LMFDB - Embedded newform 825.2.n.l.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.819390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 10x^{6} - 13x^{5} + 29x^{4} - 7x^{3} + 80x^{2} + 143x + 121 $ x^8 - 3x^7 + 10x^6 - 13x^5 + 29x^4 - 7x^3 + 80x^2 + 143*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.1
Root			$-0.575405 - 1.77091i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.l.526.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.575405 - 1.77091i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.18701 + 0.862413i) q^{4} +(-0.575405 + 1.77091i) q^{6} +(1.04263 - 0.757515i) q^{7} +(-0.802588 - 0.583114i) q^{8} +(0.309017 + 0.951057i) q^{9} +(3.04508 - 1.31433i) q^{11} +1.46722 q^{12} +(-0.312990 - 0.963285i) q^{13} +(-1.94143 - 1.41053i) q^{14} +(-1.47763 + 4.54767i) q^{16} +(2.19741 - 6.76294i) q^{17} +(1.50643 - 1.09448i) q^{18} +(-2.69344 - 1.95690i) q^{19} -1.28876 q^{21} +(-4.07972 - 4.63631i) q^{22} -4.54563 q^{23} +(0.306561 + 0.943499i) q^{24} +(-1.52580 + 1.10856i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.584321 + 1.79835i) q^{28} +(0.510402 - 0.370829i) q^{29} +(0.457371 + 1.40764i) q^{31} +6.91965 q^{32} +(-3.23607 - 0.726543i) q^{33} -13.2410 q^{34} +(-1.18701 - 0.862413i) q^{36} +(-1.56898 + 1.13993i) q^{37} +(-1.91568 + 5.89585i) q^{38} +(-0.312990 + 0.963285i) q^{39} +(-8.55794 - 6.21771i) q^{41} +(0.741559 + 2.28228i) q^{42} -1.64375 q^{43} +(-2.48105 + 4.18624i) q^{44} +(2.61558 + 8.04992i) q^{46} +(1.61161 + 1.17090i) q^{47} +(3.86848 - 2.81061i) q^{48} +(-1.64987 + 5.07778i) q^{49} +(-5.75290 + 4.17973i) q^{51} +(1.20227 + 0.873502i) q^{52} +(0.544147 + 1.67471i) q^{53} -1.86205 q^{54} -1.27852 q^{56} +(1.02880 + 3.16633i) q^{57} +(-0.950394 - 0.690501i) q^{58} +(4.79553 - 3.48416i) q^{59} +(0.939361 - 2.89105i) q^{61} +(2.22964 - 1.61993i) q^{62} +(1.04263 + 0.757515i) q^{63} +(-1.02635 - 3.15877i) q^{64} +(0.575405 + 6.14885i) q^{66} -10.6112 q^{67} +(3.22410 + 9.92275i) q^{68} +(3.67749 + 2.67186i) q^{69} +(4.99903 - 15.3854i) q^{71} +(0.306561 - 0.943499i) q^{72} +(-5.95374 + 4.32564i) q^{73} +(2.92151 + 2.12260i) q^{74} +4.88479 q^{76} +(2.17927 - 3.67705i) q^{77} +1.88599 q^{78} +(5.25535 + 16.1743i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-6.08674 + 18.7331i) q^{82} +(-2.81511 + 8.66401i) q^{83} +(1.52977 - 1.11144i) q^{84} +(0.945821 + 2.91094i) q^{86} -0.630892 q^{87} +(-3.21035 - 0.720769i) q^{88} -0.138629 q^{89} +(-1.05604 - 0.767255i) q^{91} +(5.39571 - 3.92021i) q^{92} +(0.457371 - 1.40764i) q^{93} +(1.14624 - 3.52775i) q^{94} +(-5.59812 - 4.06727i) q^{96} +(1.66709 + 5.13078i) q^{97} +9.94166 q^{98} +(2.19098 + 2.48990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 2 q^{3} - 7 q^{4} + 3 q^{6} + 7 q^{7} - 16 q^{8} - 2 q^{9} + 2 q^{11} + 18 q^{12} - 5 q^{13} - 2 q^{14} - 11 q^{16} + 8 q^{17} - 2 q^{18} - 5 q^{19} - 8 q^{21} - 8 q^{22} - 2 q^{23} + 19 q^{24}+ \cdots + 22 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 2 * q^3 - 7 * q^4 + 3 * q^6 + 7 * q^7 - 16 * q^8 - 2 * q^9 + 2 * q^11 + 18 * q^12 - 5 * q^13 - 2 * q^14 - 11 * q^16 + 8 * q^17 - 2 * q^18 - 5 * q^19 - 8 * q^21 - 8 * q^22 - 2 * q^23 + 19 * q^24 - 32 * q^26 - 2 * q^27 - 51 * q^28 - 3 * q^29 + 5 * q^31 + 16 * q^32 - 8 * q^33 - 46 * q^34 - 7 * q^36 - 19 * q^37 + 31 * q^38 - 5 * q^39 - 18 * q^41 + 23 * q^42 + 52 * q^43 - 38 * q^44 + 33 * q^46 + 18 * q^47 + 4 * q^48 - 47 * q^49 - 7 * q^51 - 29 * q^52 + 31 * q^53 - 2 * q^54 - 68 * q^56 - 5 * q^57 - 35 * q^58 - 2 * q^59 - 22 * q^61 + 14 * q^62 + 7 * q^63 - 16 * q^64 - 3 * q^66 - 38 * q^67 - 2 * q^69 + 19 * q^72 - 18 * q^73 - 12 * q^74 + 92 * q^76 + 13 * q^77 + 18 * q^78 - 18 * q^79 - 2 * q^81 + 15 * q^82 - 28 * q^83 + 39 * q^84 + 53 * q^86 + 32 * q^87 - 64 * q^88 + 34 * q^89 + 33 * q^91 - 12 * q^92 + 5 * q^93 + 12 * q^94 - 14 * q^96 - 11 * q^97 - 24 * q^98 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.575405	−	1.77091i	−0.406873	−	1.25222i	−0.919322	−	0.393507i	$-0.871262\pi$
$2$	−0.575405	−	1.77091i	−0.406873	−	1.25222i	0.512449	−	0.858718i	$-0.328738\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−1.18701	+	0.862413i	−0.593505	+	0.431207i
$5$		0			0
$5$		0			0
$6$	−0.575405	+	1.77091i	−0.234908	+	0.722972i
$7$	1.04263	−	0.757515i	0.394077	−	0.286314i	−0.373047	−	0.927812i	$-0.621687\pi$
$7$	1.04263	−	0.757515i	0.394077	−	0.286314i	0.767124	+	0.641499i	$0.221687\pi$
$8$	−0.802588	−	0.583114i	−0.283758	−	0.206162i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$12$	1.46722			0.423551
$13$	−0.312990	−	0.963285i	−0.0868079	−	0.267167i	0.898224	−	0.439537i	$-0.144858\pi$
$13$	−0.312990	−	0.963285i	−0.0868079	−	0.267167i	−0.985032	+	0.172370i	$0.944858\pi$
$14$	−1.94143	−	1.41053i	−0.518868	−	0.376980i
$15$		0			0
$16$	−1.47763	+	4.54767i	−0.369407	+	1.13692i
$17$	2.19741	−	6.76294i	0.532951	−	1.64025i	−0.215085	−	0.976595i	$-0.569003\pi$
$17$	2.19741	−	6.76294i	0.532951	−	1.64025i	0.748036	−	0.663658i	$-0.230997\pi$
$18$	1.50643	−	1.09448i	0.355069	−	0.257973i
$19$	−2.69344	−	1.95690i	−0.617917	−	0.448943i	0.234276	−	0.972170i	$-0.424728\pi$
$19$	−2.69344	−	1.95690i	−0.617917	−	0.448943i	−0.852193	+	0.523227i	$0.824728\pi$
$20$		0			0
$21$	−1.28876			−0.281231
$22$	−4.07972	−	4.63631i	−0.869799	−	0.988465i
$23$	−4.54563			−0.947830			−0.473915	−	0.880571i	$-0.657160\pi$
$23$	−4.54563			−0.947830			−0.473915	+	0.880571i	$0.657160\pi$
$24$	0.306561	+	0.943499i	0.0625766	+	0.192591i
$25$		0			0
$26$	−1.52580	+	1.10856i	−0.299234	+	0.217406i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.584321	+	1.79835i	−0.110426	+	0.339857i
$29$	0.510402	−	0.370829i	0.0947793	−	0.0688612i	−0.539386	−	0.842058i	$-0.681344\pi$
$29$	0.510402	−	0.370829i	0.0947793	−	0.0688612i	0.634166	+	0.773197i	$0.281344\pi$
$30$		0			0
$31$	0.457371	+	1.40764i	0.0821462	+	0.252820i	0.983691	−	0.179865i	$-0.0575662\pi$
$31$	0.457371	+	1.40764i	0.0821462	+	0.252820i	−0.901545	+	0.432685i	$0.857566\pi$
$32$	6.91965			1.22323
$33$	−3.23607	−	0.726543i	−0.563327	−	0.126475i
$34$	−13.2410			−2.27081
$35$		0			0
$36$	−1.18701	−	0.862413i	−0.197835	−	0.143736i
$37$	−1.56898	+	1.13993i	−0.257938	+	0.187403i	−0.709238	−	0.704970i	$-0.750961\pi$
$37$	−1.56898	+	1.13993i	−0.257938	+	0.187403i	0.451299	+	0.892373i	$0.350961\pi$
$38$	−1.91568	+	5.89585i	−0.310764	+	0.956434i
$39$	−0.312990	+	0.963285i	−0.0501186	+	0.154249i
$40$		0			0
$41$	−8.55794	−	6.21771i	−1.33653	−	0.971043i	−0.999564	−	0.0295248i	$-0.990601\pi$
$41$	−8.55794	−	6.21771i	−1.33653	−	0.971043i	−0.336962	−	0.941518i	$-0.609399\pi$
$42$	0.741559	+	2.28228i	0.114425	+	0.352164i
$43$	−1.64375			−0.250669			−0.125335	−	0.992115i	$-0.540000\pi$
$43$	−1.64375			−0.250669			−0.125335	+	0.992115i	$0.540000\pi$
$44$	−2.48105	+	4.18624i	−0.374033	+	0.631100i
$45$		0			0
$46$	2.61558	+	8.04992i	0.385646	+	1.18690i
$47$	1.61161	+	1.17090i	0.235077	+	0.170793i	0.699087	−	0.715037i	$-0.253590\pi$
$47$	1.61161	+	1.17090i	0.235077	+	0.170793i	−0.464010	+	0.885830i	$0.653590\pi$
$48$	3.86848	−	2.81061i	0.558367	−	0.405677i
$49$	−1.64987	+	5.07778i	−0.235696	+	0.725397i
$50$		0			0
$51$	−5.75290	+	4.17973i	−0.805567	+	0.585279i
$52$	1.20227	+	0.873502i	0.166725	+	0.121133i
$53$	0.544147	+	1.67471i	0.0747443	+	0.230039i	0.981448	−	0.191729i	$-0.0614095\pi$
$53$	0.544147	+	1.67471i	0.0747443	+	0.230039i	−0.906704	+	0.421769i	$0.861409\pi$
$54$	−1.86205			−0.253393
$55$		0			0
$56$	−1.27852			−0.170849
$57$	1.02880	+	3.16633i	0.136268	+	0.419390i
$58$	−0.950394	−	0.690501i	−0.124793	−	0.0906673i
$59$	4.79553	−	3.48416i	0.624325	−	0.453598i	−0.230105	−	0.973166i	$-0.573907\pi$
$59$	4.79553	−	3.48416i	0.624325	−	0.453598i	0.854429	+	0.519567i	$0.173907\pi$
$60$		0			0
$61$	0.939361	−	2.89105i	0.120273	−	0.370162i	−0.872737	−	0.488190i	$-0.837657\pi$
$61$	0.939361	−	2.89105i	0.120273	−	0.370162i	0.993010	+	0.118028i	$0.0376573\pi$
$62$	2.22964	−	1.61993i	0.283164	−	0.205731i
$63$	1.04263	+	0.757515i	0.131359	+	0.0954379i
$64$	−1.02635	−	3.15877i	−0.128293	−	0.394846i
$65$		0			0
$66$	0.575405	+	6.14885i	0.0708274	+	0.756871i
$67$	−10.6112			−1.29636			−0.648181	−	0.761486i	$-0.724470\pi$
$67$	−10.6112			−1.29636			−0.648181	+	0.761486i	$0.724470\pi$
$68$	3.22410	+	9.92275i	0.390979	+	1.20331i
$69$	3.67749	+	2.67186i	0.442718	+	0.321654i
$70$		0			0
$71$	4.99903	−	15.3854i	0.593276	−	1.82592i	0.0301476	−	0.999545i	$-0.490402\pi$
$71$	4.99903	−	15.3854i	0.593276	−	1.82592i	0.563128	−	0.826370i	$-0.309598\pi$
$72$	0.306561	−	0.943499i	0.0361286	−	0.111192i
$73$	−5.95374	+	4.32564i	−0.696832	+	0.506278i	−0.878899	−	0.477008i	$-0.841721\pi$
$73$	−5.95374	+	4.32564i	−0.696832	+	0.506278i	0.182067	+	0.983286i	$0.441721\pi$
$74$	2.92151	+	2.12260i	0.339619	+	0.246747i
$75$		0			0
$76$	4.88479			0.560324
$77$	2.17927	−	3.67705i	0.248351	−	0.419039i
$78$	1.88599			0.213546
$79$	5.25535	+	16.1743i	0.591274	+	1.81975i	0.572464	+	0.819930i	$0.305988\pi$
$79$	5.25535	+	16.1743i	0.591274	+	1.81975i	0.0188097	+	0.999823i	$0.494012\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−6.08674	+	18.7331i	−0.672169	+	2.06872i
$83$	−2.81511	+	8.66401i	−0.308998	+	0.950999i	0.669157	+	0.743121i	$0.266655\pi$
$83$	−2.81511	+	8.66401i	−0.308998	+	0.950999i	−0.978155	+	0.207877i	$0.933345\pi$
$84$	1.52977	−	1.11144i	0.166912	−	0.121268i
$85$		0			0
$86$	0.945821	+	2.91094i	0.101991	+	0.313895i
$87$	−0.630892			−0.0676387
$88$	−3.21035	−	0.720769i	−0.342225	−	0.0768342i
$89$	−0.138629			−0.0146946			−0.00734732	−	0.999973i	$-0.502339\pi$
$89$	−0.138629			−0.0146946			−0.00734732	+	0.999973i	$0.502339\pi$
$90$		0			0
$91$	−1.05604	−	0.767255i	−0.110703	−	0.0804301i
$92$	5.39571	−	3.92021i	0.562542	−	0.408710i
$93$	0.457371	−	1.40764i	0.0474271	−	0.145966i
$94$	1.14624	−	3.52775i	0.118225	−	0.363860i
$95$		0			0
$96$	−5.59812	−	4.06727i	−0.571355	−	0.415114i
$97$	1.66709	+	5.13078i	0.169268	+	0.520952i	0.999325	−	0.0367253i	$-0.0116927\pi$
$97$	1.66709	+	5.13078i	0.169268	+	0.520952i	−0.830058	+	0.557677i	$0.811693\pi$
$98$	9.94166			1.00426
$99$	2.19098	+	2.48990i	0.220202	+	0.250244i
$100$		0			0
$101$	−2.66485	−	8.20155i	−0.265162	−	0.816085i	−0.991656	−	0.128912i	$-0.958851\pi$
$101$	−2.66485	−	8.20155i	−0.265162	−	0.816085i	0.726494	−	0.687173i	$-0.241149\pi$
$102$	10.7122	+	7.78285i	1.06066	+	0.770617i
$103$	7.41999	−	5.39094i	0.731113	−	0.531185i	−0.158802	−	0.987310i	$-0.550763\pi$
$103$	7.41999	−	5.39094i	0.731113	−	0.531185i	0.889916	+	0.456125i	$0.150763\pi$
$104$	−0.310503	+	0.955630i	−0.0304473	+	0.0937073i
$105$		0			0
$106$	2.65267	−	1.92727i	0.257650	−	0.187193i
$107$	12.1039	+	8.79401i	1.17013	+	0.850149i	0.991024	−	0.133681i	$-0.0426798\pi$
$107$	12.1039	+	8.79401i	1.17013	+	0.850149i	0.179105	+	0.983830i	$0.442680\pi$
$108$	0.453397	+	1.39541i	0.0436282	+	0.134274i
$109$	−4.39550			−0.421013			−0.210506	−	0.977592i	$-0.567511\pi$
$109$	−4.39550			−0.421013			−0.210506	+	0.977592i	$0.567511\pi$
$110$		0			0
$111$	1.93936			0.184076
$112$	1.90431	+	5.86086i	0.179940	+	0.553799i
$113$	−11.5540	−	8.39445i	−1.08691	−	0.789683i	−0.108032	−	0.994147i	$-0.534455\pi$
$113$	−11.5540	−	8.39445i	−1.08691	−	0.789683i	−0.978874	+	0.204464i	$0.934455\pi$
$114$	5.01531	−	3.64384i	0.469727	−	0.341277i
$115$		0			0
$116$	−0.286045	+	0.880355i	−0.0265586	+	0.0817389i
$117$	0.819419	−	0.595343i	0.0757553	−	0.0550395i
$118$	−8.92951	−	6.48767i	−0.822028	−	0.597238i
$119$	−2.83194	−	8.71581i	−0.259603	−	0.798977i
$120$		0			0
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$	−5.66032			−0.512461
$123$	3.26884	+	10.0605i	0.294742	+	0.907122i
$124$	−1.75687	−	1.27644i	−0.157772	−	0.114628i
$125$		0			0
$126$	0.741559	−	2.28228i	0.0660633	−	0.203322i
$127$	5.31921	−	16.3708i	0.472004	−	1.45268i	−0.377953	−	0.925825i	$-0.623372\pi$
$127$	5.31921	−	16.3708i	0.472004	−	1.45268i	0.849957	−	0.526853i	$-0.176628\pi$
$128$	6.19289	−	4.49940i	0.547379	−	0.397694i
$129$	1.32982	+	0.966172i	0.117084	+	0.0850667i
$130$		0			0
$131$	3.93936			0.344184			0.172092	−	0.985081i	$-0.444947\pi$
$131$	3.93936			0.344184			0.172092	+	0.985081i	$0.444947\pi$
$132$	4.46782	−	1.92841i	0.388874	−	0.167847i
$133$	−4.29064			−0.372045
$134$	6.10572	+	18.7915i	0.527454	+	1.62334i
$135$		0			0
$136$	−5.70718	+	4.14651i	−0.489387	+	0.355560i
$137$	−6.30407	+	19.4019i	−0.538593	+	1.65762i	0.197161	+	0.980371i	$0.436828\pi$
$137$	−6.30407	+	19.4019i	−0.538593	+	1.65762i	−0.735754	+	0.677249i	$0.763172\pi$
$138$	2.61558	−	8.04992i	0.222653	−	0.685255i
$139$	9.16003	−	6.65515i	0.776944	−	0.564483i	−0.127116	−	0.991888i	$-0.540572\pi$
$139$	9.16003	−	6.65515i	0.776944	−	0.564483i	0.904060	+	0.427405i	$0.140572\pi$
$140$		0			0
$141$	−0.615578	−	1.89456i	−0.0518411	−	0.159550i
$142$	−30.1227			−2.52784
$143$	−2.21915	−	2.52191i	−0.185575	−	0.210893i
$144$	−4.78170			−0.398475
$145$		0			0
$146$	11.0861	+	8.05456i	0.917496	+	0.666600i
$147$	4.31942	−	3.13824i	0.356260	−	0.258838i
$148$	0.879301	−	2.70621i	0.0722781	−	0.222449i
$149$	6.63771	−	20.4288i	0.543782	−	1.67359i	−0.180085	−	0.983651i	$-0.557637\pi$
$149$	6.63771	−	20.4288i	0.543782	−	1.67359i	0.723867	−	0.689939i	$-0.242363\pi$
$150$		0			0
$151$	−5.29464	−	3.84678i	−0.430872	−	0.313047i	0.351126	−	0.936328i	$-0.385799\pi$
$151$	−5.29464	−	3.84678i	−0.430872	−	0.313047i	−0.781997	+	0.623282i	$0.785799\pi$
$152$	1.02063	+	3.14117i	0.0827837	+	0.254782i
$153$	7.11097			0.574888
$154$	−7.76571	−	1.74351i	−0.625778	−	0.140496i
$155$		0			0
$156$	−0.459227	−	1.41336i	−0.0367676	−	0.113159i
$157$	−11.3415	−	8.24008i	−0.905150	−	0.657630i	0.0346334	−	0.999400i	$-0.488974\pi$
$157$	−11.3415	−	8.24008i	−0.905150	−	0.657630i	−0.939784	+	0.341770i	$0.888974\pi$
$158$	25.6194	−	18.6136i	2.03817	−	1.48081i
$159$	0.544147	−	1.67471i	0.0431537	−	0.132813i
$160$		0			0
$161$	−4.73941	+	3.44338i	−0.373518	+	0.271377i
$162$	1.50643	+	1.09448i	0.118356	+	0.0859908i
$163$	−0.379172	−	1.16697i	−0.0296990	−	0.0914042i	0.935108	−	0.354362i	$-0.115302\pi$
$163$	−0.379172	−	1.16697i	−0.0296990	−	0.0914042i	−0.964807	+	0.262958i	$0.915302\pi$
$164$	15.5206			1.21195
$165$		0			0
$166$	16.9630			1.31659
$167$	−4.51137	−	13.8846i	−0.349100	−	1.07442i	−0.959352	−	0.282213i	$-0.908932\pi$
$167$	−4.51137	−	13.8846i	−0.349100	−	1.07442i	0.610251	−	0.792208i	$-0.291068\pi$
$168$	1.03434	+	0.751495i	0.0798014	+	0.0579791i
$169$	9.68727	−	7.03821i	0.745174	−	0.541401i
$170$		0			0
$171$	1.02880	−	3.16633i	0.0786745	−	0.242135i
$172$	1.95115	−	1.41759i	0.148774	−	0.108090i
$173$	4.92917	+	3.58125i	0.374758	+	0.272277i	0.759181	−	0.650880i	$-0.225600\pi$
$173$	4.92917	+	3.58125i	0.374758	+	0.272277i	−0.384423	+	0.923157i	$0.625600\pi$
$174$	0.363018	+	1.11725i	0.0275203	+	0.0846989i
$175$		0			0
$176$	1.47763	+	15.7901i	0.111380	+	1.19023i
$177$	−5.92760			−0.445546
$178$	0.0797678	+	0.245500i	0.00597885	+	0.0184010i
$179$	0.479744	+	0.348554i	0.0358577	+	0.0260522i	0.605570	−	0.795792i	$-0.292945\pi$
$179$	0.479744	+	0.348554i	0.0358577	+	0.0260522i	−0.569712	+	0.821844i	$0.692945\pi$
$180$		0			0
$181$	6.38709	−	19.6574i	0.474748	−	1.46113i	−0.371548	−	0.928414i	$-0.621173\pi$
$181$	6.38709	−	19.6574i	0.474748	−	1.46113i	0.846297	−	0.532712i	$-0.178827\pi$
$182$	−0.751094	+	2.31163i	−0.0556748	+	0.171349i
$183$	−2.45928	+	1.78677i	−0.181795	+	0.132082i
$184$	3.64827	+	2.65062i	0.268954	+	0.195407i
$185$		0			0
$186$	−2.75599			−0.202079
$187$	−2.19741	−	23.4818i	−0.160691	−	1.71716i
$188$	−2.92279			−0.213166
$189$	−0.398249	−	1.22568i	−0.0289684	−	0.0891554i
$190$		0			0
$191$	−7.03612	+	5.11204i	−0.509116	+	0.369894i	−0.812488	−	0.582978i	$-0.801887\pi$
$191$	−7.03612	+	5.11204i	−0.509116	+	0.369894i	0.303372	+	0.952872i	$0.401887\pi$
$192$	−1.02635	+	3.15877i	−0.0740702	+	0.227965i
$193$	4.95128	−	15.2385i	0.356401	−	1.09689i	−0.598792	−	0.800905i	$-0.704352\pi$
$193$	4.95128	−	15.2385i	0.356401	−	1.09689i	0.955193	−	0.295985i	$-0.0956477\pi$
$194$	8.12692	−	5.90455i	0.583479	−	0.423922i
$195$		0			0
$196$	−2.42073	−	7.45025i	−0.172909	−	0.532160i
$197$	−6.94349			−0.494703			−0.247352	−	0.968926i	$-0.579560\pi$
$197$	−6.94349			−0.494703			−0.247352	+	0.968926i	$0.579560\pi$
$198$	3.14869	−	5.31274i	0.223768	−	0.377560i
$199$	−20.6414			−1.46323			−0.731615	−	0.681718i	$-0.761233\pi$
$199$	−20.6414			−1.46323			−0.731615	+	0.681718i	$0.761233\pi$
$200$		0			0
$201$	8.58463	+	6.23710i	0.605513	+	0.439931i
$202$	−12.9909	+	9.43842i	−0.914035	+	0.664085i
$203$	0.251252	−	0.773274i	0.0176344	−	0.0542732i
$204$	3.22410	−	9.92275i	0.225732	−	0.694731i
$205$		0			0
$206$	−13.8164	−	10.0382i	−0.962633	−	0.699394i
$207$	−1.40468	−	4.32315i	−0.0976319	−	0.300480i
$208$	4.84318			0.335814
$209$	−10.7738	−	2.41886i	−0.745236	−	0.167316i
$210$		0			0
$211$	4.80256	+	14.7807i	0.330622	+	1.01755i	0.968839	+	0.247692i	$0.0796722\pi$
$211$	4.80256	+	14.7807i	0.330622	+	1.01755i	−0.638217	+	0.769856i	$0.720328\pi$
$212$	−2.09020	−	1.51862i	−0.143556	−	0.104299i
$213$	−13.0876	+	9.50872i	−0.896750	+	0.651527i
$214$	8.60878	−	26.4951i	0.588484	−	1.81117i
$215$		0			0
$216$	−0.802588	+	0.583114i	−0.0546092	+	0.0396759i
$217$	1.54318	+	1.12118i	0.104758	+	0.0761109i
$218$	2.52919	+	7.78405i	0.171298	+	0.527203i
$219$	7.35922			0.497290
$220$		0			0
$221$	−7.20241			−0.484486
$222$	−1.11592	−	3.43444i	−0.0748955	−	0.230505i
$223$	18.5525	+	13.4791i	1.24236	+	0.902630i	0.997754	−	0.0669911i	$-0.0213399\pi$
$223$	18.5525	+	13.4791i	1.24236	+	0.902630i	0.244610	+	0.969621i	$0.421340\pi$
$224$	7.21463	−	5.24174i	0.482048	−	0.350228i
$225$		0			0
$226$	−8.21764	+	25.2913i	−0.546629	+	1.68235i
$227$	−6.89728	+	5.01117i	−0.457789	+	0.332603i	−0.792663	−	0.609660i	$-0.791306\pi$
$227$	−6.89728	+	5.01117i	−0.457789	+	0.332603i	0.334875	+	0.942263i	$0.391306\pi$
$228$	−3.95188	−	2.87121i	−0.261720	−	0.190150i
$229$	0.857476	+	2.63904i	0.0566636	+	0.174393i	0.975383	−	0.220519i	$-0.0707751\pi$
$229$	0.857476	+	2.63904i	0.0566636	+	0.174393i	−0.918719	+	0.394912i	$0.870775\pi$
$230$		0			0
$231$	−3.92439	+	1.69385i	−0.258206	+	0.111447i
$232$	−0.625878			−0.0410909
$233$	−6.02496	−	18.5429i	−0.394708	−	1.21479i	−0.929189	−	0.369606i	$-0.879493\pi$
$233$	−6.02496	−	18.5429i	−0.394708	−	1.21479i	0.534480	−	0.845181i	$-0.320507\pi$
$234$	−1.52580	−	1.10856i	−0.0997446	−	0.0724687i
$235$		0			0
$236$	−2.68756	+	8.27145i	−0.174945	+	0.538426i
$237$	5.25535	−	16.1743i	0.341372	−	1.05063i
$238$	−13.8054	+	10.0302i	−0.894873	+	0.650164i
$239$	8.34767	+	6.06494i	0.539966	+	0.392308i	0.824072	−	0.566484i	$-0.191697\pi$
$239$	8.34767	+	6.06494i	0.539966	+	0.392308i	−0.284106	+	0.958793i	$0.591697\pi$
$240$		0			0
$241$	19.1814			1.23558			0.617792	−	0.786341i	$-0.288027\pi$
$241$	19.1814			1.23558			0.617792	+	0.786341i	$0.288027\pi$
$242$	−18.5167	−	8.75588i	−1.19030	−	0.562849i
$243$	1.00000			0.0641500
$244$	1.37825	+	4.24183i	0.0882336	+	0.271555i
$245$		0			0
$246$	15.9353	−	11.5777i	1.01600	−	0.738166i
$247$	−1.04203	+	3.20704i	−0.0663028	+	0.204059i
$248$	0.453736	−	1.39646i	0.0288123	−	0.0886751i
$249$	7.37005	−	5.35465i	0.467058	−	0.339337i
$250$		0			0
$251$	8.04424	+	24.7576i	0.507748	+	1.56269i	0.796101	+	0.605164i	$0.206892\pi$
$251$	8.04424	+	24.7576i	0.507748	+	1.56269i	−0.288353	+	0.957524i	$0.593108\pi$
$252$	−1.89090			−0.119116
$253$	−13.8418	+	5.97445i	−0.870229	+	0.375611i
$254$	−32.0520			−2.01112
$255$		0			0
$256$	−16.9055	−	12.2826i	−1.05659	−	0.767659i
$257$	15.2192	−	11.0574i	0.949345	−	0.689739i	−0.00130705	−	0.999999i	$-0.500416\pi$
$257$	15.2192	−	11.0574i	0.949345	−	0.689739i	0.950652	+	0.310260i	$0.100416\pi$
$258$	0.945821	−	2.91094i	0.0588843	−	0.181227i
$259$	−0.772348	+	2.37704i	−0.0479914	+	0.147702i
$260$		0			0
$261$	0.510402	+	0.370829i	0.0315931	+	0.0229537i
$262$	−2.26673	−	6.97627i	−0.140039	−	0.430995i
$263$	12.9135			0.796279			0.398140	−	0.917325i	$-0.369656\pi$
$263$	12.9135			0.796279			0.398140	+	0.917325i	$0.369656\pi$
$264$	2.17357	+	2.47011i	0.133774	+	0.152025i
$265$		0			0
$266$	2.46885	+	7.59835i	0.151375	+	0.465884i
$267$	0.112153	+	0.0814841i	0.00686366	+	0.00498674i
$268$	12.5956	−	9.15122i	0.769397	−	0.559000i
$269$	6.97551	−	21.4684i	0.425304	−	1.30895i	−0.477398	−	0.878687i	$-0.658420\pi$
$269$	6.97551	−	21.4684i	0.425304	−	1.30895i	0.902703	−	0.430265i	$-0.141580\pi$
$270$		0			0
$271$	12.4497	−	9.04522i	0.756264	−	0.549458i	−0.141498	−	0.989939i	$-0.545192\pi$
$271$	12.4497	−	9.04522i	0.756264	−	0.549458i	0.897762	+	0.440480i	$0.145192\pi$
$272$	27.5086	+	19.9862i	1.66796	+	1.21184i
$273$	0.403370	+	1.24144i	0.0244130	+	0.0751356i
$274$	37.9866			2.29485
$275$		0			0
$276$	−6.66947			−0.401455
$277$	3.95889	+	12.1842i	0.237867	+	0.732078i	0.996728	+	0.0808261i	$0.0257558\pi$
$277$	3.95889	+	12.1842i	0.237867	+	0.732078i	−0.758862	+	0.651252i	$0.774244\pi$
$278$	−17.0564	−	12.3922i	−1.02298	−	0.743236i
$279$	−1.19741	+	0.869971i	−0.0716872	+	0.0520838i
$280$		0			0
$281$	−1.97214	+	6.06961i	−0.117648	+	0.362083i	−0.992490	−	0.122325i	$-0.960965\pi$
$281$	−1.97214	+	6.06961i	−0.117648	+	0.362083i	0.874842	+	0.484408i	$0.160965\pi$
$282$	−3.00089	+	2.18027i	−0.178700	+	0.129833i
$283$	17.0876	+	12.4149i	1.01575	+	0.737989i	0.965408	−	0.260743i	$-0.0839676\pi$
$283$	17.0876	+	12.4149i	1.01575	+	0.737989i	0.0503461	+	0.998732i	$0.483968\pi$
$284$	7.33470	+	22.5739i	0.435234	+	1.33951i
$285$		0			0
$286$	−3.18918	+	5.38105i	−0.188580	+	0.318188i
$287$	−13.6328			−0.804717
$288$	2.13829	+	6.58098i	0.126000	+	0.387788i
$289$	−27.1554	−	19.7296i	−1.59738	−	1.16056i
$290$		0			0
$291$	1.66709	−	5.13078i	0.0977267	−	0.300772i
$292$	3.33665	−	10.2692i	0.195263	−	0.600957i
$293$	20.1673	−	14.6524i	1.17819	−	0.856004i	0.186223	−	0.982508i	$-0.440375\pi$
$293$	20.1673	−	14.6524i	1.17819	−	0.856004i	0.991966	+	0.126503i	$0.0403754\pi$
$294$	−8.04297	−	5.84356i	−0.469075	−	0.340803i
$295$		0			0
$296$	1.92395			0.111827
$297$	−0.309017	−	3.30220i	−0.0179310	−	0.191613i
$298$	−39.9970			−2.31696
$299$	1.42274	+	4.37874i	0.0822791	+	0.253229i
$300$		0			0
$301$	−1.71382	+	1.24516i	−0.0987830	+	0.0717701i
$302$	−3.76576	+	11.5898i	−0.216695	+	0.666919i
$303$	−2.66485	+	8.20155i	−0.153091	+	0.471167i
$304$	12.8792	−	9.35730i	0.738674	−	0.536678i
$305$		0			0
$306$	−4.09169	−	12.5929i	−0.233906	−	0.719889i
$307$	31.6395			1.80576			0.902879	−	0.429894i	$-0.141449\pi$
$307$	31.6395			1.80576			0.902879	+	0.429894i	$0.141449\pi$
$308$	0.584321	+	6.24413i	0.0332948	+	0.355792i
$309$	−9.17161			−0.521755
$310$		0			0
$311$	2.42151	+	1.75933i	0.137311	+	0.0997624i	0.654320	−	0.756217i	$-0.272955\pi$
$311$	2.42151	+	1.75933i	0.137311	+	0.0997624i	−0.517009	+	0.855980i	$0.672955\pi$
$312$	0.812908	−	0.590612i	0.0460218	−	0.0334368i
$313$	0.603659	−	1.85787i	0.0341208	−	0.105013i	−0.932546	−	0.361052i	$-0.882418\pi$
$313$	0.603659	−	1.85787i	0.0341208	−	0.105013i	0.966666	+	0.256039i	$0.0824176\pi$
$314$	−8.06652	+	24.8262i	−0.455220	+	1.40102i
$315$		0			0
$316$	−20.1871	−	14.6668i	−1.13561	−	0.825071i
$317$	7.19542	+	22.1452i	0.404135	+	1.24380i	0.921615	+	0.388105i	$0.126870\pi$
$317$	7.19542	+	22.1452i	0.404135	+	1.24380i	−0.517480	+	0.855695i	$0.673130\pi$
$318$	−3.27888			−0.183870
$319$	1.06683	−	1.80004i	0.0597309	−	0.100783i
$320$		0			0
$321$	−4.62328	−	14.2290i	−0.258047	−	0.794186i
$322$	8.82501	+	6.41175i	0.491799	+	0.357313i
$323$	−19.1530	+	13.9154i	−1.06570	+	0.774276i
$324$	0.453397	−	1.39541i	0.0251887	−	0.0775230i
$325$		0			0
$326$	−1.84843	+	1.34296i	−0.102375	+	0.0743797i
$327$	3.55604	+	2.58361i	0.196649	+	0.142874i
$328$	3.24287	+	9.98052i	0.179057	+	0.551082i
$329$	2.56728			0.141539
$330$		0			0
$331$	32.2999			1.77537			0.887683	−	0.460456i	$-0.152314\pi$
$331$	32.2999			1.77537			0.887683	+	0.460456i	$0.152314\pi$
$332$	−4.13039	−	12.7120i	−0.226685	−	0.697664i
$333$	−1.56898	−	1.13993i	−0.0859793	−	0.0624676i
$334$	−21.9925	+	15.9785i	−1.20338	+	0.874304i
$335$		0			0
$336$	1.90431	−	5.86086i	0.103888	−	0.319736i
$337$	0.949424	−	0.689797i	0.0517184	−	0.0375756i	−0.561626	−	0.827391i	$-0.689824\pi$
$337$	0.949424	−	0.689797i	0.0517184	−	0.0375756i	0.613344	+	0.789816i	$0.289824\pi$
$338$	−18.0382	−	13.1055i	−0.981147	−	0.712845i
$339$	4.41322	+	13.5825i	0.239693	+	0.737700i
$340$		0			0
$341$	3.24284	+	3.68525i	0.175609	+	0.199568i
$342$	−6.19927			−0.335218
$343$	4.91403	+	15.1238i	0.265333	+	0.816610i
$344$	1.31925	+	0.958494i	0.0711294	+	0.0516785i
$345$		0			0
$346$	3.50582	−	10.7898i	0.188474	−	0.580063i
$347$	−3.76579	+	11.5899i	−0.202158	+	0.622179i	0.797660	+	0.603107i	$0.206071\pi$
$347$	−3.76579	+	11.5899i	−0.202158	+	0.622179i	−0.999818	+	0.0190713i	$0.993929\pi$
$348$	0.748875	−	0.544089i	0.0401439	−	0.0291662i
$349$	−6.14684	−	4.46594i	−0.329033	−	0.239056i	0.410987	−	0.911641i	$-0.365184\pi$
$349$	−6.14684	−	4.46594i	−0.329033	−	0.239056i	−0.740020	+	0.672585i	$0.765184\pi$
$350$		0			0
$351$	−1.01286			−0.0540624
$352$	21.0709	−	9.09469i	1.12308	−	0.484749i
$353$	−23.7904			−1.26624			−0.633118	−	0.774055i	$-0.718225\pi$
$353$	−23.7904			−1.26624			−0.633118	+	0.774055i	$0.718225\pi$
$354$	3.41077	+	10.4973i	0.181280	+	0.557923i
$355$		0			0
$356$	0.164554	−	0.119555i	0.00872134	−	0.00633643i
$357$	−2.83194	+	8.71581i	−0.149882	+	0.461290i
$358$	0.341213	−	1.05014i	0.0180336	−	0.0555019i
$359$	−24.0920	+	17.5039i	−1.27153	+	0.923818i	−0.999262	−	0.0384041i	$-0.987773\pi$
$359$	−24.0920	+	17.5039i	−1.27153	+	0.923818i	−0.272265	+	0.962222i	$0.587773\pi$
$360$		0			0
$361$	−2.44616	−	7.52851i	−0.128745	−	0.396237i
$362$	−38.4868			−2.02282
$363$	−10.8090	+	2.04087i	−0.567326	+	0.107118i
$364$	1.91521			0.100385
$365$		0			0
$366$	4.57930	+	3.32705i	0.239364	+	0.173908i
$367$	−0.931911	+	0.677073i	−0.0486454	+	0.0353429i	−0.611842	−	0.790980i	$-0.709571\pi$
$367$	−0.931911	+	0.677073i	−0.0486454	+	0.0353429i	0.563197	+	0.826323i	$0.309571\pi$
$368$	6.71675	−	20.6720i	0.350135	−	1.07760i
$369$	3.26884	−	10.0605i	0.170169	−	0.523727i
$370$		0			0
$371$	1.83596	+	1.33390i	0.0953184	+	0.0692529i
$372$	0.671066	+	2.06533i	0.0347931	+	0.107082i
$373$	34.7216			1.79781			0.898907	−	0.438139i	$-0.144362\pi$
$373$	34.7216			1.79781			0.898907	+	0.438139i	$0.144362\pi$
$374$	−40.3199	+	17.4030i	−2.08489	+	0.899887i
$375$		0			0
$376$	−0.610687	−	1.87950i	−0.0314938	−	0.0969278i
$377$	−0.516965	−	0.375597i	−0.0266250	−	0.0193442i
$378$	−1.94143	+	1.41053i	−0.0998562	+	0.0725498i
$379$	−9.75802	+	30.0321i	−0.501236	+	1.54265i	0.305772	+	0.952105i	$0.401085\pi$
$379$	−9.75802	+	30.0321i	−0.501236	+	1.54265i	−0.807008	+	0.590540i	$0.798915\pi$
$380$		0			0
$381$	−13.9259	+	10.1177i	−0.713444	+	0.518347i
$382$	13.1016	+	9.51886i	0.670336	+	0.487027i
$383$	6.88570	+	21.1920i	0.351843	+	1.08286i	0.957818	+	0.287377i	$0.0927832\pi$
$383$	6.88570	+	21.1920i	0.351843	+	1.08286i	−0.605975	+	0.795484i	$0.707217\pi$
$384$	−7.65483			−0.390634
$385$		0			0
$386$	−29.8350			−1.51856
$387$	−0.507947	−	1.56330i	−0.0258204	−	0.0794669i
$388$	−6.40371	−	4.65257i	−0.325099	−	0.236198i
$389$	19.6422	−	14.2709i	0.995901	−	0.723564i	0.0346953	−	0.999398i	$-0.488954\pi$
$389$	19.6422	−	14.2709i	0.995901	−	0.723564i	0.961205	+	0.275834i	$0.0889539\pi$
$390$		0			0
$391$	−9.98863	+	30.7418i	−0.505147	+	1.55468i
$392$	4.28509	−	3.11330i	0.216430	−	0.157246i
$393$	−3.18701	−	2.31550i	−0.160763	−	0.116801i
$394$	3.99532	+	12.2963i	0.201281	+	0.619480i
$395$		0			0
$396$	−4.74804	−	1.06600i	−0.238598	−	0.0535686i
$397$	37.3655			1.87532			0.937660	−	0.347554i	$-0.112988\pi$
$397$	37.3655			1.87532			0.937660	+	0.347554i	$0.112988\pi$
$398$	11.8772	+	36.5541i	0.595348	+	1.83229i
$399$	3.47120	+	2.52197i	0.173777	+	0.126257i
$400$		0			0
$401$	−1.19707	+	3.68421i	−0.0597790	+	0.183981i	−0.976487	−	0.215578i	$-0.930837\pi$
$401$	−1.19707	+	3.68421i	−0.0597790	+	0.183981i	0.916708	+	0.399558i	$0.130837\pi$
$402$	6.10572	−	18.7915i	0.304526	−	0.937234i
$403$	1.21281	−	0.881157i	0.0604143	−	0.0438935i
$404$	10.2363	+	7.43712i	0.509276	+	0.370011i
$405$		0			0
$406$	−1.51397			−0.0751372
$407$	−3.27943	+	5.53332i	−0.162555	+	0.274277i
$408$	7.05447			0.349248
$409$	9.82922	+	30.2512i	0.486024	+	1.49583i	0.830493	+	0.557030i	$0.188059\pi$
$409$	9.82922	+	30.2512i	0.486024	+	1.49583i	−0.344469	+	0.938798i	$0.611941\pi$
$410$		0			0
$411$	16.5043	−	11.9911i	0.814096	−	0.591475i
$412$	−4.15839	+	12.7982i	−0.204869	+	0.630522i
$413$	2.36066	−	7.26537i	0.116160	−	0.357505i
$414$	−6.84767	+	4.97513i	−0.336545	+	0.244514i
$415$		0			0
$416$	−2.16578	−	6.66560i	−0.106186	−	0.326808i
$417$	−11.3224			−0.554461
$418$	1.91568	+	20.4712i	0.0936989	+	1.00128i
$419$	−7.52127			−0.367438			−0.183719	−	0.982979i	$-0.558814\pi$
$419$	−7.52127			−0.367438			−0.183719	+	0.982979i	$0.558814\pi$
$420$		0			0
$421$	−28.4044	−	20.6370i	−1.38434	−	1.00578i	−0.996459	−	0.0840763i	$-0.973206\pi$
$421$	−28.4044	−	20.6370i	−1.38434	−	1.00578i	−0.387884	−	0.921708i	$-0.626794\pi$
$422$	23.4120	−	17.0098i	1.13968	−	0.828025i
$423$	−0.615578	+	1.89456i	−0.0299304	+	0.0921164i
$424$	0.539823	−	1.66140i	0.0262161	−	0.0806849i
$425$		0			0
$426$	24.3698	+	17.7057i	1.18072	+	0.857844i
$427$	−1.21061	−	3.72588i	−0.0585856	−	0.180308i
$428$	−21.9515			−1.06107
$429$	0.312990	+	3.34466i	0.0151113	+	0.161482i
$430$		0			0
$431$	−9.12268	−	28.0767i	−0.439424	−	1.35241i	−0.888484	−	0.458907i	$-0.848241\pi$
$431$	−9.12268	−	28.0767i	−0.439424	−	1.35241i	0.449060	−	0.893502i	$-0.351759\pi$
$432$	3.86848	+	2.81061i	0.186122	+	0.135226i
$433$	4.43991	−	3.22578i	0.213368	−	0.155021i	−0.475968	−	0.879463i	$-0.657902\pi$
$433$	4.43991	−	3.22578i	0.213368	−	0.155021i	0.689336	+	0.724441i	$0.257902\pi$
$434$	1.09757	−	3.37797i	0.0526850	−	0.162148i
$435$		0			0
$436$	5.21750	−	3.79074i	0.249873	−	0.181543i
$437$	12.2434	+	8.89534i	0.585680	+	0.425522i
$438$	−4.23453	−	13.0325i	−0.202334	−	0.622719i
$439$	7.12848			0.340224			0.170112	−	0.985425i	$-0.445587\pi$
$439$	7.12848			0.340224			0.170112	+	0.985425i	$0.445587\pi$
$440$		0			0
$441$	−5.33910			−0.254243
$442$	4.14430	+	12.7548i	0.197124	+	0.606686i
$443$	12.5647	+	9.12880i	0.596967	+	0.433722i	0.844801	−	0.535080i	$-0.179719\pi$
$443$	12.5647	+	9.12880i	0.596967	+	0.433722i	−0.247834	+	0.968803i	$0.579719\pi$
$444$	−2.30204	+	1.67253i	−0.109250	+	0.0793748i
$445$		0			0
$446$	13.1952	−	40.6107i	0.624812	−	1.92297i
$447$	−17.3778	+	12.6257i	−0.821939	+	0.597174i
$448$	−3.46291	−	2.51595i	−0.163607	−	0.118868i
$449$	−3.32420	−	10.2308i	−0.156879	−	0.482823i	0.841468	−	0.540307i	$-0.181692\pi$
$449$	−3.32420	−	10.2308i	−0.156879	−	0.482823i	−0.998346	+	0.0574843i	$0.981692\pi$
$450$		0			0
$451$	−34.2318	−	7.68551i	−1.61191	−	0.361897i
$452$	20.9542			0.985601
$453$	2.02237	+	6.22422i	0.0950194	+	0.292440i
$454$	12.8431	+	9.33104i	0.602755	+	0.437927i
$455$		0			0
$456$	1.02063	−	3.14117i	0.0477952	−	0.147099i
$457$	−5.11267	+	15.7352i	−0.239161	+	0.736061i	0.757381	+	0.652973i	$0.226478\pi$
$457$	−5.11267	+	15.7352i	−0.239161	+	0.736061i	−0.996542	+	0.0830884i	$0.973522\pi$
$458$	4.18012	−	3.03703i	0.195324	−	0.141911i
$459$	−5.75290	−	4.17973i	−0.268522	−	0.195093i
$460$		0			0
$461$	7.85326			0.365763			0.182881	−	0.983135i	$-0.441458\pi$
$461$	7.85326			0.365763			0.182881	+	0.983135i	$0.441458\pi$
$462$	5.25778	+	5.97510i	0.244614	+	0.277987i
$463$	−15.7430			−0.731638			−0.365819	−	0.930686i	$-0.619211\pi$
$463$	−15.7430			−0.731638			−0.365819	+	0.930686i	$0.619211\pi$
$464$	0.932223	+	2.86909i	0.0432774	+	0.133194i
$465$		0			0
$466$	−29.3711	+	21.3394i	−1.36059	+	0.988527i
$467$	−2.82475	+	8.69369i	−0.130714	+	0.402296i	−0.994899	−	0.100878i	$-0.967835\pi$
$467$	−2.82475	+	8.69369i	−0.130714	+	0.402296i	0.864185	+	0.503174i	$0.167835\pi$
$468$	−0.459227	+	1.41336i	−0.0212278	+	0.0653324i
$469$	−11.0635	+	8.03813i	−0.510866	+	0.371166i
$470$		0			0
$471$	4.33207	+	13.3327i	0.199611	+	0.614340i
$472$	−5.88050			−0.270672
$473$	−5.00536	+	2.16043i	−0.230147	+	0.0993365i
$474$	−31.6673			−1.45453
$475$		0			0
$476$	10.8782	+	7.90345i	0.498600	+	0.362254i
$477$	−1.42460	+	1.03503i	−0.0652277	+	0.0473907i
$478$	5.93719	−	18.2728i	0.271561	−	0.835778i
$479$	−7.27363	+	22.3859i	−0.332340	+	1.02284i	0.635677	+	0.771955i	$0.280721\pi$
$479$	−7.27363	+	22.3859i	−0.332340	+	1.02284i	−0.968017	+	0.250883i	$0.919279\pi$
$480$		0			0
$481$	1.58915	+	1.15458i	0.0724590	+	0.0526445i
$482$	−11.0371	−	33.9687i	−0.502726	−	1.54723i
$483$	5.85823			0.266559
$484$	−2.05292	+	16.0084i	−0.0933146	+	0.727653i
$485$		0			0
$486$	−0.575405	−	1.77091i	−0.0261009	−	0.0803303i
$487$	−5.62391	−	4.08601i	−0.254844	−	0.185155i	0.453027	−	0.891497i	$-0.350344\pi$
$487$	−5.62391	−	4.08601i	−0.254844	−	0.185155i	−0.707871	+	0.706342i	$0.750344\pi$
$488$	−2.43974	+	1.77257i	−0.110442	+	0.0802405i
$489$	−0.379172	+	1.16697i	−0.0171467	+	0.0527722i
$490$		0			0
$491$	−16.4599	+	11.9588i	−0.742824	+	0.539693i	−0.893594	−	0.448876i	$-0.851825\pi$
$491$	−16.4599	+	11.9588i	−0.742824	+	0.539693i	0.150770	+	0.988569i	$0.451825\pi$
$492$	−12.5564	−	9.12278i	−0.566087	−	0.411287i
$493$	−1.38633	−	4.26668i	−0.0624371	−	0.192162i
$494$	6.27898			0.282505
$495$		0			0
$496$	−7.07731			−0.317781
$497$	−6.44255	−	19.8281i	−0.288988	−	0.889414i
$498$	−13.7234	−	9.97062i	−0.614960	−	0.446794i
$499$	10.6009	−	7.70201i	0.474562	−	0.344789i	−0.324655	−	0.945833i	$-0.605248\pi$
$499$	10.6009	−	7.70201i	0.474562	−	0.344789i	0.799217	+	0.601043i	$0.205248\pi$
$500$		0			0
$501$	−4.51137	+	13.8846i	−0.201553	+	0.620317i
$502$	39.2149	−	28.4913i	1.75025	−	1.27163i
$503$	1.53214	+	1.11317i	0.0683149	+	0.0496337i	0.621419	−	0.783479i	$-0.286557\pi$
$503$	1.53214	+	1.11317i	0.0683149	+	0.0496337i	−0.553104	+	0.833112i	$0.686557\pi$
$504$	−0.395084	−	1.21594i	−0.0175985	−	0.0541625i
$505$		0			0
$506$	18.5449	+	21.0750i	0.824421	+	0.936897i
$507$	−11.9741			−0.531789
$508$	7.80448	+	24.0197i	0.346268	+	1.06570i
$509$	−27.8663	−	20.2461i	−1.23515	−	0.897391i	−0.237888	−	0.971293i	$-0.576455\pi$
$509$	−27.8663	−	20.2461i	−1.23515	−	0.897391i	−0.997266	+	0.0739012i	$0.976455\pi$
$510$		0			0
$511$	−2.93080	+	9.02008i	−0.129651	+	0.399025i
$512$	−7.29289	+	22.4452i	−0.322303	+	0.991948i
$513$	−2.69344	+	1.95690i	−0.118918	+	0.0863991i
$514$	−28.3388	−	20.5893i	−1.24997	−	0.908157i
$515$		0			0
$516$	−2.41175			−0.106171
$517$	6.44642	+	1.44731i	0.283513	+	0.0636527i
$518$	4.65395			0.204483
$519$	−1.88277	−	5.79458i	−0.0826446	−	0.254354i
$520$		0			0
$521$	14.2222	−	10.3331i	0.623088	−	0.452700i	−0.230911	−	0.972975i	$-0.574171\pi$
$521$	14.2222	−	10.3331i	0.623088	−	0.452700i	0.853999	+	0.520275i	$0.174171\pi$
$522$	0.363018	−	1.11725i	0.0158889	−	0.0489009i
$523$	11.3427	−	34.9093i	0.495982	−	1.52648i	−0.319438	−	0.947607i	$-0.603494\pi$
$523$	11.3427	−	34.9093i	0.495982	−	1.52648i	0.815421	−	0.578869i	$-0.196506\pi$
$524$	−4.67606	+	3.39736i	−0.204275	+	0.148414i
$525$		0			0
$526$	−7.43048	−	22.8687i	−0.323984	−	0.997121i
$527$	10.5248			0.458469
$528$	8.08578	−	13.6430i	0.351888	−	0.593736i
$529$	−2.33722			−0.101618
$530$		0			0
$531$	4.79553	+	3.48416i	0.208108	+	0.151199i
$532$	5.09303	−	3.70030i	0.220811	−	0.160428i
$533$	−3.31087	+	10.1898i	−0.143410	+	0.441370i
$534$	0.0797678	−	0.245500i	0.00345189	−	0.0106238i
$535$		0			0
$536$	8.51641	+	6.18753i	0.367853	+	0.267261i
$537$	−0.183246	−	0.563973i	−0.00790764	−	0.0243372i
$538$	−42.0324			−1.81215
$539$	1.64987	+	17.6307i	0.0710650	+	0.759410i
$540$		0			0
$541$	9.52302	+	29.3088i	0.409427	+	1.26009i	0.917142	+	0.398561i	$0.130490\pi$
$541$	9.52302	+	29.3088i	0.409427	+	1.26009i	−0.507715	+	0.861525i	$0.669510\pi$
$542$	−23.1819	−	16.8426i	−0.995748	−	0.723453i
$543$	−16.7216	+	12.1490i	−0.717593	+	0.521362i
$544$	15.2053	−	46.7972i	0.651923	−	2.00641i
$545$		0			0
$546$	1.96639	−	1.42867i	0.0841537	−	0.0611412i
$547$	−5.69336	−	4.13647i	−0.243430	−	0.176862i	0.459380	−	0.888240i	$-0.348072\pi$
$547$	−5.69336	−	4.13647i	−0.243430	−	0.176862i	−0.702810	+	0.711377i	$0.748072\pi$
$548$	−9.24949	−	28.4670i	−0.395119	−	1.21605i
$549$	3.03983			0.129737
$550$		0			0
$551$	−2.10041			−0.0894805
$552$	−1.39352	−	4.28880i	−0.0593120	−	0.182543i
$553$	17.7317	+	12.8828i	0.754027	+	0.547833i
$554$	19.2992	−	14.0217i	0.819945	−	0.595725i
$555$		0			0
$556$	−5.13356	+	15.7995i	−0.217711	+	0.670046i
$557$	0.394276	−	0.286458i	0.0167060	−	0.0121376i	−0.579401	−	0.815043i	$-0.696713\pi$
$557$	0.394276	−	0.286458i	0.0167060	−	0.0121376i	0.596107	+	0.802905i	$0.296713\pi$
$558$	2.22964	+	1.61993i	0.0943881	+	0.0685770i
$559$	0.514478	+	1.58340i	0.0217601	+	0.0669707i
$560$		0			0
$561$	−12.0245	+	20.2888i	−0.507676	+	0.856594i
$562$	11.8835			0.501276
$563$	−3.24947	−	10.0009i	−0.136949	−	0.421486i	0.858939	−	0.512078i	$-0.171124\pi$
$563$	−3.24947	−	10.0009i	−0.136949	−	0.421486i	−0.995888	+	0.0905921i	$0.971124\pi$
$564$	2.36459	+	1.71797i	0.0995671	+	0.0723397i
$565$		0			0
$566$	12.1534	−	37.4043i	0.510845	−	1.57222i
$567$	−0.398249	+	1.22568i	−0.0167249	+	0.0514739i
$568$	−12.9836	+	9.43316i	−0.544781	+	0.395807i
$569$	−28.3627	−	20.6067i	−1.18903	−	0.863878i	−0.195865	−	0.980631i	$-0.562751\pi$
$569$	−28.3627	−	20.6067i	−1.18903	−	0.863878i	−0.993161	+	0.116753i	$0.962751\pi$
$570$		0			0
$571$	22.2489			0.931089			0.465544	−	0.885025i	$-0.345859\pi$
$571$	22.2489			0.931089			0.465544	+	0.885025i	$0.345859\pi$
$572$	4.80909	+	1.07971i	0.201078	+	0.0451448i
$573$	8.69712			0.363327
$574$	7.84436	+	24.1425i	0.327417	+	1.00769i
$575$		0			0
$576$	2.68701	−	1.95223i	0.111959	−	0.0813428i
$577$	0.527233	−	1.62266i	0.0219490	−	0.0675521i	−0.939482	−	0.342598i	$-0.888693\pi$
$577$	0.527233	−	1.62266i	0.0219490	−	0.0675521i	0.961431	+	0.275046i	$0.0886931\pi$
$578$	−19.3140	+	59.4424i	−0.803357	+	2.47248i
$579$	−12.9626	+	9.41790i	−0.538708	+	0.391394i
$580$		0			0
$581$	3.62800	+	11.1658i	0.150515	+	0.463237i
$582$	−10.0454			−0.416396
$583$	3.85809	+	4.38445i	0.159786	+	0.181586i
$584$	7.30074			0.302107
$585$		0			0
$586$	−37.5526	−	27.2835i	−1.55128	−	1.12707i
$587$	1.92350	−	1.39750i	0.0793913	−	0.0576812i	−0.547382	−	0.836883i	$-0.684375\pi$
$587$	1.92350	−	1.39750i	0.0793913	−	0.0576812i	0.626773	+	0.779202i	$0.284375\pi$
$588$	−2.42073	+	7.45025i	−0.0998293	+	0.307243i
$589$	1.52271	−	4.68643i	0.0627422	−	0.193101i
$590$		0			0
$591$	5.61740	+	4.08128i	0.231069	+	0.167882i
$592$	−2.86565	−	8.81957i	−0.117778	−	0.362482i
$593$	11.4985			0.472188			0.236094	−	0.971730i	$-0.424133\pi$
$593$	11.4985			0.472188			0.236094	+	0.971730i	$0.424133\pi$
$594$	−5.67010	+	2.44734i	−0.232647	+	0.100416i
$595$		0			0
$596$	9.73901	+	29.9736i	0.398926	+	1.22777i
$597$	16.6992	+	12.1327i	0.683454	+	0.496559i
$598$	6.93572	−	5.03909i	0.283623	−	0.206064i
$599$	4.51027	−	13.8812i	0.184285	−	0.567170i	−0.815651	−	0.578545i	$-0.803621\pi$
$599$	4.51027	−	13.8812i	0.184285	−	0.567170i	0.999935	+	0.0113747i	$0.00362077\pi$
$600$		0			0
$601$	4.76118	−	3.45920i	0.194213	−	0.141104i	−0.486429	−	0.873720i	$-0.661701\pi$
$601$	4.76118	−	3.45920i	0.194213	−	0.141104i	0.680642	+	0.732616i	$0.261701\pi$
$602$	3.19122	+	2.31856i	0.130064	+	0.0944973i
$603$	−3.27904	−	10.0918i	−0.133533	−	0.410971i
$604$	9.60231			0.390712
$605$		0			0
$606$	16.0576			0.652296
$607$	−6.45361	−	19.8622i	−0.261944	−	0.806180i	−0.992382	−	0.123201i	$-0.960684\pi$
$607$	−6.45361	−	19.8622i	−0.261944	−	0.806180i	0.730438	−	0.682979i	$-0.239316\pi$
$608$	−18.6377	−	13.5411i	−0.755857	−	0.549162i
$609$	−0.657786	+	0.477910i	−0.0266548	+	0.0193659i
$610$		0			0
$611$	0.623493	−	1.91892i	0.0252238	−	0.0776310i
$612$	−8.44080	+	6.13260i	−0.341199	+	0.247896i
$613$	−20.1003	−	14.6037i	−0.811843	−	0.589838i	0.102522	−	0.994731i	$-0.467309\pi$
$613$	−20.1003	−	14.6037i	−0.811843	−	0.589838i	−0.914364	+	0.404893i	$0.867309\pi$
$614$	−18.2055	−	56.0307i	−0.734714	−	2.26122i
$615$		0			0
$616$	−3.89320	+	1.68039i	−0.156862	+	0.0677050i
$617$	1.41531			0.0569783			0.0284892	−	0.999594i	$-0.490930\pi$
$617$	1.41531			0.0569783			0.0284892	+	0.999594i	$0.490930\pi$
$618$	5.27739	+	16.2421i	0.212288	+	0.653354i
$619$	9.34582	+	6.79013i	0.375640	+	0.272918i	0.759546	−	0.650454i	$-0.225421\pi$
$619$	9.34582	+	6.79013i	0.375640	+	0.272918i	−0.383906	+	0.923372i	$0.625421\pi$
$620$		0			0
$621$	−1.40468	+	4.32315i	−0.0563678	+	0.173482i
$622$	1.72227	−	5.30061i	0.0690568	−	0.212535i
$623$	−0.144539	+	0.105013i	−0.00579082	+	0.00420728i
$624$	−3.91822	−	2.84675i	−0.156854	−	0.113961i
$625$		0			0
$626$	−3.63747			−0.145383
$627$	7.29438	+	8.28955i	0.291310	+	0.331053i
$628$	20.5688			0.820785
$629$	4.26157	+	13.1158i	0.169920	+	0.522960i
$630$		0			0
$631$	−20.3672	+	14.7976i	−0.810806	+	0.589085i	−0.914064	−	0.405570i	$-0.867073\pi$
$631$	−20.3672	+	14.7976i	−0.810806	+	0.589085i	0.103258	+	0.994655i	$0.467073\pi$
$632$	5.21359	−	16.0458i	0.207386	−	0.638267i
$633$	4.80256	−	14.7807i	0.190884	−	0.587482i
$634$	35.0770	−	25.4849i	1.39309	−	1.01214i
$635$		0			0
$636$	0.798386	+	2.45718i	0.0316581	+	0.0974335i
$637$	5.40774			0.214263
$638$	−3.80157	−	0.853507i	−0.150506	−	0.0337907i
$639$	16.1772			0.639960
$640$		0			0
$641$	20.5722	+	14.9466i	0.812554	+	0.590355i	0.914570	−	0.404427i	$-0.132529\pi$
$641$	20.5722	+	14.9466i	0.812554	+	0.590355i	−0.102016	+	0.994783i	$0.532529\pi$
$642$	−22.5381	+	16.3749i	−0.889507	+	0.646265i
$643$	11.7750	−	36.2398i	0.464361	−	1.42916i	−0.395423	−	0.918499i	$-0.629402\pi$
$643$	11.7750	−	36.2398i	0.464361	−	1.42916i	0.859784	−	0.510658i	$-0.170598\pi$
$644$	2.65611	−	8.17466i	0.104665	−	0.322127i
$645$		0			0
$646$	35.6638	+	25.9112i	1.40317	+	1.01946i
$647$	−10.8153	−	33.2862i	−0.425195	−	1.30861i	−0.902808	−	0.430044i	$-0.858498\pi$
$647$	−10.8153	−	33.2862i	−0.425195	−	1.30861i	0.477613	−	0.878570i	$-0.341502\pi$
$648$	0.992053			0.0389715
$649$	10.0235	−	16.9124i	0.393456	−	0.663872i
$650$		0			0
$651$	−0.589441	−	1.81411i	−0.0231020	−	0.0711007i
$652$	1.45649	+	1.05820i	0.0570406	+	0.0414424i
$653$	−24.4530	+	17.7662i	−0.956921	+	0.695244i	−0.952434	−	0.304746i	$-0.901428\pi$
$653$	−24.4530	+	17.7662i	−0.956921	+	0.695244i	−0.00448717	+	0.999990i	$0.501428\pi$
$654$	2.52919	−	7.78405i	0.0988992	−	0.304381i
$655$		0			0
$656$	40.9215	−	29.7312i	1.59772	−	1.16081i
$657$	−5.95374	−	4.32564i	−0.232277	−	0.168759i
$658$	−1.47722	−	4.54643i	−0.0575882	−	0.177238i
$659$	27.5598			1.07358			0.536790	−	0.843716i	$-0.319637\pi$
$659$	27.5598			1.07358			0.536790	+	0.843716i	$0.319637\pi$
$660$		0			0
$661$	−16.4272			−0.638945			−0.319472	−	0.947596i	$-0.603506\pi$
$661$	−16.4272			−0.638945			−0.319472	+	0.947596i	$0.603506\pi$
$662$	−18.5855	−	57.2004i	−0.722347	−	2.22316i
$663$	5.82687	+	4.23347i	0.226297	+	0.164414i
$664$	7.31148	−	5.31210i	0.283740	−	0.206149i
$665$		0			0
$666$	−1.11592	+	3.43444i	−0.0432409	+	0.133082i
$667$	−2.32010	+	1.68565i	−0.0898347	+	0.0652687i
$668$	17.3293	+	12.5905i	0.670490	+	0.487139i
$669$	−7.08641	−	21.8097i	−0.273976	−	0.843212i
$670$		0			0
$671$	−0.939361	−	10.0381i	−0.0362636	−	0.387518i
$672$	−8.91778			−0.344011
$673$	−11.7416	−	36.1370i	−0.452606	−	1.39298i	−0.873922	−	0.486065i	$-0.838432\pi$
$673$	−11.7416	−	36.1370i	−0.452606	−	1.39298i	0.421316	−	0.906914i	$-0.361568\pi$
$674$	−1.76787	−	1.28444i	−0.0680960	−	0.0494746i
$675$		0			0
$676$	−5.42903	+	16.7088i	−0.208809	+	0.642648i
$677$	−5.50753	+	16.9504i	−0.211671	+	0.651458i	0.787702	+	0.616057i	$0.211271\pi$
$677$	−5.50753	+	16.9504i	−0.211671	+	0.651458i	−0.999373	+	0.0354010i	$0.988729\pi$
$678$	21.5141	−	15.6309i	0.826242	−	0.600300i
$679$	5.62480	+	4.08666i	0.215860	+	0.156832i
$680$		0			0
$681$	8.52551			0.326698
$682$	4.66032	−	7.86329i	0.178453	−	0.301101i
$683$	6.53811			0.250174			0.125087	−	0.992146i	$-0.460079\pi$
$683$	6.53811			0.250174			0.125087	+	0.992146i	$0.460079\pi$
$684$	1.50948	+	4.64571i	0.0577166	+	0.177633i
$685$		0			0
$686$	23.9554	−	17.4047i	0.914623	−	0.664513i
$687$	0.857476	−	2.63904i	0.0327148	−	0.100686i
$688$	2.42885	−	7.47523i	0.0925990	−	0.284990i
$689$	1.44291	−	1.04834i	0.0549706	−	0.0399385i
$690$		0			0
$691$	8.13983	+	25.0518i	0.309654	+	0.953016i	0.977900	+	0.209075i	$0.0670454\pi$
$691$	8.13983	+	25.0518i	0.309654	+	0.953016i	−0.668246	+	0.743940i	$0.732955\pi$
$692$	−8.93949			−0.339828
$693$	4.17052	+	0.936339i	0.158425	+	0.0355686i
$694$	22.6916			0.861360
$695$		0			0
$696$	0.506346	+	0.367882i	0.0191930	+	0.0139445i
$697$	−60.8553	+	44.2140i	−2.30506	+	1.67472i
$698$	−4.37187	+	13.4552i	−0.165478	+	0.509288i
$699$	−6.02496	+	18.5429i	−0.227885	+	0.701357i
$700$		0			0
$701$	−7.97700	−	5.79563i	−0.301287	−	0.218898i	0.426862	−	0.904317i	$-0.359619\pi$
$701$	−7.97700	−	5.79563i	−0.301287	−	0.218898i	−0.728149	+	0.685419i	$0.759619\pi$
$702$	0.582803	+	1.79368i	0.0219965	+	0.0676982i
$703$	6.45666			0.243518
$704$	−7.27697	−	8.26977i	−0.274261	−	0.311679i
$705$		0			0
$706$	13.6891	+	42.1308i	0.515197	+	1.58561i
$707$	−8.99124	−	6.53252i	−0.338150	−	0.245681i
$708$	7.03612	−	5.11204i	0.264433	−	0.192122i
$709$	−6.50658	+	20.0252i	−0.244360	+	0.752062i	0.751381	+	0.659868i	$0.229388\pi$
$709$	−6.50658	+	20.0252i	−0.244360	+	0.752062i	−0.995741	+	0.0921936i	$0.970612\pi$
$710$		0			0
$711$	−13.7587	+	9.99628i	−0.515991	+	0.374890i
$712$	0.111262	+	0.0808366i	0.00416972	+	0.00302948i
$713$	−2.07904	−	6.39862i	−0.0778606	−	0.239630i
$714$	17.0645			0.638621
$715$		0			0
$716$	−0.870058			−0.0325156
$717$	−3.18853	−	9.81328i	−0.119078	−	0.366484i
$718$	44.8605	+	32.5930i	1.67418	+	1.21636i
$719$	20.7601	−	15.0831i	0.774219	−	0.562503i	−0.129019	−	0.991642i	$-0.541183\pi$
$719$	20.7601	−	15.0831i	0.774219	−	0.562503i	0.903239	+	0.429139i	$0.141183\pi$
$720$		0			0
$721$	3.65259	−	11.2415i	0.136029	−	0.418655i
$722$	−11.9248	+	8.66387i	−0.443795	+	0.322436i
$723$	−15.5181	−	11.2746i	−0.577125	−	0.419306i
$724$	9.37129	+	28.8419i	0.348281	+	1.07190i
$725$		0			0
$726$	9.83376	+	17.9675i	0.364965	+	0.666837i
$727$	45.4536			1.68578			0.842891	−	0.538085i	$-0.180852\pi$
$727$	45.4536			1.68578			0.842891	+	0.538085i	$0.180852\pi$
$728$	0.400164	+	1.23158i	0.0148311	+	0.0456453i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−3.61199	+	11.1166i	−0.133594	+	0.411161i
$732$	1.37825	−	4.24183i	0.0509417	−	0.156782i
$733$	36.8435	−	26.7683i	1.36084	−	0.988711i	0.362453	−	0.932002i	$-0.381939\pi$
$733$	36.8435	−	26.7683i	1.36084	−	0.988711i	0.998391	−	0.0567093i	$-0.0180608\pi$
$734$	1.73526	+	1.26074i	0.0640498	+	0.0465349i
$735$		0			0
$736$	−31.4542			−1.15942
$737$	−32.3120	+	13.9466i	−1.19023	+	0.513729i
$738$	−19.6971			−0.725061
$739$	2.23907	+	6.89115i	0.0823656	+	0.253495i	0.983756	−	0.179513i	$-0.0574522\pi$
$739$	2.23907	+	6.89115i	0.0823656	+	0.253495i	−0.901390	+	0.433008i	$0.857452\pi$
$740$		0			0
$741$	2.72807	−	1.98206i	0.100218	−	0.0728128i
$742$	1.30581	−	4.01887i	0.0479377	−	0.147537i
$743$	−3.59014	+	11.0493i	−0.131709	+	0.405360i	−0.995064	−	0.0992384i	$-0.968359\pi$
$743$	−3.59014	+	11.0493i	−0.131709	+	0.405360i	0.863354	+	0.504598i	$0.168359\pi$
$744$	−1.18790	+	0.863057i	−0.0435504	+	0.0316412i
$745$		0			0
$746$	−19.9790	−	61.4889i	−0.731482	−	2.25127i
$747$	−9.10988			−0.333313
$748$	22.8594	+	25.9781i	0.835822	+	0.949853i
$749$	19.2815			0.704530
$750$		0			0
$751$	−23.6190	−	17.1602i	−0.861870	−	0.626185i	0.0665229	−	0.997785i	$-0.478809\pi$
$751$	−23.6190	−	17.1602i	−0.861870	−	0.626185i	−0.928393	+	0.371600i	$0.878809\pi$
$752$	−7.70621	+	5.59889i	−0.281017	+	0.204171i
$753$	8.04424	−	24.7576i	0.293149	−	0.902219i
$754$	−0.367686	+	1.13162i	−0.0133903	+	0.0412112i
$755$		0			0
$756$	1.52977	+	1.11144i	0.0556373	+	0.0404228i
$757$	13.9904	+	43.0579i	0.508488	+	1.56497i	0.794826	+	0.606837i	$0.207562\pi$
$757$	13.9904	+	43.0579i	0.508488	+	1.56497i	−0.286338	+	0.958129i	$0.592438\pi$
$758$	58.7991			2.13568
$759$	14.7100	+	3.30260i	0.533938	+	0.119877i
$760$		0			0
$761$	−5.20682	−	16.0249i	−0.188747	−	0.580903i	0.811246	−	0.584705i	$-0.198790\pi$
$761$	−5.20682	−	16.0249i	−0.188747	−	0.580903i	−0.999993	+	0.00380191i	$0.998790\pi$
$762$	25.9306	+	18.8397i	0.939368	+	0.682491i
$763$	−4.58288	+	3.32966i	−0.165911	+	0.120542i
$764$	3.94325	−	12.1361i	0.142662	−	0.439068i
$765$		0			0
$766$	33.5671	−	24.3880i	1.21283	−	0.881172i
$767$	−4.85719	−	3.52895i	−0.175383	−	0.127423i
$768$	6.45732	+	19.8736i	0.233008	+	0.717126i
$769$	−1.13686			−0.0409960			−0.0204980	−	0.999790i	$-0.506525\pi$
$769$	−1.13686			−0.0409960			−0.0204980	+	0.999790i	$0.506525\pi$
$770$		0			0
$771$	−18.8119			−0.677494
$772$	7.26464	+	22.3583i	0.261460	+	0.804692i
$773$	−40.3369	−	29.3064i	−1.45082	−	1.05408i	−0.985640	−	0.168862i	$-0.945991\pi$
$773$	−40.3369	−	29.3064i	−1.45082	−	1.05408i	−0.465176	−	0.885218i	$-0.654009\pi$
$774$	−2.47619	+	1.79906i	−0.0890049	+	0.0646658i
$775$		0			0
$776$	1.65384	−	5.09001i	0.0593696	−	0.182721i
$777$	2.02203	−	1.46909i	0.0725401	−	0.0527035i
$778$	−36.5748	−	26.5731i	−1.31127	−	0.952693i
$779$	10.8829	+	33.4940i	0.389919	+	1.20005i
$780$		0			0
$781$	−4.99903	−	53.4203i	−0.178879	−	1.91153i
$782$	60.1886			2.15234
$783$	−0.194956	−	0.600014i	−0.00696717	−	0.0214427i
$784$	−20.6542	−	15.0061i	−0.737649	−	0.535933i
$785$		0			0
$786$	−2.26673	+	6.97627i	−0.0808515	+	0.248835i
$787$	0.0979582	−	0.301484i	0.00349183	−	0.0107468i	−0.949295	−	0.314385i	$-0.898202\pi$
$787$	0.0979582	−	0.301484i	0.00349183	−	0.0107468i	0.952787	+	0.303639i	$0.0982016\pi$
$788$	8.24199	−	5.98816i	0.293609	−	0.213319i
$789$	−10.4472	−	7.59035i	−0.371931	−	0.270224i
$790$		0			0
$791$	−18.4054			−0.654422
$792$	−0.306561	−	3.27596i	−0.0108932	−	0.116406i
$793$	−3.07892			−0.109336
$794$	−21.5003	−	66.1710i	−0.763016	−	2.34832i
$795$		0			0
$796$	24.5015	−	17.8014i	0.868434	−	0.630954i
$797$	1.07175	−	3.29851i	0.0379634	−	0.116839i	−0.930279	−	0.366853i	$-0.880435\pi$
$797$	1.07175	−	3.29851i	0.0379634	−	0.116839i	0.968242	+	0.250014i	$0.0804352\pi$
$798$	2.46885	−	7.59835i	0.0873964	−	0.268979i
$799$	11.4601	−	8.32624i	0.405429	−	0.294561i
$800$		0			0
$801$	−0.0428387	−	0.131844i	−0.00151363	−	0.00465848i
$802$	7.21322			0.254708
$803$	−12.4443	+	20.9971i	−0.439151	+	0.740972i
$804$	−15.5690			−0.549076
$805$		0			0
$806$	−2.25831	−	1.64076i	−0.0795455	−	0.0577932i
$807$	−18.2621	+	13.2682i	−0.642857	+	0.467063i
$808$	−2.64367	+	8.13638i	−0.0930040	+	0.286237i
$809$	−7.95520	+	24.4836i	−0.279690	+	0.860797i	0.708250	+	0.705962i	$0.249485\pi$
$809$	−7.95520	+	24.4836i	−0.279690	+	0.860797i	−0.987940	+	0.154836i	$0.950515\pi$
$810$		0			0
$811$	14.7677	+	10.7293i	0.518563	+	0.376758i	0.816062	−	0.577964i	$-0.196153\pi$
$811$	14.7677	+	10.7293i	0.518563	+	0.376758i	−0.297499	+	0.954722i	$0.596153\pi$
$812$	0.368643	+	1.13457i	0.0129368	+	0.0398155i
$813$	−15.3887			−0.539704
$814$	11.6860	+	2.62368i	0.409595	+	0.0919599i
$815$		0			0
$816$	−10.5074	−	32.3384i	−0.367831	−	1.13207i
$817$	4.42734	+	3.21665i	0.154893	+	0.112536i
$818$	47.9165	−	34.8134i	1.67536	−	1.21722i
$819$	0.403370	−	1.24144i	0.0140949	−	0.0433796i
$820$		0			0
$821$	−10.1862	+	7.40069i	−0.355500	+	0.258286i	−0.751173	−	0.660106i	$-0.770511\pi$
$821$	−10.1862	+	7.40069i	−0.355500	+	0.258286i	0.395673	+	0.918392i	$0.370511\pi$
$822$	−30.7318	−	22.3279i	−1.07189	−	0.778776i
$823$	−1.24274	−	3.82475i	−0.0433191	−	0.133323i	0.927058	−	0.374918i	$-0.122329\pi$
$823$	−1.24274	−	3.82475i	−0.0433191	−	0.133323i	−0.970377	+	0.241596i	$0.922329\pi$
$824$	−9.09873			−0.316969
$825$		0			0
$826$	−14.2247			−0.494939
$827$	−10.7447	−	33.0688i	−0.373630	−	1.14992i	−0.944398	−	0.328804i	$-0.893354\pi$
$827$	−10.7447	−	33.0688i	−0.373630	−	1.14992i	0.570768	−	0.821111i	$-0.306646\pi$
$828$	5.39571	+	3.92021i	0.187514	+	0.136237i
$829$	−6.69049	+	4.86092i	−0.232370	+	0.168827i	−0.697877	−	0.716217i	$-0.745872\pi$
$829$	−6.69049	+	4.86092i	−0.232370	+	0.168827i	0.465507	+	0.885044i	$0.345872\pi$
$830$		0			0
$831$	3.95889	−	12.1842i	0.137332	−	0.422665i
$832$	−2.72156	+	1.97733i	−0.0943531	+	0.0685515i
$833$	30.7153	+	22.3160i	1.06422	+	0.773202i
$834$	6.51497	+	20.0510i	0.225595	+	0.694310i
$835$		0			0
$836$	14.8746	−	6.42022i	0.514449	−	0.222048i
$837$	1.48008			0.0511591
$838$	4.32778	+	13.3195i	0.149501	+	0.460115i
$839$	13.4243	+	9.75333i	0.463458	+	0.336722i	0.794886	−	0.606758i	$-0.207530\pi$
$839$	13.4243	+	9.75333i	0.463458	+	0.336722i	−0.331428	+	0.943481i	$0.607530\pi$
$840$		0			0
$841$	−8.83850	+	27.2021i	−0.304776	+	0.938003i
$842$	−20.2023	+	62.1763i	−0.696217	+	2.14274i
$843$	5.16312	−	3.75123i	0.177827	−	0.129199i
$844$	−18.4478	−	13.4031i	−0.634999	−	0.461354i
$845$		0			0
$846$	3.70930			0.127528
$847$	1.80322	−	14.0612i	0.0619593	−	0.483149i
$848$	−8.42008			−0.289147
$849$	−6.52689	−	20.0877i	−0.224002	−	0.689409i
$850$		0			0
$851$	7.13199	−	5.18169i	0.244481	−	0.177626i
$852$	7.33470	−	22.5739i	0.251283	−	0.773369i
$853$	−0.0227434	+	0.0699971i	−0.000778720	+	0.00239666i	−0.951445	−	0.307818i	$-0.900401\pi$
$853$	−0.0227434	+	0.0699971i	−0.000778720	+	0.00239666i	0.950666	+	0.310215i	$0.100401\pi$
$854$	−5.90162	+	4.28778i	−0.201949	+	0.146725i
$855$		0			0
$856$	−4.58654	−	14.1159i	−0.156765	−	0.482473i
$857$	30.2115			1.03200			0.516002	−	0.856587i	$-0.327420\pi$
$857$	30.2115			1.03200			0.516002	+	0.856587i	$0.327420\pi$
$858$	5.74300	−	2.47881i	0.196063	−	0.0846252i
$859$	6.71583			0.229141			0.114571	−	0.993415i	$-0.463451\pi$
$859$	6.71583			0.229141			0.114571	+	0.993415i	$0.463451\pi$
$860$		0			0
$861$	11.0291	+	8.01314i	0.375872	+	0.273087i
$862$	−44.4722	+	32.3110i	−1.51473	+	1.10052i
$863$	14.2721	−	43.9250i	0.485828	−	1.49523i	−0.344950	−	0.938621i	$-0.612104\pi$
$863$	14.2721	−	43.9250i	0.485828	−	1.49523i	0.830778	−	0.556604i	$-0.187896\pi$
$864$	2.13829	−	6.58098i	0.0727461	−	0.223890i
$865$		0			0
$866$	−8.26733	−	6.00656i	−0.280935	−	0.204111i
$867$	10.3725	+	31.9231i	0.352267	+	1.08417i
$868$	−2.79869			−0.0949937
$869$	37.2614	+	42.3449i	1.26400	+	1.43645i
$870$		0			0
$871$	3.32120	+	10.2216i	0.112534	+	0.346346i
$872$	3.52778	+	2.56308i	0.119466	+	0.0867968i
$873$	−4.36450	+	3.17100i	−0.147716	+	0.107322i
$874$	8.70798	−	26.8004i	0.294552	−	0.906537i
$875$		0			0
$876$	−8.73547	+	6.34669i	−0.295144	+	0.214435i
$877$	−12.3102	−	8.94385i	−0.415685	−	0.302013i	0.360215	−	0.932869i	$-0.382703\pi$
$877$	−12.3102	−	8.94385i	−0.415685	−	0.302013i	−0.775899	+	0.630857i	$0.782703\pi$
$878$	−4.10176	−	12.6239i	−0.138428	−	0.426037i
$879$	−24.9282			−0.840808
$880$		0			0
$881$	−22.7839			−0.767609			−0.383804	−	0.923414i	$-0.625386\pi$
$881$	−22.7839			−0.767609			−0.383804	+	0.923414i	$0.625386\pi$
$882$	3.07214	+	9.45508i	0.103444	+	0.318369i
$883$	−8.36163	−	6.07508i	−0.281391	−	0.204443i	0.438133	−	0.898910i	$-0.355640\pi$
$883$	−8.36163	−	6.07508i	−0.281391	−	0.204443i	−0.719524	+	0.694468i	$0.755640\pi$
$884$	8.54933	−	6.21145i	0.287545	−	0.208914i
$885$		0			0
$886$	8.93652	−	27.5038i	0.300228	−	0.924007i
$887$	−43.0389	+	31.2696i	−1.44511	+	1.04993i	−0.458162	+	0.888869i	$0.651492\pi$
$887$	−43.0389	+	31.2696i	−1.44511	+	1.04993i	−0.986944	+	0.161062i	$0.948508\pi$
$888$	−1.55651	−	1.13087i	−0.0522330	−	0.0379495i
$889$	−6.85519	−	21.0981i	−0.229916	−	0.707608i
$890$		0			0
$891$	−1.69098	+	2.85317i	−0.0566501	+	0.0955848i
$892$	−33.6465			−1.12657
$893$	−2.04943	−	6.30749i	−0.0685815	−	0.211072i
$894$	32.3582	+	23.5096i	1.08222	+	0.786279i
$895$		0			0
$896$	3.04853	−	9.38241i	0.101844	−	0.313444i
$897$	1.42274	−	4.37874i	0.0475039	−	0.146202i
$898$	−16.2052	+	11.7737i	−0.540773	+	0.392895i
$899$	0.755437	+	0.548857i	0.0251952	+	0.0183054i
$900$		0			0
$901$	12.5217			0.417158
$902$	6.08674	+	65.0438i	0.202666	+	2.16572i
$903$	2.11840			0.0704959
$904$	4.37815	+	13.4746i	0.145615	+	0.448158i
$905$		0			0
$906$	9.85888	−	7.16290i	0.327539	−	0.237971i
$907$	4.20935	−	12.9551i	0.139769	−	0.430165i	−0.856532	−	0.516094i	$-0.827386\pi$
$907$	4.20935	−	12.9551i	0.139769	−	0.430165i	0.996301	+	0.0859283i	$0.0273856\pi$
$908$	3.86544	−	11.8966i	0.128279	−	0.394803i
$909$	6.97666	−	5.06884i	0.231401	−	0.168123i
$910$		0			0
$911$	7.81952	+	24.0660i	0.259072	+	0.797342i	0.993000	+	0.118115i	$0.0376850\pi$
$911$	7.81952	+	24.0660i	0.259072	+	0.797342i	−0.733928	+	0.679227i	$0.762315\pi$
$912$	−15.9196			−0.527150
$913$	2.81511	+	30.0826i	0.0931664	+	0.995589i
$914$	30.8075			1.01902
$915$		0			0
$916$	−3.29377	−	2.39307i	−0.108829	−	0.0790692i
$917$	4.10729	−	2.98412i	0.135635	−	0.0985444i
$918$	−4.09169	+	12.5929i	−0.135046	+	0.415628i
$919$	−3.24182	+	9.97729i	−0.106938	+	0.329120i	−0.990180	−	0.139796i	$-0.955355\pi$
$919$	−3.24182	+	9.97729i	−0.106938	+	0.329120i	0.883243	+	0.468916i	$0.155355\pi$
$920$		0			0
$921$	−25.5969	−	18.5972i	−0.843445	−	0.612799i
$922$	−4.51880	−	13.9074i	−0.148819	−	0.458017i
$923$	−16.3852			−0.539326
$924$	3.19748	−	5.39506i	0.105189	−	0.177485i
$925$		0			0
$926$	9.05857	+	27.8794i	0.297683	+	0.916175i
$927$	7.41999	+	5.39094i	0.243704	+	0.177062i
$928$	3.53181	−	2.56601i	0.115937	−	0.0842333i
$929$	−5.31856	+	16.3688i	−0.174496	+	0.537044i	−0.999610	−	0.0279222i	$-0.991111\pi$
$929$	−5.31856	+	16.3688i	−0.174496	+	0.537044i	0.825114	+	0.564967i	$0.191111\pi$
$930$		0			0
$931$	14.3805	−	10.4481i	0.471303	−	0.342421i
$932$	23.1433	+	16.8146i	0.758085	+	0.550781i
$933$	−0.924934	−	2.84665i	−0.0302810	−	0.0931953i
$934$	17.0212			0.556949
$935$		0			0
$936$	−1.00481			−0.0328432
$937$	6.91607	+	21.2855i	0.225938	+	0.695366i	0.998195	+	0.0600557i	$0.0191278\pi$
$937$	6.91607	+	21.2855i	0.225938	+	0.695366i	−0.772257	+	0.635310i	$0.780872\pi$
$938$	20.6008	+	14.9674i	0.672641	+	0.488702i
$939$	−1.58040	+	1.14823i	−0.0515744	+	0.0374710i
$940$		0			0
$941$	8.75860	−	26.9562i	0.285522	−	0.878747i	−0.700719	−	0.713437i	$-0.747137\pi$
$941$	8.75860	−	26.9562i	0.285522	−	0.878747i	0.986242	−	0.165310i	$-0.0528625\pi$
$942$	21.1184	−	15.3434i	0.688075	−	0.499916i
$943$	38.9013	+	28.2634i	1.26680	+	0.920384i
$944$	8.75878	+	26.9568i	0.285074	+	0.877368i
$945$		0			0
$946$	6.70603	+	7.62094i	0.218032	+	0.247778i
$947$	34.3182			1.11519			0.557596	−	0.830113i	$-0.311724\pi$
$947$	34.3182			1.11519			0.557596	+	0.830113i	$0.311724\pi$
$948$	7.71079	+	23.7314i	0.250435	+	0.770759i
$949$	6.03029	+	4.38126i	0.195751	+	0.142222i
$950$		0			0
$951$	7.19542	−	22.1452i	0.233328	−	0.718109i
$952$	−2.80943	+	8.64655i	−0.0910543	+	0.280236i
$953$	−16.7790	+	12.1906i	−0.543524	+	0.394893i	−0.825392	−	0.564560i	$-0.809046\pi$
$953$	−16.7790	+	12.1906i	−0.543524	+	0.394893i	0.281868	+	0.959453i	$0.409046\pi$
$954$	2.65267	+	1.92727i	0.0858832	+	0.0623978i
$955$		0			0
$956$	−15.1393			−0.489638
$957$	−1.92112	+	0.829199i	−0.0621010	+	0.0268042i
$958$	43.8288			1.41604
$959$	8.12444	+	25.0045i	0.262352	+	0.807436i
$960$		0			0
$961$	23.3073	−	16.9337i	0.751847	−	0.546249i
$962$	1.13027	−	3.47860i	0.0364412	−	0.112155i
$963$	−4.62328	+	14.2290i	−0.148983	+	0.458523i
$964$	−22.7686	+	16.5423i	−0.733326	+	0.532792i
$965$		0			0
$966$	−3.37085	−	10.3744i	−0.108455	−	0.333792i
$967$	−4.38264			−0.140936			−0.0704682	−	0.997514i	$-0.522449\pi$
$967$	−4.38264			−0.140936			−0.0704682	+	0.997514i	$0.522449\pi$
$968$	−10.7231	+	2.02465i	−0.344654	+	0.0650748i
$969$	23.6744			0.760531
$970$		0			0
$971$	29.3309	+	21.3102i	0.941275	+	0.683876i	0.948727	−	0.316096i	$-0.102372\pi$
$971$	29.3309	+	21.3102i	0.941275	+	0.683876i	−0.00745250	+	0.999972i	$0.502372\pi$
$972$	−1.18701	+	0.862413i	−0.0380734	+	0.0276619i
$973$	4.50914	−	13.8777i	0.144556	−	0.444899i
$974$	−3.99995	+	12.3106i	−0.128167	+	0.394456i
$975$		0			0
$976$	11.7595	+	8.54380i	0.376413	+	0.273480i
$977$	4.47159	+	13.7621i	0.143059	+	0.440290i	0.996756	−	0.0804796i	$-0.0256452\pi$
$977$	4.47159	+	13.7621i	0.143059	+	0.440290i	−0.853697	+	0.520769i	$0.825645\pi$
$978$	2.28478			0.0730592
$979$	−0.422137	+	0.182204i	−0.0134916	+	0.00582326i
$980$		0			0
$981$	−1.35828	−	4.18037i	−0.0433667	−	0.133469i
$982$	30.6491	+	22.2679i	0.978052	+	0.710596i
$983$	−34.0822	+	24.7622i	−1.08705	+	0.789790i	−0.978899	−	0.204344i	$-0.934494\pi$
$983$	−34.0822	+	24.7622i	−1.08705	+	0.789790i	−0.108154	+	0.994134i	$0.534494\pi$
$984$	3.24287	−	9.98052i	0.103379	−	0.318167i
$985$		0			0
$986$	−6.75822	+	4.91014i	−0.215226	+	0.156371i
$987$	−2.07697	−	1.50901i	−0.0661108	−	0.0480323i
$988$	−1.52889	−	4.70545i	−0.0486405	−	0.149700i
$989$	7.47188			0.237592
$990$		0			0
$991$	−10.7710			−0.342151			−0.171076	−	0.985258i	$-0.554724\pi$
$991$	−10.7710			−0.342151			−0.171076	+	0.985258i	$0.554724\pi$
$992$	3.16485	+	9.74039i	0.100484	+	0.309258i
$993$	−26.1312	−	18.9854i	−0.829249	−	0.602484i
$994$	−31.4068	+	22.8184i	−0.996165	+	0.723756i
$995$		0			0
$996$	−4.13039	+	12.7120i	−0.130877	+	0.402797i
$997$	−15.7258	+	11.4255i	−0.498043	+	0.361849i	−0.808269	−	0.588814i	$-0.799595\pi$
$997$	−15.7258	+	11.4255i	−0.498043	+	0.361849i	0.310226	+	0.950663i	$0.399595\pi$
$998$	−19.7394	−	14.3415i	−0.624840	−	0.453973i
$999$	0.599295	+	1.84444i	0.0189609	+	0.0583555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.l.676.1	yes	8
5.2	odd	4		825.2.bx.i.49.3		16
5.3	odd	4		825.2.bx.i.49.2		16
5.4	even	2		825.2.n.h.676.2	yes	8
11.3	even	5		9075.2.a.cp.1.2		4
11.8	odd	10		9075.2.a.dh.1.3		4
11.9	even	5	inner	825.2.n.l.526.1	yes	8
55.9	even	10		825.2.n.h.526.2	✓	8
55.14	even	10		9075.2.a.de.1.3		4
55.19	odd	10		9075.2.a.cn.1.2		4
55.42	odd	20		825.2.bx.i.724.2		16
55.53	odd	20		825.2.bx.i.724.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.h.526.2	✓	8	55.9	even	10
825.2.n.h.676.2	yes	8	5.4	even	2
825.2.n.l.526.1	yes	8	11.9	even	5	inner
825.2.n.l.676.1	yes	8	1.1	even	1	trivial
825.2.bx.i.49.2		16	5.3	odd	4
825.2.bx.i.49.3		16	5.2	odd	4
825.2.bx.i.724.2		16	55.42	odd	20
825.2.bx.i.724.3		16	55.53	odd	20
9075.2.a.cn.1.2		4	55.19	odd	10
9075.2.a.cp.1.2		4	11.3	even	5
9075.2.a.de.1.3		4	55.14	even	10
9075.2.a.dh.1.3		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.575405 - 1.77091i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.18701 + 0.862413i) q^{4} +(-0.575405 + 1.77091i) q^{6} +(1.04263 - 0.757515i) q^{7} +(-0.802588 - 0.583114i) q^{8} +(0.309017 + 0.951057i) q^{9} +(3.04508 - 1.31433i) q^{11} +1.46722 q^{12} +(-0.312990 - 0.963285i) q^{13} +(-1.94143 - 1.41053i) q^{14} +(-1.47763 + 4.54767i) q^{16} +(2.19741 - 6.76294i) q^{17} +(1.50643 - 1.09448i) q^{18} +(-2.69344 - 1.95690i) q^{19} -1.28876 q^{21} +(-4.07972 - 4.63631i) q^{22} -4.54563 q^{23} +(0.306561 + 0.943499i) q^{24} +(-1.52580 + 1.10856i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.584321 + 1.79835i) q^{28} +(0.510402 - 0.370829i) q^{29} +(0.457371 + 1.40764i) q^{31} +6.91965 q^{32} +(-3.23607 - 0.726543i) q^{33} -13.2410 q^{34} +(-1.18701 - 0.862413i) q^{36} +(-1.56898 + 1.13993i) q^{37} +(-1.91568 + 5.89585i) q^{38} +(-0.312990 + 0.963285i) q^{39} +(-8.55794 - 6.21771i) q^{41} +(0.741559 + 2.28228i) q^{42} -1.64375 q^{43} +(-2.48105 + 4.18624i) q^{44} +(2.61558 + 8.04992i) q^{46} +(1.61161 + 1.17090i) q^{47} +(3.86848 - 2.81061i) q^{48} +(-1.64987 + 5.07778i) q^{49} +(-5.75290 + 4.17973i) q^{51} +(1.20227 + 0.873502i) q^{52} +(0.544147 + 1.67471i) q^{53} -1.86205 q^{54} -1.27852 q^{56} +(1.02880 + 3.16633i) q^{57} +(-0.950394 - 0.690501i) q^{58} +(4.79553 - 3.48416i) q^{59} +(0.939361 - 2.89105i) q^{61} +(2.22964 - 1.61993i) q^{62} +(1.04263 + 0.757515i) q^{63} +(-1.02635 - 3.15877i) q^{64} +(0.575405 + 6.14885i) q^{66} -10.6112 q^{67} +(3.22410 + 9.92275i) q^{68} +(3.67749 + 2.67186i) q^{69} +(4.99903 - 15.3854i) q^{71} +(0.306561 - 0.943499i) q^{72} +(-5.95374 + 4.32564i) q^{73} +(2.92151 + 2.12260i) q^{74} +4.88479 q^{76} +(2.17927 - 3.67705i) q^{77} +1.88599 q^{78} +(5.25535 + 16.1743i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-6.08674 + 18.7331i) q^{82} +(-2.81511 + 8.66401i) q^{83} +(1.52977 - 1.11144i) q^{84} +(0.945821 + 2.91094i) q^{86} -0.630892 q^{87} +(-3.21035 - 0.720769i) q^{88} -0.138629 q^{89} +(-1.05604 - 0.767255i) q^{91} +(5.39571 - 3.92021i) q^{92} +(0.457371 - 1.40764i) q^{93} +(1.14624 - 3.52775i) q^{94} +(-5.59812 - 4.06727i) q^{96} +(1.66709 + 5.13078i) q^{97} +9.94166 q^{98} +(2.19098 + 2.48990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 2 q^{3} - 7 q^{4} + 3 q^{6} + 7 q^{7} - 16 q^{8} - 2 q^{9} + 2 q^{11} + 18 q^{12} - 5 q^{13} - 2 q^{14} - 11 q^{16} + 8 q^{17} - 2 q^{18} - 5 q^{19} - 8 q^{21} - 8 q^{22} - 2 q^{23} + 19 q^{24}+ \cdots + 22 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 2 * q^3 - 7 * q^4 + 3 * q^6 + 7 * q^7 - 16 * q^8 - 2 * q^9 + 2 * q^11 + 18 * q^12 - 5 * q^13 - 2 * q^14 - 11 * q^16 + 8 * q^17 - 2 * q^18 - 5 * q^19 - 8 * q^21 - 8 * q^22 - 2 * q^23 + 19 * q^24 - 32 * q^26 - 2 * q^27 - 51 * q^28 - 3 * q^29 + 5 * q^31 + 16 * q^32 - 8 * q^33 - 46 * q^34 - 7 * q^36 - 19 * q^37 + 31 * q^38 - 5 * q^39 - 18 * q^41 + 23 * q^42 + 52 * q^43 - 38 * q^44 + 33 * q^46 + 18 * q^47 + 4 * q^48 - 47 * q^49 - 7 * q^51 - 29 * q^52 + 31 * q^53 - 2 * q^54 - 68 * q^56 - 5 * q^57 - 35 * q^58 - 2 * q^59 - 22 * q^61 + 14 * q^62 + 7 * q^63 - 16 * q^64 - 3 * q^66 - 38 * q^67 - 2 * q^69 + 19 * q^72 - 18 * q^73 - 12 * q^74 + 92 * q^76 + 13 * q^77 + 18 * q^78 - 18 * q^79 - 2 * q^81 + 15 * q^82 - 28 * q^83 + 39 * q^84 + 53 * q^86 + 32 * q^87 - 64 * q^88 + 34 * q^89 + 33 * q^91 - 12 * q^92 + 5 * q^93 + 12 * q^94 - 14 * q^96 - 11 * q^97 - 24 * q^98 + 22 * q^99

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