LMFDB - Embedded newform 315.2.j.g.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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([0, 0, 4]))

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$-0.105378 - 0.182520i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.2.j.g.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.605378 - 1.04855i) q^{2} +(0.267035 + 0.462518i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.16166 + 2.37709i) q^{7} +3.06814 q^{8} +O(q^{10})$	\(q+(0.605378 - 1.04855i) q^{2} +(0.267035 + 0.462518i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.16166 + 2.37709i) q^{7} +3.06814 q^{8} +(-0.605378 - 1.04855i) q^{10} +(0.127587 + 0.220987i) q^{11} -0.744826 q^{13} +(3.19573 + 0.220987i) q^{14} +(1.32331 - 2.29205i) q^{16} +(-0.605378 - 1.04855i) q^{17} +(-0.556279 + 0.963504i) q^{19} +0.534070 q^{20} +0.308953 q^{22} +(3.92869 - 6.80469i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.450901 + 0.780984i) q^{26} +(-0.789244 + 1.17205i) q^{28} -3.32331 q^{29} +(-3.45558 - 5.98524i) q^{31} +(1.46593 + 2.53906i) q^{32} -1.46593 q^{34} +(2.63945 + 0.182520i) q^{35} +(-4.63945 + 8.03576i) q^{37} +(0.673518 + 1.16657i) q^{38} +(1.53407 - 2.65709i) q^{40} -8.81297 q^{41} +5.70041 q^{43} +(-0.0681404 + 0.118023i) q^{44} +(-4.75669 - 8.23882i) q^{46} +(-3.95558 + 6.85127i) q^{47} +(-4.30111 + 5.52273i) q^{49} -1.21076 q^{50} +(-0.198895 - 0.344496i) q^{52} +(1.21076 + 2.09709i) q^{53} +0.255174 q^{55} +(3.56413 + 7.29324i) q^{56} +(-2.01186 + 3.48465i) q^{58} +(-5.94055 - 10.2893i) q^{59} +(5.47779 - 9.48781i) q^{61} -8.36773 q^{62} +8.84302 q^{64} +(-0.372413 + 0.645038i) q^{65} +(4.58317 + 7.93828i) q^{67} +(0.323314 - 0.559997i) q^{68} +(1.78924 - 2.65709i) q^{70} -10.5878 q^{71} +(0.217936 + 0.377477i) q^{73} +(5.61724 + 9.72934i) q^{74} -0.594184 q^{76} +(-0.377094 + 0.559997i) q^{77} +(-1.18855 + 2.05862i) q^{79} +(-1.32331 - 2.29205i) q^{80} +(-5.33518 + 9.24080i) q^{82} -10.2789 q^{83} -1.21076 q^{85} +(3.45090 - 5.97714i) q^{86} +(0.391455 + 0.678019i) q^{88} +(-7.08317 + 12.2684i) q^{89} +(-0.865233 - 1.77052i) q^{91} +4.19639 q^{92} +(4.78924 + 8.29521i) q^{94} +(0.556279 + 0.963504i) q^{95} +8.44523 q^{97} +(3.18703 + 7.85324i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8	$ 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8} - 2 q^{10} + 10 q^{11} + 14 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + q^{19} - 12 q^{20} + 4 q^{22} + 10 q^{23} - 3 q^{25} - 8 q^{28} - 8 q^{29} + q^{31} + 24 q^{32} - 24 q^{34} - q^{35} - 11 q^{37} - 28 q^{38} - 6 q^{40} - 4 q^{41} - 6 q^{43} + 30 q^{44} + 16 q^{46} - 2 q^{47} - 3 q^{49} - 4 q^{50} - 24 q^{52} + 4 q^{53} + 20 q^{55} + 42 q^{56} + 14 q^{58} + 4 q^{59} + 22 q^{61} - 60 q^{62} + 40 q^{64} + 7 q^{65} + 15 q^{67} - 10 q^{68} + 14 q^{70} - 32 q^{71} - 9 q^{73} + 6 q^{74} - 60 q^{76} + 26 q^{77} + 7 q^{79} + 4 q^{80} + 6 q^{82} - 28 q^{83} - 4 q^{85} + 18 q^{86} - 40 q^{88} - 30 q^{89} - 3 q^{91} + 36 q^{92} + 32 q^{94} - q^{95} - 8 q^{97} + 68 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8 - 2 * q^10 + 10 * q^11 + 14 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + q^19 - 12 * q^20 + 4 * q^22 + 10 * q^23 - 3 * q^25 - 8 * q^28 - 8 * q^29 + q^31 + 24 * q^32 - 24 * q^34 - q^35 - 11 * q^37 - 28 * q^38 - 6 * q^40 - 4 * q^41 - 6 * q^43 + 30 * q^44 + 16 * q^46 - 2 * q^47 - 3 * q^49 - 4 * q^50 - 24 * q^52 + 4 * q^53 + 20 * q^55 + 42 * q^56 + 14 * q^58 + 4 * q^59 + 22 * q^61 - 60 * q^62 + 40 * q^64 + 7 * q^65 + 15 * q^67 - 10 * q^68 + 14 * q^70 - 32 * q^71 - 9 * q^73 + 6 * q^74 - 60 * q^76 + 26 * q^77 + 7 * q^79 + 4 * q^80 + 6 * q^82 - 28 * q^83 - 4 * q^85 + 18 * q^86 - 40 * q^88 - 30 * q^89 - 3 * q^91 + 36 * q^92 + 32 * q^94 - q^95 - 8 * q^97 + 68 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.605378	−	1.04855i	0.428067	−	0.741434i	−0.568635	−	0.822590i	$-0.692528\pi$
$2$	0.605378	−	1.04855i	0.428067	−	0.741434i	0.996701	+	0.0811568i	$0.0258614\pi$
$3$		0			0
$3$		0			0
$4$	0.267035	+	0.462518i	0.133518	+	0.231259i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.16166	+	2.37709i	0.439065	+	0.898455i
$7$	1.16166	+	2.37709i	0.439065	+	0.898455i
$8$	3.06814			1.08475
$9$		0			0
$10$	−0.605378	−	1.04855i	−0.191437	−	0.331579i
$11$	0.127587	+	0.220987i	0.0384689	+	0.0666301i	0.884619	−	0.466315i	$-0.154419\pi$
$11$	0.127587	+	0.220987i	0.0384689	+	0.0666301i	−0.846150	+	0.532945i	$0.821085\pi$
$12$		0			0
$13$	−0.744826			−0.206578			−0.103289	−	0.994651i	$-0.532937\pi$
$13$	−0.744826			−0.206578			−0.103289	+	0.994651i	$0.532937\pi$
$14$	3.19573	+	0.220987i	0.854094	+	0.0590613i
$15$		0			0
$16$	1.32331	−	2.29205i	0.330829	−	0.573012i
$17$	−0.605378	−	1.04855i	−0.146826	−	0.254310i	0.783227	−	0.621736i	$-0.213572\pi$
$17$	−0.605378	−	1.04855i	−0.146826	−	0.254310i	−0.930053	+	0.367426i	$0.880239\pi$
$18$		0			0
$19$	−0.556279	+	0.963504i	−0.127619	+	0.221043i	−0.922754	−	0.385390i	$-0.874067\pi$
$19$	−0.556279	+	0.963504i	−0.127619	+	0.221043i	0.795135	+	0.606433i	$0.207400\pi$
$20$	0.534070			0.119422
$21$		0			0
$22$	0.308953			0.0658691
$23$	3.92869	−	6.80469i	0.819189	−	1.41888i	−0.0870916	−	0.996200i	$-0.527757\pi$
$23$	3.92869	−	6.80469i	0.819189	−	1.41888i	0.906281	−	0.422677i	$-0.138909\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.450901	+	0.780984i	−0.0884290	+	0.153164i
$27$		0			0
$28$	−0.789244	+	1.17205i	−0.149153	+	0.221497i
$29$	−3.32331			−0.617124			−0.308562	−	0.951204i	$-0.599848\pi$
$29$	−3.32331			−0.617124			−0.308562	+	0.951204i	$0.599848\pi$
$30$		0			0
$31$	−3.45558	−	5.98524i	−0.620641	−	1.07498i	−0.989367	−	0.145443i	$-0.953539\pi$
$31$	−3.45558	−	5.98524i	−0.620641	−	1.07498i	0.368726	−	0.929538i	$-0.379794\pi$
$32$	1.46593	+	2.53906i	0.259142	+	0.448848i
$33$		0			0
$34$	−1.46593			−0.251405
$35$	2.63945	+	0.182520i	0.446148	+	0.0308515i
$36$		0			0
$37$	−4.63945	+	8.03576i	−0.762721	+	1.32107i	0.178723	+	0.983899i	$0.442803\pi$
$37$	−4.63945	+	8.03576i	−0.762721	+	1.32107i	−0.941443	+	0.337171i	$0.890530\pi$
$38$	0.673518	+	1.16657i	0.109259	+	0.189242i
$39$		0			0
$40$	1.53407	−	2.65709i	0.242558	−	0.420122i
$41$	−8.81297			−1.37635			−0.688177	−	0.725543i	$-0.741589\pi$
$41$	−8.81297			−1.37635			−0.688177	+	0.725543i	$0.741589\pi$
$42$		0			0
$43$	5.70041			0.869304			0.434652	−	0.900598i	$-0.356871\pi$
$43$	5.70041			0.869304			0.434652	+	0.900598i	$0.356871\pi$
$44$	−0.0681404	+	0.118023i	−0.0102726	+	0.0177926i
$45$		0			0
$46$	−4.75669	−	8.23882i	−0.701335	−	1.21475i
$47$	−3.95558	+	6.85127i	−0.576981	+	0.999360i	0.418842	+	0.908059i	$0.362436\pi$
$47$	−3.95558	+	6.85127i	−0.576981	+	0.999360i	−0.995823	+	0.0913013i	$0.970897\pi$
$48$		0			0
$49$	−4.30111	+	5.52273i	−0.614444	+	0.788961i
$50$	−1.21076			−0.171227
$51$		0			0
$52$	−0.198895	−	0.344496i	−0.0275817	−	0.0477730i
$53$	1.21076	+	2.09709i	0.166310	+	0.288058i	0.937120	−	0.349008i	$-0.113481\pi$
$53$	1.21076	+	2.09709i	0.166310	+	0.288058i	−0.770810	+	0.637066i	$0.780148\pi$
$54$		0			0
$55$	0.255174			0.0344076
$56$	3.56413	+	7.29324i	0.476277	+	0.974601i
$57$		0			0
$58$	−2.01186	+	3.48465i	−0.264170	+	0.457556i
$59$	−5.94055	−	10.2893i	−0.773394	−	1.33956i	−0.935693	−	0.352816i	$-0.885224\pi$
$59$	−5.94055	−	10.2893i	−0.773394	−	1.33956i	0.162298	−	0.986742i	$-0.448109\pi$
$60$		0			0
$61$	5.47779	−	9.48781i	0.701359	−	1.21479i	−0.266630	−	0.963799i	$-0.585910\pi$
$61$	5.47779	−	9.48781i	0.701359	−	1.21479i	0.967989	−	0.250991i	$-0.0807564\pi$
$62$	−8.36773			−1.06270
$63$		0			0
$64$	8.84302			1.10538
$65$	−0.372413	+	0.645038i	−0.0461922	+	0.0800072i
$66$		0			0
$67$	4.58317	+	7.93828i	0.559923	+	0.969815i	0.997502	+	0.0706355i	$0.0225027\pi$
$67$	4.58317	+	7.93828i	0.559923	+	0.969815i	−0.437579	+	0.899180i	$0.644164\pi$
$68$	0.323314	−	0.559997i	0.0392076	−	0.0679096i
$69$		0			0
$70$	1.78924	−	2.65709i	0.213856	−	0.317583i
$71$	−10.5878			−1.25655			−0.628273	−	0.777993i	$-0.716238\pi$
$71$	−10.5878			−1.25655			−0.628273	+	0.777993i	$0.716238\pi$
$72$		0			0
$73$	0.217936	+	0.377477i	0.0255075	+	0.0441803i	0.878497	−	0.477747i	$-0.158546\pi$
$73$	0.217936	+	0.377477i	0.0255075	+	0.0441803i	−0.852990	+	0.521927i	$0.825213\pi$
$74$	5.61724	+	9.72934i	0.652991	+	1.13101i
$75$		0			0
$76$	−0.594184			−0.0681576
$77$	−0.377094	+	0.559997i	−0.0429738	+	0.0638176i
$78$		0			0
$79$	−1.18855	+	2.05862i	−0.133722	+	0.231613i	−0.925109	−	0.379703i	$-0.876026\pi$
$79$	−1.18855	+	2.05862i	−0.133722	+	0.231613i	0.791387	+	0.611316i	$0.209360\pi$
$80$	−1.32331	−	2.29205i	−0.147951	−	0.256259i
$81$		0			0
$82$	−5.33518	+	9.24080i	−0.589172	+	1.02048i
$83$	−10.2789			−1.12826			−0.564128	−	0.825688i	$-0.690787\pi$
$83$	−10.2789			−1.12826			−0.564128	+	0.825688i	$0.690787\pi$
$84$		0			0
$85$	−1.21076			−0.131325
$86$	3.45090	−	5.97714i	0.372120	−	0.644531i
$87$		0			0
$88$	0.391455	+	0.678019i	0.0417292	+	0.0722771i
$89$	−7.08317	+	12.2684i	−0.750814	+	1.30045i	0.196614	+	0.980481i	$0.437005\pi$
$89$	−7.08317	+	12.2684i	−0.750814	+	1.30045i	−0.947428	+	0.319968i	$0.896328\pi$
$90$		0			0
$91$	−0.865233	−	1.77052i	−0.0907010	−	0.185601i
$92$	4.19639			0.437504
$93$		0			0
$94$	4.78924	+	8.29521i	0.493973	+	0.855586i
$95$	0.556279	+	0.963504i	0.0570730	+	0.0988534i
$96$		0			0
$97$	8.44523			0.857484			0.428742	−	0.903427i	$-0.358957\pi$
$97$	8.44523			0.857484			0.428742	+	0.903427i	$0.358957\pi$
$98$	3.18703	+	7.85324i	0.321939	+	0.793297i
$99$		0			0
$100$	0.267035	−	0.462518i	0.0267035	−	0.0462518i
$101$	5.03875	+	8.72737i	0.501374	+	0.868406i	0.999999	+	0.00158781i	$0.000505415\pi$
$101$	5.03875	+	8.72737i	0.501374	+	0.868406i	−0.498624	+	0.866818i	$0.666161\pi$
$102$		0			0
$103$	2.38427	−	4.12968i	0.234930	−	0.406910i	−0.724323	−	0.689461i	$-0.757847\pi$
$103$	2.38427	−	4.12968i	0.234930	−	0.406910i	0.959252	+	0.282551i	$0.0911807\pi$
$104$	−2.28523			−0.224085
$105$		0			0
$106$	2.93186			0.284767
$107$	8.13945	−	14.0979i	0.786870	−	1.36290i	−0.141005	−	0.990009i	$-0.545033\pi$
$107$	8.13945	−	14.0979i	0.786870	−	1.36290i	0.927875	−	0.372890i	$-0.121633\pi$
$108$		0			0
$109$	0.654477	+	1.13359i	0.0626875	+	0.108578i	0.895666	−	0.444728i	$-0.146700\pi$
$109$	0.654477	+	1.13359i	0.0626875	+	0.108578i	−0.832978	+	0.553306i	$0.813366\pi$
$110$	0.154477	−	0.267561i	0.0147288	−	0.0255110i
$111$		0			0
$112$	6.98564	+	0.483063i	0.660081	+	0.0456451i
$113$	−6.64663			−0.625262			−0.312631	−	0.949875i	$-0.601210\pi$
$113$	−6.64663			−0.625262			−0.312631	+	0.949875i	$0.601210\pi$
$114$		0			0
$115$	−3.92869	−	6.80469i	−0.366352	−	0.634541i
$116$	−0.887442	−	1.53709i	−0.0823969	−	0.142716i
$117$		0			0
$118$	−14.3851			−1.32426
$119$	1.78924	−	2.65709i	0.164020	−	0.243575i
$120$		0			0
$121$	5.46744	−	9.46989i	0.497040	−	0.860899i
$122$	−6.63227	−	11.4874i	−0.600457	−	1.04002i
$123$		0			0
$124$	1.84552	−	3.19654i	0.165733	−	0.287058i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−6.09820			−0.541128			−0.270564	−	0.962702i	$-0.587210\pi$
$127$	−6.09820			−0.541128			−0.270564	+	0.962702i	$0.587210\pi$
$128$	2.42151	−	4.19418i	0.214033	−	0.370717i
$129$		0			0
$130$	0.450901	+	0.780984i	0.0395467	+	0.0684968i
$131$	10.6560	−	18.4567i	0.931018	−	1.61257i	0.149433	−	0.988772i	$-0.452255\pi$
$131$	10.6560	−	18.4567i	0.931018	−	1.61257i	0.781585	−	0.623799i	$-0.214412\pi$
$132$		0			0
$133$	−2.93654	−	0.203064i	−0.254630	−	0.0176079i
$134$	11.0982			0.958738
$135$		0			0
$136$	−1.85738	−	3.21708i	−0.159269	−	0.275863i
$137$	7.62910	+	13.2140i	0.651798	+	1.12895i	0.982686	+	0.185277i	$0.0593183\pi$
$137$	7.62910	+	13.2140i	0.651798	+	1.12895i	−0.330888	+	0.943670i	$0.607348\pi$
$138$		0			0
$139$	−12.1807			−1.03315			−0.516577	−	0.856241i	$-0.672794\pi$
$139$	−12.1807			−1.03315			−0.516577	+	0.856241i	$0.672794\pi$
$140$	0.620406	+	1.26953i	0.0524339	+	0.107295i
$141$		0			0
$142$	−6.40965	+	11.1018i	−0.537886	+	0.931646i
$143$	−0.0950301	−	0.164597i	−0.00794682	−	0.0137643i
$144$		0			0
$145$	−1.66166	+	2.87807i	−0.137993	+	0.239011i
$146$	0.527735			0.0436757
$147$		0			0
$148$	−4.95558			−0.407346
$149$	8.48965	−	14.7045i	0.695499	−	1.20464i	−0.274513	−	0.961583i	$-0.588517\pi$
$149$	8.48965	−	14.7045i	0.695499	−	1.20464i	0.970012	−	0.243057i	$-0.0781501\pi$
$150$		0			0
$151$	−0.590349	−	1.02252i	−0.0480420	−	0.0832111i	0.841004	−	0.541028i	$-0.181965\pi$
$151$	−0.590349	−	1.02252i	−0.0480420	−	0.0832111i	−0.889046	+	0.457817i	$0.848631\pi$
$152$	−1.70674	+	2.95617i	−0.138435	+	0.239777i
$153$		0			0
$154$	0.358898	+	0.734410i	0.0289208	+	0.0591804i
$155$	−6.91116			−0.555118
$156$		0			0
$157$	−8.85738	−	15.3414i	−0.706896	−	1.22438i	−0.966003	−	0.258531i	$-0.916761\pi$
$157$	−8.85738	−	15.3414i	−0.706896	−	1.22438i	0.259107	−	0.965849i	$-0.416572\pi$
$158$	1.43904	+	2.49249i	0.114484	+	0.198292i
$159$		0			0
$160$	2.93186			0.231784
$161$	20.7392	+	1.43413i	1.63447	+	0.113025i
$162$		0			0
$163$	7.74483	−	13.4144i	0.606622	−	1.05070i	−0.385171	−	0.922845i	$-0.625858\pi$
$163$	7.74483	−	13.4144i	0.606622	−	1.05070i	0.991793	−	0.127854i	$-0.0408090\pi$
$164$	−2.35337	−	4.07616i	−0.183767	−	0.318295i
$165$		0			0
$166$	−6.22262	+	10.7779i	−0.482969	+	0.836526i
$167$	11.4359			0.884934			0.442467	−	0.896785i	$-0.354103\pi$
$167$	11.4359			0.884934			0.442467	+	0.896785i	$0.354103\pi$
$168$		0			0
$169$	−12.4452			−0.957326
$170$	−0.732965	+	1.26953i	−0.0562158	+	0.0973687i
$171$		0			0
$172$	1.52221	+	2.63654i	0.116067	+	0.201035i
$173$	−5.11256	+	8.85521i	−0.388701	+	0.673249i	−0.992275	−	0.124057i	$-0.960409\pi$
$173$	−5.11256	+	8.85521i	−0.388701	+	0.673249i	0.603574	+	0.797307i	$0.293743\pi$
$174$		0			0
$175$	1.47779	−	2.19457i	0.111710	−	0.165894i
$176$	0.675351			0.0509065
$177$		0			0
$178$	8.57599	+	14.8540i	0.642798	+	1.11336i
$179$	−0.955582	−	1.65512i	−0.0714235	−	0.123709i	0.828102	−	0.560578i	$-0.189421\pi$
$179$	−0.955582	−	1.65512i	−0.0714235	−	0.123709i	−0.899525	+	0.436868i	$0.856088\pi$
$180$		0			0
$181$	5.44523			0.404741			0.202371	−	0.979309i	$-0.435135\pi$
$181$	5.44523			0.404741			0.202371	+	0.979309i	$0.435135\pi$
$182$	−2.38026	−	0.164597i	−0.176437	−	0.0122007i
$183$		0			0
$184$	12.0538	−	20.8778i	0.888616	−	1.53913i
$185$	4.63945	+	8.03576i	0.341099	+	0.590801i
$186$		0			0
$187$	0.154477	−	0.267561i	0.0112965	−	0.0195660i
$188$	−4.22512			−0.308148
$189$		0			0
$190$	1.34704			0.0977243
$191$	2.11256	−	3.65906i	0.152859	−	0.264760i	−0.779418	−	0.626504i	$-0.784485\pi$
$191$	2.11256	−	3.65906i	0.152859	−	0.264760i	0.932278	+	0.361744i	$0.117819\pi$
$192$		0			0
$193$	3.27172	+	5.66678i	0.235503	+	0.407904i	0.959419	−	0.281985i	$-0.0909928\pi$
$193$	3.27172	+	5.66678i	0.235503	+	0.407904i	−0.723916	+	0.689889i	$0.757660\pi$
$194$	5.11256	−	8.85521i	0.367060	−	0.635767i
$195$		0			0
$196$	−3.70291	−	0.514579i	−0.264493	−	0.0367556i
$197$	17.1694			1.22327			0.611633	−	0.791141i	$-0.290513\pi$
$197$	17.1694			1.22327			0.611633	+	0.791141i	$0.290513\pi$
$198$		0			0
$199$	12.5015	+	21.6533i	0.886209	+	1.53496i	0.844322	+	0.535836i	$0.180004\pi$
$199$	12.5015	+	21.6533i	0.886209	+	1.53496i	0.0418869	+	0.999122i	$0.486663\pi$
$200$	−1.53407	−	2.65709i	−0.108475	−	0.187884i
$201$		0			0
$202$	12.2014			0.858487
$203$	−3.86055	−	7.89981i	−0.270958	−	0.554458i
$204$		0			0
$205$	−4.40648	+	7.63225i	−0.307762	+	0.533060i
$206$	−2.88677	−	5.00004i	−0.201131	−	0.348369i
$207$		0			0
$208$	−0.985639	+	1.70718i	−0.0683418	+	0.118371i
$209$	−0.283896			−0.0196375
$210$		0			0
$211$	−12.2201			−0.841268			−0.420634	−	0.907231i	$-0.638192\pi$
$211$	−12.2201			−0.841268			−0.420634	+	0.907231i	$0.638192\pi$
$212$	−0.646629	+	1.11999i	−0.0444106	+	0.0769215i
$213$		0			0
$214$	−9.85488	−	17.0692i	−0.673666	−	1.16682i
$215$	2.85020	−	4.93670i	0.194382	−	0.336680i
$216$		0			0
$217$	10.2133	−	15.1670i	0.693321	−	1.02960i
$218$	1.58482			0.107338
$219$		0			0
$220$	0.0681404	+	0.118023i	0.00459402	+	0.00795708i
$221$	0.450901	+	0.780984i	0.0303309	+	0.0525347i
$222$		0			0
$223$	18.9793			1.27095			0.635474	−	0.772122i	$-0.280805\pi$
$223$	18.9793			1.27095			0.635474	+	0.772122i	$0.280805\pi$
$224$	−4.33268	+	6.43417i	−0.289489	+	0.429901i
$225$		0			0
$226$	−4.02372	+	6.96929i	−0.267654	+	0.463590i
$227$	−1.49282	−	2.58564i	−0.0990819	−	0.171615i	0.812223	−	0.583347i	$-0.198257\pi$
$227$	−1.49282	−	2.58564i	−0.0990819	−	0.171615i	−0.911305	+	0.411732i	$0.864924\pi$
$228$		0			0
$229$	−1.98965	+	3.44618i	−0.131480	+	0.227730i	−0.924247	−	0.381794i	$-0.875306\pi$
$229$	−1.98965	+	3.44618i	−0.131480	+	0.227730i	0.792767	+	0.609524i	$0.208640\pi$
$230$	−9.51337			−0.627293
$231$		0			0
$232$	−10.1964			−0.669426
$233$	−5.81297	+	10.0684i	−0.380820	+	0.659600i	−0.991180	−	0.132525i	$-0.957692\pi$
$233$	−5.81297	+	10.0684i	−0.380820	+	0.659600i	0.610360	+	0.792124i	$0.291025\pi$
$234$		0			0
$235$	3.95558	+	6.85127i	0.258034	+	0.446928i
$236$	3.17267	−	5.49523i	0.206523	−	0.357709i
$237$		0			0
$238$	−1.70291	−	3.48465i	−0.110383	−	0.225876i
$239$	−7.02070			−0.454131			−0.227066	−	0.973879i	$-0.572913\pi$
$239$	−7.02070			−0.454131			−0.227066	+	0.973879i	$0.572913\pi$
$240$		0			0
$241$	14.2908	+	24.7523i	0.920549	+	1.59444i	0.798568	+	0.601904i	$0.205591\pi$
$241$	14.2908	+	24.7523i	0.920549	+	1.59444i	0.121981	+	0.992532i	$0.461075\pi$
$242$	−6.61974	−	11.4657i	−0.425533	−	0.737045i
$243$		0			0
$244$	5.85105			0.374575
$245$	2.63227	+	6.48623i	0.168169	+	0.414390i
$246$		0			0
$247$	0.414331	−	0.717643i	0.0263633	−	0.0456625i
$248$	−10.6022	−	18.3636i	−0.673241	−	1.16609i
$249$		0			0
$250$	−0.605378	+	1.04855i	−0.0382875	+	0.0663158i
$251$	4.48029			0.282793			0.141397	−	0.989953i	$-0.454841\pi$
$251$	4.48029			0.282793			0.141397	+	0.989953i	$0.454841\pi$
$252$		0			0
$253$	2.00500			0.126053
$254$	−3.69171	+	6.39424i	−0.231639	+	0.401210i
$255$		0			0
$256$	5.91116	+	10.2384i	0.369448	+	0.639902i
$257$	−13.1188	+	22.7223i	−0.818325	+	1.41738i	0.0885901	+	0.996068i	$0.471764\pi$
$257$	−13.1188	+	22.7223i	−0.818325	+	1.41738i	−0.906915	+	0.421313i	$0.861569\pi$
$258$		0			0
$259$	−24.4912	−	1.69358i	−1.52181	−	0.105234i
$260$	−0.397789			−0.0246699
$261$		0			0
$262$	−12.9018	−	22.3466i	−0.797076	−	1.38058i
$263$	5.42151	+	9.39033i	0.334305	+	0.579033i	0.983351	−	0.181716i	$-0.0581652\pi$
$263$	5.42151	+	9.39033i	0.334305	+	0.579033i	−0.649046	+	0.760749i	$0.724832\pi$
$264$		0			0
$265$	2.42151			0.148752
$266$	−1.99064	+	2.95617i	−0.122054	+	0.181254i
$267$		0			0
$268$	−2.44773	+	4.23960i	−0.149519	+	0.258975i
$269$	13.9255	+	24.1197i	0.849054	+	1.47061i	0.882053	+	0.471150i	$0.156161\pi$
$269$	13.9255	+	24.1197i	0.849054	+	1.47061i	−0.0329990	+	0.999455i	$0.510506\pi$
$270$		0			0
$271$	−1.80111	+	3.11961i	−0.109409	+	0.189503i	−0.915531	−	0.402247i	$-0.868229\pi$
$271$	−1.80111	+	3.11961i	−0.109409	+	0.189503i	0.806122	+	0.591750i	$0.201563\pi$
$272$	−3.20442			−0.194297
$273$		0			0
$274$	18.4740			1.11605
$275$	0.127587	−	0.220987i	0.00769378	−	0.0133260i
$276$		0			0
$277$	−1.38427	−	2.39763i	−0.0831730	−	0.144060i	0.821438	−	0.570297i	$-0.193172\pi$
$277$	−1.38427	−	2.39763i	−0.0831730	−	0.144060i	−0.904611	+	0.426238i	$0.859839\pi$
$278$	−7.37393	+	12.7720i	−0.442259	+	0.766015i
$279$		0			0
$280$	8.09820	+	0.559997i	0.483960	+	0.0334662i
$281$	−26.0474			−1.55386			−0.776930	−	0.629587i	$-0.783224\pi$
$281$	−26.0474			−1.55386			−0.776930	+	0.629587i	$0.783224\pi$
$282$		0			0
$283$	1.68387	+	2.91654i	0.100095	+	0.173370i	0.911724	−	0.410804i	$-0.134752\pi$
$283$	1.68387	+	2.91654i	0.100095	+	0.173370i	−0.811628	+	0.584174i	$0.801419\pi$
$284$	−2.82733	−	4.89707i	−0.167771	−	0.290588i
$285$		0			0
$286$	−0.230116			−0.0136071
$287$	−10.2376	−	20.9492i	−0.604309	−	1.23659i
$288$		0			0
$289$	7.76704	−	13.4529i	0.456884	−	0.791347i
$290$	2.01186	+	3.48465i	0.118141	+	0.204625i
$291$		0			0
$292$	−0.116393	+	0.201599i	−0.00681140	+	0.0117977i
$293$	15.8510			0.926028			0.463014	−	0.886351i	$-0.346768\pi$
$293$	15.8510			0.926028			0.463014	+	0.886351i	$0.346768\pi$
$294$		0			0
$295$	−11.8811			−0.691745
$296$	−14.2345	+	24.6548i	−0.827362	+	1.43303i
$297$		0			0
$298$	−10.2789	−	17.8036i	−0.595440	−	1.03133i
$299$	−2.92619	+	5.06831i	−0.169226	+	0.293108i
$300$		0			0
$301$	6.62192	+	13.5504i	0.381681	+	0.781031i
$302$	−1.42954			−0.0822607
$303$		0			0
$304$	1.47226	+	2.55004i	0.0844402	+	0.146255i
$305$	−5.47779	−	9.48781i	−0.313657	−	0.543271i
$306$		0			0
$307$	22.8811			1.30589			0.652947	−	0.757404i	$-0.273532\pi$
$307$	22.8811			1.30589			0.652947	+	0.757404i	$0.273532\pi$
$308$	−0.359706	−	0.0248740i	−0.0204962	−	0.00141733i
$309$		0			0
$310$	−4.18387	+	7.24667i	−0.237628	+	0.411583i
$311$	9.82799	+	17.0226i	0.557294	+	0.965262i	0.997721	+	0.0674737i	$0.0214939\pi$
$311$	9.82799	+	17.0226i	0.557294	+	0.965262i	−0.440427	+	0.897789i	$0.645173\pi$
$312$		0			0
$313$	1.15916	−	2.00772i	0.0655194	−	0.113483i	−0.831405	−	0.555667i	$-0.812463\pi$
$313$	1.15916	−	2.00772i	0.0655194	−	0.113483i	0.896924	+	0.442184i	$0.145796\pi$
$314$	−21.4483			−1.21040
$315$		0			0
$316$	−1.26953			−0.0714169
$317$	−2.71794	+	4.70760i	−0.152655	+	0.264405i	−0.932203	−	0.361937i	$-0.882116\pi$
$317$	−2.71794	+	4.70760i	−0.152655	+	0.264405i	0.779548	+	0.626342i	$0.215449\pi$
$318$		0			0
$319$	−0.424012	−	0.734410i	−0.0237401	−	0.0411190i
$320$	4.42151	−	7.65828i	0.247170	−	0.428111i
$321$		0			0
$322$	14.0588	−	20.8778i	0.783465	−	1.16347i
$323$	1.34704			0.0749511
$324$		0			0
$325$	0.372413	+	0.645038i	0.0206578	+	0.0357803i
$326$	−9.37709	−	16.2416i	−0.519349	−	0.899539i
$327$		0			0
$328$	−27.0394			−1.49300
$329$	−20.8811	−	1.44395i	−1.15121	−	0.0796073i
$330$		0			0
$331$	−6.45558	+	11.1814i	−0.354831	+	0.614585i	−0.987089	−	0.160173i	$-0.948795\pi$
$331$	−6.45558	+	11.1814i	−0.354831	+	0.614585i	0.632258	+	0.774758i	$0.282128\pi$
$332$	−2.74483	−	4.75418i	−0.150642	−	0.260919i
$333$		0			0
$334$	6.92303	−	11.9910i	0.378811	−	0.656120i
$335$	9.16634			0.500811
$336$		0			0
$337$	−29.8604			−1.62660			−0.813300	−	0.581844i	$-0.802331\pi$
$337$	−29.8604			−1.62660			−0.813300	+	0.581844i	$0.802331\pi$
$338$	−7.53407	+	13.0494i	−0.409799	+	0.709793i
$339$		0			0
$340$	−0.323314	−	0.559997i	−0.0175342	−	0.0303701i
$341$	0.881774	−	1.52728i	0.0477508	−	0.0827067i
$342$		0			0
$343$	−18.1244	−	3.80860i	−0.978627	−	0.205645i
$344$	17.4897			0.942979
$345$		0			0
$346$	6.19006	+	10.7215i	0.332780	+	0.576391i
$347$	7.46593	+	12.9314i	0.400792	+	0.694192i	0.993822	−	0.110988i	$-0.0354016\pi$
$347$	7.46593	+	12.9314i	0.400792	+	0.694192i	−0.593030	+	0.805181i	$0.702068\pi$
$348$		0			0
$349$	−30.8304			−1.65031			−0.825156	−	0.564906i	$-0.808913\pi$
$349$	−30.8304			−1.65031			−0.825156	+	0.564906i	$0.808913\pi$
$350$	−1.40648	−	2.87807i	−0.0751797	−	0.153840i
$351$		0			0
$352$	−0.374067	+	0.647903i	−0.0199378	+	0.0345334i
$353$	3.91433	+	6.77982i	0.208339	+	0.360853i	0.951191	−	0.308602i	$-0.0998610\pi$
$353$	3.91433	+	6.77982i	0.208339	+	0.360853i	−0.742853	+	0.669455i	$0.766528\pi$
$354$		0			0
$355$	−5.29392	+	9.16935i	−0.280972	+	0.486658i
$356$	−7.56582			−0.400988
$357$		0			0
$358$	−2.31395			−0.122296
$359$	2.92619	−	5.06831i	0.154439	−	0.267495i	−0.778416	−	0.627749i	$-0.783976\pi$
$359$	2.92619	−	5.06831i	0.154439	−	0.267495i	0.932854	+	0.360254i	$0.117310\pi$
$360$		0			0
$361$	8.88111	+	15.3825i	0.467427	+	0.809607i
$362$	3.29642	−	5.70957i	0.173256	−	0.300089i
$363$		0			0
$364$	0.587850	−	0.872976i	0.0308117	−	0.0457564i
$365$	0.435873			0.0228146
$366$		0			0
$367$	−11.7495	−	20.3507i	−0.613319	−	1.06230i	−0.990677	−	0.136233i	$-0.956501\pi$
$367$	−11.7495	−	20.3507i	−0.613319	−	1.06230i	0.377358	−	0.926068i	$-0.376833\pi$
$368$	−10.3978	−	18.0095i	−0.542022	−	0.938810i
$369$		0			0
$370$	11.2345			0.584053
$371$	−3.57849	+	5.31418i	−0.185786	+	0.275898i
$372$		0			0
$373$	14.3517	−	24.8579i	0.743104	−	1.28709i	−0.207972	−	0.978135i	$-0.566686\pi$
$373$	14.3517	−	24.8579i	0.743104	−	1.28709i	0.951075	−	0.308959i	$-0.0999805\pi$
$374$	−0.187034	−	0.323952i	−0.00967127	−	0.0167511i
$375$		0			0
$376$	−12.1363	+	21.0207i	−0.625881	+	1.08406i
$377$	2.47529			0.127484
$378$		0			0
$379$	11.5103			0.591247			0.295623	−	0.955305i	$-0.404473\pi$
$379$	11.5103			0.591247			0.295623	+	0.955305i	$0.404473\pi$
$380$	−0.297092	+	0.514579i	−0.0152405	+	0.0263973i
$381$		0			0
$382$	−2.55779	−	4.43023i	−0.130868	−	0.226670i
$383$	13.8574	−	24.0017i	0.708079	−	1.22643i	−0.257489	−	0.966281i	$-0.582895\pi$
$383$	13.8574	−	24.0017i	0.708079	−	1.22643i	0.965569	−	0.260148i	$-0.0837714\pi$
$384$		0			0
$385$	0.296425	+	0.606571i	0.0151072	+	0.0309137i
$386$	7.92250			0.403245
$387$		0			0
$388$	2.25517	+	3.90608i	0.114489	+	0.198301i
$389$	−5.54910	−	9.61132i	−0.281350	−	0.487313i	0.690367	−	0.723459i	$-0.257449\pi$
$389$	−5.54910	−	9.61132i	−0.281350	−	0.487313i	−0.971718	+	0.236146i	$0.924116\pi$
$390$		0			0
$391$	−9.51337			−0.481112
$392$	−13.1964	+	16.9445i	−0.666519	+	0.855826i
$393$		0			0
$394$	10.3940	−	18.0029i	0.523640	−	0.906971i
$395$	1.18855	+	2.05862i	0.0598023	+	0.103581i
$396$		0			0
$397$	10.4287	−	18.0630i	0.523401	−	0.906557i	−0.476228	−	0.879322i	$-0.657996\pi$
$397$	10.4287	−	18.0630i	0.523401	−	0.906557i	0.999629	−	0.0272354i	$-0.00867036\pi$
$398$	30.2726			1.51743
$399$		0			0
$400$	−2.64663			−0.132331
$401$	−13.3470	+	23.1177i	−0.666519	+	1.15445i	0.312352	+	0.949966i	$0.398883\pi$
$401$	−13.3470	+	23.1177i	−0.666519	+	1.15445i	−0.978871	+	0.204479i	$0.934450\pi$
$402$		0			0
$403$	2.57381	+	4.45797i	0.128210	+	0.222067i
$404$	−2.69105	+	4.66103i	−0.133885	+	0.231895i
$405$		0			0
$406$	−10.6204	−	0.734410i	−0.527082	−	0.0364481i
$407$	−2.36773			−0.117364
$408$		0			0
$409$	2.79959	+	4.84904i	0.138431	+	0.239769i	0.926903	−	0.375301i	$-0.122461\pi$
$409$	2.79959	+	4.84904i	0.138431	+	0.239769i	−0.788472	+	0.615071i	$0.789127\pi$
$410$	5.33518	+	9.24080i	0.263486	+	0.456370i
$411$		0			0
$412$	2.54674			0.125469
$413$	17.5578	−	26.0739i	0.863962	−	1.28301i
$414$		0			0
$415$	−5.13945	+	8.90179i	−0.252286	+	0.436971i
$416$	−1.09186	−	1.89116i	−0.0535330	−	0.0927218i
$417$		0			0
$418$	−0.171864	+	0.297678i	−0.00840616	+	0.0145599i
$419$	37.4008			1.82715			0.913575	−	0.406671i	$-0.133310\pi$
$419$	37.4008			1.82715			0.913575	+	0.406671i	$0.133310\pi$
$420$		0			0
$421$	18.3357			0.893627			0.446814	−	0.894627i	$-0.352559\pi$
$421$	18.3357			0.893627			0.446814	+	0.894627i	$0.352559\pi$
$422$	−7.39779	+	12.8133i	−0.360119	+	0.623744i
$423$		0			0
$424$	3.71477	+	6.43417i	0.180405	+	0.312471i
$425$	−0.605378	+	1.04855i	−0.0293651	+	0.0508619i
$426$		0			0
$427$	28.9167	+	1.99961i	1.39938	+	0.0967680i
$428$	8.69407			0.420244
$429$		0			0
$430$	−3.45090	−	5.97714i	−0.166417	−	0.288243i
$431$	−10.3470	−	17.9216i	−0.498399	−	0.863253i	0.501599	−	0.865100i	$-0.332745\pi$
$431$	−10.3470	−	17.9216i	−0.498399	−	0.863253i	−0.999998	+	0.00184744i	$0.999412\pi$
$432$		0			0
$433$	−7.25517			−0.348661			−0.174331	−	0.984687i	$-0.555776\pi$
$433$	−7.25517			−0.348661			−0.174331	+	0.984687i	$0.555776\pi$
$434$	−9.72044	−	19.8908i	−0.466596	−	0.954791i
$435$		0			0
$436$	−0.349536	+	0.605415i	−0.0167398	+	0.0289941i
$437$	4.37090	+	7.57062i	0.209088	+	0.362152i
$438$		0			0
$439$	4.84552	−	8.39269i	0.231264	−	0.400561i	−0.726916	−	0.686726i	$-0.759047\pi$
$439$	4.84552	−	8.39269i	0.231264	−	0.400561i	0.958180	+	0.286165i	$0.0923805\pi$
$440$	0.782909			0.0373237
$441$		0			0
$442$	1.09186			0.0519346
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	−0.785916	−	0.618333i	$-0.787808\pi$
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	0.928450	+	0.371457i	$0.121142\pi$
$444$		0			0
$445$	7.08317	+	12.2684i	0.335774	+	0.581578i
$446$	11.4897	−	19.9007i	0.544051	−	0.942324i
$447$		0			0
$448$	10.2726	+	21.0207i	0.485333	+	0.993133i
$449$	16.2251			0.765711			0.382855	−	0.923808i	$-0.374941\pi$
$449$	16.2251			0.765711			0.382855	+	0.923808i	$0.374941\pi$
$450$		0			0
$451$	−1.12442	−	1.94755i	−0.0529469	−	0.0917066i
$452$	−1.77488	−	3.07419i	−0.0834835	−	0.144598i
$453$		0			0
$454$	−3.61488			−0.169655
$455$	−1.96593	−	0.135946i	−0.0921642	−	0.00637323i
$456$		0			0
$457$	−16.9158	+	29.2991i	−0.791290	+	1.37055i	0.133879	+	0.990998i	$0.457257\pi$
$457$	−16.9158	+	29.2991i	−0.791290	+	1.37055i	−0.925169	+	0.379556i	$0.876077\pi$
$458$	2.40898	+	4.17248i	0.112564	+	0.194967i
$459$		0			0
$460$	2.09820	−	3.63418i	0.0978290	−	0.169445i
$461$	14.8417			0.691246			0.345623	−	0.938373i	$-0.387668\pi$
$461$	14.8417			0.691246			0.345623	+	0.938373i	$0.387668\pi$
$462$		0			0
$463$	34.3708			1.59734			0.798672	−	0.601766i	$-0.205536\pi$
$463$	34.3708			1.59734			0.798672	+	0.601766i	$0.205536\pi$
$464$	−4.39779	+	7.61719i	−0.204162	+	0.353619i
$465$		0			0
$466$	7.03808	+	12.1903i	0.326033	+	0.564706i
$467$	1.34704	−	2.33314i	0.0623334	−	0.107965i	−0.833175	−	0.553010i	$-0.813479\pi$
$467$	1.34704	−	2.33314i	0.0623334	−	0.107965i	0.895508	+	0.445045i	$0.146812\pi$
$468$		0			0
$469$	−13.5459	+	20.1162i	−0.625493	+	0.928878i
$470$	9.57849			0.441823
$471$		0			0
$472$	−18.2265	−	31.5691i	−0.838940	−	1.45309i
$473$	0.727298	+	1.25972i	0.0334412	+	0.0579218i
$474$		0			0
$475$	1.11256			0.0510477
$476$	1.70674	+	0.118023i	0.0782284	+	0.00540956i
$477$		0			0
$478$	−4.25017	+	7.36152i	−0.194398	+	0.336708i
$479$	−7.33268	−	12.7006i	−0.335039	−	0.580304i	0.648454	−	0.761254i	$-0.275416\pi$
$479$	−7.33268	−	12.7006i	−0.335039	−	0.580304i	−0.983492	+	0.180950i	$0.942083\pi$
$480$		0			0
$481$	3.45558	−	5.98524i	0.157561	−	0.272904i
$482$	34.6052			1.57623
$483$		0			0
$484$	5.84000			0.265454
$485$	4.22262	−	7.31379i	0.191739	−	0.332102i
$486$		0			0
$487$	3.50869	+	6.07724i	0.158994	+	0.275386i	0.934506	−	0.355947i	$-0.115842\pi$
$487$	3.50869	+	6.07724i	0.158994	+	0.275386i	−0.775512	+	0.631333i	$0.782508\pi$
$488$	16.8066	−	29.1099i	0.760800	−	1.31775i
$489$		0			0
$490$	8.39462	+	1.16657i	0.379230	+	0.0527002i
$491$	−21.7148			−0.979974			−0.489987	−	0.871730i	$-0.662998\pi$
$491$	−21.7148			−0.979974			−0.489987	+	0.871730i	$0.662998\pi$
$492$		0			0
$493$	2.01186	+	3.48465i	0.0906097	+	0.156941i
$494$	−0.501654	−	0.868890i	−0.0225705	−	0.0390932i
$495$		0			0
$496$	−18.2913			−0.821303
$497$	−12.2995	−	25.1683i	−0.551706	−	1.12895i
$498$		0			0
$499$	5.66634	−	9.81439i	0.253660	−	0.439352i	−0.710871	−	0.703323i	$-0.751699\pi$
$499$	5.66634	−	9.81439i	0.253660	−	0.439352i	0.964531	+	0.263971i	$0.0850322\pi$
$500$	−0.267035	−	0.462518i	−0.0119422	−	0.0206844i
$501$		0			0
$502$	2.71227	−	4.69779i	0.121054	−	0.209673i
$503$	2.31395			0.103174			0.0515870	−	0.998669i	$-0.483572\pi$
$503$	2.31395			0.103174			0.0515870	+	0.998669i	$0.483572\pi$
$504$		0			0
$505$	10.0775			0.448443
$506$	1.21378	−	2.10233i	0.0539592	−	0.0934601i
$507$		0			0
$508$	−1.62843	−	2.82053i	−0.0722500	−	0.125141i
$509$	−4.14262	+	7.17522i	−0.183618	+	0.318036i	−0.943110	−	0.332481i	$-0.892114\pi$
$509$	−4.14262	+	7.17522i	−0.183618	+	0.318036i	0.759492	+	0.650517i	$0.225448\pi$
$510$		0			0
$511$	−0.644129	+	0.956553i	−0.0284946	+	0.0423154i
$512$	24.0000			1.06066
$513$		0			0
$514$	15.8836	+	27.5112i	0.700596	+	1.21347i
$515$	−2.38427	−	4.12968i	−0.105064	−	0.181976i
$516$		0			0
$517$	−2.01872			−0.0887833
$518$	−16.6022	+	24.6548i	−0.729459	+	1.08327i
$519$		0			0
$520$	−1.14262	+	1.97907i	−0.0501070	+	0.0867879i
$521$	9.32331	+	16.1485i	0.408462	+	0.707477i	0.994718	−	0.102649i	$-0.0327320\pi$
$521$	9.32331	+	16.1485i	0.408462	+	0.707477i	−0.586256	+	0.810126i	$0.699399\pi$
$522$		0			0
$523$	0.695727	−	1.20504i	0.0304220	−	0.0526925i	−0.850414	−	0.526115i	$-0.823648\pi$
$523$	0.695727	−	1.20504i	0.0304220	−	0.0526925i	0.880836	+	0.473422i	$0.156982\pi$
$524$	11.3821			0.497229
$525$		0			0
$526$	13.1283			0.572419
$527$	−4.18387	+	7.24667i	−0.182252	+	0.315670i
$528$		0			0
$529$	−19.3692	−	33.5485i	−0.842141	−	1.45863i
$530$	1.46593	−	2.53906i	0.0636759	−	0.110290i
$531$		0			0
$532$	−0.690238	−	1.41243i	−0.0299256	−	0.0612366i
$533$	6.56413			0.284324
$534$		0			0
$535$	−8.13945	−	14.0979i	−0.351899	−	0.609507i
$536$	14.0618	+	24.3558i	0.607377	+	1.05201i
$537$		0			0
$538$	33.7208			1.45381
$539$	−1.76922	−	0.245861i	−0.0762055	−	0.0105900i
$540$		0			0
$541$	−5.31297	+	9.20233i	−0.228422	+	0.395639i	−0.957341	−	0.288962i	$-0.906690\pi$
$541$	−5.31297	+	9.20233i	−0.228422	+	0.395639i	0.728918	+	0.684601i	$0.240023\pi$
$542$	2.18070	+	3.77708i	0.0936690	+	0.162240i
$543$		0			0
$544$	1.77488	−	3.07419i	0.0760975	−	0.131805i
$545$	1.30895			0.0560694
$546$		0			0
$547$	18.5765			0.794274			0.397137	−	0.917759i	$-0.370004\pi$
$547$	18.5765			0.794274			0.397137	+	0.917759i	$0.370004\pi$
$548$	−4.07448	+	7.05720i	−0.174053	+	0.301469i
$549$		0			0
$550$	−0.154477	−	0.267561i	−0.00658691	−	0.0114089i
$551$	1.84869	−	3.20203i	0.0787569	−	0.136411i
$552$		0			0
$553$	−6.27422	−	0.433867i	−0.266807	−	0.0184499i
$554$	−3.35204			−0.142414
$555$		0			0
$556$	−3.25267	−	5.63380i	−0.137944	−	0.238926i
$557$	−18.0681	−	31.2949i	−0.765572	−	1.32601i	−0.939944	−	0.341329i	$-0.889123\pi$
$557$	−18.0681	−	31.2949i	−0.765572	−	1.32601i	0.174372	−	0.984680i	$-0.444210\pi$
$558$		0			0
$559$	−4.24581			−0.179579
$560$	3.91116	−	5.80821i	0.165277	−	0.245442i
$561$		0			0
$562$	−15.7685	+	27.3119i	−0.665156	+	1.15208i
$563$	11.8811	+	20.5787i	0.500729	+	0.867288i	1.00000		0.000841928i	$0.000267994\pi$
$563$	11.8811	+	20.5787i	0.500729	+	0.867288i	−0.499271	+	0.866446i	$0.666399\pi$
$564$		0			0
$565$	−3.32331	+	5.75615i	−0.139813	+	0.242163i
$566$	4.07750			0.171390
$567$		0			0
$568$	−32.4850			−1.36304
$569$	−10.3414	+	17.9118i	−0.433533	+	0.750901i	−0.997175	−	0.0751185i	$-0.976066\pi$
$569$	−10.3414	+	17.9118i	−0.433533	+	0.750901i	0.563642	+	0.826019i	$0.309400\pi$
$570$		0			0
$571$	−18.6926	−	32.3765i	−0.782259	−	1.35491i	−0.930623	−	0.365980i	$-0.880734\pi$
$571$	−18.6926	−	32.3765i	−0.782259	−	1.35491i	0.148363	−	0.988933i	$-0.452599\pi$
$572$	0.0507527	−	0.0879063i	0.00212208	−	0.00367555i
$573$		0			0
$574$	−28.1638	−	1.94755i	−1.17554	−	0.0812892i
$575$	−7.85738			−0.327676
$576$		0			0
$577$	−17.3217	−	30.0020i	−0.721110	−	1.24900i	−0.960555	−	0.278089i	$-0.910299\pi$
$577$	−17.3217	−	30.0020i	−0.721110	−	1.24900i	0.239445	−	0.970910i	$-0.423035\pi$
$578$	−9.40398	−	16.2882i	−0.391154	−	0.677499i
$579$		0			0
$580$	−1.77488			−0.0736980
$581$	−11.9406	−	24.4339i	−0.495378	−	1.01369i
$582$		0			0
$583$	−0.308953	+	0.535123i	−0.0127955	+	0.0221625i
$584$	0.668659	+	1.15815i	0.0276693	+	0.0479247i
$585$		0			0
$586$	9.59588	−	16.6205i	0.396402	−	0.686588i
$587$	−15.7685			−0.650838			−0.325419	−	0.945570i	$-0.605505\pi$
$587$	−15.7685			−0.650838			−0.325419	+	0.945570i	$0.605505\pi$
$588$		0			0
$589$	7.68907			0.316823
$590$	−7.19256	+	12.4579i	−0.296113	+	0.512883i
$591$		0			0
$592$	12.2789	+	21.2677i	0.504660	+	0.874096i
$593$	−11.7179	+	20.2961i	−0.481198	+	0.833459i	−0.999767	−	0.0215763i	$-0.993132\pi$
$593$	−11.7179	+	20.2961i	−0.481198	+	0.833459i	0.518569	+	0.855036i	$0.326465\pi$
$594$		0			0
$595$	−1.40648	−	2.87807i	−0.0576602	−	0.117990i
$596$	9.06814			0.371446
$597$		0			0
$598$	3.54290	+	6.13649i	0.144880	+	0.250940i
$599$	5.50401	+	9.53323i	0.224888	+	0.389517i	0.956286	−	0.292434i	$-0.0944651\pi$
$599$	5.50401	+	9.53323i	0.224888	+	0.389517i	−0.731398	+	0.681951i	$0.761132\pi$
$600$		0			0
$601$	12.7385			0.519614			0.259807	−	0.965661i	$-0.416341\pi$
$601$	12.7385			0.519614			0.259807	+	0.965661i	$0.416341\pi$
$602$	18.2169	+	1.25972i	0.742467	+	0.0513422i
$603$		0			0
$604$	0.315288	−	0.546095i	0.0128289	−	0.0222203i
$605$	−5.46744	−	9.46989i	−0.222283	−	0.385006i
$606$		0			0
$607$	−12.8527	+	22.2615i	−0.521675	+	0.903568i	0.478007	+	0.878356i	$0.341359\pi$
$607$	−12.8527	+	22.2615i	−0.521675	+	0.903568i	−0.999682	+	0.0252118i	$0.991974\pi$
$608$	−3.26187			−0.132286
$609$		0			0
$610$	−13.2645			−0.537065
$611$	2.94622	−	5.10300i	0.119191	−	0.206445i
$612$		0			0
$613$	−11.3145	−	19.5973i	−0.456988	−	0.791526i	0.541813	−	0.840499i	$-0.317738\pi$
$613$	−11.3145	−	19.5973i	−0.456988	−	0.791526i	−0.998800	+	0.0489737i	$0.984405\pi$
$614$	13.8517	−	23.9919i	0.559010	−	0.968233i
$615$		0			0
$616$	−1.15698	+	1.71815i	−0.0466159	+	0.0692262i
$617$	−24.2726			−0.977177			−0.488588	−	0.872514i	$-0.662488\pi$
$617$	−24.2726			−0.977177			−0.488588	+	0.872514i	$0.662488\pi$
$618$		0			0
$619$	5.42552	+	9.39728i	0.218070	+	0.377709i	0.954218	−	0.299112i	$-0.0966905\pi$
$619$	5.42552	+	9.39728i	0.218070	+	0.377709i	−0.736148	+	0.676821i	$0.763357\pi$
$620$	−1.84552	−	3.19654i	−0.0741180	−	0.128376i
$621$		0			0
$622$	23.7986			0.954237
$623$	−37.3913	−	2.58564i	−1.49805	−	0.103591i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.40346	−	2.43086i	−0.0560934	−	0.0971566i
$627$		0			0
$628$	4.73047	−	8.19341i	0.188766	−	0.326952i
$629$	11.2345			0.447948
$630$		0			0
$631$	−15.4897			−0.616633			−0.308317	−	0.951284i	$-0.599766\pi$
$631$	−15.4897			−0.616633			−0.308317	+	0.951284i	$0.599766\pi$
$632$	−3.64663	+	6.31615i	−0.145055	+	0.251243i
$633$		0			0
$634$	3.29076	+	5.69976i	0.130693	+	0.226366i
$635$	−3.04910	+	5.28119i	−0.121000	+	0.209578i
$636$		0			0
$637$	3.20358	−	4.11347i	0.126930	−	0.162982i
$638$	−1.02675			−0.0406494
$639$		0			0
$640$	−2.42151	−	4.19418i	−0.0957187	−	0.165790i
$641$	−7.67602	−	13.2953i	−0.303184	−	0.525131i	0.673671	−	0.739031i	$-0.264717\pi$
$641$	−7.67602	−	13.2953i	−0.303184	−	0.525131i	−0.976855	+	0.213900i	$0.931383\pi$
$642$		0			0
$643$	−41.0775			−1.61994			−0.809969	−	0.586472i	$-0.800516\pi$
$643$	−41.0775			−1.61994			−0.809969	+	0.586472i	$0.800516\pi$
$644$	4.87477	+	9.97520i	0.192093	+	0.393078i
$645$		0			0
$646$	0.815466	−	1.41243i	0.0320841	−	0.0555713i
$647$	−3.04125	−	5.26760i	−0.119564	−	0.207091i	0.800031	−	0.599959i	$-0.204816\pi$
$647$	−3.04125	−	5.26760i	−0.119564	−	0.207091i	−0.919595	+	0.392868i	$0.871483\pi$
$648$		0			0
$649$	1.51587	−	2.62557i	0.0595033	−	0.103063i
$650$	0.901803			0.0353716
$651$		0			0
$652$	8.27256			0.323979
$653$	−2.63543	+	4.56471i	−0.103133	+	0.178631i	−0.912974	−	0.408018i	$-0.866220\pi$
$653$	−2.63543	+	4.56471i	−0.103133	+	0.178631i	0.809841	+	0.586649i	$0.199553\pi$
$654$		0			0
$655$	−10.6560	−	18.4567i	−0.416364	−	0.721164i
$656$	−11.6623	+	20.1997i	−0.455337	+	0.788667i
$657$		0			0
$658$	−14.1550	+	21.0207i	−0.551819	+	0.819470i
$659$	−44.6654			−1.73992			−0.869958	−	0.493127i	$-0.835854\pi$
$659$	−44.6654			−1.73992			−0.869958	+	0.493127i	$0.835854\pi$
$660$		0			0
$661$	−1.49750	−	2.59375i	−0.0582460	−	0.100885i	0.835432	−	0.549594i	$-0.185217\pi$
$661$	−1.49750	−	2.59375i	−0.0582460	−	0.100885i	−0.893678	+	0.448709i	$0.851884\pi$
$662$	7.81613	+	13.5379i	0.303783	+	0.526167i
$663$		0			0
$664$	−31.5371			−1.22388
$665$	−1.64413	+	2.44159i	−0.0637566	+	0.0946807i
$666$		0			0
$667$	−13.0563	+	22.6141i	−0.505541	+	0.875623i
$668$	3.05378	+	5.28930i	0.118154	+	0.204649i
$669$		0			0
$670$	5.54910	−	9.61132i	0.214380	−	0.371318i
$671$	2.79558			0.107922
$672$		0			0
$673$	40.3420			1.55507			0.777536	−	0.628839i	$-0.216470\pi$
$673$	40.3420			1.55507			0.777536	+	0.628839i	$0.216470\pi$
$674$	−18.0768	+	31.3100i	−0.696294	+	1.20602i
$675$		0			0
$676$	−3.32331	−	5.75615i	−0.127820	−	0.221390i
$677$	11.2757	−	19.5301i	0.433361	−	0.750604i	−0.563799	−	0.825912i	$-0.690661\pi$
$677$	11.2757	−	19.5301i	0.433361	−	0.750604i	0.997160	+	0.0753081i	$0.0239940\pi$
$678$		0			0
$679$	9.81047	+	20.0751i	0.376491	+	0.770411i
$680$	−3.71477			−0.142455
$681$		0			0
$682$	−1.06761	−	1.84916i	−0.0408810	−	0.0708080i
$683$	3.21392	+	5.56668i	0.122977	+	0.213003i	0.920940	−	0.389703i	$-0.127422\pi$
$683$	3.21392	+	5.56668i	0.122977	+	0.213003i	−0.797963	+	0.602706i	$0.794089\pi$
$684$		0			0
$685$	15.2582			0.582986
$686$	−14.9656	+	16.6986i	−0.571390	+	0.637557i
$687$		0			0
$688$	7.54343	−	13.0656i	0.287591	−	0.498122i
$689$	−0.901803	−	1.56197i	−0.0343559	−	0.0595062i
$690$		0			0
$691$	24.1259	−	41.7873i	0.917794	−	1.58967i	0.115035	−	0.993361i	$-0.463302\pi$
$691$	24.1259	−	41.7873i	0.917794	−	1.58967i	0.802759	−	0.596304i	$-0.203365\pi$
$692$	−5.46093			−0.207593
$693$		0			0
$694$	18.0788			0.686263
$695$	−6.09035	+	10.5488i	−0.231020	+	0.400139i
$696$		0			0
$697$	5.33518	+	9.24080i	0.202084	+	0.350020i
$698$	−18.6640	+	32.3270i	−0.706443	+	1.22360i
$699$		0			0
$700$	1.40965	+	0.0974785i	0.0532798	+	0.00368434i
$701$	42.6640			1.61140			0.805699	−	0.592325i	$-0.201790\pi$
$701$	42.6640			1.61140			0.805699	+	0.592325i	$0.201790\pi$
$702$		0			0
$703$	−5.16166	−	8.94025i	−0.194676	−	0.337188i
$704$	1.12825	+	1.95419i	0.0425227	+	0.0736515i
$705$		0			0
$706$	9.47860			0.356732
$707$	−14.8924	+	22.1158i	−0.560088	+	0.831749i
$708$		0			0
$709$	−2.48715	+	4.30787i	−0.0934070	+	0.161786i	−0.908943	−	0.416921i	$-0.863109\pi$
$709$	−2.48715	+	4.30787i	−0.0934070	+	0.161786i	0.815536	+	0.578707i	$0.196442\pi$
$710$	6.40965	+	11.1018i	0.240550	+	0.416645i
$711$		0			0
$712$	−21.7322	+	37.6412i	−0.814447	+	1.41066i
$713$	−54.3037			−2.03369
$714$		0			0
$715$	−0.190060			−0.00710785
$716$	0.510348	−	0.883948i	0.0190726	−	0.0330347i
$717$		0			0
$718$	−3.54290	−	6.13649i	−0.132220	−	0.229012i
$719$	−1.72413	+	2.98628i	−0.0642992	+	0.111370i	−0.896383	−	0.443281i	$-0.853815\pi$
$719$	−1.72413	+	2.98628i	−0.0642992	+	0.111370i	0.832084	+	0.554650i	$0.187148\pi$
$720$		0			0
$721$	12.5863	+	0.870355i	0.468740	+	0.0324137i
$722$	21.5057			0.800359
$723$		0			0
$724$	1.45407	+	2.51852i	0.0540400	+	0.0936001i
$725$	1.66166	+	2.87807i	0.0617124	+	0.106889i
$726$		0			0
$727$	34.6797			1.28620			0.643100	−	0.765782i	$-0.277648\pi$
$727$	34.6797			1.28620			0.643100	+	0.765782i	$0.277648\pi$
$728$	−2.65465	−	5.43220i	−0.0983881	−	0.201331i
$729$		0			0
$730$	0.263868	−	0.457032i	0.00976618	−	0.0169155i
$731$	−3.45090	−	5.97714i	−0.127636	−	0.221072i
$732$		0			0
$733$	−12.3818	+	21.4459i	−0.457331	+	0.792121i	−0.998819	−	0.0485877i	$-0.984528\pi$
$733$	−12.3818	+	21.4459i	−0.457331	+	0.792121i	0.541488	+	0.840709i	$0.317861\pi$
$734$	−28.4516			−1.05017
$735$		0			0
$736$	23.0367			0.849146
$737$	−1.16951	+	2.02564i	−0.0430793	+	0.0746155i
$738$		0			0
$739$	8.45808	+	14.6498i	0.311136	+	0.538903i	0.978608	−	0.205731i	$-0.0659573\pi$
$739$	8.45808	+	14.6498i	0.311136	+	0.538903i	−0.667473	+	0.744634i	$0.732624\pi$
$740$	−2.47779	+	4.29166i	−0.0910854	+	0.157765i
$741$		0			0
$742$	3.40582	+	6.96929i	0.125031	+	0.255851i
$743$	−17.2996			−0.634660			−0.317330	−	0.948315i	$-0.602786\pi$
$743$	−17.2996			−0.634660			−0.317330	+	0.948315i	$0.602786\pi$
$744$		0			0
$745$	−8.48965	−	14.7045i	−0.311037	−	0.538732i
$746$	−17.3764	−	30.0969i	−0.636196	−	1.10192i
$747$		0			0
$748$	0.165003			0.00603310
$749$	42.9673	+	2.97122i	1.56999	+	0.108566i
$750$		0			0
$751$	17.0484	−	29.5287i	0.622106	−	1.07752i	−0.366987	−	0.930226i	$-0.619611\pi$
$751$	17.0484	−	29.5287i	0.622106	−	1.07752i	0.989093	−	0.147293i	$-0.0470561\pi$
$752$	10.4690	+	18.1328i	0.381764	+	0.661234i
$753$		0			0
$754$	1.49849	−	2.59546i	0.0545717	−	0.0945209i
$755$	−1.18070			−0.0429700
$756$		0			0
$757$	−30.5578			−1.11064			−0.555321	−	0.831636i	$-0.687405\pi$
$757$	−30.5578			−1.11064			−0.555321	+	0.831636i	$0.687405\pi$
$758$	6.96811	−	12.0691i	0.253093	−	0.438370i
$759$		0			0
$760$	1.70674	+	2.95617i	0.0619101	+	0.107231i
$761$	−2.02439	+	3.50635i	−0.0733841	+	0.127105i	−0.900382	−	0.435099i	$-0.856713\pi$
$761$	−2.02439	+	3.50635i	−0.0733841	+	0.127105i	0.826998	+	0.562204i	$0.190047\pi$
$762$		0			0
$763$	−1.93436	+	2.87259i	−0.0700285	+	0.103995i
$764$	2.25651			0.0816376
$765$		0			0
$766$	−16.7779	−	29.0602i	−0.606211	−	1.04999i
$767$	4.42468	+	7.66377i	0.159766	+	0.276723i
$768$		0			0
$769$	−3.97430			−0.143317			−0.0716585	−	0.997429i	$-0.522829\pi$
$769$	−3.97430			−0.143317			−0.0716585	+	0.997429i	$0.522829\pi$
$770$	0.815466	+	0.0563901i	0.0293874	+	0.00203216i
$771$		0			0
$772$	−1.74733	+	3.02646i	−0.0628876	+	0.108925i
$773$	−0.914331	−	1.58367i	−0.0328862	−	0.0569606i	0.849114	−	0.528210i	$-0.177137\pi$
$773$	−0.914331	−	1.58367i	−0.0328862	−	0.0569606i	−0.882000	+	0.471249i	$0.843803\pi$
$774$		0			0
$775$	−3.45558	+	5.98524i	−0.124128	+	0.214996i
$776$	25.9112			0.930157
$777$		0			0
$778$	−13.4372			−0.481747
$779$	4.90247	−	8.49133i	0.175649	−	0.304233i
$780$		0			0
$781$	−1.35087	−	2.33978i	−0.0483380	−	0.0837238i
$782$	−5.75919	+	9.97520i	−0.205948	+	0.356713i
$783$		0			0
$784$	6.96663	+	17.1666i	0.248808	+	0.613094i
$785$	−17.7148			−0.632267
$786$		0			0
$787$	11.5672	+	20.0349i	0.412325	+	0.714167i	0.995143	−	0.0984350i	$-0.0313837\pi$
$787$	11.5672	+	20.0349i	0.412325	+	0.714167i	−0.582819	+	0.812602i	$0.698050\pi$
$788$	4.58482	+	7.94115i	0.163328	+	0.282892i
$789$		0			0
$790$	2.87808			0.102397
$791$	−7.72110	−	15.7996i	−0.274531	−	0.561770i
$792$		0			0
$793$	−4.08000	+	7.06677i	−0.144885	+	0.250948i
$794$	−12.6266	−	21.8699i	−0.448101	−	0.776134i
$795$		0			0
$796$	−6.67669	+	11.5644i	−0.236649	+	0.409888i
$797$	−1.07448			−0.0380599			−0.0190299	−	0.999819i	$-0.506058\pi$
$797$	−1.07448			−0.0380599			−0.0190299	+	0.999819i	$0.506058\pi$
$798$		0			0
$799$	9.57849			0.338863
$800$	1.46593	−	2.53906i	0.0518284	−	0.0897695i
$801$		0			0
$802$	16.1600	+	27.9899i	0.570630	+	0.988359i
$803$	−0.0556117	+	0.0963223i	−0.00196249	+	0.00339914i
$804$		0			0
$805$	11.6116	−	17.2436i	0.409254	−	0.607756i
$806$	6.23251			0.219531
$807$		0			0
$808$	15.4596	+	26.7768i	0.543867	+	0.942005i
$809$	−22.7098	−	39.3345i	−0.798433	−	1.38293i	−0.920636	−	0.390421i	$-0.872329\pi$
$809$	−22.7098	−	39.3345i	−0.798433	−	1.38293i	0.122203	−	0.992505i	$-0.461004\pi$
$810$		0			0
$811$	−40.2074			−1.41187			−0.705937	−	0.708274i	$-0.749474\pi$
$811$	−40.2074			−1.41187			−0.705937	+	0.708274i	$0.749474\pi$
$812$	2.62291	−	3.89510i	0.0920460	−	0.136691i
$813$		0			0
$814$	−1.43337	+	2.48267i	−0.0502397	+	0.0870177i
$815$	−7.74483	−	13.4144i	−0.271289	−	0.469887i
$816$		0			0
$817$	−3.17102	+	5.49237i	−0.110940	+	0.192154i
$818$	6.77924			0.237031
$819$		0			0
$820$	−4.70674			−0.164367
$821$	21.8961	−	37.9252i	0.764180	−	1.32360i	−0.176498	−	0.984301i	$-0.556477\pi$
$821$	21.8961	−	37.9252i	0.764180	−	1.32360i	0.940679	−	0.339298i	$-0.110190\pi$
$822$		0			0
$823$	15.1926	+	26.3143i	0.529579	+	0.917258i	0.999405	+	0.0344990i	$0.0109835\pi$
$823$	15.1926	+	26.3143i	0.529579	+	0.917258i	−0.469825	+	0.882759i	$0.655683\pi$
$824$	7.31529	−	12.6705i	0.254840	−	0.441396i
$825$		0			0
$826$	−16.7106	−	34.1947i	−0.581435	−	1.18979i
$827$	−30.3801			−1.05642			−0.528210	−	0.849114i	$-0.677137\pi$
$827$	−30.3801			−1.05642			−0.528210	+	0.849114i	$0.677137\pi$
$828$		0			0
$829$	20.3105	+	35.1788i	0.705412	+	1.22181i	0.966543	+	0.256505i	$0.0825712\pi$
$829$	20.3105	+	35.1788i	0.705412	+	1.22181i	−0.261131	+	0.965303i	$0.584095\pi$
$830$	6.22262	+	10.7779i	0.215990	+	0.374106i
$831$		0			0
$832$	−6.58651			−0.228346
$833$	8.39462	+	1.16657i	0.290856	+	0.0404192i
$834$		0			0
$835$	5.71794	−	9.90376i	0.197877	−	0.342734i
$836$	−0.0758102	−	0.131307i	−0.00262195	−	0.00454135i
$837$		0			0
$838$	22.6416	−	39.2165i	0.782142	−	1.35471i
$839$	36.0962			1.24618			0.623090	−	0.782150i	$-0.285877\pi$
$839$	36.0962			1.24618			0.623090	+	0.782150i	$0.285877\pi$
$840$		0			0
$841$	−17.9556			−0.619158
$842$	11.1000	−	19.2258i	0.382532	−	0.662565i
$843$		0			0
$844$	−3.26320	−	5.65203i	−0.112324	−	0.194551i
$845$	−6.22262	+	10.7779i	−0.214065	+	0.370771i
$846$		0			0
$847$	28.8621	+	1.99583i	0.991712	+	0.0685777i
$848$	6.40884			0.220081
$849$		0			0
$850$	0.732965	+	1.26953i	0.0251405	+	0.0435446i
$851$	36.4539	+	63.1401i	1.24962	+	2.16441i
$852$		0			0
$853$	30.4546			1.04275			0.521373	−	0.853329i	$-0.325420\pi$
$853$	30.4546			1.04275			0.521373	+	0.853329i	$0.325420\pi$
$854$	19.6022	−	29.1099i	0.670774	−	0.996122i
$855$		0			0
$856$	24.9730	−	43.2545i	0.853559	−	1.47841i
$857$	5.38026	+	9.31889i	0.183786	+	0.318327i	0.943167	−	0.332320i	$-0.107831\pi$
$857$	5.38026	+	9.31889i	0.183786	+	0.318327i	−0.759381	+	0.650647i	$0.774498\pi$
$858$		0			0
$859$	−8.89297	+	15.4031i	−0.303424	+	0.525546i	−0.976909	−	0.213655i	$-0.931463\pi$
$859$	−8.89297	+	15.4031i	−0.303424	+	0.525546i	0.673485	+	0.739201i	$0.264797\pi$
$860$	3.04442			0.103814
$861$		0			0
$862$	−25.0555			−0.853393
$863$	−9.05378	+	15.6816i	−0.308194	+	0.533808i	−0.977967	−	0.208758i	$-0.933058\pi$
$863$	−9.05378	+	15.6816i	−0.308194	+	0.533808i	0.669773	+	0.742566i	$0.266391\pi$
$864$		0			0
$865$	5.11256	+	8.85521i	0.173832	+	0.301086i
$866$	−4.39212	+	7.60738i	−0.149250	+	0.258509i
$867$		0			0
$868$	9.74233	+	0.673690i	0.330676	+	0.0228665i
$869$	−0.606572			−0.0205766
$870$		0			0
$871$	−3.41366	−	5.91264i	−0.115668	−	0.200342i
$872$	2.00803	+	3.47800i	0.0680004	+	0.117780i
$873$		0			0
$874$	10.5842			0.358015
$875$	−1.16166	−	2.37709i	−0.0392712	−	0.0803603i
$876$		0			0
$877$	−5.48029	+	9.49214i	−0.185056	+	0.320527i	−0.943595	−	0.331101i	$-0.892580\pi$
$877$	−5.48029	+	9.49214i	−0.185056	+	0.320527i	0.758539	+	0.651627i	$0.225913\pi$
$878$	−5.86675	−	10.1615i	−0.197993	−	0.342934i
$879$		0			0
$880$	0.337675	−	0.584871i	0.0113830	−	0.0197160i
$881$	−37.1570			−1.25185			−0.625925	−	0.779883i	$-0.715278\pi$
$881$	−37.1570			−1.25185			−0.625925	+	0.779883i	$0.715278\pi$
$882$		0			0
$883$	−13.9730			−0.470228			−0.235114	−	0.971968i	$-0.575546\pi$
$883$	−13.9730			−0.470228			−0.235114	+	0.971968i	$0.575546\pi$
$884$	−0.240813	+	0.417100i	−0.00809942	+	0.0140286i
$885$		0			0
$886$	−3.63227	−	6.29127i	−0.122028	−	0.211359i
$887$	19.7367	−	34.1849i	0.662692	−	1.14782i	−0.317213	−	0.948354i	$-0.602747\pi$
$887$	19.7367	−	34.1849i	0.662692	−	1.14782i	0.979906	−	0.199462i	$-0.0639195\pi$
$888$		0			0
$889$	−7.08401	−	14.4960i	−0.237590	−	0.486179i
$890$	17.1520			0.574936
$891$		0			0
$892$	5.06814	+	8.77828i	0.169694	+	0.293918i
$893$	−4.40082	−	7.62244i	−0.147268	−	0.255075i
$894$		0			0
$895$	−1.91116			−0.0638832
$896$	12.7829	+	0.883948i	0.427047	+	0.0295306i
$897$		0			0
$898$	9.82233	−	17.0128i	0.327775	−	0.567724i
$899$	11.4840	+	19.8908i	0.383012	+	0.663397i
$900$		0			0
$901$	1.46593	−	2.53906i	0.0488372	−	0.0845885i
$902$	−2.72280			−0.0906592
$903$		0			0
$904$	−20.3928			−0.678254
$905$	2.72262	−	4.71571i	0.0905029	−	0.156756i
$906$		0			0
$907$	7.24166	+	12.5429i	0.240455	+	0.416481i	0.960844	−	0.277090i	$-0.0893699\pi$
$907$	7.24166	+	12.5429i	0.240455	+	0.416481i	−0.720389	+	0.693571i	$0.756037\pi$
$908$	0.797270	−	1.38091i	0.0264583	−	0.0458272i
$909$		0			0
$910$	−1.33268	+	1.97907i	−0.0441778	+	0.0656055i
$911$	35.1043			1.16306			0.581528	−	0.813526i	$-0.302455\pi$
$911$	35.1043			1.16306			0.581528	+	0.813526i	$0.302455\pi$
$912$		0			0
$913$	−1.31145	−	2.27150i	−0.0434028	−	0.0751758i
$914$	20.4810	+	35.4741i	0.677450	+	1.17338i
$915$		0			0
$916$	−2.12523			−0.0702195
$917$	56.2519	+	3.88986i	1.85760	+	0.128455i
$918$		0			0
$919$	10.7138	−	18.5568i	0.353415	−	0.612133i	−0.633430	−	0.773800i	$-0.718354\pi$
$919$	10.7138	−	18.5568i	0.353415	−	0.612133i	0.986845	+	0.161667i	$0.0516870\pi$
$920$	−12.0538	−	20.8778i	−0.397401	−	0.688319i
$921$		0			0
$922$	8.98483	−	15.5622i	0.295900	−	0.512513i
$923$	7.88611			0.259574
$924$		0			0
$925$	9.27890			0.305088
$926$	20.8073	−	36.0393i	0.683770	−	1.18432i
$927$		0			0
$928$	−4.87175	−	8.43811i	−0.159923	−	0.276995i
$929$	−10.0150	+	17.3465i	−0.328582	+	0.569121i	−0.982231	−	0.187677i	$-0.939904\pi$
$929$	−10.0150	+	17.3465i	−0.328582	+	0.569121i	0.653648	+	0.756798i	$0.273238\pi$
$930$		0			0
$931$	−2.92855	−	7.21631i	−0.0959794	−	0.236505i
$932$	−6.20906			−0.203385
$933$		0			0
$934$	−1.63093	−	2.82486i	−0.0533657	−	0.0924322i
$935$	−0.154477	−	0.267561i	−0.00505193	−	0.00875019i
$936$		0			0
$937$	−49.4626			−1.61587			−0.807937	−	0.589269i	$-0.799416\pi$
$937$	−49.4626			−1.61587			−0.807937	+	0.589269i	$0.799416\pi$
$938$	12.8923	+	26.3814i	0.420949	+	0.861383i
$939$		0			0
$940$	−2.11256	+	3.65906i	−0.0689041	+	0.119345i
$941$	−21.2525	−	36.8105i	−0.692813	−	1.19999i	−0.970912	−	0.239435i	$-0.923038\pi$
$941$	−21.2525	−	36.8105i	−0.692813	−	1.19999i	0.278100	−	0.960552i	$-0.410295\pi$
$942$		0			0
$943$	−34.6234	+	59.9695i	−1.12749	+	1.95288i
$944$	−31.4449			−1.02344
$945$		0			0
$946$	1.76116			0.0572603
$947$	8.90497	−	15.4239i	0.289373	−	0.501208i	−0.684288	−	0.729212i	$-0.739887\pi$
$947$	8.90497	−	15.4239i	0.289373	−	0.501208i	0.973660	+	0.228004i	$0.0732200\pi$
$948$		0			0
$949$	−0.162325	−	0.281155i	−0.00526928	−	0.00912667i
$950$	0.673518	−	1.16657i	0.0218518	−	0.0378485i
$951$		0			0
$952$	5.48965	−	8.15232i	0.177921	−	0.264218i
$953$	23.4897			0.760904			0.380452	−	0.924801i	$-0.375768\pi$
$953$	23.4897			0.760904			0.380452	+	0.924801i	$0.375768\pi$
$954$		0			0
$955$	−2.11256	−	3.65906i	−0.0683608	−	0.118404i
$956$	−1.87477	−	3.24720i	−0.0606345	−	0.105022i
$957$		0			0
$958$	−17.7562			−0.573676
$959$	−22.5484	+	33.4852i	−0.728127	+	1.08129i
$960$		0			0
$961$	−8.38209	+	14.5182i	−0.270390	+	0.468329i
$962$	−4.18387	−	7.24667i	−0.134893	−	0.233642i
$963$		0			0
$964$	−7.63227	+	13.2195i	−0.245819	+	0.425771i
$965$	6.54343			0.210641
$966$		0			0
$967$	−15.5040			−0.498575			−0.249288	−	0.968429i	$-0.580196\pi$
$967$	−15.5040			−0.498575			−0.249288	+	0.968429i	$0.580196\pi$
$968$	16.7749	−	29.0549i	0.539165	−	0.933861i
$969$		0			0
$970$	−5.11256	−	8.85521i	−0.164154	−	0.284324i
$971$	−13.4690	+	23.3289i	−0.432239	+	0.748661i	−0.997066	−	0.0765492i	$-0.975610\pi$
$971$	−13.4690	+	23.3289i	−0.432239	+	0.748661i	0.564826	+	0.825210i	$0.308943\pi$
$972$		0			0
$973$	−14.1498	−	28.9546i	−0.453622	−	0.928242i
$974$	8.49634			0.272240
$975$		0			0
$976$	−14.4977	−	25.1107i	−0.464059	−	0.803774i
$977$	−21.8636	−	37.8688i	−0.699478	−	1.21153i	−0.968648	−	0.248438i	$-0.920083\pi$
$977$	−21.8636	−	37.8688i	−0.699478	−	1.21153i	0.269170	−	0.963093i	$-0.413251\pi$
$978$		0			0
$979$	−3.61488			−0.115532
$980$	−2.29709	+	2.94952i	−0.0733779	+	0.0942191i
$981$		0			0
$982$	−13.1456	+	22.7689i	−0.419494	+	0.726585i
$983$	8.63846	+	14.9623i	0.275524	+	0.477222i	0.970267	−	0.242036i	$-0.0778153\pi$
$983$	8.63846	+	14.9623i	0.275524	+	0.477222i	−0.694743	+	0.719258i	$0.744482\pi$
$984$		0			0
$985$	8.58468	−	14.8691i	0.273531	−	0.473769i
$986$	4.87175			0.155148
$987$		0			0
$988$	0.442564			0.0140798
$989$	22.3951	−	38.7895i	0.712124	−	1.23344i
$990$		0			0
$991$	−20.6037	−	35.6867i	−0.654499	−	1.13363i	−0.982019	−	0.188781i	$-0.939546\pi$
$991$	−20.6037	−	35.6867i	−0.654499	−	1.13363i	0.327520	−	0.944844i	$-0.393787\pi$
$992$	10.1313	−	17.5479i	0.321668	−	0.557146i
$993$		0			0
$994$	−33.8359	−	2.33978i	−1.07321	−	0.0742133i
$995$	25.0030			0.792649
$996$		0			0
$997$	4.68387	+	8.11269i	0.148340	+	0.256932i	0.930614	−	0.366002i	$-0.119274\pi$
$997$	4.68387	+	8.11269i	0.148340	+	0.256932i	−0.782274	+	0.622934i	$0.785940\pi$
$998$	−6.86055	−	11.8828i	−0.217167	−	0.376144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.g.226.2	yes	6
3.2	odd	2		315.2.j.f.226.2	yes	6
7.2	even	3		2205.2.a.bb.1.2		3
7.4	even	3	inner	315.2.j.g.46.2	yes	6
7.5	odd	6		2205.2.a.bc.1.2		3
21.2	odd	6		2205.2.a.be.1.2		3
21.5	even	6		2205.2.a.bd.1.2		3
21.11	odd	6		315.2.j.f.46.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.j.f.46.2	✓	6	21.11	odd	6
315.2.j.f.226.2	yes	6	3.2	odd	2
315.2.j.g.46.2	yes	6	7.4	even	3	inner
315.2.j.g.226.2	yes	6	1.1	even	1	trivial
2205.2.a.bb.1.2		3	7.2	even	3
2205.2.a.bc.1.2		3	7.5	odd	6
2205.2.a.bd.1.2		3	21.5	even	6
2205.2.a.be.1.2		3	21.2	odd	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.605378 - 1.04855i) q^{2} +(0.267035 + 0.462518i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.16166 + 2.37709i) q^{7} +3.06814 q^{8} +O(q^{10})\)	\(q+(0.605378 - 1.04855i) q^{2} +(0.267035 + 0.462518i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.16166 + 2.37709i) q^{7} +3.06814 q^{8} +(-0.605378 - 1.04855i) q^{10} +(0.127587 + 0.220987i) q^{11} -0.744826 q^{13} +(3.19573 + 0.220987i) q^{14} +(1.32331 - 2.29205i) q^{16} +(-0.605378 - 1.04855i) q^{17} +(-0.556279 + 0.963504i) q^{19} +0.534070 q^{20} +0.308953 q^{22} +(3.92869 - 6.80469i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.450901 + 0.780984i) q^{26} +(-0.789244 + 1.17205i) q^{28} -3.32331 q^{29} +(-3.45558 - 5.98524i) q^{31} +(1.46593 + 2.53906i) q^{32} -1.46593 q^{34} +(2.63945 + 0.182520i) q^{35} +(-4.63945 + 8.03576i) q^{37} +(0.673518 + 1.16657i) q^{38} +(1.53407 - 2.65709i) q^{40} -8.81297 q^{41} +5.70041 q^{43} +(-0.0681404 + 0.118023i) q^{44} +(-4.75669 - 8.23882i) q^{46} +(-3.95558 + 6.85127i) q^{47} +(-4.30111 + 5.52273i) q^{49} -1.21076 q^{50} +(-0.198895 - 0.344496i) q^{52} +(1.21076 + 2.09709i) q^{53} +0.255174 q^{55} +(3.56413 + 7.29324i) q^{56} +(-2.01186 + 3.48465i) q^{58} +(-5.94055 - 10.2893i) q^{59} +(5.47779 - 9.48781i) q^{61} -8.36773 q^{62} +8.84302 q^{64} +(-0.372413 + 0.645038i) q^{65} +(4.58317 + 7.93828i) q^{67} +(0.323314 - 0.559997i) q^{68} +(1.78924 - 2.65709i) q^{70} -10.5878 q^{71} +(0.217936 + 0.377477i) q^{73} +(5.61724 + 9.72934i) q^{74} -0.594184 q^{76} +(-0.377094 + 0.559997i) q^{77} +(-1.18855 + 2.05862i) q^{79} +(-1.32331 - 2.29205i) q^{80} +(-5.33518 + 9.24080i) q^{82} -10.2789 q^{83} -1.21076 q^{85} +(3.45090 - 5.97714i) q^{86} +(0.391455 + 0.678019i) q^{88} +(-7.08317 + 12.2684i) q^{89} +(-0.865233 - 1.77052i) q^{91} +4.19639 q^{92} +(4.78924 + 8.29521i) q^{94} +(0.556279 + 0.963504i) q^{95} +8.44523 q^{97} +(3.18703 + 7.85324i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8	\( 6 q + 2 q^{2} - 6 q^{4} + 3 q^{5} + q^{7} - 12 q^{8} - 2 q^{10} + 10 q^{11} + 14 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + q^{19} - 12 q^{20} + 4 q^{22} + 10 q^{23} - 3 q^{25} - 8 q^{28} - 8 q^{29} + q^{31} + 24 q^{32} - 24 q^{34} - q^{35} - 11 q^{37} - 28 q^{38} - 6 q^{40} - 4 q^{41} - 6 q^{43} + 30 q^{44} + 16 q^{46} - 2 q^{47} - 3 q^{49} - 4 q^{50} - 24 q^{52} + 4 q^{53} + 20 q^{55} + 42 q^{56} + 14 q^{58} + 4 q^{59} + 22 q^{61} - 60 q^{62} + 40 q^{64} + 7 q^{65} + 15 q^{67} - 10 q^{68} + 14 q^{70} - 32 q^{71} - 9 q^{73} + 6 q^{74} - 60 q^{76} + 26 q^{77} + 7 q^{79} + 4 q^{80} + 6 q^{82} - 28 q^{83} - 4 q^{85} + 18 q^{86} - 40 q^{88} - 30 q^{89} - 3 q^{91} + 36 q^{92} + 32 q^{94} - q^{95} - 8 q^{97} + 68 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 6 * q^4 + 3 * q^5 + q^7 - 12 * q^8 - 2 * q^10 + 10 * q^11 + 14 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + q^19 - 12 * q^20 + 4 * q^22 + 10 * q^23 - 3 * q^25 - 8 * q^28 - 8 * q^29 + q^31 + 24 * q^32 - 24 * q^34 - q^35 - 11 * q^37 - 28 * q^38 - 6 * q^40 - 4 * q^41 - 6 * q^43 + 30 * q^44 + 16 * q^46 - 2 * q^47 - 3 * q^49 - 4 * q^50 - 24 * q^52 + 4 * q^53 + 20 * q^55 + 42 * q^56 + 14 * q^58 + 4 * q^59 + 22 * q^61 - 60 * q^62 + 40 * q^64 + 7 * q^65 + 15 * q^67 - 10 * q^68 + 14 * q^70 - 32 * q^71 - 9 * q^73 + 6 * q^74 - 60 * q^76 + 26 * q^77 + 7 * q^79 + 4 * q^80 + 6 * q^82 - 28 * q^83 - 4 * q^85 + 18 * q^86 - 40 * q^88 - 30 * q^89 - 3 * q^91 + 36 * q^92 + 32 * q^94 - q^95 - 8 * q^97 + 68 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more