LMFDB - Embedded newform 425.2.n.f.274.3

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			274.3
Character	$\chi$	$=$	425.274
Dual form			425.2.n.f.349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09994 + 1.09994i) q^{2} +(1.15110 + 2.77900i) q^{3} -0.419729i q^{4} +(-4.32287 - 1.79059i) q^{6} +(3.19170 + 1.32205i) q^{7} +(-1.73820 - 1.73820i) q^{8} +(-4.27649 + 4.27649i) q^{9} +O(q^{10})$	\(q+(-1.09994 + 1.09994i) q^{2} +(1.15110 + 2.77900i) q^{3} -0.419729i q^{4} +(-4.32287 - 1.79059i) q^{6} +(3.19170 + 1.32205i) q^{7} +(-1.73820 - 1.73820i) q^{8} +(-4.27649 + 4.27649i) q^{9} +(-3.92026 - 1.62382i) q^{11} +(1.16643 - 0.483150i) q^{12} -0.127392 q^{13} +(-4.96485 + 2.05651i) q^{14} +4.66329 q^{16} +(-0.193278 + 4.11857i) q^{17} -9.40776i q^{18} +(-1.81966 - 1.81966i) q^{19} +10.3916i q^{21} +(6.09815 - 2.52594i) q^{22} +(-1.24457 + 3.00465i) q^{23} +(2.82962 - 6.83130i) q^{24} +(0.140123 - 0.140123i) q^{26} +(-8.47004 - 3.50841i) q^{27} +(0.554901 - 1.33965i) q^{28} +(1.87644 + 4.53013i) q^{29} +(4.95543 - 2.05261i) q^{31} +(-1.65293 + 1.65293i) q^{32} -12.7636i q^{33} +(-4.31758 - 4.74277i) q^{34} +(1.79497 + 1.79497i) q^{36} +(0.677990 + 1.63681i) q^{37} +4.00302 q^{38} +(-0.146641 - 0.354023i) q^{39} +(3.85069 - 9.29639i) q^{41} +(-11.4301 - 11.4301i) q^{42} +(1.79227 + 1.79227i) q^{43} +(-0.681566 + 1.64545i) q^{44} +(-1.93598 - 4.67388i) q^{46} +4.59479 q^{47} +(5.36791 + 12.9593i) q^{48} +(3.48941 + 3.48941i) q^{49} +(-11.6680 + 4.20377i) q^{51} +0.0534701i q^{52} +(-1.15866 + 1.15866i) q^{53} +(13.1756 - 5.45749i) q^{54} +(-3.24984 - 7.84580i) q^{56} +(2.96222 - 7.15144i) q^{57} +(-7.04683 - 2.91889i) q^{58} +(4.34287 - 4.34287i) q^{59} +(-1.54679 + 3.73428i) q^{61} +(-3.19293 + 7.70840i) q^{62} +(-19.3030 + 7.99557i) q^{63} +5.69034i q^{64} +(14.0392 + 14.0392i) q^{66} +6.88856i q^{67} +(1.72868 + 0.0811242i) q^{68} -9.78255 q^{69} +(-6.66802 + 2.76198i) q^{71} +14.8668 q^{72} +(13.5119 - 5.59682i) q^{73} +(-2.54614 - 1.05465i) q^{74} +(-0.763763 + 0.763763i) q^{76} +(-10.3655 - 10.3655i) q^{77} +(0.550699 + 0.228107i) q^{78} +(4.75854 + 1.97105i) q^{79} -9.43315i q^{81} +(5.98994 + 14.4610i) q^{82} +(-10.2150 + 10.2150i) q^{83} +4.36164 q^{84} -3.94276 q^{86} +(-10.4293 + 10.4293i) q^{87} +(3.99166 + 9.63673i) q^{88} +0.600876i q^{89} +(-0.406598 - 0.168418i) q^{91} +(1.26114 + 0.522381i) q^{92} +(11.4084 + 11.4084i) q^{93} +(-5.05398 + 5.05398i) q^{94} +(-6.49616 - 2.69080i) q^{96} +(-7.09206 + 2.93763i) q^{97} -7.67628 q^{98} +(23.7092 - 9.82068i) 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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.09994	+	1.09994i	−0.777774	+	0.777774i	−0.979452	−	0.201678i	$-0.935361\pi$
$2$	−1.09994	+	1.09994i	−0.777774	+	0.777774i	0.201678	+	0.979452i	$0.435361\pi$
$3$	1.15110	+	2.77900i	0.664588	+	1.60446i	0.790533	+	0.612419i	$0.209804\pi$
$3$	1.15110	+	2.77900i	0.664588	+	1.60446i	−0.125945	+	0.992037i	$0.540196\pi$
$4$		−	0.419729i		−	0.209865i
$5$		0			0
$5$		0			0
$6$	−4.32287	−	1.79059i	−1.76480	−	0.731006i
$7$	3.19170	+	1.32205i	1.20635	+	0.499687i	0.893046	−	0.449966i	$-0.148564\pi$
$7$	3.19170	+	1.32205i	1.20635	+	0.499687i	0.313305	+	0.949653i	$0.398564\pi$
$8$	−1.73820	−	1.73820i	−0.614547	−	0.614547i
$9$	−4.27649	+	4.27649i	−1.42550	+	1.42550i
$10$		0			0
$11$	−3.92026	−	1.62382i	−1.18200	−	0.489601i	−0.296860	−	0.954921i	$-0.595939\pi$
$11$	−3.92026	−	1.62382i	−1.18200	−	0.489601i	−0.885143	+	0.465320i	$0.845939\pi$
$12$	1.16643	−	0.483150i	0.336719	−	0.139473i
$13$	−0.127392			−0.0353322			−0.0176661	−	0.999844i	$-0.505624\pi$
$13$	−0.127392			−0.0353322			−0.0176661	+	0.999844i	$0.505624\pi$
$14$	−4.96485	+	2.05651i	−1.32691	+	0.549625i
$15$		0			0
$16$	4.66329			1.16582
$17$	−0.193278	+	4.11857i	−0.0468767	+	0.998901i
$17$	−0.193278	+	4.11857i	−0.0468767	+	0.998901i
$18$		−	9.40776i		−	2.21743i
$19$	−1.81966	−	1.81966i	−0.417458	−	0.417458i	0.466869	−	0.884327i	$-0.345382\pi$
$19$	−1.81966	−	1.81966i	−0.417458	−	0.417458i	−0.884327	+	0.466869i	$0.845382\pi$
$20$		0			0
$21$			10.3916i			2.26762i
$22$	6.09815	−	2.52594i	1.30013	−	0.538531i
$23$	−1.24457	+	3.00465i	−0.259510	+	0.626513i	−0.998906	−	0.0467576i	$-0.985111\pi$
$23$	−1.24457	+	3.00465i	−0.259510	+	0.626513i	0.739396	+	0.673271i	$0.235111\pi$
$24$	2.82962	−	6.83130i	0.577593	−	1.39443i
$25$		0			0
$26$	0.140123	−	0.140123i	0.0274805	−	0.0274805i
$27$	−8.47004	−	3.50841i	−1.63006	−	0.675193i
$28$	0.554901	−	1.33965i	0.104866	−	0.253170i
$29$	1.87644	+	4.53013i	0.348446	+	0.841224i	0.996804	+	0.0798877i	$0.0254562\pi$
$29$	1.87644	+	4.53013i	0.348446	+	0.841224i	−0.648358	+	0.761336i	$0.724544\pi$
$30$		0			0
$31$	4.95543	−	2.05261i	0.890021	−	0.368659i	0.109646	−	0.993971i	$-0.465028\pi$
$31$	4.95543	−	2.05261i	0.890021	−	0.368659i	0.780375	+	0.625312i	$0.215028\pi$
$32$	−1.65293	+	1.65293i	−0.292199	+	0.292199i
$33$		−	12.7636i		−	2.22185i
$34$	−4.31758	−	4.74277i	−0.740459	−	0.813378i
$35$		0			0
$36$	1.79497	+	1.79497i	0.299161	+	0.299161i
$37$	0.677990	+	1.63681i	0.111461	+	0.269090i	0.969761	−	0.244059i	$-0.0784789\pi$
$37$	0.677990	+	1.63681i	0.111461	+	0.269090i	−0.858300	+	0.513149i	$0.828479\pi$
$38$	4.00302			0.649376
$39$	−0.146641	−	0.354023i	−0.0234813	−	0.0566890i
$40$		0			0
$41$	3.85069	−	9.29639i	0.601377	−	1.45185i	−0.270787	−	0.962639i	$-0.587284\pi$
$41$	3.85069	−	9.29639i	0.601377	−	1.45185i	0.872164	−	0.489214i	$-0.162716\pi$
$42$	−11.4301	−	11.4301i	−1.76370	−	1.76370i
$43$	1.79227	+	1.79227i	0.273318	+	0.273318i	0.830434	−	0.557116i	$-0.188092\pi$
$43$	1.79227	+	1.79227i	0.273318	+	0.273318i	−0.557116	+	0.830434i	$0.688092\pi$
$44$	−0.681566	+	1.64545i	−0.102750	+	0.248060i
$45$		0			0
$46$	−1.93598	−	4.67388i	−0.285445	−	0.689126i
$47$	4.59479			0.670219			0.335109	−	0.942179i	$-0.391227\pi$
$47$	4.59479			0.670219			0.335109	+	0.942179i	$0.391227\pi$
$48$	5.36791	+	12.9593i	0.774791	+	1.87051i
$49$	3.48941	+	3.48941i	0.498487	+	0.498487i
$50$		0			0
$51$	−11.6680	+	4.20377i	−1.63385	+	0.588645i
$52$			0.0534701i			0.00741498i
$53$	−1.15866	+	1.15866i	−0.159155	+	0.159155i	−0.782192	−	0.623037i	$-0.785898\pi$
$53$	−1.15866	+	1.15866i	−0.159155	+	0.159155i	0.623037	+	0.782192i	$0.285898\pi$
$54$	13.1756	−	5.45749i	1.79297	−	0.742671i
$55$		0			0
$56$	−3.24984	−	7.84580i	−0.434278	−	1.04844i
$57$	2.96222	−	7.15144i	0.392356	−	0.947231i
$58$	−7.04683	−	2.91889i	−0.925294	−	0.383269i
$59$	4.34287	−	4.34287i	0.565393	−	0.565393i	−0.365441	−	0.930834i	$-0.619082\pi$
$59$	4.34287	−	4.34287i	0.565393	−	0.565393i	0.930834	+	0.365441i	$0.119082\pi$
$60$		0			0
$61$	−1.54679	+	3.73428i	−0.198046	+	0.478125i	−0.991437	−	0.130587i	$-0.958314\pi$
$61$	−1.54679	+	3.73428i	−0.198046	+	0.478125i	0.793391	+	0.608713i	$0.208314\pi$
$62$	−3.19293	+	7.70840i	−0.405502	+	0.978968i
$63$	−19.3030	+	7.99557i	−2.43195	+	1.00735i
$64$			5.69034i			0.711292i
$65$		0			0
$66$	14.0392	+	14.0392i	1.72810	+	1.72810i
$67$			6.88856i			0.841571i	0.907160	+	0.420786i	$0.138246\pi$
$67$			6.88856i			0.841571i	−0.907160	+	0.420786i	$0.861754\pi$
$68$	1.72868	+	0.0811242i	0.209634	+	0.00983776i
$69$	−9.78255			−1.17768
$70$		0			0
$71$	−6.66802	+	2.76198i	−0.791348	+	0.327787i	−0.741485	−	0.670969i	$-0.765878\pi$
$71$	−6.66802	+	2.76198i	−0.791348	+	0.327787i	−0.0498626	+	0.998756i	$0.515878\pi$
$72$	14.8668			1.75207
$73$	13.5119	−	5.59682i	1.58145	−	0.655058i	0.592807	−	0.805345i	$-0.298020\pi$
$73$	13.5119	−	5.59682i	1.58145	−	0.655058i	0.988642	+	0.150287i	$0.0480197\pi$
$74$	−2.54614	−	1.05465i	−0.295983	−	0.122600i
$75$		0			0
$76$	−0.763763	+	0.763763i	−0.0876096	+	0.0876096i
$77$	−10.3655	−	10.3655i	−1.18126	−	1.18126i
$78$	0.550699	+	0.228107i	0.0623544	+	0.0258280i
$79$	4.75854	+	1.97105i	0.535378	+	0.221761i	0.633957	−	0.773369i	$-0.281430\pi$
$79$	4.75854	+	1.97105i	0.535378	+	0.221761i	−0.0985790	+	0.995129i	$0.531430\pi$
$80$		0			0
$81$		−	9.43315i		−	1.04813i
$82$	5.98994	+	14.4610i	0.661478	+	1.59695i
$83$	−10.2150	+	10.2150i	−1.12124	+	1.12124i	−0.129685	+	0.991555i	$0.541397\pi$
$83$	−10.2150	+	10.2150i	−1.12124	+	1.12124i	−0.991555	+	0.129685i	$0.958603\pi$
$84$	4.36164			0.475893
$85$		0			0
$86$	−3.94276			−0.425159
$87$	−10.4293	+	10.4293i	−1.11813	+	1.11813i
$88$	3.99166	+	9.63673i	0.425513	+	1.02728i
$89$			0.600876i			0.0636927i	0.999493	+	0.0318463i	$0.0101387\pi$
$89$			0.600876i			0.0636927i	−0.999493	+	0.0318463i	$0.989861\pi$
$90$		0			0
$91$	−0.406598	−	0.168418i	−0.0426230	−	0.0176550i
$92$	1.26114	+	0.522381i	0.131483	+	0.0544620i
$93$	11.4084	+	11.4084i	1.18299	+	1.18299i
$94$	−5.05398	+	5.05398i	−0.521279	+	0.521279i
$95$		0			0
$96$	−6.49616	−	2.69080i	−0.663012	−	0.274628i
$97$	−7.09206	+	2.93763i	−0.720090	+	0.298271i	−0.712473	−	0.701700i	$-0.752425\pi$
$97$	−7.09206	+	2.93763i	−0.720090	+	0.298271i	−0.00761730	+	0.999971i	$0.502425\pi$
$98$	−7.67628			−0.775421
$99$	23.7092	−	9.82068i	2.38287	−	0.987016i
$100$		0			0
$101$	16.8485			1.67649			0.838243	−	0.545297i	$-0.183583\pi$
$101$	16.8485			1.67649			0.838243	+	0.545297i	$0.183583\pi$
$102$	8.21019	−	17.4580i	0.812930	−	1.72860i
$103$			4.32255i			0.425914i	0.977062	+	0.212957i	$0.0683093\pi$
$103$			4.32255i			0.425914i	−0.977062	+	0.212957i	$0.931691\pi$
$104$	0.221433	+	0.221433i	0.0217133	+	0.0217133i
$105$		0			0
$106$		−	2.54891i		−	0.247572i
$107$	4.36120	−	1.80647i	0.421613	−	0.174638i	−0.161782	−	0.986827i	$-0.551724\pi$
$107$	4.36120	−	1.80647i	0.421613	−	0.174638i	0.583395	+	0.812189i	$0.301724\pi$
$108$	−1.47258	+	3.55512i	−0.141699	+	0.342092i
$109$	5.86580	−	14.1613i	0.561842	−	1.35641i	−0.346450	−	0.938068i	$-0.612613\pi$
$109$	5.86580	−	14.1613i	0.561842	−	1.35641i	0.908292	−	0.418338i	$-0.137387\pi$
$110$		0			0
$111$	−3.76827	+	3.76827i	−0.357668	+	0.357668i
$112$	14.8838	+	6.16508i	1.40639	+	0.582545i
$113$	2.82099	−	6.81048i	0.265377	−	0.640676i	−0.733878	−	0.679282i	$-0.762291\pi$
$113$	2.82099	−	6.81048i	0.265377	−	0.640676i	0.999255	+	0.0386052i	$0.0122915\pi$
$114$	4.60788	+	11.1244i	0.431567	+	1.04190i
$115$		0			0
$116$	1.90143	−	0.787596i	0.176543	−	0.0731265i
$117$	0.544791	−	0.544791i	0.0503660	−	0.0503660i
$118$			9.55378i			0.879496i
$119$	−6.06183	+	12.8897i	−0.555687	+	1.18160i
$120$		0			0
$121$	4.95345	+	4.95345i	0.450313	+	0.450313i
$122$	−2.40610	−	5.80885i	−0.217838	−	0.525909i
$123$	30.2672			2.72910
$124$	−0.861538	−	2.07994i	−0.0773684	−	0.186784i
$125$		0			0
$126$	12.4375	−	30.0268i	1.10802	−	2.67500i
$127$	5.67103	+	5.67103i	0.503223	+	0.503223i	0.912438	−	0.409215i	$-0.134197\pi$
$127$	5.67103	+	5.67103i	0.503223	+	0.503223i	−0.409215	+	0.912438i	$0.634197\pi$
$128$	−9.56487	−	9.56487i	−0.845423	−	0.845423i
$129$	−2.91763	+	7.04378i	−0.256883	+	0.620170i
$130$		0			0
$131$	5.43762	+	13.1276i	0.475087	+	1.14696i	0.961887	+	0.273448i	$0.0881643\pi$
$131$	5.43762	+	13.1276i	0.475087	+	1.14696i	−0.486799	+	0.873514i	$0.661836\pi$
$132$	−5.35725			−0.466288
$133$	−3.40213	−	8.21348i	−0.295002	−	0.712199i
$134$	−7.57699	−	7.57699i	−0.654552	−	0.654552i
$135$		0			0
$136$	7.49486	−	6.82295i	0.642679	−	0.585063i
$137$		−	8.53083i		−	0.728838i	−0.931235	−	0.364419i	$-0.881268\pi$
$137$		−	8.53083i		−	0.728838i	0.931235	−	0.364419i	$-0.118732\pi$
$138$	10.7602	−	10.7602i	0.915969	−	0.915969i
$139$	−6.31676	+	2.61649i	−0.535781	+	0.221928i	−0.634133	−	0.773224i	$-0.718643\pi$
$139$	−6.31676	+	2.61649i	−0.535781	+	0.221928i	0.0983522	+	0.995152i	$0.468643\pi$
$140$		0			0
$141$	5.28906	+	12.7689i	0.445419	+	1.07534i
$142$	4.29640	−	10.3724i	0.360546	−	0.870434i
$143$	0.499410	+	0.206862i	0.0417627	+	0.0172987i
$144$	−19.9425	+	19.9425i	−1.66188	+	1.66188i
$145$		0			0
$146$	−8.70612	+	21.0184i	−0.720523	+	1.73950i
$147$	−5.68042	+	13.7137i	−0.468513	+	1.13109i
$148$	0.687018	−	0.284572i	0.0564725	−	0.0233917i
$149$			7.04072i			0.576798i	0.957510	+	0.288399i	$0.0931229\pi$
$149$			7.04072i			0.576798i	−0.957510	+	0.288399i	$0.906877\pi$
$150$		0			0
$151$	4.49500	+	4.49500i	0.365798	+	0.365798i	0.865942	−	0.500144i	$-0.166720\pi$
$151$	4.49500	+	4.49500i	0.365798	+	0.365798i	−0.500144	+	0.865942i	$0.666720\pi$
$152$			6.32586i			0.513095i
$153$	−16.7865	−	18.4396i	−1.35711	−	1.49075i
$154$	22.8029			1.83751
$155$		0			0
$156$	−0.148594	+	0.0615495i	−0.0118970	+	0.00492790i
$157$	−16.7739			−1.33870			−0.669351	−	0.742947i	$-0.733428\pi$
$157$	−16.7739			−1.33870			−0.669351	+	0.742947i	$0.733428\pi$
$158$	−7.40214	+	3.06607i	−0.588882	+	0.243923i
$159$	−4.55366	−	1.88619i	−0.361129	−	0.149584i
$160$		0			0
$161$	−7.94458	+	7.94458i	−0.626121	+	0.626121i
$162$	10.3759	+	10.3759i	0.815206	+	0.815206i
$163$	−4.24468	−	1.75820i	−0.332469	−	0.137713i	0.210203	−	0.977658i	$-0.432587\pi$
$163$	−4.24468	−	1.75820i	−0.332469	−	0.137713i	−0.542672	+	0.839945i	$0.682587\pi$
$164$	−3.90197	−	1.61625i	−0.304692	−	0.126208i
$165$		0			0
$166$		−	22.4717i		−	1.74414i
$167$	−8.04650	−	19.4260i	−0.622657	−	1.50323i	−0.848572	−	0.529079i	$-0.822537\pi$
$167$	−8.04650	−	19.4260i	−0.622657	−	1.50323i	0.225916	−	0.974147i	$-0.427463\pi$
$168$	18.0626	−	18.0626i	1.39356	−	1.39356i
$169$	−12.9838			−0.998752
$170$		0			0
$171$	15.5635			1.19017
$172$	0.752266	−	0.752266i	0.0573597	−	0.0573597i
$173$	−4.80360	−	11.5969i	−0.365211	−	0.881698i	−0.994520	−	0.104543i	$-0.966662\pi$
$173$	−4.80360	−	11.5969i	−0.365211	−	0.881698i	0.629309	−	0.777155i	$-0.283338\pi$
$174$		−	22.9431i		−	1.73931i
$175$		0			0
$176$	−18.2813	−	7.57236i	−1.37800	−	0.570788i
$177$	17.0679	+	7.06976i	1.28290	+	0.531396i
$178$	−0.660926	−	0.660926i	−0.0495385	−	0.0495385i
$179$	8.59390	−	8.59390i	0.642338	−	0.642338i	−0.308791	−	0.951130i	$-0.599925\pi$
$179$	8.59390	−	8.59390i	0.642338	−	0.642338i	0.951130	+	0.308791i	$0.0999245\pi$
$180$		0			0
$181$	−14.1007	−	5.84068i	−1.04809	−	0.434135i	−0.208883	−	0.977941i	$-0.566983\pi$
$181$	−14.1007	−	5.84068i	−1.04809	−	0.434135i	−0.839211	+	0.543806i	$0.816983\pi$
$182$	0.632482	−	0.261983i	0.0468827	−	0.0194194i
$183$	−12.1581			−0.898750
$184$	7.38600	−	3.05938i	0.544503	−	0.225540i
$185$		0			0
$186$	−25.0970			−1.84020
$187$	7.44554	−	15.8320i	0.544472	−	1.15775i
$188$		−	1.92857i		−	0.140655i
$189$	−22.3956	−	22.3956i	−1.62904	−	1.62904i
$190$		0			0
$191$			8.89972i			0.643961i	0.946746	+	0.321981i	$0.104349\pi$
$191$			8.89972i			0.643961i	−0.946746	+	0.321981i	$0.895651\pi$
$192$	−15.8135	+	6.55015i	−1.14124	+	0.472716i
$193$	−7.03519	+	16.9844i	−0.506404	+	1.22257i	0.439536	+	0.898225i	$0.355143\pi$
$193$	−7.03519	+	16.9844i	−0.506404	+	1.22257i	−0.945940	+	0.324342i	$0.894857\pi$
$194$	4.56962	−	11.0320i	0.328080	−	0.792054i
$195$		0			0
$196$	1.46461	−	1.46461i	0.104615	−	0.104615i
$197$	−9.87591	−	4.09074i	−0.703629	−	0.291453i	0.00203619	−	0.999998i	$-0.499352\pi$
$197$	−9.87591	−	4.09074i	−0.703629	−	0.291453i	−0.705666	+	0.708545i	$0.749352\pi$
$198$	−15.2765	+	36.8808i	−1.08566	+	2.62101i
$199$	−5.93889	−	14.3377i	−0.420996	−	1.01638i	−0.982054	−	0.188599i	$-0.939605\pi$
$199$	−5.93889	−	14.3377i	−0.420996	−	1.01638i	0.561058	−	0.827777i	$-0.310395\pi$
$200$		0			0
$201$	−19.1433	+	7.92942i	−1.35026	+	0.559298i
$202$	−18.5323	+	18.5323i	−1.30393	+	1.30393i
$203$			16.9396i			1.18892i
$204$	1.76444	+	4.89740i	0.123536	+	0.342886i
$205$		0			0
$206$	−4.75454	−	4.75454i	−0.331264	−	0.331264i
$207$	−7.52699	−	18.1718i	−0.523162	−	1.26302i
$208$	−0.594066			−0.0411910
$209$	4.17872	+	10.0883i	0.289048	+	0.697824i
$210$		0			0
$211$	3.34996	−	8.08752i	0.230621	−	0.556768i	−0.765630	−	0.643281i	$-0.777573\pi$
$211$	3.34996	−	8.08752i	0.230621	−	0.556768i	0.996251	+	0.0865134i	$0.0275726\pi$
$212$	0.486324	+	0.486324i	0.0334009	+	0.0334009i
$213$	−15.3511	−	15.3511i	−1.05184	−	1.05184i
$214$	−2.81005	+	6.78406i	−0.192091	+	0.463748i
$215$		0			0
$216$	8.62432	+	20.8209i	0.586810	+	1.41669i
$217$	18.5299			1.25789
$218$	9.12453	+	22.0286i	0.617991	+	1.49196i
$219$	31.1071	+	31.1071i	2.10202	+	2.10202i
$220$		0			0
$221$	0.0246220	−	0.524674i	0.00165626	−	0.0352934i
$222$		−	8.28973i		−	0.556370i
$223$	14.9621	−	14.9621i	1.00193	−	1.00193i	0.00193640	−	0.999998i	$-0.499384\pi$
$223$	14.9621	−	14.9621i	1.00193	−	1.00193i	0.999998	−	0.00193640i	$-0.000616375\pi$
$224$	−7.46089	+	3.09040i	−0.498502	+	0.206486i
$225$		0			0
$226$	4.38819	+	10.5940i	0.291898	+	0.704705i
$227$	−9.80944	+	23.6821i	−0.651075	+	1.57183i	0.160145	+	0.987094i	$0.448804\pi$
$227$	−9.80944	+	23.6821i	−0.651075	+	1.57183i	−0.811220	+	0.584741i	$0.801196\pi$
$228$	−3.00166	−	1.24333i	−0.198790	−	0.0823416i
$229$	5.02072	−	5.02072i	0.331779	−	0.331779i	−0.521483	−	0.853262i	$-0.674621\pi$
$229$	5.02072	−	5.02072i	0.331779	−	0.331779i	0.853262	+	0.521483i	$0.174621\pi$
$230$		0			0
$231$	16.8741	−	40.7376i	1.11023	−	2.68033i
$232$	4.61264	−	11.1359i	0.302835	−	0.731108i
$233$	21.9091	−	9.07503i	1.43531	−	0.594525i	0.476654	−	0.879091i	$-0.341849\pi$
$233$	21.9091	−	9.07503i	1.43531	−	0.594525i	0.958657	+	0.284566i	$0.0918494\pi$
$234$			1.19847i			0.0783467i
$235$		0			0
$236$	−1.82283	−	1.82283i	−0.118656	−	0.118656i
$237$			15.4929i			1.00637i
$238$	−7.51028	−	20.8456i	−0.486819	−	1.35122i
$239$	−0.109315			−0.00707103			−0.00353551	−	0.999994i	$-0.501125\pi$
$239$	−0.109315			−0.00707103			−0.00353551	+	0.999994i	$0.501125\pi$
$240$		0			0
$241$	16.1558	−	6.69194i	1.04069	−	0.431066i	0.204127	−	0.978944i	$-0.434564\pi$
$241$	16.1558	−	6.69194i	1.04069	−	0.431066i	0.836558	+	0.547878i	$0.184564\pi$
$242$	−10.8970			−0.700484
$243$	0.804604	−	0.333278i	0.0516154	−	0.0213798i
$244$	1.56739	+	0.649232i	0.100342	+	0.0415628i
$245$		0			0
$246$	−33.2921	+	33.2921i	−2.12262	+	2.12262i
$247$	0.231810	+	0.231810i	0.0147497	+	0.0147497i
$248$	−12.1814	−	5.04569i	−0.773518	−	0.320401i
$249$	−40.1459	−	16.6290i	−2.54414	−	1.05382i
$250$		0			0
$251$			3.28782i			0.207525i	0.994602	+	0.103763i	$0.0330882\pi$
$251$			3.28782i			0.207525i	−0.994602	+	0.103763i	$0.966912\pi$
$252$	3.35597	+	8.10204i	0.211406	+	0.510380i
$253$	9.75805	−	9.75805i	0.613484	−	0.613484i
$254$	−12.4756			−0.782787
$255$		0			0
$256$	9.66087			0.603804
$257$	15.1307	−	15.1307i	0.943829	−	0.943829i	−0.0546752	−	0.998504i	$-0.517412\pi$
$257$	15.1307	−	15.1307i	0.943829	−	0.943829i	0.998504	+	0.0546752i	$0.0174123\pi$
$258$	−4.53851	−	10.9569i	−0.282555	−	0.682149i
$259$			6.12055i			0.380313i
$260$		0			0
$261$	−27.3976	−	11.3485i	−1.69587	−	0.702453i
$262$	−20.4206	−	8.45848i	−1.26159	−	0.522567i
$263$	7.16800	+	7.16800i	0.441998	+	0.441998i	0.892683	−	0.450685i	$-0.148820\pi$
$263$	7.16800	+	7.16800i	0.441998	+	0.441998i	−0.450685	+	0.892683i	$0.648820\pi$
$264$	−22.1857	+	22.1857i	−1.36543	+	1.36543i
$265$		0			0
$266$	12.7765	+	5.29218i	0.783375	+	0.324484i
$267$	−1.66983	+	0.691668i	−0.102192	+	0.0423294i
$268$	2.89133			0.176616
$269$	13.9299	−	5.76996i	0.849321	−	0.351800i	0.0847993	−	0.996398i	$-0.472975\pi$
$269$	13.9299	−	5.76996i	0.849321	−	0.351800i	0.764522	+	0.644598i	$0.222975\pi$
$270$		0			0
$271$	−6.80304			−0.413255			−0.206628	−	0.978420i	$-0.566249\pi$
$271$	−6.80304			−0.413255			−0.206628	+	0.978420i	$0.566249\pi$
$272$	−0.901309	+	19.2061i	−0.0546499	+	1.16454i
$273$		−	1.32380i		−	0.0801201i
$274$	9.38338	+	9.38338i	0.566871	+	0.566871i
$275$		0			0
$276$			4.10602i			0.247153i
$277$	16.0032	−	6.62876i	0.961542	−	0.398284i	0.153985	−	0.988073i	$-0.450789\pi$
$277$	16.0032	−	6.62876i	0.961542	−	0.398284i	0.807557	+	0.589790i	$0.200789\pi$
$278$	4.07007	−	9.82602i	0.244107	−	0.589326i
$279$	−12.4139	+	29.9698i	−0.743200	+	1.79424i
$280$		0			0
$281$	12.7436	−	12.7436i	0.760218	−	0.760218i	−0.216143	−	0.976362i	$-0.569348\pi$
$281$	12.7436	−	12.7436i	0.760218	−	0.760218i	0.976362	+	0.216143i	$0.0693479\pi$
$282$	−19.8627	−	8.22738i	−1.18280	−	0.489934i
$283$	7.23322	−	17.4625i	0.429970	−	1.03804i	−0.549326	−	0.835608i	$-0.685115\pi$
$283$	7.23322	−	17.4625i	0.429970	−	1.03804i	0.979296	−	0.202432i	$-0.0648846\pi$
$284$	1.15928	+	2.79876i	0.0687909	+	0.166076i
$285$		0			0
$286$	−0.776856	+	0.321784i	−0.0459365	+	0.0190275i
$287$	24.5805	−	24.5805i	1.45094	−	1.45094i
$288$		−	14.1374i		−	0.833057i
$289$	−16.9253	−	1.59206i	−0.995605	−	0.0936504i
$290$		0			0
$291$	−16.3273	−	16.3273i	−0.957126	−	0.957126i
$292$	−2.34915	−	5.67134i	−0.137473	−	0.331890i
$293$	−7.53184			−0.440015			−0.220007	−	0.975498i	$-0.570608\pi$
$293$	−7.53184			−0.440015			−0.220007	+	0.975498i	$0.570608\pi$
$294$	−8.83616	−	21.3324i	−0.515335	−	1.24413i
$295$		0			0
$296$	1.66663	−	4.02359i	0.0968707	−	0.233866i
$297$	27.5077	+	27.5077i	1.59616	+	1.59616i
$298$	−7.74435	−	7.74435i	−0.448618	−	0.448618i
$299$	0.158548	−	0.382769i	0.00916907	−	0.0221361i
$300$		0			0
$301$	3.35092	+	8.08984i	0.193144	+	0.466290i
$302$	−9.88844			−0.569016
$303$	19.3943	+	46.8219i	1.11417	+	2.68985i
$304$	−8.48558	−	8.48558i	−0.486681	−	0.486681i
$305$		0			0
$306$	38.7465	+	1.81831i	2.21499	+	0.103946i
$307$			7.77074i			0.443499i	0.975104	+	0.221750i	$0.0711768\pi$
$307$			7.77074i			0.443499i	−0.975104	+	0.221750i	$0.928823\pi$
$308$	−4.35071	+	4.35071i	−0.247905	+	0.247905i
$309$	−12.0124	+	4.97569i	−0.683360	+	0.283057i
$310$		0			0
$311$	3.30824	+	7.98679i	0.187593	+	0.452889i	0.989495	−	0.144566i	$-0.0461786\pi$
$311$	3.30824	+	7.98679i	0.187593	+	0.452889i	−0.801902	+	0.597455i	$0.796179\pi$
$312$	−0.360471	+	0.870254i	−0.0204076	+	0.0492684i
$313$	−11.3988	−	4.72153i	−0.644298	−	0.266877i	0.0365165	−	0.999333i	$-0.488374\pi$
$313$	−11.3988	−	4.72153i	−0.644298	−	0.266877i	−0.680814	+	0.732456i	$0.738374\pi$
$314$	18.4502	−	18.4502i	1.04121	−	1.04121i
$315$		0			0
$316$	0.827308	−	1.99730i	0.0465397	−	0.112357i
$317$	−3.12750	+	7.55046i	−0.175658	+	0.424076i	−0.987047	−	0.160430i	$-0.948712\pi$
$317$	−3.12750	+	7.55046i	−0.175658	+	0.424076i	0.811389	+	0.584506i	$0.198712\pi$
$318$	7.08343	−	2.93405i	0.397219	−	0.164534i
$319$		−	20.8063i		−	1.16493i
$320$		0			0
$321$	10.0404	+	10.0404i	0.560398	+	0.560398i
$322$		−	17.4771i		−	0.973960i
$323$	7.84609	−	7.14269i	0.436568	−	0.397430i
$324$	−3.95937			−0.219965
$325$		0			0
$326$	6.60280	−	2.73497i	0.365695	−	0.151476i
$327$	46.1064			2.54969
$328$	−22.8523	+	9.46572i	−1.26181	+	0.522657i
$329$	14.6652	+	6.07452i	0.808519	+	0.334899i
$330$		0			0
$331$	16.5933	−	16.5933i	0.912049	−	0.912049i	−0.0843846	−	0.996433i	$-0.526892\pi$
$331$	16.5933	−	16.5933i	0.912049	−	0.912049i	0.996433	+	0.0843846i	$0.0268924\pi$
$332$	4.28753	+	4.28753i	0.235309	+	0.235309i
$333$	−9.89923	−	4.10040i	−0.542475	−	0.224700i
$334$	30.2180	+	12.5167i	1.65346	+	0.684884i
$335$		0			0
$336$			48.4588i			2.64364i
$337$	9.07655	+	21.9127i	0.494431	+	1.19366i	0.952443	+	0.304716i	$0.0985616\pi$
$337$	9.07655	+	21.9127i	0.494431	+	1.19366i	−0.458012	+	0.888946i	$0.651438\pi$
$338$	14.2813	−	14.2813i	0.776803	−	0.776803i
$339$	22.1736			1.20430
$340$		0			0
$341$	−22.7596			−1.23250
$342$	−17.1189	+	17.1189i	−0.925684	+	0.925684i
$343$	−2.73032	−	6.59159i	−0.147424	−	0.355912i
$344$		−	6.23063i		−	0.335933i
$345$		0			0
$346$	18.0396	+	7.47223i	0.969813	+	0.401710i
$347$	−6.48456	−	2.68599i	−0.348109	−	0.144192i	0.201776	−	0.979432i	$-0.435329\pi$
$347$	−6.48456	−	2.68599i	−0.348109	−	0.144192i	−0.549885	+	0.835240i	$0.685329\pi$
$348$	4.37746	+	4.37746i	0.234657	+	0.234657i
$349$	20.7773	−	20.7773i	1.11219	−	1.11219i	0.119331	−	0.992855i	$-0.461925\pi$
$349$	20.7773	−	20.7773i	1.11219	−	1.11219i	0.992855	−	0.119331i	$-0.0380750\pi$
$350$		0			0
$351$	1.07902	+	0.446943i	0.0575936	+	0.0238561i
$352$	9.16396	−	3.79583i	0.488440	−	0.202319i
$353$	9.09110			0.483870			0.241935	−	0.970292i	$-0.422218\pi$
$353$	9.09110			0.483870			0.241935	+	0.970292i	$0.422218\pi$
$354$	−26.5499	+	10.9973i	−1.41111	+	0.584502i
$355$		0			0
$356$	0.252205			0.0133668
$357$	−42.7984	−	2.00845i	−2.26513	−	0.106299i
$358$			18.9055i			0.999188i
$359$	−3.70529	−	3.70529i	−0.195558	−	0.195558i	0.602535	−	0.798093i	$-0.294157\pi$
$359$	−3.70529	−	3.70529i	−0.195558	−	0.195558i	−0.798093	+	0.602535i	$0.794157\pi$
$360$		0			0
$361$		−	12.3777i		−	0.651458i
$362$	21.9342	−	9.08546i	1.15284	−	0.477521i
$363$	−8.06372	+	19.4675i	−0.423235	+	1.02178i
$364$	−0.0706900	+	0.170661i	−0.00370516	+	0.00894506i
$365$		0			0
$366$	13.3731	−	13.3731i	0.699025	−	0.699025i
$367$	16.8448	+	6.97736i	0.879293	+	0.364215i	0.776223	−	0.630459i	$-0.217133\pi$
$367$	16.8448	+	6.97736i	0.879293	+	0.364215i	0.103071	+	0.994674i	$0.467133\pi$
$368$	−5.80377	+	14.0115i	−0.302543	+	0.730402i
$369$	23.2885	+	56.2234i	1.21235	+	2.92687i
$370$		0			0
$371$	−5.22991	+	2.16630i	−0.271524	+	0.112469i
$372$	4.78843	−	4.78843i	0.248268	−	0.248268i
$373$			18.5489i			0.960428i	0.877151	+	0.480214i	$0.159441\pi$
$373$			18.5489i			0.960428i	−0.877151	+	0.480214i	$0.840559\pi$
$374$	9.22462	+	25.6039i	0.476994	+	1.32395i
$375$		0			0
$376$	−7.98666	−	7.98666i	−0.411881	−	0.411881i
$377$	−0.239044	−	0.577102i	−0.0123114	−	0.0297223i
$378$	49.2675			2.53405
$379$	7.67735	+	18.5348i	0.394359	+	0.952067i	0.988978	+	0.148060i	$0.0473028\pi$
$379$	7.67735	+	18.5348i	0.394359	+	0.952067i	−0.594619	+	0.804007i	$0.702697\pi$
$380$		0			0
$381$	−9.23188	+	22.2877i	−0.472963	+	1.14183i
$382$	−9.78914	−	9.78914i	−0.500856	−	0.500856i
$383$	−7.72751	−	7.72751i	−0.394857	−	0.394857i	0.481557	−	0.876415i	$-0.340071\pi$
$383$	−7.72751	−	7.72751i	−0.394857	−	0.394857i	−0.876415	+	0.481557i	$0.840071\pi$
$384$	15.5707	−	37.5909i	0.794587	−	1.91830i
$385$		0			0
$386$	−10.9436	−	26.4201i	−0.557013	−	1.34475i
$387$	−15.3292			−0.779228
$388$	1.23301	+	2.97674i	0.0625965	+	0.151121i
$389$	−16.7947	−	16.7947i	−0.851526	−	0.851526i	0.138795	−	0.990321i	$-0.455677\pi$
$389$	−16.7947	−	16.7947i	−0.851526	−	0.851526i	−0.990321	+	0.138795i	$0.955677\pi$
$390$		0			0
$391$	−12.1343	−	5.70657i	−0.613659	−	0.288594i
$392$		−	12.1306i		−	0.612688i
$393$	−30.2223	+	30.2223i	−1.52451	+	1.52451i
$394$	15.3624	−	6.36333i	0.773949	−	0.320580i
$395$		0			0
$396$	−4.12203	−	9.95145i	−0.207140	−	0.500079i
$397$	−10.8631	+	26.2259i	−0.545205	+	1.31624i	0.375804	+	0.926699i	$0.377367\pi$
$397$	−10.8631	+	26.2259i	−0.545205	+	1.31624i	−0.921009	+	0.389542i	$0.872633\pi$
$398$	22.3030	+	9.23822i	1.11795	+	0.463070i
$399$	18.9091	−	18.9091i	0.946637	−	0.946637i
$400$		0			0
$401$	−3.33935	+	8.06191i	−0.166759	+	0.402592i	−0.985063	−	0.172193i	$-0.944915\pi$
$401$	−3.33935	+	8.06191i	−0.166759	+	0.402592i	0.818304	+	0.574786i	$0.194915\pi$
$402$	12.3346	−	29.7783i	0.615193	−	1.48521i
$403$	−0.631282	+	0.261486i	−0.0314464	+	0.0130255i
$404$		−	7.07179i		−	0.351835i
$405$		0			0
$406$	−18.6325	−	18.6325i	−0.924714	−	0.924714i
$407$		−	7.51766i		−	0.372637i
$408$	27.5883	+	12.9743i	1.36583	+	0.642325i
$409$	−10.5572			−0.522020			−0.261010	−	0.965336i	$-0.584056\pi$
$409$	−10.5572			−0.522020			−0.261010	+	0.965336i	$0.584056\pi$
$410$		0			0
$411$	23.7072	−	9.81983i	1.16939	−	0.484376i
$412$	1.81430			0.0893841
$413$	19.6026	−	8.11967i	0.964582	−	0.399543i
$414$	28.2670	+	11.7086i	1.38925	+	0.575446i
$415$		0			0
$416$	0.210570	−	0.210570i	0.0103240	−	0.0103240i
$417$	−14.5424	−	14.5424i	−0.712147	−	0.712147i
$418$	−15.6929	−	6.50020i	−0.767564	−	0.317935i
$419$	−13.2011	−	5.46806i	−0.644915	−	0.267132i	0.0361604	−	0.999346i	$-0.488487\pi$
$419$	−13.2011	−	5.46806i	−0.644915	−	0.267132i	−0.681075	+	0.732214i	$0.738487\pi$
$420$		0			0
$421$		−	18.2694i		−	0.890398i	−0.895432	−	0.445199i	$-0.853133\pi$
$421$		−	18.2694i		−	0.890398i	0.895432	−	0.445199i	$-0.146867\pi$
$422$	5.21102	+	12.5805i	0.253669	+	0.612410i
$423$	−19.6496	+	19.6496i	−0.955395	+	0.955395i
$424$	4.02798			0.195616
$425$		0			0
$426$	33.7705			1.63619
$427$	−9.87378	+	9.87378i	−0.477826	+	0.477826i
$428$	−0.758227	−	1.83052i	−0.0366503	−	0.0884816i
$429$			1.62598i			0.0785030i
$430$		0			0
$431$	19.4407	+	8.05261i	0.936427	+	0.387881i	0.798113	−	0.602508i	$-0.205832\pi$
$431$	19.4407	+	8.05261i	0.936427	+	0.387881i	0.138314	+	0.990388i	$0.455832\pi$
$432$	−39.4982	−	16.3607i	−1.90036	−	0.787154i
$433$	2.52902	+	2.52902i	0.121537	+	0.121537i	0.765259	−	0.643722i	$-0.222611\pi$
$433$	2.52902	+	2.52902i	0.121537	+	0.121537i	−0.643722	+	0.765259i	$0.722611\pi$
$434$	−20.3817	+	20.3817i	−0.978355	+	0.978355i
$435$		0			0
$436$	−5.94391	−	2.46205i	−0.284661	−	0.117911i
$437$	7.73212	−	3.20275i	0.369878	−	0.153208i
$438$	−68.4318			−3.26980
$439$	−3.03763	+	1.25823i	−0.144978	+	0.0600520i	−0.453993	−	0.891005i	$-0.650001\pi$
$439$	−3.03763	+	1.25823i	−0.144978	+	0.0600520i	0.309014	+	0.951057i	$0.400001\pi$
$440$		0			0
$441$	−29.8449			−1.42119
$442$	0.550026	+	0.604191i	0.0261621	+	0.0287384i
$443$		−	24.9391i		−	1.18489i	−0.805609	−	0.592447i	$-0.798162\pi$
$443$		−	24.9391i		−	1.18489i	0.805609	−	0.592447i	$-0.201838\pi$
$444$	1.58165	+	1.58165i	0.0750619	+	0.0750619i
$445$		0			0
$446$			32.9147i			1.55856i
$447$	−19.5662	+	8.10457i	−0.925447	+	0.383333i
$448$	−7.52289	+	18.1619i	−0.355423	+	0.858068i
$449$	−3.69533	+	8.92132i	−0.174394	+	0.421023i	−0.986773	−	0.162105i	$-0.948172\pi$
$449$	−3.69533	+	8.92132i	−0.174394	+	0.421023i	0.812380	+	0.583128i	$0.198172\pi$
$450$		0			0
$451$	−30.1914	+	30.1914i	−1.42166	+	1.42166i
$452$	−2.85856	−	1.18405i	−0.134455	−	0.0556932i
$453$	−7.31741	+	17.6658i	−0.343802	+	0.830011i
$454$	−15.2590	−	36.8386i	−0.716143	−	1.72892i
$455$		0			0
$456$	−17.5796	+	7.28169i	−0.823239	+	0.340997i
$457$	14.4798	−	14.4798i	0.677338	−	0.677338i	−0.282059	−	0.959397i	$-0.591018\pi$
$457$	14.4798	−	14.4798i	0.677338	−	0.677338i	0.959397	+	0.282059i	$0.0910175\pi$
$458$			11.0450i			0.516098i
$459$	16.0867	−	34.2064i	0.750863	−	1.59662i
$460$		0			0
$461$	−13.3288	−	13.3288i	−0.620785	−	0.620785i	0.324947	−	0.945732i	$-0.394654\pi$
$461$	−13.3288	−	13.3288i	−0.620785	−	0.620785i	−0.945732	+	0.324947i	$0.894654\pi$
$462$	26.2484	+	63.3692i	1.22119	+	2.94820i
$463$	−2.13430			−0.0991892			−0.0495946	−	0.998769i	$-0.515793\pi$
$463$	−2.13430			−0.0991892			−0.0495946	+	0.998769i	$0.515793\pi$
$464$	8.75038	+	21.1253i	0.406226	+	0.980716i
$465$		0			0
$466$	−14.1166	+	34.0806i	−0.653941	+	1.57875i
$467$	−16.4498	−	16.4498i	−0.761208	−	0.761208i	0.215333	−	0.976541i	$-0.430916\pi$
$467$	−16.4498	−	16.4498i	−0.761208	−	0.761208i	−0.976541	+	0.215333i	$0.930916\pi$
$468$	−0.228665	−	0.228665i	−0.0105700	−	0.0105700i
$469$	−9.10700	+	21.9862i	−0.420522	+	1.01523i
$470$		0			0
$471$	−19.3084	−	46.6146i	−0.889684	−	2.14789i
$472$	−15.0976			−0.694921
$473$	−4.11582	−	9.93647i	−0.189246	−	0.456879i
$474$	−17.0412	−	17.0412i	−0.782728	−	0.782728i
$475$		0			0
$476$	5.41020	+	2.54433i	0.247976	+	0.116619i
$477$		−	9.91002i		−	0.453749i
$478$	0.120240	−	0.120240i	0.00549966	−	0.00549966i
$479$	28.8369	−	11.9446i	1.31759	−	0.545763i	0.390500	−	0.920603i	$-0.372302\pi$
$479$	28.8369	−	11.9446i	1.31759	−	0.545763i	0.927090	+	0.374839i	$0.122302\pi$
$480$		0			0
$481$	−0.0863705	−	0.208517i	−0.00393816	−	0.00950755i
$482$	−10.4096	+	25.1311i	−0.474146	+	1.14469i
$483$	−31.2230	−	12.9330i	−1.42070	−	0.588471i
$484$	2.07911	−	2.07911i	0.0945048	−	0.0945048i
$485$		0			0
$486$	−0.518430	+	1.25160i	−0.0235164	+	0.0567737i
$487$	5.60737	−	13.5374i	0.254094	−	0.613438i	−0.744433	−	0.667698i	$-0.767280\pi$
$487$	5.60737	−	13.5374i	0.254094	−	0.613438i	0.998527	+	0.0542599i	$0.0172800\pi$
$488$	9.17956	−	3.80230i	0.415539	−	0.172122i
$489$		−	13.8198i		−	0.624954i
$490$		0			0
$491$	9.80148	+	9.80148i	0.442334	+	0.442334i	0.892796	−	0.450461i	$-0.148741\pi$
$491$	9.80148	+	9.80148i	0.442334	+	0.442334i	−0.450461	+	0.892796i	$0.648741\pi$
$492$		−	12.7040i		−	0.572742i
$493$	−19.0203	+	6.85268i	−0.856633	+	0.308629i
$494$	−0.509953			−0.0229439
$495$		0			0
$496$	23.1086	−	9.57188i	1.03761	−	0.429790i
$497$	−24.9338			−1.11843
$498$	62.4489	−	25.8672i	2.79840	−	1.15914i
$499$	−36.9847	−	15.3196i	−1.65566	−	0.685798i	−0.657929	−	0.753080i	$-0.728567\pi$
$499$	−36.9847	−	15.3196i	−1.65566	−	0.685798i	−0.997734	+	0.0672815i	$0.978567\pi$
$500$		0			0
$501$	44.7224	−	44.7224i	1.99805	−	1.99805i
$502$	−3.61639	−	3.61639i	−0.161408	−	0.161408i
$503$	36.2551	+	15.0174i	1.61654	+	0.669591i	0.993629	−	0.112704i	$-0.0359513\pi$
$503$	36.2551	+	15.0174i	1.61654	+	0.669591i	0.622907	+	0.782296i	$0.285951\pi$
$504$	47.4504	+	19.6546i	2.11361	+	0.875486i
$505$		0			0
$506$			21.4665i			0.954303i
$507$	−14.9456	−	36.0819i	−0.663758	−	1.60245i
$508$	2.38030	−	2.38030i	0.105609	−	0.105609i
$509$	26.7005			1.18348			0.591740	−	0.806129i	$-0.298441\pi$
$509$	26.7005			1.18348			0.591740	+	0.806129i	$0.298441\pi$
$510$		0			0
$511$	50.5253			2.23511
$512$	8.50339	−	8.50339i	0.375800	−	0.375800i
$513$	9.02847	+	21.7967i	0.398617	+	0.962346i
$514$			33.2857i			1.46817i
$515$		0			0
$516$	2.95648	+	1.22461i	0.130152	+	0.0539106i
$517$	−18.0128	−	7.46113i	−0.792200	−	0.328140i
$518$	−6.73223	−	6.73223i	−0.295797	−	0.295797i
$519$	26.6984	−	26.6984i	1.17193	−	1.17193i
$520$		0			0
$521$	4.28773	+	1.77604i	0.187849	+	0.0778096i	0.474625	−	0.880188i	$-0.342584\pi$
$521$	4.28773	+	1.77604i	0.187849	+	0.0778096i	−0.286776	+	0.957998i	$0.592584\pi$
$522$	42.6183	−	17.6531i	1.86535	−	0.772655i
$523$	9.21401			0.402900			0.201450	−	0.979499i	$-0.435435\pi$
$523$	9.21401			0.402900			0.201450	+	0.979499i	$0.435435\pi$
$524$	5.51003	−	2.28233i	0.240707	−	0.0997040i
$525$		0			0
$526$	−15.7687			−0.687549
$527$	7.49603	+	20.8060i	0.326532	+	0.906324i
$528$		−	59.5202i		−	2.59029i
$529$	8.78447	+	8.78447i	0.381934	+	0.381934i
$530$		0			0
$531$			37.1445i			1.61193i
$532$	−3.44743	+	1.42797i	−0.149465	+	0.0619105i
$533$	−0.490548	+	1.18429i	−0.0212480	+	0.0512972i
$534$	1.07592	−	2.59751i	0.0465597	−	0.112405i
$535$		0			0
$536$	11.9737	−	11.9737i	0.517185	−	0.517185i
$537$	33.7749	+	13.9900i	1.45749	+	0.603714i
$538$	−8.97544	+	21.6686i	−0.386959	+	0.934201i
$539$	−8.01321	−	19.3456i	−0.345153	−	0.833274i
$540$		0			0
$541$	−29.5380	+	12.2350i	−1.26994	+	0.526025i	−0.912945	−	0.408083i	$-0.866197\pi$
$541$	−29.5380	+	12.2350i	−1.26994	+	0.526025i	−0.356991	+	0.934108i	$0.616197\pi$
$542$	7.48292	−	7.48292i	0.321419	−	0.321419i
$543$		−	45.9089i		−	1.97014i
$544$	−6.48822	−	7.12717i	−0.278180	−	0.305575i
$545$		0			0
$546$	1.45610	+	1.45610i	0.0623153	+	0.0623153i
$547$	−3.21779	−	7.76844i	−0.137583	−	0.332155i	0.840038	−	0.542527i	$-0.182532\pi$
$547$	−3.21779	−	7.76844i	−0.137583	−	0.332155i	−0.977621	+	0.210372i	$0.932532\pi$
$548$	−3.58064			−0.152957
$549$	−9.35478	−	22.5844i	−0.399252	−	0.963881i
$550$		0			0
$551$	4.82880	−	11.6578i	0.205714	−	0.496637i
$552$	17.0040	+	17.0040i	0.723740	+	0.723740i
$553$	12.5820	+	12.5820i	0.535042	+	0.535042i
$554$	−10.3114	+	24.8938i	−0.438087	+	1.05764i
$555$		0			0
$556$	1.09822	+	2.65133i	0.0465747	+	0.112441i
$557$	−1.01642			−0.0430670			−0.0215335	−	0.999768i	$-0.506855\pi$
$557$	−1.01642			−0.0430670			−0.0215335	+	0.999768i	$0.506855\pi$
$558$	−19.3104	−	46.6194i	−0.817475	−	1.97356i
$559$	−0.228320	−	0.228320i	−0.00965692	−	0.00965692i
$560$		0			0
$561$	52.5677	+	2.46692i	2.21941	+	0.104153i
$562$			28.0343i			1.18256i
$563$	−7.34466	+	7.34466i	−0.309541	+	0.309541i	−0.844731	−	0.535191i	$-0.820240\pi$
$563$	−7.34466	+	7.34466i	−0.309541	+	0.309541i	0.535191	+	0.844731i	$0.320240\pi$
$564$	5.35949	−	2.21997i	0.225675	−	0.0934777i
$565$		0			0
$566$	11.2516	+	27.1638i	0.472941	+	1.14178i
$567$	12.4711	−	30.1078i	0.523735	−	1.26441i
$568$	16.3912	+	6.78947i	0.687761	+	0.284880i
$569$	16.9517	−	16.9517i	0.710651	−	0.710651i	−0.256020	−	0.966671i	$-0.582411\pi$
$569$	16.9517	−	16.9517i	0.710651	−	0.710651i	0.966671	+	0.256020i	$0.0824113\pi$
$570$		0			0
$571$	−4.53513	+	10.9488i	−0.189789	+	0.458192i	−0.989919	−	0.141635i	$-0.954764\pi$
$571$	−4.53513	+	10.9488i	−0.189789	+	0.458192i	0.800129	+	0.599827i	$0.204764\pi$
$572$	0.0868261	−	0.209617i	0.00363038	−	0.00876452i
$573$	−24.7323	+	10.2445i	−1.03321	+	0.427969i
$574$			54.0741i			2.25701i
$575$		0			0
$576$	−24.3347	−	24.3347i	−1.01395	−	1.01395i
$577$		−	22.5581i		−	0.939107i	−0.882904	−	0.469553i	$-0.844415\pi$
$577$		−	22.5581i		−	0.939107i	0.882904	−	0.469553i	$-0.155585\pi$
$578$	20.3679	−	16.8656i	0.847195	−	0.701517i
$579$	−55.2980			−2.29811
$580$		0			0
$581$	−46.1079	+	19.0985i	−1.91288	+	0.792340i
$582$	35.9181			1.48885
$583$	6.42372	−	2.66079i	0.266043	−	0.110199i
$584$	−33.2148	−	13.7580i	−1.37444	−	0.569311i
$585$		0			0
$586$	8.28456	−	8.28456i	0.342232	−	0.342232i
$587$	29.8211	+	29.8211i	1.23085	+	1.23085i	0.963638	+	0.267210i	$0.0861019\pi$
$587$	29.8211	+	29.8211i	1.23085	+	1.23085i	0.267210	+	0.963638i	$0.413898\pi$
$588$	5.75605	+	2.38424i	0.237376	+	0.0983242i
$589$	−12.7522	−	5.28214i	−0.525446	−	0.217647i
$590$		0			0
$591$		−	32.1540i		−	1.32264i
$592$	3.16166	+	7.63292i	0.129943	+	0.313711i
$593$	6.00168	−	6.00168i	0.246460	−	0.246460i	−0.573056	−	0.819516i	$-0.694242\pi$
$593$	6.00168	−	6.00168i	0.246460	−	0.246460i	0.819516	+	0.573056i	$0.194242\pi$
$594$	−60.5136			−2.48290
$595$		0			0
$596$	2.95519			0.121049
$597$	33.0083	−	33.0083i	1.35094	−	1.35094i
$598$	0.246629	+	0.595415i	0.0100854	+	0.0243483i
$599$			17.0226i			0.695523i	0.937583	+	0.347762i	$0.113058\pi$
$599$			17.0226i			0.695523i	−0.937583	+	0.347762i	$0.886942\pi$
$600$		0			0
$601$	−18.7530	−	7.76773i	−0.764949	−	0.316852i	−0.0341247	−	0.999418i	$-0.510864\pi$
$601$	−18.7530	−	7.76773i	−0.764949	−	0.316852i	−0.730825	+	0.682565i	$0.760864\pi$
$602$	−12.5841	−	5.21252i	−0.512891	−	0.212446i
$603$	−29.4589	−	29.4589i	−1.19966	−	1.19966i
$604$	1.88668	−	1.88668i	0.0767679	−	0.0767679i
$605$		0			0
$606$	−72.8337	−	30.1687i	−2.95867	−	1.22552i
$607$	−45.1162	+	18.6877i	−1.83121	+	0.758512i	−0.864500	+	0.502633i	$0.832365\pi$
$607$	−45.1162	+	18.6877i	−1.83121	+	0.758512i	−0.966709	+	0.255879i	$0.917635\pi$
$608$	6.01552			0.243961
$609$	−47.0750	+	19.4991i	−1.90758	+	0.790144i
$610$		0			0
$611$	−0.585340			−0.0236803
$612$	−7.73963	+	7.04578i	−0.312856	+	0.284809i
$613$		−	21.5320i		−	0.869669i	−0.900510	−	0.434834i	$-0.856807\pi$
$613$		−	21.5320i		−	0.869669i	0.900510	−	0.434834i	$-0.143193\pi$
$614$	−8.54733	−	8.54733i	−0.344942	−	0.344942i
$615$		0			0
$616$			36.0347i			1.45188i
$617$	−4.27386	+	1.77029i	−0.172059	+	0.0712692i	−0.467050	−	0.884231i	$-0.654683\pi$
$617$	−4.27386	+	1.77029i	−0.172059	+	0.0712692i	0.294991	+	0.955500i	$0.404683\pi$
$618$	7.73992	−	18.6858i	0.311345	−	0.751654i
$619$	−17.8427	+	43.0760i	−0.717158	+	1.73137i	−0.0358698	+	0.999356i	$0.511420\pi$
$619$	−17.8427	+	43.0760i	−0.717158	+	1.73137i	−0.681288	+	0.732016i	$0.738580\pi$
$620$		0			0
$621$	21.0831	−	21.0831i	0.846035	−	0.846035i
$622$	−12.4238	−	5.14612i	−0.498150	−	0.206341i
$623$	−0.794386	+	1.91782i	−0.0318264	+	0.0768357i
$624$	−0.683829	−	1.65091i	−0.0273751	−	0.0660892i
$625$		0			0
$626$	17.7314	−	7.34457i	0.708688	−	0.293548i
$627$	−23.2253	+	23.2253i	−0.927531	+	0.927531i
$628$			7.04048i			0.280946i
$629$	−6.87237	+	2.47599i	−0.274019	+	0.0987243i
$630$		0			0
$631$	18.5948	+	18.5948i	0.740246	+	0.740246i	0.972625	−	0.232380i	$-0.0746511\pi$
$631$	18.5948	+	18.5948i	0.740246	+	0.740246i	−0.232380	+	0.972625i	$0.574651\pi$
$632$	−4.84522	−	11.6974i	−0.192732	−	0.465297i
$633$	26.3314			1.04658
$634$	−4.86498	−	11.7451i	−0.193213	−	0.466457i
$635$		0			0
$636$	−0.791688	+	1.91130i	−0.0313925	+	0.0757881i
$637$	−0.444523	−	0.444523i	−0.0176127	−	0.0176127i
$638$	22.8856	+	22.8856i	0.906051	+	0.906051i
$639$	16.7041	−	40.3273i	0.660805	−	1.59532i
$640$		0			0
$641$	2.51210	+	6.06476i	0.0992222	+	0.239544i	0.965694	−	0.259682i	$-0.0836178\pi$
$641$	2.51210	+	6.06476i	0.0992222	+	0.239544i	−0.866472	+	0.499226i	$0.833618\pi$
$642$	−22.0875			−0.871726
$643$	−2.45187	−	5.91935i	−0.0966925	−	0.233436i	0.868131	−	0.496335i	$-0.165321\pi$
$643$	−2.45187	−	5.91935i	−0.0966925	−	0.233436i	−0.964823	+	0.262899i	$0.915321\pi$
$644$	3.33457	+	3.33457i	0.131400	+	0.131400i
$645$		0			0
$646$	−0.773695	+	16.4867i	−0.0304406	+	0.648662i
$647$			8.03230i			0.315782i	0.987457	+	0.157891i	$0.0504695\pi$
$647$			8.03230i			0.315782i	−0.987457	+	0.157891i	$0.949530\pi$
$648$	−16.3967	+	16.3967i	−0.644123	+	0.644123i
$649$	−24.0772	+	9.97311i	−0.945114	+	0.391479i
$650$		0			0
$651$	21.3298	+	51.4946i	0.835979	+	2.01823i
$652$	−0.737969	+	1.78161i	−0.0289011	+	0.0697734i
$653$	−42.6883	−	17.6821i	−1.67052	−	0.691953i	−0.671717	−	0.740808i	$-0.734443\pi$
$653$	−42.6883	−	17.6821i	−1.67052	−	0.691953i	−0.998806	+	0.0488551i	$0.984443\pi$
$654$	−50.7142	+	50.7142i	−1.98308	+	1.98308i
$655$		0			0
$656$	17.9569	−	43.3517i	0.701098	−	1.69260i
$657$	−33.8488	+	81.7183i	−1.32057	+	3.18814i
$658$	−22.8124	+	9.44921i	−0.889321	+	0.368369i
$659$			47.9496i			1.86785i	0.357465	+	0.933926i	$0.383641\pi$
$659$			47.9496i			1.86785i	−0.357465	+	0.933926i	$0.616359\pi$
$660$		0			0
$661$	−26.7821	−	26.7821i	−1.04170	−	1.04170i	−0.999092	−	0.0426129i	$-0.986432\pi$
$661$	−26.7821	−	26.7821i	−1.04170	−	1.04170i	−0.0426129	−	0.999092i	$-0.513568\pi$
$662$			36.5032i			1.41874i
$663$	1.48641	−	0.535527i	0.0577274	−	0.0207981i
$664$	35.5114			1.37811
$665$		0			0
$666$	15.3987	−	6.37836i	0.596689	−	0.247157i
$667$	−15.9468			−0.617463
$668$	−8.15364	+	3.37735i	−0.315474	+	0.130674i
$669$	58.8024	+	24.3568i	2.27343	+	0.941687i
$670$		0			0
$671$	12.1276	−	12.1276i	0.468182	−	0.468182i
$672$	−17.1765	−	17.1765i	−0.662596	−	0.662596i
$673$	3.75229	+	1.55425i	0.144640	+	0.0599119i	0.453829	−	0.891089i	$-0.350058\pi$
$673$	3.75229	+	1.55425i	0.144640	+	0.0599119i	−0.309189	+	0.951001i	$0.600058\pi$
$674$	−34.0863	−	14.1190i	−1.31295	−	0.543844i
$675$		0			0
$676$			5.44967i			0.209603i
$677$	−1.33382	−	3.22013i	−0.0512629	−	0.123760i	0.896173	−	0.443704i	$-0.146336\pi$
$677$	−1.33382	−	3.22013i	−0.0512629	−	0.123760i	−0.947436	+	0.319944i	$0.896336\pi$
$678$	−24.3896	+	24.3896i	−0.936676	+	0.936676i
$679$	−26.5194			−1.01772
$680$		0			0
$681$	−77.1041			−2.95464
$682$	25.0342	−	25.0342i	0.958609	−	0.958609i
$683$	−5.38880	−	13.0097i	−0.206197	−	0.497803i	0.786621	−	0.617436i	$-0.211828\pi$
$683$	−5.38880	−	13.0097i	−0.206197	−	0.497803i	−0.992818	+	0.119632i	$0.961828\pi$
$684$		−	6.53245i		−	0.249775i
$685$		0			0
$686$	10.2535	+	4.24715i	0.391482	+	0.162157i
$687$	19.7319	+	8.17324i	0.752821	+	0.311829i
$688$	8.35784	+	8.35784i	0.318640	+	0.318640i
$689$	0.147604	−	0.147604i	0.00562328	−	0.00562328i
$690$		0			0
$691$	−41.2601	−	17.0905i	−1.56961	−	0.650153i	−0.582883	−	0.812556i	$-0.698075\pi$
$691$	−41.2601	−	17.0905i	−1.56961	−	0.650153i	−0.986724	+	0.162403i	$0.948075\pi$
$692$	−4.86756	+	2.01621i	−0.185037	+	0.0766448i
$693$	88.6562			3.36777
$694$	10.0870	−	4.17819i	0.382899	−	0.158602i
$695$		0			0
$696$	36.2563			1.37429
$697$	37.5436	+	17.6561i	1.42207	+	0.668774i
$698$			45.7076i			1.73006i
$699$	50.4390	+	50.4390i	1.90778	+	1.90778i
$700$		0			0
$701$			1.84833i			0.0698103i	0.999391	+	0.0349052i	$0.0111129\pi$
$701$			1.84833i			0.0698103i	−0.999391	+	0.0349052i	$0.988887\pi$
$702$	−1.67846	+	0.695241i	−0.0633494	+	0.0262402i
$703$	1.74473	−	4.21215i	0.0658037	−	0.158864i
$704$	9.24011	−	22.3076i	0.348250	−	0.840749i
$705$		0			0
$706$	−9.99965	+	9.99965i	−0.376342	+	0.376342i
$707$	53.7753	+	22.2745i	2.02243	+	0.837717i
$708$	2.96738	−	7.16390i	0.111521	−	0.269236i
$709$	−11.4834	−	27.7233i	−0.431267	−	1.04117i	−0.978879	−	0.204438i	$-0.934463\pi$
$709$	−11.4834	−	27.7233i	−0.431267	−	1.04117i	0.547613	−	0.836732i	$-0.315537\pi$
$710$		0			0
$711$	−28.7791	+	11.9207i	−1.07930	+	0.447060i
$712$	1.04444	−	1.04444i	0.0391421	−	0.0391421i
$713$			17.4439i			0.653281i
$714$	49.2847	−	44.8664i	1.84443	−	1.67908i
$715$		0			0
$716$	−3.60711	−	3.60711i	−0.134804	−	0.134804i
$717$	−0.125833	−	0.303788i	−0.00469932	−	0.0113452i
$718$	8.15119			0.304200
$719$	−14.6916	−	35.4687i	−0.547904	−	1.32276i	−0.919034	−	0.394177i	$-0.871030\pi$
$719$	−14.6916	−	35.4687i	−0.547904	−	1.32276i	0.371130	−	0.928581i	$-0.378970\pi$
$720$		0			0
$721$	−5.71461	+	13.7963i	−0.212823	+	0.513801i
$722$	13.6147	+	13.6147i	0.506687	+	0.506687i
$723$	37.1938	+	37.1938i	1.38325	+	1.38325i
$724$	−2.45150	+	5.91846i	−0.0911094	+	0.219958i
$725$		0			0
$726$	−12.5435	−	30.2827i	−0.465533	−	1.12390i
$727$	−0.0992434			−0.00368073			−0.00184037	−	0.999998i	$-0.500586\pi$
$727$	−0.0992434			−0.00368073			−0.00184037	+	0.999998i	$0.500586\pi$
$728$	0.414004	+	0.999493i	0.0153440	+	0.0370437i
$729$	−18.1584	−	18.1584i	−0.672532	−	0.672532i
$730$		0			0
$731$	−7.72798	+	7.03517i	−0.285830	+	0.260205i
$732$			5.10310i			0.188616i
$733$	−10.2168	+	10.2168i	−0.377365	+	0.377365i	−0.870151	−	0.492786i	$-0.835979\pi$
$733$	−10.2168	+	10.2168i	−0.377365	+	0.377365i	0.492786	+	0.870151i	$0.335979\pi$
$734$	−26.2030	+	10.8536i	−0.967169	+	0.400614i
$735$		0			0
$736$	−2.90929	−	7.02364i	−0.107238	−	0.258895i
$737$	11.1858	−	27.0049i	0.412035	−	0.994739i
$738$	−87.4582	−	36.2264i	−3.21938	−	1.33351i
$739$	3.22478	−	3.22478i	0.118625	−	0.118625i	−0.645302	−	0.763928i	$-0.723268\pi$
$739$	3.22478	−	3.22478i	0.118625	−	0.118625i	0.763928	+	0.645302i	$0.223268\pi$
$740$		0			0
$741$	−0.377364	+	0.911036i	−0.0138628	+	0.0334677i
$742$	3.36978	−	8.13538i	0.123709	−	0.298659i
$743$	−30.7404	+	12.7331i	−1.12776	+	0.467131i	−0.867017	−	0.498278i	$-0.833966\pi$
$743$	−30.7404	+	12.7331i	−1.12776	+	0.467131i	−0.260738	+	0.965410i	$0.583966\pi$
$744$		−	39.6601i		−	1.45401i
$745$		0			0
$746$	−20.4027	−	20.4027i	−0.746996	−	0.746996i
$747$		−	87.3686i		−	3.19665i
$748$	−6.64516	−	3.12511i	−0.242971	−	0.114265i
$749$	16.3079			0.595877
$750$		0			0
$751$	−24.4052	+	10.1090i	−0.890558	+	0.368881i	−0.780582	−	0.625053i	$-0.785077\pi$
$751$	−24.4052	+	10.1090i	−0.890558	+	0.368881i	−0.109976	+	0.993934i	$0.535077\pi$
$752$	21.4268			0.781355
$753$	−9.13684	+	3.78460i	−0.332965	+	0.137919i
$754$	0.897710	+	0.371844i	0.0326927	+	0.0135418i
$755$		0			0
$756$	−9.40007	+	9.40007i	−0.341877	+	0.341877i
$757$	−15.6840	−	15.6840i	−0.570043	−	0.570043i	0.362097	−	0.932140i	$-0.382061\pi$
$757$	−15.6840	−	15.6840i	−0.570043	−	0.570043i	−0.932140	+	0.362097i	$0.882061\pi$
$758$	−28.8317	−	11.9425i	−1.04722	−	0.433771i
$759$	38.3501	+	15.8851i	1.39202	+	0.576594i
$760$		0			0
$761$			23.1817i			0.840337i	0.907446	+	0.420168i	$0.138029\pi$
$761$			23.1817i			0.840337i	−0.907446	+	0.420168i	$0.861971\pi$
$762$	−14.3606	−	34.6696i	−0.520231	−	1.25595i
$763$	37.4438	−	37.4438i	1.35556	−	1.35556i
$764$	3.73547			0.135145
$765$		0			0
$766$	16.9996			0.614219
$767$	−0.553247	+	0.553247i	−0.0199766	+	0.0199766i
$768$	11.1206	+	26.8475i	0.401281	+	0.968777i
$769$		−	16.7701i		−	0.604747i	−0.953190	−	0.302373i	$-0.902221\pi$
$769$		−	16.7701i		−	0.604747i	0.953190	−	0.302373i	$-0.0977789\pi$
$770$		0			0
$771$	59.4653	+	24.6313i	2.14159	+	0.887076i
$772$	7.12886	+	2.95287i	0.256573	+	0.106276i
$773$	9.68077	+	9.68077i	0.348193	+	0.348193i	0.859436	−	0.511243i	$-0.170815\pi$
$773$	9.68077	+	9.68077i	0.348193	+	0.348193i	−0.511243	+	0.859436i	$0.670815\pi$
$774$	16.8612	−	16.8612i	0.606063	−	0.606063i
$775$		0			0
$776$	17.4336	+	7.22124i	0.625830	+	0.259227i
$777$	−17.0090	+	7.04537i	−0.610195	+	0.252751i
$778$	36.9463			1.32459
$779$	−23.9232	+	9.90931i	−0.857137	+	0.355038i
$780$		0			0
$781$	30.6253			1.09586
$782$	19.6239	−	7.07014i	0.701749	−	0.252828i
$783$		−	44.9537i		−	1.60651i
$784$	16.2721	+	16.2721i	0.581147	+	0.581147i
$785$		0			0
$786$		−	66.4854i		−	2.37145i
$787$	−27.0058	+	11.1862i	−0.962651	+	0.398743i	−0.807972	−	0.589221i	$-0.799435\pi$
$787$	−27.0058	+	11.1862i	−0.962651	+	0.398743i	−0.154680	+	0.987965i	$0.549435\pi$
$788$	−1.71700	+	4.14521i	−0.0611656	+	0.147667i
$789$	−11.6688	+	28.1710i	−0.415420	+	1.00291i
$790$		0			0
$791$	18.0076	−	18.0076i	0.640275	−	0.640275i
$792$	−58.2817	−	24.1411i	−2.07095	−	0.857816i
$793$	0.197049	−	0.475718i	0.00699740	−	0.0168932i
$794$	−16.8981	−	40.7957i	−0.599692	−	1.44778i
$795$		0			0
$796$	−6.01797	+	2.49272i	−0.213301	+	0.0883522i
$797$	10.0043	−	10.0043i	0.354369	−	0.354369i	−0.507363	−	0.861732i	$-0.669380\pi$
$797$	10.0043	−	10.0043i	0.354369	−	0.354369i	0.861732	+	0.507363i	$0.169380\pi$
$798$			41.5976i			1.47254i
$799$	−0.888070	+	18.9240i	−0.0314176	+	0.669482i
$800$		0			0
$801$	−2.56964	−	2.56964i	−0.0907938	−	0.0907938i
$802$	−5.19452	−	12.5407i	−0.183425	−	0.442827i
$803$	−62.0584			−2.18999
$804$	3.32821	+	8.03500i	0.117377	+	0.283373i
$805$		0			0
$806$	0.406753	−	0.981990i	0.0143273	−	0.0345891i
$807$	32.0694	+	32.0694i	1.12890	+	1.12890i
$808$	−29.2860	−	29.2860i	−1.03028	−	1.03028i
$809$	−6.56799	+	15.8565i	−0.230918	+	0.557486i	−0.996286	−	0.0861076i	$-0.972557\pi$
$809$	−6.56799	+	15.8565i	−0.230918	+	0.557486i	0.765368	+	0.643593i	$0.222557\pi$
$810$		0			0
$811$	17.3259	+	41.8285i	0.608396	+	1.46880i	0.864744	+	0.502214i	$0.167481\pi$
$811$	17.3259	+	41.8285i	0.608396	+	1.46880i	−0.256348	+	0.966585i	$0.582519\pi$
$812$	7.11003			0.249513
$813$	−7.83097	−	18.9056i	−0.274644	−	0.663050i
$814$	8.26897	+	8.26897i	0.289827	+	0.289827i
$815$		0			0
$816$	−54.4112	+	19.6034i	−1.90477	+	0.686255i
$817$		−	6.52262i		−	0.228197i
$818$	11.6123	−	11.6123i	0.406013	−	0.406013i
$819$	2.45905	−	1.01857i	0.0859262	−	0.0355918i
$820$		0			0
$821$	−9.18115	−	22.1652i	−0.320424	−	0.773572i	−0.999229	−	0.0392539i	$-0.987502\pi$
$821$	−9.18115	−	22.1652i	−0.320424	−	0.773572i	0.678805	−	0.734319i	$-0.262498\pi$
$822$	−15.2752	+	36.8776i	−0.532784	+	1.28626i
$823$	40.0669	+	16.5962i	1.39664	+	0.578509i	0.948878	−	0.315642i	$-0.102220\pi$
$823$	40.0669	+	16.5962i	1.39664	+	0.578509i	0.447766	+	0.894151i	$0.352220\pi$
$824$	7.51346	−	7.51346i	0.261744	−	0.261744i
$825$		0			0
$826$	−12.6305	+	30.4928i	−0.439473	+	1.06098i
$827$	−14.7306	+	35.5628i	−0.512233	+	1.23664i	0.430347	+	0.902663i	$0.358391\pi$
$827$	−14.7306	+	35.5628i	−0.512233	+	1.23664i	−0.942581	+	0.333978i	$0.891609\pi$
$828$	−7.62721	+	3.15929i	−0.265064	+	0.109793i
$829$		−	54.4489i		−	1.89109i	−0.325492	−	0.945545i	$-0.605530\pi$
$829$		−	54.4489i		−	1.89109i	0.325492	−	0.945545i	$-0.394470\pi$
$830$		0			0
$831$	36.8427	+	36.8427i	1.27806	+	1.27806i
$832$		−	0.724904i		−	0.0251315i
$833$	−15.0458	+	13.6970i	−0.521307	+	0.474572i
$834$	31.9916			1.10778
$835$		0			0
$836$	4.23437	−	1.75393i	0.146449	−	0.0606610i
$837$	−49.1740			−1.69970
$838$	20.5349	−	8.50583i	0.709366	−	0.293829i
$839$	10.9808	+	4.54840i	0.379100	+	0.157028i	0.564093	−	0.825712i	$-0.309226\pi$
$839$	10.9808	+	4.54840i	0.379100	+	0.157028i	−0.184993	+	0.982740i	$0.559226\pi$
$840$		0			0
$841$	3.50507	−	3.50507i	0.120864	−	0.120864i
$842$	20.0953	+	20.0953i	0.692529	+	0.692529i
$843$	50.0835	+	20.7453i	1.72497	+	0.714505i
$844$	−3.39457	−	1.40608i	−0.116846	−	0.0483991i
$845$		0			0
$846$		−	43.2266i		−	1.48616i
$847$	9.26124	+	22.3586i	0.318220	+	0.768251i
$848$	−5.40317	+	5.40317i	−0.185546	+	0.185546i
$849$	56.8546			1.95124
$850$		0			0
$851$	−5.76186			−0.197514
$852$	−6.44330	+	6.44330i	−0.220744	+	0.220744i
$853$	−13.1561	−	31.7617i	−0.450457	−	1.08750i	−0.972149	−	0.234365i	$-0.924699\pi$
$853$	−13.1561	−	31.7617i	−0.450457	−	1.08750i	0.521692	−	0.853134i	$-0.325301\pi$
$854$		−	21.7211i		−	0.743281i
$855$		0			0
$856$	−10.7206	−	4.44064i	−0.366424	−	0.151778i
$857$	−17.0386	−	7.05760i	−0.582026	−	0.241083i	0.0721899	−	0.997391i	$-0.477001\pi$
$857$	−17.0386	−	7.05760i	−0.582026	−	0.241083i	−0.654216	+	0.756308i	$0.727001\pi$
$858$	−1.78848	−	1.78848i	−0.0610576	−	0.0610576i
$859$	−17.2644	+	17.2644i	−0.589054	+	0.589054i	−0.937375	−	0.348321i	$-0.886752\pi$
$859$	−17.2644	+	17.2644i	−0.589054	+	0.589054i	0.348321	+	0.937375i	$0.386752\pi$
$860$		0			0
$861$	96.6040	+	40.0147i	3.29225	+	1.36370i
$862$	−30.2410	+	12.5262i	−1.03001	+	0.426645i
$863$	−22.5253			−0.766770			−0.383385	−	0.923589i	$-0.625242\pi$
$863$	−22.5253			−0.766770			−0.383385	+	0.923589i	$0.625242\pi$
$864$	19.7995	−	8.20121i	0.673592	−	0.279011i
$865$		0			0
$866$	−5.56353			−0.189056
$867$	−15.0584	−	48.8680i	−0.511409	−	1.65964i
$868$		−	7.77753i		−	0.263987i
$869$	−15.4541	−	15.4541i	−0.524243	−	0.524243i
$870$		0			0
$871$		−	0.877548i		−	0.0297346i
$872$	−34.8111	+	14.4192i	−1.17885	+	0.488297i
$873$	17.7664	−	42.8919i	0.601302	−	1.45167i
$874$	−4.98203	+	12.0277i	−0.168520	+	0.406843i
$875$		0			0
$876$	13.0566	−	13.0566i	0.441140	−	0.441140i
$877$	−52.2583	−	21.6461i	−1.76464	−	0.730937i	−0.995806	−	0.0914856i	$-0.970838\pi$
$877$	−52.2583	−	21.6461i	−1.76464	−	0.730937i	−0.768832	−	0.639451i	$-0.779162\pi$
$878$	1.95724	−	4.72519i	0.0660535	−	0.159467i
$879$	−8.66990	−	20.9310i	−0.292428	−	0.705984i
$880$		0			0
$881$	30.6744	−	12.7058i	1.03345	−	0.428068i	0.199492	−	0.979899i	$-0.436071\pi$
$881$	30.6744	−	12.7058i	1.03345	−	0.428068i	0.833956	+	0.551831i	$0.186071\pi$
$882$	32.8275	−	32.8275i	1.10536	−	1.10536i
$883$		−	11.2453i		−	0.378433i	−0.981935	−	0.189217i	$-0.939405\pi$
$883$		−	11.2453i		−	0.378433i	0.981935	−	0.189217i	$-0.0605949\pi$
$884$	−0.220221	−	0.0103346i	−0.00740682	−	0.000347590i
$885$		0			0
$886$	27.4315	+	27.4315i	0.921580	+	0.921580i
$887$	0.387187	+	0.934751i	0.0130005	+	0.0313859i	0.930246	−	0.366935i	$-0.119593\pi$
$887$	0.387187	+	0.934751i	0.0130005	+	0.0313859i	−0.917246	+	0.398321i	$0.869593\pi$
$888$	13.1000			0.439608
$889$	10.6029	+	25.5976i	0.355609	+	0.858516i
$890$		0			0
$891$	−15.3178	+	36.9804i	−0.513165	+	1.23889i
$892$	−6.28002	−	6.28002i	−0.210271	−	0.210271i
$893$	−8.36094	−	8.36094i	−0.279788	−	0.279788i
$894$	12.6070	−	30.4361i	0.421642	−	1.01793i
$895$		0			0
$896$	−17.8830	−	43.1734i	−0.597430	−	1.44232i
$897$	1.24622			0.0416100
$898$	−5.74827	−	13.8775i	−0.191822	−	0.463100i
$899$	18.5971	+	18.5971i	0.620249	+	0.620249i
$900$		0			0
$901$	−4.54809	−	4.99598i	−0.151519	−	0.166440i
$902$		−	66.4174i		−	2.21146i
$903$	−18.6244	+	18.6244i	−0.619782	+	0.619782i
$904$	−16.7414	+	6.93453i	−0.556812	+	0.230639i
$905$		0			0
$906$	−11.3826	−	27.4800i	−0.378161	−	0.912961i
$907$	7.01488	−	16.9354i	0.232925	−	0.562331i	−0.763594	−	0.645697i	$-0.776567\pi$
$907$	7.01488	−	16.9354i	0.232925	−	0.562331i	0.996519	+	0.0833657i	$0.0265669\pi$
$908$	9.94006	+	4.11731i	0.329872	+	0.136638i
$909$	−72.0523	+	72.0523i	−2.38983	+	2.38983i
$910$		0			0
$911$	10.6365	−	25.6787i	0.352402	−	0.850772i	−0.643921	−	0.765092i	$-0.722694\pi$
$911$	10.6365	−	25.6787i	0.352402	−	0.850772i	0.996323	−	0.0856806i	$-0.0273065\pi$
$912$	13.8137	−	33.3492i	0.457417	−	1.10430i
$913$	56.6327	−	23.4580i	1.87427	−	0.776348i
$914$			31.8538i			1.05363i
$915$		0			0
$916$	−2.10734	−	2.10734i	−0.0696286	−	0.0696286i
$917$			49.0881i			1.62103i
$918$	19.9305	+	55.3193i	0.657806	+	1.82581i
$919$	13.6372			0.449850			0.224925	−	0.974376i	$-0.427786\pi$
$919$	13.6372			0.449850			0.224925	+	0.974376i	$0.427786\pi$
$920$		0			0
$921$	−21.5949	+	8.94489i	−0.711575	+	0.294744i
$922$	29.3218			0.965661
$923$	0.849453	−	0.351855i	0.0279601	−	0.0115814i
$924$	−17.0987	−	7.08253i	−0.562507	−	0.232998i
$925$		0			0
$926$	2.34760	−	2.34760i	0.0771468	−	0.0771468i
$927$	−18.4854	−	18.4854i	−0.607139	−	0.607139i
$928$	−10.5896	−	4.38635i	−0.347620	−	0.143989i
$929$	48.4225	+	20.0573i	1.58869	+	0.658057i	0.989760	−	0.142743i	$-0.0455922\pi$
$929$	48.4225	+	20.0573i	1.58869	+	0.658057i	0.598931	+	0.800800i	$0.295592\pi$
$930$		0			0
$931$		−	12.6991i		−	0.416195i
$932$	−3.80905	−	9.19587i	−0.124770	−	0.301221i
$933$	−18.3872	+	18.3872i	−0.601969	+	0.601969i
$934$	36.1876			1.18409
$935$		0			0
$936$	−1.89391			−0.0619045
$937$	22.9966	−	22.9966i	0.751266	−	0.751266i	−0.223450	−	0.974715i	$-0.571732\pi$
$937$	22.9966	−	22.9966i	0.751266	−	0.751266i	0.974715	+	0.223450i	$0.0717318\pi$
$938$	−14.1664	−	34.2006i	−0.462548	−	1.11669i
$939$		−	37.1122i		−	1.21111i
$940$		0			0
$941$	16.0374	+	6.64290i	0.522804	+	0.216552i	0.628448	−	0.777852i	$-0.283690\pi$
$941$	16.0374	+	6.64290i	0.522804	+	0.216552i	−0.105644	+	0.994404i	$0.533690\pi$
$942$	72.5113	+	30.0351i	2.36254	+	0.978598i
$943$	23.1400	+	23.1400i	0.753541	+	0.753541i
$944$	20.2520	−	20.2520i	0.659148	−	0.659148i
$945$		0			0
$946$	15.4566	+	6.40235i	0.502539	+	0.208158i
$947$	13.1834	−	5.46073i	0.428402	−	0.177450i	−0.158055	−	0.987430i	$-0.550522\pi$
$947$	13.1834	−	5.46073i	0.428402	−	0.177450i	0.586457	+	0.809980i	$0.300522\pi$
$948$	6.50280			0.211201
$949$	−1.72131	+	0.712990i	−0.0558761	+	0.0231446i
$950$		0			0
$951$	−24.5828			−0.797152
$952$	32.9416	−	11.8683i	1.06764	−	0.384653i
$953$			30.1090i			0.975326i	0.873032	+	0.487663i	$0.162150\pi$
$953$			30.1090i			0.975326i	−0.873032	+	0.487663i	$0.837850\pi$
$954$	10.9004	+	10.9004i	0.352914	+	0.352914i
$955$		0			0
$956$			0.0458829i			0.00148396i
$957$	57.8207	−	23.9501i	1.86908	−	0.774197i
$958$	−18.5804	+	44.8571i	−0.600306	+	1.44927i
$959$	11.2781	−	27.2279i	0.364190	−	0.879233i
$960$		0			0
$961$	−1.57724	+	1.57724i	−0.0508787	+	0.0508787i
$962$	0.324358	+	0.134354i	0.0104577	+	0.00433173i
$963$	−10.9253	+	26.3760i	−0.352063	+	0.849954i
$964$	−2.80880	−	6.78105i	−0.0904654	−	0.218403i
$965$		0			0
$966$	48.5689	−	20.1179i	1.56268	−	0.647282i
$967$	−12.3882	+	12.3882i	−0.398378	+	0.398378i	−0.877661	−	0.479282i	$-0.840897\pi$
$967$	−12.3882	+	12.3882i	−0.398378	+	0.398378i	0.479282	+	0.877661i	$0.340897\pi$
$968$		−	17.2202i		−	0.553477i
$969$	28.8812	+	13.5823i	0.927797	+	0.436328i
$970$		0			0
$971$	−8.22783	−	8.22783i	−0.264044	−	0.264044i	0.562651	−	0.826695i	$-0.309782\pi$
$971$	−8.22783	−	8.22783i	−0.264044	−	0.264044i	−0.826695	+	0.562651i	$0.809782\pi$
$972$	−0.139886	−	0.337716i	−0.00448686	−	0.0108322i
$973$	−23.6203			−0.757234
$974$	8.72253	+	21.0581i	0.279488	+	0.674744i
$975$		0			0
$976$	−7.21312	+	17.4140i	−0.230886	+	0.557409i
$977$	−30.6475	−	30.6475i	−0.980501	−	0.980501i	0.0193125	−	0.999813i	$-0.493852\pi$
$977$	−30.6475	−	30.6475i	−0.980501	−	0.980501i	−0.999813	+	0.0193125i	$0.993852\pi$
$978$	15.2010	+	15.2010i	0.486073	+	0.486073i
$979$	0.975716	−	2.35559i	0.0311840	−	0.0752849i
$980$		0			0
$981$	35.4756	+	85.6457i	1.13265	+	2.73446i
$982$	−21.5620			−0.688072
$983$	16.9881	+	41.0128i	0.541835	+	1.30811i	0.923427	+	0.383774i	$0.125376\pi$
$983$	16.9881	+	41.0128i	0.541835	+	1.30811i	−0.381592	+	0.924331i	$0.624624\pi$
$984$	−52.6105	−	52.6105i	−1.67716	−	1.67716i
$985$		0			0
$986$	13.3837	−	28.4587i	0.426223	−	0.906310i
$987$			47.7470i			1.51980i
$988$	0.0972974	−	0.0972974i	0.00309544	−	0.00309544i
$989$	−7.61573	+	3.15454i	−0.242166	+	0.100308i
$990$		0			0
$991$	−22.0859	−	53.3201i	−0.701583	−	1.69377i	−0.720033	−	0.693940i	$-0.755873\pi$
$991$	−22.0859	−	53.3201i	−0.701583	−	1.69377i	0.0184501	−	0.999830i	$-0.494127\pi$
$992$	−4.79815	+	11.5838i	−0.152341	+	0.367785i
$993$	65.2132	+	27.0122i	2.06948	+	0.857206i
$994$	27.4256	−	27.4256i	0.869889	−	0.869889i
$995$		0			0
$996$	−6.97967	+	16.8504i	−0.221159	+	0.533926i
$997$	4.46444	−	10.7781i	0.141390	−	0.341346i	−0.837283	−	0.546770i	$-0.815857\pi$
$997$	4.46444	−	10.7781i	0.141390	−	0.341346i	0.978673	+	0.205424i	$0.0658572\pi$
$998$	57.5315	−	23.8303i	1.82113	−	0.754336i
$999$		−	16.2425i		−	0.513891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.f.274.3		24
5.2	odd	4		85.2.l.a.36.3	yes	24
5.3	odd	4		425.2.m.b.376.4		24
5.4	even	2		425.2.n.c.274.4		24
15.2	even	4		765.2.be.b.631.4		24
17.9	even	8		425.2.n.c.349.4		24
85.3	even	16		7225.2.a.bq.1.9		12
85.9	even	8	inner	425.2.n.f.349.3		24
85.12	even	16		1445.2.d.j.866.17		24
85.22	even	16		1445.2.d.j.866.18		24
85.37	even	16		1445.2.a.q.1.4		12
85.43	odd	8		425.2.m.b.26.4		24
85.48	even	16		7225.2.a.bs.1.9		12
85.77	odd	8		85.2.l.a.26.3	✓	24
85.82	even	16		1445.2.a.p.1.4		12
255.77	even	8		765.2.be.b.451.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.3	✓	24	85.77	odd	8
85.2.l.a.36.3	yes	24	5.2	odd	4
425.2.m.b.26.4		24	85.43	odd	8
425.2.m.b.376.4		24	5.3	odd	4
425.2.n.c.274.4		24	5.4	even	2
425.2.n.c.349.4		24	17.9	even	8
425.2.n.f.274.3		24	1.1	even	1	trivial
425.2.n.f.349.3		24	85.9	even	8	inner
765.2.be.b.451.4		24	255.77	even	8
765.2.be.b.631.4		24	15.2	even	4
1445.2.a.p.1.4		12	85.82	even	16
1445.2.a.q.1.4		12	85.37	even	16
1445.2.d.j.866.17		24	85.12	even	16
1445.2.d.j.866.18		24	85.22	even	16
7225.2.a.bq.1.9		12	85.3	even	16
7225.2.a.bs.1.9		12	85.48	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.09994 + 1.09994i) q^{2} +(1.15110 + 2.77900i) q^{3} -0.419729i q^{4} +(-4.32287 - 1.79059i) q^{6} +(3.19170 + 1.32205i) q^{7} +(-1.73820 - 1.73820i) q^{8} +(-4.27649 + 4.27649i) q^{9} +O(q^{10})\)	\(q+(-1.09994 + 1.09994i) q^{2} +(1.15110 + 2.77900i) q^{3} -0.419729i q^{4} +(-4.32287 - 1.79059i) q^{6} +(3.19170 + 1.32205i) q^{7} +(-1.73820 - 1.73820i) q^{8} +(-4.27649 + 4.27649i) q^{9} +(-3.92026 - 1.62382i) q^{11} +(1.16643 - 0.483150i) q^{12} -0.127392 q^{13} +(-4.96485 + 2.05651i) q^{14} +4.66329 q^{16} +(-0.193278 + 4.11857i) q^{17} -9.40776i q^{18} +(-1.81966 - 1.81966i) q^{19} +10.3916i q^{21} +(6.09815 - 2.52594i) q^{22} +(-1.24457 + 3.00465i) q^{23} +(2.82962 - 6.83130i) q^{24} +(0.140123 - 0.140123i) q^{26} +(-8.47004 - 3.50841i) q^{27} +(0.554901 - 1.33965i) q^{28} +(1.87644 + 4.53013i) q^{29} +(4.95543 - 2.05261i) q^{31} +(-1.65293 + 1.65293i) q^{32} -12.7636i q^{33} +(-4.31758 - 4.74277i) q^{34} +(1.79497 + 1.79497i) q^{36} +(0.677990 + 1.63681i) q^{37} +4.00302 q^{38} +(-0.146641 - 0.354023i) q^{39} +(3.85069 - 9.29639i) q^{41} +(-11.4301 - 11.4301i) q^{42} +(1.79227 + 1.79227i) q^{43} +(-0.681566 + 1.64545i) q^{44} +(-1.93598 - 4.67388i) q^{46} +4.59479 q^{47} +(5.36791 + 12.9593i) q^{48} +(3.48941 + 3.48941i) q^{49} +(-11.6680 + 4.20377i) q^{51} +0.0534701i q^{52} +(-1.15866 + 1.15866i) q^{53} +(13.1756 - 5.45749i) q^{54} +(-3.24984 - 7.84580i) q^{56} +(2.96222 - 7.15144i) q^{57} +(-7.04683 - 2.91889i) q^{58} +(4.34287 - 4.34287i) q^{59} +(-1.54679 + 3.73428i) q^{61} +(-3.19293 + 7.70840i) q^{62} +(-19.3030 + 7.99557i) q^{63} +5.69034i q^{64} +(14.0392 + 14.0392i) q^{66} +6.88856i q^{67} +(1.72868 + 0.0811242i) q^{68} -9.78255 q^{69} +(-6.66802 + 2.76198i) q^{71} +14.8668 q^{72} +(13.5119 - 5.59682i) q^{73} +(-2.54614 - 1.05465i) q^{74} +(-0.763763 + 0.763763i) q^{76} +(-10.3655 - 10.3655i) q^{77} +(0.550699 + 0.228107i) q^{78} +(4.75854 + 1.97105i) q^{79} -9.43315i q^{81} +(5.98994 + 14.4610i) q^{82} +(-10.2150 + 10.2150i) q^{83} +4.36164 q^{84} -3.94276 q^{86} +(-10.4293 + 10.4293i) q^{87} +(3.99166 + 9.63673i) q^{88} +0.600876i q^{89} +(-0.406598 - 0.168418i) q^{91} +(1.26114 + 0.522381i) q^{92} +(11.4084 + 11.4084i) q^{93} +(-5.05398 + 5.05398i) q^{94} +(-6.49616 - 2.69080i) q^{96} +(-7.09206 + 2.93763i) q^{97} -7.67628 q^{98} +(23.7092 - 9.82068i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more