LMFDB - Embedded newform 671.2.f.a.538.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.5
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73949 - 1.73949i) q^{2} -3.20201i q^{3} +4.05165i q^{4} -0.618387i q^{5} +(-5.56987 + 5.56987i) q^{6} +(2.25367 + 2.25367i) q^{7} +(3.56882 - 3.56882i) q^{8} -7.25288 q^{9} +O(q^{10})$	\(q+(-1.73949 - 1.73949i) q^{2} -3.20201i q^{3} +4.05165i q^{4} -0.618387i q^{5} +(-5.56987 + 5.56987i) q^{6} +(2.25367 + 2.25367i) q^{7} +(3.56882 - 3.56882i) q^{8} -7.25288 q^{9} +(-1.07568 + 1.07568i) q^{10} +(-1.90745 + 2.71323i) q^{11} +12.9734 q^{12} +4.10409i q^{13} -7.84045i q^{14} -1.98008 q^{15} -4.31255 q^{16} +(-1.95964 + 1.95964i) q^{17} +(12.6163 + 12.6163i) q^{18} +2.64324 q^{19} +2.50549 q^{20} +(7.21626 - 7.21626i) q^{21} +(8.03763 - 1.40166i) q^{22} +(-5.35759 + 5.35759i) q^{23} +(-11.4274 - 11.4274i) q^{24} +4.61760 q^{25} +(7.13901 - 7.13901i) q^{26} +13.6178i q^{27} +(-9.13105 + 9.13105i) q^{28} +(-1.12842 + 1.12842i) q^{29} +(3.44433 + 3.44433i) q^{30} +(4.56592 + 4.56592i) q^{31} +(0.363997 + 0.363997i) q^{32} +(8.68781 + 6.10767i) q^{33} +6.81755 q^{34} +(1.39364 - 1.39364i) q^{35} -29.3861i q^{36} +(-0.728760 - 0.728760i) q^{37} +(-4.59790 - 4.59790i) q^{38} +13.1413 q^{39} +(-2.20691 - 2.20691i) q^{40} -5.46444 q^{41} -25.1052 q^{42} +(-7.04314 + 7.04314i) q^{43} +(-10.9931 - 7.72830i) q^{44} +4.48509i q^{45} +18.6389 q^{46} +1.71878 q^{47} +13.8088i q^{48} +3.15801i q^{49} +(-8.03226 - 8.03226i) q^{50} +(6.27480 + 6.27480i) q^{51} -16.6283 q^{52} +(-4.41144 + 4.41144i) q^{53} +(23.6880 - 23.6880i) q^{54} +(1.67783 + 1.17954i) q^{55} +16.0858 q^{56} -8.46370i q^{57} +3.92576 q^{58} +(0.135316 + 0.135316i) q^{59} -8.02260i q^{60} +(-7.15970 - 3.12068i) q^{61} -15.8847i q^{62} +(-16.3456 - 16.3456i) q^{63} +7.35876i q^{64} +2.53791 q^{65} +(-4.48813 - 25.7366i) q^{66} +(-11.1289 - 11.1289i) q^{67} +(-7.93978 - 7.93978i) q^{68} +(17.1551 + 17.1551i) q^{69} -4.84844 q^{70} +(-5.75691 - 5.75691i) q^{71} +(-25.8842 + 25.8842i) q^{72} -0.750887i q^{73} +2.53534i q^{74} -14.7856i q^{75} +10.7095i q^{76} +(-10.4135 + 1.81597i) q^{77} +(-22.8592 - 22.8592i) q^{78} +(-7.94456 - 7.94456i) q^{79} +2.66682i q^{80} +21.8456 q^{81} +(9.50534 + 9.50534i) q^{82} -0.346044i q^{83} +(29.2377 + 29.2377i) q^{84} +(1.21182 + 1.21182i) q^{85} +24.5029 q^{86} +(3.61322 + 3.61322i) q^{87} +(2.87571 + 16.4904i) q^{88} +(8.24703 + 8.24703i) q^{89} +(7.80176 - 7.80176i) q^{90} +(-9.24924 + 9.24924i) q^{91} +(-21.7071 - 21.7071i) q^{92} +(14.6201 - 14.6201i) q^{93} +(-2.98981 - 2.98981i) q^{94} -1.63455i q^{95} +(1.16552 - 1.16552i) q^{96} +14.6472i q^{97} +(5.49333 - 5.49333i) q^{98} +(13.8345 - 19.6788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.73949	−	1.73949i	−1.23000	−	1.23000i	−0.963961	−	0.266044i	$-0.914283\pi$
$2$	−1.73949	−	1.73949i	−1.23000	−	1.23000i	−0.266044	−	0.963961i	$-0.585717\pi$
$3$		−	3.20201i		−	1.84868i	−0.381567	−	0.924341i	$-0.624615\pi$
$3$		−	3.20201i		−	1.84868i	0.381567	−	0.924341i	$-0.375385\pi$
$4$			4.05165i			2.02582i
$5$		−	0.618387i		−	0.276551i	−0.990394	−	0.138276i	$-0.955844\pi$
$5$		−	0.618387i		−	0.276551i	0.990394	−	0.138276i	$-0.0441560\pi$
$6$	−5.56987	+	5.56987i	−2.27389	+	2.27389i
$7$	2.25367	+	2.25367i	0.851805	+	0.851805i	0.990355	−	0.138550i	$-0.0442442\pi$
$7$	2.25367	+	2.25367i	0.851805	+	0.851805i	−0.138550	+	0.990355i	$0.544244\pi$
$8$	3.56882	−	3.56882i	1.26177	−	1.26177i
$9$	−7.25288			−2.41763
$10$	−1.07568	+	1.07568i	−0.340159	+	0.340159i
$11$	−1.90745	+	2.71323i	−0.575117	+	0.818071i
$11$	−1.90745	+	2.71323i	−0.575117	+	0.818071i
$12$	12.9734			3.74510
$13$			4.10409i			1.13827i	0.822245	+	0.569134i	$0.192722\pi$
$13$			4.10409i			1.13827i	−0.822245	+	0.569134i	$0.807278\pi$
$14$		−	7.84045i		−	2.09545i
$15$	−1.98008			−0.511255
$16$	−4.31255			−1.07814
$17$	−1.95964	+	1.95964i	−0.475283	+	0.475283i	−0.903619	−	0.428336i	$-0.859100\pi$
$17$	−1.95964	+	1.95964i	−0.475283	+	0.475283i	0.428336	+	0.903619i	$0.359100\pi$
$18$	12.6163	+	12.6163i	2.97369	+	2.97369i
$19$	2.64324			0.606402			0.303201	−	0.952927i	$-0.401945\pi$
$19$	2.64324			0.606402			0.303201	+	0.952927i	$0.401945\pi$
$20$	2.50549			0.560244
$21$	7.21626	−	7.21626i	1.57472	−	1.57472i
$22$	8.03763	−	1.40166i	1.71363	−	0.298835i
$23$	−5.35759	+	5.35759i	−1.11714	+	1.11714i	−0.124975	+	0.992160i	$0.539885\pi$
$23$	−5.35759	+	5.35759i	−1.11714	+	1.11714i	−0.992160	+	0.124975i	$0.960115\pi$
$24$	−11.4274	−	11.4274i	−2.33261	−	2.33261i
$25$	4.61760			0.923519
$26$	7.13901	−	7.13901i	1.40008	−	1.40008i
$27$			13.6178i			2.62074i
$28$	−9.13105	+	9.13105i	−1.72561	+	1.72561i
$29$	−1.12842	+	1.12842i	−0.209543	+	0.209543i	−0.804073	−	0.594530i	$-0.797338\pi$
$29$	−1.12842	+	1.12842i	−0.209543	+	0.209543i	0.594530	+	0.804073i	$0.297338\pi$
$30$	3.44433	+	3.44433i	0.628846	+	0.628846i
$31$	4.56592	+	4.56592i	0.820063	+	0.820063i	0.986117	−	0.166054i	$-0.0531025\pi$
$31$	4.56592	+	4.56592i	0.820063	+	0.820063i	−0.166054	+	0.986117i	$0.553102\pi$
$32$	0.363997	+	0.363997i	0.0643461	+	0.0643461i
$33$	8.68781	+	6.10767i	1.51235	+	1.06321i
$34$	6.81755			1.16920
$35$	1.39364	−	1.39364i	0.235568	−	0.235568i
$36$		−	29.3861i		−	4.89768i
$37$	−0.728760	−	0.728760i	−0.119807	−	0.119807i	0.644661	−	0.764469i	$-0.276999\pi$
$37$	−0.728760	−	0.728760i	−0.119807	−	0.119807i	−0.764469	+	0.644661i	$0.776999\pi$
$38$	−4.59790	−	4.59790i	−0.745877	−	0.745877i
$39$	13.1413			2.10430
$40$	−2.20691	−	2.20691i	−0.348943	−	0.348943i
$41$	−5.46444			−0.853403			−0.426701	−	0.904393i	$-0.640324\pi$
$41$	−5.46444			−0.853403			−0.426701	+	0.904393i	$0.640324\pi$
$42$	−25.1052			−3.87382
$43$	−7.04314	+	7.04314i	−1.07407	+	1.07407i	−0.0770403	+	0.997028i	$0.524547\pi$
$43$	−7.04314	+	7.04314i	−1.07407	+	1.07407i	−0.997028	+	0.0770403i	$0.975453\pi$
$44$	−10.9931	−	7.72830i	−1.65727	−	1.16509i
$45$			4.48509i			0.668597i
$46$	18.6389			2.74816
$47$	1.71878			0.250710			0.125355	−	0.992112i	$-0.459993\pi$
$47$	1.71878			0.250710			0.125355	+	0.992112i	$0.459993\pi$
$48$			13.8088i			1.99313i
$49$			3.15801i			0.451145i
$50$	−8.03226	−	8.03226i	−1.13593	−	1.13593i
$51$	6.27480	+	6.27480i	0.878647	+	0.878647i
$52$	−16.6283			−2.30593
$53$	−4.41144	+	4.41144i	−0.605959	+	0.605959i	−0.941887	−	0.335929i	$-0.890950\pi$
$53$	−4.41144	+	4.41144i	−0.605959	+	0.605959i	0.335929	+	0.941887i	$0.390950\pi$
$54$	23.6880	−	23.6880i	3.22352	−	3.22352i
$55$	1.67783	+	1.17954i	0.226239	+	0.159049i
$56$	16.0858			2.14956
$57$		−	8.46370i		−	1.12104i
$58$	3.92576			0.515477
$59$	0.135316	+	0.135316i	0.0176166	+	0.0176166i	0.715860	−	0.698244i	$-0.246035\pi$
$59$	0.135316	+	0.135316i	0.0176166	+	0.0176166i	−0.698244	+	0.715860i	$0.746035\pi$
$60$		−	8.02260i		−	1.03571i
$61$	−7.15970	−	3.12068i	−0.916706	−	0.399562i
$61$	−7.15970	−	3.12068i	−0.916706	−	0.399562i
$62$		−	15.8847i		−	2.01736i
$63$	−16.3456	−	16.3456i	−2.05935	−	2.05935i
$64$			7.35876i			0.919845i
$65$	2.53791			0.314790
$66$	−4.48813	−	25.7366i	−0.552450	−	3.16795i
$67$	−11.1289	−	11.1289i	−1.35961	−	1.35961i	−0.874397	−	0.485210i	$-0.838743\pi$
$67$	−11.1289	−	11.1289i	−1.35961	−	1.35961i	−0.485210	−	0.874397i	$-0.661257\pi$
$68$	−7.93978	−	7.93978i	−0.962839	−	0.962839i
$69$	17.1551	+	17.1551i	2.06523	+	2.06523i
$70$	−4.84844			−0.579499
$71$	−5.75691	−	5.75691i	−0.683220	−	0.683220i	0.277504	−	0.960724i	$-0.410493\pi$
$71$	−5.75691	−	5.75691i	−0.683220	−	0.683220i	−0.960724	+	0.277504i	$0.910493\pi$
$72$	−25.8842	+	25.8842i	−3.05048	+	3.05048i
$73$		−	0.750887i		−	0.0878847i	−0.999034	−	0.0439423i	$-0.986008\pi$
$73$		−	0.750887i		−	0.0878847i	0.999034	−	0.0439423i	$-0.0139918\pi$
$74$			2.53534i			0.294727i
$75$		−	14.7856i		−	1.70729i
$76$			10.7095i			1.22846i
$77$	−10.4135	+	1.81597i	−1.18673	+	0.206949i
$78$	−22.8592	−	22.8592i	−2.58830	−	2.58830i
$79$	−7.94456	−	7.94456i	−0.893833	−	0.893833i	0.101048	−	0.994882i	$-0.467780\pi$
$79$	−7.94456	−	7.94456i	−0.893833	−	0.893833i	−0.994882	+	0.101048i	$0.967780\pi$
$80$			2.66682i			0.298160i
$81$	21.8456			2.42729
$82$	9.50534	+	9.50534i	1.04969	+	1.04969i
$83$		−	0.346044i		−	0.0379832i	−0.999820	−	0.0189916i	$-0.993954\pi$
$83$		−	0.346044i		−	0.0379832i	0.999820	−	0.0189916i	$-0.00604558\pi$
$84$	29.2377	+	29.2377i	3.19010	+	3.19010i
$85$	1.21182	+	1.21182i	0.131440	+	0.131440i
$86$	24.5029			2.64222
$87$	3.61322	+	3.61322i	0.387378	+	0.387378i
$88$	2.87571	+	16.4904i	0.306551	+	1.75788i
$89$	8.24703	+	8.24703i	0.874183	+	0.874183i	0.992925	−	0.118742i	$-0.0378861\pi$
$89$	8.24703	+	8.24703i	0.874183	+	0.874183i	−0.118742	+	0.992925i	$0.537886\pi$
$90$	7.80176	−	7.80176i	0.822378	−	0.822378i
$91$	−9.24924	+	9.24924i	−0.969583	+	0.969583i
$92$	−21.7071	−	21.7071i	−2.26312	−	2.26312i
$93$	14.6201	−	14.6201i	1.51604	−	1.51604i
$94$	−2.98981	−	2.98981i	−0.308375	−	0.308375i
$95$		−	1.63455i		−	0.167701i
$96$	1.16552	−	1.16552i	0.118956	−	0.118956i
$97$			14.6472i			1.48720i	0.668626	+	0.743599i	$0.266883\pi$
$97$			14.6472i			1.48720i	−0.668626	+	0.743599i	$0.733117\pi$
$98$	5.49333	−	5.49333i	0.554910	−	0.554910i
$99$	13.8345	−	19.6788i	1.39042	−	1.97779i
$100$			18.7089i			1.87089i
$101$	−6.62942	−	6.62942i	−0.659652	−	0.659652i	0.295645	−	0.955298i	$-0.404465\pi$
$101$	−6.62942	−	6.62942i	−0.659652	−	0.659652i	−0.955298	+	0.295645i	$0.904465\pi$
$102$		−	21.8299i		−	2.16148i
$103$	1.86977			0.184234			0.0921170	−	0.995748i	$-0.470637\pi$
$103$	1.86977			0.184234			0.0921170	+	0.995748i	$0.470637\pi$
$104$	14.6467	+	14.6467i	1.43623	+	1.43623i
$105$	−4.46244	−	4.46244i	−0.435490	−	0.435490i
$106$	15.3473			1.49066
$107$	16.4932			1.59446			0.797228	−	0.603679i	$-0.206299\pi$
$107$	16.4932			1.59446			0.797228	+	0.603679i	$0.206299\pi$
$108$	−55.1744			−5.30916
$109$	3.39202			0.324897			0.162448	−	0.986717i	$-0.448061\pi$
$109$	3.39202			0.324897			0.162448	+	0.986717i	$0.448061\pi$
$110$	−0.866768	−	4.97037i	−0.0826430	−	0.473906i
$111$	−2.33350	+	2.33350i	−0.221486	+	0.221486i
$112$	−9.71904	−	9.71904i	−0.918363	−	0.918363i
$113$			15.1941i			1.42934i	0.699463	+	0.714669i	$0.253423\pi$
$113$			15.1941i			1.42934i	−0.699463	+	0.714669i	$0.746577\pi$
$114$	−14.7225	+	14.7225i	−1.37889	+	1.37889i
$115$	3.31307	+	3.31307i	0.308945	+	0.308945i
$116$	−4.57197	−	4.57197i	−0.424497	−	0.424497i
$117$		−	29.7664i		−	2.75191i
$118$		−	0.470760i		−	0.0433370i
$119$	−8.83275			−0.809697
$120$	−7.06656	+	7.06656i	−0.645085	+	0.645085i
$121$	−3.72329	−	10.3507i	−0.338481	−	0.940973i
$122$	7.02584	+	17.8826i	0.636090	+	1.61902i
$123$			17.4972i			1.57767i
$124$	−18.4995	+	18.4995i	−1.66130	+	1.66130i
$125$		−	5.94740i		−	0.531952i
$126$			56.8659i			5.06601i
$127$	−7.81072			−0.693089			−0.346545	−	0.938033i	$-0.612645\pi$
$127$	−7.81072			−0.693089			−0.346545	+	0.938033i	$0.612645\pi$
$128$	13.5285	−	13.5285i	1.19576	−	1.19576i
$129$	22.5522	+	22.5522i	1.98561	+	1.98561i
$130$	−4.41468	−	4.41468i	−0.387193	−	0.387193i
$131$			8.70995i			0.760992i	0.924783	+	0.380496i	$0.124247\pi$
$131$			8.70995i			0.760992i	−0.924783	+	0.380496i	$0.875753\pi$
$132$	−24.7461	+	35.1999i	−2.15387	+	3.06376i
$133$	5.95699	+	5.95699i	0.516536	+	0.516536i
$134$			38.7171i			3.34465i
$135$	8.42105			0.724769
$136$			13.9872i			1.19939i
$137$	13.4118			1.14585			0.572923	−	0.819609i	$-0.305809\pi$
$137$	13.4118			1.14585			0.572923	+	0.819609i	$0.305809\pi$
$138$		−	59.6821i		−	5.08048i
$139$	5.33219	−	5.33219i	0.452271	−	0.452271i	−0.443837	−	0.896108i	$-0.646383\pi$
$139$	5.33219	−	5.33219i	0.452271	−	0.452271i	0.896108	+	0.443837i	$0.146383\pi$
$140$	5.64653	+	5.64653i	0.477219	+	0.477219i
$141$		−	5.50357i		−	0.463484i
$142$			20.0282i			1.68073i
$143$	−11.1353	−	7.82833i	−0.931185	−	0.654638i
$144$	31.2784			2.60653
$145$	0.697802	+	0.697802i	0.0579493	+	0.0579493i
$146$	−1.30616	+	1.30616i	−0.108099	+	0.108099i
$147$	10.1120			0.834023
$148$	2.95268	−	2.95268i	0.242709	−	0.242709i
$149$	17.0051			1.39311			0.696554	−	0.717504i	$-0.254716\pi$
$149$	17.0051			1.39311			0.696554	+	0.717504i	$0.254716\pi$
$150$	−25.7194	+	25.7194i	−2.09998	+	2.09998i
$151$	−3.79210	+	3.79210i	−0.308597	+	0.308597i	−0.844365	−	0.535768i	$-0.820022\pi$
$151$	−3.79210	+	3.79210i	−0.308597	+	0.308597i	0.535768	+	0.844365i	$0.320022\pi$
$152$	9.43326	−	9.43326i	0.765138	−	0.765138i
$153$	14.2130	−	14.2130i	1.14906	−	1.14906i
$154$	21.2730	+	14.9553i	1.71423	+	1.20513i
$155$	2.82351	−	2.82351i	0.226789	−	0.226789i
$156$			53.2440i			4.26293i
$157$	−13.0223	−	13.0223i	−1.03929	−	1.03929i	−0.999196	−	0.0400946i	$-0.987234\pi$
$157$	−13.0223	−	13.0223i	−1.03929	−	1.03929i	−0.0400946	−	0.999196i	$-0.512766\pi$
$158$			27.6390i			2.19884i
$159$	14.1255	+	14.1255i	1.12022	+	1.12022i
$160$	0.225091	−	0.225091i	0.0177950	−	0.0177950i
$161$	−24.1484			−1.90316
$162$	−38.0002	−	38.0002i	−2.98558	−	2.98558i
$163$		−	22.0319i		−	1.72567i	−0.505484	−	0.862836i	$-0.668686\pi$
$163$		−	22.0319i		−	1.72567i	0.505484	−	0.862836i	$-0.331314\pi$
$164$		−	22.1400i		−	1.72884i
$165$	3.77690	−	5.37243i	0.294032	−	0.418243i
$166$	−0.601940	+	0.601940i	−0.0467196	+	0.0467196i
$167$	−14.4268			−1.11638			−0.558188	−	0.829714i	$-0.688503\pi$
$167$	−14.4268			−1.11638			−0.558188	+	0.829714i	$0.688503\pi$
$168$		−	51.5071i		−	3.97386i
$169$	−3.84352			−0.295656
$170$		−	4.21589i		−	0.323344i
$171$	−19.1711			−1.46605
$172$	−28.5363	−	28.5363i	−2.17587	−	2.17587i
$173$	4.42325	+	4.42325i	0.336294	+	0.336294i	0.854970	−	0.518677i	$-0.173575\pi$
$173$	4.42325	+	4.42325i	0.336294	+	0.336294i	−0.518677	+	0.854970i	$0.673575\pi$
$174$		−	12.5703i		−	0.952954i
$175$	10.4065	+	10.4065i	0.786659	+	0.786659i
$176$	8.22596	−	11.7010i	0.620055	−	0.881993i
$177$	0.433282	−	0.433282i	0.0325675	−	0.0325675i
$178$		−	28.6912i		−	2.15050i
$179$	13.7088			1.02464			0.512322	−	0.858794i	$-0.328786\pi$
$179$	13.7088			1.02464			0.512322	+	0.858794i	$0.328786\pi$
$180$	−18.1720			−1.35446
$181$	11.2978	+	11.2978i	0.839755	+	0.839755i	0.988826	−	0.149071i	$-0.0476284\pi$
$181$	11.2978	+	11.2978i	0.839755	+	0.839755i	−0.149071	+	0.988826i	$0.547628\pi$
$182$	32.1779			2.38518
$183$	−9.99245	+	22.9255i	−0.738663	+	1.69470i
$184$			38.2405i			2.81913i
$185$	−0.450656	+	0.450656i	−0.0331329	+	0.0331329i
$186$	−50.8631			−3.72946
$187$	−1.57905	−	9.05488i	−0.115472	−	0.662159i
$188$			6.96390i			0.507895i
$189$	−30.6899	+	30.6899i	−2.23236	+	2.23236i
$190$	−2.84328	+	2.84328i	−0.206273	+	0.206273i
$191$	−6.08562	−	6.08562i	−0.440340	−	0.440340i	0.451786	−	0.892126i	$-0.350787\pi$
$191$	−6.08562	−	6.08562i	−0.440340	−	0.440340i	−0.892126	+	0.451786i	$0.850787\pi$
$192$	23.5628			1.70050
$193$	−17.4191	+	17.4191i	−1.25385	+	1.25385i	−0.299872	+	0.953980i	$0.596944\pi$
$193$	−17.4191	+	17.4191i	−1.25385	+	1.25385i	−0.953980	+	0.299872i	$0.903056\pi$
$194$	25.4787	−	25.4787i	1.82926	−	1.82926i
$195$		−	8.12643i		−	0.581946i
$196$	−12.7951			−0.913939
$197$	6.06892			0.432392			0.216196	−	0.976350i	$-0.430635\pi$
$197$	6.06892			0.432392			0.216196	+	0.976350i	$0.430635\pi$
$198$	−58.2959	+	10.1661i	−4.14291	+	0.722470i
$199$	10.2336			0.725439			0.362720	−	0.931898i	$-0.381848\pi$
$199$	10.2336			0.725439			0.362720	+	0.931898i	$0.381848\pi$
$200$	16.4794	−	16.4794i	1.16527	−	1.16527i
$201$	−35.6348	+	35.6348i	−2.51348	+	2.51348i
$202$			23.0636i			1.62275i
$203$	−5.08617			−0.356979
$204$	−25.4233	+	25.4233i	−1.77998	+	1.77998i
$205$			3.37914i			0.236010i
$206$	−3.25245	−	3.25245i	−0.226609	−	0.226609i
$207$	38.8580	−	38.8580i	2.70082	−	2.70082i
$208$		−	17.6991i		−	1.22721i
$209$	−5.04185	+	7.17174i	−0.348752	+	0.496080i
$210$			15.5247i			1.07131i
$211$	10.1554	−	10.1554i	0.699126	−	0.699126i	−0.265096	−	0.964222i	$-0.585404\pi$
$211$	10.1554	−	10.1554i	0.699126	−	0.699126i	0.964222	+	0.265096i	$0.0854037\pi$
$212$	−17.8736	−	17.8736i	−1.22757	−	1.22757i
$213$	−18.4337	+	18.4337i	−1.26306	+	1.26306i
$214$	−28.6897	−	28.6897i	−1.96119	−	1.96119i
$215$	4.35539	+	4.35539i	0.297035	+	0.297035i
$216$	48.5993	+	48.5993i	3.30677	+	3.30677i
$217$			20.5801i			1.39707i
$218$	−5.90038	−	5.90038i	−0.399624	−	0.399624i
$219$	−2.40435			−0.162471
$220$	−4.77908	+	6.79797i	−0.322206	+	0.458319i
$221$	−8.04254	−	8.04254i	−0.541000	−	0.541000i
$222$	8.11819			0.544857
$223$	−11.0292	+	11.0292i	−0.738568	+	0.738568i	−0.972301	−	0.233733i	$-0.924906\pi$
$223$	−11.0292	+	11.0292i	−0.738568	+	0.738568i	0.233733	+	0.972301i	$0.424906\pi$
$224$			1.64065i			0.109621i
$225$	−33.4909			−2.23273
$226$	26.4299	−	26.4299i	1.75809	−	1.75809i
$227$	11.3166	+	11.3166i	0.751107	+	0.751107i	0.974686	−	0.223579i	$-0.0717740\pi$
$227$	11.3166	+	11.3166i	0.751107	+	0.751107i	−0.223579	+	0.974686i	$0.571774\pi$
$228$	34.2919			2.27104
$229$		−	9.13638i		−	0.603749i	−0.953348	−	0.301874i	$-0.902388\pi$
$229$		−	9.13638i		−	0.603749i	0.953348	−	0.301874i	$-0.0976123\pi$
$230$		−	11.5261i		−	0.760008i
$231$	5.81477	+	33.3441i	0.382584	+	2.19388i
$232$			8.05427i			0.528789i
$233$	−0.343392	−	0.343392i	−0.0224963	−	0.0224963i	0.695769	−	0.718265i	$-0.255064\pi$
$233$	−0.343392	−	0.343392i	−0.0224963	−	0.0224963i	−0.718265	+	0.695769i	$0.755064\pi$
$234$	−51.7784	+	51.7784i	−3.38486	+	3.38486i
$235$		−	1.06287i		−	0.0693342i
$236$	−0.548251	+	0.548251i	−0.0356881	+	0.0356881i
$237$	−25.4386	+	25.4386i	−1.65241	+	1.65241i
$238$	15.3645	+	15.3645i	0.995931	+	0.995931i
$239$		−	17.3304i		−	1.12101i	−0.828151	−	0.560505i	$-0.810607\pi$
$239$		−	17.3304i		−	1.12101i	0.828151	−	0.560505i	$-0.189393\pi$
$240$	8.53920			0.551203
$241$			0.482312i			0.0310685i	0.999879	+	0.0155342i	$0.00494490\pi$
$241$			0.482312i			0.0310685i	−0.999879	+	0.0155342i	$0.995055\pi$
$242$	−11.5283	+	24.4816i	−0.741069	+	1.57373i
$243$		−	29.0966i		−	1.86655i
$244$	12.6439	−	29.0086i	0.809442	−	1.85708i
$245$	1.95287			0.124765
$246$	30.4362	−	30.4362i	1.94054	−	1.94054i
$247$			10.8481i			0.690248i
$248$	32.5899			2.06946
$249$	−1.10804			−0.0702190
$250$	−10.3454	+	10.3454i	−0.654303	+	0.654303i
$251$	15.0861	−	15.0861i	0.952227	−	0.952227i	−0.0466832	−	0.998910i	$-0.514865\pi$
$251$	15.0861	−	15.0861i	0.952227	−	0.952227i	0.998910	+	0.0466832i	$0.0148651\pi$
$252$	66.2264	−	66.2264i	4.17187	−	4.17187i
$253$	−4.31708	−	24.7557i	−0.271412	−	1.55638i
$254$	13.5867	+	13.5867i	0.852503	+	0.852503i
$255$	3.88025	−	3.88025i	0.242991	−	0.242991i
$256$	−32.3478			−2.02174
$257$	30.4602			1.90005			0.950026	−	0.312170i	$-0.101056\pi$
$257$	30.4602			1.90005			0.950026	+	0.312170i	$0.101056\pi$
$258$		−	78.4587i		−	4.88462i
$259$		−	3.28476i		−	0.204105i
$260$			10.2827i			0.637708i
$261$	8.18431	−	8.18431i	0.506596	−	0.506596i
$262$	15.1509	−	15.1509i	0.936023	−	0.936023i
$263$	−10.6532			−0.656905			−0.328452	−	0.944521i	$-0.606527\pi$
$263$	−10.6532			−0.656905			−0.328452	+	0.944521i	$0.606527\pi$
$264$	52.8024	−	9.20805i	3.24976	−	0.566716i
$265$	2.72798	+	2.72798i	0.167579	+	0.167579i
$266$		−	20.7242i		−	1.27068i
$267$	26.4071	−	26.4071i	1.61609	−	1.61609i
$268$	45.0902	−	45.0902i	2.75433	−	2.75433i
$269$	15.6823			0.956170			0.478085	−	0.878314i	$-0.341331\pi$
$269$	15.6823			0.956170			0.478085	+	0.878314i	$0.341331\pi$
$270$	−14.6483	−	14.6483i	−0.891469	−	0.891469i
$271$	26.2212			1.59283			0.796413	−	0.604753i	$-0.206728\pi$
$271$	26.2212			1.59283			0.796413	+	0.604753i	$0.206728\pi$
$272$	8.45105	−	8.45105i	0.512420	−	0.512420i
$273$	29.6162	+	29.6162i	1.79245	+	1.79245i
$274$	−23.3297	−	23.3297i	−1.40940	−	1.40940i
$275$	−8.80783	+	12.5286i	−0.531132	+	0.755505i
$276$	−69.5063	+	69.5063i	−4.18379	+	4.18379i
$277$	9.60517	+	9.60517i	0.577119	+	0.577119i	0.934108	−	0.356989i	$-0.116197\pi$
$277$	9.60517	+	9.60517i	0.577119	+	0.577119i	−0.356989	+	0.934108i	$0.616197\pi$
$278$	−18.5506			−1.11259
$279$	−33.1161	−	33.1161i	−1.98261	−	1.98261i
$280$		−	9.94728i		−	0.594464i
$281$	9.01175	−	9.01175i	0.537596	−	0.537596i	−0.385226	−	0.922822i	$-0.625877\pi$
$281$	9.01175	−	9.01175i	0.537596	−	0.537596i	0.922822	+	0.385226i	$0.125877\pi$
$282$	−9.57339	+	9.57339i	−0.570087	+	0.570087i
$283$	21.2678			1.26424			0.632119	−	0.774871i	$-0.282185\pi$
$283$	21.2678			1.26424			0.632119	+	0.774871i	$0.282185\pi$
$284$	23.3250	−	23.3250i	1.38408	−	1.38408i
$285$	−5.23384			−0.310026
$286$	5.75253	+	32.9871i	0.340154	+	1.95057i
$287$	−12.3150	−	12.3150i	−0.726933	−	0.726933i
$288$	−2.64002	−	2.64002i	−0.155565	−	0.155565i
$289$			9.31961i			0.548212i
$290$		−	2.42764i		−	0.142556i
$291$	46.9005			2.74936
$292$	3.04233			0.178039
$293$	−18.0865			−1.05662			−0.528312	−	0.849050i	$-0.677175\pi$
$293$	−18.0865			−1.05662			−0.528312	+	0.849050i	$0.677175\pi$
$294$	−17.5897	−	17.5897i	−1.02585	−	1.02585i
$295$	0.0836774	−	0.0836774i	0.00487189	−	0.00487189i
$296$	−5.20163			−0.302338
$297$	−36.9482	−	25.9752i	−2.14395	−	1.50723i
$298$	−29.5801	−	29.5801i	−1.71353	−	1.71353i
$299$	−21.9880	−	21.9880i	−1.27160	−	1.27160i
$300$	59.9060			3.45868
$301$	−31.7457			−1.82979
$302$	13.1927			0.759152
$303$	−21.2275	+	21.2275i	−1.21949	+	1.21949i
$304$	−11.3991			−0.653785
$305$	−1.92979	+	4.42747i	−0.110499	+	0.253516i
$306$	−49.4469			−2.82669
$307$	8.27093	+	8.27093i	0.472047	+	0.472047i	0.902576	−	0.430530i	$-0.141673\pi$
$307$	8.27093	+	8.27093i	0.472047	+	0.472047i	−0.430530	+	0.902576i	$0.641673\pi$
$308$	−7.35769	−	42.1917i	−0.419243	−	2.40410i
$309$		−	5.98703i		−	0.340590i
$310$	−9.82291			−0.557904
$311$	7.18987	+	7.18987i	0.407700	+	0.407700i	0.880936	−	0.473236i	$-0.156914\pi$
$311$	7.18987	+	7.18987i	0.407700	+	0.407700i	−0.473236	+	0.880936i	$0.656914\pi$
$312$	46.8990	−	46.8990i	2.65513	−	2.65513i
$313$	−1.46420	−	1.46420i	−0.0827613	−	0.0827613i	0.664514	−	0.747276i	$-0.268638\pi$
$313$	−1.46420	−	1.46420i	−0.0827613	−	0.0827613i	−0.747276	+	0.664514i	$0.768638\pi$
$314$			45.3042i			2.55666i
$315$	−10.1079	+	10.1079i	−0.569515	+	0.569515i
$316$	32.1886	−	32.1886i	1.81075	−	1.81075i
$317$	−4.86868			−0.273452			−0.136726	−	0.990609i	$-0.543658\pi$
$317$	−4.86868			−0.273452			−0.136726	+	0.990609i	$0.543658\pi$
$318$		−	49.1423i		−	2.75576i
$319$	−0.909268	−	5.21408i	−0.0509093	−	0.291933i
$320$	4.55056			0.254384
$321$		−	52.8113i		−	2.94764i
$322$	42.0059	+	42.0059i	2.34090	+	2.34090i
$323$	−5.17981	+	5.17981i	−0.288213	+	0.288213i
$324$			88.5107i			4.91726i
$325$			18.9510i			1.05121i
$326$	−38.3243	+	38.3243i	−2.12258	+	2.12258i
$327$		−	10.8613i		−	0.600630i
$328$	−19.5016	+	19.5016i	−1.07680	+	1.07680i
$329$	3.87356	+	3.87356i	0.213556	+	0.213556i
$330$	−15.9152	+	2.77540i	−0.876101	+	0.152781i
$331$	−2.01315	+	2.01315i	−0.110653	+	0.110653i	−0.760265	−	0.649613i	$-0.774931\pi$
$331$	−2.01315	+	2.01315i	−0.110653	+	0.110653i	0.649613	+	0.760265i	$0.274931\pi$
$332$	1.40205			0.0769473
$333$	5.28561	+	5.28561i	0.289650	+	0.289650i
$334$	25.0952	+	25.0952i	1.37315	+	1.37315i
$335$	−6.88195	+	6.88195i	−0.376001	+	0.376001i
$336$	−31.1205	+	31.1205i	−1.69776	+	1.69776i
$337$	6.49778	+	6.49778i	0.353957	+	0.353957i	0.861579	−	0.507623i	$-0.169476\pi$
$337$	6.49778	+	6.49778i	0.353957	+	0.353957i	−0.507623	+	0.861579i	$0.669476\pi$
$338$	6.68577	+	6.68577i	0.363658	+	0.363658i
$339$	48.6516			2.64239
$340$	−4.90986	+	4.90986i	−0.266274	+	0.266274i
$341$	−21.0977	+	3.67916i	−1.14250	+	0.199238i
$342$	33.3480	+	33.3480i	1.80325	+	1.80325i
$343$	8.65855	−	8.65855i	0.467518	−	0.467518i
$344$			50.2713i			2.71045i
$345$	10.6085	−	10.6085i	0.571141	−	0.571141i
$346$		−	15.3884i		−	0.827285i
$347$			9.96922i			0.535176i	0.963533	+	0.267588i	$0.0862265\pi$
$347$			9.96922i			0.535176i	−0.963533	+	0.267588i	$0.913773\pi$
$348$	−14.6395	+	14.6395i	−0.784760	+	0.784760i
$349$	−4.34917	−	4.34917i	−0.232806	−	0.232806i	0.581057	−	0.813863i	$-0.302639\pi$
$349$	−4.34917	−	4.34917i	−0.232806	−	0.232806i	−0.813863	+	0.581057i	$0.802639\pi$
$350$		−	36.2041i		−	1.93519i
$351$	−55.8885			−2.98311
$352$	−1.68191	+	0.293304i	−0.0896463	+	0.0156331i
$353$		−	0.0762552i		−	0.00405865i	−0.999998	−	0.00202933i	$-0.999354\pi$
$353$		−	0.0762552i		−	0.00405865i	0.999998	−	0.00202933i	$-0.000645955\pi$
$354$	−1.50738			−0.0801163
$355$	−3.56000	+	3.56000i	−0.188945	+	0.188945i
$356$	−33.4140	+	33.4140i	−1.77094	+	1.77094i
$357$			28.2826i			1.49687i
$358$	−23.8463	−	23.8463i	−1.26032	−	1.26032i
$359$	21.1701	−	21.1701i	1.11732	−	1.11732i	0.125182	−	0.992134i	$-0.460048\pi$
$359$	21.1701	−	21.1701i	1.11732	−	1.11732i	0.992134	−	0.125182i	$-0.0399515\pi$
$360$	16.0065	+	16.0065i	0.843615	+	0.843615i
$361$	−12.0133			−0.632277
$362$		−	39.3046i		−	2.06581i
$363$	−33.1431	+	11.9220i	−1.73956	+	0.625743i
$364$	−37.4746	−	37.4746i	−1.96420	−	1.96420i
$365$	−0.464339			−0.0243046
$366$	57.2603	−	22.4968i	2.99305	−	1.17593i
$367$	−31.0849			−1.62262			−0.811310	−	0.584616i	$-0.801245\pi$
$367$	−31.0849			−1.62262			−0.811310	+	0.584616i	$0.801245\pi$
$368$	23.1049	−	23.1049i	1.20442	−	1.20442i
$369$	39.6330			2.06321
$370$	1.56782			0.0815072
$371$	−19.8838			−1.03232
$372$	59.2356	+	59.2356i	3.07122	+	3.07122i
$373$	−8.55657	−	8.55657i	−0.443043	−	0.443043i	0.449991	−	0.893033i	$-0.351427\pi$
$373$	−8.55657	−	8.55657i	−0.443043	−	0.443043i	−0.893033	+	0.449991i	$0.851427\pi$
$374$	−13.0041	+	18.4976i	−0.672427	+	0.956489i
$375$	−19.0436			−0.983409
$376$	6.13403	−	6.13403i	0.316338	−	0.316338i
$377$	−4.63114	−	4.63114i	−0.238516	−	0.238516i
$378$	106.769			5.49163
$379$	−12.8689			−0.661032			−0.330516	−	0.943800i	$-0.607223\pi$
$379$	−12.8689			−0.661032			−0.330516	+	0.943800i	$0.607223\pi$
$380$	6.62261			0.339733
$381$			25.0100i			1.28130i
$382$			21.1717i			1.08324i
$383$	4.52043	+	4.52043i	0.230983	+	0.230983i	0.813103	−	0.582120i	$-0.197777\pi$
$383$	4.52043	+	4.52043i	0.230983	+	0.230983i	−0.582120	+	0.813103i	$0.697777\pi$
$384$	−43.3184	−	43.3184i	−2.21058	−	2.21058i
$385$	1.12298	+	6.43956i	0.0572321	+	0.328190i
$386$	60.6005			3.08449
$387$	51.0830	−	51.0830i	2.59670	−	2.59670i
$388$	−59.3453			−3.01280
$389$	−19.9375	+	19.9375i	−1.01087	+	1.01087i	−0.0109308	+	0.999940i	$0.503479\pi$
$389$	−19.9375	+	19.9375i	−1.01087	+	1.01087i	−0.999940	+	0.0109308i	$0.996521\pi$
$390$	−14.1358	+	14.1358i	−0.715796	+	0.715796i
$391$		−	20.9979i		−	1.06191i
$392$	11.2704	+	11.2704i	0.569240	+	0.569240i
$393$	27.8894			1.40683
$394$	−10.5568	−	10.5568i	−0.531845	−	0.531845i
$395$	−4.91282	+	4.91282i	−0.247191	+	0.247191i
$396$	79.7314	+	56.0525i	4.00665	+	2.81674i
$397$	−17.4951	−	17.4951i	−0.878053	−	0.878053i	0.115280	−	0.993333i	$-0.463224\pi$
$397$	−17.4951	−	17.4951i	−0.878053	−	0.878053i	−0.993333	+	0.115280i	$0.963224\pi$
$398$	−17.8012	−	17.8012i	−0.892294	−	0.892294i
$399$	19.0743	−	19.0743i	0.954912	−	0.954912i
$400$	−19.9136			−0.995681
$401$	27.7927	+	27.7927i	1.38790	+	1.38790i	0.829720	+	0.558180i	$0.188500\pi$
$401$	27.7927	+	27.7927i	1.38790	+	1.38790i	0.558180	+	0.829720i	$0.311500\pi$
$402$	123.973			6.18319
$403$	−18.7389	+	18.7389i	−0.933452	+	0.933452i
$404$	26.8601	−	26.8601i	1.33634	−	1.33634i
$405$		−	13.5091i		−	0.671270i
$406$	8.84734	+	8.84734i	0.439086	+	0.439086i
$407$	3.36737	−	0.587226i	0.166914	−	0.0291077i
$408$	44.7872			2.21730
$409$	−10.3819	+	10.3819i	−0.513352	+	0.513352i	−0.915552	−	0.402200i	$-0.868246\pi$
$409$	−10.3819	+	10.3819i	−0.513352	+	0.513352i	0.402200	+	0.915552i	$0.368246\pi$
$410$	5.87798	−	5.87798i	0.290293	−	0.290293i
$411$		−	42.9447i		−	2.11830i
$412$			7.57565i			0.373225i
$413$			0.609912i			0.0300118i
$414$	−135.186			−6.64403
$415$	−0.213989			−0.0105043
$416$	−1.49387	+	1.49387i	−0.0732432	+	0.0732432i
$417$	−17.0737	−	17.0737i	−0.836105	−	0.836105i
$418$	21.2454	−	3.70493i	1.03915	−	0.181214i
$419$	−2.46354	+	2.46354i	−0.120352	+	0.120352i	−0.764717	−	0.644366i	$-0.777121\pi$
$419$	−2.46354	+	2.46354i	−0.120352	+	0.120352i	0.644366	+	0.764717i	$0.277121\pi$
$420$	18.0802	−	18.0802i	0.882226	−	0.882226i
$421$	−22.9077	+	22.9077i	−1.11645	+	1.11645i	−0.124195	+	0.992258i	$0.539635\pi$
$421$	−22.9077	+	22.9077i	−1.11645	+	1.11645i	−0.992258	+	0.124195i	$0.960365\pi$
$422$	−35.3304			−1.71986
$423$	−12.4661			−0.606124
$424$			31.4873i			1.52916i
$425$	−9.04884	+	9.04884i	−0.438933	+	0.438933i
$426$	64.1305			3.10713
$427$	−9.10261	−	23.1685i	−0.440506	−	1.12120i
$428$			66.8245i			3.23009i
$429$	−25.0664	+	35.6555i	−1.21022	+	1.72146i
$430$		−	15.1523i		−	0.730709i
$431$	−10.1057			−0.486772			−0.243386	−	0.969929i	$-0.578258\pi$
$431$	−10.1057			−0.486772			−0.243386	+	0.969929i	$0.578258\pi$
$432$		−	58.7273i		−	2.82552i
$433$	18.1900	+	18.1900i	0.874154	+	0.874154i	0.992922	−	0.118768i	$-0.0378944\pi$
$433$	18.1900	+	18.1900i	0.874154	+	0.874154i	−0.118768	+	0.992922i	$0.537894\pi$
$434$	35.7989	−	35.7989i	1.71840	−	1.71840i
$435$	2.23437	−	2.23437i	0.107130	−	0.107130i
$436$			13.7433i			0.658183i
$437$	−14.1614	+	14.1614i	−0.677433	+	0.677433i
$438$	4.18234	+	4.18234i	0.199840	+	0.199840i
$439$		−	5.89583i		−	0.281393i	−0.990053	−	0.140696i	$-0.955066\pi$
$439$		−	5.89583i		−	0.281393i	0.990053	−	0.140696i	$-0.0449341\pi$
$440$	10.1974	−	1.77830i	0.486144	−	0.0847772i
$441$		−	22.9047i		−	1.09070i
$442$			27.9798i			1.33086i
$443$	5.06172			0.240489			0.120245	−	0.992744i	$-0.461632\pi$
$443$	5.06172			0.240489			0.120245	+	0.992744i	$0.461632\pi$
$444$	−9.45451	−	9.45451i	−0.448691	−	0.448691i
$445$	5.09986	−	5.09986i	0.241756	−	0.241756i
$446$	38.3703			1.81688
$447$		−	54.4504i		−	2.57541i
$448$	−16.5842	+	16.5842i	−0.783529	+	0.783529i
$449$	−11.6147			−0.548132			−0.274066	−	0.961711i	$-0.588369\pi$
$449$	−11.6147			−0.548132			−0.274066	+	0.961711i	$0.588369\pi$
$450$	58.2570	+	58.2570i	2.74626	+	2.74626i
$451$	10.4231	−	14.8263i	0.490807	−	0.698144i
$452$	−61.5610			−2.89559
$453$	12.1424	+	12.1424i	0.570498	+	0.570498i
$454$		−	39.3701i		−	1.84773i
$455$	5.71961	+	5.71961i	0.268139	+	0.268139i
$456$	−30.2054	−	30.2054i	−1.41450	−	1.41450i
$457$	−4.32273	−	4.32273i	−0.202209	−	0.202209i	0.598737	−	0.800946i	$-0.295669\pi$
$457$	−4.32273	−	4.32273i	−0.202209	−	0.202209i	−0.800946	+	0.598737i	$0.795669\pi$
$458$	−15.8926	+	15.8926i	−0.742614	+	0.742614i
$459$	−26.6859	−	26.6859i	−1.24559	−	1.24559i
$460$	−13.4234	+	13.4234i	−0.625868	+	0.625868i
$461$			14.3958i			0.670477i	0.942133	+	0.335239i	$0.108817\pi$
$461$			14.3958i			0.670477i	−0.942133	+	0.335239i	$0.891183\pi$
$462$	47.8869	−	68.1164i	2.22790	−	3.16906i
$463$			11.2975i			0.525040i	0.964927	+	0.262520i	$0.0845535\pi$
$463$			11.2975i			0.525040i	−0.964927	+	0.262520i	$0.915446\pi$
$464$	4.86638	−	4.86638i	0.225916	−	0.225916i
$465$	−9.04090	−	9.04090i	−0.419262	−	0.419262i
$466$			1.19465i			0.0553412i
$467$	0.0960089	−	0.0960089i	0.00444276	−	0.00444276i	−0.704882	−	0.709325i	$-0.749000\pi$
$467$	0.0960089	−	0.0960089i	0.00444276	−	0.00444276i	0.709325	+	0.704882i	$0.249000\pi$
$468$	120.603			5.57488
$469$		−	50.1615i		−	2.31624i
$470$	−1.84886	+	1.84886i	−0.0852815	+	0.0852815i
$471$	−41.6975	+	41.6975i	−1.92132	+	1.92132i
$472$	0.965833			0.0444561
$473$	−5.67527	−	32.5441i	−0.260949	−	1.49638i
$474$	88.5003			4.06495
$475$	12.2054			0.560024
$476$		−	35.7872i		−	1.64030i
$477$	31.9957	−	31.9957i	1.46498	−	1.46498i
$478$	−30.1461	+	30.1461i	−1.37885	+	1.37885i
$479$	−26.1203			−1.19347			−0.596734	−	0.802439i	$-0.703535\pi$
$479$	−26.1203			−1.19347			−0.596734	+	0.802439i	$0.703535\pi$
$480$	−0.720744	−	0.720744i	−0.0328973	−	0.0328973i
$481$	2.99089	−	2.99089i	0.136373	−	0.136373i
$482$	0.838977	−	0.838977i	0.0382144	−	0.0382144i
$483$			77.3236i			3.51834i
$484$	41.9374	−	15.0854i	1.90625	−	0.685702i
$485$	9.05765			0.411287
$486$	−50.6133	+	50.6133i	−2.29586	+	2.29586i
$487$			24.8393i			1.12557i	0.826602	+	0.562787i	$0.190271\pi$
$487$			24.8393i			1.12557i	−0.826602	+	0.562787i	$0.809729\pi$
$488$	−36.6888	+	14.4146i	−1.66082	+	0.652516i
$489$	−70.5464			−3.19022
$490$	−3.39700	−	3.39700i	−0.153461	−	0.153461i
$491$	0.345652			0.0155991			0.00779954	−	0.999970i	$-0.497517\pi$
$491$	0.345652			0.0155991			0.00779954	+	0.999970i	$0.497517\pi$
$492$	−70.8925			−3.19608
$493$		−	4.42261i		−	0.199184i
$494$	18.8702	−	18.8702i	0.849009	−	0.849009i
$495$	−12.1691	−	8.55507i	−0.546960	−	0.384522i
$496$	−19.6907	−	19.6907i	−0.884140	−	0.884140i
$497$		−	25.9483i		−	1.16394i
$498$	1.92742	+	1.92742i	0.0863696	+	0.0863696i
$499$	2.69960	+	2.69960i	0.120851	+	0.120851i	0.764946	−	0.644095i	$-0.222766\pi$
$499$	2.69960	+	2.69960i	0.120851	+	0.120851i	−0.644095	+	0.764946i	$0.722766\pi$
$500$	24.0968			1.07764
$501$			46.1947i			2.06382i
$502$	−52.4842			−2.34249
$503$		−	1.22654i		−	0.0546885i	−0.999626	−	0.0273443i	$-0.991295\pi$
$503$		−	1.22654i		−	0.0546885i	0.999626	−	0.0273443i	$-0.00870503\pi$
$504$	−116.669			−5.19684
$505$	−4.09955	+	4.09955i	−0.182428	+	0.182428i
$506$	−35.5528	+	50.5718i	−1.58052	+	2.24819i
$507$			12.3070i			0.546573i
$508$		−	31.6463i		−	1.40408i
$509$	21.6596	+	21.6596i	0.960043	+	0.960043i	0.999232	−	0.0391891i	$-0.0124775\pi$
$509$	21.6596	+	21.6596i	0.960043	+	0.960043i	−0.0391891	+	0.999232i	$0.512477\pi$
$510$	−13.4993			−0.597760
$511$	1.69225	−	1.69225i	0.0748607	−	0.0748607i
$512$	29.2116	+	29.2116i	1.29098	+	1.29098i
$513$			35.9951i			1.58922i
$514$	−52.9851	−	52.9851i	−2.33707	−	2.33707i
$515$		−	1.15624i		−	0.0509501i
$516$	−91.3736	+	91.3736i	−4.02250	+	4.02250i
$517$	−3.27849	+	4.66346i	−0.144188	+	0.205099i
$518$	−5.71381	+	5.71381i	−0.251050	+	0.251050i
$519$	14.1633	−	14.1633i	0.621700	−	0.621700i
$520$	9.05735	−	9.05735i	0.397191	−	0.397191i
$521$	−19.4296	+	19.4296i	−0.851228	+	0.851228i	−0.990284	−	0.139057i	$-0.955593\pi$
$521$	−19.4296	+	19.4296i	−0.851228	+	0.851228i	0.139057	+	0.990284i	$0.455593\pi$
$522$	−28.4731			−1.24623
$523$	14.4038	−	14.4038i	0.629835	−	0.629835i	−0.318191	−	0.948027i	$-0.603075\pi$
$523$	14.4038	−	14.4038i	0.629835	−	0.629835i	0.948027	+	0.318191i	$0.103075\pi$
$524$	−35.2896			−1.54163
$525$	33.3218	−	33.3218i	1.45428	−	1.45428i
$526$	18.5311	+	18.5311i	0.807996	+	0.807996i
$527$	−17.8951			−0.779524
$528$	−37.4666	−	26.3396i	−1.63052	−	1.14628i
$529$		−	34.4076i		−	1.49598i
$530$		−	9.49059i		−	0.412245i
$531$	−0.981428	−	0.981428i	−0.0425903	−	0.0425903i
$532$	−24.1356	+	24.1356i	−1.04641	+	1.04641i
$533$		−	22.4266i		−	0.971402i
$534$	−91.8697			−3.97559
$535$		−	10.1992i		−	0.440949i
$536$	−79.4338			−3.43102
$537$		−	43.8957i		−	1.89424i
$538$	−27.2793	−	27.2793i	−1.17609	−	1.17609i
$539$	−8.56843	−	6.02374i	−0.369068	−	0.259461i
$540$			34.1191i			1.46825i
$541$	8.54292	+	8.54292i	0.367289	+	0.367289i	0.866487	−	0.499199i	$-0.166372\pi$
$541$	8.54292	+	8.54292i	0.367289	+	0.367289i	−0.499199	+	0.866487i	$0.666372\pi$
$542$	−45.6116	−	45.6116i	−1.95918	−	1.95918i
$543$	36.1755	−	36.1755i	1.55244	−	1.55244i
$544$	−1.42661			−0.0611652
$545$		−	2.09758i		−	0.0898505i
$546$		−	103.034i		−	4.40945i
$547$	32.7659	−	32.7659i	1.40097	−	1.40097i	0.603930	−	0.797038i	$-0.293601\pi$
$547$	32.7659	−	32.7659i	1.40097	−	1.40097i	0.797038	−	0.603930i	$-0.206399\pi$
$548$			54.3398i			2.32128i
$549$	51.9285	+	22.6339i	2.21625	+	0.965991i
$550$	37.1145	−	6.47229i	1.58257	−	0.275980i
$551$	−2.98270	+	2.98270i	−0.127067	+	0.127067i
$552$	122.447			5.21168
$553$		−	35.8088i		−	1.52274i
$554$		−	33.4162i		−	1.41972i
$555$	1.44301	+	1.44301i	0.0612522	+	0.0612522i
$556$	21.6042	+	21.6042i	0.916220	+	0.916220i
$557$	29.3231	−	29.3231i	1.24246	−	1.24246i	0.283480	−	0.958978i	$-0.408511\pi$
$557$	29.3231	−	29.3231i	1.24246	−	1.24246i	0.958978	−	0.283480i	$-0.0914891\pi$
$558$			115.210i			4.87723i
$559$	−28.9056	−	28.9056i	−1.22258	−	1.22258i
$560$	−6.01013	+	6.01013i	−0.253974	+	0.253974i
$561$	−28.9938	+	5.05615i	−1.22412	+	0.213471i
$562$	−31.3517			−1.32249
$563$	−40.2928			−1.69814			−0.849069	−	0.528281i	$-0.822837\pi$
$563$	−40.2928			−1.69814			−0.849069	+	0.528281i	$0.822837\pi$
$564$	22.2985			0.938936
$565$	9.39582			0.395285
$566$	−36.9951	−	36.9951i	−1.55502	−	1.55502i
$567$	49.2327	+	49.2327i	2.06758	+	2.06758i
$568$	−41.0908			−1.72413
$569$			30.9596i			1.29789i	0.760834	+	0.648946i	$0.224790\pi$
$569$			30.9596i			1.29789i	−0.760834	+	0.648946i	$0.775210\pi$
$570$	9.10422	+	9.10422i	0.381334	+	0.381334i
$571$			4.85616i			0.203224i	0.994824	+	0.101612i	$0.0324000\pi$
$571$			4.85616i			0.203224i	−0.994824	+	0.101612i	$0.967600\pi$
$572$	31.7176	−	45.1165i	1.32618	−	1.88642i
$573$	−19.4862	+	19.4862i	−0.814048	+	0.814048i
$574$			42.8437i			1.78826i
$575$	−24.7392	+	24.7392i	−1.03170	+	1.03170i
$576$		−	53.3722i		−	2.22384i
$577$	4.89465	+	4.89465i	0.203767	+	0.203767i	0.801612	−	0.597845i	$-0.203976\pi$
$577$	4.89465	+	4.89465i	0.203767	+	0.203767i	−0.597845	+	0.801612i	$0.703976\pi$
$578$	16.2114	−	16.2114i	0.674304	−	0.674304i
$579$	55.7760	+	55.7760i	2.31797	+	2.31797i
$580$	−2.82725	+	2.82725i	−0.117395	+	0.117395i
$581$	0.779867	−	0.779867i	0.0323543	−	0.0323543i
$582$	−81.5830	−	81.5830i	−3.38172	−	3.38172i
$583$	−3.55469	−	20.3839i	−0.147220	−	0.844214i
$584$	−2.67978	−	2.67978i	−0.110890	−	0.110890i
$585$	−18.4072			−0.761044
$586$	31.4613	+	31.4613i	1.29965	+	1.29965i
$587$	5.41299	+	5.41299i	0.223418	+	0.223418i	0.809936	−	0.586518i	$-0.199502\pi$
$587$	5.41299	+	5.41299i	0.223418	+	0.223418i	−0.586518	+	0.809936i	$0.699502\pi$
$588$			40.9702i			1.68958i
$589$	12.0688	+	12.0688i	0.497288	+	0.497288i
$590$	−0.291112			−0.0119849
$591$		−	19.4327i		−	0.799356i
$592$	3.14281	+	3.14281i	0.129169	+	0.129169i
$593$	−2.18495	−	2.18495i	−0.0897250	−	0.0897250i	0.660820	−	0.750545i	$-0.270209\pi$
$593$	−2.18495	−	2.18495i	−0.0897250	−	0.0897250i	−0.750545	+	0.660820i	$0.770209\pi$
$594$	19.0875	+	109.455i	0.783168	+	4.49098i
$595$			5.46206i			0.223923i
$596$			68.8985i			2.82219i
$597$		−	32.7680i		−	1.34111i
$598$			76.4958i			3.12815i
$599$	12.7546	−	12.7546i	0.521137	−	0.521137i	−0.396778	−	0.917915i	$-0.629872\pi$
$599$	12.7546	−	12.7546i	0.521137	−	0.521137i	0.917915	+	0.396778i	$0.129872\pi$
$600$	−52.7671	−	52.7671i	−2.15421	−	2.15421i
$601$	−0.659742			−0.0269114			−0.0134557	−	0.999909i	$-0.504283\pi$
$601$	−0.659742			−0.0269114			−0.0134557	+	0.999909i	$0.504283\pi$
$602$	55.2214	+	55.2214i	2.25066	+	2.25066i
$603$	80.7163	+	80.7163i	3.28702	+	3.28702i
$604$	−15.3643	−	15.3643i	−0.625163	−	0.625163i
$605$	−6.40074	+	2.30243i	−0.260227	+	0.0936072i
$606$	73.8500			2.99995
$607$			35.9486i			1.45911i	0.683924	+	0.729553i	$0.260272\pi$
$607$			35.9486i			1.45911i	−0.683924	+	0.729553i	$0.739728\pi$
$608$	0.962132	+	0.962132i	0.0390196	+	0.0390196i
$609$			16.2860i			0.659941i
$610$	11.0584	−	4.34469i	0.447741	−	0.175911i
$611$			7.05404i			0.285376i
$612$	57.5862	+	57.5862i	2.32779	+	2.32779i
$613$	6.08709			0.245855			0.122928	−	0.992416i	$-0.460772\pi$
$613$	6.08709			0.245855			0.122928	+	0.992416i	$0.460772\pi$
$614$		−	28.7744i		−	1.16124i
$615$	10.8201			0.436307
$616$	−30.6829	+	43.6447i	−1.23625	+	1.75849i
$617$	−29.2946	+	29.2946i	−1.17936	+	1.17936i	−0.199447	+	0.979909i	$0.563915\pi$
$617$	−29.2946	+	29.2946i	−1.17936	+	1.17936i	−0.979909	+	0.199447i	$0.936085\pi$
$618$	−10.4144	+	10.4144i	−0.418927	+	0.418927i
$619$	−15.8519			−0.637140			−0.318570	−	0.947899i	$-0.603203\pi$
$619$	−15.8519			−0.637140			−0.318570	+	0.947899i	$0.603203\pi$
$620$	11.4398	+	11.4398i	0.459435	+	0.459435i
$621$	−72.9584	−	72.9584i	−2.92772	−	2.92772i
$622$		−	25.0134i		−	1.00295i
$623$			37.1721i			1.48927i
$624$	−56.6726			−2.26872
$625$	19.4102			0.776408
$626$			5.09391i			0.203594i
$627$	22.9640	+	16.1441i	0.917094	+	0.644732i
$628$	52.7617	−	52.7617i	2.10542	−	2.10542i
$629$	2.85622			0.113885
$630$	35.1651			1.40101
$631$	21.7709	+	21.7709i	0.866687	+	0.866687i	0.992104	−	0.125417i	$-0.0400269\pi$
$631$	21.7709	+	21.7709i	0.866687	+	0.866687i	−0.125417	+	0.992104i	$0.540027\pi$
$632$	−56.7054			−2.25562
$633$	−32.5177	−	32.5177i	−1.29246	−	1.29246i
$634$	8.46901	+	8.46901i	0.336347	+	0.336347i
$635$			4.83005i			0.191675i
$636$	−57.2315	+	57.2315i	−2.26938	+	2.26938i
$637$	−12.9608			−0.513524
$638$	−7.48818	+	10.6515i	−0.296460	+	0.421697i
$639$	41.7542	+	41.7542i	1.65177	+	1.65177i
$640$	−8.36584	−	8.36584i	−0.330689	−	0.330689i
$641$	−12.7972	−	12.7972i	−0.505457	−	0.505457i	0.407671	−	0.913129i	$-0.366341\pi$
$641$	−12.7972	−	12.7972i	−0.505457	−	0.505457i	−0.913129	+	0.407671i	$0.866341\pi$
$642$	−91.8648	+	91.8648i	−3.62561	+	3.62561i
$643$	0.539905	−	0.539905i	0.0212918	−	0.0212918i	−0.696381	−	0.717673i	$-0.745207\pi$
$643$	0.539905	−	0.539905i	0.0212918	−	0.0212918i	0.717673	+	0.696381i	$0.245207\pi$
$644$		−	97.8409i		−	3.85547i
$645$	13.9460	−	13.9460i	0.549123	−	0.549123i
$646$	18.0205			0.709006
$647$	−10.1226	−	10.1226i	−0.397959	−	0.397959i	0.479554	−	0.877513i	$-0.340799\pi$
$647$	−10.1226	−	10.1226i	−0.397959	−	0.397959i	−0.877513	+	0.479554i	$0.840799\pi$
$648$	77.9630	−	77.9630i	3.06268	−	3.06268i
$649$	−0.625250	+	0.109036i	−0.0245432	+	0.00428002i
$650$	32.9651	−	32.9651i	1.29300	−	1.29300i
$651$	65.8977			2.58274
$652$	89.2655			3.49591
$653$	11.7721	+	11.7721i	0.460679	+	0.460679i	0.898878	−	0.438199i	$-0.144384\pi$
$653$	11.7721	+	11.7721i	0.460679	+	0.460679i	−0.438199	+	0.898878i	$0.644384\pi$
$654$	−18.8931	+	18.8931i	−0.738778	+	0.738778i
$655$	5.38612			0.210453
$656$	23.5657			0.920085
$657$			5.44609i			0.212472i
$658$		−	13.4760i		−	0.525351i
$659$	35.7580			1.39294			0.696468	−	0.717588i	$-0.254754\pi$
$659$	35.7580			1.39294			0.696468	+	0.717588i	$0.254754\pi$
$660$	21.7672	+	15.3027i	0.847287	+	0.595656i
$661$	−2.10638	+	2.10638i	−0.0819285	+	0.0819285i	−0.746883	−	0.664955i	$-0.768451\pi$
$661$	−2.10638	+	2.10638i	−0.0819285	+	0.0819285i	0.664955	+	0.746883i	$0.268451\pi$
$662$	7.00372			0.272207
$663$	−25.7523	+	25.7523i	−1.00014	+	1.00014i
$664$	−1.23497	−	1.23497i	−0.0479260	−	0.0479260i
$665$	3.68373	−	3.68373i	0.142849	−	0.142849i
$666$		−	18.3885i		−	0.712541i
$667$		−	12.0913i		−	0.468175i
$668$		−	58.4521i		−	2.26158i
$669$	35.3155	+	35.3155i	1.36538	+	1.36538i
$670$	23.9422			0.924966
$671$	22.1239	−	13.4734i	0.854083	−	0.520136i
$672$	5.25339			0.202654
$673$	2.73046	+	2.73046i	0.105252	+	0.105252i	0.757772	−	0.652520i	$-0.226288\pi$
$673$	2.73046	+	2.73046i	0.105252	+	0.105252i	−0.652520	+	0.757772i	$0.726288\pi$
$674$		−	22.6056i		−	0.870737i
$675$			62.8814i			2.42031i
$676$		−	15.5726i		−	0.598946i
$677$	−22.7657	+	22.7657i	−0.874958	+	0.874958i	−0.993008	−	0.118049i	$-0.962336\pi$
$677$	−22.7657	+	22.7657i	−0.874958	+	0.874958i	0.118049	+	0.993008i	$0.462336\pi$
$678$	−84.6289	−	84.6289i	−3.25015	−	3.25015i
$679$	−33.0099	+	33.0099i	−1.26680	+	1.26680i
$680$	8.64951			0.331694
$681$	36.2358	−	36.2358i	1.38856	−	1.38856i
$682$	43.0990	+	30.2993i	1.65035	+	1.16022i
$683$	−6.51331			−0.249225			−0.124612	−	0.992205i	$-0.539769\pi$
$683$	−6.51331			−0.249225			−0.124612	+	0.992205i	$0.539769\pi$
$684$		−	77.6747i		−	2.96997i
$685$		−	8.29367i		−	0.316885i
$686$	−30.1229			−1.15010
$687$	−29.2548			−1.11614
$688$	30.3739	−	30.3739i	1.15799	−	1.15799i
$689$	−18.1049	−	18.1049i	−0.689744	−	0.689744i
$690$	−36.9067			−1.40501
$691$	1.35972			0.0517261			0.0258631	−	0.999665i	$-0.491767\pi$
$691$	1.35972			0.0517261			0.0258631	+	0.999665i	$0.491767\pi$
$692$	−17.9215	+	17.9215i	−0.681271	+	0.681271i
$693$	75.5276	−	13.1710i	2.86906	−	0.500327i
$694$	17.3413	−	17.3413i	0.658268	−	0.658268i
$695$	−3.29736	−	3.29736i	−0.125076	−	0.125076i
$696$	25.7899			0.977562
$697$	10.7084	−	10.7084i	0.405608	−	0.405608i
$698$			15.1307i			0.572704i
$699$	−1.09954	+	1.09954i	−0.0415886	+	0.0415886i
$700$	−42.1635	+	42.1635i	−1.59363	+	1.59363i
$701$	−26.3948	−	26.3948i	−0.996918	−	0.996918i	0.00307752	−	0.999995i	$-0.499020\pi$
$701$	−26.3948	−	26.3948i	−0.996918	−	0.996918i	−0.999995	+	0.00307752i	$0.999020\pi$
$702$	97.2175	+	97.2175i	3.66924	+	3.66924i
$703$	−1.92629	−	1.92629i	−0.0726515	−	0.0726515i
$704$	−19.9660	−	14.0365i	−0.752499	−	0.529019i
$705$	−3.40333			−0.128177
$706$	−0.132645	+	0.132645i	−0.00499216	+	0.00499216i
$707$		−	29.8810i		−	1.12379i
$708$	1.75551	+	1.75551i	0.0659760	+	0.0659760i
$709$	25.0004	+	25.0004i	0.938911	+	0.938911i	0.998239	−	0.0593280i	$-0.0188958\pi$
$709$	25.0004	+	25.0004i	0.938911	+	0.938911i	−0.0593280	+	0.998239i	$0.518896\pi$
$710$	12.3852			0.464807
$711$	57.6210	+	57.6210i	2.16096	+	2.16096i
$712$	58.8643			2.20603
$713$	−48.9246			−1.83224
$714$	49.1972	−	49.1972i	1.84116	−	1.84116i
$715$	−4.84094	+	6.88596i	−0.181041	+	0.257520i
$716$			55.5432i			2.07575i
$717$	−55.4922			−2.07239
$718$	−73.6504			−2.74861
$719$		−	35.9316i		−	1.34002i	−0.742351	−	0.670011i	$-0.766290\pi$
$719$		−	35.9316i		−	1.34002i	0.742351	−	0.670011i	$-0.233710\pi$
$720$		−	19.3422i		−	0.720840i
$721$	4.21384	+	4.21384i	0.156931	+	0.156931i
$722$	20.8969	+	20.8969i	0.777703	+	0.777703i
$723$	1.54437			0.0574357
$724$	−45.7745	+	45.7745i	−1.70120	+	1.70120i
$725$	−5.21060	+	5.21060i	−0.193517	+	0.193517i
$726$	78.3903	+	36.9138i	2.90934	+	1.37000i
$727$	−20.8684			−0.773967			−0.386983	−	0.922087i	$-0.626483\pi$
$727$	−20.8684			−0.773967			−0.386983	+	0.922087i	$0.626483\pi$
$728$			66.0177i			2.44678i
$729$	−27.6309			−1.02337
$730$	0.807713	+	0.807713i	0.0298948	+	0.0298948i
$731$		−	27.6040i		−	1.02097i
$732$	−92.8859	−	40.4859i	−3.43316	−	1.49640i
$733$		−	15.7410i		−	0.581409i	−0.956813	−	0.290704i	$-0.906110\pi$
$733$		−	15.7410i		−	0.581409i	0.956813	−	0.290704i	$-0.0938896\pi$
$734$	54.0719	+	54.0719i	1.99583	+	1.99583i
$735$		−	6.25313i		−	0.230650i
$736$	−3.90029			−0.143767
$737$	51.4230	−	8.96750i	1.89419	−	0.330322i
$738$	−68.9411	−	68.9411i	−2.53776	−	2.53776i
$739$	20.5619	+	20.5619i	0.756383	+	0.756383i	0.975662	−	0.219279i	$-0.0703706\pi$
$739$	20.5619	+	20.5619i	0.756383	+	0.756383i	−0.219279	+	0.975662i	$0.570371\pi$
$740$	−1.82590	−	1.82590i	−0.0671214	−	0.0671214i
$741$	34.7358			1.27605
$742$	34.5877	+	34.5877i	1.26976	+	1.26976i
$743$	−7.24019	+	7.24019i	−0.265617	+	0.265617i	−0.827331	−	0.561714i	$-0.810142\pi$
$743$	−7.24019	+	7.24019i	−0.265617	+	0.265617i	0.561714	+	0.827331i	$0.310142\pi$
$744$		−	104.353i		−	3.82577i
$745$		−	10.5157i		−	0.385266i
$746$			29.7681i			1.08989i
$747$			2.50981i			0.0918293i
$748$	36.6872	−	6.39777i	1.34142	−	0.233926i
$749$	37.1701	+	37.1701i	1.35817	+	1.35817i
$750$	33.1262	+	33.1262i	1.20960	+	1.20960i
$751$			6.39465i			0.233344i	0.993170	+	0.116672i	$0.0372227\pi$
$751$			6.39465i			0.233344i	−0.993170	+	0.116672i	$0.962777\pi$
$752$	−7.41234			−0.270300
$753$	−48.3059	−	48.3059i	−1.76036	−	1.76036i
$754$			16.1117i			0.586752i
$755$	2.34499	+	2.34499i	0.0853429	+	0.0853429i
$756$	−124.345	−	124.345i	−4.52237	−	4.52237i
$757$	25.1415			0.913784			0.456892	−	0.889522i	$-0.348963\pi$
$757$	25.1415			0.913784			0.456892	+	0.889522i	$0.348963\pi$
$758$	22.3854	+	22.3854i	0.813073	+	0.813073i
$759$	−79.2681	+	13.8233i	−2.87725	+	0.501755i
$760$	−5.83341	−	5.83341i	−0.211600	−	0.211600i
$761$	−12.0317	+	12.0317i	−0.436149	+	0.436149i	−0.890714	−	0.454565i	$-0.849795\pi$
$761$	−12.0317	+	12.0317i	−0.436149	+	0.436149i	0.454565	+	0.890714i	$0.349795\pi$
$762$	43.5047	−	43.5047i	1.57601	−	1.57601i
$763$	7.64448	+	7.64448i	0.276749	+	0.276749i
$764$	24.6568	−	24.6568i	0.892050	−	0.892050i
$765$	−8.78917	−	8.78917i	−0.317773	−	0.317773i
$766$		−	15.7265i		−	0.568221i
$767$	−0.555347	+	0.555347i	−0.0200524	+	0.0200524i
$768$			103.578i			3.73755i
$769$	−20.5357	+	20.5357i	−0.740537	+	0.740537i	−0.972681	−	0.232145i	$-0.925426\pi$
$769$	−20.5357	+	20.5357i	−0.740537	+	0.740537i	0.232145	+	0.972681i	$0.425426\pi$
$770$	9.24814	−	13.1549i	0.333280	−	0.474071i
$771$		−	97.5338i		−	3.51259i
$772$	−70.5759	−	70.5759i	−2.54008	−	2.54008i
$773$			3.58555i			0.128963i	0.997919	+	0.0644817i	$0.0205394\pi$
$773$			3.58555i			0.128963i	−0.997919	+	0.0644817i	$0.979461\pi$
$774$	−177.717			−6.38790
$775$	21.0836	+	21.0836i	0.757344	+	0.757344i
$776$	52.2732	+	52.2732i	1.87650	+	1.87650i
$777$	−10.5179			−0.377326
$778$	69.3621			2.48675
$779$	−14.4439			−0.517505
$780$	32.9254			1.17892
$781$	26.6009	−	4.63885i	0.951854	−	0.165991i
$782$	−36.5257	+	36.5257i	−1.30615	+	1.30615i
$783$	−15.3666	−	15.3666i	−0.549157	−	0.549157i
$784$		−	13.6191i		−	0.486396i
$785$	−8.05281	+	8.05281i	−0.287417	+	0.287417i
$786$	−48.5132	−	48.5132i	−1.73041	−	1.73041i
$787$	−4.62143	−	4.62143i	−0.164736	−	0.164736i	0.619925	−	0.784661i	$-0.287163\pi$
$787$	−4.62143	−	4.62143i	−0.164736	−	0.164736i	−0.784661	+	0.619925i	$0.787163\pi$
$788$			24.5891i			0.875951i
$789$			34.1117i			1.21441i
$790$	17.0916			0.608091
$791$	−34.2423	+	34.2423i	−1.21752	+	1.21752i
$792$	−20.8572	−	119.603i	−0.741127	−	4.24990i
$793$	12.8075	−	29.3840i	0.454809	−	1.04346i
$794$			60.8651i			2.16002i
$795$	8.73503	−	8.73503i	0.309799	−	0.309799i
$796$			41.4628i			1.46961i
$797$			24.9859i			0.885047i	0.896757	+	0.442523i	$0.145917\pi$
$797$			24.9859i			0.885047i	−0.896757	+	0.442523i	$0.854083\pi$
$798$	−66.3593			−2.34909
$799$	−3.36820	+	3.36820i	−0.119158	+	0.119158i
$800$	1.68079	+	1.68079i	0.0594249	+	0.0594249i
$801$	−59.8147	−	59.8147i	−2.11345	−	2.11345i
$802$		−	96.6901i		−	3.41425i
$803$	2.03733	+	1.43228i	0.0718959	+	0.0505440i
$804$	−144.380	−	144.380i	−5.09187	−	5.09187i
$805$			14.9331i			0.526322i
$806$	65.1923			2.29630
$807$		−	50.2151i		−	1.76765i
$808$	−47.3184			−1.66466
$809$		−	40.6716i		−	1.42994i	−0.699157	−	0.714969i	$-0.746441\pi$
$809$		−	40.6716i		−	1.42994i	0.699157	−	0.714969i	$-0.253559\pi$
$810$	−23.4989	+	23.4989i	−0.825666	+	0.825666i
$811$	−18.9565	−	18.9565i	−0.665654	−	0.665654i	0.291053	−	0.956707i	$-0.405994\pi$
$811$	−18.9565	−	18.9565i	−0.665654	−	0.665654i	−0.956707	+	0.291053i	$0.905994\pi$
$812$		−	20.6074i		−	0.723177i
$813$		−	83.9607i		−	2.94463i
$814$	−6.87898	−	4.83603i	−0.241108	−	0.169503i
$815$	−13.6242			−0.477237
$816$	−27.0604	−	27.0604i	−0.947302	−	0.947302i
$817$	−18.6167	+	18.6167i	−0.651317	+	0.651317i
$818$	36.1184			1.26285
$819$	67.0836	−	67.0836i	2.34409	−	2.34409i
$820$	−13.6911			−0.478114
$821$	22.4438	−	22.4438i	0.783295	−	0.783295i	−0.197090	−	0.980385i	$-0.563149\pi$
$821$	22.4438	−	22.4438i	0.783295	−	0.783295i	0.980385	+	0.197090i	$0.0631492\pi$
$822$	−74.7018	+	74.7018i	−2.60553	+	2.60553i
$823$	−30.6694	+	30.6694i	−1.06907	+	1.06907i	−0.0716387	+	0.997431i	$0.522823\pi$
$823$	−30.6694	+	30.6694i	−1.06907	+	1.06907i	−0.997431	+	0.0716387i	$0.977177\pi$
$824$	6.67287	−	6.67287i	0.232460	−	0.232460i
$825$	40.1168	+	28.2028i	1.39669	+	0.981894i
$826$	1.06094	−	1.06094i	0.0369147	−	0.0369147i
$827$		−	3.69062i		−	0.128335i	−0.997939	−	0.0641677i	$-0.979561\pi$
$827$		−	3.69062i		−	0.128335i	0.997939	−	0.0641677i	$-0.0204393\pi$
$828$	157.439	+	157.439i	5.47137	+	5.47137i
$829$		−	27.4634i		−	0.953843i	−0.878946	−	0.476922i	$-0.841753\pi$
$829$		−	27.4634i		−	0.953843i	0.878946	−	0.476922i	$-0.158247\pi$
$830$	0.372232	+	0.372232i	0.0129204	+	0.0129204i
$831$	30.7559	−	30.7559i	1.06691	−	1.06691i
$832$	−30.2010			−1.04703
$833$	−6.18857	−	6.18857i	−0.214421	−	0.214421i
$834$			59.3992i			2.05683i
$835$			8.92132i			0.308735i
$836$	−29.0574	−	20.4278i	−1.00497	−	0.706510i
$837$	−62.1776	+	62.1776i	−2.14917	+	2.14917i
$838$	8.57060			0.296067
$839$		−	11.3697i		−	0.392524i	−0.980551	−	0.196262i	$-0.937120\pi$
$839$		−	11.3697i		−	0.392524i	0.980551	−	0.196262i	$-0.0628803\pi$
$840$	−31.8513			−1.09897
$841$			26.4533i			0.912184i
$842$	79.6954			2.74649
$843$	−28.8557	−	28.8557i	−0.993845	−	0.993845i
$844$	41.1460	+	41.1460i	1.41631	+	1.41631i
$845$			2.37679i			0.0817639i
$846$	21.6847	+	21.6847i	0.745535	+	0.745535i
$847$	14.9360	−	31.7181i	0.513207	−	1.08985i
$848$	19.0246	−	19.0246i	0.653306	−	0.653306i
$849$		−	68.0997i		−	2.33718i
$850$	31.4807			1.07978
$851$	7.80880			0.267682
$852$	−74.6869	−	74.6869i	−2.55873	−	2.55873i
$853$	4.71123			0.161310			0.0806548	−	0.996742i	$-0.474299\pi$
$853$	4.71123			0.161310			0.0806548	+	0.996742i	$0.474299\pi$
$854$	−24.4675	+	56.1353i	−0.837262	+	1.92091i
$855$			11.8552i			0.405439i
$856$	58.8611	−	58.8611i	2.01183	−	2.01183i
$857$	21.8354			0.745884			0.372942	−	0.927855i	$-0.378349\pi$
$857$	21.8354			0.745884			0.372942	+	0.927855i	$0.378349\pi$
$858$	105.625	−	18.4197i	3.60598	−	0.628837i
$859$			40.3520i			1.37679i	0.725335	+	0.688397i	$0.241685\pi$
$859$			40.3520i			1.37679i	−0.725335	+	0.688397i	$0.758315\pi$
$860$	−17.6465	+	17.6465i	−0.601740	+	0.601740i
$861$	−39.4329	+	39.4329i	−1.34387	+	1.34387i
$862$	17.5787	+	17.5787i	0.598732	+	0.598732i
$863$	12.0122			0.408901			0.204451	−	0.978877i	$-0.434459\pi$
$863$	12.0122			0.408901			0.204451	+	0.978877i	$0.434459\pi$
$864$	−4.95682	+	4.95682i	−0.168635	+	0.168635i
$865$	2.73528	−	2.73528i	0.0930024	−	0.0930024i
$866$		−	63.2825i		−	2.15043i
$867$	29.8415			1.01347
$868$	−83.3833			−2.83021
$869$	36.7093	−	6.40163i	1.24528	−	0.217160i
$870$	−7.77333			−0.263540
$871$	45.6738	−	45.6738i	1.54760	−	1.54760i
$872$	12.1055	−	12.1055i	0.409944	−	0.409944i
$873$		−	106.234i		−	3.59549i
$874$	49.2673			1.66649
$875$	13.4034	−	13.4034i	0.453119	−	0.453119i
$876$		−	9.74158i		−	0.329137i
$877$	0.490623	+	0.490623i	0.0165672	+	0.0165672i	0.715342	−	0.698775i	$-0.246271\pi$
$877$	0.490623	+	0.490623i	0.0165672	+	0.0165672i	−0.698775	+	0.715342i	$0.746271\pi$
$878$	−10.2557	+	10.2557i	−0.346114	+	0.346114i
$879$			57.9132i			1.95336i
$880$	−7.23572	−	5.08683i	−0.243916	−	0.171477i
$881$		−	9.67265i		−	0.325880i	−0.986636	−	0.162940i	$-0.947902\pi$
$881$		−	9.67265i		−	0.325880i	0.986636	−	0.162940i	$-0.0520977\pi$
$882$	−39.8424	+	39.8424i	−1.34157	+	1.34157i
$883$	−25.6545	−	25.6545i	−0.863343	−	0.863343i	0.128382	−	0.991725i	$-0.459022\pi$
$883$	−25.6545	−	25.6545i	−0.863343	−	0.863343i	−0.991725	+	0.128382i	$0.959022\pi$
$884$	32.5855	−	32.5855i	1.09597	−	1.09597i
$885$	−0.267936	−	0.267936i	−0.00900657	−	0.00900657i
$886$	−8.80480	−	8.80480i	−0.295803	−	0.295803i
$887$	16.6520	+	16.6520i	0.559120	+	0.559120i	0.929057	−	0.369937i	$-0.120621\pi$
$887$	16.6520	+	16.6520i	0.559120	+	0.559120i	−0.369937	+	0.929057i	$0.620621\pi$
$888$			16.6557i			0.558928i
$889$	−17.6028	−	17.6028i	−0.590377	−	0.590377i
$890$	−17.7423			−0.594723
$891$	−41.6694	+	59.2723i	−1.39598	+	1.98570i
$892$	−44.6863	−	44.6863i	−1.49621	−	1.49621i
$893$	4.54317			0.152031
$894$	−94.7159	+	94.7159i	−3.16777	+	3.16777i
$895$		−	8.47734i		−	0.283366i
$896$	60.9773			2.03711
$897$	−70.4059	+	70.4059i	−2.35078	+	2.35078i
$898$	20.2037	+	20.2037i	0.674205	+	0.674205i
$899$	−10.3046			−0.343677
$900$		−	135.693i		−	4.52311i
$901$		−	17.2897i		−	0.576004i
$902$	−43.9212	+	7.65928i	−1.46242	+	0.255026i
$903$			101.650i			3.38271i
$904$	54.2249	+	54.2249i	1.80349	+	1.80349i
$905$	6.98638	−	6.98638i	0.232235	−	0.232235i
$906$		−	42.2430i		−	1.40343i
$907$	32.4960	−	32.4960i	1.07901	−	1.07901i	0.0824127	−	0.996598i	$-0.473737\pi$
$907$	32.4960	−	32.4960i	1.07901	−	1.07901i	0.996598	−	0.0824127i	$-0.0262625\pi$
$908$	−45.8507	+	45.8507i	−1.52161	+	1.52161i
$909$	48.0824	+	48.0824i	1.59479	+	1.59479i
$910$		−	19.8984i		−	0.659625i
$911$	4.25398			0.140941			0.0704703	−	0.997514i	$-0.477550\pi$
$911$	4.25398			0.140941			0.0704703	+	0.997514i	$0.477550\pi$
$912$			36.5001i			1.20864i
$913$	0.938898	+	0.660060i	0.0310730	+	0.0218448i
$914$			15.0387i			0.497435i
$915$	14.1768	+	6.17920i	0.468671	+	0.204278i
$916$	37.0174			1.22309
$917$	−19.6293	+	19.6293i	−0.648217	+	0.648217i
$918$			92.8399i			3.06417i
$919$	21.8663			0.721304			0.360652	−	0.932700i	$-0.382554\pi$
$919$	21.8663			0.721304			0.360652	+	0.932700i	$0.382554\pi$
$920$	23.6475			0.779634
$921$	26.4836	−	26.4836i	0.872665	−	0.872665i
$922$	25.0413	−	25.0413i	0.824690	−	0.824690i
$923$	23.6269	−	23.6269i	0.777688	−	0.777688i
$924$	−135.098	+	23.5594i	−4.44441	+	0.775047i
$925$	−3.36512	−	3.36512i	−0.110645	−	0.110645i
$926$	19.6519	−	19.6519i	0.645801	−	0.645801i
$927$	−13.5612			−0.445409
$928$	−0.821484			−0.0269665
$929$		−	36.2930i		−	1.19073i	−0.803454	−	0.595367i	$-0.797007\pi$
$929$		−	36.2930i		−	1.19073i	0.803454	−	0.595367i	$-0.202993\pi$
$930$			31.4531i			1.03139i
$931$			8.34740i			0.273575i
$932$	1.39130	−	1.39130i	0.0455736	−	0.0455736i
$933$	23.0220	−	23.0220i	0.753708	−	0.753708i
$934$	−0.334013			−0.0109292
$935$	−5.59942	+	0.976467i	−0.183121	+	0.0319339i
$936$	−106.231	−	106.231i	−3.47227	−	3.47227i
$937$		−	11.4463i		−	0.373935i	−0.982366	−	0.186968i	$-0.940134\pi$
$937$		−	11.4463i		−	0.373935i	0.982366	−	0.186968i	$-0.0598660\pi$
$938$	−87.2554	+	87.2554i	−2.84899	+	2.84899i
$939$	−4.68838	+	4.68838i	−0.152999	+	0.152999i
$940$	4.30639			0.140459
$941$	27.9000	+	27.9000i	0.909514	+	0.909514i	0.996233	−	0.0867186i	$-0.0276381\pi$
$941$	27.9000	+	27.9000i	0.909514	+	0.909514i	−0.0867186	+	0.996233i	$0.527638\pi$
$942$	145.065			4.72646
$943$	29.2763	−	29.2763i	0.953366	−	0.953366i
$944$	−0.583555	−	0.583555i	−0.0189931	−	0.0189931i
$945$	18.9782	+	18.9782i	0.617362	+	0.617362i
$946$	−46.7380	+	66.4822i	−1.51958	+	2.16152i
$947$	15.9522	−	15.9522i	0.518377	−	0.518377i	−0.398703	−	0.917080i	$-0.630540\pi$
$947$	15.9522	−	15.9522i	0.518377	−	0.518377i	0.917080	+	0.398703i	$0.130540\pi$
$948$	−103.068	−	103.068i	−3.34750	−	3.34750i
$949$	3.08171			0.100036
$950$	−21.2312	−	21.2312i	−0.688832	−	0.688832i
$951$			15.5896i			0.505526i
$952$	−31.5225	+	31.5225i	−1.02165	+	1.02165i
$953$	−8.09970	+	8.09970i	−0.262375	+	0.262375i	−0.826018	−	0.563643i	$-0.809399\pi$
$953$	−8.09970	+	8.09970i	−0.262375	+	0.262375i	0.563643	+	0.826018i	$0.309399\pi$
$954$	−111.312			−3.60387
$955$	−3.76327	+	3.76327i	−0.121776	+	0.121776i
$956$	70.2167			2.27097
$957$	−16.6956	+	2.91149i	−0.539691	+	0.0941151i
$958$	45.4361	+	45.4361i	1.46797	+	1.46797i
$959$	30.2257	+	30.2257i	0.976038	+	0.976038i
$960$		−	14.5710i		−	0.470276i
$961$			10.6952i			0.345007i
$962$	−10.4053			−0.335479
$963$	−119.623			−3.85480
$964$	−1.95416			−0.0629392
$965$	10.7717	+	10.7717i	0.346754	+	0.346754i
$966$	134.504	−	134.504i	4.32758	−	4.32758i
$967$	−9.19094			−0.295561			−0.147780	−	0.989020i	$-0.547213\pi$
$967$	−9.19094			−0.295561			−0.147780	+	0.989020i	$0.547213\pi$
$968$	−50.2275	−	23.6521i	−1.61437	−	0.760206i
$969$	16.5858	+	16.5858i	0.532813	+	0.532813i
$970$	−15.7557	−	15.7557i	−0.505884	−	0.505884i
$971$	−2.76003			−0.0885736			−0.0442868	−	0.999019i	$-0.514102\pi$
$971$	−2.76003			−0.0885736			−0.0442868	+	0.999019i	$0.514102\pi$
$972$	117.889			3.78130
$973$	24.0339			0.770493
$974$	43.2076	−	43.2076i	1.38446	−	1.38446i
$975$	60.6814			1.94336
$976$	30.8766	+	13.4581i	0.988335	+	0.430783i
$977$	11.7840			0.377004			0.188502	−	0.982073i	$-0.439637\pi$
$977$	11.7840			0.377004			0.188502	+	0.982073i	$0.439637\pi$
$978$	122.715	+	122.715i	3.92398	+	3.92398i
$979$	−38.1069	+	6.64535i	−1.21790	+	0.212386i
$980$			7.91236i			0.252751i
$981$	−24.6019			−0.785478
$982$	−0.601259	−	0.601259i	−0.0191869	−	0.0191869i
$983$	−27.4838	+	27.4838i	−0.876598	+	0.876598i	−0.993181	−	0.116583i	$-0.962806\pi$
$983$	−27.4838	+	27.4838i	−0.876598	+	0.876598i	0.116583	+	0.993181i	$0.462806\pi$
$984$	62.4444	+	62.4444i	1.99065	+	1.99065i
$985$		−	3.75294i		−	0.119579i
$986$	−7.69308	+	7.69308i	−0.244998	+	0.244998i
$987$	12.4032	−	12.4032i	0.394798	−	0.394798i
$988$	−43.9527			−1.39832
$989$		−	75.4685i		−	2.39976i
$990$	6.28656	+	36.0495i	0.199800	+	1.14573i
$991$	17.2683			0.548546			0.274273	−	0.961652i	$-0.411563\pi$
$991$	17.2683			0.548546			0.274273	+	0.961652i	$0.411563\pi$
$992$			3.32396i			0.105536i
$993$	6.44614	+	6.44614i	0.204562	+	0.204562i
$994$	−45.1368	+	45.1368i	−1.43165	+	1.43165i
$995$		−	6.32831i		−	0.200621i
$996$		−	4.48937i		−	0.142251i
$997$	38.9240	−	38.9240i	1.23274	−	1.23274i	0.269828	−	0.962908i	$-0.413033\pi$
$997$	38.9240	−	38.9240i	1.23274	−	1.23274i	0.962908	−	0.269828i	$-0.0869669\pi$
$998$		−	9.39185i		−	0.297294i
$999$	9.92409	−	9.92409i	0.313984	−	0.313984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.5	✓	120
11.10	odd	2	inner	671.2.f.a.538.56	yes	120
61.11	odd	4	inner	671.2.f.a.560.56	yes	120
671.560	even	4	inner	671.2.f.a.560.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.5	✓	120	1.1	even	1	trivial
671.2.f.a.538.56	yes	120	11.10	odd	2	inner
671.2.f.a.560.5	yes	120	671.560	even	4	inner
671.2.f.a.560.56	yes	120	61.11	odd	4	inner

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73949 - 1.73949i) q^{2} -3.20201i q^{3} +4.05165i q^{4} -0.618387i q^{5} +(-5.56987 + 5.56987i) q^{6} +(2.25367 + 2.25367i) q^{7} +(3.56882 - 3.56882i) q^{8} -7.25288 q^{9} +O(q^{10})\)	\(q+(-1.73949 - 1.73949i) q^{2} -3.20201i q^{3} +4.05165i q^{4} -0.618387i q^{5} +(-5.56987 + 5.56987i) q^{6} +(2.25367 + 2.25367i) q^{7} +(3.56882 - 3.56882i) q^{8} -7.25288 q^{9} +(-1.07568 + 1.07568i) q^{10} +(-1.90745 + 2.71323i) q^{11} +12.9734 q^{12} +4.10409i q^{13} -7.84045i q^{14} -1.98008 q^{15} -4.31255 q^{16} +(-1.95964 + 1.95964i) q^{17} +(12.6163 + 12.6163i) q^{18} +2.64324 q^{19} +2.50549 q^{20} +(7.21626 - 7.21626i) q^{21} +(8.03763 - 1.40166i) q^{22} +(-5.35759 + 5.35759i) q^{23} +(-11.4274 - 11.4274i) q^{24} +4.61760 q^{25} +(7.13901 - 7.13901i) q^{26} +13.6178i q^{27} +(-9.13105 + 9.13105i) q^{28} +(-1.12842 + 1.12842i) q^{29} +(3.44433 + 3.44433i) q^{30} +(4.56592 + 4.56592i) q^{31} +(0.363997 + 0.363997i) q^{32} +(8.68781 + 6.10767i) q^{33} +6.81755 q^{34} +(1.39364 - 1.39364i) q^{35} -29.3861i q^{36} +(-0.728760 - 0.728760i) q^{37} +(-4.59790 - 4.59790i) q^{38} +13.1413 q^{39} +(-2.20691 - 2.20691i) q^{40} -5.46444 q^{41} -25.1052 q^{42} +(-7.04314 + 7.04314i) q^{43} +(-10.9931 - 7.72830i) q^{44} +4.48509i q^{45} +18.6389 q^{46} +1.71878 q^{47} +13.8088i q^{48} +3.15801i q^{49} +(-8.03226 - 8.03226i) q^{50} +(6.27480 + 6.27480i) q^{51} -16.6283 q^{52} +(-4.41144 + 4.41144i) q^{53} +(23.6880 - 23.6880i) q^{54} +(1.67783 + 1.17954i) q^{55} +16.0858 q^{56} -8.46370i q^{57} +3.92576 q^{58} +(0.135316 + 0.135316i) q^{59} -8.02260i q^{60} +(-7.15970 - 3.12068i) q^{61} -15.8847i q^{62} +(-16.3456 - 16.3456i) q^{63} +7.35876i q^{64} +2.53791 q^{65} +(-4.48813 - 25.7366i) q^{66} +(-11.1289 - 11.1289i) q^{67} +(-7.93978 - 7.93978i) q^{68} +(17.1551 + 17.1551i) q^{69} -4.84844 q^{70} +(-5.75691 - 5.75691i) q^{71} +(-25.8842 + 25.8842i) q^{72} -0.750887i q^{73} +2.53534i q^{74} -14.7856i q^{75} +10.7095i q^{76} +(-10.4135 + 1.81597i) q^{77} +(-22.8592 - 22.8592i) q^{78} +(-7.94456 - 7.94456i) q^{79} +2.66682i q^{80} +21.8456 q^{81} +(9.50534 + 9.50534i) q^{82} -0.346044i q^{83} +(29.2377 + 29.2377i) q^{84} +(1.21182 + 1.21182i) q^{85} +24.5029 q^{86} +(3.61322 + 3.61322i) q^{87} +(2.87571 + 16.4904i) q^{88} +(8.24703 + 8.24703i) q^{89} +(7.80176 - 7.80176i) q^{90} +(-9.24924 + 9.24924i) q^{91} +(-21.7071 - 21.7071i) q^{92} +(14.6201 - 14.6201i) q^{93} +(-2.98981 - 2.98981i) q^{94} -1.63455i q^{95} +(1.16552 - 1.16552i) q^{96} +14.6472i q^{97} +(5.49333 - 5.49333i) q^{98} +(13.8345 - 19.6788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more