LMFDB - Embedded newform 945.2.bv.d.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(73,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 2]))

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

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

chi := DirichletCharacter("945.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bv (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	945.73
Dual form			945.2.bv.d.712.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 0.366025i) q^{2} +1.73205i q^{4} +(1.86603 - 1.23205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.36603 - 1.36603i) q^{8} +O(q^{10})$	\(q+(-0.366025 + 0.366025i) q^{2} +1.73205i q^{4} +(1.86603 - 1.23205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(-0.232051 + 1.13397i) q^{10} +(0.732051 + 1.26795i) q^{11} +(1.00000 + 0.267949i) q^{13} +(-1.36603 + 0.0980762i) q^{14} -2.46410 q^{16} +(-2.73205 + 0.732051i) q^{17} +(3.36603 + 5.83013i) q^{19} +(2.13397 + 3.23205i) q^{20} +(-0.732051 - 0.196152i) q^{22} +(2.23205 - 0.598076i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-0.464102 + 0.267949i) q^{26} +(-3.00000 + 3.46410i) q^{28} +(6.00000 + 3.46410i) q^{29} -10.1962i q^{31} +(3.63397 - 3.63397i) q^{32} +(0.732051 - 1.26795i) q^{34} +(5.86603 + 0.767949i) q^{35} +(-4.09808 - 1.09808i) q^{37} +(-3.36603 - 0.901924i) q^{38} +(-4.23205 - 0.866025i) q^{40} +(-8.19615 + 4.73205i) q^{41} +(-5.59808 + 1.50000i) q^{43} +(-2.19615 + 1.26795i) q^{44} +(-0.598076 + 1.03590i) q^{46} +(6.29423 + 6.29423i) q^{47} +(1.00000 + 6.92820i) q^{49} +(0.964102 + 2.40192i) q^{50} +(-0.464102 + 1.73205i) q^{52} +(3.36603 - 0.901924i) q^{53} +(2.92820 + 1.46410i) q^{55} +(-0.366025 - 5.09808i) q^{56} +(-3.46410 + 0.928203i) q^{58} -3.46410 q^{59} +9.39230i q^{61} +(3.73205 + 3.73205i) q^{62} -2.26795i q^{64} +(2.19615 - 0.732051i) q^{65} +(6.09808 - 6.09808i) q^{67} +(-1.26795 - 4.73205i) q^{68} +(-2.42820 + 1.86603i) q^{70} +6.00000 q^{71} +(-0.169873 - 0.633975i) q^{73} +(1.90192 - 1.09808i) q^{74} +(-10.0981 + 5.83013i) q^{76} +(-0.732051 + 3.80385i) q^{77} +11.4641i q^{79} +(-4.59808 + 3.03590i) q^{80} +(1.26795 - 4.73205i) q^{82} +(-0.366025 - 1.36603i) q^{83} +(-4.19615 + 4.73205i) q^{85} +(1.50000 - 2.59808i) q^{86} +(0.732051 - 2.73205i) q^{88} +(0.598076 + 1.03590i) q^{89} +(1.53590 + 2.26795i) q^{91} +(1.03590 + 3.86603i) q^{92} -4.60770 q^{94} +(13.4641 + 6.73205i) q^{95} +(-3.09808 + 0.830127i) q^{97} +(-2.90192 - 2.16987i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8	$ 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8} + 6 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} + 10 q^{19} + 12 q^{20} + 4 q^{22} + 2 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{28} + 24 q^{29} + 18 q^{32} - 4 q^{34} + 20 q^{35} - 6 q^{37} - 10 q^{38} - 10 q^{40} - 12 q^{41} - 12 q^{43} + 12 q^{44} + 8 q^{46} - 6 q^{47} + 4 q^{49} - 10 q^{50} + 12 q^{52} + 10 q^{53} - 16 q^{55} + 2 q^{56} + 8 q^{62} - 12 q^{65} + 14 q^{67} - 12 q^{68} + 18 q^{70} + 24 q^{71} - 18 q^{73} + 18 q^{74} - 30 q^{76} + 4 q^{77} - 8 q^{80} + 12 q^{82} + 2 q^{83} + 4 q^{85} + 6 q^{86} - 4 q^{88} - 8 q^{89} + 20 q^{91} + 18 q^{92} - 60 q^{94} + 40 q^{95} - 2 q^{97} - 22 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8 + 6 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 + 10 * q^19 + 12 * q^20 + 4 * q^22 + 2 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^28 + 24 * q^29 + 18 * q^32 - 4 * q^34 + 20 * q^35 - 6 * q^37 - 10 * q^38 - 10 * q^40 - 12 * q^41 - 12 * q^43 + 12 * q^44 + 8 * q^46 - 6 * q^47 + 4 * q^49 - 10 * q^50 + 12 * q^52 + 10 * q^53 - 16 * q^55 + 2 * q^56 + 8 * q^62 - 12 * q^65 + 14 * q^67 - 12 * q^68 + 18 * q^70 + 24 * q^71 - 18 * q^73 + 18 * q^74 - 30 * q^76 + 4 * q^77 - 8 * q^80 + 12 * q^82 + 2 * q^83 + 4 * q^85 + 6 * q^86 - 4 * q^88 - 8 * q^89 + 20 * q^91 + 18 * q^92 - 60 * q^94 + 40 * q^95 - 2 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.366025	+	0.366025i	−0.258819	+	0.258819i	−0.824574	−	0.565755i	$-0.808585\pi$
$2$	−0.366025	+	0.366025i	−0.258819	+	0.258819i	0.565755	+	0.824574i	$0.308585\pi$
$3$		0			0
$3$		0			0
$4$			1.73205i			0.866025i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	−1.36603	−	1.36603i	−0.482963	−	0.482963i
$9$		0			0
$10$	−0.232051	+	1.13397i	−0.0733809	+	0.358594i
$11$	0.732051	+	1.26795i	0.220722	+	0.382301i	0.955027	−	0.296518i	$-0.0958254\pi$
$11$	0.732051	+	1.26795i	0.220722	+	0.382301i	−0.734306	+	0.678819i	$0.762492\pi$
$12$		0			0
$13$	1.00000	+	0.267949i	0.277350	+	0.0743157i	0.394813	−	0.918762i	$-0.370809\pi$
$13$	1.00000	+	0.267949i	0.277350	+	0.0743157i	−0.117463	+	0.993077i	$0.537476\pi$
$14$	−1.36603	+	0.0980762i	−0.365086	+	0.0262120i
$15$		0			0
$16$	−2.46410			−0.616025
$17$	−2.73205	+	0.732051i	−0.662620	+	0.177548i	−0.574428	−	0.818555i	$-0.694775\pi$
$17$	−2.73205	+	0.732051i	−0.662620	+	0.177548i	−0.0881917	+	0.996104i	$0.528109\pi$
$18$		0			0
$19$	3.36603	+	5.83013i	0.772219	+	1.33752i	0.936344	+	0.351083i	$0.114187\pi$
$19$	3.36603	+	5.83013i	0.772219	+	1.33752i	−0.164125	+	0.986440i	$0.552480\pi$
$20$	2.13397	+	3.23205i	0.477171	+	0.722709i
$21$		0			0
$22$	−0.732051	−	0.196152i	−0.156074	−	0.0418198i
$23$	2.23205	−	0.598076i	0.465415	−	0.124708i	−0.0184884	−	0.999829i	$-0.505885\pi$
$23$	2.23205	−	0.598076i	0.465415	−	0.124708i	0.483903	+	0.875122i	$0.339219\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	−0.464102	+	0.267949i	−0.0910178	+	0.0525492i
$27$		0			0
$28$	−3.00000	+	3.46410i	−0.566947	+	0.654654i
$29$	6.00000	+	3.46410i	1.11417	+	0.643268i	0.939907	−	0.341431i	$-0.110912\pi$
$29$	6.00000	+	3.46410i	1.11417	+	0.643268i	0.174265	+	0.984699i	$0.444245\pi$
$30$		0			0
$31$		−	10.1962i		−	1.83128i	−0.401996	−	0.915642i	$-0.631683\pi$
$31$		−	10.1962i		−	1.83128i	0.401996	−	0.915642i	$-0.368317\pi$
$32$	3.63397	−	3.63397i	0.642402	−	0.642402i
$33$		0			0
$34$	0.732051	−	1.26795i	0.125546	−	0.217451i
$35$	5.86603	+	0.767949i	0.991539	+	0.129807i
$36$		0			0
$37$	−4.09808	−	1.09808i	−0.673720	−	0.180523i	−0.0942898	−	0.995545i	$-0.530058\pi$
$37$	−4.09808	−	1.09808i	−0.673720	−	0.180523i	−0.579430	+	0.815022i	$0.696725\pi$
$38$	−3.36603	−	0.901924i	−0.546041	−	0.146311i
$39$		0			0
$40$	−4.23205	−	0.866025i	−0.669146	−	0.136931i
$41$	−8.19615	+	4.73205i	−1.28002	+	0.739022i	−0.976853	−	0.213914i	$-0.931379\pi$
$41$	−8.19615	+	4.73205i	−1.28002	+	0.739022i	−0.303171	+	0.952936i	$0.598045\pi$
$42$		0			0
$43$	−5.59808	+	1.50000i	−0.853699	+	0.228748i	−0.659026	−	0.752120i	$-0.729031\pi$
$43$	−5.59808	+	1.50000i	−0.853699	+	0.228748i	−0.194673	+	0.980868i	$0.562365\pi$
$44$	−2.19615	+	1.26795i	−0.331082	+	0.191151i
$45$		0			0
$46$	−0.598076	+	1.03590i	−0.0881815	+	0.152735i
$47$	6.29423	+	6.29423i	0.918108	+	0.918108i	0.996892	−	0.0787841i	$-0.0251038\pi$
$47$	6.29423	+	6.29423i	0.918108	+	0.918108i	−0.0787841	+	0.996892i	$0.525104\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	0.964102	+	2.40192i	0.136345	+	0.339683i
$51$		0			0
$52$	−0.464102	+	1.73205i	−0.0643593	+	0.240192i
$53$	3.36603	−	0.901924i	0.462359	−	0.123889i	−0.0201174	−	0.999798i	$-0.506404\pi$
$53$	3.36603	−	0.901924i	0.462359	−	0.123889i	0.482477	+	0.875909i	$0.339737\pi$
$54$		0			0
$55$	2.92820	+	1.46410i	0.394839	+	0.197419i
$56$	−0.366025	−	5.09808i	−0.0489122	−	0.681259i
$57$		0			0
$58$	−3.46410	+	0.928203i	−0.454859	+	0.121879i
$59$	−3.46410			−0.450988			−0.225494	−	0.974245i	$-0.572400\pi$
$59$	−3.46410			−0.450988			−0.225494	+	0.974245i	$0.572400\pi$
$60$		0			0
$61$			9.39230i			1.20256i	0.799038	+	0.601281i	$0.205343\pi$
$61$			9.39230i			1.20256i	−0.799038	+	0.601281i	$0.794657\pi$
$62$	3.73205	+	3.73205i	0.473971	+	0.473971i
$63$		0			0
$64$		−	2.26795i		−	0.283494i
$65$	2.19615	−	0.732051i	0.272399	−	0.0907997i
$66$		0			0
$67$	6.09808	−	6.09808i	0.744999	−	0.744999i	−0.228537	−	0.973535i	$-0.573394\pi$
$67$	6.09808	−	6.09808i	0.744999	−	0.744999i	0.973535	+	0.228537i	$0.0733941\pi$
$68$	−1.26795	−	4.73205i	−0.153761	−	0.573845i
$69$		0			0
$70$	−2.42820	+	1.86603i	−0.290226	+	0.223033i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−0.169873	−	0.633975i	−0.0198821	−	0.0742011i	0.955272	−	0.295729i	$-0.0955624\pi$
$73$	−0.169873	−	0.633975i	−0.0198821	−	0.0742011i	−0.975154	+	0.221528i	$0.928896\pi$
$74$	1.90192	−	1.09808i	0.221094	−	0.127649i
$75$		0			0
$76$	−10.0981	+	5.83013i	−1.15833	+	0.668761i
$77$	−0.732051	+	3.80385i	−0.0834249	+	0.433489i
$78$		0			0
$79$			11.4641i			1.28981i	0.764262	+	0.644906i	$0.223104\pi$
$79$			11.4641i			1.28981i	−0.764262	+	0.644906i	$0.776896\pi$
$80$	−4.59808	+	3.03590i	−0.514081	+	0.339424i
$81$		0			0
$82$	1.26795	−	4.73205i	0.140022	−	0.522568i
$83$	−0.366025	−	1.36603i	−0.0401765	−	0.149941i	0.942924	−	0.333009i	$-0.108064\pi$
$83$	−0.366025	−	1.36603i	−0.0401765	−	0.149941i	−0.983100	+	0.183068i	$0.941397\pi$
$84$		0			0
$85$	−4.19615	+	4.73205i	−0.455137	+	0.513263i
$86$	1.50000	−	2.59808i	0.161749	−	0.280158i
$87$		0			0
$88$	0.732051	−	2.73205i	0.0780369	−	0.291238i
$89$	0.598076	+	1.03590i	0.0633960	+	0.109805i	0.895981	−	0.444092i	$-0.146474\pi$
$89$	0.598076	+	1.03590i	0.0633960	+	0.109805i	−0.832585	+	0.553897i	$0.813140\pi$
$90$		0			0
$91$	1.53590	+	2.26795i	0.161006	+	0.237746i
$92$	1.03590	+	3.86603i	0.108000	+	0.403061i
$93$		0			0
$94$	−4.60770			−0.475247
$95$	13.4641	+	6.73205i	1.38139	+	0.690694i
$96$		0			0
$97$	−3.09808	+	0.830127i	−0.314562	+	0.0842866i	−0.412646	−	0.910892i	$-0.635395\pi$
$97$	−3.09808	+	0.830127i	−0.314562	+	0.0842866i	0.0980839	+	0.995178i	$0.468729\pi$
$98$	−2.90192	−	2.16987i	−0.293139	−	0.219190i
$99$		0			0
$100$	7.96410	+	3.40192i	0.796410	+	0.340192i
$101$	−11.7679	+	6.79423i	−1.17095	+	0.676051i	−0.953905	−	0.300109i	$-0.902977\pi$
$101$	−11.7679	+	6.79423i	−1.17095	+	0.676051i	−0.217050	+	0.976160i	$0.569643\pi$
$102$		0			0
$103$	−2.96410	−	11.0622i	−0.292062	−	1.08999i	−0.943523	−	0.331307i	$-0.892510\pi$
$103$	−2.96410	−	11.0622i	−0.292062	−	1.08999i	0.651461	−	0.758682i	$-0.274156\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	−0.901924	+	1.56218i	−0.0876026	+	0.151732i
$107$	2.36603	+	0.633975i	0.228732	+	0.0612886i	0.371365	−	0.928487i	$-0.378890\pi$
$107$	2.36603	+	0.633975i	0.228732	+	0.0612886i	−0.142632	+	0.989776i	$0.545557\pi$
$108$		0			0
$109$	1.73205	+	1.00000i	0.165900	+	0.0957826i	0.580651	−	0.814152i	$-0.302798\pi$
$109$	1.73205	+	1.00000i	0.165900	+	0.0957826i	−0.414751	+	0.909935i	$0.636131\pi$
$110$	−1.60770	+	0.535898i	−0.153288	+	0.0510959i
$111$		0			0
$112$	−4.92820	−	4.26795i	−0.465671	−	0.403283i
$113$	1.90192	−	7.09808i	0.178918	−	0.667731i	−0.816933	−	0.576732i	$-0.804328\pi$
$113$	1.90192	−	7.09808i	0.178918	−	0.667731i	0.995851	−	0.0909984i	$-0.0290058\pi$
$114$		0			0
$115$	3.42820	−	3.86603i	0.319682	−	0.360509i
$116$	−6.00000	+	10.3923i	−0.557086	+	0.964901i
$117$		0			0
$118$	1.26795	−	1.26795i	0.116724	−	0.116724i
$119$	−6.73205	−	3.26795i	−0.617126	−	0.299572i
$120$		0			0
$121$	4.42820	−	7.66987i	0.402564	−	0.697261i
$122$	−3.43782	−	3.43782i	−0.311246	−	0.311246i
$123$		0			0
$124$	17.6603			1.58594
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	6.75833	−	6.75833i	0.599705	−	0.599705i	−0.340529	−	0.940234i	$-0.610606\pi$
$127$	6.75833	−	6.75833i	0.599705	−	0.599705i	0.940234	+	0.340529i	$0.110606\pi$
$128$	8.09808	+	8.09808i	0.715776	+	0.715776i
$129$		0			0
$130$	−0.535898	+	1.07180i	−0.0470014	+	0.0940028i
$131$	−16.3923	−	9.46410i	−1.43220	−	0.826882i	−0.434914	−	0.900472i	$-0.643221\pi$
$131$	−16.3923	−	9.46410i	−1.43220	−	0.826882i	−0.997289	+	0.0735897i	$0.976554\pi$
$132$		0			0
$133$	−3.36603	+	17.4904i	−0.291871	+	1.51661i
$134$			4.46410i			0.385640i
$135$		0			0
$136$	4.73205	+	2.73205i	0.405770	+	0.234271i
$137$	−7.46410	−	2.00000i	−0.637701	−	0.170872i	−0.0745393	−	0.997218i	$-0.523749\pi$
$137$	−7.46410	−	2.00000i	−0.637701	−	0.170872i	−0.563162	+	0.826347i	$0.690415\pi$
$138$		0			0
$139$	3.46410	+	6.00000i	0.293821	+	0.508913i	0.974710	−	0.223474i	$-0.0717396\pi$
$139$	3.46410	+	6.00000i	0.293821	+	0.508913i	−0.680889	+	0.732387i	$0.738406\pi$
$140$	−1.33013	+	10.1603i	−0.112416	+	0.858698i
$141$		0			0
$142$	−2.19615	+	2.19615i	−0.184297	+	0.184297i
$143$	0.392305	+	1.46410i	0.0328062	+	0.122434i
$144$		0			0
$145$	15.4641	−	0.928203i	1.28422	−	0.0770831i
$146$	0.294229	+	0.169873i	0.0243505	+	0.0140588i
$147$		0			0
$148$	1.90192	−	7.09808i	0.156337	−	0.583458i
$149$	17.8923	+	10.3301i	1.46579	+	0.846277i	0.999269	−	0.0382306i	$-0.0121722\pi$
$149$	17.8923	+	10.3301i	1.46579	+	0.846277i	0.466526	+	0.884508i	$0.345505\pi$
$150$		0			0
$151$	−0.633975	−	1.09808i	−0.0515921	−	0.0893602i	0.839076	−	0.544014i	$-0.183096\pi$
$151$	−0.633975	−	1.09808i	−0.0515921	−	0.0893602i	−0.890668	+	0.454654i	$0.849763\pi$
$152$	3.36603	−	12.5622i	0.273021	−	1.01893i
$153$		0			0
$154$	−1.12436	−	1.66025i	−0.0906032	−	0.133787i
$155$	−12.5622	−	19.0263i	−1.00902	−	1.52823i
$156$		0			0
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	0.666076	−	0.745884i	$-0.267973\pi$
$157$	−1.00000	−	1.00000i	−0.0798087	−	0.0798087i	−0.745884	+	0.666076i	$0.767973\pi$
$158$	−4.19615	−	4.19615i	−0.333828	−	0.333828i
$159$		0			0
$160$	2.30385	−	11.2583i	0.182135	−	0.890049i
$161$	5.50000	+	2.66987i	0.433461	+	0.210415i
$162$		0			0
$163$	−0.169873	+	0.633975i	−0.0133055	+	0.0496567i	−0.972259	−	0.233905i	$-0.924849\pi$
$163$	−0.169873	+	0.633975i	−0.0133055	+	0.0496567i	0.958954	+	0.283562i	$0.0915161\pi$
$164$	−8.19615	−	14.1962i	−0.640012	−	1.10853i
$165$		0			0
$166$	0.633975	+	0.366025i	0.0492060	+	0.0284091i
$167$	5.52628	−	20.6244i	0.427636	−	1.59596i	−0.330461	−	0.943820i	$-0.607204\pi$
$167$	5.52628	−	20.6244i	0.427636	−	1.59596i	0.758098	−	0.652141i	$-0.226129\pi$
$168$		0			0
$169$	−10.3301	−	5.96410i	−0.794625	−	0.458777i
$170$	−0.196152	−	3.26795i	−0.0150442	−	0.250640i
$171$		0			0
$172$	−2.59808	−	9.69615i	−0.198101	−	0.739325i
$173$	10.0000	−	10.0000i	0.760286	−	0.760286i	−0.216088	−	0.976374i	$-0.569330\pi$
$173$	10.0000	−	10.0000i	0.760286	−	0.760286i	0.976374	+	0.216088i	$0.0693298\pi$
$174$		0			0
$175$	11.8923	−	5.79423i	0.898974	−	0.438003i
$176$	−1.80385	−	3.12436i	−0.135970	−	0.235507i
$177$		0			0
$178$	−0.598076	−	0.160254i	−0.0448277	−	0.0120115i
$179$	−16.0981	−	9.29423i	−1.20323	−	0.694683i	−0.241955	−	0.970287i	$-0.577789\pi$
$179$	−16.0981	−	9.29423i	−1.20323	−	0.694683i	−0.961271	+	0.275604i	$0.911122\pi$
$180$		0			0
$181$			4.53590i			0.337151i	0.985689	+	0.168575i	$0.0539166\pi$
$181$			4.53590i			0.337151i	−0.985689	+	0.168575i	$0.946083\pi$
$182$	−1.39230	−	0.267949i	−0.103205	−	0.0198617i
$183$		0			0
$184$	−3.86603	−	2.23205i	−0.285007	−	0.164549i
$185$	−9.00000	+	3.00000i	−0.661693	+	0.220564i
$186$		0			0
$187$	−2.92820	−	2.92820i	−0.214131	−	0.214131i
$188$	−10.9019	+	10.9019i	−0.795105	+	0.795105i
$189$		0			0
$190$	−7.39230	+	2.46410i	−0.536294	+	0.178765i
$191$	0.339746			0.0245832			0.0122916	−	0.999924i	$-0.496087\pi$
$191$	0.339746			0.0245832			0.0122916	+	0.999924i	$0.496087\pi$
$192$		0			0
$193$	−7.53590	−	7.53590i	−0.542446	−	0.542446i	0.381799	−	0.924245i	$-0.375305\pi$
$193$	−7.53590	−	7.53590i	−0.542446	−	0.542446i	−0.924245	+	0.381799i	$0.875305\pi$
$194$	0.830127	−	1.43782i	0.0595996	−	0.103230i
$195$		0			0
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	10.5359	−	10.5359i	0.750652	−	0.750652i	−0.223949	−	0.974601i	$-0.571895\pi$
$197$	10.5359	−	10.5359i	0.750652	−	0.750652i	0.974601	+	0.223949i	$0.0718950\pi$
$198$		0			0
$199$	9.92820	−	17.1962i	0.703792	−	1.21900i	−0.263334	−	0.964705i	$-0.584822\pi$
$199$	9.92820	−	17.1962i	0.703792	−	1.21900i	0.967126	−	0.254298i	$-0.0818445\pi$
$200$	−8.96410	+	3.59808i	−0.633858	+	0.254422i
$201$		0			0
$202$	1.82051	−	6.79423i	0.128091	−	0.478040i
$203$	6.00000	+	17.3205i	0.421117	+	1.21566i
$204$		0			0
$205$	−9.46410	+	18.9282i	−0.661002	+	1.32200i
$206$	5.13397	+	2.96410i	0.357701	+	0.206519i
$207$		0			0
$208$	−2.46410	−	0.660254i	−0.170855	−	0.0457804i
$209$	−4.92820	+	8.53590i	−0.340891	+	0.590440i
$210$		0			0
$211$	2.46410	+	4.26795i	0.169636	+	0.293818i	0.938292	−	0.345845i	$-0.112408\pi$
$211$	2.46410	+	4.26795i	0.169636	+	0.293818i	−0.768656	+	0.639662i	$0.779074\pi$
$212$	1.56218	+	5.83013i	0.107291	+	0.400415i
$213$		0			0
$214$	−1.09808	+	0.633975i	−0.0750629	+	0.0433376i
$215$	−8.59808	+	9.69615i	−0.586384	+	0.661272i
$216$		0			0
$217$	17.6603	−	20.3923i	1.19886	−	1.38432i
$218$	−1.00000	+	0.267949i	−0.0677285	+	0.0181478i
$219$		0			0
$220$	−2.53590	+	5.07180i	−0.170970	+	0.341940i
$221$	−2.92820			−0.196972
$222$		0			0
$223$	−1.96410	−	7.33013i	−0.131526	−	0.490862i	0.868462	−	0.495756i	$-0.165109\pi$
$223$	−1.96410	−	7.33013i	−0.131526	−	0.490862i	−0.999988	+	0.00489404i	$0.998442\pi$
$224$	13.5622	−	0.973721i	0.906161	−	0.0650594i
$225$		0			0
$226$	1.90192	+	3.29423i	0.126514	+	0.219129i
$227$	2.43782	−	9.09808i	0.161804	−	0.603861i	−0.836622	−	0.547780i	$-0.815473\pi$
$227$	2.43782	−	9.09808i	0.161804	−	0.603861i	0.998426	−	0.0560804i	$-0.0178603\pi$
$228$		0			0
$229$	6.33013	−	10.9641i	0.418307	−	0.724528i	−0.577463	−	0.816417i	$-0.695957\pi$
$229$	6.33013	−	10.9641i	0.418307	−	0.724528i	0.995769	+	0.0918888i	$0.0292904\pi$
$230$	0.160254	+	2.66987i	0.0105668	+	0.176046i
$231$		0			0
$232$	−3.46410	−	12.9282i	−0.227429	−	0.848778i
$233$	3.16987	−	11.8301i	0.207665	−	0.775017i	−0.780955	−	0.624587i	$-0.785267\pi$
$233$	3.16987	−	11.8301i	0.207665	−	0.775017i	0.988621	−	0.150430i	$-0.0480660\pi$
$234$		0			0
$235$	19.5000	+	3.99038i	1.27204	+	0.260304i
$236$		−	6.00000i		−	0.390567i
$237$		0			0
$238$	3.66025	−	1.26795i	0.237259	−	0.0821889i
$239$	−19.0526	+	11.0000i	−1.23241	+	0.711531i	−0.967531	−	0.252752i	$-0.918664\pi$
$239$	−19.0526	+	11.0000i	−1.23241	+	0.711531i	−0.264876	+	0.964282i	$0.585331\pi$
$240$		0			0
$241$	−14.2583	+	8.23205i	−0.918460	+	0.530273i	−0.883143	−	0.469103i	$-0.844577\pi$
$241$	−14.2583	+	8.23205i	−0.918460	+	0.530273i	−0.0353164	+	0.999376i	$0.511244\pi$
$242$	1.18653	+	4.42820i	0.0762733	+	0.284656i
$243$		0			0
$244$	−16.2679			−1.04145
$245$	10.4019	+	11.6962i	0.664555	+	0.747240i
$246$		0			0
$247$	1.80385	+	6.73205i	0.114776	+	0.428350i
$248$	−13.9282	+	13.9282i	−0.884442	+	0.884442i
$249$		0			0
$250$	4.75833	+	3.29423i	0.300943	+	0.208345i
$251$		−	21.8564i		−	1.37956i	−0.724017	−	0.689782i	$-0.757706\pi$
$251$		−	21.8564i		−	1.37956i	0.724017	−	0.689782i	$-0.242294\pi$
$252$		0			0
$253$	2.39230	+	2.39230i	0.150403	+	0.150403i
$254$			4.94744i			0.310430i
$255$		0			0
$256$	−1.39230			−0.0870191
$257$	26.2224	−	7.02628i	1.63571	−	0.438287i	0.680148	−	0.733075i	$-0.261916\pi$
$257$	26.2224	−	7.02628i	1.63571	−	0.438287i	0.955563	+	0.294788i	$0.0952490\pi$
$258$		0			0
$259$	−6.29423	−	9.29423i	−0.391104	−	0.577515i
$260$	1.26795	+	3.80385i	0.0786349	+	0.235905i
$261$		0			0
$262$	9.46410	−	2.53590i	0.584694	−	0.156668i
$263$	5.45448	−	20.3564i	0.336338	−	1.25523i	−0.566074	−	0.824355i	$-0.691538\pi$
$263$	5.45448	−	20.3564i	0.336338	−	1.25523i	0.902412	−	0.430875i	$-0.141795\pi$
$264$		0			0
$265$	5.16987	−	5.83013i	0.317583	−	0.358142i
$266$	−5.16987	−	7.63397i	−0.316985	−	0.468069i
$267$		0			0
$268$	10.5622	+	10.5622i	0.645188	+	0.645188i
$269$	1.96410	−	3.40192i	0.119753	−	0.207419i	−0.799917	−	0.600111i	$-0.795123\pi$
$269$	1.96410	−	3.40192i	0.119753	−	0.207419i	0.919670	+	0.392692i	$0.128456\pi$
$270$		0			0
$271$	3.92820	−	2.26795i	0.238621	−	0.137768i	−0.375922	−	0.926651i	$-0.622674\pi$
$271$	3.92820	−	2.26795i	0.238621	−	0.137768i	0.614543	+	0.788883i	$0.289340\pi$
$272$	6.73205	−	1.80385i	0.408191	−	0.109374i
$273$		0			0
$274$	3.46410	−	2.00000i	0.209274	−	0.120824i
$275$	7.26795	−	0.875644i	0.438274	−	0.0528033i
$276$		0			0
$277$	5.19615	+	1.39230i	0.312207	+	0.0836555i	0.411520	−	0.911401i	$-0.364998\pi$
$277$	5.19615	+	1.39230i	0.312207	+	0.0836555i	−0.0993135	+	0.995056i	$0.531665\pi$
$278$	−3.46410	−	0.928203i	−0.207763	−	0.0556699i
$279$		0			0
$280$	−6.96410	−	9.06218i	−0.416185	−	0.541569i
$281$	−5.13397	+	8.89230i	−0.306267	+	0.530470i	−0.977543	−	0.210738i	$-0.932413\pi$
$281$	−5.13397	+	8.89230i	−0.306267	+	0.530470i	0.671275	+	0.741208i	$0.265747\pi$
$282$		0			0
$283$	−6.75833	+	6.75833i	−0.401741	+	0.401741i	−0.878846	−	0.477105i	$-0.841686\pi$
$283$	−6.75833	+	6.75833i	−0.401741	+	0.401741i	0.477105	+	0.878846i	$0.341686\pi$
$284$			10.3923i			0.616670i
$285$		0			0
$286$	−0.679492	−	0.392305i	−0.0401792	−	0.0231975i
$287$	−24.5885	−	4.73205i	−1.45141	−	0.279324i
$288$		0			0
$289$	−7.79423	+	4.50000i	−0.458484	+	0.264706i
$290$	−5.32051	+	6.00000i	−0.312431	+	0.352332i
$291$		0			0
$292$	1.09808	−	0.294229i	0.0642600	−	0.0172184i
$293$	−17.5622	−	4.70577i	−1.02599	−	0.274914i	−0.293696	−	0.955899i	$-0.594885\pi$
$293$	−17.5622	−	4.70577i	−1.02599	−	0.274914i	−0.732298	+	0.680985i	$0.761552\pi$
$294$		0			0
$295$	−6.46410	+	4.26795i	−0.376355	+	0.248490i
$296$	4.09808	+	7.09808i	0.238196	+	0.412567i
$297$		0			0
$298$	−10.3301	+	2.76795i	−0.598408	+	0.160343i
$299$	2.39230			0.138351
$300$		0			0
$301$	−13.7942	−	6.69615i	−0.795086	−	0.385960i
$302$	0.633975	+	0.169873i	0.0364811	+	0.00977509i
$303$		0			0
$304$	−8.29423	−	14.3660i	−0.475707	−	0.823948i
$305$	11.5718	+	17.5263i	0.662599	+	1.00355i
$306$		0			0
$307$	−24.4641	−	24.4641i	−1.39624	−	1.39624i	−0.810496	−	0.585744i	$-0.800803\pi$
$307$	−24.4641	−	24.4641i	−1.39624	−	1.39624i	−0.585744	−	0.810496i	$-0.699197\pi$
$308$	−6.58846	−	1.26795i	−0.375412	−	0.0722481i
$309$		0			0
$310$	11.5622	+	2.36603i	0.656688	+	0.134381i
$311$		−	16.0000i		−	0.907277i	−0.891186	−	0.453638i	$-0.850126\pi$
$311$		−	16.0000i		−	0.907277i	0.891186	−	0.453638i	$-0.149874\pi$
$312$		0			0
$313$	−5.19615	+	5.19615i	−0.293704	+	0.293704i	−0.838542	−	0.544838i	$-0.816591\pi$
$313$	−5.19615	+	5.19615i	−0.293704	+	0.293704i	0.544838	+	0.838542i	$0.316591\pi$
$314$	0.732051			0.0413120
$315$		0			0
$316$	−19.8564			−1.11701
$317$	−1.53590	+	1.53590i	−0.0862646	+	0.0862646i	−0.748922	−	0.662658i	$-0.769428\pi$
$317$	−1.53590	+	1.53590i	−0.0862646	+	0.0862646i	0.662658	+	0.748922i	$0.269428\pi$
$318$		0			0
$319$			10.1436i			0.567932i
$320$	−2.79423	−	4.23205i	−0.156202	−	0.236579i
$321$		0			0
$322$	−2.99038	+	1.03590i	−0.166647	+	0.0577284i
$323$	−13.4641	−	13.4641i	−0.749163	−	0.749163i
$324$		0			0
$325$	3.19615	−	4.07180i	0.177291	−	0.225863i
$326$	−0.169873	−	0.294229i	−0.00940839	−	0.0162958i
$327$		0			0
$328$	17.6603	+	4.73205i	0.975124	+	0.261284i
$329$	1.68653	+	23.4904i	0.0929816	+	1.29507i
$330$		0			0
$331$	35.6603			1.96006			0.980032	−	0.198838i	$-0.0637167\pi$
$331$	35.6603			1.96006			0.980032	+	0.198838i	$0.0637167\pi$
$332$	2.36603	−	0.633975i	0.129853	−	0.0347939i
$333$		0			0
$334$	5.52628	+	9.57180i	0.302385	+	0.523745i
$335$	3.86603	−	18.8923i	0.211224	−	1.03220i
$336$		0			0
$337$	9.19615	+	2.46410i	0.500946	+	0.134228i	0.500439	−	0.865772i	$-0.333172\pi$
$337$	9.19615	+	2.46410i	0.500946	+	0.134228i	0.000507178		1.00000i	$0.499839\pi$
$338$	5.96410	−	1.59808i	0.324404	−	0.0869239i
$339$		0			0
$340$	−8.19615	−	7.26795i	−0.444499	−	0.394160i
$341$	12.9282	−	7.46410i	0.700101	−	0.404204i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	9.69615	+	5.59808i	0.522782	+	0.301828i
$345$		0			0
$346$			7.32051i			0.393553i
$347$	6.16987	−	6.16987i	0.331216	−	0.331216i	−0.521832	−	0.853048i	$-0.674751\pi$
$347$	6.16987	−	6.16987i	0.331216	−	0.331216i	0.853048	+	0.521832i	$0.174751\pi$
$348$		0			0
$349$	4.93782	−	8.55256i	0.264316	−	0.457808i	−0.703069	−	0.711122i	$-0.748187\pi$
$349$	4.93782	−	8.55256i	0.264316	−	0.457808i	0.967384	+	0.253314i	$0.0815206\pi$
$350$	−2.23205	+	6.47372i	−0.119308	+	0.346035i
$351$		0			0
$352$	7.26795	+	1.94744i	0.387383	+	0.103799i
$353$	27.1244	+	7.26795i	1.44368	+	0.386834i	0.893822	−	0.448422i	$-0.148014\pi$
$353$	27.1244	+	7.26795i	1.44368	+	0.386834i	0.549862	+	0.835256i	$0.314680\pi$
$354$		0			0
$355$	11.1962	−	7.39230i	0.594230	−	0.392343i
$356$	−1.79423	+	1.03590i	−0.0950939	+	0.0549025i
$357$		0			0
$358$	9.29423	−	2.49038i	0.491215	−	0.131621i
$359$	14.9545	−	8.63397i	0.789267	−	0.455684i	−0.0504372	−	0.998727i	$-0.516061\pi$
$359$	14.9545	−	8.63397i	0.789267	−	0.455684i	0.839705	+	0.543043i	$0.182728\pi$
$360$		0			0
$361$	−13.1603	+	22.7942i	−0.692645	+	1.19970i
$362$	−1.66025	−	1.66025i	−0.0872610	−	0.0872610i
$363$		0			0
$364$	−3.92820	+	2.66025i	−0.205894	+	0.139435i
$365$	−1.09808	−	0.973721i	−0.0574759	−	0.0509669i
$366$		0			0
$367$	−1.40192	+	5.23205i	−0.0731798	+	0.273111i	−0.992814	−	0.119664i	$-0.961818\pi$
$367$	−1.40192	+	5.23205i	−0.0731798	+	0.273111i	0.919635	+	0.392775i	$0.128485\pi$
$368$	−5.50000	+	1.47372i	−0.286707	+	0.0768230i
$369$		0			0
$370$	2.19615	−	4.39230i	0.114173	−	0.228345i
$371$	8.29423	+	4.02628i	0.430615	+	0.209034i
$372$		0			0
$373$	−4.09808	+	1.09808i	−0.212190	+	0.0568562i	−0.363348	−	0.931653i	$-0.618366\pi$
$373$	−4.09808	+	1.09808i	−0.212190	+	0.0568562i	0.151158	+	0.988510i	$0.451700\pi$
$374$	2.14359			0.110843
$375$		0			0
$376$		−	17.1962i		−	0.886824i
$377$	5.07180	+	5.07180i	0.261211	+	0.261211i
$378$		0			0
$379$			19.4641i			0.999804i	0.866082	+	0.499902i	$0.166631\pi$
$379$			19.4641i			0.999804i	−0.866082	+	0.499902i	$0.833369\pi$
$380$	−11.6603	+	23.3205i	−0.598158	+	1.19632i
$381$		0			0
$382$	−0.124356	+	0.124356i	−0.00636259	+	0.00636259i
$383$	−0.205771	−	0.767949i	−0.0105144	−	0.0392404i	0.960469	−	0.278386i	$-0.0897994\pi$
$383$	−0.205771	−	0.767949i	−0.0105144	−	0.0392404i	−0.970984	+	0.239145i	$0.923133\pi$
$384$		0			0
$385$	3.32051	+	8.00000i	0.169229	+	0.407718i
$386$	5.51666			0.280791
$387$		0			0
$388$	−1.43782	−	5.36603i	−0.0729944	−	0.272419i
$389$	7.96410	−	4.59808i	0.403796	−	0.233132i	−0.284325	−	0.958728i	$-0.591769\pi$
$389$	7.96410	−	4.59808i	0.403796	−	0.233132i	0.688121	+	0.725596i	$0.258436\pi$
$390$		0			0
$391$	−5.66025	+	3.26795i	−0.286251	+	0.165267i
$392$	8.09808	−	10.8301i	0.409015	−	0.547004i
$393$		0			0
$394$			7.71281i			0.388566i
$395$	14.1244	+	21.3923i	0.710673	+	1.07636i
$396$		0			0
$397$	−8.78461	+	32.7846i	−0.440887	+	1.64541i	0.285686	+	0.958323i	$0.407779\pi$
$397$	−8.78461	+	32.7846i	−0.440887	+	1.64541i	−0.726573	+	0.687089i	$0.758888\pi$
$398$	2.66025	+	9.92820i	0.133346	+	0.497656i
$399$		0			0
$400$	−4.83975	+	11.3301i	−0.241987	+	0.566506i
$401$	1.30385	−	2.25833i	0.0651110	−	0.112776i	−0.831632	−	0.555327i	$-0.812593\pi$
$401$	1.30385	−	2.25833i	0.0651110	−	0.112776i	0.896743	+	0.442551i	$0.145927\pi$
$402$		0			0
$403$	2.73205	−	10.1962i	0.136093	−	0.507907i
$404$	−11.7679	−	20.3827i	−0.585477	−	1.01408i
$405$		0			0
$406$	−8.53590	−	4.14359i	−0.423630	−	0.205643i
$407$	−1.60770	−	6.00000i	−0.0796905	−	0.297409i
$408$		0			0
$409$	−15.3923			−0.761100			−0.380550	−	0.924760i	$-0.624265\pi$
$409$	−15.3923			−0.761100			−0.380550	+	0.924760i	$0.624265\pi$
$410$	−3.46410	−	10.3923i	−0.171080	−	0.513239i
$411$		0			0
$412$	19.1603	−	5.13397i	0.943958	−	0.252933i
$413$	−6.92820	−	6.00000i	−0.340915	−	0.295241i
$414$		0			0
$415$	−2.36603	−	2.09808i	−0.116144	−	0.102991i
$416$	4.60770	−	2.66025i	0.225911	−	0.130430i
$417$		0			0
$418$	−1.32051	−	4.92820i	−0.0645882	−	0.241046i
$419$	4.00000	+	6.92820i	0.195413	+	0.338465i	0.947036	−	0.321128i	$-0.104062\pi$
$419$	4.00000	+	6.92820i	0.195413	+	0.338465i	−0.751623	+	0.659593i	$0.770729\pi$
$420$		0			0
$421$	7.52628	−	13.0359i	0.366808	−	0.635331i	−0.622256	−	0.782814i	$-0.713784\pi$
$421$	7.52628	−	13.0359i	0.366808	−	0.635331i	0.989065	+	0.147483i	$0.0471171\pi$
$422$	−2.46410	−	0.660254i	−0.119951	−	0.0321407i
$423$		0			0
$424$	−5.83013	−	3.36603i	−0.283136	−	0.163469i
$425$	−2.00000	+	14.0000i	−0.0970143	+	0.679100i
$426$		0			0
$427$	−16.2679	+	18.7846i	−0.787261	+	0.909051i
$428$	−1.09808	+	4.09808i	−0.0530775	+	0.198088i
$429$		0			0
$430$	−0.401924	−	6.69615i	−0.0193825	−	0.322917i
$431$	−6.90192	+	11.9545i	−0.332454	+	0.575827i	−0.982992	−	0.183646i	$-0.941210\pi$
$431$	−6.90192	+	11.9545i	−0.332454	+	0.575827i	0.650538	+	0.759473i	$0.274543\pi$
$432$		0			0
$433$	20.1962	−	20.1962i	0.970565	−	0.970565i	−0.0290139	−	0.999579i	$-0.509237\pi$
$433$	20.1962	−	20.1962i	0.970565	−	0.970565i	0.999579	+	0.0290139i	$0.00923670\pi$
$434$	1.00000	+	13.9282i	0.0480015	+	0.668575i
$435$		0			0
$436$	−1.73205	+	3.00000i	−0.0829502	+	0.143674i
$437$	11.0000	+	11.0000i	0.526201	+	0.526201i
$438$		0			0
$439$	21.8564			1.04315			0.521575	−	0.853206i	$-0.325345\pi$
$439$	21.8564			1.04315			0.521575	+	0.853206i	$0.325345\pi$
$440$	−2.00000	−	6.00000i	−0.0953463	−	0.286039i
$441$		0			0
$442$	1.07180	−	1.07180i	0.0509802	−	0.0509802i
$443$	−16.6603	−	16.6603i	−0.791553	−	0.791553i	0.190194	−	0.981747i	$-0.439088\pi$
$443$	−16.6603	−	16.6603i	−0.791553	−	0.791553i	−0.981747	+	0.190194i	$0.939088\pi$
$444$		0			0
$445$	2.39230	+	1.19615i	0.113406	+	0.0567031i
$446$	3.40192	+	1.96410i	0.161086	+	0.0930029i
$447$		0			0
$448$	3.92820	−	4.53590i	0.185590	−	0.214301i
$449$			29.5885i			1.39637i	0.715920	+	0.698183i	$0.246008\pi$
$449$			29.5885i			1.39637i	−0.715920	+	0.698183i	$0.753992\pi$
$450$		0			0
$451$	−12.0000	−	6.92820i	−0.565058	−	0.326236i
$452$	12.2942	+	3.29423i	0.578272	+	0.154947i
$453$		0			0
$454$	2.43782	+	4.22243i	0.114413	+	0.198169i
$455$	5.66025	+	2.33975i	0.265357	+	0.109689i
$456$		0			0
$457$	−24.6603	+	24.6603i	−1.15356	+	1.15356i	−0.167724	+	0.985834i	$0.553642\pi$
$457$	−24.6603	+	24.6603i	−1.15356	+	1.15356i	−0.985834	+	0.167724i	$0.946358\pi$
$458$	1.69615	+	6.33013i	0.0792560	+	0.295787i
$459$		0			0
$460$	6.69615	+	5.93782i	0.312210	+	0.276852i
$461$	−7.96410	−	4.59808i	−0.370925	−	0.214154i	0.302937	−	0.953010i	$-0.402033\pi$
$461$	−7.96410	−	4.59808i	−0.370925	−	0.214154i	−0.673863	+	0.738857i	$0.735366\pi$
$462$		0			0
$463$	−1.18653	+	4.42820i	−0.0551429	+	0.205796i	−0.988001	−	0.154448i	$-0.950640\pi$
$463$	−1.18653	+	4.42820i	−0.0551429	+	0.205796i	0.932858	+	0.360244i	$0.117307\pi$
$464$	−14.7846	−	8.53590i	−0.686358	−	0.396269i
$465$		0			0
$466$	3.16987	+	5.49038i	0.146842	+	0.254337i
$467$	−6.03590	+	22.5263i	−0.279308	+	1.04239i	0.673591	+	0.739104i	$0.264751\pi$
$467$	−6.03590	+	22.5263i	−0.279308	+	1.04239i	−0.952899	+	0.303288i	$0.901916\pi$
$468$		0			0
$469$	22.7583	−	1.63397i	1.05088	−	0.0754499i
$470$	−8.59808	+	5.67691i	−0.396600	+	0.261857i
$471$		0			0
$472$	4.73205	+	4.73205i	0.217810	+	0.217810i
$473$	−6.00000	−	6.00000i	−0.275880	−	0.275880i
$474$		0			0
$475$	33.4186	−	4.02628i	1.53335	−	0.184738i
$476$	5.66025	−	11.6603i	0.259437	−	0.534447i
$477$		0			0
$478$	2.94744	−	11.0000i	0.134813	−	0.503128i
$479$	−4.36603	−	7.56218i	−0.199489	−	0.345525i	0.748874	−	0.662712i	$-0.230595\pi$
$479$	−4.36603	−	7.56218i	−0.199489	−	0.345525i	−0.948363	+	0.317188i	$0.897261\pi$
$480$		0			0
$481$	−3.80385	−	2.19615i	−0.173441	−	0.100136i
$482$	2.20577	−	8.23205i	0.100470	−	0.374960i
$483$		0			0
$484$	13.2846	+	7.66987i	0.603846	+	0.348631i
$485$	−4.75833	+	5.36603i	−0.216065	+	0.243659i
$486$		0			0
$487$	7.41858	+	27.6865i	0.336168	+	1.25460i	0.902597	+	0.430486i	$0.141658\pi$
$487$	7.41858	+	27.6865i	0.336168	+	1.25460i	−0.566429	+	0.824110i	$0.691675\pi$
$488$	12.8301	−	12.8301i	0.580793	−	0.580793i
$489$		0			0
$490$	−8.08846	−	0.473721i	−0.365399	−	0.0214005i
$491$	−1.53590	−	2.66025i	−0.0693141	−	0.120056i	0.829285	−	0.558825i	$-0.188748\pi$
$491$	−1.53590	−	2.66025i	−0.0693141	−	0.120056i	−0.898600	+	0.438770i	$0.855414\pi$
$492$		0			0
$493$	−18.9282	−	5.07180i	−0.852483	−	0.228422i
$494$	−3.12436	−	1.80385i	−0.140571	−	0.0811589i
$495$		0			0
$496$			25.1244i			1.12812i
$497$	12.0000	+	10.3923i	0.538274	+	0.466159i
$498$		0			0
$499$	−18.1244	−	10.4641i	−0.811358	−	0.468438i	0.0360695	−	0.999349i	$-0.488516\pi$
$499$	−18.1244	−	10.4641i	−0.811358	−	0.468438i	−0.847427	+	0.530912i	$0.821850\pi$
$500$	19.0526	−	3.46410i	0.852056	−	0.154919i
$501$		0			0
$502$	8.00000	+	8.00000i	0.357057	+	0.357057i
$503$	−23.9282	+	23.9282i	−1.06691	+	1.06691i	−0.0693107	+	0.997595i	$0.522080\pi$
$503$	−23.9282	+	23.9282i	−1.06691	+	1.06691i	−0.997595	+	0.0693107i	$0.977920\pi$
$504$		0			0
$505$	−13.5885	+	27.1769i	−0.604678	+	1.20936i
$506$	−1.75129			−0.0778543
$507$		0			0
$508$	11.7058	+	11.7058i	0.519360	+	0.519360i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	0.758330	−	1.56218i	0.0335466	−	0.0691067i
$512$	−15.6865	+	15.6865i	−0.693253	+	0.693253i
$513$		0			0
$514$	−7.02628	+	12.1699i	−0.309916	+	0.536790i
$515$	−19.1603	−	16.9904i	−0.844302	−	0.748686i
$516$		0			0
$517$	−3.37307	+	12.5885i	−0.148347	+	0.553640i
$518$	5.70577	+	1.09808i	0.250697	+	0.0482467i
$519$		0			0
$520$	−4.00000	−	2.00000i	−0.175412	−	0.0877058i
$521$	−13.3756	−	7.72243i	−0.585998	−	0.338326i	0.177516	−	0.984118i	$-0.443194\pi$
$521$	−13.3756	−	7.72243i	−0.585998	−	0.338326i	−0.763513	+	0.645792i	$0.776527\pi$
$522$		0			0
$523$	7.33013	+	1.96410i	0.320524	+	0.0858842i	0.415494	−	0.909596i	$-0.363609\pi$
$523$	7.33013	+	1.96410i	0.320524	+	0.0858842i	−0.0949698	+	0.995480i	$0.530275\pi$
$524$	16.3923	−	28.3923i	0.716101	−	1.24032i
$525$		0			0
$526$	5.45448	+	9.44744i	0.237827	+	0.411928i
$527$	7.46410	+	27.8564i	0.325141	+	1.21344i
$528$		0			0
$529$	−15.2942	+	8.83013i	−0.664966	+	0.383919i
$530$	0.241670	+	4.02628i	0.0104975	+	0.174890i
$531$		0			0
$532$	−30.2942	−	5.83013i	−1.31342	−	0.252768i
$533$	−9.46410	+	2.53590i	−0.409936	+	0.109842i
$534$		0			0
$535$	5.19615	−	1.73205i	0.224649	−	0.0748831i
$536$	−16.6603			−0.719613
$537$		0			0
$538$	0.526279	+	1.96410i	0.0226895	+	0.0846784i
$539$	−8.05256	+	6.33975i	−0.346848	+	0.273072i
$540$		0			0
$541$	−1.96410	−	3.40192i	−0.0844433	−	0.146260i	0.820711	−	0.571344i	$-0.193578\pi$
$541$	−1.96410	−	3.40192i	−0.0844433	−	0.146260i	−0.905154	+	0.425084i	$0.860245\pi$
$542$	−0.607695	+	2.26795i	−0.0261027	+	0.0974168i
$543$		0			0
$544$	−7.26795	+	12.5885i	−0.311611	+	0.539726i
$545$	4.46410	−	0.267949i	0.191221	−	0.0114777i
$546$		0			0
$547$	−10.6340	−	39.6865i	−0.454676	−	1.69687i	−0.689039	−	0.724724i	$-0.741967\pi$
$547$	−10.6340	−	39.6865i	−0.454676	−	1.69687i	0.234363	−	0.972149i	$-0.424700\pi$
$548$	3.46410	−	12.9282i	0.147979	−	0.552265i
$549$		0			0
$550$	−2.33975	+	2.98076i	−0.0997671	+	0.127100i
$551$			46.6410i			1.98697i
$552$		0			0
$553$	−19.8564	+	22.9282i	−0.844380	+	0.975006i
$554$	−2.41154	+	1.39230i	−0.102457	+	0.0591534i
$555$		0			0
$556$	−10.3923	+	6.00000i	−0.440732	+	0.254457i
$557$	−0.294229	−	1.09808i	−0.0124669	−	0.0465270i	0.959412	−	0.282007i	$-0.0910003\pi$
$557$	−0.294229	−	1.09808i	−0.0124669	−	0.0465270i	−0.971879	+	0.235480i	$0.924334\pi$
$558$		0			0
$559$	−6.00000			−0.253773
$560$	−14.4545	−	1.89230i	−0.610813	−	0.0799645i
$561$		0			0
$562$	−1.37564	−	5.13397i	−0.0580281	−	0.216564i
$563$	−23.8301	+	23.8301i	−1.00432	+	1.00432i	−0.00432948	+	0.999991i	$0.501378\pi$
$563$	−23.8301	+	23.8301i	−1.00432	+	1.00432i	−0.999991	+	0.00432948i	$0.998622\pi$
$564$		0			0
$565$	−5.19615	−	15.5885i	−0.218604	−	0.655811i
$566$		−	4.94744i		−	0.207956i
$567$		0			0
$568$	−8.19615	−	8.19615i	−0.343903	−	0.343903i
$569$			22.7846i			0.955181i	0.878583	+	0.477590i	$0.158490\pi$
$569$			22.7846i			0.955181i	−0.878583	+	0.477590i	$0.841510\pi$
$570$		0			0
$571$	28.2487			1.18217			0.591086	−	0.806609i	$-0.298699\pi$
$571$	28.2487			1.18217			0.591086	+	0.806609i	$0.298699\pi$
$572$	−2.53590	+	0.679492i	−0.106031	+	0.0284110i
$573$		0			0
$574$	10.7321	−	7.26795i	0.447947	−	0.303358i
$575$	1.63397	−	11.4378i	0.0681415	−	0.476990i
$576$		0			0
$577$	−33.3205	+	8.92820i	−1.38715	+	0.371686i	−0.873713	−	0.486441i	$-0.838295\pi$
$577$	−33.3205	+	8.92820i	−1.38715	+	0.371686i	−0.513437	+	0.858127i	$0.671628\pi$
$578$	1.20577	−	4.50000i	0.0501535	−	0.187175i
$579$		0			0
$580$	1.60770	+	26.7846i	0.0667559	+	1.11217i
$581$	1.63397	−	3.36603i	0.0677887	−	0.139646i
$582$		0			0
$583$	3.60770	+	3.60770i	0.149415	+	0.149415i
$584$	−0.633975	+	1.09808i	−0.0262341	+	0.0454387i
$585$		0			0
$586$	8.15064	−	4.70577i	0.336700	−	0.194394i
$587$	−15.6244	+	4.18653i	−0.644886	+	0.172797i	−0.566416	−	0.824120i	$-0.691670\pi$
$587$	−15.6244	+	4.18653i	−0.644886	+	0.172797i	−0.0784705	+	0.996916i	$0.525004\pi$
$588$		0			0
$589$	59.4449	−	34.3205i	2.44938	−	1.41415i
$590$	0.803848	−	3.92820i	0.0330939	−	0.161722i
$591$		0			0
$592$	10.0981	+	2.70577i	0.415028	+	0.111207i
$593$	−2.73205	−	0.732051i	−0.112192	−	0.0300617i	0.202286	−	0.979326i	$-0.435163\pi$
$593$	−2.73205	−	0.732051i	−0.112192	−	0.0300617i	−0.314478	+	0.949265i	$0.601830\pi$
$594$		0			0
$595$	−16.5885	+	2.19615i	−0.680060	+	0.0900335i
$596$	−17.8923	+	30.9904i	−0.732897	+	1.26942i
$597$		0			0
$598$	−0.875644	+	0.875644i	−0.0358078	+	0.0358078i
$599$		−	20.9808i		−	0.857251i	−0.903482	−	0.428625i	$-0.858998\pi$
$599$		−	20.9808i		−	0.857251i	0.903482	−	0.428625i	$-0.141002\pi$
$600$		0			0
$601$	3.33975	+	1.92820i	0.136231	+	0.0786531i	0.566567	−	0.824016i	$-0.308271\pi$
$601$	3.33975	+	1.92820i	0.136231	+	0.0786531i	−0.430335	+	0.902669i	$0.641605\pi$
$602$	7.50000	−	2.59808i	0.305677	−	0.105890i
$603$		0			0
$604$	1.90192	−	1.09808i	0.0773882	−	0.0446801i
$605$	−1.18653	−	19.7679i	−0.0482394	−	0.803681i
$606$		0			0
$607$	4.09808	−	1.09808i	0.166336	−	0.0445695i	−0.174690	−	0.984623i	$-0.555892\pi$
$607$	4.09808	−	1.09808i	0.166336	−	0.0445695i	0.341026	+	0.940054i	$0.389226\pi$
$608$	33.4186	+	8.95448i	1.35530	+	0.363152i
$609$		0			0
$610$	−10.6506	−	2.17949i	−0.431232	−	0.0882450i
$611$	4.60770	+	7.98076i	0.186407	+	0.322867i
$612$		0			0
$613$	−5.90192	+	1.58142i	−0.238376	+	0.0638728i	−0.376029	−	0.926608i	$-0.622711\pi$
$613$	−5.90192	+	1.58142i	−0.238376	+	0.0638728i	0.137653	+	0.990481i	$0.456044\pi$
$614$	17.9090			0.722747
$615$		0			0
$616$	6.19615	−	4.19615i	0.249650	−	0.169068i
$617$	11.5622	+	3.09808i	0.465476	+	0.124724i	0.483932	−	0.875106i	$-0.339208\pi$
$617$	11.5622	+	3.09808i	0.465476	+	0.124724i	−0.0184559	+	0.999830i	$0.505875\pi$
$618$		0			0
$619$	−13.4904	−	23.3660i	−0.542224	−	0.939160i	−0.998776	−	0.0494630i	$-0.984249\pi$
$619$	−13.4904	−	23.3660i	−0.542224	−	0.939160i	0.456552	−	0.889697i	$-0.349084\pi$
$620$	32.9545	−	21.7583i	1.32348	−	0.873836i
$621$		0			0
$622$	5.85641	+	5.85641i	0.234821	+	0.234821i
$623$	−0.598076	+	3.10770i	−0.0239614	+	0.124507i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$		−	3.80385i		−	0.152032i
$627$		0			0
$628$	1.73205	−	1.73205i	0.0691164	−	0.0691164i
$629$	12.0000			0.478471
$630$		0			0
$631$	2.67949			0.106669			0.0533344	−	0.998577i	$-0.483015\pi$
$631$	2.67949			0.106669			0.0533344	+	0.998577i	$0.483015\pi$
$632$	15.6603	−	15.6603i	0.622931	−	0.622931i
$633$		0			0
$634$		−	1.12436i		−	0.0446539i
$635$	4.28461	−	20.9378i	0.170030	−	0.830892i
$636$		0			0
$637$	−0.856406	+	7.19615i	−0.0339321	+	0.285122i
$638$	−3.71281	−	3.71281i	−0.146992	−	0.146992i
$639$		0			0
$640$	25.0885	+	5.13397i	0.991708	+	0.202938i
$641$	13.7224	+	23.7679i	0.542003	+	0.938778i	0.998789	+	0.0492007i	$0.0156674\pi$
$641$	13.7224	+	23.7679i	0.542003	+	0.938778i	−0.456785	+	0.889577i	$0.650999\pi$
$642$		0			0
$643$	−36.1865	−	9.69615i	−1.42706	−	0.382379i	−0.539076	−	0.842257i	$-0.681226\pi$
$643$	−36.1865	−	9.69615i	−1.42706	−	0.382379i	−0.887982	+	0.459878i	$0.847893\pi$
$644$	−4.62436	+	9.52628i	−0.182225	+	0.375388i
$645$		0			0
$646$	9.85641			0.387795
$647$	−37.9545	+	10.1699i	−1.49214	+	0.399819i	−0.910461	−	0.413596i	$-0.864273\pi$
$647$	−37.9545	+	10.1699i	−1.49214	+	0.399819i	−0.581684	+	0.813415i	$0.697606\pi$
$648$		0			0
$649$	−2.53590	−	4.39230i	−0.0995427	−	0.172413i
$650$	0.320508	+	2.66025i	0.0125714	+	0.104344i
$651$		0			0
$652$	−1.09808	−	0.294229i	−0.0430040	−	0.0115229i
$653$	19.4904	−	5.22243i	0.762718	−	0.204370i	0.143566	−	0.989641i	$-0.454143\pi$
$653$	19.4904	−	5.22243i	0.762718	−	0.204370i	0.619152	+	0.785271i	$0.287477\pi$
$654$		0			0
$655$	−42.2487	+	2.53590i	−1.65079	+	0.0990857i
$656$	20.1962	−	11.6603i	0.788527	−	0.455256i
$657$		0			0
$658$	−9.21539	−	7.98076i	−0.359253	−	0.311122i
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.869709	−	0.493564i	$-0.164306\pi$
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.00741531	+	0.999973i	$0.497640\pi$
$660$		0			0
$661$			11.0000i			0.427850i	0.976850	+	0.213925i	$0.0686249\pi$
$661$			11.0000i			0.427850i	−0.976850	+	0.213925i	$0.931375\pi$
$662$	−13.0526	+	13.0526i	−0.507302	+	0.507302i
$663$		0			0
$664$	−1.36603	+	2.36603i	−0.0530121	+	0.0918196i
$665$	15.2679	+	36.7846i	0.592066	+	1.42645i
$666$		0			0
$667$	15.4641	+	4.14359i	0.598772	+	0.160441i
$668$	35.7224	+	9.57180i	1.38214	+	0.370344i
$669$		0			0
$670$	5.50000	+	8.33013i	0.212484	+	0.321821i
$671$	−11.9090	+	6.87564i	−0.459741	+	0.265431i
$672$		0			0
$673$	6.92820	−	1.85641i	0.267063	−	0.0715592i	−0.122803	−	0.992431i	$-0.539188\pi$
$673$	6.92820	−	1.85641i	0.267063	−	0.0715592i	0.389865	+	0.920872i	$0.372522\pi$
$674$	−4.26795	+	2.46410i	−0.164395	+	0.0949136i
$675$		0			0
$676$	10.3301	−	17.8923i	0.397313	−	0.688166i
$677$	−29.9090	−	29.9090i	−1.14949	−	1.14949i	−0.986652	−	0.162843i	$-0.947934\pi$
$677$	−29.9090	−	29.9090i	−1.14949	−	1.14949i	−0.162843	−	0.986652i	$-0.552066\pi$
$678$		0			0
$679$	−7.63397	−	3.70577i	−0.292965	−	0.142214i
$680$	12.1962	−	0.732051i	0.467701	−	0.0280729i
$681$		0			0
$682$	−2.00000	+	7.46410i	−0.0765840	+	0.285815i
$683$	29.9904	−	8.03590i	1.14755	−	0.307485i	0.365567	−	0.930785i	$-0.380875\pi$
$683$	29.9904	−	8.03590i	1.14755	−	0.307485i	0.781983	+	0.623300i	$0.214208\pi$
$684$		0			0
$685$	−16.3923	+	5.46410i	−0.626318	+	0.208773i
$686$	−2.04552	−	9.36603i	−0.0780982	−	0.357597i
$687$		0			0
$688$	13.7942	−	3.69615i	0.525900	−	0.140914i
$689$	3.60770			0.137442
$690$		0			0
$691$		−	20.5885i		−	0.783222i	−0.920131	−	0.391611i	$-0.871918\pi$
$691$		−	20.5885i		−	0.783222i	0.920131	−	0.391611i	$-0.128082\pi$
$692$	17.3205	+	17.3205i	0.658427	+	0.658427i
$693$		0			0
$694$			4.51666i			0.171450i
$695$	13.8564	+	6.92820i	0.525603	+	0.262802i
$696$		0			0
$697$	18.9282	−	18.9282i	0.716957	−	0.716957i
$698$	1.32309	+	4.93782i	0.0500795	+	0.186899i
$699$		0			0
$700$	10.0359	+	20.5981i	0.379321	+	0.778534i
$701$	40.5359			1.53102			0.765510	−	0.643424i	$-0.222487\pi$
$701$	40.5359			1.53102			0.765510	+	0.643424i	$0.222487\pi$
$702$		0			0
$703$	−7.39230	−	27.5885i	−0.278806	−	1.04052i
$704$	2.87564	−	1.66025i	0.108380	−	0.0625732i
$705$		0			0
$706$	−12.5885	+	7.26795i	−0.473773	+	0.273533i
$707$	−35.3038	−	6.79423i	−1.32774	−	0.255523i
$708$		0			0
$709$			48.7128i			1.82945i	0.404079	+	0.914724i	$0.367592\pi$
$709$			48.7128i			1.82945i	−0.404079	+	0.914724i	$0.632408\pi$
$710$	−1.39230	+	6.80385i	−0.0522523	+	0.255344i
$711$		0			0
$712$	0.598076	−	2.23205i	0.0224139	−	0.0836496i
$713$	−6.09808	−	22.7583i	−0.228375	−	0.852306i
$714$		0			0
$715$	2.53590	+	2.24871i	0.0948372	+	0.0840970i
$716$	16.0981	−	27.8827i	0.601613	−	1.04202i
$717$		0			0
$718$	−2.31347	+	8.63397i	−0.0863378	+	0.322217i
$719$	−3.43782	−	5.95448i	−0.128209	−	0.222065i	0.794774	−	0.606906i	$-0.207590\pi$
$719$	−3.43782	−	5.95448i	−0.128209	−	0.222065i	−0.922983	+	0.384841i	$0.874256\pi$
$720$		0			0
$721$	13.2321	−	27.2583i	0.492787	−	1.01515i
$722$	−3.52628	−	13.1603i	−0.131235	−	0.489774i
$723$		0			0
$724$	−7.85641			−0.291981
$725$	27.7128	−	20.7846i	1.02923	−	0.771921i
$726$		0			0
$727$	25.6244	−	6.86603i	0.950355	−	0.254647i	0.249842	−	0.968287i	$-0.419621\pi$
$727$	25.6244	−	6.86603i	0.950355	−	0.254647i	0.700513	+	0.713640i	$0.252955\pi$
$728$	1.00000	−	5.19615i	0.0370625	−	0.192582i
$729$		0			0
$730$	0.758330	−	0.0455173i	0.0280671	−	0.00168467i
$731$	14.1962	−	8.19615i	0.525064	−	0.303146i
$732$		0			0
$733$	−0.607695	−	2.26795i	−0.0224457	−	0.0837686i	0.953794	−	0.300460i	$-0.0971402\pi$
$733$	−0.607695	−	2.26795i	−0.0224457	−	0.0837686i	−0.976240	+	0.216691i	$0.930473\pi$
$734$	−1.40192	−	2.42820i	−0.0517460	−	0.0896266i
$735$		0			0
$736$	5.93782	−	10.2846i	0.218871	−	0.379096i
$737$	12.1962	+	3.26795i	0.449251	+	0.120376i
$738$		0			0
$739$	3.12436	+	1.80385i	0.114931	+	0.0663556i	0.556364	−	0.830939i	$-0.312196\pi$
$739$	3.12436	+	1.80385i	0.114931	+	0.0663556i	−0.441432	+	0.897295i	$0.645529\pi$
$740$	−5.19615	−	15.5885i	−0.191014	−	0.573043i
$741$		0			0
$742$	−4.50962	+	1.56218i	−0.165553	+	0.0573494i
$743$	−0.169873	+	0.633975i	−0.00623204	+	0.0232583i	−0.968972	−	0.247171i	$-0.920499\pi$
$743$	−0.169873	+	0.633975i	−0.00623204	+	0.0232583i	0.962740	+	0.270429i	$0.0871657\pi$
$744$		0			0
$745$	46.1147	−	2.76795i	1.68951	−	0.101410i
$746$	1.09808	−	1.90192i	0.0402034	−	0.0696344i
$747$		0			0
$748$	5.07180	−	5.07180i	0.185443	−	0.185443i
$749$	3.63397	+	5.36603i	0.132783	+	0.196070i
$750$		0			0
$751$	11.4378	−	19.8109i	0.417372	−	0.722910i	−0.578302	−	0.815823i	$-0.696285\pi$
$751$	11.4378	−	19.8109i	0.417372	−	0.722910i	0.995674	+	0.0929130i	$0.0296179\pi$
$752$	−15.5096	−	15.5096i	−0.565578	−	0.565578i
$753$		0			0
$754$	−3.71281			−0.135213
$755$	−2.53590	−	1.26795i	−0.0922908	−	0.0461454i
$756$		0			0
$757$	−11.7321	+	11.7321i	−0.426409	+	0.426409i	−0.887403	−	0.460994i	$-0.847493\pi$
$757$	−11.7321	+	11.7321i	−0.426409	+	0.426409i	0.460994	+	0.887403i	$0.347493\pi$
$758$	−7.12436	−	7.12436i	−0.258768	−	0.258768i
$759$		0			0
$760$	−9.19615	−	27.5885i	−0.333580	−	1.00074i
$761$	−10.0359	−	5.79423i	−0.363801	−	0.210041i	0.306946	−	0.951727i	$-0.400693\pi$
$761$	−10.0359	−	5.79423i	−0.363801	−	0.210041i	−0.670747	+	0.741686i	$0.734026\pi$
$762$		0			0
$763$	1.73205	+	5.00000i	0.0627044	+	0.181012i
$764$			0.588457i			0.0212896i
$765$		0			0
$766$	0.356406	+	0.205771i	0.0128775	+	0.00743482i
$767$	−3.46410	−	0.928203i	−0.125081	−	0.0335155i
$768$		0			0
$769$	17.9904	+	31.1603i	0.648750	+	1.12367i	0.983422	+	0.181333i	$0.0580411\pi$
$769$	17.9904	+	31.1603i	0.648750	+	1.12367i	−0.334672	+	0.942335i	$0.608626\pi$
$770$	−4.14359	−	1.71281i	−0.149325	−	0.0617255i
$771$		0			0
$772$	13.0526	−	13.0526i	0.469772	−	0.469772i
$773$	−12.0263	−	44.8827i	−0.432555	−	1.61432i	−0.746850	−	0.664993i	$-0.768435\pi$
$773$	−12.0263	−	44.8827i	−0.432555	−	1.61432i	0.314295	−	0.949325i	$-0.398232\pi$
$774$		0			0
$775$	−46.8827	−	20.0263i	−1.68408	−	0.719365i
$776$	5.36603	+	3.09808i	0.192629	+	0.111214i
$777$		0			0
$778$	−1.23205	+	4.59808i	−0.0441712	+	0.164849i
$779$	−55.1769	−	31.8564i	−1.97692	−	1.14137i
$780$		0			0
$781$	4.39230	+	7.60770i	0.157169	+	0.272225i
$782$	0.875644	−	3.26795i	0.0313130	−	0.116862i
$783$		0			0
$784$	−2.46410	−	17.0718i	−0.0880036	−	0.609707i
$785$	−3.09808	−	0.633975i	−0.110575	−	0.0226275i
$786$		0			0
$787$	4.29423	+	4.29423i	0.153073	+	0.153073i	0.779489	−	0.626416i	$-0.215479\pi$
$787$	4.29423	+	4.29423i	0.153073	+	0.153073i	−0.626416	+	0.779489i	$0.715479\pi$
$788$	18.2487	+	18.2487i	0.650083	+	0.650083i
$789$		0			0
$790$	−13.0000	−	2.66025i	−0.462519	−	0.0946476i
$791$	16.0981	−	10.9019i	0.572382	−	0.387628i
$792$		0			0
$793$	−2.51666	+	9.39230i	−0.0893692	+	0.333531i
$794$	−8.78461	−	15.2154i	−0.311754	−	0.539974i
$795$		0			0
$796$	29.7846	+	17.1962i	1.05569	+	0.609501i
$797$	−12.6147	+	47.0788i	−0.446837	+	1.66762i	0.264204	+	0.964467i	$0.414891\pi$
$797$	−12.6147	+	47.0788i	−0.446837	+	1.66762i	−0.711040	+	0.703151i	$0.751776\pi$
$798$		0			0
$799$	−21.8038	−	12.5885i	−0.771365	−	0.445348i
$800$	−9.57180	−	23.8468i	−0.338414	−	0.843111i
$801$		0			0
$802$	0.349365	+	1.30385i	0.0123365	+	0.0460405i
$803$	0.679492	−	0.679492i	0.0239787	−	0.0239787i
$804$		0			0
$805$	13.5526	−	1.79423i	0.477665	−	0.0632382i
$806$	2.73205	+	4.73205i	0.0962324	+	0.166679i
$807$		0			0
$808$	25.3564	+	6.79423i	0.892035	+	0.239020i
$809$	−41.5981	−	24.0167i	−1.46251	−	0.844381i	−0.463384	−	0.886158i	$-0.653365\pi$
$809$	−41.5981	−	24.0167i	−1.46251	−	0.844381i	−0.999127	+	0.0417770i	$0.986698\pi$
$810$		0			0
$811$		−	25.8564i		−	0.907941i	−0.891017	−	0.453971i	$-0.850007\pi$
$811$		−	25.8564i		−	0.907941i	0.891017	−	0.453971i	$-0.149993\pi$
$812$	−30.0000	+	10.3923i	−1.05279	+	0.364698i
$813$		0			0
$814$	2.78461	+	1.60770i	0.0976005	+	0.0563497i
$815$	0.464102	+	1.39230i	0.0162568	+	0.0487703i
$816$		0			0
$817$	−27.5885	−	27.5885i	−0.965198	−	0.965198i
$818$	5.63397	−	5.63397i	0.196987	−	0.196987i
$819$		0			0
$820$	−32.7846	−	16.3923i	−1.14489	−	0.572444i
$821$	7.33975			0.256159			0.128079	−	0.991764i	$-0.459119\pi$
$821$	7.33975			0.256159			0.128079	+	0.991764i	$0.459119\pi$
$822$		0			0
$823$	−27.9282	−	27.9282i	−0.973516	−	0.973516i	0.0261423	−	0.999658i	$-0.491678\pi$
$823$	−27.9282	−	27.9282i	−0.973516	−	0.973516i	−0.999658	+	0.0261423i	$0.991678\pi$
$824$	−11.0622	+	19.1603i	−0.385369	+	0.667479i
$825$		0			0
$826$	4.73205	−	0.339746i	0.164649	−	0.0118213i
$827$	−0.607695	+	0.607695i	−0.0211316	+	0.0211316i	−0.717594	−	0.696462i	$-0.754756\pi$
$827$	−0.607695	+	0.607695i	−0.0211316	+	0.0211316i	0.696462	+	0.717594i	$0.254756\pi$
$828$		0			0
$829$	4.83975	−	8.38269i	0.168091	−	0.291143i	−0.769657	−	0.638457i	$-0.779573\pi$
$829$	4.83975	−	8.38269i	0.168091	−	0.291143i	0.937749	+	0.347314i	$0.112906\pi$
$830$	1.63397	−	0.0980762i	0.0567161	−	0.00340427i
$831$		0			0
$832$	0.607695	−	2.26795i	0.0210680	−	0.0786270i
$833$	−7.80385	−	18.1962i	−0.270387	−	0.630459i
$834$		0			0
$835$	−15.0981	−	45.2942i	−0.522490	−	1.56747i
$836$	−14.7846	−	8.53590i	−0.511336	−	0.295220i
$837$		0			0
$838$	−4.00000	−	1.07180i	−0.138178	−	0.0370246i
$839$	−19.0263	+	32.9545i	−0.656860	+	1.13772i	0.324564	+	0.945864i	$0.394782\pi$
$839$	−19.0263	+	32.9545i	−0.656860	+	1.13772i	−0.981424	+	0.191851i	$0.938551\pi$
$840$		0			0
$841$	9.50000	+	16.4545i	0.327586	+	0.567396i
$842$	2.01666	+	7.52628i	0.0694987	+	0.259373i
$843$		0			0
$844$	−7.39230	+	4.26795i	−0.254454	+	0.146909i
$845$	−26.6244	+	1.59808i	−0.915906	+	0.0549755i
$846$		0			0
$847$	22.1410	−	7.66987i	0.760774	−	0.263540i
$848$	−8.29423	+	2.22243i	−0.284825	+	0.0763186i
$849$		0			0
$850$	−4.39230	−	5.85641i	−0.150655	−	0.200873i
$851$	−9.80385			−0.336072
$852$		0			0
$853$	−4.51666	−	16.8564i	−0.154648	−	0.577152i	−0.999135	−	0.0415775i	$-0.986762\pi$
$853$	−4.51666	−	16.8564i	−0.154648	−	0.577152i	0.844488	−	0.535575i	$-0.179905\pi$
$854$	−0.921162	−	12.8301i	−0.0315215	−	0.439038i
$855$		0			0
$856$	−2.36603	−	4.09808i	−0.0808691	−	0.140069i
$857$	−6.24167	+	23.2942i	−0.213211	+	0.795716i	0.773577	+	0.633702i	$0.218466\pi$
$857$	−6.24167	+	23.2942i	−0.213211	+	0.795716i	−0.986789	+	0.162014i	$0.948201\pi$
$858$		0			0
$859$	−4.49038	+	7.77757i	−0.153210	+	0.265367i	−0.932406	−	0.361413i	$-0.882294\pi$
$859$	−4.49038	+	7.77757i	−0.153210	+	0.265367i	0.779196	+	0.626780i	$0.215628\pi$
$860$	−16.7942	−	14.8923i	−0.572678	−	0.507823i
$861$		0			0
$862$	−1.84936	−	6.90192i	−0.0629896	−	0.235080i
$863$	−10.5718	+	39.4545i	−0.359868	+	1.34305i	0.514378	+	0.857563i	$0.328023\pi$
$863$	−10.5718	+	39.4545i	−0.359868	+	1.34305i	−0.874246	+	0.485483i	$0.838644\pi$
$864$		0			0
$865$	6.33975	−	30.9808i	0.215558	−	1.05338i
$866$			14.7846i			0.502401i
$867$		0			0
$868$	35.3205	+	30.5885i	1.19886	+	1.03824i
$869$	−14.5359	+	8.39230i	−0.493097	+	0.284689i
$870$		0			0
$871$	7.73205	−	4.46410i	0.261991	−	0.151260i
$872$	−1.00000	−	3.73205i	−0.0338643	−	0.126383i
$873$		0			0
$874$	−8.05256			−0.272382
$875$	15.0526	−	25.4641i	0.508869	−	0.860844i
$876$		0			0
$877$	0.562178	+	2.09808i	0.0189834	+	0.0708470i	0.974768	−	0.223221i	$-0.0716573\pi$
$877$	0.562178	+	2.09808i	0.0189834	+	0.0708470i	−0.955784	+	0.294068i	$0.904991\pi$
$878$	−8.00000	+	8.00000i	−0.269987	+	0.269987i
$879$		0			0
$880$	−7.21539	−	3.60770i	−0.243231	−	0.121615i
$881$			23.7846i			0.801324i	0.916226	+	0.400662i	$0.131220\pi$
$881$			23.7846i			0.801324i	−0.916226	+	0.400662i	$0.868780\pi$
$882$		0			0
$883$	39.5429	+	39.5429i	1.33073	+	1.33073i	0.904721	+	0.426005i	$0.140079\pi$
$883$	39.5429	+	39.5429i	1.33073	+	1.33073i	0.426005	+	0.904721i	$0.359921\pi$
$884$		−	5.07180i		−	0.170583i
$885$		0			0
$886$	12.1962			0.409738
$887$	−8.23205	+	2.20577i	−0.276405	+	0.0740626i	−0.394359	−	0.918957i	$-0.629033\pi$
$887$	−8.23205	+	2.20577i	−0.276405	+	0.0740626i	0.117954	+	0.993019i	$0.462367\pi$
$888$		0			0
$889$	25.2224	−	1.81089i	0.845933	−	0.0607353i
$890$	−1.31347	+	0.437822i	−0.0440275	+	0.0146758i
$891$		0			0
$892$	12.6962	−	3.40192i	0.425099	−	0.113905i
$893$	−15.5096	+	57.8827i	−0.519010	+	1.93697i
$894$		0			0
$895$	−41.4904	+	2.49038i	−1.38687	+	0.0832443i
$896$	2.16987	+	30.2224i	0.0724904	+	1.00966i
$897$		0			0
$898$	−10.8301	−	10.8301i	−0.361406	−	0.361406i
$899$	35.3205	−	61.1769i	1.17800	−	2.04036i
$900$		0			0
$901$	−8.53590	+	4.92820i	−0.284372	+	0.164182i
$902$	6.92820	−	1.85641i	0.230684	−	0.0618116i
$903$		0			0
$904$	−12.2942	+	7.09808i	−0.408900	+	0.236079i
$905$	5.58846	+	8.46410i	0.185767	+	0.281356i
$906$		0			0
$907$	17.5622	+	4.70577i	0.583143	+	0.156253i	0.538317	−	0.842742i	$-0.319060\pi$
$907$	17.5622	+	4.70577i	0.583143	+	0.156253i	0.0448253	+	0.998995i	$0.485727\pi$
$908$	15.7583	+	4.22243i	0.522959	+	0.140126i
$909$		0			0
$910$	−2.92820	+	1.21539i	−0.0970690	+	0.0402898i
$911$	19.5622	−	33.8827i	0.648124	−	1.12258i	−0.335447	−	0.942059i	$-0.608887\pi$
$911$	19.5622	−	33.8827i	0.648124	−	1.12258i	0.983571	−	0.180524i	$-0.0577794\pi$
$912$		0			0
$913$	1.46410	−	1.46410i	0.0484547	−	0.0484547i
$914$		−	18.0526i		−	0.597126i
$915$		0			0
$916$	18.9904	+	10.9641i	0.627460	+	0.362264i
$917$	−16.3923	−	47.3205i	−0.541322	−	1.56266i
$918$		0			0
$919$	27.3731	−	15.8038i	0.902954	−	0.521321i	0.0247967	−	0.999693i	$-0.492106\pi$
$919$	27.3731	−	15.8038i	0.902954	−	0.521321i	0.878157	+	0.478372i	$0.158773\pi$
$920$	−9.96410	+	0.598076i	−0.328507	+	0.0197180i
$921$		0			0
$922$	4.59808	−	1.23205i	0.151430	−	0.0405754i
$923$	6.00000	+	1.60770i	0.197492	+	0.0529179i
$924$		0			0
$925$	−13.0981	+	16.6865i	−0.430662	+	0.548650i
$926$	−1.18653	−	2.05514i	−0.0389919	−	0.0675360i
$927$		0			0
$928$	34.3923	−	9.21539i	1.12898	−	0.302510i
$929$	1.67949			0.0551023			0.0275512	−	0.999620i	$-0.491229\pi$
$929$	1.67949			0.0551023			0.0275512	+	0.999620i	$0.491229\pi$
$930$		0			0
$931$	−37.0263	+	29.1506i	−1.21349	+	0.955373i
$932$	20.4904	+	5.49038i	0.671185	+	0.179843i
$933$		0			0
$934$	−6.03590	−	10.4545i	−0.197501	−	0.342081i
$935$	−9.07180	−	1.85641i	−0.296679	−	0.0607110i
$936$		0			0
$937$	−2.53590	−	2.53590i	−0.0828442	−	0.0828442i	0.664470	−	0.747315i	$-0.268657\pi$
$937$	−2.53590	−	2.53590i	−0.0828442	−	0.0828442i	−0.747315	+	0.664470i	$0.768657\pi$
$938$	−7.73205	+	8.92820i	−0.252460	+	0.291516i
$939$		0			0
$940$	−6.91154	+	33.7750i	−0.225430	+	1.10162i
$941$			13.9808i			0.455760i	0.973689	+	0.227880i	$0.0731794\pi$
$941$			13.9808i			0.455760i	−0.973689	+	0.227880i	$0.926821\pi$
$942$		0			0
$943$	−15.4641	+	15.4641i	−0.503580	+	0.503580i
$944$	8.53590			0.277820
$945$		0			0
$946$	4.39230			0.142806
$947$	11.2224	−	11.2224i	0.364680	−	0.364680i	−0.500853	−	0.865533i	$-0.666980\pi$
$947$	11.2224	−	11.2224i	0.364680	−	0.364680i	0.865533	+	0.500853i	$0.166980\pi$
$948$		0			0
$949$		−	0.679492i		−	0.0220572i
$950$	−10.7583	+	13.7058i	−0.349046	+	0.444674i
$951$		0			0
$952$	4.73205	+	13.6603i	0.153367	+	0.442731i
$953$	−21.0000	−	21.0000i	−0.680257	−	0.680257i	0.279801	−	0.960058i	$-0.409731\pi$
$953$	−21.0000	−	21.0000i	−0.680257	−	0.680257i	−0.960058	+	0.279801i	$0.909731\pi$
$954$		0			0
$955$	0.633975	−	0.418584i	0.0205149	−	0.0135451i
$956$	−19.0526	−	33.0000i	−0.616204	−	1.06730i
$957$		0			0
$958$	4.36603	+	1.16987i	0.141060	+	0.0377969i
$959$	−11.4641	−	16.9282i	−0.370195	−	0.546640i
$960$		0			0
$961$	−72.9615			−2.35360
$962$	2.19615	−	0.588457i	0.0708068	−	0.0189726i
$963$		0			0
$964$	−14.2583	−	24.6962i	−0.459230	−	0.795410i
$965$	−23.3468	−	4.77757i	−0.751560	−	0.153795i
$966$		0			0
$967$	38.5526	+	10.3301i	1.23977	+	0.332194i	0.818375	−	0.574684i	$-0.194875\pi$
$967$	38.5526	+	10.3301i	1.23977	+	0.332194i	0.421392	+	0.906879i	$0.361542\pi$
$968$	−16.5263	+	4.42820i	−0.531175	+	0.142328i
$969$		0			0
$970$	−0.222432	−	3.70577i	−0.00714186	−	0.118985i
$971$	9.46410	−	5.46410i	0.303717	−	0.175351i	−0.340394	−	0.940283i	$-0.610561\pi$
$971$	9.46410	−	5.46410i	0.303717	−	0.175351i	0.644112	+	0.764931i	$0.277227\pi$
$972$		0			0
$973$	−3.46410	+	18.0000i	−0.111054	+	0.577054i
$974$	−12.8494	−	7.41858i	−0.411720	−	0.237707i
$975$		0			0
$976$		−	23.1436i		−	0.740808i
$977$	−29.1769	+	29.1769i	−0.933452	+	0.933452i	−0.997920	−	0.0644676i	$-0.979465\pi$
$977$	−29.1769	+	29.1769i	−0.933452	+	0.933452i	0.0644676	+	0.997920i	$0.479465\pi$
$978$		0			0
$979$	−0.875644	+	1.51666i	−0.0279857	+	0.0484727i
$980$	−20.2583	+	18.0167i	−0.647129	+	0.575521i
$981$		0			0
$982$	1.53590	+	0.411543i	0.0490125	+	0.0131329i
$983$	−31.9545	−	8.56218i	−1.01919	−	0.273091i	−0.289725	−	0.957110i	$-0.593564\pi$
$983$	−31.9545	−	8.56218i	−1.01919	−	0.273091i	−0.729464	+	0.684019i	$0.760231\pi$
$984$		0			0
$985$	6.67949	−	32.6410i	0.212826	−	1.04003i
$986$	8.78461	−	5.07180i	0.279759	−	0.161519i
$987$		0			0
$988$	−11.6603	+	3.12436i	−0.370962	+	0.0993990i
$989$	−11.5981	+	6.69615i	−0.368797	+	0.212925i
$990$		0			0
$991$	5.26795	−	9.12436i	0.167342	−	0.289845i	−0.770143	−	0.637872i	$-0.779815\pi$
$991$	5.26795	−	9.12436i	0.167342	−	0.289845i	0.937484	+	0.348027i	$0.113148\pi$
$992$	−37.0526	−	37.0526i	−1.17642	−	1.17642i
$993$		0			0
$994$	−8.19615	+	0.588457i	−0.259966	+	0.0186647i
$995$	−2.66025	−	44.3205i	−0.0843357	−	1.40505i
$996$		0			0
$997$	−7.31347	+	27.2942i	−0.231620	+	0.864417i	0.748024	+	0.663672i	$0.231003\pi$
$997$	−7.31347	+	27.2942i	−0.231620	+	0.864417i	−0.979644	+	0.200745i	$0.935664\pi$
$998$	10.4641	−	2.80385i	0.331235	−	0.0887542i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.d.73.1		4
3.2	odd	2		315.2.bs.c.178.1	yes	4
5.2	odd	4		945.2.bv.a.262.1		4
7.5	odd	6		945.2.cj.d.208.1		4
9.4	even	3		945.2.cj.a.388.1		4
9.5	odd	6		315.2.cg.c.283.1	yes	4
15.2	even	4		315.2.bs.b.52.1	✓	4
21.5	even	6		315.2.cg.a.313.1	yes	4
35.12	even	12		945.2.cj.a.397.1		4
45.22	odd	12		945.2.cj.d.577.1		4
45.32	even	12		315.2.cg.a.157.1	yes	4
63.5	even	6		315.2.bs.b.103.1	yes	4
63.40	odd	6		945.2.bv.a.523.1		4
105.47	odd	12		315.2.cg.c.187.1	yes	4
315.257	odd	12		315.2.bs.c.292.1	yes	4
315.292	even	12	inner	945.2.bv.d.712.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.b.52.1	✓	4	15.2	even	4
315.2.bs.b.103.1	yes	4	63.5	even	6
315.2.bs.c.178.1	yes	4	3.2	odd	2
315.2.bs.c.292.1	yes	4	315.257	odd	12
315.2.cg.a.157.1	yes	4	45.32	even	12
315.2.cg.a.313.1	yes	4	21.5	even	6
315.2.cg.c.187.1	yes	4	105.47	odd	12
315.2.cg.c.283.1	yes	4	9.5	odd	6
945.2.bv.a.262.1		4	5.2	odd	4
945.2.bv.a.523.1		4	63.40	odd	6
945.2.bv.d.73.1		4	1.1	even	1	trivial
945.2.bv.d.712.1		4	315.292	even	12	inner
945.2.cj.a.388.1		4	9.4	even	3
945.2.cj.a.397.1		4	35.12	even	12
945.2.cj.d.208.1		4	7.5	odd	6
945.2.cj.d.577.1		4	45.22	odd	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bv (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 0.366025i) q^{2} +1.73205i q^{4} +(1.86603 - 1.23205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.36603 - 1.36603i) q^{8} +O(q^{10})\)	\(q+(-0.366025 + 0.366025i) q^{2} +1.73205i q^{4} +(1.86603 - 1.23205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(-0.232051 + 1.13397i) q^{10} +(0.732051 + 1.26795i) q^{11} +(1.00000 + 0.267949i) q^{13} +(-1.36603 + 0.0980762i) q^{14} -2.46410 q^{16} +(-2.73205 + 0.732051i) q^{17} +(3.36603 + 5.83013i) q^{19} +(2.13397 + 3.23205i) q^{20} +(-0.732051 - 0.196152i) q^{22} +(2.23205 - 0.598076i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-0.464102 + 0.267949i) q^{26} +(-3.00000 + 3.46410i) q^{28} +(6.00000 + 3.46410i) q^{29} -10.1962i q^{31} +(3.63397 - 3.63397i) q^{32} +(0.732051 - 1.26795i) q^{34} +(5.86603 + 0.767949i) q^{35} +(-4.09808 - 1.09808i) q^{37} +(-3.36603 - 0.901924i) q^{38} +(-4.23205 - 0.866025i) q^{40} +(-8.19615 + 4.73205i) q^{41} +(-5.59808 + 1.50000i) q^{43} +(-2.19615 + 1.26795i) q^{44} +(-0.598076 + 1.03590i) q^{46} +(6.29423 + 6.29423i) q^{47} +(1.00000 + 6.92820i) q^{49} +(0.964102 + 2.40192i) q^{50} +(-0.464102 + 1.73205i) q^{52} +(3.36603 - 0.901924i) q^{53} +(2.92820 + 1.46410i) q^{55} +(-0.366025 - 5.09808i) q^{56} +(-3.46410 + 0.928203i) q^{58} -3.46410 q^{59} +9.39230i q^{61} +(3.73205 + 3.73205i) q^{62} -2.26795i q^{64} +(2.19615 - 0.732051i) q^{65} +(6.09808 - 6.09808i) q^{67} +(-1.26795 - 4.73205i) q^{68} +(-2.42820 + 1.86603i) q^{70} +6.00000 q^{71} +(-0.169873 - 0.633975i) q^{73} +(1.90192 - 1.09808i) q^{74} +(-10.0981 + 5.83013i) q^{76} +(-0.732051 + 3.80385i) q^{77} +11.4641i q^{79} +(-4.59808 + 3.03590i) q^{80} +(1.26795 - 4.73205i) q^{82} +(-0.366025 - 1.36603i) q^{83} +(-4.19615 + 4.73205i) q^{85} +(1.50000 - 2.59808i) q^{86} +(0.732051 - 2.73205i) q^{88} +(0.598076 + 1.03590i) q^{89} +(1.53590 + 2.26795i) q^{91} +(1.03590 + 3.86603i) q^{92} -4.60770 q^{94} +(13.4641 + 6.73205i) q^{95} +(-3.09808 + 0.830127i) q^{97} +(-2.90192 - 2.16987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8	\( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{7} - 2 q^{8} + 6 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} + 10 q^{19} + 12 q^{20} + 4 q^{22} + 2 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{28} + 24 q^{29} + 18 q^{32} - 4 q^{34} + 20 q^{35} - 6 q^{37} - 10 q^{38} - 10 q^{40} - 12 q^{41} - 12 q^{43} + 12 q^{44} + 8 q^{46} - 6 q^{47} + 4 q^{49} - 10 q^{50} + 12 q^{52} + 10 q^{53} - 16 q^{55} + 2 q^{56} + 8 q^{62} - 12 q^{65} + 14 q^{67} - 12 q^{68} + 18 q^{70} + 24 q^{71} - 18 q^{73} + 18 q^{74} - 30 q^{76} + 4 q^{77} - 8 q^{80} + 12 q^{82} + 2 q^{83} + 4 q^{85} + 6 q^{86} - 4 q^{88} - 8 q^{89} + 20 q^{91} + 18 q^{92} - 60 q^{94} + 40 q^{95} - 2 q^{97} - 22 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^5 + 8 * q^7 - 2 * q^8 + 6 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 + 10 * q^19 + 12 * q^20 + 4 * q^22 + 2 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^28 + 24 * q^29 + 18 * q^32 - 4 * q^34 + 20 * q^35 - 6 * q^37 - 10 * q^38 - 10 * q^40 - 12 * q^41 - 12 * q^43 + 12 * q^44 + 8 * q^46 - 6 * q^47 + 4 * q^49 - 10 * q^50 + 12 * q^52 + 10 * q^53 - 16 * q^55 + 2 * q^56 + 8 * q^62 - 12 * q^65 + 14 * q^67 - 12 * q^68 + 18 * q^70 + 24 * q^71 - 18 * q^73 + 18 * q^74 - 30 * q^76 + 4 * q^77 - 8 * q^80 + 12 * q^82 + 2 * q^83 + 4 * q^85 + 6 * q^86 - 4 * q^88 - 8 * q^89 + 20 * q^91 + 18 * q^92 - 60 * q^94 + 40 * q^95 - 2 * q^97 - 22 * q^98

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