LMFDB - Embedded newform 3510.2.j.h.1171.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3510,2,Mod(1171,3510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3510, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3510.1171"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3510 = 2 \cdot 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3510.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,-4,-4,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$28.0274911095$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 1170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.1
Root			$-0.385731i$ of defining polynomial
Character	$\chi$	$=$	3510.1171
Dual form			3510.2.j.h.2341.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.425606 - 0.737171i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(-0.0743941 - 0.128854i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.425606 - 0.737171i) q^{14} +(-0.500000 - 0.866025i) q^{16} +0.0580138 q^{17} +1.85121 q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.0743941 - 0.128854i) q^{22} +(2.78651 - 4.82637i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +0.851212 q^{28} +(3.26851 + 5.66122i) q^{29} +(-1.59371 + 2.76039i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.0290069 + 0.0502414i) q^{34} +0.851212 q^{35} +1.73518 q^{37} +(0.925606 + 1.60320i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-4.31389 + 7.47188i) q^{41} +(1.27820 + 2.21390i) q^{43} +0.148788 q^{44} +5.57301 q^{46} +(6.55501 + 11.3536i) q^{47} +(3.13772 - 5.43469i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} +11.8452 q^{53} +0.148788 q^{55} +(0.425606 + 0.737171i) q^{56} +(-3.26851 + 5.66122i) q^{58} +(-3.17480 + 5.49891i) q^{59} +(1.10202 + 1.90876i) q^{61} -3.18742 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(2.73281 - 4.73337i) q^{67} +(-0.0290069 + 0.0502414i) q^{68} +(0.425606 + 0.737171i) q^{70} -10.8152 q^{71} -6.14279 q^{73} +(0.867592 + 1.50271i) q^{74} +(-0.925606 + 1.60320i) q^{76} +(-0.0633251 + 0.109682i) q^{77} +(-6.67342 - 11.5587i) q^{79} +1.00000 q^{80} -8.62779 q^{82} +(6.96961 + 12.0717i) q^{83} +(-0.0290069 + 0.0502414i) q^{85} +(-1.27820 + 2.21390i) q^{86} +(0.0743941 + 0.128854i) q^{88} +5.88985 q^{89} -0.851212 q^{91} +(2.78651 + 4.82637i) q^{92} +(-6.55501 + 11.3536i) q^{94} +(-0.925606 + 1.60320i) q^{95} +(1.31551 + 2.27854i) q^{97} +6.27544 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 4 q^{5} + 7 q^{7} - 8 q^{8} - 8 q^{10} - 11 q^{11} + 4 q^{13} - 7 q^{14} - 4 q^{16} + 8 q^{17} - 6 q^{19} - 4 q^{20} + 11 q^{22} + 15 q^{23} - 4 q^{25} + 8 q^{26} - 14 q^{28} - 4 q^{29}+ \cdots - 6 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 4 * q^5 + 7 * q^7 - 8 * q^8 - 8 * q^10 - 11 * q^11 + 4 * q^13 - 7 * q^14 - 4 * q^16 + 8 * q^17 - 6 * q^19 - 4 * q^20 + 11 * q^22 + 15 * q^23 - 4 * q^25 + 8 * q^26 - 14 * q^28 - 4 * q^29 - 3 * q^31 + 4 * q^32 + 4 * q^34 - 14 * q^35 - 22 * q^37 - 3 * q^38 + 4 * q^40 - 11 * q^41 + 4 * q^43 + 22 * q^44 + 30 * q^46 + 15 * q^47 - 3 * q^49 + 4 * q^50 + 4 * q^52 - 16 * q^53 + 22 * q^55 - 7 * q^56 + 4 * q^58 - 5 * q^59 - 2 * q^61 - 6 * q^62 + 8 * q^64 + 4 * q^65 + 9 * q^67 - 4 * q^68 - 7 * q^70 - 20 * q^71 + 20 * q^73 - 11 * q^74 + 3 * q^76 + 38 * q^77 - 8 * q^79 + 8 * q^80 - 22 * q^82 + 27 * q^83 - 4 * q^85 - 4 * q^86 + 11 * q^88 - 14 * q^89 + 14 * q^91 + 15 * q^92 - 15 * q^94 + 3 * q^95 + 7 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3510\mathbb{Z}\right)^\times$.

$n$	$1081$	$2081$	$2107$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.425606	−	0.737171i	−0.160864	−	0.278624i	0.774315	−	0.632801i	$-0.218095\pi$
$7$	−0.425606	−	0.737171i	−0.160864	−	0.278624i	−0.935179	+	0.354176i	$0.884761\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	−0.0743941	−	0.128854i	−0.0224307	−	0.0388511i	0.854592	−	0.519300i	$-0.173807\pi$
$11$	−0.0743941	−	0.128854i	−0.0224307	−	0.0388511i	−0.877023	+	0.480449i	$0.840474\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	0.425606	−	0.737171i	0.113748	−	0.197017i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.0580138			0.0140704			0.00703521	−	0.999975i	$-0.497761\pi$
$17$	0.0580138			0.0140704			0.00703521	+	0.999975i	$0.497761\pi$
$18$		0			0
$19$	1.85121			0.424697			0.212349	−	0.977194i	$-0.431889\pi$
$19$	1.85121			0.424697			0.212349	+	0.977194i	$0.431889\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	0.0743941	−	0.128854i	0.0158609	−	0.0274718i
$23$	2.78651	−	4.82637i	0.581027	−	1.00637i	−0.414331	−	0.910126i	$-0.635984\pi$
$23$	2.78651	−	4.82637i	0.581027	−	1.00637i	0.995358	−	0.0962420i	$-0.0306823\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000			0.196116
$27$		0			0
$28$	0.851212			0.160864
$29$	3.26851	+	5.66122i	0.606947	+	1.05126i	0.991741	+	0.128260i	$0.0409391\pi$
$29$	3.26851	+	5.66122i	0.606947	+	1.05126i	−0.384794	+	0.923002i	$0.625728\pi$
$30$		0			0
$31$	−1.59371	+	2.76039i	−0.286239	+	0.495780i	−0.972909	−	0.231189i	$-0.925738\pi$
$31$	−1.59371	+	2.76039i	−0.286239	+	0.495780i	0.686670	+	0.726969i	$0.259072\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	0.0290069	+	0.0502414i	0.00497464	+	0.00861633i
$35$	0.851212			0.143881
$36$		0			0
$37$	1.73518			0.285263			0.142631	−	0.989776i	$-0.454444\pi$
$37$	1.73518			0.285263			0.142631	+	0.989776i	$0.454444\pi$
$38$	0.925606	+	1.60320i	0.150153	+	0.260073i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−4.31389	+	7.47188i	−0.673717	+	1.16691i	0.303125	+	0.952951i	$0.401970\pi$
$41$	−4.31389	+	7.47188i	−0.673717	+	1.16691i	−0.976842	+	0.213961i	$0.931363\pi$
$42$		0			0
$43$	1.27820	+	2.21390i	0.194923	+	0.337617i	0.946875	−	0.321601i	$-0.104221\pi$
$43$	1.27820	+	2.21390i	0.194923	+	0.337617i	−0.751952	+	0.659218i	$0.770888\pi$
$44$	0.148788			0.0224307
$45$		0			0
$46$	5.57301			0.821696
$47$	6.55501	+	11.3536i	0.956147	+	1.65610i	0.731721	+	0.681604i	$0.238717\pi$
$47$	6.55501	+	11.3536i	0.956147	+	1.65610i	0.224426	+	0.974491i	$0.427949\pi$
$48$		0			0
$49$	3.13772	−	5.43469i	0.448246	−	0.776384i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	11.8452			1.62707			0.813533	−	0.581519i	$-0.197542\pi$
$53$	11.8452			1.62707			0.813533	+	0.581519i	$0.197542\pi$
$54$		0			0
$55$	0.148788			0.0200626
$56$	0.425606	+	0.737171i	0.0568740	+	0.0985086i
$57$		0			0
$58$	−3.26851	+	5.66122i	−0.429176	+	0.743355i
$59$	−3.17480	+	5.49891i	−0.413323	+	0.715897i	−0.995251	−	0.0973438i	$-0.968965\pi$
$59$	−3.17480	+	5.49891i	−0.413323	+	0.715897i	0.581928	+	0.813241i	$0.302299\pi$
$60$		0			0
$61$	1.10202	+	1.90876i	0.141099	+	0.244391i	0.927911	−	0.372802i	$-0.121603\pi$
$61$	1.10202	+	1.90876i	0.141099	+	0.244391i	−0.786811	+	0.617193i	$0.788270\pi$
$62$	−3.18742			−0.404803
$63$		0			0
$64$	1.00000			0.125000
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$		0			0
$67$	2.73281	−	4.73337i	0.333866	−	0.578273i	−0.649400	−	0.760447i	$-0.724980\pi$
$67$	2.73281	−	4.73337i	0.333866	−	0.578273i	0.983266	+	0.182174i	$0.0583134\pi$
$68$	−0.0290069	+	0.0502414i	−0.00351760	+	0.00609267i
$69$		0			0
$70$	0.425606	+	0.737171i	0.0508696	+	0.0881088i
$71$	−10.8152			−1.28353			−0.641765	−	0.766902i	$-0.721797\pi$
$71$	−10.8152			−1.28353			−0.641765	+	0.766902i	$0.721797\pi$
$72$		0			0
$73$	−6.14279			−0.718959			−0.359480	−	0.933153i	$-0.617046\pi$
$73$	−6.14279			−0.718959			−0.359480	+	0.933153i	$0.617046\pi$
$74$	0.867592	+	1.50271i	0.100856	+	0.174687i
$75$		0			0
$76$	−0.925606	+	1.60320i	−0.106174	+	0.183899i
$77$	−0.0633251	+	0.109682i	−0.00721657	+	0.0124995i
$78$		0			0
$79$	−6.67342	−	11.5587i	−0.750818	−	1.30045i	−0.947427	−	0.319973i	$-0.896326\pi$
$79$	−6.67342	−	11.5587i	−0.750818	−	1.30045i	0.196609	−	0.980482i	$-0.437007\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	−8.62779			−0.952780
$83$	6.96961	+	12.0717i	0.765015	+	1.32504i	0.940239	+	0.340515i	$0.110602\pi$
$83$	6.96961	+	12.0717i	0.765015	+	1.32504i	−0.175224	+	0.984529i	$0.556065\pi$
$84$		0			0
$85$	−0.0290069	+	0.0502414i	−0.00314624	+	0.00544945i
$86$	−1.27820	+	2.21390i	−0.137832	+	0.238731i
$87$		0			0
$88$	0.0743941	+	0.128854i	0.00793044	+	0.0137359i
$89$	5.88985			0.624322			0.312161	−	0.950029i	$-0.398947\pi$
$89$	5.88985			0.624322			0.312161	+	0.950029i	$0.398947\pi$
$90$		0			0
$91$	−0.851212			−0.0892312
$92$	2.78651	+	4.82637i	0.290513	+	0.503184i
$93$		0			0
$94$	−6.55501	+	11.3536i	−0.676098	+	1.17104i
$95$	−0.925606	+	1.60320i	−0.0949652	+	0.164484i
$96$		0			0
$97$	1.31551	+	2.27854i	0.133570	+	0.231350i	0.925050	−	0.379844i	$-0.124022\pi$
$97$	1.31551	+	2.27854i	0.133570	+	0.231350i	−0.791480	+	0.611195i	$0.790689\pi$
$98$	6.27544			0.633915
$99$		0			0
$100$	1.00000			0.100000
$101$	6.41592	+	11.1127i	0.638408	+	1.10575i	0.985782	+	0.168028i	$0.0537399\pi$
$101$	6.41592	+	11.1127i	0.638408	+	1.10575i	−0.347375	+	0.937726i	$0.612927\pi$
$102$		0			0
$103$	−5.41592	+	9.38064i	−0.533646	+	0.924302i	0.465582	+	0.885005i	$0.345845\pi$
$103$	−5.41592	+	9.38064i	−0.533646	+	0.924302i	−0.999228	+	0.0392971i	$0.987488\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$		0			0
$106$	5.92261	+	10.2583i	0.575254	+	0.996370i
$107$	−2.27820			−0.220242			−0.110121	−	0.993918i	$-0.535124\pi$
$107$	−2.27820			−0.220242			−0.110121	+	0.993918i	$0.535124\pi$
$108$		0			0
$109$	−4.56977			−0.437705			−0.218853	−	0.975758i	$-0.570231\pi$
$109$	−4.56977			−0.437705			−0.218853	+	0.975758i	$0.570231\pi$
$110$	0.0743941	+	0.128854i	0.00709320	+	0.0122858i
$111$		0			0
$112$	−0.425606	+	0.737171i	−0.0402160	+	0.0696561i
$113$	−6.22981	+	10.7903i	−0.586051	+	1.01507i	0.408692	+	0.912672i	$0.365985\pi$
$113$	−6.22981	+	10.7903i	−0.586051	+	1.01507i	−0.994743	+	0.102398i	$0.967348\pi$
$114$		0			0
$115$	2.78651	+	4.82637i	0.259843	+	0.450062i
$116$	−6.53701			−0.606947
$117$		0			0
$118$	−6.34959			−0.584527
$119$	−0.0246910	−	0.0427661i	−0.00226342	−	0.00392036i
$120$		0			0
$121$	5.48893	−	9.50711i	0.498994	−	0.864282i
$122$	−1.10202	+	1.90876i	−0.0997724	+	0.172811i
$123$		0			0
$124$	−1.59371	−	2.76039i	−0.143119	−	0.247890i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−6.23680			−0.553427			−0.276713	−	0.960952i	$-0.589245\pi$
$127$	−6.23680			−0.553427			−0.276713	+	0.960952i	$0.589245\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.500000	+	0.866025i	−0.0438529	+	0.0759555i
$131$	3.14879	−	5.45386i	0.275111	−	0.476506i	−0.695052	−	0.718959i	$-0.744619\pi$
$131$	3.14879	−	5.45386i	0.275111	−	0.476506i	0.970163	+	0.242453i	$0.0779521\pi$
$132$		0			0
$133$	−0.787887	−	1.36466i	−0.0683184	−	0.118331i
$134$	5.46562			0.472158
$135$		0			0
$136$	−0.0580138			−0.00497464
$137$	6.05070	+	10.4801i	0.516946	+	0.895377i	0.999806	+	0.0196794i	$0.00626456\pi$
$137$	6.05070	+	10.4801i	0.516946	+	0.895377i	−0.482860	+	0.875697i	$0.660402\pi$
$138$		0			0
$139$	−1.41892	+	2.45763i	−0.120351	+	0.208454i	−0.919906	−	0.392139i	$-0.871735\pi$
$139$	−1.41892	+	2.45763i	−0.120351	+	0.208454i	0.799555	+	0.600593i	$0.205069\pi$
$140$	−0.425606	+	0.737171i	−0.0359703	+	0.0623023i
$141$		0			0
$142$	−5.40761	−	9.36625i	−0.453796	−	0.785998i
$143$	−0.148788			−0.0124423
$144$		0			0
$145$	−6.53701			−0.542869
$146$	−3.07139	−	5.31981i	−0.254190	−	0.440271i
$147$		0			0
$148$	−0.867592	+	1.50271i	−0.0713156	+	0.123522i
$149$	1.91592	−	3.31846i	0.156958	−	0.271859i	−0.776812	−	0.629732i	$-0.783165\pi$
$149$	1.91592	−	3.31846i	0.156958	−	0.271859i	0.933770	+	0.357873i	$0.116498\pi$
$150$		0			0
$151$	4.71049	+	8.15881i	0.383334	+	0.663955i	0.991537	−	0.129827i	$-0.0414423\pi$
$151$	4.71049	+	8.15881i	0.383334	+	0.663955i	−0.608202	+	0.793782i	$0.708109\pi$
$152$	−1.85121			−0.150153
$153$		0			0
$154$	−0.126650			−0.0102058
$155$	−1.59371	−	2.76039i	−0.128010	−	0.221720i
$156$		0			0
$157$	−5.34152	+	9.25179i	−0.426300	+	0.738373i	−0.996541	−	0.0831044i	$-0.973516\pi$
$157$	−5.34152	+	9.25179i	−0.426300	+	0.738373i	0.570241	+	0.821477i	$0.306850\pi$
$158$	6.67342	−	11.5587i	0.530909	−	0.919561i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−4.74382			−0.373865
$162$		0			0
$163$	5.63379			0.441272			0.220636	−	0.975356i	$-0.429187\pi$
$163$	5.63379			0.441272			0.220636	+	0.975356i	$0.429187\pi$
$164$	−4.31389	−	7.47188i	−0.336859	−	0.583456i
$165$		0			0
$166$	−6.96961	+	12.0717i	−0.540947	+	0.936948i
$167$	6.05232	−	10.4829i	0.468342	−	0.811193i	−0.531003	−	0.847370i	$-0.678185\pi$
$167$	6.05232	−	10.4829i	0.468342	−	0.811193i	0.999345	+	0.0361770i	$0.0115180\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−0.0580138			−0.00444945
$171$		0			0
$172$	−2.55639			−0.194923
$173$	10.8399	+	18.7753i	0.824142	+	1.42746i	0.902573	+	0.430537i	$0.141676\pi$
$173$	10.8399	+	18.7753i	0.824142	+	1.42746i	−0.0784304	+	0.996920i	$0.524991\pi$
$174$		0			0
$175$	−0.425606	+	0.737171i	−0.0321728	+	0.0557249i
$176$	−0.0743941	+	0.128854i	−0.00560767	+	0.00971276i
$177$		0			0
$178$	2.94492	+	5.10076i	0.220731	+	0.382318i
$179$	−4.88721			−0.365287			−0.182644	−	0.983179i	$-0.558465\pi$
$179$	−4.88721			−0.365287			−0.182644	+	0.983179i	$0.558465\pi$
$180$		0			0
$181$	25.6412			1.90589			0.952947	−	0.303138i	$-0.0980344\pi$
$181$	25.6412			1.90589			0.952947	+	0.303138i	$0.0980344\pi$
$182$	−0.425606	−	0.737171i	−0.0315480	−	0.0546428i
$183$		0			0
$184$	−2.78651	+	4.82637i	−0.205424	+	0.355805i
$185$	−0.867592	+	1.50271i	−0.0637866	+	0.110482i
$186$		0			0
$187$	−0.00431588	−	0.00747533i	−0.000315609	−	0.000546650i
$188$	−13.1100			−0.956147
$189$		0			0
$190$	−1.85121			−0.134301
$191$	3.90923	+	6.77098i	0.282862	+	0.489931i	0.972088	−	0.234615i	$-0.0753829\pi$
$191$	3.90923	+	6.77098i	0.282862	+	0.489931i	−0.689227	+	0.724546i	$0.742050\pi$
$192$		0			0
$193$	−5.60709	+	9.71177i	−0.403607	+	0.699068i	−0.994158	−	0.107932i	$-0.965577\pi$
$193$	−5.60709	+	9.71177i	−0.403607	+	0.699068i	0.590551	+	0.807000i	$0.298910\pi$
$194$	−1.31551	+	2.27854i	−0.0944484	+	0.163589i
$195$		0			0
$196$	3.13772	+	5.43469i	0.224123	+	0.388192i
$197$	−24.8092			−1.76758			−0.883792	−	0.467881i	$-0.845018\pi$
$197$	−24.8092			−1.76758			−0.883792	+	0.467881i	$0.845018\pi$
$198$		0			0
$199$	5.78720			0.410244			0.205122	−	0.978736i	$-0.434241\pi$
$199$	5.78720			0.410244			0.205122	+	0.978736i	$0.434241\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	−6.41592	+	11.1127i	−0.451422	+	0.781886i
$203$	2.78219	−	4.81890i	0.195272	−	0.338220i
$204$		0			0
$205$	−4.31389	−	7.47188i	−0.301295	−	0.521859i
$206$	−10.8318			−0.754690
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	−0.137719	−	0.238537i	−0.00952624	−	0.0164999i
$210$		0			0
$211$	−1.23149	+	2.13301i	−0.0847795	+	0.146842i	−0.905297	−	0.424779i	$-0.860352\pi$
$211$	−1.23149	+	2.13301i	−0.0847795	+	0.146842i	0.820518	+	0.571621i	$0.193685\pi$
$212$	−5.92261	+	10.2583i	−0.406766	+	0.704540i
$213$		0			0
$214$	−1.13910	−	1.97298i	−0.0778672	−	0.134870i
$215$	−2.55639			−0.174345
$216$		0			0
$217$	2.71317			0.184182
$218$	−2.28489	−	3.95754i	−0.154752	−	0.268038i
$219$		0			0
$220$	−0.0743941	+	0.128854i	−0.00501565	+	0.00868736i
$221$	0.0290069	−	0.0502414i	0.00195122	−	0.00337960i
$222$		0			0
$223$	7.07433	+	12.2531i	0.473732	+	0.820528i	0.999548	−	0.0300703i	$-0.00957311\pi$
$223$	7.07433	+	12.2531i	0.473732	+	0.820528i	−0.525816	+	0.850599i	$0.676240\pi$
$224$	−0.851212			−0.0568740
$225$		0			0
$226$	−12.4596			−0.828802
$227$	−6.81089	−	11.7968i	−0.452055	−	0.782982i	0.546459	−	0.837486i	$-0.315976\pi$
$227$	−6.81089	−	11.7968i	−0.452055	−	0.782982i	−0.998514	+	0.0545040i	$0.982642\pi$
$228$		0			0
$229$	0.765570	−	1.32601i	0.0505903	−	0.0876250i	−0.839621	−	0.543172i	$-0.817223\pi$
$229$	0.765570	−	1.32601i	0.0505903	−	0.0876250i	0.890212	+	0.455547i	$0.150556\pi$
$230$	−2.78651	+	4.82637i	−0.183737	+	0.318242i
$231$		0			0
$232$	−3.26851	−	5.66122i	−0.214588	−	0.371677i
$233$	12.5509			0.822235			0.411118	−	0.911582i	$-0.365139\pi$
$233$	12.5509			0.822235			0.411118	+	0.911582i	$0.365139\pi$
$234$		0			0
$235$	−13.1100			−0.855204
$236$	−3.17480	−	5.49891i	−0.206662	−	0.357948i
$237$		0			0
$238$	0.0246910	−	0.0427661i	0.00160048	−	0.00277211i
$239$	10.1748	−	17.6233i	0.658153	−	1.13995i	−0.322941	−	0.946419i	$-0.604671\pi$
$239$	10.1748	−	17.6233i	0.658153	−	1.13995i	0.981093	−	0.193535i	$-0.0619953\pi$
$240$		0			0
$241$	−5.51638	−	9.55465i	−0.355341	−	0.615469i	0.631835	−	0.775103i	$-0.282302\pi$
$241$	−5.51638	−	9.55465i	−0.355341	−	0.615469i	−0.987176	+	0.159634i	$0.948969\pi$
$242$	10.9779			0.705684
$243$		0			0
$244$	−2.20404			−0.141099
$245$	3.13772	+	5.43469i	0.200462	+	0.347210i
$246$		0			0
$247$	0.925606	−	1.60320i	0.0588949	−	0.102009i
$248$	1.59371	−	2.76039i	0.101201	−	0.175285i
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−2.60578			−0.164475			−0.0822375	−	0.996613i	$-0.526207\pi$
$251$	−2.60578			−0.164475			−0.0822375	+	0.996613i	$0.526207\pi$
$252$		0			0
$253$	−0.829199			−0.0521313
$254$	−3.11840	−	5.40123i	−0.195666	−	0.338903i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.187422	+	0.324625i	−0.0116911	+	0.0202496i	−0.871812	−	0.489841i	$-0.837055\pi$
$257$	−0.187422	+	0.324625i	−0.0116911	+	0.0202496i	0.860121	+	0.510091i	$0.170388\pi$
$258$		0			0
$259$	−0.738505	−	1.27913i	−0.0458884	−	0.0794811i
$260$	−1.00000			−0.0620174
$261$		0			0
$262$	6.29758			0.389066
$263$	2.09509	+	3.62880i	0.129189	+	0.223762i	0.923363	−	0.383929i	$-0.125429\pi$
$263$	2.09509	+	3.62880i	0.129189	+	0.223762i	−0.794174	+	0.607691i	$0.792096\pi$
$264$		0			0
$265$	−5.92261	+	10.2583i	−0.363823	+	0.630160i
$266$	0.787887	−	1.36466i	0.0483084	−	0.0836727i
$267$		0			0
$268$	2.73281	+	4.73337i	0.166933	+	0.289136i
$269$	−18.9032			−1.15255			−0.576275	−	0.817256i	$-0.695494\pi$
$269$	−18.9032			−1.15255			−0.576275	+	0.817256i	$0.695494\pi$
$270$		0			0
$271$	13.0165			0.790696			0.395348	−	0.918531i	$-0.370624\pi$
$271$	13.0165			0.790696			0.395348	+	0.918531i	$0.370624\pi$
$272$	−0.0290069	−	0.0502414i	−0.00175880	−	0.00304633i
$273$		0			0
$274$	−6.05070	+	10.4801i	−0.365536	+	0.633127i
$275$	−0.0743941	+	0.128854i	−0.00448613	+	0.00777021i
$276$		0			0
$277$	−3.69435	−	6.39881i	−0.221972	−	0.384467i	0.733435	−	0.679760i	$-0.237916\pi$
$277$	−3.69435	−	6.39881i	−0.221972	−	0.384467i	−0.955407	+	0.295293i	$0.904583\pi$
$278$	−2.83783			−0.170202
$279$		0			0
$280$	−0.851212			−0.0508696
$281$	11.5190	+	19.9515i	0.687167	+	1.19021i	0.972751	+	0.231854i	$0.0744792\pi$
$281$	11.5190	+	19.9515i	0.687167	+	1.19021i	−0.285584	+	0.958354i	$0.592188\pi$
$282$		0			0
$283$	6.89522	−	11.9429i	0.409878	−	0.709930i	−0.584997	−	0.811035i	$-0.698905\pi$
$283$	6.89522	−	11.9429i	0.409878	−	0.709930i	0.994876	+	0.101105i	$0.0322378\pi$
$284$	5.40761	−	9.36625i	0.320882	−	0.555785i
$285$		0			0
$286$	−0.0743941	−	0.128854i	−0.00439902	−	0.00761932i
$287$	7.34408			0.433507
$288$		0			0
$289$	−16.9966			−0.999802
$290$	−3.26851	−	5.66122i	−0.191933	−	0.332438i
$291$		0			0
$292$	3.07139	−	5.31981i	0.179740	−	0.311318i
$293$	5.01638	−	8.68863i	0.293060	−	0.507595i	−0.681472	−	0.731844i	$-0.738660\pi$
$293$	5.01638	−	8.68863i	0.293060	−	0.507595i	0.974532	+	0.224250i	$0.0719931\pi$
$294$		0			0
$295$	−3.17480	−	5.49891i	−0.184844	−	0.320159i
$296$	−1.73518			−0.100856
$297$		0			0
$298$	3.83183			0.221972
$299$	−2.78651	−	4.82637i	−0.161148	−	0.279116i
$300$		0			0
$301$	1.08802	−	1.88450i	0.0627122	−	0.108621i
$302$	−4.71049	+	8.15881i	−0.271058	+	0.469487i
$303$		0			0
$304$	−0.925606	−	1.60320i	−0.0530871	−	0.0919496i
$305$	−2.20404			−0.126203
$306$		0			0
$307$	1.79307			0.102336			0.0511680	−	0.998690i	$-0.483706\pi$
$307$	1.79307			0.102336			0.0511680	+	0.998690i	$0.483706\pi$
$308$	−0.0633251	−	0.109682i	−0.00360829	−	0.00624973i
$309$		0			0
$310$	1.59371	−	2.76039i	0.0905167	−	0.156780i
$311$	−5.47900	+	9.48991i	−0.310686	+	0.538123i	−0.978511	−	0.206195i	$-0.933892\pi$
$311$	−5.47900	+	9.48991i	−0.310686	+	0.538123i	0.667825	+	0.744318i	$0.267225\pi$
$312$		0			0
$313$	3.28782	+	5.69468i	0.185839	+	0.321882i	0.943859	−	0.330349i	$-0.107166\pi$
$313$	3.28782	+	5.69468i	0.185839	+	0.321882i	−0.758020	+	0.652231i	$0.773833\pi$
$314$	−10.6830			−0.602879
$315$		0			0
$316$	13.3468			0.750818
$317$	−6.69942	−	11.6037i	−0.376277	−	0.651731i	0.614240	−	0.789119i	$-0.289463\pi$
$317$	−6.69942	−	11.6037i	−0.376277	−	0.651731i	−0.990517	+	0.137388i	$0.956129\pi$
$318$		0			0
$319$	0.486315	−	0.842323i	0.0272284	−	0.0471610i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−2.37191	−	4.10827i	−0.132181	−	0.228945i
$323$	0.107396			0.00597566
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	2.81689	+	4.87900i	0.156013	+	0.270223i
$327$		0			0
$328$	4.31389	−	7.47188i	0.238195	−	0.412566i
$329$	5.57971	−	9.66433i	0.307619	−	0.532812i
$330$		0			0
$331$	−2.58564	−	4.47846i	−0.142120	−	0.246159i	0.786175	−	0.618004i	$-0.212058\pi$
$331$	−2.58564	−	4.47846i	−0.142120	−	0.246159i	−0.928295	+	0.371845i	$0.878725\pi$
$332$	−13.9392			−0.765015
$333$		0			0
$334$	12.1046			0.662336
$335$	2.73281	+	4.73337i	0.149309	+	0.258611i
$336$		0			0
$337$	10.0644	−	17.4321i	0.548243	−	0.949584i	−0.450152	−	0.892952i	$-0.648630\pi$
$337$	10.0644	−	17.4321i	0.548243	−	0.949584i	0.998395	−	0.0566326i	$-0.0180364\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$		0			0
$340$	−0.0290069	−	0.0502414i	−0.00157312	−	0.00272472i
$341$	0.474251			0.0256821
$342$		0			0
$343$	−11.3002			−0.610154
$344$	−1.27820	−	2.21390i	−0.0689158	−	0.119366i
$345$		0			0
$346$	−10.8399	+	18.7753i	−0.582757	+	1.00936i
$347$	−3.71181	+	6.42904i	−0.199260	+	0.345129i	−0.948289	−	0.317409i	$-0.897187\pi$
$347$	−3.71181	+	6.42904i	−0.199260	+	0.345129i	0.749028	+	0.662538i	$0.230521\pi$
$348$		0			0
$349$	16.0259	+	27.7578i	0.857849	+	1.48584i	0.873976	+	0.485968i	$0.161533\pi$
$349$	16.0259	+	27.7578i	0.857849	+	1.48584i	−0.0161272	+	0.999870i	$0.505134\pi$
$350$	−0.851212			−0.0454992
$351$		0			0
$352$	−0.148788			−0.00793044
$353$	4.65704	+	8.06622i	0.247869	+	0.429322i	0.962934	−	0.269736i	$-0.0869364\pi$
$353$	4.65704	+	8.06622i	0.247869	+	0.429322i	−0.715065	+	0.699058i	$0.753603\pi$
$354$		0			0
$355$	5.40761	−	9.36625i	0.287006	−	0.497109i
$356$	−2.94492	+	5.10076i	−0.156081	+	0.270340i
$357$		0			0
$358$	−2.44361	−	4.23245i	−0.129149	−	0.223692i
$359$	5.03264			0.265612			0.132806	−	0.991142i	$-0.457601\pi$
$359$	5.03264			0.265612			0.132806	+	0.991142i	$0.457601\pi$
$360$		0			0
$361$	−15.5730			−0.819632
$362$	12.8206	+	22.2059i	0.673835	+	1.16712i
$363$		0			0
$364$	0.425606	−	0.737171i	0.0223078	−	0.0386383i
$365$	3.07139	−	5.31981i	0.160764	−	0.278452i
$366$		0			0
$367$	4.49331	+	7.78264i	0.234549	+	0.406251i	0.959141	−	0.282927i	$-0.0913054\pi$
$367$	4.49331	+	7.78264i	0.234549	+	0.406251i	−0.724593	+	0.689177i	$0.757972\pi$
$368$	−5.57301			−0.290513
$369$		0			0
$370$	−1.73518			−0.0902079
$371$	−5.04139	−	8.73195i	−0.261736	−	0.453340i
$372$		0			0
$373$	−1.70518	+	2.95346i	−0.0882910	+	0.152924i	−0.906789	−	0.421585i	$-0.861474\pi$
$373$	−1.70518	+	2.95346i	−0.0882910	+	0.152924i	0.818498	+	0.574510i	$0.194807\pi$
$374$	0.00431588	−	0.00747533i	0.000223169	−	0.000386540i
$375$		0			0
$376$	−6.55501	−	11.3536i	−0.338049	−	0.585518i
$377$	6.53701			0.336673
$378$		0			0
$379$	30.3956			1.56132			0.780659	−	0.624958i	$-0.214884\pi$
$379$	30.3956			1.56132			0.780659	+	0.624958i	$0.214884\pi$
$380$	−0.925606	−	1.60320i	−0.0474826	−	0.0822422i
$381$		0			0
$382$	−3.90923	+	6.77098i	−0.200013	+	0.346433i
$383$	5.23944	−	9.07497i	0.267723	−	0.463709i	−0.700551	−	0.713603i	$-0.747062\pi$
$383$	5.23944	−	9.07497i	0.267723	−	0.463709i	0.968273	+	0.249893i	$0.0803955\pi$
$384$		0			0
$385$	−0.0633251	−	0.109682i	−0.00322735	−	0.00558993i
$386$	−11.2142			−0.570787
$387$		0			0
$388$	−2.63103			−0.133570
$389$	−6.42392	−	11.1266i	−0.325706	−	0.564139i	0.655949	−	0.754805i	$-0.272269\pi$
$389$	−6.42392	−	11.1266i	−0.325706	−	0.564139i	−0.981655	+	0.190666i	$0.938935\pi$
$390$		0			0
$391$	0.161656	−	0.279996i	0.00817529	−	0.0141600i
$392$	−3.13772	+	5.43469i	−0.158479	+	0.274493i
$393$		0			0
$394$	−12.4046	−	21.4854i	−0.624935	−	1.08242i
$395$	13.3468			0.671552
$396$		0			0
$397$	6.59515			0.331001			0.165501	−	0.986210i	$-0.447076\pi$
$397$	6.59515			0.331001			0.165501	+	0.986210i	$0.447076\pi$
$398$	2.89360	+	5.01186i	0.145043	+	0.251222i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−7.98494	+	13.8303i	−0.398749	+	0.690653i	−0.993572	−	0.113204i	$-0.963889\pi$
$401$	−7.98494	+	13.8303i	−0.398749	+	0.690653i	0.594823	+	0.803857i	$0.297222\pi$
$402$		0			0
$403$	1.59371	+	2.76039i	0.0793884	+	0.137505i
$404$	−12.8318			−0.638408
$405$		0			0
$406$	5.56438			0.276156
$407$	−0.129087	−	0.223586i	−0.00639863	−	0.0110828i
$408$		0			0
$409$	0.484999	−	0.840043i	0.0239816	−	0.0415374i	−0.853786	−	0.520625i	$-0.825699\pi$
$409$	0.484999	−	0.840043i	0.0239816	−	0.0415374i	0.877767	+	0.479087i	$0.159032\pi$
$410$	4.31389	−	7.47188i	0.213048	−	0.369010i
$411$		0			0
$412$	−5.41592	−	9.38064i	−0.266823	−	0.462151i
$413$	5.40485			0.265955
$414$		0			0
$415$	−13.9392			−0.684250
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	0.137719	−	0.238537i	0.00673607	−	0.0116672i
$419$	11.7491	−	20.3501i	0.573982	−	0.994167i	−0.422169	−	0.906517i	$-0.638731\pi$
$419$	11.7491	−	20.3501i	0.573982	−	0.994167i	0.996151	−	0.0876496i	$-0.0279356\pi$
$420$		0			0
$421$	−0.422669	−	0.732084i	−0.0205996	−	0.0356796i	0.855542	−	0.517734i	$-0.173224\pi$
$421$	−0.422669	−	0.732084i	−0.0205996	−	0.0356796i	−0.876141	+	0.482054i	$0.839891\pi$
$422$	−2.46299			−0.119896
$423$		0			0
$424$	−11.8452			−0.575254
$425$	−0.0290069	−	0.0502414i	−0.00140704	−	0.00243707i
$426$		0			0
$427$	0.938054	−	1.62476i	0.0453956	−	0.0786275i
$428$	1.13910	−	1.97298i	0.0550604	−	0.0953674i
$429$		0			0
$430$	−1.27820	−	2.21390i	−0.0616401	−	0.106764i
$431$	34.8834			1.68027			0.840136	−	0.542375i	$-0.182475\pi$
$431$	34.8834			1.68027			0.840136	+	0.542375i	$0.182475\pi$
$432$		0			0
$433$	23.7409			1.14092			0.570458	−	0.821327i	$-0.306766\pi$
$433$	23.7409			1.14092			0.570458	+	0.821327i	$0.306766\pi$
$434$	1.35659	+	2.34968i	0.0651182	+	0.112788i
$435$		0			0
$436$	2.28489	−	3.95754i	0.109426	−	0.189532i
$437$	5.15842	−	8.93464i	0.246760	−	0.427402i
$438$		0			0
$439$	−19.4279	−	33.6500i	−0.927241	−	1.60603i	−0.787917	−	0.615782i	$-0.788840\pi$
$439$	−19.4279	−	33.6500i	−0.927241	−	1.60603i	−0.139324	−	0.990247i	$-0.544493\pi$
$440$	−0.148788			−0.00709320
$441$		0			0
$442$	0.0580138			0.00275943
$443$	8.67180	+	15.0200i	0.412009	+	0.713621i	0.995109	−	0.0987791i	$-0.0314937\pi$
$443$	8.67180	+	15.0200i	0.412009	+	0.713621i	−0.583100	+	0.812400i	$0.698160\pi$
$444$		0			0
$445$	−2.94492	+	5.10076i	−0.139603	+	0.241799i
$446$	−7.07433	+	12.2531i	−0.334979	+	0.580201i
$447$		0			0
$448$	−0.425606	−	0.737171i	−0.0201080	−	0.0348281i
$449$	4.51452			0.213053			0.106527	−	0.994310i	$-0.466027\pi$
$449$	4.51452			0.213053			0.106527	+	0.994310i	$0.466027\pi$
$450$		0			0
$451$	1.28371			0.0604477
$452$	−6.22981	−	10.7903i	−0.293026	−	0.507535i
$453$		0			0
$454$	6.81089	−	11.7968i	0.319651	−	0.553652i
$455$	0.425606	−	0.737171i	0.0199527	−	0.0345591i
$456$		0			0
$457$	12.2174	+	21.1612i	0.571507	+	0.989879i	0.996412	+	0.0846410i	$0.0269743\pi$
$457$	12.2174	+	21.1612i	0.571507	+	0.989879i	−0.424904	+	0.905238i	$0.639692\pi$
$458$	1.53114			0.0715455
$459$		0			0
$460$	−5.57301			−0.259843
$461$	−7.34446	−	12.7210i	−0.342066	−	0.592475i	0.642751	−	0.766075i	$-0.277793\pi$
$461$	−7.34446	−	12.7210i	−0.342066	−	0.592475i	−0.984816	+	0.173601i	$0.944460\pi$
$462$		0			0
$463$	−1.99400	+	3.45371i	−0.0926691	+	0.160508i	−0.908633	−	0.417595i	$-0.862873\pi$
$463$	−1.99400	+	3.45371i	−0.0926691	+	0.160508i	0.815964	+	0.578102i	$0.196207\pi$
$464$	3.26851	−	5.66122i	0.151737	−	0.262816i
$465$		0			0
$466$	6.27544	+	10.8694i	0.290704	+	0.503514i
$467$	−29.0599			−1.34473			−0.672365	−	0.740219i	$-0.734722\pi$
$467$	−29.0599			−1.34473			−0.672365	+	0.740219i	$0.734722\pi$
$468$		0			0
$469$	−4.65240			−0.214828
$470$	−6.55501	−	11.3536i	−0.302360	−	0.523703i
$471$		0			0
$472$	3.17480	−	5.49891i	0.146132	−	0.253108i
$473$	0.190181	−	0.329403i	0.00874451	−	0.0151459i
$474$		0			0
$475$	−0.925606	−	1.60320i	−0.0424697	−	0.0735597i
$476$	0.0493820			0.00226342
$477$		0			0
$478$	20.3496			0.930769
$479$	−20.6816	−	35.8216i	−0.944967	−	1.63673i	−0.755818	−	0.654781i	$-0.772761\pi$
$479$	−20.6816	−	35.8216i	−0.944967	−	1.63673i	−0.189148	−	0.981949i	$-0.560573\pi$
$480$		0			0
$481$	0.867592	−	1.50271i	0.0395588	−	0.0685178i
$482$	5.51638	−	9.55465i	0.251264	−	0.435202i
$483$		0			0
$484$	5.48893	+	9.50711i	0.249497	+	0.432141i
$485$	−2.63103			−0.119469
$486$		0			0
$487$	−42.6109			−1.93088			−0.965442	−	0.260619i	$-0.916073\pi$
$487$	−42.6109			−1.93088			−0.965442	+	0.260619i	$0.916073\pi$
$488$	−1.10202	−	1.90876i	−0.0498862	−	0.0864054i
$489$		0			0
$490$	−3.13772	+	5.43469i	−0.141748	+	0.245514i
$491$	6.02732	−	10.4396i	0.272009	−	0.471134i	−0.697367	−	0.716714i	$-0.745645\pi$
$491$	6.02732	−	10.4396i	0.272009	−	0.471134i	0.969376	+	0.245580i	$0.0789785\pi$
$492$		0			0
$493$	0.189618	+	0.328429i	0.00853999	+	0.0147917i
$494$	1.85121			0.0832900
$495$		0			0
$496$	3.18742			0.143119
$497$	4.60302	+	7.97266i	0.206474	+	0.357623i
$498$		0			0
$499$	−16.7641	+	29.0362i	−0.750463	+	1.29984i	0.197136	+	0.980376i	$0.436836\pi$
$499$	−16.7641	+	29.0362i	−0.750463	+	1.29984i	−0.947599	+	0.319463i	$0.896497\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	−1.30289	−	2.25667i	−0.0581507	−	0.100720i
$503$	−2.33310			−0.104028			−0.0520138	−	0.998646i	$-0.516564\pi$
$503$	−2.33310			−0.104028			−0.0520138	+	0.998646i	$0.516564\pi$
$504$		0			0
$505$	−12.8318			−0.571009
$506$	−0.414600	−	0.718107i	−0.0184312	−	0.0319238i
$507$		0			0
$508$	3.11840	−	5.40123i	0.138357	−	0.239641i
$509$	17.2327	−	29.8480i	0.763828	−	1.32299i	−0.177036	−	0.984204i	$-0.556651\pi$
$509$	17.2327	−	29.8480i	0.763828	−	1.32299i	0.940864	−	0.338785i	$-0.110016\pi$
$510$		0			0
$511$	2.61441	+	4.52829i	0.115655	+	0.200320i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−0.374845			−0.0165337
$515$	−5.41592	−	9.38064i	−0.238654	−	0.413360i
$516$		0			0
$517$	0.975309	−	1.68928i	0.0428940	−	0.0742947i
$518$	0.738505	−	1.27913i	0.0324480	−	0.0562016i
$519$		0			0
$520$	−0.500000	−	0.866025i	−0.0219265	−	0.0379777i
$521$	32.9659			1.44426			0.722130	−	0.691757i	$-0.243163\pi$
$521$	32.9659			1.44426			0.722130	+	0.691757i	$0.243163\pi$
$522$		0			0
$523$	5.71629			0.249956			0.124978	−	0.992160i	$-0.460114\pi$
$523$	5.71629			0.249956			0.124978	+	0.992160i	$0.460114\pi$
$524$	3.14879	+	5.45386i	0.137555	+	0.238253i
$525$		0			0
$526$	−2.09509	+	3.62880i	−0.0913503	+	0.158223i
$527$	−0.0924572	+	0.160141i	−0.00402750	+	0.00697584i
$528$		0			0
$529$	−4.02925	−	6.97886i	−0.175185	−	0.303429i
$530$	−11.8452			−0.514523
$531$		0			0
$532$	1.57577			0.0683184
$533$	4.31389	+	7.47188i	0.186855	+	0.323643i
$534$		0			0
$535$	1.13910	−	1.97298i	0.0492475	−	0.0852992i
$536$	−2.73281	+	4.73337i	−0.118039	+	0.204450i
$537$		0			0
$538$	−9.45161	−	16.3707i	−0.407488	−	0.705790i
$539$	−0.933711			−0.0402178
$540$		0			0
$541$	5.80507			0.249579			0.124790	−	0.992183i	$-0.460174\pi$
$541$	5.80507			0.249579			0.124790	+	0.992183i	$0.460174\pi$
$542$	6.50825	+	11.2726i	0.279553	+	0.484200i
$543$		0			0
$544$	0.0290069	−	0.0502414i	0.00124366	−	0.00215408i
$545$	2.28489	−	3.95754i	0.0978738	−	0.169522i
$546$		0			0
$547$	0.902294	+	1.56282i	0.0385793	+	0.0668213i	0.884670	−	0.466217i	$-0.154383\pi$
$547$	0.902294	+	1.56282i	0.0385793	+	0.0668213i	−0.846091	+	0.533038i	$0.821050\pi$
$548$	−12.1014			−0.516946
$549$		0			0
$550$	−0.148788			−0.00634435
$551$	6.05070	+	10.4801i	0.257768	+	0.446468i
$552$		0			0
$553$	−5.68049	+	9.83890i	−0.241559	+	0.418393i
$554$	3.69435	−	6.39881i	0.156958	−	0.271859i
$555$		0			0
$556$	−1.41892	−	2.45763i	−0.0601754	−	0.104227i
$557$	−21.2616			−0.900882			−0.450441	−	0.892806i	$-0.648733\pi$
$557$	−21.2616			−0.900882			−0.450441	+	0.892806i	$0.648733\pi$
$558$		0			0
$559$	2.55639			0.108124
$560$	−0.425606	−	0.737171i	−0.0179851	−	0.0311512i
$561$		0			0
$562$	−11.5190	+	19.9515i	−0.485900	+	0.841604i
$563$	4.58702	−	7.94495i	0.193320	−	0.334840i	−0.753029	−	0.657988i	$-0.771408\pi$
$563$	4.58702	−	7.94495i	0.193320	−	0.334840i	0.946348	+	0.323148i	$0.104741\pi$
$564$		0			0
$565$	−6.22981	−	10.7903i	−0.262090	−	0.453953i
$566$	13.7904			0.579655
$567$		0			0
$568$	10.8152			0.453796
$569$	10.9471	+	18.9609i	0.458924	+	0.794881i	0.998904	−	0.0467974i	$-0.0149015\pi$
$569$	10.9471	+	18.9609i	0.458924	+	0.794881i	−0.539980	+	0.841678i	$0.681568\pi$
$570$		0			0
$571$	22.5036	−	38.9773i	0.941745	−	1.63115i	0.179604	−	0.983739i	$-0.442518\pi$
$571$	22.5036	−	38.9773i	0.941745	−	1.63115i	0.762141	−	0.647411i	$-0.224148\pi$
$572$	0.0743941	−	0.128854i	0.00311057	−	0.00538767i
$573$		0			0
$574$	3.67204	+	6.36016i	0.153268	+	0.265468i
$575$	−5.57301			−0.232411
$576$		0			0
$577$	11.0993			0.462069			0.231035	−	0.972946i	$-0.425789\pi$
$577$	11.0993			0.462069			0.231035	+	0.972946i	$0.425789\pi$
$578$	−8.49832	−	14.7195i	−0.353483	−	0.612251i
$579$		0			0
$580$	3.26851	−	5.66122i	0.135717	−	0.235069i
$581$	5.93262	−	10.2756i	0.246126	−	0.426304i
$582$		0			0
$583$	−0.881214	−	1.52631i	−0.0364962	−	0.0632132i
$584$	6.14279			0.254190
$585$		0			0
$586$	10.0328			0.414450
$587$	9.08672	+	15.7387i	0.375049	+	0.649604i	0.990334	−	0.138701i	$-0.0442926\pi$
$587$	9.08672	+	15.7387i	0.375049	+	0.649604i	−0.615285	+	0.788304i	$0.710959\pi$
$588$		0			0
$589$	−2.95030	+	5.11006i	−0.121565	+	0.210557i
$590$	3.17480	−	5.49891i	0.130704	−	0.226386i
$591$		0			0
$592$	−0.867592	−	1.50271i	−0.0356578	−	0.0617611i
$593$	45.0659			1.85063			0.925317	−	0.379195i	$-0.123799\pi$
$593$	45.0659			1.85063			0.925317	+	0.379195i	$0.123799\pi$
$594$		0			0
$595$	0.0493820			0.00202447
$596$	1.91592	+	3.31846i	0.0784790	+	0.135930i
$597$		0			0
$598$	2.78651	−	4.82637i	0.113949	−	0.197365i
$599$	22.9386	−	39.7309i	0.937247	−	1.62336i	0.166669	−	0.986013i	$-0.446699\pi$
$599$	22.9386	−	39.7309i	0.937247	−	1.62336i	0.770578	−	0.637346i	$-0.219968\pi$
$600$		0			0
$601$	2.50669	+	4.34172i	0.102250	+	0.177102i	0.912611	−	0.408828i	$-0.134062\pi$
$601$	2.50669	+	4.34172i	0.102250	+	0.177102i	−0.810361	+	0.585930i	$0.800729\pi$
$602$	2.17603			0.0886885
$603$		0			0
$604$	−9.42099			−0.383334
$605$	5.48893	+	9.50711i	0.223157	+	0.386519i
$606$		0			0
$607$	5.28213	−	9.14892i	0.214395	−	0.371343i	−0.738690	−	0.674045i	$-0.764555\pi$
$607$	5.28213	−	9.14892i	0.214395	−	0.371343i	0.953085	+	0.302702i	$0.0978887\pi$
$608$	0.925606	−	1.60320i	0.0375383	−	0.0650182i
$609$		0			0
$610$	−1.10202	−	1.90876i	−0.0446196	−	0.0772833i
$611$	13.1100			0.530375
$612$		0			0
$613$	10.4736			0.423025			0.211513	−	0.977375i	$-0.432161\pi$
$613$	10.4736			0.423025			0.211513	+	0.977375i	$0.432161\pi$
$614$	0.896536	+	1.55285i	0.0361813	+	0.0626678i
$615$		0			0
$616$	0.0633251	−	0.109682i	0.00255144	−	0.00441923i
$617$	−11.1967	+	19.3933i	−0.450763	+	0.780745i	−0.998434	−	0.0559493i	$-0.982181\pi$
$617$	−11.1967	+	19.3933i	−0.450763	+	0.780745i	0.547670	+	0.836694i	$0.315515\pi$
$618$		0			0
$619$	−10.6984	−	18.5302i	−0.430006	−	0.744793i	0.566867	−	0.823809i	$-0.308155\pi$
$619$	−10.6984	−	18.5302i	−0.430006	−	0.744793i	−0.996873	+	0.0790167i	$0.974822\pi$
$620$	3.18742			0.128010
$621$		0			0
$622$	−10.9580			−0.439376
$623$	−2.50675	−	4.34182i	−0.100431	−	0.173951i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.28782	+	5.69468i	−0.131408	+	0.227605i
$627$		0			0
$628$	−5.34152	−	9.25179i	−0.213150	−	0.369187i
$629$	0.100665			0.00401376
$630$		0			0
$631$	0.0358759			0.00142820			0.000714098	−	1.00000i	$-0.499773\pi$
$631$	0.0358759			0.00142820			0.000714098		1.00000i	$0.499773\pi$
$632$	6.67342	+	11.5587i	0.265454	+	0.459780i
$633$		0			0
$634$	6.69942	−	11.6037i	0.266068	−	0.460844i
$635$	3.11840	−	5.40123i	0.123750	−	0.214341i
$636$		0			0
$637$	−3.13772	−	5.43469i	−0.124321	−	0.215330i
$638$	0.972631			0.0385068
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	−16.3066	−	28.2438i	−0.644071	−	1.11556i	−0.984515	−	0.175299i	$-0.943911\pi$
$641$	−16.3066	−	28.2438i	−0.644071	−	1.11556i	0.340444	−	0.940265i	$-0.389423\pi$
$642$		0			0
$643$	11.0464	−	19.1329i	0.435627	−	0.754529i	−0.561719	−	0.827328i	$-0.689860\pi$
$643$	11.0464	−	19.1329i	0.435627	−	0.754529i	0.997347	+	0.0727990i	$0.0231932\pi$
$644$	2.37191	−	4.10827i	0.0934663	−	0.161888i
$645$		0			0
$646$	0.0536979	+	0.0930075i	0.00211272	+	0.00365933i
$647$	−39.0330			−1.53455			−0.767273	−	0.641321i	$-0.778387\pi$
$647$	−39.0330			−1.53455			−0.767273	+	0.641321i	$0.778387\pi$
$648$		0			0
$649$	0.944744			0.0370845
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$		0			0
$652$	−2.81689	+	4.87900i	−0.110318	+	0.191076i
$653$	−20.9333	+	36.2576i	−0.819184	+	1.41887i	0.0871008	+	0.996200i	$0.472240\pi$
$653$	−20.9333	+	36.2576i	−0.819184	+	1.41887i	−0.906284	+	0.422668i	$0.861094\pi$
$654$		0			0
$655$	3.14879	+	5.45386i	0.123033	+	0.213100i
$656$	8.62779			0.336859
$657$		0			0
$658$	11.1594			0.435039
$659$	−3.84521	−	6.66010i	−0.149788	−	0.259441i	0.781361	−	0.624079i	$-0.214526\pi$
$659$	−3.84521	−	6.66010i	−0.149788	−	0.259441i	−0.931149	+	0.364639i	$0.881193\pi$
$660$		0			0
$661$	16.4913	−	28.5638i	0.641437	−	1.11100i	−0.343675	−	0.939089i	$-0.611672\pi$
$661$	16.4913	−	28.5638i	0.641437	−	1.11100i	0.985112	−	0.171913i	$-0.0549949\pi$
$662$	2.58564	−	4.47846i	0.100494	−	0.174060i
$663$		0			0
$664$	−6.96961	−	12.0717i	−0.270473	−	0.468474i
$665$	1.57577			0.0611059
$666$		0			0
$667$	36.4309			1.41061
$668$	6.05232	+	10.4829i	0.234171	+	0.405596i
$669$		0			0
$670$	−2.73281	+	4.73337i	−0.105578	+	0.182866i
$671$	0.163968	−	0.284001i	0.00632991	−	0.0109637i
$672$		0			0
$673$	−5.45699	−	9.45178i	−0.210351	−	0.364339i	0.741473	−	0.670983i	$-0.234127\pi$
$673$	−5.45699	−	9.45178i	−0.210351	−	0.364339i	−0.951825	+	0.306643i	$0.900794\pi$
$674$	20.1288			0.775332
$675$		0			0
$676$	1.00000			0.0384615
$677$	−14.0987	−	24.4197i	−0.541858	−	0.938525i	−0.998797	−	0.0490275i	$-0.984388\pi$
$677$	−14.0987	−	24.4197i	−0.541858	−	0.938525i	0.456940	−	0.889498i	$-0.348946\pi$
$678$		0			0
$679$	1.11978	−	1.93952i	0.0429733	−	0.0744319i
$680$	0.0290069	−	0.0502414i	0.00111236	−	0.00192667i
$681$		0			0
$682$	0.237125	+	0.410713i	0.00908000	+	0.0157270i
$683$	7.03552			0.269207			0.134603	−	0.990900i	$-0.457024\pi$
$683$	7.03552			0.269207			0.134603	+	0.990900i	$0.457024\pi$
$684$		0			0
$685$	−12.1014			−0.462371
$686$	−5.65010	−	9.78627i	−0.215722	−	0.373641i
$687$		0			0
$688$	1.27820	−	2.21390i	0.0487308	−	0.0844042i
$689$	5.92261	−	10.2583i	0.225633	−	0.390808i
$690$		0			0
$691$	−10.6764	−	18.4921i	−0.406150	−	0.703472i	0.588305	−	0.808639i	$-0.299796\pi$
$691$	−10.6764	−	18.4921i	−0.406150	−	0.703472i	−0.994455	+	0.105167i	$0.966462\pi$
$692$	−21.6798			−0.824142
$693$		0			0
$694$	−7.42362			−0.281797
$695$	−1.41892	−	2.45763i	−0.0538225	−	0.0932234i
$696$		0			0
$697$	−0.250265	+	0.433472i	−0.00947948	+	0.0164189i
$698$	−16.0259	+	27.7578i	−0.606591	+	1.05065i
$699$		0			0
$700$	−0.425606	−	0.737171i	−0.0160864	−	0.0278624i
$701$	−41.2962			−1.55974			−0.779868	−	0.625944i	$-0.784714\pi$
$701$	−41.2962			−1.55974			−0.779868	+	0.625944i	$0.784714\pi$
$702$		0			0
$703$	3.21219			0.121150
$704$	−0.0743941	−	0.128854i	−0.00280383	−	0.00485638i
$705$		0			0
$706$	−4.65704	+	8.06622i	−0.175270	+	0.303576i
$707$	5.46130	−	9.45925i	0.205393	−	0.355752i
$708$		0			0
$709$	−9.45137	−	16.3703i	−0.354954	−	0.614798i	0.632156	−	0.774841i	$-0.282170\pi$
$709$	−9.45137	−	16.3703i	−0.354954	−	0.614798i	−0.987110	+	0.160043i	$0.948837\pi$
$710$	10.8152			0.405888
$711$		0			0
$712$	−5.88985			−0.220731
$713$	8.88178	+	15.3837i	0.332625	+	0.576124i
$714$		0			0
$715$	0.0743941	−	0.128854i	0.00278218	−	0.00481888i
$716$	2.44361	−	4.23245i	0.0913219	−	0.158174i
$717$		0			0
$718$	2.51632	+	4.35839i	0.0939081	+	0.162654i
$719$	−40.6689			−1.51669			−0.758347	−	0.651851i	$-0.773993\pi$
$719$	−40.6689			−1.51669			−0.758347	+	0.651851i	$0.773993\pi$
$720$		0			0
$721$	9.22018			0.343378
$722$	−7.78651	−	13.4866i	−0.289784	−	0.501920i
$723$		0			0
$724$	−12.8206	+	22.2059i	−0.476473	+	0.825276i
$725$	3.26851	−	5.66122i	0.121389	−	0.210252i
$726$		0			0
$727$	7.10610	+	12.3081i	0.263551	+	0.456483i	0.967183	−	0.254081i	$-0.0817731\pi$
$727$	7.10610	+	12.3081i	0.263551	+	0.456483i	−0.703632	+	0.710564i	$0.748440\pi$
$728$	0.851212			0.0315480
$729$		0			0
$730$	6.14279			0.227355
$731$	0.0741530	+	0.128437i	0.00274265	+	0.00475041i
$732$		0			0
$733$	−6.85684	+	11.8764i	−0.253263	+	0.438665i	−0.964422	−	0.264366i	$-0.914837\pi$
$733$	−6.85684	+	11.8764i	−0.253263	+	0.438665i	0.711159	+	0.703031i	$0.248171\pi$
$734$	−4.49331	+	7.78264i	−0.165851	+	0.287262i
$735$		0			0
$736$	−2.78651	−	4.82637i	−0.102712	−	0.177902i
$737$	−0.813220			−0.0299553
$738$		0			0
$739$	−28.9640			−1.06546			−0.532729	−	0.846286i	$-0.678833\pi$
$739$	−28.9640			−1.06546			−0.532729	+	0.846286i	$0.678833\pi$
$740$	−0.867592	−	1.50271i	−0.0318933	−	0.0552408i
$741$		0			0
$742$	5.04139	−	8.73195i	0.185075	−	0.320560i
$743$	−17.4459	+	30.2172i	−0.640029	+	1.10856i	0.345396	+	0.938457i	$0.387744\pi$
$743$	−17.4459	+	30.2172i	−0.640029	+	1.10856i	−0.985426	+	0.170106i	$0.945589\pi$
$744$		0			0
$745$	1.91592	+	3.31846i	0.0701937	+	0.121579i
$746$	−3.41036			−0.124862
$747$		0			0
$748$	0.00863177			0.000315609
$749$	0.969614	+	1.67942i	0.0354289	+	0.0613647i
$750$		0			0
$751$	15.0354	−	26.0421i	0.548649	−	0.950288i	−0.449718	−	0.893171i	$-0.648476\pi$
$751$	15.0354	−	26.0421i	0.548649	−	0.950288i	0.998367	−	0.0571179i	$-0.0181911\pi$
$752$	6.55501	−	11.3536i	0.239037	−	0.414024i
$753$		0			0
$754$	3.26851	+	5.66122i	0.119032	+	0.206169i
$755$	−9.42099			−0.342865
$756$		0			0
$757$	−13.6037			−0.494433			−0.247217	−	0.968960i	$-0.579516\pi$
$757$	−13.6037			−0.494433			−0.247217	+	0.968960i	$0.579516\pi$
$758$	15.1978	+	26.3234i	0.552009	+	0.956108i
$759$		0			0
$760$	0.925606	−	1.60320i	0.0335753	−	0.0581540i
$761$	−10.6087	+	18.3748i	−0.384566	+	0.666087i	−0.991709	−	0.128505i	$-0.958982\pi$
$761$	−10.6087	+	18.3748i	−0.384566	+	0.666087i	0.607143	+	0.794592i	$0.292315\pi$
$762$		0			0
$763$	1.94492	+	3.36871i	0.0704109	+	0.121955i
$764$	−7.81845			−0.282862
$765$		0			0
$766$	10.4789			0.378617
$767$	3.17480	+	5.49891i	0.114635	+	0.198554i
$768$		0			0
$769$	−4.79889	+	8.31193i	−0.173053	+	0.299736i	−0.939486	−	0.342588i	$-0.888696\pi$
$769$	−4.79889	+	8.31193i	−0.173053	+	0.299736i	0.766433	+	0.642324i	$0.222030\pi$
$770$	0.0633251	−	0.109682i	0.00228208	−	0.00395268i
$771$		0			0
$772$	−5.60709	−	9.71177i	−0.201804	−	0.349534i
$773$	−48.6082			−1.74831			−0.874157	−	0.485643i	$-0.838585\pi$
$773$	−48.6082			−1.74831			−0.874157	+	0.485643i	$0.838585\pi$
$774$		0			0
$775$	3.18742			0.114496
$776$	−1.31551	−	2.27854i	−0.0472242	−	0.0817947i
$777$		0			0
$778$	6.42392	−	11.1266i	0.230309	−	0.398907i
$779$	−7.98593	+	13.8320i	−0.286126	+	0.495584i
$780$		0			0
$781$	0.804588	+	1.39359i	0.0287904	+	0.0498665i
$782$	0.323312			0.0115616
$783$		0			0
$784$	−6.27544			−0.224123
$785$	−5.34152	−	9.25179i	−0.190647	−	0.330210i
$786$		0			0
$787$	14.8528	−	25.7258i	0.529444	−	0.917024i	−0.469966	−	0.882684i	$-0.655734\pi$
$787$	14.8528	−	25.7258i	0.529444	−	0.917024i	0.999410	−	0.0343396i	$-0.0109328\pi$
$788$	12.4046	−	21.4854i	0.441896	−	0.765386i
$789$		0			0
$790$	6.67342	+	11.5587i	0.237430	+	0.411240i
$791$	10.6058			0.377098
$792$		0			0
$793$	2.20404			0.0782679
$794$	3.29758	+	5.71157i	0.117027	+	0.202696i
$795$		0			0
$796$	−2.89360	+	5.01186i	−0.102561	+	0.177641i
$797$	15.2340	−	26.3861i	0.539618	−	0.934645i	−0.459307	−	0.888278i	$-0.651902\pi$
$797$	15.2340	−	26.3861i	0.539618	−	0.934645i	0.998924	−	0.0463674i	$-0.0147645\pi$
$798$		0			0
$799$	0.380281	+	0.658666i	0.0134534	+	0.0233019i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$	−15.9699			−0.563916
$803$	0.456987	+	0.791525i	0.0161267	+	0.0279323i
$804$		0			0
$805$	2.37191	−	4.10827i	0.0835988	−	0.144797i
$806$	−1.59371	+	2.76039i	−0.0561361	+	0.0972305i
$807$		0			0
$808$	−6.41592	−	11.1127i	−0.225711	−	0.390943i
$809$	7.09401			0.249412			0.124706	−	0.992194i	$-0.460201\pi$
$809$	7.09401			0.249412			0.124706	+	0.992194i	$0.460201\pi$
$810$		0			0
$811$	7.57914			0.266140			0.133070	−	0.991107i	$-0.457517\pi$
$811$	7.57914			0.266140			0.133070	+	0.991107i	$0.457517\pi$
$812$	2.78219	+	4.81890i	0.0976358	+	0.169110i
$813$		0			0
$814$	0.129087	−	0.223586i	0.00452451	−	0.00783669i
$815$	−2.81689	+	4.87900i	−0.0986715	+	0.170904i
$816$		0			0
$817$	2.36621	+	4.09840i	0.0827833	+	0.143385i
$818$	0.969998			0.0339152
$819$		0			0
$820$	8.62779			0.301295
$821$	−6.27582	−	10.8700i	−0.219028	−	0.379367i	0.735483	−	0.677543i	$-0.236955\pi$
$821$	−6.27582	−	10.8700i	−0.219028	−	0.379367i	−0.954511	+	0.298176i	$0.903622\pi$
$822$		0			0
$823$	23.9253	−	41.4398i	0.833984	−	1.44450i	−0.0608717	−	0.998146i	$-0.519388\pi$
$823$	23.9253	−	41.4398i	0.833984	−	1.44450i	0.894855	−	0.446356i	$-0.147279\pi$
$824$	5.41592	−	9.38064i	0.188672	−	0.326790i
$825$		0			0
$826$	2.70242	+	4.68073i	0.0940293	+	0.162864i
$827$	24.9360			0.867109			0.433555	−	0.901127i	$-0.357259\pi$
$827$	24.9360			0.867109			0.433555	+	0.901127i	$0.357259\pi$
$828$		0			0
$829$	10.8598			0.377178			0.188589	−	0.982056i	$-0.439609\pi$
$829$	10.8598			0.377178			0.188589	+	0.982056i	$0.439609\pi$
$830$	−6.96961	−	12.0717i	−0.241919	−	0.419016i
$831$		0			0
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	0.182031	−	0.315287i	0.00630700	−	0.0109240i
$834$		0			0
$835$	6.05232	+	10.4829i	0.209449	+	0.362777i
$836$	0.275439			0.00952624
$837$		0			0
$838$	23.4983			0.811734
$839$	−9.52163	−	16.4919i	−0.328723	−	0.569365i	0.653536	−	0.756896i	$-0.273285\pi$
$839$	−9.52163	−	16.4919i	−0.328723	−	0.569365i	−0.982259	+	0.187531i	$0.939952\pi$
$840$		0			0
$841$	−6.86628	+	11.8927i	−0.236768	+	0.410094i
$842$	0.422669	−	0.732084i	0.0145661	−	0.0252293i
$843$		0			0
$844$	−1.23149	−	2.13301i	−0.0423897	−	0.0734212i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−9.34449			−0.321080
$848$	−5.92261	−	10.2583i	−0.203383	−	0.352270i
$849$		0			0
$850$	0.0290069	−	0.0502414i	0.000994928	−	0.00172327i
$851$	4.83510	−	8.37465i	0.165745	−	0.287079i
$852$		0			0
$853$	24.9101	+	43.1456i	0.852905	+	1.47728i	0.878575	+	0.477605i	$0.158495\pi$
$853$	24.9101	+	43.1456i	0.852905	+	1.47728i	−0.0256692	+	0.999670i	$0.508172\pi$
$854$	1.87611			0.0641991
$855$		0			0
$856$	2.27820			0.0778672
$857$	13.5730	+	23.5092i	0.463645	+	0.803057i	0.999139	−	0.0414818i	$-0.0132078\pi$
$857$	13.5730	+	23.5092i	0.463645	+	0.803057i	−0.535494	+	0.844539i	$0.679875\pi$
$858$		0			0
$859$	9.94993	−	17.2338i	0.339487	−	0.588009i	−0.644849	−	0.764310i	$-0.723080\pi$
$859$	9.94993	−	17.2338i	0.339487	−	0.588009i	0.984336	+	0.176301i	$0.0564131\pi$
$860$	1.27820	−	2.21390i	0.0435861	−	0.0754934i
$861$		0			0
$862$	17.4417	+	30.2099i	0.594066	+	1.02895i
$863$	2.24743			0.0765033			0.0382517	−	0.999268i	$-0.487821\pi$
$863$	2.24743			0.0765033			0.0382517	+	0.999268i	$0.487821\pi$
$864$		0			0
$865$	−21.6798			−0.737135
$866$	11.8705	+	20.5603i	0.403375	+	0.698666i
$867$		0			0
$868$	−1.35659	+	2.34968i	−0.0460455	+	0.0797532i
$869$	−0.992926	+	1.71980i	−0.0336827	+	0.0583402i
$870$		0			0
$871$	−2.73281	−	4.73337i	−0.0925977	−	0.160384i
$872$	4.56977			0.154752
$873$		0			0
$874$	10.3168			0.348972
$875$	−0.425606	−	0.737171i	−0.0143881	−	0.0249209i
$876$		0			0
$877$	20.5013	−	35.5092i	0.692278	−	1.19906i	−0.278811	−	0.960346i	$-0.589940\pi$
$877$	20.5013	−	35.5092i	0.692278	−	1.19906i	0.971090	−	0.238715i	$-0.0767262\pi$
$878$	19.4279	−	33.6500i	0.655658	−	1.13563i
$879$		0			0
$880$	−0.0743941	−	0.128854i	−0.00250783	−	0.00434368i
$881$	−33.9525			−1.14389			−0.571944	−	0.820293i	$-0.693811\pi$
$881$	−33.9525			−1.14389			−0.571944	+	0.820293i	$0.693811\pi$
$882$		0			0
$883$	27.8138			0.936010			0.468005	−	0.883726i	$-0.344973\pi$
$883$	27.8138			0.936010			0.468005	+	0.883726i	$0.344973\pi$
$884$	0.0290069	+	0.0502414i	0.000975608	+	0.00168980i
$885$		0			0
$886$	−8.67180	+	15.0200i	−0.291335	+	0.504607i
$887$	23.9454	−	41.4746i	0.804007	−	1.39258i	−0.112952	−	0.993600i	$-0.536031\pi$
$887$	23.9454	−	41.4746i	0.804007	−	1.39258i	0.916959	−	0.398981i	$-0.130636\pi$
$888$		0			0
$889$	2.65442	+	4.59759i	0.0890264	+	0.154198i
$890$	−5.88985			−0.197428
$891$		0			0
$892$	−14.1487			−0.473732
$893$	12.1347	+	21.0180i	0.406073	+	0.703339i
$894$		0			0
$895$	2.44361	−	4.23245i	0.0816808	−	0.141475i
$896$	0.425606	−	0.737171i	0.0142185	−	0.0246272i
$897$		0			0
$898$	2.25726	+	3.90969i	0.0753257	+	0.130468i
$899$	−20.8362			−0.694927
$900$		0			0
$901$	0.687186			0.0228935
$902$	0.641857	+	1.11173i	0.0213715	+	0.0370165i
$903$		0			0
$904$	6.22981	−	10.7903i	0.207200	−	0.358882i
$905$	−12.8206	+	22.2059i	−0.426171	+	0.738149i
$906$		0			0
$907$	10.7792	+	18.6701i	0.357917	+	0.619931i	0.987613	−	0.156911i	$-0.0501537\pi$
$907$	10.7792	+	18.6701i	0.357917	+	0.619931i	−0.629695	+	0.776842i	$0.716820\pi$
$908$	13.6218			0.452055
$909$		0			0
$910$	0.851212			0.0282174
$911$	19.7802	+	34.2603i	0.655347	+	1.13510i	0.981807	+	0.189884i	$0.0608111\pi$
$911$	19.7802	+	34.2603i	0.655347	+	1.13510i	−0.326459	+	0.945211i	$0.605856\pi$
$912$		0			0
$913$	1.03700	−	1.79613i	0.0343196	−	0.0594432i
$914$	−12.2174	+	21.1612i	−0.404116	+	0.699950i
$915$		0			0
$916$	0.765570	+	1.32601i	0.0252952	+	0.0438125i
$917$	−5.36057			−0.177022
$918$		0			0
$919$	−0.985977			−0.0325244			−0.0162622	−	0.999868i	$-0.505177\pi$
$919$	−0.985977			−0.0325244			−0.0162622	+	0.999868i	$0.505177\pi$
$920$	−2.78651	−	4.82637i	−0.0918684	−	0.159121i
$921$		0			0
$922$	7.34446	−	12.7210i	0.241877	−	0.418943i
$923$	−5.40761	+	9.36625i	−0.177993	+	0.308294i
$924$		0			0
$925$	−0.867592	−	1.50271i	−0.0285263	−	0.0494089i
$926$	−3.98800			−0.131054
$927$		0			0
$928$	6.53701			0.214588
$929$	−27.0874	−	46.9168i	−0.888709	−	1.53929i	−0.841403	−	0.540409i	$-0.818270\pi$
$929$	−27.0874	−	46.9168i	−0.888709	−	1.53929i	−0.0473065	−	0.998880i	$-0.515064\pi$
$930$		0			0
$931$	5.80858	−	10.0608i	0.190369	−	0.329728i
$932$	−6.27544	+	10.8694i	−0.205559	+	0.356038i
$933$		0			0
$934$	−14.5299	−	25.1666i	−0.475434	−	0.823476i
$935$	0.00863177			0.000282289
$936$		0			0
$937$	8.63366			0.282049			0.141025	−	0.990006i	$-0.454960\pi$
$937$	8.63366			0.282049			0.141025	+	0.990006i	$0.454960\pi$
$938$	−2.32620	−	4.02910i	−0.0759531	−	0.131555i
$939$		0			0
$940$	6.55501	−	11.3536i	0.213801	−	0.370314i
$941$	−1.51107	+	2.61725i	−0.0492594	+	0.0853199i	−0.889604	−	0.456733i	$-0.849019\pi$
$941$	−1.51107	+	2.61725i	−0.0492594	+	0.0853199i	0.840344	+	0.542053i	$0.182353\pi$
$942$		0			0
$943$	24.0414	+	41.6409i	0.782896	+	1.35601i
$944$	6.34959			0.206662
$945$		0			0
$946$	0.380361			0.0123666
$947$	25.9158	+	44.8875i	0.842150	+	1.45865i	0.888073	+	0.459702i	$0.152044\pi$
$947$	25.9158	+	44.8875i	0.842150	+	1.45865i	−0.0459233	+	0.998945i	$0.514623\pi$
$948$		0			0
$949$	−3.07139	+	5.31981i	−0.0997017	+	0.172688i
$950$	0.925606	−	1.60320i	0.0300306	−	0.0520146i
$951$		0			0
$952$	0.0246910	+	0.0427661i	0.000800240	+	0.00138606i
$953$	−39.5024			−1.27961			−0.639804	−	0.768538i	$-0.720985\pi$
$953$	−39.5024			−1.27961			−0.639804	+	0.768538i	$0.720985\pi$
$954$		0			0
$955$	−7.81845			−0.252999
$956$	10.1748	+	17.6233i	0.329076	+	0.569977i
$957$		0			0
$958$	20.6816	−	35.8216i	0.668192	−	1.15734i
$959$	5.15043	−	8.92080i	0.166316	−	0.288068i
$960$		0			0
$961$	10.4202	+	18.0483i	0.336134	+	0.582202i
$962$	1.73518			0.0559446
$963$		0			0
$964$	11.0328			0.355341
$965$	−5.60709	−	9.71177i	−0.180499	−	0.312633i
$966$		0			0
$967$	−4.86597	+	8.42811i	−0.156479	+	0.271030i	−0.933597	−	0.358326i	$-0.883348\pi$
$967$	−4.86597	+	8.42811i	−0.156479	+	0.271030i	0.777118	+	0.629356i	$0.216681\pi$
$968$	−5.48893	+	9.50711i	−0.176421	+	0.305570i
$969$		0			0
$970$	−1.31551	−	2.27854i	−0.0422386	−	0.0731594i
$971$	10.7765			0.345833			0.172916	−	0.984937i	$-0.444681\pi$
$971$	10.7765			0.345833			0.172916	+	0.984937i	$0.444681\pi$
$972$		0			0
$973$	2.41559			0.0774404
$974$	−21.3054	−	36.9021i	−0.682670	−	1.18242i
$975$		0			0
$976$	1.10202	−	1.90876i	0.0352749	−	0.0610979i
$977$	−17.9926	+	31.1640i	−0.575633	+	0.997026i	0.420340	+	0.907367i	$0.361911\pi$
$977$	−17.9926	+	31.1640i	−0.575633	+	0.997026i	−0.995973	+	0.0896587i	$0.971422\pi$
$978$		0			0
$979$	−0.438170	−	0.758932i	−0.0140040	−	0.0242556i
$980$	−6.27544			−0.200462
$981$		0			0
$982$	12.0546			0.384679
$983$	11.6844	+	20.2380i	0.372675	+	0.645492i	0.989976	−	0.141235i	$-0.0451072\pi$
$983$	11.6844	+	20.2380i	0.372675	+	0.645492i	−0.617301	+	0.786727i	$0.711774\pi$
$984$		0			0
$985$	12.4046	−	21.4854i	0.395244	−	0.684582i
$986$	−0.189618	+	0.328429i	−0.00603868	+	0.0104593i
$987$		0			0
$988$	0.925606	+	1.60320i	0.0294474	+	0.0510045i
$989$	14.2468			0.453023
$990$		0			0
$991$	−13.6196			−0.432642			−0.216321	−	0.976322i	$-0.569406\pi$
$991$	−13.6196			−0.432642			−0.216321	+	0.976322i	$0.569406\pi$
$992$	1.59371	+	2.76039i	0.0506004	+	0.0876424i
$993$		0			0
$994$	−4.60302	+	7.97266i	−0.145999	+	0.252877i
$995$	−2.89360	+	5.01186i	−0.0917333	+	0.158887i
$996$		0			0
$997$	−14.4871	−	25.0923i	−0.458810	−	0.794682i	0.540088	−	0.841608i	$-0.318391\pi$
$997$	−14.4871	−	25.0923i	−0.458810	−	0.794682i	−0.998898	+	0.0469260i	$0.985058\pi$
$998$	−33.5281			−1.06131
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3510.2.j.h.1171.1		8
3.2	odd	2		1170.2.j.h.391.1	✓	8
9.2	odd	6		1170.2.j.h.781.1	yes	8
9.7	even	3	inner	3510.2.j.h.2341.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.j.h.391.1	✓	8	3.2	odd	2
1170.2.j.h.781.1	yes	8	9.2	odd	6
3510.2.j.h.1171.1		8	1.1	even	1	trivial
3510.2.j.h.2341.1		8	9.7	even	3	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3510 = 2 \cdot 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3510.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.425606 - 0.737171i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(-0.0743941 - 0.128854i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.425606 - 0.737171i) q^{14} +(-0.500000 - 0.866025i) q^{16} +0.0580138 q^{17} +1.85121 q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.0743941 - 0.128854i) q^{22} +(2.78651 - 4.82637i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +0.851212 q^{28} +(3.26851 + 5.66122i) q^{29} +(-1.59371 + 2.76039i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.0290069 + 0.0502414i) q^{34} +0.851212 q^{35} +1.73518 q^{37} +(0.925606 + 1.60320i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-4.31389 + 7.47188i) q^{41} +(1.27820 + 2.21390i) q^{43} +0.148788 q^{44} +5.57301 q^{46} +(6.55501 + 11.3536i) q^{47} +(3.13772 - 5.43469i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} +11.8452 q^{53} +0.148788 q^{55} +(0.425606 + 0.737171i) q^{56} +(-3.26851 + 5.66122i) q^{58} +(-3.17480 + 5.49891i) q^{59} +(1.10202 + 1.90876i) q^{61} -3.18742 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(2.73281 - 4.73337i) q^{67} +(-0.0290069 + 0.0502414i) q^{68} +(0.425606 + 0.737171i) q^{70} -10.8152 q^{71} -6.14279 q^{73} +(0.867592 + 1.50271i) q^{74} +(-0.925606 + 1.60320i) q^{76} +(-0.0633251 + 0.109682i) q^{77} +(-6.67342 - 11.5587i) q^{79} +1.00000 q^{80} -8.62779 q^{82} +(6.96961 + 12.0717i) q^{83} +(-0.0290069 + 0.0502414i) q^{85} +(-1.27820 + 2.21390i) q^{86} +(0.0743941 + 0.128854i) q^{88} +5.88985 q^{89} -0.851212 q^{91} +(2.78651 + 4.82637i) q^{92} +(-6.55501 + 11.3536i) q^{94} +(-0.925606 + 1.60320i) q^{95} +(1.31551 + 2.27854i) q^{97} +6.27544 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 4 q^{5} + 7 q^{7} - 8 q^{8} - 8 q^{10} - 11 q^{11} + 4 q^{13} - 7 q^{14} - 4 q^{16} + 8 q^{17} - 6 q^{19} - 4 q^{20} + 11 q^{22} + 15 q^{23} - 4 q^{25} + 8 q^{26} - 14 q^{28} - 4 q^{29}+ \cdots - 6 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 4 * q^5 + 7 * q^7 - 8 * q^8 - 8 * q^10 - 11 * q^11 + 4 * q^13 - 7 * q^14 - 4 * q^16 + 8 * q^17 - 6 * q^19 - 4 * q^20 + 11 * q^22 + 15 * q^23 - 4 * q^25 + 8 * q^26 - 14 * q^28 - 4 * q^29 - 3 * q^31 + 4 * q^32 + 4 * q^34 - 14 * q^35 - 22 * q^37 - 3 * q^38 + 4 * q^40 - 11 * q^41 + 4 * q^43 + 22 * q^44 + 30 * q^46 + 15 * q^47 - 3 * q^49 + 4 * q^50 + 4 * q^52 - 16 * q^53 + 22 * q^55 - 7 * q^56 + 4 * q^58 - 5 * q^59 - 2 * q^61 - 6 * q^62 + 8 * q^64 + 4 * q^65 + 9 * q^67 - 4 * q^68 - 7 * q^70 - 20 * q^71 + 20 * q^73 - 11 * q^74 + 3 * q^76 + 38 * q^77 - 8 * q^79 + 8 * q^80 - 22 * q^82 + 27 * q^83 - 4 * q^85 - 4 * q^86 + 11 * q^88 - 14 * q^89 + 14 * q^91 + 15 * q^92 - 15 * q^94 + 3 * q^95 + 7 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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