LMFDB - Embedded newform 15.8.e.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,8,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.68577538226$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	15.2
Dual form			15.8.e.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.2671 + 13.2671i) q^{2} +(42.4163 - 19.6942i) q^{3} -224.030i q^{4} +(122.889 - 251.044i) q^{5} +(-301.455 + 824.023i) q^{6} +(796.332 + 796.332i) q^{7} +(1274.03 + 1274.03i) q^{8} +(1411.28 - 1670.71i) q^{9} +O(q^{10})$	\(q+(-13.2671 + 13.2671i) q^{2} +(42.4163 - 19.6942i) q^{3} -224.030i q^{4} +(122.889 - 251.044i) q^{5} +(-301.455 + 824.023i) q^{6} +(796.332 + 796.332i) q^{7} +(1274.03 + 1274.03i) q^{8} +(1411.28 - 1670.71i) q^{9} +(1700.24 + 4961.00i) q^{10} +2194.99i q^{11} +(-4412.09 - 9502.50i) q^{12} +(5051.41 - 5051.41i) q^{13} -21130.0 q^{14} +(268.387 - 13068.6i) q^{15} -5129.52 q^{16} +(17341.7 - 17341.7i) q^{17} +(3441.90 + 40888.9i) q^{18} +36559.5i q^{19} +(-56241.4 - 27530.9i) q^{20} +(49460.5 + 18094.3i) q^{21} +(-29121.1 - 29121.1i) q^{22} +(-9551.69 - 9551.69i) q^{23} +(79130.7 + 28948.6i) q^{24} +(-47921.4 - 61701.3i) q^{25} +134035. i q^{26} +(26957.8 - 98659.2i) q^{27} +(178402. - 178402. i) q^{28} -35370.9 q^{29} +(169821. + 176942. i) q^{30} -237710. q^{31} +(-95022.5 + 95022.5i) q^{32} +(43228.6 + 93103.4i) q^{33} +460147. i q^{34} +(297775. - 102054. i) q^{35} +(-374288. - 316168. i) q^{36} +(64138.1 + 64138.1i) q^{37} +(-485037. - 485037. i) q^{38} +(114778. - 313745. i) q^{39} +(476404. - 163274. i) q^{40} -9927.62i q^{41} +(-896254. + 416138. i) q^{42} +(-190060. + 190060. i) q^{43} +491744. q^{44} +(-245991. - 559605. i) q^{45} +253446. q^{46} +(-213766. + 213766. i) q^{47} +(-217575. + 101022. i) q^{48} +444746. i q^{49} +(1.45437e6 + 182818. i) q^{50} +(394039. - 1.07710e6i) q^{51} +(-1.13167e6 - 1.13167e6i) q^{52} +(859949. + 859949. i) q^{53} +(951266. + 1.66657e6i) q^{54} +(551041. + 269741. i) q^{55} +2.02911e6i q^{56} +(720010. + 1.55072e6i) q^{57} +(469267. - 469267. i) q^{58} -1.97483e6 q^{59} +(-2.92775e6 - 60126.6i) q^{60} -1.08141e6 q^{61} +(3.15372e6 - 3.15372e6i) q^{62} +(2.45428e6 - 206594. i) q^{63} -3.17792e6i q^{64} +(-647363. - 1.88889e6i) q^{65} +(-1.80873e6 - 661691. i) q^{66} +(-335328. - 335328. i) q^{67} +(-3.88506e6 - 3.88506e6i) q^{68} +(-593260. - 217034. i) q^{69} +(-2.59665e6 + 5.30456e6i) q^{70} +4.54224e6i q^{71} +(3.92655e6 - 330524. i) q^{72} +(-522637. + 522637. i) q^{73} -1.70185e6 q^{74} +(-3.24781e6 - 1.67336e6i) q^{75} +8.19041e6 q^{76} +(-1.74794e6 + 1.74794e6i) q^{77} +(2.63970e6 + 5.68525e6i) q^{78} +3.93381e6i q^{79} +(-630364. + 1.28774e6i) q^{80} +(-799565. - 4.71566e6i) q^{81} +(131710. + 131710. i) q^{82} +(4.46224e6 + 4.46224e6i) q^{83} +(4.05366e6 - 1.10806e7i) q^{84} +(-2.22243e6 - 6.48465e6i) q^{85} -5.04308e6i q^{86} +(-1.50030e6 + 696601. i) q^{87} +(-2.79649e6 + 2.79649e6i) q^{88} -7.73756e6 q^{89} +(1.06879e7 + 4.16074e6i) q^{90} +8.04519e6 q^{91} +(-2.13986e6 + 2.13986e6i) q^{92} +(-1.00828e7 + 4.68151e6i) q^{93} -5.67208e6i q^{94} +(9.17805e6 + 4.49277e6i) q^{95} +(-2.15911e6 + 5.90189e6i) q^{96} +(87220.9 + 87220.9i) q^{97} +(-5.90047e6 - 5.90047e6i) q^{98} +(3.66719e6 + 3.09774e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7}+O(q^{10}) $ 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7	$ 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7} - 3180 q^{10} - 2028 q^{12} + 16848 q^{13} + 37560 q^{15} - 68868 q^{16} - 106560 q^{18} + 84144 q^{21} + 166020 q^{22} - 275760 q^{25} - 264168 q^{27} + 602028 q^{28} + 892380 q^{30} - 208992 q^{31} - 877800 q^{33} - 256212 q^{36} - 635616 q^{37} - 1574040 q^{40} + 1219380 q^{42} + 1397328 q^{43} + 570240 q^{45} + 2787168 q^{46} - 476796 q^{48} - 4028016 q^{51} - 6426336 q^{52} + 2324880 q^{55} + 8457264 q^{57} + 986340 q^{58} + 2037900 q^{60} + 12157968 q^{61} - 1973952 q^{63} - 25406040 q^{66} - 16720176 q^{67} - 13165860 q^{70} + 36245880 q^{72} + 4059528 q^{73} + 11226120 q^{75} + 37968816 q^{76} - 26156280 q^{78} - 31289976 q^{81} - 53633520 q^{82} - 34181760 q^{85} + 44480160 q^{87} + 74717340 q^{88} + 71623080 q^{90} + 67599648 q^{91} - 58742592 q^{93} - 103105308 q^{96} - 75148056 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7 - 3180 * q^10 - 2028 * q^12 + 16848 * q^13 + 37560 * q^15 - 68868 * q^16 - 106560 * q^18 + 84144 * q^21 + 166020 * q^22 - 275760 * q^25 - 264168 * q^27 + 602028 * q^28 + 892380 * q^30 - 208992 * q^31 - 877800 * q^33 - 256212 * q^36 - 635616 * q^37 - 1574040 * q^40 + 1219380 * q^42 + 1397328 * q^43 + 570240 * q^45 + 2787168 * q^46 - 476796 * q^48 - 4028016 * q^51 - 6426336 * q^52 + 2324880 * q^55 + 8457264 * q^57 + 986340 * q^58 + 2037900 * q^60 + 12157968 * q^61 - 1973952 * q^63 - 25406040 * q^66 - 16720176 * q^67 - 13165860 * q^70 + 36245880 * q^72 + 4059528 * q^73 + 11226120 * q^75 + 37968816 * q^76 - 26156280 * q^78 - 31289976 * q^81 - 53633520 * q^82 - 34181760 * q^85 + 44480160 * q^87 + 74717340 * q^88 + 71623080 * q^90 + 67599648 * q^91 - 58742592 * q^93 - 103105308 * q^96 - 75148056 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−13.2671	+	13.2671i	−1.17265	+	1.17265i	−0.191079	+	0.981575i	$0.561199\pi$
$2$	−13.2671	+	13.2671i	−1.17265	+	1.17265i	−0.981575	+	0.191079i	$0.938801\pi$
$3$	42.4163	−	19.6942i	0.907001	−	0.421128i
$3$	42.4163	−	19.6942i	0.907001	−	0.421128i
$4$		−	224.030i		−	1.75023i
$5$	122.889	−	251.044i	0.439662	−	0.898163i
$5$	122.889	−	251.044i	0.439662	−	0.898163i
$6$	−301.455	+	824.023i	−0.569761	+	1.55744i
$7$	796.332	+	796.332i	0.877508	+	0.877508i	0.993276	−	0.115769i	$-0.0369331\pi$
$7$	796.332	+	796.332i	0.877508	+	0.877508i	−0.115769	+	0.993276i	$0.536933\pi$
$8$	1274.03	+	1274.03i	0.879763	+	0.879763i
$9$	1411.28	−	1670.71i	0.645303	−	0.763927i
$10$	1700.24	+	4961.00i	0.537663	+	1.56881i
$11$			2194.99i			0.497232i	0.968602	+	0.248616i	$0.0799757\pi$
$11$			2194.99i			0.497232i	−0.968602	+	0.248616i	$0.920024\pi$
$12$	−4412.09	−	9502.50i	−0.737072	−	1.58746i
$13$	5051.41	−	5051.41i	0.637691	−	0.637691i	−0.312294	−	0.949985i	$-0.601097\pi$
$13$	5051.41	−	5051.41i	0.637691	−	0.637691i	0.949985	+	0.312294i	$0.101097\pi$
$14$	−21130.0			−2.05802
$15$	268.387	−	13068.6i	0.0205325	−	0.999789i
$16$	−5129.52			−0.313081
$17$	17341.7	−	17341.7i	0.856093	−	0.856093i	−0.134782	−	0.990875i	$-0.543033\pi$
$17$	17341.7	−	17341.7i	0.856093	−	0.856093i	0.990875	+	0.134782i	$0.0430334\pi$
$18$	3441.90	+	40888.9i	0.139105	+	1.65254i
$19$			36559.5i			1.22282i	0.791314	+	0.611410i	$0.209397\pi$
$19$			36559.5i			1.22282i	−0.791314	+	0.611410i	$0.790603\pi$
$20$	−56241.4	−	27530.9i	−1.57199	−	0.769511i
$21$	49460.5	+	18094.3i	1.16544	+	0.426358i
$22$	−29121.1	−	29121.1i	−0.583081	−	0.583081i
$23$	−9551.69	−	9551.69i	−0.163694	−	0.163694i	0.620507	−	0.784201i	$-0.286927\pi$
$23$	−9551.69	−	9551.69i	−0.163694	−	0.163694i	−0.784201	+	0.620507i	$0.786927\pi$
$24$	79130.7	+	28948.6i	1.16844	+	0.427453i
$25$	−47921.4	−	61701.3i	−0.613394	−	0.789777i
$26$			134035.i			1.49558i
$27$	26957.8	−	98659.2i	0.263579	−	0.964638i
$28$	178402.	−	178402.i	1.53584	−	1.53584i
$29$	−35370.9			−0.269310			−0.134655	−	0.990893i	$-0.542993\pi$
$29$	−35370.9			−0.269310			−0.134655	+	0.990893i	$0.542993\pi$
$30$	169821.	+	176942.i	1.14833	+	1.19648i
$31$	−237710.			−1.43312			−0.716559	−	0.697526i	$-0.754284\pi$
$31$	−237710.			−1.43312			−0.716559	+	0.697526i	$0.754284\pi$
$32$	−95022.5	+	95022.5i	−0.512627	+	0.512627i
$33$	43228.6	+	93103.4i	0.209398	+	0.450990i
$34$			460147.i			2.00780i
$35$	297775.	−	102054.i	1.17395	−	0.402338i
$36$	−374288.	−	316168.i	−1.33705	−	1.12943i
$37$	64138.1	+	64138.1i	0.208166	+	0.208166i	0.803488	−	0.595321i	$-0.202975\pi$
$37$	64138.1	+	64138.1i	0.208166	+	0.208166i	−0.595321	+	0.803488i	$0.702975\pi$
$38$	−485037.	−	485037.i	−1.43394	−	1.43394i
$39$	114778.	−	313745.i	0.309837	−	0.846937i
$40$	476404.	−	163274.i	1.17697	−	0.403372i
$41$		−	9927.62i		−	0.0224958i	−0.999937	−	0.0112479i	$-0.996420\pi$
$41$		−	9927.62i		−	0.0224958i	0.999937	−	0.0112479i	$-0.00358040\pi$
$42$	−896254.	+	416138.i	−1.86663	+	0.866692i
$43$	−190060.	+	190060.i	−0.364545	+	0.364545i	−0.865483	−	0.500938i	$-0.832988\pi$
$43$	−190060.	+	190060.i	−0.364545	+	0.364545i	0.500938	+	0.865483i	$0.332988\pi$
$44$	491744.			0.870271
$45$	−245991.	−	559605.i	−0.402416	−	0.915457i
$46$	253446.			0.383913
$47$	−213766.	+	213766.i	−0.300328	+	0.300328i	−0.841142	−	0.540814i	$-0.818116\pi$
$47$	−213766.	+	213766.i	−0.300328	+	0.300328i	0.540814	+	0.841142i	$0.318116\pi$
$48$	−217575.	+	101022.i	−0.283965	+	0.131847i
$49$			444746.i			0.540039i
$50$	1.45437e6	+	182818.i	1.64543	+	0.206835i
$51$	394039.	−	1.07710e6i	0.415953	−	1.13700i
$52$	−1.13167e6	−	1.13167e6i	−1.11611	−	1.11611i
$53$	859949.	+	859949.i	0.793427	+	0.793427i	0.982050	−	0.188623i	$-0.0604023\pi$
$53$	859949.	+	859949.i	0.793427	+	0.793427i	−0.188623	+	0.982050i	$0.560402\pi$
$54$	951266.	+	1.66657e6i	0.822099	+	1.44027i
$55$	551041.	+	269741.i	0.446595	+	0.218614i
$56$			2.02911e6i			1.54400i
$57$	720010.	+	1.55072e6i	0.514964	+	1.10910i
$58$	469267.	−	469267.i	0.315807	−	0.315807i
$59$	−1.97483e6			−1.25184			−0.625918	−	0.779889i	$-0.715275\pi$
$59$	−1.97483e6			−1.25184			−0.625918	+	0.779889i	$0.715275\pi$
$60$	−2.92775e6	−	60126.6i	−1.74986	−	0.0359366i
$61$	−1.08141e6			−0.610011			−0.305005	−	0.952351i	$-0.598658\pi$
$61$	−1.08141e6			−0.610011			−0.305005	+	0.952351i	$0.598658\pi$
$62$	3.15372e6	−	3.15372e6i	1.68055	−	1.68055i
$63$	2.45428e6	−	206594.i	1.23661	−	0.104094i
$64$		−	3.17792e6i		−	1.51535i
$65$	−647363.	−	1.88889e6i	−0.292382	−	0.853120i
$66$	−1.80873e6	−	661691.i	−0.774406	−	0.283303i
$67$	−335328.	−	335328.i	−0.136210	−	0.136210i	0.635715	−	0.771924i	$-0.280706\pi$
$67$	−335328.	−	335328.i	−0.136210	−	0.136210i	−0.771924	+	0.635715i	$0.780706\pi$
$68$	−3.88506e6	−	3.88506e6i	−1.49836	−	1.49836i
$69$	−593260.	−	217034.i	−0.217407	−	0.0795346i
$70$	−2.59665e6	+	5.30456e6i	−0.904836	+	1.84844i
$71$			4.54224e6i			1.50614i	0.657940	+	0.753070i	$0.271428\pi$
$71$			4.54224e6i			1.50614i	−0.657940	+	0.753070i	$0.728572\pi$
$72$	3.92655e6	−	330524.i	1.23979	−	0.104361i
$73$	−522637.	+	522637.i	−0.157243	+	0.157243i	−0.781344	−	0.624101i	$-0.785465\pi$
$73$	−522637.	+	522637.i	−0.157243	+	0.157243i	0.624101	+	0.781344i	$0.285465\pi$
$74$	−1.70185e6			−0.488214
$75$	−3.24781e6	−	1.67336e6i	−0.888947	−	0.458011i
$76$	8.19041e6			2.14022
$77$	−1.74794e6	+	1.74794e6i	−0.436325	+	0.436325i
$78$	2.63970e6	+	5.68525e6i	0.629831	+	1.35649i
$79$			3.93381e6i			0.897674i	0.893614	+	0.448837i	$0.148162\pi$
$79$			3.93381e6i			0.897674i	−0.893614	+	0.448837i	$0.851838\pi$
$80$	−630364.	+	1.28774e6i	−0.137650	+	0.281198i
$81$	−799565.	−	4.71566e6i	−0.167169	−	0.985928i
$82$	131710.	+	131710.i	0.0263798	+	0.0263798i
$83$	4.46224e6	+	4.46224e6i	0.856603	+	0.856603i	0.990936	−	0.134333i	$-0.0428893\pi$
$83$	4.46224e6	+	4.46224e6i	0.856603	+	0.856603i	−0.134333	+	0.990936i	$0.542889\pi$
$84$	4.05366e6	−	1.10806e7i	0.746225	−	2.03980i
$85$	−2.22243e6	−	6.48465e6i	−0.392520	−	1.14530i
$86$		−	5.04308e6i		−	0.854970i
$87$	−1.50030e6	+	696601.i	−0.244265	+	0.113414i
$88$	−2.79649e6	+	2.79649e6i	−0.437446	+	0.437446i
$89$	−7.73756e6			−1.16343			−0.581713	−	0.813394i	$-0.697617\pi$
$89$	−7.73756e6			−1.16343			−0.581713	+	0.813394i	$0.697617\pi$
$90$	1.06879e7	+	4.16074e6i	1.54541	+	0.601619i
$91$	8.04519e6			1.11916
$92$	−2.13986e6	+	2.13986e6i	−0.286503	+	0.286503i
$93$	−1.00828e7	+	4.68151e6i	−1.29984	+	0.603526i
$94$		−	5.67208e6i		−	0.704361i
$95$	9.17805e6	+	4.49277e6i	1.09829	+	0.537628i
$96$	−2.15911e6	+	5.90189e6i	−0.249072	+	0.680835i
$97$	87220.9	+	87220.9i	0.00970330	+	0.00970330i	0.711942	−	0.702238i	$-0.247816\pi$
$97$	87220.9	+	87220.9i	0.00970330	+	0.00970330i	−0.702238	+	0.711942i	$0.747816\pi$
$98$	−5.90047e6	−	5.90047e6i	−0.633279	−	0.633279i
$99$	3.66719e6	+	3.09774e6i	0.379849	+	0.320865i
$100$	−1.38229e7	+	1.07358e7i	−1.38229	+	1.07358i
$101$		−	1.63053e7i		−	1.57472i	−0.616491	−	0.787362i	$-0.711446\pi$
$101$		−	1.63053e7i		−	1.57472i	0.616491	−	0.787362i	$-0.288554\pi$
$102$	9.06224e6	+	1.95177e7i	0.845541	+	1.82108i
$103$	1.09059e7	−	1.09059e7i	0.983404	−	0.983404i	−0.0164609	−	0.999865i	$-0.505240\pi$
$103$	1.09059e7	−	1.09059e7i	0.983404	−	0.983404i	0.999865	+	0.0164609i	$0.00523990\pi$
$104$	1.28713e7			1.12203
$105$	1.06206e7	−	1.01932e7i	0.895340	−	0.859305i
$106$	−2.28180e7			−1.86083
$107$	−6.48981e6	+	6.48981e6i	−0.512140	+	0.512140i	−0.915182	−	0.403042i	$-0.867953\pi$
$107$	−6.48981e6	+	6.48981e6i	−0.512140	+	0.512140i	0.403042	+	0.915182i	$0.367953\pi$
$108$	−2.21026e7	−	6.03935e6i	−1.68834	−	0.461325i
$109$		−	1.01289e6i		−	0.0749152i	−0.999298	−	0.0374576i	$-0.988074\pi$
$109$		−	1.01289e6i		−	0.0749152i	0.999298	−	0.0374576i	$-0.0119259\pi$
$110$	−1.08894e7	+	3.73201e6i	−0.780060	+	0.267343i
$111$	3.98365e6	+	1.45735e6i	0.276472	+	0.101142i
$112$	−4.08480e6	−	4.08480e6i	−0.274731	−	0.274731i
$113$	4.98667e6	+	4.98667e6i	0.325114	+	0.325114i	0.850725	−	0.525611i	$-0.176163\pi$
$113$	4.98667e6	+	4.98667e6i	0.325114	+	0.325114i	−0.525611	+	0.850725i	$0.676163\pi$
$114$	−3.01259e7	−	1.10210e7i	−1.90446	−	0.696715i
$115$	−3.57170e6	+	1.22410e6i	−0.218994	+	0.0750539i
$116$			7.92413e6i			0.471355i
$117$	−1.31049e6	−	1.55684e7i	−0.0756458	−	0.898654i
$118$	2.62002e7	−	2.62002e7i	1.46797	−	1.46797i
$119$	2.76195e7			1.50246
$120$	1.69917e7	−	1.63078e7i	0.897641	−	0.861514i
$121$	1.46692e7			0.752761
$122$	1.43472e7	−	1.43472e7i	0.715331	−	0.715331i
$123$	−195517.	−	421093.i	−0.00947362	−	0.0204037i
$124$			5.32542e7i			2.50829i
$125$	−2.13788e7	+	4.44797e6i	−0.979035	+	0.203693i
$126$	−2.98202e7	+	3.53020e7i	−1.32805	+	1.57218i
$127$	−1.56565e7	−	1.56565e7i	−0.678239	−	0.678239i	0.281363	−	0.959601i	$-0.409214\pi$
$127$	−1.56565e7	−	1.56565e7i	−0.678239	−	0.678239i	−0.959601	+	0.281363i	$0.909214\pi$
$128$	2.99987e7	+	2.99987e7i	1.26435	+	1.26435i
$129$	−4.31855e6	+	1.18047e7i	−0.177123	+	0.484163i
$130$	3.36486e7	+	1.64714e7i	1.34328	+	0.657551i
$131$		−	3.15718e6i		−	0.122701i	−0.998116	−	0.0613507i	$-0.980459\pi$
$131$		−	3.15718e6i		−	0.122701i	0.998116	−	0.0613507i	$-0.0195408\pi$
$132$	2.08579e7	−	9.68450e6i	0.789337	−	0.366495i
$133$	−2.91135e7	+	2.91135e7i	−1.07303	+	1.07303i
$134$	8.89763e6			0.319454
$135$	−2.14550e7	−	1.88918e7i	−0.750516	−	0.660852i
$136$	4.41878e7			1.50632
$137$	−4.10988e6	+	4.10988e6i	−0.136555	+	0.136555i	−0.772080	−	0.635525i	$-0.780784\pi$
$137$	−4.10988e6	+	4.10988e6i	−0.136555	+	0.136555i	0.635525	+	0.772080i	$0.280784\pi$
$138$	1.07502e7	−	4.99141e6i	0.348209	−	0.161676i
$139$			5.61722e6i			0.177406i	0.996058	+	0.0887032i	$0.0282723\pi$
$139$			5.61722e6i			0.177406i	−0.996058	+	0.0887032i	$0.971728\pi$
$140$	−2.28631e7	−	6.67105e7i	−0.704185	−	2.05469i
$141$	−4.85719e6	+	1.32771e7i	−0.145921	+	0.398874i
$142$	−6.02621e7	−	6.02621e7i	−1.76618	−	1.76618i
$143$	1.10878e7	+	1.10878e7i	0.317080	+	0.317080i
$144$	−7.23918e6	+	8.56994e6i	−0.202032	+	0.239171i
$145$	−4.34670e6	+	8.87965e6i	−0.118405	+	0.241884i
$146$		−	1.38677e7i		−	0.368782i
$147$	8.75891e6	+	1.88644e7i	0.227426	+	0.489816i
$148$	1.43688e7	−	1.43688e7i	0.364339	−	0.364339i
$149$	−3.67779e7			−0.910826			−0.455413	−	0.890280i	$-0.650508\pi$
$149$	−3.67779e7			−0.910826			−0.455413	+	0.890280i	$0.650508\pi$
$150$	6.52894e7	−	2.08882e7i	1.57951	−	0.505338i
$151$	9.65672e6			0.228250			0.114125	−	0.993466i	$-0.463594\pi$
$151$	9.65672e6			0.228250			0.114125	+	0.993466i	$0.463594\pi$
$152$	−4.65780e7	+	4.65780e7i	−1.07579	+	1.07579i
$153$	−4.49899e6	−	5.34469e7i	−0.101554	−	1.20643i
$154$		−	4.63801e7i		−	1.02332i
$155$	−2.92121e7	+	5.96758e7i	−0.630088	+	1.28717i
$156$	−7.02882e7	−	2.57138e7i	−1.48234	−	0.542287i
$157$	−1.06951e6	−	1.06951e6i	−0.0220565	−	0.0220565i	0.695993	−	0.718049i	$-0.254965\pi$
$157$	−1.06951e6	−	1.06951e6i	−0.0220565	−	0.0220565i	−0.718049	+	0.695993i	$0.754965\pi$
$158$	−5.21901e7	−	5.21901e7i	−1.05266	−	1.05266i
$159$	5.34118e7	+	1.95398e7i	1.05377	+	0.385505i
$160$	1.21776e7	+	3.55321e7i	0.235040	+	0.685805i
$161$		−	1.52126e7i		−	0.287286i
$162$	7.31709e7	+	5.19551e7i	1.35218	+	0.960121i
$163$	−3.61482e7	+	3.61482e7i	−0.653778	+	0.653778i	−0.953901	−	0.300123i	$-0.902972\pi$
$163$	−3.61482e7	+	3.61482e7i	−0.653778	+	0.653778i	0.300123	+	0.953901i	$0.402972\pi$
$164$	−2.22408e6			−0.0393729
$165$	2.86854e7	+	589107.i	0.497127	+	0.0102094i
$166$	−1.18402e8			−2.00900
$167$	5.77212e7	−	5.77212e7i	0.959020	−	0.959020i	−0.0401732	−	0.999193i	$-0.512791\pi$
$167$	5.77212e7	−	5.77212e7i	0.959020	−	0.959020i	0.999193	+	0.0401732i	$0.0127910\pi$
$168$	3.99616e7	+	8.60670e7i	0.650220	+	1.40041i
$169$			1.17151e7i			0.186699i
$170$	1.15517e8	+	5.65472e7i	1.80333	+	0.882754i
$171$	6.10802e7	+	5.15956e7i	0.934145	+	0.789089i
$172$	4.25791e7	+	4.25791e7i	0.638039	+	0.638039i
$173$	−4.69509e7	−	4.69509e7i	−0.689418	−	0.689418i	0.272685	−	0.962103i	$-0.412088\pi$
$173$	−4.69509e7	−	4.69509e7i	−0.689418	−	0.689418i	−0.962103	+	0.272685i	$0.912088\pi$
$174$	1.06627e7	−	2.91464e7i	0.153442	−	0.419433i
$175$	1.09733e7	−	8.72961e7i	0.154777	−	1.23129i
$176$		−	1.12593e7i		−	0.155674i
$177$	−8.37648e7	+	3.88927e7i	−1.13542	+	0.527183i
$178$	1.02655e8	−	1.02655e8i	1.36430	−	1.36430i
$179$	−2.05963e6			−0.0268413			−0.0134206	−	0.999910i	$-0.504272\pi$
$179$	−2.05963e6			−0.0268413			−0.0134206	+	0.999910i	$0.504272\pi$
$180$	−1.25368e8	+	5.51093e7i	−1.60226	+	0.704322i
$181$	1.11774e8			1.40109			0.700543	−	0.713610i	$-0.252941\pi$
$181$	1.11774e8			1.40109			0.700543	+	0.713610i	$0.252941\pi$
$182$	−1.06736e8	+	1.06736e8i	−1.31238	+	1.31238i
$183$	−4.58695e7	+	2.12976e7i	−0.553280	+	0.256892i
$184$		−	2.43383e7i		−	0.288024i
$185$	2.39834e7	−	8.21962e6i	0.278490	−	0.0954444i
$186$	7.16589e7	−	1.95879e8i	0.816535	−	2.23199i
$187$	3.80650e7	+	3.80650e7i	0.425677	+	0.425677i
$188$	4.78899e7	+	4.78899e7i	0.525643	+	0.525643i
$189$	1.00033e8	−	5.70981e7i	1.07777	−	0.615184i
$190$	−1.81372e8	+	6.21599e7i	−1.91837	+	0.657465i
$191$			2.33104e7i			0.242065i	0.992649	+	0.121033i	$0.0386206\pi$
$191$			2.33104e7i			0.242065i	−0.992649	+	0.121033i	$0.961379\pi$
$192$	−6.25865e7	−	1.34795e8i	−0.638156	−	1.37442i
$193$	−1.05813e8	+	1.05813e8i	−1.05947	+	1.05947i	−0.0613507	+	0.998116i	$0.519541\pi$
$193$	−1.05813e8	+	1.05813e8i	−1.05947	+	1.05947i	−0.998116	+	0.0613507i	$0.980459\pi$
$194$	−2.31433e6			−0.0227572
$195$	−6.46589e7	−	6.73704e7i	−0.624464	−	0.650650i
$196$	9.96362e7			0.945194
$197$	1.01270e8	−	1.01270e8i	0.943732	−	0.943732i	−0.0547667	−	0.998499i	$-0.517442\pi$
$197$	1.01270e8	−	1.01270e8i	0.943732	−	0.943732i	0.998499	+	0.0547667i	$0.0174415\pi$
$198$	−8.97508e7	+	7.55494e6i	−0.821694	+	0.0691676i
$199$			3.85338e7i			0.346622i	0.984867	+	0.173311i	$0.0554466\pi$
$199$			3.85338e7i			0.346622i	−0.984867	+	0.173311i	$0.944553\pi$
$200$	1.75560e7	−	1.39663e8i	0.155175	−	1.23446i
$201$	−2.08274e7	−	7.61934e6i	−0.180904	−	0.0661807i
$202$	2.16324e8	+	2.16324e8i	1.84661	+	1.84661i
$203$	−2.81669e7	−	2.81669e7i	−0.236322	−	0.236322i
$204$	−2.41303e8	−	8.82766e7i	−1.99002	−	0.728014i
$205$	−2.49227e6	−	1.22000e6i	−0.0202049	−	0.00989056i
$206$			2.89379e8i			2.30638i
$207$	−2.94382e7	+	2.47801e6i	−0.230683	+	0.0194181i
$208$	−2.59113e7	+	2.59113e7i	−0.199649	+	0.199649i
$209$	−8.02478e7			−0.608025
$210$	−5.67100e6	+	2.76138e8i	−0.0422564	+	2.05759i
$211$	−1.75300e8			−1.28467			−0.642336	−	0.766423i	$-0.722035\pi$
$211$	−1.75300e8			−1.28467			−0.642336	+	0.766423i	$0.722035\pi$
$212$	1.92654e8	−	1.92654e8i	1.38868	−	1.38868i
$213$	8.94557e7	+	1.92665e8i	0.634278	+	1.36607i
$214$		−	1.72201e8i		−	1.20113i
$215$	2.43571e7	+	7.10698e7i	0.167144	+	0.487698i
$216$	1.60040e8	−	9.13499e7i	1.08054	−	0.616765i
$217$	−1.89296e8	−	1.89296e8i	−1.25757	−	1.25757i
$218$	1.34381e7	+	1.34381e7i	0.0878496	+	0.0878496i
$219$	−1.18754e7	+	3.24612e7i	−0.0764000	+	0.208838i
$220$	6.04301e7	−	1.23449e8i	0.382625	−	0.781646i
$221$		−	1.75200e8i		−	1.09185i
$222$	−7.21860e7	+	3.35166e7i	−0.442810	+	0.205600i
$223$	2.09041e8	−	2.09041e8i	1.26230	−	1.26230i	0.312330	−	0.949974i	$-0.398891\pi$
$223$	2.09041e8	−	2.09041e8i	1.26230	−	1.26230i	0.949974	−	0.312330i	$-0.101109\pi$
$224$	−1.51339e8			−0.899668
$225$	−1.70715e8	−	7.01486e6i	−0.999157	−	0.0410563i
$226$	−1.32317e8			−0.762493
$227$	9.19929e7	−	9.19929e7i	0.521992	−	0.521992i	−0.396181	−	0.918173i	$-0.629665\pi$
$227$	9.19929e7	−	9.19929e7i	0.521992	−	0.521992i	0.918173	+	0.396181i	$0.129665\pi$
$228$	3.47407e8	−	1.61304e8i	1.94118	−	0.901306i
$229$		−	1.04935e8i		−	0.577424i	−0.957416	−	0.288712i	$-0.906773\pi$
$229$		−	1.04935e8i		−	0.577424i	0.957416	−	0.288712i	$-0.0932269\pi$
$230$	3.11458e7	−	6.36261e7i	0.168792	−	0.344816i
$231$	−3.97168e7	+	1.08566e8i	−0.211999	+	0.579495i
$232$	−4.50636e7	−	4.50636e7i	−0.236929	−	0.236929i
$233$	1.67161e8	+	1.67161e8i	0.865744	+	0.865744i	0.991998	−	0.126254i	$-0.0402955\pi$
$233$	1.67161e8	+	1.67161e8i	0.865744	+	0.865744i	−0.126254	+	0.991998i	$0.540295\pi$
$234$	2.23933e8	+	1.89160e8i	1.14252	+	0.965103i
$235$	2.73951e7	+	7.99342e7i	0.137701	+	0.401786i
$236$			4.42420e8i			2.19100i
$237$	7.74732e7	+	1.66857e8i	0.378035	+	0.814191i
$238$	−3.66430e8	+	3.66430e8i	−1.76186	+	1.76186i
$239$	5.40980e6			0.0256323			0.0128162	−	0.999918i	$-0.495920\pi$
$239$	5.40980e6			0.0256323			0.0128162	+	0.999918i	$0.495920\pi$
$240$	−1.37670e6	+	6.70355e7i	−0.00642834	+	0.313015i
$241$	2.89625e8			1.33283			0.666416	−	0.745580i	$-0.267827\pi$
$241$	2.89625e8			1.33283			0.666416	+	0.745580i	$0.267827\pi$
$242$	−1.94617e8	+	1.94617e8i	−0.882727	+	0.882727i
$243$	−1.26786e8	−	1.84274e8i	−0.566824	−	0.823839i
$244$			2.42269e8i			1.06766i
$245$	1.11651e8	+	5.46545e7i	0.485043	+	0.237435i
$246$	8.18059e6	+	2.99273e6i	0.0350358	+	0.0128172i
$247$	1.84677e8	+	1.84677e8i	0.779782	+	0.779782i
$248$	−3.02851e8	−	3.02851e8i	−1.26080	−	1.26080i
$249$	2.77152e8	+	1.01391e8i	1.13768	+	0.416200i
$250$	2.24622e8	−	3.42645e8i	0.909207	−	1.38693i
$251$		−	3.81056e8i		−	1.52101i	−0.649335	−	0.760503i	$-0.724953\pi$
$251$		−	3.81056e8i		−	1.52101i	0.649335	−	0.760503i	$-0.275047\pi$
$252$	−4.62831e7	−	5.49832e8i	−0.182188	−	2.16435i
$253$	2.09659e7	−	2.09659e7i	0.0813939	−	0.0813939i
$254$	4.15432e8			1.59068
$255$	−2.21977e8	−	2.31286e8i	−0.838335	−	0.873490i
$256$	−3.89217e8			−1.44995
$257$	−3.28549e8	+	3.28549e8i	−1.20735	+	1.20735i	−0.235471	+	0.971881i	$0.575663\pi$
$257$	−3.28549e8	+	3.28549e8i	−1.20735	+	1.20735i	−0.971881	+	0.235471i	$0.924337\pi$
$258$	−9.93194e7	−	2.13908e8i	−0.360052	−	0.775459i
$259$			1.02150e8i			0.365335i
$260$	−4.23168e8	+	1.45029e8i	−1.49316	+	0.511737i
$261$	−4.99181e7	+	5.90944e7i	−0.173787	+	0.205733i
$262$	4.18865e7	+	4.18865e7i	0.143886	+	0.143886i
$263$	−9.87239e7	−	9.87239e7i	−0.334639	−	0.334639i	0.519706	−	0.854345i	$-0.326042\pi$
$263$	−9.87239e7	−	9.87239e7i	−0.334639	−	0.334639i	−0.854345	+	0.519706i	$0.826042\pi$
$264$	−6.35421e7	+	1.73691e8i	−0.212543	+	0.580985i
$265$	3.21564e8	−	1.10207e8i	1.06147	−	0.363787i
$266$		−	7.72501e8i		−	2.51659i
$267$	−3.28198e8	+	1.52385e8i	−1.05523	+	0.489951i
$268$	−7.51235e7	+	7.51235e7i	−0.238399	+	0.238399i
$269$	−5.55168e8			−1.73897			−0.869483	−	0.493963i	$-0.835548\pi$
$269$	−5.55168e8			−1.73897			−0.869483	+	0.493963i	$0.835548\pi$
$270$	5.35283e8	−	3.40066e7i	1.65505	−	0.105145i
$271$	−1.90730e8			−0.582138			−0.291069	−	0.956702i	$-0.594011\pi$
$271$	−1.90730e8			−0.582138			−0.291069	+	0.956702i	$0.594011\pi$
$272$	−8.89548e7	+	8.89548e7i	−0.268027	+	0.268027i
$273$	3.41247e8	−	1.58444e8i	1.01508	−	0.471309i
$274$		−	1.09052e8i		−	0.320263i
$275$	1.35434e8	−	1.05187e8i	0.392702	−	0.304999i
$276$	−4.86221e7	+	1.32908e8i	−0.139204	+	0.380513i
$277$	3.26885e7	+	3.26885e7i	0.0924092	+	0.0924092i	0.751800	−	0.659391i	$-0.229186\pi$
$277$	3.26885e7	+	3.26885e7i	0.0924092	+	0.0924092i	−0.659391	+	0.751800i	$0.729186\pi$
$278$	−7.45240e7	−	7.45240e7i	−0.208036	−	0.208036i
$279$	−3.35475e8	+	3.97145e8i	−0.924795	+	1.09480i
$280$	5.09395e8	+	2.49355e8i	1.38676	+	0.678837i
$281$			3.92270e8i			1.05466i	0.849660	+	0.527331i	$0.176807\pi$
$281$			3.92270e8i			1.05466i	−0.849660	+	0.527331i	$0.823193\pi$
$282$	−1.11707e8	−	2.40589e8i	−0.296626	−	0.638856i
$283$	−1.43453e8	+	1.43453e8i	−0.376234	+	0.376234i	−0.869742	−	0.493507i	$-0.835715\pi$
$283$	−1.43453e8	+	1.43453e8i	−0.376234	+	0.376234i	0.493507	+	0.869742i	$0.335715\pi$
$284$	1.01760e9			2.63610
$285$	4.77780e8	+	9.81208e6i	1.22256	+	0.0251075i
$286$	−2.94205e8			−0.743651
$287$	7.90568e6	−	7.90568e6i	0.0197403	−	0.0197403i
$288$	2.46518e7	+	2.92858e8i	0.0608101	+	0.722409i
$289$		−	1.91132e8i		−	0.465791i
$290$	−6.01389e7	−	1.75475e8i	−0.144798	−	0.422495i
$291$	5.41733e6	+	1.98184e6i	0.0128872	+	0.00471458i
$292$	1.17086e8	+	1.17086e8i	0.275211	+	0.275211i
$293$	4.27911e8	+	4.27911e8i	0.993841	+	0.993841i	0.999981	−	0.00614032i	$-0.00195454\pi$
$293$	4.27911e8	+	4.27911e8i	0.993841	+	0.993841i	−0.00614032	+	0.999981i	$0.501955\pi$
$294$	−3.66481e8	−	1.34071e8i	−0.841076	−	0.307693i
$295$	−2.42685e8	+	4.95769e8i	−0.550384	+	1.12435i
$296$			1.63428e8i			0.366274i
$297$	2.16556e8	+	5.91722e7i	0.479648	+	0.131060i
$298$	4.87935e8	−	4.87935e8i	1.06808	−	1.06808i
$299$	−9.64990e7			−0.208773
$300$	−3.74883e8	+	7.27605e8i	−0.801626	+	1.55586i
$301$	−3.02702e8			−0.639782
$302$	−1.28116e8	+	1.28116e8i	−0.267658	+	0.267658i
$303$	−3.21120e8	−	6.91611e8i	−0.663160	−	1.42828i
$304$		−	1.87533e8i		−	0.382842i
$305$	−1.32894e8	+	2.71483e8i	−0.268199	+	0.547889i
$306$	7.68772e8	+	6.49395e8i	1.53381	+	1.29564i
$307$	−5.24432e8	−	5.24432e8i	−1.03444	−	1.03444i	−0.999385	−	0.0350528i	$-0.988840\pi$
$307$	−5.24432e8	−	5.24432e8i	−1.03444	−	1.03444i	−0.0350528	−	0.999385i	$-0.511160\pi$
$308$	3.91591e8	+	3.91591e8i	0.763670	+	0.763670i
$309$	2.47805e8	−	6.77371e8i	0.477810	−	1.30609i
$310$	−4.04164e8	−	1.17928e9i	−0.770535	−	2.24828i
$311$			3.33947e7i			0.0629529i	0.999504	+	0.0314765i	$0.0100209\pi$
$311$			3.33947e7i			0.0629529i	−0.999504	+	0.0314765i	$0.989979\pi$
$312$	5.45953e8	−	2.53490e8i	1.01769	−	0.472520i
$313$	−2.66192e8	+	2.66192e8i	−0.490670	+	0.490670i	−0.908517	−	0.417847i	$-0.862785\pi$
$313$	−2.66192e8	+	2.66192e8i	−0.490670	+	0.490670i	0.417847	+	0.908517i	$0.362785\pi$
$314$	2.83786e7			0.0517293
$315$	2.49741e8	−	6.41522e8i	0.450197	−	1.15644i
$316$	8.81290e8			1.57114
$317$	2.74734e8	−	2.74734e8i	0.484401	−	0.484401i	−0.422133	−	0.906534i	$-0.638718\pi$
$317$	2.74734e8	−	2.74734e8i	0.484401	−	0.484401i	0.906534	+	0.422133i	$0.138718\pi$
$318$	−9.67853e8	+	4.49382e8i	−1.68778	+	0.783647i
$319$		−	7.76388e7i		−	0.133910i
$320$	−7.97798e8	−	3.90532e8i	−1.36103	−	0.666241i
$321$	−1.47462e8	+	4.03085e8i	−0.248835	+	0.680188i
$322$	2.01827e8	+	2.01827e8i	0.336886	+	0.336886i
$323$	6.34004e8	+	6.34004e8i	1.04685	+	1.04685i
$324$	−1.05645e9	+	1.79126e8i	−1.72560	+	0.292585i
$325$	−5.53749e8	−	6.96077e7i	−0.894790	−	0.112477i
$326$		−	9.59161e8i		−	1.53331i
$327$	−1.99481e7	−	4.29630e7i	−0.0315489	−	0.0679482i
$328$	1.26481e7	−	1.26481e7i	0.0197910	−	0.0197910i
$329$	−3.40457e8			−0.527080
$330$	−3.88387e8	+	3.72755e8i	−0.594930	+	0.570986i
$331$	−7.04006e7			−0.106704			−0.0533518	−	0.998576i	$-0.516990\pi$
$331$	−7.04006e7			−0.106704			−0.0533518	+	0.998576i	$0.516990\pi$
$332$	9.99674e8	−	9.99674e8i	1.49925	−	1.49925i
$333$	1.97673e8	−	1.66395e7i	0.293354	−	0.0246936i
$334$			1.53158e9i			2.24920i
$335$	−1.25390e8	+	4.29739e7i	−0.182225	+	0.0624523i
$336$	−2.53709e8	−	9.28151e7i	−0.364879	−	0.133485i
$337$	9.36892e8	+	9.36892e8i	1.33347	+	1.33347i	0.902240	+	0.431235i	$0.141922\pi$
$337$	9.36892e8	+	9.36892e8i	1.33347	+	1.33347i	0.431235	+	0.902240i	$0.358078\pi$
$338$	−1.55425e8	−	1.55425e8i	−0.218934	−	0.218934i
$339$	3.09724e8	+	1.13307e8i	0.431794	+	0.157964i
$340$	−1.45276e9	+	4.97890e8i	−2.00455	+	0.687001i
$341$		−	5.21773e8i		−	0.712592i
$342$	−1.49488e9	+	1.25834e8i	−2.02076	+	0.170101i
$343$	3.01648e8	−	3.01648e8i	0.403619	−	0.403619i
$344$	−4.84285e8			−0.641426
$345$	−1.27390e8	+	1.22263e8i	−0.167021	+	0.160299i
$346$	1.24580e9			1.61690
$347$	2.74722e8	−	2.74722e8i	0.352973	−	0.352973i	−0.508242	−	0.861214i	$-0.669704\pi$
$347$	2.74722e8	−	2.74722e8i	0.352973	−	0.352973i	0.861214	+	0.508242i	$0.169704\pi$
$348$	1.56059e8	+	3.36112e8i	0.198501	+	0.427520i
$349$		−	3.41208e8i		−	0.429666i	−0.976651	−	0.214833i	$-0.931079\pi$
$349$		−	3.41208e8i		−	0.429666i	0.976651	−	0.214833i	$-0.0689206\pi$
$350$	1.01258e9	+	1.30375e9i	1.26238	+	1.62538i
$351$	−3.62193e8	−	6.34542e8i	−0.447059	−	0.783223i
$352$	−2.08574e8	−	2.08574e8i	−0.254894	−	0.254894i
$353$	−1.15012e9	−	1.15012e9i	−1.39165	−	1.39165i	−0.821626	−	0.570027i	$-0.806933\pi$
$353$	−1.15012e9	−	1.15012e9i	−1.39165	−	1.39165i	−0.570027	−	0.821626i	$-0.693067\pi$
$354$	5.95321e8	−	1.62730e9i	0.713247	−	1.94965i
$355$	1.14030e9	+	5.58192e8i	1.35276	+	0.662193i
$356$			1.73344e9i			2.03627i
$357$	1.17152e9	−	5.43945e8i	1.36273	−	0.632726i
$358$	2.73252e7	−	2.73252e7i	0.0314755	−	0.0314755i
$359$	8.30194e8			0.946998			0.473499	−	0.880794i	$-0.342991\pi$
$359$	8.30194e8			0.946998			0.473499	+	0.880794i	$0.342991\pi$
$360$	3.99555e8	−	1.02636e9i	0.451354	−	1.15942i
$361$	−4.42724e8			−0.495288
$362$	−1.48291e9	+	1.48291e9i	−1.64299	+	1.64299i
$363$	6.22211e8	−	2.88898e8i	0.682755	−	0.317008i
$364$		−	1.80236e9i		−	1.95879i
$365$	6.69785e7	+	1.95431e8i	0.0720959	+	0.210363i
$366$	3.25997e8	−	8.91110e8i	0.347560	−	0.950052i
$367$	1.64658e8	+	1.64658e8i	0.173881	+	0.173881i	0.788682	−	0.614801i	$-0.210764\pi$
$367$	1.64658e8	+	1.64658e8i	0.173881	+	0.173881i	−0.614801	+	0.788682i	$0.710764\pi$
$368$	4.89956e7	+	4.89956e7i	0.0512496	+	0.0512496i
$369$	−1.65862e7	−	1.40106e7i	−0.0171852	−	0.0145166i
$370$	−2.09139e8	+	4.27239e8i	−0.214649	+	0.438496i
$371$			1.36961e9i			1.39248i
$372$	1.04880e9	+	2.25884e9i	1.05631	+	2.27502i
$373$	−1.69793e7	+	1.69793e7i	−0.0169410	+	0.0169410i	−0.715527	−	0.698586i	$-0.753813\pi$
$373$	−1.69793e7	+	1.69793e7i	−0.0169410	+	0.0169410i	0.698586	+	0.715527i	$0.253813\pi$
$374$	−1.01002e9			−0.998343
$375$	−8.19209e8	+	6.09705e8i	−0.802205	+	0.597049i
$376$	−5.44689e8			−0.528434
$377$	−1.78673e8	+	1.78673e8i	−0.171737	+	0.171737i
$378$	−5.69617e8	+	2.08466e9i	−0.542453	+	1.98525i
$379$		−	1.84386e9i		−	1.73976i	−0.493260	−	0.869882i	$-0.664195\pi$
$379$		−	1.84386e9i		−	1.73976i	0.493260	−	0.869882i	$-0.335805\pi$
$380$	1.00651e9	−	2.05616e9i	0.940973	−	1.92227i
$381$	−9.72434e8	−	3.55749e8i	−0.900789	−	0.329538i
$382$	−3.09260e8	−	3.09260e8i	−0.283859	−	0.283859i
$383$	−3.20580e8	−	3.20580e8i	−0.291569	−	0.291569i	0.546131	−	0.837700i	$-0.316100\pi$
$383$	−3.20580e8	−	3.20580e8i	−0.291569	−	0.291569i	−0.837700	+	0.546131i	$0.816100\pi$
$384$	1.86324e9	+	6.81633e8i	1.67922	+	0.614315i
$385$	2.24008e8	+	6.53615e8i	0.200055	+	0.583726i
$386$		−	2.80765e9i		−	2.48478i
$387$	4.93076e7	+	5.85762e8i	0.0432440	+	0.513728i
$388$	1.95401e7	−	1.95401e7i	0.0169830	−	0.0169830i
$389$	6.95254e8			0.598853			0.299426	−	0.954119i	$-0.403205\pi$
$389$	6.95254e8			0.598853			0.299426	+	0.954119i	$0.403205\pi$
$390$	1.75164e9	+	3.59731e7i	1.49527	+	0.0307080i
$391$	−3.31286e8			−0.280275
$392$	−5.66620e8	+	5.66620e8i	−0.475106	+	0.475106i
$393$	−6.21781e7	−	1.33916e8i	−0.0516730	−	0.111290i
$394$			2.68711e9i			2.21334i
$395$	9.87560e8	+	4.83423e8i	0.806258	+	0.394673i
$396$	6.93987e8	−	8.21561e8i	0.561588	−	0.664824i
$397$	−1.32748e9	−	1.32748e9i	−1.06478	−	1.06478i	−0.997751	−	0.0670285i	$-0.978648\pi$
$397$	−1.32748e9	−	1.32748e9i	−1.06478	−	1.06478i	−0.0670285	−	0.997751i	$-0.521352\pi$
$398$	−5.11231e8	−	5.11231e8i	−0.406468	−	0.406468i
$399$	−6.61518e8	+	1.80825e9i	−0.521358	+	1.42513i
$400$	2.45814e8	+	3.16498e8i	0.192042	+	0.247264i
$401$			8.10449e8i			0.627654i	0.949480	+	0.313827i	$0.101611\pi$
$401$			8.10449e8i			0.627654i	−0.949480	+	0.313827i	$0.898389\pi$
$402$	3.77404e8	−	1.75232e8i	0.289745	−	0.134531i
$403$	−1.20077e9	+	1.20077e9i	−0.913887	+	0.913887i
$404$	−3.65288e9			−2.75613
$405$	−1.28210e9	−	3.78779e8i	−0.959022	−	0.283330i
$406$	7.47385e8			0.554247
$407$	−1.40783e8	+	1.40783e8i	−0.103507	+	0.103507i
$408$	1.87428e9	−	8.70244e8i	1.36623	−	0.634352i
$409$		−	5.96743e8i		−	0.431276i	−0.976473	−	0.215638i	$-0.930817\pi$
$409$		−	5.96743e8i		−	0.431276i	0.976473	−	0.215638i	$-0.0691831\pi$
$410$	4.92509e7	−	1.68793e7i	0.0352916	−	0.0120952i
$411$	−9.33850e7	+	2.55267e8i	−0.0663484	+	0.181363i
$412$	−2.44325e9	−	2.44325e9i	−1.72118	−	1.72118i
$413$	−1.57262e9	−	1.57262e9i	−1.09849	−	1.09849i
$414$	3.57682e8	−	4.23434e8i	0.247740	−	0.293281i
$415$	1.66858e9	−	5.71858e8i	1.14598	−	0.392753i
$416$			9.59994e8i			0.653796i
$417$	1.10627e8	+	2.38261e8i	0.0747108	+	0.160908i
$418$	1.06465e9	−	1.06465e9i	0.713002	−	0.713002i
$419$	7.04325e8			0.467761			0.233881	−	0.972265i	$-0.424858\pi$
$419$	7.04325e8			0.467761			0.233881	+	0.972265i	$0.424858\pi$
$420$	−2.28358e9	−	2.37934e9i	−1.50398	−	1.56705i
$421$	2.61689e9			1.70922			0.854611	−	0.519270i	$-0.173796\pi$
$421$	2.61689e9			1.70922			0.854611	+	0.519270i	$0.173796\pi$
$422$	2.32571e9	−	2.32571e9i	1.50648	−	1.50648i
$423$	5.54576e7	+	6.58823e8i	0.0356262	+	0.423231i
$424$			2.19121e9i			1.39606i
$425$	−1.90105e9	−	2.38967e8i	−1.20125	−	0.151000i
$426$	−3.74291e9	−	1.36928e9i	−2.34572	−	0.858140i
$427$	−8.61164e8	−	8.61164e8i	−0.535289	−	0.535289i
$428$	1.45391e9	+	1.45391e9i	0.896364	+	0.896364i
$429$	6.88669e8	+	2.51938e8i	0.421124	+	0.154061i
$430$	−1.26604e9	−	6.19740e8i	−0.767903	−	0.375898i
$431$			1.64472e9i			0.989513i	0.869032	+	0.494757i	$0.164743\pi$
$431$			1.64472e9i			0.989513i	−0.869032	+	0.494757i	$0.835257\pi$
$432$	−1.38281e8	+	5.06074e8i	−0.0825217	+	0.302010i
$433$	−2.76352e8	+	2.76352e8i	−0.163589	+	0.163589i	−0.784155	−	0.620565i	$-0.786903\pi$
$433$	−2.76352e8	+	2.76352e8i	−0.163589	+	0.163589i	0.620565	+	0.784155i	$0.286903\pi$
$434$	5.02281e9			2.94939
$435$	−9.49307e6	+	4.62246e8i	−0.00552961	+	0.269253i
$436$	−2.26918e8			−0.131119
$437$	3.49205e8	−	3.49205e8i	0.200168	−	0.200168i
$438$	−2.73113e8	−	5.88216e8i	−0.155304	−	0.334486i
$439$			1.73429e9i			0.978353i	0.872185	+	0.489177i	$0.162703\pi$
$439$			1.73429e9i			0.978353i	−0.872185	+	0.489177i	$0.837297\pi$
$440$	3.58384e8	+	1.04570e9i	0.200569	+	0.585226i
$441$	7.43040e8	+	6.27659e8i	0.412551	+	0.348489i
$442$	2.32439e9	+	2.32439e9i	1.28036	+	1.28036i
$443$	8.78428e8	+	8.78428e8i	0.480058	+	0.480058i	0.905150	−	0.425092i	$-0.139758\pi$
$443$	8.78428e8	+	8.78428e8i	0.480058	+	0.480058i	−0.425092	+	0.905150i	$0.639758\pi$
$444$	3.26490e8	−	8.92456e8i	0.177023	−	0.483890i
$445$	−9.50863e8	+	1.94247e9i	−0.511515	+	1.04495i
$446$			5.54671e9i			2.96049i
$447$	−1.55998e9	+	7.24312e8i	−0.826120	+	0.383574i
$448$	2.53068e9	−	2.53068e9i	1.32973	−	1.32973i
$449$	−3.69207e9			−1.92490			−0.962449	−	0.271462i	$-0.912493\pi$
$449$	−3.69207e9			−1.92490			−0.962449	+	0.271462i	$0.912493\pi$
$450$	2.35796e9	−	2.17182e9i	1.21981	−	1.12352i
$451$	2.17911e7			0.0111856
$452$	1.11716e9	−	1.11716e9i	0.569025	−	0.569025i
$453$	4.09602e8	−	1.90181e8i	0.207023	−	0.0961223i
$454$			2.44095e9i			1.22423i
$455$	9.88668e8	−	2.01970e9i	0.492051	−	1.00519i
$456$	−1.05835e9	+	2.89298e9i	−0.522698	+	1.42879i
$457$	1.11621e9	+	1.11621e9i	0.547063	+	0.547063i	0.925590	−	0.378527i	$-0.123569\pi$
$457$	1.11621e9	+	1.11621e9i	0.547063	+	0.547063i	−0.378527	+	0.925590i	$0.623569\pi$
$458$	1.39217e9	+	1.39217e9i	0.677118	+	0.677118i
$459$	−1.24343e9	−	2.17841e9i	−0.600171	−	1.05147i
$460$	2.74234e8	+	8.00167e8i	0.131362	+	0.383291i
$461$		−	2.53272e9i		−	1.20402i	−0.798487	−	0.602011i	$-0.794366\pi$
$461$		−	2.53272e9i		−	1.20402i	0.798487	−	0.602011i	$-0.205634\pi$
$462$	−9.13420e8	−	1.96727e9i	−0.430947	−	0.928148i
$463$	1.61986e9	−	1.61986e9i	0.758481	−	0.758481i	−0.217565	−	0.976046i	$-0.569811\pi$
$463$	1.61986e9	−	1.61986e9i	0.758481	−	0.758481i	0.976046	+	0.217565i	$0.0698115\pi$
$464$	1.81436e8			0.0843160
$465$	−6.37983e7	+	3.10653e9i	−0.0294255	+	1.43282i
$466$	−4.43547e9			−2.03043
$467$	1.38138e9	−	1.38138e9i	0.627631	−	0.627631i	−0.319840	−	0.947471i	$-0.603629\pi$
$467$	1.38138e9	−	1.38138e9i	0.627631	−	0.627631i	0.947471	+	0.319840i	$0.103629\pi$
$468$	−3.48778e9	+	2.93590e8i	−1.57285	+	0.132398i
$469$		−	5.34065e8i		−	0.239050i
$470$	−1.42394e9	−	6.97038e8i	−0.632631	−	0.309681i
$471$	−6.64279e7	−	2.43015e7i	−0.0292939	−	0.0107167i
$472$	−2.51599e9	−	2.51599e9i	−1.10132	−	1.10132i
$473$	−4.17181e8	−	4.17181e8i	−0.181263	−	0.181263i
$474$	−3.24155e9	−	1.18587e9i	−1.39807	−	0.511460i
$475$	2.25577e9	−	1.75198e9i	0.965755	−	0.750071i
$476$		−	6.18760e9i		−	2.62965i
$477$	2.65035e9	−	2.23098e8i	1.11812	−	0.0941199i
$478$	−7.17721e7	+	7.17721e7i	−0.0300578	+	0.0300578i
$479$	4.40903e9			1.83303			0.916513	−	0.400005i	$-0.130992\pi$
$479$	4.40903e9			1.83303			0.916513	+	0.400005i	$0.130992\pi$
$480$	1.21630e9	+	1.26731e9i	0.501993	+	0.523044i
$481$	6.47975e8			0.265492
$482$	−3.84247e9	+	3.84247e9i	−1.56295	+	1.56295i
$483$	−2.99601e8	−	6.45263e8i	−0.120984	−	0.260568i
$484$		−	3.28633e9i		−	1.31751i
$485$	3.26148e7	−	1.11778e7i	0.0129813	−	0.00444898i
$486$	4.12685e9	+	7.62700e8i	1.63077	+	0.301389i
$487$	−2.28543e9	−	2.28543e9i	−0.896639	−	0.896639i	0.0984986	−	0.995137i	$-0.468596\pi$
$487$	−2.28543e9	−	2.28543e9i	−0.896639	−	0.896639i	−0.995137	+	0.0984986i	$0.968596\pi$
$488$	−1.37776e9	−	1.37776e9i	−0.536665	−	0.536665i
$489$	−8.21361e8	+	2.24518e9i	−0.317653	+	0.868301i
$490$	−2.20638e9	+	7.56174e8i	−0.847217	+	0.290359i
$491$		−	2.17713e9i		−	0.830041i	−0.909812	−	0.415021i	$-0.863774\pi$
$491$		−	2.17713e9i		−	0.830041i	0.909812	−	0.415021i	$-0.136226\pi$
$492$	−9.43373e7	+	4.38015e7i	−0.0357113	+	0.0165810i
$493$	−6.13392e8	+	6.13392e8i	−0.230555	+	0.230555i
$494$	−4.90024e9			−1.82883
$495$	1.22833e9	−	5.39949e8i	0.455194	−	0.200094i
$496$	1.21934e9			0.448683
$497$	−3.61713e9	+	3.61713e9i	−1.32165	+	1.32165i
$498$	−5.02215e9	+	2.33182e9i	−1.82216	+	0.846044i
$499$			3.64634e9i			1.31373i	0.754009	+	0.656864i	$0.228117\pi$
$499$			3.64634e9i			1.31373i	−0.754009	+	0.656864i	$0.771883\pi$
$500$	9.96478e8	+	4.78949e9i	0.356511	+	1.71354i
$501$	1.31154e9	−	3.58509e9i	0.465962	−	1.27370i
$502$	5.05549e9	+	5.05549e9i	1.78361	+	1.78361i
$503$	1.92307e9	+	1.92307e9i	0.673763	+	0.673763i	0.958582	−	0.284818i	$-0.0919332\pi$
$503$	1.92307e9	+	1.92307e9i	0.673763	+	0.673763i	−0.284818	+	0.958582i	$0.591933\pi$
$504$	3.39004e9	+	2.86363e9i	1.17950	+	0.996345i
$505$	−4.09336e9	−	2.00375e9i	−1.41436	−	0.692347i
$506$			5.56312e8i			0.190894i
$507$	2.30720e8	+	4.96911e8i	0.0786243	+	0.169336i
$508$	−3.50753e9	+	3.50753e9i	−1.18708	+	1.18708i
$509$	5.80942e9			1.95263			0.976316	−	0.216348i	$-0.0694146\pi$
$509$	5.80942e9			1.95263			0.976316	+	0.216348i	$0.0694146\pi$
$510$	6.01346e9	+	1.23497e8i	2.00738	+	0.0412252i
$511$	−8.32385e8			−0.275963
$512$	1.32392e9	−	1.32392e9i	0.435931	−	0.435931i
$513$	3.60693e9	+	9.85563e8i	1.17958	+	0.322310i
$514$		−	8.71776e9i		−	2.83161i
$515$	−1.39765e9	−	4.07809e9i	−0.450892	−	1.31562i
$516$	2.64461e9	+	9.67485e8i	0.847398	+	0.310006i
$517$	−4.69214e8	−	4.69214e8i	−0.149332	−	0.149332i
$518$	−1.35524e9	−	1.35524e9i	−0.428411	−	0.428411i
$519$	−2.91614e9	−	1.06682e9i	−0.915637	−	0.334970i
$520$	1.58175e9	−	3.23127e9i	0.493316	−	1.00777i
$521$		−	2.41153e9i		−	0.747070i	−0.927616	−	0.373535i	$-0.878146\pi$
$521$		−	2.41153e9i		−	0.747070i	0.927616	−	0.373535i	$-0.121854\pi$
$522$	−1.21743e8	−	1.44628e9i	−0.0374625	−	0.445045i
$523$	−3.60669e9	+	3.60669e9i	−1.10244	+	1.10244i	−0.108320	+	0.994116i	$0.534547\pi$
$523$	−3.60669e9	+	3.60669e9i	−1.10244	+	1.10244i	−0.994116	+	0.108320i	$0.965453\pi$
$524$	−7.07302e8			−0.214756
$525$	−1.25378e9	−	3.91888e9i	−0.378149	−	1.18197i
$526$	2.61955e9			0.784832
$527$	−4.12231e9	+	4.12231e9i	−1.22688	+	1.22688i
$528$	−2.21742e8	−	4.77576e8i	−0.0655586	−	0.141196i
$529$		−	3.22236e9i		−	0.946408i
$530$	−2.80409e9	+	5.72832e9i	−0.818136	+	1.67133i
$531$	−2.78703e9	+	3.29936e9i	−0.807812	+	0.956311i
$532$	6.52229e9	+	6.52229e9i	1.87806	+	1.87806i
$533$	−5.01485e7	−	5.01485e7i	−0.0143454	−	0.0143454i
$534$	2.33252e9	−	6.37593e9i	0.662875	−	1.81196i
$535$	8.31701e8	+	2.42676e9i	0.234817	+	0.685154i
$536$		−	8.54438e8i		−	0.239664i
$537$	−8.73617e7	+	4.05627e7i	−0.0243451	+	0.0113036i
$538$	7.36544e9	−	7.36544e9i	2.03920	−	2.03920i
$539$	−9.76214e8			−0.268525
$540$	−4.23232e9	+	4.80656e9i	−1.15664	+	1.31358i
$541$	−1.51865e9			−0.412352			−0.206176	−	0.978515i	$-0.566102\pi$
$541$	−1.51865e9			−0.412352			−0.206176	+	0.978515i	$0.566102\pi$
$542$	2.53042e9	−	2.53042e9i	0.682646	−	0.682646i
$543$	4.74102e9	−	2.20129e9i	1.27079	−	0.590036i
$544$			3.29571e9i			0.877713i
$545$	−2.54281e8	−	1.24473e8i	−0.0672861	−	0.0329374i
$546$	−2.42526e9	+	6.62942e9i	−0.637653	+	1.74302i
$547$	−1.62510e8	−	1.62510e8i	−0.0424546	−	0.0424546i	0.685561	−	0.728015i	$-0.259557\pi$
$547$	−1.62510e8	−	1.62510e8i	−0.0424546	−	0.0424546i	−0.728015	+	0.685561i	$0.759557\pi$
$548$	9.20736e8	+	9.20736e8i	0.239003	+	0.239003i
$549$	−1.52617e9	+	1.80673e9i	−0.393641	+	0.466004i
$550$	−4.01285e8	+	3.19234e9i	−0.102845	+	0.818162i
$551$		−	1.29314e9i		−	0.329318i
$552$	−4.79324e8	−	1.03234e9i	−0.121295	−	0.261238i
$553$	−3.13262e9	+	3.13262e9i	−0.787716	+	0.787716i
$554$	−8.67360e8			−0.216728
$555$	8.55407e8	−	8.20979e8i	0.212396	−	0.203848i
$556$	1.25842e9			0.310503
$557$	5.10273e9	−	5.10273e9i	1.25115	−	1.25115i	0.295944	−	0.955205i	$-0.404366\pi$
$557$	5.10273e9	−	5.10273e9i	1.25115	−	1.25115i	0.955205	−	0.295944i	$-0.0956340\pi$
$558$	−8.18174e8	−	9.71971e9i	−0.199354	−	2.36828i
$559$			1.92014e9i			0.464935i
$560$	−1.52744e9	+	5.23488e8i	−0.367542	+	0.125965i
$561$	2.36423e9	+	8.64914e8i	0.565354	+	0.206825i
$562$	−5.20428e9	−	5.20428e9i	−1.23675	−	1.23675i
$563$	1.01937e8	+	1.01937e8i	0.0240743	+	0.0240743i	0.719041	−	0.694967i	$-0.244581\pi$
$563$	1.01937e8	+	1.01937e8i	0.0240743	+	0.0240743i	−0.694967	+	0.719041i	$0.744581\pi$
$564$	2.97446e9	+	1.08816e9i	0.698122	+	0.255396i
$565$	1.86468e9	−	6.39066e8i	0.434946	−	0.149065i
$566$		−	3.80641e9i		−	0.882384i
$567$	3.11851e9	−	4.39195e9i	0.718467	−	1.01185i
$568$	−5.78696e9	+	5.78696e9i	−1.32505	+	1.32505i
$569$	−7.01526e9			−1.59643			−0.798217	−	0.602370i	$-0.794223\pi$
$569$	−7.01526e9			−1.59643			−0.798217	+	0.602370i	$0.794223\pi$
$570$	−6.46891e9	+	6.20856e9i	−1.46308	+	1.40420i
$571$	4.86912e9			1.09452			0.547261	−	0.836962i	$-0.315671\pi$
$571$	4.86912e9			1.09452			0.547261	+	0.836962i	$0.315671\pi$
$572$	2.48400e9	−	2.48400e9i	0.554964	−	0.554964i
$573$	4.59079e8	+	9.88738e8i	0.101940	+	0.219553i
$574$			2.09770e8i			0.0462969i
$575$	−1.31621e8	+	1.04708e9i	−0.0288727	+	0.229691i
$576$	−5.30937e9	−	4.48492e9i	−1.15762	−	0.977858i
$577$	4.33343e9	+	4.33343e9i	0.939110	+	0.939110i	0.998250	−	0.0591397i	$-0.0188358\pi$
$577$	4.33343e9	+	4.33343e9i	0.939110	+	0.939110i	−0.0591397	+	0.998250i	$0.518836\pi$
$578$	2.53576e9	+	2.53576e9i	0.546211	+	0.546211i
$579$	−2.40428e9	+	6.57208e9i	−0.514767	+	1.40711i
$580$	1.98931e9	+	9.73790e8i	0.423354	+	0.207237i
$581$			7.10684e9i			1.50335i
$582$	−9.81652e7	+	4.55789e7i	−0.0206408	+	0.00958370i
$583$	−1.88758e9	+	1.88758e9i	−0.394517	+	0.394517i
$584$	−1.33171e9			−0.276672
$585$	−4.06939e9	−	1.58419e9i	−0.840396	−	0.327162i
$586$	−1.13542e10			−2.33086
$587$	−3.69878e9	+	3.69878e9i	−0.754788	+	0.754788i	−0.975369	−	0.220581i	$-0.929205\pi$
$587$	−3.69878e9	+	3.69878e9i	−0.754788	+	0.754788i	0.220581	+	0.975369i	$0.429205\pi$
$588$	4.22620e9	−	1.96226e9i	0.857292	−	0.398048i
$589$		−	8.69057e9i		−	1.75245i
$590$	−3.35768e9	−	9.79712e9i	−0.673065	−	1.96389i
$591$	2.30106e9	−	6.28992e9i	0.458534	−	1.25340i
$592$	−3.28998e8	−	3.28998e8i	−0.0651729	−	0.0651729i
$593$	4.68655e9	+	4.68655e9i	0.922915	+	0.922915i	0.997234	−	0.0743193i	$-0.0236784\pi$
$593$	4.68655e9	+	4.68655e9i	0.922915	+	0.922915i	−0.0743193	+	0.997234i	$0.523678\pi$
$594$	−3.65811e9	+	2.08802e9i	−0.716149	+	0.408774i
$595$	3.39414e9	−	6.93372e9i	0.660573	−	1.34945i
$596$			8.23935e9i			1.59416i
$597$	7.58893e8	+	1.63446e9i	0.145972	+	0.314387i
$598$	1.28026e9	−	1.28026e9i	0.244818	−	0.244818i
$599$	2.03377e9			0.386641			0.193321	−	0.981136i	$-0.438074\pi$
$599$	2.03377e9			0.386641			0.193321	+	0.981136i	$0.438074\pi$
$600$	−2.00589e9	−	6.26973e9i	−0.379121	−	1.18500i
$601$	7.28550e9			1.36899			0.684493	−	0.729020i	$-0.260024\pi$
$601$	7.28550e9			1.36899			0.684493	+	0.729020i	$0.260024\pi$
$602$	4.01596e9	−	4.01596e9i	0.750243	−	0.750243i
$603$	−1.03348e9	+	8.69947e7i	−0.191951	+	0.0161578i
$604$		−	2.16339e9i		−	0.399490i
$605$	1.80268e9	−	3.68261e9i	0.330960	−	0.676102i
$606$	1.34360e10	+	4.91532e9i	2.45253	+	0.897217i
$607$	−5.62222e9	−	5.62222e9i	−1.02035	−	1.02035i	−0.999789	−	0.0205564i	$-0.993456\pi$
$607$	−5.62222e9	−	5.62222e9i	−1.02035	−	1.02035i	−0.0205564	−	0.999789i	$-0.506544\pi$
$608$	−3.47397e9	−	3.47397e9i	−0.626850	−	0.626850i
$609$	−1.74946e9	−	6.40011e8i	−0.313866	−	0.114822i
$610$	−1.83866e9	−	5.36489e9i	−0.327980	−	0.956988i
$611$			2.15963e9i			0.383033i
$612$	−1.19737e10	+	1.00791e9i	−2.11154	+	0.177742i
$613$	−3.93275e8	+	3.93275e8i	−0.0689581	+	0.0689581i	−0.740745	−	0.671787i	$-0.765527\pi$
$613$	−3.93275e8	+	3.93275e8i	−0.0689581	+	0.0689581i	0.671787	+	0.740745i	$0.265527\pi$
$614$	1.39153e10			2.42608
$615$	−1.29740e8	−	2.66444e6i	−0.0224911	−	0.000461895i
$616$	−4.45387e9			−0.767724
$617$	1.08006e8	−	1.08006e8i	0.0185119	−	0.0185119i	−0.697790	−	0.716302i	$-0.745833\pi$
$617$	1.08006e8	−	1.08006e8i	0.0185119	−	0.0185119i	0.716302	+	0.697790i	$0.245833\pi$
$618$	5.69909e9	+	1.22744e10i	0.971282	+	2.09189i
$619$			6.81497e9i			1.15491i	0.816424	+	0.577453i	$0.195953\pi$
$619$			6.81497e9i			1.15491i	−0.816424	+	0.577453i	$0.804047\pi$
$620$	1.33692e10	+	6.54437e9i	2.25285	+	1.10280i
$621$	−1.19985e9	+	6.84870e8i	−0.201052	+	0.114759i
$622$	−4.43049e8	−	4.43049e8i	−0.0738220	−	0.0738220i
$623$	−6.16166e9	−	6.16166e9i	−1.02092	−	1.02092i
$624$	−5.88758e8	+	1.60936e9i	−0.0970042	+	0.265160i
$625$	−1.51059e9	+	5.91363e9i	−0.247494	+	0.968889i
$626$		−	7.06317e9i		−	1.15077i
$627$	−3.40381e9	+	1.58042e9i	−0.551479	+	0.256056i
$628$	−2.39603e8	+	2.39603e8i	−0.0386040	+	0.0386040i
$629$	2.22453e9			0.356419
$630$	5.19778e9	+	1.18244e10i	0.828182	+	1.88403i
$631$	1.75898e8			0.0278713			0.0139357	−	0.999903i	$-0.495564\pi$
$631$	1.75898e8			0.0278713			0.0139357	+	0.999903i	$0.495564\pi$
$632$	−5.01180e9	+	5.01180e9i	−0.789740	+	0.789740i
$633$	−7.43555e9	+	3.45239e9i	−1.16520	+	0.541011i
$634$			7.28983e9i			1.13607i
$635$	−5.85450e9	+	2.00646e9i	−0.907365	+	0.310973i
$636$	4.37750e9	−	1.19658e10i	0.674724	−	1.84435i
$637$	2.24659e9	+	2.24659e9i	0.344378	+	0.344378i
$638$	1.03004e9	+	1.03004e9i	0.157029	+	0.157029i
$639$	7.58875e9	+	6.41035e9i	1.15058	+	0.971916i
$640$	1.12175e10	−	3.84449e9i	1.69148	−	0.579707i
$641$			8.24640e9i			1.23669i	0.785906	+	0.618346i	$0.212197\pi$
$641$			8.24640e9i			1.23669i	−0.785906	+	0.618346i	$0.787803\pi$
$642$	−3.39137e9	−	7.30414e9i	−0.505827	−	1.08942i
$643$	5.92462e9	−	5.92462e9i	0.878864	−	0.878864i	−0.114553	−	0.993417i	$-0.536544\pi$
$643$	5.92462e9	−	5.92462e9i	0.878864	−	0.878864i	0.993417	+	0.114553i	$0.0365436\pi$
$644$	−3.40808e9			−0.502817
$645$	2.43280e9	+	2.53482e9i	0.356983	+	0.371953i
$646$	−1.68228e10			−2.45518
$647$	−2.44814e8	+	2.44814e8i	−0.0355362	+	0.0355362i	−0.724652	−	0.689115i	$-0.757999\pi$
$647$	−2.44814e8	+	2.44814e8i	−0.0355362	+	0.0355362i	0.689115	+	0.724652i	$0.257999\pi$
$648$	4.98924e9	−	7.02658e9i	0.720314	−	1.01445i
$649$		−	4.33473e9i		−	0.622452i
$650$	8.27011e9	−	6.42313e9i	1.18118	−	0.917382i
$651$	−1.17573e10	−	4.30120e9i	−1.67022	−	0.611021i
$652$	8.09827e9	+	8.09827e9i	1.14426	+	1.14426i
$653$	2.61385e9	+	2.61385e9i	0.367354	+	0.367354i	0.866511	−	0.499157i	$-0.166357\pi$
$653$	2.61385e9	+	2.61385e9i	0.367354	+	0.367354i	−0.499157	+	0.866511i	$0.666357\pi$
$654$	8.34646e8	+	3.05341e8i	0.116676	+	0.0426838i
$655$	−7.92592e8	−	3.87984e8i	−0.110206	−	0.0539472i
$656$			5.09240e7i			0.00704302i
$657$	1.35589e8	+	1.61076e9i	0.0186528	+	0.221591i
$658$	4.51686e9	−	4.51686e9i	0.618082	−	0.618082i
$659$	−2.23874e9			−0.304722			−0.152361	−	0.988325i	$-0.548688\pi$
$659$	−2.23874e9			−0.304722			−0.152361	+	0.988325i	$0.548688\pi$
$660$	1.31978e8	−	6.42639e9i	0.0178688	−	0.870088i
$661$	−4.36686e9			−0.588118			−0.294059	−	0.955787i	$-0.595006\pi$
$661$	−4.36686e9			−0.588118			−0.294059	+	0.955787i	$0.595006\pi$
$662$	9.34010e8	−	9.34010e8i	0.125126	−	0.125126i
$663$	−3.45043e9	−	7.43134e9i	−0.459807	−	0.990306i
$664$			1.13701e10i			1.50721i
$665$	3.73104e9	+	1.08865e10i	0.491987	+	1.43553i
$666$	−2.40178e9	+	2.84329e9i	−0.315046	+	0.372960i
$667$	3.37852e8	+	3.37852e8i	0.0440845	+	0.0440845i
$668$	−1.29313e10	−	1.29313e10i	−1.67851	−	1.67851i
$669$	4.74983e9	−	1.29836e10i	0.613320	−	1.67650i
$670$	1.09342e9	−	2.23370e9i	0.140452	−	0.286921i
$671$		−	2.37370e9i		−	0.303317i
$672$	−6.41923e9	+	2.98050e9i	−0.816000	+	0.378875i
$673$	2.24949e9	−	2.24949e9i	0.284466	−	0.284466i	−0.550421	−	0.834887i	$-0.685533\pi$
$673$	2.24949e9	−	2.24949e9i	0.284466	−	0.284466i	0.834887	+	0.550421i	$0.185533\pi$
$674$	−2.48596e10			−3.12741
$675$	−7.37926e9	+	3.06456e9i	−0.923526	+	0.383535i
$676$	2.62453e9			0.326767
$677$	−9.30302e8	+	9.30302e8i	−0.115229	+	0.115229i	−0.762370	−	0.647141i	$-0.775965\pi$
$677$	−9.30302e8	+	9.30302e8i	−0.115229	+	0.115229i	0.647141	+	0.762370i	$0.275965\pi$
$678$	−5.61238e9	+	2.60587e9i	−0.691582	+	0.321107i
$679$			1.38914e8i			0.0170294i
$680$	5.43021e9	−	1.10931e10i	0.662271	−	1.35292i
$681$	2.09027e9	−	5.71372e9i	0.253622	−	0.693272i
$682$	6.92239e9	+	6.92239e9i	0.835623	+	0.835623i
$683$	−8.26978e9	−	8.26978e9i	−0.993166	−	0.993166i	0.00681121	−	0.999977i	$-0.497832\pi$
$683$	−8.26978e9	−	8.26978e9i	−0.993166	−	0.993166i	−0.999977	+	0.00681121i	$0.997832\pi$
$684$	1.15589e10	−	1.36838e10i	1.38109	−	1.63497i
$685$	5.26702e8	+	1.53682e9i	0.0626106	+	0.182687i
$686$			8.00398e9i			0.946611i
$687$	−2.06660e9	−	4.45093e9i	−0.243169	−	0.523724i
$688$	9.74918e8	−	9.74918e8i	0.114132	−	0.114132i
$689$	8.68790e9			1.01192
$690$	6.80215e7	−	3.31217e9i	0.00788269	−	0.383832i
$691$	−1.33347e10			−1.53749			−0.768744	−	0.639557i	$-0.779118\pi$
$691$	−1.33347e10			−1.53749			−0.768744	+	0.639557i	$0.779118\pi$
$692$	−1.05184e10	+	1.05184e10i	−1.20664	+	1.20664i
$693$	4.53472e8	+	5.38713e9i	0.0517588	+	0.614882i
$694$			7.28952e9i			0.827829i
$695$	1.41017e9	+	6.90296e8i	0.159340	+	0.0779989i
$696$	−2.79892e9	−	1.02394e9i	−0.314672	−	0.115118i
$697$	−1.72162e8	−	1.72162e8i	−0.0192585	−	0.0192585i
$698$	4.52683e9	+	4.52683e9i	0.503849	+	0.503849i
$699$	1.03824e10	+	3.79824e9i	1.14982	+	0.420642i
$700$	−1.95569e10	−	2.45836e9i	−2.15505	−	0.270895i
$701$		−	7.64678e9i		−	0.838428i	−0.907888	−	0.419214i	$-0.862306\pi$
$701$		−	7.64678e9i		−	0.838428i	0.907888	−	0.419214i	$-0.137694\pi$
$702$	1.32237e10	+	3.61328e9i	1.44270	+	0.394204i
$703$	−2.34486e9	+	2.34486e9i	−0.254550	+	0.254550i
$704$	6.97551e9			0.753479
$705$	2.73624e9	+	2.85098e9i	0.294098	+	0.306431i
$706$	3.05174e10			3.26385
$707$	1.29844e10	−	1.29844e10i	1.38183	−	1.38183i
$708$	8.71311e9	+	1.87658e10i	0.922692	+	1.98724i
$709$			1.18117e7i			0.00124466i	1.00000		0.000622328i	$0.000198093\pi$
$709$			1.18117e7i			0.00124466i	−1.00000		0.000622328i	$0.999802\pi$
$710$	−2.25340e10	+	7.72289e9i	−2.36284	+	0.809796i
$711$	6.57225e9	+	5.55169e9i	0.685757	+	0.579271i
$712$	−9.85790e9	−	9.85790e9i	−1.02354	−	1.02354i
$713$	2.27054e9	+	2.27054e9i	0.234593	+	0.234593i
$714$	−8.32604e9	+	2.27591e10i	−0.856041	+	2.33998i
$715$	4.14610e9	−	1.42096e9i	0.424198	−	0.145382i
$716$			4.61418e8i			0.0469785i
$717$	2.29463e8	−	1.06542e8i	0.0232486	−	0.0107945i
$718$	−1.10142e10	+	1.10142e10i	−1.11050	+	1.11050i
$719$	−1.41252e9			−0.141724			−0.0708618	−	0.997486i	$-0.522575\pi$
$719$	−1.41252e9			−0.141724			−0.0708618	+	0.997486i	$0.522575\pi$
$720$	1.26182e9	+	2.87051e9i	0.125989	+	0.286612i
$721$	1.73695e10			1.72589
$722$	5.87365e9	−	5.87365e9i	0.580801	−	0.580801i
$723$	1.22848e10	−	5.70392e9i	1.20888	−	0.561293i
$724$		−	2.50406e10i		−	2.45223i
$725$	1.69502e9	+	2.18243e9i	0.165193	+	0.212695i
$726$	−4.42209e9	+	1.20877e10i	−0.428894	+	1.17238i
$727$	−6.14138e9	−	6.14138e9i	−0.592783	−	0.592783i	0.345599	−	0.938382i	$-0.387676\pi$
$727$	−6.14138e9	−	6.14138e9i	−0.592783	−	0.592783i	−0.938382	+	0.345599i	$0.887676\pi$
$728$	1.02498e10	+	1.02498e10i	0.984594	+	0.984594i
$729$	−9.00691e9	−	5.31927e9i	−0.861052	−	0.508517i
$730$	−3.48141e9	−	1.70419e9i	−0.331226	−	0.162139i
$731$			6.59194e9i			0.624169i
$732$	4.77129e9	+	1.02761e10i	0.449622	+	0.968369i
$733$	−3.98048e9	+	3.98048e9i	−0.373312	+	0.373312i	−0.868682	−	0.495370i	$-0.835032\pi$
$733$	−3.98048e9	+	3.98048e9i	−0.373312	+	0.373312i	0.495370	+	0.868682i	$0.335032\pi$
$734$	−4.36906e9			−0.407804
$735$	5.81219e9	+	1.19364e8i	0.539925	+	0.0110884i
$736$	1.81525e9			0.167828
$737$	7.36043e8	−	7.36043e8i	0.0677278	−	0.0677278i
$738$	4.05929e8	−	3.41698e7i	0.0371752	−	0.00312929i
$739$			2.14990e8i			0.0195958i	0.999952	+	0.00979791i	$0.00311882\pi$
$739$			2.14990e8i			0.0195958i	−0.999952	+	0.00979791i	$0.996881\pi$
$740$	−1.84144e9	−	5.37299e9i	−0.167050	−	0.487422i
$741$	1.14704e10	+	4.19624e9i	1.03565	+	0.378875i
$742$	−1.81707e10	−	1.81707e10i	−1.63289	−	1.63289i
$743$	−1.92927e9	−	1.92927e9i	−0.172557	−	0.172557i	0.615545	−	0.788102i	$-0.288936\pi$
$743$	−1.92927e9	−	1.92927e9i	−0.172557	−	0.172557i	−0.788102	+	0.615545i	$0.788936\pi$
$744$	−1.88102e10	−	6.88139e9i	−1.67451	−	0.612591i
$745$	−4.51961e9	+	9.23289e9i	−0.400455	+	0.818070i
$746$		−	4.50530e8i		−	0.0397318i
$747$	1.37526e10	−	1.15765e9i	1.20715	−	0.101614i
$748$	8.52769e9	−	8.52769e9i	0.745033	−	0.745033i
$749$	−1.03361e10			−0.898813
$750$	2.77951e9	−	1.89575e10i	0.240577	−	1.64084i
$751$	−5.80970e9			−0.500511			−0.250256	−	0.968180i	$-0.580515\pi$
$751$	−5.80970e9			−0.500511			−0.250256	+	0.968180i	$0.580515\pi$
$752$	1.09652e9	−	1.09652e9i	0.0940270	−	0.0940270i
$753$	−7.50459e9	−	1.61630e10i	−0.640538	−	1.37955i
$754$		−	4.74092e9i		−	0.402775i
$755$	1.18671e9	−	2.42426e9i	0.100353	−	0.205005i
$756$	−1.27917e10	−	2.24103e10i	−1.07672	−	1.88635i
$757$	−6.47878e9	−	6.47878e9i	−0.542822	−	0.542822i	0.381533	−	0.924355i	$-0.375396\pi$
$757$	−6.47878e9	−	6.47878e9i	−0.542822	−	0.542822i	−0.924355	+	0.381533i	$0.875396\pi$
$758$	2.44626e10	+	2.44626e10i	2.04014	+	2.04014i
$759$	4.76388e8	−	1.30220e9i	0.0395471	−	0.108102i
$760$	5.96920e9	+	1.74171e10i	0.493252	+	1.43922i
$761$		−	1.29566e10i		−	1.06573i	−0.846202	−	0.532863i	$-0.821116\pi$
$761$		−	1.29566e10i		−	1.06573i	0.846202	−	0.532863i	$-0.178884\pi$
$762$	1.76211e10	−	8.18161e9i	1.44275	−	0.669879i
$763$	8.06597e8	−	8.06597e8i	0.0657387	−	0.0657387i
$764$	5.22222e9			0.423670
$765$	−1.39704e10	−	5.43861e9i	−1.12822	−	0.439211i
$766$	8.50632e9			0.683819
$767$	−9.97566e9	+	9.97566e9i	−0.798284	+	0.798284i
$768$	−1.65091e10	+	7.66531e9i	−1.31510	+	0.610612i
$769$		−	7.79627e9i		−	0.618222i	−0.951026	−	0.309111i	$-0.899969\pi$
$769$		−	7.79627e9i		−	0.618222i	0.951026	−	0.309111i	$-0.100031\pi$
$770$	−1.16435e10	−	5.69962e9i	−0.919104	−	0.449913i
$771$	−7.46530e9	+	2.04063e10i	−0.586620	+	1.60352i
$772$	2.37052e10	+	2.37052e10i	1.85431	+	1.85431i
$773$	3.18561e9	+	3.18561e9i	0.248064	+	0.248064i	0.820176	−	0.572112i	$-0.193876\pi$
$773$	3.18561e9	+	3.18561e9i	0.248064	+	0.248064i	−0.572112	+	0.820176i	$0.693876\pi$
$774$	−8.42551e9	−	7.11718e9i	−0.653135	−	0.551715i
$775$	1.13914e10	+	1.46670e10i	0.879067	+	1.13184i
$776$			2.22245e8i			0.0170732i
$777$	2.01177e9	+	4.33284e9i	0.153853	+	0.331359i
$778$	−9.22398e9	+	9.22398e9i	−0.702247	+	0.702247i
$779$	3.62949e8			0.0275083
$780$	−1.50930e10	+	1.44855e10i	−1.13879	+	1.09296i
$781$	−9.97018e9			−0.748901
$782$	4.39519e9	−	4.39519e9i	0.328665	−	0.328665i
$783$	−9.53521e8	+	3.48966e9i	−0.0709846	+	0.259787i
$784$		−	2.28133e9i		−	0.169076i
$785$	−3.99927e8	+	1.37063e8i	−0.0295078	+	0.0101129i
$786$	2.60159e9	+	9.51747e8i	0.191100	+	0.0699105i
$787$	1.61942e10	+	1.61942e10i	1.18426	+	1.18426i	0.978630	+	0.205629i	$0.0659240\pi$
$787$	1.61942e10	+	1.61942e10i	1.18426	+	1.18426i	0.205629	+	0.978630i	$0.434076\pi$
$788$	−2.26875e10	−	2.26875e10i	−1.65175	−	1.65175i
$789$	−6.13178e9	−	2.24321e9i	−0.444444	−	0.162592i
$790$	−1.95156e10	+	6.68842e9i	−1.40828	+	0.482646i
$791$			7.94208e9i			0.570580i
$792$	7.25499e8	+	8.61875e9i	0.0518918	+	0.616462i
$793$	−5.46266e9	+	5.46266e9i	−0.388999	+	0.388999i
$794$	3.52234e10			2.49724
$795$	1.14691e10	−	1.10075e10i	0.809551	−	0.776969i
$796$	8.63273e9			0.606670
$797$	5.91307e9	−	5.91307e9i	0.413723	−	0.413723i	−0.469311	−	0.883033i	$-0.655498\pi$
$797$	5.91307e9	−	5.91307e9i	0.413723	−	0.413723i	0.883033	+	0.469311i	$0.155498\pi$
$798$	−1.52138e10	−	3.27666e10i	−1.05981	−	2.28255i
$799$			7.41413e9i			0.514217i
$800$	1.04166e10	+	1.30940e9i	0.719303	+	0.0904183i
$801$	−1.09198e10	+	1.29272e10i	−0.750762	+	0.888773i
$802$	−1.07523e10	−	1.07523e10i	−0.736021	−	0.736021i
$803$	−1.14718e9	−	1.14718e9i	−0.0781860	−	0.0781860i
$804$	−1.70696e9	+	4.66595e9i	−0.115832	+	0.316624i
$805$	−3.81904e9	−	1.86947e9i	−0.258029	−	0.126309i
$806$		−	3.18614e10i		−	2.14335i
$807$	−2.35481e10	+	1.09336e10i	−1.57724	+	0.732327i
$808$	2.07735e10	−	2.07735e10i	1.38538	−	1.38538i
$809$	−4.74682e9			−0.315198			−0.157599	−	0.987503i	$-0.550375\pi$
$809$	−4.74682e9			−0.315198			−0.157599	+	0.987503i	$0.550375\pi$
$810$	2.20350e10	−	1.19844e10i	1.45685	−	0.792353i
$811$	−1.40599e10			−0.925571			−0.462785	−	0.886470i	$-0.653150\pi$
$811$	−1.40599e10			−0.925571			−0.462785	+	0.886470i	$0.653150\pi$
$812$	−6.31023e9	+	6.31023e9i	−0.413618	+	0.413618i
$813$	−8.09004e9	+	3.75627e9i	−0.528000	+	0.245154i
$814$		−	3.73555e9i		−	0.242755i
$815$	4.63257e9	+	1.35170e10i	0.299758	+	0.874640i
$816$	−2.02123e9	+	5.52502e9i	−0.130227	+	0.355974i
$817$	−6.94850e9	−	6.94850e9i	−0.445773	−	0.445773i
$818$	7.91702e9	+	7.91702e9i	0.505738	+	0.505738i
$819$	1.13540e10	−	1.34412e10i	0.722196	−	0.854955i
$820$	−2.73316e8	+	5.58343e8i	−0.0173108	+	0.0353633i
$821$		−	2.47030e10i		−	1.55793i	−0.627067	−	0.778965i	$-0.715745\pi$
$821$		−	2.47030e10i		−	1.55793i	0.627067	−	0.778965i	$-0.284255\pi$
$822$	−2.14769e9	−	4.62558e9i	−0.134872	−	0.290479i
$823$	1.41479e10	−	1.41479e10i	0.884691	−	0.884691i	−0.109316	−	0.994007i	$-0.534866\pi$
$823$	1.41479e10	−	1.41479e10i	0.884691	−	0.884691i	0.994007	+	0.109316i	$0.0348660\pi$
$824$	2.77890e10			1.73032
$825$	3.67302e9	−	7.12891e9i	0.227738	−	0.442012i
$826$	4.17280e10			2.57631
$827$	−2.82797e6	+	2.82797e6i	−0.000173862	+	0.000173862i	−0.707194	−	0.707020i	$-0.750039\pi$
$827$	−2.82797e6	+	2.82797e6i	−0.000173862	+	0.000173862i	0.707020	+	0.707194i	$0.250039\pi$
$828$	5.55148e8	+	6.59503e9i	0.0339862	+	0.403748i
$829$			1.28461e10i			0.783126i	0.920151	+	0.391563i	$0.128065\pi$
$829$			1.28461e10i			0.783126i	−0.920151	+	0.391563i	$0.871935\pi$
$830$	−1.45503e10	+	2.97240e10i	−0.883280	+	1.80441i
$831$	2.03030e9	+	7.42749e8i	0.122731	+	0.0448992i
$832$	−1.60529e10	−	1.60529e10i	−0.966325	−	0.966325i
$833$	7.71265e9	+	7.71265e9i	0.462324	+	0.462324i
$834$	−4.62872e9	−	1.69334e9i	−0.276299	−	0.101079i
$835$	−7.39725e9	−	2.15839e10i	−0.439712	−	1.28300i
$836$			1.79779e10i			1.06418i
$837$	−6.40815e9	+	2.34523e10i	−0.377740	+	1.38244i
$838$	−9.34432e9	+	9.34432e9i	−0.548522	+	0.548522i
$839$	−2.82762e10			−1.65293			−0.826464	−	0.562989i	$-0.809651\pi$
$839$	−2.82762e10			−1.65293			−0.826464	+	0.562989i	$0.809651\pi$
$840$	2.65175e10	+	5.44585e8i	1.54367	+	0.0317021i
$841$	−1.59988e10			−0.927472
$842$	−3.47184e10	+	3.47184e10i	−2.00432	+	2.00432i
$843$	7.72545e9	+	1.66386e10i	0.444148	+	0.956580i
$844$			3.92723e10i			2.24848i
$845$	2.94101e9	+	1.43966e9i	0.167686	+	0.0820846i
$846$	−9.47640e9	−	8.00488e9i	−0.538080	−	0.454526i
$847$	1.16815e10	+	1.16815e10i	0.660553	+	0.660553i
$848$	−4.41113e9	−	4.41113e9i	−0.248407	−	0.248407i
$849$	−3.25955e9	+	8.90995e9i	−0.182802	+	0.499687i
$850$	2.83917e10	−	2.20509e10i	1.58571	−	1.23157i
$851$		−	1.22526e9i		−	0.0681512i
$852$	4.31626e10	−	2.00407e10i	2.39094	−	1.11013i
$853$	1.54968e10	−	1.54968e10i	0.854910	−	0.854910i	−0.135823	−	0.990733i	$-0.543368\pi$
$853$	1.54968e10	−	1.54968e10i	0.854910	−	0.854910i	0.990733	+	0.135823i	$0.0433678\pi$
$854$	2.28502e10			1.25542
$855$	2.04589e10	−	8.99330e9i	1.11944	−	0.492082i
$856$	−1.65365e10			−0.901123
$857$	1.33885e10	−	1.33885e10i	0.726609	−	0.726609i	−0.243334	−	0.969943i	$-0.578241\pi$
$857$	1.33885e10	−	1.33885e10i	0.726609	−	0.726609i	0.969943	+	0.243334i	$0.0782411\pi$
$858$	−1.24791e10	+	5.79414e9i	−0.674492	+	0.313172i
$859$		−	4.72940e8i		−	0.0254583i	−0.999919	−	0.0127292i	$-0.995948\pi$
$859$		−	4.72940e8i		−	0.0254583i	0.999919	−	0.0127292i	$-0.00405193\pi$
$860$	1.59218e10	−	5.45672e9i	0.853584	−	0.292541i
$861$	1.79633e8	−	4.91025e8i	0.00959126	−	0.0262176i
$862$	−2.18206e10	−	2.18206e10i	−1.16036	−	1.16036i
$863$	1.29050e10	+	1.29050e10i	0.683473	+	0.683473i	0.960781	−	0.277308i	$-0.0894422\pi$
$863$	1.29050e10	+	1.29050e10i	0.683473	+	0.683473i	−0.277308	+	0.960781i	$0.589442\pi$
$864$	6.81324e9	+	1.19364e10i	0.359381	+	0.629617i
$865$	−1.75565e10	+	6.01699e9i	−0.922321	+	0.316099i
$866$		−	7.33276e9i		−	0.383667i
$867$	−3.76419e9	−	8.10711e9i	−0.196158	−	0.422473i
$868$	−4.24080e10	+	4.24080e10i	−2.20104	+	2.20104i
$869$	−8.63469e9			−0.446352
$870$	−6.00671e9	−	6.25860e9i	−0.309257	−	0.322225i
$871$	−3.38776e9			−0.173720
$872$	1.29046e9	−	1.29046e9i	0.0659076	−	0.0659076i
$873$	2.68814e8	−	2.26279e7i	0.0136742	−	0.00115105i
$874$			9.26585e9i			0.469456i
$875$	−2.05667e10	−	1.34825e10i	−1.03785	−	0.680368i
$876$	7.27228e9	+	2.66044e9i	0.365516	+	0.133718i
$877$	2.11418e10	+	2.11418e10i	1.05838	+	1.05838i	0.998186	+	0.0601979i	$0.0191732\pi$
$877$	2.11418e10	+	2.11418e10i	1.05838	+	1.05838i	0.0601979	+	0.998186i	$0.480827\pi$
$878$	−2.30089e10	−	2.30089e10i	−1.14727	−	1.14727i
$879$	2.65777e10	+	9.72302e9i	1.31995	+	0.482881i
$880$	−2.82658e9	−	1.38364e9i	−0.139821	−	0.0684439i
$881$		−	7.02407e9i		−	0.346077i	−0.984915	−	0.173039i	$-0.944641\pi$
$881$		−	7.02407e9i		−	0.346077i	0.984915	−	0.173039i	$-0.0553585\pi$
$882$	−1.81851e10	+	1.53077e9i	−0.892435	+	0.0751224i
$883$	2.00482e10	−	2.00482e10i	0.979969	−	0.979969i	−0.0198342	−	0.999803i	$-0.506314\pi$
$883$	2.00482e10	−	2.00482e10i	0.979969	−	0.979969i	0.999803	+	0.0198342i	$0.00631384\pi$
$884$	−3.92501e10			−1.91099
$885$	−5.30018e8	+	2.58082e10i	−0.0257033	+	1.25157i
$886$	−2.33083e10			−1.12588
$887$	−1.40958e9	+	1.40958e9i	−0.0678201	+	0.0678201i	−0.740203	−	0.672383i	$-0.765271\pi$
$887$	−1.40958e9	+	1.40958e9i	−0.0678201	+	0.0678201i	0.672383	+	0.740203i	$0.265271\pi$
$888$	3.21859e9	+	6.93201e9i	0.154248	+	0.332211i
$889$		−	2.49356e10i		−	1.19032i
$890$	−1.31557e10	−	3.83860e10i	−0.625531	−	1.82519i
$891$	1.03509e10	−	1.75504e9i	0.490235	−	0.0831218i
$892$	−4.68313e10	−	4.68313e10i	−2.20932	−	2.20932i
$893$	−7.81516e9	−	7.81516e9i	−0.367247	−	0.367247i
$894$	1.10869e10	−	3.03059e10i	0.518953	−	1.41855i
$895$	−2.53106e8	+	5.17058e8i	−0.0118011	+	0.0241079i
$896$			4.77779e10i			2.21896i
$897$	−4.09313e9	+	1.90047e9i	−0.189357	+	0.0879200i
$898$	4.89829e10	−	4.89829e10i	2.25724	−	2.25724i
$899$	8.40802e9			0.385953
$900$	−1.57154e9	+	3.82453e10i	−0.0718581	+	1.74876i
$901$	2.98260e10			1.35850
$902$	−2.89103e8	+	2.89103e8i	−0.0131169	+	0.0131169i
$903$	−1.28395e10	+	5.96147e9i	−0.580283	+	0.269430i
$904$			1.27064e10i			0.572047i
$905$	1.37358e10	−	2.80601e10i	0.616004	−	1.25840i
$906$	−2.91106e9	+	7.95736e9i	−0.130048	+	0.355484i
$907$	1.70546e9	+	1.70546e9i	0.0758956	+	0.0758956i	0.744036	−	0.668140i	$-0.232909\pi$
$907$	1.70546e9	+	1.70546e9i	0.0758956	+	0.0758956i	−0.668140	+	0.744036i	$0.732909\pi$
$908$	−2.06091e10	−	2.06091e10i	−0.913607	−	0.913607i
$909$	−2.72414e10	−	2.30113e10i	−1.20297	−	1.01617i
$910$	1.36788e10	+	3.99122e10i	0.601730	+	1.75574i
$911$		−	4.57586e9i		−	0.200520i	−0.994961	−	0.100260i	$-0.968033\pi$
$911$		−	4.57586e9i		−	0.200520i	0.994961	−	0.100260i	$-0.0319675\pi$
$912$	−3.69331e9	−	7.95444e9i	−0.161225	−	0.347238i
$913$	−9.79458e9	+	9.79458e9i	−0.425930	+	0.425930i
$914$	−2.96175e10			−1.28303
$915$	−2.90237e8	+	1.41325e10i	−0.0125250	+	0.609882i
$916$	−2.35085e10			−1.01063
$917$	2.51416e9	−	2.51416e9i	0.107671	−	0.107671i
$918$	4.53978e10	+	1.24046e10i	1.93680	+	0.529215i
$919$			1.17875e10i			0.500977i	0.968120	+	0.250489i	$0.0805913\pi$
$919$			1.17875e10i			0.500977i	−0.968120	+	0.250489i	$0.919409\pi$
$920$	−6.11000e9	−	2.99092e9i	−0.258693	−	0.126633i
$921$	−3.25727e10	−	1.19162e10i	−1.37387	−	0.502606i
$922$	3.36018e10	+	3.36018e10i	1.41190	+	1.41190i
$923$	2.29447e10	+	2.29447e10i	0.960453	+	0.960453i
$924$	2.43219e10	+	8.89776e9i	1.01425	+	0.371047i
$925$	8.83815e8	−	7.03100e9i	0.0367168	−	0.292093i
$926$			4.29816e10i			1.77887i
$927$	−2.82934e9	−	3.36119e10i	−0.116656	−	1.38584i
$928$	3.36103e9	−	3.36103e9i	0.138056	−	0.138056i
$929$	2.51024e8			0.0102721			0.00513607	−	0.999987i	$-0.498365\pi$
$929$	2.51024e8			0.0102721			0.00513607	+	0.999987i	$0.498365\pi$
$930$	−4.03681e10	−	4.20610e10i	−1.64569	−	1.71470i
$931$	−1.62597e10			−0.660371
$932$	3.74491e10	−	3.74491e10i	1.51525	−	1.51525i
$933$	6.57682e8	+	1.41648e9i	0.0265112	+	0.0570984i
$934$			3.66537e10i			1.47199i
$935$	1.42338e10	−	4.87822e9i	0.569481	−	0.195173i
$936$	1.81650e10	−	2.15042e10i	0.724052	−	0.857152i
$937$	−1.45938e9	−	1.45938e9i	−0.0579534	−	0.0579534i	0.677536	−	0.735490i	$-0.263048\pi$
$937$	−1.45938e9	−	1.45938e9i	−0.0579534	−	0.0579534i	−0.735490	+	0.677536i	$0.763048\pi$
$938$	7.08547e9	+	7.08547e9i	0.280323	+	0.280323i
$939$	−6.04843e9	+	1.65333e10i	−0.238404	+	0.651673i
$940$	1.79076e10	−	6.13732e9i	0.703219	−	0.241008i
$941$			3.09909e10i			1.21247i	0.795286	+	0.606235i	$0.207321\pi$
$941$			3.09909e10i			1.21247i	−0.795286	+	0.606235i	$0.792679\pi$
$942$	1.20371e9	−	5.58893e8i	0.0469186	−	0.0217847i
$943$	−9.48256e7	+	9.48256e7i	−0.00368243	+	0.00368243i
$944$	1.01299e10			0.391926
$945$	−2.04119e9	−	3.21294e10i	−0.0786812	−	1.23849i
$946$	1.10695e10			0.425118
$947$	8.25000e9	−	8.25000e9i	0.315667	−	0.315667i	−0.531433	−	0.847100i	$-0.678346\pi$
$947$	8.25000e9	−	8.25000e9i	0.315667	−	0.315667i	0.847100	+	0.531433i	$0.178346\pi$
$948$	3.73810e10	−	1.73563e10i	1.42502	−	0.661650i
$949$			5.28010e9i			0.200544i
$950$	−6.68374e9	+	5.31711e10i	−0.252922	+	2.01207i
$951$	6.24252e9	−	1.70639e10i	0.235358	−	0.643347i
$952$	3.51882e10	+	3.51882e10i	1.32181	+	1.32181i
$953$	−3.25460e9	−	3.25460e9i	−0.121807	−	0.121807i	0.643576	−	0.765383i	$-0.277450\pi$
$953$	−3.25460e9	−	3.25460e9i	−0.121807	−	0.121807i	−0.765383	+	0.643576i	$0.777450\pi$
$954$	−3.22025e10	+	3.81222e10i	−1.20080	+	1.42154i
$955$	5.85193e9	+	2.86459e9i	0.217414	+	0.106427i
$956$		−	1.21196e9i		−	0.0448625i
$957$	−1.52903e9	−	3.29315e9i	−0.0563930	−	0.121456i
$958$	−5.84948e10	+	5.84948e10i	−2.14950	+	2.14950i
$959$	−6.54566e9			−0.239656
$960$	−4.15308e10	−	8.52911e8i	−1.51503	−	0.0311139i
$961$	2.89936e10			1.05383
$962$	−8.59673e9	+	8.59673e9i	−0.311330	+	0.311330i
$963$	1.68366e9	+	2.00015e10i	0.0607523	+	0.721723i
$964$		−	6.48845e10i		−	2.33277i
$965$	1.35604e10	+	3.95669e10i	0.485767	+	1.41738i
$966$	1.25356e10	+	4.58592e9i	0.447429	+	0.163684i
$967$	−3.10808e10	−	3.10808e10i	−1.10535	−	1.10535i	−0.993754	−	0.111597i	$-0.964403\pi$
$967$	−3.10808e10	−	3.10808e10i	−1.10535	−	1.10535i	−0.111597	−	0.993754i	$-0.535597\pi$
$968$	1.86890e10	+	1.86890e10i	0.662251	+	0.662251i
$969$	3.93783e10	+	1.44059e10i	1.39035	+	0.508635i
$970$	−2.84406e8	+	5.80999e8i	−0.0100055	+	0.0204397i
$971$		−	1.90629e10i		−	0.668224i	−0.942533	−	0.334112i	$-0.891564\pi$
$971$		−	1.90629e10i		−	0.668224i	0.942533	−	0.334112i	$-0.108436\pi$
$972$	−4.12829e10	+	2.84038e10i	−1.44191	+	0.992075i
$973$	−4.47317e9	+	4.47317e9i	−0.155676	+	0.155676i
$974$	6.06420e10			2.10289
$975$	−2.48588e10	+	7.95315e9i	−0.858943	+	0.274804i
$976$	5.54714e9			0.190983
$977$	−3.74941e9	+	3.74941e9i	−0.128627	+	0.128627i	−0.768489	−	0.639863i	$-0.778991\pi$
$977$	−3.74941e9	+	3.74941e9i	−0.128627	+	0.128627i	0.639863	+	0.768489i	$0.278991\pi$
$978$	−1.88899e10	−	4.06840e10i	−0.645719	−	1.39071i
$979$		−	1.69839e10i		−	0.578493i
$980$	1.22442e10	−	2.50131e10i	0.415566	−	0.848939i
$981$	−1.69225e9	−	1.42947e9i	−0.0572298	−	0.0483430i
$982$	2.88842e10	+	2.88842e10i	0.973351	+	0.973351i
$983$	−2.66637e10	−	2.66637e10i	−0.895331	−	0.895331i	0.0996878	−	0.995019i	$-0.468216\pi$
$983$	−2.66637e10	−	2.66637e10i	−0.895331	−	0.895331i	−0.995019	+	0.0996878i	$0.968216\pi$
$984$	2.87391e8	−	7.85580e8i	0.00961591	−	0.0262850i
$985$	−1.29782e10	−	3.78682e10i	−0.432702	−	1.26255i
$986$		−	1.62758e10i		−	0.540721i
$987$	−1.44409e10	+	6.70503e9i	−0.478062	+	0.221968i
$988$	4.13731e10	−	4.13731e10i	1.36480	−	1.36480i
$989$	3.63079e9			0.119348
$990$	−9.13279e9	+	2.34599e10i	−0.299144	+	0.768426i
$991$	1.72494e10			0.563012			0.281506	−	0.959560i	$-0.409166\pi$
$991$	1.72494e10			0.563012			0.281506	+	0.959560i	$0.409166\pi$
$992$	2.25878e10	−	2.25878e10i	0.734655	−	0.734655i
$993$	−2.98613e9	+	1.38648e9i	−0.0967802	+	0.0449358i
$994$		−	9.59773e10i		−	3.09967i
$995$	9.67370e9	+	4.73540e9i	0.311323	+	0.152397i
$996$	2.27146e10	−	6.20902e10i	0.728448	−	1.99120i
$997$	−9.38169e9	−	9.38169e9i	−0.299811	−	0.299811i	0.541129	−	0.840940i	$-0.317997\pi$
$997$	−9.38169e9	−	9.38169e9i	−0.299811	−	0.299811i	−0.840940	+	0.541129i	$0.817997\pi$
$998$	−4.83762e10	−	4.83762e10i	−1.54055	−	1.54055i
$999$	8.05684e9	−	4.59879e9i	0.255673	−	0.145937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.8.e.a.2.2	✓	24
3.2	odd	2	inner	15.8.e.a.2.11	yes	24
5.2	odd	4		75.8.e.d.68.2		24
5.3	odd	4	inner	15.8.e.a.8.11	yes	24
5.4	even	2		75.8.e.d.32.11		24
15.2	even	4		75.8.e.d.68.11		24
15.8	even	4	inner	15.8.e.a.8.2	yes	24
15.14	odd	2		75.8.e.d.32.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.8.e.a.2.2	✓	24	1.1	even	1	trivial
15.8.e.a.2.11	yes	24	3.2	odd	2	inner
15.8.e.a.8.2	yes	24	15.8	even	4	inner
15.8.e.a.8.11	yes	24	5.3	odd	4	inner
75.8.e.d.32.2		24	15.14	odd	2
75.8.e.d.32.11		24	5.4	even	2
75.8.e.d.68.2		24	5.2	odd	4
75.8.e.d.68.11		24	15.2	even	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.2671 + 13.2671i) q^{2} +(42.4163 - 19.6942i) q^{3} -224.030i q^{4} +(122.889 - 251.044i) q^{5} +(-301.455 + 824.023i) q^{6} +(796.332 + 796.332i) q^{7} +(1274.03 + 1274.03i) q^{8} +(1411.28 - 1670.71i) q^{9} +O(q^{10})\)	\(q+(-13.2671 + 13.2671i) q^{2} +(42.4163 - 19.6942i) q^{3} -224.030i q^{4} +(122.889 - 251.044i) q^{5} +(-301.455 + 824.023i) q^{6} +(796.332 + 796.332i) q^{7} +(1274.03 + 1274.03i) q^{8} +(1411.28 - 1670.71i) q^{9} +(1700.24 + 4961.00i) q^{10} +2194.99i q^{11} +(-4412.09 - 9502.50i) q^{12} +(5051.41 - 5051.41i) q^{13} -21130.0 q^{14} +(268.387 - 13068.6i) q^{15} -5129.52 q^{16} +(17341.7 - 17341.7i) q^{17} +(3441.90 + 40888.9i) q^{18} +36559.5i q^{19} +(-56241.4 - 27530.9i) q^{20} +(49460.5 + 18094.3i) q^{21} +(-29121.1 - 29121.1i) q^{22} +(-9551.69 - 9551.69i) q^{23} +(79130.7 + 28948.6i) q^{24} +(-47921.4 - 61701.3i) q^{25} +134035. i q^{26} +(26957.8 - 98659.2i) q^{27} +(178402. - 178402. i) q^{28} -35370.9 q^{29} +(169821. + 176942. i) q^{30} -237710. q^{31} +(-95022.5 + 95022.5i) q^{32} +(43228.6 + 93103.4i) q^{33} +460147. i q^{34} +(297775. - 102054. i) q^{35} +(-374288. - 316168. i) q^{36} +(64138.1 + 64138.1i) q^{37} +(-485037. - 485037. i) q^{38} +(114778. - 313745. i) q^{39} +(476404. - 163274. i) q^{40} -9927.62i q^{41} +(-896254. + 416138. i) q^{42} +(-190060. + 190060. i) q^{43} +491744. q^{44} +(-245991. - 559605. i) q^{45} +253446. q^{46} +(-213766. + 213766. i) q^{47} +(-217575. + 101022. i) q^{48} +444746. i q^{49} +(1.45437e6 + 182818. i) q^{50} +(394039. - 1.07710e6i) q^{51} +(-1.13167e6 - 1.13167e6i) q^{52} +(859949. + 859949. i) q^{53} +(951266. + 1.66657e6i) q^{54} +(551041. + 269741. i) q^{55} +2.02911e6i q^{56} +(720010. + 1.55072e6i) q^{57} +(469267. - 469267. i) q^{58} -1.97483e6 q^{59} +(-2.92775e6 - 60126.6i) q^{60} -1.08141e6 q^{61} +(3.15372e6 - 3.15372e6i) q^{62} +(2.45428e6 - 206594. i) q^{63} -3.17792e6i q^{64} +(-647363. - 1.88889e6i) q^{65} +(-1.80873e6 - 661691. i) q^{66} +(-335328. - 335328. i) q^{67} +(-3.88506e6 - 3.88506e6i) q^{68} +(-593260. - 217034. i) q^{69} +(-2.59665e6 + 5.30456e6i) q^{70} +4.54224e6i q^{71} +(3.92655e6 - 330524. i) q^{72} +(-522637. + 522637. i) q^{73} -1.70185e6 q^{74} +(-3.24781e6 - 1.67336e6i) q^{75} +8.19041e6 q^{76} +(-1.74794e6 + 1.74794e6i) q^{77} +(2.63970e6 + 5.68525e6i) q^{78} +3.93381e6i q^{79} +(-630364. + 1.28774e6i) q^{80} +(-799565. - 4.71566e6i) q^{81} +(131710. + 131710. i) q^{82} +(4.46224e6 + 4.46224e6i) q^{83} +(4.05366e6 - 1.10806e7i) q^{84} +(-2.22243e6 - 6.48465e6i) q^{85} -5.04308e6i q^{86} +(-1.50030e6 + 696601. i) q^{87} +(-2.79649e6 + 2.79649e6i) q^{88} -7.73756e6 q^{89} +(1.06879e7 + 4.16074e6i) q^{90} +8.04519e6 q^{91} +(-2.13986e6 + 2.13986e6i) q^{92} +(-1.00828e7 + 4.68151e6i) q^{93} -5.67208e6i q^{94} +(9.17805e6 + 4.49277e6i) q^{95} +(-2.15911e6 + 5.90189e6i) q^{96} +(87220.9 + 87220.9i) q^{97} +(-5.90047e6 - 5.90047e6i) q^{98} +(3.66719e6 + 3.09774e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7}+O(q^{10}) \) 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7	\( 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7} - 3180 q^{10} - 2028 q^{12} + 16848 q^{13} + 37560 q^{15} - 68868 q^{16} - 106560 q^{18} + 84144 q^{21} + 166020 q^{22} - 275760 q^{25} - 264168 q^{27} + 602028 q^{28} + 892380 q^{30} - 208992 q^{31} - 877800 q^{33} - 256212 q^{36} - 635616 q^{37} - 1574040 q^{40} + 1219380 q^{42} + 1397328 q^{43} + 570240 q^{45} + 2787168 q^{46} - 476796 q^{48} - 4028016 q^{51} - 6426336 q^{52} + 2324880 q^{55} + 8457264 q^{57} + 986340 q^{58} + 2037900 q^{60} + 12157968 q^{61} - 1973952 q^{63} - 25406040 q^{66} - 16720176 q^{67} - 13165860 q^{70} + 36245880 q^{72} + 4059528 q^{73} + 11226120 q^{75} + 37968816 q^{76} - 26156280 q^{78} - 31289976 q^{81} - 53633520 q^{82} - 34181760 q^{85} + 44480160 q^{87} + 74717340 q^{88} + 71623080 q^{90} + 67599648 q^{91} - 58742592 q^{93} - 103105308 q^{96} - 75148056 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7 - 3180 * q^10 - 2028 * q^12 + 16848 * q^13 + 37560 * q^15 - 68868 * q^16 - 106560 * q^18 + 84144 * q^21 + 166020 * q^22 - 275760 * q^25 - 264168 * q^27 + 602028 * q^28 + 892380 * q^30 - 208992 * q^31 - 877800 * q^33 - 256212 * q^36 - 635616 * q^37 - 1574040 * q^40 + 1219380 * q^42 + 1397328 * q^43 + 570240 * q^45 + 2787168 * q^46 - 476796 * q^48 - 4028016 * q^51 - 6426336 * q^52 + 2324880 * q^55 + 8457264 * q^57 + 986340 * q^58 + 2037900 * q^60 + 12157968 * q^61 - 1973952 * q^63 - 25406040 * q^66 - 16720176 * q^67 - 13165860 * q^70 + 36245880 * q^72 + 4059528 * q^73 + 11226120 * q^75 + 37968816 * q^76 - 26156280 * q^78 - 31289976 * q^81 - 53633520 * q^82 - 34181760 * q^85 + 44480160 * q^87 + 74717340 * q^88 + 71623080 * q^90 + 67599648 * q^91 - 58742592 * q^93 - 103105308 * q^96 - 75148056 * q^97

Introduction

L-functions

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