LMFDB - Embedded newform 91.8.h.a.16.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(16,91)]

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([2, 2]))

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, 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:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.13
Character	$\chi$	$=$	91.16
Dual form			91.8.h.a.74.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.8112 q^{2} +(4.92210 - 8.52533i) q^{3} +91.3725 q^{4} +(67.2870 - 116.545i) q^{5} +(-72.9024 + 126.271i) q^{6} +(-792.466 - 442.199i) q^{7} +542.499 q^{8} +(1045.05 + 1810.07i) q^{9} +O(q^{10})$	\(q-14.8112 q^{2} +(4.92210 - 8.52533i) q^{3} +91.3725 q^{4} +(67.2870 - 116.545i) q^{5} +(-72.9024 + 126.271i) q^{6} +(-792.466 - 442.199i) q^{7} +542.499 q^{8} +(1045.05 + 1810.07i) q^{9} +(-996.603 + 1726.17i) q^{10} +(3960.33 - 6859.49i) q^{11} +(449.745 - 778.980i) q^{12} +(-7782.37 - 1477.57i) q^{13} +(11737.4 + 6549.52i) q^{14} +(-662.387 - 1147.29i) q^{15} -19730.7 q^{16} +18701.7 q^{17} +(-15478.4 - 26809.4i) q^{18} +(24936.2 + 43190.8i) q^{19} +(6148.18 - 10649.0i) q^{20} +(-7670.49 + 4579.48i) q^{21} +(-58657.4 + 101598. i) q^{22} +30611.3 q^{23} +(2670.23 - 4624.98i) q^{24} +(30007.4 + 51974.4i) q^{25} +(115266. + 21884.7i) q^{26} +42104.6 q^{27} +(-72409.6 - 40404.9i) q^{28} +(41056.9 + 71112.6i) q^{29} +(9810.76 + 16992.7i) q^{30} +(-120986. - 209553. i) q^{31} +222797. q^{32} +(-38986.3 - 67526.2i) q^{33} -276995. q^{34} +(-104859. + 62603.3i) q^{35} +(95488.4 + 165391. i) q^{36} -199481. q^{37} +(-369336. - 639709. i) q^{38} +(-50902.4 + 59074.5i) q^{39} +(36503.1 - 63225.3i) q^{40} +(-279436. - 483998. i) q^{41} +(113609. - 67827.8i) q^{42} +(265282. - 459483. i) q^{43} +(361865. - 626769. i) q^{44} +281272. q^{45} -453391. q^{46} +(247824. - 429244. i) q^{47} +(-97116.7 + 168211. i) q^{48} +(432462. + 700856. i) q^{49} +(-444447. - 769804. i) q^{50} +(92051.5 - 159438. i) q^{51} +(-711094. - 135009. i) q^{52} +(-724710. - 1.25524e6i) q^{53} -623620. q^{54} +(-532958. - 923110. i) q^{55} +(-429912. - 239893. i) q^{56} +490955. q^{57} +(-608103. - 1.05327e6i) q^{58} -445078. q^{59} +(-60523.9 - 104831. i) q^{60} +(-656771. - 1.13756e6i) q^{61} +(1.79194e6 + 3.10374e6i) q^{62} +(-27750.5 - 1.89654e6i) q^{63} -774358. q^{64} +(-695855. + 807571. i) q^{65} +(577435. + 1.00015e6i) q^{66} +(1.48117e6 - 2.56546e6i) q^{67} +1.70882e6 q^{68} +(150672. - 260971. i) q^{69} +(1.55308e6 - 927232. i) q^{70} +(-234694. + 406501. i) q^{71} +(566936. + 981962. i) q^{72} +(-2.03026e6 - 3.51652e6i) q^{73} +2.95455e6 q^{74} +590798. q^{75} +(2.27849e6 + 3.94645e6i) q^{76} +(-6.17169e6 + 3.68466e6i) q^{77} +(753927. - 874966. i) q^{78} +(-1.65714e6 + 2.87025e6i) q^{79} +(-1.32762e6 + 2.29951e6i) q^{80} +(-2.07827e6 + 3.59967e6i) q^{81} +(4.13880e6 + 7.16860e6i) q^{82} +3.69672e6 q^{83} +(-700872. + 418439. i) q^{84} +(1.25838e6 - 2.17958e6i) q^{85} +(-3.92916e6 + 6.80550e6i) q^{86} +808345. q^{87} +(2.14847e6 - 3.72127e6i) q^{88} -4.54629e6 q^{89} -4.16598e6 q^{90} +(5.51388e6 + 4.61229e6i) q^{91} +2.79703e6 q^{92} -2.38201e6 q^{93} +(-3.67058e6 + 6.35764e6i) q^{94} +6.71154e6 q^{95} +(1.09663e6 - 1.89942e6i) q^{96} +(-54890.4 + 95073.0i) q^{97} +(-6.40530e6 - 1.03805e7i) q^{98} +1.65549e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) $ 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−14.8112			−1.30914			−0.654570	−	0.756001i	$-0.727150\pi$
$2$	−14.8112			−1.30914			−0.654570	+	0.756001i	$0.727150\pi$
$3$	4.92210	−	8.52533i	0.105251	−	0.182300i	−0.808590	−	0.588373i	$-0.799769\pi$
$3$	4.92210	−	8.52533i	0.105251	−	0.182300i	0.913841	+	0.406073i	$0.133102\pi$
$4$	91.3725			0.713847
$5$	67.2870	−	116.545i	0.240733	−	0.416962i	−0.720190	−	0.693777i	$-0.755945\pi$
$5$	67.2870	−	116.545i	0.240733	−	0.416962i	0.960923	+	0.276814i	$0.0892787\pi$
$6$	−72.9024	+	126.271i	−0.137788	+	0.238656i
$7$	−792.466	−	442.199i	−0.873248	−	0.487276i
$7$	−792.466	−	442.199i	−0.873248	−	0.487276i
$8$	542.499			0.374614
$9$	1045.05	+	1810.07i	0.477844	+	0.827651i
$10$	−996.603	+	1726.17i	−0.315154	+	0.545862i
$11$	3960.33	−	6859.49i	0.897133	−	1.55388i	0.0659915	−	0.997820i	$-0.478979\pi$
$11$	3960.33	−	6859.49i	0.897133	−	1.55388i	0.831142	−	0.556060i	$-0.187688\pi$
$12$	449.745	−	778.980i	0.0751331	−	0.130134i
$13$	−7782.37	−	1477.57i	−0.982449	−	0.186529i
$13$	−7782.37	−	1477.57i	−0.982449	−	0.186529i
$14$	11737.4	+	6549.52i	1.14320	+	0.637912i
$15$	−662.387	−	1147.29i	−0.0506748	−	0.0877714i
$16$	−19730.7			−1.20427
$17$	18701.7			0.923229			0.461614	−	0.887081i	$-0.347270\pi$
$17$	18701.7			0.923229			0.461614	+	0.887081i	$0.347270\pi$
$18$	−15478.4	−	26809.4i	−0.625565	−	1.08351i
$19$	24936.2	+	43190.8i	0.834052	+	1.44462i	0.894800	+	0.446468i	$0.147318\pi$
$19$	24936.2	+	43190.8i	0.834052	+	1.44462i	−0.0607475	+	0.998153i	$0.519348\pi$
$20$	6148.18	−	10649.0i	0.171847	−	0.297647i
$21$	−7670.49	+	4579.48i	−0.180741	+	0.107907i
$22$	−58657.4	+	101598.i	−1.17447	+	2.03425i
$23$	30611.3			0.524607			0.262304	−	0.964985i	$-0.415518\pi$
$23$	30611.3			0.524607			0.262304	+	0.964985i	$0.415518\pi$
$24$	2670.23	−	4624.98i	0.0394285	−	0.0682921i
$25$	30007.4	+	51974.4i	0.384095	+	0.665272i
$26$	115266.	+	21884.7i	1.28616	+	0.244193i
$27$	42104.6			0.411676
$28$	−72409.6	−	40404.9i	−0.623366	−	0.347841i
$29$	41056.9	+	71112.6i	0.312603	+	0.541444i	0.978925	−	0.204220i	$-0.0654658\pi$
$29$	41056.9	+	71112.6i	0.312603	+	0.541444i	−0.666322	+	0.745664i	$0.732132\pi$
$30$	9810.76	+	16992.7i	0.0663404	+	0.114905i
$31$	−120986.	−	209553.i	−0.729403	−	1.26336i	−0.957136	−	0.289639i	$-0.906465\pi$
$31$	−120986.	−	209553.i	−0.729403	−	1.26336i	0.227733	−	0.973724i	$-0.426869\pi$
$32$	222797.			1.20194
$33$	−38986.3	−	67526.2i	−0.188848	−	0.327095i
$34$	−276995.			−1.20864
$35$	−104859.	+	62603.3i	−0.413396	+	0.246808i
$36$	95488.4	+	165391.i	0.341108	+	0.590816i
$37$	−199481.			−0.647433			−0.323716	−	0.946154i	$-0.604932\pi$
$37$	−199481.			−0.647433			−0.323716	+	0.946154i	$0.604932\pi$
$38$	−369336.	−	639709.i	−1.09189	−	1.89121i
$39$	−50902.4	+	59074.5i	−0.137408	+	0.159468i
$40$	36503.1	−	63225.3i	0.0901820	−	0.156200i
$41$	−279436.	−	483998.i	−0.633198	−	1.09673i	−0.986894	−	0.161370i	$-0.948409\pi$
$41$	−279436.	−	483998.i	−0.633198	−	1.09673i	0.353696	−	0.935360i	$-0.384925\pi$
$42$	113609.	−	67827.8i	0.236615	−	0.141265i
$43$	265282.	−	459483.i	0.508826	−	0.881312i	−0.491122	−	0.871091i	$-0.663413\pi$
$43$	265282.	−	459483.i	0.508826	−	0.881312i	0.999948	−	0.0102211i	$-0.00325354\pi$
$44$	361865.	−	626769.i	0.640416	−	1.10923i
$45$	281272.			0.460132
$46$	−453391.			−0.686784
$47$	247824.	−	429244.i	0.348178	−	0.603062i	−0.637748	−	0.770245i	$-0.720134\pi$
$47$	247824.	−	429244.i	0.348178	−	0.603062i	0.985926	+	0.167183i	$0.0534671\pi$
$48$	−97116.7	+	168211.i	−0.126751	+	0.219538i
$49$	432462.	+	700856.i	0.525124	+	0.851026i
$50$	−444447.	−	769804.i	−0.502834	−	0.870934i
$51$	92051.5	−	159438.i	0.0971707	−	0.168305i
$52$	−711094.	−	135009.i	−0.701319	−	0.133153i
$53$	−724710.	−	1.25524e6i	−0.668650	−	1.15814i	−0.978282	−	0.207279i	$-0.933539\pi$
$53$	−724710.	−	1.25524e6i	−0.668650	−	1.15814i	0.309632	−	0.950857i	$-0.399794\pi$
$54$	−623620.			−0.538942
$55$	−532958.	−	923110.i	−0.431940	−	0.748142i
$56$	−429912.	−	239893.i	−0.327131	−	0.182540i
$57$	490955.			0.351139
$58$	−608103.	−	1.05327e6i	−0.409241	−	0.708826i
$59$	−445078.			−0.282133			−0.141066	−	0.990000i	$-0.545053\pi$
$59$	−445078.			−0.282133			−0.141066	+	0.990000i	$0.545053\pi$
$60$	−60523.9	−	104831.i	−0.0361741	−	0.0626554i
$61$	−656771.	−	1.13756e6i	−0.370475	−	0.641682i	0.619163	−	0.785262i	$-0.287472\pi$
$61$	−656771.	−	1.13756e6i	−0.370475	−	0.641682i	−0.989639	+	0.143580i	$0.954139\pi$
$62$	1.79194e6	+	3.10374e6i	0.954891	+	1.65392i
$63$	−27750.5	−	1.89654e6i	−0.0139823	−	0.955587i
$64$	−774358.			−0.369243
$65$	−695855.	+	807571.i	−0.314284	+	0.364741i
$66$	577435.	+	1.00015e6i	0.247229	+	0.428213i
$67$	1.48117e6	−	2.56546e6i	0.601648	−	1.04208i	−0.390924	−	0.920423i	$-0.627844\pi$
$67$	1.48117e6	−	2.56546e6i	0.601648	−	1.04208i	0.992572	−	0.121662i	$-0.0388223\pi$
$68$	1.70882e6			0.659044
$69$	150672.	−	260971.i	0.0552154	−	0.0956359i
$70$	1.55308e6	−	927232.i	0.541193	−	0.323106i
$71$	−234694.	+	406501.i	−0.0778211	+	0.134790i	−0.902310	−	0.431089i	$-0.858130\pi$
$71$	−234694.	+	406501.i	−0.0778211	+	0.134790i	0.824489	+	0.565879i	$0.191463\pi$
$72$	566936.	+	981962.i	0.179007	+	0.310049i
$73$	−2.03026e6	−	3.51652e6i	−0.610833	−	1.05799i	−0.991100	−	0.133117i	$-0.957501\pi$
$73$	−2.03026e6	−	3.51652e6i	−0.610833	−	1.05799i	0.380268	−	0.924876i	$-0.375832\pi$
$74$	2.95455e6			0.847580
$75$	590798.			0.161705
$76$	2.27849e6	+	3.94645e6i	0.595386	+	1.03124i
$77$	−6.17169e6	+	3.68466e6i	−1.54059	+	0.919772i
$78$	753927.	−	874966.i	0.179886	−	0.208766i
$79$	−1.65714e6	+	2.87025e6i	−0.378150	+	0.654975i	−0.990793	−	0.135385i	$-0.956773\pi$
$79$	−1.65714e6	+	2.87025e6i	−0.378150	+	0.654975i	0.612643	+	0.790360i	$0.290106\pi$
$80$	−1.32762e6	+	2.29951e6i	−0.289908	+	0.502135i
$81$	−2.07827e6	+	3.59967e6i	−0.434515	+	0.752602i
$82$	4.13880e6	+	7.16860e6i	0.828945	+	1.43577i
$83$	3.69672e6			0.709648			0.354824	−	0.934933i	$-0.384541\pi$
$83$	3.69672e6			0.709648			0.354824	+	0.934933i	$0.384541\pi$
$84$	−700872.	+	418439.i	−0.129021	+	0.0770290i
$85$	1.25838e6	−	2.17958e6i	0.222252	−	0.384952i
$86$	−3.92916e6	+	6.80550e6i	−0.666124	+	1.15376i
$87$	808345.			0.131607
$88$	2.14847e6	−	3.72127e6i	0.336079	−	0.582105i
$89$	−4.54629e6			−0.683584			−0.341792	−	0.939776i	$-0.611034\pi$
$89$	−4.54629e6			−0.683584			−0.341792	+	0.939776i	$0.611034\pi$
$90$	−4.16598e6			−0.602378
$91$	5.51388e6	+	4.61229e6i	0.767031	+	0.641610i
$92$	2.79703e6			0.374489
$93$	−2.38201e6			−0.307081
$94$	−3.67058e6	+	6.35764e6i	−0.455814	+	0.789493i
$95$	6.71154e6			0.803137
$96$	1.09663e6	−	1.89942e6i	0.126506	−	0.219114i
$97$	−54890.4	+	95073.0i	−0.00610654	+	0.0105768i	−0.869063	−	0.494702i	$-0.835277\pi$
$97$	−54890.4	+	95073.0i	−0.00610654	+	0.0105768i	0.862956	+	0.505279i	$0.168610\pi$
$98$	−6.40530e6	−	1.03805e7i	−0.687461	−	1.11411i
$99$	1.65549e7			1.71476
$100$	2.74185e6	+	4.74903e6i	0.274185	+	0.474903i
$101$	1.73056e6	−	2.99742e6i	0.167133	−	0.289482i	−0.770278	−	0.637708i	$-0.779882\pi$
$101$	1.73056e6	−	2.99742e6i	0.167133	−	0.289482i	0.937411	+	0.348226i	$0.113216\pi$
$102$	−1.36340e6	+	2.36147e6i	−0.127210	+	0.220334i
$103$	1.32720e6	−	2.29878e6i	0.119676	−	0.207285i	−0.799963	−	0.600049i	$-0.795148\pi$
$103$	1.32720e6	−	2.29878e6i	0.119676	−	0.207285i	0.919639	+	0.392764i	$0.128481\pi$
$104$	−4.22193e6	−	801581.i	−0.368039	−	0.0698765i
$105$	17589.3	+	1.20209e6i	0.00148281	+	0.101339i
$106$	1.07338e7	+	1.85916e7i	0.875356	+	1.51616i
$107$	−1.08099e7			−0.853058			−0.426529	−	0.904474i	$-0.640264\pi$
$107$	−1.08099e7			−0.853058			−0.426529	+	0.904474i	$0.640264\pi$
$108$	3.84720e6			0.293874
$109$	−2.72881e6	−	4.72643e6i	−0.201827	−	0.349575i	0.747290	−	0.664498i	$-0.231355\pi$
$109$	−2.72881e6	−	4.72643e6i	−0.201827	−	0.349575i	−0.949117	+	0.314923i	$0.898021\pi$
$110$	7.89376e6	+	1.36724e7i	0.565470	+	0.979422i
$111$	−981864.	+	1.70064e6i	−0.0681429	+	0.118027i
$112$	1.56360e7	+	8.72493e6i	1.05163	+	0.586812i
$113$	−4.58138e6	+	7.93518e6i	−0.298690	+	0.517347i	−0.975837	−	0.218501i	$-0.929883\pi$
$113$	−4.58138e6	+	7.93518e6i	−0.298690	+	0.517347i	0.677146	+	0.735849i	$0.263216\pi$
$114$	−7.27164e6			−0.459690
$115$	2.05974e6	−	3.56758e6i	0.126290	−	0.218741i
$116$	3.75147e6	+	6.49774e6i	0.223151	+	0.386508i
$117$	−5.45842e6	−	1.56308e7i	−0.315077	−	0.902257i
$118$	6.59215e6			0.369351
$119$	−1.48204e7	−	8.26987e6i	−0.806208	−	0.449867i
$120$	−359344.	−	622402.i	−0.0189835	−	0.0328804i
$121$	−2.16248e7	−	3.74553e7i	−1.10970	−	1.92205i
$122$	9.72758e6	+	1.68487e7i	0.485004	+	0.840052i
$123$	−5.50166e6			−0.266579
$124$	−1.10547e7	−	1.91474e7i	−0.520682	−	0.901848i
$125$	1.85900e7			0.851324
$126$	411019.	+	2.80901e7i	0.0183048	+	1.25100i
$127$	−1.94856e7	−	3.37501e7i	−0.844114	−	1.46205i	−0.886389	−	0.462942i	$-0.846794\pi$
$127$	−1.94856e7	−	3.37501e7i	−0.844114	−	1.46205i	0.0422752	−	0.999106i	$-0.486539\pi$
$128$	−1.70488e7			−0.718553
$129$	−2.61149e6	−	4.52324e6i	−0.107109	−	0.185518i
$130$	1.03065e7	−	1.19611e7i	0.411442	−	0.477496i
$131$	1.09293e7	−	1.89301e7i	0.424759	−	0.735705i	−0.571639	−	0.820506i	$-0.693692\pi$
$131$	1.09293e7	−	1.89301e7i	0.424759	−	0.735705i	0.996398	+	0.0848007i	$0.0270254\pi$
$132$	−3.56227e6	−	6.17004e6i	−0.134809	−	0.233496i
$133$	−662165.	−	4.52541e7i	−0.0244054	−	1.66793i
$134$	−2.19379e7	+	3.79976e7i	−0.787641	+	1.36423i
$135$	2.83309e6	−	4.90706e6i	0.0991042	−	0.171654i
$136$	1.01456e7			0.345854
$137$	5.01939e7			1.66774			0.833871	−	0.551960i	$-0.186120\pi$
$137$	5.01939e7			1.66774			0.833871	+	0.551960i	$0.186120\pi$
$138$	−2.23164e6	+	3.86531e6i	−0.0722847	+	0.125201i
$139$	−2.30687e7	+	3.99562e7i	−0.728572	+	1.26192i	0.228915	+	0.973446i	$0.426482\pi$
$139$	−2.30687e7	+	3.99562e7i	−0.728572	+	1.26192i	−0.957487	+	0.288477i	$0.906851\pi$
$140$	−9.58119e6	+	5.72022e6i	−0.295101	+	0.176183i
$141$	−2.43963e6	−	4.22557e6i	−0.0732922	−	0.126946i
$142$	3.47610e6	−	6.02079e6i	0.101879	−	0.176459i
$143$	−4.09562e7	+	4.75314e7i	−1.17123	+	1.35927i
$144$	−2.06195e7	−	3.57141e7i	−0.575453	−	0.996715i
$145$	1.10504e7			0.301016
$146$	3.00707e7	+	5.20840e7i	0.799665	+	1.38506i
$147$	8.10365e6	−	237199.i	0.210412	−	0.00615889i
$148$	−1.82270e7			−0.462168
$149$	−1.28338e7	−	2.22287e7i	−0.317835	−	0.550506i	0.662201	−	0.749326i	$-0.269622\pi$
$149$	−1.28338e7	−	2.22287e7i	−0.317835	−	0.550506i	−0.980036	+	0.198820i	$0.936289\pi$
$150$	−8.75045e6			−0.211695
$151$	6.02381e6	+	1.04335e7i	0.142381	+	0.246611i	0.928393	−	0.371600i	$-0.121191\pi$
$151$	6.02381e6	+	1.04335e7i	0.142381	+	0.246611i	−0.786012	+	0.618212i	$0.787858\pi$
$152$	1.35279e7	+	2.34310e7i	0.312447	+	0.541175i
$153$	1.95441e7	+	3.38514e7i	0.441160	+	0.764111i
$154$	9.14103e7	−	5.45744e7i	2.01685	−	1.20411i
$155$	−3.25630e7			−0.702366
$156$	−4.65108e6	+	5.39778e6i	−0.0980884	+	0.113836i
$157$	−2.34667e7	−	4.06456e7i	−0.483954	−	0.838233i	0.515876	−	0.856663i	$-0.327466\pi$
$157$	−2.34667e7	−	4.06456e7i	−0.483954	−	0.838233i	−0.999830	+	0.0184303i	$0.994133\pi$
$158$	2.45443e7	−	4.25119e7i	0.495051	−	0.857454i
$159$	−1.42684e7			−0.281504
$160$	1.49913e7	−	2.59657e7i	0.289348	−	0.501165i
$161$	−2.42584e7	−	1.35363e7i	−0.458112	−	0.255628i
$162$	3.07818e7	−	5.33156e7i	0.568841	−	0.985262i
$163$	3.87091e7	+	6.70461e7i	0.700094	+	1.21260i	0.968433	+	0.249274i	$0.0801919\pi$
$163$	3.87091e7	+	6.70461e7i	0.700094	+	1.21260i	−0.268339	+	0.963325i	$0.586475\pi$
$164$	−2.55328e7	−	4.42241e7i	−0.452007	−	0.782899i
$165$	−1.04931e7			−0.181848
$166$	−5.47529e7			−0.929028
$167$	1.73040e7	+	2.99715e7i	0.287501	+	0.497967i	0.973213	−	0.229907i	$-0.0738421\pi$
$167$	1.73040e7	+	2.99715e7i	0.287501	+	0.497967i	−0.685711	+	0.727874i	$0.740509\pi$
$168$	−4.16123e6	+	2.48436e6i	−0.0677079	+	0.0404234i
$169$	5.83821e7	+	2.29980e7i	0.930414	+	0.366511i
$170$	−1.86382e7	+	3.22822e7i	−0.290959	+	0.503956i
$171$	−5.21190e7	+	9.02728e7i	−0.797094	+	1.38061i
$172$	2.42395e7	−	4.19841e7i	0.363224	−	0.629122i
$173$	2.23232e6	+	3.86649e6i	0.0327789	+	0.0567748i	0.881949	−	0.471344i	$-0.156231\pi$
$173$	2.23232e6	+	3.86649e6i	0.0327789	+	0.0567748i	−0.849171	+	0.528119i	$0.822898\pi$
$174$	−1.19726e7			−0.172292
$175$	−796827.	−	5.44572e7i	−0.0112391	−	0.768108i
$176$	−7.81403e7	+	1.35343e8i	−1.08039	+	1.87129i
$177$	−2.19072e6	+	3.79443e6i	−0.0296948	+	0.0514328i
$178$	6.73361e7			0.894907
$179$	3.11951e7	−	5.40315e7i	0.406538	−	0.704144i	−0.587961	−	0.808889i	$-0.700069\pi$
$179$	3.11951e7	−	5.40315e7i	0.406538	−	0.704144i	0.994499	+	0.104745i	$0.0334026\pi$
$180$	2.57005e7			0.328464
$181$	−3.22864e7			−0.404711			−0.202356	−	0.979312i	$-0.564860\pi$
$181$	−3.22864e7			−0.404711			−0.202356	+	0.979312i	$0.564860\pi$
$182$	−8.16674e7	−	6.83136e7i	−1.00415	−	0.839958i
$183$	−1.29308e7			−0.155972
$184$	1.66066e7			0.196525
$185$	−1.34225e7	+	2.32484e7i	−0.155859	+	0.269955i
$186$	3.52805e7			0.402013
$187$	7.40648e7	−	1.28284e8i	0.828259	−	1.43459i
$188$	2.26443e7	−	3.92211e7i	0.248546	−	0.430494i
$189$	−3.33664e7	−	1.86186e7i	−0.359496	−	0.200600i
$190$	−9.94061e7			−1.05142
$191$	−7.99440e7	−	1.38467e8i	−0.830174	−	1.43790i	−0.897900	−	0.440200i	$-0.854908\pi$
$191$	−7.99440e7	−	1.38467e8i	−0.830174	−	1.43790i	0.0677259	−	0.997704i	$-0.478426\pi$
$192$	−3.81147e6	+	6.60166e6i	−0.0388631	+	0.0673129i
$193$	3.32381e7	−	5.75700e7i	0.332802	−	0.576429i	−0.650258	−	0.759713i	$-0.725339\pi$
$193$	3.32381e7	−	5.75700e7i	0.332802	−	0.576429i	0.983060	+	0.183284i	$0.0586727\pi$
$194$	812994.	−	1.40815e6i	0.00799432	−	0.0138466i
$195$	3.45974e6	+	9.90734e6i	0.0334135	+	0.0956833i
$196$	3.95152e7	+	6.40390e7i	0.374859	+	0.607502i
$197$	−2.09375e7	−	3.62648e7i	−0.195116	−	0.337951i	0.751822	−	0.659366i	$-0.229175\pi$
$197$	−2.09375e7	−	3.62648e7i	−0.195116	−	0.337951i	−0.946939	+	0.321415i	$0.895842\pi$
$198$	−2.45199e8			−2.24486
$199$	6.97474e7			0.627396			0.313698	−	0.949523i	$-0.398432\pi$
$199$	6.97474e7			0.627396			0.313698	+	0.949523i	$0.398432\pi$
$200$	1.62790e7	+	2.81960e7i	0.143887	+	0.249220i
$201$	−1.45809e7	−	2.52549e7i	−0.126648	−	0.219361i
$202$	−2.56317e7	+	4.43954e7i	−0.218800	+	0.378973i
$203$	−1.09024e6	−	7.45097e7i	−0.00914714	−	0.625139i
$204$	8.41098e6	−	1.45682e7i	0.0693651	−	0.120144i
$205$	−7.52098e7			−0.609727
$206$	−1.96575e7	+	3.40478e7i	−0.156673	+	0.271365i
$207$	3.19902e7	+	5.54087e7i	0.250681	+	0.434192i
$208$	1.53552e8	+	2.91536e7i	1.18313	+	0.224632i
$209$	3.95023e8			2.99302
$210$	−260518.	−	1.78045e7i	−0.00194120	−	0.132667i
$211$	3.03121e7	+	5.25021e7i	0.222140	+	0.384759i	0.955458	−	0.295128i	$-0.0953623\pi$
$211$	3.03121e7	+	5.25021e7i	0.222140	+	0.384759i	−0.733317	+	0.679887i	$0.762029\pi$
$212$	−6.62186e7	−	1.14694e8i	−0.477314	−	0.826732i
$213$	2.31037e6	+	4.00168e6i	0.0163815	+	0.0283736i
$214$	1.60108e8			1.11677
$215$	−3.57001e7	−	6.18344e7i	−0.244983	−	0.424322i
$216$	2.28417e7			0.154220
$217$	3.21269e6	+	2.19563e8i	0.0213432	+	1.45865i
$218$	4.04170e7	+	7.00042e7i	0.264220	+	0.457643i
$219$	−3.99726e7			−0.257163
$220$	−4.86976e7	−	8.43468e7i	−0.308339	−	0.534059i
$221$	−1.45543e8	−	2.76331e7i	−0.907026	−	0.172209i
$222$	1.45426e7	−	2.51885e7i	0.0892087	−	0.154514i
$223$	−9.54068e7	−	1.65249e8i	−0.576119	−	0.997868i	−0.995919	−	0.0902513i	$-0.971233\pi$
$223$	−9.54068e7	−	1.65249e8i	−0.576119	−	0.997868i	0.419800	−	0.907617i	$-0.362100\pi$
$224$	−1.76559e8	−	9.85206e7i	−1.04959	−	0.585678i
$225$	−6.27183e7	+	1.08631e8i	−0.367075	+	0.635793i
$226$	6.78558e7	−	1.17530e8i	0.391028	−	0.677280i
$227$	−3.36216e8			−1.90778			−0.953889	−	0.300159i	$-0.902960\pi$
$227$	−3.36216e8			−1.90778			−0.953889	+	0.300159i	$0.902960\pi$
$228$	4.48597e7			0.250660
$229$	−7.67084e7	+	1.32863e8i	−0.422103	+	0.731104i	−0.996145	−	0.0877216i	$-0.972041\pi$
$229$	−7.67084e7	+	1.32863e8i	−0.422103	+	0.731104i	0.574042	+	0.818826i	$0.305375\pi$
$230$	−3.05073e7	+	5.28402e7i	−0.165332	+	0.286363i
$231$	1.03526e6	+	7.07520e7i	0.00552593	+	0.377656i
$232$	2.22733e7	+	3.85785e7i	0.117105	+	0.202832i
$233$	−1.23480e8	+	2.13874e8i	−0.639515	+	1.10767i	0.346024	+	0.938226i	$0.387532\pi$
$233$	−1.23480e8	+	2.13874e8i	−0.639515	+	1.10767i	−0.985539	+	0.169447i	$0.945802\pi$
$234$	8.08459e7	+	2.31511e8i	0.412480	+	1.18118i
$235$	−3.33507e7	−	5.77651e7i	−0.167636	−	0.290354i
$236$	−4.06678e7			−0.201400
$237$	1.63132e7	+	2.82553e7i	0.0796013	+	0.137873i
$238$	2.19509e8	+	1.22487e8i	1.05544	+	0.588939i
$239$	3.18680e8			1.50995			0.754974	−	0.655755i	$-0.227649\pi$
$239$	3.18680e8			1.50995			0.754974	+	0.655755i	$0.227649\pi$
$240$	1.30694e7	+	2.26368e7i	0.0610261	+	0.105700i
$241$	2.69583e8			1.24061			0.620303	−	0.784363i	$-0.287010\pi$
$241$	2.69583e8			1.24061			0.620303	+	0.784363i	$0.287010\pi$
$242$	3.20291e8	+	5.54760e8i	1.45275	+	2.51623i
$243$	6.65003e7	+	1.15182e8i	0.297304	+	0.514946i
$244$	−6.00108e7	−	1.03942e8i	−0.264463	−	0.458063i
$245$	1.10780e8	−	3.24260e6i	0.481261	−	0.0140868i
$246$	8.14863e7			0.348989
$247$	−1.30245e8	−	3.72972e8i	−0.549950	−	1.57484i
$248$	−6.56345e7	−	1.13682e8i	−0.273244	−	0.473273i
$249$	1.81956e7	−	3.15157e7i	0.0746911	−	0.129369i
$250$	−2.75341e8			−1.11450
$251$	−1.54047e8	+	2.66817e8i	−0.614886	+	1.06501i	0.375519	+	0.926815i	$0.377465\pi$
$251$	−1.54047e8	+	2.66817e8i	−0.614886	+	1.06501i	−0.990405	+	0.138199i	$0.955869\pi$
$252$	−2.53563e6	−	1.73292e8i	−0.00998124	−	0.682143i
$253$	1.21231e8	−	2.09978e8i	0.470643	−	0.815177i
$254$	2.88606e8	+	4.99880e8i	1.10506	+	1.91402i
$255$	−1.23877e7	−	2.14562e7i	−0.0467845	−	0.0810331i
$256$	3.51631e8			1.30993
$257$	−3.30400e8			−1.21416			−0.607078	−	0.794642i	$-0.707658\pi$
$257$	−3.30400e8			−1.21416			−0.607078	+	0.794642i	$0.707658\pi$
$258$	3.86794e7	+	6.69947e7i	0.140220	+	0.242869i
$259$	1.58082e8	+	8.82102e7i	0.565370	+	0.315479i
$260$	−6.35820e7	+	7.37898e7i	−0.224351	+	0.260369i
$261$	−8.58127e7	+	1.48632e8i	−0.298751	+	0.517452i
$262$	−1.61876e8	+	2.80378e8i	−0.556069	+	0.963141i
$263$	1.36659e8	−	2.36701e8i	0.463227	−	0.802332i	−0.535893	−	0.844286i	$-0.680025\pi$
$263$	1.36659e8	−	2.36701e8i	0.463227	−	0.802332i	0.999120	+	0.0419539i	$0.0133583\pi$
$264$	−2.11500e7	−	3.66329e7i	−0.0707452	−	0.122534i
$265$	−1.95054e8			−0.643865
$266$	9.80748e6	+	6.70268e8i	0.0319501	+	2.18355i
$267$	−2.23773e7	+	3.87586e7i	−0.0719479	+	0.124617i
$268$	1.35338e8	−	2.34412e8i	0.429485	−	0.743890i
$269$	−1.16899e8			−0.366166			−0.183083	−	0.983097i	$-0.558608\pi$
$269$	−1.16899e8			−0.366166			−0.183083	+	0.983097i	$0.558608\pi$
$270$	−4.19615e7	+	7.26795e7i	−0.129741	+	0.224718i
$271$	2.40488e8			0.734010			0.367005	−	0.930219i	$-0.380383\pi$
$271$	2.40488e8			0.734010			0.367005	+	0.930219i	$0.380383\pi$
$272$	−3.68998e8			−1.11182
$273$	6.64612e7	−	2.43055e7i	0.197696	−	0.0722996i
$274$	−7.43433e8			−2.18331
$275$	4.75357e8			1.37834
$276$	1.37673e7	−	2.38456e7i	0.0394154	−	0.0682694i
$277$	2.43550e8			0.688509			0.344254	−	0.938876i	$-0.388132\pi$
$277$	2.43550e8			0.688509			0.344254	+	0.938876i	$0.388132\pi$
$278$	3.41676e8	−	5.91801e8i	0.953802	−	1.65203i
$279$	2.52871e8	−	4.37985e8i	0.697082	−	1.20738i
$280$	−5.68857e7	+	3.39622e7i	−0.154864	+	0.0924577i
$281$	−3.30801e8			−0.889395			−0.444697	−	0.895681i	$-0.646689\pi$
$281$	−3.30801e8			−0.889395			−0.444697	+	0.895681i	$0.646689\pi$
$282$	3.61340e7	+	6.25858e7i	0.0959497	+	0.166190i
$283$	−1.02344e8	+	1.77265e8i	−0.268417	+	0.464913i	−0.968453	−	0.249195i	$-0.919834\pi$
$283$	−1.02344e8	+	1.77265e8i	−0.268417	+	0.464913i	0.700036	+	0.714108i	$0.253167\pi$
$284$	−2.14445e7	+	3.71430e7i	−0.0555524	+	0.0962195i
$285$	3.30349e7	−	5.72181e7i	0.0845309	−	0.146412i
$286$	6.06611e8	−	7.03999e8i	1.53331	−	1.77947i
$287$	7.42025e6	+	5.07119e8i	0.0185281	+	1.26626i
$288$	2.32833e8	+	4.03278e8i	0.574342	+	0.994789i
$289$	−6.05859e7			−0.147649
$290$	−1.63670e8			−0.394072
$291$	540352.	+	935917.i	0.00128544	+	0.00222645i
$292$	−1.85510e8	−	3.21313e8i	−0.436041	−	0.755246i
$293$	1.35761e8	−	2.35146e8i	0.315311	−	0.546135i	−0.664192	−	0.747562i	$-0.731224\pi$
$293$	1.35761e8	−	2.35146e8i	0.315311	−	0.546135i	0.979504	+	0.201427i	$0.0645577\pi$
$294$	−1.20025e8	+	3.51321e6i	−0.275459	+	0.00806284i
$295$	−2.99479e7	+	5.18714e7i	−0.0679188	+	0.117639i
$296$	−1.08218e8			−0.242537
$297$	1.66748e8	−	2.88816e8i	0.369329	−	0.639696i
$298$	1.90084e8	+	3.29234e8i	0.416090	+	0.720690i
$299$	−2.38228e8	−	4.52304e7i	−0.515400	−	0.0978546i
$300$	5.39827e7			0.115433
$301$	−4.13410e8	+	2.46817e8i	−0.873773	+	0.521665i
$302$	−8.92200e7	−	1.54534e8i	−0.186397	−	0.322848i
$303$	−1.70360e7	−	2.95072e7i	−0.0351818	−	0.0609366i
$304$	−4.92011e8	−	8.52187e8i	−1.00442	−	1.73971i
$305$	−1.76769e8			−0.356743
$306$	−2.89472e8	−	5.01381e8i	−0.577540	−	1.00033i
$307$	−7.36870e8			−1.45347			−0.726736	−	0.686917i	$-0.758964\pi$
$307$	−7.36870e8			−1.45347			−0.726736	+	0.686917i	$0.758964\pi$
$308$	−5.63923e8	+	3.36677e8i	−1.09975	+	0.656577i
$309$	−1.30653e7	−	2.26297e7i	−0.0251920	−	0.0436339i
$310$	4.82298e8			0.919496
$311$	−1.04565e8	−	1.81112e8i	−0.197118	−	0.341418i	0.750475	−	0.660899i	$-0.229825\pi$
$311$	−1.04565e8	−	1.81112e8i	−0.197118	−	0.341418i	−0.947593	+	0.319481i	$0.896491\pi$
$312$	−2.76145e7	+	3.20478e7i	−0.0514750	+	0.0597390i
$313$	3.65487e8	−	6.33041e8i	0.673699	−	1.16688i	−0.303148	−	0.952944i	$-0.598038\pi$
$313$	3.65487e8	−	6.33041e8i	0.673699	−	1.16688i	0.976847	−	0.213938i	$-0.0686291\pi$
$314$	3.47571e8	+	6.02011e8i	0.633564	+	1.09736i
$315$	−2.22899e8	−	1.24378e8i	−0.401810	−	0.224211i
$316$	−1.51417e8	+	2.62262e8i	−0.269941	+	0.467552i
$317$	2.75057e8	−	4.76413e8i	0.484971	−	0.839994i	−0.514880	−	0.857262i	$-0.672164\pi$
$317$	2.75057e8	−	4.76413e8i	0.484971	−	0.839994i	0.999851	+	0.0172682i	$0.00549692\pi$
$318$	2.11332e8			0.368528
$319$	6.50395e8			1.12179
$320$	−5.21042e7	+	9.02472e7i	−0.0888890	+	0.153960i
$321$	−5.32074e7	+	9.21579e7i	−0.0897851	+	0.155512i
$322$	3.59297e8	+	2.00489e8i	0.599733	+	0.334653i
$323$	4.66349e8	+	8.07741e8i	0.770021	+	1.33372i
$324$	−1.89897e8	+	3.28911e8i	−0.310177	+	0.537243i
$325$	−1.56733e8	−	4.48822e8i	−0.253261	−	0.725241i
$326$	−5.73329e8	−	9.93035e8i	−0.916521	−	1.58746i
$327$	−5.37258e7			−0.0849701
$328$	−1.51594e8	−	2.62568e8i	−0.237205	−	0.410851i
$329$	−3.86204e8	+	2.30574e8i	−0.597904	+	0.356964i
$330$	1.55415e8			0.238065
$331$	1.33363e7	+	2.30991e7i	0.0202133	+	0.0350105i	0.875955	−	0.482393i	$-0.160232\pi$
$331$	1.33363e7	+	2.30991e7i	0.0202133	+	0.0350105i	−0.855742	+	0.517403i	$0.826899\pi$
$332$	3.37778e8			0.506580
$333$	−2.08466e8	−	3.61074e8i	−0.309372	−	0.535848i
$334$	−2.56294e8	−	4.43914e8i	−0.376379	−	0.651908i
$335$	−1.99327e8	−	3.45244e8i	−0.289673	−	0.501729i
$336$	1.51345e8	−	9.03567e7i	0.217660	−	0.129949i
$337$	4.09603e8			0.582986			0.291493	−	0.956573i	$-0.405848\pi$
$337$	4.09603e8			0.582986			0.291493	+	0.956573i	$0.405848\pi$
$338$	−8.64710e8	−	3.40629e8i	−1.21804	−	0.479815i
$339$	4.51000e7	+	7.81155e7i	0.0628749	+	0.108903i
$340$	1.14981e8	−	1.99153e8i	0.158654	−	0.274797i
$341$	−1.91657e9			−2.61749
$342$	7.71947e8	−	1.33705e9i	1.04351	−	1.80741i
$343$	−3.27936e7	−	7.46639e8i	−0.0438793	−	0.999037i
$344$	1.43915e8	−	2.49269e8i	0.190613	−	0.330152i
$345$	−2.02765e7	−	3.51200e7i	−0.0265844	−	0.0460455i
$346$	−3.30634e7	−	5.72674e7i	−0.0429122	−	0.0743261i
$347$	9.55491e8			1.22765			0.613823	−	0.789443i	$-0.289631\pi$
$347$	9.55491e8			1.22765			0.613823	+	0.789443i	$0.289631\pi$
$348$	7.38604e7			0.0939473
$349$	−7.88808e7	−	1.36626e8i	−0.0993304	−	0.172045i	0.812077	−	0.583550i	$-0.198337\pi$
$349$	−7.88808e7	−	1.36626e8i	−0.0993304	−	0.172045i	−0.911408	+	0.411505i	$0.865003\pi$
$350$	1.18020e7	+	8.06578e8i	0.0147135	+	1.00556i
$351$	−3.27673e8	−	6.22125e7i	−0.404451	−	0.0767897i
$352$	8.82349e8	−	1.52827e9i	1.07830	−	1.86768i
$353$	8.21397e8	−	1.42270e9i	0.993897	−	1.72148i	0.401418	−	0.915895i	$-0.368517\pi$
$353$	8.21397e8	−	1.42270e9i	0.993897	−	1.72148i	0.592479	−	0.805586i	$-0.298149\pi$
$354$	3.24472e7	−	5.62002e7i	0.0388746	−	0.0673328i
$355$	3.15837e7	+	5.47045e7i	0.0374683	+	0.0648969i
$356$	−4.15406e8			−0.487975
$357$	−1.43451e8	+	8.56440e7i	−0.166865	+	0.0996227i
$358$	−4.62038e8	+	8.00273e8i	−0.532215	+	0.921823i
$359$	−5.52596e8	+	9.57124e8i	−0.630343	+	1.09179i	0.357138	+	0.934052i	$0.383753\pi$
$359$	−5.52596e8	+	9.57124e8i	−0.630343	+	1.09179i	−0.987481	+	0.157735i	$0.949581\pi$
$360$	1.52590e8			0.172372
$361$	−7.96696e8	+	1.37992e9i	−0.891286	+	1.54375i
$362$	4.78202e8			0.529824
$363$	−4.25759e8			−0.467187
$364$	5.03817e8	+	4.21436e8i	0.547543	+	0.458012i
$365$	−5.46441e8			−0.588191
$366$	1.91521e8			0.204189
$367$	1.63398e8	−	2.83014e8i	0.172551	−	0.298866i	−0.766760	−	0.641934i	$-0.778132\pi$
$367$	1.63398e8	−	2.83014e8i	0.172551	−	0.298866i	0.939311	+	0.343067i	$0.111466\pi$
$368$	−6.03984e8			−0.631768
$369$	5.84048e8	−	1.01160e9i	0.605140	−	1.04813i
$370$	1.98803e8	−	3.44337e8i	0.204041	−	0.353409i
$371$	1.92442e7	+	1.31520e9i	0.0195655	+	1.33716i
$372$	−2.17650e8			−0.219209
$373$	7.95180e8	+	1.37729e9i	0.793387	+	1.37419i	0.923859	+	0.382734i	$0.125017\pi$
$373$	7.95180e8	+	1.37729e9i	0.793387	+	1.37419i	−0.130472	+	0.991452i	$0.541649\pi$
$374$	−1.09699e9	+	1.90004e9i	−1.08431	+	1.87808i
$375$	9.15020e7	−	1.58486e8i	0.0896027	−	0.155196i
$376$	1.34444e8	−	2.32864e8i	0.130432	−	0.225915i
$377$	−2.14446e8	−	6.14089e8i	−0.206121	−	0.590251i
$378$	4.94198e8	+	2.75764e8i	0.470630	+	0.262613i
$379$	−4.94616e8	−	8.56699e8i	−0.466692	−	0.808335i	0.532584	−	0.846377i	$-0.321221\pi$
$379$	−4.94616e8	−	8.56699e8i	−0.466692	−	0.808335i	−0.999276	+	0.0380426i	$0.987888\pi$
$380$	6.13250e8			0.573317
$381$	−3.83640e8			−0.355375
$382$	1.18407e9	+	2.05087e9i	1.08681	+	1.88242i
$383$	3.05564e8	+	5.29253e8i	0.277912	+	0.481357i	0.970866	−	0.239625i	$-0.0770244\pi$
$383$	3.05564e8	+	5.29253e8i	0.277912	+	0.481357i	−0.692954	+	0.720982i	$0.743691\pi$
$384$	−8.39159e7	+	1.45347e8i	−0.0756284	+	0.130992i
$385$	1.41523e7	+	9.67207e8i	0.0126391	+	0.863787i
$386$	−4.92297e8	+	8.52683e8i	−0.435684	+	0.754627i
$387$	1.10893e9			0.972558
$388$	−5.01547e6	+	8.68705e6i	−0.00435914	+	0.00755025i
$389$	2.31640e8	+	4.01213e8i	0.199522	+	0.345582i	0.948374	−	0.317156i	$-0.102728\pi$
$389$	2.31640e8	+	4.01213e8i	0.199522	+	0.345582i	−0.748852	+	0.662738i	$0.769394\pi$
$390$	−5.12430e7	−	1.46740e8i	−0.0437430	−	0.125263i
$391$	5.72482e8			0.484332
$392$	2.34610e8	+	3.80214e8i	0.196719	+	0.318806i
$393$	−1.07590e8	−	1.86352e8i	−0.0894127	−	0.154867i
$394$	3.10110e8	+	5.37126e8i	0.255434	+	0.442425i
$395$	2.23008e8	+	3.86261e8i	0.182067	+	0.315348i
$396$	1.51266e9			1.22408
$397$	1.28396e8	+	2.22388e8i	0.102987	+	0.178379i	0.912914	−	0.408152i	$-0.133827\pi$
$397$	1.28396e8	+	2.22388e8i	0.102987	+	0.178379i	−0.809927	+	0.586531i	$0.800493\pi$
$398$	−1.03304e9			−0.821350
$399$	−3.89065e8	−	2.17100e8i	−0.306632	−	0.171102i
$400$	−5.92069e8	−	1.02549e9i	−0.462554	−	0.801167i
$401$	1.92302e9			1.48929			0.744644	−	0.667461i	$-0.232619\pi$
$401$	1.92302e9			1.48929			0.744644	+	0.667461i	$0.232619\pi$
$402$	2.15961e8	+	3.74056e8i	0.165800	+	0.287174i
$403$	6.31924e8	+	1.80958e9i	0.480947	+	1.37725i
$404$	1.58125e8	−	2.73881e8i	0.119307	−	0.206646i
$405$	2.79681e8	+	4.84423e8i	0.209205	+	0.362353i
$406$	1.61478e7	+	1.10358e9i	0.0119749	+	0.818394i
$407$	−7.90009e8	+	1.36834e9i	−0.580834	+	1.00603i
$408$	4.99378e7	−	8.64949e7i	0.0364015	−	0.0630492i
$409$	9.12426e8			0.659426			0.329713	−	0.944081i	$-0.393048\pi$
$409$	9.12426e8			0.659426			0.329713	+	0.944081i	$0.393048\pi$
$410$	1.11395e9			0.798218
$411$	2.47059e8	−	4.27919e8i	0.175531	−	0.304029i
$412$	1.21270e8	−	2.10046e8i	0.0854305	−	0.147970i
$413$	3.52709e8	+	1.96813e8i	0.246372	+	0.137477i
$414$	−4.73814e8	−	8.20670e8i	−0.328176	−	0.568417i
$415$	2.48741e8	−	4.30832e8i	0.170836	−	0.295896i
$416$	−1.73389e9	−	3.29198e8i	−1.18085	−	0.224198i
$417$	2.27093e8	+	3.93337e8i	0.153366	+	0.265637i
$418$	−5.85077e9			−3.91829
$419$	3.17428e8	+	5.49801e8i	0.210812	+	0.365138i	0.951969	−	0.306194i	$-0.0990558\pi$
$419$	3.17428e8	+	5.49801e8i	0.210812	+	0.365138i	−0.741157	+	0.671332i	$0.765722\pi$
$420$	1.60717e6	+	1.09838e8i	0.00105850	+	0.0723405i
$421$	−7.43751e8			−0.485780			−0.242890	−	0.970054i	$-0.578095\pi$
$421$	−7.43751e8			−0.485780			−0.242890	+	0.970054i	$0.578095\pi$
$422$	−4.48960e8	−	7.77621e8i	−0.290813	−	0.503703i
$423$	1.03595e9			0.665500
$424$	−3.93154e8	−	6.80963e8i	−0.250486	−	0.433854i
$425$	5.61189e8	+	9.72008e8i	0.354607	+	0.614198i
$426$	−3.42195e7	−	5.92698e7i	−0.0214457	−	0.0371450i
$427$	1.74401e7	+	1.19190e9i	0.0108406	+	0.740871i
$428$	−9.87727e8			−0.608953
$429$	2.03631e8	+	5.83119e8i	0.124521	+	0.356580i
$430$	5.28763e8	+	9.15844e8i	0.320716	+	0.555497i
$431$	9.26573e7	−	1.60487e8i	0.0557454	−	0.0965539i	−0.836806	−	0.547499i	$-0.815580\pi$
$431$	9.26573e7	−	1.60487e8i	0.0557454	−	0.0965539i	0.892551	+	0.450946i	$0.148913\pi$
$432$	−8.30754e8			−0.495769
$433$	1.44703e9	−	2.50632e9i	0.856582	−	1.48364i	−0.0185874	−	0.999827i	$-0.505917\pi$
$433$	1.44703e9	−	2.50632e9i	0.856582	−	1.48364i	0.875169	−	0.483816i	$-0.160750\pi$
$434$	−4.75839e7	−	3.25200e9i	−0.0279413	−	1.90958i
$435$	5.43911e7	−	9.42081e7i	0.0316822	−	0.0548752i
$436$	−2.49338e8	−	4.31865e8i	−0.144074	−	0.249543i
$437$	7.63330e8	+	1.32213e9i	0.437550	+	0.757858i
$438$	5.92044e8			0.336662
$439$	−1.57053e9			−0.885975			−0.442988	−	0.896528i	$-0.646081\pi$
$439$	−1.57053e9			−0.885975			−0.442988	+	0.896528i	$0.646081\pi$
$440$	−2.89129e8	−	5.00786e8i	−0.161811	−	0.280264i
$441$	−8.16658e8	+	1.51522e9i	−0.453424	+	0.841277i
$442$	2.15568e9	+	4.09280e8i	1.18742	+	0.225446i
$443$	5.00214e8	−	8.66397e8i	0.273365	−	0.473482i	−0.696356	−	0.717696i	$-0.745197\pi$
$443$	5.00214e8	−	8.66397e8i	0.273365	−	0.473482i	0.969721	+	0.244214i	$0.0785299\pi$
$444$	−8.97153e7	+	1.55392e8i	−0.0486437	+	0.0842533i
$445$	−3.05906e8	+	5.29845e8i	−0.164562	+	0.285029i
$446$	1.41309e9	+	2.44755e9i	0.754221	+	1.30635i
$447$	−2.52676e8			−0.133810
$448$	6.13652e8	+	3.42421e8i	0.322440	+	0.179923i
$449$	−5.49874e8	+	9.52410e8i	−0.286683	+	0.496549i	−0.973016	−	0.230738i	$-0.925886\pi$
$449$	−5.49874e8	+	9.52410e8i	−0.286683	+	0.496549i	0.686333	+	0.727287i	$0.259219\pi$
$450$	9.28934e8	−	1.60896e9i	0.480553	−	0.832342i
$451$	−4.42664e9			−2.27225
$452$	−4.18612e8	+	7.25057e8i	−0.213219	+	0.369307i
$453$	1.18599e8			0.0599430
$454$	4.97977e9			2.49755
$455$	9.08549e8	−	3.32266e8i	0.452177	−	0.165366i
$456$	2.66342e8			0.131542
$457$	−1.31035e9			−0.642215			−0.321108	−	0.947043i	$-0.604055\pi$
$457$	−1.31035e9			−0.642215			−0.321108	+	0.947043i	$0.604055\pi$
$458$	1.13615e9	−	1.96786e9i	0.552592	−	0.957118i
$459$	7.87426e8			0.380071
$460$	1.88204e8	−	3.25978e8i	0.0901521	−	0.156148i
$461$	4.50115e8	−	7.79623e8i	0.213979	−	0.370622i	−0.738977	−	0.673730i	$-0.764691\pi$
$461$	4.50115e8	−	7.79623e8i	0.213979	−	0.370622i	0.952956	+	0.303108i	$0.0980243\pi$
$462$	−1.53334e7	−	1.04792e9i	−0.00723422	−	0.494405i
$463$	2.15738e9			1.01017			0.505083	−	0.863071i	$-0.331462\pi$
$463$	2.15738e9			1.01017			0.505083	+	0.863071i	$0.331462\pi$
$464$	−8.10083e8	−	1.40311e9i	−0.376458	−	0.652045i
$465$	−1.60278e8	+	2.77610e8i	−0.0739247	+	0.128041i
$466$	1.82889e9	−	3.16773e9i	0.837215	−	1.45010i
$467$	9.43434e8	−	1.63408e9i	0.428650	−	0.742443i	−0.568104	−	0.822957i	$-0.692323\pi$
$467$	9.43434e8	−	1.63408e9i	0.428650	−	0.742443i	0.996753	+	0.0805138i	$0.0256561\pi$
$468$	−4.98749e8	−	1.42822e9i	−0.224917	−	0.644074i
$469$	−2.30822e9	+	1.37807e9i	−1.03317	+	0.616830i
$470$	4.93965e8	+	8.55573e8i	0.219459	+	0.380114i
$471$	−4.62023e8			−0.203747
$472$	−2.41454e8			−0.105691
$473$	−2.10121e9	−	3.63941e9i	−0.912969	−	1.58131i
$474$	−2.41619e8	−	4.18496e8i	−0.104209	−	0.180496i
$475$	−1.49654e9	+	2.59209e9i	−0.640710	+	1.10974i
$476$	−1.35418e9	−	7.55639e8i	−0.575509	−	0.321137i
$477$	1.51471e9	−	2.62356e9i	0.639021	−	1.10682i
$478$	−4.72004e9			−1.97673
$479$	−6.16224e8	+	1.06733e9i	−0.256191	+	0.443737i	−0.965218	−	0.261445i	$-0.915801\pi$
$479$	−6.16224e8	+	1.06733e9i	−0.256191	+	0.443737i	0.709027	+	0.705181i	$0.249134\pi$
$480$	−1.47578e8	−	2.55612e8i	−0.0609083	−	0.105496i
$481$	1.55243e9	+	2.94747e8i	0.636070	+	0.120765i
$482$	−3.99286e9			−1.62413
$483$	−2.34804e8	+	1.40184e8i	−0.0948178	+	0.0566087i
$484$	−1.97592e9	−	3.42239e9i	−0.792154	−	1.37205i
$485$	7.38682e6	+	1.27944e7i	0.00294010	+	0.00509240i
$486$	−9.84951e8	−	1.70598e9i	−0.389213	−	0.674137i
$487$	1.35812e9			0.532826			0.266413	−	0.963859i	$-0.414161\pi$
$487$	1.35812e9			0.532826			0.266413	+	0.963859i	$0.414161\pi$
$488$	−3.56297e8	−	6.17125e8i	−0.138785	−	0.240383i
$489$	7.62120e8			0.294742
$490$	−1.64079e9	+	4.80269e7i	−0.630037	+	0.0184416i
$491$	2.38886e9	+	4.13764e9i	0.910765	+	1.57749i	0.812986	+	0.582283i	$0.197841\pi$
$491$	2.38886e9	+	4.13764e9i	0.910765	+	1.57749i	0.0977790	+	0.995208i	$0.468826\pi$
$492$	−5.02700e8			−0.190297
$493$	7.67833e8	+	1.32993e9i	0.288604	+	0.499877i
$494$	1.92909e9	+	5.52417e9i	0.719961	+	2.06169i
$495$	1.11393e9	−	1.92938e9i	0.412800	−	0.714991i
$496$	2.38714e9	+	4.13464e9i	0.878398	+	1.52143i
$497$	3.65742e8	−	2.18357e8i	0.133637	−	0.0797848i
$498$	−2.69499e8	+	4.66787e8i	−0.0977811	+	0.169362i
$499$	−2.34593e8	+	4.06327e8i	−0.0845207	+	0.146394i	−0.905187	−	0.425014i	$-0.860269\pi$
$499$	−2.34593e8	+	4.06327e8i	−0.0845207	+	0.146394i	0.820666	+	0.571408i	$0.193603\pi$
$500$	1.69862e9			0.607716
$501$	3.40689e8			0.121039
$502$	2.28162e9	−	3.95188e9i	0.804972	−	1.39425i
$503$	−2.37099e9	+	4.10667e9i	−0.830695	+	1.43881i	0.0667934	+	0.997767i	$0.478723\pi$
$503$	−2.37099e9	+	4.10667e9i	−0.830695	+	1.43881i	−0.897488	+	0.441039i	$0.854610\pi$
$504$	−1.50546e7	−	1.02887e9i	−0.00523797	−	0.357976i
$505$	−2.32888e8	−	4.03374e8i	−0.0804689	−	0.139376i
$506$	−1.79558e9	+	3.11003e9i	−0.616137	+	1.06718i
$507$	4.83428e8	−	3.84528e8i	0.164742	−	0.131039i
$508$	−1.78045e9	−	3.08383e9i	−0.602568	−	1.04368i
$509$	2.19966e8			0.0739337			0.0369669	−	0.999316i	$-0.488230\pi$
$509$	2.19966e8			0.0739337			0.0369669	+	0.999316i	$0.488230\pi$
$510$	1.83478e8	+	3.17793e8i	0.0612474	+	0.106084i
$511$	5.39123e7	+	3.68450e9i	0.0178737	+	1.22153i
$512$	−3.02585e9			−0.996327
$513$	1.04993e9	+	1.81853e9i	0.343360	+	0.594716i
$514$	4.89363e9			1.58950
$515$	−1.78607e8	−	3.09357e8i	−0.0576200	−	0.0998008i
$516$	−2.38619e8	−	4.13300e8i	−0.0764593	−	0.132431i
$517$	−1.96293e9	−	3.39990e9i	−0.624724	−	1.08205i
$518$	−2.34138e9	−	1.30650e9i	−0.740148	−	0.413006i
$519$	4.39508e7			0.0138001
$520$	−3.77501e8	+	4.38106e8i	−0.117735	+	0.136637i
$521$	−2.78886e9	−	4.83044e9i	−0.863961	−	1.49642i	−0.868075	−	0.496433i	$-0.834643\pi$
$521$	−2.78886e9	−	4.83044e9i	−0.863961	−	1.49642i	0.00411446	−	0.999992i	$-0.498690\pi$
$522$	1.27099e9	−	2.20142e9i	0.391107	−	0.677417i
$523$	3.80971e9			1.16449			0.582246	−	0.813013i	$-0.302174\pi$
$523$	3.80971e9			1.16449			0.582246	+	0.813013i	$0.302174\pi$
$524$	9.98638e8	−	1.72969e9i	0.303213	−	0.525181i
$525$	−4.68188e8	−	2.61251e8i	−0.141209	−	0.0787952i
$526$	−2.02409e9	+	3.50583e9i	−0.606428	+	1.05036i
$527$	−2.26263e9	−	3.91899e9i	−0.673406	−	1.16637i
$528$	7.69229e8	+	1.33234e9i	0.227424	+	0.393910i
$529$	−2.46777e9			−0.724787
$530$	2.88899e9			0.842910
$531$	−4.65127e8	−	8.05623e8i	−0.134816	−	0.233508i
$532$	−6.05037e7	−	4.13497e9i	−0.0174217	−	1.19064i
$533$	1.45954e9	+	4.17954e9i	0.417512	+	1.19559i
$534$	3.31435e8	−	5.74063e8i	0.0941899	−	0.163142i
$535$	−7.27366e8	+	1.25983e9i	−0.205359	+	0.355693i
$536$	8.03532e8	−	1.39176e9i	0.225386	−	0.390379i
$537$	−3.07091e8	−	5.31897e8i	−0.0855770	−	0.148224i
$538$	1.73142e9			0.479362
$539$	6.52021e9	−	1.90851e8i	1.79350	−	0.0524968i
$540$	2.58866e8	−	4.48370e8i	0.0707453	−	0.122534i
$541$	−2.16008e9	+	3.74136e9i	−0.586514	+	1.01587i	0.408171	+	0.912906i	$0.366167\pi$
$541$	−2.16008e9	+	3.74136e9i	−0.586514	+	1.01587i	−0.994685	+	0.102967i	$0.967166\pi$
$542$	−3.56193e9			−0.960921
$543$	−1.58917e8	+	2.75253e8i	−0.0425962	+	0.0737789i
$544$	4.16667e9			1.10967
$545$	−7.34453e8			−0.194346
$546$	−9.84371e8	+	3.59995e8i	−0.258812	+	0.0946503i
$547$	3.41840e9			0.893031			0.446516	−	0.894776i	$-0.352665\pi$
$547$	3.41840e9			0.893031			0.446516	+	0.894776i	$0.352665\pi$
$548$	4.58634e9			1.19051
$549$	1.37271e9	−	2.37761e9i	0.354059	−	0.613249i
$550$	−7.04062e9			−1.80444
$551$	−2.04761e9	+	3.54656e9i	−0.521454	+	0.903185i
$552$	8.17393e7	−	1.41577e8i	0.0206845	−	0.0358265i
$553$	2.58245e9	−	1.54179e9i	0.649372	−	0.387692i
$554$	−3.60728e9			−0.901354
$555$	1.32133e8	+	2.28862e8i	0.0328086	+	0.0568261i
$556$	−2.10785e9	+	3.65090e9i	−0.520089	+	0.900820i
$557$	1.53099e9	−	2.65176e9i	0.375388	−	0.650191i	−0.614997	−	0.788529i	$-0.710843\pi$
$557$	1.53099e9	−	2.65176e9i	0.375388	−	0.650191i	0.990385	+	0.138338i	$0.0441762\pi$
$558$	−3.74533e9	+	6.48710e9i	−0.912578	+	1.58063i
$559$	−2.74345e9	+	3.18389e9i	−0.664286	+	0.770933i
$560$	2.06894e9	−	1.23521e9i	0.497840	−	0.297223i
$561$	−7.29109e8	−	1.26285e9i	−0.174350	−	0.301983i
$562$	4.89957e9			1.16434
$563$	−3.24507e8			−0.0766381			−0.0383191	−	0.999266i	$-0.512200\pi$
$563$	−3.24507e8			−0.0766381			−0.0383191	+	0.999266i	$0.512200\pi$
$564$	−2.22915e8	−	3.86101e8i	−0.0523194	−	0.0906199i
$565$	6.16534e8	+	1.06787e9i	0.143810	+	0.249085i
$566$	1.51584e9	−	2.62552e9i	0.351396	−	0.608636i
$567$	3.23873e9	−	1.93361e9i	0.746165	−	0.445480i
$568$	−1.27321e8	+	2.20527e8i	−0.0291528	+	0.0504942i
$569$	−2.95116e9			−0.671583			−0.335791	−	0.941936i	$-0.609004\pi$
$569$	−2.95116e9			−0.671583			−0.335791	+	0.941936i	$0.609004\pi$
$570$	−4.89287e8	+	8.47470e8i	−0.110663	+	0.191674i
$571$	−1.66858e9	−	2.89007e9i	−0.375078	−	0.649654i	0.615261	−	0.788324i	$-0.289051\pi$
$571$	−1.66858e9	−	2.89007e9i	−0.375078	−	0.649654i	−0.990339	+	0.138670i	$0.955717\pi$
$572$	−3.74227e9	+	4.34307e9i	−0.836081	+	0.970309i
$573$	−1.57397e9			−0.349506
$574$	−1.09903e8	−	7.51105e9i	−0.0242559	−	1.65771i
$575$	9.18566e8	+	1.59100e9i	0.201499	+	0.349006i
$576$	−8.09240e8	−	1.40164e9i	−0.176441	−	0.305604i
$577$	−4.13241e8	−	7.15755e8i	−0.0895547	−	0.155113i	0.817768	−	0.575548i	$-0.195211\pi$
$577$	−4.13241e8	−	7.15755e8i	−0.0895547	−	0.155113i	−0.907323	+	0.420434i	$0.861878\pi$
$578$	8.97352e8			0.193293
$579$	−3.27202e8	−	5.66731e8i	−0.0700554	−	0.121339i
$580$	1.00970e9			0.214879
$581$	−2.92952e9	−	1.63469e9i	−0.619699	−	0.345794i
$582$	−8.00328e6	−	1.38621e7i	−0.00168282	−	0.00291473i
$583$	−1.14804e10			−2.39947
$584$	−1.10142e9	−	1.90771e9i	−0.228826	−	0.396339i
$585$	−2.18896e9	−	4.15600e8i	−0.452057	−	0.0858282i
$586$	−2.01079e9	+	3.48280e9i	−0.412787	+	0.714967i
$587$	6.49466e8	+	1.12491e9i	0.132533	+	0.229553i	0.924652	−	0.380813i	$-0.124356\pi$
$587$	6.49466e8	+	1.12491e9i	0.132533	+	0.229553i	−0.792120	+	0.610366i	$0.791022\pi$
$588$	7.40451e8	−	2.16735e7i	0.150202	−	0.00439650i
$589$	6.03385e9	−	1.04509e10i	1.21672	−	2.10742i
$590$	4.43566e8	−	7.68279e8i	0.0889152	−	0.154006i
$591$	−4.12226e8			−0.0821446
$592$	3.93590e9			0.779684
$593$	3.58229e9	−	6.20471e9i	0.705455	−	1.22188i	−0.261072	−	0.965319i	$-0.584076\pi$
$593$	3.58229e9	−	6.20471e9i	0.705455	−	1.22188i	0.966527	−	0.256565i	$-0.0825908\pi$
$594$	−2.46974e9	+	4.27772e9i	−0.483503	+	0.837451i
$595$	−1.96103e9	+	1.17079e9i	−0.381659	+	0.227860i
$596$	−1.17265e9	−	2.03109e9i	−0.226886	−	0.392977i
$597$	3.43303e8	−	5.94619e8i	0.0660341	−	0.114374i
$598$	3.52846e9	+	6.69918e8i	0.674731	+	0.128105i
$599$	5.42524e8	+	9.39679e8i	0.103140	+	0.178643i	0.912977	−	0.408012i	$-0.133778\pi$
$599$	5.42524e8	+	9.39679e8i	0.103140	+	0.178643i	−0.809837	+	0.586655i	$0.800445\pi$
$600$	3.20507e8			0.0605771
$601$	2.36424e9	+	4.09498e9i	0.444253	+	0.769469i	0.998000	−	0.0632159i	$-0.0201357\pi$
$601$	2.36424e9	+	4.09498e9i	0.444253	+	0.769469i	−0.553747	+	0.832685i	$0.686802\pi$
$602$	6.12312e9	−	3.65566e9i	1.14389	−	0.682933i
$603$	6.19155e9			1.14998
$604$	5.50411e8	+	9.53339e8i	0.101638	+	0.176043i
$605$	−5.82029e9			−1.06856
$606$	2.52324e8	+	4.37037e8i	0.0460579	+	0.0797746i
$607$	−3.19372e9	−	5.53168e9i	−0.579610	−	1.00391i	−0.995524	−	0.0945100i	$-0.969872\pi$
$607$	−3.19372e9	−	5.53168e9i	−0.579610	−	1.00391i	0.415914	−	0.909404i	$-0.363462\pi$
$608$	5.55571e9	+	9.62278e9i	1.00248	+	1.73635i
$609$	−6.40586e8	−	3.57449e8i	−0.114926	−	0.0641290i
$610$	2.61816e9			0.467027
$611$	−2.56290e9	+	2.97436e9i	−0.454556	+	0.527533i
$612$	1.78579e9	+	3.09309e9i	0.314921	+	0.545459i
$613$	−1.47378e9	+	2.55266e9i	−0.258417	+	0.447591i	−0.965818	−	0.259221i	$-0.916534\pi$
$613$	−1.47378e9	+	2.55266e9i	−0.258417	+	0.447591i	0.707401	+	0.706812i	$0.249868\pi$
$614$	1.09140e10			1.90280
$615$	−3.70190e8	+	6.41188e8i	−0.0641744	+	0.111153i
$616$	−3.34813e9	+	1.99892e9i	−0.577126	+	0.344559i
$617$	3.48350e9	−	6.03359e9i	0.597059	−	1.03414i	−0.396194	−	0.918167i	$-0.629669\pi$
$617$	3.48350e9	−	6.03359e9i	0.597059	−	1.03414i	0.993253	−	0.115970i	$-0.0369976\pi$
$618$	1.93513e8	+	3.35174e8i	0.0329799	+	0.0571229i
$619$	−3.85464e7	−	6.67642e7i	−0.00653230	−	0.0113143i	0.862741	−	0.505646i	$-0.168746\pi$
$619$	−3.85464e7	−	6.67642e7i	−0.00653230	−	0.0113143i	−0.869273	+	0.494332i	$0.835413\pi$
$620$	−2.97536e9			−0.501382
$621$	1.28887e9			0.215968
$622$	1.54874e9	+	2.68249e9i	0.258055	+	0.446964i
$623$	3.60278e9	+	2.01037e9i	0.596939	+	0.333094i
$624$	1.00434e9	−	1.16558e9i	0.165476	−	0.192043i
$625$	−1.09346e9	+	1.89393e9i	−0.179153	+	0.310302i
$626$	−5.41330e9	+	9.37612e9i	−0.881967	+	1.52761i
$627$	1.94434e9	−	3.36770e9i	0.315019	−	0.545628i
$628$	−2.14421e9	−	3.71389e9i	−0.345469	−	0.598370i
$629$	−3.73062e9			−0.597729
$630$	3.30140e9	+	1.84220e9i	0.526025	+	0.293524i
$631$	−3.35535e9	+	5.81163e9i	−0.531661	+	0.920863i	0.467656	+	0.883910i	$0.345099\pi$
$631$	−3.35535e9	+	5.81163e9i	−0.531661	+	0.920863i	−0.999317	+	0.0369531i	$0.988235\pi$
$632$	−8.98995e8	+	1.55711e9i	−0.141660	+	0.245363i
$633$	5.96797e8			0.0935220
$634$	−4.07393e9	+	7.05626e9i	−0.634895	+	1.09967i
$635$	−5.24451e9			−0.812825
$636$	−1.30374e9			−0.200951
$637$	−2.33002e9	−	6.09332e9i	−0.357167	−	0.934041i
$638$	−9.63315e9			−1.46857
$639$	−9.81063e8			−0.148745
$640$	−1.14716e9	+	1.98694e9i	−0.172980	+	0.299610i
$641$	4.00110e9			0.600034			0.300017	−	0.953934i	$-0.403008\pi$
$641$	4.00110e9			0.600034			0.300017	+	0.953934i	$0.403008\pi$
$642$	7.88067e8	−	1.36497e9i	0.117541	−	0.203588i
$643$	2.36056e9	−	4.08860e9i	0.350168	−	0.606508i	−0.636111	−	0.771598i	$-0.719458\pi$
$643$	2.36056e9	−	4.08860e9i	0.350168	−	0.606508i	0.986279	+	0.165090i	$0.0527913\pi$
$644$	−2.21655e9	−	1.23684e9i	−0.327022	−	0.182480i
$645$	−7.02879e8			−0.103139
$646$	−6.90721e9	−	1.19636e10i	−1.00807	−	1.74602i
$647$	4.31595e8	−	7.47544e8i	0.0626485	−	0.108510i	−0.833000	−	0.553273i	$-0.813379\pi$
$647$	4.31595e8	−	7.47544e8i	0.0626485	−	0.108510i	0.895648	+	0.444763i	$0.146712\pi$
$648$	−1.12746e9	+	1.95282e9i	−0.162775	+	0.281935i
$649$	−1.76265e9	+	3.05301e9i	−0.253111	+	0.438401i
$650$	2.32141e9	+	6.64760e9i	0.331554	+	0.949442i
$651$	1.88766e9	+	1.05332e9i	0.268158	+	0.149633i
$652$	3.53695e9	+	6.12617e9i	0.499760	+	0.865610i
$653$	4.89935e9			0.688561			0.344280	−	0.938867i	$-0.388123\pi$
$653$	4.89935e9			0.688561			0.344280	+	0.938867i	$0.388123\pi$
$654$	7.95745e8			0.111238
$655$	−1.47080e9	−	2.54750e9i	−0.204507	−	0.354217i
$656$	5.51349e9	+	9.54964e9i	0.762541	+	1.32076i
$657$	4.24344e9	−	7.34985e9i	0.583766	−	1.01111i
$658$	5.72016e9	−	3.41508e9i	0.782739	−	0.467316i
$659$	4.21250e9	−	7.29626e9i	0.573378	−	0.993119i	−0.422838	−	0.906205i	$-0.638966\pi$
$659$	4.21250e9	−	7.29626e9i	0.573378	−	0.993119i	0.996216	−	0.0869141i	$-0.0277006\pi$
$660$	−9.58779e8			−0.129812
$661$	6.59024e9	−	1.14146e10i	0.887556	−	1.53729i	0.0448011	−	0.998996i	$-0.485735\pi$
$661$	6.59024e9	−	1.14146e10i	0.887556	−	1.53729i	0.842755	−	0.538297i	$-0.180932\pi$
$662$	−1.97527e8	−	3.42127e8i	−0.0264620	−	0.0458336i
$663$	−9.51960e8	+	1.10479e9i	−0.126859	+	0.147226i
$664$	2.00546e9			0.265844
$665$	−5.31867e9	−	2.96784e9i	−0.701338	−	0.391349i
$666$	3.08764e9	+	5.34796e9i	0.405012	+	0.701501i
$667$	1.25680e9	+	2.17685e9i	0.163994	+	0.284045i
$668$	1.58111e9	+	2.73857e9i	0.205232	+	0.355472i
$669$	−1.87841e9			−0.242549
$670$	2.95227e9	+	5.11349e9i	0.379223	+	0.656834i
$671$	−1.04041e10			−1.32946
$672$	−1.70896e9	+	1.02029e9i	−0.217240	+	0.129698i
$673$	3.22296e8	+	5.58233e8i	0.0407570	+	0.0705932i	0.885684	−	0.464288i	$-0.153690\pi$
$673$	3.22296e8	+	5.58233e8i	0.0407570	+	0.0705932i	−0.844927	+	0.534881i	$0.820356\pi$
$674$	−6.06672e9			−0.763210
$675$	1.26345e9	+	2.18836e9i	0.158123	+	0.273877i
$676$	5.33451e9	+	2.10139e9i	0.664173	+	0.261633i
$677$	7.00740e7	−	1.21372e8i	0.00867953	−	0.0150334i	−0.861653	−	0.507498i	$-0.830571\pi$
$677$	7.00740e7	−	1.21372e8i	0.00867953	−	0.0150334i	0.870333	+	0.492464i	$0.163904\pi$
$678$	−6.67986e8	−	1.15699e9i	−0.0823121	−	0.142569i
$679$	8.55400e7	−	5.10696e7i	0.0104864	−	0.00626063i
$680$	6.82670e8	−	1.18242e9i	0.0832586	−	0.144208i
$681$	−1.65489e9	+	2.86635e9i	−0.200796	+	0.347788i
$682$	2.83868e10			3.42666
$683$	−8.18756e9			−0.983290			−0.491645	−	0.870796i	$-0.663604\pi$
$683$	−8.18756e9			−0.983290			−0.491645	+	0.870796i	$0.663604\pi$
$684$	−4.76224e9	+	8.24845e9i	−0.569004	+	0.985544i
$685$	3.37740e9	−	5.84982e9i	0.401481	−	0.695385i
$686$	4.85714e8	+	1.10586e10i	0.0574442	+	1.30788i
$687$	7.55133e8	+	1.30793e9i	0.0888536	+	0.153899i
$688$	−5.23422e9	+	9.06594e9i	−0.612763	+	1.06134i
$689$	3.78526e9	+	1.08395e10i	0.440889	+	1.26253i
$690$	3.00320e8	+	5.20170e8i	0.0348027	+	0.0602800i
$691$	9.09183e9			1.04828			0.524141	−	0.851631i	$-0.324386\pi$
$691$	9.09183e9			1.04828			0.524141	+	0.851631i	$0.324386\pi$
$692$	2.03972e8	+	3.53291e8i	0.0233991	+	0.0405285i
$693$	−1.31192e10	−	7.32057e9i	−1.49741	−	0.835562i
$694$	−1.41520e10			−1.60716
$695$	3.10445e9	+	5.37707e9i	0.350783	+	0.607574i
$696$	4.38526e8			0.0493018
$697$	−5.22593e9	−	9.05157e9i	−0.584587	−	1.01253i
$698$	1.16832e9	+	2.02359e9i	0.130037	+	0.225231i
$699$	1.21556e9	+	2.10542e9i	0.134619	+	0.233167i
$700$	−7.28081e7	−	4.97589e9i	−0.00802299	−	0.548312i
$701$	6.33186e9			0.694254			0.347127	−	0.937818i	$-0.387157\pi$
$701$	6.33186e9			0.694254			0.347127	+	0.937818i	$0.387157\pi$
$702$	4.85324e9	+	9.21444e8i	0.529483	+	0.100528i
$703$	−4.97430e9	−	8.61573e9i	−0.539993	−	0.935295i
$704$	−3.06671e9	+	5.31170e9i	−0.331260	+	0.573759i
$705$	−6.56622e8			−0.0705755
$706$	−1.21659e10	+	2.10719e10i	−1.30115	+	2.25366i
$707$	−2.69687e9	+	1.61010e9i	−0.287006	+	0.171350i
$708$	−2.00171e8	+	3.46707e8i	−0.0211975	+	0.0367152i
$709$	6.47572e9	+	1.12163e10i	0.682380	+	1.18192i	0.974252	+	0.225460i	$0.0723884\pi$
$709$	6.47572e9	+	1.12163e10i	0.682380	+	1.18192i	−0.291872	+	0.956457i	$0.594278\pi$
$710$	−4.67793e8	−	8.10241e8i	−0.0490512	−	0.0849592i
$711$	−6.92714e9			−0.722787
$712$	−2.46636e9			−0.256080
$713$	−3.70352e9	−	6.41469e9i	−0.382650	−	0.662769i
$714$	2.12469e9	−	1.26849e9i	0.218450	−	0.130420i
$715$	2.78371e9	+	7.97146e9i	0.284809	+	0.815581i
$716$	2.85037e9	−	4.93699e9i	0.290206	−	0.502651i
$717$	1.56857e9	−	2.71685e9i	0.158924	−	0.275264i
$718$	8.18462e9	−	1.41762e10i	0.825208	−	1.42930i
$719$	4.20668e9	+	7.28619e9i	0.422074	+	0.731054i	0.996142	−	0.0877537i	$-0.0279688\pi$
$719$	4.20668e9	+	7.28619e9i	0.422074	+	0.731054i	−0.574068	+	0.818808i	$0.694636\pi$
$720$	−5.54971e9			−0.554123
$721$	−2.06829e9	+	1.23482e9i	−0.205512	+	0.122696i
$722$	1.18000e10	−	2.04383e10i	1.16682	−	2.02099i
$723$	1.32692e9	−	2.29829e9i	0.130575	−	0.226162i
$724$	−2.95009e9			−0.288902
$725$	−2.46402e9	+	4.26781e9i	−0.240138	+	0.415932i
$726$	6.30601e9			0.611613
$727$	1.70249e10			1.64329			0.821643	−	0.570002i	$-0.193058\pi$
$727$	1.70249e10			1.64329			0.821643	+	0.570002i	$0.193058\pi$
$728$	2.99128e9	+	2.50216e9i	0.287340	+	0.240356i
$729$	−7.78108e9			−0.743864
$730$	8.09347e9			0.770025
$731$	4.96123e9	−	8.59310e9i	0.469762	−	0.813652i
$732$	−1.18152e9			−0.111340
$733$	−7.76010e9	+	1.34409e10i	−0.727785	+	1.26056i	0.230032	+	0.973183i	$0.426117\pi$
$733$	−7.76010e9	+	1.34409e10i	−0.727785	+	1.26056i	−0.957817	+	0.287378i	$0.907216\pi$
$734$	−2.42013e9	+	4.19179e9i	−0.225893	+	0.391258i
$735$	5.17626e8	−	9.60397e8i	0.0480851	−	0.0892165i
$736$	6.82010e9			0.630548
$737$	−1.17318e10	−	2.03201e10i	−1.07952	−	1.86978i
$738$	−8.65046e9	+	1.49830e10i	−0.792213	+	1.37215i
$739$	−9.56123e9	+	1.65605e10i	−0.871481	+	1.50945i	−0.0110170	+	0.999939i	$0.503507\pi$
$739$	−9.56123e9	+	1.65605e10i	−0.871481	+	1.50945i	−0.860464	+	0.509511i	$0.829826\pi$
$740$	−1.22644e9	+	2.12426e9i	−0.111259	+	0.192707i
$741$	−3.82079e9	−	7.25421e8i	−0.344977	−	0.0654978i
$742$	−2.85030e8	−	1.94797e10i	−0.0256140	−	1.75053i
$743$	5.92223e9	+	1.02576e10i	0.529693	+	0.917456i	0.999400	+	0.0346333i	$0.0110263\pi$
$743$	5.92223e9	+	1.02576e10i	0.529693	+	0.917456i	−0.469707	+	0.882822i	$0.655640\pi$
$744$	−1.29224e9			−0.115037
$745$	−3.45418e9			−0.306054
$746$	−1.17776e10	−	2.03994e10i	−1.03865	−	1.79900i
$747$	3.86324e9	+	6.69133e9i	0.339101	+	0.587341i
$748$	6.76749e9	−	1.17216e10i	0.591251	−	1.02408i
$749$	8.56648e9	+	4.78013e9i	0.744931	+	0.415674i
$750$	−1.35526e9	+	2.34737e9i	−0.117303	+	0.203174i
$751$	1.72083e10			1.48251			0.741255	−	0.671223i	$-0.234231\pi$
$751$	1.72083e10			1.48251			0.741255	+	0.671223i	$0.234231\pi$
$752$	−4.88976e9	+	8.46931e9i	−0.419300	+	0.726249i
$753$	1.51647e9	+	2.62660e9i	0.129435	+	0.224187i
$754$	3.17621e9	+	9.09542e9i	0.269842	+	0.772721i
$755$	1.62130e9			0.137103
$756$	−3.04877e9	−	1.70123e9i	−0.256625	−	0.143198i
$757$	−1.14978e10	−	1.99147e10i	−0.963335	−	1.66855i	−0.714022	−	0.700123i	$-0.753128\pi$
$757$	−1.14978e10	−	1.99147e10i	−0.963335	−	1.66855i	−0.249313	−	0.968423i	$-0.580205\pi$
$758$	7.32586e9	+	1.26888e10i	0.610965	+	1.05822i
$759$	−1.19342e9	−	2.06707e9i	−0.0990712	−	0.171596i
$760$	3.64100e9			0.300866
$761$	−5.29957e9	−	9.17913e9i	−0.435908	−	0.755014i	0.561462	−	0.827503i	$-0.310239\pi$
$761$	−5.29957e9	−	9.17913e9i	−0.435908	−	0.755014i	−0.997369	+	0.0724887i	$0.976906\pi$
$762$	5.68219e9			0.465236
$763$	7.24616e7	+	4.95221e9i	0.00590571	+	0.403611i
$764$	−7.30468e9	−	1.26521e10i	−0.592618	−	1.02644i
$765$	5.26026e9			0.424807
$766$	−4.52578e9	−	7.83888e9i	−0.363825	−	0.630164i
$767$	3.46376e9	+	6.57635e8i	0.277181	+	0.0526261i
$768$	1.73077e9	−	2.99777e9i	0.137871	−	0.238800i
$769$	−8.67007e9	−	1.50170e10i	−0.687512	−	1.19081i	−0.972640	−	0.232317i	$-0.925369\pi$
$769$	−8.67007e9	−	1.50170e10i	−0.687512	−	1.19081i	0.285128	−	0.958489i	$-0.407964\pi$
$770$	−2.09614e8	−	1.43255e10i	−0.0165463	−	1.13082i
$771$	−1.62626e9	+	2.81677e9i	−0.127791	+	0.221341i
$772$	3.03705e9	−	5.26032e9i	0.237570	−	0.411482i
$773$	−1.09172e10			−0.850125			−0.425062	−	0.905164i	$-0.639748\pi$
$773$	−1.09172e10			−0.850125			−0.425062	+	0.905164i	$0.639748\pi$
$774$	−1.64246e10			−1.27321
$775$	7.26093e9	−	1.25763e10i	0.560320	−	0.970503i
$776$	−2.97780e7	+	5.15770e7i	−0.00228759	+	0.00396223i
$777$	1.53012e9	−	9.13519e8i	0.117017	−	0.0698625i
$778$	−3.43088e9	−	5.94246e9i	−0.261202	−	0.452415i
$779$	1.39362e10	−	2.41382e10i	1.05624	−	1.82946i
$780$	3.16125e8	+	9.05258e8i	0.0238522	+	0.0683033i
$781$	1.85893e9	+	3.21976e9i	0.139632	+	0.241849i
$782$	−8.47917e9			−0.634059
$783$	1.72868e9	+	2.99416e9i	0.128691	+	0.222900i
$784$	−8.53281e9	−	1.38284e10i	−0.632391	−	1.02486i
$785$	−6.31603e9			−0.466015
$786$	1.59354e9	+	2.76010e9i	0.117054	+	0.202743i
$787$	−2.39534e9			−0.175169			−0.0875843	−	0.996157i	$-0.527915\pi$
$787$	−2.39534e9			−0.175169			−0.0875843	+	0.996157i	$0.527915\pi$
$788$	−1.91311e9	−	3.31361e9i	−0.139283	−	0.241245i
$789$	−1.34530e9	−	2.33013e9i	−0.0975101	−	0.168892i
$790$	−3.30302e9	−	5.72100e9i	−0.238351	−	0.412835i
$791$	7.13952e9	−	4.26248e9i	0.512922	−	0.306228i
$792$	8.98102e9			0.642373
$793$	3.43040e9	+	9.82334e9i	0.244281	+	0.699525i
$794$	−1.90170e9	−	3.29383e9i	−0.134825	−	0.233523i
$795$	−9.60077e8	+	1.66290e9i	−0.0677675	+	0.117377i
$796$	6.37299e9			0.447865
$797$	−6.96220e9	+	1.20589e10i	−0.487127	+	0.843729i	−0.999890	−	0.0148009i	$-0.995289\pi$
$797$	−6.96220e9	+	1.20589e10i	−0.487127	+	0.843729i	0.512763	+	0.858530i	$0.328622\pi$
$798$	5.76253e9	+	3.21552e9i	0.401424	+	0.223996i
$799$	4.63473e9	−	8.02759e9i	0.321448	−	0.556764i
$800$	6.68556e9	+	1.15797e10i	0.461660	+	0.799619i
$801$	−4.75108e9	−	8.22911e9i	−0.326647	−	0.565769i
$802$	−2.84823e10			−1.94969
$803$	−3.21620e10			−2.19199
$804$	−1.33229e9	−	2.30760e9i	−0.0904074	−	0.156590i
$805$	−3.20986e9	+	1.91637e9i	−0.216870	+	0.129477i
$806$	−9.35958e9	−	2.68022e10i	−0.629627	−	1.80301i
$807$	−5.75388e8	+	9.96602e8i	−0.0385393	+	0.0667520i
$808$	9.38826e8	−	1.62609e9i	0.0626102	−	0.108444i
$809$	−1.04169e10	+	1.80425e10i	−0.691699	+	1.19806i	0.279582	+	0.960122i	$0.409804\pi$
$809$	−1.04169e10	+	1.80425e10i	−0.691699	+	1.19806i	−0.971281	+	0.237936i	$0.923529\pi$
$810$	−4.14243e9	−	7.17489e9i	−0.273878	−	0.474371i
$811$	−8.34615e9			−0.549431			−0.274715	−	0.961526i	$-0.588584\pi$
$811$	−8.34615e9			−0.549431			−0.274715	+	0.961526i	$0.588584\pi$
$812$	−9.96178e7	−	6.80813e9i	−0.00652966	−	0.446254i
$813$	1.18371e9	−	2.05024e9i	0.0772552	−	0.133810i
$814$	1.17010e10	−	2.02667e10i	0.760393	−	1.31704i
$815$	1.04185e10			0.674144
$816$	−1.81625e9	+	3.14583e9i	−0.117020	+	0.202684i
$817$	2.64606e10			1.69755
$818$	−1.35141e10			−0.863281
$819$	−2.58631e9	+	1.48006e10i	−0.164508	+	0.941424i
$820$	−6.87210e9			−0.435252
$821$	−1.72438e10			−1.08751			−0.543753	−	0.839245i	$-0.682997\pi$
$821$	−1.72438e10			−1.08751			−0.543753	+	0.839245i	$0.682997\pi$
$822$	−3.65925e9	+	6.33801e9i	−0.229795	+	0.398017i
$823$	1.69738e10			1.06140			0.530699	−	0.847560i	$-0.321929\pi$
$823$	1.69738e10			1.06140			0.530699	+	0.847560i	$0.321929\pi$
$824$	7.20006e8	−	1.24709e9i	0.0448323	−	0.0776518i
$825$	2.33976e9	−	4.05258e9i	0.145071	−	0.251271i
$826$	−5.22405e9	−	2.91504e9i	−0.322535	−	0.179976i
$827$	2.08687e9			0.128300			0.0641498	−	0.997940i	$-0.479566\pi$
$827$	2.08687e9			0.128300			0.0641498	+	0.997940i	$0.479566\pi$
$828$	2.92302e9	+	5.06283e9i	0.178948	+	0.309947i
$829$	1.44213e10	−	2.49785e10i	0.879153	−	1.52274i	0.0268812	−	0.999639i	$-0.491442\pi$
$829$	1.44213e10	−	2.49785e10i	0.879153	−	1.52274i	0.852272	−	0.523099i	$-0.175224\pi$
$830$	−3.68416e9	+	6.38115e9i	−0.223648	+	0.387370i
$831$	1.19878e9	−	2.07635e9i	0.0724662	−	0.125515i
$832$	6.02634e9	+	1.14417e9i	0.362762	+	0.0688746i
$833$	8.08777e9	+	1.31072e10i	0.484810	+	0.785691i
$834$	−3.36353e9	−	5.82581e9i	−0.200777	−	0.347756i
$835$	4.65735e9			0.276845
$836$	3.60942e10			2.13656
$837$	−5.09404e9	−	8.82314e9i	−0.300278	−	0.520097i
$838$	−4.70150e9	−	8.14323e9i	−0.275983	−	0.478016i
$839$	−4.55815e9	+	7.89495e9i	−0.266454	+	0.461511i	−0.967943	−	0.251168i	$-0.919185\pi$
$839$	−4.55815e9	+	7.89495e9i	−0.266454	+	0.461511i	0.701490	+	0.712680i	$0.252519\pi$
$840$	9.54215e6	+	6.52134e8i	0.000555480	+	0.0379629i
$841$	5.25360e9	−	9.09951e9i	0.304559	−	0.527511i
$842$	1.10159e10			0.635955
$843$	−1.62824e9	+	2.82019e9i	−0.0936097	+	0.162137i
$844$	2.76969e9	+	4.79725e9i	0.158574	+	0.274659i
$845$	6.60865e9	−	5.25664e9i	0.376803	−	0.299716i
$846$	−1.53437e10			−0.871232
$847$	5.74234e8	+	3.92446e10i	0.0324711	+	2.21916i
$848$	1.42991e10	+	2.47667e10i	0.805235	+	1.39471i
$849$	1.00750e9	+	1.74504e9i	0.0565024	+	0.0978650i
$850$	−8.31190e9	−	1.43966e10i	−0.464231	−	0.804071i
$851$	−6.10636e9			−0.339648
$852$	2.11104e8	+	3.65644e8i	0.0116939	+	0.0202544i
$853$	−1.34950e10			−0.744479			−0.372240	−	0.928137i	$-0.621410\pi$
$853$	−1.34950e10			−0.744479			−0.372240	+	0.928137i	$0.621410\pi$
$854$	−2.58310e8	−	1.76535e10i	−0.0141918	−	0.969904i
$855$	7.01387e9	+	1.21484e10i	0.383774	+	0.664717i
$856$	−5.86436e9			−0.319567
$857$	8.63092e9	+	1.49492e10i	0.468408	+	0.811306i	0.999348	−	0.0361031i	$-0.0114945\pi$
$857$	8.63092e9	+	1.49492e10i	0.468408	+	0.811306i	−0.530940	+	0.847409i	$0.678161\pi$
$858$	−3.01602e9	−	8.63671e9i	−0.163016	−	0.466813i
$859$	−1.05181e10	+	1.82179e10i	−0.566189	+	0.980668i	0.430749	+	0.902472i	$0.358249\pi$
$859$	−1.05181e10	+	1.82179e10i	−0.566189	+	0.980668i	−0.996938	+	0.0781963i	$0.975084\pi$
$860$	−3.26201e9	−	5.64997e9i	−0.174880	−	0.302901i
$861$	4.35988e9	+	2.43283e9i	0.232789	+	0.129897i
$862$	−1.37237e9	+	2.37701e9i	−0.0729785	+	0.126403i
$863$	7.67903e9	−	1.33005e10i	0.406695	−	0.704416i	−0.587822	−	0.808990i	$-0.700015\pi$
$863$	7.67903e9	−	1.33005e10i	0.406695	−	0.704416i	0.994517	+	0.104574i	$0.0333479\pi$
$864$	9.38076e9			0.494812
$865$	6.00824e8			0.0315639
$866$	−2.14322e10	+	3.71217e10i	−1.12139	+	1.94230i
$867$	−2.98210e8	+	5.16515e8i	−0.0155402	+	0.0269163i
$868$	2.93552e8	+	2.00621e10i	0.0152358	+	1.04125i
$869$	1.31256e10	+	2.27343e10i	0.678502	+	1.17520i
$870$	−8.05599e8	+	1.39534e9i	−0.0414764	+	0.0718393i
$871$	−1.53176e10	+	1.77768e10i	−0.785468	+	0.911571i
$872$	−1.48037e9	−	2.56408e9i	−0.0756073	−	0.130956i
$873$	−2.29452e8			−0.0116719
$874$	−1.13059e10	−	1.95823e10i	−0.572814	−	0.992143i
$875$	−1.47320e10	−	8.22050e9i	−0.743417	−	0.414830i
$876$	−3.65240e9			−0.183575
$877$	1.14430e10	+	1.98199e10i	0.572851	+	0.992208i	0.996271	+	0.0862742i	$0.0274961\pi$
$877$	1.14430e10	+	1.98199e10i	0.572851	+	0.992208i	−0.423420	+	0.905933i	$0.639171\pi$
$878$	2.32615e10			1.15987
$879$	−1.33646e9	−	2.31482e9i	−0.0663737	−	0.114963i
$880$	1.05157e10	+	1.82136e10i	0.520172	+	0.900964i
$881$	−4.29784e9	−	7.44409e9i	−0.211756	−	0.366772i	0.740508	−	0.672047i	$-0.234585\pi$
$881$	−4.29784e9	−	7.44409e9i	−0.211756	−	0.366772i	−0.952264	+	0.305276i	$0.901251\pi$
$882$	1.20957e10	−	2.24422e10i	0.593596	−	1.10135i
$883$	−1.41352e10			−0.690938			−0.345469	−	0.938430i	$-0.612280\pi$
$883$	−1.41352e10			−0.690938			−0.345469	+	0.938430i	$0.612280\pi$
$884$	−1.32987e10	−	2.52490e9i	−0.647478	−	0.122931i
$885$	2.94814e8	+	5.10632e8i	0.0142970	+	0.0247632i
$886$	−7.40879e9	+	1.28324e10i	−0.357873	+	0.619855i
$887$	2.91587e10			1.40293			0.701465	−	0.712704i	$-0.252530\pi$
$887$	2.91587e10			1.40293			0.701465	+	0.712704i	$0.252530\pi$
$888$	−5.32660e8	+	9.22594e8i	−0.0255273	+	0.0442146i
$889$	5.17428e8	+	3.53623e10i	0.0246998	+	1.68805i
$890$	4.53085e9	−	7.84766e9i	0.215434	−	0.373143i
$891$	1.64613e10	+	2.85118e10i	0.779636	+	1.35037i
$892$	−8.71756e9	−	1.50993e10i	−0.411261	−	0.712326i
$893$	2.47192e10			1.16159
$894$	3.74244e9			0.175176
$895$	−4.19805e9	−	7.27124e9i	−0.195734	−	0.339022i
$896$	1.35106e10	+	7.53897e9i	0.627475	+	0.350134i
$897$	−1.55819e9	+	1.80835e9i	−0.0720852	+	0.0836581i
$898$	8.14431e9	−	1.41064e10i	0.375308	−	0.650052i
$899$	9.93458e9	−	1.72072e10i	0.456027	−	0.789862i
$900$	−5.73072e9	+	9.92590e9i	−0.262036	+	0.453859i
$901$	−1.35533e10	−	2.34750e10i	−0.617317	−	1.06922i
$902$	6.55640e10			2.97470
$903$	6.93465e7	+	4.73932e9i	0.00313413	+	0.214195i
$904$	−2.48539e9	+	4.30482e9i	−0.111894	+	0.193805i
$905$	−2.17246e9	+	3.76281e9i	−0.0974275	+	0.168749i
$906$	−1.75660e9			−0.0784737
$907$	−1.33478e10	+	2.31191e10i	−0.593997	+	1.02883i	0.399691	+	0.916650i	$0.369118\pi$
$907$	−1.33478e10	+	2.31191e10i	−0.593997	+	1.02883i	−0.993688	+	0.112183i	$0.964216\pi$
$908$	−3.07209e10			−1.36186
$909$	7.23405e9			0.319454
$910$	−1.34567e10	+	4.92127e9i	−0.591963	+	0.216487i
$911$	4.08739e10			1.79115			0.895575	−	0.444912i	$-0.146765\pi$
$911$	4.08739e10			1.79115			0.895575	+	0.444912i	$0.146765\pi$
$912$	−9.68690e9			−0.422866
$913$	1.46402e10	−	2.53576e10i	0.636649	−	1.10271i
$914$	1.94079e10			0.840750
$915$	−8.70073e8	+	1.50701e9i	−0.0375476	+	0.0650343i
$916$	−7.00904e9	+	1.21400e10i	−0.301317	+	0.521897i
$917$	−1.70320e10	+	1.01685e10i	−0.729412	+	0.435478i
$918$	−1.16627e10			−0.497567
$919$	2.32944e10	+	4.03471e10i	0.990028	+	1.71478i	0.617011	+	0.786955i	$0.288343\pi$
$919$	2.32944e10	+	4.03471e10i	0.990028	+	1.71478i	0.373017	+	0.927824i	$0.378323\pi$
$920$	1.11741e9	−	1.93541e9i	0.0473101	−	0.0819436i
$921$	−3.62695e9	+	6.28206e9i	−0.152979	+	0.264968i
$922$	−6.66676e9	+	1.15472e10i	−0.280128	+	0.485196i
$923$	2.42711e9	−	2.81677e9i	0.101598	−	0.117909i
$924$	9.45938e7	+	6.46478e9i	0.00394467	+	0.269589i
$925$	−5.98590e9	−	1.03679e10i	−0.248676	−	0.430719i
$926$	−3.19534e10			−1.32245
$927$	5.54796e9			0.228746
$928$	9.14734e9	+	1.58437e10i	0.375731	+	0.650785i
$929$	2.60342e9	+	4.50925e9i	0.106534	+	0.184523i	0.914364	−	0.404893i	$-0.132691\pi$
$929$	2.60342e9	+	4.50925e9i	0.106534	+	0.184523i	−0.807830	+	0.589416i	$0.799358\pi$
$930$	2.37392e9	−	4.11175e9i	0.0967778	−	0.167624i
$931$	−1.94866e10	+	3.61551e10i	−0.791428	+	1.46841i
$932$	−1.12827e10	+	1.95422e10i	−0.456516	+	0.790710i
$933$	−2.05872e9			−0.0829873
$934$	−1.39734e10	+	2.42027e10i	−0.561163	+	0.971962i
$935$	−9.96720e9	−	1.72637e10i	−0.398779	−	0.690706i
$936$	−2.96119e9	−	8.47968e9i	−0.118032	−	0.337998i
$937$	−1.32578e10			−0.526481			−0.263240	−	0.964730i	$-0.584791\pi$
$937$	−1.32578e10			−0.526481			−0.263240	+	0.964730i	$0.584791\pi$
$938$	3.41876e10	−	2.04109e10i	1.35257	−	0.807517i
$939$	−3.59792e9	−	6.23179e9i	−0.141815	−	0.245631i
$940$	−3.04734e9	−	5.27814e9i	−0.119667	−	0.207269i
$941$	−1.37471e10	−	2.38107e10i	−0.537834	−	0.931556i	−0.999020	−	0.0442525i	$-0.985909\pi$
$941$	−1.37471e10	−	2.38107e10i	−0.537834	−	0.931556i	0.461186	−	0.887303i	$-0.347424\pi$
$942$	6.84312e9			0.266733
$943$	−8.55391e9	−	1.48158e10i	−0.332180	−	0.575353i
$944$	8.78171e9			0.339764
$945$	−4.41502e9	+	2.63588e9i	−0.170185	+	0.101605i
$946$	3.11215e10	+	5.39041e10i	1.19520	+	2.07015i
$947$	2.76937e10			1.05963			0.529817	−	0.848112i	$-0.322261\pi$
$947$	2.76937e10			1.05963			0.529817	+	0.848112i	$0.322261\pi$
$948$	1.49058e9	+	2.58176e9i	0.0568232	+	0.0984206i
$949$	1.06043e10	+	3.03667e10i	0.402765	+	1.15336i
$950$	2.21657e10	−	3.83920e10i	0.838780	−	1.45281i
$951$	−2.70772e9	−	4.68991e9i	−0.102087	−	0.176820i
$952$	−8.04007e9	−	4.48639e9i	−0.302017	−	0.168526i
$953$	6.21371e9	−	1.07625e10i	0.232555	−	0.402797i	−0.726004	−	0.687690i	$-0.758625\pi$
$953$	6.21371e9	−	1.07625e10i	0.232555	−	0.402797i	0.958559	+	0.284893i	$0.0919580\pi$
$954$	−2.24347e10	+	3.88581e10i	−0.836569	+	1.44898i
$955$	−2.15168e10			−0.799402
$956$	2.91186e10			1.07787
$957$	3.20131e9	−	5.54483e9i	0.118069	−	0.204502i
$958$	9.12704e9	−	1.58085e10i	0.335390	−	0.580913i
$959$	−3.97770e10	−	2.21957e10i	−1.45635	−	0.812650i
$960$	5.12925e8	+	8.88411e8i	0.0187113	+	0.0324089i
$961$	−1.55187e10	+	2.68792e10i	−0.564057	+	0.976976i
$962$	−2.29934e10	−	4.36557e9i	−0.832705	−	0.158099i
$963$	−1.12968e10	−	1.95667e10i	−0.407629	−	0.706034i
$964$	2.46325e10			0.885603
$965$	−4.47298e9	−	7.74743e9i	−0.160233	−	0.277531i
$966$	3.47773e9	−	2.07630e9i	0.124130	−	0.0741087i
$967$	5.79178e9			0.205977			0.102989	−	0.994683i	$-0.467159\pi$
$967$	5.79178e9			0.205977			0.102989	+	0.994683i	$0.467159\pi$
$968$	−1.17315e10	−	2.03195e10i	−0.415708	−	0.720027i
$969$	9.18168e9			0.324182
$970$	−1.09408e8	−	1.89500e8i	−0.00384900	−	0.00666666i
$971$	6.10725e9	+	1.05781e10i	0.214081	+	0.370799i	0.952988	−	0.303008i	$-0.0979910\pi$
$971$	6.10725e9	+	1.05781e10i	0.214081	+	0.370799i	−0.738907	+	0.673808i	$0.764658\pi$
$972$	6.07629e9	+	1.05244e10i	0.212230	+	0.367593i
$973$	3.59498e10	−	2.14630e10i	1.25113	−	0.746956i
$974$	−2.01154e10			−0.697544
$975$	−4.59781e9	−	8.72947e8i	−0.158867	−	0.0301628i
$976$	1.29586e10	+	2.24449e10i	0.446152	+	0.772758i
$977$	1.62024e10	−	2.80634e10i	0.555838	−	0.962740i	−0.442000	−	0.897015i	$-0.645731\pi$
$977$	1.62024e10	−	2.80634e10i	0.555838	−	0.962740i	0.997838	−	0.0657248i	$-0.0209360\pi$
$978$	−1.12879e10			−0.385859
$979$	−1.80048e10	+	3.11852e10i	−0.613266	+	1.06221i
$980$	1.01222e10	−	2.96284e8i	0.343547	−	0.0100558i
$981$	5.70345e9	−	9.87867e9i	0.192884	−	0.334085i
$982$	−3.53820e10	−	6.12835e10i	−1.19232	−	2.06516i
$983$	2.28343e10	+	3.95502e10i	0.766745	+	1.32804i	0.939319	+	0.343045i	$0.111458\pi$
$983$	2.28343e10	+	3.95502e10i	0.766745	+	1.32804i	−0.172574	+	0.984997i	$0.555208\pi$
$984$	−2.98464e9			−0.0998641
$985$	−5.63529e9			−0.187884
$986$	−1.13725e10	−	1.96978e10i	−0.377823	−	0.654409i
$987$	6.47829e7	+	4.42742e9i	0.00214462	+	0.146569i
$988$	−1.19008e10	−	3.40794e10i	−0.392580	−	1.12420i
$989$	8.12064e9	−	1.40654e10i	0.266934	−	0.462342i
$990$	−1.64987e10	+	2.85765e10i	−0.540413	+	0.936023i
$991$	−1.99570e10	+	3.45665e10i	−0.651384	+	1.12823i	0.331404	+	0.943489i	$0.392478\pi$
$991$	−1.99570e10	+	3.45665e10i	−0.651384	+	1.12823i	−0.982787	+	0.184741i	$0.940856\pi$
$992$	−2.69552e10	−	4.66878e10i	−0.876701	−	1.51849i
$993$	2.62570e8			0.00850988
$994$	−5.41708e9	+	3.23414e9i	−0.174950	+	0.104449i
$995$	4.69309e9	−	8.12867e9i	0.151035	−	0.261601i
$996$	1.66258e9	−	2.87967e9i	0.0533181	−	0.0923496i
$997$	−4.96957e10			−1.58813			−0.794065	−	0.607833i	$-0.792039\pi$
$997$	−4.96957e10			−1.58813			−0.794065	+	0.607833i	$0.792039\pi$
$998$	3.47461e9	−	6.01820e9i	0.110649	−	0.191650i
$999$	−8.39904e9			−0.266533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.h.a.16.13	yes	126
7.4	even	3		91.8.g.a.81.51	yes	126
13.9	even	3		91.8.g.a.9.51	✓	126
91.74	even	3	inner	91.8.h.a.74.13	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.g.a.9.51	✓	126	13.9	even	3
91.8.g.a.81.51	yes	126	7.4	even	3
91.8.h.a.16.13	yes	126	1.1	even	1	trivial
91.8.h.a.74.13	yes	126	91.74	even	3	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-14.8112 q^{2} +(4.92210 - 8.52533i) q^{3} +91.3725 q^{4} +(67.2870 - 116.545i) q^{5} +(-72.9024 + 126.271i) q^{6} +(-792.466 - 442.199i) q^{7} +542.499 q^{8} +(1045.05 + 1810.07i) q^{9} +O(q^{10})\)	\(q-14.8112 q^{2} +(4.92210 - 8.52533i) q^{3} +91.3725 q^{4} +(67.2870 - 116.545i) q^{5} +(-72.9024 + 126.271i) q^{6} +(-792.466 - 442.199i) q^{7} +542.499 q^{8} +(1045.05 + 1810.07i) q^{9} +(-996.603 + 1726.17i) q^{10} +(3960.33 - 6859.49i) q^{11} +(449.745 - 778.980i) q^{12} +(-7782.37 - 1477.57i) q^{13} +(11737.4 + 6549.52i) q^{14} +(-662.387 - 1147.29i) q^{15} -19730.7 q^{16} +18701.7 q^{17} +(-15478.4 - 26809.4i) q^{18} +(24936.2 + 43190.8i) q^{19} +(6148.18 - 10649.0i) q^{20} +(-7670.49 + 4579.48i) q^{21} +(-58657.4 + 101598. i) q^{22} +30611.3 q^{23} +(2670.23 - 4624.98i) q^{24} +(30007.4 + 51974.4i) q^{25} +(115266. + 21884.7i) q^{26} +42104.6 q^{27} +(-72409.6 - 40404.9i) q^{28} +(41056.9 + 71112.6i) q^{29} +(9810.76 + 16992.7i) q^{30} +(-120986. - 209553. i) q^{31} +222797. q^{32} +(-38986.3 - 67526.2i) q^{33} -276995. q^{34} +(-104859. + 62603.3i) q^{35} +(95488.4 + 165391. i) q^{36} -199481. q^{37} +(-369336. - 639709. i) q^{38} +(-50902.4 + 59074.5i) q^{39} +(36503.1 - 63225.3i) q^{40} +(-279436. - 483998. i) q^{41} +(113609. - 67827.8i) q^{42} +(265282. - 459483. i) q^{43} +(361865. - 626769. i) q^{44} +281272. q^{45} -453391. q^{46} +(247824. - 429244. i) q^{47} +(-97116.7 + 168211. i) q^{48} +(432462. + 700856. i) q^{49} +(-444447. - 769804. i) q^{50} +(92051.5 - 159438. i) q^{51} +(-711094. - 135009. i) q^{52} +(-724710. - 1.25524e6i) q^{53} -623620. q^{54} +(-532958. - 923110. i) q^{55} +(-429912. - 239893. i) q^{56} +490955. q^{57} +(-608103. - 1.05327e6i) q^{58} -445078. q^{59} +(-60523.9 - 104831. i) q^{60} +(-656771. - 1.13756e6i) q^{61} +(1.79194e6 + 3.10374e6i) q^{62} +(-27750.5 - 1.89654e6i) q^{63} -774358. q^{64} +(-695855. + 807571. i) q^{65} +(577435. + 1.00015e6i) q^{66} +(1.48117e6 - 2.56546e6i) q^{67} +1.70882e6 q^{68} +(150672. - 260971. i) q^{69} +(1.55308e6 - 927232. i) q^{70} +(-234694. + 406501. i) q^{71} +(566936. + 981962. i) q^{72} +(-2.03026e6 - 3.51652e6i) q^{73} +2.95455e6 q^{74} +590798. q^{75} +(2.27849e6 + 3.94645e6i) q^{76} +(-6.17169e6 + 3.68466e6i) q^{77} +(753927. - 874966. i) q^{78} +(-1.65714e6 + 2.87025e6i) q^{79} +(-1.32762e6 + 2.29951e6i) q^{80} +(-2.07827e6 + 3.59967e6i) q^{81} +(4.13880e6 + 7.16860e6i) q^{82} +3.69672e6 q^{83} +(-700872. + 418439. i) q^{84} +(1.25838e6 - 2.17958e6i) q^{85} +(-3.92916e6 + 6.80550e6i) q^{86} +808345. q^{87} +(2.14847e6 - 3.72127e6i) q^{88} -4.54629e6 q^{89} -4.16598e6 q^{90} +(5.51388e6 + 4.61229e6i) q^{91} +2.79703e6 q^{92} -2.38201e6 q^{93} +(-3.67058e6 + 6.35764e6i) q^{94} +6.71154e6 q^{95} +(1.09663e6 - 1.89942e6i) q^{96} +(-54890.4 + 95073.0i) q^{97} +(-6.40530e6 - 1.03805e7i) q^{98} +1.65549e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Introduction

L-functions

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