LMFDB - Embedded newform 756.2.n.b.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(19,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 5]))

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

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

chi := DirichletCharacter("756.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07941 - 0.913714i) q^{2} +(0.330255 + 1.97254i) q^{4} -3.48216i q^{5} +(-0.638585 + 2.56753i) q^{7} +(1.44586 - 2.43094i) q^{8} +O(q^{10})$	\(q+(-1.07941 - 0.913714i) q^{2} +(0.330255 + 1.97254i) q^{4} -3.48216i q^{5} +(-0.638585 + 2.56753i) q^{7} +(1.44586 - 2.43094i) q^{8} +(-3.18169 + 3.75868i) q^{10} +1.97557i q^{11} +(5.52258 - 3.18847i) q^{13} +(3.03528 - 2.18793i) q^{14} +(-3.78186 + 1.30288i) q^{16} +(-1.04054 + 0.600755i) q^{17} +(2.25453 - 3.90496i) q^{19} +(6.86871 - 1.15000i) q^{20} +(1.80511 - 2.13246i) q^{22} +0.590265i q^{23} -7.12541 q^{25} +(-8.87448 - 1.60440i) q^{26} +(-5.27546 - 0.411699i) q^{28} +(2.00631 - 3.47503i) q^{29} +(2.63991 - 4.57246i) q^{31} +(5.27265 + 2.04919i) q^{32} +(1.67209 + 0.302292i) q^{34} +(8.94054 + 2.22365i) q^{35} +(0.506783 - 0.877774i) q^{37} +(-6.00157 + 2.15506i) q^{38} +(-8.46493 - 5.03471i) q^{40} +(-4.54294 + 2.62287i) q^{41} +(-2.66552 - 1.53894i) q^{43} +(-3.89691 + 0.652443i) q^{44} +(0.539333 - 0.637139i) q^{46} +(0.174866 + 0.302877i) q^{47} +(-6.18442 - 3.27917i) q^{49} +(7.69124 + 6.51059i) q^{50} +(8.11325 + 9.84054i) q^{52} +(-3.01662 - 5.22494i) q^{53} +6.87926 q^{55} +(5.31822 + 5.26465i) q^{56} +(-5.34081 + 1.91779i) q^{58} +(7.25888 - 12.5727i) q^{59} +(3.42577 - 1.97787i) q^{61} +(-7.02746 + 2.52344i) q^{62} +(-3.81897 - 7.02961i) q^{64} +(-11.1027 - 19.2305i) q^{65} +(-4.23532 - 2.44526i) q^{67} +(-1.52866 - 1.85410i) q^{68} +(-7.61873 - 10.5693i) q^{70} +1.47342i q^{71} +(9.61590 - 5.55174i) q^{73} +(-1.34906 + 0.484424i) q^{74} +(8.44727 + 3.15753i) q^{76} +(-5.07235 - 1.26157i) q^{77} +(0.556744 - 0.321436i) q^{79} +(4.53685 + 13.1690i) q^{80} +(7.30024 + 1.31979i) q^{82} +(-1.00577 + 1.74205i) q^{83} +(2.09192 + 3.62331i) q^{85} +(1.47104 + 4.09667i) q^{86} +(4.80251 + 2.85640i) q^{88} +(3.27016 + 1.88803i) q^{89} +(4.65984 + 16.2155i) q^{91} +(-1.16432 + 0.194938i) q^{92} +(0.0879904 - 0.486706i) q^{94} +(-13.5977 - 7.85062i) q^{95} +(-14.8094 - 8.55023i) q^{97} +(3.67930 + 9.19036i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) $ 84 * q + q^2 + q^4 + 16 * q^8	$ 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.07941	−	0.913714i	−0.763259	−	0.646093i
$2$	−1.07941	−	0.913714i	−0.763259	−	0.646093i
$3$		0			0
$3$		0			0
$4$	0.330255	+	1.97254i	0.165127	+	0.986272i
$5$		−	3.48216i		−	1.55727i	−0.627479	−	0.778634i	$-0.715913\pi$
$5$		−	3.48216i		−	1.55727i	0.627479	−	0.778634i	$-0.284087\pi$
$6$		0			0
$7$	−0.638585	+	2.56753i	−0.241362	+	0.970435i
$7$	−0.638585	+	2.56753i	−0.241362	+	0.970435i
$8$	1.44586	−	2.43094i	0.511189	−	0.859468i
$9$		0			0
$10$	−3.18169	+	3.75868i	−1.00614	+	1.18860i
$11$			1.97557i			0.595658i	0.954619	+	0.297829i	$0.0962625\pi$
$11$			1.97557i			0.595658i	−0.954619	+	0.297829i	$0.903737\pi$
$12$		0			0
$13$	5.52258	−	3.18847i	1.53169	−	0.884321i	0.532405	−	0.846490i	$-0.321288\pi$
$13$	5.52258	−	3.18847i	1.53169	−	0.884321i	0.999284	−	0.0378315i	$-0.0120450\pi$
$14$	3.03528	−	2.18793i	0.811213	−	0.584750i
$15$		0			0
$16$	−3.78186	+	1.30288i	−0.945466	+	0.325721i
$17$	−1.04054	+	0.600755i	−0.252367	+	0.145704i	−0.620848	−	0.783931i	$-0.713212\pi$
$17$	−1.04054	+	0.600755i	−0.252367	+	0.145704i	0.368480	+	0.929636i	$0.379878\pi$
$18$		0			0
$19$	2.25453	−	3.90496i	0.517224	−	0.895858i	−0.482576	−	0.875854i	$-0.660299\pi$
$19$	2.25453	−	3.90496i	0.517224	−	0.895858i	0.999800	−	0.0200042i	$-0.00636795\pi$
$20$	6.86871	−	1.15000i	1.53589	−	0.257147i
$21$		0			0
$22$	1.80511	−	2.13246i	0.384851	−	0.454641i
$23$			0.590265i			0.123079i	0.998105	+	0.0615394i	$0.0196010\pi$
$23$			0.590265i			0.123079i	−0.998105	+	0.0615394i	$0.980399\pi$
$24$		0			0
$25$	−7.12541			−1.42508
$26$	−8.87448	−	1.60440i	−1.74043	−	0.314648i
$27$		0			0
$28$	−5.27546	−	0.411699i	−0.996969	−	0.0778038i
$29$	2.00631	−	3.47503i	0.372562	−	0.645296i	−0.617397	−	0.786652i	$-0.711813\pi$
$29$	2.00631	−	3.47503i	0.372562	−	0.645296i	0.989959	+	0.141356i	$0.0451461\pi$
$30$		0			0
$31$	2.63991	−	4.57246i	0.474142	−	0.821237i	−0.525420	−	0.850843i	$-0.676092\pi$
$31$	2.63991	−	4.57246i	0.474142	−	0.821237i	0.999562	+	0.0296057i	$0.00942517\pi$
$32$	5.27265	+	2.04919i	0.932081	+	0.362250i
$33$		0			0
$34$	1.67209	+	0.302292i	0.286760	+	0.0518427i
$35$	8.94054	+	2.22365i	1.51123	+	0.375866i
$36$		0			0
$37$	0.506783	−	0.877774i	0.0833146	−	0.144305i	−0.821357	−	0.570414i	$-0.806783\pi$
$37$	0.506783	−	0.877774i	0.0833146	−	0.144305i	0.904672	+	0.426109i	$0.140116\pi$
$38$	−6.00157	+	2.15506i	−0.973584	+	0.349597i
$39$		0			0
$40$	−8.46493	−	5.03471i	−1.33842	−	0.796058i
$41$	−4.54294	+	2.62287i	−0.709488	+	0.409623i	−0.810871	−	0.585225i	$-0.801006\pi$
$41$	−4.54294	+	2.62287i	−0.709488	+	0.409623i	0.101384	+	0.994847i	$0.467673\pi$
$42$		0			0
$43$	−2.66552	−	1.53894i	−0.406488	−	0.234686i	0.282792	−	0.959181i	$-0.408739\pi$
$43$	−2.66552	−	1.53894i	−0.406488	−	0.234686i	−0.689280	+	0.724495i	$0.742073\pi$
$44$	−3.89691	+	0.652443i	−0.587481	+	0.0983594i
$45$		0			0
$46$	0.539333	−	0.637139i	0.0795204	−	0.0939410i
$47$	0.174866	+	0.302877i	0.0255068	+	0.0441791i	0.878497	−	0.477748i	$-0.158547\pi$
$47$	0.174866	+	0.302877i	0.0255068	+	0.0441791i	−0.852990	+	0.521927i	$0.825213\pi$
$48$		0			0
$49$	−6.18442	−	3.27917i	−0.883488	−	0.468453i
$50$	7.69124	+	6.51059i	1.08771	+	0.920736i
$51$		0			0
$52$	8.11325	+	9.84054i	1.12511	+	1.36464i
$53$	−3.01662	−	5.22494i	−0.414364	−	0.717700i	0.580997	−	0.813906i	$-0.302663\pi$
$53$	−3.01662	−	5.22494i	−0.414364	−	0.717700i	−0.995361	+	0.0962054i	$0.969329\pi$
$54$		0			0
$55$	6.87926			0.927599
$56$	5.31822	+	5.26465i	0.710676	+	0.703519i
$57$		0			0
$58$	−5.34081	+	1.91779i	−0.701282	+	0.251818i
$59$	7.25888	−	12.5727i	0.945025	−	1.63683i	0.189324	−	0.981915i	$-0.439370\pi$
$59$	7.25888	−	12.5727i	0.945025	−	1.63683i	0.755701	−	0.654917i	$-0.227296\pi$
$60$		0			0
$61$	3.42577	−	1.97787i	0.438625	−	0.253240i	−0.264389	−	0.964416i	$-0.585170\pi$
$61$	3.42577	−	1.97787i	0.438625	−	0.253240i	0.703014	+	0.711176i	$0.251837\pi$
$62$	−7.02746	+	2.52344i	−0.892488	+	0.320477i
$63$		0			0
$64$	−3.81897	−	7.02961i	−0.477372	−	0.878701i
$65$	−11.1027	−	19.2305i	−1.37712	−	2.38525i
$66$		0			0
$67$	−4.23532	−	2.44526i	−0.517426	−	0.298736i	0.218455	−	0.975847i	$-0.429898\pi$
$67$	−4.23532	−	2.44526i	−0.517426	−	0.298736i	−0.735881	+	0.677111i	$0.763232\pi$
$68$	−1.52866	−	1.85410i	−0.185377	−	0.224843i
$69$		0			0
$70$	−7.61873	−	10.5693i	−0.910613	−	1.26328i
$71$			1.47342i			0.174863i	0.996171	+	0.0874313i	$0.0278658\pi$
$71$			1.47342i			0.174863i	−0.996171	+	0.0874313i	$0.972134\pi$
$72$		0			0
$73$	9.61590	−	5.55174i	1.12546	−	0.649783i	0.182668	−	0.983175i	$-0.441527\pi$
$73$	9.61590	−	5.55174i	1.12546	−	0.649783i	0.942788	+	0.333392i	$0.108193\pi$
$74$	−1.34906	+	0.484424i	−0.156825	+	0.0563131i
$75$		0			0
$76$	8.44727	+	3.15753i	0.968968	+	0.362193i
$77$	−5.07235	−	1.26157i	−0.578047	−	0.143770i
$78$		0			0
$79$	0.556744	−	0.321436i	0.0626386	−	0.0361644i	−0.468354	−	0.883541i	$-0.655153\pi$
$79$	0.556744	−	0.321436i	0.0626386	−	0.0361644i	0.530992	+	0.847377i	$0.321819\pi$
$80$	4.53685	+	13.1690i	0.507235	+	1.47234i
$81$		0			0
$82$	7.30024	+	1.31979i	0.806177	+	0.145747i
$83$	−1.00577	+	1.74205i	−0.110398	+	0.191215i	−0.915931	−	0.401336i	$-0.868546\pi$
$83$	−1.00577	+	1.74205i	−0.110398	+	0.191215i	0.805533	+	0.592551i	$0.201879\pi$
$84$		0			0
$85$	2.09192	+	3.62331i	0.226901	+	0.393004i
$86$	1.47104	+	4.09667i	0.158626	+	0.441755i
$87$		0			0
$88$	4.80251	+	2.85640i	0.511949	+	0.304494i
$89$	3.27016	+	1.88803i	0.346636	+	0.200130i	0.663203	−	0.748440i	$-0.269197\pi$
$89$	3.27016	+	1.88803i	0.346636	+	0.200130i	−0.316567	+	0.948570i	$0.602530\pi$
$90$		0			0
$91$	4.65984	+	16.2155i	0.488484	+	1.69985i
$92$	−1.16432	+	0.194938i	−0.121389	+	0.0203237i
$93$		0			0
$94$	0.0879904	−	0.486706i	0.00907552	−	0.0501999i
$95$	−13.5977	−	7.85062i	−1.39509	−	0.805456i
$96$		0			0
$97$	−14.8094	−	8.55023i	−1.50367	−	0.868145i	−0.999991	−	0.00425389i	$-0.998646\pi$
$97$	−14.8094	−	8.55023i	−1.50367	−	0.868145i	−0.503679	−	0.863891i	$-0.668021\pi$
$98$	3.67930	+	9.19036i	0.371666	+	0.928367i
$99$		0			0
$100$	−2.35320	−	14.0552i	−0.235320	−	1.40552i
$101$			4.96913i			0.494447i	0.968958	+	0.247224i	$0.0795182\pi$
$101$			4.96913i			0.494447i	−0.968958	+	0.247224i	$0.920482\pi$
$102$		0			0
$103$	−15.1779			−1.49552			−0.747761	−	0.663968i	$-0.768871\pi$
$103$	−15.1779			−1.49552			−0.747761	+	0.663968i	$0.768871\pi$
$104$	0.233906	−	18.0352i	0.0229364	−	1.76849i
$105$		0			0
$106$	−1.51793	+	8.39618i	−0.147434	+	0.815509i
$107$	−9.66900	−	5.58240i	−0.934737	−	0.539671i	−0.0464307	−	0.998922i	$-0.514785\pi$
$107$	−9.66900	−	5.58240i	−0.934737	−	0.539671i	−0.888307	+	0.459251i	$0.848118\pi$
$108$		0			0
$109$	2.33905	+	4.05136i	0.224041	+	0.388050i	0.956031	−	0.293265i	$-0.0947419\pi$
$109$	2.33905	+	4.05136i	0.224041	+	0.388050i	−0.731991	+	0.681315i	$0.761409\pi$
$110$	−7.42554	−	6.28567i	−0.707998	−	0.599315i
$111$		0			0
$112$	−0.930152	−	10.5420i	−0.0878911	−	0.996130i
$113$	5.62554	+	9.74373i	0.529207	+	0.916613i	0.999420	+	0.0340600i	$0.0108437\pi$
$113$	5.62554	+	9.74373i	0.529207	+	0.916613i	−0.470213	+	0.882553i	$0.655823\pi$
$114$		0			0
$115$	2.05540			0.191667
$116$	7.51724	+	2.80989i	0.697958	+	0.260891i
$117$		0			0
$118$	−19.3232	+	6.93862i	−1.77884	+	0.638751i
$119$	−0.877984	−	3.05524i	−0.0804846	−	0.280074i
$120$		0			0
$121$	7.09711			0.645192
$122$	−5.50501	−	0.995239i	−0.498401	−	0.0901047i
$123$		0			0
$124$	9.89121	+	3.69726i	0.888257	+	0.332024i
$125$			7.40101i			0.661967i
$126$		0			0
$127$		−	10.7073i		−	0.950115i	−0.879955	−	0.475058i	$-0.842427\pi$
$127$		−	10.7073i		−	0.950115i	0.879955	−	0.475058i	$-0.157573\pi$
$128$	−2.30081	+	11.0773i	−0.203365	+	0.979103i
$129$		0			0
$130$	−5.58676	+	30.9023i	−0.489991	+	2.71031i
$131$	5.67606			0.495920			0.247960	−	0.968770i	$-0.420240\pi$
$131$	5.67606			0.495920			0.247960	+	0.968770i	$0.420240\pi$
$132$		0			0
$133$	8.58638	+	8.28221i	0.744534	+	0.718159i
$134$	2.33738	+	6.50931i	0.201919	+	0.562318i
$135$		0			0
$136$	−0.0440714	+	3.39810i	−0.00377909	+	0.291384i
$137$	7.79004			0.665548			0.332774	−	0.943007i	$-0.392015\pi$
$137$	7.79004			0.665548			0.332774	+	0.943007i	$0.392015\pi$
$138$		0			0
$139$	6.87438	+	11.9068i	0.583078	+	1.00992i	0.995112	+	0.0987517i	$0.0314850\pi$
$139$	6.87438	+	11.9068i	0.583078	+	1.00992i	−0.412035	+	0.911168i	$0.635182\pi$
$140$	−1.43360	+	18.3700i	−0.121161	+	1.55255i
$141$		0			0
$142$	1.34628	−	1.59042i	0.112978	−	0.133465i
$143$	6.29905	+	10.9103i	0.526753	+	0.912363i
$144$		0			0
$145$	−12.1006	−	6.98628i	−1.00490	−	0.580179i
$146$	−15.4522	−	2.79357i	−1.27883	−	0.231198i
$147$		0			0
$148$	1.89882	+	0.709763i	0.156082	+	0.0583422i
$149$	20.4898			1.67859			0.839293	−	0.543679i	$-0.182969\pi$
$149$	20.4898			1.67859			0.839293	+	0.543679i	$0.182969\pi$
$150$		0			0
$151$			22.0199i			1.79195i	0.444100	+	0.895977i	$0.353523\pi$
$151$			22.0199i			1.79195i	−0.444100	+	0.895977i	$0.646477\pi$
$152$	−6.23300	−	11.1267i	−0.505563	−	0.902491i
$153$		0			0
$154$	4.32243	+	5.99643i	0.348311	+	0.483206i
$155$	−15.9220	−	9.19257i	−1.27889	−	0.738365i
$156$		0			0
$157$	9.72123	+	5.61256i	0.775839	+	0.447931i	0.834954	−	0.550320i	$-0.185494\pi$
$157$	9.72123	+	5.61256i	0.775839	+	0.447931i	−0.0591146	+	0.998251i	$0.518828\pi$
$158$	−0.894656	−	0.161743i	−0.0711750	−	0.0128676i
$159$		0			0
$160$	7.13561	−	18.3602i	0.564120	−	1.45150i
$161$	−1.51552	−	0.376935i	−0.119440	−	0.0297066i
$162$		0			0
$163$	7.50110	+	4.33076i	0.587531	+	0.339211i	0.764121	−	0.645073i	$-0.223173\pi$
$163$	7.50110	+	4.33076i	0.587531	+	0.339211i	−0.176589	+	0.984285i	$0.556506\pi$
$164$	−6.67405	−	8.09493i	−0.521155	−	0.632108i
$165$		0			0
$166$	2.67738	−	0.961399i	0.207805	−	0.0746190i
$167$	12.3381	+	21.3703i	0.954754	+	1.65368i	0.734930	+	0.678143i	$0.237215\pi$
$167$	12.3381	+	21.3703i	0.954754	+	1.65368i	0.219824	+	0.975540i	$0.429452\pi$
$168$		0			0
$169$	13.8326	−	23.9588i	1.06405	−	1.84299i
$170$	1.05263	−	5.82246i	0.0807330	−	0.446562i
$171$		0			0
$172$	2.15532	−	5.76610i	0.164342	−	0.439661i
$173$	0.626093	−	0.361475i	0.0476010	−	0.0274824i	−0.476011	−	0.879440i	$-0.657918\pi$
$173$	0.626093	−	0.361475i	0.0476010	−	0.0274824i	0.523612	+	0.851957i	$0.324584\pi$
$174$		0			0
$175$	4.55018	−	18.2947i	0.343961	−	1.38295i
$176$	−2.57394	−	7.47135i	−0.194018	−	0.563174i
$177$		0			0
$178$	−1.80473	−	5.02594i	−0.135270	−	0.376710i
$179$	−10.2904	+	5.94116i	−0.769139	+	0.444063i	−0.832568	−	0.553924i	$-0.813130\pi$
$179$	−10.2904	+	5.94116i	−0.769139	+	0.444063i	0.0634282	+	0.997986i	$0.479797\pi$
$180$		0			0
$181$			5.23327i			0.388986i	0.980904	+	0.194493i	$0.0623062\pi$
$181$			5.23327i			0.388986i	−0.980904	+	0.194493i	$0.937694\pi$
$182$	9.78645	−	21.7609i	0.725420	−	1.61303i
$183$		0			0
$184$	1.43490	+	0.853441i	0.105782	+	0.0629165i
$185$	−3.05655	−	1.76470i	−0.224722	−	0.129743i
$186$		0			0
$187$	−1.18684	−	2.05566i	−0.0867900	−	0.150325i
$188$	−0.539687	+	0.444957i	−0.0393607	+	0.0324518i
$189$		0			0
$190$	7.50425	+	20.8984i	0.544416	+	1.51613i
$191$	13.7450	−	7.93569i	0.994555	−	0.574207i	0.0879222	−	0.996127i	$-0.471977\pi$
$191$	13.7450	−	7.93569i	0.994555	−	0.574207i	0.906633	+	0.421921i	$0.138644\pi$
$192$		0			0
$193$	0.442829	−	0.767002i	0.0318755	−	0.0552100i	−0.849648	−	0.527351i	$-0.823185\pi$
$193$	0.442829	−	0.767002i	0.0318755	−	0.0552100i	0.881523	+	0.472141i	$0.156519\pi$
$194$	8.17300	+	22.7608i	0.586787	+	1.63413i
$195$		0			0
$196$	4.42588	−	13.2820i	0.316134	−	0.948714i
$197$	2.17147			0.154711			0.0773553	−	0.997004i	$-0.475352\pi$
$197$	2.17147			0.154711			0.0773553	+	0.997004i	$0.475352\pi$
$198$		0			0
$199$	6.48062	+	11.2248i	0.459399	+	0.795702i	0.998929	−	0.0462638i	$-0.0147315\pi$
$199$	6.48062	+	11.2248i	0.459399	+	0.795702i	−0.539530	+	0.841966i	$0.681398\pi$
$200$	−10.3024	+	17.3215i	−0.728486	+	1.22481i
$201$		0			0
$202$	4.54037	−	5.36374i	0.319459	−	0.377391i
$203$	7.64104	+	7.37035i	0.536296	+	0.517297i
$204$		0			0
$205$	9.13323	+	15.8192i	0.637892	+	1.10486i
$206$	16.3832	+	13.8682i	1.14147	+	0.966246i
$207$		0			0
$208$	−16.7315	+	19.2536i	−1.16012	+	1.33500i
$209$	7.71453	+	4.45399i	0.533625	+	0.308089i
$210$		0			0
$211$	−8.89012	+	5.13271i	−0.612021	+	0.353350i	−0.773756	−	0.633484i	$-0.781624\pi$
$211$	−8.89012	+	5.13271i	−0.612021	+	0.353350i	0.161735	+	0.986834i	$0.448291\pi$
$212$	9.31017	−	7.67597i	0.639425	−	0.527188i
$213$		0			0
$214$	5.33611	+	14.8604i	0.364769	+	1.01584i
$215$	−5.35882	+	9.28176i	−0.365469	+	0.633010i
$216$		0			0
$217$	10.0541	+	9.69795i	0.682517	+	0.658339i
$218$	1.17698	−	6.51030i	0.0797153	−	0.440933i
$219$		0			0
$220$	2.27191	+	13.5696i	0.153172	+	0.914865i
$221$	−3.83097	+	6.63544i	−0.257699	+	0.446348i
$222$		0			0
$223$	−9.27475	+	16.0643i	−0.621083	+	1.07575i	0.368201	+	0.929746i	$0.379974\pi$
$223$	−9.27475	+	16.0643i	−0.621083	+	1.07575i	−0.989284	+	0.146001i	$0.953360\pi$
$224$	−8.62840	+	12.2291i	−0.576509	+	0.817091i
$225$		0			0
$226$	2.83071	−	15.6576i	0.188296	−	1.04153i
$227$	−6.02921			−0.400172			−0.200086	−	0.979778i	$-0.564122\pi$
$227$	−6.02921			−0.400172			−0.200086	+	0.979778i	$0.564122\pi$
$228$		0			0
$229$			2.91153i			0.192399i	0.995362	+	0.0961995i	$0.0306687\pi$
$229$			2.91153i			0.192399i	−0.995362	+	0.0961995i	$0.969331\pi$
$230$	−2.21862	−	1.87804i	−0.146291	−	0.123834i
$231$		0			0
$232$	−5.54675	−	9.90162i	−0.364162	−	0.650073i
$233$	4.64505	−	8.04547i	0.304308	−	0.527076i	−0.672799	−	0.739825i	$-0.734908\pi$
$233$	4.64505	−	8.04547i	0.304308	−	0.527076i	0.977107	+	0.212749i	$0.0682416\pi$
$234$		0			0
$235$	1.05466	−	0.608910i	0.0687987	−	0.0397209i
$236$	27.1976	+	10.1662i	1.77041	+	0.661766i
$237$		0			0
$238$	−1.84391	+	4.10009i	−0.119523	+	0.265769i
$239$	−4.84551	+	2.79756i	−0.313430	+	0.180959i	−0.648460	−	0.761248i	$-0.724587\pi$
$239$	−4.84551	+	2.79756i	−0.313430	+	0.180959i	0.335030	+	0.942207i	$0.391253\pi$
$240$		0			0
$241$		−	2.16706i		−	0.139593i	−0.997561	−	0.0697963i	$-0.977765\pi$
$241$		−	2.16706i		−	0.139593i	0.997561	−	0.0697963i	$-0.0222349\pi$
$242$	−7.66069	−	6.48472i	−0.492448	−	0.416854i
$243$		0			0
$244$	5.03281	+	6.10428i	0.322192	+	0.390786i
$245$	−11.4186	+	21.5351i	−0.729507	+	1.37583i
$246$		0			0
$247$		−	28.7539i		−	1.82957i
$248$	−7.29844	−	13.0286i	−0.463452	−	0.827317i
$249$		0			0
$250$	6.76241	−	7.98873i	0.427692	−	0.505252i
$251$	14.3444			0.905410			0.452705	−	0.891660i	$-0.350459\pi$
$251$	14.3444			0.905410			0.452705	+	0.891660i	$0.350459\pi$
$252$		0			0
$253$	−1.16611			−0.0733129
$254$	−9.78336	+	11.5575i	−0.613863	+	0.725184i
$255$		0			0
$256$	12.6050	−	9.85466i	0.787812	−	0.615916i
$257$			1.08665i			0.0677832i	0.999426	+	0.0338916i	$0.0107901\pi$
$257$			1.08665i			0.0677832i	−0.999426	+	0.0338916i	$0.989210\pi$
$258$		0			0
$259$	1.93009	+	1.86171i	0.119930	+	0.115681i
$260$	34.2663	−	28.2516i	2.12510	−	1.75209i
$261$		0			0
$262$	−6.12680	−	5.18630i	−0.378515	−	0.320411i
$263$			3.61167i			0.222705i	0.993781	+	0.111352i	$0.0355182\pi$
$263$			3.61167i			0.222705i	−0.993781	+	0.111352i	$0.964482\pi$
$264$		0			0
$265$	−18.1940	+	10.5043i	−1.11765	+	0.645276i
$266$	−1.70066	−	16.7854i	−0.104274	−	1.02918i
$267$		0			0
$268$	3.42465	−	9.16191i	0.209194	−	0.559652i
$269$	−18.9812	+	10.9588i	−1.15731	+	0.668171i	−0.950657	−	0.310244i	$-0.899589\pi$
$269$	−18.9812	+	10.9588i	−1.15731	+	0.668171i	−0.206649	+	0.978415i	$0.566256\pi$
$270$		0			0
$271$	7.49415	−	12.9802i	0.455237	−	0.788494i	−0.543465	−	0.839432i	$-0.682888\pi$
$271$	7.49415	−	12.9802i	0.455237	−	0.788494i	0.998702	+	0.0509383i	$0.0162212\pi$
$272$	3.15246	−	3.62767i	0.191146	−	0.219960i
$273$		0			0
$274$	−8.40866	−	7.11787i	−0.507986	−	0.430006i
$275$		−	14.0768i		−	0.848862i
$276$		0			0
$277$	−17.6898			−1.06288			−0.531439	−	0.847097i	$-0.678348\pi$
$277$	−17.6898			−1.06288			−0.531439	+	0.847097i	$0.678348\pi$
$278$	3.45911	−	19.1335i	0.207463	−	1.14755i
$279$		0			0
$280$	18.3323	−	18.5189i	1.09557	−	1.10671i
$281$	5.96654	−	10.3343i	0.355934	−	0.616495i	−0.631344	−	0.775503i	$-0.717496\pi$
$281$	5.96654	−	10.3343i	0.355934	−	0.616495i	0.987277	+	0.159008i	$0.0508296\pi$
$282$		0			0
$283$	9.08689	−	15.7390i	0.540160	−	0.935584i	−0.458735	−	0.888573i	$-0.651697\pi$
$283$	9.08689	−	15.7390i	0.540160	−	0.935584i	0.998894	−	0.0470106i	$-0.0149694\pi$
$284$	−2.90638	+	0.486603i	−0.172462	+	0.0288746i
$285$		0			0
$286$	3.16961	−	17.5322i	0.187423	−	1.03670i
$287$	−3.83323	−	13.3391i	−0.226269	−	0.787379i
$288$		0			0
$289$	−7.77819	+	13.4722i	−0.457540	+	0.792483i
$290$	6.67804	+	18.5975i	0.392148	+	1.09208i
$291$		0			0
$292$	14.1268	+	17.1343i	0.826706	+	1.00271i
$293$	−11.7151	+	6.76373i	−0.684405	+	0.395141i	−0.801513	−	0.597978i	$-0.795971\pi$
$293$	−11.7151	+	6.76373i	−0.684405	+	0.395141i	0.117108	+	0.993119i	$0.462638\pi$
$294$		0			0
$295$	−43.7802	−	25.2765i	−2.54898	−	1.47166i
$296$	−1.40108	−	2.50110i	−0.0814362	−	0.145373i
$297$		0			0
$298$	−22.1169	−	18.7218i	−1.28120	−	1.08452i
$299$	1.88204	+	3.25979i	0.108841	+	0.188518i
$300$		0			0
$301$	5.65343	−	5.86106i	0.325858	−	0.337826i
$302$	20.1199	−	23.7685i	1.15777	−	1.36772i
$303$		0			0
$304$	−3.43861	+	17.7054i	−0.197218	+	1.01547i
$305$	−6.88724	−	11.9291i	−0.394362	−	0.683056i
$306$		0			0
$307$	−30.1730			−1.72206			−0.861031	−	0.508553i	$-0.830181\pi$
$307$	−30.1730			−1.72206			−0.861031	+	0.508553i	$0.830181\pi$
$308$	0.813342	−	10.4221i	0.0463445	−	0.593852i
$309$		0			0
$310$	8.78700	+	24.4707i	0.499068	+	1.38984i
$311$	−10.6227	+	18.3990i	−0.602357	+	1.04331i	0.390106	+	0.920770i	$0.372438\pi$
$311$	−10.6227	+	18.3990i	−0.602357	+	1.04331i	−0.992463	+	0.122543i	$0.960895\pi$
$312$		0			0
$313$	−5.89379	+	3.40278i	−0.333137	+	0.192336i	−0.657233	−	0.753688i	$-0.728273\pi$
$313$	−5.89379	+	3.40278i	−0.333137	+	0.192336i	0.324096	+	0.946024i	$0.394940\pi$
$314$	−5.36493	−	14.9407i	−0.302761	−	0.843151i
$315$		0			0
$316$	0.817915	+	0.992046i	0.0460113	+	0.0558070i
$317$	5.88259	+	10.1889i	0.330399	+	0.572268i	0.982590	−	0.185786i	$-0.0594833\pi$
$317$	5.88259	+	10.1889i	0.330399	+	0.572268i	−0.652191	+	0.758055i	$0.726150\pi$
$318$		0			0
$319$	6.86517	+	3.96361i	0.384376	+	0.221919i
$320$	−24.4782	+	13.2983i	−1.36837	+	0.743396i
$321$		0			0
$322$	1.29146	+	1.79162i	0.0719704	+	0.0998432i
$323$			5.41767i			0.301447i
$324$		0			0
$325$	−39.3507	+	22.7191i	−2.18278	+	1.26023i
$326$	−4.13969	−	11.5285i	−0.229276	−	0.638506i
$327$		0			0
$328$	−0.192414	+	14.8359i	−0.0106243	+	0.819177i
$329$	−0.889312	+	0.255561i	−0.0490293	+	0.0140895i
$330$		0			0
$331$	−7.21741	+	4.16697i	−0.396705	+	0.229038i	−0.685061	−	0.728486i	$-0.740225\pi$
$331$	−7.21741	+	4.16697i	−0.396705	+	0.229038i	0.288356	+	0.957523i	$0.406891\pi$
$332$	−3.76843	−	1.40861i	−0.206820	−	0.0773076i
$333$		0			0
$334$	6.20840	−	34.3408i	0.339709	−	1.87905i
$335$	−8.51478	+	14.7480i	−0.465212	+	0.805771i
$336$		0			0
$337$	−8.90728	−	15.4279i	−0.485210	−	0.840409i	0.514645	−	0.857403i	$-0.327924\pi$
$337$	−8.90728	−	15.4279i	−0.485210	−	0.840409i	−0.999856	+	0.0169941i	$0.994590\pi$
$338$	−36.8226	+	13.2223i	−2.00288	+	0.719200i
$339$		0			0
$340$	−6.45628	+	5.32303i	−0.350141	+	0.288682i
$341$	9.03322	+	5.21533i	0.489177	+	0.282426i
$342$		0			0
$343$	12.3687	−	13.7846i	0.667844	−	0.744301i
$344$	−7.59504	+	4.25464i	−0.409497	+	0.229395i
$345$		0			0
$346$	−1.00610	−	0.181890i	−0.0540881	−	0.00977846i
$347$	−10.4898	−	6.05632i	−0.563125	−	0.325120i	0.191274	−	0.981537i	$-0.438738\pi$
$347$	−10.4898	−	6.05632i	−0.563125	−	0.325120i	−0.754399	+	0.656417i	$0.772071\pi$
$348$		0			0
$349$	9.68839	+	5.59359i	0.518607	+	0.299418i	0.736365	−	0.676585i	$-0.236541\pi$
$349$	9.68839	+	5.59359i	0.518607	+	0.299418i	−0.217757	+	0.976003i	$0.569874\pi$
$350$	−21.6276	+	15.5899i	−1.15605	+	0.833317i
$351$		0			0
$352$	−4.04833	+	10.4165i	−0.215777	+	0.555202i
$353$			30.1679i			1.60568i	0.596197	+	0.802838i	$0.296678\pi$
$353$			30.1679i			1.60568i	−0.596197	+	0.802838i	$0.703322\pi$
$354$		0			0
$355$	5.13067			0.272308
$356$	−2.64423	+	7.07406i	−0.140144	+	0.374925i
$357$		0			0
$358$	16.5361	+	2.98952i	0.873958	+	0.158001i
$359$	−24.5853	−	14.1944i	−1.29757	−	0.749150i	−0.317582	−	0.948231i	$-0.602871\pi$
$359$	−24.5853	−	14.1944i	−1.29757	−	0.749150i	−0.979983	+	0.199081i	$0.936204\pi$
$360$		0			0
$361$	−0.665788	−	1.15318i	−0.0350415	−	0.0606936i
$362$	4.78171	−	5.64885i	0.251321	−	0.296897i
$363$		0			0
$364$	−30.4469	+	14.5470i	−1.59585	+	0.762469i
$365$	−19.3320	−	33.4841i	−1.01189	−	1.75264i
$366$		0			0
$367$	35.2632			1.84072			0.920362	−	0.391066i	$-0.127894\pi$
$367$	35.2632			1.84072			0.920362	+	0.391066i	$0.127894\pi$
$368$	−0.769047	−	2.23230i	−0.0400894	−	0.116367i
$369$		0			0
$370$	1.68684	+	4.69764i	0.0876946	+	0.244219i
$371$	15.3415	−	4.40869i	0.796493	−	0.228888i
$372$		0			0
$373$	−11.4118			−0.590880			−0.295440	−	0.955361i	$-0.595466\pi$
$373$	−11.4118			−0.590880			−0.295440	+	0.955361i	$0.595466\pi$
$374$	−0.597201	+	3.30333i	−0.0308805	+	0.170811i
$375$		0			0
$376$	0.989108	+	0.0128282i	0.0510093	+	0.000661563i
$377$		−	25.5882i		−	1.31786i
$378$		0			0
$379$			14.3418i			0.736686i	0.929690	+	0.368343i	$0.120075\pi$
$379$			14.3418i			0.736686i	−0.929690	+	0.368343i	$0.879925\pi$
$380$	10.9950	−	29.4147i	0.564031	−	1.50894i
$381$		0			0
$382$	−22.0875	−	3.99314i	−1.13009	−	0.204307i
$383$	−18.6443			−0.952678			−0.476339	−	0.879262i	$-0.658037\pi$
$383$	−18.6443			−0.952678			−0.476339	+	0.879262i	$0.658037\pi$
$384$		0			0
$385$	−4.39299	+	17.6627i	−0.223888	+	0.900174i
$386$	−1.17881	+	0.423291i	−0.0600001	+	0.0215450i
$387$		0			0
$388$	11.9748	−	32.0360i	0.607930	−	1.62638i
$389$	15.9211			0.807231			0.403615	−	0.914929i	$-0.367753\pi$
$389$	15.9211			0.807231			0.403615	+	0.914929i	$0.367753\pi$
$390$		0			0
$391$	−0.354605	−	0.614193i	−0.0179331	−	0.0310611i
$392$	−16.9133	+	10.2927i	−0.854250	+	0.519862i
$393$		0			0
$394$	−2.34390	−	1.98410i	−0.118084	−	0.0999574i
$395$	−1.11929	−	1.93867i	−0.0563177	−	0.0975450i
$396$		0			0
$397$	−4.13873	−	2.38950i	−0.207717	−	0.119925i	0.392533	−	0.919738i	$-0.371599\pi$
$397$	−4.13873	−	2.38950i	−0.207717	−	0.119925i	−0.600250	+	0.799813i	$0.704932\pi$
$398$	3.26097	−	18.0376i	0.163458	−	0.904141i
$399$		0			0
$400$	26.9473	−	9.28358i	1.34737	−	0.464179i
$401$	33.2918			1.66251			0.831256	−	0.555890i	$-0.187622\pi$
$401$	33.2918			1.66251			0.831256	+	0.555890i	$0.187622\pi$
$402$		0			0
$403$		−	33.6690i		−	1.67717i
$404$	−9.80184	+	1.64108i	−0.487660	+	0.0816468i
$405$		0			0
$406$	−1.51342	−	14.9374i	−0.0751099	−	0.741329i
$407$	1.73411	+	1.00119i	0.0859565	+	0.0496270i
$408$		0			0
$409$	8.34763	+	4.81951i	0.412764	+	0.238309i	0.691977	−	0.721920i	$-0.256740\pi$
$409$	8.34763	+	4.81951i	0.412764	+	0.238309i	−0.279213	+	0.960229i	$0.590073\pi$
$410$	4.59573	−	25.4206i	0.226967	−	1.25543i
$411$		0			0
$412$	−5.01257	−	29.9391i	−0.246952	−	1.47499i
$413$	27.6455	+	26.6661i	1.36034	+	1.31216i
$414$		0			0
$415$	6.06609	+	3.50226i	0.297773	+	0.171919i
$416$	35.6524	−	5.49481i	1.74800	−	0.269405i
$417$		0			0
$418$	−4.25748	−	11.8566i	−0.208240	−	0.579923i
$419$	−5.29413	−	9.16971i	−0.258635	−	0.447970i	0.707241	−	0.706972i	$-0.249939\pi$
$419$	−5.29413	−	9.16971i	−0.258635	−	0.447970i	−0.965877	+	0.259003i	$0.916606\pi$
$420$		0			0
$421$	−12.4805	+	21.6168i	−0.608261	+	1.05354i	0.383266	+	0.923638i	$0.374799\pi$
$421$	−12.4805	+	21.6168i	−0.608261	+	1.05354i	−0.991527	+	0.129901i	$0.958534\pi$
$422$	14.2859	+	2.58272i	0.695428	+	0.125725i
$423$		0			0
$424$	−17.0631	−	0.221299i	−0.828659	−	0.0107472i
$425$	7.41426	−	4.28062i	0.359644	−	0.207641i
$426$		0			0
$427$	2.89059	+	10.0588i	0.139885	+	0.486779i
$428$	7.81830	−	20.9161i	0.377912	−	1.01102i
$429$		0			0
$430$	14.2652	−	5.12239i	0.687931	−	0.247024i
$431$	25.0572	−	14.4668i	1.20696	−	0.696841i	0.244870	−	0.969556i	$-0.421255\pi$
$431$	25.0572	−	14.4668i	1.20696	−	0.696841i	0.962095	+	0.272715i	$0.0879215\pi$
$432$		0			0
$433$		−	11.0967i		−	0.533275i	−0.963797	−	0.266637i	$-0.914087\pi$
$433$		−	11.0967i		−	0.533275i	0.963797	−	0.266637i	$-0.0859126\pi$
$434$	−1.99137	−	19.6546i	−0.0955887	−	0.943453i
$435$		0			0
$436$	−7.21900	+	5.95186i	−0.345727	+	0.285043i
$437$	2.30496	+	1.33077i	0.110261	+	0.0636593i
$438$		0			0
$439$	6.98423	+	12.0970i	0.333339	+	0.577361i	0.983164	−	0.182723i	$-0.0584912\pi$
$439$	6.98423	+	12.0970i	0.333339	+	0.577361i	−0.649825	+	0.760084i	$0.725158\pi$
$440$	9.94645	−	16.7231i	0.474178	−	0.797242i
$441$		0			0
$442$	10.1981	−	3.66195i	0.485073	−	0.174181i
$443$	1.79243	−	1.03486i	0.0851609	−	0.0491676i	−0.456815	−	0.889562i	$-0.651010\pi$
$443$	1.79243	−	1.03486i	0.0851609	−	0.0491676i	0.541976	+	0.840394i	$0.317676\pi$
$444$		0			0
$445$	6.57440	−	11.3872i	0.311657	−	0.539805i
$446$	24.6895	−	8.86555i	1.16908	−	0.419796i
$447$		0			0
$448$	20.4875	−	5.31633i	0.967942	−	0.251173i
$449$	−15.9634			−0.753361			−0.376680	−	0.926343i	$-0.622934\pi$
$449$	−15.9634			−0.753361			−0.376680	+	0.926343i	$0.622934\pi$
$450$		0			0
$451$	−5.18167	−	8.97491i	−0.243995	−	0.422612i
$452$	−17.3621	+	14.3145i	−0.816643	+	0.673300i
$453$		0			0
$454$	6.50799	+	5.50897i	0.305435	+	0.258549i
$455$	56.4649	−	16.2263i	2.64712	−	0.760700i
$456$		0			0
$457$	−6.54273	−	11.3323i	−0.306056	−	0.530104i	0.671440	−	0.741059i	$-0.265676\pi$
$457$	−6.54273	−	11.3323i	−0.306056	−	0.530104i	−0.977496	+	0.210955i	$0.932343\pi$
$458$	2.66030	−	3.14273i	0.124308	−	0.146850i
$459$		0			0
$460$	0.678804	+	4.05436i	0.0316494	+	0.189035i
$461$	−4.13795	−	2.38905i	−0.192724	−	0.111269i	0.400533	−	0.916282i	$-0.368825\pi$
$461$	−4.13795	−	2.38905i	−0.192724	−	0.111269i	−0.593257	+	0.805013i	$0.702158\pi$
$462$		0			0
$463$	−14.5389	+	8.39406i	−0.675681	+	0.390105i	−0.798226	−	0.602358i	$-0.794228\pi$
$463$	−14.5389	+	8.39406i	−0.675681	+	0.390105i	0.122545	+	0.992463i	$0.460895\pi$
$464$	−3.06002	+	15.7561i	−0.142058	+	0.731457i
$465$		0			0
$466$	−12.3652	+	4.44012i	−0.572806	+	0.205684i
$467$	17.1928	−	29.7788i	0.795587	−	1.37800i	−0.126879	−	0.991918i	$-0.540496\pi$
$467$	17.1928	−	29.7788i	0.795587	−	1.37800i	0.922466	−	0.386079i	$-0.126171\pi$
$468$		0			0
$469$	8.98289	−	9.31279i	0.414791	−	0.430025i
$470$	−1.69478	−	0.306396i	−0.0781746	−	0.0141330i
$471$		0			0
$472$	−20.0683	−	35.8243i	−0.923719	−	1.64895i
$473$	3.04029	−	5.26593i	0.139793	−	0.242128i
$474$		0			0
$475$	−16.0644	+	27.8244i	−0.737087	+	1.27667i
$476$	5.73665	−	2.74087i	0.262939	−	0.125628i
$477$		0			0
$478$	7.78647	+	1.40770i	0.356145	+	0.0643866i
$479$	10.2893			0.470130			0.235065	−	0.971980i	$-0.424470\pi$
$479$	10.2893			0.470130			0.235065	+	0.971980i	$0.424470\pi$
$480$		0			0
$481$		−	6.46344i		−	0.294707i
$482$	−1.98007	+	2.33915i	−0.0901899	+	0.106545i
$483$		0			0
$484$	2.34385	+	13.9994i	0.106539	+	0.636334i
$485$	−29.7732	+	51.5688i	−1.35193	+	2.34162i
$486$		0			0
$487$	23.9091	−	13.8039i	1.08343	−	0.625516i	0.151607	−	0.988441i	$-0.451555\pi$
$487$	23.9091	−	13.8039i	1.08343	−	0.625516i	0.931818	+	0.362925i	$0.118222\pi$
$488$	0.145097	−	11.1876i	0.00656821	−	0.506437i
$489$		0			0
$490$	32.0023	−	12.8119i	1.44572	−	0.578783i
$491$	−28.0754	+	16.2093i	−1.26702	+	0.731516i	−0.974424	−	0.224719i	$-0.927854\pi$
$491$	−28.0754	+	16.2093i	−1.26702	+	0.731516i	−0.292599	+	0.956235i	$0.594520\pi$
$492$		0			0
$493$			4.82119i			0.217136i
$494$	−26.2729	+	31.0373i	−1.18207	+	1.39643i
$495$		0			0
$496$	−4.02639	+	20.7319i	−0.180790	+	0.930890i
$497$	−3.78305	−	0.940903i	−0.169693	−	0.0422053i
$498$		0			0
$499$			7.13521i			0.319416i	0.987164	+	0.159708i	$0.0510552\pi$
$499$			7.13521i			0.319416i	−0.987164	+	0.159708i	$0.948945\pi$
$500$	−14.5988	+	2.44422i	−0.652879	+	0.109309i
$501$		0			0
$502$	−15.4835	−	13.1067i	−0.691062	−	0.584979i
$503$	−13.4502			−0.599716			−0.299858	−	0.953984i	$-0.596939\pi$
$503$	−13.4502			−0.599716			−0.299858	+	0.953984i	$0.596939\pi$
$504$		0			0
$505$	17.3033			0.769987
$506$	1.25871	+	1.06549i	0.0559567	+	0.0473669i
$507$		0			0
$508$	21.1205	−	3.53612i	0.937072	−	0.156890i
$509$		−	5.90623i		−	0.261789i	−0.991396	−	0.130895i	$-0.958215\pi$
$509$		−	5.90623i		−	0.261789i	0.991396	−	0.130895i	$-0.0417849\pi$
$510$		0			0
$511$	8.11370	+	28.2344i	0.358929	+	1.24902i
$512$	−22.6103	−	0.880124i	−0.999243	−	0.0388963i
$513$		0			0
$514$	0.992884	−	1.17294i	0.0437942	−	0.0517361i
$515$			52.8518i			2.32893i
$516$		0			0
$517$	−0.598355	+	0.345461i	−0.0263156	+	0.0151933i
$518$	−0.382282	−	3.77310i	−0.0167965	−	0.165780i
$519$		0			0
$520$	−62.8013	−	0.814497i	−2.75402	−	0.0357181i
$521$	37.1446	−	21.4454i	1.62733	−	0.939542i	0.642451	−	0.766327i	$-0.277918\pi$
$521$	37.1446	−	21.4454i	1.62733	−	0.939542i	0.984884	−	0.173215i	$-0.0554155\pi$
$522$		0			0
$523$	4.11355	−	7.12488i	0.179873	−	0.311549i	−0.761964	−	0.647619i	$-0.775765\pi$
$523$	4.11355	−	7.12488i	0.179873	−	0.311549i	0.941837	+	0.336070i	$0.109098\pi$
$524$	1.87455	+	11.1963i	0.0818900	+	0.489112i
$525$		0			0
$526$	3.30003	−	3.89847i	0.143888	−	0.169981i
$527$			6.34375i			0.276338i
$528$		0			0
$529$	22.6516			0.984852
$530$	29.2368	+	5.28565i	1.26997	+	0.229594i
$531$		0			0
$532$	−13.5013	+	19.6723i	−0.585357	+	0.852901i
$533$	−16.7258	+	28.9700i	−0.724476	+	1.25483i
$534$		0			0
$535$	−19.4388	+	33.6690i	−0.840412	+	1.45564i
$536$	−12.0680	+	6.76031i	−0.521257	+	0.292001i
$537$		0			0
$538$	30.5018	+	5.51434i	1.31502	+	0.237740i
$539$	6.47825	−	12.2178i	0.279038	−	0.526257i
$540$		0			0
$541$	5.48118	−	9.49369i	0.235654	−	0.408165i	−0.723808	−	0.690001i	$-0.757610\pi$
$541$	5.48118	−	9.49369i	0.235654	−	0.408165i	0.959463	+	0.281836i	$0.0909433\pi$
$542$	−19.9495	+	7.16351i	−0.856904	+	0.307699i
$543$		0			0
$544$	−6.71745	+	1.03530i	−0.288008	+	0.0443883i
$545$	14.1075	−	8.14494i	0.604297	−	0.348891i
$546$		0			0
$547$	−4.82709	−	2.78692i	−0.206391	−	0.119160i	0.393242	−	0.919435i	$-0.371354\pi$
$547$	−4.82709	−	2.78692i	−0.206391	−	0.119160i	−0.599633	+	0.800275i	$0.704687\pi$
$548$	2.57270	+	15.3662i	0.109900	+	0.656412i
$549$		0			0
$550$	−12.8621	+	15.1946i	−0.548444	+	0.647901i
$551$	−9.04655	−	15.6691i	−0.385396	−	0.667525i
$552$		0			0
$553$	0.469769	+	1.63472i	0.0199766	+	0.0695154i
$554$	19.0946	+	16.1634i	0.811251	+	0.686718i
$555$		0			0
$556$	−21.2164	+	17.4923i	−0.899774	+	0.741839i
$557$	−14.6473	−	25.3699i	−0.620626	−	1.07496i	−0.989369	−	0.145425i	$-0.953545\pi$
$557$	−14.6473	−	25.3699i	−0.620626	−	1.07496i	0.368743	−	0.929531i	$-0.379788\pi$
$558$		0			0
$559$	−19.6274			−0.830151
$560$	−36.7091	+	3.23893i	−1.55124	+	0.136870i
$561$		0			0
$562$	−15.8830	+	5.70329i	−0.669983	+	0.240579i
$563$	4.68201	−	8.10948i	0.197323	−	0.341774i	−0.750336	−	0.661056i	$-0.770108\pi$
$563$	4.68201	−	8.10948i	0.197323	−	0.341774i	0.947660	+	0.319282i	$0.103442\pi$
$564$		0			0
$565$	33.9292	−	19.5890i	1.42741	−	0.824116i
$566$	−24.1894	+	8.68598i	−1.01676	+	0.365099i
$567$		0			0
$568$	3.58180	+	2.13036i	0.150289	+	0.0893878i
$569$	−13.9962	−	24.2421i	−0.586750	−	1.01628i	−0.994655	−	0.103257i	$-0.967074\pi$
$569$	−13.9962	−	24.2421i	−0.586750	−	1.01628i	0.407905	−	0.913025i	$-0.366260\pi$
$570$		0			0
$571$	−10.7880	−	6.22848i	−0.451466	−	0.260654i	0.256983	−	0.966416i	$-0.417271\pi$
$571$	−10.7880	−	6.22848i	−0.451466	−	0.260654i	−0.708449	+	0.705762i	$0.750605\pi$
$572$	−19.4407	+	16.0283i	−0.812857	+	0.670178i
$573$		0			0
$574$	−8.05044	+	17.9008i	−0.336019	+	0.747165i
$575$		−	4.20588i		−	0.175397i
$576$		0			0
$577$	−23.8836	+	13.7892i	−0.994289	+	0.574053i	−0.906554	−	0.422091i	$-0.861296\pi$
$577$	−23.8836	+	13.7892i	−0.994289	+	0.574053i	−0.0877357	+	0.996144i	$0.527963\pi$
$578$	20.7056	−	7.43502i	0.861240	−	0.309256i
$579$		0			0
$580$	9.78446	−	26.1762i	0.406278	−	1.08691i
$581$	−3.83049	−	3.69480i	−0.158916	−	0.153286i
$582$		0			0
$583$	10.3222	−	5.95955i	0.427504	−	0.246819i
$584$	0.407276	−	31.4028i	0.0168532	−	1.29946i
$585$		0			0
$586$	18.8255	+	3.40343i	0.777676	+	0.140594i
$587$	0.790747	−	1.36961i	0.0326376	−	0.0565300i	−0.849245	−	0.527999i	$-0.822943\pi$
$587$	0.790747	−	1.36961i	0.0326376	−	0.0565300i	0.881883	+	0.471469i	$0.156276\pi$
$588$		0			0
$589$	−11.9035	−	20.6175i	−0.490475	−	0.849527i
$590$	24.1613	+	67.2864i	0.994707	+	2.77014i
$591$		0			0
$592$	−0.772946	+	3.97990i	−0.0317679	+	0.163573i
$593$	15.1545	+	8.74947i	0.622322	+	0.359298i	0.777773	−	0.628546i	$-0.216350\pi$
$593$	15.1545	+	8.74947i	0.622322	+	0.359298i	−0.155450	+	0.987844i	$0.549683\pi$
$594$		0			0
$595$	−10.6388	+	3.05728i	−0.436150	+	0.125336i
$596$	6.76684	+	40.4169i	0.277180	+	1.65554i
$597$		0			0
$598$	0.947020	−	5.23830i	0.0387265	−	0.214210i
$599$	8.75858	+	5.05677i	0.357866	+	0.206614i	0.668144	−	0.744032i	$-0.267089\pi$
$599$	8.75858	+	5.05677i	0.357866	+	0.206614i	−0.310278	+	0.950646i	$0.600422\pi$
$600$		0			0
$601$	−3.06836	−	1.77152i	−0.125161	−	0.0722618i	0.436112	−	0.899892i	$-0.356355\pi$
$601$	−3.06836	−	1.77152i	−0.125161	−	0.0722618i	−0.561273	+	0.827630i	$0.689688\pi$
$602$	−11.4577	+	1.16087i	−0.466981	+	0.0473135i
$603$		0			0
$604$	−43.4352	+	7.27218i	−1.76735	+	0.295901i
$605$		−	24.7132i		−	1.00474i
$606$		0			0
$607$	−18.5731			−0.753857			−0.376929	−	0.926242i	$-0.623020\pi$
$607$	−18.5731			−0.753857			−0.376929	+	0.926242i	$0.623020\pi$
$608$	19.8893	−	15.9695i	0.806619	−	0.647648i
$609$		0			0
$610$	−3.46558	+	19.1693i	−0.140317	+	0.776143i
$611$	1.93142	+	1.11511i	0.0781370	+	0.0451124i
$612$		0			0
$613$	13.5566	+	23.4808i	0.547548	+	0.948381i	0.998442	+	0.0558032i	$0.0177719\pi$
$613$	13.5566	+	23.4808i	0.547548	+	0.948381i	−0.450894	+	0.892578i	$0.648895\pi$
$614$	32.5690	+	27.5694i	1.31438	+	1.11261i
$615$		0			0
$616$	−10.4007	+	10.5065i	−0.419057	+	0.423320i
$617$	10.1963	+	17.6606i	0.410489	+	0.710987i	0.994943	−	0.100439i	$-0.0320248\pi$
$617$	10.1963	+	17.6606i	0.410489	+	0.710987i	−0.584454	+	0.811427i	$0.698691\pi$
$618$		0			0
$619$	24.0272			0.965734			0.482867	−	0.875694i	$-0.339595\pi$
$619$	24.0272			0.965734			0.482867	+	0.875694i	$0.339595\pi$
$620$	12.8744	−	34.4428i	0.517050	−	1.38325i
$621$		0			0
$622$	28.2777	−	10.1540i	1.13383	−	0.407139i
$623$	−6.93584	+	7.19056i	−0.277879	+	0.288084i
$624$		0			0
$625$	−9.85557			−0.394223
$626$	9.47098	+	1.71224i	0.378537	+	0.0684348i
$627$		0			0
$628$	−7.86054	+	21.0291i	−0.313670	+	0.839154i
$629$			1.21781i			0.0485572i
$630$		0			0
$631$			17.1069i			0.681016i	0.940242	+	0.340508i	$0.110599\pi$
$631$			17.1069i			0.681016i	−0.940242	+	0.340508i	$0.889401\pi$
$632$	0.0235806	−	1.81817i	0.000937985	−	0.0723227i
$633$		0			0
$634$	2.96005	−	16.3731i	0.117559	−	0.650257i
$635$	−37.2843			−1.47958
$636$		0			0
$637$	−44.6095	+	1.60930i	−1.76749	+	0.0637626i
$638$	−3.78874	−	10.5512i	−0.149997	−	0.417725i
$639$		0			0
$640$	38.5728	+	8.01178i	1.52473	+	0.316693i
$641$	−30.3467			−1.19862			−0.599311	−	0.800516i	$-0.704559\pi$
$641$	−30.3467			−1.19862			−0.599311	+	0.800516i	$0.704559\pi$
$642$		0			0
$643$	−2.71240	−	4.69801i	−0.106967	−	0.185272i	0.807573	−	0.589767i	$-0.200780\pi$
$643$	−2.71240	−	4.69801i	−0.106967	−	0.185272i	−0.914540	+	0.404496i	$0.867447\pi$
$644$	0.243012	−	3.11392i	0.00957600	−	0.122706i
$645$		0			0
$646$	4.95020	−	5.84789i	0.194763	−	0.230082i
$647$	9.98684	+	17.2977i	0.392623	+	0.680043i	0.992795	−	0.119828i	$-0.0382343\pi$
$647$	9.98684	+	17.2977i	0.392623	+	0.680043i	−0.600171	+	0.799871i	$0.704901\pi$
$648$		0			0
$649$	24.8384	+	14.3404i	0.974992	+	0.562912i
$650$	63.2343	+	11.4320i	2.48025	+	0.448399i
$651$		0			0
$652$	−6.06535	+	16.2265i	−0.237537	+	0.635479i
$653$	−32.1932			−1.25982			−0.629909	−	0.776669i	$-0.716908\pi$
$653$	−32.1932			−1.25982			−0.629909	+	0.776669i	$0.716908\pi$
$654$		0			0
$655$		−	19.7649i		−	0.772280i
$656$	13.7635	−	15.8382i	0.537374	−	0.618379i
$657$		0			0
$658$	1.19344	+	0.536721i	0.0465252	+	0.0209236i
$659$	3.30688	+	1.90923i	0.128818	+	0.0743729i	0.563024	−	0.826440i	$-0.309638\pi$
$659$	3.30688	+	1.90923i	0.128818	+	0.0743729i	−0.434206	+	0.900813i	$0.642971\pi$
$660$		0			0
$661$	35.9322	+	20.7455i	1.39760	+	0.806906i	0.994141	−	0.108092i	$-0.0344740\pi$
$661$	35.9322	+	20.7455i	1.39760	+	0.806906i	0.403460	+	0.914997i	$0.367807\pi$
$662$	11.5980	+	2.09677i	0.450768	+	0.0814933i
$663$		0			0
$664$	2.78062	+	4.96374i	0.107909	+	0.192630i
$665$	28.8400	−	29.8991i	1.11837	−	1.15944i
$666$		0			0
$667$	2.05119	+	1.18425i	0.0794223	+	0.0458545i
$668$	−38.0791	+	31.3952i	−1.47333	+	1.21472i
$669$		0			0
$670$	22.6664	−	8.13911i	0.875680	−	0.314441i
$671$	3.90742	+	6.76786i	0.150844	+	0.261270i
$672$		0			0
$673$	−3.35200	+	5.80584i	−0.129210	+	0.223799i	−0.923371	−	0.383909i	$-0.874578\pi$
$673$	−3.35200	+	5.80584i	−0.129210	+	0.223799i	0.794161	+	0.607708i	$0.207911\pi$
$674$	−4.48203	+	24.7917i	−0.172642	+	0.954941i
$675$		0			0
$676$	51.8281	+	19.3730i	1.99339	+	0.745114i
$677$	−15.7745	+	9.10739i	−0.606262	+	0.350025i	−0.771501	−	0.636228i	$-0.780494\pi$
$677$	−15.7745	+	9.10739i	−0.606262	+	0.350025i	0.165239	+	0.986253i	$0.447160\pi$
$678$		0			0
$679$	31.4101	−	32.5636i	1.20541	−	1.24968i
$680$	11.8327	+	0.153464i	0.453763	+	0.00588506i
$681$		0			0
$682$	−4.98524	−	13.8833i	−0.190895	−	0.531618i
$683$	−41.8382	+	24.1553i	−1.60090	+	0.924278i	−0.609588	+	0.792719i	$0.708665\pi$
$683$	−41.8382	+	24.1553i	−1.60090	+	0.924278i	−0.991308	+	0.131559i	$0.958002\pi$
$684$		0			0
$685$		−	27.1262i		−	1.03644i
$686$	−25.9461	+	3.57789i	−0.990626	+	0.136604i
$687$		0			0
$688$	12.0857	+	2.34719i	0.460763	+	0.0894859i
$689$	−33.3191	−	19.2368i	−1.26935	−	0.732862i
$690$		0			0
$691$	−2.71691	−	4.70582i	−0.103356	−	0.179018i	0.809709	−	0.586831i	$-0.199625\pi$
$691$	−2.71691	−	4.70582i	−0.103356	−	0.179018i	−0.913065	+	0.407813i	$0.866291\pi$
$692$	0.919796	+	1.11562i	0.0349654	+	0.0424094i
$693$		0			0
$694$	5.78911	+	16.1220i	0.219752	+	0.611982i
$695$	41.4613	−	23.9377i	1.57272	−	0.908008i
$696$		0			0
$697$	3.15140	−	5.45838i	0.119368	−	0.206751i
$698$	−5.34681	−	14.8902i	−0.202380	−	0.563602i
$699$		0			0
$700$	37.5898	+	2.93352i	1.42076	+	0.110877i
$701$	17.6328			0.665980			0.332990	−	0.942930i	$-0.391942\pi$
$701$	17.6328			0.665980			0.332990	+	0.942930i	$0.391942\pi$
$702$		0			0
$703$	−2.28511	−	3.95793i	−0.0861846	−	0.149276i
$704$	13.8875	−	7.54467i	0.523406	−	0.284350i
$705$		0			0
$706$	27.5648	−	32.5636i	1.03742	−	1.22555i
$707$	−12.7584	−	3.17322i	−0.479829	−	0.119341i
$708$		0			0
$709$	−8.40413	−	14.5564i	−0.315624	−	0.546677i	0.663946	−	0.747780i	$-0.268880\pi$
$709$	−8.40413	−	14.5564i	−0.315624	−	0.546677i	−0.979570	+	0.201104i	$0.935547\pi$
$710$	−5.53810	−	4.68797i	−0.207841	−	0.175936i
$711$		0			0
$712$	9.31788	−	5.21975i	0.349202	−	0.195618i
$713$	2.69896	+	1.55825i	0.101077	+	0.0583568i
$714$		0			0
$715$	37.9913	−	21.9343i	1.42079	−	0.820295i
$716$	−15.1176	−	18.3361i	−0.564973	−	0.685254i
$717$		0			0
$718$	13.5681	+	37.7855i	0.506357	+	1.41014i
$719$	−15.1910	+	26.3116i	−0.566530	+	0.981258i	0.430376	+	0.902650i	$0.358381\pi$
$719$	−15.1910	+	26.3116i	−0.566530	+	0.981258i	−0.996906	+	0.0786083i	$0.974952\pi$
$720$		0			0
$721$	9.69238	−	38.9697i	0.360963	−	1.45131i
$722$	−0.335016	+	1.85309i	−0.0124680	+	0.0689650i
$723$		0			0
$724$	−10.3229	+	1.72831i	−0.383646	+	0.0642322i
$725$	−14.2958	+	24.7610i	−0.530931	+	0.919600i
$726$		0			0
$727$	2.64995	−	4.58985i	0.0982812	−	0.170228i	−0.812692	−	0.582693i	$-0.801999\pi$
$727$	2.64995	−	4.58985i	0.0982812	−	0.170228i	0.910973	+	0.412465i	$0.135332\pi$
$728$	46.1565	+	12.1176i	1.71067	+	0.449106i
$729$		0			0
$730$	−9.72765	+	53.8070i	−0.360036	+	1.99149i
$731$	3.69810			0.136779
$732$		0			0
$733$			49.1128i			1.81402i	0.421105	+	0.907012i	$0.361642\pi$
$733$			49.1128i			1.81402i	−0.421105	+	0.907012i	$0.638358\pi$
$734$	−38.0635	−	32.2205i	−1.40495	−	1.18928i
$735$		0			0
$736$	−1.20957	+	3.11226i	−0.0445853	+	0.114719i
$737$	4.83079	−	8.36718i	0.177945	−	0.308209i
$738$		0			0
$739$	−24.0001	+	13.8565i	−0.882859	+	0.509719i	−0.871600	−	0.490218i	$-0.836917\pi$
$739$	−24.0001	+	13.8565i	−0.882859	+	0.509719i	−0.0112591	+	0.999937i	$0.503584\pi$
$740$	2.47151	−	6.61197i	0.0908543	−	0.243061i
$741$		0			0
$742$	−20.5881	−	9.25899i	−0.755813	−	0.339908i
$743$	−32.0177	+	18.4854i	−1.17461	+	0.678164i	−0.954763	−	0.297369i	$-0.903891\pi$
$743$	−32.0177	+	18.4854i	−1.17461	+	0.678164i	−0.219852	+	0.975533i	$0.570557\pi$
$744$		0			0
$745$		−	71.3485i		−	2.61401i
$746$	12.3180	+	10.4271i	0.450994	+	0.381764i
$747$		0			0
$748$	3.66292	−	3.01998i	0.133930	−	0.110421i
$749$	20.5075	−	21.2606i	0.749326	−	0.776846i
$750$		0			0
$751$			25.6840i			0.937222i	0.883405	+	0.468611i	$0.155245\pi$
$751$			25.6840i			0.937222i	−0.883405	+	0.468611i	$0.844755\pi$
$752$	−1.05593	−	0.917608i	−0.0385059	−	0.0334617i
$753$		0			0
$754$	−23.3803	+	27.6201i	−0.851459	+	1.00587i
$755$	76.6767			2.79055
$756$		0			0
$757$	32.8332			1.19334			0.596671	−	0.802486i	$-0.296490\pi$
$757$	32.8332			1.19334			0.596671	+	0.802486i	$0.296490\pi$
$758$	13.1043	−	15.4806i	0.475968	−	0.562282i
$759$		0			0
$760$	−38.7447	+	21.7043i	−1.40542	+	0.787296i
$761$			13.3912i			0.485432i	0.970097	+	0.242716i	$0.0780382\pi$
$761$			13.3912i			0.485432i	−0.970097	+	0.242716i	$0.921962\pi$
$762$		0			0
$763$	−11.8957	+	3.41845i	−0.430652	+	0.123756i
$764$	20.1929	+	24.4919i	0.730552	+	0.886085i
$765$		0			0
$766$	20.1248	+	17.0355i	0.727140	+	0.615519i
$767$		−	92.5787i		−	3.34282i
$768$		0			0
$769$	−1.88139	+	1.08622i	−0.0678447	+	0.0391702i	−0.533539	−	0.845776i	$-0.679138\pi$
$769$	−1.88139	+	1.08622i	−0.0678447	+	0.0391702i	0.465694	+	0.884946i	$0.345805\pi$
$770$	20.8805	−	15.0514i	0.752481	−	0.542414i
$771$		0			0
$772$	1.65919	+	0.620193i	0.0597156	+	0.0223212i
$773$	9.28632	−	5.36146i	0.334006	−	0.192838i	−0.323612	−	0.946190i	$-0.604897\pi$
$773$	9.28632	−	5.36146i	0.334006	−	0.192838i	0.657618	+	0.753351i	$0.271564\pi$
$774$		0			0
$775$	−18.8104	+	32.5806i	−0.675691	+	1.17033i
$776$	−42.1975	+	23.6385i	−1.51480	+	0.848571i
$777$		0			0
$778$	−17.1854	−	14.5473i	−0.616126	−	0.521546i
$779$			23.6533i			0.847467i
$780$		0			0
$781$	−2.91085			−0.104158
$782$	−0.178433	+	0.986974i	−0.00638074	+	0.0352941i
$783$		0			0
$784$	27.6610	+	4.34380i	0.987893	+	0.155136i
$785$	19.5438	−	33.8509i	0.697548	−	1.20819i
$786$		0			0
$787$	−12.2911	+	21.2888i	−0.438130	+	0.758863i	−0.997545	−	0.0700244i	$-0.977692\pi$
$787$	−12.2911	+	21.2888i	−0.438130	+	0.758863i	0.559416	+	0.828887i	$0.311026\pi$
$788$	0.717137	+	4.28331i	0.0255469	+	0.152587i
$789$		0			0
$790$	−0.563214	+	3.11533i	−0.0200382	+	0.110839i
$791$	−28.6097	+	8.22155i	−1.01724	+	0.292325i
$792$		0			0
$793$	12.6127	−	21.8459i	0.447891	−	0.775770i
$794$	2.28407	+	6.36086i	0.0810587	+	0.225739i
$795$		0			0
$796$	−20.0011	+	16.4903i	−0.708920	+	0.584485i
$797$	−29.3180	+	16.9267i	−1.03850	+	0.599576i	−0.919407	−	0.393308i	$-0.871331\pi$
$797$	−29.3180	+	16.9267i	−1.03850	+	0.599576i	−0.119089	+	0.992884i	$0.537997\pi$
$798$		0			0
$799$	−0.363909	−	0.210103i	−0.0128742	−	0.00743291i
$800$	−37.5698	−	14.6013i	−1.32829	−	0.516236i
$801$		0			0
$802$	−35.9355	−	30.4191i	−1.26893	−	1.07414i
$803$	10.9679	+	18.9969i	0.387048	+	0.670387i
$804$		0			0
$805$	−1.31255	+	5.27729i	−0.0462611	+	0.186000i
$806$	−30.7638	+	36.3427i	−1.08361	+	1.28012i
$807$		0			0
$808$	12.0797	+	7.18468i	0.424962	+	0.252756i
$809$	11.2283	+	19.4481i	0.394768	+	0.683758i	0.993072	−	0.117512i	$-0.0374917\pi$
$809$	11.2283	+	19.4481i	0.394768	+	0.683758i	−0.598304	+	0.801269i	$0.704158\pi$
$810$		0			0
$811$	47.6072			1.67172			0.835858	−	0.548946i	$-0.184971\pi$
$811$	47.6072			1.67172			0.835858	+	0.548946i	$0.184971\pi$
$812$	−12.0149	+	17.5064i	−0.421639	+	0.614353i
$813$		0			0
$814$	−0.957015	−	2.66517i	−0.0335434	−	0.0934141i
$815$	15.0804	−	26.1200i	0.528243	−	0.914944i
$816$		0			0
$817$	−12.0190	+	6.93916i	−0.420491	+	0.242770i
$818$	−4.60687	−	12.8296i	−0.161076	−	0.448576i
$819$		0			0
$820$	−28.1878	+	23.2401i	−0.984361	+	0.811578i
$821$	12.5572	+	21.7496i	0.438248	+	0.759068i	0.997554	−	0.0698933i	$-0.0222659\pi$
$821$	12.5572	+	21.7496i	0.438248	+	0.759068i	−0.559307	+	0.828961i	$0.688933\pi$
$822$		0			0
$823$	2.43553	+	1.40615i	0.0848972	+	0.0490154i	0.541848	−	0.840477i	$-0.317725\pi$
$823$	2.43553	+	1.40615i	0.0848972	+	0.0490154i	−0.456950	+	0.889492i	$0.651058\pi$
$824$	−21.9451	+	36.8966i	−0.764494	+	1.28535i
$825$		0			0
$826$	−5.47560	−	54.0438i	−0.190521	−	1.88042i
$827$			36.6231i			1.27351i	0.771066	+	0.636756i	$0.219724\pi$
$827$			36.6231i			1.27351i	−0.771066	+	0.636756i	$0.780276\pi$
$828$		0			0
$829$	15.8020	−	9.12326i	0.548825	−	0.316864i	−0.199823	−	0.979832i	$-0.564037\pi$
$829$	15.8020	−	9.12326i	0.548825	−	0.316864i	0.748648	+	0.662968i	$0.230703\pi$
$830$	−3.34774	−	9.32305i	−0.116202	−	0.323608i
$831$		0			0
$832$	−43.5043	−	26.6449i	−1.50824	−	0.923747i
$833$	8.40510	−	0.303215i	0.291219	−	0.0105058i
$834$		0			0
$835$	74.4147	−	42.9633i	2.57523	−	1.48681i
$836$	−6.23793	+	16.6882i	−0.215743	+	0.577174i
$837$		0			0
$838$	−2.66394	+	14.7352i	−0.0920244	+	0.509019i
$839$	−12.4481	+	21.5607i	−0.429755	+	0.744358i	−0.996851	−	0.0792938i	$-0.974733\pi$
$839$	−12.4481	+	21.5607i	−0.429755	+	0.744358i	0.567096	+	0.823652i	$0.308067\pi$
$840$		0			0
$841$	6.44946	+	11.1708i	0.222395	+	0.385200i
$842$	33.2231	−	11.9298i	1.14494	−	0.411129i
$843$		0			0
$844$	−13.0605	−	15.8411i	−0.449561	−	0.545271i
$845$	−83.4283	−	48.1674i	−2.87002	−	1.65701i
$846$		0			0
$847$	−4.53211	+	18.2220i	−0.155725	+	0.626116i
$848$	18.2159	+	15.8297i	0.625537	+	0.543594i
$849$		0			0
$850$	−11.9143	−	2.15396i	−0.408657	−	0.0738802i
$851$	0.518119	+	0.299136i	0.0177609	+	0.0102543i
$852$		0			0
$853$	38.8466	+	22.4281i	1.33008	+	0.767924i	0.985312	−	0.170763i	$-0.0546232\pi$
$853$	38.8466	+	22.4281i	1.33008	+	0.767924i	0.344771	+	0.938687i	$0.387956\pi$
$854$	6.07073	−	13.4987i	0.207736	−	0.461917i
$855$		0			0
$856$	−27.5505	+	15.4334i	−0.941657	+	0.527504i
$857$		−	7.51550i		−	0.256725i	−0.991727	−	0.128362i	$-0.959028\pi$
$857$		−	7.51550i		−	0.256725i	0.991727	−	0.128362i	$-0.0409721\pi$
$858$		0			0
$859$	30.9241			1.05512			0.527559	−	0.849519i	$-0.323107\pi$
$859$	30.9241			1.05512			0.527559	+	0.849519i	$0.323107\pi$
$860$	−20.0785	−	7.50518i	−0.684670	−	0.255924i
$861$		0			0
$862$	−40.2656	−	7.27952i	−1.37145	−	0.247941i
$863$	−37.2047	−	21.4801i	−1.26646	−	0.731192i	−0.292146	−	0.956374i	$-0.594369\pi$
$863$	−37.2047	−	21.4801i	−1.26646	−	0.731192i	−0.974317	+	0.225181i	$0.927703\pi$
$864$		0			0
$865$	−1.25871	−	2.18015i	−0.0427975	−	0.0741274i
$866$	−10.1392	+	11.9779i	−0.344545	+	0.407027i
$867$		0			0
$868$	−15.8092	+	23.0350i	−0.536600	+	0.781858i
$869$	0.635021	+	1.09989i	0.0215416	+	0.0373112i
$870$		0			0
$871$	−31.1865			−1.05671
$872$	13.2306	+	0.171593i	0.448043	+	0.00581087i
$873$		0			0
$874$	−1.27206	−	3.54252i	−0.0430279	−	0.119828i
$875$	−19.0023	−	4.72618i	−0.642396	−	0.159774i
$876$		0			0
$877$	8.25082			0.278610			0.139305	−	0.990249i	$-0.455513\pi$
$877$	8.25082			0.278610			0.139305	+	0.990249i	$0.455513\pi$
$878$	3.51438	−	19.4393i	0.118605	−	0.656044i
$879$		0			0
$880$	−26.0164	+	8.96288i	−0.877013	+	0.302138i
$881$			22.1964i			0.747816i	0.927466	+	0.373908i	$0.121982\pi$
$881$			22.1964i			0.747816i	−0.927466	+	0.373908i	$0.878018\pi$
$882$		0			0
$883$		−	48.0915i		−	1.61841i	−0.587529	−	0.809203i	$-0.699899\pi$
$883$		−	48.0915i		−	1.61841i	0.587529	−	0.809203i	$-0.300101\pi$
$884$	−14.3539	−	5.36538i	−0.482774	−	0.180457i
$885$		0			0
$886$	−2.88033	−	0.520729i	−0.0967666	−	0.0174942i
$887$	42.7483			1.43535			0.717674	−	0.696379i	$-0.245207\pi$
$887$	42.7483			1.43535			0.717674	+	0.696379i	$0.245207\pi$
$888$		0			0
$889$	27.4912	+	6.83749i	0.922025	+	0.229322i
$890$	−17.5011	+	6.28434i	−0.586639	+	0.210652i
$891$		0			0
$892$	−34.7506	−	12.9895i	−1.16354	−	0.434922i
$893$	1.57696			0.0527710
$894$		0			0
$895$	20.6880	+	35.8327i	0.691525	+	1.19776i
$896$	−26.9720	−	12.9812i	−0.901071	−	0.433671i
$897$		0			0
$898$	17.2311	+	14.5860i	0.575009	+	0.486741i
$899$	−10.5929	−	18.3475i	−0.353294	−	0.611923i
$900$		0			0
$901$	6.27781	+	3.62450i	0.209144	+	0.120749i
$902$	−2.60735	+	14.4222i	−0.0868153	+	0.480206i
$903$		0			0
$904$	31.8202	+	0.412690i	1.05832	+	0.0137259i
$905$	18.2231			0.605755
$906$		0			0
$907$		−	16.3986i		−	0.544508i	−0.962225	−	0.272254i	$-0.912231\pi$
$907$		−	16.3986i		−	0.544508i	0.962225	−	0.272254i	$-0.0877690\pi$
$908$	−1.99117	−	11.8929i	−0.0660794	−	0.394679i
$909$		0			0
$910$	−75.7750	−	34.0779i	−2.51192	−	1.12967i
$911$	−6.37439	−	3.68026i	−0.211193	−	0.121932i	0.390673	−	0.920530i	$-0.372242\pi$
$911$	−6.37439	−	3.68026i	−0.211193	−	0.121932i	−0.601866	+	0.798597i	$0.705576\pi$
$912$		0			0
$913$	−3.44155	−	1.98698i	−0.113899	−	0.0657594i
$914$	−3.29222	+	18.2104i	−0.108897	+	0.602347i
$915$		0			0
$916$	−5.74312	+	0.961545i	−0.189758	+	0.0317703i
$917$	−3.62465	+	14.5735i	−0.119696	+	0.481258i
$918$		0			0
$919$	−10.1235	−	5.84481i	−0.333944	−	0.192802i	0.323647	−	0.946178i	$-0.395091\pi$
$919$	−10.1235	−	5.84481i	−0.333944	−	0.192802i	−0.657591	+	0.753375i	$0.728424\pi$
$920$	2.97182	−	4.99655i	0.0979778	−	0.164731i
$921$		0			0
$922$	2.28364	+	6.35966i	0.0752078	+	0.209444i
$923$	4.69794	+	8.13708i	0.154635	+	0.267835i
$924$		0			0
$925$	−3.61104	+	6.25450i	−0.118730	+	0.205647i
$926$	23.3632	+	4.22379i	0.767764	+	0.138802i
$927$		0			0
$928$	17.6996	−	14.2113i	0.581016	−	0.466508i
$929$	24.5685	−	14.1846i	0.806065	−	0.465382i	−0.0395223	−	0.999219i	$-0.512584\pi$
$929$	24.5685	−	14.1846i	0.806065	−	0.465382i	0.845588	+	0.533837i	$0.179250\pi$
$930$		0			0
$931$	−26.7480	+	16.7569i	−0.876629	+	0.549185i
$932$	17.4041	+	6.50552i	0.570090	+	0.213095i
$933$		0			0
$934$	−45.7673	+	16.4342i	−1.49755	+	0.537745i
$935$	−7.15813	+	4.13275i	−0.234096	+	0.135155i
$936$		0			0
$937$		−	49.8946i		−	1.62999i	−0.579470	−	0.814993i	$-0.696741\pi$
$937$		−	49.8946i		−	1.62999i	0.579470	−	0.814993i	$-0.303259\pi$
$938$	−18.2054	+	1.84454i	−0.594429	+	0.0602263i
$939$		0			0
$940$	1.54941	+	1.87928i	0.0505362	+	0.0612952i
$941$	10.8025	+	6.23683i	0.352151	+	0.203315i	0.665632	−	0.746280i	$-0.268162\pi$
$941$	10.8025	+	6.23683i	0.352151	+	0.203315i	−0.313481	+	0.949594i	$0.601495\pi$
$942$		0			0
$943$	−1.54819	−	2.68154i	−0.0504159	−	0.0873229i
$944$	−11.0713	+	57.0059i	−0.360339	+	1.85538i
$945$		0			0
$946$	−8.09327	+	2.90615i	−0.263135	+	0.0944871i
$947$	−24.4507	+	14.1166i	−0.794541	+	0.458728i	−0.841559	−	0.540166i	$-0.818362\pi$
$947$	−24.4507	+	14.1166i	−0.794541	+	0.458728i	0.0470178	+	0.998894i	$0.485028\pi$
$948$		0			0
$949$	35.4031	−	61.3200i	1.14923	−	1.99053i
$950$	42.7637	−	15.3557i	1.38744	−	0.498204i
$951$		0			0
$952$	−8.69657	−	2.28313i	−0.281857	−	0.0739966i
$953$	2.77543			0.0899050			0.0449525	−	0.998989i	$-0.485686\pi$
$953$	2.77543			0.0899050			0.0449525	+	0.998989i	$0.485686\pi$
$954$		0			0
$955$	−27.6333	−	47.8623i	−0.894193	−	1.54879i
$956$	−7.11856	−	8.63409i	−0.230231	−	0.279246i
$957$		0			0
$958$	−11.1064	−	9.40147i	−0.358831	−	0.303748i
$959$	−4.97461	+	20.0012i	−0.160638	+	0.645871i
$960$		0			0
$961$	1.56177	+	2.70506i	0.0503796	+	0.0872601i
$962$	−5.90573	+	6.97671i	−0.190408	+	0.224938i
$963$		0			0
$964$	4.27462	−	0.715682i	0.137676	−	0.0230506i
$965$	−2.67082	−	1.54200i	−0.0859767	−	0.0496387i
$966$		0			0
$967$	−33.2406	+	19.1915i	−1.06894	+	0.617156i	−0.927893	−	0.372847i	$-0.878382\pi$
$967$	−33.2406	+	19.1915i	−1.06894	+	0.617156i	−0.141052	+	0.990002i	$0.545048\pi$
$968$	10.2614	−	17.2527i	0.329815	−	0.554522i
$969$		0			0
$970$	79.2566	−	28.4597i	2.54478	−	0.913785i
$971$	22.7039	−	39.3244i	0.728604	−	1.26198i	−0.228870	−	0.973457i	$-0.573503\pi$
$971$	22.7039	−	39.3244i	0.728604	−	1.26198i	0.957473	−	0.288522i	$-0.0931637\pi$
$972$		0			0
$973$	−34.9609	+	10.0467i	−1.12079	+	0.322082i
$974$	−38.4206	−	6.94597i	−1.23107	−	0.222563i
$975$		0			0
$976$	−10.3789	+	11.9434i	−0.332219	+	0.382299i
$977$	19.2557	−	33.3519i	0.616046	−	1.06702i	−0.374154	−	0.927366i	$-0.622067\pi$
$977$	19.2557	−	33.3519i	0.616046	−	1.06702i	0.990200	−	0.139656i	$-0.0445997\pi$
$978$		0			0
$979$	−3.72994	+	6.46044i	−0.119209	+	0.206477i
$980$	−46.2500	−	15.4116i	−1.47740	−	0.492306i
$981$		0			0
$982$	45.1155	+	8.15633i	1.43969	+	0.260279i
$983$	6.34126			0.202255			0.101127	−	0.994873i	$-0.467755\pi$
$983$	6.34126			0.202255			0.101127	+	0.994873i	$0.467755\pi$
$984$		0			0
$985$		−	7.56138i		−	0.240926i
$986$	4.40519	−	5.20405i	0.140290	−	0.165731i
$987$		0			0
$988$	56.7184	−	9.49612i	1.80445	−	0.302112i
$989$	0.908382	−	1.57336i	0.0288849	−	0.0500300i
$990$		0			0
$991$	−39.7136	+	22.9287i	−1.26154	+	0.728353i	−0.973373	−	0.229226i	$-0.926380\pi$
$991$	−39.7136	+	22.9287i	−1.26154	+	0.728353i	−0.288171	+	0.957579i	$0.593047\pi$
$992$	23.2892	−	18.6993i	0.739431	−	0.593702i
$993$		0			0
$994$	3.22374	+	4.47224i	0.102251	+	0.141851i
$995$	39.0864	−	22.5665i	1.23912	−	0.715407i
$996$		0			0
$997$			41.3718i			1.31026i	0.755518	+	0.655128i	$0.227385\pi$
$997$			41.3718i			1.31026i	−0.755518	+	0.655128i	$0.772615\pi$
$998$	6.51954	−	7.70182i	0.206372	−	0.243797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.10		84
3.2	odd	2		252.2.n.b.187.33	yes	84
4.3	odd	2	inner	756.2.n.b.19.20		84
7.3	odd	6		756.2.bj.b.451.37		84
9.4	even	3		756.2.bj.b.523.37		84
9.5	odd	6		252.2.bj.b.103.6	yes	84
12.11	even	2		252.2.n.b.187.23	yes	84
21.17	even	6		252.2.bj.b.115.6	yes	84
28.3	even	6		756.2.bj.b.451.38		84
36.23	even	6		252.2.bj.b.103.5	yes	84
36.31	odd	6		756.2.bj.b.523.38		84
63.31	odd	6	inner	756.2.n.b.199.20		84
63.59	even	6		252.2.n.b.31.23	✓	84
84.59	odd	6		252.2.bj.b.115.5	yes	84
252.31	even	6	inner	756.2.n.b.199.10		84
252.59	odd	6		252.2.n.b.31.33	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.23	✓	84	63.59	even	6
252.2.n.b.31.33	yes	84	252.59	odd	6
252.2.n.b.187.23	yes	84	12.11	even	2
252.2.n.b.187.33	yes	84	3.2	odd	2
252.2.bj.b.103.5	yes	84	36.23	even	6
252.2.bj.b.103.6	yes	84	9.5	odd	6
252.2.bj.b.115.5	yes	84	84.59	odd	6
252.2.bj.b.115.6	yes	84	21.17	even	6
756.2.n.b.19.10		84	1.1	even	1	trivial
756.2.n.b.19.20		84	4.3	odd	2	inner
756.2.n.b.199.10		84	252.31	even	6	inner
756.2.n.b.199.20		84	63.31	odd	6	inner
756.2.bj.b.451.37		84	7.3	odd	6
756.2.bj.b.451.38		84	28.3	even	6
756.2.bj.b.523.37		84	9.4	even	3
756.2.bj.b.523.38		84	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.07941 - 0.913714i) q^{2} +(0.330255 + 1.97254i) q^{4} -3.48216i q^{5} +(-0.638585 + 2.56753i) q^{7} +(1.44586 - 2.43094i) q^{8} +O(q^{10})\)	\(q+(-1.07941 - 0.913714i) q^{2} +(0.330255 + 1.97254i) q^{4} -3.48216i q^{5} +(-0.638585 + 2.56753i) q^{7} +(1.44586 - 2.43094i) q^{8} +(-3.18169 + 3.75868i) q^{10} +1.97557i q^{11} +(5.52258 - 3.18847i) q^{13} +(3.03528 - 2.18793i) q^{14} +(-3.78186 + 1.30288i) q^{16} +(-1.04054 + 0.600755i) q^{17} +(2.25453 - 3.90496i) q^{19} +(6.86871 - 1.15000i) q^{20} +(1.80511 - 2.13246i) q^{22} +0.590265i q^{23} -7.12541 q^{25} +(-8.87448 - 1.60440i) q^{26} +(-5.27546 - 0.411699i) q^{28} +(2.00631 - 3.47503i) q^{29} +(2.63991 - 4.57246i) q^{31} +(5.27265 + 2.04919i) q^{32} +(1.67209 + 0.302292i) q^{34} +(8.94054 + 2.22365i) q^{35} +(0.506783 - 0.877774i) q^{37} +(-6.00157 + 2.15506i) q^{38} +(-8.46493 - 5.03471i) q^{40} +(-4.54294 + 2.62287i) q^{41} +(-2.66552 - 1.53894i) q^{43} +(-3.89691 + 0.652443i) q^{44} +(0.539333 - 0.637139i) q^{46} +(0.174866 + 0.302877i) q^{47} +(-6.18442 - 3.27917i) q^{49} +(7.69124 + 6.51059i) q^{50} +(8.11325 + 9.84054i) q^{52} +(-3.01662 - 5.22494i) q^{53} +6.87926 q^{55} +(5.31822 + 5.26465i) q^{56} +(-5.34081 + 1.91779i) q^{58} +(7.25888 - 12.5727i) q^{59} +(3.42577 - 1.97787i) q^{61} +(-7.02746 + 2.52344i) q^{62} +(-3.81897 - 7.02961i) q^{64} +(-11.1027 - 19.2305i) q^{65} +(-4.23532 - 2.44526i) q^{67} +(-1.52866 - 1.85410i) q^{68} +(-7.61873 - 10.5693i) q^{70} +1.47342i q^{71} +(9.61590 - 5.55174i) q^{73} +(-1.34906 + 0.484424i) q^{74} +(8.44727 + 3.15753i) q^{76} +(-5.07235 - 1.26157i) q^{77} +(0.556744 - 0.321436i) q^{79} +(4.53685 + 13.1690i) q^{80} +(7.30024 + 1.31979i) q^{82} +(-1.00577 + 1.74205i) q^{83} +(2.09192 + 3.62331i) q^{85} +(1.47104 + 4.09667i) q^{86} +(4.80251 + 2.85640i) q^{88} +(3.27016 + 1.88803i) q^{89} +(4.65984 + 16.2155i) q^{91} +(-1.16432 + 0.194938i) q^{92} +(0.0879904 - 0.486706i) q^{94} +(-13.5977 - 7.85062i) q^{95} +(-14.8094 - 8.55023i) q^{97} +(3.67930 + 9.19036i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 84 * q + q^2 + q^4 + 16 * q^8	\( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

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