LMFDB - Embedded newform 867.2.i.c.158.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(65,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

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

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

chi := DirichletCharacter("867.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			158.4
Character	$\chi$	$=$	867.158
Dual form			867.2.i.c.653.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34436 - 0.556851i) q^{2} +(-0.336782 - 1.69899i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(-2.99276 - 0.595296i) q^{5} +(-1.39884 - 2.09652i) q^{6} +(0.420765 + 2.11533i) q^{7} +(-1.04834 + 2.53091i) q^{8} +(-2.77316 + 1.14438i) q^{9} +(-4.35483 + 0.866229i) q^{10} +(0.915491 - 1.37013i) q^{11} +(-0.168973 - 0.113066i) q^{12} +(3.12551 + 3.12551i) q^{13} +(1.74358 + 2.60946i) q^{14} +(-0.00349923 + 5.28516i) q^{15} +4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(0.330416 + 0.797694i) q^{19} +(-0.297816 + 0.198994i) q^{20} +(3.45222 - 1.42728i) q^{21} +(0.467790 - 2.35174i) q^{22} +(0.637394 + 0.425893i) q^{23} +(4.65306 + 0.928755i) q^{24} +(3.98282 + 1.64974i) q^{25} +(5.94226 + 2.46136i) q^{26} +(2.87824 + 4.32617i) q^{27} +(0.210501 + 0.140652i) q^{28} +(-1.55905 + 7.83789i) q^{29} +(2.93834 + 7.10709i) q^{30} +(-2.40167 + 1.60475i) q^{31} +(0.253786 + 0.612694i) q^{32} +(-2.63616 - 1.09398i) q^{33} -6.58114i q^{35} +(-0.135192 + 0.325163i) q^{36} +(-1.32318 - 1.98027i) q^{37} +(0.888394 + 0.888394i) q^{38} +(4.25761 - 6.36284i) q^{39} +(4.64406 - 6.95033i) q^{40} +(-3.02038 + 0.600791i) q^{41} +(3.84624 - 3.84115i) q^{42} +(-4.38037 + 10.5751i) q^{43} +(-0.0377359 - 0.189711i) q^{44} +(8.98063 - 1.77400i) q^{45} +(1.09405 + 0.217619i) q^{46} +(2.21238 - 2.21238i) q^{47} +(7.17143 - 1.42155i) q^{48} +(2.16958 - 0.898671i) q^{49} +6.27299 q^{50} +0.518848 q^{52} +(-5.88369 + 2.43710i) q^{53} +(6.27842 + 4.21317i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(-5.79482 - 1.15266i) q^{56} +(1.24400 - 0.830022i) q^{57} +(2.26861 + 11.4051i) q^{58} +(2.33146 - 5.62864i) q^{59} +(0.438389 + 0.438969i) q^{60} +(-5.73423 + 1.14061i) q^{61} +(-2.33510 + 3.49473i) q^{62} +(-3.58759 - 5.38462i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(-7.49329 - 11.2145i) q^{65} +(-4.15313 - 0.00274973i) q^{66} +7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(-3.66472 - 8.84742i) q^{70} +(1.80802 - 1.20808i) q^{71} +(0.0108825 - 8.21831i) q^{72} +(-2.45412 + 12.3377i) q^{73} +(-2.88154 - 1.92538i) q^{74} +(1.46155 - 7.32238i) q^{75} +(0.0936354 + 0.0387851i) q^{76} +(3.28348 + 1.36006i) q^{77} +(2.18060 - 10.9248i) q^{78} +(4.95397 + 3.31013i) q^{79} +(2.51274 - 12.6324i) q^{80} +(6.38079 - 6.34708i) q^{81} +(-3.72592 + 2.48958i) q^{82} +(-4.96993 - 11.9985i) q^{83} +(0.168074 - 0.405009i) q^{84} +16.6560i q^{86} +(13.8416 + 0.00916431i) q^{87} +(2.50793 + 3.75339i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(11.0853 - 7.38576i) q^{90} +(-5.29638 + 7.92660i) q^{91} +(0.0882551 - 0.0175550i) q^{92} +(3.53529 + 3.53997i) q^{93} +(1.74226 - 4.20619i) q^{94} +(-0.513989 - 2.58400i) q^{95} +(0.955492 - 0.637525i) q^{96} +(-3.47928 - 0.692072i) q^{97} +(2.41627 - 2.41627i) q^{98} +(-0.970853 + 4.84725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 8 q^{9} - 32 q^{10} - 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} + 48 q^{22} - 8 q^{24} - 16 q^{25} + 48 q^{27} + 64 q^{28} - 8 q^{30} - 16 q^{31} - 8 q^{36}+ \cdots - 96 q^{97}+O(q^{100}) $ 32 * q - 16 * q^4 + 8 * q^9 - 32 * q^10 - 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 + 48 * q^22 - 8 * q^24 - 16 * q^25 + 48 * q^27 + 64 * q^28 - 8 * q^30 - 16 * q^31 - 8 * q^36 + 32 * q^37 - 8 * q^39 + 64 * q^40 + 56 * q^42 - 16 * q^43 - 24 * q^45 + 80 * q^46 + 72 * q^48 + 48 * q^49 - 96 * q^52 - 48 * q^54 - 48 * q^55 - 24 * q^57 + 32 * q^58 - 32 * q^60 - 64 * q^61 + 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 + 16 * q^78 + 32 * q^79 + 48 * q^81 - 48 * q^82 + 56 * q^87 + 80 * q^88 - 104 * q^90 - 80 * q^91 + 72 * q^93 + 48 * q^94 - 72 * q^96 - 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	1.34436	−	0.556851i	0.950605	−	0.393753i	0.147147	−	0.989115i	$-0.452991\pi$
$2$	1.34436	−	0.556851i	0.950605	−	0.393753i	0.803458	+	0.595361i	$0.202991\pi$
$3$	−0.336782	−	1.69899i	−0.194441	−	0.980914i
$3$	−0.336782	−	1.69899i	−0.194441	−	0.980914i
$4$	0.0830021	−	0.0830021i	0.0415010	−	0.0415010i
$5$	−2.99276	−	0.595296i	−1.33840	−	0.266225i	−0.526578	−	0.850127i	$-0.676525\pi$
$5$	−2.99276	−	0.595296i	−1.33840	−	0.266225i	−0.811824	+	0.583902i	$0.801525\pi$
$6$	−1.39884	−	2.09652i	−0.571075	−	0.855900i
$7$	0.420765	+	2.11533i	0.159034	+	0.799519i	0.975135	+	0.221610i	$0.0711312\pi$
$7$	0.420765	+	2.11533i	0.159034	+	0.799519i	−0.816101	+	0.577909i	$0.803869\pi$
$8$	−1.04834	+	2.53091i	−0.370644	+	0.894813i
$9$	−2.77316	+	1.14438i	−0.924385	+	0.381460i
$10$	−4.35483	+	0.866229i	−1.37712	+	0.273926i
$11$	0.915491	−	1.37013i	0.276031	−	0.413110i	−0.667389	−	0.744709i	$-0.732588\pi$
$11$	0.915491	−	1.37013i	0.276031	−	0.413110i	0.943420	+	0.331599i	$0.107588\pi$
$12$	−0.168973	−	0.113066i	−0.0487784	−	0.0326395i
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	0.992124	−	0.125262i	$-0.0399772\pi$
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	−0.125262	+	0.992124i	$0.539977\pi$
$14$	1.74358	+	2.60946i	0.465992	+	0.697407i
$15$	−0.00349923	+	5.28516i	−0.000903497	+	1.36462i
$16$			4.22099i			1.05525i
$17$		0			0
$17$		0			0
$18$	−3.09087	+	3.08269i	−0.728524	+	0.726597i
$19$	0.330416	+	0.797694i	0.0758025	+	0.183004i	0.957238	−	0.289300i	$-0.0934226\pi$
$19$	0.330416	+	0.797694i	0.0758025	+	0.183004i	−0.881436	+	0.472304i	$0.843423\pi$
$20$	−0.297816	+	0.198994i	−0.0665936	+	0.0444964i
$21$	3.45222	−	1.42728i	0.753337	−	0.311458i
$22$	0.467790	−	2.35174i	0.0997331	−	0.501392i
$23$	0.637394	+	0.425893i	0.132906	+	0.0888049i	0.620246	−	0.784407i	$-0.287033\pi$
$23$	0.637394	+	0.425893i	0.132906	+	0.0888049i	−0.487340	+	0.873212i	$0.662033\pi$
$24$	4.65306	+	0.928755i	0.949803	+	0.189581i
$25$	3.98282	+	1.64974i	0.796563	+	0.329947i
$26$	5.94226	+	2.46136i	1.16537	+	0.482713i
$27$	2.87824	+	4.32617i	0.553918	+	0.832571i
$28$	0.210501	+	0.140652i	0.0397810	+	0.0265808i
$29$	−1.55905	+	7.83789i	−0.289509	+	1.45546i	0.512778	+	0.858521i	$0.328616\pi$
$29$	−1.55905	+	7.83789i	−0.289509	+	1.45546i	−0.802287	+	0.596938i	$0.796384\pi$
$30$	2.93834	+	7.10709i	0.536466	+	1.29757i
$31$	−2.40167	+	1.60475i	−0.431353	+	0.288221i	−0.752231	−	0.658900i	$-0.771022\pi$
$31$	−2.40167	+	1.60475i	−0.431353	+	0.288221i	0.320878	+	0.947121i	$0.396022\pi$
$32$	0.253786	+	0.612694i	0.0448635	+	0.108310i
$33$	−2.63616	−	1.09398i	−0.458897	−	0.190437i
$34$		0			0
$35$		−	6.58114i		−	1.11242i
$36$	−0.135192	+	0.325163i	−0.0225320	+	0.0541939i
$37$	−1.32318	−	1.98027i	−0.217529	−	0.325555i	0.706616	−	0.707597i	$-0.250221\pi$
$37$	−1.32318	−	1.98027i	−0.217529	−	0.325555i	−0.924145	+	0.382042i	$0.875221\pi$
$38$	0.888394	+	0.888394i	0.144117	+	0.144117i
$39$	4.25761	−	6.36284i	0.681763	−	1.01887i
$40$	4.64406	−	6.95033i	0.734291	−	1.09894i
$41$	−3.02038	+	0.600791i	−0.471704	+	0.0938278i	−0.425218	−	0.905091i	$-0.639802\pi$
$41$	−3.02038	+	0.600791i	−0.471704	+	0.0938278i	−0.0464865	+	0.998919i	$0.514802\pi$
$42$	3.84624	−	3.84115i	0.593488	−	0.592703i
$43$	−4.38037	+	10.5751i	−0.668000	+	1.61269i	0.116952	+	0.993138i	$0.462688\pi$
$43$	−4.38037	+	10.5751i	−0.668000	+	1.61269i	−0.784952	+	0.619557i	$0.787312\pi$
$44$	−0.0377359	−	0.189711i	−0.00568890	−	0.0286000i
$45$	8.98063	−	1.77400i	1.33875	−	0.264452i
$46$	1.09405	+	0.217619i	0.161308	+	0.0320862i
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	−0.527097	−	0.849805i	$-0.676719\pi$
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	0.849805	+	0.527097i	$0.176719\pi$
$48$	7.17143	−	1.42155i	1.03511	−	0.205183i
$49$	2.16958	−	0.898671i	0.309940	−	0.128382i
$50$	6.27299			0.887135
$51$		0			0
$52$	0.518848			0.0719513
$53$	−5.88369	+	2.43710i	−0.808187	+	0.334762i	−0.748230	−	0.663439i	$-0.769096\pi$
$53$	−5.88369	+	2.43710i	−0.808187	+	0.334762i	−0.0599567	+	0.998201i	$0.519096\pi$
$54$	6.27842	+	4.21317i	0.854385	+	0.573340i
$55$	−3.55548	+	3.55548i	−0.479420	+	0.479420i
$56$	−5.79482	−	1.15266i	−0.774365	−	0.154031i
$57$	1.24400	−	0.830022i	0.164772	−	0.109939i
$58$	2.26861	+	11.4051i	0.297884	+	1.49756i
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	−0.696356	−	0.717696i	$-0.745197\pi$
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	0.999886	−	0.0150898i	$-0.00480343\pi$
$60$	0.438389	+	0.438969i	0.0565957	+	0.0566707i
$61$	−5.73423	+	1.14061i	−0.734193	+	0.146040i	−0.548006	−	0.836474i	$-0.684613\pi$
$61$	−5.73423	+	1.14061i	−0.734193	+	0.146040i	−0.186187	+	0.982514i	$0.559613\pi$
$62$	−2.33510	+	3.49473i	−0.296558	+	0.443831i
$63$	−3.58759	−	5.38462i	−0.451993	−	0.678399i
$64$	−5.28702	−	5.28702i	−0.660877	−	0.660877i
$65$	−7.49329	−	11.2145i	−0.929429	−	1.39099i
$66$	−4.15313	−	0.00274973i	−0.511215	−	0.000338468i
$67$			7.19481i			0.878985i	0.898246	+	0.439493i	$0.144842\pi$
$67$			7.19481i			0.878985i	−0.898246	+	0.439493i	$0.855158\pi$
$68$		0			0
$69$	0.508927	−	1.22636i	0.0612676	−	0.147637i
$70$	−3.66472	−	8.84742i	−0.438018	−	1.05747i
$71$	1.80802	−	1.20808i	0.214573	−	0.143373i	−0.443639	−	0.896205i	$-0.646313\pi$
$71$	1.80802	−	1.20808i	0.214573	−	0.143373i	0.658212	+	0.752832i	$0.271313\pi$
$72$	0.0108825	−	8.21831i	0.00128251	−	0.968537i
$73$	−2.45412	+	12.3377i	−0.287233	+	1.44402i	0.520193	+	0.854049i	$0.325860\pi$
$73$	−2.45412	+	12.3377i	−0.287233	+	1.44402i	−0.807426	+	0.589969i	$0.799140\pi$
$74$	−2.88154	−	1.92538i	−0.334972	−	0.223821i
$75$	1.46155	−	7.32238i	0.168766	−	0.845516i
$76$	0.0936354	+	0.0387851i	0.0107407	+	0.00444895i
$77$	3.28348	+	1.36006i	0.374187	+	0.154994i
$78$	2.18060	−	10.9248i	0.246904	−	1.23699i
$79$	4.95397	+	3.31013i	0.557365	+	0.372419i	0.802117	−	0.597166i	$-0.203707\pi$
$79$	4.95397	+	3.31013i	0.557365	+	0.372419i	−0.244753	+	0.969586i	$0.578707\pi$
$80$	2.51274	−	12.6324i	0.280933	−	1.41234i
$81$	6.38079	−	6.34708i	0.708977	−	0.705232i
$82$	−3.72592	+	2.48958i	−0.411459	+	0.274928i
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	−0.920779	−	0.390084i	$-0.872446\pi$
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	0.375258	−	0.926920i	$-0.377554\pi$
$84$	0.168074	−	0.405009i	0.0183384	−	0.0441901i
$85$		0			0
$86$			16.6560i			1.79606i
$87$	13.8416	+	0.00916431i	1.48397	+	0.000982518i
$88$	2.50793	+	3.75339i	0.267347	+	0.400112i
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	0.502205	−	0.864749i	$-0.332522\pi$
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	−0.864749	+	0.502205i	$0.832522\pi$
$90$	11.0853	−	7.38576i	1.16850	−	0.778528i
$91$	−5.29638	+	7.92660i	−0.555212	+	0.830933i
$92$	0.0882551	−	0.0175550i	0.00920123	−	0.00183024i
$93$	3.53529	+	3.53997i	0.366592	+	0.367078i
$94$	1.74226	−	4.20619i	0.179701	−	0.433836i
$95$	−0.513989	−	2.58400i	−0.0527342	−	0.265113i
$96$	0.955492	−	0.637525i	0.0975195	−	0.0650671i
$97$	−3.47928	−	0.692072i	−0.353267	−	0.0702692i	0.0152668	−	0.999883i	$-0.495140\pi$
$97$	−3.47928	−	0.692072i	−0.353267	−	0.0702692i	−0.368534	+	0.929614i	$0.620140\pi$
$98$	2.41627	−	2.41627i	0.244080	−	0.244080i
$99$	−0.970853	+	4.84725i	−0.0975744	+	0.487167i
$100$	0.467514	−	0.193650i	0.0467514	−	0.0193650i
$101$	3.73948			0.372092			0.186046	−	0.982541i	$-0.440433\pi$
$101$	3.73948			0.372092			0.186046	+	0.982541i	$0.440433\pi$
$102$		0			0
$103$	9.33404			0.919710			0.459855	−	0.887994i	$-0.347901\pi$
$103$	9.33404			0.919710			0.459855	+	0.887994i	$0.347901\pi$
$104$	−11.1870	+	4.63380i	−1.09698	+	0.454382i
$105$	−11.1813	+	2.21641i	−1.09119	+	0.216299i
$106$	−6.55268	+	6.55268i	−0.636453	+	0.636453i
$107$	1.85365	+	0.368714i	0.179199	+	0.0356449i	0.283874	−	0.958862i	$-0.408380\pi$
$107$	1.85365	+	0.368714i	0.179199	+	0.0356449i	−0.104675	+	0.994506i	$0.533380\pi$
$108$	0.597981	+	0.120181i	0.0575407	+	0.0115644i
$109$	−0.819969	−	4.12226i	−0.0785388	−	0.394841i	−0.999980	−	0.00632347i	$-0.997987\pi$
$109$	−0.819969	−	4.12226i	−0.0785388	−	0.394841i	0.921441	−	0.388518i	$-0.127013\pi$
$110$	−2.79996	+	6.75970i	−0.266966	+	0.644513i
$111$	−2.91885	+	2.91499i	−0.277045	+	0.276678i
$112$	−8.92878	+	1.77604i	−0.843690	+	0.167820i
$113$	−9.15888	+	13.7072i	−0.861595	+	1.28947i	0.0942363	+	0.995550i	$0.469959\pi$
$113$	−9.15888	+	13.7072i	−0.861595	+	1.28947i	−0.955831	+	0.293917i	$0.905041\pi$
$114$	1.21018	−	1.80857i	0.113344	−	0.169388i
$115$	−1.65403	−	1.65403i	−0.154239	−	0.154239i
$116$	0.521156	+	0.779965i	0.0483881	+	0.0724180i
$117$	−12.2443	−	5.09076i	−1.13199	−	0.470641i
$118$		−	8.86518i		−	0.816106i
$119$		0			0
$120$	−13.3726	−	5.54949i	−1.22075	−	0.506597i
$121$	3.17039	+	7.65399i	0.288217	+	0.695817i
$122$	−7.07371	+	4.72650i	−0.640424	+	0.427917i
$123$	2.03795	+	4.92927i	0.183756	+	0.444457i
$124$	−0.0661465	+	0.332541i	−0.00594013	+	0.0298630i
$125$	1.74816	+	1.16808i	0.156360	+	0.104477i
$126$	−7.82144	−	5.24111i	−0.696789	−	0.466915i
$127$	−11.3753	−	4.71179i	−1.00939	−	0.418104i	−0.184159	−	0.982896i	$-0.558956\pi$
$127$	−11.3753	−	4.71179i	−1.00939	−	0.418104i	−0.825233	+	0.564792i	$0.808956\pi$
$128$	−11.2771	−	4.67113i	−0.996766	−	0.412874i
$129$	19.4423	+	3.88070i	1.71180	+	0.341677i
$130$	−16.3185	−	10.9037i	−1.43123	−	0.956315i
$131$	−0.687984	+	3.45873i	−0.0601094	+	0.302191i	−0.999132	−	0.0416661i	$-0.986733\pi$
$131$	−0.687984	+	3.45873i	−0.0601094	+	0.302191i	0.939022	+	0.343857i	$0.111733\pi$
$132$	−0.309609	+	0.128004i	−0.0269480	+	0.0111413i
$133$	−1.54836	+	1.03458i	−0.134260	+	0.0897094i
$134$	4.00644	+	9.67240i	0.346103	+	0.835568i
$135$	−6.03852	−	14.6606i	−0.519713	−	1.26178i
$136$		0			0
$137$		−	14.6484i		−	1.25150i	−0.780025	−	0.625748i	$-0.784794\pi$
$137$		−	14.6484i		−	1.25150i	0.780025	−	0.625748i	$-0.215206\pi$
$138$	0.00127919	−	1.93207i	0.000108892	−	0.164468i
$139$	−2.80264	−	4.19445i	−0.237717	−	0.355768i	0.693360	−	0.720591i	$-0.256130\pi$
$139$	−2.80264	−	4.19445i	−0.237717	−	0.355768i	−0.931077	+	0.364823i	$0.881130\pi$
$140$	−0.546249	−	0.546249i	−0.0461664	−	0.0461664i
$141$	−4.50390	−	3.01373i	−0.379297	−	0.253802i
$142$	1.75791	−	2.63090i	0.147520	−	0.220780i
$143$	7.14374	−	1.42098i	0.597389	−	0.118828i
$144$	−4.83041	−	11.7055i	−0.402534	−	0.975455i
$145$	9.33173	−	22.5288i	0.774958	−	1.87091i
$146$	3.57105	+	17.9529i	0.295542	+	1.48579i
$147$	−2.25751	−	3.38345i	−0.186196	−	0.279062i
$148$	−0.274193	−	0.0545404i	−0.0225385	−	0.00448319i
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	−0.865423	−	0.501041i	$-0.832950\pi$
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	0.501041	+	0.865423i	$0.332950\pi$
$150$	−2.11263	−	10.6578i	−0.172495	−	0.870203i
$151$	14.0551	−	5.82179i	1.14378	−	0.473771i	0.271339	−	0.962484i	$-0.412533\pi$
$151$	14.0551	−	5.82179i	1.14378	−	0.473771i	0.872445	+	0.488713i	$0.162533\pi$
$152$	−2.36528			−0.191850
$153$		0			0
$154$	5.17153			0.416734
$155$	8.14291	−	3.37291i	0.654055	−	0.270918i
$156$	−0.174738	−	0.881519i	−0.0139903	−	0.0705780i
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	−0.634025	−	0.773312i	$-0.718598\pi$
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	0.773312	+	0.634025i	$0.218598\pi$
$158$	8.50316	+	1.69138i	0.676475	+	0.134559i
$159$	6.12214	+	9.17558i	0.485518	+	0.727671i
$160$	−0.394786	−	1.98472i	−0.0312105	−	0.156906i
$161$	−0.632711	+	1.52750i	−0.0498646	+	0.120384i
$162$	5.04369	−	12.0859i	0.396270	−	0.949559i
$163$	−1.08953	+	0.216722i	−0.0853388	+	0.0169749i	−0.237575	−	0.971369i	$-0.576353\pi$
$163$	−1.08953	+	0.216722i	−0.0853388	+	0.0169749i	0.152236	+	0.988344i	$0.451353\pi$
$164$	−0.200831	+	0.300565i	−0.0156823	+	0.0234702i
$165$	7.23815	+	4.84331i	0.563489	+	0.377051i
$166$	−13.3627	−	13.3627i	−1.03715	−	1.03715i
$167$	11.0337	+	16.5131i	0.853815	+	1.27782i	0.959010	+	0.283373i	$0.0914534\pi$
$167$	11.0337	+	16.5131i	0.853815	+	1.27782i	−0.105195	+	0.994452i	$0.533547\pi$
$168$	−0.00677549	+	10.2335i	−0.000522740	+	0.789535i
$169$			6.53766i			0.502897i
$170$		0			0
$171$	−1.82916	−	1.83401i	−0.139879	−	0.140250i
$172$	0.514179	+	1.24134i	0.0392058	+	0.0946511i
$173$	9.67520	−	6.46476i	0.735591	−	0.491507i	−0.130465	−	0.991453i	$-0.541647\pi$
$173$	9.67520	−	6.46476i	0.735591	−	0.491507i	0.866056	+	0.499946i	$0.166647\pi$
$174$	18.6131	−	7.69538i	1.41106	−	0.583385i
$175$	−1.81391	+	9.11912i	−0.137118	+	0.689341i
$176$	5.78330	+	3.86428i	0.435933	+	0.291281i
$177$	−10.3482	−	2.06551i	−0.777819	−	0.155253i
$178$	−6.50257	−	2.69345i	−0.487389	−	0.201883i
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	0.353259	−	0.935526i	$-0.385073\pi$
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	−0.411725	+	0.911308i	$0.635073\pi$
$180$	0.598165	−	0.892656i	0.0445846	−	0.0665347i
$181$	1.19220	+	0.796600i	0.0886152	+	0.0592108i	0.599088	−	0.800683i	$-0.295530\pi$
$181$	1.19220	+	0.796600i	0.0886152	+	0.0592108i	−0.510473	+	0.859894i	$0.670530\pi$
$182$	−2.70630	+	13.6055i	−0.200604	+	1.00851i
$183$	3.86907	+	9.35828i	0.286010	+	0.691784i
$184$	−1.74610	+	1.16671i	−0.128724	+	0.0860109i
$185$	2.78110	+	6.71416i	0.204470	+	0.493635i
$186$	6.72393	+	2.79036i	0.493023	+	0.204599i
$187$		0			0
$188$		−	0.367264i		−	0.0267855i
$189$	−7.94021	+	7.90873i	−0.577565	+	0.575275i
$190$	−2.12989	−	3.18760i	−0.154518	−	0.231253i
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	0.688420	−	0.725312i	$-0.258304\pi$
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	−0.725312	+	0.688420i	$0.758304\pi$
$192$	−7.20204	+	10.7632i	−0.519762	+	0.776765i
$193$	−6.45656	+	9.66292i	−0.464753	+	0.695552i	−0.987621	−	0.156862i	$-0.949862\pi$
$193$	−6.45656	+	9.66292i	−0.464753	+	0.695552i	0.522867	+	0.852414i	$0.324862\pi$
$194$	−5.06278	+	1.00705i	−0.363486	+	0.0723019i
$195$	−16.5298	+	16.5079i	−1.18372	+	1.18215i
$196$	0.105488	−	0.254671i	0.00753488	−	0.0181908i
$197$	−4.53858	−	22.8170i	−0.323360	−	1.62564i	−0.710553	−	0.703643i	$-0.751555\pi$
$197$	−4.53858	−	22.8170i	−0.323360	−	1.62564i	0.387193	−	0.921999i	$-0.373445\pi$
$198$	1.39403	+	7.05706i	0.0990691	+	0.501524i
$199$	23.6514	+	4.70456i	1.67661	+	0.333497i	0.939570	−	0.342357i	$-0.111225\pi$
$199$	23.6514	+	4.70456i	1.67661	+	0.333497i	0.737035	+	0.675854i	$0.236225\pi$
$200$	−8.35068	+	8.35068i	−0.590482	+	0.590482i
$201$	12.2239	−	2.42308i	0.862209	−	0.170911i
$202$	5.02720	−	2.08233i	0.353712	−	0.146512i
$203$	−17.2357			−1.20971
$204$		0			0
$205$	9.39691			0.656309
$206$	12.5483	−	5.19767i	0.874281	−	0.362139i
$207$	−2.25498	−	0.451648i	−0.156732	−	0.0313917i
$208$	−13.1927	+	13.1927i	−0.914753	+	0.914753i
$209$	1.39544	+	0.277570i	0.0965244	+	0.0191999i
$210$	−13.7975	+	9.20598i	−0.952117	+	0.635273i
$211$	−3.04535	−	15.3100i	−0.209651	−	1.05398i	−0.932000	−	0.362457i	$-0.881938\pi$
$211$	−3.04535	−	15.3100i	−0.209651	−	1.05398i	0.722350	−	0.691528i	$-0.243062\pi$
$212$	−0.286074	+	0.690643i	−0.0196476	+	0.0474336i
$213$	−2.66143	−	2.66496i	−0.182358	−	0.182600i
$214$	2.69729	−	0.536524i	0.184383	−	0.0366760i
$215$	19.4047	−	29.0412i	1.32339	−	1.98059i
$216$	−13.9665	+	2.74929i	−0.950301	+	0.187065i
$217$	−4.40510	−	4.40510i	−0.299038	−	0.299038i
$218$	−3.39782	−	5.08520i	−0.230130	−	0.344413i
$219$	21.7882	+	0.0144256i	1.47231	+	0.000974794i
$220$			0.590224i			0.0397929i
$221$		0			0
$222$	−2.30077	+	5.54415i	−0.154417	+	0.372099i
$223$	−0.930718	−	2.24695i	−0.0623255	−	0.150467i	0.889648	−	0.456646i	$-0.150949\pi$
$223$	−0.930718	−	2.24695i	−0.0623255	−	0.150467i	−0.951974	+	0.306179i	$0.900949\pi$
$224$	−1.18926	+	0.794641i	−0.0794611	+	0.0530942i
$225$	−12.9329	−	0.0171254i	−0.862193	−	0.00114169i
$226$	−4.67992	+	23.5276i	−0.311304	+	1.56503i
$227$	−1.16773	−	0.780250i	−0.0775048	−	0.0517870i	0.516214	−	0.856460i	$-0.327341\pi$
$227$	−1.16773	−	0.780250i	−0.0775048	−	0.0517870i	−0.593719	+	0.804673i	$0.702341\pi$
$228$	0.0343609	−	0.172148i	0.00227560	−	0.0114008i
$229$	10.0488	+	4.16234i	0.664043	+	0.275055i	0.689139	−	0.724630i	$-0.257989\pi$
$229$	10.0488	+	4.16234i	0.664043	+	0.275055i	−0.0250960	+	0.999685i	$0.507989\pi$
$230$	−3.14466	−	1.30256i	−0.207353	−	0.0858884i
$231$	1.20492	−	6.03666i	0.0792780	−	0.397183i
$232$	−18.2026	−	12.1626i	−1.19506	−	0.798513i
$233$	2.79686	−	14.0608i	0.183228	−	0.921151i	−0.774302	−	0.632817i	$-0.781899\pi$
$233$	2.79686	−	14.0608i	0.183228	−	0.921151i	0.957530	−	0.288334i	$-0.0931014\pi$
$234$	−19.2955	−	0.0255506i	−1.26139	−	0.00167030i
$235$	−7.93813	+	5.30409i	−0.517826	+	0.346000i
$236$	−0.273673	−	0.660704i	−0.0178146	−	0.0430082i
$237$	3.95549	−	9.53155i	0.256937	−	0.619140i
$238$		0			0
$239$			23.7093i			1.53362i	0.641872	+	0.766812i	$0.278158\pi$
$239$			23.7093i			1.53362i	−0.641872	+	0.766812i	$0.721842\pi$
$240$	−22.3086	−	0.0147702i	−1.44001	−	0.000953412i
$241$	1.56359	+	2.34007i	0.100719	+	0.150737i	0.878406	−	0.477914i	$-0.158607\pi$
$241$	1.56359	+	2.34007i	0.100719	+	0.150737i	−0.777687	+	0.628652i	$0.783607\pi$
$242$	8.52427	+	8.52427i	0.547961	+	0.547961i
$243$	−12.9326	−	8.70334i	−0.829626	−	0.558320i
$244$	−0.381280	+	0.570626i	−0.0244090	+	0.0365306i
$245$	−7.02801	+	1.39796i	−0.449003	+	0.0893123i
$246$	5.48460	+	5.49187i	0.349686	+	0.350149i
$247$	−1.46048	+	3.52592i	−0.0929284	+	0.224349i
$248$	−1.54371	−	7.76073i	−0.0980254	−	0.492807i
$249$	−18.7116	+	12.4847i	−1.18580	+	0.791189i
$250$	3.00061	+	0.596858i	0.189775	+	0.0377486i
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	−0.959034	−	0.283289i	$-0.908574\pi$
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	0.283289	+	0.959034i	$0.408574\pi$
$252$	−0.744712	−	0.149158i	−0.0469124	−	0.00939606i
$253$	1.16706	−	0.483411i	0.0733723	−	0.0303918i
$254$	−17.9162			−1.12416
$255$		0			0
$256$	−2.80767			−0.175479
$257$	18.3799	−	7.61319i	1.14650	−	0.474898i	0.273145	−	0.961973i	$-0.411936\pi$
$257$	18.3799	−	7.61319i	1.14650	−	0.474898i	0.873360	+	0.487075i	$0.161936\pi$
$258$	28.2984	−	5.60943i	1.76178	−	0.349228i
$259$	3.63218	−	3.63218i	0.225693	−	0.225693i
$260$	−1.55279	−	0.308868i	−0.0962997	−	0.0191552i
$261$	−4.64602	−	23.5198i	−0.287581	−	1.45584i
$262$	1.00110	+	5.03288i	0.0618482	+	0.310932i
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	−0.925419	−	0.378946i	$-0.876287\pi$
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	0.922325	+	0.386415i	$0.126287\pi$
$264$	5.53235	−	5.52503i	0.340493	−	0.340042i
$265$	19.0593	−	3.79112i	1.17080	−	0.232887i
$266$	−1.50544	+	2.25305i	−0.0923045	+	0.138143i
$267$	−4.65908	+	6.96282i	−0.285131	+	0.426118i
$268$	0.597184	+	0.597184i	0.0364788	+	0.0364788i
$269$	−3.30317	−	4.94355i	−0.201398	−	0.301413i	0.716999	−	0.697075i	$-0.245515\pi$
$269$	−3.30317	−	4.94355i	−0.201398	−	0.301413i	−0.918396	+	0.395661i	$0.870515\pi$
$270$	−16.2817	−	16.3465i	−0.990873	−	0.994817i
$271$		−	6.87483i		−	0.417616i	−0.977957	−	0.208808i	$-0.933042\pi$
$271$		−	6.87483i		−	0.417616i	0.977957	−	0.208808i	$-0.0669584\pi$
$272$		0			0
$273$	15.2510	+	6.32899i	0.923030	+	0.383048i
$274$	−8.15697	−	19.6927i	−0.492781	−	1.18968i
$275$	5.90659	−	3.94666i	0.356181	−	0.237992i
$276$	−0.0595485	−	0.144033i	−0.00358440	−	0.00866974i
$277$	1.61874	−	8.13797i	0.0972608	−	0.488963i	−0.901195	−	0.433414i	$-0.857309\pi$
$277$	1.61874	−	8.13797i	0.0972608	−	0.488963i	0.998456	−	0.0555495i	$-0.0176911\pi$
$278$	−6.10344	−	4.07818i	−0.366060	−	0.244593i
$279$	4.82377	−	7.19863i	0.288792	−	0.430971i
$280$	16.6563	+	6.89927i	0.995404	+	0.412310i
$281$	−12.2411	−	5.07041i	−0.730240	−	0.302475i	−0.0135893	−	0.999908i	$-0.504326\pi$
$281$	−12.2411	−	5.07041i	−0.730240	−	0.302475i	−0.716651	+	0.697432i	$0.754326\pi$
$282$	−7.73306	−	1.54352i	−0.460497	−	0.0919155i
$283$	11.6680	+	7.79633i	0.693593	+	0.463444i	0.851735	−	0.523972i	$-0.175550\pi$
$283$	11.6680	+	7.79633i	0.693593	+	0.463444i	−0.158142	+	0.987416i	$0.550550\pi$
$284$	0.0497963	−	0.250343i	0.00295487	−	0.0148551i
$285$	−4.21709	+	1.74351i	−0.249799	+	0.103276i
$286$	8.81247	−	5.88830i	0.521092	−	0.348183i
$287$	−2.54174	−	6.13631i	−0.150034	−	0.362215i
$288$	−1.40494	−	1.40867i	−0.0827870	−	0.0830066i
$289$		0			0
$290$		−	35.4832i		−	2.08364i
$291$	−0.00406809	+	6.14435i	−0.000238475	+	0.360188i
$292$	0.820357	+	1.22775i	0.0480078	+	0.0718487i
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.995440	+	0.0953949i	$0.0304114\pi$
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.0953949	+	0.995440i	$0.469589\pi$
$294$	−4.91898	−	3.29147i	−0.286881	−	0.191963i
$295$	−10.3282	+	15.4572i	−0.601331	+	0.899955i
$296$	6.39904	−	1.27285i	0.371936	−	0.0739827i
$297$	8.56241	+	0.0170072i	0.496842	+	0.000986857i
$298$	−3.50271	+	8.45629i	−0.202907	+	0.489860i
$299$	0.661049	+	3.32332i	0.0382295	+	0.192193i
$300$	−0.486461	−	0.729085i	−0.0280858	−	0.0420937i
$301$	−24.2130	−	4.81627i	−1.39561	−	0.277605i
$302$	15.6531	−	15.6531i	0.900738	−	0.900738i
$303$	−1.25939	−	6.35335i	−0.0723499	−	0.364990i
$304$	−3.36705	+	1.39468i	−0.193114	+	0.0799904i
$305$	17.8402			1.02152
$306$		0			0
$307$	−24.4315			−1.39438			−0.697189	−	0.716887i	$-0.745566\pi$
$307$	−24.4315			−1.39438			−0.697189	+	0.716887i	$0.745566\pi$
$308$	0.385424	−	0.159648i	0.0219616	−	0.00909677i
$309$	−3.14353	−	15.8585i	−0.178829	−	0.902157i
$310$	9.06879	−	9.06879i	0.515073	−	0.515073i
$311$	22.8877	+	4.55265i	1.29784	+	0.258157i	0.795206	−	0.606340i	$-0.207363\pi$
$311$	22.8877	+	4.55265i	1.29784	+	0.258157i	0.502638	+	0.864497i	$0.332363\pi$
$312$	11.6404	+	17.4460i	0.659007	+	0.987688i
$313$	−0.314998	−	1.58360i	−0.0178048	−	0.0895106i	0.970861	−	0.239642i	$-0.0770302\pi$
$313$	−0.314998	−	1.58360i	−0.0178048	−	0.0895106i	−0.988666	+	0.150132i	$0.952030\pi$
$314$	1.37441	−	3.31812i	0.0775624	−	0.187252i
$315$	7.53133	+	18.2505i	0.424342	+	1.02830i
$316$	0.685937	−	0.136441i	0.0385870	−	0.00767543i
$317$	13.5476	−	20.2754i	0.760908	−	1.13878i	−0.225464	−	0.974251i	$-0.572390\pi$
$317$	13.5476	−	20.2754i	0.760908	−	1.13878i	0.986372	−	0.164528i	$-0.0526100\pi$
$318$	13.3398	+	8.92614i	0.748058	+	0.500553i
$319$	9.31162	+	9.31162i	0.521351	+	0.521351i
$320$	12.6754	+	18.9701i	0.708577	+	1.06046i
$321$	0.00216735	−	3.27351i	0.000120970	−	0.182710i
$322$			2.40583i			0.134072i
$323$		0			0
$324$	0.00279782	−	1.05644i	0.000155435	−	0.0586911i
$325$	7.29207	+	17.6046i	0.404491	+	0.976529i
$326$	−1.34404	+	0.898060i	−0.0744396	+	0.0497389i
$327$	−6.72755	+	2.78143i	−0.372034	+	0.153813i
$328$	1.64583	−	8.27415i	0.0908758	−	0.456863i
$329$	5.61080	+	3.74901i	0.309333	+	0.206690i
$330$	12.4277	+	2.48057i	0.684121	+	0.136551i
$331$	−28.1459	−	11.6584i	−1.54704	−	0.640804i	−0.564260	−	0.825597i	$-0.690839\pi$
$331$	−28.1459	−	11.6584i	−1.54704	−	0.640804i	−0.982777	+	0.184793i	$0.940839\pi$
$332$	−1.40841	−	0.583384i	−0.0772967	−	0.0320173i
$333$	5.93556	+	3.97739i	0.325267	+	0.217960i
$334$	24.0286	+	16.0554i	1.31479	+	0.878514i
$335$	4.28304	−	21.5323i	0.234008	−	1.17644i
$336$	6.02453	+	14.5718i	0.328665	+	0.794956i
$337$	14.3229	−	9.57025i	0.780218	−	0.521325i	−0.100517	−	0.994935i	$-0.532050\pi$
$337$	14.3229	−	9.57025i	0.780218	−	0.521325i	0.880734	+	0.473611i	$0.157050\pi$
$338$	3.64051	+	8.78896i	0.198018	+	0.478057i
$339$	26.3730	+	10.9445i	1.43239	+	0.594425i
$340$		0			0
$341$			4.75973i			0.257754i
$342$	−3.48031	−	1.44700i	−0.188194	−	0.0782446i
$343$	11.2015	+	16.7643i	0.604826	+	0.905186i
$344$	−22.1727	−	22.1727i	−1.19547	−	1.19547i
$345$	−2.25314	+	3.36724i	−0.121305	+	0.181286i
$346$	9.40702	−	14.0786i	0.505724	−	0.756870i
$347$	−19.8459	+	3.94759i	−1.06538	+	0.211918i	−0.696499	−	0.717558i	$-0.745260\pi$
$347$	−19.8459	+	3.94759i	−1.06538	+	0.211918i	−0.368884	+	0.929476i	$0.620260\pi$
$348$	1.14964	−	1.14812i	0.0616272	−	0.0615456i
$349$	2.90948	−	7.02410i	0.155741	−	0.375992i	−0.826680	−	0.562673i	$-0.809773\pi$
$349$	2.90948	−	7.02410i	0.155741	−	0.375992i	0.982421	+	0.186681i	$0.0597731\pi$
$350$	2.63946	+	13.2694i	0.141085	+	0.709281i
$351$	−4.52552	+	22.5175i	−0.241554	+	1.20189i
$352$	1.07181	+	0.213196i	0.0571276	+	0.0113634i
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	−0.445756	−	0.895155i	$-0.647065\pi$
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	0.895155	+	0.445756i	$0.147065\pi$
$354$	−15.0619	+	2.98563i	−0.800530	+	0.158684i
$355$	−6.13014	+	2.53919i	−0.325354	+	0.134766i
$356$	−0.567772			−0.0300919
$357$		0			0
$358$	−1.23200			−0.0651133
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.864839	−	0.502049i	$-0.832580\pi$
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.256531	+	0.966536i	$0.582580\pi$
$360$	−4.92490	+	24.5889i	−0.259565	+	1.29595i
$361$	12.9079	−	12.9079i	0.679363	−	0.679363i
$362$	2.04633	+	0.407040i	0.107553	+	0.0213935i
$363$	11.9364	−	7.96419i	0.626496	−	0.418012i
$364$	0.218313	+	1.09753i	0.0114427	+	0.0575264i
$365$	14.6892	−	35.4628i	0.768866	−	1.85621i
$366$	10.4126	+	10.4264i	0.544275	+	0.544996i
$367$	−16.0952	+	3.20154i	−0.840163	+	0.167119i	−0.596371	−	0.802709i	$-0.703391\pi$
$367$	−16.0952	+	3.20154i	−0.840163	+	0.167119i	−0.243792	+	0.969828i	$0.578391\pi$
$368$	−1.79769	+	2.69043i	−0.0937111	+	0.140249i
$369$	7.68845	−	5.12255i	0.400245	−	0.266669i
$370$	7.47758	+	7.47758i	0.388741	+	0.388741i
$371$	−7.63093	−	11.4205i	−0.396178	−	0.592923i
$372$	0.587261		0.000388817i	0.0304481		2.01592e-5i
$373$			1.61824i			0.0837894i	0.999122	+	0.0418947i	$0.0133394\pi$
$373$			1.61824i			0.0837894i	−0.999122	+	0.0418947i	$0.986661\pi$
$374$		0			0
$375$	1.39582	−	3.36351i	0.0720798	−	0.173691i
$376$	3.28001	+	7.91865i	0.169154	+	0.408373i
$377$	−29.3703	+	19.6246i	−1.51265	+	1.01072i
$378$	−6.27050	+	15.0537i	−0.322520	+	0.774278i
$379$	3.02965	−	15.2311i	0.155623	−	0.782368i	−0.821586	−	0.570085i	$-0.806910\pi$
$379$	3.02965	−	15.2311i	0.155623	−	0.782368i	0.977208	−	0.212283i	$-0.0680898\pi$
$380$	−0.257139	−	0.171815i	−0.0131910	−	0.00881393i
$381$	−4.17432	+	20.9134i	−0.213857	+	1.07142i
$382$	−0.969330	−	0.401510i	−0.0495952	−	0.0205430i
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.838247	−	0.545291i	$-0.183581\pi$
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.207151	+	0.978309i	$0.433581\pi$
$384$	−4.13830	+	20.7329i	−0.211182	+	1.05802i
$385$	−9.01702	−	6.02498i	−0.459550	−	0.307061i
$386$	−3.29912	+	16.5858i	−0.167921	+	0.844194i
$387$	0.0454712	−	34.3393i	0.00231143	−	1.74557i
$388$	−0.346231	+	0.231344i	−0.0175772	+	0.0117447i
$389$	5.80572	+	14.0162i	0.294362	+	0.710652i	0.999998	+	0.00207747i	$0.000661280\pi$
$389$	5.80572	+	14.0162i	0.294362	+	0.710652i	−0.705636	+	0.708574i	$0.749339\pi$
$390$	−13.0295	+	31.3972i	−0.659774	+	1.58986i
$391$		0			0
$392$			6.43314i			0.324922i
$393$	6.10806	+	0.00404406i	0.308111	+	0.000203996i
$394$	−18.8071	−	28.1469i	−0.947490	−	1.41802i
$395$	−12.8555	−	12.8555i	−0.646831	−	0.646831i
$396$	0.321749	+	0.482915i	0.0161685	+	0.0242674i
$397$	20.9101	−	31.2942i	1.04945	−	1.57061i	0.251526	−	0.967850i	$-0.419068\pi$
$397$	20.9101	−	31.2942i	1.04945	−	1.57061i	0.797922	−	0.602760i	$-0.205932\pi$
$398$	34.4157	−	6.84571i	1.72510	−	0.343145i
$399$	2.27920	+	2.28222i	0.114103	+	0.114254i
$400$	−6.96352	+	16.8114i	−0.348176	+	0.840571i
$401$	0.689420	+	3.46595i	0.0344280	+	0.173081i	0.994174	−	0.107789i	$-0.0343770\pi$
$401$	0.689420	+	3.46595i	0.0344280	+	0.173081i	−0.959746	+	0.280870i	$0.909377\pi$
$402$	15.0840	−	10.0644i	0.752324	−	0.501966i
$403$	−12.5221	−	2.49080i	−0.623770	−	0.124076i
$404$	0.310384	−	0.310384i	0.0154422	−	0.0154422i
$405$	−22.8746	+	15.1968i	−1.13665	+	0.755136i
$406$	−23.1710	+	9.59773i	−1.14996	+	0.476327i
$407$	−3.92459			−0.194535
$408$		0			0
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$	12.6328	−	5.23268i	0.623890	−	0.258424i
$411$	−24.8875	+	4.93331i	−1.22761	+	0.243342i
$412$	0.774744	−	0.774744i	0.0381689	−	0.0381689i
$413$	12.8874	+	2.56347i	0.634148	+	0.126140i
$414$	−3.28300	+	0.648511i	−0.161351	+	0.0318726i
$415$	7.73115	+	38.8671i	0.379507	+	1.90791i
$416$	−1.12177	+	2.70819i	−0.0549993	+	0.132780i
$417$	−6.18246	+	6.17428i	−0.302756	+	0.302356i
$418$	2.03053	−	0.403898i	0.0993165	−	0.0197553i
$419$	−17.4409	+	26.1021i	−0.852042	+	1.27517i	0.107670	+	0.994187i	$0.465661\pi$
$419$	−17.4409	+	26.1021i	−0.852042	+	1.27517i	−0.959712	+	0.280985i	$0.909339\pi$
$420$	−0.744106	+	1.11204i	−0.0363087	+	0.0542619i
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	0.918380	−	0.395699i	$-0.129498\pi$
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	−0.395699	+	0.918380i	$0.629498\pi$
$422$	−12.6194	−	18.8863i	−0.614305	−	0.919373i
$423$	−3.60347	+	8.66707i	−0.175207	+	0.421407i
$424$		−	17.4460i		−	0.847253i
$425$		0			0
$426$	−5.06191	−	2.10064i	−0.245250	−	0.101776i
$427$	−4.82553	−	11.6499i	−0.233524	−	0.563776i
$428$	0.184461	−	0.123253i	0.00891625	−	0.00595764i
$429$	−4.82011	−	11.6586i	−0.232717	−	0.562883i
$430$	9.91525	−	49.8473i	0.478156	−	2.40385i
$431$	−9.52337	−	6.36331i	−0.458724	−	0.306510i	0.304652	−	0.952464i	$-0.401460\pi$
$431$	−9.52337	−	6.36331i	−0.458724	−	0.306510i	−0.763376	+	0.645954i	$0.776460\pi$
$432$	−18.2607	+	12.1490i	−0.878568	+	0.584520i
$433$	24.7526	+	10.2528i	1.18953	+	0.492720i	0.887603	−	0.460610i	$-0.152369\pi$
$433$	24.7526	+	10.2528i	1.18953	+	0.492720i	0.301930	+	0.953330i	$0.402369\pi$
$434$	−8.37502	−	3.46905i	−0.402014	−	0.166520i
$435$	−41.4190	−	8.26727i	−1.98589	−	0.396385i
$436$	−0.410216	−	0.274097i	−0.0196458	−	0.0131269i
$437$	−0.129127	+	0.649167i	−0.00617700	+	0.0310539i
$438$	29.2991	−	12.1134i	1.39997	−	0.578799i
$439$	−7.08940	+	4.73699i	−0.338359	+	0.226084i	−0.713128	−	0.701034i	$-0.752722\pi$
$439$	−7.08940	+	4.73699i	−0.338359	+	0.226084i	0.374769	+	0.927118i	$0.377722\pi$
$440$	−5.27126	−	12.7259i	−0.251297	−	0.606685i
$441$	−4.98817	+	4.97498i	−0.237532	+	0.236904i
$442$		0			0
$443$			18.8773i			0.896886i	0.893811	+	0.448443i	$0.148021\pi$
$443$			18.8773i			0.896886i	−0.893811	+	0.448443i	$0.851979\pi$
$444$	−0.000320596		0.484221i	−1.52148e−5		0.0229801i
$445$	8.19987	+	12.2720i	0.388711	+	0.581747i
$446$	−2.50244	−	2.50244i	−0.118494	−	0.118494i
$447$	9.05482	+	6.05891i	0.428278	+	0.286577i
$448$	8.95919	−	13.4084i	0.423282	−	0.633486i
$449$	26.7408	−	5.31908i	1.26198	−	0.251023i	0.481633	−	0.876373i	$-0.340044\pi$
$449$	26.7408	−	5.31908i	1.26198	−	0.251023i	0.780345	+	0.625350i	$0.215044\pi$
$450$	−17.3960	+	7.17868i	−0.820055	+	0.338406i
$451$	−1.94197	+	4.68833i	−0.0914438	+	0.220765i
$452$	0.377522	+	1.89793i	0.0177572	+	0.0892713i
$453$	−14.6247	−	21.9188i	−0.687127	−	1.02983i
$454$	−2.00433	−	0.398685i	−0.0940677	−	0.0187112i
$455$	20.5695	−	20.5695i	0.964311	−	0.964311i
$456$	0.796583	+	4.01860i	0.0373034	+	0.188188i
$457$	−9.73907	+	4.03405i	−0.455574	+	0.188705i	−0.598657	−	0.801006i	$-0.704299\pi$
$457$	−9.73907	+	4.03405i	−0.455574	+	0.188705i	0.143082	+	0.989711i	$0.454299\pi$
$458$	15.8270			0.739546
$459$		0			0
$460$	−0.274576			−0.0128022
$461$	−9.13414	+	3.78349i	−0.425419	+	0.176215i	−0.585112	−	0.810952i	$-0.698950\pi$
$461$	−9.13414	+	3.78349i	−0.425419	+	0.176215i	0.159693	+	0.987167i	$0.448950\pi$
$462$	−1.74168	−	8.78639i	−0.0810301	−	0.408780i
$463$	−16.2123	+	16.2123i	−0.753448	+	0.753448i	−0.975121	−	0.221673i	$-0.928848\pi$
$463$	−16.2123	+	16.2123i	−0.753448	+	0.753448i	0.221673	+	0.975121i	$0.428848\pi$
$464$	−33.0836	−	6.58074i	−1.53587	−	0.305503i
$465$	−8.47293	−	12.6988i	−0.392923	−	0.588894i
$466$	−4.06977	−	20.4601i	−0.188529	−	0.947797i
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	0.511621	+	0.859211i	$0.329045\pi$
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	−0.969325	+	0.245783i	$0.920955\pi$
$468$	−1.43885	+	0.593759i	−0.0665107	+	0.0274465i
$469$	−15.2194	+	3.02732i	−0.702766	+	0.139789i
$470$	−7.71810	+	11.5509i	−0.356009	+	0.532806i
$471$	−3.55297	−	2.37742i	−0.163712	−	0.109546i
$472$	11.8014	+	11.8014i	0.543205	+	0.543205i
$473$	10.4791	+	15.6831i	0.481831	+	0.721111i
$474$	0.00994217	−	15.0164i	0.000456659	−	0.689728i
$475$			3.72217i			0.170785i
$476$		0			0
$477$	13.5274	−	13.4916i	0.619378	−	0.617740i
$478$	13.2025	+	31.8737i	0.603870	+	1.45787i
$479$	7.20443	−	4.81385i	0.329179	−	0.219950i	−0.379987	−	0.924992i	$-0.624072\pi$
$479$	7.20443	−	4.81385i	0.329179	−	0.219950i	0.709166	+	0.705041i	$0.249072\pi$
$480$	−3.23907	+	1.33916i	−0.147843	+	0.0611238i
$481$	2.05377	−	10.3250i	0.0936437	−	0.470778i
$482$	3.40509	+	2.27521i	0.155098	+	0.103633i
$483$	2.80830	+	0.560538i	0.127782	+	0.0255054i
$484$	0.898446	+	0.372148i	0.0408384	+	0.0169158i
$485$	10.0006	+	4.14240i	0.454106	+	0.188097i
$486$	−22.2325	−	4.49888i	−1.00849	−	0.204073i
$487$	32.2752	+	21.5656i	1.46253	+	0.977229i	0.995676	+	0.0928931i	$0.0296115\pi$
$487$	32.2752	+	21.5656i	1.46253	+	0.977229i	0.466851	+	0.884336i	$0.345389\pi$
$488$	3.12463	−	15.7086i	0.141445	−	0.711094i
$489$	0.735143	+	1.77812i	0.0332443	+	0.0804094i
$490$	−8.66971	+	5.79291i	−0.391658	+	0.261697i
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	0.775882	−	0.630878i	$-0.217305\pi$
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	−0.994730	+	0.102533i	$0.967305\pi$
$492$	0.578293	+	0.239986i	0.0260715	+	0.0108194i
$493$		0			0
$494$			5.55337i			0.249858i
$495$	5.79108	−	13.9287i	0.260290	−	0.626049i
$496$	−6.77361	−	10.1374i	−0.304144	−	0.455184i
$497$	3.31625	+	3.31625i	0.148754	+	0.148754i
$498$	−18.2029	+	27.2035i	−0.815691	+	1.21902i
$499$	−20.6206	+	30.8610i	−0.923106	+	1.38153i	0.00125143	+	0.999999i	$0.499602\pi$
$499$	−20.6206	+	30.8610i	−0.923106	+	1.38153i	−0.924358	+	0.381527i	$0.875398\pi$
$500$	0.242054	−	0.0481476i	0.0108250	−	0.00215323i
$501$	24.3397	−	24.3075i	1.08742	−	1.08598i
$502$	−8.43090	+	20.3540i	−0.376290	+	0.908444i
$503$	6.23297	+	31.3353i	0.277914	+	1.39717i	0.827375	+	0.561650i	$0.189833\pi$
$503$	6.23297	+	31.3353i	0.277914	+	1.39717i	−0.549460	+	0.835520i	$0.685167\pi$
$504$	17.3890	−	3.43496i	0.774568	−	0.153005i
$505$	−11.1913	−	2.22610i	−0.498008	−	0.0990600i
$506$	1.29976	−	1.29976i	0.0577812	−	0.0577812i
$507$	11.1074	−	2.20176i	0.493299	−	0.0977838i
$508$	−1.33526	+	0.553083i	−0.0592426	+	0.0245391i
$509$	−2.30289			−0.102074			−0.0510369	−	0.998697i	$-0.516253\pi$
$509$	−2.30289			−0.102074			−0.0510369	+	0.998697i	$0.516253\pi$
$510$		0			0
$511$	−27.1309			−1.20020
$512$	18.7797	−	7.77882i	0.829954	−	0.343778i
$513$	−2.49994	+	3.72539i	−0.110375	+	0.164480i
$514$	20.4697	−	20.4697i	0.902880	−	0.902880i
$515$	−27.9345	−	5.55652i	−1.23094	−	0.244849i
$516$	1.93586	−	1.29165i	0.0852214	−	0.0568616i
$517$	−1.00583	−	5.05666i	−0.0442364	−	0.222391i
$518$	2.86037	−	6.90554i	0.125677	−	0.303412i
$519$	−14.2420	−	14.2609i	−0.625155	−	0.625983i
$520$	36.2384	−	7.20827i	1.58916	−	0.316104i
$521$	−1.52929	+	2.28875i	−0.0669995	+	0.100272i	−0.863456	−	0.504423i	$-0.831705\pi$
$521$	−1.52929	+	2.28875i	−0.0669995	+	0.100272i	0.796457	+	0.604695i	$0.206705\pi$
$522$	−19.3430	−	29.0319i	−0.846619	−	1.27069i
$523$	29.8001	+	29.8001i	1.30307	+	1.30307i	0.926313	+	0.376755i	$0.122960\pi$
$523$	29.8001	+	29.8001i	1.30307	+	1.30307i	0.376755	+	0.926313i	$0.377040\pi$
$524$	0.229978	+	0.344186i	0.0100466	+	0.0150358i
$525$	16.1042	+	0.0106624i	0.702846	+	0.000465344i
$526$			0.190778i			0.00831830i
$527$		0			0
$528$	4.61767	−	11.1272i	0.200958	−	0.484249i
$529$	−8.57683	−	20.7063i	−0.372906	−	0.900274i
$530$	23.5114	−	15.7098i	1.02127	−	0.682390i
$531$	−0.0242021	+	18.2772i	−0.00105028	+	0.793161i
$532$	−0.0426446	+	0.214389i	−0.00184888	+	0.00929494i
$533$	−11.3180	−	7.56246i	−0.490238	−	0.327566i
$534$	−2.38621	+	11.9549i	−0.103262	+	0.517341i
$535$	−5.32803	−	2.20694i	−0.230351	−	0.0954144i
$536$	−18.2094	−	7.54259i	−0.786527	−	0.325790i
$537$	−0.287045	+	1.43810i	−0.0123869	+	0.0620585i
$538$	−7.19347	−	4.80652i	−0.310132	−	0.207224i
$539$	0.754939	−	3.79534i	0.0325175	−	0.163477i
$540$	−1.71807	−	0.715648i	−0.0739339	−	0.0307966i
$541$	12.1699	−	8.13164i	0.523223	−	0.349606i	−0.265742	−	0.964044i	$-0.585617\pi$
$541$	12.1699	−	8.13164i	0.523223	−	0.349606i	0.788965	+	0.614438i	$0.210617\pi$
$542$	−3.82826	−	9.24223i	−0.164438	−	0.396988i
$543$	0.951908	−	2.29381i	0.0408503	−	0.0984369i
$544$		0			0
$545$			12.8251i			0.549365i
$546$	24.0271	+	0.0159080i	1.02826	+	0.000680798i
$547$	15.2378	+	22.8049i	0.651520	+	0.975068i	0.999297	+	0.0374912i	$0.0119366\pi$
$547$	15.2378	+	22.8049i	0.651520	+	0.975068i	−0.347777	+	0.937577i	$0.613063\pi$
$548$	−1.21585	−	1.21585i	−0.0519384	−	0.0519384i
$549$	14.5966	−	9.72522i	0.622969	−	0.415062i
$550$	5.74287	−	8.59481i	0.244877	−	0.366484i
$551$	−6.76737	+	1.34611i	−0.288300	+	0.0573464i
$552$	2.57029	+	2.57369i	0.109399	+	0.109544i
$553$	−4.91757	+	11.8721i	−0.209116	+	0.504851i
$554$	−2.35547	−	11.8417i	−0.100074	−	0.503107i
$555$	10.4707	−	6.98627i	0.444456	−	0.296551i
$556$	−0.580773	−	0.115523i	−0.0246302	−	0.00489926i
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.399984	+	0.916522i	$0.630984\pi$
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.916522	+	0.399984i	$0.869016\pi$
$558$	2.47631	−	12.3637i	0.104831	−	0.523396i
$559$	−46.7436	+	19.3619i	−1.97705	+	0.818919i
$560$	27.7789			1.17387
$561$		0			0
$562$	−19.2798			−0.813270
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.957080	−	0.289825i	$-0.906403\pi$
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.471821	+	0.881695i	$0.656403\pi$
$564$	−0.623979	+	0.123688i	−0.0262742	+	0.00520819i
$565$	35.5701	−	35.5701i	1.49645	−	1.49645i
$566$	20.0274	+	3.98370i	0.841815	+	0.167448i
$567$	16.1110	+	10.8268i	0.676598	+	0.454685i
$568$	1.16213	+	5.84243i	0.0487620	+	0.245143i
$569$	−9.46803	+	22.8578i	−0.396920	+	0.958251i	0.591472	+	0.806326i	$0.298547\pi$
$569$	−9.46803	+	22.8578i	−0.396920	+	0.958251i	−0.988392	+	0.151925i	$0.951453\pi$
$570$	−4.69841	+	4.69219i	−0.196795	+	0.196534i
$571$	1.93303	−	0.384503i	0.0808947	−	0.0160910i	−0.154477	−	0.987996i	$-0.549369\pi$
$571$	1.93303	−	0.384503i	0.0808947	−	0.0160910i	0.235372	+	0.971905i	$0.424369\pi$
$572$	0.475001	−	0.710889i	0.0198608	−	0.0297238i
$573$	−0.694522	+	1.03794i	−0.0290141	+	0.0433605i
$574$	−6.83402	−	6.83402i	−0.285247	−	0.285247i
$575$	1.83601	+	2.74779i	0.0765671	+	0.114591i
$576$	20.7121	+	8.61137i	0.863003	+	0.358807i
$577$			26.8179i			1.11645i	0.829691	+	0.558223i	$0.188517\pi$
$577$			26.8179i			1.11645i	−0.829691	+	0.558223i	$0.811483\pi$
$578$		0			0
$579$	18.5917	+	7.71536i	0.772644	+	0.320639i
$580$	−1.09538	−	2.64449i	−0.0454833	−	0.109806i
$581$	23.2896	−	15.5616i	0.966214	−	0.645603i
$582$	3.41602	+	8.26247i	0.141599	+	0.342490i
$583$	−2.04732	+	10.2926i	−0.0847913	+	0.426275i
$584$	−28.6529	−	19.1452i	−1.18566	−	0.792235i
$585$	33.6137	+	22.5244i	1.38976	+	0.931270i
$586$	35.4995	+	14.7044i	1.46647	+	0.607433i
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.999994	−	0.00334911i	$-0.00106606\pi$
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.704735	+	0.709471i	$0.251066\pi$
$588$	−0.468212	−	0.0934554i	−0.0193087	−	0.00385403i
$589$	−2.07364	−	1.38557i	−0.0854430	−	0.0570912i
$590$	−5.27741	+	26.5313i	−0.217268	+	1.09228i
$591$	−37.2374	+	15.3953i	−1.53174	+	0.633280i
$592$	8.35871	−	5.58511i	0.343541	−	0.229547i
$593$	8.44534	+	20.3889i	0.346809	+	0.837270i	0.996993	+	0.0774935i	$0.0246917\pi$
$593$	8.44534	+	20.3889i	0.346809	+	0.837270i	−0.650184	+	0.759777i	$0.725308\pi$
$594$	11.5204	−	4.74513i	0.472689	−	0.194695i
$595$		0			0
$596$			0.738361i			0.0302444i
$597$	0.0276540	−	41.7680i	0.00113180	−	1.70945i
$598$	2.73928	+	4.09963i	0.112018	+	0.167646i
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	0.962655	−	0.270729i	$-0.0872649\pi$
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	−0.270729	+	0.962655i	$0.587265\pi$
$600$	17.0001	+	11.3754i	0.694026	+	0.464398i
$601$	1.46551	−	2.19329i	0.0597794	−	0.0894662i	−0.800376	−	0.599499i	$-0.795367\pi$
$601$	1.46551	−	2.19329i	0.0597794	−	0.0894662i	0.860155	+	0.510033i	$0.170367\pi$
$602$	−35.2329	+	7.00826i	−1.43599	+	0.285635i
$603$	−8.23359	−	19.9523i	−0.335298	−	0.812521i
$604$	0.683377	−	1.64982i	0.0278062	−	0.0671302i
$605$	−4.93180	−	24.7939i	−0.200506	−	1.00801i
$606$	−5.23094	−	7.83988i	−0.212492	−	0.318473i
$607$	35.5752	+	7.07635i	1.44395	+	0.287220i	0.854024	−	0.520234i	$-0.174155\pi$
$607$	35.5752	+	7.07635i	1.44395	+	0.287220i	0.589930	+	0.807454i	$0.299155\pi$
$608$	−0.404887	+	0.404887i	−0.0164203	+	0.0164203i
$609$	5.80467	+	29.2833i	0.235217	+	1.18662i
$610$	23.9836	−	9.93432i	0.971066	−	0.402229i
$611$	13.8296			0.559487
$612$		0			0
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$	−32.8447	+	13.6047i	−1.32550	+	0.549041i
$615$	−3.16471	−	15.9653i	−0.127613	−	0.643783i
$616$	−6.88440	+	6.88440i	−0.277380	+	0.277380i
$617$	−9.68025	−	1.92552i	−0.389712	−	0.0775186i	−0.00365472	−	0.999993i	$-0.501163\pi$
$617$	−9.68025	−	1.92552i	−0.389712	−	0.0775186i	−0.386057	+	0.922475i	$0.626163\pi$
$618$	−13.0568	−	19.5690i	−0.525223	−	0.787180i
$619$	−6.30326	−	31.6886i	−0.253349	−	1.27367i	−0.872583	−	0.488466i	$-0.837557\pi$
$619$	−6.30326	−	31.6886i	−0.253349	−	1.27367i	0.619233	−	0.785207i	$-0.287443\pi$
$620$	0.395921	−	0.955837i	0.0159006	−	0.0383873i
$621$	−0.00791187	+	3.98330i	−0.000317492	+	0.159844i
$622$	33.3044	−	6.62467i	1.33539	−	0.265625i
$623$	5.79580	−	8.67402i	0.232204	−	0.347517i
$624$	26.8575	+	17.9713i	1.07516	+	0.719428i
$625$	−19.7780	−	19.7780i	−0.791122	−	0.791122i
$626$	−1.30530	−	1.95352i	−0.0521704	−	0.0780785i
$627$	0.00163159	−	2.46432i	6.51594e−5	−	0.0984154i
$628$		−	0.289721i		−	0.0115611i
$629$		0			0
$630$	20.2876	+	20.3414i	0.808279	+	0.810422i
$631$	1.47845	+	3.56930i	0.0588563	+	0.142092i	0.950572	−	0.310504i	$-0.100498\pi$
$631$	1.47845	+	3.56930i	0.0588563	+	0.142092i	−0.891716	+	0.452596i	$0.850498\pi$
$632$	−13.5711	+	9.06791i	−0.539829	+	0.360702i
$633$	−24.9860	+	10.3302i	−0.993104	+	0.410587i
$634$	6.92242	−	34.8014i	0.274925	−	1.38214i
$635$	31.2385	+	20.8729i	1.23966	+	0.828316i
$636$	1.26974	+	0.253442i	0.0503486	+	0.0100496i
$637$	9.58987	+	3.97225i	0.379964	+	0.157386i
$638$	17.7033	+	7.33297i	0.700882	+	0.290315i
$639$	−3.63143	+	5.41927i	−0.143657	+	0.214383i
$640$	30.9690	+	20.6928i	1.22416	+	0.817955i
$641$	−7.30038	+	36.7015i	−0.288348	+	1.44962i	0.516575	+	0.856242i	$0.327207\pi$
$641$	−7.30038	+	36.7015i	−0.288348	+	1.44962i	−0.804922	+	0.593380i	$0.797793\pi$
$642$	−1.81995	−	4.40198i	−0.0718276	−	0.173732i
$643$	35.3195	−	23.5997i	1.39286	−	0.930682i	0.392925	−	0.919570i	$-0.371463\pi$
$643$	35.3195	−	23.5997i	1.39286	−	0.930682i	0.999938	−	0.0111111i	$-0.00353683\pi$
$644$	0.0742693	+	0.179302i	0.00292662	+	0.00706549i
$645$	−55.8760	−	23.1879i	−2.20011	−	0.913024i
$646$		0			0
$647$		−	48.3331i		−	1.90017i	−0.311989	−	0.950086i	$-0.600995\pi$
$647$		−	48.3331i		−	1.90017i	0.311989	−	0.950086i	$-0.399005\pi$
$648$	9.37469	+	22.8031i	0.368272	+	0.895791i
$649$	−5.57753	−	8.34737i	−0.218937	−	0.327663i
$650$	19.6063	+	19.6063i	0.769023	+	0.769023i
$651$	−6.00068	+	8.96780i	−0.235185	+	0.351476i
$652$	−0.0724451	+	0.108422i	−0.00283717	+	0.00424613i
$653$	6.34586	−	1.26227i	0.248333	−	0.0493965i	−0.0693542	−	0.997592i	$-0.522094\pi$
$653$	6.34586	−	1.26227i	0.248333	−	0.0493965i	0.317687	+	0.948196i	$0.397094\pi$
$654$	−7.49540	+	7.48548i	−0.293093	+	0.292705i
$655$	4.11794	−	9.94158i	0.160901	−	0.388450i
$656$	−2.53593	−	12.7490i	−0.0990114	−	0.497764i
$657$	−7.31334	−	37.0228i	−0.285321	−	1.44440i
$658$	9.63056	+	1.91564i	0.375439	+	0.0746794i
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	−0.962125	−	0.272610i	$-0.912113\pi$
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	0.272610	+	0.962125i	$0.412113\pi$
$660$	1.00279	−	0.198776i	0.0390334	−	0.00773736i
$661$	23.0223	−	9.53615i	0.895464	−	0.370913i	0.112990	−	0.993596i	$-0.463957\pi$
$661$	23.0223	−	9.53615i	0.895464	−	0.370913i	0.782474	+	0.622683i	$0.213957\pi$
$662$	−44.3302			−1.72294
$663$		0			0
$664$	35.5773			1.38067
$665$	5.24974	−	2.17451i	0.203576	−	0.0843240i
$666$	10.1943	+	2.04182i	0.395022	+	0.0791188i
$667$	−4.33184	+	4.33184i	−0.167729	+	0.167729i
$668$	2.28645	+	0.454802i	0.0884652	+	0.0175968i
$669$	−3.50411	+	2.33802i	−0.135477	+	0.0903929i
$670$	−6.23235	−	31.3321i	−0.240777	−	1.21047i
$671$	−3.68686	+	8.90086i	−0.142329	+	0.343614i
$672$	1.75061	+	1.75293i	0.0675313	+	0.0676208i
$673$	18.4220	−	3.66436i	0.710115	−	0.141251i	0.173200	−	0.984887i	$-0.444589\pi$
$673$	18.4220	−	3.66436i	0.710115	−	0.141251i	0.536915	+	0.843636i	$0.319589\pi$
$674$	13.9259	−	20.8416i	0.536405	−	0.802787i
$675$	4.32647	+	21.9787i	0.166526	+	0.845960i
$676$	0.542640	+	0.542640i	0.0208708	+	0.0208708i
$677$	−5.50607	−	8.24041i	−0.211615	−	0.316705i	0.710444	−	0.703754i	$-0.248494\pi$
$677$	−5.50607	−	8.24041i	−0.211615	−	0.316705i	−0.922059	+	0.387049i	$0.873494\pi$
$678$	41.5493	+	0.0275092i	1.59569	+	0.00105648i
$679$		−	7.65102i		−	0.293619i
$680$		0			0
$681$	−0.932371	+	2.24673i	−0.0357285	+	0.0860950i
$682$	2.65046	+	6.39878i	0.101491	+	0.245022i
$683$	1.98540	−	1.32660i	0.0759692	−	0.0507610i	−0.517006	−	0.855982i	$-0.672953\pi$
$683$	1.98540	−	1.32660i	0.0759692	−	0.0507610i	0.592975	+	0.805221i	$0.297953\pi$
$684$	−0.304050		0.000402615i	−0.0116257		1.53944e-5i
$685$	−8.72013	+	43.8391i	−0.333179	+	1.67500i
$686$	24.3941	+	16.2996i	0.931370	+	0.622322i
$687$	3.68755	−	18.4746i	0.140689	−	0.704851i
$688$	−44.6375	−	18.4895i	−1.70179	−	0.704905i
$689$	−26.0068	−	10.7724i	−0.990779	−	0.410394i
$690$	−1.15398	+	5.78144i	−0.0439313	+	0.220096i
$691$	−27.1095	−	18.1140i	−1.03129	−	0.689088i	−0.0798165	−	0.996810i	$-0.525433\pi$
$691$	−27.1095	−	18.1140i	−1.03129	−	0.689088i	−0.951476	+	0.307722i	$0.900433\pi$
$692$	0.266473	−	1.33965i	0.0101298	−	0.0509258i
$693$	−10.6620	−	0.0141184i	−0.405017	−	0.000536313i
$694$	−24.4818	+	16.3582i	−0.929315	+	0.620948i
$695$	5.89068	+	14.2214i	0.223446	+	0.539447i
$696$	−14.5338	+	35.0222i	−0.550904	+	1.32751i
$697$		0			0
$698$		−	11.0631i		−	0.418743i
$699$	−24.8311	−	0.0164403i	−0.939197	−	0.000621829i
$700$	0.606348	+	0.907464i	0.0229178	+	0.0342989i
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.974807	−	0.223051i	$-0.928398\pi$
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.223051	−	0.974807i	$-0.571602\pi$
$702$	6.45497	+	32.7916i	0.243627	+	1.23764i
$703$	1.14245	−	1.70980i	0.0430885	−	0.0644864i
$704$	−12.0841	+	2.40368i	−0.455437	+	0.0905921i
$705$	11.6850	+	11.7005i	0.440083	+	0.440667i
$706$	6.64926	−	16.0527i	0.250248	−	0.604153i
$707$	1.57344	+	7.91022i	0.0591753	+	0.297495i
$708$	−1.03036	+	0.687481i	−0.0387235	+	0.0258371i
$709$	−38.7263	−	7.70314i	−1.45440	−	0.289297i	−0.596290	−	0.802769i	$-0.703359\pi$
$709$	−38.7263	−	7.70314i	−1.45440	−	0.289297i	−0.858106	+	0.513472i	$0.828359\pi$
$710$	−6.82716	+	6.82716i	−0.256219	+	0.256219i
$711$	−17.5262	−	3.51030i	−0.657283	−	0.131647i
$712$	12.2419	−	5.07074i	0.458783	−	0.190034i
$713$	−2.21426			−0.0829248
$714$		0			0
$715$	−22.2254			−0.831182
$716$	−0.0918186	+	0.0380325i	−0.00343142	+	0.00142134i
$717$	40.2819	−	7.98484i	1.50435	−	0.298199i
$718$	−23.6628	+	23.6628i	−0.883086	+	0.883086i
$719$	−43.1030	−	8.57373i	−1.60747	−	0.319746i	−0.691929	−	0.721966i	$-0.743239\pi$
$719$	−43.1030	−	8.57373i	−1.60747	−	0.319746i	−0.915543	+	0.402220i	$0.868239\pi$
$720$	7.48802	+	37.9071i	0.279062	+	1.41271i
$721$	3.92744	+	19.7446i	0.146265	+	0.735326i
$722$	10.1650	−	24.5406i	0.378304	−	0.913307i
$723$	3.44918	−	3.44461i	0.128276	−	0.128107i
$724$	0.165074	−	0.0328353i	0.00613493	−	0.00122031i
$725$	−19.1399	+	28.6448i	−0.710837	+	1.06384i
$726$	11.6119	−	17.3535i	0.430957	−	0.644049i
$727$	−0.0802760	−	0.0802760i	−0.00297727	−	0.00297727i	0.705617	−	0.708594i	$-0.250670\pi$
$727$	−0.0802760	−	0.0802760i	−0.00297727	−	0.00297727i	−0.708594	+	0.705617i	$0.750670\pi$
$728$	−14.5091	−	21.7144i	−0.537744	−	0.804790i
$729$	−10.4315	+	24.9035i	−0.386351	+	0.922352i
$730$		−	55.8544i		−	2.06726i
$731$		0			0
$732$	1.09790	+	0.455616i	0.0405795	+	0.0168400i
$733$	3.12587	+	7.54651i	0.115457	+	0.278737i	0.971035	−	0.238936i	$-0.0767986\pi$
$733$	3.12587	+	7.54651i	0.115457	+	0.278737i	−0.855579	+	0.517673i	$0.826799\pi$
$734$	−19.8549	+	13.2667i	−0.732860	+	0.489681i
$735$	4.74203	+	11.4697i	0.174912	+	0.423068i
$736$	−0.0991804	+	0.498613i	−0.00365584	+	0.0183791i
$737$	9.85781	+	6.58678i	0.363117	+	0.242627i
$738$	7.48354	−	11.1679i	0.275473	−	0.411095i
$739$	10.8531	+	4.49550i	0.399237	+	0.165370i	0.573263	−	0.819372i	$-0.305677\pi$
$739$	10.8531	+	4.49550i	0.399237	+	0.165370i	−0.174025	+	0.984741i	$0.555677\pi$
$740$	0.788126	+	0.326452i	0.0289721	+	0.0120006i
$741$	6.48238	+	1.29389i	0.238136	+	0.0475322i
$742$	−16.6182	−	11.1039i	−0.610074	−	0.407639i
$743$	−8.00737	+	40.2557i	−0.293762	+	1.47684i	0.498623	+	0.866819i	$0.333839\pi$
$743$	−8.00737	+	40.2557i	−0.293762	+	1.47684i	−0.792385	+	0.610021i	$0.791161\pi$
$744$	−12.6655	+	5.23642i	−0.464341	+	0.191976i
$745$	15.9591	−	10.6635i	0.584697	−	0.390682i
$746$	0.901121	+	2.17550i	0.0329924	+	0.0796507i
$747$	27.5132	+	27.5862i	1.00666	+	1.00933i
$748$		0			0
$749$			4.07622i			0.148942i
$750$	0.00350841	−	5.29902i	0.000128109	−	0.193493i
$751$	−0.938366	−	1.40436i	−0.0342414	−	0.0512460i	0.813954	−	0.580929i	$-0.197311\pi$
$751$	−0.938366	−	1.40436i	−0.0342414	−	0.0512460i	−0.848195	+	0.529683i	$0.822311\pi$
$752$	9.33841	+	9.33841i	0.340537	+	0.340537i
$753$	21.7946	+	14.5836i	0.794241	+	0.531456i
$754$	−28.5562	+	42.7373i	−1.03995	+	1.55640i
$755$	−45.5290	+	9.05629i	−1.65697	+	0.329592i
$756$	−0.00261291	+	1.31549i	−9.50307e−5	+	0.0478441i
$757$	20.8300	−	50.2881i	0.757080	−	1.82775i	0.242954	−	0.970038i	$-0.421884\pi$
$757$	20.8300	−	50.2881i	0.757080	−	1.82775i	0.514126	−	0.857715i	$-0.328116\pi$
$758$	−4.40851	−	22.1631i	−0.160124	−	0.805000i
$759$	−1.21436	−	1.82002i	−0.0440783	−	0.0660625i
$760$	7.07871	+	1.40804i	0.256772	+	0.0510751i
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	−0.117963	−	0.993018i	$-0.537636\pi$
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	0.993018	+	0.117963i	$0.0376365\pi$
$762$	6.03385	+	30.4395i	0.218583	+	1.10271i
$763$	8.37493	−	3.46901i	0.303193	−	0.125587i
$764$	−0.0846370			−0.00306206
$765$		0			0
$766$	32.2229			1.16426
$767$	24.8794	−	10.3054i	0.898343	−	0.372106i
$768$	0.945571	+	4.77021i	0.0341204	+	0.172130i
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.139204	−	0.990264i	$-0.455546\pi$
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.990264	−	0.139204i	$-0.0444544\pi$
$770$	−15.4771	−	3.07859i	−0.557757	−	0.110945i
$771$	−19.1248	−	28.6633i	−0.688761	−	1.03228i
$772$	0.266135	+	1.33795i	0.00957840	+	0.0481539i
$773$	−5.31114	+	12.8222i	−0.191028	+	0.461184i	−0.990154	−	0.139980i	$-0.955296\pi$
$773$	−5.31114	+	12.8222i	−0.191028	+	0.461184i	0.799126	+	0.601164i	$0.205296\pi$
$774$	−19.0608	−	46.1897i	−0.685125	−	1.66025i
$775$	−12.2128	+	2.42928i	−0.438698	+	0.0872624i
$776$	5.39903	−	8.08023i	0.193814	−	0.290063i
$777$	−7.39431	−	4.94780i	−0.265269	−	0.177501i
$778$	15.6099	+	15.6099i	0.559643	+	0.559643i
$779$	−1.47723	−	2.21083i	−0.0529272	−	0.0792111i
$780$	−0.00181557	+	2.74219i	−6.50078e−5	+	0.0981863i
$781$		−	3.58322i		−	0.128218i
$782$		0			0
$783$	−38.3954	+	15.8146i	−1.37214	+	0.565168i
$784$	3.79328	+	9.15778i	0.135474	+	0.327064i
$785$	−6.26211	+	4.18421i	−0.223504	+	0.149341i
$786$	8.21367	−	3.39584i	0.292972	−	0.121126i
$787$	4.67010	−	23.4782i	0.166471	−	0.836907i	−0.803802	−	0.594896i	$-0.797193\pi$
$787$	4.67010	−	23.4782i	0.166471	−	0.836907i	0.970274	−	0.242011i	$-0.0778069\pi$
$788$	−2.27057	−	1.51714i	−0.0808856	−	0.0540460i
$789$	0.222692	+	0.0444496i	0.00792806	+	0.00158245i
$790$	−24.4410	−	10.1238i	−0.869572	−	0.360189i
$791$	−32.8490	−	13.6065i	−1.16798	−	0.483792i
$792$	−11.2502	−	7.53870i	−0.399758	−	0.267876i
$793$	−21.4874	−	14.3574i	−0.763040	−	0.509847i
$794$	10.6845	−	53.7144i	0.379178	−	1.90625i
$795$	−12.8599	−	31.1048i	−0.456094	−	1.10317i
$796$	2.35361	−	1.57263i	0.0834213	−	0.0557403i
$797$	−17.9210	−	43.2651i	−0.634795	−	1.53253i	−0.833529	−	0.552476i	$-0.813683\pi$
$797$	−17.9210	−	43.2651i	−0.634795	−	1.53253i	0.198734	−	0.980053i	$-0.436317\pi$
$798$	4.33492	+	1.79895i	0.153455	+	0.0636820i
$799$		0			0
$800$			2.85893i			0.101078i
$801$	13.3989	+	5.57079i	0.473426	+	0.196834i
$802$	2.85685	+	4.27557i	0.100879	+	0.150976i
$803$	14.6575	+	14.6575i	0.517252	+	0.517252i
$804$	0.813491	−	1.21573i	0.0286896	−	0.0428755i
$805$	2.80287	−	4.19478i	0.0987880	−	0.147847i
$806$	−18.2212	+	3.62442i	−0.641814	+	0.127665i
$807$	−7.28661	+	7.27696i	−0.256501	+	0.256161i
$808$	−3.92024	+	9.46429i	−0.137913	+	0.332952i
$809$	2.28565	+	11.4907i	0.0803592	+	0.403993i	0.999939	+	0.0110886i	$0.00352967\pi$
$809$	2.28565	+	11.4907i	0.0803592	+	0.403993i	−0.919579	+	0.392904i	$0.871470\pi$
$810$	−22.2892	+	33.1677i	−0.783164	+	1.16539i
$811$	18.4661	+	3.67314i	0.648434	+	0.128982i	0.508340	−	0.861157i	$-0.330259\pi$
$811$	18.4661	+	3.67314i	0.648434	+	0.128982i	0.140094	+	0.990138i	$0.455259\pi$
$812$	−1.43060	+	1.43060i	−0.0502042	+	0.0502042i
$813$	−11.6803	+	2.31531i	−0.409645	+	0.0812016i
$814$	−5.27605	+	2.18541i	−0.184926	+	0.0765987i
$815$	3.38972			0.118737
$816$		0			0
$817$	−9.88307			−0.345765
$818$	16.4118	−	6.79797i	0.573824	−	0.237686i
$819$	5.61666	−	28.0428i	0.196262	−	0.979893i
$820$	0.779963	−	0.779963i	0.0272375	−	0.0272375i
$821$	29.7119	+	5.91006i	1.03695	+	0.206263i	0.684079	−	0.729408i	$-0.260205\pi$
$821$	29.7119	+	5.91006i	1.03695	+	0.206263i	0.352874	+	0.935671i	$0.385205\pi$
$822$	−30.7106	+	20.4908i	−1.07116	+	0.714698i
$823$	−4.47717	−	22.5083i	−0.156064	−	0.784589i	−0.976945	−	0.213489i	$-0.931517\pi$
$823$	−4.47717	−	22.5083i	−0.156064	−	0.784589i	0.820881	−	0.571099i	$-0.193483\pi$
$824$	−9.78523	+	23.6236i	−0.340884	+	0.822968i
$825$	−8.69457	−	8.70609i	−0.302706	−	0.303107i
$826$	18.7528	−	3.73016i	0.652493	−	0.129789i
$827$	−9.72768	+	14.5585i	−0.338265	+	0.506249i	−0.961136	−	0.276076i	$-0.910966\pi$
$827$	−9.72768	+	14.5585i	−0.338265	+	0.506249i	0.622871	+	0.782324i	$0.285966\pi$
$828$	−0.224655	+	0.149680i	−0.00780732	+	0.00520174i
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.996380	−	0.0850121i	$-0.972907\pi$
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.0850121	−	0.996380i	$-0.527093\pi$
$830$	32.0366	+	47.9462i	1.11201	+	1.66424i
$831$	−14.3715	−	0.00951518i	−0.498542	−	0.000330078i
$832$		−	33.0493i		−	1.14578i
$833$		0			0
$834$	−4.87328	+	11.7432i	−0.168748	+	0.406632i
$835$	−23.1910	−	55.9881i	−0.802559	−	1.93755i
$836$	0.138863	−	0.0927852i	0.00480267	−	0.00320904i
$837$	−13.8550	−	5.77119i	−0.478898	−	0.199481i
$838$	−8.91178	+	44.8026i	−0.307852	+	1.54768i
$839$	−16.4446	−	10.9879i	−0.567731	−	0.379346i	0.238325	−	0.971186i	$-0.423402\pi$
$839$	−16.4446	−	10.9879i	−0.567731	−	0.379346i	−0.806056	+	0.591840i	$0.798402\pi$
$840$	6.11227	−	30.6225i	0.210893	−	1.05658i
$841$	−32.2093	−	13.3415i	−1.11067	−	0.460053i
$842$	20.3896	+	8.44564i	0.702671	+	0.291056i
$843$	−4.49203	+	22.5051i	−0.154714	+	0.775116i
$844$	−1.52353	−	1.01799i	−0.0524422	−	0.0350407i
$845$	3.89185	−	19.5656i	0.133884	−	0.673078i
$846$	−0.0180859	+	13.6582i	−0.000621805	+	0.469580i
$847$	−14.8567	+	9.92694i	−0.510483	+	0.341094i
$848$	−10.2870	−	24.8350i	−0.353257	−	0.852837i
$849$	9.31634	−	22.4496i	0.319736	−	0.770468i
$850$		0			0
$851$		−	1.82575i		−	0.0625858i
$852$	−0.442102		0.000292709i	−0.0151462		1.00281e-5i
$853$	−3.43080	−	5.13456i	−0.117469	−	0.175804i	0.768076	−	0.640359i	$-0.221214\pi$
$853$	−3.43080	−	5.13456i	−0.117469	−	0.175804i	−0.885544	+	0.464555i	$0.846214\pi$
$854$	−12.9745	−	12.9745i	−0.443977	−	0.443977i
$855$	4.38245	+	6.57763i	0.149877	+	0.224950i
$856$	−2.87643	+	4.30489i	−0.0983145	+	0.147138i
$857$	25.5035	−	5.07296i	0.871184	−	0.173289i	0.260798	−	0.965393i	$-0.416014\pi$
$857$	25.5035	−	5.07296i	0.871184	−	0.173289i	0.610386	+	0.792104i	$0.291014\pi$
$858$	−12.9721	−	12.9893i	−0.442859	−	0.443446i
$859$	1.25664	−	3.03380i	0.0428761	−	0.103512i	−0.900991	−	0.433838i	$-0.857159\pi$
$859$	1.25664	−	3.03380i	0.0428761	−	0.103512i	0.943867	+	0.330326i	$0.107159\pi$
$860$	−0.799849	−	4.02111i	−0.0272746	−	0.137119i
$861$	−9.56953	+	6.38500i	−0.326129	+	0.217600i
$862$	−16.3462	−	3.25147i	−0.556755	−	0.110745i
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	−0.507750	−	0.861504i	$-0.669523\pi$
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	0.861504	+	0.507750i	$0.169523\pi$
$864$	−1.92016	+	2.86140i	−0.0653251	+	0.0973468i
$865$	−32.8040	+	13.5878i	−1.11537	+	0.462000i
$866$	38.9856			1.32479
$867$		0			0
$868$	−0.731265			−0.0248208
$869$	9.07062	−	3.75718i	0.307700	−	0.127453i
$870$	−60.2856	+	11.9501i	−2.04387	+	0.405145i
$871$	−22.4875	+	22.4875i	−0.761958	+	0.761958i
$872$	11.2927	+	2.24626i	0.382419	+	0.0760679i
$873$	10.4406	−	2.06239i	0.353360	−	0.0698014i
$874$	0.187896	+	0.944618i	0.00635569	+	0.0319522i
$875$	−1.73532	+	4.18943i	−0.0586644	+	0.141629i
$876$	1.80966	−	1.80726i	0.0611427	−	0.0610618i
$877$	13.0801	−	2.60180i	0.441684	−	0.0878565i	0.0307618	−	0.999527i	$-0.490207\pi$
$877$	13.0801	−	2.60180i	0.441684	−	0.0878565i	0.410923	+	0.911670i	$0.365207\pi$
$878$	−6.89290	+	10.3160i	−0.232624	+	0.348146i
$879$	25.4353	−	38.0121i	0.857912	−	1.28212i
$880$	−15.0076	−	15.0076i	−0.505907	−	0.505907i
$881$	−10.9553	−	16.3958i	−0.369094	−	0.552389i	0.599709	−	0.800218i	$-0.295283\pi$
$881$	−10.9553	−	16.3958i	−0.369094	−	0.552389i	−0.968804	+	0.247829i	$0.920283\pi$
$882$	−3.93557	+	9.46583i	−0.132517	+	0.318731i
$883$		−	44.5932i		−	1.50068i	−0.661051	−	0.750341i	$-0.729889\pi$
$883$		−	44.5932i		−	1.50068i	0.661051	−	0.750341i	$-0.270111\pi$
$884$		0			0
$885$	29.7401	+	12.3418i	0.999702	+	0.414866i
$886$	10.5118	+	25.3778i	0.353152	+	0.852584i
$887$	−13.8993	+	9.28722i	−0.466693	+	0.311834i	−0.766590	−	0.642137i	$-0.778048\pi$
$887$	−13.8993	+	9.28722i	−0.466693	+	0.311834i	0.299896	+	0.953972i	$0.403048\pi$
$888$	−4.31764	−	10.4432i	−0.144890	−	0.350452i
$889$	5.18067	−	26.0450i	0.173754	−	0.873522i
$890$	17.8572	+	11.9318i	0.598575	+	0.399955i
$891$	−2.85477	−	14.5532i	−0.0956383	−	0.487551i
$892$	−0.263753	−	0.109250i	−0.00883111	−	0.00365797i
$893$	2.49580	+	1.03380i	0.0835189	+	0.0345947i
$894$	15.5468	+	3.10316i	0.519964	+	0.103785i
$895$	2.14810	+	1.43532i	0.0718032	+	0.0479773i
$896$	5.13597	−	25.8203i	0.171581	−	0.862594i
$897$	5.42367	−	2.24235i	0.181091	−	0.0748699i
$898$	32.9873	−	22.0414i	1.10080	−	0.735532i
$899$	−8.83348	−	21.3259i	−0.294613	−	0.711259i
$900$	−1.07488	+	1.07204i	−0.0358293	+	0.0357345i
$901$		0			0
$902$			7.38418i			0.245866i
$903$	−0.0283106	+	42.7598i	−0.000942119	+	1.42296i
$904$	−25.0902	−	37.5501i	−0.834487	−	1.24890i
$905$	−3.09374	−	3.09374i	−0.102839	−	0.102839i
$906$	−31.8663	−	21.3229i	−1.05869	−	0.708406i
$907$	5.11877	−	7.66078i	0.169966	−	0.254372i	−0.736702	−	0.676218i	$-0.763618\pi$
$907$	5.11877	−	7.66078i	0.169966	−	0.254372i	0.906668	+	0.421846i	$0.138618\pi$
$908$	−0.161686	+	0.0321614i	−0.00536574	+	0.00106731i
$909$	−10.3702	+	4.27938i	−0.343956	+	0.141938i
$910$	16.1986	−	39.1068i	0.536978	−	1.29638i
$911$	−0.391215	−	1.96677i	−0.0129615	−	0.0651621i	0.973763	−	0.227564i	$-0.0730760\pi$
$911$	−0.391215	−	1.96677i	−0.0129615	−	0.0651621i	−0.986725	+	0.162402i	$0.948076\pi$
$912$	3.50351	+	5.25090i	0.116013	+	0.173875i
$913$	−20.9894	−	4.17505i	−0.694648	−	0.138174i
$914$	−10.8464	+	10.8464i	−0.358768	+	0.358768i
$915$	−6.00824	−	30.3103i	−0.198626	−	1.00203i
$916$	1.17955	−	0.488587i	0.0389735	−	0.0161434i
$917$	−7.60583			−0.251167
$918$		0			0
$919$	4.18774			0.138141			0.0690703	−	0.997612i	$-0.477997\pi$
$919$	4.18774			0.138141			0.0690703	+	0.997612i	$0.477997\pi$
$920$	5.92020	−	2.45223i	0.195183	−	0.0808475i
$921$	8.22807	+	41.5089i	0.271124	+	1.36777i
$922$	−10.1727	+	10.1727i	−0.335021	+	0.335021i
$923$	9.42688	+	1.87512i	0.310290	+	0.0617204i
$924$	−0.401044	−	0.601066i	−0.0131934	−	0.0197736i
$925$	−2.00304	−	10.0700i	−0.0658595	−	0.331098i
$926$	−12.7673	+	30.8229i	−0.419558	+	1.01290i
$927$	−25.8847	+	10.6817i	−0.850166	+	0.350832i
$928$	−5.19789	+	1.03392i	−0.170629	+	0.0339402i
$929$	−13.5854	+	20.3321i	−0.445724	+	0.667073i	−0.984502	−	0.175375i	$-0.943886\pi$
$929$	−13.5854	+	20.3321i	−0.445724	+	0.667073i	0.538778	+	0.842448i	$0.318886\pi$
$930$	−18.4620	−	12.3536i	−0.605393	−	0.405091i
$931$	1.43373	+	1.43373i	0.0469885	+	0.0469885i
$932$	−0.934927	−	1.39922i	−0.0306245	−	0.0458329i
$933$	0.0267611	−	40.4193i	0.000876118	−	1.32327i
$934$			37.6099i			1.23063i
$935$		0			0
$936$	25.7205	−	25.6524i	0.840699	−	0.838476i
$937$	19.3663	+	46.7545i	0.632671	+	1.52740i	0.836252	+	0.548345i	$0.184742\pi$
$937$	19.3663	+	46.7545i	0.632671	+	1.52740i	−0.203582	+	0.979058i	$0.565258\pi$
$938$	−18.7745	+	12.5447i	−0.613010	+	0.409600i
$939$	−2.58445	+	1.06851i	−0.0843403	+	0.0348695i
$940$	−0.218631	+	1.09913i	−0.00713095	+	0.0358497i
$941$	2.99651	+	2.00221i	0.0976836	+	0.0652701i	0.603453	−	0.797399i	$-0.293791\pi$
$941$	2.99651	+	2.00221i	0.0976836	+	0.0652701i	−0.505769	+	0.862669i	$0.668791\pi$
$942$	−6.10033	−	1.21763i	−0.198760	−	0.0396726i
$943$	−2.18105	−	0.903419i	−0.0710246	−	0.0294194i
$944$	23.7584	+	9.84105i	0.773270	+	0.320299i
$945$	28.4711	−	18.9421i	0.926166	−	0.616187i
$946$	22.8209	+	15.2484i	0.741970	+	0.495769i
$947$	5.22957	−	26.2908i	0.169938	−	0.854336i	−0.797905	−	0.602783i	$-0.794059\pi$
$947$	5.22957	−	26.2908i	0.169938	−	0.854336i	0.967843	−	0.251554i	$-0.0809415\pi$
$948$	−0.462824	−	1.11945i	−0.0150318	−	0.0363581i
$949$	−46.2320	+	30.8912i	−1.50075	+	1.00277i
$950$	2.07269	+	5.00393i	0.0672471	+	0.162349i
$951$	−39.0103	−	16.1889i	−1.26500	−	0.524960i
$952$		0			0
$953$		−	24.2594i		−	0.785838i	−0.919573	−	0.392919i	$-0.871465\pi$
$953$		−	24.2594i		−	0.785838i	0.919573	−	0.392919i	$-0.128535\pi$
$954$	10.6729	−	25.6704i	0.345547	−	0.831109i
$955$	1.22234	+	1.82937i	0.0395541	+	0.0591969i
$956$	1.96792	+	1.96792i	0.0636470	+	0.0636470i
$957$	12.6844	−	18.9564i	0.410028	−	0.612772i
$958$	7.00474	−	10.4833i	0.226313	−	0.338701i
$959$	30.9862	−	6.16353i	1.00060	−	0.199031i
$960$	27.9612	−	27.9242i	0.902445	−	0.901250i
$961$	−8.67037	+	20.9321i	−0.279689	+	0.675230i
$962$	−2.98848	−	15.0241i	−0.0963525	−	0.484397i
$963$	−5.56241	+	1.09878i	−0.179246	+	0.0354076i
$964$	0.324012	+	0.0644499i	0.0104357	+	0.00207579i
$965$	25.0752	−	25.0752i	0.807200	−	0.807200i
$966$	4.08749	−	0.810240i	0.131513	−	0.0260691i
$967$	12.2636	−	5.07976i	0.394372	−	0.163354i	−0.176680	−	0.984268i	$-0.556536\pi$
$967$	12.2636	−	5.07976i	0.394372	−	0.163354i	0.571051	+	0.820914i	$0.306536\pi$
$968$	−22.6952			−0.729452
$969$		0			0
$970$	15.7512			0.505739
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	−0.600012	−	0.799991i	$-0.704837\pi$
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	0.141407	+	0.989952i	$0.454837\pi$
$972$	−1.79583	+	0.351036i	−0.0576012	+	0.0112595i
$973$	7.69338	−	7.69338i	0.246638	−	0.246638i
$974$	55.3982	+	11.0194i	1.77507	+	0.353084i
$975$	27.4543	−	18.3181i	0.879241	−	0.586649i
$976$	−4.81450	−	24.2041i	−0.154108	−	0.774755i
$977$	7.72995	−	18.6618i	0.247303	−	0.597042i	−0.750670	−	0.660677i	$-0.770269\pi$
$977$	7.72995	−	18.6618i	0.247303	−	0.597042i	0.997973	+	0.0636347i	$0.0202693\pi$
$978$	1.97845	+	1.98107i	0.0632637	+	0.0633475i
$979$	−7.81735	+	1.55497i	−0.249844	+	0.0496970i
$980$	−0.467306	+	0.699373i	−0.0149275	+	0.0223406i
$981$	6.99134	+	10.4933i	0.223216	+	0.335026i
$982$	−13.0385	−	13.0385i	−0.416075	−	0.416075i
$983$	−14.4927	−	21.6898i	−0.462244	−	0.691797i	0.524984	−	0.851112i	$-0.324071\pi$
$983$	−14.4927	−	21.6898i	−0.462244	−	0.691797i	−0.987228	+	0.159315i	$0.949071\pi$
$984$	−14.6120	−	0.00967440i	−0.465814	−	0.000308409i
$985$			70.9874i			2.26185i
$986$		0			0
$987$	4.47994	−	10.7953i	0.142598	−	0.343618i
$988$	0.171435	+	0.413882i	0.00545409	+	0.0131673i
$989$	−7.29590	+	4.87497i	−0.231996	+	0.155015i
$990$	0.0290655	−	21.9499i	0.000923762	−	0.697615i
$991$	−7.04470	+	35.4161i	−0.223782	+	1.12503i	0.691549	+	0.722329i	$0.256928\pi$
$991$	−7.04470	+	35.4161i	−0.223782	+	1.12503i	−0.915332	+	0.402701i	$0.868072\pi$
$992$	−1.59273	−	1.06423i	−0.0505692	−	0.0337892i
$993$	−10.3285	+	51.7460i	−0.327766	+	1.64211i
$994$	6.30488	+	2.61157i	0.199979	+	0.0828339i
$995$	−67.9824	−	28.1592i	−2.15519	−	0.892707i
$996$	−0.516838	+	2.58936i	−0.0163766	+	0.0820469i
$997$	−12.2838	−	8.20777i	−0.389032	−	0.259943i	0.345638	−	0.938368i	$-0.387663\pi$
$997$	−12.2838	−	8.20777i	−0.389032	−	0.259943i	−0.734669	+	0.678425i	$0.762663\pi$
$998$	−10.5365	+	52.9708i	−0.333529	+	1.67676i
$999$	4.75858	−	11.4240i	0.150555	−	0.361439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.c.158.4		32
3.2	odd	2	inner	867.2.i.c.158.1		32
17.2	even	8		867.2.i.g.224.4		32
17.3	odd	16		867.2.i.i.827.4		32
17.4	even	4		51.2.i.a.29.1	✓	32
17.5	odd	16		867.2.i.f.329.1		32
17.6	odd	16		51.2.i.a.44.4	yes	32
17.7	odd	16	inner	867.2.i.c.653.1		32
17.8	even	8		867.2.i.i.65.1		32
17.9	even	8		867.2.i.b.65.1		32
17.10	odd	16		867.2.i.d.653.1		32
17.11	odd	16		867.2.i.h.503.4		32
17.12	odd	16		867.2.i.g.329.1		32
17.13	even	4		867.2.i.h.131.1		32
17.14	odd	16		867.2.i.b.827.4		32
17.15	even	8		867.2.i.f.224.4		32
17.16	even	2		867.2.i.d.158.4		32
51.2	odd	8		867.2.i.g.224.1		32
51.5	even	16		867.2.i.f.329.4		32
51.8	odd	8		867.2.i.i.65.4		32
51.11	even	16		867.2.i.h.503.1		32
51.14	even	16		867.2.i.b.827.1		32
51.20	even	16		867.2.i.i.827.1		32
51.23	even	16		51.2.i.a.44.1	yes	32
51.26	odd	8		867.2.i.b.65.4		32
51.29	even	16		867.2.i.g.329.4		32
51.32	odd	8		867.2.i.f.224.1		32
51.38	odd	4		51.2.i.a.29.4	yes	32
51.41	even	16	inner	867.2.i.c.653.4		32
51.44	even	16		867.2.i.d.653.4		32
51.47	odd	4		867.2.i.h.131.4		32
51.50	odd	2		867.2.i.d.158.1		32
68.23	even	16		816.2.cj.c.401.3		32
68.55	odd	4		816.2.cj.c.641.4		32
204.23	odd	16		816.2.cj.c.401.4		32
204.191	even	4		816.2.cj.c.641.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	17.4	even	4
51.2.i.a.29.4	yes	32	51.38	odd	4
51.2.i.a.44.1	yes	32	51.23	even	16
51.2.i.a.44.4	yes	32	17.6	odd	16
816.2.cj.c.401.3		32	68.23	even	16
816.2.cj.c.401.4		32	204.23	odd	16
816.2.cj.c.641.3		32	204.191	even	4
816.2.cj.c.641.4		32	68.55	odd	4
867.2.i.b.65.1		32	17.9	even	8
867.2.i.b.65.4		32	51.26	odd	8
867.2.i.b.827.1		32	51.14	even	16
867.2.i.b.827.4		32	17.14	odd	16
867.2.i.c.158.1		32	3.2	odd	2	inner
867.2.i.c.158.4		32	1.1	even	1	trivial
867.2.i.c.653.1		32	17.7	odd	16	inner
867.2.i.c.653.4		32	51.41	even	16	inner
867.2.i.d.158.1		32	51.50	odd	2
867.2.i.d.158.4		32	17.16	even	2
867.2.i.d.653.1		32	17.10	odd	16
867.2.i.d.653.4		32	51.44	even	16
867.2.i.f.224.1		32	51.32	odd	8
867.2.i.f.224.4		32	17.15	even	8
867.2.i.f.329.1		32	17.5	odd	16
867.2.i.f.329.4		32	51.5	even	16
867.2.i.g.224.1		32	51.2	odd	8
867.2.i.g.224.4		32	17.2	even	8
867.2.i.g.329.1		32	17.12	odd	16
867.2.i.g.329.4		32	51.29	even	16
867.2.i.h.131.1		32	17.13	even	4
867.2.i.h.131.4		32	51.47	odd	4
867.2.i.h.503.1		32	51.11	even	16
867.2.i.h.503.4		32	17.11	odd	16
867.2.i.i.65.1		32	17.8	even	8
867.2.i.i.65.4		32	51.8	odd	8
867.2.i.i.827.1		32	51.20	even	16
867.2.i.i.827.4		32	17.3	odd	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34436 - 0.556851i) q^{2} +(-0.336782 - 1.69899i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(-2.99276 - 0.595296i) q^{5} +(-1.39884 - 2.09652i) q^{6} +(0.420765 + 2.11533i) q^{7} +(-1.04834 + 2.53091i) q^{8} +(-2.77316 + 1.14438i) q^{9} +(-4.35483 + 0.866229i) q^{10} +(0.915491 - 1.37013i) q^{11} +(-0.168973 - 0.113066i) q^{12} +(3.12551 + 3.12551i) q^{13} +(1.74358 + 2.60946i) q^{14} +(-0.00349923 + 5.28516i) q^{15} +4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(0.330416 + 0.797694i) q^{19} +(-0.297816 + 0.198994i) q^{20} +(3.45222 - 1.42728i) q^{21} +(0.467790 - 2.35174i) q^{22} +(0.637394 + 0.425893i) q^{23} +(4.65306 + 0.928755i) q^{24} +(3.98282 + 1.64974i) q^{25} +(5.94226 + 2.46136i) q^{26} +(2.87824 + 4.32617i) q^{27} +(0.210501 + 0.140652i) q^{28} +(-1.55905 + 7.83789i) q^{29} +(2.93834 + 7.10709i) q^{30} +(-2.40167 + 1.60475i) q^{31} +(0.253786 + 0.612694i) q^{32} +(-2.63616 - 1.09398i) q^{33} -6.58114i q^{35} +(-0.135192 + 0.325163i) q^{36} +(-1.32318 - 1.98027i) q^{37} +(0.888394 + 0.888394i) q^{38} +(4.25761 - 6.36284i) q^{39} +(4.64406 - 6.95033i) q^{40} +(-3.02038 + 0.600791i) q^{41} +(3.84624 - 3.84115i) q^{42} +(-4.38037 + 10.5751i) q^{43} +(-0.0377359 - 0.189711i) q^{44} +(8.98063 - 1.77400i) q^{45} +(1.09405 + 0.217619i) q^{46} +(2.21238 - 2.21238i) q^{47} +(7.17143 - 1.42155i) q^{48} +(2.16958 - 0.898671i) q^{49} +6.27299 q^{50} +0.518848 q^{52} +(-5.88369 + 2.43710i) q^{53} +(6.27842 + 4.21317i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(-5.79482 - 1.15266i) q^{56} +(1.24400 - 0.830022i) q^{57} +(2.26861 + 11.4051i) q^{58} +(2.33146 - 5.62864i) q^{59} +(0.438389 + 0.438969i) q^{60} +(-5.73423 + 1.14061i) q^{61} +(-2.33510 + 3.49473i) q^{62} +(-3.58759 - 5.38462i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(-7.49329 - 11.2145i) q^{65} +(-4.15313 - 0.00274973i) q^{66} +7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(-3.66472 - 8.84742i) q^{70} +(1.80802 - 1.20808i) q^{71} +(0.0108825 - 8.21831i) q^{72} +(-2.45412 + 12.3377i) q^{73} +(-2.88154 - 1.92538i) q^{74} +(1.46155 - 7.32238i) q^{75} +(0.0936354 + 0.0387851i) q^{76} +(3.28348 + 1.36006i) q^{77} +(2.18060 - 10.9248i) q^{78} +(4.95397 + 3.31013i) q^{79} +(2.51274 - 12.6324i) q^{80} +(6.38079 - 6.34708i) q^{81} +(-3.72592 + 2.48958i) q^{82} +(-4.96993 - 11.9985i) q^{83} +(0.168074 - 0.405009i) q^{84} +16.6560i q^{86} +(13.8416 + 0.00916431i) q^{87} +(2.50793 + 3.75339i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(11.0853 - 7.38576i) q^{90} +(-5.29638 + 7.92660i) q^{91} +(0.0882551 - 0.0175550i) q^{92} +(3.53529 + 3.53997i) q^{93} +(1.74226 - 4.20619i) q^{94} +(-0.513989 - 2.58400i) q^{95} +(0.955492 - 0.637525i) q^{96} +(-3.47928 - 0.692072i) q^{97} +(2.41627 - 2.41627i) q^{98} +(-0.970853 + 4.84725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 8 q^{9} - 32 q^{10} - 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} + 48 q^{22} - 8 q^{24} - 16 q^{25} + 48 q^{27} + 64 q^{28} - 8 q^{30} - 16 q^{31} - 8 q^{36}+ \cdots - 96 q^{97}+O(q^{100}) \) 32 * q - 16 * q^4 + 8 * q^9 - 32 * q^10 - 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 + 48 * q^22 - 8 * q^24 - 16 * q^25 + 48 * q^27 + 64 * q^28 - 8 * q^30 - 16 * q^31 - 8 * q^36 + 32 * q^37 - 8 * q^39 + 64 * q^40 + 56 * q^42 - 16 * q^43 - 24 * q^45 + 80 * q^46 + 72 * q^48 + 48 * q^49 - 96 * q^52 - 48 * q^54 - 48 * q^55 - 24 * q^57 + 32 * q^58 - 32 * q^60 - 64 * q^61 + 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 + 16 * q^78 + 32 * q^79 + 48 * q^81 - 48 * q^82 + 56 * q^87 + 80 * q^88 - 104 * q^90 - 80 * q^91 + 72 * q^93 + 48 * q^94 - 72 * q^96 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more