LMFDB - Embedded newform 490.2.s.a.223.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(13,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([21, 22]))

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

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

chi := DirichletCharacter("490.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.s (of order $28$, degree $12$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			223.8
Character	$\chi$	$=$	490.223
Dual form			490.2.s.a.167.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.330279 + 0.943883i) q^{2} +(-0.00530751 - 0.00844686i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.69250 + 1.46131i) q^{5} +(0.00972581 - 0.00221985i) q^{6} +(-2.63324 + 0.256962i) q^{7} +(0.846724 - 0.532032i) q^{8} +(1.30161 - 2.70282i) q^{9} +O(q^{10})$	\(q+(-0.330279 + 0.943883i) q^{2} +(-0.00530751 - 0.00844686i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.69250 + 1.46131i) q^{5} +(0.00972581 - 0.00221985i) q^{6} +(-2.63324 + 0.256962i) q^{7} +(0.846724 - 0.532032i) q^{8} +(1.30161 - 2.70282i) q^{9} +(-0.820308 - 2.08017i) q^{10} +(-2.11209 + 1.01713i) q^{11} +(-0.00111695 + 0.00991320i) q^{12} +(1.37482 - 3.92901i) q^{13} +(0.627163 - 2.57034i) q^{14} +(0.0213265 + 0.00654043i) q^{15} +(0.222521 + 0.974928i) q^{16} +(0.513758 - 4.55973i) q^{17} +(2.12125 + 2.12125i) q^{18} +4.64712 q^{19} +(2.23437 - 0.0872390i) q^{20} +(0.0161465 + 0.0208788i) q^{21} +(-0.262473 - 2.32951i) q^{22} +(-5.83483 + 0.657428i) q^{23} +(-0.00898800 - 0.00432839i) q^{24} +(0.729144 - 4.94655i) q^{25} +(3.25445 + 2.59534i) q^{26} +(-0.0594782 + 0.00670159i) q^{27} +(2.21897 + 1.44090i) q^{28} +(3.13758 - 2.50214i) q^{29} +(-0.0132171 + 0.0179695i) q^{30} -1.74240i q^{31} +(-0.993712 - 0.111964i) q^{32} +(0.0198015 + 0.0124421i) q^{33} +(4.13417 + 1.99091i) q^{34} +(4.08128 - 4.28289i) q^{35} +(-2.70282 + 1.30161i) q^{36} +(-9.30588 - 1.04852i) q^{37} +(-1.53485 + 4.38634i) q^{38} +(-0.0404847 + 0.00924037i) q^{39} +(-0.655621 + 2.13779i) q^{40} +(-8.12845 - 1.85527i) q^{41} +(-0.0250400 + 0.00834458i) q^{42} +(5.13016 - 8.16461i) q^{43} +(2.28547 + 0.521644i) q^{44} +(1.74668 + 6.47658i) q^{45} +(1.30659 - 5.72454i) q^{46} +(3.03915 + 1.06344i) q^{47} +(0.00705405 - 0.00705405i) q^{48} +(6.86794 - 1.35329i) q^{49} +(4.42814 + 2.32197i) q^{50} +(-0.0412422 + 0.0198612i) q^{51} +(-3.52458 + 2.21464i) q^{52} +(-13.2719 + 1.49538i) q^{53} +(0.0133189 - 0.0583539i) q^{54} +(2.08839 - 4.80793i) q^{55} +(-2.09292 + 1.61855i) q^{56} +(-0.0246647 - 0.0392536i) q^{57} +(1.32545 + 3.78791i) q^{58} +(1.51549 + 6.63980i) q^{59} +(-0.0125958 - 0.0184103i) q^{60} +(1.88094 - 1.50000i) q^{61} +(1.64462 + 0.575478i) q^{62} +(-2.73293 + 7.45164i) q^{63} +(0.433884 - 0.900969i) q^{64} +(3.41462 + 8.65891i) q^{65} +(-0.0182840 + 0.0145810i) q^{66} +(-3.04233 + 3.04233i) q^{67} +(-3.24462 + 3.24462i) q^{68} +(0.0365217 + 0.0457967i) q^{69} +(2.69459 + 5.26680i) q^{70} +(0.989548 - 1.24085i) q^{71} +(-0.335882 - 2.98104i) q^{72} +(-2.37800 + 0.832097i) q^{73} +(4.06322 - 8.43736i) q^{74} +(-0.0456527 + 0.0200949i) q^{75} +(-3.63327 - 2.89743i) q^{76} +(5.30030 - 3.22108i) q^{77} +(0.00464942 - 0.0412647i) q^{78} -0.365145i q^{79} +(-1.80129 - 1.32490i) q^{80} +(-5.61085 - 7.03578i) q^{81} +(4.43581 - 7.05955i) q^{82} +(14.6831 - 5.13782i) q^{83} +(0.000393885 - 0.0263909i) q^{84} +(5.79364 + 8.46813i) q^{85} +(6.01205 + 7.53887i) q^{86} +(-0.0377880 - 0.0132226i) q^{87} +(-1.24722 + 1.98493i) q^{88} +(-8.11511 - 3.90803i) q^{89} +(-6.69003 - 0.490421i) q^{90} +(-2.61063 + 10.6993i) q^{91} +(4.97176 + 3.12396i) q^{92} +(-0.0147178 + 0.00924781i) q^{93} +(-2.00753 + 2.51737i) q^{94} +(-7.86527 + 6.79089i) q^{95} +(0.00432839 + 0.00898800i) q^{96} +(-6.12616 - 6.12616i) q^{97} +(-0.990993 + 6.92950i) q^{98} +7.03251i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 28 q^{6} + 8 q^{7}+O(q^{10}) $ 336 * q + 28 * q^6 + 8 * q^7	$ 336 q + 28 q^{6} + 8 q^{7} + 8 q^{11} + 44 q^{15} + 56 q^{16} + 28 q^{17} - 16 q^{21} - 20 q^{22} + 8 q^{23} - 8 q^{25} - 28 q^{26} - 8 q^{28} - 24 q^{30} + 8 q^{35} + 76 q^{36} - 24 q^{37} - 56 q^{41} - 112 q^{42} - 24 q^{43} + 112 q^{45} - 68 q^{46} - 84 q^{47} - 32 q^{50} - 80 q^{51} - 100 q^{53} + 84 q^{55} - 20 q^{56} + 92 q^{57} - 80 q^{58} - 112 q^{61} - 32 q^{67} + 52 q^{70} + 16 q^{71} - 84 q^{75} + 16 q^{77} - 80 q^{78} + 12 q^{81} + 140 q^{83} + 40 q^{85} - 8 q^{86} - 28 q^{87} - 8 q^{88} - 84 q^{90} + 124 q^{91} + 8 q^{92} + 20 q^{93} - 56 q^{95} - 32 q^{98}+O(q^{100}) $ 336 * q + 28 * q^6 + 8 * q^7 + 8 * q^11 + 44 * q^15 + 56 * q^16 + 28 * q^17 - 16 * q^21 - 20 * q^22 + 8 * q^23 - 8 * q^25 - 28 * q^26 - 8 * q^28 - 24 * q^30 + 8 * q^35 + 76 * q^36 - 24 * q^37 - 56 * q^41 - 112 * q^42 - 24 * q^43 + 112 * q^45 - 68 * q^46 - 84 * q^47 - 32 * q^50 - 80 * q^51 - 100 * q^53 + 84 * q^55 - 20 * q^56 + 92 * q^57 - 80 * q^58 - 112 * q^61 - 32 * q^67 + 52 * q^70 + 16 * q^71 - 84 * q^75 + 16 * q^77 - 80 * q^78 + 12 * q^81 + 140 * q^83 + 40 * q^85 - 8 * q^86 - 28 * q^87 - 8 * q^88 - 84 * q^90 + 124 * q^91 + 8 * q^92 + 20 * q^93 - 56 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.330279	+	0.943883i	−0.233543	+	0.667426i
$2$	−0.330279	+	0.943883i	−0.233543	+	0.667426i
$3$	−0.00530751	−	0.00844686i	−0.00306429	−	0.00487680i	0.845189	−	0.534468i	$-0.179488\pi$
$3$	−0.00530751	−	0.00844686i	−0.00306429	−	0.00487680i	−0.848253	+	0.529591i	$0.822345\pi$
$4$	−0.781831	−	0.623490i	−0.390916	−	0.311745i
$5$	−1.69250	+	1.46131i	−0.756911	+	0.653518i
$5$	−1.69250	+	1.46131i	−0.756911	+	0.653518i
$6$	0.00972581	−	0.00221985i	0.00397055	−	0.000906251i
$7$	−2.63324	+	0.256962i	−0.995272	+	0.0971225i
$7$	−2.63324	+	0.256962i	−0.995272	+	0.0971225i
$8$	0.846724	−	0.532032i	0.299362	−	0.188102i
$9$	1.30161	−	2.70282i	0.433869	−	0.900939i
$10$	−0.820308	−	2.08017i	−0.259404	−	0.657807i
$11$	−2.11209	+	1.01713i	−0.636821	+	0.306677i	−0.724295	−	0.689490i	$-0.757835\pi$
$11$	−2.11209	+	1.01713i	−0.636821	+	0.306677i	0.0874745	+	0.996167i	$0.472120\pi$
$12$	−0.00111695	+	0.00991320i	−0.000322436	+	0.00286169i
$13$	1.37482	−	3.92901i	0.381307	−	1.08971i	−0.580092	−	0.814551i	$-0.696983\pi$
$13$	1.37482	−	3.92901i	0.381307	−	1.08971i	0.961398	−	0.275161i	$-0.0887310\pi$
$14$	0.627163	−	2.57034i	0.167616	−	0.686953i
$15$	0.0213265	+	0.00654043i	0.00550647	+	0.00168873i
$16$	0.222521	+	0.974928i	0.0556302	+	0.243732i
$17$	0.513758	−	4.55973i	0.124605	−	1.10590i	−0.763356	−	0.645978i	$-0.776450\pi$
$17$	0.513758	−	4.55973i	0.124605	−	1.10590i	0.887961	−	0.459919i	$-0.152122\pi$
$18$	2.12125	+	2.12125i	0.499983	+	0.499983i
$19$	4.64712			1.06612			0.533061	−	0.846077i	$-0.321041\pi$
$19$	4.64712			1.06612			0.533061	+	0.846077i	$0.321041\pi$
$20$	2.23437	−	0.0872390i	0.499619	−	0.0195072i
$21$	0.0161465	+	0.0208788i	0.00352345	+	0.00455613i
$22$	−0.262473	−	2.32951i	−0.0559593	−	0.496653i
$23$	−5.83483	+	0.657428i	−1.21665	+	0.137083i	−0.696856	−	0.717211i	$-0.745419\pi$
$23$	−5.83483	+	0.657428i	−1.21665	+	0.137083i	−0.519790	+	0.854294i	$0.673990\pi$
$24$	−0.00898800	−	0.00432839i	−0.00183467	−	0.000883530i
$25$	0.729144	−	4.94655i	0.145829	−	0.989310i
$26$	3.25445	+	2.59534i	0.638251	+	0.508988i
$27$	−0.0594782	+	0.00670159i	−0.0114466	+	0.00128972i
$28$	2.21897	+	1.44090i	0.419345	+	0.272304i
$29$	3.13758	−	2.50214i	0.582634	−	0.464635i	−0.287274	−	0.957848i	$-0.592749\pi$
$29$	3.13758	−	2.50214i	0.582634	−	0.464635i	0.869909	+	0.493213i	$0.164178\pi$
$30$	−0.0132171	+	0.0179695i	−0.00241310	+	0.00328077i
$31$		−	1.74240i		−	0.312944i	−0.987682	−	0.156472i	$-0.949988\pi$
$31$		−	1.74240i		−	0.312944i	0.987682	−	0.156472i	$-0.0500121\pi$
$32$	−0.993712	−	0.111964i	−0.175665	−	0.0197927i
$33$	0.0198015	+	0.0124421i	0.00344701	+	0.00216590i
$34$	4.13417	+	1.99091i	0.709004	+	0.341439i
$35$	4.08128	−	4.28289i	0.689862	−	0.723941i
$36$	−2.70282	+	1.30161i	−0.450469	+	0.216935i
$37$	−9.30588	−	1.04852i	−1.52988	−	0.172376i	−0.693471	−	0.720485i	$-0.743919\pi$
$37$	−9.30588	−	1.04852i	−1.52988	−	0.172376i	−0.836407	+	0.548109i	$0.815348\pi$
$38$	−1.53485	+	4.38634i	−0.248985	+	0.711558i
$39$	−0.0404847	+	0.00924037i	−0.00648274	+	0.00147964i
$40$	−0.655621	+	2.13779i	−0.103663	+	0.338015i
$41$	−8.12845	−	1.85527i	−1.26945	−	0.289744i	−0.465824	−	0.884878i	$-0.654242\pi$
$41$	−8.12845	−	1.85527i	−1.26945	−	0.289744i	−0.803627	+	0.595134i	$0.797099\pi$
$42$	−0.0250400	+	0.00834458i	−0.00386376	+	0.00128760i
$43$	5.13016	−	8.16461i	0.782342	−	1.24509i	−0.182744	−	0.983160i	$-0.558498\pi$
$43$	5.13016	−	8.16461i	0.782342	−	1.24509i	0.965087	−	0.261930i	$-0.0843591\pi$
$44$	2.28547	+	0.521644i	0.344548	+	0.0786408i
$45$	1.74668	+	6.47658i	0.260379	+	0.965472i
$46$	1.30659	−	5.72454i	0.192646	−	0.844037i
$47$	3.03915	+	1.06344i	0.443305	+	0.155119i	0.542696	−	0.839929i	$-0.317404\pi$
$47$	3.03915	+	1.06344i	0.443305	+	0.155119i	−0.0993906	+	0.995048i	$0.531689\pi$
$48$	0.00705405	−	0.00705405i	0.00101816	−	0.00101816i
$49$	6.86794	−	1.35329i	0.981134	−	0.193327i
$50$	4.42814	+	2.32197i	0.626234	+	0.328376i
$51$	−0.0412422	+	0.0198612i	−0.00577506	+	0.00278112i
$52$	−3.52458	+	2.21464i	−0.488771	+	0.307115i
$53$	−13.2719	+	1.49538i	−1.82303	+	0.205406i	−0.956104	−	0.293027i	$-0.905338\pi$
$53$	−13.2719	+	1.49538i	−1.82303	+	0.205406i	−0.866928	+	0.498433i	$0.833909\pi$
$54$	0.0133189	−	0.0583539i	0.00181247	−	0.00794096i
$55$	2.08839	−	4.80793i	0.281598	−	0.648301i
$56$	−2.09292	+	1.61855i	−0.279678	+	0.216287i
$57$	−0.0246647	−	0.0392536i	−0.00326691	−	0.00519926i
$58$	1.32545	+	3.78791i	0.174040	+	0.497378i
$59$	1.51549	+	6.63980i	0.197300	+	0.864428i	0.972535	+	0.232756i	$0.0747742\pi$
$59$	1.51549	+	6.63980i	0.197300	+	0.864428i	−0.775235	+	0.631673i	$0.782369\pi$
$60$	−0.0125958	−	0.0184103i	−0.00162611	−	0.00237677i
$61$	1.88094	−	1.50000i	0.240830	−	0.192056i	−0.495635	−	0.868531i	$-0.665065\pi$
$61$	1.88094	−	1.50000i	0.240830	−	0.192056i	0.736466	+	0.676475i	$0.236493\pi$
$62$	1.64462	+	0.575478i	0.208867	+	0.0730858i
$63$	−2.73293	+	7.45164i	−0.344317	+	0.938818i
$64$	0.433884	−	0.900969i	0.0542355	−	0.112621i
$65$	3.41462	+	8.65891i	0.423531	+	1.07401i
$66$	−0.0182840	+	0.0145810i	−0.00225060	+	0.00179479i
$67$	−3.04233	+	3.04233i	−0.371680	+	0.371680i	−0.868089	−	0.496409i	$-0.834652\pi$
$67$	−3.04233	+	3.04233i	−0.371680	+	0.371680i	0.496409	+	0.868089i	$0.334652\pi$
$68$	−3.24462	+	3.24462i	−0.393468	+	0.393468i
$69$	0.0365217	+	0.0457967i	0.00439669	+	0.00551328i
$70$	2.69459	+	5.26680i	0.322065	+	0.629503i
$71$	0.989548	−	1.24085i	0.117438	−	0.147262i	−0.719638	−	0.694350i	$-0.755692\pi$
$71$	0.989548	−	1.24085i	0.117438	−	0.147262i	0.837075	+	0.547088i	$0.184264\pi$
$72$	−0.335882	−	2.98104i	−0.0395841	−	0.351319i
$73$	−2.37800	+	0.832097i	−0.278323	+	0.0973896i	−0.465831	−	0.884874i	$-0.654245\pi$
$73$	−2.37800	+	0.832097i	−0.278323	+	0.0973896i	0.187508	+	0.982263i	$0.439959\pi$
$74$	4.06322	−	8.43736i	0.472340	−	0.980824i
$75$	−0.0456527	+	0.0200949i	−0.00527153	+	0.00232036i
$76$	−3.63327	−	2.89743i	−0.416764	−	0.332358i
$77$	5.30030	−	3.22108i	0.604025	−	0.367076i
$78$	0.00464942	−	0.0412647i	0.000526443	−	0.00467231i
$79$		−	0.365145i		−	0.0410820i	−0.999789	−	0.0205410i	$-0.993461\pi$
$79$		−	0.365145i		−	0.0410820i	0.999789	−	0.0205410i	$-0.00653886\pi$
$80$	−1.80129	−	1.32490i	−0.201390	−	0.148128i
$81$	−5.61085	−	7.03578i	−0.623428	−	0.781754i
$82$	4.43581	−	7.05955i	0.489853	−	0.779597i
$83$	14.6831	−	5.13782i	1.61167	−	0.563949i	0.633865	−	0.773444i	$-0.281468\pi$
$83$	14.6831	−	5.13782i	1.61167	−	0.563949i	0.977810	+	0.209494i	$0.0671818\pi$
$84$	0.000393885	−	0.0263909i	4.29764e−5	−	0.00287948i
$85$	5.79364	+	8.46813i	0.628409	+	0.918497i
$86$	6.01205	+	7.53887i	0.648296	+	0.812938i
$87$	−0.0377880	−	0.0132226i	−0.00405129	−	0.00141761i
$88$	−1.24722	+	1.98493i	−0.132954	+	0.211594i
$89$	−8.11511	−	3.90803i	−0.860199	−	0.414250i	−0.0488461	−	0.998806i	$-0.515554\pi$
$89$	−8.11511	−	3.90803i	−0.860199	−	0.414250i	−0.811353	+	0.584556i	$0.801269\pi$
$90$	−6.69003	−	0.490421i	−0.705191	−	0.0516949i
$91$	−2.61063	+	10.6993i	−0.273669	+	1.12159i
$92$	4.97176	+	3.12396i	0.518341	+	0.325695i
$93$	−0.0147178	+	0.00924781i	−0.00152616	+	0.000958953i
$94$	−2.00753	+	2.51737i	−0.207061	+	0.259647i
$95$	−7.86527	+	6.79089i	−0.806960	+	0.696730i
$96$	0.00432839	+	0.00898800i	0.000441765	+	0.000917334i
$97$	−6.12616	−	6.12616i	−0.622017	−	0.622017i	0.324030	−	0.946047i	$-0.394962\pi$
$97$	−6.12616	−	6.12616i	−0.622017	−	0.622017i	−0.946047	+	0.324030i	$0.894962\pi$
$98$	−0.990993	+	6.92950i	−0.100105	+	0.699985i
$99$			7.03251i			0.706794i
$100$	−3.65419	+	3.41275i	−0.365419	+	0.341275i
$101$	9.18757	+	2.09700i	0.914198	+	0.208660i	0.653646	−	0.756800i	$-0.273238\pi$
$101$	9.18757	+	2.09700i	0.914198	+	0.208660i	0.260552	+	0.965460i	$0.416096\pi$
$102$	−0.00512522	−	0.0454876i	−0.000507472	−	0.00450394i
$103$	1.79135	+	2.85091i	0.176507	+	0.280909i	0.923247	−	0.384207i	$-0.125525\pi$
$103$	1.79135	+	2.85091i	0.176507	+	0.280909i	−0.746740	+	0.665116i	$0.768382\pi$
$104$	−0.926266	−	4.05824i	−0.0908279	−	0.397943i
$105$	−0.0578384	−	0.0117424i	−0.00564445	−	0.00114594i
$106$	2.97196	−	13.0210i	0.288662	−	1.26471i
$107$	−19.2000	+	6.71839i	−1.85614	+	0.649491i	−0.867864	+	0.496802i	$0.834508\pi$
$107$	−19.2000	+	6.71839i	−1.85614	+	0.649491i	−0.988274	+	0.152689i	$0.951207\pi$
$108$	0.0506803	+	0.0318446i	0.00487672	+	0.00306424i
$109$	−1.53344	−	3.18422i	−0.146877	−	0.304993i	0.814531	−	0.580120i	$-0.196994\pi$
$109$	−1.53344	−	3.18422i	−0.146877	−	0.304993i	−0.961408	+	0.275127i	$0.911280\pi$
$110$	3.84837	+	3.55915i	0.366928	+	0.339352i
$111$	0.0405344	+	0.0841705i	0.00384735	+	0.00798911i
$112$	−0.836471	−	2.51004i	−0.0790391	−	0.237177i
$113$	4.66544	+	13.3331i	0.438888	+	1.25427i	0.924864	+	0.380298i	$0.124178\pi$
$113$	4.66544	+	13.3331i	0.438888	+	1.25427i	−0.485976	+	0.873972i	$0.661536\pi$
$114$	0.0451970	−	0.0103159i	0.00423309	−	0.000966175i
$115$	8.91478	−	9.63920i	0.831307	−	0.898860i
$116$	−4.01312			−0.372609
$117$	−8.82992	−	8.82992i	−0.816327	−	0.816327i
$118$	−6.76773	−	0.762540i	−0.623020	−	0.0701975i
$119$	−0.181174	+	12.1389i	−0.0166081	+	1.11277i
$120$	0.0215374	−	0.00580843i	0.00196608	−	0.000530235i
$121$	−3.43200	+	4.30359i	−0.312000	+	0.391236i
$122$	0.794592	+	2.27081i	0.0719389	+	0.205590i
$123$	0.0274707	+	0.0785067i	0.00247695	+	0.00707871i
$124$	−1.08637	+	1.36226i	−0.0975587	+	0.122335i
$125$	5.99436	+	9.43756i	0.536152	+	0.844121i
$126$	−6.13085	−	5.04069i	−0.546179	−	0.449060i
$127$	−20.9736	−	2.36316i	−1.86111	−	0.209697i	−0.891275	−	0.453463i	$-0.850188\pi$
$127$	−20.9736	−	2.36316i	−1.86111	−	0.209697i	−0.969834	+	0.243766i	$0.921617\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.0961937			−0.00846938
$130$	−9.30078	+	0.363141i	−0.815732	+	0.0318496i
$131$	1.67579	−	0.382488i	0.146415	−	0.0334182i	−0.148685	−	0.988885i	$-0.547504\pi$
$131$	1.67579	−	0.382488i	0.146415	−	0.0334182i	0.295100	+	0.955466i	$0.404647\pi$
$132$	−0.00772392	−	0.0220737i	−0.000672281	−	0.00192127i
$133$	−12.2370	+	1.19413i	−1.06108	+	0.103544i
$134$	−1.86679	−	3.87643i	−0.161266	−	0.334872i
$135$	0.0908741	−	0.0982586i	0.00782119	−	0.00845675i
$136$	−1.99091	−	4.13417i	−0.170719	−	0.354502i
$137$	4.00951	+	2.51934i	0.342555	+	0.215242i	0.692311	−	0.721599i	$-0.256593\pi$
$137$	4.00951	+	2.51934i	0.342555	+	0.215242i	−0.349756	+	0.936841i	$0.613735\pi$
$138$	−0.0552891	+	0.0193465i	−0.00470652	+	0.00164688i
$139$	3.80284	−	16.6614i	0.322553	−	1.41320i	−0.510440	−	0.859914i	$-0.670517\pi$
$139$	3.80284	−	16.6614i	0.322553	−	1.41320i	0.832993	−	0.553284i	$-0.186626\pi$
$140$	−5.86121	+	0.803868i	−0.495363	+	0.0679393i
$141$	−0.00714756	−	0.0313155i	−0.000601933	−	0.00263724i
$142$	0.844394	+	1.34385i	0.0708600	+	0.112773i
$143$	1.09257	+	9.69682i	0.0913652	+	0.810889i
$144$	2.92469	+	0.667541i	0.243724	+	0.0556284i
$145$	−1.65397	+	8.81986i	−0.137355	+	0.732449i
$146$		−	2.51938i		−	0.208505i
$147$	−0.0478827	−	0.0508299i	−0.00394930	−	0.00419238i
$148$	6.62189	+	6.62189i	0.544316	+	0.544316i
$149$	−1.68092	−	3.49047i	−0.137706	−	0.285950i	0.820699	−	0.571361i	$-0.193584\pi$
$149$	−1.68092	−	3.49047i	−0.137706	−	0.285950i	−0.958405	+	0.285411i	$0.907870\pi$
$150$	−0.00388909	−	0.0497278i	−0.000317543	−	0.00406026i
$151$	−4.43545	+	5.56188i	−0.360952	+	0.452619i	−0.928837	−	0.370489i	$-0.879190\pi$
$151$	−4.43545	+	5.56188i	−0.360952	+	0.452619i	0.567885	+	0.823108i	$0.307762\pi$
$152$	3.93483	−	2.47242i	0.319157	−	0.200540i
$153$	−11.6554	−	7.32358i	−0.942284	−	0.592076i
$154$	1.28975	+	6.06672i	0.103931	+	0.488870i
$155$	2.54619	+	2.94902i	0.204515	+	0.236871i
$156$	0.0374135	+	0.0180174i	0.00299548	+	0.00144255i
$157$	2.74572	−	4.36979i	0.219132	−	0.348747i	−0.719008	−	0.695001i	$-0.755404\pi$
$157$	2.74572	−	4.36979i	0.219132	−	0.348747i	0.938141	+	0.346254i	$0.112547\pi$
$158$	0.344654	+	0.120600i	0.0274192	+	0.00959440i
$159$	0.0830719	+	0.104169i	0.00658803	+	0.00826113i
$160$	1.84548	−	1.26262i	0.145898	−	0.0998190i
$161$	15.1956	−	3.23050i	1.19758	−	0.254599i
$162$	8.49410	−	2.97222i	0.667360	−	0.233519i
$163$	−2.68010	+	4.26535i	−0.209921	+	0.334088i	−0.935044	−	0.354532i	$-0.884640\pi$
$163$	−2.68010	+	4.26535i	−0.209921	+	0.334088i	0.725123	+	0.688620i	$0.241783\pi$
$164$	5.19834	+	6.51851i	0.405922	+	0.509010i
$165$	−0.0516960	+	0.00787783i	−0.00402453	+	0.000613288i
$166$			15.5560i			1.20738i
$167$	−1.77835	+	15.7833i	−0.137613	+	1.22135i	0.715121	+	0.699001i	$0.246372\pi$
$167$	−1.77835	+	15.7833i	−0.137613	+	1.22135i	−0.852734	+	0.522346i	$0.825057\pi$
$168$	0.0247798	+	0.00908814i	0.00191180	+	0.000701165i
$169$	−3.38320	−	2.69801i	−0.260246	−	0.207539i
$170$	−9.90644	+	2.67168i	−0.759790	+	0.204908i
$171$	6.04873	−	12.5603i	0.462558	−	0.960511i
$172$	−9.10147	+	3.18474i	−0.693981	+	0.242834i
$173$	−0.191296	−	1.69780i	−0.0145440	−	0.129081i	0.984342	−	0.176269i	$-0.0564028\pi$
$173$	−0.191296	−	1.69780i	−0.0145440	−	0.129081i	−0.998886	+	0.0471874i	$0.984974\pi$
$174$	0.0249611	−	0.0313003i	0.00189230	−	0.00237287i
$175$	−0.648940	+	13.2128i	−0.0490552	+	0.998796i
$176$	−1.46161	−	1.83281i	−0.110173	−	0.138153i
$177$	0.0480420	−	0.0480420i	0.00361106	−	0.00361106i
$178$	6.36897	−	6.36897i	0.477375	−	0.477375i
$179$	14.3689	−	11.4588i	1.07398	−	0.856471i	0.0838307	−	0.996480i	$-0.473285\pi$
$179$	14.3689	−	11.4588i	1.07398	−	0.856471i	0.990150	+	0.140009i	$0.0447131\pi$
$180$	2.67248	−	6.15263i	0.199195	−	0.458590i
$181$	10.0100	−	20.7860i	0.744039	−	1.54501i	−0.0916374	−	0.995792i	$-0.529210\pi$
$181$	10.0100	−	20.7860i	0.744039	−	1.54501i	0.835677	−	0.549221i	$-0.185076\pi$
$182$	−9.23667	−	5.99789i	−0.684668	−	0.444593i
$183$	−0.0226535	−	0.00792679i	−0.00167459	−	0.000585965i
$184$	−4.59072	+	3.66098i	−0.338432	+	0.269891i
$185$	17.2825	−	11.8242i	1.27063	−	0.869329i
$186$	−0.00386787	−	0.0169462i	−0.000283606	−	0.00124256i
$187$	3.55274	+	10.1531i	0.259802	+	0.742472i
$188$	−1.71306	−	2.72631i	−0.124937	−	0.198837i
$189$	0.154899	−	0.0329305i	0.0112672	−	0.00239534i
$190$	−3.81207	−	9.66679i	−0.276557	−	0.701303i
$191$	−0.0332496	+	0.145676i	−0.00240585	+	0.0105407i	−0.976117	−	0.217247i	$-0.930292\pi$
$191$	−0.0332496	+	0.145676i	−0.00240585	+	0.0105407i	0.973711	+	0.227788i	$0.0731493\pi$
$192$	−0.00991320	+	0.00111695i	−0.000715424	+	8.06089e-5i
$193$	20.2026	−	12.6941i	1.45421	−	0.913742i	0.454476	−	0.890759i	$-0.349827\pi$
$193$	20.2026	−	12.6941i	1.45421	−	0.913742i	0.999736	−	0.0229824i	$-0.00731617\pi$
$194$	7.80572	−	3.75904i	0.560418	−	0.269883i
$195$	0.0550175	−	0.0748001i	0.00393988	−	0.00535654i
$196$	−6.21333	−	3.22405i	−0.443809	−	0.230289i
$197$	8.34328	−	8.34328i	0.594434	−	0.594434i	−0.344392	−	0.938826i	$-0.611915\pi$
$197$	8.34328	−	8.34328i	0.594434	−	0.594434i	0.938826	+	0.344392i	$0.111915\pi$
$198$	−6.63787	−	2.32269i	−0.471733	−	0.165066i
$199$	−1.74852	+	7.66077i	−0.123949	+	0.543058i	0.874378	+	0.485245i	$0.161270\pi$
$199$	−1.74852	+	7.66077i	−0.123949	+	0.543058i	−0.998327	+	0.0578125i	$0.981587\pi$
$200$	−2.01434	−	4.57629i	−0.142435	−	0.323593i
$201$	0.0418454	+	0.00955093i	0.00295155	+	0.000673671i
$202$	−5.01379	+	7.97940i	−0.352769	+	0.561429i
$203$	−7.61906	+	7.39498i	−0.534753	+	0.519026i
$204$	0.0446277	+	0.0101860i	0.00312456	+	0.000713161i
$205$	16.4686	−	8.73814i	1.15021	−	0.610298i
$206$	−3.28257	+	0.749226i	−0.228708	+	0.0522010i
$207$	−5.81776	+	16.6262i	−0.404362	+	1.15560i
$208$	4.13643	+	0.466064i	0.286810	+	0.0323157i
$209$	−9.81516	+	4.72673i	−0.678929	+	0.326955i
$210$	0.0301863	−	0.0507145i	0.00208305	−	0.00349963i
$211$	6.21876	+	2.99480i	0.428117	+	0.206170i	0.635518	−	0.772086i	$-0.280786\pi$
$211$	6.21876	+	2.99480i	0.428117	+	0.206170i	−0.207402	+	0.978256i	$0.566501\pi$
$212$	11.3087	+	7.10574i	0.776686	+	0.488024i
$213$	−0.0157334	−	0.00177272i	−0.00107803	−	0.000121465i
$214$		−	20.3415i		−	1.39052i
$215$	3.24820	+	21.3154i	0.221525	+	1.45370i
$216$	−0.0467962	+	0.0373187i	−0.00318408	+	0.00253922i
$217$	0.447730	+	4.58816i	0.0303939	+	0.311465i
$218$	3.51200	−	0.395707i	0.237862	−	0.0268007i
$219$	0.0196499	+	0.0156702i	0.00132781	+	0.00105890i
$220$	−4.63046	+	2.45690i	−0.312185	+	0.165644i
$221$	−17.2089	−	8.28738i	−1.15760	−	0.557469i
$222$	−0.0928348	+	0.0104600i	−0.00623067	+	0.000702027i
$223$	−1.45213	−	12.8880i	−0.0972420	−	0.863046i	−0.943748	−	0.330667i	$-0.892726\pi$
$223$	−1.45213	−	12.8880i	−0.0972420	−	0.863046i	0.846506	−	0.532380i	$-0.178702\pi$
$224$	2.64546	+	0.0394835i	0.176757	+	0.00263810i
$225$	−12.4206	−	8.40921i	−0.828037	−	0.560614i
$226$	−14.1258			−0.939631
$227$	14.5561	+	14.5561i	0.966121	+	0.966121i	0.999445	−	0.0333234i	$-0.0106091\pi$
$227$	14.5561	+	14.5561i	0.966121	+	0.966121i	−0.0333234	+	0.999445i	$0.510609\pi$
$228$	−0.00519060	+	0.0460678i	−0.000343756	+	0.00305092i
$229$	0.914454	+	4.00649i	0.0604288	+	0.264756i	0.996113	−	0.0880821i	$-0.0280738\pi$
$229$	0.914454	+	4.00649i	0.0604288	+	0.264756i	−0.935684	+	0.352838i	$0.885217\pi$
$230$	6.15392	+	11.5981i	0.405777	+	0.764758i
$231$	−0.0553394	−	0.0276749i	−0.00364107	−	0.00182088i
$232$	1.32545	−	3.78791i	0.0870200	−	0.248689i
$233$	1.65379	−	14.6778i	0.108344	−	0.961577i	−0.815487	−	0.578775i	$-0.803531\pi$
$233$	1.65379	−	14.6778i	0.108344	−	0.961577i	0.923831	−	0.382801i	$-0.125041\pi$
$234$	11.2508	−	5.41808i	0.735485	−	0.354191i
$235$	−6.69779	+	2.64125i	−0.436916	+	0.172296i
$236$	2.95499	−	6.13610i	0.192353	−	0.399426i
$237$	−0.00308433	+	0.00193801i	−0.000200349	+	0.000125887i
$238$	−11.3979	−	4.18023i	−0.738814	−	0.270964i
$239$	9.67209	−	2.20759i	0.625636	−	0.142797i	0.102063	−	0.994778i	$-0.467456\pi$
$239$	9.67209	−	2.20759i	0.625636	−	0.142797i	0.523573	+	0.851981i	$0.324599\pi$
$240$	−0.00163086	+	0.0222472i	−0.000105271	+	0.00143605i
$241$	22.8830	+	18.2486i	1.47402	+	1.17550i	0.945080	+	0.326840i	$0.105984\pi$
$241$	22.8830	+	18.2486i	1.47402	+	1.17550i	0.528945	+	0.848656i	$0.322588\pi$
$242$	−2.92857	−	4.66079i	−0.188256	−	0.299607i
$243$	−0.0889567	+	0.254224i	−0.00570658	+	0.0163085i
$244$	−2.40582			−0.154017
$245$	−9.64645	+	12.3266i	−0.616289	+	0.787520i
$246$	−0.0831742			−0.00530299
$247$	6.38896	−	18.2586i	0.406520	−	1.16177i
$248$	−0.927012	−	1.47533i	−0.0588653	−	0.0936837i
$249$	−0.121329	−	0.0967566i	−0.00768891	−	0.00613170i
$250$	−10.8878	+	2.54095i	−0.688603	+	0.160704i
$251$	−0.825431	+	0.188399i	−0.0521008	+	0.0118917i	−0.248492	−	0.968634i	$-0.579935\pi$
$251$	−0.825431	+	0.188399i	−0.0521008	+	0.0118917i	0.196391	+	0.980526i	$0.437078\pi$
$252$	6.78271	−	4.12197i	0.427271	−	0.259660i
$253$	11.6550	−	7.32334i	0.732745	−	0.460414i
$254$	9.15770	−	19.0162i	0.574605	−	1.19318i
$255$	0.0407792	−	0.0938828i	0.00255369	−	0.00587917i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	2.50434	−	22.2266i	0.156217	−	1.38646i	−0.633858	−	0.773449i	$-0.718530\pi$
$257$	2.50434	−	22.2266i	0.156217	−	1.38646i	0.790075	−	0.613011i	$-0.210042\pi$
$258$	0.0317708	−	0.0907956i	0.00197796	−	0.00565269i
$259$	24.7741	+	0.369754i	1.53939	+	0.0229754i
$260$	2.72909	−	8.89879i	0.169251	−	0.551879i
$261$	−2.67892	−	11.7371i	−0.165821	−	0.726509i
$262$	−0.192454	+	1.70808i	−0.0118899	+	0.105525i
$263$	7.01908	+	7.01908i	0.432815	+	0.432815i	0.889585	−	0.456770i	$-0.150994\pi$
$263$	7.01908	+	7.01908i	0.432815	+	0.432815i	−0.456770	+	0.889585i	$0.650994\pi$
$264$	0.0233861			0.00143931
$265$	20.2775	−	21.9253i	1.24564	−	1.34686i
$266$	2.91450	−	11.9447i	0.178700	−	0.732376i
$267$	0.0100605	+	0.0892891i	0.000615690	+	0.00546440i
$268$	4.27545	−	0.481728i	0.261165	−	0.0294262i
$269$	−13.7340	−	6.61397i	−0.837379	−	0.403261i	−0.0345017	−	0.999405i	$-0.510984\pi$
$269$	−13.7340	−	6.61397i	−0.837379	−	0.403261i	−0.802877	+	0.596144i	$0.796699\pi$
$270$	0.0627309	+	0.118227i	0.00381768	+	0.00719508i
$271$	−10.0046	−	7.97841i	−0.607737	−	0.484654i	0.270603	−	0.962691i	$-0.412777\pi$
$271$	−10.0046	−	7.97841i	−0.607737	−	0.484654i	−0.878340	+	0.478037i	$0.841348\pi$
$272$	4.55973	−	0.513758i	0.276474	−	0.0311512i
$273$	0.104232	−	0.0347352i	0.00630839	−	0.00210227i
$274$	−3.70222	+	2.95242i	−0.223659	+	0.178362i
$275$	3.49127	+	11.1892i	0.210531	+	0.674735i
$276$		−	0.0585762i		−	0.00352587i
$277$	14.9718	+	1.68692i	0.899569	+	0.101357i	0.549623	−	0.835413i	$-0.314771\pi$
$277$	14.9718	+	1.68692i	0.899569	+	0.101357i	0.349946	+	0.936770i	$0.386200\pi$
$278$	14.4704	+	9.09234i	0.867875	+	0.545322i
$279$	−4.70939	−	2.26792i	−0.281944	−	0.135777i
$280$	1.17708	−	5.79780i	0.0703438	−	0.346485i
$281$	−23.9308	+	11.5245i	−1.42759	+	0.687492i	−0.978548	−	0.206018i	$-0.933949\pi$
$281$	−23.9308	+	11.5245i	−1.42759	+	0.687492i	−0.449043	+	0.893510i	$0.648235\pi$
$282$	0.0319189	+	0.00359639i	0.00190074	+	0.000214162i
$283$	5.62842	−	16.0851i	0.334575	−	0.956160i	−0.646565	−	0.762859i	$-0.723795\pi$
$283$	5.62842	−	16.0851i	0.334575	−	0.956160i	0.981140	−	0.193301i	$-0.0619194\pi$
$284$	−1.54732	+	0.353166i	−0.0918165	+	0.0209565i
$285$	0.0991067	+	0.0303941i	0.00587057	+	0.00180039i
$286$	−9.51352	−	2.17140i	−0.562546	−	0.128397i
$287$	21.8809	+	2.79666i	1.29159	+	0.165082i
$288$	−1.59604	+	2.54009i	−0.0940478	+	0.149676i
$289$	−3.95343	−	0.902345i	−0.232555	−	0.0530791i
$290$	−7.77865	−	4.47417i	−0.456778	−	0.262732i
$291$	−0.0192321	+	0.0842615i	−0.00112741	+	0.00493950i
$292$	2.37800	+	0.832097i	0.139162	+	0.0486948i
$293$	7.00381	−	7.00381i	0.409167	−	0.409167i	−0.472281	−	0.881448i	$-0.656569\pi$
$293$	7.00381	−	7.00381i	0.409167	−	0.409167i	0.881448	+	0.472281i	$0.156569\pi$
$294$	0.0637922	−	0.0284076i	0.00372044	−	0.00165677i
$295$	−12.2678	−	9.02329i	−0.714258	−	0.525356i
$296$	−8.43736	+	4.06322i	−0.490412	+	0.236170i
$297$	0.118807	−	0.0746515i	0.00689390	−	0.00433172i
$298$	3.84976	−	0.433764i	0.223011	−	0.0251273i
$299$	−5.43881	+	23.8290i	−0.314534	+	1.37807i
$300$	0.0482217	+	0.0127532i	0.00278408	+	0.000736306i
$301$	−11.4110	+	22.8177i	−0.657718	+	1.31519i
$302$	−3.78483	−	6.02352i	−0.217792	−	0.346614i
$303$	−0.0310501	−	0.0887360i	−0.00178378	−	0.00509775i
$304$	1.03408	+	4.53061i	0.0593087	+	0.259848i
$305$	−0.991537	+	5.28741i	−0.0567753	+	0.302756i
$306$	10.7621	−	8.58252i	0.615231	−	0.490630i
$307$	−14.2792	−	4.99651i	−0.814957	−	0.285166i	−0.109562	−	0.993980i	$-0.534945\pi$
$307$	−14.2792	−	4.99651i	−0.814957	−	0.285166i	−0.705395	+	0.708814i	$0.749230\pi$
$308$	−6.15225	−	0.786337i	−0.350557	−	0.0448057i
$309$	0.0145737	−	0.0302625i	0.000829066	−	0.00172157i
$310$	−3.62448	+	1.42930i	−0.205857	+	0.0811790i
$311$	5.89697	−	4.70268i	0.334387	−	0.266664i	−0.441873	−	0.897077i	$-0.645686\pi$
$311$	5.89697	−	4.70268i	0.334387	−	0.266664i	0.776260	+	0.630413i	$0.217114\pi$
$312$	−0.0293632	+	0.0293632i	−0.00166236	+	0.00166236i
$313$	1.54874	−	1.54874i	0.0875397	−	0.0875397i	−0.661981	−	0.749521i	$-0.730284\pi$
$313$	1.54874	−	1.54874i	0.0875397	−	0.0875397i	0.749521	+	0.661981i	$0.230284\pi$
$314$	3.21772	+	4.03489i	0.181586	+	0.227702i
$315$	−6.26366	−	16.6056i	−0.352917	−	0.935619i
$316$	−0.227664	+	0.285482i	−0.0128071	+	0.0160596i
$317$	1.07428	+	9.53448i	0.0603375	+	0.535510i	0.987128	+	0.159932i	$0.0511274\pi$
$317$	1.07428	+	9.53448i	0.0603375	+	0.535510i	−0.926791	+	0.375578i	$0.877444\pi$
$318$	−0.125760	+	0.0440054i	−0.00705228	+	0.00246770i
$319$	−4.08187	+	8.47608i	−0.228541	+	0.474570i
$320$	0.582245	+	2.15893i	0.0325485	+	0.120688i
$321$	0.158654	+	0.126522i	0.00885519	+	0.00706178i
$322$	−1.96958	+	15.4098i	−0.109760	+	0.858757i
$323$	2.38750	−	21.1896i	0.132844	−	1.17902i
$324$			8.99910i			0.499950i
$325$	−18.4326	−	9.66544i	−1.02246	−	0.536142i
$326$	−3.14081	−	3.93846i	−0.173954	−	0.218131i
$327$	−0.0187579	+	0.0298531i	−0.00103732	+	0.00165088i
$328$	−7.86961	+	2.75370i	−0.434527	+	0.152047i
$329$	−8.27608	−	2.01936i	−0.456275	−	0.111331i
$330$	0.00963836	−	0.0513969i	0.000530574	−	0.00282931i
$331$	−6.04348	−	7.57829i	−0.332180	−	0.416540i	0.587491	−	0.809231i	$-0.300116\pi$
$331$	−6.04348	−	7.57829i	−0.332180	−	0.416540i	−0.919671	+	0.392690i	$0.871544\pi$
$332$	−14.6831	−	5.13782i	−0.805837	−	0.281975i
$333$	−14.9466	+	23.7873i	−0.819067	+	1.30354i
$334$	−14.3102	−	6.89144i	−0.783021	−	0.377083i
$335$	0.703370	−	9.59495i	0.0384292	−	0.524228i
$336$	−0.0167624	+	0.0203876i	−0.000914464	+	0.00111224i
$337$	11.3400	+	7.12538i	0.617728	+	0.388144i	0.804237	−	0.594309i	$-0.202574\pi$
$337$	11.3400	+	7.12538i	0.617728	+	0.388144i	−0.186509	+	0.982453i	$0.559717\pi$
$338$	3.66400	−	2.30225i	0.199296	−	0.125226i
$339$	0.0878607	−	0.110174i	0.00477194	−	0.00598382i
$340$	0.750138	−	10.2329i	0.0406819	−	0.554958i
$341$	1.77225	+	3.68011i	0.0959726	+	0.199289i
$342$	9.85771	+	9.85771i	0.533044	+	0.533044i
$343$	−17.7372	+	5.32833i	−0.957720	+	0.287703i
$344$		−	9.64258i		−	0.519893i
$345$	−0.128736	−	0.0241417i	−0.00693093	−	0.00129974i
$346$	1.66571	+	0.380187i	0.0895489	+	0.0204390i
$347$	−0.0825059	−	0.732260i	−0.00442915	−	0.0393098i	0.991303	−	0.131597i	$-0.0420106\pi$
$347$	−0.0825059	−	0.732260i	−0.00442915	−	0.0393098i	−0.995732	+	0.0922877i	$0.970582\pi$
$348$	0.0212997	+	0.0338982i	0.00114178	+	0.00181714i
$349$	6.51287	+	28.5347i	0.348626	+	1.52743i	0.780303	+	0.625402i	$0.215065\pi$
$349$	6.51287	+	28.5347i	0.348626	+	1.52743i	−0.431677	+	0.902028i	$0.642078\pi$
$350$	−12.2570	−	4.97644i	−0.655166	−	0.266002i
$351$	−0.0554413	+	0.242904i	−0.00295924	+	0.0129653i
$352$	2.21270	−	0.774256i	0.117937	−	0.0412680i
$353$	−10.4698	−	6.57858i	−0.557249	−	0.350143i	0.223778	−	0.974640i	$-0.428161\pi$
$353$	−10.4698	−	6.57858i	−0.557249	−	0.350143i	−0.781027	+	0.624497i	$0.785304\pi$
$354$	0.0294788	+	0.0612133i	0.00156678	+	0.00325345i
$355$	0.138458	+	3.54619i	0.00734859	+	0.188212i
$356$	3.90803	+	8.11511i	0.207125	+	0.430100i
$357$	0.103497	−	0.0628970i	0.00547765	−	0.00332886i
$358$	6.07003	+	17.3472i	0.320811	+	0.916826i
$359$	−19.3707	+	4.42125i	−1.02235	+	0.233344i	−0.700656	−	0.713500i	$-0.747109\pi$
$359$	−19.3707	+	4.42125i	−1.02235	+	0.233344i	−0.321693	+	0.946844i	$0.604252\pi$
$360$	4.92470	+	4.55459i	0.259555	+	0.240048i
$361$	2.59573			0.136618
$362$	16.3135	+	16.3135i	0.857418	+	0.857418i
$363$	0.0545672	+	0.00614825i	0.00286404	+	0.000322699i
$364$	8.71199	−	6.73736i	0.456632	−	0.353134i
$365$	2.80882	−	4.88332i	0.147020	−	0.255605i
$366$	0.0149639	−	0.0187642i	0.000782177	−	0.000980819i
$367$	6.69274	+	19.1267i	0.349358	+	0.998408i	0.975748	+	0.218898i	$0.0702461\pi$
$367$	6.69274	+	19.1267i	0.349358	+	0.998408i	−0.626390	+	0.779510i	$0.715468\pi$
$368$	−1.93932	−	5.54225i	−0.101094	−	0.288910i
$369$	−15.5945	+	19.5549i	−0.811817	+	1.01799i
$370$	5.45259	+	20.2179i	0.283467	+	1.05108i
$371$	34.5638	−	7.34807i	1.79446	−	0.381493i
$372$	0.0172728	+	0.00194617i	0.000895551	+	0.000100904i
$373$	−18.2455	−	18.2455i	−0.944718	−	0.944718i	0.0538318	−	0.998550i	$-0.482857\pi$
$373$	−18.2455	−	18.2455i	−0.944718	−	0.944718i	−0.998550	+	0.0538318i	$0.982857\pi$
$374$	−10.7568			−0.556220
$375$	0.0479026	−	0.100724i	0.00247368	−	0.00520134i
$376$	3.13911	−	0.716481i	0.161887	−	0.0369497i
$377$	−5.51732	−	15.7676i	−0.284156	−	0.812072i
$378$	−0.0200772	+	0.157082i	−0.00103266	+	0.00807945i
$379$	−10.5487	−	21.9047i	−0.541853	−	1.12517i	−0.974662	−	0.223683i	$-0.928192\pi$
$379$	−10.5487	−	21.9047i	−0.541853	−	1.12517i	0.432809	−	0.901486i	$-0.357522\pi$
$380$	10.3834	−	0.405410i	0.532655	−	0.0207971i
$381$	0.0913566	+	0.189704i	0.00468034	+	0.00971882i
$382$	−0.126519	−	0.0794974i	−0.00647329	−	0.00406744i
$383$	36.4927	−	12.7694i	1.86469	−	0.652484i	0.880863	−	0.473371i	$-0.156963\pi$
$383$	36.4927	−	12.7694i	1.86469	−	0.652484i	0.983829	−	0.179112i	$-0.0573226\pi$
$384$	0.00221985	−	0.00972581i	0.000113281	−	0.000496318i
$385$	−4.26377	+	13.1971i	−0.217302	+	0.672585i
$386$	5.30927	+	23.2614i	0.270235	+	1.18398i
$387$	−15.3900	−	24.4930i	−0.782317	−	1.24505i
$388$	0.970026	+	8.60922i	0.0492456	+	0.437067i
$389$	13.1686	+	3.00565i	0.667675	+	0.152392i	0.542906	−	0.839793i	$-0.317324\pi$
$389$	13.1686	+	3.00565i	0.667675	+	0.152392i	0.124769	+	0.992186i	$0.460181\pi$
$390$	0.0524314	+	0.0766350i	0.00265497	+	0.00388056i
$391$			26.9430i			1.36257i
$392$	5.09526	−	4.79983i	0.257350	−	0.242428i
$393$	−0.0121251	−	0.0121251i	−0.000611631	−	0.000611631i
$394$	5.11947	+	10.6307i	0.257915	+	0.535567i
$395$	0.533590	+	0.618009i	0.0268478	+	0.0310954i
$396$	4.38470	−	5.49824i	0.220339	−	0.276297i
$397$	7.43919	−	4.67435i	0.373362	−	0.234599i	−0.332259	−	0.943188i	$-0.607811\pi$
$397$	7.43919	−	4.67435i	0.373362	−	0.234599i	0.705621	+	0.708589i	$0.250668\pi$
$398$	−6.65338	−	4.18059i	−0.333504	−	0.209554i
$399$	0.0750347	+	0.0970263i	0.00375643	+	0.00485739i
$400$	4.98478	−	0.389848i	0.249239	−	0.0194924i
$401$	7.91140	+	3.80993i	0.395076	+	0.190259i	0.620865	−	0.783918i	$-0.286782\pi$
$401$	7.91140	+	3.80993i	0.395076	+	0.190259i	−0.225789	+	0.974176i	$0.572496\pi$
$402$	−0.0228356	+	0.0363427i	−0.00113894	+	0.00181261i
$403$	−6.84591	−	2.39549i	−0.341019	−	0.119328i
$404$	−5.87567	−	7.36786i	−0.292326	−	0.366565i
$405$	19.7779	+	3.70890i	0.982769	+	0.184297i
$406$	−4.46358	−	9.63391i	−0.221524	−	0.478123i
$407$	20.7214	−	7.25073i	1.02712	−	0.359405i
$408$	−0.0243540	+	0.0387591i	−0.00120570	+	0.00191886i
$409$	2.86450	+	3.59197i	0.141640	+	0.177611i	0.847592	−	0.530649i	$-0.178052\pi$
$409$	2.86450	+	3.59197i	0.141640	+	0.177611i	−0.705951	+	0.708260i	$0.749480\pi$
$410$	2.80857	+	18.4304i	0.138705	+	0.910214i
$411$		−	0.0472392i		−	0.00233014i
$412$	0.376983	−	3.34582i	0.0185726	−	0.164837i
$413$	−5.69683	−	17.0948i	−0.280323	−	0.841179i
$414$	−13.7717	−	10.9826i	−0.676843	−	0.539764i
$415$	−17.3432	+	30.1523i	−0.851343	+	1.48012i
$416$	−1.80609	+	3.75038i	−0.0885507	+	0.183877i
$417$	−0.160920	+	0.0563083i	−0.00788027	+	0.00275743i
$418$	−1.21974	−	10.8255i	−0.0596595	−	0.529493i
$419$	−10.4442	+	13.0966i	−0.510232	+	0.639811i	−0.968503	−	0.249002i	$-0.919897\pi$
$419$	−10.4442	+	13.0966i	−0.510232	+	0.639811i	0.458271	+	0.888812i	$0.348469\pi$
$420$	0.0378986	+	0.0452423i	0.00184926	+	0.00220760i
$421$	−4.08177	−	5.11838i	−0.198933	−	0.249455i	0.672352	−	0.740232i	$-0.265284\pi$
$421$	−4.08177	−	5.11838i	−0.198933	−	0.249455i	−0.871285	+	0.490777i	$0.836713\pi$
$422$	−4.88066	+	4.88066i	−0.237587	+	0.237587i
$423$	6.83007	−	6.83007i	0.332090	−	0.332090i
$424$	−10.4420	+	8.32724i	−0.507110	+	0.404406i
$425$	−22.1803	−	5.86603i	−1.07590	−	0.284544i
$426$	0.00686964	−	0.0142650i	0.000332835	−	0.000691140i
$427$	−4.56754	+	4.43321i	−0.221039	+	0.214538i
$428$	19.2000	+	6.71839i	0.928069	+	0.324745i
$429$	0.0761088	−	0.0606948i	0.00367457	−	0.00293037i
$430$	−21.1921	−	3.97411i	−1.02197	−	0.191648i
$431$	2.53873	+	11.1229i	0.122286	+	0.535771i	0.998545	+	0.0539299i	$0.0171748\pi$
$431$	2.53873	+	11.1229i	0.122286	+	0.535771i	−0.876258	+	0.481841i	$0.839968\pi$
$432$	−0.0197687	−	0.0564957i	−0.000951123	−	0.00271815i
$433$	2.06103	+	3.28011i	0.0990467	+	0.157632i	0.892571	−	0.450906i	$-0.148899\pi$
$433$	2.06103	+	3.28011i	0.0990467	+	0.157632i	−0.793525	+	0.608538i	$0.791756\pi$
$434$	−4.47856	−	1.09277i	−0.214978	−	0.0524546i
$435$	0.0832786	−	0.0328407i	0.00399290	−	0.00157459i
$436$	−0.786438	+	3.44561i	−0.0376635	+	0.165015i
$437$	−27.1152	+	3.05515i	−1.29709	+	0.146147i
$438$	−0.0212808	+	0.0133716i	−0.00101684	+	0.000638921i
$439$	−24.9054	+	11.9938i	−1.18867	+	0.572433i	−0.920425	−	0.390918i	$-0.872157\pi$
$439$	−24.9054	+	11.9938i	−1.18867	+	0.572433i	−0.268243	+	0.963351i	$0.586443\pi$
$440$	−0.789684	−	5.18208i	−0.0376467	−	0.247046i
$441$	5.28168	−	20.3242i	0.251509	−	0.967821i
$442$	13.5061	−	13.5061i	0.642418	−	0.642418i
$443$	20.2076	+	7.07094i	0.960092	+	0.335951i	0.764420	−	0.644719i	$-0.223026\pi$
$443$	20.2076	+	7.07094i	0.960092	+	0.335951i	0.195672	+	0.980669i	$0.437311\pi$
$444$	0.0207884	−	0.0910800i	0.000986574	−	0.00432246i
$445$	19.4457	−	5.24433i	0.921814	−	0.248605i
$446$	12.6444	+	2.88600i	0.598730	+	0.136656i
$447$	−0.0205620	+	0.0327242i	−0.000972548	+	0.00154780i
$448$	−0.911007	+	2.48396i	−0.0430410	+	0.117356i
$449$	−7.45746	−	1.70212i	−0.351939	−	0.0803278i	0.0428967	−	0.999080i	$-0.486341\pi$
$449$	−7.45746	−	1.70212i	−0.351939	−	0.0803278i	−0.394836	+	0.918752i	$0.629199\pi$
$450$	12.0396	−	8.94617i	0.567551	−	0.421726i
$451$	19.0551	−	4.34920i	0.897270	−	0.204796i
$452$	4.66544	−	13.3331i	0.219444	−	0.627135i
$453$	0.0705216	+	0.00794587i	0.00331339	+	0.000373330i
$454$	−18.5468	+	8.93168i	−0.870445	+	0.419184i
$455$	−11.2165	−	21.9236i	−0.525839	−	1.02779i
$456$	−0.0417683	−	0.0201146i	−0.00195598	−	0.000941951i
$457$	0.981624	+	0.616795i	0.0459184	+	0.0288525i	0.554796	−	0.831987i	$-0.312796\pi$
$457$	0.981624	+	0.616795i	0.0459184	+	0.0288525i	−0.508877	+	0.860839i	$0.669939\pi$
$458$	−4.08368	−	0.460120i	−0.190818	−	0.0215000i
$459$			0.274648i			0.0128195i
$460$	−12.9798	+	1.97796i	−0.605186	+	0.0922228i
$461$	−21.2173	+	16.9202i	−0.988187	+	0.788053i	−0.977294	−	0.211888i	$-0.932039\pi$
$461$	−21.2173	+	16.9202i	−0.988187	+	0.788053i	−0.0108931	+	0.999941i	$0.503467\pi$
$462$	0.0443993	−	0.0430935i	0.00206564	−	0.00200489i
$463$	−18.3682	+	2.06960i	−0.853642	+	0.0961824i	−0.527931	−	0.849287i	$-0.677032\pi$
$463$	−18.3682	+	2.06960i	−0.853642	+	0.0961824i	−0.325711	+	0.945469i	$0.605604\pi$
$464$	3.13758	+	2.50214i	0.145659	+	0.116159i
$465$	0.0113960	−	0.0371592i	0.000528478	−	0.00172322i
$466$	13.3079	+	6.40877i	0.616479	+	0.296881i
$467$	−26.1017	+	2.94096i	−1.20784	+	0.136091i	−0.692836	−	0.721095i	$-0.743639\pi$
$467$	−26.1017	+	2.94096i	−1.20784	+	0.136091i	−0.515007	+	0.857186i	$0.672211\pi$
$468$	1.39814	+	12.4089i	0.0646293	+	0.573601i
$469$	7.22944	−	8.79297i	0.333824	−	0.406021i
$470$	−0.280895	−	7.19429i	−0.0129567	−	0.331848i
$471$	−0.0514839			−0.00237225
$472$	4.81579	+	4.81579i	0.221665	+	0.221665i
$473$	−2.53091	+	22.4625i	−0.116372	+	1.03283i
$474$	−0.000810568	−	0.00355133i	−3.72306e−5	−	0.000163118i
$475$	3.38842	−	22.9872i	0.155471	−	1.05473i
$476$	7.71013	−	9.37761i	0.353393	−	0.429822i
$477$	−13.2330	+	37.8179i	−0.605899	+	1.73156i
$478$	−1.11078	+	9.85845i	−0.0508059	+	0.450915i
$479$	−23.2115	+	11.1780i	−1.06056	+	0.510738i	−0.881052	−	0.473019i	$-0.843164\pi$
$479$	−23.2115	+	11.1780i	−1.06056	+	0.510738i	−0.179506	+	0.983757i	$0.557450\pi$
$480$	−0.0204601	−	0.00888711i	−0.000933871	−	0.000405639i
$481$	−16.9136	+	35.1214i	−0.771193	+	1.60140i
$482$	−24.7823	+	15.5718i	−1.12880	+	0.709275i
$483$	−0.107938	−	0.111209i	−0.00491137	−	0.00506019i
$484$	5.36649	−	1.22487i	0.243931	−	0.0556757i
$485$	19.3208	+	1.41633i	0.877311	+	0.0643124i
$486$	−0.210577	−	0.167930i	−0.00955197	−	0.00761744i
$487$	0.556795	+	0.886134i	0.0252308	+	0.0401546i	0.859102	−	0.511805i	$-0.171023\pi$
$487$	0.556795	+	0.886134i	0.0252308	+	0.0401546i	−0.833871	+	0.551960i	$0.813880\pi$
$488$	0.794592	−	2.27081i	0.0359695	−	0.102795i
$489$	0.0502535			0.00227254
$490$	−8.44889	−	13.1764i	−0.381682	−	0.595247i
$491$	−8.01544			−0.361732			−0.180866	−	0.983508i	$-0.557890\pi$
$491$	−8.01544			−0.361732			−0.180866	+	0.983508i	$0.557890\pi$
$492$	0.0274707	−	0.0785067i	0.00123847	−	0.00353936i
$493$	−9.79712	−	15.5920i	−0.441240	−	0.702229i
$494$	15.1238	+	12.0609i	0.680454	+	0.542644i
$495$	−10.2767	−	11.9026i	−0.461903	−	0.534980i
$496$	1.69871	−	0.387720i	0.0762745	−	0.0174092i
$497$	−2.28687	+	3.52175i	−0.102580	+	0.157972i
$498$	0.131399	−	0.0825637i	0.00588815	−	0.00369977i
$499$	5.74396	−	11.9275i	0.257135	−	0.533946i	−0.731938	−	0.681371i	$-0.761384\pi$
$499$	5.74396	−	11.9275i	0.257135	−	0.533946i	0.989073	+	0.147424i	$0.0470983\pi$
$500$	1.19764	−	11.1160i	0.0535602	−	0.497123i
$501$	0.142758	−	0.0687485i	0.00637795	−	0.00307146i
$502$	0.0947957	−	0.841335i	0.00423094	−	0.0375506i
$503$	−1.39823	+	3.99591i	−0.0623440	+	0.178169i	−0.970842	−	0.239720i	$-0.922944\pi$
$503$	−1.39823	+	3.99591i	−0.0623440	+	0.178169i	0.908498	+	0.417889i	$0.137230\pi$
$504$	1.65047	+	7.76349i	0.0735179	+	0.345813i
$505$	−18.6144	+	9.87671i	−0.828329	+	0.439508i
$506$	3.06297	+	13.4197i	0.136165	+	0.596580i
$507$	−0.00483334	+	0.0428971i	−0.000214656	+	0.00190513i
$508$	14.9244	+	14.9244i	0.662165	+	0.662165i
$509$	21.0733			0.934056			0.467028	−	0.884243i	$-0.345325\pi$
$509$	21.0733			0.934056			0.467028	+	0.884243i	$0.345325\pi$
$510$	0.0751459	+	0.0694984i	0.00332752	+	0.00307744i
$511$	6.04803	−	2.80217i	0.267549	−	0.123961i
$512$	−0.111964	−	0.993712i	−0.00494818	−	0.0439163i
$513$	−0.276402	+	0.0311431i	−0.0122035	+	0.00137500i
$514$	20.1522	+	9.70480i	0.888877	+	0.428060i
$515$	−7.19793	−	2.20747i	−0.317179	−	0.0972727i
$516$	0.0752073	+	0.0599758i	0.00331082	+	0.00264029i
$517$	−7.50063	+	0.845118i	−0.329877	+	0.0371683i
$518$	−8.53137	+	23.2617i	−0.374847	+	1.02206i
$519$	−0.0133258	+	0.0106270i	−0.000584937	+	0.000466471i
$520$	7.49806	+	5.51503i	0.328812	+	0.241850i
$521$		−	2.30480i		−	0.100975i	−0.998725	−	0.0504877i	$-0.983922\pi$
$521$		−	2.30480i		−	0.100975i	0.998725	−	0.0504877i	$-0.0160776\pi$
$522$	11.9633	+	1.34793i	0.523617	+	0.0589975i
$523$	29.5544	+	18.5703i	1.29232	+	0.812021i	0.989984	−	0.141179i	$-0.0450894\pi$
$523$	29.5544	+	18.5703i	1.29232	+	0.812021i	0.302340	+	0.953200i	$0.402232\pi$
$524$	−1.54866	−	0.745797i	−0.0676537	−	0.0325803i
$525$	0.115051	−	0.0646458i	0.00502124	−	0.00282137i
$526$	−8.94345	+	4.30694i	−0.389953	+	0.187791i
$527$	−7.94487	−	0.895172i	−0.346084	−	0.0389943i
$528$	−0.00772392	+	0.0220737i	−0.000336141	+	0.000960635i
$529$	11.1897	−	2.55398i	0.486510	−	0.111043i
$530$	13.9977	+	26.3810i	0.608020	+	1.14592i
$531$	19.9187	+	4.54632i	0.864400	+	0.197294i
$532$	10.3118	+	6.69603i	0.447073	+	0.290310i
$533$	−18.4645	+	29.3861i	−0.799787	+	1.27285i
$534$	−0.0876012	−	0.0199944i	−0.00379088	−	0.000865243i
$535$	22.6785	−	39.4281i	0.980478	−	1.70463i
$536$	−0.957398	+	4.19463i	−0.0413533	+	0.181181i
$537$	−0.173054	−	0.0605542i	−0.00746783	−	0.00261311i
$538$	10.7789	−	10.7789i	0.464710	−	0.464710i
$539$	−13.1293	+	9.84387i	−0.565518	+	0.424005i
$540$	−0.132311	+	0.0201626i	−0.00569378	+	0.000867661i
$541$	27.1617	−	13.0804i	1.16777	−	0.562369i	0.253446	−	0.967349i	$-0.418436\pi$
$541$	27.1617	−	13.0804i	1.16777	−	0.562369i	0.914325	+	0.404980i	$0.132722\pi$
$542$	10.8350	−	6.80809i	0.465403	−	0.292432i
$543$	−0.228705	+	0.0257689i	−0.00981467	+	0.00110585i
$544$	−1.02106	+	4.47354i	−0.0437774	+	0.191801i
$545$	7.24849	+	3.14848i	0.310491	+	0.134866i
$546$	−0.00163959	+	0.109855i	−7.01678e−5	+	0.00470135i
$547$	−3.31681	−	5.27868i	−0.141817	−	0.225700i	0.768262	−	0.640136i	$-0.221122\pi$
$547$	−3.31681	−	5.27868i	−0.141817	−	0.225700i	−0.910079	+	0.414436i	$0.863979\pi$
$548$	−1.56398	−	4.46959i	−0.0668098	−	0.190931i
$549$	−1.60598	−	7.03627i	−0.0685416	−	0.300301i
$550$	−11.7144	−	0.400214i	−0.499504	−	0.0170652i
$551$	14.5807	−	11.6277i	0.621160	−	0.495358i
$552$	0.0552891	+	0.0193465i	0.00235326	+	0.000823441i
$553$	0.0938283	+	0.961515i	0.00398999	+	0.0408878i
$554$	−6.53713	+	13.5745i	−0.277736	+	0.576725i
$555$	−0.191604	−	0.0832257i	−0.00813313	−	0.00353273i
$556$	−13.3614	+	10.6553i	−0.566648	+	0.451887i
$557$	28.8398	−	28.8398i	1.22198	−	1.22198i	0.255055	−	0.966927i	$-0.417906\pi$
$557$	28.8398	−	28.8398i	1.22198	−	1.22198i	0.966927	−	0.255055i	$-0.0820935\pi$
$558$	3.69606	−	3.69606i	0.156467	−	0.156467i
$559$	−25.0258	−	31.3813i	−1.05848	−	1.32729i
$560$	5.08368	+	3.02592i	0.214825	+	0.127868i
$561$	0.0669060	−	0.0838974i	0.00282477	−	0.00354215i
$562$	−2.97391	−	26.3942i	−0.125447	−	1.11337i
$563$	−33.7310	+	11.8030i	−1.42159	+	0.497436i	−0.928105	−	0.372318i	$-0.878563\pi$
$563$	−33.7310	+	11.8030i	−1.42159	+	0.497436i	−0.493485	+	0.869754i	$0.664277\pi$
$564$	−0.0139367	+	0.0289399i	−0.000586841	+	0.00121859i
$565$	−27.3800	−	15.7486i	−1.15189	−	0.662549i
$566$	13.3235	+	10.6251i	0.560029	+	0.446608i
$567$	16.5827	+	17.0852i	0.696406	+	0.717509i
$568$	0.177700	−	1.57713i	0.00745613	−	0.0661750i
$569$			7.24047i			0.303536i	0.988416	+	0.151768i	$0.0484967\pi$
$569$			7.24047i			0.303536i	−0.988416	+	0.151768i	$0.951503\pi$
$570$	−0.0614214	+	0.0835066i	−0.00257266	+	0.00349771i
$571$	−22.6979	−	28.4623i	−0.949879	−	1.19111i	−0.981471	−	0.191610i	$-0.938629\pi$
$571$	−22.6979	−	28.4623i	−0.949879	−	1.19111i	0.0315919	−	0.999501i	$-0.489942\pi$
$572$	5.19166	−	8.26248i	0.217074	−	0.345472i
$573$	0.00140698		0.000492322i	5.87773e−5		2.05671e-5i
$574$	−9.86653	+	19.7294i	−0.411821	+	0.823487i
$575$	−1.00244	+	29.3416i	−0.0418045	+	1.22363i
$576$	−1.87041	−	2.34542i	−0.0779336	−	0.0977257i
$577$	35.4983	+	12.4214i	1.47781	+	0.517110i	0.944415	−	0.328754i	$-0.106629\pi$
$577$	35.4983	+	12.4214i	1.47781	+	0.517110i	0.533399	+	0.845864i	$0.320915\pi$
$578$	2.15744	−	3.43355i	0.0897378	−	0.142817i
$579$	−0.214451	−	0.103274i	−0.00891226	−	0.00429192i
$580$	6.79222	−	5.86441i	0.282032	−	0.243506i
$581$	−37.3438	+	17.3021i	−1.54928	+	0.717813i
$582$	−0.0731810	−	0.0459827i	−0.00303345	−	0.00190604i
$583$	26.5105	−	16.6576i	1.09795	−	0.689888i
$584$	−1.57080	+	1.96973i	−0.0650004	+	0.0815079i
$585$	27.8479	+	2.04143i	1.15137	+	0.0844027i
$586$	4.29757	+	8.92400i	0.177531	+	0.368647i
$587$	1.51501	+	1.51501i	0.0625313	+	0.0625313i	0.737681	−	0.675150i	$-0.235921\pi$
$587$	1.51501	+	1.51501i	0.0625313	+	0.0625313i	−0.675150	+	0.737681i	$0.735921\pi$
$588$	0.00574426	+	0.0695948i	0.000236889	+	0.00287004i
$589$		−	8.09714i		−	0.333637i
$590$	12.5687	−	8.59915i	0.517446	−	0.354022i
$591$	−0.114757	−	0.0261924i	−0.00472046	−	0.00107741i
$592$	−1.04852	−	9.30588i	−0.0430940	−	0.382469i
$593$	−24.5728	−	39.1073i	−1.00908	−	1.60595i	−0.773199	−	0.634164i	$-0.781345\pi$
$593$	−24.5728	−	39.1073i	−1.00908	−	1.60595i	−0.235883	−	0.971781i	$-0.575798\pi$
$594$	0.0312228	+	0.136796i	0.00128109	+	0.00561281i
$595$	−17.4321	−	20.8099i	−0.714645	−	0.853123i
$596$	−0.862074	+	3.77699i	−0.0353119	+	0.154712i
$597$	0.0739898	−	0.0258901i	0.00302820	−	0.00105961i
$598$	−20.6954	−	13.0038i	−0.846300	−	0.531765i
$599$	−15.4766	−	32.1375i	−0.632356	−	1.31310i	−0.933176	−	0.359420i	$-0.882975\pi$
$599$	−15.4766	−	32.1375i	−0.632356	−	1.31310i	0.300820	−	0.953681i	$-0.402740\pi$
$600$	−0.0279642	+	0.0413036i	−0.00114163	+	0.00168621i
$601$	16.0408	+	33.3091i	0.654318	+	1.35871i	0.918957	+	0.394358i	$0.129033\pi$
$601$	16.0408	+	33.3091i	0.654318	+	1.35871i	−0.264639	+	0.964348i	$0.585253\pi$
$602$	−17.7684	−	18.3068i	−0.724186	−	0.746130i
$603$	4.26294	+	12.1828i	0.173600	+	0.496122i
$604$	6.93555	−	1.58299i	0.282203	−	0.0644111i
$605$	−0.480207	−	12.2991i	−0.0195232	−	0.500028i
$606$	0.0940117			0.00381896
$607$	11.9574	+	11.9574i	0.485337	+	0.485337i	0.906831	−	0.421494i	$-0.138494\pi$
$607$	11.9574	+	11.9574i	0.485337	+	0.485337i	−0.421494	+	0.906831i	$0.638494\pi$
$608$	−4.61790	−	0.520312i	−0.187281	−	0.0211015i
$609$	0.102903	+	0.0251082i	0.00416982	+	0.00101744i
$610$	−4.66321	−	2.68222i	−0.188808	−	0.108600i
$611$	8.35657	−	10.4788i	0.338071	−	0.423927i
$612$	4.54639	+	12.9928i	0.183777	+	0.525204i
$613$	15.6441	+	44.7084i	0.631861	+	1.80575i	0.591118	+	0.806585i	$0.298687\pi$
$613$	15.6441	+	44.7084i	0.631861	+	1.80575i	0.0407433	+	0.999170i	$0.487027\pi$
$614$	9.43224	−	11.8277i	0.380654	−	0.477325i
$615$	−0.161217	−	0.0927298i	−0.00650089	−	0.00373923i
$616$	2.77417	−	5.54730i	0.111774	−	0.223507i
$617$	5.64103	+	0.635592i	0.227099	+	0.0255880i	0.224781	−	0.974409i	$-0.427833\pi$
$617$	5.64103	+	0.635592i	0.227099	+	0.0255880i	0.00231862	+	0.999997i	$0.499262\pi$
$618$	0.0237509	+	0.0237509i	0.000955402	+	0.000955402i
$619$	38.3612			1.54186			0.770932	−	0.636917i	$-0.219791\pi$
$619$	38.3612			1.54186			0.770932	+	0.636917i	$0.219791\pi$
$620$	−0.152005	−	3.89316i	−0.00610467	−	0.156353i
$621$	0.342640	−	0.0782053i	0.0137497	−	0.00313827i
$622$	2.49113	+	7.11925i	0.0998853	+	0.285456i
$623$	22.3733	+	8.20552i	0.896366	+	0.328747i
$624$	−0.0180174	−	0.0374135i	−0.000721273	−	0.00149774i
$625$	−23.9367	−	7.21350i	−0.957468	−	0.288540i
$626$	0.950311	+	1.97334i	0.0379821	+	0.0788705i
$627$	0.0920201	+	0.0578201i	0.00367493	+	0.00230911i
$628$	−4.87121	+	1.70451i	−0.194382	+	0.0680174i
$629$	−9.56195	+	41.8936i	−0.381260	+	1.67041i
$630$	17.7425	−	0.427685i	0.706878	−	0.0170394i
$631$	8.66665	+	37.9711i	0.345014	+	1.51160i	0.788337	+	0.615243i	$0.210942\pi$
$631$	8.66665	+	37.9711i	0.345014	+	1.51160i	−0.443324	+	0.896362i	$0.646201\pi$
$632$	−0.194269	−	0.309177i	−0.00772760	−	0.0122984i
$633$	−0.00770952	−	0.0684239i	−0.000306426	−	0.00271961i
$634$	−9.35425	−	2.13505i	−0.371505	−	0.0847936i
$635$	38.9513	−	26.6493i	1.54573	−	1.05755i
$636$		−	0.133237i		−	0.00528319i
$637$	4.12511	−	28.8448i	0.163443	−	1.14287i
$638$	−6.65228	−	6.65228i	−0.263366	−	0.263366i
$639$	−2.06580	−	4.28967i	−0.0817217	−	0.169697i
$640$	−2.23008	−	0.163479i	−0.0881518	−	0.00646208i
$641$	−1.94468	+	2.43856i	−0.0768104	+	0.0963172i	−0.818752	−	0.574147i	$-0.805334\pi$
$641$	−1.94468	+	2.43856i	−0.0768104	+	0.0963172i	0.741942	+	0.670464i	$0.233905\pi$
$642$	−0.171822	+	0.107963i	−0.00678128	+	0.00426096i
$643$	−30.9730	−	19.4617i	−1.22146	−	0.767493i	−0.242222	−	0.970221i	$-0.577876\pi$
$643$	−30.9730	−	19.4617i	−1.22146	−	0.767493i	−0.979235	+	0.202728i	$0.935019\pi$
$644$	−13.8946	−	6.94860i	−0.547523	−	0.273813i
$645$	0.162808	−	0.140569i	0.00641057	−	0.00553489i
$646$	19.2120	+	9.25201i	0.755886	+	0.364015i
$647$	−8.82852	+	14.0505i	−0.347085	+	0.552382i	−0.973955	−	0.226741i	$-0.927193\pi$
$647$	−8.82852	+	14.0505i	−0.347085	+	0.552382i	0.626870	+	0.779124i	$0.284336\pi$
$648$	−8.49410	−	2.97222i	−0.333680	−	0.116760i
$649$	−9.95441	−	12.4824i	−0.390745	−	0.489978i
$650$	15.2109	−	14.2059i	0.596622	−	0.557203i
$651$	0.0363792	−	0.0281336i	0.00142581	−	0.00110264i
$652$	4.75479	−	1.66377i	0.186212	−	0.0651583i
$653$	23.5742	−	37.5181i	0.922529	−	1.46820i	0.0393138	−	0.999227i	$-0.487483\pi$
$653$	23.5742	−	37.5181i	0.922529	−	1.46820i	0.883215	−	0.468969i	$-0.155374\pi$
$654$	−0.0219825	−	0.0275651i	−0.000859582	−	0.00107788i
$655$	−2.27735	+	3.09621i	−0.0889834	+	0.120979i
$656$		−	8.33749i		−	0.325524i
$657$	−0.846213	+	7.51035i	−0.0330139	+	0.293007i
$658$	4.63946	−	7.14470i	0.180865	−	0.278529i
$659$	−24.5196	−	19.5537i	−0.955149	−	0.761706i	0.0160760	−	0.999871i	$-0.494883\pi$
$659$	−24.5196	−	19.5537i	−0.955149	−	0.761706i	−0.971225	+	0.238165i	$0.923454\pi$
$660$	0.0453293	+	0.0260728i	0.00176444	+	0.00101488i
$661$	8.71340	−	18.0936i	0.338912	−	0.703758i	−0.659957	−	0.751303i	$-0.729426\pi$
$661$	8.71340	−	18.0936i	0.338912	−	0.703758i	0.998869	+	0.0475454i	$0.0151399\pi$
$662$	9.14906	−	3.20139i	0.355588	−	0.124426i
$663$	0.0213342	+	0.189347i	0.000828553	+	0.00735361i
$664$	9.69901	−	12.1622i	0.376395	−	0.471984i
$665$	18.9662	−	19.9031i	0.735477	−	0.771810i
$666$	−17.5159	−	21.9643i	−0.678729	−	0.851099i
$667$	−16.6623	+	16.6623i	−0.645166	+	0.645166i
$668$	11.2311	−	11.2311i	0.434544	−	0.434544i
$669$	−0.101156	+	0.0806694i	−0.00391092	+	0.00311886i
$670$	8.82421	+	3.83291i	0.340909	+	0.148078i
$671$	−2.44703	+	5.08132i	−0.0944667	+	0.196162i
$672$	−0.0137073	−	0.0225554i	−0.000528770	−	0.000870092i
$673$	10.5862	+	3.70429i	0.408070	+	0.142790i	0.526505	−	0.850172i	$-0.323502\pi$
$673$	10.5862	+	3.70429i	0.408070	+	0.142790i	−0.118435	+	0.992962i	$0.537788\pi$
$674$	−10.4709	+	8.35025i	−0.403323	+	0.321640i
$675$	−0.0102185	+	0.299098i	−0.000393310	+	0.0115123i
$676$	0.962908	+	4.21878i	0.0370349	+	0.162261i
$677$	−3.73740	−	10.6809i	−0.143640	−	0.410500i	0.849477	−	0.527626i	$-0.176918\pi$
$677$	−3.73740	−	10.6809i	−0.143640	−	0.410500i	−0.993117	+	0.117126i	$0.962632\pi$
$678$	0.0749727	+	0.119318i	0.00287931	+	0.00458239i
$679$	17.7059	+	14.5575i	0.679489	+	0.558665i
$680$	9.41093	+	4.08776i	0.360893	+	0.156759i
$681$	0.0456966	−	0.200210i	0.00175110	−	0.00767206i
$682$	−4.05893	+	0.457332i	−0.155425	+	0.0175121i
$683$	−4.24896	+	2.66980i	−0.162582	+	0.102157i	−0.610866	−	0.791734i	$-0.709178\pi$
$683$	−4.24896	+	2.66980i	−0.162582	+	0.102157i	0.448283	+	0.893891i	$0.352036\pi$
$684$	−12.5603	+	6.04873i	−0.480256	+	0.231279i
$685$	−10.4677	+	1.59514i	−0.399948	+	0.0609472i
$686$	0.828908	−	18.5017i	0.0316479	−	0.706398i
$687$	0.0289887	−	0.0289887i	0.00110599	−	0.00110599i
$688$	9.10147	+	3.18474i	0.346990	+	0.121417i
$689$	−12.3711	+	54.2012i	−0.471301	+	2.06490i
$690$	0.0653058	−	0.113539i	0.00248615	−	0.00432234i
$691$	−30.4849	−	6.95799i	−1.15970	−	0.264694i	−0.400966	−	0.916093i	$-0.631326\pi$
$691$	−30.4849	−	6.95799i	−1.15970	−	0.264694i	−0.758736	+	0.651398i	$0.774183\pi$
$692$	−0.909000	+	1.44667i	−0.0345550	+	0.0549940i
$693$	−1.80709	−	18.5183i	−0.0686456	−	0.703453i
$694$	0.718418	+	0.163974i	0.0272708	+	0.00622438i
$695$	17.9111	+	33.7566i	0.679406	+	1.28046i
$696$	−0.0390308	+	0.00890853i	−0.00147946	+	0.000337677i
$697$	−12.6356	+	36.1104i	−0.478606	+	1.36778i
$698$	−29.0845	−	3.27704i	−1.10087	−	0.124038i
$699$	−0.132759	+	0.0639334i	−0.00502141	+	0.00241818i
$700$	8.74543	−	9.92560i	0.330546	−	0.375152i
$701$	21.0890	+	10.1559i	0.796522	+	0.383585i	0.787453	−	0.616374i	$-0.211399\pi$
$701$	21.0890	+	10.1559i	0.796522	+	0.383585i	0.00906835	+	0.999959i	$0.497113\pi$
$702$	−0.210962	−	0.132556i	−0.00796225	−	0.00500301i
$703$	−43.2456	−	4.87261i	−1.63104	−	0.183774i
$704$			2.34425i			0.0883522i
$705$	0.0578589	+	0.0425568i	0.00217909	+	0.00160278i
$706$	9.66736	−	7.70946i	0.363836	−	0.290149i
$707$	−24.7320	−	3.16107i	−0.930141	−	0.118884i
$708$	−0.0675144	+	0.00760705i	−0.00253735	+	0.000285890i
$709$	21.3088	+	16.9932i	0.800270	+	0.638194i	0.935781	−	0.352582i	$-0.114696\pi$
$709$	21.3088	+	16.9932i	0.800270	+	0.638194i	−0.135511	+	0.990776i	$0.543268\pi$
$710$	−3.39292	−	1.04054i	−0.127334	−	0.0390509i
$711$	−0.986920	−	0.475275i	−0.0370124	−	0.0178242i
$712$	−8.95045	+	1.00847i	−0.335432	+	0.0377942i
$713$	1.14550	+	10.1666i	0.0428994	+	0.380742i
$714$	0.0251845	+	0.118463i	0.000942507	+	0.00443336i
$715$	−16.0192	−	14.8153i	−0.599086	−	0.554062i
$716$	−18.3785			−0.686837
$717$	−0.0699820	−	0.0699820i	−0.00261353	−	0.00261353i
$718$	2.22461	−	19.7440i	0.0830217	−	0.736838i
$719$	−9.40856	−	41.2216i	−0.350880	−	1.53731i	−0.775154	−	0.631772i	$-0.782328\pi$
$719$	−9.40856	−	41.2216i	−0.350880	−	1.53731i	0.424274	−	0.905534i	$-0.360529\pi$
$720$	−5.92553	+	3.14406i	−0.220831	+	0.117172i
$721$	−5.44963	−	7.04684i	−0.202955	−	0.262438i
$722$	−0.857316	+	2.45007i	−0.0319060	+	0.0911821i
$723$	0.0326914	−	0.290144i	0.00121581	−	0.0107906i
$724$	−20.7860	+	10.0100i	−0.772507	+	0.372020i
$725$	−10.0892	−	17.3446i	−0.374703	−	0.644163i
$726$	−0.0238256	+	0.0494744i	−0.000884252	+	0.00183617i
$727$	19.8621	−	12.4802i	0.736643	−	0.462864i	−0.110737	−	0.993850i	$-0.535321\pi$
$727$	19.8621	−	12.4802i	0.736643	−	0.462864i	0.847380	+	0.530986i	$0.178178\pi$
$728$	3.48190	+	10.4483i	0.129048	+	0.387240i
$729$	−26.3178	+	6.00687i	−0.974734	+	0.222477i
$730$	3.68159	+	4.26405i	0.136262	+	0.157820i
$731$	−34.5928	−	27.5868i	−1.27946	−	1.02033i
$732$	0.0127689	+	0.0203216i	0.000471953	+	0.000751108i
$733$	5.36473	−	15.3315i	0.198151	−	0.566282i	−0.801340	−	0.598210i	$-0.795879\pi$
$733$	5.36473	−	15.3315i	0.198151	−	0.566282i	0.999490	+	0.0319278i	$0.0101647\pi$
$734$	−20.2639			−0.747954
$735$	0.155320	+	0.0160584i	0.00572907	+	0.000592324i
$736$	5.87175			0.216436
$737$	3.33124	−	9.52015i	0.122708	−	0.350679i
$738$	−13.3070	−	21.1780i	−0.489837	−	0.779571i
$739$	3.78415	+	3.01776i	0.139202	+	0.111010i	0.690615	−	0.723222i	$-0.257340\pi$
$739$	3.78415	+	3.01776i	0.139202	+	0.111010i	−0.551413	+	0.834232i	$0.685911\pi$
$740$	−20.8842	−	1.53094i	−0.767719	−	0.0562786i
$741$	−0.188137	+	0.0429411i	−0.00691140	+	0.00157748i
$742$	−4.47999	+	35.0511i	−0.164466	+	1.28677i
$743$	11.7212	−	7.36493i	0.430010	−	0.270193i	−0.299589	−	0.954068i	$-0.596850\pi$
$743$	11.7212	−	7.36493i	0.430010	−	0.270193i	0.729599	+	0.683875i	$0.239707\pi$
$744$	−0.00754179	+	0.0156607i	−0.000276495	+	0.000574149i
$745$	7.94562	+	3.45128i	0.291105	+	0.126445i
$746$	23.2478	−	11.1955i	0.851162	−	0.409898i
$747$	5.22499	−	46.3730i	0.191172	−	1.69670i
$748$	3.55274	−	10.1531i	0.129901	−	0.371236i
$749$	48.8320	−	22.6248i	1.78428	−	0.826693i
$750$	0.0792500	+	0.0784814i	0.00289380	+	0.00286573i
$751$	8.32938	+	36.4934i	0.303943	+	1.33166i	0.864118	+	0.503289i	$0.167877\pi$
$751$	8.32938	+	36.4934i	0.303943	+	1.33166i	−0.560175	+	0.828374i	$0.689266\pi$
$752$	−0.360507	+	3.19959i	−0.0131463	+	0.116677i
$753$	0.00597237	+	0.00597237i	0.000217645	+	0.000217645i
$754$	16.7050			0.608361
$755$	−0.620610	−	15.8951i	−0.0225863	−	0.578481i
$756$	−0.141636	−	0.0708315i	−0.00515127	−	0.00257612i
$757$	−2.15097	−	19.0904i	−0.0781784	−	0.693853i	−0.970274	−	0.242007i	$-0.922194\pi$
$757$	−2.15097	−	19.0904i	−0.0781784	−	0.693853i	0.892096	−	0.451846i	$-0.149234\pi$
$758$	24.1595	−	2.72212i	0.877513	−	0.0988719i
$759$	−0.123718	−	0.0595797i	−0.00449070	−	0.00216261i
$760$	−3.04675	+	9.93459i	−0.110517	+	0.360365i
$761$	−38.7375	−	30.8921i	−1.40423	−	1.11984i	−0.976398	−	0.215980i	$-0.930705\pi$
$761$	−38.7375	−	30.8921i	−1.40423	−	1.11984i	−0.427834	−	0.903857i	$-0.640723\pi$
$762$	−0.209231	+	0.0235747i	−0.00757966	+	0.000854022i
$763$	4.85615	+	7.99080i	0.175804	+	0.289286i
$764$	0.116823	−	0.0931632i	0.00422651	−	0.00337053i
$765$	30.4289	−	4.63698i	1.10016	−	0.167650i
$766$			38.6623i			1.39693i
$767$	28.1714	+	3.17415i	1.01721	+	0.114612i
$768$	0.00844686	+	0.00530751i	0.000304800	+	0.000191518i
$769$	17.7913	+	8.56785i	0.641571	+	0.308965i	0.726237	−	0.687445i	$-0.241268\pi$
$769$	17.7913	+	8.56785i	0.641571	+	0.308965i	−0.0846650	+	0.996409i	$0.526982\pi$
$770$	−11.0483	−	8.38322i	−0.398152	−	0.302110i
$771$	−0.201037	+	0.0968144i	−0.00724018	+	0.00348669i
$772$	−23.7096	−	2.67143i	−0.853328	−	0.0961470i
$773$	−5.44671	+	15.5658i	−0.195905	+	0.559863i	−0.999370	−	0.0354881i	$-0.988701\pi$
$773$	−5.44671	+	15.5658i	−0.195905	+	0.559863i	0.803465	+	0.595351i	$0.202987\pi$
$774$	28.2015	−	6.43682i	1.01368	−	0.231367i
$775$	−8.61886	−	1.27046i	−0.309599	−	0.0456363i
$776$	−8.44648	−	1.92785i	−0.303211	−	0.0692059i
$777$	−0.128366	−	0.211226i	−0.00460509	−	0.00757768i
$778$	−7.18630	+	11.4369i	−0.257641	+	0.410034i
$779$	−37.7739	−	8.62164i	−1.35339	−	0.308902i
$780$	−0.0896515	+	0.0241782i	−0.00321004	+	0.000865719i
$781$	−0.827908	+	3.62730i	−0.0296249	+	0.129795i
$782$	−25.4311	−	8.89872i	−0.909414	−	0.318218i
$783$	−0.169849	+	0.169849i	−0.00606992	+	0.00606992i
$784$	2.84762	+	6.39461i	0.101701	+	0.228379i
$785$	1.73847	+	11.4082i	0.0620488	+	0.407177i
$786$	0.0154494	−	0.00744002i	0.000551060	−	0.000265377i
$787$	1.70365	−	1.07047i	0.0607284	−	0.0381582i	−0.501326	−	0.865259i	$-0.667154\pi$
$787$	1.70365	−	1.07047i	0.0607284	−	0.0381582i	0.562054	+	0.827100i	$0.310011\pi$
$788$	−11.7250	+	1.32109i	−0.417686	+	0.0470619i
$789$	0.0220353	−	0.0965430i	0.000784478	−	0.00343702i
$790$	−0.759562	+	0.299531i	−0.0270240	+	0.0106568i
$791$	−15.7113	−	33.9104i	−0.558631	−	1.20571i
$792$	3.74152	+	5.95460i	0.132949	+	0.211587i
$793$	−3.30757	−	9.45249i	−0.117455	−	0.335668i
$794$	1.95504	+	8.56557i	0.0693816	+	0.303981i
$795$	−0.292823	−	0.0549125i	−0.0103854	−	0.00194755i
$796$	6.14346	−	4.89925i	0.217749	−	0.173649i
$797$	26.3564	+	9.22251i	0.933592	+	0.326678i	0.753858	−	0.657037i	$-0.228191\pi$
$797$	26.3564	+	9.22251i	0.933592	+	0.326678i	0.179734	+	0.983715i	$0.442476\pi$
$798$	−0.116364	+	0.0387783i	−0.00411924	+	0.00137274i
$799$	6.41041	−	13.3113i	0.226784	−	0.470922i
$800$	−1.27840	+	4.83381i	−0.0451982	+	0.170901i
$801$	−21.1254	+	16.8469i	−0.746428	+	0.595257i
$802$	−6.20909	+	6.20909i	−0.219251	+	0.219251i
$803$	4.17620	−	4.17620i	0.147375	−	0.147375i
$804$	−0.0267611	−	0.0335574i	−0.000943792	−	0.00118348i
$805$	−20.9979	+	27.6731i	−0.740078	+	0.975349i
$806$	4.52212	−	5.67056i	0.159285	−	0.199737i
$807$	0.0170264	+	0.151113i	0.000599357	+	0.00531944i
$808$	8.89502	−	3.11250i	0.312926	−	0.109497i
$809$	9.75520	−	20.2569i	0.342975	−	0.712194i	−0.656124	−	0.754653i	$-0.727805\pi$
$809$	9.75520	−	20.2569i	0.342975	−	0.712194i	0.999098	+	0.0424593i	$0.0135193\pi$
$810$	−10.0330	+	17.4430i	−0.352523	+	0.612885i
$811$	24.4856	+	19.5266i	0.859804	+	0.685671i	0.950674	−	0.310192i	$-0.100393\pi$
$811$	24.4856	+	19.5266i	0.859804	+	0.685671i	−0.0908696	+	0.995863i	$0.528965\pi$
$812$	10.5675	−	1.03122i	0.370847	−	0.0361887i
$813$	−0.0142929	+	0.126853i	−0.000501274	+	0.00444893i
$814$			21.9533i			0.769464i
$815$	−1.69692	−	11.1356i	−0.0594406	−	0.390062i
$816$	−0.0285405	−	0.0357886i	−0.000999117	−	0.00125285i
$817$	23.8405	−	37.9419i	0.834073	−	1.32742i
$818$	−4.33648	+	1.51740i	−0.151621	+	0.0530547i
$819$	25.5203	+	20.9824i	0.891751	+	0.733184i
$820$	−18.3238	−	3.43622i	−0.639894	−	0.119998i
$821$	−15.3797	−	19.2855i	−0.536754	−	0.673068i	0.437318	−	0.899307i	$-0.355928\pi$
$821$	−15.3797	−	19.2855i	−0.536754	−	0.673068i	−0.974072	+	0.226239i	$0.927357\pi$
$822$	0.0445883	+	0.0156021i	0.00155520	+	0.000544186i
$823$	−23.3123	+	37.1013i	−0.812616	+	1.29327i	0.140323	+	0.990106i	$0.455186\pi$
$823$	−23.3123	+	37.1013i	−0.812616	+	1.29327i	−0.952938	+	0.303164i	$0.901957\pi$
$824$	3.03355	+	1.46088i	0.105679	+	0.0508922i
$825$	0.0759838	−	0.0888772i	0.00264542	−	0.00309431i
$826$	18.0170	+	0.268905i	0.626893	+	0.00935639i
$827$	40.4796	+	25.4350i	1.40761	+	0.884463i	0.999594	−	0.0285101i	$-0.00907628\pi$
$827$	40.4796	+	25.4350i	1.40761	+	0.884463i	0.408021	+	0.912973i	$0.366219\pi$
$828$	14.9148	−	9.37157i	0.518324	−	0.325685i
$829$	7.37715	−	9.25066i	0.256219	−	0.321289i	−0.637040	−	0.770831i	$-0.719841\pi$
$829$	7.37715	−	9.25066i	0.256219	−	0.321289i	0.893259	+	0.449542i	$0.148413\pi$
$830$	−22.7322	−	26.3286i	−0.789045	−	0.913880i
$831$	−0.0652140	−	0.135418i	−0.00226225	−	0.00469760i
$832$	−2.94341	−	2.94341i	−0.102044	−	0.102044i
$833$	−2.64216	−	32.0112i	−0.0915454	−	1.10912i
$834$		−	0.170487i		−	0.00590348i
$835$	−20.0544	−	29.3120i	−0.694012	−	1.01438i
$836$	10.6209	+	2.42414i	0.367330	+	0.0838408i
$837$	0.0116768	+	0.103635i	0.000403611	+	0.00358214i
$838$	−8.91216	−	14.1836i	−0.307866	−	0.489965i
$839$	−2.46759	−	10.8112i	−0.0851907	−	0.373245i	0.914304	−	0.405028i	$-0.132738\pi$
$839$	−2.46759	−	10.8112i	−0.0851907	−	0.373245i	−0.999495	+	0.0317836i	$0.989881\pi$
$840$	−0.0552206	+	0.0208293i	−0.00190529	+	0.000718679i
$841$	−2.86938	+	12.5716i	−0.0989443	+	0.433503i
$842$	6.17928	−	2.16222i	0.212952	−	0.0745151i
$843$	0.224358	+	0.140974i	0.00772732	+	0.00485539i
$844$	−2.99480	−	6.21876i	−0.103085	−	0.214058i
$845$	9.66870	−	0.377507i	0.332613	−	0.0129866i
$846$	4.19096	+	8.70262i	0.144088	+	0.299202i
$847$	7.93143	−	12.2143i	0.272527	−	0.419688i
$848$	−4.41116	−	12.6064i	−0.151480	−	0.432904i
$849$	−0.165742	+	0.0378294i	−0.00568824	+	0.00129830i
$850$	12.8626	−	18.9982i	0.441182	−	0.651634i
$851$	54.9876			1.88495
$852$	0.0111956	+	0.0111956i	0.000383554	+	0.000383554i
$853$	35.2355	+	3.97009i	1.20644	+	0.135933i	0.692196	−	0.721710i	$-0.256643\pi$
$853$	35.2355	+	3.97009i	1.20644	+	0.135933i	0.514246	+	0.857643i	$0.328072\pi$
$854$	−2.67587	−	5.77542i	−0.0915662	−	0.197631i
$855$	8.11702	+	30.0975i	0.277596	+	1.02931i
$856$	−12.6827	+	15.9037i	−0.433487	+	0.543576i
$857$	−9.59620	−	27.4244i	−0.327800	−	0.936799i	−0.983362	−	0.181657i	$-0.941854\pi$
$857$	−9.59620	−	27.4244i	−0.327800	−	0.936799i	0.655562	−	0.755141i	$-0.272432\pi$
$858$	0.0321516	+	0.0918841i	0.00109764	+	0.00313687i
$859$	20.6204	−	25.8571i	0.703557	−	0.882233i	−0.293726	−	0.955890i	$-0.594895\pi$
$859$	20.6204	−	25.8571i	0.703557	−	0.882233i	0.997284	+	0.0736566i	$0.0234669\pi$
$860$	10.7504	−	18.6903i	0.366585	−	0.637333i
$861$	−0.0925102	−	0.199668i	−0.00315274	−	0.00680468i
$862$	−11.3372	−	1.27740i	−0.386147	−	0.0435083i
$863$	−7.95523	−	7.95523i	−0.270799	−	0.270799i	0.558623	−	0.829422i	$-0.311330\pi$
$863$	−7.95523	−	7.95523i	−0.270799	−	0.270799i	−0.829422	+	0.558623i	$0.811330\pi$
$864$	0.0598546			0.00203629
$865$	2.80478	+	2.59399i	0.0953655	+	0.0881984i
$866$	−3.77675	+	0.862020i	−0.128339	+	0.0292926i
$867$	0.0133609	+	0.0381833i	0.000453760	+	0.00129677i
$868$	2.51062	−	3.86632i	0.0852161	−	0.131232i
$869$	0.371400	+	0.771221i	0.0125989	+	0.0261619i
$870$	0.00349258	+	0.0894519i	0.000118409	+	0.00303270i
$871$	7.77070	+	16.1360i	0.263300	+	0.546748i
$872$	−2.99251	−	1.88032i	−0.101339	−	0.0636756i
$873$	−24.5317	+	8.58403i	−0.830274	+	0.290525i
$874$	6.07187	−	26.6026i	0.205384	−	0.899847i
$875$	−18.2097	−	23.3111i	−0.615601	−	0.788058i
$876$	−0.00559264	−	0.0245030i	−0.000188958	−	0.000827878i
$877$	−25.1437	−	40.0159i	−0.849041	−	1.35124i	−0.934892	−	0.354933i	$-0.884504\pi$
$877$	−25.1437	−	40.0159i	−0.849041	−	1.35124i	0.0858504	−	0.996308i	$-0.472639\pi$
$878$	−3.09502	−	27.4691i	−0.104452	−	0.927036i
$879$	−0.0963331	−	0.0219874i	−0.00324923	−	0.000741616i
$880$	5.15209	+	0.966162i	0.173677	+	0.0325693i
$881$		−	17.0660i		−	0.574968i	−0.957786	−	0.287484i	$-0.907181\pi$
$881$		−	17.0660i		−	0.574968i	0.957786	−	0.287484i	$-0.0928187\pi$
$882$	17.4393	+	11.6980i	0.587211	+	0.393891i
$883$	20.9315	+	20.9315i	0.704400	+	0.704400i	0.965352	−	0.260952i	$-0.0840363\pi$
$883$	20.9315	+	20.9315i	0.704400	+	0.704400i	−0.260952	+	0.965352i	$0.584036\pi$
$884$	8.28738	+	17.2089i	0.278735	+	0.578798i
$885$	−0.0111070	+	0.151515i	−0.000373359	+	0.00509314i
$886$	−13.3483	+	16.7382i	−0.448445	+	0.562332i
$887$	−36.9501	+	23.2173i	−1.24066	+	0.779560i	−0.982450	−	0.186528i	$-0.940276\pi$
$887$	−36.9501	+	23.2173i	−1.24066	+	0.779560i	−0.258213	+	0.966088i	$0.583134\pi$
$888$	0.0791029	+	0.0497036i	0.00265452	+	0.00166794i
$889$	55.8359	+	0.833353i	1.87268	+	0.0279498i
$890$	−1.47247	+	20.0866i	−0.0493573	+	0.673303i
$891$	19.0070	+	9.15327i	0.636757	+	0.306646i
$892$	−6.90023	+	10.9817i	−0.231037	+	0.367693i
$893$	14.1233	+	4.94195i	0.472618	+	0.165376i
$894$	−0.0240966	−	0.0302162i	−0.000805912	−	0.00101058i
$895$	−7.57454	+	40.3915i	−0.253189	+	1.35014i
$896$	−2.04368	−	1.68028i	−0.0682747	−	0.0561344i
$897$	0.230147	−	0.0805318i	0.00768437	−	0.00268888i
$898$	4.06964	−	6.47680i	0.135806	−	0.216133i
$899$	−4.35972	−	5.46692i	−0.145405	−	0.182332i
$900$	4.46772	+	14.3187i	0.148924	+	0.477289i
$901$			61.2845i			2.04168i
$902$	−2.18836	+	19.4222i	−0.0728645	+	0.646690i
$903$	0.253301	−	0.0247181i	0.00842934	−	0.000822567i
$904$	11.0440	+	8.80727i	0.367317	+	0.292925i
$905$	13.4328	+	49.8082i	0.446522	+	1.65568i
$906$	−0.0307918	+	0.0639398i	−0.00102299	+	0.00212426i
$907$	−9.20729	+	3.22177i	−0.305723	+	0.106977i	−0.478781	−	0.877935i	$-0.658921\pi$
$907$	−9.20729	+	3.22177i	−0.305723	+	0.106977i	0.173058	+	0.984912i	$0.444635\pi$
$908$	−2.30483	−	20.4560i	−0.0764886	−	0.678855i
$909$	17.6264	−	22.1029i	0.584632	−	0.733105i
$910$	24.3979	−	3.34619i	0.808782	−	0.110925i
$911$	−14.5597	−	18.2573i	−0.482384	−	0.604890i	0.479771	−	0.877394i	$-0.340720\pi$
$911$	−14.5597	−	18.2573i	−0.482384	−	0.604890i	−0.962155	+	0.272504i	$0.912148\pi$
$912$	0.0327810	−	0.0327810i	0.00108549	−	0.00108549i
$913$	−25.7862	+	25.7862i	−0.853397	+	0.853397i
$914$	−0.906393	+	0.722824i	−0.0299808	+	0.0239089i
$915$	0.0499246	−	0.0196876i	0.00165046	−	0.000650852i
$916$	1.78305	−	3.70255i	0.0589138	−	0.122336i
$917$	−4.31448	+	1.43780i	−0.142477	+	0.0474803i
$918$	−0.259235	−	0.0907104i	−0.00855604	−	0.00299389i
$919$	−4.96308	+	3.95792i	−0.163717	+	0.130560i	−0.701921	−	0.712254i	$-0.747674\pi$
$919$	−4.96308	+	3.95792i	−0.163717	+	0.130560i	0.538205	+	0.842814i	$0.319103\pi$
$920$	2.41999	−	12.9047i	0.0797848	−	0.425455i
$921$	0.0335822	+	0.147133i	0.00110657	+	0.00484821i
$922$	−8.96309	−	25.6150i	−0.295184	−	0.843586i
$923$	−3.51488	−	5.59390i	−0.115694	−	0.184125i
$924$	0.0260111	+	0.0561407i	0.000855701	+	0.00184689i
$925$	−11.9719	+	45.2675i	−0.393633	+	1.48839i
$926$	4.11317	−	18.0210i	0.135167	−	0.592206i
$927$	10.0371	−	1.13091i	0.329662	−	0.0371440i
$928$	−3.39800	+	2.13511i	−0.111545	+	0.0700883i
$929$	−11.7455	+	5.65633i	−0.385357	+	0.185578i	−0.616524	−	0.787336i	$-0.711460\pi$
$929$	−11.7455	+	5.65633i	−0.385357	+	0.185578i	0.231167	+	0.972914i	$0.425746\pi$
$930$	0.0313101	+	0.0230294i	0.00102670	+	0.000755165i
$931$	31.9162	−	6.28889i	1.04601	−	0.206110i
$932$	−10.4445	+	10.4445i	−0.342120	+	0.342120i
$933$	−0.0710211	−	0.0248514i	−0.00232513	−	0.000813597i
$934$	5.84493	−	25.6083i	0.191252	−	0.837929i
$935$	−20.8499	−	11.9926i	−0.681865	−	0.392200i
$936$	−12.1743	−	2.77871i	−0.397930	−	0.0908249i
$937$	−8.06348	+	12.8330i	−0.263422	+	0.419234i	−0.952079	−	0.305854i	$-0.901058\pi$
$937$	−8.06348	+	12.8330i	−0.263422	+	0.419234i	0.688656	+	0.725088i	$0.258201\pi$
$938$	5.91180	+	9.72788i	0.193027	+	0.317626i
$939$	−0.0213019	−	0.00486202i	−0.000695161	−	0.000158666i
$940$	6.88334	+	2.11099i	0.224510	+	0.0688529i
$941$	−40.5610	+	9.25779i	−1.32225	+	0.301795i	−0.824666	−	0.565620i	$-0.808637\pi$
$941$	−40.5610	+	9.25779i	−1.32225	+	0.301795i	−0.497585	+	0.867415i	$0.665780\pi$
$942$	0.0170041	−	0.0485948i	0.000554023	−	0.00158331i
$943$	48.6478	+	5.48130i	1.58419	+	0.178496i
$944$	−6.13610	+	2.95499i	−0.199713	+	0.0961767i
$945$	−0.214045	+	0.282090i	−0.00696288	+	0.00917639i
$946$	−20.3660	−	9.80777i	−0.662157	−	0.318878i
$947$	45.9851	+	28.8944i	1.49432	+	0.938941i	0.997469	+	0.0711019i	$0.0226516\pi$
$947$	45.9851	+	28.8944i	1.49432	+	0.938941i	0.496846	+	0.867839i	$0.334491\pi$
$948$	0.00361975		0.000407848i	0.000117564		1.32463e-5i
$949$			10.4872i			0.340428i
$950$	20.5781	+	10.7905i	0.667642	+	0.350089i
$951$	0.0748347	−	0.0596787i	0.00242668	−	0.00193521i
$952$	6.30488	+	10.3747i	0.204342	+	0.336246i
$953$	40.4040	−	4.55244i	1.30881	−	0.147468i	0.570149	−	0.821541i	$-0.306885\pi$
$953$	40.4040	−	4.55244i	1.30881	−	0.147468i	0.738665	+	0.674073i	$0.235457\pi$
$954$	−31.3250	−	24.9809i	−1.01419	−	0.808786i
$955$	−0.156603	−	0.295145i	−0.00506754	−	0.00955067i
$956$	−8.93836	−	4.30449i	−0.289087	−	0.139217i
$957$	0.0932609	−	0.0105080i	0.00301470	−	0.000339675i
$958$	−2.88452	−	25.6008i	−0.0931945	−	0.827124i
$959$	−11.2054	−	5.60375i	−0.361841	−	0.180954i
$960$	0.0151459	−	0.0163767i	0.000488833	−	0.000528556i
$961$	27.9640			0.902066
$962$	−27.5643	−	27.5643i	−0.888709	−	0.888709i
$963$	−6.83236	+	60.6389i	−0.220170	+	1.95406i
$964$	−6.51285	−	28.5347i	−0.209765	−	0.919040i
$965$	−15.6429	+	51.0070i	−0.503562	+	1.64197i
$966$	0.140618	−	0.0651512i	0.00452432	−	0.00209621i
$967$	−2.97875	+	8.51278i	−0.0957901	+	0.273752i	−0.981801	−	0.189912i	$-0.939180\pi$
$967$	−2.97875	+	8.51278i	−0.0957901	+	0.273752i	0.886011	+	0.463664i	$0.153466\pi$
$968$	−0.616308	+	5.46989i	−0.0198089	+	0.175809i
$969$	−0.191657	+	0.0922974i	−0.00615692	+	0.00296502i
$970$	−7.71810	+	17.7688i	−0.247813	+	0.570521i
$971$	−4.21921	+	8.76129i	−0.135401	+	0.281163i	−0.957634	−	0.287988i	$-0.907014\pi$
$971$	−4.21921	+	8.76129i	−0.135401	+	0.281163i	0.822233	+	0.569151i	$0.192728\pi$
$972$	0.228055	−	0.143297i	0.00731487	−	0.00459624i
$973$	−5.73248	+	44.8506i	−0.183775	+	1.43784i
$974$	−1.02030	+	0.232878i	−0.0326927	+	0.00746189i
$975$	0.0161887	+	0.206997i	0.000518455	+	0.00662921i
$976$	1.88094	+	1.50000i	0.0602076	+	0.0480139i
$977$	−13.2264	−	21.0497i	−0.423150	−	0.673439i	0.565318	−	0.824873i	$-0.308754\pi$
$977$	−13.2264	−	21.0497i	−0.423150	−	0.673439i	−0.988467	+	0.151434i	$0.951611\pi$
$978$	−0.0165977	+	0.0474334i	−0.000530735	+	0.00151675i
$979$	21.1148			0.674834
$980$	15.2274	−	3.62289i	0.486422	−	0.115729i
$981$	−10.6023			−0.338506
$982$	2.64733	−	7.56564i	0.0844798	−	0.241429i
$983$	−0.0587841	−	0.0935544i	−0.00187492	−	0.00298392i	0.845785	−	0.533523i	$-0.179132\pi$
$983$	−0.0587841	−	0.0935544i	−0.00187492	−	0.00298392i	−0.847660	+	0.530539i	$0.821989\pi$
$984$	0.0650282	+	0.0518582i	0.00207302	+	0.00165318i
$985$	−1.92892	+	26.3132i	−0.0614605	+	0.838407i
$986$	17.9528	−	4.09762i	0.571735	−	0.130495i
$987$	0.0268682	+	0.0806247i	0.000855223	+	0.00256631i
$988$	−16.3791	+	10.2917i	−0.521090	+	0.327422i
$989$	−24.5660	+	51.0118i	−0.781153	+	1.62208i
$990$	14.6288	−	5.76882i	0.464934	−	0.183345i
$991$	−9.64673	+	4.64562i	−0.306439	+	0.147573i	−0.580783	−	0.814058i	$-0.697253\pi$
$991$	−9.64673	+	4.64562i	−0.306439	+	0.147573i	0.274344	+	0.961632i	$0.411539\pi$
$992$	−0.195087	+	1.73144i	−0.00619401	+	0.0549734i
$993$	−0.0319369	+	0.0912703i	−0.00101349	+	0.00289638i
$994$	−2.56881	−	3.32170i	−0.0814778	−	0.105358i
$995$	−8.23539	−	15.5210i	−0.261079	−	0.492050i
$996$	0.0345320	+	0.151295i	0.00109419	+	0.00479396i
$997$	−1.24815	+	11.0776i	−0.0395294	+	0.350833i	0.958342	+	0.285623i	$0.0922004\pi$
$997$	−1.24815	+	11.0776i	−0.0395294	+	0.350833i	−0.997872	+	0.0652102i	$0.979228\pi$
$998$	9.36102	+	9.36102i	0.296318	+	0.296318i
$999$	0.560524			0.0177342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.s.a.223.8	yes	336
5.2	odd	4	inner	490.2.s.a.27.8	✓	336
49.20	odd	14	inner	490.2.s.a.363.8	yes	336
245.167	even	28	inner	490.2.s.a.167.8	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.s.a.27.8	✓	336	5.2	odd	4	inner
490.2.s.a.167.8	yes	336	245.167	even	28	inner
490.2.s.a.223.8	yes	336	1.1	even	1	trivial
490.2.s.a.363.8	yes	336	49.20	odd	14	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.330279 + 0.943883i) q^{2} +(-0.00530751 - 0.00844686i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.69250 + 1.46131i) q^{5} +(0.00972581 - 0.00221985i) q^{6} +(-2.63324 + 0.256962i) q^{7} +(0.846724 - 0.532032i) q^{8} +(1.30161 - 2.70282i) q^{9} +O(q^{10})\)	\(q+(-0.330279 + 0.943883i) q^{2} +(-0.00530751 - 0.00844686i) q^{3} +(-0.781831 - 0.623490i) q^{4} +(-1.69250 + 1.46131i) q^{5} +(0.00972581 - 0.00221985i) q^{6} +(-2.63324 + 0.256962i) q^{7} +(0.846724 - 0.532032i) q^{8} +(1.30161 - 2.70282i) q^{9} +(-0.820308 - 2.08017i) q^{10} +(-2.11209 + 1.01713i) q^{11} +(-0.00111695 + 0.00991320i) q^{12} +(1.37482 - 3.92901i) q^{13} +(0.627163 - 2.57034i) q^{14} +(0.0213265 + 0.00654043i) q^{15} +(0.222521 + 0.974928i) q^{16} +(0.513758 - 4.55973i) q^{17} +(2.12125 + 2.12125i) q^{18} +4.64712 q^{19} +(2.23437 - 0.0872390i) q^{20} +(0.0161465 + 0.0208788i) q^{21} +(-0.262473 - 2.32951i) q^{22} +(-5.83483 + 0.657428i) q^{23} +(-0.00898800 - 0.00432839i) q^{24} +(0.729144 - 4.94655i) q^{25} +(3.25445 + 2.59534i) q^{26} +(-0.0594782 + 0.00670159i) q^{27} +(2.21897 + 1.44090i) q^{28} +(3.13758 - 2.50214i) q^{29} +(-0.0132171 + 0.0179695i) q^{30} -1.74240i q^{31} +(-0.993712 - 0.111964i) q^{32} +(0.0198015 + 0.0124421i) q^{33} +(4.13417 + 1.99091i) q^{34} +(4.08128 - 4.28289i) q^{35} +(-2.70282 + 1.30161i) q^{36} +(-9.30588 - 1.04852i) q^{37} +(-1.53485 + 4.38634i) q^{38} +(-0.0404847 + 0.00924037i) q^{39} +(-0.655621 + 2.13779i) q^{40} +(-8.12845 - 1.85527i) q^{41} +(-0.0250400 + 0.00834458i) q^{42} +(5.13016 - 8.16461i) q^{43} +(2.28547 + 0.521644i) q^{44} +(1.74668 + 6.47658i) q^{45} +(1.30659 - 5.72454i) q^{46} +(3.03915 + 1.06344i) q^{47} +(0.00705405 - 0.00705405i) q^{48} +(6.86794 - 1.35329i) q^{49} +(4.42814 + 2.32197i) q^{50} +(-0.0412422 + 0.0198612i) q^{51} +(-3.52458 + 2.21464i) q^{52} +(-13.2719 + 1.49538i) q^{53} +(0.0133189 - 0.0583539i) q^{54} +(2.08839 - 4.80793i) q^{55} +(-2.09292 + 1.61855i) q^{56} +(-0.0246647 - 0.0392536i) q^{57} +(1.32545 + 3.78791i) q^{58} +(1.51549 + 6.63980i) q^{59} +(-0.0125958 - 0.0184103i) q^{60} +(1.88094 - 1.50000i) q^{61} +(1.64462 + 0.575478i) q^{62} +(-2.73293 + 7.45164i) q^{63} +(0.433884 - 0.900969i) q^{64} +(3.41462 + 8.65891i) q^{65} +(-0.0182840 + 0.0145810i) q^{66} +(-3.04233 + 3.04233i) q^{67} +(-3.24462 + 3.24462i) q^{68} +(0.0365217 + 0.0457967i) q^{69} +(2.69459 + 5.26680i) q^{70} +(0.989548 - 1.24085i) q^{71} +(-0.335882 - 2.98104i) q^{72} +(-2.37800 + 0.832097i) q^{73} +(4.06322 - 8.43736i) q^{74} +(-0.0456527 + 0.0200949i) q^{75} +(-3.63327 - 2.89743i) q^{76} +(5.30030 - 3.22108i) q^{77} +(0.00464942 - 0.0412647i) q^{78} -0.365145i q^{79} +(-1.80129 - 1.32490i) q^{80} +(-5.61085 - 7.03578i) q^{81} +(4.43581 - 7.05955i) q^{82} +(14.6831 - 5.13782i) q^{83} +(0.000393885 - 0.0263909i) q^{84} +(5.79364 + 8.46813i) q^{85} +(6.01205 + 7.53887i) q^{86} +(-0.0377880 - 0.0132226i) q^{87} +(-1.24722 + 1.98493i) q^{88} +(-8.11511 - 3.90803i) q^{89} +(-6.69003 - 0.490421i) q^{90} +(-2.61063 + 10.6993i) q^{91} +(4.97176 + 3.12396i) q^{92} +(-0.0147178 + 0.00924781i) q^{93} +(-2.00753 + 2.51737i) q^{94} +(-7.86527 + 6.79089i) q^{95} +(0.00432839 + 0.00898800i) q^{96} +(-6.12616 - 6.12616i) q^{97} +(-0.990993 + 6.92950i) q^{98} +7.03251i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 28 q^{6} + 8 q^{7}+O(q^{10}) \) 336 * q + 28 * q^6 + 8 * q^7	\( 336 q + 28 q^{6} + 8 q^{7} + 8 q^{11} + 44 q^{15} + 56 q^{16} + 28 q^{17} - 16 q^{21} - 20 q^{22} + 8 q^{23} - 8 q^{25} - 28 q^{26} - 8 q^{28} - 24 q^{30} + 8 q^{35} + 76 q^{36} - 24 q^{37} - 56 q^{41} - 112 q^{42} - 24 q^{43} + 112 q^{45} - 68 q^{46} - 84 q^{47} - 32 q^{50} - 80 q^{51} - 100 q^{53} + 84 q^{55} - 20 q^{56} + 92 q^{57} - 80 q^{58} - 112 q^{61} - 32 q^{67} + 52 q^{70} + 16 q^{71} - 84 q^{75} + 16 q^{77} - 80 q^{78} + 12 q^{81} + 140 q^{83} + 40 q^{85} - 8 q^{86} - 28 q^{87} - 8 q^{88} - 84 q^{90} + 124 q^{91} + 8 q^{92} + 20 q^{93} - 56 q^{95} - 32 q^{98}+O(q^{100}) \) 336 * q + 28 * q^6 + 8 * q^7 + 8 * q^11 + 44 * q^15 + 56 * q^16 + 28 * q^17 - 16 * q^21 - 20 * q^22 + 8 * q^23 - 8 * q^25 - 28 * q^26 - 8 * q^28 - 24 * q^30 + 8 * q^35 + 76 * q^36 - 24 * q^37 - 56 * q^41 - 112 * q^42 - 24 * q^43 + 112 * q^45 - 68 * q^46 - 84 * q^47 - 32 * q^50 - 80 * q^51 - 100 * q^53 + 84 * q^55 - 20 * q^56 + 92 * q^57 - 80 * q^58 - 112 * q^61 - 32 * q^67 + 52 * q^70 + 16 * q^71 - 84 * q^75 + 16 * q^77 - 80 * q^78 + 12 * q^81 + 140 * q^83 + 40 * q^85 - 8 * q^86 - 28 * q^87 - 8 * q^88 - 84 * q^90 + 124 * q^91 + 8 * q^92 + 20 * q^93 - 56 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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