LMFDB - Embedded newform 322.2.i.a.211.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	322.211
Dual form			322.2.i.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{2} +(-2.57385 + 0.755750i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.0741615 + 0.0476607i) q^{5} +(1.75667 + 2.02730i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(3.52977 - 2.26844i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{2} +(-2.57385 + 0.755750i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.0741615 + 0.0476607i) q^{5} +(1.75667 + 2.02730i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(3.52977 - 2.26844i) q^{9} +(0.0125459 - 0.0872586i) q^{10} +(-0.716476 + 1.56886i) q^{11} +(1.11435 - 2.44009i) q^{12} +(0.695368 - 4.83639i) q^{13} +(0.841254 - 0.540641i) q^{14} +(-0.226900 - 0.0666238i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-3.93020 - 4.53569i) q^{17} +(-3.52977 - 2.26844i) q^{18} +(0.260554 - 0.300696i) q^{19} +(-0.0845850 + 0.0248364i) q^{20} +(-1.11435 - 2.44009i) q^{21} +1.72472 q^{22} +(1.72750 - 4.47389i) q^{23} -2.68251 q^{24} +(-2.07385 - 4.54109i) q^{25} +(-4.68820 + 1.37658i) q^{26} +(-2.10070 + 2.42434i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(1.83228 + 2.11456i) q^{29} +(0.0336545 + 0.234072i) q^{30} +(-2.13436 - 0.626704i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.658432 - 4.57949i) q^{33} +(-2.49315 + 5.45923i) q^{34} +(-0.0366213 + 0.0801894i) q^{35} +(-0.597131 + 4.15314i) q^{36} +(7.46708 - 4.79880i) q^{37} +(-0.381761 - 0.112095i) q^{38} +(1.86533 + 12.9736i) q^{39} +(0.0577299 + 0.0666238i) q^{40} +(-6.22653 - 4.00155i) q^{41} +(-1.75667 + 2.02730i) q^{42} +(8.04733 - 2.36291i) q^{43} +(-0.716476 - 1.56886i) q^{44} +0.369889 q^{45} +(-4.78723 + 0.287130i) q^{46} -3.30416 q^{47} +(1.11435 + 2.44009i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(-3.26921 + 3.77287i) q^{50} +(13.5436 + 8.70393i) q^{51} +(3.19973 + 3.69269i) q^{52} +(1.30473 + 9.07459i) q^{53} +(3.07792 + 0.903759i) q^{54} +(-0.127908 + 0.0822015i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(-0.443376 + 0.970858i) q^{57} +(1.16232 - 2.54512i) q^{58} +(-0.378794 + 2.63457i) q^{59} +(0.198939 - 0.127850i) q^{60} +(-2.20579 - 0.647679i) q^{61} +(0.316574 + 2.20182i) q^{62} +(2.74769 + 3.17101i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.282075 - 0.325532i) q^{65} +(-4.43918 + 1.30346i) q^{66} +(0.401608 + 0.879398i) q^{67} +6.00158 q^{68} +(-1.06519 + 12.8207i) q^{69} +0.0881559 q^{70} +(-5.55888 - 12.1722i) q^{71} +(4.02588 - 1.18211i) q^{72} +(6.97403 - 8.04846i) q^{73} +(-7.46708 - 4.79880i) q^{74} +(8.76969 + 10.1208i) q^{75} +(0.0566239 + 0.393828i) q^{76} +(-1.65486 - 0.485911i) q^{77} +(11.0264 - 7.08621i) q^{78} +(-0.363404 + 2.52753i) q^{79} +(0.0366213 - 0.0801894i) q^{80} +(-1.65436 + 3.62254i) q^{81} +(-1.05334 + 7.32616i) q^{82} +(-6.48421 + 4.16715i) q^{83} +(2.57385 + 0.755750i) q^{84} +(-0.0752952 - 0.523690i) q^{85} +(-5.49236 - 6.33852i) q^{86} +(-6.31408 - 4.05782i) q^{87} +(-1.12945 + 1.30346i) q^{88} +(-2.88384 + 0.846773i) q^{89} +(-0.153657 - 0.336462i) q^{90} +4.88612 q^{91} +(2.24987 + 4.23534i) q^{92} +5.96714 q^{93} +(1.37260 + 3.00557i) q^{94} +(0.0336545 - 0.00988184i) q^{95} +(1.75667 - 2.02730i) q^{96} +(2.35857 + 1.51576i) q^{97} +(0.654861 + 0.755750i) q^{98} +(1.02989 + 7.16301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9} - 5 q^{10} - 11 q^{11} - 3 q^{12} + 10 q^{13} - q^{14} - 7 q^{15} - q^{16} + q^{17} - 16 q^{18} + 3 q^{19} - 6 q^{20} + 3 q^{21} + 12 q^{23} - 8 q^{24} + 2 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} - 5 q^{31} + q^{32} - 11 q^{33} - 12 q^{34} + 6 q^{35} - 6 q^{36} + 27 q^{37} - 3 q^{38} + 8 q^{39} - 5 q^{40} - 12 q^{41} - 3 q^{42} + 38 q^{43} - 11 q^{44} + 8 q^{45} + 10 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 13 q^{50} + 36 q^{51} - q^{52} - 16 q^{53} + 9 q^{54} - 11 q^{55} - q^{56} - 13 q^{57} + 9 q^{58} - 5 q^{59} - 7 q^{60} - 26 q^{61} + 5 q^{62} + 6 q^{63} - q^{64} + 5 q^{65} - 11 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 6 q^{70} + q^{71} + 6 q^{72} + 9 q^{73} - 27 q^{74} + 17 q^{75} - 8 q^{76} - 11 q^{77} + 25 q^{78} - 50 q^{79} - 6 q^{80} + 2 q^{81} + 23 q^{82} - 29 q^{83} + 3 q^{84} + 28 q^{85} + 17 q^{86} - 16 q^{87} + 11 q^{88} + 7 q^{89} - 19 q^{90} + 12 q^{91} + 23 q^{92} + 40 q^{93} + 20 q^{94} - 4 q^{95} + 3 q^{96} + 12 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9 - 5 * q^10 - 11 * q^11 - 3 * q^12 + 10 * q^13 - q^14 - 7 * q^15 - q^16 + q^17 - 16 * q^18 + 3 * q^19 - 6 * q^20 + 3 * q^21 + 12 * q^23 - 8 * q^24 + 2 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 2 * q^29 - 4 * q^30 - 5 * q^31 + q^32 - 11 * q^33 - 12 * q^34 + 6 * q^35 - 6 * q^36 + 27 * q^37 - 3 * q^38 + 8 * q^39 - 5 * q^40 - 12 * q^41 - 3 * q^42 + 38 * q^43 - 11 * q^44 + 8 * q^45 + 10 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 13 * q^50 + 36 * q^51 - q^52 - 16 * q^53 + 9 * q^54 - 11 * q^55 - q^56 - 13 * q^57 + 9 * q^58 - 5 * q^59 - 7 * q^60 - 26 * q^61 + 5 * q^62 + 6 * q^63 - q^64 + 5 * q^65 - 11 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 6 * q^70 + q^71 + 6 * q^72 + 9 * q^73 - 27 * q^74 + 17 * q^75 - 8 * q^76 - 11 * q^77 + 25 * q^78 - 50 * q^79 - 6 * q^80 + 2 * q^81 + 23 * q^82 - 29 * q^83 + 3 * q^84 + 28 * q^85 + 17 * q^86 - 16 * q^87 + 11 * q^88 + 7 * q^89 - 19 * q^90 + 12 * q^91 + 23 * q^92 + 40 * q^93 + 20 * q^94 - 4 * q^95 + 3 * q^96 + 12 * q^97 + q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$

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
$3$	−2.57385	+	0.755750i	−1.48601	+	0.436332i	−0.921266	−	0.388933i	$-0.872844\pi$
$3$	−2.57385	+	0.755750i	−1.48601	+	0.436332i	−0.564745	+	0.825265i	$0.691026\pi$
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	0.0741615	+	0.0476607i	0.0331660	+	0.0213145i	0.557119	−	0.830433i	$-0.311907\pi$
$5$	0.0741615	+	0.0476607i	0.0331660	+	0.0213145i	−0.523953	+	0.851747i	$0.675543\pi$
$6$	1.75667	+	2.02730i	0.717157	+	0.827643i
$7$	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
$9$	3.52977	−	2.26844i	1.17659	−	0.756148i
$10$	0.0125459	−	0.0872586i	0.00396736	−	0.0275936i
$11$	−0.716476	+	1.56886i	−0.216026	+	0.473030i	−0.986358	−	0.164612i	$-0.947363\pi$
$11$	−0.716476	+	1.56886i	−0.216026	+	0.473030i	0.770333	+	0.637642i	$0.220090\pi$
$12$	1.11435	−	2.44009i	0.321686	−	0.704395i
$13$	0.695368	−	4.83639i	0.192860	−	1.34137i	−0.631530	−	0.775351i	$-0.717573\pi$
$13$	0.695368	−	4.83639i	0.192860	−	1.34137i	0.824390	−	0.566022i	$-0.191518\pi$
$14$	0.841254	−	0.540641i	0.224834	−	0.144492i
$15$	−0.226900	−	0.0666238i	−0.0585853	−	0.0172022i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−3.93020	−	4.53569i	−0.953214	−	1.10007i	−0.994893	−	0.100936i	$-0.967816\pi$
$17$	−3.93020	−	4.53569i	−0.953214	−	1.10007i	0.0416792	−	0.999131i	$-0.486729\pi$
$18$	−3.52977	−	2.26844i	−0.831974	−	0.534678i
$19$	0.260554	−	0.300696i	0.0597753	−	0.0689843i	−0.725074	−	0.688671i	$-0.758195\pi$
$19$	0.260554	−	0.300696i	0.0597753	−	0.0689843i	0.784850	+	0.619686i	$0.212740\pi$
$20$	−0.0845850	+	0.0248364i	−0.0189138	+	0.00555359i
$21$	−1.11435	−	2.44009i	−0.243172	−	0.532472i
$22$	1.72472			0.367712
$23$	1.72750	−	4.47389i	0.360209	−	0.932871i
$23$	1.72750	−	4.47389i	0.360209	−	0.932871i
$24$	−2.68251			−0.547564
$25$	−2.07385	−	4.54109i	−0.414769	−	0.908218i
$26$	−4.68820	+	1.37658i	−0.919432	+	0.269970i
$27$	−2.10070	+	2.42434i	−0.404280	+	0.466564i
$28$	−0.841254	−	0.540641i	−0.158982	−	0.102172i
$29$	1.83228	+	2.11456i	0.340246	+	0.392664i	0.899925	−	0.436045i	$-0.143621\pi$
$29$	1.83228	+	2.11456i	0.340246	+	0.392664i	−0.559679	+	0.828709i	$0.689076\pi$
$30$	0.0336545	+	0.234072i	0.00614443	+	0.0427355i
$31$	−2.13436	−	0.626704i	−0.383342	−	0.112559i	0.0843832	−	0.996433i	$-0.473108\pi$
$31$	−2.13436	−	0.626704i	−0.383342	−	0.112559i	−0.467725	+	0.883874i	$0.654926\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	0.658432	−	4.57949i	0.114618	−	0.797187i
$34$	−2.49315	+	5.45923i	−0.427571	+	0.936250i
$35$	−0.0366213	+	0.0801894i	−0.00619013	+	0.0135545i
$36$	−0.597131	+	4.15314i	−0.0995218	+	0.692189i
$37$	7.46708	−	4.79880i	1.22758	−	0.788918i	0.244068	−	0.969758i	$-0.421518\pi$
$37$	7.46708	−	4.79880i	1.22758	−	0.788918i	0.983513	+	0.180840i	$0.0578815\pi$
$38$	−0.381761	−	0.112095i	−0.0619297	−	0.0181842i
$39$	1.86533	+	12.9736i	0.298692	+	2.07745i
$40$	0.0577299	+	0.0666238i	0.00912789	+	0.0105341i
$41$	−6.22653	−	4.00155i	−0.972421	−	0.624937i	−0.0450121	−	0.998986i	$-0.514333\pi$
$41$	−6.22653	−	4.00155i	−0.972421	−	0.624937i	−0.927409	+	0.374049i	$0.877969\pi$
$42$	−1.75667	+	2.02730i	−0.271060	+	0.312820i
$43$	8.04733	−	2.36291i	1.22721	−	0.360340i	0.397012	−	0.917813i	$-0.370047\pi$
$43$	8.04733	−	2.36291i	1.22721	−	0.360340i	0.830195	+	0.557473i	$0.188229\pi$
$44$	−0.716476	−	1.56886i	−0.108013	−	0.236515i
$45$	0.369889			0.0551397
$46$	−4.78723	+	0.287130i	−0.705838	+	0.0423350i
$47$	−3.30416			−0.481962			−0.240981	−	0.970530i	$-0.577469\pi$
$47$	−3.30416			−0.481962			−0.240981	+	0.970530i	$0.577469\pi$
$48$	1.11435	+	2.44009i	0.160843	+	0.352197i
$49$	−0.959493	+	0.281733i	−0.137070	+	0.0402475i
$50$	−3.26921	+	3.77287i	−0.462337	+	0.533565i
$51$	13.5436	+	8.70393i	1.89648	+	1.21879i
$52$	3.19973	+	3.69269i	0.443723	+	0.512083i
$53$	1.30473	+	9.07459i	0.179218	+	1.24649i	0.858577	+	0.512685i	$0.171349\pi$
$53$	1.30473	+	9.07459i	0.179218	+	1.24649i	−0.679358	+	0.733807i	$0.737742\pi$
$54$	3.07792	+	0.903759i	0.418852	+	0.122986i
$55$	−0.127908	+	0.0822015i	−0.0172471	+	0.0110841i
$56$	−0.142315	+	0.989821i	−0.0190176	+	0.132270i
$57$	−0.443376	+	0.970858i	−0.0587266	+	0.128593i
$58$	1.16232	−	2.54512i	0.152620	−	0.334191i
$59$	−0.378794	+	2.63457i	−0.0493147	+	0.342992i	0.950194	+	0.311658i	$0.100884\pi$
$59$	−0.378794	+	2.63457i	−0.0493147	+	0.342992i	−0.999509	+	0.0313333i	$0.990025\pi$
$60$	0.198939	−	0.127850i	0.0256829	−	0.0165054i
$61$	−2.20579	−	0.647679i	−0.282423	−	0.0829268i	0.137453	−	0.990508i	$-0.456108\pi$
$61$	−2.20579	−	0.647679i	−0.282423	−	0.0829268i	−0.419876	+	0.907581i	$0.637926\pi$
$62$	0.316574	+	2.20182i	0.0402049	+	0.279632i
$63$	2.74769	+	3.17101i	0.346177	+	0.399509i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	0.282075	−	0.325532i	0.0349871	−	0.0403773i
$66$	−4.43918	+	1.30346i	−0.546425	+	0.160445i
$67$	0.401608	+	0.879398i	0.0490642	+	0.107436i	0.932577	−	0.360972i	$-0.117555\pi$
$67$	0.401608	+	0.879398i	0.0490642	+	0.107436i	−0.883512	+	0.468408i	$0.844828\pi$
$68$	6.00158			0.727799
$69$	−1.06519	+	12.8207i	−0.128233	+	1.54343i
$70$	0.0881559			0.0105366
$71$	−5.55888	−	12.1722i	−0.659718	−	1.44458i	−0.882785	−	0.469777i	$-0.844334\pi$
$71$	−5.55888	−	12.1722i	−0.659718	−	1.44458i	0.223067	−	0.974803i	$-0.428393\pi$
$72$	4.02588	−	1.18211i	0.474455	−	0.139313i
$73$	6.97403	−	8.04846i	0.816249	−	0.942001i	−0.182905	−	0.983131i	$-0.558550\pi$
$73$	6.97403	−	8.04846i	0.816249	−	0.942001i	0.999154	+	0.0411292i	$0.0130955\pi$
$74$	−7.46708	−	4.79880i	−0.868031	−	0.557850i
$75$	8.76969	+	10.1208i	1.01264	+	1.16865i
$76$	0.0566239	+	0.393828i	0.00649520	+	0.0451751i
$77$	−1.65486	−	0.485911i	−0.188589	−	0.0553747i
$78$	11.0264	−	7.08621i	1.24849	−	0.802355i
$79$	−0.363404	+	2.52753i	−0.0408861	+	0.284369i	0.959113	+	0.283024i	$0.0913375\pi$
$79$	−0.363404	+	2.52753i	−0.0408861	+	0.284369i	−0.999999	+	0.00134579i	$0.999572\pi$
$80$	0.0366213	−	0.0801894i	0.00409439	−	0.00896545i
$81$	−1.65436	+	3.62254i	−0.183818	+	0.402505i
$82$	−1.05334	+	7.32616i	−0.116322	+	0.809039i
$83$	−6.48421	+	4.16715i	−0.711734	+	0.457404i	−0.845753	−	0.533575i	$-0.820848\pi$
$83$	−6.48421	+	4.16715i	−0.711734	+	0.457404i	0.134018	+	0.990979i	$0.457212\pi$
$84$	2.57385	+	0.755750i	0.280830	+	0.0824590i
$85$	−0.0752952	−	0.523690i	−0.00816691	−	0.0568021i
$86$	−5.49236	−	6.33852i	−0.592257	−	0.683501i
$87$	−6.31408	−	4.05782i	−0.676941	−	0.435043i
$88$	−1.12945	+	1.30346i	−0.120400	+	0.138949i
$89$	−2.88384	+	0.846773i	−0.305687	+	0.0897578i	−0.430979	−	0.902362i	$-0.641832\pi$
$89$	−2.88384	+	0.846773i	−0.305687	+	0.0897578i	0.125292	+	0.992120i	$0.460013\pi$
$90$	−0.153657	−	0.336462i	−0.0161969	−	0.0354663i
$91$	4.88612			0.512205
$92$	2.24987	+	4.23534i	0.234565	+	0.441565i
$93$	5.96714			0.618763
$94$	1.37260	+	3.00557i	0.141573	+	0.310001i
$95$	0.0336545	−	0.00988184i	0.00345287	−	0.00101386i
$96$	1.75667	−	2.02730i	0.179289	−	0.206911i
$97$	2.35857	+	1.51576i	0.239476	+	0.153902i	0.654875	−	0.755738i	$-0.272721\pi$
$97$	2.35857	+	1.51576i	0.239476	+	0.153902i	−0.415398	+	0.909640i	$0.636358\pi$
$98$	0.654861	+	0.755750i	0.0661509	+	0.0763422i
$99$	1.02989	+	7.16301i	0.103507	+	0.719910i
$100$	4.79001	+	1.40647i	0.479001	+	0.140647i
$101$	11.4109	−	7.33335i	1.13543	−	0.729695i	0.168742	−	0.985660i	$-0.446030\pi$
$101$	11.4109	−	7.33335i	1.13543	−	0.729695i	0.966686	+	0.255965i	$0.0823933\pi$
$102$	2.29117	−	15.9354i	0.226859	−	1.57784i
$103$	2.04358	−	4.47481i	0.201360	−	0.440916i	−0.781833	−	0.623488i	$-0.785715\pi$
$103$	2.04358	−	4.47481i	0.201360	−	0.440916i	0.983192	+	0.182572i	$0.0584423\pi$
$104$	2.02977	−	4.44457i	0.199035	−	0.435826i
$105$	0.0336545	−	0.234072i	0.00328434	−	0.0228431i
$106$	7.71254	−	4.95655i	0.749108	−	0.481422i
$107$	−19.1531	−	5.62387i	−1.85160	−	0.543680i	−0.999804	−	0.0198116i	$-0.993693\pi$
$107$	−19.1531	−	5.62387i	−1.85160	−	0.543680i	−0.851799	−	0.523868i	$-0.824488\pi$
$108$	−0.456526	−	3.17521i	−0.0439292	−	0.305535i
$109$	−0.803147	−	0.926881i	−0.0769276	−	0.0887791i	0.715981	−	0.698120i	$-0.245980\pi$
$109$	−0.803147	−	0.926881i	−0.0769276	−	0.0887791i	−0.792909	+	0.609341i	$0.791434\pi$
$110$	0.127908	+	0.0822015i	0.0121956	+	0.00783761i
$111$	−15.5924	+	17.9946i	−1.47997	+	1.70797i
$112$	0.959493	−	0.281733i	0.0906636	−	0.0266212i
$113$	−7.43988	−	16.2911i	−0.699885	−	1.53253i	−0.840111	−	0.542414i	$-0.817510\pi$
$113$	−7.43988	−	16.2911i	−0.699885	−	1.53253i	0.140226	−	0.990119i	$-0.455217\pi$
$114$	1.06731			0.0999626
$115$	0.341343	−	0.249457i	0.0318304	−	0.0232619i
$116$	−2.79797			−0.259785
$117$	−8.51659	−	18.6487i	−0.787359	−	1.72408i
$118$	2.55384	−	0.749876i	0.235100	−	0.0690317i
$119$	3.93020	−	4.53569i	0.360281	−	0.415786i
$120$	−0.198939	−	0.127850i	−0.0181605	−	0.0116711i
$121$	5.25547	+	6.06514i	0.477770	+	0.551376i
$122$	0.327169	+	2.27551i	0.0296205	+	0.206015i
$123$	19.0503	+	5.59367i	1.71771	+	0.504365i
$124$	1.87134	−	1.20264i	0.168051	−	0.108000i
$125$	0.125361	−	0.871908i	0.0112127	−	0.0779858i
$126$	1.74302	−	3.81667i	0.155280	−	0.340016i
$127$	−3.82561	+	8.37691i	−0.339468	+	0.743331i	−0.999972	−	0.00749154i	$-0.997615\pi$
$127$	−3.82561	+	8.37691i	−0.339468	+	0.743331i	0.660504	+	0.750822i	$0.270343\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	−18.9268	+	12.1635i	−1.66641	+	1.07094i
$130$	−0.413293	−	0.121354i	−0.0362482	−	0.0106434i
$131$	1.23660	+	8.60076i	0.108042	+	0.751451i	0.969760	+	0.244062i	$0.0784802\pi$
$131$	1.23660	+	8.60076i	0.108042	+	0.751451i	−0.861717	+	0.507389i	$0.830611\pi$
$132$	3.02977	+	3.49654i	0.263708	+	0.304335i
$133$	0.334716	+	0.215109i	0.0290235	+	0.0186523i
$134$	0.633095	−	0.730630i	0.0546911	−	0.0631169i
$135$	−0.271337	+	0.0796717i	−0.0233530	+	0.00685705i
$136$	−2.49315	−	5.45923i	−0.213786	−	0.468125i
$137$	−0.107600			−0.00919287			−0.00459643	−	0.999989i	$-0.501463\pi$
$137$	−0.107600			−0.00919287			−0.00459643	+	0.999989i	$0.501463\pi$
$138$	12.1046	−	4.35697i	1.03041	−	0.370890i
$139$	−18.1038			−1.53554			−0.767772	−	0.640724i	$-0.778634\pi$
$139$	−18.1038			−1.53554			−0.767772	+	0.640724i	$0.778634\pi$
$140$	−0.0366213	−	0.0801894i	−0.00309506	−	0.00677725i
$141$	8.50441	−	2.49712i	0.716200	−	0.210295i
$142$	−8.76303	+	10.1131i	−0.735377	+	0.848670i
$143$	7.08942	+	4.55610i	0.592847	+	0.381000i
$144$	−2.74769	−	3.17101i	−0.228974	−	0.264251i
$145$	0.0351030	+	0.244147i	0.00291515	+	0.0202753i
$146$	−10.2183	−	3.00035i	−0.845669	−	0.248311i
$147$	2.25667	−	1.45027i	0.186127	−	0.119616i
$148$	−1.26321	+	8.78579i	−0.103835	+	0.722188i
$149$	−4.27678	+	9.36485i	−0.350368	+	0.767198i	0.649608	+	0.760269i	$0.274933\pi$
$149$	−4.27678	+	9.36485i	−0.350368	+	0.767198i	−0.999976	+	0.00692928i	$0.997794\pi$
$150$	5.56311	−	12.1815i	0.454226	−	0.994616i
$151$	−2.01062	+	13.9842i	−0.163622	+	1.13802i	0.728112	+	0.685458i	$0.240398\pi$
$151$	−2.01062	+	13.9842i	−0.163622	+	1.13802i	−0.891734	+	0.452559i	$0.850511\pi$
$152$	0.334716	−	0.215109i	0.0271490	−	0.0174476i
$153$	−24.1617	−	7.09451i	−1.95336	−	0.573557i
$154$	0.245454	+	1.70717i	0.0197792	+	0.137568i
$155$	−0.128418	−	0.148202i	−0.0103148	−	0.0119039i
$156$	−11.0264	−	7.08621i	−0.882815	−	0.567351i
$157$	−12.7560	+	14.7212i	−1.01804	+	1.17488i	−0.0335519	+	0.999437i	$0.510682\pi$
$157$	−12.7560	+	14.7212i	−1.01804	+	1.17488i	−0.984489	+	0.175445i	$0.943864\pi$
$158$	2.45009	−	0.719410i	0.194918	−	0.0572332i
$159$	−10.2163	−	22.3706i	−0.810205	−	1.77410i
$160$	−0.0881559			−0.00696934
$161$	4.67421	+	1.07322i	0.368379	+	0.0845815i
$162$	3.98242			0.312889
$163$	−4.64753	−	10.1767i	−0.364023	−	0.797099i	−0.999684	−	0.0251309i	$-0.992000\pi$
$163$	−4.64753	−	10.1767i	−0.364023	−	0.797099i	0.635661	−	0.771968i	$-0.280728\pi$
$164$	7.10168	−	2.08524i	0.554548	−	0.162830i
$165$	0.267092	−	0.308241i	0.0207931	−	0.0239965i
$166$	6.48421	+	4.16715i	0.503272	+	0.323433i
$167$	−6.29370	−	7.26331i	−0.487021	−	0.562052i	0.458046	−	0.888928i	$-0.348549\pi$
$167$	−6.29370	−	7.26331i	−0.487021	−	0.562052i	−0.945067	+	0.326876i	$0.894004\pi$
$168$	−0.381761	−	2.65520i	−0.0294535	−	0.204853i
$169$	−10.4337	−	3.06361i	−0.802593	−	0.235663i
$170$	−0.445086	+	0.286040i	−0.0341366	+	0.0219382i
$171$	0.237585	−	1.65244i	0.0181686	−	0.126365i
$172$	−3.48411	+	7.62915i	−0.265661	+	0.581717i
$173$	−1.59742	+	3.49787i	−0.121450	+	0.265938i	−0.960586	−	0.277984i	$-0.910334\pi$
$173$	−1.59742	+	3.49787i	−0.121450	+	0.265938i	0.839136	+	0.543922i	$0.183061\pi$
$174$	−1.06815	+	7.42917i	−0.0809765	+	0.563204i
$175$	4.19973	−	2.69900i	0.317470	−	0.204025i
$176$	1.65486	+	0.485911i	0.124740	+	0.0366269i
$177$	−1.01612	−	7.06725i	−0.0763760	−	0.531207i
$178$	1.96824	+	2.27148i	0.147526	+	0.170254i
$179$	−0.0130114	−	0.00836195i	−0.000972521	−	0.000625002i	0.540154	−	0.841566i	$-0.318366\pi$
$179$	−0.0130114	−	0.00836195i	−0.000972521	−	0.000625002i	−0.541127	+	0.840941i	$0.682002\pi$
$180$	−0.242225	+	0.279543i	−0.0180544	+	0.0208359i
$181$	23.6098	−	6.93248i	1.75491	−	0.515287i	0.763466	−	0.645848i	$-0.223496\pi$
$181$	23.6098	−	6.93248i	1.75491	−	0.515287i	0.991440	+	0.130561i	$0.0416780\pi$
$182$	−2.02977	−	4.44457i	−0.150456	−	0.329454i
$183$	6.16685			0.455867
$184$	2.91797	−	3.80598i	0.215116	−	0.280580i
$185$	0.782484			0.0575294
$186$	−2.47884	−	5.42790i	−0.181757	−	0.397993i
$187$	9.93178	−	2.91623i	0.726284	−	0.213256i
$188$	2.16377	−	2.49712i	0.157809	−	0.182121i
$189$	−2.69862	−	1.73430i	−0.196296	−	0.126152i
$190$	−0.0229694	−	0.0265081i	−0.00166638	−	0.00192310i
$191$	−1.09030	−	7.58323i	−0.0788916	−	0.548703i	−0.990486	−	0.137613i	$-0.956057\pi$
$191$	−1.09030	−	7.58323i	−0.0788916	−	0.548703i	0.911595	−	0.411091i	$-0.134852\pi$
$192$	−2.57385	−	0.755750i	−0.185751	−	0.0545415i
$193$	15.2735	−	9.81570i	1.09941	−	0.706550i	0.140452	−	0.990088i	$-0.455145\pi$
$193$	15.2735	−	9.81570i	1.09941	−	0.706550i	0.958961	+	0.283538i	$0.0915081\pi$
$194$	0.398999	−	2.77510i	0.0286464	−	0.199240i
$195$	−0.479997	+	1.05105i	−0.0343733	+	0.0752671i
$196$	0.415415	−	0.909632i	0.0296725	−	0.0649737i
$197$	−0.829895	+	5.77204i	−0.0591275	+	0.411241i	0.938665	+	0.344831i	$0.112064\pi$
$197$	−0.829895	+	5.77204i	−0.0591275	+	0.411241i	−0.997792	+	0.0664103i	$0.978845\pi$
$198$	6.08788	−	3.91244i	0.432647	−	0.278045i
$199$	16.4963	+	4.84374i	1.16939	+	0.343364i	0.808075	−	0.589080i	$-0.200510\pi$
$199$	16.4963	+	4.84374i	1.16939	+	0.343364i	0.361315	+	0.932444i	$0.382328\pi$
$200$	−0.710468	−	4.94141i	−0.0502377	−	0.349411i
$201$	−1.69828	−	1.95992i	−0.119788	−	0.138242i
$202$	−11.4109	−	7.33335i	−0.802869	−	0.515972i
$203$	−1.83228	+	2.11456i	−0.128601	+	0.148413i
$204$	−15.4472	+	4.53569i	−1.08152	+	0.317562i
$205$	−0.271052	−	0.593522i	−0.0189311	−	0.0414533i
$206$	−4.91936			−0.342748
$207$	−4.05109	−	19.7106i	−0.281570	−	1.36998i
$208$	−4.88612			−0.338792
$209$	0.285070	+	0.624216i	0.0197187	+	0.0431779i
$210$	−0.226900	+	0.0666238i	−0.0156576	+	0.00459748i
$211$	10.2233	−	11.7984i	0.703804	−	0.812233i	−0.285457	−	0.958391i	$-0.592145\pi$
$211$	10.2233	−	11.7984i	0.703804	−	0.812233i	0.989261	+	0.146158i	$0.0466909\pi$
$212$	−7.71254	−	4.95655i	−0.529699	−	0.340417i
$213$	23.5069	+	27.1284i	1.61066	+	1.85881i
$214$	2.84085	+	19.7585i	0.194196	+	1.35067i
$215$	0.709420	+	0.208305i	0.0483821	+	0.0142063i
$216$	−2.69862	+	1.73430i	−0.183618	+	0.118004i
$217$	0.316574	−	2.20182i	0.0214904	−	0.149469i
$218$	−0.509482	+	1.11561i	−0.0345064	+	0.0755586i
$219$	−11.8675	+	25.9861i	−0.801929	+	1.75598i
$220$	0.0216382	−	0.150497i	0.00145885	−	0.0101465i
$221$	−24.6693	+	15.8540i	−1.65944	+	1.06646i
$222$	22.8458	+	6.70814i	1.53331	+	0.450221i
$223$	−3.60127	−	25.0474i	−0.241159	−	1.67730i	−0.646331	−	0.763057i	$-0.723697\pi$
$223$	−3.60127	−	25.0474i	−0.241159	−	1.67730i	0.405172	−	0.914241i	$-0.367212\pi$
$224$	−0.654861	−	0.755750i	−0.0437547	−	0.0504956i
$225$	−17.6214	−	11.3246i	−1.17476	−	0.754973i
$226$	−11.7282	+	13.5351i	−0.780150	+	0.900342i
$227$	17.9687	−	5.27610i	1.19263	−	0.350187i	0.375598	−	0.926783i	$-0.377437\pi$
$227$	17.9687	−	5.27610i	1.19263	−	0.350187i	0.817030	+	0.576596i	$0.195619\pi$
$228$	−0.443376	−	0.970858i	−0.0293633	−	0.0642967i
$229$	3.27777			0.216601			0.108301	−	0.994118i	$-0.465459\pi$
$229$	3.27777			0.216601			0.108301	+	0.994118i	$0.465459\pi$
$230$	−0.368713	−	0.206869i	−0.0243122	−	0.0136405i
$231$	4.62658			0.304407
$232$	1.16232	+	2.54512i	0.0763099	+	0.167095i
$233$	27.6698	−	8.12459i	1.81271	−	0.532260i	0.813899	−	0.581007i	$-0.197341\pi$
$233$	27.6698	−	8.12459i	1.81271	−	0.532260i	0.998811	+	0.0487473i	$0.0155229\pi$
$234$	−13.4256	+	15.4939i	−0.877657	+	1.01287i
$235$	−0.245042	−	0.157479i	−0.0159847	−	0.0102728i
$236$	−1.74302	−	2.01155i	−0.113461	−	0.130941i
$237$	−0.974834	−	6.78012i	−0.0633223	−	0.440416i
$238$	−5.75848	−	1.69084i	−0.373267	−	0.109601i
$239$	−16.4667	+	10.5825i	−1.06514	+	0.684525i	−0.951079	−	0.308949i	$-0.900023\pi$
$239$	−16.4667	+	10.5825i	−1.06514	+	0.684525i	−0.114063	+	0.993474i	$0.536387\pi$
$240$	−0.0336545	+	0.234072i	−0.00217239	+	0.0151093i
$241$	2.41834	−	5.29542i	0.155779	−	0.341108i	−0.815610	−	0.578602i	$-0.803599\pi$
$241$	2.41834	−	5.29542i	0.155779	−	0.341108i	0.971389	+	0.237494i	$0.0763259\pi$
$242$	3.33384	−	7.30009i	0.214307	−	0.469268i
$243$	2.88991	−	20.0998i	0.185388	−	1.28940i
$244$	1.93397	−	1.24289i	0.123810	−	0.0795677i
$245$	−0.0845850	−	0.0248364i	−0.00540394	−	0.00158674i
$246$	−2.82560	−	19.6525i	−0.180154	−	1.25300i
$247$	−1.27310	−	1.46924i	−0.0810054	−	0.0934852i
$248$	−1.87134	−	1.20264i	−0.118830	−	0.0763674i
$249$	13.5400	−	15.6260i	0.858065	−	0.990260i
$250$	−0.845193	+	0.248171i	−0.0534547	+	0.0156957i
$251$	6.52594	+	14.2898i	0.411913	+	0.901965i	0.995922	+	0.0902172i	$0.0287561\pi$
$251$	6.52594	+	14.2898i	0.411913	+	0.901965i	−0.584009	+	0.811747i	$0.698517\pi$
$252$	−4.19584			−0.264313
$253$	5.78122	+	5.91566i	0.363462	+	0.371914i
$254$	9.20912			0.577832
$255$	0.589577	+	1.29099i	0.0369207	+	0.0808451i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−16.5457	+	19.0948i	−1.03209	+	1.19110i	−0.0507743	+	0.998710i	$0.516169\pi$
$257$	−16.5457	+	19.0948i	−1.03209	+	1.19110i	−0.981319	+	0.192389i	$0.938377\pi$
$258$	18.9268	+	12.1635i	1.17833	+	0.757269i
$259$	5.81264	+	6.70814i	0.361180	+	0.416823i
$260$	0.0613008	+	0.426356i	0.00380171	+	0.0264415i
$261$	11.2643	+	3.30749i	0.697242	+	0.204729i
$262$	7.30982	−	4.69774i	0.451602	−	0.290227i
$263$	2.57189	−	17.8879i	0.158589	−	1.10301i	−0.742647	−	0.669684i	$-0.766430\pi$
$263$	2.57189	−	17.8879i	0.158589	−	1.10301i	0.901236	−	0.433329i	$-0.142661\pi$
$264$	1.92195	−	4.20849i	0.118288	−	0.259015i
$265$	−0.335741	+	0.735170i	−0.0206244	+	0.0451611i
$266$	0.0566239	−	0.393828i	0.00347183	−	0.0241471i
$267$	6.78263	−	4.35893i	0.415090	−	0.266762i
$268$	−0.927602	−	0.272368i	−0.0566623	−	0.0166376i
$269$	−1.19622	−	8.31991i	−0.0729350	−	0.507274i	−0.993241	−	0.116074i	$-0.962969\pi$
$269$	−1.19622	−	8.31991i	−0.0729350	−	0.507274i	0.920306	−	0.391200i	$-0.127940\pi$
$270$	0.185189	+	0.213720i	0.0112703	+	0.0130066i
$271$	22.3521	+	14.3648i	1.35779	+	0.872601i	0.998168	−	0.0604958i	$-0.0192682\pi$
$271$	22.3521	+	14.3648i	1.35779	+	0.872601i	0.359625	+	0.933097i	$0.382905\pi$
$272$	−3.93020	+	4.53569i	−0.238303	+	0.275017i
$273$	−12.5761	+	3.69269i	−0.761142	+	0.223491i
$274$	0.0446985	+	0.0978762i	0.00270034	+	0.00591292i
$275$	8.61022			0.519216
$276$	−8.99167	−	9.20077i	−0.541235	−	0.553821i
$277$	−28.4003			−1.70641			−0.853203	−	0.521578i	$-0.825343\pi$
$277$	−28.4003			−1.70641			−0.853203	+	0.521578i	$0.825343\pi$
$278$	7.52059	+	16.4678i	0.451055	+	0.987672i
$279$	−8.95543	+	2.62955i	−0.536147	+	0.157427i
$280$	−0.0577299	+	0.0666238i	−0.00345002	+	0.00398153i
$281$	4.32948	+	2.78239i	0.258275	+	0.165983i	0.663371	−	0.748291i	$-0.269125\pi$
$281$	4.32948	+	2.78239i	0.258275	+	0.165983i	−0.405095	+	0.914274i	$0.632762\pi$
$282$	−5.80432	−	6.69854i	−0.345642	−	0.398892i
$283$	−0.729260	−	5.07211i	−0.0433500	−	0.301506i	−0.999949	−	0.0100984i	$-0.996786\pi$
$283$	−0.729260	−	5.07211i	−0.0433500	−	0.301506i	0.956599	−	0.291408i	$-0.0941236\pi$
$284$	12.8395	+	3.77001i	0.761882	+	0.223709i
$285$	−0.0791532	+	0.0508687i	−0.00468863	+	0.00301320i
$286$	1.19932	−	8.34144i	0.0709171	−	0.493240i
$287$	3.07469	−	6.73263i	0.181493	−	0.397415i
$288$	−1.74302	+	3.81667i	−0.102708	+	0.224900i
$289$	−2.70668	+	18.8254i	−0.159217	+	1.10738i
$290$	0.207501	−	0.133353i	0.0121849	−	0.00783076i
$291$	−7.21612	−	2.11884i	−0.423016	−	0.124209i
$292$	1.51560	+	10.5412i	0.0886939	+	0.616880i
$293$	15.2037	+	17.5460i	0.888211	+	1.02505i	0.999511	+	0.0312630i	$0.00995293\pi$
$293$	15.2037	+	17.5460i	0.888211	+	1.02505i	−0.111301	+	0.993787i	$0.535502\pi$
$294$	−2.25667	−	1.45027i	−0.131612	−	0.0845816i
$295$	−0.153657	+	0.177330i	−0.00894627	+	0.0103245i
$296$	8.51659	−	2.50070i	0.495017	−	0.145350i
$297$	−2.29836	−	5.03270i	−0.133364	−	0.292027i
$298$	10.2952			0.596385
$299$	−20.4362	−	11.4659i	−1.18186	−	0.663089i
$300$	−13.3917			−0.773169
$301$	3.48411	+	7.62915i	0.200821	+	0.439737i
$302$	13.5557	−	3.98032i	0.780044	−	0.229041i
$303$	−23.8278	+	27.4987i	−1.36887	+	1.57976i
$304$	−0.334716	−	0.215109i	−0.0191973	−	0.0123373i
$305$	−0.132716	−	0.153162i	−0.00759929	−	0.00877005i
$306$	3.58373	+	24.9254i	0.204868	+	1.42489i
$307$	10.7206	+	3.14786i	0.611859	+	0.179658i	0.572958	−	0.819585i	$-0.305796\pi$
$307$	10.7206	+	3.14786i	0.611859	+	0.179658i	0.0389016	+	0.999243i	$0.487614\pi$
$308$	1.45093	−	0.932456i	0.0826744	−	0.0531316i
$309$	−1.87802	+	13.0619i	−0.106837	+	0.743066i
$310$	−0.0814627	+	0.178378i	−0.00462677	+	0.0101312i
$311$	−5.65778	+	12.3888i	−0.320823	+	0.702505i	−0.999490	−	0.0319414i	$-0.989831\pi$
$311$	−5.65778	+	12.3888i	−0.320823	+	0.702505i	0.678666	+	0.734447i	$0.262558\pi$
$312$	−1.86533	+	12.9736i	−0.105603	+	0.734488i
$313$	−21.4837	+	13.8068i	−1.21433	+	0.780404i	−0.981378	−	0.192084i	$-0.938475\pi$
$313$	−21.4837	+	13.8068i	−1.21433	+	0.780404i	−0.232954	+	0.972488i	$0.574839\pi$
$314$	18.6899	+	5.48786i	1.05473	+	0.309698i
$315$	0.0526406	+	0.366124i	0.00296596	+	0.0206287i
$316$	−1.67220	−	1.92982i	−0.0940687	−	0.108561i
$317$	1.91553	+	1.23104i	0.107587	+	0.0691420i	0.593328	−	0.804961i	$-0.297814\pi$
$317$	1.91553	+	1.23104i	0.107587	+	0.0691420i	−0.485741	+	0.874103i	$0.661450\pi$
$318$	−16.1050	+	18.5861i	−0.903122	+	1.04226i
$319$	−4.63025	+	1.35956i	−0.259244	+	0.0761209i
$320$	0.0366213	+	0.0801894i	0.00204719	+	0.00448273i
$321$	53.5475			2.98873
$322$	−0.965501	−	4.69764i	−0.0538053	−	0.261789i
$323$	−2.38789			−0.132866
$324$	−1.65436	−	3.62254i	−0.0919088	−	0.201252i
$325$	−23.4046	+	6.87220i	−1.29825	+	0.381201i
$326$	−7.32638	+	8.45509i	−0.405771	+	0.468284i
$327$	2.76767	+	1.77867i	0.153052	+	0.0983608i
$328$	−4.84695	−	5.59367i	−0.267628	−	0.308859i
$329$	−0.470231	−	3.27053i	−0.0259247	−	0.180310i
$330$	−0.391340	−	0.114908i	−0.0215425	−	0.00632546i
$331$	−12.0957	+	7.77346i	−0.664842	+	0.427268i	−0.829063	−	0.559156i	$-0.811125\pi$
$331$	−12.0957	+	7.77346i	−0.664842	+	0.427268i	0.164221	+	0.986424i	$0.447489\pi$
$332$	1.09693	−	7.62934i	0.0602020	−	0.418714i
$333$	15.4713	−	33.8773i	0.847820	−	1.85647i
$334$	−3.99245	+	8.74224i	−0.218457	+	0.478354i
$335$	−0.0121289	+	0.0843584i	−0.000662673	+	0.00460899i
$336$	−2.25667	+	1.45027i	−0.123111	+	0.0791189i
$337$	15.2277	+	4.47124i	0.829503	+	0.243564i	0.668803	−	0.743439i	$-0.266807\pi$
$337$	15.2277	+	4.47124i	0.829503	+	0.243564i	0.160700	+	0.987003i	$0.448625\pi$
$338$	1.54756	+	10.7635i	0.0841761	+	0.585458i
$339$	31.4611	+	36.3080i	1.70873	+	1.97198i
$340$	0.445086	+	0.286040i	0.0241382	+	0.0155127i
$341$	2.51243	−	2.89950i	0.136056	−	0.157017i
$342$	−1.60181	+	0.470333i	−0.0866158	+	0.0254327i
$343$	−0.415415	−	0.909632i	−0.0224303	−	0.0491155i
$344$	8.38707			0.452200
$345$	−0.690038	+	0.900033i	−0.0371504	+	0.0484561i
$346$	3.84537			0.206728
$347$	−0.0920910	−	0.201651i	−0.00494370	−	0.0108252i	0.907144	−	0.420820i	$-0.138258\pi$
$347$	−0.0920910	−	0.201651i	−0.00494370	−	0.0108252i	−0.912088	+	0.409995i	$0.865530\pi$
$348$	7.20154	−	2.11456i	0.386043	−	0.113352i
$349$	13.7682	−	15.8894i	0.736996	−	0.850539i	−0.256245	−	0.966612i	$-0.582485\pi$
$349$	13.7682	−	15.8894i	0.736996	−	0.850539i	0.993241	+	0.116073i	$0.0370308\pi$
$350$	−4.19973	−	2.69900i	−0.224485	−	0.144268i
$351$	10.2643	+	11.8456i	0.547867	+	0.632272i
$352$	−0.245454	−	1.70717i	−0.0130827	−	0.0909924i
$353$	−5.41030	−	1.58861i	−0.287961	−	0.0845530i	0.134562	−	0.990905i	$-0.457037\pi$
$353$	−5.41030	−	1.58861i	−0.287961	−	0.0845530i	−0.422523	+	0.906352i	$0.638855\pi$
$354$	−6.00648	+	3.86013i	−0.319241	+	0.205164i
$355$	0.167883	−	1.16765i	0.00891031	−	0.0619725i
$356$	1.24857	−	2.73398i	0.0661740	−	0.144901i
$357$	−6.68789	+	14.6444i	−0.353960	+	0.775065i
$358$	−0.00220115	+	0.0153093i	−0.000116334	+	0.000809122i
$359$	24.1929	−	15.5478i	1.27685	−	0.820582i	0.286355	−	0.958124i	$-0.407556\pi$
$359$	24.1929	−	15.5478i	1.27685	−	0.820582i	0.990496	+	0.137541i	$0.0439199\pi$
$360$	0.354905	+	0.104210i	0.0187052	+	0.00549233i
$361$	2.68145	+	18.6499i	0.141129	+	0.981574i
$362$	−16.1139	−	18.5964i	−0.846927	−	0.977406i
$363$	−18.1105	−	11.6389i	−0.950555	−	0.610884i
$364$	−3.19973	+	3.69269i	−0.167711	+	0.193549i
$365$	0.900800	−	0.264499i	0.0471500	−	0.0138445i
$366$	−2.56180	−	5.60957i	−0.133908	−	0.293217i
$367$	−24.0754			−1.25672			−0.628362	−	0.777921i	$-0.716274\pi$
$367$	−24.0754			−1.25672			−0.628362	+	0.777921i	$0.716274\pi$
$368$	−4.67421	−	1.07322i	−0.243660	−	0.0559454i
$369$	−31.0555			−1.61669
$370$	−0.325056	−	0.711773i	−0.0168988	−	0.0370033i
$371$	−8.79655	+	2.58290i	−0.456694	+	0.134097i
$372$	−3.90764	+	4.50966i	−0.202602	+	0.233815i
$373$	−6.24798	−	4.01533i	−0.323508	−	0.207906i	0.368799	−	0.929509i	$-0.379769\pi$
$373$	−6.24798	−	4.01533i	−0.323508	−	0.207906i	−0.692307	+	0.721603i	$0.743406\pi$
$374$	−6.77851	−	7.82282i	−0.350509	−	0.404508i
$375$	0.336283	+	2.33890i	0.0173656	+	0.120780i
$376$	−3.17032	−	0.930890i	−0.163497	−	0.0480070i
$377$	11.5010	−	7.39121i	0.592329	−	0.380667i
$378$	−0.456526	+	3.17521i	−0.0234812	+	0.163315i
$379$	11.7325	−	25.6905i	0.602656	−	1.31963i	−0.324829	−	0.945773i	$-0.605307\pi$
$379$	11.7325	−	25.6905i	0.602656	−	1.31963i	0.927485	−	0.373860i	$-0.121966\pi$
$380$	−0.0145708	+	0.0319056i	−0.000747465	+	0.00163672i
$381$	3.51568	−	24.4521i	0.180114	−	1.25272i
$382$	−6.44502	+	4.14196i	−0.329756	+	0.211921i
$383$	10.0159	+	2.94094i	0.511789	+	0.150275i	0.527423	−	0.849603i	$-0.323158\pi$
$383$	10.0159	+	2.94094i	0.511789	+	0.150275i	−0.0156338	+	0.999878i	$0.504977\pi$
$384$	0.381761	+	2.65520i	0.0194816	+	0.135498i
$385$	−0.0995681	−	0.114908i	−0.00507446	−	0.00585624i
$386$	−15.2735	−	9.81570i	−0.777402	−	0.499606i
$387$	23.0451	−	26.5955i	1.17145	−	1.35192i
$388$	−2.69007	+	0.789875i	−0.136567	+	0.0400998i
$389$	3.49163	+	7.64561i	0.177033	+	0.387648i	0.977259	−	0.212051i	$-0.0680143\pi$
$389$	3.49163	+	7.64561i	0.177033	+	0.387648i	−0.800226	+	0.599699i	$0.795287\pi$
$390$	1.15546			0.0585092
$391$	−27.0816	+	9.74787i	−1.36958	+	0.492971i
$392$	−1.00000			−0.0505076
$393$	−9.68284	−	21.2025i	−0.488435	−	1.06952i
$394$	5.59519	−	1.64290i	0.281881	−	0.0827679i
$395$	−0.147414	+	0.170125i	−0.00741722	+	0.00855993i
$396$	−6.08788	−	3.91244i	−0.305927	−	0.196608i
$397$	−7.90998	−	9.12860i	−0.396990	−	0.458151i	0.521700	−	0.853129i	$-0.325298\pi$
$397$	−7.90998	−	9.12860i	−0.396990	−	0.458151i	−0.918691	+	0.394977i	$0.870752\pi$
$398$	−2.44678	−	17.0177i	−0.122646	−	0.853020i
$399$	−1.02408	−	0.300696i	−0.0512679	−	0.0150536i
$400$	−4.19973	+	2.69900i	−0.209986	+	0.134950i
$401$	−0.553587	+	3.85028i	−0.0276448	+	0.192274i	−0.998964	−	0.0455050i	$-0.985510\pi$
$401$	−0.553587	+	3.85028i	−0.0276448	+	0.192274i	0.971319	+	0.237779i	$0.0764194\pi$
$402$	−1.07732	+	2.35899i	−0.0537316	+	0.117656i
$403$	−4.51514	+	9.88679i	−0.224915	+	0.492496i
$404$	−1.93038	+	13.4261i	−0.0960401	+	0.667974i
$405$	−0.295342	+	0.189805i	−0.0146757	+	0.00943149i
$406$	2.68463	+	0.788278i	0.133236	+	0.0391216i
$407$	2.17868	+	15.1531i	0.107993	+	0.751110i
$408$	10.5428	+	12.1670i	0.521946	+	0.602358i
$409$	−26.3755	−	16.9505i	−1.30419	−	0.838149i	−0.310524	−	0.950565i	$-0.600505\pi$
$409$	−26.3755	−	16.9505i	−1.30419	−	0.838149i	−0.993661	+	0.112416i	$0.964141\pi$
$410$	−0.427287	+	0.493116i	−0.0211022	+	0.0243532i
$411$	0.276945	−	0.0813185i	0.0136607	−	0.00401114i
$412$	2.04358	+	4.47481i	0.100680	+	0.220458i
$413$	−2.66166			−0.130972
$414$	−16.2465	+	11.8731i	−0.798470	+	0.583529i
$415$	−0.679488			−0.0333547
$416$	2.02977	+	4.44457i	0.0995176	+	0.217913i
$417$	46.5964	−	13.6819i	2.28183	−	0.670007i
$418$	0.449384	−	0.518617i	0.0219801	−	0.0253664i
$419$	24.0605	+	15.4628i	1.17543	+	0.755406i	0.974542	−	0.224207i	$-0.0719792\pi$
$419$	24.0605	+	15.4628i	1.17543	+	0.755406i	0.200893	+	0.979613i	$0.435616\pi$
$420$	0.154861	+	0.178719i	0.00755643	+	0.00872059i
$421$	−3.90013	−	27.1260i	−0.190081	−	1.32204i	−0.831789	−	0.555091i	$-0.812683\pi$
$421$	−3.90013	−	27.1260i	−0.190081	−	1.32204i	0.641709	−	0.766948i	$-0.278226\pi$
$422$	−14.9791	−	4.39826i	−0.729171	−	0.214104i
$423$	−11.6629	+	7.49531i	−0.567071	+	0.364434i
$424$	−1.30473	+	9.07459i	−0.0633633	+	0.440701i
$425$	−12.4464	+	27.2537i	−0.603737	+	1.32200i
$426$	14.9117	−	32.6521i	0.722476	−	1.58200i
$427$	0.327169	−	2.27551i	0.0158328	−	0.110120i
$428$	16.7929	−	10.7921i	0.811714	−	0.521657i
$429$	−21.6904	−	6.36886i	−1.04722	−	0.307492i
$430$	−0.105223	−	0.731844i	−0.00507432	−	0.0352927i
$431$	−22.8342	−	26.3520i	−1.09988	−	1.26933i	−0.960254	−	0.279129i	$-0.909954\pi$
$431$	−22.8342	−	26.3520i	−1.09988	−	1.26933i	−0.139629	−	0.990204i	$-0.544591\pi$
$432$	2.69862	+	1.73430i	0.129838	+	0.0834416i
$433$	4.48216	−	5.17268i	0.215399	−	0.248583i	−0.637760	−	0.770235i	$-0.720139\pi$
$433$	4.48216	−	5.17268i	0.215399	−	0.248583i	0.853158	+	0.521652i	$0.174684\pi$
$434$	−2.13436	+	0.626704i	−0.102452	+	0.0300827i
$435$	−0.274864	−	0.601867i	−0.0131787	−	0.0288573i
$436$	1.22644			0.0587358
$437$	−0.895172	−	1.68515i	−0.0428219	−	0.0806114i
$438$	28.5677			1.36502
$439$	−7.29847	−	15.9814i	−0.348337	−	0.762752i	−0.999991	−	0.00423547i	$-0.998652\pi$
$439$	−7.29847	−	15.9814i	−0.348337	−	0.762752i	0.651654	−	0.758516i	$-0.274075\pi$
$440$	−0.145886	+	0.0428359i	−0.00695483	+	0.00204212i
$441$	−2.74769	+	3.17101i	−0.130843	+	0.151000i
$442$	24.6693	+	15.8540i	1.17340	+	0.754098i
$443$	−6.72262	−	7.75832i	−0.319401	−	0.368609i	0.573231	−	0.819394i	$-0.305690\pi$
$443$	−6.72262	−	7.75832i	−0.319401	−	0.368609i	−0.892633	+	0.450785i	$0.851144\pi$
$444$	−3.38856	−	23.5680i	−0.160814	−	1.11849i
$445$	−0.254228	−	0.0746481i	−0.0120516	−	0.00353866i
$446$	−21.2879	+	13.6809i	−1.00801	+	0.647809i
$447$	3.93030	−	27.3359i	0.185897	−	1.29294i
$448$	−0.415415	+	0.909632i	−0.0196265	+	0.0429761i
$449$	−2.51988	+	5.51778i	−0.118921	+	0.260400i	−0.959726	−	0.280938i	$-0.909355\pi$
$449$	−2.51988	+	5.51778i	−0.118921	+	0.260400i	0.840805	+	0.541338i	$0.182082\pi$
$450$	−2.98101	+	20.7334i	−0.140526	+	0.977382i
$451$	10.7390	−	6.90157i	0.505682	−	0.324982i
$452$	17.1840	+	5.04569i	0.808269	+	0.237329i
$453$	−5.39351	−	37.5127i	−0.253409	−	1.76250i
$454$	−12.2638	−	14.1532i	−0.575568	−	0.664241i
$455$	0.362362	+	0.232876i	0.0169878	+	0.0109174i
$456$	−0.698939	+	0.806618i	−0.0327308	+	0.0377734i
$457$	17.1721	−	5.04219i	0.803279	−	0.235864i	0.145777	−	0.989317i	$-0.453432\pi$
$457$	17.1721	−	5.04219i	0.803279	−	0.235864i	0.657501	+	0.753454i	$0.271613\pi$
$458$	−1.36164	−	2.98157i	−0.0636250	−	0.139319i
$459$	19.2522			0.898618
$460$	−0.0350055	+	0.421329i	−0.00163214	+	0.0196446i
$461$	42.2374			1.96719			0.983595	−	0.180390i	$-0.0577359\pi$
$461$	42.2374			1.96719			0.983595	+	0.180390i	$0.0577359\pi$
$462$	−1.92195	−	4.20849i	−0.0894173	−	0.195797i
$463$	−35.5864	+	10.4491i	−1.65384	+	0.485611i	−0.969814	−	0.243847i	$-0.921590\pi$
$463$	−35.5864	+	10.4491i	−1.65384	+	0.485611i	−0.684025	+	0.729458i	$0.739772\pi$
$464$	1.83228	−	2.11456i	0.0850614	−	0.0981661i
$465$	0.442532	+	0.284398i	0.0205219	+	0.0131886i
$466$	−18.8848	−	21.7943i	−0.874823	−	1.00960i
$467$	3.22529	+	22.4324i	0.149249	+	1.03805i	0.917453	+	0.397843i	$0.130241\pi$
$467$	3.22529	+	22.4324i	0.149249	+	1.03805i	−0.768205	+	0.640204i	$0.778850\pi$
$468$	19.6710	+	5.77591i	0.909290	+	0.266992i
$469$	−0.813292	+	0.522671i	−0.0375544	+	0.0241347i
$470$	−0.0414537	+	0.288317i	−0.00191212	+	0.0132991i
$471$	21.7065	−	47.5305i	1.00018	−	2.19009i
$472$	−1.10569	+	2.42113i	−0.0508937	+	0.111442i
$473$	−2.05864	+	14.3181i	−0.0946563	+	0.658349i
$474$	−5.76245	+	3.70330i	−0.264678	+	0.170098i
$475$	−1.90584	−	0.559604i	−0.0874458	−	0.0256764i
$476$	0.854114	+	5.94049i	0.0391483	+	0.272282i
$477$	25.1906	+	29.0715i	1.15340	+	1.33109i
$478$	16.4667	+	10.5825i	0.753169	+	0.484032i
$479$	9.48762	−	10.9493i	0.433500	−	0.500286i	−0.496402	−	0.868093i	$-0.665346\pi$
$479$	9.48762	−	10.9493i	0.433500	−	0.500286i	0.929902	+	0.367807i	$0.119891\pi$
$480$	0.226900	−	0.0666238i	0.0103565	−	0.00304095i
$481$	−18.0165	−	39.4507i	−0.821482	−	1.79879i
$482$	−5.82150			−0.265162
$483$	−12.8418	+	0.770228i	−0.584321	+	0.0350466i
$484$	−8.02533			−0.364788
$485$	0.102673	+	0.224822i	0.00466213	+	0.0102086i
$486$	−19.4839	+	5.72099i	−0.883808	+	0.259509i
$487$	1.00264	−	1.15711i	0.0454341	−	0.0524337i	−0.732578	−	0.680683i	$-0.761683\pi$
$487$	1.00264	−	1.15711i	0.0454341	−	0.0524337i	0.778012	+	0.628250i	$0.216228\pi$
$488$	−1.93397	−	1.24289i	−0.0875467	−	0.0562628i
$489$	19.6531	+	22.6808i	0.888742	+	1.02566i
$490$	0.0125459	+	0.0872586i	0.000566766	+	0.00394194i
$491$	−32.8593	−	9.64835i	−1.48292	−	0.435424i	−0.562644	−	0.826699i	$-0.690216\pi$
$491$	−32.8593	−	9.64835i	−1.48292	−	0.435424i	−0.920274	+	0.391275i	$0.872034\pi$
$492$	−16.7027	+	10.7342i	−0.753017	+	0.483934i
$493$	2.38978	−	16.6213i	0.107630	−	0.748586i
$494$	−0.807599	+	1.76840i	−0.0363356	+	0.0795639i
$495$	−0.265016	+	0.580305i	−0.0119116	+	0.0260828i
$496$	−0.316574	+	2.20182i	−0.0142146	+	0.0988647i
$497$	11.2572	−	7.23459i	0.504956	−	0.324516i
$498$	−19.8387	−	5.82516i	−0.888992	−	0.261032i
$499$	3.59666	+	25.0153i	0.161009	+	1.11984i	0.896737	+	0.442563i	$0.145931\pi$
$499$	3.59666	+	25.0153i	0.161009	+	1.11984i	−0.735729	+	0.677276i	$0.763160\pi$
$500$	0.576850	+	0.665720i	0.0257975	+	0.0297719i
$501$	21.6883	+	13.9382i	0.968960	+	0.622713i
$502$	10.2875	−	11.8724i	0.459153	−	0.529891i
$503$	−3.30909	+	0.971636i	−0.147545	+	0.0433231i	−0.354671	−	0.934991i	$-0.615407\pi$
$503$	−3.30909	+	0.971636i	−0.147545	+	0.0433231i	0.207126	+	0.978314i	$0.433589\pi$
$504$	1.74302	+	3.81667i	0.0776401	+	0.170008i
$505$	1.19576			0.0532107
$506$	2.97947	−	7.71623i	0.132453	−	0.343028i
$507$	29.1701			1.29549
$508$	−3.82561	−	8.37691i	−0.169734	−	0.371665i
$509$	−2.31360	+	0.679336i	−0.102549	+	0.0301110i	−0.332604	−	0.943066i	$-0.607927\pi$
$509$	−2.31360	+	0.679336i	−0.102549	+	0.0301110i	0.230056	+	0.973177i	$0.426109\pi$
$510$	0.929409	−	1.07260i	0.0411549	−	0.0474953i
$511$	8.95905	+	5.75763i	0.396325	+	0.254703i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	0.181641	+	1.26334i	0.00801966	+	0.0557780i
$514$	24.2425	+	7.11825i	1.06929	+	0.313973i
$515$	0.364827	−	0.234460i	0.0160762	−	0.0103315i
$516$	3.20185	−	22.2694i	0.140954	−	0.980354i
$517$	2.36735	−	5.18378i	0.104116	−	0.227982i
$518$	3.68728	−	8.07402i	0.162010	−	0.354752i
$519$	1.46801	−	10.2102i	0.0644385	−	0.448180i
$520$	0.362362	−	0.232876i	0.0158906	−	0.0102123i
$521$	18.8051	+	5.52168i	0.823868	+	0.241909i	0.666381	−	0.745612i	$-0.267843\pi$
$521$	18.8051	+	5.52168i	0.823868	+	0.241909i	0.157487	+	0.987521i	$0.449661\pi$
$522$	−1.67075	−	11.6203i	−0.0731268	−	0.508608i
$523$	9.42536	+	10.8774i	0.412142	+	0.475637i	0.923427	−	0.383774i	$-0.125376\pi$
$523$	9.42536	+	10.8774i	0.412142	+	0.475637i	−0.511285	+	0.859411i	$0.670830\pi$
$524$	−7.30982	−	4.69774i	−0.319331	−	0.205222i
$525$	−8.76969	+	10.1208i	−0.382741	+	0.441706i
$526$	−17.3398	+	5.09141i	−0.756050	+	0.221996i
$527$	5.54591	+	12.1439i	0.241584	+	0.528995i
$528$	−4.62658			−0.201346
$529$	−17.0315	−	15.4573i	−0.740498	−	0.672058i
$530$	0.808206			0.0351062
$531$	4.63932	+	10.1587i	0.201329	+	0.440850i
$532$	−0.381761	+	0.112095i	−0.0165514	+	0.00485994i
$533$	−23.6828	+	27.3314i	−1.02581	+	1.18385i
$534$	−6.78263	−	4.35893i	−0.293513	−	0.188629i
$535$	−1.15239	−	1.32993i	−0.0498220	−	0.0574977i
$536$	0.137585	+	0.956922i	0.00594275	+	0.0413327i
$537$	0.0398090	+	0.0116890i	0.00171789	+	0.000504417i
$538$	−7.07113	+	4.54434i	−0.304858	+	0.195920i
$539$	0.245454	−	1.70717i	0.0105724	−	0.0735330i
$540$	0.117476	−	0.257237i	0.00505536	−	0.0110697i
$541$	−10.7128	+	23.4577i	−0.460577	+	1.00852i	0.526778	+	0.850003i	$0.323400\pi$
$541$	−10.7128	+	23.4577i	−0.460577	+	1.00852i	−0.987356	+	0.158521i	$0.949328\pi$
$542$	3.78131	−	26.2996i	0.162421	−	1.12966i
$543$	−55.5289	+	35.6863i	−2.38297	+	1.53144i
$544$	5.75848	+	1.69084i	0.246893	+	0.0724942i
$545$	−0.0153868	−	0.107017i	−0.000659098	−	0.00458412i
$546$	8.58330	+	9.90565i	0.367331	+	0.423923i
$547$	19.4053	+	12.4710i	0.829709	+	0.533222i	0.885185	−	0.465238i	$-0.154031\pi$
$547$	19.4053	+	12.4710i	0.829709	+	0.533222i	−0.0554764	+	0.998460i	$0.517668\pi$
$548$	0.0704628	−	0.0813185i	0.00301002	−	0.00347375i
$549$	−9.25516	+	2.71756i	−0.395000	+	0.115983i
$550$	−3.57681	−	7.83213i	−0.152516	−	0.333963i
$551$	1.11325			0.0474259
$552$	−4.63404	+	12.0013i	−0.197238	+	0.510807i
$553$	−2.55352			−0.108587
$554$	11.7979	+	25.8338i	0.501245	+	1.09757i
$555$	−2.01399	+	0.591362i	−0.0854893	+	0.0251019i
$556$	11.8555	−	13.6819i	0.502783	−	0.580243i
$557$	−2.97368	−	1.91107i	−0.125999	−	0.0809745i	0.476123	−	0.879379i	$-0.342042\pi$
$557$	−2.97368	−	1.91107i	−0.125999	−	0.0809745i	−0.602122	+	0.798404i	$0.705678\pi$
$558$	6.11214	+	7.05379i	0.258748	+	0.298611i
$559$	−5.83210	−	40.5631i	−0.246671	−	1.71564i
$560$	0.0845850	+	0.0248364i	0.00357437	+	0.00104953i
$561$	−23.3589	+	15.0119i	−0.986215	+	0.633802i
$562$	0.732418	−	5.09408i	0.0308952	−	0.214881i
$563$	14.4141	−	31.5625i	0.607482	−	1.33020i	−0.316800	−	0.948492i	$-0.602609\pi$
$563$	14.4141	−	31.5625i	0.607482	−	1.33020i	0.924283	−	0.381709i	$-0.124664\pi$
$564$	−3.68201	+	8.06247i	−0.155040	+	0.339491i
$565$	0.224691	−	1.56276i	0.00945281	−	0.0657458i
$566$	−4.31081	+	2.77039i	−0.181197	+	0.116448i
$567$	−3.82111	−	1.12198i	−0.160471	−	0.0471187i
$568$	−1.90439	−	13.2453i	−0.0799063	−	0.555761i
$569$	−7.13645	−	8.23591i	−0.299176	−	0.345267i	0.586181	−	0.810180i	$-0.300631\pi$
$569$	−7.13645	−	8.23591i	−0.299176	−	0.345267i	−0.885356	+	0.464913i	$0.846085\pi$
$570$	0.0791532	+	0.0508687i	0.00331536	+	0.00213065i
$571$	5.20302	−	6.00460i	0.217739	−	0.251285i	−0.636363	−	0.771390i	$-0.719562\pi$
$571$	5.20302	−	6.00460i	0.217739	−	0.251285i	0.854102	+	0.520105i	$0.174107\pi$
$572$	−8.08585	+	2.37422i	−0.338086	+	0.0992711i
$573$	8.53730	+	18.6941i	0.356651	+	0.780956i
$574$	−7.40149			−0.308932
$575$	−23.8989	+	1.43342i	−0.996655	+	0.0597777i
$576$	4.19584			0.174827
$577$	15.2790	+	33.4563i	0.636071	+	1.39280i	0.903233	+	0.429150i	$0.141187\pi$
$577$	15.2790	+	33.4563i	0.636071	+	1.39280i	−0.267162	+	0.963652i	$0.586086\pi$
$578$	18.2486	−	5.35827i	0.759041	−	0.222875i
$579$	−31.8935	+	36.8071i	−1.32545	+	1.52965i
$580$	−0.207501	−	0.133353i	−0.00861602	−	0.00553718i
$581$	−5.04753	−	5.82516i	−0.209407	−	0.241668i
$582$	1.07032	+	7.44421i	0.0443660	+	0.308573i
$583$	−15.1716	−	4.45479i	−0.628344	−	0.184498i
$584$	8.95905	−	5.75763i	0.370728	−	0.238253i
$585$	0.257209	−	1.78892i	0.0106343	−	0.0739629i
$586$	9.64457	−	21.1187i	0.398414	−	0.872404i
$587$	3.82011	−	8.36488i	0.157673	−	0.345255i	−0.814265	−	0.580493i	$-0.802860\pi$
$587$	3.82011	−	8.36488i	0.157673	−	0.345255i	0.971938	+	0.235238i	$0.0755869\pi$
$588$	−0.381761	+	2.65520i	−0.0157435	+	0.109499i
$589$	−0.744563	+	0.478501i	−0.0306792	+	0.0197163i
$590$	0.225136	+	0.0661060i	0.00926872	+	0.00272154i
$591$	−2.22620	−	15.4835i	−0.0915736	−	0.636908i
$592$	−5.81264	−	6.70814i	−0.238898	−	0.275703i
$593$	31.7484	+	20.4035i	1.30375	+	0.837870i	0.993615	−	0.112822i	$-0.0359890\pi$
$593$	31.7484	+	20.4035i	1.30375	+	0.837870i	0.310136	+	0.950692i	$0.399625\pi$
$594$	−3.62313	+	4.18132i	−0.148659	+	0.171561i
$595$	0.507644	−	0.149058i	0.0208114	−	0.00611077i
$596$	−4.27678	−	9.36485i	−0.175184	−	0.383599i
$597$	−46.1195			−1.88755
$598$	−1.94021	+	23.3526i	−0.0793412	+	0.954957i
$599$	22.3867			0.914696			0.457348	−	0.889288i	$-0.348799\pi$
$599$	22.3867			0.914696			0.457348	+	0.889288i	$0.348799\pi$
$600$	5.56311	+	12.1815i	0.227113	+	0.497308i
$601$	27.6655	−	8.12331i	1.12850	−	0.331357i	0.336381	−	0.941726i	$-0.390797\pi$
$601$	27.6655	−	8.12331i	1.12850	−	0.331357i	0.792117	+	0.610369i	$0.208979\pi$
$602$	5.49236	−	6.33852i	0.223852	−	0.258339i
$603$	3.41245	+	2.19305i	0.138966	+	0.0893078i
$604$	−9.25187	−	10.6772i	−0.376453	−	0.434450i
$605$	0.100685	+	0.700279i	0.00409342	+	0.0284704i
$606$	34.9121	+	10.2511i	1.41821	+	0.416423i
$607$	−6.39989	+	4.11296i	−0.259763	+	0.166940i	−0.664040	−	0.747697i	$-0.731160\pi$
$607$	−6.39989	+	4.11296i	−0.259763	+	0.166940i	0.404277	+	0.914637i	$0.367523\pi$
$608$	−0.0566239	+	0.393828i	−0.00229640	+	0.0159718i
$609$	3.11792	−	6.82730i	0.126345	−	0.276656i
$610$	−0.0841892	+	0.184349i	−0.00340872	+	0.00746406i
$611$	−2.29761	+	15.9802i	−0.0929513	+	0.646490i
$612$	21.1842	−	13.6143i	0.856320	−	0.550324i
$613$	−37.4740	−	11.0034i	−1.51356	−	0.444422i	−0.583589	−	0.812049i	$-0.698352\pi$
$613$	−37.4740	−	11.0034i	−1.51356	−	0.444422i	−0.929973	+	0.367627i	$0.880170\pi$
$614$	−1.59012	−	11.0595i	−0.0641719	−	0.446325i
$615$	1.14620	+	1.32279i	0.0462193	+	0.0533399i
$616$	−1.45093	−	0.932456i	−0.0584596	−	0.0375697i
$617$	−28.4158	+	32.7935i	−1.14398	+	1.32022i	−0.204001	+	0.978971i	$0.565395\pi$
$617$	−28.4158	+	32.7935i	−1.14398	+	1.32022i	−0.939974	+	0.341247i	$0.889151\pi$
$618$	12.6617	−	3.71780i	0.509327	−	0.149552i
$619$	−2.22299	−	4.86768i	−0.0893496	−	0.195648i	0.859682	−	0.510830i	$-0.170662\pi$
$619$	−2.22299	−	4.86768i	−0.0893496	−	0.195648i	−0.949031	+	0.315182i	$0.897935\pi$
$620$	0.196100			0.00787555
$621$	7.21727	+	13.5864i	0.289619	+	0.545202i
$622$	13.6196			0.546096
$623$	−1.24857	−	2.73398i	−0.0500228	−	0.109535i
$624$	12.5761	−	3.69269i	0.503448	−	0.147826i
$625$	−16.2952	+	18.8057i	−0.651809	+	0.752227i
$626$	21.4837	+	13.8068i	0.858662	+	0.551829i
$627$	−1.20548	−	1.39119i	−0.0481421	−	0.0555589i
$628$	−2.77215	−	19.2807i	−0.110621	−	0.769384i
$629$	−51.1130	−	15.0081i	−2.03801	−	0.598414i
$630$	0.311170	−	0.199977i	0.0123973	−	0.00796727i
$631$	1.59087	−	11.0648i	0.0633317	−	0.440481i	−0.933342	−	0.358988i	$-0.883122\pi$
$631$	1.59087	−	11.0648i	0.0633317	−	0.440481i	0.996674	−	0.0814935i	$-0.0259690\pi$
$632$	−1.06077	+	2.32276i	−0.0421952	+	0.0923946i
$633$	−17.3967	+	38.0935i	−0.691457	+	1.51408i
$634$	0.324051	−	2.25382i	0.0128697	−	0.0895107i
$635$	−0.682962	+	0.438913i	−0.0271025	+	0.0174177i
$636$	23.5968	+	6.92864i	0.935674	+	0.274739i
$637$	0.695368	+	4.83639i	0.0275515	+	0.191625i
$638$	3.16018	+	3.64704i	0.125113	+	0.144388i
$639$	−47.2336	−	30.3552i	−1.86853	−	1.20083i
$640$	0.0577299	−	0.0666238i	0.00228197	−	0.00263354i
$641$	47.6387	−	13.9880i	1.88161	−	0.552492i	0.885478	−	0.464682i	$-0.153831\pi$
$641$	47.6387	−	13.9880i	1.88161	−	0.552492i	0.996137	−	0.0878099i	$-0.0279868\pi$
$642$	−22.2444	−	48.7085i	−0.877917	−	1.92237i
$643$	−11.8828			−0.468612			−0.234306	−	0.972163i	$-0.575282\pi$
$643$	−11.8828			−0.468612			−0.234306	+	0.972163i	$0.575282\pi$
$644$	−3.87204	+	2.82972i	−0.152580	+	0.111507i
$645$	−1.98336			−0.0780949
$646$	0.991967	+	2.17210i	0.0390284	+	0.0854603i
$647$	−38.9048	+	11.4235i	−1.52951	+	0.449103i	−0.934899	−	0.354913i	$-0.884510\pi$
$647$	−38.9048	+	11.4235i	−1.52951	+	0.449103i	−0.594607	+	0.804017i	$0.702692\pi$
$648$	−2.60793	+	3.00972i	−0.102449	+	0.118233i
$649$	−3.86188	−	2.48188i	−0.151592	−	0.0974224i
$650$	15.9738	+	18.4347i	0.626543	+	0.723070i
$651$	0.849212	+	5.90640i	0.0332832	+	0.231490i
$652$	10.7345	+	3.15194i	0.420396	+	0.123439i
$653$	2.86730	−	1.84270i	0.112206	−	0.0721104i	−0.483334	−	0.875436i	$-0.660574\pi$
$653$	2.86730	−	1.84270i	0.112206	−	0.0721104i	0.595540	+	0.803325i	$0.296938\pi$
$654$	0.468206	−	3.25645i	0.0183083	−	0.127337i
$655$	−0.318210	+	0.696782i	−0.0124335	+	0.0272255i
$656$	−3.07469	+	6.73263i	−0.120047	+	0.262865i
$657$	6.35923	−	44.2294i	0.248097	−	1.72555i
$658$	−2.77964	+	1.78636i	−0.108362	+	0.0696398i
$659$	39.1841	+	11.5055i	1.52640	+	0.448191i	0.933946	−	0.357415i	$-0.116342\pi$
$659$	39.1841	+	11.5055i	1.52640	+	0.448191i	0.592452	+	0.805606i	$0.298160\pi$
$660$	0.0580447	+	0.403709i	0.00225938	+	0.0157144i
$661$	−29.8715	−	34.4735i	−1.16186	−	1.34086i	−0.929757	−	0.368173i	$-0.879983\pi$
$661$	−29.8715	−	34.4735i	−1.16186	−	1.34086i	−0.232108	−	0.972690i	$-0.574562\pi$
$662$	12.0957	+	7.77346i	0.470114	+	0.302124i
$663$	51.5134	−	59.4496i	2.00061	−	2.30883i
$664$	−7.39557	+	2.17154i	−0.287004	+	0.0842720i
$665$	0.0145708	+	0.0319056i	0.000565031	+	0.00123724i
$666$	−37.2429			−1.44313
$667$	12.6256	−	4.54451i	0.488865	−	0.175964i
$668$	9.61074			0.371851
$669$	28.1987	+	61.7465i	1.09022	+	2.38726i
$670$	0.0817736	−	0.0240109i	0.00315919	−	0.000927622i
$671$	2.59652	−	2.99654i	0.100237	−	0.115680i
$672$	2.25667	+	1.45027i	0.0870529	+	0.0559455i
$673$	17.7037	+	20.4312i	0.682427	+	0.787563i	0.986267	−	0.165160i	$-0.0528141\pi$
$673$	17.7037	+	20.4312i	0.682427	+	0.787563i	−0.303839	+	0.952723i	$0.598269\pi$
$674$	−2.25861	−	15.7090i	−0.0869984	−	0.605087i
$675$	15.3657	+	4.51177i	0.591425	+	0.173658i
$676$	9.14795	−	5.87903i	0.351844	−	0.226117i
$677$	−5.08935	+	35.3972i	−0.195600	+	1.36042i	0.621267	+	0.783599i	$0.286618\pi$
$677$	−5.08935	+	35.3972i	−0.195600	+	1.36042i	−0.816867	+	0.576826i	$0.804291\pi$
$678$	19.9575	−	43.7009i	0.766464	−	1.67832i
$679$	−1.16467	+	2.55027i	−0.0446960	+	0.0978705i
$680$	0.0752952	−	0.523690i	0.00288744	−	0.0200826i
$681$	−42.2614	+	27.1597i	−1.61946	+	1.04076i
$682$	−3.68118	−	1.08089i	−0.140960	−	0.0413894i
$683$	−0.256399	−	1.78329i	−0.00981082	−	0.0682358i	0.984328	−	0.176348i	$-0.0564285\pi$
$683$	−0.256399	−	1.78329i	−0.00981082	−	0.0682358i	−0.994139	+	0.108112i	$0.965519\pi$
$684$	1.09325	+	1.26167i	0.0418013	+	0.0482412i
$685$	−0.00797976	−	0.00512828i	−0.000304891	−	0.000195941i
$686$	−0.654861	+	0.755750i	−0.0250027	+	0.0288547i
$687$	−8.43648	+	2.47717i	−0.321872	+	0.0945101i
$688$	−3.48411	−	7.62915i	−0.132831	−	0.290858i
$689$	44.7955			1.70657
$690$	1.10535	+	0.253794i	0.0420800	+	0.00966176i
$691$	17.6296			0.670661			0.335330	−	0.942101i	$-0.391152\pi$
$691$	17.6296			0.670661			0.335330	+	0.942101i	$0.391152\pi$
$692$	−1.59742	−	3.49787i	−0.0607250	−	0.132969i
$693$	−6.94354	+	2.03881i	−0.263763	+	0.0774479i
$694$	−0.145172	+	0.167538i	−0.00551067	+	0.00635965i
$695$	−1.34260	−	0.862839i	−0.0509279	−	0.0327293i
$696$	−4.91510	−	5.67233i	−0.186306	−	0.215009i
$697$	6.32172	+	43.9685i	0.239452	+	1.66543i
$698$	−20.1730	−	5.92333i	−0.763560	−	0.224201i
$699$	−65.0777	+	41.8229i	−2.46146	+	1.58189i
$700$	−0.710468	+	4.94141i	−0.0268532	+	0.186768i
$701$	3.45996	−	7.57625i	0.130681	−	0.286151i	−0.832969	−	0.553320i	$-0.813361\pi$
$701$	3.45996	−	7.57625i	0.130681	−	0.286151i	0.963650	+	0.267169i	$0.0860881\pi$
$702$	6.51121	−	14.2576i	0.245750	−	0.538117i
$703$	0.502601	−	3.49567i	0.0189560	−	0.131842i
$704$	−1.45093	+	0.932456i	−0.0546840	+	0.0351433i
$705$	0.749714	+	0.220136i	0.0282359	+	0.00829079i
$706$	0.802472	+	5.58131i	0.0302014	+	0.210056i
$707$	8.88264	+	10.2511i	0.334066	+	0.385533i
$708$	6.00648	+	3.86013i	0.225738	+	0.145073i
$709$	−8.73450	+	10.0801i	−0.328031	+	0.378568i	−0.895677	−	0.444705i	$-0.853309\pi$
$709$	−8.73450	+	10.0801i	−0.328031	+	0.378568i	0.567646	+	0.823272i	$0.307854\pi$
$710$	−1.13187	+	0.332348i	−0.0424785	+	0.0124728i
$711$	4.45083	+	9.74596i	0.166919	+	0.365502i
$712$	−3.00559			−0.112639
$713$	−6.49091	+	8.46625i	−0.243087	+	0.317064i
$714$	16.0993			0.602501
$715$	0.308615	+	0.675774i	0.0115416	+	0.0252725i
$716$	0.0148402	−	0.00435748i	0.000554605	−	0.000162847i
$717$	34.3850	−	39.6824i	1.28413	−	1.48197i
$718$	−24.1929	−	15.5478i	−0.902870	−	0.580239i
$719$	−15.1616	−	17.4974i	−0.565431	−	0.652542i	0.398977	−	0.916961i	$-0.369365\pi$
$719$	−15.1616	−	17.4974i	−0.565431	−	0.652542i	−0.964408	+	0.264419i	$0.914820\pi$
$720$	−0.0526406	−	0.366124i	−0.00196180	−	0.0136446i
$721$	4.72009	+	1.38594i	0.175785	+	0.0516152i
$722$	15.8506	−	10.1866i	0.589900	−	0.379106i
$723$	−2.22242	+	15.4573i	−0.0826526	+	0.574862i
$724$	−10.2219	+	22.3829i	−0.379896	+	0.831855i
$725$	5.80255	−	12.7058i	0.215501	−	0.471882i
$726$	−3.06375	+	21.3089i	−0.113707	+	0.790846i
$727$	21.7402	−	13.9716i	0.806301	−	0.518178i	−0.0713656	−	0.997450i	$-0.522736\pi$
$727$	21.7402	−	13.9716i	0.806301	−	0.518178i	0.877666	+	0.479272i	$0.159099\pi$
$728$	4.68820	+	1.37658i	0.173756	+	0.0510194i
$729$	6.05193	+	42.0921i	0.224146	+	1.55897i
$730$	−0.614802	−	0.709520i	−0.0227549	−	0.0262605i
$731$	−42.3451	−	27.2135i	−1.56619	−	1.00653i
$732$	−4.03843	+	4.66060i	−0.149265	+	0.172261i
$733$	37.5100	−	11.0139i	1.38546	−	0.406808i	0.497795	−	0.867295i	$-0.334143\pi$
$733$	37.5100	−	11.0139i	1.38546	−	0.406808i	0.887667	+	0.460486i	$0.152325\pi$
$734$	10.0013	+	21.8997i	0.369154	+	0.808334i
$735$	0.236479			0.00872265
$736$	0.965501	+	4.69764i	0.0355888	+	0.173157i
$737$	−1.66740			−0.0614194
$738$	12.9009	+	28.2491i	0.474890	+	1.03986i
$739$	46.6678	−	13.7029i	1.71670	−	0.504069i	0.732446	−	0.680825i	$-0.238378\pi$
$739$	46.6678	−	13.7029i	1.71670	−	0.504069i	0.984255	+	0.176756i	$0.0565602\pi$
$740$	−0.512418	+	0.591362i	−0.0188369	+	0.0217389i
$741$	4.38714	+	2.81944i	0.161166	+	0.103575i
$742$	6.00370	+	6.92864i	0.220403	+	0.254359i
$743$	−1.46730	−	10.2053i	−0.0538300	−	0.374396i	−0.998874	−	0.0474514i	$-0.984890\pi$
$743$	−1.46730	−	10.2053i	−0.0538300	−	0.374396i	0.945044	−	0.326944i	$-0.106019\pi$
$744$	5.72543	+	1.68114i	0.209904	+	0.0616335i
$745$	−0.763508	+	0.490677i	−0.0279728	+	0.0179770i
$746$	−1.05697	+	7.35139i	−0.0386984	+	0.269154i
$747$	−13.4348	+	29.4181i	−0.491554	+	1.07635i
$748$	−4.29999	+	9.41567i	−0.157223	+	0.344271i
$749$	2.84085	−	19.7585i	0.103802	−	0.721961i
$750$	1.98784	−	1.27751i	0.0725857	−	0.0466480i
$751$	10.6071	+	3.11453i	0.387059	+	0.113651i	0.469472	−	0.882948i	$-0.344444\pi$
$751$	10.6071	+	3.11453i	0.387059	+	0.113651i	−0.0824128	+	0.996598i	$0.526263\pi$
$752$	0.470231	+	3.27053i	0.0171476	+	0.119264i
$753$	−27.5963	−	31.8478i	−1.00566	−	1.16060i
$754$	−11.5010	−	7.39121i	−0.418840	−	0.269172i
$755$	−0.815607	+	0.941261i	−0.0296830	+	0.0342560i
$756$	3.07792	−	0.903759i	0.111943	−	0.0328694i
$757$	−0.213043	−	0.466500i	−0.00774319	−	0.0169552i	0.905721	−	0.423875i	$-0.139330\pi$
$757$	−0.213043	−	0.466500i	−0.00774319	−	0.0169552i	−0.913464	+	0.406919i	$0.866603\pi$
$758$	−28.2428			−1.02582
$759$	−19.3507	−	10.8568i	−0.702387	−	0.394079i
$760$	0.0350752			0.00127231
$761$	19.7670	+	43.2838i	0.716554	+	1.56904i	0.818671	+	0.574263i	$0.194711\pi$
$761$	19.7670	+	43.2838i	0.716554	+	1.56904i	−0.102116	+	0.994772i	$0.532561\pi$
$762$	−23.7029	+	6.95979i	−0.858665	+	0.252127i
$763$	0.803147	−	0.926881i	0.0290759	−	0.0335554i
$764$	6.44502	+	4.14196i	0.233173	+	0.149851i
$765$	−1.45374	−	1.67770i	−0.0525599	−	0.0606574i
$766$	−1.48559	−	10.3325i	−0.0536765	−	0.373328i
$767$	12.4784	+	3.66399i	0.450569	+	0.132299i
$768$	2.25667	−	1.45027i	0.0814305	−	0.0523322i
$769$	−5.50710	+	38.3027i	−0.198591	+	1.38123i	0.609786	+	0.792566i	$0.291255\pi$
$769$	−5.50710	+	38.3027i	−0.198591	+	1.38123i	−0.808377	+	0.588665i	$0.799654\pi$
$770$	−0.0631616	+	0.138305i	−0.00227619	+	0.00498415i
$771$	28.1553	−	61.6514i	1.01399	−	2.22032i
$772$	−2.58382	+	17.9709i	−0.0929938	+	0.646786i
$773$	27.8171	−	17.8769i	1.00051	−	0.642989i	0.0655896	−	0.997847i	$-0.479107\pi$
$773$	27.8171	−	17.8769i	1.00051	−	0.642989i	0.934920	+	0.354858i	$0.115471\pi$
$774$	−33.7654	−	9.91440i	−1.21367	−	0.356366i
$775$	1.58041	+	10.9920i	0.0567700	+	0.394844i
$776$	1.83599	+	2.11884i	0.0659082	+	0.0760621i
$777$	−20.0305	−	12.8728i	−0.718590	−	0.461810i
$778$	5.50421	−	6.35220i	0.197336	−	0.227737i
$779$	−2.82560	+	0.829670i	−0.101238	+	0.0297260i
$780$	−0.479997	−	1.05105i	−0.0171867	−	0.0376335i
$781$	23.0794			0.825846
$782$	20.1171	+	20.5849i	0.719386	+	0.736115i
$783$	−8.97549			−0.320758
$784$	0.415415	+	0.909632i	0.0148363	+	0.0324869i
$785$	−1.64763	+	0.483788i	−0.0588064	+	0.0172671i
$786$	−15.2640	+	17.6156i	−0.544450	+	0.628329i
$787$	−18.0934	−	11.6279i	−0.644959	−	0.414490i	0.176862	−	0.984236i	$-0.443405\pi$
$787$	−18.0934	−	11.6279i	−0.644959	−	0.414490i	−0.821821	+	0.569745i	$0.807042\pi$
$788$	−3.81875	−	4.40708i	−0.136037	−	0.156996i
$789$	6.89910	+	47.9843i	0.245614	+	1.70829i
$790$	0.215990	+	0.0634203i	0.00768456	+	0.00225639i
$791$	15.0664	−	9.68261i	0.535701	−	0.344274i
$792$	−1.02989	+	7.16301i	−0.0365954	+	0.254527i
$793$	−4.66626	+	10.2177i	−0.165704	+	0.362841i
$794$	−5.01774	+	10.9873i	−0.178073	+	0.389926i
$795$	0.308541	−	2.14595i	0.0109428	−	0.0761090i
$796$	−14.4634	+	9.29507i	−0.512642	+	0.329455i
$797$	13.8573	+	4.06886i	0.490850	+	0.144126i	0.517785	−	0.855511i	$-0.326757\pi$
$797$	13.8573	+	4.06886i	0.490850	+	0.144126i	−0.0269354	+	0.999637i	$0.508575\pi$
$798$	0.151894	+	1.05645i	0.00537699	+	0.0373978i
$799$	12.9860	+	14.9867i	0.459412	+	0.530190i
$800$	4.19973	+	2.69900i	0.148483	+	0.0954241i
$801$	−8.25845	+	9.53076i	−0.291798	+	0.336753i
$802$	3.73231	−	1.09591i	0.131792	−	0.0386978i
$803$	7.63022	+	16.7078i	0.269265	+	0.589607i
$804$	2.59335			0.0914603
$805$	0.295496	+	0.302367i	0.0104149	+	0.0106570i
$806$	10.8690			0.382844
$807$	9.36666	+	20.5101i	0.329722	+	0.721991i
$808$	13.0147	−	3.82147i	0.457857	−	0.134439i
$809$	−3.72995	+	4.30459i	−0.131138	+	0.151341i	−0.817521	−	0.575899i	$-0.804652\pi$
$809$	−3.72995	+	4.30459i	−0.131138	+	0.151341i	0.686383	+	0.727241i	$0.259198\pi$
$810$	0.295342	+	0.189805i	0.0103773	+	0.00666907i
$811$	28.7522	+	33.1818i	1.00963	+	1.16517i	0.986219	+	0.165446i	$0.0529062\pi$
$811$	28.7522	+	33.1818i	1.00963	+	1.16517i	0.0234080	+	0.999726i	$0.492548\pi$
$812$	−0.398192	−	2.76949i	−0.0139738	−	0.0971900i
$813$	−68.3871	−	20.0803i	−2.39844	−	0.704246i
$814$	12.8787	−	8.27661i	0.451397	−	0.290095i
$815$	0.140360	−	0.976222i	0.00491658	−	0.0341956i
$816$	6.68789	−	14.6444i	0.234123	−	0.512657i
$817$	1.38625	−	3.03546i	0.0484988	−	0.106197i
$818$	−4.46195	+	31.0335i	−0.156008	+	1.08506i
$819$	17.2469	−	11.0839i	0.602655	−	0.387303i
$820$	0.626055	+	0.183826i	0.0218628	+	0.00641950i
$821$	−0.292144	−	2.03190i	−0.0101959	−	0.0709139i	0.984088	−	0.177680i	$-0.0568593\pi$
$821$	−0.292144	−	2.03190i	−0.0101959	−	0.0709139i	−0.994284	+	0.106767i	$0.965950\pi$
$822$	−0.189017	−	0.218137i	−0.00659273	−	0.00760841i
$823$	31.4734	+	20.2267i	1.09709	+	0.705060i	0.958444	−	0.285281i	$-0.0920870\pi$
$823$	31.4734	+	20.2267i	1.09709	+	0.705060i	0.138651	+	0.990341i	$0.455723\pi$
$824$	3.22150	−	3.71780i	0.112226	−	0.129516i
$825$	−22.1614	+	6.50717i	−0.771560	+	0.226551i
$826$	1.10569	+	2.42113i	0.0384720	+	0.0842419i
$827$	33.7835			1.17477			0.587384	−	0.809308i	$-0.300158\pi$
$827$	33.7835			1.17477			0.587384	+	0.809308i	$0.300158\pi$
$828$	17.5491	+	9.84606i	0.609875	+	0.342174i
$829$	−10.2402			−0.355657			−0.177829	−	0.984061i	$-0.556907\pi$
$829$	−10.2402			−0.355657			−0.177829	+	0.984061i	$0.556907\pi$
$830$	0.282269	+	0.618084i	0.00979771	+	0.0214540i
$831$	73.0979	−	21.4635i	2.53574	−	0.744560i
$832$	3.19973	−	3.69269i	0.110931	−	0.128021i
$833$	5.04885	+	3.24470i	0.174932	+	0.112422i
$834$	−31.8024	−	36.7019i	−1.10123	−	1.27088i
$835$	−0.120575	−	0.838620i	−0.00417268	−	0.0290216i
$836$	−0.658432	−	0.193333i	−0.0227723	−	0.00668656i
$837$	6.00299	−	3.85789i	0.207494	−	0.133348i
$838$	4.07032	−	28.3097i	0.140607	−	0.977943i
$839$	−11.7349	+	25.6959i	−0.405134	+	0.887120i	0.591589	+	0.806239i	$0.298501\pi$
$839$	−11.7349	+	25.6959i	−0.405134	+	0.887120i	−0.996724	+	0.0808810i	$0.974227\pi$
$840$	0.0982369	−	0.215109i	0.00338949	−	0.00742196i
$841$	3.01300	−	20.9559i	0.103897	−	0.722617i
$842$	−23.0545	+	14.8162i	−0.794510	+	0.510601i
$843$	−13.2462	−	3.88944i	−0.456224	−	0.133959i
$844$	2.22174	+	15.4526i	0.0764756	+	0.531900i
$845$	−0.627766	−	0.724480i	−0.0215958	−	0.0249229i
$846$	11.6629	+	7.49531i	0.400980	+	0.257694i
$847$	−5.25547	+	6.06514i	−0.180580	+	0.208401i
$848$	8.79655	−	2.58290i	0.302075	−	0.0886971i
$849$	5.71025	+	12.5037i	0.195975	+	0.429126i
$850$	29.9613			1.02766
$851$	−8.56992	−	41.6969i	−0.293773	−	1.42935i
$852$	−35.8960			−1.22978
$853$	−7.14045	−	15.6354i	−0.244484	−	0.535346i	0.747115	−	0.664695i	$-0.231439\pi$
$853$	−7.14045	−	15.6354i	−0.244484	−	0.535346i	−0.991599	+	0.129349i	$0.958711\pi$
$854$	−2.20579	+	0.647679i	−0.0754806	+	0.0221631i
$855$	0.0963760	−	0.111224i	0.00329599	−	0.00380378i
$856$	−16.7929	−	10.7921i	−0.573968	−	0.368867i
$857$	17.6532	+	20.3729i	0.603023	+	0.695926i	0.972391	−	0.233357i	$-0.0749712\pi$
$857$	17.6532	+	20.3729i	0.603023	+	0.695926i	−0.369368	+	0.929283i	$0.620426\pi$
$858$	3.21718	+	22.3760i	0.109833	+	0.763903i
$859$	6.00563	+	1.76341i	0.204910	+	0.0601669i	0.382577	−	0.923924i	$-0.375037\pi$
$859$	6.00563	+	1.76341i	0.204910	+	0.0601669i	−0.177667	+	0.984091i	$0.556855\pi$
$860$	−0.621997	+	0.399734i	−0.0212099	+	0.0136308i
$861$	−2.82560	+	19.6525i	−0.0962961	+	0.669754i
$862$	−14.4850	+	31.7177i	−0.493361	+	1.08031i
$863$	−4.67740	+	10.2421i	−0.159220	+	0.348644i	−0.972382	−	0.233393i	$-0.925017\pi$
$863$	−4.67740	+	10.2421i	−0.159220	+	0.348644i	0.813162	+	0.582037i	$0.197744\pi$
$864$	0.456526	−	3.17521i	0.0155313	−	0.108023i
$865$	−0.285178	+	0.183273i	−0.00969635	+	0.00623147i
$866$	−6.56719	−	1.92830i	−0.223162	−	0.0655264i
$867$	−7.26070	−	50.4993i	−0.246586	−	1.71505i
$868$	1.45671	+	1.68114i	0.0494441	+	0.0570615i
$869$	−3.70498	−	2.38105i	−0.125683	−	0.0807715i
$870$	−0.433295	+	0.500049i	−0.0146901	+	0.0169533i
$871$	4.53238	−	1.33083i	0.153574	−	0.0450933i
$872$	−0.509482	−	1.11561i	−0.0172532	−	0.0377793i
$873$	11.7636			0.398138
$874$	−1.16099	+	1.51431i	−0.0392712	+	0.0512224i
$875$	0.880874			0.0297790
$876$	−11.8675	−	25.9861i	−0.400965	−	0.877990i
$877$	−3.92597	+	1.15277i	−0.132571	+	0.0389262i	−0.347345	−	0.937738i	$-0.612917\pi$
$877$	−3.92597	+	1.15277i	−0.132571	+	0.0389262i	0.214774	+	0.976664i	$0.431098\pi$
$878$	−11.5053	+	13.2778i	−0.388286	+	0.448106i
$879$	−52.3924	−	33.6706i	−1.76715	−	1.13568i
$880$	0.0995681	+	0.114908i	0.00335644	+	0.00387354i
$881$	3.46398	+	24.0925i	0.116704	+	0.811697i	0.961144	+	0.276047i	$0.0890244\pi$
$881$	3.46398	+	24.0925i	0.116704	+	0.811697i	−0.844440	+	0.535650i	$0.820066\pi$
$882$	4.02588	+	1.18211i	0.135559	+	0.0398036i
$883$	5.93936	−	3.81699i	0.199875	−	0.128452i	−0.436875	−	0.899522i	$-0.643915\pi$
$883$	5.93936	−	3.81699i	0.199875	−	0.128452i	0.636750	+	0.771070i	$0.280278\pi$
$884$	4.17331	−	29.0260i	0.140364	−	0.976250i
$885$	0.261473	−	0.572546i	0.00878932	−	0.0192459i
$886$	−4.26454	+	9.33804i	−0.143270	+	0.313717i
$887$	4.65162	−	32.3527i	0.156186	−	1.08630i	−0.749394	−	0.662124i	$-0.769655\pi$
$887$	4.65162	−	32.3527i	0.156186	−	1.08630i	0.905580	−	0.424175i	$-0.139436\pi$
$888$	−20.0305	+	12.8728i	−0.672180	+	0.431984i
$889$	−8.83609	−	2.59451i	−0.296353	−	0.0870171i
$890$	0.0377078	+	0.262264i	0.00126397	+	0.00879110i
$891$	−4.49797	−	5.19093i	−0.150688	−	0.173903i
$892$	21.2879	+	13.6809i	0.712771	+	0.458070i
$893$	−0.860914	+	0.993547i	−0.0288094	+	0.0332478i
$894$	−26.4983	+	7.78060i	−0.886235	+	0.260222i
$895$	−0.000566412	−	0.00124027i	−1.89331e−5	−	4.14576e-5i
$896$	1.00000			0.0334077
$897$	61.2651	+	14.0667i	2.04558	+	0.469675i
$898$	6.06594			0.202423
$899$	−2.58553	−	5.66152i	−0.0862323	−	0.188822i
$900$	20.0981	−	5.90134i	0.669938	−	0.196711i
$901$	36.0317	−	41.5828i	1.20039	−	1.38532i
$902$	−10.7390	−	6.90157i	−0.357571	−	0.229797i
$903$	−14.7333	−	17.0031i	−0.490294	−	0.565829i
$904$	−2.54879	−	17.7272i	−0.0847714	−	0.589598i
$905$	2.08135	+	0.611139i	0.0691863	+	0.0203149i
$906$	−31.8822	+	20.4894i	−1.05922	+	0.680716i
$907$	−3.89588	+	27.0964i	−0.129361	+	0.899723i	0.817006	+	0.576629i	$0.195632\pi$
$907$	−3.89588	+	27.0964i	−0.129361	+	0.899723i	−0.946367	+	0.323094i	$0.895277\pi$
$908$	−7.77962	+	17.0350i	−0.258176	+	0.565326i
$909$	23.6426	−	51.7700i	0.784175	−	1.71710i
$910$	0.0613008	−	0.426356i	0.00203210	−	0.0141336i
$911$	−3.35900	+	2.15870i	−0.111289	+	0.0715209i	−0.595101	−	0.803651i	$-0.702888\pi$
$911$	−3.35900	+	2.15870i	−0.111289	+	0.0715209i	0.483813	+	0.875172i	$0.339252\pi$
$912$	1.02408	+	0.300696i	0.0339105	+	0.00995703i
$913$	−1.89191	−	13.1585i	−0.0626130	−	0.435483i
$914$	−11.7201	−	13.5257i	−0.387667	−	0.447391i
$915$	0.457343	+	0.293916i	0.0151193	+	0.00971658i
$916$	−2.14648	+	2.47717i	−0.0709218	+	0.0818481i
$917$	−8.33722	+	2.44803i	−0.275319	+	0.0808411i
$918$	−7.99767	−	17.5125i	−0.263962	−	0.577997i
$919$	40.8313			1.34690			0.673450	−	0.739233i	$-0.264812\pi$
$919$	40.8313			1.34690			0.673450	+	0.739233i	$0.264812\pi$
$920$	0.397796	−	0.143184i	0.0131150	−	0.00472065i
$921$	−29.9723			−0.987620
$922$	−17.5460	−	38.4205i	−0.577848	−	1.26531i
$923$	−62.7352	+	18.4207i	−2.06495	+	0.606325i
$924$	−3.02977	+	3.49654i	−0.0996721	+	0.115028i
$925$	−37.2774	−	23.9567i	−1.22567	−	0.787692i
$926$	24.2880	+	28.0298i	0.798152	+	0.921116i
$927$	−2.93750	−	20.4308i	−0.0964802	−	0.671035i
$928$	−2.68463	−	0.788278i	−0.0881273	−	0.0258765i
$929$	−0.0886650	+	0.0569816i	−0.00290901	+	0.00186950i	−0.542095	−	0.840318i	$-0.682369\pi$
$929$	−0.0886650	+	0.0569816i	−0.00290901	+	0.00186950i	0.539186	+	0.842187i	$0.318732\pi$
$930$	0.0748631	−	0.520684i	0.00245486	−	0.0170739i
$931$	−0.165284	+	0.361922i	−0.00541697	+	0.0118615i
$932$	−11.9797	+	26.2319i	−0.392409	+	0.859255i
$933$	5.19942	−	36.1628i	0.170221	−	1.18392i
$934$	19.0654	−	12.2526i	0.623839	−	0.400917i
$935$	0.875545	+	0.257083i	0.0286334	+	0.00840752i
$936$	−2.91765	−	20.2927i	−0.0953665	−	0.663289i
$937$	−22.8681	−	26.3912i	−0.747068	−	0.862162i	0.247213	−	0.968961i	$-0.420485\pi$
$937$	−22.8681	−	26.3912i	−0.747068	−	0.862162i	−0.994281	+	0.106799i	$0.965940\pi$
$938$	0.813292	+	0.522671i	0.0265549	+	0.0170658i
$939$	44.8614	−	51.7728i	1.46400	−	1.68954i
$940$	0.279482	−	0.0820635i	0.00911571	−	0.00267662i
$941$	7.67675	+	16.8097i	0.250255	+	0.547981i	0.992514	−	0.122131i	$-0.0389729\pi$
$941$	7.67675	+	16.8097i	0.250255	+	0.547981i	−0.742259	+	0.670113i	$0.766246\pi$
$942$	−52.2525			−1.70248
$943$	−28.6589	+	20.9442i	−0.933261	+	0.682035i
$944$	2.66166			0.0866297
$945$	−0.117476	−	0.257237i	−0.00382149	−	0.00836791i
$946$	13.8794	−	4.07537i	0.451259	−	0.132502i
$947$	16.9879	−	19.6050i	0.552031	−	0.637078i	−0.409324	−	0.912389i	$-0.634235\pi$
$947$	16.9879	−	19.6050i	0.552031	−	0.637078i	0.961355	+	0.275311i	$0.0887809\pi$
$948$	5.76245	+	3.70330i	0.187156	+	0.120278i
$949$	−34.0760	−	39.3258i	−1.10615	−	1.27657i
$950$	0.282679	+	1.96608i	0.00917133	+	0.0637880i
$951$	−5.86064	−	1.72084i	−0.190044	−	0.0558021i
$952$	5.04885	−	3.24470i	0.163634	−	0.105161i
$953$	7.21369	−	50.1723i	0.233674	−	1.62524i	−0.448314	−	0.893876i	$-0.647975\pi$
$953$	7.21369	−	50.1723i	0.233674	−	1.62524i	0.681988	−	0.731363i	$-0.261116\pi$
$954$	15.9798	−	34.9909i	0.517366	−	1.13287i
$955$	0.280563	−	0.614348i	0.00907882	−	0.0198798i
$956$	2.78567	−	19.3748i	0.0900950	−	0.626624i
$957$	10.8901	−	6.99861i	0.352025	−	0.226233i
$958$	−13.9011	−	4.08174i	−0.449125	−	0.131875i
$959$	−0.0153130	−	0.106505i	−0.000494484	−	0.00343921i
$960$	−0.154861	−	0.178719i	−0.00499811	−	0.00576812i
$961$	−21.9161	−	14.0846i	−0.706972	−	0.454343i
$962$	−28.4012	+	32.7768i	−0.915693	+	1.05677i
$963$	−80.3636	+	23.5969i	−2.58968	+	0.760398i
$964$	2.41834	+	5.29542i	0.0778894	+	0.170554i
$965$	1.60053			0.0515229
$966$	6.03529	+	11.3613i	0.194182	+	0.365545i
$967$	−43.2020			−1.38928			−0.694641	−	0.719357i	$-0.744437\pi$
$967$	−43.2020			−1.38928			−0.694641	+	0.719357i	$0.744437\pi$
$968$	3.33384	+	7.30009i	0.107154	+	0.234634i
$969$	6.14607	−	1.80465i	0.197440	−	0.0579737i
$970$	0.161853	−	0.186789i	0.00519680	−	0.00599742i
$971$	11.4228	+	7.34100i	0.366575	+	0.235584i	0.710941	−	0.703252i	$-0.248269\pi$
$971$	11.4228	+	7.34100i	0.366575	+	0.235584i	−0.344365	+	0.938836i	$0.611906\pi$
$972$	13.2979	+	15.3466i	0.426530	+	0.492242i
$973$	−2.57644	−	17.9195i	−0.0825968	−	0.574473i
$974$	−1.46906	−	0.431354i	−0.0470717	−	0.0138215i
$975$	55.0461	−	35.3760i	1.76289	−	1.13294i
$976$	−0.327169	+	2.27551i	−0.0104724	+	0.0728374i
$977$	7.93401	−	17.3731i	0.253832	−	0.555814i	−0.739224	−	0.673460i	$-0.764808\pi$
$977$	7.93401	−	17.3731i	0.253832	−	0.555814i	0.993056	+	0.117646i	$0.0375348\pi$
$978$	12.4670	−	27.2990i	0.398652	−	0.872926i
$979$	0.737734	−	5.13105i	0.0235781	−	0.163989i
$980$	0.0741615	−	0.0476607i	0.00236900	−	0.00152246i
$981$	−4.93750	−	1.44978i	−0.157642	−	0.0462880i
$982$	4.87378	+	33.8979i	0.155529	+	1.08173i
$983$	7.07533	+	8.16536i	0.225668	+	0.260435i	0.857281	−	0.514849i	$-0.172152\pi$
$983$	7.07533	+	8.16536i	0.225668	+	0.260435i	−0.631613	+	0.775284i	$0.717607\pi$
$984$	16.7027	+	10.7342i	0.532463	+	0.342193i
$985$	−0.336646	+	0.388510i	−0.0107264	+	0.0123790i
$986$	−16.1120	+	4.73092i	−0.513111	+	0.150663i
$987$	3.68201	+	8.06247i	0.117200	+	0.256631i
$988$	1.94408			0.0618494
$989$	3.33039	−	40.0849i	0.105900	−	1.27462i
$990$	0.637956			0.0202756
$991$	−16.4122	−	35.9377i	−0.521351	−	1.14160i	−0.968925	−	0.247353i	$-0.920439\pi$
$991$	−16.4122	−	35.9377i	−0.521351	−	1.14160i	0.447574	−	0.894247i	$-0.352288\pi$
$992$	2.13436	−	0.626704i	0.0677659	−	0.0198979i
$993$	25.2578	−	29.1490i	0.801532	−	0.925017i
$994$	−11.2572	−	7.23459i	−0.357058	−	0.229467i
$995$	0.992532	+	1.14544i	0.0314654	+	0.0363130i
$996$	2.94253	+	20.4658i	0.0932377	+	0.648482i
$997$	5.97964	+	1.75578i	0.189377	+	0.0556062i	0.375046	−	0.927006i	$-0.377627\pi$
$997$	5.97964	+	1.75578i	0.189377	+	0.0556062i	−0.185669	+	0.982612i	$0.559445\pi$
$998$	21.2606	−	13.6634i	0.672994	−	0.432507i
$999$	−4.05219	+	28.1836i	−0.128206	+	0.891690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.a.211.1	yes	10
23.6	even	11	inner	322.2.i.a.29.1	✓	10
23.11	odd	22		7406.2.a.bh.1.5		5
23.12	even	11		7406.2.a.bg.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.a.29.1	✓	10	23.6	even	11	inner
322.2.i.a.211.1	yes	10	1.1	even	1	trivial
7406.2.a.bg.1.5		5	23.12	even	11
7406.2.a.bh.1.5		5	23.11	odd	22

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)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-2.57385 + 0.755750i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.0741615 + 0.0476607i) q^{5} +(1.75667 + 2.02730i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(3.52977 - 2.26844i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{2} +(-2.57385 + 0.755750i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.0741615 + 0.0476607i) q^{5} +(1.75667 + 2.02730i) q^{6} +(0.142315 + 0.989821i) q^{7} +(0.959493 + 0.281733i) q^{8} +(3.52977 - 2.26844i) q^{9} +(0.0125459 - 0.0872586i) q^{10} +(-0.716476 + 1.56886i) q^{11} +(1.11435 - 2.44009i) q^{12} +(0.695368 - 4.83639i) q^{13} +(0.841254 - 0.540641i) q^{14} +(-0.226900 - 0.0666238i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-3.93020 - 4.53569i) q^{17} +(-3.52977 - 2.26844i) q^{18} +(0.260554 - 0.300696i) q^{19} +(-0.0845850 + 0.0248364i) q^{20} +(-1.11435 - 2.44009i) q^{21} +1.72472 q^{22} +(1.72750 - 4.47389i) q^{23} -2.68251 q^{24} +(-2.07385 - 4.54109i) q^{25} +(-4.68820 + 1.37658i) q^{26} +(-2.10070 + 2.42434i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(1.83228 + 2.11456i) q^{29} +(0.0336545 + 0.234072i) q^{30} +(-2.13436 - 0.626704i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(0.658432 - 4.57949i) q^{33} +(-2.49315 + 5.45923i) q^{34} +(-0.0366213 + 0.0801894i) q^{35} +(-0.597131 + 4.15314i) q^{36} +(7.46708 - 4.79880i) q^{37} +(-0.381761 - 0.112095i) q^{38} +(1.86533 + 12.9736i) q^{39} +(0.0577299 + 0.0666238i) q^{40} +(-6.22653 - 4.00155i) q^{41} +(-1.75667 + 2.02730i) q^{42} +(8.04733 - 2.36291i) q^{43} +(-0.716476 - 1.56886i) q^{44} +0.369889 q^{45} +(-4.78723 + 0.287130i) q^{46} -3.30416 q^{47} +(1.11435 + 2.44009i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(-3.26921 + 3.77287i) q^{50} +(13.5436 + 8.70393i) q^{51} +(3.19973 + 3.69269i) q^{52} +(1.30473 + 9.07459i) q^{53} +(3.07792 + 0.903759i) q^{54} +(-0.127908 + 0.0822015i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(-0.443376 + 0.970858i) q^{57} +(1.16232 - 2.54512i) q^{58} +(-0.378794 + 2.63457i) q^{59} +(0.198939 - 0.127850i) q^{60} +(-2.20579 - 0.647679i) q^{61} +(0.316574 + 2.20182i) q^{62} +(2.74769 + 3.17101i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.282075 - 0.325532i) q^{65} +(-4.43918 + 1.30346i) q^{66} +(0.401608 + 0.879398i) q^{67} +6.00158 q^{68} +(-1.06519 + 12.8207i) q^{69} +0.0881559 q^{70} +(-5.55888 - 12.1722i) q^{71} +(4.02588 - 1.18211i) q^{72} +(6.97403 - 8.04846i) q^{73} +(-7.46708 - 4.79880i) q^{74} +(8.76969 + 10.1208i) q^{75} +(0.0566239 + 0.393828i) q^{76} +(-1.65486 - 0.485911i) q^{77} +(11.0264 - 7.08621i) q^{78} +(-0.363404 + 2.52753i) q^{79} +(0.0366213 - 0.0801894i) q^{80} +(-1.65436 + 3.62254i) q^{81} +(-1.05334 + 7.32616i) q^{82} +(-6.48421 + 4.16715i) q^{83} +(2.57385 + 0.755750i) q^{84} +(-0.0752952 - 0.523690i) q^{85} +(-5.49236 - 6.33852i) q^{86} +(-6.31408 - 4.05782i) q^{87} +(-1.12945 + 1.30346i) q^{88} +(-2.88384 + 0.846773i) q^{89} +(-0.153657 - 0.336462i) q^{90} +4.88612 q^{91} +(2.24987 + 4.23534i) q^{92} +5.96714 q^{93} +(1.37260 + 3.00557i) q^{94} +(0.0336545 - 0.00988184i) q^{95} +(1.75667 - 2.02730i) q^{96} +(2.35857 + 1.51576i) q^{97} +(0.654861 + 0.755750i) q^{98} +(1.02989 + 7.16301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9} - 5 q^{10} - 11 q^{11} - 3 q^{12} + 10 q^{13} - q^{14} - 7 q^{15} - q^{16} + q^{17} - 16 q^{18} + 3 q^{19} - 6 q^{20} + 3 q^{21} + 12 q^{23} - 8 q^{24} + 2 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} - 5 q^{31} + q^{32} - 11 q^{33} - 12 q^{34} + 6 q^{35} - 6 q^{36} + 27 q^{37} - 3 q^{38} + 8 q^{39} - 5 q^{40} - 12 q^{41} - 3 q^{42} + 38 q^{43} - 11 q^{44} + 8 q^{45} + 10 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 13 q^{50} + 36 q^{51} - q^{52} - 16 q^{53} + 9 q^{54} - 11 q^{55} - q^{56} - 13 q^{57} + 9 q^{58} - 5 q^{59} - 7 q^{60} - 26 q^{61} + 5 q^{62} + 6 q^{63} - q^{64} + 5 q^{65} - 11 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 6 q^{70} + q^{71} + 6 q^{72} + 9 q^{73} - 27 q^{74} + 17 q^{75} - 8 q^{76} - 11 q^{77} + 25 q^{78} - 50 q^{79} - 6 q^{80} + 2 q^{81} + 23 q^{82} - 29 q^{83} + 3 q^{84} + 28 q^{85} + 17 q^{86} - 16 q^{87} + 11 q^{88} + 7 q^{89} - 19 q^{90} + 12 q^{91} + 23 q^{92} + 40 q^{93} + 20 q^{94} - 4 q^{95} + 3 q^{96} + 12 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9 - 5 * q^10 - 11 * q^11 - 3 * q^12 + 10 * q^13 - q^14 - 7 * q^15 - q^16 + q^17 - 16 * q^18 + 3 * q^19 - 6 * q^20 + 3 * q^21 + 12 * q^23 - 8 * q^24 + 2 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 2 * q^29 - 4 * q^30 - 5 * q^31 + q^32 - 11 * q^33 - 12 * q^34 + 6 * q^35 - 6 * q^36 + 27 * q^37 - 3 * q^38 + 8 * q^39 - 5 * q^40 - 12 * q^41 - 3 * q^42 + 38 * q^43 - 11 * q^44 + 8 * q^45 + 10 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 13 * q^50 + 36 * q^51 - q^52 - 16 * q^53 + 9 * q^54 - 11 * q^55 - q^56 - 13 * q^57 + 9 * q^58 - 5 * q^59 - 7 * q^60 - 26 * q^61 + 5 * q^62 + 6 * q^63 - q^64 + 5 * q^65 - 11 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 6 * q^70 + q^71 + 6 * q^72 + 9 * q^73 - 27 * q^74 + 17 * q^75 - 8 * q^76 - 11 * q^77 + 25 * q^78 - 50 * q^79 - 6 * q^80 + 2 * q^81 + 23 * q^82 - 29 * q^83 + 3 * q^84 + 28 * q^85 + 17 * q^86 - 16 * q^87 + 11 * q^88 + 7 * q^89 - 19 * q^90 + 12 * q^91 + 23 * q^92 + 40 * q^93 + 20 * q^94 - 4 * q^95 + 3 * q^96 + 12 * q^97 + q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more