LMFDB - Embedded newform 525.2.q.f.374.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 $ x^16 + 11x^14 + 85x^12 + 332x^10 + 940x^8 + 1064x^6 + 880x^4 + 128*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.7
Root			$-1.03144 - 1.78651i$ of defining polynomial
Character	$\chi$	$=$	525.374
Dual form			525.2.q.f.299.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03144 + 1.78651i) q^{2} +(1.61429 + 0.627739i) q^{3} +(-1.12774 + 1.95330i) q^{4} +(0.543588 + 3.53142i) q^{6} +(2.64573 - 0.00953166i) q^{7} -0.527019 q^{8} +(2.21189 + 2.02671i) q^{9} +O(q^{10})$	\(q+(1.03144 + 1.78651i) q^{2} +(1.61429 + 0.627739i) q^{3} +(-1.12774 + 1.95330i) q^{4} +(0.543588 + 3.53142i) q^{6} +(2.64573 - 0.00953166i) q^{7} -0.527019 q^{8} +(2.21189 + 2.02671i) q^{9} +(-4.06348 - 2.34605i) q^{11} +(-3.04666 + 2.44528i) q^{12} +0.638688 q^{13} +(2.74595 + 4.71679i) q^{14} +(1.71189 + 2.96508i) q^{16} +(-3.59334 - 2.07462i) q^{17} +(-1.33930 + 6.04198i) q^{18} +(0.776975 - 0.448587i) q^{19} +(4.27698 + 1.64544i) q^{21} -9.67925i q^{22} +(-3.40218 - 5.89275i) q^{23} +(-0.850763 - 0.330830i) q^{24} +(0.658769 + 1.14102i) q^{26} +(2.29839 + 4.66019i) q^{27} +(-2.96508 + 5.17866i) q^{28} +2.14740i q^{29} +(-2.02453 - 1.16886i) q^{31} +(-4.05844 + 7.02943i) q^{32} +(-5.08695 - 6.33802i) q^{33} -8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} +(-9.85748 + 5.69122i) q^{37} +(1.60281 + 0.925382i) q^{38} +(1.03103 + 0.400929i) q^{39} -4.10624 q^{41} +(1.47185 + 9.33802i) q^{42} -3.14924i q^{43} +(9.16509 - 5.29147i) q^{44} +(7.01829 - 12.1560i) q^{46} +(5.89714 - 3.40471i) q^{47} +(0.902197 + 5.86113i) q^{48} +(6.99982 - 0.0504365i) q^{49} +(-4.49840 - 5.60472i) q^{51} +(-0.720273 + 1.24755i) q^{52} +(1.13269 - 1.96187i) q^{53} +(-5.95481 + 8.91281i) q^{54} +(-1.39435 + 0.00502336i) q^{56} +(1.53586 - 0.236414i) q^{57} +(-3.83635 + 2.21492i) q^{58} +(0.254055 - 0.440035i) q^{59} +(4.48946 - 2.59199i) q^{61} -4.82244i q^{62} +(5.87139 + 5.34105i) q^{63} -9.89660 q^{64} +(6.07604 - 15.6252i) q^{66} +(-4.18160 - 2.41425i) q^{67} +(8.10471 - 4.67925i) q^{68} +(-1.79301 - 11.6483i) q^{69} +1.22800i q^{71} +(-1.16571 - 1.06811i) q^{72} +(7.22826 - 12.5197i) q^{73} +(-20.3348 - 11.7403i) q^{74} +2.02356i q^{76} +(-10.7733 - 6.16830i) q^{77} +(0.347183 + 2.25548i) q^{78} +(4.54056 + 7.86448i) q^{79} +(0.784903 + 8.96571i) q^{81} +(-4.23534 - 7.33583i) q^{82} -2.76359i q^{83} +(-8.03735 + 6.49859i) q^{84} +(5.62613 - 3.24825i) q^{86} +(-1.34801 + 3.46653i) q^{87} +(2.14153 + 1.23641i) q^{88} +(6.90067 + 11.9523i) q^{89} +(1.68980 - 0.00608775i) q^{91} +15.3471 q^{92} +(-2.53444 - 3.15776i) q^{93} +(12.1651 + 7.02352i) q^{94} +(-10.9642 + 8.79992i) q^{96} +12.9085 q^{97} +(7.31000 + 12.4532i) q^{98} +(-4.23321 - 13.4247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	$ 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * q^96 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.03144	+	1.78651i	0.729338	+	1.26325i	0.957163	+	0.289549i	$0.0935054\pi$
$2$	1.03144	+	1.78651i	0.729338	+	1.26325i	−0.227825	+	0.973702i	$0.573161\pi$
$3$	1.61429	+	0.627739i	0.932013	+	0.362425i
$3$	1.61429	+	0.627739i	0.932013	+	0.362425i
$4$	−1.12774	+	1.95330i	−0.563869	+	0.976650i
$5$		0			0
$5$		0			0
$6$	0.543588	+	3.53142i	0.221919	+	1.44170i
$7$	2.64573	−	0.00953166i	0.999994	−	0.00360263i
$7$	2.64573	−	0.00953166i	0.999994	−	0.00360263i
$8$	−0.527019			−0.186329
$9$	2.21189	+	2.02671i	0.737296	+	0.675570i
$10$		0			0
$11$	−4.06348	−	2.34605i	−1.22519	−	0.707362i	−0.259167	−	0.965833i	$-0.583448\pi$
$11$	−4.06348	−	2.34605i	−1.22519	−	0.707362i	−0.966019	+	0.258471i	$0.916781\pi$
$12$	−3.04666	+	2.44528i	−0.879496	+	0.705890i
$13$	0.638688			0.177140			0.0885701	−	0.996070i	$-0.471770\pi$
$13$	0.638688			0.177140			0.0885701	+	0.996070i	$0.471770\pi$
$14$	2.74595	+	4.71679i	0.733885	+	1.26062i
$15$		0			0
$16$	1.71189	+	2.96508i	0.427972	+	0.741270i
$17$	−3.59334	−	2.07462i	−0.871514	−	0.503169i	−0.00366299	−	0.999993i	$-0.501166\pi$
$17$	−3.59334	−	2.07462i	−0.871514	−	0.503169i	−0.867851	+	0.496824i	$0.834499\pi$
$18$	−1.33930	+	6.04198i	−0.315676	+	1.42411i
$19$	0.776975	−	0.448587i	0.178250	−	0.102913i	−0.408220	−	0.912884i	$-0.633850\pi$
$19$	0.776975	−	0.448587i	0.178250	−	0.102913i	0.586470	+	0.809971i	$0.300517\pi$
$20$		0			0
$21$	4.27698	+	1.64544i	0.933313	+	0.359065i
$22$		−	9.67925i		−	2.06362i
$23$	−3.40218	−	5.89275i	−0.709403	−	1.22872i	−0.965079	−	0.261960i	$-0.915631\pi$
$23$	−3.40218	−	5.89275i	−0.709403	−	1.22872i	0.255675	−	0.966763i	$-0.417702\pi$
$24$	−0.850763	−	0.330830i	−0.173661	−	0.0675304i
$25$		0			0
$26$	0.658769	+	1.14102i	0.129195	+	0.223773i
$27$	2.29839	+	4.66019i	0.442326	+	0.896854i
$28$	−2.96508	+	5.17866i	−0.560347	+	0.978675i
$29$			2.14740i			0.398762i	0.979922	+	0.199381i	$0.0638932\pi$
$29$			2.14740i			0.398762i	−0.979922	+	0.199381i	$0.936107\pi$
$30$		0			0
$31$	−2.02453	−	1.16886i	−0.363615	−	0.209933i	0.307050	−	0.951693i	$-0.400658\pi$
$31$	−2.02453	−	1.16886i	−0.363615	−	0.209933i	−0.670666	+	0.741760i	$0.733991\pi$
$32$	−4.05844	+	7.02943i	−0.717438	+	1.24264i
$33$	−5.08695	−	6.33802i	−0.885524	−	1.10331i
$34$		−	8.55938i		−	1.46792i
$35$		0			0
$36$	−6.45320	+	2.03489i	−1.07553	+	0.339148i
$37$	−9.85748	+	5.69122i	−1.62056	+	0.935631i	−0.633790	+	0.773505i	$0.718502\pi$
$37$	−9.85748	+	5.69122i	−1.62056	+	0.935631i	−0.986770	+	0.162126i	$0.948165\pi$
$38$	1.60281	+	0.925382i	0.260010	+	0.150117i
$39$	1.03103	+	0.400929i	0.165097	+	0.0642000i
$40$		0			0
$41$	−4.10624			−0.641287			−0.320643	−	0.947200i	$-0.603899\pi$
$41$	−4.10624			−0.641287			−0.320643	+	0.947200i	$0.603899\pi$
$42$	1.47185	+	9.33802i	0.227111	+	1.44089i
$43$		−	3.14924i		−	0.480254i	−0.970741	−	0.240127i	$-0.922811\pi$
$43$		−	3.14924i		−	0.480254i	0.970741	−	0.240127i	$-0.0771891\pi$
$44$	9.16509	−	5.29147i	1.38169	−	0.797719i
$45$		0			0
$46$	7.01829	−	12.1560i	1.03479	−	1.79231i
$47$	5.89714	−	3.40471i	0.860186	−	0.496629i	−0.00388861	−	0.999992i	$-0.501238\pi$
$47$	5.89714	−	3.40471i	0.860186	−	0.496629i	0.864075	+	0.503364i	$0.167904\pi$
$48$	0.902197	+	5.86113i	0.130221	+	0.845981i
$49$	6.99982	−	0.0504365i	0.999974	−	0.00720521i
$50$		0			0
$51$	−4.49840	−	5.60472i	−0.629901	−	0.784818i
$52$	−0.720273	+	1.24755i	−0.0998839	+	0.173004i
$53$	1.13269	−	1.96187i	0.155587	−	0.269484i	−0.777686	−	0.628653i	$-0.783607\pi$
$53$	1.13269	−	1.96187i	0.155587	−	0.269484i	0.933272	+	0.359169i	$0.116940\pi$
$54$	−5.95481	+	8.91281i	−0.810347	+	1.21288i
$55$		0			0
$56$	−1.39435	+	0.00502336i	−0.186328	+	0.000671275i
$57$	1.53586	−	0.236414i	0.203430	−	0.0313138i
$58$	−3.83635	+	2.21492i	−0.503737	+	0.290833i
$59$	0.254055	−	0.440035i	0.0330751	−	0.0572877i	−0.849014	−	0.528370i	$-0.822803\pi$
$59$	0.254055	−	0.440035i	0.0330751	−	0.0572877i	0.882089	+	0.471083i	$0.156137\pi$
$60$		0			0
$61$	4.48946	−	2.59199i	0.574816	−	0.331870i	−0.184255	−	0.982879i	$-0.558987\pi$
$61$	4.48946	−	2.59199i	0.574816	−	0.331870i	0.759070	+	0.651008i	$0.225654\pi$
$62$		−	4.82244i		−	0.612450i
$63$	5.87139	+	5.34105i	0.739725	+	0.672909i
$64$	−9.89660			−1.23708
$65$		0			0
$66$	6.07604	−	15.6252i	0.747909	−	1.92332i
$67$	−4.18160	−	2.41425i	−0.510863	−	0.294947i	0.222325	−	0.974973i	$-0.428635\pi$
$67$	−4.18160	−	2.41425i	−0.510863	−	0.294947i	−0.733188	+	0.680026i	$0.761969\pi$
$68$	8.10471	−	4.67925i	0.982840	−	0.567443i
$69$	−1.79301	−	11.6483i	−0.215853	−	1.40229i
$70$		0			0
$71$			1.22800i			0.145737i	0.997342	+	0.0728686i	$0.0232154\pi$
$71$			1.22800i			0.145737i	−0.997342	+	0.0728686i	$0.976785\pi$
$72$	−1.16571	−	1.06811i	−0.137380	−	0.125878i
$73$	7.22826	−	12.5197i	0.846004	−	1.46532i	−0.0387429	−	0.999249i	$-0.512335\pi$
$73$	7.22826	−	12.5197i	0.846004	−	1.46532i	0.884747	−	0.466072i	$-0.154331\pi$
$74$	−20.3348	−	11.7403i	−2.36387	−	1.36478i
$75$		0			0
$76$			2.02356i			0.232118i
$77$	−10.7733	−	6.16830i	−1.22773	−	0.702943i
$78$	0.347183	+	2.25548i	0.0393108	+	0.255382i
$79$	4.54056	+	7.86448i	0.510853	+	0.884824i	0.999921	+	0.0125778i	$0.00400373\pi$
$79$	4.54056	+	7.86448i	0.510853	+	0.884824i	−0.489068	+	0.872246i	$0.662663\pi$
$80$		0			0
$81$	0.784903	+	8.96571i	0.0872114	+	0.996190i
$82$	−4.23534	−	7.33583i	−0.467715	−	0.810107i
$83$		−	2.76359i		−	0.303343i	−0.988431	−	0.151671i	$-0.951534\pi$
$83$		−	2.76359i		−	0.303343i	0.988431	−	0.151671i	$-0.0484656\pi$
$84$	−8.03735	+	6.49859i	−0.876947	+	0.709054i
$85$		0			0
$86$	5.62613	−	3.24825i	0.606682	−	0.350268i
$87$	−1.34801	+	3.46653i	−0.144521	+	0.371652i
$88$	2.14153	+	1.23641i	0.228288	+	0.131802i
$89$	6.90067	+	11.9523i	0.731470	+	1.26694i	0.956255	+	0.292535i	$0.0944988\pi$
$89$	6.90067	+	11.9523i	0.731470	+	1.26694i	−0.224785	+	0.974408i	$0.572168\pi$
$90$		0			0
$91$	1.68980	−	0.00608775i	0.177139	−	0.000638170i
$92$	15.3471			1.60004
$93$	−2.53444	−	3.15776i	−0.262809	−	0.327444i
$94$	12.1651	+	7.02352i	1.25473	+	0.724421i
$95$		0			0
$96$	−10.9642	+	8.79992i	−1.11902	+	0.898138i
$97$	12.9085			1.31066			0.655329	−	0.755344i	$-0.272530\pi$
$97$	12.9085			1.31066			0.655329	+	0.755344i	$0.272530\pi$
$98$	7.31000	+	12.4532i	0.738422	+	1.25796i
$99$	−4.23321	−	13.4247i	−0.425453	−	1.34923i
$100$		0			0
$101$	−4.51989	+	7.82869i	−0.449746	+	0.778983i	−0.998369	−	0.0570865i	$-0.981819\pi$
$101$	−4.51989	+	7.82869i	−0.449746	+	0.778983i	0.548623	+	0.836070i	$0.315152\pi$
$102$	5.37305	−	13.8174i	0.532012	−	1.36812i
$103$	7.76030	+	13.4412i	0.764645	+	1.32440i	0.940434	+	0.339976i	$0.110419\pi$
$103$	7.76030	+	13.4412i	0.764645	+	1.32440i	−0.175789	+	0.984428i	$0.556248\pi$
$104$	−0.336601			−0.0330064
$105$		0			0
$106$	4.67320			0.453901
$107$	−2.67897	−	4.64012i	−0.258986	−	0.448577i	0.706985	−	0.707229i	$-0.250055\pi$
$107$	−2.67897	−	4.64012i	−0.258986	−	0.448577i	−0.965971	+	0.258652i	$0.916722\pi$
$108$	−11.6947	−	0.766021i	−1.12533	−	0.0737104i
$109$	0.679436	−	1.17682i	0.0650782	−	0.112719i	−0.831650	−	0.555299i	$-0.812604\pi$
$109$	0.679436	−	1.17682i	0.0650782	−	0.112719i	0.896729	+	0.442581i	$0.145937\pi$
$110$		0			0
$111$	−19.4855	+	2.99938i	−1.84948	+	0.284689i
$112$	4.55746	+	7.82849i	0.430640	+	0.739723i
$113$	−11.9390			−1.12312			−0.561562	−	0.827435i	$-0.689799\pi$
$113$	−11.9390			−1.12312			−0.561562	+	0.827435i	$0.689799\pi$
$114$	2.00650	+	2.49998i	0.187926	+	0.234145i
$115$		0			0
$116$	−4.19452	−	2.42171i	−0.389451	−	0.224850i
$117$	1.41271	+	1.29443i	0.130605	+	0.119671i
$118$	1.04817			0.0964917
$119$	−9.52681	−	5.45464i	−0.873321	−	0.500026i
$120$		0			0
$121$	5.50793	+	9.54001i	0.500721	+	0.867274i
$122$	9.26121	+	5.34696i	0.838471	+	0.484091i
$123$	−6.62868	−	2.57765i	−0.597688	−	0.232418i
$124$	4.56627	−	2.63634i	0.410063	−	0.236750i
$125$		0			0
$126$	−3.48584	+	15.9982i	−0.310543	+	1.42524i
$127$		−	16.8492i		−	1.49513i	−0.664191	−	0.747563i	$-0.731224\pi$
$127$		−	16.8492i		−	1.49513i	0.664191	−	0.747563i	$-0.268776\pi$
$128$	−2.09088	−	3.62150i	−0.184809	−	0.320099i
$129$	1.97690	−	5.08379i	0.174056	−	0.447603i
$130$		0			0
$131$	6.93473	+	12.0113i	0.605890	+	1.04943i	0.991910	+	0.126942i	$0.0405163\pi$
$131$	6.93473	+	12.0113i	0.605890	+	1.04943i	−0.386020	+	0.922490i	$0.626150\pi$
$132$	18.1168	−	2.78870i	1.57687	−	0.242725i
$133$	2.05139	−	1.19425i	0.177878	−	0.103554i
$134$		−	9.96060i		−	0.860465i
$135$		0			0
$136$	1.89376	+	1.09336i	0.162389	+	0.0937551i
$137$	2.16915	−	3.75708i	0.185323	−	0.320989i	−0.758362	−	0.651833i	$-0.774000\pi$
$137$	2.16915	−	3.75708i	0.185323	−	0.320989i	0.943685	+	0.330844i	$0.107333\pi$
$138$	18.9604	−	15.2178i	1.61402	−	1.29542i
$139$			10.9631i			0.929881i	0.885342	+	0.464941i	$0.153924\pi$
$139$			10.9631i			0.929881i	−0.885342	+	0.464941i	$0.846076\pi$
$140$		0			0
$141$	11.6570	−	1.79435i	0.981695	−	0.151111i
$142$	−2.19384	+	1.26661i	−0.184103	+	0.106292i
$143$	−2.59530	−	1.49840i	−0.217030	−	0.125302i
$144$	−2.22284	+	10.0279i	−0.185237	+	0.835660i
$145$		0			0
$146$	29.8221			2.46809
$147$	11.3314	+	4.31264i	0.934600	+	0.355700i
$148$		−	25.6728i		−	2.11029i
$149$	−7.50546	+	4.33328i	−0.614871	+	0.354996i	−0.774870	−	0.632121i	$-0.782184\pi$
$149$	−7.50546	+	4.33328i	−0.614871	+	0.354996i	0.159998	+	0.987117i	$0.448851\pi$
$150$		0			0
$151$	−6.73018	+	11.6570i	−0.547694	+	0.948634i	0.450738	+	0.892656i	$0.351161\pi$
$151$	−6.73018	+	11.6570i	−0.547694	+	0.948634i	−0.998432	+	0.0559778i	$0.982172\pi$
$152$	−0.409481	+	0.236414i	−0.0332133	+	0.0191757i
$153$	−3.74343	−	11.8715i	−0.302638	−	0.959753i
$154$	−0.0922593	−	25.6087i	−0.00743447	−	2.06361i
$155$		0			0
$156$	−1.94587	+	1.56177i	−0.155794	+	0.125042i
$157$	3.90660	−	6.76643i	0.311781	−	0.540020i	−0.666967	−	0.745087i	$-0.732408\pi$
$157$	3.90660	−	6.76643i	0.311781	−	0.540020i	0.978748	+	0.205067i	$0.0657412\pi$
$158$	−9.36664	+	16.2235i	−0.745170	+	1.29067i
$159$	3.06003	−	2.45601i	0.242677	−	0.194774i
$160$		0			0
$161$	−9.05743	−	15.5582i	−0.713825	−	1.22616i
$162$	−15.2077	+	10.6498i	−1.19483	+	0.836730i
$163$	−14.4443	+	8.33945i	−1.13137	+	0.653196i	−0.944279	−	0.329147i	$-0.893239\pi$
$163$	−14.4443	+	8.33945i	−1.13137	+	0.653196i	−0.187090	+	0.982343i	$0.559905\pi$
$164$	4.63077	−	8.02072i	0.361602	−	0.626313i
$165$		0			0
$166$	4.93717	−	2.85047i	0.383198	−	0.221240i
$167$			0.465112i			0.0359915i	0.999838	+	0.0179957i	$0.00572853\pi$
$167$			0.465112i			0.0359915i	−0.999838	+	0.0179957i	$0.994271\pi$
$168$	−2.25405	−	0.867179i	−0.173903	−	0.0669043i
$169$	−12.5921			−0.968621
$170$		0			0
$171$	2.62774	+	0.582479i	0.200948	+	0.0445432i
$172$	6.15141	+	3.55152i	0.469040	+	0.270801i
$173$	9.68576	−	5.59208i	0.736395	−	0.425158i	−0.0843622	−	0.996435i	$-0.526885\pi$
$173$	9.68576	−	5.59208i	0.736395	−	0.425158i	0.820757	+	0.571277i	$0.193552\pi$
$174$	−7.58338	+	1.16730i	−0.574894	+	0.0884929i
$175$		0			0
$176$		−	16.0647i		−	1.21092i
$177$	0.686346	−	0.550867i	0.0515889	−	0.0414057i
$178$	−14.2353	+	24.6562i	−1.06698	+	1.84806i
$179$	0.214505	+	0.123845i	0.0160329	+	0.00925660i	0.507995	−	0.861360i	$-0.330387\pi$
$179$	0.214505	+	0.123845i	0.0160329	+	0.00925660i	−0.491962	+	0.870617i	$0.663720\pi$
$180$		0			0
$181$		−	14.3385i		−	1.06578i	−0.846186	−	0.532888i	$-0.821107\pi$
$181$		−	14.3385i		−	1.06578i	0.846186	−	0.532888i	$-0.178893\pi$
$182$	1.75380	+	3.01256i	0.130000	+	0.223306i
$183$	8.87439	−	1.36603i	0.656014	−	0.100980i
$184$	1.79301	+	3.10559i	0.132183	+	0.228947i
$185$		0			0
$186$	3.02723	−	7.78483i	0.221967	−	0.570812i
$187$	9.73433	+	16.8604i	0.711845	+	1.23295i
$188$			15.3585i			1.12013i
$189$	6.12536	+	12.3077i	0.445554	+	0.895255i
$190$		0			0
$191$	14.7572	−	8.52006i	1.06779	−	0.616490i	0.140214	−	0.990121i	$-0.455221\pi$
$191$	14.7572	−	8.52006i	1.06779	−	0.616490i	0.927577	+	0.373632i	$0.121888\pi$
$192$	−15.9760	−	6.21248i	−1.15297	−	0.448347i
$193$	2.44533	+	1.41181i	0.176019	+	0.101624i	0.585421	−	0.810730i	$-0.300929\pi$
$193$	2.44533	+	1.41181i	0.176019	+	0.101624i	−0.409402	+	0.912354i	$0.634263\pi$
$194$	13.3143	+	23.0611i	0.955913	+	1.65569i
$195$		0			0
$196$	−7.79545	+	13.7296i	−0.556818	+	0.980688i
$197$	−9.59675			−0.683740			−0.341870	−	0.939747i	$-0.611060\pi$
$197$	−9.59675			−0.683740			−0.341870	+	0.939747i	$0.611060\pi$
$198$	19.6170	−	21.4094i	1.39412	−	1.52150i
$199$	−10.5777	−	6.10706i	−0.749836	−	0.432918i	0.0757989	−	0.997123i	$-0.475849\pi$
$199$	−10.5777	−	6.10706i	−0.749836	−	0.432918i	−0.825635	+	0.564205i	$0.809183\pi$
$200$		0			0
$201$	−5.23481	−	6.52225i	−0.369235	−	0.460044i
$202$	−18.6480			−1.31207
$203$	0.0204683	+	5.68145i	0.00143659	+	0.398760i
$204$	16.0207	−	2.46605i	1.12168	−	0.172658i
$205$		0			0
$206$	−16.0086	+	27.7277i	−1.11537	+	1.93188i
$207$	4.41764	−	19.9293i	0.307047	−	1.38518i
$208$	1.09336	+	1.89376i	0.0758111	+	0.131309i
$209$	−4.20964			−0.291187
$210$		0			0
$211$	5.64113			0.388351			0.194176	−	0.980967i	$-0.437797\pi$
$211$	5.64113			0.388351			0.194176	+	0.980967i	$0.437797\pi$
$212$	2.55475	+	4.42496i	0.175461	+	0.303908i
$213$	−0.770865	+	1.98236i	−0.0528188	+	0.135829i
$214$	5.52640	−	9.57200i	0.377777	−	0.654329i
$215$		0			0
$216$	−1.21130	−	2.45601i	−0.0824183	−	0.167110i
$217$	−5.36750	−	3.07320i	−0.364369	−	0.208622i
$218$	2.80319			0.189856
$219$	19.5276	−	15.6730i	1.31956	−	1.05909i
$220$		0			0
$221$	−2.29503	−	1.32503i	−0.154380	−	0.0891314i
$222$	−25.4565	−	31.7173i	−1.70853	−	2.12872i
$223$	−0.392378			−0.0262755			−0.0131378	−	0.999914i	$-0.504182\pi$
$223$	−0.392378			−0.0262755			−0.0131378	+	0.999914i	$0.504182\pi$
$224$	−10.6706	+	18.6367i	−0.712956	+	1.24522i
$225$		0			0
$226$	−12.3143	−	21.3290i	−0.819137	−	1.41879i
$227$	20.2867	+	11.7125i	1.34648	+	0.777388i	0.987749	−	0.156054i	$-0.0498773\pi$
$227$	20.2867	+	11.7125i	1.34648	+	0.777388i	0.358728	+	0.933442i	$0.383211\pi$
$228$	−1.27026	+	3.26661i	−0.0841253	+	0.216337i
$229$	−6.69286	+	3.86412i	−0.442276	+	0.255348i	−0.704563	−	0.709642i	$-0.748857\pi$
$229$	−6.69286	+	3.86412i	−0.442276	+	0.255348i	0.262286	+	0.964990i	$0.415523\pi$
$230$		0			0
$231$	−13.5191	−	16.7202i	−0.889493	−	1.10011i
$232$		−	1.13172i		−	0.0743011i
$233$	−2.03991	−	3.53323i	−0.133639	−	0.231469i	0.791438	−	0.611250i	$-0.209333\pi$
$233$	−2.03991	−	3.53323i	−0.133639	−	0.231469i	−0.925077	+	0.379780i	$0.876000\pi$
$234$	−0.855394	+	3.85894i	−0.0559188	+	0.252267i
$235$		0			0
$236$	0.573014	+	0.992490i	0.0373001	+	0.0646056i
$237$	2.39296	+	15.5459i	0.155440	+	1.00981i
$238$	−0.0815851	−	22.6458i	−0.00528837	−	1.46791i
$239$		−	5.76281i		−	0.372765i	−0.982477	−	0.186383i	$-0.940324\pi$
$239$		−	5.76281i		−	0.372765i	0.982477	−	0.186383i	$-0.0596764\pi$
$240$		0			0
$241$	−17.6840	−	10.2098i	−1.13912	−	0.657674i	−0.192911	−	0.981216i	$-0.561793\pi$
$241$	−17.6840	−	10.2098i	−1.13912	−	0.657674i	−0.946214	+	0.323542i	$0.895126\pi$
$242$	−11.3622	+	19.6799i	−0.730390	+	1.26507i
$243$	−4.36106	+	14.9660i	−0.279762	+	0.960069i
$244$			11.6923i			0.748525i
$245$		0			0
$246$	−2.23210	−	14.5009i	−0.142314	−	0.924542i
$247$	0.496245	−	0.286507i	0.0315753	−	0.0182300i
$248$	1.06696	+	0.616011i	0.0677522	+	0.0391167i
$249$	1.73481	−	4.46124i	0.109939	−	0.282720i
$250$		0			0
$251$	4.42544			0.279331			0.139666	−	0.990199i	$-0.455397\pi$
$251$	4.42544			0.279331			0.139666	+	0.990199i	$0.455397\pi$
$252$	−17.0541	+	5.44528i	−1.07431	+	0.343020i
$253$			31.9268i			2.00722i
$254$	30.1012	−	17.3790i	1.88872	−	1.09045i
$255$		0			0
$256$	−5.58338	+	9.67069i	−0.348961	+	0.604418i
$257$	−22.0904	+	12.7539i	−1.37796	+	0.795565i	−0.991914	−	0.126915i	$-0.959492\pi$
$257$	−22.0904	+	12.7539i	−1.37796	+	0.795565i	−0.386045	+	0.922480i	$0.626159\pi$
$258$	11.1213	−	1.71189i	0.692381	−	0.106578i
$259$	−26.0260	+	15.1514i	−1.61718	+	0.941463i
$260$		0			0
$261$	−4.35215	+	4.74981i	−0.269392	+	0.294006i
$262$	−14.3055	+	24.7779i	−0.883798	+	1.53078i
$263$	0.178990	−	0.310020i	0.0110370	−	0.0191166i	−0.860454	−	0.509528i	$-0.829820\pi$
$263$	0.178990	−	0.310020i	0.0110370	−	0.0191166i	0.871491	+	0.490411i	$0.163153\pi$
$264$	2.68092	+	3.34026i	0.164999	+	0.205579i
$265$		0			0
$266$	4.24942	+	2.43304i	0.260549	+	0.149179i
$267$	3.63678	+	23.6264i	0.222568	+	1.44591i
$268$	9.43149	−	5.44528i	0.576120	−	0.332623i
$269$	−4.26905	+	7.39421i	−0.260288	+	0.450833i	−0.966319	−	0.257349i	$-0.917151\pi$
$269$	−4.26905	+	7.39421i	−0.260288	+	0.450833i	0.706030	+	0.708182i	$0.250484\pi$
$270$		0			0
$271$	−7.30474	+	4.21739i	−0.443731	+	0.256188i	−0.705179	−	0.709029i	$-0.749133\pi$
$271$	−7.30474	+	4.21739i	−0.443731	+	0.256188i	0.261448	+	0.965218i	$0.415800\pi$
$272$		−	14.2061i		−	0.861369i
$273$	2.73165	+	1.05092i	0.165327	+	0.0636048i
$274$	8.94940			0.540653
$275$		0			0
$276$	24.7747	+	9.63395i	1.49126	+	0.579896i
$277$	−8.75195	−	5.05294i	−0.525853	−	0.303602i	0.213473	−	0.976949i	$-0.431523\pi$
$277$	−8.75195	−	5.05294i	−0.525853	−	0.303602i	−0.739326	+	0.673347i	$0.764856\pi$
$278$	−19.5857	+	11.3078i	−1.17467	+	0.678198i
$279$	−2.10909	−	6.68851i	−0.126268	−	0.400431i
$280$		0			0
$281$			15.1554i			0.904094i	0.891994	+	0.452047i	$0.149306\pi$
$281$			15.1554i			0.904094i	−0.891994	+	0.452047i	$0.850694\pi$
$282$	15.2291	+	18.9745i	0.906880	+	1.12992i
$283$	11.9697	−	20.7322i	0.711527	−	1.23240i	−0.252757	−	0.967530i	$-0.581337\pi$
$283$	11.9697	−	20.7322i	0.711527	−	1.23240i	0.964284	−	0.264871i	$-0.0853294\pi$
$284$	−2.39866	−	1.38487i	−0.142334	−	0.0821768i
$285$		0			0
$286$		−	6.18202i		−	0.365551i
$287$	−10.8640	+	0.0391393i	−0.641283	+	0.00231032i
$288$	−23.2234	+	7.32303i	−1.36845	+	0.431514i
$289$	0.108084	+	0.187206i	0.00635786	+	0.0110121i
$290$		0			0
$291$	20.8381	+	8.10315i	1.22155	+	0.475015i
$292$	16.3032	+	28.2379i	0.954071	+	1.65250i
$293$			21.2223i			1.23982i	0.784673	+	0.619909i	$0.212831\pi$
$293$			21.2223i			1.23982i	−0.784673	+	0.619909i	$0.787169\pi$
$294$	3.98313	+	24.6919i	0.232301	+	1.44006i
$295$		0			0
$296$	5.19508	−	2.99938i	0.301958	−	0.174335i
$297$	1.59357	−	24.3288i	0.0924681	−	1.41170i
$298$	−15.4829	−	8.93904i	−0.896899	−	0.517825i
$299$	−2.17293	−	3.76363i	−0.125664	−	0.217656i
$300$		0			0
$301$	−0.0300174	−	8.33204i	−0.00173018	−	0.480251i
$302$	−27.7671			−1.59782
$303$	−12.2108	+	9.80049i	−0.701492	+	0.563023i
$304$	2.66019	+	1.53586i	0.152572	+	0.0880877i
$305$		0			0
$306$	17.3474	−	18.9324i	0.991683	−	1.08229i
$307$	−24.2817			−1.38583			−0.692916	−	0.721019i	$-0.743674\pi$
$307$	−24.2817			−1.38583			−0.692916	+	0.721019i	$0.743674\pi$
$308$	24.1980	−	14.0872i	1.37881	−	0.802691i
$309$	4.08982	+	26.5695i	0.232662	+	1.51149i
$310$		0			0
$311$	3.55858	−	6.16364i	0.201789	−	0.349508i	−0.747316	−	0.664469i	$-0.768658\pi$
$311$	3.55858	−	6.16364i	0.201789	−	0.349508i	0.949105	+	0.314960i	$0.101991\pi$
$312$	−0.543372	−	0.211297i	−0.0307624	−	0.0119623i
$313$	−1.77362	−	3.07200i	−0.100251	−	0.173640i	0.811537	−	0.584301i	$-0.198631\pi$
$313$	−1.77362	−	3.07200i	−0.100251	−	0.173640i	−0.911788	+	0.410661i	$0.865298\pi$
$314$	16.1177			0.909575
$315$		0			0
$316$	−20.4823			−1.15222
$317$	−10.5382	−	18.2527i	−0.591885	−	1.02517i	−0.993978	−	0.109576i	$-0.965051\pi$
$317$	−10.5382	−	18.2527i	−0.591885	−	1.02517i	0.402093	−	0.915599i	$-0.368283\pi$
$318$	7.54392	+	2.93355i	0.423042	+	0.164505i
$319$	5.03791	−	8.72592i	0.282069	−	0.488558i
$320$		0			0
$321$	−1.41187	−	9.17220i	−0.0788028	−	0.511942i
$322$	18.4527	−	32.2285i	1.02833	−	1.79603i
$323$	−3.72259			−0.207130
$324$	−18.3979	−	8.57782i	−1.02210	−	0.476546i
$325$		0			0
$326$	−29.7970	−	17.2033i	−1.65030	−	0.952802i
$327$	1.83554	−	1.47322i	0.101506	−	0.0814693i
$328$	2.16407			0.119491
$329$	15.5698	−	9.06418i	0.858391	−	0.499724i
$330$		0			0
$331$	7.40412	+	12.8243i	0.406967	+	0.704888i	0.994548	−	0.104277i	$-0.0332529\pi$
$331$	7.40412	+	12.8243i	0.406967	+	0.704888i	−0.587581	+	0.809165i	$0.699920\pi$
$332$	5.39811	+	3.11660i	0.296260	+	0.171046i
$333$	−33.3381	−	7.38990i	−1.82692	−	0.404964i
$334$	−0.830926	+	0.479736i	−0.0454663	+	0.0262500i
$335$		0			0
$336$	2.44284	+	15.4984i	0.133268	+	0.845506i
$337$			20.5062i			1.11704i	0.829490	+	0.558522i	$0.188631\pi$
$337$			20.5062i			1.11704i	−0.829490	+	0.558522i	$0.811369\pi$
$338$	−12.9880	−	22.4958i	−0.706453	−	1.22361i
$339$	−19.2730	−	7.49455i	−1.04677	−	0.407048i
$340$		0			0
$341$	5.48442	+	9.49929i	0.296998	+	0.514415i
$342$	1.66975	+	5.29527i	0.0902899	+	0.286335i
$343$	18.5192	−	0.200161i	0.999942	−	0.0108077i
$344$			1.65971i			0.0894854i
$345$		0			0
$346$	19.9806	+	11.5358i	1.07416	+	0.620168i
$347$	−7.91567	+	13.7103i	−0.424935	+	0.736010i	−0.996414	−	0.0846070i	$-0.973037\pi$
$347$	−7.91567	+	13.7103i	−0.424935	+	0.736010i	0.571479	+	0.820617i	$0.306370\pi$
$348$	−5.25099	−	6.54241i	−0.281482	−	0.350710i
$349$			8.96019i			0.479628i	0.970819	+	0.239814i	$0.0770865\pi$
$349$			8.96019i			0.479628i	−0.970819	+	0.239814i	$0.922914\pi$
$350$		0			0
$351$	1.46796	+	2.97641i	0.0783538	+	0.158869i
$352$	32.9828	−	19.0426i	1.75799	−	1.01498i
$353$	−11.6545	−	6.72876i	−0.620309	−	0.358136i	0.156680	−	0.987649i	$-0.449921\pi$
$353$	−11.6545	−	6.72876i	−0.620309	−	0.358136i	−0.776989	+	0.629514i	$0.783254\pi$
$354$	1.69205	+	0.657976i	0.0899316	+	0.0349710i
$355$		0			0
$356$	−31.1286			−1.64981
$357$	−11.9550	−	14.7857i	−0.632725	−	0.782544i
$358$			0.510954i			0.0270048i
$359$	4.85824	−	2.80491i	0.256408	−	0.148037i	−0.366287	−	0.930502i	$-0.619371\pi$
$359$	4.85824	−	2.80491i	0.256408	−	0.148037i	0.622695	+	0.782465i	$0.286038\pi$
$360$		0			0
$361$	−9.09754	+	15.7574i	−0.478818	+	0.829337i
$362$	25.6159	−	14.7894i	1.34634	−	0.777311i
$363$	2.90278	+	18.8579i	0.152356	+	0.989784i
$364$	−1.89376	+	3.30755i	−0.0992600	+	0.173363i
$365$		0			0
$366$	11.5938	+	14.4452i	0.606019	+	0.755062i
$367$	0.988156	−	1.71154i	0.0515813	−	0.0893415i	−0.839082	−	0.544005i	$-0.816907\pi$
$367$	0.988156	−	1.71154i	0.0515813	−	0.0893415i	0.890663	+	0.454664i	$0.150241\pi$
$368$	11.6483	−	20.1755i	0.607210	−	1.05172i
$369$	−9.08255	−	8.32215i	−0.472818	−	0.433234i
$370$		0			0
$371$	2.97809	−	5.20139i	0.154615	−	0.270043i
$372$	9.02623	−	1.38940i	0.467988	−	0.0720370i
$373$	19.9995	−	11.5467i	1.03553	−	0.597866i	0.116969	−	0.993136i	$-0.462682\pi$
$373$	19.9995	−	11.5467i	1.03553	−	0.597866i	0.918565	+	0.395270i	$0.129349\pi$
$374$	−20.0808	+	34.7809i	−1.03835	+	1.79848i
$375$		0			0
$376$	−3.10790	+	1.79435i	−0.160278	+	0.0925364i
$377$			1.37152i			0.0706368i
$378$	−15.6699	+	23.6377i	−0.805972	+	1.21579i
$379$	17.0645			0.876547			0.438273	−	0.898842i	$-0.355590\pi$
$379$	17.0645			0.876547			0.438273	+	0.898842i	$0.355590\pi$
$380$		0			0
$381$	10.5769	−	27.1996i	0.541871	−	1.39348i
$382$	30.4423	+	17.5759i	1.55756	+	0.899259i
$383$	23.0460	−	13.3056i	1.17760	−	0.679886i	0.222139	−	0.975015i	$-0.428696\pi$
$383$	23.0460	−	13.3056i	1.17760	−	0.679886i	0.955457	+	0.295129i	$0.0953627\pi$
$384$	−1.10193	−	7.15869i	−0.0562327	−	0.365316i
$385$		0			0
$386$			5.82479i			0.296474i
$387$	6.38259	−	6.96576i	0.324445	−	0.354090i
$388$	−14.5574	+	25.2141i	−0.739040	+	1.28005i
$389$	−8.20951	−	4.73976i	−0.416239	−	0.240316i	0.277228	−	0.960804i	$-0.410584\pi$
$389$	−8.20951	−	4.73976i	−0.416239	−	0.240316i	−0.693467	+	0.720489i	$0.743918\pi$
$390$		0			0
$391$			28.2329i			1.42780i
$392$	−3.68904	+	0.0265810i	−0.186324	+	0.00134254i
$393$	3.65473	+	23.7430i	0.184357	+	1.19767i
$394$	−9.89848	−	17.1447i	−0.498678	−	0.863736i
$395$		0			0
$396$	30.9964	+	6.87083i	1.55763	+	0.345272i
$397$	6.18009	+	10.7042i	0.310170	+	0.537230i	0.978399	−	0.206726i	$-0.0662807\pi$
$397$	6.18009	+	10.7042i	0.310170	+	0.537230i	−0.668229	+	0.743956i	$0.732947\pi$
$398$		−	25.1963i		−	1.26297i
$399$	4.06123	−	0.640127i	0.203316	−	0.0320464i
$400$		0			0
$401$	7.11494	−	4.10781i	0.355303	−	0.205134i	−0.311715	−	0.950176i	$-0.600904\pi$
$401$	7.11494	−	4.10781i	0.355303	−	0.205134i	0.667019	+	0.745041i	$0.267570\pi$
$402$	6.25265	−	16.0793i	0.311854	−	0.801964i
$403$	−1.29304	−	0.746537i	−0.0644109	−	0.0371877i
$404$	−10.1945	−	17.6574i	−0.507196	−	0.878490i
$405$		0			0
$406$	−10.1288	+	5.89664i	−0.502686	+	0.292646i
$407$	53.4076			2.64732
$408$	2.37074	+	2.95379i	0.117369	+	0.146235i
$409$	17.9575	+	10.3678i	0.887942	+	0.512653i	0.873269	−	0.487239i	$-0.161996\pi$
$409$	17.9575	+	10.3678i	0.887942	+	0.512653i	0.0146731	+	0.999892i	$0.495329\pi$
$410$		0			0
$411$	5.86011	−	4.70337i	0.289058	−	0.232000i
$412$	−35.0064			−1.72464
$413$	0.667967	−	1.16664i	0.0328685	−	0.0574065i
$414$	40.1604	−	12.6638i	1.97378	−	0.622390i
$415$		0			0
$416$	−2.59208	+	4.48961i	−0.127087	+	0.220121i
$417$	−6.88198	+	17.6977i	−0.337012	+	0.866661i
$418$	−4.34199	−	7.52054i	−0.212374	−	0.367842i
$419$	−6.93924			−0.339004			−0.169502	−	0.985530i	$-0.554216\pi$
$419$	−6.93924			−0.339004			−0.169502	+	0.985530i	$0.554216\pi$
$420$		0			0
$421$	−15.2162			−0.741594			−0.370797	−	0.928714i	$-0.620915\pi$
$421$	−15.2162			−0.741594			−0.370797	+	0.928714i	$0.620915\pi$
$422$	5.81849	+	10.0779i	0.283240	+	0.490585i
$423$	19.9442	+	4.42093i	0.969719	+	0.214953i
$424$	−0.596948	+	1.03394i	−0.0289904	+	0.0502128i
$425$		0			0
$426$	−4.33660	+	0.667529i	−0.210109	+	0.0323419i
$427$	11.8532	−	6.90050i	0.573617	−	0.333939i
$428$	12.0847			0.584137
$429$	−3.24897	−	4.04802i	−0.156862	−	0.195440i
$430$		0			0
$431$	−26.9043	−	15.5332i	−1.29594	−	0.748209i	−0.316236	−	0.948681i	$-0.602419\pi$
$431$	−26.9043	−	15.5332i	−1.29594	−	0.748209i	−0.979699	+	0.200472i	$0.935752\pi$
$432$	−9.88323	+	14.7926i	−0.475507	+	0.711712i
$433$	−22.3083			−1.07207			−0.536034	−	0.844196i	$-0.680078\pi$
$433$	−22.3083			−1.07207			−0.536034	+	0.844196i	$0.680078\pi$
$434$	−0.0459658	−	12.7589i	−0.00220643	−	0.612446i
$435$		0			0
$436$	1.53245	+	2.65429i	0.0733912	+	0.127117i
$437$	−5.28682	−	3.05235i	−0.252903	−	0.146014i
$438$	48.1416	+	18.7205i	2.30029	+	0.894498i
$439$	22.4126	−	12.9399i	1.06970	−	0.617590i	0.141598	−	0.989924i	$-0.454776\pi$
$439$	22.4126	−	12.9399i	1.06970	−	0.617590i	0.928099	+	0.372334i	$0.121443\pi$
$440$		0			0
$441$	15.5850	+	14.0750i	0.742145	+	0.670240i
$442$		−	5.46677i		−	0.260028i
$443$	15.4826	+	26.8166i	0.735599	+	1.27409i	0.954460	+	0.298338i	$0.0964324\pi$
$443$	15.4826	+	26.8166i	0.735599	+	1.27409i	−0.218862	+	0.975756i	$0.570234\pi$
$444$	16.1158	−	41.4435i	0.764823	−	1.96682i
$445$		0			0
$446$	−0.404714	−	0.700985i	−0.0191638	−	0.0331926i
$447$	−14.8362	+	2.28372i	−0.701728	+	0.108016i
$448$	−26.1838	+	0.0943310i	−1.23707	+	0.00445672i
$449$			24.2032i			1.14222i	0.820874	+	0.571110i	$0.193487\pi$
$449$			24.2032i			1.14222i	−0.820874	+	0.571110i	$0.806513\pi$
$450$		0			0
$451$	16.6856	+	9.63346i	0.785696	+	0.453622i
$452$	13.4640	−	23.3204i	0.633295	−	1.09690i
$453$	−18.1820	+	14.5930i	−0.854267	+	0.685641i
$454$			48.3231i			2.26792i
$455$		0			0
$456$	−0.809428	+	0.124594i	−0.0379049	+	0.00583467i
$457$	−2.09103	+	1.20726i	−0.0978143	+	0.0564731i	−0.548109	−	0.836407i	$-0.684652\pi$
$457$	−2.09103	+	1.20726i	−0.0978143	+	0.0564731i	0.450295	+	0.892880i	$0.351319\pi$
$458$	−13.8066	−	7.97122i	−0.645138	−	0.372471i
$459$	1.40919	−	21.5140i	0.0657755	−	1.00419i
$460$		0			0
$461$	7.45376			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$461$	7.45376			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$462$	15.9267	−	41.3979i	0.740975	−	1.92601i
$463$		−	13.8862i		−	0.645345i	−0.946511	−	0.322672i	$-0.895419\pi$
$463$		−	13.8862i		−	0.645345i	0.946511	−	0.322672i	$-0.104581\pi$
$464$	−6.36721	+	3.67611i	−0.295590	+	0.170659i
$465$		0			0
$466$	4.20809	−	7.28862i	0.194936	−	0.337639i
$467$	17.4404	−	10.0692i	0.807045	−	0.465948i	−0.0388836	−	0.999244i	$-0.512380\pi$
$467$	17.4404	−	10.0692i	0.807045	−	0.465948i	0.845929	+	0.533296i	$0.179047\pi$
$468$	−4.12158	+	1.29966i	−0.190520	+	0.0600767i
$469$	−11.0864	−	6.34759i	−0.511923	−	0.293105i
$470$		0			0
$471$	10.5540	−	8.47068i	0.486300	−	0.390309i
$472$	−0.133892	+	0.231907i	−0.00616286	+	0.0106744i
$473$	−7.38828	+	12.7969i	−0.339713	+	0.588401i
$474$	−25.3046	+	20.3097i	−1.16228	+	0.932855i
$475$		0			0
$476$	21.3983	−	12.4573i	0.980789	−	0.570980i
$477$	6.48153	−	2.04382i	0.296769	−	0.0935799i
$478$	10.2953	−	5.94399i	0.470896	−	0.271872i
$479$	16.6189	−	28.7847i	0.759335	−	1.31521i	−0.183855	−	0.982953i	$-0.558858\pi$
$479$	16.6189	−	28.7847i	0.759335	−	1.31521i	0.943190	−	0.332253i	$-0.107809\pi$
$480$		0			0
$481$	−6.29586	+	3.63491i	−0.287066	+	0.165738i
$482$		−	42.1234i		−	1.91867i
$483$	−4.85486	−	30.8012i	−0.220904	−	1.40150i
$484$	−24.8460			−1.12936
$485$		0			0
$486$	−31.2350	+	7.64548i	−1.41685	+	0.346806i
$487$	27.8927	+	16.1039i	1.26394	+	0.729736i	0.973834	−	0.227259i	$-0.0729764\pi$
$487$	27.8927	+	16.1039i	1.26394	+	0.729736i	0.290105	+	0.956995i	$0.406310\pi$
$488$	−2.36603	+	1.36603i	−0.107105	+	0.0618371i
$489$	−28.5524	+	4.39504i	−1.29118	+	0.198751i
$490$		0			0
$491$			22.5003i			1.01542i	0.861527	+	0.507712i	$0.169509\pi$
$491$			22.5003i			1.01542i	−0.861527	+	0.507712i	$0.830491\pi$
$492$	12.5103	−	10.0409i	0.564009	−	0.452678i
$493$	4.45504	−	7.71635i	0.200645	−	0.347527i
$494$	1.02369	+	0.591030i	0.0460582	+	0.0265917i
$495$		0			0
$496$		−	8.00383i		−	0.359383i
$497$	0.0117049	+	3.24897i	0.000525037	+	0.145736i
$498$	9.75939	−	1.50225i	0.437329	−	0.0673176i
$499$	3.20702	+	5.55472i	0.143566	+	0.248663i	0.928837	−	0.370489i	$-0.120810\pi$
$499$	3.20702	+	5.55472i	0.143566	+	0.248663i	−0.785271	+	0.619152i	$0.787476\pi$
$500$		0			0
$501$	−0.291969	+	0.750828i	−0.0130442	+	0.0335445i
$502$	4.56458	+	7.90608i	0.203727	+	0.352866i
$503$		−	38.0103i		−	1.69479i	−0.530960	−	0.847397i	$-0.678169\pi$
$503$		−	38.0103i		−	1.69479i	0.530960	−	0.847397i	$-0.321831\pi$
$504$	−3.09433	−	2.81483i	−0.137832	−	0.125383i
$505$		0			0
$506$	−57.0374	+	32.9306i	−2.53562	+	1.46394i
$507$	−20.3273	−	7.90453i	−0.902768	−	0.351053i
$508$	32.9116	+	19.0015i	1.46022	+	0.843056i
$509$	6.34981	+	10.9982i	0.281450	+	0.487486i	0.971742	−	0.236045i	$-0.0758512\pi$
$509$	6.34981	+	10.9982i	0.281450	+	0.487486i	−0.690292	+	0.723531i	$0.742518\pi$
$510$		0			0
$511$	19.0047	−	33.1927i	0.840719	−	1.46836i
$512$	−31.3992			−1.38766
$513$	3.87630	+	2.58982i	0.171143	+	0.114344i
$514$	−45.5698	−	26.3097i	−2.01000	−	1.16047i
$515$		0			0
$516$	7.70075	+	9.59466i	0.339007	+	0.422382i
$517$	−31.9506			−1.40518
$518$	−53.9124	−	30.8679i	−2.36878	−	1.35626i
$519$	19.1460	−	2.94713i	0.840417	−	0.129365i
$520$		0			0
$521$	18.0970	−	31.3449i	0.792843	−	1.37324i	−0.131357	−	0.991335i	$-0.541933\pi$
$521$	18.0970	−	31.3449i	0.792843	−	1.37324i	0.924200	−	0.381909i	$-0.124733\pi$
$522$	−12.9746	−	2.87601i	−0.567881	−	0.125880i
$523$	2.46749	+	4.27382i	0.107896	+	0.186881i	0.914918	−	0.403640i	$-0.132255\pi$
$523$	2.46749	+	4.27382i	0.107896	+	0.186881i	−0.807022	+	0.590522i	$0.798922\pi$
$524$	−31.2823			−1.36657
$525$		0			0
$526$	0.738470			0.0321988
$527$	4.84988	+	8.40023i	0.211264	+	0.365920i
$528$	10.0844	−	25.9332i	0.438869	−	1.12860i
$529$	−11.6496	+	20.1778i	−0.506506	+	0.877295i
$530$		0			0
$531$	1.45376	−	0.458415i	0.0630880	−	0.0198935i
$532$	0.0192878	+	5.35379i	0.000836234	+	0.232116i
$533$	−2.62261			−0.113598
$534$	−38.4576	+	30.8663i	−1.66422	+	1.33572i
$535$		0			0
$536$	2.20378	+	1.27235i	0.0951888	+	0.0549573i
$537$	0.268533	+	0.334575i	0.0115880	+	0.0144380i
$538$	−17.6131			−0.759354
$539$	−28.5620	−	16.2170i	−1.23025	−	0.698515i
$540$		0			0
$541$	−8.32849	−	14.4254i	−0.358070	−	0.620195i	0.629569	−	0.776945i	$-0.283232\pi$
$541$	−8.32849	−	14.4254i	−0.358070	−	0.620195i	−0.987638	+	0.156750i	$0.949898\pi$
$542$	−15.0688	−	8.69998i	−0.647261	−	0.373696i
$543$	9.00086	−	23.1466i	0.386264	−	0.993317i
$544$	29.1668	−	16.8394i	1.25051	−	0.721985i
$545$		0			0
$546$	0.940053	+	5.96408i	0.0402306	+	0.255239i
$547$			21.2868i			0.910159i	0.890451	+	0.455079i	$0.150389\pi$
$547$			21.2868i			0.910159i	−0.890451	+	0.455079i	$0.849611\pi$
$548$	4.89247	+	8.47401i	0.208996	+	0.361992i
$549$	15.1834	+	3.36563i	0.648011	+	0.143642i
$550$		0			0
$551$	0.963296	+	1.66848i	0.0410378	+	0.0710795i
$552$	0.944951	+	6.13887i	0.0402198	+	0.261288i
$553$	12.0881	+	20.7641i	0.514037	+	0.882977i
$554$		−	20.8472i		−	0.885713i
$555$		0			0
$556$	−21.4143	−	12.3636i	−0.908169	−	0.524331i
$557$	9.58040	−	16.5937i	0.405935	−	0.703099i	−0.588495	−	0.808501i	$-0.700279\pi$
$557$	9.58040	−	16.5937i	0.405935	−	0.703099i	0.994430	+	0.105401i	$0.0336127\pi$
$558$	9.77368	−	10.6667i	0.413753	−	0.451557i
$559$		−	2.01138i		−	0.0850723i
$560$		0			0
$561$	5.13017	+	33.3282i	0.216596	+	1.40712i
$562$	−27.0752	+	15.6319i	−1.14210	+	0.659390i
$563$	23.5981	+	13.6243i	0.994540	+	0.574198i	0.906628	−	0.421930i	$-0.138647\pi$
$563$	23.5981	+	13.6243i	0.994540	+	0.574198i	0.0879116	+	0.996128i	$0.471981\pi$
$564$	−9.64113	+	24.7931i	−0.405965	+	1.04398i
$565$		0			0
$566$	49.3843			2.07578
$567$	2.16210	+	23.7134i	0.0907998	+	0.995869i
$568$		−	0.647181i		−	0.0271551i
$569$	−22.7124	+	13.1130i	−0.952153	+	0.549726i	−0.893749	−	0.448567i	$-0.851934\pi$
$569$	−22.7124	+	13.1130i	−0.952153	+	0.549726i	−0.0584038	+	0.998293i	$0.518601\pi$
$570$		0			0
$571$	13.4388	−	23.2767i	0.562397	−	0.974101i	−0.434889	−	0.900484i	$-0.643212\pi$
$571$	13.4388	−	23.2767i	0.562397	−	0.974101i	0.997287	−	0.0736170i	$-0.0234542\pi$
$572$	5.85363	−	3.37960i	0.244753	−	0.141308i
$573$	29.1708	−	4.49023i	1.21863	−	0.187582i
$574$	−11.2755	−	19.3683i	−0.470631	−	0.808416i
$575$		0			0
$576$	−21.8902	−	20.0575i	−0.912091	−	0.835731i
$577$	5.15614	−	8.93069i	0.214653	−	0.371790i	−0.738512	−	0.674240i	$-0.764471\pi$
$577$	5.15614	−	8.93069i	0.214653	−	0.371790i	0.953165	+	0.302450i	$0.0978047\pi$
$578$	−0.222964	+	0.386185i	−0.00927407	+	0.0160632i
$579$	3.06123	+	3.81410i	0.127220	+	0.158509i
$580$		0			0
$581$	−0.0263416	−	7.31171i	−0.00109283	−	0.303341i
$582$	7.01690	+	45.5853i	0.290860	+	1.88957i
$583$	−9.20532	+	5.31469i	−0.381245	+	0.220112i
$584$	−3.80943	+	6.59812i	−0.157635	+	0.273032i
$585$		0			0
$586$	−37.9138	+	21.8895i	−1.56620	+	0.904248i
$587$			22.1492i			0.914197i	0.889416	+	0.457098i	$0.151111\pi$
$587$			22.1492i			0.914197i	−0.889416	+	0.457098i	$0.848889\pi$
$588$	−21.2028	+	17.2701i	−0.874387	+	0.712209i
$589$	−2.09734			−0.0864195
$590$		0			0
$591$	−15.4920	−	6.02425i	−0.637255	−	0.247805i
$592$	−33.7498	−	19.4855i	−1.38711	−	0.800848i
$593$	2.52638	−	1.45861i	0.103746	−	0.0598978i	−0.447229	−	0.894419i	$-0.647589\pi$
$593$	2.52638	−	1.45861i	0.103746	−	0.0598978i	0.550975	+	0.834522i	$0.314256\pi$
$594$	45.1072	−	22.2467i	1.85077	−	0.912795i
$595$		0			0
$596$		−	19.5472i		−	0.800686i
$597$	−13.2419	−	16.4986i	−0.541956	−	0.675244i
$598$	4.48250	−	7.76391i	0.183303	−	0.317490i
$599$	31.4551	+	18.1606i	1.28522	+	0.742023i	0.977798	−	0.209550i	$-0.0671998\pi$
$599$	31.4551	+	18.1606i	1.28522	+	0.742023i	0.307424	+	0.951573i	$0.400533\pi$
$600$		0			0
$601$			7.15198i			0.291735i	0.989304	+	0.145868i	$0.0465974\pi$
$601$			7.15198i			0.291735i	−0.989304	+	0.145868i	$0.953403\pi$
$602$	14.8543	−	8.64763i	0.605416	−	0.352451i
$603$	−4.35625	−	13.8149i	−0.177400	−	0.562587i
$604$	−15.1798	−	26.2921i	−0.617656	−	1.06981i
$605$		0			0
$606$	−30.1034	−	11.7061i	−1.22287	−	0.475527i
$607$	−21.8382	−	37.8248i	−0.886384	−	1.53526i	−0.844119	−	0.536156i	$-0.819876\pi$
$607$	−21.8382	−	37.8248i	−0.886384	−	1.53526i	−0.0422651	−	0.999106i	$-0.513457\pi$
$608$			7.28226i			0.295334i
$609$	−3.53342	+	9.18438i	−0.143182	+	0.372170i
$610$		0			0
$611$	3.76643	−	2.17455i	0.152373	−	0.0879729i
$612$	27.4102	+	6.07589i	1.10799	+	0.245603i
$613$	−12.6080	−	7.27926i	−0.509234	−	0.294007i	0.223285	−	0.974753i	$-0.428322\pi$
$613$	−12.6080	−	7.27926i	−0.509234	−	0.294007i	−0.732519	+	0.680747i	$0.761655\pi$
$614$	−25.0452	−	43.3795i	−1.01074	−	1.75065i
$615$		0			0
$616$	5.67771	+	3.25081i	0.228761	+	0.130979i
$617$	4.68442			0.188588			0.0942938	−	0.995544i	$-0.469941\pi$
$617$	4.68442			0.188588			0.0942938	+	0.995544i	$0.469941\pi$
$618$	−43.2483	+	34.7114i	−1.73970	+	1.39630i
$619$	33.0429	+	19.0773i	1.32810	+	0.766782i	0.985006	−	0.172518i	$-0.0551902\pi$
$619$	33.0429	+	19.0773i	1.32810	+	0.766782i	0.343098	+	0.939299i	$0.388524\pi$
$620$		0			0
$621$	19.6418	−	29.3987i	0.788197	−	1.17973i
$622$	14.6819			0.588689
$623$	18.3713	+	31.5569i	0.736030	+	1.26430i
$624$	0.576223	+	3.74343i	0.0230674	+	0.149857i
$625$		0			0
$626$	3.65877	−	6.33717i	0.146234	−	0.253284i
$627$	−6.79559	−	2.64255i	−0.271390	−	0.105533i
$628$	8.81125	+	15.2615i	0.351607	+	0.609001i
$629$	47.2285			1.88312
$630$		0			0
$631$	23.9959			0.955264			0.477632	−	0.878560i	$-0.341495\pi$
$631$	23.9959			0.955264			0.477632	+	0.878560i	$0.341495\pi$
$632$	−2.39296	−	4.14473i	−0.0951869	−	0.164869i
$633$	9.10644	+	3.54115i	0.361948	+	0.140748i
$634$	21.7391	−	37.6532i	0.863369	−	1.49540i
$635$		0			0
$636$	1.34640	+	8.74690i	0.0533883	+	0.346837i
$637$	4.47070	−	0.0322132i	0.177136	−	0.00127633i
$638$	20.7852			0.822895
$639$	−2.48881	+	2.71621i	−0.0984557	+	0.107452i
$640$		0			0
$641$	20.0037	+	11.5491i	0.790099	+	0.456164i	0.839997	−	0.542590i	$-0.182556\pi$
$641$	20.0037	+	11.5491i	0.790099	+	0.456164i	−0.0498985	+	0.998754i	$0.515890\pi$
$642$	14.9299	−	11.9829i	0.589238	−	0.472927i
$643$	−22.7592			−0.897536			−0.448768	−	0.893648i	$-0.648137\pi$
$643$	−22.7592			−0.897536			−0.448768	+	0.893648i	$0.648137\pi$
$644$	40.6043	−	0.146283i	1.60003	−	0.00576436i
$645$		0			0
$646$	−3.83963	−	6.65043i	−0.151068	−	0.261658i
$647$	2.10183	+	1.21349i	0.0826315	+	0.0477073i	0.540746	−	0.841186i	$-0.318142\pi$
$647$	2.10183	+	1.21349i	0.0826315	+	0.0477073i	−0.458115	+	0.888893i	$0.651475\pi$
$648$	−0.413659	−	4.72510i	−0.0162500	−	0.185619i
$649$	−2.06469	+	1.19205i	−0.0810463	+	0.0467921i
$650$		0			0
$651$	−6.73555	−	8.33043i	−0.263987	−	0.326495i
$652$		−	37.6189i		−	1.47327i
$653$	20.0779	+	34.7760i	0.785709	+	1.36089i	0.928574	+	0.371146i	$0.121035\pi$
$653$	20.0779	+	34.7760i	0.785709	+	1.36089i	−0.142865	+	0.989742i	$0.545632\pi$
$654$	4.52517	+	1.75967i	0.176948	+	0.0688086i
$655$		0			0
$656$	−7.02943	−	12.1753i	−0.274453	−	0.475366i
$657$	41.3619	−	13.0426i	1.61368	−	0.508842i
$658$	32.2525	+	18.4664i	1.25734	+	0.719896i
$659$			0.627454i			0.0244421i	0.999925	+	0.0122211i	$0.00389018\pi$
$659$			0.627454i			0.0244421i	−0.999925	+	0.0122211i	$0.996110\pi$
$660$		0			0
$661$	−28.5745	−	16.4975i	−1.11142	−	0.641678i	−0.172222	−	0.985058i	$-0.555095\pi$
$661$	−28.5745	−	16.4975i	−1.11142	−	0.641678i	−0.939197	+	0.343380i	$0.888428\pi$
$662$	−15.2738	+	26.4550i	−0.593634	+	1.02820i
$663$	−2.87307	−	3.57967i	−0.111581	−	0.139023i
$664$			1.45646i			0.0565217i
$665$		0			0
$666$	−21.1842	−	67.1810i	−0.820869	−	2.60321i
$667$	12.6541	−	7.30584i	0.489968	−	0.282883i
$668$	−0.908504	−	0.524525i	−0.0351511	−	0.0202945i
$669$	−0.633413	−	0.246310i	−0.0244891	−	0.00952291i
$670$		0			0
$671$	−24.3238			−0.939009
$672$	−28.9244	+	23.3868i	−1.11578	+	0.902164i
$673$		−	1.14437i		−	0.0441121i	−0.999757	−	0.0220560i	$-0.992979\pi$
$673$		−	1.14437i		−	0.0441121i	0.999757	−	0.0220560i	$-0.00702123\pi$
$674$	−36.6345	+	21.1509i	−1.41111	+	0.814703i
$675$		0			0
$676$	14.2006	−	24.5961i	0.546176	−	0.946004i
$677$	−13.8375	+	7.98910i	−0.531820	+	0.307046i	−0.741757	−	0.670669i	$-0.766007\pi$
$677$	−13.8375	+	7.98910i	−0.531820	+	0.307046i	0.209938	+	0.977715i	$0.432674\pi$
$678$	−6.48988	−	42.1615i	−0.249242	−	1.61920i
$679$	34.1524	−	0.123039i	1.31065	−	0.00472181i
$680$		0			0
$681$	25.3963	+	31.6422i	0.973188	+	1.21253i
$682$	−11.3137	+	19.5959i	−0.433224	+	0.750366i
$683$	−1.13231	+	1.96122i	−0.0433268	+	0.0750442i	−0.886876	−	0.462008i	$-0.847129\pi$
$683$	−1.13231	+	1.96122i	−0.0433268	+	0.0750442i	0.843549	+	0.537053i	$0.180462\pi$
$684$	−4.10116	+	4.47588i	−0.156812	+	0.171140i
$685$		0			0
$686$	19.4590	+	32.8782i	0.742949	+	1.25530i
$687$	−13.2299	+	2.03646i	−0.504752	+	0.0776960i
$688$	9.33773	−	5.39114i	0.355998	−	0.205535i
$689$	0.723434	−	1.25303i	0.0275607	−	0.0477365i
$690$		0			0
$691$	−2.40044	+	1.38589i	−0.0913169	+	0.0527218i	−0.544963	−	0.838460i	$-0.683456\pi$
$691$	−2.40044	+	1.38589i	−0.0913169	+	0.0527218i	0.453646	+	0.891182i	$0.350123\pi$
$692$			25.2256i			0.958934i
$693$	−11.3279	−	35.4778i	−0.430311	−	1.34769i
$694$	−32.6582			−1.23969
$695$		0			0
$696$	0.710424	−	1.82693i	0.0269286	−	0.0692496i
$697$	14.7551	+	8.51888i	0.558891	+	0.322676i
$698$	−16.0075	+	9.24191i	−0.605891	+	0.349811i
$699$	−1.07507	−	6.98419i	−0.0406629	−	0.264166i
$700$		0			0
$701$			23.1184i			0.873169i	0.899663	+	0.436585i	$0.143812\pi$
$701$			23.1184i			0.873169i	−0.899663	+	0.436585i	$0.856188\pi$
$702$	−3.80326	+	5.69250i	−0.143545	+	0.214850i
$703$	−5.10602	+	8.84388i	−0.192577	+	0.333553i
$704$	40.2147	+	23.2180i	1.51565	+	0.875060i
$705$		0			0
$706$		−	27.7612i		−	1.04481i
$707$	−11.8838	+	20.7557i	−0.446937	+	0.780599i
$708$	0.301989	+	1.96187i	0.0113495	+	0.0737317i
$709$	−18.0134	−	31.2002i	−0.676508	−	1.17175i	−0.976026	−	0.217656i	$-0.930159\pi$
$709$	−18.0134	−	31.2002i	−0.676508	−	1.17175i	0.299517	−	0.954091i	$-0.403174\pi$
$710$		0			0
$711$	−5.89580	+	26.5978i	−0.221110	+	0.997494i
$712$	−3.63678	−	6.29910i	−0.136294	−	0.236069i
$713$			15.9067i			0.595710i
$714$	14.0840	−	36.6083i	0.527079	−	1.37003i
$715$		0			0
$716$	−0.483812	+	0.279329i	−0.0180809	+	0.0104390i
$717$	3.61754	−	9.30287i	0.135099	−	0.347422i
$718$	10.0220	+	5.78619i	0.374017	+	0.215939i
$719$	−8.57099	−	14.8454i	−0.319644	−	0.553640i	0.660770	−	0.750589i	$-0.270230\pi$
$719$	−8.57099	−	14.8454i	−0.319644	−	0.553640i	−0.980414	+	0.196949i	$0.936897\pi$
$720$		0			0
$721$	20.6598	+	35.4880i	0.769412	+	1.32164i
$722$	−37.5343			−1.39688
$723$	−22.1380	−	27.5826i	−0.823322	−	1.02581i
$724$	28.0075	+	16.1701i	1.04089	+	0.600958i
$725$		0			0
$726$	−30.6958	+	24.6367i	−1.13923	+	0.914352i
$727$	16.6832			0.618747			0.309374	−	0.950941i	$-0.399881\pi$
$727$	16.6832			0.618747			0.309374	+	0.950941i	$0.399881\pi$
$728$	−0.890556	+	0.00320836i	−0.0330062	+	0.000118910i
$729$	−16.4348	+	21.4219i	−0.608695	+	0.793404i
$730$		0			0
$731$	−6.53347	+	11.3163i	−0.241649	+	0.418548i
$732$	−7.33973	+	18.8749i	−0.271284	+	0.697635i
$733$	−19.0418	−	32.9814i	−0.703326	−	1.21820i	−0.967292	−	0.253664i	$-0.918364\pi$
$733$	−19.0418	−	32.9814i	−0.703326	−	1.21820i	0.263967	−	0.964532i	$-0.414969\pi$
$734$	4.07690			0.150481
$735$		0			0
$736$	55.2302			2.03581
$737$	11.3279	+	19.6205i	0.417268	+	0.722730i
$738$	5.49948	−	24.8098i	0.202439	−	0.913263i
$739$	−11.2186	+	19.4312i	−0.412684	+	0.714790i	−0.995182	−	0.0980422i	$-0.968742\pi$
$739$	−11.2186	+	19.4312i	−0.412684	+	0.714790i	0.582498	+	0.812832i	$0.302075\pi$
$740$		0			0
$741$	0.980937	−	0.150995i	0.0360356	−	0.00554693i
$742$	12.3640	−	0.0445433i	0.453898	−	0.00163524i
$743$	−6.39189			−0.234496			−0.117248	−	0.993103i	$-0.537407\pi$
$743$	−6.39189			−0.234496			−0.117248	+	0.993103i	$0.537407\pi$
$744$	1.33570	+	1.66420i	0.0489690	+	0.0610124i
$745$		0			0
$746$	41.2565	+	23.8195i	1.51051	+	0.872093i
$747$	5.60098	−	6.11275i	0.204929	−	0.223654i
$748$	−43.9111			−1.60555
$749$	−7.13207	−	12.2510i	−0.260600	−	0.447641i
$750$		0			0
$751$	5.49944	+	9.52531i	0.200677	+	0.347583i	0.948747	−	0.316037i	$-0.102352\pi$
$751$	5.49944	+	9.52531i	0.200677	+	0.347583i	−0.748069	+	0.663620i	$0.769019\pi$
$752$	20.1905	+	11.6570i	0.736271	+	0.425086i
$753$	7.14396	+	2.77802i	0.260340	+	0.101237i
$754$	−2.45023	+	1.41464i	−0.0892320	+	0.0515181i
$755$		0			0
$756$	−30.9485	−	1.91522i	−1.12559	−	0.0696558i
$757$		−	27.8216i		−	1.01119i	−0.862770	−	0.505597i	$-0.831272\pi$
$757$		−	27.8216i		−	1.01119i	0.862770	−	0.505597i	$-0.168728\pi$
$758$	17.6011	+	30.4859i	0.639299	+	1.10730i
$759$	−20.0417	+	51.5392i	−0.727466	+	1.87075i
$760$		0			0
$761$	−6.54766	−	11.3409i	−0.237352	−	0.411106i	0.722601	−	0.691265i	$-0.242946\pi$
$761$	−6.54766	−	11.3409i	−0.237352	−	0.411106i	−0.959954	+	0.280159i	$0.909613\pi$
$762$	59.5017	−	9.15904i	2.15552	−	0.331797i
$763$	1.78639	−	3.12002i	0.0646717	−	0.112952i
$764$			38.4336i			1.39048i
$765$		0			0
$766$	47.5412	+	27.4479i	1.71773	+	0.991734i
$767$	0.162262	−	0.281045i	0.00585893	−	0.0101480i
$768$	−15.0839	+	12.1064i	−0.544293	+	0.436853i
$769$			7.74247i			0.279201i	0.990208	+	0.139600i	$0.0445818\pi$
$769$			7.74247i			0.279201i	−0.990208	+	0.139600i	$0.955418\pi$
$770$		0			0
$771$	−43.6664	+	6.72153i	−1.57261	+	0.242070i
$772$	−5.51538	+	3.18431i	−0.198503	+	0.114606i
$773$	−33.2091	−	19.1733i	−1.19445	−	0.689614i	−0.235135	−	0.971963i	$-0.575553\pi$
$773$	−33.2091	−	19.1733i	−1.19445	−	0.689614i	−0.959312	+	0.282349i	$0.908887\pi$
$774$	19.0276	+	4.21777i	0.683934	+	0.151605i
$775$		0			0
$776$	−6.80301			−0.244214
$777$	−51.5248	+	8.12129i	−1.84844	+	0.291350i
$778$		−	19.5551i		−	0.701086i
$779$	−3.19045	+	1.84201i	−0.114310	+	0.0659967i
$780$		0			0
$781$	2.88096	−	4.98997i	0.103089	−	0.178555i
$782$	−50.4383	+	29.1205i	−1.80367	+	1.04135i
$783$	−10.0073	+	4.93557i	−0.357632	+	0.176383i
$784$	12.1325	+	20.6687i	0.433302	+	0.738167i
$785$		0			0
$786$	−38.6474	+	31.0187i	−1.37851	+	1.10640i
$787$	12.4811	−	21.6178i	0.444901	−	0.770592i	−0.553144	−	0.833086i	$-0.686572\pi$
$787$	12.4811	−	21.6178i	0.444901	−	0.770592i	0.998045	+	0.0624938i	$0.0199054\pi$
$788$	10.8226	−	18.7453i	0.385540	−	0.667775i
$789$	0.483554	−	0.388104i	0.0172150	−	0.0138169i
$790$		0			0
$791$	−31.5873	+	0.113798i	−1.12312	+	0.00404619i
$792$	2.23098	+	7.07507i	0.0792744	+	0.251402i
$793$	2.86736	−	1.65547i	0.101823	−	0.0587875i
$794$	−12.7488	+	22.0816i	−0.452438	+	0.783645i
$795$		0			0
$796$	23.8578	−	13.7743i	0.845619	−	0.488218i
$797$			5.81191i			0.205868i	0.994688	+	0.102934i	$0.0328231\pi$
$797$			5.81191i			0.205868i	−0.994688	+	0.102934i	$0.967177\pi$
$798$	5.33251	+	6.59516i	0.188769	+	0.233466i
$799$	−28.2539			−0.999552
$800$		0			0
$801$	−8.96035	+	40.4229i	−0.316598	+	1.42827i
$802$	14.6773	+	8.47393i	0.518273	+	0.299225i
$803$	−58.7438	+	33.9158i	−2.07302	+	1.19686i
$804$	18.6434	−	2.86976i	0.657502	−	0.101209i
$805$		0			0
$806$		−	3.08003i		−	0.108490i
$807$	−11.5331	+	9.25658i	−0.405985	+	0.325847i
$808$	2.38207	−	4.12586i	0.0838009	−	0.145147i
$809$	−1.51563	−	0.875048i	−0.0532866	−	0.0307650i	0.473120	−	0.880998i	$-0.343128\pi$
$809$	−1.51563	−	0.875048i	−0.0532866	−	0.0307650i	−0.526407	+	0.850233i	$0.676461\pi$
$810$		0			0
$811$			28.4479i			0.998940i	0.866331	+	0.499470i	$0.166472\pi$
$811$			28.4479i			0.998940i	−0.866331	+	0.499470i	$0.833528\pi$
$812$	−11.1207	−	6.36721i	−0.390259	−	0.223445i
$813$	−14.4394	+	2.22265i	−0.506412	+	0.0779516i
$814$	55.0868	+	95.4131i	1.93079	+	3.34423i
$815$		0			0
$816$	8.91769	−	22.9328i	0.312182	−	0.802807i
$817$	−1.41271	−	2.44688i	−0.0494244	−	0.0856055i
$818$			42.7750i			1.49559i
$819$	3.74998	+	3.41126i	0.131035	+	0.119199i
$820$		0			0
$821$	25.9378	−	14.9752i	0.905236	−	0.522638i	0.0263407	−	0.999653i	$-0.491615\pi$
$821$	25.9378	−	14.9752i	0.905236	−	0.522638i	0.878895	+	0.477015i	$0.158281\pi$
$822$	14.4470	+	5.61789i	0.503896	+	0.195946i
$823$	13.9652	+	8.06283i	0.486798	+	0.281053i	0.723245	−	0.690592i	$-0.242650\pi$
$823$	13.9652	+	8.06283i	0.486798	+	0.281053i	−0.236447	+	0.971644i	$0.575983\pi$
$824$	−4.08982	−	7.08378i	−0.142476	−	0.246775i
$825$		0			0
$826$	2.77318	−	0.00999078i	0.0964911	−	0.000347624i
$827$	15.9844			0.555831			0.277916	−	0.960605i	$-0.410356\pi$
$827$	15.9844			0.555831			0.277916	+	0.960605i	$0.410356\pi$
$828$	33.9460	+	31.1041i	1.17971	+	1.08094i
$829$	−18.0763	−	10.4363i	−0.627815	−	0.362469i	0.152091	−	0.988367i	$-0.451399\pi$
$829$	−18.0763	−	10.4363i	−0.627815	−	0.362469i	−0.779905	+	0.625898i	$0.784733\pi$
$830$		0			0
$831$	−10.9563	−	13.6509i	−0.380069	−	0.473543i
$832$	−6.32084			−0.219136
$833$	−25.2574	−	14.3407i	−0.875117	−	0.496876i
$834$	−38.7155	+	5.95943i	−1.34061	+	0.206358i
$835$		0			0
$836$	4.74737	−	8.22268i	0.164191	−	0.284387i
$837$	0.793953	−	12.1212i	0.0274430	−	0.418969i
$838$	−7.15741	−	12.3970i	−0.247249	−	0.428247i
$839$	14.2504			0.491977			0.245989	−	0.969273i	$-0.420887\pi$
$839$	14.2504			0.491977			0.245989	+	0.969273i	$0.420887\pi$
$840$		0			0
$841$	24.3887			0.840989
$842$	−15.6946	−	27.1839i	−0.540873	−	0.936819i
$843$	−9.51361	+	24.4652i	−0.327666	+	0.842627i
$844$	−6.36172	+	11.0188i	−0.218979	+	0.379283i
$845$		0			0
$846$	12.6732	+	40.1903i	0.435714	+	1.38177i
$847$	14.6634	+	25.1878i	0.503842	+	0.865464i
$848$	7.75614			0.266347
$849$	32.3371	−	25.9540i	1.10981	−	0.890738i
$850$		0			0
$851$	67.0739	+	38.7251i	2.29926	+	1.32748i
$852$	−3.00281	−	3.74131i	−0.102875	−	0.128175i
$853$	49.6034			1.69839			0.849194	−	0.528081i	$-0.177088\pi$
$853$	49.6034			1.69839			0.849194	+	0.528081i	$0.177088\pi$
$854$	24.5537	+	14.0584i	0.840209	+	0.481067i
$855$		0			0
$856$	1.41187	+	2.44543i	0.0482567	+	0.0835830i
$857$	4.54233	+	2.62252i	0.155163	+	0.0895834i	0.575571	−	0.817752i	$-0.304780\pi$
$857$	4.54233	+	2.62252i	0.155163	+	0.0895834i	−0.420408	+	0.907335i	$0.638113\pi$
$858$	3.88069	−	9.97960i	0.132485	−	0.340698i
$859$	10.1722	−	5.87292i	0.347071	−	0.200382i	−0.316323	−	0.948651i	$-0.602448\pi$
$859$	10.1722	−	5.87292i	0.347071	−	0.200382i	0.663394	+	0.748270i	$0.269115\pi$
$860$		0			0
$861$	−17.5623	−	6.75658i	−0.598521	−	0.230264i
$862$		−	64.0863i		−	2.18279i
$863$	−17.5454	−	30.3896i	−0.597254	−	1.03447i	−0.993225	−	0.116211i	$-0.962925\pi$
$863$	−17.5454	−	30.3896i	−0.597254	−	1.03447i	0.395971	−	0.918263i	$-0.370408\pi$
$864$	−42.0864	−	2.75671i	−1.43181	−	0.0937853i
$865$		0			0
$866$	−23.0097	−	39.8539i	−0.781901	−	1.35429i
$867$	0.0569621	+	0.370054i	0.00193454	+	0.0125677i
$868$	12.0560	−	7.01857i	0.409208	−	0.238226i
$869$		−	42.6096i		−	1.44543i
$870$		0			0
$871$	−2.67074	−	1.54195i	−0.0904944	−	0.0522470i
$872$	−0.358076	+	0.620205i	−0.0121260	+	0.0210028i
$873$	28.5521	+	26.1617i	0.966343	+	0.885440i
$874$		−	12.5933i		−	0.425973i
$875$		0			0
$876$	8.59208	+	55.8184i	0.290299	+	1.88593i
$877$	−14.5953	+	8.42662i	−0.492850	+	0.284547i	−0.725756	−	0.687952i	$-0.758510\pi$
$877$	−14.5953	+	8.42662i	−0.492850	+	0.284547i	0.232906	+	0.972499i	$0.425176\pi$
$878$	46.2346	+	26.6936i	1.56034	+	0.900864i
$879$	−13.3220	+	34.2590i	−0.449341	+	1.15553i
$880$		0			0
$881$	−51.9437			−1.75003			−0.875015	−	0.484096i	$-0.839148\pi$
$881$	−51.9437			−1.75003			−0.875015	+	0.484096i	$0.839148\pi$
$882$	−9.07011	+	42.3603i	−0.305406	+	1.42635i
$883$		−	14.9096i		−	0.501748i	−0.968020	−	0.250874i	$-0.919282\pi$
$883$		−	14.9096i		−	0.501748i	0.968020	−	0.250874i	$-0.0807181\pi$
$884$	5.17638	−	2.98858i	0.174100	−	0.100517i
$885$		0			0
$886$	−31.9387	+	55.3194i	−1.07300	+	1.85849i
$887$	11.4216	−	6.59427i	0.383500	−	0.221414i	−0.295840	−	0.955238i	$-0.595599\pi$
$887$	11.4216	−	6.59427i	0.383500	−	0.221414i	0.679340	+	0.733824i	$0.262266\pi$
$888$	10.2692	−	1.58073i	0.344612	−	0.0530458i
$889$	−0.160601	−	44.5785i	−0.00538638	−	1.49512i
$890$		0			0
$891$	17.8446	−	38.2734i	0.597816	−	1.28221i
$892$	0.442499	−	0.766431i	0.0148160	−	0.0256620i
$893$	3.05462	−	5.29076i	0.102219	−	0.177048i
$894$	−19.3825	−	24.1494i	−0.648249	−	0.807678i
$895$		0			0
$896$	−5.56642	−	9.56161i	−0.185961	−	0.319431i
$897$	−1.14518	−	7.43963i	−0.0382363	−	0.248402i
$898$	−43.2392	+	24.9642i	−1.44291	+	0.833065i
$899$	2.51001	−	4.34747i	0.0837135	−	0.144996i
$900$		0			0
$901$	−8.14028	+	4.69979i	−0.271192	+	0.156573i
$902$			39.7453i			1.32338i
$903$	5.18189	−	13.4692i	0.172442	−	0.448227i
$904$	6.29206			0.209271
$905$		0			0
$906$	−44.8243	−	17.4305i	−1.48919	−	0.579089i
$907$	−40.6527	−	23.4709i	−1.34985	−	0.779337i	−0.361623	−	0.932324i	$-0.617777\pi$
$907$	−40.6527	−	23.4709i	−1.34985	−	0.779337i	−0.988228	+	0.152987i	$0.951111\pi$
$908$	−45.7562	+	26.4174i	−1.51847	+	0.876691i
$909$	−25.8640	+	8.15567i	−0.857854	+	0.270507i
$910$		0			0
$911$		−	45.2977i		−	1.50078i	−0.660996	−	0.750389i	$-0.729866\pi$
$911$		−	45.2977i		−	1.50078i	0.660996	−	0.750389i	$-0.270134\pi$
$912$	3.33021	+	4.14924i	0.110274	+	0.137395i
$913$	−6.48352	+	11.2298i	−0.214573	+	0.371652i
$914$	−4.31355	−	2.49043i	−0.142680	−	0.0823761i
$915$		0			0
$916$		−	17.4309i		−	0.575932i
$917$	18.4619	+	31.7126i	0.609667	+	1.04724i
$918$	39.8884	−	19.6728i	1.31651	−	0.649300i
$919$	21.5911	+	37.3969i	0.712225	+	1.23361i	0.964020	+	0.265830i	$0.0856460\pi$
$919$	21.5911	+	37.3969i	0.712225	+	1.23361i	−0.251795	+	0.967781i	$0.581021\pi$
$920$		0			0
$921$	−39.1978	−	15.2426i	−1.29161	−	0.502260i
$922$	7.68811	+	13.3162i	0.253195	+	0.438546i
$923$			0.784311i			0.0258159i
$924$	47.9057	−	7.55085i	1.57598	−	0.248405i
$925$		0			0
$926$	24.8077	−	14.3227i	0.815232	−	0.470675i
$927$	−10.0765	+	45.4584i	−0.330957	+	1.49305i
$928$	−15.0950	−	8.71510i	−0.495517	−	0.286087i
$929$	4.50570	+	7.80410i	0.147827	+	0.256044i	0.930424	−	0.366484i	$-0.119439\pi$
$929$	4.50570	+	7.80410i	0.147827	+	0.256044i	−0.782597	+	0.622529i	$0.786105\pi$
$930$		0			0
$931$	5.41606	−	3.17922i	0.177504	−	0.104195i
$932$	9.20194			0.301419
$933$	9.61375	−	7.71607i	0.314740	−	0.252613i
$934$	35.9774	+	20.7716i	1.17722	+	0.679667i
$935$		0			0
$936$	−0.744523	−	0.682191i	−0.0243355	−	0.0222981i
$937$	−21.9677			−0.717654			−0.358827	−	0.933404i	$-0.616823\pi$
$937$	−21.9677			−0.717654			−0.358827	+	0.933404i	$0.616823\pi$
$938$	−0.0949410	−	26.3531i	−0.00309993	−	0.860459i
$939$	−0.934731	−	6.07248i	−0.0305038	−	0.198168i
$940$		0			0
$941$	0.823861	−	1.42697i	0.0268571	−	0.0465178i	−0.852284	−	0.523079i	$-0.824783\pi$
$941$	0.823861	−	1.42697i	0.0268571	−	0.0465178i	0.879142	+	0.476561i	$0.158117\pi$
$942$	26.0187	+	10.1177i	0.847735	+	0.329653i
$943$	13.9702	+	24.1970i	0.454931	+	0.787964i
$944$	1.73965			0.0566209
$945$		0			0
$946$	−30.4823			−0.991064
$947$	−13.6627	−	23.6645i	−0.443979	−	0.768994i	0.554002	−	0.832516i	$-0.313100\pi$
$947$	−13.6627	−	23.6645i	−0.443979	−	0.768994i	−0.997980	+	0.0635217i	$0.979767\pi$
$948$	−33.0644	−	12.8575i	−1.07388	−	0.417592i
$949$	4.61660	−	7.99619i	0.149861	−	0.259567i
$950$		0			0
$951$	−5.55384	−	36.0805i	−0.180095	−	1.16999i
$952$	5.02081	+	2.87470i	0.162725	+	0.0931695i
$953$	55.2380			1.78933			0.894667	−	0.446734i	$-0.147413\pi$
$953$	55.2380			1.78933			0.894667	+	0.446734i	$0.147413\pi$
$954$	10.3366	+	9.47122i	0.334660	+	0.306642i
$955$		0			0
$956$	11.2565	+	6.49894i	0.364061	+	0.210191i
$957$	13.6103	−	10.9237i	0.439958	−	0.353113i
$958$	68.5654			2.21525
$959$	5.70319	−	9.96091i	0.184166	−	0.321655i
$960$		0			0
$961$	−12.7675	−	22.1140i	−0.411856	−	0.713355i
$962$	−12.9876	−	7.49840i	−0.418737	−	0.241758i
$963$	3.47857	−	15.6929i	0.112096	−	0.505697i
$964$	39.8858	−	23.0281i	1.28464	−	0.741684i
$965$		0			0
$966$	50.0191	−	40.4429i	1.60934	−	1.30123i
$967$		−	34.5930i		−	1.11244i	−0.831036	−	0.556218i	$-0.812252\pi$
$967$		−	34.5930i		−	1.11244i	0.831036	−	0.556218i	$-0.187748\pi$
$968$	−2.90278	−	5.02776i	−0.0932989	−	0.161598i
$969$	−6.00935	−	2.33681i	−0.193048	−	0.0750692i
$970$		0			0
$971$	2.12246	+	3.67621i	0.0681129	+	0.117975i	0.898071	−	0.439851i	$-0.144969\pi$
$971$	2.12246	+	3.67621i	0.0681129	+	0.117975i	−0.829958	+	0.557826i	$0.811636\pi$
$972$	−24.3150	−	25.3962i	−0.779903	−	0.814583i
$973$	0.104497	+	29.0056i	0.00335002	+	0.929875i
$974$			66.4407i			2.12890i
$975$		0			0
$976$	15.3709	+	8.87439i	0.492010	+	0.284062i
$977$	19.4455	−	33.6806i	0.622118	−	1.07754i	−0.366973	−	0.930232i	$-0.619606\pi$
$977$	19.4455	−	33.6806i	0.622118	−	1.07754i	0.989091	−	0.147308i	$-0.0470607\pi$
$978$	−37.3019	−	46.4758i	−1.19278	−	1.48613i
$979$		−	64.7574i		−	2.06966i
$980$		0			0
$981$	3.88790	−	1.22597i	0.124131	−	0.0391422i
$982$	−40.1970	+	23.2077i	−1.28274	+	0.740588i
$983$	22.8429	+	13.1884i	0.728577	+	0.420644i	0.817901	−	0.575359i	$-0.195138\pi$
$983$	22.8429	+	13.1884i	0.728577	+	0.420644i	−0.0893246	+	0.996003i	$0.528471\pi$
$984$	3.49344	+	1.35847i	0.111367	+	0.0433064i
$985$		0			0
$986$	18.3804			0.585352
$987$	30.8242	−	4.85848i	0.981144	−	0.154647i
$988$			1.29242i			0.0411174i
$989$	−18.5577	+	10.7143i	−0.590099	+	0.340694i
$990$		0			0
$991$	6.90833	−	11.9656i	0.219450	−	0.380099i	−0.735190	−	0.677861i	$-0.762907\pi$
$991$	6.90833	−	11.9656i	0.219450	−	0.380099i	0.954640	+	0.297762i	$0.0962403\pi$
$992$	16.4328	−	9.48750i	0.521743	−	0.301228i
$993$	3.90211	+	25.3501i	0.123830	+	0.804460i
$994$	−5.79224	+	3.37203i	−0.183719	+	0.106954i
$995$		0			0
$996$	6.75773	+	8.41972i	0.214127	+	0.266789i
$997$	−30.6574	+	53.1001i	−0.970929	+	1.68170i	−0.278166	+	0.960533i	$0.589726\pi$
$997$	−30.6574	+	53.1001i	−0.970929	+	1.68170i	−0.692763	+	0.721165i	$0.743607\pi$
$998$	−6.61570	+	11.4587i	−0.209416	+	0.362720i
$999$	−49.1786	−	32.8571i	−1.55594	−	1.03955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.f.374.7		16
3.2	odd	2		525.2.q.e.374.2		16
5.2	odd	4		525.2.t.g.101.1		8
5.3	odd	4		105.2.s.c.101.4	yes	8
5.4	even	2	inner	525.2.q.f.374.2		16
7.5	odd	6		525.2.q.e.299.7		16
15.2	even	4		525.2.t.f.101.4		8
15.8	even	4		105.2.s.d.101.1	yes	8
15.14	odd	2		525.2.q.e.374.7		16
21.5	even	6	inner	525.2.q.f.299.2		16
35.3	even	12		735.2.b.c.146.7		8
35.12	even	12		525.2.t.f.26.4		8
35.13	even	4		735.2.s.k.521.4		8
35.18	odd	12		735.2.b.d.146.7		8
35.19	odd	6		525.2.q.e.299.2		16
35.23	odd	12		735.2.s.l.656.1		8
35.33	even	12		105.2.s.d.26.1	yes	8
105.23	even	12		735.2.s.k.656.4		8
105.38	odd	12		735.2.b.d.146.2		8
105.47	odd	12		525.2.t.g.26.1		8
105.53	even	12		735.2.b.c.146.2		8
105.68	odd	12		105.2.s.c.26.4	✓	8
105.83	odd	4		735.2.s.l.521.1		8
105.89	even	6	inner	525.2.q.f.299.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.4	✓	8	105.68	odd	12
105.2.s.c.101.4	yes	8	5.3	odd	4
105.2.s.d.26.1	yes	8	35.33	even	12
105.2.s.d.101.1	yes	8	15.8	even	4
525.2.q.e.299.2		16	35.19	odd	6
525.2.q.e.299.7		16	7.5	odd	6
525.2.q.e.374.2		16	3.2	odd	2
525.2.q.e.374.7		16	15.14	odd	2
525.2.q.f.299.2		16	21.5	even	6	inner
525.2.q.f.299.7		16	105.89	even	6	inner
525.2.q.f.374.2		16	5.4	even	2	inner
525.2.q.f.374.7		16	1.1	even	1	trivial
525.2.t.f.26.4		8	35.12	even	12
525.2.t.f.101.4		8	15.2	even	4
525.2.t.g.26.1		8	105.47	odd	12
525.2.t.g.101.1		8	5.2	odd	4
735.2.b.c.146.2		8	105.53	even	12
735.2.b.c.146.7		8	35.3	even	12
735.2.b.d.146.2		8	105.38	odd	12
735.2.b.d.146.7		8	35.18	odd	12
735.2.s.k.521.4		8	35.13	even	4
735.2.s.k.656.4		8	105.23	even	12
735.2.s.l.521.1		8	105.83	odd	4
735.2.s.l.656.1		8	35.23	odd	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03144 + 1.78651i) q^{2} +(1.61429 + 0.627739i) q^{3} +(-1.12774 + 1.95330i) q^{4} +(0.543588 + 3.53142i) q^{6} +(2.64573 - 0.00953166i) q^{7} -0.527019 q^{8} +(2.21189 + 2.02671i) q^{9} +O(q^{10})\)	\(q+(1.03144 + 1.78651i) q^{2} +(1.61429 + 0.627739i) q^{3} +(-1.12774 + 1.95330i) q^{4} +(0.543588 + 3.53142i) q^{6} +(2.64573 - 0.00953166i) q^{7} -0.527019 q^{8} +(2.21189 + 2.02671i) q^{9} +(-4.06348 - 2.34605i) q^{11} +(-3.04666 + 2.44528i) q^{12} +0.638688 q^{13} +(2.74595 + 4.71679i) q^{14} +(1.71189 + 2.96508i) q^{16} +(-3.59334 - 2.07462i) q^{17} +(-1.33930 + 6.04198i) q^{18} +(0.776975 - 0.448587i) q^{19} +(4.27698 + 1.64544i) q^{21} -9.67925i q^{22} +(-3.40218 - 5.89275i) q^{23} +(-0.850763 - 0.330830i) q^{24} +(0.658769 + 1.14102i) q^{26} +(2.29839 + 4.66019i) q^{27} +(-2.96508 + 5.17866i) q^{28} +2.14740i q^{29} +(-2.02453 - 1.16886i) q^{31} +(-4.05844 + 7.02943i) q^{32} +(-5.08695 - 6.33802i) q^{33} -8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} +(-9.85748 + 5.69122i) q^{37} +(1.60281 + 0.925382i) q^{38} +(1.03103 + 0.400929i) q^{39} -4.10624 q^{41} +(1.47185 + 9.33802i) q^{42} -3.14924i q^{43} +(9.16509 - 5.29147i) q^{44} +(7.01829 - 12.1560i) q^{46} +(5.89714 - 3.40471i) q^{47} +(0.902197 + 5.86113i) q^{48} +(6.99982 - 0.0504365i) q^{49} +(-4.49840 - 5.60472i) q^{51} +(-0.720273 + 1.24755i) q^{52} +(1.13269 - 1.96187i) q^{53} +(-5.95481 + 8.91281i) q^{54} +(-1.39435 + 0.00502336i) q^{56} +(1.53586 - 0.236414i) q^{57} +(-3.83635 + 2.21492i) q^{58} +(0.254055 - 0.440035i) q^{59} +(4.48946 - 2.59199i) q^{61} -4.82244i q^{62} +(5.87139 + 5.34105i) q^{63} -9.89660 q^{64} +(6.07604 - 15.6252i) q^{66} +(-4.18160 - 2.41425i) q^{67} +(8.10471 - 4.67925i) q^{68} +(-1.79301 - 11.6483i) q^{69} +1.22800i q^{71} +(-1.16571 - 1.06811i) q^{72} +(7.22826 - 12.5197i) q^{73} +(-20.3348 - 11.7403i) q^{74} +2.02356i q^{76} +(-10.7733 - 6.16830i) q^{77} +(0.347183 + 2.25548i) q^{78} +(4.54056 + 7.86448i) q^{79} +(0.784903 + 8.96571i) q^{81} +(-4.23534 - 7.33583i) q^{82} -2.76359i q^{83} +(-8.03735 + 6.49859i) q^{84} +(5.62613 - 3.24825i) q^{86} +(-1.34801 + 3.46653i) q^{87} +(2.14153 + 1.23641i) q^{88} +(6.90067 + 11.9523i) q^{89} +(1.68980 - 0.00608775i) q^{91} +15.3471 q^{92} +(-2.53444 - 3.15776i) q^{93} +(12.1651 + 7.02352i) q^{94} +(-10.9642 + 8.79992i) q^{96} +12.9085 q^{97} +(7.31000 + 12.4532i) q^{98} +(-4.23321 - 13.4247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * q^96 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more