LMFDB - Embedded newform 475.2.u.c.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.3
Character	$\chi$	$=$	475.99
Dual form			475.2.u.c.24.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.408399 + 1.12207i) q^{2} +(2.23864 - 0.394733i) q^{3} +(0.439845 + 0.369074i) q^{4} +(-0.471342 + 2.67312i) q^{6} +(1.90222 + 1.09825i) q^{7} +(-2.66196 + 1.53688i) q^{8} +(2.03663 - 0.741274i) q^{9} +O(q^{10})$	\(q+(-0.408399 + 1.12207i) q^{2} +(2.23864 - 0.394733i) q^{3} +(0.439845 + 0.369074i) q^{4} +(-0.471342 + 2.67312i) q^{6} +(1.90222 + 1.09825i) q^{7} +(-2.66196 + 1.53688i) q^{8} +(2.03663 - 0.741274i) q^{9} +(1.41324 + 2.44780i) q^{11} +(1.13034 + 0.652604i) q^{12} +(-4.01920 - 0.708694i) q^{13} +(-2.00917 + 1.68589i) q^{14} +(-0.437935 - 2.48365i) q^{16} +(0.130867 - 0.359555i) q^{17} +2.58797i q^{18} +(2.75520 - 3.37770i) q^{19} +(4.69190 + 1.70771i) q^{21} +(-3.32376 + 0.586069i) q^{22} +(-1.91290 + 2.27970i) q^{23} +(-5.35253 + 4.49130i) q^{24} +(2.43664 - 4.22038i) q^{26} +(-1.63920 + 0.946391i) q^{27} +(0.431347 + 1.18512i) q^{28} +(8.05787 - 2.93282i) q^{29} +(2.34622 - 4.06377i) q^{31} +(-3.08847 - 0.544580i) q^{32} +(4.12997 + 4.92191i) q^{33} +(0.349999 + 0.293684i) q^{34} +(1.16939 + 0.425623i) q^{36} -10.7694i q^{37} +(2.66478 + 4.47097i) q^{38} -9.27731 q^{39} +(0.544445 + 3.08770i) q^{41} +(-3.83233 + 4.56720i) q^{42} +(-1.29137 - 1.53900i) q^{43} +(-0.281814 + 1.59824i) q^{44} +(-1.77675 - 3.07743i) q^{46} +(3.72722 + 10.2405i) q^{47} +(-1.96076 - 5.38714i) q^{48} +(-1.08771 - 1.88398i) q^{49} +(0.151037 - 0.856574i) q^{51} +(-1.50627 - 1.79510i) q^{52} +(4.80532 - 5.72676i) q^{53} +(-0.392467 - 2.22579i) q^{54} -6.75150 q^{56} +(4.83463 - 8.64904i) q^{57} +10.2392i q^{58} +(-12.1961 - 4.43900i) q^{59} +(4.57784 + 3.84126i) q^{61} +(3.60163 + 4.29225i) q^{62} +(4.68822 + 0.826660i) q^{63} +(4.39435 - 7.61123i) q^{64} +(-7.20938 + 2.62400i) q^{66} +(-0.358925 - 0.986138i) q^{67} +(0.190264 - 0.109849i) q^{68} +(-3.38242 + 5.85853i) q^{69} +(-5.99626 + 5.03146i) q^{71} +(-4.28219 + 5.10332i) q^{72} +(-13.8755 + 2.44663i) q^{73} +(12.0840 + 4.39822i) q^{74} +(2.45848 - 0.468792i) q^{76} +6.20833i q^{77} +(3.78884 - 10.4098i) q^{78} +(2.33355 + 13.2342i) q^{79} +(-8.27685 + 6.94510i) q^{81} +(-3.68695 - 0.650110i) q^{82} +(-4.81175 - 2.77807i) q^{83} +(1.43344 + 2.48279i) q^{84} +(2.25425 - 0.820481i) q^{86} +(16.8810 - 9.74626i) q^{87} +(-7.52398 - 4.34397i) q^{88} +(1.13984 - 6.46435i) q^{89} +(-6.86708 - 5.76216i) q^{91} +(-1.68276 + 0.296716i) q^{92} +(3.64824 - 10.0235i) q^{93} -13.0127 q^{94} -7.12895 q^{96} +(4.94091 - 13.5750i) q^{97} +(2.55817 - 0.451074i) q^{98} +(4.69275 + 3.93768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.408399	+	1.12207i	−0.288782	+	0.793421i	0.707456	+	0.706757i	$0.249843\pi$
$2$	−0.408399	+	1.12207i	−0.288782	+	0.793421i	−0.996238	+	0.0866635i	$0.972380\pi$
$3$	2.23864	−	0.394733i	1.29248	−	0.227899i	0.515210	−	0.857064i	$-0.327714\pi$
$3$	2.23864	−	0.394733i	1.29248	−	0.227899i	0.777272	+	0.629165i	$0.216603\pi$
$4$	0.439845	+	0.369074i	0.219923	+	0.184537i
$5$		0			0
$5$		0			0
$6$	−0.471342	+	2.67312i	−0.192425	+	1.09129i
$7$	1.90222	+	1.09825i	0.718970	+	0.415098i	0.814374	−	0.580341i	$-0.197081\pi$
$7$	1.90222	+	1.09825i	0.718970	+	0.415098i	−0.0954033	+	0.995439i	$0.530414\pi$
$8$	−2.66196	+	1.53688i	−0.941146	+	0.543371i
$9$	2.03663	−	0.741274i	0.678878	−	0.247091i
$10$		0			0
$11$	1.41324	+	2.44780i	0.426108	+	0.738040i	0.996523	−	0.0833161i	$-0.0265511\pi$
$11$	1.41324	+	2.44780i	0.426108	+	0.738040i	−0.570415	+	0.821356i	$0.693218\pi$
$12$	1.13034	+	0.652604i	0.326302	+	0.188391i
$13$	−4.01920	−	0.708694i	−1.11473	−	0.196556i	−0.414202	−	0.910185i	$-0.635939\pi$
$13$	−4.01920	−	0.708694i	−1.11473	−	0.196556i	−0.700524	+	0.713628i	$0.747051\pi$
$14$	−2.00917	+	1.68589i	−0.536972	+	0.450573i
$15$		0			0
$16$	−0.437935	−	2.48365i	−0.109484	−	0.620913i
$17$	0.130867	−	0.359555i	0.0317400	−	0.0872049i	−0.922810	−	0.385254i	$-0.874114\pi$
$17$	0.130867	−	0.359555i	0.0317400	−	0.0872049i	0.954550	+	0.298049i	$0.0963360\pi$
$18$			2.58797i			0.609992i
$19$	2.75520	−	3.37770i	0.632087	−	0.774898i
$19$	2.75520	−	3.37770i	0.632087	−	0.774898i
$20$		0			0
$21$	4.69190	+	1.70771i	1.02386	+	0.372653i
$22$	−3.32376	+	0.586069i	−0.708628	+	0.124950i
$23$	−1.91290	+	2.27970i	−0.398867	+	0.475351i	−0.927674	−	0.373391i	$-0.878195\pi$
$23$	−1.91290	+	2.27970i	−0.398867	+	0.475351i	0.528807	+	0.848742i	$0.322639\pi$
$24$	−5.35253	+	4.49130i	−1.09258	+	0.916783i
$25$		0			0
$26$	2.43664	−	4.22038i	0.477864	−	0.827686i
$27$	−1.63920	+	0.946391i	−0.315464	+	0.182133i
$28$	0.431347	+	1.18512i	0.0815170	+	0.223966i
$29$	8.05787	−	2.93282i	1.49631	−	0.544612i	0.541207	−	0.840889i	$-0.317968\pi$
$29$	8.05787	−	2.93282i	1.49631	−	0.544612i	0.955102	+	0.296278i	$0.0957454\pi$
$30$		0			0
$31$	2.34622	−	4.06377i	0.421393	−	0.729874i	−0.574683	−	0.818376i	$-0.694875\pi$
$31$	2.34622	−	4.06377i	0.421393	−	0.729874i	0.996076	+	0.0885019i	$0.0282079\pi$
$32$	−3.08847	−	0.544580i	−0.545969	−	0.0962691i
$33$	4.12997	+	4.92191i	0.718935	+	0.856794i
$34$	0.349999	+	0.293684i	0.0600243	+	0.0503663i
$35$		0			0
$36$	1.16939	+	0.425623i	0.194898	+	0.0709372i
$37$		−	10.7694i		−	1.77048i	−0.465131	−	0.885242i	$-0.653993\pi$
$37$		−	10.7694i		−	1.77048i	0.465131	−	0.885242i	$-0.346007\pi$
$38$	2.66478	+	4.47097i	0.432285	+	0.725287i
$39$	−9.27731			−1.48556
$40$		0			0
$41$	0.544445	+	3.08770i	0.0850280	+	0.482218i	0.997351	+	0.0727454i	$0.0231760\pi$
$41$	0.544445	+	3.08770i	0.0850280	+	0.482218i	−0.912323	+	0.409472i	$0.865713\pi$
$42$	−3.83233	+	4.56720i	−0.591342	+	0.704734i
$43$	−1.29137	−	1.53900i	−0.196933	−	0.234695i	0.658537	−	0.752549i	$-0.271176\pi$
$43$	−1.29137	−	1.53900i	−0.196933	−	0.234695i	−0.855469	+	0.517853i	$0.826731\pi$
$44$	−0.281814	+	1.59824i	−0.0424850	+	0.240944i
$45$		0			0
$46$	−1.77675	−	3.07743i	−0.261968	−	0.453742i
$47$	3.72722	+	10.2405i	0.543671	+	1.49372i	0.842115	+	0.539297i	$0.181310\pi$
$47$	3.72722	+	10.2405i	0.543671	+	1.49372i	−0.298444	+	0.954427i	$0.596468\pi$
$48$	−1.96076	−	5.38714i	−0.283011	−	0.777567i
$49$	−1.08771	−	1.88398i	−0.155388	−	0.269140i
$50$		0			0
$51$	0.151037	−	0.856574i	0.0211494	−	0.119944i
$52$	−1.50627	−	1.79510i	−0.208882	−	0.248936i
$53$	4.80532	−	5.72676i	0.660062	−	0.786631i	−0.327333	−	0.944909i	$-0.606150\pi$
$53$	4.80532	−	5.72676i	0.660062	−	0.786631i	0.987395	+	0.158278i	$0.0505942\pi$
$54$	−0.392467	−	2.22579i	−0.0534080	−	0.302892i
$55$		0			0
$56$	−6.75150			−0.902208
$57$	4.83463	−	8.64904i	0.640362	−	1.14559i
$58$			10.2392i			1.34448i
$59$	−12.1961	−	4.43900i	−1.58779	−	0.577909i	−0.610912	−	0.791698i	$-0.709197\pi$
$59$	−12.1961	−	4.43900i	−1.58779	−	0.577909i	−0.976880	+	0.213789i	$0.931419\pi$
$60$		0			0
$61$	4.57784	+	3.84126i	0.586132	+	0.491823i	0.886954	−	0.461857i	$-0.152817\pi$
$61$	4.57784	+	3.84126i	0.586132	+	0.491823i	−0.300822	+	0.953680i	$0.597261\pi$
$62$	3.60163	+	4.29225i	0.457407	+	0.545116i
$63$	4.68822	+	0.826660i	0.590660	+	0.104149i
$64$	4.39435	−	7.61123i	0.549294	−	0.951404i
$65$		0			0
$66$	−7.20938	+	2.62400i	−0.887413	+	0.322992i
$67$	−0.358925	−	0.986138i	−0.0438496	−	0.120476i	0.915835	−	0.401555i	$-0.131530\pi$
$67$	−0.358925	−	0.986138i	−0.0438496	−	0.120476i	−0.959685	+	0.281079i	$0.909308\pi$
$68$	0.190264	−	0.109849i	0.0230729	−	0.0133211i
$69$	−3.38242	+	5.85853i	−0.407196	+	0.705284i
$70$		0			0
$71$	−5.99626	+	5.03146i	−0.711625	+	0.597124i	−0.925055	−	0.379834i	$-0.875981\pi$
$71$	−5.99626	+	5.03146i	−0.711625	+	0.597124i	0.213430	+	0.976958i	$0.431537\pi$
$72$	−4.28219	+	5.10332i	−0.504661	+	0.601432i
$73$	−13.8755	+	2.44663i	−1.62401	+	0.286357i	−0.910258	−	0.414042i	$-0.864117\pi$
$73$	−13.8755	+	2.44663i	−1.62401	+	0.286357i	−0.713752	+	0.700399i	$0.753005\pi$
$74$	12.0840	+	4.39822i	1.40474	+	0.511283i
$75$		0			0
$76$	2.45848	−	0.468792i	0.282008	−	0.0537741i
$77$			6.20833i			0.707505i
$78$	3.78884	−	10.4098i	0.429002	−	1.17867i
$79$	2.33355	+	13.2342i	0.262545	+	1.48897i	0.775935	+	0.630813i	$0.217278\pi$
$79$	2.33355	+	13.2342i	0.262545	+	1.48897i	−0.513390	+	0.858156i	$0.671610\pi$
$80$		0			0
$81$	−8.27685	+	6.94510i	−0.919650	+	0.771678i
$82$	−3.68695	−	0.650110i	−0.407156	−	0.0717926i
$83$	−4.81175	−	2.77807i	−0.528158	−	0.304932i	0.212108	−	0.977246i	$-0.431967\pi$
$83$	−4.81175	−	2.77807i	−0.528158	−	0.304932i	−0.740266	+	0.672314i	$0.765301\pi$
$84$	1.43344	+	2.48279i	0.156401	+	0.270894i
$85$		0			0
$86$	2.25425	−	0.820481i	0.243082	−	0.0884748i
$87$	16.8810	−	9.74626i	1.80984	−	1.04491i
$88$	−7.52398	−	4.34397i	−0.802059	−	0.463069i
$89$	1.13984	−	6.46435i	0.120823	−	0.685220i	−0.862879	−	0.505411i	$-0.831341\pi$
$89$	1.13984	−	6.46435i	0.120823	−	0.685220i	0.983702	−	0.179809i	$-0.0575479\pi$
$90$		0			0
$91$	−6.86708	−	5.76216i	−0.719865	−	0.604039i
$92$	−1.68276	+	0.296716i	−0.175440	+	0.0309347i
$93$	3.64824	−	10.0235i	0.378305	−	1.03938i
$94$	−13.0127			−1.34215
$95$		0			0
$96$	−7.12895			−0.727595
$97$	4.94091	−	13.5750i	0.501673	−	1.37834i	−0.387966	−	0.921674i	$-0.626822\pi$
$97$	4.94091	−	13.5750i	0.501673	−	1.37834i	0.889640	−	0.456663i	$-0.150955\pi$
$98$	2.55817	−	0.451074i	0.258414	−	0.0455654i
$99$	4.69275	+	3.93768i	0.471639	+	0.395752i
$100$		0			0
$101$	0.738074	−	4.18582i	0.0734411	−	0.416505i	−0.925816	−	0.377974i	$-0.876621\pi$
$101$	0.738074	−	4.18582i	0.0734411	−	0.416505i	0.999257	−	0.0385313i	$-0.0122679\pi$
$102$	0.899449	+	0.519297i	0.0890587	+	0.0514181i
$103$	12.7051	−	7.33528i	1.25187	−	0.722767i	0.280389	−	0.959887i	$-0.409537\pi$
$103$	12.7051	−	7.33528i	1.25187	−	0.722767i	0.971481	+	0.237119i	$0.0762033\pi$
$104$	11.7882	−	4.29054i	1.15592	−	0.420722i
$105$		0			0
$106$	4.46332	+	7.73070i	0.433516	+	0.750872i
$107$	5.35244	+	3.09023i	0.517439	+	0.298744i	0.735886	−	0.677105i	$-0.236766\pi$
$107$	5.35244	+	3.09023i	0.517439	+	0.298744i	−0.218447	+	0.975849i	$0.570099\pi$
$108$	−1.07028	−	0.188720i	−0.102988	−	0.0181595i
$109$	−0.577493	+	0.484574i	−0.0553138	+	0.0464138i	−0.670025	−	0.742338i	$-0.733717\pi$
$109$	−0.577493	+	0.484574i	−0.0553138	+	0.0464138i	0.614712	+	0.788752i	$0.289272\pi$
$110$		0			0
$111$	−4.25105	−	24.1089i	−0.403492	−	2.28832i
$112$	1.89461	−	5.20540i	0.179024	−	0.491864i
$113$		−	0.870003i		−	0.0818430i	−0.999162	−	0.0409215i	$-0.986971\pi$
$113$		−	0.870003i		−	0.0818430i	0.999162	−	0.0409215i	$-0.0130294\pi$
$114$	7.73034	+	8.95703i	0.724013	+	0.838903i
$115$		0			0
$116$	4.62665	+	1.68396i	0.429573	+	0.156352i
$117$	−8.71099	+	1.53598i	−0.805331	+	0.142002i
$118$	9.96171	−	11.8719i	0.917050	−	1.09290i
$119$	0.643818	−	0.540227i	0.0590187	−	0.0495225i
$120$		0			0
$121$	1.50551	−	2.60762i	0.136864	−	0.237056i
$122$	−6.17973	+	3.56787i	−0.559487	+	0.323020i
$123$	2.43764	+	6.69735i	0.219794	+	0.603880i
$124$	2.53180	−	0.921502i	0.227363	−	0.0827533i
$125$		0			0
$126$	−2.84223	+	4.92289i	−0.253206	+	0.438566i
$127$	−3.39209	−	0.598116i	−0.300999	−	0.0530743i	0.0211090	−	0.999777i	$-0.493280\pi$
$127$	−3.39209	−	0.598116i	−0.300999	−	0.0530743i	−0.322108	+	0.946703i	$0.604391\pi$
$128$	2.71395	+	3.23436i	0.239882	+	0.285880i
$129$	−3.49842	−	2.93552i	−0.308019	−	0.258458i
$130$		0			0
$131$	−9.67954	−	3.52307i	−0.845706	−	0.307812i	−0.117418	−	0.993083i	$-0.537462\pi$
$131$	−9.67954	−	3.52307i	−0.845706	−	0.307812i	−0.728288	+	0.685271i	$0.759684\pi$
$132$			3.68914i			0.321099i
$133$	8.95054	−	3.39923i	0.776110	−	0.294751i
$134$	1.25310			0.108251
$135$		0			0
$136$	0.204231	+	1.15825i	0.0175126	+	0.0993191i
$137$	−0.943562	+	1.12449i	−0.0806140	+	0.0960720i	−0.804844	−	0.593487i	$-0.797751\pi$
$137$	−0.943562	+	1.12449i	−0.0806140	+	0.0960720i	0.724230	+	0.689559i	$0.242195\pi$
$138$	−5.19228	−	6.18792i	−0.441996	−	0.526750i
$139$	1.27243	−	7.21629i	0.107926	−	0.612078i	−0.882085	−	0.471090i	$-0.843861\pi$
$139$	1.27243	−	7.21629i	0.107926	−	0.612078i	0.990011	−	0.140988i	$-0.0450281\pi$
$140$		0			0
$141$	12.3862	+	21.4535i	1.04310	+	1.80671i
$142$	−3.19677	−	8.78304i	−0.268267	−	0.737057i
$143$	−3.94535	−	10.8398i	−0.329927	−	0.906467i
$144$	−2.73298	−	4.73366i	−0.227748	−	0.394472i
$145$		0			0
$146$	2.92147	−	16.5685i	0.241783	−	1.37122i
$147$	−3.17868	−	3.78820i	−0.262173	−	0.312445i
$148$	3.97472	−	4.73689i	0.326720	−	0.389370i
$149$	−1.73507	−	9.84006i	−0.142142	−	0.806129i	−0.969617	−	0.244627i	$-0.921335\pi$
$149$	−1.73507	−	9.84006i	−0.142142	−	0.806129i	0.827475	−	0.561503i	$-0.189777\pi$
$150$		0			0
$151$	15.0689			1.22629			0.613144	−	0.789971i	$-0.289905\pi$
$151$	15.0689			1.22629			0.613144	+	0.789971i	$0.289905\pi$
$152$	−2.14311	+	13.2257i	−0.173829	+	1.07275i
$153$		−	0.829291i		−	0.0670442i
$154$	−6.96616	−	2.53548i	−0.561349	−	0.204314i
$155$		0			0
$156$	−4.08058	−	3.42402i	−0.326708	−	0.274141i
$157$	6.64935	+	7.92438i	0.530676	+	0.632435i	0.963070	−	0.269250i	$-0.0867758\pi$
$157$	6.64935	+	7.92438i	0.530676	+	0.632435i	−0.432395	+	0.901684i	$0.642331\pi$
$158$	−15.8027	−	2.78645i	−1.25720	−	0.221678i
$159$	8.49687	−	14.7170i	0.673845	−	1.16713i
$160$		0			0
$161$	−6.14242	+	2.23566i	−0.484090	+	0.176194i
$162$	−4.41261	−	12.1235i	−0.346687	−	0.952515i
$163$	5.97565	−	3.45005i	0.468049	−	0.270228i	−0.247373	−	0.968920i	$-0.579567\pi$
$163$	5.97565	−	3.45005i	0.468049	−	0.270228i	0.715423	+	0.698692i	$0.246234\pi$
$164$	−0.900118	+	1.55905i	−0.0702874	+	0.121741i
$165$		0			0
$166$	5.08229	−	4.26455i	0.394462	−	0.330993i
$167$	−7.62476	+	9.08683i	−0.590022	+	0.703160i	−0.975610	−	0.219510i	$-0.929554\pi$
$167$	−7.62476	+	9.08683i	−0.590022	+	0.703160i	0.385589	+	0.922671i	$0.373998\pi$
$168$	−15.1142	+	2.66504i	−1.16609	+	0.205613i
$169$	3.43575	+	1.25051i	0.264289	+	0.0961932i
$170$		0			0
$171$	3.10754	−	8.92150i	0.237639	−	0.682244i
$172$		−	1.15353i		−	0.0879561i
$173$	−8.68955	+	23.8744i	−0.660655	+	1.81513i	−0.0867194	+	0.996233i	$0.527638\pi$
$173$	−8.68955	+	23.8744i	−0.660655	+	1.81513i	−0.573935	+	0.818901i	$0.694584\pi$
$174$	4.04176	+	22.9220i	0.306405	+	1.73771i
$175$		0			0
$176$	5.46058	−	4.58197i	0.411607	−	0.345379i
$177$	−29.0549	−	5.12316i	−2.18390	−	0.385080i
$178$	6.78792	+	3.91901i	0.508776	+	0.293742i
$179$	−0.194400	−	0.336710i	−0.0145301	−	0.0251669i	0.858669	−	0.512531i	$-0.171292\pi$
$179$	−0.194400	−	0.336710i	−0.0145301	−	0.0251669i	−0.873199	+	0.487364i	$0.837959\pi$
$180$		0			0
$181$	−4.49536	+	1.63618i	−0.334137	+	0.121616i	−0.503640	−	0.863914i	$-0.668006\pi$
$181$	−4.49536	+	1.63618i	−0.334137	+	0.121616i	0.169502	+	0.985530i	$0.445784\pi$
$182$	9.27003	−	5.35206i	0.687141	−	0.396721i
$183$	11.7644	+	6.79219i	0.869651	+	0.502093i
$184$	1.58842	−	9.00838i	0.117100	−	0.664107i
$185$		0			0
$186$	9.75705	+	8.18714i	0.715422	+	0.600310i
$187$	1.06507	−	0.187800i	0.0778854	−	0.0137333i
$188$	−2.14009	+	5.87984i	−0.156082	+	0.428831i
$189$	−4.15748			−0.302412
$190$		0			0
$191$	−23.8516			−1.72584			−0.862921	−	0.505338i	$-0.831368\pi$
$191$	−23.8516			−1.72584			−0.862921	+	0.505338i	$0.831368\pi$
$192$	6.83297	−	18.7734i	0.493127	−	1.35486i
$193$	−11.0554	+	1.94937i	−0.795787	+	0.140319i	−0.556737	−	0.830688i	$-0.687947\pi$
$193$	−11.0554	+	1.94937i	−0.795787	+	0.140319i	−0.239050	+	0.971007i	$0.576836\pi$
$194$	13.2142	+	11.0881i	0.948727	+	0.796076i
$195$		0			0
$196$	0.216901	−	1.23011i	0.0154929	−	0.0878647i
$197$	14.6122	+	8.43639i	1.04108	+	0.601068i	0.920139	−	0.391592i	$-0.128076\pi$
$197$	14.6122	+	8.43639i	1.04108	+	0.601068i	0.120941	+	0.992660i	$0.461409\pi$
$198$	−6.33485	+	3.65743i	−0.450198	+	0.259922i
$199$	−14.7743	+	5.37740i	−1.04732	+	0.381194i	−0.807651	−	0.589660i	$-0.799262\pi$
$199$	−14.7743	+	5.37740i	−1.04732	+	0.381194i	−0.239670	+	0.970854i	$0.577039\pi$
$200$		0			0
$201$	−1.19277	−	2.06593i	−0.0841312	−	0.145720i
$202$	4.39534	+	2.53765i	0.309255	+	0.178549i
$203$	18.5488	+	3.27065i	1.30187	+	0.229555i
$204$	0.382572	−	0.321016i	0.0267854	−	0.0224756i
$205$		0			0
$206$	3.04194	+	17.2517i	0.211942	+	1.20198i
$207$	−2.20599	+	6.06090i	−0.153327	+	0.421262i
$208$			10.2927i			0.713668i
$209$	12.1617	+	1.97069i	0.841243	+	0.136316i
$210$		0			0
$211$	8.72857	+	3.17694i	0.600899	+	0.218709i	0.624517	−	0.781012i	$-0.285296\pi$
$211$	8.72857	+	3.17694i	0.600899	+	0.218709i	−0.0236172	+	0.999721i	$0.507518\pi$
$212$	4.22720	−	0.745369i	0.290325	−	0.0511922i
$213$	−11.4374	+	13.6306i	−0.783678	+	0.933951i
$214$	−5.65337	+	4.74374i	−0.386457	+	0.324276i
$215$		0			0
$216$	2.90899	−	5.03851i	0.197932	−	0.342827i
$217$	8.92603	−	5.15344i	0.605938	−	0.349839i
$218$	−0.307877	−	0.845885i	−0.0208521	−	0.0572906i
$219$	−30.0966	+	10.9543i	−2.03374	+	0.740221i
$220$		0			0
$221$	−0.780797	+	1.35238i	−0.0525221	+	0.0909710i
$222$	28.7879	+	5.07609i	1.93212	+	0.340685i
$223$	1.79399	+	2.13799i	0.120134	+	0.143170i	0.822759	−	0.568390i	$-0.192433\pi$
$223$	1.79399	+	2.13799i	0.120134	+	0.143170i	−0.702625	+	0.711560i	$0.747989\pi$
$224$	−5.27685	−	4.42781i	−0.352575	−	0.295845i
$225$		0			0
$226$	0.976201	+	0.355308i	0.0649359	+	0.0236347i
$227$		−	0.844086i		−	0.0560240i	−0.999608	−	0.0280120i	$-0.991082\pi$
$227$		−	0.844086i		−	0.0560240i	0.999608	−	0.0280120i	$-0.00891766\pi$
$228$	5.31862	−	2.01990i	0.352235	−	0.133771i
$229$	−21.9559			−1.45089			−0.725444	−	0.688282i	$-0.758365\pi$
$229$	−21.9559			−1.45089			−0.725444	+	0.688282i	$0.758365\pi$
$230$		0			0
$231$	2.45064	+	13.8982i	0.161240	+	0.914438i
$232$	−16.9423	+	20.1911i	−1.11232	+	1.32561i
$233$	2.83819	+	3.38242i	0.185936	+	0.221590i	0.850958	−	0.525234i	$-0.176022\pi$
$233$	2.83819	+	3.38242i	0.185936	+	0.221590i	−0.665022	+	0.746824i	$0.731578\pi$
$234$	1.83408	−	10.4016i	0.119898	−	0.679974i
$235$		0			0
$236$	−3.72606	−	6.45373i	−0.242546	−	0.420102i
$237$	10.4480	+	28.7056i	0.678670	+	1.86463i
$238$	0.343236	+	0.943034i	0.0222487	+	0.0611278i
$239$	9.91358	+	17.1708i	0.641256	+	1.11069i	0.985153	+	0.171681i	$0.0549198\pi$
$239$	9.91358	+	17.1708i	0.641256	+	1.11069i	−0.343896	+	0.939008i	$0.611747\pi$
$240$		0			0
$241$	−3.62651	+	20.5670i	−0.233604	+	1.32484i	0.611929	+	0.790913i	$0.290394\pi$
$241$	−3.62651	+	20.5670i	−0.233604	+	1.32484i	−0.845533	+	0.533923i	$0.820717\pi$
$242$	2.31107	+	2.75423i	0.148561	+	0.177049i
$243$	−12.1375	+	14.4649i	−0.778620	+	0.927923i
$244$	0.595830	+	3.37912i	0.0381441	+	0.216326i
$245$		0			0
$246$	−8.51040			−0.542603
$247$	−13.4675	+	11.6231i	−0.856915	+	0.739558i
$248$			14.4235i			0.915891i
$249$	−11.8684	−	4.31974i	−0.752129	−	0.273753i
$250$		0			0
$251$	4.25499	+	3.57036i	0.268573	+	0.225359i	0.767121	−	0.641503i	$-0.221689\pi$
$251$	4.25499	+	3.57036i	0.268573	+	0.225359i	−0.498548	+	0.866862i	$0.666133\pi$
$252$	1.75699	+	2.09390i	0.110680	+	0.131904i
$253$	−8.28364	−	1.46063i	−0.520788	−	0.0918290i
$254$	2.05645	−	3.56188i	0.129033	−	0.223492i
$255$		0			0
$256$	11.7798	−	4.28750i	0.736237	−	0.267969i
$257$	−6.88036	−	18.9036i	−0.429185	−	1.17918i	−0.946308	−	0.323266i	$-0.895219\pi$
$257$	−6.88036	−	18.9036i	−0.429185	−	1.17918i	0.517123	−	0.855911i	$-0.327003\pi$
$258$	4.72260	−	2.72659i	0.294016	−	0.169750i
$259$	11.8275	−	20.4858i	0.734924	−	1.27293i
$260$		0			0
$261$	14.2369	−	11.9462i	0.881242	−	0.739450i
$262$	7.90623	−	9.42228i	0.488448	−	0.582110i
$263$	11.5304	−	2.03312i	0.710995	−	0.125368i	0.193558	−	0.981089i	$-0.437997\pi$
$263$	11.5304	−	2.03312i	0.710995	−	0.125368i	0.517437	+	0.855721i	$0.326886\pi$
$264$	−18.5582	−	6.75464i	−1.14218	−	0.415719i
$265$		0			0
$266$	0.158773	+	11.4313i	0.00973499	+	0.700900i
$267$		−	14.9213i		−	0.913169i
$268$	0.206086	−	0.566218i	0.0125887	−	0.0345873i
$269$	2.23756	+	12.6898i	0.136426	+	0.773712i	0.973856	+	0.227167i	$0.0729463\pi$
$269$	2.23756	+	12.6898i	0.136426	+	0.773712i	−0.837429	+	0.546545i	$0.815943\pi$
$270$		0			0
$271$	−11.8097	+	9.90953i	−0.717389	+	0.601961i	−0.926662	−	0.375896i	$-0.877335\pi$
$271$	−11.8097	+	9.90953i	−0.717389	+	0.601961i	0.209273	+	0.977857i	$0.432890\pi$
$272$	−0.950321	−	0.167567i	−0.0576217	−	0.0101603i
$273$	−17.6475	−	10.1888i	−1.06807	−	0.616652i
$274$	−0.876407	−	1.51798i	−0.0529457	−	0.0917046i
$275$		0			0
$276$	−3.64997	+	1.32848i	−0.219703	+	0.0799652i
$277$	4.58742	−	2.64855i	0.275632	−	0.159136i	−0.355813	−	0.934557i	$-0.615796\pi$
$277$	4.58742	−	2.64855i	0.275632	−	0.159136i	0.631444	+	0.775421i	$0.282463\pi$
$278$	7.57750	+	4.37487i	0.454468	+	0.262387i
$279$	1.76602	−	10.0156i	0.105729	−	0.599618i
$280$		0			0
$281$	−4.12384	−	3.46031i	−0.246008	−	0.206425i	0.511443	−	0.859317i	$-0.329111\pi$
$281$	−4.12384	−	3.46031i	−0.246008	−	0.206425i	−0.757451	+	0.652892i	$0.773555\pi$
$282$	−29.1307	+	5.13653i	−1.73471	+	0.305876i
$283$	−6.04576	+	16.6106i	−0.359383	+	0.987397i	0.619861	+	0.784712i	$0.287189\pi$
$283$	−6.04576	+	16.6106i	−0.359383	+	0.987397i	−0.979244	+	0.202685i	$0.935033\pi$
$284$	−4.49441			−0.266694
$285$		0			0
$286$	13.7742			0.814487
$287$	−2.35540	+	6.47141i	−0.139035	+	0.381995i
$288$	−6.69377	+	1.18029i	−0.394434	+	0.0695494i
$289$	12.9106	+	10.8333i	0.759447	+	0.637252i
$290$		0			0
$291$	5.70242	−	32.3400i	0.334282	−	1.89581i
$292$	−7.00608	−	4.04496i	−0.410000	−	0.236714i
$293$	−4.07939	+	2.35524i	−0.238320	+	0.137594i	−0.614405	−	0.788991i	$-0.710604\pi$
$293$	−4.07939	+	2.35524i	−0.238320	+	0.137594i	0.376084	+	0.926586i	$0.377270\pi$
$294$	5.54878	−	2.01959i	0.323611	−	0.117785i
$295$		0			0
$296$	16.5514	+	28.6678i	0.962029	+	1.66628i
$297$	−4.63316	−	2.67495i	−0.268843	−	0.155217i
$298$	11.7498	+	2.07181i	0.680648	+	0.120017i
$299$	9.30394	−	7.80693i	0.538061	−	0.451486i
$300$		0			0
$301$	−0.766273	−	4.34575i	−0.0441673	−	0.250485i
$302$	−6.15411	+	16.9083i	−0.354129	+	0.972962i
$303$		−	9.66191i		−	0.555062i
$304$	−9.59563	−	5.36375i	−0.550347	−	0.307632i
$305$		0			0
$306$	0.930520	+	0.338681i	0.0531943	+	0.0193611i
$307$	−11.6265	+	2.05006i	−0.663557	+	0.117003i	−0.495275	−	0.868736i	$-0.664933\pi$
$307$	−11.6265	+	2.05006i	−0.663557	+	0.117003i	−0.168281	+	0.985739i	$0.553822\pi$
$308$	−2.29134	+	2.73071i	−0.130561	+	0.155596i
$309$	25.5467	−	21.4362i	1.45330	−	1.21946i
$310$		0			0
$311$	4.47006	−	7.74236i	0.253474	−	0.439029i	−0.711006	−	0.703186i	$-0.751760\pi$
$311$	4.47006	−	7.74236i	0.253474	−	0.439029i	0.964480	+	0.264157i	$0.0850936\pi$
$312$	24.6959	−	14.2582i	1.39813	−	0.807209i
$313$	−4.59349	−	12.6205i	−0.259639	−	0.713353i	−0.999190	−	0.0402519i	$-0.987184\pi$
$313$	−4.59349	−	12.6205i	−0.259639	−	0.713353i	0.739550	−	0.673101i	$-0.235038\pi$
$314$	−11.6073	+	4.22470i	−0.655036	+	0.238414i
$315$		0			0
$316$	−3.85801	+	6.68227i	−0.217030	+	0.375907i
$317$	−10.8896	−	1.92013i	−0.611622	−	0.107845i	−0.140747	−	0.990046i	$-0.544951\pi$
$317$	−10.8896	−	1.92013i	−0.611622	−	0.107845i	−0.470875	+	0.882200i	$0.656062\pi$
$318$	13.0433	+	15.5445i	0.731435	+	0.871690i
$319$	18.5667	+	15.5793i	1.03953	+	0.872273i
$320$		0			0
$321$	13.2020	+	4.80514i	0.736865	+	0.268197i
$322$		−	7.80524i		−	0.434969i
$323$	−0.853903	−	1.43268i	−0.0475124	−	0.0797163i
$324$	−6.20379			−0.344655
$325$		0			0
$326$	1.43073	+	8.11408i	0.0792408	+	0.449397i
$327$	−1.10152	+	1.31275i	−0.0609144	+	0.0725950i
$328$	−6.19473	−	7.38259i	−0.342047	−	0.407635i
$329$	−4.15655	+	23.5730i	−0.229158	+	1.29962i
$330$		0			0
$331$	1.42273	+	2.46424i	0.0782003	+	0.135447i	0.902473	−	0.430745i	$-0.141749\pi$
$331$	1.42273	+	2.46424i	0.0782003	+	0.135447i	−0.824273	+	0.566192i	$0.808416\pi$
$332$	−1.09111	−	2.99781i	−0.0598827	−	0.164526i
$333$	−7.98310	−	21.9334i	−0.437471	−	1.20194i
$334$	−7.08209	−	12.2665i	−0.387515	−	0.671195i
$335$		0			0
$336$	2.18661	−	12.4009i	0.119290	−	0.676525i
$337$	4.11760	+	4.90717i	0.224300	+	0.267311i	0.866445	−	0.499273i	$-0.166400\pi$
$337$	4.11760	+	4.90717i	0.224300	+	0.267311i	−0.642145	+	0.766584i	$0.721955\pi$
$338$	−2.80632	+	3.34444i	−0.152643	+	0.181913i
$339$	−0.343419	−	1.94763i	−0.0186520	−	0.105781i
$340$		0			0
$341$	13.2631			0.718235
$342$	8.74140	+	7.13040i	0.472681	+	0.385568i
$343$		−	20.1537i		−	1.08820i
$344$	5.80285	+	2.11206i	0.312869	+	0.113875i
$345$		0			0
$346$	−23.2398	−	19.5005i	−1.24938	−	1.04835i
$347$	10.1579	+	12.1057i	0.545305	+	0.649869i	0.966368	−	0.257162i	$-0.0827875\pi$
$347$	10.1579	+	12.1057i	0.545305	+	0.649869i	−0.421063	+	0.907031i	$0.638343\pi$
$348$	11.0221	+	1.94350i	0.590848	+	0.104182i
$349$	−13.7825	+	23.8721i	−0.737763	+	1.27784i	0.215738	+	0.976451i	$0.430784\pi$
$349$	−13.7825	+	23.8721i	−0.737763	+	1.27784i	−0.953501	+	0.301391i	$0.902549\pi$
$350$		0			0
$351$	7.25897	−	2.64205i	0.387455	−	0.141022i
$352$	−3.03172	−	8.32959i	−0.161591	−	0.443968i
$353$	3.66228	−	2.11442i	0.194924	−	0.112539i	−0.399362	−	0.916793i	$-0.630768\pi$
$353$	3.66228	−	2.11442i	0.194924	−	0.112539i	0.594285	+	0.804254i	$0.297435\pi$
$354$	17.6145	−	30.5092i	0.936200	−	1.62155i
$355$		0			0
$356$	2.88718	−	2.42263i	0.153020	−	0.128399i
$357$	1.22803	−	1.46351i	0.0649944	−	0.0774573i
$358$	0.457204	−	0.0806174i	0.0241640	−	0.00426076i
$359$	5.38553	+	1.96017i	0.284237	+	0.103454i	0.480205	−	0.877157i	$-0.340562\pi$
$359$	5.38553	+	1.96017i	0.284237	+	0.103454i	−0.195967	+	0.980610i	$0.562785\pi$
$360$		0			0
$361$	−3.81772	−	18.6125i	−0.200932	−	0.979605i
$362$		−	5.71231i		−	0.300232i
$363$	2.34099	−	6.43180i	0.122870	−	0.337582i
$364$	−0.893788	−	5.06892i	−0.0468472	−	0.265684i
$365$		0			0
$366$	−12.4259	+	10.4265i	−0.649510	+	0.545004i
$367$	−0.931253	−	0.164205i	−0.0486110	−	0.00857143i	0.149290	−	0.988793i	$-0.452301\pi$
$367$	−0.931253	−	0.164205i	−0.0486110	−	0.00857143i	−0.197901	+	0.980222i	$0.563412\pi$
$368$	6.49971	+	3.75261i	0.338821	+	0.195618i
$369$	3.39767	+	5.88493i	0.176876	+	0.306357i
$370$		0			0
$371$	15.4302	−	5.61612i	0.801094	−	0.291574i
$372$	5.30406	−	3.06230i	0.275003	−	0.158773i
$373$	0.583094	+	0.336649i	0.0301915	+	0.0174310i	0.515020	−	0.857178i	$-0.327785\pi$
$373$	0.583094	+	0.336649i	0.0301915	+	0.0174310i	−0.484828	+	0.874609i	$0.661118\pi$
$374$	−0.224248	+	1.27177i	−0.0115956	+	0.0657618i
$375$		0			0
$376$	−25.6601	−	21.5314i	−1.32332	−	1.11040i
$377$	−34.4647	+	6.07706i	−1.77502	+	0.312984i
$378$	1.69791	−	4.66497i	0.0873310	−	0.239940i
$379$	34.7701			1.78602			0.893010	−	0.450037i	$-0.148589\pi$
$379$	34.7701			1.78602			0.893010	+	0.450037i	$0.148589\pi$
$380$		0			0
$381$	−7.82977			−0.401131
$382$	9.74097	−	26.7631i	0.498392	−	1.36932i
$383$	26.8426	−	4.73308i	1.37159	−	0.241849i	0.561174	−	0.827698i	$-0.310350\pi$
$383$	26.8426	−	4.73308i	1.37159	−	0.241849i	0.810420	+	0.585849i	$0.199239\pi$
$384$	7.35229	+	6.16930i	0.375195	+	0.314826i
$385$		0			0
$386$	2.32770	−	13.2010i	0.118477	−	0.671916i
$387$	−3.77088	−	2.17712i	−0.191684	−	0.110669i
$388$	7.18343	−	4.14736i	0.364684	−	0.210550i
$389$	34.2998	−	12.4841i	1.73907	−	0.632969i	0.739860	−	0.672761i	$-0.234892\pi$
$389$	34.2998	−	12.4841i	1.73907	−	0.632969i	0.999208	+	0.0397915i	$0.0126694\pi$
$390$		0			0
$391$	0.569343	+	0.986131i	0.0287929	+	0.0498708i
$392$	5.79091	+	3.34338i	0.292485	+	0.168866i
$393$	−23.0597	−	4.06605i	−1.16321	−	0.205105i
$394$	−15.4338	+	12.9505i	−0.777544	+	0.652437i
$395$		0			0
$396$	0.610786	+	3.46394i	0.0306932	+	0.174070i
$397$	−4.73209	+	13.0013i	−0.237497	+	0.652517i	0.762488	+	0.647002i	$0.223978\pi$
$397$	−4.73209	+	13.0013i	−0.237497	+	0.652517i	−0.999985	+	0.00551465i	$0.998245\pi$
$398$		−	18.7739i		−	0.941048i
$399$	18.6953	−	11.1427i	0.935934	−	0.557835i
$400$		0			0
$401$	−22.8095	−	8.30199i	−1.13905	−	0.414582i	−0.297482	−	0.954727i	$-0.596147\pi$
$401$	−22.8095	−	8.30199i	−1.13905	−	0.414582i	−0.841572	+	0.540145i	$0.818369\pi$
$402$	2.80524	−	0.494639i	0.139912	−	0.0246703i
$403$	−12.3099	+	14.6704i	−0.613200	+	0.730783i
$404$	1.86952	−	1.56871i	0.0930120	−	0.0780463i
$405$		0			0
$406$	−11.2452	+	19.4772i	−0.558089	+	0.966638i
$407$	26.3614	−	15.2198i	1.30669	−	0.754417i
$408$	0.914400	+	2.51229i	0.0452695	+	0.124377i
$409$	−31.8875	+	11.6061i	−1.57674	+	0.573885i	−0.974491	−	0.224426i	$-0.927949\pi$
$409$	−31.8875	+	11.6061i	−1.57674	+	0.573885i	−0.602245	+	0.798311i	$0.705727\pi$
$410$		0			0
$411$	−1.66842	+	2.88980i	−0.0822973	+	0.142543i
$412$	8.29554	+	1.46273i	0.408692	+	0.0720634i
$413$	−18.3244	−	21.8382i	−0.901686	−	1.07459i
$414$	−5.89981	−	4.95053i	−0.289960	−	0.243305i
$415$		0			0
$416$	12.0272	+	4.37756i	0.589684	+	0.214628i
$417$		−	16.6570i		−	0.815696i
$418$	−7.17807	+	12.8414i	−0.351091	+	0.628094i
$419$	−21.4325			−1.04705			−0.523523	−	0.852012i	$-0.675382\pi$
$419$	−21.4325			−1.04705			−0.523523	+	0.852012i	$0.675382\pi$
$420$		0			0
$421$	−1.27528	−	7.23247i	−0.0621533	−	0.352489i	−0.999985	−	0.00539967i	$-0.998281\pi$
$421$	−1.27528	−	7.23247i	−0.0621533	−	0.352489i	0.937832	−	0.347089i	$-0.112830\pi$
$422$	−7.12947	+	8.49657i	−0.347057	+	0.413607i
$423$	15.1820	+	18.0932i	0.738173	+	0.879720i
$424$	−3.99022	+	22.6297i	−0.193782	+	1.09899i
$425$		0			0
$426$	−10.6234	−	18.4002i	−0.514704	−	0.891494i
$427$	4.48939	+	12.3345i	0.217257	+	0.596908i
$428$	1.21372	+	3.33467i	0.0586674	+	0.161187i
$429$	−13.1111	−	22.7090i	−0.633008	−	1.09640i
$430$		0			0
$431$	0.0219443	−	0.124452i	0.00105702	−	0.00599466i	−0.984275	−	0.176645i	$-0.943476\pi$
$431$	0.0219443	−	0.124452i	0.00105702	−	0.00599466i	0.985332	+	0.170650i	$0.0545868\pi$
$432$	3.06837	+	3.65674i	0.147627	+	0.175935i
$433$	3.73982	−	4.45694i	0.179724	−	0.214187i	−0.668660	−	0.743569i	$-0.733132\pi$
$433$	3.73982	−	4.45694i	0.179724	−	0.214187i	0.848384	+	0.529382i	$0.177576\pi$
$434$	2.13713	+	12.1203i	0.102585	+	0.581791i
$435$		0			0
$436$	−0.432852			−0.0207298
$437$	2.42973	+	12.7422i	0.116230	+	0.609544i
$438$		−	38.2441i		−	1.82738i
$439$	17.3872	+	6.32841i	0.829844	+	0.302039i	0.721795	−	0.692107i	$-0.243317\pi$
$439$	17.3872	+	6.32841i	0.829844	+	0.302039i	0.108049	+	0.994146i	$0.465540\pi$
$440$		0			0
$441$	−3.61182	−	3.03068i	−0.171992	−	0.144318i
$442$	−1.19858	−	1.42842i	−0.0570108	−	0.0679429i
$443$	−21.7891	−	3.84201i	−1.03523	−	0.182539i	−0.369889	−	0.929076i	$-0.620604\pi$
$443$	−21.7891	−	3.84201i	−1.03523	−	0.182539i	−0.665344	+	0.746537i	$0.731715\pi$
$444$	7.02817	−	12.1732i	0.333542	−	0.577712i
$445$		0			0
$446$	−3.13163	+	1.13982i	−0.148287	+	0.0539720i
$447$	−7.76840	−	21.3435i	−0.367433	−	1.00951i
$448$	16.7180	−	9.65214i	0.789851	−	0.456021i
$449$	−10.2840	+	17.8124i	−0.485331	+	0.840617i	−0.999858	−	0.0168567i	$-0.994634\pi$
$449$	−10.2840	+	17.8124i	−0.485331	+	0.840617i	0.514527	+	0.857474i	$0.327967\pi$
$450$		0			0
$451$	−6.78865	+	5.69635i	−0.319665	+	0.268231i
$452$	0.321096	−	0.382667i	0.0151031	−	0.0179991i
$453$	33.7339	−	5.94819i	1.58495	−	0.279470i
$454$	0.947121	+	0.344724i	0.0444506	+	0.0161787i
$455$		0			0
$456$	0.422979	+	30.4537i	0.0198078	+	1.42612i
$457$			20.3583i			0.952323i	0.879358	+	0.476161i	$0.157972\pi$
$457$			20.3583i			0.952323i	−0.879358	+	0.476161i	$0.842028\pi$
$458$	8.96676	−	24.6360i	0.418989	−	1.15116i
$459$	0.125762	+	0.713233i	0.00587008	+	0.0332909i
$460$		0			0
$461$	−4.24592	+	3.56275i	−0.197752	+	0.165934i	−0.736287	−	0.676670i	$-0.763423\pi$
$461$	−4.24592	+	3.56275i	−0.197752	+	0.165934i	0.538535	+	0.842603i	$0.318978\pi$
$462$	−16.5956	−	2.92625i	−0.772097	−	0.136142i
$463$	28.2757	+	16.3250i	1.31408	+	0.758686i	0.982770	−	0.184835i	$-0.0591751\pi$
$463$	28.2757	+	16.3250i	1.31408	+	0.758686i	0.331313	+	0.943521i	$0.392508\pi$
$464$	−10.8129	−	18.7286i	−0.501978	−	0.869451i
$465$		0			0
$466$	−4.95442	+	1.80326i	−0.229509	+	0.0835344i
$467$	24.8214	−	14.3306i	1.14860	−	0.663142i	0.200051	−	0.979785i	$-0.435889\pi$
$467$	24.8214	−	14.3306i	1.14860	−	0.663142i	0.948545	+	0.316643i	$0.102556\pi$
$468$	−4.39838	−	2.53941i	−0.203315	−	0.117384i
$469$	0.400268	−	2.27003i	0.0184827	−	0.104820i
$470$		0			0
$471$	18.0135	+	15.1152i	0.830020	+	0.696469i
$472$	39.2877	−	6.92748i	1.80836	−	0.318863i
$473$	1.94214	−	5.33600i	0.0892999	−	0.245350i
$474$	−36.4766			−1.67542
$475$		0			0
$476$	0.482564			0.0221183
$477$	5.54159	−	15.2254i	0.253732	−	0.697123i
$478$	−23.3155	+	4.11115i	−1.06643	+	0.188040i
$479$	−7.86922	−	6.60306i	−0.359554	−	0.301701i	0.445059	−	0.895501i	$-0.353183\pi$
$479$	−7.86922	−	6.60306i	−0.359554	−	0.301701i	−0.804613	+	0.593800i	$0.797627\pi$
$480$		0			0
$481$	−7.63223	+	43.2846i	−0.348000	+	1.97361i
$482$	−21.5964	−	12.4687i	−0.983691	−	0.567934i
$483$	−12.8682	+	7.42946i	−0.585523	+	0.338052i
$484$	1.62460	−	0.591304i	0.0738453	−	0.0268775i
$485$		0			0
$486$	−11.2736	−	19.5265i	−0.511382	−	0.885740i
$487$	−9.63406	−	5.56223i	−0.436561	−	0.252049i	0.265577	−	0.964090i	$-0.414438\pi$
$487$	−9.63406	−	5.56223i	−0.436561	−	0.252049i	−0.702138	+	0.712041i	$0.747771\pi$
$488$	−18.0896	−	3.18968i	−0.818878	−	0.144390i
$489$	12.0155	−	10.0822i	0.543360	−	0.455934i
$490$		0			0
$491$	2.41105	+	13.6738i	0.108809	+	0.617089i	0.989630	+	0.143639i	$0.0458804\pi$
$491$	2.41105	+	13.6738i	0.108809	+	0.617089i	−0.880821	+	0.473450i	$0.843009\pi$
$492$	−1.39964	+	3.84547i	−0.0631004	+	0.173367i
$493$		−	3.28106i		−	0.147771i
$494$	−7.54176	−	19.8583i	−0.339320	−	0.893465i
$495$		0			0
$496$	−11.1205	−	4.04752i	−0.499324	−	0.181739i
$497$	−16.9320	+	2.98556i	−0.759502	+	0.133921i
$498$	9.69408	−	11.5530i	0.434402	−	0.517700i
$499$	−9.79608	+	8.21989i	−0.438533	+	0.367973i	−0.835160	−	0.550007i	$-0.814625\pi$
$499$	−9.79608	+	8.21989i	−0.438533	+	0.367973i	0.396627	+	0.917980i	$0.370181\pi$
$500$		0			0
$501$	−13.4822	+	23.3519i	−0.602342	+	1.04329i
$502$	−5.74392	+	3.31625i	−0.256364	+	0.148012i
$503$	3.57906	+	9.83338i	0.159582	+	0.438449i	0.993554	−	0.113358i	$-0.0361608\pi$
$503$	3.57906	+	9.83338i	0.159582	+	0.438449i	−0.833972	+	0.551807i	$0.813939\pi$
$504$	−13.7503	+	5.00472i	−0.612489	+	0.222928i
$505$		0			0
$506$	5.02195	−	8.69828i	0.223253	−	0.386686i
$507$	8.18505	+	1.44324i	0.363511	+	0.0640968i
$508$	−1.27124	−	1.51501i	−0.0564024	−	0.0672177i
$509$	−21.4000	−	17.9567i	−0.948539	−	0.795919i	0.0305117	−	0.999534i	$-0.490286\pi$
$509$	−21.4000	−	17.9567i	−0.948539	−	0.795919i	−0.979051	+	0.203616i	$0.934731\pi$
$510$		0			0
$511$	−29.0813	−	10.5847i	−1.28648	−	0.468241i
$512$			23.4130i			1.03472i
$513$	−1.31970	+	8.14422i	−0.0582660	+	0.359576i
$514$	24.0211			1.05952
$515$		0			0
$516$	−0.455338	−	2.58235i	−0.0200451	−	0.113682i
$517$	−19.7992	+	23.5957i	−0.870766	+	1.03774i
$518$	18.1561	+	21.6376i	0.797733	+	0.950701i
$519$	−10.0288	+	56.8762i	−0.440216	+	2.49659i
$520$		0			0
$521$	4.03138	+	6.98256i	0.176618	+	0.305912i	0.940720	−	0.339184i	$-0.110151\pi$
$521$	4.03138	+	6.98256i	0.176618	+	0.305912i	−0.764102	+	0.645095i	$0.776818\pi$
$522$	7.59008	+	20.8536i	0.332209	+	0.912736i
$523$	−3.94751	−	10.8457i	−0.172612	−	0.474249i	0.822976	−	0.568076i	$-0.192312\pi$
$523$	−3.94751	−	10.8457i	−0.172612	−	0.474249i	−0.995588	+	0.0938274i	$0.970090\pi$
$524$	−2.95723	−	5.12207i	−0.129187	−	0.223759i
$525$		0			0
$526$	−2.42771	+	13.7682i	−0.105853	+	0.600322i
$527$	−1.15411	−	1.37541i	−0.0502736	−	0.0599138i
$528$	10.4156	−	12.4129i	0.453283	−	0.540201i
$529$	2.45604	+	13.9289i	0.106784	+	0.605605i
$530$		0			0
$531$	−28.1294			−1.22071
$532$	5.19142	+	1.80828i	0.225077	+	0.0783987i
$533$		−	12.7959i		−	0.554254i
$534$	16.7427	+	6.09385i	0.724528	+	0.263706i
$535$		0			0
$536$	2.47102	+	2.07343i	0.106732	+	0.0895587i
$537$	−0.568103	−	0.677038i	−0.0245154	−	0.0292164i
$538$	−15.1526	−	2.67182i	−0.653277	−	0.115190i
$539$	3.07440	−	5.32502i	0.132424	−	0.229365i
$540$		0			0
$541$	−32.1819	+	11.7133i	−1.38361	+	0.503593i	−0.923270	−	0.384151i	$-0.874494\pi$
$541$	−32.1819	+	11.7133i	−1.38361	+	0.503593i	−0.460339	+	0.887743i	$0.652272\pi$
$542$	−6.29608	−	17.2983i	−0.270440	−	0.743027i
$543$	−9.41766	+	5.43729i	−0.404150	+	0.233336i
$544$	−0.599987	+	1.03921i	−0.0257242	+	0.0445556i
$545$		0			0
$546$	18.6397	−	15.6405i	0.797704	−	0.669353i
$547$	17.8017	−	21.2152i	0.761146	−	0.907098i	−0.236774	−	0.971565i	$-0.576090\pi$
$547$	17.8017	−	21.2152i	0.761146	−	0.907098i	0.997920	+	0.0644666i	$0.0205346\pi$
$548$	−0.830043	+	0.146359i	−0.0354577	+	0.00625214i
$549$	12.1708	+	4.42981i	0.519437	+	0.189060i
$550$		0			0
$551$	12.2949	−	35.2976i	0.523779	−	1.50373i
$552$		−	20.7936i		−	0.885033i
$553$	−10.0955	+	27.7372i	−0.429305	+	1.17951i
$554$	1.09835	+	6.22906i	0.0466645	+	0.264647i
$555$		0			0
$556$	3.22302	−	2.70443i	0.136686	−	0.114694i
$557$	13.4285	+	2.36781i	0.568985	+	0.100327i	0.450737	−	0.892657i	$-0.351161\pi$
$557$	13.4285	+	2.36781i	0.568985	+	0.100327i	0.118248	+	0.992984i	$0.462272\pi$
$558$	10.5169	+	6.07195i	0.445217	+	0.257046i
$559$	4.09961	+	7.10074i	0.173395	+	0.300329i
$560$		0			0
$561$	2.31017	−	0.840835i	0.0975356	−	0.0355001i
$562$	5.56687	−	3.21403i	0.234824	−	0.135576i
$563$	33.7910	+	19.5093i	1.42412	+	0.822217i	0.996648	−	0.0818108i	$-0.0260703\pi$
$563$	33.7910	+	19.5093i	1.42412	+	0.822217i	0.427474	+	0.904028i	$0.359404\pi$
$564$	−2.46992	+	14.0076i	−0.104003	+	0.589828i
$565$		0			0
$566$	−16.1691	−	13.5675i	−0.679638	−	0.570284i
$567$	−23.3718	+	4.12107i	−0.981522	+	0.173069i
$568$	8.22904	−	22.6091i	0.345283	−	0.948657i
$569$	−8.86810			−0.371770			−0.185885	−	0.982572i	$-0.559515\pi$
$569$	−8.86810			−0.371770			−0.185885	+	0.982572i	$0.559515\pi$
$570$		0			0
$571$	35.4054			1.48167			0.740834	−	0.671688i	$-0.234431\pi$
$571$	35.4054			1.48167			0.740834	+	0.671688i	$0.234431\pi$
$572$	2.26533	−	6.22395i	0.0947184	−	0.260237i
$573$	−53.3953	+	9.41503i	−2.23062	+	0.393319i
$574$	−6.29941	−	5.28583i	−0.262932	−	0.220626i
$575$		0			0
$576$	3.30767	−	18.7587i	0.137820	−	0.781613i
$577$	22.5238	+	13.0041i	0.937677	+	0.541368i	0.889231	−	0.457458i	$-0.151240\pi$
$577$	22.5238	+	13.0041i	0.937677	+	0.541368i	0.0484454	+	0.998826i	$0.484573\pi$
$578$	−17.4283	+	10.0623i	−0.724923	+	0.418535i
$579$	−23.9797	+	8.72790i	−0.996562	+	0.362719i
$580$		0			0
$581$	−6.10200	−	10.5690i	−0.253153	−	0.438475i
$582$	33.9588	+	19.6061i	1.40764	+	0.812700i
$583$	20.8091	+	3.66920i	0.861823	+	0.151963i
$584$	33.1760	−	27.8379i	1.37283	−	1.15194i
$585$		0			0
$586$	−0.976714	−	5.53922i	−0.0403477	−	0.228823i
$587$	3.60512	−	9.90499i	0.148799	−	0.408823i	−0.842791	−	0.538241i	$-0.819089\pi$
$587$	3.60512	−	9.90499i	0.148799	−	0.408823i	0.991590	+	0.129419i	$0.0413111\pi$
$588$		−	2.83939i		−	0.117094i
$589$	−7.26189	−	19.1213i	−0.299221	−	0.787880i
$590$		0			0
$591$	36.0417	+	13.1181i	1.48256	+	0.539607i
$592$	−26.7475	+	4.71631i	−1.09932	+	0.193839i
$593$	−8.50064	+	10.1307i	−0.349080	+	0.416017i	−0.911803	−	0.410629i	$-0.865309\pi$
$593$	−8.50064	+	10.1307i	−0.349080	+	0.416017i	0.562723	+	0.826645i	$0.309754\pi$
$594$	4.89365	−	4.10626i	0.200789	−	0.168482i
$595$		0			0
$596$	2.86855	−	4.96848i	0.117500	−	0.203517i
$597$	−30.9517	+	17.8700i	−1.26677	+	0.731370i
$598$	4.96018	+	13.6280i	0.202837	+	0.557289i
$599$	−3.49529	+	1.27218i	−0.142814	+	0.0519800i	−0.412438	−	0.910986i	$-0.635323\pi$
$599$	−3.49529	+	1.27218i	−0.142814	+	0.0519800i	0.269624	+	0.962966i	$0.413100\pi$
$600$		0			0
$601$	21.0672	−	36.4895i	0.859349	−	1.48844i	−0.0132009	−	0.999913i	$-0.504202\pi$
$601$	21.0672	−	36.4895i	0.859349	−	1.48844i	0.872550	−	0.488524i	$-0.162465\pi$
$602$	5.18917	+	0.914990i	0.211495	+	0.0372922i
$603$	−1.46200	−	1.74234i	−0.0595371	−	0.0709536i
$604$	6.62798	+	5.56153i	0.269689	+	0.226296i
$605$		0			0
$606$	10.8413	+	3.94591i	0.440398	+	0.160292i
$607$		−	27.1082i		−	1.10029i	−0.835070	−	0.550144i	$-0.814573\pi$
$607$		−	27.1082i		−	1.10029i	0.835070	−	0.550144i	$-0.185427\pi$
$608$	−10.3488	+	8.93149i	−0.419699	+	0.362220i
$609$	42.8151			1.73496
$610$		0			0
$611$	−7.72311	−	43.8000i	−0.312444	−	1.77196i
$612$	0.306070	−	0.364760i	0.0123721	−	0.0147445i
$613$	7.22977	+	8.61611i	0.292008	+	0.348001i	0.892025	−	0.451986i	$-0.149284\pi$
$613$	7.22977	+	8.61611i	0.292008	+	0.348001i	−0.600017	+	0.799987i	$0.704840\pi$
$614$	2.44793	−	13.8829i	0.0987904	−	0.560268i
$615$		0			0
$616$	−9.54149	−	16.5263i	−0.384438	−	0.665866i
$617$	−10.4849	−	28.8071i	−0.422108	−	1.15973i	−0.950498	−	0.310730i	$-0.899427\pi$
$617$	−10.4849	−	28.8071i	−0.422108	−	1.15973i	0.528391	−	0.849001i	$-0.322796\pi$
$618$	13.6196	+	37.4196i	0.547861	+	1.50524i
$619$	−20.1384	−	34.8807i	−0.809431	−	1.40198i	−0.913259	−	0.407380i	$-0.866442\pi$
$619$	−20.1384	−	34.8807i	−0.809431	−	1.40198i	0.103828	−	0.994595i	$-0.466891\pi$
$620$		0			0
$621$	0.978126	−	5.54723i	0.0392509	−	0.222603i
$622$	6.86188	+	8.17767i	0.275136	+	0.327895i
$623$	9.26766	−	11.0448i	0.371301	−	0.442499i
$624$	4.06286	+	23.0416i	0.162644	+	0.922403i
$625$		0			0
$626$	16.0370			0.640968
$627$	28.0036	−	0.388950i	1.11836	−	0.0155332i
$628$			5.93960i			0.237016i
$629$	−3.87220	−	1.40937i	−0.154395	−	0.0561951i
$630$		0			0
$631$	29.6279	+	24.8608i	1.17947	+	0.989692i	0.999982	+	0.00593154i	$0.00188808\pi$
$631$	29.6279	+	24.8608i	1.17947	+	0.989692i	0.179487	+	0.983760i	$0.442556\pi$
$632$	−26.5513	−	31.6426i	−1.05616	−	1.25868i
$633$	20.7942	+	3.66658i	0.826495	+	0.145733i
$634$	6.60183	−	11.4347i	0.262192	−	0.454130i
$635$		0			0
$636$	9.16897	−	3.33723i	0.363573	−	0.132330i
$637$	3.03658	+	8.34295i	0.120314	+	0.330560i
$638$	−25.0636	+	14.4705i	−0.992278	+	0.572892i
$639$	−8.48250	+	14.6921i	−0.335562	+	0.581211i
$640$		0			0
$641$	−33.0725	+	27.7511i	−1.30628	+	1.09610i	−0.317261	+	0.948338i	$0.602763\pi$
$641$	−33.0725	+	27.7511i	−1.30628	+	1.09610i	−0.989023	+	0.147764i	$0.952792\pi$
$642$	−10.7834	+	12.8511i	−0.425586	+	0.507193i
$643$	4.31238	−	0.760389i	0.170064	−	0.0299868i	−0.0879678	−	0.996123i	$-0.528037\pi$
$643$	4.31238	−	0.760389i	0.170064	−	0.0299868i	0.258032	+	0.966137i	$0.416926\pi$
$644$	−3.52684	−	1.28366i	−0.138977	−	0.0505834i
$645$		0			0
$646$	1.95629	−	0.373032i	0.0769693	−	0.0146768i
$647$		−	16.4916i		−	0.648351i	−0.945997	−	0.324176i	$-0.894913\pi$
$647$		−	16.4916i		−	0.648351i	0.945997	−	0.324176i	$-0.105087\pi$
$648$	11.3588	−	31.2081i	0.446217	−	1.22597i
$649$	−6.37015	−	36.1269i	−0.250050	−	1.41811i
$650$		0			0
$651$	17.9480	−	15.0601i	0.703436	−	0.590253i
$652$	3.90169	+	0.687973i	0.152802	+	0.0269431i
$653$	1.40826	+	0.813059i	0.0551095	+	0.0318175i	0.527302	−	0.849678i	$-0.323204\pi$
$653$	1.40826	+	0.813059i	0.0551095	+	0.0318175i	−0.472192	+	0.881496i	$0.656537\pi$
$654$	−1.02313	−	1.77211i	−0.0400074	−	0.0692949i
$655$		0			0
$656$	7.43034	−	2.70442i	0.290106	−	0.105590i
$657$	−26.4458	+	15.2685i	−1.03175	+	0.595680i
$658$	−24.7529	−	14.2911i	−0.964969	−	0.557125i
$659$	0.331134	−	1.87796i	0.0128992	−	0.0731548i	−0.977679	−	0.210106i	$-0.932619\pi$
$659$	0.331134	−	1.87796i	0.0128992	−	0.0731548i	0.990578	+	0.136951i	$0.0437303\pi$
$660$		0			0
$661$	5.07136	+	4.25538i	0.197253	+	0.165515i	0.736064	−	0.676911i	$-0.236682\pi$
$661$	5.07136	+	4.25538i	0.197253	+	0.165515i	−0.538811	+	0.842426i	$0.681126\pi$
$662$	−3.34608	+	0.590004i	−0.130049	+	0.0229312i
$663$	−1.21410	+	3.33571i	−0.0471516	+	0.129548i
$664$	17.0783			0.662765
$665$		0			0
$666$	27.8710			1.07998
$667$	−8.72791	+	23.9797i	−0.337946	+	0.928499i
$668$	−6.70743	+	1.18270i	−0.259518	+	0.0457601i
$669$	4.86003	+	4.07805i	0.187900	+	0.157667i
$670$		0			0
$671$	−2.93307	+	16.6343i	−0.113230	+	0.642158i
$672$	−13.5608	−	7.82933i	−0.523119	−	0.302023i
$673$	10.7785	−	6.22298i	0.415482	−	0.239878i	−0.277661	−	0.960679i	$-0.589559\pi$
$673$	10.7785	−	6.22298i	0.415482	−	0.239878i	0.693142	+	0.720801i	$0.256226\pi$
$674$	−7.18779	+	2.61614i	−0.276864	+	0.100770i
$675$		0			0
$676$	1.04967	+	1.81808i	0.0403719	+	0.0699261i
$677$	−4.07556	−	2.35303i	−0.156637	−	0.0904342i	0.419633	−	0.907694i	$-0.362159\pi$
$677$	−4.07556	−	2.35303i	−0.156637	−	0.0904342i	−0.576270	+	0.817260i	$0.695492\pi$
$678$	2.32562	+	0.410069i	0.0893149	+	0.0157486i
$679$	24.3074	−	20.3963i	0.932833	−	0.782739i
$680$		0			0
$681$	−0.333189	−	1.88961i	−0.0127678	−	0.0724100i
$682$	−5.41662	+	14.8820i	−0.207413	+	0.569863i
$683$		−	17.6914i		−	0.676942i	−0.940977	−	0.338471i	$-0.890090\pi$
$683$		−	17.6914i		−	0.676942i	0.940977	−	0.338471i	$-0.109910\pi$
$684$	4.65953	−	2.77717i	0.178162	−	0.106188i
$685$		0			0
$686$	22.6138	+	8.23076i	0.863400	+	0.314252i
$687$	−49.1515	+	8.66673i	−1.87524	+	0.330656i
$688$	−3.25680	+	3.88130i	−0.124164	+	0.147973i
$689$	−23.3721	+	19.6115i	−0.890406	+	0.747140i
$690$		0			0
$691$	−13.0639	+	22.6273i	−0.496974	+	0.860784i	−0.999994	−	0.00349090i	$-0.998889\pi$
$691$	−13.0639	+	22.6273i	−0.496974	+	0.860784i	0.503020	+	0.864275i	$0.332222\pi$
$692$	−12.6335	+	7.29394i	−0.480252	+	0.277274i
$693$	4.60208	+	12.6441i	0.174819	+	0.480310i
$694$	−17.7319	+	6.45388i	−0.673093	+	0.244986i
$695$		0			0
$696$	−29.9578	+	51.8883i	−1.13555	+	1.96682i
$697$	1.18145	+	0.208321i	0.0447505	+	0.00789073i
$698$	−21.1573	−	25.2143i	−0.800814	−	0.954374i
$699$	7.68885	+	6.45171i	0.290819	+	0.244026i
$700$		0			0
$701$	19.9867	+	7.27458i	0.754889	+	0.274757i	0.690661	−	0.723178i	$-0.257320\pi$
$701$	19.9867	+	7.27458i	0.754889	+	0.274757i	0.0642272	+	0.997935i	$0.479542\pi$
$702$			9.22406i			0.348140i
$703$	−36.3759	−	29.6720i	−1.37194	−	1.11910i
$704$	24.8411			0.936233
$705$		0			0
$706$	0.876847	+	4.97285i	0.0330006	+	0.187156i
$707$	6.00104	−	7.15176i	0.225692	−	0.268970i
$708$	−10.8888	−	12.9768i	−0.409227	−	0.487698i
$709$	−1.84788	+	10.4798i	−0.0693985	+	0.393578i	0.930247	+	0.366935i	$0.119593\pi$
$709$	−1.84788	+	10.4798i	−0.0693985	+	0.393578i	−0.999645	+	0.0266433i	$0.991518\pi$
$710$		0			0
$711$	14.5628	+	25.2235i	0.546148	+	0.945956i
$712$	6.90075	+	18.9597i	0.258617	+	0.710543i
$713$	4.77611	+	13.1222i	0.178867	+	0.491432i
$714$	1.14063	+	1.97563i	0.0426871	+	0.0739361i
$715$		0			0
$716$	0.0387652	−	0.219848i	0.00144872	−	0.00821612i
$717$	28.9709	+	34.5261i	1.08194	+	1.28940i
$718$	−4.39889	+	5.24239i	−0.164165	+	0.195644i
$719$	6.65775	+	37.7580i	0.248292	+	1.40813i	0.812721	+	0.582653i	$0.197985\pi$
$719$	6.65775	+	37.7580i	0.248292	+	1.40813i	−0.564429	+	0.825481i	$0.690904\pi$
$720$		0			0
$721$	32.2238			1.20008
$722$	22.4436	+	3.31759i	0.835265	+	0.123468i
$723$			47.4736i			1.76556i
$724$	−2.58113	−	0.939456i	−0.0959271	−	0.0349146i
$725$		0			0
$726$	6.26086	+	5.25348i	0.232362	+	0.194975i
$727$	4.95353	+	5.90339i	0.183716	+	0.218945i	0.850040	−	0.526718i	$-0.176578\pi$
$727$	4.95353	+	5.90339i	0.183716	+	0.218945i	−0.666324	+	0.745663i	$0.732133\pi$
$728$	27.1357	+	4.78475i	1.00572	+	0.177335i
$729$	−5.25474	+	9.10148i	−0.194620	+	0.337092i
$730$		0			0
$731$	−0.722353	+	0.262915i	−0.0267172	+	0.00972427i
$732$	2.66770	+	7.32946i	0.0986012	+	0.270905i
$733$	−3.53795	+	2.04263i	−0.130677	+	0.0754464i	−0.563913	−	0.825834i	$-0.690705\pi$
$733$	−3.53795	+	2.04263i	−0.130677	+	0.0754464i	0.433236	+	0.901280i	$0.357372\pi$
$734$	0.564571	−	0.977866i	0.0208387	−	0.0360937i
$735$		0			0
$736$	7.14941	−	5.99906i	0.263531	−	0.221128i
$737$	1.90662	−	2.27223i	0.0702314	−	0.0836985i
$738$	−7.99089	+	1.40901i	−0.294149	+	0.0518663i
$739$	−23.1521	−	8.42669i	−0.851665	−	0.309981i	−0.120946	−	0.992659i	$-0.538593\pi$
$739$	−23.1521	−	8.42669i	−0.851665	−	0.309981i	−0.730719	+	0.682678i	$0.760815\pi$
$740$		0			0
$741$	−25.5609	+	31.3360i	−0.939002	+	1.15116i
$742$			19.6073i			0.719806i
$743$	8.81599	−	24.2217i	0.323427	−	0.888610i	−0.666305	−	0.745679i	$-0.732125\pi$
$743$	8.81599	−	24.2217i	0.323427	−	0.888610i	0.989733	−	0.142931i	$-0.0456525\pi$
$744$	5.69342	+	32.2890i	0.208731	+	1.18377i
$745$		0			0
$746$	−0.615878	+	0.516783i	−0.0225489	+	0.0189208i
$747$	−11.8591	−	2.09108i	−0.433901	−	0.0765085i
$748$	0.537777	+	0.310486i	0.0196631	+	0.0113525i
$749$	6.78766	+	11.7566i	0.248016	+	0.429576i
$750$		0			0
$751$	14.5890	−	5.30998i	0.532362	−	0.193764i	−0.0618308	−	0.998087i	$-0.519694\pi$
$751$	14.5890	−	5.30998i	0.532362	−	0.193764i	0.594193	+	0.804323i	$0.297472\pi$
$752$	23.8014	−	13.7418i	0.867950	−	0.501111i
$753$	10.9348	+	6.31319i	0.398485	+	0.230065i
$754$	7.25648	−	41.1535i	0.264265	−	1.49872i
$755$		0			0
$756$	−1.82865	−	1.53442i	−0.0665073	−	0.0558062i
$757$	21.3440	−	3.76351i	0.775759	−	0.136787i	0.228268	−	0.973598i	$-0.426694\pi$
$757$	21.3440	−	3.76351i	0.775759	−	0.136787i	0.547492	+	0.836811i	$0.315583\pi$
$758$	−14.2001	+	39.0143i	−0.515769	+	1.41706i
$759$	−19.1207			−0.694037
$760$		0			0
$761$	1.91229			0.0693204			0.0346602	−	0.999399i	$-0.488965\pi$
$761$	1.91229			0.0693204			0.0346602	+	0.999399i	$0.488965\pi$
$762$	3.19767	−	8.78552i	0.115839	−	0.318266i
$763$	−1.63070	+	0.287536i	−0.0590353	+	0.0104095i
$764$	−10.4910	−	8.80302i	−0.379552	−	0.318482i
$765$		0			0
$766$	−5.65167	+	32.0522i	−0.204203	+	1.15809i
$767$	45.8726	+	26.4845i	1.65636	+	0.956301i
$768$	24.6784	−	14.2481i	0.890504	−	0.514133i
$769$	23.4461	−	8.53369i	0.845489	−	0.307733i	0.117289	−	0.993098i	$-0.462580\pi$
$769$	23.4461	−	8.53369i	0.845489	−	0.307733i	0.728200	+	0.685365i	$0.240357\pi$
$770$		0			0
$771$	−22.8646	−	39.6026i	−0.823448	−	1.42625i
$772$	−5.58214	−	3.22285i	−0.200906	−	0.115993i
$773$	17.1974	+	3.03236i	0.618547	+	0.109067i	0.474136	−	0.880451i	$-0.342760\pi$
$773$	17.1974	+	3.03236i	0.618547	+	0.109067i	0.144410	+	0.989518i	$0.453871\pi$
$774$	3.98289	−	3.34204i	0.143162	−	0.120127i
$775$		0			0
$776$	7.71075	+	43.7298i	0.276800	+	1.56981i
$777$	18.3911	−	50.5291i	0.659777	−	1.81272i
$778$			43.5851i			1.56260i
$779$	11.9294	+	6.66827i	0.427414	+	0.238915i
$780$		0			0
$781$	−20.7902	−	7.56700i	−0.743931	−	0.270769i
$782$	−1.33902	+	0.236106i	−0.0478834	+	0.00844313i
$783$	−10.4328	+	12.4334i	−0.372839	+	0.444333i
$784$	−4.20279	+	3.52656i	−0.150100	+	0.125949i
$785$		0			0
$786$	13.9799	−	24.2140i	0.498648	−	0.863684i
$787$	−42.5745	+	24.5804i	−1.51762	+	0.876196i	−0.517831	+	0.855483i	$0.673260\pi$
$787$	−42.5745	+	24.5804i	−1.51762	+	0.876196i	−0.999785	+	0.0207128i	$0.993406\pi$
$788$	3.31348	+	9.10371i	0.118038	+	0.324306i
$789$	25.0099	−	9.10287i	0.890377	−	0.324071i
$790$		0			0
$791$	0.955477	−	1.65493i	0.0339728	−	0.0588427i
$792$	−18.5437	−	3.26975i	−0.658921	−	0.116185i
$793$	−15.6770	−	18.6831i	−0.556706	−	0.663456i
$794$	−12.6558	−	10.6194i	−0.449136	−	0.376870i
$795$		0			0
$796$	−8.48306	−	3.08758i	−0.300674	−	0.109436i
$797$		−	35.4304i		−	1.25501i	−0.778613	−	0.627505i	$-0.784076\pi$
$797$		−	35.4304i		−	1.25501i	0.778613	−	0.627505i	$-0.215924\pi$
$798$	4.86777	+	25.5280i	0.172317	+	0.903682i
$799$	4.16978			0.147516
$800$		0			0
$801$	−2.47042	−	14.0105i	−0.0872880	−	0.495035i
$802$	18.6308	−	22.2033i	0.657876	−	0.784026i
$803$	−25.5983	−	30.5069i	−0.903346	−	1.07657i
$804$	0.237849	−	1.34891i	0.00838829	−	0.0475724i
$805$		0			0
$806$	−11.4338	−	19.8039i	−0.402738	−	0.697562i
$807$	10.0182	+	27.5248i	0.352657	+	0.968917i
$808$	4.46840	+	12.2768i	0.157198	+	0.431898i
$809$	−18.1503	−	31.4373i	−0.638131	−	1.10528i	−0.985842	−	0.167674i	$-0.946374\pi$
$809$	−18.1503	−	31.4373i	−0.638131	−	1.10528i	0.347711	−	0.937602i	$-0.386959\pi$
$810$		0			0
$811$	−1.04633	+	5.93406i	−0.0367418	+	0.208373i	−0.997652	−	0.0684872i	$-0.978183\pi$
$811$	−1.04633	+	5.93406i	−0.0367418	+	0.208373i	0.960910	+	0.276860i	$0.0892939\pi$
$812$	6.95148	+	8.28445i	0.243949	+	0.290727i
$813$	−22.5261	+	26.8456i	−0.790026	+	0.941516i
$814$	6.31163	+	35.7950i	0.221223	+	1.25462i
$815$		0			0
$816$	−2.19357			−0.0767905
$817$	−8.75627	+	0.121618i	−0.306343	+	0.00425488i
$818$		−	40.5198i		−	1.41674i
$819$	−18.2571	−	6.64503i	−0.637954	−	0.232196i
$820$		0			0
$821$	−28.0570	−	23.5426i	−0.979196	−	0.821643i	0.00477169	−	0.999989i	$-0.498481\pi$
$821$	−28.0570	−	23.5426i	−0.979196	−	0.821643i	−0.983968	+	0.178345i	$0.942926\pi$
$822$	−2.56116	−	3.05227i	−0.0893307	−	0.106460i
$823$	15.0754	+	2.65820i	0.525495	+	0.0926590i	0.430101	−	0.902781i	$-0.358478\pi$
$823$	15.0754	+	2.65820i	0.525495	+	0.0926590i	0.0953939	+	0.995440i	$0.469589\pi$
$824$	−22.5470	+	39.0525i	−0.785461	+	1.36046i
$825$		0			0
$826$	31.9876	−	11.6425i	1.11299	−	0.405096i
$827$	−7.21472	−	19.8223i	−0.250880	−	0.689288i	−0.999650	−	0.0264579i	$-0.991577\pi$
$827$	−7.21472	−	19.8223i	−0.250880	−	0.689288i	0.748769	−	0.662831i	$-0.230645\pi$
$828$	−3.20722	+	1.85169i	−0.111458	+	0.0643506i
$829$	20.0967	−	34.8085i	0.697987	−	1.20895i	−0.271177	−	0.962530i	$-0.587413\pi$
$829$	20.0967	−	34.8085i	0.697987	−	1.20895i	0.969163	−	0.246419i	$-0.0792539\pi$
$830$		0			0
$831$	9.22414	−	7.73997i	0.319982	−	0.268497i
$832$	−23.0558	+	27.4769i	−0.799317	+	0.952589i
$833$	−0.819740	+	0.144542i	−0.0284023	+	0.00500809i
$834$	18.6902	+	6.80269i	0.647190	+	0.235558i
$835$		0			0
$836$	4.62194	+	5.35537i	0.159853	+	0.185219i
$837$			8.88176i			0.306998i
$838$	8.75300	−	24.0487i	0.302367	−	0.830747i
$839$	−4.84143	−	27.4571i	−0.167145	−	0.947925i	−0.946825	−	0.321748i	$-0.895730\pi$
$839$	−4.84143	−	27.4571i	−0.167145	−	0.947925i	0.779681	−	0.626177i	$-0.215381\pi$
$840$		0			0
$841$	34.1125	−	28.6238i	1.17629	−	0.987027i
$842$	8.63613	+	1.52278i	0.297621	+	0.0524786i
$843$	−10.5977	−	6.11859i	−0.365004	−	0.210735i
$844$	2.66669	+	4.61885i	0.0917914	+	0.158987i
$845$		0			0
$846$	−26.5021	+	9.64596i	−0.911159	+	0.331635i
$847$	5.72761	−	3.30684i	0.196803	−	0.113624i
$848$	−16.3277	−	9.42680i	−0.560696	−	0.323718i
$849$	−6.97755	+	39.5717i	−0.239469	+	1.35810i
$850$		0			0
$851$	24.5511	+	20.6008i	0.841601	+	0.706187i
$852$	−10.0614	+	1.77409i	−0.344697	+	0.0607794i
$853$	−6.88015	+	18.9031i	−0.235572	+	0.647228i	0.764425	+	0.644713i	$0.223023\pi$
$853$	−6.88015	+	18.9031i	−0.235572	+	0.647228i	−0.999997	+	0.00251570i	$0.999199\pi$
$854$	−15.6736			−0.536339
$855$		0			0
$856$	−18.9973			−0.649315
$857$	−1.48855	+	4.08976i	−0.0508480	+	0.139704i	−0.962517	−	0.271222i	$-0.912572\pi$
$857$	−1.48855	+	4.08976i	−0.0508480	+	0.139704i	0.911669	+	0.410926i	$0.134794\pi$
$858$	30.8356	−	5.43715i	1.05271	−	0.185621i
$859$	4.22949	+	3.54896i	0.144308	+	0.121089i	0.712084	−	0.702094i	$-0.247751\pi$
$859$	4.22949	+	3.54896i	0.144308	+	0.121089i	−0.567776	+	0.823183i	$0.692196\pi$
$860$		0			0
$861$	−2.71842	+	15.4169i	−0.0926435	+	0.525408i
$862$	0.130682	+	0.0754492i	0.00445104	+	0.00256981i
$863$	−31.0093	+	17.9032i	−1.05557	+	0.609433i	−0.924203	−	0.381901i	$-0.875270\pi$
$863$	−31.0093	+	17.9032i	−1.05557	+	0.609433i	−0.131366	+	0.991334i	$0.541936\pi$
$864$	5.57800	−	2.03022i	0.189767	−	0.0690697i
$865$		0			0
$866$	3.47365	+	6.01653i	0.118039	+	0.204450i
$867$	33.1785	+	19.1556i	1.12680	+	0.650559i
$868$	5.82808	+	1.02765i	0.197818	+	0.0348806i
$869$	−29.0969	+	24.4152i	−0.987046	+	0.828230i
$870$		0			0
$871$	0.743722	+	4.21786i	0.0252001	+	0.142917i
$872$	0.792530	−	2.17746i	0.0268385	−	0.0737381i
$873$		−	31.3100i		−	1.05968i
$874$	−15.2899	−	2.47759i	−0.517190	−	0.0838059i
$875$		0			0
$876$	−17.2808	−	6.28970i	−0.583864	−	0.212509i
$877$	24.1462	−	4.25763i	0.815360	−	0.143770i	0.249610	−	0.968347i	$-0.419698\pi$
$877$	24.1462	−	4.25763i	0.815360	−	0.143770i	0.565750	+	0.824577i	$0.308587\pi$
$878$	−14.2018	+	16.9250i	−0.479288	+	0.571193i
$879$	−8.20261	+	6.88280i	−0.276667	+	0.232151i
$880$		0			0
$881$	14.7421	−	25.5341i	0.496675	−	0.860266i	−0.503318	−	0.864101i	$-0.667887\pi$
$881$	14.7421	−	25.5341i	0.496675	−	0.860266i	0.999993	+	0.00383530i	$0.00122082\pi$
$882$	4.87569	−	2.81498i	0.164173	−	0.0947853i
$883$	−2.74594	−	7.54441i	−0.0924083	−	0.253890i	0.884874	−	0.465830i	$-0.154244\pi$
$883$	−2.74594	−	7.54441i	−0.0924083	−	0.253890i	−0.977283	+	0.211940i	$0.932022\pi$
$884$	−0.842559	+	0.306666i	−0.0283383	+	0.0103143i
$885$		0			0
$886$	13.2096	−	22.8798i	0.443787	−	0.768661i
$887$	20.5987	+	3.63211i	0.691638	+	0.121954i	0.508409	−	0.861116i	$-0.330234\pi$
$887$	20.5987	+	3.63211i	0.691638	+	0.121954i	0.183229	+	0.983070i	$0.441345\pi$
$888$	48.3688	+	57.6437i	1.62315	+	1.93439i
$889$	−5.79561	−	4.86309i	−0.194378	−	0.163103i
$890$		0			0
$891$	−28.6974	−	10.4450i	−0.961399	−	0.349921i
$892$			1.60250i			0.0536556i
$893$	44.8585	+	15.6251i	1.50113	+	0.522874i
$894$	27.1214			0.907077
$895$		0			0
$896$	1.61040	+	9.13305i	0.0537998	+	0.305114i
$897$	17.7465	−	21.1495i	0.592540	−	0.706162i
$898$	−15.7867	−	18.8138i	−0.526809	−	0.627826i
$899$	6.98720	−	39.6264i	0.233036	−	1.32161i
$900$		0			0
$901$	−1.43023	−	2.47723i	−0.0476478	−	0.0825283i
$902$	−3.61921	−	9.94370i	−0.120506	−	0.331089i
$903$	−3.43083	−	9.42612i	−0.114171	−	0.313682i
$904$	1.33709	+	2.31591i	0.0444711	+	0.0770262i
$905$		0			0
$906$	−7.10260	+	40.2809i	−0.235968	+	1.33824i
$907$	−0.188414	−	0.224543i	−0.00625619	−	0.00745584i	0.762907	−	0.646508i	$-0.223771\pi$
$907$	−0.188414	−	0.224543i	−0.00625619	−	0.00745584i	−0.769163	+	0.639052i	$0.779327\pi$
$908$	0.311530	−	0.371267i	0.0103385	−	0.0123209i
$909$	−1.59966	−	9.07211i	−0.0530573	−	0.300903i
$910$		0			0
$911$	−22.0356			−0.730073			−0.365037	−	0.930993i	$-0.618944\pi$
$911$	−22.0356			−0.730073			−0.365037	+	0.930993i	$0.618944\pi$
$912$	−23.5984	−	8.21981i	−0.781423	−	0.272185i
$913$		−	15.7043i		−	0.519736i
$914$	−22.8434	−	8.31432i	−0.755592	−	0.275013i
$915$		0			0
$916$	−9.65720	−	8.10336i	−0.319083	−	0.267742i
$917$	−14.5434	−	17.3321i	−0.480265	−	0.572358i
$918$	−0.851656	−	0.150170i	−0.0281089	−	0.00495635i
$919$	−0.460757	+	0.798054i	−0.0151990	+	0.0263254i	−0.873525	−	0.486780i	$-0.838171\pi$
$919$	−0.460757	+	0.798054i	−0.0151990	+	0.0263254i	0.858326	+	0.513105i	$0.171505\pi$
$920$		0			0
$921$	−25.2183	+	9.17870i	−0.830970	+	0.302448i
$922$	−2.26361	−	6.21922i	−0.0745481	−	0.204819i
$923$	27.6660	−	15.9729i	0.910636	−	0.525756i
$924$	−4.05158	+	7.01755i	−0.133287	+	0.230860i
$925$		0			0
$926$	−29.8655	+	25.0601i	−0.981440	+	0.823526i
$927$	20.4382	−	24.3573i	0.671277	−	0.799997i
$928$	−26.4836	+	4.66978i	−0.869368	+	0.153293i
$929$	−22.0825	−	8.03737i	−0.724503	−	0.263697i	−0.0466666	−	0.998911i	$-0.514860\pi$
$929$	−22.0825	−	8.03737i	−0.724503	−	0.263697i	−0.677836	+	0.735213i	$0.737082\pi$
$930$		0			0
$931$	−9.36039	−	1.51677i	−0.306774	−	0.0497100i
$932$			2.53525i			0.0830448i
$933$	6.95069	−	19.0969i	0.227556	−	0.625204i
$934$	5.94289	+	33.7038i	0.194457	+	1.10282i
$935$		0			0
$936$	20.8277	−	17.4765i	0.680774	−	0.571238i
$937$	−52.5128	−	9.25942i	−1.71552	−	0.302492i	−0.772445	−	0.635081i	$-0.780967\pi$
$937$	−52.5128	−	9.25942i	−1.71552	−	0.302492i	−0.943072	+	0.332589i	$0.892078\pi$
$938$	2.38366	+	1.37621i	0.0778293	+	0.0449348i
$939$	−15.2649	−	26.4396i	−0.498152	−	0.862824i
$940$		0			0
$941$	3.88045	−	1.41237i	0.126499	−	0.0460418i	−0.277995	−	0.960583i	$-0.589670\pi$
$941$	3.88045	−	1.41237i	0.126499	−	0.0460418i	0.404494	+	0.914541i	$0.367448\pi$
$942$	−24.3169	+	14.0394i	−0.792288	+	0.457428i
$943$	−8.08050	−	4.66528i	−0.263137	−	0.151922i
$944$	−5.68386	+	32.2348i	−0.184994	+	1.04915i
$945$		0			0
$946$	5.19418	+	4.35843i	0.168877	+	0.141705i
$947$	−8.29375	+	1.46241i	−0.269511	+	0.0475220i	−0.306770	−	0.951784i	$-0.599248\pi$
$947$	−8.29375	+	1.46241i	−0.269511	+	0.0475220i	0.0372596	+	0.999306i	$0.488137\pi$
$948$	−5.99900	+	16.4821i	−0.194838	+	0.535314i
$949$	57.5025			1.86661
$950$		0			0
$951$	−25.1359			−0.815088
$952$	−0.883552	+	2.42754i	−0.0286361	+	0.0786770i
$953$	−18.6859	+	3.29483i	−0.605296	+	0.106730i	−0.467893	−	0.883785i	$-0.654987\pi$
$953$	−18.6859	+	3.29483i	−0.605296	+	0.106730i	−0.137403	+	0.990515i	$0.543875\pi$
$954$	14.8207	+	12.4361i	0.479838	+	0.402632i
$955$		0			0
$956$	−1.97686	+	11.2114i	−0.0639364	+	0.362601i
$957$	47.7138	+	27.5476i	1.54237	+	0.890487i
$958$	10.6229	−	6.13311i	0.343209	−	0.198152i
$959$	−3.02983	+	1.10277i	−0.0978383	+	0.0356102i
$960$		0			0
$961$	4.49052	+	7.77782i	0.144856	+	0.250897i
$962$	−45.4511	−	26.2412i	−1.46540	−	0.846051i
$963$	13.1917	+	2.32605i	0.425095	+	0.0749558i
$964$	−9.18584	+	7.70784i	−0.295856	+	0.248253i
$965$		0			0
$966$	−3.08099	−	17.4732i	−0.0991292	−	0.562189i
$967$	−1.28556	+	3.53205i	−0.0413408	+	0.113583i	−0.958645	−	0.284603i	$-0.908138\pi$
$967$	−1.28556	+	3.53205i	−0.0413408	+	0.113583i	0.917305	+	0.398186i	$0.130360\pi$
$968$			9.25517i			0.297473i
$969$	−2.47711	−	2.87019i	−0.0795763	−	0.0922038i
$970$		0			0
$971$	−12.0598	−	4.38940i	−0.387016	−	0.140862i	0.141182	−	0.989984i	$-0.454910\pi$
$971$	−12.0598	−	4.38940i	−0.387016	−	0.140862i	−0.528198	+	0.849121i	$0.677132\pi$
$972$	−10.6772	+	1.88268i	−0.342472	+	0.0603871i
$973$	10.3457	−	12.3295i	0.331668	−	0.395266i
$974$	10.1757	−	8.53845i	0.326051	−	0.273590i
$975$		0			0
$976$	7.53556	−	13.0520i	0.241207	−	0.417783i
$977$	−23.8455	+	13.7672i	−0.762887	+	0.440453i	−0.830331	−	0.557270i	$-0.811849\pi$
$977$	−23.8455	+	13.7672i	−0.762887	+	0.440453i	0.0674446	+	0.997723i	$0.478515\pi$
$978$	6.40579	+	17.5998i	0.204835	+	0.562779i
$979$	17.4343	−	6.34557i	0.557203	−	0.202805i
$980$		0			0
$981$	−0.816940	+	1.41498i	−0.0260829	+	0.0451769i
$982$	−16.3276	−	2.87899i	−0.521033	−	0.0918722i
$983$	−31.0232	−	36.9720i	−0.989486	−	1.17922i	−0.983805	−	0.179239i	$-0.942636\pi$
$983$	−31.0232	−	36.9720i	−0.989486	−	1.17922i	−0.00568028	−	0.999984i	$-0.501808\pi$
$984$	−16.7819	−	14.0817i	−0.534989	−	0.448909i
$985$		0			0
$986$	3.68157	+	1.33998i	0.117245	+	0.0426737i
$987$			54.4122i			1.73196i
$988$	−10.2134	+	0.141856i	−0.324931	+	0.00451305i
$989$	5.97872			0.190112
$990$		0			0
$991$	−7.57591	−	42.9651i	−0.240657	−	1.36483i	−0.830367	−	0.557217i	$-0.811869\pi$
$991$	−7.57591	−	42.9651i	−0.240657	−	1.36483i	0.589710	−	0.807615i	$-0.299242\pi$
$992$	−9.45927	+	11.2731i	−0.300332	+	0.357922i
$993$	4.15770	+	4.95495i	0.131941	+	0.157241i
$994$	3.56499	−	20.2181i	0.113075	−	0.641279i
$995$		0			0
$996$	−3.62595	−	6.28034i	−0.114893	−	0.199000i
$997$	−10.3283	−	28.3767i	−0.327099	−	0.898698i	−0.988842	−	0.148967i	$-0.952405\pi$
$997$	−10.3283	−	28.3767i	−0.327099	−	0.898698i	0.661743	−	0.749731i	$-0.269817\pi$
$998$	−5.22255	−	14.3488i	−0.165317	−	0.454205i
$999$	10.1921	+	17.6532i	0.322464	+	0.558523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.c.99.3		36
5.2	odd	4		475.2.l.b.251.2		18
5.3	odd	4		95.2.k.b.61.2	✓	18
5.4	even	2	inner	475.2.u.c.99.4		36
15.8	even	4		855.2.bs.b.631.2		18
19.5	even	9	inner	475.2.u.c.24.4		36
95.24	even	18	inner	475.2.u.c.24.3		36
95.28	odd	36		1805.2.a.t.1.4		9
95.43	odd	36		95.2.k.b.81.2	yes	18
95.47	odd	36		9025.2.a.ce.1.6		9
95.48	even	36		1805.2.a.u.1.6		9
95.62	odd	36		475.2.l.b.176.2		18
95.67	even	36		9025.2.a.cd.1.4		9
285.233	even	36		855.2.bs.b.271.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.2	✓	18	5.3	odd	4
95.2.k.b.81.2	yes	18	95.43	odd	36
475.2.l.b.176.2		18	95.62	odd	36
475.2.l.b.251.2		18	5.2	odd	4
475.2.u.c.24.3		36	95.24	even	18	inner
475.2.u.c.24.4		36	19.5	even	9	inner
475.2.u.c.99.3		36	1.1	even	1	trivial
475.2.u.c.99.4		36	5.4	even	2	inner
855.2.bs.b.271.2		18	285.233	even	36
855.2.bs.b.631.2		18	15.8	even	4
1805.2.a.t.1.4		9	95.28	odd	36
1805.2.a.u.1.6		9	95.48	even	36
9025.2.a.cd.1.4		9	95.67	even	36
9025.2.a.ce.1.6		9	95.47	odd	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.408399 + 1.12207i) q^{2} +(2.23864 - 0.394733i) q^{3} +(0.439845 + 0.369074i) q^{4} +(-0.471342 + 2.67312i) q^{6} +(1.90222 + 1.09825i) q^{7} +(-2.66196 + 1.53688i) q^{8} +(2.03663 - 0.741274i) q^{9} +O(q^{10})\)	\(q+(-0.408399 + 1.12207i) q^{2} +(2.23864 - 0.394733i) q^{3} +(0.439845 + 0.369074i) q^{4} +(-0.471342 + 2.67312i) q^{6} +(1.90222 + 1.09825i) q^{7} +(-2.66196 + 1.53688i) q^{8} +(2.03663 - 0.741274i) q^{9} +(1.41324 + 2.44780i) q^{11} +(1.13034 + 0.652604i) q^{12} +(-4.01920 - 0.708694i) q^{13} +(-2.00917 + 1.68589i) q^{14} +(-0.437935 - 2.48365i) q^{16} +(0.130867 - 0.359555i) q^{17} +2.58797i q^{18} +(2.75520 - 3.37770i) q^{19} +(4.69190 + 1.70771i) q^{21} +(-3.32376 + 0.586069i) q^{22} +(-1.91290 + 2.27970i) q^{23} +(-5.35253 + 4.49130i) q^{24} +(2.43664 - 4.22038i) q^{26} +(-1.63920 + 0.946391i) q^{27} +(0.431347 + 1.18512i) q^{28} +(8.05787 - 2.93282i) q^{29} +(2.34622 - 4.06377i) q^{31} +(-3.08847 - 0.544580i) q^{32} +(4.12997 + 4.92191i) q^{33} +(0.349999 + 0.293684i) q^{34} +(1.16939 + 0.425623i) q^{36} -10.7694i q^{37} +(2.66478 + 4.47097i) q^{38} -9.27731 q^{39} +(0.544445 + 3.08770i) q^{41} +(-3.83233 + 4.56720i) q^{42} +(-1.29137 - 1.53900i) q^{43} +(-0.281814 + 1.59824i) q^{44} +(-1.77675 - 3.07743i) q^{46} +(3.72722 + 10.2405i) q^{47} +(-1.96076 - 5.38714i) q^{48} +(-1.08771 - 1.88398i) q^{49} +(0.151037 - 0.856574i) q^{51} +(-1.50627 - 1.79510i) q^{52} +(4.80532 - 5.72676i) q^{53} +(-0.392467 - 2.22579i) q^{54} -6.75150 q^{56} +(4.83463 - 8.64904i) q^{57} +10.2392i q^{58} +(-12.1961 - 4.43900i) q^{59} +(4.57784 + 3.84126i) q^{61} +(3.60163 + 4.29225i) q^{62} +(4.68822 + 0.826660i) q^{63} +(4.39435 - 7.61123i) q^{64} +(-7.20938 + 2.62400i) q^{66} +(-0.358925 - 0.986138i) q^{67} +(0.190264 - 0.109849i) q^{68} +(-3.38242 + 5.85853i) q^{69} +(-5.99626 + 5.03146i) q^{71} +(-4.28219 + 5.10332i) q^{72} +(-13.8755 + 2.44663i) q^{73} +(12.0840 + 4.39822i) q^{74} +(2.45848 - 0.468792i) q^{76} +6.20833i q^{77} +(3.78884 - 10.4098i) q^{78} +(2.33355 + 13.2342i) q^{79} +(-8.27685 + 6.94510i) q^{81} +(-3.68695 - 0.650110i) q^{82} +(-4.81175 - 2.77807i) q^{83} +(1.43344 + 2.48279i) q^{84} +(2.25425 - 0.820481i) q^{86} +(16.8810 - 9.74626i) q^{87} +(-7.52398 - 4.34397i) q^{88} +(1.13984 - 6.46435i) q^{89} +(-6.86708 - 5.76216i) q^{91} +(-1.68276 + 0.296716i) q^{92} +(3.64824 - 10.0235i) q^{93} -13.0127 q^{94} -7.12895 q^{96} +(4.94091 - 13.5750i) q^{97} +(2.55817 - 0.451074i) q^{98} +(4.69275 + 3.93768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more