LMFDB - Embedded newform 425.2.n.f.49.2

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			49.2
Character	$\chi$	$=$	425.49
Dual form			425.2.n.f.399.2

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

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	−0.868916	−	0.494959i	$-0.835183\pi$
$2$	−0.528855	+	0.528855i	−0.373957	+	0.373957i	0.494959	+	0.868916i	$0.335183\pi$
$3$	−2.84096	+	1.17676i	−1.64023	+	0.679404i	−0.996321	−	0.0857002i	$-0.972687\pi$
$3$	−2.84096	+	1.17676i	−1.64023	+	0.679404i	−0.643906	+	0.765105i	$0.722687\pi$
$4$			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	−0.497653	−	0.867376i	$-0.665805\pi$
$7$	1.23707	−	2.98655i	0.467569	−	1.12881i	0.965221	−	0.261434i	$-0.0841954\pi$
$8$	−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	−0.683894	−	0.729581i	$-0.739715\pi$
$11$	1.04667	−	2.52689i	0.315584	−	0.761886i	0.999478	−	0.0323052i	$-0.0102849\pi$
$12$	−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	0.802499	−	0.596653i	$-0.203503\pi$
$19$	0.897260	+	0.897260i	0.205846	+	0.205846i	−0.596653	+	0.802499i	$0.703503\pi$
$20$		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	0.334754	−	0.942306i	$-0.391347\pi$
$23$	−0.454888	−	0.188421i	−0.0948506	−	0.0392884i	−0.429604	+	0.903017i	$0.641347\pi$
$24$	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	−0.344240	−	0.938882i	$-0.611863\pi$
$29$	0.410535	−	0.170049i	0.0762345	−	0.0315774i	0.420475	+	0.907304i	$0.361863\pi$
$30$		0			0
$31$	−2.11561	−	5.10754i	−0.379975	−	0.917342i	−0.991969	−	0.126479i	$-0.959632\pi$
$31$	−2.11561	−	5.10754i	−0.379975	−	0.917342i	0.611994	−	0.790862i	$-0.290368\pi$
$32$	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	0.630481	−	0.776205i	$-0.282858\pi$
$37$	9.88545	−	4.09469i	1.62516	−	0.673162i	0.994677	+	0.103043i	$0.0328578\pi$
$38$	−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	0.220562	−	0.975373i	$-0.429211\pi$
$41$	−2.00526	−	0.830608i	−0.313170	−	0.129719i	−0.533732	+	0.845654i	$0.679211\pi$
$42$	−5.25703	−	5.25703i	−0.811178	−	0.811178i
$43$	1.52864	+	1.52864i	0.233115	+	0.233115i	0.813992	−	0.580876i	$-0.197290\pi$
$43$	1.52864	+	1.52864i	0.233115	+	0.233115i	−0.580876	+	0.813992i	$0.697290\pi$
$44$	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	−0.789820	−	0.613339i	$-0.789826\pi$
$53$	−1.28480	+	1.28480i	−0.176481	+	0.176481i	0.613339	+	0.789820i	$0.289826\pi$
$54$	−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	−0.554309	−	0.832311i	$-0.687018\pi$
$59$	2.13537	−	2.13537i	0.278001	−	0.278001i	0.832311	+	0.554309i	$0.187018\pi$
$60$		0			0
$61$	11.2928	+	4.67764i	1.44590	+	0.598910i	0.961220	−	0.275783i	$-0.0889371\pi$
$61$	11.2928	+	4.67764i	1.44590	+	0.598910i	0.484677	+	0.874693i	$0.338937\pi$
$62$	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	$0.0828672\pi$
$67$			4.21389i			0.514808i	−0.966304	+	0.257404i	$0.917133\pi$
$68$	−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	0.810536	−	0.585689i	$-0.199176\pi$
$71$	−1.48927	−	3.59542i	−0.176744	−	0.426698i	−0.987280	+	0.158991i	$0.949176\pi$
$72$	−16.6127			−1.95782
$73$	−2.47620	−	5.97807i	−0.289817	−	0.699680i	0.710173	−	0.704027i	$-0.248617\pi$
$73$	−2.47620	−	5.97807i	−0.289817	−	0.699680i	−0.999991	+	0.00434632i	$0.998617\pi$
$74$	−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	−0.688748	−	0.725001i	$-0.741839\pi$
$79$	2.76355	−	6.67180i	0.310923	−	0.750636i	0.999671	−	0.0256347i	$-0.00816068\pi$
$80$		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	−0.715880	−	0.698223i	$-0.753974\pi$
$83$	−0.160866	+	0.160866i	−0.0176574	+	0.0176574i	0.698223	+	0.715880i	$0.253974\pi$
$84$	−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	$0.249981\pi$
$89$			13.3408i			1.41413i	−0.707150	+	0.707064i	$0.750019\pi$
$90$		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	0.896943	+	0.442145i	$0.145782\pi$
$97$	5.66657	+	13.6803i	0.575353	+	1.38902i	−0.321591	+	0.946879i	$0.604218\pi$
$98$	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	$-0.755901\pi$
$103$		−	14.0842i		−	1.38775i	0.720093	−	0.693877i	$-0.244099\pi$
$104$	−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	−0.740344	−	0.672228i	$-0.765337\pi$
$107$	−7.15995	−	17.2857i	−0.692179	−	1.67107i	0.0481649	−	0.998839i	$-0.484663\pi$
$108$	−14.1437	−	5.85853i	−1.36098	−	0.563738i
$109$	3.26202	+	1.35117i	0.312444	+	0.129419i	0.533395	−	0.845866i	$-0.320916\pi$
$109$	3.26202	+	1.35117i	0.312444	+	0.129419i	−0.220951	+	0.975285i	$0.570916\pi$
$110$		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	0.502731	−	0.864443i	$-0.332329\pi$
$113$	2.62525	+	1.08741i	0.246963	+	0.102295i	−0.255769	+	0.966738i	$0.582329\pi$
$114$	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	0.514548	−	0.857462i	$-0.327960\pi$
$127$	−3.86444	−	3.86444i	−0.342914	−	0.342914i	−0.857462	+	0.514548i	$0.827960\pi$
$128$	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	0.0583689	−	0.998295i	$-0.481410\pi$
$131$	9.21986	−	3.81899i	0.805543	−	0.333667i	0.747174	+	0.664628i	$0.231410\pi$
$132$	−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	$0.0419709\pi$
$137$			3.07772i			0.262947i	−0.991320	+	0.131474i	$0.958029\pi$
$138$	−0.800709	+	0.800709i	−0.0681609	+	0.0681609i
$139$	2.56777	+	6.19915i	0.217796	+	0.525805i	0.994582	−	0.103960i	$-0.0331513\pi$
$139$	2.56777	+	6.19915i	0.217796	+	0.525805i	−0.776786	+	0.629765i	$0.783151\pi$
$140$		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	$-0.609167\pi$
$149$		−	22.9914i		−	1.88353i	0.336276	−	0.941764i	$-0.390833\pi$
$150$		0			0
$151$	0.138411	+	0.138411i	0.0112638	+	0.0112638i	0.712716	−	0.701452i	$-0.247465\pi$
$151$	0.138411	+	0.138411i	0.0112638	+	0.0112638i	−0.701452	+	0.712716i	$0.747465\pi$
$152$		−	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	−0.823312	−	0.567588i	$-0.807877\pi$
$163$	2.04533	−	4.93787i	0.160203	−	0.386764i	0.983515	+	0.180824i	$0.0578765\pi$
$164$	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	−0.756344	−	0.654174i	$-0.773016\pi$
$167$	−10.7077	+	4.43529i	−0.828589	+	0.343213i	−0.0722453	+	0.997387i	$0.523016\pi$
$168$	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	−0.734716	−	0.678375i	$-0.762685\pi$
$173$	−10.1877	+	4.21988i	−0.774556	+	0.320832i	−0.0398396	+	0.999206i	$0.512685\pi$
$174$		−	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	−0.121109	+	0.992639i	$0.538645\pi$
$179$	−14.9009	+	14.9009i	−1.11375	+	1.11375i	−0.992639	+	0.121109i	$0.961355\pi$
$180$		0			0
$181$	8.67131	−	20.9344i	0.644533	−	1.55604i	−0.175968	−	0.984396i	$-0.556305\pi$
$181$	8.67131	−	20.9344i	0.644533	−	1.55604i	0.820501	−	0.571645i	$-0.193695\pi$
$182$	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	$-0.959567\pi$
$191$		−	3.50162i		−	0.253368i	0.991943	−	0.126684i	$-0.0404335\pi$
$192$	−2.90782	−	7.02011i	−0.209854	−	0.506633i
$193$	−11.3584	−	4.70480i	−0.817595	−	0.338659i	−0.0656152	−	0.997845i	$-0.520901\pi$
$193$	−11.3584	−	4.70480i	−0.817595	−	0.338659i	−0.751980	+	0.659186i	$0.770901\pi$
$194$	−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	−0.504381	−	0.863481i	$-0.668279\pi$
$197$	6.49632	−	15.6835i	0.462843	−	1.11740i	0.967225	−	0.253922i	$-0.0817206\pi$
$198$	12.2008	+	5.05374i	0.867074	+	0.359154i
$199$	−10.6966	+	4.43067i	−0.758260	+	0.314082i	−0.728107	−	0.685464i	$-0.759600\pi$
$199$	−10.6966	+	4.43067i	−0.758260	+	0.314082i	−0.0301533	+	0.999545i	$0.509600\pi$
$200$		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	0.584397	−	0.811468i	$-0.301331\pi$
$211$	6.15655	+	2.55013i	0.423834	+	0.175558i	−0.160563	+	0.987026i	$0.551331\pi$
$212$	−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	−0.939322	−	0.343037i	$-0.888544\pi$
$223$	−8.90442	+	8.90442i	−0.596284	+	0.596284i	0.343037	+	0.939322i	$0.388544\pi$
$224$	−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	0.122213	−	0.992504i	$-0.461001\pi$
$227$	−7.43044	−	3.07779i	−0.493176	−	0.204280i	−0.615389	+	0.788224i	$0.711001\pi$
$228$	2.15116	−	5.19336i	0.142464	−	0.343939i
$229$	15.2944	−	15.2944i	1.01068	−	1.01068i	0.0107373	−	0.999942i	$-0.496582\pi$
$229$	15.2944	−	15.2944i	1.01068	−	1.01068i	0.999942	−	0.0107373i	$-0.00341786\pi$
$230$		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	−0.917247	−	0.398320i	$-0.869594\pi$
$233$	−8.40011	−	20.2797i	−0.550310	−	1.32857i	0.366937	−	0.930246i	$-0.380406\pi$
$234$			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	0.998731	+	0.0503696i	$0.0160399\pi$
$241$	5.09407	+	12.2982i	0.328138	+	0.792195i	−0.670593	+	0.741826i	$0.733960\pi$
$242$	−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	$-0.963821\pi$
$251$		−	3.59367i		−	0.226831i	0.993548	−	0.113415i	$-0.0361790\pi$
$252$	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	−0.0865680	+	0.996246i	$0.527590\pi$
$257$	−17.3588	+	17.3588i	−1.08281	+	1.08281i	−0.996246	+	0.0865680i	$0.972410\pi$
$258$	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	0.950146	−	0.311806i	$-0.100934\pi$
$263$	10.3521	+	10.3521i	0.638340	+	0.638340i	−0.311806	+	0.950146i	$0.600934\pi$
$264$	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	0.976736	+	0.214443i	$0.0687936\pi$
$269$	7.17904	+	17.3317i	0.437714	+	1.05673i	−0.539023	+	0.842291i	$0.681206\pi$
$270$		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	0.922456	−	0.386102i	$-0.126179\pi$
$277$	−0.0471663	−	0.113870i	−0.00283395	−	0.00684176i	−0.925290	+	0.379260i	$0.876179\pi$
$278$	−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	−0.744523	−	0.667597i	$-0.767323\pi$
$281$	−1.28950	+	1.28950i	−0.0769253	+	0.0769253i	0.667597	+	0.744523i	$0.267323\pi$
$282$	7.38944	−	17.8397i	0.440035	−	1.06234i
$283$	26.4486	+	10.9554i	1.57221	+	0.651229i	0.987155	−	0.159767i	$-0.0510743\pi$
$283$	26.4486	+	10.9554i	1.57221	+	0.651229i	0.585052	+	0.810996i	$0.301074\pi$
$284$	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	$0.212982\pi$
$307$			21.7364i			1.24056i	−0.784379	+	0.620281i	$0.787018\pi$
$308$	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	−0.144387	−	0.989521i	$-0.546121\pi$
$311$	7.99250	−	3.31060i	0.453213	−	0.187727i	0.597600	+	0.801794i	$0.296121\pi$
$312$	31.5696	+	13.0766i	1.78728	+	0.740315i
$313$	−3.93476	+	9.49936i	−0.222406	+	0.536936i	−0.995216	−	0.0977022i	$-0.968851\pi$
$313$	−3.93476	+	9.49936i	−0.222406	+	0.536936i	0.772810	+	0.634638i	$0.218851\pi$
$314$	−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	0.411749	−	0.911297i	$-0.364918\pi$
$317$	1.04183	+	0.431538i	0.0585147	+	0.0242376i	−0.353234	+	0.935535i	$0.614918\pi$
$318$	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	−0.427567	+	0.903984i	$0.640629\pi$
$331$	−24.2254	+	24.2254i	−1.33155	+	1.33155i	−0.903984	+	0.427567i	$0.859371\pi$
$332$	−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	−0.700753	−	0.713404i	$-0.747152\pi$
$337$	−12.6999	+	5.26046i	−0.691807	+	0.286556i	0.00894611	+	0.999960i	$0.497152\pi$
$338$	−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	−0.602566	−	0.798069i	$-0.705855\pi$
$347$	7.22453	−	17.4415i	0.387833	−	0.936311i	0.990398	−	0.138242i	$-0.0441452\pi$
$348$	−1.39194	−	1.39194i	−0.0746158	−	0.0746158i
$349$	−4.98501	+	4.98501i	−0.266842	+	0.266842i	−0.827826	−	0.560985i	$-0.810423\pi$
$349$	−4.98501	+	4.98501i	−0.266842	+	0.266842i	0.560985	+	0.827826i	$0.310423\pi$
$350$		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	0.857356	−	0.514724i	$-0.172106\pi$
$359$	6.49195	+	6.49195i	0.342632	+	0.342632i	−0.514724	+	0.857356i	$0.672106\pi$
$360$		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	−0.977221	−	0.212223i	$-0.931930\pi$
$367$	−2.60840	+	6.29722i	−0.136157	+	0.328712i	0.841064	+	0.540935i	$0.181930\pi$
$368$	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	$0.0873280\pi$
$373$			10.4647i			0.541841i	−0.962602	+	0.270920i	$0.912672\pi$
$374$	−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	−0.891851	−	0.452330i	$-0.850593\pi$
$379$	−23.4129	+	9.69794i	−1.20264	+	0.498150i	−0.310789	+	0.950479i	$0.600593\pi$
$380$		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	0.554389	−	0.832258i	$-0.312952\pi$
$383$	−5.43799	−	5.43799i	−0.277868	−	0.277868i	−0.832258	+	0.554389i	$0.812952\pi$
$384$	−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	0.363700	−	0.931516i	$-0.381513\pi$
$389$	−11.1991	−	11.1991i	−0.567816	−	0.567816i	−0.931516	+	0.363700i	$0.881513\pi$
$390$		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	−0.415355	−	0.909659i	$-0.636343\pi$
$397$	−26.9440	−	11.1606i	−1.35228	−	0.560133i	−0.936927	+	0.349526i	$0.886343\pi$
$398$	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	−0.0288034	−	0.999585i	$-0.509170\pi$
$401$	−15.1386	−	6.27060i	−0.755984	−	0.313139i	−0.727181	+	0.686446i	$0.759170\pi$
$402$	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	−0.932007	−	0.362441i	$-0.881943\pi$
$419$	−0.341711	+	0.824964i	−0.0166937	+	0.0403021i	0.915313	+	0.402743i	$0.131943\pi$
$420$		0			0
$421$		−	33.6725i		−	1.64110i	−0.571575	−	0.820550i	$-0.693668\pi$
$421$		−	33.6725i		−	1.64110i	0.571575	−	0.820550i	$-0.306332\pi$
$422$	−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	0.699538	+	0.714595i	$0.253389\pi$
$431$	−6.23658	+	15.0564i	−0.300405	+	0.725243i	−0.999943	+	0.0106472i	$0.996611\pi$
$432$	3.89036	−	9.39215i	0.187175	−	0.451880i
$433$	−24.7450	−	24.7450i	−1.18917	−	1.18917i	−0.977298	−	0.211871i	$-0.932044\pi$
$433$	−24.7450	−	24.7450i	−1.18917	−	1.18917i	−0.211871	−	0.977298i	$-0.567956\pi$
$434$	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	−0.985951	−	0.167036i	$-0.946580\pi$
$439$	−8.52530	−	20.5819i	−0.406891	−	0.982321i	0.579060	−	0.815285i	$-0.303420\pi$
$440$		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	$-0.932970\pi$
$443$		−	8.79907i		−	0.418056i	0.977910	−	0.209028i	$-0.0670300\pi$
$444$	−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	0.567513	−	0.823364i	$-0.307906\pi$
$449$	8.19189	+	3.39319i	0.386599	+	0.160135i	−0.180914	+	0.983499i	$0.557906\pi$
$450$		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	−0.943238	−	0.332118i	$-0.892237\pi$
$457$	−13.0643	+	13.0643i	−0.611120	+	0.611120i	0.332118	+	0.943238i	$0.392237\pi$
$458$			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	0.984508	−	0.175339i	$-0.0561022\pi$
$461$	17.3736	+	17.3736i	0.809169	+	0.809169i	−0.175339	+	0.984508i	$0.556102\pi$
$462$	−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	0.999309	−	0.0371777i	$-0.0118367\pi$
$467$	20.7918	+	20.7918i	0.962131	+	0.962131i	−0.0371777	+	0.999309i	$0.511837\pi$
$468$	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	0.949438	+	0.313955i	$0.101654\pi$
$479$	10.9449	+	26.4232i	0.500083	+	1.20731i	−0.449354	+	0.893354i	$0.648346\pi$
$480$		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	0.395580	−	0.918432i	$-0.370544\pi$
$487$	0.570849	+	0.236454i	0.0258677	+	0.0107147i	−0.369712	+	0.929146i	$0.620544\pi$
$488$	−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	0.985034	−	0.172359i	$-0.0551390\pi$
$491$	18.0077	+	18.0077i	0.812675	+	0.812675i	−0.172359	+	0.985034i	$0.555139\pi$
$492$			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	0.221624	+	0.975132i	$0.428864\pi$
$499$	−13.9527	+	33.6849i	−0.624611	+	1.50794i	−0.846234	+	0.532811i	$0.821136\pi$
$500$		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	0.425781	+	0.904826i	$0.359999\pi$
$503$	−11.5525	+	27.8902i	−0.515100	+	1.24356i	−0.940881	+	0.338736i	$0.890001\pi$
$504$	−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	0.288053	+	0.957614i	$0.406992\pi$
$521$	−13.5302	+	32.6647i	−0.592767	+	1.43107i	−0.880820	+	0.473451i	$0.843008\pi$
$522$	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	0.982235	+	0.187657i	$0.0600892\pi$
$541$	9.77786	+	23.6058i	0.420383	+	1.01489i	−0.561852	+	0.827238i	$0.689911\pi$
$542$	−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	−0.602696	−	0.797971i	$-0.705907\pi$
$547$	−10.8664	+	4.50103i	−0.464616	+	0.192450i	0.138080	+	0.990421i	$0.455907\pi$
$548$	−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	−0.0975306	−	0.995233i	$-0.531094\pi$
$563$	21.3003	−	21.3003i	0.897702	−	0.897702i	0.995233	+	0.0975306i	$0.0310944\pi$
$564$	−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	−0.246010	−	0.969267i	$-0.579120\pi$
$569$	17.2524	−	17.2524i	0.723257	−	0.723257i	0.969267	+	0.246010i	$0.0791197\pi$
$570$		0			0
$571$	−30.7483	−	12.7364i	−1.28678	−	0.533001i	−0.368755	−	0.929527i	$-0.620216\pi$
$571$	−30.7483	−	12.7364i	−1.28678	−	0.533001i	−0.918024	+	0.396526i	$0.870216\pi$
$572$	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	$0.122683\pi$
$577$			18.0611i			0.751895i	−0.926641	+	0.375947i	$0.877317\pi$
$578$	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	0.967335	+	0.253500i	$0.0815817\pi$
$587$	29.5785	+	29.5785i	1.22084	+	1.22084i	0.253500	+	0.967335i	$0.418418\pi$
$588$	−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	−0.940335	−	0.340250i	$-0.889488\pi$
$593$	−14.6130	+	14.6130i	−0.600085	+	0.600085i	0.340250	+	0.940335i	$0.389488\pi$
$594$	−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	$-0.939695\pi$
$599$		−	9.21817i		−	0.376644i	0.982107	−	0.188322i	$-0.0603049\pi$
$600$		0			0
$601$	−0.620216	+	1.49733i	−0.0252991	+	0.0610775i	−0.936024	−	0.351936i	$-0.885524\pi$
$601$	−0.620216	+	1.49733i	−0.0252991	+	0.0610775i	0.910725	+	0.413013i	$0.135524\pi$
$602$	−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	−0.990245	−	0.139334i	$-0.955504\pi$
$607$	−9.57311	−	23.1115i	−0.388560	−	0.938068i	0.601685	−	0.798733i	$-0.294496\pi$
$608$	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	$0.0311324\pi$
$613$			4.83538i			0.195299i	−0.995221	+	0.0976495i	$0.968868\pi$
$614$	−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	0.739843	−	0.672779i	$-0.234900\pi$
$617$	−6.43422	−	15.5336i	−0.259032	−	0.625358i	−0.998875	+	0.0474212i	$0.984900\pi$
$618$	−29.9259	−	12.3957i	−1.20380	−	0.498629i
$619$	−11.7540	−	4.86865i	−0.472431	−	0.195687i	0.133748	−	0.991015i	$-0.457299\pi$
$619$	−11.7540	−	4.86865i	−0.472431	−	0.195687i	−0.606179	+	0.795328i	$0.707299\pi$
$620$		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	0.644907	−	0.764261i	$-0.276896\pi$
$631$	−2.99812	−	2.99812i	−0.119353	−	0.119353i	−0.764261	+	0.644907i	$0.776896\pi$
$632$	−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	0.0397171	−	0.999211i	$-0.487354\pi$
$641$	19.6050	−	8.12065i	0.774350	−	0.320746i	0.734633	+	0.678465i	$0.237354\pi$
$642$	−43.0300			−1.69826
$643$	7.54502	−	3.12525i	0.297547	−	0.123248i	−0.228916	−	0.973446i	$-0.573518\pi$
$643$	7.54502	−	3.12525i	0.297547	−	0.123248i	0.526462	+	0.850198i	$0.323518\pi$
$644$	−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	$-0.847626\pi$
$647$		−	23.4331i		−	0.921249i	0.887595	−	0.460624i	$-0.152374\pi$
$648$	−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	−0.998341	−	0.0575706i	$-0.981665\pi$
$653$	−6.43188	+	15.5279i	−0.251699	+	0.607655i	0.746643	+	0.665225i	$0.231665\pi$
$654$	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	$0.0885371\pi$
$659$			14.0972i			0.549150i	−0.961566	+	0.274575i	$0.911463\pi$
$660$		0			0
$661$	−7.34734	−	7.34734i	−0.285779	−	0.285779i	0.549630	−	0.835408i	$-0.314769\pi$
$661$	−7.34734	−	7.34734i	−0.285779	−	0.285779i	−0.835408	+	0.549630i	$0.814769\pi$
$662$		−	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	−0.707563	−	0.706650i	$-0.750205\pi$
$673$	7.58646	−	18.3153i	0.292437	−	0.706005i	1.00000		0.000645530i	$0.000205479\pi$
$674$	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	−0.322489	−	0.946573i	$-0.604519\pi$
$677$	3.09124	−	1.28043i	0.118806	−	0.0492111i	0.441295	+	0.897362i	$0.354519\pi$
$678$	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	−0.784302	+	0.620380i	$0.786978\pi$
$683$	−46.4553	+	19.2424i	−1.77756	+	0.736290i	−0.993260	+	0.115910i	$0.963022\pi$
$684$			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	0.337913	+	0.941177i	$0.390279\pi$
$691$	−14.8926	+	35.9539i	−0.566540	+	1.36775i	−0.904454	+	0.426572i	$0.859721\pi$
$692$	−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	$-0.749160\pi$
$701$		−	37.5419i		−	1.41794i	0.705239	−	0.708969i	$-0.250840\pi$
$702$	−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	−0.608321	−	0.793691i	$-0.708157\pi$
$709$	−12.7076	+	5.26367i	−0.477245	+	0.197681i	0.131076	+	0.991372i	$0.458157\pi$
$710$		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	−0.373552	−	0.927609i	$-0.621860\pi$
$719$	0.488717	−	0.202433i	0.0182261	−	0.00754949i	0.391778	+	0.920060i	$0.371860\pi$
$720$		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	−0.443279	−	0.896384i	$-0.646185\pi$
$733$	12.2673	−	12.2673i	0.453105	−	0.453105i	0.896384	+	0.443279i	$0.146185\pi$
$734$	−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	−0.980961	−	0.194204i	$-0.937788\pi$
$739$	−21.3876	+	21.3876i	−0.786757	+	0.786757i	0.194204	+	0.980961i	$0.437788\pi$
$740$		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	0.966236	−	0.257657i	$-0.0829506\pi$
$743$	2.74796	+	6.63416i	0.100813	+	0.243384i	−0.865424	+	0.501041i	$0.832951\pi$
$744$		−	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	0.976967	+	0.213390i	$0.0684505\pi$
$751$	11.9767	+	28.9144i	0.437037	+	1.05510i	−0.539930	+	0.841710i	$0.681549\pi$
$752$	−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	0.831885	−	0.554948i	$-0.187262\pi$
$757$	7.61956	+	7.61956i	0.276938	+	0.276938i	−0.554948	+	0.831885i	$0.687262\pi$
$758$	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	$-0.794898\pi$
$761$		−	33.1409i		−	1.20136i	0.799491	−	0.600678i	$-0.205102\pi$
$762$	−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	$0.0664042\pi$
$769$			11.4864i			0.414210i	−0.978319	+	0.207105i	$0.933596\pi$
$770$		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	0.665121	−	0.746736i	$-0.268380\pi$
$773$	−2.26913	−	2.26913i	−0.0816149	−	0.0816149i	−0.746736	+	0.665121i	$0.768380\pi$
$774$	−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	0.899224	−	0.437489i	$-0.144132\pi$
$787$	−1.28976	−	3.11375i	−0.0459748	−	0.110993i	−0.945199	+	0.326496i	$0.894132\pi$
$788$	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	−0.921981	−	0.387234i	$-0.873431\pi$
$797$	−15.0966	+	15.0966i	−0.534747	+	0.534747i	0.387234	+	0.921981i	$0.373431\pi$
$798$		−	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	0.426575	−	0.904452i	$-0.359720\pi$
$809$	2.52190	+	1.04460i	0.0886652	+	0.0367263i	−0.337910	+	0.941178i	$0.609720\pi$
$810$		0			0
$811$	−34.4933	+	14.2876i	−1.21122	+	0.501705i	−0.894609	−	0.446849i	$-0.852546\pi$
$811$	−34.4933	+	14.2876i	−1.21122	+	0.501705i	−0.316614	+	0.948554i	$0.602546\pi$
$812$	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	−0.939505	−	0.342536i	$-0.888714\pi$
$821$	−39.0148	+	16.1605i	−1.36163	+	0.564004i	−0.422121	+	0.906540i	$0.638714\pi$
$822$	6.53952	+	2.70876i	0.228092	+	0.0944788i
$823$	−7.94473	+	19.1803i	−0.276936	+	0.668582i	−0.999748	−	0.0224627i	$-0.992849\pi$
$823$	−7.94473	+	19.1803i	−0.276936	+	0.668582i	0.722812	+	0.691045i	$0.242849\pi$
$824$	−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	0.559791	−	0.828634i	$-0.310881\pi$
$827$	10.6314	+	4.40367i	0.369690	+	0.153131i	−0.190101	+	0.981765i	$0.560881\pi$
$828$	−1.75238	−	4.23063i	−0.0608996	−	0.147025i
$829$		−	11.7508i		−	0.408121i	−0.978958	−	0.204060i	$-0.934586\pi$
$829$		−	11.7508i		−	0.408121i	0.978958	−	0.204060i	$-0.0654139\pi$
$830$		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	−0.474377	−	0.880322i	$-0.657327\pi$
$839$	14.0060	−	33.8134i	0.483540	−	1.16737i	0.957917	−	0.287046i	$-0.0926733\pi$
$840$		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	−0.892449	−	0.451149i	$-0.851014\pi$
$853$	−35.1787	+	14.5715i	−1.20450	+	0.498918i	−0.312046	+	0.950067i	$0.601014\pi$
$854$			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	−0.999202	−	0.0399356i	$-0.987285\pi$
$857$	−7.74080	+	18.6880i	−0.264421	+	0.638368i	0.734781	+	0.678304i	$0.237285\pi$
$858$	−19.2076	−	19.2076i	−0.655736	−	0.655736i
$859$	−1.84360	+	1.84360i	−0.0629028	+	0.0629028i	−0.737858	−	0.674956i	$-0.764163\pi$
$859$	−1.84360	+	1.84360i	−0.0629028	+	0.0629028i	0.674956	+	0.737858i	$0.264163\pi$
$860$		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	−0.957899	−	0.287106i	$-0.907307\pi$
$877$	−2.29651	+	5.54426i	−0.0775476	+	0.187216i	0.880351	+	0.474322i	$0.157307\pi$
$878$	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	0.975022	+	0.222109i	$0.0712941\pi$
$881$	13.1380	+	31.7181i	0.442632	+	1.06861i	−0.532390	+	0.846499i	$0.678706\pi$
$882$	11.7784	−	11.7784i	0.396598	−	0.396598i
$883$		−	11.8244i		−	0.397921i	−0.980007	−	0.198961i	$-0.936243\pi$
$883$		−	11.8244i		−	0.397921i	0.980007	−	0.198961i	$-0.0637566\pi$
$884$	−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	−0.725474	−	0.688250i	$-0.758379\pi$
$887$	−22.3904	+	9.27440i	−0.751796	+	0.311404i	−0.0263216	+	0.999654i	$0.508379\pi$
$888$	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	0.942789	−	0.333390i	$-0.108192\pi$
$907$	41.3709	+	17.1364i	1.37370	+	0.569005i	0.430910	+	0.902395i	$0.358192\pi$
$908$	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	0.529711	−	0.848178i	$-0.322300\pi$
$911$	9.19129	+	3.80716i	0.304521	+	0.126137i	−0.225190	+	0.974315i	$0.572300\pi$
$912$	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	−0.687027	−	0.726632i	$-0.741085\pi$
$929$	9.52731	−	23.0010i	0.312581	−	0.754637i	0.999608	−	0.0280049i	$-0.00891541\pi$
$930$		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	−0.968969	−	0.247181i	$-0.920496\pi$
$937$	−22.0943	+	22.0943i	−0.721788	+	0.721788i	0.247181	+	0.968969i	$0.420496\pi$
$938$	−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	−0.934325	−	0.356423i	$-0.883996\pi$
$941$	−0.663467	+	1.60175i	−0.0216284	+	0.0522156i	0.912696	+	0.408638i	$0.133996\pi$
$942$	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	0.841936	−	0.539577i	$-0.181416\pi$
$947$	−4.15260	−	10.0253i	−0.134941	−	0.325777i	−0.976877	+	0.213800i	$0.931416\pi$
$948$	−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	$-0.911742\pi$
$953$		−	16.9007i		−	0.547466i	0.961806	−	0.273733i	$-0.0882584\pi$
$954$	−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	−0.256324	−	0.966591i	$-0.582511\pi$
$967$	22.0869	−	22.0869i	0.710267	−	0.710267i	0.966591	+	0.256324i	$0.0825115\pi$
$968$		−	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	0.481731	−	0.876319i	$-0.340008\pi$
$971$	−12.2957	−	12.2957i	−0.394589	−	0.394589i	−0.876319	+	0.481731i	$0.840008\pi$
$972$	−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	0.803214	−	0.595691i	$-0.203122\pi$
$977$	6.48656	+	6.48656i	0.207523	+	0.207523i	−0.595691	+	0.803214i	$0.703122\pi$
$978$	−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	−0.857148	−	0.515070i	$-0.827766\pi$
$983$	−34.4578	+	14.2729i	−1.09903	+	0.455235i	−0.241886	+	0.970305i	$0.577766\pi$
$984$	−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	−0.832417	−	0.554149i	$-0.813044\pi$
$991$	−32.3988	+	13.4200i	−1.02918	+	0.426301i	−0.196765	+	0.980451i	$0.563044\pi$
$992$	−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	−0.237991	−	0.971267i	$-0.576489\pi$
$997$	−34.5139	−	14.2961i	−1.09307	−	0.452763i	−0.855075	+	0.518505i	$0.826489\pi$
$998$	−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.49.2		24
5.2	odd	4		85.2.l.a.66.2	✓	24
5.3	odd	4		425.2.m.b.151.5		24
5.4	even	2		425.2.n.c.49.5		24
15.2	even	4		765.2.be.b.406.5		24
17.8	even	8		425.2.n.c.399.5		24
85.8	odd	8		425.2.m.b.76.5		24
85.12	even	16		1445.2.a.q.1.9		12
85.22	even	16		1445.2.a.p.1.9		12
85.37	even	16		1445.2.d.j.866.7		24
85.42	odd	8		85.2.l.a.76.2	yes	24
85.59	even	8	inner	425.2.n.f.399.2		24
85.63	even	16		7225.2.a.bq.1.4		12
85.73	even	16		7225.2.a.bs.1.4		12
85.82	even	16		1445.2.d.j.866.8		24
255.212	even	8		765.2.be.b.586.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	5.2	odd	4
85.2.l.a.76.2	yes	24	85.42	odd	8
425.2.m.b.76.5		24	85.8	odd	8
425.2.m.b.151.5		24	5.3	odd	4
425.2.n.c.49.5		24	5.4	even	2
425.2.n.c.399.5		24	17.8	even	8
425.2.n.f.49.2		24	1.1	even	1	trivial
425.2.n.f.399.2		24	85.59	even	8	inner
765.2.be.b.406.5		24	15.2	even	4
765.2.be.b.586.5		24	255.212	even	8
1445.2.a.p.1.9		12	85.22	even	16
1445.2.a.q.1.9		12	85.12	even	16
1445.2.d.j.866.7		24	85.37	even	16
1445.2.d.j.866.8		24	85.82	even	16
7225.2.a.bq.1.4		12	85.63	even	16
7225.2.a.bs.1.4		12	85.73	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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