LMFDB - Embedded newform 15.8.e.a.2.11

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			2.11
Character	$\chi$	$=$	15.2
Dual form			15.8.e.a.8.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.2671 - 13.2671i) q^{2} +(19.6942 - 42.4163i) q^{3} -224.030i q^{4} +(-122.889 + 251.044i) q^{5} +(-301.455 - 824.023i) q^{6} +(796.332 + 796.332i) q^{7} +(-1274.03 - 1274.03i) q^{8} +(-1411.28 - 1670.71i) q^{9} +O(q^{10})$	\(q+(13.2671 - 13.2671i) q^{2} +(19.6942 - 42.4163i) 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} +(-9502.50 - 4412.09i) q^{12} +(5051.41 - 5051.41i) q^{13} +21130.0 q^{14} +(8228.15 + 10156.6i) q^{15} -5129.52 q^{16} +(-17341.7 + 17341.7i) q^{17} +(-40888.9 - 3441.90i) 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} +(-98659.2 + 26957.8i) q^{27} +(178402. - 178402. i) q^{28} +35370.9 q^{29} +(243912. + 25585.1i) q^{30} -237710. q^{31} +(95022.5 - 95022.5i) q^{32} +(-93103.4 - 43228.6i) 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} +(416138. - 896254. i) q^{42} +(-190060. + 190060. i) q^{43} -491744. q^{44} +(592853. - 148981. i) q^{45} +253446. q^{46} +(213766. - 213766. i) q^{47} +(-101022. + 217575. 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} +(1.55072e6 + 720010. i) q^{57} +(469267. - 469267. i) q^{58} +1.97483e6 q^{59} +(2.27539e6 - 1.84335e6i) q^{60} -1.08141e6 q^{61} +(-3.15372e6 + 3.15372e6i) q^{62} +(206594. - 2.45428e6i) 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} +(-330524. + 3.92655e6i) q^{72} +(-522637. + 522637. i) q^{73} +1.70185e6 q^{74} +(-3.56091e6 + 817490. i) q^{75} +8.19041e6 q^{76} +(1.74794e6 - 1.74794e6i) q^{77} +(-5.68525e6 - 2.63970e6i) 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} +(696601. - 1.50030e6i) q^{87} +(-2.79649e6 + 2.79649e6i) q^{88} +7.73756e6 q^{89} +(5.88887e6 - 9.84195e6i) q^{90} +8.04519e6 q^{91} +(2.13986e6 - 2.13986e6i) q^{92} +(-4.68151e6 + 1.00828e7i) 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	$-0.438801\pi$
$2$	13.2671	−	13.2671i	1.17265	−	1.17265i	0.981575	−	0.191079i	$-0.0611986\pi$
$3$	19.6942	−	42.4163i	0.421128	−	0.907001i
$3$	19.6942	−	42.4163i	0.421128	−	0.907001i
$4$		−	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	$-0.920024\pi$
$11$		−	2194.99i		−	0.497232i	0.968602	−	0.248616i	$-0.0799757\pi$
$12$	−9502.50	−	4412.09i	−1.58746	−	0.737072i
$13$	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
$15$	8228.15	+	10156.6i	0.629481	+	0.777016i
$16$	−5129.52			−0.313081
$17$	−17341.7	+	17341.7i	−0.856093	+	0.856093i	−0.990875	−	0.134782i	$-0.956967\pi$
$17$	−17341.7	+	17341.7i	−0.856093	+	0.856093i	0.134782	+	0.990875i	$0.456967\pi$
$18$	−40888.9	−	3441.90i	−1.65254	−	0.139105i
$19$			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	0.784201	−	0.620507i	$-0.213073\pi$
$23$	9551.69	+	9551.69i	0.163694	+	0.163694i	−0.620507	+	0.784201i	$0.713073\pi$
$24$	−79130.7	+	28948.6i	−1.16844	+	0.427453i
$25$	−47921.4	−	61701.3i	−0.613394	−	0.789777i
$26$		−	134035.i		−	1.49558i
$27$	−98659.2	+	26957.8i	−0.964638	+	0.263579i
$28$	178402.	−	178402.i	1.53584	−	1.53584i
$29$	35370.9			0.269310			0.134655	−	0.990893i	$-0.457007\pi$
$29$	35370.9			0.269310			0.134655	+	0.990893i	$0.457007\pi$
$30$	243912.	+	25585.1i	1.64933	+	0.173007i
$31$	−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
$33$	−93103.4	−	43228.6i	−0.450990	−	0.209398i
$34$			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	$0.00358040\pi$
$41$			9927.62i			0.0224958i	−0.999937	+	0.0112479i	$0.996420\pi$
$42$	416138.	−	896254.i	0.866692	−	1.86663i
$43$	−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
$45$	592853.	−	148981.i	0.969846	−	0.243717i
$46$	253446.			0.383913
$47$	213766.	−	213766.i	0.300328	−	0.300328i	−0.540814	−	0.841142i	$-0.681884\pi$
$47$	213766.	−	213766.i	0.300328	−	0.300328i	0.841142	+	0.540814i	$0.181884\pi$
$48$	−101022.	+	217575.i	−0.131847	+	0.283965i
$49$			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	0.188623	−	0.982050i	$-0.439598\pi$
$53$	−859949.	−	859949.i	−0.793427	−	0.793427i	−0.982050	+	0.188623i	$0.939598\pi$
$54$	−951266.	+	1.66657e6i	−0.822099	+	1.44027i
$55$	551041.	+	269741.i	0.446595	+	0.218614i
$56$		−	2.02911e6i		−	1.54400i
$57$	1.55072e6	+	720010.i	1.10910	+	0.514964i
$58$	469267.	−	469267.i	0.315807	−	0.315807i
$59$	1.97483e6			1.25184			0.625918	−	0.779889i	$-0.284725\pi$
$59$	1.97483e6			1.25184			0.625918	+	0.779889i	$0.284725\pi$
$60$	2.27539e6	−	1.84335e6i	1.35996	−	1.10174i
$61$	−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
$63$	206594.	−	2.45428e6i	0.104094	−	1.23661i
$64$		−	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	$-0.728572\pi$
$71$		−	4.54224e6i		−	1.50614i	0.657940	−	0.753070i	$-0.271428\pi$
$72$	−330524.	+	3.92655e6i	−0.104361	+	1.23979i
$73$	−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
$75$	−3.56091e6	+	817490.i	−0.974646	+	0.223753i
$76$	8.19041e6			2.14022
$77$	1.74794e6	−	1.74794e6i	0.436325	−	0.436325i
$78$	−5.68525e6	−	2.63970e6i	−1.35649	−	0.629831i
$79$			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	0.134333	−	0.990936i	$-0.457111\pi$
$83$	−4.46224e6	−	4.46224e6i	−0.856603	−	0.856603i	−0.990936	+	0.134333i	$0.957111\pi$
$84$	−4.05366e6	−	1.10806e7i	−0.746225	−	2.03980i
$85$	−2.22243e6	−	6.48465e6i	−0.392520	−	1.14530i
$86$			5.04308e6i			0.854970i
$87$	696601.	−	1.50030e6i	0.113414	−	0.244265i
$88$	−2.79649e6	+	2.79649e6i	−0.437446	+	0.437446i
$89$	7.73756e6			1.16343			0.581713	−	0.813394i	$-0.302383\pi$
$89$	7.73756e6			1.16343			0.581713	+	0.813394i	$0.302383\pi$
$90$	5.88887e6	−	9.84195e6i	0.851498	−	1.42309i
$91$	8.04519e6			1.11916
$92$	2.13986e6	−	2.13986e6i	0.286503	−	0.286503i
$93$	−4.68151e6	+	1.00828e7i	−0.603526	+	1.29984i
$94$		−	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	$0.288554\pi$
$101$			1.63053e7i			1.57472i	−0.616491	+	0.787362i	$0.711446\pi$
$102$	1.95177e7	+	9.06224e6i	1.82108	+	0.845541i
$103$	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
$105$	−1.53570e6	+	1.46404e7i	−0.129463	+	1.23421i
$106$	−2.28180e7			−1.86083
$107$	6.48981e6	−	6.48981e6i	0.512140	−	0.512140i	−0.403042	−	0.915182i	$-0.632047\pi$
$107$	6.48981e6	−	6.48981e6i	0.512140	−	0.512140i	0.915182	+	0.403042i	$0.132047\pi$
$108$	6.03935e6	+	2.21026e7i	0.461325	+	1.68834i
$109$		−	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	0.525611	−	0.850725i	$-0.323837\pi$
$113$	−4.98667e6	−	4.98667e6i	−0.325114	−	0.325114i	−0.850725	+	0.525611i	$0.823837\pi$
$114$	3.01259e7	−	1.10210e7i	1.90446	−	0.696715i
$115$	−3.57170e6	+	1.22410e6i	−0.218994	+	0.0750539i
$116$		−	7.92413e6i		−	0.471355i
$117$	−1.55684e7	−	1.31049e6i	−0.898654	−	0.0756458i
$118$	2.62002e7	−	2.62002e7i	1.46797	−	1.46797i
$119$	−2.76195e7			−1.50246
$120$	2.45693e6	−	2.34228e7i	0.129795	−	1.23738i
$121$	1.46692e7			0.752761
$122$	−1.43472e7	+	1.43472e7i	−0.715331	+	0.715331i
$123$	421093.	+	195517.i	0.0204037	+	0.00947362i
$124$			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	$0.0195408\pi$
$131$			3.15718e6i			0.122701i	−0.998116	+	0.0613507i	$0.980459\pi$
$132$	−9.68450e6	+	2.08579e7i	−0.366495	+	0.789337i
$133$	−2.91135e7	+	2.91135e7i	−1.07303	+	1.07303i
$134$	−8.89763e6			−0.319454
$135$	5.35655e6	−	2.80806e7i	0.187377	−	0.982288i
$136$	4.41878e7			1.50632
$137$	4.10988e6	−	4.10988e6i	0.136555	−	0.136555i	−0.635525	−	0.772080i	$-0.719216\pi$
$137$	4.10988e6	−	4.10988e6i	0.136555	−	0.136555i	0.772080	+	0.635525i	$0.219216\pi$
$138$	4.99141e6	−	1.07502e7i	0.161676	−	0.348209i
$139$			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
$147$	1.88644e7	+	8.75891e6i	0.489816	+	0.227426i
$148$	1.43688e7	−	1.43688e7i	0.364339	−	0.364339i
$149$	3.67779e7			0.910826			0.455413	−	0.890280i	$-0.349492\pi$
$149$	3.67779e7			0.910826			0.455413	+	0.890280i	$0.349492\pi$
$150$	−3.63972e7	+	5.80885e7i	−0.880538	+	1.40531i
$151$	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
$153$	5.34469e7	+	4.49899e6i	1.20643	+	0.101554i
$154$		−	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
$162$	5.19551e7	+	7.31709e7i	0.960121	+	1.35218i
$163$	−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
$165$	2.22937e7	−	1.80607e7i	0.386357	−	0.312998i
$166$	−1.18402e8			−2.00900
$167$	−5.77212e7	+	5.77212e7i	−0.959020	+	0.959020i	−0.999193	−	0.0401732i	$-0.987209\pi$
$167$	−5.77212e7	+	5.77212e7i	−0.959020	+	0.959020i	0.0401732	+	0.999193i	$0.487209\pi$
$168$	−8.60670e7	−	3.99616e7i	−1.40041	−	0.650220i
$169$			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	0.962103	−	0.272685i	$-0.0879117\pi$
$173$	4.69509e7	+	4.69509e7i	0.689418	+	0.689418i	−0.272685	+	0.962103i	$0.587912\pi$
$174$	−1.06627e7	−	2.91464e7i	−0.153442	−	0.419433i
$175$	1.09733e7	−	8.72961e7i	0.154777	−	1.23129i
$176$			1.12593e7i			0.155674i
$177$	3.88927e7	−	8.37648e7i	0.527183	−	1.13542i
$178$	1.02655e8	−	1.02655e8i	1.36430	−	1.36430i
$179$	2.05963e6			0.0268413			0.0134206	−	0.999910i	$-0.495728\pi$
$179$	2.05963e6			0.0268413			0.0134206	+	0.999910i	$0.495728\pi$
$180$	−3.33761e7	−	1.32817e8i	−0.426562	−	1.69746i
$181$	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
$183$	−2.12976e7	+	4.58695e7i	−0.256892	+	0.553280i
$184$		−	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	$-0.961379\pi$
$191$		−	2.33104e7i		−	0.242065i	0.992649	−	0.121033i	$-0.0386206\pi$
$192$	−1.34795e8	−	6.25865e7i	−1.37442	−	0.638156i
$193$	−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
$195$	9.28689e7	+	9.74149e6i	0.896911	+	0.0940815i
$196$	9.96362e7			0.945194
$197$	−1.01270e8	+	1.01270e8i	−0.943732	+	0.943732i	−0.998499	−	0.0547667i	$-0.982558\pi$
$197$	−1.01270e8	+	1.01270e8i	−0.943732	+	0.943732i	0.0547667	+	0.998499i	$0.482558\pi$
$198$	−7.55494e6	+	8.97508e7i	−0.0691676	+	0.821694i
$199$			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
$207$	2.47801e6	−	2.94382e7i	0.0194181	−	0.230683i
$208$	−2.59113e7	+	2.59113e7i	−0.199649	+	0.199649i
$209$	8.02478e7			0.608025
$210$	1.73860e8	+	2.14609e8i	1.29549	+	1.59912i
$211$	−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
$213$	−1.92665e8	−	8.94557e7i	−1.36607	−	0.634278i
$214$		−	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
$222$	3.35166e7	−	7.21860e7i	0.205600	−	0.442810i
$223$	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
$225$	−3.54545e7	+	1.67140e8i	−0.207507	+	0.978234i
$226$	−1.32317e8			−0.762493
$227$	−9.19929e7	+	9.19929e7i	−0.521992	+	0.521992i	−0.918173	−	0.396181i	$-0.870335\pi$
$227$	−9.19929e7	+	9.19929e7i	−0.521992	+	0.521992i	0.396181	+	0.918173i	$0.370335\pi$
$228$	1.61304e8	−	3.47407e8i	0.901306	−	1.94118i
$229$		−	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	0.126254	−	0.991998i	$-0.459705\pi$
$233$	−1.67161e8	−	1.67161e8i	−0.865744	−	0.865744i	−0.991998	+	0.126254i	$0.959705\pi$
$234$	−2.23933e8	+	1.89160e8i	−1.14252	+	0.965103i
$235$	2.73951e7	+	7.99342e7i	0.137701	+	0.401786i
$236$		−	4.42420e8i		−	2.19100i
$237$	1.66857e8	+	7.74732e7i	0.814191	+	0.378035i
$238$	−3.66430e8	+	3.66430e8i	−1.76186	+	1.76186i
$239$	−5.40980e6			−0.0256323			−0.0128162	−	0.999918i	$-0.504080\pi$
$239$	−5.40980e6			−0.0256323			−0.0128162	+	0.999918i	$0.504080\pi$
$240$	−4.22065e7	−	5.20986e7i	−0.197079	−	0.243269i
$241$	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
$243$	1.84274e8	+	1.26786e8i	0.823839	+	0.566824i
$244$			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	$0.275047\pi$
$251$			3.81056e8i			1.52101i	−0.649335	+	0.760503i	$0.724953\pi$
$252$	−5.49832e8	−	4.62831e7i	−2.16435	−	0.182188i
$253$	2.09659e7	−	2.09659e7i	0.0813939	−	0.0813939i
$254$	−4.15432e8			−1.59068
$255$	−3.18824e8	−	3.34430e7i	−1.20409	−	0.126303i
$256$	−3.89217e8			−1.44995
$257$	3.28549e8	−	3.28549e8i	1.20735	−	1.20735i	0.235471	−	0.971881i	$-0.424337\pi$
$257$	3.28549e8	−	3.28549e8i	1.20735	−	1.20735i	0.971881	−	0.235471i	$-0.0756634\pi$
$258$	2.13908e8	+	9.93194e7i	0.775459	+	0.360052i
$259$			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	0.854345	−	0.519706i	$-0.173958\pi$
$263$	9.87239e7	+	9.87239e7i	0.334639	+	0.334639i	−0.519706	+	0.854345i	$0.673958\pi$
$264$	6.35421e7	+	1.73691e8i	0.212543	+	0.580985i
$265$	3.21564e8	−	1.10207e8i	1.06147	−	0.363787i
$266$			7.72501e8i			2.51659i
$267$	1.52385e8	−	3.28198e8i	0.489951	−	1.05523i
$268$	−7.51235e7	+	7.51235e7i	−0.238399	+	0.238399i
$269$	5.55168e8			1.73897			0.869483	−	0.493963i	$-0.164452\pi$
$269$	5.55168e8			1.73897			0.869483	+	0.493963i	$0.164452\pi$
$270$	−3.01482e8	−	4.43613e8i	−0.932155	−	1.37161i
$271$	−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
$273$	1.58444e8	−	3.41247e8i	0.471309	−	1.01508i
$274$		−	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	$-0.823193\pi$
$281$		−	3.92270e8i		−	1.05466i	0.849660	−	0.527331i	$-0.176807\pi$
$282$	−2.40589e8	−	1.11707e8i	−0.638856	−	0.296626i
$283$	−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
$285$	−3.71321e8	+	3.00817e8i	−0.950150	+	0.769742i
$286$	−2.94205e8			−0.743651
$287$	−7.90568e6	+	7.90568e6i	−0.0197403	+	0.0197403i
$288$	−2.92858e8	−	2.46518e7i	−0.722409	−	0.0608101i
$289$		−	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	0.00614032	−	0.999981i	$-0.498045\pi$
$293$	−4.27911e8	−	4.27911e8i	−0.993841	−	0.993841i	−0.999981	+	0.00614032i	$0.998045\pi$
$294$	3.66481e8	−	1.34071e8i	0.841076	−	0.307693i
$295$	−2.42685e8	+	4.95769e8i	−0.550384	+	1.12435i
$296$		−	1.63428e8i		−	0.366274i
$297$	5.91722e7	+	2.16556e8i	0.131060	+	0.479648i
$298$	4.87935e8	−	4.87935e8i	1.06808	−	1.06808i
$299$	9.64990e7			0.208773
$300$	1.83142e8	+	7.97750e8i	0.391619	+	1.70586i
$301$	−3.02702e8			−0.639782
$302$	1.28116e8	−	1.28116e8i	0.267658	−	0.267658i
$303$	6.91611e8	+	3.21120e8i	1.42828	+	0.663160i
$304$		−	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	$-0.989979\pi$
$311$		−	3.33947e7i		−	0.0629529i	0.999504	−	0.0314765i	$-0.0100209\pi$
$312$	−2.53490e8	+	5.45953e8i	−0.472520	+	1.01769i
$313$	−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
$315$	5.90745e8	+	3.53469e8i	1.06491	+	0.637184i
$316$	8.81290e8			1.57114
$317$	−2.74734e8	+	2.74734e8i	−0.484401	+	0.484401i	−0.906534	−	0.422133i	$-0.861282\pi$
$317$	−2.74734e8	+	2.74734e8i	−0.484401	+	0.484401i	0.422133	+	0.906534i	$0.361282\pi$
$318$	−4.49382e8	+	9.67853e8i	−0.783647	+	1.68778i
$319$		−	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
$327$	−4.29630e7	−	1.99481e7i	−0.0679482	−	0.0315489i
$328$	1.26481e7	−	1.26481e7i	0.0197910	−	0.0197910i
$329$	3.40457e8			0.527080
$330$	5.61592e7	−	5.35385e8i	0.0860245	−	0.820101i
$331$	−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
$333$	1.66395e7	−	1.97673e8i	0.0246936	−	0.293354i
$334$			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
$342$	1.25834e8	−	1.49488e9i	0.170101	−	2.02076i
$343$	3.01648e8	−	3.01648e8i	0.403619	−	0.403619i
$344$	4.84285e8			0.641426
$345$	−1.84202e7	+	1.75606e8i	−0.0241505	+	0.230235i
$346$	1.24580e9			1.61690
$347$	−2.74722e8	+	2.74722e8i	−0.352973	+	0.352973i	−0.861214	−	0.508242i	$-0.830296\pi$
$347$	−2.74722e8	+	2.74722e8i	−0.352973	+	0.352973i	0.508242	+	0.861214i	$0.330296\pi$
$348$	−3.36112e8	−	1.56059e8i	−0.427520	−	0.198501i
$349$		−	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	$0.193067\pi$
$353$	1.15012e9	+	1.15012e9i	1.39165	+	1.39165i	0.570027	+	0.821626i	$0.306933\pi$
$354$	−5.95321e8	−	1.62730e9i	−0.713247	−	1.94965i
$355$	1.14030e9	+	5.58192e8i	1.35276	+	0.662193i
$356$		−	1.73344e9i		−	2.03627i
$357$	−5.43945e8	+	1.17152e9i	−0.632726	+	1.36273i
$358$	2.73252e7	−	2.73252e7i	0.0314755	−	0.0314755i
$359$	−8.30194e8			−0.946998			−0.473499	−	0.880794i	$-0.657009\pi$
$359$	−8.30194e8			−0.946998			−0.473499	+	0.880794i	$0.657009\pi$
$360$	−9.45120e8	−	5.65507e8i	−1.06765	−	0.638821i
$361$	−4.42724e8			−0.495288
$362$	1.48291e9	−	1.48291e9i	1.64299	−	1.64299i
$363$	2.88898e8	−	6.22211e8i	0.317008	−	0.682755i
$364$		−	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
$372$	2.25884e9	+	1.04880e9i	2.27502	+	1.05631i
$373$	−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
$375$	2.32372e8	−	9.94407e8i	0.227549	−	0.973767i
$376$	−5.44689e8			−0.528434
$377$	1.78673e8	−	1.78673e8i	0.171737	−	0.171737i
$378$	−2.08466e9	+	5.69617e8i	−1.98525	+	0.542453i
$379$		−	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	0.837700	−	0.546131i	$-0.183900\pi$
$383$	3.20580e8	+	3.20580e8i	0.291569	+	0.291569i	−0.546131	+	0.837700i	$0.683900\pi$
$384$	−1.86324e9	+	6.81633e8i	−1.67922	+	0.614315i
$385$	2.24008e8	+	6.53615e8i	0.200055	+	0.583726i
$386$			2.80765e9i			2.48478i
$387$	5.85762e8	+	4.93076e7i	0.513728	+	0.0432440i
$388$	1.95401e7	−	1.95401e7i	0.0169830	−	0.0169830i
$389$	−6.95254e8			−0.598853			−0.299426	−	0.954119i	$-0.596795\pi$
$389$	−6.95254e8			−0.598853			−0.299426	+	0.954119i	$0.596795\pi$
$390$	1.36134e9	−	1.10286e9i	1.16209	−	0.941441i
$391$	−3.31286e8			−0.280275
$392$	5.66620e8	−	5.66620e8i	0.475106	−	0.475106i
$393$	1.33916e8	+	6.21781e7i	0.111290	+	0.0516730i
$394$			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	$-0.898389\pi$
$401$		−	8.10449e8i		−	0.627654i	0.949480	−	0.313827i	$-0.101611\pi$
$402$	−1.75232e8	+	3.77404e8i	−0.134531	+	0.289745i
$403$	−1.20077e9	+	1.20077e9i	−0.913887	+	0.913887i
$404$	3.65288e9			2.75613
$405$	−1.08558e9	−	7.80231e8i	−0.812027	−	0.583620i
$406$	7.47385e8			0.554247
$407$	1.40783e8	−	1.40783e8i	0.103507	−	0.103507i
$408$	8.70244e8	−	1.87428e9i	0.634352	−	1.36623i
$409$		−	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
$417$	2.38261e8	+	1.10627e8i	0.160908	+	0.0747108i
$418$	1.06465e9	−	1.06465e9i	0.713002	−	0.713002i
$419$	−7.04325e8			−0.467761			−0.233881	−	0.972265i	$-0.575142\pi$
$419$	−7.04325e8			−0.467761			−0.233881	+	0.972265i	$0.575142\pi$
$420$	3.27988e9	+	3.44043e8i	2.16016	+	0.226590i
$421$	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
$423$	−6.58823e8	−	5.54576e7i	−0.423231	−	0.0356262i
$424$			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	$-0.835257\pi$
$431$		−	1.64472e9i		−	0.989513i	0.869032	−	0.494757i	$-0.164743\pi$
$432$	5.06074e8	−	1.38281e8i	0.302010	−	0.0825217i
$433$	−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
$435$	2.91037e8	+	3.59248e8i	0.169526	+	0.209258i
$436$	−2.26918e8			−0.131119
$437$	−3.49205e8	+	3.49205e8i	−0.200168	+	0.200168i
$438$	5.88216e8	+	2.73113e8i	0.334486	+	0.155304i
$439$			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	0.425092	−	0.905150i	$-0.360242\pi$
$443$	−8.78428e8	−	8.78428e8i	−0.480058	−	0.480058i	−0.905150	+	0.425092i	$0.860242\pi$
$444$	−3.26490e8	−	8.92456e8i	−0.177023	−	0.483890i
$445$	−9.50863e8	+	1.94247e9i	−0.511515	+	1.04495i
$446$		−	5.54671e9i		−	2.96049i
$447$	7.24312e8	−	1.55998e9i	0.383574	−	0.826120i
$448$	2.53068e9	−	2.53068e9i	1.32973	−	1.32973i
$449$	3.69207e9			1.92490			0.962449	−	0.271462i	$-0.0875072\pi$
$449$	3.69207e9			1.92490			0.962449	+	0.271462i	$0.0875072\pi$
$450$	1.74708e9	+	2.68784e9i	0.903796	+	1.39046i
$451$	2.17911e7			0.0111856
$452$	−1.11716e9	+	1.11716e9i	−0.569025	+	0.569025i
$453$	1.90181e8	−	4.09602e8i	0.0961223	−	0.207023i
$454$			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	$0.205634\pi$
$461$			2.53272e9i			1.20402i	−0.798487	+	0.602011i	$0.794366\pi$
$462$	−1.96727e9	−	9.13420e8i	−0.928148	−	0.430947i
$463$	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
$465$	−1.95592e9	−	2.41433e9i	−0.902121	−	1.11356i
$466$	−4.43547e9			−2.03043
$467$	−1.38138e9	+	1.38138e9i	−0.627631	+	0.627631i	−0.947471	−	0.319840i	$-0.896371\pi$
$467$	−1.38138e9	+	1.38138e9i	−0.627631	+	0.627631i	0.319840	+	0.947471i	$0.396371\pi$
$468$	−2.93590e8	+	3.48778e9i	−0.132398	+	1.57285i
$469$		−	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
$477$	−2.23098e8	+	2.65035e9i	−0.0941199	+	1.11812i
$478$	−7.17721e7	+	7.17721e7i	−0.0300578	+	0.0300578i
$479$	−4.40903e9			−1.83303			−0.916513	−	0.400005i	$-0.869008\pi$
$479$	−4.40903e9			−1.83303			−0.916513	+	0.400005i	$0.869008\pi$
$480$	1.74697e9	+	1.83248e8i	0.721008	+	0.0756301i
$481$	6.47975e8			0.265492
$482$	3.84247e9	−	3.84247e9i	1.56295	−	1.56295i
$483$	6.45263e8	+	2.99601e8i	0.260568	+	0.120984i
$484$		−	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	$0.136226\pi$
$491$			2.17713e9i			0.830041i	−0.909812	+	0.415021i	$0.863774\pi$
$492$	4.38015e7	−	9.43373e7i	0.0165810	−	0.0357113i
$493$	−6.13392e8	+	6.13392e8i	−0.230555	+	0.230555i
$494$	4.90024e9			1.82883
$495$	−3.27012e8	−	1.30131e9i	−0.121184	−	0.482238i
$496$	1.21934e9			0.448683
$497$	3.61713e9	−	3.61713e9i	1.32165	−	1.32165i
$498$	−2.33182e9	+	5.02215e9i	−0.846044	+	1.82216i
$499$			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	0.284818	−	0.958582i	$-0.408067\pi$
$503$	−1.92307e9	−	1.92307e9i	−0.673763	−	0.673763i	−0.958582	+	0.284818i	$0.908067\pi$
$504$	−3.39004e9	+	2.86363e9i	−1.17950	+	0.996345i
$505$	−4.09336e9	−	2.00375e9i	−1.41436	−	0.692347i
$506$		−	5.56312e8i		−	0.190894i
$507$	4.96911e8	+	2.30720e8i	0.169336	+	0.0786243i
$508$	−3.50753e9	+	3.50753e9i	−1.18708	+	1.18708i
$509$	−5.80942e9			−1.95263			−0.976316	−	0.216348i	$-0.930585\pi$
$509$	−5.80942e9			−1.95263			−0.976316	+	0.216348i	$0.930585\pi$
$510$	−4.67354e9	+	3.78616e9i	−1.56009	+	1.26387i
$511$	−8.32385e8			−0.275963
$512$	−1.32392e9	+	1.32392e9i	−0.435931	+	0.435931i
$513$	−9.85563e8	−	3.60693e9i	−0.322310	−	1.17958i
$514$		−	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	$0.121854\pi$
$521$			2.41153e9i			0.747070i	−0.927616	+	0.373535i	$0.878146\pi$
$522$	−1.44628e9	−	1.21743e8i	−0.445045	−	0.0374625i
$523$	−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
$525$	−3.48666e9	−	2.18467e9i	−1.05160	−	0.658915i
$526$	2.61955e9			0.784832
$527$	4.12231e9	−	4.12231e9i	1.22688	−	1.22688i
$528$	4.77576e8	+	2.21742e8i	0.141196	+	0.0655586i
$529$		−	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
$537$	4.05627e7	−	8.73617e7i	0.0113036	−	0.0243451i
$538$	7.36544e9	−	7.36544e9i	2.03920	−	2.03920i
$539$	9.76214e8			0.268525
$540$	−6.29090e9	−	1.20003e9i	−1.71923	−	0.327954i
$541$	−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
$543$	2.20129e9	−	4.74102e9i	0.590036	−	1.27079i
$544$			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
$552$	−1.03234e9	−	4.79324e8i	−0.261238	−	0.121295i
$553$	−3.13262e9	+	3.13262e9i	−0.787716	+	0.787716i
$554$	8.67360e8			0.216728
$555$	−1.23688e8	+	1.17916e9i	−0.0307117	+	0.292785i
$556$	1.25842e9			0.310503
$557$	−5.10273e9	+	5.10273e9i	−1.25115	+	1.25115i	−0.295944	+	0.955205i	$0.595634\pi$
$557$	−5.10273e9	+	5.10273e9i	−1.25115	+	1.25115i	−0.955205	+	0.295944i	$0.904366\pi$
$558$	9.71971e9	+	8.18174e8i	2.36828	+	0.199354i
$559$			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	0.694967	−	0.719041i	$-0.255419\pi$
$563$	−1.01937e8	−	1.01937e8i	−0.0240743	−	0.0240743i	−0.719041	+	0.694967i	$0.755419\pi$
$564$	−2.97446e9	+	1.08816e9i	−0.698122	+	0.255396i
$565$	1.86468e9	−	6.39066e8i	0.434946	−	0.149065i
$566$			3.80641e9i			0.882384i
$567$	−4.39195e9	+	3.11851e9i	−1.01185	+	0.718467i
$568$	−5.78696e9	+	5.78696e9i	−1.32505	+	1.32505i
$569$	7.01526e9			1.59643			0.798217	−	0.602370i	$-0.205777\pi$
$569$	7.01526e9			1.59643			0.798217	+	0.602370i	$0.205777\pi$
$570$	−9.35379e8	+	8.91729e9i	−0.211556	+	2.01684i
$571$	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
$573$	−9.88738e8	−	4.59079e8i	−0.219553	−	0.101940i
$574$			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
$582$	4.55789e7	−	9.81652e7i	0.00958370	−	0.0206408i
$583$	−1.88758e9	+	1.88758e9i	−0.394517	+	0.394517i
$584$	1.33171e9			0.276672
$585$	2.24218e9	−	3.74730e9i	0.463046	−	0.773879i
$586$	−1.13542e10			−2.33086
$587$	3.69878e9	−	3.69878e9i	0.754788	−	0.754788i	−0.220581	−	0.975369i	$-0.570795\pi$
$587$	3.69878e9	−	3.69878e9i	0.754788	−	0.754788i	0.975369	+	0.220581i	$0.0707953\pi$
$588$	1.96226e9	−	4.22620e9i	0.398048	−	0.857292i
$589$		−	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	0.0743193	−	0.997234i	$-0.476322\pi$
$593$	−4.68655e9	−	4.68655e9i	−0.922915	−	0.922915i	−0.997234	+	0.0743193i	$0.976322\pi$
$594$	3.65811e9	+	2.08802e9i	0.716149	+	0.408774i
$595$	3.39414e9	−	6.93372e9i	0.660573	−	1.34945i
$596$		−	8.23935e9i		−	1.59416i
$597$	1.63446e9	+	7.58893e8i	0.314387	+	0.145972i
$598$	1.28026e9	−	1.28026e9i	0.244818	−	0.244818i
$599$	−2.03377e9			−0.386641			−0.193321	−	0.981136i	$-0.561926\pi$
$599$	−2.03377e9			−0.386641			−0.193321	+	0.981136i	$0.561926\pi$
$600$	5.57823e9	+	3.49521e9i	1.05431	+	0.660608i
$601$	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
$603$	−8.69947e7	+	1.03348e9i	−0.0161578	+	0.191951i
$604$		−	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
$612$	1.00791e9	−	1.19737e10i	0.177742	−	2.11154i
$613$	−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
$615$	−1.00831e8	+	8.16860e7i	−0.0174796	+	0.0141607i
$616$	−4.45387e9			−0.767724
$617$	−1.08006e8	+	1.08006e8i	−0.0185119	+	0.0185119i	−0.716302	−	0.697790i	$-0.754167\pi$
$617$	−1.08006e8	+	1.08006e8i	−0.0185119	+	0.0185119i	0.697790	+	0.716302i	$0.254167\pi$
$618$	−1.22744e10	−	5.69909e9i	−2.09189	−	0.971282i
$619$			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
$627$	1.58042e9	−	3.40381e9i	0.256056	−	0.551479i
$628$	−2.39603e8	+	2.39603e8i	−0.0386040	+	0.0386040i
$629$	−2.22453e9			−0.356419
$630$	1.25270e10	−	3.14796e9i	1.99597	−	0.501576i
$631$	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
$633$	−3.45239e9	+	7.43555e9i	−0.541011	+	1.16520i
$634$			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	$-0.787803\pi$
$641$		−	8.24640e9i		−	1.23669i	0.785906	−	0.618346i	$-0.212197\pi$
$642$	−7.30414e9	−	3.39137e9i	−1.08942	−	0.505827i
$643$	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
$645$	−3.49421e9	−	3.66525e8i	−0.512732	−	0.0537830i
$646$	−1.68228e10			−2.45518
$647$	2.44814e8	−	2.44814e8i	0.0355362	−	0.0355362i	−0.689115	−	0.724652i	$-0.742001\pi$
$647$	2.44814e8	−	2.44814e8i	0.0355362	−	0.0355362i	0.724652	+	0.689115i	$0.242001\pi$
$648$	7.02658e9	−	4.98924e9i	1.01445	−	0.720314i
$649$		−	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	0.499157	−	0.866511i	$-0.333643\pi$
$653$	−2.61385e9	−	2.61385e9i	−0.367354	−	0.367354i	−0.866511	+	0.499157i	$0.833643\pi$
$654$	−8.34646e8	+	3.05341e8i	−0.116676	+	0.0426838i
$655$	−7.92592e8	−	3.87984e8i	−0.110206	−	0.0539472i
$656$		−	5.09240e7i		−	0.00704302i
$657$	1.61076e9	+	1.35589e8i	0.221591	+	0.0186528i
$658$	4.51686e9	−	4.51686e9i	0.618082	−	0.618082i
$659$	2.23874e9			0.304722			0.152361	−	0.988325i	$-0.451312\pi$
$659$	2.23874e9			0.304722			0.152361	+	0.988325i	$0.451312\pi$
$660$	−4.04614e9	−	4.99446e9i	−0.547819	−	0.676214i
$661$	−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
$663$	7.43134e9	+	3.45043e9i	0.990306	+	0.459807i
$664$			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
$672$	2.98050e9	−	6.41923e9i	0.378875	−	0.816000i
$673$	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
$675$	6.39122e9	+	4.79554e9i	0.799872	+	0.600170i
$676$	2.62453e9			0.326767
$677$	9.30302e8	−	9.30302e8i	0.115229	−	0.115229i	−0.647141	−	0.762370i	$-0.724035\pi$
$677$	9.30302e8	−	9.30302e8i	0.115229	−	0.115229i	0.762370	+	0.647141i	$0.224035\pi$
$678$	−2.60587e9	+	5.61238e9i	−0.321107	+	0.691582i
$679$			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	0.999977	−	0.00681121i	$-0.00216809\pi$
$683$	8.26978e9	+	8.26978e9i	0.993166	+	0.993166i	−0.00681121	+	0.999977i	$0.502168\pi$
$684$	−1.15589e10	−	1.36838e10i	−1.38109	−	1.63497i
$685$	5.26702e8	+	1.53682e9i	0.0626106	+	0.182687i
$686$		−	8.00398e9i		−	0.946611i
$687$	−4.45093e9	−	2.06660e9i	−0.523724	−	0.243169i
$688$	9.74918e8	−	9.74918e8i	0.114132	−	0.114132i
$689$	−8.68790e9			−1.01192
$690$	2.08539e9	+	2.57415e9i	0.241666	+	0.298306i
$691$	−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
$693$	−5.38713e9	−	4.53472e8i	−0.614882	−	0.0517588i
$694$			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	$0.137694\pi$
$701$			7.64678e9i			0.838428i	−0.907888	+	0.419214i	$0.862306\pi$
$702$	3.61328e9	+	1.32237e10i	0.394204	+	1.44270i
$703$	−2.34486e9	+	2.34486e9i	−0.254550	+	0.254550i
$704$	−6.97551e9			−0.753479
$705$	3.93003e9	+	4.12241e8i	0.422410	+	0.0443087i
$706$	3.05174e10			3.26385
$707$	−1.29844e10	+	1.29844e10i	−1.38183	+	1.38183i
$708$	−1.87658e10	−	8.71311e9i	−1.98724	−	0.922692i
$709$			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
$717$	−1.06542e8	+	2.29463e8i	−0.0107945	+	0.0232486i
$718$	−1.10142e10	+	1.10142e10i	−1.11050	+	1.11050i
$719$	1.41252e9			0.141724			0.0708618	−	0.997486i	$-0.477425\pi$
$719$	1.41252e9			0.141724			0.0708618	+	0.997486i	$0.477425\pi$
$720$	−3.04105e9	+	7.64200e8i	−0.303641	+	0.0763033i
$721$	1.73695e10			1.72589
$722$	−5.87365e9	+	5.87365e9i	−0.580801	+	0.580801i
$723$	5.70392e9	−	1.22848e10i	0.561293	−	1.20888i
$724$		−	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
$732$	1.02761e10	+	4.77129e9i	0.968369	+	0.449622i
$733$	−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
$735$	−4.51711e9	+	3.65943e9i	−0.419619	+	0.339945i
$736$	1.81525e9			0.167828
$737$	−7.36043e8	+	7.36043e8i	−0.0677278	+	0.0677278i
$738$	3.41698e7	−	4.05929e8i	0.00312929	−	0.0371752i
$739$			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	0.788102	−	0.615545i	$-0.211064\pi$
$743$	1.92927e9	+	1.92927e9i	0.172557	+	0.172557i	−0.615545	+	0.788102i	$0.711064\pi$
$744$	1.88102e10	−	6.88139e9i	1.67451	−	0.612591i
$745$	−4.51961e9	+	9.23289e9i	−0.400455	+	0.818070i
$746$			4.50530e8i			0.0397318i
$747$	−1.15765e9	+	1.37526e10i	−0.101614	+	1.20715i
$748$	8.52769e9	−	8.52769e9i	0.745033	−	0.745033i
$749$	1.03361e10			0.898813
$750$	−1.01100e10	−	1.62758e10i	−0.875055	−	1.40873i
$751$	−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
$753$	1.61630e10	+	7.50459e9i	1.37955	+	0.640538i
$754$		−	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	$0.178884\pi$
$761$			1.29566e10i			1.06573i	−0.846202	+	0.532863i	$0.821116\pi$
$762$	−8.18161e9	+	1.76211e10i	−0.669879	+	1.44275i
$763$	8.06597e8	−	8.06597e8i	0.0657387	−	0.0657387i
$764$	−5.22222e9			−0.423670
$765$	−7.69750e9	+	1.28647e10i	−0.621634	+	1.03892i
$766$	8.50632e9			0.683819
$767$	9.97566e9	−	9.97566e9i	0.798284	−	0.798284i
$768$	−7.66531e9	+	1.65091e10i	−0.610612	+	1.31510i
$769$		−	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	0.572112	−	0.820176i	$-0.306124\pi$
$773$	−3.18561e9	−	3.18561e9i	−0.248064	−	0.248064i	−0.820176	+	0.572112i	$0.806124\pi$
$774$	8.42551e9	−	7.11718e9i	0.653135	−	0.551715i
$775$	1.13914e10	+	1.46670e10i	0.879067	+	1.13184i
$776$		−	2.22245e8i		−	0.0170732i
$777$	4.33284e9	+	2.01177e9i	0.331359	+	0.153853i
$778$	−9.22398e9	+	9.22398e9i	−0.702247	+	0.702247i
$779$	−3.62949e8			−0.0275083
$780$	2.18238e9	−	2.08054e10i	0.164664	−	1.56980i
$781$	−9.97018e9			−0.748901
$782$	−4.39519e9	+	4.39519e9i	−0.328665	+	0.328665i
$783$	−3.48966e9	+	9.53521e8i	−0.259787	+	0.0709846i
$784$		−	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
$792$	8.61875e9	+	7.25499e8i	0.616462	+	0.0518918i
$793$	−5.46266e9	+	5.46266e9i	−0.388999	+	0.388999i
$794$	−3.52234e10			−2.49724
$795$	1.65839e9	−	1.58100e10i	0.117058	−	1.11595i
$796$	8.63273e9			0.606670
$797$	−5.91307e9	+	5.91307e9i	−0.413723	+	0.413723i	−0.883033	−	0.469311i	$-0.844502\pi$
$797$	−5.91307e9	+	5.91307e9i	−0.413723	+	0.413723i	0.469311	+	0.883033i	$0.344502\pi$
$798$	3.27666e10	+	1.52138e10i	2.28255	+	1.05981i
$799$			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
$807$	1.09336e10	−	2.35481e10i	0.732327	−	1.57724i
$808$	2.07735e10	−	2.07735e10i	1.38538	−	1.38538i
$809$	4.74682e9			0.315198			0.157599	−	0.987503i	$-0.449625\pi$
$809$	4.74682e9			0.315198			0.157599	+	0.987503i	$0.449625\pi$
$810$	−2.47539e10	+	4.05112e9i	−1.63661	+	0.267841i
$811$	−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
$813$	−3.75627e9	+	8.09004e9i	−0.245154	+	0.528000i
$814$		−	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	$0.284255\pi$
$821$			2.47030e10i			1.55793i	−0.627067	+	0.778965i	$0.715745\pi$
$822$	−4.62558e9	−	2.14769e9i	−0.290479	−	0.134872i
$823$	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
$825$	1.79439e9	+	7.81618e9i	0.111257	+	0.484625i
$826$	4.17280e10			2.57631
$827$	2.82797e6	−	2.82797e6i	0.000173862	−	0.000173862i	−0.707020	−	0.707194i	$-0.749961\pi$
$827$	2.82797e6	−	2.82797e6i	0.000173862	−	0.000173862i	0.707194	+	0.707020i	$0.249961\pi$
$828$	−6.59503e9	−	5.55148e8i	−0.403748	−	0.0339862i
$829$			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
$837$	2.34523e10	−	6.40815e9i	1.38244	−	0.377740i
$838$	−9.34432e9	+	9.34432e9i	−0.548522	+	0.548522i
$839$	2.82762e10			1.65293			0.826464	−	0.562989i	$-0.190349\pi$
$839$	2.82762e10			1.65293			0.826464	+	0.562989i	$0.190349\pi$
$840$	2.06088e10	−	1.66958e10i	1.19971	−	0.971917i
$841$	−1.59988e10			−0.927472
$842$	3.47184e10	−	3.47184e10i	2.00432	−	2.00432i
$843$	−1.66386e10	−	7.72545e9i	−0.956580	−	0.444148i
$844$			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
$852$	−2.00407e10	+	4.31626e10i	−1.11013	+	2.39094i
$853$	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
$855$	5.44666e9	+	2.16744e10i	0.298022	+	1.18595i
$856$	−1.65365e10			−0.901123
$857$	−1.33885e10	+	1.33885e10i	−0.726609	+	0.726609i	−0.969943	−	0.243334i	$-0.921759\pi$
$857$	−1.33885e10	+	1.33885e10i	−0.726609	+	0.726609i	0.243334	+	0.969943i	$0.421759\pi$
$858$	−5.79414e9	+	1.24791e10i	−0.313172	+	0.674492i
$859$		−	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	0.277308	−	0.960781i	$-0.410558\pi$
$863$	−1.29050e10	−	1.29050e10i	−0.683473	−	0.683473i	−0.960781	+	0.277308i	$0.910558\pi$
$864$	−6.81324e9	+	1.19364e10i	−0.359381	+	0.629617i
$865$	−1.75565e10	+	6.01699e9i	−0.922321	+	0.316099i
$866$			7.33276e9i			0.383667i
$867$	−8.10711e9	−	3.76419e9i	−0.422473	−	0.196158i
$868$	−4.24080e10	+	4.24080e10i	−2.20104	+	2.20104i
$869$	8.63469e9			0.446352
$870$	8.62737e9	+	9.04968e8i	0.444182	+	0.0465925i
$871$	−3.38776e9			−0.173720
$872$	−1.29046e9	+	1.29046e9i	−0.0659076	+	0.0659076i
$873$	2.26279e7	−	2.68814e8i	0.00115105	−	0.0136742i
$874$			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	$0.0553585\pi$
$881$			7.02407e9i			0.346077i	−0.984915	+	0.173039i	$0.944641\pi$
$882$	1.53077e9	−	1.81851e10i	0.0751224	−	0.892435i
$883$	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
$885$	1.62492e10	+	2.00576e10i	0.788007	+	0.972695i
$886$	−2.33083e10			−1.12588
$887$	1.40958e9	−	1.40958e9i	0.0678201	−	0.0678201i	−0.672383	−	0.740203i	$-0.734729\pi$
$887$	1.40958e9	−	1.40958e9i	0.0678201	−	0.0678201i	0.740203	+	0.672383i	$0.234729\pi$
$888$	−6.93201e9	−	3.21859e9i	−0.332211	−	0.154248i
$889$		−	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
$897$	1.90047e9	−	4.09313e9i	0.0879200	−	0.189357i
$898$	4.89829e10	−	4.89829e10i	2.25724	−	2.25724i
$899$	−8.40802e9			−0.385953
$900$	3.74444e10	+	7.94286e9i	1.71214	+	0.363185i
$901$	2.98260e10			1.35850
$902$	2.89103e8	−	2.89103e8i	0.0131169	−	0.0131169i
$903$	−5.96147e9	+	1.28395e10i	−0.269430	+	0.580283i
$904$			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	$0.0319675\pi$
$911$			4.57586e9i			0.200520i	−0.994961	+	0.100260i	$0.968033\pi$
$912$	−7.95444e9	−	3.69331e9i	−0.347238	−	0.161225i
$913$	−9.79458e9	+	9.79458e9i	−0.425930	+	0.425930i
$914$	2.96175e10			1.28303
$915$	−8.89803e9	−	1.09835e10i	−0.383990	−	0.473988i
$916$	−2.35085e10			−1.01063
$917$	−2.51416e9	+	2.51416e9i	−0.107671	+	0.107671i
$918$	−1.24046e10	−	4.53978e10i	−0.529215	−	1.93680i
$919$			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
$927$	−3.36119e10	−	2.82934e9i	−1.38584	−	0.116656i
$928$	3.36103e9	−	3.36103e9i	0.138056	−	0.138056i
$929$	−2.51024e8			−0.0102721			−0.00513607	−	0.999987i	$-0.501635\pi$
$929$	−2.51024e8			−0.0102721			−0.00513607	+	0.999987i	$0.501635\pi$
$930$	−5.79804e10	−	6.08185e9i	−2.36369	−	0.247939i
$931$	−1.62597e10			−0.660371
$932$	−3.74491e10	+	3.74491e10i	−1.51525	+	1.51525i
$933$	−1.41648e9	−	6.57682e8i	−0.0570984	−	0.0265112i
$934$			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	$-0.792679\pi$
$941$		−	3.09909e10i		−	1.21247i	0.795286	−	0.606235i	$-0.207321\pi$
$942$	−5.58893e8	+	1.20371e9i	−0.0217847	+	0.0469186i
$943$	−9.48256e7	+	9.48256e7i	−0.00368243	+	0.00368243i
$944$	−1.01299e10			−0.391926
$945$	2.66271e10	−	1.80959e10i	1.02639	−	0.697540i
$946$	1.10695e10			0.425118
$947$	−8.25000e9	+	8.25000e9i	−0.315667	+	0.315667i	−0.847100	−	0.531433i	$-0.821654\pi$
$947$	−8.25000e9	+	8.25000e9i	−0.315667	+	0.315667i	0.531433	+	0.847100i	$0.321654\pi$
$948$	1.73563e10	−	3.73810e10i	0.661650	−	1.42502i
$949$			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	0.765383	−	0.643576i	$-0.222550\pi$
$953$	3.25460e9	+	3.25460e9i	0.121807	+	0.121807i	−0.643576	+	0.765383i	$0.722550\pi$
$954$	3.22025e10	+	3.81222e10i	1.20080	+	1.42154i
$955$	5.85193e9	+	2.86459e9i	0.217414	+	0.106427i
$956$			1.21196e9i			0.0448625i
$957$	−3.29315e9	−	1.52903e9i	−0.121456	−	0.0563930i
$958$	−5.84948e10	+	5.84948e10i	−2.14950	+	2.14950i
$959$	6.54566e9			0.239656
$960$	3.22769e10	−	2.61484e10i	1.17745	−	0.953884i
$961$	2.89936e10			1.05383
$962$	8.59673e9	−	8.59673e9i	0.311330	−	0.311330i
$963$	−2.00015e10	−	1.68366e9i	−0.721723	−	0.0607523i
$964$		−	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	$0.108436\pi$
$971$			1.90629e10i			0.668224i	−0.942533	+	0.334112i	$0.891564\pi$
$972$	2.84038e10	−	4.12829e10i	0.992075	−	1.44191i
$973$	−4.47317e9	+	4.47317e9i	−0.155676	+	0.155676i
$974$	−6.06420e10			−2.10289
$975$	−1.38581e10	+	2.21171e10i	−0.478838	+	0.764208i
$976$	5.54714e9			0.190983
$977$	3.74941e9	−	3.74941e9i	0.128627	−	0.128627i	−0.639863	−	0.768489i	$-0.721009\pi$
$977$	3.74941e9	−	3.74941e9i	0.128627	−	0.128627i	0.768489	+	0.639863i	$0.221009\pi$
$978$	4.06840e10	+	1.88899e10i	1.39071	+	0.645719i
$979$		−	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	0.995019	−	0.0996878i	$-0.0317844\pi$
$983$	2.66637e10	+	2.66637e10i	0.895331	+	0.895331i	−0.0996878	+	0.995019i	$0.531784\pi$
$984$	−2.87391e8	−	7.85580e8i	−0.00961591	−	0.0262850i
$985$	−1.29782e10	−	3.78682e10i	−0.432702	−	1.26255i
$986$			1.62758e10i			0.540721i
$987$	6.70503e9	−	1.44409e10i	0.221968	−	0.478062i
$988$	4.13731e10	−	4.13731e10i	1.36480	−	1.36480i
$989$	−3.63079e9			−0.119348
$990$	−2.16030e10	−	1.29260e10i	−0.707605	−	0.423392i
$991$	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
$993$	−1.38648e9	+	2.98613e9i	−0.0449358	+	0.0967802i
$994$		−	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.2.11	yes	24
3.2	odd	2	inner	15.8.e.a.2.2	✓	24
5.2	odd	4		75.8.e.d.68.11		24
5.3	odd	4	inner	15.8.e.a.8.2	yes	24
5.4	even	2		75.8.e.d.32.2		24
15.2	even	4		75.8.e.d.68.2		24
15.8	even	4	inner	15.8.e.a.8.11	yes	24
15.14	odd	2		75.8.e.d.32.11		24

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

\(f(q)\)	\(=\)	\(q+(13.2671 - 13.2671i) q^{2} +(19.6942 - 42.4163i) q^{3} -224.030i q^{4} +(-122.889 + 251.044i) q^{5} +(-301.455 - 824.023i) q^{6} +(796.332 + 796.332i) q^{7} +(-1274.03 - 1274.03i) q^{8} +(-1411.28 - 1670.71i) q^{9} +O(q^{10})\)	\(q+(13.2671 - 13.2671i) q^{2} +(19.6942 - 42.4163i) 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} +(-9502.50 - 4412.09i) q^{12} +(5051.41 - 5051.41i) q^{13} +21130.0 q^{14} +(8228.15 + 10156.6i) q^{15} -5129.52 q^{16} +(-17341.7 + 17341.7i) q^{17} +(-40888.9 - 3441.90i) 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} +(-98659.2 + 26957.8i) q^{27} +(178402. - 178402. i) q^{28} +35370.9 q^{29} +(243912. + 25585.1i) q^{30} -237710. q^{31} +(95022.5 - 95022.5i) q^{32} +(-93103.4 - 43228.6i) 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} +(416138. - 896254. i) q^{42} +(-190060. + 190060. i) q^{43} -491744. q^{44} +(592853. - 148981. i) q^{45} +253446. q^{46} +(213766. - 213766. i) q^{47} +(-101022. + 217575. 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} +(1.55072e6 + 720010. i) q^{57} +(469267. - 469267. i) q^{58} +1.97483e6 q^{59} +(2.27539e6 - 1.84335e6i) q^{60} -1.08141e6 q^{61} +(-3.15372e6 + 3.15372e6i) q^{62} +(206594. - 2.45428e6i) 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} +(-330524. + 3.92655e6i) q^{72} +(-522637. + 522637. i) q^{73} +1.70185e6 q^{74} +(-3.56091e6 + 817490. i) q^{75} +8.19041e6 q^{76} +(1.74794e6 - 1.74794e6i) q^{77} +(-5.68525e6 - 2.63970e6i) 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} +(696601. - 1.50030e6i) q^{87} +(-2.79649e6 + 2.79649e6i) q^{88} +7.73756e6 q^{89} +(5.88887e6 - 9.84195e6i) q^{90} +8.04519e6 q^{91} +(2.13986e6 - 2.13986e6i) q^{92} +(-4.68151e6 + 1.00828e7i) 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

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