LMFDB - Embedded newform 975.2.bc.j.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, 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("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.191102976.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 $ x^8 - 6x^6 + 6x^4 + 36*x^2 + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$0.291439 - 1.08766i$ of defining polynomial
Character	$\chi$	$=$	975.901
Dual form			975.2.bc.j.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88389 - 1.08766i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.36603 + 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.383889 - 0.221638i) q^{7} -1.59245i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.88389 - 1.08766i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.36603 + 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.383889 - 0.221638i) q^{7} -1.59245i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.37910 - 0.796225i) q^{11} -2.73205 q^{12} +(3.39697 + 1.20856i) q^{13} -0.964273 q^{14} +(1.00000 - 1.73205i) q^{16} +(-1.88389 - 3.26299i) q^{17} +2.17533i q^{18} +(-1.33987 + 0.773575i) q^{19} +0.443277i q^{21} +(1.73205 + 3.00000i) q^{22} +(-0.352948 + 0.611324i) q^{23} +(1.37910 + 0.796225i) q^{24} +(-5.08500 - 5.97155i) q^{26} +1.00000 q^{27} +(1.04880 + 0.605528i) q^{28} +(-1.24991 + 2.16492i) q^{29} -6.18490i q^{31} +(-6.52598 + 3.76778i) q^{32} +(1.37910 - 0.796225i) q^{33} +8.19615i q^{34} +(1.36603 - 2.36603i) q^{36} +(8.96393 + 5.17533i) q^{37} +3.36556 q^{38} +(-2.74513 + 2.33758i) q^{39} +(5.21419 + 3.01041i) q^{41} +(0.482136 - 0.835085i) q^{42} +(-2.36124 - 4.08979i) q^{43} -4.35066i q^{44} +(1.32983 - 0.767778i) q^{46} -5.41712i q^{47} +(1.00000 + 1.73205i) q^{48} +(-3.40175 + 5.89201i) q^{49} +3.76778 q^{51} +(1.78086 + 9.68823i) q^{52} -5.51641 q^{53} +(-1.88389 - 1.08766i) q^{54} +(-0.352948 - 0.611324i) q^{56} -1.54715i q^{57} +(4.70940 - 2.71897i) q^{58} +(7.55359 - 4.36107i) q^{59} +(4.86603 + 8.42820i) q^{61} +(-6.72709 + 11.6517i) q^{62} +(-0.383889 - 0.221638i) q^{63} +12.3923 q^{64} -3.46410 q^{66} +(11.8611 + 6.84799i) q^{67} +(5.14688 - 8.91466i) q^{68} +(-0.352948 - 0.611324i) q^{69} +(13.1193 - 7.57442i) q^{71} +(-1.37910 + 0.796225i) q^{72} -10.7939i q^{73} +(-11.2580 - 19.4995i) q^{74} +(-3.66060 - 2.11345i) q^{76} -0.705897 q^{77} +(7.71402 - 1.41796i) q^{78} +10.7317 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.54863 - 11.3426i) q^{82} -9.12801i q^{83} +(-1.04880 + 0.605528i) q^{84} +10.2729i q^{86} +(-1.24991 - 2.16492i) q^{87} +(-1.26795 + 2.19615i) q^{88} +(-4.11927 - 2.37826i) q^{89} +(1.57192 - 0.288945i) q^{91} -1.92855 q^{92} +(5.35628 + 3.09245i) q^{93} +(-5.89201 + 10.2053i) q^{94} -7.53556i q^{96} +(7.28944 - 4.20856i) q^{97} +(12.8170 - 7.39993i) q^{98} +1.59245i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9} - 8 q^{12} + 8 q^{13} - 24 q^{14} + 8 q^{16} - 12 q^{19} - 24 q^{26} + 8 q^{27} - 12 q^{28} + 12 q^{29} + 4 q^{36} - 4 q^{39} + 36 q^{41} + 12 q^{42} - 16 q^{43} + 8 q^{48} - 4 q^{49} - 20 q^{52} + 36 q^{58} + 36 q^{59} + 32 q^{61} + 12 q^{63} + 16 q^{64} + 48 q^{67} + 36 q^{71} - 24 q^{74} - 48 q^{76} + 12 q^{78} - 16 q^{79} - 4 q^{81} + 12 q^{82} + 12 q^{84} + 12 q^{87} - 24 q^{88} + 36 q^{89} - 48 q^{92} + 12 q^{94} + 72 q^{98}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9 - 8 * q^12 + 8 * q^13 - 24 * q^14 + 8 * q^16 - 12 * q^19 - 24 * q^26 + 8 * q^27 - 12 * q^28 + 12 * q^29 + 4 * q^36 - 4 * q^39 + 36 * q^41 + 12 * q^42 - 16 * q^43 + 8 * q^48 - 4 * q^49 - 20 * q^52 + 36 * q^58 + 36 * q^59 + 32 * q^61 + 12 * q^63 + 16 * q^64 + 48 * q^67 + 36 * q^71 - 24 * q^74 - 48 * q^76 + 12 * q^78 - 16 * q^79 - 4 * q^81 + 12 * q^82 + 12 * q^84 + 12 * q^87 - 24 * q^88 + 36 * q^89 - 48 * q^92 + 12 * q^94 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−1.88389	−	1.08766i	−1.33211	−	0.769095i	−0.346488	−	0.938054i	$-0.612626\pi$
$2$	−1.88389	−	1.08766i	−1.33211	−	0.769095i	−0.985623	+	0.168960i	$0.945959\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.36603	+	2.36603i	0.683013	+	1.18301i
$5$		0			0
$5$		0			0
$6$	1.88389	−	1.08766i	0.769095	−	0.444037i
$7$	0.383889	−	0.221638i	0.145096	−	0.0837715i	−0.425694	−	0.904867i	$-0.639970\pi$
$7$	0.383889	−	0.221638i	0.145096	−	0.0837715i	0.570791	+	0.821096i	$0.306637\pi$
$8$		−	1.59245i		−	0.563016i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.37910	−	0.796225i	−0.415815	−	0.240071i	0.277470	−	0.960734i	$-0.410504\pi$
$11$	−1.37910	−	0.796225i	−0.415815	−	0.240071i	−0.693285	+	0.720663i	$0.743837\pi$
$12$	−2.73205			−0.788675
$13$	3.39697	+	1.20856i	0.942149	+	0.335195i
$13$	3.39697	+	1.20856i	0.942149	+	0.335195i
$14$	−0.964273			−0.257713
$15$		0			0
$16$	1.00000	−	1.73205i	0.250000	−	0.433013i
$17$	−1.88389	−	3.26299i	−0.456910	−	0.791392i	0.541886	−	0.840452i	$-0.317711\pi$
$17$	−1.88389	−	3.26299i	−0.456910	−	0.791392i	−0.998796	+	0.0490606i	$0.984377\pi$
$18$			2.17533i			0.512730i
$19$	−1.33987	+	0.773575i	−0.307388	+	0.177470i	−0.645757	−	0.763543i	$-0.723458\pi$
$19$	−1.33987	+	0.773575i	−0.307388	+	0.177470i	0.338369	+	0.941013i	$0.390125\pi$
$20$		0			0
$21$			0.443277i			0.0967310i
$22$	1.73205	+	3.00000i	0.369274	+	0.639602i
$23$	−0.352948	+	0.611324i	−0.0735948	+	0.127470i	−0.900474	−	0.434909i	$-0.856780\pi$
$23$	−0.352948	+	0.611324i	−0.0735948	+	0.127470i	0.826880	+	0.562379i	$0.190114\pi$
$24$	1.37910	+	0.796225i	0.281508	+	0.162529i
$25$		0			0
$26$	−5.08500	−	5.97155i	−0.997250	−	1.17112i
$27$	1.00000			0.192450
$28$	1.04880	+	0.605528i	0.198205	+	0.114434i
$29$	−1.24991	+	2.16492i	−0.232103	+	0.402015i	−0.958427	−	0.285338i	$-0.907894\pi$
$29$	−1.24991	+	2.16492i	−0.232103	+	0.402015i	0.726324	+	0.687353i	$0.241227\pi$
$30$		0			0
$31$		−	6.18490i		−	1.11084i	−0.831570	−	0.555420i	$-0.812557\pi$
$31$		−	6.18490i		−	1.11084i	0.831570	−	0.555420i	$-0.187443\pi$
$32$	−6.52598	+	3.76778i	−1.15364	+	0.666055i
$33$	1.37910	−	0.796225i	0.240071	−	0.138605i
$34$			8.19615i			1.40563i
$35$		0			0
$36$	1.36603	−	2.36603i	0.227671	−	0.394338i
$37$	8.96393	+	5.17533i	1.47366	+	0.850819i	0.999560	−	0.0296519i	$-0.00943988\pi$
$37$	8.96393	+	5.17533i	1.47366	+	0.850819i	0.474101	+	0.880471i	$0.342773\pi$
$38$	3.36556			0.545966
$39$	−2.74513	+	2.33758i	−0.439572	+	0.374312i
$40$		0			0
$41$	5.21419	+	3.01041i	0.814319	+	0.470147i	0.848454	−	0.529270i	$-0.177534\pi$
$41$	5.21419	+	3.01041i	0.814319	+	0.470147i	−0.0341343	+	0.999417i	$0.510867\pi$
$42$	0.482136	−	0.835085i	0.0743952	−	0.128856i
$43$	−2.36124	−	4.08979i	−0.360086	−	0.623686i	0.627889	−	0.778303i	$-0.283919\pi$
$43$	−2.36124	−	4.08979i	−0.360086	−	0.623686i	−0.987975	+	0.154616i	$0.950586\pi$
$44$		−	4.35066i		−	0.655886i
$45$		0			0
$46$	1.32983	−	0.767778i	0.196073	−	0.113203i
$47$		−	5.41712i		−	0.790169i	−0.918645	−	0.395084i	$-0.870715\pi$
$47$		−	5.41712i		−	0.790169i	0.918645	−	0.395084i	$-0.129285\pi$
$48$	1.00000	+	1.73205i	0.144338	+	0.250000i
$49$	−3.40175	+	5.89201i	−0.485965	+	0.841716i
$50$		0			0
$51$	3.76778			0.527594
$52$	1.78086	+	9.68823i	0.246960	+	1.34352i
$53$	−5.51641			−0.757737			−0.378869	−	0.925450i	$-0.623687\pi$
$53$	−5.51641			−0.757737			−0.378869	+	0.925450i	$0.623687\pi$
$54$	−1.88389	−	1.08766i	−0.256365	−	0.148012i
$55$		0			0
$56$	−0.352948	−	0.611324i	−0.0471647	−	0.0816917i
$57$		−	1.54715i		−	0.204925i
$58$	4.70940	−	2.71897i	0.618375	−	0.357019i
$59$	7.55359	−	4.36107i	0.983394	−	0.567763i	0.0801008	−	0.996787i	$-0.474476\pi$
$59$	7.55359	−	4.36107i	0.983394	−	0.567763i	0.903293	+	0.429024i	$0.141142\pi$
$60$		0			0
$61$	4.86603	+	8.42820i	0.623031	+	1.07912i	0.988918	+	0.148462i	$0.0474322\pi$
$61$	4.86603	+	8.42820i	0.623031	+	1.07912i	−0.365887	+	0.930659i	$0.619234\pi$
$62$	−6.72709	+	11.6517i	−0.854342	+	1.47976i
$63$	−0.383889	−	0.221638i	−0.0483655	−	0.0279238i
$64$	12.3923			1.54904
$65$		0			0
$66$	−3.46410			−0.426401
$67$	11.8611	+	6.84799i	1.44906	+	0.836615i	0.998426	−	0.0560933i	$-0.0178644\pi$
$67$	11.8611	+	6.84799i	1.44906	+	0.836615i	0.450635	+	0.892709i	$0.351198\pi$
$68$	5.14688	−	8.91466i	0.624151	−	1.08106i
$69$	−0.352948	−	0.611324i	−0.0424900	−	0.0735948i
$70$		0			0
$71$	13.1193	−	7.57442i	1.55697	−	0.898918i	0.559427	−	0.828880i	$-0.311021\pi$
$71$	13.1193	−	7.57442i	1.55697	−	0.898918i	0.997544	−	0.0700381i	$-0.0223121\pi$
$72$	−1.37910	+	0.796225i	−0.162529	+	0.0938360i
$73$		−	10.7939i		−	1.26333i	−0.775240	−	0.631667i	$-0.782371\pi$
$73$		−	10.7939i		−	1.26333i	0.775240	−	0.631667i	$-0.217629\pi$
$74$	−11.2580	−	19.4995i	−1.30872	−	2.26677i
$75$		0			0
$76$	−3.66060	−	2.11345i	−0.419899	−	0.242429i
$77$	−0.705897			−0.0804444
$78$	7.71402	−	1.41796i	0.873440	−	0.160553i
$79$	10.7317			1.20741			0.603706	−	0.797207i	$-0.293690\pi$
$79$	10.7317			1.20741			0.603706	+	0.797207i	$0.293690\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.54863	−	11.3426i	−0.723176	−	1.25258i
$83$		−	9.12801i		−	1.00193i	−0.865468	−	0.500964i	$-0.832979\pi$
$83$		−	9.12801i		−	1.00193i	0.865468	−	0.500964i	$-0.167021\pi$
$84$	−1.04880	+	0.605528i	−0.114434	+	0.0660685i
$85$		0			0
$86$			10.2729i			1.10776i
$87$	−1.24991	−	2.16492i	−0.134005	−	0.232103i
$88$	−1.26795	+	2.19615i	−0.135164	+	0.234111i
$89$	−4.11927	−	2.37826i	−0.436642	−	0.252095i	0.265530	−	0.964103i	$-0.414453\pi$
$89$	−4.11927	−	2.37826i	−0.436642	−	0.252095i	−0.702172	+	0.712007i	$0.747786\pi$
$90$		0			0
$91$	1.57192	−	0.288945i	0.164782	−	0.0302897i
$92$	−1.92855			−0.201065
$93$	5.35628	+	3.09245i	0.555420	+	0.320672i
$94$	−5.89201	+	10.2053i	−0.607714	+	1.05259i
$95$		0			0
$96$		−	7.53556i		−	0.769095i
$97$	7.28944	−	4.20856i	0.740131	−	0.427315i	−0.0819861	−	0.996633i	$-0.526126\pi$
$97$	7.28944	−	4.20856i	0.740131	−	0.427315i	0.822117	+	0.569319i	$0.192793\pi$
$98$	12.8170	−	7.39993i	1.29472	−	0.747506i
$99$			1.59245i			0.160047i
$100$		0			0
$101$	−3.35295	+	5.80748i	−0.333631	+	0.577866i	−0.983221	−	0.182419i	$-0.941607\pi$
$101$	−3.35295	+	5.80748i	−0.333631	+	0.577866i	0.649590	+	0.760285i	$0.274941\pi$
$102$	−7.09808	−	4.09808i	−0.702814	−	0.405770i
$103$	1.74197			0.171641			0.0858205	−	0.996311i	$-0.472649\pi$
$103$	1.74197			0.171641			0.0858205	+	0.996311i	$0.472649\pi$
$104$	1.92457	−	5.40950i	0.188720	−	0.530445i
$105$		0			0
$106$	10.3923	+	6.00000i	1.00939	+	0.582772i
$107$	5.95932	−	10.3218i	0.576109	−	0.997850i	−0.419811	−	0.907611i	$-0.637904\pi$
$107$	5.95932	−	10.3218i	0.576109	−	0.997850i	0.995920	−	0.0902383i	$-0.0287629\pi$
$108$	1.36603	+	2.36603i	0.131446	+	0.227671i
$109$		−	17.0407i		−	1.63220i	−0.577908	−	0.816102i	$-0.696131\pi$
$109$		−	17.0407i		−	1.63220i	0.577908	−	0.816102i	$-0.303869\pi$
$110$		0			0
$111$	−8.96393	+	5.17533i	−0.850819	+	0.491220i
$112$		−	0.886554i		−	0.0837715i
$113$	−1.73205	−	3.00000i	−0.162938	−	0.282216i	0.772983	−	0.634426i	$-0.218764\pi$
$113$	−1.73205	−	3.00000i	−0.162938	−	0.282216i	−0.935921	+	0.352210i	$0.885430\pi$
$114$	−1.68278	+	2.91466i	−0.157607	+	0.272983i
$115$		0			0
$116$	−6.82966			−0.634118
$117$	−0.651838	−	3.54614i	−0.0602625	−	0.327841i
$118$	−18.9735			−1.74665
$119$	−1.44641	−	0.835085i	−0.132592	−	0.0765521i
$120$		0			0
$121$	−4.23205	−	7.33013i	−0.384732	−	0.666375i
$122$		−	21.1704i		−	1.91668i
$123$	−5.21419	+	3.01041i	−0.470147	+	0.271440i
$124$	14.6336	−	8.44873i	1.31414	−	0.758719i
$125$		0			0
$126$	0.482136	+	0.835085i	0.0429521	+	0.0743952i
$127$	−7.12551	+	12.3418i	−0.632287	+	1.09515i	0.354796	+	0.934944i	$0.384550\pi$
$127$	−7.12551	+	12.3418i	−0.632287	+	1.09515i	−0.987083	+	0.160210i	$0.948783\pi$
$128$	−10.2938	−	5.94311i	−0.909849	−	0.525301i
$129$	4.72248			0.415791
$130$		0			0
$131$	10.0354			0.876796			0.438398	−	0.898781i	$-0.355546\pi$
$131$	10.0354			0.876796			0.438398	+	0.898781i	$0.355546\pi$
$132$	3.76778	+	2.17533i	0.327943	+	0.189338i
$133$	−0.342908	+	0.593934i	−0.0297339	+	0.0515006i
$134$	−14.8966	−	25.8017i	−1.28687	−	2.22893i
$135$		0			0
$136$	−5.19615	+	3.00000i	−0.445566	+	0.257248i
$137$	8.04034	−	4.64209i	0.686933	−	0.396601i	−0.115529	−	0.993304i	$-0.536856\pi$
$137$	8.04034	−	4.64209i	0.686933	−	0.396601i	0.802462	+	0.596703i	$0.203523\pi$
$138$			1.53556i			0.130715i
$139$	3.25821	+	5.64338i	0.276357	+	0.478665i	0.970477	−	0.241195i	$-0.0775393\pi$
$139$	3.25821	+	5.64338i	0.276357	+	0.478665i	−0.694119	+	0.719860i	$0.744206\pi$
$140$		0			0
$141$	4.69137	+	2.70856i	0.395084	+	0.228102i
$142$	−32.9537			−2.76541
$143$	−3.72248	−	4.37148i	−0.311289	−	0.365562i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−11.7402	+	20.3346i	−0.971623	+	1.68290i
$147$	−3.40175	−	5.89201i	−0.280572	−	0.485965i
$148$			28.2785i			2.32448i
$149$	−0.0492717	+	0.0284470i	−0.00403650	+	0.00233047i	−0.502017	−	0.864858i	$-0.667408\pi$
$149$	−0.0492717	+	0.0284470i	−0.00403650	+	0.00233047i	0.497980	+	0.867188i	$0.334075\pi$
$150$		0			0
$151$		−	17.3004i		−	1.40789i	−0.710255	−	0.703944i	$-0.751420\pi$
$151$		−	17.3004i		−	1.40789i	0.710255	−	0.703944i	$-0.248580\pi$
$152$	1.23188	+	2.13368i	0.0999186	+	0.173064i
$153$	−1.88389	+	3.26299i	−0.152303	+	0.263797i
$154$	1.32983	+	0.767778i	0.107161	+	0.0618693i
$155$		0			0
$156$	−9.28068	−	3.30185i	−0.743049	−	0.264360i
$157$	1.34898			0.107660			0.0538300	−	0.998550i	$-0.482857\pi$
$157$	1.34898			0.107660			0.0538300	+	0.998550i	$0.482857\pi$
$158$	−20.2173	−	11.6725i	−1.60841	−	0.928614i
$159$	2.75821	−	4.77735i	0.218740	−	0.378869i
$160$		0			0
$161$			0.312908i			0.0246606i
$162$	1.88389	−	1.08766i	0.148012	−	0.0854549i
$163$	−2.58004	+	1.48959i	−0.202084	+	0.116674i	−0.597627	−	0.801774i	$-0.703890\pi$
$163$	−2.58004	+	1.48959i	−0.202084	+	0.116674i	0.395543	+	0.918447i	$0.370556\pi$
$164$			16.4492i			1.28447i
$165$		0			0
$166$	−9.92820	+	17.1962i	−0.770578	+	1.33468i
$167$	20.6236	+	11.9070i	1.59590	+	0.921394i	0.992265	+	0.124134i	$0.0396153\pi$
$167$	20.6236	+	11.9070i	1.59590	+	0.921394i	0.603636	+	0.797260i	$0.293718\pi$
$168$	0.705897			0.0544611
$169$	10.0788	+	8.21088i	0.775289	+	0.631606i
$170$		0			0
$171$	1.33987	+	0.773575i	0.102463	+	0.0591568i
$172$	6.45102	−	11.1735i	0.491886	−	0.851972i
$173$	12.3381	+	21.3702i	0.938047	+	1.62474i	0.769109	+	0.639117i	$0.220700\pi$
$173$	12.3381	+	21.3702i	0.938047	+	1.62474i	0.168937	+	0.985627i	$0.445966\pi$
$174$			5.43795i			0.412250i
$175$		0			0
$176$	−2.75821	+	1.59245i	−0.207908	+	0.120035i
$177$			8.72214i			0.655596i
$178$	5.17350	+	8.96077i	0.387770	+	0.671638i
$179$	−1.44244	+	2.49838i	−0.107813	+	0.186737i	−0.914884	−	0.403717i	$-0.867718\pi$
$179$	−1.44244	+	2.49838i	−0.107813	+	0.186737i	0.807071	+	0.590454i	$0.201051\pi$
$180$		0			0
$181$	−7.41086			−0.550845			−0.275422	−	0.961323i	$-0.588818\pi$
$181$	−7.41086			−0.550845			−0.275422	+	0.961323i	$0.588818\pi$
$182$	−3.27560	−	1.16538i	−0.242804	−	0.0863839i
$183$	−9.73205			−0.719414
$184$	0.973504	+	0.562053i	0.0717676	+	0.0414351i
$185$		0			0
$186$	−6.72709	−	11.6517i	−0.493254	−	0.854342i
$187$			6.00000i			0.438763i
$188$	12.8170	−	7.39993i	0.934779	−	0.539695i
$189$	0.383889	−	0.221638i	0.0279238	−	0.0161218i
$190$		0			0
$191$	8.12885	+	14.0796i	0.588183	+	1.01876i	0.994470	+	0.105017i	$0.0334897\pi$
$191$	8.12885	+	14.0796i	0.588183	+	1.01876i	−0.406288	+	0.913745i	$0.633177\pi$
$192$	−6.19615	+	10.7321i	−0.447169	+	0.774519i
$193$	9.76662	+	5.63876i	0.703017	+	0.405887i	0.808470	−	0.588537i	$-0.200296\pi$
$193$	9.76662	+	5.63876i	0.703017	+	0.405887i	−0.105453	+	0.994424i	$0.533629\pi$
$194$	−18.3100			−1.31458
$195$		0			0
$196$	−18.5875			−1.32768
$197$	21.3622	+	12.3335i	1.52199	+	0.878723i	0.999662	+	0.0259791i	$0.00827032\pi$
$197$	21.3622	+	12.3335i	1.52199	+	0.878723i	0.522330	+	0.852744i	$0.325063\pi$
$198$	1.73205	−	3.00000i	0.123091	−	0.213201i
$199$	−11.0356	−	19.1141i	−0.782290	−	1.35497i	−0.930605	−	0.366026i	$-0.880718\pi$
$199$	−11.0356	−	19.1141i	−0.782290	−	1.35497i	0.148315	−	0.988940i	$-0.452615\pi$
$200$		0			0
$201$	−11.8611	+	6.84799i	−0.836615	+	0.483020i
$202$	12.6332	−	7.29376i	0.888866	−	0.513187i
$203$			1.10812i			0.0777745i
$204$	5.14688	+	8.91466i	0.360354	+	0.624151i
$205$		0			0
$206$	−3.28167	−	1.89467i	−0.228645	−	0.132008i
$207$	0.705897			0.0490632
$208$	5.49026	−	4.67516i	0.380681	−	0.324164i
$209$	2.46376			0.170422
$210$		0			0
$211$	10.7580	−	18.6335i	0.740614	−	1.28278i	−0.211603	−	0.977356i	$-0.567868\pi$
$211$	10.7580	−	18.6335i	0.740614	−	1.28278i	0.952216	−	0.305425i	$-0.0987984\pi$
$212$	−7.53556	−	13.0520i	−0.517544	−	0.896413i
$213$			15.1488i			1.03798i
$214$	−22.4534	+	12.9635i	−1.53488	+	0.886164i
$215$		0			0
$216$		−	1.59245i		−	0.108353i
$217$	−1.37081	−	2.37432i	−0.0930568	−	0.161179i
$218$	−18.5346	+	32.1028i	−1.25532	+	2.17428i
$219$	9.34782	+	5.39697i	0.631667	+	0.364693i
$220$		0			0
$221$	−2.45598	−	13.3611i	−0.165207	−	0.898763i
$222$	22.5161			1.51118
$223$	−18.3914	−	10.6183i	−1.23158	−	0.711051i	−0.264219	−	0.964463i	$-0.585114\pi$
$223$	−18.3914	−	10.6183i	−1.23158	−	0.711051i	−0.967359	+	0.253411i	$0.918447\pi$
$224$	−1.67017	+	2.89282i	−0.111593	+	0.193285i
$225$		0			0
$226$			7.53556i			0.501258i
$227$	−9.04992	+	5.22497i	−0.600664	+	0.346794i	−0.769303	−	0.638884i	$-0.779396\pi$
$227$	−9.04992	+	5.22497i	−0.600664	+	0.346794i	0.168639	+	0.985678i	$0.446063\pi$
$228$	3.66060	−	2.11345i	0.242429	−	0.139966i
$229$			21.4135i			1.41505i	0.706690	+	0.707523i	$0.250187\pi$
$229$			21.4135i			1.41505i	−0.706690	+	0.707523i	$0.749813\pi$
$230$		0			0
$231$	0.352948	−	0.611324i	0.0232223	−	0.0402222i
$232$	3.44752	+	1.99043i	0.226341	+	0.130678i
$233$	3.24179			0.212377			0.106189	−	0.994346i	$-0.466135\pi$
$233$	3.24179			0.212377			0.106189	+	0.994346i	$0.466135\pi$
$234$	−2.62902	+	7.38951i	−0.171864	+	0.483068i
$235$		0			0
$236$	20.6368	+	11.9147i	1.34334	+	0.775578i
$237$	−5.36585	+	9.29393i	−0.348550	+	0.603706i
$238$	1.81658	+	3.14641i	0.117752	+	0.203952i
$239$			18.3129i			1.18456i	0.805731	+	0.592282i	$0.201773\pi$
$239$			18.3129i			1.18456i	−0.805731	+	0.592282i	$0.798227\pi$
$240$		0			0
$241$	−5.74816	+	3.31870i	−0.370272	+	0.213777i	−0.673577	−	0.739117i	$-0.735243\pi$
$241$	−5.74816	+	3.31870i	−0.370272	+	0.213777i	0.303305	+	0.952893i	$0.401910\pi$
$242$			18.4122i			1.18358i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−13.2942	+	23.0263i	−0.851076	+	1.47411i
$245$		0			0
$246$	13.0973			0.835051
$247$	−5.48641	+	1.00849i	−0.349092	+	0.0641688i
$248$	−9.84915			−0.625422
$249$	7.90509	+	4.56400i	0.500964	+	0.289232i
$250$		0			0
$251$	−9.94081	−	17.2180i	−0.627459	−	1.08679i	−0.988060	−	0.154070i	$-0.950762\pi$
$251$	−9.94081	−	17.2180i	−0.627459	−	1.08679i	0.360601	−	0.932720i	$-0.382571\pi$
$252$		−	1.21106i		−	0.0762893i
$253$	0.973504	−	0.562053i	0.0612037	−	0.0353359i
$254$	26.8474	−	15.5003i	1.68455	−	0.972577i
$255$		0			0
$256$	0.535898	+	0.928203i	0.0334936	+	0.0580127i
$257$	−0.504787	+	0.874316i	−0.0314877	+	0.0545383i	−0.881340	−	0.472483i	$-0.843358\pi$
$257$	−0.504787	+	0.874316i	−0.0314877	+	0.0545383i	0.849852	+	0.527021i	$0.176691\pi$
$258$	−8.89662	−	5.13647i	−0.553880	−	0.319783i
$259$	4.58821			0.285097
$260$		0			0
$261$	2.49983			0.154736
$262$	−18.9056	−	10.9151i	−1.16799	−	0.674339i
$263$	−10.7859	+	18.6818i	−0.665089	+	1.15197i	0.314172	+	0.949366i	$0.398273\pi$
$263$	−10.7859	+	18.6818i	−0.665089	+	1.15197i	−0.979261	+	0.202602i	$0.935060\pi$
$264$	−1.26795	−	2.19615i	−0.0780369	−	0.135164i
$265$		0			0
$266$	1.29200	−	0.745937i	0.0792177	−	0.0457363i
$267$	4.11927	−	2.37826i	0.252095	−	0.145547i
$268$			37.4181i			2.28568i
$269$	2.32534	+	4.02761i	0.141779	+	0.245568i	0.928166	−	0.372165i	$-0.121385\pi$
$269$	2.32534	+	4.02761i	0.141779	+	0.245568i	−0.786388	+	0.617733i	$0.788051\pi$
$270$		0			0
$271$	4.60718	+	2.65996i	0.279866	+	0.161581i	0.633363	−	0.773855i	$-0.281674\pi$
$271$	4.60718	+	2.65996i	0.279866	+	0.161581i	−0.353497	+	0.935436i	$0.615007\pi$
$272$	−7.53556			−0.456910
$273$	−0.535727	+	1.50580i	−0.0324237	+	0.0911350i
$274$	−20.1962			−1.22009
$275$		0			0
$276$	0.964273	−	1.67017i	0.0580424	−	0.100532i
$277$	−4.67974	−	8.10555i	−0.281178	−	0.487015i	0.690497	−	0.723335i	$-0.257392\pi$
$277$	−4.67974	−	8.10555i	−0.281178	−	0.487015i	−0.971675	+	0.236320i	$0.924059\pi$
$278$		−	14.1753i		−	0.850180i
$279$	−5.35628	+	3.09245i	−0.320672	+	0.185140i
$280$		0			0
$281$			13.1449i			0.784161i	0.919931	+	0.392080i	$0.128244\pi$
$281$			13.1449i			0.784161i	−0.919931	+	0.392080i	$0.871756\pi$
$282$	−5.89201	−	10.2053i	−0.350864	−	0.607714i
$283$	1.82184	−	3.15551i	0.108297	−	0.187576i	−0.806783	−	0.590847i	$-0.798794\pi$
$283$	1.82184	−	3.15551i	0.108297	−	0.187576i	0.915080	+	0.403271i	$0.132127\pi$
$284$	35.8425	+	20.6937i	2.12686	+	1.22794i
$285$		0			0
$286$	2.25803	+	12.2842i	0.133520	+	0.726379i
$287$	2.66889			0.157540
$288$	6.52598	+	3.76778i	0.384547	+	0.222018i
$289$	1.40192	−	2.42820i	0.0824661	−	0.142835i
$290$		0			0
$291$			8.41712i			0.493420i
$292$	25.5387	−	14.7448i	1.49454	−	0.862873i
$293$	−17.0043	+	9.81742i	−0.993400	+	0.573540i	−0.906289	−	0.422659i	$-0.861097\pi$
$293$	−17.0043	+	9.81742i	−0.993400	+	0.573540i	−0.0871113	+	0.996199i	$0.527764\pi$
$294$			14.7999i			0.863145i
$295$		0			0
$296$	8.24145	−	14.2746i	0.479025	−	0.829695i
$297$	−1.37910	−	0.796225i	−0.0800236	−	0.0462017i
$298$	0.123763			0.00716941
$299$	−1.93778	+	1.65009i	−0.112064	+	0.0954271i
$300$		0			0
$301$	−1.81291	−	1.04668i	−0.104494	−	0.0603298i
$302$	−18.8170	+	32.5921i	−1.08280	+	1.87546i
$303$	−3.35295	−	5.80748i	−0.192622	−	0.333631i
$304$			3.09430i			0.177470i
$305$		0			0
$306$	7.09808	−	4.09808i	0.405770	−	0.234271i
$307$		−	4.74863i		−	0.271019i	−0.990776	−	0.135509i	$-0.956733\pi$
$307$		−	4.74863i		−	0.271019i	0.990776	−	0.135509i	$-0.0432671\pi$
$308$	−0.964273	−	1.67017i	−0.0549445	−	0.0951667i
$309$	−0.870983	+	1.50859i	−0.0495485	+	0.0858205i
$310$		0			0
$311$	−5.45512			−0.309332			−0.154666	−	0.987967i	$-0.549430\pi$
$311$	−5.45512			−0.309332			−0.154666	+	0.987967i	$0.549430\pi$
$312$	3.72248	+	4.37148i	0.210744	+	0.247486i
$313$	7.23855			0.409147			0.204573	−	0.978851i	$-0.434419\pi$
$313$	7.23855			0.409147			0.204573	+	0.978851i	$0.434419\pi$
$314$	−2.54132	−	1.46723i	−0.143415	−	0.0828008i
$315$		0			0
$316$	14.6598	+	25.3915i	0.824677	+	1.42838i
$317$		−	21.0142i		−	1.18028i	−0.807302	−	0.590138i	$-0.799073\pi$
$317$		−	21.0142i		−	1.18028i	0.807302	−	0.590138i	$-0.200927\pi$
$318$	−10.3923	+	6.00000i	−0.582772	+	0.336463i
$319$	3.44752	−	1.99043i	0.193024	−	0.111443i
$320$		0			0
$321$	5.95932	+	10.3218i	0.332617	+	0.576109i
$322$	0.340338	−	0.589483i	0.0189663	−	0.0328506i
$323$	5.04834	+	2.91466i	0.280897	+	0.162176i
$324$	−2.73205			−0.151781
$325$		0			0
$326$	6.48068			0.358932
$327$	14.7577	+	8.52036i	0.816102	+	0.471177i
$328$	4.79393	−	8.30333i	0.264701	−	0.458475i
$329$	−1.20064	−	2.07957i	−0.0661936	−	0.114651i
$330$		0			0
$331$	−13.4352	+	7.75682i	−0.738466	+	0.426354i	−0.821511	−	0.570192i	$-0.806869\pi$
$331$	−13.4352	+	7.75682i	−0.738466	+	0.426354i	0.0830453	+	0.996546i	$0.473535\pi$
$332$	21.5971	−	12.4691i	1.18529	−	0.684330i
$333$		−	10.3507i		−	0.567212i
$334$	−25.9017	−	44.8631i	−1.41728	−	2.45480i
$335$		0			0
$336$	0.767778	+	0.443277i	0.0418857	+	0.0241827i
$337$	−32.8124			−1.78741			−0.893703	−	0.448660i	$-0.851901\pi$
$337$	−32.8124			−1.78741			−0.893703	+	0.448660i	$0.851901\pi$
$338$	−10.0566	−	26.4307i	−0.547006	−	1.43764i
$339$	3.46410			0.188144
$340$		0			0
$341$	−4.92457	+	8.52961i	−0.266681	+	0.461904i
$342$	−1.68278	−	2.91466i	−0.0909943	−	0.157607i
$343$			6.11878i			0.330383i
$344$	−6.51278	+	3.76016i	−0.351146	+	0.202734i
$345$		0			0
$346$		−	53.6787i		−	2.88579i
$347$	−9.73171	−	16.8558i	−0.522426	−	0.904868i	−0.999660	−	0.0260913i	$-0.991694\pi$
$347$	−9.73171	−	16.8558i	−0.522426	−	0.904868i	0.477234	−	0.878776i	$-0.341639\pi$
$348$	3.41483	−	5.91466i	0.183054	−	0.317059i
$349$	−8.41876	−	4.86057i	−0.450646	−	0.260180i	0.257457	−	0.966290i	$-0.417115\pi$
$349$	−8.41876	−	4.86057i	−0.450646	−	0.260180i	−0.708103	+	0.706109i	$0.750449\pi$
$350$		0			0
$351$	3.39697	+	1.20856i	0.181317	+	0.0645082i
$352$	12.0000			0.639602
$353$	−19.9338	−	11.5088i	−1.06097	−	0.612551i	−0.135269	−	0.990809i	$-0.543190\pi$
$353$	−19.9338	−	11.5088i	−1.06097	−	0.612551i	−0.925700	+	0.378258i	$0.876523\pi$
$354$	9.48675	−	16.4315i	0.504215	−	0.873326i
$355$		0			0
$356$		−	12.9951i		−	0.688737i
$357$	1.44641	−	0.835085i	0.0765521	−	0.0441974i
$358$	5.43479	−	3.13777i	0.287237	−	0.165837i
$359$			10.4131i			0.549584i	0.961504	+	0.274792i	$0.0886090\pi$
$359$			10.4131i			0.549584i	−0.961504	+	0.274792i	$0.911391\pi$
$360$		0			0
$361$	−8.30316	+	14.3815i	−0.437009	+	0.756921i
$362$	13.9612	+	8.06052i	0.733786	+	0.423652i
$363$	8.46410			0.444250
$364$	2.83094	+	3.32450i	0.148381	+	0.174251i
$365$		0			0
$366$	18.3341	+	10.5852i	0.958339	+	0.553297i
$367$	−1.81577	+	3.14500i	−0.0947823	+	0.164168i	−0.909518	−	0.415665i	$-0.863549\pi$
$367$	−1.81577	+	3.14500i	−0.0947823	+	0.164168i	0.814735	+	0.579833i	$0.196882\pi$
$368$	0.705897	+	1.22265i	0.0367974	+	0.0637350i
$369$		−	6.02082i		−	0.313432i
$370$		0			0
$371$	−2.11769	+	1.22265i	−0.109945	+	0.0634768i
$372$			16.8975i			0.876093i
$373$	9.91945	+	17.1810i	0.513609	+	0.889598i	0.999875	+	0.0157867i	$0.00502529\pi$
$373$	9.91945	+	17.1810i	0.513609	+	0.889598i	−0.486266	+	0.873811i	$0.661641\pi$
$374$	6.52598	−	11.3033i	0.337451	−	0.584482i
$375$		0			0
$376$	−8.62650			−0.444878
$377$	−6.86235	+	5.84355i	−0.353429	+	0.300958i
$378$	−0.964273			−0.0495968
$379$	−5.91833	−	3.41695i	−0.304004	−	0.175517i	0.340236	−	0.940340i	$-0.389493\pi$
$379$	−5.91833	−	3.41695i	−0.304004	−	0.175517i	−0.644240	+	0.764823i	$0.722826\pi$
$380$		0			0
$381$	−7.12551	−	12.3418i	−0.365051	−	0.632287i
$382$		−	35.3658i		−	1.80947i
$383$	33.6744	−	19.4419i	1.72068	−	0.993437i	0.803152	−	0.595774i	$-0.203155\pi$
$383$	33.6744	−	19.4419i	1.72068	−	0.993437i	0.917531	−	0.397663i	$-0.130179\pi$
$384$	10.2938	−	5.94311i	0.525301	−	0.303283i
$385$		0			0
$386$	−12.2662	−	21.2456i	−0.624331	−	1.08137i
$387$	−2.36124	+	4.08979i	−0.120029	+	0.207895i
$388$	19.9151	+	11.4980i	1.01104	+	0.583723i
$389$	−8.84881			−0.448652			−0.224326	−	0.974514i	$-0.572018\pi$
$389$	−8.84881			−0.448652			−0.224326	+	0.974514i	$0.572018\pi$
$390$		0			0
$391$	2.65966			0.134505
$392$	9.38273	+	5.41712i	0.473900	+	0.273606i
$393$	−5.01769	+	8.69090i	−0.253109	+	0.438398i
$394$	−26.8293	−	46.4697i	−1.35164	−	2.34111i
$395$		0			0
$396$	−3.76778	+	2.17533i	−0.189338	+	0.109314i
$397$	14.7552	−	8.51890i	0.740541	−	0.427552i	−0.0817250	−	0.996655i	$-0.526043\pi$
$397$	14.7552	−	8.51890i	0.740541	−	0.427552i	0.822266	+	0.569103i	$0.192710\pi$
$398$			48.0119i			2.40662i
$399$	−0.342908	−	0.593934i	−0.0171669	−	0.0297339i
$400$		0			0
$401$	−6.66060	−	3.84550i	−0.332614	−	0.192035i	0.324387	−	0.945924i	$-0.394842\pi$
$401$	−6.66060	−	3.84550i	−0.332614	−	0.192035i	−0.657001	+	0.753890i	$0.728175\pi$
$402$	29.7932			1.48595
$403$	7.47483	−	21.0099i	0.372348	−	1.04658i
$404$	−18.3209			−0.911496
$405$		0			0
$406$	1.20526	−	2.08757i	0.0598160	−	0.103604i
$407$	−8.24145	−	14.2746i	−0.408514	−	0.707566i
$408$		−	6.00000i		−	0.297044i
$409$	7.86637	−	4.54165i	0.388967	−	0.224570i	−0.292746	−	0.956190i	$-0.594569\pi$
$409$	7.86637	−	4.54165i	0.388967	−	0.224570i	0.681712	+	0.731620i	$0.261236\pi$
$410$		0			0
$411$			9.28419i			0.457955i
$412$	2.37957	+	4.12154i	0.117233	+	0.203053i
$413$	1.93316	−	3.34833i	0.0951246	−	0.164761i
$414$	−1.32983	−	0.767778i	−0.0653576	−	0.0377342i
$415$		0			0
$416$	−26.7221	+	4.91196i	−1.31016	+	0.240829i
$417$	−6.51641			−0.319110
$418$	−4.64145	−	2.67974i	−0.227021	−	0.131070i
$419$	6.49534	−	11.2503i	0.317318	−	0.549611i	−0.662609	−	0.748965i	$-0.730551\pi$
$419$	6.49534	−	11.2503i	0.317318	−	0.549611i	0.979928	+	0.199354i	$0.0638844\pi$
$420$		0			0
$421$			19.8859i			0.969178i	0.874742	+	0.484589i	$0.161031\pi$
$421$			19.8859i			0.969178i	−0.874742	+	0.484589i	$0.838969\pi$
$422$	−40.5339	+	23.4022i	−1.97316	+	1.13920i
$423$	−4.69137	+	2.70856i	−0.228102	+	0.131695i
$424$			8.78461i			0.426618i
$425$		0			0
$426$	16.4768	−	28.5387i	0.798305	−	1.38271i
$427$	3.73603	+	2.15700i	0.180799	+	0.104384i
$428$	32.5623			1.57396
$429$	5.64705	−	1.03802i	0.272642	−	0.0501161i
$430$		0			0
$431$	−33.8858	−	19.5640i	−1.63222	−	0.942365i	−0.983405	−	0.181422i	$-0.941930\pi$
$431$	−33.8858	−	19.5640i	−1.63222	−	0.942365i	−0.648818	−	0.760943i	$-0.724737\pi$
$432$	1.00000	−	1.73205i	0.0481125	−	0.0833333i
$433$	−19.0700	−	33.0301i	−0.916444	−	1.58733i	−0.804774	−	0.593581i	$-0.797713\pi$
$433$	−19.0700	−	33.0301i	−0.916444	−	1.58733i	−0.111670	−	0.993745i	$-0.535620\pi$
$434$			5.96393i			0.286278i
$435$		0			0
$436$	40.3188	−	23.2780i	1.93092	−	1.11482i
$437$		−	1.09213i		−	0.0522436i
$438$	−11.7402	−	20.3346i	−0.560967	−	0.971623i
$439$	3.37543	−	5.84641i	0.161100	−	0.279034i	−0.774163	−	0.632986i	$-0.781829\pi$
$439$	3.37543	−	5.84641i	0.161100	−	0.279034i	0.935264	+	0.353952i	$0.115162\pi$
$440$		0			0
$441$	6.80351			0.323976
$442$	−9.90555	+	27.8421i	−0.471159	+	1.32431i
$443$	12.2647			0.582713			0.291357	−	0.956614i	$-0.405893\pi$
$443$	12.2647			0.582713			0.291357	+	0.956614i	$0.405893\pi$
$444$	−24.4899	−	14.1393i	−1.16224	−	0.671020i
$445$		0			0
$446$	23.0982	+	40.0073i	1.09373	+	1.89440i
$447$		−	0.0568941i		−	0.00269100i
$448$	4.75727	−	2.74661i	0.224760	−	0.129765i
$449$	20.2673	−	11.7013i	0.956471	−	0.552219i	0.0613861	−	0.998114i	$-0.480448\pi$
$449$	20.2673	−	11.7013i	0.956471	−	0.552219i	0.895085	+	0.445895i	$0.147115\pi$
$450$		0			0
$451$	−4.79393	−	8.30333i	−0.225737	−	0.390989i
$452$	4.73205	−	8.19615i	0.222577	−	0.385515i
$453$	14.9826	+	8.65021i	0.703944	+	0.406422i
$454$	22.7321			1.06687
$455$		0			0
$456$	−2.46376			−0.115376
$457$	−25.6023	−	14.7815i	−1.19763	−	0.691451i	−0.237602	−	0.971363i	$-0.576361\pi$
$457$	−25.6023	−	14.7815i	−1.19763	−	0.691451i	−0.960026	+	0.279912i	$0.909695\pi$
$458$	23.2907	−	40.3407i	1.08830	−	1.88500i
$459$	−1.88389	−	3.26299i	−0.0879324	−	0.152303i
$460$		0			0
$461$	−8.29218	+	4.78749i	−0.386205	+	0.222976i	−0.680515	−	0.732735i	$-0.738244\pi$
$461$	−8.29218	+	4.78749i	−0.386205	+	0.222976i	0.294309	+	0.955710i	$0.404910\pi$
$462$	−1.32983	+	0.767778i	−0.0618693	+	0.0357203i
$463$		−	20.0241i		−	0.930600i	−0.885153	−	0.465300i	$-0.845946\pi$
$463$		−	20.0241i		−	0.930600i	0.885153	−	0.465300i	$-0.154054\pi$
$464$	2.49983	+	4.32983i	0.116052	+	0.201007i
$465$		0			0
$466$	−6.10718	−	3.52598i	−0.282910	−	0.163338i
$467$	15.7942			0.730868			0.365434	−	0.930837i	$-0.380921\pi$
$467$	15.7942			0.730868			0.365434	+	0.930837i	$0.380921\pi$
$468$	7.49983	−	6.38638i	0.346680	−	0.295211i
$469$	6.07111			0.280338
$470$		0			0
$471$	−0.674489	+	1.16825i	−0.0310788	+	0.0538300i
$472$	−6.94478	−	12.0287i	−0.319660	−	0.553667i
$473$			7.52031i			0.345784i
$474$	20.2173	−	11.6725i	0.928614	−	0.536135i
$475$		0			0
$476$		−	4.56299i		−	0.209144i
$477$	2.75821	+	4.77735i	0.126290	+	0.218740i
$478$	19.9183	−	34.4995i	0.911041	−	1.57797i
$479$	23.1649	+	13.3743i	1.05843	+	0.611086i	0.924998	−	0.379972i	$-0.124066\pi$
$479$	23.1649	+	13.3743i	1.05843	+	0.611086i	0.133434	+	0.991058i	$0.457400\pi$
$480$		0			0
$481$	24.1955	+	28.4139i	1.10322	+	1.29556i
$482$	14.4385			0.657657
$483$	−0.270986	−	0.156454i	−0.0123303	−	0.00711890i
$484$	11.5622	−	20.0263i	0.525554	−	0.910285i
$485$		0			0
$486$			2.17533i			0.0986749i
$487$	−24.5291	+	14.1619i	−1.11152	+	0.641737i	−0.939223	−	0.343307i	$-0.888453\pi$
$487$	−24.5291	+	14.1619i	−1.11152	+	0.641737i	−0.172299	+	0.985045i	$0.555119\pi$
$488$	13.4215	−	7.74890i	0.607563	−	0.350776i
$489$		−	2.97918i		−	0.134723i
$490$		0			0
$491$	4.75009	−	8.22739i	0.214368	−	0.371297i	−0.738709	−	0.674025i	$-0.764564\pi$
$491$	4.75009	−	8.22739i	0.214368	−	0.371297i	0.953077	+	0.302728i	$0.0978974\pi$
$492$	−14.2454	−	8.22460i	−0.642233	−	0.370794i
$493$	9.41880			0.424201
$494$	11.4327	+	4.06748i	0.514381	+	0.183005i
$495$		0			0
$496$	−10.7126	−	6.18490i	−0.481008	−	0.277710i
$497$	3.35756	−	5.81547i	0.150607	−	0.260860i
$498$	−9.92820	−	17.1962i	−0.444893	−	0.770578i
$499$		−	23.1767i		−	1.03753i	−0.854917	−	0.518765i	$-0.826392\pi$
$499$		−	23.1767i		−	1.03753i	0.854917	−	0.518765i	$-0.173608\pi$
$500$		0			0
$501$	−20.6236	+	11.9070i	−0.921394	+	0.531967i
$502$			43.2491i			1.93030i
$503$	−20.1767	−	34.9470i	−0.899633	−	1.55821i	−0.827964	−	0.560782i	$-0.810501\pi$
$503$	−20.1767	−	34.9470i	−0.899633	−	1.55821i	−0.0716692	−	0.997428i	$-0.522833\pi$
$504$	−0.352948	+	0.611324i	−0.0157216	+	0.0272306i
$505$		0			0
$506$	−2.44530			−0.108707
$507$	−12.1502	+	4.62302i	−0.539610	+	0.205315i
$508$	−38.9345			−1.72744
$509$	−8.91466	−	5.14688i	−0.395135	−	0.228131i	0.289248	−	0.957254i	$-0.406595\pi$
$509$	−8.91466	−	5.14688i	−0.395135	−	0.228131i	−0.684383	+	0.729123i	$0.739928\pi$
$510$		0			0
$511$	−2.39235	−	4.14367i	−0.105831	−	0.183305i
$512$			21.4409i			0.947564i
$513$	−1.33987	+	0.773575i	−0.0591568	+	0.0341542i
$514$	1.90192	−	1.09808i	0.0838903	−	0.0484341i
$515$		0			0
$516$	6.45102	+	11.1735i	0.283991	+	0.491886i
$517$	−4.31325	+	7.47077i	−0.189697	+	0.328564i
$518$	−8.64367	−	4.99043i	−0.379781	−	0.219267i
$519$	−24.6762			−1.08316
$520$		0			0
$521$	43.7218			1.91549			0.957743	−	0.287624i	$-0.0928655\pi$
$521$	43.7218			1.91549			0.957743	+	0.287624i	$0.0928655\pi$
$522$	−4.70940	−	2.71897i	−0.206125	−	0.119006i
$523$	3.59778	−	6.23154i	0.157320	−	0.272486i	−0.776581	−	0.630017i	$-0.783048\pi$
$523$	3.59778	−	6.23154i	0.157320	−	0.272486i	0.933901	+	0.357531i	$0.116381\pi$
$524$	13.7086	+	23.7440i	0.598863	+	1.03726i
$525$		0			0
$526$	40.6390	−	23.4630i	1.77195	−	1.02303i
$527$	−20.1813	+	11.6517i	−0.879110	+	0.507555i
$528$		−	3.18490i		−	0.138605i
$529$	11.2509	+	19.4871i	0.489168	+	0.847263i
$530$		0			0
$531$	−7.55359	−	4.36107i	−0.327798	−	0.189254i
$532$	−1.87368			−0.0812345
$533$	14.0741	+	16.5279i	0.609619	+	0.715904i
$534$	−10.3470			−0.447759
$535$		0			0
$536$	10.9051	−	18.8882i	0.471028	−	0.815844i
$537$	−1.44244	−	2.49838i	−0.0622458	−	0.107813i
$538$		−	10.1168i		−	0.436164i
$539$	9.38273	−	5.41712i	0.404143	−	0.233332i
$540$		0			0
$541$		−	24.7159i		−	1.06262i	−0.847177	−	0.531310i	$-0.821700\pi$
$541$		−	24.7159i		−	1.06262i	0.847177	−	0.531310i	$-0.178300\pi$
$542$	−5.78628	−	10.0221i	−0.248542	−	0.430487i
$543$	3.70543	−	6.41799i	0.159015	−	0.275422i
$544$	24.5885	+	14.1962i	1.05422	+	0.608655i
$545$		0			0
$546$	2.64705	−	2.25406i	0.113283	−	0.0964650i
$547$	6.97187			0.298096			0.149048	−	0.988830i	$-0.452379\pi$
$547$	6.97187			0.298096			0.149048	+	0.988830i	$0.452379\pi$
$548$	21.9666	+	12.6824i	0.938368	+	0.541767i
$549$	4.86603	−	8.42820i	0.207677	−	0.359707i
$550$		0			0
$551$		−	3.86761i		−	0.164766i
$552$	−0.973504	+	0.562053i	−0.0414351	+	0.0239225i
$553$	4.11979	−	2.37856i	0.175191	−	0.101147i
$554$			20.3599i			0.865011i
$555$		0			0
$556$	−8.90158	+	15.4180i	−0.377511	+	0.653869i
$557$	1.45124	+	0.837875i	0.0614911	+	0.0355019i	0.530430	−	0.847729i	$-0.322030\pi$
$557$	1.45124	+	0.837875i	0.0614911	+	0.0355019i	−0.468939	+	0.883230i	$0.655364\pi$
$558$	13.4542			0.569561
$559$	−3.07829	−	16.7466i	−0.130198	−	0.708304i
$560$		0			0
$561$	−5.19615	−	3.00000i	−0.219382	−	0.126660i
$562$	14.2973	−	24.7636i	0.603094	−	1.04459i
$563$	−1.02615	−	1.77735i	−0.0432472	−	0.0749064i	0.843592	−	0.536985i	$-0.180437\pi$
$563$	−1.02615	−	1.77735i	−0.0432472	−	0.0749064i	−0.886839	+	0.462079i	$0.847104\pi$
$564$			14.7999i			0.623186i
$565$		0			0
$566$	−6.86428	+	3.96309i	−0.288527	+	0.166581i
$567$			0.443277i			0.0186159i
$568$	−12.0619	−	20.8918i	−0.506105	−	0.876600i
$569$	−20.6095	+	35.6968i	−0.863996	+	1.49649i	0.00404386	+	0.999992i	$0.498713\pi$
$569$	−20.6095	+	35.6968i	−0.863996	+	1.49649i	−0.868040	+	0.496494i	$0.834621\pi$
$570$		0			0
$571$	−30.7115			−1.28524			−0.642619	−	0.766186i	$-0.722152\pi$
$571$	−30.7115			−1.28524			−0.642619	+	0.766186i	$0.722152\pi$
$572$	5.25803	−	14.7790i	0.219849	−	0.617942i
$573$	−16.2577			−0.679175
$574$	−5.02790	−	2.90286i	−0.209860	−	0.121163i
$575$		0			0
$576$	−6.19615	−	10.7321i	−0.258173	−	0.447169i
$577$			44.8752i			1.86818i	0.357038	+	0.934090i	$0.383787\pi$
$577$			44.8752i			1.86818i	−0.357038	+	0.934090i	$0.616213\pi$
$578$	−5.28214	+	3.04964i	−0.219708	+	0.126848i
$579$	−9.76662	+	5.63876i	−0.405887	+	0.234339i
$580$		0			0
$581$	−2.02312	−	3.50414i	−0.0839331	−	0.145376i
$582$	9.15500	−	15.8569i	0.379487	−	0.657291i
$583$	7.60770	+	4.39230i	0.315079	+	0.181911i
$584$	−17.1888			−0.711278
$585$		0			0
$586$	42.7122			1.76443
$587$	20.6735	+	11.9359i	0.853287	+	0.492645i	0.861759	−	0.507319i	$-0.169363\pi$
$587$	20.6735	+	11.9359i	0.853287	+	0.492645i	−0.00847155	+	0.999964i	$0.502697\pi$
$588$	9.29376	−	16.0973i	0.383268	−	0.663840i
$589$	4.78448	+	8.28697i	0.197141	+	0.341459i
$590$		0			0
$591$	−21.3622	+	12.3335i	−0.878723	+	0.507331i
$592$	17.9279	−	10.3507i	0.736831	−	0.425409i
$593$			26.8263i			1.10162i	0.834630	+	0.550811i	$0.185682\pi$
$593$			26.8263i			1.10162i	−0.834630	+	0.550811i	$0.814318\pi$
$594$	1.73205	+	3.00000i	0.0710669	+	0.123091i
$595$		0			0
$596$	−0.134613	−	0.0777187i	−0.00551396	−	0.00318348i
$597$	22.0711			0.903311
$598$	5.44530	−	1.00093i	0.222675	−	0.0409313i
$599$	−26.4919			−1.08243			−0.541215	−	0.840885i	$-0.682035\pi$
$599$	−26.4919			−1.08243			−0.541215	+	0.840885i	$0.682035\pi$
$600$		0			0
$601$	−11.6145	+	20.1169i	−0.473765	+	0.820585i	−0.999549	−	0.0300334i	$-0.990439\pi$
$601$	−11.6145	+	20.1169i	−0.473765	+	0.820585i	0.525784	+	0.850618i	$0.323772\pi$
$602$	2.27688	+	3.94367i	0.0927986	+	0.160732i
$603$		−	13.6960i		−	0.557743i
$604$	40.9333	−	23.6328i	1.66555	−	0.961606i
$605$		0			0
$606$			14.5875i			0.592578i
$607$	5.29060	+	9.16359i	0.214739	+	0.371939i	0.953192	−	0.302366i	$-0.0977766\pi$
$607$	5.29060	+	9.16359i	0.214739	+	0.371939i	−0.738453	+	0.674305i	$0.764443\pi$
$608$	5.82932	−	10.0967i	0.236410	−	0.409474i
$609$	−0.959657	−	0.554058i	−0.0388873	−	0.0224516i
$610$		0			0
$611$	6.54693	−	18.4018i	0.264860	−	0.744456i
$612$	−10.2938			−0.416101
$613$	−5.47099	−	3.15868i	−0.220971	−	0.127578i	0.385429	−	0.922738i	$-0.374054\pi$
$613$	−5.47099	−	3.15868i	−0.220971	−	0.127578i	−0.606400	+	0.795160i	$0.707387\pi$
$614$	−5.16492	+	8.94590i	−0.208439	+	0.361027i
$615$		0			0
$616$			1.12411i			0.0452915i
$617$	−28.3430	+	16.3639i	−1.14105	+	0.658784i	−0.946690	−	0.322147i	$-0.895596\pi$
$617$	−28.3430	+	16.3639i	−1.14105	+	0.658784i	−0.194358	+	0.980931i	$0.562262\pi$
$618$	3.28167	−	1.89467i	0.132008	−	0.0762149i
$619$			21.0143i			0.844635i	0.906448	+	0.422317i	$0.138783\pi$
$619$			21.0143i			0.844635i	−0.906448	+	0.422317i	$0.861217\pi$
$620$		0			0
$621$	−0.352948	+	0.611324i	−0.0141633	+	0.0245316i
$622$	10.2768	+	5.93334i	0.412064	+	0.237905i
$623$	−2.10846			−0.0844736
$624$	1.30368	+	7.09228i	0.0521888	+	0.283918i
$625$		0			0
$626$	−13.6366	−	7.87310i	−0.545029	−	0.314673i
$627$	−1.23188	+	2.13368i	−0.0491965	+	0.0852109i
$628$	1.84274	+	3.19171i	0.0735332	+	0.127363i
$629$		−	38.9990i		−	1.55499i
$630$		0			0
$631$	13.4803	−	7.78285i	0.536642	−	0.309830i	−0.207075	−	0.978325i	$-0.566394\pi$
$631$	13.4803	−	7.78285i	0.536642	−	0.309830i	0.743717	+	0.668495i	$0.233061\pi$
$632$		−	17.0897i		−	0.679792i
$633$	10.7580	+	18.6335i	0.427593	+	0.740614i
$634$	−22.8564	+	39.5885i	−0.907744	+	1.57226i
$635$		0			0
$636$	15.0711			0.597608
$637$	−18.6765	+	15.9037i	−0.739990	+	0.630129i
$638$	−8.65966			−0.342839
$639$	−13.1193	−	7.57442i	−0.518990	−	0.299639i
$640$		0			0
$641$	6.89551	+	11.9434i	0.272356	+	0.471735i	0.969465	−	0.245231i	$-0.0788637\pi$
$641$	6.89551	+	11.9434i	0.272356	+	0.471735i	−0.697108	+	0.716966i	$0.745530\pi$
$642$		−	25.9269i		−	1.02325i
$643$	−23.9628	+	13.8349i	−0.945000	+	0.545596i	−0.891524	−	0.452973i	$-0.850363\pi$
$643$	−23.9628	+	13.8349i	−0.945000	+	0.545596i	−0.0534755	+	0.998569i	$0.517030\pi$
$644$	−0.740347	+	0.427440i	−0.0291738	+	0.0168435i
$645$		0			0
$646$	−6.34034	−	10.9818i	−0.249457	−	0.432073i
$647$	17.9147	−	31.0291i	0.704298	−	1.21988i	−0.262646	−	0.964892i	$-0.584595\pi$
$647$	17.9147	−	31.0291i	0.704298	−	1.21988i	0.966944	−	0.254988i	$-0.0820714\pi$
$648$	1.37910	+	0.796225i	0.0541763	+	0.0312787i
$649$	−13.8896			−0.545213
$650$		0			0
$651$	2.74162			0.107453
$652$	−7.04880	−	4.06963i	−0.276052	−	0.159379i
$653$	−22.6153	+	39.1708i	−0.885003	+	1.53287i	−0.0392935	+	0.999228i	$0.512511\pi$
$653$	−22.6153	+	39.1708i	−0.885003	+	1.53287i	−0.845710	+	0.533643i	$0.820823\pi$
$654$	−18.5346	−	32.1028i	−0.724759	−	1.25532i
$655$		0			0
$656$	10.4284	−	6.02082i	0.407160	−	0.235074i
$657$	−9.34782	+	5.39697i	−0.364693	+	0.210556i
$658$			5.22358i			0.203636i
$659$	1.18658	+	2.05522i	0.0462226	+	0.0800598i	0.888211	−	0.459436i	$-0.151948\pi$
$659$	1.18658	+	2.05522i	0.0462226	+	0.0800598i	−0.841988	+	0.539496i	$0.818615\pi$
$660$		0			0
$661$	11.4110	+	6.58816i	0.443838	+	0.256250i	0.705224	−	0.708984i	$-0.250846\pi$
$661$	11.4110	+	6.58816i	0.443838	+	0.256250i	−0.261386	+	0.965234i	$0.584180\pi$
$662$	33.7473			1.31162
$663$	12.7990	+	4.55359i	0.497073	+	0.176847i
$664$	−14.5359			−0.564102
$665$		0			0
$666$	−11.2580	+	19.4995i	−0.436240	+	0.755590i
$667$	−0.882310	−	1.52821i	−0.0341632	−	0.0591724i
$668$			65.0613i			2.51730i
$669$	18.3914	−	10.6183i	0.711051	−	0.410526i
$670$		0			0
$671$		−	15.4978i		−	0.598286i
$672$	−1.67017	−	2.89282i	−0.0644282	−	0.111593i
$673$	−6.39346	+	11.0738i	−0.246450	+	0.426864i	−0.962538	−	0.271146i	$-0.912597\pi$
$673$	−6.39346	+	11.0738i	−0.246450	+	0.426864i	0.716088	+	0.698010i	$0.245931\pi$
$674$	61.8149	+	35.6889i	2.38102	+	1.37468i
$675$		0			0
$676$	−5.65932	+	35.0629i	−0.217666	+	1.34857i
$677$	−16.0794			−0.617981			−0.308991	−	0.951065i	$-0.599991\pi$
$677$	−16.0794			−0.617981			−0.308991	+	0.951065i	$0.599991\pi$
$678$	−6.52598	−	3.76778i	−0.250629	−	0.144701i
$679$	1.86556	−	3.23124i	0.0715936	−	0.124004i
$680$		0			0
$681$		−	10.4499i		−	0.400443i
$682$	18.5547	−	10.7126i	0.710496	−	0.410205i
$683$	5.46602	−	3.15581i	0.209152	−	0.120754i	−0.391765	−	0.920065i	$-0.628136\pi$
$683$	5.46602	−	3.15581i	0.209152	−	0.120754i	0.600917	+	0.799311i	$0.294802\pi$
$684$			4.22689i			0.161619i
$685$		0			0
$686$	6.65517	−	11.5271i	0.254096	−	0.440107i
$687$	−18.5447	−	10.7068i	−0.707523	−	0.408489i
$688$	−9.44496			−0.360086
$689$	−18.7391	−	6.66692i	−0.713901	−	0.253989i
$690$		0			0
$691$	−31.7955	−	18.3572i	−1.20956	−	0.698339i	−0.246896	−	0.969042i	$-0.579410\pi$
$691$	−31.7955	−	18.3572i	−1.20956	−	0.698339i	−0.962663	+	0.270703i	$0.912744\pi$
$692$	−33.7082	+	58.3844i	−1.28140	+	2.21944i
$693$	0.352948	+	0.611324i	0.0134074	+	0.0232223i
$694$			42.3393i			1.60718i
$695$		0			0
$696$	−3.44752	+	1.99043i	−0.130678	+	0.0754469i
$697$		−	22.6851i		−	0.859261i
$698$	10.5733	+	18.3136i	0.400207	+	0.693178i
$699$	−1.62090	+	2.80748i	−0.0613080	+	0.106189i
$700$		0			0
$701$	52.0509			1.96594			0.982968	−	0.183774i	$-0.0588316\pi$
$701$	52.0509			1.96594			0.982968	+	0.183774i	$0.0588316\pi$
$702$	−5.08500	−	5.97155i	−0.191921	−	0.225382i
$703$	−16.0140			−0.603980
$704$	−17.0903	−	9.86707i	−0.644113	−	0.371879i
$705$		0			0
$706$	25.0354	+	43.3626i	0.942219	+	1.63197i
$707$			2.97257i			0.111795i
$708$	−20.6368	+	11.9147i	−0.775578	+	0.447780i
$709$	0.810685	−	0.468049i	0.0304459	−	0.0175779i	−0.484700	−	0.874681i	$-0.661071\pi$
$709$	0.810685	−	0.468049i	0.0304459	−	0.0175779i	0.515146	+	0.857103i	$0.327738\pi$
$710$		0			0
$711$	−5.36585	−	9.29393i	−0.201235	−	0.348550i
$712$	−3.78727	+	6.55974i	−0.141934	+	0.245837i
$713$	3.78098	+	2.18295i	0.141599	+	0.0817521i
$714$	−3.63317			−0.135968
$715$		0			0
$716$	−7.88163			−0.294550
$717$	−15.8594	−	9.15645i	−0.592282	−	0.341954i
$718$	11.3260	−	19.6172i	0.422682	−	0.732107i
$719$	0.498717	+	0.863804i	0.0185990	+	0.0322145i	0.875175	−	0.483806i	$-0.160746\pi$
$719$	0.498717	+	0.863804i	0.0185990	+	0.0322145i	−0.856576	+	0.516021i	$0.827413\pi$
$720$		0			0
$721$	0.668722	−	0.386087i	0.0249045	−	0.0143786i
$722$	31.2845	−	18.0621i	1.16429	−	0.672202i
$723$		−	6.63741i		−	0.246848i
$724$	−10.1234	−	17.5343i	−0.376234	−	0.651656i
$725$		0			0
$726$	−15.9454	−	9.20610i	−0.591790	−	0.341670i
$727$	15.4879			0.574416			0.287208	−	0.957868i	$-0.407273\pi$
$727$	15.4879			0.574416			0.287208	+	0.957868i	$0.407273\pi$
$728$	−0.460130	−	2.50321i	−0.0170536	−	0.0927751i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−8.89662	+	15.4094i	−0.329054	+	0.569937i
$732$	−13.2942	−	23.0263i	−0.491369	−	0.851076i
$733$		−	3.34533i		−	0.123562i	−0.998090	−	0.0617812i	$-0.980322\pi$
$733$		−	3.34533i		−	0.123562i	0.998090	−	0.0617812i	$-0.0196781\pi$
$734$	6.84141	−	3.94989i	0.252521	−	0.145793i
$735$		0			0
$736$		−	5.31932i		−	0.196073i
$737$	−10.9051	−	18.8882i	−0.401694	−	0.695754i
$738$	−6.54863	+	11.3426i	−0.241059	+	0.417526i
$739$	−11.3394	−	6.54681i	−0.417127	−	0.240828i	0.276721	−	0.960950i	$-0.410752\pi$
$739$	−11.3394	−	6.54681i	−0.417127	−	0.240828i	−0.693847	+	0.720122i	$0.744086\pi$
$740$		0			0
$741$	1.86983	−	5.25562i	0.0686898	−	0.193070i
$742$	5.31932			0.195279
$743$	−4.39398	−	2.53686i	−0.161199	−	0.0930685i	0.417230	−	0.908801i	$-0.363001\pi$
$743$	−4.39398	−	2.53686i	−0.161199	−	0.0930685i	−0.578430	+	0.815732i	$0.696334\pi$
$744$	4.92457	−	8.52961i	0.180544	−	0.312711i
$745$		0			0
$746$		−	43.1561i		−	1.58006i
$747$	−7.90509	+	4.56400i	−0.289232	+	0.166988i
$748$	−14.1962	+	8.19615i	−0.519063	+	0.299681i
$749$		−	5.28325i		−	0.193046i
$750$		0			0
$751$	9.51688	−	16.4837i	0.347276	−	0.601499i	−0.638489	−	0.769631i	$-0.720440\pi$
$751$	9.51688	−	16.4837i	0.347276	−	0.601499i	0.985765	+	0.168132i	$0.0537734\pi$
$752$	−9.38273	−	5.41712i	−0.342153	−	0.197542i
$753$	19.8816			0.724527
$754$	19.2837	−	3.54466i	0.702272	−	0.129089i
$755$		0			0
$756$	1.04880	+	0.605528i	0.0381447	+	0.0220228i
$757$	22.4044	−	38.8056i	0.814303	−	1.41042i	−0.0955235	−	0.995427i	$-0.530452\pi$
$757$	22.4044	−	38.8056i	0.814303	−	1.41042i	0.909827	−	0.414988i	$-0.136214\pi$
$758$	7.43299	+	12.8743i	0.269978	+	0.467616i
$759$			1.12411i			0.0408024i
$760$		0			0
$761$	32.8763	−	18.9811i	1.19176	−	0.688065i	0.233058	−	0.972463i	$-0.425127\pi$
$761$	32.8763	−	18.9811i	1.19176	−	0.688065i	0.958706	+	0.284398i	$0.0917936\pi$
$762$			31.0007i			1.12304i
$763$	−3.77688	−	6.54174i	−0.136732	−	0.236827i
$764$	−22.2084	+	38.4661i	−0.803472	+	1.39166i
$765$		0			0
$766$	−84.5852			−3.05619
$767$	30.9299	−	5.68542i	1.11681	−	0.205289i
$768$	−1.07180			−0.0386751
$769$	21.5337	+	12.4325i	0.776525	+	0.448327i	0.835197	−	0.549950i	$-0.185353\pi$
$769$	21.5337	+	12.4325i	0.776525	+	0.448327i	−0.0586721	+	0.998277i	$0.518687\pi$
$770$		0			0
$771$	−0.504787	−	0.874316i	−0.0181794	−	0.0314877i
$772$			30.8108i			1.10890i
$773$	25.3768	−	14.6513i	0.912740	−	0.526970i	0.0314280	−	0.999506i	$-0.489995\pi$
$773$	25.3768	−	14.6513i	0.912740	−	0.526970i	0.881312	+	0.472536i	$0.156661\pi$
$774$	8.89662	−	5.13647i	0.319783	−	0.184627i
$775$		0			0
$776$	−6.70193	−	11.6081i	−0.240585	−	0.416706i
$777$	−2.29410	+	3.97350i	−0.0823005	+	0.142549i
$778$	16.6702	+	9.62453i	0.597655	+	0.345056i
$779$	−9.31512			−0.333749
$780$		0			0
$781$	−24.1238			−0.863216
$782$	−5.01051	−	2.89282i	−0.179175	−	0.103447i
$783$	−1.24991	+	2.16492i	−0.0446683	+	0.0773678i
$784$	6.80351	+	11.7840i	0.242982	+	0.420858i
$785$		0			0
$786$	18.9056	−	10.9151i	0.674339	−	0.389330i
$787$	−9.24064	+	5.33508i	−0.329393	+	0.190175i	−0.655572	−	0.755133i	$-0.727572\pi$
$787$	−9.24064	+	5.33508i	−0.329393	+	0.190175i	0.326179	+	0.945308i	$0.394239\pi$
$788$			67.3913i			2.40071i
$789$	−10.7859	−	18.6818i	−0.383990	−	0.665089i
$790$		0			0
$791$	−1.32983	−	0.767778i	−0.0472833	−	0.0272990i
$792$	2.53590			0.0901092
$793$	6.34372	+	34.5112i	0.225272	+	1.22553i
$794$	−37.0628			−1.31531
$795$		0			0
$796$	30.1497	−	52.2208i	1.06863	−	1.85092i
$797$	−9.44000	−	16.3506i	−0.334382	−	0.579166i	0.648984	−	0.760802i	$-0.275194\pi$
$797$	−9.44000	−	16.3506i	−0.334382	−	0.579166i	−0.983366	+	0.181636i	$0.941861\pi$
$798$			1.49187i			0.0528118i
$799$	−17.6760	+	10.2053i	−0.625333	+	0.361036i
$800$		0			0
$801$			4.75653i			0.168064i
$802$	8.36522	+	14.4890i	0.295386	+	0.511624i
$803$	−8.59440	+	14.8859i	−0.303290	+	0.525313i
$804$	−32.4050	−	18.7091i	−1.14284	−	0.659818i
$805$		0			0
$806$	−36.9335	+	31.4502i	−1.30093	+	1.10779i
$807$	−4.65068			−0.163712
$808$	9.24812	+	5.33940i	0.325348	+	0.187840i
$809$	−21.8102	+	37.7763i	−0.766805	+	1.32814i	0.172482	+	0.985013i	$0.444821\pi$
$809$	−21.8102	+	37.7763i	−0.766805	+	1.32814i	−0.939287	+	0.343132i	$0.888512\pi$
$810$		0			0
$811$		−	3.31656i		−	0.116460i	−0.998303	−	0.0582301i	$-0.981454\pi$
$811$		−	3.31656i		−	0.116460i	0.998303	−	0.0582301i	$-0.0185457\pi$
$812$	−2.62183	+	1.51372i	−0.0920083	+	0.0531210i
$813$	−4.60718	+	2.65996i	−0.161581	+	0.0932888i
$814$			35.8557i			1.25674i
$815$		0			0
$816$	3.76778	−	6.52598i	0.131899	−	0.228455i
$817$	6.32751	+	3.65319i	0.221372	+	0.127809i
$818$	−19.7592			−0.690863
$819$	−1.03619	−	1.21685i	−0.0362076	−	0.0425202i
$820$		0			0
$821$	6.24179	+	3.60370i	0.217840	+	0.125770i	0.604950	−	0.796264i	$-0.293193\pi$
$821$	6.24179	+	3.60370i	0.217840	+	0.125770i	−0.387110	+	0.922034i	$0.626527\pi$
$822$	10.0981	−	17.4904i	0.352211	−	0.610047i
$823$	−4.90146	−	8.48957i	−0.170854	−	0.295928i	0.767865	−	0.640612i	$-0.221319\pi$
$823$	−4.90146	−	8.48957i	−0.170854	−	0.295928i	−0.938719	+	0.344684i	$0.887986\pi$
$824$		−	2.77399i		−	0.0966367i
$825$		0			0
$826$	−7.28372	+	4.20526i	−0.253433	+	0.146320i
$827$			3.92322i			0.136424i	0.997671	+	0.0682118i	$0.0217294\pi$
$827$			3.92322i			0.136424i	−0.997671	+	0.0682118i	$0.978271\pi$
$828$	0.964273	+	1.67017i	0.0335108	+	0.0580424i
$829$	5.21210	−	9.02761i	0.181024	−	0.313542i	−0.761206	−	0.648510i	$-0.775392\pi$
$829$	5.21210	−	9.02761i	0.181024	−	0.313542i	0.942229	+	0.334968i	$0.108726\pi$
$830$		0			0
$831$	9.35948			0.324677
$832$	42.0962	+	14.9769i	1.45942	+	0.519229i
$833$	25.6341			0.888169
$834$	12.2762	+	7.08766i	0.425090	+	0.245426i
$835$		0			0
$836$	3.36556	+	5.82932i	0.116400	+	0.201611i
$837$		−	6.18490i		−	0.213781i
$838$	−24.4730	+	14.1295i	−0.845406	+	0.488095i
$839$	−8.87859	+	5.12606i	−0.306523	+	0.176971i	−0.645369	−	0.763871i	$-0.723297\pi$
$839$	−8.87859	+	5.12606i	−0.306523	+	0.176971i	0.338847	+	0.940842i	$0.389963\pi$
$840$		0			0
$841$	11.3754	+	19.7028i	0.392256	+	0.679408i
$842$	21.6291	−	37.4628i	0.745389	−	1.29105i
$843$	−11.3838	−	6.57246i	−0.392080	−	0.226368i
$844$	58.7830			2.02339
$845$		0			0
$846$	11.7840			0.405143
$847$	−3.24928	−	1.87597i	−0.111646	−	0.0644591i
$848$	−5.51641	+	9.55470i	−0.189434	+	0.328110i
$849$	1.82184	+	3.15551i	0.0625253	+	0.108297i
$850$		0			0
$851$	−6.32761	+	3.65325i	−0.216908	+	0.125232i
$852$	−35.8425	+	20.6937i	−1.22794	+	0.708954i
$853$			26.3671i			0.902792i	0.892324	+	0.451396i	$0.149074\pi$
$853$			26.3671i			0.902792i	−0.892324	+	0.451396i	$0.850926\pi$
$854$	−4.69218	−	8.12709i	−0.160563	−	0.278103i
$855$		0			0
$856$	−16.4370	−	9.48991i	−0.561806	−	0.324359i
$857$	1.04855			0.0358178			0.0179089	−	0.999840i	$-0.494299\pi$
$857$	1.04855			0.0358178			0.0179089	+	0.999840i	$0.494299\pi$
$858$	−11.7674	−	4.18658i	−0.401734	−	0.142927i
$859$	−19.6076			−0.669003			−0.334501	−	0.942395i	$-0.608568\pi$
$859$	−19.6076			−0.669003			−0.334501	+	0.942395i	$0.608568\pi$
$860$		0			0
$861$	−1.33445	+	2.31133i	−0.0454778	+	0.0787699i
$862$	42.5581	+	73.7128i	1.44954	+	2.51067i
$863$		−	25.6925i		−	0.874582i	−0.899320	−	0.437291i	$-0.855938\pi$
$863$		−	25.6925i		−	0.874582i	0.899320	−	0.437291i	$-0.144062\pi$
$864$	−6.52598	+	3.76778i	−0.222018	+	0.128182i
$865$		0			0
$866$			82.9668i			2.81933i
$867$	1.40192	+	2.42820i	0.0476118	+	0.0824661i
$868$	3.74513	−	6.48675i	0.127118	−	0.220175i
$869$	−14.8001	−	8.54486i	−0.502060	−	0.289864i
$870$		0			0
$871$	32.0154	+	37.5972i	1.08480	+	1.27393i
$872$	−27.1365			−0.918958
$873$	−7.28944	−	4.20856i	−0.246710	−	0.142438i
$874$	−1.18787	+	2.05745i	−0.0401802	+	0.0695942i
$875$		0			0
$876$			29.4896i			0.996360i
$877$	31.5356	−	18.2071i	1.06488	−	0.614809i	0.138102	−	0.990418i	$-0.455900\pi$
$877$	31.5356	−	18.2071i	1.06488	−	0.614809i	0.926778	+	0.375609i	$0.122567\pi$
$878$	−12.7179	+	7.34266i	−0.429207	+	0.247803i
$879$		−	19.6348i		−	0.662267i
$880$		0			0
$881$	8.01915	−	13.8896i	0.270172	−	0.467951i	−0.698734	−	0.715382i	$-0.746253\pi$
$881$	8.01915	−	13.8896i	0.270172	−	0.467951i	0.968906	+	0.247430i	$0.0795861\pi$
$882$	−12.8170	−	7.39993i	−0.431573	−	0.249169i
$883$	27.4548			0.923927			0.461963	−	0.886899i	$-0.347145\pi$
$883$	27.4548			0.923927			0.461963	+	0.886899i	$0.347145\pi$
$884$	28.2577	−	24.0625i	0.950409	−	0.809309i
$885$		0			0
$886$	−23.1053	−	13.3399i	−0.776239	−	0.448162i
$887$	−15.9821	+	27.6818i	−0.536626	+	0.929464i	0.462457	+	0.886642i	$0.346968\pi$
$887$	−15.9821	+	27.6818i	−0.536626	+	0.929464i	−0.999083	+	0.0428217i	$0.986365\pi$
$888$	8.24145	+	14.2746i	0.276565	+	0.479025i
$889$			6.31715i			0.211870i
$890$		0			0
$891$	1.37910	−	0.796225i	0.0462017	−	0.0266745i
$892$		−	58.0193i		−	1.94263i
$893$	4.19055	+	7.25825i	0.140231	+	0.242888i
$894$	−0.0618816	+	0.107182i	−0.00206963	+	0.00358471i
$895$		0			0
$896$	−5.26888			−0.176021
$897$	−0.460130	−	2.50321i	−0.0153633	−	0.0835797i
$898$	−50.9084			−1.69883
$899$	13.3898	+	7.73060i	0.446574	+	0.257830i
$900$		0			0
$901$	10.3923	+	18.0000i	0.346218	+	0.599667i
$902$			20.8567i			0.694454i
$903$	1.81291	−	1.04668i	0.0603298	−	0.0348314i
$904$	−4.77735	+	2.75821i	−0.158892	+	0.0917365i
$905$		0			0
$906$	−18.8170	−	32.5921i	−0.625155	−	1.08280i
$907$	−15.8398	+	27.4354i	−0.525953	+	0.910977i	0.473590	+	0.880745i	$0.342958\pi$
$907$	−15.8398	+	27.4354i	−0.525953	+	0.910977i	−0.999543	+	0.0302317i	$0.990375\pi$
$908$	−24.7248	−	14.2749i	−0.820522	−	0.473729i
$909$	6.70590			0.222421
$910$		0			0
$911$	−25.9227			−0.858858			−0.429429	−	0.903101i	$-0.641285\pi$
$911$	−25.9227			−0.858858			−0.429429	+	0.903101i	$0.641285\pi$
$912$	−2.67974	−	1.54715i	−0.0887351	−	0.0512313i
$913$	−7.26795	+	12.5885i	−0.240534	+	0.416617i
$914$	32.1547	+	55.6935i	1.06358	+	1.84218i
$915$		0			0
$916$	−50.6650	+	29.2514i	−1.67402	+	0.966494i
$917$	3.85247	−	2.22423i	0.127220	−	0.0734505i
$918$			8.19615i			0.270513i
$919$	6.00970	+	10.4091i	0.198242	+	0.343365i	0.947958	−	0.318394i	$-0.103144\pi$
$919$	6.00970	+	10.4091i	0.198242	+	0.343365i	−0.749717	+	0.661759i	$0.769810\pi$
$920$		0			0
$921$	4.11244	+	2.37432i	0.135509	+	0.0782364i
$922$	20.8287			0.685958
$923$	53.7199	−	9.87459i	1.76821	−	0.325026i
$924$	1.92855			0.0634445
$925$		0			0
$926$	−21.7795	+	37.7232i	−0.715720	+	1.23966i
$927$	−0.870983	−	1.50859i	−0.0286068	−	0.0495485i
$928$		−	18.8376i		−	0.618375i
$929$	−18.4962	+	10.6788i	−0.606842	+	0.350360i	−0.771728	−	0.635952i	$-0.780608\pi$
$929$	−18.4962	+	10.6788i	−0.606842	+	0.350360i	0.164887	+	0.986313i	$0.447274\pi$
$930$		0			0
$931$		−	10.5260i		−	0.344977i
$932$	4.42837	+	7.67017i	0.145056	+	0.251245i
$933$	2.72756	−	4.72427i	0.0892963	−	0.154666i
$934$	−29.7545	−	17.1788i	−0.973597	−	0.562106i
$935$		0			0
$936$	−5.64705	+	1.03802i	−0.184580	+	0.0339288i
$937$	−15.8029			−0.516259			−0.258129	−	0.966110i	$-0.583106\pi$
$937$	−15.8029			−0.516259			−0.258129	+	0.966110i	$0.583106\pi$
$938$	−11.4373	−	6.60333i	−0.373441	−	0.215606i
$939$	−3.61927	+	6.26876i	−0.118111	+	0.204573i
$940$		0			0
$941$		−	6.50590i		−	0.212086i	−0.994362	−	0.106043i	$-0.966182\pi$
$941$		−	6.50590i		−	0.212086i	0.994362	−	0.106043i	$-0.0338182\pi$
$942$	2.54132	−	1.46723i	0.0828008	−	0.0478051i
$943$	−3.68068	+	2.12504i	−0.119859	+	0.0692008i
$944$		−	17.4443i		−	0.567763i
$945$		0			0
$946$	8.17957	−	14.1674i	0.265941	−	0.460623i
$947$	−24.1479	−	13.9418i	−0.784701	−	0.453048i	0.0533924	−	0.998574i	$-0.482997\pi$
$947$	−24.1479	−	13.9418i	−0.784701	−	0.453048i	−0.838094	+	0.545526i	$0.816330\pi$
$948$	−29.3196			−0.952255
$949$	13.0451	−	36.6666i	0.423463	−	1.19025i
$950$		0			0
$951$	18.1988	+	10.5071i	0.590138	+	0.340716i
$952$	−1.32983	+	2.30333i	−0.0431001	+	0.0746515i
$953$	−25.9430	−	44.9347i	−0.840377	−	1.45558i	−0.889576	−	0.456787i	$-0.849000\pi$
$953$	−25.9430	−	44.9347i	−0.840377	−	1.45558i	0.0491986	−	0.998789i	$-0.484333\pi$
$954$		−	12.0000i		−	0.388514i
$955$		0			0
$956$	−43.3288	+	25.0159i	−1.40135	+	0.809072i
$957$			3.98085i			0.128683i
$958$	−29.0934	−	50.3913i	−0.939966	−	1.62807i
$959$	2.05773	−	3.56410i	0.0664477	−	0.115091i
$960$		0			0
$961$	−7.25300			−0.233968
$962$	−14.6768	−	79.8451i	−0.473200	−	2.57431i
$963$	−11.9186			−0.384072
$964$	−15.7043	−	9.06687i	−0.505801	−	0.292024i
$965$		0			0
$966$	0.340338	+	0.589483i	0.0109502	+	0.0189663i
$967$			21.4251i			0.688986i	0.938789	+	0.344493i	$0.111949\pi$
$967$			21.4251i			0.688986i	−0.938789	+	0.344493i	$0.888051\pi$
$968$	−11.6729	+	6.73933i	−0.375180	+	0.216610i
$969$	−5.04834	+	2.91466i	−0.162176	+	0.0936323i
$970$		0			0
$971$	3.33637	+	5.77876i	0.107069	+	0.185449i	0.914582	−	0.404401i	$-0.132520\pi$
$971$	3.33637	+	5.77876i	0.107069	+	0.185449i	−0.807513	+	0.589850i	$0.799187\pi$
$972$	1.36603	−	2.36603i	0.0438153	−	0.0758903i
$973$	2.50158	+	1.44429i	0.0801969	+	0.0463017i
$974$	61.6136			1.97423
$975$		0			0
$976$	19.4641			0.623031
$977$	−8.50906	−	4.91271i	−0.272229	−	0.157171i	0.357671	−	0.933848i	$-0.383571\pi$
$977$	−8.50906	−	4.91271i	−0.272229	−	0.157171i	−0.629900	+	0.776676i	$0.716904\pi$
$978$	−3.24034	+	5.61244i	−0.103615	+	0.179466i
$979$	3.78727	+	6.55974i	0.121042	+	0.209650i
$980$		0			0
$981$	−14.7577	+	8.52036i	−0.471177	+	0.272034i
$982$	−17.8973	+	10.3330i	−0.571125	+	0.329739i
$983$		−	8.83034i		−	0.281644i	−0.990035	−	0.140822i	$-0.955025\pi$
$983$		−	8.83034i		−	0.281644i	0.990035	−	0.140822i	$-0.0449746\pi$
$984$	4.79393	+	8.30333i	0.152825	+	0.264701i
$985$		0			0
$986$	−17.7440	−	10.2445i	−0.565083	−	0.326251i
$987$	2.40129			0.0764338
$988$	−9.88069	−	11.6034i	−0.314347	−	0.369152i
$989$	3.33358			0.106002
$990$		0			0
$991$	−6.16662	+	10.6809i	−0.195889	+	0.339290i	−0.947192	−	0.320668i	$-0.896093\pi$
$991$	−6.16662	+	10.6809i	−0.195889	+	0.339290i	0.751302	+	0.659958i	$0.229426\pi$
$992$	23.3033	+	40.3626i	0.739882	+	1.28151i
$993$		−	15.5136i		−	0.492311i
$994$	−12.6506	+	7.30380i	−0.401251	+	0.231663i
$995$		0			0
$996$			24.9382i			0.790196i
$997$	−6.52517	−	11.3019i	−0.206654	−	0.357935i	0.744004	−	0.668175i	$-0.232924\pi$
$997$	−6.52517	−	11.3019i	−0.206654	−	0.357935i	−0.950658	+	0.310239i	$0.899591\pi$
$998$	−25.2084	+	43.6623i	−0.797959	+	1.38210i
$999$	8.96393	+	5.17533i	0.283606	+	0.163740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.j.901.1		8
5.2	odd	4		975.2.w.i.199.4		8
5.3	odd	4		975.2.w.h.199.1		8
5.4	even	2		195.2.bb.b.121.4	✓	8
13.10	even	6	inner	975.2.bc.j.751.1		8
15.14	odd	2		585.2.bu.d.316.1		8
65.19	odd	12		2535.2.a.bk.1.1		4
65.23	odd	12		975.2.w.i.49.4		8
65.49	even	6		195.2.bb.b.166.4	yes	8
65.59	odd	12		2535.2.a.bj.1.4		4
65.62	odd	12		975.2.w.h.49.1		8
195.59	even	12		7605.2.a.ci.1.1		4
195.149	even	12		7605.2.a.ch.1.4		4
195.179	odd	6		585.2.bu.d.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.b.121.4	✓	8	5.4	even	2
195.2.bb.b.166.4	yes	8	65.49	even	6
585.2.bu.d.316.1		8	15.14	odd	2
585.2.bu.d.361.1		8	195.179	odd	6
975.2.w.h.49.1		8	65.62	odd	12
975.2.w.h.199.1		8	5.3	odd	4
975.2.w.i.49.4		8	65.23	odd	12
975.2.w.i.199.4		8	5.2	odd	4
975.2.bc.j.751.1		8	13.10	even	6	inner
975.2.bc.j.901.1		8	1.1	even	1	trivial
2535.2.a.bj.1.4		4	65.59	odd	12
2535.2.a.bk.1.1		4	65.19	odd	12
7605.2.a.ch.1.4		4	195.149	even	12
7605.2.a.ci.1.1		4	195.59	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88389 - 1.08766i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.36603 + 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.383889 - 0.221638i) q^{7} -1.59245i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.88389 - 1.08766i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.36603 + 2.36603i) q^{4} +(1.88389 - 1.08766i) q^{6} +(0.383889 - 0.221638i) q^{7} -1.59245i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.37910 - 0.796225i) q^{11} -2.73205 q^{12} +(3.39697 + 1.20856i) q^{13} -0.964273 q^{14} +(1.00000 - 1.73205i) q^{16} +(-1.88389 - 3.26299i) q^{17} +2.17533i q^{18} +(-1.33987 + 0.773575i) q^{19} +0.443277i q^{21} +(1.73205 + 3.00000i) q^{22} +(-0.352948 + 0.611324i) q^{23} +(1.37910 + 0.796225i) q^{24} +(-5.08500 - 5.97155i) q^{26} +1.00000 q^{27} +(1.04880 + 0.605528i) q^{28} +(-1.24991 + 2.16492i) q^{29} -6.18490i q^{31} +(-6.52598 + 3.76778i) q^{32} +(1.37910 - 0.796225i) q^{33} +8.19615i q^{34} +(1.36603 - 2.36603i) q^{36} +(8.96393 + 5.17533i) q^{37} +3.36556 q^{38} +(-2.74513 + 2.33758i) q^{39} +(5.21419 + 3.01041i) q^{41} +(0.482136 - 0.835085i) q^{42} +(-2.36124 - 4.08979i) q^{43} -4.35066i q^{44} +(1.32983 - 0.767778i) q^{46} -5.41712i q^{47} +(1.00000 + 1.73205i) q^{48} +(-3.40175 + 5.89201i) q^{49} +3.76778 q^{51} +(1.78086 + 9.68823i) q^{52} -5.51641 q^{53} +(-1.88389 - 1.08766i) q^{54} +(-0.352948 - 0.611324i) q^{56} -1.54715i q^{57} +(4.70940 - 2.71897i) q^{58} +(7.55359 - 4.36107i) q^{59} +(4.86603 + 8.42820i) q^{61} +(-6.72709 + 11.6517i) q^{62} +(-0.383889 - 0.221638i) q^{63} +12.3923 q^{64} -3.46410 q^{66} +(11.8611 + 6.84799i) q^{67} +(5.14688 - 8.91466i) q^{68} +(-0.352948 - 0.611324i) q^{69} +(13.1193 - 7.57442i) q^{71} +(-1.37910 + 0.796225i) q^{72} -10.7939i q^{73} +(-11.2580 - 19.4995i) q^{74} +(-3.66060 - 2.11345i) q^{76} -0.705897 q^{77} +(7.71402 - 1.41796i) q^{78} +10.7317 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.54863 - 11.3426i) q^{82} -9.12801i q^{83} +(-1.04880 + 0.605528i) q^{84} +10.2729i q^{86} +(-1.24991 - 2.16492i) q^{87} +(-1.26795 + 2.19615i) q^{88} +(-4.11927 - 2.37826i) q^{89} +(1.57192 - 0.288945i) q^{91} -1.92855 q^{92} +(5.35628 + 3.09245i) q^{93} +(-5.89201 + 10.2053i) q^{94} -7.53556i q^{96} +(7.28944 - 4.20856i) q^{97} +(12.8170 - 7.39993i) q^{98} +1.59245i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 12 q^{7} - 4 q^{9} - 8 q^{12} + 8 q^{13} - 24 q^{14} + 8 q^{16} - 12 q^{19} - 24 q^{26} + 8 q^{27} - 12 q^{28} + 12 q^{29} + 4 q^{36} - 4 q^{39} + 36 q^{41} + 12 q^{42} - 16 q^{43} + 8 q^{48} - 4 q^{49} - 20 q^{52} + 36 q^{58} + 36 q^{59} + 32 q^{61} + 12 q^{63} + 16 q^{64} + 48 q^{67} + 36 q^{71} - 24 q^{74} - 48 q^{76} + 12 q^{78} - 16 q^{79} - 4 q^{81} + 12 q^{82} + 12 q^{84} + 12 q^{87} - 24 q^{88} + 36 q^{89} - 48 q^{92} + 12 q^{94} + 72 q^{98}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 12 * q^7 - 4 * q^9 - 8 * q^12 + 8 * q^13 - 24 * q^14 + 8 * q^16 - 12 * q^19 - 24 * q^26 + 8 * q^27 - 12 * q^28 + 12 * q^29 + 4 * q^36 - 4 * q^39 + 36 * q^41 + 12 * q^42 - 16 * q^43 + 8 * q^48 - 4 * q^49 - 20 * q^52 + 36 * q^58 + 36 * q^59 + 32 * q^61 + 12 * q^63 + 16 * q^64 + 48 * q^67 + 36 * q^71 - 24 * q^74 - 48 * q^76 + 12 * q^78 - 16 * q^79 - 4 * q^81 + 12 * q^82 + 12 * q^84 + 12 * q^87 - 24 * q^88 + 36 * q^89 - 48 * q^92 + 12 * q^94 + 72 * q^98

Introduction

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