LMFDB - Embedded newform 315.2.bj.a.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(26,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("315.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bj (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 312x^{2} + 36 $ x^12 + 20x^10 + 144x^8 + 452x^6 + 604x^4 + 312*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.5
Root			$1.99567i$ of defining polynomial
Character	$\chi$	$=$	315.26
Dual form			315.2.bj.a.206.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72830 + 0.997835i) q^{2} +(0.991350 + 1.71707i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.78020 + 1.95727i) q^{7} -0.0345244i q^{8} +O(q^{10})$	\(q+(1.72830 + 0.997835i) q^{2} +(0.991350 + 1.71707i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.78020 + 1.95727i) q^{7} -0.0345244i q^{8} +(-1.72830 + 0.997835i) q^{10} +(1.56652 - 0.904429i) q^{11} +5.33881i q^{13} +(1.12369 + 5.15909i) q^{14} +(2.01715 - 3.49381i) q^{16} +(-0.932008 - 1.61429i) q^{17} +(-1.79482 - 1.03624i) q^{19} -1.98270 q^{20} +3.60989 q^{22} +(-7.16531 - 4.13690i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.32725 + 9.22706i) q^{26} +(-1.59596 + 4.99706i) q^{28} -2.79369i q^{29} +(6.71938 - 3.87944i) q^{31} +(6.91269 - 3.99104i) q^{32} -3.71996i q^{34} +(-2.58514 + 0.563064i) q^{35} +(3.73210 - 6.46419i) q^{37} +(-2.06799 - 3.58187i) q^{38} +(0.0298990 + 0.0172622i) q^{40} -3.78017 q^{41} -3.14243 q^{43} +(3.10594 + 1.79321i) q^{44} +(-8.25588 - 14.2996i) q^{46} +(-2.69021 + 4.65958i) q^{47} +(-0.661784 + 6.96865i) q^{49} -1.99567i q^{50} +(-9.16710 + 5.29263i) q^{52} +(4.42119 - 2.55257i) q^{53} +1.80886i q^{55} +(0.0675734 - 0.0614603i) q^{56} +(2.78764 - 4.82834i) q^{58} +(-4.12369 - 7.14244i) q^{59} +(-6.75422 - 3.89955i) q^{61} +15.4842 q^{62} +7.86101 q^{64} +(-4.62354 - 2.66940i) q^{65} +(5.60962 + 9.71614i) q^{67} +(1.84789 - 3.20064i) q^{68} +(-5.02975 - 1.60640i) q^{70} +9.97319i q^{71} +(-14.2718 + 8.23984i) q^{73} +(12.9004 - 7.44805i) q^{74} -4.10910i q^{76} +(4.55892 + 1.45603i) q^{77} +(2.11854 - 3.66941i) q^{79} +(2.01715 + 3.49381i) q^{80} +(-6.53327 - 3.77199i) q^{82} +9.01001 q^{83} +1.86402 q^{85} +(-5.43107 - 3.13563i) q^{86} +(-0.0312249 - 0.0540831i) q^{88} +(3.37674 - 5.84868i) q^{89} +(-10.4495 + 9.50414i) q^{91} -16.4045i q^{92} +(-9.29898 + 5.36877i) q^{94} +(1.79482 - 1.03624i) q^{95} +2.19212i q^{97} +(-8.09732 + 11.3836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7	$ 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7} + 12 q^{11} - 12 q^{14} - 16 q^{16} + 6 q^{19} - 16 q^{20} + 32 q^{22} + 12 q^{23} - 6 q^{25} - 20 q^{28} + 6 q^{31} + 60 q^{32} - 2 q^{35} - 10 q^{37} - 36 q^{38} + 24 q^{41} - 4 q^{43} + 12 q^{44} - 4 q^{46} + 6 q^{49} + 12 q^{53} - 60 q^{56} + 20 q^{58} - 24 q^{59} + 24 q^{62} - 56 q^{64} + 18 q^{65} + 6 q^{67} - 60 q^{68} - 12 q^{70} - 42 q^{73} + 84 q^{74} - 36 q^{77} + 18 q^{79} - 16 q^{80} - 72 q^{82} - 24 q^{83} - 84 q^{86} + 4 q^{88} + 12 q^{89} - 18 q^{91} + 12 q^{94} - 6 q^{95} + 12 q^{98}+O(q^{100}) $ 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7 + 12 * q^11 - 12 * q^14 - 16 * q^16 + 6 * q^19 - 16 * q^20 + 32 * q^22 + 12 * q^23 - 6 * q^25 - 20 * q^28 + 6 * q^31 + 60 * q^32 - 2 * q^35 - 10 * q^37 - 36 * q^38 + 24 * q^41 - 4 * q^43 + 12 * q^44 - 4 * q^46 + 6 * q^49 + 12 * q^53 - 60 * q^56 + 20 * q^58 - 24 * q^59 + 24 * q^62 - 56 * q^64 + 18 * q^65 + 6 * q^67 - 60 * q^68 - 12 * q^70 - 42 * q^73 + 84 * q^74 - 36 * q^77 + 18 * q^79 - 16 * q^80 - 72 * q^82 - 24 * q^83 - 84 * q^86 + 4 * q^88 + 12 * q^89 - 18 * q^91 + 12 * q^94 - 6 * q^95 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.72830	+	0.997835i	1.22209	+	0.705576i	0.965364	−	0.260907i	$-0.0840217\pi$
$2$	1.72830	+	0.997835i	1.22209	+	0.705576i	0.256730	+	0.966483i	$0.417355\pi$
$3$		0			0
$3$		0			0
$4$	0.991350	+	1.71707i	0.495675	+	0.858534i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.78020	+	1.95727i	0.672852	+	0.739777i
$7$	1.78020	+	1.95727i	0.672852	+	0.739777i
$8$		−	0.0345244i		−	0.0122062i
$9$		0			0
$10$	−1.72830	+	0.997835i	−0.546537	+	0.315543i
$11$	1.56652	−	0.904429i	0.472323	−	0.272696i	−0.244889	−	0.969551i	$-0.578751\pi$
$11$	1.56652	−	0.904429i	0.472323	−	0.272696i	0.717212	+	0.696855i	$0.245418\pi$
$12$		0			0
$13$			5.33881i			1.48072i	0.672212	+	0.740359i	$0.265345\pi$
$13$			5.33881i			1.48072i	−0.672212	+	0.740359i	$0.734655\pi$
$14$	1.12369	+	5.15909i	0.300319	+	1.37883i
$15$		0			0
$16$	2.01715	−	3.49381i	0.504288	−	0.873452i
$17$	−0.932008	−	1.61429i	−0.226045	−	0.391522i	0.730587	−	0.682819i	$-0.239246\pi$
$17$	−0.932008	−	1.61429i	−0.226045	−	0.391522i	−0.956632	+	0.291298i	$0.905913\pi$
$18$		0			0
$19$	−1.79482	−	1.03624i	−0.411760	−	0.237730i	0.279786	−	0.960062i	$-0.409737\pi$
$19$	−1.79482	−	1.03624i	−0.411760	−	0.237730i	−0.691546	+	0.722333i	$0.743070\pi$
$20$	−1.98270			−0.443345
$21$		0			0
$22$	3.60989			0.769630
$23$	−7.16531	−	4.13690i	−1.49407	−	0.862603i	−0.494095	−	0.869408i	$-0.664500\pi$
$23$	−7.16531	−	4.13690i	−1.49407	−	0.862603i	−0.999977	+	0.00680565i	$0.997834\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−5.32725	+	9.22706i	−1.04476	+	1.80958i
$27$		0			0
$28$	−1.59596	+	4.99706i	−0.301608	+	0.944356i
$29$		−	2.79369i		−	0.518775i	−0.965773	−	0.259388i	$-0.916479\pi$
$29$		−	2.79369i		−	0.518775i	0.965773	−	0.259388i	$-0.0835207\pi$
$30$		0			0
$31$	6.71938	−	3.87944i	1.20684	−	0.696767i	0.244770	−	0.969581i	$-0.421288\pi$
$31$	6.71938	−	3.87944i	1.20684	−	0.696767i	0.962067	+	0.272814i	$0.0879543\pi$
$32$	6.91269	−	3.99104i	1.22200	−	0.705523i
$33$		0			0
$34$		−	3.71996i		−	0.637968i
$35$	−2.58514	+	0.563064i	−0.436969	+	0.0951752i
$36$		0			0
$37$	3.73210	−	6.46419i	0.613554	−	1.06271i	−0.377083	−	0.926180i	$-0.623073\pi$
$37$	3.73210	−	6.46419i	0.613554	−	1.06271i	0.990636	−	0.136527i	$-0.0435940\pi$
$38$	−2.06799	−	3.58187i	−0.335473	−	0.581056i
$39$		0			0
$40$	0.0298990	+	0.0172622i	0.00472745	+	0.00272939i
$41$	−3.78017			−0.590363			−0.295182	−	0.955441i	$-0.595380\pi$
$41$	−3.78017			−0.590363			−0.295182	+	0.955441i	$0.595380\pi$
$42$		0			0
$43$	−3.14243			−0.479217			−0.239608	−	0.970870i	$-0.577019\pi$
$43$	−3.14243			−0.479217			−0.239608	+	0.970870i	$0.577019\pi$
$44$	3.10594	+	1.79321i	0.468237	+	0.270337i
$45$		0			0
$46$	−8.25588	−	14.2996i	−1.21726	−	2.10836i
$47$	−2.69021	+	4.65958i	−0.392407	+	0.679669i	−0.992766	−	0.120061i	$-0.961691\pi$
$47$	−2.69021	+	4.65958i	−0.392407	+	0.679669i	0.600359	+	0.799730i	$0.295024\pi$
$48$		0			0
$49$	−0.661784	+	6.96865i	−0.0945405	+	0.995521i
$50$		−	1.99567i		−	0.282230i
$51$		0			0
$52$	−9.16710	+	5.29263i	−1.27125	+	0.733955i
$53$	4.42119	−	2.55257i	0.607297	−	0.350623i	−0.164610	−	0.986359i	$-0.552636\pi$
$53$	4.42119	−	2.55257i	0.607297	−	0.350623i	0.771907	+	0.635736i	$0.219303\pi$
$54$		0			0
$55$			1.80886i			0.243906i
$56$	0.0675734	−	0.0614603i	0.00902988	−	0.00821298i
$57$		0			0
$58$	2.78764	−	4.82834i	0.366036	−	0.633992i
$59$	−4.12369	−	7.14244i	−0.536859	−	0.929867i	−0.999071	−	0.0430973i	$-0.986277\pi$
$59$	−4.12369	−	7.14244i	−0.536859	−	0.929867i	0.462212	−	0.886769i	$-0.347056\pi$
$60$		0			0
$61$	−6.75422	−	3.89955i	−0.864789	−	0.499286i	0.000823881	−	1.00000i	$-0.499738\pi$
$61$	−6.75422	−	3.89955i	−0.864789	−	0.499286i	−0.865613	+	0.500713i	$0.833071\pi$
$62$	15.4842			1.96649
$63$		0			0
$64$	7.86101			0.982626
$65$	−4.62354	−	2.66940i	−0.573480	−	0.331099i
$66$		0			0
$67$	5.60962	+	9.71614i	0.685324	+	1.18702i	0.973335	+	0.229388i	$0.0736726\pi$
$67$	5.60962	+	9.71614i	0.685324	+	1.18702i	−0.288011	+	0.957627i	$0.592994\pi$
$68$	1.84789	−	3.20064i	0.224090	−	0.388135i
$69$		0			0
$70$	−5.02975	−	1.60640i	−0.601170	−	0.192002i
$71$			9.97319i			1.18360i	0.806085	+	0.591800i	$0.201583\pi$
$71$			9.97319i			1.18360i	−0.806085	+	0.591800i	$0.798417\pi$
$72$		0			0
$73$	−14.2718	+	8.23984i	−1.67039	+	0.964401i	−0.702973	+	0.711217i	$0.748144\pi$
$73$	−14.2718	+	8.23984i	−1.67039	+	0.964401i	−0.967418	+	0.253184i	$0.918522\pi$
$74$	12.9004	−	7.44805i	1.49964	−	0.865818i
$75$		0			0
$76$		−	4.10910i		−	0.471347i
$77$	4.55892	+	1.45603i	0.519537	+	0.165930i
$78$		0			0
$79$	2.11854	−	3.66941i	0.238354	−	0.412841i	−0.721888	−	0.692010i	$-0.756726\pi$
$79$	2.11854	−	3.66941i	0.238354	−	0.412841i	0.960242	+	0.279169i	$0.0900589\pi$
$80$	2.01715	+	3.49381i	0.225524	+	0.390619i
$81$		0			0
$82$	−6.53327	−	3.77199i	−0.721479	−	0.416546i
$83$	9.01001			0.988977			0.494489	−	0.869184i	$-0.335355\pi$
$83$	9.01001			0.988977			0.494489	+	0.869184i	$0.335355\pi$
$84$		0			0
$85$	1.86402			0.202181
$86$	−5.43107	−	3.13563i	−0.585648	−	0.338124i
$87$		0			0
$88$	−0.0312249	−	0.0540831i	−0.00332858	−	0.00576528i
$89$	3.37674	−	5.84868i	0.357933	−	0.619959i	−0.629682	−	0.776853i	$-0.716815\pi$
$89$	3.37674	−	5.84868i	0.357933	−	0.619959i	0.987615	+	0.156894i	$0.0501482\pi$
$90$		0			0
$91$	−10.4495	+	9.50414i	−1.09540	+	0.996304i
$92$		−	16.4045i		−	1.71028i
$93$		0			0
$94$	−9.29898	+	5.36877i	−0.959117	+	0.553746i
$95$	1.79482	−	1.03624i	0.184145	−	0.106316i
$96$		0			0
$97$			2.19212i			0.222576i	0.993788	+	0.111288i	$0.0354976\pi$
$97$			2.19212i			0.222576i	−0.993788	+	0.111288i	$0.964502\pi$
$98$	−8.09732	+	11.3836i	−0.817953	+	1.14991i
$99$		0			0
$100$	0.991350	−	1.71707i	0.0991350	−	0.171707i
$101$	−2.63704	−	4.56749i	−0.262395	−	0.454482i	0.704483	−	0.709721i	$-0.251179\pi$
$101$	−2.63704	−	4.56749i	−0.262395	−	0.454482i	−0.966878	+	0.255239i	$0.917846\pi$
$102$		0			0
$103$	5.68990	+	3.28507i	0.560643	+	0.323687i	0.753403	−	0.657559i	$-0.228411\pi$
$103$	5.68990	+	3.28507i	0.560643	+	0.323687i	−0.192761	+	0.981246i	$0.561744\pi$
$104$	0.184319			0.0180740
$105$		0			0
$106$	10.1882			0.989565
$107$	8.50847	+	4.91237i	0.822545	+	0.474897i	0.851293	−	0.524690i	$-0.175819\pi$
$107$	8.50847	+	4.91237i	0.822545	+	0.474897i	−0.0287483	+	0.999587i	$0.509152\pi$
$108$		0			0
$109$	−1.55799	−	2.69851i	−0.149228	−	0.258471i	0.781714	−	0.623637i	$-0.214346\pi$
$109$	−1.55799	−	2.69851i	−0.149228	−	0.258471i	−0.930942	+	0.365166i	$0.881012\pi$
$110$	−1.80494	+	3.12625i	−0.172095	+	0.298077i
$111$		0			0
$112$	10.4292	−	2.27157i	0.985470	−	0.214643i
$113$			16.5865i			1.56032i	0.625578	+	0.780161i	$0.284863\pi$
$113$			16.5865i			1.56032i	−0.625578	+	0.780161i	$0.715137\pi$
$114$		0			0
$115$	7.16531	−	4.13690i	0.668169	−	0.385768i
$116$	4.79696	−	2.76953i	0.445387	−	0.257144i
$117$		0			0
$118$		−	16.4591i		−	1.51518i
$119$	1.50043	−	4.69794i	0.137544	−	0.430659i
$120$		0			0
$121$	−3.86401	+	6.69267i	−0.351274	+	0.608425i
$122$	−7.78222	−	13.4792i	−0.704569	−	1.22035i
$123$		0			0
$124$	13.3225	+	7.69176i	1.19640	+	0.690740i
$125$	1.00000			0.0894427
$126$		0			0
$127$	14.5361			1.28987			0.644933	−	0.764239i	$-0.276885\pi$
$127$	14.5361			1.28987			0.644933	+	0.764239i	$0.276885\pi$
$128$	−0.239183	−	0.138092i	−0.0211410	−	0.0122058i
$129$		0			0
$130$	−5.32725	−	9.22706i	−0.467231	−	0.809267i
$131$	−6.99970	+	12.1238i	−0.611567	+	1.05926i	0.379410	+	0.925229i	$0.376127\pi$
$131$	−6.99970	+	12.1238i	−0.611567	+	1.05926i	−0.990976	+	0.134036i	$0.957206\pi$
$132$		0			0
$133$	−1.16694	−	5.35765i	−0.101186	−	0.464567i
$134$			22.3899i			1.93419i
$135$		0			0
$136$	−0.0557322	+	0.0321770i	−0.00477900	+	0.00275916i
$137$	−19.5272	+	11.2740i	−1.66832	+	0.963206i	−0.699778	+	0.714361i	$0.746718\pi$
$137$	−19.5272	+	11.2740i	−1.66832	+	0.963206i	−0.968543	+	0.248845i	$0.919949\pi$
$138$		0			0
$139$		−	7.47837i		−	0.634307i	−0.948374	−	0.317154i	$-0.897273\pi$
$139$		−	7.47837i		−	0.634307i	0.948374	−	0.317154i	$-0.102727\pi$
$140$	−3.52960	−	3.88067i	−0.298306	−	0.327977i
$141$		0			0
$142$	−9.95160	+	17.2367i	−0.835120	+	1.44647i
$143$	4.82857	+	8.36333i	0.403786	+	0.699377i
$144$		0			0
$145$	2.41941	+	1.39685i	0.200921	+	0.116002i
$146$	−32.8880			−2.72183
$147$		0			0
$148$	14.7993			1.21649
$149$	−10.4752	−	6.04787i	−0.858164	−	0.495461i	0.00523309	−	0.999986i	$-0.498334\pi$
$149$	−10.4752	−	6.04787i	−0.858164	−	0.495461i	−0.863397	+	0.504525i	$0.831668\pi$
$150$		0			0
$151$	−6.22818	−	10.7875i	−0.506842	−	0.877876i	−0.999969	−	0.00791876i	$-0.997479\pi$
$151$	−6.22818	−	10.7875i	−0.506842	−	0.877876i	0.493126	−	0.869958i	$-0.335854\pi$
$152$	−0.0357755	+	0.0619650i	−0.00290178	+	0.00502603i
$153$		0			0
$154$	6.42632	+	7.06551i	0.517847	+	0.569355i
$155$			7.75887i			0.623208i
$156$		0			0
$157$	−14.4669	+	8.35248i	−1.15459	+	0.666600i	−0.950000	−	0.312249i	$-0.898918\pi$
$157$	−14.4669	+	8.35248i	−1.15459	+	0.666600i	−0.204585	+	0.978849i	$0.565584\pi$
$158$	7.32294	−	4.22790i	0.582582	−	0.336354i
$159$		0			0
$160$			7.98208i			0.631039i
$161$	−4.65868	−	21.3889i	−0.367155	−	1.68568i
$162$		0			0
$163$	9.69006	−	16.7837i	0.758984	−	1.31460i	−0.184385	−	0.982854i	$-0.559029\pi$
$163$	9.69006	−	16.7837i	0.758984	−	1.31460i	0.943369	−	0.331745i	$-0.107637\pi$
$164$	−3.74747	−	6.49081i	−0.292628	−	0.506847i
$165$		0			0
$166$	15.5720	+	8.99051i	1.20862	+	0.697799i
$167$	21.3710			1.65373			0.826867	−	0.562397i	$-0.190121\pi$
$167$	21.3710			1.65373			0.826867	+	0.562397i	$0.190121\pi$
$168$		0			0
$169$	−15.5028			−1.19253
$170$	3.22158	+	1.85998i	0.247084	+	0.142654i
$171$		0			0
$172$	−3.11525	−	5.39577i	−0.237536	−	0.411424i
$173$	8.43701	−	14.6133i	0.641454	−	1.11103i	−0.343654	−	0.939096i	$-0.611665\pi$
$173$	8.43701	−	14.6133i	0.641454	−	1.11103i	0.985108	−	0.171935i	$-0.0550019\pi$
$174$		0			0
$175$	0.804943	−	2.52033i	0.0608480	−	0.190519i
$176$		−	7.29748i		−	0.550068i
$177$		0			0
$178$	11.6720	−	6.73885i	0.874856	−	0.505098i
$179$	−16.6564	+	9.61657i	−1.24496	+	0.718776i	−0.970099	−	0.242708i	$-0.921964\pi$
$179$	−16.6564	+	9.61657i	−1.24496	+	0.718776i	−0.274858	+	0.961485i	$0.588631\pi$
$180$		0			0
$181$			22.3009i			1.65762i	0.559533	+	0.828808i	$0.310980\pi$
$181$			22.3009i			1.65762i	−0.559533	+	0.828808i	$0.689020\pi$
$182$	−27.5434	+	5.99917i	−2.04165	+	0.444688i
$183$		0			0
$184$	−0.142824	+	0.247378i	−0.0105291	+	0.0182370i
$185$	3.73210	+	6.46419i	0.274390	+	0.475257i
$186$		0			0
$187$	−2.92001	−	1.68587i	−0.213533	−	0.123283i
$188$	−10.6678			−0.778026
$189$		0			0
$190$	4.13598			0.300056
$191$	15.9342	+	9.19964i	1.15296	+	0.665662i	0.949607	−	0.313443i	$-0.101482\pi$
$191$	15.9342	+	9.19964i	1.15296	+	0.665662i	0.203354	+	0.979105i	$0.434816\pi$
$192$		0			0
$193$	2.12854	+	3.68674i	0.153216	+	0.265377i	0.932408	−	0.361408i	$-0.117704\pi$
$193$	2.12854	+	3.68674i	0.153216	+	0.265377i	−0.779192	+	0.626785i	$0.784370\pi$
$194$	−2.18737	+	3.78864i	−0.157044	+	0.272008i
$195$		0			0
$196$	−12.6217	+	5.77204i	−0.901550	+	0.412289i
$197$			1.54805i			0.110294i	0.998478	+	0.0551471i	$0.0175628\pi$
$197$			1.54805i			0.110294i	−0.998478	+	0.0551471i	$0.982437\pi$
$198$		0			0
$199$	−1.13199	+	0.653554i	−0.0802445	+	0.0463292i	−0.539585	−	0.841931i	$-0.681419\pi$
$199$	−1.13199	+	0.653554i	−0.0802445	+	0.0463292i	0.459341	+	0.888260i	$0.348086\pi$
$200$	−0.0298990	+	0.0172622i	−0.00211418	+	0.00122062i
$201$		0			0
$202$		−	10.5253i		−	0.740559i
$203$	5.46800	−	4.97333i	0.383778	−	0.349059i
$204$		0			0
$205$	1.89008	−	3.27372i	0.132009	−	0.228647i
$206$	6.55591	+	11.3552i	0.456772	+	0.791152i
$207$		0			0
$208$	18.6528	+	10.7692i	1.29334	+	0.746708i
$209$	−3.74882			−0.259311
$210$		0			0
$211$	−7.71043			−0.530808			−0.265404	−	0.964137i	$-0.585505\pi$
$211$	−7.71043			−0.530808			−0.265404	+	0.964137i	$0.585505\pi$
$212$	8.76589	+	5.06099i	0.602044	+	0.347590i
$213$		0			0
$214$	9.80347	+	16.9801i	0.670151	+	1.16074i
$215$	1.57122	−	2.72143i	0.107156	−	0.185600i
$216$		0			0
$217$	19.5549	+	6.24545i	1.32747	+	0.423969i
$218$		−	6.21846i		−	0.421167i
$219$		0			0
$220$	−3.10594	+	1.79321i	−0.209402	+	0.120898i
$221$	8.61836	−	4.97581i	0.579733	−	0.334709i
$222$		0			0
$223$		−	4.20752i		−	0.281756i	−0.990027	−	0.140878i	$-0.955007\pi$
$223$		−	4.20752i		−	0.281756i	0.990027	−	0.140878i	$-0.0449926\pi$
$224$	20.1175	+	6.42512i	1.34416	+	0.429297i
$225$		0			0
$226$	−16.5506	+	28.6664i	−1.10093	+	1.90686i
$227$	−1.77198	−	3.06915i	−0.117610	−	0.203707i	0.801210	−	0.598383i	$-0.204190\pi$
$227$	−1.77198	−	3.06915i	−0.117610	−	0.203707i	−0.918820	+	0.394677i	$0.870857\pi$
$228$		0			0
$229$	−19.4045	−	11.2032i	−1.28229	−	0.740329i	−0.305021	−	0.952346i	$-0.598664\pi$
$229$	−19.4045	−	11.2032i	−1.28229	−	0.740329i	−0.977266	+	0.212017i	$0.931997\pi$
$230$	16.5118			1.08875
$231$		0			0
$232$	−0.0964505			−0.00633229
$233$	20.8118	+	12.0157i	1.36343	+	0.787175i	0.990078	−	0.140516i	$-0.0448760\pi$
$233$	20.8118	+	12.0157i	1.36343	+	0.787175i	0.373349	+	0.927691i	$0.378209\pi$
$234$		0			0
$235$	−2.69021	−	4.65958i	−0.175490	−	0.303957i
$236$	8.17604	−	14.1613i	0.532215	−	0.921824i
$237$		0			0
$238$	7.28096	−	6.62227i	0.471954	−	0.429258i
$239$			12.0933i			0.782249i	0.920338	+	0.391125i	$0.127914\pi$
$239$			12.0933i			0.782249i	−0.920338	+	0.391125i	$0.872086\pi$
$240$		0			0
$241$	22.3791	−	12.9206i	1.44156	−	0.832287i	0.443609	−	0.896221i	$-0.353698\pi$
$241$	22.3791	−	12.9206i	1.44156	−	0.832287i	0.997954	+	0.0639341i	$0.0203647\pi$
$242$	−13.3564	+	7.71130i	−0.858580	+	0.495701i
$243$		0			0
$244$		−	15.4633i		−	0.989935i
$245$	−5.70413	−	4.05744i	−0.364424	−	0.259221i
$246$		0			0
$247$	5.53228	−	9.58219i	0.352011	−	0.609700i
$248$	−0.133935	−	0.231983i	−0.00850490	−	0.0147309i
$249$		0			0
$250$	1.72830	+	0.997835i	0.109307	+	0.0631086i
$251$	8.73604			0.551414			0.275707	−	0.961242i	$-0.411088\pi$
$251$	8.73604			0.551414			0.275707	+	0.961242i	$0.411088\pi$
$252$		0			0
$253$	−14.9661			−0.940912
$254$	25.1227	+	14.5046i	1.57634	+	0.910099i
$255$		0			0
$256$	−8.13660	−	14.0930i	−0.508537	−	0.880812i
$257$	1.59437	−	2.76152i	0.0994538	−	0.172259i	−0.812005	−	0.583651i	$-0.801624\pi$
$257$	1.59437	−	2.76152i	0.0994538	−	0.172259i	0.911459	+	0.411392i	$0.134957\pi$
$258$		0			0
$259$	19.2960	−	4.20283i	1.19900	−	0.261151i
$260$		−	10.5853i		−	0.656469i
$261$		0			0
$262$	−24.1952	+	13.9691i	−1.49478	+	0.863014i
$263$	−3.69226	+	2.13173i	−0.227674	+	0.131448i	−0.609499	−	0.792787i	$-0.708629\pi$
$263$	−3.69226	+	2.13173i	−0.227674	+	0.131448i	0.381824	+	0.924235i	$0.375296\pi$
$264$		0			0
$265$			5.10515i			0.313607i
$266$	3.32923	−	10.4240i	0.204128	−	0.639139i
$267$		0			0
$268$	−11.1222	+	19.2642i	−0.679396	+	1.17675i
$269$	−7.60636	−	13.1746i	−0.463768	−	0.803270i	0.535377	−	0.844613i	$-0.320170\pi$
$269$	−7.60636	−	13.1746i	−0.463768	−	0.803270i	−0.999145	+	0.0413434i	$0.986836\pi$
$270$		0			0
$271$	12.7593	+	7.36660i	0.775074	+	0.447489i	0.834682	−	0.550733i	$-0.185652\pi$
$271$	12.7593	+	7.36660i	0.775074	+	0.447489i	−0.0596080	+	0.998222i	$0.518985\pi$
$272$	−7.52000			−0.455967
$273$		0			0
$274$	−44.9985			−2.71846
$275$	−1.56652	−	0.904429i	−0.0944646	−	0.0545391i
$276$		0			0
$277$	−0.556865	−	0.964519i	−0.0334588	−	0.0579523i	0.848811	−	0.528696i	$-0.177319\pi$
$277$	−0.556865	−	0.964519i	−0.0334588	−	0.0579523i	−0.882270	+	0.470744i	$0.843986\pi$
$278$	7.46218	−	12.9249i	0.447552	−	0.775183i
$279$		0			0
$280$	0.0194395	+	0.0892505i	0.00116173	+	0.00533374i
$281$		−	2.52283i		−	0.150499i	−0.997165	−	0.0752496i	$-0.976025\pi$
$281$		−	2.52283i		−	0.150499i	0.997165	−	0.0752496i	$-0.0239753\pi$
$282$		0			0
$283$	−2.73524	+	1.57919i	−0.162593	+	0.0938731i	−0.579089	−	0.815265i	$-0.696591\pi$
$283$	−2.73524	+	1.57919i	−0.162593	+	0.0938731i	0.416496	+	0.909138i	$0.363258\pi$
$284$	−17.1247	+	9.88693i	−1.01616	+	0.586681i
$285$		0			0
$286$			19.2725i			1.13961i
$287$	−6.72945	−	7.39880i	−0.397227	−	0.436737i
$288$		0			0
$289$	6.76272	−	11.7134i	0.397807	−	0.689022i
$290$	2.78764	+	4.82834i	0.163696	+	0.283530i
$291$		0			0
$292$	−28.2968	−	16.3371i	−1.65594	−	0.956059i
$293$	−19.0936			−1.11546			−0.557731	−	0.830022i	$-0.688328\pi$
$293$	−19.0936			−1.11546			−0.557731	+	0.830022i	$0.688328\pi$
$294$		0			0
$295$	8.24738			0.480181
$296$	−0.223172	−	0.128849i	−0.0129716	−	0.00748917i
$297$		0			0
$298$	−12.0696	−	20.9051i	−0.699171	−	1.21100i
$299$	22.0861	−	38.2542i	1.27727	−	2.21230i
$300$		0			0
$301$	−5.59416	−	6.15058i	−0.322442	−	0.354513i
$302$		−	24.8588i		−	1.43046i
$303$		0			0
$304$	−7.24084	+	4.18050i	−0.415291	+	0.239768i
$305$	6.75422	−	3.89955i	0.386746	−	0.223288i
$306$		0			0
$307$		−	7.53113i		−	0.429825i	−0.976633	−	0.214912i	$-0.931053\pi$
$307$		−	7.53113i		−	0.429825i	0.976633	−	0.214912i	$-0.0689466\pi$
$308$	2.01939	+	9.27142i	0.115065	+	0.528288i
$309$		0			0
$310$	−7.74208	+	13.4097i	−0.439720	+	0.761618i
$311$	5.05582	+	8.75693i	0.286689	+	0.496560i	0.973017	−	0.230732i	$-0.0741120\pi$
$311$	5.05582	+	8.75693i	0.286689	+	0.496560i	−0.686328	+	0.727292i	$0.740779\pi$
$312$		0			0
$313$	−11.8782	−	6.85785i	−0.671393	−	0.387629i	0.125211	−	0.992130i	$-0.460039\pi$
$313$	−11.8782	−	6.85785i	−0.671393	−	0.387629i	−0.796604	+	0.604501i	$0.793372\pi$
$314$	−33.3376			−1.88135
$315$		0			0
$316$	8.40084			0.472584
$317$	2.60874	+	1.50616i	0.146521	+	0.0845942i	0.571468	−	0.820624i	$-0.306374\pi$
$317$	2.60874	+	1.50616i	0.146521	+	0.0845942i	−0.424947	+	0.905218i	$0.639707\pi$
$318$		0			0
$319$	−2.52670	−	4.37637i	−0.141468	−	0.245029i
$320$	−3.93050	+	6.80783i	−0.219722	+	0.380569i
$321$		0			0
$322$	13.2910	−	41.6151i	0.740680	−	2.31912i
$323$			3.86313i			0.214950i
$324$		0			0
$325$	4.62354	−	2.66940i	0.256468	−	0.148072i
$326$	33.4947	−	19.3382i	1.85510	−	1.07104i
$327$		0			0
$328$			0.130508i			0.00720610i
$329$	−13.9091	+	3.02952i	−0.766836	+	0.167023i
$330$		0			0
$331$	5.57680	−	9.65930i	0.306529	−	0.530923i	−0.671072	−	0.741392i	$-0.734166\pi$
$331$	5.57680	−	9.65930i	0.306529	−	0.530923i	0.977600	+	0.210469i	$0.0674992\pi$
$332$	8.93208	+	15.4708i	0.490211	+	0.849071i
$333$		0			0
$334$	36.9355	+	21.3247i	2.02102	+	1.16684i
$335$	−11.2192			−0.612972
$336$		0			0
$337$	−13.3801			−0.728858			−0.364429	−	0.931231i	$-0.618736\pi$
$337$	−13.3801			−0.728858			−0.364429	+	0.931231i	$0.618736\pi$
$338$	−26.7936	−	15.4693i	−1.45738	−	0.841418i
$339$		0			0
$340$	1.84789	+	3.20064i	0.100216	+	0.173579i
$341$	7.01735	−	12.1544i	0.380011	−	0.658198i
$342$		0			0
$343$	−14.8176	+	11.1103i	−0.800075	+	0.599899i
$344$			0.108491i			0.00584942i
$345$		0			0
$346$	29.1634	−	16.8375i	1.56783	−	0.905189i
$347$	−21.2782	+	12.2850i	−1.14227	+	0.659491i	−0.946992	−	0.321257i	$-0.895895\pi$
$347$	−21.2782	+	12.2850i	−1.14227	+	0.659491i	−0.195279	+	0.980748i	$0.562561\pi$
$348$		0			0
$349$		−	19.2270i		−	1.02920i	−0.857431	−	0.514599i	$-0.827941\pi$
$349$		−	19.2270i		−	1.02920i	0.857431	−	0.514599i	$-0.172059\pi$
$350$	3.90606	−	3.55269i	0.208788	−	0.189899i
$351$		0			0
$352$	7.21923	−	12.5041i	0.384786	−	0.666469i
$353$	0.255875	+	0.443188i	0.0136188	+	0.0235885i	0.872755	−	0.488159i	$-0.162332\pi$
$353$	0.255875	+	0.443188i	0.0136188	+	0.0235885i	−0.859136	+	0.511748i	$0.828998\pi$
$354$		0			0
$355$	−8.63704	−	4.98660i	−0.458406	−	0.264661i
$356$	13.3901			0.709674
$357$		0			0
$358$	−38.3830			−2.02861
$359$	−17.1761	−	9.91665i	−0.906522	−	0.523381i	−0.0272117	−	0.999630i	$-0.508663\pi$
$359$	−17.1761	−	9.91665i	−0.906522	−	0.523381i	−0.879311	+	0.476249i	$0.841996\pi$
$360$		0			0
$361$	−7.35242	−	12.7348i	−0.386969	−	0.670250i
$362$	−22.2527	+	38.5427i	−1.16957	+	2.02576i
$363$		0			0
$364$	−26.6783	−	8.52052i	−1.39832	−	0.446597i
$365$		−	16.4797i		−	0.862586i
$366$		0			0
$367$	17.6842	−	10.2100i	0.923110	−	0.532958i	0.0384841	−	0.999259i	$-0.487747\pi$
$367$	17.6842	−	10.2100i	0.923110	−	0.532958i	0.884626	+	0.466301i	$0.154414\pi$
$368$	−28.9070	+	16.6895i	−1.50688	+	0.869999i
$369$		0			0
$370$			14.8961i			0.774411i
$371$	12.8667	+	4.10935i	0.668004	+	0.213347i
$372$		0			0
$373$	0.637766	−	1.10464i	0.0330223	−	0.0571962i	−0.849042	−	0.528325i	$-0.822820\pi$
$373$	0.637766	−	1.10464i	0.0330223	−	0.0571962i	0.882064	+	0.471129i	$0.156153\pi$
$374$	−3.36444	−	5.82739i	−0.173971	−	0.301327i
$375$		0			0
$376$	0.160869	+	0.0928778i	0.00829619	+	0.00478981i
$377$	14.9150			0.768160
$378$		0			0
$379$	35.4590			1.82140			0.910702	−	0.413063i	$-0.135541\pi$
$379$	35.4590			1.82140			0.910702	+	0.413063i	$0.135541\pi$
$380$	3.55859	+	2.05455i	0.182552	+	0.105396i
$381$		0			0
$382$	18.3594	+	31.7995i	0.939351	+	1.62700i
$383$	−7.98563	+	13.8315i	−0.408046	+	0.706757i	−0.994671	−	0.103102i	$-0.967123\pi$
$383$	−7.98563	+	13.8315i	−0.408046	+	0.706757i	0.586624	+	0.809859i	$0.300457\pi$
$384$		0			0
$385$	−3.54042	+	3.22013i	−0.180436	+	0.164113i
$386$			8.49573i			0.432421i
$387$		0			0
$388$	−3.76401	+	2.17315i	−0.191089	+	0.110325i
$389$	9.81632	−	5.66745i	0.497707	−	0.287351i	−0.230059	−	0.973177i	$-0.573892\pi$
$389$	9.81632	−	5.66745i	0.497707	−	0.287351i	0.727766	+	0.685825i	$0.240559\pi$
$390$		0			0
$391$			15.4225i			0.779949i
$392$	0.240588	+	0.0228477i	0.0121515	+	0.00115398i
$393$		0			0
$394$	−1.54470	+	2.67550i	−0.0778210	+	0.134790i
$395$	2.11854	+	3.66941i	0.106595	+	0.184628i
$396$		0			0
$397$	−26.1694	−	15.1089i	−1.31341	−	0.758295i	−0.330747	−	0.943719i	$-0.607301\pi$
$397$	−26.1694	−	15.1089i	−1.31341	−	0.758295i	−0.982659	+	0.185424i	$0.940634\pi$
$398$	−2.60855			−0.130755
$399$		0			0
$400$	−4.03430			−0.201715
$401$	−1.14576	−	0.661503i	−0.0572163	−	0.0330339i	0.471119	−	0.882070i	$-0.343850\pi$
$401$	−1.14576	−	0.661503i	−0.0572163	−	0.0330339i	−0.528335	+	0.849036i	$0.677184\pi$
$402$		0			0
$403$	20.7116	+	35.8735i	1.03172	+	1.78698i
$404$	5.22846	−	9.05596i	0.260126	−	0.450551i
$405$		0			0
$406$	14.4129	−	3.13924i	0.715301	−	0.155798i
$407$		−	13.5017i		−	0.669254i
$408$		0			0
$409$	29.6927	−	17.1431i	1.46821	−	0.847671i	0.468844	−	0.883281i	$-0.344671\pi$
$409$	29.6927	−	17.1431i	1.46821	−	0.847671i	0.999366	+	0.0356099i	$0.0113374\pi$
$410$	6.53327	−	3.77199i	0.322655	−	0.186285i
$411$		0			0
$412$			13.0266i			0.641775i
$413$	6.63867	−	20.7861i	0.326668	−	1.02282i
$414$		0			0
$415$	−4.50501	+	7.80290i	−0.221142	+	0.383029i
$416$	21.3074	+	36.9055i	1.04468	+	1.80944i
$417$		0			0
$418$	−6.47909	−	3.74071i	−0.316903	−	0.182964i
$419$	−0.342185			−0.0167168			−0.00835841	−	0.999965i	$-0.502661\pi$
$419$	−0.342185			−0.0167168			−0.00835841	+	0.999965i	$0.502661\pi$
$420$		0			0
$421$	−7.27017			−0.354326			−0.177163	−	0.984181i	$-0.556692\pi$
$421$	−7.27017			−0.354326			−0.177163	+	0.984181i	$0.556692\pi$
$422$	−13.3260	−	7.69374i	−0.648697	−	0.374526i
$423$		0			0
$424$	−0.0881261	−	0.152639i	−0.00427978	−	0.00741280i
$425$	−0.932008	+	1.61429i	−0.0452090	+	0.0783043i
$426$		0			0
$427$	−4.39140	−	20.1618i	−0.212515	−	0.975697i
$428$			19.4795i			0.941578i
$429$		0			0
$430$	5.43107	−	3.13563i	0.261910	−	0.151214i
$431$	−3.38713	+	1.95556i	−0.163152	+	0.0941960i	−0.579353	−	0.815077i	$-0.696695\pi$
$431$	−3.38713	+	1.95556i	−0.163152	+	0.0941960i	0.416201	+	0.909273i	$0.363361\pi$
$432$		0			0
$433$			24.8856i			1.19592i	0.801525	+	0.597962i	$0.204023\pi$
$433$			24.8856i			1.19592i	−0.801525	+	0.597962i	$0.795977\pi$
$434$	27.5649	+	30.3066i	1.32316	+	1.45476i
$435$		0			0
$436$	3.08902	−	5.35035i	0.147937	−	0.256235i
$437$	8.57363	+	14.8500i	0.410132	+	0.710370i
$438$		0			0
$439$	−12.2143	−	7.05192i	−0.582956	−	0.336570i	0.179351	−	0.983785i	$-0.442600\pi$
$439$	−12.2143	−	7.05192i	−0.582956	−	0.336570i	−0.762307	+	0.647215i	$0.775933\pi$
$440$	0.0624498			0.00297718
$441$		0			0
$442$	19.8602			0.944651
$443$	10.0493	+	5.80194i	0.477454	+	0.275658i	0.719355	−	0.694643i	$-0.244437\pi$
$443$	10.0493	+	5.80194i	0.477454	+	0.275658i	−0.241901	+	0.970301i	$0.577771\pi$
$444$		0			0
$445$	3.37674	+	5.84868i	0.160073	+	0.277254i
$446$	4.19841	−	7.27186i	0.198801	−	0.344333i
$447$		0			0
$448$	13.9942	+	15.3861i	0.661162	+	0.726924i
$449$			7.84978i			0.370454i	0.982696	+	0.185227i	$0.0593021\pi$
$449$			7.84978i			0.370454i	−0.982696	+	0.185227i	$0.940698\pi$
$450$		0			0
$451$	−5.92170	+	3.41890i	−0.278842	+	0.160990i
$452$	−28.4801	+	16.4430i	−1.33959	+	0.773413i
$453$		0			0
$454$		−	7.07256i		−	0.331932i
$455$	−3.00609	−	13.8016i	−0.140928	−	0.647028i
$456$		0			0
$457$	0.774175	−	1.34091i	0.0362144	−	0.0627252i	−0.847350	−	0.531035i	$-0.821803\pi$
$457$	0.774175	−	1.34091i	0.0362144	−	0.0627252i	0.883565	+	0.468309i	$0.155137\pi$
$458$	−22.3579	−	38.7250i	−1.04472	−	1.80950i
$459$		0			0
$460$	14.2067	+	8.20223i	0.662389	+	0.382431i
$461$	10.5782			0.492678			0.246339	−	0.969184i	$-0.420772\pi$
$461$	10.5782			0.492678			0.246339	+	0.969184i	$0.420772\pi$
$462$		0			0
$463$	7.32833			0.340576			0.170288	−	0.985394i	$-0.445530\pi$
$463$	7.32833			0.340576			0.170288	+	0.985394i	$0.445530\pi$
$464$	−9.76062	−	5.63529i	−0.453125	−	0.261612i
$465$		0			0
$466$	23.9794	+	41.5335i	1.11082	+	1.92400i
$467$	1.92851	−	3.34028i	0.0892409	−	0.154570i	−0.817950	−	0.575290i	$-0.804889\pi$
$467$	1.92851	−	3.34028i	0.0892409	−	0.154570i	0.907190	+	0.420720i	$0.138223\pi$
$468$		0			0
$469$	−9.03084	+	28.2762i	−0.417006	+	1.30567i
$470$		−	10.7375i		−	0.495286i
$471$		0			0
$472$	−0.246589	+	0.142368i	−0.0113502	+	0.00655302i
$473$	−4.92268	+	2.84211i	−0.226345	+	0.130680i
$474$		0			0
$475$			2.07248i			0.0950918i
$476$	9.55413	−	2.08096i	0.437913	−	0.0953809i
$477$		0			0
$478$	−12.0671	+	20.9008i	−0.551936	+	0.955982i
$479$	9.52418	+	16.4964i	0.435171	+	0.753738i	0.997310	−	0.0733051i	$-0.0233547\pi$
$479$	9.52418	+	16.4964i	0.435171	+	0.753738i	−0.562139	+	0.827043i	$0.690021\pi$
$480$		0			0
$481$	34.5111	+	19.9250i	1.57357	+	0.908500i
$482$	51.5704			2.34897
$483$		0			0
$484$	−15.3224			−0.696471
$485$	−1.89843	−	1.09606i	−0.0862032	−	0.0497694i
$486$		0			0
$487$	3.79075	+	6.56577i	0.171775	+	0.297523i	0.939041	−	0.343806i	$-0.111716\pi$
$487$	3.79075	+	6.56577i	0.171775	+	0.297523i	−0.767265	+	0.641330i	$0.778383\pi$
$488$	−0.134630	+	0.233185i	−0.00609440	+	0.0105558i
$489$		0			0
$490$	−5.80980	−	12.7043i	−0.262460	−	0.573921i
$491$			22.2505i			1.00415i	0.864824	+	0.502075i	$0.167430\pi$
$491$			22.2505i			1.00415i	−0.864824	+	0.502075i	$0.832570\pi$
$492$		0			0
$493$	−4.50981	+	2.60374i	−0.203112	+	0.117267i
$494$	19.1229	−	11.0406i	0.860380	−	0.496740i
$495$		0			0
$496$		−	31.3016i		−	1.40548i
$497$	−19.5202	+	17.7543i	−0.875601	+	0.796388i
$498$		0			0
$499$	−13.7031	+	23.7344i	−0.613434	+	1.06250i	0.377223	+	0.926123i	$0.376879\pi$
$499$	−13.7031	+	23.7344i	−0.613434	+	1.06250i	−0.990657	+	0.136377i	$0.956454\pi$
$500$	0.991350	+	1.71707i	0.0443345	+	0.0767897i
$501$		0			0
$502$	15.0985	+	8.71713i	0.673880	+	0.389065i
$503$	17.6283			0.786008			0.393004	−	0.919537i	$-0.371436\pi$
$503$	17.6283			0.786008			0.393004	+	0.919537i	$0.371436\pi$
$504$		0			0
$505$	5.27408			0.234693
$506$	−25.8660	−	14.9337i	−1.14988	−	0.663885i
$507$		0			0
$508$	14.4103	+	24.9594i	0.639354	+	1.10739i
$509$	−18.0257	+	31.2214i	−0.798974	+	1.38386i	0.121310	+	0.992615i	$0.461290\pi$
$509$	−18.0257	+	31.2214i	−0.798974	+	1.38386i	−0.920285	+	0.391250i	$0.872043\pi$
$510$		0			0
$511$	−41.5343	−	13.2652i	−1.83737	−	0.586818i
$512$		−	31.9236i		−	1.41084i
$513$		0			0
$514$	5.51109	−	3.18183i	0.243084	−	0.140344i
$515$	−5.68990	+	3.28507i	−0.250727	+	0.144757i
$516$		0			0
$517$			9.73241i			0.428031i
$518$	37.5431	+	11.9905i	1.64955	+	0.526833i
$519$		0			0
$520$	−0.0921595	+	0.159625i	−0.00404146	+	0.00700002i
$521$	0.602560	+	1.04366i	0.0263986	+	0.0457238i	0.878923	−	0.476964i	$-0.158263\pi$
$521$	0.602560	+	1.04366i	0.0263986	+	0.0457238i	−0.852524	+	0.522688i	$0.824929\pi$
$522$		0			0
$523$	−14.4149	−	8.32246i	−0.630321	−	0.363916i	0.150556	−	0.988602i	$-0.451894\pi$
$523$	−14.4149	−	8.32246i	−0.630321	−	0.363916i	−0.780876	+	0.624686i	$0.785227\pi$
$524$	−27.7566			−1.21255
$525$		0			0
$526$	−8.50844			−0.370986
$527$	−12.5250	−	7.23133i	−0.545599	−	0.315002i
$528$		0			0
$529$	22.7278	+	39.3657i	0.988166	+	1.71155i
$530$	−5.09410	+	8.82324i	−0.221273	+	0.383257i
$531$		0			0
$532$	8.04261	−	7.31502i	0.348691	−	0.317146i
$533$		−	20.1816i		−	0.874162i
$534$		0			0
$535$	−8.50847	+	4.91237i	−0.367853	+	0.212380i
$536$	0.335444	−	0.193669i	0.0144890	−	0.00836521i
$537$		0			0
$538$		−	30.3596i		−	1.30889i
$539$	5.26595	+	11.5150i	0.226821	+	0.495988i
$540$		0			0
$541$	16.3861	−	28.3815i	0.704492	−	1.22022i	−0.262383	−	0.964964i	$-0.584508\pi$
$541$	16.3861	−	28.3815i	0.704492	−	1.22022i	0.966875	−	0.255252i	$-0.0821583\pi$
$542$	14.7013	+	25.4634i	0.631475	+	1.09375i
$543$		0			0
$544$	−12.8854	−	7.43937i	−0.552455	−	0.318960i
$545$	3.11598			0.133474
$546$		0			0
$547$	6.72308			0.287458			0.143729	−	0.989617i	$-0.454091\pi$
$547$	6.72308			0.287458			0.143729	+	0.989617i	$0.454091\pi$
$548$	−38.7166	−	22.3530i	−1.65389	−	0.954874i
$549$		0			0
$550$	−1.80494	−	3.12625i	−0.0769630	−	0.133304i
$551$	−2.89493	+	5.01417i	−0.123328	+	0.213611i
$552$		0			0
$553$	10.9534	−	2.38574i	0.465787	−	0.101452i
$554$		−	2.22264i		−	0.0944309i
$555$		0			0
$556$	12.8409	−	7.41369i	0.544575	−	0.314410i
$557$	11.7751	−	6.79833i	0.498925	−	0.288054i	−0.229345	−	0.973345i	$-0.573658\pi$
$557$	11.7751	−	6.79833i	0.498925	−	0.288054i	0.728269	+	0.685291i	$0.240325\pi$
$558$		0			0
$559$		−	16.7768i		−	0.709585i
$560$	−3.24738	+	10.1678i	−0.137227	+	0.429667i
$561$		0			0
$562$	2.51736	−	4.36020i	0.106189	−	0.183924i
$563$	−7.57270	−	13.1163i	−0.319151	−	0.552786i	0.661160	−	0.750245i	$-0.270064\pi$
$563$	−7.57270	−	13.1163i	−0.319151	−	0.552786i	−0.980311	+	0.197459i	$0.936731\pi$
$564$		0			0
$565$	−14.3643	−	8.29323i	−0.604310	−	0.348899i
$566$	−6.30308			−0.264938
$567$		0			0
$568$	0.344319			0.0144473
$569$	−12.4624	−	7.19517i	−0.522451	−	0.301637i	0.215486	−	0.976507i	$-0.430866\pi$
$569$	−12.4624	−	7.19517i	−0.522451	−	0.301637i	−0.737937	+	0.674870i	$0.764200\pi$
$570$		0			0
$571$	8.14329	+	14.1046i	0.340786	+	0.590259i	0.984579	−	0.174941i	$-0.0559735\pi$
$571$	8.14329	+	14.1046i	0.340786	+	0.590259i	−0.643793	+	0.765200i	$0.722640\pi$
$572$	−9.57361	+	16.5820i	−0.400293	+	0.693328i
$573$		0			0
$574$	−4.24774	−	19.5022i	−0.177297	−	0.814008i
$575$			8.27379i			0.345041i
$576$		0			0
$577$	−32.3542	+	18.6797i	−1.34692	+	0.777646i	−0.987812	−	0.155649i	$-0.950253\pi$
$577$	−32.3542	+	18.6797i	−1.34692	+	0.777646i	−0.359110	+	0.933295i	$0.616920\pi$
$578$	23.3760	−	13.4962i	0.972315	−	0.561366i
$579$		0			0
$580$			5.53905i			0.229997i
$581$	16.0396	+	17.6350i	0.665435	+	0.731623i
$582$		0			0
$583$	4.61725	−	7.99731i	0.191227	−	0.331215i
$584$	0.284476	+	0.492726i	0.0117717	+	0.0203892i
$585$		0			0
$586$	−32.9996	−	19.0523i	−1.36320	−	0.787043i
$587$	−0.949011			−0.0391699			−0.0195849	−	0.999808i	$-0.506234\pi$
$587$	−0.949011			−0.0391699			−0.0195849	+	0.999808i	$0.506234\pi$
$588$		0			0
$589$	−16.0801			−0.662569
$590$	14.2540	+	8.22953i	0.586826	+	0.338804i
$591$		0			0
$592$	−15.0564	−	26.0785i	−0.618815	−	1.07182i
$593$	−22.4865	+	38.9477i	−0.923409	+	1.59939i	−0.129310	+	0.991604i	$0.541276\pi$
$593$	−22.4865	+	38.9477i	−0.923409	+	1.59939i	−0.794100	+	0.607788i	$0.792057\pi$
$594$		0			0
$595$	3.31832	+	3.64838i	0.136038	+	0.149569i
$596$		−	23.9822i		−	0.982351i
$597$		0			0
$598$	76.3428	−	44.0765i	3.12189	−	1.80242i
$599$	−9.36411	+	5.40637i	−0.382607	+	0.220898i	−0.678952	−	0.734183i	$-0.737566\pi$
$599$	−9.36411	+	5.40637i	−0.382607	+	0.220898i	0.296345	+	0.955081i	$0.404232\pi$
$600$		0			0
$601$			26.8186i			1.09395i	0.837148	+	0.546976i	$0.184221\pi$
$601$			26.8186i			1.09395i	−0.837148	+	0.546976i	$0.815779\pi$
$602$	−3.53112	−	16.2121i	−0.143918	−	0.660756i
$603$		0			0
$604$	12.3486	−	21.3884i	0.502458	−	0.870283i
$605$	−3.86401	−	6.69267i	−0.157095	−	0.272096i
$606$		0			0
$607$	−5.15663	−	2.97718i	−0.209301	−	0.120840i	0.391685	−	0.920099i	$-0.371892\pi$
$607$	−5.15663	−	2.97718i	−0.209301	−	0.120840i	−0.600987	+	0.799259i	$0.705225\pi$
$608$	−16.5427			−0.670895
$609$		0			0
$610$	15.5644			0.630186
$611$	−24.8766	−	14.3625i	−1.00640	−	0.581045i
$612$		0			0
$613$	−1.10422	−	1.91257i	−0.0445991	−	0.0772478i	0.842864	−	0.538126i	$-0.180868\pi$
$613$	−1.10422	−	1.91257i	−0.0445991	−	0.0772478i	−0.887463	+	0.460879i	$0.847534\pi$
$614$	7.51483	−	13.0161i	0.303274	−	0.525286i
$615$		0			0
$616$	0.0502685	−	0.157394i	0.00202538	−	0.00634159i
$617$		−	4.90850i		−	0.197609i	−0.995107	−	0.0988043i	$-0.968498\pi$
$617$		−	4.90850i		−	0.197609i	0.995107	−	0.0988043i	$-0.0315018\pi$
$618$		0			0
$619$	18.3950	−	10.6203i	0.739357	−	0.426868i	−0.0824787	−	0.996593i	$-0.526284\pi$
$619$	18.3950	−	10.6203i	0.739357	−	0.426868i	0.821835	+	0.569725i	$0.192950\pi$
$620$	−13.3225	+	7.69176i	−0.535045	+	0.308909i
$621$		0			0
$622$			20.1795i			0.809124i
$623$	17.4587	−	3.80264i	0.699467	−	0.152350i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.6860	−	23.7049i	−0.547003	−	0.947437i
$627$		0			0
$628$	−28.6836	−	16.5605i	−1.14460	−	0.660834i
$629$	−13.9134			−0.554764
$630$		0			0
$631$	18.6373			0.741941			0.370971	−	0.928645i	$-0.379025\pi$
$631$	18.6373			0.741941			0.370971	+	0.928645i	$0.379025\pi$
$632$	−0.126684	−	0.0731412i	−0.00503923	−	0.00290940i
$633$		0			0
$634$	3.00579	+	5.20619i	0.119375	+	0.206764i
$635$	−7.26803	+	12.5886i	−0.288423	+	0.499563i
$636$		0			0
$637$	−37.2043	−	3.53313i	−1.47409	−	0.139988i
$638$		−	10.0849i		−	0.399265i
$639$		0			0
$640$	0.239183	−	0.138092i	0.00945454	−	0.00545858i
$641$	−22.2460	+	12.8438i	−0.878665	+	0.507298i	−0.870218	−	0.492667i	$-0.836022\pi$
$641$	−22.2460	+	12.8438i	−0.878665	+	0.507298i	−0.00844724	+	0.999964i	$0.502689\pi$
$642$		0			0
$643$		−	13.6090i		−	0.536688i	−0.963323	−	0.268344i	$-0.913524\pi$
$643$		−	13.6090i		−	0.536688i	0.963323	−	0.268344i	$-0.0864763\pi$
$644$	32.1079	−	29.2032i	1.26523	−	1.15077i
$645$		0			0
$646$	−3.85477	+	6.67666i	−0.151664	+	0.262690i
$647$	−24.1947	−	41.9064i	−0.951190	−	1.64751i	−0.742855	−	0.669452i	$-0.766529\pi$
$647$	−24.1947	−	41.9064i	−0.951190	−	1.64751i	−0.208335	−	0.978057i	$-0.566805\pi$
$648$		0			0
$649$	−12.9197	−	7.45917i	−0.507141	−	0.292798i
$650$	10.6545			0.417904
$651$		0			0
$652$	38.4250			1.50484
$653$	30.6260	+	17.6819i	1.19849	+	0.691948i	0.960218	−	0.279251i	$-0.0900862\pi$
$653$	30.6260	+	17.6819i	1.19849	+	0.691948i	0.238271	+	0.971199i	$0.423420\pi$
$654$		0			0
$655$	−6.99970	−	12.1238i	−0.273501	−	0.473718i
$656$	−7.62517	+	13.2072i	−0.297713	+	0.515654i
$657$		0			0
$658$	−27.0621	−	8.64311i	−1.05499	−	0.336943i
$659$			13.1110i			0.510733i	0.966844	+	0.255366i	$0.0821961\pi$
$659$			13.1110i			0.510733i	−0.966844	+	0.255366i	$0.917804\pi$
$660$		0			0
$661$	−16.8985	+	9.75637i	−0.657277	+	0.379479i	−0.791239	−	0.611508i	$-0.790563\pi$
$661$	−16.8985	+	9.75637i	−0.657277	+	0.379479i	0.133962	+	0.990987i	$0.457230\pi$
$662$	19.2768	−	11.1295i	0.749213	−	0.432558i
$663$		0			0
$664$		−	0.311065i		−	0.0120717i
$665$	5.22333	+	1.66823i	0.202552	+	0.0646911i
$666$		0			0
$667$	−11.5572	+	20.0177i	−0.447497	+	0.775088i
$668$	21.1861	+	36.6954i	0.819715	+	1.41979i
$669$		0			0
$670$	−19.3902	−	11.1949i	−0.749109	−	0.432498i
$671$	−14.1075			−0.544613
$672$		0			0
$673$	4.89071			0.188523			0.0942615	−	0.995547i	$-0.469951\pi$
$673$	4.89071			0.188523			0.0942615	+	0.995547i	$0.469951\pi$
$674$	−23.1248	−	13.3511i	−0.890733	−	0.514265i
$675$		0			0
$676$	−15.3687	−	26.6194i	−0.591106	−	1.02382i
$677$	2.74948	−	4.76225i	0.105671	−	0.183028i	−0.808341	−	0.588715i	$-0.799634\pi$
$677$	2.74948	−	4.76225i	0.105671	−	0.183028i	0.914012	+	0.405687i	$0.132968\pi$
$678$		0			0
$679$	−4.29056	+	3.90240i	−0.164656	+	0.149760i
$680$		−	0.0643540i		−	0.00246786i
$681$		0			0
$682$	24.2562	−	14.0043i	0.928818	−	0.536253i
$683$	24.6812	−	14.2497i	0.944398	−	0.545249i	0.0530621	−	0.998591i	$-0.483102\pi$
$683$	24.6812	−	14.2497i	0.944398	−	0.545249i	0.891336	+	0.453343i	$0.149769\pi$
$684$		0			0
$685$		−	22.5481i		−	0.861517i
$686$	−36.6955	+	4.41640i	−1.40104	+	0.168619i
$687$		0			0
$688$	−6.33876	+	10.9791i	−0.241663	+	0.418572i
$689$	13.6277	+	23.6039i	0.519174	+	0.899236i
$690$		0			0
$691$	−25.0876	−	14.4843i	−0.954377	−	0.551010i	−0.0599391	−	0.998202i	$-0.519091\pi$
$691$	−25.0876	−	14.4843i	−0.954377	−	0.551010i	−0.894438	+	0.447192i	$0.852424\pi$
$692$	33.4561			1.27181
$693$		0			0
$694$	−49.0334			−1.86128
$695$	6.47646	+	3.73919i	0.245666	+	0.141835i
$696$		0			0
$697$	3.52315	+	6.10227i	0.133449	+	0.231140i
$698$	19.1854	−	33.2301i	0.726178	−	1.25778i
$699$		0			0
$700$	5.12556	−	1.11639i	0.193728	−	0.0421955i
$701$		−	48.8594i		−	1.84539i	−0.385527	−	0.922697i	$-0.625980\pi$
$701$		−	48.8594i		−	1.84539i	0.385527	−	0.922697i	$-0.374020\pi$
$702$		0			0
$703$	−13.3969	+	7.73470i	−0.505274	+	0.291720i
$704$	12.3144	−	7.10973i	0.464117	−	0.267958i
$705$		0			0
$706$			1.02128i			0.0384365i
$707$	4.24533	−	13.2924i	0.159662	−	0.499913i
$708$		0			0
$709$	0.120139	−	0.208086i	0.00451191	−	0.00781485i	−0.863761	−	0.503902i	$-0.831897\pi$
$709$	0.120139	−	0.208086i	0.00451191	−	0.00781485i	0.868273	+	0.496087i	$0.165230\pi$
$710$	−9.95160	−	17.2367i	−0.373477	−	0.646881i
$711$		0			0
$712$	−0.201922	−	0.116580i	−0.00756735	−	0.00436901i
$713$	−64.1953			−2.40413
$714$		0			0
$715$	−9.65715			−0.361157
$716$	−33.0246	−	19.0668i	−1.23419	−	0.712559i
$717$		0			0
$718$	−19.7904	−	34.2779i	−0.738570	−	1.27924i
$719$	23.5088	−	40.7184i	0.876729	−	1.51854i	0.0218189	−	0.999762i	$-0.493054\pi$
$719$	23.5088	−	40.7184i	0.876729	−	1.51854i	0.854910	−	0.518777i	$-0.173612\pi$
$720$		0			0
$721$	3.69941	+	16.9847i	0.137773	+	0.632544i
$722$		−	29.3460i		−	1.09215i
$723$		0			0
$724$	−38.2923	+	22.1080i	−1.42312	+	0.821639i
$725$	−2.41941	+	1.39685i	−0.0898545	+	0.0518775i
$726$		0			0
$727$			46.1941i			1.71325i	0.515943	+	0.856623i	$0.327441\pi$
$727$			46.1941i			1.71325i	−0.515943	+	0.856623i	$0.672559\pi$
$728$	0.328125	+	0.360761i	0.0121611	+	0.0133707i
$729$		0			0
$730$	16.4440	−	28.4819i	0.608620	−	1.05416i
$731$	2.92877	+	5.07278i	0.108325	+	0.187624i
$732$		0			0
$733$	34.6161	+	19.9856i	1.27857	+	0.738185i	0.976586	−	0.215127i	$-0.0690164\pi$
$733$	34.6161	+	19.9856i	1.27857	+	0.738185i	0.301988	+	0.953312i	$0.402350\pi$
$734$	40.7516			1.50417
$735$		0			0
$736$	−66.0421			−2.43434
$737$	17.5751	+	10.1470i	0.647388	+	0.373770i
$738$		0			0
$739$	7.71338	+	13.3600i	0.283741	+	0.491455i	0.972303	−	0.233723i	$-0.0750909\pi$
$739$	7.71338	+	13.3600i	0.283741	+	0.491455i	−0.688562	+	0.725178i	$0.741758\pi$
$740$	−7.39964	+	12.8166i	−0.272016	+	0.471146i
$741$		0			0
$742$	18.1370	+	19.9410i	0.665831	+	0.732058i
$743$			22.5672i			0.827912i	0.910297	+	0.413956i	$0.135853\pi$
$743$			22.5672i			0.827912i	−0.910297	+	0.413956i	$0.864147\pi$
$744$		0			0
$745$	10.4752	−	6.04787i	0.383783	−	0.221577i
$746$	2.20450	−	1.27277i	0.0807126	−	0.0465994i
$747$		0			0
$748$		−	6.68515i		−	0.244433i
$749$	5.53196	+	25.3983i	0.202133	+	0.928035i
$750$		0			0
$751$	−5.95375	+	10.3122i	−0.217255	+	0.376297i	−0.953968	−	0.299909i	$-0.903044\pi$
$751$	−5.95375	+	10.3122i	−0.217255	+	0.376297i	0.736713	+	0.676206i	$0.236377\pi$
$752$	10.8531	+	18.7981i	0.395772	+	0.685497i
$753$		0			0
$754$	25.7776	+	14.8827i	0.938764	+	0.541995i
$755$	12.4564			0.453333
$756$		0			0
$757$	−21.0491			−0.765042			−0.382521	−	0.923947i	$-0.624944\pi$
$757$	−21.0491			−0.765042			−0.382521	+	0.923947i	$0.624944\pi$
$758$	61.2838	+	35.3822i	2.22593	+	1.28514i
$759$		0			0
$760$	−0.0357755	−	0.0619650i	−0.00129772	−	0.00224771i
$761$	23.7347	−	41.1097i	0.860382	−	1.49023i	−0.0111779	−	0.999938i	$-0.503558\pi$
$761$	23.7347	−	41.1097i	0.860382	−	1.49023i	0.871560	−	0.490288i	$-0.163109\pi$
$762$		0			0
$763$	2.50818	−	7.85329i	0.0908023	−	0.284308i
$764$			36.4802i			1.31981i
$765$		0			0
$766$	−27.6031	+	15.9367i	−0.997342	+	0.575816i
$767$	38.1321	−	22.0156i	1.37687	−	0.794937i
$768$		0			0
$769$			16.1340i			0.581809i	0.956752	+	0.290904i	$0.0939561\pi$
$769$			16.1340i			0.581809i	−0.956752	+	0.290904i	$0.906044\pi$
$770$	−9.33207	+	2.03260i	−0.336304	+	0.0732497i
$771$		0			0
$772$	−4.22026	+	7.30970i	−0.151890	+	0.263082i
$773$	13.4018	+	23.2126i	0.482030	+	0.834901i	0.999787	−	0.0206271i	$-0.00656626\pi$
$773$	13.4018	+	23.2126i	0.482030	+	0.834901i	−0.517757	+	0.855528i	$0.673233\pi$
$774$		0			0
$775$	−6.71938	−	3.87944i	−0.241367	−	0.139353i
$776$	0.0756815			0.00271681
$777$		0			0
$778$	22.6207			0.810993
$779$	6.78472	+	3.91716i	0.243088	+	0.140347i
$780$		0			0
$781$	9.02005	+	15.6232i	0.322763	+	0.559042i
$782$	−15.3891	+	26.6547i	−0.550313	+	0.953170i
$783$		0			0
$784$	23.0122	+	16.3690i	0.821864	+	0.584605i
$785$		−	16.7050i		−	0.596225i
$786$		0			0
$787$	1.99556	−	1.15213i	0.0711339	−	0.0410692i	−0.464011	−	0.885829i	$-0.653590\pi$
$787$	1.99556	−	1.15213i	0.0711339	−	0.0410692i	0.535145	+	0.844760i	$0.320257\pi$
$788$	−2.65811	+	1.53466i	−0.0946914	+	0.0546701i
$789$		0			0
$790$			8.45580i			0.300844i
$791$	−32.4641	+	29.5272i	−1.15429	+	1.04987i
$792$		0			0
$793$	20.8189	−	36.0595i	0.739302	−	1.28051i
$794$	−30.1524	−	52.2255i	−1.07007	−	1.85341i
$795$		0			0
$796$	−2.24439	−	1.29580i	−0.0795504	−	0.0459284i
$797$	−2.87866			−0.101967			−0.0509837	−	0.998699i	$-0.516236\pi$
$797$	−2.87866			−0.101967			−0.0509837	+	0.998699i	$0.516236\pi$
$798$		0			0
$799$	10.0292			0.354807
$800$	−6.91269	−	3.99104i	−0.244400	−	0.141105i
$801$		0			0
$802$	−1.32014	−	2.28655i	−0.0466158	−	0.0807409i
$803$	−14.9047	+	25.8157i	−0.525976	+	0.911017i
$804$		0			0
$805$	20.8527	+	6.65993i	0.734961	+	0.234732i
$806$			82.6669i			2.91182i
$807$		0			0
$808$	−0.157690	+	0.0910422i	−0.00554751	+	0.00320285i
$809$	13.1435	−	7.58843i	0.462102	−	0.266795i	−0.250825	−	0.968032i	$-0.580702\pi$
$809$	13.1435	−	7.58843i	0.462102	−	0.266795i	0.712928	+	0.701237i	$0.247369\pi$
$810$		0			0
$811$		−	30.0791i		−	1.05622i	−0.849176	−	0.528110i	$-0.822901\pi$
$811$		−	30.0791i		−	1.05622i	0.849176	−	0.528110i	$-0.177099\pi$
$812$	13.9602	+	4.45862i	0.489909	+	0.156467i
$813$		0			0
$814$	13.4725	−	23.3350i	0.472210	−	0.817891i
$815$	9.69006	+	16.7837i	0.339428	+	0.587906i
$816$		0			0
$817$	5.64010	+	3.25631i	0.197322	+	0.113924i
$818$	68.4239			2.39239
$819$		0			0
$820$	7.49494			0.261735
$821$	25.7001	+	14.8379i	0.896939	+	0.517848i	0.876206	−	0.481937i	$-0.160067\pi$
$821$	25.7001	+	14.8379i	0.896939	+	0.517848i	0.0207329	+	0.999785i	$0.493400\pi$
$822$		0			0
$823$	0.946045	+	1.63860i	0.0329771	+	0.0571179i	0.882043	−	0.471169i	$-0.156168\pi$
$823$	0.946045	+	1.63860i	0.0329771	+	0.0571179i	−0.849066	+	0.528287i	$0.822835\pi$
$824$	0.113415	−	0.196440i	0.00395100	−	0.00684333i
$825$		0			0
$826$	32.2148	−	29.3004i	1.12089	−	1.01949i
$827$		−	38.5939i		−	1.34204i	−0.741439	−	0.671020i	$-0.765856\pi$
$827$		−	38.5939i		−	1.34204i	0.741439	−	0.671020i	$-0.234144\pi$
$828$		0			0
$829$	26.3366	−	15.2054i	0.914708	−	0.528107i	0.0327650	−	0.999463i	$-0.489569\pi$
$829$	26.3366	−	15.2054i	0.914708	−	0.528107i	0.881943	+	0.471356i	$0.156235\pi$
$830$	−15.5720	+	8.99051i	−0.540512	+	0.312065i
$831$		0			0
$832$			41.9684i			1.45499i
$833$	11.8662	−	5.42653i	0.411139	−	0.188018i
$834$		0			0
$835$	−10.6855	+	18.5078i	−0.369786	+	0.640489i
$836$	−3.71639	−	6.43698i	−0.128534	−	0.222628i
$837$		0			0
$838$	−0.591398	−	0.341444i	−0.0204295	−	0.0117950i
$839$	−15.0305			−0.518909			−0.259455	−	0.965755i	$-0.583543\pi$
$839$	−15.0305			−0.518909			−0.259455	+	0.965755i	$0.583543\pi$
$840$		0			0
$841$	21.1953			0.730872
$842$	−12.5650	−	7.25443i	−0.433020	−	0.250004i
$843$		0			0
$844$	−7.64374	−	13.2393i	−0.263108	−	0.455717i
$845$	7.75142	−	13.4259i	0.266657	−	0.461863i
$846$		0			0
$847$	−19.9781	+	4.35138i	−0.686454	+	0.149515i
$848$		−	20.5957i		−	0.707259i
$849$		0			0
$850$	−3.22158	+	1.85998i	−0.110499	+	0.0637968i
$851$	−53.4834	+	30.8786i	−1.83339	+	1.05851i
$852$		0			0
$853$		−	34.4211i		−	1.17856i	−0.807930	−	0.589278i	$-0.799412\pi$
$853$		−	34.4211i		−	1.17856i	0.807930	−	0.589278i	$-0.200588\pi$
$854$	12.5285	−	39.2275i	0.428716	−	1.34234i
$855$		0			0
$856$	0.169597	−	0.293750i	0.00579669	−	0.0100402i
$857$	10.9059	+	18.8896i	0.372539	+	0.645256i	0.989955	−	0.141380i	$-0.0451540\pi$
$857$	10.9059	+	18.8896i	0.372539	+	0.645256i	−0.617417	+	0.786636i	$0.711821\pi$
$858$		0			0
$859$	33.8026	+	19.5160i	1.15333	+	0.665876i	0.949697	−	0.313171i	$-0.101391\pi$
$859$	33.8026	+	19.5160i	1.15333	+	0.665876i	0.203635	+	0.979047i	$0.434725\pi$
$860$	6.23050			0.212458
$861$		0			0
$862$	−7.80531			−0.265850
$863$	−0.941464	−	0.543555i	−0.0320478	−	0.0185028i	0.483890	−	0.875129i	$-0.339223\pi$
$863$	−0.941464	−	0.543555i	−0.0320478	−	0.0185028i	−0.515938	+	0.856626i	$0.672557\pi$
$864$		0			0
$865$	8.43701	+	14.6133i	0.286867	+	0.496868i
$866$	−24.8317	+	43.0097i	−0.843815	+	1.46153i
$867$		0			0
$868$	8.66191	+	39.7686i	0.294004	+	1.34983i
$869$		−	7.66426i		−	0.259992i
$870$		0			0
$871$	−51.8726	+	29.9486i	−1.75764	+	1.01477i
$872$	−0.0931646	+	0.0537886i	−0.00315495	+	0.00182151i
$873$		0			0
$874$			34.2203i			1.15752i
$875$	1.78020	+	1.95727i	0.0601817	+	0.0661677i
$876$		0			0
$877$	5.64382	−	9.77538i	0.190578	−	0.330091i	−0.754864	−	0.655882i	$-0.772297\pi$
$877$	5.64382	−	9.77538i	0.190578	−	0.330091i	0.945442	+	0.325790i	$0.105630\pi$
$878$	−14.0733	−	24.3757i	−0.474951	−	0.822639i
$879$		0			0
$880$	6.31980	+	3.64874i	0.213040	+	0.122999i
$881$	−38.1260			−1.28450			−0.642249	−	0.766496i	$-0.721998\pi$
$881$	−38.1260			−1.28450			−0.642249	+	0.766496i	$0.721998\pi$
$882$		0			0
$883$	−8.78789			−0.295736			−0.147868	−	0.989007i	$-0.547241\pi$
$883$	−8.78789			−0.295736			−0.147868	+	0.989007i	$0.547241\pi$
$884$	17.0876	+	9.86554i	0.574719	+	0.331814i
$885$		0			0
$886$	11.5788	+	20.0550i	0.388996	+	0.673761i
$887$	17.2377	−	29.8566i	0.578787	−	1.00249i	−0.416832	−	0.908983i	$-0.636860\pi$
$887$	17.2377	−	29.8566i	0.578787	−	1.00249i	0.995619	−	0.0935043i	$-0.0298069\pi$
$888$		0			0
$889$	25.8771	+	28.4509i	0.867889	+	0.954213i
$890$			13.4777i			0.451774i
$891$		0			0
$892$	7.22460	−	4.17112i	0.241897	−	0.139660i
$893$	9.65687	−	5.57540i	0.323155	−	0.186574i
$894$		0			0
$895$		−	19.2331i		−	0.642893i
$896$	−0.155510	−	0.713977i	−0.00519522	−	0.0238523i
$897$		0			0
$898$	−7.83279	+	13.5668i	−0.261384	+	0.452730i
$899$	−10.8379	−	18.7719i	−0.361466	−	0.626077i
$900$		0			0
$901$	−8.24117	−	4.75804i	−0.274553	−	0.158513i
$902$	−13.6460			−0.454361
$903$		0			0
$904$	0.572637			0.0190456
$905$	−19.3132	−	11.1505i	−0.641992	−	0.370654i
$906$		0			0
$907$	−5.84886	−	10.1305i	−0.194208	−	0.336378i	0.752432	−	0.658669i	$-0.228880\pi$
$907$	−5.84886	−	10.1305i	−0.194208	−	0.336378i	−0.946641	+	0.322291i	$0.895547\pi$
$908$	3.51330	−	6.08521i	0.116593	−	0.201945i
$909$		0			0
$910$	8.57626	−	26.8529i	0.284300	−	0.890163i
$911$		−	17.0203i		−	0.563908i	−0.959428	−	0.281954i	$-0.909017\pi$
$911$		−	17.0203i		−	0.563908i	0.959428	−	0.281954i	$-0.0909826\pi$
$912$		0			0
$913$	14.1143	−	8.14892i	0.467117	−	0.269690i
$914$	2.67602	−	1.54500i	0.0885148	−	0.0511040i
$915$		0			0
$916$		−	44.4252i		−	1.46785i
$917$	−36.1904	+	7.88256i	−1.19511	+	0.260305i
$918$		0			0
$919$	−14.8185	+	25.6665i	−0.488819	+	0.846658i	−0.999917	−	0.0128635i	$-0.995905\pi$
$919$	−14.8185	+	25.6665i	−0.488819	+	0.846658i	0.511099	+	0.859522i	$0.329239\pi$
$920$	−0.142824	−	0.247378i	−0.00470876	−	0.00815582i
$921$		0			0
$922$	18.2824	+	10.5553i	0.602099	+	0.347622i
$923$	−53.2449			−1.75258
$924$		0			0
$925$	−7.46420			−0.245422
$926$	12.6656	+	7.31246i	0.416216	+	0.240302i
$927$		0			0
$928$	−11.1497	−	19.3119i	−0.366008	−	0.633945i
$929$	−0.569167	+	0.985826i	−0.0186738	+	0.0323439i	−0.875211	−	0.483741i	$-0.839278\pi$
$929$	−0.569167	+	0.985826i	−0.0186738	+	0.0323439i	0.856538	+	0.516085i	$0.172611\pi$
$930$		0			0
$931$	8.40897	−	11.8217i	0.275593	−	0.387440i
$932$			47.6471i			1.56073i
$933$		0			0
$934$	6.66610	−	3.84867i	0.218121	−	0.125932i
$935$	2.92001	−	1.68587i	0.0954947	−	0.0551339i
$936$		0			0
$937$			10.1424i			0.331338i	0.986181	+	0.165669i	$0.0529783\pi$
$937$			10.1424i			0.331338i	−0.986181	+	0.165669i	$0.947022\pi$
$938$	−43.8230	+	39.8585i	−1.43087	+	1.30142i
$939$		0			0
$940$	5.33388	−	9.23855i	0.173972	−	0.301328i
$941$	−18.3854	−	31.8444i	−0.599346	−	1.03810i	−0.992918	−	0.118804i	$-0.962094\pi$
$941$	−18.3854	−	31.8444i	−0.599346	−	1.03810i	0.393572	−	0.919294i	$-0.371239\pi$
$942$		0			0
$943$	27.0861	+	15.6382i	0.882045	+	0.509249i
$944$	−33.2724			−1.08292
$945$		0			0
$946$	−11.3438			−0.368820
$947$	21.0056	+	12.1276i	0.682590	+	0.394094i	0.800830	−	0.598891i	$-0.204392\pi$
$947$	21.0056	+	12.1276i	0.682590	+	0.394094i	−0.118240	+	0.992985i	$0.537725\pi$
$948$		0			0
$949$	−43.9909	−	76.1945i	−1.42801	−	2.47338i
$950$	−2.06799	+	3.58187i	−0.0670945	+	0.116211i
$951$		0			0
$952$	−0.162193	−	0.0518013i	−0.00525672	−	0.00167889i
$953$		−	4.33668i		−	0.140479i	−0.997530	−	0.0702394i	$-0.977624\pi$
$953$		−	4.33668i		−	0.140479i	0.997530	−	0.0702394i	$-0.0223763\pi$
$954$		0			0
$955$	−15.9342	+	9.19964i	−0.515620	+	0.297693i
$956$	−20.7650	+	11.9887i	−0.671588	+	0.387741i
$957$		0			0
$958$			38.0142i			1.22818i
$959$	−56.8286	−	18.1499i	−1.83509	−	0.586091i
$960$		0			0
$961$	14.6001	−	25.2880i	0.470970	−	0.815743i
$962$	39.7637	+	68.8727i	1.28203	+	2.22054i
$963$		0			0
$964$	44.3710	+	25.6176i	1.42909	+	0.825087i
$965$	−4.25708			−0.137040
$966$		0			0
$967$	32.4312			1.04292			0.521458	−	0.853277i	$-0.325388\pi$
$967$	32.4312			1.04292			0.521458	+	0.853277i	$0.325388\pi$
$968$	0.231060	+	0.133403i	0.00742656	+	0.00428773i
$969$		0			0
$970$	−2.18737	−	3.78864i	−0.0702322	−	0.121646i
$971$	−0.500111	+	0.866217i	−0.0160493	+	0.0277982i	−0.873939	−	0.486036i	$-0.838442\pi$
$971$	−0.500111	+	0.866217i	−0.0160493	+	0.0277982i	0.857889	+	0.513835i	$0.171776\pi$
$972$		0			0
$973$	14.6372	−	13.3130i	0.469246	−	0.426795i
$974$			15.1302i			0.484802i
$975$		0			0
$976$	−27.2486	+	15.7320i	−0.872205	+	0.503568i
$977$	−19.4306	+	11.2183i	−0.621641	+	0.358905i	−0.777508	−	0.628874i	$-0.783516\pi$
$977$	−19.4306	+	11.2183i	−0.621641	+	0.358905i	0.155867	+	0.987778i	$0.450183\pi$
$978$		0			0
$979$		−	12.2161i		−	0.390428i
$980$	1.31212	−	13.8167i	0.0419141	−	0.441360i
$981$		0			0
$982$	−22.2023	+	38.4555i	−0.708504	+	1.22716i
$983$	−9.56124	−	16.5606i	−0.304956	−	0.528200i	0.672295	−	0.740283i	$-0.265308\pi$
$983$	−9.56124	−	16.5606i	−0.304956	−	0.528200i	−0.977252	+	0.212083i	$0.931975\pi$
$984$		0			0
$985$	−1.34065	−	0.774027i	−0.0427168	−	0.0246625i
$986$	−10.3924			−0.330962
$987$		0			0
$988$	21.9377			0.697931
$989$	22.5165	+	12.9999i	0.715984	+	0.413373i
$990$		0			0
$991$	−3.45280	−	5.98043i	−0.109682	−	0.189975i	0.805959	−	0.591971i	$-0.201650\pi$
$991$	−3.45280	−	5.98043i	−0.109682	−	0.189975i	−0.915641	+	0.401996i	$0.868317\pi$
$992$	30.9660	−	53.6347i	0.983171	−	1.70290i
$993$		0			0
$994$	−51.4526	+	11.2068i	−1.63198	+	0.355458i
$995$		−	1.30711i		−	0.0414381i
$996$		0			0
$997$	34.3034	−	19.8051i	1.08640	−	0.627233i	0.153784	−	0.988104i	$-0.450854\pi$
$997$	34.3034	−	19.8051i	1.08640	−	0.627233i	0.932616	+	0.360871i	$0.117521\pi$
$998$	−47.3661	+	27.3468i	−1.49935	+	0.865649i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bj.a.26.5	✓	12
3.2	odd	2		315.2.bj.b.26.2	yes	12
5.2	odd	4		1575.2.bc.d.1349.3		24
5.3	odd	4		1575.2.bc.d.1349.10		24
5.4	even	2		1575.2.bk.f.26.2		12
7.2	even	3		2205.2.b.b.881.3		12
7.3	odd	6		315.2.bj.b.206.2	yes	12
7.5	odd	6		2205.2.b.a.881.3		12
15.2	even	4		1575.2.bc.c.1349.10		24
15.8	even	4		1575.2.bc.c.1349.3		24
15.14	odd	2		1575.2.bk.e.26.5		12
21.2	odd	6		2205.2.b.a.881.10		12
21.5	even	6		2205.2.b.b.881.10		12
21.17	even	6	inner	315.2.bj.a.206.5	yes	12
35.3	even	12		1575.2.bc.c.899.10		24
35.17	even	12		1575.2.bc.c.899.3		24
35.24	odd	6		1575.2.bk.e.1151.5		12
105.17	odd	12		1575.2.bc.d.899.10		24
105.38	odd	12		1575.2.bc.d.899.3		24
105.59	even	6		1575.2.bk.f.1151.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bj.a.26.5	✓	12	1.1	even	1	trivial
315.2.bj.a.206.5	yes	12	21.17	even	6	inner
315.2.bj.b.26.2	yes	12	3.2	odd	2
315.2.bj.b.206.2	yes	12	7.3	odd	6
1575.2.bc.c.899.3		24	35.17	even	12
1575.2.bc.c.899.10		24	35.3	even	12
1575.2.bc.c.1349.3		24	15.8	even	4
1575.2.bc.c.1349.10		24	15.2	even	4
1575.2.bc.d.899.3		24	105.38	odd	12
1575.2.bc.d.899.10		24	105.17	odd	12
1575.2.bc.d.1349.3		24	5.2	odd	4
1575.2.bc.d.1349.10		24	5.3	odd	4
1575.2.bk.e.26.5		12	15.14	odd	2
1575.2.bk.e.1151.5		12	35.24	odd	6
1575.2.bk.f.26.2		12	5.4	even	2
1575.2.bk.f.1151.2		12	105.59	even	6
2205.2.b.a.881.3		12	7.5	odd	6
2205.2.b.a.881.10		12	21.2	odd	6
2205.2.b.b.881.3		12	7.2	even	3
2205.2.b.b.881.10		12	21.5	even	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72830 + 0.997835i) q^{2} +(0.991350 + 1.71707i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.78020 + 1.95727i) q^{7} -0.0345244i q^{8} +O(q^{10})\)	\(q+(1.72830 + 0.997835i) q^{2} +(0.991350 + 1.71707i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.78020 + 1.95727i) q^{7} -0.0345244i q^{8} +(-1.72830 + 0.997835i) q^{10} +(1.56652 - 0.904429i) q^{11} +5.33881i q^{13} +(1.12369 + 5.15909i) q^{14} +(2.01715 - 3.49381i) q^{16} +(-0.932008 - 1.61429i) q^{17} +(-1.79482 - 1.03624i) q^{19} -1.98270 q^{20} +3.60989 q^{22} +(-7.16531 - 4.13690i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-5.32725 + 9.22706i) q^{26} +(-1.59596 + 4.99706i) q^{28} -2.79369i q^{29} +(6.71938 - 3.87944i) q^{31} +(6.91269 - 3.99104i) q^{32} -3.71996i q^{34} +(-2.58514 + 0.563064i) q^{35} +(3.73210 - 6.46419i) q^{37} +(-2.06799 - 3.58187i) q^{38} +(0.0298990 + 0.0172622i) q^{40} -3.78017 q^{41} -3.14243 q^{43} +(3.10594 + 1.79321i) q^{44} +(-8.25588 - 14.2996i) q^{46} +(-2.69021 + 4.65958i) q^{47} +(-0.661784 + 6.96865i) q^{49} -1.99567i q^{50} +(-9.16710 + 5.29263i) q^{52} +(4.42119 - 2.55257i) q^{53} +1.80886i q^{55} +(0.0675734 - 0.0614603i) q^{56} +(2.78764 - 4.82834i) q^{58} +(-4.12369 - 7.14244i) q^{59} +(-6.75422 - 3.89955i) q^{61} +15.4842 q^{62} +7.86101 q^{64} +(-4.62354 - 2.66940i) q^{65} +(5.60962 + 9.71614i) q^{67} +(1.84789 - 3.20064i) q^{68} +(-5.02975 - 1.60640i) q^{70} +9.97319i q^{71} +(-14.2718 + 8.23984i) q^{73} +(12.9004 - 7.44805i) q^{74} -4.10910i q^{76} +(4.55892 + 1.45603i) q^{77} +(2.11854 - 3.66941i) q^{79} +(2.01715 + 3.49381i) q^{80} +(-6.53327 - 3.77199i) q^{82} +9.01001 q^{83} +1.86402 q^{85} +(-5.43107 - 3.13563i) q^{86} +(-0.0312249 - 0.0540831i) q^{88} +(3.37674 - 5.84868i) q^{89} +(-10.4495 + 9.50414i) q^{91} -16.4045i q^{92} +(-9.29898 + 5.36877i) q^{94} +(1.79482 - 1.03624i) q^{95} +2.19212i q^{97} +(-8.09732 + 11.3836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7	\( 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7} + 12 q^{11} - 12 q^{14} - 16 q^{16} + 6 q^{19} - 16 q^{20} + 32 q^{22} + 12 q^{23} - 6 q^{25} - 20 q^{28} + 6 q^{31} + 60 q^{32} - 2 q^{35} - 10 q^{37} - 36 q^{38} + 24 q^{41} - 4 q^{43} + 12 q^{44} - 4 q^{46} + 6 q^{49} + 12 q^{53} - 60 q^{56} + 20 q^{58} - 24 q^{59} + 24 q^{62} - 56 q^{64} + 18 q^{65} + 6 q^{67} - 60 q^{68} - 12 q^{70} - 42 q^{73} + 84 q^{74} - 36 q^{77} + 18 q^{79} - 16 q^{80} - 72 q^{82} - 24 q^{83} - 84 q^{86} + 4 q^{88} + 12 q^{89} - 18 q^{91} + 12 q^{94} - 6 q^{95} + 12 q^{98}+O(q^{100}) \) 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7 + 12 * q^11 - 12 * q^14 - 16 * q^16 + 6 * q^19 - 16 * q^20 + 32 * q^22 + 12 * q^23 - 6 * q^25 - 20 * q^28 + 6 * q^31 + 60 * q^32 - 2 * q^35 - 10 * q^37 - 36 * q^38 + 24 * q^41 - 4 * q^43 + 12 * q^44 - 4 * q^46 + 6 * q^49 + 12 * q^53 - 60 * q^56 + 20 * q^58 - 24 * q^59 + 24 * q^62 - 56 * q^64 + 18 * q^65 + 6 * q^67 - 60 * q^68 - 12 * q^70 - 42 * q^73 + 84 * q^74 - 36 * q^77 + 18 * q^79 - 16 * q^80 - 72 * q^82 - 24 * q^83 - 84 * q^86 + 4 * q^88 + 12 * q^89 - 18 * q^91 + 12 * q^94 - 6 * q^95 + 12 * q^98

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