LMFDB - Embedded newform 69.6.e.b.58.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(4,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.6
Character	$\chi$	$=$	69.58
Dual form			69.6.e.b.25.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53574 - 0.986959i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-11.9089 + 26.0768i) q^{4} +(85.2534 - 25.0326i) q^{5} +(6.82520 + 14.9451i) q^{6} +(-23.0904 - 26.6477i) q^{7} +(15.7614 + 109.623i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(1.53574 - 0.986959i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-11.9089 + 26.0768i) q^{4} +(85.2534 - 25.0326i) q^{5} +(6.82520 + 14.9451i) q^{6} +(-23.0904 - 26.6477i) q^{7} +(15.7614 + 109.623i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(106.221 - 122.585i) q^{10} +(289.925 + 186.323i) q^{11} +(-217.049 - 139.489i) q^{12} +(-504.291 + 581.983i) q^{13} +(-61.7611 - 18.1347i) q^{14} +(113.805 + 791.533i) q^{15} +(-468.342 - 540.496i) q^{16} +(878.900 + 1924.52i) q^{17} +(-141.879 + 41.6593i) q^{18} +(-478.069 + 1046.82i) q^{19} +(-362.500 + 2521.25i) q^{20} +(266.964 - 171.567i) q^{21} +629.142 q^{22} +(1071.63 - 2299.55i) q^{23} -996.755 q^{24} +(4012.59 - 2578.73i) q^{25} +(-200.066 + 1391.49i) q^{26} +(302.838 - 663.122i) q^{27} +(969.869 - 284.779i) q^{28} +(-1051.10 - 2301.59i) q^{29} +(955.986 + 1103.27i) q^{30} +(1059.64 + 7369.93i) q^{31} +(-4653.16 - 1366.29i) q^{32} +(-2031.19 + 2344.11i) q^{33} +(3249.19 + 2088.13i) q^{34} +(-2635.60 - 1693.80i) q^{35} +(1520.63 - 1754.90i) q^{36} +(674.505 + 198.053i) q^{37} +(298.985 + 2079.48i) q^{38} +(-4538.62 - 5237.85i) q^{39} +(4087.88 + 8951.20i) q^{40} +(-3864.38 + 1134.68i) q^{41} +(240.657 - 526.964i) q^{42} +(1628.91 - 11329.3i) q^{43} +(-8311.39 + 5341.41i) q^{44} -7197.05 q^{45} +(-623.824 - 4589.17i) q^{46} +14729.5 q^{47} +(5414.82 - 3479.89i) q^{48} +(2214.95 - 15405.3i) q^{49} +(3617.18 - 7920.52i) q^{50} +(-18270.1 + 5364.59i) q^{51} +(-9170.72 - 20081.1i) q^{52} +(-16465.3 - 19002.0i) q^{53} +(-189.395 - 1317.27i) q^{54} +(29381.2 + 8627.10i) q^{55} +(2557.27 - 2951.25i) q^{56} +(-8713.20 - 5599.63i) q^{57} +(-3885.80 - 2497.25i) q^{58} +(25528.2 - 29461.1i) q^{59} +(-21995.9 - 6458.59i) q^{60} +(3114.05 + 21658.7i) q^{61} +(8901.15 + 10272.5i) q^{62} +(1186.45 + 2597.96i) q^{63} +(13464.2 - 3953.44i) q^{64} +(-28423.9 + 62239.8i) q^{65} +(-805.826 + 5604.64i) q^{66} +(40695.4 - 26153.3i) q^{67} -60652.1 q^{68} +(19112.8 + 12491.8i) q^{69} -5719.30 q^{70} +(14253.5 - 9160.19i) q^{71} +(1276.68 - 8879.48i) q^{72} +(-434.760 + 951.991i) q^{73} +(1231.33 - 361.552i) q^{74} +(17832.9 + 39048.6i) q^{75} +(-21604.6 - 24933.0i) q^{76} +(-1729.38 - 12028.1i) q^{77} +(-12139.7 - 3564.53i) q^{78} +(44845.8 - 51754.9i) q^{79} +(-53457.8 - 34355.2i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-4814.79 + 5556.56i) q^{82} +(-13574.0 - 3985.68i) q^{83} +(1294.68 + 9004.73i) q^{84} +(123105. + 142071. i) q^{85} +(-8679.99 - 19006.5i) q^{86} +(21849.8 - 6415.68i) q^{87} +(-15855.7 + 34719.2i) q^{88} +(-3919.60 + 27261.5i) q^{89} +(-11052.8 + 7103.20i) q^{90} +27152.8 q^{91} +(47203.1 + 55329.8i) q^{92} -67011.5 q^{93} +(22620.7 - 14537.5i) q^{94} +(-14552.2 + 101213. i) q^{95} +(18131.4 - 39702.2i) q^{96} +(-141921. + 41671.8i) q^{97} +(-11802.8 - 25844.6i) q^{98} +(-18280.7 - 21097.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) $ 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.53574	−	0.986959i	0.271483	−	0.174471i	−0.397815	−	0.917466i	$-0.630231\pi$
$2$	1.53574	−	0.986959i	0.271483	−	0.174471i	0.669298	+	0.742994i	$0.266595\pi$
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$4$	−11.9089	+	26.0768i	−0.372152	+	0.814900i
$5$	85.2534	−	25.0326i	1.52506	−	0.447798i	0.591525	−	0.806287i	$-0.298526\pi$
$5$	85.2534	−	25.0326i	1.52506	−	0.447798i	0.933534	+	0.358489i	$0.116708\pi$
$6$	6.82520	+	14.9451i	0.0773993	+	0.169481i
$7$	−23.0904	−	26.6477i	−0.178109	−	0.205549i	0.659674	−	0.751552i	$-0.270694\pi$
$7$	−23.0904	−	26.6477i	−0.178109	−	0.205549i	−0.837783	+	0.546003i	$0.816149\pi$
$8$	15.7614	+	109.623i	0.0870705	+	0.605589i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	106.221	−	122.585i	0.335899	−	0.387648i
$11$	289.925	+	186.323i	0.722443	+	0.464286i	0.849486	−	0.527612i	$-0.176912\pi$
$11$	289.925	+	186.323i	0.722443	+	0.464286i	−0.127043	+	0.991897i	$0.540549\pi$
$12$	−217.049	−	139.489i	−0.435116	−	0.279632i
$13$	−504.291	+	581.983i	−0.827605	+	0.955107i	−0.999550	−	0.0299996i	$-0.990449\pi$
$13$	−504.291	+	581.983i	−0.827605	+	0.955107i	0.171945	+	0.985107i	$0.444995\pi$
$14$	−61.7611	−	18.1347i	−0.0842160	−	0.0247280i
$15$	113.805	+	791.533i	0.130597	+	0.908324i
$16$	−468.342	−	540.496i	−0.457365	−	0.527828i
$17$	878.900	+	1924.52i	0.737594	+	1.61511i	0.787473	+	0.616350i	$0.211389\pi$
$17$	878.900	+	1924.52i	0.737594	+	1.61511i	−0.0498788	+	0.998755i	$0.515883\pi$
$18$	−141.879	+	41.6593i	−0.103213	+	0.0303062i
$19$	−478.069	+	1046.82i	−0.303813	+	0.665258i	−0.998540	−	0.0540157i	$-0.982798\pi$
$19$	−478.069	+	1046.82i	−0.303813	+	0.665258i	0.694727	+	0.719273i	$0.255525\pi$
$20$	−362.500	+	2521.25i	−0.202644	+	1.40942i
$21$	266.964	−	171.567i	0.132100	−	0.0848957i
$22$	629.142			0.277135
$23$	1071.63	−	2299.55i	0.422401	−	0.906409i
$23$	1071.63	−	2299.55i	0.422401	−	0.906409i
$24$	−996.755			−0.353232
$25$	4012.59	−	2578.73i	1.28403	−	0.825194i
$26$	−200.066	+	1391.49i	−0.0580416	+	0.403688i
$27$	302.838	−	663.122i	0.0799467	−	0.175059i
$28$	969.869	−	284.779i	0.233786	−	0.0686457i
$29$	−1051.10	−	2301.59i	−0.232087	−	0.508199i	0.757377	−	0.652977i	$-0.226480\pi$
$29$	−1051.10	−	2301.59i	−0.232087	−	0.508199i	−0.989464	+	0.144778i	$0.953753\pi$
$30$	955.986	+	1103.27i	0.193932	+	0.223809i
$31$	1059.64	+	7369.93i	0.198040	+	1.37740i	0.809963	+	0.586480i	$0.199487\pi$
$31$	1059.64	+	7369.93i	0.198040	+	1.37740i	−0.611924	+	0.790917i	$0.709604\pi$
$32$	−4653.16	−	1366.29i	−0.803291	−	0.235868i
$33$	−2031.19	+	2344.11i	−0.324687	+	0.374709i
$34$	3249.19	+	2088.13i	0.482034	+	0.309784i
$35$	−2635.60	−	1693.80i	−0.363671	−	0.233717i
$36$	1520.63	−	1754.90i	0.195554	−	0.225681i
$37$	674.505	+	198.053i	0.0809992	+	0.0237835i	0.321981	−	0.946746i	$-0.395651\pi$
$37$	674.505	+	198.053i	0.0809992	+	0.0237835i	−0.240982	+	0.970530i	$0.577469\pi$
$38$	298.985	+	2079.48i	0.0335884	+	0.233613i
$39$	−4538.62	−	5237.85i	−0.477818	−	0.551431i
$40$	4087.88	+	8951.20i	0.403969	+	0.884568i
$41$	−3864.38	+	1134.68i	−0.359021	+	0.105418i	−0.456269	−	0.889842i	$-0.650814\pi$
$41$	−3864.38	+	1134.68i	−0.359021	+	0.105418i	0.0972475	+	0.995260i	$0.468996\pi$
$42$	240.657	−	526.964i	0.0210511	−	0.0460954i
$43$	1628.91	−	11329.3i	0.134346	−	0.934399i	−0.805450	−	0.592664i	$-0.798076\pi$
$43$	1628.91	−	11329.3i	0.134346	−	0.934399i	0.939796	−	0.341735i	$-0.111015\pi$
$44$	−8311.39	+	5341.41i	−0.647205	+	0.415933i
$45$	−7197.05			−0.529814
$46$	−623.824	−	4589.17i	−0.0434678	−	0.319771i
$47$	14729.5			0.972623			0.486312	−	0.873786i	$-0.338342\pi$
$47$	14729.5			0.972623			0.486312	+	0.873786i	$0.338342\pi$
$48$	5414.82	−	3479.89i	0.339219	−	0.218003i
$49$	2214.95	−	15405.3i	0.131787	−	0.916601i
$50$	3617.18	−	7920.52i	0.204619	−	0.448052i
$51$	−18270.1	+	5364.59i	−0.983595	+	0.288809i
$52$	−9170.72	−	20081.1i	−0.470322	−	1.02986i
$53$	−16465.3	−	19002.0i	−0.805156	−	0.929200i	0.193496	−	0.981101i	$-0.438017\pi$
$53$	−16465.3	−	19002.0i	−0.805156	−	0.929200i	−0.998652	+	0.0519015i	$0.983472\pi$
$54$	−189.395	−	1317.27i	−0.00883860	−	0.0614738i
$55$	29381.2	+	8627.10i	1.30967	+	0.384555i
$56$	2557.27	−	2951.25i	0.108970	−	0.125758i
$57$	−8713.20	−	5599.63i	−0.355214	−	0.228282i
$58$	−3885.80	−	2497.25i	−0.151674	−	0.0974748i
$59$	25528.2	−	29461.1i	0.954751	−	1.10184i	−0.0399671	−	0.999201i	$-0.512725\pi$
$59$	25528.2	−	29461.1i	0.954751	−	1.10184i	0.994718	−	0.102641i	$-0.0327292\pi$
$60$	−21995.9	−	6458.59i	−0.788796	−	0.231611i
$61$	3114.05	+	21658.7i	0.107152	+	0.745261i	0.970578	+	0.240785i	$0.0774050\pi$
$61$	3114.05	+	21658.7i	0.107152	+	0.745261i	−0.863426	+	0.504475i	$0.831686\pi$
$62$	8901.15	+	10272.5i	0.294081	+	0.339387i
$63$	1186.45	+	2597.96i	0.0376616	+	0.0824673i
$64$	13464.2	−	3953.44i	0.410894	−	0.120649i
$65$	−28423.9	+	62239.8i	−0.834451	+	1.82719i
$66$	−805.826	+	5604.64i	−0.0227710	+	0.158376i
$67$	40695.4	−	26153.3i	1.10754	−	0.711770i	0.146781	−	0.989169i	$-0.453109\pi$
$67$	40695.4	−	26153.3i	1.10754	−	0.711770i	0.960755	+	0.277399i	$0.0894723\pi$
$68$	−60652.1			−1.59065
$69$	19112.8	+	12491.8i	0.483282	+	0.315867i
$70$	−5719.30			−0.139508
$71$	14253.5	−	9160.19i	0.335565	−	0.215655i	−0.361996	−	0.932179i	$-0.617905\pi$
$71$	14253.5	−	9160.19i	0.335565	−	0.215655i	0.697562	+	0.716525i	$0.254268\pi$
$72$	1276.68	−	8879.48i	0.0290235	−	0.201863i
$73$	−434.760	+	951.991i	−0.00954865	+	0.0209086i	−0.914346	−	0.404933i	$-0.867295\pi$
$73$	−434.760	+	951.991i	−0.00954865	+	0.0209086i	0.904798	+	0.425842i	$0.140022\pi$
$74$	1231.33	−	361.552i	0.0261394	−	0.00767523i
$75$	17832.9	+	39048.6i	0.366074	+	0.801590i
$76$	−21604.6	−	24933.0i	−0.429054	−	0.495155i
$77$	−1729.38	−	12028.1i	−0.0332402	−	0.231191i
$78$	−12139.7	−	3564.53i	−0.225928	−	0.0663385i
$79$	44845.8	−	51754.9i	0.808453	−	0.933004i	−0.190360	−	0.981714i	$-0.560966\pi$
$79$	44845.8	−	51754.9i	0.808453	−	0.933004i	0.998813	+	0.0487103i	$0.0155111\pi$
$80$	−53457.8	−	34355.2i	−0.933869	−	0.600161i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	−4814.79	+	5556.56i	−0.0790756	+	0.0912581i
$83$	−13574.0	−	3985.68i	−0.216278	−	0.0635049i	0.171799	−	0.985132i	$-0.445042\pi$
$83$	−13574.0	−	3985.68i	−0.216278	−	0.0635049i	−0.388076	+	0.921627i	$0.626860\pi$
$84$	1294.68	+	9004.73i	0.0200201	+	0.139243i
$85$	123105.	+	142071.i	1.84811	+	2.13284i
$86$	−8679.99	−	19006.5i	−0.126553	−	0.277113i
$87$	21849.8	−	6415.68i	0.309492	−	0.0908750i
$88$	−15855.7	+	34719.2i	−0.218263	+	0.477929i
$89$	−3919.60	+	27261.5i	−0.0524526	+	0.364816i	0.946643	+	0.322285i	$0.104451\pi$
$89$	−3919.60	+	27261.5i	−0.0524526	+	0.364816i	−0.999095	+	0.0425306i	$0.986458\pi$
$90$	−11052.8	+	7103.20i	−0.143835	+	0.0924374i
$91$	27152.8			0.343725
$92$	47203.1	+	55329.8i	0.581435	+	0.681537i
$93$	−67011.5			−0.803418
$94$	22620.7	−	14537.5i	0.264050	−	0.169695i
$95$	−14552.2	+	101213.i	−0.165432	+	1.15060i
$96$	18131.4	−	39702.2i	0.200795	−	0.439679i
$97$	−141921.	+	41671.8i	−1.53150	+	0.449690i	−0.935510	−	0.353300i	$-0.885059\pi$
$97$	−141921.	+	41671.8i	−1.53150	+	0.449690i	−0.595993	+	0.802990i	$0.703241\pi$
$98$	−11802.8	−	25844.6i	−0.124143	−	0.271835i
$99$	−18280.7	−	21097.0i	−0.187458	−	0.216338i
$100$	19459.7	+	135345.i	0.194597	+	1.35345i
$101$	−87664.7	−	25740.7i	−0.855109	−	0.251083i	−0.175339	−	0.984508i	$-0.556102\pi$
$101$	−87664.7	−	25740.7i	−0.855109	−	0.251083i	−0.679770	+	0.733426i	$0.737920\pi$
$102$	−22763.5	+	26270.5i	−0.216640	+	0.250016i
$103$	135573.	+	87127.2i	1.25915	+	0.809209i	0.988168	−	0.153375i	$-0.0490142\pi$
$103$	135573.	+	87127.2i	1.25915	+	0.809209i	0.270985	+	0.962584i	$0.412651\pi$
$104$	−71747.3	−	46109.2i	−0.650462	−	0.418027i
$105$	18464.8	−	21309.5i	0.163445	−	0.188625i
$106$	−44040.6	−	12931.5i	−0.380705	−	0.111785i
$107$	30749.9	+	213870.i	0.259648	+	1.80589i	0.535333	+	0.844641i	$0.320186\pi$
$107$	30749.9	+	213870.i	0.259648	+	1.80589i	−0.275685	+	0.961248i	$0.588905\pi$
$108$	13685.6	+	15794.1i	0.112903	+	0.130297i
$109$	−39198.7	−	85833.2i	−0.316014	−	0.691973i	0.683256	−	0.730179i	$-0.260563\pi$
$109$	−39198.7	−	85833.2i	−0.316014	−	0.691973i	−0.999270	+	0.0382055i	$0.987836\pi$
$110$	53636.5	−	15749.1i	0.422648	−	0.124101i
$111$	−2628.26	+	5755.08i	−0.0202470	+	0.0443347i
$112$	−3588.78	+	24960.5i	−0.0270335	+	0.188022i
$113$	190642.	−	122518.i	1.40450	−	0.902620i	0.404575	−	0.914505i	$-0.367420\pi$
$113$	190642.	−	122518.i	1.40450	−	0.902620i	0.999929	+	0.0118848i	$0.00378314\pi$
$114$	−18907.8			−0.136263
$115$	33796.1	−	222871.i	0.238299	−	1.57148i
$116$	72535.6			0.500503
$117$	52474.0	−	33723.0i	0.354389	−	0.227752i
$118$	10127.7	−	70439.9i	0.0669587	−	0.465708i
$119$	30990.0	−	67858.7i	0.200611	−	0.439277i
$120$	−84976.7	+	24951.4i	−0.538700	+	0.158177i
$121$	−17563.1	−	38457.8i	−0.109053	−	0.238792i
$122$	26158.6	+	30188.7i	0.159117	+	0.183630i
$123$	−5158.58	−	35878.7i	−0.0307445	−	0.213833i
$124$	−204803.	−	60135.7i	−1.19614	−	0.351219i
$125$	95702.7	−	110447.i	0.547834	−	0.632234i
$126$	4386.16	+	2818.82i	0.0246127	+	0.0158176i
$127$	−200900.	−	129111.i	−1.10528	−	0.710318i	−0.145018	−	0.989429i	$-0.546324\pi$
$127$	−200900.	−	129111.i	−1.10528	−	0.710318i	−0.960259	+	0.279111i	$0.909960\pi$
$128$	118402.	−	136643.i	0.638752	−	0.737160i
$129$	98839.6	+	29021.9i	0.522946	+	0.153551i
$130$	17776.4	+	123637.i	0.0922538	+	0.641640i
$131$	13885.6	+	16024.8i	0.0706945	+	0.0815858i	0.789995	−	0.613113i	$-0.210083\pi$
$131$	13885.6	+	16024.8i	0.0706945	+	0.0815858i	−0.719301	+	0.694699i	$0.755538\pi$
$132$	−36937.8	−	80882.6i	−0.184517	−	0.404036i
$133$	38934.3	−	11432.1i	0.190855	−	0.0560401i
$134$	36685.2	−	80329.3i	0.176493	−	0.386467i
$135$	9218.23	−	64114.2i	0.0435324	−	0.302775i
$136$	−197120.	+	126681.i	−0.913867	+	0.587307i
$137$	−198802.			−0.904938			−0.452469	−	0.891780i	$-0.649457\pi$
$137$	−198802.			−0.904938			−0.452469	+	0.891780i	$0.649457\pi$
$138$	41681.1	+	320.693i	0.186312	+	0.00143348i
$139$	−32535.3			−0.142829			−0.0714147	−	0.997447i	$-0.522751\pi$
$139$	−32535.3			−0.142829			−0.0714147	+	0.997447i	$0.522751\pi$
$140$	75555.8	−	48556.8i	0.325797	−	0.209377i
$141$	−18866.1	+	131217.i	−0.0799161	+	0.555828i
$142$	12849.0	−	28135.3i	0.0534746	−	0.117093i
$143$	−254643.	+	74770.1i	−1.04134	+	0.305765i
$144$	24064.8	+	52694.5i	0.0967109	+	0.211767i
$145$	−147225.	−	169907.i	−0.581516	−	0.671105i
$146$	271.899	+	1891.10i	0.00105566	+	0.00734230i
$147$	134400.	+	39463.3i	0.512985	+	0.150626i
$148$	−13197.2	+	15230.3i	−0.0495252	+	0.0571552i
$149$	−28193.7	−	18119.0i	−0.104037	−	0.0668603i	0.487588	−	0.873074i	$-0.337877\pi$
$149$	−28193.7	−	18119.0i	−0.104037	−	0.0668603i	−0.591625	+	0.806214i	$0.701513\pi$
$150$	65926.1	+	42368.1i	0.239237	+	0.153749i
$151$	627.300	−	723.943i	0.00223889	−	0.00258382i	−0.754629	−	0.656152i	$-0.772183\pi$
$151$	627.300	−	723.943i	0.00223889	−	0.00258382i	0.756868	+	0.653568i	$0.226729\pi$
$152$	−122291.	−	35908.0i	−0.429326	−	0.126061i
$153$	−24388.9	−	169629.i	−0.0842295	−	0.585829i
$154$	−14527.1	−	16765.2i	−0.0493604	−	0.0569649i
$155$	274826.	+	601786.i	0.918818	+	2.01193i
$156$	190636.	−	55975.8i	0.627182	−	0.184157i
$157$	129576.	−	283732.i	0.419542	−	0.918668i	−0.575368	−	0.817895i	$-0.695141\pi$
$157$	129576.	−	283732.i	0.419542	−	0.918668i	0.994909	−	0.100773i	$-0.0321316\pi$
$158$	17791.6	−	123743.i	0.0566984	−	0.394346i
$159$	190366.	−	122341.i	0.597169	−	0.383777i
$160$	−430899.			−1.33069
$161$	−86022.3	+	24541.1i	−0.261545	+	0.0746157i
$162$	11977.3			0.0358569
$163$	−31363.3	+	20156.0i	−0.0924597	+	0.0594203i	−0.586054	−	0.810272i	$-0.699319\pi$
$163$	−31363.3	+	20156.0i	−0.0924597	+	0.0594203i	0.493594	+	0.869692i	$0.335683\pi$
$164$	16431.5	−	114283.i	0.0477053	−	0.331798i
$165$	−114486.	+	250690.i	−0.327373	+	0.716847i
$166$	−24779.8	+	7276.00i	−0.0697955	+	0.0204938i
$167$	−201098.	−	440344.i	−0.557979	−	1.22180i	−0.952955	−	0.303111i	$-0.901975\pi$
$167$	−201098.	−	440344.i	−0.557979	−	1.22180i	0.394977	−	0.918691i	$-0.370753\pi$
$168$	23015.5	+	26561.3i	0.0629139	+	0.0726065i
$169$	−31554.2	−	219464.i	−0.0849846	−	0.591081i
$170$	329275.	+	96684.0i	0.873850	+	0.256586i
$171$	61043.9	−	70448.4i	0.159644	−	0.184239i
$172$	276034.	+	177396.i	0.711445	+	0.457218i
$173$	255687.	+	164320.i	0.649521	+	0.417422i	0.823491	−	0.567329i	$-0.192023\pi$
$173$	255687.	+	164320.i	0.649521	+	0.417422i	−0.173970	+	0.984751i	$0.555660\pi$
$174$	27223.6	−	31417.7i	0.0681666	−	0.0786685i
$175$	−161370.	−	47382.4i	−0.398315	−	0.116956i
$176$	−35077.0	−	243966.i	−0.0853574	−	0.593674i
$177$	229754.	+	265150.i	0.551226	+	0.636149i
$178$	20886.5	+	45735.0i	0.0494100	+	0.108193i
$179$	111318.	−	32685.9i	0.259676	−	0.0762478i	−0.149303	−	0.988791i	$-0.547703\pi$
$179$	111318.	−	32685.9i	0.259676	−	0.0762478i	0.408979	+	0.912544i	$0.365885\pi$
$180$	85708.8	−	187676.i	0.197172	−	0.431746i
$181$	−106917.	+	743621.i	−0.242576	+	1.68716i	0.396518	+	0.918027i	$0.370219\pi$
$181$	−106917.	+	743621.i	−0.242576	+	1.68716i	−0.639094	+	0.769129i	$0.720691\pi$
$182$	41699.6	−	26798.7i	0.0933155	−	0.0599702i
$183$	−196933.			−0.434701
$184$	268975.	+	81231.2i	0.585690	+	0.176880i
$185$	62461.6			0.134179
$186$	−102912.	+	66137.6i	−0.218114	+	0.140174i
$187$	−103769.	+	721726.i	−0.217001	+	1.50927i
$188$	−175412.	+	384099.i	−0.361964	+	0.792591i
$189$	−24663.3	+	7241.81i	−0.0502224	+	0.0147466i
$190$	77544.4	+	169799.i	0.155836	+	0.341232i
$191$	244184.	+	281804.i	0.484323	+	0.558938i	0.944340	−	0.328972i	$-0.106702\pi$
$191$	244184.	+	281804.i	0.484323	+	0.558938i	−0.460017	+	0.887910i	$0.652157\pi$
$192$	17973.4	+	125008.i	0.0351866	+	0.244728i
$193$	−745339.	−	218851.i	−1.44033	−	0.422918i	−0.533995	−	0.845487i	$-0.679310\pi$
$193$	−745339.	−	218851.i	−1.44033	−	0.422918i	−0.906330	+	0.422570i	$0.861128\pi$
$194$	−176825.	+	204067.i	−0.337319	+	0.389286i
$195$	−518050.	−	332930.i	−0.975630	−	0.626999i
$196$	375344.	+	241219.i	0.697893	+	0.448509i
$197$	43569.1	−	50281.4i	0.0799858	−	0.0923085i	−0.714346	−	0.699793i	$-0.753276\pi$
$197$	43569.1	−	50281.4i	0.0799858	−	0.0923085i	0.794332	+	0.607484i	$0.207821\pi$
$198$	−48896.2	−	14357.2i	−0.0886365	−	0.0260260i
$199$	−52363.7	−	364198.i	−0.0937342	−	0.651935i	−0.981475	−	0.191591i	$-0.938635\pi$
$199$	−52363.7	−	364198.i	−0.0937342	−	0.651935i	0.887741	−	0.460344i	$-0.152274\pi$
$200$	345933.	+	399228.i	0.611529	+	0.705743i
$201$	180860.	+	396028.i	0.315757	+	0.691411i
$202$	−160035.	+	46990.5i	−0.275954	+	0.0810274i
$203$	−37061.9	+	81154.2i	−0.0631230	+	0.138220i
$204$	77685.3	−	540313.i	0.130696	−	0.909013i
$205$	−301047.	+	193471.i	−0.500322	+	0.321538i
$206$	294195.			0.483022
$207$	−135763.	+	154264.i	−0.220219	+	0.250230i
$208$	550740.			0.882650
$209$	−333652.	+	214425.i	−0.528357	+	0.339555i
$210$	7325.47	−	50949.7i	0.0114627	−	0.0797249i
$211$	80392.7	−	176035.i	0.124311	−	0.272204i	−0.837237	−	0.546841i	$-0.815830\pi$
$211$	80392.7	−	176035.i	0.124311	−	0.272204i	0.961548	+	0.274637i	$0.0885577\pi$
$212$	691594.	−	203070.i	1.05685	−	0.310318i
$213$	63346.2	+	138709.i	0.0956691	+	0.209486i
$214$	258305.	+	298100.i	0.385566	+	0.444967i
$215$	−144733.	−	1.00664e6i	−0.213536	−	1.48517i
$216$	77466.7	+	22746.3i	0.112975	+	0.0331723i
$217$	171925.	−	198412.i	0.247850	−	0.286034i
$218$	−144913.	−	93129.9i	−0.206522	−	0.132723i
$219$	−7923.85	−	5092.35i	−0.0111642	−	0.00717477i
$220$	−574864.	+	663429.i	−0.800772	+	0.924140i
$221$	−1.56326e6	−	459015.i	−2.15303	−	0.632188i
$222$	1643.71	+	11432.3i	0.00223843	+	0.0155686i
$223$	−825424.	−	952590.i	−1.11151	−	1.28276i	−0.955497	−	0.295001i	$-0.904680\pi$
$223$	−825424.	−	952590.i	−1.11151	−	1.28276i	−0.156017	−	0.987754i	$-0.549865\pi$
$224$	71034.7	+	155544.i	0.0945912	+	0.207126i
$225$	−370701.	+	108848.i	−0.488167	+	0.143339i
$226$	171856.	−	376312.i	0.223817	−	0.490092i
$227$	−2732.96	+	19008.2i	−0.00352021	+	0.0244836i	−0.991506	−	0.130062i	$-0.958482\pi$
$227$	−2732.96	+	19008.2i	−0.00352021	+	0.0244836i	0.987986	+	0.154546i	$0.0493914\pi$
$228$	249785.	−	160527.i	0.318221	−	0.204508i
$229$	1.03076e6			1.29888			0.649442	−	0.760411i	$-0.275003\pi$
$229$	1.03076e6			1.29888			0.649442	+	0.760411i	$0.275003\pi$
$230$	−168062.	−	375626.i	−0.209484	−	0.468205i
$231$	109366.			0.134851
$232$	235741.	−	151502.i	0.287552	−	0.184798i
$233$	−82067.9	+	570795.i	−0.0990338	+	0.688795i	0.878458	+	0.477820i	$0.158573\pi$
$233$	−82067.9	+	570795.i	−0.0990338	+	0.688795i	−0.977491	+	0.210975i	$0.932336\pi$
$234$	47303.2	−	103579.i	0.0564742	−	0.123661i
$235$	1.25574e6	−	368719.i	1.48331	−	0.435538i
$236$	464240.	+	1.01654e6i	0.542578	+	1.18808i
$237$	403613.	+	465794.i	0.466760	+	0.538670i
$238$	−19381.2	−	134799.i	−0.0221788	−	0.154257i
$239$	739046.	+	217003.i	0.836906	+	0.245738i	0.671981	−	0.740568i	$-0.265444\pi$
$239$	739046.	+	217003.i	0.836906	+	0.245738i	0.164925	+	0.986306i	$0.447262\pi$
$240$	374520.	−	432220.i	0.419708	−	0.484369i
$241$	1.01224e6	+	650525.i	1.12264	+	0.721475i	0.964011	−	0.265864i	$-0.0856571\pi$
$241$	1.01224e6	+	650525.i	1.12264	+	0.721475i	0.158627	+	0.987339i	$0.449293\pi$
$242$	−64928.5	−	41727.0i	−0.0712684	−	0.0458014i
$243$	−38668.9	+	44626.3i	−0.0420093	+	0.0484814i
$244$	−601875.	−	176726.i	−0.647190	−	0.190032i
$245$	−196804.	−	1.36880e6i	−0.209468	−	1.45688i
$246$	−43333.1	−	50009.0i	−0.0456543	−	0.0526879i
$247$	−368148.	−	806133.i	−0.383955	−	0.840745i
$248$	−791215.	+	232322.i	−0.816893	+	0.239861i
$249$	52892.0	−	115817.i	0.0540619	−	0.118379i
$250$	37967.8	−	264072.i	0.0384207	−	0.267222i
$251$	−449592.	+	288935.i	−0.450437	+	0.289479i	−0.746125	−	0.665806i	$-0.768088\pi$
$251$	−449592.	+	288935.i	−0.450437	+	0.289479i	0.295687	+	0.955285i	$0.404451\pi$
$252$	−81875.9			−0.0812185
$253$	739152.	−	467028.i	0.725993	−	0.458714i
$254$	−435957.			−0.423994
$255$	−1.42330e6	+	914699.i	−1.37071	+	0.880903i
$256$	−16932.3	+	117767.i	−0.0161479	+	0.112311i
$257$	−730760.	+	1.60014e6i	−0.690148	+	1.51121i	0.161374	+	0.986893i	$0.448407\pi$
$257$	−730760.	+	1.60014e6i	−0.690148	+	1.51121i	−0.851522	+	0.524319i	$0.824320\pi$
$258$	180435.	−	52980.6i	0.168761	−	0.0495527i
$259$	−10296.9	−	22547.1i	−0.00953803	−	0.0208854i
$260$	−1.28452e6	−	1.48241e6i	−1.17844	−	1.35999i
$261$	29167.4	+	202864.i	0.0265031	+	0.184333i
$262$	37140.4	+	10905.4i	0.0334267	+	0.00981497i
$263$	617239.	−	712332.i	0.550255	−	0.635028i	−0.410688	−	0.911776i	$-0.634711\pi$
$263$	617239.	−	712332.i	0.550255	−	0.635028i	0.960943	+	0.276748i	$0.0892568\pi$
$264$	−288984.	−	185719.i	−0.255190	−	0.164001i
$265$	−1.87939e6	−	1.20781e6i	−1.64400	−	1.05654i
$266$	48509.9	−	55983.4i	0.0420364	−	0.0485126i
$267$	−237835.	−	69834.8i	−0.204173	−	0.0599506i
$268$	197359.	+	1.37266e6i	0.167849	+	1.16742i
$269$	−908480.	−	1.04844e6i	−0.765482	−	0.883413i	0.230491	−	0.973075i	$-0.425967\pi$
$269$	−908480.	−	1.04844e6i	−0.765482	−	0.883413i	−0.995972	+	0.0896615i	$0.971421\pi$
$270$	−49121.3	−	107561.i	−0.0410072	−	0.0897933i
$271$	1.48538e6	−	436148.i	1.22861	−	0.360754i	0.397888	−	0.917434i	$-0.369743\pi$
$271$	1.48538e6	−	436148.i	1.22861	−	0.360754i	0.830727	+	0.556680i	$0.187925\pi$
$272$	628570.	−	1.37638e6i	0.515147	−	1.12802i
$273$	−34778.2	+	241888.i	−0.0282424	+	0.196430i
$274$	−305308.	+	196209.i	−0.245675	+	0.157886i
$275$	1.64383e6			1.31076
$276$	−553359.	+	349636.i	−0.437254	+	0.276276i
$277$	2.32713e6			1.82230			0.911151	−	0.412073i	$-0.135195\pi$
$277$	2.32713e6			1.82230			0.911151	+	0.412073i	$0.135195\pi$
$278$	−49965.7	+	32111.0i	−0.0387757	+	0.0249196i
$279$	85830.5	−	596965.i	0.0660133	−	0.459132i
$280$	144139.	−	315620.i	0.109872	−	0.240585i
$281$	−711146.	+	208811.i	−0.537270	+	0.157757i	−0.539100	−	0.842242i	$-0.681236\pi$
$281$	−711146.	+	208811.i	−0.537270	+	0.157757i	0.00183001	+	0.999998i	$0.499417\pi$
$282$	100532.	+	220134.i	0.0752803	+	0.164841i
$283$	−628936.	−	725831.i	−0.466811	−	0.538728i	0.472711	−	0.881217i	$-0.343275\pi$
$283$	−628936.	−	725831.i	−0.466811	−	0.538728i	−0.939522	+	0.342489i	$0.888730\pi$
$284$	69124.9	+	480774.i	0.0508556	+	0.353708i
$285$	−883003.	−	259273.i	−0.643947	−	0.189080i
$286$	−317271.	+	366150.i	−0.229359	+	0.264694i
$287$	119467.	+	76776.6i	0.0856135	+	0.0550205i
$288$	330459.	+	212373.i	0.234767	+	0.150875i
$289$	−2.00151e6	+	2.30987e6i	−1.40966	+	1.62683i
$290$	−393790.	−	115627.i	−0.274960	−	0.0807356i
$291$	−189451.	−	1.31766e6i	−0.131149	−	0.912162i
$292$	−19647.4	−	22674.3i	−0.0134849	−	0.0155624i
$293$	429487.	+	940446.i	0.292268	+	0.639978i	0.997625	−	0.0688742i	$-0.0219407\pi$
$293$	429487.	+	940446.i	0.292268	+	0.639978i	−0.705357	+	0.708852i	$0.749213\pi$
$294$	245351.	−	72041.6i	0.165547	−	0.0486088i
$295$	1.43888e6	−	3.15070e6i	0.962650	−	2.10791i
$296$	−11080.0	+	77063.0i	−0.00735039	+	0.0511231i
$297$	211355.	−	135830.i	0.139034	−	0.0893518i
$298$	−61180.9			−0.0399094
$299$	797889.	+	1.78332e6i	0.516136	+	1.15359i
$300$	−1.23063e6			−0.789451
$301$	−339513.	+	218192.i	−0.215993	+	0.138810i
$302$	248.867	−	1730.91i	0.000157018	−	0.00109208i
$303$	341592.	−	747982.i	0.213748	−	0.468042i
$304$	789704.	−	231878.i	0.490095	−	0.143905i
$305$	807659.	+	1.76853e6i	0.497140	+	1.08858i
$306$	−204872.	−	236434.i	−0.125077	−	0.144347i
$307$	158326.	+	1.10118e6i	0.0958755	+	0.666829i	0.979915	+	0.199416i	$0.0639046\pi$
$307$	158326.	+	1.10118e6i	0.0958755	+	0.666829i	−0.884039	+	0.467412i	$0.845186\pi$
$308$	334250.	+	98144.6i	0.200768	+	0.0589508i
$309$	−949809.	+	1.09614e6i	−0.565900	+	0.653084i
$310$	1.01600e6	+	652944.i	0.600467	+	0.385897i
$311$	927100.	+	595811.i	0.543533	+	0.349307i	0.783419	−	0.621494i	$-0.213474\pi$
$311$	927100.	+	595811.i	0.543533	+	0.349307i	−0.239887	+	0.970801i	$0.577110\pi$
$312$	502655.	−	580095.i	0.292337	−	0.337375i
$313$	1.59044e6	+	466996.i	0.917608	+	0.269434i	0.706240	−	0.707973i	$-0.250390\pi$
$313$	1.59044e6	+	466996.i	0.917608	+	0.269434i	0.211368	+	0.977407i	$0.432208\pi$
$314$	−81036.8	−	563624.i	−0.0463830	−	0.322601i
$315$	166183.	+	191785.i	0.0943648	+	0.108903i
$316$	815538.	+	1.78578e6i	0.459437	+	1.00603i
$317$	−10292.9	+	3022.25i	−0.00575291	+	0.00168921i	−0.284608	−	0.958644i	$-0.591863\pi$
$317$	−10292.9	+	3022.25i	−0.00575291	+	0.00168921i	0.278855	+	0.960333i	$0.410045\pi$
$318$	171607.	−	375768.i	0.0951630	−	0.208378i
$319$	124100.	−	863133.i	0.0682802	−	0.474899i
$320$	1.04890e6	−	674087.i	0.572611	−	0.367994i
$321$	−1.94463e6			−1.05335
$322$	−107887.	+	122589.i	−0.0579867	+	0.0658890i
$323$	−2.43481e6			−1.29855
$324$	−158229.	+	101687.i	−0.0837381	+	0.0538152i
$325$	−522733.	+	3.63569e6i	−0.274519	+	1.90932i
$326$	−28272.7	+	61908.6i	−0.0147341	+	0.0322632i
$327$	814843.	−	239260.i	0.421410	−	0.123737i
$328$	−185296.	−	405741.i	−0.0951002	−	0.208240i
$329$	−340111.	−	392509.i	−0.173233	−	0.199922i
$330$	71599.7	+	497987.i	0.0361931	+	0.251729i
$331$	2.58625e6	+	759391.i	1.29748	+	0.380974i	0.856316	−	0.516453i	$-0.172748\pi$
$331$	2.58625e6	+	759391.i	1.29748	+	0.380974i	0.441163	+	0.897427i	$0.354566\pi$
$332$	265585.	−	306501.i	0.132238	−	0.152611i
$333$	−47902.2	−	30784.9i	−0.0236725	−	0.0152134i
$334$	−743436.	−	477778.i	−0.364651	−	0.234347i
$335$	2.81473e6	−	3.24837e6i	1.37033	−	1.58144i
$336$	−217762.	−	63940.6i	−0.105228	−	0.0308978i
$337$	−257646.	−	1.79196e6i	−0.123580	−	0.859518i	−0.953448	−	0.301558i	$-0.902493\pi$
$337$	−257646.	−	1.79196e6i	−0.123580	−	0.859518i	0.829868	−	0.557960i	$-0.188416\pi$
$338$	−265061.	−	305897.i	−0.126199	−	0.145641i
$339$	847261.	+	1.85524e6i	0.400422	+	0.876801i
$340$	−5.17080e6	+	1.51828e6i	−2.42583	+	0.712288i
$341$	−1.06597e6	+	2.33416e6i	−0.496433	+	1.08704i
$342$	24217.8	−	168438.i	0.0111961	−	0.0778709i
$343$	−960201.	+	617083.i	−0.440683	+	0.283210i
$344$	1.26763e6			0.577559
$345$	1.94213e6	+	586529.i	0.878478	+	0.265303i
$346$	554845.			0.249162
$347$	−3.28864e6	+	2.11348e6i	−1.46620	+	0.942269i	−0.467911	+	0.883775i	$0.654993\pi$
$347$	−3.28864e6	+	2.11348e6i	−1.46620	+	0.942269i	−0.998288	+	0.0584936i	$0.981370\pi$
$348$	−92906.1	+	646176.i	−0.0411241	+	0.286024i
$349$	690510.	−	1.51201e6i	0.303463	−	0.664492i	−0.695052	−	0.718959i	$-0.744619\pi$
$349$	690510.	−	1.51201e6i	0.303463	−	0.664492i	0.998516	+	0.0544673i	$0.0173461\pi$
$350$	−294586.	+	86498.3i	−0.128541	+	0.0377431i
$351$	233207.	+	510653.i	0.101036	+	0.221237i
$352$	−1.09449e6	−	1.26311e6i	−0.470822	−	0.543357i
$353$	128578.	+	894281.i	0.0549200	+	0.381977i	0.998681	+	0.0513481i	$0.0163518\pi$
$353$	128578.	+	894281.i	0.0549200	+	0.381977i	−0.943761	+	0.330629i	$0.892739\pi$
$354$	614534.	+	180444.i	0.260638	+	0.0765303i
$355$	985858.	−	1.13774e6i	0.415187	−	0.479151i
$356$	−664213.	−	426864.i	−0.277768	−	0.178511i
$357$	564819.	+	362987.i	0.234552	+	0.150737i
$358$	138696.	−	160063.i	0.0571946	−	0.0660061i
$359$	−2.21723e6	−	651039.i	−0.907978	−	0.266607i	−0.205789	−	0.978596i	$-0.565976\pi$
$359$	−2.21723e6	−	651039.i	−0.907978	−	0.266607i	−0.702190	+	0.711990i	$0.747794\pi$
$360$	−113436.	−	788965.i	−0.0461312	−	0.320849i
$361$	754208.	+	870402.i	0.304595	+	0.351522i
$362$	569728.	+	1.24753e6i	0.228505	+	0.500356i
$363$	365092.	−	107201.i	0.145424	−	0.0427003i
$364$	−323360.	+	708059.i	−0.127918	+	0.280102i
$365$	−13233.9	+	92043.6i	−0.00519942	+	0.0361628i
$366$	−302438.	+	194365.i	−0.118014	+	0.0758429i
$367$	144565.			0.0560272			0.0280136	−	0.999608i	$-0.491082\pi$
$367$	144565.			0.0560272			0.0280136	+	0.999608i	$0.491082\pi$
$368$	−1.74479e6	+	497767.i	−0.671620	+	0.191605i
$369$	326229.			0.124726
$370$	95924.7	−	61647.0i	0.0364272	−	0.0234104i
$371$	−126169.	+	877526.i	−0.0475903	+	0.330998i
$372$	798031.	−	1.74744e6i	0.298994	−	0.654706i
$373$	−4.78921e6	+	1.40624e6i	−1.78235	+	0.523344i	−0.995581	−	0.0939084i	$-0.970064\pi$
$373$	−4.78921e6	+	1.40624e6i	−1.78235	+	0.523344i	−0.786765	+	0.617252i	$0.788246\pi$
$374$	552953.	+	1.21080e6i	0.204413	+	0.447603i
$375$	861324.	+	994021.i	0.316292	+	0.365021i
$376$	232159.	+	1.61470e6i	0.0846868	+	0.589010i
$377$	1.86955e6	+	548950.i	0.677460	+	0.198920i
$378$	−30729.1	+	35463.2i	−0.0110616	+	0.0127658i
$379$	1.99556e6	+	1.28247e6i	0.713621	+	0.458616i	0.846413	−	0.532528i	$-0.178758\pi$
$379$	1.99556e6	+	1.28247e6i	0.713621	+	0.458616i	−0.132792	+	0.991144i	$0.542394\pi$
$380$	−2.46600e6	−	1.58480e6i	−0.876061	−	0.563010i
$381$	1.40749e6	−	1.62433e6i	0.496744	−	0.573273i
$382$	653133.	+	191777.i	0.229004	+	0.0672416i
$383$	−109129.	−	759011.i	−0.0380141	−	0.264394i	0.961947	−	0.273237i	$-0.0880942\pi$
$383$	−109129.	−	759011.i	−0.0380141	−	0.264394i	−0.999961	+	0.00884298i	$0.997185\pi$
$384$	1.06561e6	+	1.22978e6i	0.368784	+	0.425599i
$385$	−448531.	−	982146.i	−0.154220	−	0.337695i
$386$	−1.36064e6	+	399521.i	−0.464811	+	0.136481i
$387$	−385136.	+	843330.i	−0.130718	+	0.286233i
$388$	603454.	−	4.19711e6i	0.203500	−	1.41537i
$389$	2.54390e6	−	1.63487e6i	0.852367	−	0.547783i	−0.0399448	−	0.999202i	$-0.512718\pi$
$389$	2.54390e6	−	1.63487e6i	0.852367	−	0.547783i	0.892312	+	0.451419i	$0.149082\pi$
$390$	−1.12418e6			−0.374260
$391$	5.36740e6	+	41296.6i	1.77551	+	0.0136607i
$392$	1.72369e6			0.566558
$393$	−160540.	+	103173.i	−0.0524328	+	0.0336965i
$394$	17285.0	−	120220.i	0.00560957	−	0.0390154i
$395$	2.52770e6	−	5.53489e6i	0.815141	−	1.78491i
$396$	767845.	−	225460.i	0.246057	−	0.0722488i
$397$	−2.18019e6	−	4.77394e6i	−0.694252	−	1.52020i	−0.846804	−	0.531905i	$-0.821476\pi$
$397$	−2.18019e6	−	4.77394e6i	−0.694252	−	1.52020i	0.152552	−	0.988295i	$-0.451251\pi$
$398$	−439865.	−	507632.i	−0.139191	−	0.160635i
$399$	51973.7	+	361485.i	0.0163437	+	0.113673i
$400$	−3.27306e6	−	961056.i	−1.02283	−	0.300330i
$401$	1.39207e6	−	1.60653e6i	0.432314	−	0.498917i	−0.497235	−	0.867616i	$-0.665651\pi$
$401$	1.39207e6	−	1.60653e6i	0.432314	−	0.498917i	0.929549	+	0.368699i	$0.120197\pi$
$402$	668618.	+	429694.i	0.206354	+	0.132616i
$403$	−4.82354e6	−	3.09990e6i	−1.47946	−	0.950792i
$404$	1.71522e6	−	1.97947e6i	0.522838	−	0.603387i
$405$	559347.	+	164239.i	0.169451	+	0.0497553i
$406$	23178.5	+	161210.i	0.00697864	+	0.0485375i
$407$	158654.	+	183096.i	0.0474749	+	0.0547890i
$408$	−876048.	−	1.91828e6i	−0.260542	−	0.570507i
$409$	−3.34596e6	+	982462.i	−0.989036	+	0.290407i	−0.735950	−	0.677036i	$-0.763264\pi$
$409$	−3.34596e6	+	982462.i	−0.989036	+	0.290407i	−0.253087	+	0.967444i	$0.581446\pi$
$410$	−271381.	+	594242.i	−0.0797298	+	0.174584i
$411$	254632.	−	1.77100e6i	0.0743547	−	0.517148i
$412$	−3.88651e6	+	2.49771e6i	−1.12802	+	0.724935i
$413$	−1.37453e6			−0.396533
$414$	−56243.5	+	370901.i	−0.0161277	+	0.106355i
$415$	−1.25700e6			−0.358274
$416$	3.14171e6	−	2.01905e6i	0.890086	−	0.572024i
$417$	41672.3	−	289837.i	0.0117356	−	0.0816232i
$418$	−300773.	+	658601.i	−0.0841973	+	0.184366i
$419$	1.29086e6	−	379032.i	0.359208	−	0.105473i	−0.0971490	−	0.995270i	$-0.530972\pi$
$419$	1.29086e6	−	379032.i	0.359208	−	0.105473i	0.456357	+	0.889797i	$0.349154\pi$
$420$	335788.	+	735274.i	0.0928843	+	0.203388i
$421$	−127694.	−	147367.i	−0.0351128	−	0.0405223i	0.737922	−	0.674887i	$-0.235807\pi$
$421$	−127694.	−	147367.i	−0.0351128	−	0.0405223i	−0.773034	+	0.634364i	$0.781262\pi$
$422$	−50277.6	−	349689.i	−0.0137434	−	0.0955873i
$423$	−1.14476e6	−	336133.i	−0.311075	−	0.0913399i
$424$	1.82354e6	−	2.10448e6i	0.492607	−	0.568499i
$425$	8.48949e6	+	5.45587e6i	2.27987	+	1.46518i
$426$	234183.	+	150500.i	0.0625218	+	0.0401803i
$427$	505251.	−	583091.i	0.134103	−	0.154763i
$428$	−5.94325e6	−	1.74510e6i	−1.56825	−	0.460479i
$429$	−339925.	−	2.36423e6i	−0.0891744	−	0.620221i
$430$	−1.21578e6	−	1.40309e6i	−0.317092	−	0.365943i
$431$	551322.	+	1.20723e6i	0.142959	+	0.313037i	0.967545	−	0.252701i	$-0.0813188\pi$
$431$	551322.	+	1.20723e6i	0.142959	+	0.313037i	−0.824585	+	0.565738i	$0.808591\pi$
$432$	−500246.	+	146885.i	−0.128966	+	0.0378678i
$433$	693137.	−	1.51776e6i	0.177664	−	0.389030i	−0.799759	−	0.600321i	$-0.795040\pi$
$433$	693137.	−	1.51776e6i	0.177664	−	0.389030i	0.977423	+	0.211291i	$0.0677668\pi$
$434$	68207.1	−	474391.i	0.0173822	−	0.120896i
$435$	1.70217e6	−	1.09392e6i	0.431299	−	0.277179i
$436$	2.70507e6			0.681494
$437$	1.89492e6	+	2.22115e6i	0.474665	+	0.556385i
$438$	−17194.9			−0.00428267
$439$	−4.65050e6	+	2.98869e6i	−1.15170	+	0.740150i	−0.969976	−	0.243200i	$-0.921803\pi$
$439$	−4.65050e6	+	2.98869e6i	−1.15170	+	0.740150i	−0.181720	+	0.983350i	$0.558166\pi$
$440$	−482641.	+	3.35684e6i	−0.118848	+	0.826607i
$441$	−523698.	+	1.14674e6i	−0.128228	+	0.280781i
$442$	−2.85379e6	+	837948.i	−0.694810	+	0.204015i
$443$	−1.85993e6	−	4.07268e6i	−0.450285	−	0.985986i	−0.989595	−	0.143879i	$-0.954042\pi$
$443$	−1.85993e6	−	4.07268e6i	−0.450285	−	0.985986i	0.539310	−	0.842107i	$-0.318685\pi$
$444$	−118775.	−	137073.i	−0.0285934	−	0.0329986i
$445$	348267.	+	2.42225e6i	0.0833704	+	0.579854i
$446$	−2.20780e6	−	648269.i	−0.525561	−	0.154319i
$447$	197523.	−	227953.i	0.0467571	−	0.0539606i
$448$	−416243.	−	267503.i	−0.0979833	−	0.0629700i
$449$	−5.27847e6	−	3.39227e6i	−1.23564	−	0.794098i	−0.250881	−	0.968018i	$-0.580720\pi$
$449$	−5.27847e6	−	3.39227e6i	−1.23564	−	0.794098i	−0.984760	+	0.173920i	$0.944357\pi$
$450$	−461872.	+	533029.i	−0.107520	+	0.124085i
$451$	−1.33180e6	−	391051.i	−0.308316	−	0.0905298i
$452$	924551.	+	6.43040e6i	0.212856	+	1.48044i
$453$	5645.70	+	6515.49i	0.00129262	+	0.00149177i
$454$	14563.2	+	31888.9i	0.00331601	+	0.00726106i
$455$	2.31487e6	−	679707.i	0.524201	−	0.153919i
$456$	476517.	−	1.04343e6i	0.107317	−	0.234990i
$457$	22701.7	−	157894.i	0.00508473	−	0.0353651i	−0.987121	−	0.159975i	$-0.948859\pi$
$457$	22701.7	−	157894.i	0.00508473	−	0.0353651i	0.992206	+	0.124610i	$0.0397678\pi$
$458$	1.58298e6	−	1.01732e6i	0.352625	−	0.226618i
$459$	1.54236e6			0.341706
$460$	5.40928e6	+	3.53543e6i	1.19191	+	0.779019i
$461$	4.05721e6			0.889150			0.444575	−	0.895742i	$-0.353355\pi$
$461$	4.05721e6			0.889150			0.444575	+	0.895742i	$0.353355\pi$
$462$	167958.	−	107940.i	0.0366096	−	0.0235276i
$463$	−490641.	+	3.41248e6i	−0.106368	+	0.739806i	0.864922	+	0.501907i	$0.167368\pi$
$463$	−490641.	+	3.41248e6i	−0.106368	+	0.739806i	−0.971290	+	0.237899i	$0.923541\pi$
$464$	−751726.	+	1.64605e6i	−0.162093	+	0.354934i
$465$	−5.71295e6	+	1.67747e6i	−1.22526	+	0.359769i
$466$	437316.	+	957589.i	0.0932891	+	0.204275i
$467$	−4.26492e6	−	4.92198e6i	−0.904938	−	1.04435i	−0.998810	−	0.0487703i	$-0.984470\pi$
$467$	−4.26492e6	−	4.92198e6i	−0.904938	−	1.04435i	0.0938716	−	0.995584i	$-0.470076\pi$
$468$	254482.	+	1.76996e6i	0.0537083	+	0.373550i
$469$	−1.63660e6	−	480549.i	−0.343566	−	0.100880i
$470$	1.56458e6	−	1.80562e6i	0.326703	−	0.377036i
$471$	2.36163e6	+	1.51773e6i	0.490523	+	0.315240i
$472$	3.63199e6	+	2.33414e6i	0.750394	+	0.482249i
$473$	2.58318e6	−	2.98114e6i	0.530886	−	0.612675i
$474$	1.07956e6	+	316988.i	0.220700	+	0.0648033i
$475$	781189.	+	5.43329e6i	0.158863	+	1.10491i
$476$	1.40048e6	+	1.61624e6i	0.283309	+	0.326956i
$477$	846034.	+	1.85256e6i	0.170252	+	0.372800i
$478$	1.34915e6	−	396147.i	0.270080	−	0.0793025i
$479$	−1.55655e6	+	3.40838e6i	−0.309974	+	0.678748i	−0.998939	−	0.0460460i	$-0.985338\pi$
$479$	−1.55655e6	+	3.40838e6i	−0.309974	+	0.678748i	0.688965	+	0.724794i	$0.258065\pi$
$480$	551910.	−	3.83862e6i	0.109337	−	0.760452i
$481$	−455410.	+	292674.i	−0.0897512	+	0.0576796i
$482$	2.19657e6			0.430653
$483$	−108442.	−	797754.i	−0.0211509	−	0.155597i
$484$	1.21201e6			0.235176
$485$	−1.10561e7	+	7.10532e6i	−2.13426	+	1.37161i
$486$	−15341.0	+	106699.i	−0.00294620	+	0.0204913i
$487$	−427542.	+	936187.i	−0.0816877	+	0.178871i	−0.946068	−	0.323967i	$-0.894983\pi$
$487$	−427542.	+	936187.i	−0.0816877	+	0.178871i	0.864381	+	0.502838i	$0.167711\pi$
$488$	−2.32522e6	+	682746.i	−0.441992	+	0.129780i
$489$	−139386.	−	305213.i	−0.0263601	−	0.0577206i
$490$	−1.65319e6	−	1.90788e6i	−0.311052	−	0.358973i
$491$	−530010.	−	3.68630e6i	−0.0992156	−	0.690060i	−0.977347	−	0.211641i	$-0.932119\pi$
$491$	−530010.	−	3.68630e6i	−0.0992156	−	0.690060i	0.878132	−	0.478419i	$-0.158790\pi$
$492$	997036.	+	292756.i	0.185694	+	0.0545247i
$493$	3.50566e6	−	4.04574e6i	0.649609	−	0.749689i
$494$	−1.36100e6	−	874661.i	−0.250923	−	0.161258i
$495$	−2.08660e6	−	1.34098e6i	−0.382760	−	0.245985i
$496$	3.48714e6	−	4.02438e6i	0.636452	−	0.734505i
$497$	−573218.	−	168312.i	−0.104095	−	0.0305650i
$498$	−33078.7	−	230067.i	−0.00597689	−	0.0415702i
$499$	668733.	+	771759.i	0.120227	+	0.138749i	0.812672	−	0.582721i	$-0.198012\pi$
$499$	668733.	+	771759.i	0.120227	+	0.138749i	−0.692445	+	0.721470i	$0.743467\pi$
$500$	1.74039e6	+	3.81092e6i	0.311330	+	0.681717i
$501$	4.18033e6	−	1.22746e6i	0.744075	−	0.218480i
$502$	−405289.	+	887458.i	−0.0717803	+	0.157177i
$503$	758362.	−	5.27453e6i	0.133646	−	0.929530i	−0.807099	−	0.590416i	$-0.798964\pi$
$503$	758362.	−	5.27453e6i	0.133646	−	0.929530i	0.940745	−	0.339114i	$-0.110127\pi$
$504$	−266097.	+	171010.i	−0.0466621	+	0.0299879i
$505$	−8.11807e6			−1.41653
$506$	674207.	−	1.44675e6i	0.117062	−	0.251198i
$507$	1.99549e6			0.344770
$508$	5.75929e6	−	3.70127e6i	0.990170	−	0.636343i
$509$	−916206.	+	6.37235e6i	−0.156747	+	1.09020i	0.747831	+	0.663889i	$0.231095\pi$
$509$	−916206.	+	6.37235e6i	−0.156747	+	1.09020i	−0.904578	+	0.426309i	$0.859814\pi$
$510$	−1.28305e6	+	2.80948e6i	−0.218432	+	0.478300i
$511$	35407.2	−	10396.5i	0.00599845	−	0.00176130i
$512$	2.49371e6	+	5.46046e6i	0.420408	+	0.920565i
$513$	549395.	+	634036.i	0.0921704	+	0.106370i
$514$	457018.	+	3.17863e6i	0.0763002	+	0.530679i
$515$	1.37390e7	+	4.03415e6i	2.28264	+	0.670245i
$516$	−1.93387e6	+	2.23180e6i	−0.319744	+	0.369004i
$517$	4.27046e6	+	2.74446e6i	0.702664	+	0.451575i
$518$	−38066.5	−	24463.9i	−0.00623331	−	0.00400591i
$519$	−1.79132e6	+	2.06729e6i	−0.291914	+	0.336887i
$520$	−7.27093e6	−	2.13494e6i	−1.17918	−	0.346240i
$521$	554558.	+	3.85703e6i	0.0895061	+	0.622529i	0.984360	+	0.176169i	$0.0563706\pi$
$521$	554558.	+	3.85703e6i	0.0895061	+	0.622529i	−0.894854	+	0.446359i	$0.852720\pi$
$522$	245012.	+	282759.i	0.0393560	+	0.0454193i
$523$	−370996.	−	812368.i	−0.0593083	−	0.129867i	0.877657	−	0.479289i	$-0.159105\pi$
$523$	−370996.	−	812368.i	−0.0593083	−	0.129867i	−0.936966	+	0.349422i	$0.886378\pi$
$524$	−583237.	+	171254.i	−0.0927934	+	0.0272466i
$525$	628789.	−	1.37686e6i	0.0995649	−	0.218017i
$526$	244875.	−	1.70314e6i	0.0385905	−	0.268403i
$527$	−1.32523e7	+	8.51673e6i	−2.07857	+	1.33581i
$528$	2.21827e6			0.346282
$529$	−4.13956e6	−	4.92854e6i	−0.643154	−	0.765736i
$530$	−4.07832e6			−0.630654
$531$	−2.65634e6	+	1.70712e6i	−0.408834	+	0.262742i
$532$	−165550.	+	1.15143e6i	−0.0253601	+	0.176383i
$533$	1.28841e6	−	2.82121e6i	0.196442	−	0.430148i
$534$	−434177.	+	127486.i	−0.0658891	+	0.0193468i
$535$	7.97528e6	+	1.74634e7i	1.20465	+	2.63782i
$536$	3.50843e6	+	4.04894e6i	0.527474	+	0.608737i
$537$	148599.	+	1.03353e6i	0.0222372	+	0.154663i
$538$	−2.42996e6	−	713500.i	−0.361945	−	0.106277i
$539$	3.51254e6	−	4.05368e6i	0.520774	−	0.601005i
$540$	1.56211e6	+	1.00391e6i	0.230530	+	0.148153i
$541$	869321.	+	558679.i	0.127699	+	0.0820671i	0.602931	−	0.797793i	$-0.293999\pi$
$541$	869321.	+	558679.i	0.127699	+	0.0820671i	−0.475232	+	0.879861i	$0.657636\pi$
$542$	1.85070e6	−	2.13582e6i	0.270606	−	0.312296i
$543$	−6.48753e6	−	1.90491e6i	−0.944234	−	0.277252i
$544$	−1.46020e6	−	1.01559e7i	−0.211552	−	1.47137i
$545$	−5.49046e6	−	6.33632e6i	−0.791803	−	0.913789i
$546$	185323.	+	405801.i	0.0266041	+	0.0582548i
$547$	4.27280e6	−	1.25461e6i	0.610583	−	0.179283i	0.0382004	−	0.999270i	$-0.487837\pi$
$547$	4.27280e6	−	1.25461e6i	0.610583	−	0.179283i	0.572382	+	0.819987i	$0.306019\pi$
$548$	2.36751e6	−	5.18412e6i	0.336775	−	0.737434i
$549$	252238.	−	1.75436e6i	0.0357174	−	0.248420i
$550$	2.52449e6	−	1.62239e6i	0.355849	−	0.228691i
$551$	2.91186e6			0.408594
$552$	−1.06815e6	+	2.29209e6i	−0.149206	+	0.320173i
$553$	−2.41466e6			−0.335771
$554$	3.57386e6	−	2.29678e6i	0.494724	−	0.317940i
$555$	−80002.9	+	556432.i	−0.0110249	+	0.0766796i
$556$	387459.	−	848416.i	0.0531543	−	0.116392i
$557$	−2.29456e6	+	673743.i	−0.313373	+	0.0920145i	−0.434637	−	0.900606i	$-0.643123\pi$
$557$	−2.29456e6	+	673743.i	−0.313373	+	0.0920145i	0.121264	+	0.992620i	$0.461305\pi$
$558$	−457366.	−	1.00149e6i	−0.0621840	−	0.136164i
$559$	5.77203e6	+	6.66127e6i	0.781266	+	0.901629i
$560$	318872.	+	2.21781e6i	0.0429682	+	0.298850i
$561$	−6.29651e6	−	1.84882e6i	−0.844681	−	0.248021i
$562$	−886046.	+	1.02255e6i	−0.118336	+	0.136567i
$563$	−8.33141e6	−	5.35427e6i	−1.10776	−	0.711917i	−0.146960	−	0.989142i	$-0.546949\pi$
$563$	−8.33141e6	−	5.35427e6i	−1.10776	−	0.711917i	−0.960805	+	0.277225i	$0.910585\pi$
$564$	−3.19703e6	−	2.05461e6i	−0.423204	−	0.271976i
$565$	1.31859e7	−	1.52174e7i	1.73776	−	2.00548i
$566$	−1.68225e6	−	493953.i	−0.220724	−	0.0648103i
$567$	−32923.3	−	228986.i	−0.00430076	−	0.0299124i
$568$	1.22883e6	+	1.41814e6i	0.159816	+	0.184437i
$569$	3.90516e6	+	8.55110e6i	0.505659	+	1.10724i	0.974588	+	0.224003i	$0.0719127\pi$
$569$	3.90516e6	+	8.55110e6i	0.505659	+	1.10724i	−0.468929	+	0.883236i	$0.655360\pi$
$570$	−1.61195e6	+	473312.i	−0.207810	+	0.0610184i
$571$	2.40808e6	−	5.27296e6i	0.309087	−	0.676806i	−0.689799	−	0.724001i	$-0.742301\pi$
$571$	2.40808e6	−	5.27296e6i	0.309087	−	0.676806i	0.998886	+	0.0471952i	$0.0150283\pi$
$572$	1.08275e6	−	7.53071e6i	0.138369	−	0.962379i
$573$	−2.82318e6	+	1.81435e6i	−0.359213	+	0.230852i
$574$	259245.			0.0328421
$575$	−1.62993e6	−	1.19906e7i	−0.205589	−	1.51242i
$576$	−1.13664e6			−0.142747
$577$	−1.01587e7	+	6.52862e6i	−1.27028	+	0.816361i	−0.989657	−	0.143457i	$-0.954178\pi$
$577$	−1.01587e7	+	6.52862e6i	−1.27028	+	0.816361i	−0.280625	+	0.959817i	$0.590542\pi$
$578$	−794054.	+	5.52277e6i	−0.0988623	+	0.687602i
$579$	2.90427e6	−	6.35946e6i	0.360031	−	0.788359i
$580$	6.18391e6	−	1.81576e6i	0.763296	−	0.224124i
$581$	207219.	+	453747.i	0.0254677	+	0.0557665i
$582$	−1.59143e6	−	1.83661e6i	−0.194751	−	0.224755i
$583$	−1.23319e6	−	8.57701e6i	−0.150265	−	1.04512i
$584$	−111213.	−	32655.0i	−0.0134934	−	0.00396203i
$585$	3.62941e6	−	4.18856e6i	0.438477	−	0.506029i
$586$	1.58776e6	+	1.02039e6i	0.191004	+	0.122751i
$587$	1.43336e6	+	921167.i	0.171696	+	0.110343i	0.623667	−	0.781690i	$-0.285642\pi$
$587$	1.43336e6	+	921167.i	0.171696	+	0.110343i	−0.451970	+	0.892033i	$0.649279\pi$
$588$	−2.62962e6	+	3.03475e6i	−0.313654	+	0.361976i
$589$	−8.22161e6	−	2.41408e6i	−0.976491	−	0.286724i
$590$	−899874.	−	6.25876e6i	−0.106427	−	0.740216i
$591$	392122.	+	452533.i	0.0461798	+	0.0532944i
$592$	−208853.	−	457323.i	−0.0244926	−	0.0536314i
$593$	−1.32606e7	+	3.89367e6i	−1.54856	+	0.454698i	−0.940669	−	0.339325i	$-0.889801\pi$
$593$	−1.32606e7	+	3.89367e6i	−1.54856	+	0.454698i	−0.607889	+	0.794022i	$0.707983\pi$
$594$	190528.	−	417198.i	0.0221560	−	0.0485150i
$595$	943322.	−	6.56095e6i	0.109236	−	0.759756i
$596$	808241.	−	519425.i	0.0932020	−	0.0598973i
$597$	3.31149e6			0.380266
$598$	2.98541e6	+	1.95122e6i	0.341390	+	0.223128i
$599$	9.47438e6			1.07891			0.539453	−	0.842016i	$-0.318631\pi$
$599$	9.47438e6			1.07891			0.539453	+	0.842016i	$0.318631\pi$
$600$	−3.99957e6	+	2.57036e6i	−0.453560	+	0.291485i
$601$	−2.49881e6	+	1.73796e7i	−0.282193	+	1.96270i	−0.0118612	+	0.999930i	$0.503776\pi$
$601$	−2.49881e6	+	1.73796e7i	−0.282193	+	1.96270i	−0.270332	+	0.962767i	$0.587133\pi$
$602$	−306057.	+	670171.i	−0.0344200	+	0.0753693i
$603$	−3.75963e6	+	1.10393e6i	−0.421067	+	0.123637i
$604$	11407.7	+	24979.3i	0.00127234	+	0.00278605i
$605$	−2.46001e6	−	2.83900e6i	−0.273243	−	0.315339i
$606$	−213632.	−	1.48584e6i	−0.0236311	−	0.164358i
$607$	9.14318e6	+	2.68468e6i	1.00722	+	0.295747i	0.743417	−	0.668829i	$-0.233204\pi$
$607$	9.14318e6	+	2.68468e6i	1.00722	+	0.295747i	0.263806	+	0.964576i	$0.415022\pi$
$608$	3.65480e6	−	4.21786e6i	0.400963	−	0.462736i
$609$	−675484.	−	434107.i	−0.0738026	−	0.0474300i
$610$	2.98582e6	+	1.91887e6i	0.324892	+	0.208795i
$611$	−7.42798e6	+	8.57234e6i	−0.804948	+	0.928959i
$612$	4.71382e6	+	1.38410e6i	0.508738	+	0.149379i
$613$	−1.91091e6	−	1.32907e7i	−0.205395	−	1.42855i	−0.787940	−	0.615752i	$-0.788852\pi$
$613$	−1.91091e6	−	1.32907e7i	−0.205395	−	1.42855i	0.582545	−	0.812798i	$-0.302057\pi$
$614$	1.32997e6	+	1.53487e6i	0.142371	+	0.164305i
$615$	−1.33793e6	−	2.92965e6i	−0.142641	−	0.312340i
$616$	1.29130e6	−	379161.i	0.137112	−	0.0402598i
$617$	4.53511e6	−	9.93051e6i	0.479596	−	1.05017i	−0.502979	−	0.864299i	$-0.667763\pi$
$617$	4.53511e6	−	9.93051e6i	0.479596	−	1.05017i	0.982574	−	0.185869i	$-0.0595101\pi$
$618$	−376815.	+	2.62080e6i	−0.0396878	+	0.276034i
$619$	−28525.6	+	18332.3i	−0.00299232	+	0.00192305i	−0.542136	−	0.840291i	$-0.682384\pi$
$619$	−28525.6	+	18332.3i	−0.00299232	+	0.00192305i	0.539144	+	0.842214i	$0.318748\pi$
$620$	−1.89655e7			−1.98146
$621$	−1.20036e6	−	1.40701e6i	−0.124905	−	0.146409i
$622$	2.01182e6			0.208504
$623$	816961.	−	525029.i	0.0843299	−	0.0541955i
$624$	−705407.	+	4.90621e6i	−0.0725234	+	0.504411i
$625$	−797783.	+	1.74690e6i	−0.0816930	+	0.178883i
$626$	2.90341e6	−	852518.i	0.296123	−	0.0869496i
$627$	−1.48283e6	−	3.24694e6i	−0.150634	−	0.329842i
$628$	5.85571e6	+	6.75785e6i	0.592489	+	0.683769i
$629$	211666.	+	1.47217e6i	0.0213316	+	0.148365i
$630$	444498.	+	130516.i	0.0446188	+	0.0131013i
$631$	−7.86093e6	+	9.07199e6i	−0.785960	+	0.907046i	−0.997525	−	0.0703180i	$-0.977599\pi$
$631$	−7.86093e6	+	9.07199e6i	−0.785960	+	0.907046i	0.211565	+	0.977364i	$0.432144\pi$
$632$	6.38037e6	+	4.10042e6i	0.635409	+	0.408353i
$633$	1.46522e6	+	941641.i	0.145343	+	0.0934063i
$634$	−12824.3	+	14800.0i	−0.00126710	+	0.00146231i
$635$	−2.03594e7	−	5.97806e6i	−2.00369	−	0.588337i
$636$	923213.	+	6.42109e6i	0.0905022	+	0.629457i
$637$	7.84865e6	+	9.05783e6i	0.766384	+	0.884455i
$638$	−661293.	−	1.44803e6i	−0.0643194	−	0.140840i
$639$	−1.31681e6	+	386650.i	−0.127576	+	0.0374598i
$640$	6.67361e6	−	1.46132e7i	0.644037	−	1.41024i
$641$	−609436.	+	4.23872e6i	−0.0585845	+	0.407464i	0.939335	+	0.343000i	$0.111443\pi$
$641$	−609436.	+	4.23872e6i	−0.0585845	+	0.407464i	−0.997920	+	0.0644645i	$0.979466\pi$
$642$	−2.98644e6	+	1.91927e6i	−0.285967	+	0.183780i
$643$	−570191.			−0.0543867			−0.0271934	−	0.999630i	$-0.508657\pi$
$643$	−570191.			−0.0543867			−0.0271934	+	0.999630i	$0.508657\pi$
$644$	384475.	−	2.53544e6i	0.0365303	−	0.240901i
$645$	9.15291e6			0.866283
$646$	−3.73924e6	+	2.40306e6i	−0.352534	+	0.226560i
$647$	1.38013e6	−	9.59902e6i	0.129616	−	0.901501i	−0.816424	−	0.577453i	$-0.804047\pi$
$647$	1.38013e6	−	9.59902e6i	0.129616	−	0.901501i	0.946041	−	0.324048i	$-0.105044\pi$
$648$	−301855.	+	660970.i	−0.0282397	+	0.0618364i
$649$	1.28905e7	−	3.78501e6i	1.20132	−	0.352740i
$650$	2.78550e6	+	6.09939e6i	0.258594	+	0.566243i
$651$	1.54732e6	+	1.78570e6i	0.143096	+	0.165142i
$652$	−152102.	−	1.05789e6i	−0.0140125	−	0.0974588i
$653$	−1.11161e7	−	3.26398e6i	−1.02016	−	0.299547i	−0.271458	−	0.962450i	$-0.587506\pi$
$653$	−1.11161e7	−	3.26398e6i	−1.02016	−	0.299547i	−0.748705	+	0.662904i	$0.769324\pi$
$654$	1.01525e6	−	1.17166e6i	0.0928169	−	0.107116i
$655$	1.58494e6	+	1.01858e6i	0.144347	+	0.0927663i
$656$	2.42314e6	+	1.55726e6i	0.219846	+	0.141287i
$657$	55513.8	−	64066.3i	0.00501750	−	0.00579051i
$658$	−909712.	−	267116.i	−0.0819104	−	0.0240511i
$659$	120812.	+	840265.i	0.0108367	+	0.0753708i	0.994522	−	0.104526i	$-0.0333326\pi$
$659$	120812.	+	840265.i	0.0108367	+	0.0753708i	−0.983685	+	0.179897i	$0.942424\pi$
$660$	−5.17378e6	−	5.97086e6i	−0.462326	−	0.533552i
$661$	2.28674e6	+	5.00726e6i	0.203570	+	0.445756i	0.983690	−	0.179875i	$-0.0575692\pi$
$661$	2.28674e6	+	5.00726e6i	0.203570	+	0.445756i	−0.780120	+	0.625630i	$0.784842\pi$
$662$	4.72129e6	−	1.38630e6i	0.418712	−	0.122945i
$663$	6.09136e6	−	1.33382e7i	0.538184	−	1.17846i
$664$	222978.	−	1.55084e6i	0.0196264	−	0.136505i
$665$	3.03310e6	−	1.94926e6i	0.265970	−	0.170929i
$666$	−103949.			−0.00908099
$667$	−6.41903e6	−	49387.8i	−0.558670	−	0.00429839i
$668$	1.38776e7			1.20330
$669$	9.54328e6	−	6.13309e6i	0.824389	−	0.529803i
$670$	1.11668e6	−	7.76667e6i	0.0961040	−	0.668418i
$671$	−3.13268e6	+	6.85962e6i	−0.268602	+	0.588157i
$672$	−1.47663e6	+	433579.i	−0.126139	+	0.0370378i
$673$	−4.72208e6	−	1.03399e7i	−0.401879	−	0.879992i	−0.997076	−	0.0764127i	$-0.975653\pi$
$673$	−4.72208e6	−	1.03399e7i	−0.401879	−	0.879992i	0.595197	−	0.803580i	$-0.297074\pi$
$674$	−2.16427e6	−	2.49770e6i	−0.183511	−	0.211783i
$675$	−494852.	−	3.44177e6i	−0.0418038	−	0.290752i
$676$	6.09870e6	+	1.79074e6i	0.513299	+	0.150718i
$677$	−1.51497e6	+	1.74837e6i	−0.127037	+	0.146609i	−0.815705	−	0.578468i	$-0.803651\pi$
$677$	−1.51497e6	+	1.74837e6i	−0.127037	+	0.146609i	0.688667	+	0.725077i	$0.258196\pi$
$678$	3.13222e6	+	2.01295e6i	0.261684	+	0.168174i
$679$	4.38748e6	+	2.81966e6i	0.365208	+	0.234705i
$680$	−1.36340e7	+	1.57344e7i	−1.13071	+	1.30490i
$681$	−165832.	−	48692.6i	−0.0137025	−	0.00402342i
$682$	666661.	+	4.63673e6i	0.0548838	+	0.381725i
$683$	−1.33812e7	−	1.54427e7i	−1.09760	−	1.26670i	−0.961143	−	0.276051i	$-0.910974\pi$
$683$	−1.33812e7	−	1.54427e7i	−1.09760	−	1.26670i	−0.136456	−	0.990646i	$-0.543571\pi$
$684$	1.11010e6	+	2.43079e6i	0.0907243	+	0.198659i
$685$	−1.69485e7	+	4.97654e6i	−1.38008	+	0.405229i
$686$	−865581.	+	1.89536e6i	−0.0702259	+	0.153773i
$687$	−1.32024e6	+	9.18245e6i	−0.106723	+	0.742278i
$688$	−6.88633e6	+	4.42558e6i	−0.554647	+	0.356450i
$689$	1.93621e7			1.55384
$690$	3.56149e6	−	1.01605e6i	0.284779	−	0.0812441i
$691$	1.35760e7			1.08163			0.540813	−	0.841143i	$-0.318117\pi$
$691$	1.35760e7			1.08163			0.540813	+	0.841143i	$0.318117\pi$
$692$	−7.32988e6	+	4.71063e6i	−0.581878	+	0.373950i
$693$	−140080.	+	974277.i	−0.0110801	+	0.0770636i
$694$	−2.96457e6	+	6.49151e6i	−0.233649	+	0.511620i
$695$	−2.77374e6	+	814444.i	−0.217823	+	0.0639587i
$696$	1.04769e6	+	2.29412e6i	0.0819805	+	0.179512i
$697$	−5.58013e6	−	6.43981e6i	−0.435073	−	0.502101i
$698$	−431845.	−	3.00355e6i	−0.0335498	−	0.233344i
$699$	−4.97975e6	−	1.46219e6i	−0.385491	−	0.113190i
$700$	3.15731e6	−	3.64373e6i	0.243541	−	0.281062i
$701$	1.70806e7	+	1.09770e7i	1.31283	+	0.843703i	0.994547	−	0.104293i	$-0.0332579\pi$
$701$	1.70806e7	+	1.09770e7i	1.31283	+	0.843703i	0.318281	+	0.947996i	$0.396894\pi$
$702$	862139.	+	554063.i	0.0660290	+	0.0424342i
$703$	−529786.	+	611406.i	−0.0404308	+	0.0466596i
$704$	4.64021e6	+	1.36249e6i	0.352863	+	0.103610i
$705$	1.67630e6	+	1.16589e7i	0.127022	+	0.883457i
$706$	1.08008e6	+	1.24648e6i	0.0815539	+	0.0941182i
$707$	1.33828e6	+	2.93043e6i	0.100693	+	0.220487i
$708$	−9.65038e6	+	2.83361e6i	−0.723538	+	0.212450i
$709$	−6.76298e6	+	1.48089e7i	−0.505269	+	1.10638i	0.469452	+	0.882958i	$0.344451\pi$
$709$	−6.76298e6	+	1.48089e7i	−0.505269	+	1.10638i	−0.974721	+	0.223426i	$0.928276\pi$
$710$	391116.	−	2.72027e6i	0.0291179	−	0.202520i
$711$	−4.66643e6	+	2.99894e6i	−0.346187	+	0.222481i
$712$	−3.05027e6			−0.225496
$713$	1.80831e7	+	5.46115e6i	1.33214	+	0.402309i
$714$	1.22567e6			0.0899761
$715$	−1.98375e7	+	1.27488e7i	−1.45118	+	0.932619i
$716$	−473328.	+	3.29207e6i	−0.0345048	+	0.239986i
$717$	−2.87975e6	+	6.30576e6i	−0.209197	+	0.458078i
$718$	−4.04764e6	+	1.18849e6i	−0.293016	+	0.0860372i
$719$	1.07123e7	+	2.34567e7i	0.772788	+	1.69217i	0.720415	+	0.693543i	$0.243951\pi$
$719$	1.07123e7	+	2.34567e7i	0.772788	+	1.69217i	0.0523730	+	0.998628i	$0.483322\pi$
$720$	3.37068e6	+	3.88998e6i	0.242319	+	0.279651i
$721$	−808681.	−	5.62450e6i	−0.0579348	−	0.402945i
$722$	2.01732e6	+	592338.i	0.144023	+	0.0422889i
$723$	−7.09164e6	+	8.18419e6i	−0.504546	+	0.582277i
$724$	−1.81180e7	−	1.16437e7i	−1.28459	−	0.825555i
$725$	−1.01528e7	−	6.52483e6i	−0.717368	−	0.461025i
$726$	454884.	−	524964.i	0.0320301	−	0.0369647i
$727$	−3.34818e6	−	983115.i	−0.234949	−	0.0689872i	0.162139	−	0.986768i	$-0.448161\pi$
$727$	−3.34818e6	−	983115.i	−0.234949	−	0.0689872i	−0.397087	+	0.917781i	$0.629979\pi$
$728$	427968.	+	2.97658e6i	0.0299283	+	0.208156i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	70519.5	+	154416.i	0.00489781	+	0.0107247i
$731$	2.32352e7	−	6.82246e6i	1.60825	−	0.472224i
$732$	2.34525e6	−	5.13538e6i	0.161775	−	0.354238i
$733$	482969.	−	3.35912e6i	0.0332016	−	0.230922i	−0.966463	−	0.256805i	$-0.917330\pi$
$733$	482969.	−	3.35912e6i	0.0332016	−	0.230922i	0.999665	+	0.0258821i	$0.00823944\pi$
$734$	222015.	−	142680.i	0.0152104	−	0.00977514i
$735$	1.24459e7			0.849782
$736$	−8.12832e6	+	9.23604e6i	−0.553103	+	0.628479i
$737$	1.66716e7			1.13060
$738$	501003.	−	321975.i	0.0338610	−	0.0217611i
$739$	−1.76098e6	+	1.22479e7i	−0.118616	+	0.824995i	0.840465	+	0.541865i	$0.182282\pi$
$739$	−1.76098e6	+	1.22479e7i	−0.118616	+	0.824995i	−0.959082	+	0.283129i	$0.908627\pi$
$740$	−743847.	+	1.62880e6i	−0.0499349	+	0.109342i
$741$	7.65288e6	−	2.24709e6i	0.512011	−	0.150340i
$742$	672320.	+	1.47217e6i	0.0448297	+	0.0981634i
$743$	1.12065e7	+	1.29330e7i	0.744732	+	0.859466i	0.994047	−	0.108956i	$-0.0347509\pi$
$743$	1.12065e7	+	1.29330e7i	0.744732	+	0.859466i	−0.249315	+	0.968422i	$0.580205\pi$
$744$	−1.05620e6	−	7.34602e6i	−0.0699541	−	0.486541i
$745$	−2.85717e6	−	838942.i	−0.188602	−	0.0553785i
$746$	−5.96708e6	+	6.88637e6i	−0.392568	+	0.453047i
$747$	964001.	+	619526.i	0.0632085	+	0.0406217i
$748$	−1.75845e7	−	1.13009e7i	−1.14915	−	0.738514i
$749$	4.98913e6	−	5.75777e6i	0.324953	−	0.375016i
$750$	2.30383e6	+	676464.i	0.149553	+	0.0439129i
$751$	−3.76487e6	−	2.61852e7i	−0.243585	−	1.69417i	−0.633842	−	0.773463i	$-0.718523\pi$
$751$	−3.76487e6	−	2.61852e7i	−0.243585	−	1.69417i	0.390257	−	0.920706i	$-0.372386\pi$
$752$	−6.89846e6	−	7.96125e6i	−0.444844	−	0.513377i
$753$	−1.99810e6	−	4.37522e6i	−0.128419	−	0.281198i
$754$	3.41293e6	−	1.00213e6i	0.218625	−	0.0641940i
$755$	35357.2	−	77421.5i	0.00225741	−	0.00494304i
$756$	104869.	−	729383.i	0.00667336	−	0.0464142i
$757$	1.70162e7	−	1.09357e7i	1.07925	−	0.693595i	0.124869	−	0.992173i	$-0.460149\pi$
$757$	1.70162e7	−	1.09357e7i	1.07925	−	0.693595i	0.954385	+	0.298579i	$0.0965125\pi$
$758$	4.33041e6			0.273751
$759$	3.21374e6	+	7.18284e6i	0.202491	+	0.452577i
$760$	−1.13246e7			−0.711197
$761$	1.04672e7	−	6.72687e6i	0.655193	−	0.421067i	−0.170368	−	0.985381i	$-0.554495\pi$
$761$	1.04672e7	−	6.72687e6i	0.655193	−	0.421067i	0.825560	+	0.564314i	$0.190859\pi$
$762$	558389.	−	3.88368e6i	0.0348377	−	0.242301i
$763$	−1.38215e6	+	3.02648e6i	−0.0859494	+	0.188203i
$764$	−1.02565e7	+	3.01158e6i	−0.635720	+	0.186664i
$765$	−6.32549e6	−	1.38509e7i	−0.390788	−	0.855705i
$766$	−916707.	−	1.05794e6i	−0.0564493	−	0.0651460i
$767$	4.27222e6	+	2.97140e7i	0.262220	+	1.82378i
$768$	−1.02743e6	−	301680.i	−0.0628562	−	0.0184562i
$769$	−9.08315e6	+	1.04825e7i	−0.553886	+	0.639219i	−0.961784	−	0.273809i	$-0.911716\pi$
$769$	−9.08315e6	+	1.04825e7i	−0.553886	+	0.639219i	0.407898	+	0.913028i	$0.366262\pi$
$770$	−1.65816e6	−	1.06564e6i	−0.100786	−	0.0647713i
$771$	−1.33187e7	−	8.55941e6i	−0.806912	−	0.518571i
$772$	1.45831e7	−	1.68298e7i	0.880656	−	1.01633i
$773$	−1.86197e6	−	546724.i	−0.112079	−	0.0329093i	0.225212	−	0.974310i	$-0.427692\pi$
$773$	−1.86197e6	−	546724.i	−0.112079	−	0.0329093i	−0.337291	+	0.941400i	$0.609511\pi$
$774$	240864.	+	1.67525e6i	0.0144517	+	0.100514i
$775$	2.32570e7	+	2.68400e7i	1.39091	+	1.60519i
$776$	−6.80508e6	−	1.49011e7i	−0.405676	−	0.888306i
$777$	214048.	−	62850.0i	0.0127191	−	0.00373468i
$778$	2.29322e6	−	5.02146e6i	0.135831	−	0.297427i
$779$	659624.	−	4.58778e6i	0.0389451	−	0.270869i
$780$	1.48512e7	−	9.54426e6i	0.874025	−	0.561702i
$781$	5.83921e6			0.342552
$782$	8.28368e6	−	5.23399e6i	0.484403	−	0.306066i
$783$	−1.84455e6			−0.107519
$784$	−9.36386e6	+	6.01779e6i	−0.544083	+	0.349661i
$785$	3.94423e6	−	2.74327e7i	0.228448	−	1.58889i
$786$	−144720.	+	316894.i	−0.00835552	+	0.0182960i
$787$	−1.64612e7	+	4.83344e6i	−0.947381	+	0.278176i	−0.718696	−	0.695324i	$-0.755261\pi$
$787$	−1.64612e7	+	4.83344e6i	−0.947381	+	0.278176i	−0.228685	+	0.973500i	$0.573443\pi$
$788$	792320.	+	1.73494e6i	0.0454553	+	0.0995333i
$789$	5.55515e6	+	6.41099e6i	0.317690	+	0.366634i
$790$	−1.58082e6	−	1.09949e7i	−0.0901189	−	0.626791i
$791$	−7.66684e6	−	2.25119e6i	−0.435688	−	0.127929i
$792$	2.02459e6	−	2.33651e6i	0.114690	−	0.132359i
$793$	−1.41754e7	−	9.10998e6i	−0.800483	−	0.514439i
$794$	−8.05988e6	−	5.17977e6i	−0.453709	−	0.291581i
$795$	1.31669e7	−	1.51954e7i	0.738863	−	0.852694i
$796$	1.01207e7	+	2.97171e6i	0.566146	+	0.166235i
$797$	−2.66174e6	−	1.85128e7i	−0.148429	−	1.03235i	−0.918792	−	0.394742i	$-0.870834\pi$
$797$	−2.66174e6	−	1.85128e7i	−0.148429	−	1.03235i	0.770363	−	0.637606i	$-0.220075\pi$
$798$	436589.	+	503850.i	0.0242698	+	0.0280088i
$799$	1.29458e7	+	2.83473e7i	0.717401	+	1.57089i
$800$	−2.21945e7	+	6.51689e6i	−1.22608	+	0.360011i
$801$	926743.	−	2.02928e6i	0.0510362	−	0.111754i
$802$	552271.	−	3.84113e6i	0.0303191	−	0.210874i
$803$	−303426.	+	195000.i	−0.0166059	+	0.0106720i
$804$	−1.24810e7			−0.680940
$805$	−6.71936e6	+	4.24558e6i	−0.365459	+	0.230912i
$806$	−1.04672e7			−0.567534
$807$	1.05035e7	−	6.75022e6i	0.567743	−	0.364867i
$808$	1.44006e6	−	1.00158e7i	0.0775980	−	0.539706i
$809$	8.40224e6	−	1.83983e7i	0.451361	−	0.988342i	−0.538011	−	0.842938i	$-0.680824\pi$
$809$	8.40224e6	−	1.83983e7i	0.451361	−	0.988342i	0.989372	−	0.145405i	$-0.0464485\pi$
$810$	1.02111e6	−	299825.i	0.0546839	−	0.0160566i
$811$	2.44110e6	+	5.34526e6i	0.130327	+	0.285376i	0.963534	−	0.267584i	$-0.0862254\pi$
$811$	2.44110e6	+	5.34526e6i	0.130327	+	0.285376i	−0.833208	+	0.552960i	$0.813498\pi$
$812$	−1.67488e6	−	1.93291e6i	−0.0891442	−	0.102878i
$813$	1.98285e6	+	1.37910e7i	0.105212	+	0.731762i
$814$	424359.	+	124603.i	0.0224477	+	0.00659125i
$815$	−2.16927e6	+	2.50347e6i	−0.114398	+	0.132023i
$816$	1.14562e7	+	7.36246e6i	0.602304	+	0.387077i
$817$	1.10811e7	+	7.12138e6i	0.580800	+	0.373258i
$818$	−4.16887e6	+	4.81113e6i	−0.217839	+	0.251399i
$819$	−2.11029e6	−	619637.i	−0.109934	−	0.0322795i
$820$	−1.45998e6	−	1.01544e7i	−0.0758249	−	0.527374i
$821$	1.13128e7	+	1.30556e7i	0.585748	+	0.675989i	0.968830	−	0.247725i	$-0.0796829\pi$
$821$	1.13128e7	+	1.30556e7i	0.585748	+	0.675989i	−0.383082	+	0.923714i	$0.625137\pi$
$822$	−1.35686e6	−	2.97111e6i	−0.0700416	−	0.153370i
$823$	−2.23059e7	+	6.54960e6i	−1.14794	+	0.337066i	−0.799736	−	0.600352i	$-0.795027\pi$
$823$	−2.23059e7	+	6.54960e6i	−1.14794	+	0.337066i	−0.348206	+	0.937418i	$0.613209\pi$
$824$	−7.41435e6	+	1.62352e7i	−0.380413	+	0.832987i
$825$	−2.10547e6	+	1.46438e7i	−0.107699	+	0.749066i
$826$	−2.11092e6	+	1.35660e6i	−0.107652	+	0.0691836i
$827$	−1.48783e7			−0.756464			−0.378232	−	0.925711i	$-0.623468\pi$
$827$	−1.48783e7			−0.756464			−0.378232	+	0.925711i	$0.623468\pi$
$828$	−2.40593e6	−	5.37736e6i	−0.121957	−	0.272580i
$829$	−2.68689e7			−1.35788			−0.678942	−	0.734192i	$-0.737561\pi$
$829$	−2.68689e7			−1.35788			−0.678942	+	0.734192i	$0.737561\pi$
$830$	−1.93042e6	+	1.24061e6i	−0.0972651	+	0.0625085i
$831$	−2.98066e6	+	2.07309e7i	−0.149730	+	1.04140i
$832$	−4.48903e6	+	9.82960e6i	−0.224825	+	0.492297i
$833$	3.15946e7	−	9.27701e6i	1.57761	−	0.463229i
$834$	−222060.	−	486243.i	−0.0110549	−	0.0242068i
$835$	−2.81673e7	−	3.25068e7i	−1.39807	−	1.61346i
$836$	−1.61810e6	−	1.12541e7i	−0.0800736	−	0.556924i
$837$	5.20806e6	+	1.52922e6i	0.256958	+	0.0754497i
$838$	1.60834e6	−	1.85612e6i	0.0791167	−	0.0913055i
$839$	−3.01726e7	−	1.93908e7i	−1.47982	−	0.951021i	−0.997168	−	0.0752077i	$-0.976038\pi$
$839$	−3.01726e7	−	1.93908e7i	−1.47982	−	0.951021i	−0.482650	−	0.875813i	$-0.660326\pi$
$840$	2.62705e6	+	1.68830e6i	0.128460	+	0.0825565i
$841$	9.23943e6	−	1.06629e7i	0.450459	−	0.519857i
$842$	−341550.	−	100288.i	−0.0166025	−	0.00487494i
$843$	−949313.	−	6.60262e6i	−0.0460088	−	0.319998i
$844$	3.63305e6	+	4.19277e6i	0.175556	+	0.202602i
$845$	−8.18387e6	−	1.79202e7i	−0.394291	−	0.863377i
$846$	−2.08981e6	+	613623.i	−0.100388	+	0.0294765i
$847$	−619274.	+	1.35602e6i	−0.0296602	+	0.0649468i
$848$	−2.55909e6	+	1.77988e7i	−0.122207	+	0.849967i
$849$	7.27155e6	−	4.67314e6i	0.346225	−	0.222505i
$850$	1.84224e7			0.874577
$851$	1.17825e6	−	1.33882e6i	0.0557718	−	0.0633722i
$852$	−4.37146e6			−0.206314
$853$	2.27909e7	−	1.46468e7i	1.07248	−	0.689242i	0.119672	−	0.992813i	$-0.461816\pi$
$853$	2.27909e7	−	1.46468e7i	1.07248	−	0.689242i	0.952809	+	0.303572i	$0.0981792\pi$
$854$	200447.	−	1.39414e6i	0.00940490	−	0.0654125i
$855$	3.44069e6	−	7.53405e6i	0.160964	−	0.352463i
$856$	−2.29605e7	+	6.74181e6i	−1.07102	+	0.314479i
$857$	−991132.	−	2.17028e6i	−0.0460977	−	0.100940i	0.885182	−	0.465245i	$-0.154034\pi$
$857$	−991132.	−	2.17028e6i	−0.0460977	−	0.100940i	−0.931280	+	0.364305i	$0.881307\pi$
$858$	−2.85544e6	−	3.29535e6i	−0.132420	−	0.152821i
$859$	−2.79745e6	−	1.94567e7i	−0.129354	−	0.899675i	−0.946376	−	0.323068i	$-0.895286\pi$
$859$	−2.79745e6	−	1.94567e7i	−0.129354	−	0.899675i	0.817022	−	0.576607i	$-0.195623\pi$
$860$	2.79735e7	+	8.21376e6i	1.28974	+	0.378701i
$861$	−836974.	+	965919.i	−0.0384772	+	0.0444051i
$862$	2.03817e6	+	1.30985e6i	0.0934270	+	0.0600419i
$863$	−1.66694e7	−	1.07128e7i	−0.761891	−	0.489637i	0.101088	−	0.994877i	$-0.467768\pi$
$863$	−1.66694e7	−	1.07128e7i	−0.761891	−	0.489637i	−0.862979	+	0.505240i	$0.831404\pi$
$864$	−2.31517e6	+	2.67185e6i	−0.105511	+	0.121766i
$865$	2.59115e7	+	7.60831e6i	1.17748	+	0.345739i
$866$	−433488.	−	3.01498e6i	−0.0196419	−	0.136612i
$867$	−1.80136e7	−	2.07888e7i	−0.813867	−	0.939253i
$868$	3.12651e6	+	6.84610e6i	0.140851	+	0.308421i
$869$	2.26450e7	−	6.64919e6i	1.01724	−	0.298689i
$870$	1.53443e6	−	3.35994e6i	0.0687305	−	0.150499i
$871$	−5.30152e6	+	3.68729e7i	−0.236786	+	1.64688i
$872$	8.79149e6	−	5.64995e6i	0.391536	−	0.251625i
$873$	1.19809e7			0.532053
$874$	5.10229e6	+	1.54090e6i	0.225936	+	0.0682334i
$875$	−5.15297e6			−0.227529
$876$	227156.	−	145985.i	0.0100015	−	0.00642757i
$877$	1.84499e6	−	1.28322e7i	0.0810017	−	0.563379i	−0.908392	−	0.418120i	$-0.862689\pi$
$877$	1.84499e6	−	1.28322e7i	0.0810017	−	0.563379i	0.989394	−	0.145259i	$-0.0464016\pi$
$878$	−4.19223e6	+	9.17970e6i	−0.183531	+	0.401876i
$879$	−8.92797e6	+	2.62149e6i	−0.389745	+	0.114439i
$880$	−9.09755e6	−	1.99209e7i	−0.396021	−	0.867164i
$881$	−2.18860e7	−	2.52578e7i	−0.950005	−	1.09636i	−0.995246	−	0.0973884i	$-0.968951\pi$
$881$	−2.18860e7	−	2.52578e7i	−0.950005	−	1.09636i	0.0452412	−	0.998976i	$-0.485594\pi$
$882$	327521.	+	2.27796e6i	0.0141765	+	0.0985995i
$883$	6.64088e6	+	1.94994e6i	0.286632	+	0.0841626i	0.421888	−	0.906648i	$-0.361368\pi$
$883$	6.64088e6	+	1.94994e6i	0.286632	+	0.0841626i	−0.135256	+	0.990811i	$0.543186\pi$
$884$	3.05863e7	−	3.52985e7i	1.31643	−	1.51924i
$885$	2.62247e7	+	1.68536e7i	1.12552	+	0.723326i
$886$	−6.87593e6	−	4.41889e6i	−0.294271	−	0.189116i
$887$	−2.16950e7	+	2.50374e7i	−0.925871	+	1.06851i	0.0716000	+	0.997433i	$0.477190\pi$
$887$	−2.16950e7	+	2.50374e7i	−0.925871	+	1.06851i	−0.997471	+	0.0710784i	$0.977356\pi$
$888$	−672316.	−	197410.i	−0.0286115	−	0.00840110i
$889$	1.19836e6	+	8.33475e6i	0.0508548	+	0.353703i
$890$	2.92551e6	+	3.37622e6i	0.123802	+	0.142875i
$891$	939313.	+	2.05681e6i	0.0396384	+	0.0867960i
$892$	3.46704e7	−	1.01801e7i	1.45897	−	0.428392i
$893$	−7.04173e6	+	1.54192e7i	−0.295496	+	0.647045i
$894$	78362.5	−	545023.i	0.00327917	−	0.0228072i
$895$	8.67201e6	−	5.57316e6i	0.361878	−	0.232565i
$896$	−6.37516e6			−0.265290
$897$	−1.69084e7	+	4.82378e6i	−0.701653	+	0.200173i
$898$	−1.14544e7			−0.474003
$899$	1.58488e7	−	1.01854e7i	0.654029	−	0.420319i
$900$	1.57624e6	−	1.09630e7i	0.0648657	−	0.451151i
$901$	2.20984e7	−	4.83887e7i	0.906877	−	1.98578i
$902$	−2.43124e6	+	713877.i	−0.0994974	+	0.0292151i
$903$	−1.50888e6	−	3.30398e6i	−0.0615793	−	0.134840i
$904$	1.64357e7	+	1.89678e7i	0.668907	+	0.771960i
$905$	9.49981e6	+	6.60726e7i	0.385561	+	2.68164i
$906$	15100.8	+	4434.01i	0.000611196	+	0.000179463i
$907$	−6.70955e6	+	7.74323e6i	−0.270816	+	0.312539i	−0.874825	−	0.484439i	$-0.839024\pi$
$907$	−6.70955e6	+	7.74323e6i	−0.270816	+	0.312539i	0.604009	+	0.796978i	$0.293569\pi$
$908$	−463126.	−	297633.i	−0.0186416	−	0.0119803i
$909$	6.22580e6	+	4.00108e6i	0.249911	+	0.160608i
$910$	2.88419e6	−	3.32853e6i	0.115457	−	0.133245i
$911$	5.47852e6	+	1.60864e6i	0.218709	+	0.0642188i	0.389251	−	0.921132i	$-0.372734\pi$
$911$	5.47852e6	+	1.60864e6i	0.218709	+	0.0642188i	−0.170542	+	0.985350i	$0.554552\pi$
$912$	1.05418e6	+	7.33199e6i	0.0419690	+	0.291900i
$913$	−3.19281e6	−	3.68469e6i	−0.126764	−	0.146293i
$914$	−120971.	−	264889.i	−0.00478978	−	0.0104881i
$915$	−1.67892e7	+	4.92975e6i	−0.662945	+	0.194658i
$916$	−1.22752e7	+	2.68790e7i	−0.483383	+	1.05846i
$917$	106401.	−	740038.i	0.00417854	−	0.0290624i
$918$	2.36866e6	−	1.52224e6i	0.0927674	−	0.0596180i
$919$	−2.56840e7			−1.00317			−0.501584	−	0.865109i	$-0.667249\pi$
$919$	−2.56840e7			−1.00317			−0.501584	+	0.865109i	$0.667249\pi$
$920$	2.49645e7	+	192076.i	0.972418	+	0.00748175i
$921$	−1.00126e7			−0.388953
$922$	6.23081e6	−	4.00430e6i	0.241389	−	0.155131i
$923$	−1.85686e6	+	1.29147e7i	−0.0717421	+	0.498977i
$924$	−1.30243e6	+	2.85192e6i	−0.0501850	+	0.109890i
$925$	3.21723e6	−	944665.i	0.123631	−	0.0363014i
$926$	2.61448e6	+	5.72492e6i	0.100198	+	0.219403i
$927$	−8.54828e6	−	9.86524e6i	−0.326723	−	0.377058i
$928$	1.74630e6	+	1.21458e7i	0.0665655	+	0.462973i
$929$	2.86425e7	+	8.41019e6i	1.08886	+	0.319717i	0.776417	−	0.630220i	$-0.217035\pi$
$929$	2.86425e7	+	8.41019e6i	1.08886	+	0.319717i	0.312441	+	0.949937i	$0.398853\pi$
$930$	−7.11800e6	+	8.21461e6i	−0.269868	+	0.311444i
$931$	1.50678e7	+	9.68346e6i	0.569737	+	0.366148i
$932$	−1.39072e7	−	8.93759e6i	−0.524444	−	0.337040i
$933$	−6.49518e6	+	7.49584e6i	−0.244280	+	0.281914i
$934$	−1.14076e7	−	3.34957e6i	−0.427885	−	0.125638i
$935$	9.22010e6	+	6.41272e7i	0.344911	+	2.39891i
$936$	4.52389e6	+	5.22085e6i	0.168781	+	0.194783i
$937$	−1.16471e7	−	2.55037e7i	−0.433381	−	0.948972i	−0.992766	−	0.120064i	$-0.961690\pi$
$937$	−1.16471e7	−	2.55037e7i	−0.433381	−	0.948972i	0.559385	−	0.828908i	$-0.311037\pi$
$938$	−2.98767e6	+	877259.i	−0.110873	+	0.0325552i
$939$	−6.19728e6	+	1.35701e7i	−0.229370	+	0.502251i
$940$	−5.33946e6	+	3.71368e7i	−0.197096	+	1.37083i
$941$	−2.24400e7	+	1.44213e7i	−0.826132	+	0.530923i	−0.884047	−	0.467399i	$-0.845191\pi$
$941$	−2.24400e7	+	1.44213e7i	−0.826132	+	0.530923i	0.0579144	+	0.998322i	$0.481555\pi$
$942$	5.12478e6			0.188169
$943$	−1.53191e6	+	1.01023e7i	−0.0560990	+	0.369949i
$944$	−2.78795e7			−1.01825
$945$	−1.92135e6	+	1.23478e6i	−0.0699886	+	0.0449789i
$946$	1.02482e6	−	7.12775e6i	0.0372321	−	0.258955i
$947$	7.99575e6	−	1.75083e7i	0.289724	−	0.634407i	−0.707671	−	0.706542i	$-0.750254\pi$
$947$	7.99575e6	−	1.75083e7i	0.289724	−	0.634407i	0.997395	+	0.0721352i	$0.0229813\pi$
$948$	−1.69530e7	+	4.97785e6i	−0.612668	+	0.179896i
$949$	−334797.	−	733103.i	−0.0120675	−	0.0264241i
$950$	6.56213e6	+	7.57311e6i	0.235904	+	0.272248i
$951$	−13740.0	−	95563.8i	−0.000492646	−	0.00342643i
$952$	7.92734e6	+	2.32768e6i	0.283488	+	0.0832397i
$953$	1.32162e6	−	1.52524e6i	0.0471385	−	0.0544007i	−0.731691	−	0.681637i	$-0.761268\pi$
$953$	1.32162e6	−	1.52524e6i	0.0471385	−	0.0544007i	0.778829	+	0.627236i	$0.215814\pi$
$954$	3.12769e6	+	2.01004e6i	0.111263	+	0.0715046i
$955$	2.78718e7	+	1.79121e7i	0.988911	+	0.635535i
$956$	−1.44600e7	+	1.66877e7i	−0.511708	+	0.590543i
$957$	7.53018e6	+	2.21106e6i	0.265782	+	0.0780406i
$958$	973470.	+	6.77063e6i	0.0342696	+	0.238350i
$959$	4.59041e6	+	5.29762e6i	0.161178	+	0.186009i
$960$	4.66157e6	+	1.02074e7i	0.163250	+	0.357468i
$961$	−2.57236e7	+	7.55313e6i	−0.898511	+	0.263827i
$962$	−410533.	+	898943.i	−0.0143025	+	0.0313180i
$963$	2.49074e6	−	1.73235e7i	0.0865492	−	0.601963i
$964$	−2.90182e7	+	1.86489e7i	−1.00572	+	0.646338i
$965$	−6.90211e7			−2.38596
$966$	−953889.	−	1.11811e6i	−0.0328893	−	0.0385517i
$967$	5.45040e7			1.87440			0.937200	−	0.348793i	$-0.113409\pi$
$967$	5.45040e7			1.87440			0.937200	+	0.348793i	$0.113409\pi$
$968$	3.93905e6	−	2.53147e6i	0.135115	−	0.0868330i
$969$	3.11859e6	−	2.16903e7i	0.106696	−	0.742088i
$970$	−9.96661e6	+	2.18238e7i	−0.340109	+	0.744735i
$971$	1.18725e7	−	3.48607e6i	0.404103	−	0.118655i	−0.0733634	−	0.997305i	$-0.523373\pi$
$971$	1.18725e7	−	3.48607e6i	0.404103	−	0.118655i	0.477467	+	0.878650i	$0.341555\pi$
$972$	−703207.	−	1.53981e6i	−0.0238736	−	0.0522759i
$973$	751253.	+	866992.i	0.0254392	+	0.0293584i
$974$	267385.	+	1.85971e6i	0.00903109	+	0.0628126i
$975$	−3.17186e7	−	9.31343e6i	−1.06857	−	0.313760i
$976$	1.02480e7	−	1.18268e7i	0.344362	−	0.397414i
$977$	−2.76577e7	−	1.77745e7i	−0.927001	−	0.595747i	−0.0123200	−	0.999924i	$-0.503922\pi$
$977$	−2.76577e7	−	1.77745e7i	−0.927001	−	0.595747i	−0.914681	+	0.404177i	$0.867558\pi$
$978$	−515293.	−	331159.i	−0.0172269	−	0.0110711i
$979$	−6.21583e6	+	7.17345e6i	−0.207273	+	0.239206i
$980$	3.80377e7	+	1.11689e7i	1.26517	+	0.371487i
$981$	1.08774e6	+	7.56539e6i	0.0360871	+	0.250992i
$982$	−4.45218e6	−	5.13809e6i	−0.147331	−	0.170029i
$983$	233231.	+	510705.i	0.00769844	+	0.0168572i	0.913442	−	0.406969i	$-0.133414\pi$
$983$	233231.	+	510705.i	0.00769844	+	0.0168572i	−0.905744	+	0.423826i	$0.860687\pi$
$984$	3.85184e6	−	1.13100e6i	0.126818	−	0.0372371i
$985$	2.45574e6	−	5.37731e6i	0.0806475	−	0.176593i
$986$	1.39079e6	−	9.67314e6i	0.0455584	−	0.316866i
$987$	3.93225e6	−	2.52710e6i	0.128484	−	0.0825715i
$988$	2.54056e7			0.828013
$989$	−2.43068e7	−	1.58866e7i	−0.790200	−	0.516464i
$990$	−4.52797e6			−0.146830
$991$	1.65654e7	−	1.06459e7i	0.535817	−	0.344349i	−0.244584	−	0.969628i	$-0.578651\pi$
$991$	1.65654e7	−	1.06459e7i	0.535817	−	0.344349i	0.780401	+	0.625279i	$0.215015\pi$
$992$	5.13881e6	−	3.57412e7i	0.165800	−	1.15316i
$993$	−1.00775e7	+	2.20667e7i	−0.324325	+	0.710172i
$994$	−1.04643e6	+	307260.i	−0.0335927	+	0.00986370i
$995$	−1.35810e7	−	2.97383e7i	−0.434885	−	0.952266i
$996$	2.39026e6	+	2.75851e6i	0.0763479	+	0.0881102i
$997$	−4.70611e6	−	3.27317e7i	−0.149942	−	1.04287i	−0.916310	−	0.400470i	$-0.868847\pi$
$997$	−4.70611e6	−	3.27317e7i	−0.149942	−	1.04287i	0.766368	−	0.642402i	$-0.222062\pi$
$998$	1.78869e6	+	525208.i	0.0568473	+	0.0166919i
$999$	335598.	−	387301.i	0.0106391	−	0.0122782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.b.58.6	yes	100
23.2	even	11	inner	69.6.e.b.25.6	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.b.25.6	✓	100	23.2	even	11	inner
69.6.e.b.58.6	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.53574 - 0.986959i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-11.9089 + 26.0768i) q^{4} +(85.2534 - 25.0326i) q^{5} +(6.82520 + 14.9451i) q^{6} +(-23.0904 - 26.6477i) q^{7} +(15.7614 + 109.623i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(1.53574 - 0.986959i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(-11.9089 + 26.0768i) q^{4} +(85.2534 - 25.0326i) q^{5} +(6.82520 + 14.9451i) q^{6} +(-23.0904 - 26.6477i) q^{7} +(15.7614 + 109.623i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(106.221 - 122.585i) q^{10} +(289.925 + 186.323i) q^{11} +(-217.049 - 139.489i) q^{12} +(-504.291 + 581.983i) q^{13} +(-61.7611 - 18.1347i) q^{14} +(113.805 + 791.533i) q^{15} +(-468.342 - 540.496i) q^{16} +(878.900 + 1924.52i) q^{17} +(-141.879 + 41.6593i) q^{18} +(-478.069 + 1046.82i) q^{19} +(-362.500 + 2521.25i) q^{20} +(266.964 - 171.567i) q^{21} +629.142 q^{22} +(1071.63 - 2299.55i) q^{23} -996.755 q^{24} +(4012.59 - 2578.73i) q^{25} +(-200.066 + 1391.49i) q^{26} +(302.838 - 663.122i) q^{27} +(969.869 - 284.779i) q^{28} +(-1051.10 - 2301.59i) q^{29} +(955.986 + 1103.27i) q^{30} +(1059.64 + 7369.93i) q^{31} +(-4653.16 - 1366.29i) q^{32} +(-2031.19 + 2344.11i) q^{33} +(3249.19 + 2088.13i) q^{34} +(-2635.60 - 1693.80i) q^{35} +(1520.63 - 1754.90i) q^{36} +(674.505 + 198.053i) q^{37} +(298.985 + 2079.48i) q^{38} +(-4538.62 - 5237.85i) q^{39} +(4087.88 + 8951.20i) q^{40} +(-3864.38 + 1134.68i) q^{41} +(240.657 - 526.964i) q^{42} +(1628.91 - 11329.3i) q^{43} +(-8311.39 + 5341.41i) q^{44} -7197.05 q^{45} +(-623.824 - 4589.17i) q^{46} +14729.5 q^{47} +(5414.82 - 3479.89i) q^{48} +(2214.95 - 15405.3i) q^{49} +(3617.18 - 7920.52i) q^{50} +(-18270.1 + 5364.59i) q^{51} +(-9170.72 - 20081.1i) q^{52} +(-16465.3 - 19002.0i) q^{53} +(-189.395 - 1317.27i) q^{54} +(29381.2 + 8627.10i) q^{55} +(2557.27 - 2951.25i) q^{56} +(-8713.20 - 5599.63i) q^{57} +(-3885.80 - 2497.25i) q^{58} +(25528.2 - 29461.1i) q^{59} +(-21995.9 - 6458.59i) q^{60} +(3114.05 + 21658.7i) q^{61} +(8901.15 + 10272.5i) q^{62} +(1186.45 + 2597.96i) q^{63} +(13464.2 - 3953.44i) q^{64} +(-28423.9 + 62239.8i) q^{65} +(-805.826 + 5604.64i) q^{66} +(40695.4 - 26153.3i) q^{67} -60652.1 q^{68} +(19112.8 + 12491.8i) q^{69} -5719.30 q^{70} +(14253.5 - 9160.19i) q^{71} +(1276.68 - 8879.48i) q^{72} +(-434.760 + 951.991i) q^{73} +(1231.33 - 361.552i) q^{74} +(17832.9 + 39048.6i) q^{75} +(-21604.6 - 24933.0i) q^{76} +(-1729.38 - 12028.1i) q^{77} +(-12139.7 - 3564.53i) q^{78} +(44845.8 - 51754.9i) q^{79} +(-53457.8 - 34355.2i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-4814.79 + 5556.56i) q^{82} +(-13574.0 - 3985.68i) q^{83} +(1294.68 + 9004.73i) q^{84} +(123105. + 142071. i) q^{85} +(-8679.99 - 19006.5i) q^{86} +(21849.8 - 6415.68i) q^{87} +(-15855.7 + 34719.2i) q^{88} +(-3919.60 + 27261.5i) q^{89} +(-11052.8 + 7103.20i) q^{90} +27152.8 q^{91} +(47203.1 + 55329.8i) q^{92} -67011.5 q^{93} +(22620.7 - 14537.5i) q^{94} +(-14552.2 + 101213. i) q^{95} +(18131.4 - 39702.2i) q^{96} +(-141921. + 41671.8i) q^{97} +(-11802.8 - 25844.6i) q^{98} +(-18280.7 - 21097.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9	\( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) 100 * q + 12 * q^2 - 90 * q^3 - 148 * q^4 - 50 * q^5 + 9 * q^6 - 78 * q^7 - 1844 * q^8 - 810 * q^9 - 38 * q^10 + 404 * q^11 - 1332 * q^12 - 2850 * q^13 - 724 * q^14 + 639 * q^15 - 5556 * q^16 - 2519 * q^17 + 972 * q^18 + 1117 * q^19 - 22411 * q^20 - 702 * q^21 + 32798 * q^22 + 12040 * q^23 - 756 * q^24 - 5928 * q^25 - 788 * q^26 - 7290 * q^27 - 54024 * q^28 + 13774 * q^29 - 342 * q^30 + 12501 * q^31 + 37412 * q^32 - 4185 * q^33 + 9441 * q^34 + 28894 * q^35 - 21789 * q^36 - 38902 * q^37 - 15042 * q^38 - 25650 * q^39 - 133835 * q^40 - 19456 * q^41 + 85950 * q^42 - 8126 * q^43 + 120643 * q^44 + 40500 * q^45 + 90500 * q^46 + 60846 * q^47 + 62955 * q^48 - 25762 * q^49 - 110197 * q^50 - 51084 * q^51 + 91725 * q^52 - 83896 * q^53 - 31347 * q^54 + 190331 * q^55 - 358140 * q^56 - 40437 * q^57 + 150977 * q^58 + 248368 * q^59 + 122625 * q^60 - 81516 * q^61 + 82657 * q^62 - 6318 * q^63 - 298028 * q^64 - 25475 * q^65 - 6669 * q^66 + 51337 * q^67 + 491228 * q^68 + 17082 * q^69 + 395832 * q^70 - 206653 * q^71 - 149364 * q^72 - 121007 * q^73 + 716844 * q^74 - 59490 * q^75 + 171145 * q^76 + 71982 * q^77 + 11916 * q^78 - 661118 * q^79 - 1386592 * q^80 - 65610 * q^81 - 136394 * q^82 - 368400 * q^83 + 165204 * q^84 + 45505 * q^85 - 99668 * q^86 + 50112 * q^87 - 474416 * q^88 + 328408 * q^89 - 3078 * q^90 + 1042320 * q^91 + 1554071 * q^92 + 160722 * q^93 - 299081 * q^94 - 434011 * q^95 + 412740 * q^96 - 88136 * q^97 + 515807 * q^98 - 37665 * q^99

Introduction

L-functions

Modular forms

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