LMFDB - Embedded newform 289.2.h.a.132.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(4,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([27]))

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

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

chi := DirichletCharacter("289.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.h (of order $68$, degree $32$, 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$24$ over $\Q(\zeta_{68})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{68}]$

Embedding invariants

Embedding label			132.6
Character	$\chi$	$=$	289.132
Dual form			289.2.h.a.208.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54901 - 1.16976i) q^{2} +(0.0205619 + 0.444748i) q^{3} +(0.483774 + 1.70029i) q^{4} +(0.215937 + 0.0953453i) q^{5} +(0.488397 - 0.712972i) q^{6} +(-0.568933 - 0.472436i) q^{7} +(-0.162838 + 0.420332i) q^{8} +(2.78982 - 0.258515i) q^{9} +O(q^{10})$	\(q+(-1.54901 - 1.16976i) q^{2} +(0.0205619 + 0.444748i) q^{3} +(0.483774 + 1.70029i) q^{4} +(0.215937 + 0.0953453i) q^{5} +(0.488397 - 0.712972i) q^{6} +(-0.568933 - 0.472436i) q^{7} +(-0.162838 + 0.420332i) q^{8} +(2.78982 - 0.258515i) q^{9} +(-0.222957 - 0.400285i) q^{10} +(1.33125 + 0.741501i) q^{11} +(-0.746252 + 0.250118i) q^{12} +(-1.70952 - 0.662273i) q^{13} +(0.328647 + 1.39732i) q^{14} +(-0.0379645 + 0.0979977i) q^{15} +(3.74990 - 2.32184i) q^{16} +(3.80255 + 1.59393i) q^{17} +(-4.62387 - 2.86298i) q^{18} +(4.08607 - 3.08566i) q^{19} +(-0.0576501 + 0.413280i) q^{20} +(0.198416 - 0.262746i) q^{21} +(-1.19474 - 2.70583i) q^{22} +(3.39449 + 2.81875i) q^{23} +(-0.190290 - 0.0637788i) q^{24} +(-3.33094 - 3.65387i) q^{25} +(1.87337 + 3.02560i) q^{26} +(0.356869 + 2.55831i) q^{27} +(0.528043 - 1.19590i) q^{28} +(4.33713 - 7.78663i) q^{29} +(0.173441 - 0.107390i) q^{30} +(-1.00950 - 2.28630i) q^{31} +(-7.62694 - 0.706740i) q^{32} +(-0.302408 + 0.607317i) q^{33} +(-4.02567 - 6.91709i) q^{34} +(-0.0778089 - 0.156261i) q^{35} +(1.78919 + 4.61844i) q^{36} +(-0.0591478 + 0.176473i) q^{37} -9.93884 q^{38} +(0.259393 - 0.773924i) q^{39} +(-0.0752392 + 0.0752392i) q^{40} +(2.73674 - 0.126527i) q^{41} +(-0.614699 + 0.174897i) q^{42} +(2.84295 - 4.59153i) q^{43} +(-0.616742 + 2.62223i) q^{44} +(0.627073 + 0.210174i) q^{45} +(-1.96085 - 8.33700i) q^{46} +(-1.11515 + 12.0344i) q^{47} +(1.10974 + 1.62002i) q^{48} +(-1.18576 - 6.34324i) q^{49} +(0.885520 + 9.55628i) q^{50} +(-0.630710 + 1.72395i) q^{51} +(0.299032 - 3.22707i) q^{52} +(4.89173 - 0.453285i) q^{53} +(2.43981 - 4.38030i) q^{54} +(0.216767 + 0.287046i) q^{55} +(0.291224 - 0.162211i) q^{56} +(1.45636 + 1.75382i) q^{57} +(-15.8267 + 6.98819i) q^{58} +(-0.696220 + 3.72445i) q^{59} +(-0.184991 - 0.0171419i) q^{60} +(-6.73735 + 9.83531i) q^{61} +(-1.11069 + 4.72237i) q^{62} +(-1.70936 - 1.17094i) q^{63} +(4.46867 + 4.07373i) q^{64} +(-0.306004 - 0.306004i) q^{65} +(1.17885 - 0.586996i) q^{66} +(6.80481 + 9.01102i) q^{67} +(-0.870572 + 7.23653i) q^{68} +(-1.18383 + 1.56765i) q^{69} +(-0.0622612 + 0.333068i) q^{70} +(-9.67169 + 11.6472i) q^{71} +(-0.345626 + 1.21475i) q^{72} +(6.54718 + 1.53988i) q^{73} +(0.298051 - 0.204170i) q^{74} +(1.55656 - 1.55656i) q^{75} +(7.22324 + 5.45474i) q^{76} +(-0.407080 - 1.05079i) q^{77} +(-1.30711 + 0.895389i) q^{78} +(2.03126 + 0.283349i) q^{79} +(1.03112 - 0.143835i) q^{80} +(7.13175 - 1.33315i) q^{81} +(-4.38725 - 3.00534i) q^{82} +(-3.89156 - 4.26884i) q^{83} +(0.542732 + 0.210256i) q^{84} +(0.669135 + 0.706743i) q^{85} +(-9.77475 + 3.78676i) q^{86} +(3.55227 + 1.76882i) q^{87} +(-0.528454 + 0.438823i) q^{88} +(-6.44647 + 2.49737i) q^{89} +(-0.725491 - 1.05909i) q^{90} +(0.659723 + 1.18443i) q^{91} +(-3.15052 + 7.13525i) q^{92} +(0.996068 - 0.495983i) q^{93} +(15.8048 - 17.3370i) q^{94} +(1.17653 - 0.276718i) q^{95} +(0.157496 - 3.40660i) q^{96} +(4.75929 - 5.73139i) q^{97} +(-5.58331 + 11.2128i) q^{98} +(3.90564 + 1.72451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9}+O(q^{10}) $ 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + 34 q^{10} - 34 q^{11} - 34 q^{12} - 30 q^{13} - 34 q^{14} - 34 q^{15} - 82 q^{16} - 34 q^{17} - 42 q^{18} - 34 q^{19} - 34 q^{20} - 26 q^{21} - 34 q^{22} - 34 q^{23} - 204 q^{24} + 170 q^{25} - 34 q^{26} - 34 q^{27} - 34 q^{28} - 34 q^{29} - 14 q^{30} - 34 q^{31} - 34 q^{32} + 56 q^{33} - 34 q^{34} - 42 q^{35} - 34 q^{36} - 34 q^{37} + 144 q^{38} - 170 q^{39} - 34 q^{40} - 34 q^{41} - 34 q^{42} - 34 q^{43} - 34 q^{44} - 34 q^{45} + 102 q^{46} - 30 q^{47} - 34 q^{48} - 34 q^{49} - 62 q^{50} + 238 q^{51} - 50 q^{52} + 136 q^{54} - 14 q^{55} - 34 q^{56} - 34 q^{57} - 34 q^{58} - 34 q^{59} - 34 q^{60} - 34 q^{61} - 238 q^{62} - 34 q^{63} + 38 q^{64} - 34 q^{65} + 476 q^{66} + 82 q^{67} - 34 q^{68} - 62 q^{69} - 34 q^{70} - 34 q^{71} + 10 q^{72} - 34 q^{73} - 34 q^{74} + 102 q^{75} - 102 q^{76} - 374 q^{77} - 34 q^{78} + 68 q^{79} - 34 q^{80} + 30 q^{81} - 34 q^{82} + 102 q^{83} - 82 q^{84} - 204 q^{85} - 62 q^{86} - 34 q^{87} + 170 q^{88} - 22 q^{89} - 34 q^{90} - 34 q^{91} + 34 q^{92} - 34 q^{93} + 238 q^{94} - 34 q^{95} + 544 q^{96} - 34 q^{97} + 10 q^{98} - 34 q^{99}+O(q^{100}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9 + 34 * q^10 - 34 * q^11 - 34 * q^12 - 30 * q^13 - 34 * q^14 - 34 * q^15 - 82 * q^16 - 34 * q^17 - 42 * q^18 - 34 * q^19 - 34 * q^20 - 26 * q^21 - 34 * q^22 - 34 * q^23 - 204 * q^24 + 170 * q^25 - 34 * q^26 - 34 * q^27 - 34 * q^28 - 34 * q^29 - 14 * q^30 - 34 * q^31 - 34 * q^32 + 56 * q^33 - 34 * q^34 - 42 * q^35 - 34 * q^36 - 34 * q^37 + 144 * q^38 - 170 * q^39 - 34 * q^40 - 34 * q^41 - 34 * q^42 - 34 * q^43 - 34 * q^44 - 34 * q^45 + 102 * q^46 - 30 * q^47 - 34 * q^48 - 34 * q^49 - 62 * q^50 + 238 * q^51 - 50 * q^52 + 136 * q^54 - 14 * q^55 - 34 * q^56 - 34 * q^57 - 34 * q^58 - 34 * q^59 - 34 * q^60 - 34 * q^61 - 238 * q^62 - 34 * q^63 + 38 * q^64 - 34 * q^65 + 476 * q^66 + 82 * q^67 - 34 * q^68 - 62 * q^69 - 34 * q^70 - 34 * q^71 + 10 * q^72 - 34 * q^73 - 34 * q^74 + 102 * q^75 - 102 * q^76 - 374 * q^77 - 34 * q^78 + 68 * q^79 - 34 * q^80 + 30 * q^81 - 34 * q^82 + 102 * q^83 - 82 * q^84 - 204 * q^85 - 62 * q^86 - 34 * q^87 + 170 * q^88 - 22 * q^89 - 34 * q^90 - 34 * q^91 + 34 * q^92 - 34 * q^93 + 238 * q^94 - 34 * q^95 + 544 * q^96 - 34 * q^97 + 10 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{33}{68}\right)$

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 $

$2$	−1.54901	−	1.16976i	−1.09532	−	0.827145i	−0.109336	−	0.994005i	$-0.534872\pi$
$2$	−1.54901	−	1.16976i	−1.09532	−	0.827145i	−0.985981	+	0.166860i	$0.946637\pi$
$3$	0.0205619	+	0.444748i	0.0118714	+	0.256775i	0.996584	+	0.0825871i	$0.0263183\pi$
$3$	0.0205619	+	0.444748i	0.0118714	+	0.256775i	−0.984712	+	0.174188i	$0.944270\pi$
$4$	0.483774	+	1.70029i	0.241887	+	0.850144i
$5$	0.215937	+	0.0953453i	0.0965697	+	0.0426397i	0.451643	−	0.892199i	$-0.350838\pi$
$5$	0.215937	+	0.0953453i	0.0965697	+	0.0426397i	−0.355073	+	0.934839i	$0.615544\pi$
$6$	0.488397	−	0.712972i	0.199387	−	0.291069i
$7$	−0.568933	−	0.472436i	−0.215037	−	0.178564i	0.525059	−	0.851066i	$-0.324043\pi$
$7$	−0.568933	−	0.472436i	−0.215037	−	0.178564i	−0.740095	+	0.672502i	$0.765220\pi$
$8$	−0.162838	+	0.420332i	−0.0575718	+	0.148610i
$9$	2.78982	−	0.258515i	0.929942	−	0.0861718i
$10$	−0.222957	−	0.400285i	−0.0705052	−	0.126581i
$11$	1.33125	+	0.741501i	0.401387	+	0.223571i	0.674284	−	0.738472i	$-0.264452\pi$
$11$	1.33125	+	0.741501i	0.401387	+	0.223571i	−0.272897	+	0.962043i	$0.587982\pi$
$12$	−0.746252	+	0.250118i	−0.215424	+	0.0722030i
$13$	−1.70952	−	0.662273i	−0.474136	−	0.183681i	0.112304	−	0.993674i	$-0.464177\pi$
$13$	−1.70952	−	0.662273i	−0.474136	−	0.183681i	−0.586440	+	0.809993i	$0.699471\pi$
$14$	0.328647	+	1.39732i	0.0878347	+	0.373450i
$15$	−0.0379645	+	0.0979977i	−0.00980240	+	0.0253029i
$16$	3.74990	−	2.32184i	0.937476	−	0.580461i
$17$	3.80255	+	1.59393i	0.922254	+	0.386585i
$17$	3.80255	+	1.59393i	0.922254	+	0.386585i
$18$	−4.62387	−	2.86298i	−1.08986	−	0.674811i
$19$	4.08607	−	3.08566i	0.937409	−	0.707898i	−0.0190339	−	0.999819i	$-0.506059\pi$
$19$	4.08607	−	3.08566i	0.937409	−	0.707898i	0.956443	+	0.291921i	$0.0942943\pi$
$20$	−0.0576501	+	0.413280i	−0.0128910	+	0.0924122i
$21$	0.198416	−	0.262746i	0.0432980	−	0.0573358i
$22$	−1.19474	−	2.70583i	−0.254720	−	0.576886i
$23$	3.39449	+	2.81875i	0.707800	+	0.587749i	0.921141	−	0.389228i	$-0.127258\pi$
$23$	3.39449	+	2.81875i	0.707800	+	0.587749i	−0.213342	+	0.976978i	$0.568435\pi$
$24$	−0.190290	−	0.0637788i	−0.0388428	−	0.0130188i
$25$	−3.33094	−	3.65387i	−0.666188	−	0.730774i
$26$	1.87337	+	3.02560i	0.367398	+	0.593368i
$27$	0.356869	+	2.55831i	0.0686795	+	0.492347i
$28$	0.528043	−	1.19590i	0.0997907	−	0.226004i
$29$	4.33713	−	7.78663i	0.805384	−	1.44594i	−0.0877460	−	0.996143i	$-0.527966\pi$
$29$	4.33713	−	7.78663i	0.805384	−	1.44594i	0.893130	−	0.449799i	$-0.148504\pi$
$30$	0.173441	−	0.107390i	0.0316659	−	0.0196067i
$31$	−1.00950	−	2.28630i	−0.181311	−	0.410631i	0.800800	−	0.598932i	$-0.204408\pi$
$31$	−1.00950	−	2.28630i	−0.181311	−	0.410631i	−0.982111	+	0.188301i	$0.939702\pi$
$32$	−7.62694	−	0.706740i	−1.34827	−	0.124935i
$33$	−0.302408	+	0.607317i	−0.0526424	+	0.105720i
$34$	−4.02567	−	6.91709i	−0.690397	−	1.18627i
$35$	−0.0778089	−	0.156261i	−0.0131521	−	0.0264130i
$36$	1.78919	+	4.61844i	0.298199	+	0.769741i
$37$	−0.0591478	+	0.176473i	−0.00972383	+	0.0290120i	−0.952912	−	0.303248i	$-0.901929\pi$
$37$	−0.0591478	+	0.176473i	−0.00972383	+	0.0290120i	0.943188	+	0.332260i	$0.107811\pi$
$38$	−9.93884			−1.61229
$39$	0.259393	−	0.773924i	0.0415361	−	0.123927i
$40$	−0.0752392	+	0.0752392i	−0.0118964	+	0.0118964i
$41$	2.73674	−	0.126527i	0.427408	−	0.0197602i	0.168590	−	0.985686i	$-0.446079\pi$
$41$	2.73674	−	0.126527i	0.427408	−	0.0197602i	0.258818	+	0.965926i	$0.416667\pi$
$42$	−0.614699	+	0.174897i	−0.0948501	+	0.0269872i
$43$	2.84295	−	4.59153i	0.433546	−	0.700201i	−0.558016	−	0.829830i	$-0.688437\pi$
$43$	2.84295	−	4.59153i	0.433546	−	0.700201i	0.991563	+	0.129629i	$0.0413785\pi$
$44$	−0.616742	+	2.62223i	−0.0929774	+	0.395316i
$45$	0.627073	+	0.210174i	0.0934786	+	0.0313309i
$46$	−1.96085	−	8.33700i	−0.289111	−	1.22922i
$47$	−1.11515	+	12.0344i	−0.162662	+	1.75540i	0.388911	+	0.921275i	$0.372851\pi$
$47$	−1.11515	+	12.0344i	−0.162662	+	1.75540i	−0.551573	+	0.834127i	$0.685972\pi$
$48$	1.10974	+	1.62002i	0.160177	+	0.233830i
$49$	−1.18576	−	6.34324i	−0.169394	−	0.906178i
$50$	0.885520	+	9.55628i	0.125231	+	1.35146i
$51$	−0.630710	+	1.72395i	−0.0883171	+	0.241401i
$52$	0.299032	−	3.22707i	0.0414683	−	0.447514i
$53$	4.89173	−	0.453285i	0.671930	−	0.0622635i	0.249108	−	0.968476i	$-0.419863\pi$
$53$	4.89173	−	0.453285i	0.671930	−	0.0622635i	0.422823	+	0.906212i	$0.361039\pi$
$54$	2.43981	−	4.38030i	0.332017	−	0.596084i
$55$	0.216767	+	0.287046i	0.0292288	+	0.0387052i
$56$	0.291224	−	0.162211i	0.0389164	−	0.0216763i
$57$	1.45636	+	1.75382i	0.192899	+	0.232299i
$58$	−15.8267	+	6.98819i	−2.07815	+	0.917594i
$59$	−0.696220	+	3.72445i	−0.0906402	+	0.484882i	0.907286	+	0.420514i	$0.138150\pi$
$59$	−0.696220	+	3.72445i	−0.0906402	+	0.484882i	−0.997926	+	0.0643680i	$0.979497\pi$
$60$	−0.184991	−	0.0171419i	−0.0238822	−	0.00221301i
$61$	−6.73735	+	9.83531i	−0.862629	+	1.25928i	0.101764	+	0.994809i	$0.467551\pi$
$61$	−6.73735	+	9.83531i	−0.862629	+	1.25928i	−0.964393	+	0.264474i	$0.914802\pi$
$62$	−1.11069	+	4.72237i	−0.141058	+	0.599742i
$63$	−1.70936	−	1.17094i	−0.215359	−	0.147524i
$64$	4.46867	+	4.07373i	0.558584	+	0.509216i
$65$	−0.306004	−	0.306004i	−0.0379551	−	0.0379551i
$66$	1.17885	−	0.586996i	0.145106	−	0.0722542i
$67$	6.80481	+	9.01102i	0.831340	+	1.10087i	0.993469	+	0.114102i	$0.0363992\pi$
$67$	6.80481	+	9.01102i	0.831340	+	1.10087i	−0.162129	+	0.986770i	$0.551836\pi$
$68$	−0.870572	+	7.23653i	−0.105572	+	0.877559i
$69$	−1.18383	+	1.56765i	−0.142517	+	0.188723i
$70$	−0.0622612	+	0.333068i	−0.00744164	+	0.0398093i
$71$	−9.67169	+	11.6472i	−1.14782	+	1.38226i	−0.235958	+	0.971763i	$0.575823\pi$
$71$	−9.67169	+	11.6472i	−1.14782	+	1.38226i	−0.911860	+	0.410502i	$0.865354\pi$
$72$	−0.345626	+	1.21475i	−0.0407324	+	0.143160i
$73$	6.54718	+	1.53988i	0.766289	+	0.180230i	0.593615	−	0.804749i	$-0.297700\pi$
$73$	6.54718	+	1.53988i	0.766289	+	0.180230i	0.172675	+	0.984979i	$0.444759\pi$
$74$	0.298051	−	0.204170i	0.0346478	−	0.0237343i
$75$	1.55656	−	1.55656i	0.179736	−	0.179736i
$76$	7.22324	+	5.45474i	0.828562	+	0.625701i
$77$	−0.407080	−	1.05079i	−0.0463911	−	0.119749i
$78$	−1.30711	+	0.895389i	−0.148001	+	0.101383i
$79$	2.03126	+	0.283349i	0.228535	+	0.0318793i	0.251501	−	0.967857i	$-0.419076\pi$
$79$	2.03126	+	0.283349i	0.228535	+	0.0318793i	−0.0229663	+	0.999736i	$0.507311\pi$
$80$	1.03112	−	0.143835i	0.115283	−	0.0160812i
$81$	7.13175	−	1.33315i	0.792417	−	0.148128i
$82$	−4.38725	−	3.00534i	−0.484491	−	0.331884i
$83$	−3.89156	−	4.26884i	−0.427154	−	0.468566i	0.487312	−	0.873228i	$-0.337977\pi$
$83$	−3.89156	−	4.26884i	−0.427154	−	0.468566i	−0.914466	+	0.404662i	$0.867389\pi$
$84$	0.542732	+	0.210256i	0.0592170	+	0.0229408i
$85$	0.669135	+	0.706743i	0.0725779	+	0.0766571i
$86$	−9.77475	+	3.78676i	−1.05404	+	0.408337i
$87$	3.55227	+	1.76882i	0.380843	+	0.189637i
$88$	−0.528454	+	0.438823i	−0.0563334	+	0.0467786i
$89$	−6.44647	+	2.49737i	−0.683324	+	0.264721i	−0.677781	−	0.735263i	$-0.737058\pi$
$89$	−6.44647	+	2.49737i	−0.683324	+	0.264721i	−0.00554271	+	0.999985i	$0.501764\pi$
$90$	−0.725491	−	1.05909i	−0.0764735	−	0.111637i
$91$	0.659723	+	1.18443i	0.0691577	+	0.124162i
$92$	−3.15052	+	7.13525i	−0.328464	+	0.743901i
$93$	0.996068	−	0.495983i	0.103287	−	0.0514310i
$94$	15.8048	−	17.3370i	1.63014	−	1.78818i
$95$	1.17653	−	0.276718i	0.120710	−	0.0283907i
$96$	0.157496	−	3.40660i	0.0160744	−	0.347684i
$97$	4.75929	−	5.73139i	0.483232	−	0.581935i	−0.470573	−	0.882361i	$-0.655953\pi$
$97$	4.75929	−	5.73139i	0.483232	−	0.581935i	0.953805	+	0.300427i	$0.0971291\pi$
$98$	−5.58331	+	11.2128i	−0.564000	+	1.13266i
$99$	3.90564	+	1.72451i	0.392532	+	0.173320i
$100$	4.60121	−	7.43121i	0.460121	−	0.743121i
$101$	2.98307	−	0.557632i	0.296826	−	0.0554865i	−0.0332298	−	0.999448i	$-0.510579\pi$
$101$	2.98307	−	0.557632i	0.296826	−	0.0554865i	0.330056	+	0.943961i	$0.392932\pi$
$102$	2.99358	−	1.93264i	0.296409	−	0.191360i
$103$	−17.2245	−	3.21981i	−1.69718	−	0.317258i	−0.755849	−	0.654746i	$-0.772775\pi$
$103$	−17.2245	−	3.21981i	−1.69718	−	0.317258i	−0.941330	+	0.337489i	$0.890423\pi$
$104$	0.556749	−	0.610724i	0.0545937	−	0.0598865i
$105$	0.0678969	−	0.0378183i	0.00662606	−	0.00369069i
$106$	−8.10758	−	5.02000i	−0.787477	−	0.487585i
$107$	0.606965	−	4.35119i	0.0586775	−	0.420645i	−0.938482	−	0.345328i	$-0.887768\pi$
$107$	0.606965	−	4.35119i	0.0586775	−	0.420645i	0.997160	−	0.0753175i	$-0.0239970\pi$
$108$	−4.17722	+	1.84443i	−0.401954	+	0.177480i
$109$	−0.193953	+	4.19513i	−0.0185773	+	0.401821i	0.969232	+	0.246150i	$0.0791657\pi$
$109$	−0.193953	+	4.19513i	−0.0185773	+	0.401821i	−0.987809	+	0.155671i	$0.950246\pi$
$110$		−	0.698202i		−	0.0665709i
$111$	−0.0797021	−	0.0226772i	−0.00756499	−	0.00215242i
$112$	−3.23037	−	0.450617i	−0.305241	−	0.0425793i
$113$	−14.1542	+	0.654388i	−1.33151	+	0.0615596i	−0.700189	−	0.713958i	$-0.746901\pi$
$113$	−14.1542	+	0.654388i	−1.33151	+	0.0615596i	−0.631326	+	0.775518i	$0.717489\pi$
$114$	−0.204362	−	4.42028i	−0.0191402	−	0.413997i
$115$	0.464240	+	0.932319i	0.0432906	+	0.0869392i
$116$	15.3377	+	3.60740i	1.42407	+	0.334938i
$117$	−4.94048	−	1.40569i	−0.456747	−	0.129956i
$118$	5.43516	−	4.95480i	0.500347	−	0.456127i
$119$	−1.41036	−	2.70330i	−0.129288	−	0.247811i
$120$	−0.0350095	−	0.0319154i	−0.00319592	−	0.00291347i
$121$	−4.56835	−	7.37814i	−0.415305	−	0.670740i
$122$	21.9412	−	7.35394i	1.98646	−	0.665794i
$123$	0.112545	+	1.21456i	0.0101479	+	0.109513i
$124$	3.39900	−	2.82249i	0.305239	−	0.253467i
$125$	−0.745965	−	2.22566i	−0.0667211	−	0.199069i
$126$	1.27810	+	3.81333i	0.113862	+	0.339718i
$127$	−13.6275	−	6.78569i	−1.20925	−	0.602133i	−0.275926	−	0.961179i	$-0.588984\pi$
$127$	−13.6275	−	6.78569i	−1.20925	−	0.602133i	−0.933320	+	0.359046i	$0.883102\pi$
$128$	0.658166	+	3.52088i	0.0581742	+	0.311204i
$129$	2.10053	+	1.16999i	0.184941	+	0.103012i
$130$	0.116053	+	0.831954i	0.0101785	+	0.0729672i
$131$	−1.79570	−	1.79570i	−0.156891	−	0.156891i	0.624297	−	0.781187i	$-0.285386\pi$
$131$	−1.79570	−	1.79570i	−0.156891	−	0.156891i	−0.781187	+	0.624297i	$0.785386\pi$
$132$	−1.17891	−	0.220377i	−0.102611	−	0.0191813i
$133$	−3.78248	−	0.174874i	−0.327982	−	0.0151635i
$134$		−	21.9182i		−	1.89344i
$135$	−0.166862	+	0.586459i	−0.0143612	+	0.0504743i
$136$	−1.28918	+	1.33878i	−0.110546	+	0.114800i
$137$	−1.83744	−	6.45794i	−0.156983	−	0.551739i	−0.999906	−	0.0137045i	$-0.995638\pi$
$137$	−1.83744	−	6.45794i	−0.156983	−	0.551739i	0.842923	−	0.538035i	$-0.180833\pi$
$138$	3.66754	−	1.04351i	0.312202	−	0.0888291i
$139$	11.2317	−	1.56676i	0.952662	−	0.132891i	0.355202	−	0.934789i	$-0.384412\pi$
$139$	11.2317	−	1.56676i	0.952662	−	0.132891i	0.597460	+	0.801899i	$0.296177\pi$
$140$	0.228047	−	0.207893i	0.0192735	−	0.0175701i
$141$	−5.37521	−	0.248511i	−0.452675	−	0.0209284i
$142$	28.6059	−	6.72805i	2.40056	−	0.564606i
$143$	−1.78473	−	2.14926i	−0.149246	−	0.179730i
$144$	9.86135	−	7.44694i	0.821779	−	0.620579i
$145$	1.67896	−	1.26789i	0.139430	−	0.105293i
$146$	−8.34036	−	10.0439i	−0.690253	−	0.831241i
$147$	2.79676	−	0.657792i	0.230673	−	0.0542538i
$148$	−0.328669	−	0.0151953i	−0.0270164	−	0.00124904i
$149$	7.65541	−	6.97882i	0.627155	−	0.571728i	−0.296461	−	0.955045i	$-0.595807\pi$
$149$	7.65541	−	6.97882i	0.627155	−	0.571728i	0.923617	+	0.383317i	$0.125218\pi$
$150$	−4.23192	+	0.590328i	−0.345535	+	0.0482001i
$151$	−4.95175	+	1.40889i	−0.402967	+	0.114654i	−0.469075	−	0.883158i	$-0.655413\pi$
$151$	−4.95175	+	1.40889i	−0.402967	+	0.114654i	0.0661074	+	0.997813i	$0.478942\pi$
$152$	0.631635	+	2.21997i	0.0512324	+	0.180063i
$153$	11.0205	+	3.46378i	0.890955	+	0.280030i
$154$	−0.598605	+	2.10388i	−0.0482370	+	0.169535i
$155$		−	0.589946i		−	0.0473856i
$156$	1.44138	+	0.0666391i	0.115403	+	0.00533540i
$157$	−7.51669	−	1.40511i	−0.599897	−	0.112140i	−0.124963	−	0.992161i	$-0.539881\pi$
$157$	−7.51669	−	1.40511i	−0.599897	−	0.112140i	−0.474935	+	0.880021i	$0.657528\pi$
$158$	−2.81500	−	2.81500i	−0.223949	−	0.223949i
$159$	0.302181	+	2.16626i	0.0239645	+	0.171796i
$160$	−1.57955	−	0.879804i	−0.124874	−	0.0695546i
$161$	−0.599559	−	3.20736i	−0.0472519	−	0.252775i
$162$	−12.6066	−	6.27736i	−0.990470	−	0.493196i
$163$	6.23929	+	18.6155i	0.488699	+	1.45808i	0.850575	+	0.525854i	$0.176254\pi$
$163$	6.23929	+	18.6155i	0.488699	+	1.45808i	−0.361876	+	0.932226i	$0.617864\pi$
$164$	1.53910	+	4.59204i	0.120183	+	0.358578i
$165$	−0.123206	+	0.102309i	−0.00959155	+	0.00796472i
$166$	1.03456	+	11.1647i	0.0802973	+	0.866546i
$167$	3.25407	−	1.09065i	0.251807	−	0.0843973i	−0.189074	−	0.981963i	$-0.560548\pi$
$167$	3.25407	−	1.09065i	0.251807	−	0.0843973i	0.440881	+	0.897566i	$0.354666\pi$
$168$	0.0781309	+	0.126186i	0.00602793	+	0.00973543i
$169$	−7.12325	−	6.49370i	−0.547943	−	0.499516i
$170$	−0.209778	−	1.87748i	−0.0160893	−	0.143996i
$171$	10.6017	−	9.66475i	0.810734	−	0.739082i
$172$	9.18227	+	2.61258i	0.700141	+	0.199207i
$173$	−9.22970	−	2.17081i	−0.701721	−	0.165043i	−0.137299	−	0.990530i	$-0.543842\pi$
$173$	−9.22970	−	2.17081i	−0.701721	−	0.165043i	−0.564422	+	0.825486i	$0.690901\pi$
$174$	−3.43341	−	6.89521i	−0.260286	−	0.522725i
$175$	0.168864	+	3.65246i	0.0127649	+	0.276100i
$176$	6.71371	−	0.310393i	0.506065	−	0.0233968i
$177$	−1.67076	−	0.233060i	−0.125582	−	0.0175179i
$178$	12.9070	+	3.67235i	0.967419	+	0.275254i
$179$			2.81951i			0.210740i	0.994433	+	0.105370i	$0.0336026\pi$
$179$			2.81951i			0.210740i	−0.994433	+	0.105370i	$0.966397\pi$
$180$	−0.0539945	+	1.16788i	−0.00402451	+	0.0870488i
$181$	18.7111	−	8.26177i	1.39079	−	0.614092i	0.432953	−	0.901417i	$-0.357472\pi$
$181$	18.7111	−	8.26177i	1.39079	−	0.614092i	0.957833	+	0.287324i	$0.0927658\pi$
$182$	0.363579	−	2.60641i	0.0269502	−	0.193200i
$183$	−4.51276	−	2.79419i	−0.333593	−	0.206552i
$184$	−1.73756	+	0.967814i	−0.128095	+	0.0713482i
$185$	−0.0295980	+	0.0324675i	−0.00217609	+	0.00238706i
$186$	−2.12310	−	0.396876i	−0.155673	−	0.0291004i
$187$	3.88024	+	4.94152i	0.283751	+	0.361359i
$188$	−21.0015	+	3.92586i	−1.53169	+	0.286323i
$189$	1.00560	−	1.62411i	0.0731469	−	0.118136i
$190$	−2.14616	−	0.947622i	−0.155699	−	0.0687477i
$191$	−2.01456	+	4.04578i	−0.145768	+	0.292742i	−0.956000	−	0.293368i	$-0.905224\pi$
$191$	−2.01456	+	4.04578i	−0.145768	+	0.292742i	0.810231	+	0.586110i	$0.199342\pi$
$192$	−1.71990	+	2.07119i	−0.124123	+	0.149476i
$193$	0.302862	−	6.55080i	0.0218005	−	0.471537i	−0.959811	−	0.280647i	$-0.909451\pi$
$193$	0.302862	−	6.55080i	0.0218005	−	0.471537i	0.981612	−	0.190890i	$-0.0611372\pi$
$194$	−14.0765	+	3.31077i	−1.01064	+	0.237700i
$195$	0.129802	−	0.142386i	0.00929535	−	0.0101965i
$196$	10.2117	−	5.08482i	0.729407	−	0.363202i
$197$	−8.39191	+	19.0059i	−0.597899	+	1.35411i	0.316227	+	0.948683i	$0.397584\pi$
$197$	−8.39191	+	19.0059i	−0.597899	+	1.35411i	−0.914127	+	0.405429i	$0.867122\pi$
$198$	−4.03262	−	7.23994i	−0.286586	−	0.514520i
$199$	2.19586	+	3.20556i	0.155661	+	0.227236i	0.894967	−	0.446133i	$-0.147199\pi$
$199$	2.19586	+	3.20556i	0.155661	+	0.227236i	−0.739306	+	0.673370i	$0.764846\pi$
$200$	2.07824	−	0.805114i	0.146954	−	0.0569302i
$201$	−3.86771	+	3.21171i	−0.272807	+	0.226536i
$202$	−5.27310	−	2.62569i	−0.371014	−	0.184743i
$203$	−6.14622	+	2.38106i	−0.431380	+	0.167118i
$204$	−3.23633	−	0.238388i	−0.226589	−	0.0166905i
$205$	0.603027	+	0.233614i	0.0421172	+	0.0163163i
$206$	22.9145	+	25.1360i	1.59653	+	1.75131i
$207$	10.1987	+	6.98628i	0.708860	+	0.485580i
$208$	−7.94824	+	1.48578i	−0.551111	+	0.103021i
$209$	7.72759	−	1.07795i	0.534529	−	0.0745636i
$210$	−0.149411	−	0.0208420i	−0.0103104	−	0.00143824i
$211$	−16.2950	+	11.1624i	−1.12180	+	0.768448i	−0.975327	−	0.220767i	$-0.929144\pi$
$211$	−16.2950	+	11.1624i	−1.12180	+	0.768448i	−0.146470	+	0.989215i	$0.546791\pi$
$212$	3.13721	+	8.09806i	0.215464	+	0.556177i
$213$	−5.37892	−	4.06197i	−0.368557	−	0.278322i
$214$	−6.03004	+	6.03004i	−0.412205	+	0.412205i
$215$	1.05168	−	0.720416i	0.0717238	−	0.0491320i
$216$	−1.13345	−	0.266586i	−0.0771217	−	0.0181388i
$217$	−0.505792	+	1.77767i	−0.0343354	+	0.120676i
$218$	5.20773	−	6.27143i	0.352712	−	0.424755i
$219$	−0.550236	+	2.94351i	−0.0371815	+	0.198904i
$220$	−0.383194	+	0.507431i	−0.0258349	+	0.0342110i
$221$	−5.44493	−	5.24319i	−0.366265	−	0.352695i
$222$	0.0969326	+	0.128359i	0.00650569	+	0.00861493i
$223$	−13.4550	+	6.69979i	−0.901013	+	0.448651i	−0.835683	−	0.549213i	$-0.814928\pi$
$223$	−13.4550	+	6.69979i	−0.901013	+	0.448651i	−0.0653303	+	0.997864i	$0.520810\pi$
$224$	4.00533	+	4.00533i	0.267617	+	0.267617i
$225$	−10.2373	−	9.33255i	−0.682488	−	0.622170i
$226$	22.6905	+	15.5433i	1.50935	+	1.03393i
$227$	1.76342	−	7.49760i	0.117042	−	0.497633i	−0.882580	−	0.470162i	$-0.844196\pi$
$227$	1.76342	−	7.49760i	0.117042	−	0.497633i	0.999623	−	0.0274715i	$-0.00874556\pi$
$228$	−2.27746	+	3.32468i	−0.150828	+	0.220182i
$229$	7.56037	+	0.700572i	0.499603	+	0.0462951i	0.339119	−	0.940743i	$-0.389871\pi$
$229$	7.56037	+	0.700572i	0.499603	+	0.0462951i	0.160484	+	0.987038i	$0.448694\pi$
$230$	0.371476	−	1.98722i	0.0244944	−	0.131033i
$231$	0.458968	−	0.202654i	0.0301979	−	0.0133337i
$232$	2.56672	+	3.09099i	0.168514	+	0.202933i
$233$	5.87706	−	3.27350i	0.385019	−	0.214454i	−0.282134	−	0.959375i	$-0.591042\pi$
$233$	5.87706	−	3.27350i	0.385019	−	0.214454i	0.667153	+	0.744921i	$0.267513\pi$
$234$	6.00854	+	7.95659i	0.392791	+	0.520139i
$235$	−1.38823	+	2.49235i	−0.0905581	+	0.162583i
$236$	−6.66945	+	0.618016i	−0.434144	+	0.0402294i
$237$	−0.0842522	+	0.909226i	−0.00547277	+	0.0590606i
$238$	−0.977541	+	5.83723i	−0.0633646	+	0.378372i
$239$	−0.694742	−	7.49746i	−0.0449391	−	0.484970i	−0.988227	−	0.152995i	$-0.951108\pi$
$239$	−0.694742	−	7.49746i	−0.0449391	−	0.484970i	0.943288	−	0.331976i	$-0.107715\pi$
$240$	0.0851720	+	0.455630i	0.00549783	+	0.0294108i
$241$	−1.85222	−	2.70391i	−0.119312	−	0.174174i	0.760732	−	0.649066i	$-0.224840\pi$
$241$	−1.85222	−	2.70391i	−0.119312	−	0.174174i	−0.880044	+	0.474892i	$0.842487\pi$
$242$	−1.55422	+	16.7727i	−0.0999090	+	1.07819i
$243$	2.51375	+	10.6878i	0.161257	+	0.685624i
$244$	−19.9822	−	6.69737i	−1.27923	−	0.428755i
$245$	0.348750	−	1.48279i	0.0222808	−	0.0947322i
$246$	1.24641	−	2.01302i	0.0794680	−	0.128345i
$247$	−9.02877	+	2.56891i	−0.574487	+	0.163456i
$248$	1.12539	−	0.0520299i	0.0714622	−	0.00330390i
$249$	1.81854	−	1.81854i	0.115245	−	0.115245i
$250$	−1.44797	+	4.32017i	−0.0915779	+	0.273231i
$251$	−20.2447			−1.27783			−0.638917	−	0.769275i	$-0.720617\pi$
$251$	−20.2447			−1.27783			−0.638917	+	0.769275i	$0.720617\pi$
$252$	1.16399	−	3.47287i	0.0733243	−	0.218770i
$253$	2.42881	+	6.26947i	0.152698	+	0.394158i
$254$	13.1715	+	26.4520i	0.826455	+	1.65975i
$255$	−0.300564	+	0.312128i	−0.0188220	+	0.0195462i
$256$	8.48969	−	17.0496i	0.530606	−	1.06560i
$257$	−11.9564	−	1.10792i	−0.745818	−	0.0691102i	−0.287356	−	0.957824i	$-0.592776\pi$
$257$	−11.9564	−	1.10792i	−0.745818	−	0.0691102i	−0.458462	+	0.888714i	$0.651600\pi$
$258$	−1.88514	−	4.26943i	−0.117364	−	0.265803i
$259$	0.117023	−	0.0724578i	0.00727147	−	0.00450231i
$260$	0.372258	−	0.668331i	0.0230865	−	0.0414482i
$261$	10.0869	−	22.8446i	0.624361	−	1.41404i
$262$	0.681021	+	4.88208i	0.0420736	+	0.301616i
$263$	−5.43589	−	8.77927i	−0.335191	−	0.541353i	0.638384	−	0.769718i	$-0.279603\pi$
$263$	−5.43589	−	8.77927i	−0.335191	−	0.541353i	−0.973576	+	0.228365i	$0.926662\pi$
$264$	−0.206031	−	0.226006i	−0.0126804	−	0.0139097i
$265$	1.09952	+	0.368522i	0.0675431	+	0.0226381i
$266$	5.65454	+	4.69547i	0.346702	+	0.287898i
$267$	−1.24325	−	2.81570i	−0.0760859	−	0.172318i
$268$	−12.0294	+	15.9294i	−0.734810	+	0.973045i
$269$	−0.872722	+	6.25634i	−0.0532108	+	0.381456i	0.945267	+	0.326298i	$0.105801\pi$
$269$	−0.872722	+	6.25634i	−0.0532108	+	0.381456i	−0.998478	+	0.0551575i	$0.982434\pi$
$270$	0.944486	−	0.713243i	0.0574796	−	0.0434066i
$271$	18.4240	+	11.4076i	1.11918	+	0.692965i	0.955923	−	0.293619i	$-0.0948596\pi$
$271$	18.4240	+	11.4076i	1.11918	+	0.692965i	0.163255	+	0.986584i	$0.447801\pi$
$272$	17.9601	−	2.85183i	1.08899	−	0.172917i
$273$	−0.513207	+	0.317764i	−0.0310607	+	0.0192320i
$274$	−4.70801	+	12.1528i	−0.284422	+	0.734177i
$275$	−1.72497	−	7.33410i	−0.104019	−	0.442263i
$276$	−3.23816	−	1.25447i	−0.194915	−	0.0755103i
$277$	11.6491	−	3.90439i	0.699927	−	0.234592i	0.0546112	−	0.998508i	$-0.482608\pi$
$277$	11.6491	−	3.90439i	0.699927	−	0.234592i	0.645316	+	0.763916i	$0.276726\pi$
$278$	−19.2308	−	10.7115i	−1.15339	−	0.642432i
$279$	−3.40737	−	6.11740i	−0.203994	−	0.366239i
$280$	0.0783518	−	0.00726037i	0.00468242	−	0.000433890i
$281$	4.35488	−	11.2412i	0.259790	−	0.670595i	−0.740208	−	0.672378i	$-0.765273\pi$
$281$	4.35488	−	11.2412i	0.259790	−	0.670595i	0.999998	+	0.00178211i	$0.000567262\pi$
$282$	8.03557	+	6.67265i	0.478511	+	0.397351i
$283$	−12.2477	+	17.8795i	−0.728051	+	1.06282i	0.267023	+	0.963690i	$0.413960\pi$
$283$	−12.2477	+	17.8795i	−0.728051	+	1.06282i	−0.995074	+	0.0991338i	$0.968393\pi$
$284$	−24.4825	−	10.8101i	−1.45277	−	0.641459i
$285$	0.147262	+	0.517571i	0.00872303	+	0.0306583i
$286$	0.250440	+	5.41693i	0.0148088	+	0.320310i
$287$	−1.61680	−	1.22095i	−0.0954367	−	0.0720704i
$288$	−21.4605			−1.26457
$289$	11.9188	+	12.1220i	0.701103	+	0.713060i
$290$	−4.08386			−0.239813
$291$	2.64688	+	1.99883i	0.155163	+	0.117174i
$292$	0.549109	+	11.8770i	0.0321342	+	0.695052i
$293$	2.41017	+	8.47089i	0.140804	+	0.494874i	0.999855	−	0.0170150i	$-0.00541631\pi$
$293$	2.41017	+	8.47089i	0.140804	+	0.494874i	−0.859051	+	0.511889i	$0.828946\pi$
$294$	−5.10167	−	2.25261i	−0.297536	−	0.131375i
$295$	−0.505448	+	0.737863i	−0.0294283	+	0.0429601i
$296$	−0.0645458	−	0.0535981i	−0.00375165	−	0.00311533i
$297$	−1.42191	+	3.67037i	−0.0825075	+	0.212976i
$298$	−20.0219	+	1.85530i	−1.15983	+	0.107475i
$299$	−3.93618	−	7.06679i	−0.227635	−	0.408683i
$300$	3.39962	+	1.89358i	0.196277	+	0.109326i
$301$	−3.78665	+	1.26916i	−0.218259	+	0.0731531i
$302$	9.31838	+	3.60996i	0.536212	+	0.207730i
$303$	0.309343	+	1.31525i	0.0177713	+	0.0755590i
$304$	8.15796	−	21.0581i	0.467891	−	1.20777i
$305$	−2.39259	+	1.48143i	−0.136999	+	0.0848264i
$306$	−13.0191	−	18.2568i	−0.744252	−	1.04367i
$307$	−19.1489	−	11.8565i	−1.09288	−	0.676684i	−0.143136	−	0.989703i	$-0.545719\pi$
$307$	−19.1489	−	11.8565i	−1.09288	−	0.676684i	−0.949747	+	0.313019i	$0.898660\pi$
$308$	1.58972	−	1.20050i	0.0905827	−	0.0684049i
$309$	1.07784	−	7.72675i	0.0613159	−	0.439559i
$310$	−0.690095	+	0.913833i	−0.0391948	+	0.0519022i
$311$	10.3206	+	23.3739i	0.585228	+	1.32541i	0.923222	+	0.384266i	$0.125545\pi$
$311$	10.3206	+	23.3739i	0.585228	+	1.32541i	−0.337995	+	0.941148i	$0.609749\pi$
$312$	0.283066	+	0.235055i	0.0160255	+	0.0133074i
$313$	−14.9820	−	5.02145i	−0.846830	−	0.283829i	−0.139071	−	0.990282i	$-0.544412\pi$
$313$	−14.9820	−	5.02145i	−0.846830	−	0.283829i	−0.707759	+	0.706454i	$0.750294\pi$
$314$	9.99980	+	10.9693i	0.564321	+	0.619031i
$315$	−0.257469	−	0.415827i	−0.0145067	−	0.0234292i
$316$	0.500897	+	3.59081i	0.0281776	+	0.201999i
$317$	11.1635	−	25.2828i	0.627002	−	1.42002i	−0.263327	−	0.964707i	$-0.584820\pi$
$317$	11.1635	−	25.2828i	0.627002	−	1.42002i	0.890329	−	0.455318i	$-0.150474\pi$
$318$	2.06592	−	3.70905i	0.115851	−	0.207993i
$319$	11.5476	−	7.14997i	0.646541	−	0.400321i
$320$	0.576538	+	1.30573i	0.0322295	+	0.0729927i
$321$	1.94766	+	0.180477i	0.108708	+	0.0100733i
$322$	−2.82311	+	5.66957i	−0.157326	+	0.315953i
$323$	20.4558	−	5.22044i	1.13819	−	0.290473i
$324$	5.71690	+	11.4811i	0.317606	+	0.637838i
$325$	3.27446	+	8.45236i	0.181634	+	0.468853i
$326$	12.1109	−	36.1341i	0.670763	−	2.00128i
$327$	−1.86976			−0.103398
$328$	−0.392461	+	1.17094i	−0.0216700	+	0.0646546i
$329$	6.31995	−	6.31995i	0.348430	−	0.348430i
$330$	0.310523	−	0.0143564i	0.0170938	−	0.000790292i
$331$	3.79149	−	1.07877i	0.208399	−	0.0592946i	−0.167853	−	0.985812i	$-0.553683\pi$
$331$	3.79149	−	1.07877i	0.208399	−	0.0592946i	0.376252	+	0.926517i	$0.377213\pi$
$332$	5.37562	−	8.68193i	0.295026	−	0.476483i
$333$	−0.119391	+	0.507619i	−0.00654258	+	0.0278174i
$334$	−6.31639	−	2.11704i	−0.345617	−	0.115839i
$335$	0.610248	+	2.59462i	0.0333414	+	0.141759i
$336$	0.133988	−	1.44596i	0.00730966	−	0.0788838i
$337$	−12.7280	−	18.5806i	−0.693339	−	1.01215i	−0.998213	−	0.0597577i	$-0.980967\pi$
$337$	−12.7280	−	18.5806i	−0.693339	−	1.01215i	0.304874	−	0.952393i	$-0.401386\pi$
$338$	3.43793	+	18.3913i	0.186999	+	1.00036i
$339$	−0.582075	−	6.28159i	−0.0316140	−	0.341169i
$340$	−0.877958	+	1.47963i	−0.0476139	+	0.0802440i
$341$	0.351397	−	3.79218i	0.0190292	−	0.205358i
$342$	−27.7276	+	2.56934i	−1.49934	+	0.138934i
$343$	−4.84111	+	8.69147i	−0.261396	+	0.469295i
$344$	1.46703	+	1.94266i	0.0790968	+	0.104741i
$345$	−0.405101	+	0.225640i	−0.0218099	+	0.0121480i
$346$	11.7576	+	14.1591i	0.632092	+	0.761200i
$347$	32.0996	−	14.1734i	1.72320	−	0.760867i	0.725870	−	0.687832i	$-0.241437\pi$
$347$	32.0996	−	14.1734i	1.72320	−	0.760867i	0.997329	−	0.0730350i	$-0.0232685\pi$
$348$	−1.28901	+	6.89559i	−0.0690981	+	0.369642i
$349$	−18.0225	−	1.67003i	−0.964723	−	0.0893948i	−0.401643	−	0.915797i	$-0.631561\pi$
$349$	−18.0225	−	1.67003i	−0.964723	−	0.0893948i	−0.563081	+	0.826402i	$0.690384\pi$
$350$	4.01093	−	5.85524i	0.214393	−	0.312975i
$351$	1.08422	−	4.60984i	0.0578716	−	0.246055i
$352$	−9.62932	−	6.59623i	−0.513244	−	0.351580i
$353$	−13.7955	−	12.5762i	−0.734259	−	0.669365i	0.217553	−	0.976049i	$-0.430193\pi$
$353$	−13.7955	−	12.5762i	−0.734259	−	0.669365i	−0.951812	+	0.306683i	$0.900781\pi$
$354$	2.31539	+	2.31539i	0.123062	+	0.123062i
$355$	−3.19897	+	1.59290i	−0.169784	+	0.0845423i
$356$	−7.36489	−	9.75269i	−0.390338	−	0.516892i
$357$	1.17329	−	0.682841i	0.0620970	−	0.0361398i
$358$	3.29814	−	4.36745i	0.174312	−	0.230827i
$359$	0.671210	−	3.59066i	0.0354251	−	0.189508i	−0.960683	−	0.277648i	$-0.910445\pi$
$359$	0.671210	−	3.59066i	0.0354251	−	0.189508i	0.996108	+	0.0881401i	$0.0280923\pi$
$360$	−0.190454	+	0.229355i	−0.0100378	+	0.0120881i
$361$	1.97509	−	6.94173i	0.103952	−	0.365354i
$362$	−38.6480	−	9.08993i	−2.03129	−	0.477756i
$363$	3.18748	−	2.18347i	0.167299	−	0.114603i
$364$	−1.69471	+	1.69471i	−0.0888272	+	0.0888272i
$365$	1.26695	+	0.956760i	0.0663154	+	0.0500791i
$366$	3.72180	+	9.60707i	0.194542	+	0.502170i
$367$	14.2120	−	9.73543i	0.741859	−	0.508185i	−0.133864	−	0.991000i	$-0.542738\pi$
$367$	14.2120	−	9.73543i	0.741859	−	0.508185i	0.875723	+	0.482814i	$0.160385\pi$
$368$	19.2737	+	2.68857i	1.00471	+	0.140151i
$369$	7.60233	−	1.06048i	0.395761	−	0.0552063i
$370$	0.0838268	−	0.0156699i	0.00435795	−	0.000814642i
$371$	−2.99721	−	2.05314i	−0.155608	−	0.106594i
$372$	1.32519	+	1.45366i	0.0687077	+	0.0753687i
$373$	−3.28336	−	1.27198i	−0.170006	−	0.0658607i	0.274735	−	0.961520i	$-0.411410\pi$
$373$	−3.28336	−	1.27198i	−0.170006	−	0.0658607i	−0.444741	+	0.895659i	$0.646704\pi$
$374$	−0.230150	−	12.1934i	−0.0119008	−	0.630506i
$375$	0.974517	−	0.377530i	0.0503238	−	0.0194956i
$376$	−4.87687	−	2.42839i	−0.251505	−	0.125235i
$377$	−12.5713	+	10.4391i	−0.647454	+	0.537639i
$378$	−3.45750	+	1.33944i	−0.177835	+	0.0688936i
$379$	18.6518	+	27.2283i	0.958078	+	1.39862i	0.916743	+	0.399476i	$0.130808\pi$
$379$	18.6518	+	27.2283i	0.958078	+	1.39862i	0.0413347	+	0.999145i	$0.486839\pi$
$380$	1.03968	+	1.86658i	0.0533343	+	0.0957535i
$381$	2.73771	−	6.20033i	0.140257	−	0.317652i
$382$	7.85316	−	3.91041i	0.401803	−	0.200074i
$383$	−0.923858	+	1.01342i	−0.0472069	+	0.0517835i	−0.762159	−	0.647390i	$-0.775860\pi$
$383$	−0.923858	+	1.01342i	−0.0472069	+	0.0517835i	0.714952	+	0.699174i	$0.246449\pi$
$384$	−1.55237	+	0.365114i	−0.0792189	+	0.0186321i
$385$	0.0122849	−	0.265718i	0.000626096	−	0.0135422i
$386$	−8.13199	+	9.79298i	−0.413907	+	0.498450i
$387$	6.74436	−	13.5445i	0.342835	−	0.688506i
$388$	12.0474	+	5.31946i	0.611616	+	0.270055i
$389$	−13.9752	+	22.5708i	−0.708573	+	1.14438i	0.274573	+	0.961566i	$0.411463\pi$
$389$	−13.9752	+	22.5708i	−0.708573	+	1.14438i	−0.983147	+	0.182819i	$0.941478\pi$
$390$	−0.367623	+	0.0687207i	−0.0186153	+	0.00347981i
$391$	8.41481	+	16.1290i	0.425555	+	0.815679i
$392$	2.85935	+	0.534506i	0.144419	+	0.0269966i
$393$	0.761708	−	0.835554i	0.0384231	−	0.0421481i
$394$	35.2315	−	19.6238i	1.77494	−	0.988632i
$395$	0.411608	+	0.254857i	0.0207102	+	0.0128232i
$396$	−1.04272	+	7.47499i	−0.0523985	+	0.375632i
$397$	−8.74611	+	3.86178i	−0.438954	+	0.193817i	−0.611601	−	0.791167i	$-0.709474\pi$
$397$	−8.74611	+	3.86178i	−0.438954	+	0.193817i	0.172646	+	0.984984i	$0.444768\pi$
$398$	0.348322	−	7.53408i	0.0174598	−	0.377650i
$399$		−	1.68584i		−	0.0843977i
$400$	−20.9744	−	5.96774i	−1.04872	−	0.298387i
$401$	−19.5225	−	2.72327i	−0.974906	−	0.135994i	−0.367188	−	0.930147i	$-0.619680\pi$
$401$	−19.5225	−	2.72327i	−0.974906	−	0.135994i	−0.607718	+	0.794153i	$0.707915\pi$
$402$	9.74805	−	0.450680i	0.486189	−	0.0224779i
$403$	0.211609	+	4.57704i	0.0105410	+	0.227999i
$404$	2.39127	+	4.80231i	0.118970	+	0.238924i
$405$	1.66711	+	0.392102i	0.0828396	+	0.0194837i
$406$	12.3058	+	3.50131i	0.610728	+	0.173767i
$407$	−0.209595	+	0.191071i	−0.0103893	+	0.00947106i
$408$	−0.621928	−	0.545831i	−0.0307900	−	0.0270227i
$409$	26.4363	+	24.0999i	1.30719	+	1.19166i	0.968001	+	0.250947i	$0.0807420\pi$
$409$	26.4363	+	24.0999i	1.30719	+	1.19166i	0.339192	+	0.940717i	$0.389846\pi$
$410$	−0.660823	−	1.06727i	−0.0326357	−	0.0527085i
$411$	2.83437	−	0.949986i	0.139809	−	0.0468593i
$412$	−2.85814	−	30.8442i	−0.140810	−	1.51959i
$413$	2.15567	−	1.79004i	0.106073	−	0.0880823i
$414$	−7.62566	−	22.7519i	−0.374781	−	1.11819i
$415$	−0.433316	−	1.29284i	−0.0212707	−	0.0634630i
$416$	12.5704	+	6.25931i	0.616314	+	0.306888i
$417$	0.927758	+	4.96307i	0.0454325	+	0.243042i
$418$	−13.2311	−	7.36966i	−0.647153	−	0.360462i
$419$	3.80660	+	27.2886i	0.185965	+	1.33314i	0.825512	+	0.564385i	$0.190886\pi$
$419$	3.80660	+	27.2886i	0.185965	+	1.33314i	−0.639547	+	0.768752i	$0.720878\pi$
$420$	0.0971489	+	0.0971489i	0.00474038	+	0.00474038i
$421$	−27.1517	−	5.07554i	−1.32329	−	0.247367i	−0.525756	−	0.850635i	$-0.676218\pi$
$421$	−27.1517	−	5.07554i	−1.32329	−	0.247367i	−0.797538	+	0.603269i	$0.793865\pi$
$422$	38.2985	+	1.77064i	1.86434	+	0.0861936i
$423$			33.8622i			1.64644i
$424$	−0.606026	+	2.12996i	−0.0294312	+	0.103440i
$425$	−6.84205	−	19.2033i	−0.331888	−	0.931497i
$426$	3.58048	+	12.5841i	0.173475	+	0.609701i
$427$	8.47966	−	2.41267i	0.410359	−	0.116757i
$428$	7.69191	−	1.07298i	0.371803	−	0.0518643i
$429$	0.919182	−	0.837945i	0.0443785	−	0.0404564i
$430$	−2.47177	−	0.114277i	−0.119200	−	0.00551093i
$431$	−22.1242	+	5.20356i	−1.06568	+	0.250647i	−0.724447	−	0.689330i	$-0.757905\pi$
$431$	−22.1242	+	5.20356i	−1.06568	+	0.250647i	−0.341238	+	0.939977i	$0.610846\pi$
$432$	7.27822	+	8.76483i	0.350174	+	0.421698i
$433$	−13.1034	+	9.89525i	−0.629710	+	0.475535i	−0.868602	−	0.495511i	$-0.834981\pi$
$433$	−13.1034	+	9.89525i	−0.629710	+	0.475535i	0.238891	+	0.971046i	$0.423216\pi$
$434$	2.86293	−	2.16198i	0.137425	−	0.103778i
$435$	0.598415	+	0.720644i	0.0286918	+	0.0345522i
$436$	−7.22677	+	1.69972i	−0.346099	+	0.0814019i
$437$	22.5678	+	1.04337i	1.07956	+	0.0499113i
$438$	4.29551	−	3.91588i	0.205248	−	0.187108i
$439$	7.21136	−	1.00594i	0.344179	−	0.0480110i	0.0360348	−	0.999351i	$-0.488527\pi$
$439$	7.21136	−	1.00594i	0.344179	−	0.0480110i	0.308144	+	0.951340i	$0.400292\pi$
$440$	−0.155952	+	0.0443722i	−0.00743473	+	0.00211536i
$441$	−4.94788	−	17.3900i	−0.235613	−	0.828095i
$442$	2.30099	+	14.4910i	0.109447	+	0.689267i
$443$	−2.86262	+	10.0611i	−0.136007	+	0.478016i	−0.999660	−	0.0260712i	$-0.991700\pi$
$443$	−2.86262	+	10.0611i	−0.136007	+	0.478016i	0.863653	+	0.504087i	$0.168171\pi$
$444$		−	0.146487i		−	0.00695198i
$445$	−1.63014	−	0.0753659i	−0.0772761	−	0.00357269i
$446$	28.6791	+	5.36105i	1.35799	+	0.253853i
$447$	3.26123	+	3.26123i	0.154251	+	0.154251i
$448$	−0.617797	−	4.42884i	−0.0291882	−	0.209243i
$449$	21.4786	+	11.9635i	1.01364	+	0.564593i	0.903169	−	0.429286i	$-0.141235\pi$
$449$	21.4786	+	11.9635i	1.01364	+	0.564593i	0.110471	+	0.993879i	$0.464764\pi$
$450$	4.94089	+	26.4314i	0.232916	+	1.24599i
$451$	3.73711	+	1.86086i	0.175974	+	0.0876244i
$452$	−7.96008	−	23.7496i	−0.374411	−	1.11709i
$453$	−0.728419	−	2.17331i	−0.0342241	−	0.102111i
$454$	−11.5019	+	9.55109i	−0.539813	+	0.448255i
$455$	0.0295285	+	0.318663i	0.00138432	+	0.0149391i
$456$	−0.974337	+	0.326565i	−0.0456275	+	0.0152928i
$457$	2.05933	+	3.32593i	0.0963312	+	0.155580i	0.894817	−	0.446434i	$-0.147306\pi$
$457$	2.05933	+	3.32593i	0.0963312	+	0.155580i	−0.798485	+	0.602014i	$0.794365\pi$
$458$	−10.8916	−	9.92901i	−0.508931	−	0.463952i
$459$	−2.72076	+	10.2969i	−0.126994	+	0.480620i
$460$	−1.36062	+	1.24037i	−0.0634394	+	0.0578327i
$461$	15.7674	+	4.48620i	0.734359	+	0.208943i	0.620117	−	0.784510i	$-0.287085\pi$
$461$	15.7674	+	4.48620i	0.734359	+	0.208943i	0.114243	+	0.993453i	$0.463556\pi$
$462$	−0.948003	−	0.222968i	−0.0441051	−	0.0103734i
$463$	−2.69644	−	5.41518i	−0.125314	−	0.251665i	0.823618	−	0.567145i	$-0.191952\pi$
$463$	−2.69644	−	5.41518i	−0.125314	−	0.251665i	−0.948932	+	0.315480i	$0.897834\pi$
$464$	−1.81553	−	39.2693i	−0.0842837	−	1.82303i
$465$	0.262377	−	0.0121304i	0.0121674	−	0.000562535i
$466$	−12.9328	−	1.80405i	−0.599102	−	0.0835712i
$467$	9.02620	+	2.56817i	0.417683	+	0.118841i	0.475975	−	0.879459i	$-0.342095\pi$
$467$	9.02620	+	2.56817i	0.417683	+	0.118841i	−0.0582928	+	0.998300i	$0.518566\pi$
$468$		−	9.08027i		−	0.419736i
$469$	0.385651	−	8.34151i	0.0178077	−	0.385175i
$470$	5.06583	−	2.23678i	0.233669	−	0.103175i
$471$	0.470363	−	3.37192i	0.0216732	−	0.155370i
$472$	−1.45213	−	0.899124i	−0.0668399	−	0.0413855i
$473$	7.18930	−	4.00442i	0.330564	−	0.184123i
$474$	1.19408	−	1.30985i	0.0548460	−	0.0601632i
$475$	−24.8850	−	4.65182i	−1.14180	−	0.213440i
$476$	3.91410	−	3.70581i	0.179402	−	0.169856i
$477$	13.5299	−	2.52917i	0.619491	−	0.115803i
$478$	−7.69406	+	12.4263i	−0.351918	+	0.568367i
$479$	−37.3619	−	16.4969i	−1.70711	−	0.753762i	−0.998857	−	0.0478013i	$-0.984779\pi$
$479$	−37.3619	−	16.4969i	−1.70711	−	0.753762i	−0.708251	−	0.705961i	$-0.750516\pi$
$480$	0.358812	−	0.720592i	0.0163775	−	0.0328904i
$481$	0.217988	−	0.262513i	0.00993938	−	0.0119695i
$482$	−0.293811	+	6.35504i	−0.0133827	+	0.289464i
$483$	1.41414	−	0.332602i	0.0643454	−	0.0151339i
$484$	10.3349	−	11.3369i	0.469769	−	0.515312i
$485$	1.57417	−	0.783841i	0.0714792	−	0.0355924i
$486$	8.60835	−	19.4961i	0.390483	−	0.884359i
$487$	−5.98625	−	10.7474i	−0.271263	−	0.487010i	0.703369	−	0.710825i	$-0.251678\pi$
$487$	−5.98625	−	10.7474i	−0.271263	−	0.487010i	−0.974632	+	0.223815i	$0.928149\pi$
$488$	−3.03700	−	4.43348i	−0.137479	−	0.200694i
$489$	−8.15092	+	3.15768i	−0.368597	+	0.142795i
$490$	−2.27473	+	1.88891i	−0.102762	+	0.0853323i
$491$	−7.49396	−	3.73155i	−0.338198	−	0.168402i	0.268614	−	0.963248i	$-0.413434\pi$
$491$	−7.49396	−	3.73155i	−0.338198	−	0.168402i	−0.606812	+	0.794845i	$0.707552\pi$
$492$	−2.01065	+	0.778931i	−0.0906472	+	0.0351169i
$493$	28.9035	−	22.6960i	1.30175	−	1.02217i
$494$	16.9907	+	6.58222i	0.764447	+	0.296148i
$495$	0.678947	+	0.744769i	0.0305164	+	0.0334749i
$496$	−9.09395	−	6.22950i	−0.408330	−	0.279713i
$497$	11.0051	−	2.05721i	0.493646	−	0.0922784i
$498$	−4.94419	+	0.689685i	−0.221554	+	0.0309055i
$499$	2.71454	+	0.378661i	0.121519	+	0.0169512i	0.198656	−	0.980069i	$-0.436342\pi$
$499$	2.71454	+	0.378661i	0.121519	+	0.0169512i	−0.0771365	+	0.997021i	$0.524578\pi$
$500$	3.42338	−	2.34507i	0.153098	−	0.104875i
$501$	0.551975	+	1.42481i	0.0246604	+	0.0636559i
$502$	31.3593	+	23.6814i	1.39963	+	1.05695i
$503$	−4.17689	+	4.17689i	−0.186238	+	0.186238i	−0.794068	−	0.607829i	$-0.792041\pi$
$503$	−4.17689	+	4.17689i	−0.186238	+	0.186238i	0.607829	+	0.794068i	$0.292041\pi$
$504$	0.770529	−	0.527825i	0.0343221	−	0.0235112i
$505$	0.697321	+	0.164008i	0.0310304	+	0.00729828i
$506$	3.57152	−	12.5526i	0.158774	−	0.558031i
$507$	2.74159	−	3.30157i	0.121758	−	0.146628i
$508$	4.94500	−	26.4534i	0.219399	−	1.17368i
$509$	−22.4840	+	29.7736i	−0.996586	+	1.31969i	−0.0494791	+	0.998775i	$0.515756\pi$
$509$	−22.4840	+	29.7736i	−0.996586	+	1.31969i	−0.947107	+	0.320918i	$0.896009\pi$
$510$	0.830691	−	0.131903i	0.0367836	−	0.00584077i
$511$	−2.99741	−	3.96921i	−0.132598	−	0.175588i
$512$	−26.6818	+	13.2860i	−1.17918	+	0.587163i
$513$	9.35226	+	9.35226i	0.412913	+	0.412913i
$514$	17.2246	+	15.7023i	0.759743	+	0.692597i
$515$	−3.41240	−	2.33755i	−0.150368	−	0.103005i
$516$	−0.973134	+	4.13751i	−0.0428398	+	0.182144i
$517$	−10.4081	+	15.1939i	−0.457747	+	0.668229i
$518$	−0.266029	−	0.0246512i	−0.0116886	−	0.00108311i
$519$	0.775681	−	4.14952i	0.0340486	−	0.182144i
$520$	0.178452	−	0.0787943i	0.00782564	−	0.00345536i
$521$	16.3772	+	19.7224i	0.717500	+	0.864053i	0.995325	−	0.0965789i	$-0.0307900\pi$
$521$	16.3772	+	19.7224i	0.717500	+	0.864053i	−0.277825	+	0.960632i	$0.589614\pi$
$522$	−42.3473	+	23.5873i	−1.85349	+	1.03239i
$523$	−4.48881	−	5.94414i	−0.196282	−	0.259919i	0.689223	−	0.724549i	$-0.257952\pi$
$523$	−4.48881	−	5.94414i	−0.196282	−	0.259919i	−0.885505	+	0.464630i	$0.846187\pi$
$524$	2.18449	−	3.92191i	0.0954299	−	0.171329i
$525$	−1.62095	+	0.150203i	−0.0707441	+	0.00655541i
$526$	−1.84937	+	19.9579i	−0.0806363	+	0.870204i
$527$	−0.194466	−	10.3028i	−0.00847105	−	0.448798i
$528$	0.276093	+	2.97952i	0.0120154	+	0.129667i
$529$	−0.649025	−	3.47198i	−0.0282185	−	0.150955i
$530$	−1.27209	−	1.85702i	−0.0552560	−	0.0806638i
$531$	−0.979505	+	10.5705i	−0.0425069	+	0.458723i
$532$	−1.53253	−	6.51590i	−0.0664434	−	0.282500i
$533$	−4.76232	−	1.59617i	−0.206279	−	0.0691378i
$534$	−1.36788	+	5.81586i	−0.0591938	+	0.251677i
$535$	0.545931	−	0.881710i	0.0236027	−	0.0381196i
$536$	−4.89570	+	1.39295i	−0.211462	+	0.0601661i
$537$	−1.25397	+	0.0579745i	−0.0541127	+	0.00250178i
$538$	8.67027	−	8.67027i	0.373802	−	0.373802i
$539$	3.12498	−	9.32368i	0.134603	−	0.401599i
$540$	−1.07787			−0.0463842
$541$	11.4144	−	34.0559i	0.490742	−	1.46418i	−0.357170	−	0.934039i	$-0.616258\pi$
$541$	11.4144	−	34.0559i	0.490742	−	1.46418i	0.847912	−	0.530137i	$-0.177859\pi$
$542$	−15.1948	−	39.2222i	−0.652671	−	1.68474i
$543$	4.05914	+	8.15185i	0.174194	+	0.349829i
$544$	−27.8753	−	14.8442i	−1.19514	−	0.636442i
$545$	−0.441868	+	0.887390i	−0.0189275	+	0.0380116i
$546$	1.16667	+	0.108108i	0.0499289	+	0.00462659i
$547$	−13.7656	−	31.1762i	−0.588576	−	1.33300i	−0.920888	−	0.389828i	$-0.872534\pi$
$547$	−13.7656	−	31.1762i	−0.588576	−	1.33300i	0.332312	−	0.943170i	$-0.392171\pi$
$548$	10.0915	−	6.24836i	0.431086	−	0.266917i
$549$	−16.2534	+	29.1805i	−0.693680	+	1.24539i
$550$	−5.90714	+	13.3784i	−0.251881	+	0.570457i
$551$	−6.30508	−	45.1996i	−0.268605	−	1.92557i
$552$	−0.466161	−	0.752875i	−0.0198411	−	0.0320445i
$553$	−1.02179	−	1.12085i	−0.0434509	−	0.0476633i
$554$	−22.6118	−	7.57871i	−0.960683	−	0.321989i
$555$	−0.0150484	−	0.0124961i	−0.000638770	−	0.000530428i
$556$	8.09756	+	18.3392i	0.343413	+	0.777756i
$557$	3.29005	−	4.35674i	0.139404	−	0.184601i	−0.722959	−	0.690891i	$-0.757219\pi$
$557$	3.29005	−	4.35674i	0.139404	−	0.184601i	0.862363	+	0.506290i	$0.168983\pi$
$558$	−1.87783	+	13.4617i	−0.0794949	+	0.569880i
$559$	−7.90094	+	5.96651i	−0.334174	+	0.252357i
$560$	−0.654590	−	0.405305i	−0.0276615	−	0.0171273i
$561$	−2.11794	+	1.82733i	−0.0894196	+	0.0771501i
$562$	−19.8953	+	12.3186i	−0.839232	+	0.519630i
$563$	16.9023	−	43.6298i	0.712346	−	1.83878i	0.200512	−	0.979691i	$-0.435739\pi$
$563$	16.9023	−	43.6298i	0.712346	−	1.83878i	0.511833	−	0.859085i	$-0.328967\pi$
$564$	−2.17785	−	9.25964i	−0.0917039	−	0.389901i
$565$	−3.11880	−	1.20823i	−0.131209	−	0.0508306i
$566$	39.8865	−	13.3686i	1.67656	−	0.561925i
$567$	−4.68732	−	2.61082i	−0.196849	−	0.109644i
$568$	−3.32077	−	5.96192i	−0.139336	−	0.250156i
$569$	−32.3837	+	3.00079i	−1.35760	+	0.125800i	−0.746304	−	0.665605i	$-0.768174\pi$
$569$	−32.3837	+	3.00079i	−1.35760	+	0.125800i	−0.611292	+	0.791405i	$0.709350\pi$
$570$	0.377323	−	0.973984i	0.0158043	−	0.0407957i
$571$	17.4044	+	14.4525i	0.728353	+	0.604816i	0.926915	−	0.375272i	$-0.122451\pi$
$571$	17.4044	+	14.4525i	0.728353	+	0.604816i	−0.198562	+	0.980088i	$0.563627\pi$
$572$	2.79096	−	4.07431i	0.116696	−	0.170355i
$573$	−1.84077	−	0.812781i	−0.0768994	−	0.0339544i
$574$	1.07622	+	3.78253i	0.0449207	+	0.157880i
$575$	−1.00751	−	21.7921i	−0.0420160	−	0.908793i
$576$	13.5199	+	10.2098i	0.563330	+	0.425407i
$577$	37.1998			1.54865			0.774325	−	0.632788i	$-0.218090\pi$
$577$	37.1998			1.54865			0.774325	+	0.632788i	$0.218090\pi$
$578$	−4.28245	−	32.7192i	−0.178127	−	1.36094i
$579$	2.91968			0.121338
$580$	2.96802	+	2.24135i	0.123240	+	0.0930669i
$581$	0.197284	+	4.26720i	0.00818474	+	0.177033i
$582$	−1.76190	−	6.19243i	−0.0730330	−	0.256684i
$583$	6.84822	+	3.02379i	0.283624	+	0.125232i
$584$	−1.71339	+	2.50124i	−0.0709005	+	0.103502i
$585$	−0.932804	−	0.774590i	−0.0385667	−	0.0320254i
$586$	6.17551	−	15.9408i	0.255108	−	0.658509i
$587$	−5.24273	+	0.485811i	−0.216391	+	0.0200516i	−0.199917	−	0.979813i	$-0.564067\pi$
$587$	−5.24273	+	0.485811i	−0.216391	+	0.0200516i	−0.0164733	+	0.999864i	$0.505244\pi$
$588$	2.47144	+	4.43708i	0.101920	+	0.182982i
$589$	−11.1796	−	6.22700i	−0.460648	−	0.256579i
$590$	1.64607	−	0.551706i	0.0677675	−	0.0227134i
$591$	−8.62537	−	3.34149i	−0.354800	−	0.137450i
$592$	0.187944	+	0.799088i	0.00772445	+	0.0328423i
$593$	−16.7617	+	43.2669i	−0.688320	+	1.77676i	−0.0608095	+	0.998149i	$0.519368\pi$
$593$	−16.7617	+	43.2669i	−0.688320	+	1.77676i	−0.627510	+	0.778608i	$0.715926\pi$
$594$	6.49600	−	4.02215i	0.266534	−	0.165031i
$595$	−0.0468021	−	0.718213i	−0.00191870	−	0.0294439i
$596$	15.5695	+	9.64023i	0.637752	+	0.394879i
$597$	−1.38052	+	1.04252i	−0.0565007	+	0.0426674i
$598$	−2.16926	+	15.5509i	−0.0887076	+	0.635924i
$599$	5.21876	−	6.91076i	0.213233	−	0.282366i	−0.678813	−	0.734311i	$-0.737505\pi$
$599$	5.21876	−	6.91076i	0.213233	−	0.282366i	0.892045	+	0.451946i	$0.149270\pi$
$600$	0.400805	+	0.907737i	0.0163628	+	0.0370582i
$601$	2.89865	+	2.40701i	0.118238	+	0.0981838i	0.696077	−	0.717967i	$-0.254927\pi$
$601$	2.89865	+	2.40701i	0.118238	+	0.0981838i	−0.577839	+	0.816151i	$0.696104\pi$
$602$	7.35018	+	2.46353i	0.299571	+	0.100406i
$603$	21.3137	+	23.3800i	0.867962	+	0.952109i
$604$	−4.79105	−	7.73781i	−0.194945	−	0.314847i
$605$	−0.283003	−	2.02878i	−0.0115057	−	0.0824817i
$606$	1.05935	−	2.39919i	0.0430330	−	0.0974604i
$607$	−15.3972	+	27.6433i	−0.624954	+	1.12201i	0.357217	+	0.934021i	$0.383726\pi$
$607$	−15.3972	+	27.6433i	−0.624954	+	1.12201i	−0.982172	+	0.187987i	$0.939804\pi$
$608$	−33.3450	+	20.6463i	−1.35232	+	0.837320i
$609$	−1.18535	−	2.68456i	−0.0480327	−	0.108784i
$610$	5.43906	+	0.504003i	0.220221	+	0.0204065i
$611$	9.87646	−	19.8346i	0.399559	−	0.802422i
$612$	−0.557988	+	20.4137i	−0.0225553	+	0.825176i
$613$	−6.82043	−	13.6973i	−0.275475	−	0.553228i	0.713616	−	0.700537i	$-0.247056\pi$
$613$	−6.82043	−	13.6973i	−0.275475	−	0.553228i	−0.989090	+	0.147310i	$0.952939\pi$
$614$	15.7926	+	40.7653i	0.637337	+	1.64516i
$615$	−0.0914998	+	0.272998i	−0.00368963	+	0.0110083i
$616$	0.507971			0.0204667
$617$	−12.0880	+	36.0658i	−0.486646	+	1.45195i	0.366566	+	0.930392i	$0.380533\pi$
$617$	−12.0880	+	36.0658i	−0.486646	+	1.45195i	−0.853213	+	0.521563i	$0.825349\pi$
$618$	−10.7080	+	10.7080i	−0.430740	+	0.430740i
$619$	26.2508	−	1.21365i	1.05511	−	0.0487806i	0.488337	−	0.872655i	$-0.337604\pi$
$619$	26.2508	−	1.21365i	1.05511	−	0.0487806i	0.566772	+	0.823875i	$0.308192\pi$
$620$	1.00308	−	0.285401i	0.0402846	−	0.0114620i
$621$	−5.99985	+	9.69008i	−0.240766	+	0.388850i
$622$	11.3551	−	48.2791i	0.455300	−	1.93582i
$623$	4.84746	+	1.62470i	0.194209	+	0.0650924i
$624$	−0.824230	−	3.50441i	−0.0329956	−	0.140289i
$625$	−2.22988	+	24.0642i	−0.0891951	+	0.962569i
$626$	17.3333	+	25.3036i	0.692780	+	1.01133i
$627$	0.638311	+	3.41466i	0.0254917	+	0.136369i
$628$	−1.24728	−	13.4603i	−0.0497719	−	0.537125i
$629$	−0.506198	+	0.576769i	−0.0201834	+	0.0229973i
$630$	−0.0875947	+	0.945297i	−0.00348986	+	0.0376615i
$631$	−18.1312	+	1.68011i	−0.721793	+	0.0668839i	−0.446891	−	0.894588i	$-0.647469\pi$
$631$	−18.1312	+	1.68011i	−0.721793	+	0.0668839i	−0.274902	+	0.961472i	$0.588645\pi$
$632$	−0.449867	+	0.807665i	−0.0178947	+	0.0321272i
$633$	−5.29949	−	7.01766i	−0.210636	−	0.278927i
$634$	−46.8671	+	26.1048i	−1.86133	+	1.03675i
$635$	−2.29569	−	2.76460i	−0.0911017	−	0.109710i
$636$	−3.53709	+	1.56178i	−0.140255	+	0.0619285i
$637$	−2.17388	+	11.6292i	−0.0861321	+	0.460766i
$638$	−26.2511	−	2.43252i	−1.03929	−	0.0963045i
$639$	−23.9713	+	34.9938i	−0.948292	+	1.38434i
$640$	−0.193577	+	0.823039i	−0.00765180	+	0.0325335i
$641$	13.0425	+	8.93433i	0.515148	+	0.352885i	0.794461	−	0.607315i	$-0.207754\pi$
$641$	13.0425	+	8.93433i	0.515148	+	0.352885i	−0.279312	+	0.960200i	$0.590106\pi$
$642$	−2.80583	−	2.55786i	−0.110737	−	0.100951i
$643$	8.12653	+	8.12653i	0.320479	+	0.320479i	0.848951	−	0.528472i	$-0.177235\pi$
$643$	8.12653	+	8.12653i	0.320479	+	0.320479i	−0.528472	+	0.848951i	$0.677235\pi$
$644$	5.16338	−	2.57106i	0.203466	−	0.101314i
$645$	0.342028	+	0.452918i	0.0134673	+	0.0178336i
$646$	−37.7929	−	15.8418i	−1.48694	−	0.623289i
$647$	−16.4217	+	21.7458i	−0.645602	+	0.854915i	−0.996679	−	0.0814313i	$-0.974051\pi$
$647$	−16.4217	+	21.7458i	−0.645602	+	0.854915i	0.351077	+	0.936347i	$0.385816\pi$
$648$	−0.600948	+	3.21479i	−0.0236075	+	0.126289i
$649$	−3.68853	+	4.44192i	−0.144787	+	0.174361i
$650$	4.81505	−	16.9231i	0.188862	−	0.663780i
$651$	−0.801016	−	0.188397i	−0.0313943	−	0.00738387i
$652$	−28.6333	+	19.6143i	−1.12137	+	0.768155i
$653$	35.8185	−	35.8185i	1.40169	−	1.40169i	0.606940	−	0.794747i	$-0.292397\pi$
$653$	35.8185	−	35.8185i	1.40169	−	1.40169i	0.794747	−	0.606940i	$-0.207603\pi$
$654$	2.89629	+	2.18717i	0.113254	+	0.0855253i
$655$	−0.216545	−	0.558967i	−0.00846112	−	0.0218407i
$656$	9.96875	−	6.82875i	0.389214	−	0.266618i
$657$	18.6636	+	2.60346i	0.728135	+	0.101571i
$658$	−17.1825	+	2.39685i	−0.669843	+	0.0934391i
$659$	7.21137	−	1.34804i	0.280915	−	0.0525121i	−0.0414065	−	0.999142i	$-0.513184\pi$
$659$	7.21137	−	1.34804i	0.280915	−	0.0525121i	0.322321	+	0.946630i	$0.395537\pi$
$660$	−0.233558	−	0.159991i	−0.00909123	−	0.00622764i
$661$	7.36987	+	8.08436i	0.286655	+	0.314445i	0.865418	−	0.501050i	$-0.167053\pi$
$661$	7.36987	+	8.08436i	0.286655	+	0.314445i	−0.578764	+	0.815495i	$0.696465\pi$
$662$	−7.13496	−	2.76410i	−0.277308	−	0.107430i
$663$	2.21994	−	2.52943i	0.0862152	−	0.0982348i
$664$	2.42802	−	0.940621i	0.0942255	−	0.0365032i
$665$	−0.800101	−	0.398403i	−0.0310266	−	0.0154494i
$666$	0.778730	−	0.646649i	0.0301752	−	0.0250571i
$667$	36.6709	−	14.2064i	1.41990	−	0.550073i
$668$	3.42866	+	5.00522i	0.132659	+	0.193658i
$669$	−3.25638	−	5.84632i	−0.125899	−	0.226032i
$670$	2.08979	−	4.73293i	0.0807358	−	0.182849i
$671$	−16.2620	+	8.09750i	−0.627787	+	0.312601i
$672$	−1.69900	+	1.86372i	−0.0655405	+	0.0718945i
$673$	2.87731	−	0.676738i	0.110912	−	0.0260863i	−0.173123	−	0.984900i	$-0.555386\pi$
$673$	2.87731	−	0.676738i	0.110912	−	0.0260863i	0.284035	+	0.958814i	$0.408327\pi$
$674$	−2.01900	+	43.6703i	−0.0777689	+	1.68212i
$675$	8.15902	−	9.82554i	0.314041	−	0.378185i
$676$	7.59513	−	15.2531i	0.292120	−	0.586656i
$677$	28.8195	+	12.7251i	1.10762	+	0.489064i	0.875303	−	0.483575i	$-0.160662\pi$
$677$	28.8195	+	12.7251i	1.10762	+	0.489064i	0.232322	+	0.972639i	$0.425368\pi$
$678$	−6.44630	+	10.4111i	−0.247569	+	0.399837i
$679$	−5.41543	+	1.01232i	−0.207825	+	0.0388493i
$680$	−0.406027	+	0.166175i	−0.0155704	+	0.00637251i
$681$	3.37080	+	0.630111i	0.129169	+	0.0241459i
$682$	−4.98025	+	5.46308i	−0.190704	+	0.209192i
$683$	−18.3718	+	10.2330i	−0.702976	+	0.391555i	−0.796971	−	0.604018i	$-0.793566\pi$
$683$	−18.3718	+	10.2330i	−0.702976	+	0.391555i	0.0939949	+	0.995573i	$0.470036\pi$
$684$	21.5617	+	13.3504i	0.824433	+	0.510467i
$685$	0.218963	−	1.56970i	0.00836616	−	0.0599750i
$686$	17.6659	−	7.80024i	0.674486	−	0.297815i
$687$	−0.156122	+	3.37686i	−0.00595642	+	0.128835i
$688$		−	23.8187i		−	0.908079i
$689$	−8.66272	−	2.46476i	−0.330023	−	0.0938997i
$690$	0.891450	+	0.124352i	0.0339369	+	0.00473400i
$691$	22.8438	−	1.05613i	0.869021	−	0.0401773i	0.392925	−	0.919571i	$-0.371463\pi$
$691$	22.8438	−	1.05613i	0.869021	−	0.0401773i	0.476096	+	0.879393i	$0.342051\pi$
$692$	−0.774091	−	16.7433i	−0.0294265	−	0.636486i
$693$	−1.40733	−	2.82630i	−0.0534600	−	0.107362i
$694$	−66.3022	−	15.5941i	−2.51680	−	0.591945i
$695$	2.57472	+	0.732572i	0.0976648	+	0.0277880i
$696$	−1.32193	+	1.20510i	−0.0501077	+	0.0456792i
$697$	10.6083	+	3.88106i	0.401817	+	0.147006i
$698$	25.9636	+	23.6689i	0.982735	+	0.895881i
$699$	1.57672	+	2.54650i	0.0596372	+	0.0963174i
$700$	−6.12855	+	2.05408i	−0.231637	+	0.0776370i
$701$	2.80161	+	30.2341i	0.105815	+	1.14193i	0.868681	+	0.495371i	$0.164968\pi$
$701$	2.80161	+	30.2341i	0.105815	+	1.14193i	−0.762866	+	0.646556i	$0.776208\pi$
$702$	−7.07187	+	5.87241i	−0.266911	+	0.221640i
$703$	0.302853	+	0.903590i	0.0114223	+	0.0340796i
$704$	2.92824	+	8.73668i	0.110362	+	0.329276i
$705$	−1.13701	−	0.566164i	−0.0428223	−	0.0213230i
$706$	6.65818	+	35.6181i	0.250584	+	1.34051i
$707$	−1.96061	−	1.09205i	−0.0737364	−	0.0410709i
$708$	−0.411998	−	2.95351i	−0.0154838	−	0.111000i
$709$	18.4366	+	18.4366i	0.692401	+	0.692401i	0.962760	−	0.270359i	$-0.0871424\pi$
$709$	18.4366	+	18.4366i	0.692401	+	0.692401i	−0.270359	+	0.962760i	$0.587142\pi$
$710$	6.81855	+	1.27461i	0.255896	+	0.0478352i
$711$	5.74012	+	0.265382i	0.215271	+	0.00995259i
$712$		−	3.11632i		−	0.116789i
$713$	3.01776	−	10.6063i	0.113016	−	0.397210i
$714$	−2.61620	−	0.314734i	−0.0979086	−	0.0117786i
$715$	−0.180465	−	0.634270i	−0.00674902	−	0.0237203i
$716$	−4.79397	+	1.36400i	−0.179159	+	0.0509752i
$717$	3.32019	−	0.463147i	0.123995	−	0.0172965i
$718$	−5.23991	+	4.77681i	−0.195552	+	0.178269i
$719$	−28.1511	−	1.30150i	−1.04986	−	0.0485379i	−0.485637	−	0.874161i	$-0.661412\pi$
$719$	−28.1511	−	1.30150i	−1.04986	−	0.0485379i	−0.564223	+	0.825623i	$0.690824\pi$
$720$	2.83946	−	0.667834i	0.105820	−	0.0248887i
$721$	8.27842	+	9.96932i	0.308304	+	0.371277i
$722$	−11.1796	+	8.44243i	−0.416061	+	0.314195i
$723$	1.16447	−	0.879369i	0.0433072	−	0.0327041i
$724$	23.0993	+	27.8175i	0.858480	+	1.03383i
$725$	−42.8980	+	10.0895i	−1.59319	+	0.374716i
$726$	−7.49158	−	0.346356i	−0.278038	−	0.0128545i
$727$	−1.20181	+	1.09559i	−0.0445726	+	0.0406333i	−0.695676	−	0.718356i	$-0.744895\pi$
$727$	−1.20181	+	1.09559i	−0.0445726	+	0.0406333i	0.651103	+	0.758989i	$0.274307\pi$
$728$	−0.605281	+	0.0844331i	−0.0224332	+	0.00312930i
$729$	16.2333	−	4.61876i	0.601232	−	0.171065i
$730$	−0.843349	−	2.96406i	−0.0312137	−	0.109705i
$731$	18.1291	−	12.9280i	0.670527	−	0.478161i
$732$	2.56776	−	9.02476i	0.0949073	−	0.333565i
$733$		−	13.5095i		−	0.498985i	−0.968377	−	0.249492i	$-0.919736\pi$
$733$		−	13.5095i		−	0.498985i	0.968377	−	0.249492i	$-0.0802638\pi$
$734$	−33.4026	−	1.54430i	−1.23291	−	0.0570010i
$735$	0.666640	+	0.124617i	0.0245894	+	0.00459655i
$736$	−23.8974	−	23.8974i	−0.880872	−	0.880872i
$737$	2.37721	+	17.0417i	0.0875658	+	0.627739i
$738$	−13.0166	−	7.25019i	−0.479147	−	0.266883i
$739$	0.334559	+	1.78973i	0.0123069	+	0.0658363i	0.988575	−	0.150728i	$-0.0481619\pi$
$739$	0.334559	+	1.78973i	0.0123069	+	0.0658363i	−0.976268	+	0.216565i	$0.930515\pi$
$740$	−0.0695229	−	0.0346183i	−0.00255571	−	0.00127259i
$741$	−1.32816	−	3.96270i	−0.0487913	−	0.145574i
$742$	2.24104	+	6.68635i	0.0822712	+	0.245464i
$743$	34.2724	−	28.4594i	1.25733	−	1.04407i	0.260423	−	0.965495i	$-0.416138\pi$
$743$	34.2724	−	28.4594i	1.25733	−	1.04407i	0.996908	−	0.0785799i	$-0.0250386\pi$
$744$	0.0462803	+	0.499444i	0.00169672	+	0.0183105i
$745$	2.31848	−	0.777076i	0.0849425	−	0.0284699i
$746$	3.59805	+	5.81105i	0.131734	+	0.212758i
$747$	−11.9603	−	10.9033i	−0.437606	−	0.398930i
$748$	−6.52485	+	8.98810i	−0.238572	+	0.328638i
$749$	−2.40098	+	2.18878i	−0.0877300	+	0.0799764i
$750$	−1.95116	−	0.555152i	−0.0712462	−	0.0202713i
$751$	−40.2450	−	9.46554i	−1.46856	−	0.345403i	−0.583972	−	0.811774i	$-0.698502\pi$
$751$	−40.2450	−	9.46554i	−1.46856	−	0.345403i	−0.884589	+	0.466371i	$0.845561\pi$
$752$	23.7603	+	47.7172i	0.866450	+	1.74007i
$753$	−0.416270	−	9.00379i	−0.0151697	−	0.328116i
$754$	31.6843	−	1.46485i	1.15387	−	0.0533468i
$755$	−1.20359	−	0.167894i	−0.0438033	−	0.00611030i
$756$	3.24793	+	0.924117i	0.118126	+	0.0336098i
$757$		−	20.1852i		−	0.733643i	−0.930291	−	0.366822i	$-0.880446\pi$
$757$		−	20.1852i		−	0.733643i	0.930291	−	0.366822i	$-0.119554\pi$
$758$	2.95867	−	63.9950i	0.107464	−	2.32440i
$759$	−2.73839	+	1.20912i	−0.0993973	+	0.0438882i
$760$	−0.0752703	+	0.539595i	−0.00273034	+	0.0195732i
$761$	−29.0622	−	17.9945i	−1.05350	−	0.652301i	−0.113524	−	0.993535i	$-0.536214\pi$
$761$	−29.0622	−	17.9945i	−1.05350	−	0.652301i	−0.939978	+	0.341234i	$0.889155\pi$
$762$	−11.4936	+	6.40191i	−0.416370	+	0.231917i
$763$	2.09228	−	2.29512i	0.0757456	−	0.0830890i
$764$	−7.85358	−	1.46809i	−0.284133	−	0.0531136i
$765$	2.04947	+	1.79871i	0.0740989	+	0.0650325i
$766$	2.61653	−	0.489114i	0.0945390	−	0.0176724i
$767$	3.65681	−	5.90594i	0.132040	−	0.213251i
$768$	7.75733	+	3.42520i	0.279919	+	0.123596i
$769$	−2.75098	+	5.52471i	−0.0992029	+	0.199226i	−0.939205	−	0.343357i	$-0.888436\pi$
$769$	−2.75098	+	5.52471i	−0.0992029	+	0.199226i	0.840002	+	0.542583i	$0.182554\pi$
$770$	−0.329856	+	0.397230i	−0.0118872	+	0.0143152i
$771$	0.246899	−	5.34035i	0.00889186	−	0.192328i
$772$	11.2848	−	2.65415i	0.406147	−	0.0955250i
$773$	−30.8244	+	33.8127i	−1.10868	+	1.21616i	−0.134370	+	0.990931i	$0.542901\pi$
$773$	−30.8244	+	33.8127i	−1.10868	+	1.21616i	−0.974306	+	0.225228i	$0.927687\pi$
$774$	−26.2909	+	13.0913i	−0.945007	+	0.470558i
$775$	−4.99125	+	11.3041i	−0.179291	+	0.406055i
$776$	1.63410	+	2.93377i	0.0586607	+	0.105316i
$777$	0.0346316	+	0.0505560i	0.00124240	+	0.00181368i
$778$	48.0502	−	18.6148i	1.72268	−	0.667371i
$779$	10.7921	−	8.96165i	0.386667	−	0.321084i
$780$	0.304893	+	0.151819i	0.0109169	+	0.00543598i
$781$	−21.5118	+	8.33372i	−0.769753	+	0.298204i
$782$	5.83241	−	34.8273i	0.208567	−	1.24542i
$783$	21.4684	+	8.31691i	0.767219	+	0.297222i
$784$	−19.1745	−	21.0334i	−0.684803	−	0.751193i
$785$	−1.48916	−	1.02010i	−0.0531503	−	0.0364088i
$786$	−2.15729	+	0.403268i	−0.0769480	+	0.0143841i
$787$	38.5716	−	5.38051i	1.37493	−	0.191794i	0.588012	−	0.808852i	$-0.299911\pi$
$787$	38.5716	−	5.38051i	1.37493	−	0.191794i	0.786918	+	0.617058i	$0.211676\pi$
$788$	−36.3753	−	5.07413i	−1.29581	−	0.180758i
$789$	3.79279	−	2.59812i	0.135027	−	0.0924955i
$790$	−0.339464	−	0.876258i	−0.0120776	−	0.0311759i
$791$	8.36195	+	6.31465i	0.297317	+	0.224523i
$792$	−1.36085	+	1.36085i	−0.0483558	+	0.0483558i
$793$	18.0313	−	12.3517i	0.640310	−	0.438623i
$794$	18.0652	+	4.24889i	0.641109	+	0.150787i
$795$	−0.141291	+	0.496587i	−0.00501108	+	0.0176121i
$796$	−4.38808	+	5.28437i	−0.155531	+	0.187299i
$797$	1.57992	−	8.45181i	0.0559636	−	0.299379i	−0.943527	−	0.331296i	$-0.892514\pi$
$797$	1.57992	−	8.45181i	0.0559636	−	0.299379i	0.999491	+	0.0319172i	$0.0101613\pi$
$798$	−1.97203	+	2.61139i	−0.0698091	+	0.0924422i
$799$	−23.4225	+	43.9840i	−0.828629	+	1.55604i
$800$	22.8226	+	30.2220i	0.806899	+	1.06851i
$801$	−17.3389	+	8.63375i	−0.612640	+	0.305058i
$802$	27.0550	+	27.0550i	0.955344	+	0.955344i
$803$	7.57410	+	6.90471i	0.267284	+	0.243662i
$804$	−7.33193	−	5.02249i	−0.258577	−	0.177129i
$805$	0.176340	−	0.749751i	0.00621516	−	0.0264252i
$806$	5.02625	−	7.33742i	0.177042	−	0.258450i
$807$	−2.80044	−	0.259499i	−0.0985801	−	0.00913479i
$808$	−0.251365	+	1.34468i	−0.00884298	+	0.0473058i
$809$	50.7557	−	22.4108i	1.78448	−	0.787923i	0.803096	−	0.595850i	$-0.203185\pi$
$809$	50.7557	−	22.4108i	1.78448	−	0.787923i	0.981381	−	0.192074i	$-0.0615213\pi$
$810$	−2.12372	−	2.55749i	−0.0746197	−	0.0898611i
$811$	4.66146	−	2.59642i	0.163686	−	0.0911726i	−0.402621	−	0.915367i	$-0.631901\pi$
$811$	4.66146	−	2.59642i	0.163686	−	0.0911726i	0.566308	+	0.824194i	$0.308371\pi$
$812$	−7.02187	−	9.29845i	−0.246419	−	0.326312i
$813$	−4.69469	+	8.42859i	−0.164650	+	0.295603i
$814$	0.548173	−	0.0507957i	0.0192134	−	0.00178039i
$815$	−0.427611	+	4.61466i	−0.0149786	+	0.161644i
$816$	1.63764	+	7.92905i	0.0573287	+	0.277572i
$817$	−2.55137	−	27.5337i	−0.0892612	−	0.963281i
$818$	−12.7591	−	68.2552i	−0.446112	−	2.38649i
$819$	2.14670	+	3.13380i	0.0750119	+	0.109504i
$820$	−0.105482	+	1.13834i	−0.00368360	+	0.0397524i
$821$	−10.4350	−	44.3670i	−0.364185	−	1.54842i	−0.772162	−	0.635426i	$-0.780824\pi$
$821$	−10.4350	−	44.3670i	−0.364185	−	1.54842i	0.407977	−	0.912992i	$-0.366234\pi$
$822$	−5.50173	−	1.84399i	−0.191895	−	0.0643167i
$823$	7.03135	−	29.8955i	0.245098	−	1.04209i	−0.699700	−	0.714437i	$-0.746683\pi$
$823$	7.03135	−	29.8955i	0.245098	−	1.04209i	0.944798	−	0.327654i	$-0.106258\pi$
$824$	4.15818	−	6.71569i	0.144857	−	0.233952i
$825$	3.22636	−	0.917978i	0.112327	−	0.0319599i
$826$	−5.43307	+	0.251186i	−0.189041	+	0.00873988i
$827$	−13.7830	+	13.7830i	−0.479283	+	0.479283i	−0.904902	−	0.425619i	$-0.860056\pi$
$827$	−13.7830	+	13.7830i	−0.479283	+	0.479283i	0.425619	+	0.904902i	$0.360056\pi$
$828$	−6.94483	+	20.7205i	−0.241349	+	0.720089i
$829$	12.8877			0.447607			0.223804	−	0.974634i	$-0.428153\pi$
$829$	12.8877			0.447607			0.223804	+	0.974634i	$0.428153\pi$
$830$	−0.841100	+	2.50950i	−0.0291950	+	0.0871060i
$831$	1.97600	+	5.10063i	0.0685465	+	0.176939i
$832$	−4.94137	−	9.92361i	−0.171311	−	0.344039i
$833$	5.60180	−	26.0105i	0.194091	−	0.901211i
$834$	4.36848	−	8.77310i	0.151268	−	0.303788i
$835$	0.806660	+	0.0747481i	0.0279156	+	0.00258676i
$836$	5.57124	+	12.6177i	0.192685	+	0.436391i
$837$	5.48880	−	3.39852i	0.189721	−	0.117470i
$838$	26.0246	−	46.7232i	0.899006	−	1.61403i
$839$	−13.3379	+	30.2074i	−0.460474	+	1.04287i	0.521395	+	0.853315i	$0.325412\pi$
$839$	−13.3379	+	30.2074i	−0.460474	+	1.04287i	−0.981869	+	0.189559i	$0.939294\pi$
$840$	0.00484009	+	0.0346975i	0.000166999	+	0.00119718i
$841$	−26.5545	−	42.8869i	−0.915671	−	1.47886i
$842$	36.1212	+	39.6230i	1.24482	+	1.36550i
$843$	5.08905	+	1.70568i	0.175276	+	0.0587467i
$844$	−26.8623	−	22.3062i	−0.924640	−	0.767811i
$845$	−0.919026	−	2.08140i	−0.0316155	−	0.0716022i
$846$	39.6107	−	52.4530i	1.36184	−	1.80337i
$847$	−0.886614	+	6.35592i	−0.0304644	+	0.218392i
$848$	17.2911	−	13.0576i	0.593777	−	0.448400i
$849$	−8.20369	−	5.07951i	−0.281550	−	0.174328i
$850$	−11.8648	+	37.7497i	−0.406960	+	1.29480i
$851$	−0.698209	+	0.432313i	−0.0239343	+	0.0148195i
$852$	4.30434	−	11.1108i	0.147464	−	0.380649i
$853$	10.4780	+	44.5497i	0.358760	+	1.52535i	0.784281	+	0.620406i	$0.213032\pi$
$853$	10.4780	+	44.5497i	0.358760	+	1.52535i	−0.425521	+	0.904949i	$0.639909\pi$
$854$	−15.9573	−	6.18190i	−0.546048	−	0.211540i
$855$	3.21079	−	1.07615i	0.109807	−	0.0368035i
$856$	1.73011	+	0.963664i	0.0591339	+	0.0329374i
$857$	4.20964	+	7.55776i	0.143799	+	0.258168i	0.935933	−	0.352179i	$-0.114559\pi$
$857$	4.20964	+	7.55776i	0.143799	+	0.258168i	−0.792134	+	0.610347i	$0.791030\pi$
$858$	−2.40402	+	0.222765i	−0.0820718	+	0.00760507i
$859$	11.3020	−	29.1739i	0.385620	−	0.995401i	−0.595732	−	0.803183i	$-0.703138\pi$
$859$	11.3020	−	29.1739i	0.385620	−	0.995401i	0.981352	−	0.192218i	$-0.0615680\pi$
$860$	1.73369	+	1.43964i	0.0591183	+	0.0490912i
$861$	0.509770	−	0.744173i	0.0173729	−	0.0253613i
$862$	40.3575	+	17.8196i	1.37458	+	0.606938i
$863$	−0.596932	−	2.09800i	−0.0203198	−	0.0714167i	0.951003	−	0.309183i	$-0.100055\pi$
$863$	−0.596932	−	2.09800i	−0.0203198	−	0.0714167i	−0.971322	+	0.237766i	$0.923585\pi$
$864$	−0.913759	−	19.7643i	−0.0310867	−	0.672396i
$865$	−1.78605	−	1.34877i	−0.0607277	−	0.0458594i
$866$	31.8724			1.08307
$867$	−5.14616	+	5.55009i	−0.174773	+	0.188491i
$868$	−3.26725			−0.110898
$869$	2.49401	+	1.88339i	0.0846037	+	0.0638897i
$870$	−0.0839721	−	1.81629i	−0.00284692	−	0.0615779i
$871$	−5.66522	−	19.9112i	−0.191959	−	0.674665i
$872$	−1.73177	−	0.764650i	−0.0586450	−	0.0258943i
$873$	11.7959	−	17.2199i	0.399232	−	0.582806i
$874$	−33.7373	−	28.0151i	−1.14118	−	0.947624i
$875$	−0.627076	+	1.61867i	−0.0211990	+	0.0547210i
$876$	−5.27100	+	0.488430i	−0.178091	+	0.0165025i
$877$	9.91189	+	17.7953i	0.334701	+	0.600903i	0.987683	−	0.156470i	$-0.0500116\pi$
$877$	9.91189	+	17.7953i	0.334701	+	0.600903i	−0.652982	+	0.757374i	$0.726482\pi$
$878$	−12.3472	−	6.87734i	−0.416697	−	0.232099i
$879$	−3.71785	+	1.24610i	−0.125400	+	0.0420298i
$880$	1.47933	+	0.573095i	0.0498682	+	0.0193190i
$881$	4.78830	+	20.3586i	0.161322	+	0.685899i	0.991686	+	0.128678i	$0.0410735\pi$
$881$	4.78830	+	20.3586i	0.161322	+	0.685899i	−0.830364	+	0.557221i	$0.811868\pi$
$882$	−12.6778	+	32.7251i	−0.426883	+	1.10191i
$883$	36.8160	−	22.7955i	1.23896	−	0.767129i	0.258910	−	0.965902i	$-0.416637\pi$
$883$	36.8160	−	22.7955i	1.23896	−	0.767129i	0.980046	+	0.198773i	$0.0636956\pi$
$884$	6.28082	−	11.7945i	0.211247	−	0.396691i
$885$	−0.338556	−	0.209625i	−0.0113804	−	0.00704647i
$886$	16.2033	−	12.2361i	0.544359	−	0.411081i
$887$	−1.73168	+	12.4140i	−0.0581442	+	0.416822i	0.939162	+	0.343474i	$0.111604\pi$
$887$	−1.73168	+	12.4140i	−0.0581442	+	0.416822i	−0.997306	+	0.0733482i	$0.976632\pi$
$888$	0.0225104	−	0.0298086i	0.000755401	−	0.00100031i
$889$	4.54733	+	10.2987i	0.152513	+	0.345408i
$890$	2.43695	+	2.02361i	0.0816866	+	0.0678317i
$891$	10.4827	+	3.51344i	0.351183	+	0.117705i
$892$	−17.9008	−	19.6362i	−0.599361	−	0.657468i
$893$	32.5775	+	52.6145i	1.09017	+	1.76068i
$894$	−1.23683	−	8.86652i	−0.0413657	−	0.296541i
$895$	−0.268827	+	0.608834i	−0.00898588	+	0.0203511i
$896$	1.28894	−	2.31408i	0.0430603	−	0.0773081i
$897$	3.06200	−	1.89591i	0.102237	−	0.0633026i
$898$	−19.2762	−	43.6564i	−0.643255	−	1.45683i
$899$	−22.1809	−	2.05536i	−0.739774	−	0.0685502i
$900$	10.9155	−	21.9212i	0.363849	−	0.730708i
$901$	19.3235	+	6.07344i	0.643760	+	0.202336i
$902$	−3.61207	−	7.25401i	−0.120269	−	0.241532i
$903$	−0.642316	−	1.65801i	−0.0213749	−	0.0551751i
$904$	2.02977	−	6.05602i	0.0675093	−	0.201420i
$905$	4.82813			0.160493
$906$	−1.41392	+	4.21855i	−0.0469742	+	0.140152i
$907$	17.8902	−	17.8902i	0.594034	−	0.594034i	−0.344684	−	0.938719i	$-0.612014\pi$
$907$	17.8902	−	17.8902i	0.594034	−	0.594034i	0.938719	+	0.344684i	$0.112014\pi$
$908$	13.6012	−	0.628820i	0.451371	−	0.0208681i
$909$	8.17808	−	2.32687i	0.271250	−	0.0771773i
$910$	0.327019	−	0.528154i	0.0108406	−	0.0175081i
$911$	10.8605	−	46.1758i	0.359823	−	1.52987i	−0.422130	−	0.906535i	$-0.638717\pi$
$911$	10.8605	−	46.1758i	0.359823	−	1.52987i	0.781953	−	0.623338i	$-0.214224\pi$
$912$	9.53330	+	3.19524i	0.315679	+	0.105805i
$913$	−2.01529	−	8.56849i	−0.0666963	−	0.283575i
$914$	0.700612	−	7.56081i	0.0231742	−	0.250089i
$915$	−0.708058	−	1.03364i	−0.0234077	−	0.0341710i
$916$	2.46634	+	13.1937i	0.0814900	+	0.435933i
$917$	0.173279	+	1.86998i	0.00572219	+	0.0617522i
$918$	16.2594	−	12.7674i	0.536641	−	0.421388i
$919$	4.35844	−	47.0350i	0.143772	−	1.55154i	−0.552346	−	0.833615i	$-0.686267\pi$
$919$	4.35844	−	47.0350i	0.143772	−	1.55154i	0.696118	−	0.717928i	$-0.254909\pi$
$920$	−0.467479	+	0.0433183i	−0.0154123	+	0.00142816i
$921$	4.87940	−	8.76020i	0.160782	−	0.288658i
$922$	−19.1760	−	25.3932i	−0.631529	−	0.836280i
$923$	24.2476	−	13.5058i	0.798119	−	0.444549i
$924$	0.566607	+	0.682339i	0.0186400	+	0.0224473i
$925$	0.841826	−	0.371703i	0.0276791	−	0.0122215i
$926$	−2.15764	+	11.5424i	−0.0709045	+	0.379306i
$927$	−48.8856	−	4.52992i	−1.60562	−	0.148782i
$928$	−38.5821	+	56.3230i	−1.26652	+	1.84889i
$929$	1.66128	−	7.06334i	0.0545049	−	0.231741i	−0.939265	−	0.343193i	$-0.888491\pi$
$929$	1.66128	−	7.06334i	0.0545049	−	0.231741i	0.993770	+	0.111453i	$0.0355503\pi$
$930$	−0.420615	−	0.288128i	−0.0137925	−	0.00944808i
$931$	−24.4182	−	22.2601i	−0.800273	−	0.729545i
$932$	8.40906	+	8.40906i	0.275448	+	0.275448i
$933$	−10.1833	+	5.07068i	−0.333386	+	0.166006i
$934$	−10.9775	−	14.5366i	−0.359196	−	0.475652i
$935$	0.366735	+	1.43702i	0.0119935	+	0.0469955i
$936$	1.39535	−	1.84774i	0.0456084	−	0.0603953i
$937$	−1.86557	+	9.97992i	−0.0609455	+	0.326030i	−0.999835	−	0.0181902i	$-0.994210\pi$
$937$	−1.86557	+	9.97992i	−0.0609455	+	0.326030i	0.938889	+	0.344220i	$0.111857\pi$
$938$	−10.3549	+	12.4700i	−0.338101	+	0.407159i
$939$	1.92522	−	6.76644i	0.0628271	−	0.220814i
$940$	−4.90930	−	1.15466i	−0.160124	−	0.0376608i
$941$	7.35850	−	5.04069i	0.239880	−	0.164322i	−0.439192	−	0.898393i	$-0.644735\pi$
$941$	7.35850	−	5.04069i	0.239880	−	0.164322i	0.679072	+	0.734071i	$0.262382\pi$
$942$	−4.67294	+	4.67294i	−0.152252	+	0.152252i
$943$	9.64649	+	7.28469i	0.314133	+	0.237222i
$944$	6.03683	+	15.5828i	0.196482	+	0.507178i
$945$	0.371998	−	0.254824i	0.0121011	−	0.00828943i
$946$	−15.8205	−	2.20687i	−0.514369	−	0.0717514i
$947$	−21.9868	+	3.06702i	−0.714474	+	0.0996649i	−0.486093	−	0.873907i	$-0.661578\pi$
$947$	−21.9868	+	3.06702i	−0.714474	+	0.0996649i	−0.228381	+	0.973572i	$0.573343\pi$
$948$	−1.58671	+	0.296607i	−0.0515338	+	0.00963334i
$949$	−10.1727	−	6.96848i	−0.330221	−	0.226207i
$950$	33.1057	+	36.3152i	1.07409	+	1.17822i
$951$	11.4740	+	4.44506i	0.372070	+	0.144141i
$952$	1.36594	−	0.152623i	0.0442705	−	0.00494652i
$953$	−33.9701	+	13.1601i	−1.10040	+	0.426297i	−0.841856	−	0.539703i	$-0.818537\pi$
$953$	−33.9701	+	13.1601i	−1.10040	+	0.426297i	−0.258543	+	0.966000i	$0.583243\pi$
$954$	−23.9165	−	11.9090i	−0.774324	−	0.385568i
$955$	−0.820763	+	0.681553i	−0.0265593	+	0.0220545i
$956$	12.4117	−	4.80834i	0.401425	−	0.155513i
$957$	3.41737	+	4.98875i	0.110468	+	0.161263i
$958$	38.5766	+	69.2583i	1.24635	+	2.23763i
$959$	−2.00558	+	4.54221i	−0.0647636	+	0.146676i
$960$	−0.568867	+	0.283262i	−0.0183601	+	0.00914225i
$961$	16.6765	−	18.2932i	0.537951	−	0.590105i
$962$	−0.644742	+	0.151642i	−0.0207873	+	0.00488913i
$963$	0.568477	−	12.2960i	0.0183189	−	0.396232i
$964$	3.70137	−	4.45739i	0.119213	−	0.143563i
$965$	0.689986	−	1.38568i	0.0222114	−	0.0446066i
$966$	−2.57958	−	1.13899i	−0.0829965	−	0.0366466i
$967$	15.0908	−	24.3726i	0.485289	−	0.783768i	−0.511873	−	0.859061i	$-0.671048\pi$
$967$	15.0908	−	24.3726i	0.485289	−	0.783768i	0.997161	+	0.0752930i	$0.0239892\pi$
$968$	3.84517	−	0.718787i	0.123588	−	0.0231027i
$969$	2.74239	+	8.99033i	0.0880982	+	0.288811i
$970$	−3.35531	−	0.627215i	−0.107732	−	0.0201387i
$971$	−2.81715	+	3.09027i	−0.0904066	+	0.0991713i	−0.782547	−	0.622592i	$-0.786080\pi$
$971$	−2.81715	+	3.09027i	−0.0904066	+	0.0991713i	0.692140	+	0.721763i	$0.256668\pi$
$972$	−16.9563	+	9.44460i	−0.543874	+	0.302936i
$973$	−7.13029	−	4.41489i	−0.228587	−	0.141535i
$974$	−3.29908	+	23.6503i	−0.105709	+	0.757804i
$975$	−3.69184	+	1.63011i	−0.118233	+	0.0522052i
$976$	−2.42836	+	52.5245i	−0.0777298	+	1.68127i
$977$		−	33.5736i		−	1.07411i	−0.843546	−	0.537057i	$-0.819536\pi$
$977$		−	33.5736i		−	1.07411i	0.843546	−	0.537057i	$-0.180464\pi$
$978$	16.3196	+	4.64332i	0.521843	+	0.148477i
$979$	−10.4337	−	1.45543i	−0.333461	−	0.0465159i
$980$	2.68989	−	0.124361i	0.0859255	−	0.00397258i
$981$	0.543412	+	11.7538i	0.0173498	+	0.375271i
$982$	7.24322	+	14.5463i	0.231140	+	0.464192i
$983$	−49.0790	−	11.5433i	−1.56538	−	0.368173i	−0.646561	−	0.762862i	$-0.723793\pi$
$983$	−49.0790	−	11.5433i	−1.56538	−	0.368173i	−0.918815	+	0.394689i	$0.870852\pi$
$984$	−0.528844	−	0.150469i	−0.0168589	−	0.00479678i
$985$	−3.62424	+	3.30393i	−0.115478	+	0.105272i
$986$	−71.3207	+	1.34617i	−2.27131	+	0.0428709i
$987$	2.94073	+	2.68083i	0.0936045	+	0.0853318i
$988$	−8.73577	−	14.1088i	−0.277922	−	0.448859i
$989$	22.5927	−	7.57232i	0.718407	−	0.240786i
$990$	−0.180496	−	1.94786i	−0.00573653	−	0.0619071i
$991$	−26.5181	+	22.0204i	−0.842375	+	0.699500i	−0.955791	−	0.294048i	$-0.904997\pi$
$991$	−26.5181	+	22.0204i	−0.842375	+	0.699500i	0.113415	+	0.993548i	$0.463821\pi$
$992$	6.08357	+	18.1509i	0.193154	+	0.576292i
$993$	0.557741	+	1.66407i	0.0176994	+	0.0528078i
$994$	−19.4534	−	9.68666i	−0.617026	−	0.307242i
$995$	0.168531	+	0.901563i	0.00534281	+	0.0285815i
$996$	3.97180	+	2.21228i	0.125851	+	0.0700987i
$997$	−7.86345	−	56.3712i	−0.249038	−	1.78529i	−0.553580	−	0.832796i	$-0.686739\pi$
$997$	−7.86345	−	56.3712i	−0.249038	−	1.78529i	0.304542	−	0.952499i	$-0.401496\pi$
$998$	−3.76190	−	3.76190i	−0.119081	−	0.119081i
$999$	−0.472581	−	0.0883407i	−0.0149518	−	0.00279497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.h.a.132.6	✓	768
289.208	even	68	inner	289.2.h.a.208.6	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.h.a.132.6	✓	768	1.1	even	1	trivial
289.2.h.a.208.6	yes	768	289.208	even	68	inner

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.h (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54901 - 1.16976i) q^{2} +(0.0205619 + 0.444748i) q^{3} +(0.483774 + 1.70029i) q^{4} +(0.215937 + 0.0953453i) q^{5} +(0.488397 - 0.712972i) q^{6} +(-0.568933 - 0.472436i) q^{7} +(-0.162838 + 0.420332i) q^{8} +(2.78982 - 0.258515i) q^{9} +O(q^{10})\)	\(q+(-1.54901 - 1.16976i) q^{2} +(0.0205619 + 0.444748i) q^{3} +(0.483774 + 1.70029i) q^{4} +(0.215937 + 0.0953453i) q^{5} +(0.488397 - 0.712972i) q^{6} +(-0.568933 - 0.472436i) q^{7} +(-0.162838 + 0.420332i) q^{8} +(2.78982 - 0.258515i) q^{9} +(-0.222957 - 0.400285i) q^{10} +(1.33125 + 0.741501i) q^{11} +(-0.746252 + 0.250118i) q^{12} +(-1.70952 - 0.662273i) q^{13} +(0.328647 + 1.39732i) q^{14} +(-0.0379645 + 0.0979977i) q^{15} +(3.74990 - 2.32184i) q^{16} +(3.80255 + 1.59393i) q^{17} +(-4.62387 - 2.86298i) q^{18} +(4.08607 - 3.08566i) q^{19} +(-0.0576501 + 0.413280i) q^{20} +(0.198416 - 0.262746i) q^{21} +(-1.19474 - 2.70583i) q^{22} +(3.39449 + 2.81875i) q^{23} +(-0.190290 - 0.0637788i) q^{24} +(-3.33094 - 3.65387i) q^{25} +(1.87337 + 3.02560i) q^{26} +(0.356869 + 2.55831i) q^{27} +(0.528043 - 1.19590i) q^{28} +(4.33713 - 7.78663i) q^{29} +(0.173441 - 0.107390i) q^{30} +(-1.00950 - 2.28630i) q^{31} +(-7.62694 - 0.706740i) q^{32} +(-0.302408 + 0.607317i) q^{33} +(-4.02567 - 6.91709i) q^{34} +(-0.0778089 - 0.156261i) q^{35} +(1.78919 + 4.61844i) q^{36} +(-0.0591478 + 0.176473i) q^{37} -9.93884 q^{38} +(0.259393 - 0.773924i) q^{39} +(-0.0752392 + 0.0752392i) q^{40} +(2.73674 - 0.126527i) q^{41} +(-0.614699 + 0.174897i) q^{42} +(2.84295 - 4.59153i) q^{43} +(-0.616742 + 2.62223i) q^{44} +(0.627073 + 0.210174i) q^{45} +(-1.96085 - 8.33700i) q^{46} +(-1.11515 + 12.0344i) q^{47} +(1.10974 + 1.62002i) q^{48} +(-1.18576 - 6.34324i) q^{49} +(0.885520 + 9.55628i) q^{50} +(-0.630710 + 1.72395i) q^{51} +(0.299032 - 3.22707i) q^{52} +(4.89173 - 0.453285i) q^{53} +(2.43981 - 4.38030i) q^{54} +(0.216767 + 0.287046i) q^{55} +(0.291224 - 0.162211i) q^{56} +(1.45636 + 1.75382i) q^{57} +(-15.8267 + 6.98819i) q^{58} +(-0.696220 + 3.72445i) q^{59} +(-0.184991 - 0.0171419i) q^{60} +(-6.73735 + 9.83531i) q^{61} +(-1.11069 + 4.72237i) q^{62} +(-1.70936 - 1.17094i) q^{63} +(4.46867 + 4.07373i) q^{64} +(-0.306004 - 0.306004i) q^{65} +(1.17885 - 0.586996i) q^{66} +(6.80481 + 9.01102i) q^{67} +(-0.870572 + 7.23653i) q^{68} +(-1.18383 + 1.56765i) q^{69} +(-0.0622612 + 0.333068i) q^{70} +(-9.67169 + 11.6472i) q^{71} +(-0.345626 + 1.21475i) q^{72} +(6.54718 + 1.53988i) q^{73} +(0.298051 - 0.204170i) q^{74} +(1.55656 - 1.55656i) q^{75} +(7.22324 + 5.45474i) q^{76} +(-0.407080 - 1.05079i) q^{77} +(-1.30711 + 0.895389i) q^{78} +(2.03126 + 0.283349i) q^{79} +(1.03112 - 0.143835i) q^{80} +(7.13175 - 1.33315i) q^{81} +(-4.38725 - 3.00534i) q^{82} +(-3.89156 - 4.26884i) q^{83} +(0.542732 + 0.210256i) q^{84} +(0.669135 + 0.706743i) q^{85} +(-9.77475 + 3.78676i) q^{86} +(3.55227 + 1.76882i) q^{87} +(-0.528454 + 0.438823i) q^{88} +(-6.44647 + 2.49737i) q^{89} +(-0.725491 - 1.05909i) q^{90} +(0.659723 + 1.18443i) q^{91} +(-3.15052 + 7.13525i) q^{92} +(0.996068 - 0.495983i) q^{93} +(15.8048 - 17.3370i) q^{94} +(1.17653 - 0.276718i) q^{95} +(0.157496 - 3.40660i) q^{96} +(4.75929 - 5.73139i) q^{97} +(-5.58331 + 11.2128i) q^{98} +(3.90564 + 1.72451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9}+O(q^{10}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + 34 q^{10} - 34 q^{11} - 34 q^{12} - 30 q^{13} - 34 q^{14} - 34 q^{15} - 82 q^{16} - 34 q^{17} - 42 q^{18} - 34 q^{19} - 34 q^{20} - 26 q^{21} - 34 q^{22} - 34 q^{23} - 204 q^{24} + 170 q^{25} - 34 q^{26} - 34 q^{27} - 34 q^{28} - 34 q^{29} - 14 q^{30} - 34 q^{31} - 34 q^{32} + 56 q^{33} - 34 q^{34} - 42 q^{35} - 34 q^{36} - 34 q^{37} + 144 q^{38} - 170 q^{39} - 34 q^{40} - 34 q^{41} - 34 q^{42} - 34 q^{43} - 34 q^{44} - 34 q^{45} + 102 q^{46} - 30 q^{47} - 34 q^{48} - 34 q^{49} - 62 q^{50} + 238 q^{51} - 50 q^{52} + 136 q^{54} - 14 q^{55} - 34 q^{56} - 34 q^{57} - 34 q^{58} - 34 q^{59} - 34 q^{60} - 34 q^{61} - 238 q^{62} - 34 q^{63} + 38 q^{64} - 34 q^{65} + 476 q^{66} + 82 q^{67} - 34 q^{68} - 62 q^{69} - 34 q^{70} - 34 q^{71} + 10 q^{72} - 34 q^{73} - 34 q^{74} + 102 q^{75} - 102 q^{76} - 374 q^{77} - 34 q^{78} + 68 q^{79} - 34 q^{80} + 30 q^{81} - 34 q^{82} + 102 q^{83} - 82 q^{84} - 204 q^{85} - 62 q^{86} - 34 q^{87} + 170 q^{88} - 22 q^{89} - 34 q^{90} - 34 q^{91} + 34 q^{92} - 34 q^{93} + 238 q^{94} - 34 q^{95} + 544 q^{96} - 34 q^{97} + 10 q^{98} - 34 q^{99}+O(q^{100}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9 + 34 * q^10 - 34 * q^11 - 34 * q^12 - 30 * q^13 - 34 * q^14 - 34 * q^15 - 82 * q^16 - 34 * q^17 - 42 * q^18 - 34 * q^19 - 34 * q^20 - 26 * q^21 - 34 * q^22 - 34 * q^23 - 204 * q^24 + 170 * q^25 - 34 * q^26 - 34 * q^27 - 34 * q^28 - 34 * q^29 - 14 * q^30 - 34 * q^31 - 34 * q^32 + 56 * q^33 - 34 * q^34 - 42 * q^35 - 34 * q^36 - 34 * q^37 + 144 * q^38 - 170 * q^39 - 34 * q^40 - 34 * q^41 - 34 * q^42 - 34 * q^43 - 34 * q^44 - 34 * q^45 + 102 * q^46 - 30 * q^47 - 34 * q^48 - 34 * q^49 - 62 * q^50 + 238 * q^51 - 50 * q^52 + 136 * q^54 - 14 * q^55 - 34 * q^56 - 34 * q^57 - 34 * q^58 - 34 * q^59 - 34 * q^60 - 34 * q^61 - 238 * q^62 - 34 * q^63 + 38 * q^64 - 34 * q^65 + 476 * q^66 + 82 * q^67 - 34 * q^68 - 62 * q^69 - 34 * q^70 - 34 * q^71 + 10 * q^72 - 34 * q^73 - 34 * q^74 + 102 * q^75 - 102 * q^76 - 374 * q^77 - 34 * q^78 + 68 * q^79 - 34 * q^80 + 30 * q^81 - 34 * q^82 + 102 * q^83 - 82 * q^84 - 204 * q^85 - 62 * q^86 - 34 * q^87 + 170 * q^88 - 22 * q^89 - 34 * q^90 - 34 * q^91 + 34 * q^92 - 34 * q^93 + 238 * q^94 - 34 * q^95 + 544 * q^96 - 34 * q^97 + 10 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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