LMFDB - Embedded newform 637.2.w.b.92.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(92,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.w (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			92.4
Character	$\chi$	$=$	637.92
Dual form			637.2.w.b.547.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42465 + 1.78645i) q^{2} +(-2.04852 - 0.986513i) q^{3} +(-0.716746 - 3.14027i) q^{4} +(0.342127 + 0.164760i) q^{5} +(4.68077 - 2.25414i) q^{6} +(2.57961 - 0.587895i) q^{7} +(2.51370 + 1.21053i) q^{8} +(1.35274 + 1.69628i) q^{9} +O(q^{10})$	\(q+(-1.42465 + 1.78645i) q^{2} +(-2.04852 - 0.986513i) q^{3} +(-0.716746 - 3.14027i) q^{4} +(0.342127 + 0.164760i) q^{5} +(4.68077 - 2.25414i) q^{6} +(2.57961 - 0.587895i) q^{7} +(2.51370 + 1.21053i) q^{8} +(1.35274 + 1.69628i) q^{9} +(-0.781746 + 0.376469i) q^{10} +(-3.17977 + 3.98731i) q^{11} +(-1.62965 + 7.13997i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-2.62479 + 5.44589i) q^{14} +(-0.538315 - 0.675026i) q^{15} +(0.0603961 - 0.0290853i) q^{16} +(-0.381145 + 1.66991i) q^{17} -4.95749 q^{18} -0.294813 q^{19} +(0.272172 - 1.19246i) q^{20} +(-5.86433 - 1.34050i) q^{21} +(-2.59308 - 11.3610i) q^{22} +(-0.799940 - 3.50477i) q^{23} +(-3.95514 - 4.95959i) q^{24} +(-3.02754 - 3.79642i) q^{25} +(0.508451 + 2.22767i) q^{26} +(0.420123 + 1.84068i) q^{27} +(-3.69507 - 7.67929i) q^{28} +(1.63903 - 7.18105i) q^{29} +1.97281 q^{30} -3.73869 q^{31} +(-1.27575 + 5.58942i) q^{32} +(10.4473 - 5.03118i) q^{33} +(-2.44021 - 3.05993i) q^{34} +(0.979416 + 0.223881i) q^{35} +(4.35720 - 5.46376i) q^{36} +(-0.592362 + 2.59531i) q^{37} +(0.420004 - 0.526669i) q^{38} +(-2.04852 + 0.986513i) q^{39} +(0.660558 + 0.828314i) q^{40} +(-0.435772 - 0.209857i) q^{41} +(10.7494 - 8.56660i) q^{42} +(10.8256 - 5.21335i) q^{43} +(14.8003 + 7.12746i) q^{44} +(0.183330 + 0.803220i) q^{45} +(7.40073 + 3.56400i) q^{46} +(-4.84677 + 6.07766i) q^{47} -0.152415 q^{48} +(6.30876 - 3.03308i) q^{49} +11.0953 q^{50} +(2.42817 - 3.04483i) q^{51} +(-2.90205 - 1.39755i) q^{52} +(-0.994949 - 4.35915i) q^{53} +(-3.88681 - 1.87179i) q^{54} +(-1.74484 + 0.840269i) q^{55} +(7.19603 + 1.64491i) q^{56} +(0.603929 + 0.290837i) q^{57} +(10.4936 + 13.1585i) q^{58} +(7.94230 - 3.82481i) q^{59} +(-1.73393 + 2.17428i) q^{60} +(3.09941 - 13.5794i) q^{61} +(5.32632 - 6.67900i) q^{62} +(4.48677 + 3.58047i) q^{63} +(-8.08415 - 10.1372i) q^{64} +(0.342127 - 0.164760i) q^{65} +(-5.89583 + 25.8313i) q^{66} +4.69720 q^{67} +5.51715 q^{68} +(-1.81881 + 7.96872i) q^{69} +(-1.79527 + 1.43073i) q^{70} +(-3.32209 - 14.5550i) q^{71} +(1.34697 + 5.90147i) q^{72} +(-3.62196 - 4.54180i) q^{73} +(-3.79248 - 4.75562i) q^{74} +(2.45675 + 10.7637i) q^{75} +(0.211306 + 0.925792i) q^{76} +(-5.85845 + 12.1551i) q^{77} +(1.15605 - 5.06501i) q^{78} -4.18378 q^{79} +0.0254553 q^{80} +(2.40358 - 10.5308i) q^{81} +(0.995720 - 0.479513i) q^{82} +(7.46352 + 9.35896i) q^{83} +(-0.00630680 + 19.3764i) q^{84} +(-0.405534 + 0.508524i) q^{85} +(-6.10931 + 26.7666i) q^{86} +(-10.4418 + 13.0936i) q^{87} +(-12.8198 + 6.17367i) q^{88} +(-9.72985 - 12.2008i) q^{89} +(-1.69609 - 0.816796i) q^{90} +(1.14872 - 2.38337i) q^{91} +(-10.4326 + 5.02406i) q^{92} +(7.65877 + 3.68827i) q^{93} +(-3.95250 - 17.3170i) q^{94} +(-0.100864 - 0.0485733i) q^{95} +(8.12743 - 10.1915i) q^{96} -4.64839 q^{97} +(-3.56931 + 15.5914i) q^{98} -11.0650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) $ 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{7}\right)$

Coefficient data

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

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

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

$2$	−1.42465	+	1.78645i	−1.00738	+	1.26321i	−0.0428912	+	0.999080i	$0.513657\pi$
$2$	−1.42465	+	1.78645i	−1.00738	+	1.26321i	−0.964487	+	0.264132i	$0.914915\pi$
$3$	−2.04852	−	0.986513i	−1.18271	−	0.569564i	−0.264011	−	0.964520i	$-0.585045\pi$
$3$	−2.04852	−	0.986513i	−1.18271	−	0.569564i	−0.918700	+	0.394956i	$0.870760\pi$
$4$	−0.716746	−	3.14027i	−0.358373	−	1.57014i
$5$	0.342127	+	0.164760i	0.153004	+	0.0736829i	0.508819	−	0.860874i	$-0.330082\pi$
$5$	0.342127	+	0.164760i	0.153004	+	0.0736829i	−0.355815	+	0.934556i	$0.615797\pi$
$6$	4.68077	−	2.25414i	1.91092	−	0.920249i
$7$	2.57961	−	0.587895i	0.975000	−	0.222204i
$7$	2.57961	−	0.587895i	0.975000	−	0.222204i
$8$	2.51370	+	1.21053i	0.888727	+	0.427988i
$9$	1.35274	+	1.69628i	0.450912	+	0.565426i
$10$	−0.781746	+	0.376469i	−0.247210	+	0.119050i
$11$	−3.17977	+	3.98731i	−0.958738	+	1.20222i	0.0205591	+	0.999789i	$0.493455\pi$
$11$	−3.17977	+	3.98731i	−0.958738	+	1.20222i	−0.979297	+	0.202430i	$0.935116\pi$
$12$	−1.62965	+	7.13997i	−0.470440	+	2.06113i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$14$	−2.62479	+	5.44589i	−0.701503	+	1.45547i
$15$	−0.538315	−	0.675026i	−0.138992	−	0.174291i
$16$	0.0603961	−	0.0290853i	0.0150990	−	0.00727131i
$17$	−0.381145	+	1.66991i	−0.0924414	+	0.405012i	−0.999885	−	0.0151616i	$-0.995174\pi$
$17$	−0.381145	+	1.66991i	−0.0924414	+	0.405012i	0.907444	+	0.420174i	$0.138031\pi$
$18$	−4.95749			−1.16849
$19$	−0.294813			−0.0676347			−0.0338174	−	0.999428i	$-0.510766\pi$
$19$	−0.294813			−0.0676347			−0.0338174	+	0.999428i	$0.510766\pi$
$20$	0.272172	−	1.19246i	0.0608595	−	0.266643i
$21$	−5.86433	−	1.34050i	−1.27970	−	0.292522i
$22$	−2.59308	−	11.3610i	−0.552846	−	2.42218i
$23$	−0.799940	−	3.50477i	−0.166799	−	0.730794i	−0.987263	−	0.159096i	$-0.949142\pi$
$23$	−0.799940	−	3.50477i	−0.166799	−	0.730794i	0.820464	−	0.571698i	$-0.193715\pi$
$24$	−3.95514	−	4.95959i	−0.807341	−	1.01237i
$25$	−3.02754	−	3.79642i	−0.605509	−	0.759284i
$26$	0.508451	+	2.22767i	0.0997154	+	0.436882i
$27$	0.420123	+	1.84068i	0.0808526	+	0.354238i
$28$	−3.69507	−	7.67929i	−0.698304	−	1.45125i
$29$	1.63903	−	7.18105i	0.304360	−	1.33349i	−0.559113	−	0.829092i	$-0.688858\pi$
$29$	1.63903	−	7.18105i	0.304360	−	1.33349i	0.863472	−	0.504396i	$-0.168285\pi$
$30$	1.97281			0.360184
$31$	−3.73869			−0.671489			−0.335745	−	0.941953i	$-0.608988\pi$
$31$	−3.73869			−0.671489			−0.335745	+	0.941953i	$0.608988\pi$
$32$	−1.27575	+	5.58942i	−0.225523	+	0.988079i
$33$	10.4473	−	5.03118i	1.81865	−	0.875815i
$34$	−2.44021	−	3.05993i	−0.418493	−	0.524773i
$35$	0.979416	+	0.223881i	0.165552	+	0.0378428i
$36$	4.35720	−	5.46376i	0.726201	−	0.910627i
$37$	−0.592362	+	2.59531i	−0.0973837	+	0.426666i	−0.999993	−	0.00379539i	$-0.998792\pi$
$37$	−0.592362	+	2.59531i	−0.0973837	+	0.426666i	0.902609	+	0.430461i	$0.141649\pi$
$38$	0.420004	−	0.526669i	0.0681337	−	0.0854370i
$39$	−2.04852	+	0.986513i	−0.328025	+	0.157968i
$40$	0.660558	+	0.828314i	0.104443	+	0.130968i
$41$	−0.435772	−	0.209857i	−0.0680561	−	0.0327741i	0.399546	−	0.916713i	$-0.369168\pi$
$41$	−0.435772	−	0.209857i	−0.0680561	−	0.0327741i	−0.467602	+	0.883939i	$0.654882\pi$
$42$	10.7494	−	8.56660i	1.65866	−	1.32186i
$43$	10.8256	−	5.21335i	1.65089	−	0.795028i	0.651557	−	0.758600i	$-0.274116\pi$
$43$	10.8256	−	5.21335i	1.65089	−	0.795028i	0.999336	−	0.0364286i	$-0.0115981\pi$
$44$	14.8003	+	7.12746i	2.23123	+	1.07450i
$45$	0.183330	+	0.803220i	0.0273292	+	0.119737i
$46$	7.40073	+	3.56400i	1.09118	+	0.525484i
$47$	−4.84677	+	6.07766i	−0.706974	+	0.886517i	−0.997523	−	0.0703429i	$-0.977591\pi$
$47$	−4.84677	+	6.07766i	−0.706974	+	0.886517i	0.290549	+	0.956860i	$0.406162\pi$
$48$	−0.152415			−0.0219993
$49$	6.30876	−	3.03308i	0.901251	−	0.433297i
$50$	11.0953			1.56911
$51$	2.42817	−	3.04483i	0.340011	−	0.426361i
$52$	−2.90205	−	1.39755i	−0.402441	−	0.193806i
$53$	−0.994949	−	4.35915i	−0.136667	−	0.598776i	−0.996154	−	0.0876190i	$-0.972074\pi$
$53$	−0.994949	−	4.35915i	−0.136667	−	0.598776i	0.859487	−	0.511157i	$-0.170783\pi$
$54$	−3.88681	−	1.87179i	−0.528927	−	0.254718i
$55$	−1.74484	+	0.840269i	−0.235274	+	0.113302i
$56$	7.19603	+	1.64491i	0.961610	+	0.219810i
$57$	0.603929	+	0.290837i	0.0799923	+	0.0385223i
$58$	10.4936	+	13.1585i	1.37787	+	1.72780i
$59$	7.94230	−	3.82481i	1.03400	−	0.497948i	0.161659	−	0.986847i	$-0.448316\pi$
$59$	7.94230	−	3.82481i	1.03400	−	0.497948i	0.872340	+	0.488899i	$0.162601\pi$
$60$	−1.73393	+	2.17428i	−0.223849	+	0.280698i
$61$	3.09941	−	13.5794i	0.396839	−	1.73867i	−0.242879	−	0.970057i	$-0.578092\pi$
$61$	3.09941	−	13.5794i	0.396839	−	1.73867i	0.639718	−	0.768610i	$-0.279051\pi$
$62$	5.32632	−	6.67900i	0.676443	−	0.848233i
$63$	4.48677	+	3.58047i	0.565280	+	0.451096i
$64$	−8.08415	−	10.1372i	−1.01052	−	1.26715i
$65$	0.342127	−	0.164760i	0.0424357	−	0.0204359i
$66$	−5.89583	+	25.8313i	−0.725727	+	3.17962i
$67$	4.69720			0.573855			0.286927	−	0.957952i	$-0.407366\pi$
$67$	4.69720			0.573855			0.286927	+	0.957952i	$0.407366\pi$
$68$	5.51715			0.669052
$69$	−1.81881	+	7.96872i	−0.218959	+	0.959321i
$70$	−1.79527	+	1.43073i	−0.214576	+	0.171005i
$71$	−3.32209	−	14.5550i	−0.394260	−	1.72736i	−0.649388	−	0.760457i	$-0.724975\pi$
$71$	−3.32209	−	14.5550i	−0.394260	−	1.72736i	0.255128	−	0.966907i	$-0.417882\pi$
$72$	1.34697	+	5.90147i	0.158742	+	0.695495i
$73$	−3.62196	−	4.54180i	−0.423919	−	0.531577i	0.523307	−	0.852144i	$-0.324698\pi$
$73$	−3.62196	−	4.54180i	−0.423919	−	0.531577i	−0.947226	+	0.320567i	$0.896127\pi$
$74$	−3.79248	−	4.75562i	−0.440867	−	0.552830i
$75$	2.45675	+	10.7637i	0.283681	+	1.24289i
$76$	0.211306	+	0.925792i	0.0242385	+	0.106196i
$77$	−5.85845	+	12.1551i	−0.667632	+	1.38520i
$78$	1.15605	−	5.06501i	0.130897	−	0.573499i
$79$	−4.18378			−0.470712			−0.235356	−	0.971909i	$-0.575626\pi$
$79$	−4.18378			−0.470712			−0.235356	+	0.971909i	$0.575626\pi$
$80$	0.0254553			0.00284598
$81$	2.40358	−	10.5308i	0.267065	−	1.17009i
$82$	0.995720	−	0.479513i	0.109959	−	0.0529534i
$83$	7.46352	+	9.35896i	0.819228	+	1.02728i	0.999050	+	0.0435804i	$0.0138765\pi$
$83$	7.46352	+	9.35896i	0.819228	+	1.02728i	−0.179822	+	0.983699i	$0.557552\pi$
$84$	−0.00630680	+	19.3764i	−0.000688128	+	2.11414i
$85$	−0.405534	+	0.508524i	−0.0439863	+	0.0551571i
$86$	−6.10931	+	26.7666i	−0.658784	+	2.88632i
$87$	−10.4418	+	13.0936i	−1.11948	+	1.40378i
$88$	−12.8198	+	6.17367i	−1.36659	+	0.658116i
$89$	−9.72985	−	12.2008i	−1.03136	−	1.29329i	−0.955127	−	0.296197i	$-0.904282\pi$
$89$	−9.72985	−	12.2008i	−1.03136	−	1.29329i	−0.0762347	−	0.997090i	$-0.524290\pi$
$90$	−1.69609	−	0.816796i	−0.178784	−	0.0860979i
$91$	1.14872	−	2.38337i	0.120419	−	0.249845i
$92$	−10.4326	+	5.02406i	−1.08767	+	0.523794i
$93$	7.65877	+	3.68827i	0.794178	+	0.382456i
$94$	−3.95250	−	17.3170i	−0.407669	−	1.78612i
$95$	−0.100864	−	0.0485733i	−0.0103484	−	0.00498352i
$96$	8.12743	−	10.1915i	0.829502	−	1.04016i
$97$	−4.64839			−0.471973			−0.235986	−	0.971756i	$-0.575832\pi$
$97$	−4.64839			−0.471973			−0.235986	+	0.971756i	$0.575832\pi$
$98$	−3.56931	+	15.5914i	−0.360554	+	1.57496i
$99$	−11.0650			−1.11207
$100$	−9.75180	+	12.2284i	−0.975180	+	1.22284i
$101$	1.85292	+	0.892317i	0.184372	+	0.0887889i	0.523793	−	0.851846i	$-0.324517\pi$
$101$	1.85292	+	0.892317i	0.184372	+	0.0887889i	−0.339421	+	0.940635i	$0.610231\pi$
$102$	1.98015	+	8.67561i	0.196064	+	0.859013i
$103$	−3.47482	−	1.67338i	−0.342384	−	0.164883i	0.254787	−	0.966997i	$-0.417994\pi$
$103$	−3.47482	−	1.67338i	−0.342384	−	0.164883i	−0.597171	+	0.802114i	$0.703709\pi$
$104$	2.51370	−	1.21053i	0.246489	−	0.118703i
$105$	−1.78549	−	1.42483i	−0.174246	−	0.139049i
$106$	9.20487	+	4.43283i	0.894056	+	0.430555i
$107$	−7.61672	−	9.55107i	−0.736337	−	0.923337i	0.262801	−	0.964850i	$-0.415354\pi$
$107$	−7.61672	−	9.55107i	−0.736337	−	0.923337i	−0.999138	+	0.0415131i	$0.986782\pi$
$108$	5.47910	−	2.63860i	0.527227	−	0.253899i
$109$	9.96651	−	12.4976i	0.954618	−	1.19705i	−0.0257081	−	0.999669i	$-0.508184\pi$
$109$	9.96651	−	12.4976i	0.954618	−	1.19705i	0.980326	−	0.197384i	$-0.0632445\pi$
$110$	0.984677	−	4.31415i	0.0938853	−	0.411338i
$111$	3.77376	−	4.73215i	0.358190	−	0.449156i
$112$	0.138699	−	0.110535i	0.0131059	−	0.0104446i
$113$	−2.77194	−	3.47590i	−0.260762	−	0.326985i	0.634165	−	0.773198i	$-0.281344\pi$
$113$	−2.77194	−	3.47590i	−0.260762	−	0.326985i	−0.894927	+	0.446213i	$0.852773\pi$
$114$	−1.37995	+	0.664549i	−0.129244	+	0.0622408i
$115$	0.303764	−	1.33087i	0.0283261	−	0.124105i
$116$	−23.7252			−2.20283
$117$	2.16962			0.200582
$118$	−4.48214	+	19.6375i	−0.412614	+	1.80778i
$119$	−0.00147504	+	4.53178i	−0.000135217	+	0.415428i
$120$	−0.536021	−	2.34846i	−0.0489318	−	0.214384i
$121$	−3.33995	−	14.6333i	−0.303632	−	1.33030i
$122$	19.8434	+	24.8828i	1.79654	+	2.25279i
$123$	0.685659	+	0.859789i	0.0618238	+	0.0775246i
$124$	2.67970	+	11.7405i	0.240644	+	1.05433i
$125$	−0.832800	−	3.64874i	−0.0744879	−	0.326353i
$126$	−12.7884	+	2.91449i	−1.13928	+	0.259643i
$127$	−1.34550	+	5.89501i	−0.119394	+	0.523098i	0.879493	+	0.475913i	$0.157882\pi$
$127$	−1.34550	+	5.89501i	−0.119394	+	0.523098i	−0.998886	+	0.0471850i	$0.984975\pi$
$128$	18.1603			1.60516
$129$	−27.3195			−2.40535
$130$	−0.193075	+	0.845919i	−0.0169338	+	0.0741920i
$131$	9.46738	−	4.55925i	0.827169	−	0.398343i	0.0281162	−	0.999605i	$-0.491049\pi$
$131$	9.46738	−	4.55925i	0.827169	−	0.398343i	0.799053	+	0.601261i	$0.205335\pi$
$132$	−23.2873	−	29.2014i	−2.02690	−	2.54166i
$133$	−0.760502	+	0.173319i	−0.0659439	+	0.0150287i
$134$	−6.69186	+	8.39132i	−0.578088	+	0.724900i
$135$	−0.159534	+	0.698965i	−0.0137305	+	0.0601574i
$136$	−2.97957	+	3.73626i	−0.255496	+	0.320381i
$137$	2.29452	−	1.10498i	0.196034	−	0.0944049i	−0.333292	−	0.942824i	$-0.608159\pi$
$137$	2.29452	−	1.10498i	0.196034	−	0.0944049i	0.529325	+	0.848419i	$0.322445\pi$
$138$	−11.6446	−	14.6018i	−0.991252	−	1.24299i
$139$	−8.14196	−	3.92096i	−0.690592	−	0.332572i	0.0554585	−	0.998461i	$-0.482338\pi$
$139$	−8.14196	−	3.92096i	−0.690592	−	0.332572i	−0.746050	+	0.665889i	$0.768052\pi$
$140$	0.00105331	−	3.23610i	8.90212e−5	−	0.273500i
$141$	15.9244	−	7.66877i	1.34107	−	0.645827i
$142$	30.7347	+	14.8010i	2.57920	+	1.24208i
$143$	1.13485	+	4.97209i	0.0949007	+	0.415787i
$144$	0.131037	+	0.0631040i	0.0109197	+	0.00525867i
$145$	1.74391	−	2.18679i	0.144823	−	0.181603i
$146$	13.2737			1.09854
$147$	−15.9158	−	0.0103608i	−1.31271	−	0.000854545i
$148$	8.57454			0.704822
$149$	2.14754	−	2.69293i	0.175933	−	0.220613i	−0.686044	−	0.727560i	$-0.740654\pi$
$149$	2.14754	−	2.69293i	0.175933	−	0.220613i	0.861977	+	0.506947i	$0.169226\pi$
$150$	−22.7289	−	10.9457i	−1.85581	−	0.893709i
$151$	0.0786648	+	0.344653i	0.00640165	+	0.0280475i	0.978028	−	0.208474i	$-0.0668497\pi$
$151$	0.0786648	+	0.344653i	0.00640165	+	0.0280475i	−0.971626	+	0.236522i	$0.923993\pi$
$152$	−0.741071	−	0.356881i	−0.0601088	−	0.0289469i
$153$	−3.34822	+	1.61242i	−0.270687	+	0.130356i
$154$	−13.3682	−	27.7825i	−1.07724	−	2.23878i
$155$	−1.27911	−	0.615987i	−0.102741	−	0.0494773i
$156$	4.56618	+	5.72581i	0.365587	+	0.458432i
$157$	−1.41641	+	0.682106i	−0.113042	+	0.0544380i	−0.489550	−	0.871975i	$-0.662839\pi$
$157$	−1.41641	+	0.682106i	−0.113042	+	0.0544380i	0.376508	+	0.926413i	$0.377125\pi$
$158$	5.96041	−	7.47412i	0.474185	−	0.594609i
$159$	−2.26220	+	9.91132i	−0.179404	+	0.786019i
$160$	−1.35738	+	1.70210i	−0.107310	+	0.134563i
$161$	−4.12397	−	8.57064i	−0.325014	−	0.675461i
$162$	15.3885	+	19.2965i	1.20903	+	1.51608i
$163$	−9.91691	+	4.77573i	−0.776752	+	0.374064i	−0.779878	−	0.625931i	$-0.784719\pi$
$163$	−9.91691	+	4.77573i	−0.776752	+	0.374064i	0.00312629	+	0.999995i	$0.499005\pi$
$164$	−0.346669	+	1.51886i	−0.0270703	+	0.118603i
$165$	4.40326			0.342793
$166$	−27.3522			−2.12294
$167$	−3.63301	+	15.9173i	−0.281131	+	1.23172i	0.615215	+	0.788359i	$0.289069\pi$
$167$	−3.63301	+	15.9173i	−0.281131	+	1.23172i	−0.896346	+	0.443356i	$0.853788\pi$
$168$	−13.1184	−	10.4686i	−1.01211	−	0.807670i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	−0.330710	−	1.44893i	−0.0253643	−	0.111128i
$171$	−0.398804	−	0.500085i	−0.0304973	−	0.0382424i
$172$	−24.1306	−	30.2588i	−1.83994	−	2.30721i
$173$	−2.50714	−	10.9845i	−0.190615	−	0.835137i	−0.976285	−	0.216491i	$-0.930539\pi$
$173$	−2.50714	−	10.9845i	−0.190615	−	0.835137i	0.785670	−	0.618646i	$-0.212318\pi$
$174$	−8.51518	−	37.3074i	−0.645534	−	2.82827i
$175$	−10.0418	−	8.01340i	−0.759087	−	0.605756i
$176$	−0.0760741	+	0.333303i	−0.00573430	+	0.0251236i
$177$	−20.0431			−1.50653
$178$	35.6578			2.67267
$179$	−2.60702	+	11.4221i	−0.194858	+	0.853728i	0.779082	+	0.626922i	$0.215686\pi$
$179$	−2.60702	+	11.4221i	−0.194858	+	0.853728i	−0.973940	+	0.226806i	$0.927172\pi$
$180$	2.39093	−	1.15141i	0.178209	−	0.0858211i
$181$	11.1793	+	14.0184i	0.830952	+	1.04198i	0.998425	+	0.0561042i	$0.0178679\pi$
$181$	11.1793	+	14.0184i	0.830952	+	1.04198i	−0.167473	+	0.985877i	$0.553561\pi$
$182$	2.62124	+	5.44760i	0.194299	+	0.403803i
$183$	−19.7455	+	24.7600i	−1.45963	+	1.83031i
$184$	2.23183	−	9.77829i	0.164533	−	0.720865i
$185$	−0.630265	+	0.790328i	−0.0463380	+	0.0581061i
$186$	−17.5000	+	8.42754i	−1.28316	+	0.617937i
$187$	−5.44648	−	6.82967i	−0.398286	−	0.499435i
$188$	22.5594	+	10.8640i	1.64531	+	0.792341i
$189$	2.16588	+	4.50124i	0.157544	+	0.327417i
$190$	0.230469	−	0.110988i	0.0167200	−	0.00805191i
$191$	16.8089	+	8.09473i	1.21625	+	0.585714i	0.928264	−	0.371921i	$-0.121301\pi$
$191$	16.8089	+	8.09473i	1.21625	+	0.585714i	0.287983	+	0.957635i	$0.407015\pi$
$192$	6.56002	+	28.7413i	0.473429	+	2.07423i
$193$	−1.88497	−	0.907755i	−0.135683	−	0.0653416i	0.364810	−	0.931082i	$-0.381134\pi$
$193$	−1.88497	−	0.907755i	−0.135683	−	0.0653416i	−0.500494	+	0.865740i	$0.666848\pi$
$194$	6.62232	−	8.30412i	0.475455	−	0.596201i
$195$	−0.863391			−0.0618287
$196$	−14.0465	−	17.6373i	−1.00332	−	1.25980i
$197$	17.3903			1.23901			0.619504	−	0.784993i	$-0.287334\pi$
$197$	17.3903			1.23901			0.619504	+	0.784993i	$0.287334\pi$
$198$	15.7637	−	19.7671i	1.12028	−	1.40478i
$199$	−22.9566	−	11.0553i	−1.62735	−	0.783690i	−0.999988	−	0.00496269i	$-0.998420\pi$
$199$	−22.9566	−	11.0553i	−1.62735	−	0.783690i	−0.627362	−	0.778728i	$-0.715865\pi$
$200$	−3.01464	−	13.2080i	−0.213167	−	0.933947i
$201$	−9.62229	−	4.63385i	−0.678704	−	0.326847i
$202$	−4.23383	+	2.03891i	−0.297891	+	0.143457i
$203$	0.00634309	−	19.4879i	0.000445197	−	1.36778i
$204$	−11.3020	−	5.44273i	−0.791295	−	0.381068i
$205$	−0.114514	−	0.143595i	−0.00799797	−	0.0100291i
$206$	7.93981	−	3.82361i	0.553193	−	0.266404i
$207$	4.86295	−	6.09795i	0.337999	−	0.423837i
$208$	0.0149166	−	0.0653540i	0.00103428	−	0.00453148i
$209$	0.937438	−	1.17551i	0.0648439	−	0.0813117i
$210$	5.08908	−	1.15981i	0.351180	−	0.0800343i
$211$	3.76310	+	4.71878i	0.259062	+	0.324854i	0.894304	−	0.447459i	$-0.147671\pi$
$211$	3.76310	+	4.71878i	0.259062	+	0.324854i	−0.635242	+	0.772313i	$0.719100\pi$
$212$	−12.9758	+	6.24882i	−0.891181	+	0.429170i
$213$	−7.55337	+	33.0935i	−0.517549	+	2.26753i
$214$	27.9137			1.90814
$215$	4.56270			0.311173
$216$	−1.17214	+	5.13548i	−0.0797541	+	0.349425i
$217$	−9.64437	+	2.19796i	−0.654702	+	0.149207i
$218$	8.12760	+	35.6094i	0.550471	+	2.41177i
$219$	2.93910	+	12.8771i	0.198606	+	0.870151i
$220$	3.88928	+	4.87700i	0.262215	+	0.328807i
$221$	1.06795	+	1.33916i	0.0718378	+	0.0900818i
$222$	3.07747	+	13.4833i	0.206547	+	0.904939i
$223$	1.61056	+	7.05635i	0.107851	+	0.472528i	0.999792	+	0.0203761i	$0.00648635\pi$
$223$	1.61056	+	7.05635i	0.107851	+	0.472528i	−0.891941	+	0.452152i	$0.850657\pi$
$224$	−0.00493719	+	15.1685i	−0.000329880	+	1.01349i
$225$	2.34432	−	10.2711i	0.156288	−	0.684741i
$226$	10.1586			0.675737
$227$	−0.613557			−0.0407232			−0.0203616	−	0.999793i	$-0.506482\pi$
$227$	−0.613557			−0.0407232			−0.0203616	+	0.999793i	$0.506482\pi$
$228$	0.480442	−	2.10496i	0.0318181	−	0.139404i
$229$	−23.7678	+	11.4460i	−1.57062	+	0.756371i	−0.997986	−	0.0634399i	$-0.979793\pi$
$229$	−23.7678	+	11.4460i	−1.57062	+	0.756371i	−0.572635	+	0.819811i	$0.694079\pi$
$230$	1.94479	+	2.43869i	0.128235	+	0.160802i
$231$	23.9923	−	19.1204i	1.57857	−	1.25803i
$232$	12.8129	−	16.0669i	0.841210	−	1.05484i
$233$	3.07285	−	13.4630i	0.201309	−	0.881993i	−0.768832	−	0.639451i	$-0.779162\pi$
$233$	3.07285	−	13.4630i	0.201309	−	0.881993i	0.970141	−	0.242542i	$-0.0779813\pi$
$234$	−3.09095	+	3.87592i	−0.202061	+	0.253377i
$235$	−2.65957	+	1.28078i	−0.173491	+	0.0835488i
$236$	−17.7035	−	22.1995i	−1.15240	−	1.44507i
$237$	8.57054	+	4.12736i	0.556717	+	0.268101i
$238$	−8.09370	−	6.45882i	−0.524637	−	0.418663i
$239$	11.0159	−	5.30497i	0.712559	−	0.343150i	−0.0422391	−	0.999108i	$-0.513449\pi$
$239$	11.0159	−	5.30497i	0.712559	−	0.343150i	0.754798	+	0.655957i	$0.227735\pi$
$240$	−0.0521455	−	0.0251119i	−0.00336598	−	0.00162097i
$241$	−1.50057	−	6.57443i	−0.0966603	−	0.423496i	0.903325	−	0.428957i	$-0.141119\pi$
$241$	−1.50057	−	6.57443i	−0.0966603	−	0.423496i	−0.999985	+	0.00546089i	$0.998262\pi$
$242$	30.8999	+	14.8806i	1.98632	+	0.956561i
$243$	−11.7811	+	14.7730i	−0.755756	+	0.947687i
$244$	−44.8645			−2.87216
$245$	2.65813	+	0.00173038i	0.169822	+	0.000110550i
$246$	−2.51279			−0.160210
$247$	−0.183813	+	0.230494i	−0.0116957	+	0.0146660i
$248$	−9.39796	−	4.52582i	−0.596771	−	0.287390i
$249$	−6.05640	−	26.5348i	−0.383809	−	1.68158i
$250$	7.70474	+	3.71041i	0.487290	+	0.234667i
$251$	−2.75490	+	1.32669i	−0.173888	+	0.0837399i	−0.518803	−	0.854894i	$-0.673622\pi$
$251$	−2.75490	+	1.32669i	−0.173888	+	0.0837399i	0.344915	+	0.938634i	$0.387908\pi$
$252$	8.02776	−	16.6559i	0.505701	−	1.04923i
$253$	16.5182	+	7.95475i	1.03849	+	0.500111i
$254$	−8.61429	−	10.8020i	−0.540509	−	0.677776i
$255$	1.33241	−	0.641654i	0.0834386	−	0.0401819i
$256$	−9.70379	+	12.1682i	−0.606487	+	0.760510i
$257$	−2.35873	+	10.3343i	−0.147134	+	0.644635i	0.846540	+	0.532326i	$0.178682\pi$
$257$	−2.35873	+	10.3343i	−0.147134	+	0.644635i	−0.993673	+	0.112309i	$0.964175\pi$
$258$	38.9207	−	48.8050i	2.42309	−	3.03846i
$259$	−0.00229246	+	7.04312i	−0.000142446	+	0.437638i
$260$	−0.762609	−	0.956281i	−0.0472950	−	0.0593061i
$261$	14.3982	−	6.93383i	0.891229	−	0.429193i
$262$	−5.34280	+	23.4083i	−0.330079	+	1.44617i
$263$	3.11324			0.191971			0.0959853	−	0.995383i	$-0.469400\pi$
$263$	3.11324			0.191971			0.0959853	+	0.995383i	$0.469400\pi$
$264$	32.3519			1.99112
$265$	0.377815	−	1.65531i	0.0232090	−	0.101685i
$266$	0.773821	−	1.60552i	0.0474460	−	0.0984406i
$267$	7.89545	+	34.5922i	0.483194	+	2.11701i
$268$	−3.36670	−	14.7505i	−0.205654	−	0.901029i
$269$	−2.38816	−	2.99465i	−0.145608	−	0.182587i	0.703679	−	0.710518i	$-0.251539\pi$
$269$	−2.38816	−	2.99465i	−0.145608	−	0.182587i	−0.849287	+	0.527931i	$0.822968\pi$
$270$	−1.02139	−	1.28078i	−0.0621597	−	0.0779458i
$271$	−2.76940	−	12.1335i	−0.168229	−	0.737058i	−0.986705	−	0.162519i	$-0.948038\pi$
$271$	−2.76940	−	12.1335i	−0.168229	−	0.737058i	0.818477	−	0.574540i	$-0.194819\pi$
$272$	0.0255500	+	0.111942i	0.00154919	+	0.00678746i
$273$	−4.70440	+	3.74913i	−0.284723	+	0.226908i
$274$	−1.29488	+	5.67325i	−0.0782267	+	0.342733i
$275$	24.7644			1.49335
$276$	26.3276			1.58473
$277$	−5.84911	+	25.6266i	−0.351439	+	1.53976i	0.422422	+	0.906399i	$0.361180\pi$
$277$	−5.84911	+	25.6266i	−0.351439	+	1.53976i	−0.773861	+	0.633356i	$0.781677\pi$
$278$	18.6040	−	8.95923i	1.11580	−	0.537339i
$279$	−5.05747	−	6.34187i	−0.302783	−	0.379678i
$280$	2.19094	+	1.74839i	0.130934	+	0.104486i
$281$	−0.836748	+	1.04925i	−0.0499162	+	0.0625929i	−0.806163	−	0.591694i	$-0.798460\pi$
$281$	−0.836748	+	1.04925i	−0.0499162	+	0.0625929i	0.756247	+	0.654287i	$0.227031\pi$
$282$	−8.98672	+	39.3734i	−0.535151	+	2.34465i
$283$	0.0540291	−	0.0677503i	0.00321170	−	0.00402734i	−0.780223	−	0.625501i	$-0.784894\pi$
$283$	0.0540291	−	0.0677503i	0.00321170	−	0.00402734i	0.783435	+	0.621474i	$0.213466\pi$
$284$	−43.3256	+	20.8645i	−2.57090	+	1.23808i
$285$	0.158702	+	0.199006i	0.00940071	+	0.0117881i
$286$	−10.4992	−	5.05613i	−0.620828	−	0.298975i
$287$	−1.24749	−	0.285160i	−0.0736373	−	0.0168324i
$288$	−11.2070	+	5.39699i	−0.660377	+	0.318021i
$289$	12.6732	+	6.10307i	0.745480	+	0.359004i
$290$	1.42214	+	6.23080i	0.0835110	+	0.365885i
$291$	9.52230	+	4.58570i	0.558207	+	0.268818i
$292$	−11.6664	+	14.6293i	−0.682727	+	0.856112i
$293$	12.6315			0.737942			0.368971	−	0.929441i	$-0.379710\pi$
$293$	12.6315			0.737942			0.368971	+	0.929441i	$0.379710\pi$
$294$	22.6929	−	28.4180i	1.32347	−	1.65737i
$295$	3.34745			0.194896
$296$	−4.63073	+	5.80675i	−0.269155	+	0.337510i
$297$	−8.67524	−	4.17778i	−0.503389	−	0.242419i
$298$	1.75130	+	7.67294i	0.101450	+	0.444481i
$299$	−3.23889	−	1.55977i	−0.187310	−	0.0902037i
$300$	32.0402	−	15.4297i	1.84984	−	0.890836i
$301$	24.8610	−	19.8127i	1.43296	−	1.14199i
$302$	−0.727775	−	0.350478i	−0.0418788	−	0.0201677i
$303$	−2.91544	−	3.65585i	−0.167488	−	0.210023i
$304$	−0.0178056	+	0.00857471i	−0.00102122	+	0.000491793i
$305$	3.29774	−	4.13523i	0.188828	−	0.236783i
$306$	1.88953	−	8.27856i	0.108017	−	0.473253i
$307$	−5.47860	+	6.86995i	−0.312680	+	0.392089i	−0.913194	−	0.407526i	$-0.866391\pi$
$307$	−5.47860	+	6.86995i	−0.312680	+	0.392089i	0.600513	+	0.799615i	$0.294963\pi$
$308$	42.3692	+	9.68501i	2.41421	+	0.551855i
$309$	5.46740	+	6.85590i	0.311030	+	0.390019i
$310$	2.92271	−	1.40750i	0.165999	−	0.0799408i
$311$	−6.58492	+	28.8504i	−0.373397	+	1.63596i	0.343768	+	0.939055i	$0.388297\pi$
$311$	−6.58492	+	28.8504i	−0.373397	+	1.63596i	−0.717165	+	0.696903i	$0.754561\pi$
$312$	−6.34356			−0.359133
$313$	22.9727			1.29849			0.649247	−	0.760577i	$-0.275084\pi$
$313$	22.9727			1.29849			0.649247	+	0.760577i	$0.275084\pi$
$314$	0.799332	−	3.50210i	0.0451089	−	0.197635i
$315$	0.945129	+	1.96422i	0.0532520	+	0.110671i
$316$	2.99871	+	13.1382i	0.168691	+	0.739082i
$317$	−5.25332	−	23.0163i	−0.295056	−	1.29272i	−0.877391	−	0.479775i	$-0.840718\pi$
$317$	−5.25332	−	23.0163i	−0.295056	−	1.29272i	0.582336	−	0.812948i	$-0.302139\pi$
$318$	−14.4833	−	18.1614i	−0.812181	−	1.01844i
$319$	23.4213	+	29.3694i	1.31134	+	1.64437i
$320$	−1.09560	−	4.80016i	−0.0612461	−	0.268337i
$321$	6.18072	+	27.0795i	0.344974	+	1.51143i
$322$	21.1862	+	4.84288i	1.18066	+	0.269883i
$323$	0.112367	−	0.492310i	0.00625224	−	0.0273929i
$324$	−34.7923			−1.93290
$325$	−4.85580			−0.269351
$326$	5.59649	−	24.5198i	0.309961	−	1.35803i
$327$	−32.7456	+	15.7694i	−1.81084	+	0.872052i
$328$	−0.841361	−	1.05503i	−0.0464564	−	0.0582545i
$329$	−8.92974	+	18.5274i	−0.492312	+	1.02145i
$330$	−6.27309	+	7.86621i	−0.345322	+	0.433020i
$331$	3.11569	−	13.6507i	0.171254	−	0.750312i	−0.814230	−	0.580543i	$-0.802840\pi$
$331$	3.11569	−	13.6507i	0.171254	−	0.750312i	0.985484	−	0.169770i	$-0.0543024\pi$
$332$	24.0402	−	30.1455i	1.31938	−	1.65445i
$333$	−5.20367	+	2.50596i	−0.285160	+	0.137326i
$334$	−23.2597	−	29.1667i	−1.27271	−	1.59593i
$335$	1.60704	+	0.773910i	0.0878021	+	0.0422832i
$336$	−0.393172	+	0.0896043i	−0.0214493	+	0.00488832i
$337$	29.8656	−	14.3825i	1.62688	−	0.783465i	0.626891	−	0.779107i	$-0.284327\pi$
$337$	29.8656	−	14.3825i	1.62688	−	0.783465i	0.999991	−	0.00435732i	$-0.00138698\pi$
$338$	2.05868	+	0.991406i	0.111977	+	0.0539254i
$339$	2.24934	+	9.85498i	0.122167	+	0.535249i
$340$	1.88757	+	0.909004i	0.102368	+	0.0492977i
$341$	11.8882	−	14.9073i	0.643782	−	0.807277i
$342$	1.46153			0.0790306
$343$	14.4910	−	11.5330i	0.782440	−	0.622726i
$344$	33.5233			1.80746
$345$	−1.93519	+	2.42665i	−0.104187	+	0.130646i
$346$	23.1951	+	11.1702i	1.24698	+	0.600512i
$347$	−2.09218	−	9.16644i	−0.112314	−	0.492081i	−0.999528	−	0.0307220i	$-0.990219\pi$
$347$	−2.09218	−	9.16644i	−0.112314	−	0.492081i	0.887214	−	0.461359i	$-0.152638\pi$
$348$	48.6014	+	23.4052i	2.60531	+	1.25465i
$349$	−5.34248	+	2.57280i	−0.285976	+	0.137719i	−0.571373	−	0.820691i	$-0.693589\pi$
$349$	−5.34248	+	2.57280i	−0.285976	+	0.137719i	0.285397	+	0.958410i	$0.407875\pi$
$350$	28.6215	−	6.52288i	1.52989	−	0.348662i
$351$	1.70104	+	0.819178i	0.0907949	+	0.0437245i
$352$	−18.2302	−	22.8599i	−0.971671	−	1.21844i
$353$	−14.7357	+	7.09632i	−0.784300	+	0.377699i	−0.782779	−	0.622300i	$-0.786198\pi$
$353$	−14.7357	+	7.09632i	−0.784300	+	0.377699i	−0.00152086	+	0.999999i	$0.500484\pi$
$354$	28.5544	−	35.8061i	1.51765	−	1.90307i
$355$	1.26151	−	5.52702i	0.0669538	−	0.293344i
$356$	−31.3401	+	39.2993i	−1.66102	+	2.08286i
$357$	4.47368	−	9.28197i	0.236772	−	0.491254i
$358$	−16.6909	−	20.9298i	−0.882144	−	1.10617i
$359$	−17.5686	+	8.46059i	−0.927235	+	0.446533i	−0.835649	−	0.549265i	$-0.814908\pi$
$359$	−17.5686	+	8.46059i	−0.927235	+	0.446533i	−0.0915860	+	0.995797i	$0.529194\pi$
$360$	−0.511489	+	2.24098i	−0.0269579	+	0.118110i
$361$	−18.9131			−0.995426
$362$	−40.9698			−2.15333
$363$	−7.59397	+	33.2714i	−0.398580	+	1.74629i
$364$	−8.30776	−	1.89904i	−0.435445	−	0.0995365i
$365$	−0.490867	−	2.15063i	−0.0256931	−	0.112569i
$366$	−16.1023	−	70.5486i	−0.841679	−	3.68764i
$367$	0.889583	+	1.11550i	0.0464358	+	0.0582287i	0.804507	−	0.593943i	$-0.202430\pi$
$367$	0.889583	+	1.11550i	0.0464358	+	0.0582287i	−0.758071	+	0.652172i	$0.773858\pi$
$368$	−0.150250	−	0.188408i	−0.00783234	−	0.00982144i
$369$	−0.233509	−	1.02307i	−0.0121560	−	0.0532590i
$370$	−0.513976	−	2.25188i	−0.0267204	−	0.117070i
$371$	−5.12931	−	10.6600i	−0.266300	−	0.553439i
$372$	6.09277	−	26.6942i	0.315895	−	1.38403i
$373$	−16.4875			−0.853690			−0.426845	−	0.904325i	$-0.640375\pi$
$373$	−16.4875			−0.853690			−0.426845	+	0.904325i	$0.640375\pi$
$374$	19.9602			1.03212
$375$	−1.89352	+	8.29606i	−0.0977811	+	0.428407i
$376$	−19.5405	+	9.41022i	−1.00773	+	0.485295i
$377$	−4.59245	−	5.75876i	−0.236523	−	0.296591i
$378$	−11.1269	−	2.54344i	−0.572304	−	0.130821i
$379$	8.11968	−	10.1818i	0.417080	−	0.523002i	−0.528262	−	0.849081i	$-0.677156\pi$
$379$	8.11968	−	10.1818i	0.417080	−	0.523002i	0.945342	+	0.326079i	$0.105728\pi$
$380$	−0.0802398	+	0.351554i	−0.00411622	+	0.0180343i
$381$	8.57178	−	10.7487i	0.439145	−	0.550671i
$382$	−38.4076	+	18.4961i	−1.96510	+	0.946343i
$383$	−9.67877	−	12.1368i	−0.494562	−	0.620161i	0.470431	−	0.882437i	$-0.344099\pi$
$383$	−9.67877	−	12.1368i	−0.494562	−	0.620161i	−0.964993	+	0.262275i	$0.915527\pi$
$384$	−37.2017	−	17.9154i	−1.89844	−	0.914242i
$385$	−4.00700	+	3.19335i	−0.204216	+	0.162748i
$386$	4.30708	−	2.07418i	0.219225	−	0.105573i
$387$	23.4875	+	11.3110i	1.19394	+	0.574970i
$388$	3.33172	+	14.5972i	0.169142	+	0.741061i
$389$	−1.95748	−	0.942671i	−0.0992480	−	0.0477953i	0.383601	−	0.923499i	$-0.374684\pi$
$389$	−1.95748	−	0.942671i	−0.0992480	−	0.0477953i	−0.482849	+	0.875704i	$0.660398\pi$
$390$	1.23003	−	1.54241i	0.0622849	−	0.0781028i
$391$	6.15753			0.311400
$392$	19.5300	+	0.0127136i	0.986412	+	0.000642133i
$393$	−23.8918			−1.20518
$394$	−24.7751	+	31.0669i	−1.24815	+	1.56513i
$395$	−1.43139	−	0.689320i	−0.0720209	−	0.0346834i
$396$	7.93079	+	34.7470i	0.398537	+	1.74610i
$397$	28.1583	+	13.5603i	1.41323	+	0.680574i	0.975797	−	0.218679i	$-0.0701747\pi$
$397$	28.1583	+	13.5603i	1.41323	+	0.680574i	0.437429	+	0.899253i	$0.355889\pi$
$398$	52.4548	−	25.2609i	2.62932	−	1.26622i
$399$	1.72888	+	0.395198i	0.0865523	+	0.0197846i
$400$	−0.293272	−	0.141232i	−0.0146636	−	0.00706161i
$401$	−7.95249	−	9.97210i	−0.397128	−	0.497983i	0.542559	−	0.840018i	$-0.317455\pi$
$401$	−7.95249	−	9.97210i	−0.397128	−	0.497983i	−0.939687	+	0.342035i	$0.888884\pi$
$402$	21.9865	−	10.5881i	1.09659	−	0.528089i
$403$	−2.33104	+	2.92303i	−0.116117	+	0.145606i
$404$	1.47405	−	6.45822i	0.0733366	−	0.321309i
$405$	2.55738	−	3.20686i	0.127077	−	0.159350i
$406$	34.8051	+	27.7747i	1.72735	+	1.37843i
$407$	−8.46471	−	10.6144i	−0.419580	−	0.526137i
$408$	9.78955	−	4.71440i	0.484655	−	0.233398i
$409$	−1.20201	+	5.26633i	−0.0594353	+	0.260403i	−0.995912	−	0.0903260i	$-0.971209\pi$
$409$	−1.20201	+	5.26633i	−0.0594353	+	0.260403i	0.936477	+	0.350729i	$0.114066\pi$
$410$	0.419668			0.0207259
$411$	−5.79043			−0.285621
$412$	−2.76432	+	12.1113i	−0.136188	+	0.596679i
$413$	18.2394	−	14.5358i	0.897504	−	0.715258i
$414$	3.96570	+	17.3749i	0.194903	+	0.853928i
$415$	1.01149	+	4.43165i	0.0496523	+	0.217541i
$416$	3.57457	+	4.48237i	0.175258	+	0.219766i
$417$	12.8108	+	16.0643i	0.627350	+	0.786672i
$418$	0.764473	+	3.34937i	0.0373916	+	0.163823i
$419$	1.95811	+	8.57906i	0.0956602	+	0.419115i	0.999970	−	0.00776239i	$-0.00247087\pi$
$419$	1.95811	+	8.57906i	0.0956602	+	0.419115i	−0.904310	+	0.426877i	$0.859614\pi$
$420$	−3.19461	+	6.62816i	−0.155881	+	0.323421i
$421$	7.96187	−	34.8832i	0.388038	−	1.70010i	−0.283365	−	0.959012i	$-0.591451\pi$
$421$	7.96187	−	34.8832i	0.388038	−	1.70010i	0.671403	−	0.741093i	$-0.265692\pi$
$422$	−13.7910			−0.671333
$423$	−16.8658			−0.820043
$424$	2.77590	−	12.1620i	0.134810	−	0.590640i
$425$	7.49360	−	3.60873i	0.363493	−	0.175049i
$426$	−48.3590	−	60.6403i	−2.34300	−	2.93803i
$427$	0.0119948	−	36.8517i	0.000580470	−	1.78338i
$428$	−24.5337	+	30.7643i	−1.18588	+	1.48705i
$429$	2.58028	−	11.3050i	0.124577	−	0.545808i
$430$	−6.50023	+	8.15103i	−0.313469	+	0.393078i
$431$	−29.1468	+	14.0364i	−1.40395	+	0.676108i	−0.973959	−	0.226723i	$-0.927199\pi$
$431$	−29.1468	+	14.0364i	−1.40395	+	0.676108i	−0.429994	+	0.902832i	$0.641484\pi$
$432$	0.0789103	+	0.0989504i	0.00379658	+	0.00476076i
$433$	14.2909	+	6.88212i	0.686775	+	0.330734i	0.744522	−	0.667598i	$-0.232677\pi$
$433$	14.2909	+	6.88212i	0.686775	+	0.330734i	−0.0577470	+	0.998331i	$0.518392\pi$
$434$	9.81327	−	20.3605i	0.471052	−	0.977336i
$435$	−5.72971	+	2.75928i	−0.274719	+	0.132298i
$436$	−46.3893	−	22.3399i	−2.22164	−	1.06989i
$437$	0.235833	+	1.03325i	0.0112814	+	0.0494271i
$438$	−27.1914	−	13.0947i	−1.29926	−	0.625689i
$439$	−23.8290	+	29.8806i	−1.13729	+	1.42612i	−0.248017	+	0.968756i	$0.579779\pi$
$439$	−23.8290	+	29.8806i	−1.13729	+	1.42612i	−0.889278	+	0.457367i	$0.848793\pi$
$440$	−5.40317			−0.257586
$441$	13.6790	+	6.59845i	0.651383	+	0.314212i
$442$	−3.91379			−0.186160
$443$	12.1383	−	15.2210i	0.576709	−	0.723171i	−0.404838	−	0.914388i	$-0.632672\pi$
$443$	12.1383	−	15.2210i	0.576709	−	0.723171i	0.981548	+	0.191218i	$0.0612436\pi$
$444$	−17.5651	−	8.45889i	−0.833601	−	0.401441i
$445$	−1.31864	−	5.77733i	−0.0625094	−	0.273872i
$446$	−14.9003	−	7.17561i	−0.705550	−	0.339775i
$447$	−7.05587	+	3.39793i	−0.333731	+	0.160716i
$448$	−26.8135	−	21.3974i	−1.26682	−	1.01093i
$449$	−32.9273	−	15.8570i	−1.55394	−	0.748337i	−0.557303	−	0.830309i	$-0.688164\pi$
$449$	−32.9273	−	15.8570i	−1.55394	−	0.748337i	−0.996635	+	0.0819727i	$0.973878\pi$
$450$	15.0090	+	18.8207i	0.707532	+	0.887217i
$451$	2.22242	−	1.07026i	0.104650	−	0.0503966i
$452$	−8.92849	+	11.1960i	−0.419961	+	0.526614i
$453$	0.178859	−	0.783630i	0.00840351	−	0.0368182i
$454$	0.874103	−	1.09609i	0.0410237	−	0.0514421i
$455$	0.785693	−	0.626151i	0.0368339	−	0.0293544i
$456$	1.16603	+	1.46215i	0.0546042	+	0.0684716i
$457$	30.7070	−	14.7877i	1.43642	−	0.691741i	0.456237	−	0.889858i	$-0.349197\pi$
$457$	30.7070	−	14.7877i	1.43642	−	0.691741i	0.980178	+	0.198117i	$0.0634827\pi$
$458$	13.4131	−	58.7665i	0.626751	−	2.74598i
$459$	−3.23389			−0.150945
$460$	−4.39703			−0.205012
$461$	−2.94005	+	12.8812i	−0.136932	+	0.599937i	0.859167	+	0.511695i	$0.170982\pi$
$461$	−2.94005	+	12.8812i	−0.136932	+	0.599937i	−0.996099	+	0.0882424i	$0.971875\pi$
$462$	−0.0228170	+	70.1008i	−0.00106154	+	3.26139i
$463$	7.96345	+	34.8902i	0.370093	+	1.62148i	0.726509	+	0.687157i	$0.241141\pi$
$463$	7.96345	+	34.8902i	0.370093	+	1.62148i	−0.356416	+	0.934327i	$0.616001\pi$
$464$	−0.109872	−	0.481379i	−0.00510067	−	0.0223475i
$465$	2.01260	+	2.52372i	0.0933320	+	0.117035i
$466$	19.6733	+	24.6696i	0.911350	+	1.14280i
$467$	3.29311	+	14.4280i	0.152387	+	0.667650i	0.992188	+	0.124755i	$0.0398146\pi$
$467$	3.29311	+	14.4280i	0.152387	+	0.667650i	−0.839801	+	0.542895i	$0.817328\pi$
$468$	−1.55507	−	6.81320i	−0.0718831	−	0.314940i
$469$	12.1169	−	2.76146i	0.559508	−	0.127513i
$470$	1.50089	−	6.57584i	0.0692311	−	0.303321i
$471$	3.57444			0.164701
$472$	24.5946			1.13206
$473$	−13.6358	+	59.7424i	−0.626975	+	2.74696i
$474$	−19.5833	+	9.43083i	−0.899492	+	0.433172i
$475$	0.892559	+	1.11923i	0.0409534	+	0.0513540i
$476$	14.2321	−	3.24350i	0.652326	−	0.148666i
$477$	6.04844	−	7.58450i	0.276939	−	0.347270i
$478$	−6.21668	+	27.2371i	−0.284345	+	1.24579i
$479$	22.7755	−	28.5596i	1.04064	−	1.30492i	0.0895585	−	0.995982i	$-0.471454\pi$
$479$	22.7755	−	28.5596i	1.04064	−	1.30492i	0.951082	−	0.308940i	$-0.0999742\pi$
$480$	4.45976	−	2.14771i	0.203559	−	0.0980290i
$481$	1.65976	+	2.08127i	0.0756786	+	0.0948979i
$482$	13.8827	+	6.68555i	0.632339	+	0.304518i
$483$	−0.00703884	+	21.6254i	−0.000320278	+	0.983992i
$484$	−43.5585	+	20.9767i	−1.97993	+	0.953485i
$485$	−1.59034	−	0.765868i	−0.0722137	−	0.0347763i
$486$	−9.60736	−	42.0926i	−0.435799	−	1.90936i
$487$	3.51815	+	1.69425i	0.159422	+	0.0767738i	0.511894	−	0.859049i	$-0.328944\pi$
$487$	3.51815	+	1.69425i	0.159422	+	0.0767738i	−0.352471	+	0.935823i	$0.614659\pi$
$488$	24.2293	−	30.3826i	1.09681	−	1.37536i
$489$	25.0263			1.13173
$490$	−3.78999	+	4.74615i	−0.171214	+	0.214409i
$491$	−36.5862			−1.65111			−0.825556	−	0.564320i	$-0.809138\pi$
$491$	−36.5862			−1.65111			−0.825556	+	0.564320i	$0.809138\pi$
$492$	2.20853	−	2.76940i	0.0995681	−	0.124854i
$493$	11.3670	+	5.47405i	0.511943	+	0.246539i
$494$	−0.149898	−	0.656745i	−0.00674422	−	0.0295484i
$495$	−3.78563	−	1.82307i	−0.170152	−	0.0819407i
$496$	−0.225803	+	0.108741i	−0.0101388	+	0.00488261i
$497$	−17.1265	−	35.5932i	−0.768230	−	1.59658i
$498$	56.0314	+	26.9833i	2.51083	+	1.20915i
$499$	10.8727	+	13.6340i	0.486731	+	0.610341i	0.963179	−	0.268861i	$-0.0866473\pi$
$499$	10.8727	+	13.6340i	0.486731	+	0.610341i	−0.476448	+	0.879203i	$0.658076\pi$
$500$	−10.8611	+	5.23044i	−0.485724	+	0.233912i
$501$	23.1449	−	29.0227i	1.03404	−	1.29664i
$502$	1.55469	−	6.81156i	0.0693894	−	0.304015i
$503$	10.0487	−	12.6007i	0.448050	−	0.561837i	−0.505595	−	0.862771i	$-0.668727\pi$
$503$	10.0487	−	12.6007i	0.448050	−	0.561837i	0.953645	+	0.300934i	$0.0972984\pi$
$504$	6.94411	+	14.4316i	0.309315	+	0.642835i
$505$	0.486915	+	0.610572i	0.0216674	+	0.0271701i
$506$	−37.7434	+	18.1763i	−1.67790	+	0.808034i
$507$	−0.505941	+	2.21667i	−0.0224696	+	0.0984460i
$508$	19.4763			0.864121
$509$	22.6910			1.00576			0.502880	−	0.864356i	$-0.332274\pi$
$509$	22.6910			1.00576			0.502880	+	0.864356i	$0.332274\pi$
$510$	−0.751928	+	3.29441i	−0.0332959	+	0.145879i
$511$	−12.0133	−	9.58672i	−0.531439	−	0.424092i
$512$	0.168754	+	0.739360i	0.00745794	+	0.0326754i
$513$	−0.123858	−	0.542655i	−0.00546844	−	0.0239588i
$514$	−15.1013	−	18.9365i	−0.666091	−	0.835252i
$515$	−0.913124	−	1.14502i	−0.0402370	−	0.0504556i
$516$	19.5812	+	85.7906i	0.862012	+	3.77672i
$517$	−8.82187	−	38.6511i	−0.387985	−	1.69987i
$518$	−12.5789	−	10.0381i	−0.552686	−	0.441047i
$519$	−5.70044	+	24.9753i	−0.250222	+	1.09629i
$520$	1.05945			0.0464601
$521$	−18.7159			−0.819957			−0.409978	−	0.912095i	$-0.634464\pi$
$521$	−18.7159			−0.819957			−0.409978	+	0.912095i	$0.634464\pi$
$522$	−8.12547	+	35.6000i	−0.355642	+	1.55817i
$523$	−6.00663	+	2.89264i	−0.262652	+	0.126486i	−0.560576	−	0.828103i	$-0.689420\pi$
$523$	−6.00663	+	2.89264i	−0.262652	+	0.126486i	0.297924	+	0.954590i	$0.403706\pi$
$524$	−21.1030	−	26.4623i	−0.921888	−	1.15601i
$525$	12.6654	+	26.3219i	0.552764	+	1.14878i
$526$	−4.43527	+	5.56165i	−0.193387	+	0.242500i
$527$	1.42499	−	6.24327i	0.0620734	−	0.271961i
$528$	0.484646	−	0.607727i	0.0210915	−	0.0264479i
$529$	9.07880	−	4.37212i	0.394730	−	0.190092i
$530$	2.41889	+	3.03319i	0.105070	+	0.131753i
$531$	17.2318	+	8.29839i	0.747796	+	0.360120i
$532$	1.08936	+	2.26396i	0.0472296	+	0.0981549i
$533$	−0.435772	+	0.209857i	−0.0188754	+	0.00908990i
$534$	−73.0456	−	35.1769i	−3.16099	−	1.52225i
$535$	−1.03226	−	4.52261i	−0.0446284	−	0.195530i
$536$	11.8074	+	5.68612i	0.510000	+	0.245603i
$537$	16.6086	−	20.8265i	0.716713	−	0.898730i
$538$	8.75208			0.377329
$539$	−7.96659	+	34.7995i	−0.343145	+	1.49892i
$540$	2.30929			0.0993758
$541$	−14.2737	+	17.8986i	−0.613673	+	0.769522i	−0.987439	−	0.158001i	$-0.949495\pi$
$541$	−14.2737	+	17.8986i	−0.613673	+	0.769522i	0.373766	+	0.927523i	$0.378066\pi$
$542$	25.6213	+	12.3386i	1.10053	+	0.529988i
$543$	−9.07165	−	39.7455i	−0.389302	−	1.70564i
$544$	−8.84757	−	4.26077i	−0.379336	−	0.182679i
$545$	5.46892	−	2.63369i	0.234263	−	0.112815i
$546$	0.00447396	−	13.7454i	0.000191468	−	0.588248i
$547$	−13.3698	−	6.43856i	−0.571652	−	0.275293i	0.125645	−	0.992075i	$-0.459900\pi$
$547$	−13.3698	−	6.43856i	−0.571652	−	0.275293i	−0.697297	+	0.716782i	$0.745614\pi$
$548$	−5.11452	−	6.41341i	−0.218482	−	0.273967i
$549$	27.2272	−	13.1119i	1.16203	−	0.559603i
$550$	−35.2805	+	44.2404i	−1.50437	+	1.88642i
$551$	−0.483207	+	2.11707i	−0.0205853	+	0.0901901i
$552$	−14.2183	+	17.8292i	−0.605173	+	0.758863i
$553$	−10.7925	+	2.45963i	−0.458945	+	0.104594i
$554$	−37.4478	−	46.9581i	−1.59101	−	1.99506i
$555$	2.07078	−	0.997234i	0.0878996	−	0.0423302i
$556$	−6.47716	+	28.3783i	−0.274693	+	1.20351i
$557$	23.2239			0.984028			0.492014	−	0.870587i	$-0.336261\pi$
$557$	23.2239			0.984028			0.492014	+	0.870587i	$0.336261\pi$
$558$	18.5346			0.784630
$559$	2.67371	−	11.7143i	0.113086	−	0.495462i
$560$	0.0656646	−	0.0149650i	0.00277484	−	0.000632388i
$561$	4.41964	+	19.3637i	0.186597	+	0.817536i
$562$	−0.682361	−	2.98962i	−0.0287837	−	0.126109i
$563$	−26.8212	−	33.6328i	−1.13038	−	1.41745i	−0.895293	−	0.445477i	$-0.853034\pi$
$563$	−26.8212	−	33.6328i	−1.13038	−	1.41745i	−0.235087	−	0.971974i	$-0.575537\pi$
$564$	−35.4957	−	44.5102i	−1.49464	−	1.87422i
$565$	−0.375667	−	1.64590i	−0.0158044	−	0.0692437i
$566$	0.0440603	+	0.193041i	0.00185199	+	0.00811410i
$567$	0.00930194	−	28.5784i	0.000390645	−	1.20018i
$568$	9.26862	−	40.6085i	0.388903	−	1.70389i
$569$	37.2739			1.56260			0.781302	−	0.624153i	$-0.214556\pi$
$569$	37.2739			1.56260			0.781302	+	0.624153i	$0.214556\pi$
$570$	−0.581610			−0.0243610
$571$	2.89728	−	12.6938i	0.121247	−	0.531219i	−0.877426	−	0.479713i	$-0.840741\pi$
$571$	2.89728	−	12.6938i	0.121247	−	0.531219i	0.998673	−	0.0515057i	$-0.0164020\pi$
$572$	14.8003	−	7.12746i	0.618832	−	0.298014i
$573$	−26.4477	−	33.1643i	−1.10487	−	1.38546i
$574$	2.28666	−	1.82234i	0.0954435	−	0.0760628i
$575$	−10.8837	+	13.6477i	−0.453882	+	0.569150i
$576$	6.25979	−	27.4259i	0.260825	−	1.14275i
$577$	16.0749	−	20.1572i	0.669205	−	0.839156i	−0.325105	−	0.945678i	$-0.605400\pi$
$577$	16.0749	−	20.1572i	0.669205	−	0.839156i	0.994310	+	0.106521i	$0.0339712\pi$
$578$	−28.9576	+	13.9452i	−1.20448	+	0.580046i
$579$	2.96588	+	3.71910i	0.123258	+	0.154561i
$580$	−8.11704	−	3.90896i	−0.337042	−	0.162311i
$581$	24.7551	+	19.7547i	1.02701	+	0.819562i
$582$	−21.7580	+	10.4781i	−0.901900	+	0.434332i
$583$	20.5450	+	9.89395i	0.850887	+	0.409766i
$584$	−3.60653	−	15.8012i	−0.149239	−	0.653859i
$585$	0.742287	+	0.357467i	0.0306898	+	0.0147794i
$586$	−17.9955	+	22.5656i	−0.743386	+	0.932177i
$587$	−7.60830			−0.314028			−0.157014	−	0.987596i	$-0.550187\pi$
$587$	−7.60830			−0.314028			−0.157014	+	0.987596i	$0.550187\pi$
$588$	11.3750	+	49.9872i	0.469098	+	2.06144i
$589$	1.10222			0.0454160
$590$	−4.76894	+	5.98006i	−0.196334	+	0.246195i
$591$	−35.6243	−	17.1558i	−1.46539	−	0.705694i
$592$	0.0397088	+	0.173975i	0.00163202	+	0.00715035i
$593$	−7.76213	−	3.73805i	−0.318753	−	0.153503i	0.267665	−	0.963512i	$-0.413748\pi$
$593$	−7.76213	−	3.73805i	−0.318753	−	0.153503i	−0.586418	+	0.810009i	$0.699462\pi$
$594$	19.8226	−	9.54604i	0.813329	−	0.391679i
$595$	−0.747160	+	1.55020i	−0.0306306	+	0.0635521i
$596$	−9.99575	−	4.81370i	−0.409442	−	0.197177i
$597$	36.1207	+	45.2940i	1.47832	+	1.85376i
$598$	7.40073	−	3.56400i	0.302638	−	0.145743i
$599$	19.0884	−	23.9361i	0.779930	−	0.978001i	−0.220067	−	0.975485i	$-0.570628\pi$
$599$	19.0884	−	23.9361i	0.779930	−	0.978001i	0.999997	−	0.00251604i	$-0.000800882\pi$
$600$	−6.85433	+	30.0308i	−0.279827	+	1.22600i
$601$	−23.9491	+	30.0313i	−0.976906	+	1.22500i	−0.00254767	+	0.999997i	$0.500811\pi$
$601$	−23.9491	+	30.0313i	−0.976906	+	1.22500i	−0.974358	+	0.225004i	$0.927760\pi$
$602$	−0.0236432	+	72.6391i	−0.000963625	+	2.96055i
$603$	6.35408	+	7.96777i	0.258758	+	0.324472i
$604$	1.02592	−	0.494057i	0.0417441	−	0.0201029i
$605$	1.26829	−	5.55673i	0.0515632	−	0.225913i
$606$	10.6845			0.434027
$607$	−18.7252			−0.760032			−0.380016	−	0.924980i	$-0.624082\pi$
$607$	−18.7252			−0.760032			−0.380016	+	0.924980i	$0.624082\pi$
$608$	0.376107	−	1.64783i	0.0152532	−	0.0668285i
$609$	−19.2380	+	39.9149i	−0.779564	+	1.61744i
$610$	2.68928	+	11.7825i	0.108886	+	0.477059i
$611$	1.72979	+	7.57871i	0.0699799	+	0.306602i
$612$	7.46325	+	9.35862i	0.301684	+	0.378300i
$613$	−17.8094	−	22.3323i	−0.719317	−	0.901995i	0.278982	−	0.960296i	$-0.410003\pi$
$613$	−17.8094	−	22.3323i	−0.719317	−	0.901995i	−0.998299	+	0.0583014i	$0.981432\pi$
$614$	−4.46775	−	19.5745i	−0.180304	−	0.789962i
$615$	0.0929240	+	0.407126i	0.00374706	+	0.0164169i
$616$	−29.4405	+	23.4623i	−1.18619	+	0.945325i
$617$	−10.6605	+	46.7066i	−0.429174	+	1.88033i	0.0434236	+	0.999057i	$0.486173\pi$
$617$	−10.6605	+	46.7066i	−0.429174	+	1.88033i	−0.472598	+	0.881278i	$0.656684\pi$
$618$	−20.0369			−0.806001
$619$	44.6904			1.79626			0.898129	−	0.439732i	$-0.144926\pi$
$619$	44.6904			1.79626			0.898129	+	0.439732i	$0.144926\pi$
$620$	−1.01757	+	4.45826i	−0.0408665	+	0.179048i
$621$	6.11507	−	2.94486i	0.245389	−	0.118173i
$622$	−42.1587	−	52.8653i	−1.69041	−	2.11971i
$623$	−32.2720	−	25.7533i	−1.29295	−	1.03178i
$624$	−0.0950294	+	0.119163i	−0.00380422	+	0.00477034i
$625$	−5.08635	+	22.2847i	−0.203454	+	0.891390i
$626$	−32.7280	+	41.0396i	−1.30807	+	1.64027i
$627$	−3.08001	+	1.48326i	−0.123004	+	0.0592355i
$628$	3.15720	+	3.95901i	0.125986	+	0.157982i
$629$	−4.10815	−	1.97838i	−0.163802	−	0.0788831i
$630$	−4.85545	−	1.10989i	−0.193446	−	0.0442190i
$631$	−10.4888	+	5.05112i	−0.417551	+	0.201082i	−0.630850	−	0.775905i	$-0.717293\pi$
$631$	−10.4888	+	5.05112i	−0.417551	+	0.201082i	0.213299	+	0.976987i	$0.431579\pi$
$632$	−10.5168	−	5.06461i	−0.418335	−	0.201459i
$633$	−3.05363	−	13.3788i	−0.121371	−	0.531761i
$634$	48.6016	+	23.4053i	1.93022	+	0.929543i
$635$	−1.43159	+	1.79516i	−0.0568110	+	0.0712388i
$636$	32.7457			1.29845
$637$	1.56209	−	6.82348i	0.0618922	−	0.270356i
$638$	−85.8342			−3.39821
$639$	20.1955	−	25.3243i	0.798921	−	1.00182i
$640$	6.21315	+	2.99210i	0.245596	+	0.118273i
$641$	−0.707988	−	3.10190i	−0.0279638	−	0.122518i	0.959020	−	0.283340i	$-0.0914425\pi$
$641$	−0.707988	−	3.10190i	−0.0279638	−	0.122518i	−0.986983	+	0.160822i	$0.948585\pi$
$642$	−57.1816	−	27.5372i	−2.25678	−	1.08681i
$643$	40.8590	−	19.6766i	1.61132	−	0.775971i	0.611438	−	0.791292i	$-0.290591\pi$
$643$	40.8590	−	19.6766i	1.61132	−	0.775971i	0.999883	+	0.0153211i	$0.00487704\pi$
$644$	−23.9583	+	19.0934i	−0.944089	+	0.752384i
$645$	−9.34675	−	4.50116i	−0.368028	−	0.177233i
$646$	0.719405	+	0.902106i	0.0283046	+	0.0354929i
$647$	−0.933110	+	0.449362i	−0.0366843	+	0.0176662i	−0.452136	−	0.891949i	$-0.649338\pi$
$647$	−0.933110	+	0.449362i	−0.0366843	+	0.0176662i	0.415452	+	0.909615i	$0.363624\pi$
$648$	18.7898	−	23.5616i	0.738132	−	0.925588i
$649$	−10.0040	+	43.8304i	−0.392692	+	1.72049i
$650$	6.91781	−	8.67466i	0.271339	−	0.340248i
$651$	21.9250	+	5.01174i	0.859307	+	0.196425i
$652$	22.1050	+	27.7188i	0.865698	+	1.08555i
$653$	−29.0031	+	13.9672i	−1.13498	+	0.546577i	−0.904489	−	0.426497i	$-0.859747\pi$
$653$	−29.0031	+	13.9672i	−1.13498	+	0.546577i	−0.230490	+	0.973075i	$0.574033\pi$
$654$	18.4796	−	80.9643i	0.722608	−	3.16595i
$655$	3.99023			0.155911
$656$	−0.0324227			−0.00126589
$657$	2.80459	−	12.2877i	0.109418	−	0.479390i
$658$	−20.3765	−	42.3475i	−0.794359	−	1.65088i
$659$	−4.49077	−	19.6754i	−0.174936	−	0.766443i	−0.983920	−	0.178612i	$-0.942839\pi$
$659$	−4.49077	−	19.6754i	−0.174936	−	0.766443i	0.808984	−	0.587831i	$-0.200018\pi$
$660$	−3.15602	−	13.8274i	−0.122848	−	0.538232i
$661$	14.2680	+	17.8915i	0.554962	+	0.695901i	0.977618	−	0.210390i	$-0.0674733\pi$
$661$	14.2680	+	17.8915i	0.554962	+	0.695901i	−0.422655	+	0.906290i	$0.638902\pi$
$662$	19.9476	+	25.0135i	0.775286	+	0.972178i
$663$	−0.866603	−	3.79684i	−0.0336561	−	0.147457i
$664$	7.43171	+	32.5605i	0.288406	+	1.26359i
$665$	−0.288745	−	0.0660029i	−0.0111970	−	0.00255948i
$666$	2.93663	−	12.8662i	0.113792	−	0.498556i
$667$	−26.4790			−1.02527
$668$	52.5885			2.03471
$669$	3.66191	−	16.0439i	0.141578	−	0.620292i
$670$	−3.67202	+	1.76835i	−0.141863	+	0.0683174i
$671$	44.2899	+	55.5378i	1.70979	+	2.14401i
$672$	14.9741	−	31.0681i	0.577637	−	1.19848i
$673$	11.2382	−	14.0922i	0.433199	−	0.543215i	−0.516537	−	0.856265i	$-0.672779\pi$
$673$	11.2382	−	14.0922i	0.433199	−	0.543215i	0.949737	+	0.313050i	$0.101351\pi$
$674$	−16.8543	+	73.8434i	−0.649202	+	2.84434i
$675$	5.71604	−	7.16769i	0.220011	−	0.275885i
$676$	−2.90205	+	1.39755i	−0.111617	+	0.0537520i
$677$	−3.26691	−	4.09658i	−0.125558	−	0.157444i	0.715079	−	0.699043i	$-0.246391\pi$
$677$	−3.26691	−	4.09658i	−0.125558	−	0.157444i	−0.840637	+	0.541599i	$0.817819\pi$
$678$	−20.8100	−	10.0215i	−0.799202	−	0.384875i
$679$	−11.9910	+	2.73277i	−0.460173	+	0.104874i
$680$	−1.63498	+	0.787363i	−0.0626985	+	0.0301940i
$681$	1.25688	+	0.605282i	0.0481638	+	0.0231945i
$682$	9.69473	+	42.4754i	0.371230	+	1.62647i
$683$	−10.6292	−	5.11876i	−0.406715	−	0.195864i	0.219329	−	0.975651i	$-0.429613\pi$
$683$	−10.6292	−	5.11876i	−0.406715	−	0.195864i	−0.626045	+	0.779787i	$0.715327\pi$
$684$	−1.28456	+	1.61079i	−0.0491164	+	0.0615900i
$685$	0.967073			0.0369500
$686$	−0.0413221	+	42.3180i	−0.00157768	+	1.61571i
$687$	59.9803			2.28839
$688$	0.502195	−	0.629732i	0.0191460	−	0.0240083i
$689$	−4.02846	−	1.94001i	−0.153472	−	0.0739084i
$690$	−1.57813	−	6.91424i	−0.0600784	−	0.263221i
$691$	37.8648	+	18.2347i	1.44044	+	0.693681i	0.980907	−	0.194477i	$-0.0623011\pi$
$691$	37.8648	+	18.2347i	1.44044	+	0.693681i	0.459537	+	0.888159i	$0.348015\pi$
$692$	−32.6973	+	15.7462i	−1.24297	+	0.598581i
$693$	−28.5433	+	6.50505i	−1.08427	+	0.247107i
$694$	19.3560	+	9.32137i	0.734745	+	0.353834i
$695$	−2.13957	−	2.68294i	−0.0811585	−	0.101770i
$696$	−42.0977	+	20.2732i	−1.59571	+	0.768453i
$697$	0.516534	−	0.647713i	0.0195651	−	0.0245339i
$698$	3.01496	−	13.2094i	0.114118	−	0.499984i
$699$	−19.5763	+	24.5478i	−0.740442	+	0.928485i
$700$	−17.9668	+	37.2775i	−0.679082	+	1.40896i
$701$	−10.8917	−	13.6577i	−0.411373	−	0.515845i	0.532376	−	0.846508i	$-0.321299\pi$
$701$	−10.8917	−	13.6577i	−0.411373	−	0.515845i	−0.943749	+	0.330663i	$0.892728\pi$
$702$	−3.88681	+	1.87179i	−0.146698	+	0.0706461i
$703$	0.174636	−	0.765130i	0.00658652	−	0.0288574i
$704$	66.1259			2.49221
$705$	6.71167			0.252776
$706$	8.31589	−	36.4343i	0.312972	−	1.37122i
$707$	5.30439	+	1.21251i	0.199492	+	0.0456011i
$708$	14.3658	+	62.9409i	0.539902	+	2.36546i
$709$	−6.29199	−	27.5670i	−0.236301	−	1.03530i	−0.944299	−	0.329087i	$-0.893259\pi$
$709$	−6.29199	−	27.5670i	−0.236301	−	1.03530i	0.707999	−	0.706214i	$-0.249598\pi$
$710$	8.07655	+	10.1277i	0.303108	+	0.380085i
$711$	−5.65956	−	7.09686i	−0.212250	−	0.266153i
$712$	−9.68838	−	42.4476i	−0.363087	−	1.59079i
$713$	2.99073	+	13.1033i	0.112004	+	0.490721i
$714$	10.2084	+	21.2155i	0.382038	+	0.793972i
$715$	−0.430939	+	1.88807i	−0.0161162	+	0.0706097i
$716$	37.7371			1.41030
$717$	−27.7997			−1.03820
$718$	9.91462	−	43.4388i	0.370010	−	1.62112i
$719$	44.4763	−	21.4186i	1.65869	−	0.798781i	0.659807	−	0.751435i	$-0.270638\pi$
$719$	44.4763	−	21.4186i	1.65869	−	0.798781i	0.998879	−	0.0473453i	$-0.0150761\pi$
$720$	0.0344343	+	0.0431792i	0.00128329	+	0.00160919i
$721$	−9.94744	−	2.27385i	−0.370462	−	0.0846824i
$722$	26.9445	−	33.7873i	1.00277	−	1.25743i
$723$	−3.41182	+	14.9482i	−0.126887	+	0.555928i
$724$	36.0089	−	45.1537i	1.33826	−	1.67812i
$725$	−32.2245	+	15.5185i	−1.19679	+	0.576343i
$726$	−48.6189	−	60.9662i	−1.80442	−	2.26267i
$727$	−27.4613	−	13.2247i	−1.01849	−	0.490477i	−0.151313	−	0.988486i	$-0.548350\pi$
$727$	−27.4613	−	13.2247i	−1.01849	−	0.490477i	−0.867172	+	0.498009i	$0.834065\pi$
$728$	5.77269	−	4.60050i	0.213950	−	0.170506i
$729$	9.51170	−	4.58059i	0.352285	−	0.169652i
$730$	4.54130	+	2.18698i	0.168081	+	0.0809436i
$731$	4.57967	+	20.0648i	0.169385	+	0.742125i
$732$	91.9057	+	44.2594i	3.39693	+	1.63588i
$733$	−31.2295	+	39.1605i	−1.15349	+	1.44643i	−0.279721	+	0.960081i	$0.590242\pi$
$733$	−31.2295	+	39.1605i	−1.15349	+	1.44643i	−0.873766	+	0.486346i	$0.838329\pi$
$734$	−3.26013			−0.120334
$735$	−5.44351	−	2.62582i	−0.200787	−	0.0968549i
$736$	20.6101			0.759700
$737$	−14.9360	+	18.7292i	−0.550176	+	0.689899i
$738$	2.16034	+	1.04036i	0.0795231	+	0.0382963i
$739$	9.38275	+	41.1085i	0.345150	+	1.51220i	0.788040	+	0.615624i	$0.211096\pi$
$739$	9.38275	+	41.1085i	0.345150	+	1.51220i	−0.442890	+	0.896576i	$0.646047\pi$
$740$	2.93358	+	1.41274i	0.107841	+	0.0519333i
$741$	0.603929	−	0.290837i	0.0221859	−	0.0106842i
$742$	26.3510	+	6.02347i	0.967376	+	0.221128i
$743$	15.6465	+	7.53495i	0.574014	+	0.276430i	0.698287	−	0.715818i	$-0.253946\pi$
$743$	15.6465	+	7.53495i	0.574014	+	0.276430i	−0.124274	+	0.992248i	$0.539660\pi$
$744$	14.7871	+	18.5424i	0.542121	+	0.679798i
$745$	1.17842	−	0.567496i	0.0431739	−	0.0207914i
$746$	23.4889	−	29.4541i	0.859988	−	1.07839i
$747$	−5.77922	+	25.3204i	−0.211451	+	0.926426i
$748$	−17.5433	+	21.9986i	−0.641445	+	0.804347i
$749$	−25.2632	−	20.1602i	−0.923097	−	0.736637i
$750$	−12.1229	−	15.2016i	−0.442666	−	0.555086i
$751$	−9.22893	+	4.44442i	−0.336768	+	0.162179i	−0.594623	−	0.804005i	$-0.702699\pi$
$751$	−9.22893	+	4.44442i	−0.336768	+	0.162179i	0.257855	+	0.966184i	$0.416984\pi$
$752$	−0.115956	+	0.508036i	−0.00422848	+	0.0185262i
$753$	6.95225			0.253354
$754$	16.8304			0.612926
$755$	−0.0298716	+	0.130876i	−0.00108714	+	0.00476307i
$756$	12.5827	−	10.0277i	0.457629	−	0.364703i
$757$	3.50547	+	15.3585i	0.127408	+	0.558213i	0.997826	+	0.0658993i	$0.0209916\pi$
$757$	3.50547	+	15.3585i	0.127408	+	0.558213i	−0.870418	+	0.492314i	$0.836151\pi$
$758$	6.62153	+	29.0108i	0.240505	+	1.05372i
$759$	−25.9904	−	32.5909i	−0.943390	−	1.18297i
$760$	−0.194741	−	0.244198i	−0.00706400	−	0.00885798i
$761$	−3.34991	−	14.6769i	−0.121434	−	0.532037i	−0.998650	−	0.0519416i	$-0.983459\pi$
$761$	−3.34991	−	14.6769i	−0.121434	−	0.532037i	0.877216	−	0.480096i	$-0.159398\pi$
$762$	6.99021	+	30.6261i	0.253229	+	1.10947i
$763$	18.3624	−	38.0982i	0.664763	−	1.37925i
$764$	13.3719	−	58.5863i	0.483780	−	2.11958i
$765$	−1.41118			−0.0510213
$766$	35.4706			1.28161
$767$	1.96159	−	8.59427i	0.0708288	−	0.310321i
$768$	31.8824	−	15.3538i	1.15046	−	0.554031i
$769$	−1.66761	−	2.09111i	−0.0601355	−	0.0754075i	0.750854	−	0.660468i	$-0.229642\pi$
$769$	−1.66761	−	2.09111i	−0.0601355	−	0.0754075i	−0.810990	+	0.585061i	$0.801071\pi$
$770$	0.00381073	−	11.7077i	0.000137329	−	0.421916i
$771$	15.0268	−	18.8430i	0.541177	−	0.678615i
$772$	−1.49955	+	6.56995i	−0.0539699	+	0.236458i
$773$	−0.618813	+	0.775967i	−0.0222572	+	0.0279096i	−0.792836	−	0.609436i	$-0.791396\pi$
$773$	−0.618813	+	0.775967i	−0.0222572	+	0.0279096i	0.770578	+	0.637345i	$0.219967\pi$
$774$	−53.6680	+	25.8451i	−1.92906	+	0.928984i
$775$	11.3191	+	14.1937i	0.406593	+	0.509851i
$776$	−11.6847	−	5.62704i	−0.419455	−	0.201999i
$777$	6.95282	−	14.4257i	0.249431	−	0.517518i
$778$	4.47275	−	2.15396i	0.160356	−	0.0772233i
$779$	0.128471	+	0.0618684i	0.00460296	+	0.00221667i
$780$	0.618832	+	2.71128i	0.0221577	+	0.0970794i
$781$	68.5989	+	33.0355i	2.45466	+	1.18210i
$782$	−8.77231	+	11.0001i	−0.313697	+	0.393364i
$783$	13.9066			0.496981
$784$	0.292807	−	0.366678i	0.0104574	−	0.0130956i
$785$	−0.596976			−0.0213070
$786$	34.0374	−	42.6816i	1.21407	−	1.52240i
$787$	37.8502	+	18.2277i	1.34921	+	0.649747i	0.962204	−	0.272328i	$-0.0877937\pi$
$787$	37.8502	+	18.2277i	1.34921	+	0.649747i	0.387010	+	0.922076i	$0.373508\pi$
$788$	−12.4644	−	54.6103i	−0.444027	−	1.94541i
$789$	−6.37752	−	3.07125i	−0.227046	−	0.109339i
$790$	3.27066	−	1.57507i	0.116365	−	0.0560383i
$791$	−9.19398	−	7.33685i	−0.326900	−	0.260868i
$792$	−27.8141	−	13.3945i	−0.988329	−	0.475954i
$793$	−8.68436	−	10.8898i	−0.308391	−	0.386710i
$794$	−64.3406	+	30.9848i	−2.28336	+	1.09961i
$795$	−2.40695	+	3.01822i	−0.0853656	+	0.107045i
$796$	−18.2626	+	80.0138i	−0.647301	+	2.83601i
$797$	−12.0611	+	15.1241i	−0.427225	+	0.535723i	−0.948126	−	0.317894i	$-0.897025\pi$
$797$	−12.0611	+	15.1241i	−0.427225	+	0.535723i	0.520901	+	0.853617i	$0.325596\pi$
$798$	−3.16905	+	2.52554i	−0.112183	+	0.0894033i
$799$	−8.30180	−	10.4101i	−0.293697	−	0.368284i
$800$	25.0822	−	12.0789i	0.886789	−	0.427055i
$801$	7.53410	−	33.0091i	0.266204	−	1.16632i
$802$	29.1442			1.02912
$803$	29.6266			1.04550
$804$	−7.65480	+	33.5379i	−0.269964	+	1.18279i
$805$	0.00117557	−	3.61172i	4.14335e−5	−	0.127296i
$806$	−1.90094	−	8.32857i	−0.0669578	−	0.293361i
$807$	1.93791	+	8.49054i	0.0682177	+	0.298881i
$808$	3.57749	+	4.48604i	0.125856	+	0.157818i
$809$	−29.0545	−	36.4332i	−1.02150	−	1.28092i	−0.959158	−	0.282869i	$-0.908714\pi$
$809$	−29.0545	−	36.4332i	−1.02150	−	1.28092i	−0.0623445	−	0.998055i	$-0.519858\pi$
$810$	2.08552	+	9.13728i	0.0732779	+	0.321051i
$811$	−10.4782	−	45.9080i	−0.367940	−	1.61205i	−0.732431	−	0.680842i	$-0.761614\pi$
$811$	−10.4782	−	45.9080i	−0.367940	−	1.61205i	0.364491	−	0.931207i	$-0.381243\pi$
$812$	−61.2017	+	13.9479i	−2.14776	+	0.489477i
$813$	−6.29672	+	27.5877i	−0.220836	+	0.967544i
$814$	31.0214			1.08730
$815$	−4.17969			−0.146408
$816$	0.0580924	−	0.254520i	0.00203364	−	0.00890997i
$817$	−3.19154	+	1.53696i	−0.111658	+	0.0537715i
$818$	−7.69561	−	9.64999i	−0.269071	−	0.337404i
$819$	5.59678	−	1.27551i	0.195567	−	0.0445700i
$820$	−0.368851	+	0.462525i	−0.0128808	+	0.0161521i
$821$	−4.49162	+	19.6791i	−0.156759	+	0.686804i	0.834068	+	0.551662i	$0.186006\pi$
$821$	−4.49162	+	19.6791i	−0.156759	+	0.686804i	−0.990826	+	0.135142i	$0.956851\pi$
$822$	8.24932	−	10.3443i	0.287728	−	0.360799i
$823$	39.0997	−	18.8294i	1.36293	−	0.656352i	0.397641	−	0.917541i	$-0.369829\pi$
$823$	39.0997	−	18.8294i	1.36293	−	0.656352i	0.965288	+	0.261189i	$0.0841146\pi$
$824$	−6.70896	−	8.41277i	−0.233718	−	0.293073i
$825$	−50.7302	−	24.4304i	−1.76620	−	0.850557i
$826$	−0.0173460	+	53.2922i	−0.000603545	+	1.85427i
$827$	−14.7057	+	7.08187i	−0.511366	+	0.246261i	−0.671729	−	0.740797i	$-0.734448\pi$
$827$	−14.7057	+	7.08187i	−0.511366	+	0.246261i	0.160363	+	0.987058i	$0.448734\pi$
$828$	−22.6347	−	10.9003i	−0.786611	−	0.378812i
$829$	7.67482	+	33.6256i	0.266558	+	1.16786i	0.913988	+	0.405741i	$0.132986\pi$
$829$	7.67482	+	33.6256i	0.266558	+	1.16786i	−0.647431	+	0.762124i	$0.724156\pi$
$830$	−9.35794	−	4.50655i	−0.324819	−	0.156425i
$831$	37.2630	−	46.7263i	1.29264	−	1.62092i
$832$	−12.9660			−0.449514
$833$	2.66041	+	11.6911i	0.0921777	+	0.405072i
$834$	−46.9490			−1.62571
$835$	−3.86548	+	4.84716i	−0.133770	+	0.167743i
$836$	−4.36332	−	2.10127i	−0.150909	−	0.0726738i
$837$	−1.57071	−	6.88173i	−0.0542917	−	0.237867i
$838$	−18.1157	−	8.72406i	−0.625796	−	0.301368i
$839$	20.6348	−	9.93720i	0.712393	−	0.343070i	−0.0423395	−	0.999103i	$-0.513481\pi$
$839$	20.6348	−	9.93720i	0.712393	−	0.343070i	0.754732	+	0.656033i	$0.227767\pi$
$840$	−2.76338	−	5.74299i	−0.0953455	−	0.198152i
$841$	−22.7530	−	10.9573i	−0.784585	−	0.377836i
$842$	50.9743	+	63.9198i	1.75669	+	2.20282i
$843$	2.74919	−	1.32394i	0.0946871	−	0.0455989i
$844$	12.1210	−	15.1993i	0.417224	−	0.523182i
$845$	0.0844985	−	0.370212i	0.00290684	−	0.0127357i
$846$	24.0278	−	30.1299i	0.826094	−	1.03589i
$847$	−17.2186	−	35.7846i	−0.591638	−	1.22957i
$848$	−0.186878	−	0.234338i	−0.00641742	−	0.00804719i
$849$	−0.177516	+	0.0854872i	−0.00609233	+	0.00293391i
$850$	−4.22892	+	18.5281i	−0.145051	+	0.635509i
$851$	9.56980			0.328048
$852$	109.336			3.74580
$853$	−7.94987	+	34.8306i	−0.272198	+	1.19258i	0.635214	+	0.772336i	$0.280912\pi$
$853$	−7.94987	+	34.8306i	−0.272198	+	1.19258i	−0.907412	+	0.420242i	$0.861945\pi$
$854$	65.8167	+	52.5221i	2.25220	+	1.79727i
$855$	−0.0540480	−	0.236800i	−0.00184840	−	0.00809838i
$856$	−7.58426	−	33.2288i	−0.259225	−	1.13574i
$857$	25.5697	+	32.0634i	0.873444	+	1.09526i	0.994718	+	0.102645i	$0.0327305\pi$
$857$	25.5697	+	32.0634i	0.873444	+	1.09526i	−0.121274	+	0.992619i	$0.538698\pi$
$858$	16.5198	+	20.7151i	0.563975	+	0.707202i
$859$	−0.488961	−	2.14228i	−0.0166831	−	0.0730937i	0.965901	−	0.258911i	$-0.0833638\pi$
$859$	−0.488961	−	2.14228i	−0.0166831	−	0.0730937i	−0.982584	+	0.185818i	$0.940507\pi$
$860$	−3.27029	−	14.3281i	−0.111516	−	0.488584i
$861$	2.27420	+	1.81482i	0.0775044	+	0.0618490i
$862$	16.4487	−	72.0663i	0.560243	−	2.45459i
$863$	−49.0797			−1.67069			−0.835346	−	0.549725i	$-0.814732\pi$
$863$	−49.0797			−1.67069			−0.835346	+	0.549725i	$0.814732\pi$
$864$	−10.8243			−0.368250
$865$	0.952044	−	4.17118i	0.0323705	−	0.141824i
$866$	−32.6540	+	15.7253i	−1.10963	+	0.534369i
$867$	−19.9404	−	25.0045i	−0.677211	−	0.849196i
$868$	13.8148	+	28.7105i	0.468903	+	0.974499i
$869$	13.3035	−	16.6820i	0.451290	−	0.565899i
$870$	3.23349	−	14.1669i	0.109626	−	0.480301i
$871$	2.92866	−	3.67242i	0.0992338	−	0.124435i
$872$	40.1816	−	19.3504i	1.36072	−	0.655288i
$873$	−6.28805	−	7.88497i	−0.212818	−	0.266866i
$874$	−2.18183	−	1.05071i	−0.0738015	−	0.0355409i
$875$	−4.29338	−	8.92271i	−0.145143	−	0.301643i
$876$	38.3308	−	18.4592i	1.29508	−	0.623677i
$877$	−14.9326	−	7.19115i	−0.504237	−	0.242828i	0.164431	−	0.986389i	$-0.447421\pi$
$877$	−14.9326	−	7.19115i	−0.504237	−	0.242828i	−0.668668	+	0.743561i	$0.733135\pi$
$878$	−19.4323	−	85.1386i	−0.655809	−	2.87329i
$879$	−25.8759	−	12.4612i	−0.872772	−	0.420305i
$880$	−0.0809419	+	0.101498i	−0.00272855	+	0.00342150i
$881$	29.7452			1.00214			0.501070	−	0.865407i	$-0.332940\pi$
$881$	29.7452			1.00214			0.501070	+	0.865407i	$0.332940\pi$
$882$	−31.2756	+	15.0365i	−1.05311	+	0.506304i
$883$	−4.22965			−0.142339			−0.0711695	−	0.997464i	$-0.522673\pi$
$883$	−4.22965			−0.142339			−0.0711695	+	0.997464i	$0.522673\pi$
$884$	3.43988	−	4.31348i	0.115696	−	0.145078i
$885$	−6.85731	−	3.30231i	−0.230506	−	0.111006i
$886$	9.89871	+	43.3691i	0.332554	+	1.45701i
$887$	−33.8126	−	16.2833i	−1.13532	−	0.546739i	−0.230725	−	0.973019i	$-0.574110\pi$
$887$	−33.8126	−	16.2833i	−1.13532	−	0.546739i	−0.904591	+	0.426280i	$0.859824\pi$
$888$	15.2145	−	7.32694i	0.510567	−	0.245876i
$889$	−0.00520711	+	15.9978i	−0.000174641	+	0.536550i
$890$	12.1995	+	5.87498i	0.408929	+	0.196930i
$891$	34.3467	+	43.0693i	1.15066	+	1.44288i
$892$	21.0045	−	10.1152i	0.703282	−	0.338683i
$893$	1.42889	−	1.79177i	0.0478160	−	0.0599593i
$894$	3.98189	−	17.4458i	0.133174	−	0.583475i
$895$	−2.77384	+	3.47828i	−0.0927192	+	0.116266i
$896$	46.8466	−	10.6764i	1.56503	−	0.356673i
$897$	5.09619	+	6.39042i	0.170157	+	0.213370i
$898$	75.2376	−	36.2325i	2.51071	−	1.20909i
$899$	−6.12783	+	26.8478i	−0.204374	+	0.895423i
$900$	−33.9344			−1.13115
$901$	7.65861			0.255145
$902$	−1.25419	+	5.49499i	−0.0417601	+	0.182963i
$903$	−70.4736	+	16.0610i	−2.34522	+	0.534477i
$904$	−2.76012	−	12.0929i	−0.0918003	−	0.402204i
$905$	1.51508	+	6.63799i	0.0503629	+	0.220654i
$906$	1.14511	+	1.43592i	0.0380436	+	0.0477052i
$907$	−28.3346	−	35.5305i	−0.940836	−	1.17977i	−0.983541	−	0.180684i	$-0.942169\pi$
$907$	−28.3346	−	35.5305i	−0.940836	−	1.17977i	0.0427050	−	0.999088i	$-0.486402\pi$
$908$	0.439765	+	1.92674i	0.0145941	+	0.0639410i
$909$	0.992890	+	4.35013i	0.0329321	+	0.144285i
$910$	−0.000747207		2.29565i	−2.47697e−5		0.0761000i
$911$	−0.0164762	+	0.0721869i	−0.000545881	+	0.00239166i	−0.975200	−	0.221325i	$-0.928962\pi$
$911$	−0.0164762	+	0.0721869i	−0.000545881	+	0.00239166i	0.974654	+	0.223717i	$0.0718190\pi$
$912$	0.0449340			0.00148791
$913$	−61.0494			−2.02044
$914$	−17.3291	+	75.9239i	−0.573197	+	2.51134i
$915$	−10.8349	+	5.21782i	−0.358192	+	0.172496i
$916$	52.9789	+	66.4334i	1.75047	+	2.19502i
$917$	21.7418	−	17.3269i	0.717976	−	0.572185i
$918$	4.60715	−	5.77718i	0.152059	−	0.190675i
$919$	−3.30009	+	14.4587i	−0.108860	+	0.476947i	0.890882	+	0.454235i	$0.150087\pi$
$919$	−3.30009	+	14.4587i	−0.108860	+	0.476947i	−0.999742	+	0.0227123i	$0.992770\pi$
$920$	2.37464	−	2.97770i	0.0782895	−	0.0981720i
$921$	18.0003	−	8.66848i	0.593129	−	0.285636i
$922$	−18.8231	−	23.6034i	−0.619906	−	0.777337i
$923$	−13.4509	−	6.47760i	−0.442741	−	0.213213i
$924$	−77.2396	−	61.6377i	−2.54100	−	2.02773i
$925$	11.6463	−	5.60855i	0.382927	−	0.184408i
$926$	−73.6747	−	35.4799i	−2.42110	−	1.16594i
$927$	−1.86199	−	8.15791i	−0.0611558	−	0.267941i
$928$	38.0469	+	18.3224i	1.24895	+	0.601463i
$929$	24.8791	−	31.1974i	0.816257	−	1.02355i	−0.182926	−	0.983127i	$-0.558557\pi$
$929$	24.8791	−	31.1974i	0.816257	−	1.02355i	0.999182	−	0.0404269i	$-0.0128718\pi$
$930$	−7.37574			−0.241860
$931$	−1.85990	+	0.894191i	−0.0609559	+	0.0293059i
$932$	−44.4801			−1.45699
$933$	41.9506	−	52.6044i	1.37340	−	1.72219i
$934$	−30.4665	−	14.6719i	−0.996894	−	0.480079i
$935$	−0.738135	−	3.23398i	−0.0241396	−	0.105762i
$936$	5.45378	+	2.62640i	0.178262	+	0.0858466i
$937$	17.8039	−	8.57389i	0.581627	−	0.280097i	−0.119846	−	0.992792i	$-0.538240\pi$
$937$	17.8039	−	8.57389i	0.581627	−	0.280097i	0.701473	+	0.712696i	$0.252526\pi$
$938$	−12.3291	+	25.5804i	−0.402561	+	0.835231i
$939$	−47.0600	−	22.6629i	−1.53574	−	0.739575i
$940$	5.92823	+	7.43376i	0.193357	+	0.242463i
$941$	−15.1703	+	7.30564i	−0.494538	+	0.238157i	−0.664492	−	0.747295i	$-0.731352\pi$
$941$	−15.1703	+	7.30564i	−0.494538	+	0.238157i	0.169954	+	0.985452i	$0.445638\pi$
$942$	−5.09232	+	6.38556i	−0.165917	+	0.208053i
$943$	−0.386907	+	1.69515i	−0.0125994	+	0.0552017i
$944$	0.368439	−	0.462008i	0.0119917	−	0.0150371i
$945$	−0.000617402		1.89685i	−2.00841e−5		0.0617044i
$946$	−87.3007	−	109.472i	−2.83839	−	3.55923i
$947$	18.3097	−	8.81749i	0.594986	−	0.286530i	−0.112056	−	0.993702i	$-0.535744\pi$
$947$	18.3097	−	8.81749i	0.594986	−	0.286530i	0.707042	+	0.707172i	$0.250029\pi$
$948$	6.81811	−	29.8721i	0.221442	−	0.970200i
$949$	−5.80918			−0.188574
$950$	−3.27104			−0.106126
$951$	−11.9444	+	52.3317i	−0.387323	+	1.69697i
$952$	−5.48958	+	11.3898i	−0.177918	+	0.369144i
$953$	4.22498	+	18.5109i	0.136861	+	0.599625i	0.996114	+	0.0880750i	$0.0280715\pi$
$953$	4.22498	+	18.5109i	0.136861	+	0.599625i	−0.859253	+	0.511550i	$0.829071\pi$
$954$	4.93245	+	21.6105i	0.159694	+	0.699665i
$955$	4.41709	+	5.53886i	0.142934	+	0.179233i
$956$	−24.5547	−	30.7906i	−0.794154	−	0.995838i
$957$	−19.0056	−	83.2692i	−0.614365	−	2.69171i
$958$	18.5732	+	81.3747i	0.600074	+	2.62910i
$959$	5.26934	−	4.19935i	0.170156	−	0.135604i
$960$	−2.49105	+	10.9140i	−0.0803984	+	0.352249i
$961$	−17.0222			−0.549102
$962$	−6.08267			−0.196113
$963$	5.89785	−	25.8402i	0.190056	−	0.832688i
$964$	−19.5700	+	9.42440i	−0.630306	+	0.303539i
$965$	−0.495339	−	0.621136i	−0.0159455	−	0.0199951i
$966$	−38.6228	−	30.8212i	−1.24267	−	0.991656i
$967$	−27.5766	+	34.5800i	−0.886804	+	1.11202i	0.106248	+	0.994340i	$0.466116\pi$
$967$	−27.5766	+	34.5800i	−0.886804	+	1.11202i	−0.993052	+	0.117677i	$0.962455\pi$
$968$	9.31844	−	40.8268i	0.299506	−	1.31222i
$969$	−0.715855	+	0.897654i	−0.0229966	+	0.0288368i
$970$	3.63386	−	1.74998i	0.116676	−	0.0561883i
$971$	−4.63959	−	5.81787i	−0.148892	−	0.186704i	0.701792	−	0.712381i	$-0.252383\pi$
$971$	−4.63959	−	5.81787i	−0.148892	−	0.186704i	−0.850684	+	0.525677i	$0.823812\pi$
$972$	54.8352	+	26.4072i	1.75884	+	0.847013i
$973$	−23.3082	−	5.32792i	−0.747226	−	0.170805i
$974$	−8.03881	+	3.87129i	−0.257580	+	0.124044i
$975$	9.94719	+	4.79031i	0.318565	+	0.153413i
$976$	−0.207768	−	0.910292i	−0.00665050	−	0.0291377i
$977$	−25.9576	−	12.5005i	−0.830457	−	0.399927i	−0.0301703	−	0.999545i	$-0.509605\pi$
$977$	−25.9576	−	12.5005i	−0.830457	−	0.399927i	−0.800286	+	0.599618i	$0.795319\pi$
$978$	−35.6536	+	44.7082i	−1.14008	+	1.42961i
$979$	79.5872			2.54362
$980$	−1.89977	−	8.34848i	−0.0606859	−	0.266683i
$981$	34.6815			1.10729
$982$	52.1224	−	65.3595i	1.66329	−	2.08570i
$983$	−37.1379	−	17.8847i	−1.18451	−	0.570432i	−0.265291	−	0.964169i	$-0.585468\pi$
$983$	−37.1379	−	17.8847i	−1.18451	−	0.570432i	−0.919223	+	0.393737i	$0.871182\pi$
$984$	0.682737	+	2.99127i	0.0217649	+	0.0953581i
$985$	5.94970	+	2.86523i	0.189573	+	0.0912937i
$986$	−25.9731	+	12.5080i	−0.827151	+	0.398335i
$987$	36.5702	−	29.1443i	1.16404	−	0.927673i
$988$	0.855561	+	0.412016i	0.0272190	+	0.0131080i
$989$	−26.9314	−	33.7709i	−0.856370	−	1.07385i
$990$	8.65001	−	4.16563i	0.274915	−	0.132392i
$991$	1.59498	−	2.00004i	0.0506662	−	0.0635334i	−0.755853	−	0.654742i	$-0.772777\pi$
$991$	1.59498	−	2.00004i	0.0506662	−	0.0635334i	0.806519	+	0.591208i	$0.201349\pi$
$992$	4.76964	−	20.8971i	0.151436	−	0.663485i
$993$	−19.8492	+	24.8901i	−0.629894	+	0.789863i
$994$	87.9849	+	20.1121i	2.79071	+	0.637917i
$995$	−6.03261	−	7.56465i	−0.191247	−	0.239816i
$996$	−78.9857	+	38.0375i	−2.50276	+	1.20526i
$997$	−1.33900	+	5.86655i	−0.0424066	+	0.185795i	−0.991695	−	0.128611i	$-0.958948\pi$
$997$	−1.33900	+	5.86655i	−0.0424066	+	0.185795i	0.949289	+	0.314406i	$0.101805\pi$
$998$	−39.8463			−1.26131
$999$	−5.02599			−0.159015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.w.b.92.4	✓	174
49.8	even	7	inner	637.2.w.b.547.4	yes	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.w.b.92.4	✓	174	1.1	even	1	trivial
637.2.w.b.547.4	yes	174	49.8	even	7	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.w (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42465 + 1.78645i) q^{2} +(-2.04852 - 0.986513i) q^{3} +(-0.716746 - 3.14027i) q^{4} +(0.342127 + 0.164760i) q^{5} +(4.68077 - 2.25414i) q^{6} +(2.57961 - 0.587895i) q^{7} +(2.51370 + 1.21053i) q^{8} +(1.35274 + 1.69628i) q^{9} +O(q^{10})\)	\(q+(-1.42465 + 1.78645i) q^{2} +(-2.04852 - 0.986513i) q^{3} +(-0.716746 - 3.14027i) q^{4} +(0.342127 + 0.164760i) q^{5} +(4.68077 - 2.25414i) q^{6} +(2.57961 - 0.587895i) q^{7} +(2.51370 + 1.21053i) q^{8} +(1.35274 + 1.69628i) q^{9} +(-0.781746 + 0.376469i) q^{10} +(-3.17977 + 3.98731i) q^{11} +(-1.62965 + 7.13997i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-2.62479 + 5.44589i) q^{14} +(-0.538315 - 0.675026i) q^{15} +(0.0603961 - 0.0290853i) q^{16} +(-0.381145 + 1.66991i) q^{17} -4.95749 q^{18} -0.294813 q^{19} +(0.272172 - 1.19246i) q^{20} +(-5.86433 - 1.34050i) q^{21} +(-2.59308 - 11.3610i) q^{22} +(-0.799940 - 3.50477i) q^{23} +(-3.95514 - 4.95959i) q^{24} +(-3.02754 - 3.79642i) q^{25} +(0.508451 + 2.22767i) q^{26} +(0.420123 + 1.84068i) q^{27} +(-3.69507 - 7.67929i) q^{28} +(1.63903 - 7.18105i) q^{29} +1.97281 q^{30} -3.73869 q^{31} +(-1.27575 + 5.58942i) q^{32} +(10.4473 - 5.03118i) q^{33} +(-2.44021 - 3.05993i) q^{34} +(0.979416 + 0.223881i) q^{35} +(4.35720 - 5.46376i) q^{36} +(-0.592362 + 2.59531i) q^{37} +(0.420004 - 0.526669i) q^{38} +(-2.04852 + 0.986513i) q^{39} +(0.660558 + 0.828314i) q^{40} +(-0.435772 - 0.209857i) q^{41} +(10.7494 - 8.56660i) q^{42} +(10.8256 - 5.21335i) q^{43} +(14.8003 + 7.12746i) q^{44} +(0.183330 + 0.803220i) q^{45} +(7.40073 + 3.56400i) q^{46} +(-4.84677 + 6.07766i) q^{47} -0.152415 q^{48} +(6.30876 - 3.03308i) q^{49} +11.0953 q^{50} +(2.42817 - 3.04483i) q^{51} +(-2.90205 - 1.39755i) q^{52} +(-0.994949 - 4.35915i) q^{53} +(-3.88681 - 1.87179i) q^{54} +(-1.74484 + 0.840269i) q^{55} +(7.19603 + 1.64491i) q^{56} +(0.603929 + 0.290837i) q^{57} +(10.4936 + 13.1585i) q^{58} +(7.94230 - 3.82481i) q^{59} +(-1.73393 + 2.17428i) q^{60} +(3.09941 - 13.5794i) q^{61} +(5.32632 - 6.67900i) q^{62} +(4.48677 + 3.58047i) q^{63} +(-8.08415 - 10.1372i) q^{64} +(0.342127 - 0.164760i) q^{65} +(-5.89583 + 25.8313i) q^{66} +4.69720 q^{67} +5.51715 q^{68} +(-1.81881 + 7.96872i) q^{69} +(-1.79527 + 1.43073i) q^{70} +(-3.32209 - 14.5550i) q^{71} +(1.34697 + 5.90147i) q^{72} +(-3.62196 - 4.54180i) q^{73} +(-3.79248 - 4.75562i) q^{74} +(2.45675 + 10.7637i) q^{75} +(0.211306 + 0.925792i) q^{76} +(-5.85845 + 12.1551i) q^{77} +(1.15605 - 5.06501i) q^{78} -4.18378 q^{79} +0.0254553 q^{80} +(2.40358 - 10.5308i) q^{81} +(0.995720 - 0.479513i) q^{82} +(7.46352 + 9.35896i) q^{83} +(-0.00630680 + 19.3764i) q^{84} +(-0.405534 + 0.508524i) q^{85} +(-6.10931 + 26.7666i) q^{86} +(-10.4418 + 13.0936i) q^{87} +(-12.8198 + 6.17367i) q^{88} +(-9.72985 - 12.2008i) q^{89} +(-1.69609 - 0.816796i) q^{90} +(1.14872 - 2.38337i) q^{91} +(-10.4326 + 5.02406i) q^{92} +(7.65877 + 3.68827i) q^{93} +(-3.95250 - 17.3170i) q^{94} +(-0.100864 - 0.0485733i) q^{95} +(8.12743 - 10.1915i) q^{96} -4.64839 q^{97} +(-3.56931 + 15.5914i) q^{98} -11.0650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Introduction

L-functions

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