LMFDB - Embedded newform 69.6.e.b.58.2

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			58.2
Character	$\chi$	$=$	69.58
Dual form			69.6.e.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.63772 + 4.90846i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(20.9484 - 45.8707i) q^{4} +(-88.8509 + 26.0890i) q^{5} +(-33.9439 - 74.3267i) q^{6} +(33.6833 + 38.8726i) q^{7} +(23.8100 + 165.602i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(-7.63772 + 4.90846i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(20.9484 - 45.8707i) q^{4} +(-88.8509 + 26.0890i) q^{5} +(-33.9439 - 74.3267i) q^{6} +(33.6833 + 38.8726i) q^{7} +(23.8100 + 165.602i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(550.561 - 635.382i) q^{10} +(-603.268 - 387.697i) q^{11} +(381.803 + 245.370i) q^{12} +(84.9788 - 98.0707i) q^{13} +(-448.069 - 131.565i) q^{14} +(-118.608 - 824.934i) q^{15} +(62.0350 + 71.5922i) q^{16} +(187.444 + 410.445i) q^{17} +(705.608 - 207.185i) q^{18} +(-544.522 + 1192.34i) q^{19} +(-664.569 + 4622.18i) q^{20} +(-389.435 + 250.275i) q^{21} +6510.59 q^{22} +(2536.64 + 42.4453i) q^{23} -1505.75 q^{24} +(4584.93 - 2946.56i) q^{25} +(-167.667 + 1166.15i) q^{26} +(302.838 - 663.122i) q^{27} +(2488.73 - 730.757i) q^{28} +(1995.53 + 4369.60i) q^{29} +(4955.05 + 5718.43i) q^{30} +(740.974 + 5153.58i) q^{31} +(-5962.11 - 1750.63i) q^{32} +(4226.44 - 4877.57i) q^{33} +(-3446.30 - 2214.80i) q^{34} +(-4006.94 - 2575.10i) q^{35} +(-2674.88 + 3086.97i) q^{36} +(-11899.7 - 3494.06i) q^{37} +(-1693.64 - 11779.5i) q^{38} +(764.809 + 882.637i) q^{39} +(-6435.93 - 14092.7i) q^{40} +(10711.4 - 3145.15i) q^{41} +(1745.93 - 3823.06i) q^{42} +(2330.91 - 16211.9i) q^{43} +(-30421.4 + 19550.7i) q^{44} +7500.76 q^{45} +(-19582.5 + 12126.8i) q^{46} +10494.1 q^{47} +(-717.228 + 460.935i) q^{48} +(2015.37 - 14017.2i) q^{49} +(-20555.3 + 45009.9i) q^{50} +(-3896.49 + 1144.11i) q^{51} +(-2718.40 - 5952.47i) q^{52} +(-4293.86 - 4955.38i) q^{53} +(941.921 + 6551.20i) q^{54} +(63715.5 + 18708.6i) q^{55} +(-5635.39 + 6503.59i) q^{56} +(-9924.36 - 6378.00i) q^{57} +(-36689.3 - 23578.8i) q^{58} +(6040.11 - 6970.66i) q^{59} +(-40325.0 - 11840.5i) q^{60} +(-7774.01 - 54069.4i) q^{61} +(-30955.5 - 35724.6i) q^{62} +(-1730.75 - 3789.80i) q^{63} +(51221.3 - 15039.9i) q^{64} +(-4991.88 + 10930.7i) q^{65} +(-8338.98 + 57998.9i) q^{66} +(-11270.2 + 7242.94i) q^{67} +22754.0 q^{68} +(-3627.13 + 22543.0i) q^{69} +43243.7 q^{70} +(-7875.27 + 5061.13i) q^{71} +(1928.61 - 13413.8i) q^{72} +(-10977.1 + 24036.5i) q^{73} +(108037. - 31722.5i) q^{74} +(20376.5 + 44618.4i) q^{75} +(43286.4 + 49955.2i) q^{76} +(-5249.28 - 36509.5i) q^{77} +(-10173.8 - 2987.29i) q^{78} +(-23955.9 + 27646.6i) q^{79} +(-7379.64 - 4742.60i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-66372.7 + 76598.2i) q^{82} +(81421.9 + 23907.6i) q^{83} +(3322.22 + 23106.5i) q^{84} +(-27362.6 - 31578.2i) q^{85} +(61772.5 + 135263. i) q^{86} +(-41482.0 + 12180.2i) q^{87} +(49839.6 - 109134. i) q^{88} +(1799.84 - 12518.2i) q^{89} +(-57288.7 + 36817.2i) q^{90} +6674.64 q^{91} +(55085.7 - 115468. i) q^{92} -46859.2 q^{93} +(-80150.9 + 51509.8i) q^{94} +(17274.4 - 120146. i) q^{95} +(23231.8 - 50870.5i) q^{96} +(61955.7 - 18191.8i) q^{97} +(53410.1 + 116952. i) q^{98} +(38038.0 + 43898.2i) 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 $

$2$	−7.63772	+	4.90846i	−1.35017	+	0.867702i	−0.997678	−	0.0681126i	$-0.978302\pi$
$2$	−7.63772	+	4.90846i	−1.35017	+	0.867702i	−0.352493	+	0.935814i	$0.614666\pi$
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$3$	−1.28083	+	8.90839i	−0.0821655	+	0.571474i
$4$	20.9484	−	45.8707i	0.654639	−	1.43346i
$5$	−88.8509	+	26.0890i	−1.58941	+	0.466694i	−0.952575	−	0.304304i	$-0.901576\pi$
$5$	−88.8509	+	26.0890i	−1.58941	+	0.466694i	−0.636838	+	0.770998i	$0.719758\pi$
$6$	−33.9439	−	74.3267i	−0.384931	−	0.842882i
$7$	33.6833	+	38.8726i	0.259818	+	0.299846i	0.870639	−	0.491923i	$-0.163706\pi$
$7$	33.6833	+	38.8726i	0.259818	+	0.299846i	−0.610820	+	0.791769i	$0.709160\pi$
$8$	23.8100	+	165.602i	0.131533	+	0.914831i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	550.561	−	635.382i	1.74103	−	2.00925i
$11$	−603.268	−	387.697i	−1.50324	−	0.966074i	−0.994453	−	0.105182i	$-0.966457\pi$
$11$	−603.268	−	387.697i	−1.50324	−	0.966074i	−0.508788	−	0.860892i	$-0.669906\pi$
$12$	381.803	+	245.370i	0.765395	+	0.491890i
$13$	84.9788	−	98.0707i	0.139461	−	0.160946i	−0.681723	−	0.731611i	$-0.738769\pi$
$13$	84.9788	−	98.0707i	0.139461	−	0.160946i	0.821183	+	0.570664i	$0.193314\pi$
$14$	−448.069	−	131.565i	−0.610976	−	0.179399i
$15$	−118.608	−	824.934i	−0.136108	−	0.946654i
$16$	62.0350	+	71.5922i	0.0605811	+	0.0699143i
$17$	187.444	+	410.445i	0.157307	+	0.344455i	0.971832	−	0.235674i	$-0.0757296\pi$
$17$	187.444	+	410.445i	0.157307	+	0.344455i	−0.814525	+	0.580128i	$0.803002\pi$
$18$	705.608	−	207.185i	0.513313	−	0.150722i
$19$	−544.522	+	1192.34i	−0.346044	+	0.757731i	0.653955	+	0.756533i	$0.273108\pi$
$19$	−544.522	+	1192.34i	−0.346044	+	0.757731i	−0.999999	+	0.00119762i	$0.999619\pi$
$20$	−664.569	+	4622.18i	−0.371505	+	2.58387i
$21$	−389.435	+	250.275i	−0.192702	+	0.123842i
$22$	6510.59			2.86790
$23$	2536.64	+	42.4453i	0.999860	+	0.0167305i
$23$	2536.64	+	42.4453i	0.999860	+	0.0167305i
$24$	−1505.75			−0.533609
$25$	4584.93	−	2946.56i	1.46718	−	0.942898i
$26$	−167.667	+	1166.15i	−0.0486424	+	0.338315i
$27$	302.838	−	663.122i	0.0799467	−	0.175059i
$28$	2488.73	−	730.757i	0.599905	−	0.176148i
$29$	1995.53	+	4369.60i	0.440618	+	0.964820i	0.991484	+	0.130226i	$0.0415703\pi$
$29$	1995.53	+	4369.60i	0.440618	+	0.964820i	−0.550866	+	0.834594i	$0.685702\pi$
$30$	4955.05	+	5718.43i	1.00518	+	1.16004i
$31$	740.974	+	5153.58i	0.138484	+	0.963175i	0.934008	+	0.357253i	$0.116287\pi$
$31$	740.974	+	5153.58i	0.138484	+	0.963175i	−0.795524	+	0.605922i	$0.792804\pi$
$32$	−5962.11	−	1750.63i	−1.02926	−	0.302218i
$33$	4226.44	−	4877.57i	0.675601	−	0.779685i
$34$	−3446.30	−	2214.80i	−0.511276	−	0.328577i
$35$	−4006.94	−	2575.10i	−0.552895	−	0.355324i
$36$	−2674.88	+	3086.97i	−0.343991	+	0.396987i
$37$	−11899.7	−	3494.06i	−1.42899	−	0.419591i	−0.526457	−	0.850202i	$-0.676480\pi$
$37$	−11899.7	−	3494.06i	−1.42899	−	0.419591i	−0.902538	+	0.430611i	$0.858298\pi$
$38$	−1693.64	−	11779.5i	−0.190266	−	1.32333i
$39$	764.809	+	882.637i	0.0805177	+	0.0929224i
$40$	−6435.93	−	14092.7i	−0.636006	−	1.39266i
$41$	10711.4	−	3145.15i	0.995144	−	0.292201i	0.256682	−	0.966496i	$-0.417371\pi$
$41$	10711.4	−	3145.15i	0.995144	−	0.292201i	0.738462	+	0.674295i	$0.235552\pi$
$42$	1745.93	−	3823.06i	0.152723	−	0.334417i
$43$	2330.91	−	16211.9i	0.192245	−	1.33709i	−0.633803	−	0.773494i	$-0.718507\pi$
$43$	2330.91	−	16211.9i	0.192245	−	1.33709i	0.826048	−	0.563599i	$-0.190584\pi$
$44$	−30421.4	+	19550.7i	−2.36891	+	1.52240i
$45$	7500.76			0.552171
$46$	−19582.5	+	12126.8i	−1.36450	+	0.844991i
$47$	10494.1			0.692947			0.346473	−	0.938060i	$-0.387379\pi$
$47$	10494.1			0.692947			0.346473	+	0.938060i	$0.387379\pi$
$48$	−717.228	+	460.935i	−0.0449319	+	0.0288759i
$49$	2015.37	−	14017.2i	0.119913	−	0.834010i
$50$	−20555.3	+	45009.9i	−1.16279	+	2.54615i
$51$	−3896.49	+	1144.11i	−0.209772	+	0.0615946i
$52$	−2718.40	−	5952.47i	−0.139414	−	0.305273i
$53$	−4293.86	−	4955.38i	−0.209971	−	0.242319i	0.640989	−	0.767550i	$-0.278524\pi$
$53$	−4293.86	−	4955.38i	−0.209971	−	0.242319i	−0.850960	+	0.525231i	$0.823979\pi$
$54$	941.921	+	6551.20i	0.0439572	+	0.305729i
$55$	63715.5	+	18708.6i	2.84013	+	0.833938i
$56$	−5635.39	+	6503.59i	−0.240134	+	0.277130i
$57$	−9924.36	−	6378.00i	−0.404590	−	0.260014i
$58$	−36689.3	−	23578.8i	−1.43209	−	0.920346i
$59$	6040.11	−	6970.66i	0.225899	−	0.260702i	−0.631474	−	0.775397i	$-0.717550\pi$
$59$	6040.11	−	6970.66i	0.225899	−	0.260702i	0.857373	+	0.514696i	$0.172095\pi$
$60$	−40325.0	−	11840.5i	−1.44609	−	0.424611i
$61$	−7774.01	−	54069.4i	−0.267498	−	1.86049i	−0.471967	−	0.881616i	$-0.656456\pi$
$61$	−7774.01	−	54069.4i	−0.267498	−	1.86049i	0.204469	−	0.978873i	$-0.434453\pi$
$62$	−30955.5	−	35724.6i	−1.02273	−	1.18029i
$63$	−1730.75	−	3789.80i	−0.0549391	−	0.120300i
$64$	51221.3	−	15039.9i	1.56315	−	0.458982i
$65$	−4991.88	+	10930.7i	−0.146548	+	0.320896i
$66$	−8338.98	+	57998.9i	−0.235642	+	1.63893i
$67$	−11270.2	+	7242.94i	−0.306723	+	0.197119i	−0.684942	−	0.728597i	$-0.740173\pi$
$67$	−11270.2	+	7242.94i	−0.306723	+	0.197119i	0.378220	+	0.925716i	$0.376536\pi$
$68$	22754.0			0.596741
$69$	−3627.13	+	22543.0i	−0.0917151	+	0.570019i
$70$	43243.7			1.05482
$71$	−7875.27	+	5061.13i	−0.185404	+	0.119152i	−0.630050	−	0.776554i	$-0.716966\pi$
$71$	−7875.27	+	5061.13i	−0.185404	+	0.119152i	0.444646	+	0.895706i	$0.353329\pi$
$72$	1928.61	−	13413.8i	0.0438443	−	0.304944i
$73$	−10977.1	+	24036.5i	−0.241090	+	0.527914i	−0.991038	−	0.133583i	$-0.957352\pi$
$73$	−10977.1	+	24036.5i	−0.241090	+	0.527914i	0.749947	+	0.661498i	$0.230079\pi$
$74$	108037.	−	31722.5i	2.29347	−	0.673422i
$75$	20376.5	+	44618.4i	0.418290	+	0.915927i
$76$	43286.4	+	49955.2i	0.859642	+	0.992080i
$77$	−5249.28	−	36509.5i	−0.100896	−	0.701745i
$78$	−10173.8	−	2987.29i	−0.189342	−	0.0555957i
$79$	−23955.9	+	27646.6i	−0.431862	+	0.498395i	−0.929414	−	0.369039i	$-0.879687\pi$
$79$	−23955.9	+	27646.6i	−0.431862	+	0.498395i	0.497552	+	0.867434i	$0.334232\pi$
$80$	−7379.64	−	4742.60i	−0.128917	−	0.0828499i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	−66372.7	+	76598.2i	−1.09007	+	1.25801i
$83$	81421.9	+	23907.6i	1.29732	+	0.380927i	0.856257	−	0.516551i	$-0.172784\pi$
$83$	81421.9	+	23907.6i	1.29732	+	0.380927i	0.441061	+	0.897477i	$0.354602\pi$
$84$	3322.22	+	23106.5i	0.0513724	+	0.357303i
$85$	−27362.6	−	31578.2i	−0.410781	−	0.474067i
$86$	61772.5	+	135263.i	0.900635	+	1.97212i
$87$	−41482.0	+	12180.2i	−0.587573	+	0.172527i
$88$	49839.6	−	109134.i	0.686069	−	1.50228i
$89$	1799.84	−	12518.2i	0.0240857	−	0.167519i	−0.974228	−	0.225564i	$-0.927577\pi$
$89$	1799.84	−	12518.2i	0.0240857	−	0.167519i	0.998314	+	0.0580446i	$0.0184866\pi$
$90$	−57288.7	+	36817.2i	−0.745525	+	0.479120i
$91$	6674.64			0.0844937
$92$	55085.7	−	115468.i	0.678530	−	1.42231i
$93$	−46859.2			−0.561808
$94$	−80150.9	+	51509.8i	−0.935597	+	0.601271i
$95$	17274.4	−	120146.i	0.196379	−	1.36584i
$96$	23231.8	−	50870.5i	0.257279	−	0.563363i
$97$	61955.7	−	18191.8i	0.668578	−	0.196312i	0.0702081	−	0.997532i	$-0.477634\pi$
$97$	61955.7	−	18191.8i	0.668578	−	0.196312i	0.598370	+	0.801220i	$0.295815\pi$
$98$	53410.1	+	116952.i	0.561770	+	1.23010i
$99$	38038.0	+	43898.2i	0.390058	+	0.450151i
$100$	−39113.4	−	272040.i	−0.391134	−	2.72040i
$101$	−90544.4	−	26586.2i	−0.883198	−	0.259330i	−0.191479	−	0.981497i	$-0.561328\pi$
$101$	−90544.4	−	26586.2i	−0.883198	−	0.259330i	−0.691719	+	0.722167i	$0.743146\pi$
$102$	24144.4	−	27864.2i	0.229782	−	0.265183i
$103$	−37005.8	−	23782.2i	−0.343698	−	0.220881i	0.357391	−	0.933955i	$-0.383666\pi$
$103$	−37005.8	−	23782.2i	−0.343698	−	0.220881i	−0.701089	+	0.713073i	$0.747303\pi$
$104$	18264.1	+	11737.6i	0.165582	+	0.106413i
$105$	28072.3	−	32397.1i	0.248487	−	0.286770i
$106$	57118.6	+	16771.5i	0.493757	+	0.144980i
$107$	−25251.2	−	175626.i	−0.213217	−	1.48296i	−0.762318	−	0.647203i	$-0.775939\pi$
$107$	−25251.2	−	175626.i	−0.213217	−	1.48296i	0.549101	−	0.835756i	$-0.314970\pi$
$108$	−24073.9	−	27782.7i	−0.198603	−	0.229201i
$109$	22215.3	+	48644.7i	0.179096	+	0.392165i	0.977795	−	0.209566i	$-0.0672051\pi$
$109$	22215.3	+	48644.7i	0.179096	+	0.392165i	−0.798699	+	0.601731i	$0.794478\pi$
$110$	−578471.	+	169855.i	−4.55827	+	1.33843i
$111$	46367.9	−	101532.i	0.357199	−	0.782157i
$112$	−693.433	+	4822.93i	−0.00522347	+	0.0363300i
$113$	195607.	−	125709.i	1.44108	−	0.926126i	0.441497	−	0.897263i	$-0.354448\pi$
$113$	195607.	−	125709.i	1.44108	−	0.926126i	0.999583	−	0.0288634i	$-0.00918879\pi$
$114$	107106.			0.771881
$115$	−226490.	+	62407.0i	−1.59700	+	0.440037i
$116$	242240.			1.67148
$117$	−8842.47	+	5682.71i	−0.0597185	+	0.0383787i
$118$	−11917.4	+	82887.6i	−0.0787913	+	0.548005i
$119$	−9641.33	+	21111.6i	−0.0624122	+	0.136664i
$120$	133787.	−	39283.4i	0.848126	−	0.249032i
$121$	146720.	+	321273.i	0.911019	+	1.99485i
$122$	324773.	+	374809.i	1.97552	+	2.27987i
$123$	14298.7	+	99449.6i	0.0852185	+	0.592707i
$124$	251921.	+	73970.6i	1.47133	+	0.432021i
$125$	−140998.	+	162721.i	−0.807121	+	0.931467i
$126$	31821.1	+	20450.2i	0.178562	+	0.114755i
$127$	−101119.	−	64985.0i	−0.556316	−	0.357523i	0.232074	−	0.972698i	$-0.425449\pi$
$127$	−101119.	−	64985.0i	−0.556316	−	0.357523i	−0.788390	+	0.615175i	$0.789085\pi$
$128$	−187177.	+	216014.i	−1.00978	+	1.16535i
$129$	141436.	+	41529.4i	0.748318	+	0.219726i
$130$	−15526.3	−	107988.i	−0.0805768	−	0.560424i
$131$	−206293.	−	238075.i	−1.05028	−	1.21209i	−0.976657	−	0.214806i	$-0.931088\pi$
$131$	−206293.	−	238075.i	−1.05028	−	1.21209i	−0.0736270	−	0.997286i	$-0.523457\pi$
$132$	−135200.	−	296047.i	−0.675372	−	1.47886i
$133$	−64690.6	+	18994.9i	−0.317112	+	0.0931124i
$134$	50527.1	−	110639.i	0.243088	−	0.532287i
$135$	−9607.22	+	66819.7i	−0.0453694	+	0.315551i
$136$	−63507.5	+	40813.8i	−0.294427	+	0.189217i
$137$	−426301.			−1.94050			−0.970252	−	0.242098i	$-0.922164\pi$
$137$	−426301.			−1.94050			−0.970252	+	0.242098i	$0.922164\pi$
$138$	−82948.6	−	189981.i	−0.370776	−	0.849204i
$139$	369905.			1.62388			0.811939	−	0.583743i	$-0.198412\pi$
$139$	369905.			1.62388			0.811939	+	0.583743i	$0.198412\pi$
$140$	−202061.	+	129857.i	−0.871289	+	0.559944i
$141$	−13441.2	+	93485.4i	−0.0569363	+	0.396001i
$142$	35306.7	−	77310.9i	0.146939	−	0.321751i
$143$	−89286.7	+	26216.9i	−0.365129	+	0.107212i
$144$	−3187.54	−	6979.73i	−0.0128100	−	0.0280500i
$145$	−291303.	−	336181.i	−1.15060	−	1.32786i
$146$	−34142.2	−	237464.i	−0.132559	−	0.921969i
$147$	122289.	+	35907.4i	0.466762	+	0.137054i
$148$	−409554.	+	472651.i	−1.53694	+	1.77372i
$149$	411682.	+	264572.i	1.51913	+	0.976288i	0.991963	+	0.126528i	$0.0403833\pi$
$149$	411682.	+	264572.i	1.51913	+	0.976288i	0.527170	+	0.849760i	$0.323253\pi$
$150$	−374638.	−	240765.i	−1.35951	−	0.873707i
$151$	237641.	−	274252.i	0.848161	−	0.978831i	−0.151793	−	0.988412i	$-0.548505\pi$
$151$	237641.	−	274252.i	0.848161	−	0.978831i	0.999954	+	0.00958183i	$0.00305004\pi$
$152$	−210419.	−	61784.5i	−0.738712	−	0.216905i
$153$	−5201.45	−	36176.8i	−0.0179637	−	0.124940i
$154$	219298.	+	253084.i	0.745132	+	0.859928i
$155$	−200288.	−	438569.i	−0.669616	−	1.46625i
$156$	56508.7	−	16592.5i	0.185911	−	0.0545883i
$157$	86102.4	−	188538.i	0.278783	−	0.610449i	−0.717503	−	0.696555i	$-0.754715\pi$
$157$	86102.4	−	188538.i	0.278783	−	0.610449i	0.996286	+	0.0861059i	$0.0274423\pi$
$158$	47266.2	−	328744.i	0.150629	−	1.04765i
$159$	49644.2	−	31904.4i	0.155731	−	0.100082i
$160$	575411.			1.77696
$161$	83792.5	+	100036.i	0.254765	+	0.304151i
$162$	−59567.1			−0.178328
$163$	−273832.	+	175981.i	−0.807262	+	0.518796i	−0.877978	−	0.478701i	$-0.841108\pi$
$163$	−273832.	+	175981.i	−0.807262	+	0.518796i	0.0707162	+	0.997496i	$0.477472\pi$
$164$	80116.8	−	557225.i	0.232602	−	1.61778i
$165$	−248272.	+	543640.i	−0.709934	+	1.55454i
$166$	−739227.	+	217057.i	−2.08213	+	0.611369i
$167$	−29938.3	−	65555.7i	−0.0830684	−	0.181894i	0.863540	−	0.504281i	$-0.168242\pi$
$167$	−29938.3	−	65555.7i	−0.0830684	−	0.181894i	−0.946608	+	0.322386i	$0.895515\pi$
$168$	−50718.5	−	58532.3i	−0.138642	−	0.160001i
$169$	50444.0	+	350846.i	0.135860	+	0.944930i
$170$	363988.	+	106877.i	0.965973	+	0.283635i
$171$	69529.2	−	80241.0i	0.181835	−	0.209849i
$172$	−694820.	−	446534.i	−1.79082	−	1.15089i
$173$	165190.	+	106161.i	0.419631	+	0.269681i	0.733371	−	0.679828i	$-0.237946\pi$
$173$	165190.	+	106161.i	0.419631	+	0.269681i	−0.313740	+	0.949509i	$0.601582\pi$
$174$	257042.	−	296642.i	0.643622	−	0.742779i
$175$	268976.	+	78978.5i	0.663924	+	0.194946i
$176$	−9667.66	−	67240.1i	−0.0235256	−	0.163624i
$177$	54361.0	+	62736.0i	0.130423	+	0.150516i
$178$	47698.2	+	104445.i	0.112837	+	0.247079i
$179$	−420537.	+	123481.i	−0.981006	+	0.288049i	−0.732639	−	0.680617i	$-0.761712\pi$
$179$	−420537.	+	123481.i	−0.981006	+	0.288049i	−0.248366	+	0.968666i	$0.579894\pi$
$180$	157129.	−	344065.i	0.361473	−	0.791515i
$181$	−62729.6	+	436294.i	−0.142323	+	0.989880i	0.786032	+	0.618186i	$0.212132\pi$
$181$	−62729.6	+	436294.i	−0.142323	+	0.989880i	−0.928355	+	0.371694i	$0.878777\pi$
$182$	−50979.0	+	32762.2i	−0.114081	+	0.0733153i
$183$	491629.			1.08520
$184$	53368.3	+	421084.i	0.116209	+	0.916904i
$185$	1.14845e6			2.46708
$186$	357898.	−	230007.i	0.758536	−	0.487482i
$187$	46049.2	−	320279.i	0.0962982	−	0.669769i
$188$	219835.	−	481371.i	0.453630	−	0.993311i
$189$	35977.9	−	10564.1i	0.0732624	−	0.0215118i
$190$	457796.	+	1.00243e6i	0.920001	+	2.01452i
$191$	144948.	+	167279.i	0.287494	+	0.331786i	0.881064	−	0.472996i	$-0.156828\pi$
$191$	144948.	+	167279.i	0.287494	+	0.331786i	−0.593570	+	0.804782i	$0.702282\pi$
$192$	68375.6	+	475563.i	0.133859	+	0.931011i
$193$	−546944.	−	160597.i	−1.05694	−	0.310345i	−0.293320	−	0.956014i	$-0.594760\pi$
$193$	−546944.	−	160597.i	−1.05694	−	0.310345i	−0.763617	+	0.645669i	$0.776578\pi$
$194$	−383906.	+	443051.i	−0.732353	+	0.845181i
$195$	−90981.1	−	58470.0i	−0.171342	−	0.110115i
$196$	−600760.	−	386085.i	−1.11702	−	0.717865i
$197$	248492.	−	286775.i	0.456190	−	0.526472i	−0.480329	−	0.877089i	$-0.659483\pi$
$197$	248492.	−	286775.i	0.456190	−	0.526472i	0.936519	+	0.350617i	$0.114028\pi$
$198$	−505996.	−	148574.i	−0.917242	−	0.269327i
$199$	−54546.7	−	379381.i	−0.0976418	−	0.679114i	−0.978578	−	0.205878i	$-0.933995\pi$
$199$	−54546.7	−	379381.i	−0.0976418	−	0.679114i	0.880936	−	0.473236i	$-0.156914\pi$
$200$	597123.	+	689116.i	1.05557	+	1.21820i
$201$	−50087.6	−	109677.i	−0.0874461	−	0.191480i
$202$	822050.	−	241376.i	1.41749	−	0.416212i
$203$	−102642.	+	224754.i	−0.174817	+	0.382796i
$204$	−29144.1	+	202702.i	−0.0490316	+	0.341022i
$205$	−869662.	+	558898.i	−1.44533	+	0.928855i
$206$	399374.			0.655710
$207$	−196176.	−	61185.8i	−0.318215	−	0.0992487i
$208$	12292.8			0.0197011
$209$	790758.	−	508189.i	1.25221	−	0.804748i
$210$	−55388.0	+	385232.i	−0.0866697	+	0.602801i
$211$	293802.	−	643336.i	0.454306	−	0.994791i	−0.534443	−	0.845205i	$-0.679478\pi$
$211$	293802.	−	643336.i	0.454306	−	0.994791i	0.988749	−	0.149587i	$-0.0477943\pi$
$212$	−317256.	+	93154.9i	−0.484809	+	0.142353i
$213$	−34999.6	−	76638.4i	−0.0528584	−	0.115744i
$214$	1.05491e6	+	1.21744e6i	1.57465	+	1.81724i
$215$	215847.	+	1.50125e6i	0.318456	+	2.21491i
$216$	117025.	+	34361.6i	0.170665	+	0.0501117i
$217$	−175375.	+	202394.i	−0.252824	+	0.291774i
$218$	−408445.	−	262492.i	−0.582093	−	0.374088i
$219$	−200066.	−	128575.i	−0.281880	−	0.181153i
$220$	2.19292e6	−	2.53076e6i	3.05468	−	3.52528i
$221$	56181.4	+	16496.3i	0.0773769	+	0.0227199i
$222$	144219.	+	1.00307e6i	0.196399	+	1.36599i
$223$	−148740.	−	171655.i	−0.200293	−	0.231151i	0.646713	−	0.762733i	$-0.276143\pi$
$223$	−148740.	−	171655.i	−0.200293	−	0.231151i	−0.847007	+	0.531583i	$0.821598\pi$
$224$	−132772.	−	290730.i	−0.176802	−	0.387142i
$225$	−423577.	+	124373.i	−0.557797	+	0.163784i
$226$	−876953.	+	1.92026e6i	−1.14210	+	2.50086i
$227$	142630.	−	992012.i	0.183715	−	1.27777i	−0.664167	−	0.747584i	$-0.731214\pi$
$227$	142630.	−	992012.i	0.183715	−	1.27777i	0.847882	−	0.530184i	$-0.177877\pi$
$228$	−500463.	+	321628.i	−0.637581	+	0.409748i
$229$	722584.			0.910541			0.455271	−	0.890353i	$-0.349542\pi$
$229$	722584.			0.910541			0.455271	+	0.890353i	$0.349542\pi$
$230$	1.42354e6	−	1.58837e6i	1.77440	−	1.97984i
$231$	331965.			0.409319
$232$	−676101.	+	434504.i	−0.824691	+	0.529997i
$233$	−57701.2	+	401321.i	−0.0696298	+	0.484286i	0.924932	+	0.380134i	$0.124122\pi$
$233$	−57701.2	+	401321.i	−0.0696298	+	0.484286i	−0.994561	+	0.104152i	$0.966787\pi$
$234$	39642.9	−	86805.9i	0.0473288	−	0.103636i
$235$	−932409.	+	273780.i	−1.10138	+	0.323394i
$236$	−193218.	−	423089.i	−0.225823	−	0.494483i
$237$	−215603.	−	248819.i	−0.249336	−	0.287749i
$238$	−29987.6	−	208568.i	−0.0343162	−	0.238675i
$239$	−111201.	−	32651.6i	−0.125926	−	0.0369751i	0.218162	−	0.975912i	$-0.429994\pi$
$239$	−111201.	−	32651.6i	−0.125926	−	0.0369751i	−0.344088	+	0.938937i	$0.611812\pi$
$240$	51701.1	−	59666.2i	0.0579390	−	0.0668652i
$241$	16266.8	+	10454.1i	0.0180410	+	0.0115942i	0.549630	−	0.835408i	$-0.314769\pi$
$241$	16266.8	+	10454.1i	0.0180410	+	0.0115942i	−0.531589	+	0.847002i	$0.678405\pi$
$242$	−2.69757e6	−	1.73362e6i	−2.96097	−	1.90290i
$243$	−38668.9	+	44626.3i	−0.0420093	+	0.0484814i
$244$	−2.64306e6	−	776071.i	−2.84205	−	0.834501i
$245$	186627.	+	1.29802e6i	0.198637	+	1.38155i
$246$	−597354.	−	689384.i	−0.629353	−	0.726312i
$247$	70660.6	+	154725.i	0.0736944	+	0.161368i
$248$	−835802.	+	245414.i	−0.862927	+	0.253378i
$249$	−317267.	+	694717.i	−0.324284	+	0.710084i
$250$	278196.	−	1.93490e6i	0.281515	−	1.95798i
$251$	−1.41968e6	+	912376.i	−1.42235	+	0.914091i	−0.422382	+	0.906418i	$0.638806\pi$
$251$	−1.41968e6	+	912376.i	−1.42235	+	0.914091i	−0.999971	+	0.00767309i	$0.997558\pi$
$252$	−210097.			−0.208410
$253$	−1.51382e6	−	1.00905e6i	−1.48687	−	0.991089i
$254$	1.09129e6			1.06134
$255$	316358.	−	203311.i	0.304669	−	0.195799i
$256$	126196.	−	877712.i	0.120350	−	0.837051i
$257$	−51658.7	+	113117.i	−0.0487878	+	0.106830i	−0.932456	−	0.361283i	$-0.882339\pi$
$257$	−51658.7	+	113117.i	−0.0487878	+	0.106830i	0.883668	+	0.468113i	$0.155066\pi$
$258$	−1.28409e6	+	377044.i	−1.20101	+	0.352649i
$259$	−264997.	−	580263.i	−0.245466	−	0.537496i
$260$	396826.	+	457962.i	0.364055	+	0.420142i
$261$	−55374.6	−	385139.i	−0.0503164	−	0.349958i
$262$	2.74419e6	+	805767.i	2.46980	+	0.725198i
$263$	12507.2	−	14434.0i	0.0111499	−	0.0128676i	−0.750147	−	0.661271i	$-0.770017\pi$
$263$	12507.2	−	14434.0i	0.0111499	−	0.0128676i	0.761297	+	0.648403i	$0.224563\pi$
$264$	908368.	+	583773.i	0.802143	+	0.515506i
$265$	510794.	+	328268.i	0.446819	+	0.287153i
$266$	400853.	−	462609.i	0.347361	−	0.400876i
$267$	109211.	+	32067.3i	0.0937540	+	0.0275286i
$268$	96144.7	+	668701.i	0.0817690	+	0.568716i
$269$	132173.	+	152535.i	0.111368	+	0.128526i	0.808696	−	0.588226i	$-0.200174\pi$
$269$	132173.	+	152535.i	0.111368	+	0.128526i	−0.697328	+	0.716752i	$0.745628\pi$
$270$	−254605.	−	557507.i	−0.212548	−	0.465415i
$271$	−1.11496e6	+	327382.i	−0.922223	+	0.270789i	−0.708178	−	0.706034i	$-0.750482\pi$
$271$	−1.11496e6	+	327382.i	−0.922223	+	0.270789i	−0.214046	+	0.976824i	$0.568664\pi$
$272$	−17756.6	+	38881.5i	−0.0145525	+	0.0318655i
$273$	−8549.10	+	59460.3i	−0.00694247	+	0.0482859i
$274$	3.25596e6	−	2.09248e6i	2.62001	−	1.68378i
$275$	−3.90831e6			−3.11643
$276$	958081.	+	638620.i	0.757059	+	0.504626i
$277$	988227.			0.773851			0.386925	−	0.922111i	$-0.373537\pi$
$277$	988227.			0.773851			0.386925	+	0.922111i	$0.373537\pi$
$278$	−2.82523e6	+	1.81566e6i	−2.19251	+	1.40904i
$279$	60018.9	−	417440.i	0.0461612	−	0.321058i
$280$	331038.	−	724871.i	0.252338	−	0.552543i
$281$	−1.56694e6	+	460096.i	−1.18382	+	0.347602i	−0.813647	−	0.581359i	$-0.802521\pi$
$281$	−1.56694e6	+	460096.i	−1.18382	+	0.347602i	−0.370178	+	0.928961i	$0.620703\pi$
$282$	−356210.	−	779991.i	−0.266737	−	0.584073i
$283$	−154789.	−	178636.i	−0.114888	−	0.132588i	0.695392	−	0.718630i	$-0.255231\pi$
$283$	−154789.	−	178636.i	−0.114888	−	0.132588i	−0.810280	+	0.586042i	$0.800685\pi$
$284$	67182.8	+	467267.i	0.0494268	+	0.343771i
$285$	1.04818e6	+	307775.i	0.764408	+	0.224451i
$286$	553262.	−	638498.i	0.399959	−	0.461577i
$287$	483055.	+	310441.i	0.346172	+	0.222471i
$288$	423419.	+	272115.i	0.300808	+	0.193317i
$289$	796479.	−	919186.i	0.560957	−	0.647379i
$290$	3.87502e6	+	1.13781e6i	2.70570	+	0.794464i
$291$	82705.1	+	575226.i	0.0572532	+	0.398205i
$292$	872616.	+	1.00705e6i	0.598916	+	0.691186i
$293$	−548415.	−	1.20086e6i	−0.373199	−	0.817191i	−0.999299	−	0.0374481i	$-0.988077\pi$
$293$	−548415.	−	1.20086e6i	−0.373199	−	0.817191i	0.626100	−	0.779743i	$-0.284650\pi$
$294$	−1.11026e6	+	326003.i	−0.749130	+	0.219965i
$295$	−354812.	+	776930.i	−0.237380	+	0.519789i
$296$	295292.	−	2.05380e6i	0.195895	−	1.36248i
$297$	−439782.	+	282631.i	−0.289299	+	0.185921i
$298$	−4.44295e6			−2.89822
$299$	219723.	−	245163.i	0.142134	−	0.158591i
$300$	2.47353e6			1.58677
$301$	708711.	−	455461.i	0.450872	−	0.289758i
$302$	−468877.	+	3.26111e6i	−0.295830	+	2.05754i
$303$	352813.	−	772552.i	0.220769	−	0.483416i
$304$	−119142.	+	34983.1i	−0.0739399	+	0.0217107i
$305$	2.10134e6	+	4.60130e6i	1.29344	+	2.83225i
$306$	217300.	+	250777.i	0.132665	+	0.153103i
$307$	−147688.	−	1.02719e6i	−0.0894331	−	0.622021i	−0.984407	−	0.175903i	$-0.943715\pi$
$307$	−147688.	−	1.02719e6i	−0.0894331	−	0.622021i	0.894974	−	0.446118i	$-0.147194\pi$
$308$	−1.78468e6	−	524030.i	−1.07197	−	0.314760i
$309$	259260.	−	299202.i	0.154468	−	0.178266i
$310$	3.68244e6	+	2.36656e6i	2.17637	+	1.39867i
$311$	2.06054e6	+	1.32423e6i	1.20804	+	0.776358i	0.980329	−	0.197371i	$-0.0632404\pi$
$311$	2.06054e6	+	1.32423e6i	1.20804	+	0.776358i	0.227708	+	0.973729i	$0.426877\pi$
$312$	−127956.	+	147670.i	−0.0744176	+	0.0858825i
$313$	−2.18965e6	−	642938.i	−1.26332	−	0.370944i	−0.419590	−	0.907714i	$-0.637826\pi$
$313$	−2.18965e6	−	642938.i	−1.26332	−	0.370944i	−0.843729	+	0.536770i	$0.819644\pi$
$314$	267806.	+	1.86263e6i	0.153284	+	1.06611i
$315$	252650.	+	291574.i	0.143464	+	0.165567i
$316$	766329.	+	1.67803e6i	0.431716	+	0.945325i
$317$	2.59985e6	−	763384.i	1.45311	−	0.426672i	0.542543	−	0.840028i	$-0.317461\pi$
$317$	2.59985e6	−	763384.i	1.45311	−	0.426672i	0.910570	+	0.413355i	$0.135643\pi$
$318$	−222567.	+	487353.i	−0.123422	+	0.270257i
$319$	490240.	−	3.40970e6i	0.269732	−	1.87603i
$320$	−4.15868e6	+	2.67262e6i	−2.27029	+	1.45902i
$321$	1.59689e6			0.864991
$322$	−1.13100e6	−	352751.i	−0.607890	−	0.189596i
$323$	−591456.			−0.315439
$324$	278334.	−	178875.i	0.147300	−	0.0946642i
$325$	100651.	−	700042.i	0.0528578	−	0.367634i
$326$	1.22765e6	−	2.68818e6i	0.639781	−	1.40093i
$327$	−461800.	+	135597.i	−0.238828	+	0.0701261i
$328$	775881.	+	1.69894e6i	0.398208	+	0.871955i
$329$	353476.	+	407933.i	0.180040	+	0.207778i
$330$	−772205.	−	5.37081e6i	−0.390344	−	2.71490i
$331$	−1.78178e6	−	523177.i	−0.893888	−	0.262469i	−0.197644	−	0.980274i	$-0.563329\pi$
$331$	−1.78178e6	−	523177.i	−0.893888	−	0.262469i	−0.696244	+	0.717805i	$0.745147\pi$
$332$	2.80232e6	−	3.23405e6i	1.39532	−	1.61028i
$333$	845094.	+	543109.i	0.417633	+	0.268396i
$334$	550438.	+	353745.i	0.269987	+	0.173510i
$335$	812409.	−	937570.i	0.395515	−	0.456448i
$336$	−42076.4	−	12354.7i	−0.0203325	−	0.00597015i
$337$	−66767.5	−	464378.i	−0.0320251	−	0.222739i	0.967524	−	0.252781i	$-0.0813452\pi$
$337$	−66767.5	−	464378.i	−0.0320251	−	0.222739i	−0.999549	+	0.0300415i	$0.990436\pi$
$338$	−2.10739e6	−	2.43206e6i	−1.00335	−	1.15793i
$339$	869325.	+	1.90356e6i	0.410850	+	0.899635i
$340$	−2.02172e6	+	593629.i	−0.948469	+	0.278495i
$341$	1.55102e6	−	3.39627e6i	0.722324	−	1.58167i
$342$	−137185.	+	954140.i	−0.0634220	+	0.441110i
$343$	1.34002e6	−	861178.i	0.615001	−	0.395237i
$344$	2.74022e6			1.24850
$345$	−265850.	−	2.09760e6i	−0.120251	−	0.948799i
$346$	−1.78276e6			−0.800576
$347$	196528.	−	126301.i	0.0876196	−	0.0563097i	−0.496097	−	0.868267i	$-0.665234\pi$
$347$	196528.	−	126301.i	0.0876196	−	0.0563097i	0.583717	+	0.811957i	$0.301598\pi$
$348$	−310269.	+	2.15797e6i	−0.137338	+	0.955205i
$349$	−463460.	+	1.01484e6i	−0.203680	+	0.445997i	−0.983714	−	0.179740i	$-0.942474\pi$
$349$	−463460.	+	1.01484e6i	−0.203680	+	0.445997i	0.780034	+	0.625737i	$0.215202\pi$
$350$	−2.44203e6	+	717044.i	−1.06557	+	0.312878i
$351$	−39298.1	−	86050.8i	−0.0170256	−	0.0372810i
$352$	2.91804e6	+	3.36759e6i	1.25526	+	1.44865i
$353$	214160.	+	1.48952e6i	0.0914749	+	0.636222i	0.983048	+	0.183346i	$0.0586929\pi$
$353$	214160.	+	1.48952e6i	0.0914749	+	0.636222i	−0.891573	+	0.452876i	$0.850398\pi$
$354$	−723131.	−	212331.i	−0.306697	−	0.0900543i
$355$	567685.	−	655143.i	0.239076	−	0.275909i
$356$	−536513.	−	344796.i	−0.224365	−	0.144191i
$357$	−175721.	−	112929.i	−0.0729716	−	0.0468960i
$358$	2.60584e6	−	3.00730e6i	1.07458	−	1.24014i
$359$	94816.5	+	27840.6i	0.0388283	+	0.0114010i	0.301089	−	0.953596i	$-0.402650\pi$
$359$	94816.5	+	27840.6i	0.0388283	+	0.0114010i	−0.262261	+	0.964997i	$0.584468\pi$
$360$	178593.	+	1.24214e6i	0.0726286	+	0.505143i
$361$	496337.	+	572803.i	0.200451	+	0.231333i
$362$	−1.66242e6	−	3.64020e6i	−0.666760	−	1.46000i
$363$	−3.04995e6	+	895546.i	−1.21486	+	0.356715i
$364$	139823.	−	306170.i	0.0553128	−	0.121118i
$365$	348237.	−	2.42204e6i	0.136818	−	0.951589i
$366$	−3.75492e6	+	2.41314e6i	−1.46520	+	0.941630i
$367$	4.74149e6			1.83760			0.918798	−	0.394729i	$-0.129162\pi$
$367$	4.74149e6			1.83760			0.918798	+	0.394729i	$0.129162\pi$
$368$	154322.	+	184237.i	0.0594029	+	0.0709181i
$369$	−904251.			−0.345719
$370$	−8.77156e6	+	5.63714e6i	−3.33098	+	2.14069i
$371$	47997.1	−	333827.i	0.0181043	−	0.125918i
$372$	−981628.	+	2.14947e6i	−0.367781	+	0.805328i
$373$	−810817.	+	238077.i	−0.301753	+	0.0886026i	−0.429104	−	0.903255i	$-0.641171\pi$
$373$	−810817.	+	238077.i	−0.301753	+	0.0886026i	0.127351	+	0.991858i	$0.459352\pi$
$374$	1.22037e6	+	2.67224e6i	0.451141	+	0.987861i
$375$	−1.26898e6	−	1.46449e6i	−0.465991	−	0.537783i
$376$	249864.	+	1.73784e6i	0.0911453	+	0.633929i
$377$	598107.	+	175620.i	0.216733	+	0.0636386i
$378$	−222936.	+	257281.i	−0.0802509	+	0.0926144i
$379$	−690733.	−	443907.i	−0.247009	−	0.158743i	0.411279	−	0.911510i	$-0.365082\pi$
$379$	−690733.	−	443907.i	−0.247009	−	0.158743i	−0.658287	+	0.752767i	$0.728719\pi$
$380$	−5.14932e6	−	3.30927e6i	−1.82932	−	1.17564i
$381$	708428.	−	817569.i	0.250025	−	0.288544i
$382$	−1.92815e6	−	566157.i	−0.676057	−	0.198508i
$383$	−685487.	−	4.76767e6i	−0.238782	−	1.66077i	−0.658101	−	0.752929i	$-0.728640\pi$
$383$	−685487.	−	4.76767e6i	−0.238782	−	1.66077i	0.419319	−	0.907839i	$-0.362269\pi$
$384$	−1.68459e6	−	1.94412e6i	−0.582997	−	0.672815i
$385$	1.41890e6	+	3.10696e6i	0.487865	+	1.06828i
$386$	4.96569e6	−	1.45806e6i	1.69633	−	0.498088i
$387$	−551116.	+	1.20678e6i	−0.187054	+	0.409590i
$388$	463403.	−	3.22304e6i	0.156272	−	1.08689i
$389$	−1.75410e6	+	1.12729e6i	−0.587732	+	0.377712i	−0.800449	−	0.599401i	$-0.795405\pi$
$389$	−1.75410e6	+	1.12729e6i	−0.587732	+	0.377712i	0.212716	+	0.977114i	$0.431769\pi$
$390$	981885.			0.326888
$391$	458056.	+	1.04911e6i	0.151522	+	0.347038i
$392$	2.36927e6			0.778751
$393$	2.38509e6	−	1.53281e6i	0.778976	−	0.500617i
$394$	−490286.	+	3.41002e6i	−0.159114	+	1.10666i
$395$	1.40723e6	−	3.08141e6i	0.453809	−	0.993703i
$396$	2.81048e6	−	825230.i	0.900620	−	0.264446i
$397$	689194.	+	1.50912e6i	0.219465	+	0.480561i	0.987055	−	0.160380i	$-0.0512718\pi$
$397$	689194.	+	1.50912e6i	0.219465	+	0.480561i	−0.767591	+	0.640940i	$0.778545\pi$
$398$	2.27879e6	+	2.62986e6i	0.721101	+	0.832195i
$399$	−86355.9	−	600619.i	−0.0271556	−	0.188872i
$400$	495377.	+	145456.i	0.154805	+	0.0454549i
$401$	−2.54964e6	+	2.94244e6i	−0.791805	+	0.913792i	−0.997902	−	0.0647399i	$-0.979378\pi$
$401$	−2.54964e6	+	2.94244e6i	−0.791805	+	0.913792i	0.206097	+	0.978532i	$0.433924\pi$
$402$	920899.	+	591826.i	0.284215	+	0.182654i
$403$	568383.	+	365278.i	0.174333	+	0.112037i
$404$	−3.11629e6	+	3.59639e6i	−0.949915	+	1.09626i
$405$	−582951.	−	171170.i	−0.176601	−	0.0518549i
$406$	−319248.	−	2.22042e6i	−0.0961199	−	0.668529i
$407$	5.82405e6	+	6.72132e6i	1.74277	+	2.01126i
$408$	−282243.	−	618025.i	−0.0839406	−	0.183804i
$409$	−1.39358e6	+	409193.i	−0.411931	+	0.120954i	−0.481131	−	0.876649i	$-0.659774\pi$
$409$	−1.39358e6	+	409193.i	−0.411931	+	0.120954i	0.0691994	+	0.997603i	$0.477956\pi$
$410$	3.89891e6	−	8.53741e6i	1.14547	−	2.50823i
$411$	546020.	−	3.79765e6i	0.159442	−	1.10895i
$412$	−1.86612e6	+	1.19928e6i	−0.541623	+	0.348080i
$413$	474419.			0.136863
$414$	1.79867e6	−	495605.i	0.515763	−	0.142113i
$415$	−7.85814e6			−2.23975
$416$	−678339.	+	435942.i	−0.192182	+	0.123508i
$417$	−473787.	+	3.29526e6i	−0.133427	+	0.928003i
$418$	−3.54516e6	+	7.76281e6i	−0.992419	+	2.17309i
$419$	4.93629e6	−	1.44943e6i	1.37362	−	0.403330i	0.490074	−	0.871681i	$-0.336970\pi$
$419$	4.93629e6	−	1.44943e6i	1.37362	−	0.403330i	0.883543	+	0.468351i	$0.155152\pi$
$420$	−898008.	−	1.96636e6i	−0.248403	−	0.543927i
$421$	2.34423e6	+	2.70538e6i	0.644606	+	0.743916i	0.980182	−	0.198098i	$-0.0634763\pi$
$421$	2.34423e6	+	2.70538e6i	0.644606	+	0.743916i	−0.335576	+	0.942013i	$0.608931\pi$
$422$	913817.	+	6.35574e6i	0.249792	+	1.73734i
$423$	−815589.	−	239479.i	−0.221626	−	0.0650752i
$424$	718385.	−	829060.i	0.194063	−	0.223960i
$425$	2.06881e6	+	1.32955e6i	0.555583	+	0.357052i
$426$	643494.	+	413548.i	0.171799	+	0.110408i
$427$	1.83997e6	−	2.12343e6i	0.488360	−	0.563598i
$428$	−8.58505e6	−	2.52080e6i	−2.26534	−	0.665164i
$429$	−119189.	−	828980.i	−0.0312676	−	0.217471i
$430$	−9.01741e6	−	1.04066e7i	−2.35186	−	2.71419i
$431$	−2.05335e6	−	4.49622e6i	−0.532440	−	1.16588i	−0.964511	−	0.264041i	$-0.914944\pi$
$431$	−2.05335e6	−	4.49622e6i	−0.532440	−	1.16588i	0.432072	−	0.901839i	$-0.357783\pi$
$432$	66260.9	−	19456.0i	0.0170824	−	0.00501583i
$433$	1.42202e6	−	3.11380e6i	0.364491	−	0.798124i	−0.635177	−	0.772366i	$-0.719073\pi$
$433$	1.42202e6	−	3.11380e6i	0.364491	−	0.798124i	0.999668	−	0.0257576i	$-0.00819980\pi$
$434$	346023.	−	2.40665e6i	0.0881823	−	0.613321i
$435$	3.36794e6	−	2.16445e6i	0.853379	−	0.548433i
$436$	2.69674e6			0.679396
$437$	−1.43187e6	+	3.00142e6i	−0.358673	+	0.751835i
$438$	2.15916e6			0.537773
$439$	3.71037e6	−	2.38451e6i	0.918875	−	0.590525i	0.00654400	−	0.999979i	$-0.497917\pi$
$439$	3.71037e6	−	2.38451e6i	0.918875	−	0.590525i	0.912331	+	0.409453i	$0.134281\pi$
$440$	−1.58111e6	+	1.09969e7i	−0.389342	+	2.70793i
$441$	−476510.	+	1.04341e6i	−0.116674	+	0.255481i
$442$	−510069.	+	149770.i	−0.124186	+	0.0364643i
$443$	−2.39889e6	−	5.25283e6i	−0.580766	−	1.27170i	−0.940864	−	0.338785i	$-0.889984\pi$
$443$	−2.39889e6	−	5.25283e6i	−0.580766	−	1.27170i	0.360098	−	0.932914i	$-0.382743\pi$
$444$	−3.68599e6	−	4.25386e6i	−0.887354	−	1.02406i
$445$	166669.	+	1.15921e6i	0.0398982	+	0.277498i
$446$	1.97860e6	+	580969.i	0.471000	+	0.138298i
$447$	−2.88420e6	+	3.32855e6i	−0.682743	+	0.787927i
$448$	2.30994e6	+	1.48451e6i	0.543759	+	0.349453i
$449$	−381761.	−	245343.i	−0.0893666	−	0.0574324i	0.495194	−	0.868782i	$-0.335097\pi$
$449$	−381761.	−	245343.i	−0.0893666	−	0.0574324i	−0.584561	+	0.811350i	$0.698733\pi$
$450$	2.62468e6	−	3.02904e6i	0.611006	−	0.705138i
$451$	−7.68120e6	−	2.25540e6i	−1.77823	−	0.522135i
$452$	−1.66870e6	−	1.16060e7i	−0.384177	−	2.67201i
$453$	2.13877e6	+	2.46827e6i	0.489686	+	0.565128i
$454$	3.77989e6	+	8.27680e6i	0.860675	+	1.88462i
$455$	−593047.	+	174134.i	−0.134295	+	0.0394327i
$456$	819912.	−	1.79536e6i	0.184652	−	0.404332i
$457$	−667621.	+	4.64340e6i	−0.149534	+	1.04003i	0.767451	+	0.641108i	$0.221525\pi$
$457$	−667621.	+	4.64340e6i	−0.149534	+	1.04003i	−0.916985	+	0.398922i	$0.869384\pi$
$458$	−5.51889e6	+	3.54678e6i	−1.22939	+	0.790079i
$459$	328940.			0.0728760
$460$	−1.88196e6	+	1.16966e7i	−0.414683	+	2.57730i
$461$	1.86664e6			0.409079			0.204539	−	0.978858i	$-0.434430\pi$
$461$	1.86664e6			0.409079			0.204539	+	0.978858i	$0.434430\pi$
$462$	−2.53545e6	+	1.62944e6i	−0.552651	+	0.355167i
$463$	1.01990e6	−	7.09356e6i	0.221108	−	1.53784i	−0.512749	−	0.858539i	$-0.671373\pi$
$463$	1.01990e6	−	7.09356e6i	0.221108	−	1.53784i	0.733857	−	0.679304i	$-0.237718\pi$
$464$	−189037.	+	413932.i	−0.0407616	+	0.0892554i
$465$	4.16348e6	−	1.22251e6i	0.892945	−	0.262192i
$466$	−1.52916e6	−	3.34840e6i	−0.326204	−	0.714286i
$467$	−4.84462e6	−	5.59099e6i	−1.02794	−	1.18630i	−0.982294	−	0.187347i	$-0.940011\pi$
$467$	−4.84462e6	−	5.59099e6i	−1.02794	−	1.18630i	−0.0456453	−	0.998958i	$-0.514534\pi$
$468$	75433.9	+	524654.i	0.0159203	+	0.110728i
$469$	−661171.	−	194137.i	−0.138797	−	0.0407546i
$470$	5.77764e6	−	6.66775e6i	1.20644	−	1.39231i
$471$	1.56929e6	+	1.00852e6i	0.325949	+	0.209475i
$472$	1.29817e6	+	834284.i	0.268211	+	0.172369i
$473$	−7.69145e6	+	8.87641e6i	−1.58072	+	1.82425i
$474$	2.86804e6	+	842131.i	0.586326	+	0.172161i
$475$	1.01669e6	+	7.07124e6i	0.206755	+	1.43801i
$476$	766432.	+	884509.i	0.155044	+	0.178931i
$477$	220631.	+	483114.i	0.0443987	+	0.0972196i
$478$	1.00959e6	−	296443.i	0.202105	−	0.0593433i
$479$	−344384.	+	754096.i	−0.0685811	+	0.150172i	−0.940818	−	0.338912i	$-0.889941\pi$
$479$	−344384.	+	754096.i	−0.0685811	+	0.150172i	0.872237	+	0.489083i	$0.162669\pi$
$480$	−737006.	+	5.12599e6i	−0.146005	+	1.01549i
$481$	−1.35388e6	+	870089.i	−0.266820	+	0.171475i
$482$	−175555.			−0.0344188
$483$	−998480.	+	618328.i	−0.194747	+	0.120601i
$484$	1.78106e7			3.45593
$485$	−5.03021e6	+	3.23272e6i	−0.971028	+	0.624042i
$486$	76295.6	−	530648.i	0.0146524	−	0.101910i
$487$	2.42218e6	−	5.30384e6i	0.462791	−	1.01337i	−0.524052	−	0.851686i	$-0.675580\pi$
$487$	2.42218e6	−	5.30384e6i	0.462791	−	1.01337i	0.986843	−	0.161684i	$-0.0516925\pi$
$488$	8.76891e6	−	2.57478e6i	1.66685	−	0.489431i
$489$	−1.21697e6	−	2.66480e6i	−0.230149	−	0.503956i
$490$	−7.79669e6	−	8.99786e6i	−1.46697	−	1.69297i
$491$	160332.	+	1.11514e6i	0.0300136	+	0.208749i	0.999310	−	0.0371470i	$-0.0118270\pi$
$491$	160332.	+	1.11514e6i	0.0300136	+	0.208749i	−0.969296	+	0.245896i	$0.920918\pi$
$492$	4.86136e6	+	1.42742e6i	0.905409	+	0.265852i
$493$	−1.41943e6	+	1.63811e6i	−0.263024	+	0.303546i
$494$	−1.29915e6	−	834911.i	−0.239520	−	0.153930i
$495$	−4.52497e6	−	2.90802e6i	−0.830046	−	0.533438i
$496$	−322990.	+	372751.i	−0.0589502	+	0.0680322i
$497$	−462004.	−	135657.i	−0.0838987	−	0.0246349i
$498$	−986800.	−	6.86334e6i	−0.178302	−	1.24012i
$499$	−5.06086e6	−	5.84055e6i	−0.909857	−	1.05003i	−0.998542	−	0.0539718i	$-0.982812\pi$
$499$	−5.06086e6	−	5.84055e6i	−0.909857	−	1.05003i	0.0886850	−	0.996060i	$-0.471734\pi$
$500$	4.51041e6	+	9.87643e6i	0.806847	+	1.76675i
$501$	622342.	−	182736.i	0.110773	−	0.0325260i
$502$	6.36478e6	−	1.39369e7i	1.12726	−	2.46836i
$503$	−269758.	+	1.87621e6i	−0.0475395	+	0.330644i	0.952148	+	0.305638i	$0.0988697\pi$
$503$	−269758.	+	1.87621e6i	−0.0475395	+	0.330644i	−0.999687	+	0.0250063i	$0.992039\pi$
$504$	586391.	−	376850.i	0.102828	−	0.0660834i
$505$	8.73855e6			1.52479
$506$	1.65150e7	+	276344.i	2.86749	+	0.0479814i
$507$	−3.19008e6			−0.551166
$508$	−5.09918e6	+	3.27705e6i	−0.876680	+	0.563408i
$509$	700538.	−	4.87235e6i	0.119850	−	0.833573i	−0.837870	−	0.545870i	$-0.816199\pi$
$509$	700538.	−	4.87235e6i	0.119850	−	0.833573i	0.957720	−	0.287703i	$-0.0928917\pi$
$510$	−1.41831e6	+	3.10566e6i	−0.241460	+	0.528723i
$511$	−1.30411e6	+	382920.i	−0.220933	+	0.0648717i
$512$	−455211.	−	996772.i	−0.0767428	−	0.168043i
$513$	625763.	+	722169.i	0.104982	+	0.121156i
$514$	−160675.	−	1.11752e6i	−0.0268251	−	0.186572i
$515$	3.90846e6	+	1.14763e6i	0.649362	+	0.190670i
$516$	4.86785e6	−	5.61780e6i	0.804846	−	0.928842i
$517$	−6.33075e6	−	4.06852e6i	−1.04167	−	0.669438i
$518$	4.87217e6	+	3.13116e6i	0.797808	+	0.512720i
$519$	−1.15730e6	+	1.33560e6i	−0.188595	+	0.217650i
$520$	−1.92900e6	−	566406.i	−0.312841	−	0.0918585i
$521$	−515705.	−	3.58681e6i	−0.0832352	−	0.578914i	−0.988170	−	0.153363i	$-0.950990\pi$
$521$	−515705.	−	3.58681e6i	−0.0832352	−	0.578914i	0.904935	−	0.425551i	$-0.139920\pi$
$522$	2.31338e6	+	2.66978e6i	0.371595	+	0.428844i
$523$	4.74119e6	+	1.03818e7i	0.757937	+	1.65965i	0.751554	+	0.659671i	$0.229305\pi$
$523$	4.74119e6	+	1.03818e7i	0.757937	+	1.65965i	0.00638316	+	0.999980i	$0.497968\pi$
$524$	−1.52422e7	+	4.47551e6i	−2.42504	+	0.712056i
$525$	−1.04808e6	+	2.29499e6i	−0.165958	+	0.363397i
$526$	−24677.3	+	171634.i	−0.00388895	+	0.0270482i
$527$	−1.97637e6	+	1.27014e6i	−0.309986	+	0.199216i
$528$	611384.			0.0954397
$529$	6.43274e6	+	215337.i	0.999440	+	0.0334564i
$530$	−5.51259e6			−0.852445
$531$	−628504.	+	403915.i	−0.0967324	+	0.0621661i
$532$	−483859.	+	3.36532e6i	−0.0741208	+	0.515521i
$533$	601794.	−	1.31774e6i	0.0917550	−	0.200915i
$534$	−991527.	+	291139.i	−0.150470	+	0.0441821i
$535$	6.82549e6	+	1.49457e7i	1.03098	+	2.25753i
$536$	−1.46779e6	−	1.69392e6i	−0.220674	−	0.254672i
$537$	−561378.	−	3.90447e6i	−0.0840077	−	0.584287i
$538$	−1.75821e6	−	516257.i	−0.261888	−	0.0768972i
$539$	−6.65024e6	+	7.67478e6i	−0.985973	+	1.13787i
$540$	2.86381e6	+	1.84046e6i	0.422629	+	0.271607i
$541$	2.78783e6	+	1.79163e6i	0.409518	+	0.263181i	0.729141	−	0.684363i	$-0.239920\pi$
$541$	2.78783e6	+	1.79163e6i	0.409518	+	0.263181i	−0.319623	+	0.947545i	$0.603556\pi$
$542$	6.90881e6	−	7.97319e6i	1.01019	−	1.16583i
$543$	−3.80633e6	−	1.11764e6i	−0.553997	−	0.162668i
$544$	−399022.	−	2.77526e6i	−0.0578096	−	0.402075i
$545$	−3.24294e6	−	3.74255e6i	−0.467678	−	0.539730i
$546$	−226563.	−	496104.i	−0.0325243	−	0.0712182i
$547$	2.51126e6	−	737371.i	0.358858	−	0.105370i	−0.0973335	−	0.995252i	$-0.531031\pi$
$547$	2.51126e6	−	737371.i	0.358858	−	0.105370i	0.456192	+	0.889882i	$0.349213\pi$
$548$	−8.93033e6	+	1.95547e7i	−1.27033	+	2.78163i
$549$	−629695.	+	4.37962e6i	−0.0891660	+	0.620163i
$550$	2.98506e7	−	1.91838e7i	4.20771	−	2.70413i
$551$	−6.29664e6			−0.883547
$552$	−3.81953e6	−	63911.8i	−0.533535	−	0.00892757i
$553$	−1.88161e6			−0.261648
$554$	−7.54780e6	+	4.85067e6i	−1.04483	+	0.671472i
$555$	−1.47098e6	+	1.02309e7i	−0.202709	+	1.40987i
$556$	7.74893e6	−	1.69678e7i	1.06305	−	2.32776i
$557$	6.00639e6	−	1.76363e6i	0.820305	−	0.240863i	0.155458	−	0.987843i	$-0.450315\pi$
$557$	6.00639e6	−	1.76363e6i	0.820305	−	0.240863i	0.664847	+	0.746979i	$0.268497\pi$
$558$	1.59058e6	+	3.48289e6i	0.216257	+	0.473538i
$559$	−1.39183e6	−	1.60626e6i	−0.188390	−	0.217413i
$560$	−64213.2	−	446613.i	−0.00865275	−	0.0601812i
$561$	2.79419e6	+	820449.i	0.374843	+	0.110064i
$562$	9.70951e6	−	1.12054e7i	1.29675	−	1.49653i
$563$	3.94720e6	+	2.53671e6i	0.524830	+	0.337288i	0.776080	−	0.630634i	$-0.217205\pi$
$563$	3.94720e6	+	2.53671e6i	0.524830	+	0.337288i	−0.251250	+	0.967922i	$0.580842\pi$
$564$	4.00667e6	+	2.57493e6i	0.530378	+	0.340854i
$565$	−1.41002e7	+	1.62725e7i	−1.85825	+	2.14454i
$566$	2.05907e6	+	604597.i	0.270165	+	0.0793277i
$567$	48027.1	+	334036.i	0.00627377	+	0.0436350i
$568$	−1.02564e6	−	1.18366e6i	−0.133391	−	0.153941i
$569$	2.03391e6	+	4.45363e6i	0.263360	+	0.576679i	0.994403	−	0.105653i	$-0.0336933\pi$
$569$	2.03391e6	+	4.45363e6i	0.263360	+	0.576679i	−0.731043	+	0.682332i	$0.760966\pi$
$570$	−9.51644e6	+	2.79428e6i	−1.22684	+	0.360232i
$571$	−1.43967e6	+	3.15243e6i	−0.184787	+	0.404627i	−0.979242	−	0.202696i	$-0.935030\pi$
$571$	−1.43967e6	+	3.15243e6i	−0.184787	+	0.404627i	0.794454	+	0.607324i	$0.207757\pi$
$572$	−667828.	+	4.64485e6i	−0.0853443	+	0.593583i
$573$	−1.67584e6	+	1.07700e6i	−0.213229	+	0.137034i
$574$	−5.21323e6			−0.660430
$575$	1.17554e7	−	7.27974e6i	1.48275	−	0.918219i
$576$	−4.32408e6			−0.543047
$577$	2.64178e6	−	1.69777e6i	0.330337	−	0.212295i	−0.364949	−	0.931027i	$-0.618914\pi$
$577$	2.64178e6	−	1.69777e6i	0.330337	−	0.212295i	0.695287	+	0.718732i	$0.255277\pi$
$578$	−1.57149e6	+	1.09300e7i	−0.195656	+	1.36082i
$579$	2.13121e6	−	4.66669e6i	0.264198	−	0.578512i
$580$	−2.15232e7	+	6.31978e6i	−2.65667	+	0.780067i
$581$	1.81321e6	+	3.97037e6i	0.222847	+	0.487968i
$582$	−3.45515e6	−	3.98746e6i	−0.422824	−	0.487965i
$583$	669164.	+	4.65414e6i	0.0815382	+	0.567111i
$584$	−4.24185e6	−	1.24552e6i	−0.514664	−	0.151119i
$585$	637405.	−	735605.i	0.0770062	−	0.0888699i
$586$	1.00830e7	+	6.47996e6i	1.21296	+	0.779522i
$587$	−6.59074e6	−	4.23561e6i	−0.789477	−	0.507366i	0.0826897	−	0.996575i	$-0.473649\pi$
$587$	−6.59074e6	−	4.23561e6i	−0.789477	−	0.507366i	−0.872166	+	0.489210i	$0.837285\pi$
$588$	4.20887e6	−	4.85730e6i	0.502022	−	0.579364i
$589$	−6.54829e6	−	1.92275e6i	−0.777749	−	0.228368i
$590$	−1.10358e6	−	7.67555e6i	−0.130519	−	0.907778i
$591$	2.23642e6	+	2.58097e6i	0.263382	+	0.303959i
$592$	−488049.	−	1.06868e6i	−0.0572346	−	0.125326i
$593$	−1.05639e7	+	3.10183e6i	−1.23363	+	0.362228i	−0.832620	−	0.553844i	$-0.813160\pi$
$593$	−1.05639e7	+	3.10183e6i	−1.23363	+	0.362228i	−0.401014	+	0.916072i	$0.631342\pi$
$594$	1.97165e6	−	4.31731e6i	0.229279	−	0.502050i
$595$	305862.	−	2.12731e6i	0.0354187	−	0.246343i
$596$	2.07602e7	−	1.33418e7i	2.39395	−	1.53850i
$597$	3.44954e6			0.396118
$598$	−474809.	+	2.95099e6i	−0.0542958	+	0.337454i
$599$	2.30518e6			0.262505			0.131252	−	0.991349i	$-0.458100\pi$
$599$	2.30518e6			0.262505			0.131252	+	0.991349i	$0.458100\pi$
$600$	−6.90374e6	+	4.43676e6i	−0.782900	+	0.503139i
$601$	−1.50648e6	+	1.04778e7i	−0.170128	+	1.18327i	0.708483	+	0.705728i	$0.249380\pi$
$601$	−1.50648e6	+	1.04778e7i	−0.170128	+	1.18327i	−0.878611	+	0.477538i	$0.841529\pi$
$602$	−3.17732e6	+	6.95736e6i	−0.357330	+	0.782444i
$603$	1.04120e6	−	305723.i	0.116611	−	0.0342401i
$604$	−7.60193e6	−	1.66459e7i	−0.847874	−	1.85659i
$605$	−2.14179e7	−	2.47176e7i	−2.37897	−	2.74548i
$606$	1.09736e6	+	7.63230e6i	0.121386	+	0.844256i
$607$	−8.15963e6	−	2.39588e6i	−0.898874	−	0.263933i	−0.200523	−	0.979689i	$-0.564264\pi$
$607$	−8.15963e6	−	2.39588e6i	−0.898874	−	0.263933i	−0.698351	+	0.715756i	$0.746082\pi$
$608$	5.33385e6	−	6.15559e6i	0.585169	−	0.675321i
$609$	−1.87073e6	−	1.20224e6i	−0.204394	−	0.131356i
$610$	−3.86348e7	−	2.48291e7i	−4.20391	−	2.70169i
$611$	891775.	−	1.02916e6i	0.0966389	−	0.111527i
$612$	−1.76842e6	−	519255.i	−0.190856	−	0.0560405i
$613$	−356872.	−	2.48210e6i	−0.0383585	−	0.266789i	0.961612	−	0.274411i	$-0.0884829\pi$
$613$	−356872.	−	2.48210e6i	−0.0383585	−	0.266789i	−0.999971	+	0.00762200i	$0.997574\pi$
$614$	6.16993e6	+	7.12047e6i	0.660479	+	0.762233i
$615$	−3.86499e6	−	8.46315e6i	−0.412060	−	0.902286i
$616$	5.92107e6	−	1.73858e6i	0.628707	−	0.184605i
$617$	7.34112e6	−	1.60748e7i	0.776335	−	1.69994i	0.0641554	−	0.997940i	$-0.479565\pi$
$617$	7.34112e6	−	1.60748e7i	0.776335	−	1.69994i	0.712180	−	0.701997i	$-0.247708\pi$
$618$	−511532.	+	3.55778e6i	−0.0538768	+	0.374721i
$619$	6.54131e6	−	4.20385e6i	0.686180	−	0.440981i	−0.150546	−	0.988603i	$-0.548103\pi$
$619$	6.54131e6	−	4.20385e6i	0.686180	−	0.440981i	0.836726	+	0.547622i	$0.184467\pi$
$620$	−2.43132e7			−2.54017
$621$	796336.	−	1.66925e6i	0.0828643	−	0.173697i
$622$	−2.22378e7			−2.30470
$623$	547238.	−	351689.i	0.0564880	−	0.0363026i
$624$	−15745.0	+	109509.i	−0.00161875	+	0.0112587i
$625$	1.20741e6	−	2.64387e6i	0.123639	−	0.270732i
$626$	1.98797e7	−	5.83721e6i	2.02756	−	0.595347i
$627$	3.51432e6	+	7.69529e6i	0.357004	+	0.781729i
$628$	−6.84466e6	−	7.89915e6i	−0.692552	−	0.799248i
$629$	−796402.	−	5.53909e6i	−0.0802612	−	0.558229i
$630$	−3.36085e6	−	986836.i	−0.337364	−	0.0990589i
$631$	−5.24443e6	+	6.05239e6i	−0.524354	+	0.605137i	−0.954716	−	0.297520i	$-0.903841\pi$
$631$	−5.24443e6	+	6.05239e6i	−0.524354	+	0.605137i	0.430361	+	0.902657i	$0.358386\pi$
$632$	−5.14872e6	−	3.30888e6i	−0.512751	−	0.329525i
$633$	5.35478e6	+	3.44131e6i	0.531169	+	0.341361i
$634$	−1.61098e7	+	1.85918e7i	−1.59173	+	1.83695i
$635$	1.06799e7	+	3.13589e6i	1.05107	+	0.308622i
$636$	−423508.	−	2.94556e6i	−0.0415163	−	0.288752i
$637$	−1.20341e6	−	1.38881e6i	−0.117508	−	0.135611i
$638$	1.29921e7	+	2.84486e7i	1.26365	+	2.76700i
$639$	727554.	−	213629.i	0.0704876	−	0.0206970i
$640$	1.09953e7	−	2.40763e7i	1.06110	−	2.32348i
$641$	1.38319e6	−	9.62030e6i	0.132965	−	0.924791i	−0.808696	−	0.588227i	$-0.799826\pi$
$641$	1.38319e6	−	9.62030e6i	0.132965	−	0.924791i	0.941661	−	0.336564i	$-0.109265\pi$
$642$	−1.21966e7	+	7.83826e6i	−1.16789	+	0.750554i
$643$	1.12171e7			1.06992			0.534962	−	0.844876i	$-0.320326\pi$
$643$	1.12171e7			1.06992			0.534962	+	0.844876i	$0.320326\pi$
$644$	6.34402e6	−	1.74803e6i	0.602768	−	0.166087i
$645$	−1.36502e7			−1.29193
$646$	4.51737e6	−	2.90314e6i	0.425897	−	0.273707i
$647$	2.96646e6	−	2.06322e7i	0.278597	−	1.93769i	−0.0634028	−	0.997988i	$-0.520195\pi$
$647$	2.96646e6	−	2.06322e7i	0.278597	−	1.93769i	0.342000	−	0.939700i	$-0.388896\pi$
$648$	−455996.	+	998492.i	−0.0426603	+	0.0934130i
$649$	−6.34631e6	+	1.86345e6i	−0.591439	+	0.173662i
$650$	2.66739e6	+	5.84076e6i	0.247630	+	0.542233i
$651$	−1.57837e6	−	1.82154e6i	−0.145968	−	0.168456i
$652$	2.33602e6	+	1.62474e7i	0.215207	+	1.49680i
$653$	6.95744e6	+	2.04289e6i	0.638508	+	0.187483i	0.584934	−	0.811081i	$-0.301120\pi$
$653$	6.95744e6	+	2.04289e6i	0.638508	+	0.187483i	0.0535741	+	0.998564i	$0.482939\pi$
$654$	2.86153e6	−	3.30238e6i	0.261610	−	0.301913i
$655$	2.45405e7	+	1.57712e7i	2.23501	+	1.43635i
$656$	889649.	+	571743.i	0.0807159	+	0.0518730i
$657$	1.40165e6	−	1.61759e6i	0.126685	−	0.146202i
$658$	−4.70207e6	−	1.38065e6i	−0.423374	−	0.124314i
$659$	572183.	+	3.97962e6i	0.0513241	+	0.356967i	0.999259	+	0.0385014i	$0.0122584\pi$
$659$	572183.	+	3.97962e6i	0.0513241	+	0.356967i	−0.947934	+	0.318465i	$0.896833\pi$
$660$	1.97362e7	+	2.27768e7i	1.76362	+	2.03532i
$661$	−2.71814e6	−	5.95189e6i	−0.241973	−	0.529848i	0.749212	−	0.662330i	$-0.230432\pi$
$661$	−2.71814e6	−	5.95189e6i	−0.241973	−	0.529848i	−0.991185	+	0.132482i	$0.957705\pi$
$662$	1.61767e7	−	4.74991e6i	1.43465	−	0.421250i
$663$	−218915.	+	479357.i	−0.0193415	+	0.0423521i
$664$	−2.02050e6	+	1.40529e7i	−0.177844	+	1.23693i
$665$	5.25226e6	−	3.37542e6i	0.460566	−	0.295988i
$666$	−9.12042e6			−0.796763
$667$	4.87647e6	+	1.11688e7i	0.424415	+	0.972057i
$668$	−3.63425e6			−0.315118
$669$	1.71968e6	−	1.10517e6i	0.148554	−	0.0954697i
$670$	−1.60292e6	+	1.11486e7i	−0.137951	+	0.959472i
$671$	−1.62727e7	+	3.56323e7i	−1.39526	+	3.05519i
$672$	2.76000e6	−	810408.i	0.235768	−	0.0692278i
$673$	−2.95020e6	−	6.46004e6i	−0.251081	−	0.549791i	0.741560	−	0.670887i	$-0.234086\pi$
$673$	−2.95020e6	−	6.46004e6i	−0.251081	−	0.549791i	−0.992641	+	0.121096i	$0.961359\pi$
$674$	2.78933e6	+	3.21906e6i	0.236511	+	0.272948i
$675$	−565436.	−	3.93269e6i	−0.0477666	−	0.332224i
$676$	1.71503e7	+	5.03577e6i	1.44346	+	0.423838i
$677$	1.34650e7	−	1.55394e7i	1.12910	−	1.30305i	0.181577	−	0.983377i	$-0.441880\pi$
$677$	1.34650e7	−	1.55394e7i	1.12910	−	1.30305i	0.947526	−	0.319678i	$-0.103575\pi$
$678$	−1.59832e7	−	1.02718e7i	−1.33533	−	0.858166i
$679$	2.79404e6	+	1.79562e6i	0.232572	+	0.149465i
$680$	4.57791e6	−	5.28318e6i	0.379660	−	0.438151i
$681$	8.65455e6	+	2.54120e6i	0.715116	+	0.209977i
$682$	4.82417e6	+	3.35529e7i	0.397157	+	2.76229i
$683$	6.05058e6	+	6.98275e6i	0.496301	+	0.572762i	0.947538	−	0.319642i	$-0.103563\pi$
$683$	6.05058e6	+	6.98275e6i	0.496301	+	0.572762i	−0.451237	+	0.892404i	$0.649017\pi$
$684$	−2.22418e6	−	4.87028e6i	−0.181773	−	0.398028i
$685$	3.78772e7	−	1.11217e7i	3.08426	−	0.905621i
$686$	−6.00763e6	+	1.31549e7i	−0.487408	+	1.06727i
$687$	−925510.	+	6.43706e6i	−0.0748151	+	0.520350i
$688$	1.30524e6	−	838828.i	0.105128	−	0.0675619i
$689$	−850865.			−0.0682830
$690$	1.23265e7	+	1.47159e7i	0.985634	+	1.17670i
$691$	5.46474e6			0.435386			0.217693	−	0.976017i	$-0.430147\pi$
$691$	5.46474e6			0.435386			0.217693	+	0.976017i	$0.430147\pi$
$692$	8.33015e6	−	5.35346e6i	0.661283	−	0.424981i
$693$	−425192.	+	2.95727e6i	−0.0336319	+	0.233915i
$694$	−881083.	+	1.92930e6i	−0.0694414	+	0.152055i
$695$	−3.28664e7	+	9.65044e6i	−2.58101	+	0.757853i
$696$	−3.00476e6	−	6.57950e6i	−0.235118	−	0.514837i
$697$	3.29869e6	+	3.80689e6i	0.257193	+	0.296817i
$698$	−1.44151e6	−	1.00259e7i	−0.111990	−	0.778906i
$699$	−3.50122e6	−	1.02805e6i	−0.271035	−	0.0795832i
$700$	9.25743e6	−	1.06836e7i	0.714077	−	0.824089i
$701$	4.68783e6	+	3.01269e6i	0.360310	+	0.231557i	0.708254	−	0.705958i	$-0.249483\pi$
$701$	4.68783e6	+	3.01269e6i	0.360310	+	0.231557i	−0.347943	+	0.937516i	$0.613120\pi$
$702$	722525.	+	464338.i	0.0553363	+	0.0355625i
$703$	1.06457e7	−	1.22858e7i	0.812432	−	0.937596i
$704$	−3.67311e7	−	1.07852e7i	−2.79320	−	0.820157i
$705$	−1.24468e6	−	8.65693e6i	−0.0943158	−	0.655981i
$706$	−8.94694e6	−	1.03253e7i	−0.675558	−	0.779635i
$707$	−2.01636e6	−	4.41521e6i	−0.151712	−	0.332202i
$708$	4.01652e6	−	1.17936e6i	0.301139	−	0.0884224i
$709$	412451.	−	903141.i	0.0308146	−	0.0674745i	−0.893599	−	0.448866i	$-0.851828\pi$
$709$	412451.	−	903141.i	0.0308146	−	0.0674745i	0.924413	+	0.381392i	$0.124555\pi$
$710$	−1.12007e6	+	7.79026e6i	−0.0833872	+	0.579971i
$711$	2.49273e6	−	1.60198e6i	0.184928	−	0.118846i
$712$	2.11589e6			0.156420
$713$	1.66084e6	+	1.31042e7i	0.122350	+	0.965357i
$714$	1.89642e6			0.139216
$715$	7.24923e6	−	4.65880e6i	0.530306	−	0.340807i
$716$	−3.14544e6	+	2.18771e7i	−0.229298	+	1.59480i
$717$	433303.	−	948802.i	0.0314771	−	0.0689252i
$718$	−860837.	+	252764.i	−0.0623174	+	0.0182981i
$719$	−6.25671e6	−	1.37003e7i	−0.451361	−	0.988342i	−0.989372	−	0.145404i	$-0.953552\pi$
$719$	−6.25671e6	−	1.37003e7i	−0.451361	−	0.988342i	0.538012	−	0.842937i	$-0.319176\pi$
$720$	465310.	+	536996.i	0.0334511	+	0.0386047i
$721$	−322003.	−	2.23958e6i	−0.0230686	−	0.160446i
$722$	−6.60246e6	−	1.93866e6i	−0.471371	−	0.138407i
$723$	−113964.	+	131521.i	−0.00810815	+	0.00935731i
$724$	1.86990e7	+	1.20171e7i	1.32578	+	0.852029i
$725$	2.20246e7	+	1.41544e7i	1.55619	+	1.00010i
$726$	1.88989e7	−	2.18105e7i	1.33075	−	1.53576i
$727$	−1.05919e7	−	3.11007e6i	−0.743256	−	0.218240i	−0.111885	−	0.993721i	$-0.535689\pi$
$727$	−1.05919e7	−	3.11007e6i	−0.743256	−	0.218240i	−0.631370	+	0.775482i	$0.717507\pi$
$728$	158923.	+	1.10533e6i	0.0111137	+	0.0772974i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	9.22877e6	+	2.02082e7i	0.640968	+	1.40352i
$731$	7.09099e6	−	2.08210e6i	0.490810	−	0.144115i
$732$	1.02989e7	−	2.25514e7i	0.710414	−	1.55559i
$733$	159274.	−	1.10778e6i	0.0109493	−	0.0761539i	−0.983614	−	0.180286i	$-0.942298\pi$
$733$	159274.	−	1.10778e6i	0.0109493	−	0.0761539i	0.994563	+	0.104133i	$0.0332066\pi$
$734$	−3.62142e7	+	2.32734e7i	−2.48107	+	1.59448i
$735$	−1.18023e7			−0.805840
$736$	−1.50494e7	−	4.69379e6i	−1.02406	−	0.319396i
$737$	9.60703e6			0.651509
$738$	6.90641e6	−	4.43848e6i	0.466779	−	0.299981i
$739$	2.34000e6	−	1.62750e7i	0.157617	−	1.09625i	−0.745390	−	0.666629i	$-0.767737\pi$
$739$	2.34000e6	−	1.62750e7i	0.157617	−	1.09625i	0.903008	−	0.429625i	$-0.141354\pi$
$740$	2.40583e7	−	5.26803e7i	1.61505	−	3.53646i
$741$	−1.46886e6	+	431295.i	−0.0982729	+	0.0288555i
$742$	1.27199e6	+	2.78527e6i	0.0848153	+	0.185720i
$743$	−4.94786e6	−	5.71013e6i	−0.328810	−	0.379467i	0.567140	−	0.823621i	$-0.308050\pi$
$743$	−4.94786e6	−	5.71013e6i	−0.328810	−	0.379467i	−0.895950	+	0.444154i	$0.853504\pi$
$744$	−1.11572e6	−	7.75999e6i	−0.0738962	−	0.513959i
$745$	−4.34807e7	−	1.27671e7i	−2.87016	−	0.842754i
$746$	5.02420e6	−	5.79824e6i	0.330537	−	0.381460i
$747$	−5.78245e6	−	3.71615e6i	−0.379149	−	0.243664i
$748$	−1.37268e7	−	8.82167e6i	−0.897046	−	0.576496i
$749$	5.97650e6	−	6.89725e6i	0.389262	−	0.449232i
$750$	1.68805e7	+	4.95657e6i	1.09580	+	0.321757i
$751$	−3.63405e6	−	2.52753e7i	−0.235121	−	1.63530i	−0.675409	−	0.737443i	$-0.736033\pi$
$751$	−3.63405e6	−	2.52753e7i	−0.235121	−	1.63530i	0.440289	−	0.897856i	$-0.354876\pi$
$752$	651001.	+	751295.i	0.0419795	+	0.0484469i
$753$	−6.30942e6	−	1.38157e7i	−0.405510	−	0.887944i
$754$	−5.43020e6	+	1.59445e6i	−0.347846	+	0.102137i
$755$	−1.39596e7	+	3.05673e7i	−0.891265	+	1.95160i
$756$	269100.	−	1.87163e6i	0.0171241	−	0.119101i
$757$	−1.88601e7	+	1.21206e7i	−1.19620	+	0.768751i	−0.978295	−	0.207219i	$-0.933559\pi$
$757$	−1.88601e7	+	1.21206e7i	−1.19620	+	0.768751i	−0.217905	+	0.975970i	$0.569922\pi$
$758$	7.45452e6			0.471245
$759$	1.09280e7	−	1.21933e7i	0.688551	−	0.768272i
$760$	2.03078e7			1.27535
$761$	−1.33890e7	+	8.60461e6i	−0.838084	+	0.538604i	−0.887837	−	0.460158i	$-0.847793\pi$
$761$	−1.33890e7	+	8.60461e6i	−0.838084	+	0.538604i	0.0497535	+	0.998762i	$0.484156\pi$
$762$	−1.39776e6	+	9.72166e6i	−0.0872060	+	0.606531i
$763$	−1.14266e6	+	2.50208e6i	−0.0710570	+	0.155593i
$764$	1.07096e7	−	3.14463e6i	0.663806	−	0.194911i
$765$	1.40597e6	+	3.07864e6i	0.0868605	+	0.190198i
$766$	2.86375e7	+	3.30494e7i	1.76345	+	2.03513i
$767$	−170337.	−	1.18472e6i	−0.0104549	−	0.0727154i
$768$	7.65736e6	+	2.24841e6i	0.468464	+	0.137553i
$769$	1.00924e6	−	1.16473e6i	0.0615432	−	0.0710247i	−0.724143	−	0.689650i	$-0.757765\pi$
$769$	1.00924e6	−	1.16473e6i	0.0615432	−	0.0710247i	0.785686	+	0.618625i	$0.212310\pi$
$770$	−2.60875e7	−	1.67654e7i	−1.58565	−	1.01903i
$771$	−941523.	−	605080.i	−0.0570421	−	0.0366587i
$772$	−1.88243e7	+	2.17244e7i	−1.13678	+	1.31191i
$773$	−4.62340e6	−	1.35755e6i	−0.278300	−	0.0817162i	0.139604	−	0.990207i	$-0.455417\pi$
$773$	−4.62340e6	−	1.35755e6i	−0.278300	−	0.0817162i	−0.417904	+	0.908491i	$0.637235\pi$
$774$	−1.71415e6	−	1.19222e7i	−0.102848	−	0.715323i
$775$	1.85826e7	+	2.14455e7i	1.11136	+	1.28257i
$776$	4.48777e6	+	9.82684e6i	0.267532	+	0.585814i
$777$	5.50863e6	−	1.61748e6i	0.327334	−	0.0961139i
$778$	7.86403e6	−	1.72198e7i	0.465797	−	1.01995i
$779$	−2.08251e6	+	1.44842e7i	−0.122954	+	0.855166i
$780$	−4.58797e6	+	2.94851e6i	−0.270013	+	0.173527i
$781$	6.71308e6			0.393817
$782$	−8.64800e6	−	5.76443e6i	−0.505707	−	0.337085i
$783$	3.50189e6			0.204126
$784$	1.12855e6	−	725273.i	0.0655737	−	0.0421416i
$785$	−2.73151e6	+	1.89981e7i	−0.158208	+	1.10036i
$786$	−1.06929e7	+	2.34143e7i	−0.617364	+	1.35184i
$787$	−1.84364e7	+	5.41342e6i	−1.06106	+	0.311555i	−0.765277	−	0.643701i	$-0.777398\pi$
$787$	−1.84364e7	+	5.41342e6i	−1.06106	+	0.311555i	−0.295782	+	0.955256i	$0.595580\pi$
$788$	−7.94904e6	−	1.74060e7i	−0.456036	−	0.998579i
$789$	112564.	+	129906.i	0.00643738	+	0.00742913i
$790$	4.37694e6	+	3.04423e7i	0.249519	+	1.73544i
$791$	1.14753e7	+	3.36946e6i	0.652115	+	0.191478i
$792$	−6.36394e6	+	7.34438e6i	−0.360507	+	0.416047i
$793$	−5.96325e6	−	3.83235e6i	−0.336744	−	0.216412i
$794$	−1.26713e7	−	8.14338e6i	−0.713299	−	0.458409i
$795$	−3.57858e6	+	4.12990e6i	−0.200813	+	0.231751i
$796$	−1.85451e7	−	5.44534e6i	−1.03740	−	0.304609i
$797$	−1.93257e6	−	1.34413e7i	−0.107768	−	0.749542i	−0.970013	−	0.243051i	$-0.921852\pi$
$797$	−1.93257e6	−	1.34413e7i	−0.107768	−	0.749542i	0.862246	−	0.506490i	$-0.169057\pi$
$798$	3.60768e6	+	4.16348e6i	0.200549	+	0.231446i
$799$	1.96705e6	+	4.30724e6i	0.109006	+	0.238689i
$800$	−3.24942e7	+	9.54115e6i	−1.79507	+	0.527079i
$801$	−425550.	+	931825.i	−0.0234352	+	0.0513160i
$802$	5.03057e6	−	3.49884e7i	0.276173	−	1.92083i
$803$	1.59410e7	−	1.02446e7i	0.872421	−	0.560671i
$804$	−6.08020e6			−0.331725
$805$	−1.00549e7	−	6.70219e6i	−0.546873	−	0.364525i
$806$	−6.13410e6			−0.332593
$807$	−1.52814e6	+	982073.i	−0.0825996	+	0.0530835i
$808$	2.24687e6	−	1.56274e7i	0.121074	−	0.842087i
$809$	−1.20309e7	+	2.63440e7i	−0.646288	+	1.41517i	0.248478	+	0.968638i	$0.420070\pi$
$809$	−1.20309e7	+	2.63440e7i	−0.646288	+	1.41517i	−0.894766	+	0.446536i	$0.852658\pi$
$810$	5.29259e6	−	1.55405e6i	0.283437	−	0.0832245i
$811$	−6.64514e6	−	1.45508e7i	−0.354774	−	0.776847i	−0.999918	−	0.0127861i	$-0.995930\pi$
$811$	−6.64514e6	−	1.45508e7i	−0.354774	−	0.776847i	0.645144	−	0.764061i	$-0.276797\pi$
$812$	8.15944e6	+	9.41649e6i	0.434280	+	0.501186i
$813$	−1.48837e6	−	1.03518e7i	−0.0789740	−	0.549276i
$814$	−7.74738e7	−	2.27484e7i	−4.09821	−	1.20334i
$815$	1.97390e7	−	2.27800e7i	1.04095	−	1.20132i
$816$	−323628.	−	207983.i	−0.0170146	−	0.0109346i
$817$	1.80608e7	+	1.16070e7i	0.946632	+	0.608363i
$818$	8.63529e6	−	9.96565e6i	0.451225	−	0.520742i
$819$	−518746.	−	152317.i	−0.0270237	−	0.00793487i
$820$	7.41897e6	+	5.16001e7i	0.385309	+	2.67988i
$821$	789833.	+	911516.i	0.0408957	+	0.0471961i	0.775829	−	0.630943i	$-0.217332\pi$
$821$	789833.	+	911516.i	0.0408957	+	0.0471961i	−0.734933	+	0.678139i	$0.762787\pi$
$822$	1.44703e7	+	3.16855e7i	0.746961	+	1.63562i
$823$	9.38033e6	−	2.75431e6i	0.482746	−	0.141747i	−0.0312994	−	0.999510i	$-0.509965\pi$
$823$	9.38033e6	−	2.75431e6i	0.482746	−	0.141747i	0.514045	+	0.857763i	$0.328146\pi$
$824$	3.05728e6	−	6.69450e6i	0.156862	−	0.343479i
$825$	5.00590e6	−	3.48168e7i	0.256063	−	1.78096i
$826$	−3.62348e6	+	2.32867e6i	−0.184789	+	0.118757i
$827$	5.46121e6			0.277668			0.138834	−	0.990316i	$-0.455665\pi$
$827$	5.46121e6			0.277668			0.138834	+	0.990316i	$0.455665\pi$
$828$	−6.91622e6	+	7.71700e6i	−0.350585	+	0.391176i
$829$	1.05831e7			0.534843			0.267421	−	0.963580i	$-0.413828\pi$
$829$	1.05831e7			0.534843			0.267421	+	0.963580i	$0.413828\pi$
$830$	6.00182e7	−	3.85714e7i	3.02404	−	1.94343i
$831$	−1.26575e6	+	8.80351e6i	−0.0635838	+	0.442235i
$832$	2.87774e6	−	6.30138e6i	0.144127	−	0.315593i
$833$	6.13106e6	−	1.80024e6i	0.306142	−	0.0898914i
$834$	−1.25560e7	−	2.74938e7i	−0.625081	−	1.36874i
$835$	4.37033e6	+	5.04363e6i	0.216919	+	0.250338i
$836$	−6.74585e6	−	4.69184e7i	−0.333826	−	2.32181i
$837$	3.64185e6	+	1.06934e6i	0.179684	+	0.0527598i
$838$	−3.05875e7	+	3.52999e7i	−1.50465	+	1.73645i
$839$	8.71268e6	+	5.59930e6i	0.427314	+	0.274618i	0.736571	−	0.676361i	$-0.236444\pi$
$839$	8.71268e6	+	5.59930e6i	0.427314	+	0.274618i	−0.309257	+	0.950979i	$0.600080\pi$
$840$	6.03343e6	+	3.87745e6i	0.295030	+	0.189604i
$841$	−1.67929e6	+	1.93800e6i	−0.0818721	+	0.0944854i
$842$	−3.11838e7	−	9.15640e6i	−1.51583	−	0.445087i
$843$	−2.09172e6	−	1.45483e7i	−0.101376	−	0.705086i
$844$	−2.33556e7	−	2.69538e7i	−1.12859	−	1.30246i
$845$	−1.36352e7	−	2.98569e7i	−0.656931	−	1.43848i
$846$	7.40471e6	−	2.17422e6i	0.355699	−	0.104443i
$847$	−7.54669e6	+	1.65250e7i	−0.361450	+	0.791465i
$848$	88396.9	−	614814.i	0.00422131	−	0.0293599i
$849$	1.78962e6	−	1.15012e6i	0.0852103	−	0.0547613i
$850$	−2.23270e7			−1.05995
$851$	−3.00369e7	−	9.36825e6i	−1.42177	−	0.443440i
$852$	−4.24864e6			−0.200517
$853$	−2.35161e7	+	1.51129e7i	−1.10661	+	0.711172i	−0.960551	−	0.278104i	$-0.910294\pi$
$853$	−2.35161e7	+	1.51129e7i	−1.10661	+	0.711172i	−0.146055	+	0.989277i	$0.546658\pi$
$854$	−3.63034e6	+	2.52496e7i	−0.170335	+	1.18470i
$855$	−4.08433e6	+	8.94343e6i	−0.191076	+	0.418397i
$856$	2.84828e7	−	8.36330e6i	1.32861	−	0.390116i
$857$	1.66090e7	+	3.63686e7i	0.772487	+	1.69151i	0.721100	+	0.692831i	$0.243637\pi$
$857$	1.66090e7	+	3.63686e7i	0.772487	+	1.69151i	0.0513869	+	0.998679i	$0.483636\pi$
$858$	4.97936e6	+	5.74648e6i	0.230916	+	0.266492i
$859$	3.33834e6	+	2.32187e7i	0.154365	+	1.07363i	0.908793	+	0.417247i	$0.137005\pi$
$859$	3.33834e6	+	2.32187e7i	0.154365	+	1.07363i	−0.754429	+	0.656382i	$0.772086\pi$
$860$	7.33850e7	+	2.15478e7i	3.38346	+	0.993474i
$861$	−3.38424e6	+	3.90562e6i	−0.155580	+	0.179549i
$862$	3.77525e7	+	2.42620e7i	1.73052	+	1.11214i
$863$	1.64276e7	+	1.05574e7i	0.750841	+	0.482536i	0.859241	−	0.511571i	$-0.170936\pi$
$863$	1.64276e7	+	1.05574e7i	0.750841	+	0.482536i	−0.108400	+	0.994107i	$0.534573\pi$
$864$	−2.96643e6	+	3.42345e6i	−0.135192	+	0.156020i
$865$	−1.74469e7	−	5.12287e6i	−0.792826	−	0.232795i
$866$	4.42294e6	+	3.07622e7i	0.200409	+	1.39387i
$867$	7.16831e6	+	8.27267e6i	0.323869	+	0.373764i
$868$	5.61010e6	+	1.22844e7i	0.252738	+	0.553420i
$869$	2.51703e7	−	7.39067e6i	1.13068	−	0.331997i
$870$	−1.50993e7	+	3.30629e7i	−0.676330	+	1.48096i
$871$	−247410.	+	1.72078e6i	−0.0110503	+	0.0768562i
$872$	−7.52672e6	+	4.83713e6i	−0.335208	+	0.215425i
$873$	−5.23027e6			−0.232268
$874$	−3.79616e6	−	2.99522e7i	−0.168099	−	1.32633i
$875$	−1.10747e7			−0.489002
$876$	−1.00889e7	+	6.48374e6i	−0.444205	+	0.285473i
$877$	2.67302e6	−	1.85913e7i	0.117355	−	0.816225i	−0.843093	−	0.537768i	$-0.819268\pi$
$877$	2.67302e6	−	1.85913e7i	0.117355	−	0.816225i	0.960449	−	0.278458i	$-0.0898231\pi$
$878$	−1.66345e7	+	3.64245e7i	−0.728238	+	1.59462i
$879$	1.14002e7	−	3.34739e6i	0.497667	−	0.146128i
$880$	2.61321e6	+	5.72212e6i	0.113754	+	0.249087i
$881$	−6.64130e6	−	7.66446e6i	−0.288279	−	0.332692i	0.593076	−	0.805147i	$-0.297913\pi$
$881$	−6.64130e6	−	7.66446e6i	−0.288279	−	0.332692i	−0.881355	+	0.472455i	$0.843368\pi$
$882$	−1.48210e6	−	1.03082e7i	−0.0641513	−	0.446182i
$883$	2.78593e6	+	818022.i	0.120245	+	0.0353072i	0.341302	−	0.939954i	$-0.389132\pi$
$883$	2.78593e6	+	818022.i	0.120245	+	0.0353072i	−0.221056	+	0.975261i	$0.570950\pi$
$884$	1.93361e6	−	2.23151e6i	0.0832220	−	0.0960433i
$885$	−6.46674e6	−	4.15592e6i	−0.277541	−	0.178365i
$886$	4.41054e7	+	2.83448e7i	1.88759	+	1.21308i
$887$	−1.27501e6	+	1.47144e6i	−0.0544132	+	0.0627962i	−0.782304	−	0.622897i	$-0.785955\pi$
$887$	−1.27501e6	+	1.47144e6i	−0.0544132	+	0.0627962i	0.727890	+	0.685693i	$0.240501\pi$
$888$	1.79179e7	+	5.26116e6i	0.762525	+	0.223897i
$889$	−879874.	−	6.11966e6i	−0.0373393	−	0.259700i
$890$	−6.96288e6	−	8.03560e6i	−0.294655	−	0.340050i
$891$	−1.95450e6	−	4.27976e6i	−0.0824786	−	0.180603i
$892$	−1.09898e7	+	3.22690e6i	−0.462465	+	0.135792i
$893$	−5.71426e6	+	1.25125e7i	−0.239790	+	0.525067i
$894$	5.69068e6	−	3.95795e7i	0.238133	−	1.65625i
$895$	3.41436e7	−	2.19428e7i	1.42479	−	0.915659i
$896$	−1.47018e7			−0.611786
$897$	1.90258e6	+	2.27139e6i	0.0789518	+	0.0942565i
$898$	4.12004e6			0.170494
$899$	−2.10404e7	+	1.35219e7i	−0.868272	+	0.558005i
$900$	−3.16818e6	+	2.20352e7i	−0.130378	+	0.906799i
$901$	1.22905e6	−	2.69125e6i	0.0504380	−	0.110444i
$902$	6.97374e7	−	2.04767e7i	2.85397	−	0.838001i
$903$	3.14968e6	+	6.89684e6i	0.128543	+	0.281469i
$904$	2.54751e7	+	2.93998e7i	1.03680	+	1.19653i
$905$	−5.80888e6	−	4.04017e7i	−0.235760	−	1.63975i
$906$	−2.84507e7	−	8.35388e6i	−1.15152	−	0.338118i
$907$	1.47566e7	−	1.70300e7i	0.595617	−	0.687378i	−0.375271	−	0.926915i	$-0.622450\pi$
$907$	1.47566e7	−	1.70300e7i	0.595617	−	0.687378i	0.970887	+	0.239537i	$0.0769957\pi$
$908$	−4.25164e7	−	2.73236e7i	−1.71136	−	1.09983i
$909$	6.43030e6	+	4.13251e6i	0.258120	+	0.165884i
$910$	3.67480e6	−	4.24094e6i	0.147106	−	0.169769i
$911$	5.35790e6	+	1.57322e6i	0.213894	+	0.0628049i	0.386924	−	0.922112i	$-0.373538\pi$
$911$	5.35790e6	+	1.57322e6i	0.213894	+	0.0628049i	−0.173030	+	0.984917i	$0.555356\pi$
$912$	−159043.	−	1.10617e6i	−0.00633180	−	0.0440386i
$913$	−3.98503e7	−	4.59897e7i	−1.58218	−	1.82593i
$914$	−1.76929e7	−	3.87420e7i	−0.700540	−	1.53397i
$915$	−4.36817e7	+	1.28261e7i	−1.72483	+	0.506456i
$916$	1.51370e7	−	3.31454e7i	0.596076	−	1.30522i
$917$	2.30596e6	−	1.60383e7i	0.0905584	−	0.629848i
$918$	−2.51235e6	+	1.61459e6i	−0.0983951	+	0.0632347i
$919$	1.42454e7			0.556400			0.278200	−	0.960523i	$-0.410262\pi$
$919$	1.42454e7			0.556400			0.278200	+	0.960523i	$0.410262\pi$
$920$	−1.57275e7	−	3.60213e7i	−0.612617	−	1.40310i
$921$	9.33978e6			0.362817
$922$	−1.42568e7	+	9.16231e6i	−0.552326	+	0.354959i
$923$	−172882.	+	1.20242e6i	−0.00667953	+	0.0464571i
$924$	6.95414e6	−	1.52275e7i	0.267956	−	0.586742i
$925$	−6.48546e7	+	1.90430e7i	−2.49222	+	0.731782i
$926$	2.70288e7	+	5.91848e7i	1.03585	+	2.26821i
$927$	2.33334e6	+	2.69281e6i	0.0891822	+	0.102922i
$928$	−4.24799e6	−	2.95454e7i	−0.161925	−	1.12621i
$929$	4.38680e7	+	1.28808e7i	1.66766	+	0.489670i	0.973220	−	0.229876i	$-0.0738321\pi$
$929$	4.38680e7	+	1.28808e7i	1.66766	+	0.489670i	0.694444	+	0.719547i	$0.255650\pi$
$930$	−2.57989e7	+	2.97735e7i	−0.978123	+	1.12881i
$931$	1.56158e7	+	1.00357e7i	0.590460	+	0.379466i
$932$	1.72001e7	+	1.10538e7i	0.648622	+	0.416844i
$933$	−1.44360e7	+	1.66600e7i	−0.542927	+	0.626572i
$934$	6.44450e7	+	1.89228e7i	2.41725	+	0.709769i
$935$	4.26425e6	+	2.96585e7i	0.159519	+	1.10948i
$936$	−1.15161e6	−	1.32903e6i	−0.0429650	−	0.0495843i
$937$	−4.10862e6	−	8.99662e6i	−0.152879	−	0.334758i	0.817661	−	0.575701i	$-0.195271\pi$
$937$	−4.10862e6	−	8.99662e6i	−0.152879	−	0.334758i	−0.970539	+	0.240943i	$0.922543\pi$
$938$	6.00275e6	−	1.76257e6i	0.222763	−	0.0654092i
$939$	8.53211e6	−	1.86827e7i	0.315786	−	0.691475i
$940$	−6.97404e6	+	4.85055e7i	−0.257433	+	1.79049i
$941$	−2.28850e7	+	1.47073e7i	−0.842512	+	0.541450i	−0.889231	−	0.457458i	$-0.848760\pi$
$941$	−2.28850e7	+	1.47073e7i	−0.842512	+	0.541450i	0.0467187	+	0.998908i	$0.485124\pi$
$942$	−1.69361e7			−0.621849
$943$	2.73044e7	−	7.52346e6i	0.999894	−	0.275510i
$944$	873744.			0.0319120
$945$	−2.92106e6	+	1.87725e6i	−0.106405	+	0.0683822i
$946$	1.51756e7	−	1.05549e8i	0.551339	−	3.83464i
$947$	1.30039e6	−	2.84745e6i	0.0471192	−	0.103177i	−0.884608	−	0.466335i	$-0.845574\pi$
$947$	1.30039e6	−	2.84745e6i	0.0471192	−	0.103177i	0.931728	+	0.363158i	$0.118301\pi$
$948$	−1.59301e7	+	4.67749e6i	−0.575701	+	0.169041i
$949$	1.42445e6	+	3.11912e6i	0.0513432	+	0.112426i
$950$	−4.24741e7	−	4.90178e7i	−1.52692	−	1.76216i
$951$	3.47055e6	+	2.41382e7i	0.124436	+	0.865474i
$952$	−3.72568e6	−	1.09396e6i	−0.133233	−	0.0391209i
$953$	−2.95154e7	+	3.40626e7i	−1.05273	+	1.21491i	−0.0767483	+	0.997051i	$0.524454\pi$
$953$	−2.95154e7	+	3.40626e7i	−1.05273	+	1.21491i	−0.975980	+	0.217862i	$0.930092\pi$
$954$	−4.05646e6	−	2.60693e6i	−0.144303	−	0.0927382i
$955$	−1.72429e7	−	1.10813e7i	−0.611789	−	0.393173i
$956$	−3.82724e6	+	4.41687e6i	−0.135438	+	0.156304i
$957$	2.97470e7	+	8.73451e6i	1.04994	+	0.308289i
$958$	−1.07114e6	−	7.44997e6i	−0.0377080	−	0.262265i
$959$	−1.43592e7	−	1.65714e7i	−0.504179	−	0.581853i
$960$	−1.84822e7	−	4.04703e7i	−0.647255	−	1.41729i
$961$	1.45907e6	−	428423.i	0.0509646	−	0.0149646i
$962$	6.06979e6	−	1.32910e7i	0.211464	−	0.463041i
$963$	−2.04535e6	+	1.42257e7i	−0.0710724	+	0.494320i
$964$	820300.	−	527175.i	0.0284302	−	0.0182710i
$965$	5.27862e7			1.82475
$966$	4.59107e6	−	9.62362e6i	0.158297	−	0.331815i
$967$	3.23134e7			1.11126			0.555631	−	0.831429i	$-0.312477\pi$
$967$	3.23134e7			1.11126			0.555631	+	0.831429i	$0.312477\pi$
$968$	−4.97101e7	+	3.19467e7i	−1.70512	+	1.09582i
$969$	757556.	−	5.26892e6i	0.0259182	−	0.180265i
$970$	2.25516e7	−	4.93812e7i	0.769571	−	1.68513i
$971$	−4.33532e7	+	1.27296e7i	−1.47561	+	0.433280i	−0.917920	−	0.396766i	$-0.870132\pi$
$971$	−4.33532e7	+	1.27296e7i	−1.47561	+	0.433280i	−0.557695	+	0.830046i	$0.688314\pi$
$972$	1.23698e6	+	2.70862e6i	0.0419951	+	0.0919564i
$973$	1.24596e7	+	1.43792e7i	0.421913	+	0.486914i
$974$	7.53376e6	+	5.23984e7i	0.254457	+	1.76979i
$975$	6.10733e6	+	1.79327e6i	0.205750	+	0.0604137i
$976$	3.38869e6	−	3.91076e6i	0.113869	−	0.131412i
$977$	6.24900e6	+	4.01599e6i	0.209447	+	0.134603i	0.641159	−	0.767408i	$-0.278454\pi$
$977$	6.24900e6	+	4.01599e6i	0.209447	+	0.134603i	−0.431712	+	0.902011i	$0.642090\pi$
$978$	2.23750e7	+	1.43795e7i	0.748024	+	0.480726i
$979$	−5.93903e6	+	6.85401e6i	−0.198043	+	0.228554i
$980$	6.34507e7	+	1.86308e7i	2.11043	+	0.619678i
$981$	−616460.	−	4.28757e6i	−0.0204518	−	0.142246i
$982$	−6.69818e6	−	7.73011e6i	−0.221655	−	0.255804i
$983$	−1.65075e7	−	3.61463e7i	−0.544874	−	1.19311i	−0.959135	−	0.282950i	$-0.908687\pi$
$983$	−1.65075e7	−	3.61463e7i	−0.544874	−	1.19311i	0.414260	−	0.910158i	$-0.364040\pi$
$984$	−1.61286e7	+	4.73579e6i	−0.531018	+	0.155921i
$985$	−1.45970e7	+	3.19631e7i	−0.479374	+	1.04968i
$986$	2.80060e6	−	1.94786e7i	0.0917401	−	0.638066i
$987$	−4.08677e6	+	2.62641e6i	−0.133533	+	0.0858162i
$988$	8.57757e6			0.279558
$989$	6.60081e6	−	4.10247e7i	0.214588	−	1.33369i
$990$	4.88343e7			1.58357
$991$	−1.64665e7	+	1.05823e7i	−0.532618	+	0.342293i	−0.779146	−	0.626843i	$-0.784347\pi$
$991$	−1.64665e7	+	1.05823e7i	−0.532618	+	0.342293i	0.246528	+	0.969136i	$0.420710\pi$
$992$	4.60427e6	−	3.20234e7i	0.148553	−	1.03321i
$993$	6.94282e6	−	1.52027e7i	0.223441	−	0.489268i
$994$	4.19453e6	−	1.23162e6i	0.134653	−	0.0395378i
$995$	1.47442e7	+	3.22852e7i	0.472131	+	1.03382i
$996$	2.52209e7	+	2.91065e7i	0.805587	+	0.929697i
$997$	−894262.	−	6.21973e6i	−0.0284923	−	0.198168i	0.970604	−	0.240684i	$-0.0773717\pi$
$997$	−894262.	−	6.21973e6i	−0.0284923	−	0.198168i	−0.999096	+	0.0425160i	$0.986463\pi$
$998$	6.73216e7	+	1.97674e7i	2.13958	+	0.628237i
$999$	−5.92065e6	+	6.83280e6i	−0.187696	+	0.216613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.b.58.2	yes	100
23.2	even	11	inner	69.6.e.b.25.2	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.b.25.2	✓	100	23.2	even	11	inner
69.6.e.b.58.2	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)

\(f(q)\)	\(=\)	\(q+(-7.63772 + 4.90846i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(20.9484 - 45.8707i) q^{4} +(-88.8509 + 26.0890i) q^{5} +(-33.9439 - 74.3267i) q^{6} +(33.6833 + 38.8726i) q^{7} +(23.8100 + 165.602i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(-7.63772 + 4.90846i) q^{2} +(-1.28083 + 8.90839i) q^{3} +(20.9484 - 45.8707i) q^{4} +(-88.8509 + 26.0890i) q^{5} +(-33.9439 - 74.3267i) q^{6} +(33.6833 + 38.8726i) q^{7} +(23.8100 + 165.602i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(550.561 - 635.382i) q^{10} +(-603.268 - 387.697i) q^{11} +(381.803 + 245.370i) q^{12} +(84.9788 - 98.0707i) q^{13} +(-448.069 - 131.565i) q^{14} +(-118.608 - 824.934i) q^{15} +(62.0350 + 71.5922i) q^{16} +(187.444 + 410.445i) q^{17} +(705.608 - 207.185i) q^{18} +(-544.522 + 1192.34i) q^{19} +(-664.569 + 4622.18i) q^{20} +(-389.435 + 250.275i) q^{21} +6510.59 q^{22} +(2536.64 + 42.4453i) q^{23} -1505.75 q^{24} +(4584.93 - 2946.56i) q^{25} +(-167.667 + 1166.15i) q^{26} +(302.838 - 663.122i) q^{27} +(2488.73 - 730.757i) q^{28} +(1995.53 + 4369.60i) q^{29} +(4955.05 + 5718.43i) q^{30} +(740.974 + 5153.58i) q^{31} +(-5962.11 - 1750.63i) q^{32} +(4226.44 - 4877.57i) q^{33} +(-3446.30 - 2214.80i) q^{34} +(-4006.94 - 2575.10i) q^{35} +(-2674.88 + 3086.97i) q^{36} +(-11899.7 - 3494.06i) q^{37} +(-1693.64 - 11779.5i) q^{38} +(764.809 + 882.637i) q^{39} +(-6435.93 - 14092.7i) q^{40} +(10711.4 - 3145.15i) q^{41} +(1745.93 - 3823.06i) q^{42} +(2330.91 - 16211.9i) q^{43} +(-30421.4 + 19550.7i) q^{44} +7500.76 q^{45} +(-19582.5 + 12126.8i) q^{46} +10494.1 q^{47} +(-717.228 + 460.935i) q^{48} +(2015.37 - 14017.2i) q^{49} +(-20555.3 + 45009.9i) q^{50} +(-3896.49 + 1144.11i) q^{51} +(-2718.40 - 5952.47i) q^{52} +(-4293.86 - 4955.38i) q^{53} +(941.921 + 6551.20i) q^{54} +(63715.5 + 18708.6i) q^{55} +(-5635.39 + 6503.59i) q^{56} +(-9924.36 - 6378.00i) q^{57} +(-36689.3 - 23578.8i) q^{58} +(6040.11 - 6970.66i) q^{59} +(-40325.0 - 11840.5i) q^{60} +(-7774.01 - 54069.4i) q^{61} +(-30955.5 - 35724.6i) q^{62} +(-1730.75 - 3789.80i) q^{63} +(51221.3 - 15039.9i) q^{64} +(-4991.88 + 10930.7i) q^{65} +(-8338.98 + 57998.9i) q^{66} +(-11270.2 + 7242.94i) q^{67} +22754.0 q^{68} +(-3627.13 + 22543.0i) q^{69} +43243.7 q^{70} +(-7875.27 + 5061.13i) q^{71} +(1928.61 - 13413.8i) q^{72} +(-10977.1 + 24036.5i) q^{73} +(108037. - 31722.5i) q^{74} +(20376.5 + 44618.4i) q^{75} +(43286.4 + 49955.2i) q^{76} +(-5249.28 - 36509.5i) q^{77} +(-10173.8 - 2987.29i) q^{78} +(-23955.9 + 27646.6i) q^{79} +(-7379.64 - 4742.60i) q^{80} +(5519.46 + 3547.14i) q^{81} +(-66372.7 + 76598.2i) q^{82} +(81421.9 + 23907.6i) q^{83} +(3322.22 + 23106.5i) q^{84} +(-27362.6 - 31578.2i) q^{85} +(61772.5 + 135263. i) q^{86} +(-41482.0 + 12180.2i) q^{87} +(49839.6 - 109134. i) q^{88} +(1799.84 - 12518.2i) q^{89} +(-57288.7 + 36817.2i) q^{90} +6674.64 q^{91} +(55085.7 - 115468. i) q^{92} -46859.2 q^{93} +(-80150.9 + 51509.8i) q^{94} +(17274.4 - 120146. i) q^{95} +(23231.8 - 50870.5i) q^{96} +(61955.7 - 18191.8i) q^{97} +(53410.1 + 116952. i) q^{98} +(38038.0 + 43898.2i) 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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