LMFDB - Embedded newform 1950.2.z.n.1849.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.z (of order $6$, degree $2$, not 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1849.4
Root			$1.35234 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.n.1699.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(0.486319 + 0.280776i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(0.486319 + 0.280776i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.06155 - 3.57071i) q^{11} +1.00000i q^{12} +(-2.21837 - 2.84233i) q^{13} +0.561553 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.70469 + 1.56155i) q^{17} -1.00000i q^{18} +(0.280776 - 0.486319i) q^{19} -0.561553 q^{21} +(-3.57071 - 2.06155i) q^{22} +(-4.05703 + 2.34233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.34233 - 1.35234i) q^{26} +1.00000i q^{27} +(0.486319 - 0.280776i) q^{28} +(1.21922 + 2.11176i) q^{29} -6.68466 q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.57071 + 2.06155i) q^{33} +3.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.57071 + 2.06155i) q^{37} -0.561553i q^{38} +(3.34233 + 1.35234i) q^{39} +(-6.12311 - 10.6055i) q^{41} +(-0.486319 + 0.280776i) q^{42} +(0.379706 + 0.219224i) q^{43} -4.12311 q^{44} +(-2.34233 + 4.05703i) q^{46} +7.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.34233 - 5.78908i) q^{49} -3.12311 q^{51} +(-3.57071 + 0.500000i) q^{52} -8.56155i q^{53} +(0.500000 + 0.866025i) q^{54} +(0.280776 - 0.486319i) q^{56} +0.561553i q^{57} +(2.11176 + 1.21922i) q^{58} +(3.21922 - 5.57586i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-5.78908 + 3.34233i) q^{62} +(0.486319 - 0.280776i) q^{63} -1.00000 q^{64} +4.12311 q^{66} +(-1.94528 + 1.12311i) q^{67} +(2.70469 - 1.56155i) q^{68} +(2.34233 - 4.05703i) q^{69} +(6.56155 - 11.3649i) q^{71} +(-0.866025 - 0.500000i) q^{72} -9.36932i q^{73} +(-2.06155 + 3.57071i) q^{74} +(-0.280776 - 0.486319i) q^{76} -2.31534i q^{77} +(3.57071 - 0.500000i) q^{78} -11.5616 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-10.6055 - 6.12311i) q^{82} +7.12311i q^{83} +(-0.280776 + 0.486319i) q^{84} +0.438447 q^{86} +(-2.11176 - 1.21922i) q^{87} +(-3.57071 + 2.06155i) q^{88} +(-9.40388 - 16.2880i) q^{89} +(-0.280776 - 2.00514i) q^{91} +4.68466i q^{92} +(5.78908 - 3.34233i) q^{93} +(3.50000 + 6.06218i) q^{94} +1.00000 q^{96} +(6.16879 + 3.56155i) q^{97} +(-5.78908 - 3.34233i) q^{98} -4.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{14} - 4 q^{16} - 6 q^{19} + 12 q^{21} + 4 q^{24} - 2 q^{26} + 18 q^{29} - 4 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 16 q^{41} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} - 6 q^{56} + 34 q^{59} - 24 q^{61} - 8 q^{64} - 6 q^{69} + 36 q^{71} + 6 q^{76} - 76 q^{79} - 4 q^{81} + 6 q^{84} + 20 q^{86} - 34 q^{89} + 6 q^{91} + 28 q^{94} + 8 q^{96}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^14 - 4 * q^16 - 6 * q^19 + 12 * q^21 + 4 * q^24 - 2 * q^26 + 18 * q^29 - 4 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 16 * q^41 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 - 6 * q^56 + 34 * q^59 - 24 * q^61 - 8 * q^64 - 6 * q^69 + 36 * q^71 + 6 * q^76 - 76 * q^79 - 4 * q^81 + 6 * q^84 + 20 * q^86 - 34 * q^89 + 6 * q^91 + 28 * q^94 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	0.486319	+	0.280776i	0.183811	+	0.106124i	0.589082	−	0.808073i	$-0.299489\pi$
$7$	0.486319	+	0.280776i	0.183811	+	0.106124i	−0.405271	+	0.914197i	$0.632823\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.06155	−	3.57071i	−0.621582	−	1.07661i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−2.06155	−	3.57071i	−0.621582	−	1.07661i	0.367610	−	0.929980i	$-0.380176\pi$
$12$			1.00000i			0.288675i
$13$	−2.21837	−	2.84233i	−0.615265	−	0.788320i
$13$	−2.21837	−	2.84233i	−0.615265	−	0.788320i
$14$	0.561553			0.150081
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.70469	+	1.56155i	0.655983	+	0.378732i	0.790745	−	0.612146i	$-0.209693\pi$
$17$	2.70469	+	1.56155i	0.655983	+	0.378732i	−0.134761	+	0.990878i	$0.543027\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.280776	−	0.486319i	0.0644145	−	0.111569i	−0.832020	−	0.554746i	$-0.812815\pi$
$19$	0.280776	−	0.486319i	0.0644145	−	0.111569i	0.896434	+	0.443177i	$0.146149\pi$
$20$		0			0
$21$	−0.561553			−0.122541
$22$	−3.57071	−	2.06155i	−0.761279	−	0.439525i
$23$	−4.05703	+	2.34233i	−0.845950	+	0.488409i	−0.859282	−	0.511502i	$-0.829089\pi$
$23$	−4.05703	+	2.34233i	−0.845950	+	0.488409i	0.0133324	+	0.999911i	$0.495756\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	−3.34233	−	1.35234i	−0.655485	−	0.265217i
$27$			1.00000i			0.192450i
$28$	0.486319	−	0.280776i	0.0919057	−	0.0530618i
$29$	1.21922	+	2.11176i	0.226404	+	0.392143i	0.956740	−	0.290945i	$-0.0939697\pi$
$29$	1.21922	+	2.11176i	0.226404	+	0.392143i	−0.730336	+	0.683088i	$0.760636\pi$
$30$		0			0
$31$	−6.68466			−1.20060			−0.600300	−	0.799775i	$-0.704952\pi$
$31$	−6.68466			−1.20060			−0.600300	+	0.799775i	$0.704952\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	3.57071	+	2.06155i	0.621582	+	0.358870i
$34$	3.12311			0.535608
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.57071	+	2.06155i	−0.587022	+	0.338917i	−0.763919	−	0.645312i	$-0.776727\pi$
$37$	−3.57071	+	2.06155i	−0.587022	+	0.338917i	0.176897	+	0.984229i	$0.443394\pi$
$38$		−	0.561553i		−	0.0910959i
$39$	3.34233	+	1.35234i	0.535201	+	0.216548i
$40$		0			0
$41$	−6.12311	−	10.6055i	−0.956268	−	1.65631i	−0.731438	−	0.681908i	$-0.761151\pi$
$41$	−6.12311	−	10.6055i	−0.956268	−	1.65631i	−0.224830	−	0.974398i	$-0.572183\pi$
$42$	−0.486319	+	0.280776i	−0.0750407	+	0.0433247i
$43$	0.379706	+	0.219224i	0.0579047	+	0.0334313i	0.528673	−	0.848826i	$-0.322690\pi$
$43$	0.379706	+	0.219224i	0.0579047	+	0.0334313i	−0.470768	+	0.882257i	$0.656023\pi$
$44$	−4.12311			−0.621582
$45$		0			0
$46$	−2.34233	+	4.05703i	−0.345358	+	0.598177i
$47$			7.00000i			1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$			7.00000i			1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−3.34233	−	5.78908i	−0.477476	−	0.827012i
$50$		0			0
$51$	−3.12311			−0.437322
$52$	−3.57071	+	0.500000i	−0.495169	+	0.0693375i
$53$		−	8.56155i		−	1.17602i	−0.808854	−	0.588010i	$-0.799912\pi$
$53$		−	8.56155i		−	1.17602i	0.808854	−	0.588010i	$-0.200088\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	0.280776	−	0.486319i	0.0375203	−	0.0649871i
$57$			0.561553i			0.0743795i
$58$	2.11176	+	1.21922i	0.277287	+	0.160092i
$59$	3.21922	−	5.57586i	0.419107	−	0.725915i	−0.576743	−	0.816926i	$-0.695676\pi$
$59$	3.21922	−	5.57586i	0.419107	−	0.725915i	0.995850	+	0.0910109i	$0.0290098\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	−5.78908	+	3.34233i	−0.735214	+	0.424476i
$63$	0.486319	−	0.280776i	0.0612704	−	0.0353745i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.12311			0.507519
$67$	−1.94528	+	1.12311i	−0.237653	+	0.137209i	−0.614098	−	0.789230i	$-0.710480\pi$
$67$	−1.94528	+	1.12311i	−0.237653	+	0.137209i	0.376444	+	0.926439i	$0.377147\pi$
$68$	2.70469	−	1.56155i	0.327992	−	0.189366i
$69$	2.34233	−	4.05703i	0.281983	−	0.488409i
$70$		0			0
$71$	6.56155	−	11.3649i	0.778713	−	1.34877i	−0.153971	−	0.988075i	$-0.549206\pi$
$71$	6.56155	−	11.3649i	0.778713	−	1.34877i	0.932684	−	0.360695i	$-0.117461\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	9.36932i		−	1.09660i	−0.836283	−	0.548298i	$-0.815276\pi$
$73$		−	9.36932i		−	1.09660i	0.836283	−	0.548298i	$-0.184724\pi$
$74$	−2.06155	+	3.57071i	−0.239651	+	0.415087i
$75$		0			0
$76$	−0.280776	−	0.486319i	−0.0322073	−	0.0557846i
$77$		−	2.31534i		−	0.263858i
$78$	3.57071	−	0.500000i	0.404304	−	0.0566139i
$79$	−11.5616			−1.30078			−0.650388	−	0.759602i	$-0.725394\pi$
$79$	−11.5616			−1.30078			−0.650388	+	0.759602i	$0.725394\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.6055	−	6.12311i	−1.17118	−	0.676184i
$83$			7.12311i			0.781862i	0.920420	+	0.390931i	$0.127847\pi$
$83$			7.12311i			0.781862i	−0.920420	+	0.390931i	$0.872153\pi$
$84$	−0.280776	+	0.486319i	−0.0306352	+	0.0530618i
$85$		0			0
$86$	0.438447			0.0472790
$87$	−2.11176	−	1.21922i	−0.226404	−	0.130714i
$88$	−3.57071	+	2.06155i	−0.380639	+	0.219762i
$89$	−9.40388	−	16.2880i	−0.996810	−	1.72652i	−0.567529	−	0.823354i	$-0.692100\pi$
$89$	−9.40388	−	16.2880i	−0.996810	−	1.72652i	−0.429281	−	0.903171i	$-0.641233\pi$
$90$		0			0
$91$	−0.280776	−	2.00514i	−0.0294334	−	0.210196i
$92$			4.68466i			0.488409i
$93$	5.78908	−	3.34233i	0.600300	−	0.346583i
$94$	3.50000	+	6.06218i	0.360997	+	0.625266i
$95$		0			0
$96$	1.00000			0.102062
$97$	6.16879	+	3.56155i	0.626346	+	0.361621i	0.779335	−	0.626607i	$-0.215557\pi$
$97$	6.16879	+	3.56155i	0.626346	+	0.361621i	−0.152990	+	0.988228i	$0.548890\pi$
$98$	−5.78908	−	3.34233i	−0.584786	−	0.337626i
$99$	−4.12311			−0.414388
$100$		0			0
$101$	4.43845	+	7.68762i	0.441642	+	0.764946i	0.997812	−	0.0661225i	$-0.0210628\pi$
$101$	4.43845	+	7.68762i	0.441642	+	0.764946i	−0.556170	+	0.831069i	$0.687729\pi$
$102$	−2.70469	+	1.56155i	−0.267804	+	0.154617i
$103$		−	4.56155i		−	0.449463i	−0.974421	−	0.224732i	$-0.927849\pi$
$103$		−	4.56155i		−	0.449463i	0.974421	−	0.224732i	$-0.0721505\pi$
$104$	−2.84233	+	2.21837i	−0.278713	+	0.217529i
$105$		0			0
$106$	−4.28078	−	7.41452i	−0.415786	−	0.720162i
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	−0.413936	−	0.910306i	$-0.635846\pi$
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	0.581380	+	0.813632i	$0.302513\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	3.75379			0.359548			0.179774	−	0.983708i	$-0.442463\pi$
$109$	3.75379			0.359548			0.179774	+	0.983708i	$0.442463\pi$
$110$		0			0
$111$	2.06155	−	3.57071i	0.195674	−	0.338917i
$112$		−	0.561553i		−	0.0530618i
$113$	7.52113	+	4.34233i	0.707529	+	0.408492i	0.810145	−	0.586229i	$-0.199388\pi$
$113$	7.52113	+	4.34233i	0.707529	+	0.408492i	−0.102617	+	0.994721i	$0.532721\pi$
$114$	0.280776	+	0.486319i	0.0262971	+	0.0455479i
$115$		0			0
$116$	2.43845			0.226404
$117$	−3.57071	+	0.500000i	−0.330113	+	0.0462250i
$118$		−	6.43845i		−	0.592707i
$119$	0.876894	+	1.51883i	0.0803848	+	0.139231i
$120$		0			0
$121$	−3.00000	+	5.19615i	−0.272727	+	0.472377i
$122$			6.00000i			0.543214i
$123$	10.6055	+	6.12311i	0.956268	+	0.552102i
$124$	−3.34233	+	5.78908i	−0.300150	+	0.519875i
$125$		0			0
$126$	0.280776	−	0.486319i	0.0250136	−	0.0433247i
$127$	−7.41452	+	4.28078i	−0.657932	+	0.379857i	−0.791489	−	0.611184i	$-0.790694\pi$
$127$	−7.41452	+	4.28078i	−0.657932	+	0.379857i	0.133556	+	0.991041i	$0.457360\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−0.438447			−0.0386031
$130$		0			0
$131$	−2.12311			−0.185497			−0.0927483	−	0.995690i	$-0.529565\pi$
$131$	−2.12311			−0.185497			−0.0927483	+	0.995690i	$0.529565\pi$
$132$	3.57071	−	2.06155i	0.310791	−	0.179435i
$133$	0.273094	−	0.157671i	0.0236802	−	0.0136718i
$134$	−1.12311	+	1.94528i	−0.0970215	+	0.168046i
$135$		0			0
$136$	1.56155	−	2.70469i	0.133902	−	0.231925i
$137$	−10.2258	−	5.90388i	−0.873651	−	0.504403i	−0.00509126	−	0.999987i	$-0.501621\pi$
$137$	−10.2258	−	5.90388i	−0.873651	−	0.504403i	−0.868560	+	0.495584i	$0.834954\pi$
$138$		−	4.68466i		−	0.398785i
$139$	6.28078	−	10.8786i	0.532729	−	0.922713i	−0.466541	−	0.884500i	$-0.654500\pi$
$139$	6.28078	−	10.8786i	0.532729	−	0.922713i	0.999270	−	0.0382133i	$-0.0121666\pi$
$140$		0			0
$141$	−3.50000	−	6.06218i	−0.294753	−	0.510527i
$142$		−	13.1231i		−	1.10127i
$143$	−5.57586	+	13.7808i	−0.466277	+	1.15241i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−4.68466	−	8.11407i	−0.387705	−	0.671525i
$147$	5.78908	+	3.34233i	0.477476	+	0.275671i
$148$			4.12311i			0.338917i
$149$	−1.09612	+	1.89853i	−0.0897975	+	0.155534i	−0.907425	−	0.420213i	$-0.861955\pi$
$149$	−1.09612	+	1.89853i	−0.0897975	+	0.155534i	0.817628	+	0.575747i	$0.195289\pi$
$150$		0			0
$151$	−15.3693			−1.25074			−0.625369	−	0.780329i	$-0.715051\pi$
$151$	−15.3693			−1.25074			−0.625369	+	0.780329i	$0.715051\pi$
$152$	−0.486319	−	0.280776i	−0.0394457	−	0.0227740i
$153$	2.70469	−	1.56155i	0.218661	−	0.126244i
$154$	−1.15767	−	2.00514i	−0.0932878	−	0.161579i
$155$		0			0
$156$	2.84233	−	2.21837i	0.227568	−	0.177612i
$157$			13.8769i			1.10750i	0.832684	+	0.553748i	$0.186803\pi$
$157$			13.8769i			1.10750i	−0.832684	+	0.553748i	$0.813197\pi$
$158$	−10.0126	+	5.78078i	−0.796560	+	0.459894i
$159$	4.28078	+	7.41452i	0.339488	+	0.588010i
$160$		0			0
$161$	−2.63068			−0.207327
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−12.5041	−	7.21922i	−0.979394	−	0.565453i	−0.0773067	−	0.997007i	$-0.524632\pi$
$163$	−12.5041	−	7.21922i	−0.979394	−	0.565453i	−0.902087	+	0.431554i	$0.857965\pi$
$164$	−12.2462			−0.956268
$165$		0			0
$166$	3.56155	+	6.16879i	0.276430	+	0.478791i
$167$	3.78394	−	2.18466i	0.292810	−	0.169054i	−0.346398	−	0.938087i	$-0.612595\pi$
$167$	3.78394	−	2.18466i	0.292810	−	0.169054i	0.639208	+	0.769034i	$0.279262\pi$
$168$			0.561553i			0.0433247i
$169$	−3.15767	+	12.6107i	−0.242898	+	0.970052i
$170$		0			0
$171$	−0.280776	−	0.486319i	−0.0214715	−	0.0371897i
$172$	0.379706	−	0.219224i	0.0289523	−	0.0167156i
$173$	17.4739	+	10.0885i	1.32851	+	0.767018i	0.985070	−	0.172156i	$-0.0550732\pi$
$173$	17.4739	+	10.0885i	1.32851	+	0.767018i	0.343444	+	0.939173i	$0.388407\pi$
$174$	−2.43845			−0.184858
$175$		0			0
$176$	−2.06155	+	3.57071i	−0.155395	+	0.269153i
$177$			6.43845i			0.483943i
$178$	−16.2880	−	9.40388i	−1.22084	−	0.704851i
$179$	−6.34233	−	10.9852i	−0.474048	−	0.821075i	0.525511	−	0.850787i	$-0.323874\pi$
$179$	−6.34233	−	10.9852i	−0.474048	−	0.821075i	−0.999559	+	0.0297120i	$0.990541\pi$
$180$		0			0
$181$	2.87689			0.213838			0.106919	−	0.994268i	$-0.465901\pi$
$181$	2.87689			0.213838			0.106919	+	0.994268i	$0.465901\pi$
$182$	−1.24573	−	1.59612i	−0.0923398	−	0.118312i
$183$		−	6.00000i		−	0.443533i
$184$	2.34233	+	4.05703i	0.172679	+	0.299088i
$185$		0			0
$186$	3.34233	−	5.78908i	0.245071	−	0.424476i
$187$		−	12.8769i		−	0.941652i
$188$	6.06218	+	3.50000i	0.442130	+	0.255264i
$189$	−0.280776	+	0.486319i	−0.0204235	+	0.0353745i
$190$		0			0
$191$	−5.43845	+	9.41967i	−0.393512	+	0.681583i	−0.992910	−	0.118868i	$-0.962073\pi$
$191$	−5.43845	+	9.41967i	−0.393512	+	0.681583i	0.599398	+	0.800451i	$0.295407\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	7.12311			0.511409
$195$		0			0
$196$	−6.68466			−0.477476
$197$	11.0918	−	6.40388i	0.790262	−	0.456258i	−0.0497931	−	0.998760i	$-0.515856\pi$
$197$	11.0918	−	6.40388i	0.790262	−	0.456258i	0.840055	+	0.542502i	$0.182523\pi$
$198$	−3.57071	+	2.06155i	−0.253760	+	0.146508i
$199$	1.43845	−	2.49146i	0.101969	−	0.176615i	−0.810527	−	0.585701i	$-0.800819\pi$
$199$	1.43845	−	2.49146i	0.101969	−	0.176615i	0.912496	+	0.409086i	$0.134152\pi$
$200$		0			0
$201$	1.12311	−	1.94528i	0.0792178	−	0.137209i
$202$	7.68762	+	4.43845i	0.540899	+	0.312288i
$203$			1.36932i			0.0961072i
$204$	−1.56155	+	2.70469i	−0.109331	+	0.189366i
$205$		0			0
$206$	−2.28078	−	3.95042i	−0.158909	−	0.275239i
$207$			4.68466i			0.325606i
$208$	−1.35234	+	3.34233i	−0.0937682	+	0.231749i
$209$	−2.31534			−0.160156
$210$		0			0
$211$	10.9654	+	18.9927i	0.754892	+	1.30751i	0.945428	+	0.325831i	$0.105644\pi$
$211$	10.9654	+	18.9927i	0.754892	+	1.30751i	−0.190536	+	0.981680i	$0.561023\pi$
$212$	−7.41452	−	4.28078i	−0.509231	−	0.294005i
$213$			13.1231i			0.899180i
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−3.25088	−	1.87689i	−0.220684	−	0.127412i
$218$	3.25088	−	1.87689i	0.220177	−	0.127119i
$219$	4.68466	+	8.11407i	0.316560	+	0.548298i
$220$		0			0
$221$	−1.56155	−	11.1517i	−0.105041	−	0.750146i
$222$		−	4.12311i		−	0.276725i
$223$	−23.6427	+	13.6501i	−1.58323	+	0.914078i	−0.588845	+	0.808246i	$0.700417\pi$
$223$	−23.6427	+	13.6501i	−1.58323	+	0.914078i	−0.994384	+	0.105832i	$0.966249\pi$
$224$	−0.280776	−	0.486319i	−0.0187602	−	0.0324936i
$225$		0			0
$226$	8.68466			0.577695
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.948790	−	0.315906i	$-0.102309\pi$
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.200812	+	0.979630i	$0.435642\pi$
$228$	0.486319	+	0.280776i	0.0322073	+	0.0185949i
$229$	24.2462			1.60223			0.801117	−	0.598507i	$-0.204239\pi$
$229$	24.2462			1.60223			0.801117	+	0.598507i	$0.204239\pi$
$230$		0			0
$231$	1.15767	+	2.00514i	0.0761691	+	0.131929i
$232$	2.11176	−	1.21922i	0.138644	−	0.0800460i
$233$			5.31534i			0.348220i	0.984726	+	0.174110i	$0.0557048\pi$
$233$			5.31534i			0.348220i	−0.984726	+	0.174110i	$0.944295\pi$
$234$	−2.84233	+	2.21837i	−0.185809	+	0.145019i
$235$		0			0
$236$	−3.21922	−	5.57586i	−0.209554	−	0.362957i
$237$	10.0126	−	5.78078i	0.650388	−	0.375502i
$238$	1.51883	+	0.876894i	0.0984508	+	0.0568406i
$239$	11.3693			0.735420			0.367710	−	0.929941i	$-0.380142\pi$
$239$	11.3693			0.735420			0.367710	+	0.929941i	$0.380142\pi$
$240$		0			0
$241$	14.0616	−	24.3553i	0.905784	−	1.56886i	0.0859232	−	0.996302i	$-0.472616\pi$
$241$	14.0616	−	24.3553i	0.905784	−	1.56886i	0.819861	−	0.572563i	$-0.194051\pi$
$242$			6.00000i			0.385695i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	3.00000	+	5.19615i	0.192055	+	0.332650i
$245$		0			0
$246$	12.2462			0.780790
$247$	−2.00514	+	0.280776i	−0.127584	+	0.0178654i
$248$			6.68466i			0.424476i
$249$	−3.56155	−	6.16879i	−0.225704	−	0.390931i
$250$		0			0
$251$	4.06155	−	7.03482i	0.256363	−	0.444034i	−0.708902	−	0.705307i	$-0.750809\pi$
$251$	4.06155	−	7.03482i	0.256363	−	0.444034i	0.965265	+	0.261273i	$0.0841424\pi$
$252$		−	0.561553i		−	0.0353745i
$253$	16.7276	+	9.65767i	1.05165	+	0.607173i
$254$	−4.28078	+	7.41452i	−0.268600	+	0.465229i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.81645	+	2.78078i	−0.300442	+	0.173460i	−0.642641	−	0.766167i	$-0.722161\pi$
$257$	−4.81645	+	2.78078i	−0.300442	+	0.173460i	0.342200	+	0.939627i	$0.388828\pi$
$258$	−0.379706	+	0.219224i	−0.0236395	+	0.0136483i
$259$	−2.31534			−0.143868
$260$		0			0
$261$	2.43845			0.150936
$262$	−1.83866	+	1.06155i	−0.113593	+	0.0655830i
$263$	11.2583	−	6.50000i	0.694218	−	0.400807i	−0.110972	−	0.993824i	$-0.535396\pi$
$263$	11.2583	−	6.50000i	0.694218	−	0.400807i	0.805190	+	0.593016i	$0.202063\pi$
$264$	2.06155	−	3.57071i	0.126880	−	0.219762i
$265$		0			0
$266$	0.157671	−	0.273094i	0.00966742	−	0.0167445i
$267$	16.2880	+	9.40388i	0.996810	+	0.575508i
$268$			2.24621i			0.137209i
$269$	10.6847	−	18.5064i	0.651455	−	1.12835i	−0.331315	−	0.943520i	$-0.607492\pi$
$269$	10.6847	−	18.5064i	0.651455	−	1.12835i	0.982770	−	0.184833i	$-0.0591745\pi$
$270$		0			0
$271$	6.58854	+	11.4117i	0.400225	+	0.693211i	0.993753	−	0.111603i	$-0.0355985\pi$
$271$	6.58854	+	11.4117i	0.400225	+	0.693211i	−0.593528	+	0.804814i	$0.702265\pi$
$272$		−	3.12311i		−	0.189366i
$273$	1.24573	+	1.59612i	0.0753951	+	0.0966015i
$274$	−11.8078			−0.713333
$275$		0			0
$276$	−2.34233	−	4.05703i	−0.140992	−	0.244205i
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	0.525792	−	0.850613i	$-0.323769\pi$
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	−0.473757	+	0.880656i	$0.657103\pi$
$278$		−	12.5616i		−	0.753392i
$279$	−3.34233	+	5.78908i	−0.200100	+	0.346583i
$280$		0			0
$281$	16.2462			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$281$	16.2462			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$282$	−6.06218	−	3.50000i	−0.360997	−	0.208422i
$283$	−13.4767	+	7.78078i	−0.801107	+	0.462519i	−0.843858	−	0.536567i	$-0.819721\pi$
$283$	−13.4767	+	7.78078i	−0.801107	+	0.462519i	0.0427513	+	0.999086i	$0.486388\pi$
$284$	−6.56155	−	11.3649i	−0.389357	−	0.674385i
$285$		0			0
$286$	2.06155	+	14.7224i	0.121902	+	0.870556i
$287$		−	6.87689i		−	0.405930i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−3.62311	−	6.27540i	−0.213124	−	0.369141i
$290$		0			0
$291$	−7.12311			−0.417564
$292$	−8.11407	−	4.68466i	−0.474840	−	0.274149i
$293$	3.40423	+	1.96543i	0.198877	+	0.114822i	0.596132	−	0.802887i	$-0.296704\pi$
$293$	3.40423	+	1.96543i	0.198877	+	0.114822i	−0.397254	+	0.917709i	$0.630037\pi$
$294$	6.68466			0.389857
$295$		0			0
$296$	2.06155	+	3.57071i	0.119825	+	0.207544i
$297$	3.57071	−	2.06155i	0.207194	−	0.119623i
$298$			2.19224i			0.126993i
$299$	15.6577	+	6.33527i	0.905506	+	0.366378i
$300$		0			0
$301$	0.123106	+	0.213225i	0.00709569	+	0.0122901i
$302$	−13.3102	+	7.68466i	−0.765917	+	0.442202i
$303$	−7.68762	−	4.43845i	−0.441642	−	0.254982i
$304$	−0.561553			−0.0322073
$305$		0			0
$306$	1.56155	−	2.70469i	0.0892680	−	0.154617i
$307$			25.6155i			1.46196i	0.682401	+	0.730978i	$0.260936\pi$
$307$			25.6155i			1.46196i	−0.682401	+	0.730978i	$0.739064\pi$
$308$	−2.00514	−	1.15767i	−0.114254	−	0.0659644i
$309$	2.28078	+	3.95042i	0.129749	+	0.224732i
$310$		0			0
$311$	30.7386			1.74303			0.871514	−	0.490371i	$-0.163139\pi$
$311$	30.7386			1.74303			0.871514	+	0.490371i	$0.163139\pi$
$312$	1.35234	−	3.34233i	0.0765614	−	0.189222i
$313$		−	31.3693i		−	1.77310i	−0.462634	−	0.886549i	$-0.653096\pi$
$313$		−	31.3693i		−	1.77310i	0.462634	−	0.886549i	$-0.346904\pi$
$314$	6.93845	+	12.0177i	0.391559	+	0.678200i
$315$		0			0
$316$	−5.78078	+	10.0126i	−0.325194	+	0.563253i
$317$		−	24.8078i		−	1.39334i	−0.717390	−	0.696671i	$-0.754664\pi$
$317$		−	24.8078i		−	1.39334i	0.717390	−	0.696671i	$-0.245336\pi$
$318$	7.41452	+	4.28078i	0.415786	+	0.240054i
$319$	5.02699	−	8.70700i	0.281457	−	0.487498i
$320$		0			0
$321$	−1.00000	+	1.73205i	−0.0558146	+	0.0966736i
$322$	−2.27824	+	1.31534i	−0.126961	+	0.0733011i
$323$	1.51883	−	0.876894i	0.0845097	−	0.0487917i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−14.4384			−0.799672
$327$	−3.25088	+	1.87689i	−0.179774	+	0.103792i
$328$	−10.6055	+	6.12311i	−0.585592	+	0.338092i
$329$	−1.96543	+	3.40423i	−0.108358	+	0.187681i
$330$		0			0
$331$	−15.3693	+	26.6204i	−0.844774	+	1.46319i	0.0410432	+	0.999157i	$0.486932\pi$
$331$	−15.3693	+	26.6204i	−0.844774	+	1.46319i	−0.885817	+	0.464034i	$0.846401\pi$
$332$	6.16879	+	3.56155i	0.338556	+	0.195466i
$333$			4.12311i			0.225945i
$334$	2.18466	−	3.78394i	0.119539	−	0.207048i
$335$		0			0
$336$	0.280776	+	0.486319i	0.0153176	+	0.0265309i
$337$		−	6.00000i		−	0.326841i	−0.986557	−	0.163420i	$-0.947747\pi$
$337$		−	6.00000i		−	0.326841i	0.986557	−	0.163420i	$-0.0522527\pi$
$338$	3.57071	+	12.5000i	0.194221	+	0.679910i
$339$	−8.68466			−0.471686
$340$		0			0
$341$	13.7808	+	23.8690i	0.746271	+	1.29258i
$342$	−0.486319	−	0.280776i	−0.0262971	−	0.0151826i
$343$		−	7.68466i		−	0.414933i
$344$	0.219224	−	0.379706i	0.0118197	−	0.0204724i
$345$		0			0
$346$	20.1771			1.08473
$347$	−0.759413	−	0.438447i	−0.0407674	−	0.0235371i	0.479478	−	0.877554i	$-0.340826\pi$
$347$	−0.759413	−	0.438447i	−0.0407674	−	0.0235371i	−0.520245	+	0.854017i	$0.674159\pi$
$348$	−2.11176	+	1.21922i	−0.113202	+	0.0653572i
$349$	4.24621	+	7.35465i	0.227294	+	0.393686i	0.957005	−	0.290070i	$-0.0936787\pi$
$349$	4.24621	+	7.35465i	0.227294	+	0.393686i	−0.729711	+	0.683756i	$0.760345\pi$
$350$		0			0
$351$	2.84233	−	2.21837i	0.151712	−	0.118408i
$352$			4.12311i			0.219762i
$353$	22.3969	−	12.9309i	1.19207	−	0.688241i	0.233293	−	0.972407i	$-0.425050\pi$
$353$	22.3969	−	12.9309i	1.19207	−	0.688241i	0.958775	+	0.284166i	$0.0917166\pi$
$354$	3.21922	+	5.57586i	0.171100	+	0.296354i
$355$		0			0
$356$	−18.8078			−0.996810
$357$	−1.51883	−	0.876894i	−0.0803848	−	0.0464102i
$358$	−10.9852	−	6.34233i	−0.580588	−	0.335203i
$359$	−13.1231			−0.692611			−0.346306	−	0.938122i	$-0.612564\pi$
$359$	−13.1231			−0.692611			−0.346306	+	0.938122i	$0.612564\pi$
$360$		0			0
$361$	9.34233	+	16.1814i	0.491702	+	0.851652i
$362$	2.49146	−	1.43845i	0.130948	−	0.0756031i
$363$		−	6.00000i		−	0.314918i
$364$	−1.87689	−	0.759413i	−0.0983760	−	0.0398040i
$365$		0			0
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	10.8188	−	6.24621i	0.564734	−	0.326050i	−0.190309	−	0.981724i	$-0.560949\pi$
$367$	10.8188	−	6.24621i	0.564734	−	0.326050i	0.755044	+	0.655675i	$0.227616\pi$
$368$	4.05703	+	2.34233i	0.211487	+	0.122102i
$369$	−12.2462			−0.637512
$370$		0			0
$371$	2.40388	−	4.16365i	0.124803	−	0.216166i
$372$		−	6.68466i		−	0.346583i
$373$	−22.3502	−	12.9039i	−1.15725	−	0.668138i	−0.206605	−	0.978424i	$-0.566242\pi$
$373$	−22.3502	−	12.9039i	−1.15725	−	0.668138i	−0.950643	+	0.310287i	$0.899575\pi$
$374$	−6.43845	−	11.1517i	−0.332924	−	0.576642i
$375$		0			0
$376$	7.00000			0.360997
$377$	3.29762	−	8.15009i	0.169836	−	0.419751i
$378$			0.561553i			0.0288832i
$379$	−8.84233	−	15.3154i	−0.454200	−	0.786697i	0.544442	−	0.838799i	$-0.316741\pi$
$379$	−8.84233	−	15.3154i	−0.454200	−	0.786697i	−0.998642	+	0.0521012i	$0.983408\pi$
$380$		0			0
$381$	4.28078	−	7.41452i	0.219311	−	0.379857i
$382$			10.8769i			0.556510i
$383$	0.166481	+	0.0961180i	0.00850679	+	0.00491140i	0.504247	−	0.863559i	$-0.331770\pi$
$383$	0.166481	+	0.0961180i	0.00850679	+	0.00491140i	−0.495741	+	0.868471i	$0.665103\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$		0			0
$387$	0.379706	−	0.219224i	0.0193016	−	0.0111438i
$388$	6.16879	−	3.56155i	0.313173	−	0.180810i
$389$	18.0540			0.915373			0.457686	−	0.889114i	$-0.348678\pi$
$389$	18.0540			0.915373			0.457686	+	0.889114i	$0.348678\pi$
$390$		0			0
$391$	−14.6307			−0.739905
$392$	−5.78908	+	3.34233i	−0.292393	+	0.168813i
$393$	1.83866	−	1.06155i	0.0927483	−	0.0535483i
$394$	6.40388	−	11.0918i	0.322623	−	0.558799i
$395$		0			0
$396$	−2.06155	+	3.57071i	−0.103597	+	0.179435i
$397$	17.4271	+	10.0616i	0.874642	+	0.504975i	0.868888	−	0.495009i	$-0.164835\pi$
$397$	17.4271	+	10.0616i	0.874642	+	0.504975i	0.00575403	+	0.999983i	$0.498168\pi$
$398$		−	2.87689i		−	0.144206i
$399$	−0.157671	+	0.273094i	−0.00789341	+	0.0136718i
$400$		0			0
$401$	−0.157671	−	0.273094i	−0.00787370	−	0.0136377i	0.862062	−	0.506803i	$-0.169173\pi$
$401$	−0.157671	−	0.273094i	−0.00787370	−	0.0136377i	−0.869935	+	0.493166i	$0.835840\pi$
$402$		−	2.24621i		−	0.112031i
$403$	14.8290	+	19.0000i	0.738687	+	0.946457i
$404$	8.87689			0.441642
$405$		0			0
$406$	0.684658	+	1.18586i	0.0339790	+	0.0588534i
$407$	14.7224	+	8.50000i	0.729764	+	0.421329i
$408$			3.12311i			0.154617i
$409$	−9.40388	+	16.2880i	−0.464992	+	0.805390i	−0.999201	−	0.0399625i	$-0.987276\pi$
$409$	−9.40388	+	16.2880i	−0.464992	+	0.805390i	0.534209	+	0.845352i	$0.320609\pi$
$410$		0			0
$411$	11.8078			0.582434
$412$	−3.95042	−	2.28078i	−0.194623	−	0.112366i
$413$	3.13114	−	1.80776i	0.154073	−	0.0889543i
$414$	2.34233	+	4.05703i	0.115119	+	0.199392i
$415$		0			0
$416$	0.500000	+	3.57071i	0.0245145	+	0.175069i
$417$			12.5616i			0.615142i
$418$	−2.00514	+	1.15767i	−0.0980748	+	0.0566235i
$419$	16.2462	+	28.1393i	0.793679	+	1.37469i	0.923674	+	0.383178i	$0.125171\pi$
$419$	16.2462	+	28.1393i	0.793679	+	1.37469i	−0.129995	+	0.991515i	$0.541496\pi$
$420$		0			0
$421$	−32.4924			−1.58358			−0.791792	−	0.610791i	$-0.790852\pi$
$421$	−32.4924			−1.58358			−0.791792	+	0.610791i	$0.790852\pi$
$422$	18.9927	+	10.9654i	0.924550	+	0.533789i
$423$	6.06218	+	3.50000i	0.294753	+	0.170176i
$424$	−8.56155			−0.415786
$425$		0			0
$426$	6.56155	+	11.3649i	0.317908	+	0.550633i
$427$	−2.91791	+	1.68466i	−0.141208	+	0.0815263i
$428$		−	2.00000i		−	0.0966736i
$429$	−2.06155	−	14.7224i	−0.0995327	−	0.710806i
$430$		0			0
$431$	11.3693	+	19.6922i	0.547641	+	0.948542i	0.998436	+	0.0559140i	$0.0178073\pi$
$431$	11.3693	+	19.6922i	0.547641	+	0.948542i	−0.450795	+	0.892628i	$0.648859\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−16.2281	−	9.36932i	−0.779874	−	0.450261i	0.0565114	−	0.998402i	$-0.482002\pi$
$433$	−16.2281	−	9.36932i	−0.779874	−	0.450261i	−0.836386	+	0.548141i	$0.815336\pi$
$434$	−3.75379			−0.180188
$435$		0			0
$436$	1.87689	−	3.25088i	0.0898869	−	0.155689i
$437$			2.63068i			0.125843i
$438$	8.11407	+	4.68466i	0.387705	+	0.223842i
$439$	12.5616	+	21.7572i	0.599530	+	1.03842i	0.992890	+	0.119032i	$0.0379792\pi$
$439$	12.5616	+	21.7572i	0.599530	+	1.03842i	−0.393360	+	0.919384i	$0.628687\pi$
$440$		0			0
$441$	−6.68466			−0.318317
$442$	−6.92820	−	8.87689i	−0.329541	−	0.422231i
$443$			13.1231i			0.623498i	0.950165	+	0.311749i	$0.100915\pi$
$443$			13.1231i			0.623498i	−0.950165	+	0.311749i	$0.899085\pi$
$444$	−2.06155	−	3.57071i	−0.0978370	−	0.169459i
$445$		0			0
$446$	−13.6501	+	23.6427i	−0.646351	+	1.11951i
$447$		−	2.19224i		−	0.103689i
$448$	−0.486319	−	0.280776i	−0.0229764	−	0.0132654i
$449$	−10.0885	+	17.4739i	−0.476108	+	0.824643i	−0.999625	−	0.0273722i	$-0.991286\pi$
$449$	−10.0885	+	17.4739i	−0.476108	+	0.824643i	0.523518	+	0.852015i	$0.324619\pi$
$450$		0			0
$451$	−25.2462	+	43.7277i	−1.18880	+	2.05906i
$452$	7.52113	−	4.34233i	0.353764	−	0.204246i
$453$	13.3102	−	7.68466i	0.625369	−	0.361057i
$454$	20.0000			0.938647
$455$		0			0
$456$	0.561553			0.0262971
$457$	17.5337	−	10.1231i	0.820193	−	0.473539i	−0.0302897	−	0.999541i	$-0.509643\pi$
$457$	17.5337	−	10.1231i	0.820193	−	0.473539i	0.850483	+	0.526002i	$0.176310\pi$
$458$	20.9978	−	12.1231i	0.981164	−	0.566476i
$459$	−1.56155	+	2.70469i	−0.0728870	+	0.126244i
$460$		0			0
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	−0.268632	−	0.963243i	$-0.586572\pi$
$461$	15.0270	−	26.0275i	0.699877	−	1.21222i	0.968509	−	0.248979i	$-0.0800950\pi$
$462$	2.00514	+	1.15767i	0.0932878	+	0.0538597i
$463$			7.61553i			0.353924i	0.984218	+	0.176962i	$0.0566269\pi$
$463$			7.61553i			0.353924i	−0.984218	+	0.176962i	$0.943373\pi$
$464$	1.21922	−	2.11176i	0.0566010	−	0.0980359i
$465$		0			0
$466$	2.65767	+	4.60322i	0.123114	+	0.213240i
$467$		−	17.8617i		−	0.826543i	−0.910608	−	0.413271i	$-0.864386\pi$
$467$		−	17.8617i		−	0.826543i	0.910608	−	0.413271i	$-0.135614\pi$
$468$	−1.35234	+	3.34233i	−0.0625121	+	0.154499i
$469$	−1.26137			−0.0582445
$470$		0			0
$471$	−6.93845	−	12.0177i	−0.319707	−	0.553748i
$472$	−5.57586	−	3.21922i	−0.256650	−	0.148177i
$473$		−	1.80776i		−	0.0831211i
$474$	5.78078	−	10.0126i	0.265520	−	0.459894i
$475$		0			0
$476$	1.75379			0.0803848
$477$	−7.41452	−	4.28078i	−0.339488	−	0.196003i
$478$	9.84612	−	5.68466i	0.450351	−	0.260010i
$479$	−19.1231	−	33.1222i	−0.873757	−	1.51339i	−0.858081	−	0.513514i	$-0.828343\pi$
$479$	−19.1231	−	33.1222i	−0.873757	−	1.51339i	−0.0156760	−	0.999877i	$-0.504990\pi$
$480$		0			0
$481$	13.7808	+	5.57586i	0.628349	+	0.254237i
$482$		−	28.1231i		−	1.28097i
$483$	2.27824	−	1.31534i	0.103663	−	0.0598501i
$484$	3.00000	+	5.19615i	0.136364	+	0.236189i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−11.3051	−	6.52699i	−0.512282	−	0.295766i	0.221489	−	0.975163i	$-0.428908\pi$
$487$	−11.3051	−	6.52699i	−0.512282	−	0.295766i	−0.733771	+	0.679397i	$0.762242\pi$
$488$	5.19615	+	3.00000i	0.235219	+	0.135804i
$489$	14.4384			0.652929
$490$		0			0
$491$	8.71922	+	15.1021i	0.393493	+	0.681550i	0.992908	−	0.118889i	$-0.0379332\pi$
$491$	8.71922	+	15.1021i	0.393493	+	0.681550i	−0.599415	+	0.800439i	$0.704600\pi$
$492$	10.6055	−	6.12311i	0.478134	−	0.276051i
$493$			7.61553i			0.342986i
$494$	−1.59612	+	1.24573i	−0.0718127	+	0.0560481i
$495$		0			0
$496$	3.34233	+	5.78908i	0.150075	+	0.259938i
$497$	6.38202	−	3.68466i	0.286273	−	0.165280i
$498$	−6.16879	−	3.56155i	−0.276430	−	0.159597i
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$	−2.18466	+	3.78394i	−0.0976033	+	0.169054i
$502$		−	8.12311i		−	0.362552i
$503$	−37.2858	−	21.5270i	−1.66249	−	0.959841i	−0.971519	−	0.236962i	$-0.923848\pi$
$503$	−37.2858	−	21.5270i	−1.66249	−	0.959841i	−0.690974	−	0.722879i	$-0.742818\pi$
$504$	−0.280776	−	0.486319i	−0.0125068	−	0.0216624i
$505$		0			0
$506$	19.3153			0.858672
$507$	−3.57071	−	12.5000i	−0.158581	−	0.555144i
$508$			8.56155i			0.379857i
$509$	20.2732	+	35.1142i	0.898594	+	1.55641i	0.829293	+	0.558814i	$0.188744\pi$
$509$	20.2732	+	35.1142i	0.898594	+	1.55641i	0.0693009	+	0.997596i	$0.477923\pi$
$510$		0			0
$511$	2.63068	−	4.55648i	0.116375	−	0.201567i
$512$			1.00000i			0.0441942i
$513$	0.486319	+	0.280776i	0.0214715	+	0.0123966i
$514$	−2.78078	+	4.81645i	−0.122655	+	0.212444i
$515$		0			0
$516$	−0.219224	+	0.379706i	−0.00965078	+	0.0167156i
$517$	24.9950	−	14.4309i	1.09928	−	0.634669i
$518$	−2.00514	+	1.15767i	−0.0881010	+	0.0508651i
$519$	−20.1771			−0.885676
$520$		0			0
$521$	−6.31534			−0.276680			−0.138340	−	0.990385i	$-0.544177\pi$
$521$	−6.31534			−0.276680			−0.138340	+	0.990385i	$0.544177\pi$
$522$	2.11176	−	1.21922i	0.0924291	−	0.0533640i
$523$	25.8143	−	14.9039i	1.12878	−	0.651701i	0.185152	−	0.982710i	$-0.440722\pi$
$523$	25.8143	−	14.9039i	1.12878	−	0.651701i	0.943628	+	0.331009i	$0.107389\pi$
$524$	−1.06155	+	1.83866i	−0.0463741	+	0.0803224i
$525$		0			0
$526$	6.50000	−	11.2583i	0.283413	−	0.490887i
$527$	−18.0799	−	10.4384i	−0.787574	−	0.454706i
$528$		−	4.12311i		−	0.179435i
$529$	−0.526988	+	0.912769i	−0.0229125	+	0.0396856i
$530$		0			0
$531$	−3.21922	−	5.57586i	−0.139702	−	0.241972i
$532$		−	0.315342i		−	0.0136718i
$533$	−16.5611	+	40.9309i	−0.717341	+	1.77291i
$534$	18.8078			0.813892
$535$		0			0
$536$	1.12311	+	1.94528i	0.0485108	+	0.0840231i
$537$	10.9852	+	6.34233i	0.474048	+	0.273692i
$538$		−	21.3693i		−	0.921297i
$539$	−13.7808	+	23.8690i	−0.593580	+	1.02811i
$540$		0			0
$541$	−27.3693			−1.17670			−0.588349	−	0.808607i	$-0.700222\pi$
$541$	−27.3693			−1.17670			−0.588349	+	0.808607i	$0.700222\pi$
$542$	11.4117	+	6.58854i	0.490174	+	0.283002i
$543$	−2.49146	+	1.43845i	−0.106919	+	0.0617297i
$544$	−1.56155	−	2.70469i	−0.0669510	−	0.115963i
$545$		0			0
$546$	1.87689	+	0.759413i	0.0803237	+	0.0324999i
$547$		−	5.61553i		−	0.240103i	−0.992768	−	0.120051i	$-0.961694\pi$
$547$		−	5.61553i		−	0.240103i	0.992768	−	0.120051i	$-0.0383059\pi$
$548$	−10.2258	+	5.90388i	−0.436826	+	0.252201i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$		0			0
$551$	1.36932			0.0583349
$552$	−4.05703	−	2.34233i	−0.172679	−	0.0996962i
$553$	−5.62260	−	3.24621i	−0.239097	−	0.138043i
$554$	1.00000			0.0424859
$555$		0			0
$556$	−6.28078	−	10.8786i	−0.266364	−	0.461356i
$557$	−7.41452	+	4.28078i	−0.314163	+	0.181382i	−0.648788	−	0.760969i	$-0.724724\pi$
$557$	−7.41452	+	4.28078i	−0.314163	+	0.181382i	0.334625	+	0.942352i	$0.391390\pi$
$558$			6.68466i			0.282984i
$559$	−0.219224	−	1.56557i	−0.00927217	−	0.0662165i
$560$		0			0
$561$	6.43845	+	11.1517i	0.271831	+	0.470826i
$562$	14.0696	−	8.12311i	0.593492	−	0.342653i
$563$	−28.5657	−	16.4924i	−1.20390	−	0.695073i	−0.242481	−	0.970156i	$-0.577961\pi$
$563$	−28.5657	−	16.4924i	−1.20390	−	0.695073i	−0.961420	+	0.275083i	$0.911295\pi$
$564$	−7.00000			−0.294753
$565$		0			0
$566$	−7.78078	+	13.4767i	−0.327050	+	0.566468i
$567$		−	0.561553i		−	0.0235830i
$568$	−11.3649	−	6.56155i	−0.476862	−	0.275317i
$569$	13.0885	+	22.6700i	0.548700	+	0.950377i	0.998364	+	0.0571787i	$0.0182105\pi$
$569$	13.0885	+	22.6700i	0.548700	+	0.950377i	−0.449664	+	0.893198i	$0.648456\pi$
$570$		0			0
$571$	23.6847			0.991172			0.495586	−	0.868559i	$-0.334953\pi$
$571$	23.6847			0.991172			0.495586	+	0.868559i	$0.334953\pi$
$572$	9.14657	+	11.7192i	0.382437	+	0.490005i
$573$		−	10.8769i		−	0.454389i
$574$	−3.43845	−	5.95557i	−0.143518	−	0.248580i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$		−	40.7386i		−	1.69597i	−0.530019	−	0.847986i	$-0.677815\pi$
$577$		−	40.7386i		−	1.69597i	0.530019	−	0.847986i	$-0.322185\pi$
$578$	−6.27540	−	3.62311i	−0.261022	−	0.150701i
$579$		0			0
$580$		0			0
$581$	−2.00000	+	3.46410i	−0.0829740	+	0.143715i
$582$	−6.16879	+	3.56155i	−0.255705	+	0.147631i
$583$	−30.5709	+	17.6501i	−1.26612	+	0.730992i
$584$	−9.36932			−0.387705
$585$		0			0
$586$	3.93087			0.162383
$587$	−34.8542	+	20.1231i	−1.43859	+	0.830569i	−0.997752	−	0.0670179i	$-0.978652\pi$
$587$	−34.8542	+	20.1231i	−1.43859	+	0.830569i	−0.440837	+	0.897587i	$0.645318\pi$
$588$	5.78908	−	3.34233i	0.238738	−	0.137835i
$589$	−1.87689	+	3.25088i	−0.0773361	+	0.133950i
$590$		0			0
$591$	−6.40388	+	11.0918i	−0.263421	+	0.456258i
$592$	3.57071	+	2.06155i	0.146755	+	0.0847293i
$593$		−	33.1771i		−	1.36242i	−0.732088	−	0.681210i	$-0.761454\pi$
$593$		−	33.1771i		−	1.36242i	0.732088	−	0.681210i	$-0.238546\pi$
$594$	2.06155	−	3.57071i	0.0845865	−	0.146508i
$595$		0			0
$596$	1.09612	+	1.89853i	0.0448987	+	0.0777669i
$597$			2.87689i			0.117743i
$598$	16.7276	−	2.34233i	0.684041	−	0.0957850i
$599$	14.0000			0.572024			0.286012	−	0.958226i	$-0.407670\pi$
$599$	14.0000			0.572024			0.286012	+	0.958226i	$0.407670\pi$
$600$		0			0
$601$	−14.9924	−	25.9676i	−0.611554	−	1.05924i	−0.990979	−	0.134020i	$-0.957212\pi$
$601$	−14.9924	−	25.9676i	−0.611554	−	1.05924i	0.379425	−	0.925222i	$-0.376122\pi$
$602$	0.213225	+	0.123106i	0.00869041	+	0.00501741i
$603$			2.24621i			0.0914728i
$604$	−7.68466	+	13.3102i	−0.312684	+	0.541585i
$605$		0			0
$606$	−8.87689			−0.360599
$607$	−28.0794	−	16.2116i	−1.13971	−	0.658010i	−0.193349	−	0.981130i	$-0.561935\pi$
$607$	−28.0794	−	16.2116i	−1.13971	−	0.658010i	−0.946358	+	0.323120i	$0.895268\pi$
$608$	−0.486319	+	0.280776i	−0.0197228	+	0.0113870i
$609$	−0.684658	−	1.18586i	−0.0277438	−	0.0480536i
$610$		0			0
$611$	19.8963	−	15.5286i	0.804918	−	0.628219i
$612$		−	3.12311i		−	0.126244i
$613$	−17.2139	+	9.93845i	−0.695263	+	0.401410i	−0.805581	−	0.592486i	$-0.798146\pi$
$613$	−17.2139	+	9.93845i	−0.695263	+	0.401410i	0.110318	+	0.993896i	$0.464813\pi$
$614$	12.8078	+	22.1837i	0.516879	+	0.895261i
$615$		0			0
$616$	−2.31534			−0.0932878
$617$	25.3878	+	14.6577i	1.02208	+	0.590096i	0.914704	−	0.404123i	$-0.132423\pi$
$617$	25.3878	+	14.6577i	1.02208	+	0.590096i	0.107371	+	0.994219i	$0.465757\pi$
$618$	3.95042	+	2.28078i	0.158909	+	0.0917463i
$619$	20.5616			0.826439			0.413219	−	0.910632i	$-0.364404\pi$
$619$	20.5616			0.826439			0.413219	+	0.910632i	$0.364404\pi$
$620$		0			0
$621$	−2.34233	−	4.05703i	−0.0939944	−	0.162803i
$622$	26.6204	−	15.3693i	1.06738	−	0.616253i
$623$		−	10.5616i		−	0.423140i
$624$	−0.500000	−	3.57071i	−0.0200160	−	0.142943i
$625$		0			0
$626$	−15.6847	−	27.1666i	−0.626885	−	1.08580i
$627$	2.00514	−	1.15767i	0.0800778	−	0.0462329i
$628$	12.0177	+	6.93845i	0.479560	+	0.276874i
$629$	−12.8769			−0.513435
$630$		0			0
$631$	6.87689	−	11.9111i	0.273765	−	0.474175i	−0.696058	−	0.717986i	$-0.745064\pi$
$631$	6.87689	−	11.9111i	0.273765	−	0.474175i	0.969823	+	0.243811i	$0.0783977\pi$
$632$			11.5616i			0.459894i
$633$	−18.9927	−	10.9654i	−0.754892	−	0.435837i
$634$	−12.4039	−	21.4842i	−0.492621	−	0.853245i
$635$		0			0
$636$	8.56155			0.339488
$637$	−9.03996	+	22.3423i	−0.358176	+	0.885235i
$638$		−	10.0540i		−	0.398041i
$639$	−6.56155	−	11.3649i	−0.259571	−	0.449590i
$640$		0			0
$641$	5.71922	−	9.90599i	0.225896	−	0.391263i	−0.730692	−	0.682707i	$-0.760802\pi$
$641$	5.71922	−	9.90599i	0.225896	−	0.391263i	0.956588	+	0.291444i	$0.0941358\pi$
$642$			2.00000i			0.0789337i
$643$	18.8393	+	10.8769i	0.742951	+	0.428943i	0.823141	−	0.567837i	$-0.192220\pi$
$643$	18.8393	+	10.8769i	0.742951	+	0.428943i	−0.0801904	+	0.996780i	$0.525553\pi$
$644$	−1.31534	+	2.27824i	−0.0518317	+	0.0897752i
$645$		0			0
$646$	0.876894	−	1.51883i	0.0345009	−	0.0597574i
$647$	30.3576	−	17.5270i	1.19348	−	0.689057i	0.234387	−	0.972143i	$-0.424692\pi$
$647$	30.3576	−	17.5270i	1.19348	−	0.689057i	0.959094	+	0.283086i	$0.0913583\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−26.5464			−1.04204
$650$		0			0
$651$	3.75379			0.147123
$652$	−12.5041	+	7.21922i	−0.489697	+	0.282727i
$653$	38.5914	−	22.2808i	1.51020	−	0.871914i	0.510270	−	0.860014i	$-0.329545\pi$
$653$	38.5914	−	22.2808i	1.51020	−	0.871914i	0.999929	−	0.0119002i	$-0.00378803\pi$
$654$	−1.87689	+	3.25088i	−0.0733924	+	0.127119i
$655$		0			0
$656$	−6.12311	+	10.6055i	−0.239067	+	0.414076i
$657$	−8.11407	−	4.68466i	−0.316560	−	0.182766i
$658$			3.93087i			0.153241i
$659$	−3.02699	+	5.24290i	−0.117915	+	0.204234i	−0.918941	−	0.394395i	$-0.870954\pi$
$659$	−3.02699	+	5.24290i	−0.117915	+	0.204234i	0.801026	+	0.598629i	$0.204288\pi$
$660$		0			0
$661$	−14.8078	−	25.6478i	−0.575955	−	0.997584i	−0.995937	−	0.0900513i	$-0.971297\pi$
$661$	−14.8078	−	25.6478i	−0.575955	−	0.997584i	0.419982	−	0.907532i	$-0.362036\pi$
$662$			30.7386i			1.19469i
$663$	6.92820	+	8.87689i	0.269069	+	0.344750i
$664$	7.12311			0.276430
$665$		0			0
$666$	2.06155	+	3.57071i	0.0798835	+	0.138362i
$667$	−9.89286	−	5.71165i	−0.383053	−	0.221156i
$668$		−	4.36932i		−	0.169054i
$669$	13.6501	−	23.6427i	0.527743	−	0.914078i
$670$		0			0
$671$	24.7386			0.955024
$672$	0.486319	+	0.280776i	0.0187602	+	0.0108312i
$673$	−22.3034	+	12.8769i	−0.859734	+	0.496368i	−0.863923	−	0.503623i	$-0.832000\pi$
$673$	−22.3034	+	12.8769i	−0.859734	+	0.496368i	0.00418904	+	0.999991i	$0.498667\pi$
$674$	−3.00000	−	5.19615i	−0.115556	−	0.200148i
$675$		0			0
$676$	9.34233	+	9.03996i	0.359320	+	0.347691i
$677$		−	37.1231i		−	1.42676i	−0.700779	−	0.713378i	$-0.747164\pi$
$677$		−	37.1231i		−	1.42676i	0.700779	−	0.713378i	$-0.252836\pi$
$678$	−7.52113	+	4.34233i	−0.288847	+	0.166766i
$679$	2.00000	+	3.46410i	0.0767530	+	0.132940i
$680$		0			0
$681$	−20.0000			−0.766402
$682$	23.8690	+	13.7808i	0.913991	+	0.527693i
$683$	14.8290	+	8.56155i	0.567418	+	0.327599i	0.756117	−	0.654436i	$-0.227094\pi$
$683$	14.8290	+	8.56155i	0.567418	+	0.327599i	−0.188700	+	0.982035i	$0.560427\pi$
$684$	−0.561553			−0.0214715
$685$		0			0
$686$	−3.84233	−	6.65511i	−0.146701	−	0.254093i
$687$	−20.9978	+	12.1231i	−0.801117	+	0.462525i
$688$		−	0.438447i		−	0.0167156i
$689$	−24.3348	+	18.9927i	−0.927080	+	0.723564i
$690$		0			0
$691$	10.2808	+	17.8068i	0.391099	+	0.677404i	0.992595	−	0.121472i	$-0.0387616\pi$
$691$	10.2808	+	17.8068i	0.391099	+	0.677404i	−0.601496	+	0.798876i	$0.705428\pi$
$692$	17.4739	−	10.0885i	0.664257	−	0.383509i
$693$	−2.00514	−	1.15767i	−0.0761691	−	0.0439763i
$694$	−0.876894			−0.0332865
$695$		0			0
$696$	−1.21922	+	2.11176i	−0.0462146	+	0.0800460i
$697$		−	38.2462i		−	1.44868i
$698$	7.35465	+	4.24621i	0.278378	+	0.160721i
$699$	−2.65767	−	4.60322i	−0.100522	−	0.174110i
$700$		0			0
$701$	−36.3002			−1.37104			−0.685520	−	0.728054i	$-0.740425\pi$
$701$	−36.3002			−1.37104			−0.685520	+	0.728054i	$0.740425\pi$
$702$	1.35234	−	3.34233i	0.0510410	−	0.126148i
$703$			2.31534i			0.0873248i
$704$	2.06155	+	3.57071i	0.0776977	+	0.134576i
$705$		0			0
$706$	12.9309	−	22.3969i	0.486660	−	0.842919i
$707$			4.98485i			0.187474i
$708$	5.57586	+	3.21922i	0.209554	+	0.120986i
$709$	17.1231	−	29.6581i	0.643072	−	1.11383i	−0.341672	−	0.939819i	$-0.610993\pi$
$709$	17.1231	−	29.6581i	0.643072	−	1.11383i	0.984743	−	0.174013i	$-0.0556736\pi$
$710$		0			0
$711$	−5.78078	+	10.0126i	−0.216796	+	0.375502i
$712$	−16.2880	+	9.40388i	−0.610419	+	0.352425i
$713$	27.1199	−	15.6577i	1.01565	−	0.586384i
$714$	−1.75379			−0.0656339
$715$		0			0
$716$	−12.6847			−0.474048
$717$	−9.84612	+	5.68466i	−0.367710	+	0.212297i
$718$	−11.3649	+	6.56155i	−0.424136	+	0.244875i
$719$	22.4924	−	38.9580i	0.838826	−	1.45289i	−0.0520512	−	0.998644i	$-0.516576\pi$
$719$	22.4924	−	38.9580i	0.838826	−	1.45289i	0.890877	−	0.454245i	$-0.150091\pi$
$720$		0			0
$721$	1.28078	−	2.21837i	0.0476986	−	0.0826164i
$722$	16.1814	+	9.34233i	0.602209	+	0.347685i
$723$			28.1231i			1.04591i
$724$	1.43845	−	2.49146i	0.0534595	−	0.0925945i
$725$		0			0
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$			38.4233i			1.42504i	0.701651	+	0.712521i	$0.252446\pi$
$727$			38.4233i			1.42504i	−0.701651	+	0.712521i	$0.747554\pi$
$728$	−2.00514	+	0.280776i	−0.0743156	+	0.0104063i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	0.684658	+	1.18586i	0.0253230	+	0.0438607i
$732$	−5.19615	−	3.00000i	−0.192055	−	0.110883i
$733$		−	20.0691i		−	0.741270i	−0.928779	−	0.370635i	$-0.879140\pi$
$733$		−	20.0691i		−	0.741270i	0.928779	−	0.370635i	$-0.120860\pi$
$734$	6.24621	−	10.8188i	0.230552	−	0.399328i
$735$		0			0
$736$	4.68466			0.172679
$737$	8.02058	+	4.63068i	0.295442	+	0.170573i
$738$	−10.6055	+	6.12311i	−0.390395	+	0.225395i
$739$	−13.7732	−	23.8559i	−0.506655	−	0.877553i	−0.999970	−	0.00770202i	$-0.997548\pi$
$739$	−13.7732	−	23.8559i	−0.506655	−	0.877553i	0.493315	−	0.869851i	$-0.335785\pi$
$740$		0			0
$741$	1.59612	−	1.24573i	0.0586349	−	0.0457631i
$742$		−	4.80776i		−	0.176499i
$743$	−11.4117	+	6.58854i	−0.418654	+	0.241710i	−0.694501	−	0.719491i	$-0.744375\pi$
$743$	−11.4117	+	6.58854i	−0.418654	+	0.241710i	0.275847	+	0.961202i	$0.411042\pi$
$744$	−3.34233	−	5.78908i	−0.122536	−	0.212238i
$745$		0			0
$746$	−25.8078			−0.944889
$747$	6.16879	+	3.56155i	0.225704	+	0.130310i
$748$	−11.1517	−	6.43845i	−0.407747	−	0.235413i
$749$	1.12311			0.0410374
$750$		0			0
$751$	11.9039	+	20.6181i	0.434379	+	0.752366i	0.997245	−	0.0741820i	$-0.0236346\pi$
$751$	11.9039	+	20.6181i	0.434379	+	0.752366i	−0.562866	+	0.826548i	$0.690301\pi$
$752$	6.06218	−	3.50000i	0.221065	−	0.127632i
$753$			8.12311i			0.296022i
$754$	−1.21922	−	8.70700i	−0.0444015	−	0.317090i
$755$		0			0
$756$	0.280776	+	0.486319i	0.0102117	+	0.0176873i
$757$	−24.6153	+	14.2116i	−0.894658	+	0.516531i	−0.875463	−	0.483285i	$-0.839444\pi$
$757$	−24.6153	+	14.2116i	−0.894658	+	0.516531i	−0.0191948	+	0.999816i	$0.506110\pi$
$758$	−15.3154	−	8.84233i	−0.556279	−	0.321168i
$759$	−19.3153			−0.701102
$760$		0			0
$761$	8.96543	−	15.5286i	0.324997	−	0.562911i	−0.656515	−	0.754313i	$-0.727970\pi$
$761$	8.96543	−	15.5286i	0.324997	−	0.562911i	0.981512	+	0.191402i	$0.0613035\pi$
$762$		−	8.56155i		−	0.310152i
$763$	1.82554	+	1.05398i	0.0660889	+	0.0381565i
$764$	5.43845	+	9.41967i	0.196756	+	0.340792i
$765$		0			0
$766$	0.192236			0.00694577
$767$	−22.9899	+	3.21922i	−0.830116	+	0.116239i
$768$		−	1.00000i		−	0.0360844i
$769$	−16.6577	−	28.8519i	−0.600691	−	1.04043i	−0.992717	−	0.120473i	$-0.961559\pi$
$769$	−16.6577	−	28.8519i	−0.600691	−	1.04043i	0.392026	−	0.919954i	$-0.371774\pi$
$770$		0			0
$771$	2.78078	−	4.81645i	0.100147	−	0.173460i
$772$		0			0
$773$	20.9380	+	12.0885i	0.753086	+	0.434795i	0.826808	−	0.562484i	$-0.190154\pi$
$773$	20.9380	+	12.0885i	0.753086	+	0.434795i	−0.0737217	+	0.997279i	$0.523488\pi$
$774$	0.219224	−	0.379706i	0.00787983	−	0.0136483i
$775$		0			0
$776$	3.56155	−	6.16879i	0.127852	−	0.221447i
$777$	2.00514	−	1.15767i	0.0719342	−	0.0415312i
$778$	15.6352	−	9.02699i	0.560549	−	0.323633i
$779$	−6.87689			−0.246390
$780$		0			0
$781$	−54.1080			−1.93613
$782$	−12.6705	+	7.31534i	−0.453098	+	0.261596i
$783$	−2.11176	+	1.21922i	−0.0754680	+	0.0435715i
$784$	−3.34233	+	5.78908i	−0.119369	+	0.206753i
$785$		0			0
$786$	1.06155	−	1.83866i	0.0378643	−	0.0655830i
$787$	−27.1199	−	15.6577i	−0.966719	−	0.558136i	−0.0684848	−	0.997652i	$-0.521816\pi$
$787$	−27.1199	−	15.6577i	−0.966719	−	0.558136i	−0.898235	+	0.439516i	$0.855150\pi$
$788$		−	12.8078i		−	0.456258i
$789$	−6.50000	+	11.2583i	−0.231406	+	0.400807i
$790$		0			0
$791$	2.43845	+	4.22351i	0.0867012	+	0.150171i
$792$			4.12311i			0.146508i
$793$	21.4243	−	3.00000i	0.760799	−	0.106533i
$794$	20.1231			0.714142
$795$		0			0
$796$	−1.43845	−	2.49146i	−0.0509844	−	0.0883076i
$797$	−11.3649	−	6.56155i	−0.402567	−	0.232422i	0.285024	−	0.958520i	$-0.407998\pi$
$797$	−11.3649	−	6.56155i	−0.402567	−	0.232422i	−0.687591	+	0.726098i	$0.741332\pi$
$798$			0.315342i			0.0111630i
$799$	−10.9309	+	18.9328i	−0.386706	+	0.669795i
$800$		0			0
$801$	−18.8078			−0.664540
$802$	−0.273094	−	0.157671i	−0.00964328	−	0.00556755i
$803$	−33.4552	+	19.3153i	−1.18061	+	0.681624i
$804$	−1.12311	−	1.94528i	−0.0396089	−	0.0686046i
$805$		0			0
$806$	22.3423	+	9.03996i	0.786975	+	0.318419i
$807$			21.3693i			0.752236i
$808$	7.68762	−	4.43845i	0.270449	−	0.156144i
$809$	−7.24621	−	12.5508i	−0.254763	−	0.441263i	0.710068	−	0.704133i	$-0.248664\pi$
$809$	−7.24621	−	12.5508i	−0.254763	−	0.441263i	−0.964831	+	0.262870i	$0.915331\pi$
$810$		0			0
$811$	47.5464			1.66958			0.834790	−	0.550569i	$-0.185589\pi$
$811$	47.5464			1.66958			0.834790	+	0.550569i	$0.185589\pi$
$812$	1.18586	+	0.684658i	0.0416156	+	0.0240268i
$813$	−11.4117	−	6.58854i	−0.400225	−	0.231070i
$814$	17.0000			0.595850
$815$		0			0
$816$	1.56155	+	2.70469i	0.0546653	+	0.0946830i
$817$	0.213225	−	0.123106i	0.00745981	−	0.00430692i
$818$			18.8078i			0.657598i
$819$	−1.87689	−	0.759413i	−0.0655840	−	0.0265360i
$820$		0			0
$821$	4.21922	+	7.30791i	0.147252	+	0.255048i	0.930211	−	0.367026i	$-0.119624\pi$
$821$	4.21922	+	7.30791i	0.147252	+	0.255048i	−0.782959	+	0.622073i	$0.786291\pi$
$822$	10.2258	−	5.90388i	0.356667	−	0.205922i
$823$	4.37687	+	2.52699i	0.152568	+	0.0880853i	0.574341	−	0.818616i	$-0.305259\pi$
$823$	4.37687	+	2.52699i	0.152568	+	0.0880853i	−0.421772	+	0.906702i	$0.638592\pi$
$824$	−4.56155			−0.158909
$825$		0			0
$826$	1.80776	−	3.13114i	0.0629002	−	0.108946i
$827$		−	28.2462i		−	0.982217i	−0.871098	−	0.491109i	$-0.836592\pi$
$827$		−	28.2462i		−	0.982217i	0.871098	−	0.491109i	$-0.163408\pi$
$828$	4.05703	+	2.34233i	0.140992	+	0.0814016i
$829$	6.19224	+	10.7253i	0.215065	+	0.372504i	0.953293	−	0.302048i	$-0.0976702\pi$
$829$	6.19224	+	10.7253i	0.215065	+	0.372504i	−0.738228	+	0.674552i	$0.764337\pi$
$830$		0			0
$831$	−1.00000			−0.0346896
$832$	2.21837	+	2.84233i	0.0769081	+	0.0985400i
$833$		−	20.8769i		−	0.723342i
$834$	6.28078	+	10.8786i	0.217486	+	0.376696i
$835$		0			0
$836$	−1.15767	+	2.00514i	−0.0400389	+	0.0693494i
$837$		−	6.68466i		−	0.231056i
$838$	28.1393	+	16.2462i	0.972055	+	0.561216i
$839$	18.3693	−	31.8166i	0.634179	−	1.09843i	−0.352509	−	0.935808i	$-0.614671\pi$
$839$	18.3693	−	31.8166i	0.634179	−	1.09843i	0.986688	−	0.162622i	$-0.0519952\pi$
$840$		0			0
$841$	11.5270	−	19.9653i	0.397482	−	0.688460i
$842$	−28.1393	+	16.2462i	−0.969743	+	0.559881i
$843$	−14.0696	+	8.12311i	−0.484584	+	0.279775i
$844$	21.9309			0.754892
$845$		0			0
$846$	7.00000			0.240665
$847$	−2.91791	+	1.68466i	−0.100261	+	0.0578855i
$848$	−7.41452	+	4.28078i	−0.254616	+	0.147002i
$849$	7.78078	−	13.4767i	0.267036	−	0.462519i
$850$		0			0
$851$	9.65767	−	16.7276i	0.331061	−	0.573414i
$852$	11.3649	+	6.56155i	0.389357	+	0.224795i
$853$		−	2.30019i		−	0.0787569i	−0.999224	−	0.0393784i	$-0.987462\pi$
$853$		−	2.30019i		−	0.0787569i	0.999224	−	0.0393784i	$-0.0125378\pi$
$854$	−1.68466	+	2.91791i	−0.0576478	+	0.0998490i
$855$		0			0
$856$	−1.00000	−	1.73205i	−0.0341793	−	0.0592003i
$857$		−	6.19224i		−	0.211523i	−0.994392	−	0.105761i	$-0.966272\pi$
$857$		−	6.19224i		−	0.211523i	0.994392	−	0.105761i	$-0.0337280\pi$
$858$	−9.14657	−	11.7192i	−0.312259	−	0.400088i
$859$	−39.7926			−1.35771			−0.678853	−	0.734274i	$-0.737523\pi$
$859$	−39.7926			−1.35771			−0.678853	+	0.734274i	$0.737523\pi$
$860$		0			0
$861$	3.43845	+	5.95557i	0.117182	+	0.202965i
$862$	19.6922	+	11.3693i	0.670720	+	0.387240i
$863$		−	2.43845i		−	0.0830057i	−0.999138	−	0.0415029i	$-0.986785\pi$
$863$		−	2.43845i		−	0.0830057i	0.999138	−	0.0415029i	$-0.0132146\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−18.7386			−0.636765
$867$	6.27540	+	3.62311i	0.213124	+	0.123047i
$868$	−3.25088	+	1.87689i	−0.110342	+	0.0637059i
$869$	23.8348	+	41.2830i	0.808539	+	1.40043i
$870$		0			0
$871$	7.50758	+	3.03765i	0.254385	+	0.102927i
$872$		−	3.75379i		−	0.127119i
$873$	6.16879	−	3.56155i	0.208782	−	0.120540i
$874$	1.31534	+	2.27824i	0.0444921	+	0.0770626i
$875$		0			0
$876$	9.36932			0.316560
$877$	−7.30791	−	4.21922i	−0.246771	−	0.142473i	0.371514	−	0.928427i	$-0.378839\pi$
$877$	−7.30791	−	4.21922i	−0.246771	−	0.142473i	−0.618285	+	0.785954i	$0.712172\pi$
$878$	21.7572	+	12.5616i	0.734272	+	0.423932i
$879$	−3.93087			−0.132585
$880$		0			0
$881$	12.2808	+	21.2709i	0.413750	+	0.716636i	0.995296	−	0.0968774i	$-0.0308855\pi$
$881$	12.2808	+	21.2709i	0.413750	+	0.716636i	−0.581546	+	0.813513i	$0.697552\pi$
$882$	−5.78908	+	3.34233i	−0.194929	+	0.112542i
$883$			19.1771i			0.645360i	0.946508	+	0.322680i	$0.104584\pi$
$883$			19.1771i			0.645360i	−0.946508	+	0.322680i	$0.895416\pi$
$884$	−10.4384	−	4.22351i	−0.351083	−	0.142052i
$885$		0			0
$886$	6.56155	+	11.3649i	0.220440	+	0.381813i
$887$	−28.6723	+	16.5540i	−0.962722	+	0.555828i	−0.897010	−	0.442010i	$-0.854265\pi$
$887$	−28.6723	+	16.5540i	−0.962722	+	0.555828i	−0.0657126	+	0.997839i	$0.520932\pi$
$888$	−3.57071	−	2.06155i	−0.119825	−	0.0691812i
$889$	−4.80776			−0.161247
$890$		0			0
$891$	−2.06155	+	3.57071i	−0.0690646	+	0.119623i
$892$			27.3002i			0.914078i
$893$	3.40423	+	1.96543i	0.113918	+	0.0657708i
$894$	−1.09612	−	1.89853i	−0.0366597	−	0.0634964i
$895$		0			0
$896$	−0.561553			−0.0187602
$897$	−16.7276	+	2.34233i	−0.558518	+	0.0782081i
$898$			20.1771i			0.673318i
$899$	−8.15009	−	14.1164i	−0.271821	−	0.470807i
$900$		0			0
$901$	13.3693	−	23.1563i	0.445397	−	0.771449i
$902$			50.4924i			1.68121i
$903$	−0.213225	−	0.123106i	−0.00709569	−	0.00409670i
$904$	4.34233	−	7.52113i	0.144424	−	0.250149i
$905$		0			0
$906$	7.68466	−	13.3102i	0.255306	−	0.442202i
$907$	−46.6924	+	26.9579i	−1.55039	+	0.895121i	−0.552286	+	0.833655i	$0.686244\pi$
$907$	−46.6924	+	26.9579i	−1.55039	+	0.895121i	−0.998109	+	0.0614661i	$0.980422\pi$
$908$	17.3205	−	10.0000i	0.574801	−	0.331862i
$909$	8.87689			0.294428
$910$		0			0
$911$	−18.6307			−0.617262			−0.308631	−	0.951182i	$-0.599871\pi$
$911$	−18.6307			−0.617262			−0.308631	+	0.951182i	$0.599871\pi$
$912$	0.486319	−	0.280776i	0.0161036	−	0.00929744i
$913$	25.4346	−	14.6847i	0.841762	−	0.485991i
$914$	10.1231	−	17.5337i	0.334843	−	0.579964i
$915$		0			0
$916$	12.1231	−	20.9978i	0.400559	−	0.693788i
$917$	−1.03251	−	0.596118i	−0.0340964	−	0.0196855i
$918$			3.12311i			0.103078i
$919$	8.31534	−	14.4026i	0.274298	−	0.475098i	−0.695660	−	0.718371i	$-0.744888\pi$
$919$	8.31534	−	14.4026i	0.274298	−	0.475098i	0.969958	+	0.243274i	$0.0782213\pi$
$920$		0			0
$921$	−12.8078	−	22.1837i	−0.422030	−	0.730978i
$922$		−	30.0540i		−	0.989775i
$923$	−46.8589	+	6.56155i	−1.54238	+	0.215976i
$924$	2.31534			0.0761691
$925$		0			0
$926$	3.80776	+	6.59524i	0.125131	+	0.216733i
$927$	−3.95042	−	2.28078i	−0.129749	−	0.0749105i
$928$		−	2.43845i		−	0.0800460i
$929$	−12.5616	+	21.7572i	−0.412131	+	0.713832i	−0.995123	−	0.0986462i	$-0.968549\pi$
$929$	−12.5616	+	21.7572i	−0.412131	+	0.713832i	0.582991	+	0.812478i	$0.301882\pi$
$930$		0			0
$931$	−3.75379			−0.123025
$932$	4.60322	+	2.65767i	0.150784	+	0.0870549i
$933$	−26.6204	+	15.3693i	−0.871514	+	0.503169i
$934$	−8.93087	−	15.4687i	−0.292227	−	0.506152i
$935$		0			0
$936$	0.500000	+	3.57071i	0.0163430	+	0.116712i
$937$			53.2311i			1.73898i	0.493948	+	0.869491i	$0.335553\pi$
$937$			53.2311i			1.73898i	−0.493948	+	0.869491i	$0.664447\pi$
$938$	−1.09238	+	0.630683i	−0.0356673	+	0.0205925i
$939$	15.6847	+	27.1666i	0.511849	+	0.886549i
$940$		0			0
$941$	−25.3693			−0.827016			−0.413508	−	0.910500i	$-0.635697\pi$
$941$	−25.3693			−0.827016			−0.413508	+	0.910500i	$0.635697\pi$
$942$	−12.0177	−	6.93845i	−0.391559	−	0.226067i
$943$	49.6833	+	28.6847i	1.61791	+	0.934101i
$944$	−6.43845			−0.209554
$945$		0			0
$946$	−0.903882	−	1.56557i	−0.0293877	−	0.0509011i
$947$	−37.9854	+	21.9309i	−1.23436	+	0.712658i	−0.967936	−	0.251199i	$-0.919175\pi$
$947$	−37.9854	+	21.9309i	−1.23436	+	0.712658i	−0.266423	+	0.963856i	$0.585842\pi$
$948$		−	11.5616i		−	0.375502i
$949$	−26.6307	+	20.7846i	−0.864469	+	0.674697i
$950$		0			0
$951$	12.4039	+	21.4842i	0.402223	+	0.696671i
$952$	1.51883	−	0.876894i	0.0492254	−	0.0284203i
$953$	44.3207	+	25.5885i	1.43569	+	0.828894i	0.997546	−	0.0700123i	$-0.0223039\pi$
$953$	44.3207	+	25.5885i	1.43569	+	0.828894i	0.438141	+	0.898906i	$0.355637\pi$
$954$	−8.56155			−0.277191
$955$		0			0
$956$	5.68466	−	9.84612i	0.183855	−	0.318446i
$957$			10.0540i			0.324999i
$958$	−33.1222	−	19.1231i	−1.07013	−	0.617839i
$959$	−3.31534	−	5.74234i	−0.107058	−	0.185430i
$960$		0			0
$961$	13.6847			0.441441
$962$	14.7224	−	2.06155i	0.474670	−	0.0664671i
$963$		−	2.00000i		−	0.0644491i
$964$	−14.0616	−	24.3553i	−0.452892	−	0.784432i
$965$		0			0
$966$	1.31534	−	2.27824i	0.0423204	−	0.0733011i
$967$			15.6847i			0.504385i	0.967677	+	0.252192i	$0.0811516\pi$
$967$			15.6847i			0.504385i	−0.967677	+	0.252192i	$0.918848\pi$
$968$	5.19615	+	3.00000i	0.167011	+	0.0964237i
$969$	−0.876894	+	1.51883i	−0.0281699	+	0.0487917i
$970$		0			0
$971$	2.15767	−	3.73720i	0.0692430	−	0.119932i	−0.829325	−	0.558766i	$-0.811275\pi$
$971$	2.15767	−	3.73720i	0.0692430	−	0.119932i	0.898568	+	0.438834i	$0.144608\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	6.10892	−	3.52699i	0.195843	−	0.113070i
$974$	−13.0540			−0.418276
$975$		0			0
$976$	6.00000			0.192055
$977$	−41.8292	+	24.1501i	−1.33823	+	0.772630i	−0.986545	−	0.163487i	$-0.947726\pi$
$977$	−41.8292	+	24.1501i	−1.33823	+	0.772630i	−0.351689	+	0.936117i	$0.614392\pi$
$978$	12.5041	−	7.21922i	0.399836	−	0.230845i
$979$	−38.7732	+	67.1572i	−1.23920	+	2.14635i
$980$		0			0
$981$	1.87689	−	3.25088i	0.0599246	−	0.103792i
$982$	15.1021	+	8.71922i	0.481929	+	0.278242i
$983$		−	32.1231i		−	1.02457i	−0.858816	−	0.512284i	$-0.828800\pi$
$983$		−	32.1231i		−	1.02457i	0.858816	−	0.512284i	$-0.171200\pi$
$984$	6.12311	−	10.6055i	0.195197	−	0.338092i
$985$		0			0
$986$	3.80776	+	6.59524i	0.121264	+	0.210035i
$987$		−	3.93087i		−	0.125121i
$988$	−0.759413	+	1.87689i	−0.0241601	+	0.0597120i
$989$	−2.05398			−0.0653126
$990$		0			0
$991$	−24.7116	−	42.8018i	−0.784991	−	1.35964i	−0.929004	−	0.370069i	$-0.879334\pi$
$991$	−24.7116	−	42.8018i	−0.784991	−	1.35964i	0.144013	−	0.989576i	$-0.453999\pi$
$992$	5.78908	+	3.34233i	0.183804	+	0.106119i
$993$		−	30.7386i		−	0.975461i
$994$	3.68466	−	6.38202i	0.116870	−	0.202425i
$995$		0			0
$996$	−7.12311			−0.225704
$997$	32.5161	+	18.7732i	1.02980	+	0.594553i	0.916926	−	0.399057i	$-0.130662\pi$
$997$	32.5161	+	18.7732i	1.02980	+	0.594553i	0.112870	+	0.993610i	$0.463996\pi$
$998$	−3.46410	+	2.00000i	−0.109654	+	0.0633089i
$999$	−2.06155	−	3.57071i	−0.0652246	−	0.112972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.n.1849.4		8
5.2	odd	4		1950.2.i.bi.601.1		4
5.3	odd	4		390.2.i.g.211.2	yes	4
5.4	even	2	inner	1950.2.z.n.1849.1		8
13.9	even	3	inner	1950.2.z.n.1699.1		8
15.8	even	4		1170.2.i.o.991.2		4
65.3	odd	12		5070.2.a.bi.1.1		2
65.9	even	6	inner	1950.2.z.n.1699.4		8
65.22	odd	12		1950.2.i.bi.451.1		4
65.23	odd	12		5070.2.a.bb.1.2		2
65.28	even	12		5070.2.b.r.1351.1		4
65.48	odd	12		390.2.i.g.61.2	✓	4
65.63	even	12		5070.2.b.r.1351.4		4
195.113	even	12		1170.2.i.o.451.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.g.61.2	✓	4	65.48	odd	12
390.2.i.g.211.2	yes	4	5.3	odd	4
1170.2.i.o.451.2		4	195.113	even	12
1170.2.i.o.991.2		4	15.8	even	4
1950.2.i.bi.451.1		4	65.22	odd	12
1950.2.i.bi.601.1		4	5.2	odd	4
1950.2.z.n.1699.1		8	13.9	even	3	inner
1950.2.z.n.1699.4		8	65.9	even	6	inner
1950.2.z.n.1849.1		8	5.4	even	2	inner
1950.2.z.n.1849.4		8	1.1	even	1	trivial
5070.2.a.bb.1.2		2	65.23	odd	12
5070.2.a.bi.1.1		2	65.3	odd	12
5070.2.b.r.1351.1		4	65.28	even	12
5070.2.b.r.1351.4		4	65.63	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(0.486319 + 0.280776i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(0.486319 + 0.280776i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.06155 - 3.57071i) q^{11} +1.00000i q^{12} +(-2.21837 - 2.84233i) q^{13} +0.561553 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.70469 + 1.56155i) q^{17} -1.00000i q^{18} +(0.280776 - 0.486319i) q^{19} -0.561553 q^{21} +(-3.57071 - 2.06155i) q^{22} +(-4.05703 + 2.34233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.34233 - 1.35234i) q^{26} +1.00000i q^{27} +(0.486319 - 0.280776i) q^{28} +(1.21922 + 2.11176i) q^{29} -6.68466 q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.57071 + 2.06155i) q^{33} +3.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.57071 + 2.06155i) q^{37} -0.561553i q^{38} +(3.34233 + 1.35234i) q^{39} +(-6.12311 - 10.6055i) q^{41} +(-0.486319 + 0.280776i) q^{42} +(0.379706 + 0.219224i) q^{43} -4.12311 q^{44} +(-2.34233 + 4.05703i) q^{46} +7.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.34233 - 5.78908i) q^{49} -3.12311 q^{51} +(-3.57071 + 0.500000i) q^{52} -8.56155i q^{53} +(0.500000 + 0.866025i) q^{54} +(0.280776 - 0.486319i) q^{56} +0.561553i q^{57} +(2.11176 + 1.21922i) q^{58} +(3.21922 - 5.57586i) q^{59} +(-3.00000 + 5.19615i) q^{61} +(-5.78908 + 3.34233i) q^{62} +(0.486319 - 0.280776i) q^{63} -1.00000 q^{64} +4.12311 q^{66} +(-1.94528 + 1.12311i) q^{67} +(2.70469 - 1.56155i) q^{68} +(2.34233 - 4.05703i) q^{69} +(6.56155 - 11.3649i) q^{71} +(-0.866025 - 0.500000i) q^{72} -9.36932i q^{73} +(-2.06155 + 3.57071i) q^{74} +(-0.280776 - 0.486319i) q^{76} -2.31534i q^{77} +(3.57071 - 0.500000i) q^{78} -11.5616 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-10.6055 - 6.12311i) q^{82} +7.12311i q^{83} +(-0.280776 + 0.486319i) q^{84} +0.438447 q^{86} +(-2.11176 - 1.21922i) q^{87} +(-3.57071 + 2.06155i) q^{88} +(-9.40388 - 16.2880i) q^{89} +(-0.280776 - 2.00514i) q^{91} +4.68466i q^{92} +(5.78908 - 3.34233i) q^{93} +(3.50000 + 6.06218i) q^{94} +1.00000 q^{96} +(6.16879 + 3.56155i) q^{97} +(-5.78908 - 3.34233i) q^{98} -4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{14} - 4 q^{16} - 6 q^{19} + 12 q^{21} + 4 q^{24} - 2 q^{26} + 18 q^{29} - 4 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 16 q^{41} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} - 6 q^{56} + 34 q^{59} - 24 q^{61} - 8 q^{64} - 6 q^{69} + 36 q^{71} + 6 q^{76} - 76 q^{79} - 4 q^{81} + 6 q^{84} + 20 q^{86} - 34 q^{89} + 6 q^{91} + 28 q^{94} + 8 q^{96}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^14 - 4 * q^16 - 6 * q^19 + 12 * q^21 + 4 * q^24 - 2 * q^26 + 18 * q^29 - 4 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 16 * q^41 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 - 6 * q^56 + 34 * q^59 - 24 * q^61 - 8 * q^64 - 6 * q^69 + 36 * q^71 + 6 * q^76 - 76 * q^79 - 4 * q^81 + 6 * q^84 + 20 * q^86 - 34 * q^89 + 6 * q^91 + 28 * q^94 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more