LMFDB - Embedded newform 315.2.ce.a.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(53,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("315.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.5
Character	$\chi$	$=$	315.53
Dual form			315.2.ce.a.107.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.364480 + 1.36026i) q^{2} +(0.0145936 + 0.00842564i) q^{4} +(-2.23601 - 0.0163814i) q^{5} +(-2.58285 - 0.573503i) q^{7} +(-2.00834 + 2.00834i) q^{8} +(0.837263 - 3.03558i) q^{10} +(-1.18008 - 0.681321i) q^{11} +(0.106323 + 0.106323i) q^{13} +(1.72151 - 3.30431i) q^{14} +(-1.98301 - 3.43467i) q^{16} +(-7.24761 + 1.94199i) q^{17} +(-2.03121 + 1.17272i) q^{19} +(-0.0324934 - 0.0190789i) q^{20} +(1.35689 - 1.35689i) q^{22} +(4.94811 + 1.32584i) q^{23} +(4.99946 + 0.0732577i) q^{25} +(-0.183379 + 0.105874i) q^{26} +(-0.0328610 - 0.0301316i) q^{28} +4.97834 q^{29} +(-3.40473 + 5.89716i) q^{31} +(-0.0920746 + 0.0246713i) q^{32} -10.5664i q^{34} +(5.76587 + 1.32467i) q^{35} +(-9.92059 - 2.65821i) q^{37} +(-0.854866 - 3.19040i) q^{38} +(4.52356 - 4.45776i) q^{40} -7.03642i q^{41} +(2.50280 + 2.50280i) q^{43} +(-0.0114811 - 0.0198859i) q^{44} +(-3.60698 + 6.24747i) q^{46} +(0.560444 - 2.09160i) q^{47} +(6.34219 + 2.96254i) q^{49} +(-1.92185 + 6.77386i) q^{50} +(0.000655798 + 0.00244747i) q^{52} +(1.62383 + 6.06020i) q^{53} +(2.62751 + 1.54277i) q^{55} +(6.33901 - 4.03544i) q^{56} +(-1.81451 + 6.77183i) q^{58} +(1.32684 - 2.29815i) q^{59} +(5.85558 + 10.1422i) q^{61} +(-6.78071 - 6.78071i) q^{62} -8.06626i q^{64} +(-0.235997 - 0.239480i) q^{65} +(3.16583 + 11.8150i) q^{67} +(-0.122132 - 0.0327250i) q^{68} +(-3.90343 + 7.36026i) q^{70} +4.94291i q^{71} +(-5.43505 + 1.45632i) q^{73} +(7.23171 - 12.5257i) q^{74} -0.0395236 q^{76} +(2.65723 + 2.43653i) q^{77} +(-10.4803 + 6.05078i) q^{79} +(4.37775 + 7.71243i) q^{80} +(9.57135 + 2.56463i) q^{82} +(-8.06859 + 8.06859i) q^{83} +(16.2375 - 4.22358i) q^{85} +(-4.31668 + 2.49224i) q^{86} +(3.73832 - 1.00168i) q^{88} +(1.38011 + 2.39042i) q^{89} +(-0.213639 - 0.335591i) q^{91} +(0.0610399 + 0.0610399i) q^{92} +(2.64085 + 1.52470i) q^{94} +(4.56101 - 2.58894i) q^{95} +(3.68206 - 3.68206i) q^{97} +(-6.34142 + 7.54723i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) $ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.364480	+	1.36026i	−0.257726	+	0.961848i	0.708827	+	0.705382i	$0.249225\pi$
$2$	−0.364480	+	1.36026i	−0.257726	+	0.961848i	−0.966553	+	0.256466i	$0.917442\pi$
$3$		0			0
$3$		0			0
$4$	0.0145936	+	0.00842564i	0.00729681	+	0.00421282i
$5$	−2.23601	−	0.0163814i	−0.999973	−	0.00732597i
$5$	−2.23601	−	0.0163814i	−0.999973	−	0.00732597i
$6$		0			0
$7$	−2.58285	−	0.573503i	−0.976224	−	0.216764i
$7$	−2.58285	−	0.573503i	−0.976224	−	0.216764i
$8$	−2.00834	+	2.00834i	−0.710054	+	0.710054i
$9$		0			0
$10$	0.837263	−	3.03558i	0.264766	−	0.959934i
$11$	−1.18008	−	0.681321i	−0.355808	−	0.205426i	0.311432	−	0.950268i	$-0.399191\pi$
$11$	−1.18008	−	0.681321i	−0.355808	−	0.205426i	−0.667240	+	0.744842i	$0.732525\pi$
$12$		0			0
$13$	0.106323	+	0.106323i	0.0294886	+	0.0294886i	0.721697	−	0.692209i	$-0.243362\pi$
$13$	0.106323	+	0.106323i	0.0294886	+	0.0294886i	−0.692209	+	0.721697i	$0.743362\pi$
$14$	1.72151	−	3.30431i	0.460092	−	0.883113i
$15$		0			0
$16$	−1.98301	−	3.43467i	−0.495752	−	0.858667i
$17$	−7.24761	+	1.94199i	−1.75780	+	0.471002i	−0.986264	−	0.165178i	$-0.947180\pi$
$17$	−7.24761	+	1.94199i	−1.75780	+	0.471002i	−0.771541	+	0.636180i	$0.780514\pi$
$18$		0			0
$19$	−2.03121	+	1.17272i	−0.465992	+	0.269040i	−0.714560	−	0.699574i	$-0.753373\pi$
$19$	−2.03121	+	1.17272i	−0.465992	+	0.269040i	0.248569	+	0.968614i	$0.420040\pi$
$20$	−0.0324934	−	0.0190789i	−0.00726576	−	0.00426616i
$21$		0			0
$22$	1.35689	−	1.35689i	0.289290	−	0.289290i
$23$	4.94811	+	1.32584i	1.03175	+	0.276457i	0.734692	−	0.678401i	$-0.237327\pi$
$23$	4.94811	+	1.32584i	1.03175	+	0.276457i	0.297061	+	0.954858i	$0.403993\pi$
$24$		0			0
$25$	4.99946	+	0.0732577i	0.999893	+	0.0146515i
$26$	−0.183379	+	0.105874i	−0.0359635	+	0.0207636i
$27$		0			0
$28$	−0.0328610	−	0.0301316i	−0.00621014	−	0.00569434i
$29$	4.97834			0.924454			0.462227	−	0.886762i	$-0.347051\pi$
$29$	4.97834			0.924454			0.462227	+	0.886762i	$0.347051\pi$
$30$		0			0
$31$	−3.40473	+	5.89716i	−0.611507	+	1.05916i	0.379479	+	0.925200i	$0.376103\pi$
$31$	−3.40473	+	5.89716i	−0.611507	+	1.05916i	−0.990987	+	0.133962i	$0.957230\pi$
$32$	−0.0920746	+	0.0246713i	−0.0162766	+	0.00436131i
$33$		0			0
$34$		−	10.5664i		−	1.81213i
$35$	5.76587	+	1.32467i	0.974610	+	0.223910i
$36$		0			0
$37$	−9.92059	−	2.65821i	−1.63093	−	0.437008i	−0.676747	−	0.736216i	$-0.736611\pi$
$37$	−9.92059	−	2.65821i	−1.63093	−	0.437008i	−0.954188	+	0.299208i	$0.903277\pi$
$38$	−0.854866	−	3.19040i	−0.138678	−	0.517552i
$39$		0			0
$40$	4.52356	−	4.45776i	0.715237	−	0.704833i
$41$		−	7.03642i		−	1.09890i	−0.835525	−	0.549452i	$-0.814837\pi$
$41$		−	7.03642i		−	1.09890i	0.835525	−	0.549452i	$-0.185163\pi$
$42$		0			0
$43$	2.50280	+	2.50280i	0.381674	+	0.381674i	0.871705	−	0.490031i	$-0.163015\pi$
$43$	2.50280	+	2.50280i	0.381674	+	0.381674i	−0.490031	+	0.871705i	$0.663015\pi$
$44$	−0.0114811	−	0.0198859i	−0.00173084	−	0.00299791i
$45$		0			0
$46$	−3.60698	+	6.24747i	−0.531820	+	0.921139i
$47$	0.560444	−	2.09160i	0.0817491	−	0.305092i	−0.912930	−	0.408117i	$-0.866186\pi$
$47$	0.560444	−	2.09160i	0.0817491	−	0.305092i	0.994679	+	0.103025i	$0.0328522\pi$
$48$		0			0
$49$	6.34219	+	2.96254i	0.906027	+	0.423220i
$50$	−1.92185	+	6.77386i	−0.271791	+	0.957969i
$51$		0			0
$52$	0.000655798		0.00244747i	9.09428e−5		0.000339403i
$53$	1.62383	+	6.06020i	0.223050	+	0.832433i	0.983177	+	0.182658i	$0.0584701\pi$
$53$	1.62383	+	6.06020i	0.223050	+	0.832433i	−0.760127	+	0.649775i	$0.774863\pi$
$54$		0			0
$55$	2.62751	+	1.54277i	0.354294	+	0.208027i
$56$	6.33901	−	4.03544i	0.847086	−	0.539258i
$57$		0			0
$58$	−1.81451	+	6.77183i	−0.238256	+	0.889184i
$59$	1.32684	−	2.29815i	0.172739	−	0.299193i	−0.766637	−	0.642080i	$-0.778072\pi$
$59$	1.32684	−	2.29815i	0.172739	−	0.299193i	0.939377	+	0.342887i	$0.111405\pi$
$60$		0			0
$61$	5.85558	+	10.1422i	0.749730	+	1.29857i	0.947952	+	0.318414i	$0.103150\pi$
$61$	5.85558	+	10.1422i	0.749730	+	1.29857i	−0.198222	+	0.980157i	$0.563517\pi$
$62$	−6.78071	−	6.78071i	−0.861151	−	0.861151i
$63$		0			0
$64$		−	8.06626i		−	1.00828i
$65$	−0.235997	−	0.239480i	−0.0292718	−	0.0297038i
$66$		0			0
$67$	3.16583	+	11.8150i	0.386767	+	1.44343i	0.835362	+	0.549700i	$0.185258\pi$
$67$	3.16583	+	11.8150i	0.386767	+	1.44343i	−0.448595	+	0.893735i	$0.648076\pi$
$68$	−0.122132	−	0.0327250i	−0.0148106	−	0.00396849i
$69$		0			0
$70$	−3.90343	+	7.36026i	−0.466550	+	0.879719i
$71$			4.94291i			0.586616i	0.956018	+	0.293308i	$0.0947561\pi$
$71$			4.94291i			0.586616i	−0.956018	+	0.293308i	$0.905244\pi$
$72$		0			0
$73$	−5.43505	+	1.45632i	−0.636125	+	0.170449i	−0.562447	−	0.826833i	$-0.690140\pi$
$73$	−5.43505	+	1.45632i	−0.636125	+	0.170449i	−0.0736773	+	0.997282i	$0.523473\pi$
$74$	7.23171	−	12.5257i	0.840670	−	1.45608i
$75$		0			0
$76$	−0.0395236			−0.00453367
$77$	2.65723	+	2.43653i	0.302820	+	0.277668i
$78$		0			0
$79$	−10.4803	+	6.05078i	−1.17912	+	0.680766i	−0.955811	−	0.293981i	$-0.905020\pi$
$79$	−10.4803	+	6.05078i	−1.17912	+	0.680766i	−0.223310	+	0.974747i	$0.571686\pi$
$80$	4.37775	+	7.71243i	0.489448	+	0.862276i
$81$		0			0
$82$	9.57135	+	2.56463i	1.05698	+	0.283217i
$83$	−8.06859	+	8.06859i	−0.885643	+	0.885643i	−0.994101	−	0.108458i	$-0.965409\pi$
$83$	−8.06859	+	8.06859i	−0.885643	+	0.885643i	0.108458	+	0.994101i	$0.465409\pi$
$84$		0			0
$85$	16.2375	−	4.22358i	1.76121	−	0.458112i
$86$	−4.31668	+	2.49224i	−0.465480	+	0.268745i
$87$		0			0
$88$	3.73832	−	1.00168i	0.398507	−	0.106780i
$89$	1.38011	+	2.39042i	0.146291	+	0.253384i	0.929854	−	0.367929i	$-0.119933\pi$
$89$	1.38011	+	2.39042i	0.146291	+	0.253384i	−0.783563	+	0.621313i	$0.786600\pi$
$90$		0			0
$91$	−0.213639	−	0.335591i	−0.0223954	−	0.0351795i
$92$	0.0610399	+	0.0610399i	0.00636385	+	0.00636385i
$93$		0			0
$94$	2.64085	+	1.52470i	0.272383	+	0.157260i
$95$	4.56101	−	2.58894i	0.467950	−	0.265619i
$96$		0			0
$97$	3.68206	−	3.68206i	0.373856	−	0.373856i	−0.495023	−	0.868880i	$-0.664840\pi$
$97$	3.68206	−	3.68206i	0.373856	−	0.373856i	0.868880	+	0.495023i	$0.164840\pi$
$98$	−6.34142	+	7.54723i	−0.640580	+	0.762385i
$99$		0			0
$100$	0.0723431	+	0.0431928i	0.00723431	+	0.00431928i
$101$	−8.26084	−	4.76940i	−0.821984	−	0.474573i	0.0291161	−	0.999576i	$-0.490731\pi$
$101$	−8.26084	−	4.76940i	−0.821984	−	0.474573i	−0.851100	+	0.525003i	$0.824064\pi$
$102$		0			0
$103$	2.14544	−	8.00688i	0.211396	−	0.788941i	−0.776008	−	0.630723i	$-0.782758\pi$
$103$	2.14544	−	8.00688i	0.211396	−	0.788941i	0.987404	−	0.158218i	$-0.0505749\pi$
$104$	−0.427063			−0.0418770
$105$		0			0
$106$	−8.83529			−0.858159
$107$	0.0580815	−	0.216763i	0.00561495	−	0.0209553i	−0.963062	−	0.269281i	$-0.913214\pi$
$107$	0.0580815	−	0.216763i	0.00561495	−	0.0209553i	0.968676	+	0.248326i	$0.0798805\pi$
$108$		0			0
$109$	−4.69145	−	2.70861i	−0.449359	−	0.259438i	0.258200	−	0.966091i	$-0.416871\pi$
$109$	−4.69145	−	2.70861i	−0.449359	−	0.259438i	−0.707560	+	0.706654i	$0.750204\pi$
$110$	−3.05624	+	3.01179i	−0.291401	+	0.287163i
$111$		0			0
$112$	3.15201	+	10.0085i	0.297837	+	0.945712i
$113$	7.70220	−	7.70220i	0.724562	−	0.724562i	−0.244969	−	0.969531i	$-0.578778\pi$
$113$	7.70220	−	7.70220i	0.724562	−	0.724562i	0.969531	+	0.244969i	$0.0787778\pi$
$114$		0			0
$115$	−11.0423	−	3.04565i	−1.02970	−	0.284009i
$116$	0.0726520	+	0.0419457i	0.00674557	+	0.00389456i
$117$		0			0
$118$	2.64247	+	2.64247i	0.243259	+	0.243259i
$119$	19.8332	−	0.859342i	1.81811	−	0.0787757i
$120$		0			0
$121$	−4.57160	−	7.91825i	−0.415600	−	0.719841i
$122$	−15.9302	+	4.26849i	−1.44225	+	0.386450i
$123$		0			0
$124$	−0.0993747	+	0.0573740i	−0.00892411	+	0.00515234i
$125$	−11.1776	−	0.245703i	−0.999758	−	0.0219763i
$126$		0			0
$127$	−9.41937	+	9.41937i	−0.835834	+	0.835834i	−0.988308	−	0.152474i	$-0.951276\pi$
$127$	−9.41937	+	9.41937i	−0.835834	+	0.835834i	0.152474	+	0.988308i	$0.451276\pi$
$128$	10.7881	+	2.89065i	0.953538	+	0.255500i
$129$		0			0
$130$	0.411771	−	0.233731i	0.0361147	−	0.0204995i
$131$	6.41212	−	3.70204i	0.560230	−	0.323449i	−0.193008	−	0.981197i	$-0.561824\pi$
$131$	6.41212	−	3.70204i	0.560230	−	0.323449i	0.753238	+	0.657748i	$0.228491\pi$
$132$		0			0
$133$	5.91886	−	1.86405i	0.513230	−	0.161634i
$134$	−17.2254			−1.48804
$135$		0			0
$136$	10.6555	−	18.4558i	0.913699	−	1.58257i
$137$	8.57248	−	2.29699i	0.732396	−	0.196245i	0.126700	−	0.991941i	$-0.459561\pi$
$137$	8.57248	−	2.29699i	0.732396	−	0.196245i	0.605696	+	0.795696i	$0.292895\pi$
$138$		0			0
$139$		−	8.29182i		−	0.703303i	−0.936131	−	0.351652i	$-0.885620\pi$
$139$		−	8.29182i		−	0.703303i	0.936131	−	0.351652i	$-0.114380\pi$
$140$	0.0729838	+	0.0679128i	0.00616826	+	0.00573968i
$141$		0			0
$142$	−6.72364	−	1.80159i	−0.564235	−	0.151186i
$143$	−0.0530296	−	0.197909i	−0.00443456	−	0.0165500i
$144$		0			0
$145$	−11.1316	−	0.0815520i	−0.924429	−	0.00677252i
$146$		−	7.92387i		−	0.655785i
$147$		0			0
$148$	−0.122380	−	0.122380i	−0.0100596	−	0.0100596i
$149$	2.30099	+	3.98543i	0.188505	+	0.326500i	0.944752	−	0.327786i	$-0.106303\pi$
$149$	2.30099	+	3.98543i	0.188505	+	0.326500i	−0.756247	+	0.654286i	$0.772969\pi$
$150$		0			0
$151$	0.237053	−	0.410587i	0.0192911	−	0.0334131i	−0.856219	−	0.516614i	$-0.827192\pi$
$151$	0.237053	−	0.410587i	0.0192911	−	0.0334131i	0.875510	+	0.483200i	$0.160526\pi$
$152$	1.72414	−	6.43457i	0.139846	−	0.521912i
$153$		0			0
$154$	−4.28281	+	2.72646i	−0.345119	+	0.219704i
$155$	7.70961	−	13.1303i	0.619250	−	1.05465i
$156$		0			0
$157$	−2.86177	−	10.6803i	−0.228394	−	0.852379i	−0.981016	−	0.193926i	$-0.937878\pi$
$157$	−2.86177	−	10.6803i	−0.228394	−	0.852379i	0.752622	−	0.658453i	$-0.228789\pi$
$158$	−4.41078	−	16.4613i	−0.350903	−	1.30959i
$159$		0			0
$160$	0.206284	−	0.0536570i	0.0163082	−	0.00424195i
$161$	−12.0198	−	6.26220i	−0.947296	−	0.493531i
$162$		0			0
$163$	4.92872	−	18.3943i	0.386048	−	1.44075i	−0.450462	−	0.892796i	$-0.648741\pi$
$163$	4.92872	−	18.3943i	0.386048	−	1.44075i	0.836509	−	0.547953i	$-0.184593\pi$
$164$	0.0592863	−	0.102687i	0.00462948	−	0.00801850i
$165$		0			0
$166$	−8.03453	−	13.9162i	−0.623601	−	1.08011i
$167$	4.99821	+	4.99821i	0.386773	+	0.386773i	0.873535	−	0.486762i	$-0.161822\pi$
$167$	4.99821	+	4.99821i	0.386773	+	0.386773i	−0.486762	+	0.873535i	$0.661822\pi$
$168$		0			0
$169$		−	12.9774i		−	0.998261i
$170$	−0.173093	+	23.6267i	−0.0132756	+	1.81208i
$171$		0			0
$172$	0.0154373	+	0.0576127i	0.00117708	+	0.00439292i
$173$	−10.4408	−	2.79761i	−0.793801	−	0.212698i	−0.160940	−	0.986964i	$-0.551453\pi$
$173$	−10.4408	−	2.79761i	−0.793801	−	0.212698i	−0.632861	+	0.774266i	$0.718119\pi$
$174$		0			0
$175$	−12.8708	−	3.05642i	−0.972943	−	0.231044i
$176$			5.40425i			0.407361i
$177$		0			0
$178$	−3.75461	+	1.00604i	−0.281420	+	0.0754062i
$179$	−8.39647	+	14.5431i	−0.627582	+	1.08700i	0.360454	+	0.932777i	$0.382622\pi$
$179$	−8.39647	+	14.5431i	−0.627582	+	1.08700i	−0.988036	+	0.154227i	$0.950711\pi$
$180$		0			0
$181$	1.56378			0.116235			0.0581174	−	0.998310i	$-0.481490\pi$
$181$	1.56378			0.116235			0.0581174	+	0.998310i	$0.481490\pi$
$182$	0.534358	−	0.168288i	0.0396093	−	0.0124743i
$183$		0			0
$184$	−12.6002	+	7.27474i	−0.928900	+	0.536301i
$185$	22.1390	+	6.10630i	1.62769	+	0.448944i
$186$		0			0
$187$	9.87590	+	2.64624i	0.722197	+	0.193512i
$188$	0.0258020	−	0.0258020i	0.00188180	−	0.00188180i
$189$		0			0
$190$	1.85922	+	7.14777i	0.134882	+	0.518554i
$191$	−22.3265	+	12.8902i	−1.61549	+	0.932703i	−0.627422	+	0.778680i	$0.715890\pi$
$191$	−22.3265	+	12.8902i	−1.61549	+	0.932703i	−0.988067	+	0.154023i	$0.950777\pi$
$192$		0			0
$193$	15.7846	−	4.22947i	1.13620	−	0.304444i	0.358777	−	0.933423i	$-0.383194\pi$
$193$	15.7846	−	4.22947i	1.13620	−	0.304444i	0.777422	+	0.628980i	$0.216527\pi$
$194$	3.66651	+	6.35059i	0.263240	+	0.455946i
$195$		0			0
$196$	0.0675943	+	0.0966712i	0.00482816	+	0.00690508i
$197$	−5.06226	−	5.06226i	−0.360671	−	0.360671i	0.503389	−	0.864060i	$-0.332086\pi$
$197$	−5.06226	−	5.06226i	−0.360671	−	0.360671i	−0.864060	+	0.503389i	$0.832086\pi$
$198$		0			0
$199$	12.6245	+	7.28877i	0.894928	+	0.516687i	0.875551	−	0.483125i	$-0.160498\pi$
$199$	12.6245	+	7.28877i	0.894928	+	0.516687i	0.0193768	+	0.999812i	$0.493832\pi$
$200$	−10.1877	+	9.89348i	−0.720381	+	0.699575i
$201$		0			0
$202$	9.49852	−	9.49852i	0.668314	−	0.668314i
$203$	−12.8583	−	2.85509i	−0.902474	−	0.200388i
$204$		0			0
$205$	−0.115266	+	15.7335i	−0.00805054	+	1.09887i
$206$	10.1095	+	5.83670i	0.704359	+	0.406662i
$207$		0			0
$208$	0.154345	−	0.576022i	0.0107019	−	0.0399399i
$209$	3.19599			0.221071
$210$		0			0
$211$	−3.83207			−0.263810			−0.131905	−	0.991262i	$-0.542109\pi$
$211$	−3.83207			−0.263810			−0.131905	+	0.991262i	$0.542109\pi$
$212$	−0.0273635	+	0.102122i	−0.00187934	+	0.00701377i
$213$		0			0
$214$	0.273684	+	0.158012i	0.0187087	+	0.0108015i
$215$	−5.55529	−	5.63729i	−0.378867	−	0.384460i
$216$		0			0
$217$	12.1759	−	13.2788i	0.826556	−	0.901427i
$218$	5.39435	−	5.39435i	0.365351	−	0.365351i
$219$		0			0
$220$	0.0253461	+	0.0446531i	0.00170883	+	0.00301051i
$221$	−0.977063	−	0.564108i	−0.0657244	−	0.0379460i
$222$		0			0
$223$	−1.22784	−	1.22784i	−0.0822223	−	0.0822223i	0.664800	−	0.747022i	$-0.268517\pi$
$223$	−1.22784	−	1.22784i	−0.0822223	−	0.0822223i	−0.747022	+	0.664800i	$0.768517\pi$
$224$	0.251964	−	0.0109172i	0.0168350	−	0.000729435i
$225$		0			0
$226$	7.66968	+	13.2843i	0.510180	+	0.883657i
$227$	12.1577	−	3.25763i	0.806932	−	0.216217i	0.168307	−	0.985735i	$-0.446170\pi$
$227$	12.1577	−	3.25763i	0.806932	−	0.216217i	0.638625	+	0.769518i	$0.279503\pi$
$228$		0			0
$229$	−22.7534	+	13.1367i	−1.50359	+	0.868097i	−0.503597	+	0.863939i	$0.667990\pi$
$229$	−22.7534	+	13.1367i	−1.50359	+	0.868097i	−0.999991	+	0.00415788i	$0.998677\pi$
$230$	8.16757	−	13.9103i	0.538554	−	0.917218i
$231$		0			0
$232$	−9.99818	+	9.99818i	−0.656413	+	0.656413i
$233$	−3.76896	−	1.00989i	−0.246913	−	0.0661600i	0.133240	−	0.991084i	$-0.457462\pi$
$233$	−3.76896	−	1.00989i	−0.246913	−	0.0661600i	−0.380153	+	0.924924i	$0.624129\pi$
$234$		0			0
$235$	−1.28742	+	4.66766i	−0.0839820	+	0.304485i
$236$	0.0387267	−	0.0223589i	0.00252089	−	0.00145544i
$237$		0			0
$238$	−6.05988	+	27.2915i	−0.392804	+	1.76905i
$239$	−18.9197			−1.22382			−0.611908	−	0.790929i	$-0.709598\pi$
$239$	−18.9197			−1.22382			−0.611908	+	0.790929i	$0.709598\pi$
$240$		0			0
$241$	6.77167	−	11.7289i	0.436202	−	0.755523i	−0.561191	−	0.827686i	$-0.689657\pi$
$241$	6.77167	−	11.7289i	0.436202	−	0.755523i	0.997393	+	0.0721629i	$0.0229901\pi$
$242$	12.4371	−	3.33252i	0.799489	−	0.214222i
$243$		0			0
$244$			0.197348i			0.0126339i
$245$	−14.1327	−	6.72815i	−0.902902	−	0.429846i
$246$		0			0
$247$	−0.340650	−	0.0912770i	−0.0216751	−	0.00580781i
$248$	−5.00565	−	18.6813i	−0.317859	−	1.18627i
$249$		0			0
$250$	4.40825	−	15.1149i	0.278802	−	0.955952i
$251$			20.2767i			1.27985i	0.768437	+	0.639925i	$0.221035\pi$
$251$			20.2767i			1.27985i	−0.768437	+	0.639925i	$0.778965\pi$
$252$		0			0
$253$	−4.93585	−	4.93585i	−0.310315	−	0.310315i
$254$	−9.37960	−	16.2460i	−0.588529	−	1.01936i
$255$		0			0
$256$	0.202201	−	0.350222i	0.0126376	−	0.0218889i
$257$	6.39725	−	23.8748i	0.399049	−	1.48927i	−0.415723	−	0.909491i	$-0.636472\pi$
$257$	6.39725	−	23.8748i	0.399049	−	1.48927i	0.814773	−	0.579781i	$-0.196862\pi$
$258$		0			0
$259$	24.0989	+	12.5552i	1.49743	+	0.780145i
$260$	−0.00142628	−	0.00548330i	−8.84539e−5	−	0.000340060i
$261$		0			0
$262$	2.69864	+	10.0715i	0.166723	+	0.622217i
$263$	7.93511	+	29.6142i	0.489300	+	1.82609i	0.559864	+	0.828584i	$0.310853\pi$
$263$	7.93511	+	29.6142i	0.489300	+	1.82609i	−0.0705646	+	0.997507i	$0.522480\pi$
$264$		0			0
$265$	−3.53161	−	13.5773i	−0.216945	−	0.834044i
$266$	0.378283	+	8.73059i	0.0231940	+	0.535307i
$267$		0			0
$268$	−0.0533482	+	0.199098i	−0.00325876	+	0.0121619i
$269$	−11.7450	+	20.3429i	−0.716104	+	1.24033i	0.246428	+	0.969161i	$0.420743\pi$
$269$	−11.7450	+	20.3429i	−0.716104	+	1.24033i	−0.962532	+	0.271167i	$0.912590\pi$
$270$		0			0
$271$	14.2279	+	24.6434i	0.864282	+	1.49698i	0.867758	+	0.496987i	$0.165560\pi$
$271$	14.2279	+	24.6434i	0.864282	+	1.49698i	−0.00347606	+	0.999994i	$0.501106\pi$
$272$	21.0422	+	21.0422i	1.27587	+	1.27587i
$273$		0			0
$274$			12.4980i			0.755031i
$275$	−5.84986	−	3.49269i	−0.352760	−	0.210617i
$276$		0			0
$277$	0.761143	+	2.84063i	0.0457327	+	0.170677i	0.985015	−	0.172469i	$-0.0551743\pi$
$277$	0.761143	+	2.84063i	0.0457327	+	0.170677i	−0.939282	+	0.343145i	$0.888508\pi$
$278$	11.2790	+	3.02220i	0.676471	+	0.181260i
$279$		0			0
$280$	−14.2402	+	8.91943i	−0.851014	+	0.533038i
$281$		−	18.1830i		−	1.08471i	−0.840150	−	0.542354i	$-0.817533\pi$
$281$		−	18.1830i		−	1.08471i	0.840150	−	0.542354i	$-0.182467\pi$
$282$		0			0
$283$	−29.6744	+	7.95124i	−1.76396	+	0.472652i	−0.987514	−	0.157529i	$-0.949647\pi$
$283$	−29.6744	+	7.95124i	−1.76396	+	0.472652i	−0.776448	+	0.630182i	$0.782980\pi$
$284$	−0.0416472	+	0.0721350i	−0.00247131	+	0.00428043i
$285$		0			0
$286$	0.288536			0.0170615
$287$	−4.03540	+	18.1740i	−0.238202	+	1.07278i
$288$		0			0
$289$	34.0341	−	19.6496i	2.00201	−	1.15586i
$290$	4.16818	−	15.1121i	0.244764	−	0.887415i
$291$		0			0
$292$	−0.0915875	−	0.0245408i	−0.00535976	−	0.00143614i
$293$	−2.15360	+	2.15360i	−0.125815	+	0.125815i	−0.767210	−	0.641396i	$-0.778356\pi$
$293$	−2.15360	+	2.15360i	−0.125815	+	0.125815i	0.641396	+	0.767210i	$0.278356\pi$
$294$		0			0
$295$	−3.00446	+	5.11694i	−0.174927	+	0.297920i
$296$	25.2625	−	14.5853i	1.46835	−	0.847753i
$297$		0			0
$298$	−6.25989	+	1.67733i	−0.362626	+	0.0971652i
$299$	0.385129	+	0.667064i	0.0222726	+	0.0385773i
$300$		0			0
$301$	−5.02899	−	7.89972i	−0.289866	−	0.455332i
$302$	0.472103	+	0.472103i	0.0271665	+	0.0271665i
$303$		0			0
$304$	8.05581	+	4.65102i	0.462032	+	0.266754i
$305$	−12.9270	−	22.7739i	−0.740197	−	1.30403i
$306$		0			0
$307$	−7.16976	+	7.16976i	−0.409200	+	0.409200i	−0.881460	−	0.472260i	$-0.843438\pi$
$307$	−7.16976	+	7.16976i	−0.409200	+	0.409200i	0.472260	+	0.881460i	$0.343438\pi$
$308$	0.0182494	+	0.0579466i	0.00103985	+	0.00330182i
$309$		0			0
$310$	15.0506	+	15.2728i	0.854819	+	0.867437i
$311$	20.1351	+	11.6250i	1.14176	+	0.659193i	0.946865	−	0.321631i	$-0.104231\pi$
$311$	20.1351	+	11.6250i	1.14176	+	0.659193i	0.194892	+	0.980825i	$0.437565\pi$
$312$		0			0
$313$	4.23480	−	15.8045i	0.239365	−	0.893323i	−0.736767	−	0.676147i	$-0.763649\pi$
$313$	4.23480	−	15.8045i	0.239365	−	0.893323i	0.976132	−	0.217177i	$-0.0696848\pi$
$314$	15.5710			0.878723
$315$		0			0
$316$	−0.203927			−0.0114718
$317$	0.257510	−	0.961041i	0.0144632	−	0.0539775i	−0.958317	−	0.285707i	$-0.907772\pi$
$317$	0.257510	−	0.961041i	0.0144632	−	0.0539775i	0.972780	+	0.231729i	$0.0744383\pi$
$318$		0			0
$319$	−5.87485	−	3.39184i	−0.328928	−	0.189907i
$320$	−0.132136	+	18.0362i	−0.00738665	+	1.00826i
$321$		0			0
$322$	12.8992	−	14.0676i	0.718845	−	0.783959i
$323$	12.4440	−	12.4440i	0.692403	−	0.692403i
$324$		0			0
$325$	0.523767	+	0.539345i	0.0290534	+	0.0299175i
$326$	23.2245	+	13.4087i	1.28629	+	0.742638i
$327$		0			0
$328$	14.1315	+	14.1315i	0.780281	+	0.780281i
$329$	−2.64708	+	5.08088i	−0.145938	+	0.280118i
$330$		0			0
$331$	8.83110	+	15.2959i	0.485401	+	0.840739i	0.999859	−	0.0167761i	$-0.00534024\pi$
$331$	8.83110	+	15.2959i	0.485401	+	0.840739i	−0.514458	+	0.857515i	$0.672007\pi$
$332$	−0.185733	+	0.0497670i	−0.0101934	+	0.00273132i
$333$		0			0
$334$	−8.62060	+	4.97710i	−0.471698	+	0.272335i
$335$	−6.88526	−	26.4703i	−0.376182	−	1.44623i
$336$		0			0
$337$	3.21477	−	3.21477i	0.175119	−	0.175119i	−0.614105	−	0.789224i	$-0.710483\pi$
$337$	3.21477	−	3.21477i	0.175119	−	0.175119i	0.789224	+	0.614105i	$0.210483\pi$
$338$	17.6526	+	4.73000i	0.960175	+	0.257278i
$339$		0			0
$340$	0.272551	+	0.0751741i	0.0147812	+	0.00407689i
$341$	8.03572	−	4.63942i	0.435159	−	0.251239i
$342$		0			0
$343$	−14.6819	−	11.2890i	−0.792747	−	0.609551i
$344$	−10.0529			−0.542018
$345$		0			0
$346$	7.61095	−	13.1825i	0.409167	−	0.708698i
$347$	−0.639400	+	0.171327i	−0.0343248	+	0.00919729i	−0.275941	−	0.961175i	$-0.588989\pi$
$347$	−0.639400	+	0.171327i	−0.0343248	+	0.00919729i	0.241616	+	0.970372i	$0.422323\pi$
$348$		0			0
$349$			10.8004i			0.578130i	0.957309	+	0.289065i	$0.0933444\pi$
$349$			10.8004i			0.578130i	−0.957309	+	0.289065i	$0.906656\pi$
$350$	8.84868	−	16.3937i	0.472982	−	0.876278i
$351$		0			0
$352$	0.125465	+	0.0336182i	0.00668729	+	0.00179185i
$353$	−0.660082	−	2.46346i	−0.0351326	−	0.131117i	0.946132	−	0.323781i	$-0.104954\pi$
$353$	−0.660082	−	2.46346i	−0.0351326	−	0.131117i	−0.981265	+	0.192664i	$0.938287\pi$
$354$		0			0
$355$	0.0809717	−	11.0524i	0.00429753	−	0.586600i
$356$			0.0465132i			0.00246519i
$357$		0			0
$358$	−16.7220	−	16.7220i	−0.883788	−	0.883788i
$359$	−15.4836	−	26.8184i	−0.817194	−	1.41542i	−0.907742	−	0.419529i	$-0.862195\pi$
$359$	−15.4836	−	26.8184i	−0.817194	−	1.41542i	0.0905479	−	0.995892i	$-0.471138\pi$
$360$		0			0
$361$	−6.74946	+	11.6904i	−0.355235	+	0.615284i
$362$	−0.569967	+	2.12715i	−0.0299568	+	0.111800i
$363$		0			0
$364$	−0.000290194	−	0.00669754i	−1.52103e−5	−	0.000351046i
$365$	12.1767	−	3.16730i	0.637356	−	0.165784i
$366$		0			0
$367$	1.30619	+	4.87477i	0.0681826	+	0.254461i	0.991601	−	0.129333i	$-0.0412838\pi$
$367$	1.30619	+	4.87477i	0.0681826	+	0.254461i	−0.923419	+	0.383795i	$0.874617\pi$
$368$	−5.25831	−	19.6243i	−0.274108	−	1.02299i
$369$		0			0
$370$	−16.3754	+	27.8891i	−0.851314	+	1.44988i
$371$	−0.718551	−	16.5838i	−0.0373053	−	0.860990i
$372$		0			0
$373$	0.304003	−	1.13455i	0.0157407	−	0.0587449i	−0.957609	−	0.288072i	$-0.906986\pi$
$373$	0.304003	−	1.13455i	0.0157407	−	0.0587449i	0.973349	+	0.229327i	$0.0736525\pi$
$374$	−7.19914	+	12.4693i	−0.372259	+	0.644771i
$375$		0			0
$376$	3.07509	+	5.32620i	0.158585	+	0.274678i
$377$	0.529310	+	0.529310i	0.0272609	+	0.0272609i
$378$		0			0
$379$			12.4955i			0.641851i	0.947105	+	0.320925i	$0.103994\pi$
$379$			12.4955i			0.641851i	−0.947105	+	0.320925i	$0.896006\pi$
$380$	0.0883752		0.000647451i	0.00453355		3.32135e-5i
$381$		0			0
$382$	−9.39645	−	35.0680i	−0.480764	−	1.79424i
$383$	18.9066	+	5.06600i	0.966080	+	0.258860i	0.707172	−	0.707042i	$-0.249971\pi$
$383$	18.9066	+	5.06600i	0.966080	+	0.258860i	0.258908	+	0.965902i	$0.416637\pi$
$384$		0			0
$385$	−5.90168	−	5.49162i	−0.300777	−	0.279879i
$386$			23.0127i			1.17131i
$387$		0			0
$388$	0.0847583	−	0.0227109i	0.00430295	−	0.00115297i
$389$	−5.66554	+	9.81300i	−0.287254	+	0.497539i	−0.973153	−	0.230158i	$-0.926076\pi$
$389$	−5.66554	+	9.81300i	−0.287254	+	0.497539i	0.685899	+	0.727697i	$0.259409\pi$
$390$		0			0
$391$	−38.4368			−1.94383
$392$	−18.6870	+	6.78748i	−0.943837	+	0.342819i
$393$		0			0
$394$	8.73108	−	5.04089i	0.439865	−	0.253956i
$395$	23.5331	−	13.3579i	1.18408	−	0.672110i
$396$		0			0
$397$	−11.8070	−	3.16369i	−0.592578	−	0.158781i	−0.0499470	−	0.998752i	$-0.515905\pi$
$397$	−11.8070	−	3.16369i	−0.592578	−	0.158781i	−0.542631	+	0.839971i	$0.682572\pi$
$398$	−14.5160	+	14.5160i	−0.727621	+	0.727621i
$399$		0			0
$400$	−9.66235	−	17.3168i	−0.483118	−	0.865838i
$401$	−17.5382	+	10.1257i	−0.875816	+	0.505653i	−0.869277	−	0.494326i	$-0.835415\pi$
$401$	−17.5382	+	10.1257i	−0.875816	+	0.505653i	−0.00653958	+	0.999979i	$0.502082\pi$
$402$		0			0
$403$	−0.989002	+	0.265002i	−0.0492657	+	0.0132007i
$404$	−0.0803704	−	0.139206i	−0.00399858	−	0.00692574i
$405$		0			0
$406$	8.57025	−	16.4500i	0.425334	−	0.816398i
$407$	9.89601	+	9.89601i	0.490527	+	0.490527i
$408$		0			0
$409$	19.9017	+	11.4903i	0.984077	+	0.568157i	0.903499	−	0.428591i	$-0.140990\pi$
$409$	19.9017	+	11.4903i	0.984077	+	0.568157i	0.0805784	+	0.996748i	$0.474323\pi$
$410$	−21.3596	−	5.89134i	−1.05488	−	0.290952i
$411$		0			0
$412$	0.0987728	−	0.0987728i	0.00486618	−	0.00486618i
$413$	−4.74501	+	5.17482i	−0.233486	+	0.254636i
$414$		0			0
$415$	18.1736	−	17.9093i	0.892108	−	0.879131i
$416$	−0.0124127	−	0.00716650i	−0.000608585	−	0.000351366i
$417$		0			0
$418$	−1.16488	+	4.34738i	−0.0569759	+	0.212637i
$419$	−16.8385			−0.822617			−0.411308	−	0.911496i	$-0.634928\pi$
$419$	−16.8385			−0.822617			−0.411308	+	0.911496i	$0.634928\pi$
$420$		0			0
$421$	33.5542			1.63533			0.817667	−	0.575692i	$-0.195267\pi$
$421$	33.5542			1.63533			0.817667	+	0.575692i	$0.195267\pi$
$422$	1.39671	−	5.21260i	0.0679909	−	0.253745i
$423$		0			0
$424$	−15.4321	−	8.90973i	−0.749450	−	0.432695i
$425$	−36.3764	+	9.17798i	−1.76452	+	0.445197i
$426$		0			0
$427$	−9.30751	−	29.5538i	−0.450422	−	1.43021i
$428$	0.00267399	−	0.00267399i	0.000129252	−	0.000129252i
$429$		0			0
$430$	9.69296	−	5.50195i	0.467436	−	0.265327i
$431$	−11.5363	−	6.66051i	−0.555686	−	0.320826i	0.195726	−	0.980659i	$-0.437294\pi$
$431$	−11.5363	−	6.66051i	−0.555686	−	0.320826i	−0.751412	+	0.659833i	$0.770627\pi$
$432$		0			0
$433$	23.3937	+	23.3937i	1.12423	+	1.12423i	0.991099	+	0.133129i	$0.0425025\pi$
$433$	23.3937	+	23.3937i	1.12423	+	1.12423i	0.133129	+	0.991099i	$0.457497\pi$
$434$	13.6248	+	21.4023i	0.654010	+	1.02734i
$435$		0			0
$436$	−0.0456435	−	0.0790569i	−0.00218593	−	0.00378614i
$437$	−11.6055	+	3.10968i	−0.555166	+	0.148756i
$438$		0			0
$439$	−2.48600	+	1.43529i	−0.118650	+	0.0685027i	−0.558151	−	0.829740i	$-0.688489\pi$
$439$	−2.48600	+	1.43529i	−0.118650	+	0.0685027i	0.439500	+	0.898242i	$0.355155\pi$
$440$	−8.37533	+	2.17853i	−0.399278	+	0.103857i
$441$		0			0
$442$	1.12345	−	1.12345i	0.0534372	−	0.0534372i
$443$	16.6068	+	4.44977i	0.789011	+	0.211415i	0.630754	−	0.775983i	$-0.282746\pi$
$443$	16.6068	+	4.44977i	0.789011	+	0.211415i	0.158257	+	0.987398i	$0.449413\pi$
$444$		0			0
$445$	−3.04678	−	5.36760i	−0.144431	−	0.254449i
$446$	2.11770	−	1.22266i	0.100276	−	0.0578945i
$447$		0			0
$448$	−4.62602	+	20.8339i	−0.218559	+	0.984310i
$449$	0.314555			0.0148448			0.00742239	−	0.999972i	$-0.497637\pi$
$449$	0.314555			0.0148448			0.00742239	+	0.999972i	$0.497637\pi$
$450$		0			0
$451$	−4.79406	+	8.30355i	−0.225743	+	0.390999i
$452$	0.177299	−	0.0475071i	0.00833944	−	0.00223455i
$453$		0			0
$454$			17.7249i			0.831871i
$455$	0.472201	+	0.753885i	0.0221371	+	0.0353427i
$456$		0			0
$457$	−17.6258	−	4.72282i	−0.824501	−	0.220924i	−0.178188	−	0.983997i	$-0.557023\pi$
$457$	−17.6258	−	4.72282i	−0.824501	−	0.220924i	−0.646313	+	0.763072i	$0.723690\pi$
$458$	−9.57612	−	35.7386i	−0.447463	−	1.66995i
$459$		0			0
$460$	−0.135486	−	0.137486i	−0.00631705	−	0.00641030i
$461$			15.4893i			0.721410i	0.932680	+	0.360705i	$0.117464\pi$
$461$			15.4893i			0.721410i	−0.932680	+	0.360705i	$0.882536\pi$
$462$		0			0
$463$	21.9975	+	21.9975i	1.02231	+	1.02231i	0.999745	+	0.0225635i	$0.00718281\pi$
$463$	21.9975	+	21.9975i	1.02231	+	1.02231i	0.0225635	+	0.999745i	$0.492817\pi$
$464$	−9.87208	−	17.0989i	−0.458300	−	0.793798i
$465$		0			0
$466$	2.74742	−	4.75867i	0.127272	−	0.220441i
$467$	−8.28740	+	30.9290i	−0.383495	+	1.43122i	0.457030	+	0.889451i	$0.348913\pi$
$467$	−8.28740	+	30.9290i	−0.383495	+	1.43122i	−0.840525	+	0.541772i	$0.817754\pi$
$468$		0			0
$469$	−1.40089	−	32.3320i	−0.0646873	−	1.49295i
$470$	−5.87999	−	3.45249i	−0.271224	−	0.159252i
$471$		0			0
$472$	1.95072	+	7.28018i	0.0897892	+	0.335098i
$473$	−1.24830	−	4.65872i	−0.0573969	−	0.214208i
$474$		0			0
$475$	−10.2409	+	5.71417i	−0.469883	+	0.262184i
$476$	0.296679	+	0.154566i	0.0135983	+	0.00708454i
$477$		0			0
$478$	6.89586	−	25.7357i	0.315409	−	1.17712i
$479$	−5.51544	+	9.55302i	−0.252007	+	0.436489i	−0.964078	−	0.265618i	$-0.914424\pi$
$479$	−5.51544	+	9.55302i	−0.252007	+	0.436489i	0.712071	+	0.702107i	$0.247757\pi$
$480$		0			0
$481$	−0.772155	−	1.33741i	−0.0352072	−	0.0609807i
$482$	13.4862	+	13.4862i	0.614278	+	0.614278i
$483$		0			0
$484$		−	0.154075i		−	0.00700340i
$485$	−8.29343	+	8.17280i	−0.376585	+	0.371108i
$486$		0			0
$487$	−10.2546	−	38.2705i	−0.464678	−	1.73420i	−0.657953	−	0.753059i	$-0.728578\pi$
$487$	−10.2546	−	38.2705i	−0.464678	−	1.73420i	0.193275	−	0.981145i	$-0.438089\pi$
$488$	−32.1289	−	8.60890i	−1.45440	−	0.389707i
$489$		0			0
$490$	14.3031	−	16.7718i	0.646148	−	0.757672i
$491$			36.6693i			1.65486i	0.561567	+	0.827431i	$0.310199\pi$
$491$			36.6693i			1.65486i	−0.561567	+	0.827431i	$0.689801\pi$
$492$		0			0
$493$	−36.0811	+	9.66789i	−1.62501	+	0.435420i
$494$	0.248321	−	0.430104i	0.0111725	−	0.0193513i
$495$		0			0
$496$	27.0064			1.21262
$497$	2.83477	−	12.7668i	0.127157	−	0.572669i
$498$		0			0
$499$	−16.0187	+	9.24839i	−0.717094	+	0.414015i	−0.813682	−	0.581310i	$-0.802540\pi$
$499$	−16.0187	+	9.24839i	−0.717094	+	0.414015i	0.0965879	+	0.995324i	$0.469207\pi$
$500$	−0.161052	−	0.0977644i	−0.00720247	−	0.00437216i
$501$		0			0
$502$	−27.5815	−	7.39044i	−1.23102	−	0.329851i
$503$	12.8656	−	12.8656i	0.573650	−	0.573650i	−0.359497	−	0.933146i	$-0.617052\pi$
$503$	12.8656	−	12.8656i	0.573650	−	0.573650i	0.933146	+	0.359497i	$0.117052\pi$
$504$		0			0
$505$	18.3932	+	10.7997i	0.818485	+	0.480582i
$506$	8.51306	−	4.91502i	0.378452	−	0.218499i
$507$		0			0
$508$	−0.216827	+	0.0580986i	−0.00962014	+	0.00257771i
$509$	11.6839	+	20.2371i	0.517879	+	0.896994i	0.999784	+	0.0207700i	$0.00661177\pi$
$509$	11.6839	+	20.2371i	0.517879	+	0.896994i	−0.481905	+	0.876224i	$0.660055\pi$
$510$		0			0
$511$	14.8731	−	0.644428i	0.657948	−	0.0285078i
$512$	16.1975	+	16.1975i	0.715835	+	0.715835i
$513$		0			0
$514$	30.1443	+	17.4038i	1.32961	+	0.767649i
$515$	−4.92838	+	17.8683i	−0.217170	+	0.787371i
$516$		0			0
$517$	−2.08642	+	2.08642i	−0.0917607	+	0.0917607i
$518$	−25.8619	+	28.2045i	−1.13631	+	1.23924i
$519$		0			0
$520$	0.954917	+	0.00699588i	0.0418759	+	0.000306790i
$521$	−10.3332	−	5.96588i	−0.452706	−	0.261370i	0.256267	−	0.966606i	$-0.417508\pi$
$521$	−10.3332	−	5.96588i	−0.452706	−	0.261370i	−0.708972	+	0.705236i	$0.750841\pi$
$522$		0			0
$523$	1.33330	−	4.97594i	0.0583011	−	0.217583i	−0.930629	−	0.365964i	$-0.880739\pi$
$523$	1.33330	−	4.97594i	0.0583011	−	0.217583i	0.988930	+	0.148381i	$0.0474062\pi$
$524$	0.124768			0.00545052
$525$		0			0
$526$	−43.1752			−1.88253
$527$	13.2239	−	49.3523i	0.576043	−	2.14982i
$528$		0			0
$529$	2.80738	+	1.62084i	0.122060	+	0.0704713i
$530$	19.7558	+	0.144734i	0.858136	+	0.00628685i
$531$		0			0
$532$	0.102083	+	0.0226669i	0.00442588	+	0.000982735i
$533$	0.748131	−	0.748131i	0.0324051	−	0.0324051i
$534$		0			0
$535$	−0.133422	+	0.483733i	−0.00576832	+	0.0209136i
$536$	−30.0866	−	17.3705i	−1.29954	−	0.750291i
$537$		0			0
$538$	−23.3908	−	23.3908i	−1.00845	−	1.00845i
$539$	−5.46586	−	7.81710i	−0.235431	−	0.336706i
$540$		0			0
$541$	−1.79429	−	3.10781i	−0.0771427	−	0.133615i	0.824873	−	0.565318i	$-0.191246\pi$
$541$	−1.79429	−	3.10781i	−0.0771427	−	0.133615i	−0.902016	+	0.431703i	$0.857913\pi$
$542$	−38.7072	+	10.3716i	−1.66262	+	0.445497i
$543$		0			0
$544$	0.619410	−	0.357616i	0.0265570	−	0.0153327i
$545$	10.4457	+	6.13333i	0.447447	+	0.262723i
$546$		0			0
$547$	−6.56221	+	6.56221i	−0.280580	+	0.280580i	−0.833340	−	0.552761i	$-0.813574\pi$
$547$	−6.56221	+	6.56221i	−0.280580	+	0.280580i	0.552761	+	0.833340i	$0.313574\pi$
$548$	0.144457	+	0.0387072i	0.00617090	+	0.00165349i
$549$		0			0
$550$	6.88312	−	6.68431i	0.293497	−	0.285020i
$551$	−10.1120	+	5.83819i	−0.430788	+	0.248715i
$552$		0			0
$553$	30.5390	−	9.61778i	1.29865	−	0.408990i
$554$	−4.14141			−0.175951
$555$		0			0
$556$	0.0698639	−	0.121008i	0.00296289	−	0.00513187i
$557$	−4.41306	+	1.18248i	−0.186987	+	0.0501031i	−0.351097	−	0.936339i	$-0.614191\pi$
$557$	−4.41306	+	1.18248i	−0.186987	+	0.0501031i	0.164110	+	0.986442i	$0.447525\pi$
$558$		0			0
$559$			0.532209i			0.0225101i
$560$	−6.88397	−	22.4307i	−0.290901	−	0.947869i
$561$		0			0
$562$	24.7336	+	6.62735i	1.04332	+	0.279558i
$563$	−4.87949	−	18.2105i	−0.205646	−	0.767480i	−0.989252	−	0.146222i	$-0.953289\pi$
$563$	−4.87949	−	18.2105i	−0.205646	−	0.767480i	0.783606	−	0.621258i	$-0.213378\pi$
$564$		0			0
$565$	−17.3484	+	17.0960i	−0.729851	+	0.719234i
$566$		−	43.2630i		−	1.81848i
$567$		0			0
$568$	−9.92703	−	9.92703i	−0.416529	−	0.416529i
$569$	−5.64958	−	9.78536i	−0.236843	−	0.410224i	0.722964	−	0.690886i	$-0.242779\pi$
$569$	−5.64958	−	9.78536i	−0.236843	−	0.410224i	−0.959807	+	0.280662i	$0.909446\pi$
$570$		0			0
$571$	7.98119	−	13.8238i	0.334002	−	0.578509i	−0.649290	−	0.760541i	$-0.724934\pi$
$571$	7.98119	−	13.8238i	0.334002	−	0.578509i	0.983293	+	0.182032i	$0.0582673\pi$
$572$	0.000893617	−	0.00333502i	3.73640e−5	−	0.000139444i
$573$		0			0
$574$	−23.2505	−	12.1133i	−0.970457	−	0.505597i
$575$	24.6408	+	6.99099i	1.02759	+	0.291544i
$576$		0			0
$577$	2.86742	+	10.7014i	0.119372	+	0.445503i	0.999577	−	0.0290913i	$-0.00926136\pi$
$577$	2.86742	+	10.7014i	0.119372	+	0.445503i	−0.880205	+	0.474595i	$0.842595\pi$
$578$	14.3238	+	53.4571i	0.595791	+	2.22352i
$579$		0			0
$580$	−0.161763	−	0.0949810i	−0.00671686	−	0.00394387i
$581$	25.4673	−	16.2126i	1.05656	−	0.672611i
$582$		0			0
$583$	2.21269	−	8.25788i	0.0916403	−	0.342006i
$584$	7.99064	−	13.8402i	0.330655	−	0.572711i
$585$		0			0
$586$	−2.14451	−	3.71440i	−0.0885890	−	0.153441i
$587$	6.15146	+	6.15146i	0.253898	+	0.253898i	0.822567	−	0.568669i	$-0.192541\pi$
$587$	6.15146	+	6.15146i	0.253898	+	0.253898i	−0.568669	+	0.822567i	$0.692541\pi$
$588$		0			0
$589$		−	15.9712i		−	0.658081i
$590$	−5.86529	−	5.95187i	−0.241470	−	0.245034i
$591$		0			0
$592$	10.5425	+	39.3452i	0.433294	+	1.61708i
$593$	24.5364	+	6.57452i	1.00759	+	0.269983i	0.724622	−	0.689146i	$-0.242014\pi$
$593$	24.5364	+	6.57452i	1.00759	+	0.269983i	0.282968	+	0.959129i	$0.408681\pi$
$594$		0			0
$595$	−44.3613	+	1.59660i	−1.81864	+	0.0654542i
$596$			0.0775493i			0.00317654i
$597$		0			0
$598$	−1.04775	+	0.280744i	−0.0428457	+	0.0114805i
$599$	4.21188	−	7.29518i	0.172093	−	0.298073i	−0.767059	−	0.641577i	$-0.778280\pi$
$599$	4.21188	−	7.29518i	0.172093	−	0.298073i	0.939151	+	0.343504i	$0.111614\pi$
$600$		0			0
$601$	−33.7338			−1.37603			−0.688016	−	0.725696i	$-0.741518\pi$
$601$	−33.7338			−1.37603			−0.688016	+	0.725696i	$0.741518\pi$
$602$	12.5786	−	3.96144i	0.512666	−	0.161456i
$603$		0			0
$604$	0.00691891	−	0.00399464i	0.000281527	−	0.000162539i
$605$	10.0924	+	17.7802i	0.410316	+	0.722866i
$606$		0			0
$607$	41.6118	+	11.1499i	1.68897	+	0.452558i	0.970124	−	0.242610i	$-0.0780034\pi$
$607$	41.6118	+	11.1499i	1.68897	+	0.452558i	0.718847	+	0.695168i	$0.244670\pi$
$608$	0.158090	−	0.158090i	0.00641141	−	0.00641141i
$609$		0			0
$610$	35.6900	−	9.28341i	1.44505	−	0.375874i
$611$	0.281973	−	0.162797i	0.0114074	−	0.00658606i
$612$		0			0
$613$	−19.7127	+	5.28200i	−0.796188	+	0.213338i	−0.633910	−	0.773407i	$-0.718551\pi$
$613$	−19.7127	+	5.28200i	−0.796188	+	0.213338i	−0.162278	+	0.986745i	$0.551884\pi$
$614$	−7.13949	−	12.3660i	−0.288127	−	0.499050i
$615$		0			0
$616$	−10.2300	+	0.443249i	−0.412178	+	0.0178590i
$617$	−11.0864	−	11.0864i	−0.446321	−	0.446321i	0.447808	−	0.894130i	$-0.352205\pi$
$617$	−11.0864	−	11.0864i	−0.446321	−	0.446321i	−0.894130	+	0.447808i	$0.852205\pi$
$618$		0			0
$619$	5.11052	+	2.95056i	0.205409	+	0.118593i	0.599176	−	0.800617i	$-0.295495\pi$
$619$	5.11052	+	2.95056i	0.205409	+	0.118593i	−0.393767	+	0.919210i	$0.628828\pi$
$620$	0.223143	−	0.126661i	0.00896162	−	0.00508682i
$621$		0			0
$622$	−23.1519	+	23.1519i	−0.928305	+	0.928305i
$623$	−2.19370	−	6.96558i	−0.0878886	−	0.279070i
$624$		0			0
$625$	24.9893	+	0.732499i	0.999571	+	0.0292999i
$626$	19.9547	+	11.5209i	0.797550	+	0.460466i
$627$		0			0
$628$	0.0482245	−	0.179976i	0.00192437	−	0.00718184i
$629$	77.0628			3.07270
$630$		0			0
$631$	26.3658			1.04961			0.524803	−	0.851224i	$-0.324139\pi$
$631$	26.3658			1.04961			0.524803	+	0.851224i	$0.324139\pi$
$632$	8.89589	−	33.1999i	0.353859	−	1.32062i
$633$		0			0
$634$	1.21341	+	0.700561i	0.0481906	+	0.0278228i
$635$	21.2161	−	20.9075i	0.841935	−	0.829688i
$636$		0			0
$637$	0.359333	+	0.989303i	0.0142373	+	0.0391976i
$638$	6.75505	−	6.75505i	0.267435	−	0.267435i
$639$		0			0
$640$	−24.0748	−	6.64024i	−0.951641	−	0.262479i
$641$	11.1623	+	6.44455i	0.440884	+	0.254544i	0.703972	−	0.710227i	$-0.251408\pi$
$641$	11.1623	+	6.44455i	0.440884	+	0.254544i	−0.263089	+	0.964772i	$0.584741\pi$
$642$		0			0
$643$	13.4467	+	13.4467i	0.530286	+	0.530286i	0.920657	−	0.390372i	$-0.127654\pi$
$643$	13.4467	+	13.4467i	0.530286	+	0.530286i	−0.390372	+	0.920657i	$0.627654\pi$
$644$	−0.122650	−	0.192663i	−0.00483309	−	0.00759199i
$645$		0			0
$646$	12.3915	+	21.4627i	0.487536	+	0.844437i
$647$	3.87299	−	1.03777i	0.152263	−	0.0407988i	−0.181882	−	0.983320i	$-0.558219\pi$
$647$	3.87299	−	1.03777i	0.152263	−	0.0407988i	0.334145	+	0.942522i	$0.391552\pi$
$648$		0			0
$649$	−3.13155	+	1.80800i	−0.122924	+	0.0709702i
$650$	−0.924552	+	0.515878i	−0.0362639	+	0.0202344i
$651$		0			0
$652$	0.226911	−	0.226911i	0.00888653	−	0.00888653i
$653$	34.1463	+	9.14947i	1.33625	+	0.358047i	0.855041	−	0.518561i	$-0.173532\pi$
$653$	34.1463	+	9.14947i	1.33625	+	0.358047i	0.481207	+	0.876607i	$0.340199\pi$
$654$		0			0
$655$	−14.3982	+	8.17275i	−0.562584	+	0.319336i
$656$	−24.1678	+	13.9533i	−0.943593	+	0.544783i
$657$		0			0
$658$	−5.94650	−	5.45259i	−0.231819	−	0.212564i
$659$	9.12406			0.355423			0.177712	−	0.984083i	$-0.443131\pi$
$659$	9.12406			0.355423			0.177712	+	0.984083i	$0.443131\pi$
$660$		0			0
$661$	−9.28949	+	16.0899i	−0.361319	+	0.625823i	−0.988178	−	0.153310i	$-0.951007\pi$
$661$	−9.28949	+	16.0899i	−0.361319	+	0.625823i	0.626859	+	0.779133i	$0.284340\pi$
$662$	−24.0252	+	6.43752i	−0.933764	+	0.250201i
$663$		0			0
$664$		−	32.4089i		−	1.25771i
$665$	−13.2652	+	4.07107i	−0.514401	+	0.157869i
$666$		0			0
$667$	24.6334	+	6.60049i	0.953808	+	0.255572i
$668$	0.0308289	+	0.115055i	0.00119281	+	0.00445161i
$669$		0			0
$670$	38.5160	+	0.282175i	1.48800	+	0.0109014i
$671$		−	15.9581i		−	0.616056i
$672$		0			0
$673$	7.94341	+	7.94341i	0.306196	+	0.306196i	0.843432	−	0.537236i	$-0.180532\pi$
$673$	7.94341	+	7.94341i	0.306196	+	0.306196i	−0.537236	+	0.843432i	$0.680532\pi$
$674$	3.20119	+	5.54463i	0.123305	+	0.213571i
$675$		0			0
$676$	0.109343	−	0.189387i	0.00420549	−	0.00728412i
$677$	−2.38854	+	8.91415i	−0.0917991	+	0.342599i	−0.996515	−	0.0834172i	$-0.973417\pi$
$677$	−2.38854	+	8.91415i	−0.0917991	+	0.342599i	0.904716	+	0.426016i	$0.140083\pi$
$678$		0			0
$679$	−11.6219	+	7.39852i	−0.446006	+	0.283929i
$680$	−24.1281	+	41.0928i	−0.925269	+	1.57584i
$681$		0			0
$682$	3.38196	+	12.6216i	0.129502	+	0.483307i
$683$	−3.44703	−	12.8645i	−0.131897	−	0.492246i	0.868094	−	0.496399i	$-0.165345\pi$
$683$	−3.44703	−	12.8645i	−0.131897	−	0.492246i	−0.999991	+	0.00415310i	$0.998678\pi$
$684$		0			0
$685$	−19.2058	+	4.99566i	−0.733814	+	0.190874i
$686$	20.7073	−	15.8565i	0.790607	−	0.605404i
$687$		0			0
$688$	3.63322	−	13.5594i	0.138515	−	0.516946i
$689$	−0.471687	+	0.816986i	−0.0179699	+	0.0311247i
$690$		0			0
$691$	−8.15132	−	14.1185i	−0.310091	−	0.537093i	0.668291	−	0.743900i	$-0.267026\pi$
$691$	−8.15132	−	14.1185i	−0.310091	−	0.537093i	−0.978382	+	0.206807i	$0.933693\pi$
$692$	−0.128798	−	0.128798i	−0.00489616	−	0.00489616i
$693$		0			0
$694$		−	0.932194i		−	0.0353856i
$695$	−0.135831	+	18.5406i	−0.00515238	+	0.703284i
$696$		0			0
$697$	13.6647	+	50.9972i	0.517586	+	1.93166i
$698$	−14.6913	−	3.93652i	−0.556073	−	0.148999i
$699$		0			0
$700$	−0.162080	−	0.153049i	−0.00612604	−	0.00578472i
$701$		−	6.83585i		−	0.258186i	−0.991632	−	0.129093i	$-0.958793\pi$
$701$		−	6.83585i		−	0.258186i	0.991632	−	0.129093i	$-0.0412066\pi$
$702$		0			0
$703$	23.2681	−	6.23468i	0.877574	−	0.235145i
$704$	−5.49571	+	9.51885i	−0.207127	+	0.358755i
$705$		0			0
$706$	3.59153			0.135169
$707$	18.6012	+	17.0562i	0.699571	+	0.641466i
$708$		0			0
$709$	−12.3735	+	7.14386i	−0.464697	+	0.268293i	−0.714017	−	0.700128i	$-0.753126\pi$
$709$	−12.3735	+	7.14386i	−0.464697	+	0.268293i	0.249320	+	0.968421i	$0.419793\pi$
$710$	15.0046	+	4.13852i	0.563113	+	0.155316i
$711$		0			0
$712$	−7.57249	−	2.02904i	−0.283791	−	0.0760416i
$713$	−24.6657	+	24.6657i	−0.923738	+	0.923738i
$714$		0			0
$715$	0.115333	+	0.443395i	0.00431320	+	0.0165820i
$716$	−0.245070	+	0.141491i	−0.00915870	+	0.00528778i
$717$		0			0
$718$	42.1234	−	11.2869i	1.57203	−	0.421225i
$719$	−13.6899	−	23.7117i	−0.510549	−	0.884297i	−0.999925	−	0.0122240i	$-0.996109\pi$
$719$	−13.6899	−	23.7117i	−0.510549	−	0.884297i	0.489376	−	0.872073i	$-0.337224\pi$
$720$		0			0
$721$	−10.1333	+	19.4501i	−0.377384	+	0.724360i
$722$	−13.4419	−	13.4419i	−0.500257	−	0.500257i
$723$		0			0
$724$	0.0228212	+	0.0131758i	0.000848145	+	0.000489676i
$725$	24.8890	+	0.364702i	0.924355	+	0.0135447i
$726$		0			0
$727$	23.4350	−	23.4350i	0.869155	−	0.869155i	−0.123224	−	0.992379i	$-0.539323\pi$
$727$	23.4350	−	23.4350i	0.869155	−	0.869155i	0.992379	+	0.123224i	$0.0393235\pi$
$728$	1.10304	+	0.244922i	0.0408813	+	0.00907741i
$729$		0			0
$730$	−0.129804	+	17.7178i	−0.00480426	+	0.655767i
$731$	−22.9998	−	13.2789i	−0.850677	−	0.491139i
$732$		0			0
$733$	−12.4724	+	46.5476i	−0.460678	+	1.71927i	0.210157	+	0.977668i	$0.432603\pi$
$733$	−12.4724	+	46.5476i	−0.460678	+	1.71927i	−0.670835	+	0.741607i	$0.734064\pi$
$734$	−7.10703			−0.262325
$735$		0			0
$736$	−0.488306			−0.0179992
$737$	4.31388	−	16.0996i	0.158904	−	0.593038i
$738$		0			0
$739$	−28.9487	−	16.7136i	−1.06490	−	0.614818i	−0.138114	−	0.990416i	$-0.544104\pi$
$739$	−28.9487	−	16.7136i	−1.06490	−	0.614818i	−0.926783	+	0.375598i	$0.877437\pi$
$740$	0.271638	+	0.275648i	0.00998563	+	0.0101330i
$741$		0			0
$742$	22.8202	+	5.06706i	0.837756	+	0.186018i
$743$	−4.26258	+	4.26258i	−0.156379	+	0.156379i	−0.780960	−	0.624581i	$-0.785270\pi$
$743$	−4.26258	+	4.26258i	−0.156379	+	0.156379i	0.624581	+	0.780960i	$0.285270\pi$
$744$		0			0
$745$	−5.07975	−	8.94916i	−0.186108	−	0.327872i
$746$	1.43248	+	0.827044i	0.0524469	+	0.0302802i
$747$		0			0
$748$	0.121829	+	0.121829i	0.00445451	+	0.00445451i
$749$	−0.274330	+	0.526556i	−0.0100238	+	0.0192399i
$750$		0			0
$751$	−17.2308	−	29.8447i	−0.628762	−	1.08905i	−0.987800	−	0.155725i	$-0.950229\pi$
$751$	−17.2308	−	29.8447i	−0.628762	−	1.08905i	0.359039	−	0.933323i	$-0.383105\pi$
$752$	−8.29533	+	2.22273i	−0.302500	+	0.0810545i
$753$		0			0
$754$	−0.912922	+	0.527075i	−0.0332466	+	0.0191950i
$755$	−0.536777	+	0.914193i	−0.0195353	+	0.0332709i
$756$		0			0
$757$	−13.7624	+	13.7624i	−0.500202	+	0.500202i	−0.911501	−	0.411299i	$-0.865075\pi$
$757$	−13.7624	+	13.7624i	−0.500202	+	0.500202i	0.411299	+	0.911501i	$0.365075\pi$
$758$	−16.9971	−	4.55436i	−0.617363	−	0.165422i
$759$		0			0
$760$	−3.96059	+	14.3595i	−0.143666	+	0.520874i
$761$	10.6969	−	6.17587i	0.387763	−	0.223875i	−0.293427	−	0.955981i	$-0.594796\pi$
$761$	10.6969	−	6.17587i	0.387763	−	0.223875i	0.681190	+	0.732106i	$0.261463\pi$
$762$		0			0
$763$	10.5639	+	9.68648i	0.382439	+	0.350674i
$764$	−0.434433			−0.0157172
$765$		0			0
$766$	−13.7821	+	23.8714i	−0.497969	+	0.862507i
$767$	0.385418	−	0.103272i	0.0139166	−	0.00372895i
$768$		0			0
$769$		−	6.22694i		−	0.224549i	−0.993677	−	0.112275i	$-0.964186\pi$
$769$		−	6.22694i		−	0.224549i	0.993677	−	0.112275i	$-0.0358136\pi$
$770$	9.62107	−	6.02622i	0.346719	−	0.217170i
$771$		0			0
$772$	0.265990	+	0.0712719i	0.00957320	+	0.00256513i
$773$	−2.27482	−	8.48975i	−0.0818197	−	0.305355i	0.912873	−	0.408243i	$-0.133858\pi$
$773$	−2.27482	−	8.48975i	−0.0818197	−	0.305355i	−0.994693	+	0.102888i	$0.967192\pi$
$774$		0			0
$775$	−17.4538	+	29.2332i	−0.626960	+	1.05009i
$776$			14.7896i			0.530917i
$777$		0			0
$778$	−11.2832	−	11.2832i	−0.404524	−	0.404524i
$779$	8.25175	+	14.2924i	0.295649	+	0.512080i
$780$		0			0
$781$	3.36771	−	5.83304i	0.120506	−	0.208723i
$782$	14.0094	−	52.2840i	0.500977	−	1.86967i
$783$		0			0
$784$	−2.40127	−	27.6581i	−0.0857595	−	0.987788i
$785$	6.22399	+	23.9281i	0.222144	+	0.854030i
$786$		0			0
$787$	9.63721	+	35.9666i	0.343530	+	1.28207i	0.894321	+	0.447427i	$0.147659\pi$
$787$	9.63721	+	35.9666i	0.343530	+	1.28207i	−0.550791	+	0.834643i	$0.685674\pi$
$788$	−0.0312240	−	0.116530i	−0.00111231	−	0.00415119i
$789$		0			0
$790$	9.59288	+	36.8797i	0.341299	+	1.31212i
$791$	−24.3108	+	15.4764i	−0.864393	+	0.550276i
$792$		0			0
$793$	−0.455761	+	1.70092i	−0.0161845	+	0.0604015i
$794$	8.60686	−	14.9075i	0.305446	−	0.529048i
$795$		0			0
$796$	0.122825	+	0.212739i	0.00435342	+	0.00754034i
$797$	−15.8626	−	15.8626i	−0.561880	−	0.561880i	0.367961	−	0.929841i	$-0.380056\pi$
$797$	−15.8626	−	15.8626i	−0.561880	−	0.561880i	−0.929841	+	0.367961i	$0.880056\pi$
$798$		0			0
$799$			16.2475i			0.574796i
$800$	−0.462131	+	0.116598i	−0.0163388	+	0.00412237i
$801$		0			0
$802$	−7.38122	−	27.5471i	−0.260640	−	0.972722i
$803$	7.40603	+	1.98444i	0.261353	+	0.0700293i
$804$		0			0
$805$	26.7739	+	14.1992i	0.943655	+	0.500457i
$806$		−	1.44189i		−	0.0507883i
$807$		0			0
$808$	26.1691	−	7.01199i	0.920626	−	0.246681i
$809$	20.0158	−	34.6684i	0.703718	−	1.21888i	−0.263434	−	0.964678i	$-0.584855\pi$
$809$	20.0158	−	34.6684i	0.703718	−	1.21888i	0.967152	−	0.254199i	$-0.0818117\pi$
$810$		0			0
$811$	32.9623			1.15746			0.578732	−	0.815518i	$-0.303548\pi$
$811$	32.9623			1.15746			0.578732	+	0.815518i	$0.303548\pi$
$812$	−0.163593	−	0.150005i	−0.00574099	−	0.00526415i
$813$		0			0
$814$	−17.0680	+	9.85423i	−0.598234	+	0.345391i
$815$	−11.3220	+	41.0490i	−0.396592	+	1.43788i
$816$		0			0
$817$	−8.01880	−	2.14863i	−0.280542	−	0.0751711i
$818$	−22.8835	+	22.8835i	−0.800103	+	0.800103i
$819$		0			0
$820$	−0.134247	+	0.228637i	−0.00468810	+	0.00798437i
$821$	−4.48457	+	2.58917i	−0.156513	+	0.0903625i	−0.576211	−	0.817301i	$-0.695469\pi$
$821$	−4.48457	+	2.58917i	−0.156513	+	0.0903625i	0.419698	+	0.907664i	$0.362136\pi$
$822$		0			0
$823$	−6.85811	+	1.83762i	−0.239059	+	0.0640556i	−0.376359	−	0.926474i	$-0.622824\pi$
$823$	−6.85811	+	1.83762i	−0.239059	+	0.0640556i	0.137300	+	0.990529i	$0.456157\pi$
$824$	11.7717	+	20.3893i	0.410088	+	0.710294i
$825$		0			0
$826$	−5.30963	−	8.34055i	−0.184746	−	0.290205i
$827$	−19.9878	−	19.9878i	−0.695043	−	0.695043i	0.268294	−	0.963337i	$-0.413540\pi$
$827$	−19.9878	−	19.9878i	−0.695043	−	0.695043i	−0.963337	+	0.268294i	$0.913540\pi$
$828$		0			0
$829$	−31.9596	−	18.4519i	−1.11000	−	0.640860i	−0.171173	−	0.985241i	$-0.554756\pi$
$829$	−31.9596	−	18.4519i	−1.11000	−	0.640860i	−0.938830	+	0.344381i	$0.888089\pi$
$830$	17.7373	+	31.2484i	0.615671	+	1.08465i
$831$		0			0
$832$	0.857627	−	0.857627i	0.0297329	−	0.0297329i
$833$	−51.7190	−	9.15485i	−1.79196	−	0.317197i
$834$		0			0
$835$	−11.0941	−	11.2579i	−0.383929	−	0.389596i
$836$	0.0466411	+	0.0269283i	0.00161312	+	0.000931334i
$837$		0			0
$838$	6.13731	−	22.9048i	0.212010	−	0.791232i
$839$	−20.5318			−0.708836			−0.354418	−	0.935087i	$-0.615321\pi$
$839$	−20.5318			−0.708836			−0.354418	+	0.935087i	$0.615321\pi$
$840$		0			0
$841$	−4.21616			−0.145385
$842$	−12.2299	+	45.6424i	−0.421469	+	1.57294i
$843$		0			0
$844$	−0.0559238	−	0.0322876i	−0.00192497	−	0.00111138i
$845$	−0.212587	+	29.0175i	−0.00731323	+	0.998234i
$846$		0			0
$847$	7.26661	+	23.0735i	0.249684	+	0.792813i
$848$	17.5947	−	17.5947i	0.604205	−	0.604205i
$849$		0			0
$850$	0.774074	−	52.8266i	0.0265505	−	1.81194i
$851$	−45.5638	−	26.3063i	−1.56191	−	0.901768i
$852$		0			0
$853$	8.22782	+	8.22782i	0.281715	+	0.281715i	0.833793	−	0.552078i	$-0.186165\pi$
$853$	8.22782	+	8.22782i	0.281715	+	0.281715i	−0.552078	+	0.833793i	$0.686165\pi$
$854$	43.5933	−	1.88883i	1.49173	−	0.0646343i
$855$		0			0
$856$	0.318686	+	0.551981i	0.0108925	+	0.0188663i
$857$	0.952220	−	0.255147i	0.0325272	−	0.00871564i	−0.242519	−	0.970147i	$-0.577974\pi$
$857$	0.952220	−	0.255147i	0.0325272	−	0.00871564i	0.275046	+	0.961431i	$0.411307\pi$
$858$		0			0
$859$	29.3440	−	16.9418i	1.00121	−	0.578046i	0.0926009	−	0.995703i	$-0.470482\pi$
$859$	29.3440	−	16.9418i	1.00121	−	0.578046i	0.908605	+	0.417657i	$0.137149\pi$
$860$	−0.0335741	−	0.129075i	−0.00114487	−	0.00440143i
$861$		0			0
$862$	13.2648	−	13.2648i	0.451800	−	0.451800i
$863$	10.1675	+	2.72438i	0.346106	+	0.0927388i	0.427684	−	0.903928i	$-0.359329\pi$
$863$	10.1675	+	2.72438i	0.346106	+	0.0927388i	−0.0815784	+	0.996667i	$0.525996\pi$
$864$		0			0
$865$	23.2999	+	6.42651i	0.792222	+	0.218508i
$866$	−40.3480	+	23.2949i	−1.37108	+	0.791593i
$867$		0			0
$868$	0.289574	−	0.0911966i	0.00982877	−	0.00309541i
$869$	16.4901			0.559388
$870$		0			0
$871$	−0.919605	+	1.59280i	−0.0311596	+	0.0539701i
$872$	14.8618	−	3.98221i	0.503284	−	0.134855i
$873$		0			0
$874$		−	16.9199i		−	0.572324i
$875$	28.7292	+	7.04502i	0.971225	+	0.238165i
$876$		0			0
$877$	−21.2308	−	5.68877i	−0.716912	−	0.192096i	−0.118119	−	0.992999i	$-0.537686\pi$
$877$	−21.2308	−	5.68877i	−0.716912	−	0.192096i	−0.598793	+	0.800904i	$0.704353\pi$
$878$	−1.04627	−	3.90473i	−0.0353099	−	0.131778i
$879$		0			0
$880$	0.0885290	−	12.0840i	0.00298431	−	0.407350i
$881$		−	6.52365i		−	0.219787i	−0.993943	−	0.109894i	$-0.964949\pi$
$881$		−	6.52365i		−	0.219787i	0.993943	−	0.109894i	$-0.0350510\pi$
$882$		0			0
$883$	−10.6633	−	10.6633i	−0.358849	−	0.358849i	0.504540	−	0.863388i	$-0.331662\pi$
$883$	−10.6633	−	10.6633i	−0.358849	−	0.358849i	−0.863388	+	0.504540i	$0.831662\pi$
$884$	−0.00950593	−	0.0164648i	−0.000319719	−	0.000553770i
$885$		0			0
$886$	−12.1057	+	20.9676i	−0.406698	+	0.704421i
$887$	−5.81970	+	21.7194i	−0.195406	+	0.729267i	0.796755	+	0.604303i	$0.206548\pi$
$887$	−5.81970	+	21.7194i	−0.195406	+	0.729267i	−0.992161	+	0.124964i	$0.960118\pi$
$888$		0			0
$889$	29.7308	−	18.9268i	0.997140	−	0.634783i
$890$	8.41182	−	2.18802i	0.281965	−	0.0733425i
$891$		0			0
$892$	−0.00757331	−	0.0282640i	−0.000253573	−	0.000946348i
$893$	1.31449	+	4.90573i	0.0439876	+	0.164164i
$894$		0			0
$895$	19.0128	−	32.3810i	0.635528	−	1.08238i
$896$	−26.2061	−	13.6531i	−0.875484	−	0.456118i
$897$		0			0
$898$	−0.114649	+	0.427877i	−0.00382589	+	0.0142784i
$899$	−16.9499	+	29.3581i	−0.565311	+	0.979147i
$900$		0			0
$901$	−23.5377	−	40.7685i	−0.784155	−	1.35820i
$902$	−9.54764	−	9.54764i	−0.317901	−	0.317901i
$903$		0			0
$904$			30.9372i			1.02896i
$905$	−3.49663	−	0.0256169i	−0.116232	−	0.000851533i
$906$		0			0
$907$	−10.1119	−	37.7381i	−0.335760	−	1.25307i	−0.903043	−	0.429550i	$-0.858672\pi$
$907$	−10.1119	−	37.7381i	−0.335760	−	1.25307i	0.567283	−	0.823523i	$-0.307994\pi$
$908$	0.204872	+	0.0548953i	0.00679892	+	0.00182176i
$909$		0			0
$910$	−1.19759	+	0.367539i	−0.0396996	+	0.0121838i
$911$		−	45.1293i		−	1.49520i	−0.664148	−	0.747601i	$-0.731206\pi$
$911$		−	45.1293i		−	1.49520i	0.664148	−	0.747601i	$-0.268794\pi$
$912$		0			0
$913$	15.0189	−	4.02430i	0.497053	−	0.133185i
$914$	12.8485	−	22.2543i	0.424991	−	0.736106i
$915$		0			0
$916$	−0.442740			−0.0146285
$917$	−18.6846	+	5.88443i	−0.617022	+	0.194321i
$918$		0			0
$919$	−11.3866	+	6.57407i	−0.375610	+	0.216859i	−0.675907	−	0.736987i	$-0.736248\pi$
$919$	−11.3866	+	6.57407i	−0.375610	+	0.216859i	0.300296	+	0.953846i	$0.402914\pi$
$920$	28.2934	−	16.0600i	0.932804	−	0.529481i
$921$		0			0
$922$	−21.0695	−	5.64555i	−0.693886	−	0.185926i
$923$	−0.525544	+	0.525544i	−0.0172985	+	0.0172985i
$924$		0			0
$925$	−49.4029	−	14.0164i	−1.62436	−	0.460856i
$926$	−37.9399	+	21.9046i	−1.24678	+	0.719830i
$927$		0			0
$928$	−0.458378	+	0.122822i	−0.0150470	+	0.00403183i
$929$	−9.19334	−	15.9233i	−0.301624	−	0.522428i	0.674880	−	0.737927i	$-0.264195\pi$
$929$	−9.19334	−	15.9233i	−0.301624	−	0.522428i	−0.976504	+	0.215500i	$0.930862\pi$
$930$		0			0
$931$	−16.3565	+	1.42007i	−0.536064	+	0.0465410i
$932$	−0.0464938	−	0.0464938i	−0.00152296	−	0.00152296i
$933$		0			0
$934$	−39.0508	−	22.5460i	−1.27778	−	0.737728i
$935$	−22.0392	−	6.07879i	−0.720760	−	0.198798i
$936$		0			0
$937$	−12.8792	+	12.8792i	−0.420745	+	0.420745i	−0.885460	−	0.464715i	$-0.846157\pi$
$937$	−12.8792	+	12.8792i	−0.420745	+	0.420745i	0.464715	+	0.885460i	$0.346157\pi$
$938$	44.4905	+	9.87879i	1.45267	+	0.322554i
$939$		0			0
$940$	−0.0581161	+	0.0572708i	−0.00189554	+	0.00186797i
$941$	41.7477	+	24.1030i	1.36094	+	0.785736i	0.989748	−	0.142822i	$-0.0456176\pi$
$941$	41.7477	+	24.1030i	1.36094	+	0.785736i	0.371187	+	0.928558i	$0.378951\pi$
$942$		0			0
$943$	9.32919	−	34.8170i	0.303800	−	1.13380i
$944$	−10.5245			−0.342543
$945$		0			0
$946$	6.79205			0.220829
$947$	−10.2186	+	38.1363i	−0.332059	+	1.23926i	0.574963	+	0.818179i	$0.305016\pi$
$947$	−10.2186	+	38.1363i	−0.332059	+	1.23926i	−0.907022	+	0.421083i	$0.861650\pi$
$948$		0			0
$949$	−0.732709	−	0.423030i	−0.0237847	−	0.0137321i
$950$	−4.04015	−	16.0129i	−0.131080	−	0.519528i
$951$		0			0
$952$	−38.1059	+	41.5576i	−1.23502	+	1.34689i
$953$	−32.6743	+	32.6743i	−1.05843	+	1.05843i	−0.0602421	+	0.998184i	$0.519187\pi$
$953$	−32.6743	+	32.6743i	−1.05843	+	1.05843i	−0.998184	+	0.0602421i	$0.980813\pi$
$954$		0			0
$955$	50.1334	−	28.4569i	1.62228	−	0.920843i
$956$	−0.276107	−	0.159411i	−0.00892995	−	0.00515571i
$957$		0			0
$958$	−10.9843	−	10.9843i	−0.354887	−	0.354887i
$959$	−23.4587	+	1.01643i	−0.757522	+	0.0328222i
$960$		0			0
$961$	−7.68437	−	13.3097i	−0.247883	−	0.429346i
$962$	2.10066	−	0.562870i	0.0677280	−	0.0181477i
$963$		0			0
$964$	0.197646	−	0.114111i	0.00636576	−	0.00367528i
$965$	−35.3637	+	9.19855i	−1.13840	+	0.296112i
$966$		0			0
$967$	1.01300	−	1.01300i	0.0325759	−	0.0325759i	−0.690631	−	0.723207i	$-0.742667\pi$
$967$	1.01300	−	1.01300i	0.0325759	−	0.0325759i	0.723207	+	0.690631i	$0.242667\pi$
$968$	25.0838	+	6.72119i	0.806225	+	0.216027i
$969$		0			0
$970$	−8.09432	−	14.2600i	−0.259893	−	0.457862i
$971$	50.0760	−	28.9114i	1.60702	−	0.927811i	0.616983	−	0.786976i	$-0.288355\pi$
$971$	50.0760	−	28.9114i	1.60702	−	0.927811i	0.990033	−	0.140835i	$-0.0449787\pi$
$972$		0			0
$973$	−4.75538	+	21.4165i	−0.152451	+	0.686581i
$974$	55.7954			1.78780
$975$		0			0
$976$	23.2233	−	40.2240i	0.743360	−	1.28754i
$977$	31.6484	−	8.48016i	1.01252	−	0.271304i	0.285839	−	0.958278i	$-0.407728\pi$
$977$	31.6484	−	8.48016i	1.01252	−	0.271304i	0.726682	+	0.686973i	$0.241061\pi$
$978$		0			0
$979$		−	3.76119i		−	0.120208i
$980$	−0.149558	−	0.217265i	−0.00477745	−	0.00694027i
$981$		0			0
$982$	−49.8797	−	13.3652i	−1.59173	−	0.426502i
$983$	−10.1297	−	37.8045i	−0.323087	−	1.20578i	−0.916221	−	0.400672i	$-0.868777\pi$
$983$	−10.1297	−	37.8045i	−0.323087	−	1.20578i	0.593135	−	0.805103i	$-0.297890\pi$
$984$		0			0
$985$	11.2363	+	11.4022i	0.358019	+	0.363304i
$986$		−	52.6033i		−	1.67523i
$987$		0			0
$988$	−0.00420226	−	0.00420226i	−0.000133692	−	0.000133692i
$989$	9.06583	+	15.7025i	0.288276	+	0.499310i
$990$		0			0
$991$	6.11042	−	10.5836i	0.194104	−	0.336198i	−0.752502	−	0.658589i	$-0.771153\pi$
$991$	6.11042	−	10.5836i	0.194104	−	0.336198i	0.946606	+	0.322391i	$0.104487\pi$
$992$	0.167998	−	0.626978i	0.00533395	−	0.0199066i
$993$		0			0
$994$	16.3329	+	8.50926i	0.518048	+	0.269897i
$995$	−28.1091	−	16.5045i	−0.891119	−	0.523229i
$996$		0			0
$997$	−2.50867	−	9.36249i	−0.0794504	−	0.296513i	0.914755	−	0.404009i	$-0.132383\pi$
$997$	−2.50867	−	9.36249i	−0.0794504	−	0.296513i	−0.994206	+	0.107496i	$0.965717\pi$
$998$	−6.74171	−	25.1604i	−0.213405	−	0.796438i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.53.5	✓	64
3.2	odd	2	inner	315.2.ce.a.53.12	yes	64
5.2	odd	4	inner	315.2.ce.a.242.5	yes	64
7.2	even	3	inner	315.2.ce.a.233.12	yes	64
15.2	even	4	inner	315.2.ce.a.242.12	yes	64
21.2	odd	6	inner	315.2.ce.a.233.5	yes	64
35.2	odd	12	inner	315.2.ce.a.107.12	yes	64
105.2	even	12	inner	315.2.ce.a.107.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.5	✓	64	1.1	even	1	trivial
315.2.ce.a.53.12	yes	64	3.2	odd	2	inner
315.2.ce.a.107.5	yes	64	105.2	even	12	inner
315.2.ce.a.107.12	yes	64	35.2	odd	12	inner
315.2.ce.a.233.5	yes	64	21.2	odd	6	inner
315.2.ce.a.233.12	yes	64	7.2	even	3	inner
315.2.ce.a.242.5	yes	64	5.2	odd	4	inner
315.2.ce.a.242.12	yes	64	15.2	even	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.364480 + 1.36026i) q^{2} +(0.0145936 + 0.00842564i) q^{4} +(-2.23601 - 0.0163814i) q^{5} +(-2.58285 - 0.573503i) q^{7} +(-2.00834 + 2.00834i) q^{8} +(0.837263 - 3.03558i) q^{10} +(-1.18008 - 0.681321i) q^{11} +(0.106323 + 0.106323i) q^{13} +(1.72151 - 3.30431i) q^{14} +(-1.98301 - 3.43467i) q^{16} +(-7.24761 + 1.94199i) q^{17} +(-2.03121 + 1.17272i) q^{19} +(-0.0324934 - 0.0190789i) q^{20} +(1.35689 - 1.35689i) q^{22} +(4.94811 + 1.32584i) q^{23} +(4.99946 + 0.0732577i) q^{25} +(-0.183379 + 0.105874i) q^{26} +(-0.0328610 - 0.0301316i) q^{28} +4.97834 q^{29} +(-3.40473 + 5.89716i) q^{31} +(-0.0920746 + 0.0246713i) q^{32} -10.5664i q^{34} +(5.76587 + 1.32467i) q^{35} +(-9.92059 - 2.65821i) q^{37} +(-0.854866 - 3.19040i) q^{38} +(4.52356 - 4.45776i) q^{40} -7.03642i q^{41} +(2.50280 + 2.50280i) q^{43} +(-0.0114811 - 0.0198859i) q^{44} +(-3.60698 + 6.24747i) q^{46} +(0.560444 - 2.09160i) q^{47} +(6.34219 + 2.96254i) q^{49} +(-1.92185 + 6.77386i) q^{50} +(0.000655798 + 0.00244747i) q^{52} +(1.62383 + 6.06020i) q^{53} +(2.62751 + 1.54277i) q^{55} +(6.33901 - 4.03544i) q^{56} +(-1.81451 + 6.77183i) q^{58} +(1.32684 - 2.29815i) q^{59} +(5.85558 + 10.1422i) q^{61} +(-6.78071 - 6.78071i) q^{62} -8.06626i q^{64} +(-0.235997 - 0.239480i) q^{65} +(3.16583 + 11.8150i) q^{67} +(-0.122132 - 0.0327250i) q^{68} +(-3.90343 + 7.36026i) q^{70} +4.94291i q^{71} +(-5.43505 + 1.45632i) q^{73} +(7.23171 - 12.5257i) q^{74} -0.0395236 q^{76} +(2.65723 + 2.43653i) q^{77} +(-10.4803 + 6.05078i) q^{79} +(4.37775 + 7.71243i) q^{80} +(9.57135 + 2.56463i) q^{82} +(-8.06859 + 8.06859i) q^{83} +(16.2375 - 4.22358i) q^{85} +(-4.31668 + 2.49224i) q^{86} +(3.73832 - 1.00168i) q^{88} +(1.38011 + 2.39042i) q^{89} +(-0.213639 - 0.335591i) q^{91} +(0.0610399 + 0.0610399i) q^{92} +(2.64085 + 1.52470i) q^{94} +(4.56101 - 2.58894i) q^{95} +(3.68206 - 3.68206i) q^{97} +(-6.34142 + 7.54723i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) \) 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more