LMFDB - Embedded newform 69.6.e.b.58.10

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			58.10
Character	$\chi$	$=$	69.58
Dual form			69.6.e.b.25.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.36123 - 6.01610i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(38.1459 - 83.5279i) q^{4} +(9.60568 - 2.82048i) q^{5} +(41.6036 + 91.0991i) q^{6} +(-91.0258 - 105.049i) q^{7} +(-94.7428 - 658.950i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(9.36123 - 6.01610i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(38.1459 - 83.5279i) q^{4} +(9.60568 - 2.82048i) q^{5} +(41.6036 + 91.0991i) q^{6} +(-91.0258 - 105.049i) q^{7} +(-94.7428 - 658.950i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(72.9526 - 84.1918i) q^{10} +(477.199 + 306.677i) q^{11} +(695.240 + 446.804i) q^{12} +(332.041 - 383.195i) q^{13} +(-1484.10 - 435.771i) q^{14} +(12.8227 + 89.1837i) q^{15} +(-2926.95 - 3377.88i) q^{16} +(578.349 + 1266.41i) q^{17} +(-864.834 + 253.938i) q^{18} +(387.268 - 847.998i) q^{19} +(130.828 - 909.931i) q^{20} +(1052.41 - 676.343i) q^{21} +6312.17 q^{22} +(-1213.02 + 2228.21i) q^{23} +5991.54 q^{24} +(-2544.60 + 1635.32i) q^{25} +(802.968 - 5584.77i) q^{26} +(302.838 - 663.122i) q^{27} +(-12246.8 + 3595.99i) q^{28} +(1141.22 + 2498.93i) q^{29} +(656.574 + 757.727i) q^{30} +(959.899 + 6676.24i) q^{31} +(-27281.2 - 8010.49i) q^{32} +(-3343.22 + 3858.28i) q^{33} +(13032.9 + 8375.73i) q^{34} +(-1170.65 - 752.334i) q^{35} +(-4870.79 + 5621.19i) q^{36} +(9826.59 + 2885.35i) q^{37} +(-1476.34 - 10268.1i) q^{38} +(2988.37 + 3448.76i) q^{39} +(-2768.63 - 6062.44i) q^{40} +(2495.93 - 732.872i) q^{41} +(5782.91 - 12662.8i) q^{42} +(736.418 - 5121.90i) q^{43} +(43819.3 - 28161.0i) q^{44} -810.907 q^{45} +(2049.72 + 28156.4i) q^{46} +3824.03 q^{47} +(33840.5 - 21747.9i) q^{48} +(-357.789 + 2488.48i) q^{49} +(-13982.4 + 30617.2i) q^{50} +(-12022.4 + 3530.10i) q^{51} +(-19341.5 - 42352.0i) q^{52} +(-2683.03 - 3096.38i) q^{53} +(-1154.47 - 8029.53i) q^{54} +(5448.80 + 1599.91i) q^{55} +(-60598.3 + 69934.1i) q^{56} +(7058.27 + 4536.08i) q^{57} +(25717.1 + 16527.4i) q^{58} +(23041.4 - 26591.2i) q^{59} +(7938.46 + 2330.94i) q^{60} +(-4663.11 - 32432.7i) q^{61} +(49150.8 + 56723.0i) q^{62} +(4677.17 + 10241.6i) q^{63} +(-166345. + 48843.2i) q^{64} +(2108.68 - 4617.37i) q^{65} +(-8084.84 + 56231.3i) q^{66} +(-18595.0 + 11950.3i) q^{67} +127842. q^{68} +(-18296.1 - 13660.1i) q^{69} -15484.9 q^{70} +(-67726.0 + 43524.9i) q^{71} +(-7674.16 + 53375.0i) q^{72} +(-11883.8 + 26021.9i) q^{73} +(109348. - 32107.3i) q^{74} +(-11308.8 - 24762.9i) q^{75} +(-56058.8 - 64695.3i) q^{76} +(-11221.2 - 78045.1i) q^{77} +(48722.8 + 14306.3i) q^{78} +(-33866.2 + 39083.7i) q^{79} +(-37642.6 - 24191.4i) q^{80} +(5519.46 + 3547.14i) q^{81} +(18956.0 - 21876.3i) q^{82} +(78820.9 + 23143.9i) q^{83} +(-16348.3 - 113705. i) q^{84} +(9127.31 + 10533.5i) q^{85} +(-23920.1 - 52377.6i) q^{86} +(-23723.2 + 6965.75i) q^{87} +(156874. - 343506. i) q^{88} +(13.5230 - 94.0545i) q^{89} +(-7591.09 + 4878.50i) q^{90} -70478.7 q^{91} +(139846. + 186318. i) q^{92} -60704.1 q^{93} +(35797.6 - 23005.7i) q^{94} +(1328.21 - 9237.87i) q^{95} +(106303. - 232772. i) q^{96} +(44675.2 - 13117.8i) q^{97} +(11621.6 + 25447.7i) q^{98} +(-30088.9 - 34724.5i) 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 $

$2$	9.36123	−	6.01610i	1.65485	−	1.06351i	0.729794	−	0.683667i	$-0.239616\pi$
$2$	9.36123	−	6.01610i	1.65485	−	1.06351i	0.925053	−	0.379839i	$-0.124020\pi$
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$4$	38.1459	−	83.5279i	1.19206	−	2.61025i
$5$	9.60568	−	2.82048i	0.171832	−	0.0504543i	−0.194685	−	0.980866i	$-0.562368\pi$
$5$	9.60568	−	2.82048i	0.171832	−	0.0504543i	0.366517	+	0.930412i	$0.380550\pi$
$6$	41.6036	+	91.0991i	0.471794	+	1.03308i
$7$	−91.0258	−	105.049i	−0.702133	−	0.810305i	0.286906	−	0.957959i	$-0.407373\pi$
$7$	−91.0258	−	105.049i	−0.702133	−	0.810305i	−0.989039	+	0.147654i	$0.952828\pi$
$8$	−94.7428	−	658.950i	−0.523385	−	3.64022i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	72.9526	−	84.1918i	0.230697	−	0.266238i
$11$	477.199	+	306.677i	1.18910	+	0.764188i	0.977037	−	0.213068i	$-0.0683457\pi$
$11$	477.199	+	306.677i	1.18910	+	0.764188i	0.212062	+	0.977256i	$0.431982\pi$
$12$	695.240	+	446.804i	1.39374	+	0.895703i
$13$	332.041	−	383.195i	0.544920	−	0.628871i	−0.414772	−	0.909925i	$-0.636139\pi$
$13$	332.041	−	383.195i	0.544920	−	0.628871i	0.959692	+	0.281054i	$0.0906840\pi$
$14$	−1484.10	−	435.771i	−2.02369	−	0.594208i
$15$	12.8227	+	89.1837i	0.0147147	+	0.102343i
$16$	−2926.95	−	3377.88i	−2.85835	−	3.29872i
$17$	578.349	+	1266.41i	0.485364	+	1.06280i	0.980954	+	0.194242i	$0.0622248\pi$
$17$	578.349	+	1266.41i	0.485364	+	1.06280i	−0.495589	+	0.868557i	$0.665048\pi$
$18$	−864.834	+	253.938i	−0.629146	+	0.184734i
$19$	387.268	−	847.998i	0.246109	−	0.538903i	−0.745753	−	0.666223i	$-0.767910\pi$
$19$	387.268	−	847.998i	0.246109	−	0.538903i	0.991862	+	0.127319i	$0.0406373\pi$
$20$	130.828	−	909.931i	0.0731353	−	0.508667i
$21$	1052.41	−	676.343i	0.520759	−	0.334671i
$22$	6312.17			2.78050
$23$	−1213.02	+	2228.21i	−0.478134	+	0.878287i
$23$	−1213.02	+	2228.21i	−0.478134	+	0.878287i
$24$	5991.54			2.12329
$25$	−2544.60	+	1635.32i	−0.814273	+	0.523302i
$26$	802.968	−	5584.77i	0.232951	−	1.62021i
$27$	302.838	−	663.122i	0.0799467	−	0.175059i
$28$	−12246.8	+	3595.99i	−2.95208	+	0.866808i
$29$	1141.22	+	2498.93i	0.251986	+	0.551771i	0.992778	−	0.119962i	$-0.0382773\pi$
$29$	1141.22	+	2498.93i	0.251986	+	0.551771i	−0.740793	+	0.671734i	$0.765550\pi$
$30$	656.574	+	757.727i	0.133193	+	0.153713i
$31$	959.899	+	6676.24i	0.179400	+	1.24775i	0.858156	+	0.513388i	$0.171610\pi$
$31$	959.899	+	6676.24i	0.179400	+	1.24775i	−0.678757	+	0.734363i	$0.737481\pi$
$32$	−27281.2	−	8010.49i	−4.70965	−	1.38288i
$33$	−3343.22	+	3858.28i	−0.534416	+	0.616749i
$34$	13032.9	+	8375.73i	1.93350	+	1.24258i
$35$	−1170.65	−	752.334i	−0.161532	−	0.103810i
$36$	−4870.79	+	5621.19i	−0.626388	+	0.722890i
$37$	9826.59	+	2885.35i	1.18005	+	0.346493i	0.812191	−	0.583391i	$-0.198274\pi$
$37$	9826.59	+	2885.35i	1.18005	+	0.346493i	0.367854	+	0.929884i	$0.380093\pi$
$38$	−1476.34	−	10268.1i	−0.165854	−	1.15354i
$39$	2988.37	+	3448.76i	0.314610	+	0.363079i
$40$	−2768.63	−	6062.44i	−0.273599	−	0.599098i
$41$	2495.93	−	732.872i	0.231885	−	0.0680877i	−0.163725	−	0.986506i	$-0.552351\pi$
$41$	2495.93	−	732.872i	0.231885	−	0.0680877i	0.395611	+	0.918418i	$0.370533\pi$
$42$	5782.91	−	12662.8i	0.505851	−	1.10766i
$43$	736.418	−	5121.90i	0.0607370	−	0.422435i	−0.936655	−	0.350254i	$-0.886095\pi$
$43$	736.418	−	5121.90i	0.0607370	−	0.422435i	0.997392	−	0.0721806i	$-0.0229958\pi$
$44$	43819.3	−	28161.0i	3.41220	−	2.19288i
$45$	−810.907			−0.0596953
$46$	2049.72	+	28156.4i	0.142824	+	1.96193i
$47$	3824.03			0.252509			0.126254	−	0.991998i	$-0.459704\pi$
$47$	3824.03			0.252509			0.126254	+	0.991998i	$0.459704\pi$
$48$	33840.5	−	21747.9i	2.11999	−	1.36243i
$49$	−357.789	+	2488.48i	−0.0212881	+	0.148062i
$50$	−13982.4	+	30617.2i	−0.790963	+	1.73197i
$51$	−12022.4	+	3530.10i	−0.647242	+	0.190047i
$52$	−19341.5	−	42352.0i	−0.991932	−	2.17203i
$53$	−2683.03	−	3096.38i	−0.131201	−	0.151414i	0.686348	−	0.727273i	$-0.259213\pi$
$53$	−2683.03	−	3096.38i	−0.131201	−	0.151414i	−0.817548	+	0.575860i	$0.804667\pi$
$54$	−1154.47	−	8029.53i	−0.0538765	−	0.374719i
$55$	5448.80	+	1599.91i	0.242881	+	0.0713164i
$56$	−60598.3	+	69934.1i	−2.58220	+	2.98002i
$57$	7058.27	+	4536.08i	0.287747	+	0.184924i
$58$	25717.1	+	16527.4i	1.00381	+	0.645109i
$59$	23041.4	−	26591.2i	0.861745	−	0.994506i	−0.138247	−	0.990398i	$-0.544147\pi$
$59$	23041.4	−	26591.2i	0.861745	−	0.994506i	0.999992	−	0.00410858i	$-0.00130780\pi$
$60$	7938.46	+	2330.94i	0.284681	+	0.0835898i
$61$	−4663.11	−	32432.7i	−0.160454	−	1.11598i	−0.897779	−	0.440446i	$-0.854820\pi$
$61$	−4663.11	−	32432.7i	−0.160454	−	1.11598i	0.737325	−	0.675538i	$-0.236089\pi$
$62$	49150.8	+	56723.0i	1.62387	+	1.87404i
$63$	4677.17	+	10241.6i	0.148467	+	0.325098i
$64$	−166345.	+	48843.2i	−5.07644	+	1.49058i
$65$	2108.68	−	4617.37i	0.0619052	−	0.135554i
$66$	−8084.84	+	56231.3i	−0.228461	+	1.58898i
$67$	−18595.0	+	11950.3i	−0.506067	+	0.325230i	−0.768639	−	0.639683i	$-0.779066\pi$
$67$	−18595.0	+	11950.3i	−0.506067	+	0.325230i	0.262572	+	0.964912i	$0.415429\pi$
$68$	127842.			3.35275
$69$	−18296.1	−	13660.1i	−0.462632	−	0.345406i
$70$	−15484.9			−0.377714
$71$	−67726.0	+	43524.9i	−1.59444	+	1.02469i	−0.624606	+	0.780940i	$0.714741\pi$
$71$	−67726.0	+	43524.9i	−1.59444	+	1.02469i	−0.969839	+	0.243748i	$0.921623\pi$
$72$	−7674.16	+	53375.0i	−0.174462	+	1.21341i
$73$	−11883.8	+	26021.9i	−0.261005	+	0.571521i	−0.994083	−	0.108624i	$-0.965356\pi$
$73$	−11883.8	+	26021.9i	−0.261005	+	0.571521i	0.733078	+	0.680145i	$0.238083\pi$
$74$	109348.	−	32107.3i	2.32129	−	0.681593i
$75$	−11308.8	−	24762.9i	−0.232148	−	0.508333i
$76$	−56058.8	−	64695.3i	−1.11329	−	1.28481i
$77$	−11221.2	−	78045.1i	−0.215681	−	1.50009i
$78$	48722.8	+	14306.3i	0.906768	+	0.266251i
$79$	−33866.2	+	39083.7i	−0.610519	+	0.704577i	−0.973878	−	0.227073i	$-0.927084\pi$
$79$	−33866.2	+	39083.7i	−0.610519	+	0.704577i	0.363359	+	0.931649i	$0.381630\pi$
$80$	−37642.6	−	24191.4i	−0.657590	−	0.422607i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	18956.0	−	21876.3i	0.311323	−	0.359286i
$83$	78820.9	+	23143.9i	1.25587	+	0.368758i	0.840958	−	0.541101i	$-0.181992\pi$
$83$	78820.9	+	23143.9i	1.25587	+	0.368758i	0.414917	+	0.909859i	$0.363811\pi$
$84$	−16348.3	−	113705.i	−0.252799	−	1.75826i
$85$	9127.31	+	10533.5i	0.137024	+	0.158134i
$86$	−23920.1	−	52377.6i	−0.348752	−	0.763660i
$87$	−23723.2	+	6965.75i	−0.336027	+	0.0986665i
$88$	156874.	−	343506.i	2.15946	−	4.72855i
$89$	13.5230	−	94.0545i	0.000180966	−	0.00125865i	−0.989731	−	0.142944i	$-0.954343\pi$
$89$	13.5230	−	94.0545i	0.000180966	−	0.00125865i	0.989912	+	0.141685i	$0.0452522\pi$
$90$	−7591.09	+	4878.50i	−0.0987865	+	0.0634862i
$91$	−70478.7			−0.892184
$92$	139846.	+	186318.i	1.72258	+	2.29502i
$93$	−60704.1			−0.727797
$94$	35797.6	−	23005.7i	0.417863	−	0.268544i
$95$	1328.21	−	9237.87i	0.0150993	−	0.105018i
$96$	106303.	−	232772.i	1.17725	−	2.57782i
$97$	44675.2	−	13117.8i	0.482100	−	0.141557i	−0.0316468	−	0.999499i	$-0.510075\pi$
$97$	44675.2	−	13117.8i	0.482100	−	0.141557i	0.513747	+	0.857942i	$0.328257\pi$
$98$	11621.6	+	25447.7i	0.122236	+	0.267660i
$99$	−30088.9	−	34724.5i	−0.308545	−	0.356080i
$100$	39528.4	+	274926.i	0.395284	+	2.74926i
$101$	−148524.	−	43610.5i	−1.44875	−	0.425391i	−0.539620	−	0.841909i	$-0.681432\pi$
$101$	−148524.	−	43610.5i	−1.44875	−	0.425391i	−0.909127	+	0.416518i	$0.863250\pi$
$102$	−91307.2	+	105374.i	−0.868970	+	1.00284i
$103$	−180202.	−	115809.i	−1.67366	−	1.07560i	−0.892195	−	0.451651i	$-0.850835\pi$
$103$	−180202.	−	115809.i	−1.67366	−	1.07560i	−0.781467	−	0.623947i	$-0.785528\pi$
$104$	−283965.	−	182493.i	−2.57443	−	1.65449i
$105$	8201.50	−	9465.03i	0.0725972	−	0.0837816i
$106$	−43744.6	−	12844.6i	−0.378146	−	0.111034i
$107$	−10380.9	−	72200.6i	−0.0876546	−	0.609651i	−0.985543	−	0.169427i	$-0.945808\pi$
$107$	−10380.9	−	72200.6i	−0.0876546	−	0.609651i	0.897888	−	0.440224i	$-0.145101\pi$
$108$	−43837.1	−	50590.7i	−0.361645	−	0.417361i
$109$	46716.6	+	102295.i	0.376622	+	0.824687i	0.999115	+	0.0420615i	$0.0133925\pi$
$109$	46716.6	+	102295.i	0.376622	+	0.824687i	−0.622493	+	0.782625i	$0.713880\pi$
$110$	60632.7	−	17803.4i	0.477777	−	0.140288i
$111$	−38290.0	+	83843.5i	−0.294970	+	0.645895i
$112$	−88416.3	+	614949.i	−0.666020	+	4.63227i
$113$	135532.	−	87100.8i	0.998491	−	0.641691i	0.0641014	−	0.997943i	$-0.479582\pi$
$113$	135532.	−	87100.8i	0.998491	−	0.641691i	0.934390	+	0.356252i	$0.115946\pi$
$114$	93363.6			0.672845
$115$	−5367.30	+	24824.8i	−0.0378452	+	0.175041i
$116$	252263.			1.74064
$117$	−34550.5	+	22204.3i	−0.233340	+	0.149959i
$118$	55720.6	−	387545.i	0.368392	−	2.56223i
$119$	80390.6	−	176031.i	0.520401	−	1.13952i
$120$	57552.8	−	16899.0i	0.364849	−	0.107129i
$121$	66765.2	+	146195.i	0.414560	+	0.907759i
$122$	−238771.	−	275556.i	−1.45238	−	1.67614i
$123$	3331.84	+	23173.4i	0.0198573	+	0.138111i
$124$	594269.	+	174493.i	3.47079	+	1.01912i
$125$	−40317.6	+	46529.0i	−0.230791	+	0.266347i
$126$	105398.	+	67735.3i	0.591435	+	0.380092i
$127$	−147168.	−	94578.8i	−0.809660	−	0.520337i	0.0690950	−	0.997610i	$-0.477989\pi$
$127$	−147168.	−	94578.8i	−0.809660	−	0.520337i	−0.878755	+	0.477273i	$0.841625\pi$
$128$	−667517.	+	770356.i	−3.60112	+	4.15591i
$129$	44684.7	+	13120.6i	0.236420	+	0.0694192i
$130$	−8038.68	−	55910.2i	−0.0417183	−	0.290157i
$131$	−151284.	−	174591.i	−0.770220	−	0.888881i	0.226143	−	0.974094i	$-0.427388\pi$
$131$	−151284.	−	174591.i	−0.770220	−	0.888881i	−0.996363	+	0.0852130i	$0.972843\pi$
$132$	194744.	+	426429.i	0.972811	+	2.13016i
$133$	−124333.	+	36507.5i	−0.609477	+	0.178959i
$134$	−102178.	+	223738.i	−0.491580	+	1.07641i
$135$	1038.64	−	7223.88i	0.00490489	−	0.0341143i
$136$	779705.	−	501086.i	3.61479	−	2.32309i
$137$	232720.			1.05933			0.529667	−	0.848206i	$-0.322317\pi$
$137$	232720.			1.05933			0.529667	+	0.848206i	$0.322317\pi$
$138$	−253454.	−	17804.0i	−1.13293	−	0.0795828i
$139$	−168789.			−0.740981			−0.370491	−	0.928836i	$-0.620810\pi$
$139$	−168789.			−0.740981			−0.370491	+	0.928836i	$0.620810\pi$
$140$	−107496.	+	69083.8i	−0.463526	+	0.297890i
$141$	−4897.94	+	34065.9i	−0.0207475	+	0.144302i
$142$	−372149.	+	814892.i	−1.54880	+	3.39140i
$143$	275967.	−	81031.2i	1.12854	−	0.331369i
$144$	150395.	+	329320.i	0.604405	+	1.32346i
$145$	18010.4	+	20785.1i	0.0711383	+	0.0820980i
$146$	45303.3	+	315091.i	0.175893	+	1.22336i
$147$	−21710.1	−	6374.65i	−0.0828643	−	0.0243312i
$148$	615851.	−	710730.i	2.31111	−	2.66717i
$149$	−49476.7	−	31796.7i	−0.182572	−	0.117332i	0.446162	−	0.894952i	$-0.352790\pi$
$149$	−49476.7	−	31796.7i	−0.182572	−	0.117332i	−0.628735	+	0.777620i	$0.716427\pi$
$150$	−254841.	−	163776.i	−0.924784	−	0.594323i
$151$	−215659.	+	248884.i	−0.769708	+	0.888290i	−0.996321	−	0.0856947i	$-0.972689\pi$
$151$	−215659.	+	248884.i	−0.769708	+	0.888290i	0.226614	+	0.973985i	$0.427234\pi$
$152$	−595479.	−	174848.i	−2.09054	−	0.613837i
$153$	−16048.8	−	111622.i	−0.0554261	−	0.385497i
$154$	−574571.	−	663090.i	−1.95228	−	2.25305i
$155$	28050.7	+	61422.5i	0.0937809	+	0.205352i
$156$	402061.	−	118056.i	1.32276	−	0.388397i
$157$	−40804.8	+	89350.0i	−0.132118	+	0.289298i	−0.964116	−	0.265480i	$-0.914470\pi$
$157$	−40804.8	+	89350.0i	−0.132118	+	0.289298i	0.831998	+	0.554778i	$0.187197\pi$
$158$	−81898.1	+	569614.i	−0.260994	+	1.81526i
$159$	31020.3	−	19935.5i	0.0973090	−	0.0625367i
$160$	−284648.			−0.879040
$161$	344488.	−	75397.1i	1.04739	−	0.229240i
$162$	73008.9			0.218569
$163$	96663.1	−	62121.6i	0.284965	−	0.183136i	−0.390347	−	0.920668i	$-0.627645\pi$
$163$	96663.1	−	62121.6i	0.284965	−	0.183136i	0.675313	+	0.737532i	$0.264009\pi$
$164$	33994.4	−	236436.i	0.0986955	−	0.686442i
$165$	−21231.7	+	46490.8i	−0.0607119	+	0.132941i
$166$	877097.	−	257539.i	2.47046	−	0.725392i
$167$	170448.	+	373230.i	0.472935	+	1.03558i	0.984346	+	0.176247i	$0.0563957\pi$
$167$	170448.	+	373230.i	0.472935	+	1.03558i	−0.511411	+	0.859336i	$0.670877\pi$
$168$	−545385.	−	629407.i	−1.49084	−	1.72052i
$169$	16252.8	+	113041.i	0.0437736	+	0.304452i
$170$	148813.	+	43695.5i	0.394929	+	0.115962i
$171$	−49449.6	+	57067.9i	−0.129322	+	0.149246i
$172$	−399730.	−	256891.i	−1.03026	−	0.662106i
$173$	−49807.0	−	32009.0i	−0.126525	−	0.0813124i	0.475848	−	0.879528i	$-0.342141\pi$
$173$	−49807.0	−	32009.0i	−0.126525	−	0.0813124i	−0.602372	+	0.798215i	$0.705778\pi$
$174$	−180171.	+	207929.i	−0.451141	+	0.520645i
$175$	403414.	+	118453.i	0.995762	+	0.292382i
$176$	−360820.	−	2.50956e6i	−0.878028	−	6.10682i
$177$	207372.	+	239321.i	0.497529	+	0.574179i
$178$	−439.249	−	961.821i	−0.00103911	−	0.00227533i
$179$	392763.	−	115326.i	0.916216	−	0.269025i	0.210561	−	0.977581i	$-0.432471\pi$
$179$	392763.	−	115326.i	0.916216	−	0.269025i	0.705655	+	0.708555i	$0.250653\pi$
$180$	−30932.8	+	67733.4i	−0.0711603	+	0.155819i
$181$	86287.3	−	600141.i	0.195772	−	1.36162i	−0.620614	−	0.784116i	$-0.713116\pi$
$181$	86287.3	−	600141.i	0.195772	−	1.36162i	0.816386	−	0.577507i	$-0.195974\pi$
$182$	−659767.	+	424007.i	−1.47643	+	0.948843i
$183$	294896.			0.650939
$184$	1.58320e6	+	588216.i	3.44741	+	1.28083i
$185$	102529.			0.220251
$186$	−568265.	+	365202.i	−1.20439	+	0.774017i
$187$	−112391.	+	781696.i	−0.235032	+	1.63468i
$188$	145871.	−	319413.i	0.301005	−	0.659110i
$189$	−97226.5	+	28548.3i	−0.197984	+	0.0581334i
$190$	−43142.3	−	94468.5i	−0.0867000	−	0.189847i
$191$	61514.8	+	70991.9i	0.122010	+	0.140807i	0.813468	−	0.581609i	$-0.197577\pi$
$191$	61514.8	+	70991.9i	0.122010	+	0.140807i	−0.691458	+	0.722417i	$0.743031\pi$
$192$	−222055.	−	1.54442e6i	−0.434717	−	3.02352i
$193$	21177.9	+	6218.40i	0.0409252	+	0.0120167i	0.302131	−	0.953266i	$-0.402302\pi$
$193$	21177.9	+	6218.40i	0.0409252	+	0.0120167i	−0.261206	+	0.965283i	$0.584120\pi$
$194$	339297.	−	391569.i	0.647255	−	0.746972i
$195$	38432.4	+	24699.0i	0.0723788	+	0.0465150i
$196$	194209.	+	124811.i	0.361101	+	0.232066i
$197$	−114711.	+	132384.i	−0.210591	+	0.243035i	−0.851212	−	0.524822i	$-0.824132\pi$
$197$	−114711.	+	132384.i	−0.210591	+	0.243035i	0.640620	+	0.767858i	$0.278677\pi$
$198$	−490575.	−	144046.i	−0.889289	−	0.261119i
$199$	122261.	+	850346.i	0.218855	+	1.52217i	0.742276	+	0.670095i	$0.233746\pi$
$199$	122261.	+	850346.i	0.218855	+	1.52217i	−0.523421	+	0.852074i	$0.675344\pi$
$200$	1.31868e6	+	1.52183e6i	2.33111	+	2.69025i
$201$	−82640.5	−	180957.i	−0.144279	−	0.315927i
$202$	−1.65273e6	+	485285.i	−2.84986	+	0.836795i
$203$	158630.	−	347352.i	0.270176	−	0.591602i
$204$	−163744.	+	1.13887e6i	−0.275480	+	1.91601i
$205$	21908.1	−	14079.5i	0.0364099	−	0.0233992i
$206$	−2.38364e6			−3.91356
$207$	145123.	−	145492.i	0.235403	−	0.236001i
$208$	−2.26626e6			−3.63204
$209$	444866.	−	285898.i	0.704471	−	0.452736i
$210$	19833.5	−	137945.i	0.0310350	−	0.215853i
$211$	−450852.	+	987229.i	−0.697153	+	1.52655i	0.146236	+	0.989250i	$0.453284\pi$
$211$	−450852.	+	987229.i	−0.697153	+	1.52655i	−0.843389	+	0.537303i	$0.819443\pi$
$212$	−360981.	+	105993.i	−0.551625	+	0.161972i
$213$	−300991.	−	659078.i	−0.454574	−	0.995377i
$214$	−531544.	−	613434.i	−0.793422	−	0.915658i
$215$	−7372.43	−	51276.4i	−0.0108771	−	0.0756521i
$216$	−465656.	−	136729.i	−0.679095	−	0.199400i
$217$	613960.	−	708547.i	0.885096	−	1.02146i
$218$	1.05274e6	+	676557.i	1.50031	+	0.964191i
$219$	−216592.	−	139195.i	−0.305164	−	0.196117i
$220$	341487.	−	394097.i	0.475682	−	0.548967i
$221$	677317.	+	198878.i	0.932849	+	0.273909i
$222$	145969.	+	1.01523e6i	0.198782	+	1.38256i
$223$	115363.	+	133135.i	0.155347	+	0.179280i	0.828088	−	0.560598i	$-0.189429\pi$
$223$	115363.	+	133135.i	0.155347	+	0.179280i	−0.672741	+	0.739878i	$0.734883\pi$
$224$	1.64180e6	+	3.59504e6i	2.18625	+	4.78722i
$225$	235082.	−	69026.4i	0.309573	−	0.0908990i
$226$	744735.	−	1.63074e6i	0.969908	−	2.12380i
$227$	−85580.3	+	595224.i	−0.110232	+	0.766683i	0.857460	+	0.514550i	$0.172041\pi$
$227$	−85580.3	+	595224.i	−0.110232	+	0.766683i	−0.967693	+	0.252133i	$0.918868\pi$
$228$	648133.	−	416530.i	0.825709	−	0.530651i
$229$	1.04089e6			1.31165			0.655823	−	0.754914i	$-0.272322\pi$
$229$	1.04089e6			1.31165			0.655823	+	0.754914i	$0.272322\pi$
$230$	99103.7	+	264680.i	0.123529	+	0.329915i
$231$	709629.			0.874986
$232$	1.53855e6	−	988765.i	1.87668	−	1.20607i
$233$	30737.3	−	213783.i	0.0370917	−	0.257978i	−0.962835	−	0.270090i	$-0.912946\pi$
$233$	30737.3	−	213783.i	0.0370917	−	0.257978i	0.999927	+	0.0121121i	$0.00385550\pi$
$234$	−189852.	+	415718.i	−0.226660	+	0.496317i
$235$	36732.4	−	10785.6i	0.0433890	−	0.0127402i
$236$	−1.34217e6	−	2.93894e6i	−1.56866	−	3.43488i
$237$	−304796.	−	351753.i	−0.352483	−	0.406787i
$238$	−306464.	−	2.13150e6i	−0.350701	−	2.43918i
$239$	−1.26719e6	−	372079.i	−1.43498	−	0.421348i	−0.530434	−	0.847726i	$-0.677971\pi$
$239$	−1.26719e6	−	372079.i	−1.43498	−	0.421348i	−0.904545	+	0.426379i	$0.859789\pi$
$240$	263721.	−	304350.i	0.295540	−	0.341071i
$241$	62900.1	+	40423.4i	0.0697603	+	0.0448322i	0.575056	−	0.818114i	$-0.304980\pi$
$241$	62900.1	+	40423.4i	0.0697603	+	0.0448322i	−0.505296	+	0.862946i	$0.668617\pi$
$242$	1.50453e6	+	966903.i	1.65144	+	1.06132i
$243$	−38668.9	+	44626.3i	−0.0420093	+	0.0484814i
$244$	−2.88691e6	−	847673.i	−3.10426	−	0.911494i
$245$	3581.90	+	24912.6i	0.00381239	+	0.0265158i
$246$	170604.	+	196887.i	0.179742	+	0.207434i
$247$	−196360.	−	429969.i	−0.204791	−	0.448430i
$248$	4.30837e6	−	1.26505e6i	4.44819	−	1.30611i
$249$	−307132.	+	672524.i	−0.313925	+	0.687400i
$250$	−97499.3	+	678123.i	−0.0986624	+	0.686212i
$251$	142252.	−	91419.9i	0.142520	−	0.0915917i	−0.467438	−	0.884026i	$-0.654823\pi$
$251$	142252.	−	91419.9i	0.142520	−	0.0915917i	0.609957	+	0.792434i	$0.291187\pi$
$252$	1.03387e6			1.02557
$253$	−1.26220e6	+	691293.i	−1.23973	+	0.678986i
$254$	−1.94666e6			−1.89324
$255$	−105527.	+	67818.1i	−0.101628	+	0.0653123i
$256$	−824718.	+	5.73604e6i	−0.786512	+	5.47031i
$257$	539434.	−	1.18120e6i	0.509455	−	1.11555i	−0.463825	−	0.885927i	$-0.653523\pi$
$257$	539434.	−	1.18120e6i	0.509455	−	1.11555i	0.973280	−	0.229623i	$-0.0737494\pi$
$258$	497238.	−	146002.i	0.465067	−	0.136556i
$259$	−591369.	−	1.29492e6i	−0.547784	−	1.19948i
$260$	−305241.	−	352267.i	−0.280033	−	0.323176i
$261$	−31668.2	−	220257.i	−0.0287755	−	0.200138i
$262$	−2.46656e6	−	724247.i	−2.21993	−	0.651829i
$263$	−1.42811e6	+	1.64813e6i	−1.27313	+	1.46927i	−0.459167	+	0.888350i	$0.651852\pi$
$263$	−1.42811e6	+	1.64813e6i	−1.27313	+	1.46927i	−0.813961	+	0.580919i	$0.802693\pi$
$264$	2.85916e6	+	1.83747e6i	2.52481	+	1.62260i
$265$	−34505.6	−	22175.4i	−0.0301839	−	0.0193980i
$266$	−944277.	+	1.08975e6i	−0.818268	+	0.944331i
$267$	820.554	+	240.936i	0.000704415	+	0.000206835i
$268$	288858.	+	2.00905e6i	0.245667	+	1.70865i
$269$	−557793.	−	643727.i	−0.469994	−	0.542402i	0.470416	−	0.882445i	$-0.344104\pi$
$269$	−557793.	−	643727.i	−0.469994	−	0.542402i	−0.940410	+	0.340043i	$0.889558\pi$
$270$	−33736.6	−	73872.9i	−0.0281639	−	0.0616703i
$271$	685190.	−	201190.i	0.566745	−	0.166411i	0.0142073	−	0.999899i	$-0.495478\pi$
$271$	685190.	−	201190.i	0.566745	−	0.166411i	0.552538	+	0.833488i	$0.313659\pi$
$272$	2.58498e6	−	5.66031e6i	2.11853	−	4.63893i
$273$	90271.5	−	627852.i	0.0733067	−	0.509860i
$274$	2.17855e6	−	1.40007e6i	1.75303	−	1.12661i
$275$	−1.71580e6			−1.36815
$276$	−1.83892e6	+	1.00716e6i	−1.45308	+	0.795838i
$277$	546504.			0.427951			0.213975	−	0.976839i	$-0.431359\pi$
$277$	546504.			0.427951			0.213975	+	0.976839i	$0.431359\pi$
$278$	−1.58007e6	+	1.01545e6i	−1.22621	+	0.788038i
$279$	77751.8	−	540776.i	0.0597998	−	0.415917i
$280$	−384840.	+	842681.i	−0.293349	+	0.642345i
$281$	−1.01966e6	+	299399.i	−0.770352	+	0.226196i	−0.643211	−	0.765689i	$-0.722398\pi$
$281$	−1.01966e6	+	299399.i	−0.770352	+	0.226196i	−0.127141	+	0.991885i	$0.540580\pi$
$282$	159093.	+	348366.i	0.119132	+	0.260863i
$283$	1.29476e6	+	1.49424e6i	0.961003	+	1.10906i	0.993976	+	0.109601i	$0.0349572\pi$
$283$	1.29476e6	+	1.49424e6i	0.961003	+	1.10906i	−0.0329725	+	0.999456i	$0.510497\pi$
$284$	1.05207e6	+	7.31730e6i	0.774013	+	5.38338i
$285$	80593.4	+	23664.4i	0.0587743	+	0.0172577i
$286$	2.09590e6	−	2.41880e6i	1.51515	−	1.74857i
$287$	−304182.	−	195486.i	−0.217986	−	0.140091i
$288$	1.93747e6	+	1.24513e6i	1.37643	+	0.884575i
$289$	−339492.	+	391795.i	−0.239103	+	0.275940i
$290$	293645.	+	86221.9i	0.205035	+	0.0602036i
$291$	59637.2	+	414786.i	0.0412843	+	0.287139i
$292$	1.72024e6	+	1.98526e6i	1.18068	+	1.36257i
$293$	−499879.	−	1.09458e6i	−0.340170	−	0.744868i	0.659809	−	0.751434i	$-0.270637\pi$
$293$	−499879.	−	1.09458e6i	−0.340170	−	0.744868i	−0.999978	+	0.00656568i	$0.997910\pi$
$294$	−241583.	+	70935.3i	−0.163004	+	0.0478623i
$295$	146328.	−	320414.i	0.0978978	−	0.214366i
$296$	970303.	−	6.74860e6i	0.643692	−	4.47697i
$297$	347878.	−	223568.i	0.228842	−	0.147068i
$298$	−654454.			−0.426912
$299$	451066.	+	1.20468e6i	0.291784	+	0.779281i
$300$	−2.49978e6			−1.60361
$301$	−605085.	+	388865.i	−0.384947	+	0.247390i
$302$	−521525.	+	3.62729e6i	−0.329047	+	2.28857i
$303$	578734.	−	1.26725e6i	0.362137	−	0.792969i
$304$	−3.99795e6	+	1.17390e6i	−2.48115	+	0.728533i
$305$	−136268.	−	298386.i	−0.0838773	−	0.183666i
$306$	−821765.	−	948367.i	−0.501700	−	0.578993i
$307$	−318493.	−	2.21517e6i	−0.192865	−	1.34141i	−0.824377	−	0.566042i	$-0.808474\pi$
$307$	−318493.	−	2.21517e6i	−0.192865	−	1.34141i	0.631511	−	0.775367i	$-0.282435\pi$
$308$	−6.94698e6	−	2.03982e6i	−4.17272	−	1.22522i
$309$	1.26248e6	−	1.45698e6i	0.752193	−	0.868077i
$310$	632112.	+	406234.i	0.373586	+	0.240089i
$311$	−270704.	−	173971.i	−0.158706	−	0.101994i	0.458877	−	0.888500i	$-0.348252\pi$
$311$	−270704.	−	173971.i	−0.158706	−	0.101994i	−0.617583	+	0.786505i	$0.711888\pi$
$312$	1.98943e6	−	2.29593e6i	1.15703	−	1.33528i
$313$	−1.27944e6	−	375678.i	−0.738177	−	0.216748i	−0.109034	−	0.994038i	$-0.534776\pi$
$313$	−1.27944e6	−	375678.i	−0.738177	−	0.216748i	−0.629143	+	0.777290i	$0.716594\pi$
$314$	155555.	+	1.08191e6i	0.0890350	+	0.619252i
$315$	73813.5	+	85185.3i	0.0419140	+	0.0483714i
$316$	1.97272e6	+	4.31966e6i	1.11134	+	2.43350i
$317$	1.16848e6	−	343096.i	0.653090	−	0.191764i	0.0616301	−	0.998099i	$-0.480370\pi$
$317$	1.16848e6	−	343096.i	0.653090	−	0.191764i	0.591460	+	0.806335i	$0.298552\pi$
$318$	170454.	−	373242.i	0.0945234	−	0.206977i
$319$	−221775.	+	1.54248e6i	−0.122021	+	0.848676i
$320$	−1.46009e6	+	938344.i	−0.797086	+	0.512256i
$321$	656488.			0.355602
$322$	2.77124e6	−	2.77828e6i	1.48948	−	1.49327i
$323$	1.29789e6			0.692198
$324$	506830.	−	325720.i	0.268225	−	0.172378i
$325$	−218266.	+	1.51807e6i	−0.114624	+	0.797231i
$326$	531156.	−	1.16307e6i	0.276808	−	0.606124i
$327$	−971122.	+	285147.i	−0.502232	+	0.147469i
$328$	−719398.	−	1.57526e6i	−0.369219	−	0.808477i
$329$	−348085.	−	401712.i	−0.177295	−	0.204609i
$330$	80939.0	+	562943.i	0.0409141	+	0.284564i
$331$	534399.	+	156914.i	0.268099	+	0.0787211i	0.413019	−	0.910722i	$-0.364474\pi$
$331$	534399.	+	156914.i	0.268099	+	0.0787211i	−0.144920	+	0.989443i	$0.546292\pi$
$332$	4.93986e6	−	5.70090e6i	2.45963	−	2.83856i
$333$	−697868.	−	448492.i	−0.344876	−	0.221638i
$334$	3.84099e6	+	2.46845e6i	1.88398	+	1.21076i
$335$	−144912.	+	167237.i	−0.0705491	+	0.0814180i
$336$	−5.36496e6	−	1.57530e6i	−2.59250	−	0.761226i
$337$	−321510.	−	2.23615e6i	−0.154213	−	1.07257i	−0.909058	−	0.416670i	$-0.863197\pi$
$337$	−321510.	−	2.23615e6i	−0.154213	−	1.07257i	0.754845	−	0.655903i	$-0.227712\pi$
$338$	832211.	+	960423.i	0.396225	+	0.457268i
$339$	602335.	+	1.31893e6i	0.284668	+	0.623336i
$340$	1.22801e6	−	360576.i	0.576108	−	0.169161i
$341$	−1.58939e6	+	3.48028e6i	−0.740192	+	1.62080i
$342$	−119583.	+	831719.i	−0.0552847	+	0.384513i
$343$	−1.67134e6	+	1.07410e6i	−0.767059	+	0.492959i
$344$	−3.44485e6			−1.56955
$345$	−214274.	−	79610.4i	−0.0969219	−	0.0360099i
$346$	−658824.			−0.295855
$347$	−1.17637e6	+	756006.i	−0.524469	+	0.337056i	−0.775938	−	0.630810i	$-0.782723\pi$
$347$	−1.17637e6	+	756006.i	−0.524469	+	0.337056i	0.251469	+	0.967865i	$0.419087\pi$
$348$	−323107.	+	2.24726e6i	−0.143021	+	0.994730i
$349$	332096.	−	727190.i	0.145949	−	0.319583i	−0.822513	−	0.568747i	$-0.807428\pi$
$349$	332096.	−	727190.i	0.145949	−	0.319583i	0.968461	+	0.249163i	$0.0801557\pi$
$350$	4.48907e6	−	1.31811e6i	1.95878	−	0.575151i
$351$	−153551.	−	336229.i	−0.0665249	−	0.145669i
$352$	−1.05620e7	−	1.21891e7i	−4.54347	−	5.24344i
$353$	−276034.	−	1.91986e6i	−0.117903	−	0.820036i	−0.959858	−	0.280487i	$-0.909504\pi$
$353$	−276034.	−	1.91986e6i	−0.117903	−	0.820036i	0.841954	−	0.539549i	$-0.181405\pi$
$354$	3.38104e6	+	992762.i	1.43398	+	0.421053i
$355$	−527793.	+	609106.i	−0.222276	+	0.256520i
$356$	−7340.32	−	4717.34i	−0.00306966	−	0.00197275i
$357$	1.46519e6	+	941618.i	0.608446	+	0.391025i
$358$	2.98293e6	−	3.44249e6i	1.23009	−	1.41960i
$359$	−2.44153e6	−	716897.i	−0.999829	−	0.293576i	−0.259443	−	0.965758i	$-0.583539\pi$
$359$	−2.44153e6	−	716897.i	−0.999829	−	0.293576i	−0.740386	+	0.672182i	$0.765357\pi$
$360$	76827.6	+	534348.i	0.0312436	+	0.217304i
$361$	1.05238e6	+	1.21451e6i	0.425014	+	0.490492i
$362$	−2.80275e6	−	6.13717e6i	−1.12412	−	2.46148i
$363$	−1.38788e6	+	407519.i	−0.552823	+	0.162323i
$364$	−2.68847e6	+	5.88694e6i	−1.06354	+	2.32882i
$365$	−40757.7	+	283476.i	−0.0160132	+	0.111374i
$366$	2.76059e6	−	1.77412e6i	1.07721	−	0.692278i
$367$	399287.			0.154746			0.0773731	−	0.997002i	$-0.475347\pi$
$367$	399287.			0.154746			0.0773731	+	0.997002i	$0.475347\pi$
$368$	1.10771e7	−	2.42441e6i	4.26389	−	0.933225i
$369$	−210706.			−0.0805583
$370$	959799.	−	616825.i	0.364482	−	0.234238i
$371$	−81048.0	+	563701.i	−0.0305708	+	0.212625i
$372$	−2.31561e6	+	5.07048e6i	−0.867578	+	1.89973i
$373$	3.22196e6	−	946052.i	1.19908	−	0.352081i	0.379578	−	0.925160i	$-0.376069\pi$
$373$	3.22196e6	−	946052.i	1.19908	−	0.352081i	0.819500	+	0.573079i	$0.194251\pi$
$374$	3.65064e6	+	7.99378e6i	1.34955	+	2.95511i
$375$	−362858.	−	418761.i	−0.133247	−	0.153776i
$376$	−362299.	−	2.51984e6i	−0.132159	−	0.919188i
$377$	1.33651e6	+	392435.i	0.484305	+	0.142205i
$378$	−738411.	+	852171.i	−0.265808	+	0.306759i
$379$	−1.52077e6	−	977343.i	−0.543835	−	0.349501i	0.239702	−	0.970846i	$-0.422950\pi$
$379$	−1.52077e6	−	977343.i	−0.543835	−	0.349501i	−0.783537	+	0.621345i	$0.786587\pi$
$380$	−720954.	−	463329.i	−0.256123	−	0.164600i
$381$	1.03104e6	−	1.18989e6i	0.363885	−	0.419946i
$382$	1.00295e6	+	294492.i	0.351658	+	0.103256i
$383$	505066.	+	3.51281e6i	0.175935	+	1.22365i	0.866052	+	0.499955i	$0.166650\pi$
$383$	505066.	+	3.51281e6i	0.175935	+	1.22365i	−0.690117	+	0.723698i	$0.742441\pi$
$384$	−6.00765e6	−	6.93320e6i	−2.07911	−	2.39942i
$385$	−327912.	−	718027.i	−0.112747	−	0.246882i
$386$	235662.	−	69196.6i	0.0805047	−	0.0236383i
$387$	−174117.	+	381263.i	−0.0590968	+	0.129404i
$388$	608472.	−	4.23202e6i	0.205192	−	1.42714i
$389$	2.88846e6	−	1.85630e6i	0.967817	−	0.621978i	0.0416659	−	0.999132i	$-0.486733\pi$
$389$	2.88846e6	−	1.85630e6i	0.967817	−	0.621978i	0.926151	+	0.377154i	$0.123097\pi$
$390$	508367.			0.169245
$391$	−3.52337e6	−	247501.i	−1.16551	−	0.0818718i
$392$	1.67368e6			0.550120
$393$	1.74910e6	−	1.12408e6i	0.571258	−	0.367125i
$394$	−277404.	+	1.92939e6i	−0.0900269	+	0.626151i
$395$	−215073.	+	470945.i	−0.0693575	+	0.151872i
$396$	−4.04823e6	+	1.18867e6i	−1.29726	+	0.380910i
$397$	324059.	+	709590.i	0.103192	+	0.225960i	0.954185	−	0.299218i	$-0.0967259\pi$
$397$	324059.	+	709590.i	0.103192	+	0.225960i	−0.850992	+	0.525178i	$0.823999\pi$
$398$	6.26028e6	+	7.22474e6i	1.98101	+	2.28620i
$399$	−165973.	−	1.15437e6i	−0.0521921	−	0.363004i
$400$	1.29718e7	+	3.80888e6i	4.05370	+	1.19027i
$401$	528452.	−	609866.i	0.164113	−	0.189397i	−0.667736	−	0.744398i	$-0.732737\pi$
$401$	528452.	−	609866.i	0.164113	−	0.189397i	0.831850	+	0.555001i	$0.187282\pi$
$402$	−1.86227e6	−	1.19681e6i	−0.574749	−	0.369369i
$403$	2.87703e6	+	1.84896e6i	0.882434	+	0.567106i
$404$	−9.30827e6	+	1.07423e7i	−2.83737	+	3.27450i
$405$	63022.8	+	18505.2i	0.0190924	+	0.00560603i
$406$	−604728.	−	4.20598e6i	−0.182073	−	1.26634i
$407$	3.80437e6	+	4.39048e6i	1.13841	+	1.31379i
$408$	3.46520e6	+	7.58773e6i	1.03057	+	2.25664i
$409$	3.51100e6	−	1.03092e6i	1.03782	−	0.304732i	0.281935	−	0.959434i	$-0.409024\pi$
$409$	3.51100e6	−	1.03092e6i	1.03782	−	0.304732i	0.755888	+	0.654701i	$0.227206\pi$
$410$	120383.	−	263602.i	0.0353676	−	0.0774442i
$411$	−298076.	+	2.07316e6i	−0.0870406	+	0.605381i
$412$	−1.65473e7	+	1.06343e7i	−4.80268	+	3.08649i
$413$	−4.89075e6			−1.41091
$414$	483237.	−	2.23506e6i	0.138567	−	0.640898i
$415$	822406.			0.234404
$416$	−1.21281e7	+	7.79423e6i	−3.43604	+	2.20821i
$417$	216191.	−	1.50364e6i	0.0608831	−	0.423451i
$418$	2.44450e6	−	5.35271e6i	0.684305	−	1.49842i
$419$	2.90264e6	−	852293.i	0.807716	−	0.237167i	0.148297	−	0.988943i	$-0.452621\pi$
$419$	2.90264e6	−	852293.i	0.807716	−	0.237167i	0.659419	+	0.751776i	$0.270803\pi$
$420$	−477741.	−	1.04611e6i	−0.132151	−	0.289369i
$421$	−2.05028e6	−	2.36615e6i	−0.563777	−	0.650634i	0.400260	−	0.916402i	$-0.368920\pi$
$421$	−2.05028e6	−	2.36615e6i	−0.563777	−	0.650634i	−0.964037	+	0.265768i	$0.914374\pi$
$422$	1.71873e6	+	1.19540e7i	0.469815	+	3.26764i
$423$	−297199.	−	87265.6i	−0.0807601	−	0.0237133i
$424$	−1.78616e6	+	2.06134e6i	−0.482510	+	0.556846i
$425$	−3.54265e6	−	2.27672e6i	−0.951383	−	0.611417i
$426$	−6.78272e6	−	4.35899e6i	−1.81084	−	1.16376i
$427$	−2.98257e6	+	3.44207e6i	−0.791627	+	0.913586i
$428$	−6.42675e6	−	1.88706e6i	−1.69583	−	0.497940i
$429$	368390.	+	2.56221e6i	0.0966418	+	0.672158i
$430$	−377499.	−	435657.i	−0.0984564	−	0.113625i
$431$	−267354.	−	585423.i	−0.0693255	−	0.151802i	0.871797	−	0.489867i	$-0.162955\pi$
$431$	−267354.	−	585423.i	−0.0693255	−	0.151802i	−0.941123	+	0.338065i	$0.890227\pi$
$432$	−3.12634e6	+	917976.i	−0.805985	+	0.236658i
$433$	−981087.	+	2.14828e6i	−0.251471	+	0.550644i	−0.992700	−	0.120607i	$-0.961516\pi$
$433$	−981087.	+	2.14828e6i	−0.251471	+	0.550644i	0.741229	+	0.671252i	$0.234243\pi$
$434$	1.48473e6	−	1.03265e7i	0.378375	−	2.63166i
$435$	−208230.	+	133822.i	−0.0527620	+	0.0339081i
$436$	1.03265e7			2.60159
$437$	1.41975e6	+	1.89156e6i	0.355638	+	0.473822i
$438$	−2.86498e6			−0.713570
$439$	−5.10179e6	+	3.27872e6i	−1.26346	+	0.811976i	−0.988754	−	0.149553i	$-0.952217\pi$
$439$	−5.10179e6	+	3.27872e6i	−1.26346	+	0.811976i	−0.274705	+	0.961529i	$0.588580\pi$
$440$	538028.	−	3.74207e6i	0.132487	−	0.921468i
$441$	84594.9	−	185237.i	0.0207132	−	0.0453556i
$442$	7.53699e6	−	2.21306e6i	1.83503	−	0.538812i
$443$	−1.53794e6	−	3.36761e6i	−0.372331	−	0.815292i	−0.999342	−	0.0362808i	$-0.988449\pi$
$443$	−1.53794e6	−	3.36761e6i	−0.372331	−	0.815292i	0.627010	−	0.779011i	$-0.284278\pi$
$444$	5.54266e6	+	6.39657e6i	1.33432	+	1.53989i
$445$	−135.381	−	941.598i	−3.24085e−5	−	0.000225406i
$446$	1.88089e6	+	552279.i	0.447741	+	0.131468i
$447$	346629.	−	400031.i	0.0820533	−	0.0946946i
$448$	2.02726e7	+	1.30284e7i	4.77216	+	3.06688i
$449$	−3.72000e6	−	2.39070e6i	−0.870818	−	0.559641i	0.0271851	−	0.999630i	$-0.491346\pi$
$449$	−3.72000e6	−	2.39070e6i	−0.870818	−	0.559641i	−0.898003	+	0.439990i	$0.854982\pi$
$450$	1.78539e6	−	2.06045e6i	0.415625	−	0.479657i
$451$	1.41581e6	+	415720.i	0.327766	+	0.0962409i
$452$	−2.10537e6	−	1.46432e7i	−0.484711	−	3.37124i
$453$	−1.94093e6	−	2.23996e6i	−0.444391	−	0.512854i
$454$	2.77979e6	+	6.08689e6i	0.632954	+	1.38598i
$455$	−676996.	+	198784.i	−0.153305	+	0.0450145i
$456$	2.32033e6	−	5.08081e6i	0.522562	−	1.14425i
$457$	−280804.	+	1.95304e6i	−0.0628946	+	0.437442i	0.933906	+	0.357518i	$0.116377\pi$
$457$	−280804.	+	1.95304e6i	−0.0628946	+	0.437442i	−0.996801	+	0.0799239i	$0.974532\pi$
$458$	9.74403e6	−	6.26211e6i	2.17057	−	1.39494i
$459$	1.01493e6			0.224856
$460$	1.86882e6	+	1.39528e6i	0.411787	+	0.307445i
$461$	1.66384e6			0.364635			0.182318	−	0.983240i	$-0.441640\pi$
$461$	1.66384e6			0.364635			0.182318	+	0.983240i	$0.441640\pi$
$462$	6.64299e6	−	4.26919e6i	1.44797	−	0.930553i
$463$	588982.	−	4.09646e6i	0.127688	−	0.888088i	−0.820787	−	0.571235i	$-0.806465\pi$
$463$	588982.	−	4.09646e6i	0.127688	−	0.888088i	0.948475	−	0.316853i	$-0.102626\pi$
$464$	5.10079e6	−	1.11692e7i	1.09987	−	2.40839i
$465$	−583104.	+	171215.i	−0.125059	+	0.0367205i
$466$	−998399.	−	2.18619e6i	−0.212980	−	0.466362i
$467$	1.21765e6	+	1.40524e6i	0.258363	+	0.298167i	0.870081	−	0.492909i	$-0.164067\pi$
$467$	1.21765e6	+	1.40524e6i	0.258363	+	0.298167i	−0.611718	+	0.791076i	$0.709521\pi$
$468$	536714.	+	3.73293e6i	0.113274	+	0.787835i
$469$	2.94799e6	+	865607.i	0.618862	+	0.181714i
$470$	278973.	−	321952.i	0.0582529	−	0.0672274i
$471$	−743701.	−	477947.i	−0.154471	−	0.0992723i
$472$	−1.97053e7	−	1.26638e7i	−4.07125	−	2.61643i
$473$	1.92219e6	−	2.21833e6i	0.395042	−	0.455903i
$474$	−4.96945e6	−	1.45916e6i	−1.01593	−	0.298303i
$475$	401303.	+	2.79112e6i	0.0816091	+	0.567603i
$476$	−1.16369e7	−	1.34297e7i	−2.35408	−	2.71675i
$477$	137862.	+	301875.i	0.0277426	+	0.0607479i
$478$	−1.41009e7	+	4.14039e6i	−2.82278	+	0.828842i
$479$	2.84333e6	−	6.22602e6i	0.566224	−	1.23986i	−0.382559	−	0.923931i	$-0.624957\pi$
$479$	2.84333e6	−	6.22602e6i	0.566224	−	1.23986i	0.948783	−	0.315927i	$-0.102316\pi$
$480$	364587.	−	2.53576e6i	0.0722267	−	0.502348i
$481$	4.36848e6	−	2.80745e6i	0.860930	−	0.553286i
$482$	832013.			0.163122
$483$	230435.	+	3.16541e6i	0.0449448	+	0.617394i
$484$	1.47582e7			2.86365
$485$	392137.	−	252011.i	0.0756979	−	0.0486481i
$486$	−93512.3	+	650392.i	−0.0179588	+	0.124906i
$487$	−393997.	+	862733.i	−0.0752784	+	0.164837i	−0.943530	−	0.331288i	$-0.892517\pi$
$487$	−393997.	+	862733.i	−0.0752784	+	0.164837i	0.868251	+	0.496125i	$0.165244\pi$
$488$	−2.09297e7	+	6.14552e6i	−3.97845	+	1.16818i
$489$	429594.	+	940680.i	0.0812431	+	0.177898i
$490$	183408.	+	211664.i	0.0345086	+	0.0398251i
$491$	−62743.1	−	436388.i	−0.0117453	−	0.0816901i	0.983106	−	0.183039i	$-0.0585933\pi$
$491$	−62743.1	−	436388.i	−0.0117453	−	0.0816901i	−0.994851	+	0.101349i	$0.967684\pi$
$492$	2.06272e6	+	605670.i	0.384174	+	0.112804i
$493$	−2.50464e6	+	2.89051e6i	−0.464118	+	0.535620i
$494$	−4.42491e6	−	2.84372e6i	−0.815806	−	0.524287i
$495$	−386965.	−	248687.i	−0.0709836	−	0.0456184i
$496$	1.97420e7	−	2.27835e7i	3.60319	−	4.15830i
$497$	1.07371e7	+	3.15269e6i	1.94982	+	0.572519i
$498$	1.17084e6	+	8.14339e6i	0.211556	+	1.47140i
$499$	−5.68893e6	−	6.56537e6i	−1.02277	−	1.18034i	−0.983462	−	0.181115i	$-0.942029\pi$
$499$	−5.68893e6	−	6.56537e6i	−1.02277	−	1.18034i	−0.0393105	−	0.999227i	$-0.512516\pi$
$500$	2.34851e6	+	5.14253e6i	0.420115	+	0.919924i
$501$	−3.54319e6	+	1.04038e6i	−0.630667	+	0.185181i
$502$	781664.	−	1.71160e6i	0.138440	−	0.303141i
$503$	−312673.	+	2.17469e6i	−0.0551024	+	0.383246i	0.943545	+	0.331245i	$0.107469\pi$
$503$	−312673.	+	2.17469e6i	−0.0551024	+	0.383246i	−0.998647	+	0.0520004i	$0.983440\pi$
$504$	6.30555e6	−	4.05233e6i	1.10572	−	0.710606i
$505$	−1.54967e6			−0.270403
$506$	−7.65682e6	+	1.40648e7i	−1.32945	+	2.44207i
$507$	−1.02783e6			−0.177583
$508$	−1.35138e7	+	8.68479e6i	−2.32337	+	1.49314i
$509$	1.14656e6	−	7.97453e6i	0.196157	−	1.36430i	−0.619149	−	0.785273i	$-0.712522\pi$
$509$	1.14656e6	−	7.97453e6i	0.196157	−	1.36430i	0.815306	−	0.579030i	$-0.196569\pi$
$510$	−579862.	+	1.26972e6i	−0.0987186	+	0.216164i
$511$	3.81532e6	−	1.12028e6i	0.646366	−	0.189790i
$512$	1.32380e7	+	2.89871e7i	2.23176	+	4.88686i
$513$	−445047.	−	513611.i	−0.0746641	−	0.0861670i
$514$	−2.05642e6	−	1.43027e7i	−0.343324	−	2.38787i
$515$	−2.05760e6	−	604167.i	−0.341856	−	0.100378i
$516$	2.80047e6	−	3.23192e6i	0.463028	−	0.534363i
$517$	1.82482e6	+	1.17274e6i	0.300258	+	0.192964i
$518$	−1.33263e7	−	8.56429e6i	−2.18215	−	1.40238i
$519$	348943.	−	402702.i	0.0568639	−	0.0656244i
$520$	−3.24240e6	−	952054.i	−0.525845	−	0.154402i
$521$	147475.	+	1.02571e6i	0.0238026	+	0.165551i	0.998256	−	0.0590411i	$-0.0188043\pi$
$521$	147475.	+	1.02571e6i	0.0238026	+	0.165551i	−0.974453	+	0.224592i	$0.927895\pi$
$522$	−1.62154e6	−	1.87136e6i	−0.260467	−	0.300595i
$523$	−2.21526e6	−	4.85073e6i	−0.354136	−	0.775449i	−0.999929	−	0.0119364i	$-0.996200\pi$
$523$	−2.21526e6	−	4.85073e6i	−0.354136	−	0.775449i	0.645793	−	0.763512i	$-0.276527\pi$
$524$	−2.03541e7	+	5.97650e6i	−3.23835	+	0.950864i
$525$	−1.57193e6	+	3.44205e6i	−0.248906	+	0.545028i
$526$	−3.45357e6	+	2.40201e7i	−0.544258	+	3.78539i
$527$	−7.89969e6	+	5.07682e6i	−1.23903	+	0.796279i
$528$	2.28183e7			3.56203
$529$	−3.49349e6	−	5.40574e6i	−0.542775	−	0.839878i
$530$	−456424.			−0.0705795
$531$	−2.39757e6	+	1.54083e6i	−0.369008	+	0.237147i
$532$	−1.69340e6	+	1.17779e7i	−0.259407	+	1.80421i
$533$	547918.	−	1.19977e6i	0.0835406	−	0.182928i
$534$	9130.88	−	2681.07i	0.00138567	−	0.000406869i
$535$	−303356.	−	664257.i	−0.0458214	−	0.100335i
$536$	9.63636e6	+	1.11210e7i	1.44878	+	1.67198i
$537$	524302.	+	3.64660e6i	0.0784595	+	0.545698i
$538$	−9.09435e6	−	2.67034e6i	−1.35462	−	0.397751i
$539$	−933896.	+	1.07777e6i	−0.138461	+	0.159792i
$540$	−563776.	−	362317.i	−0.0831997	−	0.0534692i
$541$	−2.32331e6	−	1.49310e6i	−0.341283	−	0.219329i	0.358760	−	0.933430i	$-0.383200\pi$
$541$	−2.32331e6	−	1.49310e6i	−0.341283	−	0.219329i	−0.700043	+	0.714101i	$0.746836\pi$
$542$	5.20385e6	−	6.00556e6i	0.760897	−	0.878123i
$543$	5.23578e6	+	1.53736e6i	0.762046	+	0.223757i
$544$	−5.63352e6	−	3.91820e7i	−0.816174	−	5.67662i
$545$	737267.	+	850851.i	0.106325	+	0.122705i
$546$	−2.93217e6	−	6.42055e6i	−0.420927	−	0.921702i
$547$	−409929.	+	120366.i	−0.0585787	+	0.0172003i	−0.310891	−	0.950446i	$-0.600627\pi$
$547$	−409929.	+	120366.i	−0.0585787	+	0.0172003i	0.252312	+	0.967646i	$0.418809\pi$
$548$	8.87732e6	−	1.94386e7i	1.26279	−	2.76512i
$549$	−377712.	+	2.62705e6i	−0.0534848	+	0.371995i
$550$	−1.60620e7	+	1.03224e7i	−2.26408	+	1.45504i
$551$	2.56105e6			0.359367
$552$	−7.26788e6	+	1.33504e7i	−1.01522	+	1.86486i
$553$	7.18842e6			0.999587
$554$	5.11595e6	−	3.28782e6i	0.708193	−	0.455128i
$555$	−131323.	+	913370.i	−0.0180970	+	0.125868i
$556$	−6.43861e6	+	1.40986e7i	−0.883294	+	1.93414i
$557$	4.36864e6	−	1.28275e6i	0.596634	−	0.175188i	0.0305476	−	0.999533i	$-0.490275\pi$
$557$	4.36864e6	−	1.28275e6i	0.596634	−	0.175188i	0.566087	+	0.824346i	$0.308457\pi$
$558$	−2.52551e6	−	5.53009e6i	−0.343370	−	0.751877i
$559$	−1.71817e6	−	1.98287e6i	−0.232561	−	0.268389i
$560$	885154.	+	6.15638e6i	0.119275	+	0.829574i
$561$	−6.81970e6	−	2.00244e6i	−0.914867	−	0.268629i
$562$	−7.74405e6	+	8.93711e6i	−1.03425	+	1.19359i
$563$	4.33047e6	+	2.78303e6i	0.575790	+	0.370038i	0.795892	−	0.605439i	$-0.207002\pi$
$563$	4.33047e6	+	2.78303e6i	0.575790	+	0.370038i	−0.220101	+	0.975477i	$0.570639\pi$
$564$	2.65862e6	+	1.70859e6i	0.351932	+	0.226173i
$565$	1.05621e6	−	1.21893e6i	0.139196	−	0.160641i
$566$	2.11101e7	+	6.19848e6i	2.76980	+	0.813287i
$567$	−129788.	−	902698.i	−0.0169542	−	0.117919i
$568$	3.50973e7	+	4.05044e7i	4.56460	+	5.26783i
$569$	2.20918e6	+	4.83744e6i	0.286056	+	0.626375i	0.997044	−	0.0768286i	$-0.0244794\pi$
$569$	2.20918e6	+	4.83744e6i	0.286056	+	0.626375i	−0.710988	+	0.703204i	$0.751752\pi$
$570$	896820.	−	263330.i	0.115616	−	0.0339479i
$571$	3.50228e6	−	7.66892e6i	0.449532	−	0.984337i	−0.540218	−	0.841525i	$-0.681658\pi$
$571$	3.50228e6	−	7.66892e6i	0.449532	−	0.984337i	0.989750	−	0.142812i	$-0.0456144\pi$
$572$	3.75864e6	−	2.61419e7i	0.480332	−	3.34078i
$573$	−711214.	+	457070.i	−0.0904927	+	0.0581562i
$574$	−4.02358e6			−0.509721
$575$	−557164.	−	7.65359e6i	−0.0702770	−	0.965374i
$576$	1.40428e7			1.76358
$577$	1.68930e6	−	1.08565e6i	0.211235	−	0.135753i	−0.430745	−	0.902474i	$-0.641749\pi$
$577$	1.68930e6	−	1.08565e6i	0.211235	−	0.135753i	0.641981	+	0.766721i	$0.278113\pi$
$578$	−820988.	+	5.71010e6i	−0.102216	+	0.710925i
$579$	−82521.4	+	180697.i	−0.0102299	+	0.0224003i
$580$	2.42316e6	−	711504.i	0.299097	−	0.0878228i
$581$	−4.74349e6	−	1.03868e7i	−0.582985	−	1.27656i
$582$	3.05367e6	+	3.52412e6i	0.373693	+	0.431264i
$583$	−330750.	−	2.30042e6i	−0.0403021	−	0.280308i
$584$	1.82731e7	+	5.36545e6i	2.21707	+	0.650990i
$585$	−269254.	+	310736.i	−0.0325292	+	0.0375407i
$586$	−1.12646e7	−	7.23931e6i	−1.35510	−	0.870870i
$587$	4.28730e6	+	2.75528e6i	0.513557	+	0.330043i	0.771619	−	0.636085i	$-0.219447\pi$
$587$	4.28730e6	+	2.75528e6i	0.513557	+	0.330043i	−0.258061	+	0.966129i	$0.583084\pi$
$588$	−1.36061e6	+	1.57023e6i	−0.162290	+	0.187292i
$589$	6.03318e6	+	1.77150e6i	0.716569	+	0.210404i
$590$	−557830.	−	3.87979e6i	−0.0659739	−	0.458858i
$591$	−1.03240e6	−	1.19145e6i	−0.121585	−	0.140316i
$592$	−1.90156e7	−	4.16384e7i	−2.23001	−	4.88303i
$593$	1.16356e6	−	341651.i	0.135878	−	0.0398975i	−0.213086	−	0.977033i	$-0.568352\pi$
$593$	1.16356e6	−	341651.i	0.135878	−	0.0398975i	0.348965	+	0.937136i	$0.386533\pi$
$594$	1.91156e6	−	4.18574e6i	0.222291	−	0.486750i
$595$	275715.	−	1.91764e6i	0.0319277	−	0.222062i
$596$	−4.54324e6	+	2.91976e6i	−0.523902	+	0.336692i
$597$	−7.73181e6			−0.887862
$598$	1.14700e7	+	8.56364e6i	1.31163	+	0.979277i
$599$	3.89425e6			0.443462			0.221731	−	0.975108i	$-0.428829\pi$
$599$	3.89425e6			0.443462			0.221731	+	0.975108i	$0.428829\pi$
$600$	−1.52461e7	+	9.79807e6i	−1.72894	+	1.11112i
$601$	−2.08578e6	+	1.45069e7i	−0.235550	+	1.63829i	0.437879	+	0.899034i	$0.355730\pi$
$601$	−2.08578e6	+	1.45069e7i	−0.235550	+	1.63829i	−0.673429	+	0.739252i	$0.735179\pi$
$602$	−3.32489e6	+	7.28050e6i	−0.373927	+	0.818786i
$603$	1.71789e6	−	504418.i	0.192399	−	0.0564933i
$604$	1.25622e7	+	2.75075e7i	1.40112	+	3.06802i
$605$	1.05367e6	+	1.21600e6i	0.117035	+	0.135065i
$606$	−2.20624e6	−	1.53447e7i	−0.244046	−	1.69738i
$607$	1.63236e6	+	479304.i	0.179822	+	0.0528006i	0.370404	−	0.928871i	$-0.379219\pi$
$607$	1.63236e6	+	479304.i	0.179822	+	0.0528006i	−0.190582	+	0.981671i	$0.561037\pi$
$608$	−1.73580e7	+	2.00322e7i	−1.90433	+	2.19771i
$609$	2.89117e6	+	1.85804e6i	0.315886	+	0.203008i
$610$	−3.07075e6	−	1.97345e6i	−0.334134	−	0.214735i
$611$	1.26973e6	−	1.46535e6i	0.137597	−	0.158796i
$612$	−9.93574e6	−	2.91740e6i	−1.07231	−	0.314860i
$613$	290063.	+	2.01743e6i	0.0311775	+	0.216844i	0.999454	−	0.0330364i	$-0.0105177\pi$
$613$	290063.	+	2.01743e6i	0.0311775	+	0.216844i	−0.968277	+	0.249881i	$0.919609\pi$
$614$	−1.63082e7	−	1.88206e7i	−1.74576	−	2.01471i
$615$	97364.8	+	213199.i	0.0103804	+	0.0227299i
$616$	−5.03647e7	+	1.47884e7i	−5.34779	+	1.57025i
$617$	1.38056e6	−	3.02301e6i	0.145997	−	0.319688i	−0.822479	−	0.568795i	$-0.807410\pi$
$617$	1.38056e6	−	3.02301e6i	0.145997	−	0.319688i	0.968476	+	0.249107i	$0.0801371\pi$
$618$	3.05304e6	−	2.12344e7i	0.321559	−	2.23650i
$619$	−2.25384e6	+	1.44846e6i	−0.236427	+	0.151942i	−0.653490	−	0.756935i	$-0.726696\pi$
$619$	−2.25384e6	+	1.44846e6i	−0.236427	+	0.151942i	0.417063	+	0.908878i	$0.363059\pi$
$620$	6.20051e6			0.647810
$621$	1.11022e6	+	1.47917e6i	0.115527	+	0.153918i
$622$	−3.58075e6			−0.371106
$623$	−11111.3	+	7140.80i	−0.00114695	+	0.000737101i
$624$	2.90270e6	−	2.01887e7i	0.298429	−	2.07562i
$625$	3.67064e6	−	8.03757e6i	0.375873	−	0.823047i
$626$	−1.42373e7	+	4.18044e6i	−1.45208	+	0.426370i
$627$	1.97709e6	+	4.32923e6i	0.200844	+	0.439786i
$628$	5.90668e6	+	6.81667e6i	0.597646	+	0.689721i
$629$	2.02917e6	+	1.41132e7i	0.204500	+	1.42233i
$630$	1.20347e6	+	353370.i	0.120804	+	0.0354714i
$631$	−6.17807e6	+	7.12988e6i	−0.617703	+	0.712867i	−0.975269	−	0.221021i	$-0.929061\pi$
$631$	−6.17807e6	+	7.12988e6i	−0.617703	+	0.712867i	0.357566	+	0.933888i	$0.383607\pi$
$632$	2.89628e7	+	1.86133e7i	2.88435	+	1.85366i
$633$	−8.21716e6	−	5.28085e6i	−0.815103	−	0.523835i
$634$	8.87430e6	−	1.02415e7i	0.876821	−	1.01191i
$635$	−1.68040e6	−	493410.i	−0.165378	−	0.0485595i
$636$	−481875.	−	3.35152e6i	−0.0472380	−	0.328548i
$637$	834772.	+	963379.i	0.0815116	+	0.0940694i
$638$	7.20360e6	+	1.57737e7i	0.700645	+	1.53420i
$639$	6.25684e6	−	1.83718e6i	0.606182	−	0.177991i
$640$	−4.23918e6	+	9.28251e6i	−0.409102	+	0.895809i
$641$	−1.92749e6	+	1.34060e7i	−0.185288	+	1.28870i	0.658726	+	0.752383i	$0.271096\pi$
$641$	−1.92749e6	+	1.34060e7i	−0.185288	+	1.28870i	−0.844014	+	0.536321i	$0.819813\pi$
$642$	6.14553e6	−	3.94949e6i	0.588467	−	0.378184i
$643$	9.19677e6			0.877219			0.438610	−	0.898678i	$-0.355471\pi$
$643$	9.19677e6			0.877219			0.438610	+	0.898678i	$0.355471\pi$
$644$	6.84306e6	−	3.16505e7i	0.650183	−	3.00722i
$645$	466233.			0.0441269
$646$	1.21498e7	−	7.80821e6i	1.14548	−	0.736157i
$647$	583042.	−	4.05514e6i	0.0547569	−	0.380843i	−0.943954	−	0.330078i	$-0.892925\pi$
$647$	583042.	−	4.05514e6i	0.0547569	−	0.380843i	0.998711	−	0.0507648i	$-0.0161659\pi$
$648$	1.81446e6	−	3.97312e6i	0.169750	−	0.371701i
$649$	1.91503e7	−	5.62302e6i	1.78469	−	0.524032i
$650$	7.08963e6	+	1.55241e7i	0.658173	+	1.44120i
$651$	5.52564e6	+	6.37693e6i	0.511011	+	0.589738i
$652$	−1.50158e6	−	1.04437e7i	−0.138335	−	0.962138i
$653$	1.45560e6	+	427402.i	0.133585	+	0.0392242i	0.347842	−	0.937553i	$-0.386915\pi$
$653$	1.45560e6	+	427402.i	0.133585	+	0.0392242i	−0.214256	+	0.976777i	$0.568733\pi$
$654$	−7.37542e6	+	8.51169e6i	−0.674283	+	0.778165i
$655$	−1.94562e6	−	1.25037e6i	−0.177196	−	0.113877i
$656$	−9.78103e6	−	6.28589e6i	−0.887412	−	0.570305i
$657$	1.51743e6	−	1.75120e6i	0.137149	−	0.158279i
$658$	−5.67524e6	−	1.66640e6i	−0.510998	−	0.150043i
$659$	1.66017e6	+	1.15467e7i	0.148915	+	1.03573i	0.918000	+	0.396581i	$0.129804\pi$
$659$	1.66017e6	+	1.15467e7i	0.148915	+	1.03573i	−0.769084	+	0.639147i	$0.779287\pi$
$660$	3.07338e6	+	3.54687e6i	0.274635	+	0.316946i
$661$	2.76366e6	+	6.05158e6i	0.246026	+	0.538722i	0.991848	−	0.127423i	$-0.0406705\pi$
$661$	2.76366e6	+	6.05158e6i	0.246026	+	0.538722i	−0.745822	+	0.666145i	$0.767943\pi$
$662$	5.94664e6	−	1.74609e6i	0.527384	−	0.154854i
$663$	−2.63922e6	+	5.77908e6i	−0.233180	+	0.510593i
$664$	7.78298e6	−	5.41318e7i	0.685055	−	4.76466i
$665$	−1.09133e6	+	701358.i	−0.0956982	+	0.0615015i
$666$	−9.23107e6			−0.806430
$667$	−6.95247e6	−	488379.i	−0.605097	−	0.0425052i
$668$	3.76770e7			3.26689
$669$	−1.33378e6	+	857170.i	−0.115218	+	0.0740461i
$670$	−350438.	+	2.43735e6i	−0.0301595	+	0.209764i
$671$	7.72113e6	−	1.69069e7i	0.662026	−	1.44963i
$672$	−3.41289e7	+	1.00211e7i	−2.91541	+	0.856040i
$673$	−6.10644e6	−	1.33712e7i	−0.519697	−	1.13798i	−0.969554	−	0.244877i	$-0.921252\pi$
$673$	−6.10644e6	−	1.33712e7i	−0.519697	−	1.13798i	0.449857	−	0.893101i	$-0.351475\pi$
$674$	−1.64626e7	−	1.89989e7i	−1.39589	−	1.61094i
$675$	313813.	+	2.18262e6i	0.0265101	+	0.184382i
$676$	1.00620e7	+	2.95448e6i	0.846875	+	0.248665i
$677$	1.00863e6	−	1.16402e6i	0.0845787	−	0.0976090i	−0.711883	−	0.702298i	$-0.752157\pi$
$677$	1.00863e6	−	1.16402e6i	0.0845787	−	0.0976090i	0.796461	+	0.604689i	$0.206703\pi$
$678$	1.35734e7	+	8.72310e6i	1.13400	+	0.728780i
$679$	−5.44462e6	−	3.49904e6i	−0.453203	−	0.291256i
$680$	6.07629e6	−	7.01242e6i	0.503926	−	0.581561i
$681$	−5.19287e6	−	1.52477e6i	−0.429082	−	0.125990i
$682$	6.05905e6	+	4.21416e7i	0.498820	+	3.46937i
$683$	5.22299e6	+	6.02765e6i	0.428418	+	0.494420i	0.928383	−	0.371625i	$-0.121199\pi$
$683$	5.22299e6	+	6.02765e6i	0.428418	+	0.494420i	−0.499965	+	0.866045i	$0.666654\pi$
$684$	2.88046e6	+	6.30733e6i	0.235408	+	0.515472i
$685$	2.23543e6	−	656383.i	0.182027	−	0.0534479i
$686$	−9.18386e6	+	2.01098e7i	−0.745100	+	1.63154i
$687$	−1.33321e6	+	9.27267e6i	−0.107772	+	0.749572i
$688$	−1.94566e7	+	1.25040e7i	−1.56710	+	1.00711i
$689$	−2.07739e6			−0.166713
$690$	−2.48481e6	+	543843.i	−0.198688	+	0.0434861i
$691$	−4.20053e6			−0.334664			−0.167332	−	0.985901i	$-0.553515\pi$
$691$	−4.20053e6			−0.334664			−0.167332	+	0.985901i	$0.553515\pi$
$692$	−4.57358e6	+	2.93926e6i	−0.363070	+	0.233331i
$693$	−908916.	+	6.32165e6i	−0.0718937	+	0.500032i
$694$	−6.46405e6	+	1.41543e7i	−0.509455	+	1.11555i
$695$	−1.62133e6	+	476066.i	−0.127324	+	0.0373857i
$696$	6.83768e6	+	1.49724e7i	0.535040	+	1.17157i
$697$	2.37163e6	+	2.73701e6i	0.184912	+	0.213400i
$698$	−1.26601e6	−	8.80531e6i	−0.0983557	−	0.684079i
$699$	1.86509e6	+	547641.i	0.144380	+	0.0423938i
$700$	2.52827e7	−	2.91778e7i	1.95020	−	2.25065i
$701$	−8.70096e6	−	5.59177e6i	−0.668763	−	0.429788i	0.161716	−	0.986837i	$-0.448297\pi$
$701$	−8.70096e6	−	5.59177e6i	−0.668763	−	0.429788i	−0.830479	+	0.557049i	$0.811933\pi$
$702$	−3.46021e6	−	2.22374e6i	−0.265009	−	0.170311i
$703$	6.25229e6	−	7.21553e6i	0.477145	−	0.550655i
$704$	−9.43587e7	−	2.77062e7i	−7.17547	−	2.10691i
$705$	49034.3	+	341041.i	0.00371558	+	0.0258425i
$706$	−1.41341e7	−	1.63116e7i	−1.06723	−	1.23164i
$707$	8.93824e6	+	1.95720e7i	0.672517	+	1.47261i
$708$	2.79003e7	−	8.19228e6i	2.09183	−	0.614217i
$709$	−1.00561e7	+	2.20198e7i	−0.751300	+	1.64512i	0.0127151	+	0.999919i	$0.495953\pi$
$709$	−1.00561e7	+	2.20198e7i	−0.751300	+	1.64512i	−0.764015	+	0.645198i	$0.776775\pi$
$710$	−1.27635e6	+	8.87723e6i	−0.0950222	+	0.660894i
$711$	3.52395e6	−	2.26471e6i	0.261430	−	0.168011i
$712$	−63258.4			−0.00467647
$713$	−1.60404e7	−	5.95959e6i	−1.18166	−	0.439028i
$714$	1.93808e7			1.42274
$715$	2.42230e6	−	1.55672e6i	0.177200	−	0.113879i
$716$	5.34939e6	−	3.72059e7i	0.389962	−	2.71224i
$717$	4.93768e6	−	1.08120e7i	0.358695	−	0.785432i
$718$	−2.71686e7	+	7.97743e6i	−1.96678	+	0.577500i
$719$	−2.69110e6	−	5.89268e6i	−0.194136	−	0.425100i	0.787382	−	0.616465i	$-0.211436\pi$
$719$	−2.69110e6	−	5.89268e6i	−0.194136	−	0.425100i	−0.981519	+	0.191365i	$0.938708\pi$
$720$	2.37349e6	+	2.73915e6i	0.170630	+	0.196918i
$721$	4.23740e6	+	2.94718e7i	0.303572	+	2.11139i
$722$	1.71581e7	+	5.03808e6i	1.22497	+	0.359685i
$723$	−440672.	+	508563.i	−0.0313523	+	0.0361825i
$724$	−4.68370e7	−	3.01003e7i	−3.32080	−	2.13415i
$725$	−6.99051e6	−	4.49253e6i	−0.493928	−	0.317428i
$726$	−1.05406e7	+	1.21645e7i	−0.742205	+	0.856551i
$727$	14262.5	+	4187.85i	0.00100083	+	0.000293870i	0.282233	−	0.959346i	$-0.408925\pi$
$727$	14262.5	+	4187.85i	0.00100083	+	0.000293870i	−0.281232	+	0.959640i	$0.590743\pi$
$728$	6.67735e6	+	4.64420e7i	0.466955	+	3.24775i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	1.32388e6	+	2.89889e6i	0.0919477	+	0.201337i
$731$	6.91232e6	−	2.02964e6i	0.478443	−	0.140484i
$732$	1.12491e7	−	2.46320e7i	0.775958	−	1.69911i
$733$	135642.	−	943410.i	0.00932468	−	0.0648546i	−0.984628	−	0.174666i	$-0.944116\pi$
$733$	135642.	−	943410.i	0.00932468	−	0.0648546i	0.993952	+	0.109811i	$0.0350246\pi$
$734$	3.73782e6	−	2.40215e6i	0.256081	−	0.164573i
$735$	−226519.			−0.0154663
$736$	5.09418e7	−	5.10714e7i	3.46641	−	3.47523i
$737$	−1.25384e7			−0.850301
$738$	−1.97246e6	+	1.26762e6i	−0.133312	+	0.0856742i
$739$	−632873.	+	4.40173e6i	−0.0426291	+	0.296492i	0.957343	+	0.288955i	$0.0933079\pi$
$739$	−632873.	+	4.40173e6i	−0.0426291	+	0.296492i	−0.999972	+	0.00753616i	$0.997601\pi$
$740$	3.91107e6	−	8.56404e6i	0.262552	−	0.574909i
$741$	4.08184e6	−	1.19854e6i	0.273093	−	0.0801873i
$742$	2.63257e6	+	5.76453e6i	0.175538	+	0.384374i
$743$	1.32267e7	+	1.52645e7i	0.878983	+	1.01440i	0.999764	+	0.0217217i	$0.00691478\pi$
$743$	1.32267e7	+	1.52645e7i	0.878983	+	1.01440i	−0.120781	+	0.992679i	$0.538540\pi$
$744$	5.75127e6	+	4.00010e7i	0.380918	+	2.64934i
$745$	−564939.	−	165881.i	−0.0372916	−	0.0109498i
$746$	2.44699e7	−	2.82398e7i	1.60985	−	1.85787i
$747$	−5.59773e6	−	3.59744e6i	−0.367037	−	0.235881i
$748$	6.10061e7	+	3.92062e7i	3.98675	+	2.56213i
$749$	−6.63970e6	+	7.66262e6i	−0.432458	+	0.499083i
$750$	−5.91610e6	−	1.73712e6i	−0.384045	−	0.112766i
$751$	−3.64495e6	−	2.53512e7i	−0.235826	−	1.64021i	−0.672148	−	0.740417i	$-0.734628\pi$
$751$	−3.64495e6	−	2.53512e7i	−0.235826	−	1.64021i	0.436321	−	0.899791i	$-0.356281\pi$
$752$	−1.11928e7	−	1.29171e7i	−0.721759	−	0.832954i
$753$	632203.	+	1.38433e6i	0.0406321	+	0.0889718i
$754$	1.48723e7	−	4.36691e6i	0.952687	−	0.279734i
$755$	−1.36958e6	+	2.99896e6i	−0.0874420	+	0.191471i
$756$	−1.32422e6	+	9.21013e6i	−0.0842664	+	0.586086i
$757$	1.37694e7	−	8.84907e6i	0.873325	−	0.561252i	−0.0254432	−	0.999676i	$-0.508100\pi$
$757$	1.37694e7	−	8.84907e6i	0.873325	−	0.561252i	0.898768	+	0.438425i	$0.144463\pi$
$758$	−2.01161e7			−1.27166
$759$	−4.54165e6	−	1.21296e7i	−0.286160	−	0.764260i
$760$	−6.21314e6			−0.390191
$761$	−2.40510e7	+	1.54567e7i	−1.50547	+	0.967507i	−0.511332	+	0.859383i	$0.670848\pi$
$761$	−2.40510e7	+	1.54567e7i	−1.50547	+	0.967507i	−0.994137	+	0.108124i	$0.965516\pi$
$762$	2.49335e6	−	1.73416e7i	0.155559	−	1.08194i
$763$	6.49363e6	−	1.42191e7i	0.403809	−	0.884218i
$764$	8.27634e6	−	2.43015e6i	0.512985	−	0.150626i
$765$	−468987.	−	1.02694e6i	−0.0289739	−	0.0634441i
$766$	2.58615e7	+	2.98457e7i	1.59251	+	1.83785i
$767$	−2.53894e6	−	1.76587e7i	−0.155835	−	1.08385i
$768$	−5.00425e7	−	1.46938e7i	−3.06151	−	0.898942i
$769$	983400.	−	1.13490e6i	0.0599673	−	0.0692059i	−0.724973	−	0.688777i	$-0.758148\pi$
$769$	983400.	−	1.13490e6i	0.0599673	−	0.0692059i	0.784941	+	0.619571i	$0.212693\pi$
$770$	−7.38937e6	−	4.74886e6i	−0.449139	−	0.288644i
$771$	9.83163e6	+	6.31841e6i	0.595648	+	0.382800i
$772$	1.32726e6	−	1.53174e6i	0.0801518	−	0.0925001i
$773$	−1.51727e7	−	4.45509e6i	−0.913299	−	0.268169i	−0.208870	−	0.977943i	$-0.566979\pi$
$773$	−1.51727e7	−	4.45509e6i	−0.913299	−	0.268169i	−0.704429	+	0.709775i	$0.748797\pi$
$774$	663767.	+	4.61660e6i	0.0398257	+	0.276994i
$775$	−1.33603e7	−	1.54187e7i	−0.799030	−	0.922130i
$776$	−1.28766e7	−	2.81959e7i	−0.767624	−	1.68086i
$777$	1.22931e7	−	3.60958e6i	0.730480	−	0.214488i
$778$	1.58719e7	−	3.47546e7i	0.940111	−	2.05856i
$779$	345120.	−	2.40036e6i	0.0203764	−	0.141721i
$780$	3.52910e6	−	2.26801e6i	0.207695	−	0.133478i
$781$	−4.56669e7			−2.67901
$782$	−3.44721e7	+	1.88800e7i	−2.01581	+	1.10404i
$783$	2.00270e6			0.116738
$784$	9.45302e6	−	6.07509e6i	0.549263	−	0.352990i
$785$	−139948.	+	973356.i	−0.00810571	+	0.0563764i
$786$	9.61113e6	−	2.10454e7i	0.554904	−	1.21507i
$787$	2.32126e7	−	6.81583e6i	1.33594	−	0.392267i	0.465721	−	0.884932i	$-0.345795\pi$
$787$	2.32126e7	−	6.81583e6i	1.33594	−	0.392267i	0.870219	+	0.492664i	$0.163977\pi$
$788$	6.68197e6	+	1.46315e7i	0.383345	+	0.839407i
$789$	−1.28530e7	−	1.48331e7i	−0.735041	−	0.848283i
$790$	819899.	+	5.70252e6i	0.0467404	+	0.325087i
$791$	−2.14868e7	−	6.30908e6i	−1.22104	−	0.358529i
$792$	−2.00310e7	+	2.31170e7i	−1.13472	+	1.30954i
$793$	−1.39764e7	−	8.98208e6i	−0.789245	−	0.507217i
$794$	7.30255e6	+	4.69307e6i	0.411077	+	0.264183i
$795$	241743.	−	278986.i	0.0135655	−	0.0156554i
$796$	7.56913e7	+	2.22250e7i	4.23412	+	1.24325i
$797$	1.67767e6	+	1.16685e7i	0.0935538	+	0.650681i	0.981603	+	0.190933i	$0.0611512\pi$
$797$	1.67767e6	+	1.16685e7i	0.0935538	+	0.650681i	−0.888049	+	0.459748i	$0.847940\pi$
$798$	−8.49849e6	−	9.80778e6i	−0.472427	−	0.545210i
$799$	2.21162e6	+	4.84278e6i	0.122559	+	0.268366i
$800$	8.25196e7	−	2.42299e7i	4.55861	−	1.33853i
$801$	−3197.35	+	7001.21i	−0.000176079	+	0.000385560i
$802$	1.27795e6	−	8.88831e6i	0.0701579	−	0.487959i
$803$	−1.36513e7	+	8.77315e6i	−0.747110	+	0.480139i
$804$	−1.82674e7			−0.996636
$805$	3.09639e6	−	1.69586e6i	0.168409	−	0.0922361i
$806$	3.80560e7			2.06341
$807$	6.44902e6	−	4.14453e6i	0.348586	−	0.224022i
$808$	−1.46656e7	+	1.02002e8i	−0.790264	+	5.49640i
$809$	2.89927e6	−	6.34852e6i	0.155746	−	0.341037i	−0.815633	−	0.578569i	$-0.803611\pi$
$809$	2.89927e6	−	6.34852e6i	0.155746	−	0.341037i	0.971380	+	0.237532i	$0.0763386\pi$
$810$	701300.	−	205920.i	0.0375570	−	0.0110277i
$811$	−1.22996e7	−	2.69323e7i	−0.656656	−	1.43788i	−0.885606	−	0.464438i	$-0.846256\pi$
$811$	−1.22996e7	−	2.69323e7i	−0.656656	−	1.43788i	0.228950	−	0.973438i	$-0.426471\pi$
$812$	−2.29625e7	−	2.65001e7i	−1.22216	−	1.41045i
$813$	914665.	+	6.36164e6i	0.0485329	+	0.337553i
$814$	6.20272e7	+	1.82128e7i	3.28111	+	0.963421i
$815$	753302.	−	869357.i	0.0397260	−	0.0458463i
$816$	4.71134e7	+	3.02779e7i	2.47696	+	1.59184i
$817$	−4.05817e6	−	2.60803e6i	−0.212704	−	0.136696i
$818$	2.66652e7	−	3.07732e7i	1.39335	−	1.60802i
$819$	5.47753e6	+	1.60835e6i	0.285348	+	0.0837858i
$820$	−340324.	−	2.36701e6i	−0.0176750	−	0.122932i
$821$	4.95667e6	+	5.72030e6i	0.256644	+	0.296184i	0.869420	−	0.494073i	$-0.164493\pi$
$821$	4.95667e6	+	5.72030e6i	0.256644	+	0.296184i	−0.612776	+	0.790257i	$0.709947\pi$
$822$	9.68199e6	+	2.12006e7i	0.499787	+	1.09438i
$823$	−2.88037e7	+	8.45752e6i	−1.48234	+	0.435255i	−0.920089	−	0.391710i	$-0.871884\pi$
$823$	−2.88037e7	+	8.45752e6i	−1.48234	+	0.435255i	−0.562253	+	0.826965i	$0.690065\pi$
$824$	−5.92396e7	+	1.29717e8i	−3.03944	+	6.65545i
$825$	2.19765e6	−	1.52850e7i	0.112415	−	0.781863i
$826$	−4.57834e7	+	2.94232e7i	−2.33484	+	1.50051i
$827$	1.50185e7			0.763596			0.381798	−	0.924246i	$-0.375305\pi$
$827$	1.50185e7			0.763596			0.381798	+	0.924246i	$0.375305\pi$
$828$	−6.61681e6	−	1.76718e7i	−0.335407	−	0.895787i
$829$	9.92523e6			0.501596			0.250798	−	0.968039i	$-0.419307\pi$
$829$	9.92523e6			0.501596			0.250798	+	0.968039i	$0.419307\pi$
$830$	7.69873e6	−	4.94767e6i	0.387903	−	0.249290i
$831$	−699981.	+	4.86847e6i	−0.0351628	+	0.244563i
$832$	−3.65167e7	+	7.99605e7i	−1.82887	+	4.00467i
$833$	−3.35835e6	+	986101.i	−0.167693	+	0.0492390i
$834$	−7.02223e6	−	1.53765e7i	−0.349591	−	0.765497i
$835$	2.68996e6	+	3.10438e6i	0.133515	+	0.154084i
$836$	−6.91063e6	−	4.80645e7i	−0.341981	−	2.37853i
$837$	4.71786e6	+	1.38529e6i	0.232772	+	0.0683481i
$838$	2.20448e7	−	2.54411e7i	1.08442	−	1.25149i
$839$	−1.90999e7	−	1.22748e7i	−0.936756	−	0.602017i	−0.0192828	−	0.999814i	$-0.506138\pi$
$839$	−1.90999e7	−	1.22748e7i	−0.936756	−	0.602017i	−0.917473	+	0.397798i	$0.869775\pi$
$840$	−7.01402e6	−	4.50764e6i	−0.342980	−	0.220420i
$841$	8.48968e6	−	9.79761e6i	0.413906	−	0.477673i
$842$	−3.34281e7	−	9.81538e6i	−1.62492	−	0.477119i
$843$	−1.36115e6	−	9.46700e6i	−0.0659685	−	0.458821i
$844$	6.52630e7	+	7.53175e7i	3.15363	+	3.63948i
$845$	474949.	+	1.03999e6i	0.0228826	+	0.0501059i
$846$	−3.30715e6	+	971067.i	−0.158865	+	0.0466469i
$847$	9.28038e6	−	2.03212e7i	0.444485	−	0.973287i
$848$	−2.60611e6	+	1.81259e7i	−0.124453	+	0.865586i
$849$	−1.49696e7	+	9.62040e6i	−0.712758	+	0.458062i
$850$	−4.68605e7			−2.22464
$851$	−1.83491e7	+	1.83957e7i	−0.868540	+	0.870748i
$852$	−6.65329e7			−3.14006
$853$	1.70315e7	−	1.09455e7i	0.801457	−	0.515065i	−0.0746340	−	0.997211i	$-0.523779\pi$
$853$	1.70315e7	−	1.09455e7i	0.801457	−	0.515065i	0.876091	+	0.482146i	$0.160142\pi$
$854$	−7.21269e6	+	5.01654e7i	−0.338417	+	2.35375i
$855$	−314038.	+	687648.i	−0.0146915	+	0.0321700i
$856$	−4.65931e7	+	1.36810e7i	−2.17339	+	0.638164i
$857$	−1.22371e7	−	2.67954e7i	−0.569148	−	1.24626i	−0.947250	−	0.320496i	$-0.896150\pi$
$857$	−1.22371e7	−	2.67954e7i	−0.569148	−	1.24626i	0.378102	−	0.925764i	$-0.376577\pi$
$858$	1.88631e7	+	2.17692e7i	0.874771	+	1.00954i
$859$	152456.	+	1.06035e6i	0.00704955	+	0.0490307i	0.993043	−	0.117756i	$-0.0375700\pi$
$859$	152456.	+	1.06035e6i	0.00704955	+	0.0490307i	−0.985993	+	0.166787i	$0.946661\pi$
$860$	−4.56423e6	−	1.34018e6i	−0.210437	−	0.0617898i
$861$	2.13107e6	−	2.45939e6i	0.0979693	−	0.113063i
$862$	−6.02472e6	−	3.87185e6i	−0.276165	−	0.177481i
$863$	3.58385e7	+	2.30320e7i	1.63803	+	1.05270i	0.942500	+	0.334206i	$0.108468\pi$
$863$	3.58385e7	+	2.30320e7i	1.63803	+	1.05270i	0.695533	+	0.718494i	$0.255168\pi$
$864$	−1.35737e7	+	1.56649e7i	−0.618606	+	0.713910i
$865$	−568711.	−	166989.i	−0.0258435	−	0.00758833i
$866$	3.74008e6	+	2.60129e7i	0.169468	+	1.17867i
$867$	−3.05543e6	−	3.52615e6i	−0.138046	−	0.159314i
$868$	−3.57634e7	−	7.83109e7i	−1.61116	−	3.52795i
$869$	−2.81470e7	+	8.26472e6i	−1.26440	+	0.371260i
$870$	−1.14421e6	+	2.50547e6i	−0.0512516	+	0.112225i
$871$	−1.59500e6	+	1.10935e7i	−0.0712386	+	0.495475i
$872$	6.29814e7	−	4.04757e7i	2.80492	−	1.80261i
$873$	−3.77146e6			−0.167484
$874$	2.46704e7	+	9.16592e6i	1.09244	+	0.405880i
$875$	8.55778e6			0.377869
$876$	−1.98888e7	+	1.27818e7i	−0.875686	+	0.562769i
$877$	−810243.	+	5.63536e6i	−0.0355726	+	0.247413i	−0.999847	−	0.0174924i	$-0.994432\pi$
$877$	−810243.	+	5.63536e6i	−0.0355726	+	0.247413i	0.964274	+	0.264906i	$0.0853408\pi$
$878$	−2.80339e7	+	6.13857e7i	−1.22729	+	2.68739i
$879$	1.03912e7	−	3.05114e6i	0.453623	−	0.133196i
$880$	−1.05441e7	−	2.30883e7i	−0.458988	−	1.00504i
$881$	−1.39026e7	−	1.60444e7i	−0.603470	−	0.696442i	0.369010	−	0.929425i	$-0.379697\pi$
$881$	−1.39026e7	−	1.60444e7i	−0.603470	−	0.696442i	−0.972481	+	0.232983i	$0.925151\pi$
$882$	−322491.	−	2.24298e6i	−0.0139587	−	0.0970852i
$883$	−1.10945e7	−	3.25764e6i	−0.478857	−	0.140605i	0.0333915	−	0.999442i	$-0.489369\pi$
$883$	−1.10945e7	−	3.25764e6i	−0.478857	−	0.140605i	−0.512249	+	0.858837i	$0.671187\pi$
$884$	4.24487e7	−	4.89884e7i	1.82698	−	2.10845i
$885$	2.66695e6	+	1.71395e6i	0.114461	+	0.0735595i
$886$	−3.46569e7	−	2.22726e7i	−1.48322	−	0.953207i
$887$	2.94470e7	−	3.39837e7i	1.25670	−	1.45031i	0.415500	−	0.909593i	$-0.363607\pi$
$887$	2.94470e7	−	3.39837e7i	1.25670	−	1.45031i	0.841203	−	0.540719i	$-0.181848\pi$
$888$	5.88764e7	+	1.72877e7i	2.50558	+	0.735706i
$889$	3.46059e6	+	2.40690e7i	0.146858	+	1.02142i
$890$	−6932.08	−	8000.05i	−0.000293352	−	0.000338546i
$891$	1.54606e6	+	3.38539e6i	0.0652426	+	0.142861i
$892$	1.55211e7	−	4.55741e6i	0.653147	−	0.191781i
$893$	1.48092e6	−	3.24277e6i	0.0621446	−	0.136078i
$894$	838247.	−	5.83014e6i	0.0350775	−	0.243969i
$895$	3.44748e6	−	2.21556e6i	0.143861	−	0.0924541i
$896$	1.41687e8			5.89602
$897$	−1.13095e7	+	2.47528e6i	−0.469313	+	0.102717i
$898$	−4.92065e7			−2.03625
$899$	−1.55880e7	+	1.00178e7i	−0.643267	+	0.413403i
$900$	3.20180e6	−	2.22690e7i	0.131761	−	0.916420i
$901$	2.36955e6	−	5.18860e6i	0.0972421	−	0.212931i
$902$	1.57548e7	−	4.62601e6i	0.644756	−	0.189317i
$903$	−2.68915e6	−	5.88841e6i	−0.109748	−	0.240314i
$904$	−7.02358e7	−	8.10564e7i	−2.85849	−	3.29888i
$905$	−863839.	−	6.00814e6i	−0.0350600	−	0.243847i
$906$	−3.16453e7	−	9.29190e6i	−1.28082	−	0.376083i
$907$	1.68322e7	−	1.94254e7i	0.679397	−	0.784066i	−0.306419	−	0.951897i	$-0.599131\pi$
$907$	1.68322e7	−	1.94254e7i	0.679397	−	0.784066i	0.985816	+	0.167831i	$0.0536763\pi$
$908$	4.64532e7	+	2.98537e7i	1.86983	+	1.20166i
$909$	1.05479e7	+	6.77873e6i	0.423406	+	0.272106i
$910$	−5.14161e6	+	5.93373e6i	−0.205824	+	0.237533i
$911$	−2.01041e7	−	5.90309e6i	−0.802580	−	0.235659i	−0.145381	−	0.989376i	$-0.546441\pi$
$911$	−2.01041e7	−	5.90309e6i	−0.802580	−	0.235659i	−0.657199	+	0.753717i	$0.728259\pi$
$912$	−5.33689e6	−	3.71189e7i	−0.212472	−	1.47777i
$913$	3.05156e7	+	3.52169e7i	1.21156	+	1.39821i
$914$	9.12099e6	+	1.99722e7i	0.361141	+	0.790788i
$915$	2.83267e6	−	831748.i	0.111852	−	0.0328427i
$916$	3.97058e7	−	8.69435e7i	1.56356	−	3.42372i
$917$	−4.56993e6	+	3.17846e7i	−0.179468	+	1.24823i
$918$	9.50097e6	−	6.10591e6i	0.372102	−	0.239135i
$919$	−3.10959e7			−1.21455			−0.607273	−	0.794493i	$-0.707737\pi$
$919$	−3.10959e7			−1.21455			−0.607273	+	0.794493i	$0.707737\pi$
$920$	1.68668e7	+	1.18481e6i	0.656997	+	0.0461510i
$921$	2.01415e7			0.782426
$922$	1.55756e7	−	1.00098e7i	0.603415	−	0.387792i
$923$	−5.80926e6	+	4.04043e7i	−0.224449	+	1.56107i
$924$	2.70694e7	−	5.92738e7i	1.04304	−	2.28393i
$925$	−2.97232e7	+	8.72753e6i	−1.14220	+	0.335380i
$926$	−1.91311e7	−	4.18912e7i	−0.733183	−	1.60545i
$927$	1.13623e7	+	1.31128e7i	0.434279	+	0.501184i
$928$	−1.11163e7	−	7.73157e7i	−0.423732	−	2.94712i
$929$	4.04640e7	+	1.18813e7i	1.53826	+	0.451673i	0.937566	−	0.347807i	$-0.113073\pi$
$929$	4.04640e7	+	1.18813e7i	1.53826	+	0.451673i	0.600692	+	0.799480i	$0.294892\pi$
$930$	−4.42852e6	+	5.11079e6i	−0.167900	+	0.193767i
$931$	1.97166e6	+	1.26711e6i	0.0745519	+	0.0479116i
$932$	−1.66843e7	−	1.07224e7i	−0.629171	−	0.404344i
$933$	1.89653e6	−	2.18871e6i	0.0713273	−	0.0823161i
$934$	1.98528e7	+	5.82930e6i	0.744653	+	0.218650i
$935$	1.12517e6	+	7.82571e6i	0.0420909	+	0.292749i
$936$	1.79049e7	+	2.06634e7i	0.668009	+	0.770924i
$937$	1.13271e7	+	2.48028e7i	0.421471	+	0.922894i	0.994634	+	0.103452i	$0.0329889\pi$
$937$	1.13271e7	+	2.48028e7i	0.421471	+	0.922894i	−0.573163	+	0.819441i	$0.694284\pi$
$938$	3.28044e7	−	9.63223e6i	1.21738	−	0.357454i
$939$	4.98545e6	−	1.09166e7i	0.184519	−	0.404039i
$940$	500291.	−	3.47960e6i	0.0184673	−	0.128443i
$941$	1.14951e7	−	7.38744e6i	0.423192	−	0.271969i	−0.311663	−	0.950193i	$-0.600886\pi$
$941$	1.14951e7	−	7.38744e6i	0.423192	−	0.271969i	0.734856	+	0.678223i	$0.237250\pi$
$942$	−9.83733e6			−0.361202
$943$	−1.39463e6	+	6.45045e6i	−0.0510718	+	0.236217i
$944$	−1.57263e8			−5.74376
$945$	−853407.	+	548451.i	−0.0310868	+	0.0199783i
$946$	4.64840e6	−	3.23303e7i	0.168879	−	1.17458i
$947$	2.06961e7	−	4.53182e7i	0.749918	−	1.64209i	−0.0165941	−	0.999862i	$-0.505282\pi$
$947$	2.06961e7	−	4.53182e7i	0.749918	−	1.64209i	0.766512	−	0.642230i	$-0.221990\pi$
$948$	−4.10079e7	+	1.20410e7i	−1.48200	+	0.435153i
$949$	6.02557e6	+	1.31942e7i	0.217186	+	0.475572i
$950$	2.05484e7	+	2.37141e7i	0.738700	+	0.852505i
$951$	1.55981e6	+	1.08487e7i	0.0559269	+	0.388980i
$952$	−1.23612e8	−	3.62958e7i	−4.42047	−	1.29797i
$953$	−2.13311e7	+	2.46174e7i	−0.760819	+	0.878032i	−0.995570	−	0.0940236i	$-0.970027\pi$
$953$	−2.13311e7	+	2.46174e7i	−0.760819	+	0.878032i	0.234751	+	0.972056i	$0.424573\pi$
$954$	3.10666e6	+	1.99653e6i	0.110516	+	0.0710240i
$955$	791123.	+	508424.i	0.0280696	+	0.0180392i
$956$	−7.94169e7	+	9.16520e7i	−2.81040	+	3.24338i
$957$	−1.34569e7	−	3.95131e6i	−0.474970	−	0.139464i
$958$	−1.08393e7	−	7.53890e7i	−0.381582	−	2.65396i
$959$	−2.11835e7	−	2.44471e7i	−0.743793	−	0.858383i
$960$	−6.48901e6	−	1.42089e7i	−0.227248	−	0.497604i
$961$	−1.61814e7	+	4.75128e6i	−0.565206	+	0.165959i
$962$	2.40044e7	−	5.25624e7i	0.836284	−	1.83121i
$963$	−840851.	+	5.84825e6i	−0.0292182	+	0.203217i
$964$	5.77586e6	−	3.71192e6i	0.200182	−	0.128649i
$965$	220967.			0.00763853
$966$	2.12006e7	+	2.82458e7i	0.730978	+	0.973893i
$967$	4.69737e7			1.61543			0.807717	−	0.589571i	$-0.200703\pi$
$967$	4.69737e7			1.61543			0.807717	+	0.589571i	$0.200703\pi$
$968$	9.00100e7	−	5.78459e7i	3.08747	−	1.98420i
$969$	−1.66238e6	+	1.15621e7i	−0.0568748	+	0.395573i
$970$	2.15476e6	−	4.71827e6i	0.0735309	−	0.161010i
$971$	1.88348e7	−	5.53041e6i	0.641082	−	0.188239i	0.0549949	−	0.998487i	$-0.482486\pi$
$971$	1.88348e7	−	5.53041e6i	0.641082	−	0.188239i	0.586087	+	0.810248i	$0.300668\pi$
$972$	2.25248e6	+	4.93224e6i	0.0764706	+	0.167447i
$973$	1.53642e7	+	1.77312e7i	0.520268	+	0.600421i
$974$	1.50199e6	+	1.04466e7i	0.0507305	+	0.352838i
$975$	−1.32440e7	−	3.88880e6i	−0.446178	−	0.131010i
$976$	−9.59051e7	+	1.10680e8i	−3.22268	+	3.71917i
$977$	3.78679e7	+	2.43362e7i	1.26921	+	0.815674i	0.989517	−	0.144414i	$-0.0461297\pi$
$977$	3.78679e7	+	2.43362e7i	1.26921	+	0.815674i	0.279697	+	0.960088i	$0.409766\pi$
$978$	9.68075e6	+	6.22144e6i	0.323640	+	0.207991i
$979$	35297.6	−	40735.5i	0.00117703	−	0.00135837i
$980$	2.21753e6	+	651127.i	0.0737573	+	0.0216571i
$981$	−1.29636e6	−	9.01636e6i	−0.0430083	−	0.299129i
$982$	−3.21271e6	−	3.70766e6i	−0.106314	−	0.122693i
$983$	567245.	+	1.24209e6i	0.0187235	+	0.0409987i	0.918763	−	0.394810i	$-0.129190\pi$
$983$	567245.	+	1.24209e6i	0.0187235	+	0.0409987i	−0.900039	+	0.435809i	$0.856462\pi$
$984$	1.49545e7	−	4.39103e6i	0.492361	−	0.144570i
$985$	−728493.	+	1.59518e6i	−0.0239241	+	0.0523864i
$986$	−6.05693e6	+	4.21269e7i	−0.198408	+	1.37996i
$987$	4.02445e6	−	2.58635e6i	0.131496	−	0.0845075i
$988$	−4.34047e7			−1.41464
$989$	1.05194e7	+	7.85388e6i	0.341979	+	0.255325i
$990$	−5.11859e6			−0.165982
$991$	−2.78552e7	+	1.79014e7i	−0.900994	+	0.579034i	−0.907085	−	0.420948i	$-0.861698\pi$
$991$	−2.78552e7	+	1.79014e7i	−0.900994	+	0.579034i	0.00609073	+	0.999981i	$0.498061\pi$
$992$	2.72928e7	−	1.89825e8i	0.880580	−	6.12457i
$993$	−2.08233e6	+	4.55966e6i	−0.0670156	+	0.146744i
$994$	1.19479e8	−	3.50822e7i	3.83553	−	1.12621i
$995$	3.57279e6	+	7.82331e6i	0.114406	+	0.250514i
$996$	4.44587e7	+	5.13081e7i	1.42007	+	1.63884i
$997$	212534.	+	1.47820e6i	0.00677158	+	0.0470974i	0.992927	−	0.118726i	$-0.0378810\pi$
$997$	212534.	+	1.47820e6i	0.00677158	+	0.0470974i	−0.986155	+	0.165823i	$0.946972\pi$
$998$	−9.27532e7	−	2.72348e7i	−2.94783	−	0.865562i
$999$	4.88920e6	−	5.64244e6i	0.154997	−	0.178876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.b.58.10	yes	100
23.2	even	11	inner	69.6.e.b.25.10	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.b.25.10	✓	100	23.2	even	11	inner
69.6.e.b.58.10	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)

\(f(q)\)	\(=\)	\(q+(9.36123 - 6.01610i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(38.1459 - 83.5279i) q^{4} +(9.60568 - 2.82048i) q^{5} +(41.6036 + 91.0991i) q^{6} +(-91.0258 - 105.049i) q^{7} +(-94.7428 - 658.950i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(9.36123 - 6.01610i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(38.1459 - 83.5279i) q^{4} +(9.60568 - 2.82048i) q^{5} +(41.6036 + 91.0991i) q^{6} +(-91.0258 - 105.049i) q^{7} +(-94.7428 - 658.950i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(72.9526 - 84.1918i) q^{10} +(477.199 + 306.677i) q^{11} +(695.240 + 446.804i) q^{12} +(332.041 - 383.195i) q^{13} +(-1484.10 - 435.771i) q^{14} +(12.8227 + 89.1837i) q^{15} +(-2926.95 - 3377.88i) q^{16} +(578.349 + 1266.41i) q^{17} +(-864.834 + 253.938i) q^{18} +(387.268 - 847.998i) q^{19} +(130.828 - 909.931i) q^{20} +(1052.41 - 676.343i) q^{21} +6312.17 q^{22} +(-1213.02 + 2228.21i) q^{23} +5991.54 q^{24} +(-2544.60 + 1635.32i) q^{25} +(802.968 - 5584.77i) q^{26} +(302.838 - 663.122i) q^{27} +(-12246.8 + 3595.99i) q^{28} +(1141.22 + 2498.93i) q^{29} +(656.574 + 757.727i) q^{30} +(959.899 + 6676.24i) q^{31} +(-27281.2 - 8010.49i) q^{32} +(-3343.22 + 3858.28i) q^{33} +(13032.9 + 8375.73i) q^{34} +(-1170.65 - 752.334i) q^{35} +(-4870.79 + 5621.19i) q^{36} +(9826.59 + 2885.35i) q^{37} +(-1476.34 - 10268.1i) q^{38} +(2988.37 + 3448.76i) q^{39} +(-2768.63 - 6062.44i) q^{40} +(2495.93 - 732.872i) q^{41} +(5782.91 - 12662.8i) q^{42} +(736.418 - 5121.90i) q^{43} +(43819.3 - 28161.0i) q^{44} -810.907 q^{45} +(2049.72 + 28156.4i) q^{46} +3824.03 q^{47} +(33840.5 - 21747.9i) q^{48} +(-357.789 + 2488.48i) q^{49} +(-13982.4 + 30617.2i) q^{50} +(-12022.4 + 3530.10i) q^{51} +(-19341.5 - 42352.0i) q^{52} +(-2683.03 - 3096.38i) q^{53} +(-1154.47 - 8029.53i) q^{54} +(5448.80 + 1599.91i) q^{55} +(-60598.3 + 69934.1i) q^{56} +(7058.27 + 4536.08i) q^{57} +(25717.1 + 16527.4i) q^{58} +(23041.4 - 26591.2i) q^{59} +(7938.46 + 2330.94i) q^{60} +(-4663.11 - 32432.7i) q^{61} +(49150.8 + 56723.0i) q^{62} +(4677.17 + 10241.6i) q^{63} +(-166345. + 48843.2i) q^{64} +(2108.68 - 4617.37i) q^{65} +(-8084.84 + 56231.3i) q^{66} +(-18595.0 + 11950.3i) q^{67} +127842. q^{68} +(-18296.1 - 13660.1i) q^{69} -15484.9 q^{70} +(-67726.0 + 43524.9i) q^{71} +(-7674.16 + 53375.0i) q^{72} +(-11883.8 + 26021.9i) q^{73} +(109348. - 32107.3i) q^{74} +(-11308.8 - 24762.9i) q^{75} +(-56058.8 - 64695.3i) q^{76} +(-11221.2 - 78045.1i) q^{77} +(48722.8 + 14306.3i) q^{78} +(-33866.2 + 39083.7i) q^{79} +(-37642.6 - 24191.4i) q^{80} +(5519.46 + 3547.14i) q^{81} +(18956.0 - 21876.3i) q^{82} +(78820.9 + 23143.9i) q^{83} +(-16348.3 - 113705. i) q^{84} +(9127.31 + 10533.5i) q^{85} +(-23920.1 - 52377.6i) q^{86} +(-23723.2 + 6965.75i) q^{87} +(156874. - 343506. i) q^{88} +(13.5230 - 94.0545i) q^{89} +(-7591.09 + 4878.50i) q^{90} -70478.7 q^{91} +(139846. + 186318. i) q^{92} -60704.1 q^{93} +(35797.6 - 23005.7i) q^{94} +(1328.21 - 9237.87i) q^{95} +(106303. - 232772. i) q^{96} +(44675.2 - 13117.8i) q^{97} +(11621.6 + 25447.7i) q^{98} +(-30088.9 - 34724.5i) 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

Varieties

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Database

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