LMFDB - Embedded newform 507.2.t.b.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.8
Character	$\chi$	$=$	507.127
Dual form			507.2.t.b.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.208145 + 0.00838797i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.95026 + 0.157441i) q^{4} +(-1.53730 + 0.583019i) q^{5} +(0.0659665 + 0.197594i) q^{6} +(-0.815402 + 1.91382i) q^{7} +(0.818208 - 0.0993485i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})$	\(q+(-0.208145 + 0.00838797i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.95026 + 0.157441i) q^{4} +(-1.53730 + 0.583019i) q^{5} +(0.0659665 + 0.197594i) q^{6} +(-0.815402 + 1.91382i) q^{7} +(0.818208 - 0.0993485i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(0.315091 - 0.134248i) q^{10} +(1.34892 - 2.13314i) q^{11} +(0.693822 + 1.82946i) q^{12} +(1.58449 - 3.23873i) q^{13} +(0.153669 - 0.405192i) q^{14} +(0.987703 + 1.31439i) q^{15} +(3.69306 - 0.600181i) q^{16} +(5.49344 + 2.34054i) q^{17} +(0.171439 - 0.118336i) q^{18} +(-0.388136 - 0.224090i) q^{19} +(2.90633 - 1.37907i) q^{20} +(2.06512 + 0.250750i) q^{21} +(-0.262878 + 0.455318i) q^{22} +(3.86471 + 6.69388i) q^{23} +(-0.323066 - 0.758263i) q^{24} +(-1.71919 + 1.52307i) q^{25} +(-0.302638 + 0.687418i) q^{26} +(0.748511 + 0.663123i) q^{27} +(1.28893 - 3.86082i) q^{28} +(-0.198630 - 4.92895i) q^{29} +(-0.216611 - 0.265300i) q^{30} +(4.74859 - 5.36005i) q^{31} +(-2.37878 + 0.485632i) q^{32} +(-2.42421 - 0.702182i) q^{33} +(-1.16307 - 0.441093i) q^{34} +(0.137720 - 3.41750i) q^{35} +(1.56419 - 1.17542i) q^{36} +(8.46325 + 1.72779i) q^{37} +(0.0826684 + 0.0433877i) q^{38} +(-3.55169 - 0.620861i) q^{39} +(-1.19991 + 0.629759i) q^{40} +(2.43536 - 0.705409i) q^{41} +(-0.431948 - 0.0348704i) q^{42} +(-1.69076 - 8.28190i) q^{43} +(-2.29489 + 4.37256i) q^{44} +(0.987703 - 1.31439i) q^{45} +(-0.860570 - 1.36088i) q^{46} +(1.89522 + 1.30818i) q^{47} +(-1.60396 - 3.38027i) q^{48} +(1.85125 + 1.92736i) q^{49} +(0.345066 - 0.331440i) q^{50} +(0.719756 - 5.92772i) q^{51} +(-2.58026 + 6.56584i) q^{52} +(0.771182 + 6.35126i) q^{53} +(-0.161361 - 0.131747i) q^{54} +(-0.830021 + 4.06571i) q^{55} +(-0.477033 + 1.64691i) q^{56} +(-0.107257 + 0.435157i) q^{57} +(0.0826878 + 1.02427i) q^{58} +(-1.36645 + 8.40813i) q^{59} +(-2.13322 - 2.40790i) q^{60} +(-10.2850 - 7.72868i) q^{61} +(-0.943437 + 1.15550i) q^{62} +(-0.333701 - 2.05334i) q^{63} +(-6.77453 + 1.66977i) q^{64} +(-0.547589 + 5.90268i) q^{65} +(0.510479 + 0.125822i) q^{66} +(0.919668 - 11.3921i) q^{67} +(-11.0821 - 3.69976i) q^{68} +(5.35436 - 5.57448i) q^{69} +0.712492i q^{70} +(10.8092 + 10.3824i) q^{71} +(-0.638443 + 0.521273i) q^{72} +(0.199294 + 0.379723i) q^{73} +(-1.77608 - 0.288641i) q^{74} +(1.94124 + 1.22757i) q^{75} +(0.792247 + 0.375926i) q^{76} +(2.98254 + 4.32095i) q^{77} +(0.744477 + 0.0994379i) q^{78} +(-8.80074 + 12.7501i) q^{79} +(-5.32741 + 3.07578i) q^{80} +(0.428693 - 0.903450i) q^{81} +(-0.500991 + 0.167255i) q^{82} +(2.34971 + 9.53313i) q^{83} +(-4.06699 - 0.163894i) q^{84} +(-9.80961 - 0.395314i) q^{85} +(0.421393 + 1.70966i) q^{86} +(-4.67908 + 1.56211i) q^{87} +(0.891771 - 1.87937i) q^{88} +(14.7538 - 8.51808i) q^{89} +(-0.194561 + 0.281870i) q^{90} +(4.90635 + 5.67330i) q^{91} +(-8.59109 - 12.4463i) q^{92} +(-6.46956 - 3.06985i) q^{93} +(-0.405454 - 0.256394i) q^{94} +(0.727328 + 0.118202i) q^{95} +(1.12828 + 2.14975i) q^{96} +(5.01899 - 4.09788i) q^{97} +(-0.401496 - 0.385642i) q^{98} +2.52386i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

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 $

$2$	−0.208145	+	0.00838797i	−0.147181	+	0.00593119i	−0.113747	−	0.993510i	$-0.536285\pi$
$2$	−0.208145	+	0.00838797i	−0.147181	+	0.00593119i	−0.0334339	+	0.999441i	$0.510644\pi$
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$4$	−1.95026	+	0.157441i	−0.975130	+	0.0787207i
$5$	−1.53730	+	0.583019i	−0.687499	+	0.260734i	−0.673521	−	0.739168i	$-0.735219\pi$
$5$	−1.53730	+	0.583019i	−0.687499	+	0.260734i	−0.0139784	+	0.999902i	$0.504450\pi$
$6$	0.0659665	+	0.197594i	0.0269307	+	0.0806673i
$7$	−0.815402	+	1.91382i	−0.308193	+	0.723355i	0.691806	+	0.722083i	$0.256815\pi$
$7$	−0.815402	+	1.91382i	−0.308193	+	0.723355i	−0.999999	+	0.00127210i	$0.999595\pi$
$8$	0.818208	−	0.0993485i	0.289280	−	0.0351250i
$9$	−0.845190	+	0.534466i	−0.281730	+	0.178155i
$10$	0.315091	−	0.134248i	0.0996404	−	0.0424528i
$11$	1.34892	−	2.13314i	0.406714	−	0.643166i	−0.578264	−	0.815850i	$-0.696269\pi$
$11$	1.34892	−	2.13314i	0.406714	−	0.643166i	0.984977	+	0.172684i	$0.0552438\pi$
$12$	0.693822	+	1.82946i	0.200289	+	0.528119i
$13$	1.58449	−	3.23873i	0.439459	−	0.898263i
$13$	1.58449	−	3.23873i	0.439459	−	0.898263i
$14$	0.153669	−	0.405192i	0.0410698	−	0.108292i
$15$	0.987703	+	1.31439i	0.255024	+	0.339375i
$16$	3.69306	−	0.600181i	0.923266	−	0.150045i
$17$	5.49344	+	2.34054i	1.33235	+	0.567663i	0.936506	−	0.350653i	$-0.114040\pi$
$17$	5.49344	+	2.34054i	1.33235	+	0.567663i	0.395849	+	0.918316i	$0.370450\pi$
$18$	0.171439	−	0.118336i	0.0404086	−	0.0278921i
$19$	−0.388136	−	0.224090i	−0.0890444	−	0.0514098i	0.454817	−	0.890585i	$-0.349705\pi$
$19$	−0.388136	−	0.224090i	−0.0890444	−	0.0514098i	−0.543861	+	0.839175i	$0.683038\pi$
$20$	2.90633	−	1.37907i	0.649876	−	0.308370i
$21$	2.06512	+	0.250750i	0.450645	+	0.0547182i
$22$	−0.262878	+	0.455318i	−0.0560458	+	0.0970742i
$23$	3.86471	+	6.69388i	0.805848	+	1.39577i	0.915717	+	0.401824i	$0.131624\pi$
$23$	3.86471	+	6.69388i	0.805848	+	1.39577i	−0.109869	+	0.993946i	$0.535043\pi$
$24$	−0.323066	−	0.758263i	−0.0659455	−	0.154780i
$25$	−1.71919	+	1.52307i	−0.343838	+	0.304614i
$26$	−0.302638	+	0.687418i	−0.0593523	+	0.134814i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	1.28893	−	3.86082i	0.243585	−	0.729627i
$29$	−0.198630	−	4.92895i	−0.0368847	−	0.915283i	−0.906667	−	0.421847i	$-0.861382\pi$
$29$	−0.198630	−	4.92895i	−0.0368847	−	0.915283i	0.869782	−	0.493436i	$-0.164259\pi$
$30$	−0.216611	−	0.265300i	−0.0395476	−	0.0484370i
$31$	4.74859	−	5.36005i	0.852872	−	0.962693i	−0.146778	−	0.989170i	$-0.546890\pi$
$31$	4.74859	−	5.36005i	0.852872	−	0.962693i	0.999649	+	0.0264763i	$0.00842865\pi$
$32$	−2.37878	+	0.485632i	−0.420513	+	0.0858484i
$33$	−2.42421	−	0.702182i	−0.422001	−	0.122234i
$34$	−1.16307	−	0.441093i	−0.199464	−	0.0756468i
$35$	0.137720	−	3.41750i	0.0232790	−	0.577663i
$36$	1.56419	−	1.17542i	0.260699	−	0.195903i
$37$	8.46325	+	1.72779i	1.39135	+	0.284046i	0.836529	−	0.547923i	$-0.184581\pi$
$37$	8.46325	+	1.72779i	1.39135	+	0.284046i	0.554822	+	0.831969i	$0.312786\pi$
$38$	0.0826684	+	0.0433877i	0.0134106	+	0.00703841i
$39$	−3.55169	−	0.620861i	−0.568726	−	0.0994173i
$40$	−1.19991	+	0.629759i	−0.189722	+	0.0995736i
$41$	2.43536	−	0.705409i	0.380339	−	0.110166i	−0.0825407	−	0.996588i	$-0.526303\pi$
$41$	2.43536	−	0.705409i	0.380339	−	0.110166i	0.462879	+	0.886421i	$0.346816\pi$
$42$	−0.431948	−	0.0348704i	−0.0666510	−	0.00538062i
$43$	−1.69076	−	8.28190i	−0.257839	−	1.26298i	−0.878060	−	0.478551i	$-0.841162\pi$
$43$	−1.69076	−	8.28190i	−0.257839	−	1.26298i	0.620221	−	0.784427i	$-0.287043\pi$
$44$	−2.29489	+	4.37256i	−0.345968	+	0.659188i
$45$	0.987703	−	1.31439i	0.147238	−	0.195938i
$46$	−0.860570	−	1.36088i	−0.126884	−	0.200651i
$47$	1.89522	+	1.30818i	0.276446	+	0.190817i	0.698218	−	0.715885i	$-0.253976\pi$
$47$	1.89522	+	1.30818i	0.276446	+	0.190817i	−0.421772	+	0.906702i	$0.638592\pi$
$48$	−1.60396	−	3.38027i	−0.231512	−	0.487900i
$49$	1.85125	+	1.92736i	0.264464	+	0.275337i
$50$	0.345066	−	0.331440i	0.0487997	−	0.0468727i
$51$	0.719756	−	5.92772i	0.100786	−	0.830047i
$52$	−2.58026	+	6.56584i	−0.357818	+	0.910518i
$53$	0.771182	+	6.35126i	0.105930	+	0.872413i	0.944702	+	0.327930i	$0.106351\pi$
$53$	0.771182	+	6.35126i	0.105930	+	0.872413i	−0.838772	+	0.544483i	$0.816726\pi$
$54$	−0.161361	−	0.131747i	−0.0219585	−	0.0179286i
$55$	−0.830021	+	4.06571i	−0.111920	+	0.548221i
$56$	−0.477033	+	1.64691i	−0.0637463	+	0.220078i
$57$	−0.107257	+	0.435157i	−0.0142065	+	0.0576380i
$58$	0.0826878	+	1.02427i	0.0108574	+	0.134494i
$59$	−1.36645	+	8.40813i	−0.177897	+	1.09465i	0.732456	+	0.680814i	$0.238374\pi$
$59$	−1.36645	+	8.40813i	−0.177897	+	1.09465i	−0.910354	+	0.413831i	$0.864190\pi$
$60$	−2.13322	−	2.40790i	−0.275397	−	0.310859i
$61$	−10.2850	−	7.72868i	−1.31686	−	0.989557i	−0.999144	−	0.0413711i	$-0.986827\pi$
$61$	−10.2850	−	7.72868i	−1.31686	−	0.989557i	−0.317717	−	0.948186i	$-0.602916\pi$
$62$	−0.943437	+	1.15550i	−0.119817	+	0.146749i
$63$	−0.333701	−	2.05334i	−0.0420424	−	0.258697i
$64$	−6.77453	+	1.66977i	−0.846816	+	0.208721i
$65$	−0.547589	+	5.90268i	−0.0679200	+	0.732137i
$66$	0.510479	+	0.125822i	0.0628356	+	0.0154876i
$67$	0.919668	−	11.3921i	0.112355	−	1.39177i	−0.657453	−	0.753495i	$-0.728366\pi$
$67$	0.919668	−	11.3921i	0.112355	−	1.39177i	0.769809	−	0.638275i	$-0.220352\pi$
$68$	−11.0821	−	3.69976i	−1.34391	−	0.448662i
$69$	5.35436	−	5.57448i	0.644589	−	0.671088i
$70$			0.712492i			0.0851591i
$71$	10.8092	+	10.3824i	1.28282	+	1.23216i	0.958128	+	0.286340i	$0.0924386\pi$
$71$	10.8092	+	10.3824i	1.28282	+	1.23216i	0.324688	+	0.945821i	$0.394741\pi$
$72$	−0.638443	+	0.521273i	−0.0752412	+	0.0614326i
$73$	0.199294	+	0.379723i	0.0233256	+	0.0444432i	0.896840	−	0.442355i	$-0.145857\pi$
$73$	0.199294	+	0.379723i	0.0233256	+	0.0444432i	−0.873514	+	0.486798i	$0.838165\pi$
$74$	−1.77608	−	0.288641i	−0.206465	−	0.0335539i
$75$	1.94124	+	1.22757i	0.224155	+	0.141747i
$76$	0.792247	+	0.375926i	0.0908769	+	0.0431216i
$77$	2.98254	+	4.32095i	0.339891	+	0.492418i
$78$	0.744477	+	0.0994379i	0.0842954	+	0.0112591i
$79$	−8.80074	+	12.7501i	−0.990161	+	1.43450i	−0.0915237	+	0.995803i	$0.529174\pi$
$79$	−8.80074	+	12.7501i	−0.990161	+	1.43450i	−0.898637	+	0.438693i	$0.855442\pi$
$80$	−5.32741	+	3.07578i	−0.595623	+	0.343883i
$81$	0.428693	−	0.903450i	0.0476325	−	0.100383i
$82$	−0.500991	+	0.167255i	−0.0553252	+	0.0184703i
$83$	2.34971	+	9.53313i	0.257914	+	1.04640i	0.946876	+	0.321600i	$0.104221\pi$
$83$	2.34971	+	9.53313i	0.257914	+	1.04640i	−0.688962	+	0.724798i	$0.741933\pi$
$84$	−4.06699	−	0.163894i	−0.443745	−	0.0178823i
$85$	−9.80961	−	0.395314i	−1.06400	−	0.0428778i
$86$	0.421393	+	1.70966i	0.0454400	+	0.184357i
$87$	−4.67908	+	1.56211i	−0.501651	+	0.167476i
$88$	0.891771	−	1.87937i	0.0950631	−	0.200341i
$89$	14.7538	−	8.51808i	1.56389	−	0.902915i	0.567037	−	0.823692i	$-0.308089\pi$
$89$	14.7538	−	8.51808i	1.56389	−	0.902915i	0.996857	−	0.0792229i	$-0.0252439\pi$
$90$	−0.194561	+	0.281870i	−0.0205085	+	0.0297117i
$91$	4.90635	+	5.67330i	0.514325	+	0.594723i
$92$	−8.59109	−	12.4463i	−0.895683	−	1.29762i
$93$	−6.46956	−	3.06985i	−0.670863	−	0.318328i
$94$	−0.405454	−	0.256394i	−0.0418194	−	0.0264450i
$95$	0.727328	+	0.118202i	0.0746223	+	0.0121273i
$96$	1.12828	+	2.14975i	0.115154	+	0.219408i
$97$	5.01899	−	4.09788i	0.509601	−	0.416076i	−0.342449	−	0.939536i	$-0.611257\pi$
$97$	5.01899	−	4.09788i	0.509601	−	0.416076i	0.852050	+	0.523460i	$0.175359\pi$
$98$	−0.401496	−	0.385642i	−0.0405572	−	0.0389558i
$99$			2.52386i			0.253657i
$100$	3.11307	−	3.24105i	0.311307	−	0.324105i
$101$	−3.05923	−	1.02132i	−0.304405	−	0.101625i	0.160362	−	0.987058i	$-0.448734\pi$
$101$	−3.05923	−	1.02132i	−0.304405	−	0.101625i	−0.464767	+	0.885433i	$0.653862\pi$
$102$	−0.100092	+	1.23987i	−0.00991062	+	0.122765i
$103$	3.59981	+	0.887274i	0.354700	+	0.0874257i	0.412640	−	0.910894i	$-0.364607\pi$
$103$	3.59981	+	0.887274i	0.354700	+	0.0874257i	−0.0579395	+	0.998320i	$0.518453\pi$
$104$	0.974681	−	2.80737i	0.0955753	−	0.275286i
$105$	−3.32088	+	0.818525i	−0.324085	+	0.0798798i
$106$	−0.213792	−	1.31552i	−0.0207653	−	0.127774i
$107$	−4.30980	+	5.27855i	−0.416644	+	0.510297i	−0.939699	−	0.342003i	$-0.888895\pi$
$107$	−4.30980	+	5.27855i	−0.416644	+	0.510297i	0.523055	+	0.852299i	$0.324792\pi$
$108$	−1.56419	−	1.17542i	−0.150515	−	0.113104i
$109$	−2.00801	−	2.26657i	−0.192332	−	0.217098i	0.644432	−	0.764662i	$-0.277094\pi$
$109$	−2.00801	−	2.26657i	−0.192332	−	0.217098i	−0.836764	+	0.547563i	$0.815555\pi$
$110$	0.138662	−	0.853222i	0.0132209	−	0.0813515i
$111$	−0.695056	−	8.60981i	−0.0659718	−	0.817207i
$112$	−1.86269	+	7.55724i	−0.176008	+	0.714092i
$113$	1.57437	−	5.43537i	0.148105	−	0.511317i	−0.851817	−	0.523840i	$-0.824499\pi$
$113$	1.57437	−	5.43537i	0.148105	−	0.511317i	0.999922	+	0.0125230i	$0.00398629\pi$
$114$	0.0186749	−	0.0914757i	0.00174906	−	0.00856748i
$115$	−9.84386	−	8.03726i	−0.917945	−	0.749479i
$116$	1.16340	+	9.58147i	0.108019	+	0.889617i
$117$	0.391795	+	3.58420i	0.0362215	+	0.331359i
$118$	0.213894	−	1.76158i	0.0196905	−	0.162166i
$119$	−8.95872	+	8.60496i	−0.821244	+	0.788816i
$120$	0.938730	+	0.977321i	0.0856939	+	0.0892168i
$121$	1.98490	+	4.18309i	0.180446	+	0.380281i
$122$	2.20561	+	1.52242i	0.199686	+	0.137833i
$123$	−1.35512	−	2.14295i	−0.122187	−	0.193223i
$124$	−8.41709	+	11.2011i	−0.755877	+	1.00589i
$125$	5.57527	−	10.6228i	0.498667	−	0.950131i
$126$	0.0866817	+	0.424595i	0.00772222	+	0.0378259i
$127$	9.08458	+	0.733383i	0.806126	+	0.0650772i	0.476657	−	0.879089i	$-0.341848\pi$
$127$	9.08458	+	0.733383i	0.806126	+	0.0650772i	0.329469	+	0.944167i	$0.393130\pi$
$128$	6.06006	−	1.75532i	0.535639	−	0.155150i
$129$	−7.48452	+	3.92818i	−0.658975	+	0.345857i
$130$	0.0644666	−	1.23321i	0.00565409	−	0.108160i
$131$	4.80318	+	2.52090i	0.419656	+	0.220252i	0.661314	−	0.750109i	$-0.269999\pi$
$131$	4.80318	+	2.52090i	0.419656	+	0.220252i	−0.241659	+	0.970361i	$0.577691\pi$
$132$	4.83840	+	0.987766i	0.421129	+	0.0859740i
$133$	0.745355	−	0.560098i	0.0646304	−	0.0485666i
$134$	−0.0958678	+	2.37893i	−0.00828171	+	0.205509i
$135$	−1.53730	−	0.583019i	−0.132309	−	0.0501783i
$136$	4.72731	+	1.36928i	0.405363	+	0.117415i
$137$	−10.1802	+	2.07831i	−0.869757	+	0.177562i	−0.614122	−	0.789211i	$-0.710490\pi$
$137$	−10.1802	+	2.07831i	−0.869757	+	0.177562i	−0.255635	+	0.966773i	$0.582285\pi$
$138$	−1.06773	+	1.20521i	−0.0908910	+	0.102595i
$139$	−10.8204	−	13.2526i	−0.917774	−	1.12407i	−0.991925	−	0.126823i	$-0.959522\pi$
$139$	−10.8204	−	13.2526i	−0.917774	−	1.12407i	0.0741510	−	0.997247i	$-0.476375\pi$
$140$	0.269465	+	6.68669i	0.0227739	+	0.565129i
$141$	0.729244	−	2.18435i	0.0614134	−	0.183956i
$142$	−2.33697	−	2.07038i	−0.196114	−	0.173742i
$143$	−4.77133	−	7.74873i	−0.398998	−	0.647981i
$144$	−2.80056	+	2.48108i	−0.233380	+	0.206757i
$145$	3.17903	+	7.46145i	0.264004	+	0.619640i
$146$	−0.0446672	−	0.0773658i	−0.00369668	−	0.00640284i
$147$	1.33621	−	2.31438i	0.110209	−	0.190887i
$148$	−16.7776	−	2.03717i	−1.37911	−	0.167454i
$149$	14.7836	−	7.01489i	1.21112	−	0.574682i	0.287419	−	0.957805i	$-0.407203\pi$
$149$	14.7836	−	7.01489i	1.21112	−	0.574682i	0.923697	+	0.383123i	$0.125151\pi$
$150$	−0.414358	−	0.239230i	−0.0338322	−	0.0195330i
$151$	12.1446	−	8.38279i	0.988311	−	0.682182i	0.0398927	−	0.999204i	$-0.487298\pi$
$151$	12.1446	−	8.38279i	0.988311	−	0.682182i	0.948418	+	0.317022i	$0.102683\pi$
$152$	−0.339839	−	0.144792i	−0.0275646	−	0.0117442i
$153$	−5.89394	+	0.957858i	−0.476496	+	0.0774382i
$154$	−0.657045	−	0.874368i	−0.0529462	−	0.0704586i
$155$	−4.17497	+	11.0085i	−0.335342	+	0.884224i
$156$	7.02448	+	0.651657i	0.562408	+	0.0521744i
$157$	−2.71638	−	7.16251i	−0.216791	−	0.571630i	0.781866	−	0.623447i	$-0.214268\pi$
$157$	−2.71638	−	7.16251i	−0.216791	−	0.571630i	−0.998657	+	0.0518165i	$0.983499\pi$
$158$	1.72489	−	2.72769i	0.137225	−	0.217003i
$159$	5.88594	−	2.50777i	0.466786	−	0.198879i
$160$	3.37376	−	2.13343i	0.266719	−	0.168663i
$161$	−15.9622	+	1.93816i	−1.25799	+	0.152748i
$162$	−0.0816523	+	0.191645i	−0.00641521	+	0.0150570i
$163$	−2.97220	−	8.90283i	−0.232801	−	0.697324i	−0.998532	−	0.0541630i	$-0.982751\pi$
$163$	−2.97220	−	8.90283i	−0.232801	−	0.697324i	0.765731	−	0.643161i	$-0.222377\pi$
$164$	−4.63852	+	1.75916i	−0.362207	+	0.137367i
$165$	4.13612	−	0.333902i	0.321996	−	0.0259942i
$166$	−0.569044	−	1.96457i	−0.0441664	−	0.152480i
$167$	−23.6725	+	0.953968i	−1.83183	+	0.0738203i	−0.932009	−	0.362436i	$-0.881945\pi$
$167$	−23.6725	+	0.953968i	−1.83183	+	0.0738203i	−0.899823	+	0.436256i	$0.856304\pi$
$168$	1.71461			0.132285
$169$	−7.97877	−	10.2635i	−0.613752	−	0.789499i
$170$	2.04514			0.156855
$171$	0.447817	−	0.0180464i	0.0342454	−	0.00138004i
$172$	4.60134	+	15.8857i	0.350849	+	1.21127i
$173$	15.2650	−	1.23232i	1.16057	−	0.0936912i	0.514862	−	0.857273i	$-0.327843\pi$
$173$	15.2650	−	1.23232i	1.16057	−	0.0936912i	0.645711	+	0.763582i	$0.276561\pi$
$174$	0.960827	−	0.364394i	0.0728401	−	0.0276246i
$175$	−1.51305	−	4.53213i	−0.114376	−	0.342597i
$176$	3.70136	−	8.68742i	0.279001	−	0.654839i
$177$	8.45633	−	1.02678i	0.635617	−	0.0771779i
$178$	−2.99948	+	1.89675i	−0.224820	+	0.142168i
$179$	−13.5949	+	5.79223i	−1.01613	+	0.432931i	−0.834836	−	0.550498i	$-0.814438\pi$
$179$	−13.5949	+	5.79223i	−1.01613	+	0.432931i	−0.181291	+	0.983430i	$0.558028\pi$
$180$	−1.71934	+	2.71892i	−0.128152	+	0.202656i
$181$	6.47715	+	17.0788i	0.481443	+	1.26946i	0.927288	+	0.374350i	$0.122134\pi$
$181$	6.47715	+	17.0788i	0.481443	+	1.26946i	−0.445845	+	0.895110i	$0.647097\pi$
$182$	−1.06882	−	1.13972i	−0.0792263	−	0.0844814i
$183$	−4.56207	+	12.0292i	−0.337238	+	0.889224i
$184$	3.82717	+	5.09303i	0.282142	+	0.375463i
$185$	−14.0179	+	2.27812i	−1.03061	+	0.167491i
$186$	1.37236	+	0.584708i	0.100626	+	0.0428729i
$187$	12.4029	−	8.56109i	0.906989	−	0.626049i
$188$	−3.90213	−	2.25290i	−0.284592	−	0.164310i
$189$	−1.87943	+	0.891802i	−0.136709	+	0.0648690i
$190$	−0.152382	−	0.0185025i	−0.0110549	−	0.00134231i
$191$	7.89385	−	13.6726i	0.571179	−	0.989311i	−0.425266	−	0.905068i	$-0.639819\pi$
$191$	7.89385	−	13.6726i	0.571179	−	0.989311i	0.996445	−	0.0842430i	$-0.0268472\pi$
$192$	3.48864	+	6.04249i	0.251771	+	0.436080i
$193$	−0.165904	−	0.389391i	−0.0119420	−	0.0280290i	0.913902	−	0.405936i	$-0.133054\pi$
$193$	−0.165904	−	0.389391i	−0.0119420	−	0.0280290i	−0.925844	+	0.377907i	$0.876644\pi$
$194$	−1.01031	+	0.895053i	−0.0725358	+	0.0642611i
$195$	5.82198	−	1.11626i	0.416920	−	0.0799370i
$196$	−3.91387	−	3.46738i	−0.279562	−	0.247670i
$197$	5.08627	−	15.2352i	0.362382	−	1.08547i	−0.596731	−	0.802441i	$-0.703534\pi$
$197$	5.08627	−	15.2352i	0.362382	−	1.08547i	0.959113	−	0.283024i	$-0.0913376\pi$
$198$	−0.0211701	−	0.525330i	−0.00150449	−	0.0373336i
$199$	13.5716	+	16.6222i	0.962063	+	1.17831i	0.983930	+	0.178553i	$0.0571415\pi$
$199$	13.5716	+	16.6222i	0.962063	+	1.17831i	−0.0218670	+	0.999761i	$0.506961\pi$
$200$	−1.25534	+	1.41699i	−0.0887659	+	0.100196i
$201$	−11.1982	+	2.28613i	−0.789861	+	0.161251i
$202$	0.645332	+	0.186923i	0.0454054	+	0.0131518i
$203$	9.59508	+	3.63893i	0.673443	+	0.255403i
$204$	−0.470443	+	11.6739i	−0.0329376	+	0.817338i
$205$	−3.33259	+	2.50428i	−0.232758	+	0.174907i
$206$	−0.756727	−	0.154487i	−0.0527237	−	0.0107636i
$207$	−6.84406	−	3.59204i	−0.475695	−	0.249664i
$208$	3.90780	−	12.9118i	0.270957	−	0.895274i
$209$	−1.00158	+	0.525669i	−0.0692807	+	0.0363613i
$210$	0.684361	−	0.198228i	0.0472254	−	0.0136790i
$211$	−24.0852	−	1.94436i	−1.65810	−	0.133855i	−0.784377	−	0.620285i	$-0.787017\pi$
$211$	−24.0852	−	1.94436i	−1.65810	−	0.133855i	−0.873720	+	0.486429i	$0.838299\pi$
$212$	−2.50396	−	12.2652i	−0.171972	−	0.842377i
$213$	6.96515	−	13.2710i	0.477244	−	0.909313i
$214$	0.852789	−	1.13486i	0.0582955	−	0.0775772i
$215$	7.42771	+	11.7460i	0.506566	+	0.801069i
$216$	0.678318	+	0.468209i	0.0461537	+	0.0318576i
$217$	6.38615	+	13.4585i	0.433520	+	0.913624i
$218$	0.436970	+	0.454934i	0.0295953	+	0.0308120i
$219$	0.309283	−	0.297071i	0.0208994	−	0.0200742i
$220$	0.978646	−	8.05988i	0.0659803	−	0.543397i
$221$	16.2847	−	14.0832i	1.09543	−	0.947340i
$222$	0.216892	+	1.78626i	0.0145568	+	0.119886i
$223$	6.11422	+	4.99211i	0.409439	+	0.334296i	0.814677	−	0.579915i	$-0.196914\pi$
$223$	6.11422	+	4.99211i	0.409439	+	0.334296i	−0.405238	+	0.914211i	$0.632812\pi$
$224$	1.01025	−	4.94854i	0.0675003	−	0.330638i
$225$	0.639013	−	2.20613i	0.0426009	−	0.147075i
$226$	−0.282107	+	1.14455i	−0.0187655	+	0.0761346i
$227$	−0.604461	−	7.48759i	−0.0401195	−	0.496969i	−0.985348	−	0.170558i	$-0.945443\pi$
$227$	−0.604461	−	7.48759i	−0.0401195	−	0.496969i	0.945228	−	0.326411i	$-0.105839\pi$
$228$	0.140667	−	0.865557i	0.00931588	−	0.0573229i
$229$	16.3388	+	18.4427i	1.07970	+	1.21873i	0.974527	+	0.224272i	$0.0720005\pi$
$229$	16.3388	+	18.4427i	1.07970	+	1.21873i	0.105171	+	0.994454i	$0.466461\pi$
$230$	2.11637	+	1.59035i	0.139549	+	0.104865i
$231$	3.32056	−	4.06694i	0.218477	−	0.267585i
$232$	−0.652204	−	4.01318i	−0.0428193	−	0.263478i
$233$	11.7837	−	2.90441i	0.771973	−	0.190274i	0.166394	−	0.986059i	$-0.446788\pi$
$233$	11.7837	−	2.90441i	0.771973	−	0.190274i	0.605579	+	0.795785i	$0.292941\pi$
$234$	−0.111615	−	0.742749i	−0.00729647	−	0.0485550i
$235$	−3.67621	−	0.906103i	−0.239809	−	0.0591077i
$236$	1.34115	−	16.6132i	0.0873017	−	1.08143i
$237$	14.6952	+	4.90598i	0.954556	+	0.318678i
$238$	1.79254	−	1.86623i	0.116193	−	0.120970i
$239$			11.4571i			0.741101i	0.928812	+	0.370551i	$0.120831\pi$
$239$			11.4571i			0.741101i	−0.928812	+	0.370551i	$0.879169\pi$
$240$	4.43652	+	4.26134i	0.286376	+	0.275068i
$241$	5.79721	−	4.73328i	0.373431	−	0.304897i	−0.427081	−	0.904213i	$-0.640458\pi$
$241$	5.79721	−	4.73328i	0.373431	−	0.304897i	0.800512	+	0.599316i	$0.204561\pi$
$242$	−0.448236	−	0.854042i	−0.0288137	−	0.0548999i
$243$	−0.987050	−	0.160411i	−0.0633193	−	0.0102904i
$244$	21.2753	+	13.4537i	1.36201	+	0.861283i
$245$	−3.96961	−	1.88360i	−0.253609	−	0.120339i
$246$	0.300036	+	0.434678i	0.0191296	+	0.0277140i
$247$	−1.34077	+	0.901999i	−0.0853109	+	0.0573928i
$248$	3.35282	−	4.85740i	0.212904	−	0.308445i
$249$	8.50302	−	4.90922i	0.538857	−	0.311109i
$250$	−1.07136	+	2.25785i	−0.0677589	+	0.142799i
$251$	−19.0630	+	6.36418i	−1.20325	+	0.401703i	−0.846445	−	0.532476i	$-0.821262\pi$
$251$	−19.0630	+	6.36418i	−1.20325	+	0.401703i	−0.356803	+	0.934180i	$0.616133\pi$
$252$	0.974085	+	3.95202i	0.0613616	+	0.248954i
$253$	19.4922	+	0.785507i	1.22546	+	0.0493844i
$254$	−1.89706	−	0.0764491i	−0.119032	−	0.00479684i
$255$	2.34950	+	9.53229i	0.147131	+	0.596935i
$256$	11.9897	−	4.00276i	0.749359	−	0.250173i
$257$	−0.198997	+	0.419377i	−0.0124131	+	0.0261600i	−0.909562	−	0.415568i	$-0.863583\pi$
$257$	−0.198997	+	0.419377i	−0.0124131	+	0.0261600i	0.897149	+	0.441728i	$0.145634\pi$
$258$	1.52492	−	0.880412i	0.0949373	−	0.0548121i
$259$	−10.2076	+	14.7883i	−0.634270	+	0.918899i
$260$	0.138615	−	11.5980i	0.00859655	−	0.719276i
$261$	2.80224	+	4.05974i	0.173454	+	0.251292i
$262$	−1.02090	−	0.484425i	−0.0630717	−	0.0299279i
$263$	1.89390	+	1.19763i	0.116783	+	0.0738489i	0.591580	−	0.806246i	$-0.298504\pi$
$263$	1.89390	+	1.19763i	0.116783	+	0.0738489i	−0.474797	+	0.880095i	$0.657479\pi$
$264$	−2.05327	−	0.333689i	−0.126370	−	0.0205372i
$265$	−4.88844	−	9.31415i	−0.300295	−	0.572163i
$266$	−0.150444	+	0.122834i	−0.00922432	+	0.00753142i
$267$	−12.2865	−	11.8014i	−0.751923	−	0.722232i
$268$			22.3624i			1.36600i
$269$	−7.26055	+	7.55903i	−0.442683	+	0.460882i	−0.904738	−	0.425969i	$-0.859933\pi$
$269$	−7.26055	+	7.55903i	−0.442683	+	0.460882i	0.462054	+	0.886852i	$0.347113\pi$
$270$	0.324871	+	0.108458i	0.0197710	+	0.00660054i
$271$	−0.489456	+	6.06300i	−0.0297323	+	0.368301i	0.964733	+	0.263232i	$0.0847884\pi$
$271$	−0.489456	+	6.06300i	−0.0297323	+	0.368301i	−0.994465	+	0.105069i	$0.966494\pi$
$272$	21.6924	+	5.34668i	1.31529	+	0.324190i
$273$	4.08427	−	6.29104i	0.247191	−	0.380751i
$274$	2.10154	−	0.517983i	0.126959	−	0.0312925i
$275$	0.929877	+	5.72177i	0.0560737	+	0.345035i
$276$	−9.56474	+	11.7147i	−0.575730	+	0.705141i
$277$	−6.51166	−	4.89319i	−0.391248	−	0.294003i	0.386855	−	0.922140i	$-0.373561\pi$
$277$	−6.51166	−	4.89319i	−0.391248	−	0.294003i	−0.778103	+	0.628137i	$0.783818\pi$
$278$	2.36338	+	2.66770i	0.141746	+	0.159998i
$279$	−1.14870	+	7.06822i	−0.0687707	+	0.423163i
$280$	−0.226839	−	2.80991i	−0.0135562	−	0.167924i
$281$	1.71661	−	6.96456i	0.102404	−	0.415471i	−0.897257	−	0.441510i	$-0.854443\pi$
$281$	1.71661	−	6.96456i	0.102404	−	0.415471i	0.999661	+	0.0260386i	$0.00828929\pi$
$282$	−0.133466	+	0.460780i	−0.00794781	+	0.0274390i
$283$	−0.946827	+	4.63787i	−0.0562830	+	0.275693i	−0.998187	−	0.0601899i	$-0.980829\pi$
$283$	−0.946827	+	4.63787i	−0.0562830	+	0.275693i	0.941904	+	0.335882i	$0.109035\pi$
$284$	−22.7154	−	18.5465i	−1.34791	−	1.10053i
$285$	−0.0888199	−	0.731498i	−0.00526124	−	0.0433302i
$286$	1.05813	+	1.57284i	0.0625683	+	0.0930040i
$287$	−0.635768	+	5.23602i	−0.0375282	+	0.309072i
$288$	1.75097	−	1.68183i	0.103177	−	0.0991027i
$289$	12.9234	+	13.4547i	0.760203	+	0.791455i
$290$	−0.724286	−	1.52640i	−0.0425316	−	0.0896333i
$291$	−5.33245	−	3.68073i	−0.312594	−	0.215768i
$292$	−0.448459	−	0.709181i	−0.0262441	−	0.0415017i
$293$	12.3865	−	16.4835i	0.723628	−	0.962974i	−0.276370	−	0.961051i	$-0.589132\pi$
$293$	12.3865	−	16.4835i	0.723628	−	0.962974i	0.999998	−	0.00192278i	$-0.000612040\pi$
$294$	−0.258713	+	0.492937i	−0.0150885	+	0.0287487i
$295$	−2.80146	−	13.7224i	−0.163107	−	0.798952i
$296$	7.09636	+	0.572877i	0.412467	+	0.0332978i
$297$	2.42421	−	0.702182i	0.140667	−	0.0407447i
$298$	−3.01829	+	1.58412i	−0.174845	+	0.0917657i
$299$	27.8033	−	1.91037i	1.60790	−	0.110480i
$300$	−3.97920	−	2.08844i	−0.229739	−	0.120576i
$301$	17.2287	+	3.51727i	0.993046	+	0.202732i
$302$	−2.45752	+	1.84671i	−0.141414	+	0.106266i
$303$	−0.129866	+	3.22260i	−0.00746062	+	0.185133i
$304$	−1.56790	−	0.594628i	−0.0899255	−	0.0341042i
$305$	20.3171	+	5.88491i	1.16335	+	0.336969i
$306$	1.21876	−	0.248812i	0.0696719	−	0.0142236i
$307$	−7.05302	+	7.96122i	−0.402537	+	0.454371i	−0.914469	−	0.404655i	$-0.867392\pi$
$307$	−7.05302	+	7.96122i	−0.402537	+	0.454371i	0.511932	+	0.859026i	$0.328930\pi$
$308$	−6.49702	−	7.95740i	−0.370202	−	0.453415i
$309$	−0.149288	−	3.70454i	−0.00849269	−	0.210744i
$310$	0.776662	−	2.32639i	0.0441115	−	0.132130i
$311$	−0.905367	−	0.802085i	−0.0513386	−	0.0454821i	0.637063	−	0.770811i	$-0.280149\pi$
$311$	−0.905367	−	0.802085i	−0.0513386	−	0.0454821i	−0.688402	+	0.725329i	$0.741687\pi$
$312$	−2.96771	−	0.155138i	−0.168013	−	0.00878298i
$313$	4.93329	−	4.37051i	0.278846	−	0.247036i	−0.512095	−	0.858929i	$-0.671130\pi$
$313$	4.93329	−	4.37051i	0.278846	−	0.247036i	0.790940	+	0.611893i	$0.209592\pi$
$314$	0.625481	+	1.46806i	0.0352979	+	0.0828473i
$315$	1.71014	+	2.96204i	0.0963552	+	0.166892i
$316$	15.1564	−	26.2516i	0.852611	−	1.47677i
$317$	−14.9828	−	1.81924i	−0.841518	−	0.102179i	−0.311585	−	0.950218i	$-0.600860\pi$
$317$	−14.9828	−	1.81924i	−0.841518	−	0.102179i	−0.529933	+	0.848039i	$0.677783\pi$
$318$	−1.20410	+	0.571351i	−0.0675224	+	0.0320398i
$319$	−10.7821	−	6.22504i	−0.603681	−	0.348535i
$320$	9.44094	−	6.51661i	0.527764	−	0.364289i
$321$	6.26920	+	2.67106i	0.349913	+	0.149084i
$322$	3.30619	−	0.537309i	0.184247	−	0.0299430i
$323$	−1.60771	−	2.13947i	−0.0894553	−	0.119043i
$324$	−0.693822	+	1.82946i	−0.0385457	+	0.101637i
$325$	2.20877	+	7.98128i	0.122521	+	0.442722i
$326$	0.693327	+	1.82815i	0.0383998	+	0.101252i
$327$	−1.61842	+	2.55933i	−0.0894989	+	0.141531i
$328$	1.92255	−	0.819121i	0.106155	−	0.0452284i
$329$	−4.04898	+	2.56042i	−0.223227	+	0.141160i
$330$	−0.858113	+	0.104194i	−0.0472376	+	0.00573568i
$331$	−5.92073	+	13.8965i	−0.325433	+	0.763819i	0.674247	+	0.738506i	$0.264468\pi$
$331$	−5.92073	+	13.8965i	−0.325433	+	0.763819i	−0.999680	+	0.0253128i	$0.991942\pi$
$332$	−6.08345	−	18.2222i	−0.333873	−	1.00007i
$333$	−8.07650	+	3.06301i	−0.442589	+	0.167852i
$334$	4.91932	−	0.397128i	0.269173	−	0.0217299i
$335$	5.22803	+	18.0492i	0.285638	+	0.986136i
$336$	7.77710	−	0.313406i	0.424275	−	0.0170977i
$337$	0.148769			0.00810395			0.00405197	−	0.999992i	$-0.498710\pi$
$337$	0.148769			0.00810395			0.00405197	+	0.999992i	$0.498710\pi$
$338$	1.74683	+	2.06937i	0.0950153	+	0.112559i
$339$	−5.65879			−0.307343
$340$	19.1935	−	0.773473i	1.04092	−	0.0419475i
$341$	−5.02829	−	17.3597i	−0.272297	−	0.940079i
$342$	−0.0930597	+	0.00751256i	−0.00503209	+	0.000406233i
$343$	−18.8138	+	7.13514i	−1.01585	+	0.385261i
$344$	−2.20619	−	6.60835i	−0.118950	−	0.356298i
$345$	−4.98120	+	11.6913i	−0.268179	+	0.629439i
$346$	−3.16700	+	0.384543i	−0.170259	+	0.0206732i
$347$	−4.08518	+	2.58331i	−0.219304	+	0.138679i	−0.639601	−	0.768707i	$-0.720900\pi$
$347$	−4.08518	+	2.58331i	−0.219304	+	0.138679i	0.420297	+	0.907387i	$0.361926\pi$
$348$	8.87949	−	3.78320i	0.475991	−	0.202801i
$349$	7.54063	−	11.9246i	0.403641	−	0.638307i	−0.580795	−	0.814050i	$-0.697258\pi$
$349$	7.54063	−	11.9246i	0.403641	−	0.638307i	0.984436	+	0.175743i	$0.0562328\pi$
$350$	0.352949	+	0.930650i	0.0188659	+	0.0497453i
$351$	3.33369	−	1.37351i	0.177939	−	0.0733127i
$352$	−2.17286	+	5.72935i	−0.115814	+	0.305376i
$353$	−11.7451	−	15.6299i	−0.625131	−	0.831898i	0.370146	−	0.928974i	$-0.379308\pi$
$353$	−11.7451	−	15.6299i	−0.625131	−	0.831898i	−0.995277	+	0.0970753i	$0.969051\pi$
$354$	−1.75153	+	0.284652i	−0.0930930	+	0.0151291i
$355$	−22.6701	−	9.65881i	−1.20320	−	0.512636i
$356$	−27.4326	+	18.9353i	−1.45392	+	1.00357i
$357$	10.7577	+	6.21096i	0.569358	+	0.328719i
$358$	2.78112	−	1.31966i	0.146987	−	0.0697461i
$359$	−10.6806	−	1.29686i	−0.563701	−	0.0684456i	−0.166274	−	0.986080i	$-0.553174\pi$
$359$	−10.6806	−	1.29686i	−0.563701	−	0.0684456i	−0.397427	+	0.917634i	$0.630097\pi$
$360$	0.677564	−	1.17357i	0.0357107	−	0.0618528i
$361$	−9.39957	−	16.2805i	−0.494714	−	0.856870i
$362$	−1.49145	−	3.50055i	−0.0783887	−	0.183985i
$363$	3.46570	−	3.07034i	0.181902	−	0.161151i
$364$	−10.4619	−	10.2919i	−0.548351	−	0.539444i
$365$	−0.527759	−	0.467554i	−0.0276242	−	0.0244729i
$366$	0.848674	−	2.54209i	0.0443609	−	0.132877i
$367$	−0.585879	−	14.5384i	−0.0305826	−	0.758900i	−0.939627	−	0.342201i	$-0.888828\pi$
$367$	−0.585879	−	14.5384i	−0.0305826	−	0.758900i	0.909044	−	0.416700i	$-0.136813\pi$
$368$	18.2902	+	22.4014i	0.953440	+	1.16775i
$369$	−1.68132	+	1.89782i	−0.0875261	+	0.0987965i
$370$	2.89864	−	0.591762i	0.150693	−	0.0307643i
$371$	−12.7840	−	3.70292i	−0.663711	−	0.192246i
$372$	13.1007	+	4.96842i	0.679237	+	0.257601i
$373$	−0.722105	+	17.9188i	−0.0373892	+	0.927802i	0.866277	+	0.499564i	$0.166507\pi$
$373$	−0.722105	+	17.9188i	−0.0373892	+	0.927802i	−0.903666	+	0.428238i	$0.859134\pi$
$374$	−2.50979	+	1.88599i	−0.129778	+	0.0975221i
$375$	−11.7545	−	2.39970i	−0.607000	−	0.123920i
$376$	1.68065	+	0.882073i	0.0866729	+	0.0454895i
$377$	−16.2783	−	7.16657i	−0.838374	−	0.369097i
$378$	0.383715	−	0.201389i	0.0197362	−	0.0103583i
$379$	−2.16612	+	0.627425i	−0.111266	+	0.0322286i	−0.333383	−	0.942791i	$-0.608190\pi$
$379$	−2.16612	+	0.627425i	−0.111266	+	0.0322286i	0.222117	+	0.975020i	$0.428703\pi$
$380$	−1.43709	−	0.116014i	−0.0737211	−	0.00595138i
$381$	−1.82306	−	8.92994i	−0.0933982	−	0.457495i
$382$	−1.52838	+	2.91209i	−0.0781990	+	0.148996i
$383$	10.0616	−	13.3896i	0.514124	−	0.684174i	−0.465493	−	0.885052i	$-0.654123\pi$
$383$	10.0616	−	13.3896i	0.514124	−	0.684174i	0.979616	+	0.200877i	$0.0643793\pi$
$384$	−3.37203	−	5.33244i	−0.172078	−	0.272120i
$385$	−7.10423	−	4.90370i	−0.362065	−	0.249916i
$386$	0.0377984	+	0.0796584i	0.00192389	+	0.00405451i
$387$	5.85541	+	6.09613i	0.297647	+	0.309884i
$388$	−9.14316	+	8.78212i	−0.464173	+	0.445845i
$389$	−3.55078	+	29.2433i	−0.180032	+	1.48269i	0.570193	+	0.821511i	$0.306869\pi$
$389$	−3.55078	+	29.2433i	−0.180032	+	1.48269i	−0.750224	+	0.661183i	$0.770055\pi$
$390$	−1.20245	+	0.281179i	−0.0608887	+	0.0142380i
$391$	5.56330	+	45.8179i	0.281348	+	2.31711i
$392$	1.70619	+	1.39306i	0.0861756	+	0.0703602i
$393$	1.08504	−	5.31490i	0.0547332	−	0.268101i
$394$	−0.930891	+	3.21381i	−0.0468976	+	0.161909i
$395$	6.09580	−	24.7316i	0.306713	−	1.24438i
$396$	−0.397360	−	4.92218i	−0.0199681	−	0.247349i
$397$	−0.662021	+	4.07358i	−0.0332259	+	0.204447i	−0.998356	−	0.0573252i	$-0.981743\pi$
$397$	−0.662021	+	4.07358i	−0.0332259	+	0.204447i	0.965130	+	0.261772i	$0.0843069\pi$
$398$	−2.96429	−	3.34599i	−0.148586	−	0.167719i
$399$	−0.745355	−	0.560098i	−0.0373144	−	0.0280400i
$400$	−5.43495	+	6.65661i	−0.271748	+	0.332830i
$401$	1.60843	+	9.89707i	0.0803212	+	0.494236i	0.995776	+	0.0918154i	$0.0292670\pi$
$401$	1.60843	+	9.89707i	0.0803212	+	0.494236i	−0.915455	+	0.402421i	$0.868169\pi$
$402$	2.31168	−	0.569778i	0.115296	−	0.0284180i
$403$	−9.83566	−	23.8724i	−0.489949	−	1.18917i
$404$	6.12710	+	1.51019i	0.304835	+	0.0751350i
$405$	−0.132298	+	1.63881i	−0.00657395	+	0.0814329i
$406$	−2.02770	−	0.676944i	−0.100633	−	0.0335962i
$407$	15.1018	−	15.7227i	0.748570	−	0.779344i
$408$		−	4.92162i		−	0.243657i
$409$	−18.2361	−	17.5160i	−0.901717	−	0.866110i	0.0898174	−	0.995958i	$-0.471372\pi$
$409$	−18.2361	−	17.5160i	−0.901717	−	0.866110i	−0.991534	+	0.129848i	$0.958551\pi$
$410$	0.672658	−	0.549209i	0.0332202	−	0.0271235i
$411$	4.82858	+	9.20008i	0.238176	+	0.453807i
$412$	−7.16027	−	1.16366i	−0.352761	−	0.0573292i
$413$	−14.9774	−	9.47115i	−0.736991	−	0.466045i
$414$	1.45469	+	0.690259i	0.0714941	+	0.0339244i
$415$	−9.17019	−	13.2853i	−0.450147	−	0.652151i
$416$	−2.19633	+	8.47372i	−0.107684	+	0.415458i
$417$	−9.71892	+	14.0803i	−0.475938	+	0.689515i
$418$	0.204065	−	0.117817i	0.00998114	−	0.00576261i
$419$	−8.44198	+	17.7911i	−0.412418	+	0.869151i	0.585856	+	0.810415i	$0.300758\pi$
$419$	−8.44198	+	17.7911i	−0.412418	+	0.869151i	−0.998274	+	0.0587363i	$0.981293\pi$
$420$	6.34772	−	2.11918i	0.309737	−	0.103405i
$421$	−0.847987	−	3.44042i	−0.0413283	−	0.167676i	0.946651	−	0.322260i	$-0.104442\pi$
$421$	−0.847987	−	3.44042i	−0.0413283	−	0.167676i	−0.987980	+	0.154584i	$0.950596\pi$
$422$	5.02954	+	0.202684i	0.244834	+	0.00986649i
$423$	−2.30100	−	0.0927270i	−0.111878	−	0.00450854i
$424$	1.26198	+	5.12004i	0.0612870	+	0.248651i
$425$	−13.0091	+	4.34306i	−0.631032	+	0.210669i
$426$	−1.33845	+	2.82072i	−0.0648480	+	0.136664i
$427$	23.1777	−	13.3817i	1.12165	−	0.647584i
$428$	7.57417	−	10.9731i	0.366112	−	0.530404i
$429$	−6.11533	+	6.73878i	−0.295251	+	0.325351i
$430$	−1.64457	−	2.38257i	−0.0793081	−	0.114898i
$431$	−10.8122	−	5.13047i	−0.520807	−	0.247126i	0.150096	−	0.988671i	$-0.452042\pi$
$431$	−10.8122	−	5.13047i	−0.520807	−	0.247126i	−0.670902	+	0.741546i	$0.734093\pi$
$432$	3.16229	+	1.99971i	0.152146	+	0.0962112i
$433$	21.0922	+	3.42781i	1.01363	+	0.164730i	0.644464	−	0.764635i	$-0.277081\pi$
$433$	21.0922	+	3.42781i	1.01363	+	0.164730i	0.369162	+	0.929365i	$0.379645\pi$
$434$	−1.44214	−	2.74776i	−0.0692248	−	0.131897i
$435$	6.28240	−	5.12942i	0.301218	−	0.245937i
$436$	4.27299	+	4.10426i	0.204639	+	0.196559i
$437$		−	3.46418i		−	0.165714i
$438$	−0.0618841	+	0.0644282i	−0.00295694	+	0.00307850i
$439$	−10.0320	−	3.34917i	−0.478801	−	0.159847i	0.0670154	−	0.997752i	$-0.478652\pi$
$439$	−10.0320	−	3.34917i	−0.478801	−	0.159847i	−0.545817	+	0.837905i	$0.683781\pi$
$440$	−0.275208	+	3.40906i	−0.0131200	+	0.162521i
$441$	−2.59477	−	0.639552i	−0.123560	−	0.0304549i
$442$	−3.27145	+	3.06795i	−0.155607	+	0.145928i
$443$	29.6955	−	7.31928i	1.41087	−	0.347749i	0.541000	−	0.841022i	$-0.318046\pi$
$443$	29.6955	−	7.31928i	1.41087	−	0.347749i	0.869875	+	0.493273i	$0.164200\pi$
$444$	2.71108	+	16.6819i	0.128662	+	0.791690i
$445$	−17.7147	+	21.6965i	−0.839756	+	1.02851i
$446$	−1.31452	−	0.987799i	−0.0622444	−	0.0467736i
$447$	−10.8510	−	12.2482i	−0.513233	−	0.579321i
$448$	2.32832	−	14.3267i	0.110003	−	0.676875i
$449$	0.688774	+	8.53200i	0.0325053	+	0.402650i	0.992466	+	0.122517i	$0.0390966\pi$
$449$	0.688774	+	8.53200i	0.0325053	+	0.402650i	−0.959961	+	0.280133i	$0.909621\pi$
$450$	−0.114503	+	0.464556i	−0.00539771	+	0.0218994i
$451$	1.78035	−	6.14650i	0.0838336	−	0.289427i
$452$	−2.21469	+	10.8483i	−0.104170	+	0.510259i
$453$	−11.4307	−	9.33284i	−0.537059	−	0.438495i
$454$	0.188622	+	1.55344i	0.00885245	+	0.0729065i
$455$	−10.8501	−	5.86104i	−0.508663	−	0.274770i
$456$	−0.0445261	+	0.366705i	−0.00208512	+	0.0171725i
$457$	−18.6838	+	17.9460i	−0.873989	+	0.839478i	−0.988072	−	0.153993i	$-0.950787\pi$
$457$	−18.6838	+	17.9460i	−0.873989	+	0.839478i	0.114083	+	0.993471i	$0.463607\pi$
$458$	−3.55554	−	3.70171i	−0.166140	−	0.172970i
$459$	2.55984	+	5.39474i	0.119483	+	0.251805i
$460$	20.4635	+	14.1249i	0.954115	+	0.658578i
$461$	21.7516	+	34.3974i	1.01307	+	1.60205i	0.776179	+	0.630512i	$0.217155\pi$
$461$	21.7516	+	34.3974i	1.01307	+	1.60205i	0.236894	+	0.971535i	$0.423871\pi$
$462$	−0.657045	+	0.874368i	−0.0305685	+	0.0406793i
$463$	−4.76557	+	9.08003i	−0.221475	+	0.421985i	−0.970688	−	0.240344i	$-0.922740\pi$
$463$	−4.76557	+	9.08003i	−0.221475	+	0.421985i	0.749213	+	0.662329i	$0.230432\pi$
$464$	−3.69182	−	18.0837i	−0.171388	−	0.839515i
$465$	11.7354	+	0.947380i	0.544217	+	0.0439337i
$466$	−2.42835	+	0.703381i	−0.112491	+	0.0325835i
$467$	−16.6903	+	8.75974i	−0.772334	+	0.405352i	−0.804366	−	0.594134i	$-0.797495\pi$
$467$	−16.6903	+	8.75974i	−0.772334	+	0.405352i	0.0320313	+	0.999487i	$0.489802\pi$
$468$	−1.32840	−	6.92844i	−0.0614055	−	0.320267i
$469$	21.0526	+	11.0492i	0.972117	+	0.510206i
$470$	0.772786	+	0.157765i	0.0356459	+	0.00727717i
$471$	−6.12397	+	4.60187i	−0.282178	+	0.212043i
$472$	−0.282709	+	7.01536i	−0.0130127	+	0.322908i
$473$	−19.9472	−	7.56496i	−0.917172	−	0.347837i
$474$	−3.09989	−	0.897894i	−0.142383	−	0.0412416i
$475$	1.00858	−	0.205904i	0.0462770	−	0.00944751i
$476$	16.1171	−	18.1924i	0.738724	−	0.833847i
$477$	−4.04633	−	4.95585i	−0.185269	−	0.226913i
$478$	−0.0961023	−	2.38475i	−0.00439562	−	0.109076i
$479$	−6.28136	+	18.8150i	−0.287003	+	0.859678i	0.702052	+	0.712126i	$0.252268\pi$
$479$	−6.28136	+	18.8150i	−0.287003	+	0.859678i	−0.989054	+	0.147552i	$0.952861\pi$
$480$	−2.98784	−	2.64700i	−0.136376	−	0.120818i
$481$	19.0058	−	24.6725i	0.866589	−	1.12497i
$482$	−1.16696	+	1.03384i	−0.0531536	+	0.0470900i
$483$	6.30258	+	14.7927i	0.286777	+	0.673092i
$484$	−4.52967	−	7.84562i	−0.205894	−	0.356619i
$485$	−5.32652	+	9.22581i	−0.241865	+	0.418922i
$486$	0.206796	+	0.0251095i	0.00938044	+	0.00113899i
$487$	−12.3060	+	5.83926i	−0.557637	+	0.264602i	−0.686585	−	0.727049i	$-0.740891\pi$
$487$	−12.3060	+	5.83926i	−0.557637	+	0.264602i	0.128948	+	0.991651i	$0.458840\pi$
$488$	−9.18311	−	5.30187i	−0.415700	−	0.240005i
$489$	−7.72441	+	5.33178i	−0.349310	+	0.241111i
$490$	0.842055	+	0.358766i	0.0380402	+	0.0162074i
$491$	−31.6379	+	5.14166i	−1.42780	+	0.232040i	−0.824675	−	0.565607i	$-0.808642\pi$
$491$	−31.6379	+	5.14166i	−1.42780	+	0.232040i	−0.603125	+	0.797647i	$0.706078\pi$
$492$	2.98022	+	3.96595i	0.134359	+	0.178799i
$493$	10.4452	−	27.5418i	0.470429	−	1.24042i
$494$	0.271508	−	0.198993i	0.0122157	−	0.00895313i
$495$	−1.47146	−	3.87992i	−0.0661372	−	0.174389i
$496$	14.3198	−	22.6450i	0.642980	−	1.01679i
$497$	−28.6838	+	12.2210i	−1.28664	+	0.548188i
$498$	−1.72869	+	1.09315i	−0.0774643	+	0.0489854i
$499$	−24.8830	+	3.02134i	−1.11392	+	0.135254i	−0.656736	−	0.754120i	$-0.728064\pi$
$499$	−24.8830	+	3.02134i	−1.11392	+	0.135254i	−0.457180	+	0.889374i	$0.651141\pi$
$500$	−9.20076	+	21.5950i	−0.411470	+	0.965756i
$501$	7.50240	+	22.4724i	0.335183	+	1.00399i
$502$	3.91450	−	1.48457i	0.174713	−	0.0662598i
$503$	6.47647	−	0.522835i	0.288771	−	0.0233120i	0.0647678	−	0.997900i	$-0.479369\pi$
$503$	6.47647	−	0.522835i	0.288771	−	0.0233120i	0.224004	+	0.974588i	$0.428087\pi$
$504$	−0.477033	−	1.64691i	−0.0212488	−	0.0733592i
$505$	5.29839	−	0.213518i	0.235775	−	0.00950143i
$506$	−4.06379			−0.180658
$507$	−7.63843	+	10.5192i	−0.339235	+	0.467176i
$508$	−17.8328			−0.791201
$509$	17.7068	−	0.713561i	0.784841	−	0.0316280i	0.355390	−	0.934718i	$-0.384348\pi$
$509$	17.7068	−	0.713561i	0.784841	−	0.0316280i	0.429451	+	0.903090i	$0.358707\pi$
$510$	−0.568994	−	1.96440i	−0.0251955	−	0.0869849i
$511$	−0.889224	+	0.0717856i	−0.0393370	+	0.00317561i
$512$	−14.2604	+	5.40824i	−0.630225	+	0.239013i
$513$	−0.141924	−	0.425116i	−0.00626612	−	0.0187693i
$514$	0.0379026	−	0.0889606i	0.00167181	−	0.00392388i
$515$	−6.05127	+	0.734757i	−0.266651	+	0.0323773i
$516$	13.9783	−	8.83934i	0.615360	−	0.389130i
$517$	5.34702	−	2.27815i	0.235162	−	0.100193i
$518$	2.00063	−	3.16374i	0.0879024	−	0.139007i
$519$	−5.43064	−	14.3194i	−0.238379	−	0.628553i
$520$	0.138380	+	4.88402i	0.00606838	+	0.214178i
$521$	−0.256716	+	0.676904i	−0.0112469	+	0.0296557i	−0.940522	−	0.339732i	$-0.889663\pi$
$521$	−0.256716	+	0.676904i	−0.0112469	+	0.0296557i	0.929275	+	0.369388i	$0.120433\pi$
$522$	−0.617326	−	0.821511i	−0.0270196	−	0.0359566i
$523$	7.96513	−	1.29446i	0.348291	−	0.0566027i	0.0162504	−	0.999868i	$-0.494827\pi$
$523$	7.96513	−	1.29446i	0.348291	−	0.0566027i	0.332040	+	0.943265i	$0.392263\pi$
$524$	−9.76434	−	4.16020i	−0.426557	−	0.181739i
$525$	−3.93223	+	2.71422i	−0.171617	+	0.118458i
$526$	−0.404252	−	0.233395i	−0.0176262	−	0.0101765i
$527$	38.6315	−	18.3309i	1.68281	−	0.798505i
$528$	−9.37421	−	1.13823i	−0.407960	−	0.0495353i
$529$	−18.3720	+	31.8212i	−0.798782	+	1.38353i
$530$	1.09563	+	1.89769i	0.0475913	+	0.0824305i
$531$	−3.33894	−	7.83679i	−0.144898	−	0.340088i
$532$	−1.36545	+	1.20969i	−0.0591999	+	0.0524465i
$533$	1.57417	−	9.00518i	0.0681848	−	0.390058i
$534$	2.65637	+	2.35334i	0.114953	+	0.101839i
$535$	3.54794	−	10.6274i	0.153391	−	0.459462i
$536$	−0.379311	−	9.41250i	−0.0163837	−	0.406558i
$537$	9.34586	+	11.4466i	0.403304	+	0.493957i
$538$	1.44785	−	1.63428i	0.0624210	−	0.0704588i
$539$	6.60851	−	1.34914i	0.284649	−	0.0581114i
$540$	3.08992	+	0.895005i	0.132969	+	0.0385149i
$541$	29.8206	+	11.3095i	1.28209	+	0.486232i	0.899190	−	0.437559i	$-0.144157\pi$
$541$	29.8206	+	11.3095i	1.28209	+	0.486232i	0.382898	+	0.923791i	$0.374926\pi$
$542$	0.0510217	−	1.26609i	0.00219157	−	0.0543833i
$543$	14.6025	−	10.9731i	0.626652	−	0.470899i
$544$	−14.2043	−	2.89983i	−0.609006	−	0.124329i
$545$	4.40836	+	2.31368i	0.188833	+	0.0991073i
$546$	−0.797354	+	1.34371i	−0.0341236	+	0.0575055i
$547$	−33.3625	+	17.5100i	−1.42648	+	0.748673i	−0.988629	−	0.150376i	$-0.951952\pi$
$547$	−33.3625	+	17.5100i	−1.42648	+	0.748673i	−0.437848	+	0.899049i	$0.644259\pi$
$548$	19.5269	−	5.65604i	0.834148	−	0.241614i
$549$	12.8235	+	1.03522i	0.547294	+	0.0441821i
$550$	−0.241544	−	1.18316i	−0.0102995	−	0.0504501i
$551$	−1.02743	+	1.95761i	−0.0437702	+	0.0833971i
$552$	3.82717	−	5.09303i	0.162895	−	0.216774i
$553$	−17.2252	−	27.2395i	−0.732489	−	1.15834i
$554$	1.39642	+	0.963876i	0.0593280	+	0.0409512i
$555$	6.08819	+	12.8306i	0.258429	+	0.544628i
$556$	23.1891	+	24.1424i	0.983437	+	1.02387i
$557$	−3.70508	+	3.55878i	−0.156989	+	0.150790i	−0.767104	−	0.641523i	$-0.778303\pi$
$557$	−3.70508	+	3.55878i	−0.156989	+	0.150790i	0.610115	+	0.792313i	$0.291123\pi$
$558$	0.179808	−	1.48085i	0.00761188	−	0.0626895i
$559$	−29.5019	−	7.64668i	−1.24780	−	0.323420i
$560$	−1.54251	−	12.7037i	−0.0651828	−	0.536829i
$561$	−11.6738	−	9.53135i	−0.492868	−	0.402414i
$562$	−0.298886	+	1.46404i	−0.0126077	+	0.0617568i
$563$	−6.89324	+	23.7982i	−0.290515	+	1.00298i	0.673952	+	0.738775i	$0.264595\pi$
$563$	−6.89324	+	23.7982i	−0.290515	+	1.00298i	−0.964468	+	0.264201i	$0.914892\pi$
$564$	−1.07831	+	4.37487i	−0.0454049	+	0.184215i
$565$	0.748647	+	9.27366i	0.0314958	+	0.390146i
$566$	0.158175	−	0.973293i	0.00664861	−	0.0409106i
$567$	1.37948	+	1.55711i	0.0579328	+	0.0653927i
$568$	9.87565	+	7.42107i	0.414373	+	0.311381i
$569$	−8.95138	+	10.9634i	−0.375261	+	0.459612i	−0.927362	−	0.374166i	$-0.877929\pi$
$569$	−8.95138	+	10.9634i	−0.375261	+	0.459612i	0.552100	+	0.833778i	$0.313826\pi$
$570$	0.0246232	+	0.151513i	0.00103135	+	0.00634618i
$571$	−27.3352	+	6.73752i	−1.14394	+	0.281956i	−0.765354	−	0.643609i	$-0.777436\pi$
$571$	−27.3352	+	6.73752i	−1.14394	+	0.281956i	−0.378588	+	0.925565i	$0.623590\pi$
$572$	10.5253	+	14.3608i	0.440085	+	0.600456i
$573$	−15.3289	−	3.77825i	−0.640376	−	0.157838i
$574$	0.0884126	−	1.09519i	0.00369027	−	0.0457122i
$575$	−16.8394	−	5.62182i	−0.702251	−	0.234446i
$576$	4.83333	−	5.03203i	0.201389	−	0.209668i
$577$		−	16.8985i		−	0.703492i	−0.936095	−	0.351746i	$-0.885588\pi$
$577$		−	16.8985i		−	0.703492i	0.936095	−	0.351746i	$-0.114412\pi$
$578$	−2.80281	−	2.69214i	−0.116582	−	0.111978i
$579$	−0.327860	+	0.267689i	−0.0136254	+	0.0111248i
$580$	−7.37467	−	14.0513i	−0.306216	−	0.583447i
$581$	−20.1606	−	3.27642i	−0.836404	−	0.135929i
$582$	1.14080	+	0.721398i	0.0472877	+	0.0299029i
$583$	14.5884	+	6.92228i	0.604190	+	0.286692i
$584$	0.200789	+	0.290893i	0.00830869	+	0.0120372i
$585$	−2.69196	−	5.28155i	−0.111299	−	0.218365i
$586$	−2.43993	+	3.53486i	−0.100793	+	0.146024i
$587$	31.2046	−	18.0160i	1.28795	−	0.743600i	0.309664	−	0.950846i	$-0.399784\pi$
$587$	31.2046	−	18.0160i	1.28795	−	0.743600i	0.978289	+	0.207246i	$0.0664502\pi$
$588$	−2.24158	+	4.72403i	−0.0924412	+	0.194816i
$589$	−3.04423	+	1.01631i	−0.125435	+	0.0418765i
$590$	0.698214	+	2.83277i	0.0287450	+	0.116623i
$591$	−16.0488	−	0.646745i	−0.660159	−	0.0266035i
$592$	32.2923	+	1.30134i	1.32721	+	0.0534846i
$593$	−5.65294	−	22.9349i	−0.232139	−	0.941823i	−0.965169	−	0.261627i	$-0.915741\pi$
$593$	−5.65294	−	22.9349i	−0.232139	−	0.941823i	0.733030	−	0.680196i	$-0.238105\pi$
$594$	−0.498699	+	0.166490i	−0.0204619	+	0.00683118i
$595$	8.75533	−	18.4515i	0.358934	−	0.756437i
$596$	−27.7274	+	16.0084i	−1.13576	+	0.655730i
$597$	12.1900	−	17.6603i	0.498905	−	0.722789i
$598$	−5.77110	+	0.630849i	−0.235998	+	0.0257973i
$599$	−11.8488	−	17.1660i	−0.484131	−	0.701385i	0.502459	−	0.864601i	$-0.332429\pi$
$599$	−11.8488	−	17.1660i	−0.484131	−	0.701385i	−0.986590	+	0.163216i	$0.947813\pi$
$600$	1.71030	+	0.811546i	0.0698226	+	0.0331312i
$601$	15.1081	+	9.55381i	0.616274	+	0.389708i	0.805817	−	0.592164i	$-0.201726\pi$
$601$	15.1081	+	9.55381i	0.616274	+	0.389708i	−0.189543	+	0.981872i	$0.560701\pi$
$602$	−3.61558	−	0.587589i	−0.147360	−	0.0239483i
$603$	5.31141	+	10.1200i	0.216297	+	0.412120i
$604$	−22.3653	+	18.2607i	−0.910030	+	0.743016i
$605$	−5.49020	−	5.27341i	−0.223209	−	0.214395i
$606$		−	0.671858i		−	0.0272924i
$607$	−8.35185	+	8.69520i	−0.338991	+	0.352927i	−0.868776	−	0.495205i	$-0.835093\pi$
$607$	−8.35185	+	8.69520i	−0.338991	+	0.352927i	0.529785	+	0.848132i	$0.322273\pi$
$608$	1.03212	+	0.344571i	0.0418578	+	0.0139742i
$609$	0.825743	−	10.2287i	0.0334608	−	0.414486i
$610$	−4.27827	−	1.05450i	−0.173222	−	0.0426954i
$611$	7.23979	−	4.06532i	0.292891	−	0.164465i
$612$	11.3439	−	2.79602i	0.458550	−	0.113022i
$613$	−5.52586	−	34.0020i	−0.223188	−	1.37333i	−0.820650	−	0.571431i	$-0.806388\pi$
$613$	−5.52586	−	34.0020i	−0.223188	−	1.37333i	0.597462	−	0.801897i	$-0.296176\pi$
$614$	1.40128	−	1.71625i	0.0565509	−	0.0692623i
$615$	3.33259	+	2.50428i	0.134383	+	0.100982i
$616$	2.86961	+	3.23913i	0.115620	+	0.130508i
$617$	5.82849	−	35.8642i	0.234646	−	1.44384i	−0.555806	−	0.831312i	$-0.687590\pi$
$617$	5.82849	−	35.8642i	0.234646	−	1.44384i	0.790452	−	0.612524i	$-0.209846\pi$
$618$	0.0621472	+	0.769831i	0.00249993	+	0.0309671i
$619$	5.73003	−	23.2476i	0.230309	−	0.934402i	−0.735992	−	0.676990i	$-0.763284\pi$
$619$	5.73003	−	23.2476i	0.230309	−	0.934402i	0.966302	−	0.257412i	$-0.0828698\pi$
$620$	6.40909	−	22.1267i	0.257395	−	0.888632i
$621$	−1.54608	+	7.57322i	−0.0620422	+	0.303903i
$622$	0.195176	+	0.159356i	0.00782584	+	0.00638960i
$623$	4.27183	+	35.1816i	0.171147	+	1.40952i
$624$	−13.4893	−	0.161219i	−0.540002	−	0.00645393i
$625$	−0.993294	+	8.18051i	−0.0397317	+	0.327220i
$626$	−0.990181	+	0.951082i	−0.0395756	+	0.0380129i
$627$	0.783572	+	0.815785i	0.0312928	+	0.0325793i
$628$	6.42532	+	13.5411i	0.256398	+	0.540348i
$629$	42.4484	+	29.3000i	1.69253	+	1.16827i
$630$	−0.380803	−	0.602191i	−0.0151715	−	0.0239919i
$631$	−15.5110	+	20.6414i	−0.617485	+	0.821723i	−0.994528	−	0.104473i	$-0.966684\pi$
$631$	−15.5110	+	20.6414i	−0.617485	+	0.821723i	0.377043	+	0.926196i	$0.376941\pi$
$632$	−5.93414	+	11.3066i	−0.236047	+	0.449751i
$633$	4.83334	+	23.6753i	0.192108	+	0.941007i
$634$	3.13386	+	0.252992i	0.124462	+	0.0100476i
$635$	−14.3933	+	4.16906i	−0.571179	+	0.165444i
$636$	−11.0843	+	5.81749i	−0.439521	+	0.230678i
$637$	9.17548	−	2.94183i	0.363546	−	0.116559i
$638$	2.29646	+	1.20527i	0.0909176	+	0.0477173i
$639$	−14.6849	−	2.99793i	−0.580924	−	0.118596i
$640$	−8.29272	+	6.23157i	−0.327799	+	0.246325i
$641$	1.04325	−	25.8879i	0.0412057	−	1.02251i	−0.837882	−	0.545851i	$-0.816207\pi$
$641$	1.04325	−	25.8879i	0.0412057	−	1.02251i	0.879088	−	0.476659i	$-0.158152\pi$
$642$	−1.32731	−	0.503383i	−0.0523848	−	0.0198669i
$643$	17.8292	+	5.16430i	0.703117	+	0.203660i	0.610471	−	0.792039i	$-0.290980\pi$
$643$	17.8292	+	5.16430i	0.703117	+	0.203660i	0.0926461	+	0.995699i	$0.470467\pi$
$644$	30.8252	−	6.29301i	1.21468	−	0.247979i
$645$	9.21571	−	10.4024i	0.362868	−	0.409594i
$646$	0.352583	+	0.431836i	0.0138722	+	0.0169904i
$647$	−1.35408	−	33.6012i	−0.0532345	−	1.32100i	−0.776363	−	0.630286i	$-0.782937\pi$
$647$	−1.35408	−	33.6012i	−0.0532345	−	1.32100i	0.723128	−	0.690714i	$-0.242704\pi$
$648$	0.261003	−	0.781801i	0.0102532	−	0.0307120i
$649$	16.0925	+	14.2567i	0.631686	+	0.559625i
$650$	−0.526692	−	1.64274i	−0.0206586	−	0.0644336i
$651$	11.1504	−	9.87841i	0.437019	−	0.387165i
$652$	7.19824	+	16.8949i	0.281905	+	0.661655i
$653$	19.7364	+	34.1845i	0.772347	+	1.33774i	0.936274	+	0.351271i	$0.114250\pi$
$653$	19.7364	+	34.1845i	0.772347	+	1.33774i	−0.163927	+	0.986472i	$0.552416\pi$
$654$	0.315399	−	0.546288i	0.0123331	−	0.0213615i
$655$	−8.85363	−	1.07503i	−0.345940	−	0.0420047i
$656$	8.57055	−	4.06678i	0.334624	−	0.158781i
$657$	−0.371390	−	0.214422i	−0.0144893	−	0.00836540i
$658$	0.821299	−	0.566902i	0.0320176	−	0.0221001i
$659$	−21.5745	−	9.19202i	−0.840422	−	0.358070i	−0.0715217	−	0.997439i	$-0.522786\pi$
$659$	−21.5745	−	9.19202i	−0.840422	−	0.358070i	−0.768900	+	0.639369i	$0.779196\pi$
$660$	−8.01394	+	1.30239i	−0.311942	+	0.0506955i
$661$	−14.3733	−	19.1274i	−0.559057	−	0.743969i	0.428099	−	0.903732i	$-0.359184\pi$
$661$	−14.3733	−	19.1274i	−0.559057	−	0.743969i	−0.987155	+	0.159763i	$0.948927\pi$
$662$	1.11581	−	2.94215i	0.0433672	−	0.114350i
$663$	−18.0579	−	11.7235i	−0.701309	−	0.455304i
$664$	2.86965	+	7.56665i	0.111364	+	0.293643i
$665$	−0.819282	+	1.29559i	−0.0317704	+	0.0502409i
$666$	1.65539	−	0.705298i	0.0641452	−	0.0273297i
$667$	32.2261	−	20.3786i	1.24780	−	0.789062i
$668$	46.0173	−	5.58751i	1.78046	−	0.216187i
$669$	3.09393	−	7.26172i	0.119618	−	0.280754i
$670$	−1.23959	−	3.71302i	−0.0478894	−	0.143446i
$671$	−30.3600	+	11.5140i	−1.17204	+	0.444494i
$672$	−5.03423	+	0.406405i	−0.194200	+	0.0156774i
$673$	9.75182	+	33.6672i	0.375905	+	1.29778i	0.896147	+	0.443756i	$0.146354\pi$
$673$	9.75182	+	33.6672i	0.375905	+	1.29778i	−0.520242	+	0.854019i	$0.674158\pi$
$674$	−0.0309655	+	0.00124787i	−0.00119275	+	4.80661e-5i
$675$	−2.29681			−0.0884043
$676$	17.1766	+	18.7603i	0.660638	+	0.721550i
$677$	−7.39709			−0.284293			−0.142147	−	0.989846i	$-0.545400\pi$
$677$	−7.39709			−0.284293			−0.142147	+	0.989846i	$0.545400\pi$
$678$	1.17785	−	0.0474658i	0.0452351	−	0.00182291i
$679$	3.75010	+	12.9468i	0.143916	+	0.496854i
$680$	−8.06558	+	0.651121i	−0.309301	+	0.0249693i
$681$	−7.02380	+	2.66377i	−0.269152	+	0.102076i
$682$	1.19223	+	3.57116i	0.0456528	+	0.136747i
$683$	−3.75398	+	8.81092i	−0.143642	+	0.337140i	−0.976225	−	0.216760i	$-0.930451\pi$
$683$	−3.75398	+	8.81092i	−0.143642	+	0.337140i	0.832583	+	0.553901i	$0.186861\pi$
$684$	−0.870519	+	0.105700i	−0.0332851	+	0.00404154i
$685$	14.4383	−	9.13025i	0.551661	−	0.348849i
$686$	3.85616	−	1.64296i	0.147229	−	0.0627284i
$687$	13.1688	−	20.8248i	0.502421	−	0.794515i
$688$	−11.2147	−	29.5708i	−0.427558	−	1.12738i
$689$	21.7920	+	7.56586i	0.830208	+	0.288236i
$690$	0.938748	−	2.47528i	0.0357375	−	0.0942321i
$691$	14.7251	+	19.5956i	0.560170	+	0.745450i	0.987322	−	0.158729i	$-0.0507397\pi$
$691$	14.7251	+	19.5956i	0.560170	+	0.745450i	−0.427153	+	0.904180i	$0.640483\pi$
$692$	−29.5766	+	4.80667i	−1.12434	+	0.182722i
$693$	−4.83021	−	2.05796i	−0.183484	−	0.0781754i
$694$	0.828642	−	0.571970i	0.0314548	−	0.0217117i
$695$	24.3607	+	14.0646i	0.924053	+	0.533502i
$696$	−3.67327	+	1.74299i	−0.139235	+	0.0660679i
$697$	15.0295	+	1.82491i	0.569283	+	0.0691235i
$698$	−1.46952	+	2.54529i	−0.0556223	+	0.0963407i
$699$	−6.06816	−	10.5104i	−0.229519	−	0.397538i
$700$	3.66438	+	8.60061i	0.138500	+	0.325073i
$701$	−0.840140	+	0.744299i	−0.0317317	+	0.0281118i	−0.678840	−	0.734287i	$-0.737517\pi$
$701$	−0.840140	+	0.744299i	−0.0317317	+	0.0281118i	0.647108	+	0.762398i	$0.275978\pi$
$702$	−0.682371	+	0.313853i	−0.0257544	+	0.0118456i
$703$	−2.89771	−	2.56715i	−0.109289	−	0.0968218i
$704$	−5.57642	+	16.7034i	−0.210169	+	0.629533i
$705$	0.152456	+	3.78316i	0.00574182	+	0.142482i
$706$	2.57580	+	3.15478i	0.0969416	+	0.118732i
$707$	4.44913	−	5.02203i	0.167327	−	0.188873i
$708$	−16.3304	+	3.33387i	−0.613734	+	0.125295i
$709$	−35.7972	−	10.3688i	−1.34439	−	0.389408i	−0.473462	−	0.880814i	$-0.656996\pi$
$709$	−35.7972	−	10.3688i	−1.34439	−	0.389408i	−0.870930	+	0.491407i	$0.836483\pi$
$710$	4.79969	+	1.82028i	0.180129	+	0.0683139i
$711$	0.623820	−	15.4799i	0.0233951	−	0.580543i
$712$	11.2254	−	8.43533i	0.420689	−	0.316127i
$713$	54.2314	+	11.0714i	2.03098	+	0.414628i
$714$	−2.29126	−	1.20255i	−0.0857483	−	0.0450042i
$715$	11.8526	+	9.13030i	0.443262	+	0.341454i
$716$	25.6016	−	13.4367i	0.956776	−	0.502155i
$717$	11.0048	−	3.18758i	0.410982	−	0.119042i
$718$	2.23400	+	0.180347i	0.0833720	+	0.00673048i
$719$	10.3798	+	50.8435i	0.387100	+	1.89614i	0.440837	+	0.897587i	$0.354682\pi$
$719$	10.3798	+	50.8435i	0.387100	+	1.89614i	−0.0537368	+	0.998555i	$0.517113\pi$
$720$	2.85877	−	5.44694i	0.106540	−	0.202995i
$721$	−4.63337	+	6.16590i	−0.172556	+	0.229630i
$722$	2.09304	+	3.30987i	0.0778948	+	0.123181i
$723$	−6.15928	−	4.25145i	−0.229066	−	0.158113i
$724$	−15.3210	−	32.2884i	−0.569402	−	1.19999i
$725$	7.84861	+	8.17127i	0.291490	+	0.303473i
$726$	−0.695616	+	0.668148i	−0.0258167	+	0.0247973i
$727$	1.97809	−	16.2910i	0.0733631	−	0.604200i	−0.908943	−	0.416920i	$-0.863110\pi$
$727$	1.97809	−	16.2910i	0.0733631	−	0.604200i	0.982307	−	0.187280i	$-0.0599672\pi$
$728$	4.57805	+	4.15450i	0.169674	+	0.153976i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	0.113772	+	0.0928923i	0.00421091	+	0.00343810i
$731$	10.0960	−	49.4534i	0.373414	−	1.82910i
$732$	7.00334	−	24.1783i	0.258851	−	0.893657i
$733$	9.28149	−	37.6565i	0.342820	−	1.39087i	−0.506156	−	0.862442i	$-0.668934\pi$
$733$	9.28149	−	37.6565i	0.342820	−	1.39087i	0.848976	−	0.528432i	$-0.177220\pi$
$734$	0.243896	+	3.02120i	0.00900237	+	0.111514i
$735$	−0.704820	+	4.33693i	−0.0259977	+	0.159970i
$736$	−12.4441	−	14.0464i	−0.458694	−	0.517759i
$737$	−23.0605	−	17.3288i	−0.849443	−	0.638315i
$738$	0.334041	−	0.409125i	0.0122962	−	0.0150601i
$739$	−4.43348	−	27.2803i	−0.163088	−	1.00352i	−0.931547	−	0.363622i	$-0.881540\pi$
$739$	−4.43348	−	27.2803i	−0.163088	−	1.00352i	0.768458	−	0.639900i	$-0.221024\pi$
$740$	26.9798	−	6.64992i	0.991797	−	0.244456i
$741$	1.23941	+	1.03688i	0.0455309	+	0.0380907i
$742$	2.69199	+	0.663515i	0.0988259	+	0.0243584i
$743$	−0.569123	+	7.04985i	−0.0208791	+	0.258634i	0.977894	+	0.209104i	$0.0670546\pi$
$743$	−0.569123	+	7.04985i	−0.0208791	+	0.258634i	−0.998773	+	0.0495306i	$0.984227\pi$
$744$	−5.59844	−	1.86903i	−0.205249	−	0.0685221i
$745$	−18.6369	+	19.4031i	−0.682803	+	0.710873i
$746$		−	3.73578i		−	0.136777i
$747$	−7.08108	−	6.80147i	−0.259083	−	0.248853i
$748$	−22.8410	+	18.6491i	−0.835149	+	0.681878i
$749$	−6.58796	−	12.5523i	−0.240719	−	0.458651i
$750$	2.46678	+	0.400890i	0.0900739	+	0.0146384i
$751$	−31.8265	−	20.1258i	−1.16136	−	0.734402i	−0.192330	−	0.981330i	$-0.561604\pi$
$751$	−31.8265	−	20.1258i	−1.16136	−	0.734402i	−0.969034	+	0.246928i	$0.920579\pi$
$752$	7.78431	+	3.69370i	0.283865	+	0.134695i
$753$	11.4166	+	16.5398i	0.416043	+	0.602743i
$754$	3.44836	+	1.35515i	0.125582	+	0.0493516i
$755$	−13.7825	+	19.9673i	−0.501595	+	0.726686i
$756$	3.52498	−	2.03515i	0.128202	−	0.0740176i
$757$	15.0603	−	31.7390i	0.547377	−	1.15357i	−0.421682	−	0.906744i	$-0.638560\pi$
$757$	15.0603	−	31.7390i	0.547377	−	1.15357i	0.969059	−	0.246829i	$-0.0793885\pi$
$758$	0.445605	−	0.148765i	0.0161851	−	0.00540339i
$759$	−4.66857	−	18.9411i	−0.169458	−	0.687519i
$760$	0.606849	+	0.0244552i	0.0220127	+	0.000887083i
$761$	2.28079	+	0.0919127i	0.0826786	+	0.00333183i	0.0815708	−	0.996668i	$-0.474006\pi$
$761$	2.28079	+	0.0919127i	0.0826786	+	0.00333183i	0.00110784	+	0.999999i	$0.499647\pi$
$762$	0.454366	+	1.84343i	0.0164599	+	0.0667806i
$763$	5.97514	−	1.99479i	0.216315	−	0.0722164i
$764$	−13.2424	+	27.9079i	−0.479095	+	1.00967i
$765$	8.50227	−	4.90879i	0.307400	−	0.177478i
$766$	−1.98196	+	2.87137i	−0.0716113	+	0.103747i
$767$	25.0665	+	17.7482i	0.905100	+	0.640850i
$768$	−7.18048	−	10.4027i	−0.259103	−	0.375376i
$769$	−40.0152	−	18.9875i	−1.44299	−	0.684706i	−0.463478	−	0.886108i	$-0.653399\pi$
$769$	−40.0152	−	18.9875i	−1.44299	−	0.684706i	−0.979508	+	0.201403i	$0.935450\pi$
$770$	1.51985	+	0.961092i	0.0547714	+	0.0346354i
$771$	0.458184	+	0.0744621i	0.0165011	+	0.00268169i
$772$	0.384862	+	0.733294i	0.0138515	+	0.0263918i
$773$	−21.6260	+	17.6571i	−0.777834	+	0.635082i	−0.935868	−	0.352352i	$-0.885382\pi$
$773$	−21.6260	+	17.6571i	−0.777834	+	0.635082i	0.158033	+	0.987434i	$0.449485\pi$
$774$	−1.26991	−	1.21977i	−0.0456460	−	0.0438436i
$775$			16.4474i			0.590807i
$776$	3.69946	−	3.85154i	0.132803	−	0.138262i
$777$	17.0444	+	5.69024i	0.611463	+	0.204136i
$778$	0.493787	−	6.11664i	0.0177031	−	0.219292i
$779$	−1.10332	−	0.271945i	−0.0395307	−	0.00974344i
$780$	−11.1786	+	3.09362i	−0.400259	+	0.110769i
$781$	36.7278	−	9.05259i	1.31422	−	0.323927i
$782$	−1.54229	−	9.49012i	−0.0551523	−	0.339366i
$783$	3.11982	−	3.82109i	0.111493	−	0.136555i
$784$	7.99355	+	6.00676i	0.285484	+	0.214527i
$785$	8.35176	+	9.42718i	0.298087	+	0.336471i
$786$	−0.181266	+	1.11537i	−0.00646554	+	0.0397840i
$787$	1.30657	+	16.1848i	0.0465742	+	0.576925i	0.977391	+	0.211439i	$0.0678150\pi$
$787$	1.30657	+	16.1848i	0.0465742	+	0.576925i	−0.930817	+	0.365486i	$0.880903\pi$
$788$	−7.52089	+	30.5135i	−0.267921	+	1.08700i
$789$	0.623428	−	2.15232i	0.0221946	−	0.0766247i
$790$	−1.06136	+	5.19891i	−0.0377617	+	0.184969i
$791$	9.11856	+	7.44508i	0.324219	+	0.264716i
$792$	0.250742	+	2.06504i	0.00890972	+	0.0733781i
$793$	−41.3277	+	21.0644i	−1.46759	+	0.748017i
$794$	0.103628	−	0.853450i	0.00367761	−	0.0302878i
$795$	−7.58636	+	7.28679i	−0.269060	+	0.258436i
$796$	−29.0851	−	30.2808i	−1.03089	−	1.07328i
$797$	−4.01026	−	8.45145i	−0.142051	−	0.299366i	0.819939	−	0.572451i	$-0.194007\pi$
$797$	−4.01026	−	8.45145i	−0.142051	−	0.299366i	−0.961990	+	0.273085i	$0.911956\pi$
$798$	0.159840	+	0.110330i	0.00565828	+	0.00390563i
$799$	7.34944	+	11.6222i	0.260005	+	0.411164i
$800$	3.34992	−	4.45794i	0.118438	−	0.157612i
$801$	−7.91710	+	15.0848i	−0.279737	+	0.532994i
$802$	−0.417804	−	2.04654i	−0.0147532	−	0.0722658i
$803$	1.07883	+	0.0870924i	0.0380712	+	0.00307342i
$804$	21.4795	−	6.22161i	0.757524	−	0.219419i
$805$	23.4086	−	12.2858i	0.825043	−	0.433016i
$806$	2.24749	+	4.88642i	0.0791644	+	0.172117i
$807$	9.28060	+	4.87083i	0.326693	+	0.171461i
$808$	−2.60456	−	0.531724i	−0.0916280	−	0.0187060i
$809$	3.58697	−	2.69544i	0.126111	−	0.0947665i	−0.535815	−	0.844335i	$-0.679996\pi$
$809$	3.58697	−	2.69544i	0.126111	−	0.0947665i	0.661926	+	0.749569i	$0.269739\pi$
$810$	0.0137910	−	0.342220i	0.000484566	−	0.0120244i
$811$	38.3693	+	14.5515i	1.34733	+	0.510974i	0.919572	−	0.392921i	$-0.128535\pi$
$811$	38.3693	+	14.5515i	1.34733	+	0.510974i	0.427755	+	0.903895i	$0.359305\pi$
$812$	−19.2858	−	5.58621i	−0.676800	−	0.196037i
$813$	5.95980	−	1.21670i	0.209019	−	0.0426716i
$814$	−3.01150	+	3.39928i	−0.105553	+	0.119145i
$815$	9.75967	+	11.9534i	0.341866	+	0.418710i
$816$	−0.899604	−	22.3234i	−0.0314924	−	0.781477i
$817$	−1.19965	+	3.59339i	−0.0419704	+	0.125717i
$818$	3.94268	+	3.49291i	0.137853	+	0.122127i
$819$	−7.17898	−	2.17274i	−0.250854	−	0.0759216i
$820$	6.10515	−	5.40869i	0.213201	−	0.188880i
$821$	−12.4752	−	29.2804i	−0.435388	−	1.02189i	−0.982740	−	0.184991i	$-0.940774\pi$
$821$	−12.4752	−	29.2804i	−0.435388	−	1.02189i	0.547352	−	0.836902i	$-0.315636\pi$
$822$	−1.08222	−	1.87445i	−0.0377466	−	0.0653791i
$823$	25.0349	−	43.3617i	0.872662	−	1.51149i	0.0134293	−	0.999910i	$-0.495725\pi$
$823$	25.0349	−	43.3617i	0.872662	−	1.51149i	0.859233	−	0.511585i	$-0.170941\pi$
$824$	3.03355	+	0.368339i	0.105679	+	0.0128317i
$825$	5.23715	−	2.48506i	0.182334	−	0.0865186i
$826$	3.19693	+	1.84575i	0.111235	+	0.0642217i
$827$	25.7449	−	17.7704i	0.895237	−	0.617938i	−0.0290740	−	0.999577i	$-0.509256\pi$
$827$	25.7449	−	17.7704i	0.895237	−	0.617938i	0.924311	+	0.381640i	$0.124640\pi$
$828$	13.9132	+	5.92788i	0.483519	+	0.206008i
$829$	5.83557	−	0.948372i	0.202678	−	0.0329383i	−0.0582248	−	0.998303i	$-0.518544\pi$
$829$	5.83557	−	0.948372i	0.202678	−	0.0329383i	0.260902	+	0.965365i	$0.415980\pi$
$830$	2.02017	+	2.68836i	0.0701211	+	0.0933143i
$831$	−2.88834	+	7.61594i	−0.100196	+	0.264194i
$832$	−5.32624	+	24.5866i	−0.184654	+	0.852387i
$833$	5.65869	+	14.9207i	0.196062	+	0.516973i
$834$	1.90484	−	3.01227i	0.0659594	−	0.104306i
$835$	35.8354	−	15.2680i	1.24014	−	0.528372i
$836$	1.87058	−	1.18288i	0.0646953	−	0.0409108i
$837$	7.10874	−	0.863157i	0.245714	−	0.0298351i
$838$	1.60793	−	3.77394i	0.0555449	−	0.130369i
$839$	15.4108	+	46.1610i	0.532041	+	1.59366i	0.780594	+	0.625038i	$0.214917\pi$
$839$	15.4108	+	46.1610i	0.532041	+	1.59366i	−0.248554	+	0.968618i	$0.579955\pi$
$840$	−2.63586	+	0.999648i	−0.0909457	+	0.0344911i
$841$	4.65085	−	0.375456i	0.160374	−	0.0129467i
$842$	0.205363	+	0.708994i	0.00707727	+	0.0244336i
$843$	−7.16718	+	0.288827i	−0.246851	+	0.00994774i
$844$	47.2786			1.62740
$845$	18.2495	+	11.1262i	0.627803	+	0.382754i
$846$	0.479720			0.0164931
$847$	−9.62417	+	0.387841i	−0.330690	+	0.0133264i
$848$	6.65993	+	22.9927i	0.228703	+	0.789574i
$849$	4.71818	−	0.380891i	0.161927	−	0.0130721i
$850$	2.67135	−	1.01311i	0.0916264	−	0.0347493i
$851$	21.1424	+	63.3294i	0.724754	+	2.17090i
$852$	−11.4945	+	26.9785i	−0.393794	+	0.924268i
$853$	20.0479	−	2.43426i	0.686427	−	0.0833473i	0.230110	−	0.973165i	$-0.426091\pi$
$853$	20.0479	−	2.43426i	0.686427	−	0.0833473i	0.456317	+	0.889817i	$0.349168\pi$
$854$	−4.71209	+	2.97975i	−0.161244	+	0.101965i
$855$	−0.677906	+	0.288829i	−0.0231839	+	0.00987773i
$856$	−3.00190	+	4.74712i	−0.102603	+	0.162253i
$857$	9.35139	+	24.6576i	0.319437	+	0.842287i	0.994520	+	0.104545i	$0.0333387\pi$
$857$	9.35139	+	24.6576i	0.319437	+	0.842287i	−0.675083	+	0.737742i	$0.735892\pi$
$858$	1.21635	−	1.45394i	0.0415256	−	0.0496367i
$859$	7.12105	−	18.7767i	0.242967	−	0.640651i	−0.756951	−	0.653472i	$-0.773312\pi$
$859$	7.12105	−	18.7767i	0.242967	−	0.640651i	0.999918	+	0.0128206i	$0.00408105\pi$
$860$	−16.3353	−	21.7383i	−0.557028	−	0.741270i
$861$	5.20617	−	0.846086i	0.177426	−	0.0288345i
$862$	2.29355	+	0.977191i	0.0781186	+	0.0332832i
$863$	5.09338	−	3.51571i	0.173381	−	0.119676i	−0.478214	−	0.878243i	$-0.658716\pi$
$863$	5.09338	−	3.51571i	0.173381	−	0.119676i	0.651595	+	0.758567i	$0.274100\pi$
$864$	−2.10258	−	1.21392i	−0.0715311	−	0.0412985i
$865$	−22.7483	+	10.7942i	−0.773465	+	0.367014i
$866$	−4.41900	−	0.536563i	−0.150164	−	0.0182332i
$867$	9.32798	−	16.1565i	0.316795	−	0.548705i
$868$	−14.5736	−	25.2422i	−0.494660	−	0.856776i
$869$	15.3262	+	35.9720i	0.519907	+	1.22027i
$870$	−1.26463	+	1.12036i	−0.0428749	+	0.0379838i
$871$	−35.4388	−	21.0293i	−1.20080	−	0.712550i
$872$	−1.86815	−	1.65504i	−0.0632635	−	0.0560466i
$873$	−2.05182	+	6.14596i	−0.0694437	+	0.208009i
$874$	0.0290574	+	0.721053i	0.000982882	+	0.0243900i
$875$	15.7840	+	19.3319i	0.533596	+	0.653537i
$876$	−0.556412	+	0.628059i	−0.0187994	+	0.0212202i
$877$	7.43614	−	1.51810i	0.251101	−	0.0512625i	−0.0728264	−	0.997345i	$-0.523202\pi$
$877$	7.43614	−	1.51810i	0.251101	−	0.0512625i	0.323927	+	0.946082i	$0.394997\pi$
$878$	2.11621	+	0.612967i	0.0714186	+	0.0206866i
$879$	−19.2788	−	7.31149i	−0.650258	−	0.246610i
$880$	−0.625156	+	15.5131i	−0.0210740	+	0.522946i
$881$	−7.80720	+	5.86673i	−0.263031	+	0.197655i	−0.724073	−	0.689723i	$-0.757732\pi$
$881$	−7.80720	+	5.86673i	−0.263031	+	0.197655i	0.461042	+	0.887378i	$0.347476\pi$
$882$	0.545453	+	0.111355i	0.0183664	+	0.00374952i
$883$	−0.989810	−	0.519492i	−0.0333098	−	0.0174823i	0.447986	−	0.894041i	$-0.352141\pi$
$883$	−0.989810	−	0.519492i	−0.0333098	−	0.0174823i	−0.481296	+	0.876558i	$0.659834\pi$
$884$	−29.5421	+	30.0298i	−0.993608	+	1.01001i
$885$	−12.4012	+	6.50867i	−0.416863	+	0.218787i
$886$	−6.11958	+	1.77256i	−0.205591	+	0.0595503i
$887$	−0.523580	−	0.0422678i	−0.0175801	−	0.00141921i	0.0716734	−	0.997428i	$-0.477166\pi$
$887$	−0.523580	−	0.0422678i	−0.0175801	−	0.00141921i	−0.0892535	+	0.996009i	$0.528448\pi$
$888$	−1.42407	−	6.97556i	−0.0477887	−	0.234085i
$889$	−8.81114	+	16.7882i	−0.295516	+	0.563059i
$890$	3.50524	−	4.66462i	0.117496	−	0.156359i
$891$	−1.34892	−	2.13314i	−0.0451904	−	0.0714629i
$892$	−12.7103	−	8.77328i	−0.425572	−	0.293751i
$893$	−0.442453	−	0.932451i	−0.0148061	−	0.0312033i
$894$	2.36132	+	2.45839i	0.0789743	+	0.0822210i
$895$	17.5223	−	16.8304i	0.585707	−	0.562579i
$896$	−1.58202	+	13.0291i	−0.0528517	+	0.435273i
$897$	−9.57031	−	26.1741i	−0.319543	−	0.873926i
$898$	−0.214931	−	1.77012i	−0.00717236	−	0.0590697i
$899$	−27.3626	−	22.3409i	−0.912595	−	0.745111i
$900$	−0.898906	+	4.40313i	−0.0299635	+	0.146771i
$901$	−10.6289	+	36.6952i	−0.354100	+	1.22250i
$902$	−0.319016	+	1.29430i	−0.0106221	+	0.0430954i
$903$	−1.41493	−	17.5270i	−0.0470859	−	0.583264i
$904$	0.748170	−	4.60368i	0.0248838	−	0.153116i
$905$	−19.9146	−	22.4789i	−0.661983	−	0.747224i
$906$	2.45752	+	1.84671i	0.0816457	+	0.0613528i
$907$	16.1858	−	19.8241i	0.537442	−	0.658247i	−0.432485	−	0.901641i	$-0.642363\pi$
$907$	16.1858	−	19.8241i	0.537442	−	0.658247i	0.969928	+	0.243394i	$0.0782607\pi$
$908$	2.35771	+	14.5076i	0.0782434	+	0.481451i
$909$	3.13149	−	0.771844i	0.103865	−	0.0256005i
$910$	2.30757	+	1.12894i	0.0764952	+	0.0374239i
$911$	4.35932	+	1.07447i	0.144431	+	0.0355989i	0.310868	−	0.950453i	$-0.399380\pi$
$911$	4.35932	+	1.07447i	0.144431	+	0.0355989i	−0.166438	+	0.986052i	$0.553226\pi$
$912$	−0.134932	+	1.67144i	−0.00446805	+	0.0553468i
$913$	23.5051	+	7.84715i	0.777905	+	0.259703i
$914$	3.73841	−	3.89210i	0.123656	−	0.128739i
$915$		−	21.1522i		−	0.699270i
$916$	−34.7685	−	33.3956i	−1.14878	−	1.10342i
$917$	−8.74106	+	7.13686i	−0.288655	+	0.235680i
$918$	−0.578069	−	1.10142i	−0.0190791	−	0.0363522i
$919$	47.7211	+	7.75543i	1.57417	+	0.255828i	0.883884	−	0.467706i	$-0.154919\pi$
$919$	47.7211	+	7.75543i	1.57417	+	0.255828i	0.690289	+	0.723534i	$0.257483\pi$
$920$	−8.85282	−	5.59818i	−0.291869	−	0.184567i
$921$	9.60917	+	4.55961i	0.316633	+	0.150244i
$922$	−4.81602	−	6.97721i	−0.158607	−	0.229782i
$923$	50.7528	−	18.5573i	1.67055	−	0.610821i
$924$	−5.83564	+	8.45439i	−0.191979	+	0.278129i
$925$	−17.1815	+	9.91972i	−0.564923	+	0.326158i
$926$	0.915769	−	1.92994i	0.0300940	−	0.0634218i
$927$	−3.51674	+	1.17406i	−0.115505	+	0.0385612i
$928$	2.86615	+	11.6284i	0.0940861	+	0.381722i
$929$	−15.5001	−	0.624634i	−0.508543	−	0.0204936i	−0.215331	−	0.976541i	$-0.569083\pi$
$929$	−15.5001	−	0.624634i	−0.508543	−	0.0204936i	−0.293212	+	0.956048i	$0.594724\pi$
$930$	−2.45062	−	0.0987566i	−0.0803590	−	0.00323836i
$931$	−0.286635	−	1.16292i	−0.00939408	−	0.0381133i
$932$	−22.5239	+	7.51959i	−0.737796	+	0.246312i
$933$	−0.518528	+	1.09277i	−0.0169759	+	0.0357758i
$934$	3.40053	−	1.96330i	0.111269	−	0.0642411i
$935$	−14.0756	+	20.3920i	−0.460322	+	0.666891i
$936$	0.676655	+	2.89370i	0.0221172	+	0.0945835i
$937$	−18.1952	−	26.3603i	−0.594411	−	0.861153i	0.404155	−	0.914691i	$-0.367566\pi$
$937$	−18.1952	−	26.3603i	−0.594411	−	0.861153i	−0.998566	+	0.0535377i	$0.982950\pi$
$938$	−4.47468	−	2.12326i	−0.146103	−	0.0693269i
$939$	−5.57048	−	3.52256i	−0.181786	−	0.114954i
$940$	7.31222	+	1.18835i	0.238498	+	0.0387597i
$941$	4.72442	+	9.00163i	0.154012	+	0.293445i	0.950221	−	0.311576i	$-0.100857\pi$
$941$	4.72442	+	9.00163i	0.154012	+	0.293445i	−0.796209	+	0.605021i	$0.793165\pi$
$942$	1.23608	−	1.00923i	0.0402735	−	0.0328823i
$943$	14.1339	+	13.5758i	0.460262	+	0.442088i
$944$			31.8719i			1.03734i
$945$	2.36931	−	2.46671i	0.0770735	−	0.0802420i
$946$	4.21537	+	1.40730i	0.137053	+	0.0457551i
$947$	−2.97289	+	36.8259i	−0.0966061	+	1.19668i	0.748888	+	0.662696i	$0.230588\pi$
$947$	−2.97289	+	36.8259i	−0.0966061	+	1.19668i	−0.845494	+	0.533985i	$0.820694\pi$
$948$	−29.4319	−	7.25430i	−0.955903	−	0.235609i
$949$	1.54560	−	0.0437919i	0.0501723	−	0.00142155i
$950$	−0.208205	+	0.0513179i	−0.00675506	+	0.00166497i
$951$	2.42106	+	14.8974i	0.0785084	+	0.483081i
$952$	−6.47521	+	7.93069i	−0.209863	+	0.257035i
$953$	−45.7257	−	34.3606i	−1.48120	−	1.11305i	−0.966811	−	0.255491i	$-0.917763\pi$
$953$	−45.7257	−	34.3606i	−1.48120	−	1.11305i	−0.514388	−	0.857558i	$-0.671981\pi$
$954$	0.883794	+	0.997597i	0.0286139	+	0.0322984i
$955$	−4.16382	+	25.6210i	−0.134738	+	0.829077i
$956$	−1.80383	−	22.3444i	−0.0583400	−	0.722670i
$957$	−2.97950	+	12.0883i	−0.0963135	+	0.390759i
$958$	1.14962	−	3.96894i	0.0371424	−	0.128231i
$959$	4.32348	−	21.1778i	0.139612	−	0.683866i
$960$	−8.88595	−	7.25516i	−0.286793	−	0.234159i
$961$	−2.44439	−	20.1314i	−0.0788513	−	0.649399i
$962$	−3.74902	+	5.29490i	−0.120873	+	0.170714i
$963$	0.821398	−	6.76482i	0.0264692	−	0.217993i
$964$	−10.5609	+	10.1438i	−0.340142	+	0.326711i
$965$	0.482066	+	0.501884i	0.0155183	+	0.0161562i
$966$	−1.43593	−	3.02617i	−0.0462004	−	0.0973654i
$967$	−21.6228	−	14.9251i	−0.695341	−	0.479959i	0.167215	−	0.985920i	$-0.446522\pi$
$967$	−21.6228	−	14.9251i	−0.695341	−	0.479959i	−0.862556	+	0.505961i	$0.831138\pi$
$968$	2.03965	+	3.22544i	0.0655568	+	0.103670i
$969$	−1.60771	+	2.13947i	−0.0516470	+	0.0687297i
$970$	1.03131	−	1.96499i	0.0331132	−	0.0630920i
$971$	−5.62223	−	27.5395i	−0.180426	−	0.883785i	−0.964696	−	0.263365i	$-0.915168\pi$
$971$	−5.62223	−	27.5395i	−0.180426	−	0.883785i	0.784270	−	0.620419i	$-0.213038\pi$
$972$	1.95026	+	0.157441i	0.0625546	+	0.00504993i
$973$	34.1860	−	9.90210i	1.09595	−	0.317447i
$974$	2.51245	−	1.31864i	0.0805042	−	0.0422519i
$975$	7.05165	−	4.34210i	0.225833	−	0.139058i
$976$	−42.6218	−	22.3696i	−1.36429	−	0.716035i
$977$	−47.2961	−	9.65556i	−1.51314	−	0.308909i	−0.629469	−	0.777026i	$-0.716727\pi$
$977$	−47.2961	−	9.65556i	−1.51314	−	0.308909i	−0.883666	+	0.468117i	$0.844933\pi$
$978$	1.56308	−	1.17458i	0.0499817	−	0.0375588i
$979$	1.73131	−	42.9620i	0.0553329	−	1.37307i
$980$	8.03832	+	3.04853i	0.256775	+	0.0973818i
$981$	2.90855	+	0.842473i	0.0928630	+	0.0268981i
$982$	6.54216	−	1.33559i	0.208769	−	0.0426205i
$983$	25.8345	−	29.1611i	0.823993	−	0.930096i	−0.174517	−	0.984654i	$-0.555837\pi$
$983$	25.8345	−	29.1611i	0.823993	−	0.930096i	0.998511	+	0.0545580i	$0.0173750\pi$
$984$	−1.32167	−	1.61875i	−0.0421332	−	0.0516038i
$985$	1.06334	+	26.3864i	0.0338807	+	0.840742i
$986$	−1.94311	+	5.82031i	−0.0618811	+	0.185357i
$987$	3.58582	+	3.17676i	0.114138	+	0.101117i
$988$	2.47283	−	1.97022i	0.0786713	−	0.0626812i
$989$	48.9037	−	43.3249i	1.55505	−	1.37765i
$990$	0.338822	+	0.795245i	0.0107685	+	0.0252745i
$991$	−18.5534	−	32.1354i	−0.589368	−	1.02082i	−0.994315	−	0.106475i	$-0.966043\pi$
$991$	−18.5534	−	32.1354i	−0.589368	−	1.02082i	0.404947	−	0.914340i	$-0.367290\pi$
$992$	−8.69285	+	15.0565i	−0.275998	+	0.478043i
$993$	14.9951	+	1.82073i	0.475854	+	0.0577791i
$994$	5.86789	−	2.78435i	0.186118	−	0.0883142i
$995$	−30.5546	−	17.6407i	−0.968644	−	0.559247i
$996$	−15.8102	+	10.9130i	−0.500965	+	0.345791i
$997$	25.1354	+	10.7092i	0.796046	+	0.339163i	0.751406	−	0.659840i	$-0.229376\pi$
$997$	25.1354	+	10.7092i	0.796046	+	0.339163i	0.0446393	+	0.999003i	$0.485786\pi$
$998$	5.15394	−	0.837597i	0.163145	−	0.0265137i
$999$	5.18910	+	6.90544i	0.164176	+	0.218478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.127.8	yes	360
169.4	even	78	inner	507.2.t.b.4.8	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.8	✓	360	169.4	even	78	inner
507.2.t.b.127.8	yes	360	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.208145 + 0.00838797i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.95026 + 0.157441i) q^{4} +(-1.53730 + 0.583019i) q^{5} +(0.0659665 + 0.197594i) q^{6} +(-0.815402 + 1.91382i) q^{7} +(0.818208 - 0.0993485i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})\)	\(q+(-0.208145 + 0.00838797i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(-1.95026 + 0.157441i) q^{4} +(-1.53730 + 0.583019i) q^{5} +(0.0659665 + 0.197594i) q^{6} +(-0.815402 + 1.91382i) q^{7} +(0.818208 - 0.0993485i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(0.315091 - 0.134248i) q^{10} +(1.34892 - 2.13314i) q^{11} +(0.693822 + 1.82946i) q^{12} +(1.58449 - 3.23873i) q^{13} +(0.153669 - 0.405192i) q^{14} +(0.987703 + 1.31439i) q^{15} +(3.69306 - 0.600181i) q^{16} +(5.49344 + 2.34054i) q^{17} +(0.171439 - 0.118336i) q^{18} +(-0.388136 - 0.224090i) q^{19} +(2.90633 - 1.37907i) q^{20} +(2.06512 + 0.250750i) q^{21} +(-0.262878 + 0.455318i) q^{22} +(3.86471 + 6.69388i) q^{23} +(-0.323066 - 0.758263i) q^{24} +(-1.71919 + 1.52307i) q^{25} +(-0.302638 + 0.687418i) q^{26} +(0.748511 + 0.663123i) q^{27} +(1.28893 - 3.86082i) q^{28} +(-0.198630 - 4.92895i) q^{29} +(-0.216611 - 0.265300i) q^{30} +(4.74859 - 5.36005i) q^{31} +(-2.37878 + 0.485632i) q^{32} +(-2.42421 - 0.702182i) q^{33} +(-1.16307 - 0.441093i) q^{34} +(0.137720 - 3.41750i) q^{35} +(1.56419 - 1.17542i) q^{36} +(8.46325 + 1.72779i) q^{37} +(0.0826684 + 0.0433877i) q^{38} +(-3.55169 - 0.620861i) q^{39} +(-1.19991 + 0.629759i) q^{40} +(2.43536 - 0.705409i) q^{41} +(-0.431948 - 0.0348704i) q^{42} +(-1.69076 - 8.28190i) q^{43} +(-2.29489 + 4.37256i) q^{44} +(0.987703 - 1.31439i) q^{45} +(-0.860570 - 1.36088i) q^{46} +(1.89522 + 1.30818i) q^{47} +(-1.60396 - 3.38027i) q^{48} +(1.85125 + 1.92736i) q^{49} +(0.345066 - 0.331440i) q^{50} +(0.719756 - 5.92772i) q^{51} +(-2.58026 + 6.56584i) q^{52} +(0.771182 + 6.35126i) q^{53} +(-0.161361 - 0.131747i) q^{54} +(-0.830021 + 4.06571i) q^{55} +(-0.477033 + 1.64691i) q^{56} +(-0.107257 + 0.435157i) q^{57} +(0.0826878 + 1.02427i) q^{58} +(-1.36645 + 8.40813i) q^{59} +(-2.13322 - 2.40790i) q^{60} +(-10.2850 - 7.72868i) q^{61} +(-0.943437 + 1.15550i) q^{62} +(-0.333701 - 2.05334i) q^{63} +(-6.77453 + 1.66977i) q^{64} +(-0.547589 + 5.90268i) q^{65} +(0.510479 + 0.125822i) q^{66} +(0.919668 - 11.3921i) q^{67} +(-11.0821 - 3.69976i) q^{68} +(5.35436 - 5.57448i) q^{69} +0.712492i q^{70} +(10.8092 + 10.3824i) q^{71} +(-0.638443 + 0.521273i) q^{72} +(0.199294 + 0.379723i) q^{73} +(-1.77608 - 0.288641i) q^{74} +(1.94124 + 1.22757i) q^{75} +(0.792247 + 0.375926i) q^{76} +(2.98254 + 4.32095i) q^{77} +(0.744477 + 0.0994379i) q^{78} +(-8.80074 + 12.7501i) q^{79} +(-5.32741 + 3.07578i) q^{80} +(0.428693 - 0.903450i) q^{81} +(-0.500991 + 0.167255i) q^{82} +(2.34971 + 9.53313i) q^{83} +(-4.06699 - 0.163894i) q^{84} +(-9.80961 - 0.395314i) q^{85} +(0.421393 + 1.70966i) q^{86} +(-4.67908 + 1.56211i) q^{87} +(0.891771 - 1.87937i) q^{88} +(14.7538 - 8.51808i) q^{89} +(-0.194561 + 0.281870i) q^{90} +(4.90635 + 5.67330i) q^{91} +(-8.59109 - 12.4463i) q^{92} +(-6.46956 - 3.06985i) q^{93} +(-0.405454 - 0.256394i) q^{94} +(0.727328 + 0.118202i) q^{95} +(1.12828 + 2.14975i) q^{96} +(5.01899 - 4.09788i) q^{97} +(-0.401496 - 0.385642i) q^{98} +2.52386i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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