LMFDB - Embedded newform 425.2.n.f.399.2

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:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			399.2
Character	$\chi$	$=$	425.399
Dual form			425.2.n.f.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.528855 - 0.528855i) q^{2} +(-2.84096 - 1.17676i) q^{3} -1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(1.23707 + 2.98655i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(4.56494 + 4.56494i) q^{9} +O(q^{10})$	\(q+(-0.528855 - 0.528855i) q^{2} +(-2.84096 - 1.17676i) q^{3} -1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(1.23707 + 2.98655i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(4.56494 + 4.56494i) q^{9} +(1.04667 + 2.52689i) q^{11} +(-1.69527 + 4.09275i) q^{12} +4.31833 q^{13} +(0.925222 - 2.23368i) q^{14} -0.956646 q^{16} +(-2.22453 - 3.47152i) q^{17} -4.82839i q^{18} +(0.897260 - 0.897260i) q^{19} -9.94040i q^{21} +(0.782821 - 1.88990i) q^{22} +(-0.454888 + 0.188421i) q^{23} +(7.31061 - 3.02815i) q^{24} +(-2.28377 - 2.28377i) q^{26} +(-4.06666 - 9.81779i) q^{27} +(4.30250 - 1.78215i) q^{28} +(0.410535 + 0.170049i) q^{29} +(-2.11561 + 5.10754i) q^{31} +(4.14511 + 4.14511i) q^{32} -8.41047i q^{33} +(-0.659477 + 3.01239i) q^{34} +(6.57637 - 6.57637i) q^{36} +(9.88545 + 4.09469i) q^{37} -0.949042 q^{38} +(-12.2682 - 5.08165i) q^{39} +(-2.00526 + 0.830608i) q^{41} +(-5.25703 + 5.25703i) q^{42} +(1.52864 - 1.52864i) q^{43} +(3.64030 - 1.50786i) q^{44} +(0.340217 + 0.140922i) q^{46} +8.39597 q^{47} +(2.71779 + 1.12575i) q^{48} +(-2.43940 + 2.43940i) q^{49} +(2.23464 + 12.4802i) q^{51} -6.22109i q^{52} +(-1.28480 - 1.28480i) q^{53} +(-3.04152 + 7.34287i) q^{54} +(-7.68527 - 3.18334i) q^{56} +(-3.60494 + 1.49321i) q^{57} +(-0.127182 - 0.307045i) q^{58} +(2.13537 + 2.13537i) q^{59} +(11.2928 - 4.67764i) q^{61} +(3.82000 - 1.58230i) q^{62} +(-7.98628 + 19.2806i) q^{63} -2.47104i q^{64} +(-4.44792 + 4.44792i) q^{66} -4.21389i q^{67} +(-5.00116 + 3.20471i) q^{68} +1.51404 q^{69} +(-1.48927 + 3.59542i) q^{71} -16.6127 q^{72} +(-2.47620 + 5.97807i) q^{73} +(-3.06247 - 7.39347i) q^{74} +(-1.29261 - 1.29261i) q^{76} +(-6.25188 + 6.25188i) q^{77} +(3.80064 + 9.17555i) q^{78} +(2.76355 + 6.67180i) q^{79} +13.3100i q^{81} +(1.49977 + 0.621223i) q^{82} +(-0.160866 - 0.160866i) q^{83} -14.3204 q^{84} -1.61686 q^{86} +(-0.966206 - 0.966206i) q^{87} +(-6.50243 - 2.69339i) q^{88} -13.3408i q^{89} +(5.34208 + 12.8969i) q^{91} +(0.271443 + 0.655322i) q^{92} +(12.0207 - 12.0207i) q^{93} +(-4.44025 - 4.44025i) q^{94} +(-6.89827 - 16.6539i) q^{96} +(5.66657 - 13.6803i) q^{97} +2.58018 q^{98} +(-6.75711 + 16.3131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9	$ 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37} + 48 q^{38} - 8 q^{39} + 16 q^{41} + 24 q^{42} + 8 q^{43} - 16 q^{44} + 8 q^{46} + 64 q^{47} + 8 q^{48} - 56 q^{51} - 24 q^{53} + 32 q^{54} + 64 q^{56} - 16 q^{57} - 56 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 80 q^{63} + 96 q^{66} - 24 q^{68} - 96 q^{69} - 24 q^{71} + 24 q^{72} + 64 q^{73} + 64 q^{74} - 8 q^{76} - 24 q^{77} - 8 q^{78} + 16 q^{82} + 96 q^{83} + 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} - 112 q^{92} + 64 q^{93} - 56 q^{94} - 168 q^{96} - 48 q^{97} - 120 q^{98} + 8 q^{99}+O(q^{100}) $ 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 8 * 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 $

$2$	−0.528855	−	0.528855i	−0.373957	−	0.373957i	0.494959	−	0.868916i	$-0.335183\pi$
$2$	−0.528855	−	0.528855i	−0.373957	−	0.373957i	−0.868916	+	0.494959i	$0.835183\pi$
$3$	−2.84096	−	1.17676i	−1.64023	−	0.679404i	−0.643906	−	0.765105i	$-0.722687\pi$
$3$	−2.84096	−	1.17676i	−1.64023	−	0.679404i	−0.996321	+	0.0857002i	$0.972687\pi$
$4$		−	1.44062i		−	0.720312i
$5$		0			0
$5$		0			0
$6$	0.880118	+	2.12479i	0.359307	+	0.867443i
$7$	1.23707	+	2.98655i	0.467569	+	1.12881i	0.965221	+	0.261434i	$0.0841954\pi$
$7$	1.23707	+	2.98655i	0.467569	+	1.12881i	−0.497653	+	0.867376i	$0.665805\pi$
$8$	−1.81959	+	1.81959i	−0.643323	+	0.643323i
$9$	4.56494	+	4.56494i	1.52165	+	1.52165i
$10$		0			0
$11$	1.04667	+	2.52689i	0.315584	+	0.761886i	0.999478	+	0.0323052i	$0.0102849\pi$
$11$	1.04667	+	2.52689i	0.315584	+	0.761886i	−0.683894	+	0.729581i	$0.739715\pi$
$12$	−1.69527	+	4.09275i	−0.489383	+	1.18148i
$13$	4.31833			1.19769			0.598845	−	0.800865i	$-0.295627\pi$
$13$	4.31833			1.19769			0.598845	+	0.800865i	$0.295627\pi$
$14$	0.925222	−	2.23368i	0.247276	−	0.596977i
$15$		0			0
$16$	−0.956646			−0.239162
$17$	−2.22453	−	3.47152i	−0.539528	−	0.841968i
$17$	−2.22453	−	3.47152i	−0.539528	−	0.841968i
$18$		−	4.82839i		−	1.13806i
$19$	0.897260	−	0.897260i	0.205846	−	0.205846i	−0.596653	−	0.802499i	$-0.703503\pi$
$19$	0.897260	−	0.897260i	0.205846	−	0.205846i	0.802499	+	0.596653i	$0.203503\pi$
$20$		0			0
$21$		−	9.94040i		−	2.16917i
$22$	0.782821	−	1.88990i	0.166898	−	0.402928i
$23$	−0.454888	+	0.188421i	−0.0948506	+	0.0392884i	−0.429604	−	0.903017i	$-0.641347\pi$
$23$	−0.454888	+	0.188421i	−0.0948506	+	0.0392884i	0.334754	+	0.942306i	$0.391347\pi$
$24$	7.31061	−	3.02815i	1.49227	−	0.618119i
$25$		0			0
$26$	−2.28377	−	2.28377i	−0.447884	−	0.447884i
$27$	−4.06666	−	9.81779i	−0.782630	−	1.88943i
$28$	4.30250	−	1.78215i	0.813096	−	0.336795i
$29$	0.410535	+	0.170049i	0.0762345	+	0.0315774i	0.420475	−	0.907304i	$-0.361863\pi$
$29$	0.410535	+	0.170049i	0.0762345	+	0.0315774i	−0.344240	+	0.938882i	$0.611863\pi$
$30$		0			0
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	0.611994	+	0.790862i	$0.290368\pi$
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	−0.991969	+	0.126479i	$0.959632\pi$
$32$	4.14511	+	4.14511i	0.732759	+	0.732759i
$33$		−	8.41047i		−	1.46408i
$34$	−0.659477	+	3.01239i	−0.113099	+	0.516620i
$35$		0			0
$36$	6.57637	−	6.57637i	1.09606	−	1.09606i
$37$	9.88545	+	4.09469i	1.62516	+	0.673162i	0.994677	−	0.103043i	$-0.0328578\pi$
$37$	9.88545	+	4.09469i	1.62516	+	0.673162i	0.630481	+	0.776205i	$0.282858\pi$
$38$	−0.949042			−0.153955
$39$	−12.2682	−	5.08165i	−1.96448	−	0.813715i
$40$		0			0
$41$	−2.00526	+	0.830608i	−0.313170	+	0.129719i	−0.533732	−	0.845654i	$-0.679211\pi$
$41$	−2.00526	+	0.830608i	−0.313170	+	0.129719i	0.220562	+	0.975373i	$0.429211\pi$
$42$	−5.25703	+	5.25703i	−0.811178	+	0.811178i
$43$	1.52864	−	1.52864i	0.233115	−	0.233115i	−0.580876	−	0.813992i	$-0.697290\pi$
$43$	1.52864	−	1.52864i	0.233115	−	0.233115i	0.813992	+	0.580876i	$0.197290\pi$
$44$	3.64030	−	1.50786i	0.548796	−	0.227319i
$45$		0			0
$46$	0.340217	+	0.140922i	0.0501622	+	0.0207779i
$47$	8.39597			1.22468			0.612339	−	0.790595i	$-0.290229\pi$
$47$	8.39597			1.22468			0.612339	+	0.790595i	$0.290229\pi$
$48$	2.71779	+	1.12575i	0.392279	+	0.162487i
$49$	−2.43940	+	2.43940i	−0.348485	+	0.348485i
$50$		0			0
$51$	2.23464	+	12.4802i	0.312912	+	1.74758i
$52$		−	6.22109i		−	0.862710i
$53$	−1.28480	−	1.28480i	−0.176481	−	0.176481i	0.613339	−	0.789820i	$-0.289826\pi$
$53$	−1.28480	−	1.28480i	−0.176481	−	0.176481i	−0.789820	+	0.613339i	$0.789826\pi$
$54$	−3.04152	+	7.34287i	−0.413898	+	0.999238i
$55$		0			0
$56$	−7.68527	−	3.18334i	−1.02699	−	0.425392i
$57$	−3.60494	+	1.49321i	−0.477486	+	0.197781i
$58$	−0.127182	−	0.307045i	−0.0166999	−	0.0403170i
$59$	2.13537	+	2.13537i	0.278001	+	0.278001i	0.832311	−	0.554309i	$-0.187018\pi$
$59$	2.13537	+	2.13537i	0.278001	+	0.278001i	−0.554309	+	0.832311i	$0.687018\pi$
$60$		0			0
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.484677	−	0.874693i	$-0.338937\pi$
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.961220	+	0.275783i	$0.0889371\pi$
$62$	3.82000	−	1.58230i	0.485141	−	0.200952i
$63$	−7.98628	+	19.2806i	−1.00618	+	2.42913i
$64$		−	2.47104i		−	0.308880i
$65$		0			0
$66$	−4.44792	+	4.44792i	−0.547501	+	0.547501i
$67$		−	4.21389i		−	0.514808i	−0.966304	−	0.257404i	$-0.917133\pi$
$67$		−	4.21389i		−	0.514808i	0.966304	−	0.257404i	$-0.0828672\pi$
$68$	−5.00116	+	3.20471i	−0.606479	+	0.388629i
$69$	1.51404			0.182269
$70$		0			0
$71$	−1.48927	+	3.59542i	−0.176744	+	0.426698i	−0.987280	−	0.158991i	$-0.949176\pi$
$71$	−1.48927	+	3.59542i	−0.176744	+	0.426698i	0.810536	+	0.585689i	$0.199176\pi$
$72$	−16.6127			−1.95782
$73$	−2.47620	+	5.97807i	−0.289817	+	0.699680i	−0.999991	−	0.00434632i	$-0.998617\pi$
$73$	−2.47620	+	5.97807i	−0.289817	+	0.699680i	0.710173	+	0.704027i	$0.248617\pi$
$74$	−3.06247	−	7.39347i	−0.356005	−	0.859473i
$75$		0			0
$76$	−1.29261	−	1.29261i	−0.148273	−	0.148273i
$77$	−6.25188	+	6.25188i	−0.712468	+	0.712468i
$78$	3.80064	+	9.17555i	0.430338	+	1.03893i
$79$	2.76355	+	6.67180i	0.310923	+	0.750636i	0.999671	+	0.0256347i	$0.00816068\pi$
$79$	2.76355	+	6.67180i	0.310923	+	0.750636i	−0.688748	+	0.725001i	$0.741839\pi$
$80$		0			0
$81$			13.3100i			1.47889i
$82$	1.49977	+	0.621223i	0.165621	+	0.0686026i
$83$	−0.160866	−	0.160866i	−0.0176574	−	0.0176574i	0.698223	−	0.715880i	$-0.253974\pi$
$83$	−0.160866	−	0.160866i	−0.0176574	−	0.0176574i	−0.715880	+	0.698223i	$0.753974\pi$
$84$	−14.3204			−1.56248
$85$		0			0
$86$	−1.61686			−0.174350
$87$	−0.966206	−	0.966206i	−0.103588	−	0.103588i
$88$	−6.50243	−	2.69339i	−0.693161	−	0.287117i
$89$		−	13.3408i		−	1.41413i	−0.707150	−	0.707064i	$-0.750019\pi$
$89$		−	13.3408i		−	1.41413i	0.707150	−	0.707064i	$-0.249981\pi$
$90$		0			0
$91$	5.34208	+	12.8969i	0.560002	+	1.35196i
$92$	0.271443	+	0.655322i	0.0282999	+	0.0683220i
$93$	12.0207	−	12.0207i	1.24649	−	1.24649i
$94$	−4.44025	−	4.44025i	−0.457977	−	0.457977i
$95$		0			0
$96$	−6.89827	−	16.6539i	−0.704052	−	1.69973i
$97$	5.66657	−	13.6803i	0.575353	−	1.38902i	−0.321591	−	0.946879i	$-0.604218\pi$
$97$	5.66657	−	13.6803i	0.575353	−	1.38902i	0.896943	−	0.442145i	$-0.145782\pi$
$98$	2.58018			0.260637
$99$	−6.75711	+	16.3131i	−0.679115	+	1.63953i
$100$		0			0
$101$	−0.284213			−0.0282803			−0.0141401	−	0.999900i	$-0.504501\pi$
$101$	−0.284213			−0.0282803			−0.0141401	+	0.999900i	$0.504501\pi$
$102$	5.41841	−	7.78201i	0.536503	−	0.770534i
$103$			14.0842i			1.38775i	0.720093	+	0.693877i	$0.244099\pi$
$103$			14.0842i			1.38775i	−0.720093	+	0.693877i	$0.755901\pi$
$104$	−7.85760	+	7.85760i	−0.770501	+	0.770501i
$105$		0			0
$106$			1.35894i			0.131992i
$107$	−7.15995	+	17.2857i	−0.692179	+	1.67107i	0.0481649	+	0.998839i	$0.484663\pi$
$107$	−7.15995	+	17.2857i	−0.692179	+	1.67107i	−0.740344	+	0.672228i	$0.765337\pi$
$108$	−14.1437	+	5.85853i	−1.36098	+	0.563738i
$109$	3.26202	−	1.35117i	0.312444	−	0.129419i	−0.220951	−	0.975285i	$-0.570916\pi$
$109$	3.26202	−	1.35117i	0.312444	−	0.129419i	0.533395	+	0.845866i	$0.320916\pi$
$110$		0			0
$111$	−23.2657	−	23.2657i	−2.20828	−	2.20828i
$112$	−1.18344	−	2.85707i	−0.111824	−	0.269968i
$113$	2.62525	−	1.08741i	0.246963	−	0.102295i	−0.255769	−	0.966738i	$-0.582329\pi$
$113$	2.62525	−	1.08741i	0.246963	−	0.102295i	0.502731	+	0.864443i	$0.332329\pi$
$114$	2.69619	+	1.11680i	0.252521	+	0.104598i
$115$		0			0
$116$	0.244977	−	0.591427i	0.0227456	−	0.0549126i
$117$	19.7129	+	19.7129i	1.82246	+	1.82246i
$118$		−	2.25860i		−	0.207921i
$119$	7.61598	−	10.9382i	0.698155	−	1.00270i
$120$		0			0
$121$	2.48852	−	2.48852i	0.226229	−	0.226229i
$122$	−8.44606	−	3.49847i	−0.764670	−	0.316737i
$123$	6.67430			0.601801
$124$	7.35805	+	3.04780i	0.660772	+	0.273701i
$125$		0			0
$126$	14.4202	−	5.97306i	1.28466	−	0.532122i
$127$	−3.86444	+	3.86444i	−0.342914	+	0.342914i	−0.857462	−	0.514548i	$-0.827960\pi$
$127$	−3.86444	+	3.86444i	−0.342914	+	0.342914i	0.514548	+	0.857462i	$0.327960\pi$
$128$	6.98340	−	6.98340i	0.617251	−	0.617251i
$129$	−6.14164	+	2.54395i	−0.540742	+	0.223983i
$130$		0			0
$131$	9.21986	+	3.81899i	0.805543	+	0.333667i	0.747174	−	0.664628i	$-0.231410\pi$
$131$	9.21986	+	3.81899i	0.805543	+	0.333667i	0.0583689	+	0.998295i	$0.481410\pi$
$132$	−12.1163			−1.05459
$133$	3.78969	+	1.56974i	0.328608	+	0.136114i
$134$	−2.22854	+	2.22854i	−0.192516	+	0.192516i
$135$		0			0
$136$	10.3645	+	2.26901i	0.888748	+	0.194566i
$137$		−	3.07772i		−	0.262947i	−0.991320	−	0.131474i	$-0.958029\pi$
$137$		−	3.07772i		−	0.262947i	0.991320	−	0.131474i	$-0.0419709\pi$
$138$	−0.800709	−	0.800709i	−0.0681609	−	0.0681609i
$139$	2.56777	−	6.19915i	0.217796	−	0.525805i	−0.776786	−	0.629765i	$-0.783151\pi$
$139$	2.56777	−	6.19915i	0.217796	−	0.525805i	0.994582	+	0.103960i	$0.0331513\pi$
$140$		0			0
$141$	−23.8526	−	9.88006i	−2.00875	−	0.832051i
$142$	2.68907	−	1.11385i	0.225661	−	0.0934720i
$143$	4.51988	+	10.9119i	0.377971	+	0.912503i
$144$	−4.36704	−	4.36704i	−0.363920	−	0.363920i
$145$		0			0
$146$	4.47109	−	1.85198i	0.370030	−	0.153271i
$147$	9.80082	−	4.05963i	0.808358	−	0.334833i
$148$	5.89890	−	14.2412i	0.484887	−	1.17062i
$149$			22.9914i			1.88353i	0.336276	+	0.941764i	$0.390833\pi$
$149$			22.9914i			1.88353i	−0.336276	+	0.941764i	$0.609167\pi$
$150$		0			0
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	−0.701452	−	0.712716i	$-0.747465\pi$
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	0.712716	+	0.701452i	$0.247465\pi$
$152$			3.26530i			0.264850i
$153$	5.69244	−	26.0022i	0.460207	−	2.10215i
$154$	6.61268			0.532865
$155$		0			0
$156$	−7.32075	+	17.6738i	−0.586129	+	1.41504i
$157$	11.8582			0.946391			0.473196	−	0.880957i	$-0.343100\pi$
$157$	11.8582			0.946391			0.473196	+	0.880957i	$0.343100\pi$
$158$	2.06690	−	4.98993i	0.164434	−	0.396978i
$159$	2.13815	+	5.16196i	0.169567	+	0.409370i
$160$		0			0
$161$	−1.12546	−	1.12546i	−0.0886983	−	0.0886983i
$162$	7.03907	−	7.03907i	0.553041	−	0.553041i
$163$	2.04533	+	4.93787i	0.160203	+	0.386764i	0.983515	−	0.180824i	$-0.0578765\pi$
$163$	2.04533	+	4.93787i	0.160203	+	0.386764i	−0.823312	+	0.567588i	$0.807877\pi$
$164$	1.19659	+	2.88883i	0.0934382	+	0.225580i
$165$		0			0
$166$			0.170150i			0.0132062i
$167$	−10.7077	−	4.43529i	−0.828589	−	0.343213i	−0.0722453	−	0.997387i	$-0.523016\pi$
$167$	−10.7077	−	4.43529i	−0.828589	−	0.343213i	−0.756344	+	0.654174i	$0.773016\pi$
$168$	18.0875	+	18.0875i	1.39548	+	1.39548i
$169$	5.64797			0.434459
$170$		0			0
$171$	8.19188			0.626449
$172$	−2.20220	−	2.20220i	−0.167916	−	0.167916i
$173$	−10.1877	−	4.21988i	−0.774556	−	0.320832i	−0.0398396	−	0.999206i	$-0.512685\pi$
$173$	−10.1877	−	4.21988i	−0.774556	−	0.320832i	−0.734716	+	0.678375i	$0.762685\pi$
$174$			1.02197i			0.0774750i
$175$		0			0
$176$	−1.00130	−	2.41734i	−0.0754755	−	0.182214i
$177$	−3.55367	−	8.57932i	−0.267110	−	0.644861i
$178$	−7.05538	+	7.05538i	−0.528823	+	0.528823i
$179$	−14.9009	−	14.9009i	−1.11375	−	1.11375i	−0.992639	−	0.121109i	$-0.961355\pi$
$179$	−14.9009	−	14.9009i	−1.11375	−	1.11375i	−0.121109	−	0.992639i	$-0.538645\pi$
$180$		0			0
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	0.820501	+	0.571645i	$0.193695\pi$
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	−0.175968	+	0.984396i	$0.556305\pi$
$182$	3.99542	−	9.64579i	0.296160	−	0.714993i
$183$	−37.5869			−2.77850
$184$	0.484861	−	1.17056i	0.0357444	−	0.0862947i
$185$		0			0
$186$	−12.7145			−0.932269
$187$	6.44380	−	9.25469i	0.471217	−	0.676770i
$188$		−	12.0954i		−	0.882150i
$189$	24.2906	−	24.2906i	1.76688	−	1.76688i
$190$		0			0
$191$			3.50162i			0.253368i	0.991943	+	0.126684i	$0.0404335\pi$
$191$			3.50162i			0.253368i	−0.991943	+	0.126684i	$0.959567\pi$
$192$	−2.90782	+	7.02011i	−0.209854	+	0.506633i
$193$	−11.3584	+	4.70480i	−0.817595	+	0.338659i	−0.751980	−	0.659186i	$-0.770901\pi$
$193$	−11.3584	+	4.70480i	−0.817595	+	0.338659i	−0.0656152	+	0.997845i	$0.520901\pi$
$194$	−10.2317	+	4.23811i	−0.734593	+	0.304278i
$195$		0			0
$196$	3.51426	+	3.51426i	0.251018	+	0.251018i
$197$	6.49632	+	15.6835i	0.462843	+	1.11740i	0.967225	+	0.253922i	$0.0817206\pi$
$197$	6.49632	+	15.6835i	0.462843	+	1.11740i	−0.504381	+	0.863481i	$0.668279\pi$
$198$	12.2008	−	5.05374i	0.867074	−	0.359154i
$199$	−10.6966	−	4.43067i	−0.758260	−	0.314082i	−0.0301533	−	0.999545i	$-0.509600\pi$
$199$	−10.6966	−	4.43067i	−0.758260	−	0.314082i	−0.728107	+	0.685464i	$0.759600\pi$
$200$		0			0
$201$	−4.95875	+	11.9715i	−0.349763	+	0.844403i
$202$	0.150308	+	0.150308i	0.0105756	+	0.0105756i
$203$			1.43645i			0.100819i
$204$	17.9793	−	3.21928i	1.25880	−	0.225394i
$205$		0			0
$206$	7.44849	−	7.44849i	0.518961	−	0.518961i
$207$	−2.93667	−	1.21641i	−0.204112	−	0.0845461i
$208$	−4.13111			−0.286441
$209$	3.20642	+	1.32814i	0.221792	+	0.0918694i
$210$		0			0
$211$	6.15655	−	2.55013i	0.423834	−	0.175558i	−0.160563	−	0.987026i	$-0.551331\pi$
$211$	6.15655	−	2.55013i	0.423834	−	0.175558i	0.584397	+	0.811468i	$0.301331\pi$
$212$	−1.85091	+	1.85091i	−0.127121	+	0.127121i
$213$	8.46191	−	8.46191i	0.579800	−	0.579800i
$214$	12.9282	−	5.35503i	0.883753	−	0.366063i
$215$		0			0
$216$	25.2640	+	10.4647i	1.71900	+	0.712033i
$217$	−17.8711			−1.21317
$218$	−2.43971	−	1.01056i	−0.165238	−	0.0684438i
$219$	14.0695	−	14.0695i	0.950732	−	0.950732i
$220$		0			0
$221$	−9.60626	−	14.9912i	−0.646187	−	1.00842i
$222$			24.6083i			1.65160i
$223$	−8.90442	−	8.90442i	−0.596284	−	0.596284i	0.343037	−	0.939322i	$-0.388544\pi$
$223$	−8.90442	−	8.90442i	−0.596284	−	0.596284i	−0.939322	+	0.343037i	$0.888544\pi$
$224$	−7.25180	+	17.5074i	−0.484531	+	1.16976i
$225$		0			0
$226$	−1.96346	−	0.813292i	−0.130607	−	0.0540994i
$227$	−7.43044	+	3.07779i	−0.493176	+	0.204280i	−0.615389	−	0.788224i	$-0.711001\pi$
$227$	−7.43044	+	3.07779i	−0.493176	+	0.204280i	0.122213	+	0.992504i	$0.461001\pi$
$228$	2.15116	+	5.19336i	0.142464	+	0.343939i
$229$	15.2944	+	15.2944i	1.01068	+	1.01068i	0.999942	+	0.0107373i	$0.00341786\pi$
$229$	15.2944	+	15.2944i	1.01068	+	1.01068i	0.0107373	+	0.999942i	$0.496582\pi$
$230$		0			0
$231$	25.1183	−	10.4043i	1.65266	−	0.684555i
$232$	−1.05643	+	0.437587i	−0.0693579	+	0.0287290i
$233$	−8.40011	+	20.2797i	−0.550310	+	1.32857i	0.366937	+	0.930246i	$0.380406\pi$
$233$	−8.40011	+	20.2797i	−0.550310	+	1.32857i	−0.917247	+	0.398320i	$0.869594\pi$
$234$		−	20.8506i		−	1.36304i
$235$		0			0
$236$	3.07626	−	3.07626i	0.200248	−	0.200248i
$237$		−	22.2063i		−	1.44246i
$238$	−9.81247	+	1.75697i	−0.636048	+	0.113888i
$239$	−5.90132			−0.381725			−0.190862	−	0.981617i	$-0.561128\pi$
$239$	−5.90132			−0.381725			−0.190862	+	0.981617i	$0.561128\pi$
$240$		0			0
$241$	5.09407	−	12.2982i	0.328138	−	0.792195i	−0.670593	−	0.741826i	$-0.733960\pi$
$241$	5.09407	−	12.2982i	0.328138	−	0.792195i	0.998731	−	0.0503696i	$-0.0160399\pi$
$242$	−2.63214			−0.169200
$243$	3.46273	−	8.35977i	0.222134	−	0.536279i
$244$	−6.73872	−	16.2687i	−0.431402	−	1.04150i
$245$		0			0
$246$	−3.52974	−	3.52974i	−0.225048	−	0.225048i
$247$	3.87467	−	3.87467i	0.246539	−	0.246539i
$248$	−5.44409	−	13.1432i	−0.345700	−	0.834594i
$249$	0.267712	+	0.646315i	0.0169656	+	0.0409586i
$250$		0			0
$251$			3.59367i			0.226831i	0.993548	+	0.113415i	$0.0361790\pi$
$251$			3.59367i			0.226831i	−0.993548	+	0.113415i	$0.963821\pi$
$252$	27.7761	+	11.5052i	1.74973	+	0.724761i
$253$	−0.952236	−	0.952236i	−0.0598666	−	0.0598666i
$254$	4.08746			0.256470
$255$		0			0
$256$	−12.3285			−0.770531
$257$	−17.3588	−	17.3588i	−1.08281	−	1.08281i	−0.996246	−	0.0865680i	$-0.972410\pi$
$257$	−17.3588	−	17.3588i	−1.08281	−	1.08281i	−0.0865680	−	0.996246i	$-0.527590\pi$
$258$	4.59342	+	1.90266i	0.285974	+	0.118454i
$259$			34.5888i			2.14924i
$260$		0			0
$261$	1.09781	+	2.65034i	0.0679524	+	0.164052i
$262$	−2.85628	−	6.89567i	−0.176462	−	0.426016i
$263$	10.3521	−	10.3521i	0.638340	−	0.638340i	−0.311806	−	0.950146i	$-0.600934\pi$
$263$	10.3521	−	10.3521i	0.638340	−	0.638340i	0.950146	+	0.311806i	$0.100934\pi$
$264$	15.3036	+	15.3036i	0.941873	+	0.941873i
$265$		0			0
$266$	−1.17403	−	2.83436i	−0.0719845	−	0.173786i
$267$	−15.6990	+	37.9008i	−0.960764	+	2.31949i
$268$	−6.07063			−0.370823
$269$	7.17904	−	17.3317i	0.437714	−	1.05673i	−0.539023	−	0.842291i	$-0.681206\pi$
$269$	7.17904	−	17.3317i	0.437714	−	1.05673i	0.976736	−	0.214443i	$-0.0687936\pi$
$270$		0			0
$271$	5.76388			0.350131			0.175065	−	0.984557i	$-0.443986\pi$
$271$	5.76388			0.350131			0.175065	+	0.984557i	$0.443986\pi$
$272$	2.12809	+	3.32102i	0.129034	+	0.201366i
$273$		−	42.9259i		−	2.59800i
$274$	−1.62767	+	1.62767i	−0.0983311	+	0.0983311i
$275$		0			0
$276$		−	2.18117i		−	0.131291i
$277$	−0.0471663	+	0.113870i	−0.00283395	+	0.00684176i	−0.925290	−	0.379260i	$-0.876179\pi$
$277$	−0.0471663	+	0.113870i	−0.00283395	+	0.00684176i	0.922456	+	0.386102i	$0.126179\pi$
$278$	−4.63643	+	1.92047i	−0.278075	+	0.115182i
$279$	−32.9733	+	13.6580i	−1.97406	+	0.817682i
$280$		0			0
$281$	−1.28950	−	1.28950i	−0.0769253	−	0.0769253i	0.667597	−	0.744523i	$-0.267323\pi$
$281$	−1.28950	−	1.28950i	−0.0769253	−	0.0769253i	−0.744523	+	0.667597i	$0.767323\pi$
$282$	7.38944	+	17.8397i	0.440035	+	1.06234i
$283$	26.4486	−	10.9554i	1.57221	−	0.651229i	0.585052	−	0.810996i	$-0.301074\pi$
$283$	26.4486	−	10.9554i	1.57221	−	0.651229i	0.987155	+	0.159767i	$0.0510743\pi$
$284$	5.17965	+	2.14548i	0.307355	+	0.127311i
$285$		0			0
$286$	3.38048	−	8.16120i	0.199892	−	0.482582i
$287$	−4.96130	−	4.96130i	−0.292856	−	0.292856i
$288$			37.8444i			2.23000i
$289$	−7.10292	+	15.4450i	−0.417819	+	0.908530i
$290$		0			0
$291$	−32.1969	+	32.1969i	−1.88742	+	1.88742i
$292$	8.61216	+	3.56727i	0.503988	+	0.208759i
$293$	1.41607			0.0827278			0.0413639	−	0.999144i	$-0.486830\pi$
$293$	1.41607			0.0827278			0.0413639	+	0.999144i	$0.486830\pi$
$294$	−7.33017	−	3.03626i	−0.427504	−	0.177078i
$295$		0			0
$296$	−25.4381	+	10.5368i	−1.47856	+	0.612440i
$297$	20.5520	−	20.5520i	1.19255	−	1.19255i
$298$	12.1591	−	12.1591i	0.704358	−	0.704358i
$299$	−1.96435	+	0.813662i	−0.113602	+	0.0470553i
$300$		0			0
$301$	6.45639	+	2.67433i	0.372140	+	0.154146i
$302$	−0.146399			−0.00842433
$303$	0.807438	+	0.334452i	0.0463861	+	0.0192138i
$304$	−0.858361	+	0.858361i	−0.0492304	+	0.0492304i
$305$		0			0
$306$	−16.7619	+	10.7409i	−0.958212	+	0.614017i
$307$		−	21.7364i		−	1.24056i	−0.784379	−	0.620281i	$-0.787018\pi$
$307$		−	21.7364i		−	1.24056i	0.784379	−	0.620281i	$-0.212982\pi$
$308$	9.00661	+	9.00661i	0.513199	+	0.513199i
$309$	16.5737	−	40.0125i	0.942846	−	2.27623i
$310$		0			0
$311$	7.99250	+	3.31060i	0.453213	+	0.187727i	0.597600	−	0.801794i	$-0.296121\pi$
$311$	7.99250	+	3.31060i	0.453213	+	0.187727i	−0.144387	+	0.989521i	$0.546121\pi$
$312$	31.5696	−	13.0766i	1.78728	−	0.740315i
$313$	−3.93476	−	9.49936i	−0.222406	−	0.536936i	0.772810	−	0.634638i	$-0.218851\pi$
$313$	−3.93476	−	9.49936i	−0.222406	−	0.536936i	−0.995216	+	0.0977022i	$0.968851\pi$
$314$	−6.27130	−	6.27130i	−0.353910	−	0.353910i
$315$		0			0
$316$	9.61155	−	3.98123i	0.540692	−	0.223962i
$317$	1.04183	−	0.431538i	0.0585147	−	0.0242376i	−0.353234	−	0.935535i	$-0.614918\pi$
$317$	1.04183	−	0.431538i	0.0585147	−	0.0242376i	0.411749	+	0.911297i	$0.364918\pi$
$318$	1.59916	−	3.86070i	0.0896762	−	0.216497i
$319$			1.21536i			0.0680473i
$320$		0			0
$321$	40.6822	−	40.6822i	2.27066	−	2.27066i
$322$			1.19041i			0.0663387i
$323$	−5.11084	−	1.11887i	−0.284375	−	0.0622559i
$324$	19.1747			1.06526
$325$		0			0
$326$	1.52974	−	3.69311i	0.0847242	−	0.204542i
$327$	−10.8573			−0.600407
$328$	2.13740	−	5.16013i	0.118018	−	0.284921i
$329$	10.3864	+	25.0750i	0.572621	+	1.38243i
$330$		0			0
$331$	−24.2254	−	24.2254i	−1.33155	−	1.33155i	−0.903984	−	0.427567i	$-0.859371\pi$
$331$	−24.2254	−	24.2254i	−1.33155	−	1.33155i	−0.427567	−	0.903984i	$-0.640629\pi$
$332$	−0.231748	+	0.231748i	−0.0127188	+	0.0127188i
$333$	26.4345	+	63.8185i	1.44860	+	3.49723i
$334$	3.31722	+	8.00847i	0.181510	+	0.438204i
$335$		0			0
$336$			9.50945i			0.518783i
$337$	−12.6999	−	5.26046i	−0.691807	−	0.286556i	0.00894611	−	0.999960i	$-0.497152\pi$
$337$	−12.6999	−	5.26046i	−0.691807	−	0.286556i	−0.700753	+	0.713404i	$0.747152\pi$
$338$	−2.98696	−	2.98696i	−0.162469	−	0.162469i
$339$	−8.73784			−0.474574
$340$		0			0
$341$	−15.1206			−0.818824
$342$	−4.33232	−	4.33232i	−0.234265	−	0.234265i
$343$	10.6028	+	4.39181i	0.572495	+	0.237135i
$344$			5.56300i			0.299937i
$345$		0			0
$346$	3.15611	+	7.61952i	0.169673	+	0.409628i
$347$	7.22453	+	17.4415i	0.387833	+	0.936311i	0.990398	+	0.138242i	$0.0441452\pi$
$347$	7.22453	+	17.4415i	0.387833	+	0.936311i	−0.602566	+	0.798069i	$0.705855\pi$
$348$	−1.39194	+	1.39194i	−0.0746158	+	0.0746158i
$349$	−4.98501	−	4.98501i	−0.266842	−	0.266842i	0.560985	−	0.827826i	$-0.310423\pi$
$349$	−4.98501	−	4.98501i	−0.266842	−	0.266842i	−0.827826	+	0.560985i	$0.810423\pi$
$350$		0			0
$351$	−17.5612	−	42.3965i	−0.937347	−	2.26296i
$352$	−6.13567	+	14.8128i	−0.327032	+	0.789526i
$353$	8.60779			0.458146			0.229073	−	0.973409i	$-0.426431\pi$
$353$	8.60779			0.458146			0.229073	+	0.973409i	$0.426431\pi$
$354$	−2.65784	+	6.41659i	−0.141263	+	0.341038i
$355$		0			0
$356$	−19.2191			−1.01861
$357$	−34.5083	+	22.1127i	−1.82637	+	1.17033i
$358$			15.7609i			0.832988i
$359$	6.49195	−	6.49195i	0.342632	−	0.342632i	−0.514724	−	0.857356i	$-0.672106\pi$
$359$	6.49195	−	6.49195i	0.342632	−	0.342632i	0.857356	+	0.514724i	$0.172106\pi$
$360$		0			0
$361$			17.3898i			0.915255i
$362$	6.48540	−	15.6571i	0.340865	−	0.822921i
$363$	−9.99818	+	4.14138i	−0.524769	+	0.217366i
$364$	18.5796	−	7.69592i	0.973836	−	0.403376i
$365$		0			0
$366$	19.8780	+	19.8780i	1.03904	+	1.03904i
$367$	−2.60840	−	6.29722i	−0.136157	−	0.328712i	0.841064	−	0.540935i	$-0.181930\pi$
$367$	−2.60840	−	6.29722i	−0.136157	−	0.328712i	−0.977221	+	0.212223i	$0.931930\pi$
$368$	0.435166	−	0.180252i	0.0226846	−	0.00939628i
$369$	−12.9456	−	5.36224i	−0.673921	−	0.279147i
$370$		0			0
$371$	2.24773	−	5.42650i	0.116696	−	0.281730i
$372$	−17.3174	−	17.3174i	−0.897863	−	0.897863i
$373$		−	10.4647i		−	0.541841i	−0.962602	−	0.270920i	$-0.912672\pi$
$373$		−	10.4647i		−	0.541841i	0.962602	−	0.270920i	$-0.0873280\pi$
$374$	−8.30223	+	1.48656i	−0.429298	+	0.0768680i
$375$		0			0
$376$	−15.2772	+	15.2772i	−0.787863	+	0.787863i
$377$	1.77283	+	0.734329i	0.0913053	+	0.0378199i
$378$	−25.6924			−1.32148
$379$	−23.4129	−	9.69794i	−1.20264	−	0.498150i	−0.310789	−	0.950479i	$-0.600593\pi$
$379$	−23.4129	−	9.69794i	−1.20264	−	0.498150i	−0.891851	+	0.452330i	$0.850593\pi$
$380$		0			0
$381$	15.5263	−	6.43119i	0.795434	−	0.329480i
$382$	1.85185	−	1.85185i	0.0947489	−	0.0947489i
$383$	−5.43799	+	5.43799i	−0.277868	+	0.277868i	−0.832258	−	0.554389i	$-0.812952\pi$
$383$	−5.43799	+	5.43799i	−0.277868	+	0.277868i	0.554389	+	0.832258i	$0.312952\pi$
$384$	−28.0574	+	11.6217i	−1.43180	+	0.593069i
$385$		0			0
$386$	8.49511	+	3.51879i	0.432389	+	0.179102i
$387$	13.9563			0.709439
$388$	−19.7082	−	8.16339i	−1.00053	−	0.414433i
$389$	−11.1991	+	11.1991i	−0.567816	+	0.567816i	−0.931516	−	0.363700i	$-0.881513\pi$
$389$	−11.1991	+	11.1991i	−0.567816	+	0.567816i	0.363700	+	0.931516i	$0.381513\pi$
$390$		0			0
$391$	1.66602	+	1.16000i	0.0842541	+	0.0586639i
$392$		−	8.87742i		−	0.448377i
$393$	−21.6992	−	21.6992i	−1.09458	−	1.09458i
$394$	4.85869	−	11.7299i	0.244777	−	0.590944i
$395$		0			0
$396$	23.5011	+	9.73446i	1.18097	+	0.489175i
$397$	−26.9440	+	11.1606i	−1.35228	+	0.560133i	−0.936927	−	0.349526i	$-0.886343\pi$
$397$	−26.9440	+	11.1606i	−1.35228	+	0.560133i	−0.415355	+	0.909659i	$0.636343\pi$
$398$	3.31376	+	8.00012i	0.166104	+	0.401010i
$399$	−8.91913	−	8.91913i	−0.446515	−	0.446515i
$400$		0			0
$401$	−15.1386	+	6.27060i	−0.755984	+	0.313139i	−0.727181	−	0.686446i	$-0.759170\pi$
$401$	−15.1386	+	6.27060i	−0.755984	+	0.313139i	−0.0288034	+	0.999585i	$0.509170\pi$
$402$	8.95364	−	3.70872i	0.446567	−	0.184974i
$403$	−9.13592	+	22.0561i	−0.455092	+	1.09869i
$404$			0.409445i			0.0203706i
$405$		0			0
$406$	0.759673	−	0.759673i	0.0377019	−	0.0377019i
$407$			29.2652i			1.45062i
$408$	−26.7750	−	18.6427i	−1.32556	−	0.922952i
$409$	−33.9971			−1.68105			−0.840525	−	0.541772i	$-0.817753\pi$
$409$	−33.9971			−1.68105			−0.840525	+	0.541772i	$0.817753\pi$
$410$		0			0
$411$	−3.62175	+	8.74367i	−0.178648	+	0.431294i
$412$	20.2900			0.999616
$413$	−3.73579	+	9.01899i	−0.183826	+	0.443796i
$414$	0.909768	+	2.19637i	0.0447127	+	0.107946i
$415$		0			0
$416$	17.9000	+	17.9000i	0.877618	+	0.877618i
$417$	−14.5899	+	14.5899i	−0.714468	+	0.714468i
$418$	−0.993336	−	2.39812i	−0.0485856	−	0.117296i
$419$	−0.341711	−	0.824964i	−0.0166937	−	0.0403021i	0.915313	−	0.402743i	$-0.131943\pi$
$419$	−0.341711	−	0.824964i	−0.0166937	−	0.0403021i	−0.932007	+	0.362441i	$0.881943\pi$
$420$		0			0
$421$			33.6725i			1.64110i	0.571575	+	0.820550i	$0.306332\pi$
$421$			33.6725i			1.64110i	−0.571575	+	0.820550i	$0.693668\pi$
$422$	−4.60457	−	1.90728i	−0.224147	−	0.0928448i
$423$	38.3271	+	38.3271i	1.86353	+	1.86353i
$424$	4.67562			0.227068
$425$		0			0
$426$	−8.95025			−0.433641
$427$	27.9400	+	27.9400i	1.35211	+	1.35211i
$428$	24.9021	+	10.3148i	1.20369	+	0.498585i
$429$		−	36.3192i		−	1.75351i
$430$		0			0
$431$	−6.23658	−	15.0564i	−0.300405	−	0.725243i	−0.999943	−	0.0106472i	$-0.996611\pi$
$431$	−6.23658	−	15.0564i	−0.300405	−	0.725243i	0.699538	−	0.714595i	$-0.253389\pi$
$432$	3.89036	+	9.39215i	0.187175	+	0.451880i
$433$	−24.7450	+	24.7450i	−1.18917	+	1.18917i	−0.211871	+	0.977298i	$0.567956\pi$
$433$	−24.7450	+	24.7450i	−1.18917	+	1.18917i	−0.977298	+	0.211871i	$0.932044\pi$
$434$	9.45122	+	9.45122i	0.453673	+	0.453673i
$435$		0			0
$436$	−1.94653	−	4.69934i	−0.0932219	−	0.225057i
$437$	−0.239090	+	0.577215i	−0.0114372	+	0.0276119i
$438$	−14.8815			−0.711066
$439$	−8.52530	+	20.5819i	−0.406891	+	0.982321i	0.579060	+	0.815285i	$0.303420\pi$
$439$	−8.52530	+	20.5819i	−0.406891	+	0.982321i	−0.985951	+	0.167036i	$0.946580\pi$
$440$		0			0
$441$	−22.2714			−1.06054
$442$	−2.84784	+	13.0085i	−0.135458	+	0.618750i
$443$			8.79907i			0.418056i	0.977910	+	0.209028i	$0.0670300\pi$
$443$			8.79907i			0.418056i	−0.977910	+	0.209028i	$0.932970\pi$
$444$	−33.5171	+	33.5171i	−1.59065	+	1.59065i
$445$		0			0
$446$			9.41830i			0.445970i
$447$	27.0554	−	65.3175i	1.27968	−	3.08941i
$448$	7.37988	−	3.05685i	0.348666	−	0.144422i
$449$	8.19189	−	3.39319i	0.386599	−	0.160135i	−0.180914	−	0.983499i	$-0.557906\pi$
$449$	8.19189	−	3.39319i	0.386599	−	0.160135i	0.567513	+	0.823364i	$0.307906\pi$
$450$		0			0
$451$	−4.19771	−	4.19771i	−0.197662	−	0.197662i
$452$	−1.56655	−	3.78200i	−0.0736845	−	0.177890i
$453$	−0.556098	+	0.230343i	−0.0261278	+	0.0108225i
$454$	5.55733	+	2.30192i	0.260819	+	0.108035i
$455$		0			0
$456$	3.84248	−	9.27656i	0.179941	−	0.434415i
$457$	−13.0643	−	13.0643i	−0.611120	−	0.611120i	0.332118	−	0.943238i	$-0.392237\pi$
$457$	−13.0643	−	13.0643i	−0.611120	−	0.611120i	−0.943238	+	0.332118i	$0.892237\pi$
$458$		−	16.1770i		−	0.755902i
$459$	−25.0363	+	35.9575i	−1.16859	+	1.67835i
$460$		0			0
$461$	17.3736	−	17.3736i	0.809169	−	0.809169i	−0.175339	−	0.984508i	$-0.556102\pi$
$461$	17.3736	−	17.3736i	0.809169	−	0.809169i	0.984508	+	0.175339i	$0.0561022\pi$
$462$	−18.7863	−	7.78156i	−0.874020	−	0.362031i
$463$	9.90931			0.460525			0.230262	−	0.973129i	$-0.426042\pi$
$463$	9.90931			0.460525			0.230262	+	0.973129i	$0.426042\pi$
$464$	−0.392737	−	0.162677i	−0.0182324	−	0.00755209i
$465$		0			0
$466$	15.1675	−	6.28257i	0.702619	−	0.291034i
$467$	20.7918	−	20.7918i	0.962131	−	0.962131i	−0.0371777	−	0.999309i	$-0.511837\pi$
$467$	20.7918	−	20.7918i	0.962131	−	0.962131i	0.999309	+	0.0371777i	$0.0118367\pi$
$468$	28.3989	−	28.3989i	1.31274	−	1.31274i
$469$	12.5850	−	5.21287i	0.581121	−	0.240708i
$470$		0			0
$471$	−33.6888	−	13.9543i	−1.55230	−	0.642982i
$472$	−7.77100			−0.357689
$473$	5.46269	+	2.26272i	0.251175	+	0.104040i
$474$	−11.7439	+	11.7439i	−0.539417	+	0.539417i
$475$		0			0
$476$	−15.7578	−	10.9718i	−0.722259	−	0.502890i
$477$		−	11.7301i		−	0.537083i
$478$	3.12095	+	3.12095i	0.142749	+	0.142749i
$479$	10.9449	−	26.4232i	0.500083	−	1.20731i	−0.449354	−	0.893354i	$-0.648346\pi$
$479$	10.9449	−	26.4232i	0.500083	−	1.20731i	0.949438	−	0.313955i	$-0.101654\pi$
$480$		0			0
$481$	42.6886	+	17.6822i	1.94643	+	0.806239i
$482$	−9.19799	+	3.80993i	−0.418957	+	0.173538i
$483$	1.87298	+	4.52176i	0.0852234	+	0.205747i
$484$	−3.58503	−	3.58503i	−0.162956	−	0.162956i
$485$		0			0
$486$	−6.25239	+	2.58982i	−0.283614	+	0.117477i
$487$	0.570849	−	0.236454i	0.0258677	−	0.0107147i	−0.369712	−	0.929146i	$-0.620544\pi$
$487$	0.570849	−	0.236454i	0.0258677	−	0.0107147i	0.395580	+	0.918432i	$0.370544\pi$
$488$	−12.0369	+	29.0597i	−0.544886	+	1.31547i
$489$		−	16.4352i		−	0.743224i
$490$		0			0
$491$	18.0077	−	18.0077i	0.812675	−	0.812675i	−0.172359	−	0.985034i	$-0.555139\pi$
$491$	18.0077	−	18.0077i	0.812675	−	0.812675i	0.985034	+	0.172359i	$0.0551390\pi$
$492$		−	9.61515i		−	0.433485i
$493$	−0.322919	−	1.80346i	−0.0145435	−	0.0812239i
$494$	−4.09827			−0.184390
$495$		0			0
$496$	2.02389	−	4.88611i	0.0908755	−	0.219393i
$497$	−12.5802			−0.564301
$498$	0.200226	−	0.483388i	0.00897234	−	0.0216611i
$499$	−13.9527	−	33.6849i	−0.624611	−	1.50794i	−0.846234	−	0.532811i	$-0.821136\pi$
$499$	−13.9527	−	33.6849i	−0.624611	−	1.50794i	0.221624	−	0.975132i	$-0.428864\pi$
$500$		0			0
$501$	25.2009	+	25.2009i	1.12589	+	1.12589i
$502$	1.90053	−	1.90053i	0.0848249	−	0.0848249i
$503$	−11.5525	−	27.8902i	−0.515100	−	1.24356i	−0.940881	−	0.338736i	$-0.890001\pi$
$503$	−11.5525	−	27.8902i	−0.515100	−	1.24356i	0.425781	−	0.904826i	$-0.359999\pi$
$504$	−20.5510	−	49.6146i	−0.915416	−	2.21001i
$505$		0			0
$506$			1.00719i			0.0447751i
$507$	−16.0456	−	6.64632i	−0.712612	−	0.295174i
$508$	5.56721	+	5.56721i	0.247005	+	0.247005i
$509$	40.1857			1.78120			0.890600	−	0.454787i	$-0.150285\pi$
$509$	40.1857			1.78120			0.890600	+	0.454787i	$0.150285\pi$
$510$		0			0
$511$	−20.9171			−0.925316
$512$	−7.44682	−	7.44682i	−0.329106	−	0.329106i
$513$	−12.4580	−	5.16026i	−0.550033	−	0.227831i
$514$			18.3606i			0.809852i
$515$		0			0
$516$	3.66488	+	8.84780i	0.161337	+	0.389503i
$517$	8.78783	+	21.2157i	0.386488	+	0.933065i
$518$	18.2925	−	18.2925i	0.803725	−	0.803725i
$519$	23.9770	+	23.9770i	1.05247	+	1.05247i
$520$		0			0
$521$	−13.5302	−	32.6647i	−0.592767	−	1.43107i	−0.880820	−	0.473451i	$-0.843008\pi$
$521$	−13.5302	−	32.6647i	−0.592767	−	1.43107i	0.288053	−	0.957614i	$-0.406992\pi$
$522$	0.821064	−	1.98222i	0.0359370	−	0.0867596i
$523$	24.5035			1.07146			0.535732	−	0.844388i	$-0.320036\pi$
$523$	24.5035			1.07146			0.535732	+	0.844388i	$0.320036\pi$
$524$	5.50173	−	13.2824i	0.240344	−	0.580243i
$525$		0			0
$526$	−10.9496			−0.477424
$527$	22.4372	−	4.01749i	0.977379	−	0.175005i
$528$			8.04585i			0.350150i
$529$	−16.0920	+	16.0920i	−0.699654	+	0.699654i
$530$		0			0
$531$			19.4957i			0.846041i
$532$	2.26140	−	5.45951i	0.0980443	−	0.236700i
$533$	−8.65939	+	3.58684i	−0.375080	+	0.155363i
$534$	28.3465	−	11.7415i	1.22667	−	0.508105i
$535$		0			0
$536$	7.66756	+	7.66756i	0.331188	+	0.331188i
$537$	24.7981	+	59.8678i	1.07011	+	2.58349i
$538$	−12.9626	+	5.36930i	−0.558859	+	0.231487i
$539$	−8.71734	−	3.61084i	−0.375483	−	0.155530i
$540$		0			0
$541$	9.77786	−	23.6058i	0.420383	−	1.01489i	−0.561852	−	0.827238i	$-0.689911\pi$
$541$	9.77786	−	23.6058i	0.420383	−	1.01489i	0.982235	−	0.187657i	$-0.0600892\pi$
$542$	−3.04826	−	3.04826i	−0.130934	−	0.130934i
$543$		−	69.6778i		−	2.99016i
$544$	5.16891	−	23.6108i	0.221615	−	1.01230i
$545$		0			0
$546$	−22.7016	+	22.7016i	−0.971539	+	0.971539i
$547$	−10.8664	−	4.50103i	−0.464616	−	0.192450i	0.138080	−	0.990421i	$-0.455907\pi$
$547$	−10.8664	−	4.50103i	−0.464616	−	0.192450i	−0.602696	+	0.797971i	$0.705907\pi$
$548$	−4.43384			−0.189404
$549$	72.9042	+	30.1979i	3.11148	+	1.28882i
$550$		0			0
$551$	0.520936	−	0.215779i	0.0221926	−	0.00919248i
$552$	−2.75494	+	2.75494i	−0.117258	+	0.117258i
$553$	−16.5070	+	16.5070i	−0.701947	+	0.701947i
$554$	0.0851647	−	0.0352764i	0.00361830	−	0.00149875i
$555$		0			0
$556$	−8.93065	−	3.69919i	−0.378744	−	0.156881i
$557$	35.6812			1.51186			0.755931	−	0.654651i	$-0.227184\pi$
$557$	35.6812			1.51186			0.755931	+	0.654651i	$0.227184\pi$
$558$	24.6612	+	10.2150i	1.04399	+	0.432436i
$559$	6.60117	−	6.60117i	0.279200	−	0.279200i
$560$		0			0
$561$	−29.1971	+	18.7094i	−1.23270	+	0.789910i
$562$			1.36392i			0.0575335i
$563$	21.3003	+	21.3003i	0.897702	+	0.897702i	0.995233	−	0.0975306i	$-0.0310944\pi$
$563$	21.3003	+	21.3003i	0.897702	+	0.897702i	−0.0975306	+	0.995233i	$0.531094\pi$
$564$	−14.2335	+	34.3626i	−0.599337	+	1.44693i
$565$		0			0
$566$	−19.7813	−	8.19368i	−0.831470	−	0.344406i
$567$	−39.7510	+	16.4654i	−1.66939	+	0.691482i
$568$	−3.83233	−	9.25206i	−0.160801	−	0.388208i
$569$	17.2524	+	17.2524i	0.723257	+	0.723257i	0.969267	−	0.246010i	$-0.0791197\pi$
$569$	17.2524	+	17.2524i	0.723257	+	0.723257i	−0.246010	+	0.969267i	$0.579120\pi$
$570$		0			0
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.918024	−	0.396526i	$-0.870216\pi$
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.368755	+	0.929527i	$0.620216\pi$
$572$	15.7200	−	6.51144i	0.657287	−	0.272257i
$573$	4.12058	−	9.94795i	0.172140	−	0.415582i
$574$			5.24762i			0.219032i
$575$		0			0
$576$	11.2801	−	11.2801i	0.470006	−	0.470006i
$577$		−	18.0611i		−	0.751895i	−0.926641	−	0.375947i	$-0.877317\pi$
$577$		−	18.0611i		−	0.751895i	0.926641	−	0.375947i	$-0.122683\pi$
$578$	11.9246	−	4.41176i	0.495998	−	0.183505i
$579$	37.8051			1.57113
$580$		0			0
$581$	0.281432	−	0.679438i	0.0116758	−	0.0281878i
$582$	34.0550			1.41163
$583$	1.90178	−	4.59131i	0.0787637	−	0.190152i
$584$	−6.37198	−	15.3833i	−0.263675	−	0.636567i
$585$		0			0
$586$	−0.748897	−	0.748897i	−0.0309366	−	0.0309366i
$587$	29.5785	−	29.5785i	1.22084	−	1.22084i	0.253500	−	0.967335i	$-0.418418\pi$
$587$	29.5785	−	29.5785i	1.22084	−	1.22084i	0.967335	−	0.253500i	$-0.0815817\pi$
$588$	−5.84840	−	14.1193i	−0.241184	−	0.582270i
$589$	2.68454	+	6.48105i	0.110614	+	0.267047i
$590$		0			0
$591$		−	52.2008i		−	2.14725i
$592$	−9.45688	−	3.91717i	−0.388675	−	0.160995i
$593$	−14.6130	−	14.6130i	−0.600085	−	0.600085i	0.340250	−	0.940335i	$-0.389488\pi$
$593$	−14.6130	−	14.6130i	−0.600085	−	0.600085i	−0.940335	+	0.340250i	$0.889488\pi$
$594$	−21.7381			−0.891925
$595$		0			0
$596$	33.1219			1.35673
$597$	25.1747	+	25.1747i	1.03033	+	1.03033i
$598$	1.46917	+	0.608550i	0.0600788	+	0.0248854i
$599$			9.21817i			0.376644i	0.982107	+	0.188322i	$0.0603049\pi$
$599$			9.21817i			0.376644i	−0.982107	+	0.188322i	$0.939695\pi$
$600$		0			0
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	0.910725	−	0.413013i	$-0.135524\pi$
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	−0.936024	+	0.351936i	$0.885524\pi$
$602$	−2.00017	−	4.82883i	−0.0815207	−	0.196808i
$603$	19.2362	−	19.2362i	0.783357	−	0.783357i
$604$	−0.199399	−	0.199399i	−0.00811342	−	0.00811342i
$605$		0			0
$606$	−0.250141	−	0.603894i	−0.0101613	−	0.0245315i
$607$	−9.57311	+	23.1115i	−0.388560	+	0.938068i	0.601685	+	0.798733i	$0.294496\pi$
$607$	−9.57311	+	23.1115i	−0.388560	+	0.938068i	−0.990245	+	0.139334i	$0.955504\pi$
$608$	7.43849			0.301671
$609$	1.69036	−	4.08089i	0.0684968	−	0.165366i
$610$		0			0
$611$	36.2566			1.46678
$612$	−37.4593	−	8.20067i	−1.51420	−	0.331492i
$613$		−	4.83538i		−	0.195299i	−0.995221	−	0.0976495i	$-0.968868\pi$
$613$		−	4.83538i		−	0.195299i	0.995221	−	0.0976495i	$-0.0311324\pi$
$614$	−11.4954	+	11.4954i	−0.463917	+	0.463917i
$615$		0			0
$616$		−	22.7517i		−	0.916694i
$617$	−6.43422	+	15.5336i	−0.259032	+	0.625358i	−0.998875	−	0.0474212i	$-0.984900\pi$
$617$	−6.43422	+	15.5336i	−0.259032	+	0.625358i	0.739843	+	0.672779i	$0.234900\pi$
$618$	−29.9259	+	12.3957i	−1.20380	+	0.498629i
$619$	−11.7540	+	4.86865i	−0.472431	+	0.195687i	−0.606179	−	0.795328i	$-0.707299\pi$
$619$	−11.7540	+	4.86865i	−0.472431	+	0.195687i	0.133748	+	0.991015i	$0.457299\pi$
$620$		0			0
$621$	3.69975	+	3.69975i	0.148466	+	0.148466i
$622$	−2.47605	−	5.97771i	−0.0992804	−	0.239684i
$623$	39.8431	−	16.5036i	1.59628	−	0.661201i
$624$	11.7363	+	4.86134i	0.469829	+	0.194609i
$625$		0			0
$626$	−2.94287	+	7.10471i	−0.117621	+	0.283961i
$627$	−7.54638	−	7.54638i	−0.301373	−	0.301373i
$628$		−	17.0833i		−	0.681697i
$629$	−7.77569	−	43.4263i	−0.310037	−	1.73152i
$630$		0			0
$631$	−2.99812	+	2.99812i	−0.119353	+	0.119353i	−0.764261	−	0.644907i	$-0.776896\pi$
$631$	−2.99812	+	2.99812i	−0.119353	+	0.119353i	0.644907	+	0.764261i	$0.276896\pi$
$632$	−17.1685	−	7.11142i	−0.682925	−	0.282877i
$633$	−20.4914			−0.814459
$634$	−0.779196	−	0.322754i	−0.0309458	−	0.0128182i
$635$		0			0
$636$	7.43644	−	3.08028i	0.294874	−	0.122141i
$637$	−10.5341	+	10.5341i	−0.417377	+	0.417377i
$638$	0.642752	−	0.642752i	0.0254468	−	0.0254468i
$639$	−23.2113	+	9.61444i	−0.918226	+	0.380342i
$640$		0			0
$641$	19.6050	+	8.12065i	0.774350	+	0.320746i	0.734633	−	0.678465i	$-0.237354\pi$
$641$	19.6050	+	8.12065i	0.774350	+	0.320746i	0.0397171	+	0.999211i	$0.487354\pi$
$642$	−43.0300			−1.69826
$643$	7.54502	+	3.12525i	0.297547	+	0.123248i	0.526462	−	0.850198i	$-0.323518\pi$
$643$	7.54502	+	3.12525i	0.297547	+	0.123248i	−0.228916	+	0.973446i	$0.573518\pi$
$644$	−1.62136	+	1.62136i	−0.0638905	+	0.0638905i
$645$		0			0
$646$	2.11117	+	3.29462i	0.0830630	+	0.129625i
$647$			23.4331i			0.921249i	0.887595	+	0.460624i	$0.152374\pi$
$647$			23.4331i			0.921249i	−0.887595	+	0.460624i	$0.847626\pi$
$648$	−24.2188	−	24.2188i	−0.951404	−	0.951404i
$649$	−3.16081	+	7.63088i	−0.124073	+	0.299538i
$650$		0			0
$651$	50.7710	+	21.0300i	1.98987	+	0.824232i
$652$	7.11362	−	2.94656i	0.278591	−	0.115396i
$653$	−6.43188	−	15.5279i	−0.251699	−	0.607655i	0.746643	−	0.665225i	$-0.231665\pi$
$653$	−6.43188	−	15.5279i	−0.251699	−	0.607655i	−0.998341	+	0.0575706i	$0.981665\pi$
$654$	5.74192	+	5.74192i	0.224527	+	0.224527i
$655$		0			0
$656$	1.91833	−	0.794598i	0.0748981	−	0.0310238i
$657$	−38.5933	+	15.9859i	−1.50567	+	0.623668i
$658$	7.76814	−	18.7539i	0.302833	−	0.731105i
$659$		−	14.0972i		−	0.549150i	−0.961566	−	0.274575i	$-0.911463\pi$
$659$		−	14.0972i		−	0.549150i	0.961566	−	0.274575i	$-0.0885371\pi$
$660$		0			0
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	−0.835408	−	0.549630i	$-0.814769\pi$
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	0.549630	+	0.835408i	$0.314769\pi$
$662$			25.6235i			0.995886i
$663$	9.64991	+	53.8936i	0.374771	+	2.09305i
$664$	0.585422			0.0227188
$665$		0			0
$666$	19.7707	−	47.7308i	0.766101	−	1.84953i
$667$	−0.218788			−0.00847151
$668$	−6.38959	+	15.4258i	−0.247220	+	0.596843i
$669$	14.8187	+	35.7755i	0.572923	+	1.38316i
$670$		0			0
$671$	23.6398	+	23.6398i	0.912603	+	0.912603i
$672$	41.2041	−	41.2041i	1.58948	−	1.58948i
$673$	7.58646	+	18.3153i	0.292437	+	0.706005i	1.00000		0.000645530i	$-0.000205479\pi$
$673$	7.58646	+	18.3153i	0.292437	+	0.706005i	−0.707563	+	0.706650i	$0.750205\pi$
$674$	3.93438	+	9.49842i	0.151546	+	0.365866i
$675$		0			0
$676$		−	8.13660i		−	0.312946i
$677$	3.09124	+	1.28043i	0.118806	+	0.0492111i	0.441295	−	0.897362i	$-0.354519\pi$
$677$	3.09124	+	1.28043i	0.118806	+	0.0492111i	−0.322489	+	0.946573i	$0.604519\pi$
$678$	4.62105	+	4.62105i	0.177471	+	0.177471i
$679$	47.8669			1.83696
$680$		0			0
$681$	24.7314			0.947709
$682$	7.99658	+	7.99658i	0.306205	+	0.306205i
$683$	−46.4553	−	19.2424i	−1.77756	−	0.736290i	−0.993260	−	0.115910i	$-0.963022\pi$
$683$	−46.4553	−	19.2424i	−1.77756	−	0.736290i	−0.784302	−	0.620380i	$-0.786978\pi$
$684$		−	11.8014i		−	0.451239i
$685$		0			0
$686$	−3.28470	−	7.92996i	−0.125410	−	0.302767i
$687$	−25.4528	−	61.4484i	−0.971084	−	2.34440i
$688$	−1.46237	+	1.46237i	−0.0557522	+	0.0557522i
$689$	−5.54818	−	5.54818i	−0.211369	−	0.211369i
$690$		0			0
$691$	−14.8926	−	35.9539i	−0.566540	−	1.36775i	−0.904454	−	0.426572i	$-0.859721\pi$
$691$	−14.8926	−	35.9539i	−0.566540	−	1.36775i	0.337913	−	0.941177i	$-0.390279\pi$
$692$	−6.07926	+	14.6766i	−0.231099	+	0.557922i
$693$	−57.0790			−2.16825
$694$	5.40333	−	13.0448i	0.205107	−	0.495173i
$695$		0			0
$696$	3.51620			0.133281
$697$	7.34424	+	5.11360i	0.278183	+	0.193692i
$698$			5.27270i			0.199575i
$699$	47.7287	−	47.7287i	1.80527	−	1.80527i
$700$		0			0
$701$			37.5419i			1.41794i	0.705239	+	0.708969i	$0.250840\pi$
$701$			37.5419i			1.41794i	−0.705239	+	0.708969i	$0.749160\pi$
$702$	−13.1343	+	31.7089i	−0.495721	+	1.19678i
$703$	12.5438	−	5.19582i	0.473099	−	0.195964i
$704$	6.24404	−	2.58637i	0.235331	−	0.0974773i
$705$		0			0
$706$	−4.55227	−	4.55227i	−0.171327	−	0.171327i
$707$	−0.351592	−	0.848818i	−0.0132230	−	0.0319231i
$708$	−12.3596	+	5.11950i	−0.464501	+	0.192403i
$709$	−12.7076	−	5.26367i	−0.477245	−	0.197681i	0.131076	−	0.991372i	$-0.458157\pi$
$709$	−12.7076	−	5.26367i	−0.477245	−	0.197681i	−0.608321	+	0.793691i	$0.708157\pi$
$710$		0			0
$711$	−17.8409	+	43.0718i	−0.669087	+	1.61532i
$712$	24.2749	+	24.2749i	0.909741	+	0.909741i
$713$		−	2.72198i		−	0.101939i
$714$	29.9443	+	6.55547i	1.12064	+	0.245332i
$715$		0			0
$716$	−21.4667	+	21.4667i	−0.802246	+	0.802246i
$717$	16.7654	+	6.94446i	0.626116	+	0.259346i
$718$	−6.86660			−0.256259
$719$	0.488717	+	0.202433i	0.0182261	+	0.00754949i	0.391778	−	0.920060i	$-0.371860\pi$
$719$	0.488717	+	0.202433i	0.0182261	+	0.00754949i	−0.373552	+	0.927609i	$0.621860\pi$
$720$		0			0
$721$	−42.0631	+	17.4231i	−1.56651	+	0.648870i
$722$	9.19671	−	9.19671i	0.342266	−	0.342266i
$723$	−28.9441	+	28.9441i	−1.07644	+	1.07644i
$724$	30.1586	−	12.4921i	1.12084	−	0.464265i
$725$		0			0
$726$	7.47778	+	3.09740i	0.277527	+	0.114955i
$727$	−26.7632			−0.992591			−0.496296	−	0.868154i	$-0.665307\pi$
$727$	−26.7632			−0.992591			−0.496296	+	0.868154i	$0.665307\pi$
$728$	−33.1875	−	13.7467i	−1.23001	−	0.509487i
$729$	8.55986	−	8.55986i	0.317032	−	0.317032i
$730$		0			0
$731$	−8.70721	−	1.90620i	−0.322048	−	0.0705033i
$732$			54.1486i			2.00139i
$733$	12.2673	+	12.2673i	0.453105	+	0.453105i	0.896384	−	0.443279i	$-0.146185\pi$
$733$	12.2673	+	12.2673i	0.453105	+	0.453105i	−0.443279	+	0.896384i	$0.646185\pi$
$734$	−1.95086	+	4.70978i	−0.0720074	+	0.173841i
$735$		0			0
$736$	−2.66658	−	1.10454i	−0.0982916	−	0.0407137i
$737$	10.6480	−	4.41056i	0.392225	−	0.162465i
$738$	4.01050	+	9.68219i	0.147628	+	0.356407i
$739$	−21.3876	−	21.3876i	−0.786757	−	0.786757i	0.194204	−	0.980961i	$-0.437788\pi$
$739$	−21.3876	−	21.3876i	−0.786757	−	0.786757i	−0.980961	+	0.194204i	$0.937788\pi$
$740$		0			0
$741$	−15.5673	+	6.44819i	−0.571880	+	0.236880i
$742$	−4.05856	+	1.68111i	−0.148994	+	0.0617155i
$743$	2.74796	−	6.63416i	0.100813	−	0.243384i	−0.865424	−	0.501041i	$-0.832951\pi$
$743$	2.74796	−	6.63416i	0.100813	−	0.243384i	0.966236	+	0.257657i	$0.0829506\pi$
$744$			43.7457i			1.60379i
$745$		0			0
$746$	−5.53430	+	5.53430i	−0.202625	+	0.202625i
$747$		−	1.46869i		−	0.0537366i
$748$	−13.3325	−	9.28309i	−0.487486	−	0.339423i
$749$	−60.4819			−2.20996
$750$		0			0
$751$	11.9767	−	28.9144i	0.437037	−	1.05510i	−0.539930	−	0.841710i	$-0.681549\pi$
$751$	11.9767	−	28.9144i	0.437037	−	1.05510i	0.976967	−	0.213390i	$-0.0684505\pi$
$752$	−8.03197			−0.292896
$753$	4.22890	−	10.2095i	0.154110	−	0.372054i
$754$	−0.549215	−	1.32592i	−0.0200012	−	0.0482873i
$755$		0			0
$756$	−34.9936	−	34.9936i	−1.27271	−	1.27271i
$757$	7.61956	−	7.61956i	0.276938	−	0.276938i	−0.554948	−	0.831885i	$-0.687262\pi$
$757$	7.61956	−	7.61956i	0.276938	−	0.276938i	0.831885	+	0.554948i	$0.187262\pi$
$758$	7.25323	+	17.5108i	0.263449	+	0.636022i
$759$	1.58471	+	3.82582i	0.0575212	+	0.138868i
$760$		0			0
$761$			33.1409i			1.20136i	0.799491	+	0.600678i	$0.205102\pi$
$761$			33.1409i			1.20136i	−0.799491	+	0.600678i	$0.794898\pi$
$762$	−11.6123	−	4.80998i	−0.420670	−	0.174247i
$763$	8.07068	+	8.07068i	0.292178	+	0.292178i
$764$	5.04452			0.182504
$765$		0			0
$766$	5.75182			0.207822
$767$	9.22123	+	9.22123i	0.332959	+	0.332959i
$768$	35.0247	+	14.5077i	1.26385	+	0.523502i
$769$		−	11.4864i		−	0.414210i	−0.978319	−	0.207105i	$-0.933596\pi$
$769$		−	11.4864i		−	0.414210i	0.978319	−	0.207105i	$-0.0664042\pi$
$770$		0			0
$771$	28.8885	+	69.7429i	1.04039	+	2.51173i
$772$	6.77785	+	16.3632i	0.243940	+	0.588924i
$773$	−2.26913	+	2.26913i	−0.0816149	+	0.0816149i	−0.746736	−	0.665121i	$-0.768380\pi$
$773$	−2.26913	+	2.26913i	−0.0816149	+	0.0816149i	0.665121	+	0.746736i	$0.268380\pi$
$774$	−7.38087	−	7.38087i	−0.265300	−	0.265300i
$775$		0			0
$776$	14.5817	+	35.2034i	0.523454	+	1.26373i
$777$	40.7028	−	98.2653i	1.46021	−	3.52525i
$778$	11.8454			0.424678
$779$	−1.05397	+	2.54451i	−0.0377625	+	0.0911667i
$780$		0			0
$781$	−10.6440			−0.380873
$782$	−0.267608	−	1.49456i	−0.00956963	−	0.0534452i
$783$		−	4.72208i		−	0.168754i
$784$	2.33364	−	2.33364i	0.0833443	−	0.0833443i
$785$		0			0
$786$			22.9515i			0.818651i
$787$	−1.28976	+	3.11375i	−0.0459748	+	0.110993i	−0.945199	−	0.326496i	$-0.894132\pi$
$787$	−1.28976	+	3.11375i	−0.0459748	+	0.110993i	0.899224	+	0.437489i	$0.144132\pi$
$788$	22.5940	−	9.35875i	0.804879	−	0.333392i
$789$	−41.5920	+	17.2280i	−1.48071	+	0.613332i
$790$		0			0
$791$	6.49523	+	6.49523i	0.230944	+	0.230944i
$792$	−17.3880	−	41.9784i	−0.617857	−	1.49164i
$793$	48.7661	−	20.1996i	1.73174	−	0.717308i
$794$	20.1518	+	8.34716i	0.715161	+	0.296230i
$795$		0			0
$796$	−6.38293	+	15.4097i	−0.226237	+	0.546184i
$797$	−15.0966	−	15.0966i	−0.534747	−	0.534747i	0.387234	−	0.921981i	$-0.373431\pi$
$797$	−15.0966	−	15.0966i	−0.534747	−	0.534747i	−0.921981	+	0.387234i	$0.873431\pi$
$798$			9.43385i			0.333955i
$799$	−18.6771	−	29.1468i	−0.660748	−	1.03114i
$800$		0			0
$801$	60.9002	−	60.9002i	2.15180	−	2.15180i
$802$	11.3224	+	4.68987i	0.399806	+	0.165605i
$803$	−17.6977			−0.624538
$804$	17.2464	+	7.14369i	0.608233	+	0.251939i
$805$		0			0
$806$	16.4960	−	6.83288i	0.581048	−	0.240678i
$807$	−40.7907	+	40.7907i	−1.43590	+	1.43590i
$808$	0.517153	−	0.517153i	0.0181934	−	0.0181934i
$809$	2.52190	−	1.04460i	0.0886652	−	0.0367263i	−0.337910	−	0.941178i	$-0.609720\pi$
$809$	2.52190	−	1.04460i	0.0886652	−	0.0367263i	0.426575	+	0.904452i	$0.359720\pi$
$810$		0			0
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.316614	−	0.948554i	$-0.602546\pi$
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.894609	+	0.446849i	$0.852546\pi$
$812$	2.06938			0.0726211
$813$	−16.3749	−	6.78272i	−0.574294	−	0.237880i
$814$	15.4771	−	15.4771i	0.542471	−	0.542471i
$815$		0			0
$816$	−2.13776	−	11.9391i	−0.0748365	−	0.417953i
$817$		−	2.74317i		−	0.0959715i
$818$	17.9796	+	17.9796i	0.628641	+	0.628641i
$819$	−34.4874	+	83.2600i	−1.20509	+	2.90934i
$820$		0			0
$821$	−39.0148	−	16.1605i	−1.36163	−	0.564004i	−0.422121	−	0.906540i	$-0.638714\pi$
$821$	−39.0148	−	16.1605i	−1.36163	−	0.564004i	−0.939505	+	0.342536i	$0.888714\pi$
$822$	6.53952	−	2.70876i	0.228092	−	0.0944788i
$823$	−7.94473	−	19.1803i	−0.276936	−	0.668582i	0.722812	−	0.691045i	$-0.242849\pi$
$823$	−7.94473	−	19.1803i	−0.276936	−	0.668582i	−0.999748	+	0.0224627i	$0.992849\pi$
$824$	−25.6275	−	25.6275i	−0.892775	−	0.892775i
$825$		0			0
$826$	6.74543	−	2.79405i	0.234704	−	0.0972174i
$827$	10.6314	−	4.40367i	0.369690	−	0.153131i	−0.190101	−	0.981765i	$-0.560881\pi$
$827$	10.6314	−	4.40367i	0.369690	−	0.153131i	0.559791	+	0.828634i	$0.310881\pi$
$828$	−1.75238	+	4.23063i	−0.0608996	+	0.147025i
$829$			11.7508i			0.408121i	0.978958	+	0.204060i	$0.0654139\pi$
$829$			11.7508i			0.408121i	−0.978958	+	0.204060i	$0.934586\pi$
$830$		0			0
$831$	0.267995	−	0.267995i	0.00929664	−	0.00929664i
$832$		−	10.6708i		−	0.369942i
$833$	13.8949	+	3.04191i	0.481431	+	0.105396i
$834$	15.4318			0.534361
$835$		0			0
$836$	1.91335	−	4.61924i	0.0661747	−	0.159760i
$837$	58.7483			2.03064
$838$	−0.255571	+	0.617003i	−0.00882855	+	0.0213140i
$839$	14.0060	+	33.8134i	0.483540	+	1.16737i	0.957917	+	0.287046i	$0.0926733\pi$
$839$	14.0060	+	33.8134i	0.483540	+	1.16737i	−0.474377	+	0.880322i	$0.657327\pi$
$840$		0			0
$841$	−20.3665	−	20.3665i	−0.702292	−	0.702292i
$842$	17.8079	−	17.8079i	0.613701	−	0.613701i
$843$	2.14598	+	5.18086i	0.0739116	+	0.178438i
$844$	−3.67377	−	8.86927i	−0.126457	−	0.305293i
$845$		0			0
$846$		−	40.5390i		−	1.39376i
$847$	10.5106	+	4.35362i	0.361148	+	0.149592i
$848$	1.22910	+	1.22910i	0.0422074	+	0.0422074i
$849$	−88.0312			−3.02122
$850$		0			0
$851$	−5.26829			−0.180595
$852$	−12.1904	−	12.1904i	−0.417637	−	0.417637i
$853$	−35.1787	−	14.5715i	−1.20450	−	0.498918i	−0.312046	−	0.950067i	$-0.601014\pi$
$853$	−35.1787	−	14.5715i	−1.20450	−	0.498918i	−0.892449	+	0.451149i	$0.851014\pi$
$854$		−	29.5524i		−	1.01126i
$855$		0			0
$856$	−18.4247	−	44.4811i	−0.629742	−	1.52033i
$857$	−7.74080	−	18.6880i	−0.264421	−	0.638368i	0.734781	−	0.678304i	$-0.237285\pi$
$857$	−7.74080	−	18.6880i	−0.264421	−	0.638368i	−0.999202	+	0.0399356i	$0.987285\pi$
$858$	−19.2076	+	19.2076i	−0.655736	+	0.655736i
$859$	−1.84360	−	1.84360i	−0.0629028	−	0.0629028i	0.674956	−	0.737858i	$-0.264163\pi$
$859$	−1.84360	−	1.84360i	−0.0629028	−	0.0629028i	−0.737858	+	0.674956i	$0.764163\pi$
$860$		0			0
$861$	8.25657	+	19.9331i	0.281383	+	0.679319i
$862$	−4.66443	+	11.2609i	−0.158871	+	0.383548i
$863$	11.2563			0.383169			0.191584	−	0.981476i	$-0.438637\pi$
$863$	11.2563			0.383169			0.191584	+	0.981476i	$0.438637\pi$
$864$	23.8391	−	57.5526i	0.811022	−	1.95798i
$865$		0			0
$866$	26.1730			0.889396
$867$	38.3542	−	35.5202i	1.30258	−	1.20633i
$868$			25.7455i			0.873860i
$869$	−13.9664	+	13.9664i	−0.473777	+	0.473777i
$870$		0			0
$871$		−	18.1970i		−	0.616580i
$872$	−3.47696	+	8.39412i	−0.117745	+	0.284261i
$873$	88.3174	−	36.5822i	2.98909	−	1.23812i
$874$	0.431707	−	0.178819i	0.0146027	−	0.00604864i
$875$		0			0
$876$	−20.2689	−	20.2689i	−0.684824	−	0.684824i
$877$	−2.29651	−	5.54426i	−0.0775476	−	0.187216i	0.880351	−	0.474322i	$-0.157307\pi$
$877$	−2.29651	−	5.54426i	−0.0775476	−	0.187216i	−0.957899	+	0.287106i	$0.907307\pi$
$878$	15.3935	−	6.37620i	0.519506	−	0.215186i
$879$	−4.02300	−	1.66638i	−0.135692	−	0.0562056i
$880$		0			0
$881$	13.1380	−	31.7181i	0.442632	−	1.06861i	−0.532390	−	0.846499i	$-0.678706\pi$
$881$	13.1380	−	31.7181i	0.442632	−	1.06861i	0.975022	−	0.222109i	$-0.0712941\pi$
$882$	11.7784	+	11.7784i	0.396598	+	0.396598i
$883$			11.8244i			0.397921i	0.980007	+	0.198961i	$0.0637566\pi$
$883$			11.8244i			0.397921i	−0.980007	+	0.198961i	$0.936243\pi$
$884$	−21.5966	+	13.8390i	−0.726374	+	0.465456i
$885$		0			0
$886$	4.65343	−	4.65343i	0.156335	−	0.156335i
$887$	−22.3904	−	9.27440i	−0.751796	−	0.311404i	−0.0263216	−	0.999654i	$-0.508379\pi$
$887$	−22.3904	−	9.27440i	−0.751796	−	0.311404i	−0.725474	+	0.688250i	$0.758379\pi$
$888$	84.6680			2.84127
$889$	−16.3220	−	6.76077i	−0.547421	−	0.226749i
$890$		0			0
$891$	−33.6329	+	13.9312i	−1.12675	+	0.466713i
$892$	−12.8279	+	12.8279i	−0.429511	+	0.429511i
$893$	7.53337	−	7.53337i	0.252095	−	0.252095i
$894$	−48.8519	+	20.2351i	−1.63385	+	0.676764i
$895$		0			0
$896$	29.4952	+	12.2173i	0.985367	+	0.408152i
$897$	6.53813			0.218302
$898$	−6.12683	−	2.53782i	−0.204455	−	0.0846880i
$899$	−1.73707	+	1.73707i	−0.0579345	+	0.0579345i
$900$		0			0
$901$	−1.60213	+	7.31828i	−0.0533747	+	0.243807i
$902$			4.43996i			0.147835i
$903$	−15.1953	−	15.1953i	−0.505668	−	0.505668i
$904$	−2.79823	+	6.75553i	−0.0930678	+	0.224686i
$905$		0			0
$906$	0.415914	+	0.172277i	0.0138178	+	0.00572353i
$907$	41.3709	−	17.1364i	1.37370	−	0.569005i	0.430910	−	0.902395i	$-0.358192\pi$
$907$	41.3709	−	17.1364i	1.37370	−	0.569005i	0.942789	+	0.333390i	$0.108192\pi$
$908$	4.43394	+	10.7045i	0.147145	+	0.355240i
$909$	−1.29742	−	1.29742i	−0.0430326	−	0.0430326i
$910$		0			0
$911$	9.19129	−	3.80716i	0.304521	−	0.126137i	−0.225190	−	0.974315i	$-0.572300\pi$
$911$	9.19129	−	3.80716i	0.304521	−	0.126137i	0.529711	+	0.848178i	$0.322300\pi$
$912$	3.44865	−	1.42848i	0.114196	−	0.0473016i
$913$	0.238117	−	0.574865i	0.00788052	−	0.0190253i
$914$			13.8182i			0.457066i
$915$		0			0
$916$	22.0334	−	22.0334i	0.728005	−	0.728005i
$917$			32.2600i			1.06532i
$918$	32.2569	−	5.77575i	1.06464	−	0.190628i
$919$	33.3601			1.10045			0.550224	−	0.835017i	$-0.314542\pi$
$919$	33.3601			1.10045			0.550224	+	0.835017i	$0.314542\pi$
$920$		0			0
$921$	−25.5786	+	61.7522i	−0.842844	+	2.03480i
$922$	−18.3762			−0.605189
$923$	−6.43116	+	15.5262i	−0.211684	+	0.511051i
$924$	−14.9887	−	36.1860i	−0.493094	−	1.19043i
$925$		0			0
$926$	−5.24059	−	5.24059i	−0.172217	−	0.172217i
$927$	−64.2934	+	64.2934i	−2.11167	+	2.11167i
$928$	0.996842	+	2.40659i	0.0327229	+	0.0790001i
$929$	9.52731	+	23.0010i	0.312581	+	0.754637i	0.999608	+	0.0280049i	$0.00891541\pi$
$929$	9.52731	+	23.0010i	0.312581	+	0.754637i	−0.687027	+	0.726632i	$0.741085\pi$
$930$		0			0
$931$			4.37755i			0.143468i
$932$	29.2154	+	12.1014i	0.956982	+	0.396395i
$933$	−18.8106	−	18.8106i	−0.615830	−	0.615830i
$934$	−21.9917			−0.719592
$935$		0			0
$936$	−71.7390			−2.34486
$937$	−22.0943	−	22.0943i	−0.721788	−	0.721788i	0.247181	−	0.968969i	$-0.420496\pi$
$937$	−22.0943	−	22.0943i	−0.721788	−	0.721788i	−0.968969	+	0.247181i	$0.920496\pi$
$938$	−9.41250	−	3.89878i	−0.307329	−	0.127300i
$939$			31.6176i			1.03180i
$940$		0			0
$941$	−0.663467	−	1.60175i	−0.0216284	−	0.0522156i	0.912696	−	0.408638i	$-0.133996\pi$
$941$	−0.663467	−	1.60175i	−0.0216284	−	0.0522156i	−0.934325	+	0.356423i	$0.883996\pi$
$942$	10.4367	+	25.1963i	0.340045	+	0.820940i
$943$	0.755666	−	0.755666i	0.0246079	−	0.0246079i
$944$	−2.04279	−	2.04279i	−0.0664873	−	0.0664873i
$945$		0			0
$946$	−1.69232	−	4.08562i	−0.0550221	−	0.132835i
$947$	−4.15260	+	10.0253i	−0.134941	+	0.325777i	−0.976877	−	0.213800i	$-0.931416\pi$
$947$	−4.15260	+	10.0253i	−0.134941	+	0.325777i	0.841936	+	0.539577i	$0.181416\pi$
$948$	−31.9910			−1.03902
$949$	−10.6930	+	25.8153i	−0.347111	+	0.838000i
$950$		0			0
$951$	−3.46760			−0.112445
$952$	6.04508	+	33.7610i	0.195922	+	1.09420i
$953$			16.9007i			0.547466i	0.961806	+	0.273733i	$0.0882584\pi$
$953$			16.9007i			0.547466i	−0.961806	+	0.273733i	$0.911742\pi$
$954$	−6.20351	+	6.20351i	−0.200846	+	0.200846i
$955$		0			0
$956$			8.50159i			0.274961i
$957$	1.43020	−	3.45280i	0.0462316	−	0.111613i
$958$	−19.7623	+	8.18582i	−0.638491	+	0.264472i
$959$	9.19177	−	3.80736i	0.296818	−	0.122946i
$960$		0			0
$961$	0.309144	+	0.309144i	0.00997239	+	0.00997239i
$962$	−13.2248	−	31.9274i	−0.426384	−	1.02938i
$963$	−111.593	+	46.2233i	−3.59603	+	1.48952i
$964$	−17.7171	−	7.33864i	−0.570628	−	0.236362i
$965$		0			0
$966$	1.40083	−	3.38189i	0.0450708	−	0.108811i
$967$	22.0869	+	22.0869i	0.710267	+	0.710267i	0.966591	−	0.256324i	$-0.0825115\pi$
$967$	22.0869	+	22.0869i	0.710267	+	0.710267i	−0.256324	+	0.966591i	$0.582511\pi$
$968$			9.05619i			0.291077i
$969$	13.2030	+	9.19292i	0.424142	+	0.295319i
$970$		0			0
$971$	−12.2957	+	12.2957i	−0.394589	+	0.394589i	−0.876319	−	0.481731i	$-0.840008\pi$
$971$	−12.2957	+	12.2957i	−0.394589	+	0.394589i	0.481731	+	0.876319i	$0.340008\pi$
$972$	−12.0433	−	4.98849i	−0.386288	−	0.160006i
$973$	21.6906			0.695368
$974$	−0.426947	−	0.176847i	−0.0136802	−	0.00566654i
$975$		0			0
$976$	−10.8032	+	4.47485i	−0.345803	+	0.143236i
$977$	6.48656	−	6.48656i	0.207523	−	0.207523i	−0.595691	−	0.803214i	$-0.703122\pi$
$977$	6.48656	−	6.48656i	0.207523	−	0.207523i	0.803214	+	0.595691i	$0.203122\pi$
$978$	−8.69182	+	8.69182i	−0.277934	+	0.277934i
$979$	33.7109	−	13.9635i	1.07740	−	0.446275i
$980$		0			0
$981$	21.0589	+	8.72290i	0.672360	+	0.278501i
$982$	−19.0469			−0.607811
$983$	−34.4578	−	14.2729i	−1.09903	−	0.455235i	−0.241886	−	0.970305i	$-0.577766\pi$
$983$	−34.4578	−	14.2729i	−1.09903	−	0.455235i	−0.857148	+	0.515070i	$0.827766\pi$
$984$	−12.1445	+	12.1445i	−0.387152	+	0.387152i
$985$		0			0
$986$	−0.782993	+	1.12455i	−0.0249356	+	0.0358129i
$987$		−	83.4593i		−	2.65654i
$988$	−5.58194	−	5.58194i	−0.177585	−	0.177585i
$989$	−0.407332	+	0.983386i	−0.0129524	+	0.0312699i
$990$		0			0
$991$	−32.3988	−	13.4200i	−1.02918	−	0.426301i	−0.196765	−	0.980451i	$-0.563044\pi$
$991$	−32.3988	−	13.4200i	−1.02918	−	0.426301i	−0.832417	+	0.554149i	$0.813044\pi$
$992$	−29.9408	+	12.4019i	−0.950621	+	0.393760i
$993$	40.3158	+	97.3310i	1.27938	+	3.08871i
$994$	6.65312	+	6.65312i	0.211024	+	0.211024i
$995$		0			0
$996$	0.931097	−	0.385673i	0.0295029	−	0.0122205i
$997$	−34.5139	+	14.2961i	−1.09307	+	0.452763i	−0.855075	−	0.518505i	$-0.826489\pi$
$997$	−34.5139	+	14.2961i	−1.09307	+	0.452763i	−0.237991	+	0.971267i	$0.576489\pi$
$998$	−10.4355	+	25.1934i	−0.330329	+	0.797484i
$999$		−	113.705i		−	3.59747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.f.399.2		24
5.2	odd	4		425.2.m.b.76.5		24
5.3	odd	4		85.2.l.a.76.2	yes	24
5.4	even	2		425.2.n.c.399.5		24
15.8	even	4		765.2.be.b.586.5		24
17.15	even	8		425.2.n.c.49.5		24
85.7	even	16		7225.2.a.bs.1.4		12
85.23	even	16		1445.2.d.j.866.8		24
85.27	even	16		7225.2.a.bq.1.4		12
85.28	even	16		1445.2.d.j.866.7		24
85.32	odd	8		425.2.m.b.151.5		24
85.49	even	8	inner	425.2.n.f.49.2		24
85.58	even	16		1445.2.a.p.1.9		12
85.78	even	16		1445.2.a.q.1.9		12
85.83	odd	8		85.2.l.a.66.2	✓	24
255.83	even	8		765.2.be.b.406.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	85.83	odd	8
85.2.l.a.76.2	yes	24	5.3	odd	4
425.2.m.b.76.5		24	5.2	odd	4
425.2.m.b.151.5		24	85.32	odd	8
425.2.n.c.49.5		24	17.15	even	8
425.2.n.c.399.5		24	5.4	even	2
425.2.n.f.49.2		24	85.49	even	8	inner
425.2.n.f.399.2		24	1.1	even	1	trivial
765.2.be.b.406.5		24	255.83	even	8
765.2.be.b.586.5		24	15.8	even	4
1445.2.a.p.1.9		12	85.58	even	16
1445.2.a.q.1.9		12	85.78	even	16
1445.2.d.j.866.7		24	85.28	even	16
1445.2.d.j.866.8		24	85.23	even	16
7225.2.a.bq.1.4		12	85.27	even	16
7225.2.a.bs.1.4		12	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)

\(f(q)\)	\(=\)	\(q+(-0.528855 - 0.528855i) q^{2} +(-2.84096 - 1.17676i) q^{3} -1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(1.23707 + 2.98655i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(4.56494 + 4.56494i) q^{9} +O(q^{10})\)	\(q+(-0.528855 - 0.528855i) q^{2} +(-2.84096 - 1.17676i) q^{3} -1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(1.23707 + 2.98655i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(4.56494 + 4.56494i) q^{9} +(1.04667 + 2.52689i) q^{11} +(-1.69527 + 4.09275i) q^{12} +4.31833 q^{13} +(0.925222 - 2.23368i) q^{14} -0.956646 q^{16} +(-2.22453 - 3.47152i) q^{17} -4.82839i q^{18} +(0.897260 - 0.897260i) q^{19} -9.94040i q^{21} +(0.782821 - 1.88990i) q^{22} +(-0.454888 + 0.188421i) q^{23} +(7.31061 - 3.02815i) q^{24} +(-2.28377 - 2.28377i) q^{26} +(-4.06666 - 9.81779i) q^{27} +(4.30250 - 1.78215i) q^{28} +(0.410535 + 0.170049i) q^{29} +(-2.11561 + 5.10754i) q^{31} +(4.14511 + 4.14511i) q^{32} -8.41047i q^{33} +(-0.659477 + 3.01239i) q^{34} +(6.57637 - 6.57637i) q^{36} +(9.88545 + 4.09469i) q^{37} -0.949042 q^{38} +(-12.2682 - 5.08165i) q^{39} +(-2.00526 + 0.830608i) q^{41} +(-5.25703 + 5.25703i) q^{42} +(1.52864 - 1.52864i) q^{43} +(3.64030 - 1.50786i) q^{44} +(0.340217 + 0.140922i) q^{46} +8.39597 q^{47} +(2.71779 + 1.12575i) q^{48} +(-2.43940 + 2.43940i) q^{49} +(2.23464 + 12.4802i) q^{51} -6.22109i q^{52} +(-1.28480 - 1.28480i) q^{53} +(-3.04152 + 7.34287i) q^{54} +(-7.68527 - 3.18334i) q^{56} +(-3.60494 + 1.49321i) q^{57} +(-0.127182 - 0.307045i) q^{58} +(2.13537 + 2.13537i) q^{59} +(11.2928 - 4.67764i) q^{61} +(3.82000 - 1.58230i) q^{62} +(-7.98628 + 19.2806i) q^{63} -2.47104i q^{64} +(-4.44792 + 4.44792i) q^{66} -4.21389i q^{67} +(-5.00116 + 3.20471i) q^{68} +1.51404 q^{69} +(-1.48927 + 3.59542i) q^{71} -16.6127 q^{72} +(-2.47620 + 5.97807i) q^{73} +(-3.06247 - 7.39347i) q^{74} +(-1.29261 - 1.29261i) q^{76} +(-6.25188 + 6.25188i) q^{77} +(3.80064 + 9.17555i) q^{78} +(2.76355 + 6.67180i) q^{79} +13.3100i q^{81} +(1.49977 + 0.621223i) q^{82} +(-0.160866 - 0.160866i) q^{83} -14.3204 q^{84} -1.61686 q^{86} +(-0.966206 - 0.966206i) q^{87} +(-6.50243 - 2.69339i) q^{88} -13.3408i q^{89} +(5.34208 + 12.8969i) q^{91} +(0.271443 + 0.655322i) q^{92} +(12.0207 - 12.0207i) q^{93} +(-4.44025 - 4.44025i) q^{94} +(-6.89827 - 16.6539i) q^{96} +(5.66657 - 13.6803i) q^{97} +2.58018 q^{98} +(-6.75711 + 16.3131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9	\( 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37} + 48 q^{38} - 8 q^{39} + 16 q^{41} + 24 q^{42} + 8 q^{43} - 16 q^{44} + 8 q^{46} + 64 q^{47} + 8 q^{48} - 56 q^{51} - 24 q^{53} + 32 q^{54} + 64 q^{56} - 16 q^{57} - 56 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 80 q^{63} + 96 q^{66} - 24 q^{68} - 96 q^{69} - 24 q^{71} + 24 q^{72} + 64 q^{73} + 64 q^{74} - 8 q^{76} - 24 q^{77} - 8 q^{78} + 16 q^{82} + 96 q^{83} + 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} - 112 q^{92} + 64 q^{93} - 56 q^{94} - 168 q^{96} - 48 q^{97} - 120 q^{98} + 8 q^{99}+O(q^{100}) \) 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 8 * q^99

Introduction

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