LMFDB - Embedded newform 1170.2.bs.c.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1170.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.901
Dual form			1170.2.bs.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(3.50000 - 0.866025i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.09808 - 1.90192i) q^{17} +(-5.59808 + 3.23205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(1.26795 - 2.19615i) q^{23} -1.00000 q^{25} +(-3.46410 - 1.00000i) q^{26} +(-2.59808 - 1.50000i) q^{28} +(-4.73205 + 8.19615i) q^{29} -1.26795i q^{31} +(0.866025 - 0.500000i) q^{32} +2.19615i q^{34} +(1.50000 + 2.59808i) q^{35} +(9.69615 + 5.59808i) q^{37} +6.46410 q^{38} -1.00000 q^{40} +(9.00000 + 5.19615i) q^{41} +(-1.00000 - 1.73205i) q^{43} +3.00000i q^{44} +(-2.19615 + 1.26795i) q^{46} +3.00000i q^{47} +(1.00000 - 1.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.50000 + 2.59808i) q^{52} +6.46410 q^{53} +(1.50000 - 2.59808i) q^{55} +(1.50000 + 2.59808i) q^{56} +(8.19615 - 4.73205i) q^{58} +(-9.00000 + 5.19615i) q^{59} +(2.09808 + 3.63397i) q^{61} +(-0.633975 + 1.09808i) q^{62} -1.00000 q^{64} +(-0.866025 - 3.50000i) q^{65} +(1.09808 - 1.90192i) q^{68} -3.00000i q^{70} +(-5.19615 + 3.00000i) q^{71} +5.66025i q^{73} +(-5.59808 - 9.69615i) q^{74} +(-5.59808 - 3.23205i) q^{76} -9.00000 q^{77} +6.19615 q^{79} +(0.866025 + 0.500000i) q^{80} +(-5.19615 - 9.00000i) q^{82} +2.19615i q^{83} +(-1.90192 + 1.09808i) q^{85} +2.00000i q^{86} +(1.50000 - 2.59808i) q^{88} +(14.8923 + 8.59808i) q^{89} +(-7.79423 + 7.50000i) q^{91} +2.53590 q^{92} +(1.50000 - 2.59808i) q^{94} +(3.23205 + 5.59808i) q^{95} +(13.0981 - 7.56218i) q^{97} +(-1.73205 + 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} + 14 q^{13} + 12 q^{14} - 2 q^{16} + 6 q^{17} - 12 q^{19} - 6 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{29} + 6 q^{35} + 18 q^{37} + 12 q^{38} - 4 q^{40} + 36 q^{41} - 4 q^{43} + 12 q^{46} + 4 q^{49} + 10 q^{52} + 12 q^{53} + 6 q^{55} + 6 q^{56} + 12 q^{58} - 36 q^{59} - 2 q^{61} - 6 q^{62} - 4 q^{64} - 6 q^{68} - 12 q^{74} - 12 q^{76} - 36 q^{77} + 4 q^{79} - 18 q^{85} + 6 q^{88} + 18 q^{89} + 24 q^{92} + 6 q^{94} + 6 q^{95} + 42 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 + 14 * q^13 + 12 * q^14 - 2 * q^16 + 6 * q^17 - 12 * q^19 - 6 * q^22 + 12 * q^23 - 4 * q^25 - 12 * q^29 + 6 * q^35 + 18 * q^37 + 12 * q^38 - 4 * q^40 + 36 * q^41 - 4 * q^43 + 12 * q^46 + 4 * q^49 + 10 * q^52 + 12 * q^53 + 6 * q^55 + 6 * q^56 + 12 * q^58 - 36 * q^59 - 2 * q^61 - 6 * q^62 - 4 * q^64 - 6 * q^68 - 12 * q^74 - 12 * q^76 - 36 * q^77 + 4 * q^79 - 18 * q^85 + 6 * q^88 + 18 * q^89 + 24 * q^92 + 6 * q^94 + 6 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.902867	−	0.429919i	$-0.858542\pi$
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.0791130	+	0.996866i	$0.525209\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.09808	−	1.90192i	−0.266323	−	0.461284i	0.701587	−	0.712584i	$-0.252475\pi$
$17$	−1.09808	−	1.90192i	−0.266323	−	0.461284i	−0.967909	+	0.251300i	$0.919142\pi$
$18$		0			0
$19$	−5.59808	+	3.23205i	−1.28429	+	0.741483i	−0.977629	−	0.210337i	$-0.932544\pi$
$19$	−5.59808	+	3.23205i	−1.28429	+	0.741483i	−0.306658	+	0.951820i	$0.599211\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	−0.703017	−	0.711173i	$-0.748164\pi$
$23$	1.26795	−	2.19615i	0.264386	−	0.457929i	0.967402	+	0.253244i	$0.0814975\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.46410	−	1.00000i	−0.679366	−	0.196116i
$27$		0			0
$28$	−2.59808	−	1.50000i	−0.490990	−	0.283473i
$29$	−4.73205	+	8.19615i	−0.878720	+	1.52199i	−0.0259731	+	0.999663i	$0.508268\pi$
$29$	−4.73205	+	8.19615i	−0.878720	+	1.52199i	−0.852747	+	0.522325i	$0.825065\pi$
$30$		0			0
$31$		−	1.26795i		−	0.227730i	−0.993496	−	0.113865i	$-0.963677\pi$
$31$		−	1.26795i		−	0.227730i	0.993496	−	0.113865i	$-0.0363232\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			2.19615i			0.376637i
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$		0			0
$37$	9.69615	+	5.59808i	1.59404	+	0.920318i	0.992604	+	0.121395i	$0.0387368\pi$
$37$	9.69615	+	5.59808i	1.59404	+	0.920318i	0.601433	+	0.798923i	$0.294597\pi$
$38$	6.46410			1.04862
$39$		0			0
$40$	−1.00000			−0.158114
$41$	9.00000	+	5.19615i	1.40556	+	0.811503i	0.994956	−	0.100309i	$-0.0319833\pi$
$41$	9.00000	+	5.19615i	1.40556	+	0.811503i	0.410608	+	0.911812i	$0.365317\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	−2.19615	+	1.26795i	−0.323805	+	0.186949i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$		0			0
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$	6.46410			0.887913			0.443956	−	0.896048i	$-0.353575\pi$
$53$	6.46410			0.887913			0.443956	+	0.896048i	$0.353575\pi$
$54$		0			0
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$		0			0
$58$	8.19615	−	4.73205i	1.07621	−	0.621349i
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.954080	−	0.299552i	$-0.903163\pi$
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.217620	+	0.976034i	$0.569829\pi$
$60$		0			0
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	0.968509	−	0.248980i	$-0.0800954\pi$
$61$	2.09808	+	3.63397i	0.268631	+	0.465283i	−0.699877	+	0.714263i	$0.746762\pi$
$62$	−0.633975	+	1.09808i	−0.0805149	+	0.139456i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.866025	−	3.50000i	−0.107417	−	0.434122i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	1.09808	−	1.90192i	0.133161	−	0.230642i
$69$		0			0
$70$		−	3.00000i		−	0.358569i
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	−0.775571	−	0.631260i	$-0.782538\pi$
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	0.158901	+	0.987294i	$0.449205\pi$
$72$		0			0
$73$			5.66025i			0.662483i	0.943546	+	0.331241i	$0.107467\pi$
$73$			5.66025i			0.662483i	−0.943546	+	0.331241i	$0.892533\pi$
$74$	−5.59808	−	9.69615i	−0.650763	−	1.12715i
$75$		0			0
$76$	−5.59808	−	3.23205i	−0.642143	−	0.370742i
$77$	−9.00000			−1.02565
$78$		0			0
$79$	6.19615			0.697122			0.348561	−	0.937286i	$-0.386670\pi$
$79$	6.19615			0.697122			0.348561	+	0.937286i	$0.386670\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$		0			0
$82$	−5.19615	−	9.00000i	−0.573819	−	0.993884i
$83$			2.19615i			0.241059i	0.992710	+	0.120530i	$0.0384592\pi$
$83$			2.19615i			0.241059i	−0.992710	+	0.120530i	$0.961541\pi$
$84$		0			0
$85$	−1.90192	+	1.09808i	−0.206293	+	0.119103i
$86$			2.00000i			0.215666i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.995058	+	0.0992979i	$0.0316597\pi$
$89$	14.8923	+	8.59808i	1.57858	+	0.911394i	0.583523	+	0.812096i	$0.301674\pi$
$90$		0			0
$91$	−7.79423	+	7.50000i	−0.817057	+	0.786214i
$92$	2.53590			0.264386
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	3.23205	+	5.59808i	0.331601	+	0.574351i
$96$		0			0
$97$	13.0981	−	7.56218i	1.32991	−	0.767823i	0.344623	−	0.938741i	$-0.388007\pi$
$97$	13.0981	−	7.56218i	1.32991	−	0.767823i	0.985285	+	0.170918i	$0.0546734\pi$
$98$	−1.73205	+	1.00000i	−0.174964	+	0.101015i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.63397	−	6.29423i	0.361594	−	0.626299i	−0.626629	−	0.779317i	$-0.715566\pi$
$101$	3.63397	−	6.29423i	0.361594	−	0.626299i	0.988223	+	0.153018i	$0.0488993\pi$
$102$		0			0
$103$	1.19615			0.117860			0.0589302	−	0.998262i	$-0.481231\pi$
$103$	1.19615			0.117860			0.0589302	+	0.998262i	$0.481231\pi$
$104$	−0.866025	−	3.50000i	−0.0849208	−	0.343203i
$105$		0			0
$106$	−5.59808	−	3.23205i	−0.543733	−	0.313925i
$107$	0.169873	−	0.294229i	0.0164222	−	0.0284442i	−0.857697	−	0.514155i	$-0.828106\pi$
$107$	0.169873	−	0.294229i	0.0164222	−	0.0284442i	0.874120	+	0.485710i	$0.161439\pi$
$108$		0			0
$109$			15.4641i			1.48119i	0.671950	+	0.740596i	$0.265457\pi$
$109$			15.4641i			1.48119i	−0.671950	+	0.740596i	$0.734543\pi$
$110$	−2.59808	+	1.50000i	−0.247717	+	0.143019i
$111$		0			0
$112$		−	3.00000i		−	0.283473i
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	0.655814	−	0.754923i	$-0.272326\pi$
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	−0.981689	+	0.190490i	$0.938992\pi$
$114$		0			0
$115$	−2.19615	−	1.26795i	−0.204792	−	0.118237i
$116$	−9.46410			−0.878720
$117$		0			0
$118$	10.3923			0.956689
$119$	5.70577	+	3.29423i	0.523047	+	0.301981i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		−	4.19615i		−	0.379902i
$123$		0			0
$124$	1.09808	−	0.633975i	0.0986102	−	0.0569326i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−10.5981	+	18.3564i	−0.940427	+	1.62887i	−0.175769	+	0.984431i	$0.556241\pi$
$127$	−10.5981	+	18.3564i	−0.940427	+	1.62887i	−0.764658	+	0.644436i	$0.777092\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.00000	+	3.46410i	−0.0877058	+	0.303822i
$131$	18.1244			1.58353			0.791766	−	0.610824i	$-0.209162\pi$
$131$	18.1244			1.58353			0.791766	+	0.610824i	$0.209162\pi$
$132$		0			0
$133$	9.69615	−	16.7942i	0.840763	−	1.45624i
$134$		0			0
$135$		0			0
$136$	−1.90192	+	1.09808i	−0.163089	+	0.0941593i
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	−0.771567	−	0.636148i	$-0.780527\pi$
$137$	−7.09808	+	4.09808i	−0.606430	+	0.350122i	0.165137	+	0.986271i	$0.447193\pi$
$138$		0			0
$139$	4.59808	+	7.96410i	0.390004	+	0.675506i	0.992450	−	0.122653i	$-0.0391404\pi$
$139$	4.59808	+	7.96410i	0.390004	+	0.675506i	−0.602446	+	0.798160i	$0.705807\pi$
$140$	−1.50000	+	2.59808i	−0.126773	+	0.219578i
$141$		0			0
$142$	6.00000			0.503509
$143$	10.3923	+	3.00000i	0.869048	+	0.250873i
$144$		0			0
$145$	8.19615	+	4.73205i	0.680653	+	0.392975i
$146$	2.83013	−	4.90192i	0.234223	−	0.405686i
$147$		0			0
$148$			11.1962i			0.920318i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$		0			0
$151$			6.33975i			0.515921i	0.966155	+	0.257961i	$0.0830505\pi$
$151$			6.33975i			0.515921i	−0.966155	+	0.257961i	$0.916950\pi$
$152$	3.23205	+	5.59808i	0.262154	+	0.454064i
$153$		0			0
$154$	7.79423	+	4.50000i	0.628077	+	0.362620i
$155$	−1.26795			−0.101844
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	−5.36603	−	3.09808i	−0.426898	−	0.246470i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$			7.60770i			0.599570i
$162$		0			0
$163$	6.29423	−	3.63397i	0.493002	−	0.284635i	−0.232817	−	0.972521i	$-0.574794\pi$
$163$	6.29423	−	3.63397i	0.493002	−	0.284635i	0.725819	+	0.687886i	$0.241461\pi$
$164$			10.3923i			0.811503i
$165$		0			0
$166$	1.09808	−	1.90192i	0.0852272	−	0.147618i
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	0.597143	−	0.802135i	$-0.296303\pi$
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	−0.396098	+	0.918208i	$0.629636\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	2.19615			0.168437
$171$		0			0
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		0			0
$175$	2.59808	−	1.50000i	0.196396	−	0.113389i
$176$	−2.59808	+	1.50000i	−0.195837	+	0.113067i
$177$		0			0
$178$	−8.59808	−	14.8923i	−0.644453	−	1.11623i
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	−0.909513	−	0.415675i	$-0.863545\pi$
$179$	−1.26795	+	2.19615i	−0.0947710	+	0.164148i	0.814742	+	0.579824i	$0.196879\pi$
$180$		0			0
$181$	−16.5885			−1.23301			−0.616505	−	0.787351i	$-0.711452\pi$
$181$	−16.5885			−1.23301			−0.616505	+	0.787351i	$0.711452\pi$
$182$	10.5000	−	2.59808i	0.778312	−	0.192582i
$183$		0			0
$184$	−2.19615	−	1.26795i	−0.161903	−	0.0934745i
$185$	5.59808	−	9.69615i	0.411579	−	0.712875i
$186$		0			0
$187$		−	6.58846i		−	0.481796i
$188$	−2.59808	+	1.50000i	−0.189484	+	0.109399i
$189$		0			0
$190$		−	6.46410i		−	0.468955i
$191$	−9.63397	−	16.6865i	−0.697090	−	1.20740i	−0.969471	−	0.245206i	$-0.921144\pi$
$191$	−9.63397	−	16.6865i	−0.697090	−	1.20740i	0.272381	−	0.962189i	$-0.412189\pi$
$192$		0			0
$193$	−3.80385	−	2.19615i	−0.273807	−	0.158083i	0.356809	−	0.934177i	$-0.383865\pi$
$193$	−3.80385	−	2.19615i	−0.273807	−	0.158083i	−0.630616	+	0.776095i	$0.717198\pi$
$194$	−15.1244			−1.08587
$195$		0			0
$196$	2.00000			0.142857
$197$	−8.30385	−	4.79423i	−0.591625	−	0.341575i	0.174115	−	0.984725i	$-0.444294\pi$
$197$	−8.30385	−	4.79423i	−0.591625	−	0.341575i	−0.765740	+	0.643151i	$0.777627\pi$
$198$		0			0
$199$	−7.19615	−	12.4641i	−0.510122	−	0.883557i	−0.999931	−	0.0117273i	$-0.996267\pi$
$199$	−7.19615	−	12.4641i	−0.510122	−	0.883557i	0.489810	−	0.871829i	$-0.337066\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−6.29423	+	3.63397i	−0.442860	+	0.255686i
$203$		−	28.3923i		−	1.99275i
$204$		0			0
$205$	5.19615	−	9.00000i	0.362915	−	0.628587i
$206$	−1.03590	−	0.598076i	−0.0721745	−	0.0416699i
$207$		0			0
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	−19.3923			−1.34139
$210$		0			0
$211$	−6.79423	+	11.7679i	−0.467734	+	0.810139i	−0.999320	−	0.0368651i	$-0.988263\pi$
$211$	−6.79423	+	11.7679i	−0.467734	+	0.810139i	0.531586	+	0.847004i	$0.321596\pi$
$212$	3.23205	+	5.59808i	0.221978	+	0.384477i
$213$		0			0
$214$	−0.294229	+	0.169873i	−0.0201131	+	0.0116123i
$215$	−1.73205	+	1.00000i	−0.118125	+	0.0681994i
$216$		0			0
$217$	1.90192	+	3.29423i	0.129111	+	0.223627i
$218$	7.73205	−	13.3923i	0.523681	−	0.907041i
$219$		0			0
$220$	3.00000			0.202260
$221$	−5.49038	−	5.70577i	−0.369323	−	0.383812i
$222$		0			0
$223$	−0.401924	−	0.232051i	−0.0269148	−	0.0155393i	0.486482	−	0.873690i	$-0.338280\pi$
$223$	−0.401924	−	0.232051i	−0.0269148	−	0.0155393i	−0.513397	+	0.858151i	$0.671613\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$		0			0
$226$			6.92820i			0.460857i
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	−0.620895	−	0.783894i	$-0.713231\pi$
$227$	−3.80385	+	2.19615i	−0.252470	+	0.145764i	0.368425	+	0.929658i	$0.379897\pi$
$228$		0			0
$229$			4.73205i			0.312703i	0.987701	+	0.156351i	$0.0499732\pi$
$229$			4.73205i			0.312703i	−0.987701	+	0.156351i	$0.950027\pi$
$230$	1.26795	+	2.19615i	0.0836061	+	0.144810i
$231$		0			0
$232$	8.19615	+	4.73205i	0.538104	+	0.310674i
$233$	−1.26795			−0.0830661			−0.0415331	−	0.999137i	$-0.513224\pi$
$233$	−1.26795			−0.0830661			−0.0415331	+	0.999137i	$0.513224\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−9.00000	−	5.19615i	−0.585850	−	0.338241i
$237$		0			0
$238$	−3.29423	−	5.70577i	−0.213533	−	0.369850i
$239$		−	8.19615i		−	0.530165i	−0.964226	−	0.265083i	$-0.914601\pi$
$239$		−	8.19615i		−	0.530165i	0.964226	−	0.265083i	$-0.0853992\pi$
$240$		0			0
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	−0.721715	−	0.692191i	$-0.756646\pi$
$241$	−7.50000	+	4.33013i	−0.483117	+	0.278928i	0.238597	+	0.971119i	$0.423312\pi$
$242$			2.00000i			0.128565i
$243$		0			0
$244$	−2.09808	+	3.63397i	−0.134316	+	0.232641i
$245$	−1.73205	−	1.00000i	−0.110657	−	0.0638877i
$246$		0			0
$247$	−16.7942	+	16.1603i	−1.06859	+	1.02825i
$248$	−1.26795			−0.0805149
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	3.40192	+	5.89230i	0.214728	+	0.371919i	0.953188	−	0.302378i	$-0.0977803\pi$
$251$	3.40192	+	5.89230i	0.214728	+	0.371919i	−0.738461	+	0.674296i	$0.764447\pi$
$252$		0			0
$253$	6.58846	−	3.80385i	0.414213	−	0.239146i
$254$	18.3564	−	10.5981i	1.15178	−	0.664982i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	−0.564890	−	0.825166i	$-0.691082\pi$
$257$	6.92820	−	12.0000i	0.432169	−	0.748539i	0.997060	+	0.0766265i	$0.0244149\pi$
$258$		0			0
$259$	−33.5885			−2.08709
$260$	2.59808	−	2.50000i	0.161126	−	0.155043i
$261$		0			0
$262$	−15.6962	−	9.06218i	−0.969712	−	0.559863i
$263$	−13.7942	+	23.8923i	−0.850589	+	1.47326i	0.0300894	+	0.999547i	$0.490421\pi$
$263$	−13.7942	+	23.8923i	−0.850589	+	1.47326i	−0.880678	+	0.473715i	$0.842913\pi$
$264$		0			0
$265$		−	6.46410i		−	0.397087i
$266$	−16.7942	+	9.69615i	−1.02972	+	0.594509i
$267$		0			0
$268$		0			0
$269$	−1.43782	−	2.49038i	−0.0876656	−	0.151841i	0.818858	−	0.573996i	$-0.194607\pi$
$269$	−1.43782	−	2.49038i	−0.0876656	−	0.151841i	−0.906524	+	0.422154i	$0.861274\pi$
$270$		0			0
$271$	−2.19615	−	1.26795i	−0.133407	−	0.0770224i	0.431811	−	0.901964i	$-0.357875\pi$
$271$	−2.19615	−	1.26795i	−0.133407	−	0.0770224i	−0.565218	+	0.824942i	$0.691208\pi$
$272$	2.19615			0.133161
$273$		0			0
$274$	8.19615			0.495148
$275$	−2.59808	−	1.50000i	−0.156670	−	0.0904534i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$		−	9.19615i		−	0.551549i
$279$		0			0
$280$	2.59808	−	1.50000i	0.155265	−	0.0896421i
$281$			10.3923i			0.619953i	0.950744	+	0.309976i	$0.100321\pi$
$281$			10.3923i			0.619953i	−0.950744	+	0.309976i	$0.899679\pi$
$282$		0			0
$283$	15.1962	−	26.3205i	0.903317	−	1.56459i	0.0801576	−	0.996782i	$-0.474458\pi$
$283$	15.1962	−	26.3205i	0.903317	−	1.56459i	0.823160	−	0.567810i	$-0.192209\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$	−7.50000	−	7.79423i	−0.443484	−	0.460882i
$287$	−31.1769			−1.84032
$288$		0			0
$289$	6.08846	−	10.5455i	0.358145	−	0.620325i
$290$	−4.73205	−	8.19615i	−0.277876	−	0.481295i
$291$		0			0
$292$	−4.90192	+	2.83013i	−0.286863	+	0.165621i
$293$	0.696152	−	0.401924i	0.0406697	−	0.0234806i	−0.479527	−	0.877527i	$-0.659192\pi$
$293$	0.696152	−	0.401924i	0.0406697	−	0.0234806i	0.520197	+	0.854046i	$0.325859\pi$
$294$		0			0
$295$	5.19615	+	9.00000i	0.302532	+	0.524000i
$296$	5.59808	−	9.69615i	0.325382	−	0.563577i
$297$		0			0
$298$	−6.00000			−0.347571
$299$	2.53590	−	8.78461i	0.146655	−	0.508027i
$300$		0			0
$301$	5.19615	+	3.00000i	0.299501	+	0.172917i
$302$	3.16987	−	5.49038i	0.182406	−	0.315936i
$303$		0			0
$304$		−	6.46410i		−	0.370742i
$305$	3.63397	−	2.09808i	0.208081	−	0.120135i
$306$		0			0
$307$			20.5359i			1.17205i	0.810295	+	0.586023i	$0.199307\pi$
$307$			20.5359i			1.17205i	−0.810295	+	0.586023i	$0.800693\pi$
$308$	−4.50000	−	7.79423i	−0.256411	−	0.444117i
$309$		0			0
$310$	1.09808	+	0.633975i	0.0623665	+	0.0360073i
$311$	−15.1244			−0.857624			−0.428812	−	0.903394i	$-0.641068\pi$
$311$	−15.1244			−0.857624			−0.428812	+	0.903394i	$0.641068\pi$
$312$		0			0
$313$	5.60770			0.316966			0.158483	−	0.987362i	$-0.449340\pi$
$313$	5.60770			0.316966			0.158483	+	0.987362i	$0.449340\pi$
$314$	11.2583	+	6.50000i	0.635344	+	0.366816i
$315$		0			0
$316$	3.09808	+	5.36603i	0.174280	+	0.301863i
$317$		−	12.8038i		−	0.719136i	−0.933119	−	0.359568i	$-0.882924\pi$
$317$		−	12.8038i		−	0.719136i	0.933119	−	0.359568i	$-0.117076\pi$
$318$		0			0
$319$	−24.5885	+	14.1962i	−1.37669	+	0.794832i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	3.80385	−	6.58846i	0.211980	−	0.367160i
$323$	12.2942	+	7.09808i	0.684069	+	0.394948i
$324$		0			0
$325$	−3.50000	+	0.866025i	−0.194145	+	0.0480384i
$326$	−7.26795			−0.402534
$327$		0			0
$328$	5.19615	−	9.00000i	0.286910	−	0.496942i
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$		0			0
$331$	0.803848	−	0.464102i	0.0441835	−	0.0255093i	−0.477746	−	0.878498i	$-0.658546\pi$
$331$	0.803848	−	0.464102i	0.0441835	−	0.0255093i	0.521929	+	0.852989i	$0.325213\pi$
$332$	−1.90192	+	1.09808i	−0.104382	+	0.0602648i
$333$		0			0
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$		0			0
$337$	−4.19615			−0.228579			−0.114289	−	0.993447i	$-0.536459\pi$
$337$	−4.19615			−0.228579			−0.114289	+	0.993447i	$0.536459\pi$
$338$	−12.9904	−	0.500000i	−0.706584	−	0.0271964i
$339$		0			0
$340$	−1.90192	−	1.09808i	−0.103146	−	0.0595515i
$341$	1.90192	−	3.29423i	0.102995	−	0.178392i
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	−1.73205	+	1.00000i	−0.0933859	+	0.0539164i
$345$		0			0
$346$			15.0000i			0.806405i
$347$	−12.6340	−	21.8827i	−0.678227	−	1.17472i	−0.975514	−	0.219936i	$-0.929415\pi$
$347$	−12.6340	−	21.8827i	−0.678227	−	1.17472i	0.297287	−	0.954788i	$-0.403918\pi$
$348$		0			0
$349$	−29.4904	−	17.0263i	−1.57858	−	0.911396i	−0.995057	−	0.0993018i	$-0.968339\pi$
$349$	−29.4904	−	17.0263i	−1.57858	−	0.911396i	−0.583527	−	0.812094i	$-0.698328\pi$
$350$	−3.00000			−0.160357
$351$		0			0
$352$	3.00000			0.159901
$353$	17.4904	+	10.0981i	0.930919	+	0.537466i	0.887102	−	0.461573i	$-0.152715\pi$
$353$	17.4904	+	10.0981i	0.930919	+	0.537466i	0.0438169	+	0.999040i	$0.486048\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$			17.1962i			0.911394i
$357$		0			0
$358$	2.19615	−	1.26795i	0.116070	−	0.0670132i
$359$			22.3923i			1.18182i	0.806737	+	0.590910i	$0.201231\pi$
$359$			22.3923i			1.18182i	−0.806737	+	0.590910i	$0.798769\pi$
$360$		0			0
$361$	11.3923	−	19.7321i	0.599595	−	1.03853i
$362$	14.3660	+	8.29423i	0.755062	+	0.435935i
$363$		0			0
$364$	−10.3923	−	3.00000i	−0.544705	−	0.157243i
$365$	5.66025			0.296271
$366$		0			0
$367$	13.1962	−	22.8564i	0.688834	−	1.19309i	−0.283382	−	0.959007i	$-0.591456\pi$
$367$	13.1962	−	22.8564i	0.688834	−	1.19309i	0.972216	−	0.234088i	$-0.0752102\pi$
$368$	1.26795	+	2.19615i	0.0660964	+	0.114482i
$369$		0			0
$370$	−9.69615	+	5.59808i	−0.504079	+	0.291030i
$371$	−16.7942	+	9.69615i	−0.871913	+	0.503399i
$372$		0			0
$373$	−10.1962	−	17.6603i	−0.527937	−	0.914413i	−0.999470	−	0.0325648i	$-0.989632\pi$
$373$	−10.1962	−	17.6603i	−0.527937	−	0.914413i	0.471533	−	0.881848i	$-0.343701\pi$
$374$	−3.29423	+	5.70577i	−0.170341	+	0.295038i
$375$		0			0
$376$	3.00000			0.154713
$377$	−9.46410	+	32.7846i	−0.487426	+	1.68849i
$378$		0			0
$379$	10.2058	+	5.89230i	0.524235	+	0.302667i	0.738666	−	0.674072i	$-0.235456\pi$
$379$	10.2058	+	5.89230i	0.524235	+	0.302667i	−0.214430	+	0.976739i	$0.568790\pi$
$380$	−3.23205	+	5.59808i	−0.165801	+	0.287175i
$381$		0			0
$382$			19.2679i			0.985834i
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	−0.464006	−	0.885832i	$-0.653589\pi$
$383$	1.39230	−	0.803848i	0.0711435	−	0.0410747i	0.535150	+	0.844757i	$0.320255\pi$
$384$		0			0
$385$			9.00000i			0.458682i
$386$	2.19615	+	3.80385i	0.111781	+	0.193611i
$387$		0			0
$388$	13.0981	+	7.56218i	0.664954	+	0.383911i
$389$	−19.2679			−0.976924			−0.488462	−	0.872585i	$-0.662442\pi$
$389$	−19.2679			−0.976924			−0.488462	+	0.872585i	$0.662442\pi$
$390$		0			0
$391$	−5.56922			−0.281648
$392$	−1.73205	−	1.00000i	−0.0874818	−	0.0505076i
$393$		0			0
$394$	4.79423	+	8.30385i	0.241530	+	0.418342i
$395$		−	6.19615i		−	0.311762i
$396$		0			0
$397$	0.696152	−	0.401924i	0.0349389	−	0.0201720i	−0.482429	−	0.875935i	$-0.660245\pi$
$397$	0.696152	−	0.401924i	0.0349389	−	0.0201720i	0.517368	+	0.855763i	$0.326912\pi$
$398$			14.3923i			0.721421i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	4.50000	+	2.59808i	0.224719	+	0.129742i	0.608134	−	0.793835i	$-0.291919\pi$
$401$	4.50000	+	2.59808i	0.224719	+	0.129742i	−0.383414	+	0.923576i	$0.625252\pi$
$402$		0			0
$403$	−1.09808	−	4.43782i	−0.0546991	−	0.221064i
$404$	7.26795			0.361594
$405$		0			0
$406$	−14.1962	+	24.5885i	−0.704543	+	1.22030i
$407$	16.7942	+	29.0885i	0.832459	+	1.44186i
$408$		0			0
$409$	17.0885	−	9.86603i	0.844970	−	0.487844i	−0.0139806	−	0.999902i	$-0.504450\pi$
$409$	17.0885	−	9.86603i	0.844970	−	0.487844i	0.858950	+	0.512059i	$0.171117\pi$
$410$	−9.00000	+	5.19615i	−0.444478	+	0.256620i
$411$		0			0
$412$	0.598076	+	1.03590i	0.0294651	+	0.0510351i
$413$	15.5885	−	27.0000i	0.767058	−	1.32858i
$414$		0			0
$415$	2.19615			0.107805
$416$	2.59808	−	2.50000i	0.127381	−	0.122573i
$417$		0			0
$418$	16.7942	+	9.69615i	0.821433	+	0.474254i
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	−0.573158	−	0.819445i	$-0.694282\pi$
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	0.996239	+	0.0866469i	$0.0276152\pi$
$420$		0			0
$421$		−	27.1244i		−	1.32196i	−0.750403	−	0.660980i	$-0.770141\pi$
$421$		−	27.1244i		−	1.32196i	0.750403	−	0.660980i	$-0.229859\pi$
$422$	11.7679	−	6.79423i	0.572855	−	0.330738i
$423$		0			0
$424$		−	6.46410i		−	0.313925i
$425$	1.09808	+	1.90192i	0.0532645	+	0.0922569i
$426$		0			0
$427$	−10.9019	−	6.29423i	−0.527581	−	0.304599i
$428$	0.339746			0.0164222
$429$		0			0
$430$	2.00000			0.0964486
$431$	1.90192	+	1.09808i	0.0916124	+	0.0528925i	0.545106	−	0.838367i	$-0.316489\pi$
$431$	1.90192	+	1.09808i	0.0916124	+	0.0528925i	−0.453494	+	0.891259i	$0.649823\pi$
$432$		0			0
$433$	6.19615	+	10.7321i	0.297768	+	0.515749i	0.975625	−	0.219444i	$-0.0704245\pi$
$433$	6.19615	+	10.7321i	0.297768	+	0.515749i	−0.677857	+	0.735194i	$0.737091\pi$
$434$		−	3.80385i		−	0.182591i
$435$		0			0
$436$	−13.3923	+	7.73205i	−0.641375	+	0.370298i
$437$			16.3923i			0.784150i
$438$		0			0
$439$	17.2942	−	29.9545i	0.825408	−	1.42965i	−0.0761982	−	0.997093i	$-0.524278\pi$
$439$	17.2942	−	29.9545i	0.825408	−	1.42965i	0.901607	−	0.432557i	$-0.142388\pi$
$440$	−2.59808	−	1.50000i	−0.123858	−	0.0715097i
$441$		0			0
$442$	1.90192	+	7.68653i	0.0904653	+	0.365611i
$443$	1.60770			0.0763839			0.0381920	−	0.999270i	$-0.487840\pi$
$443$	1.60770			0.0763839			0.0381920	+	0.999270i	$0.487840\pi$
$444$		0			0
$445$	8.59808	−	14.8923i	0.407588	−	0.705963i
$446$	0.232051	+	0.401924i	0.0109879	+	0.0190316i
$447$		0			0
$448$	2.59808	−	1.50000i	0.122748	−	0.0708683i
$449$	−13.5000	+	7.79423i	−0.637104	+	0.367832i	−0.783498	−	0.621394i	$-0.786567\pi$
$449$	−13.5000	+	7.79423i	−0.637104	+	0.367832i	0.146394	+	0.989226i	$0.453233\pi$
$450$		0			0
$451$	15.5885	+	27.0000i	0.734032	+	1.27138i
$452$	3.46410	−	6.00000i	0.162938	−	0.282216i
$453$		0			0
$454$	4.39230			0.206141
$455$	7.50000	+	7.79423i	0.351605	+	0.365399i
$456$		0			0
$457$	−30.8827	−	17.8301i	−1.44463	−	0.834058i	−0.446477	−	0.894795i	$-0.647322\pi$
$457$	−30.8827	−	17.8301i	−1.44463	−	0.834058i	−0.998154	+	0.0607368i	$0.980655\pi$
$458$	2.36603	−	4.09808i	0.110557	−	0.191491i
$459$		0			0
$460$		−	2.53590i		−	0.118237i
$461$	0.509619	−	0.294229i	0.0237353	−	0.0137036i	−0.488085	−	0.872796i	$-0.662305\pi$
$461$	0.509619	−	0.294229i	0.0237353	−	0.0137036i	0.511821	+	0.859092i	$0.328971\pi$
$462$		0			0
$463$			0.928203i			0.0431373i	0.999767	+	0.0215686i	$0.00686604\pi$
$463$			0.928203i			0.0431373i	−0.999767	+	0.0215686i	$0.993134\pi$
$464$	−4.73205	−	8.19615i	−0.219680	−	0.380497i
$465$		0			0
$466$	1.09808	+	0.633975i	0.0508674	+	0.0293683i
$467$	10.1436			0.469390			0.234695	−	0.972069i	$-0.424591\pi$
$467$	10.1436			0.469390			0.234695	+	0.972069i	$0.424591\pi$
$468$		0			0
$469$		0			0
$470$	−2.59808	−	1.50000i	−0.119840	−	0.0691898i
$471$		0			0
$472$	5.19615	+	9.00000i	0.239172	+	0.414259i
$473$		−	6.00000i		−	0.275880i
$474$		0			0
$475$	5.59808	−	3.23205i	0.256857	−	0.148297i
$476$			6.58846i			0.301981i
$477$		0			0
$478$	−4.09808	+	7.09808i	−0.187442	+	0.324658i
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	0.701264	−	0.712901i	$-0.252619\pi$
$479$	9.50962	+	5.49038i	0.434506	+	0.250862i	−0.266759	+	0.963763i	$0.585953\pi$
$480$		0			0
$481$	38.7846	+	11.1962i	1.76843	+	0.510501i
$482$	8.66025			0.394464
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−7.56218	−	13.0981i	−0.343381	−	0.594753i
$486$		0			0
$487$	−28.7942	+	16.6244i	−1.30479	+	0.753321i	−0.981222	−	0.192883i	$-0.938216\pi$
$487$	−28.7942	+	16.6244i	−1.30479	+	0.753321i	−0.323569	+	0.946204i	$0.604883\pi$
$488$	3.63397	−	2.09808i	0.164502	−	0.0949754i
$489$		0			0
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	1.66987	−	2.89230i	0.0753603	−	0.130528i	−0.825883	−	0.563842i	$-0.809323\pi$
$491$	1.66987	−	2.89230i	0.0753603	−	0.130528i	0.901243	+	0.433314i	$0.142656\pi$
$492$		0			0
$493$	20.7846			0.936092
$494$	22.6244	−	5.59808i	1.01792	−	0.251869i
$495$		0			0
$496$	1.09808	+	0.633975i	0.0493051	+	0.0284663i
$497$	9.00000	−	15.5885i	0.403705	−	0.699238i
$498$		0			0
$499$			1.85641i			0.0831042i	0.999136	+	0.0415521i	$0.0132302\pi$
$499$			1.85641i			0.0831042i	−0.999136	+	0.0415521i	$0.986770\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$		0			0
$502$		−	6.80385i		−	0.303671i
$503$	−4.66987	−	8.08846i	−0.208219	−	0.360646i	0.742934	−	0.669364i	$-0.233433\pi$
$503$	−4.66987	−	8.08846i	−0.208219	−	0.360646i	−0.951154	+	0.308718i	$0.900100\pi$
$504$		0			0
$505$	−6.29423	−	3.63397i	−0.280089	−	0.161710i
$506$	−7.60770			−0.338203
$507$		0			0
$508$	−21.1962			−0.940427
$509$	−1.39230	−	0.803848i	−0.0617128	−	0.0356299i	0.468826	−	0.883290i	$-0.344677\pi$
$509$	−1.39230	−	0.803848i	−0.0617128	−	0.0356299i	−0.530539	+	0.847661i	$0.678010\pi$
$510$		0			0
$511$	−8.49038	−	14.7058i	−0.375592	−	0.650545i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.0000	+	6.92820i	−0.529297	+	0.305590i
$515$		−	1.19615i		−	0.0527088i
$516$		0			0
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$	29.0885	+	16.7942i	1.27807	+	0.737896i
$519$		0			0
$520$	−3.50000	+	0.866025i	−0.153485	+	0.0379777i
$521$	0.464102			0.0203327			0.0101663	−	0.999948i	$-0.496764\pi$
$521$	0.464102			0.0203327			0.0101663	+	0.999948i	$0.496764\pi$
$522$		0			0
$523$	−9.19615	+	15.9282i	−0.402120	+	0.696492i	−0.993982	−	0.109548i	$-0.965060\pi$
$523$	−9.19615	+	15.9282i	−0.402120	+	0.696492i	0.591862	+	0.806039i	$0.298393\pi$
$524$	9.06218	+	15.6962i	0.395883	+	0.685690i
$525$		0			0
$526$	23.8923	−	13.7942i	1.04175	−	0.601457i
$527$	−2.41154	+	1.39230i	−0.105048	+	0.0606498i
$528$		0			0
$529$	8.28461	+	14.3494i	0.360200	+	0.623885i
$530$	−3.23205	+	5.59808i	−0.140391	+	0.243165i
$531$		0			0
$532$	19.3923			0.840763
$533$	36.0000	+	10.3923i	1.55933	+	0.450141i
$534$		0			0
$535$	−0.294229	−	0.169873i	−0.0127206	−	0.00734425i
$536$		0			0
$537$		0			0
$538$			2.87564i			0.123978i
$539$	5.19615	−	3.00000i	0.223814	−	0.129219i
$540$		0			0
$541$			16.0526i			0.690153i	0.938574	+	0.345077i	$0.112147\pi$
$541$			16.0526i			0.690153i	−0.938574	+	0.345077i	$0.887853\pi$
$542$	1.26795	+	2.19615i	0.0544631	+	0.0943328i
$543$		0			0
$544$	−1.90192	−	1.09808i	−0.0815443	−	0.0470796i
$545$	15.4641			0.662409
$546$		0			0
$547$	34.7846			1.48728			0.743641	−	0.668579i	$-0.233097\pi$
$547$	34.7846			1.48728			0.743641	+	0.668579i	$0.233097\pi$
$548$	−7.09808	−	4.09808i	−0.303215	−	0.175061i
$549$		0			0
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$		−	61.1769i		−	2.60622i
$552$		0			0
$553$	−16.0981	+	9.29423i	−0.684560	+	0.395231i
$554$		−	1.00000i		−	0.0424859i
$555$		0			0
$556$	−4.59808	+	7.96410i	−0.195002	+	0.337753i
$557$	−14.8923	−	8.59808i	−0.631007	−	0.364312i	0.150135	−	0.988666i	$-0.452029\pi$
$557$	−14.8923	−	8.59808i	−0.631007	−	0.364312i	−0.781142	+	0.624353i	$0.785363\pi$
$558$		0			0
$559$	−5.00000	−	5.19615i	−0.211477	−	0.219774i
$560$	−3.00000			−0.126773
$561$		0			0
$562$	5.19615	−	9.00000i	0.219186	−	0.379642i
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	0.998529	−	0.0542274i	$-0.0172696\pi$
$563$	10.7321	+	18.5885i	0.452302	+	0.783410i	−0.546227	+	0.837637i	$0.683936\pi$
$564$		0			0
$565$	−6.00000	+	3.46410i	−0.252422	+	0.145736i
$566$	−26.3205	+	15.1962i	−1.10633	+	0.638742i
$567$		0			0
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	10.6244	−	18.4019i	0.445396	−	0.771449i	−0.552684	−	0.833391i	$-0.686396\pi$
$569$	10.6244	−	18.4019i	0.445396	−	0.771449i	0.998080	+	0.0619424i	$0.0197295\pi$
$570$		0			0
$571$	34.3731			1.43847			0.719234	−	0.694768i	$-0.244493\pi$
$571$	34.3731			1.43847			0.719234	+	0.694768i	$0.244493\pi$
$572$	2.59808	+	10.5000i	0.108631	+	0.439027i
$573$		0			0
$574$	27.0000	+	15.5885i	1.12696	+	0.650650i
$575$	−1.26795	+	2.19615i	−0.0528771	+	0.0915859i
$576$		0			0
$577$		−	32.4449i		−	1.35070i	−0.737499	−	0.675349i	$-0.763993\pi$
$577$		−	32.4449i		−	1.35070i	0.737499	−	0.675349i	$-0.236007\pi$
$578$	−10.5455	+	6.08846i	−0.438636	+	0.253246i
$579$		0			0
$580$			9.46410i			0.392975i
$581$	−3.29423	−	5.70577i	−0.136668	−	0.236715i
$582$		0			0
$583$	16.7942	+	9.69615i	0.695546	+	0.401574i
$584$	5.66025			0.234223
$585$		0			0
$586$	−0.803848			−0.0332066
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.928820	−	0.370531i	$-0.120824\pi$
$587$	25.9808	+	15.0000i	1.07234	+	0.619116i	0.143521	+	0.989647i	$0.454158\pi$
$588$		0			0
$589$	4.09808	+	7.09808i	0.168858	+	0.292471i
$590$		−	10.3923i		−	0.427844i
$591$		0			0
$592$	−9.69615	+	5.59808i	−0.398509	+	0.230080i
$593$			20.7846i			0.853522i	0.904365	+	0.426761i	$0.140345\pi$
$593$			20.7846i			0.853522i	−0.904365	+	0.426761i	$0.859655\pi$
$594$		0			0
$595$	3.29423	−	5.70577i	0.135050	−	0.233914i
$596$	5.19615	+	3.00000i	0.212843	+	0.122885i
$597$		0			0
$598$	−6.58846	+	6.33975i	−0.269422	+	0.259251i
$599$	−7.85641			−0.321004			−0.160502	−	0.987036i	$-0.551311\pi$
$599$	−7.85641			−0.321004			−0.160502	+	0.987036i	$0.551311\pi$
$600$		0			0
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	−0.902036	−	0.431661i	$-0.857928\pi$
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	0.824847	+	0.565356i	$0.191261\pi$
$602$	−3.00000	−	5.19615i	−0.122271	−	0.211779i
$603$		0			0
$604$	−5.49038	+	3.16987i	−0.223400	+	0.128980i
$605$	−1.73205	+	1.00000i	−0.0704179	+	0.0406558i
$606$		0			0
$607$	3.20577	+	5.55256i	0.130118	+	0.225371i	0.923722	−	0.383064i	$-0.125131\pi$
$607$	3.20577	+	5.55256i	0.130118	+	0.225371i	−0.793604	+	0.608435i	$0.791798\pi$
$608$	−3.23205	+	5.59808i	−0.131077	+	0.227032i
$609$		0			0
$610$	−4.19615			−0.169897
$611$	2.59808	+	10.5000i	0.105107	+	0.424785i
$612$		0			0
$613$	23.3038	+	13.4545i	0.941234	+	0.543421i	0.890347	−	0.455283i	$-0.150462\pi$
$613$	23.3038	+	13.4545i	0.941234	+	0.543421i	0.0508868	+	0.998704i	$0.483795\pi$
$614$	10.2679	−	17.7846i	0.414381	−	0.717728i
$615$		0			0
$616$			9.00000i			0.362620i
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	−0.152242	−	0.988343i	$-0.548649\pi$
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	0.779809	+	0.626017i	$0.215316\pi$
$618$		0			0
$619$			10.6077i			0.426359i	0.977013	+	0.213180i	$0.0683820\pi$
$619$			10.6077i			0.426359i	−0.977013	+	0.213180i	$0.931618\pi$
$620$	−0.633975	−	1.09808i	−0.0254610	−	0.0440998i
$621$		0			0
$622$	13.0981	+	7.56218i	0.525185	+	0.303216i
$623$	−51.5885			−2.06685
$624$		0			0
$625$	1.00000			0.0400000
$626$	−4.85641	−	2.80385i	−0.194101	−	0.112064i
$627$		0			0
$628$	−6.50000	−	11.2583i	−0.259378	−	0.449256i
$629$		−	24.5885i		−	0.980406i
$630$		0			0
$631$	−18.0000	+	10.3923i	−0.716569	+	0.413711i	−0.813488	−	0.581581i	$-0.802434\pi$
$631$	−18.0000	+	10.3923i	−0.716569	+	0.413711i	0.0969198	+	0.995292i	$0.469101\pi$
$632$		−	6.19615i		−	0.246470i
$633$		0			0
$634$	−6.40192	+	11.0885i	−0.254253	+	0.440379i
$635$	18.3564	+	10.5981i	0.728452	+	0.420572i
$636$		0			0
$637$	2.00000	−	6.92820i	0.0792429	−	0.274505i
$638$	28.3923			1.12406
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	22.9641	+	39.7750i	0.907027	+	1.57102i	0.818172	+	0.574973i	$0.194988\pi$
$641$	22.9641	+	39.7750i	0.907027	+	1.57102i	0.0888552	+	0.996045i	$0.471679\pi$
$642$		0			0
$643$	6.29423	−	3.63397i	0.248220	−	0.143310i	−0.370729	−	0.928741i	$-0.620892\pi$
$643$	6.29423	−	3.63397i	0.248220	−	0.143310i	0.618949	+	0.785431i	$0.287559\pi$
$644$	−6.58846	+	3.80385i	−0.259622	+	0.149893i
$645$		0			0
$646$	−7.09808	−	12.2942i	−0.279270	−	0.483710i
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	−0.954833	−	0.297143i	$-0.903966\pi$
$647$	−5.59808	+	9.69615i	−0.220083	+	0.381195i	0.734750	+	0.678338i	$0.237300\pi$
$648$		0			0
$649$	−31.1769			−1.22380
$650$	3.46410	+	1.00000i	0.135873	+	0.0392232i
$651$		0			0
$652$	6.29423	+	3.63397i	0.246501	+	0.142317i
$653$	−9.69615	+	16.7942i	−0.379440	+	0.657209i	−0.990981	−	0.134004i	$-0.957217\pi$
$653$	−9.69615	+	16.7942i	−0.379440	+	0.657209i	0.611541	+	0.791213i	$0.290550\pi$
$654$		0			0
$655$		−	18.1244i		−	0.708177i
$656$	−9.00000	+	5.19615i	−0.351391	+	0.202876i
$657$		0			0
$658$			9.00000i			0.350857i
$659$	14.6603	+	25.3923i	0.571082	+	0.989144i	0.996455	+	0.0841255i	$0.0268097\pi$
$659$	14.6603	+	25.3923i	0.571082	+	0.989144i	−0.425373	+	0.905018i	$0.639857\pi$
$660$		0			0
$661$	25.9019	+	14.9545i	1.00747	+	0.581662i	0.910449	−	0.413621i	$-0.135736\pi$
$661$	25.9019	+	14.9545i	1.00747	+	0.581662i	0.0970187	+	0.995283i	$0.469069\pi$
$662$	−0.928203			−0.0360756
$663$		0			0
$664$	2.19615			0.0852272
$665$	−16.7942	−	9.69615i	−0.651252	−	0.376001i
$666$		0			0
$667$	12.0000	+	20.7846i	0.464642	+	0.804783i
$668$			3.00000i			0.116073i
$669$		0			0
$670$		0			0
$671$			12.5885i			0.485972i
$672$		0			0
$673$	−1.80385	+	3.12436i	−0.0695332	+	0.120435i	−0.898696	−	0.438572i	$-0.855484\pi$
$673$	−1.80385	+	3.12436i	−0.0695332	+	0.120435i	0.829163	+	0.559007i	$0.188818\pi$
$674$	3.63397	+	2.09808i	0.139975	+	0.0808149i
$675$		0			0
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	−1.85641			−0.0713475			−0.0356737	−	0.999363i	$-0.511358\pi$
$677$	−1.85641			−0.0713475			−0.0356737	+	0.999363i	$0.511358\pi$
$678$		0			0
$679$	−22.6865	+	39.2942i	−0.870629	+	1.50797i
$680$	1.09808	+	1.90192i	0.0421093	+	0.0729354i
$681$		0			0
$682$	−3.29423	+	1.90192i	−0.126143	+	0.0728284i
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.917879	−	0.396861i	$-0.870099\pi$
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.115248	+	0.993337i	$0.536766\pi$
$684$		0			0
$685$	4.09808	+	7.09808i	0.156579	+	0.271204i
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$		0			0
$688$	2.00000			0.0762493
$689$	22.6244	−	5.59808i	0.861919	−	0.213270i
$690$		0			0
$691$	−16.2058	−	9.35641i	−0.616497	−	0.355934i	0.159007	−	0.987277i	$-0.449171\pi$
$691$	−16.2058	−	9.35641i	−0.616497	−	0.355934i	−0.775504	+	0.631343i	$0.782504\pi$
$692$	7.50000	−	12.9904i	0.285107	−	0.493820i
$693$		0			0
$694$			25.2679i			0.959158i
$695$	7.96410	−	4.59808i	0.302096	−	0.174415i
$696$		0			0
$697$		−	22.8231i		−	0.864486i
$698$	17.0263	+	29.4904i	0.644454	+	1.11623i
$699$		0			0
$700$	2.59808	+	1.50000i	0.0981981	+	0.0566947i
$701$	29.9090			1.12965			0.564823	−	0.825212i	$-0.308944\pi$
$701$	29.9090			1.12965			0.564823	+	0.825212i	$0.308944\pi$
$702$		0			0
$703$	−72.3731			−2.72960
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$	−10.0981	−	17.4904i	−0.380046	−	0.658259i
$707$			21.8038i			0.820018i
$708$		0			0
$709$	35.4904	−	20.4904i	1.33287	−	0.769532i	0.347131	−	0.937817i	$-0.387156\pi$
$709$	35.4904	−	20.4904i	1.33287	−	0.769532i	0.985738	+	0.168284i	$0.0538227\pi$
$710$		−	6.00000i		−	0.225176i
$711$		0			0
$712$	8.59808	−	14.8923i	0.322227	−	0.558113i
$713$	−2.78461	−	1.60770i	−0.104284	−	0.0602087i
$714$		0			0
$715$	3.00000	−	10.3923i	0.112194	−	0.388650i
$716$	−2.53590			−0.0947710
$717$		0			0
$718$	11.1962	−	19.3923i	0.417837	−	0.723714i
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	0.848198	−	0.529679i	$-0.177688\pi$
$719$	−0.928203	−	1.60770i	−0.0346161	−	0.0599569i	−0.882814	+	0.469722i	$0.844354\pi$
$720$		0			0
$721$	−3.10770	+	1.79423i	−0.115737	+	0.0668206i
$722$	−19.7321	+	11.3923i	−0.734351	+	0.423978i
$723$		0			0
$724$	−8.29423	−	14.3660i	−0.308253	−	0.533909i
$725$	4.73205	−	8.19615i	0.175744	−	0.304397i
$726$		0			0
$727$	−38.3731			−1.42318			−0.711589	−	0.702596i	$-0.752024\pi$
$727$	−38.3731			−1.42318			−0.711589	+	0.702596i	$0.752024\pi$
$728$	7.50000	+	7.79423i	0.277968	+	0.288873i
$729$		0			0
$730$	−4.90192	−	2.83013i	−0.181428	−	0.104748i
$731$	−2.19615	+	3.80385i	−0.0812276	+	0.140690i
$732$		0			0
$733$			50.9090i			1.88037i	0.340670	+	0.940183i	$0.389346\pi$
$733$			50.9090i			1.88037i	−0.340670	+	0.940183i	$0.610654\pi$
$734$	−22.8564	+	13.1962i	−0.843645	+	0.487079i
$735$		0			0
$736$		−	2.53590i		−	0.0934745i
$737$		0			0
$738$		0			0
$739$	43.7942	+	25.2846i	1.61100	+	0.930109i	0.989140	+	0.146979i	$0.0469549\pi$
$739$	43.7942	+	25.2846i	1.61100	+	0.930109i	0.621857	+	0.783131i	$0.286378\pi$
$740$	11.1962			0.411579
$741$		0			0
$742$	19.3923			0.711914
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.158400	−	0.987375i	$-0.550633\pi$
$743$	−29.7846	−	17.1962i	−1.09269	−	0.630866i	−0.934292	+	0.356509i	$0.883967\pi$
$744$		0			0
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$			20.3923i			0.746615i
$747$		0			0
$748$	5.70577	−	3.29423i	0.208624	−	0.120449i
$749$			1.01924i			0.0372421i
$750$		0			0
$751$	−0.196152	+	0.339746i	−0.00715770	+	0.0123975i	−0.869582	−	0.493788i	$-0.835612\pi$
$751$	−0.196152	+	0.339746i	−0.00715770	+	0.0123975i	0.862424	+	0.506186i	$0.168945\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$		0			0
$754$	24.5885	−	23.6603i	0.895459	−	0.861656i
$755$	6.33975			0.230727
$756$		0			0
$757$	−1.89230	+	3.27757i	−0.0687770	+	0.119125i	−0.898363	−	0.439253i	$-0.855243\pi$
$757$	−1.89230	+	3.27757i	−0.0687770	+	0.119125i	0.829586	+	0.558379i	$0.188576\pi$
$758$	−5.89230	−	10.2058i	−0.214018	−	0.370690i
$759$		0			0
$760$	5.59808	−	3.23205i	0.203064	−	0.117239i
$761$	25.2846	−	14.5981i	0.916566	−	0.529180i	0.0340283	−	0.999421i	$-0.489166\pi$
$761$	25.2846	−	14.5981i	0.916566	−	0.529180i	0.882538	+	0.470241i	$0.155833\pi$
$762$		0			0
$763$	−23.1962	−	40.1769i	−0.839757	−	1.45450i
$764$	9.63397	−	16.6865i	0.348545	−	0.603698i
$765$		0			0
$766$	−1.60770			−0.0580884
$767$	−27.0000	+	25.9808i	−0.974913	+	0.938111i
$768$		0			0
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.231701	−	0.972787i	$-0.574429\pi$
$769$	−33.0000	−	19.0526i	−1.19001	−	0.687053i	−0.958309	+	0.285734i	$0.907763\pi$
$770$	4.50000	−	7.79423i	0.162169	−	0.280885i
$771$		0			0
$772$		−	4.39230i		−	0.158083i
$773$	29.0885	−	16.7942i	1.04624	−	0.604046i	0.124645	−	0.992201i	$-0.460221\pi$
$773$	29.0885	−	16.7942i	1.04624	−	0.604046i	0.921594	+	0.388155i	$0.126887\pi$
$774$		0			0
$775$			1.26795i			0.0455461i
$776$	−7.56218	−	13.0981i	−0.271466	−	0.470194i
$777$		0			0
$778$	16.6865	+	9.63397i	0.598241	+	0.345395i
$779$	−67.1769			−2.40686
$780$		0			0
$781$	−18.0000			−0.644091
$782$	4.82309	+	2.78461i	0.172473	+	0.0995774i
$783$		0			0
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$			13.0000i			0.463990i
$786$		0			0
$787$	−31.9019	+	18.4186i	−1.13718	+	0.656552i	−0.945731	−	0.324951i	$-0.894652\pi$
$787$	−31.9019	+	18.4186i	−1.13718	+	0.656552i	−0.191450	+	0.981502i	$0.561319\pi$
$788$		−	9.58846i		−	0.341575i
$789$		0			0
$790$	−3.09808	+	5.36603i	−0.110225	+	0.190915i
$791$	18.0000	+	10.3923i	0.640006	+	0.369508i
$792$		0			0
$793$	10.4904	+	10.9019i	0.372524	+	0.387139i
$794$	−0.803848			−0.0285275
$795$		0			0
$796$	7.19615	−	12.4641i	0.255061	−	0.441778i
$797$	0.464102	+	0.803848i	0.0164393	+	0.0284737i	0.874128	−	0.485696i	$-0.161434\pi$
$797$	0.464102	+	0.803848i	0.0164393	+	0.0284737i	−0.857689	+	0.514169i	$0.828100\pi$
$798$		0			0
$799$	5.70577	−	3.29423i	0.201856	−	0.116541i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−2.59808	−	4.50000i	−0.0917413	−	0.158901i
$803$	−8.49038	+	14.7058i	−0.299619	+	0.518955i
$804$		0			0
$805$	7.60770			0.268136
$806$	−1.26795	+	4.39230i	−0.0446616	+	0.154712i
$807$		0			0
$808$	−6.29423	−	3.63397i	−0.221430	−	0.127843i
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	−0.574228	−	0.818696i	$-0.694698\pi$
$809$	12.0000	−	20.7846i	0.421898	−	0.730748i	0.996125	+	0.0879478i	$0.0280309\pi$
$810$		0			0
$811$		−	22.6077i		−	0.793864i	−0.917848	−	0.396932i	$-0.870075\pi$
$811$		−	22.6077i		−	0.793864i	0.917848	−	0.396932i	$-0.129925\pi$
$812$	24.5885	−	14.1962i	0.862886	−	0.498187i
$813$		0			0
$814$		−	33.5885i		−	1.17727i
$815$	−3.63397	−	6.29423i	−0.127293	−	0.220477i
$816$		0			0
$817$	11.1962	+	6.46410i	0.391704	+	0.226150i
$818$	−19.7321			−0.689915
$819$		0			0
$820$	10.3923			0.362915
$821$	8.49038	+	4.90192i	0.296316	+	0.171078i	0.640787	−	0.767719i	$-0.278608\pi$
$821$	8.49038	+	4.90192i	0.296316	+	0.171078i	−0.344471	+	0.938797i	$0.611942\pi$
$822$		0			0
$823$	8.40192	+	14.5526i	0.292873	+	0.507270i	0.974488	−	0.224441i	$-0.0720555\pi$
$823$	8.40192	+	14.5526i	0.292873	+	0.507270i	−0.681615	+	0.731711i	$0.738722\pi$
$824$		−	1.19615i		−	0.0416699i
$825$		0			0
$826$	−27.0000	+	15.5885i	−0.939450	+	0.542392i
$827$		−	11.4115i		−	0.396818i	−0.980119	−	0.198409i	$-0.936423\pi$
$827$		−	11.4115i		−	0.396818i	0.980119	−	0.198409i	$-0.0635775\pi$
$828$		0			0
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$	−1.90192	−	1.09808i	−0.0660167	−	0.0381148i
$831$		0			0
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$	−4.39230			−0.152184
$834$		0			0
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	−9.69615	−	16.7942i	−0.335348	−	0.580841i
$837$		0			0
$838$	−15.0000	+	8.66025i	−0.518166	+	0.299164i
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.0656397	−	0.997843i	$-0.479091\pi$
$839$	27.8827	−	16.0981i	0.962617	−	0.555767i	0.896978	+	0.442076i	$0.145758\pi$
$840$		0			0
$841$	−30.2846	−	52.4545i	−1.04430	−	1.80878i
$842$	−13.5622	+	23.4904i	−0.467384	+	0.809532i
$843$		0			0
$844$	−13.5885			−0.467734
$845$	−6.06218	−	11.5000i	−0.208545	−	0.395612i
$846$		0			0
$847$	5.19615	+	3.00000i	0.178542	+	0.103081i
$848$	−3.23205	+	5.59808i	−0.110989	+	0.192239i
$849$		0			0
$850$		−	2.19615i		−	0.0753274i
$851$	24.5885	−	14.1962i	0.842881	−	0.486638i
$852$		0			0
$853$			13.8564i			0.474434i	0.971457	+	0.237217i	$0.0762353\pi$
$853$			13.8564i			0.474434i	−0.971457	+	0.237217i	$0.923765\pi$
$854$	6.29423	+	10.9019i	0.215384	+	0.373056i
$855$		0			0
$856$	−0.294229	−	0.169873i	−0.0100565	−	0.00580614i
$857$	13.2679			0.453225			0.226612	−	0.973985i	$-0.427235\pi$
$857$	13.2679			0.453225			0.226612	+	0.973985i	$0.427235\pi$
$858$		0			0
$859$	52.3731			1.78695			0.893473	−	0.449117i	$-0.148261\pi$
$859$	52.3731			1.78695			0.893473	+	0.449117i	$0.148261\pi$
$860$	−1.73205	−	1.00000i	−0.0590624	−	0.0340997i
$861$		0			0
$862$	−1.09808	−	1.90192i	−0.0374006	−	0.0647798i
$863$		−	19.1769i		−	0.652790i	−0.945234	−	0.326395i	$-0.894166\pi$
$863$		−	19.1769i		−	0.652790i	0.945234	−	0.326395i	$-0.105834\pi$
$864$		0			0
$865$	−12.9904	+	7.50000i	−0.441686	+	0.255008i
$866$		−	12.3923i		−	0.421108i
$867$		0			0
$868$	−1.90192	+	3.29423i	−0.0645555	+	0.111813i
$869$	16.0981	+	9.29423i	0.546090	+	0.315285i
$870$		0			0
$871$		0			0
$872$	15.4641			0.523681
$873$		0			0
$874$	8.19615	−	14.1962i	0.277239	−	0.480192i
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$		0			0
$877$	17.7846	−	10.2679i	0.600544	−	0.346724i	−0.168712	−	0.985665i	$-0.553961\pi$
$877$	17.7846	−	10.2679i	0.600544	−	0.346724i	0.769255	+	0.638941i	$0.220627\pi$
$878$	−29.9545	+	17.2942i	−1.01091	+	0.583652i
$879$		0			0
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−4.16025	+	7.20577i	−0.140163	+	0.242769i	−0.927558	−	0.373680i	$-0.878096\pi$
$881$	−4.16025	+	7.20577i	−0.140163	+	0.242769i	0.787395	+	0.616449i	$0.211429\pi$
$882$		0			0
$883$	−26.5885			−0.894773			−0.447386	−	0.894341i	$-0.647645\pi$
$883$	−26.5885			−0.894773			−0.447386	+	0.894341i	$0.647645\pi$
$884$	2.19615	−	7.60770i	0.0738646	−	0.255874i
$885$		0			0
$886$	−1.39230	−	0.803848i	−0.0467754	−	0.0270058i
$887$	26.3827	−	45.6962i	0.885844	−	1.53433i	0.0411005	−	0.999155i	$-0.486914\pi$
$887$	26.3827	−	45.6962i	0.885844	−	1.53433i	0.844743	−	0.535172i	$-0.179753\pi$
$888$		0			0
$889$		−	63.5885i		−	2.13269i
$890$	−14.8923	+	8.59808i	−0.499191	+	0.288208i
$891$		0			0
$892$		−	0.464102i		−	0.0155393i
$893$	−9.69615	−	16.7942i	−0.324469	−	0.561997i
$894$		0			0
$895$	2.19615	+	1.26795i	0.0734093	+	0.0423829i
$896$	−3.00000			−0.100223
$897$		0			0
$898$	15.5885			0.520194
$899$	10.3923	+	6.00000i	0.346603	+	0.200111i
$900$		0			0
$901$	−7.09808	−	12.2942i	−0.236471	−	0.409580i
$902$		−	31.1769i		−	1.03808i
$903$		0			0
$904$	−6.00000	+	3.46410i	−0.199557	+	0.115214i
$905$			16.5885i			0.551419i
$906$		0			0
$907$	13.2942	−	23.0263i	0.441428	−	0.764575i	−0.556368	−	0.830936i	$-0.687806\pi$
$907$	13.2942	−	23.0263i	0.441428	−	0.764575i	0.997796	+	0.0663609i	$0.0211389\pi$
$908$	−3.80385	−	2.19615i	−0.126235	−	0.0728819i
$909$		0			0
$910$	−2.59808	−	10.5000i	−0.0861254	−	0.348072i
$911$	14.5359			0.481596			0.240798	−	0.970575i	$-0.422591\pi$
$911$	14.5359			0.481596			0.240798	+	0.970575i	$0.422591\pi$
$912$		0			0
$913$	−3.29423	+	5.70577i	−0.109023	+	0.188833i
$914$	17.8301	+	30.8827i	0.589768	+	1.02151i
$915$		0			0
$916$	−4.09808	+	2.36603i	−0.135404	+	0.0781757i
$917$	−47.0885	+	27.1865i	−1.55500	+	0.897778i
$918$		0			0
$919$	5.39230	+	9.33975i	0.177876	+	0.308090i	0.941153	−	0.337982i	$-0.109744\pi$
$919$	5.39230	+	9.33975i	0.177876	+	0.308090i	−0.763277	+	0.646071i	$0.776411\pi$
$920$	−1.26795	+	2.19615i	−0.0418030	+	0.0724050i
$921$		0			0
$922$	−0.588457			−0.0193798
$923$	−15.5885	+	15.0000i	−0.513100	+	0.493731i
$924$		0			0
$925$	−9.69615	−	5.59808i	−0.318808	−	0.184064i
$926$	0.464102	−	0.803848i	0.0152513	−	0.0264161i
$927$		0			0
$928$			9.46410i			0.310674i
$929$	−38.7846	+	22.3923i	−1.27248	+	0.734668i	−0.975454	−	0.220201i	$-0.929329\pi$
$929$	−38.7846	+	22.3923i	−1.27248	+	0.734668i	−0.297027	+	0.954869i	$0.595995\pi$
$930$		0			0
$931$			12.9282i			0.423705i
$932$	−0.633975	−	1.09808i	−0.0207665	−	0.0359687i
$933$		0			0
$934$	−8.78461	−	5.07180i	−0.287441	−	0.165954i
$935$	−6.58846			−0.215466
$936$		0			0
$937$	−30.3923			−0.992873			−0.496437	−	0.868073i	$-0.665359\pi$
$937$	−30.3923			−0.992873			−0.496437	+	0.868073i	$0.665359\pi$
$938$		0			0
$939$		0			0
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$			44.7846i			1.45994i	0.683481	+	0.729968i	$0.260465\pi$
$941$			44.7846i			1.45994i	−0.683481	+	0.729968i	$0.739535\pi$
$942$		0			0
$943$	22.8231	−	13.1769i	0.743222	−	0.429099i
$944$		−	10.3923i		−	0.338241i
$945$		0			0
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.988286	−	0.152612i	$-0.951231\pi$
$947$	−49.6865	−	28.6865i	−1.61460	−	0.932187i	−0.626309	−	0.779575i	$-0.715435\pi$
$948$		0			0
$949$	4.90192	+	19.8109i	0.159123	+	0.643089i
$950$	−6.46410			−0.209723
$951$		0			0
$952$	3.29423	−	5.70577i	0.106767	−	0.184925i
$953$	12.2942	+	21.2942i	0.398249	+	0.689788i	0.993510	−	0.113745i	$-0.0362846\pi$
$953$	12.2942	+	21.2942i	0.398249	+	0.689788i	−0.595261	+	0.803533i	$0.702951\pi$
$954$		0			0
$955$	−16.6865	+	9.63397i	−0.539964	+	0.311748i
$956$	7.09808	−	4.09808i	0.229568	−	0.132541i
$957$		0			0
$958$	−5.49038	−	9.50962i	−0.177386	−	0.307242i
$959$	12.2942	−	21.2942i	0.397001	−	0.687627i
$960$		0			0
$961$	29.3923			0.948139
$962$	−27.9904	−	29.0885i	−0.902446	−	0.937850i
$963$		0			0
$964$	−7.50000	−	4.33013i	−0.241559	−	0.139464i
$965$	−2.19615	+	3.80385i	−0.0706966	+	0.122450i
$966$		0			0
$967$		−	38.5692i		−	1.24030i	−0.784482	−	0.620151i	$-0.787071\pi$
$967$		−	38.5692i		−	1.24030i	0.784482	−	0.620151i	$-0.212929\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$		0			0
$970$			15.1244i			0.485614i
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	−0.947636	−	0.319354i	$-0.896534\pi$
$971$	−23.3827	−	40.5000i	−0.750386	−	1.29971i	0.197250	−	0.980353i	$-0.436799\pi$
$972$		0			0
$973$	−23.8923	−	13.7942i	−0.765952	−	0.442223i
$974$	33.2487			1.06536
$975$		0			0
$976$	−4.19615			−0.134316
$977$	−3.80385	−	2.19615i	−0.121696	−	0.0702611i	0.437916	−	0.899016i	$-0.355717\pi$
$977$	−3.80385	−	2.19615i	−0.121696	−	0.0702611i	−0.559612	+	0.828755i	$0.689050\pi$
$978$		0			0
$979$	25.7942	+	44.6769i	0.824387	+	1.42788i
$980$		−	2.00000i		−	0.0638877i
$981$		0			0
$982$	−2.89230	+	1.66987i	−0.0922972	+	0.0532878i
$983$		−	38.5692i		−	1.23017i	−0.788462	−	0.615084i	$-0.789122\pi$
$983$		−	38.5692i		−	1.23017i	0.788462	−	0.615084i	$-0.210878\pi$
$984$		0			0
$985$	−4.79423	+	8.30385i	−0.152757	+	0.264583i
$986$	−18.0000	−	10.3923i	−0.573237	−	0.330958i
$987$		0			0
$988$	−22.3923	−	6.46410i	−0.712394	−	0.205650i
$989$	−5.07180			−0.161274
$990$		0			0
$991$	−25.5885	+	44.3205i	−0.812844	+	1.40789i	0.0980215	+	0.995184i	$0.468749\pi$
$991$	−25.5885	+	44.3205i	−0.812844	+	1.40789i	−0.910866	+	0.412703i	$0.864585\pi$
$992$	−0.633975	−	1.09808i	−0.0201287	−	0.0348640i
$993$		0			0
$994$	−15.5885	+	9.00000i	−0.494436	+	0.285463i
$995$	−12.4641	+	7.19615i	−0.395139	+	0.228133i
$996$		0			0
$997$	21.2846	+	36.8660i	0.674090	+	1.16756i	0.976734	+	0.214455i	$0.0687975\pi$
$997$	21.2846	+	36.8660i	0.674090	+	1.16756i	−0.302644	+	0.953104i	$0.597869\pi$
$998$	0.928203	−	1.60770i	0.0293818	−	0.0508907i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.c.901.1		4
3.2	odd	2		130.2.l.a.121.2	yes	4
12.11	even	2		1040.2.da.a.641.1		4
13.10	even	6	inner	1170.2.bs.c.361.1		4
15.2	even	4		650.2.n.a.199.1		4
15.8	even	4		650.2.n.b.199.2		4
15.14	odd	2		650.2.m.a.251.1		4
39.2	even	12		1690.2.e.n.991.2		4
39.5	even	4		1690.2.e.n.191.2		4
39.8	even	4		1690.2.e.l.191.2		4
39.11	even	12		1690.2.e.l.991.2		4
39.17	odd	6		1690.2.d.f.1351.3		4
39.20	even	12		1690.2.a.m.1.1		2
39.23	odd	6		130.2.l.a.101.2	✓	4
39.29	odd	6		1690.2.l.g.361.1		4
39.32	even	12		1690.2.a.j.1.1		2
39.35	odd	6		1690.2.d.f.1351.1		4
39.38	odd	2		1690.2.l.g.1161.1		4
156.23	even	6		1040.2.da.a.881.1		4
195.23	even	12		650.2.n.a.49.1		4
195.59	even	12		8450.2.a.bf.1.2		2
195.62	even	12		650.2.n.b.49.2		4
195.149	even	12		8450.2.a.bm.1.2		2
195.179	odd	6		650.2.m.a.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.2	✓	4	39.23	odd	6
130.2.l.a.121.2	yes	4	3.2	odd	2
650.2.m.a.101.1		4	195.179	odd	6
650.2.m.a.251.1		4	15.14	odd	2
650.2.n.a.49.1		4	195.23	even	12
650.2.n.a.199.1		4	15.2	even	4
650.2.n.b.49.2		4	195.62	even	12
650.2.n.b.199.2		4	15.8	even	4
1040.2.da.a.641.1		4	12.11	even	2
1040.2.da.a.881.1		4	156.23	even	6
1170.2.bs.c.361.1		4	13.10	even	6	inner
1170.2.bs.c.901.1		4	1.1	even	1	trivial
1690.2.a.j.1.1		2	39.32	even	12
1690.2.a.m.1.1		2	39.20	even	12
1690.2.d.f.1351.1		4	39.35	odd	6
1690.2.d.f.1351.3		4	39.17	odd	6
1690.2.e.l.191.2		4	39.8	even	4
1690.2.e.l.991.2		4	39.11	even	12
1690.2.e.n.191.2		4	39.5	even	4
1690.2.e.n.991.2		4	39.2	even	12
1690.2.l.g.361.1		4	39.29	odd	6
1690.2.l.g.1161.1		4	39.38	odd	2
8450.2.a.bf.1.2		2	195.59	even	12
8450.2.a.bm.1.2		2	195.149	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(3.50000 - 0.866025i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.09808 - 1.90192i) q^{17} +(-5.59808 + 3.23205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(1.26795 - 2.19615i) q^{23} -1.00000 q^{25} +(-3.46410 - 1.00000i) q^{26} +(-2.59808 - 1.50000i) q^{28} +(-4.73205 + 8.19615i) q^{29} -1.26795i q^{31} +(0.866025 - 0.500000i) q^{32} +2.19615i q^{34} +(1.50000 + 2.59808i) q^{35} +(9.69615 + 5.59808i) q^{37} +6.46410 q^{38} -1.00000 q^{40} +(9.00000 + 5.19615i) q^{41} +(-1.00000 - 1.73205i) q^{43} +3.00000i q^{44} +(-2.19615 + 1.26795i) q^{46} +3.00000i q^{47} +(1.00000 - 1.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.50000 + 2.59808i) q^{52} +6.46410 q^{53} +(1.50000 - 2.59808i) q^{55} +(1.50000 + 2.59808i) q^{56} +(8.19615 - 4.73205i) q^{58} +(-9.00000 + 5.19615i) q^{59} +(2.09808 + 3.63397i) q^{61} +(-0.633975 + 1.09808i) q^{62} -1.00000 q^{64} +(-0.866025 - 3.50000i) q^{65} +(1.09808 - 1.90192i) q^{68} -3.00000i q^{70} +(-5.19615 + 3.00000i) q^{71} +5.66025i q^{73} +(-5.59808 - 9.69615i) q^{74} +(-5.59808 - 3.23205i) q^{76} -9.00000 q^{77} +6.19615 q^{79} +(0.866025 + 0.500000i) q^{80} +(-5.19615 - 9.00000i) q^{82} +2.19615i q^{83} +(-1.90192 + 1.09808i) q^{85} +2.00000i q^{86} +(1.50000 - 2.59808i) q^{88} +(14.8923 + 8.59808i) q^{89} +(-7.79423 + 7.50000i) q^{91} +2.53590 q^{92} +(1.50000 - 2.59808i) q^{94} +(3.23205 + 5.59808i) q^{95} +(13.0981 - 7.56218i) q^{97} +(-1.73205 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} + 14 q^{13} + 12 q^{14} - 2 q^{16} + 6 q^{17} - 12 q^{19} - 6 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{29} + 6 q^{35} + 18 q^{37} + 12 q^{38} - 4 q^{40} + 36 q^{41} - 4 q^{43} + 12 q^{46} + 4 q^{49} + 10 q^{52} + 12 q^{53} + 6 q^{55} + 6 q^{56} + 12 q^{58} - 36 q^{59} - 2 q^{61} - 6 q^{62} - 4 q^{64} - 6 q^{68} - 12 q^{74} - 12 q^{76} - 36 q^{77} + 4 q^{79} - 18 q^{85} + 6 q^{88} + 18 q^{89} + 24 q^{92} + 6 q^{94} + 6 q^{95} + 42 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 + 14 * q^13 + 12 * q^14 - 2 * q^16 + 6 * q^17 - 12 * q^19 - 6 * q^22 + 12 * q^23 - 4 * q^25 - 12 * q^29 + 6 * q^35 + 18 * q^37 + 12 * q^38 - 4 * q^40 + 36 * q^41 - 4 * q^43 + 12 * q^46 + 4 * q^49 + 10 * q^52 + 12 * q^53 + 6 * q^55 + 6 * q^56 + 12 * q^58 - 36 * q^59 - 2 * q^61 - 6 * q^62 - 4 * q^64 - 6 * q^68 - 12 * q^74 - 12 * q^76 - 36 * q^77 + 4 * q^79 - 18 * q^85 + 6 * q^88 + 18 * q^89 + 24 * q^92 + 6 * q^94 + 6 * q^95 + 42 * q^97

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