LMFDB - Embedded newform 430.2.q.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	430.101
Dual form			430.2.q.a.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 - 0.781831i) q^{2} +(-0.0251063 + 0.0639697i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(0.0343600 + 0.0595134i) q^{6} +(1.80548 - 3.12719i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(2.19569 + 2.03731i) q^{9} +O(q^{10})$	\(q+(0.623490 - 0.781831i) q^{2} +(-0.0251063 + 0.0639697i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(0.0343600 + 0.0595134i) q^{6} +(1.80548 - 3.12719i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(2.19569 + 2.03731i) q^{9} +(0.826239 + 0.563320i) q^{10} +(-0.806458 + 3.53332i) q^{11} +(0.0679526 + 0.0102422i) q^{12} +(3.70335 - 2.52490i) q^{13} +(-1.31923 - 3.36135i) q^{14} +(-0.0656671 - 0.0202556i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.537687 - 7.17494i) q^{17} +(2.96182 - 0.446423i) q^{18} +(-0.431503 + 0.400376i) q^{19} +(0.955573 - 0.294755i) q^{20} +(0.154716 + 0.194008i) q^{21} +(2.25965 + 2.83351i) q^{22} +(-3.64048 + 1.12294i) q^{23} +(0.0503754 - 0.0467415i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.334954 - 4.46965i) q^{26} +(-0.371196 + 0.178758i) q^{27} +(-3.45054 - 1.06435i) q^{28} +(-3.13362 - 7.98433i) q^{29} +(-0.0567792 + 0.0387114i) q^{30} +(7.37151 + 1.11108i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-0.205779 - 0.140297i) q^{33} +(-5.27435 - 4.89388i) q^{34} +(3.25337 + 1.56674i) q^{35} +(1.49764 - 2.59399i) q^{36} +(5.77585 + 10.0041i) q^{37} +(0.0439890 + 0.586993i) q^{38} +(0.0685400 + 0.300293i) q^{39} +(0.365341 - 0.930874i) q^{40} +(-1.30072 + 1.63105i) q^{41} +0.248146 q^{42} +(1.50824 + 6.38163i) q^{43} +3.62419 q^{44} +(-1.86753 + 2.34180i) q^{45} +(-1.39185 + 3.54638i) q^{46} +(0.732659 + 3.20999i) q^{47} +(-0.00513546 - 0.0685279i) q^{48} +(-3.01954 - 5.22999i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.445480 + 0.214532i) q^{51} +(-3.28567 - 3.04866i) q^{52} +(-9.40582 - 6.41278i) q^{53} +(-0.0916778 + 0.401666i) q^{54} +(-3.58371 - 0.540157i) q^{55} +(-2.98352 + 2.03413i) q^{56} +(-0.0147785 - 0.0376551i) q^{57} +(-8.19618 - 2.52819i) q^{58} +(-10.5903 + 5.10003i) q^{59} +(-0.00513546 + 0.0685279i) q^{60} +(-3.37696 + 0.508995i) q^{61} +(5.46473 - 5.07053i) q^{62} +(10.3353 - 3.18803i) q^{63} +(0.623490 + 0.781831i) q^{64} +(2.79460 + 3.50431i) q^{65} +(-0.237990 + 0.0734101i) q^{66} +(-3.29395 + 3.05634i) q^{67} +(-7.11469 + 1.07237i) q^{68} +(0.0195647 - 0.261073i) q^{69} +(3.25337 - 1.56674i) q^{70} +(-8.48895 - 2.61850i) q^{71} +(-1.09430 - 2.78823i) q^{72} +(-2.27650 + 1.55209i) q^{73} +(11.4227 + 1.72169i) q^{74} +(0.0152917 - 0.0669971i) q^{75} +(0.486356 + 0.331592i) q^{76} +(9.59332 + 8.90130i) q^{77} +(0.277513 + 0.133643i) q^{78} +(-3.01935 + 5.22967i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(0.669396 + 8.93247i) q^{81} +(0.464220 + 2.03388i) q^{82} +(-5.11029 + 13.0208i) q^{83} +(0.154716 - 0.194008i) q^{84} +7.19506 q^{85} +(5.92973 + 2.79969i) q^{86} +0.589429 q^{87} +(2.25965 - 2.83351i) q^{88} +(-1.74550 + 4.44746i) q^{89} +(0.666512 + 2.92018i) q^{90} +(-1.20951 - 16.1398i) q^{91} +(1.90487 + 3.29933i) q^{92} +(-0.256146 + 0.443658i) q^{93} +(2.96648 + 1.42858i) q^{94} +(-0.431503 - 0.400376i) q^{95} +(-0.0567792 - 0.0387114i) q^{96} +(1.08267 - 4.74347i) q^{97} +(-5.97163 - 0.900078i) q^{98} +(-8.96920 + 6.11509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$3$	−0.0251063	+	0.0639697i	−0.0144951	+	0.0369329i	−0.937938	−	0.346803i	$-0.887267\pi$
$3$	−0.0251063	+	0.0639697i	−0.0144951	+	0.0369329i	0.923443	+	0.383736i	$0.125363\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	0.0747301	+	0.997204i	0.0334203	+	0.445963i
$5$	0.0747301	+	0.997204i	0.0334203	+	0.445963i
$6$	0.0343600	+	0.0595134i	0.0140274	+	0.0242962i
$7$	1.80548	−	3.12719i	0.682408	−	1.18197i	−0.291835	−	0.956469i	$-0.594266\pi$
$7$	1.80548	−	3.12719i	0.682408	−	1.18197i	0.974244	−	0.225498i	$-0.0724008\pi$
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	2.19569	+	2.03731i	0.731898	+	0.679102i
$10$	0.826239	+	0.563320i	0.261280	+	0.178137i
$11$	−0.806458	+	3.53332i	−0.243156	+	1.06534i	0.694969	+	0.719040i	$0.255418\pi$
$11$	−0.806458	+	3.53332i	−0.243156	+	1.06534i	−0.938125	+	0.346297i	$0.887439\pi$
$12$	0.0679526	+	0.0102422i	0.0196162	+	0.00295667i
$13$	3.70335	−	2.52490i	1.02713	−	0.700282i	0.0722797	−	0.997384i	$-0.476973\pi$
$13$	3.70335	−	2.52490i	1.02713	−	0.700282i	0.954846	+	0.297102i	$0.0960202\pi$
$14$	−1.31923	−	3.36135i	−0.352580	−	0.898360i
$15$	−0.0656671	−	0.0202556i	−0.0169552	−	0.00522997i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.537687	−	7.17494i	0.130408	−	1.74018i	−0.421993	−	0.906599i	$-0.638669\pi$
$17$	0.537687	−	7.17494i	0.130408	−	1.74018i	0.552401	−	0.833579i	$-0.313712\pi$
$18$	2.96182	−	0.446423i	0.698108	−	0.105223i
$19$	−0.431503	+	0.400376i	−0.0989935	+	0.0918525i	−0.728117	−	0.685453i	$-0.759604\pi$
$19$	−0.431503	+	0.400376i	−0.0989935	+	0.0918525i	0.629124	+	0.777305i	$0.283414\pi$
$20$	0.955573	−	0.294755i	0.213673	−	0.0659093i
$21$	0.154716	+	0.194008i	0.0337619	+	0.0423361i
$22$	2.25965	+	2.83351i	0.481758	+	0.604105i
$23$	−3.64048	+	1.12294i	−0.759092	+	0.234149i	−0.650053	−	0.759889i	$-0.725253\pi$
$23$	−3.64048	+	1.12294i	−0.759092	+	0.234149i	−0.109039	+	0.994038i	$0.534777\pi$
$24$	0.0503754	−	0.0467415i	0.0102828	−	0.00954108i
$25$	−0.988831	+	0.149042i	−0.197766	+	0.0298085i
$26$	0.334954	−	4.46965i	0.0656899	−	0.876570i
$27$	−0.371196	+	0.178758i	−0.0714366	+	0.0344021i
$28$	−3.45054	−	1.06435i	−0.652091	−	0.201143i
$29$	−3.13362	−	7.98433i	−0.581898	−	1.48265i	−0.853942	−	0.520368i	$-0.825795\pi$
$29$	−3.13362	−	7.98433i	−0.581898	−	1.48265i	0.272044	−	0.962285i	$-0.412300\pi$
$30$	−0.0567792	+	0.0387114i	−0.0103664	+	0.00706770i
$31$	7.37151	+	1.11108i	1.32396	+	0.199555i	0.772697	−	0.634775i	$-0.218907\pi$
$31$	7.37151	+	1.11108i	1.32396	+	0.199555i	0.551265	+	0.834330i	$0.314145\pi$
$32$	−0.222521	+	0.974928i	−0.0393365	+	0.172345i
$33$	−0.205779	−	0.140297i	−0.0358215	−	0.0244227i
$34$	−5.27435	−	4.89388i	−0.904543	−	0.839294i
$35$	3.25337	+	1.56674i	0.549920	+	0.264827i
$36$	1.49764	−	2.59399i	0.249606	−	0.432331i
$37$	5.77585	+	10.0041i	0.949544	+	1.64466i	0.746388	+	0.665511i	$0.231786\pi$
$37$	5.77585	+	10.0041i	0.949544	+	1.64466i	0.203156	+	0.979146i	$0.434880\pi$
$38$	0.0439890	+	0.586993i	0.00713596	+	0.0952228i
$39$	0.0685400	+	0.300293i	0.0109752	+	0.0480854i
$40$	0.365341	−	0.930874i	0.0577655	−	0.147184i
$41$	−1.30072	+	1.63105i	−0.203138	+	0.254727i	−0.872957	−	0.487798i	$-0.837800\pi$
$41$	−1.30072	+	1.63105i	−0.203138	+	0.254727i	0.669819	+	0.742524i	$0.266372\pi$
$42$	0.248146			0.0382898
$43$	1.50824	+	6.38163i	0.230004	+	0.973190i
$43$	1.50824	+	6.38163i	0.230004	+	0.973190i
$44$	3.62419			0.546367
$45$	−1.86753	+	2.34180i	−0.278394	+	0.349095i
$46$	−1.39185	+	3.54638i	−0.205217	+	0.522885i
$47$	0.732659	+	3.20999i	0.106869	+	0.468225i	0.999836	+	0.0181026i	$0.00576254\pi$
$47$	0.732659	+	3.20999i	0.106869	+	0.468225i	−0.892967	+	0.450122i	$0.851380\pi$
$48$	−0.00513546	−	0.0685279i	−0.000741240	−	0.00989116i
$49$	−3.01954	−	5.22999i	−0.431363	−	0.747142i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.445480	+	0.214532i	0.0623796	+	0.0300404i
$52$	−3.28567	−	3.04866i	−0.455641	−	0.422773i
$53$	−9.40582	−	6.41278i	−1.29199	−	0.880863i	−0.294783	−	0.955564i	$-0.595247\pi$
$53$	−9.40582	−	6.41278i	−1.29199	−	0.880863i	−0.997206	+	0.0747016i	$0.976200\pi$
$54$	−0.0916778	+	0.401666i	−0.0124758	+	0.0546599i
$55$	−3.58371	−	0.540157i	−0.483227	−	0.0728348i
$56$	−2.98352	+	2.03413i	−0.398690	+	0.271822i
$57$	−0.0147785	−	0.0376551i	−0.00195746	−	0.00498753i
$58$	−8.19618	−	2.52819i	−1.07621	−	0.331967i
$59$	−10.5903	+	5.10003i	−1.37874	+	0.663968i	−0.968731	−	0.248113i	$-0.920190\pi$
$59$	−10.5903	+	5.10003i	−1.37874	+	0.663968i	−0.410012	+	0.912080i	$0.634475\pi$
$60$	−0.00513546	+	0.0685279i	−0.000662985	+	0.00884692i
$61$	−3.37696	+	0.508995i	−0.432375	+	0.0651701i	−0.361624	−	0.932324i	$-0.617778\pi$
$61$	−3.37696	+	0.508995i	−0.432375	+	0.0651701i	−0.0707511	+	0.997494i	$0.522540\pi$
$62$	5.46473	−	5.07053i	0.694022	−	0.643958i
$63$	10.3353	−	3.18803i	1.30213	−	0.401654i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	2.79460	+	3.50431i	0.346627	+	0.434656i
$66$	−0.237990	+	0.0734101i	−0.0292945	+	0.00903616i
$67$	−3.29395	+	3.05634i	−0.402420	+	0.373392i	−0.855259	−	0.518201i	$-0.826602\pi$
$67$	−3.29395	+	3.05634i	−0.402420	+	0.373392i	0.452838	+	0.891593i	$0.350411\pi$
$68$	−7.11469	+	1.07237i	−0.862783	+	0.130044i
$69$	0.0195647	−	0.261073i	0.00235532	−	0.0314295i
$70$	3.25337	−	1.56674i	0.388852	−	0.187261i
$71$	−8.48895	−	2.61850i	−1.00745	−	0.310758i	−0.253251	−	0.967401i	$-0.581500\pi$
$71$	−8.48895	−	2.61850i	−1.00745	−	0.310758i	−0.754202	+	0.656642i	$0.771976\pi$
$72$	−1.09430	−	2.78823i	−0.128964	−	0.328595i
$73$	−2.27650	+	1.55209i	−0.266445	+	0.181659i	−0.689171	−	0.724598i	$-0.742025\pi$
$73$	−2.27650	+	1.55209i	−0.266445	+	0.181659i	0.422727	+	0.906257i	$0.361073\pi$
$74$	11.4227	+	1.72169i	1.32786	+	0.200143i
$75$	0.0152917	−	0.0669971i	0.00176573	−	0.00773616i
$76$	0.486356	+	0.331592i	0.0557889	+	0.0380362i
$77$	9.59332	+	8.90130i	1.09326	+	1.01440i
$78$	0.277513	+	0.133643i	0.0314221	+	0.0151321i
$79$	−3.01935	+	5.22967i	−0.339704	+	0.588384i	−0.984377	−	0.176074i	$-0.943660\pi$
$79$	−3.01935	+	5.22967i	−0.339704	+	0.588384i	0.644673	+	0.764458i	$0.276993\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	0.669396	+	8.93247i	0.0743774	+	0.992497i
$82$	0.464220	+	2.03388i	0.0512645	+	0.224605i
$83$	−5.11029	+	13.0208i	−0.560927	+	1.42922i	0.316075	+	0.948734i	$0.397635\pi$
$83$	−5.11029	+	13.0208i	−0.560927	+	1.42922i	−0.877003	+	0.480485i	$0.840460\pi$
$84$	0.154716	−	0.194008i	0.0168810	−	0.0211680i
$85$	7.19506			0.780413
$86$	5.92973	+	2.79969i	0.639419	+	0.301899i
$87$	0.589429			0.0631934
$88$	2.25965	−	2.83351i	0.240879	−	0.302053i
$89$	−1.74550	+	4.44746i	−0.185023	+	0.471430i	−0.993047	−	0.117719i	$-0.962442\pi$
$89$	−1.74550	+	4.44746i	−0.185023	+	0.471430i	0.808024	+	0.589149i	$0.200537\pi$
$90$	0.666512	+	2.92018i	0.0702565	+	0.307814i
$91$	−1.20951	−	16.1398i	−0.126791	−	1.69191i
$92$	1.90487	+	3.29933i	0.198596	+	0.343978i
$93$	−0.256146	+	0.443658i	−0.0265611	+	0.0460052i
$94$	2.96648	+	1.42858i	0.305969	+	0.147347i
$95$	−0.431503	−	0.400376i	−0.0442712	−	0.0410777i
$96$	−0.0567792	−	0.0387114i	−0.00579500	−	0.00395097i
$97$	1.08267	−	4.74347i	0.109928	−	0.481627i	−0.889755	−	0.456439i	$-0.849125\pi$
$97$	1.08267	−	4.74347i	0.109928	−	0.481627i	0.999683	−	0.0251875i	$-0.00801829\pi$
$98$	−5.97163	−	0.900078i	−0.603225	−	0.0909216i
$99$	−8.96920	+	6.11509i	−0.901438	+	0.614590i
$100$	0.365341	+	0.930874i	0.0365341	+	0.0930874i
$101$	13.8832	+	4.28239i	1.38143	+	0.426114i	0.894398	−	0.447272i	$-0.147604\pi$
$101$	13.8832	+	4.28239i	1.38143	+	0.426114i	0.487029	+	0.873386i	$0.338081\pi$
$102$	0.445480	−	0.214532i	0.0441090	−	0.0212418i
$103$	1.08162	−	14.4333i	0.106576	−	1.42215i	−0.645845	−	0.763469i	$-0.723495\pi$
$103$	1.08162	−	14.4333i	0.106576	−	1.42215i	0.752420	−	0.658683i	$-0.228886\pi$
$104$	−4.43212	+	0.668035i	−0.434605	+	0.0655062i
$105$	−0.181904	+	0.168782i	−0.0177520	+	0.0164714i
$106$	−10.8781	+	3.35546i	−1.05658	+	0.325911i
$107$	7.06165	+	8.85503i	0.682675	+	0.856048i	0.995598	−	0.0937308i	$-0.0298793\pi$
$107$	7.06165	+	8.85503i	0.682675	+	0.856048i	−0.312922	+	0.949779i	$0.601308\pi$
$108$	0.256875	+	0.322111i	0.0247178	+	0.0309952i
$109$	−2.05497	+	0.633874i	−0.196830	+	0.0607141i	−0.391603	−	0.920134i	$-0.628079\pi$
$109$	−2.05497	+	0.633874i	−0.196830	+	0.0607141i	0.194773	+	0.980848i	$0.437603\pi$
$110$	−2.65672	+	2.46507i	−0.253308	+	0.235036i
$111$	−0.784967	+	0.118315i	−0.0745058	+	0.0112299i
$112$	−0.269848	+	3.60087i	−0.0254982	+	0.340250i
$113$	15.1761	−	7.30843i	1.42765	−	0.687520i	0.449090	−	0.893486i	$-0.351748\pi$
$113$	15.1761	−	7.30843i	1.42765	−	0.687520i	0.978559	+	0.205967i	$0.0660338\pi$
$114$	−0.0386542	−	0.0119232i	−0.00362029	−	0.00111671i
$115$	−1.39185	−	3.54638i	−0.129791	−	0.330702i
$116$	−7.08685	+	4.83173i	−0.657997	+	0.448615i
$117$	13.2754	+	2.00095i	1.22731	+	0.184988i
$118$	−2.61559	+	11.4597i	−0.240785	+	1.05495i
$119$	−21.4666	−	14.6357i	−1.96784	−	1.34165i
$120$	0.0503754	+	0.0467415i	0.00459862	+	0.00426690i
$121$	−1.92334	−	0.926232i	−0.174849	−	0.0842029i
$122$	−1.70755	+	2.95757i	−0.154594	+	0.267765i
$123$	−0.0716815	−	0.124156i	−0.00646330	−	0.0111948i
$124$	−0.557096	−	7.43392i	−0.0500287	−	0.667586i
$125$	−0.222521	−	0.974928i	−0.0199029	−	0.0872002i
$126$	3.95147	−	10.0682i	0.352025	−	0.896945i
$127$	−0.124627	+	0.156278i	−0.0110589	+	0.0138674i	−0.787330	−	0.616532i	$-0.788537\pi$
$127$	−0.124627	+	0.156278i	−0.0110589	+	0.0138674i	0.776271	+	0.630399i	$0.217109\pi$
$128$	1.00000			0.0883883
$129$	−0.446098	−	0.0637373i	−0.0392767	−	0.00561176i
$130$	4.48218			0.393113
$131$	−5.98208	+	7.50129i	−0.522657	+	0.655391i	−0.971171	−	0.238385i	$-0.923382\pi$
$131$	−5.98208	+	7.50129i	−0.522657	+	0.655391i	0.448514	+	0.893776i	$0.351953\pi$
$132$	−0.0909899	+	0.231838i	−0.00791965	+	0.0201789i
$133$	0.472980	+	2.07226i	0.0410126	+	0.179688i
$134$	0.335798	+	4.48091i	0.0290085	+	0.387092i
$135$	−0.205998	−	0.356799i	−0.0177295	−	0.0307084i
$136$	−3.59753	+	6.23110i	−0.308485	+	0.534313i
$137$	−19.2073	−	9.24974i	−1.64099	−	0.790259i	−0.999737	−	0.0229278i	$-0.992701\pi$
$137$	−19.2073	−	9.24974i	−1.64099	−	0.790259i	−0.641252	−	0.767331i	$-0.721584\pi$
$138$	−0.191917	−	0.178073i	−0.0163370	−	0.0151586i
$139$	−7.17018	−	4.88854i	−0.608166	−	0.414641i	0.219699	−	0.975568i	$-0.429492\pi$
$139$	−7.17018	−	4.88854i	−0.608166	−	0.414641i	−0.827865	+	0.560927i	$0.810445\pi$
$140$	0.803516	−	3.52043i	0.0679095	−	0.297531i
$141$	−0.223736	−	0.0337229i	−0.0188420	−	0.00283998i
$142$	−7.34000	+	5.00433i	−0.615959	+	0.419954i
$143$	5.93470	+	15.1214i	0.496285	+	1.26451i
$144$	−2.86221	−	0.882874i	−0.238517	−	0.0735728i
$145$	7.72783	−	3.72153i	0.641761	−	0.309056i
$146$	−0.205901	+	2.74756i	−0.0170405	+	0.227389i
$147$	0.410371	−	0.0618534i	0.0338468	−	0.00510158i
$148$	8.46799	−	7.85715i	0.696065	−	0.645854i
$149$	1.65259	−	0.509756i	0.135385	−	0.0417608i	−0.226322	−	0.974053i	$-0.572670\pi$
$149$	1.65259	−	0.509756i	0.135385	−	0.0417608i	0.361707	+	0.932292i	$0.382194\pi$
$150$	−0.0428463	−	0.0537275i	−0.00349838	−	0.00438684i
$151$	−6.32727	−	7.93414i	−0.514906	−	0.645671i	0.454613	−	0.890689i	$-0.349778\pi$
$151$	−6.32727	−	7.93414i	−0.514906	−	0.645671i	−0.969519	+	0.245018i	$0.921206\pi$
$152$	0.562487	−	0.173504i	0.0456237	−	0.0140731i
$153$	15.7981	−	14.6585i	1.27720	−	1.18507i
$154$	12.9407	−	1.95049i	1.04279	−	0.157175i
$155$	−0.557096	+	7.43392i	−0.0447470	+	0.597107i
$156$	0.277513	−	0.133643i	0.0222188	−	0.0107000i
$157$	5.53778	+	1.70818i	0.441963	+	0.136327i	0.507747	−	0.861506i	$-0.330479\pi$
$157$	5.53778	+	1.70818i	0.441963	+	0.136327i	−0.0657840	+	0.997834i	$0.520955\pi$
$158$	2.20619	+	5.62127i	0.175515	+	0.447204i
$159$	0.646369	−	0.440687i	0.0512604	−	0.0349487i
$160$	−0.988831	−	0.149042i	−0.0781739	−	0.0117828i
$161$	−3.06118	+	13.4119i	−0.241255	+	1.05701i
$162$	7.40105	+	5.04595i	0.581481	+	0.396447i
$163$	−12.9308	−	11.9980i	−1.01282	−	0.939758i	−0.0146275	−	0.999893i	$-0.504656\pi$
$163$	−12.9308	−	11.9980i	−1.01282	−	0.939758i	−0.998190	+	0.0601355i	$0.980847\pi$
$164$	1.87959	+	0.905162i	0.146771	+	0.0706813i
$165$	0.124527	−	0.215688i	0.00969444	−	0.0167913i
$166$	6.99386	+	12.1137i	0.542829	+	0.940208i
$167$	0.584712	+	7.80243i	0.0452463	+	0.603770i	0.973034	+	0.230662i	$0.0740891\pi$
$167$	0.584712	+	7.80243i	0.0452463	+	0.603770i	−0.927788	+	0.373109i	$0.878292\pi$
$168$	−0.0552177	−	0.241924i	−0.00426014	−	0.0186649i
$169$	2.59025	−	6.59986i	0.199250	−	0.507681i
$170$	4.48604	−	5.62532i	0.344064	−	0.431442i
$171$	−1.76314			−0.134830
$172$	5.88602	−	2.89047i	0.448804	−	0.220396i
$173$	−1.11322			−0.0846367			−0.0423184	−	0.999104i	$-0.513474\pi$
$173$	−1.11322			−0.0846367			−0.0423184	+	0.999104i	$0.513474\pi$
$174$	0.367503	−	0.460834i	0.0278603	−	0.0349357i
$175$	−1.31923	+	3.36135i	−0.0997247	+	0.254094i
$176$	−0.806458	−	3.53332i	−0.0607891	−	0.266334i
$177$	−0.0603641	−	0.805503i	−0.00453724	−	0.0605453i
$178$	2.38887	+	4.13764i	0.179053	+	0.310129i
$179$	3.99994	−	6.92810i	0.298969	−	0.517830i	−0.676931	−	0.736047i	$-0.736690\pi$
$179$	3.99994	−	6.92810i	0.298969	−	0.517830i	0.975900	+	0.218216i	$0.0700238\pi$
$180$	2.69865	+	1.29960i	0.201146	+	0.0968666i
$181$	9.57637	+	8.88557i	0.711806	+	0.660459i	0.950532	−	0.310628i	$-0.100539\pi$
$181$	9.57637	+	8.88557i	0.711806	+	0.660459i	−0.238726	+	0.971087i	$0.576730\pi$
$182$	−13.3727	−	9.11734i	−0.991249	−	0.675822i
$183$	0.0522226	−	0.228802i	0.00386041	−	0.0169135i
$184$	3.76718	+	0.567811i	0.277720	+	0.0418596i
$185$	−9.54446	+	6.50730i	−0.701723	+	0.478426i
$186$	0.187161	+	0.476880i	0.0137233	+	0.0349665i
$187$	24.9178	+	7.68611i	1.82217	+	0.562064i
$188$	2.96648	−	1.42858i	0.216352	−	0.104190i
$189$	−0.111176	+	1.48354i	−0.00808688	+	0.107912i
$190$	−0.582064	+	0.0877320i	−0.0422274	+	0.00636475i
$191$	19.9507	−	18.5116i	1.44358	−	1.33945i	0.603036	−	0.797714i	$-0.293957\pi$
$191$	19.9507	−	18.5116i	1.44358	−	1.33945i	0.840548	−	0.541737i	$-0.182233\pi$
$192$	−0.0656671	+	0.0202556i	−0.00473911	+	0.00146182i
$193$	−13.4349	−	16.8469i	−0.967068	−	1.21266i	−0.977114	−	0.212715i	$-0.931769\pi$
$193$	−13.4349	−	16.8469i	−0.967068	−	1.21266i	0.0100467	−	0.999950i	$-0.496802\pi$
$194$	−3.03357	−	3.80397i	−0.217797	−	0.273109i
$195$	−0.294332	+	0.0907893i	−0.0210775	+	0.00650156i
$196$	−4.42696	+	4.10762i	−0.316211	+	0.293401i
$197$	−0.176560	+	0.0266122i	−0.0125794	+	0.00189604i	−0.155329	−	0.987863i	$-0.549644\pi$
$197$	−0.176560	+	0.0266122i	−0.0125794	+	0.00189604i	0.142750	+	0.989759i	$0.454406\pi$
$198$	−0.811229	+	10.8251i	−0.0576515	+	0.769306i
$199$	−15.0175	+	7.23203i	−1.06456	+	0.512665i	−0.882350	−	0.470595i	$-0.844039\pi$
$199$	−15.0175	+	7.23203i	−1.06456	+	0.512665i	−0.182210	+	0.983260i	$0.558325\pi$
$200$	0.955573	+	0.294755i	0.0675692	+	0.0208423i
$201$	−0.112814	−	0.287447i	−0.00795732	−	0.0202749i
$202$	12.0041	−	8.18427i	0.844607	−	0.575843i
$203$	−30.6262	−	4.61616i	−2.14954	−	0.323991i
$204$	0.110024	−	0.482048i	0.00770325	−	0.0337501i
$205$	−1.72369	−	1.17519i	−0.120388	−	0.0820789i
$206$	−10.6100	−	9.84464i	−0.739234	−	0.685909i
$207$	−10.2811	−	4.95114i	−0.714589	−	0.344128i
$208$	−2.24109	+	3.88168i	−0.155392	+	0.269146i
$209$	−1.06667	−	1.84752i	−0.0737830	−	0.127796i
$210$	0.0185440	+	0.247452i	0.00127966	+	0.0170758i
$211$	−0.406196	−	1.77966i	−0.0279637	−	0.122517i	0.959020	−	0.283340i	$-0.0914424\pi$
$211$	−0.406196	−	1.77966i	−0.0279637	−	0.122517i	−0.986983	+	0.160823i	$0.948585\pi$
$212$	−4.15900	+	10.5970i	−0.285642	+	0.727803i
$213$	0.380630	−	0.477295i	0.0260804	−	0.0327037i
$214$	11.3260			0.774230
$215$	−6.25108	+	1.98092i	−0.426320	+	0.135098i
$216$	0.411996			0.0280328
$217$	16.7837	−	21.0461i	1.13935	−	1.42870i
$218$	−0.785670	+	2.00185i	−0.0532123	+	0.135583i
$219$	−0.0421325	−	0.184595i	−0.00284705	−	0.0124737i
$220$	0.270836	+	3.61406i	0.0182598	+	0.243660i
$221$	−16.1248	−	27.9289i	−1.08467	−	1.87870i
$222$	−0.396917	+	0.687480i	−0.0266393	+	0.0461406i
$223$	13.0044	+	6.26260i	0.870840	+	0.419374i	0.815270	−	0.579080i	$-0.196588\pi$
$223$	13.0044	+	6.26260i	0.870840	+	0.419374i	0.0555695	+	0.998455i	$0.482303\pi$
$224$	2.64703	+	2.45608i	0.176862	+	0.164104i
$225$	−2.47481	−	1.68730i	−0.164988	−	0.112487i
$226$	3.74819	−	16.4219i	0.249326	−	1.09237i
$227$	5.17608	+	0.780169i	0.343549	+	0.0517816i	0.318551	−	0.947906i	$-0.396804\pi$
$227$	5.17608	+	0.780169i	0.343549	+	0.0517816i	0.0249981	+	0.999687i	$0.492042\pi$
$228$	−0.0334224	+	0.0227870i	−0.00221346	+	0.00150911i
$229$	−1.73533	−	4.42155i	−0.114674	−	0.292184i	0.862001	−	0.506906i	$-0.169211\pi$
$229$	−1.73533	−	4.42155i	−0.114674	−	0.292184i	−0.976675	+	0.214722i	$0.931116\pi$
$230$	−3.64048	−	1.12294i	−0.240046	−	0.0740444i
$231$	−0.810266	+	0.390204i	−0.0533116	+	0.0256735i
$232$	−0.640978	+	8.55326i	−0.0420823	+	0.561549i
$233$	12.3689	−	1.86432i	0.810316	−	0.122136i	0.269201	−	0.963084i	$-0.413240\pi$
$233$	12.3689	−	1.86432i	0.810316	−	0.122136i	0.541115	+	0.840948i	$0.318002\pi$
$234$	9.84150	−	9.13158i	0.643359	−	0.596950i
$235$	−3.14626	+	0.970493i	−0.205239	+	0.0633080i
$236$	7.32873	+	9.18994i	0.477060	+	0.598214i
$237$	−0.258736	−	0.324445i	−0.0168067	−	0.0210749i
$238$	−24.8268	+	7.65807i	−1.60928	+	0.496399i
$239$	−4.41730	+	4.09865i	−0.285731	+	0.265120i	−0.809996	−	0.586436i	$-0.800531\pi$
$239$	−4.41730	+	4.09865i	−0.285731	+	0.265120i	0.524265	+	0.851555i	$0.324340\pi$
$240$	0.0679526	−	0.0102422i	0.00438632	−	0.000661131i
$241$	0.563287	−	7.51655i	0.0362845	−	0.484183i	−0.949229	−	0.314586i	$-0.898134\pi$
$241$	0.563287	−	7.51655i	0.0362845	−	0.484183i	0.985513	−	0.169597i	$-0.0542467\pi$
$242$	−1.92334	+	0.926232i	−0.123637	+	0.0595405i
$243$	−1.76929	−	0.545754i	−0.113500	−	0.0350101i
$244$	1.24768	+	3.17903i	0.0798744	+	0.203517i
$245$	4.98972	−	3.40193i	0.318781	−	0.217342i
$246$	−0.141762	−	0.0213671i	−0.00903839	−	0.00136232i
$247$	−0.587096	+	2.57224i	−0.0373560	+	0.163667i
$248$	−6.15942	−	4.19942i	−0.391124	−	0.266664i
$249$	−0.704637	−	0.653808i	−0.0446546	−	0.0414334i
$250$	−0.900969	−	0.433884i	−0.0569823	−	0.0274412i
$251$	13.9212	−	24.1123i	0.878700	−	1.52195i	0.0259318	−	0.999664i	$-0.491745\pi$
$251$	13.9212	−	24.1123i	0.878700	−	1.52195i	0.852768	−	0.522289i	$-0.174922\pi$
$252$	−5.40792	−	9.36680i	−0.340667	−	0.590053i
$253$	−1.03181	−	13.7686i	−0.0648695	−	0.865624i
$254$	0.0444790	+	0.194875i	0.00279086	+	0.0122276i
$255$	−0.180641	+	0.460266i	−0.0113122	+	0.0288230i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−24.9886			−1.55875			−0.779374	−	0.626560i	$-0.784463\pi$
$257$	−24.9886			−1.55875			−0.779374	+	0.626560i	$0.784463\pi$
$258$	−0.327969	+	0.309034i	−0.0204185	+	0.0192396i
$259$	41.7128			2.59191
$260$	2.79460	−	3.50431i	0.173313	−	0.217328i
$261$	9.38606	−	23.9153i	0.580982	−	1.48032i
$262$	2.13498	+	9.35396i	0.131900	+	0.577890i
$263$	0.804535	+	10.7358i	0.0496098	+	0.661996i	0.965473	+	0.260505i	$0.0838890\pi$
$263$	0.804535	+	10.7358i	0.0496098	+	0.661996i	−0.915863	+	0.401492i	$0.868492\pi$
$264$	0.124527	+	0.215688i	0.00766413	+	0.0132747i
$265$	5.69195	−	9.85874i	0.349654	−	0.605618i
$266$	1.91506	+	0.922243i	0.117420	+	0.0565464i
$267$	−0.240680	−	0.223319i	−0.0147294	−	0.0136669i
$268$	3.71269	+	2.53127i	0.226788	+	0.154622i
$269$	−2.80402	+	12.2852i	−0.170964	+	0.749043i	0.814639	+	0.579968i	$0.196935\pi$
$269$	−2.80402	+	12.2852i	−0.170964	+	0.749043i	−0.985603	+	0.169075i	$0.945922\pi$
$270$	−0.407394	−	0.0614048i	−0.0247932	−	0.00373698i
$271$	−16.5687	+	11.2963i	−1.00648	+	0.686203i	−0.950016	−	0.312201i	$-0.898934\pi$
$271$	−16.5687	+	11.2963i	−1.00648	+	0.686203i	−0.0564596	+	0.998405i	$0.517981\pi$
$272$	2.62865	+	6.69769i	0.159385	+	0.406107i
$273$	1.06282	+	0.327837i	0.0643249	+	0.0198416i
$274$	−19.2073	+	9.24974i	−1.16035	+	0.558797i
$275$	0.270836	−	3.61406i	0.0163320	−	0.217936i
$276$	−0.258881	+	0.0390200i	−0.0155828	+	0.00234873i
$277$	−8.27488	+	7.67797i	−0.497189	+	0.461324i	−0.888462	−	0.458951i	$-0.848225\pi$
$277$	−8.27488	+	7.67797i	−0.497189	+	0.461324i	0.391272	+	0.920275i	$0.372035\pi$
$278$	−8.29255	+	2.55791i	−0.497354	+	0.153413i
$279$	13.9220	+	17.4576i	0.833486	+	1.04516i
$280$	−2.25140	−	2.82317i	−0.134547	−	0.168717i
$281$	5.67292	−	1.74987i	0.338418	−	0.104388i	−0.120888	−	0.992666i	$-0.538574\pi$
$281$	5.67292	−	1.74987i	0.338418	−	0.104388i	0.459306	+	0.888278i	$0.348098\pi$
$282$	−0.165863	+	0.153898i	−0.00987700	+	0.00916452i
$283$	8.85391	−	1.33451i	0.526310	−	0.0793285i	0.119488	−	0.992836i	$-0.461875\pi$
$283$	8.85391	−	1.33451i	0.526310	−	0.0793285i	0.406823	+	0.913507i	$0.366637\pi$
$284$	−0.663874	+	8.85879i	−0.0393937	+	0.525672i
$285$	0.0364454	−	0.0175512i	0.00215884	−	0.00103964i
$286$	15.5226	+	4.78809i	0.917870	+	0.283125i
$287$	2.75217	+	7.01241i	0.162455	+	0.413929i
$288$	−2.47481	+	1.68730i	−0.145830	+	0.0994251i
$289$	−34.3805	−	5.18203i	−2.02238	−	0.304825i
$290$	1.90862	−	8.36219i	0.112078	−	0.491045i
$291$	0.276257	+	0.188349i	0.0161945	+	0.0110412i
$292$	2.01975	+	1.87405i	0.118197	+	0.109671i
$293$	29.4963	+	14.2047i	1.72319	+	0.829846i	0.988459	+	0.151491i	$0.0484075\pi$
$293$	29.4963	+	14.2047i	1.72319	+	0.829846i	0.734735	+	0.678355i	$0.237307\pi$
$294$	0.207503	−	0.359406i	0.0121018	−	0.0209610i
$295$	−5.87719	−	10.1796i	−0.342183	−	0.592678i
$296$	−0.863259	−	11.5194i	−0.0501759	−	0.669551i
$297$	−0.332258	−	1.45572i	−0.0192795	−	0.0844692i
$298$	0.631829	−	1.60987i	0.0366009	−	0.0932575i
$299$	−10.6467	+	13.3505i	−0.615712	+	0.772079i
$300$	−0.0687201			−0.00396756
$301$	22.6797	+	6.80538i	1.30723	+	0.392256i
$302$	−10.1482			−0.583960
$303$	−0.622498	+	0.780588i	−0.0357616	+	0.0448436i
$304$	0.215054	−	0.547948i	0.0123342	−	0.0314270i
$305$	−0.759932	−	3.32948i	−0.0435136	−	0.190645i
$306$	−1.61052	−	21.4909i	−0.0920674	−	1.22855i
$307$	0.143342	+	0.248276i	0.00818096	+	0.0141698i	0.870087	−	0.492898i	$-0.164063\pi$
$307$	0.143342	+	0.248276i	0.00818096	+	0.0141698i	−0.861906	+	0.507068i	$0.830729\pi$
$308$	6.54341	−	11.3335i	0.372846	−	0.645787i
$309$	0.896137	+	0.431557i	0.0509794	+	0.0245504i
$310$	5.46473	+	5.07053i	0.310376	+	0.287987i
$311$	−8.12546	−	5.53984i	−0.460752	−	0.314136i	0.310604	−	0.950540i	$-0.399469\pi$
$311$	−8.12546	−	5.53984i	−0.460752	−	0.314136i	−0.771356	+	0.636404i	$0.780421\pi$
$312$	0.0685400	−	0.300293i	0.00388031	−	0.0170008i
$313$	8.63981	+	1.30224i	0.488351	+	0.0736071i	0.388602	−	0.921406i	$-0.372958\pi$
$313$	8.63981	+	1.30224i	0.488351	+	0.0736071i	0.0997488	+	0.995013i	$0.468196\pi$
$314$	4.78825	−	3.26458i	0.270217	−	0.184231i
$315$	3.95147	+	10.0682i	0.222640	+	0.567278i
$316$	5.77042	+	1.77994i	0.324612	+	0.100129i
$317$	−6.92149	+	3.33322i	−0.388750	+	0.187212i	−0.618041	−	0.786146i	$-0.712073\pi$
$317$	−6.92149	+	3.33322i	−0.388750	+	0.187212i	0.229291	+	0.973358i	$0.426359\pi$
$318$	0.0584615	−	0.780115i	0.00327836	−	0.0437467i
$319$	30.7383	−	4.63306i	1.72102	−	0.259402i
$320$	−0.733052	+	0.680173i	−0.0409788	+	0.0380228i
$321$	−0.743746	+	0.229415i	−0.0415118	+	0.0128047i
$322$	8.57724	+	10.7555i	0.477991	+	0.599381i
$323$	2.64066	+	3.31128i	0.146930	+	0.184245i
$324$	8.55956	−	2.64028i	0.475531	−	0.146682i
$325$	−3.28567	+	3.04866i	−0.182256	+	0.169109i
$326$	−17.4426	+	2.62906i	−0.966059	+	0.145610i
$327$	0.0110439	−	0.147370i	0.000610727	−	0.00814958i
$328$	1.87959	−	0.905162i	0.103783	−	0.0499792i
$329$	11.3610	+	3.50442i	0.626355	+	0.193205i
$330$	−0.0909899	−	0.231838i	−0.00500883	−	0.0127623i
$331$	6.14503	−	4.18961i	0.337761	−	0.230282i	−0.382547	−	0.923936i	$-0.624953\pi$
$331$	6.14503	−	4.18961i	0.337761	−	0.230282i	0.720308	+	0.693654i	$0.244000\pi$
$332$	13.8315	+	2.08476i	0.759102	+	0.114416i
$333$	−7.69934	+	33.7330i	−0.421921	+	1.84856i
$334$	6.46475	+	4.40759i	0.353735	+	0.241173i
$335$	−3.29395	−	3.05634i	−0.179968	−	0.166986i
$336$	−0.223572	−	0.107666i	−0.0121968	−	0.00587369i
$337$	1.10779	−	1.91875i	0.0603453	−	0.104521i	−0.834274	−	0.551349i	$-0.814113\pi$
$337$	1.10779	−	1.91875i	0.0603453	−	0.104521i	0.894620	+	0.446828i	$0.147446\pi$
$338$	−3.54498	−	6.14009i	−0.192822	−	0.333977i
$339$	0.0865028	+	1.15430i	0.00469819	+	0.0626930i
$340$	−1.60105	−	7.01466i	−0.0868292	−	0.380423i
$341$	−9.87060	+	25.1499i	−0.534523	+	1.36194i
$342$	−1.09930	+	1.37848i	−0.0594432	+	0.0745394i
$343$	3.46986			0.187355
$344$	1.41001	−	6.40405i	0.0760226	−	0.345283i
$345$	0.261805			0.0140951
$346$	−0.694083	+	0.870352i	−0.0373141	+	0.0467904i
$347$	12.5795	−	32.0522i	0.675306	−	1.72065i	−0.0178276	−	0.999841i	$-0.505675\pi$
$347$	12.5795	−	32.0522i	0.675306	−	1.72065i	0.693133	−	0.720809i	$-0.256230\pi$
$348$	−0.131160	−	0.574651i	−0.00703093	−	0.0308045i
$349$	1.57431	+	21.0077i	0.0842710	+	1.12452i	0.865713	+	0.500540i	$0.166865\pi$
$349$	1.57431	+	21.0077i	0.0842710	+	1.12452i	−0.781442	+	0.623978i	$0.785516\pi$
$350$	1.80548	+	3.12719i	0.0965071	+	0.167155i
$351$	−0.923321	+	1.59924i	−0.0492832	+	0.0853610i
$352$	−3.26528	−	1.57248i	−0.174040	−	0.0838133i
$353$	13.5526	+	12.5750i	0.721334	+	0.669301i	0.952819	−	0.303538i	$-0.0981679\pi$
$353$	13.5526	+	12.5750i	0.721334	+	0.669301i	−0.231485	+	0.972839i	$0.574358\pi$
$354$	−0.667404	−	0.455028i	−0.0354721	−	0.0241845i
$355$	1.97679	−	8.66090i	0.104917	−	0.459673i
$356$	4.72437	+	0.712084i	0.250391	+	0.0377404i
$357$	1.47519	−	1.00577i	0.0780752	−	0.0532307i
$358$	−2.92268	−	7.44688i	−0.154469	−	0.393580i
$359$	12.2991	+	3.79377i	0.649122	+	0.200228i	0.601793	−	0.798652i	$-0.294453\pi$
$359$	12.2991	+	3.79377i	0.649122	+	0.200228i	0.0473285	+	0.998879i	$0.484929\pi$
$360$	2.69865	−	1.29960i	0.142231	−	0.0684951i
$361$	−1.39398	+	18.6013i	−0.0733673	+	0.979018i
$362$	12.9178	−	1.94704i	0.678944	−	0.102334i
$363$	0.107539	−	0.0997814i	0.00564432	−	0.00523717i
$364$	−15.4660	+	4.77062i	−0.810636	+	0.250048i
$365$	−1.71788	−	2.15415i	−0.0899178	−	0.112753i
$366$	−0.146324	−	0.183485i	−0.00764850	−	0.00959092i
$367$	−21.9524	+	6.77142i	−1.14591	+	0.353465i	−0.808847	−	0.588019i	$-0.799908\pi$
$367$	−21.9524	+	6.77142i	−1.14591	+	0.353465i	−0.337059	+	0.941484i	$0.609432\pi$
$368$	2.79273	−	2.59128i	0.145581	−	0.135080i
$369$	−6.17891	+	0.931321i	−0.321661	+	0.0484827i
$370$	−0.863259	+	11.5194i	−0.0448787	+	0.598865i
$371$	−37.0360	+	17.8356i	−1.92281	+	0.925978i
$372$	0.489533	+	0.151001i	0.0253811	+	0.00782903i
$373$	−6.96896	−	17.7566i	−0.360839	−	0.919403i	−0.989864	−	0.142018i	$-0.954641\pi$
$373$	−6.96896	−	17.7566i	−0.360839	−	0.919403i	0.629025	−	0.777385i	$-0.283454\pi$
$374$	21.5452	−	14.6893i	1.11408	−	0.759564i
$375$	0.0679526	+	0.0102422i	0.00350905	+	0.000528905i
$376$	0.732659	−	3.20999i	0.0377840	−	0.165543i
$377$	−31.7646	−	21.6567i	−1.63596	−	1.11538i
$378$	1.09056	+	1.01190i	0.0560926	+	0.0520463i
$379$	−30.4750	−	14.6760i	−1.56540	−	0.753855i	−0.567801	−	0.823166i	$-0.692206\pi$
$379$	−30.4750	−	14.6760i	−1.56540	−	0.753855i	−0.997595	+	0.0693110i	$0.977920\pi$
$380$	−0.294319	+	0.509776i	−0.0150983	+	0.0261510i
$381$	−0.00686812	−	0.0118959i	−0.000351864	−	0.000609447i
$382$	−2.03385	−	27.1399i	−0.104061	−	1.38860i
$383$	0.0345691	+	0.151457i	0.00176640	+	0.00773911i	0.975803	−	0.218650i	$-0.0701652\pi$
$383$	0.0345691	+	0.151457i	0.00176640	+	0.00773911i	−0.974037	+	0.226389i	$0.927308\pi$
$384$	−0.0251063	+	0.0639697i	−0.00128120	+	0.00326444i
$385$	−8.15950	+	10.2317i	−0.415847	+	0.521455i
$386$	−21.5480			−1.09676
$387$	−9.68971	+	17.0849i	−0.492555	+	0.868472i
$388$	−4.86546			−0.247006
$389$	1.01874	−	1.27745i	0.0516520	−	0.0647695i	−0.755334	−	0.655339i	$-0.772526\pi$
$389$	1.01874	−	1.27745i	0.0516520	−	0.0647695i	0.806986	+	0.590570i	$0.201097\pi$
$390$	−0.112531	+	0.286724i	−0.00569822	+	0.0145188i
$391$	6.09958	+	26.7240i	0.308469	+	1.35149i
$392$	0.451301	+	6.02219i	0.0227941	+	0.304167i
$393$	−0.329668	−	0.571002i	−0.0166295	−	0.0288032i
$394$	−0.0892774	+	0.154633i	−0.00449773	+	0.00779029i
$395$	−5.44068	−	2.62010i	−0.273750	−	0.131831i
$396$	7.95761	+	7.38358i	0.399885	+	0.371039i
$397$	−6.37615	−	4.34718i	−0.320010	−	0.218179i	0.392651	−	0.919687i	$-0.371558\pi$
$397$	−6.37615	−	4.34718i	−0.320010	−	0.218179i	−0.712661	+	0.701508i	$0.752510\pi$
$398$	−3.70901	+	16.2502i	−0.185916	+	0.814550i
$399$	−0.144437	−	0.0217704i	−0.00723089	−	0.00108988i
$400$	0.826239	−	0.563320i	0.0413119	−	0.0281660i
$401$	−3.43910	−	8.76269i	−0.171741	−	0.437588i	0.818925	−	0.573900i	$-0.194570\pi$
$401$	−3.43910	−	8.76269i	−0.171741	−	0.437588i	−0.990666	+	0.136312i	$0.956475\pi$
$402$	−0.295074	−	0.0910181i	−0.0147169	−	0.00453957i
$403$	30.1046	−	14.4976i	1.49962	−	0.722179i
$404$	1.08573	−	14.4880i	0.0540169	−	0.720805i
$405$	−8.85747	+	1.33505i	−0.440131	+	0.0663391i
$406$	−22.7042	+	21.0664i	−1.12679	+	1.04551i
$407$	−40.0056	+	12.3401i	−1.98300	+	0.611675i
$408$	−0.308281	−	0.386573i	−0.0152622	−	0.0191382i
$409$	4.02948	+	5.05281i	0.199245	+	0.249845i	0.871409	−	0.490557i	$-0.163207\pi$
$409$	4.02948	+	5.05281i	0.199245	+	0.249845i	−0.672164	+	0.740402i	$0.734635\pi$
$410$	−1.99350	+	0.614914i	−0.0984521	+	0.0303684i
$411$	1.07393	−	0.996458i	0.0529729	−	0.0491517i
$412$	−14.3121	+	2.15720i	−0.705106	+	0.106278i
$413$	−3.17189	+	42.3260i	−0.156079	+	2.08272i
$414$	−10.2811	+	4.95114i	−0.505291	+	0.243335i
$415$	−13.3663	−	4.12296i	−0.656126	−	0.202388i
$416$	1.63753	+	4.17235i	0.0802863	+	0.204566i
$417$	0.492735	−	0.335941i	0.0241293	−	0.0164511i
$418$	−2.10951	−	0.317958i	−0.103180	−	0.0155518i
$419$	−0.944059	+	4.13619i	−0.0461203	+	0.202066i	−0.992739	−	0.120290i	$-0.961618\pi$
$419$	−0.944059	+	4.13619i	−0.0461203	+	0.202066i	0.946619	+	0.322356i	$0.104475\pi$
$420$	0.205028	+	0.139786i	0.0100043	+	0.00682084i
$421$	21.2966	+	19.7603i	1.03793	+	0.963059i	0.999345	−	0.0361963i	$-0.0115242\pi$
$421$	21.2966	+	19.7603i	1.03793	+	0.963059i	0.0385860	+	0.999255i	$0.487715\pi$
$422$	−1.64466	−	0.792024i	−0.0800606	−	0.0385551i
$423$	−4.93104	+	8.54080i	−0.239755	+	0.415268i
$424$	5.69195	+	9.85874i	0.276425	+	0.478783i
$425$	0.537687	+	7.17494i	0.0260817	+	0.348036i
$426$	−0.135845	−	0.595178i	−0.00658173	−	0.0288365i
$427$	−4.50532	+	11.4794i	−0.218028	+	0.555526i
$428$	7.06165	−	8.85503i	0.341338	−	0.428024i
$429$	−1.11631			−0.0538959
$430$	−2.34874	+	6.12237i	−0.113266	+	0.295247i
$431$	−10.7167			−0.516207			−0.258104	−	0.966117i	$-0.583098\pi$
$431$	−10.7167			−0.516207			−0.258104	+	0.966117i	$0.583098\pi$
$432$	0.256875	−	0.322111i	0.0123589	−	0.0154976i
$433$	7.14700	−	18.2102i	0.343463	−	0.875129i	−0.649891	−	0.760027i	$-0.725186\pi$
$433$	7.14700	−	18.2102i	0.343463	−	0.875129i	0.993354	−	0.115101i	$-0.0367193\pi$
$434$	−5.99002	−	26.2440i	−0.287530	−	1.25975i
$435$	0.0440481	+	0.587781i	0.00211194	+	0.0281819i
$436$	1.07525	+	1.86240i	0.0514954	+	0.0891926i
$437$	1.12128	−	1.94211i	0.0536380	−	0.0929037i
$438$	−0.170591	−	0.0821523i	−0.00815116	−	0.00392539i
$439$	18.1306	+	16.8227i	0.865327	+	0.802906i	0.981727	−	0.190297i	$-0.0609449\pi$
$439$	18.1306	+	16.8227i	0.865327	+	0.802906i	−0.116400	+	0.993202i	$0.537135\pi$
$440$	2.99445	+	2.04158i	0.142755	+	0.0973284i
$441$	4.02512	−	17.6352i	0.191672	−	0.839771i
$442$	−31.8894	−	4.80655i	−1.51682	−	0.228624i
$443$	10.1172	−	6.89780i	0.480683	−	0.327724i	−0.298619	−	0.954372i	$-0.596526\pi$
$443$	10.1172	−	6.89780i	0.480683	−	0.327724i	0.779302	+	0.626648i	$0.215574\pi$
$444$	0.290020	+	0.738959i	0.0137637	+	0.0350694i
$445$	−4.56547	−	1.40826i	−0.216424	−	0.0667580i
$446$	13.0044	−	6.26260i	0.615777	−	0.296542i
$447$	−0.00888137	+	0.118514i	−0.000420075	+	0.00560551i
$448$	3.57063	−	0.538187i	0.168697	−	0.0254269i
$449$	5.02592	−	4.66337i	0.237188	−	0.220078i	−0.552619	−	0.833434i	$-0.686371\pi$
$449$	5.02592	−	4.66337i	0.237188	−	0.220078i	0.789806	+	0.613356i	$0.210181\pi$
$450$	−2.86221	+	0.882874i	−0.134926	+	0.0416191i
$451$	−4.71404	−	5.91122i	−0.221975	−	0.278348i
$452$	−10.5022	−	13.1693i	−0.493982	−	0.619434i
$453$	0.666399	−	0.205557i	0.0313102	−	0.00965791i
$454$	3.83720	−	3.56040i	0.180089	−	0.167098i
$455$	16.0042	−	2.41225i	0.750290	−	0.113088i
$456$	−0.00302293	+	0.0403382i	−0.000141562	+	0.00188901i
$457$	28.7743	−	13.8570i	1.34600	−	0.648201i	0.384534	−	0.923111i	$-0.374362\pi$
$457$	28.7743	−	13.8570i	1.34600	−	0.648201i	0.961470	+	0.274910i	$0.0886480\pi$
$458$	−4.53887	−	1.40005i	−0.212087	−	0.0654203i
$459$	1.08299	+	2.75942i	0.0505498	+	0.128799i
$460$	−3.14775	+	2.14610i	−0.146765	+	0.100062i
$461$	30.4191	+	4.58494i	1.41676	+	0.213542i	0.812367	−	0.583146i	$-0.198179\pi$
$461$	30.4191	+	4.58494i	1.41676	+	0.213542i	0.604391	+	0.796688i	$0.293417\pi$
$462$	−0.200119	+	0.876780i	−0.00931039	+	0.0407915i
$463$	2.94558	+	2.00826i	0.136893	+	0.0933317i	0.629830	−	0.776733i	$-0.283125\pi$
$463$	2.94558	+	2.00826i	0.136893	+	0.0933317i	−0.492938	+	0.870065i	$0.664077\pi$
$464$	6.28756	+	5.83401i	0.291893	+	0.270837i
$465$	−0.461560	−	0.222275i	−0.0214043	−	0.0103078i
$466$	6.25433	−	10.8328i	0.289726	−	0.501820i
$467$	5.81196	+	10.0666i	0.268945	+	0.465827i	0.968590	−	0.248664i	$-0.0799915\pi$
$467$	5.81196	+	10.0666i	0.268945	+	0.465827i	−0.699644	+	0.714491i	$0.746658\pi$
$468$	−1.00328	−	13.3878i	−0.0463766	−	0.618853i
$469$	3.61058	+	15.8190i	0.166721	+	0.730453i
$470$	−1.20290	+	3.06494i	−0.0554856	+	0.141375i
$471$	−0.248305	+	0.311364i	−0.0114413	+	0.0143469i
$472$	11.7544			0.541039
$473$	−23.7647	+	0.182578i	−1.09270	+	0.00839496i
$474$	−0.414980			−0.0190607
$475$	0.367010	−	0.460216i	0.0168396	−	0.0211162i
$476$	−9.49196	+	24.1851i	−0.435063	+	1.10852i
$477$	−7.58750	−	33.2430i	−0.347408	−	1.52209i
$478$	0.450316	+	6.00905i	0.0205970	+	0.274848i
$479$	−1.97183	−	3.41530i	−0.0900950	−	0.156049i	0.817456	−	0.575991i	$-0.195384\pi$
$479$	−1.97183	−	3.41530i	−0.0900950	−	0.156049i	−0.907551	+	0.419942i	$0.862050\pi$
$480$	0.0343600	−	0.0595134i	0.00156831	−	0.00271640i
$481$	46.6493	+	22.4651i	2.12702	+	1.02432i
$482$	−5.52547	−	5.12688i	−0.251678	−	0.233523i
$483$	−0.781101	−	0.532546i	−0.0355413	−	0.0242317i
$484$	−0.475026	+	2.08123i	−0.0215921	+	0.0946011i
$485$	4.81112	+	0.725159i	0.218462	+	0.0329278i
$486$	−1.52982	+	1.04302i	−0.0693941	+	0.0473121i
$487$	6.96540	+	17.7475i	0.315632	+	0.804218i	0.997360	+	0.0726123i	$0.0231336\pi$
$487$	6.96540	+	17.7475i	0.315632	+	0.804218i	−0.681728	+	0.731606i	$0.738771\pi$
$488$	3.26338	+	1.00662i	0.147726	+	0.0455675i
$489$	1.09215	−	0.525954i	0.0493889	−	0.0237845i
$490$	0.451301	−	6.02219i	0.0203877	−	0.272055i
$491$	−11.6878	+	1.76165i	−0.527462	+	0.0795021i	−0.407374	−	0.913261i	$-0.633556\pi$
$491$	−11.6878	+	1.76165i	−0.527462	+	0.0795021i	−0.120087	+	0.992763i	$0.538317\pi$
$492$	−0.105092	+	0.0975115i	−0.00473793	+	0.00439616i
$493$	−58.9720	+	18.1904i	−2.65596	+	0.819256i
$494$	1.64501	+	2.06277i	0.0740124	+	0.0928086i
$495$	−6.76826	−	8.48713i	−0.304211	−	0.381468i
$496$	−7.12358	+	2.19733i	−0.319858	+	0.0986631i
$497$	−23.5152	+	21.8189i	−1.05480	+	0.978712i
$498$	−0.950502	+	0.143265i	−0.0425930	+	0.00641986i
$499$	−1.07957	+	14.4058i	−0.0483280	+	0.644892i	0.919469	+	0.393162i	$0.128619\pi$
$499$	−1.07957	+	14.4058i	−0.0483280	+	0.644892i	−0.967797	+	0.251730i	$0.919000\pi$
$500$	−0.900969	+	0.433884i	−0.0402926	+	0.0194039i
$501$	−0.513800	−	0.158486i	−0.0229549	−	0.00708064i
$502$	−10.1720	−	25.9178i	−0.453998	−	1.15677i
$503$	−14.7833	+	10.0791i	−0.659157	+	0.449406i	−0.846142	−	0.532957i	$-0.821081\pi$
$503$	−14.7833	+	10.0791i	−0.659157	+	0.449406i	0.186985	+	0.982363i	$0.440128\pi$
$504$	−10.6950	−	1.61202i	−0.476395	−	0.0718050i
$505$	−3.23292	+	14.1644i	−0.143863	+	0.630306i
$506$	−11.4080	−	7.77787i	−0.507149	−	0.345768i
$507$	0.357160	+	0.331396i	0.0158620	+	0.0147178i
$508$	0.180092	+	0.0867276i	0.00799028	+	0.00384791i
$509$	12.1221	−	20.9960i	0.537301	−	0.930633i	−0.461747	−	0.887012i	$-0.652777\pi$
$509$	12.1221	−	20.9960i	0.537301	−	0.930633i	0.999048	−	0.0436211i	$-0.0138894\pi$
$510$	0.247222	+	0.428202i	0.0109472	+	0.0189611i
$511$	0.743501	+	9.92133i	0.0328906	+	0.438894i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	0.0886013	−	0.225753i	0.00391184	−	0.00996722i
$514$	−15.5801	+	19.5369i	−0.687211	+	0.861735i
$515$	14.4737			0.637789
$516$	0.0371267	+	0.449096i	0.00163441	+	0.0197703i
$517$	−11.9328			−0.524803
$518$	26.0075	−	32.6124i	1.14270	−	1.43291i
$519$	0.0279489	−	0.0712125i	0.00122682	−	0.00312588i
$520$	−0.997379	−	4.36980i	−0.0437380	−	0.191629i
$521$	−0.0864509	−	1.15361i	−0.00378748	−	0.0505405i	0.994990	−	0.0999763i	$-0.0318767\pi$
$521$	−0.0864509	−	1.15361i	−0.00378748	−	0.0505405i	−0.998777	+	0.0494359i	$0.984258\pi$
$522$	−12.8456	−	22.2492i	−0.562237	−	0.973823i
$523$	15.4189	−	26.7063i	0.674220	−	1.16778i	−0.302476	−	0.953157i	$-0.597813\pi$
$523$	15.4189	−	26.7063i	0.674220	−	1.16778i	0.976696	−	0.214626i	$-0.0688534\pi$
$524$	8.64436	+	4.16290i	0.377631	+	0.181857i
$525$	−0.181904	−	0.168782i	−0.00793894	−	0.00736626i
$526$	8.89519	+	6.06464i	0.387849	+	0.264431i
$527$	11.9355	−	52.2927i	0.519917	−	2.27791i
$528$	0.246273	+	0.0371197i	0.0107177	+	0.00161543i
$529$	−7.01141	+	4.78030i	−0.304844	+	0.207839i
$530$	−4.15900	−	10.5970i	−0.180656	−	0.460303i
$531$	−33.6434	−	10.3776i	−1.46000	−	0.450351i
$532$	1.91506	−	0.922243i	0.0830283	−	0.0399843i
$533$	−0.698776	+	9.32452i	−0.0302674	+	0.403890i
$534$	−0.324659	+	0.0489345i	−0.0140494	+	0.00211760i
$535$	−8.30255	+	7.70364i	−0.358951	+	0.333057i
$536$	4.29385	−	1.32448i	0.185466	−	0.0572087i
$537$	0.342765	+	0.429814i	0.0147914	+	0.0185478i
$538$	7.85669	+	9.85198i	0.338726	+	0.424749i
$539$	20.9144	−	6.45124i	0.900847	−	0.277874i
$540$	−0.302014	+	0.280228i	−0.0129966	+	0.0120591i
$541$	−12.2845	+	1.85159i	−0.528152	+	0.0796061i	−0.407705	−	0.913114i	$-0.633671\pi$
$541$	−12.2845	+	1.85159i	−0.528152	+	0.0796061i	−0.120447	+	0.992720i	$0.538433\pi$
$542$	−1.49857	+	19.9971i	−0.0643692	+	0.858947i
$543$	−0.808835	+	0.389514i	−0.0347104	+	0.0167157i
$544$	6.87540	+	2.12078i	0.294780	+	0.0909277i
$545$	−0.785670	−	2.00185i	−0.0336544	−	0.0857500i
$546$	0.918972	−	0.626545i	0.0393284	−	0.0268136i
$547$	−9.59166	−	1.44571i	−0.410110	−	0.0618141i	−0.0592525	−	0.998243i	$-0.518872\pi$
$547$	−9.59166	−	1.44571i	−0.410110	−	0.0618141i	−0.350857	+	0.936429i	$0.614110\pi$
$548$	−4.74381	+	20.7840i	−0.202645	+	0.887847i
$549$	−8.45175	−	5.76230i	−0.360712	−	0.245929i
$550$	−2.65672	−	2.46507i	−0.113283	−	0.105111i
$551$	4.54890	+	2.19063i	0.193790	+	0.0933241i
$552$	−0.130903	+	0.226730i	−0.00557159	+	0.00965027i
$553$	10.9028	+	18.8842i	0.463633	+	0.803036i
$554$	0.843573	+	11.2567i	0.0358400	+	0.478251i
$555$	−0.176645	−	0.773931i	−0.00749815	−	0.0328515i
$556$	−3.17046	+	8.07821i	−0.134458	+	0.342592i
$557$	−3.56915	+	4.47557i	−0.151230	+	0.189636i	−0.851675	−	0.524070i	$-0.824413\pi$
$557$	−3.56915	+	4.47557i	−0.151230	+	0.189636i	0.700446	+	0.713706i	$0.252985\pi$
$558$	22.3291			0.945266
$559$	21.6985	+	19.8253i	0.917751	+	0.838520i
$560$	−3.61097			−0.152591
$561$	−1.11727	+	1.40101i	−0.0471712	+	0.0591508i
$562$	2.16891	−	5.52629i	0.0914900	−	0.233113i
$563$	−6.61369	−	28.9765i	−0.278734	−	1.22121i	−0.899396	−	0.437135i	$-0.855993\pi$
$563$	−6.61369	−	28.9765i	−0.278734	−	1.22121i	0.620662	−	0.784078i	$-0.286864\pi$
$564$	0.0169087	+	0.225631i	0.000711985	+	0.00950078i
$565$	8.42211	+	14.5875i	0.354321	+	0.613702i
$566$	4.47696	−	7.75432i	0.188181	−	0.325938i
$567$	29.1421	+	14.0341i	1.22385	+	0.589377i
$568$	6.51216	+	6.04240i	0.273244	+	0.253534i
$569$	0.640803	+	0.436892i	0.0268639	+	0.0183155i	0.576678	−	0.816972i	$-0.304349\pi$
$569$	0.640803	+	0.436892i	0.0268639	+	0.0183155i	−0.549814	+	0.835287i	$0.685301\pi$
$570$	0.00900126	−	0.0394371i	0.000377021	−	0.00165184i
$571$	−0.470480	−	0.0709134i	−0.0196890	−	0.00296763i	0.139190	−	0.990266i	$-0.455550\pi$
$571$	−0.470480	−	0.0709134i	−0.0196890	−	0.00296763i	−0.158879	+	0.987298i	$0.550788\pi$
$572$	13.4217	−	9.15073i	0.561187	−	0.382611i
$573$	0.683292	+	1.74100i	0.0285449	+	0.0727313i
$574$	7.19847	+	2.22043i	0.300458	+	0.0926791i
$575$	3.43245	−	1.65298i	0.143143	−	0.0689341i
$576$	−0.223837	+	2.98690i	−0.00932656	+	0.124454i
$577$	6.51510	−	0.981993i	0.271227	−	0.0408809i	−0.0120204	−	0.999928i	$-0.503826\pi$
$577$	6.51510	−	0.981993i	0.271227	−	0.0408809i	0.283248	+	0.959047i	$0.408588\pi$
$578$	−25.4874	+	23.6488i	−1.06013	+	0.983661i
$579$	1.41499	−	0.436467i	0.0588050	−	0.0181389i
$580$	−5.34782	−	6.70596i	−0.222056	−	0.278450i
$581$	31.4920	+	39.4897i	1.30651	+	1.63831i
$582$	0.319501	−	0.0985529i	0.0132437	−	0.00408515i
$583$	30.2438	−	28.0622i	1.25257	−	1.16222i
$584$	2.72449	−	0.410650i	0.112740	−	0.0169928i
$585$	−1.00328	+	13.3878i	−0.0414805	+	0.553519i
$586$	29.4963	−	14.2047i	1.21848	−	0.586790i
$587$	8.99448	+	2.77443i	0.371242	+	0.114513i	0.474762	−	0.880114i	$-0.342534\pi$
$587$	8.99448	+	2.77443i	0.371242	+	0.114513i	−0.103520	+	0.994627i	$0.533010\pi$
$588$	−0.151619	−	0.386318i	−0.00625265	−	0.0159315i
$589$	−3.62567	+	2.47194i	−0.149393	+	0.101855i
$590$	−11.6231	−	1.75190i	−0.478515	−	0.0721245i
$591$	0.00273040	−	0.0119627i	0.000112314	−	0.000492078i
$592$	−9.54446	−	6.50730i	−0.392275	−	0.267448i
$593$	−12.9294	−	11.9967i	−0.530945	−	0.492645i	0.368531	−	0.929616i	$-0.379861\pi$
$593$	−12.9294	−	11.9967i	−0.530945	−	0.492645i	−0.899476	+	0.436971i	$0.856051\pi$
$594$	−1.34528	−	0.647854i	−0.0551976	−	0.0265818i
$595$	12.9906	−	22.5003i	0.532561	−	0.922422i
$596$	−0.864711	−	1.49772i	−0.0354199	−	0.0613491i
$597$	−0.0855985	−	1.14223i	−0.00350331	−	0.0467485i
$598$	3.79975	+	16.6478i	0.155383	+	0.680779i
$599$	13.9232	−	35.4757i	0.568885	−	1.44950i	−0.299737	−	0.954022i	$-0.596899\pi$
$599$	13.9232	−	35.4757i	0.568885	−	1.44950i	0.868623	−	0.495474i	$-0.165006\pi$
$600$	−0.0428463	+	0.0537275i	−0.00174919	+	0.00219342i
$601$	−38.1506			−1.55620			−0.778099	−	0.628142i	$-0.783816\pi$
$601$	−38.1506			−1.55620			−0.778099	+	0.628142i	$0.783816\pi$
$602$	19.4612	−	13.4886i	0.793179	−	0.549754i
$603$	−13.4592			−0.548102
$604$	−6.32727	+	7.93414i	−0.257453	+	0.322836i
$605$	0.779911	−	1.98718i	0.0317079	−	0.0807904i
$606$	0.222167	+	0.973377i	0.00902491	+	0.0395407i
$607$	−2.03498	−	27.1549i	−0.0825972	−	1.10218i	−0.872390	−	0.488810i	$-0.837431\pi$
$607$	−2.03498	−	27.1549i	−0.0825972	−	1.10218i	0.789793	−	0.613373i	$-0.210188\pi$
$608$	−0.294319	−	0.509776i	−0.0119362	−	0.0206741i
$609$	1.06420	−	1.84326i	0.0431237	−	0.0746925i
$610$	−3.07690	−	1.48176i	−0.124580	−	0.0599946i
$611$	10.8182	+	10.0378i	0.437658	+	0.406087i
$612$	−17.8064	−	12.1402i	−0.719782	−	0.490739i
$613$	9.34369	−	40.9374i	0.377388	−	1.65345i	−0.328040	−	0.944664i	$-0.606388\pi$
$613$	9.34369	−	40.9374i	0.377388	−	1.65345i	0.705428	−	0.708781i	$-0.250755\pi$
$614$	0.283482	+	0.0427280i	0.0114404	+	0.00172436i
$615$	0.118452	−	0.0807592i	0.00477645	−	0.00325653i
$616$	−4.78115	−	12.1822i	−0.192638	−	0.490834i
$617$	−17.6471	−	5.44342i	−0.710447	−	0.219144i	−0.0815912	−	0.996666i	$-0.526000\pi$
$617$	−17.6471	−	5.44342i	−0.710447	−	0.219144i	−0.628856	+	0.777522i	$0.716476\pi$
$618$	0.896137	−	0.431557i	0.0360479	−	0.0173598i
$619$	−2.76611	+	36.9112i	−0.111179	+	1.48358i	0.610863	+	0.791736i	$0.290822\pi$
$619$	−2.76611	+	36.9112i	−0.111179	+	1.48358i	−0.722043	+	0.691848i	$0.756797\pi$
$620$	7.37151	−	1.11108i	0.296047	−	0.0446219i
$621$	1.15059	−	1.06760i	0.0461718	−	0.0428411i
$622$	−9.39736	+	2.89870i	−0.376800	+	0.116227i
$623$	10.7566	+	13.4883i	0.430954	+	0.540399i
$624$	−0.192045	−	0.240817i	−0.00768795	−	0.00964038i
$625$	0.955573	−	0.294755i	0.0382229	−	0.0117902i
$626$	6.40497	−	5.94294i	0.255994	−	0.237528i
$627$	0.144966	−	0.0218501i	0.00578937	−	0.000872608i
$628$	0.433079	−	5.77904i	0.0172817	−	0.230609i
$629$	74.8841	−	36.0623i	2.98583	−	1.43790i
$630$	10.3353	+	3.18803i	0.411769	+	0.127014i
$631$	−7.10740	−	18.1094i	−0.282941	−	0.720923i	−0.999721	−	0.0236229i	$-0.992480\pi$
$631$	−7.10740	−	18.1094i	−0.282941	−	0.720923i	0.716780	−	0.697300i	$-0.245615\pi$
$632$	4.98941	−	3.40172i	0.198468	−	0.135313i
$633$	0.124043	+	0.0186964i	0.00493025	+	0.000743116i
$634$	−1.70947	+	7.48967i	−0.0678916	+	0.297453i
$635$	−0.165154	−	0.112600i	−0.00655394	−	0.00446840i
$636$	−0.573468	−	0.532101i	−0.0227395	−	0.0210992i
$637$	−24.3876	−	11.7445i	−0.966274	−	0.465333i
$638$	15.5428	−	26.9209i	0.615344	−	1.06581i
$639$	−13.3045	−	23.0440i	−0.526317	−	0.911607i
$640$	0.0747301	+	0.997204i	0.00295397	+	0.0394179i
$641$	−2.66776	−	11.6882i	−0.105370	−	0.461657i	−0.999893	−	0.0146347i	$-0.995341\pi$
$641$	−2.66776	−	11.6882i	−0.105370	−	0.461657i	0.894523	−	0.447023i	$-0.147516\pi$
$642$	−0.284354	+	0.724522i	−0.0112225	+	0.0285946i
$643$	14.3879	−	18.0418i	0.567403	−	0.711500i	−0.412504	−	0.910956i	$-0.635346\pi$
$643$	14.3879	−	18.0418i	0.567403	−	0.711500i	0.979907	+	0.199455i	$0.0639173\pi$
$644$	13.7568			0.542095
$645$	0.0302222	−	0.449613i	0.00119000	−	0.0177035i
$646$	4.23529			0.166635
$647$	0.349823	−	0.438664i	0.0137530	−	0.0172457i	−0.774907	−	0.632075i	$-0.782204\pi$
$647$	0.349823	−	0.438664i	0.0137530	−	0.0172457i	0.788660	+	0.614829i	$0.210775\pi$
$648$	3.27255	−	8.33832i	0.128558	−	0.327560i
$649$	−9.47941	−	41.5320i	−0.372099	−	1.63027i
$650$	0.334954	+	4.46965i	0.0131380	+	0.175314i
$651$	0.924936	+	1.60204i	0.0362511	+	0.0627887i
$652$	−8.81983	+	15.2764i	−0.345411	+	0.598270i
$653$	39.2598	+	18.9065i	1.53636	+	0.739870i	0.994901	−	0.100860i	$-0.0321594\pi$
$653$	39.2598	+	18.9065i	1.53636	+	0.739870i	0.541455	+	0.840730i	$0.317874\pi$
$654$	−0.108333	−	0.100518i	−0.00423615	−	0.00393057i
$655$	−7.92736	−	5.40478i	−0.309748	−	0.211182i
$656$	0.464220	−	2.03388i	0.0181247	−	0.0794097i
$657$	−8.16059	−	1.23001i	−0.318375	−	0.0479873i
$658$	9.82336	−	6.69745i	0.382954	−	0.261094i
$659$	15.1041	+	38.4847i	0.588373	+	1.49915i	0.846150	+	0.532945i	$0.178915\pi$
$659$	15.1041	+	38.4847i	0.588373	+	1.49915i	−0.257777	+	0.966204i	$0.582990\pi$
$660$	−0.237990	−	0.0734101i	−0.00926374	−	0.00285749i
$661$	−6.82909	+	3.28872i	−0.265621	+	0.127916i	−0.561954	−	0.827168i	$-0.689950\pi$
$661$	−6.82909	+	3.28872i	−0.265621	+	0.127916i	0.296333	+	0.955085i	$0.404236\pi$
$662$	0.555794	−	7.41656i	0.0216015	−	0.288253i
$663$	2.19144	−	0.330306i	0.0851085	−	0.0128280i
$664$	10.2537	−	9.51407i	0.397922	−	0.369218i
$665$	−2.03112	+	0.626518i	−0.0787635	+	0.0242953i
$666$	21.5731	+	27.0518i	0.835940	+	1.04824i
$667$	20.3738	+	25.5479i	0.788876	+	0.989219i
$668$	7.47670	−	2.30626i	0.289282	−	0.0892317i
$669$	−0.727109	+	0.674658i	−0.0281117	+	0.0260838i
$670$	−4.44329	+	0.669718i	−0.171659	+	0.0258735i
$671$	0.924933	−	12.3424i	0.0357066	−	0.476472i
$672$	−0.223572	+	0.107666i	−0.00862447	+	0.00415333i
$673$	−26.9766	−	8.32117i	−1.03987	−	0.320758i	−0.272631	−	0.962119i	$-0.587894\pi$
$673$	−26.9766	−	8.32117i	−1.03987	−	0.320758i	−0.767239	+	0.641361i	$0.778370\pi$
$674$	−0.809444	−	2.06243i	−0.0311786	−	0.0794418i
$675$	0.340407	−	0.232086i	0.0131023	−	0.00893298i
$676$	−7.01077	−	1.05670i	−0.269645	−	0.0406425i
$677$	4.87782	−	21.3711i	0.187470	−	0.821359i	−0.790475	−	0.612495i	$-0.790166\pi$
$677$	4.87782	−	21.3711i	0.187470	−	0.821359i	0.977945	−	0.208864i	$-0.0669768\pi$
$678$	0.956402	+	0.652064i	0.0367304	+	0.0250424i
$679$	−12.8790	−	11.9500i	−0.494251	−	0.458598i
$680$	−6.48252	−	3.12182i	−0.248593	−	0.119716i
$681$	−0.179859	+	0.311526i	−0.00689223	+	0.0119377i
$682$	13.5087	+	23.3978i	0.517277	+	0.895950i
$683$	3.22333	+	43.0123i	0.123337	+	1.64582i	0.624905	+	0.780701i	$0.285138\pi$
$683$	3.22333	+	43.0123i	0.123337	+	1.64582i	−0.501568	+	0.865118i	$0.667243\pi$
$684$	0.392335	+	1.71893i	0.0150013	+	0.0657250i
$685$	7.78851	−	19.8448i	0.297584	−	0.758231i
$686$	2.16342	−	2.71285i	0.0825999	−	0.103577i
$687$	0.326413			0.0124534
$688$	−4.12776	−	5.09525i	−0.157369	−	0.194255i
$689$	−51.0247			−1.94389
$690$	0.163233	−	0.204688i	0.00621417	−	0.00779232i
$691$	9.84438	−	25.0831i	0.374498	−	0.954205i	−0.612063	−	0.790809i	$-0.709660\pi$
$691$	9.84438	−	25.0831i	0.374498	−	0.954205i	0.986561	−	0.163396i	$-0.0522447\pi$
$692$	0.247715	+	1.08531i	0.00941672	+	0.0412574i
$693$	2.92932	+	39.0891i	0.111276	+	1.48487i
$694$	−17.2162	−	29.8193i	−0.653517	−	1.13192i
$695$	4.33905	−	7.51545i	0.164589	−	0.285077i
$696$	−0.531057	−	0.255744i	−0.0201297	−	0.00969394i
$697$	11.0033	+	10.2095i	0.416779	+	0.386714i
$698$	17.4061	+	11.8673i	0.658830	+	0.449182i
$699$	−0.191278	+	0.838044i	−0.00723480	+	0.0316977i
$700$	3.57063	+	0.538187i	0.134957	+	0.0203415i
$701$	−28.3364	+	19.3194i	−1.07025	+	0.729685i	−0.964334	−	0.264689i	$-0.914731\pi$
$701$	−28.3364	+	19.3194i	−1.07025	+	0.729685i	−0.105918	+	0.994375i	$0.533778\pi$
$702$	0.674654	+	1.71899i	0.0254632	+	0.0648791i
$703$	−6.49768	−	2.00427i	−0.245065	−	0.0755924i
$704$	−3.26528	+	1.57248i	−0.123065	+	0.0592649i
$705$	0.0169087	−	0.225631i	0.000636819	−	0.00849775i
$706$	18.2815	−	2.75549i	0.688033	−	0.103704i
$707$	38.4577	−	35.6835i	1.44635	−	1.34202i
$708$	−0.771875	+	0.238092i	−0.0290088	+	0.00894804i
$709$	−11.0690	−	13.8801i	−0.415705	−	0.521277i	0.529255	−	0.848463i	$-0.322471\pi$
$709$	−11.0690	−	13.8801i	−0.415705	−	0.521277i	−0.944960	+	0.327185i	$0.893900\pi$
$710$	−5.53885	−	6.94550i	−0.207869	−	0.260660i
$711$	−17.2840	+	5.33141i	−0.648201	+	0.199944i
$712$	3.50232	−	3.24968i	0.131255	−	0.121787i
$713$	−28.0835	+	4.23290i	−1.05173	+	0.158523i
$714$	0.133425	−	1.78043i	0.00499330	−	0.0666310i
$715$	−14.6356	+	7.04813i	−0.547340	+	0.263585i
$716$	−7.64447	−	2.35801i	−0.285687	−	0.0881228i
$717$	−0.151288	−	0.385475i	−0.00564995	−	0.0143958i
$718$	10.6345	−	7.25045i	0.396874	−	0.270584i
$719$	32.6478	+	4.92087i	1.21756	+	0.183517i	0.726227	−	0.687455i	$-0.241272\pi$
$719$	32.6478	+	4.92087i	1.21756	+	0.183517i	0.491332	+	0.870972i	$0.336510\pi$
$720$	0.666512	−	2.92018i	0.0248394	−	0.108829i
$721$	−43.1827	−	29.4415i	−1.60821	−	1.09646i
$722$	13.6740	+	12.6876i	0.508893	+	0.472184i
$723$	0.466689	+	0.224746i	0.0173564	+	0.00835838i
$724$	6.53185	−	11.3135i	0.242754	−	0.420463i
$725$	4.28862	+	7.42811i	0.159275	+	0.275873i
$726$	−0.0109629	−	0.146290i	−0.000406872	−	0.00542933i
$727$	0.428704	+	1.87828i	0.0158998	+	0.0696614i	0.982255	−	0.187548i	$-0.0600541\pi$
$727$	0.428704	+	1.87828i	0.0158998	+	0.0696614i	−0.966356	+	0.257210i	$0.917197\pi$
$728$	−5.91305	+	15.0662i	−0.219152	+	0.558391i
$729$	−16.6754	+	20.9103i	−0.617609	+	0.774457i
$730$	−2.75526			−0.101977
$731$	46.5988	−	7.39020i	1.72352	−	0.273336i
$732$	−0.234686			−0.00867425
$733$	22.0288	−	27.6232i	0.813651	−	1.02029i	−0.185639	−	0.982618i	$-0.559435\pi$
$733$	22.0288	−	27.6232i	0.813651	−	1.02029i	0.999290	−	0.0376686i	$-0.0119931\pi$
$734$	−8.39299	+	21.3850i	−0.309791	+	0.789334i
$735$	0.0923475	+	0.404601i	0.00340629	+	0.0149239i
$736$	−0.284702	−	3.79908i	−0.0104942	−	0.140036i
$737$	−8.14261	−	14.1034i	−0.299937	−	0.519506i
$738$	−3.12435	+	5.41154i	−0.115009	+	0.199201i
$739$	−19.3132	−	9.30075i	−0.710447	−	0.342133i	0.0435134	−	0.999053i	$-0.486145\pi$
$739$	−19.3132	−	9.30075i	−0.710447	−	0.342133i	−0.753961	+	0.656919i	$0.771859\pi$
$740$	8.46799	+	7.85715i	0.311290	+	0.288835i
$741$	−0.149805	−	0.102136i	−0.00550324	−	0.00375205i
$742$	−9.14714	+	40.0762i	−0.335802	+	1.47124i
$743$	0.934961	+	0.140923i	0.0343004	+	0.00516995i	0.166170	−	0.986097i	$-0.446860\pi$
$743$	0.934961	+	0.140923i	0.0343004	+	0.00516995i	−0.131870	+	0.991267i	$0.542098\pi$
$744$	0.423276	−	0.288585i	0.0155180	−	0.0105800i
$745$	0.631829	+	1.60987i	0.0231484	+	0.0589812i
$746$	−18.2278	−	5.62252i	−0.667366	−	0.205855i
$747$	−37.7480	+	18.1785i	−1.38113	+	0.665116i
$748$	1.94868	−	26.0033i	0.0712508	−	0.950776i
$749$	40.4410	−	6.09551i	1.47768	−	0.222725i
$750$	0.0503754	−	0.0467415i	0.00183945	−	0.00170676i
$751$	31.0743	−	9.58516i	1.13392	−	0.349768i	0.329691	−	0.944089i	$-0.393055\pi$
$751$	31.0743	−	9.58516i	1.13392	−	0.349768i	0.804228	+	0.594321i	$0.202579\pi$
$752$	−2.05287	−	2.57421i	−0.0748603	−	0.0938718i
$753$	1.19295	+	1.49591i	0.0434734	+	0.0545139i
$754$	−36.7368	+	11.3318i	−1.33787	+	0.412680i
$755$	7.43912	−	6.90250i	0.270737	−	0.251208i
$756$	1.47109	−	0.221731i	0.0535029	−	0.00806427i
$757$	1.50154	−	20.0366i	0.0545743	−	0.728243i	−0.901061	−	0.433692i	$-0.857211\pi$
$757$	1.50154	−	20.0366i	0.0545743	−	0.728243i	0.955636	−	0.294551i	$-0.0951702\pi$
$758$	−30.4750	+	14.6760i	−1.10690	+	0.533056i
$759$	0.906678	+	0.279673i	0.0329103	+	0.0101515i
$760$	0.215054	+	0.547948i	0.00780082	+	0.0198762i
$761$	19.3349	−	13.1823i	0.700890	−	0.477859i	−0.159694	−	0.987167i	$-0.551051\pi$
$761$	19.3349	−	13.1823i	0.700890	−	0.477859i	0.860585	+	0.509308i	$0.170098\pi$
$762$	−0.0135828	−	0.00204728i	−0.000492053	−	7.41651e-5i
$763$	−1.72797	+	7.57072i	−0.0625567	+	0.274079i
$764$	−22.4869	−	15.3313i	−0.813548	−	0.554667i
$765$	15.7981	+	14.6585i	0.571183	+	0.529980i
$766$	0.139968	+	0.0674049i	0.00505724	+	0.00243544i
$767$	−26.3426	+	45.6268i	−0.951177	+	1.64749i
$768$	0.0343600	+	0.0595134i	0.00123986	+	0.00214750i
$769$	1.95256	+	26.0551i	0.0704112	+	0.939572i	0.914817	+	0.403868i	$0.132334\pi$
$769$	1.95256	+	26.0551i	0.0704112	+	0.939572i	−0.844406	+	0.535704i	$0.820046\pi$
$770$	2.91209	+	12.7587i	0.104945	+	0.459792i
$771$	0.627371	−	1.59852i	0.0225942	−	0.0575691i
$772$	−13.4349	+	16.8469i	−0.483534	+	0.606332i
$773$	−14.1315			−0.508274			−0.254137	−	0.967168i	$-0.581791\pi$
$773$	−14.1315			−0.508274			−0.254137	+	0.967168i	$0.581791\pi$
$774$	7.31604	+	18.2279i	0.262970	+	0.655190i
$775$	−7.45477			−0.267783
$776$	−3.03357	+	3.80397i	−0.108899	+	0.136555i
$777$	−1.04725	+	2.66836i	−0.0375700	+	0.0957267i
$778$	−0.363583	−	1.59296i	−0.0130351	−	0.0571104i
$779$	−0.0917693	−	1.22458i	−0.00328798	−	0.0438750i
$780$	0.154008	+	0.266750i	0.00551437	+	0.00955117i
$781$	16.0980	−	27.8825i	0.576031	−	0.997715i
$782$	24.6967	+	11.8933i	0.883151	+	0.425303i
$783$	2.59045	+	2.40359i	0.0925752	+	0.0858972i
$784$	4.98972	+	3.40193i	0.178204	+	0.121498i
$785$	−1.28956	+	5.64994i	−0.0460265	+	0.201655i
$786$	−0.651972	−	0.0982689i	−0.0232551	−	0.00350514i
$787$	6.98539	−	4.76256i	0.249002	−	0.169767i	−0.432387	−	0.901688i	$-0.642329\pi$
$787$	6.98539	−	4.76256i	0.249002	−	0.169767i	0.681389	+	0.731921i	$0.261376\pi$
$788$	0.0652334	+	0.166212i	0.00232384	+	0.00592105i
$789$	−0.706964	−	0.218069i	−0.0251686	−	0.00776348i
$790$	−5.44068	+	2.62010i	−0.193571	+	0.0932188i
$791$	4.54538	−	60.6538i	0.161615	−	2.15660i
$792$	10.7342	−	1.61792i	0.381423	−	0.0574903i
$793$	−11.2209	+	10.4115i	−0.398466	+	0.369723i
$794$	−7.37423	+	2.27465i	−0.261702	+	0.0807243i
$795$	0.487758	+	0.611629i	0.0172990	+	0.0216922i
$796$	10.3924	+	13.0317i	0.368349	+	0.461895i
$797$	−0.535956	+	0.165321i	−0.0189845	+	0.00585596i	−0.304233	−	0.952598i	$-0.598400\pi$
$797$	−0.535956	+	0.165321i	−0.0189845	+	0.00585596i	0.285248	+	0.958454i	$0.407924\pi$
$798$	−0.107076	+	0.0993517i	−0.00379044	+	0.00351701i
$799$	23.4254	−	3.53081i	0.828731	−	0.124911i
$800$	0.0747301	−	0.997204i	0.00264211	−	0.0352565i
$801$	−12.8934	+	6.20915i	−0.455567	+	0.219390i
$802$	−8.99520	−	2.77465i	−0.317631	−	0.0979763i
$803$	−3.64814	−	9.29532i	−0.128740	−	0.328025i
$804$	−0.255136	+	0.173949i	−0.00899796	+	0.00613470i
$805$	−13.6032	−	2.05035i	−0.479449	−	0.0722652i
$806$	7.43523	−	32.5759i	0.261895	−	1.14744i
$807$	−0.715483	−	0.487808i	−0.0251862	−	0.0171717i
$808$	−10.6502	−	9.88198i	−0.374674	−	0.347647i
$809$	−32.4006	−	15.6033i	−1.13914	−	0.548583i	−0.233389	−	0.972383i	$-0.574981\pi$
$809$	−32.4006	−	15.6033i	−1.13914	−	0.548583i	−0.905756	+	0.423800i	$0.860696\pi$
$810$	−4.47876	+	7.75744i	−0.157368	+	0.272569i
$811$	16.4417	+	28.4779i	0.577347	+	0.999995i	0.995782	+	0.0917480i	$0.0292454\pi$
$811$	16.4417	+	28.4779i	0.577347	+	0.999995i	−0.418435	+	0.908247i	$0.637421\pi$
$812$	2.31455	+	30.8855i	0.0812248	+	1.08387i
$813$	−0.306646	−	1.34350i	−0.0107545	−	0.0471187i
$814$	−15.2952	+	38.9715i	−0.536096	+	1.36595i
$815$	10.9982	−	13.7912i	0.385249	−	0.483086i
$816$	−0.494445			−0.0173090
$817$	−3.20586	−	2.14983i	−0.112159	−	0.0752130i
$818$	6.46279			0.225966
$819$	30.2259	−	37.9021i	1.05618	−	1.32441i
$820$	−0.762169	+	1.94198i	−0.0266161	+	0.0678167i
$821$	7.40494	+	32.4432i	0.258434	+	1.13227i	0.922926	+	0.384978i	$0.125791\pi$
$821$	7.40494	+	32.4432i	0.258434	+	1.13227i	−0.664492	+	0.747296i	$0.731352\pi$
$822$	−0.109480	−	1.46091i	−0.00381856	−	0.0509551i
$823$	−10.4659	−	18.1274i	−0.364817	−	0.631881i	0.623930	−	0.781480i	$-0.285535\pi$
$823$	−10.4659	−	18.1274i	−0.364817	−	0.631881i	−0.988747	+	0.149599i	$0.952202\pi$
$824$	−7.23687	+	12.5346i	−0.252108	+	0.436664i
$825$	0.224390	+	0.108061i	0.00781227	+	0.00376219i
$826$	31.1141	+	28.8697i	1.08260	+	1.00450i
$827$	5.28375	+	3.60240i	0.183734	+	0.125268i	0.651694	−	0.758482i	$-0.274059\pi$
$827$	5.28375	+	3.60240i	0.183734	+	0.125268i	−0.467960	+	0.883750i	$0.655011\pi$
$828$	−2.53923	+	11.1251i	−0.0882444	+	0.386624i
$829$	14.2185	+	2.14310i	0.493831	+	0.0744330i	0.391236	−	0.920290i	$-0.372048\pi$
$829$	14.2185	+	2.14310i	0.493831	+	0.0744330i	0.102594	+	0.994723i	$0.467286\pi$
$830$	−11.5572	+	7.87957i	−0.401156	+	0.273504i
$831$	−0.283406	−	0.722107i	−0.00983125	−	0.0250496i
$832$	4.28305	+	1.32115i	0.148488	+	0.0458025i
$833$	−39.1484	+	18.8529i	−1.35641	+	0.653214i
$834$	0.0445660	−	0.594692i	0.00154319	−	0.0205925i
$835$	−7.73692	+	1.16615i	−0.267747	+	0.0403564i
$836$	−1.56385	+	1.45104i	−0.0540868	+	0.0501852i
$837$	−2.93489	+	0.905292i	−0.101444	+	0.0312915i
$838$	2.64520	+	3.31697i	0.0913768	+	0.114583i
$839$	9.14606	+	11.4688i	0.315757	+	0.395947i	0.914230	−	0.405197i	$-0.132797\pi$
$839$	9.14606	+	11.4688i	0.315757	+	0.395947i	−0.598473	+	0.801143i	$0.704225\pi$
$840$	0.237122	−	0.0731423i	0.00818147	−	0.00252365i
$841$	−32.6714	+	30.3147i	−1.12660	+	1.04533i
$842$	28.7274	−	4.32996i	0.990012	−	0.149220i
$843$	−0.0304875	+	0.406828i	−0.00105005	+	0.0140119i
$844$	−1.64466	+	0.792024i	−0.0566114	+	0.0272626i
$845$	6.77497	+	2.08980i	0.233066	+	0.0718914i
$846$	3.60302	+	9.18034i	0.123874	+	0.315627i
$847$	−6.36906	+	4.34235i	−0.218844	+	0.149205i
$848$	11.2567	+	1.69668i	0.386558	+	0.0582643i
$849$	−0.136920	+	0.599887i	−0.00469909	+	0.0205881i
$850$	5.94483	+	4.05312i	0.203906	+	0.139021i
$851$	−32.2608	−	29.9336i	−1.10589	−	1.02611i
$852$	−0.550027	−	0.264879i	−0.0188436	−	0.00907460i
$853$	9.46397	−	16.3921i	0.324040	−	0.561254i	−0.657277	−	0.753649i	$-0.728292\pi$
$853$	9.46397	−	16.3921i	0.324040	−	0.561254i	0.981318	+	0.192394i	$0.0616253\pi$
$854$	6.16591	+	10.6797i	0.210993	+	0.365451i
$855$	−0.131759	−	1.75821i	−0.00450607	−	0.0601294i
$856$	−2.52027	−	11.0420i	−0.0861412	−	0.377409i
$857$	9.41124	−	23.9795i	0.321482	−	0.819123i	−0.675193	−	0.737641i	$-0.735940\pi$
$857$	9.41124	−	23.9795i	0.321482	−	0.819123i	0.996675	−	0.0814814i	$-0.0259651\pi$
$858$	−0.696007	+	0.872765i	−0.0237613	+	0.0297957i
$859$	−10.3271			−0.352357			−0.176178	−	0.984358i	$-0.556374\pi$
$859$	−10.3271			−0.352357			−0.176178	+	0.984358i	$0.556374\pi$
$860$	3.32225	+	5.65355i	0.113288	+	0.192785i
$861$	−0.517679			−0.0176424
$862$	−6.68178	+	8.37869i	−0.227582	+	0.285379i
$863$	−8.33519	+	21.2377i	−0.283733	+	0.722940i	0.715959	+	0.698142i	$0.245990\pi$
$863$	−8.33519	+	21.2377i	−0.283733	+	0.722940i	−0.999692	+	0.0247982i	$0.992106\pi$
$864$	−0.0916778	−	0.401666i	−0.00311894	−	0.0136650i
$865$	−0.0831912	−	1.11011i	−0.00282859	−	0.0377449i
$866$	−9.78127	−	16.9416i	−0.332381	−	0.575701i
$867$	1.19466	−	2.06921i	0.0405727	−	0.0702740i
$868$	−24.2531	−	11.6797i	−0.823204	−	0.396434i
$869$	−16.0431	−	14.8859i	−0.544226	−	0.504968i
$870$	0.487009	+	0.332037i	0.0165112	+	0.0112571i
$871$	−4.48170	+	19.6356i	−0.151857	+	0.665328i
$872$	2.12649	+	0.320517i	0.0720121	+	0.0108541i
$873$	12.0411	−	8.20949i	0.407530	−	0.277849i
$874$	−0.819298	−	2.08754i	−0.0277132	−	0.0706120i
$875$	−3.45054	−	1.06435i	−0.116650	−	0.0359816i
$876$	−0.170591	+	0.0821523i	−0.00576374	+	0.00277567i
$877$	−3.04476	+	40.6295i	−0.102814	+	1.37196i	0.672365	+	0.740219i	$0.265278\pi$
$877$	−3.04476	+	40.6295i	−0.102814	+	1.37196i	−0.775180	+	0.631741i	$0.782341\pi$
$878$	24.4568	−	3.68627i	0.825377	−	0.124406i
$879$	−1.64921	+	1.53025i	−0.0556265	+	0.0516139i
$880$	3.46318	−	1.06825i	0.116744	−	0.0360107i
$881$	1.98192	+	2.48525i	0.0667725	+	0.0837301i	0.814096	−	0.580730i	$-0.197233\pi$
$881$	1.98192	+	2.48525i	0.0667725	+	0.0837301i	−0.747324	+	0.664460i	$0.768661\pi$
$882$	−11.2781	−	14.1423i	−0.379754	−	0.476197i
$883$	−21.6992	+	6.69332i	−0.730236	+	0.225248i	−0.637508	−	0.770443i	$-0.720035\pi$
$883$	−21.6992	+	6.69332i	−0.730236	+	0.225248i	−0.0927278	+	0.995691i	$0.529559\pi$
$884$	−23.6406	+	21.9353i	−0.795119	+	0.737763i
$885$	0.798740	−	0.120391i	0.0268493	−	0.00404689i
$886$	0.915063	−	12.2107i	0.0307421	−	0.410225i
$887$	11.9468	−	5.75326i	0.401133	−	0.193176i	−0.222430	−	0.974949i	$-0.571399\pi$
$887$	11.9468	−	5.75326i	0.401133	−	0.193176i	0.623563	+	0.781773i	$0.285684\pi$
$888$	0.758566	+	0.233987i	0.0254558	+	0.00785208i
$889$	0.263697	+	0.671890i	0.00884413	+	0.0225345i
$890$	−3.94755	+	2.69139i	−0.132322	+	0.0902157i
$891$	−32.1012	−	4.83847i	−1.07543	−	0.162095i
$892$	3.21182	−	14.0719i	0.107540	−	0.471163i
$893$	−1.60135	−	1.09178i	−0.0535870	−	0.0365350i
$894$	0.0871203	+	0.0808358i	0.00291374	+	0.00270355i
$895$	7.20764	+	3.47102i	0.240925	+	0.116023i
$896$	1.80548	−	3.12719i	0.0603170	−	0.104472i
$897$	−0.586729	−	1.01625i	−0.0195903	−	0.0339314i
$898$	−0.512361	−	6.83698i	−0.0170977	−	0.228153i
$899$	−14.2283	−	62.3382i	−0.474540	−	2.07910i
$900$	−1.09430	+	2.78823i	−0.0364766	+	0.0929408i
$901$	−51.0687	+	64.0381i	−1.70134	+	2.13342i
$902$	−7.56073			−0.251745
$903$	−1.00474	+	1.27995i	−0.0334357	+	0.0425942i
$904$	−16.8442			−0.560231
$905$	−8.14508	+	10.2136i	−0.270752	+	0.339512i
$906$	0.254782	−	0.649175i	0.00846457	−	0.0215674i
$907$	−0.634902	−	2.78169i	−0.0210816	−	0.0923644i	0.963293	−	0.268453i	$-0.0865125\pi$
$907$	−0.634902	−	2.78169i	−0.0210816	−	0.0923644i	−0.984374	+	0.176089i	$0.943655\pi$
$908$	−0.391178	−	5.21991i	−0.0129817	−	0.173229i
$909$	21.7586	+	37.6871i	0.721689	+	1.25000i
$910$	8.09250	−	14.0166i	0.268264	−	0.464647i
$911$	−3.72476	−	1.79375i	−0.123407	−	0.0594296i	0.371162	−	0.928568i	$-0.378960\pi$
$911$	−3.72476	−	1.79375i	−0.123407	−	0.0594296i	−0.494568	+	0.869139i	$0.664674\pi$
$912$	0.0296529	+	0.0275139i	0.000981906	+	0.000911075i
$913$	−41.8855	−	28.5570i	−1.38621	−	0.945100i
$914$	7.10666	−	31.1363i	0.235067	−	1.02990i
$915$	0.232065	+	0.0349782i	0.00767183	+	0.00115634i
$916$	−3.92454	+	2.67571i	−0.129671	+	0.0884079i
$917$	12.6574	+	32.2506i	0.417984	+	1.06501i
$918$	2.83264	+	0.873753i	0.0934910	+	0.0288381i
$919$	13.8996	−	6.69371i	0.458507	−	0.220805i	−0.190349	−	0.981716i	$-0.560962\pi$
$919$	13.8996	−	6.69371i	0.458507	−	0.220805i	0.648856	+	0.760911i	$0.275248\pi$
$920$	−0.284702	+	3.79908i	−0.00938634	+	0.125252i
$921$	−0.0194809	+	0.00293627i	−0.000641918	+	9.67535e-5i
$922$	22.5506	−	20.9239i	0.742666	−	0.689093i
$923$	−38.0490	+	11.7366i	−1.25240	+	0.386314i
$924$	0.560722	+	0.703123i	0.0184464	+	0.0231310i
$925$	−7.20236	−	9.03148i	−0.236812	−	0.296953i
$926$	3.40666	−	1.05081i	0.111950	−	0.0345319i
$927$	31.7799	−	29.4874i	1.04379	−	0.968494i
$928$	8.48144	−	1.27837i	0.278417	−	0.0419646i
$929$	−0.635166	+	8.47570i	−0.0208391	+	0.278079i	0.977044	+	0.213039i	$0.0683363\pi$
$929$	−0.635166	+	8.47570i	−0.0208391	+	0.278079i	−0.997883	+	0.0650392i	$0.979283\pi$
$930$	−0.461560	+	0.222275i	−0.0151351	+	0.00728870i
$931$	3.39690	+	1.04781i	0.111329	+	0.0343404i
$932$	−4.56992	−	11.6440i	−0.149693	−	0.381411i
$933$	0.558382	−	0.380699i	0.0182806	−	0.0124635i
$934$	11.4941	+	1.73246i	0.376098	+	0.0566877i
$935$	−5.80251	+	25.4225i	−0.189762	+	0.831403i
$936$	−11.0926	−	7.56279i	−0.362572	−	0.247197i
$937$	−28.0412	−	26.0184i	−0.916065	−	0.849984i	0.0730197	−	0.997331i	$-0.476736\pi$
$937$	−28.0412	−	26.0184i	−0.916065	−	0.849984i	−0.989085	+	0.147346i	$0.952927\pi$
$938$	14.6189	+	7.04011i	0.477325	+	0.229868i
$939$	−0.300218	+	0.519992i	−0.00979723	+	0.0169693i
$940$	1.64627	+	2.85142i	0.0536954	+	0.0930032i
$941$	2.23810	+	29.8654i	0.0729601	+	0.973585i	0.906795	+	0.421571i	$0.138521\pi$
$941$	2.23810	+	29.8654i	0.0729601	+	0.973585i	−0.833835	+	0.552013i	$0.813860\pi$
$942$	0.0886189	+	0.388265i	0.00288736	+	0.0126503i
$943$	2.90366	−	7.39841i	0.0945562	−	0.240925i
$944$	7.32873	−	9.18994i	0.238530	−	0.299107i
$945$	−1.48770			−0.0483950
$946$	−14.6743	+	18.6938i	−0.477103	+	0.607789i
$947$	−4.00330			−0.130090			−0.0650449	−	0.997882i	$-0.520719\pi$
$947$	−4.00330			−0.130090			−0.0650449	+	0.997882i	$0.520719\pi$
$948$	−0.258736	+	0.324445i	−0.00840335	+	0.0105375i
$949$	−4.51181	+	11.4959i	−0.146460	+	0.373173i
$950$	−0.130984	−	0.573880i	−0.00424970	−	0.0186191i
$951$	−0.0394520	−	0.526451i	−0.00127932	−	0.0170713i
$952$	12.9906	+	22.5003i	0.421026	+	0.729239i
$953$	1.85922	−	3.22027i	0.0602261	−	0.104315i	−0.834340	−	0.551250i	$-0.814151\pi$
$953$	1.85922	−	3.22027i	0.0602261	−	0.104315i	0.894566	+	0.446935i	$0.147484\pi$
$954$	−30.7212	−	14.7945i	−0.994635	−	0.478991i
$955$	19.9507	+	18.5116i	0.645591	+	0.599021i
$956$	4.97883	+	3.39451i	0.161027	+	0.109786i
$957$	−0.475350	+	2.08264i	−0.0153659	+	0.0673223i
$958$	−3.89960	−	0.587771i	−0.125990	−	0.0189900i
$959$	−63.6041	+	43.3645i	−2.05388	+	1.40031i
$960$	−0.0251063	−	0.0639697i	−0.000810301	−	0.00206461i
$961$	23.4819	+	7.24319i	0.757479	+	0.233651i
$962$	46.6493	−	22.4651i	1.50403	−	0.724304i
$963$	−2.53518	+	33.8297i	−0.0816952	+	1.09015i
$964$	−7.45343	+	1.12342i	−0.240059	+	0.0361831i
$965$	15.7958	−	14.6563i	0.508484	−	0.471804i
$966$	−0.903370	+	0.278653i	−0.0290654	+	0.00896550i
$967$	25.9936	+	32.5949i	0.835897	+	1.04818i	0.998112	+	0.0614261i	$0.0195648\pi$
$967$	25.9936	+	32.5949i	0.835897	+	1.04818i	−0.162215	+	0.986755i	$0.551864\pi$
$968$	1.33099	+	1.66901i	0.0427798	+	0.0536441i
$969$	−0.278119	+	0.0857883i	−0.00893447	+	0.00275592i
$970$	3.56664	−	3.30935i	0.114518	−	0.106257i
$971$	−41.3912	+	6.23873i	−1.32831	+	0.200210i	−0.774574	−	0.632483i	$-0.782036\pi$
$971$	−41.3912	+	6.23873i	−1.32831	+	0.200210i	−0.553734	+	0.832694i	$0.686798\pi$
$972$	−0.138366	+	1.84637i	−0.00443811	+	0.0592224i
$973$	−28.2330	+	13.5963i	−0.905109	+	0.435878i
$974$	18.2184	+	5.61965i	0.583757	+	0.180065i
$975$	−0.112531	−	0.286724i	−0.00360387	−	0.00918252i
$976$	2.82169	−	1.92380i	0.0903201	−	0.0615792i
$977$	24.1274	+	3.63662i	0.771904	+	0.116346i	0.523173	−	0.852227i	$-0.324748\pi$
$977$	24.1274	+	3.63662i	0.771904	+	0.116346i	0.248731	+	0.968573i	$0.419986\pi$
$978$	0.269740	−	1.18181i	0.00862533	−	0.0377900i
$979$	−14.3067	−	9.75411i	−0.457243	−	0.311743i
$980$	−4.42696	−	4.10762i	−0.141414	−	0.131213i
$981$	−5.80348	−	2.79481i	−0.185291	−	0.0892313i
$982$	−5.90989	+	10.2362i	−0.188592	+	0.326651i
$983$	−15.5794	−	26.9844i	−0.496907	−	0.860668i	0.503087	−	0.864236i	$-0.332198\pi$
$983$	−15.5794	−	26.9844i	−0.496907	−	0.860668i	−0.999994	+	0.00356794i	$0.998864\pi$
$984$	0.0107135	+	0.142962i	0.000341535	+	0.00455746i
$985$	−0.0397322	−	0.174078i	−0.00126597	−	0.00554659i
$986$	−22.5466	+	57.4477i	−0.718029	+	1.82951i
$987$	−0.509410	+	0.638780i	−0.0162147	+	0.0203326i
$988$	2.63839			0.0839382
$989$	−12.6569	−	21.5385i	−0.402466	−	0.684885i
$990$	−10.8555			−0.345009
$991$	17.6967	−	22.1909i	0.562154	−	0.704918i	−0.416801	−	0.908998i	$-0.636849\pi$
$991$	17.6967	−	22.1909i	0.562154	−	0.704918i	0.978954	+	0.204080i	$0.0654201\pi$
$992$	−2.72353	+	6.93945i	−0.0864723	+	0.220328i
$993$	0.113729	+	0.498281i	0.00360910	+	0.0158125i
$994$	2.39723	+	31.9888i	0.0760355	+	1.01462i
$995$	−8.33406	−	14.4350i	−0.264208	−	0.457621i
$996$	−0.480619	+	0.832457i	−0.0152290	+	0.0263774i
$997$	−33.3138	−	16.0431i	−1.05506	−	0.508090i	−0.175797	−	0.984426i	$-0.556250\pi$
$997$	−33.3138	−	16.0431i	−1.05506	−	0.508090i	−0.879263	+	0.476336i	$0.841964\pi$
$998$	10.5898	+	9.82591i	0.335215	+	0.311034i
$999$	−3.93228	−	2.68098i	−0.124412	−	0.0848225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.101.2	✓	36
43.23	even	21	inner	430.2.q.a.281.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.101.2	✓	36	1.1	even	1	trivial
430.2.q.a.281.2	yes	36	43.23	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.0251063 + 0.0639697i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(0.0343600 + 0.0595134i) q^{6} +(1.80548 - 3.12719i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(2.19569 + 2.03731i) q^{9} +O(q^{10})\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.0251063 + 0.0639697i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.0747301 + 0.997204i) q^{5} +(0.0343600 + 0.0595134i) q^{6} +(1.80548 - 3.12719i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(2.19569 + 2.03731i) q^{9} +(0.826239 + 0.563320i) q^{10} +(-0.806458 + 3.53332i) q^{11} +(0.0679526 + 0.0102422i) q^{12} +(3.70335 - 2.52490i) q^{13} +(-1.31923 - 3.36135i) q^{14} +(-0.0656671 - 0.0202556i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.537687 - 7.17494i) q^{17} +(2.96182 - 0.446423i) q^{18} +(-0.431503 + 0.400376i) q^{19} +(0.955573 - 0.294755i) q^{20} +(0.154716 + 0.194008i) q^{21} +(2.25965 + 2.83351i) q^{22} +(-3.64048 + 1.12294i) q^{23} +(0.0503754 - 0.0467415i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(0.334954 - 4.46965i) q^{26} +(-0.371196 + 0.178758i) q^{27} +(-3.45054 - 1.06435i) q^{28} +(-3.13362 - 7.98433i) q^{29} +(-0.0567792 + 0.0387114i) q^{30} +(7.37151 + 1.11108i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-0.205779 - 0.140297i) q^{33} +(-5.27435 - 4.89388i) q^{34} +(3.25337 + 1.56674i) q^{35} +(1.49764 - 2.59399i) q^{36} +(5.77585 + 10.0041i) q^{37} +(0.0439890 + 0.586993i) q^{38} +(0.0685400 + 0.300293i) q^{39} +(0.365341 - 0.930874i) q^{40} +(-1.30072 + 1.63105i) q^{41} +0.248146 q^{42} +(1.50824 + 6.38163i) q^{43} +3.62419 q^{44} +(-1.86753 + 2.34180i) q^{45} +(-1.39185 + 3.54638i) q^{46} +(0.732659 + 3.20999i) q^{47} +(-0.00513546 - 0.0685279i) q^{48} +(-3.01954 - 5.22999i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.445480 + 0.214532i) q^{51} +(-3.28567 - 3.04866i) q^{52} +(-9.40582 - 6.41278i) q^{53} +(-0.0916778 + 0.401666i) q^{54} +(-3.58371 - 0.540157i) q^{55} +(-2.98352 + 2.03413i) q^{56} +(-0.0147785 - 0.0376551i) q^{57} +(-8.19618 - 2.52819i) q^{58} +(-10.5903 + 5.10003i) q^{59} +(-0.00513546 + 0.0685279i) q^{60} +(-3.37696 + 0.508995i) q^{61} +(5.46473 - 5.07053i) q^{62} +(10.3353 - 3.18803i) q^{63} +(0.623490 + 0.781831i) q^{64} +(2.79460 + 3.50431i) q^{65} +(-0.237990 + 0.0734101i) q^{66} +(-3.29395 + 3.05634i) q^{67} +(-7.11469 + 1.07237i) q^{68} +(0.0195647 - 0.261073i) q^{69} +(3.25337 - 1.56674i) q^{70} +(-8.48895 - 2.61850i) q^{71} +(-1.09430 - 2.78823i) q^{72} +(-2.27650 + 1.55209i) q^{73} +(11.4227 + 1.72169i) q^{74} +(0.0152917 - 0.0669971i) q^{75} +(0.486356 + 0.331592i) q^{76} +(9.59332 + 8.90130i) q^{77} +(0.277513 + 0.133643i) q^{78} +(-3.01935 + 5.22967i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(0.669396 + 8.93247i) q^{81} +(0.464220 + 2.03388i) q^{82} +(-5.11029 + 13.0208i) q^{83} +(0.154716 - 0.194008i) q^{84} +7.19506 q^{85} +(5.92973 + 2.79969i) q^{86} +0.589429 q^{87} +(2.25965 - 2.83351i) q^{88} +(-1.74550 + 4.44746i) q^{89} +(0.666512 + 2.92018i) q^{90} +(-1.20951 - 16.1398i) q^{91} +(1.90487 + 3.29933i) q^{92} +(-0.256146 + 0.443658i) q^{93} +(2.96648 + 1.42858i) q^{94} +(-0.431503 - 0.400376i) q^{95} +(-0.0567792 - 0.0387114i) q^{96} +(1.08267 - 4.74347i) q^{97} +(-5.97163 - 0.900078i) q^{98} +(-8.96920 + 6.11509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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