LMFDB - Embedded newform 425.2.n.a.399.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			399.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	425.399
Dual form			425.2.n.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 - 0.414214i) q^{3} +3.82843i q^{4} +(1.00000 + 2.41421i) q^{6} +(-1.00000 - 2.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 - 1.29289i) q^{9} +O(q^{10})$	\(q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 - 0.414214i) q^{3} +3.82843i q^{4} +(1.00000 + 2.41421i) q^{6} +(-1.00000 - 2.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 - 1.29289i) q^{9} +(-1.00000 - 2.41421i) q^{11} +(1.58579 - 3.82843i) q^{12} +1.41421 q^{13} +(-2.41421 + 5.82843i) q^{14} -3.00000 q^{16} +(-3.00000 + 2.82843i) q^{17} +4.41421i q^{18} +(-0.585786 + 0.585786i) q^{19} +2.82843i q^{21} +(-2.41421 + 5.82843i) q^{22} +(-4.41421 + 1.82843i) q^{23} +(-4.41421 + 1.82843i) q^{24} +(-2.41421 - 2.41421i) q^{26} +(2.00000 + 4.82843i) q^{27} +(9.24264 - 3.82843i) q^{28} +(0.292893 + 0.121320i) q^{29} +(-3.00000 + 7.24264i) q^{31} +(-1.12132 - 1.12132i) q^{32} +2.82843i q^{33} +(9.94975 + 0.292893i) q^{34} +(4.94975 - 4.94975i) q^{36} +(8.53553 + 3.53553i) q^{37} +2.00000 q^{38} +(-1.41421 - 0.585786i) q^{39} +(1.12132 - 0.464466i) q^{41} +(4.82843 - 4.82843i) q^{42} +(-0.585786 + 0.585786i) q^{43} +(9.24264 - 3.82843i) q^{44} +(10.6569 + 4.41421i) q^{46} -5.17157 q^{47} +(3.00000 + 1.24264i) q^{48} +(0.121320 - 0.121320i) q^{49} +(4.17157 - 1.58579i) q^{51} +5.41421i q^{52} +(1.00000 + 1.00000i) q^{53} +(4.82843 - 11.6569i) q^{54} +(-10.6569 - 4.41421i) q^{56} +(0.828427 - 0.343146i) q^{57} +(-0.292893 - 0.707107i) q^{58} +(-4.24264 - 4.24264i) q^{59} +(-3.53553 + 1.46447i) q^{61} +(17.4853 - 7.24264i) q^{62} +(-1.82843 + 4.41421i) q^{63} +9.82843i q^{64} +(4.82843 - 4.82843i) q^{66} +1.17157i q^{67} +(-10.8284 - 11.4853i) q^{68} +5.17157 q^{69} +(-2.07107 + 5.00000i) q^{71} -8.07107 q^{72} +(-4.94975 + 11.9497i) q^{73} +(-8.53553 - 20.6066i) q^{74} +(-2.24264 - 2.24264i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(1.41421 + 3.41421i) q^{78} +(-1.82843 - 4.41421i) q^{79} -0.171573i q^{81} +(-2.70711 - 1.12132i) q^{82} +(-8.24264 - 8.24264i) q^{83} -10.8284 q^{84} +2.00000 q^{86} +(-0.242641 - 0.242641i) q^{87} +(-10.6569 - 4.41421i) q^{88} +6.58579i q^{89} +(-1.41421 - 3.41421i) q^{91} +(-7.00000 - 16.8995i) q^{92} +(6.00000 - 6.00000i) q^{93} +(8.82843 + 8.82843i) q^{94} +(0.656854 + 1.58579i) q^{96} +(-3.94975 + 9.53553i) q^{97} -0.414214 q^{98} +(-1.82843 + 4.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} - 4 q^{11} + 12 q^{12} - 4 q^{14} - 12 q^{16} - 12 q^{17} - 8 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 4 q^{26} + 8 q^{27} + 20 q^{28} + 4 q^{29} - 12 q^{31} + 4 q^{32} + 20 q^{34} + 20 q^{37} + 8 q^{38} - 4 q^{41} + 8 q^{42} - 8 q^{43} + 20 q^{44} + 20 q^{46} - 32 q^{47} + 12 q^{48} - 8 q^{49} + 28 q^{51} + 4 q^{53} + 8 q^{54} - 20 q^{56} - 8 q^{57} - 4 q^{58} + 36 q^{62} + 4 q^{63} + 8 q^{66} - 32 q^{68} + 32 q^{69} + 20 q^{71} - 4 q^{72} - 20 q^{74} + 8 q^{76} - 8 q^{77} + 4 q^{79} - 8 q^{82} - 16 q^{83} - 32 q^{84} + 8 q^{86} + 16 q^{87} - 20 q^{88} - 28 q^{92} + 24 q^{93} + 24 q^{94} - 20 q^{96} + 4 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 - 4 * q^11 + 12 * q^12 - 4 * q^14 - 12 * q^16 - 12 * q^17 - 8 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 4 * q^26 + 8 * q^27 + 20 * q^28 + 4 * q^29 - 12 * q^31 + 4 * q^32 + 20 * q^34 + 20 * q^37 + 8 * q^38 - 4 * q^41 + 8 * q^42 - 8 * q^43 + 20 * q^44 + 20 * q^46 - 32 * q^47 + 12 * q^48 - 8 * q^49 + 28 * q^51 + 4 * q^53 + 8 * q^54 - 20 * q^56 - 8 * q^57 - 4 * q^58 + 36 * q^62 + 4 * q^63 + 8 * q^66 - 32 * q^68 + 32 * q^69 + 20 * q^71 - 4 * q^72 - 20 * q^74 + 8 * q^76 - 8 * q^77 + 4 * q^79 - 8 * q^82 - 16 * q^83 - 32 * q^84 + 8 * q^86 + 16 * q^87 - 20 * q^88 - 28 * q^92 + 24 * q^93 + 24 * q^94 - 20 * q^96 + 4 * q^97 + 4 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.971960	−	0.235147i	$-0.924443\pi$
$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.235147	−	0.971960i	$-0.575557\pi$
$3$	−1.00000	−	0.414214i	−0.577350	−	0.239146i	0.0748477	−	0.997195i	$-0.476153\pi$
$3$	−1.00000	−	0.414214i	−0.577350	−	0.239146i	−0.652198	+	0.758049i	$0.726153\pi$
$4$			3.82843i			1.91421i
$5$		0			0
$5$		0			0
$6$	1.00000	+	2.41421i	0.408248	+	0.985599i
$7$	−1.00000	−	2.41421i	−0.377964	−	0.912487i	−0.992347	−	0.123479i	$-0.960595\pi$
$7$	−1.00000	−	2.41421i	−0.377964	−	0.912487i	0.614383	−	0.789008i	$-0.289405\pi$
$8$	3.12132	−	3.12132i	1.10355	−	1.10355i
$9$	−1.29289	−	1.29289i	−0.430964	−	0.430964i
$10$		0			0
$11$	−1.00000	−	2.41421i	−0.301511	−	0.727913i	−0.999925	−	0.0122188i	$-0.996111\pi$
$11$	−1.00000	−	2.41421i	−0.301511	−	0.727913i	0.698414	−	0.715694i	$-0.253889\pi$
$12$	1.58579	−	3.82843i	0.457777	−	1.10517i
$13$	1.41421			0.392232			0.196116	−	0.980581i	$-0.437167\pi$
$13$	1.41421			0.392232			0.196116	+	0.980581i	$0.437167\pi$
$14$	−2.41421	+	5.82843i	−0.645226	+	1.55771i
$15$		0			0
$16$	−3.00000			−0.750000
$17$	−3.00000	+	2.82843i	−0.727607	+	0.685994i
$17$	−3.00000	+	2.82843i	−0.727607	+	0.685994i
$18$			4.41421i			1.04044i
$19$	−0.585786	+	0.585786i	−0.134389	+	0.134389i	−0.771101	−	0.636713i	$-0.780294\pi$
$19$	−0.585786	+	0.585786i	−0.134389	+	0.134389i	0.636713	+	0.771101i	$0.280294\pi$
$20$		0			0
$21$			2.82843i			0.617213i
$22$	−2.41421	+	5.82843i	−0.514712	+	1.24262i
$23$	−4.41421	+	1.82843i	−0.920427	+	0.381253i	−0.792039	−	0.610471i	$-0.790980\pi$
$23$	−4.41421	+	1.82843i	−0.920427	+	0.381253i	−0.128388	+	0.991724i	$0.540980\pi$
$24$	−4.41421	+	1.82843i	−0.901048	+	0.373226i
$25$		0			0
$26$	−2.41421	−	2.41421i	−0.473466	−	0.473466i
$27$	2.00000	+	4.82843i	0.384900	+	0.929231i
$28$	9.24264	−	3.82843i	1.74669	−	0.723505i
$29$	0.292893	+	0.121320i	0.0543889	+	0.0225286i	0.409712	−	0.912215i	$-0.365629\pi$
$29$	0.292893	+	0.121320i	0.0543889	+	0.0225286i	−0.355323	+	0.934744i	$0.615629\pi$
$30$		0			0
$31$	−3.00000	+	7.24264i	−0.538816	+	1.30082i	0.386734	+	0.922191i	$0.373603\pi$
$31$	−3.00000	+	7.24264i	−0.538816	+	1.30082i	−0.925550	+	0.378625i	$0.876397\pi$
$32$	−1.12132	−	1.12132i	−0.198223	−	0.198223i
$33$			2.82843i			0.492366i
$34$	9.94975	+	0.292893i	1.70637	+	0.0502308i
$35$		0			0
$36$	4.94975	−	4.94975i	0.824958	−	0.824958i
$37$	8.53553	+	3.53553i	1.40323	+	0.581238i	0.950589	−	0.310453i	$-0.100481\pi$
$37$	8.53553	+	3.53553i	1.40323	+	0.581238i	0.452644	+	0.891691i	$0.350481\pi$
$38$	2.00000			0.324443
$39$	−1.41421	−	0.585786i	−0.226455	−	0.0938009i
$40$		0			0
$41$	1.12132	−	0.464466i	0.175121	−	0.0725374i	−0.293400	−	0.955990i	$-0.594787\pi$
$41$	1.12132	−	0.464466i	0.175121	−	0.0725374i	0.468521	+	0.883452i	$0.344787\pi$
$42$	4.82843	−	4.82843i	0.745042	−	0.745042i
$43$	−0.585786	+	0.585786i	−0.0893316	+	0.0893316i	−0.750360	−	0.661029i	$-0.770120\pi$
$43$	−0.585786	+	0.585786i	−0.0893316	+	0.0893316i	0.661029	+	0.750360i	$0.270120\pi$
$44$	9.24264	−	3.82843i	1.39338	−	0.577157i
$45$		0			0
$46$	10.6569	+	4.41421i	1.57127	+	0.650840i
$47$	−5.17157			−0.754351			−0.377176	−	0.926142i	$-0.623105\pi$
$47$	−5.17157			−0.754351			−0.377176	+	0.926142i	$0.623105\pi$
$48$	3.00000	+	1.24264i	0.433013	+	0.179360i
$49$	0.121320	−	0.121320i	0.0173315	−	0.0173315i
$50$		0			0
$51$	4.17157	−	1.58579i	0.584137	−	0.222055i
$52$			5.41421i			0.750816i
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$	4.82843	−	11.6569i	0.657066	−	1.58630i
$55$		0			0
$56$	−10.6569	−	4.41421i	−1.42408	−	0.589874i
$57$	0.828427	−	0.343146i	0.109728	−	0.0454508i
$58$	−0.292893	−	0.707107i	−0.0384588	−	0.0928477i
$59$	−4.24264	−	4.24264i	−0.552345	−	0.552345i	0.374772	−	0.927117i	$-0.377721\pi$
$59$	−4.24264	−	4.24264i	−0.552345	−	0.552345i	−0.927117	+	0.374772i	$0.877721\pi$
$60$		0			0
$61$	−3.53553	+	1.46447i	−0.452679	+	0.187506i	−0.597361	−	0.801973i	$-0.703784\pi$
$61$	−3.53553	+	1.46447i	−0.452679	+	0.187506i	0.144682	+	0.989478i	$0.453784\pi$
$62$	17.4853	−	7.24264i	2.22063	−	0.919816i
$63$	−1.82843	+	4.41421i	−0.230360	+	0.556139i
$64$			9.82843i			1.22855i
$65$		0			0
$66$	4.82843	−	4.82843i	0.594338	−	0.594338i
$67$			1.17157i			0.143130i	0.997436	+	0.0715652i	$0.0227994\pi$
$67$			1.17157i			0.143130i	−0.997436	+	0.0715652i	$0.977201\pi$
$68$	−10.8284	−	11.4853i	−1.31314	−	1.39279i
$69$	5.17157			0.622584
$70$		0			0
$71$	−2.07107	+	5.00000i	−0.245791	+	0.593391i	−0.997838	−	0.0657178i	$-0.979066\pi$
$71$	−2.07107	+	5.00000i	−0.245791	+	0.593391i	0.752048	+	0.659109i	$0.229066\pi$
$72$	−8.07107			−0.951184
$73$	−4.94975	+	11.9497i	−0.579324	+	1.39861i	0.314097	+	0.949391i	$0.398298\pi$
$73$	−4.94975	+	11.9497i	−0.579324	+	1.39861i	−0.893421	+	0.449221i	$0.851702\pi$
$74$	−8.53553	−	20.6066i	−0.992236	−	2.39547i
$75$		0			0
$76$	−2.24264	−	2.24264i	−0.257249	−	0.257249i
$77$	−4.82843	+	4.82843i	−0.550250	+	0.550250i
$78$	1.41421	+	3.41421i	0.160128	+	0.386584i
$79$	−1.82843	−	4.41421i	−0.205714	−	0.496638i	0.787026	−	0.616920i	$-0.211620\pi$
$79$	−1.82843	−	4.41421i	−0.205714	−	0.496638i	−0.992740	+	0.120283i	$0.961620\pi$
$80$		0			0
$81$		−	0.171573i		−	0.0190637i
$82$	−2.70711	−	1.12132i	−0.298950	−	0.123829i
$83$	−8.24264	−	8.24264i	−0.904747	−	0.904747i	0.0910949	−	0.995842i	$-0.470963\pi$
$83$	−8.24264	−	8.24264i	−0.904747	−	0.904747i	−0.995842	+	0.0910949i	$0.970963\pi$
$84$	−10.8284			−1.18148
$85$		0			0
$86$	2.00000			0.215666
$87$	−0.242641	−	0.242641i	−0.0260138	−	0.0260138i
$88$	−10.6569	−	4.41421i	−1.13602	−	0.470557i
$89$			6.58579i			0.698092i	0.937106	+	0.349046i	$0.113494\pi$
$89$			6.58579i			0.698092i	−0.937106	+	0.349046i	$0.886506\pi$
$90$		0			0
$91$	−1.41421	−	3.41421i	−0.148250	−	0.357907i
$92$	−7.00000	−	16.8995i	−0.729800	−	1.76189i
$93$	6.00000	−	6.00000i	0.622171	−	0.622171i
$94$	8.82843	+	8.82843i	0.910583	+	0.910583i
$95$		0			0
$96$	0.656854	+	1.58579i	0.0670399	+	0.161849i
$97$	−3.94975	+	9.53553i	−0.401036	+	0.968187i	0.586379	+	0.810037i	$0.300553\pi$
$97$	−3.94975	+	9.53553i	−0.401036	+	0.968187i	−0.987415	+	0.158150i	$0.949447\pi$
$98$	−0.414214			−0.0418419
$99$	−1.82843	+	4.41421i	−0.183764	+	0.443645i
$100$		0			0
$101$	−10.5858			−1.05333			−0.526663	−	0.850074i	$-0.676557\pi$
$101$	−10.5858			−1.05333			−0.526663	+	0.850074i	$0.676557\pi$
$102$	−9.82843	−	4.41421i	−0.973159	−	0.437072i
$103$		−	12.4853i		−	1.23021i	−0.788445	−	0.615106i	$-0.789113\pi$
$103$		−	12.4853i		−	1.23021i	0.788445	−	0.615106i	$-0.210887\pi$
$104$	4.41421	−	4.41421i	0.432849	−	0.432849i
$105$		0			0
$106$		−	3.41421i		−	0.331618i
$107$	−0.171573	+	0.414214i	−0.0165866	+	0.0400435i	−0.931956	−	0.362572i	$-0.881899\pi$
$107$	−0.171573	+	0.414214i	−0.0165866	+	0.0400435i	0.915369	+	0.402615i	$0.131899\pi$
$108$	−18.4853	+	7.65685i	−1.77875	+	0.736781i
$109$	−14.3640	+	5.94975i	−1.37582	+	0.569882i	−0.943360	−	0.331772i	$-0.892354\pi$
$109$	−14.3640	+	5.94975i	−1.37582	+	0.569882i	−0.432458	+	0.901654i	$0.642354\pi$
$110$		0			0
$111$	−7.07107	−	7.07107i	−0.671156	−	0.671156i
$112$	3.00000	+	7.24264i	0.283473	+	0.684365i
$113$	12.1924	−	5.05025i	1.14696	−	0.475088i	0.273449	−	0.961886i	$-0.411835\pi$
$113$	12.1924	−	5.05025i	1.14696	−	0.475088i	0.873514	+	0.486799i	$0.161835\pi$
$114$	−2.00000	−	0.828427i	−0.187317	−	0.0775893i
$115$		0			0
$116$	−0.464466	+	1.12132i	−0.0431246	+	0.104112i
$117$	−1.82843	−	1.82843i	−0.169038	−	0.169038i
$118$			14.4853i			1.33348i
$119$	9.82843	+	4.41421i	0.900970	+	0.404650i
$120$		0			0
$121$	2.94975	−	2.94975i	0.268159	−	0.268159i
$122$	8.53553	+	3.53553i	0.772771	+	0.320092i
$123$	−1.31371			−0.118453
$124$	−27.7279	−	11.4853i	−2.49004	−	1.03141i
$125$		0			0
$126$	10.6569	−	4.41421i	0.949388	−	0.393249i
$127$	3.75736	−	3.75736i	0.333412	−	0.333412i	−0.520469	−	0.853881i	$-0.674243\pi$
$127$	3.75736	−	3.75736i	0.333412	−	0.333412i	0.853881	+	0.520469i	$0.174243\pi$
$128$	14.5355	−	14.5355i	1.28477	−	1.28477i
$129$	0.828427	−	0.343146i	0.0729389	−	0.0302123i
$130$		0			0
$131$	−14.0711	−	5.82843i	−1.22939	−	0.509232i	−0.329010	−	0.944326i	$-0.606715\pi$
$131$	−14.0711	−	5.82843i	−1.22939	−	0.509232i	−0.900385	+	0.435094i	$0.856715\pi$
$132$	−10.8284			−0.942494
$133$	2.00000	+	0.828427i	0.173422	+	0.0718337i
$134$	2.00000	−	2.00000i	0.172774	−	0.172774i
$135$		0			0
$136$	−0.535534	+	18.1924i	−0.0459217	+	1.55998i
$137$		−	16.7279i		−	1.42916i	−0.699552	−	0.714581i	$-0.746617\pi$
$137$		−	16.7279i		−	1.42916i	0.699552	−	0.714581i	$-0.253383\pi$
$138$	−8.82843	−	8.82843i	−0.751526	−	0.751526i
$139$	8.17157	−	19.7279i	0.693104	−	1.67330i	−0.0453279	−	0.998972i	$-0.514433\pi$
$139$	8.17157	−	19.7279i	0.693104	−	1.67330i	0.738432	−	0.674328i	$-0.235567\pi$
$140$		0			0
$141$	5.17157	+	2.14214i	0.435525	+	0.180400i
$142$	12.0711	−	5.00000i	1.01298	−	0.419591i
$143$	−1.41421	−	3.41421i	−0.118262	−	0.285511i
$144$	3.87868	+	3.87868i	0.323223	+	0.323223i
$145$		0			0
$146$	28.8492	−	11.9497i	2.38758	−	0.988968i
$147$	−0.171573	+	0.0710678i	−0.0141511	+	0.00586157i
$148$	−13.5355	+	32.6777i	−1.11261	+	2.68609i
$149$			16.9706i			1.39028i	0.718873	+	0.695141i	$0.244658\pi$
$149$			16.9706i			1.39028i	−0.718873	+	0.695141i	$0.755342\pi$
$150$		0			0
$151$	5.07107	−	5.07107i	0.412678	−	0.412678i	−0.469993	−	0.882670i	$-0.655743\pi$
$151$	5.07107	−	5.07107i	0.412678	−	0.412678i	0.882670	+	0.469993i	$0.155743\pi$
$152$			3.65685i			0.296610i
$153$	7.53553	+	0.221825i	0.609212	+	0.0179335i
$154$	16.4853			1.32842
$155$		0			0
$156$	2.24264	−	5.41421i	0.179555	−	0.433484i
$157$	−9.65685			−0.770701			−0.385350	−	0.922770i	$-0.625919\pi$
$157$	−9.65685			−0.770701			−0.385350	+	0.922770i	$0.625919\pi$
$158$	−4.41421	+	10.6569i	−0.351176	+	0.847814i
$159$	−0.585786	−	1.41421i	−0.0464559	−	0.112154i
$160$		0			0
$161$	8.82843	+	8.82843i	0.695778	+	0.695778i
$162$	−0.292893	+	0.292893i	−0.0230119	+	0.0230119i
$163$	3.24264	+	7.82843i	0.253983	+	0.613170i	0.998518	−	0.0544134i	$-0.0173289\pi$
$163$	3.24264	+	7.82843i	0.253983	+	0.613170i	−0.744535	+	0.667583i	$0.767329\pi$
$164$	1.77817	+	4.29289i	0.138852	+	0.335219i
$165$		0			0
$166$			28.1421i			2.18425i
$167$	1.82843	+	0.757359i	0.141488	+	0.0586062i	0.452304	−	0.891864i	$-0.350602\pi$
$167$	1.82843	+	0.757359i	0.141488	+	0.0586062i	−0.310816	+	0.950470i	$0.600602\pi$
$168$	8.82843	+	8.82843i	0.681128	+	0.681128i
$169$	−11.0000			−0.846154
$170$		0			0
$171$	1.51472			0.115833
$172$	−2.24264	−	2.24264i	−0.171000	−	0.171000i
$173$	−2.70711	−	1.12132i	−0.205818	−	0.0852524i	0.277393	−	0.960756i	$-0.410530\pi$
$173$	−2.70711	−	1.12132i	−0.205818	−	0.0852524i	−0.483211	+	0.875504i	$0.660530\pi$
$174$			0.828427i			0.0628029i
$175$		0			0
$176$	3.00000	+	7.24264i	0.226134	+	0.545935i
$177$	2.48528	+	6.00000i	0.186805	+	0.450988i
$178$	11.2426	−	11.2426i	0.842672	−	0.842672i
$179$	4.24264	+	4.24264i	0.317110	+	0.317110i	0.847656	−	0.530546i	$-0.178013\pi$
$179$	4.24264	+	4.24264i	0.317110	+	0.317110i	−0.530546	+	0.847656i	$0.678013\pi$
$180$		0			0
$181$	−4.46447	−	10.7782i	−0.331841	−	0.801135i	−0.998446	−	0.0557243i	$-0.982253\pi$
$181$	−4.46447	−	10.7782i	−0.331841	−	0.801135i	0.666605	−	0.745411i	$-0.267747\pi$
$182$	−3.41421	+	8.24264i	−0.253078	+	0.610985i
$183$	4.14214			0.306195
$184$	−8.07107	+	19.4853i	−0.595007	+	1.43647i
$185$		0			0
$186$	−20.4853			−1.50205
$187$	9.82843	+	4.41421i	0.718726	+	0.322799i
$188$		−	19.7990i		−	1.44399i
$189$	9.65685	−	9.65685i	0.702433	−	0.702433i
$190$		0			0
$191$		−	20.0000i		−	1.44715i	−0.690246	−	0.723575i	$-0.742498\pi$
$191$		−	20.0000i		−	1.44715i	0.690246	−	0.723575i	$-0.257502\pi$
$192$	4.07107	−	9.82843i	0.293804	−	0.709306i
$193$	2.12132	−	0.878680i	0.152696	−	0.0632487i	−0.305027	−	0.952344i	$-0.598665\pi$
$193$	2.12132	−	0.878680i	0.152696	−	0.0632487i	0.457722	+	0.889095i	$0.348665\pi$
$194$	23.0208	−	9.53553i	1.65280	−	0.684611i
$195$		0			0
$196$	0.464466	+	0.464466i	0.0331761	+	0.0331761i
$197$	−1.77817	−	4.29289i	−0.126690	−	0.305856i	0.847790	−	0.530332i	$-0.177933\pi$
$197$	−1.77817	−	4.29289i	−0.126690	−	0.305856i	−0.974480	+	0.224476i	$0.927933\pi$
$198$	10.6569	−	4.41421i	0.757350	−	0.313704i
$199$	−10.6569	−	4.41421i	−0.755444	−	0.312915i	−0.0284836	−	0.999594i	$-0.509068\pi$
$199$	−10.6569	−	4.41421i	−0.755444	−	0.312915i	−0.726961	+	0.686679i	$0.759068\pi$
$200$		0			0
$201$	0.485281	−	1.17157i	0.0342291	−	0.0826364i
$202$	18.0711	+	18.0711i	1.27148	+	1.27148i
$203$		−	0.828427i		−	0.0581442i
$204$	6.07107	+	15.9706i	0.425060	+	1.11816i
$205$		0			0
$206$	−21.3137	+	21.3137i	−1.48500	+	1.48500i
$207$	8.07107	+	3.34315i	0.560978	+	0.232365i
$208$	−4.24264			−0.294174
$209$	2.00000	+	0.828427i	0.138343	+	0.0573035i
$210$		0			0
$211$	−19.7279	+	8.17157i	−1.35813	+	0.562554i	−0.938543	−	0.345163i	$-0.887824\pi$
$211$	−19.7279	+	8.17157i	−1.35813	+	0.562554i	−0.419583	+	0.907717i	$0.637824\pi$
$212$	−3.82843	+	3.82843i	−0.262937	+	0.262937i
$213$	4.14214	−	4.14214i	0.283814	−	0.283814i
$214$	1.00000	−	0.414214i	0.0683586	−	0.0283151i
$215$		0			0
$216$	21.3137	+	8.82843i	1.45021	+	0.600698i
$217$	20.4853			1.39063
$218$	34.6777	+	14.3640i	2.34867	+	0.972850i
$219$	9.89949	−	9.89949i	0.668946	−	0.668946i
$220$		0			0
$221$	−4.24264	+	4.00000i	−0.285391	+	0.269069i
$222$			24.1421i			1.62031i
$223$	−3.41421	−	3.41421i	−0.228633	−	0.228633i	0.583489	−	0.812121i	$-0.301687\pi$
$223$	−3.41421	−	3.41421i	−0.228633	−	0.228633i	−0.812121	+	0.583489i	$0.801687\pi$
$224$	−1.58579	+	3.82843i	−0.105955	+	0.255798i
$225$		0			0
$226$	−29.4350	−	12.1924i	−1.95799	−	0.811026i
$227$	−16.0711	+	6.65685i	−1.06667	+	0.441831i	−0.845816	−	0.533475i	$-0.820886\pi$
$227$	−16.0711	+	6.65685i	−1.06667	+	0.441831i	−0.220858	+	0.975306i	$0.570886\pi$
$228$	1.31371	+	3.17157i	0.0870025	+	0.210043i
$229$	12.1421	+	12.1421i	0.802375	+	0.802375i	0.983466	−	0.181091i	$-0.0579630\pi$
$229$	12.1421	+	12.1421i	0.802375	+	0.802375i	−0.181091	+	0.983466i	$0.557963\pi$
$230$		0			0
$231$	6.82843	−	2.82843i	0.449278	−	0.186097i
$232$	1.29289	−	0.535534i	0.0848826	−	0.0351595i
$233$	3.36396	−	8.12132i	0.220380	−	0.532045i	−0.774561	−	0.632499i	$-0.782029\pi$
$233$	3.36396	−	8.12132i	0.220380	−	0.532045i	0.994942	+	0.100453i	$0.0320293\pi$
$234$			6.24264i			0.408094i
$235$		0			0
$236$	16.2426	−	16.2426i	1.05731	−	1.05731i
$237$			5.17157i			0.335930i
$238$	−9.24264	−	24.3137i	−0.599111	−	1.57602i
$239$	−14.8284			−0.959171			−0.479586	−	0.877495i	$-0.659213\pi$
$239$	−14.8284			−0.959171			−0.479586	+	0.877495i	$0.659213\pi$
$240$		0			0
$241$	−1.36396	+	3.29289i	−0.0878605	+	0.212114i	−0.961702	−	0.274097i	$-0.911621\pi$
$241$	−1.36396	+	3.29289i	−0.0878605	+	0.212114i	0.873842	+	0.486211i	$0.161621\pi$
$242$	−10.0711			−0.647393
$243$	5.92893	−	14.3137i	0.380341	−	0.918225i
$244$	−5.60660	−	13.5355i	−0.358926	−	0.866524i
$245$		0			0
$246$	2.24264	+	2.24264i	0.142986	+	0.142986i
$247$	−0.828427	+	0.828427i	−0.0527116	+	0.0527116i
$248$	13.2426	+	31.9706i	0.840909	+	2.03013i
$249$	4.82843	+	11.6569i	0.305989	+	0.738723i
$250$		0			0
$251$			20.4853i			1.29302i	0.762906	+	0.646510i	$0.223772\pi$
$251$			20.4853i			1.29302i	−0.762906	+	0.646510i	$0.776228\pi$
$252$	−16.8995	−	7.00000i	−1.06457	−	0.440959i
$253$	8.82843	+	8.82843i	0.555038	+	0.555038i
$254$	−12.8284			−0.804927
$255$		0			0
$256$	−29.9706			−1.87316
$257$	−4.34315	−	4.34315i	−0.270918	−	0.270918i	0.558552	−	0.829470i	$-0.311357\pi$
$257$	−4.34315	−	4.34315i	−0.270918	−	0.270918i	−0.829470	+	0.558552i	$0.811357\pi$
$258$	−2.00000	−	0.828427i	−0.124515	−	0.0515756i
$259$		−	24.1421i		−	1.50012i
$260$		0			0
$261$	−0.221825	−	0.535534i	−0.0137306	−	0.0331487i
$262$	14.0711	+	33.9706i	0.869313	+	2.09871i
$263$	−7.41421	+	7.41421i	−0.457180	+	0.457180i	−0.897729	−	0.440549i	$-0.854784\pi$
$263$	−7.41421	+	7.41421i	−0.457180	+	0.457180i	0.440549	+	0.897729i	$0.354784\pi$
$264$	8.82843	+	8.82843i	0.543352	+	0.543352i
$265$		0			0
$266$	−2.00000	−	4.82843i	−0.122628	−	0.296050i
$267$	2.72792	−	6.58579i	0.166946	−	0.403044i
$268$	−4.48528			−0.273982
$269$	−10.1213	+	24.4350i	−0.617108	+	1.48983i	0.237939	+	0.971280i	$0.423528\pi$
$269$	−10.1213	+	24.4350i	−0.617108	+	1.48983i	−0.855047	+	0.518550i	$0.826472\pi$
$270$		0			0
$271$	22.1421			1.34504			0.672519	−	0.740079i	$-0.265212\pi$
$271$	22.1421			1.34504			0.672519	+	0.740079i	$0.265212\pi$
$272$	9.00000	−	8.48528i	0.545705	−	0.514496i
$273$			4.00000i			0.242091i
$274$	−28.5563	+	28.5563i	−1.72515	+	1.72515i
$275$		0			0
$276$			19.7990i			1.19176i
$277$	7.63604	−	18.4350i	0.458805	−	1.10765i	−0.510077	−	0.860129i	$-0.670383\pi$
$277$	7.63604	−	18.4350i	0.458805	−	1.10765i	0.968882	−	0.247525i	$-0.0796171\pi$
$278$	−47.6274	+	19.7279i	−2.85650	+	1.18320i
$279$	13.2426	−	5.48528i	0.792816	−	0.328395i
$280$		0			0
$281$	−1.34315	−	1.34315i	−0.0801254	−	0.0801254i	0.665908	−	0.746034i	$-0.268044\pi$
$281$	−1.34315	−	1.34315i	−0.0801254	−	0.0801254i	−0.746034	+	0.665908i	$0.768044\pi$
$282$	−5.17157	−	12.4853i	−0.307963	−	0.743488i
$283$	−17.2426	+	7.14214i	−1.02497	+	0.424556i	−0.830894	−	0.556431i	$-0.812170\pi$
$283$	−17.2426	+	7.14214i	−1.02497	+	0.424556i	−0.194075	+	0.980987i	$0.562170\pi$
$284$	−19.1421	−	7.92893i	−1.13588	−	0.470496i
$285$		0			0
$286$	−3.41421	+	8.24264i	−0.201887	+	0.487398i
$287$	−2.24264	−	2.24264i	−0.132379	−	0.132379i
$288$			2.89949i			0.170854i
$289$	1.00000	−	16.9706i	0.0588235	−	0.998268i
$290$		0			0
$291$	7.89949	−	7.89949i	0.463077	−	0.463077i
$292$	−45.7487	−	18.9497i	−2.67724	−	1.10895i
$293$	12.3431			0.721094			0.360547	−	0.932741i	$-0.382590\pi$
$293$	12.3431			0.721094			0.360547	+	0.932741i	$0.382590\pi$
$294$	0.414214	+	0.171573i	0.0241574	+	0.0100063i
$295$		0			0
$296$	37.6777	−	15.6066i	2.18997	−	0.907115i
$297$	9.65685	−	9.65685i	0.560348	−	0.560348i
$298$	28.9706	−	28.9706i	1.67822	−	1.67822i
$299$	−6.24264	+	2.58579i	−0.361021	+	0.149540i
$300$		0			0
$301$	2.00000	+	0.828427i	0.115278	+	0.0477497i
$302$	−17.3137			−0.996292
$303$	10.5858	+	4.38478i	0.608138	+	0.251899i
$304$	1.75736	−	1.75736i	0.100791	−	0.100791i
$305$		0			0
$306$	−12.4853	−	13.2426i	−0.713736	−	0.757031i
$307$		−	26.1421i		−	1.49201i	−0.665940	−	0.746005i	$-0.731969\pi$
$307$		−	26.1421i		−	1.49201i	0.665940	−	0.746005i	$-0.268031\pi$
$308$	−18.4853	−	18.4853i	−1.05330	−	1.05330i
$309$	−5.17157	+	12.4853i	−0.294201	+	0.710263i
$310$		0			0
$311$	23.7279	+	9.82843i	1.34549	+	0.557319i	0.935032	−	0.354562i	$-0.115370\pi$
$311$	23.7279	+	9.82843i	1.34549	+	0.557319i	0.410455	+	0.911881i	$0.365370\pi$
$312$	−6.24264	+	2.58579i	−0.353420	+	0.146391i
$313$	3.77817	+	9.12132i	0.213555	+	0.515568i	0.993965	−	0.109701i	$-0.0349894\pi$
$313$	3.77817	+	9.12132i	0.213555	+	0.515568i	−0.780410	+	0.625269i	$0.784989\pi$
$314$	16.4853	+	16.4853i	0.930318	+	0.930318i
$315$		0			0
$316$	16.8995	−	7.00000i	0.950671	−	0.393781i
$317$	−17.7782	+	7.36396i	−0.998522	+	0.413601i	−0.821255	−	0.570562i	$-0.806726\pi$
$317$	−17.7782	+	7.36396i	−0.998522	+	0.413601i	−0.177267	+	0.984163i	$0.556726\pi$
$318$	−1.41421	+	3.41421i	−0.0793052	+	0.191460i
$319$		−	0.828427i		−	0.0463830i
$320$		0			0
$321$	0.343146	−	0.343146i	0.0191525	−	0.0191525i
$322$		−	30.1421i		−	1.67976i
$323$	0.100505	−	3.41421i	0.00559225	−	0.189972i
$324$	0.656854			0.0364919
$325$		0			0
$326$	7.82843	−	18.8995i	0.433576	−	1.04675i
$327$	16.8284			0.930614
$328$	2.05025	−	4.94975i	0.113206	−	0.273304i
$329$	5.17157	+	12.4853i	0.285118	+	0.688336i
$330$		0			0
$331$	−15.4142	−	15.4142i	−0.847242	−	0.847242i	0.142546	−	0.989788i	$-0.454471\pi$
$331$	−15.4142	−	15.4142i	−0.847242	−	0.847242i	−0.989788	+	0.142546i	$0.954471\pi$
$332$	31.5563	−	31.5563i	1.73188	−	1.73188i
$333$	−6.46447	−	15.6066i	−0.354251	−	0.855237i
$334$	−1.82843	−	4.41421i	−0.100047	−	0.241535i
$335$		0			0
$336$		−	8.48528i		−	0.462910i
$337$	−5.19239	−	2.15076i	−0.282847	−	0.117159i	0.236750	−	0.971571i	$-0.423918\pi$
$337$	−5.19239	−	2.15076i	−0.282847	−	0.117159i	−0.519597	+	0.854411i	$0.673918\pi$
$338$	18.7782	+	18.7782i	1.02140	+	1.02140i
$339$	−14.2843			−0.775815
$340$		0			0
$341$	20.4853			1.10934
$342$	−2.58579	−	2.58579i	−0.139823	−	0.139823i
$343$	−17.3137	−	7.17157i	−0.934852	−	0.387229i
$344$			3.65685i			0.197164i
$345$		0			0
$346$	2.70711	+	6.53553i	0.145535	+	0.351352i
$347$	6.41421	+	15.4853i	0.344333	+	0.831293i	0.997267	+	0.0738788i	$0.0235378\pi$
$347$	6.41421	+	15.4853i	0.344333	+	0.831293i	−0.652934	+	0.757415i	$0.726462\pi$
$348$	0.928932	−	0.928932i	0.0497960	−	0.0497960i
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	0.622240	−	0.782826i	$-0.286223\pi$
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	−0.782826	+	0.622240i	$0.786223\pi$
$350$		0			0
$351$	2.82843	+	6.82843i	0.150970	+	0.364474i
$352$	−1.58579	+	3.82843i	−0.0845227	+	0.204056i
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$	6.00000	−	14.4853i	0.318896	−	0.769884i
$355$		0			0
$356$	−25.2132			−1.33630
$357$	−8.00000	−	8.48528i	−0.423405	−	0.449089i
$358$		−	14.4853i		−	0.765571i
$359$	20.3848	−	20.3848i	1.07587	−	1.07587i	0.0789921	−	0.996875i	$-0.474830\pi$
$359$	20.3848	−	20.3848i	1.07587	−	1.07587i	0.996875	−	0.0789921i	$-0.0251702\pi$
$360$		0			0
$361$			18.3137i			0.963879i
$362$	−10.7782	+	26.0208i	−0.566488	+	1.36762i
$363$	−4.17157	+	1.72792i	−0.218951	+	0.0906924i
$364$	13.0711	−	5.41421i	0.685110	−	0.283782i
$365$		0			0
$366$	−7.07107	−	7.07107i	−0.369611	−	0.369611i
$367$	−1.68629	−	4.07107i	−0.0880237	−	0.212508i	0.873737	−	0.486398i	$-0.161690\pi$
$367$	−1.68629	−	4.07107i	−0.0880237	−	0.212508i	−0.961761	+	0.273890i	$0.911690\pi$
$368$	13.2426	−	5.48528i	0.690320	−	0.285940i
$369$	−2.05025	−	0.849242i	−0.106732	−	0.0442098i
$370$		0			0
$371$	1.41421	−	3.41421i	0.0734223	−	0.177257i
$372$	22.9706	+	22.9706i	1.19097	+	1.19097i
$373$		−	11.5563i		−	0.598365i	−0.954196	−	0.299183i	$-0.903286\pi$
$373$		−	11.5563i		−	0.598365i	0.954196	−	0.299183i	$-0.0967140\pi$
$374$	−9.24264	−	24.3137i	−0.477926	−	1.25723i
$375$		0			0
$376$	−16.1421	+	16.1421i	−0.832467	+	0.832467i
$377$	0.414214	+	0.171573i	0.0213331	+	0.00883645i
$378$	−32.9706			−1.69582
$379$	2.41421	+	1.00000i	0.124010	+	0.0513665i	0.443826	−	0.896113i	$-0.353621\pi$
$379$	2.41421	+	1.00000i	0.124010	+	0.0513665i	−0.319816	+	0.947480i	$0.603621\pi$
$380$		0			0
$381$	−5.31371	+	2.20101i	−0.272230	+	0.112761i
$382$	−34.1421	+	34.1421i	−1.74686	+	1.74686i
$383$	−15.8995	+	15.8995i	−0.812426	+	0.812426i	−0.984997	−	0.172571i	$-0.944793\pi$
$383$	−15.8995	+	15.8995i	−0.812426	+	0.812426i	0.172571	+	0.984997i	$0.444793\pi$
$384$	−20.5563	+	8.51472i	−1.04901	+	0.434515i
$385$		0			0
$386$	−5.12132	−	2.12132i	−0.260668	−	0.107972i
$387$	1.51472			0.0769975
$388$	−36.5061	−	15.1213i	−1.85332	−	0.767669i
$389$	8.58579	−	8.58579i	0.435317	−	0.435317i	−0.455116	−	0.890432i	$-0.650402\pi$
$389$	8.58579	−	8.58579i	0.435317	−	0.435317i	0.890432	+	0.455116i	$0.150402\pi$
$390$		0			0
$391$	8.07107	−	17.9706i	0.408171	−	0.908810i
$392$		−	0.757359i		−	0.0382524i
$393$	11.6569	+	11.6569i	0.588011	+	0.588011i
$394$	−4.29289	+	10.3640i	−0.216273	+	0.522129i
$395$		0			0
$396$	−16.8995	−	7.00000i	−0.849232	−	0.351763i
$397$	−16.4350	+	6.80761i	−0.824850	+	0.341664i	−0.754862	−	0.655884i	$-0.772296\pi$
$397$	−16.4350	+	6.80761i	−0.824850	+	0.341664i	−0.0699884	+	0.997548i	$0.522296\pi$
$398$	10.6569	+	25.7279i	0.534180	+	1.28962i
$399$	−1.65685	−	1.65685i	−0.0829465	−	0.0829465i
$400$		0			0
$401$	−0.535534	+	0.221825i	−0.0267433	+	0.0110774i	−0.396015	−	0.918244i	$-0.629607\pi$
$401$	−0.535534	+	0.221825i	−0.0267433	+	0.0110774i	0.369272	+	0.929321i	$0.379607\pi$
$402$	−2.82843	+	1.17157i	−0.141069	+	0.0584327i
$403$	−4.24264	+	10.2426i	−0.211341	+	0.510222i
$404$		−	40.5269i		−	2.01629i
$405$		0			0
$406$	−1.41421	+	1.41421i	−0.0701862	+	0.0701862i
$407$		−	24.1421i		−	1.19668i
$408$	8.07107	−	17.9706i	0.399577	−	0.889675i
$409$	3.31371			0.163852			0.0819262	−	0.996638i	$-0.473893\pi$
$409$	3.31371			0.163852			0.0819262	+	0.996638i	$0.473893\pi$
$410$		0			0
$411$	−6.92893	+	16.7279i	−0.341779	+	0.825128i
$412$	47.7990			2.35489
$413$	−6.00000	+	14.4853i	−0.295241	+	0.712774i
$414$	−8.07107	−	19.4853i	−0.396671	−	0.957649i
$415$		0			0
$416$	−1.58579	−	1.58579i	−0.0777496	−	0.0777496i
$417$	−16.3431	+	16.3431i	−0.800327	+	0.800327i
$418$	−2.00000	−	4.82843i	−0.0978232	−	0.236166i
$419$	5.10051	+	12.3137i	0.249176	+	0.601564i	0.998135	−	0.0610528i	$-0.0194458\pi$
$419$	5.10051	+	12.3137i	0.249176	+	0.601564i	−0.748959	+	0.662617i	$0.769446\pi$
$420$		0			0
$421$			14.5858i			0.710868i	0.934701	+	0.355434i	$0.115667\pi$
$421$			14.5858i			0.710868i	−0.934701	+	0.355434i	$0.884333\pi$
$422$	47.6274	+	19.7279i	2.31847	+	0.960340i
$423$	6.68629	+	6.68629i	0.325099	+	0.325099i
$424$	6.24264			0.303169
$425$		0			0
$426$	−14.1421			−0.685189
$427$	7.07107	+	7.07107i	0.342193	+	0.342193i
$428$	−1.58579	−	0.656854i	−0.0766519	−	0.0317502i
$429$			4.00000i			0.193122i
$430$		0			0
$431$	2.79899	+	6.75736i	0.134823	+	0.325491i	0.976844	−	0.213954i	$-0.0686343\pi$
$431$	2.79899	+	6.75736i	0.134823	+	0.325491i	−0.842021	+	0.539445i	$0.818634\pi$
$432$	−6.00000	−	14.4853i	−0.288675	−	0.696923i
$433$	14.7279	−	14.7279i	0.707779	−	0.707779i	−0.258289	−	0.966068i	$-0.583159\pi$
$433$	14.7279	−	14.7279i	0.707779	−	0.707779i	0.966068	+	0.258289i	$0.0831587\pi$
$434$	−34.9706	−	34.9706i	−1.67864	−	1.67864i
$435$		0			0
$436$	−22.7782	−	54.9914i	−1.09088	−	2.63361i
$437$	1.51472	−	3.65685i	0.0724588	−	0.174931i
$438$	−33.7990			−1.61498
$439$	4.07107	−	9.82843i	0.194301	−	0.469085i	−0.796462	−	0.604689i	$-0.793297\pi$
$439$	4.07107	−	9.82843i	0.194301	−	0.469085i	0.990763	+	0.135604i	$0.0432974\pi$
$440$		0			0
$441$	−0.313708			−0.0149385
$442$	14.0711	+	0.414214i	0.669292	+	0.0197021i
$443$			23.7990i			1.13072i	0.824843	+	0.565362i	$0.191264\pi$
$443$			23.7990i			1.13072i	−0.824843	+	0.565362i	$0.808736\pi$
$444$	27.0711	−	27.0711i	1.28474	−	1.28474i
$445$		0			0
$446$			11.6569i			0.551968i
$447$	7.02944	−	16.9706i	0.332481	−	0.802680i
$448$	23.7279	−	9.82843i	1.12104	−	0.464350i
$449$	−11.1924	+	4.63604i	−0.528201	+	0.218788i	−0.630815	−	0.775933i	$-0.717279\pi$
$449$	−11.1924	+	4.63604i	−0.528201	+	0.218788i	0.102614	+	0.994721i	$0.467279\pi$
$450$		0			0
$451$	−2.24264	−	2.24264i	−0.105602	−	0.105602i
$452$	19.3345	+	46.6777i	0.909419	+	2.19553i
$453$	−7.17157	+	2.97056i	−0.336950	+	0.139569i
$454$	38.7990	+	16.0711i	1.82093	+	0.754253i
$455$		0			0
$456$	1.51472	−	3.65685i	0.0709332	−	0.171248i
$457$	9.31371	+	9.31371i	0.435677	+	0.435677i	0.890554	−	0.454877i	$-0.150317\pi$
$457$	9.31371	+	9.31371i	0.435677	+	0.435677i	−0.454877	+	0.890554i	$0.650317\pi$
$458$		−	41.4558i		−	1.93710i
$459$	−19.6569	−	8.82843i	−0.917503	−	0.412076i
$460$		0			0
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	−0.190013	−	0.981782i	$-0.560853\pi$
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	0.981782	+	0.190013i	$0.0608529\pi$
$462$	−16.4853	−	6.82843i	−0.766965	−	0.317687i
$463$	−14.6274			−0.679794			−0.339897	−	0.940463i	$-0.610392\pi$
$463$	−14.6274			−0.679794			−0.339897	+	0.940463i	$0.610392\pi$
$464$	−0.878680	−	0.363961i	−0.0407917	−	0.0168965i
$465$		0			0
$466$	−19.6066	+	8.12132i	−0.908258	+	0.376213i
$467$	−23.0711	+	23.0711i	−1.06760	+	1.06760i	−0.0700588	+	0.997543i	$0.522319\pi$
$467$	−23.0711	+	23.0711i	−1.06760	+	1.06760i	−0.997543	+	0.0700588i	$0.977681\pi$
$468$	7.00000	−	7.00000i	0.323575	−	0.323575i
$469$	2.82843	−	1.17157i	0.130605	−	0.0540982i
$470$		0			0
$471$	9.65685	+	4.00000i	0.444964	+	0.184310i
$472$	−26.4853			−1.21908
$473$	2.00000	+	0.828427i	0.0919601	+	0.0380911i
$474$	8.82843	−	8.82843i	0.405503	−	0.405503i
$475$		0			0
$476$	−16.8995	+	37.6274i	−0.774587	+	1.72465i
$477$		−	2.58579i		−	0.118395i
$478$	25.3137	+	25.3137i	1.15782	+	1.15782i
$479$	−1.97056	+	4.75736i	−0.0900373	+	0.217369i	−0.962483	−	0.271342i	$-0.912533\pi$
$479$	−1.97056	+	4.75736i	−0.0900373	+	0.217369i	0.872446	+	0.488711i	$0.162533\pi$
$480$		0			0
$481$	12.0711	+	5.00000i	0.550393	+	0.227980i
$482$	7.94975	−	3.29289i	0.362101	−	0.149987i
$483$	−5.17157	−	12.4853i	−0.235315	−	0.568100i
$484$	11.2929	+	11.2929i	0.513313	+	0.513313i
$485$		0			0
$486$	−34.5563	+	14.3137i	−1.56751	+	0.649283i
$487$	−24.3137	+	10.0711i	−1.10176	+	0.456364i	−0.858092	−	0.513495i	$-0.828350\pi$
$487$	−24.3137	+	10.0711i	−1.10176	+	0.456364i	−0.243667	+	0.969859i	$0.578350\pi$
$488$	−6.46447	+	15.6066i	−0.292633	+	0.706478i
$489$		−	9.17157i		−	0.414753i
$490$		0			0
$491$	26.2426	−	26.2426i	1.18431	−	1.18431i	0.205698	−	0.978615i	$-0.434053\pi$
$491$	26.2426	−	26.2426i	1.18431	−	1.18431i	0.978615	−	0.205698i	$-0.0659466\pi$
$492$		−	5.02944i		−	0.226745i
$493$	−1.22183	+	0.464466i	−0.0550282	+	0.0209185i
$494$	2.82843			0.127257
$495$		0			0
$496$	9.00000	−	21.7279i	0.404112	−	0.975613i
$497$	14.1421			0.634361
$498$	11.6569	−	28.1421i	0.522356	−	1.26108i
$499$	8.21320	+	19.8284i	0.367673	+	0.887642i	0.994131	+	0.108186i	$0.0345043\pi$
$499$	8.21320	+	19.8284i	0.367673	+	0.887642i	−0.626457	+	0.779456i	$0.715496\pi$
$500$		0			0
$501$	−1.51472	−	1.51472i	−0.0676726	−	0.0676726i
$502$	34.9706	−	34.9706i	1.56081	−	1.56081i
$503$	8.17157	+	19.7279i	0.364352	+	0.879625i	0.994653	+	0.103273i	$0.0329317\pi$
$503$	8.17157	+	19.7279i	0.364352	+	0.879625i	−0.630301	+	0.776351i	$0.717068\pi$
$504$	8.07107	+	19.4853i	0.359514	+	0.867943i
$505$		0			0
$506$		−	30.1421i		−	1.33998i
$507$	11.0000	+	4.55635i	0.488527	+	0.202355i
$508$	14.3848	+	14.3848i	0.638221	+	0.638221i
$509$	36.9706			1.63869			0.819346	−	0.573300i	$-0.194337\pi$
$509$	36.9706			1.63869			0.819346	+	0.573300i	$0.194337\pi$
$510$		0			0
$511$	33.7990			1.49518
$512$	22.0919	+	22.0919i	0.976333	+	0.976333i
$513$	−4.00000	−	1.65685i	−0.176604	−	0.0731519i
$514$			14.8284i			0.654054i
$515$		0			0
$516$	1.31371	+	3.17157i	0.0578328	+	0.139621i
$517$	5.17157	+	12.4853i	0.227446	+	0.549102i
$518$	−41.2132	+	41.2132i	−1.81080	+	1.81080i
$519$	2.24264	+	2.24264i	0.0984410	+	0.0984410i
$520$		0			0
$521$	7.12132	+	17.1924i	0.311991	+	0.753212i	0.999631	+	0.0271607i	$0.00864660\pi$
$521$	7.12132	+	17.1924i	0.311991	+	0.753212i	−0.687640	+	0.726051i	$0.741353\pi$
$522$	−0.535534	+	1.29289i	−0.0234397	+	0.0565884i
$523$	1.17157			0.0512293			0.0256147	−	0.999672i	$-0.491846\pi$
$523$	1.17157			0.0512293			0.0256147	+	0.999672i	$0.491846\pi$
$524$	22.3137	−	53.8701i	0.974779	−	2.35332i
$525$		0			0
$526$	25.3137			1.10373
$527$	−11.4853	−	30.2132i	−0.500307	−	1.31611i
$528$		−	8.48528i		−	0.369274i
$529$	−0.121320	+	0.121320i	−0.00527480	+	0.00527480i
$530$		0			0
$531$			10.9706i			0.476082i
$532$	−3.17157	+	7.65685i	−0.137505	+	0.331967i
$533$	1.58579	−	0.656854i	0.0686880	−	0.0284515i
$534$	−15.8995	+	6.58579i	−0.688038	+	0.284995i
$535$		0			0
$536$	3.65685	+	3.65685i	0.157952	+	0.157952i
$537$	−2.48528	−	6.00000i	−0.107248	−	0.258919i
$538$	58.9914	−	24.4350i	2.54330	−	1.05347i
$539$	−0.414214	−	0.171573i	−0.0178414	−	0.00739017i
$540$		0			0
$541$	−7.05025	+	17.0208i	−0.303114	+	0.731782i	0.696781	+	0.717284i	$0.254615\pi$
$541$	−7.05025	+	17.0208i	−0.303114	+	0.731782i	−0.999895	+	0.0144979i	$0.995385\pi$
$542$	−37.7990	−	37.7990i	−1.62361	−	1.62361i
$543$			12.6274i			0.541894i
$544$	6.53553	+	0.192388i	0.280209	+	0.00824857i
$545$		0			0
$546$	6.82843	−	6.82843i	0.292230	−	0.292230i
$547$	7.48528	+	3.10051i	0.320048	+	0.132568i	0.536923	−	0.843631i	$-0.319587\pi$
$547$	7.48528	+	3.10051i	0.320048	+	0.132568i	−0.216875	+	0.976199i	$0.569587\pi$
$548$	64.0416			2.73572
$549$	6.46447	+	2.67767i	0.275897	+	0.114280i
$550$		0			0
$551$	−0.242641	+	0.100505i	−0.0103368	+	0.00428166i
$552$	16.1421	−	16.1421i	0.687055	−	0.687055i
$553$	−8.82843	+	8.82843i	−0.375423	+	0.375423i
$554$	−44.5061	+	18.4350i	−1.89088	+	0.783229i
$555$		0			0
$556$	75.5269	+	31.2843i	3.20305	+	1.32675i
$557$	19.7574			0.837146			0.418573	−	0.908183i	$-0.362530\pi$
$557$	19.7574			0.837146			0.418573	+	0.908183i	$0.362530\pi$
$558$	−31.9706	−	13.2426i	−1.35342	−	0.560606i
$559$	−0.828427	+	0.828427i	−0.0350387	+	0.0350387i
$560$		0			0
$561$	−8.00000	−	8.48528i	−0.337760	−	0.358249i
$562$			4.58579i			0.193440i
$563$	−24.5858	−	24.5858i	−1.03617	−	1.03617i	−0.999321	−	0.0368464i	$-0.988269\pi$
$563$	−24.5858	−	24.5858i	−1.03617	−	1.03617i	−0.0368464	−	0.999321i	$-0.511731\pi$
$564$	−8.20101	+	19.7990i	−0.345325	+	0.833688i
$565$		0			0
$566$	41.6274	+	17.2426i	1.74973	+	0.724762i
$567$	−0.414214	+	0.171573i	−0.0173953	+	0.00720538i
$568$	9.14214	+	22.0711i	0.383595	+	0.926081i
$569$	−8.51472	−	8.51472i	−0.356956	−	0.356956i	0.505734	−	0.862690i	$-0.331222\pi$
$569$	−8.51472	−	8.51472i	−0.356956	−	0.356956i	−0.862690	+	0.505734i	$0.831222\pi$
$570$		0			0
$571$	−3.92893	+	1.62742i	−0.164421	+	0.0681053i	−0.463376	−	0.886162i	$-0.653362\pi$
$571$	−3.92893	+	1.62742i	−0.164421	+	0.0681053i	0.298955	+	0.954267i	$0.403362\pi$
$572$	13.0711	−	5.41421i	0.546529	−	0.226380i
$573$	−8.28427	+	20.0000i	−0.346080	+	0.835512i
$574$			7.65685i			0.319591i
$575$		0			0
$576$	12.7071	−	12.7071i	0.529463	−	0.529463i
$577$		−	27.0711i		−	1.12698i	−0.826122	−	0.563492i	$-0.809458\pi$
$577$		−	27.0711i		−	1.12698i	0.826122	−	0.563492i	$-0.190542\pi$
$578$	−30.6777	+	27.2635i	−1.27602	+	1.13401i
$579$	−2.48528			−0.103285
$580$		0			0
$581$	−11.6569	+	28.1421i	−0.483608	+	1.16753i
$582$	−26.9706			−1.11797
$583$	1.41421	−	3.41421i	0.0585707	−	0.141402i
$584$	21.8492	+	52.7487i	0.904128	+	2.18276i
$585$		0			0
$586$	−21.0711	−	21.0711i	−0.870438	−	0.870438i
$587$	−32.0416	+	32.0416i	−1.32250	+	1.32250i	−0.410753	+	0.911747i	$0.634734\pi$
$587$	−32.0416	+	32.0416i	−1.32250	+	1.32250i	−0.911747	+	0.410753i	$0.865266\pi$
$588$	−0.272078	−	0.656854i	−0.0112203	−	0.0270882i
$589$	−2.48528	−	6.00000i	−0.102404	−	0.247226i
$590$		0			0
$591$			5.02944i			0.206883i
$592$	−25.6066	−	10.6066i	−1.05242	−	0.435929i
$593$	−9.14214	−	9.14214i	−0.375423	−	0.375423i	0.494025	−	0.869448i	$-0.335525\pi$
$593$	−9.14214	−	9.14214i	−0.375423	−	0.375423i	−0.869448	+	0.494025i	$0.835525\pi$
$594$	−32.9706			−1.35280
$595$		0			0
$596$	−64.9706			−2.66130
$597$	8.82843	+	8.82843i	0.361323	+	0.361323i
$598$	15.0711	+	6.24264i	0.616302	+	0.255281i
$599$		−	10.6274i		−	0.434224i	−0.976147	−	0.217112i	$-0.930336\pi$
$599$		−	10.6274i		−	0.434224i	0.976147	−	0.217112i	$-0.0696638\pi$
$600$		0			0
$601$	−3.22183	−	7.77817i	−0.131421	−	0.317278i	0.844447	−	0.535639i	$-0.179929\pi$
$601$	−3.22183	−	7.77817i	−0.131421	−	0.317278i	−0.975868	+	0.218360i	$0.929929\pi$
$602$	−2.00000	−	4.82843i	−0.0815139	−	0.196792i
$603$	1.51472	−	1.51472i	0.0616841	−	0.0616841i
$604$	19.4142	+	19.4142i	0.789953	+	0.789953i
$605$		0			0
$606$	−10.5858	−	25.5563i	−0.430018	−	1.03816i
$607$	−6.27208	+	15.1421i	−0.254576	+	0.614600i	−0.998563	−	0.0535937i	$-0.982932\pi$
$607$	−6.27208	+	15.1421i	−0.254576	+	0.614600i	0.743987	+	0.668194i	$0.232932\pi$
$608$	1.31371			0.0532779
$609$	−0.343146	+	0.828427i	−0.0139050	+	0.0335696i
$610$		0			0
$611$	−7.31371			−0.295881
$612$	−0.849242	+	28.8492i	−0.0343286	+	1.16616i
$613$		−	5.31371i		−	0.214619i	−0.994226	−	0.107309i	$-0.965776\pi$
$613$		−	5.31371i		−	0.214619i	0.994226	−	0.107309i	$-0.0342235\pi$
$614$	−44.6274	+	44.6274i	−1.80102	+	1.80102i
$615$		0			0
$616$			30.1421i			1.21446i
$617$	1.12132	−	2.70711i	0.0451427	−	0.108984i	−0.899700	−	0.436509i	$-0.856215\pi$
$617$	1.12132	−	2.70711i	0.0451427	−	0.108984i	0.944842	+	0.327525i	$0.106215\pi$
$618$	30.1421	−	12.4853i	1.21249	−	0.502232i
$619$	−26.3137	+	10.8995i	−1.05764	+	0.438088i	−0.842612	−	0.538521i	$-0.818983\pi$
$619$	−26.3137	+	10.8995i	−1.05764	+	0.438088i	−0.215025	+	0.976609i	$0.568983\pi$
$620$		0			0
$621$	−17.6569	−	17.6569i	−0.708545	−	0.708545i
$622$	−23.7279	−	57.2843i	−0.951403	−	2.29689i
$623$	15.8995	−	6.58579i	0.637000	−	0.263854i
$624$	4.24264	+	1.75736i	0.169842	+	0.0703507i
$625$		0			0
$626$	9.12132	−	22.0208i	0.364561	−	0.880129i
$627$	−1.65685	−	1.65685i	−0.0661684	−	0.0661684i
$628$		−	36.9706i		−	1.47529i
$629$	−35.6066	+	13.5355i	−1.41973	+	0.539697i
$630$		0			0
$631$	−20.7279	+	20.7279i	−0.825166	+	0.825166i	−0.986844	−	0.161678i	$-0.948309\pi$
$631$	−20.7279	+	20.7279i	−0.825166	+	0.825166i	0.161678	+	0.986844i	$0.448309\pi$
$632$	−19.4853	−	8.07107i	−0.775083	−	0.321050i
$633$	23.1127			0.918647
$634$	42.9203	+	17.7782i	1.70458	+	0.706062i
$635$		0			0
$636$	5.41421	−	2.24264i	0.214688	−	0.0889265i
$637$	0.171573	−	0.171573i	0.00679796	−	0.00679796i
$638$	−1.41421	+	1.41421i	−0.0559893	+	0.0559893i
$639$	9.14214	−	3.78680i	0.361657	−	0.149803i
$640$		0			0
$641$	−38.2635	−	15.8492i	−1.51132	−	0.626007i	−0.535487	−	0.844544i	$-0.679872\pi$
$641$	−38.2635	−	15.8492i	−1.51132	−	0.626007i	−0.975829	+	0.218536i	$0.929872\pi$
$642$	−1.17157			−0.0462383
$643$	−26.6569	−	11.0416i	−1.05124	−	0.435439i	−0.210908	−	0.977506i	$-0.567642\pi$
$643$	−26.6569	−	11.0416i	−1.05124	−	0.435439i	−0.840336	+	0.542066i	$0.817642\pi$
$644$	−33.7990	+	33.7990i	−1.33187	+	1.33187i
$645$		0			0
$646$	−6.00000	+	5.65685i	−0.236067	+	0.222566i
$647$		−	2.82843i		−	0.111197i	−0.998453	−	0.0555985i	$-0.982293\pi$
$647$		−	2.82843i		−	0.111197i	0.998453	−	0.0555985i	$-0.0177067\pi$
$648$	−0.535534	−	0.535534i	−0.0210378	−	0.0210378i
$649$	−6.00000	+	14.4853i	−0.235521	+	0.568597i
$650$		0			0
$651$	−20.4853	−	8.48528i	−0.802881	−	0.332564i
$652$	−29.9706	+	12.4142i	−1.17374	+	0.486178i
$653$	−3.63604	−	8.77817i	−0.142289	−	0.343517i	0.836629	−	0.547770i	$-0.184523\pi$
$653$	−3.63604	−	8.77817i	−0.142289	−	0.343517i	−0.978918	+	0.204254i	$0.934523\pi$
$654$	−28.7279	−	28.7279i	−1.12335	−	1.12335i
$655$		0			0
$656$	−3.36396	+	1.39340i	−0.131341	+	0.0544031i
$657$	21.8492	−	9.05025i	0.852420	−	0.353084i
$658$	12.4853	−	30.1421i	0.486727	−	1.17506i
$659$			8.48528i			0.330540i	0.986248	+	0.165270i	$0.0528495\pi$
$659$			8.48528i			0.330540i	−0.986248	+	0.165270i	$0.947151\pi$
$660$		0			0
$661$	0.857864	−	0.857864i	0.0333671	−	0.0333671i	−0.690226	−	0.723593i	$-0.742489\pi$
$661$	0.857864	−	0.857864i	0.0333671	−	0.0333671i	0.723593	+	0.690226i	$0.242489\pi$
$662$			52.6274i			2.04542i
$663$	5.89949	−	2.24264i	0.229117	−	0.0870969i
$664$	−51.4558			−1.99687
$665$		0			0
$666$	−15.6066	+	37.6777i	−0.604744	+	1.45998i
$667$	−1.51472			−0.0586501
$668$	−2.89949	+	7.00000i	−0.112185	+	0.270838i
$669$	2.00000	+	4.82843i	0.0773245	+	0.186678i
$670$		0			0
$671$	7.07107	+	7.07107i	0.272976	+	0.272976i
$672$	3.17157	−	3.17157i	0.122346	−	0.122346i
$673$	−1.70711	−	4.12132i	−0.0658041	−	0.158865i	0.887556	−	0.460699i	$-0.152401\pi$
$673$	−1.70711	−	4.12132i	−0.0658041	−	0.158865i	−0.953361	+	0.301834i	$0.902401\pi$
$674$	5.19239	+	12.5355i	0.200003	+	0.482851i
$675$		0			0
$676$		−	42.1127i		−	1.61972i
$677$	−35.1924	−	14.5772i	−1.35255	−	0.560246i	−0.415551	−	0.909570i	$-0.636411\pi$
$677$	−35.1924	−	14.5772i	−1.35255	−	0.560246i	−0.937002	+	0.349324i	$0.886411\pi$
$678$	24.3848	+	24.3848i	0.936492	+	0.936492i
$679$	26.9706			1.03504
$680$		0			0
$681$	18.8284			0.721507
$682$	−34.9706	−	34.9706i	−1.33909	−	1.33909i
$683$	21.9706	+	9.10051i	0.840680	+	0.348221i	0.761122	−	0.648609i	$-0.224649\pi$
$683$	21.9706	+	9.10051i	0.840680	+	0.348221i	0.0795585	+	0.996830i	$0.474649\pi$
$684$			5.79899i			0.221730i
$685$		0			0
$686$	17.3137	+	41.7990i	0.661040	+	1.59589i
$687$	−7.11270	−	17.1716i	−0.271366	−	0.655136i
$688$	1.75736	−	1.75736i	0.0669987	−	0.0669987i
$689$	1.41421	+	1.41421i	0.0538772	+	0.0538772i
$690$		0			0
$691$	−7.62742	−	18.4142i	−0.290161	−	0.700510i	0.709832	−	0.704371i	$-0.248771\pi$
$691$	−7.62742	−	18.4142i	−0.290161	−	0.700510i	−0.999993	+	0.00386139i	$0.998771\pi$
$692$	4.29289	−	10.3640i	0.163191	−	0.393979i
$693$	12.4853			0.474277
$694$	15.4853	−	37.3848i	0.587813	−	1.41911i
$695$		0			0
$696$	−1.51472			−0.0574153
$697$	−2.05025	+	4.56497i	−0.0776589	+	0.172911i
$698$			10.2426i			0.387690i
$699$	−6.72792	+	6.72792i	−0.254473	+	0.254473i
$700$		0			0
$701$		−	37.6985i		−	1.42385i	−0.702254	−	0.711926i	$-0.747823\pi$
$701$		−	37.6985i		−	1.42385i	0.702254	−	0.711926i	$-0.252177\pi$
$702$	6.82843	−	16.4853i	0.257722	−	0.622197i
$703$	−7.07107	+	2.92893i	−0.266690	+	0.110467i
$704$	23.7279	−	9.82843i	0.894280	−	0.370423i
$705$		0			0
$706$	23.8995	+	23.8995i	0.899469	+	0.899469i
$707$	10.5858	+	25.5563i	0.398119	+	0.961145i
$708$	−22.9706	+	9.51472i	−0.863287	+	0.357585i
$709$	−22.4350	−	9.29289i	−0.842565	−	0.349002i	−0.0807007	−	0.996738i	$-0.525716\pi$
$709$	−22.4350	−	9.29289i	−0.842565	−	0.349002i	−0.761864	+	0.647736i	$0.775716\pi$
$710$		0			0
$711$	−3.34315	+	8.07107i	−0.125378	+	0.302689i
$712$	20.5563	+	20.5563i	0.770382	+	0.770382i
$713$		−	37.4558i		−	1.40273i
$714$	−0.828427	+	28.1421i	−0.0310031	+	1.05319i
$715$		0			0
$716$	−16.2426	+	16.2426i	−0.607016	+	0.607016i
$717$	14.8284	+	6.14214i	0.553778	+	0.229382i
$718$	−69.5980			−2.59737
$719$	31.3848	+	13.0000i	1.17045	+	0.484818i	0.881343	−	0.472477i	$-0.156640\pi$
$719$	31.3848	+	13.0000i	1.17045	+	0.484818i	0.289112	+	0.957295i	$0.406640\pi$
$720$		0			0
$721$	−30.1421	+	12.4853i	−1.12255	+	0.464976i
$722$	31.2635	−	31.2635i	1.16351	−	1.16351i
$723$	2.72792	−	2.72792i	0.101453	−	0.101453i
$724$	41.2635	−	17.0919i	1.53354	−	0.635215i
$725$		0			0
$726$	10.0711	+	4.17157i	0.373772	+	0.154822i
$727$	43.1127			1.59896			0.799481	−	0.600692i	$-0.205108\pi$
$727$	43.1127			1.59896			0.799481	+	0.600692i	$0.205108\pi$
$728$	−15.0711	−	6.24264i	−0.558571	−	0.231368i
$729$	−12.2218	+	12.2218i	−0.452660	+	0.452660i
$730$		0			0
$731$	0.100505	−	3.41421i	0.00371731	−	0.126279i
$732$			15.8579i			0.586124i
$733$	25.4853	+	25.4853i	0.941320	+	0.941320i	0.998371	−	0.0570509i	$-0.0181697\pi$
$733$	25.4853	+	25.4853i	0.941320	+	0.941320i	−0.0570509	+	0.998371i	$0.518170\pi$
$734$	−4.07107	+	9.82843i	−0.150266	+	0.362774i
$735$		0			0
$736$	7.00000	+	2.89949i	0.258023	+	0.106877i
$737$	2.82843	−	1.17157i	0.104186	−	0.0431554i
$738$	2.05025	+	4.94975i	0.0754708	+	0.182203i
$739$	−15.7574	−	15.7574i	−0.579644	−	0.579644i	0.355161	−	0.934805i	$-0.384426\pi$
$739$	−15.7574	−	15.7574i	−0.579644	−	0.579644i	−0.934805	+	0.355161i	$0.884426\pi$
$740$		0			0
$741$	1.17157	−	0.485281i	0.0430388	−	0.0178273i
$742$	−8.24264	+	3.41421i	−0.302597	+	0.125340i
$743$	19.5269	−	47.1421i	0.716373	−	1.72948i	0.0329473	−	0.999457i	$-0.489511\pi$
$743$	19.5269	−	47.1421i	0.716373	−	1.72948i	0.683426	−	0.730020i	$-0.260489\pi$
$744$		−	37.4558i		−	1.37320i
$745$		0			0
$746$	−19.7279	+	19.7279i	−0.722291	+	0.722291i
$747$			21.3137i			0.779828i
$748$	−16.8995	+	37.6274i	−0.617907	+	1.37579i
$749$	1.17157			0.0428083
$750$		0			0
$751$	18.2132	−	43.9706i	0.664609	−	1.60451i	−0.125889	−	0.992044i	$-0.540178\pi$
$751$	18.2132	−	43.9706i	0.664609	−	1.60451i	0.790498	−	0.612464i	$-0.209822\pi$
$752$	15.5147			0.565764
$753$	8.48528	−	20.4853i	0.309221	−	0.746525i
$754$	−0.414214	−	1.00000i	−0.0150848	−	0.0364179i
$755$		0			0
$756$	36.9706	+	36.9706i	1.34461	+	1.34461i
$757$	1.79899	−	1.79899i	0.0653854	−	0.0653854i	−0.673658	−	0.739043i	$-0.735278\pi$
$757$	1.79899	−	1.79899i	0.0653854	−	0.0653854i	0.739043	+	0.673658i	$0.235278\pi$
$758$	−2.41421	−	5.82843i	−0.0876882	−	0.211698i
$759$	−5.17157	−	12.4853i	−0.187716	−	0.453187i
$760$		0			0
$761$			37.6985i			1.36657i	0.730152	+	0.683285i	$0.239449\pi$
$761$			37.6985i			1.36657i	−0.730152	+	0.683285i	$0.760551\pi$
$762$	12.8284	+	5.31371i	0.464725	+	0.192495i
$763$	28.7279	+	28.7279i	1.04002	+	1.04002i
$764$	76.5685			2.77015
$765$		0			0
$766$	54.2843			1.96137
$767$	−6.00000	−	6.00000i	−0.216647	−	0.216647i
$768$	29.9706	+	12.4142i	1.08147	+	0.447959i
$769$			12.7279i			0.458981i	0.973311	+	0.229490i	$0.0737059\pi$
$769$			12.7279i			0.458981i	−0.973311	+	0.229490i	$0.926294\pi$
$770$		0			0
$771$	2.54416	+	6.14214i	0.0916255	+	0.221204i
$772$	3.36396	+	8.12132i	0.121072	+	0.292293i
$773$	−0.585786	+	0.585786i	−0.0210693	+	0.0210693i	−0.717563	−	0.696494i	$-0.754742\pi$
$773$	−0.585786	+	0.585786i	−0.0210693	+	0.0210693i	0.696494	+	0.717563i	$0.254742\pi$
$774$	−2.58579	−	2.58579i	−0.0929442	−	0.0929442i
$775$		0			0
$776$	17.4350	+	42.0919i	0.625881	+	1.51101i
$777$	−10.0000	+	24.1421i	−0.358748	+	0.866094i
$778$	−29.3137			−1.05095
$779$	−0.384776	+	0.928932i	−0.0137860	+	0.0332824i
$780$		0			0
$781$	14.1421			0.506045
$782$	−44.4558	+	16.8995i	−1.58974	+	0.604325i
$783$			1.65685i			0.0592111i
$784$	−0.363961	+	0.363961i	−0.0129986	+	0.0129986i
$785$		0			0
$786$		−	39.7990i		−	1.41958i
$787$	7.87006	−	19.0000i	0.280537	−	0.677277i	−0.719311	−	0.694688i	$-0.755542\pi$
$787$	7.87006	−	19.0000i	0.280537	−	0.677277i	0.999848	+	0.0174112i	$0.00554243\pi$
$788$	16.4350	−	6.80761i	0.585474	−	0.242511i
$789$	10.4853	−	4.34315i	0.373286	−	0.154620i
$790$		0			0
$791$	−24.3848	−	24.3848i	−0.867023	−	0.867023i
$792$	8.07107	+	19.4853i	0.286793	+	0.692379i
$793$	−5.00000	+	2.07107i	−0.177555	+	0.0735458i
$794$	39.6777	+	16.4350i	1.40811	+	0.583257i
$795$		0			0
$796$	16.8995	−	40.7990i	0.598987	−	1.44608i
$797$	−17.8284	−	17.8284i	−0.631515	−	0.631515i	0.316933	−	0.948448i	$-0.397347\pi$
$797$	−17.8284	−	17.8284i	−0.631515	−	0.631515i	−0.948448	+	0.316933i	$0.897347\pi$
$798$			5.65685i			0.200250i
$799$	15.5147	−	14.6274i	0.548871	−	0.517481i
$800$		0			0
$801$	8.51472	−	8.51472i	0.300853	−	0.300853i
$802$	1.29289	+	0.535534i	0.0456536	+	0.0189104i
$803$	33.7990			1.19274
$804$	4.48528	+	1.85786i	0.158184	+	0.0655218i
$805$		0			0
$806$	24.7279	−	10.2426i	0.871004	−	0.360782i
$807$	20.2426	−	20.2426i	0.712575	−	0.712575i
$808$	−33.0416	+	33.0416i	−1.16240	+	1.16240i
$809$	32.6066	−	13.5061i	1.14639	−	0.474849i	0.273067	−	0.961995i	$-0.411962\pi$
$809$	32.6066	−	13.5061i	1.14639	−	0.474849i	0.873321	+	0.487146i	$0.161962\pi$
$810$		0			0
$811$	−50.9411	−	21.1005i	−1.78878	−	0.740939i	−0.990304	−	0.138919i	$-0.955637\pi$
$811$	−50.9411	−	21.1005i	−1.78878	−	0.740939i	−0.798481	−	0.602020i	$-0.794363\pi$
$812$	3.17157			0.111300
$813$	−22.1421	−	9.17157i	−0.776559	−	0.321661i
$814$	−41.2132	+	41.2132i	−1.44452	+	1.44452i
$815$		0			0
$816$	−12.5147	+	4.75736i	−0.438103	+	0.166541i
$817$		−	0.686292i		−	0.0240103i
$818$	−5.65685	−	5.65685i	−0.197787	−	0.197787i
$819$	−2.58579	+	6.24264i	−0.0903547	+	0.218136i
$820$		0			0
$821$	35.5061	+	14.7071i	1.23917	+	0.513282i	0.903456	−	0.428682i	$-0.141022\pi$
$821$	35.5061	+	14.7071i	1.23917	+	0.513282i	0.335716	+	0.941963i	$0.391022\pi$
$822$	40.3848	−	16.7279i	1.40858	−	0.583453i
$823$	−3.72792	−	9.00000i	−0.129947	−	0.313720i	0.845492	−	0.533987i	$-0.179307\pi$
$823$	−3.72792	−	9.00000i	−0.129947	−	0.313720i	−0.975440	+	0.220267i	$0.929307\pi$
$824$	−38.9706	−	38.9706i	−1.35760	−	1.35760i
$825$		0			0
$826$	34.9706	−	14.4853i	1.21678	−	0.504007i
$827$	43.2843	−	17.9289i	1.50514	−	0.623450i	0.530593	−	0.847627i	$-0.321969\pi$
$827$	43.2843	−	17.9289i	1.50514	−	0.623450i	0.974549	+	0.224177i	$0.0719693\pi$
$828$	−12.7990	+	30.8995i	−0.444796	+	1.07383i
$829$		−	53.9411i		−	1.87345i	−0.350062	−	0.936726i	$-0.613840\pi$
$829$		−	53.9411i		−	1.87345i	0.350062	−	0.936726i	$-0.386160\pi$
$830$		0			0
$831$	−15.2721	+	15.2721i	−0.529783	+	0.529783i
$832$			13.8995i			0.481878i
$833$	−0.0208153	+	0.707107i	−0.000721207	+	0.0244998i
$834$	55.7990			1.93216
$835$		0			0
$836$	−3.17157	+	7.65685i	−0.109691	+	0.264818i
$837$	−40.9706			−1.41615
$838$	12.3137	−	29.7279i	0.425370	−	1.02693i
$839$	6.41421	+	15.4853i	0.221443	+	0.534611i	0.995086	−	0.0990102i	$-0.0315677\pi$
$839$	6.41421	+	15.4853i	0.221443	+	0.534611i	−0.773643	+	0.633622i	$0.781568\pi$
$840$		0			0
$841$	−20.4350	−	20.4350i	−0.704656	−	0.704656i
$842$	24.8995	−	24.8995i	0.858093	−	0.858093i
$843$	0.786797	+	1.89949i	0.0270987	+	0.0654221i
$844$	−31.2843	−	75.5269i	−1.07685	−	2.59974i
$845$		0			0
$846$		−	22.8284i		−	0.784857i
$847$	−10.0711	−	4.17157i	−0.346046	−	0.143337i
$848$	−3.00000	−	3.00000i	−0.103020	−	0.103020i
$849$	20.2010			0.693297
$850$		0			0
$851$	−44.1421			−1.51317
$852$	15.8579	+	15.8579i	0.543281	+	0.543281i
$853$	17.7071	+	7.33452i	0.606280	+	0.251129i	0.664637	−	0.747166i	$-0.268586\pi$
$853$	17.7071	+	7.33452i	0.606280	+	0.251129i	−0.0583572	+	0.998296i	$0.518586\pi$
$854$		−	24.1421i		−	0.826127i
$855$		0			0
$856$	0.757359	+	1.82843i	0.0258860	+	0.0624944i
$857$	−3.53553	−	8.53553i	−0.120772	−	0.291568i	0.851919	−	0.523673i	$-0.175439\pi$
$857$	−3.53553	−	8.53553i	−0.120772	−	0.291568i	−0.972691	+	0.232105i	$0.925439\pi$
$858$	6.82843	−	6.82843i	0.233119	−	0.233119i
$859$	−24.7279	−	24.7279i	−0.843706	−	0.843706i	0.145633	−	0.989339i	$-0.453478\pi$
$859$	−24.7279	−	24.7279i	−0.843706	−	0.843706i	−0.989339	+	0.145633i	$0.953478\pi$
$860$		0			0
$861$	1.31371	+	3.17157i	0.0447711	+	0.108087i
$862$	6.75736	−	16.3137i	0.230157	−	0.555647i
$863$	−10.6274			−0.361761			−0.180881	−	0.983505i	$-0.557895\pi$
$863$	−10.6274			−0.361761			−0.180881	+	0.983505i	$0.557895\pi$
$864$	3.17157	−	7.65685i	0.107899	−	0.260491i
$865$		0			0
$866$	−50.2843			−1.70873
$867$	−8.02944	+	16.5563i	−0.272694	+	0.562283i
$868$			78.4264i			2.66197i
$869$	−8.82843	+	8.82843i	−0.299484	+	0.299484i
$870$		0			0
$871$			1.65685i			0.0561404i
$872$	−26.2635	+	63.4056i	−0.889393	+	2.14718i
$873$	17.4350	−	7.22183i	0.590086	−	0.244422i
$874$	−8.82843	+	3.65685i	−0.298626	+	0.123695i
$875$		0			0
$876$	37.8995	+	37.8995i	1.28051	+	1.28051i
$877$	19.2218	+	46.4056i	0.649075	+	1.56701i	0.814105	+	0.580717i	$0.197228\pi$
$877$	19.2218	+	46.4056i	0.649075	+	1.56701i	−0.165031	+	0.986288i	$0.552772\pi$
$878$	−23.7279	+	9.82843i	−0.800779	+	0.331693i
$879$	−12.3431	−	5.11270i	−0.416324	−	0.172447i
$880$		0			0
$881$	12.8787	−	31.0919i	0.433894	−	1.04751i	−0.544127	−	0.839003i	$-0.683139\pi$
$881$	12.8787	−	31.0919i	0.433894	−	1.04751i	0.978020	−	0.208509i	$-0.0668611\pi$
$882$	0.535534	+	0.535534i	0.0180324	+	0.0180324i
$883$		−	8.00000i		−	0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$		−	8.00000i		−	0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	−15.3137	−	16.2426i	−0.515056	−	0.546299i
$885$		0			0
$886$	40.6274	−	40.6274i	1.36490	−	1.36490i
$887$	40.6985	+	16.8579i	1.36652	+	0.566032i	0.940843	−	0.338843i	$-0.110035\pi$
$887$	40.6985	+	16.8579i	1.36652	+	0.566032i	0.425678	+	0.904875i	$0.360035\pi$
$888$	−44.1421			−1.48131
$889$	−12.8284	−	5.31371i	−0.430252	−	0.178216i
$890$		0			0
$891$	−0.414214	+	0.171573i	−0.0138767	+	0.00574791i
$892$	13.0711	−	13.0711i	0.437652	−	0.437652i
$893$	3.02944	−	3.02944i	0.101376	−	0.101376i
$894$	−40.9706	+	16.9706i	−1.37026	+	0.567581i
$895$		0			0
$896$	−49.6274	−	20.5563i	−1.65794	−	0.686739i
$897$	7.31371			0.244198
$898$	27.0208	+	11.1924i	0.901696	+	0.373495i
$899$	−1.75736	+	1.75736i	−0.0586112	+	0.0586112i
$900$		0			0
$901$	−5.82843	−	0.171573i	−0.194173	−	0.00571592i
$902$			7.65685i			0.254945i
$903$	−1.65685	−	1.65685i	−0.0551367	−	0.0551367i
$904$	22.2929	−	53.8198i	0.741451	−	1.79002i
$905$		0			0
$906$	17.3137	+	7.17157i	0.575209	+	0.238260i
$907$	−12.4142	+	5.14214i	−0.412207	+	0.170742i	−0.579143	−	0.815226i	$-0.696613\pi$
$907$	−12.4142	+	5.14214i	−0.412207	+	0.170742i	0.166936	+	0.985968i	$0.446613\pi$
$908$	−25.4853	−	61.5269i	−0.845759	−	2.04184i
$909$	13.6863	+	13.6863i	0.453946	+	0.453946i
$910$		0			0
$911$	5.24264	−	2.17157i	0.173696	−	0.0719474i	−0.294141	−	0.955762i	$-0.595033\pi$
$911$	5.24264	−	2.17157i	0.173696	−	0.0719474i	0.467837	+	0.883815i	$0.345033\pi$
$912$	−2.48528	+	1.02944i	−0.0822959	+	0.0340881i
$913$	−11.6569	+	28.1421i	−0.385786	+	0.931369i
$914$		−	31.7990i		−	1.05182i
$915$		0			0
$916$	−46.4853	+	46.4853i	−1.53592	+	1.53592i
$917$			39.7990i			1.31428i
$918$	18.4853	+	48.6274i	0.610105	+	1.60494i
$919$	−19.3137			−0.637100			−0.318550	−	0.947906i	$-0.603196\pi$
$919$	−19.3137			−0.637100			−0.318550	+	0.947906i	$0.603196\pi$
$920$		0			0
$921$	−10.8284	+	26.1421i	−0.356809	+	0.861413i
$922$	−58.0416			−1.91150
$923$	−2.92893	+	7.07107i	−0.0964070	+	0.232747i
$924$	10.8284	+	26.1421i	0.356229	+	0.860013i
$925$		0			0
$926$	24.9706	+	24.9706i	0.820584	+	0.820584i
$927$	−16.1421	+	16.1421i	−0.530177	+	0.530177i
$928$	−0.192388	−	0.464466i	−0.00631545	−	0.0152468i
$929$	−6.63604	−	16.0208i	−0.217721	−	0.525626i	0.776850	−	0.629686i	$-0.216817\pi$
$929$	−6.63604	−	16.0208i	−0.217721	−	0.525626i	−0.994571	+	0.104060i	$0.966817\pi$
$930$		0			0
$931$			0.142136i			0.00465831i
$932$	31.0919	+	12.8787i	1.01845	+	0.421855i
$933$	−19.6569	−	19.6569i	−0.643537	−	0.643537i
$934$	78.7696			2.57742
$935$		0			0
$936$	−11.4142			−0.373085
$937$	19.4853	+	19.4853i	0.636556	+	0.636556i	0.949704	−	0.313148i	$-0.101384\pi$
$937$	19.4853	+	19.4853i	0.636556	+	0.636556i	−0.313148	+	0.949704i	$0.601384\pi$
$938$	−6.82843	−	2.82843i	−0.222956	−	0.0923514i
$939$		−	10.6863i		−	0.348734i
$940$		0			0
$941$	−15.2635	−	36.8492i	−0.497574	−	1.20125i	−0.950786	−	0.309848i	$-0.899722\pi$
$941$	−15.2635	−	36.8492i	−0.497574	−	1.20125i	0.453212	−	0.891403i	$-0.350278\pi$
$942$	−9.65685	−	23.3137i	−0.314637	−	0.759602i
$943$	−4.10051	+	4.10051i	−0.133531	+	0.133531i
$944$	12.7279	+	12.7279i	0.414259	+	0.414259i
$945$		0			0
$946$	−2.00000	−	4.82843i	−0.0650256	−	0.156986i
$947$	−11.7279	+	28.3137i	−0.381106	+	0.920072i	0.610646	+	0.791904i	$0.290910\pi$
$947$	−11.7279	+	28.3137i	−0.381106	+	0.920072i	−0.991752	+	0.128168i	$0.959090\pi$
$948$	−19.7990			−0.643041
$949$	−7.00000	+	16.8995i	−0.227230	+	0.548581i
$950$		0			0
$951$	20.8284			0.675408
$952$	44.4558	−	16.8995i	1.44082	−	0.547716i
$953$		−	49.6985i		−	1.60989i	−0.593348	−	0.804946i	$-0.702194\pi$
$953$		−	49.6985i		−	1.60989i	0.593348	−	0.804946i	$-0.297806\pi$
$954$	−4.41421	+	4.41421i	−0.142915	+	0.142915i
$955$		0			0
$956$		−	56.7696i		−	1.83606i
$957$	−0.343146	+	0.828427i	−0.0110923	+	0.0267792i
$958$	11.4853	−	4.75736i	0.371073	−	0.153703i
$959$	−40.3848	+	16.7279i	−1.30409	+	0.540173i
$960$		0			0
$961$	−21.5355	−	21.5355i	−0.694695	−	0.694695i
$962$	−12.0711	−	29.1421i	−0.389187	−	0.939580i
$963$	0.757359	−	0.313708i	0.0244056	−	0.0101091i
$964$	−12.6066	−	5.22183i	−0.406031	−	0.168184i
$965$		0			0
$966$	−12.4853	+	30.1421i	−0.401707	+	0.969807i
$967$	−30.8701	−	30.8701i	−0.992714	−	0.992714i	0.00725952	−	0.999974i	$-0.497689\pi$
$967$	−30.8701	−	30.8701i	−0.992714	−	0.992714i	−0.999974	+	0.00725952i	$0.997689\pi$
$968$		−	18.4142i		−	0.591855i
$969$	−1.51472	+	3.37258i	−0.0486598	+	0.108343i
$970$		0			0
$971$	−36.5858	+	36.5858i	−1.17409	+	1.17409i	−0.192869	+	0.981224i	$0.561779\pi$
$971$	−36.5858	+	36.5858i	−1.17409	+	1.17409i	−0.981224	+	0.192869i	$0.938221\pi$
$972$	54.7990	+	22.6985i	1.75768	+	0.728054i
$973$	−55.7990			−1.78883
$974$	58.6985	+	24.3137i	1.88082	+	0.779061i
$975$		0			0
$976$	10.6066	−	4.39340i	0.339509	−	0.140629i
$977$	27.1421	−	27.1421i	0.868354	−	0.868354i	−0.123936	−	0.992290i	$-0.539552\pi$
$977$	27.1421	−	27.1421i	0.868354	−	0.868354i	0.992290	+	0.123936i	$0.0395519\pi$
$978$	−15.6569	+	15.6569i	−0.500651	+	0.500651i
$979$	15.8995	−	6.58579i	0.508150	−	0.210483i
$980$		0			0
$981$	26.2635	+	10.8787i	0.838528	+	0.347330i
$982$	−89.5980			−2.85919
$983$	−9.00000	−	3.72792i	−0.287055	−	0.118902i	0.234510	−	0.972114i	$-0.424652\pi$
$983$	−9.00000	−	3.72792i	−0.287055	−	0.118902i	−0.521565	+	0.853212i	$0.674652\pi$
$984$	−4.10051	+	4.10051i	−0.130719	+	0.130719i
$985$		0			0
$986$	2.87868	+	1.29289i	0.0916758	+	0.0411741i
$987$		−	14.6274i		−	0.465596i
$988$	−3.17157	−	3.17157i	−0.100901	−	0.100901i
$989$	1.51472	−	3.65685i	0.0481653	−	0.116281i
$990$		0			0
$991$	37.7279	+	15.6274i	1.19847	+	0.496421i	0.890503	−	0.454977i	$-0.150352\pi$
$991$	37.7279	+	15.6274i	1.19847	+	0.496421i	0.307964	+	0.951398i	$0.400352\pi$
$992$	11.4853	−	4.75736i	0.364658	−	0.151046i
$993$	9.02944	+	21.7990i	0.286541	+	0.691770i
$994$	−24.1421	−	24.1421i	−0.765742	−	0.765742i
$995$		0			0
$996$	−44.6274	+	18.4853i	−1.41407	+	0.585729i
$997$	6.94975	−	2.87868i	0.220101	−	0.0911687i	−0.269908	−	0.962886i	$-0.586993\pi$
$997$	6.94975	−	2.87868i	0.220101	−	0.0911687i	0.490009	+	0.871717i	$0.336993\pi$
$998$	19.8284	−	47.8701i	0.627658	−	1.51530i
$999$			48.2843i			1.52765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.a.399.1		4
5.2	odd	4		425.2.m.a.76.1		4
5.3	odd	4		17.2.d.a.8.1	✓	4
5.4	even	2		425.2.n.b.399.1		4
15.8	even	4		153.2.l.c.127.1		4
17.15	even	8		425.2.n.b.49.1		4
20.3	even	4		272.2.v.d.161.1		4
35.3	even	12		833.2.v.a.569.1		8
35.13	even	4		833.2.l.a.246.1		4
35.18	odd	12		833.2.v.b.569.1		8
35.23	odd	12		833.2.v.b.263.1		8
35.33	even	12		833.2.v.a.263.1		8
85.3	even	16		289.2.c.c.38.4		8
85.7	even	16		7225.2.a.u.1.2		4
85.8	odd	8		289.2.d.b.155.1		4
85.13	odd	4		289.2.d.c.179.1		4
85.23	even	16		289.2.b.b.288.1		4
85.27	even	16		7225.2.a.u.1.1		4
85.28	even	16		289.2.b.b.288.2		4
85.32	odd	8		425.2.m.a.151.1		4
85.33	odd	4		289.2.d.a.110.1		4
85.38	odd	4		289.2.d.b.179.1		4
85.43	odd	8		289.2.d.c.155.1		4
85.48	even	16		289.2.c.c.38.3		8
85.49	even	8	inner	425.2.n.a.49.1		4
85.53	odd	8		289.2.d.a.134.1		4
85.58	even	16		289.2.a.f.1.3		4
85.63	even	16		289.2.c.c.251.1		8
85.73	even	16		289.2.c.c.251.2		8
85.78	even	16		289.2.a.f.1.4		4
85.83	odd	8		17.2.d.a.15.1	yes	4
255.83	even	8		153.2.l.c.100.1		4
255.143	odd	16		2601.2.a.bb.1.1		4
255.248	odd	16		2601.2.a.bb.1.2		4
340.83	even	8		272.2.v.d.49.1		4
340.143	odd	16		4624.2.a.bp.1.3		4
340.163	odd	16		4624.2.a.bp.1.2		4
595.83	even	8		833.2.l.a.491.1		4
595.338	odd	24		833.2.v.b.508.1		8
595.423	even	24		833.2.v.a.814.1		8
595.508	odd	24		833.2.v.b.814.1		8
595.593	even	24		833.2.v.a.508.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	5.3	odd	4
17.2.d.a.15.1	yes	4	85.83	odd	8
153.2.l.c.100.1		4	255.83	even	8
153.2.l.c.127.1		4	15.8	even	4
272.2.v.d.49.1		4	340.83	even	8
272.2.v.d.161.1		4	20.3	even	4
289.2.a.f.1.3		4	85.58	even	16
289.2.a.f.1.4		4	85.78	even	16
289.2.b.b.288.1		4	85.23	even	16
289.2.b.b.288.2		4	85.28	even	16
289.2.c.c.38.3		8	85.48	even	16
289.2.c.c.38.4		8	85.3	even	16
289.2.c.c.251.1		8	85.63	even	16
289.2.c.c.251.2		8	85.73	even	16
289.2.d.a.110.1		4	85.33	odd	4
289.2.d.a.134.1		4	85.53	odd	8
289.2.d.b.155.1		4	85.8	odd	8
289.2.d.b.179.1		4	85.38	odd	4
289.2.d.c.155.1		4	85.43	odd	8
289.2.d.c.179.1		4	85.13	odd	4
425.2.m.a.76.1		4	5.2	odd	4
425.2.m.a.151.1		4	85.32	odd	8
425.2.n.a.49.1		4	85.49	even	8	inner
425.2.n.a.399.1		4	1.1	even	1	trivial
425.2.n.b.49.1		4	17.15	even	8
425.2.n.b.399.1		4	5.4	even	2
833.2.l.a.246.1		4	35.13	even	4
833.2.l.a.491.1		4	595.83	even	8
833.2.v.a.263.1		8	35.33	even	12
833.2.v.a.508.1		8	595.593	even	24
833.2.v.a.569.1		8	35.3	even	12
833.2.v.a.814.1		8	595.423	even	24
833.2.v.b.263.1		8	35.23	odd	12
833.2.v.b.508.1		8	595.338	odd	24
833.2.v.b.569.1		8	35.18	odd	12
833.2.v.b.814.1		8	595.508	odd	24
2601.2.a.bb.1.1		4	255.143	odd	16
2601.2.a.bb.1.2		4	255.248	odd	16
4624.2.a.bp.1.2		4	340.163	odd	16
4624.2.a.bp.1.3		4	340.143	odd	16
7225.2.a.u.1.1		4	85.27	even	16
7225.2.a.u.1.2		4	85.7	even	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 - 0.414214i) q^{3} +3.82843i q^{4} +(1.00000 + 2.41421i) q^{6} +(-1.00000 - 2.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 - 1.29289i) q^{9} +O(q^{10})\)	\(q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 - 0.414214i) q^{3} +3.82843i q^{4} +(1.00000 + 2.41421i) q^{6} +(-1.00000 - 2.41421i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 - 1.29289i) q^{9} +(-1.00000 - 2.41421i) q^{11} +(1.58579 - 3.82843i) q^{12} +1.41421 q^{13} +(-2.41421 + 5.82843i) q^{14} -3.00000 q^{16} +(-3.00000 + 2.82843i) q^{17} +4.41421i q^{18} +(-0.585786 + 0.585786i) q^{19} +2.82843i q^{21} +(-2.41421 + 5.82843i) q^{22} +(-4.41421 + 1.82843i) q^{23} +(-4.41421 + 1.82843i) q^{24} +(-2.41421 - 2.41421i) q^{26} +(2.00000 + 4.82843i) q^{27} +(9.24264 - 3.82843i) q^{28} +(0.292893 + 0.121320i) q^{29} +(-3.00000 + 7.24264i) q^{31} +(-1.12132 - 1.12132i) q^{32} +2.82843i q^{33} +(9.94975 + 0.292893i) q^{34} +(4.94975 - 4.94975i) q^{36} +(8.53553 + 3.53553i) q^{37} +2.00000 q^{38} +(-1.41421 - 0.585786i) q^{39} +(1.12132 - 0.464466i) q^{41} +(4.82843 - 4.82843i) q^{42} +(-0.585786 + 0.585786i) q^{43} +(9.24264 - 3.82843i) q^{44} +(10.6569 + 4.41421i) q^{46} -5.17157 q^{47} +(3.00000 + 1.24264i) q^{48} +(0.121320 - 0.121320i) q^{49} +(4.17157 - 1.58579i) q^{51} +5.41421i q^{52} +(1.00000 + 1.00000i) q^{53} +(4.82843 - 11.6569i) q^{54} +(-10.6569 - 4.41421i) q^{56} +(0.828427 - 0.343146i) q^{57} +(-0.292893 - 0.707107i) q^{58} +(-4.24264 - 4.24264i) q^{59} +(-3.53553 + 1.46447i) q^{61} +(17.4853 - 7.24264i) q^{62} +(-1.82843 + 4.41421i) q^{63} +9.82843i q^{64} +(4.82843 - 4.82843i) q^{66} +1.17157i q^{67} +(-10.8284 - 11.4853i) q^{68} +5.17157 q^{69} +(-2.07107 + 5.00000i) q^{71} -8.07107 q^{72} +(-4.94975 + 11.9497i) q^{73} +(-8.53553 - 20.6066i) q^{74} +(-2.24264 - 2.24264i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(1.41421 + 3.41421i) q^{78} +(-1.82843 - 4.41421i) q^{79} -0.171573i q^{81} +(-2.70711 - 1.12132i) q^{82} +(-8.24264 - 8.24264i) q^{83} -10.8284 q^{84} +2.00000 q^{86} +(-0.242641 - 0.242641i) q^{87} +(-10.6569 - 4.41421i) q^{88} +6.58579i q^{89} +(-1.41421 - 3.41421i) q^{91} +(-7.00000 - 16.8995i) q^{92} +(6.00000 - 6.00000i) q^{93} +(8.82843 + 8.82843i) q^{94} +(0.656854 + 1.58579i) q^{96} +(-3.94975 + 9.53553i) q^{97} -0.414214 q^{98} +(-1.82843 + 4.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} - 4 q^{11} + 12 q^{12} - 4 q^{14} - 12 q^{16} - 12 q^{17} - 8 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 4 q^{26} + 8 q^{27} + 20 q^{28} + 4 q^{29} - 12 q^{31} + 4 q^{32} + 20 q^{34} + 20 q^{37} + 8 q^{38} - 4 q^{41} + 8 q^{42} - 8 q^{43} + 20 q^{44} + 20 q^{46} - 32 q^{47} + 12 q^{48} - 8 q^{49} + 28 q^{51} + 4 q^{53} + 8 q^{54} - 20 q^{56} - 8 q^{57} - 4 q^{58} + 36 q^{62} + 4 q^{63} + 8 q^{66} - 32 q^{68} + 32 q^{69} + 20 q^{71} - 4 q^{72} - 20 q^{74} + 8 q^{76} - 8 q^{77} + 4 q^{79} - 8 q^{82} - 16 q^{83} - 32 q^{84} + 8 q^{86} + 16 q^{87} - 20 q^{88} - 28 q^{92} + 24 q^{93} + 24 q^{94} - 20 q^{96} + 4 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 - 4 * q^11 + 12 * q^12 - 4 * q^14 - 12 * q^16 - 12 * q^17 - 8 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 4 * q^26 + 8 * q^27 + 20 * q^28 + 4 * q^29 - 12 * q^31 + 4 * q^32 + 20 * q^34 + 20 * q^37 + 8 * q^38 - 4 * q^41 + 8 * q^42 - 8 * q^43 + 20 * q^44 + 20 * q^46 - 32 * q^47 + 12 * q^48 - 8 * q^49 + 28 * q^51 + 4 * q^53 + 8 * q^54 - 20 * q^56 - 8 * q^57 - 4 * q^58 + 36 * q^62 + 4 * q^63 + 8 * q^66 - 32 * q^68 + 32 * q^69 + 20 * q^71 - 4 * q^72 - 20 * q^74 + 8 * q^76 - 8 * q^77 + 4 * q^79 - 8 * q^82 - 16 * q^83 - 32 * q^84 + 8 * q^86 + 16 * q^87 - 20 * q^88 - 28 * q^92 + 24 * q^93 + 24 * q^94 - 20 * q^96 + 4 * q^97 + 4 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more