LMFDB - Embedded newform 425.2.m.d.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, 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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.6
Character	$\chi$	$=$	425.151
Dual form			425.2.m.d.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33351 + 1.33351i) q^{2} +(-0.723051 - 1.74560i) q^{3} +1.55648i q^{4} +(1.36358 - 3.29196i) q^{6} +(-0.309803 - 0.128325i) q^{7} +(0.591431 - 0.591431i) q^{8} +(-0.402996 + 0.402996i) q^{9} +O(q^{10})$	\(q+(1.33351 + 1.33351i) q^{2} +(-0.723051 - 1.74560i) q^{3} +1.55648i q^{4} +(1.36358 - 3.29196i) q^{6} +(-0.309803 - 0.128325i) q^{7} +(0.591431 - 0.591431i) q^{8} +(-0.402996 + 0.402996i) q^{9} +(1.45699 - 3.51749i) q^{11} +(2.71700 - 1.12542i) q^{12} +0.558802i q^{13} +(-0.242003 - 0.584247i) q^{14} +4.69032 q^{16} +(-2.12362 - 3.53415i) q^{17} -1.07480 q^{18} +(2.64081 + 2.64081i) q^{19} +0.633578i q^{21} +(6.63350 - 2.74769i) q^{22} +(-0.476856 + 1.15123i) q^{23} +(-1.46004 - 0.604767i) q^{24} +(-0.745166 + 0.745166i) q^{26} +(-4.24194 - 1.75707i) q^{27} +(0.199736 - 0.482204i) q^{28} +(3.68273 - 1.52544i) q^{29} +(3.58304 + 8.65022i) q^{31} +(5.07172 + 5.07172i) q^{32} -7.19360 q^{33} +(1.88096 - 7.54468i) q^{34} +(-0.627257 - 0.627257i) q^{36} +(-2.59150 - 6.25643i) q^{37} +7.04307i q^{38} +(0.975444 - 0.404042i) q^{39} +(1.55259 + 0.643105i) q^{41} +(-0.844881 + 0.844881i) q^{42} +(-4.00791 + 4.00791i) q^{43} +(5.47491 + 2.26778i) q^{44} +(-2.17107 + 0.899286i) q^{46} +9.50560i q^{47} +(-3.39134 - 8.18743i) q^{48} +(-4.87024 - 4.87024i) q^{49} +(-4.63373 + 6.26236i) q^{51} -0.869767 q^{52} +(5.16482 + 5.16482i) q^{53} +(-3.31360 - 7.99973i) q^{54} +(-0.259122 + 0.107332i) q^{56} +(2.70035 - 6.51923i) q^{57} +(6.94514 + 2.87677i) q^{58} +(-6.60087 + 6.60087i) q^{59} +(0.687270 + 0.284676i) q^{61} +(-6.75712 + 16.3131i) q^{62} +(0.176564 - 0.0731351i) q^{63} +4.14571i q^{64} +(-9.59272 - 9.59272i) q^{66} -7.29434 q^{67} +(5.50086 - 3.30538i) q^{68} +2.35438 q^{69} +(-5.95517 - 14.3771i) q^{71} +0.476688i q^{72} +(-10.3022 + 4.26733i) q^{73} +(4.88721 - 11.7988i) q^{74} +(-4.11038 + 4.11038i) q^{76} +(-0.902761 + 0.902761i) q^{77} +(1.83956 + 0.761969i) q^{78} +(-4.58769 + 11.0757i) q^{79} +10.3850i q^{81} +(1.21281 + 2.92798i) q^{82} +(8.29190 + 8.29190i) q^{83} -0.986155 q^{84} -10.6892 q^{86} +(-5.32561 - 5.32561i) q^{87} +(-1.21864 - 2.94206i) q^{88} +13.1316i q^{89} +(0.0717081 - 0.173119i) q^{91} +(-1.79188 - 0.742219i) q^{92} +(12.5091 - 12.5091i) q^{93} +(-12.6758 + 12.6758i) q^{94} +(5.18608 - 12.5203i) q^{96} +(9.81153 - 4.06407i) q^{97} -12.9890i q^{98} +(0.830371 + 2.00469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^6 + 12 * q^9	$ 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * 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 $

$2$	1.33351	+	1.33351i	0.942932	+	0.942932i	0.998457	−	0.0555250i	$-0.0176833\pi$
$2$	1.33351	+	1.33351i	0.942932	+	0.942932i	−0.0555250	+	0.998457i	$0.517683\pi$
$3$	−0.723051	−	1.74560i	−0.417454	−	1.00782i	−0.983083	−	0.183163i	$-0.941367\pi$
$3$	−0.723051	−	1.74560i	−0.417454	−	1.00782i	0.565629	−	0.824660i	$-0.308633\pi$
$4$			1.55648i			0.778242i
$5$		0			0
$5$		0			0
$6$	1.36358	−	3.29196i	0.556678	−	1.34394i
$7$	−0.309803	−	0.128325i	−0.117095	−	0.0485022i	0.323367	−	0.946274i	$-0.395185\pi$
$7$	−0.309803	−	0.128325i	−0.117095	−	0.0485022i	−0.440462	+	0.897771i	$0.645185\pi$
$8$	0.591431	−	0.591431i	0.209102	−	0.209102i
$9$	−0.402996	+	0.402996i	−0.134332	+	0.134332i
$10$		0			0
$11$	1.45699	−	3.51749i	0.439299	−	1.06056i	−0.536892	−	0.843651i	$-0.680402\pi$
$11$	1.45699	−	3.51749i	0.439299	−	1.06056i	0.976191	−	0.216911i	$-0.0695982\pi$
$12$	2.71700	−	1.12542i	0.784330	−	0.324880i
$13$			0.558802i			0.154984i	0.996993	+	0.0774919i	$0.0246912\pi$
$13$			0.558802i			0.154984i	−0.996993	+	0.0774919i	$0.975309\pi$
$14$	−0.242003	−	0.584247i	−0.0646781	−	0.156147i
$15$		0			0
$16$	4.69032			1.17258
$17$	−2.12362	−	3.53415i	−0.515053	−	0.857158i
$17$	−2.12362	−	3.53415i	−0.515053	−	0.857158i
$18$	−1.07480			−0.253332
$19$	2.64081	+	2.64081i	0.605842	+	0.605842i	0.941857	−	0.336014i	$-0.109079\pi$
$19$	2.64081	+	2.64081i	0.605842	+	0.605842i	−0.336014	+	0.941857i	$0.609079\pi$
$20$		0			0
$21$			0.633578i			0.138258i
$22$	6.63350	−	2.74769i	1.41427	−	0.585809i
$23$	−0.476856	+	1.15123i	−0.0994314	+	0.240049i	−0.965766	−	0.259416i	$-0.916470\pi$
$23$	−0.476856	+	1.15123i	−0.0994314	+	0.240049i	0.866334	+	0.499465i	$0.166470\pi$
$24$	−1.46004	−	0.604767i	−0.298029	−	0.123447i
$25$		0			0
$26$	−0.745166	+	0.745166i	−0.146139	+	0.146139i
$27$	−4.24194	−	1.75707i	−0.816363	−	0.338148i
$28$	0.199736	−	0.482204i	0.0377465	−	0.0911281i
$29$	3.68273	−	1.52544i	0.683867	−	0.283267i	−0.0135756	−	0.999908i	$-0.504321\pi$
$29$	3.68273	−	1.52544i	0.683867	−	0.283267i	0.697442	+	0.716641i	$0.254321\pi$
$30$		0			0
$31$	3.58304	+	8.65022i	0.643532	+	1.55362i	0.821882	+	0.569657i	$0.192924\pi$
$31$	3.58304	+	8.65022i	0.643532	+	1.55362i	−0.178350	+	0.983967i	$0.557076\pi$
$32$	5.07172	+	5.07172i	0.896562	+	0.896562i
$33$	−7.19360			−1.25225
$34$	1.88096	−	7.54468i	0.322582	−	1.29390i
$35$		0			0
$36$	−0.627257	−	0.627257i	−0.104543	−	0.104543i
$37$	−2.59150	−	6.25643i	−0.426040	−	1.02855i	−0.980532	−	0.196361i	$-0.937087\pi$
$37$	−2.59150	−	6.25643i	−0.426040	−	1.02855i	0.554492	−	0.832189i	$-0.312913\pi$
$38$			7.04307i			1.14254i
$39$	0.975444	−	0.404042i	0.156196	−	0.0646985i
$40$		0			0
$41$	1.55259	+	0.643105i	0.242474	+	0.100436i	0.500611	−	0.865672i	$-0.333109\pi$
$41$	1.55259	+	0.643105i	0.242474	+	0.100436i	−0.258137	+	0.966108i	$0.583109\pi$
$42$	−0.844881	+	0.844881i	−0.130368	+	0.130368i
$43$	−4.00791	+	4.00791i	−0.611200	+	0.611200i	−0.943259	−	0.332058i	$-0.892257\pi$
$43$	−4.00791	+	4.00791i	−0.611200	+	0.611200i	0.332058	+	0.943259i	$0.392257\pi$
$44$	5.47491	+	2.26778i	0.825374	+	0.341881i
$45$		0			0
$46$	−2.17107	+	0.899286i	−0.320107	+	0.132592i
$47$			9.50560i			1.38653i	0.720680	+	0.693267i	$0.243830\pi$
$47$			9.50560i			1.38653i	−0.720680	+	0.693267i	$0.756170\pi$
$48$	−3.39134	−	8.18743i	−0.489498	−	1.18175i
$49$	−4.87024	−	4.87024i	−0.695748	−	0.695748i
$50$		0			0
$51$	−4.63373	+	6.26236i	−0.648852	+	0.876906i
$52$	−0.869767			−0.120615
$53$	5.16482	+	5.16482i	0.709443	+	0.709443i	0.966418	−	0.256975i	$-0.0827259\pi$
$53$	5.16482	+	5.16482i	0.709443	+	0.709443i	−0.256975	+	0.966418i	$0.582726\pi$
$54$	−3.31360	−	7.99973i	−0.450923	−	1.08863i
$55$		0			0
$56$	−0.259122	+	0.107332i	−0.0346267	+	0.0143428i
$57$	2.70035	−	6.51923i	0.357670	−	0.863493i
$58$	6.94514	+	2.87677i	0.911941	+	0.377738i
$59$	−6.60087	+	6.60087i	−0.859360	+	0.859360i	−0.991263	−	0.131903i	$-0.957891\pi$
$59$	−6.60087	+	6.60087i	−0.859360	+	0.859360i	0.131903	+	0.991263i	$0.457891\pi$
$60$		0			0
$61$	0.687270	+	0.284676i	0.0879958	+	0.0364491i	0.426247	−	0.904607i	$-0.359835\pi$
$61$	0.687270	+	0.284676i	0.0879958	+	0.0364491i	−0.338251	+	0.941056i	$0.609835\pi$
$62$	−6.75712	+	16.3131i	−0.858155	+	2.07177i
$63$	0.176564	−	0.0731351i	0.0222449	−	0.00921416i
$64$			4.14571i			0.518214i
$65$		0			0
$66$	−9.59272	−	9.59272i	−1.18078	−	1.18078i
$67$	−7.29434			−0.891146			−0.445573	−	0.895246i	$-0.647000\pi$
$67$	−7.29434			−0.891146			−0.445573	+	0.895246i	$0.647000\pi$
$68$	5.50086	−	3.30538i	0.667077	−	0.400836i
$69$	2.35438			0.283434
$70$		0			0
$71$	−5.95517	−	14.3771i	−0.706749	−	1.70624i	−0.707970	−	0.706243i	$-0.750389\pi$
$71$	−5.95517	−	14.3771i	−0.706749	−	1.70624i	0.00122104	−	0.999999i	$-0.499611\pi$
$72$			0.476688i			0.0561782i
$73$	−10.3022	+	4.26733i	−1.20579	+	0.499453i	−0.892865	−	0.450325i	$-0.851308\pi$
$73$	−10.3022	+	4.26733i	−1.20579	+	0.499453i	−0.312922	+	0.949779i	$0.601308\pi$
$74$	4.88721	−	11.7988i	0.568127	−	1.37158i
$75$		0			0
$76$	−4.11038	+	4.11038i	−0.471492	+	0.471492i
$77$	−0.902761	+	0.902761i	−0.102879	+	0.102879i
$78$	1.83956	+	0.761969i	0.208289	+	0.0862760i
$79$	−4.58769	+	11.0757i	−0.516155	+	1.24611i	0.424093	+	0.905619i	$0.360593\pi$
$79$	−4.58769	+	11.0757i	−0.516155	+	1.24611i	−0.940248	+	0.340490i	$0.889407\pi$
$80$		0			0
$81$			10.3850i			1.15388i
$82$	1.21281	+	2.92798i	0.133932	+	0.323341i
$83$	8.29190	+	8.29190i	0.910155	+	0.910155i	0.996284	−	0.0861294i	$-0.0274498\pi$
$83$	8.29190	+	8.29190i	0.910155	+	0.910155i	−0.0861294	+	0.996284i	$0.527450\pi$
$84$	−0.986155			−0.107598
$85$		0			0
$86$	−10.6892			−1.15264
$87$	−5.32561	−	5.32561i	−0.570965	−	0.570965i
$88$	−1.21864	−	2.94206i	−0.129907	−	0.313624i
$89$			13.1316i			1.39195i	0.718066	+	0.695975i	$0.245028\pi$
$89$			13.1316i			1.39195i	−0.718066	+	0.695975i	$0.754972\pi$
$90$		0			0
$91$	0.0717081	−	0.173119i	0.00751705	−	0.0181478i
$92$	−1.79188	−	0.742219i	−0.186816	−	0.0773817i
$93$	12.5091	−	12.5091i	1.29713	−	1.29713i
$94$	−12.6758	+	12.6758i	−1.30741	+	1.30741i
$95$		0			0
$96$	5.18608	−	12.5203i	0.529302	−	1.27785i
$97$	9.81153	−	4.06407i	0.996210	−	0.412644i	0.175804	−	0.984425i	$-0.443748\pi$
$97$	9.81153	−	4.06407i	0.996210	−	0.412644i	0.820406	+	0.571782i	$0.193748\pi$
$98$		−	12.9890i		−	1.31209i
$99$	0.830371	+	2.00469i	0.0834554	+	0.201479i
$100$		0			0
$101$	12.6689			1.26060			0.630300	−	0.776352i	$-0.282932\pi$
$101$	12.6689			1.26060			0.630300	+	0.776352i	$0.282932\pi$
$102$	−14.5300	+	2.17179i	−1.43869	+	0.215039i
$103$	13.2397			1.30455			0.652273	−	0.757985i	$-0.273816\pi$
$103$	13.2397			1.30455			0.652273	+	0.757985i	$0.273816\pi$
$104$	0.330492	+	0.330492i	0.0324075	+	0.0324075i
$105$		0			0
$106$			13.7747i			1.33791i
$107$	8.18993	−	3.39238i	0.791751	−	0.327954i	0.0501034	−	0.998744i	$-0.484045\pi$
$107$	8.18993	−	3.39238i	0.791751	−	0.327954i	0.741647	+	0.670790i	$0.234045\pi$
$108$	2.73485	−	6.60252i	0.263161	−	0.635328i
$109$	−2.36586	−	0.979971i	−0.226608	−	0.0938642i	0.266491	−	0.963838i	$-0.414136\pi$
$109$	−2.36586	−	0.979971i	−0.226608	−	0.0938642i	−0.493099	+	0.869973i	$0.664136\pi$
$110$		0			0
$111$	−9.04743	+	9.04743i	−0.858744	+	0.858744i
$112$	−1.45308	−	0.601885i	−0.137303	−	0.0568728i
$113$	2.71030	−	6.54324i	0.254963	−	0.615536i	−0.743628	−	0.668594i	$-0.766897\pi$
$113$	2.71030	−	6.54324i	0.254963	−	0.615536i	0.998591	+	0.0530573i	$0.0168966\pi$
$114$	12.2944	−	5.09250i	1.15147	−	0.476956i
$115$		0			0
$116$	2.37432	+	5.73212i	0.220450	+	0.532214i
$117$	−0.225195	−	0.225195i	−0.0208193	−	0.0208193i
$118$	−17.6046			−1.62064
$119$	0.204385	+	1.36741i	0.0187359	+	0.125350i
$120$		0			0
$121$	−2.47171	−	2.47171i	−0.224701	−	0.224701i
$122$	0.536861	+	1.29610i	0.0486051	+	0.117343i
$123$		−	3.17520i		−	0.286298i
$124$	−13.4639	+	5.57694i	−1.20910	+	0.500824i
$125$		0			0
$126$	0.332975	+	0.137923i	0.0296638	+	0.0122871i
$127$	0.310015	−	0.310015i	0.0275094	−	0.0275094i	−0.693218	−	0.720728i	$-0.743808\pi$
$127$	0.310015	−	0.310015i	0.0275094	−	0.0275094i	0.720728	+	0.693218i	$0.243808\pi$
$128$	4.61511	−	4.61511i	0.407922	−	0.407922i
$129$	9.89413	+	4.09828i	0.871129	+	0.360834i
$130$		0			0
$131$	3.66708	−	1.51896i	0.320394	−	0.132712i	−0.216689	−	0.976241i	$-0.569526\pi$
$131$	3.66708	−	1.51896i	0.320394	−	0.132712i	0.537084	+	0.843529i	$0.319526\pi$
$132$		−	11.1967i		−	0.974550i
$133$	−0.479250	−	1.15701i	−0.0415562	−	0.100326i
$134$	−9.72706	−	9.72706i	−0.840290	−	0.840290i
$135$		0			0
$136$	−3.34618	−	0.834234i	−0.286933	−	0.0715349i
$137$	−4.65140			−0.397396			−0.198698	−	0.980061i	$-0.563671\pi$
$137$	−4.65140			−0.397396			−0.198698	+	0.980061i	$0.563671\pi$
$138$	3.13959	+	3.13959i	0.267259	+	0.267259i
$139$	−1.66516	−	4.02004i	−0.141237	−	0.340976i	0.837394	−	0.546599i	$-0.184078\pi$
$139$	−1.66516	−	4.02004i	−0.141237	−	0.340976i	−0.978631	+	0.205623i	$0.934078\pi$
$140$		0			0
$141$	16.5930	−	6.87304i	1.39738	−	0.578814i
$142$	11.2306	−	27.1132i	0.942455	−	2.27529i
$143$	1.96558	+	0.814169i	0.164370	+	0.0680842i
$144$	−1.89018	+	1.89018i	−0.157515	+	0.157515i
$145$		0			0
$146$	−19.4286	−	8.04761i	−1.60793	−	0.666025i
$147$	−4.98005	+	12.0229i	−0.410748	+	0.991633i
$148$	9.73804	−	4.03363i	0.800462	−	0.331562i
$149$		−	15.0861i		−	1.23590i	−0.786217	−	0.617950i	$-0.787963\pi$
$149$		−	15.0861i		−	1.23590i	0.786217	−	0.617950i	$-0.212037\pi$
$150$		0			0
$151$	−14.3011	−	14.3011i	−1.16381	−	1.16381i	−0.983634	−	0.180176i	$-0.942333\pi$
$151$	−14.3011	−	14.3011i	−1.16381	−	1.16381i	−0.180176	−	0.983634i	$-0.557667\pi$
$152$	3.12371			0.253366
$153$	2.28006	+	0.568439i	0.184332	+	0.0459556i
$154$	−2.40768			−0.194016
$155$		0			0
$156$	0.628886	+	1.51826i	0.0503512	+	0.121558i
$157$		−	11.6845i		−	0.932525i	−0.884646	−	0.466263i	$-0.845600\pi$
$157$		−	11.6845i		−	0.932525i	0.884646	−	0.466263i	$-0.154400\pi$
$158$	−20.8872	+	8.65175i	−1.66170	+	0.688297i
$159$	5.28128	−	12.7501i	0.418833	−	1.01115i
$160$		0			0
$161$	0.295463	−	0.295463i	0.0232858	−	0.0232858i
$162$	−13.8484	+	13.8484i	−1.08803	+	1.08803i
$163$	10.7048	+	4.43407i	0.838464	+	0.347303i	0.760248	−	0.649633i	$-0.225078\pi$
$163$	10.7048	+	4.43407i	0.838464	+	0.347303i	0.0782160	+	0.996936i	$0.475078\pi$
$164$	−1.00098	+	2.41659i	−0.0781636	+	0.188704i
$165$		0			0
$166$			22.1146i			1.71643i
$167$	7.09236	+	17.1225i	0.548823	+	1.32498i	0.918355	+	0.395758i	$0.129518\pi$
$167$	7.09236	+	17.1225i	0.548823	+	1.32498i	−0.369532	+	0.929218i	$0.620482\pi$
$168$	0.374718	+	0.374718i	0.0289101	+	0.0289101i
$169$	12.6877			0.975980
$170$		0			0
$171$	−2.12847			−0.162768
$172$	−6.23825	−	6.23825i	−0.475662	−	0.475662i
$173$	−0.516258	−	1.24636i	−0.0392504	−	0.0947589i	0.903039	−	0.429559i	$-0.141331\pi$
$173$	−0.516258	−	1.24636i	−0.0392504	−	0.0947589i	−0.942289	+	0.334800i	$0.891331\pi$
$174$		−	14.2035i		−	1.07676i
$175$		0			0
$176$	6.83376	−	16.4982i	0.515114	−	1.24359i
$177$	16.2952	+	6.74971i	1.22483	+	0.507339i
$178$	−17.5111	+	17.5111i	−1.31251	+	1.31251i
$179$	−6.30106	+	6.30106i	−0.470963	+	0.470963i	−0.902226	−	0.431263i	$-0.858068\pi$
$179$	−6.30106	+	6.30106i	−0.470963	+	0.470963i	0.431263	+	0.902226i	$0.358068\pi$
$180$		0			0
$181$	−2.98099	+	7.19675i	−0.221575	+	0.534930i	−0.995104	−	0.0988310i	$-0.968490\pi$
$181$	−2.98099	+	7.19675i	−0.221575	+	0.534930i	0.773529	+	0.633761i	$0.218490\pi$
$182$	0.326478	−	0.135232i	0.0242002	−	0.0100240i
$183$		−	1.40553i		−	0.103900i
$184$	0.398847	+	0.962901i	0.0294034	+	0.0709860i
$185$		0			0
$186$	33.3619			2.44622
$187$	−15.5254	+	2.32057i	−1.13533	+	0.169697i
$188$	−14.7953			−1.07906
$189$	1.08869	+	1.08869i	0.0791908	+	0.0791908i
$190$		0			0
$191$			2.88897i			0.209038i	0.994523	+	0.104519i	$0.0333304\pi$
$191$			2.88897i			0.209038i	−0.994523	+	0.104519i	$0.966670\pi$
$192$	7.23675	−	2.99756i	0.522268	−	0.216330i
$193$	−6.73687	+	16.2642i	−0.484931	+	1.17073i	0.472310	+	0.881433i	$0.343420\pi$
$193$	−6.73687	+	16.2642i	−0.484931	+	1.17073i	−0.957240	+	0.289294i	$0.906580\pi$
$194$	18.5032	+	7.66428i	1.32845	+	0.550263i
$195$		0			0
$196$	7.58045	−	7.58045i	0.541461	−	0.541461i
$197$	22.8712	+	9.47357i	1.62951	+	0.674964i	0.995177	−	0.0980974i	$-0.0312757\pi$
$197$	22.8712	+	9.47357i	1.62951	+	0.674964i	0.634331	+	0.773062i	$0.281276\pi$
$198$	−1.56597	+	3.78058i	−0.111288	+	0.268674i
$199$	−2.20365	+	0.912782i	−0.156213	+	0.0647054i	−0.459420	−	0.888219i	$-0.651943\pi$
$199$	−2.20365	+	0.912782i	−0.156213	+	0.0647054i	0.303207	+	0.952925i	$0.401943\pi$
$200$		0			0
$201$	5.27418	+	12.7330i	0.372012	+	0.898117i
$202$	16.8940	+	16.8940i	1.18866	+	1.18866i
$203$	−1.33668			−0.0938162
$204$	−9.74727	−	7.21234i	−0.682446	−	0.504965i
$205$		0			0
$206$	17.6552	+	17.6552i	1.23010	+	1.23010i
$207$	−0.271771	−	0.656113i	−0.0188894	−	0.0456030i
$208$			2.62096i			0.181731i
$209$	13.1366	−	5.44137i	0.908680	−	0.376387i
$210$		0			0
$211$	−9.17536	−	3.80056i	−0.631658	−	0.261641i	0.0437994	−	0.999040i	$-0.486054\pi$
$211$	−9.17536	−	3.80056i	−0.631658	−	0.261641i	−0.675457	+	0.737399i	$0.736054\pi$
$212$	−8.03896	+	8.03896i	−0.552118	+	0.552118i
$213$	−20.7907	+	20.7907i	−1.42455	+	1.42455i
$214$	15.4451	+	6.39757i	1.05581	+	0.437329i
$215$		0			0
$216$	−3.54800	+	1.46963i	−0.241411	+	0.0999957i
$217$		−	3.13966i		−	0.213134i
$218$	−1.84809	−	4.46169i	−0.125169	−	0.302184i
$219$	14.8981	+	14.8981i	1.00672	+	1.00672i
$220$		0			0
$221$	1.97489	−	1.18668i	0.132846	−	0.0798249i
$222$	−24.1296			−1.61948
$223$	−8.07535	−	8.07535i	−0.540765	−	0.540765i	0.382988	−	0.923753i	$-0.374895\pi$
$223$	−8.07535	−	8.07535i	−0.540765	−	0.540765i	−0.923753	+	0.382988i	$0.874895\pi$
$224$	−0.920409	−	2.22206i	−0.0614974	−	0.148468i
$225$		0			0
$226$	12.3397	−	5.11126i	0.820822	−	0.339996i
$227$	−0.364094	+	0.879001i	−0.0241658	+	0.0583413i	−0.935502	−	0.353322i	$-0.885052\pi$
$227$	−0.364094	+	0.879001i	−0.0241658	+	0.0583413i	0.911336	+	0.411663i	$0.135052\pi$
$228$	10.1471	+	4.20306i	0.672007	+	0.278354i
$229$	−12.2351	+	12.2351i	−0.808520	+	0.808520i	−0.984410	−	0.175890i	$-0.943720\pi$
$229$	−12.2351	+	12.2351i	−0.808520	+	0.808520i	0.175890	+	0.984410i	$0.443720\pi$
$230$		0			0
$231$	2.22860	+	0.923117i	0.146631	+	0.0607367i
$232$	1.27589	−	3.08027i	0.0837663	−	0.202230i
$233$	−14.7233	+	6.09859i	−0.964556	+	0.399532i	−0.808683	−	0.588245i	$-0.799819\pi$
$233$	−14.7233	+	6.09859i	−0.964556	+	0.399532i	−0.155873	+	0.987777i	$0.549819\pi$
$234$		−	0.600598i		−	0.0392623i
$235$		0			0
$236$	−10.2742	−	10.2742i	−0.668790	−	0.668790i
$237$	22.6508			1.47133
$238$	−1.55090	+	2.09600i	−0.100530	+	0.135863i
$239$	−9.77203			−0.632100			−0.316050	−	0.948743i	$-0.602357\pi$
$239$	−9.77203			−0.632100			−0.316050	+	0.948743i	$0.602357\pi$
$240$		0			0
$241$	−10.0230	−	24.1978i	−0.645641	−	1.55872i	−0.818960	−	0.573850i	$-0.805449\pi$
$241$	−10.0230	−	24.1978i	−0.645641	−	1.55872i	0.173319	−	0.984866i	$-0.444551\pi$
$242$		−	6.59209i		−	0.423756i
$243$	5.40214	−	2.23764i	0.346548	−	0.143545i
$244$	−0.443094	+	1.06972i	−0.0283662	+	0.0684821i
$245$		0			0
$246$	4.23416	−	4.23416i	0.269960	−	0.269960i
$247$	−1.47569	+	1.47569i	−0.0938957	+	0.0938957i
$248$	7.23512	+	2.99688i	0.459431	+	0.190302i
$249$	8.47887	−	20.4698i	0.537327	−	1.29722i
$250$		0			0
$251$			18.3573i			1.15870i	0.815078	+	0.579351i	$0.196694\pi$
$251$			18.3573i			1.15870i	−0.815078	+	0.579351i	$0.803306\pi$
$252$	0.113834	+	0.274819i	0.00717085	+	0.0173120i
$253$	3.35467	+	3.35467i	0.210906	+	0.210906i
$254$	0.826814			0.0518789
$255$		0			0
$256$	20.6000			1.28750
$257$	−14.3446	−	14.3446i	−0.894791	−	0.894791i	0.100179	−	0.994969i	$-0.468058\pi$
$257$	−14.3446	−	14.3446i	−0.894791	−	0.894791i	−0.994969	+	0.100179i	$0.968058\pi$
$258$	7.72880	+	18.6590i	0.481174	+	1.16166i
$259$			2.27082i			0.141102i
$260$		0			0
$261$	−0.869381	+	2.09887i	−0.0538133	+	0.129917i
$262$	6.91562	+	2.86454i	0.427248	+	0.176972i
$263$	8.02655	−	8.02655i	0.494938	−	0.494938i	−0.414920	−	0.909858i	$-0.636190\pi$
$263$	8.02655	−	8.02655i	0.494938	−	0.494938i	0.909858	+	0.414920i	$0.136190\pi$
$264$	−4.25452	+	4.25452i	−0.261847	+	0.261847i
$265$		0			0
$266$	0.903801	−	2.18197i	0.0554156	−	0.133785i
$267$	22.9226	−	9.49484i	1.40284	−	0.581075i
$268$		−	11.3535i		−	0.693527i
$269$	0.536103	+	1.29427i	0.0326868	+	0.0789128i	0.939380	−	0.342878i	$-0.111402\pi$
$269$	0.536103	+	1.29427i	0.0326868	+	0.0789128i	−0.906693	+	0.421791i	$0.861402\pi$
$270$		0			0
$271$	−3.64441			−0.221382			−0.110691	−	0.993855i	$-0.535306\pi$
$271$	−3.64441			−0.221382			−0.110691	+	0.993855i	$0.535306\pi$
$272$	−9.96046	−	16.5763i	−0.603942	−	1.00509i
$273$	−0.354045			−0.0214278
$274$	−6.20268	−	6.20268i	−0.374718	−	0.374718i
$275$		0			0
$276$			3.66456i			0.220581i
$277$	−11.8638	+	4.91416i	−0.712829	+	0.295263i	−0.709475	−	0.704731i	$-0.751068\pi$
$277$	−11.8638	+	4.91416i	−0.712829	+	0.295263i	−0.00335413	+	0.999994i	$0.501068\pi$
$278$	3.14026	−	7.58126i	0.188340	−	0.454694i
$279$	−4.92995	−	2.04205i	−0.295148	−	0.122254i
$280$		0			0
$281$	15.1581	−	15.1581i	0.904255	−	0.904255i	−0.0915454	−	0.995801i	$-0.529181\pi$
$281$	15.1581	−	15.1581i	0.904255	−	0.904255i	0.995801	+	0.0915454i	$0.0291807\pi$
$282$	31.2921	+	12.9616i	1.86342	+	0.771853i
$283$	−3.58976	+	8.66646i	−0.213389	+	0.515167i	−0.993940	−	0.109925i	$-0.964939\pi$
$283$	−3.58976	+	8.66646i	−0.213389	+	0.515167i	0.780551	+	0.625093i	$0.214939\pi$
$284$	22.3777	−	9.26913i	1.32787	−	0.550022i
$285$		0			0
$286$	1.53541	+	3.70681i	0.0907908	+	0.219188i
$287$	−0.398472	−	0.398472i	−0.0235211	−	0.0235211i
$288$	−4.08776			−0.240874
$289$	−7.98049	+	15.0104i	−0.469440	+	0.882964i
$290$		0			0
$291$	−14.1885	−	14.1885i	−0.831743	−	0.831743i
$292$	−6.64204	−	16.0353i	−0.388696	−	0.938395i
$293$		−	22.0519i		−	1.28828i	−0.764906	−	0.644142i	$-0.777214\pi$
$293$		−	22.0519i		−	1.28828i	0.764906	−	0.644142i	$-0.222786\pi$
$294$	−22.6736	+	9.39171i	−1.32235	+	0.547736i
$295$		0			0
$296$	−5.23293	−	2.16755i	−0.304158	−	0.125986i
$297$	−12.3609	+	12.3609i	−0.717255	+	0.717255i
$298$	20.1174	−	20.1174i	1.16537	−	1.16537i
$299$	−0.643311	−	0.266468i	−0.0372036	−	0.0154102i
$300$		0			0
$301$	1.75598	−	0.727350i	0.101213	−	0.0419238i
$302$		−	38.1414i		−	2.19479i
$303$	−9.16024	−	22.1148i	−0.526242	−	1.27046i
$304$	12.3862	+	12.3862i	0.710399	+	0.710399i
$305$		0			0
$306$	2.28246	+	3.79849i	0.130479	+	0.217145i
$307$	−4.89164			−0.279181			−0.139590	−	0.990209i	$-0.544579\pi$
$307$	−4.89164			−0.279181			−0.139590	+	0.990209i	$0.544579\pi$
$308$	−1.40513	−	1.40513i	−0.0800650	−	0.0800650i
$309$	−9.57297	−	23.1112i	−0.544587	−	1.31475i
$310$		0			0
$311$	4.49000	−	1.85982i	0.254604	−	0.105461i	−0.251731	−	0.967797i	$-0.581000\pi$
$311$	4.49000	−	1.85982i	0.254604	−	0.105461i	0.506335	+	0.862337i	$0.331000\pi$
$312$	0.337945	−	0.815871i	0.0191323	−	0.0461896i
$313$	−20.8833	−	8.65013i	−1.18039	−	0.488935i	−0.295777	−	0.955257i	$-0.595579\pi$
$313$	−20.8833	−	8.65013i	−1.18039	−	0.488935i	−0.884615	+	0.466322i	$0.845579\pi$
$314$	15.5814	−	15.5814i	0.879308	−	0.879308i
$315$		0			0
$316$	−17.2391	−	7.14066i	−0.969775	−	0.401694i
$317$	1.95102	−	4.71017i	0.109580	−	0.264549i	−0.859571	−	0.511016i	$-0.829269\pi$
$317$	1.95102	−	4.71017i	0.109580	−	0.264549i	0.969151	+	0.246466i	$0.0792694\pi$
$318$	24.0450	−	9.95978i	1.34838	−	0.558517i
$319$		−	15.1765i		−	0.849722i
$320$		0			0
$321$	−11.8435	−	11.8435i	−0.661039	−	0.661039i
$322$	0.788005			0.0439138
$323$	3.72495	−	14.9411i	0.207262	−	0.831344i
$324$	−16.1640			−0.898001
$325$		0			0
$326$	8.36205	+	20.1878i	0.463131	+	1.11810i
$327$			4.83841i			0.267565i
$328$	1.29860	−	0.537899i	0.0717033	−	0.0297005i
$329$	1.21980	−	2.94487i	0.0672500	−	0.162356i
$330$		0			0
$331$	−24.0968	+	24.0968i	−1.32448	+	1.32448i	−0.414371	+	0.910108i	$0.635998\pi$
$331$	−24.0968	+	24.0968i	−1.32448	+	1.32448i	−0.910108	+	0.414371i	$0.864002\pi$
$332$	−12.9062	+	12.9062i	−0.708321	+	0.708321i
$333$	3.56567	+	1.47695i	0.195398	+	0.0809364i
$334$	−13.3752	+	32.2906i	−0.731860	+	1.76687i
$335$		0			0
$336$			2.97169i			0.162119i
$337$	4.30033	+	10.3819i	0.234254	+	0.565539i	0.996669	−	0.0815491i	$-0.0259867\pi$
$337$	4.30033	+	10.3819i	0.234254	+	0.565539i	−0.762416	+	0.647088i	$0.775987\pi$
$338$	16.9192	+	16.9192i	0.920283	+	0.920283i
$339$	−13.3816			−0.726787
$340$		0			0
$341$	35.6475			1.93042
$342$	−2.83833	−	2.83833i	−0.153479	−	0.153479i
$343$	1.78212	+	4.30241i	0.0962253	+	0.232308i
$344$			4.74080i			0.255607i
$345$		0			0
$346$	0.973594	−	2.35046i	0.0523407	−	0.126362i
$347$	−14.6652	−	6.07454i	−0.787272	−	0.326099i	−0.0474255	−	0.998875i	$-0.515102\pi$
$347$	−14.6652	−	6.07454i	−0.787272	−	0.326099i	−0.739846	+	0.672776i	$0.765102\pi$
$348$	8.28923	−	8.28923i	0.444349	−	0.444349i
$349$	2.24304	−	2.24304i	0.120067	−	0.120067i	−0.644520	−	0.764587i	$-0.722943\pi$
$349$	2.24304	−	2.24304i	0.120067	−	0.120067i	0.764587	+	0.644520i	$0.222943\pi$
$350$		0			0
$351$	0.981854	−	2.37041i	0.0524075	−	0.126523i
$352$	25.2292	−	10.4503i	1.34472	−	0.557001i
$353$		−	34.6534i		−	1.84441i	−0.386696	−	0.922207i	$-0.626384\pi$
$353$		−	34.6534i		−	1.84441i	0.386696	−	0.922207i	$-0.373616\pi$
$354$	12.7290	+	30.7306i	0.676541	+	1.63331i
$355$		0			0
$356$	−20.4392			−1.08327
$357$	2.23916	−	1.34548i	0.118509	−	0.0712103i
$358$	−16.8050			−0.888173
$359$	−15.4968	−	15.4968i	−0.817888	−	0.817888i	0.167914	−	0.985802i	$-0.446297\pi$
$359$	−15.4968	−	15.4968i	−0.817888	−	0.817888i	−0.985802	+	0.167914i	$0.946297\pi$
$360$		0			0
$361$		−	5.05229i		−	0.265910i
$362$	−13.5721	+	5.62174i	−0.713333	+	0.295472i
$363$	−2.52745	+	6.10179i	−0.132656	+	0.320261i
$364$	0.269457	+	0.111613i	0.0141234	+	0.00585009i
$365$		0			0
$366$	1.87429	−	1.87429i	0.0979707	−	0.0979707i
$367$	−6.34751	−	2.62922i	−0.331337	−	0.137244i	0.210812	−	0.977527i	$-0.432389\pi$
$367$	−6.34751	−	2.62922i	−0.331337	−	0.137244i	−0.542149	+	0.840282i	$0.682389\pi$
$368$	−2.23661	+	5.39965i	−0.116591	+	0.281476i
$369$	−0.884856	+	0.366519i	−0.0460638	+	0.0190802i
$370$		0			0
$371$	−0.937305	−	2.26285i	−0.0486624	−	0.117482i
$372$	19.4702	+	19.4702i	1.00948	+	1.00948i
$373$	34.8389			1.80389			0.901946	−	0.431850i	$-0.142139\pi$
$373$	34.8389			1.80389			0.901946	+	0.431850i	$0.142139\pi$
$374$	−23.7978	−	17.6088i	−1.23055	−	0.910528i
$375$		0			0
$376$	5.62191	+	5.62191i	0.289928	+	0.289928i
$377$	0.852418	+	2.05792i	0.0439017	+	0.105988i
$378$			2.90356i			0.149343i
$379$	21.9470	−	9.09076i	1.12734	−	0.466961i	0.260467	−	0.965483i	$-0.416124\pi$
$379$	21.9470	−	9.09076i	1.12734	−	0.466961i	0.866877	+	0.498522i	$0.166124\pi$
$380$		0			0
$381$	−0.765318	−	0.317005i	−0.0392084	−	0.0162407i
$382$	−3.85246	+	3.85246i	−0.197109	+	0.197109i
$383$	−3.76978	+	3.76978i	−0.192627	+	0.192627i	−0.796830	−	0.604203i	$-0.793491\pi$
$383$	−3.76978	+	3.76978i	−0.192627	+	0.192627i	0.604203	+	0.796830i	$0.293491\pi$
$384$	−11.3931	−	4.71917i	−0.581401	−	0.240824i
$385$		0			0
$386$	−30.6722	+	12.7048i	−1.56117	+	0.646659i
$387$		−	3.23034i		−	0.164207i
$388$	6.32566	+	15.2715i	0.321137	+	0.775293i
$389$	14.5321	+	14.5321i	0.736808	+	0.736808i	0.971959	−	0.235150i	$-0.0755583\pi$
$389$	14.5321	+	14.5321i	0.736808	+	0.736808i	−0.235150	+	0.971959i	$0.575558\pi$
$390$		0			0
$391$	5.08129	−	0.759496i	0.256972	−	0.0384094i
$392$	−5.76081			−0.290965
$393$	−5.30298	−	5.30298i	−0.267500	−	0.267500i
$394$	17.8659	+	43.1320i	0.900070	+	2.17296i
$395$		0			0
$396$	−3.12027	+	1.29246i	−0.156800	+	0.0649485i
$397$	−3.08280	+	7.44253i	−0.154721	+	0.373530i	−0.982166	−	0.188017i	$-0.939794\pi$
$397$	−3.08280	+	7.44253i	−0.154721	+	0.373530i	0.827444	+	0.561548i	$0.189794\pi$
$398$	−4.15579	−	1.72138i	−0.208311	−	0.0862852i
$399$	−1.67316	+	1.67316i	−0.0837626	+	0.0837626i
$400$		0			0
$401$	−12.4455	−	5.15508i	−0.621497	−	0.257432i	0.0496387	−	0.998767i	$-0.484193\pi$
$401$	−12.4455	−	5.15508i	−0.621497	−	0.257432i	−0.671135	+	0.741335i	$0.734193\pi$
$402$	−9.94639	+	24.0127i	−0.496081	+	1.19765i
$403$	−4.83376	+	2.00221i	−0.240787	+	0.0997370i
$404$			19.7189i			0.981053i
$405$		0			0
$406$	−1.78247	−	1.78247i	−0.0884623	−	0.0884623i
$407$	−25.7827			−1.27800
$408$	0.963221	+	6.44429i	0.0476866	+	0.319040i
$409$	−7.88198			−0.389739			−0.194869	−	0.980829i	$-0.562428\pi$
$409$	−7.88198			−0.389739			−0.194869	+	0.980829i	$0.562428\pi$
$410$		0			0
$411$	3.36320	+	8.11948i	0.165894	+	0.400505i
$412$			20.6074i			1.01525i
$413$	2.89203	−	1.19792i	0.142307	−	0.0589456i
$414$	0.512523	−	1.23734i	0.0251891	−	0.0608119i
$415$		0			0
$416$	−2.83409	+	2.83409i	−0.138953	+	0.138953i
$417$	−5.81340	+	5.81340i	−0.284683	+	0.284683i
$418$	24.7739	+	10.2617i	1.21173	+	0.501915i
$419$	−2.09753	+	5.06389i	−0.102471	+	0.247387i	−0.966797	−	0.255544i	$-0.917745\pi$
$419$	−2.09753	+	5.06389i	−0.102471	+	0.247387i	0.864326	+	0.502932i	$0.167745\pi$
$420$		0			0
$421$		−	13.5189i		−	0.658873i	−0.944178	−	0.329437i	$-0.893141\pi$
$421$		−	13.5189i		−	0.658873i	0.944178	−	0.329437i	$-0.106859\pi$
$422$	−7.16734	−	17.3035i	−0.348901	−	0.842321i
$423$	−3.83072	−	3.83072i	−0.186256	−	0.186256i
$424$	6.10927			0.296692
$425$		0			0
$426$	−55.4491			−2.68652
$427$	−0.176387	−	0.176387i	−0.00853599	−	0.00853599i
$428$	5.28019	+	12.7475i	0.255228	+	0.616174i
$429$		−	4.01980i		−	0.194078i
$430$		0			0
$431$	−15.5636	+	37.5740i	−0.749674	+	1.80987i	−0.188712	+	0.982032i	$0.560431\pi$
$431$	−15.5636	+	37.5740i	−0.749674	+	1.80987i	−0.560962	+	0.827841i	$0.689569\pi$
$432$	−19.8961	−	8.24123i	−0.957251	−	0.396506i
$433$	−22.7592	+	22.7592i	−1.09374	+	1.09374i	−0.0986088	+	0.995126i	$0.531439\pi$
$433$	−22.7592	+	22.7592i	−1.09374	+	1.09374i	−0.995126	+	0.0986088i	$0.968561\pi$
$434$	4.18676	−	4.18676i	0.200971	−	0.200971i
$435$		0			0
$436$	1.52531	−	3.68242i	0.0730491	−	0.176356i
$437$	−4.29947	+	1.78090i	−0.205671	+	0.0851919i
$438$			39.7335i			1.89854i
$439$	−14.6236	−	35.3045i	−0.697946	−	1.68499i	−0.728123	−	0.685446i	$-0.759607\pi$
$439$	−14.6236	−	35.3045i	−0.697946	−	1.68499i	0.0301772	−	0.999545i	$-0.490393\pi$
$440$		0			0
$441$	3.92537			0.186922
$442$	4.21598	+	1.05108i	0.200534	+	0.0499949i
$443$	39.5730			1.88017			0.940086	−	0.340938i	$-0.110745\pi$
$443$	39.5730			1.88017			0.940086	+	0.340938i	$0.110745\pi$
$444$	−14.0822	−	14.0822i	−0.668311	−	0.668311i
$445$		0			0
$446$		−	21.5371i		−	1.01981i
$447$	−26.3343	+	10.9080i	−1.24557	+	0.515931i
$448$	0.531997	−	1.28436i	0.0251345	−	0.0606801i
$449$	−10.4743	−	4.33859i	−0.494312	−	0.204751i	0.121580	−	0.992582i	$-0.461204\pi$
$449$	−10.4743	−	4.33859i	−0.494312	−	0.204751i	−0.615891	+	0.787831i	$0.711204\pi$
$450$		0			0
$451$	4.52422	−	4.52422i	0.213037	−	0.213037i
$452$	10.1845	+	4.21854i	0.479037	+	0.198423i
$453$	−14.6236	+	35.3045i	−0.687077	+	1.65875i
$454$	−1.65768	+	0.686632i	−0.0777986	+	0.0322252i
$455$		0			0
$456$	−2.25860	−	5.45274i	−0.105769	−	0.255348i
$457$	2.78590	+	2.78590i	0.130319	+	0.130319i	0.769258	−	0.638939i	$-0.220626\pi$
$457$	2.78590	+	2.78590i	0.130319	+	0.130319i	−0.638939	+	0.769258i	$0.720626\pi$
$458$	−32.6313			−1.52476
$459$	2.79851	+	18.7230i	0.130623	+	0.873916i
$460$		0			0
$461$	7.34660	+	7.34660i	0.342165	+	0.342165i	0.857181	−	0.515016i	$-0.172214\pi$
$461$	7.34660	+	7.34660i	0.342165	+	0.342165i	−0.515016	+	0.857181i	$0.672214\pi$
$462$	1.74087	+	4.20284i	0.0809928	+	0.195534i
$463$		−	9.30604i		−	0.432488i	−0.976339	−	0.216244i	$-0.930619\pi$
$463$		−	9.30604i		−	0.432488i	0.976339	−	0.216244i	$-0.0693807\pi$
$464$	17.2732	−	7.15480i	0.801889	−	0.332153i
$465$		0			0
$466$	−27.7662	−	11.5011i	−1.28624	−	0.532779i
$467$	6.20595	−	6.20595i	0.287177	−	0.287177i	−0.548786	−	0.835963i	$-0.684910\pi$
$467$	6.20595	−	6.20595i	0.287177	−	0.287177i	0.835963	+	0.548786i	$0.184910\pi$
$468$	0.350512	−	0.350512i	0.0162024	−	0.0162024i
$469$	2.25981	+	0.936045i	0.104348	+	0.0432225i
$470$		0			0
$471$	−20.3965	+	8.44850i	−0.939820	+	0.389286i
$472$			7.80791i			0.359388i
$473$	8.25828	+	19.9372i	0.379716	+	0.916716i
$474$	30.2050	+	30.2050i	1.38736	+	1.38736i
$475$		0			0
$476$	−2.12835	+	0.318122i	−0.0975526	+	0.0145811i
$477$	−4.16280			−0.190601
$478$	−13.0311	−	13.0311i	−0.596028	−	0.596028i
$479$	−12.1048	−	29.2235i	−0.553081	−	1.33525i	−0.915154	−	0.403105i	$-0.867931\pi$
$479$	−12.1048	−	29.2235i	−0.553081	−	1.33525i	0.362073	−	0.932150i	$-0.382069\pi$
$480$		0			0
$481$	3.49610	−	1.44813i	0.159409	−	0.0660292i
$482$	18.9021	−	45.6337i	0.860967	−	2.07856i
$483$	−0.729396	−	0.302126i	−0.0331887	−	0.0137472i
$484$	3.84718	−	3.84718i	0.174872	−	0.174872i
$485$		0			0
$486$	10.1877	+	4.21989i	0.462124	+	0.191418i
$487$	−13.6803	+	33.0273i	−0.619916	+	1.49661i	0.231885	+	0.972743i	$0.425511\pi$
$487$	−13.6803	+	33.0273i	−0.619916	+	1.49661i	−0.851801	+	0.523866i	$0.824489\pi$
$488$	0.574839	−	0.238106i	0.0260217	−	0.0107785i
$489$		−	21.8923i		−	0.990005i
$490$		0			0
$491$	10.8870	+	10.8870i	0.491324	+	0.491324i	0.908723	−	0.417399i	$-0.137058\pi$
$491$	10.8870	+	10.8870i	0.491324	+	0.491324i	−0.417399	+	0.908723i	$0.637058\pi$
$492$	4.94215			0.222810
$493$	−13.2119	−	9.77590i	−0.595032	−	0.440284i
$494$	−3.93568			−0.177075
$495$		0			0
$496$	16.8056	+	40.5723i	0.754594	+	1.82175i
$497$			5.21826i			0.234071i
$498$	38.6033	−	15.9900i	1.72986	−	0.716529i
$499$	4.27770	−	10.3273i	0.191496	−	0.462313i	−0.798746	−	0.601668i	$-0.794503\pi$
$499$	4.27770	−	10.3273i	0.191496	−	0.462313i	0.990242	+	0.139355i	$0.0445030\pi$
$500$		0			0
$501$	24.7608	−	24.7608i	1.10623	−	1.10623i
$502$	−24.4796	+	24.4796i	−1.09258	+	1.09258i
$503$	−18.0038	−	7.45742i	−0.802750	−	0.332510i	−0.0566928	−	0.998392i	$-0.518056\pi$
$503$	−18.0038	−	7.45742i	−0.802750	−	0.332510i	−0.746057	+	0.665882i	$0.768056\pi$
$504$	0.0611709	−	0.147680i	0.00272477	−	0.00657817i
$505$		0			0
$506$			8.94695i			0.397741i
$507$	−9.17389	−	22.1477i	−0.407427	−	0.983615i
$508$	0.482533	+	0.482533i	0.0214090	+	0.0214090i
$509$	−38.3851			−1.70139			−0.850695	−	0.525660i	$-0.823818\pi$
$509$	−38.3851			−1.70139			−0.850695	+	0.525660i	$0.823818\pi$
$510$		0			0
$511$	3.73928			0.165416
$512$	18.2400	+	18.2400i	0.806103	+	0.806103i
$513$	−6.56207	−	15.8422i	−0.289722	−	0.699452i
$514$		−	38.2572i		−	1.68745i
$515$		0			0
$516$	−6.37891	+	15.4001i	−0.280816	+	0.677950i
$517$	33.4358	+	13.8496i	1.47051	+	0.609104i
$518$	−3.02815	+	3.02815i	−0.133049	+	0.133049i
$519$	−1.80236	+	1.80236i	−0.0791149	+	0.0791149i
$520$		0			0
$521$	−2.33657	+	5.64099i	−0.102367	+	0.247136i	−0.966762	−	0.255677i	$-0.917702\pi$
$521$	−2.33657	+	5.64099i	−0.102367	+	0.247136i	0.864395	+	0.502813i	$0.167702\pi$
$522$	−3.95819	+	1.63953i	−0.173245	+	0.0717605i
$523$		−	16.2004i		−	0.708392i	−0.935171	−	0.354196i	$-0.884755\pi$
$523$		−	16.2004i		−	0.708392i	0.935171	−	0.354196i	$-0.115245\pi$
$524$	2.36423	+	5.70776i	0.103282	+	0.249345i
$525$		0			0
$526$	21.4069			0.933387
$527$	22.9622	−	31.0328i	1.00025	−	1.35181i
$528$	−33.7403			−1.46836
$529$	15.1655	+	15.1655i	0.659370	+	0.659370i
$530$		0			0
$531$		−	5.32024i		−	0.230879i
$532$	1.80087	−	0.745945i	0.0780777	−	0.0323408i
$533$	−0.359368	+	0.867591i	−0.0155660	+	0.0375795i
$534$	43.2289	+	17.9060i	1.87070	+	0.774868i
$535$		0			0
$536$	−4.31410	+	4.31410i	−0.186341	+	0.186341i
$537$	15.5551	+	6.44314i	0.671253	+	0.278042i
$538$	−1.01102	+	2.44081i	−0.0435880	+	0.105231i
$539$	−24.2269	+	10.0351i	−1.04353	+	0.432242i
$540$		0			0
$541$	−1.49263	−	3.60353i	−0.0641731	−	0.154928i	0.888540	−	0.458800i	$-0.151720\pi$
$541$	−1.49263	−	3.60353i	−0.0641731	−	0.154928i	−0.952713	+	0.303872i	$0.901720\pi$
$542$	−4.85984	−	4.85984i	−0.208748	−	0.208748i
$543$	14.7180			0.631612
$544$	7.15384	−	28.6946i	0.306718	−	1.23027i
$545$		0			0
$546$	−0.472121	−	0.472121i	−0.0202049	−	0.0202049i
$547$	−6.02751	−	14.5517i	−0.257718	−	0.622185i	0.741069	−	0.671429i	$-0.234319\pi$
$547$	−6.02751	−	14.5517i	−0.257718	−	0.622185i	−0.998787	+	0.0492434i	$0.984319\pi$
$548$		−	7.23984i		−	0.309270i
$549$	−0.391690	+	0.162243i	−0.0167169	+	0.00692437i
$550$		0			0
$551$	13.7538	+	5.69700i	0.585930	+	0.242700i
$552$	1.39245	−	1.39245i	0.0592668	−	0.0592668i
$553$	2.84256	−	2.84256i	0.120878	−	0.120878i
$554$	−22.3736	−	9.26744i	−0.950562	−	0.393736i
$555$		0			0
$556$	6.25714	−	2.59179i	0.265362	−	0.109916i
$557$			4.05067i			0.171632i	0.996311	+	0.0858161i	$0.0273498\pi$
$557$			4.05067i			0.171632i	−0.996311	+	0.0858161i	$0.972650\pi$
$558$	−3.85103	−	9.29721i	−0.163027	−	0.393582i
$559$	−2.23963	−	2.23963i	−0.0947261	−	0.0947261i
$560$		0			0
$561$	15.2765	+	25.4233i	0.644973	+	1.07337i
$562$	40.4268			1.70530
$563$	−3.40955	−	3.40955i	−0.143696	−	0.143696i	0.631599	−	0.775295i	$-0.282399\pi$
$563$	−3.40955	−	3.40955i	−0.143696	−	0.143696i	−0.775295	+	0.631599i	$0.782399\pi$
$564$	10.6978	+	25.8267i	0.450458	+	1.08750i
$565$		0			0
$566$	−16.3438	+	6.76981i	−0.686980	+	0.284556i
$567$	1.33265	−	3.21730i	0.0559659	−	0.135114i
$568$	−12.0251	−	4.98096i	−0.504562	−	0.208996i
$569$	30.6954	−	30.6954i	1.28682	−	1.28682i	0.350106	−	0.936710i	$-0.386146\pi$
$569$	30.6954	−	30.6954i	1.28682	−	1.28682i	0.936710	−	0.350106i	$-0.113854\pi$
$570$		0			0
$571$	10.6100	+	4.39481i	0.444015	+	0.183917i	0.593478	−	0.804850i	$-0.297754\pi$
$571$	10.6100	+	4.39481i	0.444015	+	0.183917i	−0.149463	+	0.988767i	$0.547754\pi$
$572$	−1.26724	+	3.05939i	−0.0529860	+	0.127920i
$573$	5.04298	−	2.08887i	0.210674	−	0.0872639i
$574$		−	1.06273i		−	0.0443575i
$575$		0			0
$576$	−1.67070	−	1.67070i	−0.0696126	−	0.0696126i
$577$	−36.7718			−1.53083			−0.765415	−	0.643537i	$-0.777466\pi$
$577$	−36.7718			−1.53083			−0.765415	+	0.643537i	$0.777466\pi$
$578$	−30.6585	+	9.37443i	−1.27523	+	0.389925i
$579$	33.2620			1.38232
$580$		0			0
$581$	−1.50480	−	3.63292i	−0.0624298	−	0.150719i
$582$		−	37.8409i		−	1.56855i
$583$	25.6923	−	10.6421i	1.06407	−	0.440750i
$584$	−3.56924	+	8.61690i	−0.147696	+	0.356570i
$585$		0			0
$586$	29.4063	−	29.4063i	1.21477	−	1.21477i
$587$	13.3065	−	13.3065i	0.549219	−	0.549219i	−0.376996	−	0.926215i	$-0.623043\pi$
$587$	13.3065	−	13.3065i	0.549219	−	0.549219i	0.926215	+	0.376996i	$0.123043\pi$
$588$	−18.7135	−	7.75138i	−0.771731	−	0.319662i
$589$	−13.3814	+	32.3056i	−0.551372	+	1.33113i
$590$		0			0
$591$		−	46.7739i		−	1.92402i
$592$	−12.1550	−	29.3447i	−0.499566	−	1.20606i
$593$	−0.366973	−	0.366973i	−0.0150698	−	0.0150698i	0.699532	−	0.714602i	$-0.253392\pi$
$593$	−0.366973	−	0.366973i	−0.0150698	−	0.0150698i	−0.714602	+	0.699532i	$0.753392\pi$
$594$	−32.9668			−1.35265
$595$		0			0
$596$	23.4813			0.961830
$597$	3.18671	+	3.18671i	0.130423	+	0.130423i
$598$	−0.502523	−	1.21320i	−0.0205497	−	0.0496113i
$599$			5.36433i			0.219180i	0.993977	+	0.109590i	$0.0349539\pi$
$599$			5.36433i			0.219180i	−0.993977	+	0.109590i	$0.965046\pi$
$600$		0			0
$601$	−6.43273	+	15.5300i	−0.262396	+	0.633481i	−0.999086	−	0.0427504i	$-0.986388\pi$
$601$	−6.43273	+	15.5300i	−0.262396	+	0.633481i	0.736689	+	0.676231i	$0.236388\pi$
$602$	3.31154	+	1.37168i	0.134968	+	0.0559056i
$603$	2.93959	−	2.93959i	0.119709	−	0.119709i
$604$	22.2595	−	22.2595i	0.905727	−	0.905727i
$605$		0			0
$606$	17.2750	−	41.7055i	0.701748	−	1.69417i
$607$	22.8532	−	9.46610i	0.927582	−	0.384217i	0.132822	−	0.991140i	$-0.457596\pi$
$607$	22.8532	−	9.46610i	0.927582	−	0.384217i	0.794761	+	0.606923i	$0.207596\pi$
$608$			26.7869i			1.08635i
$609$	0.966485	+	2.33330i	0.0391639	+	0.0945501i
$610$		0			0
$611$	−5.31175			−0.214890
$612$	−0.884767	+	3.54888i	−0.0357646	+	0.143455i
$613$	5.46570			0.220757			0.110379	−	0.993890i	$-0.464794\pi$
$613$	5.46570			0.220757			0.110379	+	0.993890i	$0.464794\pi$
$614$	−6.52304	−	6.52304i	−0.263249	−	0.263249i
$615$		0			0
$616$			1.06784i			0.0430246i
$617$	18.8491	−	7.80755i	0.758836	−	0.314320i	0.0304947	−	0.999535i	$-0.490292\pi$
$617$	18.8491	−	7.80755i	0.758836	−	0.314320i	0.728341	+	0.685215i	$0.240292\pi$
$618$	18.0533	−	43.5846i	0.726211	−	1.75323i
$619$	−35.1548	−	14.5616i	−1.41299	−	0.585279i	−0.459900	−	0.887971i	$-0.652115\pi$
$619$	−35.1548	−	14.5616i	−1.41299	−	0.585279i	−0.953089	+	0.302691i	$0.902115\pi$
$620$		0			0
$621$	4.04559	−	4.04559i	0.162344	−	0.162344i
$622$	8.46753	+	3.50737i	0.339517	+	0.140633i
$623$	1.68511	−	4.06822i	0.0675126	−	0.162990i
$624$	4.57515	−	1.89509i	0.183153	−	0.0758643i
$625$		0			0
$626$	−16.3130	−	39.3830i	−0.651998	−	1.57406i
$627$	−18.9969	−	18.9969i	−0.758663	−	0.758663i
$628$	18.1868			0.725731
$629$	−16.6078	+	22.4450i	−0.662197	+	0.894941i
$630$		0			0
$631$	−26.0820	−	26.0820i	−1.03831	−	1.03831i	−0.999236	−	0.0390728i	$-0.987560\pi$
$631$	−26.0820	−	26.0820i	−1.03831	−	1.03831i	−0.0390728	−	0.999236i	$-0.512440\pi$
$632$	3.83718	+	9.26378i	0.152635	+	0.368493i
$633$			18.7645i			0.745822i
$634$	8.88274	−	3.67935i	0.352779	−	0.146126i
$635$		0			0
$636$	19.8454	+	8.22023i	0.786921	+	0.325953i
$637$	2.72150	−	2.72150i	0.107830	−	0.107830i
$638$	20.2380	−	20.2380i	0.801230	−	0.801230i
$639$	8.19380	+	3.39398i	0.324142	+	0.134264i
$640$		0			0
$641$	28.5131	−	11.8105i	1.12620	−	0.466486i	0.259711	−	0.965686i	$-0.416373\pi$
$641$	28.5131	−	11.8105i	1.12620	−	0.466486i	0.866487	+	0.499200i	$0.166373\pi$
$642$		−	31.5867i		−	1.24663i
$643$	14.8876	+	35.9418i	0.587109	+	1.41741i	0.886254	+	0.463199i	$0.153299\pi$
$643$	14.8876	+	35.9418i	0.587109	+	1.41741i	−0.299145	+	0.954208i	$0.596701\pi$
$644$	0.459884	+	0.459884i	0.0181220	+	0.0181220i
$645$		0			0
$646$	24.8913	−	14.9568i	0.979335	−	0.588467i
$647$	24.3986			0.959209			0.479605	−	0.877485i	$-0.340780\pi$
$647$	24.3986			0.959209			0.479605	+	0.877485i	$0.340780\pi$
$648$	6.14198	+	6.14198i	0.241280	+	0.241280i
$649$	13.6011	+	32.8359i	0.533888	+	1.28892i
$650$		0			0
$651$	−5.48059	+	2.27013i	−0.214801	+	0.0889736i
$652$	−6.90156	+	16.6618i	−0.270286	+	0.652528i
$653$	14.6879	+	6.08392i	0.574781	+	0.238082i	0.651088	−	0.759002i	$-0.274313\pi$
$653$	14.6879	+	6.08392i	0.574781	+	0.238082i	−0.0763070	+	0.997084i	$0.524313\pi$
$654$	−6.45206	+	6.45206i	−0.252295	+	0.252295i
$655$		0			0
$656$	7.28216	+	3.01637i	0.284321	+	0.117769i
$657$	2.43205	−	5.87148i	0.0948831	−	0.229068i
$658$	5.55362	−	2.30039i	0.216503	−	0.0896784i
$659$			31.1072i			1.21176i	0.795554	+	0.605882i	$0.207180\pi$
$659$			31.1072i			1.21176i	−0.795554	+	0.605882i	$0.792820\pi$
$660$		0			0
$661$	14.4062	+	14.4062i	0.560336	+	0.560336i	0.929403	−	0.369067i	$-0.120323\pi$
$661$	14.4062	+	14.4062i	0.560336	+	0.560336i	−0.369067	+	0.929403i	$0.620323\pi$
$662$	−64.2665			−2.49779
$663$	−3.49942	−	2.58934i	−0.135906	−	0.100562i
$664$	9.80817			0.380631
$665$		0			0
$666$	2.78533	+	6.72438i	0.107929	+	0.260564i
$667$			4.96710i			0.192327i
$668$	−26.6509	+	11.0391i	−1.03115	+	0.427117i
$669$	−8.25744	+	19.9352i	−0.319251	+	0.770740i
$670$		0			0
$671$	2.00269	−	2.00269i	0.0773130	−	0.0773130i
$672$	−3.21333	+	3.21333i	−0.123957	+	0.123957i
$673$	−39.9541	−	16.5495i	−1.54012	−	0.637938i	−0.558623	−	0.829422i	$-0.688670\pi$
$673$	−39.9541	−	16.5495i	−1.54012	−	0.637938i	−0.981496	+	0.191484i	$0.938670\pi$
$674$	−8.10984	+	19.5789i	−0.312379	+	0.754150i
$675$		0			0
$676$			19.7483i			0.759549i
$677$	−1.37905	−	3.32933i	−0.0530013	−	0.127957i	0.895161	−	0.445743i	$-0.147060\pi$
$677$	−1.37905	−	3.32933i	−0.0530013	−	0.127957i	−0.948162	+	0.317786i	$0.897060\pi$
$678$	−17.8444	−	17.8444i	−0.685311	−	0.685311i
$679$	−3.56117			−0.136665
$680$		0			0
$681$	1.79764			0.0688858
$682$	47.5362	+	47.5362i	1.82025	+	1.82025i
$683$	0.0868787	+	0.209744i	0.00332432	+	0.00802562i	0.925533	−	0.378667i	$-0.123617\pi$
$683$	0.0868787	+	0.209744i	0.00332432	+	0.00802562i	−0.922209	+	0.386693i	$0.873617\pi$
$684$		−	3.31293i		−	0.126673i
$685$		0			0
$686$	−3.36083	+	8.11377i	−0.128317	+	0.309785i
$687$	30.2043	+	12.5110i	1.15236	+	0.477325i
$688$	−18.7984	+	18.7984i	−0.716682	+	0.716682i
$689$	−2.88611	+	2.88611i	−0.109952	+	0.109952i
$690$		0			0
$691$	0.792297	−	1.91277i	0.0301404	−	0.0727653i	−0.908093	−	0.418769i	$-0.862462\pi$
$691$	0.792297	−	1.91277i	0.0301404	−	0.0727653i	0.938233	+	0.346004i	$0.112462\pi$
$692$	1.93994	−	0.803549i	0.0737454	−	0.0305463i
$693$		−	0.727618i		−	0.0276399i
$694$	−11.4558	−	27.6567i	−0.434855	−	1.04983i
$695$		0			0
$696$	−6.29946			−0.238780
$697$	−1.02428	−	6.85281i	−0.0387975	−	0.259569i
$698$	5.98222			0.226430
$699$	21.2914	+	21.2914i	0.805315	+	0.805315i
$700$		0			0
$701$			8.10138i			0.305985i	0.988227	+	0.152992i	$0.0488910\pi$
$701$			8.10138i			0.305985i	−0.988227	+	0.152992i	$0.951109\pi$
$702$	4.47026	−	1.85164i	0.168719	−	0.0698858i
$703$	9.67837	−	23.3657i	0.365027	−	0.881252i
$704$	14.5825	+	6.04026i	0.549598	+	0.227651i
$705$		0			0
$706$	46.2106	−	46.2106i	1.73916	−	1.73916i
$707$	−3.92486	−	1.62573i	−0.147610	−	0.0611419i
$708$	−10.5058	+	25.3633i	−0.394833	+	0.953211i
$709$	30.5996	−	12.6748i	1.14919	−	0.476011i	0.274929	−	0.961464i	$-0.411346\pi$
$709$	30.5996	−	12.6748i	1.14919	−	0.476011i	0.874262	+	0.485454i	$0.161346\pi$
$710$		0			0
$711$	−2.61462	−	6.31226i	−0.0980560	−	0.236728i
$712$	7.76645	+	7.76645i	0.291060	+	0.291060i
$713$	−11.6670			−0.436933
$714$	4.78015	+	1.19173i	0.178893	+	0.0445996i
$715$		0			0
$716$	−9.80751	−	9.80751i	−0.366524	−	0.366524i
$717$	7.06568	+	17.0581i	0.263873	+	0.637045i
$718$		−	41.3301i		−	1.54243i
$719$	25.4683	−	10.5493i	0.949807	−	0.393423i	0.146649	−	0.989189i	$-0.453151\pi$
$719$	25.4683	−	10.5493i	0.949807	−	0.393423i	0.803158	+	0.595766i	$0.203151\pi$
$720$		0			0
$721$	−4.10170	−	1.69898i	−0.152755	−	0.0632733i
$722$	6.73726	−	6.73726i	0.250735	−	0.250735i
$723$	−34.9925	+	34.9925i	−1.30138	+	1.30138i
$724$	−11.2016	−	4.63987i	−0.416305	−	0.172439i
$725$		0			0
$726$	−11.5072	+	4.76642i	−0.427071	+	0.176898i
$727$			7.87140i			0.291934i	0.989289	+	0.145967i	$0.0466294\pi$
$727$			7.87140i			0.291934i	−0.989289	+	0.145967i	$0.953371\pi$
$728$	−0.0599773	−	0.144798i	−0.00222291	−	0.00536657i
$729$	14.2178	+	14.2178i	0.526584	+	0.526584i
$730$		0			0
$731$	22.6758	+	5.65330i	0.838696	+	0.209095i
$732$	2.18769			0.0808594
$733$	17.1792	+	17.1792i	0.634529	+	0.634529i	0.949201	−	0.314672i	$-0.101894\pi$
$733$	17.1792	+	17.1792i	0.634529	+	0.634529i	−0.314672	+	0.949201i	$0.601894\pi$
$734$	−4.95836	−	11.9705i	−0.183016	−	0.441841i
$735$		0			0
$736$	−8.25721	+	3.42025i	−0.304365	+	0.126072i
$737$	−10.6278	+	25.6577i	−0.391480	+	0.945115i
$738$	−1.66872	−	0.691206i	−0.0614264	−	0.0254436i
$739$	−25.6967	+	25.6967i	−0.945268	+	0.945268i	−0.998578	−	0.0533099i	$-0.983023\pi$
$739$	−25.6967	+	25.6967i	−0.945268	+	0.945268i	0.0533099	+	0.998578i	$0.483023\pi$
$740$		0			0
$741$	3.64296	+	1.50896i	0.133827	+	0.0554331i
$742$	1.76763	−	4.26744i	0.0648917	−	0.156662i
$743$	−23.1520	+	9.58988i	−0.849366	+	0.351819i	−0.764539	−	0.644577i	$-0.777034\pi$
$743$	−23.1520	+	9.58988i	−0.849366	+	0.351819i	−0.0848262	+	0.996396i	$0.527034\pi$
$744$		−	14.7965i		−	0.542467i
$745$		0			0
$746$	46.4580	+	46.4580i	1.70095	+	1.70095i
$747$	−6.68320			−0.244526
$748$	−3.61193	−	24.1651i	−0.132065	−	0.883563i
$749$	−2.97260			−0.108616
$750$		0			0
$751$	4.19911	+	10.1376i	0.153228	+	0.369925i	0.981789	−	0.189974i	$-0.0608402\pi$
$751$	4.19911	+	10.1376i	0.153228	+	0.369925i	−0.828561	+	0.559898i	$0.810840\pi$
$752$			44.5844i			1.62582i
$753$	32.0445	−	13.2733i	1.16777	−	0.483704i
$754$	−1.60754	+	3.88095i	−0.0585433	+	0.141336i
$755$		0			0
$756$	−1.69453	+	1.69453i	−0.0616296	+	0.0616296i
$757$	15.0037	−	15.0037i	0.545317	−	0.545317i	−0.379765	−	0.925083i	$-0.623995\pi$
$757$	15.0037	−	15.0037i	0.545317	−	0.545317i	0.925083	+	0.379765i	$0.123995\pi$
$758$	41.3892	+	17.1439i	1.50332	+	0.622696i
$759$	3.43031	−	8.28151i	0.124512	−	0.300600i
$760$		0			0
$761$		−	37.2293i		−	1.34956i	−0.738019	−	0.674780i	$-0.764238\pi$
$761$		−	37.2293i		−	1.34956i	0.738019	−	0.674780i	$-0.235762\pi$
$762$	−0.597829	−	1.44329i	−0.0216571	−	0.0522847i
$763$	0.607197	+	0.607197i	0.0219820	+	0.0219820i
$764$	−4.49664			−0.162683
$765$		0			0
$766$	−10.0541			−0.363268
$767$	−3.68858	−	3.68858i	−0.133187	−	0.133187i
$768$	−14.8948	−	35.9593i	−0.537471	−	1.29757i
$769$		−	28.9604i		−	1.04434i	−0.852842	−	0.522169i	$-0.825123\pi$
$769$		−	28.9604i		−	1.04434i	0.852842	−	0.522169i	$-0.174877\pi$
$770$		0			0
$771$	−14.6680	+	35.4118i	−0.528256	+	1.27532i
$772$	−25.3151	−	10.4858i	−0.911109	−	0.377394i
$773$	20.6896	−	20.6896i	0.744152	−	0.744152i	−0.229222	−	0.973374i	$-0.573618\pi$
$773$	20.6896	−	20.6896i	0.744152	−	0.744152i	0.973374	+	0.229222i	$0.0736182\pi$
$774$	4.30768	−	4.30768i	0.154836	−	0.154836i
$775$		0			0
$776$	3.39922	−	8.20645i	0.122025	−	0.294595i
$777$	3.96394	−	1.64192i	0.142205	−	0.0589034i
$778$			38.7574i			1.38952i
$779$	2.40178	+	5.79841i	0.0860527	+	0.207750i
$780$		0			0
$781$	−59.2477			−2.12005
$782$	7.78874	+	5.76315i	0.278525	+	0.206090i
$783$	−18.3023			−0.654069
$784$	−22.8430	−	22.8430i	−0.815821	−	0.815821i
$785$		0			0
$786$		−	14.1431i		−	0.504468i
$787$	−38.0333	+	15.7539i	−1.35574	+	0.561567i	−0.937885	−	0.346946i	$-0.887219\pi$
$787$	−38.0333	+	15.7539i	−1.35574	+	0.561567i	−0.417857	+	0.908513i	$0.637219\pi$
$788$	−14.7455	+	35.5987i	−0.525286	+	1.26815i
$789$	−19.8148	−	8.20754i	−0.705424	−	0.292196i
$790$		0			0
$791$	−1.67932	+	1.67932i	−0.0597098	+	0.0597098i
$792$	1.67674	+	0.694530i	0.0595805	+	0.0246790i
$793$	−0.159078	+	0.384047i	−0.00564901	+	0.0136379i
$794$	−14.0356	+	5.81374i	−0.498105	+	0.206322i
$795$		0			0
$796$	−1.42073	−	3.42995i	−0.0503565	−	0.121571i
$797$	19.9292	+	19.9292i	0.705928	+	0.705928i	0.965676	−	0.259748i	$-0.0836396\pi$
$797$	19.9292	+	19.9292i	0.705928	+	0.705928i	−0.259748	+	0.965676i	$0.583640\pi$
$798$	−4.46234			−0.157965
$799$	33.5943	−	20.1863i	1.18848	−	0.714139i
$800$		0			0
$801$	−5.29199	−	5.29199i	−0.186983	−	0.186983i
$802$	−9.72178	−	23.4705i	−0.343288	−	0.828770i
$803$			42.4555i			1.49822i
$804$	−19.8187	+	8.20919i	−0.698953	+	0.289516i
$805$		0			0
$806$	−9.11581	−	3.77589i	−0.321091	−	0.133000i
$807$	1.87164	−	1.87164i	0.0658849	−	0.0658849i
$808$	7.49276	−	7.49276i	0.263594	−	0.263594i
$809$	33.6793	+	13.9504i	1.18410	+	0.490471i	0.885830	−	0.464010i	$-0.153590\pi$
$809$	33.6793	+	13.9504i	1.18410	+	0.490471i	0.298272	+	0.954481i	$0.403590\pi$
$810$		0			0
$811$	−36.5807	+	15.1522i	−1.28452	+	0.532066i	−0.917348	−	0.398087i	$-0.869674\pi$
$811$	−36.5807	+	15.1522i	−1.28452	+	0.532066i	−0.367173	+	0.930153i	$0.619674\pi$
$812$		−	2.08052i		−	0.0730118i
$813$	2.63509	+	6.36168i	0.0924167	+	0.223114i
$814$	−34.3814	−	34.3814i	−1.20507	−	1.20507i
$815$		0			0
$816$	−21.7337	+	29.3725i	−0.760832	+	1.02824i
$817$	−21.1682			−0.740582
$818$	−10.5107	−	10.5107i	−0.367497	−	0.367497i
$819$	0.0408680	+	0.0986641i	0.00142804	+	0.00344760i
$820$		0			0
$821$	−47.9994	+	19.8820i	−1.67519	+	0.693886i	−0.999079	−	0.0429141i	$-0.986336\pi$
$821$	−47.9994	+	19.8820i	−1.67519	+	0.693886i	−0.676111	+	0.736800i	$0.736336\pi$
$822$	−6.34254	+	15.3122i	−0.221222	+	0.534076i
$823$	12.3527	+	5.11665i	0.430587	+	0.178355i	0.587441	−	0.809267i	$-0.300135\pi$
$823$	12.3527	+	5.11665i	0.430587	+	0.178355i	−0.156854	+	0.987622i	$0.550135\pi$
$824$	7.83036	−	7.83036i	0.272783	−	0.272783i
$825$		0			0
$826$	5.45397	+	2.25911i	0.189768	+	0.0786045i
$827$	−3.15215	+	7.60996i	−0.109611	+	0.264624i	−0.969161	−	0.246427i	$-0.920744\pi$
$827$	−3.15215	+	7.60996i	−0.109611	+	0.264624i	0.859551	+	0.511051i	$0.170744\pi$
$828$	1.02123	−	0.423007i	0.0354902	−	0.0147005i
$829$		−	45.0159i		−	1.56347i	−0.623612	−	0.781734i	$-0.714335\pi$
$829$		−	45.0159i		−	1.56347i	0.623612	−	0.781734i	$-0.285665\pi$
$830$		0			0
$831$	17.1563	+	17.1563i	0.595146	+	0.595146i
$832$	−2.31663			−0.0803147
$833$	−6.86964	+	27.5547i	−0.238019	+	0.954713i
$834$	−15.5044			−0.536874
$835$		0			0
$836$	8.46941	+	20.4470i	0.292921	+	0.707173i
$837$		−	42.9894i		−	1.48593i
$838$	−9.54981	+	3.95566i	−0.329893	+	0.136646i
$839$	1.06357	−	2.56768i	0.0367184	−	0.0886461i	−0.904457	−	0.426566i	$-0.859723\pi$
$839$	1.06357	−	2.56768i	0.0367184	−	0.0886461i	0.941175	+	0.337920i	$0.109723\pi$
$840$		0			0
$841$	−9.27053	+	9.27053i	−0.319673	+	0.319673i
$842$	18.0276	−	18.0276i	0.621273	−	0.621273i
$843$	−37.4200	−	15.4999i	−1.28881	−	0.533844i
$844$	5.91551	−	14.2813i	0.203620	−	0.491583i
$845$		0			0
$846$		−	10.2166i		−	0.351253i
$847$	0.448563	+	1.08293i	0.0154128	+	0.0372098i
$848$	24.2247	+	24.2247i	0.831879	+	0.831879i
$849$	17.7237			0.608277
$850$		0			0
$851$	8.43837			0.289264
$852$	−32.3604	−	32.3604i	−1.10865	−	1.10865i
$853$	2.10429	+	5.08020i	0.0720494	+	0.173943i	0.955802	−	0.294013i	$-0.0949908\pi$
$853$	2.10429	+	5.08020i	0.0720494	+	0.173943i	−0.883752	+	0.467955i	$0.844991\pi$
$854$		−	0.470428i		−	0.0160977i
$855$		0			0
$856$	2.83742	−	6.85013i	0.0969810	−	0.234133i
$857$	10.4033	+	4.30921i	0.355372	+	0.147200i	0.553225	−	0.833032i	$-0.313397\pi$
$857$	10.4033	+	4.30921i	0.355372	+	0.147200i	−0.197853	+	0.980232i	$0.563397\pi$
$858$	5.36043	−	5.36043i	0.183002	−	0.183002i
$859$	20.5171	−	20.5171i	0.700033	−	0.700033i	−0.264384	−	0.964417i	$-0.585169\pi$
$859$	20.5171	−	20.5171i	0.700033	−	0.700033i	0.964417	+	0.264384i	$0.0851688\pi$
$860$		0			0
$861$	−0.407457	+	0.983689i	−0.0138861	+	0.0335240i
$862$	−70.8594	+	29.3509i	−2.41348	+	0.999696i
$863$			2.49653i			0.0849829i	0.999097	+	0.0424914i	$0.0135295\pi$
$863$			2.49653i			0.0849829i	−0.999097	+	0.0424914i	$0.986470\pi$
$864$	−12.6026	−	30.4253i	−0.428749	−	1.03509i
$865$		0			0
$866$	−60.6990			−2.06264
$867$	31.9724	+	3.07746i	1.08584	+	0.104516i
$868$	4.88683			0.165870
$869$	32.2742	+	32.2742i	1.09483	+	1.09483i
$870$		0			0
$871$		−	4.07609i		−	0.138113i
$872$	−1.97883	+	0.819657i	−0.0670115	+	0.0277571i
$873$	−2.31620	+	5.59180i	−0.0783915	+	0.189254i
$874$	−8.10821	−	3.35853i	−0.274264	−	0.113604i
$875$		0			0
$876$	−23.1887	+	23.1887i	−0.783473	+	0.783473i
$877$	−52.1751	−	21.6116i	−1.76183	−	0.729773i	−0.996259	−	0.0864199i	$-0.972457\pi$
$877$	−52.1751	−	21.6116i	−1.76183	−	0.729773i	−0.765569	−	0.643353i	$-0.777543\pi$
$878$	27.5781	−	66.5795i	0.930716	−	2.24695i
$879$	−38.4938	+	15.9446i	−1.29836	+	0.537799i
$880$		0			0
$881$	−7.06706	−	17.0614i	−0.238095	−	0.574813i	0.758990	−	0.651102i	$-0.225693\pi$
$881$	−7.06706	−	17.0614i	−0.238095	−	0.574813i	−0.997086	+	0.0762888i	$0.975693\pi$
$882$	5.23451	+	5.23451i	0.176255	+	0.176255i
$883$	38.2887			1.28852			0.644259	−	0.764808i	$-0.277166\pi$
$883$	38.2887			1.28852			0.644259	+	0.764808i	$0.277166\pi$
$884$	1.84705	+	3.07389i	0.0621231	+	0.103386i
$885$		0			0
$886$	52.7709	+	52.7709i	1.77287	+	1.77287i
$887$	12.3661	+	29.8544i	0.415213	+	1.00241i	0.983716	+	0.179731i	$0.0575228\pi$
$887$	12.3661	+	29.8544i	0.415213	+	1.00241i	−0.568503	+	0.822681i	$0.692477\pi$
$888$			10.7019i			0.359131i
$889$	−0.135826	+	0.0562611i	−0.00455546	+	0.00188694i
$890$		0			0
$891$	36.5289	+	15.1308i	1.22377	+	0.506900i
$892$	12.5692	−	12.5692i	0.420847	−	0.420847i
$893$	−25.1025	+	25.1025i	−0.840022	+	0.840022i
$894$	−49.6629	−	20.5710i	−1.66098	−	0.687998i
$895$		0			0
$896$	−2.02201	+	0.837544i	−0.0675506	+	0.0279804i
$897$			1.31563i			0.0439277i
$898$	−8.18199	−	19.7531i	−0.273036	−	0.659168i
$899$	26.3907	+	26.3907i	0.880181	+	0.880181i
$900$		0			0
$901$	7.28516	−	29.2214i	0.242704	−	0.973505i
$902$	12.0662			0.401760
$903$	−2.53932	−	2.53932i	−0.0845034	−	0.0845034i
$904$	−2.26692	−	5.47283i	−0.0753966	−	0.182024i
$905$		0			0
$906$	−66.5796	+	27.5782i	−2.21196	+	0.916223i
$907$	7.97415	−	19.2513i	0.264777	−	0.639229i	−0.734445	−	0.678669i	$-0.762557\pi$
$907$	7.97415	−	19.2513i	0.264777	−	0.639229i	0.999222	+	0.0394396i	$0.0125573\pi$
$908$	−1.36815	−	0.566707i	−0.0454037	−	0.0188068i
$909$	−5.10550	+	5.10550i	−0.169339	+	0.169339i
$910$		0			0
$911$	−43.8597	−	18.1673i	−1.45314	−	0.601908i	−0.490193	−	0.871614i	$-0.663074\pi$
$911$	−43.8597	−	18.1673i	−1.45314	−	0.601908i	−0.962943	+	0.269706i	$0.913074\pi$
$912$	12.6655	−	30.5773i	0.419398	−	1.01252i
$913$	41.2479	−	17.0854i	1.36511	−	0.565445i
$914$			7.43005i			0.245764i
$915$		0			0
$916$	−19.0438	−	19.0438i	−0.629225	−	0.629225i
$917$	−1.33099			−0.0439533
$918$	−21.2355	+	28.6991i	−0.700875	+	0.947213i
$919$	28.1486			0.928538			0.464269	−	0.885694i	$-0.346317\pi$
$919$	28.1486			0.928538			0.464269	+	0.885694i	$0.346317\pi$
$920$		0			0
$921$	3.53691	+	8.53885i	0.116545	+	0.281365i
$922$			19.5935i			0.645277i
$923$	8.03392	−	3.32776i	0.264440	−	0.109535i
$924$	−1.43682	+	3.46879i	−0.0472679	+	0.114115i
$925$		0			0
$926$	12.4097	−	12.4097i	0.407807	−	0.407807i
$927$	−5.33554	+	5.33554i	−0.175242	+	0.175242i
$928$	26.4144	+	10.9412i	0.867095	+	0.359163i
$929$	1.61712	−	3.90407i	0.0530559	−	0.128088i	−0.895129	−	0.445807i	$-0.852917\pi$
$929$	1.61712	−	3.90407i	0.0530559	−	0.128088i	0.948185	+	0.317719i	$0.102917\pi$
$930$		0			0
$931$		−	25.7227i		−	0.843027i
$932$	−9.49237	−	22.9166i	−0.310933	−	0.750659i
$933$	−6.49300	−	6.49300i	−0.212571	−	0.212571i
$934$	16.5514			0.541577
$935$		0			0
$936$	−0.266374			−0.00870671
$937$	−17.4547	−	17.4547i	−0.570219	−	0.570219i	0.361970	−	0.932190i	$-0.382104\pi$
$937$	−17.4547	−	17.4547i	−0.570219	−	0.570219i	−0.932190	+	0.361970i	$0.882104\pi$
$938$	1.76525	+	4.26170i	0.0576376	+	0.139149i
$939$			42.7083i			1.39373i
$940$		0			0
$941$	−8.71889	+	21.0493i	−0.284228	+	0.686187i	−0.999925	−	0.0122238i	$-0.996109\pi$
$941$	−8.71889	+	21.0493i	−0.284228	+	0.686187i	0.715697	+	0.698410i	$0.246109\pi$
$942$	−38.4650	−	15.9327i	−1.25326	−	0.519116i
$943$	−1.48073	+	1.48073i	−0.0482191	+	0.0482191i
$944$	−30.9602	+	30.9602i	−1.00767	+	1.00767i
$945$		0			0
$946$	−15.5740	+	37.5989i	−0.506354	+	1.22245i
$947$	−8.76683	+	3.63134i	−0.284884	+	0.118003i	−0.520550	−	0.853831i	$-0.674273\pi$
$947$	−8.76683	+	3.63134i	−0.284884	+	0.118003i	0.235666	+	0.971834i	$0.424273\pi$
$948$			35.2556i			1.14505i
$949$	−2.38459	−	5.75691i	−0.0774071	−	0.186877i
$950$		0			0
$951$	−9.63275			−0.312363
$952$	0.929605	+	0.687846i	0.0301287	+	0.0222932i
$953$	−15.0041			−0.486031			−0.243016	−	0.970022i	$-0.578137\pi$
$953$	−15.0041			−0.486031			−0.243016	+	0.970022i	$0.578137\pi$
$954$	−5.55112	−	5.55112i	−0.179724	−	0.179724i
$955$		0			0
$956$		−	15.2100i		−	0.491927i
$957$	−26.4921	+	10.9734i	−0.856369	+	0.354720i
$958$	22.8279	−	55.1115i	0.737537	−	1.78057i
$959$	1.44102	+	0.596890i	0.0465330	+	0.0192746i
$960$		0			0
$961$	−40.0678	+	40.0678i	−1.29251	+	1.29251i
$962$	6.59318	+	2.73098i	0.212573	+	0.0880504i
$963$	−1.93339	+	4.66762i	−0.0623027	+	0.150412i
$964$	37.6635	−	15.6007i	1.21306	−	0.502465i
$965$		0			0
$966$	−0.569768	−	1.37554i	−0.0183320	−	0.0442573i
$967$	19.9524	+	19.9524i	0.641625	+	0.641625i	0.950955	−	0.309330i	$-0.100105\pi$
$967$	19.9524	+	19.9524i	0.641625	+	0.641625i	−0.309330	+	0.950955i	$0.600105\pi$
$968$	−2.92369			−0.0939710
$969$	−28.7745	+	4.30089i	−0.924369	+	0.138165i
$970$		0			0
$971$	35.3096	+	35.3096i	1.13314	+	1.13314i	0.989652	+	0.143489i	$0.0458320\pi$
$971$	35.3096	+	35.3096i	1.13314	+	1.13314i	0.143489	+	0.989652i	$0.454168\pi$
$972$	3.48285	+	8.40835i	0.111713	+	0.269698i
$973$			1.45910i			0.0467768i
$974$	−62.2850	+	25.7993i	−1.99574	+	0.826662i
$975$		0			0
$976$	3.22352	+	1.33522i	0.103182	+	0.0427395i
$977$	6.20642	−	6.20642i	0.198561	−	0.198561i	−0.600822	−	0.799383i	$-0.705160\pi$
$977$	6.20642	−	6.20642i	0.198561	−	0.198561i	0.799383	+	0.600822i	$0.205160\pi$
$978$	29.1936	−	29.1936i	0.933508	−	0.933508i
$979$	46.1903	+	19.1327i	1.47625	+	0.611482i
$980$		0			0
$981$	1.34835	−	0.558507i	0.0430496	−	0.0178317i
$982$			29.0358i			0.926571i
$983$	3.27415	+	7.90450i	0.104429	+	0.252114i	0.967454	−	0.253047i	$-0.0814328\pi$
$983$	3.27415	+	7.90450i	0.104429	+	0.252114i	−0.863025	+	0.505162i	$0.831433\pi$
$984$	−1.87791	−	1.87791i	−0.0598656	−	0.0598656i
$985$		0			0
$986$	−4.58188	−	30.6543i	−0.145917	−	0.976233i
$987$	−6.02254			−0.191700
$988$	−2.29688	−	2.29688i	−0.0730736	−	0.0730736i
$989$	−2.70284	−	6.52523i	−0.0859453	−	0.207490i
$990$		0			0
$991$	34.1352	−	14.1393i	1.08434	−	0.449149i	0.232311	−	0.972642i	$-0.425371\pi$
$991$	34.1352	−	14.1393i	1.08434	−	0.449149i	0.852030	+	0.523493i	$0.175371\pi$
$992$	−25.6993	+	62.0437i	−0.815954	+	1.96989i
$993$	59.4866	+	24.6401i	1.88775	+	0.781931i
$994$	−6.95858	+	6.95858i	−0.220713	+	0.220713i
$995$		0			0
$996$	31.8610	+	13.1972i	1.00955	+	0.418171i
$997$	20.9413	−	50.5568i	0.663217	−	1.60115i	−0.129514	−	0.991578i	$-0.541342\pi$
$997$	20.9413	−	50.5568i	0.663217	−	1.60115i	0.792731	−	0.609571i	$-0.208658\pi$
$998$	19.4759	−	8.06717i	0.616498	−	0.255362i
$999$			31.0929i			0.983735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.d.151.6	yes	24
5.2	odd	4		425.2.n.d.49.1		24
5.3	odd	4		425.2.n.e.49.6		24
5.4	even	2		425.2.m.c.151.1	yes	24
17.5	odd	16		7225.2.a.cb.1.4		24
17.8	even	8	inner	425.2.m.d.76.6	yes	24
17.12	odd	16		7225.2.a.cb.1.3		24
85.8	odd	8		425.2.n.d.399.1		24
85.29	odd	16		7225.2.a.bx.1.22		24
85.39	odd	16		7225.2.a.bx.1.21		24
85.42	odd	8		425.2.n.e.399.6		24
85.59	even	8		425.2.m.c.76.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.1	✓	24	85.59	even	8
425.2.m.c.151.1	yes	24	5.4	even	2
425.2.m.d.76.6	yes	24	17.8	even	8	inner
425.2.m.d.151.6	yes	24	1.1	even	1	trivial
425.2.n.d.49.1		24	5.2	odd	4
425.2.n.d.399.1		24	85.8	odd	8
425.2.n.e.49.6		24	5.3	odd	4
425.2.n.e.399.6		24	85.42	odd	8
7225.2.a.bx.1.21		24	85.39	odd	16
7225.2.a.bx.1.22		24	85.29	odd	16
7225.2.a.cb.1.3		24	17.12	odd	16
7225.2.a.cb.1.4		24	17.5	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33351 + 1.33351i) q^{2} +(-0.723051 - 1.74560i) q^{3} +1.55648i q^{4} +(1.36358 - 3.29196i) q^{6} +(-0.309803 - 0.128325i) q^{7} +(0.591431 - 0.591431i) q^{8} +(-0.402996 + 0.402996i) q^{9} +O(q^{10})\)	\(q+(1.33351 + 1.33351i) q^{2} +(-0.723051 - 1.74560i) q^{3} +1.55648i q^{4} +(1.36358 - 3.29196i) q^{6} +(-0.309803 - 0.128325i) q^{7} +(0.591431 - 0.591431i) q^{8} +(-0.402996 + 0.402996i) q^{9} +(1.45699 - 3.51749i) q^{11} +(2.71700 - 1.12542i) q^{12} +0.558802i q^{13} +(-0.242003 - 0.584247i) q^{14} +4.69032 q^{16} +(-2.12362 - 3.53415i) q^{17} -1.07480 q^{18} +(2.64081 + 2.64081i) q^{19} +0.633578i q^{21} +(6.63350 - 2.74769i) q^{22} +(-0.476856 + 1.15123i) q^{23} +(-1.46004 - 0.604767i) q^{24} +(-0.745166 + 0.745166i) q^{26} +(-4.24194 - 1.75707i) q^{27} +(0.199736 - 0.482204i) q^{28} +(3.68273 - 1.52544i) q^{29} +(3.58304 + 8.65022i) q^{31} +(5.07172 + 5.07172i) q^{32} -7.19360 q^{33} +(1.88096 - 7.54468i) q^{34} +(-0.627257 - 0.627257i) q^{36} +(-2.59150 - 6.25643i) q^{37} +7.04307i q^{38} +(0.975444 - 0.404042i) q^{39} +(1.55259 + 0.643105i) q^{41} +(-0.844881 + 0.844881i) q^{42} +(-4.00791 + 4.00791i) q^{43} +(5.47491 + 2.26778i) q^{44} +(-2.17107 + 0.899286i) q^{46} +9.50560i q^{47} +(-3.39134 - 8.18743i) q^{48} +(-4.87024 - 4.87024i) q^{49} +(-4.63373 + 6.26236i) q^{51} -0.869767 q^{52} +(5.16482 + 5.16482i) q^{53} +(-3.31360 - 7.99973i) q^{54} +(-0.259122 + 0.107332i) q^{56} +(2.70035 - 6.51923i) q^{57} +(6.94514 + 2.87677i) q^{58} +(-6.60087 + 6.60087i) q^{59} +(0.687270 + 0.284676i) q^{61} +(-6.75712 + 16.3131i) q^{62} +(0.176564 - 0.0731351i) q^{63} +4.14571i q^{64} +(-9.59272 - 9.59272i) q^{66} -7.29434 q^{67} +(5.50086 - 3.30538i) q^{68} +2.35438 q^{69} +(-5.95517 - 14.3771i) q^{71} +0.476688i q^{72} +(-10.3022 + 4.26733i) q^{73} +(4.88721 - 11.7988i) q^{74} +(-4.11038 + 4.11038i) q^{76} +(-0.902761 + 0.902761i) q^{77} +(1.83956 + 0.761969i) q^{78} +(-4.58769 + 11.0757i) q^{79} +10.3850i q^{81} +(1.21281 + 2.92798i) q^{82} +(8.29190 + 8.29190i) q^{83} -0.986155 q^{84} -10.6892 q^{86} +(-5.32561 - 5.32561i) q^{87} +(-1.21864 - 2.94206i) q^{88} +13.1316i q^{89} +(0.0717081 - 0.173119i) q^{91} +(-1.79188 - 0.742219i) q^{92} +(12.5091 - 12.5091i) q^{93} +(-12.6758 + 12.6758i) q^{94} +(5.18608 - 12.5203i) q^{96} +(9.81153 - 4.06407i) q^{97} -12.9890i q^{98} +(0.830371 + 2.00469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^6 + 12 * q^9	\( 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more