LMFDB - Embedded newform 1950.2.bc.a.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.a.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.23205 - 1.86603i) q^{11} -1.00000 q^{12} +(0.866025 + 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-1.96410 + 1.13397i) q^{19} +3.00000i q^{21} +(-1.86603 - 3.23205i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(2.59808 + 1.50000i) q^{28} +(2.73205 - 4.73205i) q^{29} +8.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.23205 - 1.86603i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(6.86603 + 3.96410i) q^{37} -2.26795 q^{38} +(-3.46410 - 1.00000i) q^{39} +(3.46410 + 2.00000i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(3.00000 + 5.19615i) q^{43} -3.73205i q^{44} +(-3.00000 + 1.73205i) q^{46} +0.464102i q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{49} -4.00000 q^{51} +(-2.59808 + 2.50000i) q^{52} +3.73205 q^{53} +(0.866025 + 0.500000i) q^{54} +(1.50000 + 2.59808i) q^{56} -2.26795i q^{57} +(4.73205 - 2.73205i) q^{58} +(3.92820 - 2.26795i) q^{59} +(3.73205 + 6.46410i) q^{61} +(-4.46410 + 7.73205i) q^{62} +(-2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +3.73205 q^{66} +(-4.73205 - 2.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-1.73205 - 3.00000i) q^{69} +(-0.803848 + 0.464102i) q^{71} +(0.866025 - 0.500000i) q^{72} +6.92820i q^{73} +(3.96410 + 6.86603i) q^{74} +(-1.96410 - 1.13397i) q^{76} -11.1962 q^{77} +(-2.50000 - 2.59808i) q^{78} +16.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +2.53590i q^{83} +(-2.59808 + 1.50000i) q^{84} +6.00000i q^{86} +(2.73205 + 4.73205i) q^{87} +(1.86603 - 3.23205i) q^{88} +(-8.76795 - 5.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} -3.46410 q^{92} +(-7.73205 - 4.46410i) q^{93} +(-0.232051 + 0.401924i) q^{94} -1.00000i q^{96} +(-10.7321 + 6.19615i) q^{97} +(1.73205 - 1.00000i) q^{98} +3.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 6 q^{11} - 4 q^{12} + 12 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} - 4 q^{22} - 4 q^{26} + 4 q^{27} + 4 q^{29} + 6 q^{33} + 2 q^{36} + 24 q^{37} - 16 q^{38} - 6 q^{42} + 12 q^{43} - 12 q^{46} - 2 q^{48} + 4 q^{49} - 16 q^{51} + 8 q^{53} + 6 q^{56} + 12 q^{58} - 12 q^{59} + 8 q^{61} - 4 q^{62} - 4 q^{64} + 8 q^{66} - 12 q^{67} - 8 q^{68} - 24 q^{71} + 2 q^{74} + 6 q^{76} - 24 q^{77} - 10 q^{78} + 40 q^{79} - 2 q^{81} + 8 q^{82} + 4 q^{87} + 4 q^{88} - 42 q^{89} + 30 q^{91} - 24 q^{93} + 6 q^{94} - 36 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 6 * q^11 - 4 * q^12 + 12 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 - 4 * q^22 - 4 * q^26 + 4 * q^27 + 4 * q^29 + 6 * q^33 + 2 * q^36 + 24 * q^37 - 16 * q^38 - 6 * q^42 + 12 * q^43 - 12 * q^46 - 2 * q^48 + 4 * q^49 - 16 * q^51 + 8 * q^53 + 6 * q^56 + 12 * q^58 - 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 8 * q^66 - 12 * q^67 - 8 * q^68 - 24 * q^71 + 2 * q^74 + 6 * q^76 - 24 * q^77 - 10 * q^78 + 40 * q^79 - 2 * q^81 + 8 * q^82 + 4 * q^87 + 4 * q^88 - 42 * q^89 + 30 * q^91 - 24 * q^93 + 6 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.0791130	−	0.996866i	$-0.474791\pi$
$7$	2.59808	−	1.50000i	0.981981	−	0.566947i	0.902867	+	0.429919i	$0.141458\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.23205	−	1.86603i	−0.974500	−	0.562628i	−0.0738948	−	0.997266i	$-0.523543\pi$
$11$	−3.23205	−	1.86603i	−0.974500	−	0.562628i	−0.900605	+	0.434638i	$0.856876\pi$
$12$	−1.00000			−0.288675
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	−0.708082	−	0.706130i	$-0.750439\pi$
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	0.257486	+	0.966282i	$0.417106\pi$
$20$		0			0
$21$			3.00000i			0.654654i
$22$	−1.86603	−	3.23205i	−0.397838	−	0.689076i
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	−0.988152	−	0.153481i	$-0.950952\pi$
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	0.626994	+	0.779024i	$0.284285\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	1.00000			0.192450
$28$	2.59808	+	1.50000i	0.490990	+	0.283473i
$29$	2.73205	−	4.73205i	0.507329	−	0.878720i	−0.492635	−	0.870236i	$-0.663966\pi$
$29$	2.73205	−	4.73205i	0.507329	−	0.878720i	0.999964	−	0.00848369i	$-0.00270048\pi$
$30$		0			0
$31$			8.92820i			1.60355i	0.597624	+	0.801776i	$0.296111\pi$
$31$			8.92820i			1.60355i	−0.597624	+	0.801776i	$0.703889\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.23205	−	1.86603i	0.562628	−	0.324833i
$34$			4.00000i			0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	6.86603	+	3.96410i	1.12877	+	0.651694i	0.943625	−	0.331017i	$-0.107392\pi$
$37$	6.86603	+	3.96410i	1.12877	+	0.651694i	0.185143	+	0.982712i	$0.440725\pi$
$38$	−2.26795			−0.367910
$39$	−3.46410	−	1.00000i	−0.554700	−	0.160128i
$40$		0			0
$41$	3.46410	+	2.00000i	0.541002	+	0.312348i	0.745485	−	0.666523i	$-0.232218\pi$
$41$	3.46410	+	2.00000i	0.541002	+	0.312348i	−0.204483	+	0.978870i	$0.565551\pi$
$42$	−1.50000	+	2.59808i	−0.231455	+	0.400892i
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	0.998828	−	0.0484030i	$-0.0154132\pi$
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	−0.541332	+	0.840809i	$0.682080\pi$
$44$		−	3.73205i		−	0.562628i
$45$		0			0
$46$	−3.00000	+	1.73205i	−0.442326	+	0.255377i
$47$			0.464102i			0.0676962i	0.999427	+	0.0338481i	$0.0107762\pi$
$47$			0.464102i			0.0676962i	−0.999427	+	0.0338481i	$0.989224\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	−2.59808	+	2.50000i	−0.360288	+	0.346688i
$53$	3.73205			0.512637			0.256318	−	0.966592i	$-0.417490\pi$
$53$	3.73205			0.512637			0.256318	+	0.966592i	$0.417490\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$		−	2.26795i		−	0.300397i
$58$	4.73205	−	2.73205i	0.621349	−	0.358736i
$59$	3.92820	−	2.26795i	0.511409	−	0.295262i	−0.222004	−	0.975046i	$-0.571260\pi$
$59$	3.92820	−	2.26795i	0.511409	−	0.295262i	0.733412	+	0.679784i	$0.237926\pi$
$60$		0			0
$61$	3.73205	+	6.46410i	0.477840	+	0.827643i	0.999677	−	0.0254017i	$-0.00808648\pi$
$61$	3.73205	+	6.46410i	0.477840	+	0.827643i	−0.521837	+	0.853045i	$0.674753\pi$
$62$	−4.46410	+	7.73205i	−0.566941	+	0.981971i
$63$	−2.59808	−	1.50000i	−0.327327	−	0.188982i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.73205			0.459384
$67$	−4.73205	−	2.73205i	−0.578112	−	0.333773i	0.182271	−	0.983248i	$-0.441655\pi$
$67$	−4.73205	−	2.73205i	−0.578112	−	0.333773i	−0.760383	+	0.649475i	$0.774989\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	−1.73205	−	3.00000i	−0.208514	−	0.361158i
$70$		0			0
$71$	−0.803848	+	0.464102i	−0.0953992	+	0.0550787i	−0.546941	−	0.837171i	$-0.684208\pi$
$71$	−0.803848	+	0.464102i	−0.0953992	+	0.0550787i	0.451541	+	0.892250i	$0.350874\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	3.96410	+	6.86603i	0.460817	+	0.798159i
$75$		0			0
$76$	−1.96410	−	1.13397i	−0.225298	−	0.130076i
$77$	−11.1962			−1.27592
$78$	−2.50000	−	2.59808i	−0.283069	−	0.294174i
$79$	16.9282			1.90457			0.952286	−	0.305208i	$-0.0987259\pi$
$79$	16.9282			1.90457			0.952286	+	0.305208i	$0.0987259\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.00000	+	3.46410i	0.220863	+	0.382546i
$83$			2.53590i			0.278351i	0.990268	+	0.139176i	$0.0444452\pi$
$83$			2.53590i			0.278351i	−0.990268	+	0.139176i	$0.955555\pi$
$84$	−2.59808	+	1.50000i	−0.283473	+	0.163663i
$85$		0			0
$86$			6.00000i			0.646997i
$87$	2.73205	+	4.73205i	0.292907	+	0.507329i
$88$	1.86603	−	3.23205i	0.198919	−	0.344538i
$89$	−8.76795	−	5.06218i	−0.929401	−	0.536590i	−0.0427788	−	0.999085i	$-0.513621\pi$
$89$	−8.76795	−	5.06218i	−0.929401	−	0.536590i	−0.886622	+	0.462495i	$0.846954\pi$
$90$		0			0
$91$	7.50000	+	7.79423i	0.786214	+	0.817057i
$92$	−3.46410			−0.361158
$93$	−7.73205	−	4.46410i	−0.801776	−	0.462906i
$94$	−0.232051	+	0.401924i	−0.0239342	+	0.0414553i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−10.7321	+	6.19615i	−1.08967	+	0.629124i	−0.933490	−	0.358604i	$-0.883253\pi$
$97$	−10.7321	+	6.19615i	−1.08967	+	0.629124i	−0.156185	+	0.987728i	$0.549920\pi$
$98$	1.73205	−	1.00000i	0.174964	−	0.101015i
$99$			3.73205i			0.375085i
$100$		0			0
$101$	4.19615	−	7.26795i	0.417533	−	0.723188i	−0.578158	−	0.815925i	$-0.696228\pi$
$101$	4.19615	−	7.26795i	0.417533	−	0.723188i	0.995691	+	0.0927369i	$0.0295616\pi$
$102$	−3.46410	−	2.00000i	−0.342997	−	0.198030i
$103$	−19.5885			−1.93011			−0.965054	−	0.262051i	$-0.915601\pi$
$103$	−19.5885			−1.93011			−0.965054	+	0.262051i	$0.915601\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$		0			0
$106$	3.23205	+	1.86603i	0.313925	+	0.181244i
$107$	0.464102	−	0.803848i	0.0448664	−	0.0777109i	−0.842720	−	0.538352i	$-0.819047\pi$
$107$	0.464102	−	0.803848i	0.0448664	−	0.0777109i	0.887587	+	0.460641i	$0.152380\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$		0			0
$111$	−6.86603	+	3.96410i	−0.651694	+	0.376256i
$112$			3.00000i			0.283473i
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$	1.13397	−	1.96410i	0.106206	−	0.183955i
$115$		0			0
$116$	5.46410			0.507329
$117$	2.59808	−	2.50000i	0.240192	−	0.231125i
$118$	4.53590			0.417563
$119$	10.3923	+	6.00000i	0.952661	+	0.550019i
$120$		0			0
$121$	1.46410	+	2.53590i	0.133100	+	0.230536i
$122$			7.46410i			0.675768i
$123$	−3.46410	+	2.00000i	−0.312348	+	0.180334i
$124$	−7.73205	+	4.46410i	−0.694359	+	0.400888i
$125$		0			0
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	2.33013	−	4.03590i	0.206765	−	0.358128i	−0.743928	−	0.668259i	$-0.767040\pi$
$127$	2.33013	−	4.03590i	0.206765	−	0.358128i	0.950694	+	0.310131i	$0.100373\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−6.00000			−0.528271
$130$		0			0
$131$	−20.3205			−1.77541			−0.887706	−	0.460412i	$-0.847702\pi$
$131$	−20.3205			−1.77541			−0.887706	+	0.460412i	$0.847702\pi$
$132$	3.23205	+	1.86603i	0.281314	+	0.162417i
$133$	−3.40192	+	5.89230i	−0.294984	+	0.510928i
$134$	−2.73205	−	4.73205i	−0.236013	−	0.408787i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	5.66025	−	3.26795i	0.483588	−	0.279200i	−0.238322	−	0.971186i	$-0.576598\pi$
$137$	5.66025	−	3.26795i	0.483588	−	0.279200i	0.721911	+	0.691986i	$0.243264\pi$
$138$		−	3.46410i		−	0.294884i
$139$	−10.8923	−	18.8660i	−0.923873	−	1.60020i	−0.793363	−	0.608748i	$-0.791672\pi$
$139$	−10.8923	−	18.8660i	−0.923873	−	1.60020i	−0.130510	−	0.991447i	$-0.541661\pi$
$140$		0			0
$141$	−0.401924	−	0.232051i	−0.0338481	−	0.0195422i
$142$	−0.928203			−0.0778931
$143$	3.73205	−	12.9282i	0.312090	−	1.08111i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−3.46410	+	6.00000i	−0.286691	+	0.496564i
$147$	1.00000	+	1.73205i	0.0824786	+	0.142857i
$148$			7.92820i			0.651694i
$149$	19.7321	−	11.3923i	1.61651	−	0.933294i	0.628700	−	0.777648i	$-0.283587\pi$
$149$	19.7321	−	11.3923i	1.61651	−	0.933294i	0.987813	−	0.155646i	$-0.0497458\pi$
$150$		0			0
$151$			18.7846i			1.52867i	0.644819	+	0.764335i	$0.276933\pi$
$151$			18.7846i			1.52867i	−0.644819	+	0.764335i	$0.723067\pi$
$152$	−1.13397	−	1.96410i	−0.0919775	−	0.159310i
$153$	2.00000	−	3.46410i	0.161690	−	0.280056i
$154$	−9.69615	−	5.59808i	−0.781338	−	0.451106i
$155$		0			0
$156$	−0.866025	−	3.50000i	−0.0693375	−	0.280224i
$157$	−10.8038			−0.862241			−0.431120	−	0.902294i	$-0.641882\pi$
$157$	−10.8038			−0.862241			−0.431120	+	0.902294i	$0.641882\pi$
$158$	14.6603	+	8.46410i	1.16631	+	0.673368i
$159$	−1.86603	+	3.23205i	−0.147985	+	0.256318i
$160$		0			0
$161$			10.3923i			0.819028i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	9.46410	−	5.46410i	0.741286	−	0.427981i	−0.0812509	−	0.996694i	$-0.525892\pi$
$163$	9.46410	−	5.46410i	0.741286	−	0.427981i	0.822537	+	0.568712i	$0.192558\pi$
$164$			4.00000i			0.312348i
$165$		0			0
$166$	−1.26795	+	2.19615i	−0.0984119	+	0.170454i
$167$	5.59808	+	3.23205i	0.433192	+	0.250104i	0.700706	−	0.713451i	$-0.252869\pi$
$167$	5.59808	+	3.23205i	0.433192	+	0.250104i	−0.267513	+	0.963554i	$0.586202\pi$
$168$	−3.00000			−0.231455
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$		0			0
$171$	1.96410	+	1.13397i	0.150199	+	0.0867172i
$172$	−3.00000	+	5.19615i	−0.228748	+	0.396203i
$173$	11.0622	+	19.1603i	0.841042	+	1.45673i	0.889015	+	0.457879i	$0.151391\pi$
$173$	11.0622	+	19.1603i	0.841042	+	1.45673i	−0.0479730	+	0.998849i	$0.515276\pi$
$174$			5.46410i			0.414232i
$175$		0			0
$176$	3.23205	−	1.86603i	0.243625	−	0.140657i
$177$			4.53590i			0.340939i
$178$	−5.06218	−	8.76795i	−0.379426	−	0.657186i
$179$	−11.4641	+	19.8564i	−0.856867	+	1.48414i	0.0180347	+	0.999837i	$0.494259\pi$
$179$	−11.4641	+	19.8564i	−0.856867	+	1.48414i	−0.874902	+	0.484300i	$0.839074\pi$
$180$		0			0
$181$	3.07180			0.228325			0.114162	−	0.993462i	$-0.463582\pi$
$181$	3.07180			0.228325			0.114162	+	0.993462i	$0.463582\pi$
$182$	2.59808	+	10.5000i	0.192582	+	0.778312i
$183$	−7.46410			−0.551762
$184$	−3.00000	−	1.73205i	−0.221163	−	0.127688i
$185$		0			0
$186$	−4.46410	−	7.73205i	−0.327324	−	0.566941i
$187$		−	14.9282i		−	1.09166i
$188$	−0.401924	+	0.232051i	−0.0293133	+	0.0169240i
$189$	2.59808	−	1.50000i	0.188982	−	0.109109i
$190$		0			0
$191$	−8.66025	−	15.0000i	−0.626634	−	1.08536i	−0.988222	−	0.153024i	$-0.951099\pi$
$191$	−8.66025	−	15.0000i	−0.626634	−	1.08536i	0.361588	−	0.932338i	$-0.382235\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	15.4641	+	8.92820i	1.11313	+	0.642666i	0.939638	−	0.342169i	$-0.111162\pi$
$193$	15.4641	+	8.92820i	1.11313	+	0.642666i	0.173492	+	0.984835i	$0.444495\pi$
$194$	−12.3923			−0.889716
$195$		0			0
$196$	2.00000			0.142857
$197$	8.13397	+	4.69615i	0.579522	+	0.334587i	0.760943	−	0.648818i	$-0.224737\pi$
$197$	8.13397	+	4.69615i	0.579522	+	0.334587i	−0.181422	+	0.983405i	$0.558070\pi$
$198$	−1.86603	+	3.23205i	−0.132613	+	0.229692i
$199$	5.53590	+	9.58846i	0.392429	+	0.679708i	0.992769	−	0.120037i	$-0.0383014\pi$
$199$	5.53590	+	9.58846i	0.392429	+	0.679708i	−0.600340	+	0.799745i	$0.704968\pi$
$200$		0			0
$201$	4.73205	−	2.73205i	0.333773	−	0.192704i
$202$	7.26795	−	4.19615i	0.511371	−	0.295240i
$203$		−	16.3923i		−	1.15051i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$		0			0
$206$	−16.9641	−	9.79423i	−1.18194	−	0.682396i
$207$	3.46410			0.240772
$208$	−3.46410	−	1.00000i	−0.240192	−	0.0693375i
$209$	8.46410			0.585474
$210$		0			0
$211$	10.9641	−	18.9904i	0.754800	−	1.30735i	−0.190674	−	0.981653i	$-0.561067\pi$
$211$	10.9641	−	18.9904i	0.754800	−	1.30735i	0.945474	−	0.325698i	$-0.105599\pi$
$212$	1.86603	+	3.23205i	0.128159	+	0.221978i
$213$		−	0.928203i		−	0.0635994i
$214$	0.803848	−	0.464102i	0.0549499	−	0.0317253i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	13.3923	+	23.1962i	0.909129	+	1.57466i
$218$	5.19615	−	9.00000i	0.351928	−	0.609557i
$219$	−6.00000	−	3.46410i	−0.405442	−	0.234082i
$220$		0			0
$221$	−10.3923	+	10.0000i	−0.699062	+	0.672673i
$222$	−7.92820			−0.532106
$223$	7.66987	+	4.42820i	0.513613	+	0.296534i	0.734317	−	0.678806i	$-0.237502\pi$
$223$	7.66987	+	4.42820i	0.513613	+	0.296534i	−0.220705	+	0.975341i	$0.570836\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$		0			0
$226$		−	12.0000i		−	0.798228i
$227$	11.6603	−	6.73205i	0.773918	−	0.446822i	−0.0603523	−	0.998177i	$-0.519222\pi$
$227$	11.6603	−	6.73205i	0.773918	−	0.446822i	0.834271	+	0.551355i	$0.185889\pi$
$228$	1.96410	−	1.13397i	0.130076	−	0.0750993i
$229$		−	11.4641i		−	0.757569i	−0.925485	−	0.378785i	$-0.876342\pi$
$229$		−	11.4641i		−	0.757569i	0.925485	−	0.378785i	$-0.123658\pi$
$230$		0			0
$231$	5.59808	−	9.69615i	0.368326	−	0.637960i
$232$	4.73205	+	2.73205i	0.310674	+	0.179368i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$		0			0
$236$	3.92820	+	2.26795i	0.255704	+	0.147631i
$237$	−8.46410	+	14.6603i	−0.549802	+	0.952286i
$238$	6.00000	+	10.3923i	0.388922	+	0.673633i
$239$		−	3.46410i		−	0.224074i	−0.993704	−	0.112037i	$-0.964262\pi$
$239$		−	3.46410i		−	0.224074i	0.993704	−	0.112037i	$-0.0357375\pi$
$240$		0			0
$241$	12.8205	−	7.40192i	0.825842	−	0.476800i	−0.0265852	−	0.999647i	$-0.508463\pi$
$241$	12.8205	−	7.40192i	0.825842	−	0.476800i	0.852427	+	0.522847i	$0.175130\pi$
$242$			2.92820i			0.188232i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.73205	+	6.46410i	−0.238920	+	0.413822i
$245$		0			0
$246$	−4.00000			−0.255031
$247$	−5.66987	−	5.89230i	−0.360765	−	0.374918i
$248$	−8.92820			−0.566941
$249$	−2.19615	−	1.26795i	−0.139176	−	0.0803530i
$250$		0			0
$251$	−13.2321	−	22.9186i	−0.835200	−	1.44661i	−0.893868	−	0.448331i	$-0.852019\pi$
$251$	−13.2321	−	22.9186i	−0.835200	−	1.44661i	0.0586681	−	0.998278i	$-0.481315\pi$
$252$		−	3.00000i		−	0.188982i
$253$	11.1962	−	6.46410i	0.703896	−	0.406395i
$254$	4.03590	−	2.33013i	0.253235	−	0.146205i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.7321	−	18.5885i	0.669447	−	1.15952i	−0.308612	−	0.951188i	$-0.599864\pi$
$257$	10.7321	−	18.5885i	0.669447	−	1.15952i	0.978059	−	0.208328i	$-0.0668022\pi$
$258$	−5.19615	−	3.00000i	−0.323498	−	0.186772i
$259$	23.7846			1.47790
$260$		0			0
$261$	−5.46410			−0.338219
$262$	−17.5981	−	10.1603i	−1.08721	−	0.627703i
$263$	10.2583	−	17.7679i	0.632556	−	1.09562i	−0.354472	−	0.935067i	$-0.615339\pi$
$263$	10.2583	−	17.7679i	0.632556	−	1.09562i	0.987027	−	0.160552i	$-0.0513274\pi$
$264$	1.86603	+	3.23205i	0.114846	+	0.198919i
$265$		0			0
$266$	−5.89230	+	3.40192i	−0.361280	+	0.208585i
$267$	8.76795	−	5.06218i	0.536590	−	0.309800i
$268$		−	5.46410i		−	0.333773i
$269$	15.4641	+	26.7846i	0.942863	+	1.63309i	0.759975	+	0.649953i	$0.225211\pi$
$269$	15.4641	+	26.7846i	0.942863	+	1.63309i	0.182888	+	0.983134i	$0.441455\pi$
$270$		0			0
$271$	−3.12436	−	1.80385i	−0.189791	−	0.109576i	0.402094	−	0.915599i	$-0.368283\pi$
$271$	−3.12436	−	1.80385i	−0.189791	−	0.109576i	−0.591885	+	0.806023i	$0.701616\pi$
$272$	−4.00000			−0.242536
$273$	−10.5000	+	2.59808i	−0.635489	+	0.157243i
$274$	6.53590			0.394848
$275$		0			0
$276$	1.73205	−	3.00000i	0.104257	−	0.180579i
$277$	−9.79423	−	16.9641i	−0.588478	−	1.01927i	−0.994432	−	0.105380i	$-0.966394\pi$
$277$	−9.79423	−	16.9641i	−0.588478	−	1.01927i	0.405954	−	0.913894i	$-0.366939\pi$
$278$		−	21.7846i		−	1.30655i
$279$	7.73205	−	4.46410i	0.462906	−	0.267259i
$280$		0			0
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$	−0.232051	−	0.401924i	−0.0138184	−	0.0239342i
$283$	7.19615	−	12.4641i	0.427767	−	0.740914i	−0.568907	−	0.822402i	$-0.692634\pi$
$283$	7.19615	−	12.4641i	0.427767	−	0.740914i	0.996674	+	0.0814876i	$0.0259671\pi$
$284$	−0.803848	−	0.464102i	−0.0476996	−	0.0275394i
$285$		0			0
$286$	9.69615	−	9.33013i	0.573346	−	0.551702i
$287$	12.0000			0.708338
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$		−	12.3923i		−	0.726450i
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	−16.6699	+	9.62436i	−0.973864	+	0.562261i	−0.900412	−	0.435038i	$-0.856735\pi$
$293$	−16.6699	+	9.62436i	−0.973864	+	0.562261i	−0.0734522	+	0.997299i	$0.523402\pi$
$294$			2.00000i			0.116642i
$295$		0			0
$296$	−3.96410	+	6.86603i	−0.230409	+	0.399080i
$297$	−3.23205	−	1.86603i	−0.187543	−	0.108278i
$298$	22.7846			1.31988
$299$	−12.0000	−	3.46410i	−0.693978	−	0.200334i
$300$		0			0
$301$	15.5885	+	9.00000i	0.898504	+	0.518751i
$302$	−9.39230	+	16.2679i	−0.540466	+	0.936115i
$303$	4.19615	+	7.26795i	0.241063	+	0.417533i
$304$		−	2.26795i		−	0.130076i
$305$		0			0
$306$	3.46410	−	2.00000i	0.198030	−	0.114332i
$307$		−	20.2487i		−	1.15565i	−0.816159	−	0.577827i	$-0.803901\pi$
$307$		−	20.2487i		−	1.15565i	0.816159	−	0.577827i	$-0.196099\pi$
$308$	−5.59808	−	9.69615i	−0.318980	−	0.552490i
$309$	9.79423	−	16.9641i	0.557174	−	0.965054i
$310$		0			0
$311$	5.07180			0.287595			0.143798	−	0.989607i	$-0.454069\pi$
$311$	5.07180			0.287595			0.143798	+	0.989607i	$0.454069\pi$
$312$	1.00000	−	3.46410i	0.0566139	−	0.196116i
$313$	−1.32051			−0.0746395			−0.0373198	−	0.999303i	$-0.511882\pi$
$313$	−1.32051			−0.0746395			−0.0373198	+	0.999303i	$0.511882\pi$
$314$	−9.35641	−	5.40192i	−0.528013	−	0.304848i
$315$		0			0
$316$	8.46410	+	14.6603i	0.476143	+	0.824704i
$317$		−	23.5359i		−	1.32191i	−0.750427	−	0.660954i	$-0.770152\pi$
$317$		−	23.5359i		−	1.32191i	0.750427	−	0.660954i	$-0.229848\pi$
$318$	−3.23205	+	1.86603i	−0.181244	+	0.104642i
$319$	−17.6603	+	10.1962i	−0.988784	+	0.570875i
$320$		0			0
$321$	0.464102	+	0.803848i	0.0259036	+	0.0448664i
$322$	−5.19615	+	9.00000i	−0.289570	+	0.501550i
$323$	−7.85641	−	4.53590i	−0.437142	−	0.252384i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	10.9282			0.605257
$327$	9.00000	+	5.19615i	0.497701	+	0.287348i
$328$	−2.00000	+	3.46410i	−0.110432	+	0.191273i
$329$	0.696152	+	1.20577i	0.0383801	+	0.0664763i
$330$		0			0
$331$	5.53590	−	3.19615i	0.304280	−	0.175676i	−0.340084	−	0.940395i	$-0.610455\pi$
$331$	5.53590	−	3.19615i	0.304280	−	0.175676i	0.644364	+	0.764719i	$0.277122\pi$
$332$	−2.19615	+	1.26795i	−0.120530	+	0.0695878i
$333$		−	7.92820i		−	0.434463i
$334$	3.23205	+	5.59808i	0.176850	+	0.306313i
$335$		0			0
$336$	−2.59808	−	1.50000i	−0.141737	−	0.0818317i
$337$	5.60770			0.305471			0.152735	−	0.988267i	$-0.451192\pi$
$337$	5.60770			0.305471			0.152735	+	0.988267i	$0.451192\pi$
$338$	−12.9904	−	0.500000i	−0.706584	−	0.0271964i
$339$	12.0000			0.651751
$340$		0			0
$341$	16.6603	−	28.8564i	0.902203	−	1.56266i
$342$	1.13397	+	1.96410i	0.0613183	+	0.106206i
$343$			15.0000i			0.809924i
$344$	−5.19615	+	3.00000i	−0.280158	+	0.161749i
$345$		0			0
$346$			22.1244i			1.18941i
$347$	−8.19615	−	14.1962i	−0.439993	−	0.762089i	0.557696	−	0.830045i	$-0.311686\pi$
$347$	−8.19615	−	14.1962i	−0.439993	−	0.762089i	−0.997688	+	0.0679560i	$0.978352\pi$
$348$	−2.73205	+	4.73205i	−0.146453	+	0.253665i
$349$	15.1244	+	8.73205i	0.809588	+	0.467416i	0.846813	−	0.531891i	$-0.178518\pi$
$349$	15.1244	+	8.73205i	0.809588	+	0.467416i	−0.0372247	+	0.999307i	$0.511852\pi$
$350$		0			0
$351$	0.866025	+	3.50000i	0.0462250	+	0.186816i
$352$	3.73205			0.198919
$353$	24.5885	+	14.1962i	1.30871	+	0.755585i	0.981881	−	0.189498i	$-0.0606861\pi$
$353$	24.5885	+	14.1962i	1.30871	+	0.755585i	0.326830	+	0.945083i	$0.394019\pi$
$354$	−2.26795	+	3.92820i	−0.120540	+	0.208782i
$355$		0			0
$356$		−	10.1244i		−	0.536590i
$357$	−10.3923	+	6.00000i	−0.550019	+	0.317554i
$358$	−19.8564	+	11.4641i	−1.04944	+	0.605897i
$359$		−	12.9282i		−	0.682324i	−0.940004	−	0.341162i	$-0.889179\pi$
$359$		−	12.9282i		−	0.682324i	0.940004	−	0.341162i	$-0.110821\pi$
$360$		0			0
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	2.66025	+	1.53590i	0.139820	+	0.0807250i
$363$	−2.92820			−0.153691
$364$	−3.00000	+	10.3923i	−0.157243	+	0.544705i
$365$		0			0
$366$	−6.46410	−	3.73205i	−0.337884	−	0.195077i
$367$	−6.66025	+	11.5359i	−0.347662	+	0.602169i	−0.985834	−	0.167725i	$-0.946358\pi$
$367$	−6.66025	+	11.5359i	−0.347662	+	0.602169i	0.638171	+	0.769894i	$0.279691\pi$
$368$	−1.73205	−	3.00000i	−0.0902894	−	0.156386i
$369$		−	4.00000i		−	0.208232i
$370$		0			0
$371$	9.69615	−	5.59808i	0.503399	−	0.290638i
$372$		−	8.92820i		−	0.462906i
$373$	11.4641	+	19.8564i	0.593589	+	1.02813i	0.993744	+	0.111679i	$0.0356227\pi$
$373$	11.4641	+	19.8564i	0.593589	+	1.02813i	−0.400156	+	0.916447i	$0.631044\pi$
$374$	7.46410	−	12.9282i	0.385960	−	0.668501i
$375$		0			0
$376$	−0.464102			−0.0239342
$377$	18.9282	+	5.46410i	0.974852	+	0.281416i
$378$	3.00000			0.154303
$379$	5.42820	+	3.13397i	0.278828	+	0.160981i	0.632893	−	0.774239i	$-0.281867\pi$
$379$	5.42820	+	3.13397i	0.278828	+	0.160981i	−0.354065	+	0.935221i	$0.615201\pi$
$380$		0			0
$381$	2.33013	+	4.03590i	0.119376	+	0.206765i
$382$		−	17.3205i		−	0.886194i
$383$	−31.8564	+	18.3923i	−1.62779	+	0.939803i	−0.643035	+	0.765837i	$0.722325\pi$
$383$	−31.8564	+	18.3923i	−1.62779	+	0.939803i	−0.984752	+	0.173966i	$0.944342\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	8.92820	+	15.4641i	0.454434	+	0.787102i
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	−10.7321	−	6.19615i	−0.544837	−	0.314562i
$389$	−9.85641			−0.499740			−0.249870	−	0.968279i	$-0.580388\pi$
$389$	−9.85641			−0.499740			−0.249870	+	0.968279i	$0.580388\pi$
$390$		0			0
$391$	−13.8564			−0.700749
$392$	1.73205	+	1.00000i	0.0874818	+	0.0505076i
$393$	10.1603	−	17.5981i	0.512517	−	0.887706i
$394$	4.69615	+	8.13397i	0.236589	+	0.409784i
$395$		0			0
$396$	−3.23205	+	1.86603i	−0.162417	+	0.0937713i
$397$	6.86603	−	3.96410i	0.344596	−	0.198953i	−0.317707	−	0.948189i	$-0.602913\pi$
$397$	6.86603	−	3.96410i	0.344596	−	0.198953i	0.662303	+	0.749237i	$0.269579\pi$
$398$			11.0718i			0.554979i
$399$	−3.40192	−	5.89230i	−0.170309	−	0.294984i
$400$		0			0
$401$	−1.83975	−	1.06218i	−0.0918725	−	0.0530426i	0.453360	−	0.891328i	$-0.350225\pi$
$401$	−1.83975	−	1.06218i	−0.0918725	−	0.0530426i	−0.545232	+	0.838285i	$0.683559\pi$
$402$	5.46410			0.272525
$403$	−31.2487	+	7.73205i	−1.55661	+	0.385161i
$404$	8.39230			0.417533
$405$		0			0
$406$	8.19615	−	14.1962i	0.406768	−	0.704543i
$407$	−14.7942	−	25.6244i	−0.733323	−	1.27015i
$408$		−	4.00000i		−	0.198030i
$409$	0.820508	−	0.473721i	0.0405715	−	0.0234240i	−0.479577	−	0.877500i	$-0.659210\pi$
$409$	0.820508	−	0.473721i	0.0405715	−	0.0234240i	0.520149	+	0.854076i	$0.325877\pi$
$410$		0			0
$411$			6.53590i			0.322392i
$412$	−9.79423	−	16.9641i	−0.482527	−	0.835761i
$413$	6.80385	−	11.7846i	0.334795	−	0.579883i
$414$	3.00000	+	1.73205i	0.147442	+	0.0851257i
$415$		0			0
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	21.7846			1.06680
$418$	7.33013	+	4.23205i	0.358528	+	0.206996i
$419$	8.92820	−	15.4641i	0.436171	−	0.755471i	−0.561219	−	0.827667i	$-0.689668\pi$
$419$	8.92820	−	15.4641i	0.436171	−	0.755471i	0.997390	+	0.0721964i	$0.0230008\pi$
$420$		0			0
$421$		−	5.85641i		−	0.285424i	−0.989764	−	0.142712i	$-0.954418\pi$
$421$		−	5.85641i		−	0.285424i	0.989764	−	0.142712i	$-0.0455822\pi$
$422$	18.9904	−	10.9641i	0.924437	−	0.533724i
$423$	0.401924	−	0.232051i	0.0195422	−	0.0112827i
$424$			3.73205i			0.181244i
$425$		0			0
$426$	0.464102	−	0.803848i	0.0224858	−	0.0389465i
$427$	19.3923	+	11.1962i	0.938459	+	0.541820i
$428$	0.928203			0.0448664
$429$	9.33013	+	9.69615i	0.450463	+	0.468135i
$430$		0			0
$431$	−12.0000	−	6.92820i	−0.578020	−	0.333720i	0.182326	−	0.983238i	$-0.441637\pi$
$431$	−12.0000	−	6.92820i	−0.578020	−	0.333720i	−0.760346	+	0.649518i	$0.774971\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	16.3923	+	28.3923i	0.787764	+	1.36445i	0.927334	+	0.374235i	$0.122095\pi$
$433$	16.3923	+	28.3923i	0.787764	+	1.36445i	−0.139570	+	0.990212i	$0.544572\pi$
$434$			26.7846i			1.28570i
$435$		0			0
$436$	9.00000	−	5.19615i	0.431022	−	0.248851i
$437$		−	7.85641i		−	0.375823i
$438$	−3.46410	−	6.00000i	−0.165521	−	0.286691i
$439$	−10.6603	+	18.4641i	−0.508786	+	0.881243i	0.491162	+	0.871068i	$0.336572\pi$
$439$	−10.6603	+	18.4641i	−0.508786	+	0.881243i	−0.999948	+	0.0101753i	$0.996761\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$	−14.0000	+	3.46410i	−0.665912	+	0.164771i
$443$	−7.85641			−0.373269			−0.186635	−	0.982429i	$-0.559758\pi$
$443$	−7.85641			−0.373269			−0.186635	+	0.982429i	$0.559758\pi$
$444$	−6.86603	−	3.96410i	−0.325847	−	0.188128i
$445$		0			0
$446$	4.42820	+	7.66987i	0.209682	+	0.363179i
$447$			22.7846i			1.07768i
$448$	−2.59808	+	1.50000i	−0.122748	+	0.0708683i
$449$	−15.6962	+	9.06218i	−0.740747	+	0.427671i	−0.822341	−	0.568995i	$-0.807332\pi$
$449$	−15.6962	+	9.06218i	−0.740747	+	0.427671i	0.0815937	+	0.996666i	$0.473999\pi$
$450$		0			0
$451$	−7.46410	−	12.9282i	−0.351471	−	0.608765i
$452$	6.00000	−	10.3923i	0.282216	−	0.488813i
$453$	−16.2679	−	9.39230i	−0.764335	−	0.441289i
$454$	13.4641			0.631902
$455$		0			0
$456$	2.26795			0.106206
$457$	−0.464102	−	0.267949i	−0.0217098	−	0.0125341i	0.489106	−	0.872224i	$-0.337323\pi$
$457$	−0.464102	−	0.267949i	−0.0217098	−	0.0125341i	−0.510816	+	0.859690i	$0.670657\pi$
$458$	5.73205	−	9.92820i	0.267841	−	0.463914i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	28.0526	−	16.1962i	1.30654	−	0.754330i	0.325021	−	0.945707i	$-0.394629\pi$
$461$	28.0526	−	16.1962i	1.30654	−	0.754330i	0.981517	+	0.191377i	$0.0612952\pi$
$462$	9.69615	−	5.59808i	0.451106	−	0.260446i
$463$		−	0.784610i		−	0.0364639i	−0.999834	−	0.0182320i	$-0.994196\pi$
$463$		−	0.784610i		−	0.0364639i	0.999834	−	0.0182320i	$-0.00580373\pi$
$464$	2.73205	+	4.73205i	0.126832	+	0.219680i
$465$		0			0
$466$	−15.5885	−	9.00000i	−0.722121	−	0.416917i
$467$	−3.60770			−0.166944			−0.0834721	−	0.996510i	$-0.526601\pi$
$467$	−3.60770			−0.166944			−0.0834721	+	0.996510i	$0.526601\pi$
$468$	3.46410	+	1.00000i	0.160128	+	0.0462250i
$469$	−16.3923			−0.756926
$470$		0			0
$471$	5.40192	−	9.35641i	0.248908	−	0.431120i
$472$	2.26795	+	3.92820i	0.104391	+	0.180810i
$473$		−	22.3923i		−	1.02960i
$474$	−14.6603	+	8.46410i	−0.673368	+	0.388769i
$475$		0			0
$476$			12.0000i			0.550019i
$477$	−1.86603	−	3.23205i	−0.0854394	−	0.147985i
$478$	1.73205	−	3.00000i	0.0792222	−	0.137217i
$479$	−22.7321	−	13.1244i	−1.03865	−	0.599667i	−0.119202	−	0.992870i	$-0.538034\pi$
$479$	−22.7321	−	13.1244i	−1.03865	−	0.599667i	−0.919452	+	0.393203i	$0.871367\pi$
$480$		0			0
$481$	−7.92820	+	27.4641i	−0.361495	+	1.25226i
$482$	14.8038			0.674297
$483$	−9.00000	−	5.19615i	−0.409514	−	0.236433i
$484$	−1.46410	+	2.53590i	−0.0665501	+	0.115268i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	18.1865	−	10.5000i	0.824110	−	0.475800i	−0.0277214	−	0.999616i	$-0.508825\pi$
$487$	18.1865	−	10.5000i	0.824110	−	0.475800i	0.851832	+	0.523815i	$0.175492\pi$
$488$	−6.46410	+	3.73205i	−0.292616	+	0.168942i
$489$			10.9282i			0.494190i
$490$		0			0
$491$	7.69615	−	13.3301i	0.347322	−	0.601580i	−0.638450	−	0.769663i	$-0.720424\pi$
$491$	7.69615	−	13.3301i	0.347322	−	0.601580i	0.985773	+	0.168083i	$0.0537576\pi$
$492$	−3.46410	−	2.00000i	−0.156174	−	0.0901670i
$493$	21.8564			0.984363
$494$	−1.96410	−	7.93782i	−0.0883691	−	0.357140i
$495$		0			0
$496$	−7.73205	−	4.46410i	−0.347179	−	0.200444i
$497$	−1.39230	+	2.41154i	−0.0624534	+	0.108172i
$498$	−1.26795	−	2.19615i	−0.0568182	−	0.0984119i
$499$		−	1.32051i		−	0.0591141i	−0.999563	−	0.0295570i	$-0.990590\pi$
$499$		−	1.32051i		−	0.0591141i	0.999563	−	0.0295570i	$-0.00940967\pi$
$500$		0			0
$501$	−5.59808	+	3.23205i	−0.250104	+	0.144397i
$502$		−	26.4641i		−	1.18115i
$503$	0.133975	+	0.232051i	0.00597363	+	0.0103466i	0.868997	−	0.494818i	$-0.164765\pi$
$503$	0.133975	+	0.232051i	0.00597363	+	0.0103466i	−0.863023	+	0.505164i	$0.831432\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	12.9282			0.574729
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$	4.66025			0.206765
$509$	4.60770	+	2.66025i	0.204232	+	0.117914i	0.598628	−	0.801027i	$-0.295713\pi$
$509$	4.60770	+	2.66025i	0.204232	+	0.117914i	−0.394396	+	0.918941i	$0.629046\pi$
$510$		0			0
$511$	10.3923	+	18.0000i	0.459728	+	0.796273i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.96410	+	1.13397i	−0.0867172	+	0.0500662i
$514$	18.5885	−	10.7321i	0.819902	−	0.473370i
$515$		0			0
$516$	−3.00000	−	5.19615i	−0.132068	−	0.228748i
$517$	0.866025	−	1.50000i	0.0380878	−	0.0659699i
$518$	20.5981	+	11.8923i	0.905028	+	0.522518i
$519$	−22.1244			−0.971151
$520$		0			0
$521$	−27.3923			−1.20008			−0.600039	−	0.799970i	$-0.704848\pi$
$521$	−27.3923			−1.20008			−0.600039	+	0.799970i	$0.704848\pi$
$522$	−4.73205	−	2.73205i	−0.207116	−	0.119579i
$523$	6.85641	−	11.8756i	0.299810	−	0.519286i	−0.676283	−	0.736642i	$-0.736410\pi$
$523$	6.85641	−	11.8756i	0.299810	−	0.519286i	0.976092	+	0.217357i	$0.0697435\pi$
$524$	−10.1603	−	17.5981i	−0.443853	−	0.768776i
$525$		0			0
$526$	17.7679	−	10.2583i	0.774719	−	0.447284i
$527$	−30.9282	+	17.8564i	−1.34725	+	0.777837i
$528$			3.73205i			0.162417i
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$		0			0
$531$	−3.92820	−	2.26795i	−0.170470	−	0.0984206i
$532$	−6.80385			−0.294984
$533$	−4.00000	+	13.8564i	−0.173259	+	0.600188i
$534$	10.1244			0.438124
$535$		0			0
$536$	2.73205	−	4.73205i	0.118007	−	0.204393i
$537$	−11.4641	−	19.8564i	−0.494713	−	0.856867i
$538$			30.9282i			1.33341i
$539$	−6.46410	+	3.73205i	−0.278429	+	0.160751i
$540$		0			0
$541$		−	26.7846i		−	1.15156i	−0.817605	−	0.575780i	$-0.804698\pi$
$541$		−	26.7846i		−	1.15156i	0.817605	−	0.575780i	$-0.195302\pi$
$542$	−1.80385	−	3.12436i	−0.0774819	−	0.134203i
$543$	−1.53590	+	2.66025i	−0.0659117	+	0.114162i
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$		0			0
$546$	−10.3923	−	3.00000i	−0.444750	−	0.128388i
$547$	−29.3205			−1.25365			−0.626827	−	0.779158i	$-0.715647\pi$
$547$	−29.3205			−1.25365			−0.626827	+	0.779158i	$0.715647\pi$
$548$	5.66025	+	3.26795i	0.241794	+	0.139600i
$549$	3.73205	−	6.46410i	0.159280	−	0.275881i
$550$		0			0
$551$			12.3923i			0.527930i
$552$	3.00000	−	1.73205i	0.127688	−	0.0737210i
$553$	43.9808	−	25.3923i	1.87025	−	1.07979i
$554$		−	19.5885i		−	0.832234i
$555$		0			0
$556$	10.8923	−	18.8660i	0.461937	−	0.800098i
$557$	−37.5788	−	21.6962i	−1.59227	−	0.919295i	−0.992917	−	0.118808i	$-0.962093\pi$
$557$	−37.5788	−	21.6962i	−1.59227	−	0.919295i	−0.599349	−	0.800488i	$-0.704574\pi$
$558$	8.92820			0.377961
$559$	−15.5885	+	15.0000i	−0.659321	+	0.634432i
$560$		0			0
$561$	12.9282	+	7.46410i	0.545829	+	0.315135i
$562$	3.46410	−	6.00000i	0.146124	−	0.253095i
$563$	9.66025	+	16.7321i	0.407131	+	0.705172i	0.994567	−	0.104099i	$-0.0331959\pi$
$563$	9.66025	+	16.7321i	0.407131	+	0.705172i	−0.587436	+	0.809271i	$0.699863\pi$
$564$		−	0.464102i		−	0.0195422i
$565$		0			0
$566$	12.4641	−	7.19615i	0.523905	−	0.302477i
$567$			3.00000i			0.125988i
$568$	−0.464102	−	0.803848i	−0.0194733	−	0.0337287i
$569$	−9.16025	+	15.8660i	−0.384018	+	0.665138i	−0.991632	−	0.129094i	$-0.958793\pi$
$569$	−9.16025	+	15.8660i	−0.384018	+	0.665138i	0.607615	+	0.794232i	$0.292127\pi$
$570$		0			0
$571$	−16.8564			−0.705419			−0.352709	−	0.935733i	$-0.614740\pi$
$571$	−16.8564			−0.705419			−0.352709	+	0.935733i	$0.614740\pi$
$572$	13.0622	−	3.23205i	0.546157	−	0.135139i
$573$	17.3205			0.723575
$574$	10.3923	+	6.00000i	0.433766	+	0.250435i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	25.3205i		−	1.05411i	−0.849832	−	0.527053i	$-0.823297\pi$
$577$		−	25.3205i		−	1.05411i	0.849832	−	0.527053i	$-0.176703\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$	−15.4641	+	8.92820i	−0.642666	+	0.371043i
$580$		0			0
$581$	3.80385	+	6.58846i	0.157810	+	0.273335i
$582$	6.19615	−	10.7321i	0.256839	−	0.444858i
$583$	−12.0622	−	6.96410i	−0.499564	−	0.288424i
$584$	−6.92820			−0.286691
$585$		0			0
$586$	−19.2487			−0.795157
$587$	4.26795	+	2.46410i	0.176157	+	0.101704i	0.585486	−	0.810683i	$-0.300904\pi$
$587$	4.26795	+	2.46410i	0.176157	+	0.101704i	−0.409329	+	0.912387i	$0.634237\pi$
$588$	−1.00000	+	1.73205i	−0.0412393	+	0.0714286i
$589$	−10.1244	−	17.5359i	−0.417167	−	0.722554i
$590$		0			0
$591$	−8.13397	+	4.69615i	−0.334587	+	0.193174i
$592$	−6.86603	+	3.96410i	−0.282192	+	0.162924i
$593$			3.21539i			0.132040i	0.997818	+	0.0660201i	$0.0210302\pi$
$593$			3.21539i			0.132040i	−0.997818	+	0.0660201i	$0.978970\pi$
$594$	−1.86603	−	3.23205i	−0.0765639	−	0.132613i
$595$		0			0
$596$	19.7321	+	11.3923i	0.808256	+	0.466647i
$597$	−11.0718			−0.453138
$598$	−8.66025	−	9.00000i	−0.354144	−	0.368037i
$599$	15.0718			0.615817			0.307908	−	0.951416i	$-0.400371\pi$
$599$	15.0718			0.615817			0.307908	+	0.951416i	$0.400371\pi$
$600$		0			0
$601$	12.3564	−	21.4019i	0.504028	−	0.873003i	−0.495961	−	0.868345i	$-0.665184\pi$
$601$	12.3564	−	21.4019i	0.504028	−	0.873003i	0.999989	−	0.00465778i	$-0.00148262\pi$
$602$	9.00000	+	15.5885i	0.366813	+	0.635338i
$603$			5.46410i			0.222515i
$604$	−16.2679	+	9.39230i	−0.661933	+	0.382167i
$605$		0			0
$606$			8.39230i			0.340914i
$607$	18.7224	+	32.4282i	0.759920	+	1.31622i	0.942891	+	0.333102i	$0.108095\pi$
$607$	18.7224	+	32.4282i	0.759920	+	1.31622i	−0.182971	+	0.983118i	$0.558571\pi$
$608$	1.13397	−	1.96410i	0.0459887	−	0.0796548i
$609$	14.1962	+	8.19615i	0.575257	+	0.332125i
$610$		0			0
$611$	−1.62436	+	0.401924i	−0.0657144	+	0.0162601i
$612$	4.00000			0.161690
$613$	38.9711	+	22.5000i	1.57403	+	0.908766i	0.995667	+	0.0929864i	$0.0296413\pi$
$613$	38.9711	+	22.5000i	1.57403	+	0.908766i	0.578362	+	0.815780i	$0.303692\pi$
$614$	10.1244	−	17.5359i	0.408586	−	0.707691i
$615$		0			0
$616$		−	11.1962i		−	0.451106i
$617$	−24.7128	+	14.2679i	−0.994900	+	0.574406i	−0.906735	−	0.421700i	$-0.861434\pi$
$617$	−24.7128	+	14.2679i	−0.994900	+	0.574406i	−0.0881649	+	0.996106i	$0.528100\pi$
$618$	16.9641	−	9.79423i	0.682396	−	0.393982i
$619$		−	42.5167i		−	1.70889i	−0.519543	−	0.854444i	$-0.673898\pi$
$619$		−	42.5167i		−	1.70889i	0.519543	−	0.854444i	$-0.326102\pi$
$620$		0			0
$621$	−1.73205	+	3.00000i	−0.0695048	+	0.120386i
$622$	4.39230	+	2.53590i	0.176115	+	0.101680i
$623$	−30.3731			−1.21687
$624$	2.59808	−	2.50000i	0.104006	−	0.100080i
$625$		0			0
$626$	−1.14359	−	0.660254i	−0.0457072	−	0.0263891i
$627$	−4.23205	+	7.33013i	−0.169012	+	0.292737i
$628$	−5.40192	−	9.35641i	−0.215560	−	0.373361i
$629$			31.7128i			1.26447i
$630$		0			0
$631$	6.92820	−	4.00000i	0.275807	−	0.159237i	−0.355716	−	0.934594i	$-0.615763\pi$
$631$	6.92820	−	4.00000i	0.275807	−	0.159237i	0.631524	+	0.775356i	$0.282430\pi$
$632$			16.9282i			0.673368i
$633$	10.9641	+	18.9904i	0.435784	+	0.754800i
$634$	11.7679	−	20.3827i	0.467365	−	0.809500i
$635$		0			0
$636$	−3.73205			−0.147985
$637$	6.92820	+	2.00000i	0.274505	+	0.0792429i
$638$	−20.3923			−0.807339
$639$	0.803848	+	0.464102i	0.0317997	+	0.0183596i
$640$		0			0
$641$	−3.76795	−	6.52628i	−0.148825	−	0.257773i	0.781968	−	0.623318i	$-0.214216\pi$
$641$	−3.76795	−	6.52628i	−0.148825	−	0.257773i	−0.930793	+	0.365546i	$0.880882\pi$
$642$			0.928203i			0.0366333i
$643$	−24.9282	+	14.3923i	−0.983072	+	0.567577i	−0.903196	−	0.429228i	$-0.858786\pi$
$643$	−24.9282	+	14.3923i	−0.983072	+	0.567577i	−0.0798761	+	0.996805i	$0.525452\pi$
$644$	−9.00000	+	5.19615i	−0.354650	+	0.204757i
$645$		0			0
$646$	−4.53590	−	7.85641i	−0.178463	−	0.309106i
$647$	−16.1340	+	27.9449i	−0.634292	+	1.09863i	0.352373	+	0.935860i	$0.385375\pi$
$647$	−16.1340	+	27.9449i	−0.634292	+	1.09863i	−0.986665	+	0.162766i	$0.947958\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−16.9282			−0.664490
$650$		0			0
$651$	−26.7846			−1.04977
$652$	9.46410	+	5.46410i	0.370643	+	0.213991i
$653$	14.7942	−	25.6244i	0.578943	−	1.00276i	−0.416658	−	0.909063i	$-0.636799\pi$
$653$	14.7942	−	25.6244i	0.578943	−	1.00276i	0.995601	−	0.0936952i	$-0.0298679\pi$
$654$	5.19615	+	9.00000i	0.203186	+	0.351928i
$655$		0			0
$656$	−3.46410	+	2.00000i	−0.135250	+	0.0780869i
$657$	6.00000	−	3.46410i	0.234082	−	0.135147i
$658$			1.39230i			0.0542777i
$659$	−7.85641	−	13.6077i	−0.306042	−	0.530081i	0.671451	−	0.741049i	$-0.265672\pi$
$659$	−7.85641	−	13.6077i	−0.306042	−	0.530081i	−0.977493	+	0.210969i	$0.932338\pi$
$660$		0			0
$661$	36.7128	+	21.1962i	1.42796	+	0.824435i	0.996960	−	0.0779157i	$-0.0248265\pi$
$661$	36.7128	+	21.1962i	1.42796	+	0.824435i	0.431003	+	0.902351i	$0.358160\pi$
$662$	6.39230			0.248444
$663$	−3.46410	−	14.0000i	−0.134535	−	0.543715i
$664$	−2.53590			−0.0984119
$665$		0			0
$666$	3.96410	−	6.86603i	0.153606	−	0.266053i
$667$	9.46410	+	16.3923i	0.366451	+	0.634713i
$668$			6.46410i			0.250104i
$669$	−7.66987	+	4.42820i	−0.296534	+	0.171204i
$670$		0			0
$671$		−	27.8564i		−	1.07538i
$672$	−1.50000	−	2.59808i	−0.0578638	−	0.100223i
$673$	12.3923	−	21.4641i	0.477688	−	0.827380i	−0.521985	−	0.852955i	$-0.674808\pi$
$673$	12.3923	−	21.4641i	0.477688	−	0.827380i	0.999673	+	0.0255746i	$0.00814152\pi$
$674$	4.85641	+	2.80385i	0.187062	+	0.108000i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	2.92820			0.112540			0.0562700	−	0.998416i	$-0.482079\pi$
$677$	2.92820			0.112540			0.0562700	+	0.998416i	$0.482079\pi$
$678$	10.3923	+	6.00000i	0.399114	+	0.230429i
$679$	−18.5885	+	32.1962i	−0.713360	+	1.23557i
$680$		0			0
$681$			13.4641i			0.515945i
$682$	28.8564	−	16.6603i	1.10497	−	0.637954i
$683$	5.78461	−	3.33975i	0.221342	−	0.127792i	−0.385230	−	0.922821i	$-0.625878\pi$
$683$	5.78461	−	3.33975i	0.221342	−	0.127792i	0.606571	+	0.795029i	$0.292544\pi$
$684$			2.26795i			0.0867172i
$685$		0			0
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	9.92820	+	5.73205i	0.378785	+	0.218691i
$688$	−6.00000			−0.228748
$689$	3.23205	+	13.0622i	0.123131	+	0.497629i
$690$		0			0
$691$	19.9641	+	11.5263i	0.759470	+	0.438480i	0.829106	−	0.559092i	$-0.188850\pi$
$691$	19.9641	+	11.5263i	0.759470	+	0.438480i	−0.0696353	+	0.997573i	$0.522184\pi$
$692$	−11.0622	+	19.1603i	−0.420521	+	0.728364i
$693$	5.59808	+	9.69615i	0.212653	+	0.368326i
$694$		−	16.3923i		−	0.622243i
$695$		0			0
$696$	−4.73205	+	2.73205i	−0.179368	+	0.103558i
$697$			16.0000i			0.606043i
$698$	8.73205	+	15.1244i	0.330513	+	0.572465i
$699$	9.00000	−	15.5885i	0.340411	−	0.589610i
$700$		0			0
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$	−1.00000	+	3.46410i	−0.0377426	+	0.130744i
$703$	−17.9808			−0.678157
$704$	3.23205	+	1.86603i	0.121812	+	0.0703285i
$705$		0			0
$706$	14.1962	+	24.5885i	0.534279	+	0.925399i
$707$		−	25.1769i		−	0.946875i
$708$	−3.92820	+	2.26795i	−0.147631	+	0.0852348i
$709$	−6.33975	+	3.66025i	−0.238094	+	0.137464i	−0.614300	−	0.789072i	$-0.710562\pi$
$709$	−6.33975	+	3.66025i	−0.238094	+	0.137464i	0.376206	+	0.926536i	$0.377228\pi$
$710$		0			0
$711$	−8.46410	−	14.6603i	−0.317429	−	0.549802i
$712$	5.06218	−	8.76795i	0.189713	−	0.328593i
$713$	−26.7846	−	15.4641i	−1.00309	−	0.579135i
$714$	−12.0000			−0.449089
$715$		0			0
$716$	−22.9282			−0.856867
$717$	3.00000	+	1.73205i	0.112037	+	0.0646846i
$718$	6.46410	−	11.1962i	0.241238	−	0.417837i
$719$	−8.00000	−	13.8564i	−0.298350	−	0.516757i	0.677409	−	0.735607i	$-0.263103\pi$
$719$	−8.00000	−	13.8564i	−0.298350	−	0.516757i	−0.975759	+	0.218850i	$0.929769\pi$
$720$		0			0
$721$	−50.8923	+	29.3827i	−1.89533	+	1.09427i
$722$	−12.0000	+	6.92820i	−0.446594	+	0.257841i
$723$			14.8038i			0.550561i
$724$	1.53590	+	2.66025i	0.0570812	+	0.0988676i
$725$		0			0
$726$	−2.53590	−	1.46410i	−0.0941160	−	0.0543379i
$727$	−12.6603			−0.469543			−0.234771	−	0.972051i	$-0.575434\pi$
$727$	−12.6603			−0.469543			−0.234771	+	0.972051i	$0.575434\pi$
$728$	−7.79423	+	7.50000i	−0.288873	+	0.277968i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	−3.73205	−	6.46410i	−0.137941	−	0.238920i
$733$			6.85641i			0.253247i	0.991951	+	0.126624i	$0.0404140\pi$
$733$			6.85641i			0.253247i	−0.991951	+	0.126624i	$0.959586\pi$
$734$	−11.5359	+	6.66025i	−0.425798	+	0.245834i
$735$		0			0
$736$		−	3.46410i		−	0.127688i
$737$	10.1962	+	17.6603i	0.375580	+	0.650524i
$738$	2.00000	−	3.46410i	0.0736210	−	0.127515i
$739$	37.9641	+	21.9186i	1.39653	+	0.806288i	0.994028	−	0.109130i	$-0.0348064\pi$
$739$	37.9641	+	21.9186i	1.39653	+	0.806288i	0.402505	+	0.915418i	$0.368140\pi$
$740$		0			0
$741$	7.93782	−	1.96410i	0.291603	−	0.0721531i
$742$	11.1962			0.411024
$743$	2.53590	+	1.46410i	0.0930331	+	0.0537127i	0.545795	−	0.837919i	$-0.316228\pi$
$743$	2.53590	+	1.46410i	0.0930331	+	0.0537127i	−0.452762	+	0.891632i	$0.649561\pi$
$744$	4.46410	−	7.73205i	0.163662	−	0.283471i
$745$		0			0
$746$			22.9282i			0.839461i
$747$	2.19615	−	1.26795i	0.0803530	−	0.0463918i
$748$	12.9282	−	7.46410i	0.472702	−	0.272915i
$749$		−	2.78461i		−	0.101747i
$750$		0			0
$751$	−20.5885	+	35.6603i	−0.751283	+	1.30126i	0.195917	+	0.980620i	$0.437232\pi$
$751$	−20.5885	+	35.6603i	−0.751283	+	1.30126i	−0.947201	+	0.320641i	$0.896102\pi$
$752$	−0.401924	−	0.232051i	−0.0146567	−	0.00846202i
$753$	26.4641			0.964405
$754$	13.6603	+	14.1962i	0.497477	+	0.516993i
$755$		0			0
$756$	2.59808	+	1.50000i	0.0944911	+	0.0545545i
$757$	9.13397	−	15.8205i	0.331980	−	0.575006i	−0.650920	−	0.759146i	$-0.725617\pi$
$757$	9.13397	−	15.8205i	0.331980	−	0.575006i	0.982900	+	0.184140i	$0.0589500\pi$
$758$	3.13397	+	5.42820i	0.113831	+	0.197161i
$759$			12.9282i			0.469264i
$760$		0			0
$761$	38.0885	−	21.9904i	1.38071	−	0.797151i	0.388463	−	0.921465i	$-0.373006\pi$
$761$	38.0885	−	21.9904i	1.38071	−	0.797151i	0.992243	+	0.124314i	$0.0396730\pi$
$762$			4.66025i			0.168823i
$763$	−15.5885	−	27.0000i	−0.564340	−	0.977466i
$764$	8.66025	−	15.0000i	0.313317	−	0.542681i
$765$		0			0
$766$	−36.7846			−1.32908
$767$	11.3397	+	11.7846i	0.409454	+	0.425518i
$768$	1.00000			0.0360844
$769$	34.3923	+	19.8564i	1.24022	+	0.716040i	0.969139	−	0.246517i	$-0.0792860\pi$
$769$	34.3923	+	19.8564i	1.24022	+	0.716040i	0.271080	+	0.962557i	$0.412619\pi$
$770$		0			0
$771$	10.7321	+	18.5885i	0.386505	+	0.669447i
$772$			17.8564i			0.642666i
$773$	−46.2391	+	26.6962i	−1.66310	+	0.960194i	−0.691885	+	0.722008i	$0.743220\pi$
$773$	−46.2391	+	26.6962i	−1.66310	+	0.960194i	−0.971220	+	0.238186i	$0.923447\pi$
$774$	5.19615	−	3.00000i	0.186772	−	0.107833i
$775$		0			0
$776$	−6.19615	−	10.7321i	−0.222429	−	0.385258i
$777$	−11.8923	+	20.5981i	−0.426634	+	0.738952i
$778$	−8.53590	−	4.92820i	−0.306027	−	0.176685i
$779$	−9.07180			−0.325031
$780$		0			0
$781$	3.46410			0.123955
$782$	−12.0000	−	6.92820i	−0.429119	−	0.247752i
$783$	2.73205	−	4.73205i	0.0976355	−	0.169110i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$		0			0
$786$	17.5981	−	10.1603i	0.627703	−	0.362404i
$787$	−4.73205	+	2.73205i	−0.168679	+	0.0973871i	−0.581963	−	0.813215i	$-0.697715\pi$
$787$	−4.73205	+	2.73205i	−0.168679	+	0.0973871i	0.413284	+	0.910602i	$0.364382\pi$
$788$			9.39230i			0.334587i
$789$	10.2583	+	17.7679i	0.365206	+	0.632556i
$790$		0			0
$791$	−31.1769	−	18.0000i	−1.10852	−	0.640006i
$792$	−3.73205			−0.132613
$793$	−19.3923	+	18.6603i	−0.688641	+	0.662645i
$794$	7.92820			0.281361
$795$		0			0
$796$	−5.53590	+	9.58846i	−0.196215	+	0.339854i
$797$	−18.9282	−	32.7846i	−0.670471	−	1.16129i	−0.977771	−	0.209678i	$-0.932759\pi$
$797$	−18.9282	−	32.7846i	−0.670471	−	1.16129i	0.307299	−	0.951613i	$-0.400575\pi$
$798$		−	6.80385i		−	0.240854i
$799$	−1.60770	+	0.928203i	−0.0568762	+	0.0328375i
$800$		0			0
$801$			10.1244i			0.357727i
$802$	−1.06218	−	1.83975i	−0.0375068	−	0.0649637i
$803$	12.9282	−	22.3923i	0.456226	−	0.790207i
$804$	4.73205	+	2.73205i	0.166887	+	0.0963520i
$805$		0			0
$806$	−30.9282	−	8.92820i	−1.08940	−	0.314483i
$807$	−30.9282			−1.08872
$808$	7.26795	+	4.19615i	0.255686	+	0.147620i
$809$	−17.3923	+	30.1244i	−0.611481	+	1.05912i	0.379510	+	0.925188i	$0.376093\pi$
$809$	−17.3923	+	30.1244i	−0.611481	+	1.05912i	−0.990991	+	0.133928i	$0.957241\pi$
$810$		0			0
$811$		−	7.58846i		−	0.266467i	−0.991085	−	0.133233i	$-0.957464\pi$
$811$		−	7.58846i		−	0.266467i	0.991085	−	0.133233i	$-0.0425360\pi$
$812$	14.1962	−	8.19615i	0.498187	−	0.287629i
$813$	3.12436	−	1.80385i	0.109576	−	0.0632637i
$814$		−	29.5885i		−	1.03707i
$815$		0			0
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	−11.7846	−	6.80385i	−0.412291	−	0.238036i
$818$	0.947441			0.0331265
$819$	3.00000	−	10.3923i	0.104828	−	0.363137i
$820$		0			0
$821$	42.7128	+	24.6603i	1.49069	+	0.860649i	0.999943	−	0.0106549i	$-0.00339162\pi$
$821$	42.7128	+	24.6603i	1.49069	+	0.860649i	0.490744	+	0.871304i	$0.336725\pi$
$822$	−3.26795	+	5.66025i	−0.113983	+	0.197424i
$823$	−19.7942	−	34.2846i	−0.689983	−	1.19509i	−0.971843	−	0.235631i	$-0.924284\pi$
$823$	−19.7942	−	34.2846i	−0.689983	−	1.19509i	0.281859	−	0.959456i	$-0.409049\pi$
$824$		−	19.5885i		−	0.682396i
$825$		0			0
$826$	11.7846	−	6.80385i	0.410039	−	0.236736i
$827$			50.4974i			1.75597i	0.478690	+	0.877984i	$0.341112\pi$
$827$			50.4974i			1.75597i	−0.478690	+	0.877984i	$0.658888\pi$
$828$	1.73205	+	3.00000i	0.0601929	+	0.104257i
$829$	19.6603	−	34.0526i	0.682829	−	1.18269i	−0.291285	−	0.956636i	$-0.594083\pi$
$829$	19.6603	−	34.0526i	0.682829	−	1.18269i	0.974114	−	0.226058i	$-0.0725839\pi$
$830$		0			0
$831$	19.5885			0.679516
$832$	−0.866025	−	3.50000i	−0.0300240	−	0.121341i
$833$	8.00000			0.277184
$834$	18.8660	+	10.8923i	0.653277	+	0.377170i
$835$		0			0
$836$	4.23205	+	7.33013i	0.146369	+	0.253518i
$837$			8.92820i			0.308604i
$838$	15.4641	−	8.92820i	0.534199	−	0.308420i
$839$	37.3923	−	21.5885i	1.29093	−	0.745316i	0.312107	−	0.950047i	$-0.398965\pi$
$839$	37.3923	−	21.5885i	1.29093	−	0.745316i	0.978818	+	0.204731i	$0.0656318\pi$
$840$		0			0
$841$	−0.428203	−	0.741670i	−0.0147656	−	0.0255748i
$842$	2.92820	−	5.07180i	0.100913	−	0.174786i
$843$	6.00000	+	3.46410i	0.206651	+	0.119310i
$844$	21.9282			0.754800
$845$		0			0
$846$	0.464102			0.0159561
$847$	7.60770	+	4.39230i	0.261403	+	0.150921i
$848$	−1.86603	+	3.23205i	−0.0640796	+	0.110989i
$849$	7.19615	+	12.4641i	0.246971	+	0.427767i
$850$		0			0
$851$	−23.7846	+	13.7321i	−0.815326	+	0.470729i
$852$	0.803848	−	0.464102i	0.0275394	−	0.0158999i
$853$		−	44.6410i		−	1.52848i	−0.644932	−	0.764240i	$-0.723114\pi$
$853$		−	44.6410i		−	1.52848i	0.644932	−	0.764240i	$-0.276886\pi$
$854$	11.1962	+	19.3923i	0.383124	+	0.663591i
$855$		0			0
$856$	0.803848	+	0.464102i	0.0274749	+	0.0158627i
$857$	15.0718			0.514843			0.257421	−	0.966299i	$-0.417127\pi$
$857$	15.0718			0.514843			0.257421	+	0.966299i	$0.417127\pi$
$858$	3.23205	+	13.0622i	0.110340	+	0.445935i
$859$	−19.9282			−0.679942			−0.339971	−	0.940436i	$-0.610417\pi$
$859$	−19.9282			−0.679942			−0.339971	+	0.940436i	$0.610417\pi$
$860$		0			0
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$	−6.92820	−	12.0000i	−0.235976	−	0.408722i
$863$			10.9282i			0.372000i	0.982550	+	0.186000i	$0.0595525\pi$
$863$			10.9282i			0.372000i	−0.982550	+	0.186000i	$0.940447\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$			32.7846i			1.11407i
$867$	0.500000	+	0.866025i	0.0169809	+	0.0294118i
$868$	−13.3923	+	23.1962i	−0.454564	+	0.787329i
$869$	−54.7128	−	31.5885i	−1.85601	−	1.07157i
$870$		0			0
$871$	5.46410	−	18.9282i	0.185144	−	0.641358i
$872$	10.3923			0.351928
$873$	10.7321	+	6.19615i	0.363225	+	0.209708i
$874$	3.92820	−	6.80385i	0.132873	−	0.230144i
$875$		0			0
$876$		−	6.92820i		−	0.234082i
$877$	−29.1962	+	16.8564i	−0.985884	+	0.569200i	−0.904041	−	0.427445i	$-0.859414\pi$
$877$	−29.1962	+	16.8564i	−0.985884	+	0.569200i	−0.0818426	+	0.996645i	$0.526080\pi$
$878$	−18.4641	+	10.6603i	−0.623133	+	0.359766i
$879$		−	19.2487i		−	0.649243i
$880$		0			0
$881$	18.5526	−	32.1340i	0.625052	−	1.08262i	−0.363479	−	0.931602i	$-0.618411\pi$
$881$	18.5526	−	32.1340i	0.625052	−	1.08262i	0.988531	−	0.151019i	$-0.0482554\pi$
$882$	−1.73205	−	1.00000i	−0.0583212	−	0.0336718i
$883$	−21.3205			−0.717492			−0.358746	−	0.933435i	$-0.616796\pi$
$883$	−21.3205			−0.717492			−0.358746	+	0.933435i	$0.616796\pi$
$884$	−13.8564	−	4.00000i	−0.466041	−	0.134535i
$885$		0			0
$886$	−6.80385	−	3.92820i	−0.228580	−	0.131971i
$887$	26.1340	−	45.2654i	0.877493	−	1.51986i	0.0234098	−	0.999726i	$-0.492548\pi$
$887$	26.1340	−	45.2654i	0.877493	−	1.51986i	0.854083	−	0.520136i	$-0.174119\pi$
$888$	−3.96410	−	6.86603i	−0.133027	−	0.230409i
$889$		−	13.9808i		−	0.468900i
$890$		0			0
$891$	3.23205	−	1.86603i	0.108278	−	0.0625142i
$892$			8.85641i			0.296534i
$893$	−0.526279	−	0.911543i	−0.0176113	−	0.0305036i
$894$	−11.3923	+	19.7321i	−0.381016	+	0.659939i
$895$		0			0
$896$	−3.00000			−0.100223
$897$	9.00000	−	8.66025i	0.300501	−	0.289157i
$898$	−18.1244			−0.604818
$899$	42.2487	+	24.3923i	1.40907	+	0.813529i
$900$		0			0
$901$	7.46410	+	12.9282i	0.248665	+	0.430701i
$902$		−	14.9282i		−	0.497055i
$903$	−15.5885	+	9.00000i	−0.518751	+	0.299501i
$904$	10.3923	−	6.00000i	0.345643	−	0.199557i
$905$		0			0
$906$	−9.39230	−	16.2679i	−0.312038	−	0.540466i
$907$	3.53590	−	6.12436i	0.117408	−	0.203356i	−0.801332	−	0.598220i	$-0.795875\pi$
$907$	3.53590	−	6.12436i	0.117408	−	0.203356i	0.918740	+	0.394864i	$0.129208\pi$
$908$	11.6603	+	6.73205i	0.386959	+	0.223411i
$909$	−8.39230			−0.278355
$910$		0			0
$911$	−28.7846			−0.953677			−0.476838	−	0.878991i	$-0.658217\pi$
$911$	−28.7846			−0.953677			−0.476838	+	0.878991i	$0.658217\pi$
$912$	1.96410	+	1.13397i	0.0650379	+	0.0375497i
$913$	4.73205	−	8.19615i	0.156608	−	0.271253i
$914$	−0.267949	−	0.464102i	−0.00886297	−	0.0153511i
$915$		0			0
$916$	9.92820	−	5.73205i	0.328037	−	0.189392i
$917$	−52.7942	+	30.4808i	−1.74342	+	1.00656i
$918$			4.00000i			0.132020i
$919$	−27.9808	−	48.4641i	−0.923000	−	1.59868i	−0.794746	−	0.606942i	$-0.792396\pi$
$919$	−27.9808	−	48.4641i	−0.923000	−	1.59868i	−0.128254	−	0.991741i	$-0.540937\pi$
$920$		0			0
$921$	17.5359	+	10.1244i	0.577827	+	0.333609i
$922$	32.3923			1.06678
$923$	−2.32051	−	2.41154i	−0.0763805	−	0.0793769i
$924$	11.1962			0.368326
$925$		0			0
$926$	0.392305	−	0.679492i	0.0128919	−	0.0223295i
$927$	9.79423	+	16.9641i	0.321685	+	0.557174i
$928$			5.46410i			0.179368i
$929$	−26.1051	+	15.0718i	−0.856481	+	0.494490i	−0.862832	−	0.505490i	$-0.831312\pi$
$929$	−26.1051	+	15.0718i	−0.856481	+	0.494490i	0.00635120	+	0.999980i	$0.497978\pi$
$930$		0			0
$931$			4.53590i			0.148658i
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$	−2.53590	+	4.39230i	−0.0830216	+	0.143798i
$934$	−3.12436	−	1.80385i	−0.102232	−	0.0590237i
$935$		0			0
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$	−33.7128			−1.10135			−0.550675	−	0.834720i	$-0.685630\pi$
$937$	−33.7128			−1.10135			−0.550675	+	0.834720i	$0.685630\pi$
$938$	−14.1962	−	8.19615i	−0.463521	−	0.267614i
$939$	0.660254	−	1.14359i	0.0215466	−	0.0373198i
$940$		0			0
$941$			36.4974i			1.18978i	0.803806	+	0.594891i	$0.202805\pi$
$941$			36.4974i			1.18978i	−0.803806	+	0.594891i	$0.797195\pi$
$942$	9.35641	−	5.40192i	0.304848	−	0.176004i
$943$	−12.0000	+	6.92820i	−0.390774	+	0.225613i
$944$			4.53590i			0.147631i
$945$		0			0
$946$	11.1962	−	19.3923i	0.364018	−	0.630498i
$947$	11.7846	+	6.80385i	0.382948	+	0.221095i	0.679100	−	0.734046i	$-0.262370\pi$
$947$	11.7846	+	6.80385i	0.382948	+	0.221095i	−0.296152	+	0.955141i	$0.595703\pi$
$948$	−16.9282			−0.549802
$949$	−24.2487	+	6.00000i	−0.787146	+	0.194768i
$950$		0			0
$951$	20.3827	+	11.7679i	0.660954	+	0.381602i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	−9.33975	−	16.1769i	−0.302544	−	0.524022i	0.674167	−	0.738579i	$-0.264503\pi$
$953$	−9.33975	−	16.1769i	−0.302544	−	0.524022i	−0.976711	+	0.214557i	$0.931169\pi$
$954$		−	3.73205i		−	0.120830i
$955$		0			0
$956$	3.00000	−	1.73205i	0.0970269	−	0.0560185i
$957$		−	20.3923i		−	0.659190i
$958$	−13.1244	−	22.7321i	−0.424029	−	0.734439i
$959$	9.80385	−	16.9808i	0.316583	−	0.548337i
$960$		0			0
$961$	−48.7128			−1.57138
$962$	−20.5981	+	19.8205i	−0.664109	+	0.639039i
$963$	−0.928203			−0.0299109
$964$	12.8205	+	7.40192i	0.412921	+	0.238400i
$965$		0			0
$966$	−5.19615	−	9.00000i	−0.167183	−	0.289570i
$967$			28.8564i			0.927959i	0.885846	+	0.463980i	$0.153579\pi$
$967$			28.8564i			0.927959i	−0.885846	+	0.463980i	$0.846421\pi$
$968$	−2.53590	+	1.46410i	−0.0815069	+	0.0470580i
$969$	7.85641	−	4.53590i	0.252384	−	0.145714i
$970$		0			0
$971$	10.3038	+	17.8468i	0.330666	+	0.572731i	0.982643	−	0.185509i	$-0.0593932\pi$
$971$	10.3038	+	17.8468i	0.330666	+	0.572731i	−0.651976	+	0.758239i	$0.726060\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−56.5981	−	32.6769i	−1.81445	−	1.04757i
$974$	21.0000			0.672883
$975$		0			0
$976$	−7.46410			−0.238920
$977$	1.26795	+	0.732051i	0.0405653	+	0.0234204i	0.520145	−	0.854078i	$-0.325878\pi$
$977$	1.26795	+	0.732051i	0.0405653	+	0.0234204i	−0.479580	+	0.877498i	$0.659211\pi$
$978$	−5.46410	+	9.46410i	−0.174723	+	0.302629i
$979$	18.8923	+	32.7224i	0.603801	+	1.04581i
$980$		0			0
$981$	−9.00000	+	5.19615i	−0.287348	+	0.165900i
$982$	13.3301	−	7.69615i	0.425381	−	0.245594i
$983$			16.1769i			0.515963i	0.966150	+	0.257982i	$0.0830574\pi$
$983$			16.1769i			0.515963i	−0.966150	+	0.257982i	$0.916943\pi$
$984$	−2.00000	−	3.46410i	−0.0637577	−	0.110432i
$985$		0			0
$986$	18.9282	+	10.9282i	0.602797	+	0.348025i
$987$	−1.39230			−0.0443176
$988$	2.26795	−	7.85641i	0.0721531	−	0.249946i
$989$	−20.7846			−0.660912
$990$		0			0
$991$	11.5885	−	20.0718i	0.368119	−	0.637602i	−0.621152	−	0.783690i	$-0.713335\pi$
$991$	11.5885	−	20.0718i	0.368119	−	0.637602i	0.989272	+	0.146088i	$0.0466684\pi$
$992$	−4.46410	−	7.73205i	−0.141735	−	0.245493i
$993$			6.39230i			0.202854i
$994$	−2.41154	+	1.39230i	−0.0764895	+	0.0441612i
$995$		0			0
$996$		−	2.53590i		−	0.0803530i
$997$	5.00962	+	8.67691i	0.158656	+	0.274801i	0.934384	−	0.356267i	$-0.115951\pi$
$997$	5.00962	+	8.67691i	0.158656	+	0.274801i	−0.775728	+	0.631067i	$0.782617\pi$
$998$	0.660254	−	1.14359i	0.0209000	−	0.0361998i
$999$	6.86603	+	3.96410i	0.217231	+	0.125419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.a.901.2		4
5.2	odd	4		1950.2.y.d.199.2		4
5.3	odd	4		1950.2.y.e.199.1		4
5.4	even	2		390.2.bb.a.121.1	✓	4
13.10	even	6	inner	1950.2.bc.a.751.2		4
15.14	odd	2		1170.2.bs.d.901.2		4
65.4	even	6		5070.2.b.p.1351.1		4
65.9	even	6		5070.2.b.p.1351.4		4
65.19	odd	12		5070.2.a.be.1.1		2
65.23	odd	12		1950.2.y.d.49.2		4
65.49	even	6		390.2.bb.a.361.1	yes	4
65.59	odd	12		5070.2.a.ba.1.2		2
65.62	odd	12		1950.2.y.e.49.1		4
195.179	odd	6		1170.2.bs.d.361.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.a.121.1	✓	4	5.4	even	2
390.2.bb.a.361.1	yes	4	65.49	even	6
1170.2.bs.d.361.2		4	195.179	odd	6
1170.2.bs.d.901.2		4	15.14	odd	2
1950.2.y.d.49.2		4	65.23	odd	12
1950.2.y.d.199.2		4	5.2	odd	4
1950.2.y.e.49.1		4	65.62	odd	12
1950.2.y.e.199.1		4	5.3	odd	4
1950.2.bc.a.751.2		4	13.10	even	6	inner
1950.2.bc.a.901.2		4	1.1	even	1	trivial
5070.2.a.ba.1.2		2	65.59	odd	12
5070.2.a.be.1.1		2	65.19	odd	12
5070.2.b.p.1351.1		4	65.4	even	6
5070.2.b.p.1351.4		4	65.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.23205 - 1.86603i) q^{11} -1.00000 q^{12} +(0.866025 + 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-1.96410 + 1.13397i) q^{19} +3.00000i q^{21} +(-1.86603 - 3.23205i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(2.59808 + 1.50000i) q^{28} +(2.73205 - 4.73205i) q^{29} +8.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.23205 - 1.86603i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(6.86603 + 3.96410i) q^{37} -2.26795 q^{38} +(-3.46410 - 1.00000i) q^{39} +(3.46410 + 2.00000i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(3.00000 + 5.19615i) q^{43} -3.73205i q^{44} +(-3.00000 + 1.73205i) q^{46} +0.464102i q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{49} -4.00000 q^{51} +(-2.59808 + 2.50000i) q^{52} +3.73205 q^{53} +(0.866025 + 0.500000i) q^{54} +(1.50000 + 2.59808i) q^{56} -2.26795i q^{57} +(4.73205 - 2.73205i) q^{58} +(3.92820 - 2.26795i) q^{59} +(3.73205 + 6.46410i) q^{61} +(-4.46410 + 7.73205i) q^{62} +(-2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +3.73205 q^{66} +(-4.73205 - 2.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-1.73205 - 3.00000i) q^{69} +(-0.803848 + 0.464102i) q^{71} +(0.866025 - 0.500000i) q^{72} +6.92820i q^{73} +(3.96410 + 6.86603i) q^{74} +(-1.96410 - 1.13397i) q^{76} -11.1962 q^{77} +(-2.50000 - 2.59808i) q^{78} +16.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +2.53590i q^{83} +(-2.59808 + 1.50000i) q^{84} +6.00000i q^{86} +(2.73205 + 4.73205i) q^{87} +(1.86603 - 3.23205i) q^{88} +(-8.76795 - 5.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} -3.46410 q^{92} +(-7.73205 - 4.46410i) q^{93} +(-0.232051 + 0.401924i) q^{94} -1.00000i q^{96} +(-10.7321 + 6.19615i) q^{97} +(1.73205 - 1.00000i) q^{98} +3.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 6 q^{11} - 4 q^{12} + 12 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} - 4 q^{22} - 4 q^{26} + 4 q^{27} + 4 q^{29} + 6 q^{33} + 2 q^{36} + 24 q^{37} - 16 q^{38} - 6 q^{42} + 12 q^{43} - 12 q^{46} - 2 q^{48} + 4 q^{49} - 16 q^{51} + 8 q^{53} + 6 q^{56} + 12 q^{58} - 12 q^{59} + 8 q^{61} - 4 q^{62} - 4 q^{64} + 8 q^{66} - 12 q^{67} - 8 q^{68} - 24 q^{71} + 2 q^{74} + 6 q^{76} - 24 q^{77} - 10 q^{78} + 40 q^{79} - 2 q^{81} + 8 q^{82} + 4 q^{87} + 4 q^{88} - 42 q^{89} + 30 q^{91} - 24 q^{93} + 6 q^{94} - 36 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 6 * q^11 - 4 * q^12 + 12 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 - 4 * q^22 - 4 * q^26 + 4 * q^27 + 4 * q^29 + 6 * q^33 + 2 * q^36 + 24 * q^37 - 16 * q^38 - 6 * q^42 + 12 * q^43 - 12 * q^46 - 2 * q^48 + 4 * q^49 - 16 * q^51 + 8 * q^53 + 6 * q^56 + 12 * q^58 - 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 8 * q^66 - 12 * q^67 - 8 * q^68 - 24 * q^71 + 2 * q^74 + 6 * q^76 - 24 * q^77 - 10 * q^78 + 40 * q^79 - 2 * q^81 + 8 * q^82 + 4 * q^87 + 4 * q^88 - 42 * q^89 + 30 * q^91 - 24 * q^93 + 6 * q^94 - 36 * q^97

Introduction

L-functions

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