LMFDB - Embedded newform 322.2.i.e.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	322.29
Dual form			322.2.i.e.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.427601 - 0.125555i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.0300272 + 0.0192973i) q^{5} +(0.291841 - 0.336802i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.35668 - 1.51455i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.427601 - 0.125555i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.0300272 + 0.0192973i) q^{5} +(0.291841 - 0.336802i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.35668 - 1.51455i) q^{9} +(-0.00507970 - 0.0353301i) q^{10} +(2.36051 + 5.16879i) q^{11} +(0.185131 + 0.405381i) q^{12} +(0.862757 + 6.00061i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(0.0152626 - 0.00448149i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.549556 + 0.634221i) q^{17} +(2.35668 - 1.51455i) q^{18} +(0.597408 + 0.689446i) q^{19} +(0.0342476 + 0.0100560i) q^{20} +(0.185131 - 0.405381i) q^{21} -5.68229 q^{22} +(-2.15628 - 4.28375i) q^{23} -0.445654 q^{24} +(-2.07655 + 4.54700i) q^{25} +(-5.81675 - 1.70795i) q^{26} +(1.69308 + 1.95392i) q^{27} +(0.841254 - 0.540641i) q^{28} +(-4.70073 + 5.42494i) q^{29} +(-0.00226379 + 0.0157450i) q^{30} +(6.50732 - 1.91072i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.360388 - 2.50656i) q^{33} +(-0.348614 - 0.763358i) q^{34} +(-0.0148276 - 0.0324679i) q^{35} +(0.398680 + 2.77288i) q^{36} +(2.05803 + 1.32262i) q^{37} +(-0.875314 + 0.257015i) q^{38} +(0.384491 - 2.67419i) q^{39} +(-0.0233742 + 0.0269753i) q^{40} +(4.25603 - 2.73519i) q^{41} +(0.291841 + 0.336802i) q^{42} +(-3.47983 - 1.02177i) q^{43} +(2.36051 - 5.16879i) q^{44} +0.0999913 q^{45} +(4.79238 - 0.181884i) q^{46} -8.21030 q^{47} +(0.185131 - 0.405381i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-3.27347 - 3.77779i) q^{50} +(0.314620 - 0.202194i) q^{51} +(3.96997 - 4.58159i) q^{52} +(-0.647498 + 4.50345i) q^{53} +(-2.48068 + 0.728395i) q^{54} +(-0.170623 - 0.109653i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-0.168889 - 0.369816i) q^{57} +(-2.98194 - 6.52954i) q^{58} +(-1.49528 - 10.3999i) q^{59} +(-0.0133817 - 0.00859992i) q^{60} +(13.1470 - 3.86029i) q^{61} +(-0.965186 + 6.71301i) q^{62} +(1.83452 - 2.11715i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.141702 - 0.163533i) q^{65} +(2.42975 + 0.713440i) q^{66} +(3.90092 - 8.54181i) q^{67} +0.839195 q^{68} +(0.384180 + 2.10247i) q^{69} +0.0356934 q^{70} +(2.65590 - 5.81560i) q^{71} +(-2.68792 - 0.789244i) q^{72} +(8.88150 + 10.2498i) q^{73} +(-2.05803 + 1.32262i) q^{74} +(1.45883 - 1.68358i) q^{75} +(0.129829 - 0.902982i) q^{76} +(-5.45211 + 1.60089i) q^{77} +(2.27281 + 1.46064i) q^{78} +(-0.872513 - 6.06846i) q^{79} +(-0.0148276 - 0.0324679i) q^{80} +(3.01258 + 6.59663i) q^{81} +(0.719993 + 5.00766i) q^{82} +(15.1735 + 9.75145i) q^{83} +(-0.427601 + 0.125555i) q^{84} +(0.00426286 - 0.0296488i) q^{85} +(2.37501 - 2.74090i) q^{86} +(2.69117 - 1.72951i) q^{87} +(3.72111 + 4.29439i) q^{88} +(-1.89017 - 0.555003i) q^{89} +(-0.0415379 + 0.0909552i) q^{90} -6.06231 q^{91} +(-1.82538 + 4.43486i) q^{92} -3.02244 q^{93} +(3.41068 - 7.46835i) q^{94} +(-0.0312429 - 0.00917375i) q^{95} +(0.291841 + 0.336802i) q^{96} +(3.42207 - 2.19923i) q^{97} +(0.654861 - 0.755750i) q^{98} +(2.26541 - 15.7563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−0.427601	−	0.125555i	−0.246876	−	0.0724893i	0.155954	−	0.987764i	$-0.450155\pi$
$3$	−0.427601	−	0.125555i	−0.246876	−	0.0724893i	−0.402829	+	0.915275i	$0.631973\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.0300272	+	0.0192973i	−0.0134286	+	0.00863002i	−0.547338	−	0.836912i	$-0.684359\pi$
$5$	−0.0300272	+	0.0192973i	−0.0134286	+	0.00863002i	0.533909	+	0.845542i	$0.320722\pi$
$6$	0.291841	−	0.336802i	0.119144	−	0.137499i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−2.35668	−	1.51455i	−0.785561	−	0.504849i
$10$	−0.00507970	−	0.0353301i	−0.00160634	−	0.0111724i
$11$	2.36051	+	5.16879i	0.711720	+	1.55845i	0.825157	+	0.564904i	$0.191087\pi$
$11$	2.36051	+	5.16879i	0.711720	+	1.55845i	−0.113437	+	0.993545i	$0.536186\pi$
$12$	0.185131	+	0.405381i	0.0534428	+	0.117023i
$13$	0.862757	+	6.00061i	0.239286	+	1.66427i	0.655645	+	0.755069i	$0.272397\pi$
$13$	0.862757	+	6.00061i	0.239286	+	1.66427i	−0.416360	+	0.909200i	$0.636694\pi$
$14$	−0.841254	−	0.540641i	−0.224834	−	0.144492i
$15$	0.0152626	−	0.00448149i	0.00394077	−	0.00115712i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−0.549556	+	0.634221i	−0.133287	+	0.153821i	−0.818469	−	0.574550i	$-0.805177\pi$
$17$	−0.549556	+	0.634221i	−0.133287	+	0.153821i	0.685182	+	0.728371i	$0.259722\pi$
$18$	2.35668	−	1.51455i	0.555475	−	0.356982i
$19$	0.597408	+	0.689446i	0.137055	+	0.158170i	0.820128	−	0.572181i	$-0.193902\pi$
$19$	0.597408	+	0.689446i	0.137055	+	0.158170i	−0.683073	+	0.730350i	$0.739357\pi$
$20$	0.0342476	+	0.0100560i	0.00765799	+	0.00224859i
$21$	0.185131	−	0.405381i	0.0403989	−	0.0884613i
$22$	−5.68229			−1.21147
$23$	−2.15628	−	4.28375i	−0.449614	−	0.893223i
$23$	−2.15628	−	4.28375i	−0.449614	−	0.893223i
$24$	−0.445654			−0.0909686
$25$	−2.07655	+	4.54700i	−0.415309	+	0.909400i
$26$	−5.81675	−	1.70795i	−1.14076	−	0.334957i
$27$	1.69308	+	1.95392i	0.325834	+	0.376033i
$28$	0.841254	−	0.540641i	0.158982	−	0.102172i
$29$	−4.70073	+	5.42494i	−0.872905	+	1.00739i	0.126976	+	0.991906i	$0.459473\pi$
$29$	−4.70073	+	5.42494i	−0.872905	+	1.00739i	−0.999880	+	0.0154797i	$0.995072\pi$
$30$	−0.00226379	+	0.0157450i	−0.000413309	+	0.00287463i
$31$	6.50732	−	1.91072i	1.16875	−	0.343176i	0.360923	−	0.932596i	$-0.382462\pi$
$31$	6.50732	−	1.91072i	1.16875	−	0.343176i	0.807827	+	0.589420i	$0.200644\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−0.360388	−	2.50656i	−0.0627356	−	0.436335i
$34$	−0.348614	−	0.763358i	−0.0597868	−	0.130915i
$35$	−0.0148276	−	0.0324679i	−0.00250632	−	0.00548807i
$36$	0.398680	+	2.77288i	0.0664466	+	0.462146i
$37$	2.05803	+	1.32262i	0.338339	+	0.217437i	0.698766	−	0.715350i	$-0.253733\pi$
$37$	2.05803	+	1.32262i	0.338339	+	0.217437i	−0.360427	+	0.932787i	$0.617369\pi$
$38$	−0.875314	+	0.257015i	−0.141995	+	0.0416934i
$39$	0.384491	−	2.67419i	0.0615678	−	0.428213i
$40$	−0.0233742	+	0.0269753i	−0.00369579	+	0.00426517i
$41$	4.25603	−	2.73519i	0.664681	−	0.427164i	−0.164324	−	0.986406i	$-0.552544\pi$
$41$	4.25603	−	2.73519i	0.664681	−	0.427164i	0.829004	+	0.559242i	$0.188908\pi$
$42$	0.291841	+	0.336802i	0.0450320	+	0.0519697i
$43$	−3.47983	−	1.02177i	−0.530669	−	0.155818i	0.00541160	−	0.999985i	$-0.498277\pi$
$43$	−3.47983	−	1.02177i	−0.530669	−	0.155818i	−0.536080	+	0.844167i	$0.680096\pi$
$44$	2.36051	−	5.16879i	0.355860	−	0.779224i
$45$	0.0999913			0.0149058
$46$	4.79238	−	0.181884i	0.706598	−	0.0268174i
$47$	−8.21030			−1.19760			−0.598798	−	0.800900i	$-0.704355\pi$
$47$	−8.21030			−1.19760			−0.598798	+	0.800900i	$0.704355\pi$
$48$	0.185131	−	0.405381i	0.0267214	−	0.0585117i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−3.27347	−	3.77779i	−0.462938	−	0.534259i
$51$	0.314620	−	0.202194i	0.0440557	−	0.0283129i
$52$	3.96997	−	4.58159i	0.550536	−	0.635352i
$53$	−0.647498	+	4.50345i	−0.0889407	+	0.618596i	0.895785	+	0.444487i	$0.146614\pi$
$53$	−0.647498	+	4.50345i	−0.0889407	+	0.618596i	−0.984726	+	0.174110i	$0.944295\pi$
$54$	−2.48068	+	0.728395i	−0.337578	+	0.0991219i
$55$	−0.170623	−	0.109653i	−0.0230068	−	0.0147856i
$56$	0.142315	+	0.989821i	0.0190176	+	0.132270i
$57$	−0.168889	−	0.369816i	−0.0223699	−	0.0489833i
$58$	−2.98194	−	6.52954i	−0.391548	−	0.857370i
$59$	−1.49528	−	10.3999i	−0.194669	−	1.35395i	−0.819449	−	0.573152i	$-0.805720\pi$
$59$	−1.49528	−	10.3999i	−0.194669	−	1.35395i	0.624780	−	0.780801i	$-0.285189\pi$
$60$	−0.0133817	−	0.00859992i	−0.00172757	−	0.00111024i
$61$	13.1470	−	3.86029i	1.68330	−	0.494260i	0.706370	−	0.707843i	$-0.250331\pi$
$61$	13.1470	−	3.86029i	1.68330	−	0.494260i	0.976925	+	0.213583i	$0.0685133\pi$
$62$	−0.965186	+	6.71301i	−0.122579	+	0.852554i
$63$	1.83452	−	2.11715i	0.231128	−	0.266736i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.141702	−	0.163533i	−0.0175759	−	0.0202837i
$66$	2.42975	+	0.713440i	0.299082	+	0.0878184i
$67$	3.90092	−	8.54181i	0.476573	−	1.04355i	−0.506819	−	0.862053i	$-0.669179\pi$
$67$	3.90092	−	8.54181i	0.476573	−	1.04355i	0.983392	−	0.181496i	$-0.0580940\pi$
$68$	0.839195			0.101767
$69$	0.384180	+	2.10247i	0.0462499	+	0.253107i
$70$	0.0356934			0.00426618
$71$	2.65590	−	5.81560i	0.315197	−	0.690185i	−0.684032	−	0.729452i	$-0.739775\pi$
$71$	2.65590	−	5.81560i	0.315197	−	0.690185i	0.999229	+	0.0392673i	$0.0125024\pi$
$72$	−2.68792	−	0.789244i	−0.316774	−	0.0930132i
$73$	8.88150	+	10.2498i	1.03950	+	1.19965i	0.979499	+	0.201450i	$0.0645654\pi$
$73$	8.88150	+	10.2498i	1.03950	+	1.19965i	0.0600025	+	0.998198i	$0.480889\pi$
$74$	−2.05803	+	1.32262i	−0.239242	+	0.153751i
$75$	1.45883	−	1.68358i	0.168452	−	0.194403i
$76$	0.129829	−	0.902982i	0.0148924	−	0.103579i
$77$	−5.45211	+	1.60089i	−0.621326	+	0.182438i
$78$	2.27281	+	1.46064i	0.257345	+	0.165385i
$79$	−0.872513	−	6.06846i	−0.0981654	−	0.682755i	−0.978172	−	0.207795i	$-0.933371\pi$
$79$	−0.872513	−	6.06846i	−0.0981654	−	0.682755i	0.880007	−	0.474961i	$-0.157538\pi$
$80$	−0.0148276	−	0.0324679i	−0.00165777	−	0.00363002i
$81$	3.01258	+	6.59663i	0.334731	+	0.732959i
$82$	0.719993	+	5.00766i	0.0795099	+	0.553004i
$83$	15.1735	+	9.75145i	1.66551	+	1.07036i	0.909403	+	0.415916i	$0.136539\pi$
$83$	15.1735	+	9.75145i	1.66551	+	1.07036i	0.756110	+	0.654444i	$0.227097\pi$
$84$	−0.427601	+	0.125555i	−0.0466551	+	0.0136992i
$85$	0.00426286	−	0.0296488i	0.000462372	−	0.00321587i
$86$	2.37501	−	2.74090i	0.256104	−	0.295559i
$87$	2.69117	−	1.72951i	0.288524	−	0.185423i
$88$	3.72111	+	4.29439i	0.396671	+	0.457783i
$89$	−1.89017	−	0.555003i	−0.200357	−	0.0588302i	0.180014	−	0.983664i	$-0.442386\pi$
$89$	−1.89017	−	0.555003i	−0.200357	−	0.0588302i	−0.380371	+	0.924834i	$0.624204\pi$
$90$	−0.0415379	+	0.0909552i	−0.00437848	+	0.00958752i
$91$	−6.06231			−0.635503
$92$	−1.82538	+	4.43486i	−0.190309	+	0.462366i
$93$	−3.02244			−0.313413
$94$	3.41068	−	7.46835i	0.351785	−	0.770302i
$95$	−0.0312429	−	0.00917375i	−0.00320546	−	0.000941207i
$96$	0.291841	+	0.336802i	0.0297859	+	0.0343748i
$97$	3.42207	−	2.19923i	0.347459	−	0.223298i	−0.355257	−	0.934769i	$-0.615607\pi$
$97$	3.42207	−	2.19923i	0.347459	−	0.223298i	0.702716	+	0.711470i	$0.251970\pi$
$98$	0.654861	−	0.755750i	0.0661509	−	0.0763422i
$99$	2.26541	−	15.7563i	0.227683	−	1.58357i
$100$	4.79624	−	1.40830i	0.479624	−	0.140830i
$101$	−12.1131	−	7.78462i	−1.20530	−	0.774599i	−0.225434	−	0.974258i	$-0.572380\pi$
$101$	−12.1131	−	7.78462i	−1.20530	−	0.774599i	−0.979865	+	0.199660i	$0.936016\pi$
$102$	0.0532243	+	0.370183i	0.00526999	+	0.0366536i
$103$	−1.78862	−	3.91653i	−0.176238	−	0.385907i	0.800813	−	0.598915i	$-0.204401\pi$
$103$	−1.78862	−	3.91653i	−0.176238	−	0.385907i	−0.977050	+	0.213008i	$0.931674\pi$
$104$	2.51838	+	5.51447i	0.246947	+	0.540739i
$105$	0.00226379	+	0.0157450i	0.000220923	+	0.00153655i
$106$	−3.82750	−	2.45979i	−0.371760	−	0.238916i
$107$	−16.3945	+	4.81387i	−1.58492	+	0.465375i	−0.951299	−	0.308269i	$-0.900250\pi$
$107$	−16.3945	+	4.81387i	−1.58492	+	0.465375i	−0.633621	+	0.773643i	$0.718432\pi$
$108$	0.367942	−	2.55910i	0.0354053	−	0.246249i
$109$	−3.82931	+	4.41926i	−0.366782	+	0.423289i	−0.908900	−	0.417013i	$-0.863077\pi$
$109$	−3.82931	+	4.41926i	−0.366782	+	0.423289i	0.542119	+	0.840302i	$0.317622\pi$
$110$	0.170623	−	0.109653i	0.0162683	−	0.0104550i
$111$	−0.713957	−	0.823950i	−0.0677658	−	0.0782059i
$112$	−0.959493	−	0.281733i	−0.0906636	−	0.0266212i
$113$	2.93178	−	6.41971i	0.275799	−	0.603916i	−0.720152	−	0.693817i	$-0.755928\pi$
$113$	2.93178	−	6.41971i	0.275799	−	0.603916i	0.995951	+	0.0899011i	$0.0286551\pi$
$114$	0.406555			0.0380774
$115$	0.147412	+	0.0870186i	0.0137462	+	0.00811453i
$116$	7.17822			0.666481
$117$	7.05496	−	15.4482i	0.652231	−	1.42819i
$118$	10.0813	+	2.96012i	0.928055	+	0.272502i
$119$	−0.549556	−	0.634221i	−0.0503777	−	0.0581389i
$120$	0.0133817	−	0.00859992i	0.00122158	−	0.000785061i
$121$	−13.9409	+	16.0887i	−1.26736	+	1.46261i
$122$	−1.95000	+	13.5625i	−0.176544	+	1.22789i
$123$	−2.16330	+	0.635203i	−0.195058	+	0.0572743i
$124$	−5.70542	−	3.66665i	−0.512362	−	0.329275i
$125$	−0.0507905	−	0.353256i	−0.00454284	−	0.0315962i
$126$	1.16374	+	2.54824i	0.103674	+	0.227015i
$127$	1.72253	+	3.77181i	0.152850	+	0.334694i	0.970531	−	0.240977i	$-0.0774680\pi$
$127$	1.72253	+	3.77181i	0.152850	+	0.334694i	−0.817681	+	0.575672i	$0.804741\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	1.35969	+	0.873820i	0.119714	+	0.0769356i
$130$	0.207619	−	0.0609626i	0.0182094	−	0.00534677i
$131$	−0.229577	+	1.59674i	−0.0200582	+	0.139508i	−0.997390	−	0.0722069i	$-0.976996\pi$
$131$	−0.229577	+	1.59674i	−0.0200582	+	0.139508i	0.977331	+	0.211715i	$0.0679049\pi$
$132$	−1.65832	+	1.91381i	−0.144339	+	0.166576i
$133$	−0.767448	+	0.493209i	−0.0665462	+	0.0427666i
$134$	6.14941	+	7.09680i	0.531228	+	0.613070i
$135$	−0.0885441	−	0.0259989i	−0.00762066	−	0.00223763i
$136$	−0.348614	+	0.763358i	−0.0298934	+	0.0654574i
$137$	−19.2406			−1.64384			−0.821920	−	0.569603i	$-0.807097\pi$
$137$	−19.2406			−1.64384			−0.821920	+	0.569603i	$0.807097\pi$
$138$	−2.07207	−	0.523934i	−0.176386	−	0.0446002i
$139$	21.6710			1.83811			0.919055	−	0.394129i	$-0.128954\pi$
$139$	21.6710			1.83811			0.919055	+	0.394129i	$0.128954\pi$
$140$	−0.0148276	+	0.0324679i	−0.00125316	+	0.00274404i
$141$	3.51074	+	1.03085i	0.295657	+	0.0868128i
$142$	4.18676	+	4.83178i	0.351345	+	0.405474i
$143$	−28.9793	+	18.6239i	−2.42337	+	1.55741i
$144$	1.83452	−	2.11715i	0.152877	−	0.176429i
$145$	0.0364632	−	0.253607i	0.00302811	−	0.0210609i
$146$	−13.0131	+	3.82098i	−1.07697	+	0.316226i
$147$	0.374908	+	0.240938i	0.0309219	+	0.0198723i
$148$	−0.348158	−	2.42149i	−0.0286184	−	0.199045i
$149$	−7.04840	−	15.4338i	−0.577428	−	1.26439i	−0.942747	−	0.333508i	$-0.891768\pi$
$149$	−7.04840	−	15.4338i	−0.577428	−	1.26439i	0.365320	−	0.930882i	$-0.380960\pi$
$150$	0.925420	+	2.02639i	0.0755602	+	0.165454i
$151$	1.02826	+	7.15169i	0.0836785	+	0.581997i	0.987919	+	0.154973i	$0.0495289\pi$
$151$	1.02826	+	7.15169i	0.0836785	+	0.581997i	−0.904240	+	0.427024i	$0.859562\pi$
$152$	0.767448	+	0.493209i	0.0622483	+	0.0400045i
$153$	2.25569	−	0.662329i	0.182361	−	0.0535461i
$154$	0.808674	−	5.62445i	0.0651648	−	0.453231i
$155$	−0.158525	+	0.182948i	−0.0127330	+	0.0146947i
$156$	−2.27281	+	1.46064i	−0.181970	+	0.116945i
$157$	8.59051	+	9.91398i	0.685597	+	0.791221i	0.986732	−	0.162360i	$-0.0519107\pi$
$157$	8.59051	+	9.91398i	0.685597	+	0.791221i	−0.301134	+	0.953582i	$0.597365\pi$
$158$	5.88252	+	1.72726i	0.467988	+	0.137414i
$159$	0.842302	−	1.84439i	0.0667989	−	0.146269i
$160$	0.0356934			0.00282181
$161$	4.54701	−	1.52469i	0.358355	−	0.120162i
$162$	−7.25198			−0.569769
$163$	7.74164	−	16.9518i	0.606372	−	1.32777i	−0.318656	−	0.947870i	$-0.603231\pi$
$163$	7.74164	−	16.9518i	0.606372	−	1.32777i	0.925028	−	0.379899i	$-0.124041\pi$
$164$	−4.85422	−	1.42533i	−0.379051	−	0.111299i
$165$	0.0591912	+	0.0683103i	0.00460803	+	0.00531795i
$166$	−15.1735	+	9.75145i	−1.17770	+	0.756859i
$167$	−0.150785	+	0.174016i	−0.0116681	+	0.0134657i	−0.761554	−	0.648102i	$-0.775563\pi$
$167$	−0.150785	+	0.174016i	−0.0116681	+	0.0134657i	0.749886	+	0.661568i	$0.230109\pi$
$168$	0.0634231	−	0.441117i	0.00489320	−	0.0340329i
$169$	−22.7895	+	6.69161i	−1.75304	+	0.514739i
$170$	0.0251987	+	0.0161942i	0.00193265	+	0.00124204i
$171$	−0.363703	−	2.52961i	−0.0278130	−	0.193444i
$172$	1.50660	+	3.29900i	0.114877	+	0.251546i
$173$	6.08216	+	13.3181i	0.462418	+	1.01255i	0.986930	+	0.161151i	$0.0515208\pi$
$173$	6.08216	+	13.3181i	0.462418	+	1.01255i	−0.524511	+	0.851403i	$0.675752\pi$
$174$	0.455265	+	3.16644i	0.0345136	+	0.240047i
$175$	−4.20520	−	2.70252i	−0.317883	−	0.204291i
$176$	−5.45211	+	1.60089i	−0.410969	+	0.120671i
$177$	−0.666378	+	4.63476i	−0.0500880	+	0.348370i
$178$	1.29005	−	1.48880i	0.0966934	−	0.111590i
$179$	13.7130	−	8.81280i	1.02496	−	0.658699i	0.0837344	−	0.996488i	$-0.473315\pi$
$179$	13.7130	−	8.81280i	1.02496	−	0.658699i	0.941222	+	0.337789i	$0.109679\pi$
$180$	−0.0654803	−	0.0755683i	−0.00488062	−	0.00563253i
$181$	−14.1642	−	4.15898i	−1.05282	−	0.309134i	−0.290861	−	0.956765i	$-0.593942\pi$
$181$	−14.1642	−	4.15898i	−1.05282	−	0.309134i	−0.761954	+	0.647631i	$0.775760\pi$
$182$	2.51838	−	5.51447i	0.186674	−	0.408760i
$183$	−6.10634			−0.451393
$184$	−3.27580	−	3.50273i	−0.241495	−	0.258225i
$185$	−0.0873200			−0.00641990
$186$	1.25557	−	2.74931i	0.0920627	−	0.201589i
$187$	−4.57539	−	1.34345i	−0.334585	−	0.0982431i
$188$	5.37660	+	6.20493i	0.392129	+	0.452541i
$189$	−2.17499	+	1.39778i	−0.158207	+	0.101673i
$190$	0.0213235	−	0.0246087i	0.00154697	−	0.00178530i
$191$	−1.45276	+	10.1042i	−0.105118	+	0.731112i	0.867286	+	0.497810i	$0.165862\pi$
$191$	−1.45276	+	10.1042i	−0.105118	+	0.731112i	−0.972404	+	0.233302i	$0.925047\pi$
$192$	−0.427601	+	0.125555i	−0.0308595	+	0.00906116i
$193$	1.82265	+	1.17135i	0.131198	+	0.0843155i	0.604593	−	0.796534i	$-0.293336\pi$
$193$	1.82265	+	1.17135i	0.131198	+	0.0843155i	−0.473396	+	0.880850i	$0.656972\pi$
$194$	0.578912	+	4.02642i	0.0415635	+	0.289080i
$195$	0.0400595	+	0.0877181i	0.00286872	+	0.00628163i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	1.57242	+	10.9364i	0.112030	+	0.779186i	0.965940	+	0.258766i	$0.0833158\pi$
$197$	1.57242	+	10.9364i	0.112030	+	0.779186i	−0.853910	+	0.520421i	$0.825775\pi$
$198$	13.3913	+	8.60609i	0.951681	+	0.611608i
$199$	8.97572	−	2.63551i	0.636272	−	0.186826i	0.0523407	−	0.998629i	$-0.483332\pi$
$199$	8.97572	−	2.63551i	0.636272	−	0.186826i	0.583932	+	0.811803i	$0.301514\pi$
$200$	−0.711393	+	4.94785i	−0.0503031	+	0.349866i
$201$	−2.74051	+	3.16271i	−0.193300	+	0.223081i
$202$	12.1131	−	7.78462i	0.852275	−	0.547724i
$203$	−4.70073	−	5.42494i	−0.329927	−	0.380756i
$204$	−0.358841	−	0.105365i	−0.0251239	−	0.00737704i
$205$	−0.0750150	+	0.164260i	−0.00523928	+	0.0114724i
$206$	4.30562			0.299987
$207$	−1.40628	+	13.3612i	−0.0977434	+	0.928668i
$208$	−6.06231			−0.420346
$209$	−2.15341	+	4.71532i	−0.148955	+	0.326165i
$210$	−0.0152626	−	0.00448149i	−0.00105322	−	0.000309252i
$211$	−3.39024	−	3.91255i	−0.233394	−	0.269351i	0.626956	−	0.779054i	$-0.284300\pi$
$211$	−3.39024	−	3.91255i	−0.233394	−	0.269351i	−0.860350	+	0.509704i	$0.829755\pi$
$212$	3.82750	−	2.45979i	0.262874	−	0.168939i
$213$	−1.86584	+	2.15330i	−0.127845	+	0.147542i
$214$	2.43169	−	16.9128i	0.166227	−	1.15613i
$215$	0.124207	−	0.0364704i	0.00847084	−	0.00248726i
$216$	2.17499	+	1.39778i	0.147989	+	0.0951068i
$217$	0.965186	+	6.71301i	0.0655211	+	0.455709i
$218$	−2.42915	−	5.31909i	−0.164523	−	0.360254i
$219$	−2.51083	−	5.49795i	−0.169666	−	0.371517i
$220$	0.0288643	+	0.200756i	0.00194603	+	0.0135350i
$221$	−4.27984	−	2.75049i	−0.287893	−	0.185018i
$222$	1.04608	−	0.307157i	0.0702083	−	0.0206150i
$223$	−1.81878	+	12.6499i	−0.121794	+	0.847097i	0.833727	+	0.552176i	$0.186202\pi$
$223$	−1.81878	+	12.6499i	−0.121794	+	0.847097i	−0.955522	+	0.294921i	$0.904707\pi$
$224$	0.654861	−	0.755750i	0.0437547	−	0.0504956i
$225$	11.7804	−	7.57081i	0.785360	−	0.504720i
$226$	4.62167	+	5.33369i	0.307429	+	0.354792i
$227$	12.9209	+	3.79393i	0.857592	+	0.251812i	0.680830	−	0.732442i	$-0.261619\pi$
$227$	12.9209	+	3.79393i	0.857592	+	0.251812i	0.176763	+	0.984254i	$0.443437\pi$
$228$	−0.168889	+	0.369816i	−0.0111850	+	0.0244916i
$229$	−6.21575			−0.410748			−0.205374	−	0.978684i	$-0.565841\pi$
$229$	−6.21575			−0.410748			−0.205374	+	0.978684i	$0.565841\pi$
$230$	−0.140392	+	0.0979416i	−0.00925717	+	0.00645807i
$231$	2.53233			0.166615
$232$	−2.98194	+	6.52954i	−0.195774	+	0.428685i
$233$	15.5811	+	4.57501i	1.02075	+	0.299719i	0.748944	−	0.662633i	$-0.230561\pi$
$233$	15.5811	+	4.57501i	1.02075	+	0.299719i	0.271805	+	0.962352i	$0.412379\pi$
$234$	11.1214	+	12.8348i	0.727032	+	0.839039i
$235$	0.246532	−	0.158437i	0.0160820	−	0.0103353i
$236$	−6.88053	+	7.94055i	−0.447884	+	0.516886i
$237$	−0.388839	+	2.70443i	−0.0252578	+	0.175672i
$238$	0.805201	−	0.236428i	0.0521934	−	0.0153254i
$239$	3.46612	+	2.22754i	0.224204	+	0.144087i	0.647921	−	0.761707i	$-0.275639\pi$
$239$	3.46612	+	2.22754i	0.224204	+	0.144087i	−0.423717	+	0.905795i	$0.639275\pi$
$240$	0.00226379	+	0.0157450i	0.000146127	+	0.00101633i
$241$	−2.32099	−	5.08227i	−0.149508	−	0.327378i	0.820029	−	0.572322i	$-0.193957\pi$
$241$	−2.32099	−	5.08227i	−0.149508	−	0.327378i	−0.969537	+	0.244945i	$0.921230\pi$
$242$	−8.84352	−	19.3646i	−0.568483	−	1.24480i
$243$	−1.56377	−	10.8763i	−0.100316	−	0.697713i
$244$	−11.5268	−	7.40785i	−0.737930	−	0.474239i
$245$	0.0342476	−	0.0100560i	0.00218800	−	0.000642454i
$246$	0.320867	−	2.23168i	0.0204578	−	0.142287i
$247$	−3.62167	+	4.17963i	−0.230442	+	0.265944i
$248$	5.70542	−	3.66665i	0.362294	−	0.232833i
$249$	−5.26389	−	6.07485i	−0.333585	−	0.384978i
$250$	0.342432	+	0.100547i	0.0216573	+	0.00635916i
$251$	9.39114	−	20.5637i	0.592764	−	1.29797i	−0.340994	−	0.940065i	$-0.610764\pi$
$251$	9.39114	−	20.5637i	0.592764	−	1.29797i	0.933758	−	0.357906i	$-0.116509\pi$
$252$	−2.80139			−0.176471
$253$	17.0519	−	21.2571i	1.07204	−	1.33643i
$254$	−4.14653			−0.260176
$255$	−0.00554537	+	0.0121427i	−0.000347264	+	0.000760403i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	4.96545	+	5.73044i	0.309737	+	0.357455i	0.889180	−	0.457557i	$-0.151276\pi$
$257$	4.96545	+	5.73044i	0.309737	+	0.357455i	−0.579444	+	0.815012i	$0.696730\pi$
$258$	−1.35969	+	0.873820i	−0.0846507	+	0.0544017i
$259$	−1.60205	+	1.84886i	−0.0995462	+	0.114882i
$260$	−0.0307947	+	0.214182i	−0.00190981	+	0.0132830i
$261$	19.2945	−	5.66536i	1.19430	−	0.350677i
$262$	−1.35708	−	0.872142i	−0.0838407	−	0.0538811i
$263$	−0.0401944	−	0.279558i	−0.00247849	−	0.0172383i	0.988545	−	0.150929i	$-0.0482264\pi$
$263$	−0.0401944	−	0.279558i	−0.00247849	−	0.0172383i	−0.991023	+	0.133690i	$0.957317\pi$
$264$	−1.05197	−	2.30349i	−0.0647442	−	0.141770i
$265$	−0.0674619	−	0.147721i	−0.00414415	−	0.00907443i
$266$	−0.129829	−	0.902982i	−0.00796034	−	0.0553654i
$267$	0.738554	+	0.474640i	0.0451988	+	0.0290475i
$268$	−9.01003	+	2.64558i	−0.550375	+	0.161605i
$269$	0.883638	−	6.14584i	0.0538764	−	0.374718i	−0.944989	−	0.327101i	$-0.893928\pi$
$269$	0.883638	−	6.14584i	0.0538764	−	0.374718i	0.998866	−	0.0476171i	$-0.0151627\pi$
$270$	0.0604319	−	0.0697422i	0.00367777	−	0.00424437i
$271$	16.4130	−	10.5480i	0.997018	−	0.640745i	0.0630163	−	0.998012i	$-0.479928\pi$
$271$	16.4130	−	10.5480i	0.997018	−	0.640745i	0.934002	+	0.357268i	$0.116292\pi$
$272$	−0.549556	−	0.634221i	−0.0333217	−	0.0384553i
$273$	2.59225	+	0.761154i	0.156890	+	0.0460672i
$274$	7.99285	−	17.5019i	0.482866	−	1.05733i
$275$	−28.4042			−1.71284
$276$	1.33735	−	1.66717i	0.0804993	−	0.100352i
$277$	24.7612			1.48775			0.743877	−	0.668316i	$-0.232985\pi$
$277$	24.7612			1.48775			0.743877	+	0.668316i	$0.232985\pi$
$278$	−9.00246	+	19.7126i	−0.539932	+	1.18229i
$279$	−18.2296	−	5.35269i	−1.09138	−	0.320457i
$280$	−0.0233742	−	0.0269753i	−0.00139688	−	0.00161208i
$281$	17.4901	−	11.2402i	1.04337	−	0.670536i	0.0975548	−	0.995230i	$-0.468898\pi$
$281$	17.4901	−	11.2402i	1.04337	−	0.670536i	0.945819	+	0.324695i	$0.105262\pi$
$282$	−2.39610	+	2.76525i	−0.142686	+	0.164668i
$283$	−2.18563	+	15.2014i	−0.129922	+	0.903627i	0.815727	+	0.578437i	$0.196337\pi$
$283$	−2.18563	+	15.2014i	−0.129922	+	0.903627i	−0.945649	+	0.325190i	$0.894572\pi$
$284$	−6.13438	+	1.80122i	−0.364008	+	0.106883i
$285$	0.0122077	+	0.00784542i	0.000723123	+	0.000464723i
$286$	−4.90243	−	34.0972i	−0.289887	−	2.01621i
$287$	2.10165	+	4.60197i	0.124056	+	0.271646i
$288$	1.16374	+	2.54824i	0.0685741	+	0.150156i
$289$	2.31913	+	16.1299i	0.136419	+	0.948817i
$290$	0.215542	+	0.138520i	0.0126571	+	0.00813420i
$291$	−1.73941	+	0.510736i	−0.101966	+	0.0299399i
$292$	1.93013	−	13.4244i	0.112953	−	0.785603i
$293$	−14.9718	+	17.2784i	−0.874661	+	1.00941i	0.125189	+	0.992133i	$0.460046\pi$
$293$	−14.9718	+	17.2784i	−0.874661	+	1.00941i	−0.999851	+	0.0172803i	$0.994499\pi$
$294$	−0.374908	+	0.240938i	−0.0218651	+	0.0140518i
$295$	0.245590	+	0.283425i	0.0142988	+	0.0165017i
$296$	2.34729	+	0.689228i	0.136434	+	0.0400606i
$297$	−6.10288	+	13.3634i	−0.354125	+	0.775426i
$298$	16.9671			0.982880
$299$	23.8447	−	16.6348i	1.37898	−	0.962015i
$300$	−2.22770			−0.128616
$301$	1.50660	−	3.29900i	0.0868390	−	0.190151i
$302$	−6.93256	−	2.03558i	−0.398924	−	0.117135i
$303$	4.20218	+	4.84958i	0.241409	+	0.278601i
$304$	−0.767448	+	0.493209i	−0.0440162	+	0.0282875i
$305$	−0.320273	+	0.369615i	−0.0183388	+	0.0211641i
$306$	−0.334570	+	2.32698i	−0.0191261	+	0.133025i
$307$	21.1739	−	6.21722i	1.20846	−	0.354836i	0.385378	−	0.922759i	$-0.374071\pi$
$307$	21.1739	−	6.21722i	1.20846	−	0.354836i	0.823081	+	0.567923i	$0.192253\pi$
$308$	4.78024	+	3.07208i	0.272380	+	0.175048i
$309$	0.273076	+	1.89928i	0.0155347	+	0.108046i
$310$	−0.100561	−	0.220198i	−0.00571150	−	0.0125064i
$311$	0.949615	+	2.07937i	0.0538477	+	0.117910i	0.934643	−	0.355587i	$-0.115719\pi$
$311$	0.949615	+	2.07937i	0.0538477	+	0.117910i	−0.880796	+	0.473497i	$0.842992\pi$
$312$	−0.384491	−	2.67419i	−0.0217675	−	0.151396i
$313$	−7.40328	−	4.75780i	−0.418458	−	0.268927i	0.314424	−	0.949283i	$-0.398189\pi$
$313$	−7.40328	−	4.75780i	−0.418458	−	0.268927i	−0.732882	+	0.680356i	$0.761825\pi$
$314$	−12.5867	+	3.69579i	−0.710308	+	0.208565i
$315$	−0.0142302	+	0.0989735i	−0.000801783	+	0.00557652i
$316$	−4.01486	+	4.63340i	−0.225854	+	0.260649i
$317$	1.26587	−	0.813526i	0.0710984	−	0.0456922i	−0.504609	−	0.863348i	$-0.668363\pi$
$317$	1.26587	−	0.813526i	0.0710984	−	0.0456922i	0.575707	+	0.817656i	$0.304727\pi$
$318$	1.32781	+	1.53237i	0.0744597	+	0.0859311i
$319$	−39.1365	−	11.4915i	−2.19122	−	0.643401i
$320$	−0.0148276	+	0.0324679i	−0.000828887	+	0.00181501i
$321$	7.61474			0.425013
$322$	−0.501994	+	4.76949i	−0.0279750	+	0.265793i
$323$	−0.765570			−0.0425974
$324$	3.01258	−	6.59663i	0.167366	−	0.366480i
$325$	−29.0763	−	8.53758i	−1.61286	−	0.473580i
$326$	12.2039	+	14.0841i	0.675913	+	0.780045i
$327$	2.19228	−	1.40889i	0.121233	−	0.0779120i
$328$	3.31304	−	3.82345i	0.182932	−	0.211115i
$329$	1.16845	−	8.12673i	0.0644186	−	0.448041i
$330$	−0.0867262	+	0.0254651i	−0.00477412	+	0.00140181i
$331$	21.1658	+	13.6024i	1.16338	+	0.747656i	0.972258	−	0.233911i	$-0.0751524\pi$
$331$	21.1658	+	13.6024i	1.16338	+	0.747656i	0.191118	+	0.981567i	$0.438789\pi$
$332$	−2.56691	−	17.8532i	−0.140877	−	0.979824i
$333$	−2.84696	−	6.23398i	−0.156013	−	0.341620i
$334$	−0.0956517	−	0.209448i	−0.00523383	−	0.0114605i
$335$	0.0477005	+	0.331764i	0.00260615	+	0.0181262i
$336$	0.374908	+	0.240938i	0.0204529	+	0.0131443i
$337$	13.4203	−	3.94054i	0.731048	−	0.214655i	0.105036	−	0.994468i	$-0.466504\pi$
$337$	13.4203	−	3.94054i	0.731048	−	0.214655i	0.626012	+	0.779813i	$0.284686\pi$
$338$	3.38021	−	23.5099i	0.183859	−	1.27877i
$339$	−2.05966	+	2.37698i	−0.111865	+	0.129100i
$340$	−0.0251987	+	0.0161942i	−0.00136659	+	0.000878254i
$341$	25.2367	+	29.1247i	1.36664	+	1.57719i
$342$	2.45210	+	0.720001i	0.132594	+	0.0389332i
$343$	0.415415	−	0.909632i	0.0224303	−	0.0491155i
$344$	−3.62674			−0.195541
$345$	−0.0521078	−	0.0557176i	−0.00280539	−	0.00299973i
$346$	−14.6412			−0.787114
$347$	0.605812	−	1.32654i	0.0325217	−	0.0712126i	−0.892674	−	0.450703i	$-0.851173\pi$
$347$	0.605812	−	1.32654i	0.0325217	−	0.0712126i	0.925196	+	0.379490i	$0.123901\pi$
$348$	−3.06942	−	0.901262i	−0.164538	−	0.0483127i
$349$	−10.4745	−	12.0882i	−0.560688	−	0.647068i	0.402652	−	0.915353i	$-0.368089\pi$
$349$	−10.4745	−	12.0882i	−0.560688	−	0.647068i	−0.963340	+	0.268285i	$0.913543\pi$
$350$	4.20520	−	2.70252i	0.224777	−	0.144456i
$351$	−10.2640	+	11.8453i	−0.547852	+	0.632255i
$352$	0.808674	−	5.62445i	0.0431025	−	0.299784i
$353$	24.8949	−	7.30980i	1.32502	−	0.389061i	0.458719	−	0.888582i	$-0.348309\pi$
$353$	24.8949	−	7.30980i	1.32502	−	0.389061i	0.866302	+	0.499520i	$0.166490\pi$
$354$	−3.93910	−	2.53151i	−0.209361	−	0.134548i
$355$	0.0324763	+	0.225878i	0.00172366	+	0.0119884i
$356$	0.818352	+	1.79194i	0.0433726	+	0.0949727i
$357$	0.155361	+	0.340193i	0.00822258	+	0.0180049i
$358$	2.31982	+	16.1347i	0.122607	+	0.852747i
$359$	6.09194	+	3.91505i	0.321520	+	0.206628i	0.691438	−	0.722436i	$-0.256978\pi$
$359$	6.09194	+	3.91505i	0.321520	+	0.206628i	−0.369917	+	0.929065i	$0.620614\pi$
$360$	0.0959409	−	0.0281708i	0.00505653	−	0.00148473i
$361$	2.58554	−	17.9828i	0.136081	−	0.946466i
$362$	9.66715	−	11.1565i	0.508094	−	0.586372i
$363$	7.98118	−	5.12919i	0.418903	−	0.269213i
$364$	3.96997	+	4.58159i	0.208083	+	0.240141i
$365$	−0.464480	−	0.136384i	−0.0243120	−	0.00713865i
$366$	2.53666	−	5.55452i	0.132594	−	0.290339i
$367$	−19.2685			−1.00581			−0.502903	−	0.864343i	$-0.667735\pi$
$367$	−19.2685			−1.00581			−0.502903	+	0.864343i	$0.667735\pi$
$368$	4.54701	−	1.52469i	0.237029	−	0.0794798i
$369$	−14.1727			−0.737800
$370$	0.0362740	−	0.0794291i	0.00188580	−	0.00412932i
$371$	−4.36546	−	1.28182i	−0.226644	−	0.0665486i
$372$	1.97928	+	2.28421i	0.102621	+	0.118431i
$373$	−25.5396	+	16.4133i	−1.32239	+	0.849850i	−0.995458	−	0.0951976i	$-0.969652\pi$
$373$	−25.5396	+	16.4133i	−1.32239	+	0.849850i	−0.326934	+	0.945047i	$0.606015\pi$
$374$	3.12273	−	3.60383i	0.161473	−	0.186349i
$375$	−0.0226350	+	0.157430i	−0.00116887	+	0.00812964i
$376$	−7.87773	+	2.31311i	−0.406263	+	0.119289i
$377$	−36.6085	−	23.5269i	−1.88543	−	1.21169i
$378$	−0.367942	−	2.55910i	−0.0189249	−	0.131626i
$379$	0.485794	+	1.06374i	0.0249535	+	0.0546406i	0.921698	−	0.387907i	$-0.126802\pi$
$379$	0.485794	+	1.06374i	0.0249535	+	0.0546406i	−0.896745	+	0.442548i	$0.854075\pi$
$380$	0.0135267	+	0.0296194i	0.000693906	+	0.00151944i
$381$	−0.262986	−	1.82910i	−0.0134732	−	0.0937079i
$382$	−8.58758	−	5.51890i	−0.439379	−	0.282372i
$383$	−2.29389	+	0.673547i	−0.117212	+	0.0344167i	−0.339813	−	0.940493i	$-0.610364\pi$
$383$	−2.29389	+	0.673547i	−0.117212	+	0.0344167i	0.222600	+	0.974910i	$0.428546\pi$
$384$	0.0634231	−	0.441117i	0.00323655	−	0.0225107i
$385$	0.132819	−	0.153281i	0.00676908	−	0.00781194i
$386$	−1.82265	+	1.17135i	−0.0927707	+	0.0596201i
$387$	6.65333	+	7.67835i	0.338208	+	0.390312i
$388$	−3.90305	−	1.14604i	−0.198147	−	0.0581813i
$389$	9.92230	−	21.7268i	0.503081	−	1.10159i	−0.472375	−	0.881398i	$-0.656603\pi$
$389$	9.92230	−	21.7268i	0.503081	−	1.10159i	0.975456	−	0.220195i	$-0.0706695\pi$
$390$	−0.0964326			−0.00488305
$391$	3.90183	+	0.986602i	0.197324	+	0.0498946i
$392$	−1.00000			−0.0505076
$393$	0.298647	−	0.653945i	0.0150647	−	0.0329872i
$394$	−10.6013	−	3.11282i	−0.534086	−	0.156822i
$395$	0.143304	+	0.165382i	0.00721041	+	0.00832126i
$396$	−13.3913	+	8.60609i	−0.672940	+	0.432472i
$397$	−2.48261	+	2.86508i	−0.124598	+	0.143794i	−0.814621	−	0.579993i	$-0.803055\pi$
$397$	−2.48261	+	2.86508i	−0.124598	+	0.143794i	0.690023	+	0.723788i	$0.257601\pi$
$398$	−1.33131	+	9.25944i	−0.0667323	+	0.464134i
$399$	0.390087	−	0.114540i	0.0195288	−	0.00573416i
$400$	−4.20520	−	2.70252i	−0.210260	−	0.135126i
$401$	−2.15820	−	15.0106i	−0.107775	−	0.749594i	−0.970007	−	0.243079i	$-0.921843\pi$
$401$	−2.15820	−	15.0106i	−0.107775	−	0.749594i	0.862231	−	0.506515i	$-0.169067\pi$
$402$	−1.73846	−	3.80669i	−0.0867063	−	0.189860i
$403$	17.0797	+	37.3994i	0.850802	+	1.86300i
$404$	2.04917	+	14.2523i	0.101950	+	0.709079i
$405$	−0.217757	−	0.139944i	−0.0108204	−	0.00695386i
$406$	6.88745	−	2.02234i	0.341819	−	0.100367i
$407$	−1.97833	+	13.7596i	−0.0980623	+	0.682038i
$408$	0.244911	−	0.282643i	0.0121249	−	0.0139929i
$409$	−14.9107	+	9.58252i	−0.737286	+	0.473825i	−0.854611	−	0.519269i	$-0.826204\pi$
$409$	−14.9107	+	9.58252i	−0.737286	+	0.473825i	0.117325	+	0.993094i	$0.462568\pi$
$410$	−0.118254	−	0.136472i	−0.00584014	−	0.00673988i
$411$	8.22733	+	2.41576i	0.405824	+	0.119161i
$412$	−1.78862	+	3.91653i	−0.0881189	+	0.192953i
$413$	10.5069			0.517009
$414$	−11.5696	−	6.82964i	−0.568614	−	0.335659i
$415$	−0.643796			−0.0316027
$416$	2.51838	−	5.51447i	0.123474	−	0.270369i
$417$	−9.26655	−	2.72090i	−0.453785	−	0.133243i
$418$	−3.39464	−	3.91763i	−0.166037	−	0.191617i
$419$	2.03447	−	1.30748i	0.0993905	−	0.0638744i	−0.490001	−	0.871722i	$-0.663004\pi$
$419$	2.03447	−	1.30748i	0.0993905	−	0.0638744i	0.589392	+	0.807847i	$0.299367\pi$
$420$	0.0104168	−	0.0120216i	0.000508288	−	0.000586595i
$421$	−3.58641	+	24.9441i	−0.174791	+	1.21570i	0.693799	+	0.720168i	$0.255935\pi$
$421$	−3.58641	+	24.9441i	−0.174791	+	1.21570i	−0.868591	+	0.495530i	$0.834974\pi$
$422$	4.96733	−	1.45854i	0.241806	−	0.0710006i
$423$	19.3491	+	12.4349i	0.940784	+	0.604605i
$424$	0.647498	+	4.50345i	0.0314453	+	0.218707i
$425$	−1.74263	−	3.81582i	−0.0845298	−	0.185094i
$426$	−1.18361	−	2.59174i	−0.0573461	−	0.125570i
$427$	1.95000	+	13.5625i	0.0943669	+	0.656336i
$428$	14.3742	+	9.23775i	0.694804	+	0.446524i
$429$	14.7299	−	4.32510i	0.711168	−	0.208818i
$430$	−0.0184227	+	0.128133i	−0.000888423	+	0.00617912i
$431$	−6.47976	+	7.47804i	−0.312119	+	0.360205i	−0.890035	−	0.455891i	$-0.849321\pi$
$431$	−6.47976	+	7.47804i	−0.312119	+	0.360205i	0.577916	+	0.816096i	$0.303866\pi$
$432$	−2.17499	+	1.39778i	−0.104644	+	0.0672507i
$433$	−3.31349	−	3.82398i	−0.159236	−	0.183769i	0.670525	−	0.741887i	$-0.266069\pi$
$433$	−3.31349	−	3.82398i	−0.159236	−	0.183769i	−0.829761	+	0.558118i	$0.811523\pi$
$434$	−6.50732	−	1.91072i	−0.312362	−	0.0917176i
$435$	−0.0474334	+	0.103865i	−0.00227426	+	0.00497993i
$436$	5.84752			0.280046
$437$	1.66523	−	4.04578i	0.0796589	−	0.193536i
$438$	6.04414			0.288800
$439$	−4.78974	+	10.4881i	−0.228602	+	0.500568i	−0.988823	−	0.149097i	$-0.952363\pi$
$439$	−4.78974	+	10.4881i	−0.228602	+	0.500568i	0.760221	+	0.649665i	$0.225091\pi$
$440$	−0.194605	−	0.0571410i	−0.00927741	−	0.00272409i
$441$	1.83452	+	2.11715i	0.0873582	+	0.100817i
$442$	4.27984	−	2.75049i	0.203571	−	0.130827i
$443$	−4.36950	+	5.04267i	−0.207601	+	0.239585i	−0.849996	−	0.526789i	$-0.823396\pi$
$443$	−4.36950	+	5.04267i	−0.207601	+	0.239585i	0.642395	+	0.766374i	$0.277941\pi$
$444$	−0.155158	+	1.07915i	−0.00736346	+	0.0512140i
$445$	0.0674664	−	0.0198099i	0.00319822	−	0.000939081i
$446$	−10.7512	−	6.90936i	−0.509083	−	0.327168i
$447$	1.07611	+	7.48450i	0.0508982	+	0.354005i
$448$	0.415415	+	0.909632i	0.0196265	+	0.0429761i
$449$	5.31612	+	11.6407i	0.250883	+	0.549358i	0.992611	−	0.121344i	$-0.0387203\pi$
$449$	5.31612	+	11.6407i	0.250883	+	0.549358i	−0.741727	+	0.670702i	$0.765993\pi$
$450$	1.99289	+	13.8609i	0.0939458	+	0.653407i
$451$	24.1840	+	15.5421i	1.13878	+	0.731850i
$452$	−6.77160	+	1.98832i	−0.318509	+	0.0935228i
$453$	0.458247	−	3.18718i	0.0215303	−	0.149747i
$454$	−8.81863	+	10.1772i	−0.413879	+	0.477642i
$455$	0.182034	−	0.116986i	0.00853390	−	0.00548440i
$456$	−0.266237	−	0.307254i	−0.0124677	−	0.0143885i
$457$	17.2907	+	5.07699i	0.808823	+	0.237492i	0.659897	−	0.751356i	$-0.270600\pi$
$457$	17.2907	+	5.07699i	0.808823	+	0.237492i	0.148926	+	0.988848i	$0.452418\pi$
$458$	2.58212	−	5.65405i	0.120654	−	0.264196i
$459$	−2.16966			−0.101271
$460$	−0.0307699	−	0.168391i	−0.00143465	−	0.00785129i
$461$	−0.691203			−0.0321925			−0.0160963	−	0.999870i	$-0.505124\pi$
$461$	−0.691203			−0.0321925			−0.0160963	+	0.999870i	$0.505124\pi$
$462$	−1.05197	+	2.30349i	−0.0489420	+	0.107168i
$463$	−9.87073	−	2.89831i	−0.458732	−	0.134696i	0.0441986	−	0.999023i	$-0.485927\pi$
$463$	−9.87073	−	2.89831i	−0.458732	−	0.134696i	−0.502930	+	0.864327i	$0.667745\pi$
$464$	−4.70073	−	5.42494i	−0.218226	−	0.251846i
$465$	0.0907555	−	0.0583250i	0.00420868	−	0.00270476i
$466$	−10.6342	+	12.2725i	−0.492619	+	0.568513i
$467$	−1.04818	+	7.29028i	−0.0485042	+	0.337354i	0.951091	+	0.308910i	$0.0999643\pi$
$467$	−1.04818	+	7.29028i	−0.0485042	+	0.337354i	−0.999595	+	0.0284438i	$0.990945\pi$
$468$	−16.2950	+	4.78464i	−0.753236	+	0.221170i
$469$	7.89971	+	5.07684i	0.364775	+	0.234427i
$470$	0.0417059	+	0.290071i	0.00192375	+	0.0133800i
$471$	−2.42856	−	5.31781i	−0.111902	−	0.245032i
$472$	−4.36471	−	9.55737i	−0.200902	−	0.439914i
$473$	−2.93285	−	20.3984i	−0.134852	−	0.937919i
$474$	−2.29851	−	1.47716i	−0.105574	−	0.0678483i
$475$	−4.37545	+	1.28475i	−0.200760	+	0.0589483i
$476$	−0.119430	+	0.830653i	−0.00547406	+	0.0380729i
$477$	8.34664	−	9.63253i	0.382166	−	0.441043i
$478$	−3.46612	+	2.22754i	−0.158536	+	0.101885i
$479$	−19.7183	−	22.7561i	−0.900953	−	1.03976i	−0.999006	−	0.0445739i	$-0.985807\pi$
$479$	−19.7183	−	22.7561i	−0.900953	−	1.03976i	0.0980532	−	0.995181i	$-0.468738\pi$
$480$	−0.0152626	−	0.00448149i	−0.000696637	−	0.000204551i
$481$	−6.16093	+	13.4906i	−0.280914	+	0.615116i
$482$	5.58717			0.254489
$483$	−2.13574	+	0.0810574i	−0.0971796	+	0.00368824i
$484$	21.2884			0.967654
$485$	−0.0603160	+	0.132074i	−0.00273881	+	0.00599715i
$486$	10.5430	+	3.09571i	0.478241	+	0.140424i
$487$	4.94826	+	5.71060i	0.224227	+	0.258772i	0.856705	−	0.515806i	$-0.172508\pi$
$487$	4.94826	+	5.71060i	0.224227	+	0.258772i	−0.632478	+	0.774578i	$0.717962\pi$
$488$	11.5268	−	7.40785i	0.521796	−	0.335338i
$489$	−5.43872	+	6.27662i	−0.245948	+	0.283839i
$490$	−0.00507970	+	0.0353301i	−0.000229478	+	0.00159605i
$491$	4.10244	−	1.20458i	0.185141	−	0.0543622i	−0.187848	−	0.982198i	$-0.560151\pi$
$491$	4.10244	−	1.20458i	0.185141	−	0.0543622i	0.372989	+	0.927836i	$0.378333\pi$
$492$	1.89672	+	1.21895i	0.0855106	+	0.0549543i
$493$	−0.857294	−	5.96261i	−0.0386106	−	0.268542i
$494$	−2.29743	−	5.03067i	−0.103366	−	0.226341i
$495$	0.236030	+	0.516834i	0.0106088	+	0.0232300i
$496$	0.965186	+	6.71301i	0.0433381	+	0.301423i
$497$	5.37843	+	3.45651i	0.241256	+	0.155046i
$498$	7.71257	−	2.26462i	0.345609	−	0.101480i
$499$	0.159164	−	1.10701i	0.00712517	−	0.0495567i	−0.985949	−	0.167049i	$-0.946576\pi$
$499$	0.159164	−	1.10701i	0.00712517	−	0.0495567i	0.993074	+	0.117492i	$0.0374854\pi$
$500$	−0.233712	+	0.269718i	−0.0104519	+	0.0120622i
$501$	0.0863246	−	0.0554775i	0.00385670	−	0.00247855i
$502$	14.8042	+	17.0850i	0.660744	+	0.762539i
$503$	−33.5270	−	9.84440i	−1.49489	−	0.438940i	−0.570794	−	0.821093i	$-0.693364\pi$
$503$	−33.5270	−	9.84440i	−1.49489	−	0.438940i	−0.924099	+	0.382153i	$0.875183\pi$
$504$	1.16374	−	2.54824i	0.0518371	−	0.113507i
$505$	0.513945			0.0228703
$506$	12.2526	+	24.3415i	0.544693	+	1.08211i
$507$	10.5850			0.470096
$508$	1.72253	−	3.77181i	0.0764249	−	0.167347i
$509$	27.3990	+	8.04508i	1.21444	+	0.356592i	0.825357	−	0.564611i	$-0.190974\pi$
$509$	27.3990	+	8.04508i	1.21444	+	0.356592i	0.389083	+	0.921203i	$0.372792\pi$
$510$	−0.00874172	−	0.0100885i	−0.000387090	−	0.000446726i
$511$	−11.4094	+	7.33240i	−0.504724	+	0.324366i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−0.335662	+	2.33458i	−0.0148198	+	0.103074i
$514$	−7.27532	+	2.13623i	−0.320900	+	0.0942249i
$515$	0.129286	+	0.0830869i	0.00569701	+	0.00366124i
$516$	−0.230019	−	1.59982i	−0.0101260	−	0.0704280i
$517$	−19.3805	−	42.4373i	−0.852352	−	1.86639i
$518$	−1.01627	−	2.22532i	−0.0446522	−	0.0977747i
$519$	−0.928589	−	6.45848i	−0.0407605	−	0.283496i
$520$	−0.182034	−	0.116986i	−0.00798273	−	0.00513019i
$521$	12.4045	−	3.64229i	0.543450	−	0.159571i	0.00152630	−	0.999999i	$-0.499514\pi$
$521$	12.4045	−	3.64229i	0.543450	−	0.159571i	0.541924	+	0.840427i	$0.317696\pi$
$522$	−2.86181	+	19.9043i	−0.125258	+	0.871189i
$523$	−4.91018	+	5.66665i	−0.214707	+	0.247785i	−0.852879	−	0.522109i	$-0.825146\pi$
$523$	−4.91018	+	5.66665i	−0.214707	+	0.247785i	0.638172	+	0.769894i	$0.279691\pi$
$524$	1.35708	−	0.872142i	0.0592843	−	0.0380997i
$525$	1.45883	+	1.68358i	0.0636687	+	0.0734776i
$526$	0.270992	+	0.0795705i	0.0118158	+	0.00346944i
$527$	−2.36432	+	5.17713i	−0.102991	+	0.225519i
$528$	2.53233			0.110206
$529$	−13.7010	+	18.4739i	−0.595694	+	0.803212i
$530$	0.162396			0.00705405
$531$	−12.2273	+	26.7740i	−0.530618	+	1.16189i
$532$	0.875314	+	0.257015i	0.0379497	+	0.0111430i
$533$	20.0847	+	23.1790i	0.869965	+	1.00399i
$534$	−0.738554	+	0.474640i	−0.0319604	+	0.0205397i
$535$	0.399388	−	0.460918i	0.0172670	−	0.0199272i
$536$	1.33639	−	9.29483i	0.0577234	−	0.401475i
$537$	−6.97018	+	2.04663i	−0.300786	+	0.0883186i
$538$	5.22337	+	3.35686i	0.225196	+	0.144724i
$539$	−0.808674	−	5.62445i	−0.0348320	−	0.242262i
$540$	0.0383354	+	0.0839428i	0.00164969	+	0.00361232i
$541$	10.3840	+	22.7379i	0.446445	+	0.977577i	0.990370	+	0.138444i	$0.0442101\pi$
$541$	10.3840	+	22.7379i	0.446445	+	0.977577i	−0.543926	+	0.839133i	$0.683063\pi$
$542$	2.77659	+	19.3116i	0.119265	+	0.829503i
$543$	5.53444	+	3.55677i	0.237506	+	0.152636i
$544$	0.805201	−	0.236428i	0.0345227	−	0.0101368i
$545$	0.0297037	−	0.206594i	0.00127237	−	0.00884949i
$546$	−1.76923	+	2.04180i	−0.0757161	+	0.0873811i
$547$	−9.19355	+	5.90833i	−0.393088	+	0.252622i	−0.722222	−	0.691661i	$-0.756879\pi$
$547$	−9.19355	+	5.90833i	−0.393088	+	0.252622i	0.329135	+	0.944283i	$0.393243\pi$
$548$	12.5999	+	14.5411i	0.538243	+	0.621166i
$549$	−36.8298	−	10.8142i	−1.57186	−	0.461539i
$550$	11.7995	−	25.8374i	0.503134	−	1.10171i
$551$	−6.54846			−0.278974
$552$	0.960952	+	1.90907i	0.0409008	+	0.0812553i
$553$	6.13087			0.260711
$554$	−10.2862	+	22.5235i	−0.437017	+	0.956934i
$555$	0.0373382	+	0.0109635i	0.00158492	+	0.000465374i
$556$	−14.1915	−	16.3778i	−0.601853	−	0.694575i
$557$	−21.7639	+	13.9868i	−0.922165	+	0.592640i	−0.913285	−	0.407321i	$-0.866463\pi$
$557$	−21.7639	+	13.9868i	−0.922165	+	0.592640i	−0.00888021	+	0.999961i	$0.502827\pi$
$558$	12.4418	−	14.3586i	0.526704	−	0.607849i
$559$	3.12899	−	21.7626i	0.132342	−	0.920461i
$560$	0.0342476	−	0.0100560i	0.00144722	−	0.000424943i
$561$	1.78776	+	1.14893i	0.0754794	+	0.0485077i
$562$	2.95880	+	20.5789i	0.124810	+	0.868070i
$563$	−9.88048	−	21.6352i	−0.416413	−	0.911817i	−0.995339	−	0.0964368i	$-0.969255\pi$
$563$	−9.88048	−	21.6352i	−0.416413	−	0.911817i	0.578926	−	0.815380i	$-0.303472\pi$
$564$	−1.51998	−	3.32830i	−0.0640028	−	0.140147i
$565$	0.0358499	+	0.249341i	0.00150822	+	0.0104899i
$566$	−12.9197	−	8.30299i	−0.543056	−	0.349001i
$567$	−6.95822	+	2.04312i	−0.292218	+	0.0858029i
$568$	0.909869	−	6.32828i	0.0381773	−	0.265529i
$569$	28.5564	−	32.9559i	1.19715	−	1.38158i	0.292037	−	0.956407i	$-0.405667\pi$
$569$	28.5564	−	32.9559i	1.19715	−	1.38158i	0.905111	−	0.425175i	$-0.139787\pi$
$570$	−0.0122077	+	0.00784542i	−0.000511325	+	0.000328609i
$571$	−16.6351	−	19.1979i	−0.696156	−	0.803407i	0.292072	−	0.956396i	$-0.405655\pi$
$571$	−16.6351	−	19.1979i	−0.696156	−	0.803407i	−0.988228	+	0.152990i	$0.951110\pi$
$572$	33.0524	+	9.70507i	1.38199	+	0.405789i
$573$	1.88983	−	4.13816i	0.0789489	−	0.172874i
$574$	−5.05916			−0.211165
$575$	23.9558	−	0.909190i	0.999026	−	0.0379159i
$576$	−2.80139			−0.116725
$577$	12.1835	−	26.6781i	0.507205	−	1.11062i	−0.466855	−	0.884334i	$-0.654613\pi$
$577$	12.1835	−	26.6781i	0.507205	−	1.11062i	0.974060	−	0.226290i	$-0.0726595\pi$
$578$	−15.6357	−	4.59104i	−0.650358	−	0.190962i
$579$	−0.632301	−	0.729714i	−0.0262775	−	0.0303259i
$580$	−0.215542	+	0.138520i	−0.00894989	+	0.00575174i
$581$	−11.8116	+	13.6313i	−0.490028	+	0.565523i
$582$	0.257994	−	1.79439i	0.0106942	−	0.0743798i
$583$	−24.8058	+	7.28364i	−1.02735	+	0.301658i
$584$	11.4094	+	7.33240i	0.472126	+	0.303417i
$585$	0.0862682	+	0.600008i	0.00356675	+	0.0248073i
$586$	−9.49745	−	20.7965i	−0.392336	−	0.859096i
$587$	9.29421	+	20.3515i	0.383613	+	0.839996i	0.998672	+	0.0515146i	$0.0164049\pi$
$587$	9.29421	+	20.3515i	0.383613	+	0.839996i	−0.615059	+	0.788481i	$0.710868\pi$
$588$	−0.0634231	−	0.441117i	−0.00261553	−	0.0181914i
$589$	5.20487	+	3.34496i	0.214463	+	0.137827i
$590$	−0.359834	+	0.105657i	−0.0148141	+	0.00434983i
$591$	0.700753	−	4.87385i	0.0288251	−	0.200483i
$592$	−1.60205	+	1.84886i	−0.0658437	+	0.0759876i
$593$	16.0272	−	10.3001i	0.658159	−	0.422973i	−0.168480	−	0.985705i	$-0.553886\pi$
$593$	16.0272	−	10.3001i	0.658159	−	0.422973i	0.826640	+	0.562732i	$0.190250\pi$
$594$	−9.62059	−	11.1028i	−0.394738	−	0.455552i
$595$	0.0287404	+	0.00843894i	0.00117824	+	0.000345963i
$596$	−7.04840	+	15.4338i	−0.288714	+	0.632195i
$597$	−4.16893			−0.170623
$598$	5.22608	+	28.6003i	0.213710	+	1.16955i
$599$	−11.0938			−0.453282			−0.226641	−	0.973978i	$-0.572774\pi$
$599$	−11.0938			−0.453282			−0.226641	+	0.973978i	$0.572774\pi$
$600$	0.925420	−	2.02639i	0.0377801	−	0.0827269i
$601$	−39.4221	−	11.5754i	−1.60806	−	0.472170i	−0.650287	−	0.759688i	$-0.725352\pi$
$601$	−39.4221	−	11.5754i	−1.60806	−	0.472170i	−0.957775	+	0.287518i	$0.907170\pi$
$602$	2.37501	+	2.74090i	0.0967981	+	0.111711i
$603$	−22.1302	+	14.2222i	−0.901211	+	0.579173i
$604$	4.73152	−	5.46047i	0.192523	−	0.222183i
$605$	0.108139	−	0.752121i	0.00439646	−	0.0305781i
$606$	−6.15698	+	1.80785i	−0.250110	+	0.0734390i
$607$	−6.31762	−	4.06009i	−0.256424	−	0.164794i	0.406113	−	0.913823i	$-0.366884\pi$
$607$	−6.31762	−	4.06009i	−0.256424	−	0.164794i	−0.662537	+	0.749029i	$0.730520\pi$
$608$	−0.129829	−	0.902982i	−0.00526527	−	0.0366207i
$609$	1.32891	+	2.90991i	0.0538502	+	0.117916i
$610$	−0.203167	−	0.444874i	−0.00822600	−	0.0180124i
$611$	−7.08349	−	49.2668i	−0.286567	−	1.99312i
$612$	−1.97771	−	1.27100i	−0.0799444	−	0.0513771i
$613$	−22.7758	+	6.68758i	−0.919906	+	0.270109i	−0.707205	−	0.707009i	$-0.750044\pi$
$613$	−22.7758	+	6.68758i	−0.919906	+	0.270109i	−0.212701	+	0.977117i	$0.568226\pi$
$614$	−3.14058	+	21.8432i	−0.126743	+	0.881520i
$615$	0.0527002	−	0.0608193i	0.00212508	−	0.00245247i
$616$	−4.78024	+	3.07208i	−0.192602	+	0.123777i
$617$	0.382871	+	0.441857i	0.0154138	+	0.0177885i	0.763404	−	0.645921i	$-0.223527\pi$
$617$	0.382871	+	0.441857i	0.0154138	+	0.0177885i	−0.747990	+	0.663710i	$0.768981\pi$
$618$	−1.84109	−	0.540592i	−0.0740594	−	0.0217458i
$619$	12.5707	−	27.5261i	0.505260	−	1.10637i	−0.469463	−	0.882952i	$-0.655553\pi$
$619$	12.5707	−	27.5261i	0.505260	−	1.10637i	0.974724	−	0.223414i	$-0.0717201\pi$
$620$	0.242074			0.00972194
$621$	4.71936	−	11.4659i	0.189381	−	0.460112i
$622$	−2.28594			−0.0916580
$623$	0.818352	−	1.79194i	0.0327866	−	0.0717926i
$624$	2.59225	+	0.761154i	0.103773	+	0.0304706i
$625$	−16.3590	−	18.8793i	−0.654360	−	0.755172i
$626$	7.40328	−	4.75780i	0.295894	−	0.190160i
$627$	1.51283	−	1.74590i	0.0604168	−	0.0697247i
$628$	1.86690	−	12.9845i	0.0744973	−	0.518140i
$629$	−1.96984	+	0.578396i	−0.0785425	+	0.0230622i
$630$	−0.0841180	−	0.0540594i	−0.00335134	−	0.00215378i
$631$	0.566313	+	3.93880i	0.0225446	+	0.156801i	0.997984	−	0.0634672i	$-0.0202158\pi$
$631$	0.566313	+	3.93880i	0.0225446	+	0.156801i	−0.975439	+	0.220268i	$0.929307\pi$
$632$	−2.54685	−	5.57683i	−0.101308	−	0.221834i
$633$	0.958431	+	2.09867i	0.0380942	+	0.0834147i
$634$	0.214147	+	1.48943i	0.00850488	+	0.0591527i
$635$	−0.124509	−	0.0800168i	−0.00494097	−	0.00317537i
$636$	−1.94548	+	0.571246i	−0.0771435	+	0.0226514i
$637$	0.862757	−	6.00061i	0.0341837	−	0.237753i
$638$	26.7109	−	30.8261i	1.05750	−	1.22042i
$639$	−15.0671	+	9.68304i	−0.596045	+	0.383055i
$640$	−0.0233742	−	0.0269753i	−0.000923947	−	0.00106629i
$641$	2.99740	+	0.880116i	0.118390	+	0.0347625i	0.340391	−	0.940284i	$-0.389441\pi$
$641$	2.99740	+	0.880116i	0.118390	+	0.0347625i	−0.222001	+	0.975046i	$0.571259\pi$
$642$	−3.16328	+	6.92661i	−0.124845	+	0.273371i
$643$	21.1340			0.833445			0.416722	−	0.909034i	$-0.363179\pi$
$643$	21.1340			0.833445			0.416722	+	0.909034i	$0.363179\pi$
$644$	−4.12994	−	2.43795i	−0.162743	−	0.0960685i
$645$	−0.0576901			−0.00227155
$646$	0.318029	−	0.696387i	0.0125127	−	0.0273990i
$647$	1.21717	+	0.357393i	0.0478518	+	0.0140506i	0.305571	−	0.952169i	$-0.401153\pi$
$647$	1.21717	+	0.357393i	0.0478518	+	0.0140506i	−0.257719	+	0.966220i	$0.582971\pi$
$648$	4.74904	+	5.48068i	0.186560	+	0.215302i
$649$	50.2254	−	32.2779i	1.97152	−	1.26702i
$650$	19.8448	−	22.9021i	0.778377	−	0.898295i
$651$	0.430138	−	2.99168i	0.0168585	−	0.117253i
$652$	−17.8810	+	5.25034i	−0.700275	+	0.205619i
$653$	21.6185	+	13.8934i	0.845997	+	0.543689i	0.890324	−	0.455328i	$-0.150478\pi$
$653$	21.6185	+	13.8934i	0.845997	+	0.543689i	−0.0443269	+	0.999017i	$0.514114\pi$
$654$	0.370868	+	2.57944i	0.0145021	+	0.100864i
$655$	−0.0239193	−	0.0523760i	−0.000934605	−	0.00204650i
$656$	2.10165	+	4.60197i	0.0820556	+	0.179677i
$657$	−5.40707	−	37.6070i	−0.210950	−	1.46719i
$658$	6.90694	+	4.43882i	0.269261	+	0.173043i
$659$	−10.8748	+	3.19314i	−0.423624	+	0.124387i	−0.486594	−	0.873628i	$-0.661761\pi$
$659$	−10.8748	+	3.19314i	−0.423624	+	0.124387i	0.0629703	+	0.998015i	$0.479943\pi$
$660$	0.0128635	−	0.0894675i	0.000500711	−	0.00348252i
$661$	10.3242	−	11.9148i	0.401565	−	0.463431i	−0.518568	−	0.855036i	$-0.673535\pi$
$661$	10.3242	−	11.9148i	0.401565	−	0.463431i	0.920133	+	0.391605i	$0.128080\pi$
$662$	−21.1658	+	13.6024i	−0.822631	+	0.528673i
$663$	1.48473	+	1.71347i	0.0576621	+	0.0665456i
$664$	17.3062	+	5.08156i	0.671611	+	0.197203i
$665$	0.0135267	−	0.0296194i	0.000524543	−	0.00114859i
$666$	6.85330			0.265560
$667$	33.3751	+	8.43910i	1.29229	+	0.326763i
$668$	0.230256			0.00890886
$669$	2.36597	−	5.18074i	0.0914735	−	0.200299i
$670$	−0.321599	−	0.0944299i	−0.0124244	−	0.00364814i
$671$	50.9865	+	58.8416i	1.96831	+	2.27155i
$672$	−0.374908	+	0.240938i	−0.0144624	+	0.00929440i
$673$	−9.92546	+	11.4546i	−0.382598	+	0.441542i	−0.914084	−	0.405525i	$-0.867089\pi$
$673$	−9.92546	+	11.4546i	−0.382598	+	0.441542i	0.531485	+	0.847067i	$0.321634\pi$
$674$	−1.99053	+	13.8444i	−0.0766724	+	0.533268i
$675$	−12.4003	+	3.64104i	−0.477286	+	0.140144i
$676$	19.9811	+	12.8411i	0.768506	+	0.493889i
$677$	−2.95862	−	20.5776i	−0.113709	−	0.790862i	−0.964258	−	0.264966i	$-0.914639\pi$
$677$	−2.95862	−	20.5776i	−0.113709	−	0.790862i	0.850549	−	0.525896i	$-0.176270\pi$
$678$	−1.30656	−	2.86097i	−0.0501781	−	0.109875i
$679$	1.68984	+	3.70022i	0.0648500	+	0.142002i
$680$	−0.00426286	−	0.0296488i	−0.000163473	−	0.00113698i
$681$	−5.04866	−	3.24458i	−0.193465	−	0.124333i
$682$	−36.9765	+	10.8573i	−1.41590	+	0.415747i
$683$	1.54422	−	10.7403i	0.0590880	−	0.410966i	−0.938714	−	0.344698i	$-0.887981\pi$
$683$	1.54422	−	10.7403i	0.0590880	−	0.410966i	0.997802	−	0.0662687i	$-0.0211094\pi$
$684$	−1.67357	+	1.93141i	−0.0639907	+	0.0738492i
$685$	0.577743	−	0.371293i	0.0220744	−	0.0141864i
$686$	0.654861	+	0.755750i	0.0250027	+	0.0288547i
$687$	2.65786	+	0.780419i	0.101404	+	0.0297749i
$688$	1.50660	−	3.29900i	0.0574386	−	0.125773i
$689$	−27.5821			−1.05079
$690$	0.0723289	−	0.0242530i	0.00275351	−	0.000923297i
$691$	−8.92288			−0.339442			−0.169721	−	0.985492i	$-0.554287\pi$
$691$	−8.92288			−0.339442			−0.169721	+	0.985492i	$0.554287\pi$
$692$	6.08216	−	13.3181i	0.231209	−	0.506277i
$693$	15.2735	+	4.48471i	0.580193	+	0.170360i
$694$	0.955003	+	1.10213i	0.0362514	+	0.0418363i
$695$	−0.650719	+	0.418192i	−0.0246832	+	0.0158629i
$696$	2.09490	−	2.41764i	0.0794069	−	0.0916405i
$697$	−0.604214	+	4.20240i	−0.0228862	+	0.159177i
$698$	15.3471	−	4.50632i	0.580897	−	0.170567i
$699$	−6.08807	−	3.91256i	−0.230272	−	0.147987i
$700$	0.711393	+	4.94785i	0.0268881	+	0.187011i
$701$	0.830148	+	1.81777i	0.0313543	+	0.0686562i	0.924661	−	0.380791i	$-0.124348\pi$
$701$	0.830148	+	1.81777i	0.0313543	+	0.0686562i	−0.893307	+	0.449447i	$0.851621\pi$
$702$	−6.51104	−	14.2572i	−0.245743	−	0.538103i
$703$	0.317613	+	2.20905i	0.0119790	+	0.0833157i
$704$	4.78024	+	3.07208i	0.180162	+	0.115783i
$705$	−0.125310	+	0.0367944i	−0.00471945	+	0.00138576i
$706$	−3.69248	+	25.6818i	−0.138968	+	0.966547i
$707$	9.42926	−	10.8819i	0.354624	−	0.409258i
$708$	3.93910	−	2.53151i	0.148040	−	0.0951398i
$709$	−14.7830	−	17.0605i	−0.555187	−	0.640720i	0.406896	−	0.913474i	$-0.366611\pi$
$709$	−14.7830	−	17.0605i	−0.555187	−	0.640720i	−0.962084	+	0.272754i	$0.912066\pi$
$710$	−0.218957	−	0.0642915i	−0.00821731	−	0.00241282i
$711$	−7.13474	+	15.6229i	−0.267574	+	0.585904i
$712$	−1.96996			−0.0738275
$713$	−22.2166	−	23.7557i	−0.832019	−	0.889657i
$714$	−0.373990			−0.0139962
$715$	0.510777	−	1.11845i	0.0191020	−	0.0418275i
$716$	−15.6404	−	4.59242i	−0.584508	−	0.171627i
$717$	−1.20244	−	1.38769i	−0.0449059	−	0.0518241i
$718$	−6.09194	+	3.91505i	−0.227349	+	0.146108i
$719$	−27.6395	+	31.8977i	−1.03078	+	1.18958i	−0.0491477	+	0.998792i	$0.515651\pi$
$719$	−27.6395	+	31.8977i	−1.03078	+	1.18958i	−0.981631	+	0.190790i	$0.938895\pi$
$720$	−0.0142302	+	0.0989735i	−0.000530330	+	0.00368852i
$721$	4.13121	−	1.21303i	0.153854	−	0.0451757i
$722$	15.2837	+	9.82224i	0.568800	+	0.365546i
$723$	0.354356	+	2.46460i	0.0131786	+	0.0916594i
$724$	6.13242	+	13.4281i	0.227910	+	0.499052i
$725$	−14.9059	−	32.6394i	−0.553591	−	1.21220i
$726$	1.35018	+	9.39068i	0.0501097	+	0.348521i
$727$	−19.3416	−	12.4301i	−0.717340	−	0.461006i	0.130371	−	0.991465i	$-0.458383\pi$
$727$	−19.3416	−	12.4301i	−0.717340	−	0.461006i	−0.847711	+	0.530459i	$0.822020\pi$
$728$	−5.81675	+	1.70795i	−0.215583	+	0.0633009i
$729$	2.39929	−	16.6875i	0.0888627	−	0.618054i
$730$	0.317011	−	0.365850i	0.0117331	−	0.0135407i
$731$	2.56039	−	1.64546i	0.0946993	−	0.0608596i
$732$	3.99880	+	4.61486i	0.147800	+	0.170570i
$733$	−48.7757	−	14.3218i	−1.80157	−	0.528989i	−0.803751	−	0.594965i	$-0.797166\pi$
$733$	−48.7757	−	14.3218i	−1.80157	−	0.528989i	−0.997821	+	0.0659759i	$0.978984\pi$
$734$	8.00441	−	17.5272i	0.295448	−	0.646941i
$735$	−0.0159069			−0.000586735
$736$	−0.501994	+	4.76949i	−0.0185037	+	0.175806i
$737$	53.3590			1.96550
$738$	5.88755	−	12.8919i	0.216724	−	0.474558i
$739$	36.5339	+	10.7273i	1.34392	+	0.394611i	0.873067	−	0.487600i	$-0.162127\pi$
$739$	36.5339	+	10.7273i	1.34392	+	0.394611i	0.470855	+	0.882211i	$0.343946\pi$
$740$	0.0571824	+	0.0659921i	0.00210207	+	0.00242592i
$741$	2.07341	−	1.33250i	0.0761685	−	0.0489505i
$742$	2.97946	−	3.43848i	0.109379	−	0.126231i
$743$	2.70607	−	18.8211i	0.0992761	−	0.690480i	−0.878023	−	0.478618i	$-0.841138\pi$
$743$	2.70607	−	18.8211i	0.0992761	−	0.690480i	0.977299	−	0.211863i	$-0.0679530\pi$
$744$	−2.90001	+	0.851520i	−0.106320	+	0.0312183i
$745$	0.509476	+	0.327420i	0.0186657	+	0.0119957i
$746$	−4.32054	−	30.0500i	−0.158186	−	1.10021i
$747$	−20.9902	−	45.9621i	−0.767991	−	1.68167i
$748$	1.98093	+	4.33762i	0.0724298	+	0.158599i
$749$	−2.43169	−	16.9128i	−0.0888519	−	0.617979i
$750$	−0.133800	−	0.0859882i	−0.00488569	−	0.00313984i
$751$	23.9216	−	7.02403i	0.872913	−	0.256310i	0.185559	−	0.982633i	$-0.440590\pi$
$751$	23.9216	−	7.02403i	0.872913	−	0.256310i	0.687354	+	0.726323i	$0.258772\pi$
$752$	1.16845	−	8.12673i	0.0426089	−	0.296351i
$753$	−6.59755	+	7.61398i	−0.240428	+	0.277469i
$754$	36.6085	−	23.5269i	1.33320	−	0.856798i
$755$	−0.168884	−	0.194903i	−0.00614633	−	0.00709324i
$756$	2.48068	+	0.728395i	0.0902216	+	0.0264915i
$757$	−12.4217	+	27.1997i	−0.451474	+	0.988590i	0.537875	+	0.843025i	$0.319227\pi$
$757$	−12.4217	+	27.1997i	−0.451474	+	0.988590i	−0.989349	+	0.145565i	$0.953500\pi$
$758$	−1.16942			−0.0424752
$759$	−9.96035	+	6.94864i	−0.361538	+	0.252220i
$760$	−0.0325619			−0.00118115
$761$	−3.14288	+	6.88195i	−0.113929	+	0.249470i	−0.958004	−	0.286756i	$-0.907423\pi$
$761$	−3.14288	+	6.88195i	−0.113929	+	0.249470i	0.844074	+	0.536226i	$0.180151\pi$
$762$	1.77306	+	0.520618i	0.0642312	+	0.0188600i
$763$	−3.82931	−	4.41926i	−0.138630	−	0.159988i
$764$	8.58758	−	5.51890i	0.310688	−	0.199667i
$765$	−0.0549507	+	0.0634165i	−0.00198675	+	0.00229283i
$766$	0.340237	−	2.36640i	0.0122933	−	0.0855015i
$767$	61.1157	−	17.9452i	2.20676	−	0.647964i
$768$	0.374908	+	0.240938i	0.0135283	+	0.00869412i
$769$	4.26075	+	29.6342i	0.153647	+	1.06863i	0.910041	+	0.414519i	$0.136050\pi$
$769$	4.26075	+	29.6342i	0.153647	+	1.06863i	−0.756394	+	0.654116i	$0.773041\pi$
$770$	0.0842545	+	0.184492i	0.00303632	+	0.00664862i
$771$	−1.40375	−	3.07378i	−0.0505548	−	0.110700i
$772$	−0.308338	−	2.14454i	−0.0110973	−	0.0771837i
$773$	−33.6421	−	21.6205i	−1.21002	−	0.777635i	−0.229361	−	0.973342i	$-0.573663\pi$
$773$	−33.6421	−	21.6205i	−1.21002	−	0.777635i	−0.980662	+	0.195707i	$0.937300\pi$
$774$	−9.74837	+	2.86238i	−0.350398	+	0.102886i
$775$	−4.82470	+	33.5565i	−0.173308	+	1.20539i
$776$	2.66386	−	3.07426i	0.0956270	−	0.110359i
$777$	0.917171	−	0.589430i	0.0329033	−	0.0211457i
$778$	15.6415	+	18.0513i	0.560776	+	0.647170i
$779$	4.42835	+	1.30028i	0.158662	+	0.0465874i
$780$	0.0400595	−	0.0877181i	0.00143436	−	0.00314081i
$781$	36.3289			1.29995
$782$	−2.51832	+	3.13938i	−0.0900551	+	0.112264i
$783$	−18.5587			−0.663232
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	−0.449262	−	0.131915i	−0.0160349	−	0.00470826i
$786$	0.470787	+	0.543318i	0.0167924	+	0.0193795i
$787$	44.1792	−	28.3922i	1.57482	−	1.01207i	0.597095	−	0.802171i	$-0.296322\pi$
$787$	44.1792	−	28.3922i	1.57482	−	1.01207i	0.977722	−	0.209903i	$-0.0673147\pi$
$788$	7.23547	−	8.35017i	0.257753	−	0.297463i
$789$	−0.0179128	+	0.124586i	−0.000637711	+	0.00443538i
$790$	−0.209967	+	0.0616520i	−0.00747030	+	0.00219348i
$791$	5.93713	+	3.81556i	0.211100	+	0.135666i
$792$	−2.26541	−	15.7563i	−0.0804979	−	0.559876i
$793$	34.5067	+	75.5592i	1.22537	+	2.68319i
$794$	−1.57486	−	3.44846i	−0.0558896	−	0.122381i
$795$	0.0102997	+	0.0716359i	0.000365292	+	0.00254066i
$796$	−7.86964	−	5.05751i	−0.278932	−	0.179259i
$797$	4.62323	−	1.35750i	0.163763	−	0.0480853i	−0.198823	−	0.980035i	$-0.563712\pi$
$797$	4.62323	−	1.35750i	0.163763	−	0.0480853i	0.362586	+	0.931950i	$0.381894\pi$
$798$	−0.0578588	+	0.402417i	−0.00204818	+	0.0142454i
$799$	4.51202	−	5.20714i	0.159624	−	0.184216i
$800$	4.20520	−	2.70252i	0.148676	−	0.0955483i
$801$	3.61394	+	4.17071i	0.127692	+	0.147365i
$802$	14.5507	+	4.27246i	0.513802	+	0.150866i
$803$	−32.0142	+	70.1014i	−1.12976	+	2.47382i
$804$	4.18487			0.147589
$805$	−0.107112	+	0.133527i	−0.00377519	+	0.00470622i
$806$	−41.1149			−1.44821
$807$	−1.14949	+	2.51702i	−0.0404638	+	0.0886034i
$808$	−13.8156	−	4.05663i	−0.486032	−	0.142712i
$809$	−12.4191	−	14.3324i	−0.436633	−	0.503901i	0.494199	−	0.869349i	$-0.335461\pi$
$809$	−12.4191	−	14.3324i	−0.436633	−	0.503901i	−0.930832	+	0.365447i	$0.880916\pi$
$810$	0.217757	−	0.139944i	0.00765119	−	0.00491712i
$811$	2.95590	−	3.41129i	0.103796	−	0.119787i	−0.701475	−	0.712694i	$-0.747475\pi$
$811$	2.95590	−	3.41129i	0.103796	−	0.119787i	0.805270	+	0.592908i	$0.202020\pi$
$812$	−1.02157	+	7.10516i	−0.0358500	+	0.249342i
$813$	−8.34257	+	2.44960i	−0.292587	+	0.0859112i
$814$	−11.6943	−	7.51550i	−0.409887	−	0.263418i
$815$	0.0946649	+	0.658409i	0.00331597	+	0.0230631i
$816$	0.155361	+	0.340193i	0.00543873	+	0.0119091i
$817$	−1.37442	−	3.00957i	−0.0480850	−	0.105291i
$818$	−2.52244	−	17.5440i	−0.0881951	−	0.613410i
$819$	14.2869	+	9.18166i	0.499226	+	0.320833i
$820$	0.173264	−	0.0508748i	0.00605063	−	0.00177663i
$821$	6.08020	−	42.2887i	0.212200	−	1.47589i	−0.553586	−	0.832792i	$-0.686741\pi$
$821$	6.08020	−	42.2887i	0.212200	−	1.47589i	0.765787	−	0.643095i	$-0.222350\pi$
$822$	−5.61521	+	6.48030i	−0.195853	+	0.226026i
$823$	7.80423	−	5.01547i	0.272038	−	0.174828i	−0.397508	−	0.917599i	$-0.630125\pi$
$823$	7.80423	−	5.01547i	0.272038	−	0.174828i	0.669546	+	0.742770i	$0.266489\pi$
$824$	−2.81958	−	3.25397i	−0.0982247	−	0.113357i
$825$	12.1457	+	3.56629i	0.422858	+	0.124162i
$826$	−4.36471	+	9.55737i	−0.151868	+	0.332544i
$827$	24.6491			0.857132			0.428566	−	0.903510i	$-0.359019\pi$
$827$	24.6491			0.857132			0.428566	+	0.903510i	$0.359019\pi$
$828$	11.0186	−	7.68693i	0.382924	−	0.267139i
$829$	50.8574			1.76635			0.883176	−	0.469042i	$-0.155401\pi$
$829$	50.8574			1.76635			0.883176	+	0.469042i	$0.155401\pi$
$830$	0.267442	−	0.585617i	0.00928306	−	0.0203271i
$831$	−10.5879	−	3.10889i	−0.367291	−	0.107846i
$832$	3.96997	+	4.58159i	0.137634	+	0.158838i
$833$	0.705975	−	0.453703i	0.0244606	−	0.0157199i
$834$	6.32449	−	7.29885i	0.218999	−	0.252738i
$835$	0.00116963	−	0.00813495i	4.04767e−5	−	0.000281522i
$836$	4.97379	−	1.46044i	0.172022	−	0.0505102i
$837$	14.7509	+	9.47980i	0.509864	+	0.327670i
$838$	0.344172	+	2.39377i	0.0118892	+	0.0826913i
$839$	15.6342	+	34.2342i	0.539754	+	1.18190i	0.961405	+	0.275137i	$0.0887234\pi$
$839$	15.6342	+	34.2342i	0.539754	+	1.18190i	−0.421651	+	0.906758i	$0.638549\pi$
$840$	0.00660796	+	0.0144694i	0.000227996	+	0.000499242i
$841$	−3.20591	−	22.2976i	−0.110548	−	0.768881i
$842$	−21.2001	−	13.6245i	−0.730602	−	0.469530i
$843$	−8.89007	+	2.61036i	−0.306190	+	0.0899056i
$844$	−0.736770	+	5.12434i	−0.0253607	+	0.176387i
$845$	0.555176	−	0.640707i	0.0190986	−	0.0220410i
$846$	−19.3491	+	12.4349i	−0.665235	+	0.427520i
$847$	−13.9409	−	16.0887i	−0.479016	−	0.552814i
$848$	−4.36546	−	1.28182i	−0.149911	−	0.0440177i
$849$	2.84319	−	6.22571i	0.0975779	−	0.213666i
$850$	4.19490			0.143884
$851$	1.22807	−	11.6680i	0.0420978	−	0.399975i
$852$	2.84922			0.0976127
$853$	2.92830	−	6.41208i	0.100263	−	0.219546i	−0.852853	−	0.522152i	$-0.825129\pi$
$853$	2.92830	−	6.41208i	0.100263	−	0.219546i	0.953116	+	0.302606i	$0.0978567\pi$
$854$	−13.1470	−	3.86029i	−0.449880	−	0.132097i
$855$	0.0597356	+	0.0689385i	0.00204291	+	0.00235765i
$856$	−14.3742	+	9.23775i	−0.491301	+	0.315740i
$857$	7.94450	−	9.16844i	0.271379	−	0.313188i	−0.603659	−	0.797243i	$-0.706291\pi$
$857$	7.94450	−	9.16844i	0.271379	−	0.313188i	0.875038	+	0.484055i	$0.160836\pi$
$858$	−2.18479	+	15.1955i	−0.0745874	+	0.518767i
$859$	−45.4362	+	13.3413i	−1.55026	+	0.455199i	−0.941180	−	0.337906i	$-0.890281\pi$
$859$	−45.4362	+	13.3413i	−1.55026	+	0.455199i	−0.609085	+	0.793105i	$0.708463\pi$
$860$	−0.108901	−	0.0699863i	−0.00371348	−	0.00238651i
$861$	−0.320867	−	2.23168i	−0.0109351	−	0.0760555i
$862$	−4.11048	−	9.00069i	−0.140003	−	0.306565i
$863$	−8.68662	−	19.0210i	−0.295696	−	0.647484i	0.702224	−	0.711957i	$-0.252191\pi$
$863$	−8.68662	−	19.0210i	−0.295696	−	0.647484i	−0.997919	+	0.0644727i	$0.979463\pi$
$864$	−0.367942	−	2.55910i	−0.0125177	−	0.0870622i
$865$	−0.439634	−	0.282535i	−0.0149480	−	0.00960649i
$866$	4.85489	−	1.42552i	0.164976	−	0.0484412i
$867$	1.03353	−	7.18834i	0.0351004	−	0.244129i
$868$	4.44129	−	5.12553i	0.150747	−	0.173972i
$869$	29.3070	−	18.8345i	0.994173	−	0.638916i
$870$	−0.0747741	−	0.0862939i	−0.00253508	−	0.00292564i
$871$	54.6216	+	16.0384i	1.85078	+	0.543439i
$872$	−2.42915	+	5.31909i	−0.0822613	+	0.180127i
$873$	−11.3956			−0.385682
$874$	2.98841	+	3.19543i	0.101084	+	0.108087i
$875$	0.356889			0.0120650
$876$	−2.51083	+	5.49795i	−0.0848330	+	0.185758i
$877$	−23.4561	−	6.88733i	−0.792055	−	0.232568i	−0.139413	−	0.990234i	$-0.544522\pi$
$877$	−23.4561	−	6.88733i	−0.792055	−	0.232568i	−0.652643	+	0.757666i	$0.726340\pi$
$878$	−7.55055	−	8.71380i	−0.254819	−	0.294076i
$879$	8.57135	−	5.50847i	0.289104	−	0.185796i
$880$	0.132819	−	0.153281i	0.00447733	−	0.00516711i
$881$	−5.01368	+	34.8709i	−0.168915	+	1.17483i	0.712217	+	0.701960i	$0.247691\pi$
$881$	−5.01368	+	34.8709i	−0.168915	+	1.17483i	−0.881132	+	0.472871i	$0.843218\pi$
$882$	−2.68792	+	0.789244i	−0.0905069	+	0.0265752i
$883$	−33.0010	−	21.2084i	−1.11057	−	0.713721i	−0.149154	−	0.988814i	$-0.547655\pi$
$883$	−33.0010	−	21.2084i	−1.11057	−	0.713721i	−0.961418	+	0.275093i	$0.911291\pi$
$884$	0.724021	+	5.03568i	0.0243515	+	0.169368i
$885$	−0.0694289	−	0.152028i	−0.00233383	−	0.00511037i
$886$	−2.77182	−	6.06944i	−0.0931211	−	0.203907i
$887$	4.33166	+	30.1273i	0.145443	+	1.01158i	0.923559	+	0.383456i	$0.125266\pi$
$887$	4.33166	+	30.1273i	0.145443	+	1.01158i	−0.778116	+	0.628120i	$0.783825\pi$
$888$	−0.917171	−	0.589430i	−0.0307782	−	0.0197800i
$889$	−3.97856	+	1.16821i	−0.133437	+	0.0391805i
$890$	−0.0100068	+	0.0695990i	−0.000335429	+	0.00233296i
$891$	−26.9854	+	31.1428i	−0.904045	+	1.04332i
$892$	10.7512	−	6.90936i	0.359976	−	0.231342i
$893$	−4.90490	−	5.66055i	−0.164136	−	0.189423i
$894$	−7.25517	−	2.13031i	−0.242649	−	0.0712482i
$895$	−0.241699	+	0.529247i	−0.00807911	+	0.0176908i
$896$	−1.00000			−0.0334077
$897$	−12.2846	+	4.11923i	−0.410172	+	0.137537i
$898$	−12.7971			−0.427046
$899$	−20.2237	+	44.2836i	−0.674497	+	1.47694i
$900$	−13.4362	−	3.94521i	−0.447872	−	0.131507i
$901$	−2.50035	−	2.88555i	−0.0832986	−	0.0961317i
$902$	−24.1840	+	15.5421i	−0.805239	+	0.517496i
$903$	−1.05843	+	1.22149i	−0.0352224	+	0.0406488i
$904$	1.00438	−	6.98565i	0.0334053	−	0.232339i
$905$	0.505568	−	0.148448i	0.0168056	−	0.00493458i
$906$	2.70880	+	1.74084i	0.0899937	+	0.0578355i
$907$	−4.07715	−	28.3572i	−0.135379	−	0.941585i	−0.938380	−	0.345606i	$-0.887673\pi$
$907$	−4.07715	−	28.3572i	−0.135379	−	0.941585i	0.803000	−	0.595979i	$-0.203236\pi$
$908$	−5.59415	−	12.2495i	−0.185648	−	0.406513i
$909$	16.7566	+	36.6918i	0.555780	+	1.21699i
$910$	0.0307947	+	0.214182i	0.00102084	+	0.00710007i
$911$	−15.7251	−	10.1059i	−0.520995	−	0.334823i	0.253571	−	0.967317i	$-0.418395\pi$
$911$	−15.7251	−	10.1059i	−0.520995	−	0.334823i	−0.774565	+	0.632494i	$0.782031\pi$
$912$	0.390087	−	0.114540i	0.0129171	−	0.00379279i
$913$	−14.5859	+	101.447i	−0.482723	+	3.35741i
$914$	−11.8010	+	13.6191i	−0.390342	+	0.450479i
$915$	0.183356	−	0.117836i	0.00606157	−	0.00389553i
$916$	4.07045	+	4.69755i	0.134491	+	0.155211i
$917$	−1.54782	−	0.454481i	−0.0511135	−	0.0150083i
$918$	0.901311	−	1.97360i	0.0297477	−	0.0651383i
$919$	−43.3330			−1.42942			−0.714712	−	0.699419i	$-0.753442\pi$
$919$	−43.3330			−1.42942			−0.714712	+	0.699419i	$0.753442\pi$
$920$	0.165956	+	0.0419631i	0.00547142	+	0.00138348i
$921$	−9.83460			−0.324061
$922$	0.287136	−	0.628740i	0.00945633	−	0.0207065i
$923$	37.1885	+	10.9195i	1.22408	+	0.359421i
$924$	−1.65832	−	1.91381i	−0.0545549	−	0.0629597i
$925$	−10.2876	+	6.61141i	−0.338253	+	0.217382i
$926$	6.73684	−	7.77473i	0.221386	−	0.255493i
$927$	−1.71656	+	11.9390i	−0.0563793	+	0.392127i
$928$	6.88745	−	2.02234i	0.226092	−	0.0663865i
$929$	21.9435	+	14.1022i	0.719943	+	0.462679i	0.848617	−	0.529008i	$-0.177436\pi$
$929$	21.9435	+	14.1022i	0.719943	+	0.462679i	−0.128674	+	0.991687i	$0.541072\pi$
$930$	0.0153531	+	0.106783i	0.000503448	+	0.00350156i
$931$	−0.378970	−	0.829827i	−0.0124202	−	0.0271965i
$932$	−6.74586	−	14.7714i	−0.220968	−	0.483853i
$933$	−0.144982	−	1.00837i	−0.00474649	−	0.0330125i
$934$	−6.19604	−	3.98195i	−0.202741	−	0.130294i
$935$	0.163311	−	0.0479525i	0.00534084	−	0.00156821i
$936$	2.41692	−	16.8101i	0.0789995	−	0.549454i
$937$	1.15588	−	1.33395i	0.0377609	−	0.0435784i	−0.736555	−	0.676378i	$-0.763549\pi$
$937$	1.15588	−	1.33395i	0.0377609	−	0.0435784i	0.774316	+	0.632799i	$0.218094\pi$
$938$	−7.89971	+	5.07684i	−0.257935	+	0.165765i
$939$	2.56829	+	2.96396i	0.0838128	+	0.0967252i
$940$	−0.281183	−	0.0825627i	−0.00917117	−	0.00269290i
$941$	11.6061	−	25.4137i	0.378347	−	0.828464i	−0.620667	−	0.784074i	$-0.713138\pi$
$941$	11.6061	−	25.4137i	0.378347	−	0.828464i	0.999014	−	0.0443903i	$-0.0141345\pi$
$942$	5.84611			0.190477
$943$	−20.8940	−	12.3339i	−0.680403	−	0.401649i
$944$	10.5069			0.341969
$945$	0.0383354	−	0.0839428i	0.00124705	−	0.00273066i
$946$	19.7734	+	5.80599i	0.642888	+	0.188769i
$947$	−7.37603	−	8.51239i	−0.239689	−	0.276616i	0.623142	−	0.782109i	$-0.285856\pi$
$947$	−7.37603	−	8.51239i	−0.239689	−	0.276616i	−0.862830	+	0.505493i	$0.831311\pi$
$948$	2.29851	−	1.47716i	0.0746521	−	0.0479760i
$949$	−53.8424	+	62.1375i	−1.74780	+	2.01707i
$950$	0.648980	−	4.51376i	0.0210557	−	0.146446i
$951$	−0.643431	+	0.188928i	−0.0208647	+	0.00612642i
$952$	−0.705975	−	0.453703i	−0.0228808	−	0.0147046i
$953$	2.20720	+	15.3514i	0.0714983	+	0.497282i	0.993833	+	0.110889i	$0.0353699\pi$
$953$	2.20720	+	15.3514i	0.0714983	+	0.497282i	−0.922334	+	0.386392i	$0.873721\pi$
$954$	5.29474	+	11.5939i	0.171424	+	0.375365i
$955$	−0.151361	−	0.331434i	−0.00489793	−	0.0107250i
$956$	−0.586363	−	4.07824i	−0.0189643	−	0.131900i
$957$	15.2920	+	9.82757i	0.494320	+	0.317680i
$958$	28.8910	−	8.48316i	0.933426	−	0.274079i
$959$	2.73823	−	19.0448i	0.0884221	−	0.614989i
$960$	0.0104168	−	0.0120216i	0.000336201	−	0.000387996i
$961$	12.6155	−	8.10752i	0.406953	−	0.261533i
$962$	−9.71210	−	11.2084i	−0.313131	−	0.361372i
$963$	45.9276	+	13.4855i	1.48000	+	0.434566i
$964$	−2.32099	+	5.08227i	−0.0747542	+	0.163689i
$965$	−0.0773331			−0.00248944
$966$	0.813487	−	1.97641i	0.0261735	−	0.0635900i
$967$	−58.4958			−1.88110			−0.940548	−	0.339660i	$-0.889688\pi$
$967$	−58.4958			−1.88110			−0.940548	+	0.339660i	$0.889688\pi$
$968$	−8.84352	+	19.3646i	−0.284241	+	0.622402i
$969$	0.327359	+	0.0961212i	0.0105163	+	0.00308786i
$970$	−0.0950822	−	0.109731i	−0.00305291	−	0.00352324i
$971$	11.7180	−	7.53069i	0.376048	−	0.241671i	−0.338940	−	0.940808i	$-0.610068\pi$
$971$	11.7180	−	7.53069i	0.376048	−	0.241671i	0.714988	+	0.699137i	$0.246432\pi$
$972$	−7.19568	+	8.30426i	−0.230801	+	0.266359i
$973$	−3.08410	+	21.4504i	−0.0988718	+	0.687669i
$974$	−7.25013	+	2.12883i	−0.232309	+	0.0682121i
$975$	11.3611	+	7.30136i	0.363848	+	0.233831i
$976$	1.95000	+	13.5625i	0.0624178	+	0.434126i
$977$	13.8825	+	30.3984i	0.444140	+	0.972532i	0.990820	+	0.135190i	$0.0431644\pi$
$977$	13.8825	+	30.3984i	0.444140	+	0.972532i	−0.546679	+	0.837342i	$0.684108\pi$
$978$	−3.45009	−	7.55464i	−0.110322	−	0.241571i
$979$	−1.59306	−	11.0800i	−0.0509143	−	0.354117i
$980$	−0.0300272	−	0.0192973i	−0.000959184	−	0.000616430i
$981$	15.7177	−	4.61512i	0.501826	−	0.147349i
$982$	−0.608486	+	4.23211i	−0.0194176	+	0.135052i
$983$	−24.9751	+	28.8227i	−0.796581	+	0.919303i	−0.998189	−	0.0601634i	$-0.980838\pi$
$983$	−24.9751	+	28.8227i	−0.796581	+	0.919303i	0.201608	+	0.979466i	$0.435383\pi$
$984$	−1.89672	+	1.21895i	−0.0604651	+	0.0388586i
$985$	−0.258258	−	0.298046i	−0.00822880	−	0.00949654i
$986$	5.77991	+	1.69714i	0.184070	+	0.0540478i
$987$	−1.51998	+	3.32830i	−0.0483816	+	0.105941i
$988$	5.53045			0.175947
$989$	3.12646	+	17.1099i	0.0994158	+	0.544064i
$990$	−0.568179			−0.0180579
$991$	−13.2892	+	29.0993i	−0.422145	+	0.924369i	0.572391	+	0.819981i	$0.306016\pi$
$991$	−13.2892	+	29.0993i	−0.422145	+	0.924369i	−0.994537	+	0.104389i	$0.966711\pi$
$992$	−6.50732	−	1.91072i	−0.206608	−	0.0606655i
$993$	−7.34266	−	8.47388i	−0.233012	−	0.268911i
$994$	−5.37843	+	3.45651i	−0.170594	+	0.109634i
$995$	−0.218658	+	0.252344i	−0.00693191	+	0.00799985i
$996$	−1.14395	+	7.95636i	−0.0362475	+	0.252107i
$997$	33.6445	−	9.87892i	1.06553	−	0.312868i	0.298455	−	0.954424i	$-0.403529\pi$
$997$	33.6445	−	9.87892i	1.06553	−	0.312868i	0.767077	+	0.641555i	$0.221710\pi$
$998$	0.940854	+	0.604650i	0.0297822	+	0.0191399i
$999$	0.900131	+	6.26055i	0.0284789	+	0.198075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.e.29.3	✓	40
23.2	even	11		7406.2.a.bt.1.11		20
23.4	even	11	inner	322.2.i.e.211.3	yes	40
23.21	odd	22		7406.2.a.bs.1.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.29.3	✓	40	1.1	even	1	trivial
322.2.i.e.211.3	yes	40	23.4	even	11	inner
7406.2.a.bs.1.11		20	23.21	odd	22
7406.2.a.bt.1.11		20	23.2	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.427601 - 0.125555i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.0300272 + 0.0192973i) q^{5} +(0.291841 - 0.336802i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.35668 - 1.51455i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.427601 - 0.125555i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.0300272 + 0.0192973i) q^{5} +(0.291841 - 0.336802i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-2.35668 - 1.51455i) q^{9} +(-0.00507970 - 0.0353301i) q^{10} +(2.36051 + 5.16879i) q^{11} +(0.185131 + 0.405381i) q^{12} +(0.862757 + 6.00061i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(0.0152626 - 0.00448149i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.549556 + 0.634221i) q^{17} +(2.35668 - 1.51455i) q^{18} +(0.597408 + 0.689446i) q^{19} +(0.0342476 + 0.0100560i) q^{20} +(0.185131 - 0.405381i) q^{21} -5.68229 q^{22} +(-2.15628 - 4.28375i) q^{23} -0.445654 q^{24} +(-2.07655 + 4.54700i) q^{25} +(-5.81675 - 1.70795i) q^{26} +(1.69308 + 1.95392i) q^{27} +(0.841254 - 0.540641i) q^{28} +(-4.70073 + 5.42494i) q^{29} +(-0.00226379 + 0.0157450i) q^{30} +(6.50732 - 1.91072i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.360388 - 2.50656i) q^{33} +(-0.348614 - 0.763358i) q^{34} +(-0.0148276 - 0.0324679i) q^{35} +(0.398680 + 2.77288i) q^{36} +(2.05803 + 1.32262i) q^{37} +(-0.875314 + 0.257015i) q^{38} +(0.384491 - 2.67419i) q^{39} +(-0.0233742 + 0.0269753i) q^{40} +(4.25603 - 2.73519i) q^{41} +(0.291841 + 0.336802i) q^{42} +(-3.47983 - 1.02177i) q^{43} +(2.36051 - 5.16879i) q^{44} +0.0999913 q^{45} +(4.79238 - 0.181884i) q^{46} -8.21030 q^{47} +(0.185131 - 0.405381i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-3.27347 - 3.77779i) q^{50} +(0.314620 - 0.202194i) q^{51} +(3.96997 - 4.58159i) q^{52} +(-0.647498 + 4.50345i) q^{53} +(-2.48068 + 0.728395i) q^{54} +(-0.170623 - 0.109653i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-0.168889 - 0.369816i) q^{57} +(-2.98194 - 6.52954i) q^{58} +(-1.49528 - 10.3999i) q^{59} +(-0.0133817 - 0.00859992i) q^{60} +(13.1470 - 3.86029i) q^{61} +(-0.965186 + 6.71301i) q^{62} +(1.83452 - 2.11715i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.141702 - 0.163533i) q^{65} +(2.42975 + 0.713440i) q^{66} +(3.90092 - 8.54181i) q^{67} +0.839195 q^{68} +(0.384180 + 2.10247i) q^{69} +0.0356934 q^{70} +(2.65590 - 5.81560i) q^{71} +(-2.68792 - 0.789244i) q^{72} +(8.88150 + 10.2498i) q^{73} +(-2.05803 + 1.32262i) q^{74} +(1.45883 - 1.68358i) q^{75} +(0.129829 - 0.902982i) q^{76} +(-5.45211 + 1.60089i) q^{77} +(2.27281 + 1.46064i) q^{78} +(-0.872513 - 6.06846i) q^{79} +(-0.0148276 - 0.0324679i) q^{80} +(3.01258 + 6.59663i) q^{81} +(0.719993 + 5.00766i) q^{82} +(15.1735 + 9.75145i) q^{83} +(-0.427601 + 0.125555i) q^{84} +(0.00426286 - 0.0296488i) q^{85} +(2.37501 - 2.74090i) q^{86} +(2.69117 - 1.72951i) q^{87} +(3.72111 + 4.29439i) q^{88} +(-1.89017 - 0.555003i) q^{89} +(-0.0415379 + 0.0909552i) q^{90} -6.06231 q^{91} +(-1.82538 + 4.43486i) q^{92} -3.02244 q^{93} +(3.41068 - 7.46835i) q^{94} +(-0.0312429 - 0.00917375i) q^{95} +(0.291841 + 0.336802i) q^{96} +(3.42207 - 2.19923i) q^{97} +(0.654861 - 0.755750i) q^{98} +(2.26541 - 15.7563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Introduction

L-functions

Modular forms

Varieties

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