LMFDB - Embedded newform 432.2.k.c.325.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (of order $4$, degree $2$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			325.5
Character	$\chi$	$=$	432.325
Dual form			432.2.k.c.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.936391 + 1.05980i) q^{2} +(-0.246343 - 1.98477i) q^{4} +(1.12951 + 1.12951i) q^{5} -1.33035i q^{7} +(2.33413 + 1.59745i) q^{8} +O(q^{10})$	\(q+(-0.936391 + 1.05980i) q^{2} +(-0.246343 - 1.98477i) q^{4} +(1.12951 + 1.12951i) q^{5} -1.33035i q^{7} +(2.33413 + 1.59745i) q^{8} +(-2.25471 + 0.139389i) q^{10} +(-0.386575 - 0.386575i) q^{11} +(2.49269 - 2.49269i) q^{13} +(1.40990 + 1.24573i) q^{14} +(-3.87863 + 0.977868i) q^{16} +5.71255 q^{17} +(-0.755633 + 0.755633i) q^{19} +(1.96357 - 2.52006i) q^{20} +(0.771676 - 0.0477059i) q^{22} +2.22699i q^{23} -2.44842i q^{25} +(0.307614 + 4.97587i) q^{26} +(-2.64044 + 0.327723i) q^{28} +(0.659445 - 0.659445i) q^{29} +9.38313 q^{31} +(2.59557 - 5.02623i) q^{32} +(-5.34918 + 6.05415i) q^{34} +(1.50264 - 1.50264i) q^{35} +(5.75774 + 5.75774i) q^{37} +(-0.0932501 - 1.50839i) q^{38} +(0.832087 + 4.44075i) q^{40} +9.62854i q^{41} +(-0.132699 - 0.132699i) q^{43} +(-0.672032 + 0.862492i) q^{44} +(-2.36016 - 2.08533i) q^{46} -10.0768 q^{47} +5.23016 q^{49} +(2.59483 + 2.29268i) q^{50} +(-5.56147 - 4.33335i) q^{52} +(2.31529 + 2.31529i) q^{53} -0.873279i q^{55} +(2.12517 - 3.10521i) q^{56} +(0.0813798 + 1.31638i) q^{58} +(-7.72476 - 7.72476i) q^{59} +(-6.74143 + 6.74143i) q^{61} +(-8.78628 + 9.94422i) q^{62} +(2.89632 + 7.45730i) q^{64} +5.63102 q^{65} +(-3.59541 + 3.59541i) q^{67} +(-1.40725 - 11.3381i) q^{68} +(0.185436 + 2.99956i) q^{70} -9.17515i q^{71} -12.9932i q^{73} +(-11.4935 + 0.710543i) q^{74} +(1.68590 + 1.31361i) q^{76} +(-0.514280 + 0.514280i) q^{77} +14.6526 q^{79} +(-5.48545 - 3.27643i) q^{80} +(-10.2043 - 9.01608i) q^{82} +(-1.58041 + 1.58041i) q^{83} +(6.45238 + 6.45238i) q^{85} +(0.264893 - 0.0163760i) q^{86} +(-0.284782 - 1.51985i) q^{88} -9.68886i q^{89} +(-3.31615 - 3.31615i) q^{91} +(4.42006 - 0.548603i) q^{92} +(9.43582 - 10.6794i) q^{94} -1.70699 q^{95} -17.0818 q^{97} +(-4.89748 + 5.54292i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{4}+O(q^{10}) $ 24 * q + 16 * q^4	$ 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) $ 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.936391	+	1.05980i	−0.662129	+	0.749390i
$2$	−0.936391	+	1.05980i	−0.662129	+	0.749390i
$3$		0			0
$3$		0			0
$4$	−0.246343	−	1.98477i	−0.123171	−	0.992385i
$5$	1.12951	+	1.12951i	0.505131	+	0.505131i	0.913028	−	0.407897i	$-0.133738\pi$
$5$	1.12951	+	1.12951i	0.505131	+	0.505131i	−0.407897	+	0.913028i	$0.633738\pi$
$6$		0			0
$7$		−	1.33035i		−	0.502826i	−0.967880	−	0.251413i	$-0.919105\pi$
$7$		−	1.33035i		−	0.502826i	0.967880	−	0.251413i	$-0.0808952\pi$
$8$	2.33413	+	1.59745i	0.825239	+	0.564783i
$9$		0			0
$10$	−2.25471	+	0.139389i	−0.713002	+	0.0440786i
$11$	−0.386575	−	0.386575i	−0.116557	−	0.116557i	0.646423	−	0.762979i	$-0.276264\pi$
$11$	−0.386575	−	0.386575i	−0.116557	−	0.116557i	−0.762979	+	0.646423i	$0.776264\pi$
$12$		0			0
$13$	2.49269	−	2.49269i	0.691347	−	0.691347i	−0.271182	−	0.962528i	$-0.587414\pi$
$13$	2.49269	−	2.49269i	0.691347	−	0.691347i	0.962528	+	0.271182i	$0.0874144\pi$
$14$	1.40990	+	1.24573i	0.376813	+	0.332935i
$15$		0			0
$16$	−3.87863	+	0.977868i	−0.969658	+	0.244467i
$17$	5.71255			1.38550			0.692749	−	0.721179i	$-0.256399\pi$
$17$	5.71255			1.38550			0.692749	+	0.721179i	$0.256399\pi$
$18$		0			0
$19$	−0.755633	+	0.755633i	−0.173354	+	0.173354i	−0.788451	−	0.615097i	$-0.789117\pi$
$19$	−0.755633	+	0.755633i	−0.173354	+	0.173354i	0.615097	+	0.788451i	$0.289117\pi$
$20$	1.96357	−	2.52006i	0.439067	−	0.563503i
$21$		0			0
$22$	0.771676	−	0.0477059i	0.164522	−	0.0101709i
$23$			2.22699i			0.464359i	0.972673	+	0.232180i	$0.0745857\pi$
$23$			2.22699i			0.464359i	−0.972673	+	0.232180i	$0.925414\pi$
$24$		0			0
$25$		−	2.44842i		−	0.489685i
$26$	0.307614	+	4.97587i	0.0603280	+	0.975849i
$27$		0			0
$28$	−2.64044	+	0.327723i	−0.498997	+	0.0619338i
$29$	0.659445	−	0.659445i	0.122456	−	0.122456i	−0.643223	−	0.765679i	$-0.722403\pi$
$29$	0.659445	−	0.659445i	0.122456	−	0.122456i	0.765679	+	0.643223i	$0.222403\pi$
$30$		0			0
$31$	9.38313			1.68526			0.842630	−	0.538493i	$-0.181006\pi$
$31$	9.38313			1.68526			0.842630	+	0.538493i	$0.181006\pi$
$32$	2.59557	−	5.02623i	0.458837	−	0.888521i
$33$		0			0
$34$	−5.34918	+	6.05415i	−0.917378	+	1.03828i
$35$	1.50264	−	1.50264i	0.253993	−	0.253993i
$36$		0			0
$37$	5.75774	+	5.75774i	0.946567	+	0.946567i	0.998643	−	0.0520760i	$-0.0165838\pi$
$37$	5.75774	+	5.75774i	0.946567	+	0.946567i	−0.0520760	+	0.998643i	$0.516584\pi$
$38$	−0.0932501	−	1.50839i	−0.0151272	−	0.244693i
$39$		0			0
$40$	0.832087	+	4.44075i	0.131565	+	0.702144i
$41$			9.62854i			1.50373i	0.659319	+	0.751863i	$0.270845\pi$
$41$			9.62854i			1.50373i	−0.659319	+	0.751863i	$0.729155\pi$
$42$		0			0
$43$	−0.132699	−	0.132699i	−0.0202364	−	0.0202364i	0.696916	−	0.717153i	$-0.254555\pi$
$43$	−0.132699	−	0.132699i	−0.0202364	−	0.0202364i	−0.717153	+	0.696916i	$0.754555\pi$
$44$	−0.672032	+	0.862492i	−0.101313	+	0.130026i
$45$		0			0
$46$	−2.36016	−	2.08533i	−0.347986	−	0.307465i
$47$	−10.0768			−1.46985			−0.734926	−	0.678148i	$-0.762783\pi$
$47$	−10.0768			−1.46985			−0.734926	+	0.678148i	$0.762783\pi$
$48$		0			0
$49$	5.23016			0.747166
$50$	2.59483	+	2.29268i	0.366965	+	0.324234i
$51$		0			0
$52$	−5.56147	−	4.33335i	−0.771237	−	0.600928i
$53$	2.31529	+	2.31529i	0.318029	+	0.318029i	0.848010	−	0.529980i	$-0.177801\pi$
$53$	2.31529	+	2.31529i	0.318029	+	0.318029i	−0.529980	+	0.848010i	$0.677801\pi$
$54$		0			0
$55$		−	0.873279i		−	0.117753i
$56$	2.12517	−	3.10521i	0.283988	−	0.414952i
$57$		0			0
$58$	0.0813798	+	1.31638i	0.0106857	+	0.172849i
$59$	−7.72476	−	7.72476i	−1.00568	−	1.00568i	−0.999984	−	0.00569380i	$-0.998188\pi$
$59$	−7.72476	−	7.72476i	−1.00568	−	1.00568i	−0.00569380	−	0.999984i	$-0.501812\pi$
$60$		0			0
$61$	−6.74143	+	6.74143i	−0.863152	+	0.863152i	−0.991703	−	0.128551i	$-0.958967\pi$
$61$	−6.74143	+	6.74143i	−0.863152	+	0.863152i	0.128551	+	0.991703i	$0.458967\pi$
$62$	−8.78628	+	9.94422i	−1.11586	+	1.26292i
$63$		0			0
$64$	2.89632	+	7.45730i	0.362040	+	0.932163i
$65$	5.63102			0.698442
$66$		0			0
$67$	−3.59541	+	3.59541i	−0.439249	+	0.439249i	−0.891759	−	0.452510i	$-0.850529\pi$
$67$	−3.59541	+	3.59541i	−0.439249	+	0.439249i	0.452510	+	0.891759i	$0.350529\pi$
$68$	−1.40725	−	11.3381i	−0.170654	−	1.37495i
$69$		0			0
$70$	0.185436	+	2.99956i	0.0221639	+	0.358516i
$71$		−	9.17515i		−	1.08889i	−0.838797	−	0.544445i	$-0.816740\pi$
$71$		−	9.17515i		−	1.08889i	0.838797	−	0.544445i	$-0.183260\pi$
$72$		0			0
$73$		−	12.9932i		−	1.52073i	−0.649493	−	0.760367i	$-0.725019\pi$
$73$		−	12.9932i		−	1.52073i	0.649493	−	0.760367i	$-0.274981\pi$
$74$	−11.4935	+	0.710543i	−1.33610	+	0.0825990i
$75$		0			0
$76$	1.68590	+	1.31361i	0.193386	+	0.150682i
$77$	−0.514280	+	0.514280i	−0.0586077	+	0.0586077i
$78$		0			0
$79$	14.6526			1.64854			0.824271	−	0.566195i	$-0.191585\pi$
$79$	14.6526			1.64854			0.824271	+	0.566195i	$0.191585\pi$
$80$	−5.48545	−	3.27643i	−0.613293	−	0.366316i
$81$		0			0
$82$	−10.2043	−	9.01608i	−1.12688	−	0.995660i
$83$	−1.58041	+	1.58041i	−0.173473	+	0.173473i	−0.788503	−	0.615030i	$-0.789144\pi$
$83$	−1.58041	+	1.58041i	−0.173473	+	0.173473i	0.615030	+	0.788503i	$0.289144\pi$
$84$		0			0
$85$	6.45238	+	6.45238i	0.699858	+	0.699858i
$86$	0.264893	−	0.0163760i	0.0285641	−	0.00176587i
$87$		0			0
$88$	−0.284782	−	1.51985i	−0.0303579	−	0.162016i
$89$		−	9.68886i		−	1.02702i	−0.858085	−	0.513508i	$-0.828346\pi$
$89$		−	9.68886i		−	1.02702i	0.858085	−	0.513508i	$-0.171654\pi$
$90$		0			0
$91$	−3.31615	−	3.31615i	−0.347627	−	0.347627i
$92$	4.42006	−	0.548603i	0.460823	−	0.0571958i
$93$		0			0
$94$	9.43582	−	10.6794i	0.973231	−	1.10149i
$95$	−1.70699			−0.175133
$96$		0			0
$97$	−17.0818			−1.73439			−0.867197	−	0.497965i	$-0.834081\pi$
$97$	−17.0818			−1.73439			−0.867197	+	0.497965i	$0.834081\pi$
$98$	−4.89748	+	5.54292i	−0.494720	+	0.559919i
$99$		0			0
$100$	−4.85956	+	0.603152i	−0.485956	+	0.0603152i
$101$	5.68899	+	5.68899i	0.566076	+	0.566076i	0.931027	−	0.364951i	$-0.118914\pi$
$101$	5.68899	+	5.68899i	0.566076	+	0.566076i	−0.364951	+	0.931027i	$0.618914\pi$
$102$		0			0
$103$		−	6.44808i		−	0.635348i	−0.948200	−	0.317674i	$-0.897098\pi$
$103$		−	6.44808i		−	0.635348i	0.948200	−	0.317674i	$-0.102902\pi$
$104$	9.80019	−	1.83631i	0.960987	−	0.180065i
$105$		0			0
$106$	−4.62175	+	0.285722i	−0.448904	+	0.0277518i
$107$	−8.37271	−	8.37271i	−0.809421	−	0.809421i	0.175125	−	0.984546i	$-0.443967\pi$
$107$	−8.37271	−	8.37271i	−0.809421	−	0.809421i	−0.984546	+	0.175125i	$0.943967\pi$
$108$		0			0
$109$	1.37899	−	1.37899i	0.132084	−	0.132084i	−0.637974	−	0.770058i	$-0.720227\pi$
$109$	1.37899	−	1.37899i	0.132084	−	0.132084i	0.770058	+	0.637974i	$0.220227\pi$
$110$	0.925499	+	0.817730i	0.0882428	+	0.0779675i
$111$		0			0
$112$	1.30091	+	5.15994i	0.122924	+	0.487569i
$113$	−6.09777			−0.573629			−0.286815	−	0.957986i	$-0.592596\pi$
$113$	−6.09777			−0.573629			−0.286815	+	0.957986i	$0.592596\pi$
$114$		0			0
$115$	−2.51540	+	2.51540i	−0.234562	+	0.234562i
$116$	−1.47130	−	1.14640i	−0.136606	−	0.106440i
$117$		0			0
$118$	15.4201	−	0.953286i	1.41953	−	0.0877571i
$119$		−	7.59971i		−	0.696664i
$120$		0			0
$121$		−	10.7011i		−	0.972829i
$122$	−0.831937	−	13.4572i	−0.0753200	−	1.21835i
$123$		0			0
$124$	−2.31147	−	18.6234i	−0.207576	−	1.67243i
$125$	8.41305	−	8.41305i	0.752486	−	0.752486i
$126$		0			0
$127$	−8.83207			−0.783719			−0.391860	−	0.920025i	$-0.628168\pi$
$127$	−8.83207			−0.783719			−0.391860	+	0.920025i	$0.628168\pi$
$128$	−10.6153	−	3.91344i	−0.938270	−	0.345903i
$129$		0			0
$130$	−5.27284	+	5.96774i	−0.462458	+	0.523405i
$131$	−13.3128	+	13.3128i	−1.16314	+	1.16314i	−0.179362	+	0.983783i	$0.557403\pi$
$131$	−13.3128	+	13.3128i	−1.16314	+	1.16314i	−0.983783	+	0.179362i	$0.942597\pi$
$132$		0			0
$133$	1.00526	+	1.00526i	0.0871669	+	0.0871669i
$134$	−0.443697	−	7.17712i	−0.0383296	−	0.620008i
$135$		0			0
$136$	13.3338	+	9.12551i	1.14337	+	0.782506i
$137$		−	0.709950i		−	0.0606551i	−0.999540	−	0.0303276i	$-0.990345\pi$
$137$		−	0.709950i		−	0.0606551i	0.999540	−	0.0303276i	$-0.00965504\pi$
$138$		0			0
$139$	−5.06740	−	5.06740i	−0.429812	−	0.429812i	0.458752	−	0.888564i	$-0.348296\pi$
$139$	−5.06740	−	5.06740i	−0.429812	−	0.429812i	−0.888564	+	0.458752i	$0.848296\pi$
$140$	−3.35257	−	2.61224i	−0.283344	−	0.220774i
$141$		0			0
$142$	9.72380	+	8.59153i	0.816003	+	0.720985i
$143$	−1.92722			−0.161162
$144$		0			0
$145$	1.48970			0.123713
$146$	13.7701	+	12.1667i	1.13962	+	1.00692i
$147$		0			0
$148$	10.0094	−	12.8462i	0.822769	−	1.05595i
$149$	3.19413	+	3.19413i	0.261673	+	0.261673i	0.825734	−	0.564060i	$-0.190761\pi$
$149$	3.19413	+	3.19413i	0.261673	+	0.261673i	−0.564060	+	0.825734i	$0.690761\pi$
$150$		0			0
$151$		−	4.65825i		−	0.379083i	−0.981873	−	0.189542i	$-0.939300\pi$
$151$		−	4.65825i		−	0.379083i	0.981873	−	0.189542i	$-0.0607002\pi$
$152$	−2.97083	+	0.556661i	−0.240966	+	0.0451511i
$153$		0			0
$154$	−0.0634656	−	1.02660i	−0.00511420	−	0.0827259i
$155$	10.5983	+	10.5983i	0.851277	+	0.851277i
$156$		0			0
$157$	−7.67859	+	7.67859i	−0.612818	+	0.612818i	−0.943679	−	0.330861i	$-0.892661\pi$
$157$	−7.67859	+	7.67859i	−0.612818	+	0.612818i	0.330861	+	0.943679i	$0.392661\pi$
$158$	−13.7205	+	15.5288i	−1.09155	+	1.23540i
$159$		0			0
$160$	8.60889	−	2.74545i	0.680592	−	0.217047i
$161$	2.96268			0.233492
$162$		0			0
$163$	−17.4589	+	17.4589i	−1.36748	+	1.36748i	−0.503472	+	0.864011i	$0.667944\pi$
$163$	−17.4589	+	17.4589i	−1.36748	+	1.36748i	−0.864011	+	0.503472i	$0.832056\pi$
$164$	19.1105	−	2.37192i	1.49228	−	0.185216i
$165$		0			0
$166$	−0.195033	−	3.15480i	−0.0151375	−	0.244860i
$167$			6.38911i			0.494404i	0.968964	+	0.247202i	$0.0795112\pi$
$167$			6.38911i			0.494404i	−0.968964	+	0.247202i	$0.920489\pi$
$168$		0			0
$169$			0.573035i			0.0440796i
$170$	−12.8802	+	0.796266i	−0.987863	+	0.0610708i
$171$		0			0
$172$	−0.230688	+	0.296067i	−0.0175898	+	0.0225749i
$173$	−12.5838	+	12.5838i	−0.956725	+	0.956725i	−0.999102	−	0.0423765i	$-0.986507\pi$
$173$	−12.5838	+	12.5838i	−0.956725	+	0.956725i	0.0423765	+	0.999102i	$0.486507\pi$
$174$		0			0
$175$	−3.25726			−0.246226
$176$	1.87740	+	1.12136i	0.141514	+	0.0845258i
$177$		0			0
$178$	10.2682	+	9.07256i	0.769636	+	0.680017i
$179$	8.37271	−	8.37271i	0.625806	−	0.625806i	−0.321204	−	0.947010i	$-0.604088\pi$
$179$	8.37271	−	8.37271i	0.625806	−	0.625806i	0.947010	+	0.321204i	$0.104088\pi$
$180$		0			0
$181$	12.0336	+	12.0336i	0.894449	+	0.894449i	0.994938	−	0.100489i	$-0.0320408\pi$
$181$	12.0336	+	12.0336i	0.894449	+	0.894449i	−0.100489	+	0.994938i	$0.532041\pi$
$182$	6.61966	−	0.409235i	0.490682	−	0.0303345i
$183$		0			0
$184$	−3.55750	+	5.19808i	−0.262262	+	0.383207i
$185$			13.0068i			0.956282i
$186$		0			0
$187$	−2.20833	−	2.20833i	−0.161489	−	0.161489i
$188$	2.48235	+	20.0001i	0.181044	+	1.45866i
$189$		0			0
$190$	1.59841	−	1.80906i	0.115961	−	0.131243i
$191$	−3.66573			−0.265243			−0.132621	−	0.991167i	$-0.542339\pi$
$191$	−3.66573			−0.265243			−0.132621	+	0.991167i	$0.542339\pi$
$192$		0			0
$193$	−11.4192			−0.821970			−0.410985	−	0.911642i	$-0.634815\pi$
$193$	−11.4192			−0.821970			−0.410985	+	0.911642i	$0.634815\pi$
$194$	15.9952	−	18.1033i	1.14839	−	1.29974i
$195$		0			0
$196$	−1.28841	−	10.3807i	−0.0920296	−	0.741477i
$197$	−0.432745	−	0.432745i	−0.0308318	−	0.0308318i	0.691523	−	0.722355i	$-0.256940\pi$
$197$	−0.432745	−	0.432745i	−0.0308318	−	0.0308318i	−0.722355	+	0.691523i	$0.756940\pi$
$198$		0			0
$199$			9.36286i			0.663716i	0.943329	+	0.331858i	$0.107675\pi$
$199$			9.36286i			0.663716i	−0.943329	+	0.331858i	$0.892325\pi$
$200$	3.91123	−	5.71493i	0.276566	−	0.404107i
$201$		0			0
$202$	−11.3563	+	0.702059i	−0.799026	+	0.0493967i
$203$	−0.877293	−	0.877293i	−0.0615739	−	0.0615739i
$204$		0			0
$205$	−10.8755	+	10.8755i	−0.759579	+	0.759579i
$206$	6.83366	+	6.03793i	0.476124	+	0.420682i
$207$		0			0
$208$	−7.23069	+	12.1057i	−0.501358	+	0.839381i
$209$	0.584217			0.0404112
$210$		0			0
$211$	−18.4545	+	18.4545i	−1.27046	+	1.27046i	−0.324612	+	0.945847i	$0.605234\pi$
$211$	−18.4545	+	18.4545i	−1.27046	+	1.27046i	−0.945847	+	0.324612i	$0.894766\pi$
$212$	4.02496	−	5.16567i	0.276436	−	0.354780i
$213$		0			0
$214$	16.7135	−	1.03325i	1.14251	−	0.0706314i
$215$		−	0.299770i		−	0.0204441i
$216$		0			0
$217$		−	12.4829i		−	0.847392i
$218$	0.170177	+	2.75273i	0.0115258	+	0.186438i
$219$		0			0
$220$	−1.73326	+	0.215126i	−0.116856	+	0.0145038i
$221$	14.2396	−	14.2396i	0.957859	−	0.957859i
$222$		0			0
$223$	21.4422			1.43588			0.717938	−	0.696107i	$-0.245086\pi$
$223$	21.4422			1.43588			0.717938	+	0.696107i	$0.245086\pi$
$224$	−6.68666	−	3.45302i	−0.446771	−	0.230715i
$225$		0			0
$226$	5.70989	−	6.46240i	0.379816	−	0.429872i
$227$	7.93134	−	7.93134i	0.526422	−	0.526422i	−0.393082	−	0.919503i	$-0.628591\pi$
$227$	7.93134	−	7.93134i	0.526422	−	0.526422i	0.919503	+	0.393082i	$0.128591\pi$
$228$		0			0
$229$	−3.47637	−	3.47637i	−0.229725	−	0.229725i	0.582853	−	0.812578i	$-0.301936\pi$
$229$	−3.47637	−	3.47637i	−0.229725	−	0.229725i	−0.812578	+	0.582853i	$0.801936\pi$
$230$	−0.310417	−	5.02122i	−0.0204683	−	0.331089i
$231$		0			0
$232$	2.59266	−	0.485800i	0.170216	−	0.0318944i
$233$			3.02299i			0.198043i	0.995085	+	0.0990214i	$0.0315712\pi$
$233$			3.02299i			0.198043i	−0.995085	+	0.0990214i	$0.968429\pi$
$234$		0			0
$235$	−11.3818	−	11.3818i	−0.742468	−	0.742468i
$236$	−13.4289	+	17.2348i	−0.874149	+	1.12189i
$237$		0			0
$238$	8.05415	+	7.11630i	0.522073	+	0.461281i
$239$	24.6699			1.59576			0.797881	−	0.602815i	$-0.205954\pi$
$239$	24.6699			1.59576			0.797881	+	0.602815i	$0.205954\pi$
$240$		0			0
$241$	−8.58938			−0.553291			−0.276645	−	0.960972i	$-0.589223\pi$
$241$	−8.58938			−0.553291			−0.276645	+	0.960972i	$0.589223\pi$
$242$	11.3410	+	10.0204i	0.729029	+	0.644138i
$243$		0			0
$244$	15.0409	+	11.7195i	0.962895	+	0.750264i
$245$	5.90751	+	5.90751i	0.377417	+	0.377417i
$246$		0			0
$247$			3.76711i			0.239696i
$248$	21.9014	+	14.9891i	1.39074	+	0.951806i
$249$		0			0
$250$	1.03823	+	16.7940i	0.0656632	+	1.06215i
$251$	14.5948	+	14.5948i	0.921217	+	0.921217i	0.997116	−	0.0758982i	$-0.0241824\pi$
$251$	14.5948	+	14.5948i	0.921217	+	0.921217i	−0.0758982	+	0.997116i	$0.524182\pi$
$252$		0			0
$253$	0.860897	−	0.860897i	0.0541242	−	0.0541242i
$254$	8.27027	−	9.36020i	0.518923	−	0.587311i
$255$		0			0
$256$	14.0875	−	7.58558i	0.880472	−	0.474099i
$257$	−2.23893			−0.139661			−0.0698303	−	0.997559i	$-0.522246\pi$
$257$	−2.23893			−0.139661			−0.0698303	+	0.997559i	$0.522246\pi$
$258$		0			0
$259$	7.65982	−	7.65982i	0.475958	−	0.475958i
$260$	−1.38716	−	11.1763i	−0.0860281	−	0.693123i
$261$		0			0
$262$	−1.64289	−	26.5749i	−0.101498	−	1.64180i
$263$		−	0.517619i		−	0.0319178i	−0.999873	−	0.0159589i	$-0.994920\pi$
$263$		−	0.517619i		−	0.0319178i	0.999873	−	0.0159589i	$-0.00508009\pi$
$264$		0			0
$265$			5.23028i			0.321293i
$266$	−2.00669	+	0.124055i	−0.123038	+	0.00760633i
$267$		0			0
$268$	8.02177	+	6.25036i	0.490007	+	0.381801i
$269$	−7.20201	+	7.20201i	−0.439114	+	0.439114i	−0.891714	−	0.452600i	$-0.850497\pi$
$269$	−7.20201	+	7.20201i	−0.439114	+	0.439114i	0.452600	+	0.891714i	$0.350497\pi$
$270$		0			0
$271$	5.44404			0.330702			0.165351	−	0.986235i	$-0.447124\pi$
$271$	5.44404			0.330702			0.165351	+	0.986235i	$0.447124\pi$
$272$	−22.1569	+	5.58613i	−1.34346	+	0.338709i
$273$		0			0
$274$	0.752403	+	0.664791i	0.0454544	+	0.0401615i
$275$	−0.946498	+	0.946498i	−0.0570760	+	0.0570760i
$276$		0			0
$277$	0.590066	+	0.590066i	0.0354537	+	0.0354537i	0.724611	−	0.689158i	$-0.242019\pi$
$277$	0.590066	+	0.590066i	0.0354537	+	0.0354537i	−0.689158	+	0.724611i	$0.742019\pi$
$278$	10.1155	−	0.625351i	0.606687	−	0.0375061i
$279$		0			0
$280$	5.90776	−	1.10697i	0.353056	−	0.0661540i
$281$		−	30.6449i		−	1.82812i	−0.405580	−	0.914059i	$-0.632930\pi$
$281$		−	30.6449i		−	1.82812i	0.405580	−	0.914059i	$-0.367070\pi$
$282$		0			0
$283$	−9.41959	−	9.41959i	−0.559937	−	0.559937i	0.369353	−	0.929289i	$-0.379579\pi$
$283$	−9.41959	−	9.41959i	−0.559937	−	0.559937i	−0.929289	+	0.369353i	$0.879579\pi$
$284$	−18.2106	+	2.26023i	−1.08060	+	0.134120i
$285$		0			0
$286$	1.80463	−	2.04246i	0.106710	−	0.120773i
$287$	12.8094			0.756112
$288$		0			0
$289$	15.6333			0.919604
$290$	−1.39494	+	1.57878i	−0.0819136	+	0.0927090i
$291$		0			0
$292$	−25.7885	+	3.20077i	−1.50916	+	0.187311i
$293$	−22.7949	−	22.7949i	−1.33169	−	1.33169i	−0.903856	−	0.427837i	$-0.859276\pi$
$293$	−22.7949	−	22.7949i	−1.33169	−	1.33169i	−0.427837	−	0.903856i	$-0.640724\pi$
$294$		0			0
$295$		−	17.4503i		−	1.01600i
$296$	4.24162	+	22.6370i	0.246539	+	1.31575i
$297$		0			0
$298$	−6.37608	+	0.394176i	−0.369357	+	0.0228340i
$299$	5.55118	+	5.55118i	0.321033	+	0.321033i
$300$		0			0
$301$	−0.176537	+	0.176537i	−0.0101754	+	0.0101754i
$302$	4.93681	+	4.36195i	0.284081	+	0.251002i
$303$		0			0
$304$	2.19191	−	3.66973i	0.125715	−	0.210474i
$305$	−15.2290			−0.872010
$306$		0			0
$307$	−4.80812	+	4.80812i	−0.274414	+	0.274414i	−0.830874	−	0.556460i	$-0.812159\pi$
$307$	−4.80812	+	4.80812i	−0.274414	+	0.274414i	0.556460	+	0.830874i	$0.312159\pi$
$308$	1.14742	+	0.894039i	0.0653802	+	0.0509426i
$309$		0			0
$310$	−21.1562	+	1.30790i	−1.20159	+	0.0742839i
$311$			26.6526i			1.51133i	0.654957	+	0.755666i	$0.272687\pi$
$311$			26.6526i			1.51133i	−0.654957	+	0.755666i	$0.727313\pi$
$312$		0			0
$313$		−	16.5077i		−	0.933070i	−0.884503	−	0.466535i	$-0.845502\pi$
$313$		−	16.5077i		−	0.933070i	0.884503	−	0.466535i	$-0.154498\pi$
$314$	−0.947588	−	15.3279i	−0.0534755	−	0.865004i
$315$		0			0
$316$	−3.60956	−	29.0820i	−0.203053	−	1.63599i
$317$	−16.0855	+	16.0855i	−0.903454	+	0.903454i	−0.995733	−	0.0922795i	$-0.970585\pi$
$317$	−16.0855	+	16.0855i	−0.903454	+	0.903454i	0.0922795	+	0.995733i	$0.470585\pi$
$318$		0			0
$319$	−0.509849			−0.0285461
$320$	−5.15167	+	11.6945i	−0.287987	+	0.653742i
$321$		0			0
$322$	−2.77423	+	3.13984i	−0.154602	+	0.174976i
$323$	−4.31660	+	4.31660i	−0.240182	+	0.240182i
$324$		0			0
$325$	−6.10315	−	6.10315i	−0.338542	−	0.338542i
$326$	−2.15454	−	34.8512i	−0.119329	−	1.93023i
$327$		0			0
$328$	−15.3811	+	22.4743i	−0.849279	+	1.24093i
$329$			13.4057i			0.739079i
$330$		0			0
$331$	18.0425	+	18.0425i	0.991707	+	0.991707i	0.999966	−	0.00825899i	$-0.00262895\pi$
$331$	18.0425	+	18.0425i	0.991707	+	0.991707i	−0.00825899	+	0.999966i	$0.502629\pi$
$332$	3.52608	+	2.74743i	0.193519	+	0.150785i
$333$		0			0
$334$	−6.77117	−	5.98271i	−0.370502	−	0.327359i
$335$	−8.12209			−0.443757
$336$		0			0
$337$	−9.54474			−0.519935			−0.259968	−	0.965617i	$-0.583712\pi$
$337$	−9.54474			−0.519935			−0.259968	+	0.965617i	$0.583712\pi$
$338$	−0.607301	−	0.536585i	−0.0330328	−	0.0291864i
$339$		0			0
$340$	11.2170	−	14.3960i	0.608327	−	0.780732i
$341$	−3.62728	−	3.62728i	−0.196428	−	0.196428i
$342$		0			0
$343$		−	16.2704i		−	0.878520i
$344$	−0.0977570	−	0.521717i	−0.00527070	−	0.0281291i
$345$		0			0
$346$	−1.55292	−	25.1196i	−0.0834854	−	1.35044i
$347$	−16.4451	−	16.4451i	−0.882821	−	0.882821i	0.110999	−	0.993821i	$-0.464595\pi$
$347$	−16.4451	−	16.4451i	−0.882821	−	0.882821i	−0.993821	+	0.110999i	$0.964595\pi$
$348$		0			0
$349$	−2.01728	+	2.01728i	−0.107982	+	0.107982i	−0.759034	−	0.651051i	$-0.774328\pi$
$349$	−2.01728	+	2.01728i	−0.107982	+	0.107982i	0.651051	+	0.759034i	$0.274328\pi$
$350$	3.05007	−	3.45204i	0.163033	−	0.184519i
$351$		0			0
$352$	−2.94640	+	0.939631i	−0.157043	+	0.0500825i
$353$	5.85456			0.311607			0.155803	−	0.987788i	$-0.450203\pi$
$353$	5.85456			0.311607			0.155803	+	0.987788i	$0.450203\pi$
$354$		0			0
$355$	10.3634	−	10.3634i	0.550032	−	0.550032i
$356$	−19.2302	+	2.38678i	−1.01920	+	0.126499i
$357$		0			0
$358$	1.03325	+	16.7135i	0.0546089	+	0.883337i
$359$			6.70632i			0.353946i	0.984216	+	0.176973i	$0.0566305\pi$
$359$			6.70632i			0.353946i	−0.984216	+	0.176973i	$0.943369\pi$
$360$		0			0
$361$			17.8580i			0.939897i
$362$	−24.0213	+	1.48502i	−1.26253	+	0.0780511i
$363$		0			0
$364$	−5.76489	+	7.39871i	−0.302162	+	0.387798i
$365$	14.6759	−	14.6759i	0.768171	−	0.768171i
$366$		0			0
$367$	12.7921			0.667742			0.333871	−	0.942619i	$-0.391645\pi$
$367$	12.7921			0.667742			0.333871	+	0.942619i	$0.391645\pi$
$368$	−2.17770	−	8.63766i	−0.113521	−	0.450269i
$369$		0			0
$370$	−13.7846	−	12.1795i	−0.716628	−	0.633181i
$371$	3.08015	−	3.08015i	0.159913	−	0.159913i
$372$		0			0
$373$	7.42579	+	7.42579i	0.384493	+	0.384493i	0.872718	−	0.488225i	$-0.162355\pi$
$373$	7.42579	+	7.42579i	0.384493	+	0.384493i	−0.488225	+	0.872718i	$0.662355\pi$
$374$	4.40824	−	0.272522i	0.227945	−	0.0140918i
$375$		0			0
$376$	−23.5205	−	16.0972i	−1.21298	−	0.830148i
$377$		−	3.28758i		−	0.169319i
$378$		0			0
$379$	6.90419	+	6.90419i	0.354644	+	0.354644i	0.861834	−	0.507190i	$-0.169316\pi$
$379$	6.90419	+	6.90419i	0.354644	+	0.354644i	−0.507190	+	0.861834i	$0.669316\pi$
$380$	0.420504	+	3.38798i	0.0215714	+	0.173800i
$381$		0			0
$382$	3.43256	−	3.88493i	0.175625	−	0.198770i
$383$	16.3296			0.834401			0.417201	−	0.908814i	$-0.363011\pi$
$383$	16.3296			0.834401			0.417201	+	0.908814i	$0.363011\pi$
$384$		0			0
$385$	−1.16177			−0.0592092
$386$	10.6928	−	12.1020i	0.544250	−	0.615976i
$387$		0			0
$388$	4.20798	+	33.9035i	0.213628	+	1.72119i
$389$	−26.6841	−	26.6841i	−1.35294	−	1.35294i	−0.882356	−	0.470583i	$-0.844044\pi$
$389$	−26.6841	−	26.6841i	−1.35294	−	1.35294i	−0.470583	−	0.882356i	$-0.655956\pi$
$390$		0			0
$391$			12.7218i			0.643369i
$392$	12.2079	+	8.35492i	0.616591	+	0.421987i
$393$		0			0
$394$	0.863841	−	0.0534036i	0.0435197	−	0.00269044i
$395$	16.5502	+	16.5502i	0.832730	+	0.832730i
$396$		0			0
$397$	18.3638	−	18.3638i	0.921655	−	0.921655i	−0.0754913	−	0.997146i	$-0.524053\pi$
$397$	18.3638	−	18.3638i	0.921655	−	0.921655i	0.997146	+	0.0754913i	$0.0240525\pi$
$398$	−9.92274	−	8.76730i	−0.497382	−	0.439465i
$399$		0			0
$400$	2.39424	+	9.49653i	0.119712	+	0.474826i
$401$	−33.0099			−1.64844			−0.824219	−	0.566271i	$-0.808386\pi$
$401$	−33.0099			−1.64844			−0.824219	+	0.566271i	$0.808386\pi$
$402$		0			0
$403$	23.3892	−	23.3892i	1.16510	−	1.16510i
$404$	9.88990	−	12.6928i	0.492041	−	0.631490i
$405$		0			0
$406$	1.75124	−	0.108264i	0.0869128	−	0.00537304i
$407$		−	4.45160i		−	0.220657i
$408$		0			0
$409$		−	8.97074i		−	0.443575i	−0.975095	−	0.221787i	$-0.928811\pi$
$409$		−	8.97074i		−	0.443575i	0.975095	−	0.221787i	$-0.0711891\pi$
$410$	−1.34211	−	21.7096i	−0.0662821	−	1.07216i
$411$		0			0
$412$	−12.7980	+	1.58844i	−0.630510	+	0.0782568i
$413$	−10.2766	+	10.2766i	−0.505681	+	0.505681i
$414$		0			0
$415$	−3.57018			−0.175253
$416$	−6.05887	−	18.9988i	−0.297060	−	0.931491i
$417$		0			0
$418$	−0.547056	+	0.619152i	−0.0267574	+	0.0302837i
$419$	18.9265	−	18.9265i	0.924621	−	0.924621i	−0.0727306	−	0.997352i	$-0.523171\pi$
$419$	18.9265	−	18.9265i	0.924621	−	0.924621i	0.997352	+	0.0727306i	$0.0231713\pi$
$420$		0			0
$421$	−1.62365	−	1.62365i	−0.0791320	−	0.0791320i	0.666433	−	0.745565i	$-0.267820\pi$
$421$	−1.62365	−	1.62365i	−0.0791320	−	0.0791320i	−0.745565	+	0.666433i	$0.767820\pi$
$422$	−2.27741	−	36.8386i	−0.110862	−	1.79328i
$423$		0			0
$424$	1.70563	+	9.10274i	0.0828327	+	0.442068i
$425$		−	13.9867i		−	0.678457i
$426$		0			0
$427$	8.96847	+	8.96847i	0.434015	+	0.434015i
$428$	−14.5554	+	18.6805i	−0.703560	+	0.902955i
$429$		0			0
$430$	0.317695	+	0.280702i	0.0153206	+	0.0135366i
$431$	−32.0624			−1.54439			−0.772196	−	0.635384i	$-0.780842\pi$
$431$	−32.0624			−1.54439			−0.772196	+	0.635384i	$0.780842\pi$
$432$		0			0
$433$	15.2680			0.733732			0.366866	−	0.930274i	$-0.380431\pi$
$433$	15.2680			0.733732			0.366866	+	0.930274i	$0.380431\pi$
$434$	13.2293	+	11.6888i	0.635027	+	0.561082i
$435$		0			0
$436$	−3.07669	−	2.39728i	−0.147347	−	0.114809i
$437$	−1.68279	−	1.68279i	−0.0804986	−	0.0804986i
$438$		0			0
$439$			24.1930i			1.15467i	0.816507	+	0.577335i	$0.195907\pi$
$439$			24.1930i			1.15467i	−0.816507	+	0.577335i	$0.804093\pi$
$440$	1.39502	−	2.03834i	0.0665048	−	0.0971743i
$441$		0			0
$442$	1.75726	+	28.4249i	0.0835844	+	1.35204i
$443$	13.4825	+	13.4825i	0.640574	+	0.640574i	0.950697	−	0.310123i	$-0.100370\pi$
$443$	13.4825	+	13.4825i	0.640574	+	0.640574i	−0.310123	+	0.950697i	$0.600370\pi$
$444$		0			0
$445$	10.9436	−	10.9436i	0.518778	−	0.518778i
$446$	−20.0783	+	22.7244i	−0.950735	+	1.07603i
$447$		0			0
$448$	9.92083	−	3.85312i	0.468715	−	0.182043i
$449$	17.4996			0.825858			0.412929	−	0.910763i	$-0.364506\pi$
$449$	17.4996			0.825858			0.412929	+	0.910763i	$0.364506\pi$
$450$		0			0
$451$	3.72215	−	3.72215i	0.175269	−	0.175269i
$452$	1.50214	+	12.1027i	0.0706548	+	0.569262i
$453$		0			0
$454$	0.978780	+	15.8325i	0.0459364	+	0.743054i
$455$		−	7.49123i		−	0.351195i
$456$		0			0
$457$			21.7443i			1.01716i	0.861016	+	0.508578i	$0.169829\pi$
$457$			21.7443i			1.01716i	−0.861016	+	0.508578i	$0.830171\pi$
$458$	6.93950	−	0.429007i	0.324262	−	0.0200462i
$459$		0			0
$460$	5.61215	+	4.37284i	0.261668	+	0.203885i
$461$	−9.71242	+	9.71242i	−0.452353	+	0.452353i	−0.896135	−	0.443782i	$-0.853636\pi$
$461$	−9.71242	+	9.71242i	−0.452353	+	0.452353i	0.443782	+	0.896135i	$0.353636\pi$
$462$		0			0
$463$	−20.0438			−0.931516			−0.465758	−	0.884912i	$-0.654218\pi$
$463$	−20.0438			−0.931516			−0.465758	+	0.884912i	$0.654218\pi$
$464$	−1.91289	+	3.20259i	−0.0888038	+	0.148677i
$465$		0			0
$466$	−3.20376	−	2.83070i	−0.148411	−	0.131130i
$467$	−2.41971	+	2.41971i	−0.111971	+	0.111971i	−0.760872	−	0.648902i	$-0.775229\pi$
$467$	−2.41971	+	2.41971i	−0.111971	+	0.111971i	0.648902	+	0.760872i	$0.275229\pi$
$468$		0			0
$469$	4.78316	+	4.78316i	0.220866	+	0.220866i
$470$	22.7203	−	1.40459i	1.04801	−	0.0647890i
$471$		0			0
$472$	−5.69068	−	30.3705i	−0.261935	−	1.39791i
$473$			0.102596i			0.00471738i
$474$		0			0
$475$	1.85011	+	1.85011i	0.0848889	+	0.0848889i
$476$	−15.0837	+	1.87213i	−0.691359	+	0.0858091i
$477$		0			0
$478$	−23.1007	+	26.1451i	−1.05660	+	1.19585i
$479$	−6.14282			−0.280673			−0.140336	−	0.990104i	$-0.544818\pi$
$479$	−6.14282			−0.280673			−0.140336	+	0.990104i	$0.544818\pi$
$480$		0			0
$481$	28.7045			1.30881
$482$	8.04302	−	9.10301i	0.366350	−	0.414631i
$483$		0			0
$484$	−21.2393	+	2.63615i	−0.965421	+	0.119825i
$485$	−19.2940	−	19.2940i	−0.876097	−	0.876097i
$486$		0			0
$487$			4.67510i			0.211849i	0.994374	+	0.105925i	$0.0337802\pi$
$487$			4.67510i			0.211849i	−0.994374	+	0.105925i	$0.966220\pi$
$488$	−26.5045	+	4.96628i	−1.19980	+	0.224813i
$489$		0			0
$490$	−11.7925	+	0.729026i	−0.532731	+	0.0329340i
$491$	−12.5982	−	12.5982i	−0.568549	−	0.568549i	0.363172	−	0.931722i	$-0.381694\pi$
$491$	−12.5982	−	12.5982i	−0.568549	−	0.568549i	−0.931722	+	0.363172i	$0.881694\pi$
$492$		0			0
$493$	3.76711	−	3.76711i	0.169662	−	0.169662i
$494$	−3.99238	−	3.52749i	−0.179626	−	0.158709i
$495$		0			0
$496$	−36.3937	+	9.17546i	−1.63412	+	0.411991i
$497$	−12.2062			−0.547522
$498$		0			0
$499$	13.5597	−	13.5597i	0.607014	−	0.607014i	−0.335151	−	0.942164i	$-0.608787\pi$
$499$	13.5597	−	13.5597i	0.607014	−	0.607014i	0.942164	+	0.335151i	$0.108787\pi$
$500$	−18.7705	−	14.6255i	−0.839441	−	0.654072i
$501$		0			0
$502$	−29.1340	+	1.80110i	−1.30032	+	0.0803869i
$503$			18.0201i			0.803478i	0.915754	+	0.401739i	$0.131594\pi$
$503$			18.0201i			0.803478i	−0.915754	+	0.401739i	$0.868406\pi$
$504$		0			0
$505$			12.8515i			0.571885i
$506$	0.106240	+	1.71851i	0.00472296	+	0.0763973i
$507$		0			0
$508$	2.17572	+	17.5296i	0.0965318	+	0.777751i
$509$	23.0735	−	23.0735i	1.02271	−	1.02271i	0.0229783	−	0.999736i	$-0.492685\pi$
$509$	23.0735	−	23.0735i	1.02271	−	1.02271i	0.999736	−	0.0229783i	$-0.00731486\pi$
$510$		0			0
$511$	−17.2855			−0.764665
$512$	−5.15227	+	22.0330i	−0.227700	+	0.973731i
$513$		0			0
$514$	2.09652	−	2.37281i	0.0924733	−	0.104660i
$515$	7.28316	−	7.28316i	0.320934	−	0.320934i
$516$		0			0
$517$	3.89543	+	3.89543i	0.171321	+	0.171321i
$518$	0.945273	+	15.2905i	0.0415329	+	0.671824i
$519$		0			0
$520$	13.1435	+	8.99526i	0.576382	+	0.394468i
$521$			7.56756i			0.331541i	0.986164	+	0.165770i	$0.0530111\pi$
$521$			7.56756i			0.331541i	−0.986164	+	0.165770i	$0.946989\pi$
$522$		0			0
$523$	−3.95670	−	3.95670i	−0.173014	−	0.173014i	0.615288	−	0.788302i	$-0.289040\pi$
$523$	−3.95670	−	3.95670i	−0.173014	−	0.173014i	−0.788302	+	0.615288i	$0.789040\pi$
$524$	29.7024	+	23.1433i	1.29755	+	1.01102i
$525$		0			0
$526$	0.548572	+	0.484694i	0.0239189	+	0.0211337i
$527$	53.6016			2.33492
$528$		0			0
$529$	18.0405			0.784371
$530$	−5.54303	−	4.89758i	−0.240774	−	0.212737i
$531$		0			0
$532$	1.74757	−	2.24285i	0.0757667	−	0.0972397i
$533$	24.0009	+	24.0009i	1.03960	+	1.03960i
$534$		0			0
$535$		−	18.9141i		−	0.817728i
$536$	−14.1356	+	2.64867i	−0.610566	+	0.114405i
$537$		0			0
$538$	−0.888776	−	14.3766i	−0.0383178	−	0.619818i
$539$	−2.02185	−	2.02185i	−0.0870872	−	0.0870872i
$540$		0			0
$541$	1.57544	−	1.57544i	0.0677334	−	0.0677334i	−0.672429	−	0.740162i	$-0.734749\pi$
$541$	1.57544	−	1.57544i	0.0677334	−	0.0677334i	0.740162	+	0.672429i	$0.234749\pi$
$542$	−5.09776	+	5.76959i	−0.218967	+	0.247825i
$543$		0			0
$544$	14.8273	−	28.7126i	0.635717	−	1.23104i
$545$	3.11517			0.133439
$546$		0			0
$547$	−14.3006	+	14.3006i	−0.611448	+	0.611448i	−0.943323	−	0.331876i	$-0.892319\pi$
$547$	−14.3006	+	14.3006i	−0.611448	+	0.611448i	0.331876	+	0.943323i	$0.392319\pi$
$548$	−1.40909	+	0.174891i	−0.0601933	+	0.00747098i
$549$		0			0
$550$	−0.116804	−	1.88939i	−0.00498055	−	0.0805638i
$551$			0.996597i			0.0424565i
$552$		0			0
$553$		−	19.4931i		−	0.828929i
$554$	−1.17788	+	0.0728181i	−0.0500435	+	0.00309374i
$555$		0			0
$556$	−8.80932	+	11.3060i	−0.373598	+	0.479479i
$557$	−23.8827	+	23.8827i	−1.01194	+	1.01194i	−0.0120126	+	0.999928i	$0.503824\pi$
$557$	−23.8827	+	23.8827i	−1.01194	+	1.01194i	−0.999928	+	0.0120126i	$0.996176\pi$
$558$		0			0
$559$	−0.661555			−0.0279808
$560$	−4.35881	+	7.29758i	−0.184193	+	0.308379i
$561$		0			0
$562$	32.4774	+	28.6956i	1.36997	+	1.21045i
$563$	−11.2588	+	11.2588i	−0.474500	+	0.474500i	−0.903368	−	0.428867i	$-0.858913\pi$
$563$	−11.2588	+	11.2588i	−0.474500	+	0.474500i	0.428867	+	0.903368i	$0.358913\pi$
$564$		0			0
$565$	−6.88748	−	6.88748i	−0.289758	−	0.289758i
$566$	18.8033	−	1.16244i	0.790361	−	0.0488610i
$567$		0			0
$568$	14.6568	−	21.4160i	0.614987	−	0.898594i
$569$		−	28.3175i		−	1.18713i	−0.804785	−	0.593566i	$-0.797719\pi$
$569$		−	28.3175i		−	1.18713i	0.804785	−	0.593566i	$-0.202281\pi$
$570$		0			0
$571$	24.6894	+	24.6894i	1.03322	+	1.03322i	0.999429	+	0.0337889i	$0.0107574\pi$
$571$	24.6894	+	24.6894i	1.03322	+	1.03322i	0.0337889	+	0.999429i	$0.489243\pi$
$572$	0.474757	+	3.82509i	0.0198506	+	0.159935i
$573$		0			0
$574$	−11.9946	+	13.5753i	−0.500643	+	0.566623i
$575$	5.45261			0.227390
$576$		0			0
$577$	−7.79877			−0.324667			−0.162334	−	0.986736i	$-0.551902\pi$
$577$	−7.79877			−0.324667			−0.162334	+	0.986736i	$0.551902\pi$
$578$	−14.6388	+	16.5681i	−0.608896	+	0.689142i
$579$		0			0
$580$	−0.366976	−	2.95671i	−0.0152379	−	0.122771i
$581$	2.10251	+	2.10251i	0.0872266	+	0.0872266i
$582$		0			0
$583$		−	1.79006i		−	0.0741369i
$584$	20.7559	−	30.3277i	0.858886	−	1.25497i
$585$		0			0
$586$	45.5029	−	2.81304i	1.87971	−	0.116206i
$587$	25.6905	+	25.6905i	1.06036	+	1.06036i	0.998057	+	0.0623048i	$0.0198451\pi$
$587$	25.6905	+	25.6905i	1.06036	+	1.06036i	0.0623048	+	0.998057i	$0.480155\pi$
$588$		0			0
$589$	−7.09020	+	7.09020i	−0.292147	+	0.292147i
$590$	18.4938	+	16.3404i	0.761379	+	0.672722i
$591$		0			0
$592$	−27.9625	−	16.7018i	−1.14925	−	0.686441i
$593$	−37.5946			−1.54382			−0.771912	−	0.635729i	$-0.780700\pi$
$593$	−37.5946			−1.54382			−0.771912	+	0.635729i	$0.780700\pi$
$594$		0			0
$595$	8.58393	−	8.58393i	0.351907	−	0.351907i
$596$	5.55276	−	7.12646i	0.227450	−	0.291911i
$597$		0			0
$598$	−11.0812	+	0.685053i	−0.453144	+	0.0280139i
$599$		−	30.8830i		−	1.26184i	−0.775847	−	0.630922i	$-0.782677\pi$
$599$		−	30.8830i		−	1.26184i	0.775847	−	0.630922i	$-0.217323\pi$
$600$		0			0
$601$			17.2179i			0.702334i	0.936313	+	0.351167i	$0.114215\pi$
$601$			17.2179i			0.702334i	−0.936313	+	0.351167i	$0.885785\pi$
$602$	−0.0217858	−	0.352401i	−0.000887923	−	0.0143628i
$603$		0			0
$604$	−9.24556	+	1.14753i	−0.376197	+	0.0466922i
$605$	12.0870	−	12.0870i	0.491407	−	0.491407i
$606$		0			0
$607$	3.64130			0.147796			0.0738978	−	0.997266i	$-0.476456\pi$
$607$	3.64130			0.147796			0.0738978	+	0.997266i	$0.476456\pi$
$608$	1.83669	+	5.75929i	0.0744875	+	0.233570i
$609$		0			0
$610$	14.2603	−	16.1397i	0.577383	−	0.653476i
$611$	−25.1183	+	25.1183i	−1.01618	+	1.01618i
$612$		0			0
$613$	−28.8956	−	28.8956i	−1.16708	−	1.16708i	−0.982890	−	0.184194i	$-0.941032\pi$
$613$	−28.8956	−	28.8956i	−1.16708	−	1.16708i	−0.184194	−	0.982890i	$-0.558968\pi$
$614$	−0.593353	−	9.59791i	−0.0239458	−	0.387340i
$615$		0			0
$616$	−2.02193	+	0.378860i	−0.0814660	+	0.0152647i
$617$			27.8052i			1.11939i	0.828697	+	0.559697i	$0.189083\pi$
$617$			27.8052i			1.11939i	−0.828697	+	0.559697i	$0.810917\pi$
$618$		0			0
$619$	−20.6887	−	20.6887i	−0.831548	−	0.831548i	0.156180	−	0.987729i	$-0.450082\pi$
$619$	−20.6887	−	20.6887i	−0.831548	−	0.831548i	−0.987729	+	0.156180i	$0.950082\pi$
$620$	18.4244	−	23.6461i	0.739942	−	0.949648i
$621$		0			0
$622$	−28.2464	−	24.9573i	−1.13258	−	1.00070i
$623$	−12.8896			−0.516411
$624$		0			0
$625$	6.76311			0.270525
$626$	17.4948	+	15.4577i	0.699233	+	0.617812i
$627$		0			0
$628$	17.1318	+	13.3487i	0.683633	+	0.532670i
$629$	32.8914	+	32.8914i	1.31147	+	1.31147i
$630$		0			0
$631$			18.8206i			0.749238i	0.927179	+	0.374619i	$0.122226\pi$
$631$			18.8206i			0.749238i	−0.927179	+	0.374619i	$0.877774\pi$
$632$	34.2010	+	23.4067i	1.36044	+	0.931069i
$633$		0			0
$634$	−1.98506	−	32.1098i	−0.0788369	−	1.27524i
$635$	−9.97589	−	9.97589i	−0.395881	−	0.395881i
$636$		0			0
$637$	13.0372	−	13.0372i	0.516551	−	0.516551i
$638$	0.477418	−	0.540337i	0.0189012	−	0.0213922i
$639$		0			0
$640$	−7.56983	−	16.4104i	−0.299224	−	0.648676i
$641$	49.0450			1.93716			0.968581	−	0.248697i	$-0.0800023\pi$
$641$	49.0450			1.93716			0.968581	+	0.248697i	$0.0800023\pi$
$642$		0			0
$643$	33.3634	−	33.3634i	1.31573	−	1.31573i	0.398601	−	0.917125i	$-0.369496\pi$
$643$	33.3634	−	33.3634i	1.31573	−	1.31573i	0.917125	−	0.398601i	$-0.130504\pi$
$644$	−0.729835	−	5.88024i	−0.0287595	−	0.231714i
$645$		0			0
$646$	−0.532696	−	8.61674i	−0.0209587	−	0.339021i
$647$		−	7.59115i		−	0.298439i	−0.988804	−	0.149220i	$-0.952324\pi$
$647$		−	7.59115i		−	0.298439i	0.988804	−	0.149220i	$-0.0476761\pi$
$648$		0			0
$649$			5.97239i			0.234437i
$650$	12.1830	−	0.753169i	0.477858	−	0.0295417i
$651$		0			0
$652$	38.9527	+	30.3510i	1.52551	+	1.18864i
$653$	1.73048	−	1.73048i	0.0677189	−	0.0677189i	−0.672436	−	0.740155i	$-0.734752\pi$
$653$	1.73048	−	1.73048i	0.0677189	−	0.0677189i	0.740155	+	0.672436i	$0.234752\pi$
$654$		0			0
$655$	−30.0738			−1.17508
$656$	−9.41545	−	37.3456i	−0.367612	−	1.45810i
$657$		0			0
$658$	−14.2073	−	12.5530i	−0.553859	−	0.489365i
$659$	−4.27667	+	4.27667i	−0.166595	+	0.166595i	−0.785481	−	0.618886i	$-0.787584\pi$
$659$	−4.27667	+	4.27667i	−0.166595	+	0.166595i	0.618886	+	0.785481i	$0.287584\pi$
$660$		0			0
$661$	−18.6988	−	18.6988i	−0.727297	−	0.727297i	0.242783	−	0.970081i	$-0.421940\pi$
$661$	−18.6988	−	18.6988i	−0.727297	−	0.727297i	−0.970081	+	0.242783i	$0.921940\pi$
$662$	−36.0163	+	2.22657i	−1.39981	+	0.0865380i
$663$		0			0
$664$	−6.21352	+	1.16426i	−0.241131	+	0.0451821i
$665$			2.27089i			0.0880615i
$666$		0			0
$667$	1.46858	+	1.46858i	0.0568635	+	0.0568635i
$668$	12.6809	−	1.57391i	0.490640	−	0.0608965i
$669$		0			0
$670$	7.60545	−	8.60777i	0.293824	−	0.332547i
$671$	5.21213			0.201212
$672$		0			0
$673$	−16.2787			−0.627499			−0.313750	−	0.949506i	$-0.601585\pi$
$673$	−16.2787			−0.627499			−0.313750	+	0.949506i	$0.601585\pi$
$674$	8.93761	−	10.1155i	0.344264	−	0.389634i
$675$		0			0
$676$	1.13734	−	0.141163i	0.0437439	−	0.00542935i
$677$	21.1966	+	21.1966i	0.814652	+	0.814652i	0.985327	−	0.170675i	$-0.0545949\pi$
$677$	21.1966	+	21.1966i	0.814652	+	0.814652i	−0.170675	+	0.985327i	$0.554595\pi$
$678$		0			0
$679$			22.7248i			0.872098i
$680$	4.75334	+	25.3680i	0.182282	+	0.972819i
$681$		0			0
$682$	7.24074	−	0.447630i	0.277262	−	0.0171406i
$683$	−12.0643	−	12.0643i	−0.461629	−	0.461629i	0.437560	−	0.899189i	$-0.355843\pi$
$683$	−12.0643	−	12.0643i	−0.461629	−	0.461629i	−0.899189	+	0.437560i	$0.855843\pi$
$684$		0			0
$685$	0.801894	−	0.801894i	0.0306388	−	0.0306388i
$686$	17.2434	+	15.2355i	0.658354	+	0.581693i
$687$		0			0
$688$	0.644454	+	0.384929i	0.0245696	+	0.0146753i
$689$	11.5426			0.439737
$690$		0			0
$691$	1.12973	−	1.12973i	0.0429770	−	0.0429770i	−0.685292	−	0.728269i	$-0.740325\pi$
$691$	1.12973	−	1.12973i	0.0429770	−	0.0429770i	0.728269	+	0.685292i	$0.240325\pi$
$692$	28.0758	+	21.8760i	1.06728	+	0.831599i
$693$		0			0
$694$	32.8276	−	2.02944i	1.24612	−	0.0770364i
$695$		−	11.4473i		−	0.434223i
$696$		0			0
$697$			55.0036i			2.08341i
$698$	−0.248945	−	4.02686i	−0.00942271	−	0.152419i
$699$		0			0
$700$	0.802404	+	6.46492i	0.0303280	+	0.244351i
$701$	13.1963	−	13.1963i	0.498416	−	0.498416i	−0.412529	−	0.910945i	$-0.635354\pi$
$701$	13.1963	−	13.1963i	0.498416	−	0.498416i	0.910945	+	0.412529i	$0.135354\pi$
$702$		0			0
$703$	−8.70148			−0.328183
$704$	1.76316	−	4.00245i	0.0664516	−	0.150848i
$705$		0			0
$706$	−5.48216	+	6.20465i	−0.206324	+	0.233515i
$707$	7.56836	−	7.56836i	0.284637	−	0.284637i
$708$		0			0
$709$	−12.5191	−	12.5191i	−0.470163	−	0.470163i	0.431804	−	0.901967i	$-0.357877\pi$
$709$	−12.5191	−	12.5191i	−0.470163	−	0.470163i	−0.901967	+	0.431804i	$0.857877\pi$
$710$	1.27891	+	20.6873i	0.0479967	+	0.776381i
$711$		0			0
$712$	15.4774	−	22.6150i	0.580042	−	0.847535i
$713$			20.8961i			0.782566i
$714$		0			0
$715$	−2.17681	−	2.17681i	−0.0814080	−	0.0814080i
$716$	−18.6805	−	14.5554i	−0.698122	−	0.543959i
$717$		0			0
$718$	−7.10734	−	6.27974i	−0.265244	−	0.234358i
$719$	8.23354			0.307059			0.153530	−	0.988144i	$-0.450936\pi$
$719$	8.23354			0.307059			0.153530	+	0.988144i	$0.450936\pi$
$720$		0			0
$721$	−8.57822			−0.319469
$722$	−18.9259	−	16.7221i	−0.704349	−	0.622332i
$723$		0			0
$724$	20.9195	−	26.8483i	0.777468	−	0.997809i
$725$	−1.61460	−	1.61460i	−0.0599647	−	0.0599647i
$726$		0			0
$727$			2.03041i			0.0753037i	0.999291	+	0.0376519i	$0.0119878\pi$
$727$			2.03041i			0.0753037i	−0.999291	+	0.0376519i	$0.988012\pi$
$728$	−2.44294	−	13.0377i	−0.0905415	−	0.483209i
$729$		0			0
$730$	1.81110	+	29.2958i	0.0670319	+	1.08429i
$731$	−0.758051	−	0.758051i	−0.0280375	−	0.0280375i
$732$		0			0
$733$	8.14418	−	8.14418i	0.300812	−	0.300812i	−0.540519	−	0.841332i	$-0.681772\pi$
$733$	8.14418	−	8.14418i	0.300812	−	0.300812i	0.841332	+	0.540519i	$0.181772\pi$
$734$	−11.9784	+	13.5570i	−0.442131	+	0.500399i
$735$		0			0
$736$	11.1934	+	5.78031i	0.412593	+	0.213065i
$737$	2.77979			0.102395
$738$		0			0
$739$	8.59464	−	8.59464i	0.316159	−	0.316159i	−0.531131	−	0.847290i	$-0.678233\pi$
$739$	8.59464	−	8.59464i	0.316159	−	0.316159i	0.847290	+	0.531131i	$0.178233\pi$
$740$	25.8156	−	3.20414i	0.949000	−	0.117787i
$741$		0			0
$742$	0.380111	+	6.14856i	0.0139543	+	0.225721i
$743$			34.3833i			1.26140i	0.776026	+	0.630701i	$0.217233\pi$
$743$			34.3833i			1.26140i	−0.776026	+	0.630701i	$0.782767\pi$
$744$		0			0
$745$			7.21559i			0.264359i
$746$	−14.8233	+	0.916392i	−0.542719	+	0.0335515i
$747$		0			0
$748$	−3.83902	+	4.92703i	−0.140368	+	0.180150i
$749$	−11.1387	+	11.1387i	−0.406998	+	0.406998i
$750$		0			0
$751$	−23.0603			−0.841481			−0.420741	−	0.907181i	$-0.638230\pi$
$751$	−23.0603			−0.841481			−0.420741	+	0.907181i	$0.638230\pi$
$752$	39.0842	−	9.85378i	1.42525	−	0.359330i
$753$		0			0
$754$	3.48417	+	3.07846i	0.126886	+	0.112111i
$755$	5.26153	−	5.26153i	0.191487	−	0.191487i
$756$		0			0
$757$	−24.0737	−	24.0737i	−0.874972	−	0.874972i	0.118037	−	0.993009i	$-0.462340\pi$
$757$	−24.0737	−	24.0737i	−0.874972	−	0.874972i	−0.993009	+	0.118037i	$0.962340\pi$
$758$	−13.7821	+	0.852023i	−0.500587	+	0.0309469i
$759$		0			0
$760$	−3.98433	−	2.72683i	−0.144527	−	0.0989123i
$761$		−	17.2279i		−	0.624510i	−0.949998	−	0.312255i	$-0.898916\pi$
$761$		−	17.2279i		−	0.624510i	0.949998	−	0.312255i	$-0.101084\pi$
$762$		0			0
$763$	−1.83455	−	1.83455i	−0.0664150	−	0.0664150i
$764$	0.903026	+	7.27563i	0.0326703	+	0.263223i
$765$		0			0
$766$	−15.2909	+	17.3060i	−0.552481	+	0.625292i
$767$	−38.5108			−1.39054
$768$		0			0
$769$	−8.40722			−0.303172			−0.151586	−	0.988444i	$-0.548438\pi$
$769$	−8.40722			−0.303172			−0.151586	+	0.988444i	$0.548438\pi$
$770$	1.08787	−	1.23124i	0.0392041	−	0.0443708i
$771$		0			0
$772$	2.81303	+	22.6644i	0.101243	+	0.815711i
$773$	3.45742	+	3.45742i	0.124355	+	0.124355i	0.766545	−	0.642190i	$-0.221974\pi$
$773$	3.45742	+	3.45742i	0.124355	+	0.124355i	−0.642190	+	0.766545i	$0.721974\pi$
$774$		0			0
$775$		−	22.9739i		−	0.825246i
$776$	−39.8711	−	27.2873i	−1.43129	−	0.979557i
$777$		0			0
$778$	53.2665	−	3.29300i	1.90970	−	0.118060i
$779$	−7.27565	−	7.27565i	−0.260677	−	0.260677i
$780$		0			0
$781$	−3.54688	+	3.54688i	−0.126917	+	0.126917i
$782$	−13.4825	−	11.9126i	−0.482134	−	0.425993i
$783$		0			0
$784$	−20.2859	+	5.11441i	−0.724495	+	0.182658i
$785$	−17.3461			−0.619107
$786$		0			0
$787$	−15.8427	+	15.8427i	−0.564730	+	0.564730i	−0.930647	−	0.365918i	$-0.880755\pi$
$787$	−15.8427	+	15.8427i	−0.564730	+	0.564730i	0.365918	+	0.930647i	$0.380755\pi$
$788$	−0.752296	+	0.965504i	−0.0267994	+	0.0343946i
$789$		0			0
$790$	−33.0373	+	2.04240i	−1.17541	+	0.0726654i
$791$			8.11217i			0.288436i
$792$		0			0
$793$			33.6085i			1.19347i
$794$	2.26622	+	36.6577i	0.0804251	+	1.30093i
$795$		0			0
$796$	18.5831	−	2.30648i	0.658662	−	0.0817508i
$797$	20.3368	−	20.3368i	0.720366	−	0.720366i	−0.248313	−	0.968680i	$-0.579876\pi$
$797$	20.3368	−	20.3368i	0.720366	−	0.720366i	0.968680	+	0.248313i	$0.0798763\pi$
$798$		0			0
$799$	−57.5642			−2.03648
$800$	−12.3063	−	6.35506i	−0.435095	−	0.224685i
$801$		0			0
$802$	30.9102	−	34.9839i	1.09148	−	1.23532i
$803$	−5.02283	+	5.02283i	−0.177252	+	0.177252i
$804$		0			0
$805$	3.34637	+	3.34637i	0.117944	+	0.117944i
$806$	2.88638	+	46.6892i	0.101668	+	1.64456i
$807$		0			0
$808$	4.19097	+	22.3667i	0.147438	+	0.786858i
$809$			9.58203i			0.336886i	0.985711	+	0.168443i	$0.0538739\pi$
$809$			9.58203i			0.336886i	−0.985711	+	0.168443i	$0.946126\pi$
$810$		0			0
$811$	29.0350	+	29.0350i	1.01956	+	1.01956i	0.999805	+	0.0197508i	$0.00628728\pi$
$811$	29.0350	+	29.0350i	1.01956	+	1.01956i	0.0197508	+	0.999805i	$0.493713\pi$
$812$	−1.52511	+	1.95734i	−0.0535209	+	0.0686892i
$813$		0			0
$814$	4.71779	+	4.16843i	0.165358	+	0.146104i
$815$	−39.4399			−1.38152
$816$		0			0
$817$	0.200544			0.00701614
$818$	9.50717	+	8.40013i	0.332411	+	0.293703i
$819$		0			0
$820$	24.2645	+	18.9063i	0.847354	+	0.660237i
$821$	−11.6443	−	11.6443i	−0.406390	−	0.406390i	0.474088	−	0.880478i	$-0.342778\pi$
$821$	−11.6443	−	11.6443i	−0.406390	−	0.406390i	−0.880478	+	0.474088i	$0.842778\pi$
$822$		0			0
$823$		−	9.78505i		−	0.341085i	−0.985350	−	0.170543i	$-0.945448\pi$
$823$		−	9.78505i		−	0.341085i	0.985350	−	0.170543i	$-0.0545521\pi$
$824$	10.3005	−	15.0507i	0.358834	−	0.524314i
$825$		0			0
$826$	−1.26821	−	20.5141i	−0.0441265	−	0.713778i
$827$	−4.52046	−	4.52046i	−0.157192	−	0.157192i	0.624129	−	0.781321i	$-0.285454\pi$
$827$	−4.52046	−	4.52046i	−0.157192	−	0.157192i	−0.781321	+	0.624129i	$0.785454\pi$
$828$		0			0
$829$	−32.0727	+	32.0727i	−1.11393	+	1.11393i	−0.121317	+	0.992614i	$0.538712\pi$
$829$	−32.0727	+	32.0727i	−1.11393	+	1.11393i	−0.992614	+	0.121317i	$0.961288\pi$
$830$	3.34308	−	3.78367i	0.116040	−	0.131333i
$831$		0			0
$832$	25.8083	+	11.3691i	0.894743	+	0.394153i
$833$	29.8776			1.03520
$834$		0			0
$835$	−7.21655	+	7.21655i	−0.249739	+	0.249739i
$836$	−0.143918	−	1.15954i	−0.00497750	−	0.0401035i
$837$		0			0
$838$	2.33566	+	37.7809i	0.0806840	+	1.30512i
$839$		−	25.4507i		−	0.878655i	−0.898327	−	0.439328i	$-0.855217\pi$
$839$		−	25.4507i		−	0.878655i	0.898327	−	0.439328i	$-0.144783\pi$
$840$		0			0
$841$			28.1303i			0.970009i
$842$	3.24112	−	0.200370i	0.111696	−	0.00690519i
$843$		0			0
$844$	41.1741	+	32.0818i	1.41727	+	1.10430i
$845$	−0.647247	+	0.647247i	−0.0222660	+	0.0222660i
$846$		0			0
$847$	−14.2363			−0.489163
$848$	−11.2442	−	6.71610i	−0.386127	−	0.230632i
$849$		0			0
$850$	14.8231	+	13.0971i	0.508429	+	0.449226i
$851$	−12.8224	+	12.8224i	−0.439547	+	0.439547i
$852$		0			0
$853$	−30.2651	−	30.2651i	−1.03626	−	1.03626i	−0.999318	−	0.0369381i	$-0.988240\pi$
$853$	−30.2651	−	30.2651i	−1.03626	−	1.03626i	−0.0369381	−	0.999318i	$-0.511760\pi$
$854$	−17.9028	+	1.10677i	−0.612620	+	0.0378729i
$855$		0			0
$856$	−6.16802	−	32.9180i	−0.210819	−	1.12511i
$857$			4.83762i			0.165250i	0.996581	+	0.0826250i	$0.0263304\pi$
$857$			4.83762i			0.165250i	−0.996581	+	0.0826250i	$0.973670\pi$
$858$		0			0
$859$	−3.06295	−	3.06295i	−0.104506	−	0.104506i	0.652920	−	0.757427i	$-0.273544\pi$
$859$	−3.06295	−	3.06295i	−0.104506	−	0.104506i	−0.757427	+	0.652920i	$0.773544\pi$
$860$	−0.594974	+	0.0738461i	−0.0202885	+	0.00251813i
$861$		0			0
$862$	30.0230	−	33.9797i	1.02259	−	1.15735i
$863$	−30.0882			−1.02422			−0.512108	−	0.858921i	$-0.671135\pi$
$863$	−30.0882			−1.02422			−0.512108	+	0.858921i	$0.671135\pi$
$864$		0			0
$865$	−28.4269			−0.966544
$866$	−14.2968	+	16.1810i	−0.485825	+	0.549851i
$867$		0			0
$868$	−24.7756	+	3.07506i	−0.840939	+	0.104374i
$869$	−5.66431	−	5.66431i	−0.192149	−	0.192149i
$870$		0			0
$871$			17.9244i			0.607347i
$872$	5.42162	−	1.01588i	0.183599	−	0.0344020i
$873$		0			0
$874$	3.35916	−	0.207667i	0.113625	−	0.00702444i
$875$	−11.1923	−	11.1923i	−0.378370	−	0.378370i
$876$		0			0
$877$	18.7402	−	18.7402i	0.632813	−	0.632813i	−0.315960	−	0.948773i	$-0.602327\pi$
$877$	18.7402	−	18.7402i	0.632813	−	0.632813i	0.948773	+	0.315960i	$0.102327\pi$
$878$	−25.6397	−	22.6541i	−0.865299	−	0.764541i
$879$		0			0
$880$	0.853952	+	3.38712i	0.0287867	+	0.114180i
$881$	34.3249			1.15644			0.578218	−	0.815882i	$-0.303748\pi$
$881$	34.3249			1.15644			0.578218	+	0.815882i	$0.303748\pi$
$882$		0			0
$883$	16.2996	−	16.2996i	0.548525	−	0.548525i	−0.377489	−	0.926014i	$-0.623213\pi$
$883$	16.2996	−	16.2996i	0.548525	−	0.548525i	0.926014	+	0.377489i	$0.123213\pi$
$884$	−31.7702	−	24.7545i	−1.06855	−	0.832585i
$885$		0			0
$886$	−26.9137	+	1.66383i	−0.904182	+	0.0558975i
$887$		−	44.8326i		−	1.50533i	−0.658402	−	0.752666i	$-0.728767\pi$
$887$		−	44.8326i		−	1.50533i	0.658402	−	0.752666i	$-0.271233\pi$
$888$		0			0
$889$			11.7498i			0.394074i
$890$	1.35052	+	21.8456i	0.0452695	+	0.732266i
$891$		0			0
$892$	−5.28214	−	42.5579i	−0.176859	−	1.42494i
$893$	7.61436	−	7.61436i	0.254805	−	0.254805i
$894$		0			0
$895$	18.9141			0.632229
$896$	−5.20625	+	14.1221i	−0.173929	+	0.471787i
$897$		0			0
$898$	−16.3865	+	18.5461i	−0.546824	+	0.618890i
$899$	6.18765	−	6.18765i	0.206370	−	0.206370i
$900$		0			0
$901$	13.2262	+	13.2262i	0.440629	+	0.440629i
$902$	0.459338	+	7.43012i	0.0152943	+	0.247396i
$903$		0			0
$904$	−14.2330	−	9.74086i	−0.473382	−	0.323976i
$905$			27.1841i			0.903629i
$906$		0			0
$907$	28.0738	+	28.0738i	0.932175	+	0.932175i	0.997842	−	0.0656663i	$-0.0209173\pi$
$907$	28.0738	+	28.0738i	0.932175	+	0.932175i	−0.0656663	+	0.997842i	$0.520917\pi$
$908$	−17.6957	−	13.7881i	−0.587253	−	0.457573i
$909$		0			0
$910$	7.93919	+	7.01473i	0.263182	+	0.232536i
$911$	17.3772			0.575731			0.287866	−	0.957671i	$-0.407054\pi$
$911$	17.3772			0.575731			0.287866	+	0.957671i	$0.407054\pi$
$912$		0			0
$913$	1.22190			0.0404388
$914$	−23.0446	−	20.3612i	−0.762247	−	0.673488i
$915$		0			0
$916$	−6.04343	+	7.75619i	−0.199680	+	0.256272i
$917$	17.7107	+	17.7107i	0.584859	+	0.584859i
$918$		0			0
$919$			43.5500i			1.43658i	0.695743	+	0.718291i	$0.255075\pi$
$919$			43.5500i			1.43658i	−0.695743	+	0.718291i	$0.744925\pi$
$920$	−9.88950	+	1.85305i	−0.326047	+	0.0610932i
$921$		0			0
$922$	−1.19858	−	19.3878i	−0.0394730	−	0.638504i
$923$	−22.8708	−	22.8708i	−0.752800	−	0.752800i
$924$		0			0
$925$	14.0974	−	14.0974i	0.463519	−	0.463519i
$926$	18.7689	−	21.2424i	0.616783	−	0.698069i
$927$		0			0
$928$	−1.60289	−	5.02616i	−0.0526173	−	0.164992i
$929$	1.72866			0.0567156			0.0283578	−	0.999598i	$-0.490972\pi$
$929$	1.72866			0.0567156			0.0283578	+	0.999598i	$0.490972\pi$
$930$		0			0
$931$	−3.95209	+	3.95209i	−0.129524	+	0.129524i
$932$	5.99994	−	0.744692i	0.196535	−	0.0243932i
$933$		0			0
$934$	−0.298608	−	4.83019i	−0.00977074	−	0.158049i
$935$		−	4.98865i		−	0.163146i
$936$		0			0
$937$		−	4.24612i		−	0.138715i	−0.997592	−	0.0693573i	$-0.977905\pi$
$937$		−	4.24612i		−	0.138715i	0.997592	−	0.0693573i	$-0.0220949\pi$
$938$	−9.54809	+	0.590273i	−0.311756	+	0.0192731i
$939$		0			0
$940$	−19.7865	+	25.3941i	−0.645364	+	0.828266i
$941$	−12.6874	+	12.6874i	−0.413597	+	0.413597i	−0.882989	−	0.469393i	$-0.844473\pi$
$941$	−12.6874	+	12.6874i	−0.413597	+	0.413597i	0.469393	+	0.882989i	$0.344473\pi$
$942$		0			0
$943$	−21.4427			−0.698269
$944$	37.5153	+	22.4077i	1.22102	+	0.729308i
$945$		0			0
$946$	−0.108731	−	0.0960703i	−0.00353516	−	0.00312352i
$947$	23.6818	−	23.6818i	0.769555	−	0.769555i	−0.208473	−	0.978028i	$-0.566849\pi$
$947$	23.6818	−	23.6818i	0.769555	−	0.769555i	0.978028	+	0.208473i	$0.0668495\pi$
$948$		0			0
$949$	−32.3879	−	32.3879i	−1.05136	−	1.05136i
$950$	−3.69317	+	0.228316i	−0.119822	+	0.00740754i
$951$		0			0
$952$	12.1401	−	17.7387i	0.393464	−	0.574914i
$953$		−	18.1209i		−	0.586993i	−0.955960	−	0.293497i	$-0.905181\pi$
$953$		−	18.1209i		−	0.586993i	0.955960	−	0.293497i	$-0.0948189\pi$
$954$		0			0
$955$	−4.14047	−	4.14047i	−0.133982	−	0.133982i
$956$	−6.07725	−	48.9640i	−0.196552	−	1.58361i
$957$		0			0
$958$	5.75208	−	6.51015i	0.185841	−	0.210333i
$959$	−0.944483			−0.0304990
$960$		0			0
$961$	57.0431			1.84010
$962$	−26.8786	+	30.4210i	−0.866602	+	0.980811i
$963$		0			0
$964$	2.11593	+	17.0480i	0.0681496	+	0.549078i
$965$	−12.8980	−	12.8980i	−0.415203	−	0.415203i
$966$		0			0
$967$			6.87864i			0.221202i	0.993865	+	0.110601i	$0.0352776\pi$
$967$			6.87864i			0.221202i	−0.993865	+	0.110601i	$0.964722\pi$
$968$	17.0945	−	24.9778i	0.549438	−	0.802817i
$969$		0			0
$970$	38.5145	−	2.38101i	1.23663	−	0.0764496i
$971$	−32.3037	−	32.3037i	−1.03667	−	1.03667i	−0.999301	−	0.0373735i	$-0.988101\pi$
$971$	−32.3037	−	32.3037i	−1.03667	−	1.03667i	−0.0373735	−	0.999301i	$-0.511899\pi$
$972$		0			0
$973$	−6.74143	+	6.74143i	−0.216120	+	0.216120i
$974$	−4.95466	−	4.37772i	−0.158758	−	0.140271i
$975$		0			0
$976$	19.5553	−	32.7397i	0.625949	−	1.04797i
$977$	−23.0971			−0.738941			−0.369471	−	0.929242i	$-0.620461\pi$
$977$	−23.0971			−0.738941			−0.369471	+	0.929242i	$0.620461\pi$
$978$		0			0
$979$	−3.74547	+	3.74547i	−0.119706	+	0.119706i
$980$	10.2698	−	13.1803i	0.328056	−	0.421030i
$981$		0			0
$982$	25.1484	−	1.55470i	0.802518	−	0.0496126i
$983$		−	26.4581i		−	0.843883i	−0.906623	−	0.421941i	$-0.861349\pi$
$983$		−	26.4581i		−	0.843883i	0.906623	−	0.421941i	$-0.138651\pi$
$984$		0			0
$985$		−	0.977578i		−	0.0311482i
$986$	0.464887	+	7.51987i	0.0148050	+	0.239481i
$987$		0			0
$988$	7.47686	−	0.928002i	0.237870	−	0.0295237i
$989$	0.295520	−	0.295520i	0.00939698	−	0.00939698i
$990$		0			0
$991$	−16.3794			−0.520309			−0.260155	−	0.965567i	$-0.583774\pi$
$991$	−16.3794			−0.520309			−0.260155	+	0.965567i	$0.583774\pi$
$992$	24.3546	−	47.1618i	0.773259	−	1.49739i
$993$		0			0
$994$	11.4298	−	12.9361i	0.362530	−	0.410307i
$995$	−10.5754	+	10.5754i	−0.335264	+	0.335264i
$996$		0			0
$997$	40.9945	+	40.9945i	1.29831	+	1.29831i	0.929509	+	0.368800i	$0.120231\pi$
$997$	40.9945	+	40.9945i	1.29831	+	1.29831i	0.368800	+	0.929509i	$0.379769\pi$
$998$	1.67335	+	27.0676i	0.0529690	+	0.856811i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.c.325.5	yes	24
3.2	odd	2	inner	432.2.k.c.325.8	yes	24
4.3	odd	2		1728.2.k.c.433.8		24
12.11	even	2		1728.2.k.c.433.5		24
16.3	odd	4		1728.2.k.c.1297.8		24
16.13	even	4	inner	432.2.k.c.109.5	✓	24
48.29	odd	4	inner	432.2.k.c.109.8	yes	24
48.35	even	4		1728.2.k.c.1297.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.c.109.5	✓	24	16.13	even	4	inner
432.2.k.c.109.8	yes	24	48.29	odd	4	inner
432.2.k.c.325.5	yes	24	1.1	even	1	trivial
432.2.k.c.325.8	yes	24	3.2	odd	2	inner
1728.2.k.c.433.5		24	12.11	even	2
1728.2.k.c.433.8		24	4.3	odd	2
1728.2.k.c.1297.5		24	48.35	even	4
1728.2.k.c.1297.8		24	16.3	odd	4

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936391 + 1.05980i) q^{2} +(-0.246343 - 1.98477i) q^{4} +(1.12951 + 1.12951i) q^{5} -1.33035i q^{7} +(2.33413 + 1.59745i) q^{8} +O(q^{10})\)	\(q+(-0.936391 + 1.05980i) q^{2} +(-0.246343 - 1.98477i) q^{4} +(1.12951 + 1.12951i) q^{5} -1.33035i q^{7} +(2.33413 + 1.59745i) q^{8} +(-2.25471 + 0.139389i) q^{10} +(-0.386575 - 0.386575i) q^{11} +(2.49269 - 2.49269i) q^{13} +(1.40990 + 1.24573i) q^{14} +(-3.87863 + 0.977868i) q^{16} +5.71255 q^{17} +(-0.755633 + 0.755633i) q^{19} +(1.96357 - 2.52006i) q^{20} +(0.771676 - 0.0477059i) q^{22} +2.22699i q^{23} -2.44842i q^{25} +(0.307614 + 4.97587i) q^{26} +(-2.64044 + 0.327723i) q^{28} +(0.659445 - 0.659445i) q^{29} +9.38313 q^{31} +(2.59557 - 5.02623i) q^{32} +(-5.34918 + 6.05415i) q^{34} +(1.50264 - 1.50264i) q^{35} +(5.75774 + 5.75774i) q^{37} +(-0.0932501 - 1.50839i) q^{38} +(0.832087 + 4.44075i) q^{40} +9.62854i q^{41} +(-0.132699 - 0.132699i) q^{43} +(-0.672032 + 0.862492i) q^{44} +(-2.36016 - 2.08533i) q^{46} -10.0768 q^{47} +5.23016 q^{49} +(2.59483 + 2.29268i) q^{50} +(-5.56147 - 4.33335i) q^{52} +(2.31529 + 2.31529i) q^{53} -0.873279i q^{55} +(2.12517 - 3.10521i) q^{56} +(0.0813798 + 1.31638i) q^{58} +(-7.72476 - 7.72476i) q^{59} +(-6.74143 + 6.74143i) q^{61} +(-8.78628 + 9.94422i) q^{62} +(2.89632 + 7.45730i) q^{64} +5.63102 q^{65} +(-3.59541 + 3.59541i) q^{67} +(-1.40725 - 11.3381i) q^{68} +(0.185436 + 2.99956i) q^{70} -9.17515i q^{71} -12.9932i q^{73} +(-11.4935 + 0.710543i) q^{74} +(1.68590 + 1.31361i) q^{76} +(-0.514280 + 0.514280i) q^{77} +14.6526 q^{79} +(-5.48545 - 3.27643i) q^{80} +(-10.2043 - 9.01608i) q^{82} +(-1.58041 + 1.58041i) q^{83} +(6.45238 + 6.45238i) q^{85} +(0.264893 - 0.0163760i) q^{86} +(-0.284782 - 1.51985i) q^{88} -9.68886i q^{89} +(-3.31615 - 3.31615i) q^{91} +(4.42006 - 0.548603i) q^{92} +(9.43582 - 10.6794i) q^{94} -1.70699 q^{95} -17.0818 q^{97} +(-4.89748 + 5.54292i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{4}+O(q^{10}) \) 24 * q + 16 * q^4	\( 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) \) 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

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