LMFDB - Embedded newform 370.2.e.b.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(121,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("370.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	370.211
Dual form			370.2.e.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +1.00000 q^{10} +(-0.500000 - 0.866025i) q^{12} +(-2.50000 + 4.33013i) q^{13} -2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{21} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{26} -5.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +6.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} -1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{35} -2.00000 q^{36} +(5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-2.50000 - 4.33013i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(1.00000 - 1.73205i) q^{42} -1.00000 q^{43} +2.00000 q^{45} -6.00000 q^{47} +1.00000 q^{48} +(1.50000 + 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.50000 - 4.33013i) q^{52} +(4.50000 + 7.79423i) q^{53} +(-2.50000 - 4.33013i) q^{54} +(1.00000 - 1.73205i) q^{56} +(-1.00000 - 1.73205i) q^{57} +(3.00000 + 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} -1.00000 q^{60} +(5.00000 - 8.66025i) q^{61} +(-0.500000 - 0.866025i) q^{62} -4.00000 q^{63} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.00000 + 1.73205i) q^{70} +(6.00000 - 10.3923i) q^{71} +(-1.00000 - 1.73205i) q^{72} +8.00000 q^{73} +(5.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(2.50000 - 4.33013i) q^{78} +(2.00000 - 3.46410i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +9.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +2.00000 q^{84} +(-0.500000 - 0.866025i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(1.00000 + 1.73205i) q^{90} +(-5.00000 - 8.66025i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - q^{12} - 5 q^{13} - 4 q^{14} + q^{15} - q^{16} - 2 q^{18} - 2 q^{19} + q^{20} - 2 q^{21} + q^{24} - q^{25} - 10 q^{26} - 10 q^{27} - 2 q^{28} + 12 q^{29} - q^{30} - 2 q^{31} + q^{32} + 2 q^{35} - 4 q^{36} + 11 q^{37} - 4 q^{38} - 5 q^{39} - q^{40} + 9 q^{41} + 2 q^{42} - 2 q^{43} + 4 q^{45} - 12 q^{47} + 2 q^{48} + 3 q^{49} + q^{50} - 5 q^{52} + 9 q^{53} - 5 q^{54} + 2 q^{56} - 2 q^{57} + 6 q^{58} + 12 q^{59} - 2 q^{60} + 10 q^{61} - q^{62} - 8 q^{63} + 2 q^{64} + 5 q^{65} + 4 q^{67} - 2 q^{70} + 12 q^{71} - 2 q^{72} + 16 q^{73} + 10 q^{74} + 2 q^{75} - 2 q^{76} + 5 q^{78} + 4 q^{79} - 2 q^{80} - q^{81} + 18 q^{82} + 12 q^{83} + 4 q^{84} - q^{86} - 6 q^{87} - 6 q^{89} + 2 q^{90} - 10 q^{91} + q^{93} - 6 q^{94} + 2 q^{95} + q^{96} + 4 q^{97} - 3 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - q^12 - 5 * q^13 - 4 * q^14 + q^15 - q^16 - 2 * q^18 - 2 * q^19 + q^20 - 2 * q^21 + q^24 - q^25 - 10 * q^26 - 10 * q^27 - 2 * q^28 + 12 * q^29 - q^30 - 2 * q^31 + q^32 + 2 * q^35 - 4 * q^36 + 11 * q^37 - 4 * q^38 - 5 * q^39 - q^40 + 9 * q^41 + 2 * q^42 - 2 * q^43 + 4 * q^45 - 12 * q^47 + 2 * q^48 + 3 * q^49 + q^50 - 5 * q^52 + 9 * q^53 - 5 * q^54 + 2 * q^56 - 2 * q^57 + 6 * q^58 + 12 * q^59 - 2 * q^60 + 10 * q^61 - q^62 - 8 * q^63 + 2 * q^64 + 5 * q^65 + 4 * q^67 - 2 * q^70 + 12 * q^71 - 2 * q^72 + 16 * q^73 + 10 * q^74 + 2 * q^75 - 2 * q^76 + 5 * q^78 + 4 * q^79 - 2 * q^80 - q^81 + 18 * q^82 + 12 * q^83 + 4 * q^84 - q^86 - 6 * q^87 - 6 * q^89 + 2 * q^90 - 10 * q^91 + q^93 - 6 * q^94 + 2 * q^95 + q^96 + 4 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	1.00000			0.316228
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−2.00000			−0.534522
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−1.00000	+	1.73205i	−0.235702	+	0.408248i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.00000	−	1.73205i	−0.218218	−	0.377964i
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−5.00000			−0.980581
$27$	−5.00000			−0.962250
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−1.00000			−0.179605			−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000			−0.179605			−0.0898027	+	0.995960i	$0.528624\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	−2.00000			−0.333333
$37$	5.50000	−	2.59808i	0.904194	−	0.427121i
$37$	5.50000	−	2.59808i	0.904194	−	0.427121i
$38$	−2.00000			−0.324443
$39$	−2.50000	−	4.33013i	−0.400320	−	0.693375i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.00000			0.144338
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$		0			0
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$	−1.00000	−	1.73205i	−0.132453	−	0.229416i
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	−1.00000			−0.129099
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	−0.500000	−	0.866025i	−0.0635001	−	0.109985i
$63$	−4.00000			−0.503953
$64$	1.00000			0.125000
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		0			0
$69$		0			0
$70$	−1.00000	+	1.73205i	−0.119523	+	0.207020i
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	−0.252010	−	0.967725i	$-0.581092\pi$
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	0.964079	−	0.265615i	$-0.0855750\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	1.00000			0.115470
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$		0			0
$78$	2.50000	−	4.33013i	0.283069	−	0.490290i
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	9.00000			0.993884
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$	2.00000			0.218218
$85$		0			0
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	1.00000	+	1.73205i	0.105409	+	0.182574i
$91$	−5.00000	−	8.66025i	−0.524142	−	0.907841i
$92$		0			0
$93$	0.500000	−	0.866025i	0.0518476	−	0.0898027i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$		0			0
$100$	1.00000			0.100000
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	2.50000	−	4.33013i	0.245145	−	0.424604i
$105$	−2.00000			−0.195180
$106$	−4.50000	+	7.79423i	−0.437079	+	0.757042i
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$		0			0
$111$	−0.500000	+	6.06218i	−0.0474579	+	0.575396i
$112$	2.00000			0.188982
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	−10.0000			−0.924500
$118$	−6.00000	+	10.3923i	−0.552345	+	0.956689i
$119$		0			0
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−11.0000			−1.00000
$122$	10.0000			0.905357
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$	0.500000	−	0.866025i	0.0449013	−	0.0777714i
$125$	−1.00000			−0.0894427
$126$	−2.00000	−	3.46410i	−0.178174	−	0.308607i
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.500000	−	0.866025i	0.0440225	−	0.0762493i
$130$	−2.50000	+	4.33013i	−0.219265	+	0.379777i
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	4.00000			0.345547
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$		0			0
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$		0			0
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	0.975417	+	0.220366i	$0.0707252\pi$
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	−0.296866	+	0.954919i	$0.595942\pi$
$140$	−2.00000			−0.169031
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	12.0000			1.00702
$143$		0			0
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	4.00000	+	6.92820i	0.331042	+	0.573382i
$147$	−3.00000			−0.247436
$148$	−0.500000	+	6.06218i	−0.0410997	+	0.498308i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	−0.687741	−	0.725956i	$-0.741398\pi$
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	0.972567	+	0.232623i	$0.0747309\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$		0			0
$154$		0			0
$155$	−0.500000	+	0.866025i	−0.0401610	+	0.0695608i
$156$	5.00000			0.400320
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	−0.975470	−	0.220131i	$-0.929352\pi$
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	0.297097	−	0.954847i	$-0.403982\pi$
$158$	4.00000			0.318223
$159$	−9.00000			−0.713746
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$	1.00000	+	1.73205i	0.0771517	+	0.133631i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	−4.00000			−0.305888
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	−6.00000			−0.454859
$175$	2.00000			0.151186
$176$		0			0
$177$	−12.0000			−0.901975
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	−7.00000	+	12.1244i	−0.520306	+	0.901196i	0.479415	+	0.877588i	$0.340849\pi$
$181$	−7.00000	+	12.1244i	−0.520306	+	0.901196i	−0.999721	+	0.0236082i	$0.992485\pi$
$182$	5.00000	−	8.66025i	0.370625	−	0.641941i
$183$	5.00000	+	8.66025i	0.369611	+	0.640184i
$184$		0			0
$185$	0.500000	−	6.06218i	0.0367607	−	0.445700i
$186$	1.00000			0.0733236
$187$		0			0
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	5.00000	−	8.66025i	0.363696	−	0.629941i
$190$	−1.00000	+	1.73205i	−0.0725476	+	0.125656i
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−4.00000			−0.287926			−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000			−0.287926			−0.143963	+	0.989583i	$0.545985\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$	−5.00000			−0.358057
$196$	−3.00000			−0.214286
$197$	7.50000	+	12.9904i	0.534353	+	0.925526i	0.999194	+	0.0401324i	$0.0127780\pi$
$197$	7.50000	+	12.9904i	0.534353	+	0.925526i	−0.464841	+	0.885394i	$0.653889\pi$
$198$		0			0
$199$	−13.0000			−0.921546			−0.460773	−	0.887518i	$-0.652428\pi$
$199$	−13.0000			−0.921546			−0.460773	+	0.887518i	$0.652428\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$		0			0
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$		0			0
$208$	5.00000			0.346688
$209$		0			0
$210$	−1.00000	−	1.73205i	−0.0690066	−	0.119523i
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−9.00000			−0.618123
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$	−3.00000			−0.205076
$215$	−0.500000	+	0.866025i	−0.0340997	+	0.0590624i
$216$	5.00000			0.340207
$217$	1.00000	−	1.73205i	0.0678844	−	0.117579i
$218$	7.00000	−	12.1244i	0.474100	−	0.821165i
$219$	−4.00000	+	6.92820i	−0.270295	+	0.468165i
$220$		0			0
$221$		0			0
$222$	−5.50000	+	2.59808i	−0.369136	+	0.174371i
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$		0			0
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$	2.00000			0.132453
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	−5.00000	−	8.66025i	−0.326860	−	0.566139i
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$	−12.0000			−0.781133
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$		0			0
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	5.00000	+	8.66025i	0.320092	+	0.554416i
$245$	3.00000			0.191663
$246$	−4.50000	+	7.79423i	−0.286910	+	0.496942i
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	1.00000			0.0635001
$249$	−12.0000			−0.760469
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	2.00000	−	3.46410i	0.125988	−	0.218218i
$253$		0			0
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	1.00000			0.0622573
$259$	−1.00000	+	12.1244i	−0.0621370	+	0.753371i
$260$	−5.00000			−0.310087
$261$	6.00000	+	10.3923i	0.371391	+	0.643268i
$262$	3.00000	−	5.19615i	0.185341	−	0.321019i
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	−0.442943	−	0.896550i	$-0.646065\pi$
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	0.997906	−	0.0646755i	$-0.0206012\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	6.00000			0.367194
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−24.0000			−1.46331			−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000			−1.46331			−0.731653	+	0.681677i	$0.761251\pi$
$270$	−5.00000			−0.304290
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		0			0
$273$	10.0000			0.605228
$274$	6.00000	+	10.3923i	0.362473	+	0.627822i
$275$		0			0
$276$		0			0
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	−8.00000	+	13.8564i	−0.479808	+	0.831052i
$279$	−1.00000	−	1.73205i	−0.0598684	−	0.103695i
$280$	−1.00000	−	1.73205i	−0.0597614	−	0.103510i
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$	6.00000			0.357295
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	−0.930714	−	0.365748i	$-0.880813\pi$
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	0.782104	+	0.623148i	$0.214146\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$	−2.00000			−0.118470
$286$		0			0
$287$	9.00000	+	15.5885i	0.531253	+	0.920158i
$288$	2.00000			0.117851
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	6.00000			0.352332
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$	−4.00000	+	6.92820i	−0.234082	+	0.405442i
$293$	7.50000	−	12.9904i	0.438155	−	0.758906i	−0.559393	−	0.828903i	$-0.688966\pi$
$293$	7.50000	−	12.9904i	0.438155	−	0.758906i	0.997547	+	0.0699967i	$0.0222989\pi$
$294$	−1.50000	−	2.59808i	−0.0874818	−	0.151523i
$295$	12.0000			0.698667
$296$	−5.50000	+	2.59808i	−0.319681	+	0.151010i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	7.00000			0.402805
$303$		0			0
$304$	2.00000			0.114708
$305$	−5.00000	−	8.66025i	−0.286299	−	0.495885i
$306$		0			0
$307$	29.0000			1.65512			0.827559	−	0.561379i	$-0.189729\pi$
$307$	29.0000			1.65512			0.827559	+	0.561379i	$0.189729\pi$
$308$		0			0
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$	−1.00000			−0.0567962
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$	2.50000	+	4.33013i	0.141535	+	0.245145i
$313$	−13.0000	−	22.5167i	−0.734803	−	1.27272i	−0.954810	−	0.297218i	$-0.903941\pi$
$313$	−13.0000	−	22.5167i	−0.734803	−	1.27272i	0.220006	−	0.975499i	$-0.429392\pi$
$314$	8.50000	−	14.7224i	0.479683	−	0.830835i
$315$	−2.00000	+	3.46410i	−0.112687	+	0.195180i
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	0.820822	−	0.571184i	$-0.193516\pi$
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	−0.905071	+	0.425261i	$0.860182\pi$
$318$	−4.50000	−	7.79423i	−0.252347	−	0.437079i
$319$		0			0
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−1.50000	−	2.59808i	−0.0837218	−	0.145010i
$322$		0			0
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	5.00000			0.277350
$326$	5.50000	−	9.52628i	0.304617	−	0.527612i
$327$	14.0000			0.774202
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$		0			0
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	0.992112	+	0.125353i	$0.0400062\pi$
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	−0.387498	+	0.921871i	$0.626660\pi$
$332$	−12.0000			−0.658586
$333$	10.0000	+	6.92820i	0.547997	+	0.379663i
$334$	−18.0000			−0.984916
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	−0.991250	−	0.131995i	$-0.957862\pi$
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	0.609936	+	0.792451i	$0.291195\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−2.00000	−	3.46410i	−0.108148	−	0.187317i
$343$	−20.0000			−1.07990
$344$	1.00000			0.0539164
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	1.00000	+	1.73205i	0.0534522	+	0.0925820i
$351$	12.5000	−	21.6506i	0.667201	−	1.15563i
$352$		0			0
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	6.00000			0.317999
$357$		0			0
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	27.0000			1.42501			0.712503	−	0.701669i	$-0.247562\pi$
$359$	27.0000			1.42501			0.712503	+	0.701669i	$0.247562\pi$
$360$	−2.00000			−0.105409
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−14.0000			−0.735824
$363$	5.50000	−	9.52628i	0.288675	−	0.500000i
$364$	10.0000			0.524142
$365$	4.00000	−	6.92820i	0.209370	−	0.362639i
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	17.0000	−	29.4449i	0.887393	−	1.53701i	0.0444464	−	0.999012i	$-0.485848\pi$
$367$	17.0000	−	29.4449i	0.887393	−	1.53701i	0.842946	−	0.537998i	$-0.180819\pi$
$368$		0			0
$369$	18.0000			0.937043
$370$	5.50000	−	2.59808i	0.285931	−	0.135068i
$371$	−18.0000			−0.934513
$372$	0.500000	+	0.866025i	0.0259238	+	0.0449013i
$373$	−2.50000	+	4.33013i	−0.129445	+	0.224205i	−0.923462	−	0.383691i	$-0.874653\pi$
$373$	−2.50000	+	4.33013i	−0.129445	+	0.224205i	0.794017	+	0.607896i	$0.207986\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	6.00000			0.309426
$377$	−15.0000	+	25.9808i	−0.772539	+	1.33808i
$378$	10.0000			0.514344
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	0.994992	−	0.0999550i	$-0.0318699\pi$
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	−0.584060	+	0.811711i	$0.698537\pi$
$380$	−2.00000			−0.102598
$381$	8.00000			0.409852
$382$	1.50000	+	2.59808i	0.0767467	+	0.132929i
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	−0.173005	−	0.984921i	$-0.555348\pi$
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	0.939469	−	0.342634i	$-0.111319\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	−0.383076	−	0.923717i	$-0.625135\pi$
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	0.991500	−	0.130105i	$-0.0415314\pi$
$390$	−2.50000	−	4.33013i	−0.126592	−	0.219265i
$391$		0			0
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$	6.00000			0.302660
$394$	−7.50000	+	12.9904i	−0.377845	+	0.654446i
$395$	−2.00000	−	3.46410i	−0.100631	−	0.174298i
$396$		0			0
$397$	−13.0000			−0.652451			−0.326226	−	0.945292i	$-0.605777\pi$
$397$	−13.0000			−0.652451			−0.326226	+	0.945292i	$0.605777\pi$
$398$	−6.50000	−	11.2583i	−0.325816	−	0.564329i
$399$	4.00000			0.200250
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$	−2.00000	+	3.46410i	−0.0997509	+	0.172774i
$403$	2.50000	−	4.33013i	0.124534	−	0.215699i
$404$		0			0
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	−12.0000			−0.595550
$407$		0			0
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$	−6.00000	+	10.3923i	−0.295958	+	0.512615i
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	−24.0000			−1.18096
$414$		0			0
$415$	12.0000			0.589057
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	−16.0000			−0.783523
$418$		0			0
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.852047	+	0.523465i	$0.175361\pi$
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.0273103	+	0.999627i	$0.491306\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	7.00000	+	12.1244i	0.340755	+	0.590204i
$423$	−6.00000	−	10.3923i	−0.291730	−	0.505291i
$424$	−4.50000	−	7.79423i	−0.218539	−	0.378521i
$425$		0			0
$426$	−6.00000	+	10.3923i	−0.290701	+	0.503509i
$427$	10.0000	+	17.3205i	0.483934	+	0.838198i
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$		0			0
$430$	−1.00000			−0.0482243
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	2.00000			0.0960031
$435$	3.00000	+	5.19615i	0.143839	+	0.249136i
$436$	14.0000			0.670478
$437$		0			0
$438$	−8.00000			−0.382255
$439$	9.50000	−	16.4545i	0.453410	−	0.785330i	−0.545185	−	0.838316i	$-0.683541\pi$
$439$	9.50000	−	16.4545i	0.453410	−	0.785330i	0.998595	+	0.0529862i	$0.0168739\pi$
$440$		0			0
$441$	−3.00000	+	5.19615i	−0.142857	+	0.247436i
$442$		0			0
$443$	15.0000			0.712672			0.356336	−	0.934358i	$-0.384026\pi$
$443$	15.0000			0.712672			0.356336	+	0.934358i	$0.384026\pi$
$444$	−5.00000	−	3.46410i	−0.237289	−	0.164399i
$445$	−6.00000			−0.284427
$446$	−14.0000	−	24.2487i	−0.662919	−	1.14821i
$447$		0			0
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	−0.632990	−	0.774160i	$-0.718173\pi$
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	0.986937	+	0.161106i	$0.0515060\pi$
$450$	2.00000			0.0942809
$451$		0			0
$452$		0			0
$453$	3.50000	+	6.06218i	0.164444	+	0.284826i
$454$	−3.00000			−0.140797
$455$	−10.0000			−0.468807
$456$	1.00000	+	1.73205i	0.0468293	+	0.0811107i
$457$	14.0000	−	24.2487i	0.654892	−	1.13431i	−0.327028	−	0.945015i	$-0.606047\pi$
$457$	14.0000	−	24.2487i	0.654892	−	1.13431i	0.981921	−	0.189292i	$-0.0606194\pi$
$458$	−26.0000			−1.21490
$459$		0			0
$460$		0			0
$461$	9.00000	+	15.5885i	0.419172	+	0.726027i	0.995856	−	0.0909401i	$-0.0289872\pi$
$461$	9.00000	+	15.5885i	0.419172	+	0.726027i	−0.576685	+	0.816967i	$0.695654\pi$
$462$		0			0
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	−0.618050	−	0.786139i	$-0.712077\pi$
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	0.989841	+	0.142177i	$0.0454103\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	−0.500000	−	0.866025i	−0.0231869	−	0.0401610i
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$	5.00000	−	8.66025i	0.231125	−	0.400320i
$469$	4.00000	+	6.92820i	0.184703	+	0.319915i
$470$	−6.00000			−0.276759
$471$	17.0000			0.783319
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$		0			0
$474$	−2.00000	+	3.46410i	−0.0918630	+	0.159111i
$475$	2.00000			0.0917663
$476$		0			0
$477$	−9.00000	+	15.5885i	−0.412082	+	0.713746i
$478$		0			0
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	0.984930	−	0.172953i	$-0.0553307\pi$
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	−0.642246	+	0.766498i	$0.721997\pi$
$480$	1.00000			0.0456435
$481$	−2.50000	+	30.3109i	−0.113990	+	1.38206i
$482$	10.0000			0.455488
$483$		0			0
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	−34.0000			−1.54069			−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000			−1.54069			−0.770344	+	0.637629i	$0.779915\pi$
$488$	−5.00000	+	8.66025i	−0.226339	+	0.392031i
$489$	11.0000			0.497437
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	−9.00000			−0.405751
$493$		0			0
$494$	5.00000	−	8.66025i	0.224961	−	0.389643i
$495$		0			0
$496$	0.500000	+	0.866025i	0.0224507	+	0.0388857i
$497$	12.0000	+	20.7846i	0.538274	+	0.932317i
$498$	−6.00000	−	10.3923i	−0.268866	−	0.465690i
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	0.246214	+	0.969216i	$0.420813\pi$
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−9.00000	−	15.5885i	−0.402090	−	0.696441i
$502$	9.00000	+	15.5885i	0.401690	+	0.695747i
$503$	−15.0000	−	25.9808i	−0.668817	−	1.15842i	−0.978235	−	0.207499i	$-0.933468\pi$
$503$	−15.0000	−	25.9808i	−0.668817	−	1.15842i	0.309418	−	0.950926i	$-0.399866\pi$
$504$	4.00000			0.178174
$505$		0			0
$506$		0			0
$507$	12.0000			0.532939
$508$	8.00000			0.354943
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	−8.00000	+	13.8564i	−0.353899	+	0.612971i
$512$	−1.00000			−0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$	−2.00000	+	3.46410i	−0.0881305	+	0.152647i
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$		0			0
$518$	−11.0000	+	5.19615i	−0.483312	+	0.228306i
$519$	−6.00000			−0.263371
$520$	−2.50000	−	4.33013i	−0.109632	−	0.189889i
$521$	−22.5000	+	38.9711i	−0.985743	+	1.70736i	−0.347155	+	0.937808i	$0.612852\pi$
$521$	−22.5000	+	38.9711i	−0.985743	+	1.70736i	−0.638588	+	0.769549i	$0.720481\pi$
$522$	−6.00000	+	10.3923i	−0.262613	+	0.454859i
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	−0.688196	−	0.725525i	$-0.741597\pi$
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	0.972421	+	0.233233i	$0.0749303\pi$
$524$	6.00000			0.262111
$525$	−1.00000	+	1.73205i	−0.0436436	+	0.0755929i
$526$	18.0000			0.784837
$527$		0			0
$528$		0			0
$529$	−23.0000			−1.00000
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$	−12.0000	+	20.7846i	−0.520756	+	0.901975i
$532$	4.00000			0.173422
$533$	22.5000	+	38.9711i	0.974583	+	1.68803i
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$	−12.0000	−	20.7846i	−0.517357	−	0.896088i
$539$		0			0
$540$	−2.50000	−	4.33013i	−0.107583	−	0.186339i
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$	−0.500000	+	0.866025i	−0.0214768	+	0.0371990i
$543$	−7.00000	−	12.1244i	−0.300399	−	0.520306i
$544$		0			0
$545$	−14.0000			−0.599694
$546$	5.00000	+	8.66025i	0.213980	+	0.370625i
$547$	41.0000			1.75303			0.876517	−	0.481371i	$-0.159861\pi$
$547$	41.0000			1.75303			0.876517	+	0.481371i	$0.159861\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$	20.0000			0.853579
$550$		0			0
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$		0			0
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	1.00000			0.0424859
$555$	5.00000	+	3.46410i	0.212238	+	0.147043i
$556$	−16.0000			−0.678551
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$	1.00000	−	1.73205i	0.0423334	−	0.0733236i
$559$	2.50000	−	4.33013i	0.105739	−	0.183145i
$560$	1.00000	−	1.73205i	0.0422577	−	0.0731925i
$561$		0			0
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$	−36.0000			−1.51722			−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000			−1.51722			−0.758610	+	0.651546i	$0.774121\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$		0			0
$566$	−5.00000			−0.210166
$567$	−1.00000	−	1.73205i	−0.0419961	−	0.0727393i
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	−15.0000			−0.628833			−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000			−0.628833			−0.314416	+	0.949285i	$0.601809\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	0.994765	+	0.102190i	$0.0325850\pi$
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	−0.408883	+	0.912587i	$0.634082\pi$
$572$		0			0
$573$	−1.50000	+	2.59808i	−0.0626634	+	0.108536i
$574$	−9.00000	+	15.5885i	−0.375653	+	0.650650i
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	0.844459	−	0.535620i	$-0.179922\pi$
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	−0.886090	+	0.463513i	$0.846589\pi$
$578$	17.0000			0.707107
$579$	2.00000	−	3.46410i	0.0831172	−	0.143963i
$580$	3.00000	+	5.19615i	0.124568	+	0.215758i
$581$	−24.0000			−0.995688
$582$	−2.00000			−0.0829027
$583$		0			0
$584$	−8.00000			−0.331042
$585$	−5.00000	+	8.66025i	−0.206725	+	0.358057i
$586$	15.0000			0.619644
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$	1.50000	−	2.59808i	0.0618590	−	0.107143i
$589$	1.00000	−	1.73205i	0.0412043	−	0.0713679i
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$	−15.0000			−0.617018
$592$	−5.00000	−	3.46410i	−0.205499	−	0.142374i
$593$	−24.0000			−0.985562			−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000			−0.985562			−0.492781	+	0.870153i	$0.664020\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.50000	−	11.2583i	0.266027	−	0.460773i
$598$		0			0
$599$	−7.50000	+	12.9904i	−0.306442	+	0.530773i	−0.977581	−	0.210558i	$-0.932472\pi$
$599$	−7.50000	+	12.9904i	−0.306442	+	0.530773i	0.671140	+	0.741331i	$0.265805\pi$
$600$	−1.00000			−0.0408248
$601$	3.50000	+	6.06218i	0.142768	+	0.247281i	0.928538	−	0.371237i	$-0.121066\pi$
$601$	3.50000	+	6.06218i	0.142768	+	0.247281i	−0.785770	+	0.618519i	$0.787733\pi$
$602$	2.00000			0.0815139
$603$	8.00000			0.325785
$604$	3.50000	+	6.06218i	0.142413	+	0.246667i
$605$	−5.50000	+	9.52628i	−0.223607	+	0.387298i
$606$		0			0
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	−6.00000	−	10.3923i	−0.243132	−	0.421117i
$610$	5.00000	−	8.66025i	0.202444	−	0.350643i
$611$	15.0000	−	25.9808i	0.606835	−	1.05107i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	14.5000	+	25.1147i	0.585172	+	1.01355i
$615$	9.00000			0.362915
$616$		0			0
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	0.988343	−	0.152242i	$-0.0486493\pi$
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	−0.626017	+	0.779809i	$0.715316\pi$
$618$	4.00000			0.160904
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	−0.500000	−	0.866025i	−0.0200805	−	0.0347804i
$621$		0			0
$622$	10.5000	−	18.1865i	0.421012	−	0.729214i
$623$	12.0000			0.480770
$624$	−2.50000	+	4.33013i	−0.100080	+	0.173344i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	13.0000	−	22.5167i	0.519584	−	0.899947i
$627$		0			0
$628$	17.0000			0.678374
$629$		0			0
$630$	−4.00000			−0.159364
$631$	−2.50000	−	4.33013i	−0.0995234	−	0.172380i	0.811964	−	0.583707i	$-0.198398\pi$
$631$	−2.50000	−	4.33013i	−0.0995234	−	0.172380i	−0.911487	+	0.411328i	$0.865065\pi$
$632$	−2.00000	+	3.46410i	−0.0795557	+	0.137795i
$633$	−7.00000	+	12.1244i	−0.278225	+	0.481900i
$634$	1.50000	−	2.59808i	0.0595726	−	0.103183i
$635$	−8.00000			−0.317470
$636$	4.50000	−	7.79423i	0.178437	−	0.309061i
$637$	−15.0000			−0.594322
$638$		0			0
$639$	24.0000			0.949425
$640$	1.00000			0.0395285
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	0.679039	−	0.734103i	$-0.262397\pi$
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	−0.975271	+	0.221013i	$0.929064\pi$
$642$	1.50000	−	2.59808i	0.0592003	−	0.102538i
$643$	29.0000			1.14365			0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000			1.14365			0.571824	+	0.820376i	$0.306236\pi$
$644$		0			0
$645$	−0.500000	−	0.866025i	−0.0196875	−	0.0340997i
$646$		0			0
$647$	18.0000	−	31.1769i	0.707653	−	1.22569i	−0.258073	−	0.966126i	$-0.583087\pi$
$647$	18.0000	−	31.1769i	0.707653	−	1.22569i	0.965726	−	0.259565i	$-0.0835793\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$		0			0
$650$	2.50000	+	4.33013i	0.0980581	+	0.169842i
$651$	1.00000	+	1.73205i	0.0391931	+	0.0678844i
$652$	11.0000			0.430793
$653$	−16.5000	+	28.5788i	−0.645695	+	1.11838i	0.338446	+	0.940986i	$0.390099\pi$
$653$	−16.5000	+	28.5788i	−0.645695	+	1.11838i	−0.984141	+	0.177390i	$0.943234\pi$
$654$	7.00000	+	12.1244i	0.273722	+	0.474100i
$655$	−6.00000			−0.234439
$656$	−9.00000			−0.351391
$657$	8.00000	+	13.8564i	0.312110	+	0.540590i
$658$	12.0000			0.467809
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	−11.0000	+	19.0526i	−0.427527	+	0.740499i
$663$		0			0
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	−4.00000			−0.155113
$666$	−1.00000	+	12.1244i	−0.0387492	+	0.469809i
$667$		0			0
$668$	−9.00000	−	15.5885i	−0.348220	−	0.603136i
$669$	14.0000	−	24.2487i	0.541271	−	0.937509i
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$		0			0
$672$	−2.00000			−0.0771517
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	0.498886	+	0.866668i	$0.333743\pi$
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$	−14.0000			−0.539260
$675$	2.50000	+	4.33013i	0.0962250	+	0.166667i
$676$	12.0000			0.461538
$677$	30.0000			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$678$		0			0
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$		0			0
$681$	−1.50000	−	2.59808i	−0.0574801	−	0.0995585i
$682$		0			0
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$	6.00000	−	10.3923i	0.229248	−	0.397070i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−13.0000	−	22.5167i	−0.495981	−	0.859064i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−45.0000			−1.71436
$690$		0			0
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.743170	−	0.669102i	$-0.766679\pi$
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.207875	−	0.978155i	$-0.566655\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−6.00000	−	10.3923i	−0.227757	−	0.394486i
$695$	16.0000			0.606915
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$		0			0
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	−9.00000	+	15.5885i	−0.340411	+	0.589610i
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	0.996904	+	0.0786236i	$0.0250525\pi$
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	−0.430362	+	0.902656i	$0.641614\pi$
$702$	25.0000			0.943564
$703$	−1.00000	+	12.1244i	−0.0377157	+	0.457279i
$704$		0			0
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$		0			0
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	−16.0000			−0.600893			−0.300446	−	0.953799i	$-0.597136\pi$
$709$	−16.0000			−0.600893			−0.300446	+	0.953799i	$0.597136\pi$
$710$	6.00000	−	10.3923i	0.225176	−	0.390016i
$711$	8.00000			0.300023
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	13.5000	+	23.3827i	0.503816	+	0.872634i
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	0.601075	−	0.799193i	$-0.294739\pi$
$719$	−10.5000	−	18.1865i	−0.391584	−	0.678243i	−0.992659	+	0.120950i	$0.961406\pi$
$720$	−1.00000	−	1.73205i	−0.0372678	−	0.0645497i
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$	5.00000	+	8.66025i	0.185952	+	0.322078i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	11.0000			0.408248
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	−0.480519	−	0.876984i	$-0.659552\pi$
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	0.999750	−	0.0223506i	$-0.00711500\pi$
$728$	5.00000	+	8.66025i	0.185312	+	0.320970i
$729$	13.0000			0.481481
$730$	8.00000			0.296093
$731$		0			0
$732$	−10.0000			−0.369611
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	−0.883902	−	0.467671i	$-0.845093\pi$
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	0.846967	+	0.531646i	$0.178426\pi$
$734$	34.0000			1.25496
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$		0			0
$737$		0			0
$738$	9.00000	+	15.5885i	0.331295	+	0.573819i
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	5.00000	+	3.46410i	0.183804	+	0.127343i
$741$	10.0000			0.367359
$742$	−9.00000	−	15.5885i	−0.330400	−	0.572270i
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$	−0.500000	+	0.866025i	−0.0183309	+	0.0317500i
$745$		0			0
$746$	−5.00000			−0.183063
$747$	−12.0000	+	20.7846i	−0.439057	+	0.760469i
$748$		0			0
$749$	−3.00000	−	5.19615i	−0.109618	−	0.189863i
$750$	1.00000			0.0365148
$751$	−7.00000			−0.255434			−0.127717	−	0.991811i	$-0.540765\pi$
$751$	−7.00000			−0.255434			−0.127717	+	0.991811i	$0.540765\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	−9.00000	+	15.5885i	−0.327978	+	0.568075i
$754$	−30.0000			−1.09254
$755$	−3.50000	−	6.06218i	−0.127378	−	0.220625i
$756$	5.00000	+	8.66025i	0.181848	+	0.314970i
$757$	−23.5000	−	40.7032i	−0.854122	−	1.47938i	−0.877457	−	0.479655i	$-0.840762\pi$
$757$	−23.5000	−	40.7032i	−0.854122	−	1.47938i	0.0233351	−	0.999728i	$-0.492572\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$		0			0
$760$	−1.00000	−	1.73205i	−0.0362738	−	0.0628281i
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$	4.00000	+	6.92820i	0.144905	+	0.250982i
$763$	28.0000			1.01367
$764$	−1.50000	+	2.59808i	−0.0542681	+	0.0939951i
$765$		0			0
$766$	30.0000			1.08394
$767$	−60.0000			−2.16647
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	0.500000	+	0.866025i	0.0179605	+	0.0311086i
$776$	−2.00000			−0.0717958
$777$	−10.0000	−	6.92820i	−0.358748	−	0.248548i
$778$	24.0000			0.860442
$779$	9.00000	+	15.5885i	0.322458	+	0.558514i
$780$	2.50000	−	4.33013i	0.0895144	−	0.155043i
$781$		0			0
$782$		0			0
$783$	−30.0000			−1.07211
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	−17.0000			−0.606756
$786$	3.00000	+	5.19615i	0.107006	+	0.185341i
$787$	53.0000			1.88925			0.944623	−	0.328158i	$-0.106428\pi$
$787$	53.0000			1.88925			0.944623	+	0.328158i	$0.106428\pi$
$788$	−15.0000			−0.534353
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$	2.00000	−	3.46410i	0.0711568	−	0.123247i
$791$		0			0
$792$		0			0
$793$	25.0000	+	43.3013i	0.887776	+	1.53767i
$794$	−6.50000	−	11.2583i	−0.230676	−	0.399543i
$795$	−4.50000	+	7.79423i	−0.159599	+	0.276433i
$796$	6.50000	−	11.2583i	0.230386	−	0.399041i
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$	2.00000	+	3.46410i	0.0707992	+	0.122628i
$799$		0			0
$800$	−1.00000			−0.0353553
$801$	6.00000	−	10.3923i	0.212000	−	0.367194i
$802$	15.0000	+	25.9808i	0.529668	+	0.917413i
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	5.00000			0.176117
$807$	12.0000	−	20.7846i	0.422420	−	0.731653i
$808$		0			0
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	−0.134255	−	0.990947i	$-0.542864\pi$
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	0.925312	−	0.379206i	$-0.123803\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	−0.690693	−	0.723148i	$-0.742694\pi$
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	0.971611	+	0.236584i	$0.0760278\pi$
$812$	−6.00000	−	10.3923i	−0.210559	−	0.364698i
$813$	−1.00000			−0.0350715
$814$		0			0
$815$	−11.0000			−0.385313
$816$		0			0
$817$	1.00000	−	1.73205i	0.0349856	−	0.0605968i
$818$	2.50000	−	4.33013i	0.0874105	−	0.151399i
$819$	10.0000	−	17.3205i	0.349428	−	0.605228i
$820$	9.00000			0.314294
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	−12.0000			−0.418548
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$	−12.0000	−	20.7846i	−0.417533	−	0.723189i
$827$	−6.00000	+	10.3923i	−0.208640	+	0.361376i	−0.951286	−	0.308308i	$-0.900237\pi$
$827$	−6.00000	+	10.3923i	−0.208640	+	0.361376i	0.742646	+	0.669684i	$0.233571\pi$
$828$		0			0
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	0.546971	−	0.837151i	$-0.315781\pi$
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	−0.998480	+	0.0551154i	$0.982447\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$	0.500000	+	0.866025i	0.0173448	+	0.0300421i
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$		0			0
$834$	−8.00000	−	13.8564i	−0.277017	−	0.479808i
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$		0			0
$837$	5.00000			0.172825
$838$	−18.0000	+	31.1769i	−0.621800	+	1.07699i
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	−0.976987	−	0.213298i	$-0.931580\pi$
$839$	−19.5000	−	33.7750i	−0.673215	−	1.16604i	0.303773	−	0.952745i	$-0.401754\pi$
$840$	2.00000			0.0690066
$841$	7.00000			0.241379
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$	−15.0000			−0.516627
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	−12.0000			−0.412813
$846$	6.00000	−	10.3923i	0.206284	−	0.357295i
$847$	11.0000	−	19.0526i	0.377964	−	0.654654i
$848$	4.50000	−	7.79423i	0.154531	−	0.267655i
$849$	−2.50000	−	4.33013i	−0.0857998	−	0.148610i
$850$		0			0
$851$		0			0
$852$	−12.0000			−0.411113
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	0.986846	+	0.161664i	$0.0516860\pi$
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	−0.353418	+	0.935466i	$0.614981\pi$
$854$	−10.0000	+	17.3205i	−0.342193	+	0.592696i
$855$	−2.00000	+	3.46410i	−0.0683986	+	0.118470i
$856$	1.50000	−	2.59808i	0.0512689	−	0.0888004i
$857$	−12.0000			−0.409912			−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$	−0.500000	−	0.866025i	−0.0170499	−	0.0295312i
$861$	−18.0000			−0.613438
$862$	9.00000			0.306541
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	0.994720	−	0.102624i	$-0.0327240\pi$
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	−0.586235	+	0.810141i	$0.699391\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$	6.00000			0.204006
$866$	−8.00000	−	13.8564i	−0.271851	−	0.470860i
$867$	8.50000	+	14.7224i	0.288675	+	0.500000i
$868$	1.00000	+	1.73205i	0.0339422	+	0.0587896i
$869$		0			0
$870$	−3.00000	+	5.19615i	−0.101710	+	0.176166i
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	2.00000	+	3.46410i	0.0676897	+	0.117242i
$874$		0			0
$875$	1.00000	−	1.73205i	0.0338062	−	0.0585540i
$876$	−4.00000	−	6.92820i	−0.135147	−	0.234082i
$877$	53.0000			1.78968			0.894841	−	0.446384i	$-0.147289\pi$
$877$	53.0000			1.78968			0.894841	+	0.446384i	$0.147289\pi$
$878$	19.0000			0.641219
$879$	7.50000	+	12.9904i	0.252969	+	0.438155i
$880$		0			0
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	−0.976863	−	0.213866i	$-0.931394\pi$
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	0.673645	+	0.739055i	$0.264728\pi$
$882$	−6.00000			−0.202031
$883$	21.5000	−	37.2391i	0.723533	−	1.25320i	−0.236043	−	0.971743i	$-0.575850\pi$
$883$	21.5000	−	37.2391i	0.723533	−	1.25320i	0.959575	−	0.281453i	$-0.0908162\pi$
$884$		0			0
$885$	−6.00000	+	10.3923i	−0.201688	+	0.349334i
$886$	7.50000	+	12.9904i	0.251967	+	0.436420i
$887$	−42.0000			−1.41022			−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000			−1.41022			−0.705111	+	0.709097i	$0.749103\pi$
$888$	0.500000	−	6.06218i	0.0167789	−	0.203433i
$889$	16.0000			0.536623
$890$	−3.00000	−	5.19615i	−0.100560	−	0.174175i
$891$		0			0
$892$	14.0000	−	24.2487i	0.468755	−	0.811907i
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$	−2.00000			−0.0668153
$897$		0			0
$898$	15.0000			0.500556
$899$	−6.00000			−0.200111
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$		0			0
$902$		0			0
$903$	1.00000	+	1.73205i	0.0332779	+	0.0576390i
$904$		0			0
$905$	7.00000	+	12.1244i	0.232688	+	0.403027i
$906$	−3.50000	+	6.06218i	−0.116280	+	0.201402i
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	−0.830909	−	0.556408i	$-0.812179\pi$
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	0.897318	+	0.441384i	$0.145512\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$		0			0
$910$	−5.00000	−	8.66025i	−0.165748	−	0.287085i
$911$	51.0000			1.68971			0.844853	−	0.534999i	$-0.179688\pi$
$911$	51.0000			1.68971			0.844853	+	0.534999i	$0.179688\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$		0			0
$914$	28.0000			0.926158
$915$	10.0000			0.330590
$916$	−13.0000	−	22.5167i	−0.429532	−	0.743971i
$917$	12.0000			0.396275
$918$		0			0
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$		0			0
$921$	−14.5000	+	25.1147i	−0.477791	+	0.827559i
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$	30.0000	+	51.9615i	0.987462	+	1.71033i
$924$		0			0
$925$	−5.00000	−	3.46410i	−0.164399	−	0.113899i
$926$	16.0000			0.525793
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$	0.500000	−	0.866025i	0.0163956	−	0.0283981i
$931$	−6.00000			−0.196642
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$	21.0000			0.687509
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$		0			0
$936$	10.0000			0.326860
$937$	17.0000	+	29.4449i	0.555366	+	0.961922i	0.997875	+	0.0651578i	$0.0207551\pi$
$937$	17.0000	+	29.4449i	0.555366	+	0.961922i	−0.442509	+	0.896764i	$0.645912\pi$
$938$	−4.00000	+	6.92820i	−0.130605	+	0.226214i
$939$	26.0000			0.848478
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	18.0000	+	31.1769i	0.586783	+	1.01634i	0.994651	+	0.103297i	$0.0329393\pi$
$941$	18.0000	+	31.1769i	0.586783	+	1.01634i	−0.407867	+	0.913041i	$0.633727\pi$
$942$	8.50000	+	14.7224i	0.276945	+	0.479683i
$943$		0			0
$944$	6.00000	−	10.3923i	0.195283	−	0.338241i
$945$	−5.00000	−	8.66025i	−0.162650	−	0.281718i
$946$		0			0
$947$	10.5000	+	18.1865i	0.341204	+	0.590983i	0.984657	−	0.174503i	$-0.0558319\pi$
$947$	10.5000	+	18.1865i	0.341204	+	0.590983i	−0.643452	+	0.765486i	$0.722499\pi$
$948$	−4.00000			−0.129914
$949$	−20.0000	+	34.6410i	−0.649227	+	1.12449i
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$	3.00000			0.0972817
$952$		0			0
$953$	18.0000	+	31.1769i	0.583077	+	1.00992i	0.995112	+	0.0987513i	$0.0314848\pi$
$953$	18.0000	+	31.1769i	0.583077	+	1.00992i	−0.412035	+	0.911168i	$0.635182\pi$
$954$	−18.0000			−0.582772
$955$	1.50000	−	2.59808i	0.0485389	−	0.0840718i
$956$		0			0
$957$		0			0
$958$	−7.50000	+	12.9904i	−0.242314	+	0.419700i
$959$	−12.0000	+	20.7846i	−0.387500	+	0.671170i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−30.0000			−0.967742
$962$	−27.5000	+	12.9904i	−0.886636	+	0.418827i
$963$	−6.00000			−0.193347
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$	11.0000			0.353553
$969$		0			0
$970$	2.00000			0.0642161
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	16.0000			0.513200
$973$	−32.0000			−1.02587
$974$	−17.0000	−	29.4449i	−0.544715	−	0.943474i
$975$	−2.50000	+	4.33013i	−0.0800641	+	0.138675i
$976$	−10.0000			−0.320092
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$	5.50000	+	9.52628i	0.175871	+	0.304617i
$979$		0			0
$980$	−1.50000	+	2.59808i	−0.0479157	+	0.0829925i
$981$	14.0000	−	24.2487i	0.446986	−	0.774202i
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	0.977961	+	0.208788i	$0.0669518\pi$
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	−0.308165	+	0.951333i	$0.599715\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$	15.0000			0.477940
$986$		0			0
$987$	6.00000	+	10.3923i	0.190982	+	0.330791i
$988$	10.0000			0.318142
$989$		0			0
$990$		0			0
$991$	47.0000			1.49300			0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000			1.49300			0.746502	+	0.665383i	$0.231732\pi$
$992$	−0.500000	+	0.866025i	−0.0158750	+	0.0274963i
$993$	−22.0000			−0.698149
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$	−6.50000	+	11.2583i	−0.206064	+	0.356913i
$996$	6.00000	−	10.3923i	0.190117	−	0.329293i
$997$	−26.5000	−	45.8993i	−0.839263	−	1.45365i	−0.890511	−	0.454961i	$-0.849653\pi$
$997$	−26.5000	−	45.8993i	−0.839263	−	1.45365i	0.0512480	−	0.998686i	$-0.483680\pi$
$998$	−32.0000			−1.01294
$999$	−27.5000	+	12.9904i	−0.870061	+	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.e.b.211.1	yes	2
37.10	even	3	inner	370.2.e.b.121.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.e.b.121.1	✓	2	37.10	even	3	inner
370.2.e.b.211.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +1.00000 q^{10} +(-0.500000 - 0.866025i) q^{12} +(-2.50000 + 4.33013i) q^{13} -2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{21} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{26} -5.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +6.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} -1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{35} -2.00000 q^{36} +(5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-2.50000 - 4.33013i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(1.00000 - 1.73205i) q^{42} -1.00000 q^{43} +2.00000 q^{45} -6.00000 q^{47} +1.00000 q^{48} +(1.50000 + 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.50000 - 4.33013i) q^{52} +(4.50000 + 7.79423i) q^{53} +(-2.50000 - 4.33013i) q^{54} +(1.00000 - 1.73205i) q^{56} +(-1.00000 - 1.73205i) q^{57} +(3.00000 + 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} -1.00000 q^{60} +(5.00000 - 8.66025i) q^{61} +(-0.500000 - 0.866025i) q^{62} -4.00000 q^{63} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.00000 + 1.73205i) q^{70} +(6.00000 - 10.3923i) q^{71} +(-1.00000 - 1.73205i) q^{72} +8.00000 q^{73} +(5.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(2.50000 - 4.33013i) q^{78} +(2.00000 - 3.46410i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +9.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +2.00000 q^{84} +(-0.500000 - 0.866025i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(1.00000 + 1.73205i) q^{90} +(-5.00000 - 8.66025i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - q^{12} - 5 q^{13} - 4 q^{14} + q^{15} - q^{16} - 2 q^{18} - 2 q^{19} + q^{20} - 2 q^{21} + q^{24} - q^{25} - 10 q^{26} - 10 q^{27} - 2 q^{28} + 12 q^{29} - q^{30} - 2 q^{31} + q^{32} + 2 q^{35} - 4 q^{36} + 11 q^{37} - 4 q^{38} - 5 q^{39} - q^{40} + 9 q^{41} + 2 q^{42} - 2 q^{43} + 4 q^{45} - 12 q^{47} + 2 q^{48} + 3 q^{49} + q^{50} - 5 q^{52} + 9 q^{53} - 5 q^{54} + 2 q^{56} - 2 q^{57} + 6 q^{58} + 12 q^{59} - 2 q^{60} + 10 q^{61} - q^{62} - 8 q^{63} + 2 q^{64} + 5 q^{65} + 4 q^{67} - 2 q^{70} + 12 q^{71} - 2 q^{72} + 16 q^{73} + 10 q^{74} + 2 q^{75} - 2 q^{76} + 5 q^{78} + 4 q^{79} - 2 q^{80} - q^{81} + 18 q^{82} + 12 q^{83} + 4 q^{84} - q^{86} - 6 q^{87} - 6 q^{89} + 2 q^{90} - 10 q^{91} + q^{93} - 6 q^{94} + 2 q^{95} + q^{96} + 4 q^{97} - 3 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - q^12 - 5 * q^13 - 4 * q^14 + q^15 - q^16 - 2 * q^18 - 2 * q^19 + q^20 - 2 * q^21 + q^24 - q^25 - 10 * q^26 - 10 * q^27 - 2 * q^28 + 12 * q^29 - q^30 - 2 * q^31 + q^32 + 2 * q^35 - 4 * q^36 + 11 * q^37 - 4 * q^38 - 5 * q^39 - q^40 + 9 * q^41 + 2 * q^42 - 2 * q^43 + 4 * q^45 - 12 * q^47 + 2 * q^48 + 3 * q^49 + q^50 - 5 * q^52 + 9 * q^53 - 5 * q^54 + 2 * q^56 - 2 * q^57 + 6 * q^58 + 12 * q^59 - 2 * q^60 + 10 * q^61 - q^62 - 8 * q^63 + 2 * q^64 + 5 * q^65 + 4 * q^67 - 2 * q^70 + 12 * q^71 - 2 * q^72 + 16 * q^73 + 10 * q^74 + 2 * q^75 - 2 * q^76 + 5 * q^78 + 4 * q^79 - 2 * q^80 - q^81 + 18 * q^82 + 12 * q^83 + 4 * q^84 - q^86 - 6 * q^87 - 6 * q^89 + 2 * q^90 - 10 * q^91 + q^93 - 6 * q^94 + 2 * q^95 + q^96 + 4 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more