LMFDB - Embedded newform 91.8.q.a.36.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$50$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.7
Character	$\chi$	$=$	91.36
Dual form			91.8.q.a.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.2280 + 9.36923i) q^{2} +(5.55186 + 9.61610i) q^{3} +(111.565 - 193.236i) q^{4} +117.996i q^{5} +(-180.191 - 104.033i) q^{6} +(-297.047 - 171.500i) q^{7} +1782.59i q^{8} +(1031.85 - 1787.22i) q^{9} +O(q^{10})$	\(q+(-16.2280 + 9.36923i) q^{2} +(5.55186 + 9.61610i) q^{3} +(111.565 - 193.236i) q^{4} +117.996i q^{5} +(-180.191 - 104.033i) q^{6} +(-297.047 - 171.500i) q^{7} +1782.59i q^{8} +(1031.85 - 1787.22i) q^{9} +(-1105.54 - 1914.85i) q^{10} +(-2543.24 + 1468.34i) q^{11} +2477.57 q^{12} +(-7088.58 - 3535.61i) q^{13} +6427.29 q^{14} +(-1134.67 + 655.100i) q^{15} +(-2421.19 - 4193.63i) q^{16} +(10112.5 - 17515.4i) q^{17} +38670.7i q^{18} +(7066.68 + 4079.95i) q^{19} +(22801.2 + 13164.3i) q^{20} -3808.57i q^{21} +(27514.5 - 47656.5i) q^{22} +(47059.5 + 81509.5i) q^{23} +(-17141.6 + 9896.70i) q^{24} +64201.8 q^{25} +(148159. - 9038.64i) q^{26} +47198.6 q^{27} +(-66280.1 + 38266.8i) q^{28} +(91481.6 + 158451. i) q^{29} +(12275.6 - 21261.9i) q^{30} -192913. i q^{31} +(-119020. - 68716.4i) q^{32} +(-28239.4 - 16304.1i) q^{33} +378986. i q^{34} +(20236.4 - 35050.5i) q^{35} +(-230238. - 398783. i) q^{36} +(-317361. + 183228. i) q^{37} -152904. q^{38} +(-5355.96 - 87793.7i) q^{39} -210340. q^{40} +(-634619. + 366398. i) q^{41} +(35683.4 + 61805.5i) q^{42} +(-214251. + 371093. i) q^{43} +655263. i q^{44} +(210886. + 121755. i) q^{45} +(-1.52736e6 - 881823. i) q^{46} -1.36239e6i q^{47} +(26884.3 - 46564.9i) q^{48} +(58824.5 + 101887. i) q^{49} +(-1.04187e6 + 601522. i) q^{50} +224573. q^{51} +(-1.47405e6 + 975320. i) q^{52} +492899. q^{53} +(-765939. + 442215. i) q^{54} +(-173259. - 300094. i) q^{55} +(305715. - 529513. i) q^{56} +90605.3i q^{57} +(-2.96912e6 - 1.71422e6i) q^{58} +(1.72841e6 + 997896. i) q^{59} +292345. i q^{60} +(-1.54275e6 + 2.67213e6i) q^{61} +(1.80745e6 + 3.13060e6i) q^{62} +(-613018. + 353926. i) q^{63} +3.19511e6 q^{64} +(417190. - 836427. i) q^{65} +611026. q^{66} +(-2.37890e6 + 1.37346e6i) q^{67} +(-2.25641e6 - 3.90821e6i) q^{68} +(-522536. + 905058. i) q^{69} +758398. i q^{70} +(1.53573e6 + 886653. i) q^{71} +(3.18589e6 + 1.83937e6i) q^{72} +2.30546e6i q^{73} +(3.43342e6 - 5.94686e6i) q^{74} +(356439. + 617371. i) q^{75} +(1.57679e6 - 910360. i) q^{76} +1.00728e6 q^{77} +(909476. + 1.37453e6i) q^{78} -6.57557e6 q^{79} +(494834. - 285692. i) q^{80} +(-1.99462e6 - 3.45479e6i) q^{81} +(6.86573e6 - 1.18918e7i) q^{82} -1.03682e6i q^{83} +(-735955. - 424904. i) q^{84} +(2.06676e6 + 1.19324e6i) q^{85} -8.02945e6i q^{86} +(-1.01579e6 + 1.75939e6i) q^{87} +(-2.61745e6 - 4.53356e6i) q^{88} +(-4.09549e6 + 2.36453e6i) q^{89} -4.56301e6 q^{90} +(1.49928e6 + 2.26593e6i) q^{91} +2.10008e7 q^{92} +(1.85507e6 - 1.07103e6i) q^{93} +(1.27646e7 + 2.21089e7i) q^{94} +(-481420. + 833844. i) q^{95} -1.52602e6i q^{96} +(8.09804e6 + 4.67541e6i) q^{97} +(-1.90921e6 - 1.10228e6i) q^{98} +6.06046e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9}+O(q^{10}) $ 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9} - 2728 q^{10} - 3954 q^{11} - 54708 q^{12} - 32008 q^{13} + 21952 q^{14} + 46398 q^{15} - 228808 q^{16} + 16832 q^{17} - 203520 q^{20} + 148982 q^{22} + 154164 q^{23} - 436560 q^{24} - 1918852 q^{25} - 624246 q^{26} + 661404 q^{27} - 451396 q^{29} + 313736 q^{30} + 1854432 q^{32} + 315450 q^{33} - 372498 q^{35} + 2704174 q^{36} + 1777146 q^{37} - 338468 q^{38} + 189708 q^{39} - 2875580 q^{40} - 2158998 q^{41} - 296352 q^{42} + 1876346 q^{43} + 7252980 q^{45} + 234336 q^{46} + 1316674 q^{48} + 5882450 q^{49} + 6432894 q^{50} - 3602684 q^{51} - 14093326 q^{52} + 1719628 q^{53} - 14915976 q^{54} - 1225470 q^{55} + 2107392 q^{56} + 18792564 q^{58} + 5131962 q^{59} + 886858 q^{61} + 3663272 q^{62} - 1848084 q^{63} - 38282980 q^{64} - 17072760 q^{65} + 54390948 q^{66} - 15529368 q^{67} + 2633716 q^{68} + 12342620 q^{69} + 20194104 q^{71} + 12742440 q^{72} - 23243862 q^{74} - 12055866 q^{75} - 7828698 q^{76} - 11143384 q^{77} - 32361130 q^{78} + 38408264 q^{79} - 38368944 q^{80} - 55140914 q^{81} + 27439818 q^{82} + 46422306 q^{84} + 16353300 q^{85} - 15866954 q^{87} - 39468942 q^{88} + 11465844 q^{89} - 22072424 q^{90} - 3481450 q^{91} + 67780968 q^{92} - 71319114 q^{93} - 6119236 q^{94} + 60860930 q^{95} + 45060702 q^{97}+O(q^{100}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9 - 2728 * q^10 - 3954 * q^11 - 54708 * q^12 - 32008 * q^13 + 21952 * q^14 + 46398 * q^15 - 228808 * q^16 + 16832 * q^17 - 203520 * q^20 + 148982 * q^22 + 154164 * q^23 - 436560 * q^24 - 1918852 * q^25 - 624246 * q^26 + 661404 * q^27 - 451396 * q^29 + 313736 * q^30 + 1854432 * q^32 + 315450 * q^33 - 372498 * q^35 + 2704174 * q^36 + 1777146 * q^37 - 338468 * q^38 + 189708 * q^39 - 2875580 * q^40 - 2158998 * q^41 - 296352 * q^42 + 1876346 * q^43 + 7252980 * q^45 + 234336 * q^46 + 1316674 * q^48 + 5882450 * q^49 + 6432894 * q^50 - 3602684 * q^51 - 14093326 * q^52 + 1719628 * q^53 - 14915976 * q^54 - 1225470 * q^55 + 2107392 * q^56 + 18792564 * q^58 + 5131962 * q^59 + 886858 * q^61 + 3663272 * q^62 - 1848084 * q^63 - 38282980 * q^64 - 17072760 * q^65 + 54390948 * q^66 - 15529368 * q^67 + 2633716 * q^68 + 12342620 * q^69 + 20194104 * q^71 + 12742440 * q^72 - 23243862 * q^74 - 12055866 * q^75 - 7828698 * q^76 - 11143384 * q^77 - 32361130 * q^78 + 38408264 * q^79 - 38368944 * q^80 - 55140914 * q^81 + 27439818 * q^82 + 46422306 * q^84 + 16353300 * q^85 - 15866954 * q^87 - 39468942 * q^88 + 11465844 * q^89 - 22072424 * q^90 - 3481450 * q^91 + 67780968 * q^92 - 71319114 * q^93 - 6119236 * q^94 + 60860930 * q^95 + 45060702 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−16.2280	+	9.36923i	−1.43436	+	0.828131i	−0.997450	−	0.0713717i	$-0.977262\pi$
$2$	−16.2280	+	9.36923i	−1.43436	+	0.828131i	−0.436915	+	0.899503i	$0.643929\pi$
$3$	5.55186	+	9.61610i	0.118717	+	0.205624i	0.919260	−	0.393652i	$-0.128788\pi$
$3$	5.55186	+	9.61610i	0.118717	+	0.205624i	−0.800542	+	0.599276i	$0.795455\pi$
$4$	111.565	−	193.236i	0.871602	−	1.50966i
$5$			117.996i			0.422157i	0.977469	+	0.211079i	$0.0676976\pi$
$5$			117.996i			0.422157i	−0.977469	+	0.211079i	$0.932302\pi$
$6$	−180.191	−	104.033i	−0.340568	−	0.196627i
$7$	−297.047	−	171.500i	−0.327327	−	0.188982i
$7$	−297.047	−	171.500i	−0.327327	−	0.188982i
$8$			1782.59i			1.23094i
$9$	1031.85	−	1787.22i	0.471812	−	0.817203i
$10$	−1105.54	−	1914.85i	−0.349601	−	0.605527i
$11$	−2543.24	+	1468.34i	−0.576121	+	0.332623i	−0.759590	−	0.650402i	$-0.774600\pi$
$11$	−2543.24	+	1468.34i	−0.576121	+	0.332623i	0.183470	+	0.983025i	$0.441267\pi$
$12$	2477.57			0.413897
$13$	−7088.58	−	3535.61i	−0.894865	−	0.446337i
$13$	−7088.58	−	3535.61i	−0.894865	−	0.446337i
$14$	6427.29			0.626008
$15$	−1134.67	+	655.100i	−0.0868058	+	0.0501173i
$16$	−2421.19	−	4193.63i	−0.147778	−	0.255959i
$17$	10112.5	−	17515.4i	0.499216	−	0.864667i	−0.500784	−	0.865572i	$-0.666955\pi$
$17$	10112.5	−	17515.4i	0.499216	−	0.864667i	1.00000		0.000905451i	$0.000288214\pi$
$18$			38670.7i			1.56289i
$19$	7066.68	+	4079.95i	0.236362	+	0.136464i	0.613504	−	0.789692i	$-0.289760\pi$
$19$	7066.68	+	4079.95i	0.236362	+	0.136464i	−0.377141	+	0.926156i	$0.623093\pi$
$20$	22801.2	+	13164.3i	0.637313	+	0.367953i
$21$		−	3808.57i		−	0.0897418i
$22$	27514.5	−	47656.5i	0.550911	−	0.954207i
$23$	47059.5	+	81509.5i	0.806492	+	1.39689i	0.915279	+	0.402820i	$0.131970\pi$
$23$	47059.5	+	81509.5i	0.806492	+	1.39689i	−0.108787	+	0.994065i	$0.534697\pi$
$24$	−17141.6	+	9896.70i	−0.253111	+	0.146134i
$25$	64201.8			0.821783
$26$	148159.	−	9038.64i	1.65319	−	0.100855i
$27$	47198.6			0.461484
$28$	−66280.1	+	38266.8i	−0.570597	+	0.329435i
$29$	91481.6	+	158451.i	0.696531	+	1.20643i	0.969662	+	0.244451i	$0.0786076\pi$
$29$	91481.6	+	158451.i	0.696531	+	1.20643i	−0.273130	+	0.961977i	$0.588059\pi$
$30$	12275.6	−	21261.9i	0.0830074	−	0.143773i
$31$		−	192913.i		−	1.16304i	−0.813531	−	0.581522i	$-0.802457\pi$
$31$		−	192913.i		−	1.16304i	0.813531	−	0.581522i	$-0.197543\pi$
$32$	−119020.	−	68716.4i	−0.642091	−	0.370711i
$33$	−28239.4	−	16304.1i	−0.136791	−	0.0789763i
$34$			378986.i			1.65366i
$35$	20236.4	−	35050.5i	0.0797802	−	0.138183i
$36$	−230238.	−	398783.i	−0.822465	−	1.42455i
$37$	−317361.	+	183228.i	−1.03002	+	0.594685i	−0.916992	−	0.398906i	$-0.869390\pi$
$37$	−317361.	+	183228.i	−1.03002	+	0.594685i	−0.113033	+	0.993591i	$0.536057\pi$
$38$	−152904.			−0.452040
$39$	−5355.96	−	87793.7i	−0.0144581	−	0.236994i
$40$	−210340.			−0.519650
$41$	−634619.	+	366398.i	−1.43804	+	0.830251i	−0.997713	−	0.0675888i	$-0.978469\pi$
$41$	−634619.	+	366398.i	−1.43804	+	0.830251i	−0.440323	+	0.897839i	$0.645136\pi$
$42$	35683.4	+	61805.5i	0.0743180	+	0.128723i
$43$	−214251.	+	371093.i	−0.410944	+	0.711775i	−0.994993	−	0.0999428i	$-0.968134\pi$
$43$	−214251.	+	371093.i	−0.410944	+	0.711775i	0.584050	+	0.811718i	$0.301467\pi$
$44$			655263.i			1.15966i
$45$	210886.	+	121755.i	0.344988	+	0.199179i
$46$	−1.52736e6	−	881823.i	−2.31361	−	1.33576i
$47$		−	1.36239e6i		−	1.91408i	−0.289954	−	0.957040i	$-0.593640\pi$
$47$		−	1.36239e6i		−	1.91408i	0.289954	−	0.957040i	$-0.406360\pi$
$48$	26884.3	−	46564.9i	0.0350876	−	0.0607735i
$49$	58824.5	+	101887.i	0.0714286	+	0.123718i
$50$	−1.04187e6	+	601522.i	−1.17874	+	0.680544i
$51$	224573.			0.237062
$52$	−1.47405e6	+	975320.i	−1.45378	+	0.961912i
$53$	492899.			0.454771			0.227385	−	0.973805i	$-0.426982\pi$
$53$	492899.			0.454771			0.227385	+	0.973805i	$0.426982\pi$
$54$	−765939.	+	442215.i	−0.661936	+	0.382169i
$55$	−173259.	−	300094.i	−0.140419	−	0.243213i
$56$	305715.	−	529513.i	0.232626	−	0.402920i
$57$			90605.3i			0.0648025i
$58$	−2.96912e6	−	1.71422e6i	−1.99816	−	1.15364i
$59$	1.72841e6	+	997896.i	1.09563	+	0.632562i	0.935070	−	0.354464i	$-0.115337\pi$
$59$	1.72841e6	+	997896.i	1.09563	+	0.632562i	0.160560	+	0.987026i	$0.448670\pi$
$60$			292345.i			0.174729i
$61$	−1.54275e6	+	2.67213e6i	−0.870247	+	1.50731i	−0.00850550	+	0.999964i	$0.502707\pi$
$61$	−1.54275e6	+	2.67213e6i	−0.870247	+	1.50731i	−0.861741	+	0.507348i	$0.830626\pi$
$62$	1.80745e6	+	3.13060e6i	0.963153	+	1.66823i
$63$	−613018.	+	353926.i	−0.308874	+	0.178328i
$64$	3.19511e6			1.52355
$65$	417190.	−	836427.i	0.188424	−	0.377773i
$66$	611026.			0.261611
$67$	−2.37890e6	+	1.37346e6i	−0.966305	+	0.557896i	−0.898108	−	0.439775i	$-0.855058\pi$
$67$	−2.37890e6	+	1.37346e6i	−0.966305	+	0.557896i	−0.0681972	+	0.997672i	$0.521725\pi$
$68$	−2.25641e6	−	3.90821e6i	−0.870235	−	1.50729i
$69$	−522536.	+	905058.i	−0.191489	+	0.331669i
$70$			758398.i			0.264274i
$71$	1.53573e6	+	886653.i	0.509225	+	0.294001i	0.732515	−	0.680751i	$-0.238346\pi$
$71$	1.53573e6	+	886653.i	0.509225	+	0.294001i	−0.223290	+	0.974752i	$0.571680\pi$
$72$	3.18589e6	+	1.83937e6i	1.00593	+	0.580773i
$73$			2.30546e6i			0.693629i	0.937934	+	0.346815i	$0.112737\pi$
$73$			2.30546e6i			0.693629i	−0.937934	+	0.346815i	$0.887263\pi$
$74$	3.43342e6	−	5.94686e6i	0.984954	−	1.70599i
$75$	356439.	+	617371.i	0.0975599	+	0.168979i
$76$	1.57679e6	−	910360.i	0.412028	−	0.237884i
$77$	1.00728e6			0.251440
$78$	909476.	+	1.37453e6i	0.217000	+	0.327963i
$79$	−6.57557e6			−1.50051			−0.750255	−	0.661149i	$-0.770069\pi$
$79$	−6.57557e6			−1.50051			−0.750255	+	0.661149i	$0.770069\pi$
$80$	494834.	−	285692.i	0.108055	−	0.0623855i
$81$	−1.99462e6	−	3.45479e6i	−0.417026	−	0.722311i
$82$	6.86573e6	−	1.18918e7i	1.37511	−	2.38176i
$83$		−	1.03682e6i		−	0.199036i	−0.995036	−	0.0995181i	$-0.968270\pi$
$83$		−	1.03682e6i		−	0.199036i	0.995036	−	0.0995181i	$-0.0317301\pi$
$84$	−735955.	−	424904.i	−0.135480	−	0.0782192i
$85$	2.06676e6	+	1.19324e6i	0.365025	+	0.210747i
$86$		−	8.02945e6i		−	1.36126i
$87$	−1.01579e6	+	1.75939e6i	−0.165381	+	0.286448i
$88$	−2.61745e6	−	4.53356e6i	−0.409440	−	0.709170i
$89$	−4.09549e6	+	2.36453e6i	−0.615801	+	0.355533i	−0.775232	−	0.631676i	$-0.782367\pi$
$89$	−4.09549e6	+	2.36453e6i	−0.615801	+	0.355533i	0.159431	+	0.987209i	$0.449034\pi$
$90$	−4.56301e6			−0.659785
$91$	1.49928e6	+	2.26593e6i	0.208563	+	0.315212i
$92$	2.10008e7			2.81176
$93$	1.85507e6	−	1.07103e6i	0.239150	−	0.138073i
$94$	1.27646e7	+	2.21089e7i	1.58511	+	2.74549i
$95$	−481420.	+	833844.i	−0.0576092	+	0.0997820i
$96$		−	1.52602e6i		−	0.176039i
$97$	8.09804e6	+	4.67541e6i	0.900905	+	0.520138i	0.877494	−	0.479588i	$-0.159214\pi$
$97$	8.09804e6	+	4.67541e6i	0.900905	+	0.520138i	0.0234111	+	0.999726i	$0.492547\pi$
$98$	−1.90921e6	−	1.10228e6i	−0.204909	−	0.118304i
$99$			6.06046e6i			0.627743i
$100$	7.16268e6	−	1.24061e7i	0.716268	−	1.24061i
$101$	7.23104e6	+	1.25245e7i	0.698354	+	1.20958i	0.969037	+	0.246916i	$0.0794173\pi$
$101$	7.23104e6	+	1.25245e7i	0.698354	+	1.20958i	−0.270683	+	0.962669i	$0.587249\pi$
$102$	−3.64437e6	+	2.10408e6i	−0.340034	+	0.196318i
$103$	−2.64877e6			−0.238844			−0.119422	−	0.992844i	$-0.538104\pi$
$103$	−2.64877e6			−0.238844			−0.119422	+	0.992844i	$0.538104\pi$
$104$	6.30256e6	−	1.26360e7i	0.549415	−	1.10153i
$105$	449398.			0.0378851
$106$	−7.99876e6	+	4.61809e6i	−0.652307	+	0.376610i
$107$	−3.96224e6	−	6.86280e6i	−0.312678	−	0.541575i	0.666263	−	0.745717i	$-0.267893\pi$
$107$	−3.96224e6	−	6.86280e6i	−0.312678	−	0.541575i	−0.978941	+	0.204142i	$0.934560\pi$
$108$	5.26572e6	−	9.12049e6i	0.402230	−	0.696683i
$109$		−	1.11745e7i		−	0.826488i	−0.910620	−	0.413244i	$-0.864396\pi$
$109$		−	1.11745e7i		−	0.826488i	0.910620	−	0.413244i	$-0.135604\pi$
$110$	5.62330e6	+	3.24661e6i	0.402825	+	0.232571i
$111$	−3.52389e6	−	2.03452e6i	−0.244563	−	0.141199i
$112$			1.66094e6i			0.111710i
$113$	−3.72810e6	+	6.45726e6i	−0.243060	+	0.420992i	−0.961584	−	0.274510i	$-0.911484\pi$
$113$	−3.72810e6	+	6.45726e6i	−0.243060	+	0.420992i	0.718524	+	0.695502i	$0.244818\pi$
$114$	−848902.	−	1.47034e6i	−0.0536649	−	0.0929504i
$115$	−9.61783e6	+	5.55286e6i	−0.589705	+	0.340466i
$116$	4.08246e7			2.42839
$117$	−1.36333e7	+	9.02063e6i	−0.786957	+	0.520699i
$118$	−3.73981e7			−2.09538
$119$	−6.00778e6	+	3.46859e6i	−0.326813	+	0.188686i
$120$	−1.16778e6	−	2.02265e6i	−0.0616915	−	0.106853i
$121$	−5.43153e6	+	9.40769e6i	−0.278723	+	0.482763i
$122$		−	5.78177e7i		−	2.88271i
$123$	−7.04663e6	−	4.06838e6i	−0.341440	−	0.197130i
$124$	−3.72779e7	−	2.15224e7i	−1.75580	−	1.01371i
$125$			1.67941e7i			0.769079i
$126$	6.63203e6	−	1.14870e7i	0.295358	−	0.511576i
$127$	1.62382e7	+	2.81253e7i	0.703435	+	1.21839i	0.967253	+	0.253813i	$0.0816848\pi$
$127$	1.62382e7	+	2.81253e7i	0.703435	+	1.21839i	−0.263818	+	0.964572i	$0.584982\pi$
$128$	−3.66155e7	+	2.11400e7i	−1.54323	+	0.890984i
$129$	−4.75795e6			−0.195144
$130$	1.06653e6	+	1.74823e7i	0.0425765	+	0.697905i
$131$	−3.18866e6			−0.123925			−0.0619624	−	0.998078i	$-0.519736\pi$
$131$	−3.18866e6			−0.123925			−0.0619624	+	0.998078i	$0.519736\pi$
$132$	−6.30107e6	+	3.63792e6i	−0.238455	+	0.137672i
$133$	−1.39942e6	−	2.42387e6i	−0.0515785	−	0.0893365i
$134$	2.57365e7	−	4.45769e7i	0.924023	−	1.60045i
$135$			5.56927e6i			0.194819i
$136$	3.12228e7	+	1.80265e7i	1.06435	+	0.614505i
$137$	−2.82436e7	−	1.63065e7i	−0.938422	−	0.541798i	−0.0489566	−	0.998801i	$-0.515590\pi$
$137$	−2.82436e7	−	1.63065e7i	−0.938422	−	0.541798i	−0.889465	+	0.457003i	$0.848923\pi$
$138$		−	1.95830e7i		−	0.634312i
$139$	5.94044e6	−	1.02891e7i	0.187615	−	0.324958i	−0.756840	−	0.653600i	$-0.773258\pi$
$139$	5.94044e6	−	1.02891e7i	0.187615	−	0.324958i	0.944454	+	0.328642i	$0.106591\pi$
$140$	−4.51535e6	−	7.82081e6i	−0.139073	−	0.240882i
$141$	1.31009e7	−	7.56382e6i	0.393582	−	0.227234i
$142$	−3.32290e7			−0.973887
$143$	2.32195e7	−	1.41653e6i	0.664012	−	0.0405089i
$144$	−9.99327e6			−0.278894
$145$	−1.86966e7	+	1.07945e7i	−0.509302	+	0.294046i
$146$	−2.16004e7	−	3.74129e7i	−0.574416	−	0.994917i
$147$	−653171.	+	1.13132e6i	−0.0169596	+	0.0293749i
$148$			8.17676e7i			2.07331i
$149$	6.53840e7	+	3.77495e7i	1.61927	+	0.934886i	0.987109	+	0.160050i	$0.0511656\pi$
$149$	6.53840e7	+	3.77495e7i	1.61927	+	0.934886i	0.632162	+	0.774836i	$0.282168\pi$
$150$	−1.15686e7	−	6.67913e6i	−0.279873	−	0.161585i
$151$			6.80179e7i			1.60770i	0.594834	+	0.803848i	$0.297218\pi$
$151$			6.80179e7i			1.60770i	−0.594834	+	0.803848i	$0.702782\pi$
$152$	−7.27289e6	+	1.25970e7i	−0.167979	+	0.290948i
$153$	−2.08693e7	−	3.61467e7i	−0.471072	−	0.815921i
$154$	−1.63462e7	+	9.43746e6i	−0.360656	+	0.208225i
$155$	2.27631e7			0.490987
$156$	−1.75625e7	−	8.75974e6i	−0.370382	−	0.184738i
$157$	1.16736e7			0.240745			0.120373	−	0.992729i	$-0.461591\pi$
$157$	1.16736e7			0.240745			0.120373	+	0.992729i	$0.461591\pi$
$158$	1.06708e8	−	6.16081e7i	2.15228	−	1.24262i
$159$	2.73651e6	+	4.73977e6i	0.0539892	+	0.0935120i
$160$	8.10830e6	−	1.40440e7i	0.156498	−	0.271063i
$161$		−	3.22828e7i		−	0.609651i
$162$	6.47375e7	+	3.73762e7i	1.19634	+	0.690705i
$163$	−7.03933e7	−	4.06416e7i	−1.27314	−	0.735045i	−0.297558	−	0.954704i	$-0.596172\pi$
$163$	−7.03933e7	−	4.06416e7i	−1.27314	−	0.735045i	−0.975577	+	0.219659i	$0.929506\pi$
$164$			1.63509e8i			2.89459i
$165$	1.92382e6	−	3.33216e6i	0.0333404	−	0.0577473i
$166$	9.71425e6	+	1.68256e7i	0.164828	+	0.285490i
$167$	−4.43496e7	+	2.56052e7i	−0.736855	+	0.425423i	−0.820925	−	0.571037i	$-0.806541\pi$
$167$	−4.43496e7	+	2.56052e7i	−0.736855	+	0.425423i	0.0840698	+	0.996460i	$0.473208\pi$
$168$	6.78914e6			0.110467
$169$	3.77474e7	+	5.01250e7i	0.601566	+	0.798823i
$170$	−4.47190e7			−0.698106
$171$	1.45836e7	−	8.41983e6i	0.223037	−	0.128771i
$172$	4.78057e7	+	8.28020e7i	0.716359	+	1.24077i
$173$	4.64758e7	−	8.04984e7i	0.682441	−	1.18202i	−0.291792	−	0.956482i	$-0.594252\pi$
$173$	4.64758e7	−	8.04984e7i	0.682441	−	1.18202i	0.974234	−	0.225541i	$-0.0724151\pi$
$174$		−	3.80685e7i		−	0.547827i
$175$	−1.90709e7	−	1.10106e7i	−0.268992	−	0.155302i
$176$	1.23154e7	+	7.11028e6i	0.170276	+	0.0983088i
$177$			2.21607e7i			0.300384i
$178$	4.43077e7	−	7.67431e7i	0.588856	−	1.01993i
$179$	4.39450e7	+	7.61150e7i	0.572696	+	0.991938i	0.996288	+	0.0860850i	$0.0274357\pi$
$179$	4.39450e7	+	7.61150e7i	0.572696	+	0.991938i	−0.423592	+	0.905853i	$0.639231\pi$
$180$	4.70550e7	−	2.71672e7i	0.601384	−	0.347209i
$181$	4.54030e7			0.569128			0.284564	−	0.958657i	$-0.408151\pi$
$181$	4.54030e7			0.569128			0.284564	+	0.958657i	$0.408151\pi$
$182$	−4.55604e7	−	2.27244e7i	−0.560193	−	0.279411i
$183$	−3.42606e7			−0.413253
$184$	−1.45298e8	+	8.38879e7i	−1.71948	+	0.992744i
$185$	−2.16203e7	−	3.74475e7i	−0.251050	−	0.434832i
$186$	−2.00694e7	+	3.47612e7i	−0.228686	+	0.396096i
$187$			5.93945e7i			0.664203i
$188$	−2.63264e8	−	1.51996e8i	−2.88961	−	1.66832i
$189$	−1.40202e7	−	8.09457e6i	−0.151056	−	0.0872122i
$190$		−	1.80421e7i		−	0.190832i
$191$	1.52735e7	−	2.64546e7i	0.158607	−	0.274716i	−0.775759	−	0.631029i	$-0.782633\pi$
$191$	1.52735e7	−	2.64546e7i	0.158607	−	0.274716i	0.934367	+	0.356313i	$0.115966\pi$
$192$	1.77388e7	+	3.07245e7i	0.180871	+	0.313278i
$193$	−1.16381e8	+	6.71927e7i	−1.16529	+	0.672778i	−0.952565	−	0.304336i	$-0.901566\pi$
$193$	−1.16381e8	+	6.71927e7i	−1.16529	+	0.672778i	−0.212720	+	0.977113i	$0.568232\pi$
$194$	−1.75220e8			−1.72297
$195$	1.03593e7	−	631984.i	0.100049	−	0.00610359i
$196$	2.62510e7			0.249029
$197$	1.00097e8	−	5.77912e7i	0.932805	−	0.538555i	0.0451073	−	0.998982i	$-0.485637\pi$
$197$	1.00097e8	−	5.77912e7i	0.932805	−	0.538555i	0.887698	+	0.460427i	$0.152304\pi$
$198$	−5.67818e7	−	9.83490e7i	−0.519854	−	0.900413i
$199$	1.59635e7	−	2.76496e7i	0.143596	−	0.248716i	−0.785252	−	0.619176i	$-0.787467\pi$
$199$	1.59635e7	−	2.76496e7i	0.143596	−	0.248716i	0.928848	+	0.370460i	$0.120800\pi$
$200$			1.14446e8i			1.01157i
$201$	−2.64146e7	−	1.52505e7i	−0.229434	−	0.132464i
$202$	−2.34690e8	−	1.35499e8i	−2.00339	−	1.15666i
$203$		−	6.27564e7i		−	0.526528i
$204$	2.50545e7	−	4.33957e7i	0.206624	−	0.357883i
$205$	−4.32336e7	−	7.48829e7i	−0.350496	−	0.607077i
$206$	4.29842e7	−	2.48170e7i	0.342589	−	0.197794i
$207$	1.94234e8			1.52205
$208$	2.33576e6	+	3.82873e7i	0.0179973	+	0.295007i
$209$	−2.39631e7			−0.181564
$210$	−7.29283e6	+	4.21052e6i	−0.0543411	+	0.0313739i
$211$	3.25183e7	+	5.63233e7i	0.238308	+	0.412762i	0.960229	−	0.279214i	$-0.0900738\pi$
$211$	3.25183e7	+	5.63233e7i	0.238308	+	0.412762i	−0.721921	+	0.691976i	$0.756740\pi$
$212$	5.49903e7	−	9.52460e7i	0.396379	−	0.686549i
$213$			1.96903e7i			0.139612i
$214$	1.28598e8	+	7.42463e7i	0.896990	+	0.517877i
$215$	−4.37876e7	−	2.52808e7i	−0.300481	−	0.173483i
$216$			8.41359e7i			0.568059i
$217$	−3.30846e7	+	5.73043e7i	−0.219795	+	0.380696i
$218$	1.04697e8	+	1.81340e8i	0.684440	+	1.18549i
$219$	−2.21695e7	+	1.27996e7i	−0.142627	+	0.0823458i
$220$	−7.73187e7			−0.489559
$221$	−1.33611e8	+	8.84053e7i	−0.832664	+	0.550941i
$222$	7.62475e7			0.467724
$223$	−4.84981e6	+	2.80004e6i	−0.0292859	+	0.0169082i	−0.514571	−	0.857447i	$-0.672049\pi$
$223$	−4.84981e6	+	2.80004e6i	−0.0292859	+	0.0169082i	0.485286	+	0.874356i	$0.338716\pi$
$224$	2.35697e7	+	4.08240e7i	0.140116	+	0.242687i
$225$	6.62469e7	−	1.14743e8i	0.387728	−	0.671564i
$226$		−	1.39718e8i		−	0.805142i
$227$	1.14301e8	+	6.59916e7i	0.648573	+	0.374454i	0.787909	−	0.615791i	$-0.211164\pi$
$227$	1.14301e8	+	6.59916e7i	0.648573	+	0.374454i	−0.139336	+	0.990245i	$0.544497\pi$
$228$	1.75082e7	+	1.01084e7i	0.0978296	+	0.0564819i
$229$			2.48638e8i			1.36818i	0.729398	+	0.684090i	$0.239800\pi$
$229$			2.48638e8i			1.36818i	−0.729398	+	0.684090i	$0.760200\pi$
$230$	1.04052e8	−	1.80223e8i	0.563901	−	0.976706i
$231$	5.59229e6	+	9.68613e6i	0.0298502	+	0.0517021i
$232$	−2.82453e8	+	1.63074e8i	−1.48504	+	0.857389i
$233$	−1.59608e8			−0.826625			−0.413313	−	0.910589i	$-0.635628\pi$
$233$	−1.59608e8			−0.826625			−0.413313	+	0.910589i	$0.635628\pi$
$234$	1.36725e8	−	2.74120e8i	0.697576	−	1.39858i
$235$	1.60758e8			0.808043
$236$	3.85660e8	−	2.22661e8i	1.90991	−	1.10269i
$237$	−3.65066e7	−	6.32314e7i	−0.178136	−	0.308541i
$238$	6.49961e7	−	1.12577e8i	0.312513	−	0.541289i
$239$		−	1.04549e6i		−	0.00495366i	−0.999997	−	0.00247683i	$-0.999212\pi$
$239$		−	1.04549e6i		−	0.00495366i	0.999997	−	0.00247683i	$-0.000788400\pi$
$240$	5.49449e6	+	3.17225e6i	0.0256560	+	0.0148125i
$241$	2.98925e8	+	1.72584e8i	1.37563	+	0.794222i	0.991630	−	0.129110i	$-0.0412121\pi$
$241$	2.98925e8	+	1.72584e8i	1.37563	+	0.794222i	0.384002	+	0.923332i	$0.374545\pi$
$242$		−	2.03557e8i		−	0.923278i
$243$	7.37595e7	−	1.27755e8i	0.329758	−	0.571158i
$244$	3.44235e8	+	5.96233e8i	1.51702	+	2.62755i
$245$	−1.20223e7	+	6.94108e6i	−0.0522284	+	0.0301541i
$246$	1.52470e8			0.652999
$247$	−3.56676e7	−	5.39061e7i	−0.150603	−	0.227614i
$248$	3.43886e8			1.43164
$249$	9.97021e6	−	5.75630e6i	0.0409267	−	0.0236290i
$250$	−1.57348e8	−	2.72534e8i	−0.636898	−	1.10314i
$251$	−8.58889e7	+	1.48764e8i	−0.342830	+	0.593799i	−0.984957	−	0.172799i	$-0.944719\pi$
$251$	−8.58889e7	+	1.48764e8i	−0.342830	+	0.593799i	0.642127	+	0.766598i	$0.278052\pi$
$252$			1.57943e8i			0.621725i
$253$	−2.39368e8	−	1.38199e8i	−0.929273	−	0.536516i
$254$	−5.27026e8	−	3.04278e8i	−2.01797	−	1.16507i
$255$			2.64988e7i			0.100077i
$256$	1.91644e8	−	3.31938e8i	0.713930	−	1.23656i
$257$	2.96735e7	+	5.13961e7i	0.109044	+	0.188871i	0.915383	−	0.402583i	$-0.131888\pi$
$257$	2.96735e7	+	5.13961e7i	0.109044	+	0.188871i	−0.806339	+	0.591454i	$0.798554\pi$
$258$	7.72120e7	−	4.45784e7i	0.279908	−	0.161605i
$259$	1.25695e8			0.449540
$260$	−1.15084e8	−	1.73932e8i	−0.406078	−	0.613725i
$261$	3.77582e8			1.31453
$262$	5.17455e7	−	2.98753e7i	0.177753	−	0.102626i
$263$	−1.72538e8	−	2.98845e8i	−0.584844	−	1.01298i	−0.994895	−	0.100917i	$-0.967822\pi$
$263$	−1.72538e8	−	2.98845e8i	−0.584844	−	1.01298i	0.410051	−	0.912063i	$-0.365511\pi$
$264$	2.90635e7	−	5.03394e7i	0.0972151	−	0.168382i
$265$			5.81604e7i			0.191985i
$266$	4.54197e7	+	2.62231e7i	0.147965	+	0.0854275i
$267$	−4.54751e7	−	2.62551e7i	−0.146212	−	0.0844158i
$268$			6.12920e8i			1.94505i
$269$	−7.58054e7	+	1.31299e8i	−0.237447	+	0.411270i	−0.959981	−	0.280065i	$-0.909644\pi$
$269$	−7.58054e7	+	1.31299e8i	−0.237447	+	0.411270i	0.722534	+	0.691335i	$0.242977\pi$
$270$	−5.21798e7	−	9.03781e7i	−0.161335	−	0.279441i
$271$	5.54862e7	−	3.20350e7i	0.169353	−	0.0977759i	−0.412928	−	0.910764i	$-0.635494\pi$
$271$	5.54862e7	−	3.20350e7i	0.169353	−	0.0977759i	0.582281	+	0.812988i	$0.302161\pi$
$272$	−9.79375e7			−0.295092
$273$	−1.34657e7	+	2.69974e7i	−0.0400551	+	0.0803068i
$274$	6.11116e8			1.79472
$275$	−1.63281e8	+	9.42702e7i	−0.473446	+	0.273344i
$276$	1.16593e8	+	2.01946e8i	0.333805	+	0.578166i
$277$	1.33533e8	−	2.31285e8i	0.377492	−	0.653835i	−0.613205	−	0.789924i	$-0.710120\pi$
$277$	1.33533e8	−	2.31285e8i	0.377492	−	0.653835i	0.990697	+	0.136089i	$0.0434532\pi$
$278$			2.22629e8i			0.621478i
$279$	−3.44779e8	−	1.99058e8i	−0.950443	−	0.548739i
$280$	6.24807e7	+	3.60732e7i	0.170095	+	0.0982047i
$281$			2.47147e8i			0.664482i	0.943194	+	0.332241i	$0.107805\pi$
$281$			2.47147e8i			0.664482i	−0.943194	+	0.332241i	$0.892195\pi$
$282$	−1.41734e8	+	2.45491e8i	−0.376360	+	0.651874i
$283$	8.79947e7	+	1.52411e8i	0.230783	+	0.399728i	0.958039	−	0.286638i	$-0.0925378\pi$
$283$	8.79947e7	+	1.52411e8i	0.230783	+	0.399728i	−0.727256	+	0.686367i	$0.759205\pi$
$284$	3.42667e8	−	1.97839e8i	0.887684	−	0.512504i
$285$	−1.06911e7			−0.0273568
$286$	−3.63533e8	+	2.40536e8i	−0.918889	+	0.607994i
$287$	2.51349e8			0.627610
$288$	−2.45623e8	+	1.41811e8i	−0.605893	+	0.349812i
$289$	643192.	+	1.11404e6i	0.00156747	+	0.00271493i
$290$	2.02272e8	−	3.50346e8i	0.487017	−	0.843537i
$291$			1.03829e8i			0.246997i
$292$	4.45498e8	+	2.57209e8i	1.04714	+	0.604568i
$293$	6.83867e8	+	3.94831e8i	1.58831	+	0.917011i	0.993586	+	0.113081i	$0.0360719\pi$
$293$	6.83867e8	+	3.94831e8i	1.58831	+	0.917011i	0.594724	+	0.803930i	$0.297261\pi$
$294$		−	2.44788e7i		−	0.0561791i
$295$	−1.17748e8	+	2.03946e8i	−0.267041	+	0.462528i
$296$	−3.26622e8	−	5.65725e8i	−0.732022	−	1.26790i
$297$	−1.20038e8	+	6.93037e7i	−0.265870	+	0.153500i
$298$	−1.41473e9			−3.09683
$299$	−4.53990e7	−	7.44171e8i	−0.0982194	−	1.60999i
$300$	1.59065e8			0.340134
$301$	1.27285e8	−	7.34879e7i	0.269026	−	0.155322i
$302$	−6.37276e8	−	1.10379e9i	−1.33138	−	2.30602i
$303$	−8.02914e7	+	1.39069e8i	−0.165813	+	0.287197i
$304$		−	3.95134e7i		−	0.0806654i
$305$	−3.15302e8	−	1.82040e8i	−0.636322	−	0.367381i
$306$	6.77333e8	+	3.91058e8i	1.35138	+	0.780219i
$307$			5.48723e8i			1.08235i	0.840909	+	0.541176i	$0.182021\pi$
$307$			5.48723e8i			1.08235i	−0.840909	+	0.541176i	$0.817979\pi$
$308$	1.12378e8	−	1.94644e8i	0.219155	−	0.379588i
$309$	−1.47056e7	−	2.54709e7i	−0.0283549	−	0.0491121i
$310$	−3.69399e8	+	2.13273e8i	−0.704255	+	0.406602i
$311$	−9.06115e7			−0.170813			−0.0854067	−	0.996346i	$-0.527219\pi$
$311$	−9.06115e7			−0.170813			−0.0854067	+	0.996346i	$0.527219\pi$
$312$	1.56500e8	−	9.54749e6i	0.291725	−	0.0177971i
$313$	−5.15292e8			−0.949836			−0.474918	−	0.880030i	$-0.657522\pi$
$313$	−5.15292e8			−0.949836			−0.474918	+	0.880030i	$0.657522\pi$
$314$	−1.89440e8	+	1.09373e8i	−0.345316	+	0.199368i
$315$	−4.17620e7	−	7.23339e7i	−0.0752826	−	0.130393i
$316$	−7.33604e8	+	1.27064e9i	−1.30785	+	2.26526i
$317$			5.88505e8i			1.03763i	0.854886	+	0.518816i	$0.173627\pi$
$317$			5.88505e8i			1.03763i	−0.854886	+	0.518816i	$0.826373\pi$
$318$	−8.88160e7	−	5.12779e7i	−0.154880	−	0.0894202i
$319$	−4.65320e8	−	2.68652e8i	−0.802572	−	0.463365i
$320$			3.77011e8i			0.643176i
$321$	4.39956e7	−	7.62026e7i	0.0742406	−	0.128589i
$322$	3.02465e8	+	5.23885e8i	0.504871	+	0.874462i
$323$	1.42924e8	−	8.25172e7i	0.235991	−	0.136250i
$324$	−8.90121e8			−1.45392
$325$	−4.55100e8	−	2.26993e8i	−0.735385	−	0.366793i
$326$	1.52312e9			2.43485
$327$	1.07455e8	−	6.20394e7i	0.169946	−	0.0981184i
$328$	−6.53138e8	−	1.13127e9i	−1.02199	−	1.77014i
$329$	−2.33651e8	+	4.04695e8i	−0.361727	+	0.626530i
$330$			7.20989e7i			0.110441i
$331$	−2.86241e8	−	1.65261e8i	−0.433844	−	0.250480i	0.267139	−	0.963658i	$-0.413922\pi$
$331$	−2.86241e8	−	1.65261e8i	−0.433844	−	0.250480i	−0.700983	+	0.713178i	$0.747255\pi$
$332$	−2.00352e8	−	1.15673e8i	−0.300477	−	0.173480i
$333$			7.56260e8i			1.12232i
$334$	4.79803e8	−	8.31043e8i	0.704613	−	1.22042i
$335$	−1.62063e8	−	2.80702e8i	−0.235520	−	0.407932i
$336$	−1.59718e7	+	9.22130e6i	−0.0229702	+	0.0132619i
$337$	−1.09443e9			−1.55770			−0.778851	−	0.627209i	$-0.784197\pi$
$337$	−1.09443e9			−1.55770			−0.778851	+	0.627209i	$0.784197\pi$
$338$	−1.08220e9	−	4.59763e8i	−1.52440	−	0.647628i
$339$	−8.27916e7			−0.115422
$340$	4.61155e8	−	2.66248e8i	0.636313	−	0.367376i
$341$	2.83263e8	+	4.90625e8i	0.386856	+	0.670054i
$342$	−1.57775e8	+	2.73274e8i	−0.213278	+	0.369408i
$343$		−	4.03536e7i		−	0.0539949i
$344$	−6.61507e8	−	3.81921e8i	−0.876153	−	0.505847i
$345$	−1.06794e8	−	6.16574e7i	−0.140016	−	0.0808385i
$346$			1.74177e9i			2.26060i
$347$	−2.54208e8	+	4.40300e8i	−0.326614	+	0.565713i	−0.981838	−	0.189723i	$-0.939241\pi$
$347$	−2.54208e8	+	4.40300e8i	−0.326614	+	0.565713i	0.655223	+	0.755435i	$0.272574\pi$
$348$	2.26652e8	+	3.92573e8i	0.288292	+	0.499337i
$349$	−9.99116e7	+	5.76840e7i	−0.125813	+	0.0726384i	−0.561586	−	0.827418i	$-0.689809\pi$
$349$	−9.99116e7	+	5.76840e7i	−0.125813	+	0.0726384i	0.435772	+	0.900057i	$0.356475\pi$
$350$	4.12644e8			0.514443
$351$	−3.34571e8	−	1.66876e8i	−0.412966	−	0.205977i
$352$	4.03597e8			0.493229
$353$	1.19860e9	−	6.92011e8i	1.45032	−	0.837340i	0.451816	−	0.892111i	$-0.350776\pi$
$353$	1.19860e9	−	6.92011e8i	1.45032	−	0.837340i	0.998499	+	0.0547713i	$0.0174430\pi$
$354$	−2.07629e8	−	3.59624e8i	−0.248758	−	0.430861i
$355$	−1.04622e8	+	1.81211e8i	−0.124115	+	0.214973i
$356$			1.05520e9i			1.23953i
$357$	−6.67087e7	−	3.85143e7i	−0.0775968	−	0.0448005i
$358$	−1.42628e9	−	8.23462e8i	−1.64291	−	0.948534i
$359$		−	4.02305e8i		−	0.458907i	−0.973320	−	0.229454i	$-0.926306\pi$
$359$		−	4.02305e8i		−	0.458907i	0.973320	−	0.229454i	$-0.0736939\pi$
$360$	−2.17040e8	+	3.75924e8i	−0.245177	+	0.424660i
$361$	−4.13644e8	−	7.16452e8i	−0.462755	−	0.801516i
$362$	−7.36800e8	+	4.25391e8i	−0.816337	+	0.471312i
$363$	−1.20620e8			−0.132357
$364$	6.05128e8	−	3.69166e7i	0.657646	−	0.0401205i
$365$	−2.72036e8			−0.292820
$366$	5.55981e8	−	3.20996e8i	0.592756	−	0.342228i
$367$	−2.01015e8	−	3.48168e8i	−0.212274	−	0.367669i	0.740152	−	0.672440i	$-0.234754\pi$
$367$	−2.01015e8	−	3.48168e8i	−0.212274	−	0.367669i	−0.952426	+	0.304770i	$0.901420\pi$
$368$	2.27880e8	−	3.94701e8i	0.238364	−	0.412858i
$369$			1.51228e9i			1.56689i
$370$	7.01708e8	+	4.05132e8i	0.720196	+	0.415805i
$371$	−1.46414e8	−	8.45322e7i	−0.148859	−	0.0859436i
$372$		−	4.77957e8i		−	0.481380i
$373$	1.78686e8	−	3.09494e8i	0.178283	−	0.308796i	−0.763009	−	0.646387i	$-0.776279\pi$
$373$	1.78686e8	−	3.09494e8i	0.178283	−	0.308796i	0.941293	+	0.337592i	$0.109612\pi$
$374$	−5.56481e8	−	9.63854e8i	−0.550047	−	0.952710i
$375$	−1.61493e8	+	9.32383e7i	−0.158141	+	0.0913029i
$376$	2.42859e9			2.35612
$377$	−8.82536e7	−	1.44663e9i	−0.0848277	−	1.39048i
$378$	3.03360e8			0.288893
$379$	4.29962e8	−	2.48239e8i	0.405689	−	0.234224i	−0.283247	−	0.959047i	$-0.591412\pi$
$379$	4.29962e8	−	2.48239e8i	0.405689	−	0.234224i	0.688936	+	0.724823i	$0.258078\pi$
$380$	1.07419e8	+	1.86056e8i	0.100425	+	0.173940i
$381$	−1.80304e8	+	3.12296e8i	−0.167020	+	0.289287i
$382$			5.72406e8i			0.525390i
$383$	1.45082e9	+	8.37633e8i	1.31953	+	0.761830i	0.983653	−	0.180077i	$-0.0576346\pi$
$383$	1.45082e9	+	8.37633e8i	1.31953	+	0.761830i	0.335875	+	0.941906i	$0.390968\pi$
$384$	−4.06569e8	−	2.34733e8i	−0.366416	−	0.211550i
$385$			1.18856e8i			0.106147i
$386$	1.25909e9	−	2.18080e9i	1.11430	−	1.93002i
$387$	4.42150e8	+	7.65827e8i	0.387777	+	0.671649i
$388$	1.80692e9	−	1.04322e9i	1.57046	−	0.906706i
$389$	1.25914e9			1.08455			0.542274	−	0.840202i	$-0.317563\pi$
$389$	1.25914e9			1.08455			0.542274	+	0.840202i	$0.317563\pi$
$390$	−1.62190e8	+	1.07315e8i	−0.138452	+	0.0916082i
$391$	1.90356e9			1.61045
$392$	−1.81623e8	+	1.04860e8i	−0.152289	+	0.0879243i
$393$	−1.77030e7	−	3.06624e7i	−0.0147120	−	0.0254820i
$394$	−1.08292e9	+	1.87567e9i	−0.891988	+	1.54497i
$395$		−	7.75894e8i		−	0.633451i
$396$	1.17110e9	+	6.76135e8i	0.947678	+	0.547142i
$397$	3.69629e8	+	2.13405e8i	0.296483	+	0.171174i	0.640862	−	0.767656i	$-0.278577\pi$
$397$	3.69629e8	+	2.13405e8i	0.296483	+	0.171174i	−0.344379	+	0.938831i	$0.611911\pi$
$398$			5.98263e8i			0.475666i
$399$	1.55388e7	−	2.69140e7i	0.0122465	−	0.0212116i
$400$	−1.55445e8	−	2.69239e8i	−0.121441	−	0.210343i
$401$	7.56992e8	−	4.37050e8i	0.586254	−	0.338474i	−0.177361	−	0.984146i	$-0.556756\pi$
$401$	7.56992e8	−	4.37050e8i	0.586254	−	0.338474i	0.763615	+	0.645672i	$0.223423\pi$
$402$	5.71542e8			0.438790
$403$	−6.82067e8	+	1.36748e9i	−0.519110	+	1.04077i
$404$	3.22692e9			2.43475
$405$	4.07653e8	−	2.35359e8i	0.304929	−	0.176051i
$406$	5.87979e8	+	1.01841e9i	0.436034	+	0.755234i
$407$	5.38084e8	−	9.31989e8i	0.395612	−	0.685220i
$408$			4.00322e8i			0.291809i
$409$	−3.22435e8	−	1.86158e8i	−0.233029	−	0.134539i	0.378940	−	0.925421i	$-0.376289\pi$
$409$	−3.22435e8	−	1.86158e8i	−0.233029	−	0.134539i	−0.611969	+	0.790882i	$0.709622\pi$
$410$	1.40319e9	+	8.10132e8i	1.00548	+	0.580513i
$411$		−	3.62124e8i		−	0.257283i
$412$	−2.95510e8	+	5.11839e8i	−0.208177	+	0.360573i
$413$	−3.42278e8	−	5.92844e8i	−0.239086	−	0.414109i
$414$	−3.15203e9	+	1.81983e9i	−2.18318	+	1.26046i
$415$	1.22342e8			0.0840245
$416$	6.00730e8	+	9.07912e8i	0.409122	+	0.618325i
$417$	1.31922e8			0.0890924
$418$	3.88872e8	−	2.24515e8i	0.260429	−	0.150359i
$419$	−5.02561e8	−	8.70461e8i	−0.333764	−	0.578096i	0.649483	−	0.760377i	$-0.274986\pi$
$419$	−5.02561e8	−	8.70461e8i	−0.333764	−	0.578096i	−0.983247	+	0.182280i	$0.941652\pi$
$420$	5.01372e7	−	8.68401e7i	0.0330208	−	0.0571936i
$421$		−	1.88721e9i		−	1.23263i	−0.787500	−	0.616315i	$-0.788625\pi$
$421$		−	1.88721e9i		−	1.23263i	0.787500	−	0.616315i	$-0.211375\pi$
$422$	−1.05541e9	−	6.09343e8i	−0.683642	−	0.394701i
$423$	−2.43490e9	−	1.40579e9i	−1.56419	−	0.903087i
$424$			8.78638e8i			0.559796i
$425$	6.49242e8	−	1.12452e9i	0.410247	−	0.710569i
$426$	−1.84483e8	−	3.19534e8i	−0.115617	−	0.200255i
$427$	9.16540e8	−	5.29165e8i	0.569710	−	0.328922i
$428$	−1.76819e9			−1.09012
$429$	1.42533e8	+	2.15416e8i	0.0871593	+	0.131728i
$430$	9.47447e8			0.574666
$431$	−1.69055e9	+	9.76037e8i	−1.01708	+	0.587213i	−0.913258	−	0.407382i	$-0.866442\pi$
$431$	−1.69055e9	+	9.76037e8i	−1.01708	+	0.587213i	−0.103825	+	0.994596i	$0.533108\pi$
$432$	−1.14277e8	−	1.97934e8i	−0.0681971	−	0.118121i
$433$	9.57085e8	−	1.65772e9i	0.566556	−	0.981304i	−0.430347	−	0.902663i	$-0.641609\pi$
$433$	9.57085e8	−	1.65772e9i	0.566556	−	0.981304i	0.996903	−	0.0786401i	$-0.0250578\pi$
$434$		−	1.23991e9i		−	0.728075i
$435$	−2.07602e8	−	1.19859e8i	−0.120926	−	0.0698166i
$436$	−2.15933e9	−	1.24669e9i	−1.24772	−	0.720369i
$437$			7.68002e8i			0.440228i
$438$	2.39844e8	−	4.15423e8i	0.136386	−	0.236228i
$439$	5.42939e7	+	9.40397e7i	0.0306284	+	0.0530500i	0.880933	−	0.473240i	$-0.156916\pi$
$439$	5.42939e7	+	9.40397e7i	0.0306284	+	0.0530500i	−0.850305	+	0.526290i	$0.823582\pi$
$440$	5.34945e8	−	3.08850e8i	0.299381	−	0.172848i
$441$	2.42793e8			0.134804
$442$	1.33995e9	−	2.68647e9i	0.738092	−	1.47981i
$443$	−1.04312e9			−0.570062			−0.285031	−	0.958518i	$-0.592004\pi$
$443$	−1.04312e9			−0.570062			−0.285031	+	0.958518i	$0.592004\pi$
$444$	−7.86285e8	+	4.53962e8i	−0.426324	+	0.246138i
$445$	−2.79006e8	−	4.83253e8i	−0.150091	−	0.259965i
$446$	5.24685e7	−	9.08781e7i	0.0280044	−	0.0485051i
$447$			8.38319e8i			0.443949i
$448$	−9.49096e8	−	5.47961e8i	−0.498697	−	0.287923i
$449$	1.64219e9	+	9.48121e8i	0.856174	+	0.494312i	0.862729	−	0.505666i	$-0.168753\pi$
$449$	1.64219e9	+	9.48121e8i	0.856174	+	0.494312i	−0.00655516	+	0.999979i	$0.502087\pi$
$450$			2.48273e9i			1.28436i
$451$	1.07599e9	−	1.86368e9i	0.552322	−	0.956649i
$452$	8.31852e8	+	1.44081e9i	0.423703	+	0.733875i
$453$	−6.54067e8	+	3.77626e8i	−0.330582	+	0.190861i
$454$	−2.47316e9			−1.24039
$455$	−2.67372e8	+	1.76910e8i	−0.133069	+	0.0880465i
$456$	−1.61512e8			−0.0797680
$457$	−5.56419e8	+	3.21249e8i	−0.272706	+	0.157447i	−0.630117	−	0.776500i	$-0.716993\pi$
$457$	−5.56419e8	+	3.21249e8i	−0.272706	+	0.157447i	0.357410	+	0.933947i	$0.383660\pi$
$458$	−2.32955e9	−	4.03489e9i	−1.13303	−	1.96247i
$459$	4.77297e8	−	8.26703e8i	0.230380	−	0.399030i
$460$			2.47802e9i			1.18700i
$461$	−1.23837e9	−	7.14976e8i	−0.588707	−	0.339890i	0.175879	−	0.984412i	$-0.443723\pi$
$461$	−1.23837e9	−	7.14976e8i	−0.588707	−	0.339890i	−0.764586	+	0.644522i	$0.777056\pi$
$462$	−1.81503e8	−	1.04791e8i	−0.0856323	−	0.0494398i
$463$		−	2.30027e8i		−	0.107707i	−0.998549	−	0.0538537i	$-0.982850\pi$
$463$		−	2.30027e8i		−	0.107707i	0.998549	−	0.0538537i	$-0.0171505\pi$
$464$	4.42989e8	−	7.67280e8i	0.205864	−	0.356567i
$465$	1.26377e8	+	2.18892e8i	0.0582887	+	0.100959i
$466$	2.59012e9	−	1.49540e9i	1.18568	−	0.684554i
$467$	−3.56140e9			−1.61812			−0.809061	−	0.587725i	$-0.800024\pi$
$467$	−3.56140e9			−1.61812			−0.809061	+	0.587725i	$0.800024\pi$
$468$	2.22114e8	+	3.64084e9i	0.100165	+	1.64188i
$469$	9.42192e8			0.421730
$470$	−2.60877e9	+	1.50618e9i	−1.15903	+	0.669165i
$471$	6.48104e7	+	1.12255e8i	0.0285806	+	0.0495030i
$472$	−1.77884e9	+	3.08104e9i	−0.778647	+	1.34866i
$473$		−	1.25837e9i		−	0.546758i
$474$	1.18486e9	+	6.84078e8i	0.511025	+	0.295041i
$475$	4.53694e8	+	2.61940e8i	0.194239	+	0.112144i
$476$			1.54790e9i			0.657836i
$477$	5.08600e8	−	8.80921e8i	0.214567	−	0.371640i
$478$	9.79542e6	+	1.69662e7i	0.00410228	+	0.00710536i
$479$	1.07850e9	−	6.22673e8i	0.448380	−	0.258872i	−0.258766	−	0.965940i	$-0.583316\pi$
$479$	1.07850e9	−	6.22673e8i	0.448380	−	0.258872i	0.707146	+	0.707068i	$0.249982\pi$
$480$	1.80064e8			0.0743162
$481$	2.89746e9	−	1.76763e8i	1.18716	−	0.0724243i
$482$	−6.46793e9			−2.63088
$483$	3.10435e8	−	1.79230e8i	0.125359	−	0.0723761i
$484$	1.21194e9	+	2.09914e9i	0.485872	+	0.841554i
$485$	−5.51681e8	+	9.55540e8i	−0.219580	+	0.380323i
$486$			2.76428e9i			1.09233i
$487$	−2.52030e9	−	1.45510e9i	−0.988784	−	0.570875i	−0.0838734	−	0.996476i	$-0.526729\pi$
$487$	−2.52030e9	−	1.45510e9i	−0.988784	−	0.570875i	−0.904911	+	0.425602i	$0.860062\pi$
$488$	−4.76332e9	−	2.75010e9i	−1.85541	−	1.07122i
$489$		−	9.02545e8i		−	0.349050i
$490$	1.30065e8	−	2.25280e8i	0.0499430	−	0.0865039i
$491$	1.51302e9	+	2.62062e9i	0.576845	+	0.999124i	0.995839	+	0.0911350i	$0.0290495\pi$
$491$	1.51302e9	+	2.62062e9i	0.576845	+	0.999124i	−0.418994	+	0.907989i	$0.637617\pi$
$492$	−1.57232e9	+	9.07777e8i	−0.595199	+	0.343638i
$493$	3.70044e9			1.39088
$494$	1.08387e9	+	5.40610e8i	0.404514	+	0.201762i
$495$	−7.15112e8			−0.265006
$496$	−8.09007e8	+	4.67081e8i	−0.297692	+	0.171872i
$497$	−3.04122e8	−	5.26755e8i	−0.111122	−	0.192469i
$498$	−1.07864e8	+	1.86826e8i	−0.0391359	+	0.0677853i
$499$		−	3.33505e9i		−	1.20158i	−0.799409	−	0.600788i	$-0.794854\pi$
$499$		−	3.33505e9i		−	1.20158i	0.799409	−	0.600788i	$-0.205146\pi$
$500$	3.24522e9	+	1.87363e9i	1.16105	+	0.670331i
$501$	−4.92445e8	−	2.84313e8i	−0.174955	−	0.101010i
$502$		−	3.21885e9i		−	1.13563i
$503$	5.24757e8	−	9.08905e8i	0.183853	−	0.318442i	−0.759337	−	0.650698i	$-0.774476\pi$
$503$	5.24757e8	−	9.08905e8i	0.183853	−	0.318442i	0.943189	+	0.332256i	$0.107810\pi$
$504$	−6.30905e8	−	1.09276e9i	−0.219512	−	0.380205i
$505$	−1.47785e9	+	8.53237e8i	−0.510635	+	0.294815i
$506$	5.17927e9			1.77722
$507$	−2.72439e8	+	6.41269e8i	−0.0928412	+	0.218531i
$508$	7.24645e9			2.45246
$509$	−2.50482e9	+	1.44616e9i	−0.841906	+	0.486075i	−0.857912	−	0.513797i	$-0.828238\pi$
$509$	−2.50482e9	+	1.44616e9i	−0.841906	+	0.486075i	0.0160054	+	0.999872i	$0.494905\pi$
$510$	−2.48274e8	−	4.30023e8i	−0.0828772	−	0.143548i
$511$	3.95386e8	−	6.84829e8i	0.131084	−	0.227043i
$512$			1.77040e9i			0.582944i
$513$	3.33538e8	+	1.92568e8i	0.109077	+	0.0629758i
$514$	−9.63084e8	−	5.56037e8i	−0.312819	−	0.180606i
$515$		−	3.12546e8i		−	0.100830i
$516$	−5.30821e8	+	9.19409e8i	−0.170088	+	0.294602i
$517$	2.00046e9	+	3.46490e9i	0.636668	+	1.10274i
$518$	−2.03977e9	+	1.17766e9i	−0.644804	+	0.372278i
$519$	1.03211e9			0.324070
$520$	1.49101e9	+	7.43680e8i	0.465017	+	0.231939i
$521$	2.96067e9			0.917186			0.458593	−	0.888646i	$-0.348354\pi$
$521$	2.96067e9			0.917186			0.458593	+	0.888646i	$0.348354\pi$
$522$	−6.12740e9	+	3.53766e9i	−1.88551	+	1.08860i
$523$	−2.56245e9	−	4.43829e9i	−0.783249	−	1.35663i	−0.930040	−	0.367459i	$-0.880228\pi$
$523$	−2.56245e9	−	4.43829e9i	−0.783249	−	1.35663i	0.146791	−	0.989167i	$-0.453105\pi$
$524$	−3.55743e8	+	6.16164e8i	−0.108013	+	0.187084i
$525$		−	2.44517e8i		−	0.0737484i
$526$	5.59990e9	+	3.23310e9i	1.67776	+	0.968655i
$527$	−3.37895e9	−	1.95084e9i	−1.00565	−	0.580610i
$528$			1.57901e8i			0.0466838i
$529$	−2.72678e9	+	4.72293e9i	−0.800859	+	1.38713i
$530$	−5.44918e8	−	9.43826e8i	−0.158988	−	0.275376i
$531$	3.56693e9	−	2.05937e9i	1.03386	−	0.596902i
$532$	−6.24507e8			−0.179824
$533$	5.79399e9	−	3.53469e8i	1.65742	−	0.101113i
$534$	9.83959e8			0.279629
$535$	8.09787e8	−	4.67531e8i	0.228630	−	0.131999i
$536$	−2.44832e9	−	4.24061e9i	−0.686737	−	1.18946i
$537$	−4.87953e8	+	8.45159e8i	−0.135978	+	0.235520i
$538$		−	2.84095e9i		−	0.786549i
$539$	−2.99210e8	−	1.72749e8i	−0.0823029	−	0.0475176i
$540$	1.07619e9	+	6.21336e8i	0.294110	+	0.169804i
$541$		−	2.93988e9i		−	0.798251i	−0.916896	−	0.399126i	$-0.869314\pi$
$541$		−	2.93988e9i		−	0.798251i	0.916896	−	0.399126i	$-0.130686\pi$
$542$	−6.00286e8	+	1.03973e9i	−0.161942	+	0.280493i
$543$	2.52071e8	+	4.36600e8i	0.0675653	+	0.117027i
$544$	−2.40719e9	+	1.38979e9i	−0.641083	+	0.370130i
$545$	1.31856e9			0.348908
$546$	−3.44243e7	−	5.64276e8i	−0.00905089	−	0.148360i
$547$	−4.35776e9			−1.13843			−0.569217	−	0.822188i	$-0.692753\pi$
$547$	−4.35776e9			−1.13843			−0.569217	+	0.822188i	$0.692753\pi$
$548$	−6.30200e9	+	3.63846e9i	−1.63586	+	0.944465i
$549$	3.18379e9	+	5.51449e9i	0.821187	+	1.42234i
$550$	1.76648e9	−	3.05963e9i	0.452730	−	0.784151i
$551$			1.49296e9i			0.380205i
$552$	−1.61335e9	−	9.31468e8i	−0.408265	−	0.235712i
$553$	1.95325e9	+	1.12771e9i	0.491157	+	0.283570i
$554$			5.00439e9i			1.25045i
$555$	2.40066e8	−	4.15806e8i	0.0596081	−	0.103244i
$556$	−1.32549e9	−	2.29582e9i	−0.327051	−	0.566468i
$557$	−1.42532e9	+	8.22909e8i	−0.349478	+	0.201771i	−0.664455	−	0.747328i	$-0.731336\pi$
$557$	−1.42532e9	+	8.22909e8i	−0.349478	+	0.201771i	0.314977	+	0.949099i	$0.398003\pi$
$558$	7.46010e9			1.81771
$559$	2.83077e9	−	1.87301e9i	0.685431	−	0.453523i
$560$	−1.95985e8			−0.0471590
$561$	−5.71144e8	+	3.29750e8i	−0.136576	+	0.0788524i
$562$	−2.31558e9	−	4.01070e9i	−0.550279	−	0.953110i
$563$	−1.17449e9	+	2.03427e9i	−0.277376	+	0.480430i	−0.970732	−	0.240166i	$-0.922798\pi$
$563$	−1.17449e9	+	2.03427e9i	−0.277376	+	0.480430i	0.693355	+	0.720596i	$0.256132\pi$
$564$		−	3.37543e9i		−	0.792232i
$565$	−7.61934e8	−	4.39903e8i	−0.177725	−	0.102609i
$566$	−2.85596e9	−	1.64889e9i	−0.662055	−	0.382237i
$567$			1.36831e9i			0.315242i
$568$	−1.58054e9	+	2.73758e9i	−0.361898	+	0.626826i
$569$	−2.69414e9	−	4.66639e9i	−0.613095	−	1.06191i	−0.990716	−	0.135951i	$-0.956591\pi$
$569$	−2.69414e9	−	4.66639e9i	−0.613095	−	1.06191i	0.377621	−	0.925960i	$-0.376742\pi$
$570$	1.73495e8	−	1.00167e8i	0.0392397	−	0.0226550i
$571$	−1.34601e9			−0.302568			−0.151284	−	0.988490i	$-0.548341\pi$
$571$	−1.34601e9			−0.302568			−0.151284	+	0.988490i	$0.548341\pi$
$572$	2.31676e9	−	4.64488e9i	0.517600	−	1.03774i
$573$	3.39186e8			0.0753177
$574$	−4.07889e9	+	2.35495e9i	−0.900222	+	0.519744i
$575$	3.02131e9	+	5.23306e9i	0.662762	+	1.14794i
$576$	3.29688e9	−	5.71037e9i	0.718828	−	1.24505i
$577$		−	3.17797e9i		−	0.688707i	−0.938840	−	0.344354i	$-0.888098\pi$
$577$		−	3.17797e9i		−	0.688707i	0.938840	−	0.344354i	$-0.111902\pi$
$578$	−2.08754e7	−	1.20524e7i	−0.00449664	−	0.00259614i
$579$	−1.29226e9	−	7.46089e8i	−0.276679	−	0.159741i
$580$			4.81716e9i			1.02516i
$581$	−1.77815e8	+	3.07985e8i	−0.0376143	+	0.0651499i
$582$	−9.72796e8	−	1.68493e9i	−0.204546	−	0.354284i
$583$	−1.25356e9	+	7.23745e8i	−0.262003	+	0.151267i
$584$	−4.10969e9			−0.853816
$585$	−1.06440e9	−	1.60868e9i	−0.219817	−	0.332219i
$586$	−1.47971e10			−3.03762
$587$	−5.01508e9	+	2.89546e9i	−1.02340	+	0.590859i	−0.915087	−	0.403258i	$-0.867878\pi$
$587$	−5.01508e9	+	2.89546e9i	−1.02340	+	0.590859i	−0.108312	+	0.994117i	$0.534545\pi$
$588$	1.45742e8	+	2.52433e8i	0.0295641	+	0.0512065i
$589$	7.87077e8	−	1.36326e9i	0.158713	−	0.274900i
$590$		−	4.41284e9i		−	0.884579i
$591$	1.11145e9	+	6.41698e8i	0.221480	+	0.127872i
$592$	1.53679e9	+	8.87263e8i	0.304430	+	0.175763i
$593$		−	1.02442e9i		−	0.201737i	−0.994900	−	0.100869i	$-0.967838\pi$
$593$		−	1.02442e9i		−	0.201737i	0.994900	−	0.100869i	$-0.0321622\pi$
$594$	1.29865e9	−	2.24932e9i	0.254237	−	0.440351i
$595$	−4.09282e8	−	7.08897e8i	−0.0796550	−	0.137967i
$596$	1.45891e10	−	8.42304e9i	2.82272	−	1.62970i
$597$	3.54509e8			0.0681894
$598$	7.70904e9	+	1.16510e10i	1.47417	+	2.22798i
$599$	−4.47406e9			−0.850565			−0.425282	−	0.905061i	$-0.639825\pi$
$599$	−4.47406e9			−0.850565			−0.425282	+	0.905061i	$0.639825\pi$
$600$	−1.10052e9	+	6.35386e8i	−0.208003	+	0.120090i
$601$	3.91150e7	+	6.77492e7i	0.00734992	+	0.0127304i	0.869677	−	0.493621i	$-0.164327\pi$
$601$	3.91150e7	+	6.77492e7i	0.00734992	+	0.0127304i	−0.862327	+	0.506352i	$0.830994\pi$
$602$	−1.37705e9	+	2.38512e9i	−0.257254	+	0.445577i
$603$			5.66883e9i			1.05289i
$604$	1.31435e10	+	7.58842e9i	2.42707	+	1.40127i
$605$	−1.11007e9	−	6.40901e8i	−0.203802	−	0.117665i
$606$		−	3.00907e9i		−	0.549261i
$607$	4.97806e8	−	8.62225e8i	0.0903441	−	0.156481i	−0.817312	−	0.576196i	$-0.804537\pi$
$607$	4.97806e8	−	8.62225e8i	0.0903441	−	0.156481i	0.907656	+	0.419715i	$0.137870\pi$
$608$	−5.60720e8	−	9.71195e8i	−0.101177	−	0.175244i
$609$	6.03472e8	−	3.48414e8i	0.108267	−	0.0625080i
$610$	6.82229e9			1.21696
$611$	−4.81690e9	+	9.65744e9i	−0.854326	+	1.71284i
$612$	−9.31313e9			−1.64235
$613$	−6.56114e9	+	3.78808e9i	−1.15045	+	0.664212i	−0.948997	−	0.315286i	$-0.897900\pi$
$613$	−6.56114e9	+	3.78808e9i	−1.15045	+	0.664212i	−0.201453	+	0.979498i	$0.564566\pi$
$614$	−5.14111e9	−	8.90467e9i	−0.896330	−	1.55249i
$615$	4.80054e8	−	8.31478e8i	0.0832199	−	0.144141i
$616$			1.79557e9i			0.309507i
$617$	3.73376e9	+	2.15569e9i	0.639953	+	0.369477i	0.784596	−	0.620007i	$-0.212870\pi$
$617$	3.73376e9	+	2.15569e9i	0.639953	+	0.369477i	−0.144644	+	0.989484i	$0.546204\pi$
$618$	4.77285e8	+	2.75561e8i	0.0813426	+	0.0469632i
$619$			1.23713e9i			0.209652i	0.994491	+	0.104826i	$0.0334285\pi$
$619$			1.23713e9i			0.209652i	−0.994491	+	0.104826i	$0.966571\pi$
$620$	2.53957e9	−	4.39866e9i	0.427946	−	0.741223i
$621$	2.22115e9	+	3.84714e9i	0.372183	+	0.644640i
$622$	1.47044e9	−	8.48960e8i	0.245009	−	0.141456i
$623$	1.62207e9			0.268758
$624$	−3.55207e8	+	2.35027e8i	−0.0585241	+	0.0387232i
$625$	3.03413e9			0.497111
$626$	8.36216e9	−	4.82790e9i	1.36241	−	0.786589i
$627$	−1.33039e8	−	2.30431e8i	−0.0215548	−	0.0373340i
$628$	1.30237e9	−	2.25577e9i	0.209834	−	0.363443i
$629$			7.41161e9i			1.18750i
$630$	1.35543e9	+	7.82556e8i	0.215965	+	0.124688i
$631$	−3.66922e8	−	2.11842e8i	−0.0581394	−	0.0335668i	0.470649	−	0.882321i	$-0.344020\pi$
$631$	−3.66922e8	−	2.11842e8i	−0.0581394	−	0.0335668i	−0.528788	+	0.848754i	$0.677353\pi$
$632$		−	1.17216e10i		−	1.84704i
$633$	−3.61074e8	+	6.25398e8i	−0.0565826	+	0.0980040i
$634$	−5.51384e9	−	9.55026e9i	−0.859295	−	1.48834i
$635$	−3.31869e9	+	1.91605e9i	−0.514350	+	0.296960i
$636$	1.22119e9			0.188228
$637$	−5.67489e7	−	9.30215e8i	−0.00869900	−	0.142592i
$638$	1.00683e10			1.53491
$639$	3.16929e9	−	1.82979e9i	0.480518	−	0.277427i
$640$	−2.49445e9	−	4.32051e9i	−0.376135	−	0.651485i
$641$	−2.18647e9	+	3.78707e9i	−0.327899	+	0.567938i	−0.982095	−	0.188388i	$-0.939674\pi$
$641$	−2.18647e9	+	3.78707e9i	−0.327899	+	0.567938i	0.654196	+	0.756325i	$0.273007\pi$
$642$			1.64882e9i			0.245924i
$643$	−5.90195e9	−	3.40749e9i	−0.875502	−	0.505471i	−0.00632899	−	0.999980i	$-0.502015\pi$
$643$	−5.90195e9	−	3.40749e9i	−0.875502	−	0.505471i	−0.869173	+	0.494509i	$0.835348\pi$
$644$	−6.23822e9	−	3.60164e9i	−0.920365	−	0.531373i
$645$		−	5.61422e8i		−	0.0823816i
$646$	−1.54625e9	+	2.67818e9i	−0.225665	+	0.390864i
$647$	−4.07535e9	−	7.05872e9i	−0.591562	−	1.02462i	−0.994022	−	0.109178i	$-0.965178\pi$
$647$	−4.07535e9	−	7.05872e9i	−0.591562	−	1.02462i	0.402460	−	0.915438i	$-0.368155\pi$
$648$	6.15848e9	−	3.55560e9i	0.889122	−	0.513335i
$649$	−5.86101e9			−0.841620
$650$	9.51210e9	−	5.80297e8i	1.35856	−	0.0828807i
$651$	−7.34725e8			−0.104374
$652$	−1.57069e10	+	9.06836e9i	−2.21933	+	1.28133i
$653$	5.23699e9	+	9.07073e9i	0.736013	+	1.27481i	0.954277	+	0.298923i	$0.0966272\pi$
$653$	5.23699e9	+	9.07073e9i	0.736013	+	1.27481i	−0.218264	+	0.975890i	$0.570039\pi$
$654$	−1.16252e9	+	2.01355e9i	−0.162510	+	0.281475i
$655$		−	3.76250e8i		−	0.0523157i
$656$	3.07307e9	+	1.77424e9i	0.425020	+	0.245385i
$657$	4.12037e9	+	2.37890e9i	0.566836	+	0.327263i
$658$		−	8.75651e9i		−	1.19823i
$659$	3.15187e9	−	5.45920e9i	0.429012	−	0.743071i	−0.567774	−	0.823185i	$-0.692195\pi$
$659$	3.15187e9	−	5.45920e9i	0.429012	−	0.743071i	0.996786	+	0.0801141i	$0.0255285\pi$
$660$	−4.29262e8	−	7.43504e8i	−0.0581191	−	0.100665i
$661$	2.74311e9	−	1.58374e9i	0.369436	−	0.213294i	−0.303776	−	0.952743i	$-0.598248\pi$
$661$	2.74311e9	−	1.58374e9i	0.369436	−	0.213294i	0.673212	+	0.739450i	$0.264914\pi$
$662$	6.19348e9			0.829721
$663$	−1.59190e9	−	7.94004e8i	−0.212139	−	0.105810i
$664$	1.84823e9			0.245002
$665$	2.86008e8	−	1.65127e8i	0.0377140	−	0.0217742i
$666$	−7.08558e9	−	1.22726e10i	−0.929427	−	1.60981i
$667$	−8.61016e9	+	1.49132e10i	−1.12349	+	1.94595i
$668$			1.14266e10i			1.48320i
$669$	−5.38510e7	−	3.10909e7i	−0.00695348	−	0.00401459i
$670$	5.25992e9	+	3.03682e9i	0.675643	+	0.390083i
$671$		−	9.06116e9i		−	1.15786i
$672$	−2.61712e8	+	4.53298e8i	−0.0332683	+	0.0576224i
$673$	3.78265e9	+	6.55173e9i	0.478347	+	0.828521i	0.999692	−	0.0248249i	$-0.00790283\pi$
$673$	3.78265e9	+	6.55173e9i	0.478347	+	0.828521i	−0.521345	+	0.853346i	$0.674569\pi$
$674$	1.77604e10	−	1.02540e10i	2.23431	−	1.28998i
$675$	3.03024e9			0.379240
$676$	1.38973e10	−	1.70197e9i	1.73028	−	0.211904i
$677$	−1.09285e10			−1.35363			−0.676814	−	0.736154i	$-0.736640\pi$
$677$	−1.09285e10			−1.35363			−0.676814	+	0.736154i	$0.736640\pi$
$678$	1.34354e9	−	7.75694e8i	0.165557	−	0.0955842i
$679$	−1.60366e9	−	2.77763e9i	−0.196594	−	0.340510i
$680$	−2.12706e9	+	3.68418e9i	−0.259417	+	0.449324i
$681$			1.46550e9i			0.177816i
$682$	−9.19357e9	−	5.30791e9i	−1.10978	−	0.640734i
$683$	4.47048e9	+	2.58103e9i	0.536886	+	0.309971i	0.743816	−	0.668385i	$-0.233014\pi$
$683$	4.47048e9	+	2.58103e9i	0.536886	+	0.309971i	−0.206930	+	0.978356i	$0.566347\pi$
$684$		−	3.75743e9i		−	0.448947i
$685$	1.92410e9	−	3.33265e9i	0.228724	−	0.396161i
$686$	3.78082e8	+	6.54858e8i	0.0447149	+	0.0774484i
$687$	−2.39093e9	+	1.38040e9i	−0.281331	+	0.162427i
$688$	2.07497e9			0.242914
$689$	−3.49395e9	−	1.74270e9i	−0.406958	−	0.202981i
$690$	2.31073e9			0.267779
$691$	1.18551e10	−	6.84452e9i	1.36688	−	0.789168i	0.376352	−	0.926477i	$-0.377178\pi$
$691$	1.18551e10	−	6.84452e9i	1.36688	−	0.789168i	0.990528	+	0.137308i	$0.0438452\pi$
$692$	−1.03701e10	−	1.79616e10i	−1.18963	−	2.06051i
$693$	1.03937e9	−	1.80024e9i	0.118632	−	0.205477i
$694$		−	9.52692e9i		−	1.08192i
$695$	1.21408e9	+	7.00951e8i	0.137183	+	0.0792028i
$696$	−3.13628e9	−	1.81073e9i	−0.352600	−	0.203574i
$697$			1.48208e10i			1.65790i
$698$	1.08091e9	−	1.87219e9i	0.120308	−	0.208380i
$699$	−8.86120e8	−	1.53481e9i	−0.0981347	−	0.169974i
$700$	−4.25530e9	+	2.45680e9i	−0.468908	+	0.270724i
$701$	8.96296e9			0.982739			0.491369	−	0.870951i	$-0.336496\pi$
$701$	8.96296e9			0.982739			0.491369	+	0.870951i	$0.336496\pi$
$702$	6.99292e9	−	4.26611e8i	0.762920	−	0.0465428i
$703$	−2.99025e9			−0.324612
$704$	−8.12593e9	+	4.69151e9i	−0.877746	+	0.506767i
$705$	8.92504e8	+	1.54586e9i	0.0959286	+	0.166153i
$706$	−1.29672e10	+	2.24599e10i	−1.38685	+	2.40210i
$707$		−	4.96049e9i		−	0.527906i
$708$	4.28225e9	+	2.47236e9i	0.453478	+	0.261816i
$709$	3.50664e8	+	2.02456e8i	0.0369513	+	0.0213338i	0.518362	−	0.855161i	$-0.326542\pi$
$709$	3.50664e8	+	2.02456e8i	0.0369513	+	0.0213338i	−0.481411	+	0.876495i	$0.659875\pi$
$710$		−	3.92091e9i		−	0.411133i
$711$	−6.78503e9	+	1.17520e10i	−0.707959	+	1.22622i
$712$	−4.21499e9	−	7.30058e9i	−0.437640	−	0.758014i
$713$	1.57243e10	−	9.07841e9i	1.62464	−	0.937986i
$714$	1.44340e9			0.148403
$715$	1.67146e8	+	2.73982e9i	0.0171011	+	0.280317i
$716$	1.96109e10			1.99665
$717$	1.00535e7	−	5.80440e6i	0.00101859	−	0.000588085i
$718$	3.76929e9	+	6.52860e9i	0.380035	+	0.658241i
$719$	−4.57745e9	+	7.92837e9i	−0.459275	+	0.795487i	−0.998923	−	0.0464038i	$-0.985224\pi$
$719$	−4.57745e9	+	7.92837e9i	−0.459275	+	0.795487i	0.539648	+	0.841891i	$0.318557\pi$
$720$		−	1.17917e9i		−	0.117737i
$721$	7.86809e8	+	4.54264e8i	0.0781800	+	0.0451373i
$722$	1.34252e10	+	7.75105e9i	1.32752	+	0.766444i
$723$			3.83266e9i			0.377151i
$724$	5.06539e9	−	8.77351e9i	0.496053	−	0.859189i
$725$	5.87329e9	+	1.01728e10i	0.572398	+	0.991422i
$726$	1.95743e9	−	1.13012e9i	0.189848	−	0.109609i
$727$	9.29133e9			0.896824			0.448412	−	0.893827i	$-0.351990\pi$
$727$	9.29133e9			0.896824			0.448412	+	0.893827i	$0.351990\pi$
$728$	−4.03924e9	+	2.67261e9i	−0.388007	+	0.256729i
$729$	−7.08648e9			−0.677461
$730$	4.41460e9	−	2.54877e9i	0.420011	−	0.242494i
$731$	4.33323e9	+	7.50537e9i	0.410299	+	0.710659i
$732$	−3.82229e9	+	6.62040e9i	−0.360192	+	0.623872i
$733$			1.38056e10i			1.29477i	0.762164	+	0.647383i	$0.224137\pi$
$733$			1.38056e10i			1.29477i	−0.762164	+	0.647383i	$0.775863\pi$
$734$	6.52413e9	+	3.76671e9i	0.608957	+	0.351581i
$735$	−1.33492e8	−	7.70718e7i	−0.0124008	−	0.00715962i
$736$		−	1.29350e10i		−	1.19590i
$737$	4.03341e9	−	6.98607e9i	0.371139	−	0.642831i
$738$	−1.41689e10	−	2.45412e10i	−1.29759	−	2.24749i
$739$	2.65736e9	−	1.53423e9i	0.242211	−	0.139841i	−0.373981	−	0.927436i	$-0.622008\pi$
$739$	2.65736e9	−	1.53423e9i	0.242211	−	0.139841i	0.616193	+	0.787595i	$0.288674\pi$
$740$	−9.64829e9			−0.875264
$741$	3.20345e8	−	6.42263e8i	0.0289238	−	0.0579894i
$742$	3.16801e9			0.284690
$743$	−5.96530e9	+	3.44407e9i	−0.533546	+	0.308043i	−0.742459	−	0.669891i	$-0.766341\pi$
$743$	−5.96530e9	+	3.44407e9i	−0.533546	+	0.308043i	0.208913	+	0.977934i	$0.433007\pi$
$744$	1.90921e9	+	3.30684e9i	0.169960	+	0.294380i
$745$	−4.45430e9	+	7.71508e9i	−0.394669	+	0.683587i
$746$			6.69661e9i			0.590567i
$747$	−1.85304e9	−	1.06985e9i	−0.162653	−	0.0939077i
$748$	1.14772e10	+	6.62636e9i	1.00272	+	0.578921i
$749$			2.71810e9i			0.236363i
$750$	1.74714e9	−	3.02614e9i	0.151222	−	0.261923i
$751$	−7.83360e9	−	1.35682e10i	−0.674872	−	1.16891i	−0.976506	−	0.215490i	$-0.930865\pi$
$751$	−7.83360e9	−	1.35682e10i	−0.674872	−	1.16891i	0.301634	−	0.953424i	$-0.402468\pi$
$752$	−5.71338e9	+	3.29862e9i	−0.489926	+	0.282859i
$753$	−1.90737e9			−0.162800
$754$	1.49860e10	+	2.26491e10i	1.27317	+	1.92420i
$755$	−8.02588e9			−0.678701
$756$	−3.12833e9	+	1.80614e9i	−0.263321	+	0.152029i
$757$	−8.03633e9	−	1.39193e10i	−0.673321	−	1.16623i	−0.976957	−	0.213438i	$-0.931534\pi$
$757$	−8.03633e9	−	1.39193e10i	−0.673321	−	1.16623i	0.303635	−	0.952788i	$-0.401800\pi$
$758$	−4.65161e9	+	8.05683e9i	−0.387937	+	0.671927i
$759$		−	3.06904e9i		−	0.254775i
$760$	−1.48640e9	−	8.58176e8i	−0.122826	−	0.0709134i
$761$	8.95589e9	+	5.17069e9i	0.736652	+	0.425306i	0.820851	−	0.571143i	$-0.193500\pi$
$761$	8.95589e9	+	5.17069e9i	0.736652	+	0.425306i	−0.0841986	+	0.996449i	$0.526833\pi$
$762$		−	6.75724e9i		−	0.553257i
$763$	−1.91643e9	+	3.31936e9i	−0.156192	+	0.270532i
$764$	−3.40799e9	−	5.90281e9i	−0.276485	−	0.478886i
$765$	4.26518e9	−	2.46250e9i	0.344447	−	0.198866i
$766$	−3.13919e10			−2.52358
$767$	−8.72377e9	−	1.31846e10i	−0.698105	−	1.05508i
$768$	4.25593e9			0.339024
$769$	−3.17308e8	+	1.83198e8i	−0.0251616	+	0.0145271i	−0.512528	−	0.858670i	$-0.671291\pi$
$769$	−3.17308e8	+	1.83198e8i	−0.0251616	+	0.0145271i	0.487366	+	0.873198i	$0.337958\pi$
$770$	−1.11359e9	−	1.92879e9i	−0.0879036	−	0.152254i
$771$	−3.29487e8	+	5.70688e8i	−0.0258909	+	0.0448444i
$772$			2.99854e10i			2.34558i
$773$	1.72595e10	+	9.96477e9i	1.34400	+	0.775960i	0.987392	−	0.158294i	$-0.0505993\pi$
$773$	1.72595e10	+	9.96477e9i	1.34400	+	0.775960i	0.356610	+	0.934253i	$0.383933\pi$
$774$	−1.43504e10	−	8.28522e9i	−1.11243	−	0.642260i
$775$		−	1.23854e10i		−	0.955771i
$776$	−8.33434e9	+	1.44355e10i	−0.640258	+	1.10896i
$777$	6.97839e8	+	1.20869e9i	0.0533681	+	0.0924363i
$778$	−2.04332e10	+	1.17971e10i	−1.55564	+	0.898148i
$779$	−5.97954e9			−0.453197
$780$	1.03362e9	−	2.07231e9i	0.0779883	−	0.156359i
$781$	−5.20764e9			−0.391167
$782$	−3.08910e10	+	1.78349e10i	−2.30998	+	1.33367i
$783$	4.31781e9	+	7.47866e9i	0.321438	+	0.556747i
$784$	2.84851e8	−	4.93377e8i	0.0211111	−	0.0365656i
$785$			1.37745e9i			0.101632i
$786$	5.74567e8	+	3.31726e8i	0.0422048	+	0.0243669i
$787$	−1.13627e10	−	6.56026e9i	−0.830941	−	0.479744i	0.0232335	−	0.999730i	$-0.492604\pi$
$787$	−1.13627e10	−	6.56026e9i	−0.830941	−	0.479744i	−0.854175	+	0.519986i	$0.825937\pi$
$788$		−	2.57899e10i		−	1.87762i
$789$	1.91582e9	−	3.31829e9i	0.138862	−	0.240516i
$790$	7.26953e9	+	1.25912e10i	0.524580	+	0.908599i
$791$	2.21484e9	−	1.27874e9i	0.159120	−	0.0918680i
$792$	−1.08033e10			−0.772715
$793$	2.03836e10	−	1.34870e10i	1.45152	−	0.960417i
$794$	−7.99778e9			−0.567019
$795$	−5.59276e8	+	3.22898e8i	−0.0394767	+	0.0227919i
$796$	−3.56194e9	−	6.16946e9i	−0.250317	−	0.433562i
$797$	−1.17043e9	+	2.02725e9i	−0.0818922	+	0.141841i	−0.904063	−	0.427400i	$-0.859430\pi$
$797$	−1.17043e9	+	2.02725e9i	−0.0818922	+	0.141841i	0.822170	+	0.569241i	$0.192763\pi$
$798$			5.82347e8i			0.0405669i
$799$	−2.38629e10	−	1.37772e10i	−1.65504	−	0.955539i
$800$	−7.64132e9	−	4.41172e9i	−0.527659	−	0.304644i
$801$			9.75939e9i			0.670979i
$802$	−8.18964e9	+	1.41849e10i	−0.560602	+	0.970991i
$803$	−3.38520e9	−	5.86334e9i	−0.230717	−	0.399614i
$804$	−5.89390e9	+	3.40284e9i	−0.399951	+	0.230912i
$805$	3.80926e9			0.257368
$806$	−1.74367e9	−	2.85819e10i	−0.117299	−	1.92273i
$807$	−1.68344e9			−0.112756
$808$	−2.23261e10	+	1.28900e10i	−1.48893	+	0.859632i
$809$	−9.33499e8	−	1.61687e9i	−0.0619860	−	0.107363i	0.833367	−	0.552720i	$-0.186410\pi$
$809$	−9.33499e8	−	1.61687e9i	−0.0619860	−	0.107363i	−0.895353	+	0.445357i	$0.853077\pi$
$810$	−4.41026e9	+	7.63879e9i	−0.291586	+	0.505042i
$811$		−	2.18089e10i		−	1.43569i	−0.696201	−	0.717847i	$-0.745128\pi$
$811$		−	2.18089e10i		−	1.43569i	0.696201	−	0.717847i	$-0.254872\pi$
$812$	−1.21268e10	−	7.00142e9i	−0.794878	−	0.458923i
$813$	6.16103e8	+	3.55707e8i	0.0402102	+	0.0232154i
$814$			2.01657e10i			1.31047i
$815$	4.79556e9	−	8.30616e9i	0.310304	−	0.537463i
$816$	−5.43735e8	−	9.41777e8i	−0.0350326	−	0.0606782i
$817$	−3.02808e9	+	1.74826e9i	−0.194263	+	0.112158i
$818$	6.97662e9			0.445665
$819$	5.59677e9	−	3.41437e8i	0.355995	−	0.0217179i
$820$	−1.92935e10			−1.22197
$821$	3.03143e9	−	1.75019e9i	0.191182	−	0.110379i	−0.401354	−	0.915923i	$-0.631460\pi$
$821$	3.03143e9	−	1.75019e9i	0.191182	−	0.110379i	0.592536	+	0.805544i	$0.298127\pi$
$822$	3.39283e9	+	5.87655e9i	0.213064	+	0.369038i
$823$	−1.13818e10	+	1.97138e10i	−0.711723	+	1.23274i	0.252486	+	0.967600i	$0.418752\pi$
$823$	−1.13818e10	+	1.97138e10i	−0.711723	+	1.23274i	−0.964210	+	0.265141i	$0.914582\pi$
$824$		−	4.72168e9i		−	0.294003i
$825$	−1.81302e9	−	1.04675e9i	−0.112413	−	0.0649014i
$826$	1.11090e10	+	6.41377e9i	0.685873	+	0.395989i
$827$		−	8.28321e9i		−	0.509248i	−0.967040	−	0.254624i	$-0.918048\pi$
$827$		−	8.28321e9i		−	0.509248i	0.967040	−	0.254624i	$-0.0819517\pi$
$828$	2.16697e10	−	3.75331e10i	1.32662	−	2.29778i
$829$	−1.40745e10	−	2.43777e10i	−0.858008	−	1.48611i	−0.873827	−	0.486238i	$-0.838369\pi$
$829$	−1.40745e10	−	2.43777e10i	−0.858008	−	1.48611i	0.0158190	−	0.999875i	$-0.494964\pi$
$830$	−1.98536e9	+	1.14625e9i	−0.120522	+	0.0695833i
$831$	2.96541e9			0.179259
$832$	−2.26488e10	−	1.12967e10i	−1.36337	−	0.680015i
$833$	2.37946e9			0.142633
$834$	−2.14083e9	+	1.23601e9i	−0.127791	+	0.0737802i
$835$	−3.02133e9	−	5.23310e9i	−0.179595	−	0.311068i
$836$	−2.67344e9	+	4.63053e9i	−0.158252	+	0.274100i
$837$		−	9.10525e9i		−	0.536726i
$838$	1.63111e10	+	9.41722e9i	0.957479	+	0.552801i
$839$	1.76812e10	+	1.02082e10i	1.03358	+	0.596737i	0.918008	−	0.396562i	$-0.129797\pi$
$839$	1.76812e10	+	1.02082e10i	1.03358	+	0.596737i	0.115571	+	0.993299i	$0.463130\pi$
$840$			8.01094e8i			0.0466344i
$841$	−8.11282e9	+	1.40518e10i	−0.470312	+	0.814604i
$842$	1.76817e10	+	3.06256e10i	1.02078	+	1.76804i
$843$	−2.37659e9	+	1.37213e9i	−0.136634	+	0.0788856i
$844$	1.45116e10			0.830840
$845$	−5.91457e9	+	4.45406e9i	−0.337229	+	0.253955i
$846$	5.26848e10			2.99150
$847$	3.22684e9	−	1.86301e9i	0.182467	−	0.105348i
$848$	−1.19340e9	−	2.06704e9i	−0.0672051	−	0.116403i
$849$	−9.77069e8	+	1.69233e9i	−0.0547959	+	0.0949093i
$850$			2.43316e10i			1.35895i
$851$	−2.98697e10	−	1.72453e10i	−1.66141	−	0.959217i
$852$	3.80488e9	+	2.19675e9i	0.210767	+	0.121686i
$853$		−	1.48351e10i		−	0.818407i	−0.912443	−	0.409204i	$-0.865807\pi$
$853$		−	1.48351e10i		−	0.818407i	0.912443	−	0.409204i	$-0.134193\pi$
$854$	−9.91574e9	+	1.71746e10i	−0.544782	+	0.943590i
$855$	9.93510e8	+	1.72081e9i	0.0543614	+	0.0941568i
$856$	1.22336e10	−	7.06306e9i	0.666646	−	0.384888i
$857$	−1.27844e10			−0.693823			−0.346912	−	0.937898i	$-0.612770\pi$
$857$	−1.27844e10			−0.693823			−0.346912	+	0.937898i	$0.612770\pi$
$858$	−4.33130e9	−	2.16035e9i	−0.234106	−	0.116767i
$859$	2.70324e10			1.45515			0.727577	−	0.686026i	$-0.240646\pi$
$859$	2.70324e10			1.45515			0.727577	+	0.686026i	$0.240646\pi$
$860$	−9.77034e9	+	5.64091e9i	−0.523800	+	0.302416i
$861$	1.39545e9	+	2.41700e9i	0.0745082	+	0.129052i
$862$	1.82894e10	−	3.16782e10i	0.972579	−	1.68456i
$863$		−	2.53729e10i		−	1.34379i	−0.740646	−	0.671896i	$-0.765480\pi$
$863$		−	2.53729e10i		−	1.34379i	0.740646	−	0.671896i	$-0.234520\pi$
$864$	−5.61760e9	−	3.24332e9i	−0.296314	−	0.171077i
$865$	9.49853e9	+	5.48398e9i	0.498999	+	0.288097i
$866$			3.58686e10i			1.87673i
$867$	−7.14183e6	+	1.23700e7i	−0.000372171	+	0.000644619i
$868$	7.38218e9	+	1.27863e10i	0.383147	+	0.663630i
$869$	1.67233e10	−	9.65519e9i	0.864474	−	0.499104i
$870$	4.49195e9			0.231269
$871$	2.17190e10	−	1.32500e9i	1.11372	−	0.0679440i
$872$	1.99196e10			1.01736
$873$	1.67120e10	−	9.64867e9i	0.850116	−	0.490815i
$874$	−7.19559e9	−	1.24631e10i	−0.364566	−	0.631447i
$875$	2.88018e9	−	4.98862e9i	0.145342	−	0.251740i
$876$			5.71194e9i			0.287091i
$877$	1.89863e10	+	1.09617e10i	0.950475	+	0.548757i	0.893229	−	0.449603i	$-0.148434\pi$
$877$	1.89863e10	+	1.09617e10i	0.950475	+	0.548757i	0.0572468	+	0.998360i	$0.481768\pi$
$878$	−1.76216e9	−	1.01738e9i	−0.0878647	−	0.0507287i
$879$			8.76818e9i			0.435460i
$880$	−8.38988e8	+	1.45317e9i	−0.0415018	+	0.0718832i
$881$	1.50514e10	+	2.60698e10i	0.741586	+	1.28447i	0.951773	+	0.306804i	$0.0992596\pi$
$881$	1.50514e10	+	2.60698e10i	0.741586	+	1.28447i	−0.210186	+	0.977661i	$0.567407\pi$
$882$	−3.94004e9	+	2.27479e9i	−0.193357	+	0.111635i
$883$	−1.23081e10			−0.601628			−0.300814	−	0.953683i	$-0.597258\pi$
$883$	−1.23081e10			−0.601628			−0.300814	+	0.953683i	$0.597258\pi$
$884$	2.17679e9	+	3.56815e10i	0.105982	+	1.73724i
$885$	−2.61489e9			−0.126809
$886$	1.69278e10	−	9.77326e9i	0.817678	−	0.472086i
$887$	1.08948e10	+	1.88704e10i	0.524188	+	0.907921i	0.999603	+	0.0281592i	$0.00896453\pi$
$887$	1.08948e10	+	1.88704e10i	0.524188	+	0.907921i	−0.475415	+	0.879762i	$0.657702\pi$
$888$	3.62671e9	−	6.28165e9i	0.173807	−	0.301043i
$889$		−	1.11394e10i		−	0.531747i
$890$	9.05542e9	+	5.22815e9i	0.430570	+	0.248590i
$891$	1.01456e10	+	5.85758e9i	0.480515	+	0.277425i
$892$			1.24955e9i			0.0589489i
$893$	5.55850e9	−	9.62761e9i	0.261203	−	0.452416i
$894$	−7.85440e9	−	1.36042e10i	−0.367648	−	0.636785i
$895$	−8.98130e9	+	5.18536e9i	−0.418754	+	0.241768i
$896$	1.45020e10			0.673521
$897$	6.90397e9	−	4.56809e9i	0.319393	−	0.211330i
$898$	−3.55327e10			−1.63742
$899$	3.05673e10	−	1.76480e10i	1.40313	−	0.810097i
$900$	−1.47817e10	−	2.56026e10i	−0.675888	−	1.17067i
$901$	4.98445e9	−	8.63333e9i	0.227029	−	0.393225i
$902$			4.03250e10i			1.82958i
$903$	1.41333e9	+	8.15989e8i	0.0638760	+	0.0368788i
$904$	−1.15107e10	−	6.64569e9i	−0.518216	−	0.299192i
$905$			5.35740e9i			0.240261i
$906$	7.07613e9	−	1.22562e10i	0.316116	−	0.547530i
$907$	−7.27391e9	−	1.25988e10i	−0.323700	−	0.560664i	0.657549	−	0.753412i	$-0.271593\pi$
$907$	−7.27391e9	−	1.25988e10i	−0.323700	−	0.560664i	−0.981248	+	0.192748i	$0.938260\pi$
$908$	2.55039e10	−	1.47247e10i	1.13059	−	0.652749i
$909$	2.98455e10			1.31797
$910$	2.68140e9	−	5.37596e9i	0.117955	−	0.236489i
$911$	2.70671e10			1.18612			0.593058	−	0.805159i	$-0.297920\pi$
$911$	2.70671e10			1.18612			0.593058	+	0.805159i	$0.297920\pi$
$912$	3.79965e8	−	2.19373e8i	0.0165868	−	0.00957637i
$913$	1.52241e9	+	2.63690e9i	0.0662041	+	0.114669i
$914$	6.01971e9	−	1.04264e10i	0.260774	−	0.451673i
$915$		−	4.04263e9i		−	0.174458i
$916$	4.80459e10	+	2.77393e10i	2.06548	+	1.19251i
$917$	9.47180e8	+	5.46854e8i	0.0405639	+	0.0234196i
$918$			1.78876e10i			0.763139i
$919$	−8.18157e9	+	1.41709e10i	−0.347722	+	0.602273i	−0.985844	−	0.167662i	$-0.946378\pi$
$919$	−8.18157e9	+	1.41709e10i	−0.347722	+	0.602273i	0.638122	+	0.769935i	$0.279711\pi$
$920$	−9.89848e9	−	1.71447e10i	−0.419094	−	0.725892i
$921$	−5.27658e9	+	3.04643e9i	−0.222558	+	0.128494i
$922$	2.67951e10			1.12589
$923$	−7.75127e9	−	1.17149e10i	−0.324464	−	0.490378i
$924$	2.49562e9			0.104070
$925$	−2.03752e10	+	1.17636e10i	−0.846457	+	0.488702i
$926$	2.15518e9	+	3.73288e9i	0.0891959	+	0.154492i
$927$	−2.73315e9	+	4.73395e9i	−0.112690	+	0.195184i
$928$		−	2.51452e10i		−	1.03285i
$929$	−2.73163e10	−	1.57711e10i	−1.11781	−	0.645367i	−0.176967	−	0.984217i	$-0.556629\pi$
$929$	−2.73163e10	−	1.57711e10i	−1.11781	−	0.645367i	−0.940840	+	0.338850i	$0.889962\pi$
$930$	−4.10170e9	−	2.36812e9i	−0.167215	−	0.0965413i
$931$			9.60005e8i			0.0389897i
$932$	−1.78067e10	+	3.08420e10i	−0.720488	+	1.24792i
$933$	−5.03062e8	−	8.71329e8i	−0.0202785	−	0.0351234i
$934$	5.77943e10	−	3.33676e10i	2.32098	−	1.34002i
$935$	−7.00835e9			−0.280398
$936$	−1.60801e10	−	2.43026e10i	−0.640949	−	0.968697i
$937$	2.07753e10			0.825011			0.412505	−	0.910955i	$-0.364654\pi$
$937$	2.07753e10			0.825011			0.412505	+	0.910955i	$0.364654\pi$
$938$	−1.52899e10	+	8.82762e9i	−0.604915	+	0.349248i
$939$	−2.86083e9	−	4.95510e9i	−0.112762	−	0.195309i
$940$	1.79349e10	−	3.10642e10i	0.704292	−	1.21987i
$941$			1.61468e10i			0.631719i	0.948806	+	0.315860i	$0.102293\pi$
$941$			1.61468e10i			0.631719i	−0.948806	+	0.315860i	$0.897707\pi$
$942$	−2.10348e9	−	1.21445e9i	−0.0819900	−	0.0473370i
$943$	−5.97298e10	−	3.44850e10i	−2.31953	−	1.33918i
$944$		−	9.66440e9i		−	0.373915i
$945$	9.55131e8	−	1.65433e9i	0.0368173	−	0.0637694i
$946$	1.17900e10	+	2.04208e10i	0.452787	+	0.784250i
$947$	−9.81360e9	+	5.66588e9i	−0.375494	+	0.216792i	−0.675856	−	0.737034i	$-0.736226\pi$
$947$	−9.81360e9	+	5.66588e9i	−0.375494	+	0.216792i	0.300362	+	0.953825i	$0.402893\pi$
$948$	−1.62915e10			−0.621056
$949$	8.15121e9	−	1.63424e10i	0.309593	−	0.620704i
$950$	−9.81672e9			−0.371479
$951$	−5.65913e9	+	3.26730e9i	−0.213362	+	0.123185i
$952$	−6.18309e9	−	1.07094e10i	−0.232261	−	0.402288i
$953$	−1.27373e10	+	2.20616e10i	−0.476707	+	0.825682i	−0.999644	−	0.0266902i	$-0.991503\pi$
$953$	−1.27373e10	+	2.20616e10i	−0.476707	+	0.825682i	0.522936	+	0.852372i	$0.324837\pi$
$954$			1.90608e10i			0.710757i
$955$	3.12155e9	+	1.80222e9i	0.115973	+	0.0669572i
$956$	−2.02026e8	−	1.16640e8i	−0.00747834	−	0.00431762i
$957$		−	5.96608e9i		−	0.220038i
$958$	−1.16679e10	+	2.02095e10i	−0.428760	+	0.742635i
$959$	5.59311e9	+	9.68756e9i	0.204780	+	0.354690i
$960$	−3.62538e9	+	2.09311e9i	−0.132253	+	0.0763561i
$961$	−9.70294e9			−0.352672
$962$	−4.53639e10	+	3.00155e10i	−1.64285	+	1.08701i
$963$	−1.63538e10			−0.590102
$964$	6.66991e10	−	3.85088e10i	2.39801	−	1.38449i
$965$	−7.92850e9	−	1.37326e10i	−0.284018	−	0.491933i
$966$	−3.35849e9	+	5.81707e9i	−0.119874	+	0.207627i
$967$		−	3.49389e10i		−	1.24256i	−0.783590	−	0.621278i	$-0.786614\pi$
$967$		−	3.49389e10i		−	1.24256i	0.783590	−	0.621278i	$-0.213386\pi$
$968$	−1.67701e10	−	9.68220e9i	−0.594253	−	0.343092i
$969$	1.58699e9	+	9.16248e8i	0.0560325	+	0.0323504i
$970$		−	2.06753e10i		−	0.727363i
$971$	1.52063e10	−	2.63380e10i	0.533035	−	0.923244i	−0.466221	−	0.884668i	$-0.654385\pi$
$971$	1.52063e10	−	2.63380e10i	0.533035	−	0.923244i	0.999256	−	0.0385751i	$-0.0122819\pi$
$972$	−1.64580e10	−	2.85060e10i	−0.574836	−	0.995645i
$973$	−3.52918e9	+	2.03757e9i	−0.122823	+	0.0709117i
$974$	5.45326e10			1.89104
$975$	−3.43862e8	−	5.63652e9i	−0.0118814	−	0.194758i
$976$	1.49412e10			0.514413
$977$	−8.01952e9	+	4.63007e9i	−0.275117	+	0.158839i	−0.631211	−	0.775611i	$-0.717442\pi$
$977$	−8.01952e9	+	4.63007e9i	−0.275117	+	0.158839i	0.356094	+	0.934450i	$0.384108\pi$
$978$	8.45615e9	+	1.46465e10i	0.289059	+	0.500665i
$979$	6.94387e9	−	1.20271e10i	0.236517	−	0.409660i
$980$			3.09753e9i			0.105129i
$981$	−1.99714e10	−	1.15305e10i	−0.675409	−	0.389947i
$982$	−4.91065e10	−	2.83516e10i	−1.65481	−	0.955406i
$983$			5.40203e10i			1.81393i	0.421209	+	0.906963i	$0.361606\pi$
$983$			5.40203e10i			1.81393i	−0.421209	+	0.906963i	$0.638394\pi$
$984$	7.25225e9	−	1.25613e10i	0.242656	−	0.420292i
$985$	6.81916e9	+	1.18111e10i	0.227355	+	0.393790i
$986$	−6.00507e10	+	3.46703e10i	−1.99503	+	1.15183i
$987$	−5.18878e9			−0.171773
$988$	−1.43959e10	+	8.78238e8i	−0.474886	+	0.0289710i
$989$	−4.03301e10			−1.32569
$990$	1.16048e10	−	6.70006e9i	0.380116	−	0.219460i
$991$	−1.89414e10	−	3.28075e10i	−0.618236	−	1.07082i	−0.989807	−	0.142412i	$-0.954514\pi$
$991$	−1.89414e10	−	3.28075e10i	−0.618236	−	1.07082i	0.371571	−	0.928405i	$-0.378819\pi$
$992$	−1.32563e10	+	2.29606e10i	−0.431154	+	0.746780i
$993$		−	3.67003e9i		−	0.118945i
$994$	9.87058e9	+	5.69878e9i	0.318779	+	0.184047i
$995$	3.26256e9	+	1.88364e9i	0.104997	+	0.0606201i
$996$		−	2.56881e9i		−	0.0823804i
$997$	2.06617e10	−	3.57871e10i	0.660287	−	1.14365i	−0.320253	−	0.947332i	$-0.603768\pi$
$997$	2.06617e10	−	3.57871e10i	0.660287	−	1.14365i	0.980540	−	0.196319i	$-0.0628988\pi$
$998$	3.12469e10	+	5.41212e10i	0.995062	+	1.72350i
$999$	−1.49790e10	+	8.64814e9i	−0.475340	+	0.274437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.q.a.36.7	✓	100
13.4	even	6	inner	91.8.q.a.43.7	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.q.a.36.7	✓	100	1.1	even	1	trivial
91.8.q.a.43.7	yes	100	13.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.2280 + 9.36923i) q^{2} +(5.55186 + 9.61610i) q^{3} +(111.565 - 193.236i) q^{4} +117.996i q^{5} +(-180.191 - 104.033i) q^{6} +(-297.047 - 171.500i) q^{7} +1782.59i q^{8} +(1031.85 - 1787.22i) q^{9} +O(q^{10})\)	\(q+(-16.2280 + 9.36923i) q^{2} +(5.55186 + 9.61610i) q^{3} +(111.565 - 193.236i) q^{4} +117.996i q^{5} +(-180.191 - 104.033i) q^{6} +(-297.047 - 171.500i) q^{7} +1782.59i q^{8} +(1031.85 - 1787.22i) q^{9} +(-1105.54 - 1914.85i) q^{10} +(-2543.24 + 1468.34i) q^{11} +2477.57 q^{12} +(-7088.58 - 3535.61i) q^{13} +6427.29 q^{14} +(-1134.67 + 655.100i) q^{15} +(-2421.19 - 4193.63i) q^{16} +(10112.5 - 17515.4i) q^{17} +38670.7i q^{18} +(7066.68 + 4079.95i) q^{19} +(22801.2 + 13164.3i) q^{20} -3808.57i q^{21} +(27514.5 - 47656.5i) q^{22} +(47059.5 + 81509.5i) q^{23} +(-17141.6 + 9896.70i) q^{24} +64201.8 q^{25} +(148159. - 9038.64i) q^{26} +47198.6 q^{27} +(-66280.1 + 38266.8i) q^{28} +(91481.6 + 158451. i) q^{29} +(12275.6 - 21261.9i) q^{30} -192913. i q^{31} +(-119020. - 68716.4i) q^{32} +(-28239.4 - 16304.1i) q^{33} +378986. i q^{34} +(20236.4 - 35050.5i) q^{35} +(-230238. - 398783. i) q^{36} +(-317361. + 183228. i) q^{37} -152904. q^{38} +(-5355.96 - 87793.7i) q^{39} -210340. q^{40} +(-634619. + 366398. i) q^{41} +(35683.4 + 61805.5i) q^{42} +(-214251. + 371093. i) q^{43} +655263. i q^{44} +(210886. + 121755. i) q^{45} +(-1.52736e6 - 881823. i) q^{46} -1.36239e6i q^{47} +(26884.3 - 46564.9i) q^{48} +(58824.5 + 101887. i) q^{49} +(-1.04187e6 + 601522. i) q^{50} +224573. q^{51} +(-1.47405e6 + 975320. i) q^{52} +492899. q^{53} +(-765939. + 442215. i) q^{54} +(-173259. - 300094. i) q^{55} +(305715. - 529513. i) q^{56} +90605.3i q^{57} +(-2.96912e6 - 1.71422e6i) q^{58} +(1.72841e6 + 997896. i) q^{59} +292345. i q^{60} +(-1.54275e6 + 2.67213e6i) q^{61} +(1.80745e6 + 3.13060e6i) q^{62} +(-613018. + 353926. i) q^{63} +3.19511e6 q^{64} +(417190. - 836427. i) q^{65} +611026. q^{66} +(-2.37890e6 + 1.37346e6i) q^{67} +(-2.25641e6 - 3.90821e6i) q^{68} +(-522536. + 905058. i) q^{69} +758398. i q^{70} +(1.53573e6 + 886653. i) q^{71} +(3.18589e6 + 1.83937e6i) q^{72} +2.30546e6i q^{73} +(3.43342e6 - 5.94686e6i) q^{74} +(356439. + 617371. i) q^{75} +(1.57679e6 - 910360. i) q^{76} +1.00728e6 q^{77} +(909476. + 1.37453e6i) q^{78} -6.57557e6 q^{79} +(494834. - 285692. i) q^{80} +(-1.99462e6 - 3.45479e6i) q^{81} +(6.86573e6 - 1.18918e7i) q^{82} -1.03682e6i q^{83} +(-735955. - 424904. i) q^{84} +(2.06676e6 + 1.19324e6i) q^{85} -8.02945e6i q^{86} +(-1.01579e6 + 1.75939e6i) q^{87} +(-2.61745e6 - 4.53356e6i) q^{88} +(-4.09549e6 + 2.36453e6i) q^{89} -4.56301e6 q^{90} +(1.49928e6 + 2.26593e6i) q^{91} +2.10008e7 q^{92} +(1.85507e6 - 1.07103e6i) q^{93} +(1.27646e7 + 2.21089e7i) q^{94} +(-481420. + 833844. i) q^{95} -1.52602e6i q^{96} +(8.09804e6 + 4.67541e6i) q^{97} +(-1.90921e6 - 1.10228e6i) q^{98} +6.06046e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9}+O(q^{10}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9} - 2728 q^{10} - 3954 q^{11} - 54708 q^{12} - 32008 q^{13} + 21952 q^{14} + 46398 q^{15} - 228808 q^{16} + 16832 q^{17} - 203520 q^{20} + 148982 q^{22} + 154164 q^{23} - 436560 q^{24} - 1918852 q^{25} - 624246 q^{26} + 661404 q^{27} - 451396 q^{29} + 313736 q^{30} + 1854432 q^{32} + 315450 q^{33} - 372498 q^{35} + 2704174 q^{36} + 1777146 q^{37} - 338468 q^{38} + 189708 q^{39} - 2875580 q^{40} - 2158998 q^{41} - 296352 q^{42} + 1876346 q^{43} + 7252980 q^{45} + 234336 q^{46} + 1316674 q^{48} + 5882450 q^{49} + 6432894 q^{50} - 3602684 q^{51} - 14093326 q^{52} + 1719628 q^{53} - 14915976 q^{54} - 1225470 q^{55} + 2107392 q^{56} + 18792564 q^{58} + 5131962 q^{59} + 886858 q^{61} + 3663272 q^{62} - 1848084 q^{63} - 38282980 q^{64} - 17072760 q^{65} + 54390948 q^{66} - 15529368 q^{67} + 2633716 q^{68} + 12342620 q^{69} + 20194104 q^{71} + 12742440 q^{72} - 23243862 q^{74} - 12055866 q^{75} - 7828698 q^{76} - 11143384 q^{77} - 32361130 q^{78} + 38408264 q^{79} - 38368944 q^{80} - 55140914 q^{81} + 27439818 q^{82} + 46422306 q^{84} + 16353300 q^{85} - 15866954 q^{87} - 39468942 q^{88} + 11465844 q^{89} - 22072424 q^{90} - 3481450 q^{91} + 67780968 q^{92} - 71319114 q^{93} - 6119236 q^{94} + 60860930 q^{95} + 45060702 q^{97}+O(q^{100}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9 - 2728 * q^10 - 3954 * q^11 - 54708 * q^12 - 32008 * q^13 + 21952 * q^14 + 46398 * q^15 - 228808 * q^16 + 16832 * q^17 - 203520 * q^20 + 148982 * q^22 + 154164 * q^23 - 436560 * q^24 - 1918852 * q^25 - 624246 * q^26 + 661404 * q^27 - 451396 * q^29 + 313736 * q^30 + 1854432 * q^32 + 315450 * q^33 - 372498 * q^35 + 2704174 * q^36 + 1777146 * q^37 - 338468 * q^38 + 189708 * q^39 - 2875580 * q^40 - 2158998 * q^41 - 296352 * q^42 + 1876346 * q^43 + 7252980 * q^45 + 234336 * q^46 + 1316674 * q^48 + 5882450 * q^49 + 6432894 * q^50 - 3602684 * q^51 - 14093326 * q^52 + 1719628 * q^53 - 14915976 * q^54 - 1225470 * q^55 + 2107392 * q^56 + 18792564 * q^58 + 5131962 * q^59 + 886858 * q^61 + 3663272 * q^62 - 1848084 * q^63 - 38282980 * q^64 - 17072760 * q^65 + 54390948 * q^66 - 15529368 * q^67 + 2633716 * q^68 + 12342620 * q^69 + 20194104 * q^71 + 12742440 * q^72 - 23243862 * q^74 - 12055866 * q^75 - 7828698 * q^76 - 11143384 * q^77 - 32361130 * q^78 + 38408264 * q^79 - 38368944 * q^80 - 55140914 * q^81 + 27439818 * q^82 + 46422306 * q^84 + 16353300 * q^85 - 15866954 * q^87 - 39468942 * q^88 + 11465844 * q^89 - 22072424 * q^90 - 3481450 * q^91 + 67780968 * q^92 - 71319114 * q^93 - 6119236 * q^94 + 60860930 * q^95 + 45060702 * q^97

Introduction

L-functions

Modular forms

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