LMFDB - Embedded newform 756.2.n.b.19.20

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			19.20
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.251594 - 1.39165i) q^{2} +(-1.87340 + 0.700263i) q^{4} -3.48216i q^{5} +(0.638585 - 2.56753i) q^{7} +(1.44586 + 2.43094i) q^{8} +O(q^{10})$	\(q+(-0.251594 - 1.39165i) q^{2} +(-1.87340 + 0.700263i) q^{4} -3.48216i q^{5} +(0.638585 - 2.56753i) q^{7} +(1.44586 + 2.43094i) q^{8} +(-4.84596 + 0.876089i) q^{10} -1.97557i q^{11} +(5.52258 - 3.18847i) q^{13} +(-3.73378 - 0.242715i) q^{14} +(3.01926 - 2.62375i) q^{16} +(-1.04054 + 0.600755i) q^{17} +(-2.25453 + 3.90496i) q^{19} +(2.43843 + 6.52347i) q^{20} +(-2.74932 + 0.497042i) q^{22} -0.590265i q^{23} -7.12541 q^{25} +(-5.82669 - 6.88333i) q^{26} +(0.601621 + 5.25719i) q^{28} +(2.00631 - 3.47503i) q^{29} +(-2.63991 + 4.57246i) q^{31} +(-4.41098 - 3.54165i) q^{32} +(1.09784 + 1.29692i) q^{34} +(-8.94054 - 2.22365i) q^{35} +(0.506783 - 0.877774i) q^{37} +(6.00157 + 2.15506i) q^{38} +(8.46493 - 5.03471i) q^{40} +(-4.54294 + 2.62287i) q^{41} +(2.66552 + 1.53894i) q^{43} +(1.38342 + 3.70104i) q^{44} +(-0.821445 + 0.148507i) q^{46} +(-0.174866 - 0.302877i) q^{47} +(-6.18442 - 3.27917i) q^{49} +(1.79271 + 9.91611i) q^{50} +(-8.11325 + 9.84054i) q^{52} +(-3.01662 - 5.22494i) q^{53} -6.87926 q^{55} +(7.16483 - 2.15993i) q^{56} +(-5.34081 - 1.91779i) q^{58} +(-7.25888 + 12.5727i) q^{59} +(3.42577 - 1.97787i) q^{61} +(7.02746 + 2.52344i) q^{62} +(-3.81897 + 7.02961i) q^{64} +(-11.1027 - 19.2305i) q^{65} +(4.23532 + 2.44526i) q^{67} +(1.52866 - 1.85410i) q^{68} +(-0.845170 + 13.0016i) q^{70} -1.47342i q^{71} +(9.61590 - 5.55174i) q^{73} +(-1.34906 - 0.484424i) q^{74} +(1.48914 - 8.89431i) q^{76} +(-5.07235 - 1.26157i) q^{77} +(-0.556744 + 0.321436i) q^{79} +(-9.13630 - 10.5135i) q^{80} +(4.79310 + 5.66230i) q^{82} +(1.00577 - 1.74205i) q^{83} +(2.09192 + 3.62331i) q^{85} +(1.47104 - 4.09667i) q^{86} +(4.80251 - 2.85640i) q^{88} +(3.27016 + 1.88803i) q^{89} +(-4.65984 - 16.2155i) q^{91} +(0.413341 + 1.10580i) q^{92} +(-0.377504 + 0.319555i) q^{94} +(13.5977 + 7.85062i) q^{95} +(-14.8094 - 8.55023i) q^{97} +(-3.00751 + 9.43159i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.251594	−	1.39165i	−0.177904	−	0.984048i
$2$	−0.251594	−	1.39165i	−0.177904	−	0.984048i
$3$		0			0
$3$		0			0
$4$	−1.87340	+	0.700263i	−0.936700	+	0.350132i
$5$		−	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
$10$	−4.84596	+	0.876089i	−1.53243	+	0.277044i
$11$		−	1.97557i		−	0.595658i	−0.954619	−	0.297829i	$-0.903737\pi$
$11$		−	1.97557i		−	0.595658i	0.954619	−	0.297829i	$-0.0962625\pi$
$12$		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	$-0.0120450\pi$
$14$	−3.73378	−	0.242715i	−0.997894	−	0.0648682i
$15$		0			0
$16$	3.01926	−	2.62375i	0.754816	−	0.655937i
$17$	−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	$0.339701\pi$
$19$	−2.25453	+	3.90496i	−0.517224	+	0.895858i	−0.999800	+	0.0200042i	$0.993632\pi$
$20$	2.43843	+	6.52347i	0.545249	+	1.45869i
$21$		0			0
$22$	−2.74932	+	0.497042i	−0.586156	+	0.105970i
$23$		−	0.590265i		−	0.123079i	−0.998105	−	0.0615394i	$-0.980399\pi$
$23$		−	0.590265i		−	0.123079i	0.998105	−	0.0615394i	$-0.0196010\pi$
$24$		0			0
$25$	−7.12541			−1.42508
$26$	−5.82669	−	6.88333i	−1.14271	−	1.34993i
$27$		0			0
$28$	0.601621	+	5.25719i	0.113696	+	0.993516i
$29$	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	−0.999562	−	0.0296057i	$-0.990575\pi$
$31$	−2.63991	+	4.57246i	−0.474142	+	0.821237i	0.525420	+	0.850843i	$0.323908\pi$
$32$	−4.41098	−	3.54165i	−0.779758	−	0.626081i
$33$		0			0
$34$	1.09784	+	1.29692i	0.188277	+	0.222420i
$35$	−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	0.689280	−	0.724495i	$-0.257927\pi$
$43$	2.66552	+	1.53894i	0.406488	+	0.234686i	−0.282792	+	0.959181i	$0.591261\pi$
$44$	1.38342	+	3.70104i	0.208559	+	0.557953i
$45$		0			0
$46$	−0.821445	+	0.148507i	−0.121115	+	0.0218962i
$47$	−0.174866	−	0.302877i	−0.0255068	−	0.0441791i	0.852990	−	0.521927i	$-0.174787\pi$
$47$	−0.174866	−	0.302877i	−0.0255068	−	0.0441791i	−0.878497	+	0.477748i	$0.841453\pi$
$48$		0			0
$49$	−6.18442	−	3.27917i	−0.883488	−	0.468453i
$50$	1.79271	+	9.91611i	0.253527	+	1.40235i
$51$		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
$56$	7.16483	−	2.15993i	0.957440	−	0.288632i
$57$		0			0
$58$	−5.34081	−	1.91779i	−0.701282	−	0.251818i
$59$	−7.25888	+	12.5727i	−0.945025	+	1.63683i	−0.189324	+	0.981915i	$0.560630\pi$
$59$	−7.25888	+	12.5727i	−0.945025	+	1.63683i	−0.755701	+	0.654917i	$0.772704\pi$
$60$		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	0.735881	−	0.677111i	$-0.236768\pi$
$67$	4.23532	+	2.44526i	0.517426	+	0.298736i	−0.218455	+	0.975847i	$0.570102\pi$
$68$	1.52866	−	1.85410i	0.185377	−	0.224843i
$69$		0			0
$70$	−0.845170	+	13.0016i	−0.101017	+	1.55399i
$71$		−	1.47342i		−	0.174863i	−0.996171	−	0.0874313i	$-0.972134\pi$
$71$		−	1.47342i		−	0.174863i	0.996171	−	0.0874313i	$-0.0278658\pi$
$72$		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
$76$	1.48914	−	8.89431i	0.170816	−	1.02025i
$77$	−5.07235	−	1.26157i	−0.578047	−	0.143770i
$78$		0			0
$79$	−0.556744	+	0.321436i	−0.0626386	+	0.0361644i	−0.530992	−	0.847377i	$-0.678181\pi$
$79$	−0.556744	+	0.321436i	−0.0626386	+	0.0361644i	0.468354	+	0.883541i	$0.344847\pi$
$80$	−9.13630	−	10.5135i	−1.02147	−	1.17545i
$81$		0			0
$82$	4.79310	+	5.66230i	0.529309	+	0.625296i
$83$	1.00577	−	1.74205i	0.110398	−	0.191215i	−0.805533	−	0.592551i	$-0.798121\pi$
$83$	1.00577	−	1.74205i	0.110398	−	0.191215i	0.915931	+	0.401336i	$0.131454\pi$
$84$		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
$92$	0.413341	+	1.10580i	0.0430938	+	0.115288i
$93$		0			0
$94$	−0.377504	+	0.319555i	−0.0389366	+	0.0329596i
$95$	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	$-0.668021\pi$
$98$	−3.00751	+	9.43159i	−0.303805	+	0.952734i
$99$		0			0
$100$	13.3488	−	4.98966i	1.33488	−	0.498966i
$101$			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	$-0.231129\pi$
$103$	15.1779			1.49552			0.747761	+	0.663968i	$0.231129\pi$
$104$	15.7359	+	8.81502i	1.54303	+	0.864383i
$105$		0			0
$106$	−6.51234	+	5.51265i	−0.632534	+	0.535436i
$107$	9.66900	+	5.58240i	0.934737	+	0.539671i	0.888307	−	0.459251i	$-0.151882\pi$
$107$	9.66900	+	5.58240i	0.934737	+	0.539671i	0.0464307	+	0.998922i	$0.485215\pi$
$108$		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	$0.761409\pi$
$110$	1.73078	+	9.57355i	0.165023	+	0.912802i
$111$		0			0
$112$	−4.80849	−	9.42753i	−0.454360	−	0.890818i
$113$	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
$116$	−1.32518	+	7.91506i	−0.123040	+	0.734895i
$117$		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
$122$	−3.61441	−	4.26986i	−0.327233	−	0.386575i
$123$		0			0
$124$	1.74368	−	10.4147i	0.156587	−	0.935265i
$125$			7.40101i			0.661967i
$126$		0			0
$127$			10.7073i			0.950115i	0.879955	+	0.475058i	$0.157573\pi$
$127$			10.7073i			0.950115i	−0.879955	+	0.475058i	$0.842427\pi$
$128$	10.7436	+	3.54608i	0.949610	+	0.313432i
$129$		0			0
$130$	−23.9688	+	20.2894i	−2.10220	+	1.77950i
$131$	−5.67606			−0.495920			−0.247960	−	0.968770i	$-0.579760\pi$
$131$	−5.67606			−0.495920			−0.247960	+	0.968770i	$0.579760\pi$
$132$		0			0
$133$	8.58638	+	8.28221i	0.744534	+	0.718159i
$134$	2.33738	−	6.50931i	0.201919	−	0.562318i
$135$		0			0
$136$	−2.96487	−	1.66088i	−0.254236	−	0.142419i
$137$	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	$-0.968515\pi$
$139$	−6.87438	−	11.9068i	−0.583078	−	1.00992i	0.412035	−	0.911168i	$-0.364818\pi$
$140$	18.3064	−	2.09494i	1.54717	−	0.177055i
$141$		0			0
$142$	−2.05049	+	0.370703i	−0.172073	+	0.0311087i
$143$	−6.29905	−	10.9103i	−0.526753	−	0.912363i
$144$		0			0
$145$	−12.1006	−	6.98628i	−1.00490	−	0.580179i
$146$	−10.1454	−	11.9852i	−0.839640	−	0.991904i
$147$		0			0
$148$	−0.334735	+	1.99930i	−0.0275150	+	0.164342i
$149$	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	$-0.646477\pi$
$151$		−	22.0199i		−	1.79195i	0.444100	−	0.895977i	$-0.353523\pi$
$152$	−12.7525	+	0.165392i	−1.03436	+	0.0134151i
$153$		0			0
$154$	−0.479501	+	7.37635i	−0.0386393	+	0.594403i
$155$	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	$0.518828\pi$
$158$	0.587401	+	0.693923i	0.0467311	+	0.0552056i
$159$		0			0
$160$	−12.3326	+	15.3597i	−0.974976	+	1.21429i
$161$	−1.51552	−	0.376935i	−0.119440	−	0.0297066i
$162$		0			0
$163$	−7.50110	−	4.33076i	−0.587531	−	0.339211i	0.176589	−	0.984285i	$-0.443494\pi$
$163$	−7.50110	−	4.33076i	−0.587531	−	0.339211i	−0.764121	+	0.645073i	$0.776827\pi$
$164$	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	$-0.762785\pi$
$167$	−12.3381	−	21.3703i	−0.954754	−	1.65368i	−0.219824	−	0.975540i	$-0.570548\pi$
$168$		0			0
$169$	13.8326	−	23.9588i	1.06405	−	1.84299i
$170$	4.51609	−	3.82284i	0.346368	−	0.293198i
$171$		0			0
$172$	−6.07125	−	1.01648i	−0.462928	−	0.0775061i
$173$	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
$176$	−5.18341	−	5.96478i	−0.390714	−	0.449612i
$177$		0			0
$178$	1.80473	−	5.02594i	0.135270	−	0.376710i
$179$	10.2904	−	5.94116i	0.769139	−	0.444063i	−0.0634282	−	0.997986i	$-0.520203\pi$
$179$	10.2904	−	5.94116i	0.769139	−	0.444063i	0.832568	+	0.553924i	$0.186870\pi$
$180$		0			0
$181$			5.23327i			0.388986i	0.980904	+	0.194493i	$0.0623062\pi$
$181$			5.23327i			0.388986i	−0.980904	+	0.194493i	$0.937694\pi$
$182$	−21.3940	+	10.5646i	−1.58583	+	0.783101i
$183$		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	−0.906633	−	0.421921i	$-0.861356\pi$
$191$	−13.7450	+	7.93569i	−0.994555	+	0.574207i	−0.0879222	+	0.996127i	$0.528023\pi$
$192$		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
$196$	13.8822	+	1.81248i	0.991584	+	0.129463i
$197$	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	0.539530	−	0.841966i	$-0.318602\pi$
$199$	−6.48062	−	11.2248i	−0.459399	−	0.795702i	−0.998929	+	0.0462638i	$0.985269\pi$
$200$	−10.3024	−	17.3215i	−0.728486	−	1.22481i
$201$		0			0
$202$	6.91532	−	1.25020i	0.486560	−	0.0879641i
$203$	−7.64104	−	7.37035i	−0.536296	−	0.517297i
$204$		0			0
$205$	9.13323	+	15.8192i	0.637892	+	1.10486i
$206$	−3.81867	−	21.1224i	−0.266059	−	1.47167i
$207$		0			0
$208$	8.30840	−	24.1167i	0.576084	−	1.67219i
$209$	7.71453	+	4.45399i	0.533625	+	0.308089i
$210$		0			0
$211$	8.89012	−	5.13271i	0.612021	−	0.353350i	−0.161735	−	0.986834i	$-0.551709\pi$
$211$	8.89012	−	5.13271i	0.612021	−	0.353350i	0.773756	+	0.633484i	$0.218376\pi$
$212$	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
$218$	5.04959	−	4.27445i	0.342002	−	0.289502i
$219$		0			0
$220$	12.8876	−	4.81729i	0.868882	−	0.324782i
$221$	−3.83097	+	6.63544i	−0.257699	+	0.446348i
$222$		0			0
$223$	9.27475	−	16.0643i	0.621083	−	1.07575i	−0.368201	−	0.929746i	$-0.620026\pi$
$223$	9.27475	−	16.0643i	0.621083	−	1.07575i	0.989284	−	0.146001i	$-0.0466403\pi$
$224$	−11.9101	+	9.06367i	−0.795775	+	0.605592i
$225$		0			0
$226$	12.1445	−	10.2803i	0.807843	−	0.683834i
$227$	6.02921			0.400172			0.200086	−	0.979778i	$-0.435878\pi$
$227$	6.02921			0.400172			0.200086	+	0.979778i	$0.435878\pi$
$228$		0			0
$229$			2.91153i			0.192399i	0.995362	+	0.0961995i	$0.0306687\pi$
$229$			2.91153i			0.192399i	−0.995362	+	0.0961995i	$0.969331\pi$
$230$	0.517125	+	2.86040i	0.0340982	+	0.188609i
$231$		0			0
$232$	11.3484	−	0.147183i	0.745061	−	0.00966303i
$233$	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
$236$	4.79455	−	28.6369i	0.312099	−	1.86410i
$237$		0			0
$238$	4.03095	−	1.99053i	0.261288	−	0.129027i
$239$	4.84551	−	2.79756i	0.313430	−	0.180959i	−0.335030	−	0.942207i	$-0.608747\pi$
$239$	4.84551	−	2.79756i	0.313430	−	0.180959i	0.648460	+	0.761248i	$0.275413\pi$
$240$		0			0
$241$		−	2.16706i		−	0.139593i	−0.997561	−	0.0697963i	$-0.977765\pi$
$241$		−	2.16706i		−	0.139593i	0.997561	−	0.0697963i	$-0.0222349\pi$
$242$	−1.78559	−	9.87672i	−0.114782	−	0.634899i
$243$		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
$248$	−14.9323	+	0.193664i	−0.948203	+	0.0122977i
$249$		0			0
$250$	10.2996	−	1.86205i	0.651407	−	0.117766i
$251$	−14.3444			−0.905410			−0.452705	−	0.891660i	$-0.649541\pi$
$251$	−14.3444			−0.905410			−0.452705	+	0.891660i	$0.649541\pi$
$252$		0			0
$253$	−1.16611			−0.0733129
$254$	14.9008	−	2.69388i	0.934959	−	0.169029i
$255$		0			0
$256$	2.23189	−	15.8436i	0.139493	−	0.990223i
$257$			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
$262$	1.42806	+	7.89912i	0.0882260	+	0.488009i
$263$		−	3.61167i		−	0.222705i	−0.993781	−	0.111352i	$-0.964482\pi$
$263$		−	3.61167i		−	0.222705i	0.993781	−	0.111352i	$-0.0355182\pi$
$264$		0			0
$265$	−18.1940	+	10.5043i	−1.11765	+	0.645276i
$266$	9.36569	−	14.0330i	0.574247	−	0.860420i
$267$		0			0
$268$	−9.64677	−	1.61512i	−0.589270	−	0.0986590i
$269$	−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	−0.998702	−	0.0509383i	$-0.983779\pi$
$271$	−7.49415	+	12.9802i	−0.455237	+	0.788494i	0.543465	+	0.839432i	$0.317112\pi$
$272$	−1.56543	+	4.54395i	−0.0949180	+	0.275517i
$273$		0			0
$274$	−1.95993	−	10.8410i	−0.118404	−	0.654932i
$275$			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	$0.678348\pi$
$278$	−14.8406	+	12.5624i	−0.890078	+	0.753445i
$279$		0			0
$280$	−7.52120	−	24.9490i	−0.449477	−	1.49099i
$281$	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	$0.348303\pi$
$283$	−9.08689	+	15.7390i	−0.540160	+	0.935584i	−0.998894	+	0.0470106i	$0.985031\pi$
$284$	1.03178	+	2.76030i	0.0612249	+	0.163794i
$285$		0			0
$286$	−13.5985	+	11.5111i	−0.804098	+	0.680663i
$287$	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
$296$	2.86656	−	0.0371776i	0.166615	−	0.00216091i
$297$		0			0
$298$	−5.15510	−	28.5146i	−0.298627	−	1.65181i
$299$	−1.88204	−	3.25979i	−0.108841	−	0.188518i
$300$		0			0
$301$	5.65343	−	5.86106i	0.325858	−	0.337826i
$302$	−30.6441	+	5.54007i	−1.76337	+	0.318795i
$303$		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	$-0.169819\pi$
$307$	30.1730			1.72206			0.861031	+	0.508553i	$0.169819\pi$
$308$	10.3860	−	1.18855i	0.591796	−	0.0677237i
$309$		0			0
$310$	8.78700	−	24.4707i	0.499068	−	1.38984i
$311$	10.6227	−	18.3990i	0.602357	−	1.04331i	−0.390106	−	0.920770i	$-0.627562\pi$
$311$	10.6227	−	18.3990i	0.602357	−	1.04331i	0.992463	−	0.122543i	$-0.0391051\pi$
$312$		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
$322$	−0.143266	+	2.20392i	−0.00798390	+	0.122820i
$323$		−	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
$328$	−12.9445	−	7.25133i	−0.714740	−	0.400388i
$329$	−0.889312	+	0.255561i	−0.0490293	+	0.0140895i
$330$		0			0
$331$	7.21741	−	4.16697i	0.396705	−	0.229038i	−0.288356	−	0.957523i	$-0.593109\pi$
$331$	7.21741	−	4.16697i	0.396705	−	0.229038i	0.685061	+	0.728486i	$0.259775\pi$
$332$	−0.664323	+	3.96786i	−0.0364594	+	0.217765i
$333$		0			0
$334$	−26.6358	+	22.5471i	−1.45745	+	1.23372i
$335$	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
$344$	0.112897	+	8.70482i	0.00608698	+	0.469332i
$345$		0			0
$346$	−0.660569	−	0.780360i	−0.0355124	−	0.0419524i
$347$	10.4898	+	6.05632i	0.563125	+	0.325120i	0.754399	−	0.656417i	$-0.227929\pi$
$347$	10.4898	+	6.05632i	0.563125	+	0.325120i	−0.191274	+	0.981537i	$0.561262\pi$
$348$		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	$0.569874\pi$
$350$	26.6047	+	1.72944i	1.42208	+	0.0924425i
$351$		0			0
$352$	−6.99679	+	8.71421i	−0.372930	+	0.464469i
$353$			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
$356$	−7.44843	−	1.24706i	−0.394766	−	0.0660940i
$357$		0			0
$358$	−10.8570	−	12.8259i	−0.573812	−	0.677869i
$359$	24.5853	+	14.1944i	1.29757	+	0.749150i	0.979983	−	0.199081i	$-0.0637958\pi$
$359$	24.5853	+	14.1944i	1.29757	+	0.749150i	0.317582	+	0.948231i	$0.397129\pi$
$360$		0			0
$361$	−0.665788	−	1.15318i	−0.0350415	−	0.0606936i
$362$	7.28290	−	1.31666i	0.382781	−	0.0692021i
$363$		0			0
$364$	20.0849	+	27.1150i	1.05273	+	1.42121i
$365$	−19.3320	−	33.4841i	−1.01189	−	1.75264i
$366$		0			0
$367$	−35.2632			−1.84072			−0.920362	−	0.391066i	$-0.872106\pi$
$367$	−35.2632			−1.84072			−0.920362	+	0.391066i	$0.872106\pi$
$368$	−1.54871	−	1.78217i	−0.0807319	−	0.0929018i
$369$		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	$0.595466\pi$
$374$	2.56217	−	2.16886i	0.132486	−	0.112149i
$375$		0			0
$376$	0.483444	−	0.863007i	0.0249317	−	0.0445062i
$377$		−	25.5882i		−	1.31786i
$378$		0			0
$379$		−	14.3418i		−	0.736686i	−0.929690	−	0.368343i	$-0.879925\pi$
$379$		−	14.3418i		−	0.736686i	0.929690	−	0.368343i	$-0.120075\pi$
$380$	−30.9714	−	5.18541i	−1.58880	−	0.266006i
$381$		0			0
$382$	14.5019	+	17.1317i	0.741982	+	0.876536i
$383$	18.6443			0.952678			0.476339	−	0.879262i	$-0.341963\pi$
$383$	18.6443			0.952678			0.476339	+	0.879262i	$0.341963\pi$
$384$		0			0
$385$	−4.39299	+	17.6627i	−0.223888	+	0.900174i
$386$	−1.17881	−	0.423291i	−0.0600001	−	0.0215450i
$387$		0			0
$388$	33.7314	+	5.64751i	1.71245	+	0.286709i
$389$	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
$392$	−0.970321	−	19.7752i	−0.0490086	−	0.998798i
$393$		0			0
$394$	−0.546328	−	3.02193i	−0.0275236	−	0.152243i
$395$	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	$0.704932\pi$
$398$	−13.9905	+	11.8429i	−0.701280	+	0.593629i
$399$		0			0
$400$	−21.5135	+	18.6953i	−1.07567	+	0.934764i
$401$	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
$404$	−3.47970	−	9.30918i	−0.173122	−	0.463149i
$405$		0			0
$406$	−8.33454	+	12.4880i	−0.413636	+	0.619770i
$407$	−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	$0.590073\pi$
$410$	19.7170	−	16.6903i	0.973754	−	0.824276i
$411$		0			0
$412$	−28.4343	+	10.6285i	−1.40086	+	0.523630i
$413$	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	0.965877	−	0.259003i	$-0.0833938\pi$
$419$	5.29413	+	9.16971i	0.258635	+	0.447970i	−0.707241	+	0.706972i	$0.750061\pi$
$420$		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	$0.958534\pi$
$422$	−9.37966	−	11.0806i	−0.456595	−	0.539396i
$423$		0			0
$424$	8.33992	−	14.8878i	0.405022	−	0.723013i
$425$	7.41426	−	4.28062i	0.359644	−	0.207641i
$426$		0			0
$427$	−2.89059	−	10.0588i	−0.139885	−	0.486779i
$428$	−22.0231	−	3.68723i	−1.06452	−	0.178229i
$429$		0			0
$430$	−14.2652	−	5.12239i	−0.687931	−	0.247024i
$431$	−25.0572	+	14.4668i	−1.20696	+	0.696841i	−0.962095	−	0.272715i	$-0.912079\pi$
$431$	−25.0572	+	14.4668i	−1.20696	+	0.696841i	−0.244870	+	0.969556i	$0.578745\pi$
$432$		0			0
$433$		−	11.0967i		−	0.533275i	−0.963797	−	0.266637i	$-0.914087\pi$
$433$		−	11.0967i		−	0.533275i	0.963797	−	0.266637i	$-0.0859126\pi$
$434$	10.9666	−	16.4318i	0.526415	−	0.788751i
$435$		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	0.649825	−	0.760084i	$-0.274842\pi$
$439$	−6.98423	−	12.0970i	−0.333339	−	0.577361i	−0.983164	+	0.182723i	$0.941509\pi$
$440$	−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	−0.541976	−	0.840394i	$-0.682324\pi$
$443$	−1.79243	+	1.03486i	−0.0851609	+	0.0491676i	0.456815	+	0.889562i	$0.348990\pi$
$444$		0			0
$445$	6.57440	−	11.3872i	0.311657	−	0.539805i
$446$	−24.6895	−	8.86555i	−1.16908	−	0.419796i
$447$		0			0
$448$	15.6100	+	14.2943i	0.737503	+	0.675344i
$449$	−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
$454$	−1.51691	−	8.39057i	−0.0711922	−	0.393789i
$455$	−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	$0.932343\pi$
$458$	4.05184	−	0.732522i	0.189330	−	0.0342285i
$459$		0			0
$460$	3.85058	−	1.43932i	0.179534	−	0.0671086i
$461$	−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	−0.122545	−	0.992463i	$-0.539105\pi$
$463$	14.5389	−	8.39406i	0.675681	−	0.390105i	0.798226	+	0.602358i	$0.205772\pi$
$464$	−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	$0.459504\pi$
$467$	−17.1928	+	29.7788i	−0.795587	+	1.37800i	−0.922466	+	0.386079i	$0.873829\pi$
$468$		0			0
$469$	8.98289	−	9.31279i	0.414791	−	0.430025i
$470$	1.11274	+	1.31453i	0.0513268	+	0.0606347i
$471$		0			0
$472$	−41.0589	+	0.532512i	−1.88989	+	0.0245108i
$473$	3.04029	−	5.26593i	0.139793	−	0.242128i
$474$		0			0
$475$	16.0644	−	27.8244i	0.737087	−	1.27667i
$476$	−3.78429	−	5.10888i	−0.173453	−	0.234165i
$477$		0			0
$478$	−5.11234	−	6.03943i	−0.233833	−	0.276237i
$479$	−10.2893			−0.470130			−0.235065	−	0.971980i	$-0.575530\pi$
$479$	−10.2893			−0.470130			−0.235065	+	0.971980i	$0.575530\pi$
$480$		0			0
$481$		−	6.46344i		−	0.294707i
$482$	−3.01580	+	0.545219i	−0.137366	+	0.0248341i
$483$		0			0
$484$	−13.2957	+	4.96984i	−0.604351	+	0.225902i
$485$	−29.7732	+	51.5688i	−1.35193	+	2.34162i
$486$		0			0
$487$	−23.9091	+	13.8039i	−1.08343	+	0.625516i	−0.931818	−	0.362925i	$-0.881778\pi$
$487$	−23.9091	+	13.8039i	−1.08343	+	0.625516i	−0.151607	+	0.988441i	$0.548445\pi$
$488$	9.76127	+	5.46813i	0.441872	+	0.247530i
$489$		0			0
$490$	32.8423	+	10.4726i	1.48366	+	0.473105i
$491$	28.0754	−	16.2093i	1.26702	−	0.731516i	0.292599	−	0.956235i	$-0.405480\pi$
$491$	28.0754	−	16.2093i	1.26702	−	0.731516i	0.974424	+	0.224719i	$0.0721464\pi$
$492$		0			0
$493$			4.82119i			0.217136i
$494$	40.0155	−	7.23431i	1.80038	−	0.325487i
$495$		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	$-0.948945\pi$
$499$		−	7.13521i		−	0.319416i	0.987164	−	0.159708i	$-0.0510552\pi$
$500$	−5.18266	−	13.8651i	−0.231776	−	0.620065i
$501$		0			0
$502$	3.60896	+	19.9624i	0.161076	+	0.890967i
$503$	13.4502			0.599716			0.299858	−	0.953984i	$-0.403061\pi$
$503$	13.4502			0.599716			0.299858	+	0.953984i	$0.403061\pi$
$504$		0			0
$505$	17.3033			0.769987
$506$	0.293387	+	1.62283i	0.0130426	+	0.0721434i
$507$		0			0
$508$	−7.49790	−	20.0590i	−0.332665	−	0.889973i
$509$		−	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
$514$	1.51224	−	0.273394i	0.0667019	−	0.0120589i
$515$		−	52.8518i		−	2.32893i
$516$		0			0
$517$	−0.598355	+	0.345461i	−0.0263156	+	0.0151933i
$518$	−2.10526	+	3.15441i	−0.0924999	+	0.138597i
$519$		0			0
$520$	30.6953	−	54.7947i	1.34608	−	2.40291i
$521$	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	−0.941837	−	0.336070i	$-0.890902\pi$
$523$	−4.11355	+	7.12488i	−0.179873	+	0.311549i	0.761964	+	0.647619i	$0.224235\pi$
$524$	10.6335	−	3.97474i	0.464529	−	0.173637i
$525$		0			0
$526$	−5.02619	+	0.908673i	−0.219152	+	0.0396200i
$527$		−	6.34375i		−	0.276338i
$528$		0			0
$529$	22.6516			0.984852
$530$	19.1959	+	22.6770i	0.833817	+	0.985025i
$531$		0			0
$532$	−21.8855	−	9.50318i	−0.948855	−	0.412015i
$533$	−16.7258	+	28.9700i	−0.724476	+	1.25483i
$534$		0			0
$535$	19.4388	−	33.6690i	0.840412	−	1.45564i
$536$	0.179384	+	13.8313i	0.00774823	+	0.597422i
$537$		0			0
$538$	20.0264	+	23.6581i	0.863401	+	1.01997i
$539$	−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	0.599633	−	0.800275i	$-0.295313\pi$
$547$	4.82709	+	2.78692i	0.206391	+	0.119160i	−0.393242	+	0.919435i	$0.628646\pi$
$548$	−14.5939	+	5.45508i	−0.623420	+	0.233030i
$549$		0			0
$550$	19.5900	−	3.54163i	0.835321	−	0.151016i
$551$	9.04655	+	15.6691i	0.385396	+	0.667525i
$552$		0			0
$553$	0.469769	+	1.63472i	0.0199766	+	0.0695154i
$554$	4.45065	+	24.6181i	0.189090	+	1.04592i
$555$		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
$560$	−32.8281	+	16.7439i	−1.38724	+	0.707560i
$561$		0			0
$562$	−15.8830	−	5.70329i	−0.669983	−	0.240579i
$563$	−4.68201	+	8.10948i	−0.197323	+	0.341774i	−0.947660	−	0.319282i	$-0.896558\pi$
$563$	−4.68201	+	8.10948i	−0.197323	+	0.341774i	0.750336	+	0.661056i	$0.229892\pi$
$564$		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	0.708449	−	0.705762i	$-0.249395\pi$
$571$	10.7880	+	6.22848i	0.451466	+	0.260654i	−0.256983	+	0.966416i	$0.582729\pi$
$572$	19.4407	+	16.0283i	0.812857	+	0.670178i
$573$		0			0
$574$	17.5989	−	8.69056i	0.734565	−	0.362737i
$575$			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
$580$	27.5615	+	4.61450i	1.14443	+	0.191607i
$581$	−3.83049	−	3.69480i	−0.158916	−	0.153286i
$582$		0			0
$583$	−10.3222	+	5.95955i	−0.427504	+	0.246819i
$584$	27.3992	+	15.3487i	1.13379	+	0.635133i
$585$		0			0
$586$	12.3602	+	14.6017i	0.510596	+	0.603190i
$587$	−0.790747	+	1.36961i	−0.0326376	+	0.0565300i	−0.881883	−	0.471469i	$-0.843724\pi$
$587$	−0.790747	+	1.36961i	−0.0326376	+	0.0565300i	0.849245	+	0.527999i	$0.177057\pi$
$588$		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
$596$	−38.3855	+	14.3482i	−1.57233	+	0.587726i
$597$		0			0
$598$	−4.06299	+	3.43929i	−0.166148	+	0.140643i
$599$	−8.75858	−	5.05677i	−0.357866	−	0.206614i	0.310278	−	0.950646i	$-0.399578\pi$
$599$	−8.75858	−	5.05677i	−0.357866	−	0.206614i	−0.668144	+	0.744032i	$0.732911\pi$
$600$		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	$0.689688\pi$
$602$	−9.57893	−	6.39301i	−0.390408	−	0.260560i
$603$		0			0
$604$	15.4197	+	41.2521i	0.627420	+	1.67852i
$605$		−	24.7132i		−	1.00474i
$606$		0			0
$607$	18.5731			0.753857			0.376929	−	0.926242i	$-0.376980\pi$
$607$	18.5731			0.753857			0.376929	+	0.926242i	$0.376980\pi$
$608$	23.7747	−	9.23993i	0.964190	−	0.374729i
$609$		0			0
$610$	−14.8683	+	12.5859i	−0.602001	+	0.509590i
$611$	−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	$0.648895\pi$
$614$	−7.59133	−	41.9903i	−0.306361	−	1.69459i
$615$		0			0
$616$	−4.26709	−	14.1546i	−0.171926	−	0.570307i
$617$	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	$-0.660405\pi$
$619$	−24.0272			−0.965734			−0.482867	+	0.875694i	$0.660405\pi$
$620$	−36.2655	−	6.07178i	−1.45646	−	0.243849i
$621$		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
$626$	6.21833	+	7.34599i	0.248535	+	0.293605i
$627$		0			0
$628$	−22.1420	−	3.70715i	−0.883564	−	0.147931i
$629$			1.21781i			0.0485572i
$630$		0			0
$631$		−	17.1069i		−	0.681016i	−0.940242	−	0.340508i	$-0.889401\pi$
$631$		−	17.1069i		−	0.681016i	0.940242	−	0.340508i	$-0.110599\pi$
$632$	−1.58637	−	0.888661i	−0.0631023	−	0.0353490i
$633$		0			0
$634$	12.6995	−	10.7500i	0.504360	−	0.426937i
$635$	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
$640$	12.3480	−	37.4109i	0.488098	−	1.47880i
$641$	−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	0.914540	−	0.404496i	$-0.132553\pi$
$643$	2.71240	+	4.69801i	0.106967	+	0.185272i	−0.807573	+	0.589767i	$0.799220\pi$
$644$	3.10314	−	0.355116i	0.122281	−	0.0139935i
$645$		0			0
$646$	−7.53952	+	1.36305i	−0.296639	+	0.0536286i
$647$	−9.98684	−	17.2977i	−0.392623	−	0.680043i	0.600171	−	0.799871i	$-0.295099\pi$
$647$	−9.98684	−	17.2977i	−0.392623	−	0.680043i	−0.992795	+	0.119828i	$0.961766\pi$
$648$		0			0
$649$	24.8384	+	14.3404i	0.974992	+	0.562912i
$650$	41.5176	+	49.0465i	1.62845	+	1.92376i
$651$		0			0
$652$	17.0852	+	2.86051i	0.669110	+	0.112026i
$653$	−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
$656$	−6.83458	+	19.8386i	−0.266846	+	0.774569i
$657$		0			0
$658$	0.579398	+	1.17332i	0.0225873	+	0.0457406i
$659$	−3.30688	−	1.90923i	−0.128818	−	0.0743729i	0.434206	−	0.900813i	$-0.357029\pi$
$659$	−3.30688	−	1.90923i	−0.128818	−	0.0743729i	−0.563024	+	0.826440i	$0.690362\pi$
$660$		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	$0.367807\pi$
$662$	−7.61484	−	8.99575i	−0.295959	−	0.349630i
$663$		0			0
$664$	5.68903	−	0.0737836i	0.220777	−	0.00286336i
$665$	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	$0.207911\pi$
$674$	−19.2292	+	16.2774i	−0.740682	+	0.626982i
$675$		0			0
$676$	−9.13658	+	54.5709i	−0.351407	+	2.09888i
$677$	−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
$680$	−5.78345	+	10.3242i	−0.221785	+	0.395913i
$681$		0			0
$682$	4.98524	−	13.8833i	0.190895	−	0.531618i
$683$	41.8382	−	24.1553i	1.60090	−	0.924278i	0.609588	−	0.792719i	$-0.291335\pi$
$683$	41.8382	−	24.1553i	1.60090	−	0.924278i	0.991308	−	0.131559i	$-0.0419983\pi$
$684$		0			0
$685$		−	27.1262i		−	1.03644i
$686$	22.2953	+	13.7447i	0.851240	+	0.524777i
$687$		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	0.913065	−	0.407813i	$-0.133709\pi$
$691$	2.71691	+	4.70582i	0.103356	+	0.179018i	−0.809709	+	0.586831i	$0.800375\pi$
$692$	−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
$700$	−4.28680	−	37.4596i	−0.162026	−	1.41584i
$701$	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
$706$	41.9833	−	7.59006i	1.58006	−	0.285656i
$707$	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	$0.935547\pi$
$710$	1.29085	+	7.14012i	0.0484446	+	0.267964i
$711$		0			0
$712$	0.138506	+	10.6794i	0.00519072	+	0.400227i
$713$	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	$-0.641619\pi$
$719$	15.1910	−	26.3116i	0.566530	−	0.981258i	0.996906	−	0.0786083i	$-0.0250476\pi$
$720$		0			0
$721$	9.69238	−	38.9697i	0.360963	−	1.45131i
$722$	−1.43732	+	1.21668i	−0.0534914	+	0.0452801i
$723$		0			0
$724$	−3.66467	−	9.80402i	−0.136196	−	0.364363i
$725$	−14.2958	+	24.7610i	−0.530931	+	0.919600i
$726$		0			0
$727$	−2.64995	+	4.58985i	−0.0982812	+	0.170228i	−0.910973	−	0.412465i	$-0.864668\pi$
$727$	−2.64995	+	4.58985i	−0.0982812	+	0.170228i	0.812692	+	0.582693i	$0.198001\pi$
$728$	32.6815	−	34.7732i	1.21126	−	1.28878i
$729$		0			0
$730$	−41.7344	+	35.3279i	−1.54466	+	1.30754i
$731$	−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	$0.638358\pi$
$734$	8.87201	+	49.0742i	0.327472	+	1.81136i
$735$		0			0
$736$	−2.09051	+	2.60365i	−0.0770573	+	0.0959717i
$737$	4.83079	−	8.36718i	0.177945	−	0.308209i
$738$		0			0
$739$	24.0001	−	13.8565i	0.882859	−	0.509719i	0.0112591	−	0.999937i	$-0.496416\pi$
$739$	24.0001	−	13.8565i	0.882859	−	0.509719i	0.871600	+	0.490218i	$0.163083\pi$
$740$	6.96189	+	1.16560i	0.255924	+	0.0428483i
$741$		0			0
$742$	9.99521	+	20.2409i	0.366936	+	0.743068i
$743$	32.0177	−	18.4854i	1.17461	−	0.678164i	0.219852	−	0.975533i	$-0.429443\pi$
$743$	32.0177	−	18.4854i	1.17461	−	0.678164i	0.954763	+	0.297369i	$0.0961092\pi$
$744$		0			0
$745$		−	71.3485i		−	2.61401i
$746$	2.87114	+	15.8813i	0.105120	+	0.581454i
$747$		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	$-0.844755\pi$
$751$		−	25.6840i		−	0.937222i	0.883405	−	0.468611i	$-0.155245\pi$
$752$	−1.32264	−	0.455660i	−0.0482316	−	0.0166162i
$753$		0			0
$754$	−35.6099	+	6.43783i	−1.29683	+	0.234452i
$755$	−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	$0.296490\pi$
$758$	−19.9588	+	3.60830i	−0.724935	+	0.131059i
$759$		0			0
$760$	0.575922	+	44.4061i	0.0208909	+	1.61078i
$761$			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
$766$	−4.69079	−	25.9464i	−0.169485	−	0.937481i
$767$			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	$0.345805\pi$
$770$	25.6856	+	1.66970i	0.925645	+	0.0601717i
$771$		0			0
$772$	−0.292492	+	1.74700i	−0.0105270	+	0.0628759i
$773$	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
$776$	−0.627246	−	48.3633i	−0.0225168	−	1.73614i
$777$		0			0
$778$	−4.00565	−	22.1566i	−0.143609	−	0.794354i
$779$		−	23.6533i		−	0.847467i
$780$		0			0
$781$	−2.91085			−0.104158
$782$	0.765528	−	0.648014i	0.0273752	−	0.0231729i
$783$		0			0
$784$	−27.2761	+	6.32567i	−0.974147	+	0.225917i
$785$	19.5438	−	33.8509i	0.697548	−	1.20819i
$786$		0			0
$787$	12.2911	−	21.2888i	0.438130	−	0.758863i	−0.559416	−	0.828887i	$-0.688974\pi$
$787$	12.2911	−	21.2888i	0.438130	−	0.758863i	0.997545	+	0.0700244i	$0.0223077\pi$
$788$	−4.06803	+	1.52060i	−0.144917	+	0.0541691i
$789$		0			0
$790$	2.41635	−	2.04542i	0.0859699	−	0.0727729i
$791$	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
$800$	31.4300	+	25.2357i	1.11122	+	0.892217i
$801$		0			0
$802$	−8.37601	−	46.3306i	−0.295767	−	1.63599i
$803$	−10.9679	−	18.9969i	−0.387048	−	0.670387i
$804$		0			0
$805$	−1.31255	+	5.27729i	−0.0462611	+	0.186000i
$806$	46.8556	−	8.47092i	1.65042	−	0.298376i
$807$		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	$-0.815029\pi$
$811$	−47.6072			−1.67172			−0.835858	+	0.548946i	$0.815029\pi$
$812$	19.4759	+	8.45689i	0.683470	+	0.296779i
$813$		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	0.456950	−	0.889492i	$-0.348942\pi$
$823$	−2.43553	−	1.40615i	−0.0848972	−	0.0490154i	−0.541848	+	0.840477i	$0.682275\pi$
$824$	21.9451	+	36.8966i	0.764494	+	1.28535i
$825$		0			0
$826$	30.1546	−	45.1820i	1.04921	−	1.57208i
$827$		−	36.6231i		−	1.27351i	−0.771066	−	0.636756i	$-0.780276\pi$
$827$		−	36.6231i		−	1.27351i	0.771066	−	0.636756i	$-0.219724\pi$
$828$		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
$832$	1.32306	+	50.9983i	0.0458689	+	1.76805i
$833$	8.40510	−	0.303215i	0.291219	−	0.0105058i
$834$		0			0
$835$	−74.4147	+	42.9633i	−2.57523	+	1.48681i
$836$	−17.5714	−	2.94190i	−0.607719	−	0.101748i
$837$		0			0
$838$	11.4291	−	9.67465i	0.394811	−	0.334205i
$839$	12.4481	−	21.5607i	0.429755	−	0.744358i	−0.567096	−	0.823652i	$-0.691933\pi$
$839$	12.4481	−	21.5607i	0.429755	−	0.744358i	0.996851	+	0.0792938i	$0.0252665\pi$
$840$		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
$848$	−22.8169	−	7.86061i	−0.783535	−	0.269934i
$849$		0			0
$850$	−7.82253	−	9.24110i	−0.268311	−	0.316967i
$851$	−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	$0.387956\pi$
$854$	−13.2711	+	6.55343i	−0.454128	+	0.224254i
$855$		0			0
$856$	0.409525	+	31.5762i	0.0139973	+	1.07925i
$857$		−	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	$-0.676893\pi$
$859$	−30.9241			−1.05512			−0.527559	+	0.849519i	$0.676893\pi$
$860$	−3.53955	+	21.1410i	−0.120698	+	0.720903i
$861$		0			0
$862$	26.4370	+	31.2312i	0.900449	+	1.06374i
$863$	37.2047	+	21.4801i	1.26646	+	0.731192i	0.974317	−	0.225181i	$-0.0722975\pi$
$863$	37.2047	+	21.4801i	1.26646	+	0.731192i	0.292146	+	0.956374i	$0.405631\pi$
$864$		0			0
$865$	−1.25871	−	2.18015i	−0.0427975	−	0.0741274i
$866$	−15.4428	+	2.79187i	−0.524768	+	0.0948716i
$867$		0			0
$868$	−25.6265	−	11.1276i	−0.869820	−	0.377696i
$869$	0.635021	+	1.09989i	0.0215416	+	0.0373112i
$870$		0			0
$871$	31.1865			1.05671
$872$	−6.46668	+	11.5438i	−0.218989	+	0.390922i
$873$		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	$0.455513\pi$
$878$	−15.0777	+	12.7632i	−0.508848	+	0.430736i
$879$		0			0
$880$	−20.7703	+	18.0494i	−0.700166	+	0.608446i
$881$			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	$0.300101\pi$
$883$			48.0915i			1.61841i	−0.587529	+	0.809203i	$0.699899\pi$
$884$	2.53039	−	15.1135i	0.0851063	−	0.508323i
$885$		0			0
$886$	1.89113	+	2.23408i	0.0635338	+	0.0750552i
$887$	−42.7483			−1.43535			−0.717674	−	0.696379i	$-0.754793\pi$
$887$	−42.7483			−1.43535			−0.717674	+	0.696379i	$0.754793\pi$
$888$		0			0
$889$	27.4912	+	6.83749i	0.922025	+	0.229322i
$890$	−17.5011	−	6.28434i	−0.586639	−	0.210652i
$891$		0			0
$892$	−6.12606	+	36.5897i	−0.205116	+	1.22511i
$893$	1.57696			0.0527710
$894$		0			0
$895$	−20.6880	−	35.8327i	−0.691525	−	1.19776i
$896$	15.9654	−	25.3201i	0.533366	−	0.845884i
$897$		0			0
$898$	4.01630	+	22.2156i	0.134026	+	0.741343i
$899$	10.5929	+	18.3475i	0.353294	+	0.611923i
$900$		0			0
$901$	6.27781	+	3.62450i	0.209144	+	0.120749i
$902$	11.1863	−	9.46912i	0.372463	−	0.315287i
$903$		0			0
$904$	−15.5527	+	27.7635i	−0.517275	+	0.923399i
$905$	18.2231			0.605755
$906$		0			0
$907$			16.3986i			0.544508i	0.962225	+	0.272254i	$0.0877690\pi$
$907$			16.3986i			0.544508i	−0.962225	+	0.272254i	$0.912231\pi$
$908$	−11.2951	+	4.22203i	−0.374842	+	0.140113i
$909$		0			0
$910$	36.7876	+	74.4972i	1.21950	+	2.46956i
$911$	6.37439	+	3.68026i	0.211193	+	0.121932i	0.601866	−	0.798597i	$-0.294424\pi$
$911$	6.37439	+	3.68026i	0.211193	+	0.121932i	−0.390673	+	0.920530i	$0.627758\pi$
$912$		0			0
$913$	−3.44155	−	1.98698i	−0.113899	−	0.0657594i
$914$	−14.1246	+	11.9564i	−0.467199	+	0.395481i
$915$		0			0
$916$	−2.03884	−	5.45446i	−0.0673650	−	0.180220i
$917$	−3.62465	+	14.5735i	−0.119696	+	0.481258i
$918$		0			0
$919$	10.1235	+	5.84481i	0.333944	+	0.192802i	0.657591	−	0.753375i	$-0.271576\pi$
$919$	10.1235	+	5.84481i	0.333944	+	0.192802i	−0.323647	+	0.946178i	$0.604909\pi$
$920$	−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
$926$	−15.3395	−	18.1213i	−0.504088	−	0.595502i
$927$		0			0
$928$	−21.1571	+	8.22262i	−0.694516	+	0.269921i
$929$	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
$932$	−3.06810	+	18.3251i	−0.100499	+	0.600260i
$933$		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	$-0.303259\pi$
$938$	−15.2202	−	10.1580i	−0.496958	−	0.331671i
$939$		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	−0.0470178	−	0.998894i	$-0.514972\pi$
$947$	24.4507	−	14.1166i	0.794541	−	0.458728i	0.841559	+	0.540166i	$0.181638\pi$
$948$		0			0
$949$	35.4031	−	61.3200i	1.14923	−	1.99053i
$950$	−42.7637	−	15.3557i	−1.38744	−	0.498204i
$951$		0			0
$952$	−6.15769	+	6.55179i	−0.199572	+	0.212345i
$953$	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
$958$	2.58872	+	14.3191i	0.0836379	+	0.462630i
$959$	4.97461	−	20.0012i	0.160638	−	0.645871i
$960$		0			0
$961$	1.56177	+	2.70506i	0.0503796	+	0.0872601i
$962$	−8.99487	+	1.62616i	−0.290006	+	0.0524296i
$963$		0			0
$964$	1.51751	+	4.05977i	0.0488758	+	0.130757i
$965$	−2.67082	−	1.54200i	−0.0859767	−	0.0496387i
$966$		0			0
$967$	33.2406	−	19.1915i	1.06894	−	0.617156i	0.141052	−	0.990002i	$-0.454952\pi$
$967$	33.2406	−	19.1915i	1.06894	−	0.617156i	0.927893	+	0.372847i	$0.121618\pi$
$968$	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	$0.426497\pi$
$971$	−22.7039	+	39.3244i	−0.728604	+	1.26198i	−0.957473	+	0.288522i	$0.906836\pi$
$972$		0			0
$973$	−34.9609	+	10.0467i	−1.12079	+	0.322082i
$974$	25.2257	+	29.8002i	0.808283	+	0.954861i
$975$		0			0
$976$	5.15386	−	14.9601i	0.164971	−	0.478860i
$977$	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
$980$	6.31135	−	48.3399i	0.201609	−	1.54416i
$981$		0			0
$982$	−29.6213	−	34.9930i	−0.945255	−	1.11667i
$983$	−6.34126			−0.202255			−0.101127	−	0.994873i	$-0.532245\pi$
$983$	−6.34126			−0.202255			−0.101127	+	0.994873i	$0.532245\pi$
$984$		0			0
$985$		−	7.56138i		−	0.240926i
$986$	6.70943	−	1.21298i	0.213672	−	0.0386293i
$987$		0			0
$988$	−20.1353	−	53.8676i	−0.640590	−	1.71376i
$989$	0.908382	−	1.57336i	0.0288849	−	0.0500300i
$990$		0			0
$991$	39.7136	−	22.9287i	1.26154	−	0.728353i	0.288171	−	0.957579i	$-0.406953\pi$
$991$	39.7136	−	22.9287i	1.26154	−	0.728353i	0.973373	+	0.229226i	$0.0736196\pi$
$992$	27.8386	−	10.8194i	0.883877	−	0.343515i
$993$		0			0
$994$	−0.357620	+	5.50141i	−0.0113430	+	0.174494i
$995$	−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	$0.772615\pi$
$998$	−9.92974	+	1.79517i	−0.314320	+	0.0568253i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.251594 - 1.39165i) q^{2} +(-1.87340 + 0.700263i) q^{4} -3.48216i q^{5} +(0.638585 - 2.56753i) q^{7} +(1.44586 + 2.43094i) q^{8} +O(q^{10})\)	\(q+(-0.251594 - 1.39165i) q^{2} +(-1.87340 + 0.700263i) q^{4} -3.48216i q^{5} +(0.638585 - 2.56753i) q^{7} +(1.44586 + 2.43094i) q^{8} +(-4.84596 + 0.876089i) q^{10} -1.97557i q^{11} +(5.52258 - 3.18847i) q^{13} +(-3.73378 - 0.242715i) q^{14} +(3.01926 - 2.62375i) q^{16} +(-1.04054 + 0.600755i) q^{17} +(-2.25453 + 3.90496i) q^{19} +(2.43843 + 6.52347i) q^{20} +(-2.74932 + 0.497042i) q^{22} -0.590265i q^{23} -7.12541 q^{25} +(-5.82669 - 6.88333i) q^{26} +(0.601621 + 5.25719i) q^{28} +(2.00631 - 3.47503i) q^{29} +(-2.63991 + 4.57246i) q^{31} +(-4.41098 - 3.54165i) q^{32} +(1.09784 + 1.29692i) q^{34} +(-8.94054 - 2.22365i) q^{35} +(0.506783 - 0.877774i) q^{37} +(6.00157 + 2.15506i) q^{38} +(8.46493 - 5.03471i) q^{40} +(-4.54294 + 2.62287i) q^{41} +(2.66552 + 1.53894i) q^{43} +(1.38342 + 3.70104i) q^{44} +(-0.821445 + 0.148507i) q^{46} +(-0.174866 - 0.302877i) q^{47} +(-6.18442 - 3.27917i) q^{49} +(1.79271 + 9.91611i) q^{50} +(-8.11325 + 9.84054i) q^{52} +(-3.01662 - 5.22494i) q^{53} -6.87926 q^{55} +(7.16483 - 2.15993i) q^{56} +(-5.34081 - 1.91779i) q^{58} +(-7.25888 + 12.5727i) q^{59} +(3.42577 - 1.97787i) q^{61} +(7.02746 + 2.52344i) q^{62} +(-3.81897 + 7.02961i) q^{64} +(-11.1027 - 19.2305i) q^{65} +(4.23532 + 2.44526i) q^{67} +(1.52866 - 1.85410i) q^{68} +(-0.845170 + 13.0016i) q^{70} -1.47342i q^{71} +(9.61590 - 5.55174i) q^{73} +(-1.34906 - 0.484424i) q^{74} +(1.48914 - 8.89431i) q^{76} +(-5.07235 - 1.26157i) q^{77} +(-0.556744 + 0.321436i) q^{79} +(-9.13630 - 10.5135i) q^{80} +(4.79310 + 5.66230i) q^{82} +(1.00577 - 1.74205i) q^{83} +(2.09192 + 3.62331i) q^{85} +(1.47104 - 4.09667i) q^{86} +(4.80251 - 2.85640i) q^{88} +(3.27016 + 1.88803i) q^{89} +(-4.65984 - 16.2155i) q^{91} +(0.413341 + 1.10580i) q^{92} +(-0.377504 + 0.319555i) q^{94} +(13.5977 + 7.85062i) q^{95} +(-14.8094 - 8.55023i) q^{97} +(-3.00751 + 9.43159i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 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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