LMFDB - Embedded newform 1950.2.bc.d.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 78)
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.d.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} +(-2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.09808 + 0.633975i) q^{11} +1.00000 q^{12} +(2.59808 - 2.50000i) q^{13} -2.73205 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} -1.00000i q^{18} +(4.09808 - 2.36603i) q^{19} +2.73205i q^{21} +(0.633975 + 1.09808i) q^{22} +(-2.09808 + 3.63397i) q^{23} +(0.866025 + 0.500000i) q^{24} +(3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(-2.36603 - 1.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +1.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.09808 - 0.633975i) q^{33} +5.73205i q^{34} +(0.500000 - 0.866025i) q^{36} +(-3.06218 - 1.76795i) q^{37} +4.73205 q^{38} +(-0.866025 - 3.50000i) q^{39} +(8.13397 + 4.69615i) q^{41} +(-1.36603 + 2.36603i) q^{42} +(4.83013 + 8.36603i) q^{43} +1.26795i q^{44} +(-3.63397 + 2.09808i) q^{46} +2.19615i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.232051 - 0.401924i) q^{49} +5.73205 q^{51} +(3.46410 + 1.00000i) q^{52} +6.46410 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.36603 - 2.36603i) q^{56} -4.73205i q^{57} +(3.86603 - 2.23205i) q^{58} +(-6.92820 + 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(-0.732051 + 1.26795i) q^{62} +(2.36603 + 1.36603i) q^{63} -1.00000 q^{64} +1.26795 q^{66} +(11.3660 + 6.56218i) q^{67} +(-2.86603 + 4.96410i) q^{68} +(2.09808 + 3.63397i) q^{69} +(4.09808 - 2.36603i) q^{71} +(0.866025 - 0.500000i) q^{72} -6.26795i q^{73} +(-1.76795 - 3.06218i) q^{74} +(4.09808 + 2.36603i) q^{76} -3.46410 q^{77} +(1.00000 - 3.46410i) q^{78} -2.53590 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.69615 + 8.13397i) q^{82} +0.196152i q^{83} +(-2.36603 + 1.36603i) q^{84} +9.66025i q^{86} +(-2.23205 - 3.86603i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} +(-2.73205 + 9.46410i) q^{91} -4.19615 q^{92} +(1.26795 + 0.732051i) q^{93} +(-1.09808 + 1.90192i) q^{94} +1.00000i q^{96} +(5.19615 - 3.00000i) q^{97} +(0.401924 - 0.232051i) q^{98} -1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{22} + 2 q^{23} + 14 q^{26} - 4 q^{27} - 6 q^{28} + 2 q^{29} - 6 q^{33} + 2 q^{36} + 12 q^{37}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^22 + 2 * q^23 + 14 * q^26 - 4 * q^27 - 6 * q^28 + 2 * q^29 - 6 * q^33 + 2 * q^36 + 12 * q^37 + 12 * q^38 + 36 * q^41 - 2 * q^42 + 2 * q^43 - 18 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 12 * q^53 - 2 * q^56 + 12 * q^58 + 8 * q^61 + 4 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^66 + 42 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 6 * q^76 + 4 * q^78 - 24 * q^79 - 2 * q^81 - 2 * q^82 - 6 * q^84 - 2 * q^87 - 6 * q^88 - 12 * q^89 - 4 * q^91 + 4 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^98

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
$7$	−2.36603	+	1.36603i	−0.894274	+	0.516309i	−0.875338	−	0.483512i	$-0.839361\pi$
$7$	−2.36603	+	1.36603i	−0.894274	+	0.516309i	−0.0189356	+	0.999821i	$0.506028\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	0.656322	−	0.754481i	$-0.272111\pi$
$11$	1.09808	+	0.633975i	0.331082	+	0.191151i	−0.325239	+	0.945632i	$0.605445\pi$
$12$	1.00000			0.288675
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$14$	−2.73205			−0.730171
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.0501517	−	0.998742i	$-0.484030\pi$
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.890011	+	0.455938i	$0.150696\pi$
$20$		0			0
$21$			2.73205i			0.596182i
$22$	0.633975	+	1.09808i	0.135164	+	0.234111i
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	−0.997494	−	0.0707462i	$-0.977462\pi$
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	0.560015	+	0.828482i	$0.310795\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$	−1.00000			−0.192450
$28$	−2.36603	−	1.36603i	−0.447137	−	0.258155i
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	−0.580892	−	0.813980i	$-0.697296\pi$
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	0.995374	+	0.0960774i	$0.0306296\pi$
$30$		0			0
$31$			1.46410i			0.262960i	0.991319	+	0.131480i	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.09808	−	0.633975i	0.191151	−	0.110361i
$34$			5.73205i			0.983039i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−3.06218	−	1.76795i	−0.503419	−	0.290649i	0.226705	−	0.973963i	$-0.427205\pi$
$37$	−3.06218	−	1.76795i	−0.503419	−	0.290649i	−0.730124	+	0.683314i	$0.760538\pi$
$38$	4.73205			0.767640
$39$	−0.866025	−	3.50000i	−0.138675	−	0.560449i
$40$		0			0
$41$	8.13397	+	4.69615i	1.27031	+	0.733416i	0.975047	−	0.221999i	$-0.0712582\pi$
$41$	8.13397	+	4.69615i	1.27031	+	0.733416i	0.295267	+	0.955415i	$0.404592\pi$
$42$	−1.36603	+	2.36603i	−0.210782	+	0.365086i
$43$	4.83013	+	8.36603i	0.736587	+	1.27581i	0.954023	+	0.299732i	$0.0968974\pi$
$43$	4.83013	+	8.36603i	0.736587	+	1.27581i	−0.217436	+	0.976075i	$0.569769\pi$
$44$			1.26795i			0.191151i
$45$		0			0
$46$	−3.63397	+	2.09808i	−0.535800	+	0.309344i
$47$			2.19615i			0.320342i	0.987089	+	0.160171i	$0.0512045\pi$
$47$			2.19615i			0.320342i	−0.987089	+	0.160171i	$0.948795\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	0.232051	−	0.401924i	0.0331501	−	0.0574177i
$50$		0			0
$51$	5.73205			0.802648
$52$	3.46410	+	1.00000i	0.480384	+	0.138675i
$53$	6.46410			0.887913			0.443956	−	0.896048i	$-0.353575\pi$
$53$	6.46410			0.887913			0.443956	+	0.896048i	$0.353575\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−1.36603	−	2.36603i	−0.182543	−	0.316173i
$57$		−	4.73205i		−	0.626775i
$58$	3.86603	−	2.23205i	0.507634	−	0.293083i
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.877841	−	0.478953i	$-0.841016\pi$
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.0241347	+	0.999709i	$0.507683\pi$
$60$		0			0
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	0.994400	+	0.105682i	$0.0337026\pi$
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	−0.405677	+	0.914017i	$0.632964\pi$
$62$	−0.732051	+	1.26795i	−0.0929705	+	0.161030i
$63$	2.36603	+	1.36603i	0.298091	+	0.172103i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.26795			0.156074
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.993155	−	0.116800i	$-0.0372638\pi$
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.395426	+	0.918498i	$0.370597\pi$
$68$	−2.86603	+	4.96410i	−0.347557	+	0.601986i
$69$	2.09808	+	3.63397i	0.252579	+	0.437479i
$70$		0			0
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	−0.236708	−	0.971581i	$-0.576068\pi$
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	0.723060	+	0.690785i	$0.242735\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	6.26795i		−	0.733608i	−0.930298	−	0.366804i	$-0.880452\pi$
$73$		−	6.26795i		−	0.733608i	0.930298	−	0.366804i	$-0.119548\pi$
$74$	−1.76795	−	3.06218i	−0.205520	−	0.355971i
$75$		0			0
$76$	4.09808	+	2.36603i	0.470082	+	0.271402i
$77$	−3.46410			−0.394771
$78$	1.00000	−	3.46410i	0.113228	−	0.392232i
$79$	−2.53590			−0.285311			−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590			−0.285311			−0.142655	+	0.989772i	$0.545564\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.69615	+	8.13397i	0.518603	+	0.898247i
$83$			0.196152i			0.0215305i	0.999942	+	0.0107653i	$0.00342676\pi$
$83$			0.196152i			0.0215305i	−0.999942	+	0.0107653i	$0.996573\pi$
$84$	−2.36603	+	1.36603i	−0.258155	+	0.149046i
$85$		0			0
$86$			9.66025i			1.04169i
$87$	−2.23205	−	3.86603i	−0.239301	−	0.414481i
$88$	−0.633975	+	1.09808i	−0.0675819	+	0.117055i
$89$	−8.19615	−	4.73205i	−0.868790	−	0.501596i	−0.00184433	−	0.999998i	$-0.500587\pi$
$89$	−8.19615	−	4.73205i	−0.868790	−	0.501596i	−0.866946	+	0.498402i	$0.833920\pi$
$90$		0			0
$91$	−2.73205	+	9.46410i	−0.286397	+	0.992107i
$92$	−4.19615			−0.437479
$93$	1.26795	+	0.732051i	0.131480	+	0.0759101i
$94$	−1.09808	+	1.90192i	−0.113258	+	0.196168i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$	0.401924	−	0.232051i	0.0406004	−	0.0234407i
$99$		−	1.26795i		−	0.127434i
$100$		0			0
$101$	0.964102	−	1.66987i	0.0959317	−	0.166159i	−0.814065	−	0.580773i	$-0.802750\pi$
$101$	0.964102	−	1.66987i	0.0959317	−	0.166159i	0.909997	+	0.414615i	$0.136084\pi$
$102$	4.96410	+	2.86603i	0.491519	+	0.283779i
$103$	−15.2679			−1.50440			−0.752198	−	0.658937i	$-0.771006\pi$
$103$	−15.2679			−1.50440			−0.752198	+	0.658937i	$0.771006\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$		0			0
$106$	5.59808	+	3.23205i	0.543733	+	0.313925i
$107$	5.09808	−	8.83013i	0.492850	−	0.853641i	−0.507116	−	0.861878i	$-0.669289\pi$
$107$	5.09808	−	8.83013i	0.492850	−	0.853641i	0.999966	+	0.00823695i	$0.00262193\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			1.46410i			0.140236i	0.997539	+	0.0701178i	$0.0223375\pi$
$109$			1.46410i			0.140236i	−0.997539	+	0.0701178i	$0.977662\pi$
$110$		0			0
$111$	−3.06218	+	1.76795i	−0.290649	+	0.167806i
$112$		−	2.73205i		−	0.258155i
$113$	−0.669873	−	1.16025i	−0.0630163	−	0.109148i	0.832796	−	0.553580i	$-0.186739\pi$
$113$	−0.669873	−	1.16025i	−0.0630163	−	0.109148i	−0.895812	+	0.444432i	$0.853405\pi$
$114$	2.36603	−	4.09808i	0.221599	−	0.383820i
$115$		0			0
$116$	4.46410			0.414481
$117$	−3.46410	−	1.00000i	−0.320256	−	0.0924500i
$118$	−8.00000			−0.736460
$119$	−13.5622	−	7.83013i	−1.24324	−	0.717787i
$120$		0			0
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$			9.19615i			0.832581i
$123$	8.13397	−	4.69615i	0.733416	−	0.423438i
$124$	−1.26795	+	0.732051i	−0.113865	+	0.0657401i
$125$		0			0
$126$	1.36603	+	2.36603i	0.121695	+	0.210782i
$127$	4.92820	−	8.53590i	0.437307	−	0.757438i	−0.560173	−	0.828375i	$-0.689266\pi$
$127$	4.92820	−	8.53590i	0.437307	−	0.757438i	0.997481	+	0.0709368i	$0.0225989\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	9.66025			0.850538
$130$		0			0
$131$	6.53590			0.571044			0.285522	−	0.958372i	$-0.407833\pi$
$131$	6.53590			0.571044			0.285522	+	0.958372i	$0.407833\pi$
$132$	1.09808	+	0.633975i	0.0955753	+	0.0551804i
$133$	−6.46410	+	11.1962i	−0.560509	+	0.970830i
$134$	6.56218	+	11.3660i	0.566886	+	0.981875i
$135$		0			0
$136$	−4.96410	+	2.86603i	−0.425668	+	0.245760i
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.0110599	−	0.999939i	$-0.496479\pi$
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.871502	+	0.490391i	$0.163146\pi$
$138$			4.19615i			0.357200i
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	−0.944233	−	0.329279i	$-0.893194\pi$
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	0.186952	−	0.982369i	$-0.440139\pi$
$140$		0			0
$141$	1.90192	+	1.09808i	0.160171	+	0.0924747i
$142$	4.73205			0.397105
$143$	4.43782	−	1.09808i	0.371109	−	0.0918257i
$144$	1.00000			0.0833333
$145$		0			0
$146$	3.13397	−	5.42820i	0.259370	−	0.449241i
$147$	−0.232051	−	0.401924i	−0.0191392	−	0.0331501i
$148$		−	3.53590i		−	0.290649i
$149$	11.4282	−	6.59808i	0.936235	−	0.540535i	0.0474568	−	0.998873i	$-0.484888\pi$
$149$	11.4282	−	6.59808i	0.936235	−	0.540535i	0.888778	+	0.458338i	$0.151555\pi$
$150$		0			0
$151$		−	6.73205i		−	0.547847i	−0.961752	−	0.273923i	$-0.911679\pi$
$151$		−	6.73205i		−	0.547847i	0.961752	−	0.273923i	$-0.0883214\pi$
$152$	2.36603	+	4.09808i	0.191910	+	0.332398i
$153$	2.86603	−	4.96410i	0.231704	−	0.401324i
$154$	−3.00000	−	1.73205i	−0.241747	−	0.139573i
$155$		0			0
$156$	2.59808	−	2.50000i	0.208013	−	0.200160i
$157$	−7.58846			−0.605625			−0.302812	−	0.953050i	$-0.597926\pi$
$157$	−7.58846			−0.605625			−0.302812	+	0.953050i	$0.597926\pi$
$158$	−2.19615	−	1.26795i	−0.174717	−	0.100873i
$159$	3.23205	−	5.59808i	0.256318	−	0.443956i
$160$		0			0
$161$		−	11.4641i		−	0.903498i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	−11.6603	+	6.73205i	−0.913302	+	0.527295i	−0.881492	−	0.472199i	$-0.843460\pi$
$163$	−11.6603	+	6.73205i	−0.913302	+	0.527295i	−0.0318096	+	0.999494i	$0.510127\pi$
$164$			9.39230i			0.733416i
$165$		0			0
$166$	−0.0980762	+	0.169873i	−0.00761219	+	0.0131847i
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	0.782391	−	0.622787i	$-0.214000\pi$
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	−0.148154	+	0.988964i	$0.547333\pi$
$168$	−2.73205			−0.210782
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$	−4.09808	−	2.36603i	−0.313388	−	0.180934i
$172$	−4.83013	+	8.36603i	−0.368294	+	0.637903i
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	0.770383	−	0.637582i	$-0.220065\pi$
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	−0.937353	+	0.348380i	$0.886732\pi$
$174$		−	4.46410i		−	0.338423i
$175$		0			0
$176$	−1.09808	+	0.633975i	−0.0827706	+	0.0477876i
$177$			8.00000i			0.601317i
$178$	−4.73205	−	8.19615i	−0.354682	−	0.614328i
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	0.392921	+	0.919572i	$0.371465\pi$
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	−0.992833	+	0.119506i	$0.961869\pi$
$180$		0			0
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$	−7.09808	+	6.83013i	−0.526144	+	0.506283i
$183$	9.19615			0.679799
$184$	−3.63397	−	2.09808i	−0.267900	−	0.154672i
$185$		0			0
$186$	0.732051	+	1.26795i	0.0536766	+	0.0929705i
$187$			7.26795i			0.531485i
$188$	−1.90192	+	1.09808i	−0.138712	+	0.0800854i
$189$	2.36603	−	1.36603i	0.172103	−	0.0993637i
$190$		0			0
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	0.963706	−	0.266966i	$-0.0860212\pi$
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	−0.713052	+	0.701111i	$0.752688\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	10.1603	+	5.86603i	0.731351	+	0.422246i	0.818916	−	0.573913i	$-0.194575\pi$
$193$	10.1603	+	5.86603i	0.731351	+	0.422246i	−0.0875652	+	0.996159i	$0.527909\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	0.464102			0.0331501
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.165086	−	0.986279i	$-0.552790\pi$
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.936686	+	0.350171i	$0.886123\pi$
$198$	0.633975	−	1.09808i	0.0450546	−	0.0780369i
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	−0.999993	−	0.00366345i	$-0.998834\pi$
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	0.496824	−	0.867851i	$-0.334499\pi$
$200$		0			0
$201$	11.3660	−	6.56218i	0.801698	−	0.462860i
$202$	1.66987	−	0.964102i	0.117492	−	0.0678340i
$203$			12.1962i			0.856002i
$204$	2.86603	+	4.96410i	0.200662	+	0.347557i
$205$		0			0
$206$	−13.2224	−	7.63397i	−0.921250	−	0.531884i
$207$	4.19615			0.291653
$208$	0.866025	+	3.50000i	0.0600481	+	0.242681i
$209$	6.00000			0.415029
$210$		0			0
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	0.432873	+	0.901455i	$0.357500\pi$
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	−0.997119	+	0.0758485i	$0.975833\pi$
$212$	3.23205	+	5.59808i	0.221978	+	0.384477i
$213$		−	4.73205i		−	0.324235i
$214$	8.83013	−	5.09808i	0.603615	−	0.348497i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	−0.732051	+	1.26795i	−0.0495807	+	0.0858764i
$219$	−5.42820	−	3.13397i	−0.366804	−	0.211774i
$220$		0			0
$221$	19.8564	+	5.73205i	1.33569	+	0.385579i
$222$	−3.53590			−0.237314
$223$	−23.3205	−	13.4641i	−1.56166	−	0.901623i	−0.997090	−	0.0762356i	$-0.975710\pi$
$223$	−23.3205	−	13.4641i	−1.56166	−	0.901623i	−0.564567	−	0.825387i	$-0.690957\pi$
$224$	1.36603	−	2.36603i	0.0912714	−	0.158087i
$225$		0			0
$226$		−	1.33975i		−	0.0891186i
$227$	10.5622	−	6.09808i	0.701036	−	0.404744i	−0.106697	−	0.994292i	$-0.534027\pi$
$227$	10.5622	−	6.09808i	0.701036	−	0.404744i	0.807733	+	0.589548i	$0.200694\pi$
$228$	4.09808	−	2.36603i	0.271402	−	0.156694i
$229$			11.8564i			0.783493i	0.920073	+	0.391747i	$0.128129\pi$
$229$			11.8564i			0.783493i	−0.920073	+	0.391747i	$0.871871\pi$
$230$		0			0
$231$	−1.73205	+	3.00000i	−0.113961	+	0.197386i
$232$	3.86603	+	2.23205i	0.253817	+	0.146541i
$233$	−7.85641			−0.514690			−0.257345	−	0.966320i	$-0.582848\pi$
$233$	−7.85641			−0.514690			−0.257345	+	0.966320i	$0.582848\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$		0			0
$236$	−6.92820	−	4.00000i	−0.450988	−	0.260378i
$237$	−1.26795	+	2.19615i	−0.0823622	+	0.142655i
$238$	−7.83013	−	13.5622i	−0.507552	−	0.879105i
$239$			7.66025i			0.495501i	0.968824	+	0.247750i	$0.0796913\pi$
$239$			7.66025i			0.495501i	−0.968824	+	0.247750i	$0.920309\pi$
$240$		0			0
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	−0.828592	−	0.559853i	$-0.810857\pi$
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	0.0705514	+	0.997508i	$0.477524\pi$
$242$		−	9.39230i		−	0.603760i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.59808	+	7.96410i	−0.294362	+	0.509849i
$245$		0			0
$246$	9.39230			0.598831
$247$	4.73205	−	16.3923i	0.301093	−	1.04302i
$248$	−1.46410			−0.0929705
$249$	0.169873	+	0.0980762i	0.0107653	+	0.00621533i
$250$		0			0
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	0.996413	−	0.0846203i	$-0.0269677\pi$
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	−0.571490	+	0.820609i	$0.693634\pi$
$252$			2.73205i			0.172103i
$253$	−4.60770	+	2.66025i	−0.289683	+	0.167249i
$254$	8.53590	−	4.92820i	0.535590	−	0.309223i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	−0.974117	−	0.226044i	$-0.927421\pi$
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	0.682818	+	0.730588i	$0.260754\pi$
$258$	8.36603	+	4.83013i	0.520846	+	0.300711i
$259$	9.66025			0.600259
$260$		0			0
$261$	−4.46410			−0.276321
$262$	5.66025	+	3.26795i	0.349692	+	0.201895i
$263$	−5.02628	+	8.70577i	−0.309934	+	0.536821i	−0.978348	−	0.206969i	$-0.933640\pi$
$263$	−5.02628	+	8.70577i	−0.309934	+	0.536821i	0.668414	+	0.743790i	$0.266974\pi$
$264$	0.633975	+	1.09808i	0.0390184	+	0.0675819i
$265$		0			0
$266$	−11.1962	+	6.46410i	−0.686480	+	0.396339i
$267$	−8.19615	+	4.73205i	−0.501596	+	0.289597i
$268$			13.1244i			0.801698i
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	0.770638	−	0.637273i	$-0.219938\pi$
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	−0.937214	+	0.348755i	$0.886604\pi$
$270$		0			0
$271$	−18.9282	−	10.9282i	−1.14981	−	0.663841i	−0.200966	−	0.979598i	$-0.564408\pi$
$271$	−18.9282	−	10.9282i	−1.14981	−	0.663841i	−0.948840	+	0.315757i	$0.897742\pi$
$272$	−5.73205			−0.347557
$273$	6.83013	+	7.09808i	0.413378	+	0.429595i
$274$	11.9282			0.720609
$275$		0			0
$276$	−2.09808	+	3.63397i	−0.126289	+	0.218740i
$277$	2.86603	+	4.96410i	0.172203	+	0.298264i	0.939190	−	0.343399i	$-0.111578\pi$
$277$	2.86603	+	4.96410i	0.172203	+	0.298264i	−0.766987	+	0.641663i	$0.778245\pi$
$278$		−	17.8564i		−	1.07096i
$279$	1.26795	−	0.732051i	0.0759101	−	0.0438267i
$280$		0			0
$281$		−	12.3205i		−	0.734980i	−0.930027	−	0.367490i	$-0.880217\pi$
$281$		−	12.3205i		−	0.734980i	0.930027	−	0.367490i	$-0.119783\pi$
$282$	1.09808	+	1.90192i	0.0653895	+	0.113258i
$283$	−12.8301	+	22.2224i	−0.762672	+	1.32099i	0.178797	+	0.983886i	$0.442780\pi$
$283$	−12.8301	+	22.2224i	−0.762672	+	1.32099i	−0.941469	+	0.337100i	$0.890554\pi$
$284$	4.09808	+	2.36603i	0.243176	+	0.140398i
$285$		0			0
$286$	4.39230	+	1.26795i	0.259722	+	0.0749754i
$287$	−25.6603			−1.51468
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−7.92820	+	13.7321i	−0.466365	+	0.807768i
$290$		0			0
$291$		−	6.00000i		−	0.351726i
$292$	5.42820	−	3.13397i	0.317662	−	0.183402i
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.545368	−	0.838196i	$-0.316390\pi$
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.998584	−	0.0532048i	$-0.0169436\pi$
$294$		−	0.464102i		−	0.0270670i
$295$		0			0
$296$	1.76795	−	3.06218i	0.102760	−	0.177985i
$297$	−1.09808	−	0.633975i	−0.0637168	−	0.0367869i
$298$	13.1962			0.764433
$299$	3.63397	+	14.6865i	0.210158	+	0.849344i
$300$		0			0
$301$	−22.8564	−	13.1962i	−1.31742	−	0.760614i
$302$	3.36603	−	5.83013i	0.193693	−	0.335486i
$303$	−0.964102	−	1.66987i	−0.0553862	−	0.0959317i
$304$			4.73205i			0.271402i
$305$		0			0
$306$	4.96410	−	2.86603i	0.283779	−	0.163840i
$307$		−	22.5885i		−	1.28919i	−0.764524	−	0.644596i	$-0.777026\pi$
$307$		−	22.5885i		−	1.28919i	0.764524	−	0.644596i	$-0.222974\pi$
$308$	−1.73205	−	3.00000i	−0.0986928	−	0.170941i
$309$	−7.63397	+	13.2224i	−0.434282	+	0.752198i
$310$		0			0
$311$	1.66025			0.0941444			0.0470722	−	0.998891i	$-0.485011\pi$
$311$	1.66025			0.0941444			0.0470722	+	0.998891i	$0.485011\pi$
$312$	3.50000	−	0.866025i	0.198148	−	0.0490290i
$313$	−6.53590			−0.369431			−0.184715	−	0.982792i	$-0.559136\pi$
$313$	−6.53590			−0.369431			−0.184715	+	0.982792i	$0.559136\pi$
$314$	−6.57180	−	3.79423i	−0.370868	−	0.214121i
$315$		0			0
$316$	−1.26795	−	2.19615i	−0.0713277	−	0.123543i
$317$		−	20.6603i		−	1.16040i	−0.814476	−	0.580198i	$-0.802975\pi$
$317$		−	20.6603i		−	1.16040i	0.814476	−	0.580198i	$-0.197025\pi$
$318$	5.59808	−	3.23205i	0.313925	−	0.181244i
$319$	4.90192	−	2.83013i	0.274455	−	0.158457i
$320$		0			0
$321$	−5.09808	−	8.83013i	−0.284547	−	0.492850i
$322$	5.73205	−	9.92820i	0.319435	−	0.553277i
$323$	23.4904	+	13.5622i	1.30704	+	0.754620i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−13.4641			−0.745708
$327$	1.26795	+	0.732051i	0.0701178	+	0.0404825i
$328$	−4.69615	+	8.13397i	−0.259302	+	0.449124i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.0583130	−	0.998298i	$-0.481428\pi$
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.893708	+	0.448649i	$0.148095\pi$
$332$	−0.169873	+	0.0980762i	−0.00932299	+	0.00538263i
$333$			3.53590i			0.193766i
$334$	4.73205	+	8.19615i	0.258926	+	0.448474i
$335$		0			0
$336$	−2.36603	−	1.36603i	−0.129077	−	0.0745228i
$337$	−20.8564			−1.13612			−0.568060	−	0.822987i	$-0.692306\pi$
$337$	−20.8564			−1.13612			−0.568060	+	0.822987i	$0.692306\pi$
$338$	6.92820	−	11.0000i	0.376845	−	0.598321i
$339$	−1.33975			−0.0727650
$340$		0			0
$341$	−0.928203	+	1.60770i	−0.0502650	+	0.0870616i
$342$	−2.36603	−	4.09808i	−0.127940	−	0.221599i
$343$		−	17.8564i		−	0.964155i
$344$	−8.36603	+	4.83013i	−0.451066	+	0.260423i
$345$		0			0
$346$		−	4.39230i		−	0.236132i
$347$	16.5622	+	28.6865i	0.889104	+	1.53997i	0.840936	+	0.541135i	$0.182005\pi$
$347$	16.5622	+	28.6865i	0.889104	+	1.53997i	0.0481683	+	0.998839i	$0.484662\pi$
$348$	2.23205	−	3.86603i	0.119650	−	0.207241i
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	0.811141	−	0.584850i	$-0.198847\pi$
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	−0.100924	+	0.994894i	$0.532180\pi$
$350$		0			0
$351$	−2.59808	+	2.50000i	−0.138675	+	0.133440i
$352$	−1.26795			−0.0675819
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.0946674	−	0.995509i	$-0.530179\pi$
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.909470	+	0.415770i	$0.863512\pi$
$354$	−4.00000	+	6.92820i	−0.212598	+	0.368230i
$355$		0			0
$356$		−	9.46410i		−	0.501596i
$357$	−13.5622	+	7.83013i	−0.717787	+	0.414414i
$358$	−13.9019	+	8.02628i	−0.734740	+	0.424202i
$359$			1.12436i			0.0593412i	0.999560	+	0.0296706i	$0.00944584\pi$
$359$			1.12436i			0.0593412i	−0.999560	+	0.0296706i	$0.990554\pi$
$360$		0			0
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	−16.6244	−	9.59808i	−0.873757	−	0.504464i
$363$	−9.39230			−0.492968
$364$	−9.56218	+	2.36603i	−0.501194	+	0.124013i
$365$		0			0
$366$	7.96410	+	4.59808i	0.416290	+	0.240345i
$367$	−5.63397	+	9.75833i	−0.294091	+	0.509381i	−0.974773	−	0.223198i	$-0.928350\pi$
$367$	−5.63397	+	9.75833i	−0.294091	+	0.509381i	0.680682	+	0.732579i	$0.261684\pi$
$368$	−2.09808	−	3.63397i	−0.109370	−	0.189434i
$369$		−	9.39230i		−	0.488944i
$370$		0			0
$371$	−15.2942	+	8.83013i	−0.794037	+	0.458437i
$372$			1.46410i			0.0759101i
$373$	−6.86603	−	11.8923i	−0.355509	−	0.615760i	0.631696	−	0.775216i	$-0.282359\pi$
$373$	−6.86603	−	11.8923i	−0.355509	−	0.615760i	−0.987205	+	0.159456i	$0.949026\pi$
$374$	−3.63397	+	6.29423i	−0.187908	+	0.325467i
$375$		0			0
$376$	−2.19615			−0.113258
$377$	−3.86603	−	15.6244i	−0.199110	−	0.804695i
$378$	2.73205			0.140522
$379$	4.73205	+	2.73205i	0.243069	+	0.140336i	0.616587	−	0.787287i	$-0.288515\pi$
$379$	4.73205	+	2.73205i	0.243069	+	0.140336i	−0.373517	+	0.927623i	$0.621848\pi$
$380$		0			0
$381$	−4.92820	−	8.53590i	−0.252479	−	0.437307i
$382$			6.92820i			0.354478i
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	−0.467255	−	0.884122i	$-0.654757\pi$
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	0.532045	+	0.846716i	$0.321424\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	5.86603	+	10.1603i	0.298573	+	0.517143i
$387$	4.83013	−	8.36603i	0.245529	−	0.425269i
$388$	5.19615	+	3.00000i	0.263795	+	0.152302i
$389$	−11.7846			−0.597503			−0.298752	−	0.954331i	$-0.596570\pi$
$389$	−11.7846			−0.597503			−0.298752	+	0.954331i	$0.596570\pi$
$390$		0			0
$391$	−24.0526			−1.21639
$392$	0.401924	+	0.232051i	0.0203002	+	0.0117203i
$393$	3.26795	−	5.66025i	0.164846	−	0.285522i
$394$	−8.92820	−	15.4641i	−0.449796	−	0.779070i
$395$		0			0
$396$	1.09808	−	0.633975i	0.0551804	−	0.0318584i
$397$	17.6603	−	10.1962i	0.886343	−	0.511730i	0.0135983	−	0.999908i	$-0.495671\pi$
$397$	17.6603	−	10.1962i	0.886343	−	0.511730i	0.872744	+	0.488177i	$0.162338\pi$
$398$		−	14.1962i		−	0.711589i
$399$	6.46410	+	11.1962i	0.323610	+	0.560509i
$400$		0			0
$401$	6.99038	+	4.03590i	0.349083	+	0.201543i	0.664281	−	0.747483i	$-0.268738\pi$
$401$	6.99038	+	4.03590i	0.349083	+	0.201543i	−0.315198	+	0.949026i	$0.602071\pi$
$402$	13.1244			0.654583
$403$	3.66025	+	3.80385i	0.182330	+	0.189483i
$404$	1.92820			0.0959317
$405$		0			0
$406$	−6.09808	+	10.5622i	−0.302642	+	0.524192i
$407$	−2.24167	−	3.88269i	−0.111115	−	0.192458i
$408$			5.73205i			0.283779i
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	−0.0697281	−	0.997566i	$-0.522213\pi$
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	0.829053	+	0.559169i	$0.188880\pi$
$410$		0			0
$411$		−	11.9282i		−	0.588375i
$412$	−7.63397	−	13.2224i	−0.376099	−	0.651422i
$413$	10.9282	−	18.9282i	0.537742	−	0.931396i
$414$	3.63397	+	2.09808i	0.178600	+	0.103115i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	−17.8564			−0.874432
$418$	5.19615	+	3.00000i	0.254152	+	0.146735i
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	−0.569979	−	0.821659i	$-0.693049\pi$
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	0.996567	+	0.0827863i	$0.0263819\pi$
$420$		0			0
$421$		−	22.7128i		−	1.10695i	−0.832864	−	0.553477i	$-0.813301\pi$
$421$		−	22.7128i		−	1.10695i	0.832864	−	0.553477i	$-0.186699\pi$
$422$	−14.1962	+	8.19615i	−0.691058	+	0.398982i
$423$	1.90192	−	1.09808i	0.0924747	−	0.0533903i
$424$			6.46410i			0.313925i
$425$		0			0
$426$	2.36603	−	4.09808i	0.114634	−	0.198552i
$427$	−21.7583	−	12.5622i	−1.05296	−	0.607926i
$428$	10.1962			0.492850
$429$	1.26795	−	4.39230i	0.0612172	−	0.212062i
$430$		0			0
$431$	−11.3660	−	6.56218i	−0.547482	−	0.316089i	0.200624	−	0.979668i	$-0.435703\pi$
$431$	−11.3660	−	6.56218i	−0.547482	−	0.316089i	−0.748106	+	0.663579i	$0.769036\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−6.42820	−	11.1340i	−0.308920	−	0.535065i	0.669207	−	0.743076i	$-0.266634\pi$
$433$	−6.42820	−	11.1340i	−0.308920	−	0.535065i	−0.978126	+	0.208012i	$0.933301\pi$
$434$		−	4.00000i		−	0.192006i
$435$		0			0
$436$	−1.26795	+	0.732051i	−0.0607238	+	0.0350589i
$437$			19.8564i			0.949861i
$438$	−3.13397	−	5.42820i	−0.149747	−	0.259370i
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	−0.870051	−	0.492962i	$-0.835914\pi$
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	0.861943	+	0.507005i	$0.169247\pi$
$440$		0			0
$441$	−0.464102			−0.0221001
$442$	14.3301	+	14.8923i	0.681615	+	0.708355i
$443$	−15.6077			−0.741544			−0.370772	−	0.928724i	$-0.620907\pi$
$443$	−15.6077			−0.741544			−0.370772	+	0.928724i	$0.620907\pi$
$444$	−3.06218	−	1.76795i	−0.145325	−	0.0839032i
$445$		0			0
$446$	−13.4641	−	23.3205i	−0.637544	−	1.10426i
$447$		−	13.1962i		−	0.624157i
$448$	2.36603	−	1.36603i	0.111784	−	0.0645386i
$449$	−9.80385	+	5.66025i	−0.462672	+	0.267124i	−0.713167	−	0.700994i	$-0.752740\pi$
$449$	−9.80385	+	5.66025i	−0.462672	+	0.267124i	0.250495	+	0.968118i	$0.419407\pi$
$450$		0			0
$451$	5.95448	+	10.3135i	0.280386	+	0.485642i
$452$	0.669873	−	1.16025i	0.0315082	−	0.0545738i
$453$	−5.83013	−	3.36603i	−0.273923	−	0.158150i
$454$	12.1962			0.572394
$455$		0			0
$456$	4.73205			0.221599
$457$	1.16025	+	0.669873i	0.0542744	+	0.0313353i	0.526892	−	0.849932i	$-0.323357\pi$
$457$	1.16025	+	0.669873i	0.0542744	+	0.0313353i	−0.472617	+	0.881268i	$0.656691\pi$
$458$	−5.92820	+	10.2679i	−0.277007	+	0.479790i
$459$	−2.86603	−	4.96410i	−0.133775	−	0.231704i
$460$		0			0
$461$	19.2846	−	11.1340i	0.898174	−	0.518561i	0.0215666	−	0.999767i	$-0.493135\pi$
$461$	19.2846	−	11.1340i	0.898174	−	0.518561i	0.876607	+	0.481207i	$0.159801\pi$
$462$	−3.00000	+	1.73205i	−0.139573	+	0.0805823i
$463$			10.0526i			0.467182i	0.972335	+	0.233591i	$0.0750477\pi$
$463$			10.0526i			0.467182i	−0.972335	+	0.233591i	$0.924952\pi$
$464$	2.23205	+	3.86603i	0.103620	+	0.179476i
$465$		0			0
$466$	−6.80385	−	3.92820i	−0.315182	−	0.181971i
$467$	18.5885			0.860171			0.430086	−	0.902788i	$-0.358483\pi$
$467$	18.5885			0.860171			0.430086	+	0.902788i	$0.358483\pi$
$468$	−0.866025	−	3.50000i	−0.0400320	−	0.161788i
$469$	−35.8564			−1.65570
$470$		0			0
$471$	−3.79423	+	6.57180i	−0.174829	+	0.302812i
$472$	−4.00000	−	6.92820i	−0.184115	−	0.318896i
$473$			12.2487i			0.563196i
$474$	−2.19615	+	1.26795i	−0.100873	+	0.0582388i
$475$		0			0
$476$		−	15.6603i		−	0.717787i
$477$	−3.23205	−	5.59808i	−0.147985	−	0.256318i
$478$	−3.83013	+	6.63397i	−0.175186	+	0.303431i
$479$	28.9808	+	16.7321i	1.32416	+	0.764507i	0.984390	−	0.176000i	$-0.0563159\pi$
$479$	28.9808	+	16.7321i	1.32416	+	0.764507i	0.339775	+	0.940507i	$0.389649\pi$
$480$		0			0
$481$	−12.3756	+	3.06218i	−0.564281	+	0.139623i
$482$	−13.5885			−0.618937
$483$	−9.92820	−	5.73205i	−0.451749	−	0.260817i
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	2.70577	−	1.56218i	0.122610	−	0.0707890i	−0.437441	−	0.899247i	$-0.644115\pi$
$487$	2.70577	−	1.56218i	0.122610	−	0.0707890i	0.560051	+	0.828458i	$0.310782\pi$
$488$	−7.96410	+	4.59808i	−0.360518	+	0.208145i
$489$			13.4641i			0.608868i
$490$		0			0
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	−0.750530	−	0.660836i	$-0.770202\pi$
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	0.947566	+	0.319560i	$0.103535\pi$
$492$	8.13397	+	4.69615i	0.366708	+	0.211719i
$493$	25.5885			1.15245
$494$	12.2942	−	11.8301i	0.553143	−	0.532263i
$495$		0			0
$496$	−1.26795	−	0.732051i	−0.0569326	−	0.0328701i
$497$	−6.46410	+	11.1962i	−0.289955	+	0.502216i
$498$	0.0980762	+	0.169873i	0.00439490	+	0.00761219i
$499$			32.0000i			1.43252i	0.697835	+	0.716258i	$0.254147\pi$
$499$			32.0000i			1.43252i	−0.697835	+	0.716258i	$0.745853\pi$
$500$		0			0
$501$	8.19615	−	4.73205i	0.366177	−	0.211412i
$502$			13.4641i			0.600932i
$503$	20.4904	+	35.4904i	0.913621	+	1.58244i	0.808908	+	0.587935i	$0.200059\pi$
$503$	20.4904	+	35.4904i	0.913621	+	1.58244i	0.104713	+	0.994502i	$0.466608\pi$
$504$	−1.36603	+	2.36603i	−0.0608476	+	0.105391i
$505$		0			0
$506$	−5.32051			−0.236525
$507$	−11.0000	−	6.92820i	−0.488527	−	0.307692i
$508$	9.85641			0.437307
$509$	−11.8923	−	6.86603i	−0.527117	−	0.304331i	0.212725	−	0.977112i	$-0.431766\pi$
$509$	−11.8923	−	6.86603i	−0.527117	−	0.304331i	−0.739842	+	0.672781i	$0.765100\pi$
$510$		0			0
$511$	8.56218	+	14.8301i	0.378768	+	0.656046i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.09808	+	2.36603i	−0.180934	+	0.104463i
$514$	−8.08846	+	4.66987i	−0.356767	+	0.205979i
$515$		0			0
$516$	4.83013	+	8.36603i	0.212634	+	0.368294i
$517$	−1.39230	+	2.41154i	−0.0612335	+	0.106060i
$518$	8.36603	+	4.83013i	0.367582	+	0.212224i
$519$	−4.39230			−0.192801
$520$		0			0
$521$	41.4449			1.81573			0.907866	−	0.419260i	$-0.137710\pi$
$521$	41.4449			1.81573			0.907866	+	0.419260i	$0.137710\pi$
$522$	−3.86603	−	2.23205i	−0.169211	−	0.0976942i
$523$	−11.2224	+	19.4378i	−0.490723	+	0.849957i	−0.999943	−	0.0106796i	$-0.996601\pi$
$523$	−11.2224	+	19.4378i	−0.490723	+	0.849957i	0.509220	+	0.860636i	$0.329934\pi$
$524$	3.26795	+	5.66025i	0.142761	+	0.247269i
$525$		0			0
$526$	−8.70577	+	5.02628i	−0.379590	+	0.219156i
$527$	−7.26795	+	4.19615i	−0.316597	+	0.182787i
$528$			1.26795i			0.0551804i
$529$	2.69615	+	4.66987i	0.117224	+	0.203038i
$530$		0			0
$531$	6.92820	+	4.00000i	0.300658	+	0.173585i
$532$	−12.9282			−0.560509
$533$	32.8731	−	8.13397i	1.42389	−	0.352322i
$534$	−9.46410			−0.409552
$535$		0			0
$536$	−6.56218	+	11.3660i	−0.283443	+	0.490938i
$537$	8.02628	+	13.9019i	0.346360	+	0.599912i
$538$		−	5.46410i		−	0.235574i
$539$	0.509619	−	0.294229i	0.0219508	−	0.0126733i
$540$		0			0
$541$		−	5.67949i		−	0.244180i	−0.992519	−	0.122090i	$-0.961040\pi$
$541$		−	5.67949i		−	0.244180i	0.992519	−	0.122090i	$-0.0389597\pi$
$542$	−10.9282	−	18.9282i	−0.469407	−	0.813036i
$543$	−9.59808	+	16.6244i	−0.411893	+	0.713419i
$544$	−4.96410	−	2.86603i	−0.212834	−	0.122880i
$545$		0			0
$546$	2.36603	+	9.56218i	0.101257	+	0.409223i
$547$	4.19615			0.179415			0.0897073	−	0.995968i	$-0.471407\pi$
$547$	4.19615			0.179415			0.0897073	+	0.995968i	$0.471407\pi$
$548$	10.3301	+	5.96410i	0.441281	+	0.254774i
$549$	4.59808	−	7.96410i	0.196241	−	0.339900i
$550$		0			0
$551$		−	21.1244i		−	0.899928i
$552$	−3.63397	+	2.09808i	−0.154672	+	0.0893001i
$553$	6.00000	−	3.46410i	0.255146	−	0.147309i
$554$			5.73205i			0.243532i
$555$		0			0
$556$	8.92820	−	15.4641i	0.378640	−	0.655824i
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.997734	−	0.0672780i	$-0.978569\pi$
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.557132	−	0.830424i	$-0.688098\pi$
$558$	1.46410			0.0619804
$559$	33.4641	+	9.66025i	1.41538	+	0.408585i
$560$		0			0
$561$	6.29423	+	3.63397i	0.265743	+	0.153427i
$562$	6.16025	−	10.6699i	0.259855	−	0.450081i
$563$	−17.4641	−	30.2487i	−0.736024	−	1.27483i	−0.954273	−	0.298938i	$-0.903368\pi$
$563$	−17.4641	−	30.2487i	−0.736024	−	1.27483i	0.218248	−	0.975893i	$-0.429966\pi$
$564$			2.19615i			0.0924747i
$565$		0			0
$566$	−22.2224	+	12.8301i	−0.934078	+	0.539290i
$567$		−	2.73205i		−	0.114735i
$568$	2.36603	+	4.09808i	0.0992762	+	0.171951i
$569$	15.3205	−	26.5359i	0.642269	−	1.11244i	−0.342656	−	0.939461i	$-0.611326\pi$
$569$	15.3205	−	26.5359i	0.642269	−	1.11244i	0.984925	−	0.172982i	$-0.0553402\pi$
$570$		0			0
$571$	−14.0526			−0.588081			−0.294041	−	0.955793i	$-0.595000\pi$
$571$	−14.0526			−0.588081			−0.294041	+	0.955793i	$0.595000\pi$
$572$	3.16987	+	3.29423i	0.132539	+	0.137739i
$573$	6.92820			0.289430
$574$	−22.2224	−	12.8301i	−0.927546	−	0.535519i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	3.73205i		−	0.155367i	−0.996978	−	0.0776837i	$-0.975248\pi$
$577$		−	3.73205i		−	0.155367i	0.996978	−	0.0776837i	$-0.0247524\pi$
$578$	−13.7321	+	7.92820i	−0.571178	+	0.329770i
$579$	10.1603	−	5.86603i	0.422246	−	0.243784i
$580$		0			0
$581$	−0.267949	−	0.464102i	−0.0111164	−	0.0192542i
$582$	3.00000	−	5.19615i	0.124354	−	0.215387i
$583$	7.09808	+	4.09808i	0.293972	+	0.169725i
$584$	6.26795			0.259370
$585$		0			0
$586$	30.5167			1.26063
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	0.757914	−	0.652355i	$-0.226219\pi$
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	−0.185999	+	0.982550i	$0.559552\pi$
$588$	0.232051	−	0.401924i	0.00956961	−	0.0165751i
$589$	3.46410	+	6.00000i	0.142736	+	0.247226i
$590$		0			0
$591$	−15.4641	+	8.92820i	−0.636108	+	0.367257i
$592$	3.06218	−	1.76795i	0.125855	−	0.0726623i
$593$		−	9.14359i		−	0.375482i	−0.982219	−	0.187741i	$-0.939883\pi$
$593$		−	9.14359i		−	0.375482i	0.982219	−	0.187741i	$-0.0601166\pi$
$594$	−0.633975	−	1.09808i	−0.0260123	−	0.0450546i
$595$		0			0
$596$	11.4282	+	6.59808i	0.468117	+	0.270268i
$597$	−14.1962			−0.581010
$598$	−4.19615	+	14.5359i	−0.171593	+	0.594417i
$599$	−2.53590			−0.103614			−0.0518070	−	0.998657i	$-0.516498\pi$
$599$	−2.53590			−0.103614			−0.0518070	+	0.998657i	$0.516498\pi$
$600$		0			0
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	−0.935478	−	0.353385i	$-0.885031\pi$
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	0.773779	+	0.633456i	$0.218364\pi$
$602$	−13.1962	−	22.8564i	−0.537835	−	0.931558i
$603$		−	13.1244i		−	0.534465i
$604$	5.83013	−	3.36603i	0.237225	−	0.136962i
$605$		0			0
$606$		−	1.92820i		−	0.0783279i
$607$	−20.3923	−	35.3205i	−0.827698	−	1.43362i	−0.899840	−	0.436221i	$-0.856317\pi$
$607$	−20.3923	−	35.3205i	−0.827698	−	1.43362i	0.0721415	−	0.997394i	$-0.477017\pi$
$608$	−2.36603	+	4.09808i	−0.0959550	+	0.166199i
$609$	10.5622	+	6.09808i	0.428001	+	0.247107i
$610$		0			0
$611$	5.49038	+	5.70577i	0.222117	+	0.230831i
$612$	5.73205			0.231704
$613$	−8.13397	−	4.69615i	−0.328528	−	0.189676i	0.326659	−	0.945142i	$-0.394077\pi$
$613$	−8.13397	−	4.69615i	−0.328528	−	0.189676i	−0.655187	+	0.755466i	$0.727410\pi$
$614$	11.2942	−	19.5622i	0.455798	−	0.789465i
$615$		0			0
$616$		−	3.46410i		−	0.139573i
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	−0.250934	−	0.968004i	$-0.580738\pi$
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	0.712849	+	0.701318i	$0.247404\pi$
$618$	−13.2224	+	7.63397i	−0.531884	+	0.307083i
$619$		−	17.4641i		−	0.701942i	−0.936386	−	0.350971i	$-0.885852\pi$
$619$		−	17.4641i		−	0.701942i	0.936386	−	0.350971i	$-0.114148\pi$
$620$		0			0
$621$	2.09808	−	3.63397i	0.0841929	−	0.145826i
$622$	1.43782	+	0.830127i	0.0576514	+	0.0332851i
$623$	25.8564			1.03592
$624$	3.46410	+	1.00000i	0.138675	+	0.0400320i
$625$		0			0
$626$	−5.66025	−	3.26795i	−0.226229	−	0.130614i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	−3.79423	−	6.57180i	−0.151406	−	0.262243i
$629$		−	20.2679i		−	0.808136i
$630$		0			0
$631$	6.67949	−	3.85641i	0.265906	−	0.153521i	−0.361119	−	0.932520i	$-0.617605\pi$
$631$	6.67949	−	3.85641i	0.265906	−	0.153521i	0.627026	+	0.778998i	$0.284272\pi$
$632$		−	2.53590i		−	0.100873i
$633$	8.19615	+	14.1962i	0.325768	+	0.564246i
$634$	10.3301	−	17.8923i	0.410262	−	0.710594i
$635$		0			0
$636$	6.46410			0.256318
$637$	−0.401924	−	1.62436i	−0.0159248	−	0.0643593i
$638$	5.66025			0.224092
$639$	−4.09808	−	2.36603i	−0.162117	−	0.0935985i
$640$		0			0
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	−0.999885	−	0.0151806i	$-0.995168\pi$
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	0.486796	−	0.873516i	$-0.338166\pi$
$642$		−	10.1962i		−	0.402410i
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	−0.244359	−	0.969685i	$-0.578577\pi$
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	0.717592	+	0.696463i	$0.245244\pi$
$644$	9.92820	−	5.73205i	0.391226	−	0.225874i
$645$		0			0
$646$	13.5622	+	23.4904i	0.533597	+	0.924217i
$647$	11.1244	−	19.2679i	0.437344	−	0.757501i	−0.560140	−	0.828398i	$-0.689253\pi$
$647$	11.1244	−	19.2679i	0.437344	−	0.757501i	0.997484	+	0.0708966i	$0.0225860\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−10.1436			−0.398171
$650$		0			0
$651$	−4.00000			−0.156772
$652$	−11.6603	−	6.73205i	−0.456651	−	0.263647i
$653$	−8.73205	+	15.1244i	−0.341712	+	0.591862i	−0.984751	−	0.173972i	$-0.944340\pi$
$653$	−8.73205	+	15.1244i	−0.341712	+	0.591862i	0.643039	+	0.765833i	$0.277673\pi$
$654$	0.732051	+	1.26795i	0.0286255	+	0.0495807i
$655$		0			0
$656$	−8.13397	+	4.69615i	−0.317578	+	0.183354i
$657$	−5.42820	+	3.13397i	−0.211774	+	0.122268i
$658$		−	6.00000i		−	0.233904i
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	0.948404	−	0.317064i	$-0.102697\pi$
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	−0.748788	+	0.662810i	$0.769364\pi$
$660$		0			0
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	0.679446	−	0.733726i	$-0.262220\pi$
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	−0.295702	+	0.955280i	$0.595554\pi$
$662$	20.0000			0.777322
$663$	14.8923	−	14.3301i	0.578369	−	0.556536i
$664$	−0.196152			−0.00761219
$665$		0			0
$666$	−1.76795	+	3.06218i	−0.0685066	+	0.118657i
$667$	9.36603	+	16.2224i	0.362654	+	0.628135i
$668$			9.46410i			0.366177i
$669$	−23.3205	+	13.4641i	−0.901623	+	0.520552i
$670$		0			0
$671$			11.6603i			0.450139i
$672$	−1.36603	−	2.36603i	−0.0526956	−	0.0912714i
$673$	−13.9641	+	24.1865i	−0.538277	+	0.932322i	0.460720	+	0.887545i	$0.347591\pi$
$673$	−13.9641	+	24.1865i	−0.538277	+	0.932322i	−0.998997	+	0.0447770i	$0.985742\pi$
$674$	−18.0622	−	10.4282i	−0.695729	−	0.401679i
$675$		0			0
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	45.4641			1.74733			0.873664	−	0.486530i	$-0.161738\pi$
$677$	45.4641			1.74733			0.873664	+	0.486530i	$0.161738\pi$
$678$	−1.16025	−	0.669873i	−0.0445593	−	0.0257263i
$679$	−8.19615	+	14.1962i	−0.314539	+	0.544798i
$680$		0			0
$681$		−	12.1962i		−	0.467358i
$682$	−1.60770	+	0.928203i	−0.0615618	+	0.0355427i
$683$	−8.78461	+	5.07180i	−0.336134	+	0.194067i	−0.658561	−	0.752527i	$-0.728835\pi$
$683$	−8.78461	+	5.07180i	−0.336134	+	0.194067i	0.322427	+	0.946594i	$0.395501\pi$
$684$		−	4.73205i		−	0.180934i
$685$		0			0
$686$	8.92820	−	15.4641i	0.340880	−	0.590422i
$687$	10.2679	+	5.92820i	0.391747	+	0.226175i
$688$	−9.66025			−0.368294
$689$	16.7942	−	16.1603i	0.639809	−	0.615657i
$690$		0			0
$691$	−37.8109	−	21.8301i	−1.43839	−	0.830457i	−0.440656	−	0.897676i	$-0.645254\pi$
$691$	−37.8109	−	21.8301i	−1.43839	−	0.830457i	−0.997738	+	0.0672190i	$0.978587\pi$
$692$	2.19615	−	3.80385i	0.0834852	−	0.144601i
$693$	1.73205	+	3.00000i	0.0657952	+	0.113961i
$694$			33.1244i			1.25738i
$695$		0			0
$696$	3.86603	−	2.23205i	0.146541	−	0.0846057i
$697$			53.8372i			2.03923i
$698$	7.66025	+	13.2679i	0.289945	+	0.502199i
$699$	−3.92820	+	6.80385i	−0.148578	+	0.257345i
$700$		0			0
$701$	3.32051			0.125414			0.0627069	−	0.998032i	$-0.480027\pi$
$701$	3.32051			0.125414			0.0627069	+	0.998032i	$0.480027\pi$
$702$	−3.50000	+	0.866025i	−0.132099	+	0.0326860i
$703$	−16.7321			−0.631061
$704$	−1.09808	−	0.633975i	−0.0413853	−	0.0238938i
$705$		0			0
$706$	−10.8923	−	18.8660i	−0.409937	−	0.710032i
$707$			5.26795i			0.198122i
$708$	−6.92820	+	4.00000i	−0.260378	+	0.150329i
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	−0.698275	−	0.715830i	$-0.746049\pi$
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	0.270789	+	0.962639i	$0.412715\pi$
$710$		0			0
$711$	1.26795	+	2.19615i	0.0475518	+	0.0823622i
$712$	4.73205	−	8.19615i	0.177341	−	0.307164i
$713$	−5.32051	−	3.07180i	−0.199255	−	0.115040i
$714$	−15.6603			−0.586070
$715$		0			0
$716$	−16.0526			−0.599912
$717$	6.63397	+	3.83013i	0.247750	+	0.143039i
$718$	−0.562178	+	0.973721i	−0.0209803	+	0.0363389i
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	−0.998315	−	0.0580299i	$-0.981518\pi$
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	0.448902	−	0.893581i	$-0.351815\pi$
$720$		0			0
$721$	36.1244	−	20.8564i	1.34534	−	0.776733i
$722$	2.93782	−	1.69615i	0.109334	−	0.0631243i
$723$			13.5885i			0.505360i
$724$	−9.59808	−	16.6244i	−0.356710	−	0.617839i
$725$		0			0
$726$	−8.13397	−	4.69615i	−0.301880	−	0.174291i
$727$	−30.9808			−1.14901			−0.574506	−	0.818500i	$-0.694806\pi$
$727$	−30.9808			−1.14901			−0.574506	+	0.818500i	$0.694806\pi$
$728$	−9.46410	−	2.73205i	−0.350763	−	0.101257i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−27.6865	+	47.9545i	−1.02402	+	1.77366i
$732$	4.59808	+	7.96410i	0.169950	+	0.294362i
$733$		−	19.0000i		−	0.701781i	−0.936416	−	0.350891i	$-0.885879\pi$
$733$		−	19.0000i		−	0.701781i	0.936416	−	0.350891i	$-0.114121\pi$
$734$	−9.75833	+	5.63397i	−0.360187	+	0.207954i
$735$		0			0
$736$		−	4.19615i		−	0.154672i
$737$	8.32051	+	14.4115i	0.306490	+	0.530856i
$738$	4.69615	−	8.13397i	0.172868	−	0.299416i
$739$	2.53590	+	1.46410i	0.0932845	+	0.0538578i	0.545917	−	0.837840i	$-0.316182\pi$
$739$	2.53590	+	1.46410i	0.0932845	+	0.0538578i	−0.452632	+	0.891697i	$0.649515\pi$
$740$		0			0
$741$	−11.8301	−	12.2942i	−0.434591	−	0.451640i
$742$	−17.6603			−0.648328
$743$	−41.9090	−	24.1962i	−1.53749	−	0.887671i	−0.998985	−	0.0450491i	$-0.985656\pi$
$743$	−41.9090	−	24.1962i	−1.53749	−	0.887671i	−0.538506	−	0.842622i	$-0.681011\pi$
$744$	−0.732051	+	1.26795i	−0.0268383	+	0.0464853i
$745$		0			0
$746$		−	13.7321i		−	0.502766i
$747$	0.169873	−	0.0980762i	0.00621533	−	0.00358842i
$748$	−6.29423	+	3.63397i	−0.230140	+	0.132871i
$749$			27.8564i			1.01785i
$750$		0			0
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.0973862	+	0.995247i	$0.531048\pi$
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.813216	+	0.581962i	$0.802285\pi$
$752$	−1.90192	−	1.09808i	−0.0693560	−	0.0400427i
$753$	13.4641			0.490659
$754$	4.46410	−	15.4641i	0.162573	−	0.563169i
$755$		0			0
$756$	2.36603	+	1.36603i	0.0860515	+	0.0496819i
$757$	10.4641	−	18.1244i	0.380324	−	0.658741i	−0.610784	−	0.791797i	$-0.709146\pi$
$757$	10.4641	−	18.1244i	0.380324	−	0.658741i	0.991109	+	0.133056i	$0.0424791\pi$
$758$	2.73205	+	4.73205i	0.0992326	+	0.171876i
$759$			5.32051i			0.193122i
$760$		0			0
$761$	−9.80385	+	5.66025i	−0.355389	+	0.205184i	−0.667056	−	0.745007i	$-0.732446\pi$
$761$	−9.80385	+	5.66025i	−0.355389	+	0.205184i	0.311667	+	0.950191i	$0.399113\pi$
$762$		−	9.85641i		−	0.357060i
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	−3.46410	+	6.00000i	−0.125327	+	0.217072i
$765$		0			0
$766$	1.46410			0.0529001
$767$	−8.00000	+	27.7128i	−0.288863	+	1.00065i
$768$	−1.00000			−0.0360844
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.990879	−	0.134751i	$-0.0430235\pi$
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.378742	+	0.925502i	$0.376357\pi$
$770$		0			0
$771$	4.66987	+	8.08846i	0.168181	+	0.291299i
$772$			11.7321i			0.422246i
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.524459	−	0.851436i	$-0.324268\pi$
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.999594	−	0.0284768i	$-0.00906566\pi$
$774$	8.36603	−	4.83013i	0.300711	−	0.173615i
$775$		0			0
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	4.83013	−	8.36603i	0.173280	−	0.300129i
$778$	−10.2058	−	5.89230i	−0.365895	−	0.211249i
$779$	44.4449			1.59240
$780$		0			0
$781$	6.00000			0.214697
$782$	−20.8301	−	12.0263i	−0.744884	−	0.430059i
$783$	−2.23205	+	3.86603i	−0.0797670	+	0.138160i
$784$	0.232051	+	0.401924i	0.00828753	+	0.0143544i
$785$		0			0
$786$	5.66025	−	3.26795i	0.201895	−	0.116564i
$787$	4.05256	−	2.33975i	0.144458	−	0.0834029i	−0.426029	−	0.904710i	$-0.640088\pi$
$787$	4.05256	−	2.33975i	0.144458	−	0.0834029i	0.570487	+	0.821307i	$0.306754\pi$
$788$		−	17.8564i		−	0.636108i
$789$	5.02628	+	8.70577i	0.178940	+	0.309934i
$790$		0			0
$791$	3.16987	+	1.83013i	0.112708	+	0.0650718i
$792$	1.26795			0.0450546
$793$	31.8564	+	9.19615i	1.13125	+	0.326565i
$794$	20.3923			0.723696
$795$		0			0
$796$	7.09808	−	12.2942i	0.251585	−	0.435757i
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$			12.9282i			0.457653i
$799$	−10.9019	+	6.29423i	−0.385682	+	0.222674i
$800$		0			0
$801$			9.46410i			0.334398i
$802$	4.03590	+	6.99038i	0.142513	+	0.246839i
$803$	3.97372	−	6.88269i	0.140230	−	0.242885i
$804$	11.3660	+	6.56218i	0.400849	+	0.231430i
$805$		0			0
$806$	1.26795	+	5.12436i	0.0446616	+	0.180498i
$807$	−5.46410			−0.192345
$808$	1.66987	+	0.964102i	0.0587459	+	0.0339170i
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.180453	−	0.983584i	$-0.442244\pi$
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.761582	−	0.648069i	$-0.224423\pi$
$810$		0			0
$811$			17.1769i			0.603163i	0.953440	+	0.301582i	$0.0975145\pi$
$811$			17.1769i			0.603163i	−0.953440	+	0.301582i	$0.902485\pi$
$812$	−10.5622	+	6.09808i	−0.370660	+	0.214001i
$813$	−18.9282	+	10.9282i	−0.663841	+	0.383269i
$814$		−	4.48334i		−	0.157141i
$815$		0			0
$816$	−2.86603	+	4.96410i	−0.100331	+	0.173778i
$817$	39.5885	+	22.8564i	1.38502	+	0.799644i
$818$	17.7321			0.619987
$819$	9.56218	−	2.36603i	0.334130	−	0.0826756i
$820$		0			0
$821$	0.803848	+	0.464102i	0.0280545	+	0.0161973i	0.513962	−	0.857813i	$-0.328177\pi$
$821$	0.803848	+	0.464102i	0.0280545	+	0.0161973i	−0.485907	+	0.874010i	$0.661511\pi$
$822$	5.96410	−	10.3301i	0.208022	−	0.360305i
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	−0.959177	−	0.282806i	$-0.908735\pi$
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	0.234671	−	0.972075i	$-0.424599\pi$
$824$		−	15.2679i		−	0.531884i
$825$		0			0
$826$	18.9282	−	10.9282i	0.658596	−	0.380241i
$827$			26.5359i			0.922744i	0.887207	+	0.461372i	$0.152643\pi$
$827$			26.5359i			0.922744i	−0.887207	+	0.461372i	$0.847357\pi$
$828$	2.09808	+	3.63397i	0.0729132	+	0.126289i
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	−0.951886	−	0.306452i	$-0.900858\pi$
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	0.741338	+	0.671132i	$0.234192\pi$
$830$		0			0
$831$	5.73205			0.198843
$832$	−2.59808	+	2.50000i	−0.0900721	+	0.0866719i
$833$	2.66025			0.0921723
$834$	−15.4641	−	8.92820i	−0.535478	−	0.309158i
$835$		0			0
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$		−	1.46410i		−	0.0506068i
$838$	15.1244	−	8.73205i	0.522462	−	0.301644i
$839$	−36.2487	+	20.9282i	−1.25144	+	0.722522i	−0.971396	−	0.237464i	$-0.923684\pi$
$839$	−36.2487	+	20.9282i	−1.25144	+	0.722522i	−0.280048	+	0.959986i	$0.590350\pi$
$840$		0			0
$841$	4.53590	+	7.85641i	0.156410	+	0.270911i
$842$	11.3564	−	19.6699i	0.391368	−	0.677869i
$843$	−10.6699	−	6.16025i	−0.367490	−	0.212170i
$844$	−16.3923			−0.564246
$845$		0			0
$846$	2.19615			0.0755053
$847$	22.2224	+	12.8301i	0.763572	+	0.440848i
$848$	−3.23205	+	5.59808i	−0.110989	+	0.192239i
$849$	12.8301	+	22.2224i	0.440329	+	0.762672i
$850$		0			0
$851$	12.8494	−	7.41858i	0.440471	−	0.254306i
$852$	4.09808	−	2.36603i	0.140398	−	0.0810587i
$853$		−	54.1769i		−	1.85498i	−0.373845	−	0.927491i	$-0.621961\pi$
$853$		−	54.1769i		−	1.85498i	0.373845	−	0.927491i	$-0.378039\pi$
$854$	−12.5622	−	21.7583i	−0.429869	−	0.744555i
$855$		0			0
$856$	8.83013	+	5.09808i	0.301808	+	0.174249i
$857$	39.4449			1.34741			0.673705	−	0.739000i	$-0.264702\pi$
$857$	39.4449			1.34741			0.673705	+	0.739000i	$0.264702\pi$
$858$	3.29423	−	3.16987i	0.112463	−	0.108218i
$859$	−47.1244			−1.60786			−0.803931	−	0.594722i	$-0.797262\pi$
$859$	−47.1244			−1.60786			−0.803931	+	0.594722i	$0.797262\pi$
$860$		0			0
$861$	−12.8301	+	22.2224i	−0.437250	+	0.757338i
$862$	−6.56218	−	11.3660i	−0.223509	−	0.387128i
$863$			17.1244i			0.582920i	0.956583	+	0.291460i	$0.0941410\pi$
$863$			17.1244i			0.582920i	−0.956583	+	0.291460i	$0.905859\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	12.8564i		−	0.436878i
$867$	7.92820	+	13.7321i	0.269256	+	0.466365i
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	−2.78461	−	1.60770i	−0.0944614	−	0.0545373i
$870$		0			0
$871$	45.9352	−	11.3660i	1.55646	−	0.385123i
$872$	−1.46410			−0.0495807
$873$	−5.19615	−	3.00000i	−0.175863	−	0.101535i
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$		0			0
$876$		−	6.26795i		−	0.211774i
$877$	−20.7224	+	11.9641i	−0.699747	+	0.403999i	−0.807253	−	0.590205i	$-0.799047\pi$
$877$	−20.7224	+	11.9641i	−0.699747	+	0.403999i	0.107506	+	0.994204i	$0.465713\pi$
$878$	−0.294229	+	0.169873i	−0.00992974	+	0.00573294i
$879$		−	30.5167i		−	1.02930i
$880$		0			0
$881$	−13.9186	+	24.1077i	−0.468929	+	0.812209i	−0.999369	−	0.0355135i	$-0.988693\pi$
$881$	−13.9186	+	24.1077i	−0.468929	+	0.812209i	0.530440	+	0.847722i	$0.322027\pi$
$882$	−0.401924	−	0.232051i	−0.0135335	−	0.00781356i
$883$	42.9282			1.44465			0.722325	−	0.691554i	$-0.243074\pi$
$883$	42.9282			1.44465			0.722325	+	0.691554i	$0.243074\pi$
$884$	4.96410	+	20.0622i	0.166961	+	0.674764i
$885$		0			0
$886$	−13.5167	−	7.80385i	−0.454101	−	0.262175i
$887$	18.9282	−	32.7846i	0.635547	−	1.10080i	−0.350852	−	0.936431i	$-0.614108\pi$
$887$	18.9282	−	32.7846i	0.635547	−	1.10080i	0.986399	−	0.164369i	$-0.0525586\pi$
$888$	−1.76795	−	3.06218i	−0.0593285	−	0.102760i
$889$			26.9282i			0.903143i
$890$		0			0
$891$	−1.09808	+	0.633975i	−0.0367869	+	0.0212389i
$892$		−	26.9282i		−	0.901623i
$893$	5.19615	+	9.00000i	0.173883	+	0.301174i
$894$	6.59808	−	11.4282i	0.220673	−	0.382216i
$895$		0			0
$896$	2.73205			0.0912714
$897$	14.5359	+	4.19615i	0.485340	+	0.140105i
$898$	−11.3205			−0.377770
$899$	5.66025	+	3.26795i	0.188780	+	0.108992i
$900$		0			0
$901$	18.5263	+	32.0885i	0.617200	+	1.06902i
$902$			11.9090i			0.396525i
$903$	−22.8564	+	13.1962i	−0.760614	+	0.439140i
$904$	1.16025	−	0.669873i	0.0385895	−	0.0222796i
$905$		0			0
$906$	−3.36603	−	5.83013i	−0.111829	−	0.193693i
$907$	−18.1962	+	31.5167i	−0.604193	+	1.04649i	0.387985	+	0.921666i	$0.373171\pi$
$907$	−18.1962	+	31.5167i	−0.604193	+	1.04649i	−0.992178	+	0.124828i	$0.960162\pi$
$908$	10.5622	+	6.09808i	0.350518	+	0.202372i
$909$	−1.92820			−0.0639545
$910$		0			0
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$	4.09808	+	2.36603i	0.135701	+	0.0783469i
$913$	−0.124356	+	0.215390i	−0.00411557	+	0.00712838i
$914$	0.669873	+	1.16025i	0.0221574	+	0.0383778i
$915$		0			0
$916$	−10.2679	+	5.92820i	−0.339263	+	0.195873i
$917$	−15.4641	+	8.92820i	−0.510670	+	0.294835i
$918$		−	5.73205i		−	0.189186i
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	−0.943836	−	0.330415i	$-0.892811\pi$
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	0.185770	−	0.982593i	$-0.440522\pi$
$920$		0			0
$921$	−19.5622	−	11.2942i	−0.644596	−	0.372157i
$922$	22.2679			0.733356
$923$	4.73205	−	16.3923i	0.155757	−	0.539559i
$924$	−3.46410			−0.113961
$925$		0			0
$926$	−5.02628	+	8.70577i	−0.165174	+	0.286089i
$927$	7.63397	+	13.2224i	0.250733	+	0.434282i
$928$			4.46410i			0.146541i
$929$	−33.9904	+	19.6244i	−1.11519	+	0.643854i	−0.940168	−	0.340711i	$-0.889332\pi$
$929$	−33.9904	+	19.6244i	−1.11519	+	0.643854i	−0.175020	+	0.984565i	$0.555999\pi$
$930$		0			0
$931$		−	2.19615i		−	0.0719760i
$932$	−3.92820	−	6.80385i	−0.128673	−	0.222867i
$933$	0.830127	−	1.43782i	0.0271771	−	0.0470722i
$934$	16.0981	+	9.29423i	0.526745	+	0.304116i
$935$		0			0
$936$	1.00000	−	3.46410i	0.0326860	−	0.113228i
$937$	5.24871			0.171468			0.0857340	−	0.996318i	$-0.472676\pi$
$937$	5.24871			0.171468			0.0857340	+	0.996318i	$0.472676\pi$
$938$	−31.0526	−	17.9282i	−1.01390	−	0.585377i
$939$	−3.26795	+	5.66025i	−0.106645	+	0.184715i
$940$		0			0
$941$			12.6410i			0.412085i	0.978543	+	0.206043i	$0.0660586\pi$
$941$			12.6410i			0.412085i	−0.978543	+	0.206043i	$0.933941\pi$
$942$	−6.57180	+	3.79423i	−0.214121	+	0.123623i
$943$	−34.1314	+	19.7058i	−1.11147	+	0.641708i
$944$		−	8.00000i		−	0.260378i
$945$		0			0
$946$	−6.12436	+	10.6077i	−0.199120	+	0.344886i
$947$	−18.2487	−	10.5359i	−0.593003	−	0.342371i	0.173281	−	0.984872i	$-0.444563\pi$
$947$	−18.2487	−	10.5359i	−0.593003	−	0.342371i	−0.766284	+	0.642502i	$0.777897\pi$
$948$	−2.53590			−0.0823622
$949$	−15.6699	−	16.2846i	−0.508666	−	0.528621i
$950$		0			0
$951$	−17.8923	−	10.3301i	−0.580198	−	0.334977i
$952$	7.83013	−	13.5622i	0.253776	−	0.439553i
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	−0.976969	−	0.213383i	$-0.931552\pi$
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	0.303689	−	0.952771i	$-0.401782\pi$
$954$		−	6.46410i		−	0.209283i
$955$		0			0
$956$	−6.63397	+	3.83013i	−0.214558	+	0.123875i
$957$		−	5.66025i		−	0.182970i
$958$	16.7321	+	28.9808i	0.540588	+	0.936326i
$959$	−16.2942	+	28.2224i	−0.526168	+	0.911350i
$960$		0			0
$961$	28.8564			0.930852
$962$	−12.2487	−	3.53590i	−0.394914	−	0.114002i
$963$	−10.1962			−0.328566
$964$	−11.7679	−	6.79423i	−0.379020	−	0.218827i
$965$		0			0
$966$	−5.73205	−	9.92820i	−0.184426	−	0.319435i
$967$			43.1244i			1.38679i	0.720560	+	0.693393i	$0.243885\pi$
$967$			43.1244i			1.38679i	−0.720560	+	0.693393i	$0.756115\pi$
$968$	8.13397	−	4.69615i	0.261436	−	0.150940i
$969$	23.4904	−	13.5622i	0.754620	−	0.435680i
$970$		0			0
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	0.514495	−	0.857493i	$-0.327979\pi$
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	−0.999859	+	0.0168189i	$0.994646\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	42.2487	+	24.3923i	1.35443	+	0.781981i
$974$	3.12436			0.100111
$975$		0			0
$976$	−9.19615			−0.294362
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.975461	−	0.220174i	$-0.0706625\pi$
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.297054	+	0.954861i	$0.403996\pi$
$978$	−6.73205	+	11.6603i	−0.215267	+	0.372854i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		0			0
$981$	1.26795	−	0.732051i	0.0404825	−	0.0233726i
$982$	7.56218	−	4.36603i	0.241319	−	0.139325i
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$	4.69615	+	8.13397i	0.149708	+	0.259302i
$985$		0			0
$986$	22.1603	+	12.7942i	0.705726	+	0.407451i
$987$	−6.00000			−0.190982
$988$	16.5622	−	4.09808i	0.526913	−	0.130377i
$989$	−40.5359			−1.28897
$990$		0			0
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	−0.987756	−	0.156006i	$-0.950138\pi$
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	0.628983	+	0.777419i	$0.283471\pi$
$992$	−0.732051	−	1.26795i	−0.0232426	−	0.0402574i
$993$		−	20.0000i		−	0.634681i
$994$	−11.1962	+	6.46410i	−0.355120	+	0.205029i
$995$		0			0
$996$			0.196152i			0.00621533i
$997$	10.6699	+	18.4808i	0.337918	+	0.585292i	0.984041	−	0.177942i	$-0.0569439\pi$
$997$	10.6699	+	18.4808i	0.337918	+	0.585292i	−0.646123	+	0.763234i	$0.723611\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$	3.06218	+	1.76795i	0.0968830	+	0.0559354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.d.901.2		4
5.2	odd	4		1950.2.y.b.199.1		4
5.3	odd	4		1950.2.y.g.199.2		4
5.4	even	2		78.2.i.a.43.1	✓	4
13.10	even	6	inner	1950.2.bc.d.751.2		4
15.14	odd	2		234.2.l.c.199.2		4
20.19	odd	2		624.2.bv.e.433.2		4
60.59	even	2		1872.2.by.h.433.1		4
65.4	even	6		1014.2.b.e.337.1		4
65.9	even	6		1014.2.b.e.337.4		4
65.19	odd	12		1014.2.a.k.1.2		2
65.23	odd	12		1950.2.y.b.49.1		4
65.24	odd	12		1014.2.e.i.991.1		4
65.29	even	6		1014.2.i.a.361.2		4
65.34	odd	4		1014.2.e.i.529.1		4
65.44	odd	4		1014.2.e.g.529.2		4
65.49	even	6		78.2.i.a.49.1	yes	4
65.54	odd	12		1014.2.e.g.991.2		4
65.59	odd	12		1014.2.a.i.1.1		2
65.62	odd	12		1950.2.y.g.49.2		4
65.64	even	2		1014.2.i.a.823.2		4
195.59	even	12		3042.2.a.y.1.2		2
195.74	odd	6		3042.2.b.i.1351.1		4
195.134	odd	6		3042.2.b.i.1351.4		4
195.149	even	12		3042.2.a.p.1.1		2
195.179	odd	6		234.2.l.c.127.2		4
260.19	even	12		8112.2.a.bp.1.2		2
260.59	even	12		8112.2.a.bj.1.1		2
260.179	odd	6		624.2.bv.e.49.1		4
780.179	even	6		1872.2.by.h.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	5.4	even	2
78.2.i.a.49.1	yes	4	65.49	even	6
234.2.l.c.127.2		4	195.179	odd	6
234.2.l.c.199.2		4	15.14	odd	2
624.2.bv.e.49.1		4	260.179	odd	6
624.2.bv.e.433.2		4	20.19	odd	2
1014.2.a.i.1.1		2	65.59	odd	12
1014.2.a.k.1.2		2	65.19	odd	12
1014.2.b.e.337.1		4	65.4	even	6
1014.2.b.e.337.4		4	65.9	even	6
1014.2.e.g.529.2		4	65.44	odd	4
1014.2.e.g.991.2		4	65.54	odd	12
1014.2.e.i.529.1		4	65.34	odd	4
1014.2.e.i.991.1		4	65.24	odd	12
1014.2.i.a.361.2		4	65.29	even	6
1014.2.i.a.823.2		4	65.64	even	2
1872.2.by.h.433.1		4	60.59	even	2
1872.2.by.h.1297.2		4	780.179	even	6
1950.2.y.b.49.1		4	65.23	odd	12
1950.2.y.b.199.1		4	5.2	odd	4
1950.2.y.g.49.2		4	65.62	odd	12
1950.2.y.g.199.2		4	5.3	odd	4
1950.2.bc.d.751.2		4	13.10	even	6	inner
1950.2.bc.d.901.2		4	1.1	even	1	trivial
3042.2.a.p.1.1		2	195.149	even	12
3042.2.a.y.1.2		2	195.59	even	12
3042.2.b.i.1351.1		4	195.74	odd	6
3042.2.b.i.1351.4		4	195.134	odd	6
8112.2.a.bj.1.1		2	260.59	even	12
8112.2.a.bp.1.2		2	260.19	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.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} +(-2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.09808 + 0.633975i) q^{11} +1.00000 q^{12} +(2.59808 - 2.50000i) q^{13} -2.73205 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} -1.00000i q^{18} +(4.09808 - 2.36603i) q^{19} +2.73205i q^{21} +(0.633975 + 1.09808i) q^{22} +(-2.09808 + 3.63397i) q^{23} +(0.866025 + 0.500000i) q^{24} +(3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(-2.36603 - 1.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +1.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.09808 - 0.633975i) q^{33} +5.73205i q^{34} +(0.500000 - 0.866025i) q^{36} +(-3.06218 - 1.76795i) q^{37} +4.73205 q^{38} +(-0.866025 - 3.50000i) q^{39} +(8.13397 + 4.69615i) q^{41} +(-1.36603 + 2.36603i) q^{42} +(4.83013 + 8.36603i) q^{43} +1.26795i q^{44} +(-3.63397 + 2.09808i) q^{46} +2.19615i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.232051 - 0.401924i) q^{49} +5.73205 q^{51} +(3.46410 + 1.00000i) q^{52} +6.46410 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.36603 - 2.36603i) q^{56} -4.73205i q^{57} +(3.86603 - 2.23205i) q^{58} +(-6.92820 + 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(-0.732051 + 1.26795i) q^{62} +(2.36603 + 1.36603i) q^{63} -1.00000 q^{64} +1.26795 q^{66} +(11.3660 + 6.56218i) q^{67} +(-2.86603 + 4.96410i) q^{68} +(2.09808 + 3.63397i) q^{69} +(4.09808 - 2.36603i) q^{71} +(0.866025 - 0.500000i) q^{72} -6.26795i q^{73} +(-1.76795 - 3.06218i) q^{74} +(4.09808 + 2.36603i) q^{76} -3.46410 q^{77} +(1.00000 - 3.46410i) q^{78} -2.53590 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.69615 + 8.13397i) q^{82} +0.196152i q^{83} +(-2.36603 + 1.36603i) q^{84} +9.66025i q^{86} +(-2.23205 - 3.86603i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} +(-2.73205 + 9.46410i) q^{91} -4.19615 q^{92} +(1.26795 + 0.732051i) q^{93} +(-1.09808 + 1.90192i) q^{94} +1.00000i q^{96} +(5.19615 - 3.00000i) q^{97} +(0.401924 - 0.232051i) q^{98} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{22} + 2 q^{23} + 14 q^{26} - 4 q^{27} - 6 q^{28} + 2 q^{29} - 6 q^{33} + 2 q^{36} + 12 q^{37}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^22 + 2 * q^23 + 14 * q^26 - 4 * q^27 - 6 * q^28 + 2 * q^29 - 6 * q^33 + 2 * q^36 + 12 * q^37 + 12 * q^38 + 36 * q^41 - 2 * q^42 + 2 * q^43 - 18 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 12 * q^53 - 2 * q^56 + 12 * q^58 + 8 * q^61 + 4 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^66 + 42 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 6 * q^76 + 4 * q^78 - 24 * q^79 - 2 * q^81 - 2 * q^82 - 6 * q^84 - 2 * q^87 - 6 * q^88 - 12 * q^89 - 4 * q^91 + 4 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^98

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