LMFDB - Embedded newform 16.7.f.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,7,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68086533792$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	16.11
Dual form			16.7.f.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.06674 - 6.88924i) q^{2} +(23.4827 + 23.4827i) q^{3} +(-30.9232 + 56.0335i) q^{4} +(55.3108 + 55.3108i) q^{5} +(66.2800 - 257.276i) q^{6} +386.163 q^{7} +(511.785 - 14.8363i) q^{8} +373.878i q^{9} +O(q^{10})$	\(q+(-4.06674 - 6.88924i) q^{2} +(23.4827 + 23.4827i) q^{3} +(-30.9232 + 56.0335i) q^{4} +(55.3108 + 55.3108i) q^{5} +(66.2800 - 257.276i) q^{6} +386.163 q^{7} +(511.785 - 14.8363i) q^{8} +373.878i q^{9} +(156.115 - 605.984i) q^{10} +(-208.354 + 208.354i) q^{11} +(-2041.98 + 589.658i) q^{12} +(-1973.22 + 1973.22i) q^{13} +(-1570.43 - 2660.37i) q^{14} +2597.70i q^{15} +(-2183.51 - 3465.47i) q^{16} +8608.75 q^{17} +(2575.74 - 1520.47i) q^{18} +(-7114.07 - 7114.07i) q^{19} +(-4809.65 + 1388.87i) q^{20} +(9068.17 + 9068.17i) q^{21} +(2282.72 + 588.078i) q^{22} -14537.9 q^{23} +(12366.5 + 11669.7i) q^{24} -9506.43i q^{25} +(21618.5 + 5569.40i) q^{26} +(8339.23 - 8339.23i) q^{27} +(-11941.4 + 21638.1i) q^{28} +(-4509.49 + 4509.49i) q^{29} +(17896.2 - 10564.2i) q^{30} -44764.2i q^{31} +(-14994.7 + 29135.9i) q^{32} -9785.44 q^{33} +(-35009.6 - 59307.7i) q^{34} +(21359.0 + 21359.0i) q^{35} +(-20949.7 - 11561.5i) q^{36} +(14995.3 + 14995.3i) q^{37} +(-20079.4 + 77941.6i) q^{38} -92673.0 q^{39} +(29127.8 + 27486.6i) q^{40} -16022.1i q^{41} +(25594.9 - 99350.7i) q^{42} +(18011.9 - 18011.9i) q^{43} +(-5231.82 - 18117.8i) q^{44} +(-20679.5 + 20679.5i) q^{45} +(59121.8 + 100155. i) q^{46} +49745.6i q^{47} +(30104.1 - 132654. i) q^{48} +31473.0 q^{49} +(-65492.1 + 38660.2i) q^{50} +(202157. + 202157. i) q^{51} +(-49548.0 - 171584. i) q^{52} +(103698. + 103698. i) q^{53} +(-91364.5 - 23537.5i) q^{54} -23048.4 q^{55} +(197633. - 5729.22i) q^{56} -334116. i q^{57} +(49405.8 + 12728.0i) q^{58} +(103267. - 103267. i) q^{59} +(-145558. - 80329.2i) q^{60} +(-261802. + 261802. i) q^{61} +(-308391. + 182044. i) q^{62} +144378. i q^{63} +(261704. - 15186.0i) q^{64} -218280. q^{65} +(39794.9 + 67414.2i) q^{66} +(-82606.9 - 82606.9i) q^{67} +(-266210. + 482378. i) q^{68} +(-341390. - 341390. i) q^{69} +(60285.7 - 234009. i) q^{70} +21573.8 q^{71} +(5546.96 + 191345. i) q^{72} -431926. i q^{73} +(42324.2 - 164288. i) q^{74} +(223237. - 223237. i) q^{75} +(618616. - 178636. i) q^{76} +(-80458.6 + 80458.6i) q^{77} +(376877. + 638447. i) q^{78} -122330. i q^{79} +(70906.6 - 312450. i) q^{80} +664213. q^{81} +(-110380. + 65157.6i) q^{82} +(-80492.3 - 80492.3i) q^{83} +(-788539. + 227704. i) q^{84} +(476157. + 476157. i) q^{85} +(-197338. - 50838.4i) q^{86} -211790. q^{87} +(-103541. + 109724. i) q^{88} +1.23273e6i q^{89} +(226564. + 58367.9i) q^{90} +(-761983. + 761983. i) q^{91} +(449559. - 814609. i) q^{92} +(1.05119e6 - 1.05119e6i) q^{93} +(342709. - 202303. i) q^{94} -786970. i q^{95} +(-1.03631e6 + 332074. i) q^{96} -788704. q^{97} +(-127993. - 216825. i) q^{98} +(-77899.0 - 77899.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) $ 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−4.06674	−	6.88924i	−0.508343	−	0.861155i
$2$	−4.06674	−	6.88924i	−0.508343	−	0.861155i
$3$	23.4827	+	23.4827i	0.869731	+	0.869731i	0.992442	−	0.122711i	$-0.0391589\pi$
$3$	23.4827	+	23.4827i	0.869731	+	0.869731i	−0.122711	+	0.992442i	$0.539159\pi$
$4$	−30.9232	+	56.0335i	−0.483175	+	0.875524i
$5$	55.3108	+	55.3108i	0.442486	+	0.442486i	0.892847	−	0.450360i	$-0.148705\pi$
$5$	55.3108	+	55.3108i	0.442486	+	0.442486i	−0.450360	+	0.892847i	$0.648705\pi$
$6$	66.2800	−	257.276i	0.306852	−	1.19109i
$7$	386.163			1.12584			0.562920	−	0.826511i	$-0.309678\pi$
$7$	386.163			1.12584			0.562920	+	0.826511i	$0.309678\pi$
$8$	511.785	−	14.8363i	0.999580	−	0.0289771i
$9$			373.878i			0.512865i
$10$	156.115	−	605.984i	0.156115	−	0.605984i
$11$	−208.354	+	208.354i	−0.156539	+	0.156539i	−0.781031	−	0.624492i	$-0.785306\pi$
$11$	−208.354	+	208.354i	−0.156539	+	0.156539i	0.624492	+	0.781031i	$0.285306\pi$
$12$	−2041.98	+	589.658i	−1.18170	+	0.341237i
$13$	−1973.22	+	1973.22i	−0.898141	+	0.898141i	−0.995272	−	0.0971308i	$-0.969033\pi$
$13$	−1973.22	+	1973.22i	−0.898141	+	0.898141i	0.0971308	+	0.995272i	$0.469033\pi$
$14$	−1570.43	−	2660.37i	−0.572313	−	0.969523i
$15$			2597.70i			0.769688i
$16$	−2183.51	−	3465.47i	−0.533083	−	0.846063i
$17$	8608.75			1.75224			0.876119	−	0.482094i	$-0.160124\pi$
$17$	8608.75			1.75224			0.876119	+	0.482094i	$0.160124\pi$
$18$	2575.74	−	1520.47i	0.441656	−	0.260711i
$19$	−7114.07	−	7114.07i	−1.03719	−	1.03719i	−0.999281	−	0.0379064i	$-0.987931\pi$
$19$	−7114.07	−	7114.07i	−1.03719	−	1.03719i	−0.0379064	−	0.999281i	$-0.512069\pi$
$20$	−4809.65	+	1388.87i	−0.601206	+	0.173609i
$21$	9068.17	+	9068.17i	0.979178	+	0.979178i
$22$	2282.72	+	588.078i	0.214380	+	0.0552290i
$23$	−14537.9			−1.19486			−0.597431	−	0.801920i	$-0.703812\pi$
$23$	−14537.9			−1.19486			−0.597431	+	0.801920i	$0.703812\pi$
$24$	12366.5	+	11669.7i	0.894568	+	0.844164i
$25$		−	9506.43i		−	0.608412i
$26$	21618.5	+	5569.40i	1.23000	+	0.316875i
$27$	8339.23	−	8339.23i	0.423677	−	0.423677i
$28$	−11941.4	+	21638.1i	−0.543978	+	0.985700i
$29$	−4509.49	+	4509.49i	−0.184898	+	0.184898i	−0.793486	−	0.608588i	$-0.791736\pi$
$29$	−4509.49	+	4509.49i	−0.184898	+	0.184898i	0.608588	+	0.793486i	$0.291736\pi$
$30$	17896.2	−	10564.2i	0.662821	−	0.391265i
$31$		−	44764.2i		−	1.50261i	−0.659957	−	0.751304i	$-0.729425\pi$
$31$		−	44764.2i		−	1.50261i	0.659957	−	0.751304i	$-0.270575\pi$
$32$	−14994.7	+	29135.9i	−0.457602	+	0.889157i
$33$	−9785.44			−0.272294
$34$	−35009.6	−	59307.7i	−0.890738	−	1.50895i
$35$	21359.0	+	21359.0i	0.498169	+	0.498169i
$36$	−20949.7	−	11561.5i	−0.449025	−	0.247804i
$37$	14995.3	+	14995.3i	0.296040	+	0.296040i	0.839460	−	0.543421i	$-0.182871\pi$
$37$	14995.3	+	14995.3i	0.296040	+	0.296040i	−0.543421	+	0.839460i	$0.682871\pi$
$38$	−20079.4	+	77941.6i	−0.365932	+	1.42043i
$39$	−92673.0			−1.56228
$40$	29127.8	+	27486.6i	0.455123	+	0.429479i
$41$		−	16022.1i		−	0.232470i	−0.993222	−	0.116235i	$-0.962917\pi$
$41$		−	16022.1i		−	0.232470i	0.993222	−	0.116235i	$-0.0370826\pi$
$42$	25594.9	−	99350.7i	0.345466	−	1.34098i
$43$	18011.9	−	18011.9i	0.226544	−	0.226544i	−0.584703	−	0.811247i	$-0.698789\pi$
$43$	18011.9	−	18011.9i	0.226544	−	0.226544i	0.811247	+	0.584703i	$0.198789\pi$
$44$	−5231.82	−	18117.8i	−0.0614179	−	0.212690i
$45$	−20679.5	+	20679.5i	−0.226936	+	0.226936i
$46$	59121.8	+	100155.i	0.607400	+	1.02896i
$47$			49745.6i			0.479139i	0.970879	+	0.239569i	$0.0770062\pi$
$47$			49745.6i			0.479139i	−0.970879	+	0.239569i	$0.922994\pi$
$48$	30104.1	−	132654.i	0.272208	−	1.19949i
$49$	31473.0			0.267516
$50$	−65492.1	+	38660.2i	−0.523937	+	0.309282i
$51$	202157.	+	202157.i	1.52398	+	1.52398i
$52$	−49548.0	−	171584.i	−0.352384	−	1.22030i
$53$	103698.	+	103698.i	0.696532	+	0.696532i	0.963661	−	0.267129i	$-0.0860749\pi$
$53$	103698.	+	103698.i	0.696532	+	0.696532i	−0.267129	+	0.963661i	$0.586075\pi$
$54$	−91364.5	−	23537.5i	−0.580224	−	0.149478i
$55$	−23048.4			−0.138533
$56$	197633.	−	5729.22i	1.12537	−	0.0326236i
$57$		−	334116.i		−	1.80415i
$58$	49405.8	+	12728.0i	0.253218	+	0.0652344i
$59$	103267.	−	103267.i	0.502814	−	0.502814i	−0.409497	−	0.912311i	$-0.634296\pi$
$59$	103267.	−	103267.i	0.502814	−	0.502814i	0.912311	+	0.409497i	$0.134296\pi$
$60$	−145558.	−	80329.2i	−0.673880	−	0.371895i
$61$	−261802.	+	261802.i	−1.15341	+	1.15341i	−0.167544	+	0.985865i	$0.553584\pi$
$61$	−261802.	+	261802.i	−1.15341	+	1.15341i	−0.985865	+	0.167544i	$0.946416\pi$
$62$	−308391.	+	182044.i	−1.29398	+	0.763839i
$63$			144378.i			0.577404i
$64$	261704.	−	15186.0i	0.998321	−	0.0579298i
$65$	−218280.			−0.794830
$66$	39794.9	+	67414.2i	0.138419	+	0.234488i
$67$	−82606.9	−	82606.9i	−0.274658	−	0.274658i	0.556314	−	0.830972i	$-0.312215\pi$
$67$	−82606.9	−	82606.9i	−0.274658	−	0.274658i	−0.830972	+	0.556314i	$0.812215\pi$
$68$	−266210.	+	482378.i	−0.846639	+	1.53413i
$69$	−341390.	−	341390.i	−1.03921	−	1.03921i
$70$	60285.7	−	234009.i	0.175760	−	0.682241i
$71$	21573.8			0.0602769			0.0301384	−	0.999546i	$-0.490405\pi$
$71$	21573.8			0.0602769			0.0301384	+	0.999546i	$0.490405\pi$
$72$	5546.96	+	191345.i	0.0148613	+	0.512649i
$73$		−	431926.i		−	1.11030i	−0.831750	−	0.555151i	$-0.812660\pi$
$73$		−	431926.i		−	1.11030i	0.831750	−	0.555151i	$-0.187340\pi$
$74$	42324.2	−	164288.i	0.104446	−	0.405426i
$75$	223237.	−	223237.i	0.529155	−	0.529155i
$76$	618616.	−	178636.i	1.40923	−	0.406939i
$77$	−80458.6	+	80458.6i	−0.176238	+	0.176238i
$78$	376877.	+	638447.i	0.794175	+	1.34537i
$79$		−	122330.i		−	0.248114i	−0.992275	−	0.124057i	$-0.960409\pi$
$79$		−	122330.i		−	0.248114i	0.992275	−	0.124057i	$-0.0395905\pi$
$80$	70906.6	−	312450.i	0.138489	−	0.610253i
$81$	664213.			1.24983
$82$	−110380.	+	65157.6i	−0.200193	+	0.118174i
$83$	−80492.3	−	80492.3i	−0.140773	−	0.140773i	0.633208	−	0.773981i	$-0.281738\pi$
$83$	−80492.3	−	80492.3i	−0.140773	−	0.140773i	−0.773981	+	0.633208i	$0.781738\pi$
$84$	−788539.	+	227704.i	−1.33041	+	0.384179i
$85$	476157.	+	476157.i	0.775342	+	0.775342i
$86$	−197338.	−	50838.4i	−0.310252	−	0.0799276i
$87$	−211790.			−0.321624
$88$	−103541.	+	109724.i	−0.151938	+	0.161010i
$89$			1.23273e6i			1.74863i	0.485359	+	0.874315i	$0.338689\pi$
$89$			1.23273e6i			1.74863i	−0.485359	+	0.874315i	$0.661311\pi$
$90$	226564.	+	58367.9i	0.310788	+	0.0800656i
$91$	−761983.	+	761983.i	−1.01116	+	1.01116i
$92$	449559.	−	814609.i	0.577328	−	1.04613i
$93$	1.05119e6	−	1.05119e6i	1.30686	−	1.30686i
$94$	342709.	−	202303.i	0.412613	−	0.243567i
$95$		−	786970.i		−	0.917883i
$96$	−1.03631e6	+	332074.i	−1.17132	+	0.375336i
$97$	−788704.			−0.864169			−0.432085	−	0.901833i	$-0.642222\pi$
$97$	−788704.			−0.864169			−0.432085	+	0.901833i	$0.642222\pi$
$98$	−127993.	−	216825.i	−0.135990	−	0.230373i
$99$	−77899.0	−	77899.0i	−0.0802835	−	0.0802835i
$100$	532679.	+	293970.i	0.532679	+	0.293970i
$101$	378507.	+	378507.i	0.367375	+	0.367375i	0.866519	−	0.499144i	$-0.166352\pi$
$101$	378507.	+	378507.i	0.367375	+	0.367375i	−0.499144	+	0.866519i	$0.666352\pi$
$102$	570588.	−	2.21483e6i	0.537678	−	2.08708i
$103$	−545537.			−0.499244			−0.249622	−	0.968343i	$-0.580306\pi$
$103$	−545537.			−0.499244			−0.249622	+	0.968343i	$0.580306\pi$
$104$	−980587.	+	1.03914e6i	−0.871738	+	0.923789i
$105$			1.00314e6i			0.866546i
$106$	292686.	−	1.13611e6i	0.245745	−	0.953899i
$107$	45375.5	−	45375.5i	0.0370399	−	0.0370399i	−0.688344	−	0.725384i	$-0.741662\pi$
$107$	45375.5	−	45375.5i	0.0370399	−	0.0370399i	0.725384	+	0.688344i	$0.241662\pi$
$108$	209400.	+	725152.i	0.166229	+	0.575649i
$109$	−442028.	+	442028.i	−0.341326	+	0.341326i	−0.856866	−	0.515539i	$-0.827592\pi$
$109$	−442028.	+	442028.i	−0.341326	+	0.341326i	0.515539	+	0.856866i	$0.327592\pi$
$110$	93732.0	+	158786.i	0.0704223	+	0.119298i
$111$			704261.i			0.514950i
$112$	−843190.	−	1.33824e6i	−0.600166	−	0.952532i
$113$	223283.			0.154746			0.0773731	−	0.997002i	$-0.475347\pi$
$113$	223283.			0.154746			0.0773731	+	0.997002i	$0.475347\pi$
$114$	−2.30180e6	+	1.35876e6i	−1.55365	+	0.917126i
$115$	−804102.	−	804102.i	−0.528710	−	0.528710i
$116$	−113234.	−	392130.i	−0.0725445	−	0.251221i
$117$	−737742.	−	737742.i	−0.460625	−	0.460625i
$118$	−1.13140e6	−	291472.i	−0.688603	−	0.177399i
$119$	3.32438e6			1.97274
$120$	38540.1	+	1.32946e6i	0.0223033	+	0.769365i
$121$			1.68474e6i			0.950991i
$122$	2.86830e6	+	738935.i	1.57959	+	0.406937i
$123$	376242.	−	376242.i	0.202186	−	0.202186i
$124$	2.50829e6	+	1.38425e6i	1.31557	+	0.726023i
$125$	1.39004e6	−	1.39004e6i	0.711700	−	0.711700i
$126$	994655.	−	587148.i	0.497234	−	0.293519i
$127$			825027.i			0.402770i	0.979512	+	0.201385i	$0.0645442\pi$
$127$			825027.i			0.402770i	−0.979512	+	0.201385i	$0.935456\pi$
$128$	−1.16890e6	−	1.74118e6i	−0.557376	−	0.830261i
$129$	845936.			0.394065
$130$	887689.	+	1.50378e6i	0.404046	+	0.684472i
$131$	−2.06195e6	−	2.06195e6i	−0.917202	−	0.917202i	0.0796235	−	0.996825i	$-0.474628\pi$
$131$	−2.06195e6	−	2.06195e6i	−0.917202	−	0.917202i	−0.996825	+	0.0796235i	$0.974628\pi$
$132$	302597.	−	548313.i	0.131566	−	0.238400i
$133$	−2.74719e6	−	2.74719e6i	−1.16771	−	1.16771i
$134$	−233158.	+	905039.i	−0.0969026	+	0.376143i
$135$	922499.			0.374942
$136$	4.40583e6	−	127722.i	1.75150	−	0.0507748i
$137$		−	4.09881e6i		−	1.59403i	−0.603961	−	0.797014i	$-0.706412\pi$
$137$		−	4.09881e6i		−	1.59403i	0.603961	−	0.797014i	$-0.293588\pi$
$138$	−963571.	+	3.74026e6i	−0.366646	+	1.42319i
$139$	−2.83303e6	+	2.83303e6i	−1.05489	+	1.05489i	−0.0564838	+	0.998404i	$0.517989\pi$
$139$	−2.83303e6	+	2.83303e6i	−1.05489	+	1.05489i	−0.998404	+	0.0564838i	$0.982011\pi$
$140$	−1.85731e6	+	536330.i	−0.676862	+	0.195456i
$141$	−1.16816e6	+	1.16816e6i	−0.416722	+	0.416722i
$142$	−87734.9	−	148627.i	−0.0306413	−	0.0519077i
$143$		−	822254.i		−	0.281189i
$144$	1.29567e6	−	816366.i	0.433916	−	0.273399i
$145$	−498847.			−0.163630
$146$	−2.97564e6	+	1.75653e6i	−0.956142	+	0.564414i
$147$	739073.	+	739073.i	0.232667	+	0.232667i
$148$	−1.30394e6	+	376536.i	−0.402229	+	0.116151i
$149$	827653.	+	827653.i	0.250201	+	0.250201i	0.821053	−	0.570852i	$-0.193387\pi$
$149$	827653.	+	827653.i	0.250201	+	0.250201i	−0.570852	+	0.821053i	$0.693387\pi$
$150$	−2.44578e6	−	630086.i	−0.724676	−	0.186692i
$151$	425926.			0.123710			0.0618548	−	0.998085i	$-0.480298\pi$
$151$	425926.			0.123710			0.0618548	+	0.998085i	$0.480298\pi$
$152$	−3.74642e6	−	3.53533e6i	−1.06681	−	1.00670i
$153$			3.21862e6i			0.898661i
$154$	881503.	+	227094.i	0.241358	+	0.0621790i
$155$	2.47594e6	−	2.47594e6i	0.664883	−	0.664883i
$156$	2.86575e6	−	5.19279e6i	0.754856	−	1.36781i
$157$	1.30293e6	−	1.30293e6i	0.336685	−	0.336685i	−0.518433	−	0.855118i	$-0.673485\pi$
$157$	1.30293e6	−	1.30293e6i	0.336685	−	0.336685i	0.855118	+	0.518433i	$0.173485\pi$
$158$	−842759.	+	497484.i	−0.213664	+	0.126127i
$159$			4.87021e6i			1.21159i
$160$	−2.44090e6	+	782160.i	−0.595923	+	0.190957i
$161$	−5.61400e6			−1.34522
$162$	−2.70118e6	−	4.57592e6i	−0.635344	−	1.07630i
$163$	4.49889e6	+	4.49889e6i	1.03883	+	1.03883i	0.999215	+	0.0396113i	$0.0126120\pi$
$163$	4.49889e6	+	4.49889e6i	1.03883	+	1.03883i	0.0396113	+	0.999215i	$0.487388\pi$
$164$	897772.	+	495454.i	0.203533	+	0.112324i
$165$	−541240.	−	541240.i	−0.120487	−	0.120487i
$166$	−227189.	+	881872.i	−0.0496665	+	0.192788i
$167$	1.82644e6			0.392153			0.196076	−	0.980589i	$-0.437180\pi$
$167$	1.82644e6			0.392153			0.196076	+	0.980589i	$0.437180\pi$
$168$	4.77549e6	+	4.50642e6i	1.00714	+	0.950393i
$169$		−	2.96035e6i		−	0.613314i
$170$	1.34395e6	−	5.21676e6i	0.273550	−	1.06183i
$171$	2.65980e6	−	2.65980e6i	0.531937	−	0.531937i
$172$	452283.	+	1.56625e6i	0.0888843	+	0.307806i
$173$	−4.21958e6	+	4.21958e6i	−0.814951	+	0.814951i	−0.985371	−	0.170421i	$-0.945487\pi$
$173$	−4.21958e6	+	4.21958e6i	−0.814951	+	0.814951i	0.170421	+	0.985371i	$0.445487\pi$
$174$	861296.	+	1.45907e6i	0.163495	+	0.276968i
$175$		−	3.67103e6i		−	0.684974i
$176$	1.17699e6	+	267103.i	0.215891	+	0.0489937i
$177$	4.85000e6			0.874626
$178$	8.49257e6	−	5.01319e6i	1.50584	−	0.888903i
$179$	4.68971e6	+	4.68971e6i	0.817687	+	0.817687i	0.985772	−	0.168086i	$-0.0537585\pi$
$179$	4.68971e6	+	4.68971e6i	0.817687	+	0.817687i	−0.168086	+	0.985772i	$0.553759\pi$
$180$	−519268.	−	1.79822e6i	−0.0890377	−	0.308337i
$181$	5.53132e6	+	5.53132e6i	0.932809	+	0.932809i	0.997881	−	0.0650713i	$-0.0207275\pi$
$181$	5.53132e6	+	5.53132e6i	0.932809	+	0.932809i	−0.0650713	+	0.997881i	$0.520727\pi$
$182$	8.34827e6	+	2.15070e6i	1.38479	+	0.356751i
$183$	−1.22956e7			−2.00631
$184$	−7.44027e6	+	215688.i	−1.19436	+	0.0346236i
$185$			1.65880e6i			0.261987i
$186$	−1.15168e7	−	2.96697e6i	−1.78975	−	0.461078i
$187$	−1.79367e6	+	1.79367e6i	−0.274294	+	0.274294i
$188$	−2.78742e6	−	1.53830e6i	−0.419497	−	0.231508i
$189$	3.22030e6	−	3.22030e6i	0.476992	−	0.476992i
$190$	−5.42162e6	+	3.20040e6i	−0.790439	+	0.466599i
$191$		−	7.01967e6i		−	1.00743i	−0.863869	−	0.503717i	$-0.831965\pi$
$191$		−	7.01967e6i		−	1.00743i	0.863869	−	0.503717i	$-0.168035\pi$
$192$	6.50213e6	+	5.78891e6i	0.918654	+	0.817887i
$193$	2.08486e6			0.290005			0.145002	−	0.989431i	$-0.453681\pi$
$193$	2.08486e6			0.290005			0.145002	+	0.989431i	$0.453681\pi$
$194$	3.20746e6	+	5.43357e6i	0.439294	+	0.744184i
$195$	−5.12582e6	−	5.12582e6i	−0.691289	−	0.691289i
$196$	−973247.	+	1.76354e6i	−0.129257	+	0.234217i
$197$	3.50857e6	+	3.50857e6i	0.458914	+	0.458914i	0.898299	−	0.439385i	$-0.144804\pi$
$197$	3.50857e6	+	3.50857e6i	0.458914	+	0.458914i	−0.439385	+	0.898299i	$0.644804\pi$
$198$	−219870.	+	853460.i	−0.0283250	+	0.109948i
$199$	−9.22350e6			−1.17041			−0.585203	−	0.810887i	$-0.698985\pi$
$199$	−9.22350e6			−1.17041			−0.585203	+	0.810887i	$0.698985\pi$
$200$	−141040.	−	4.86525e6i	−0.0176300	−	0.608156i
$201$		−	3.87967e6i		−	0.477757i
$202$	1.06834e6	−	4.14692e6i	0.129615	−	0.503120i
$203$	−1.74140e6	+	1.74140e6i	−0.208166	+	0.208166i
$204$	−1.75789e7	+	5.07622e6i	−2.07063	+	0.597929i
$205$	886193.	−	886193.i	0.102865	−	0.102865i
$206$	2.21856e6	+	3.75834e6i	0.253787	+	0.429926i
$207$		−	5.43540e6i		−	0.612803i
$208$	1.11467e7	+	2.52960e6i	1.23867	+	0.281100i
$209$	2.96449e6			0.324721
$210$	6.91084e6	−	4.07949e6i	0.746230	−	0.440502i
$211$	−4.56499e6	−	4.56499e6i	−0.485951	−	0.485951i	0.421075	−	0.907026i	$-0.361653\pi$
$211$	−4.56499e6	−	4.56499e6i	−0.485951	−	0.485951i	−0.907026	+	0.421075i	$0.861653\pi$
$212$	−9.01721e6	+	2.60388e6i	−0.946377	+	0.273283i
$213$	506611.	+	506611.i	0.0524247	+	0.0524247i
$214$	−497133.	−	128072.i	−0.0507261	−	0.0130681i
$215$	1.99250e6			0.200486
$216$	4.14417e6	−	4.39162e6i	0.411222	−	0.435776i
$217$		−	1.72863e7i		−	1.69170i
$218$	4.84285e6	+	1.24762e6i	0.467446	+	0.120424i
$219$	1.01428e7	−	1.01428e7i	0.965664	−	0.965664i
$220$	712732.	−	1.29148e6i	0.0669358	−	0.121289i
$221$	−1.69869e7	+	1.69869e7i	−1.57376	+	1.57376i
$222$	4.85183e6	−	2.86405e6i	0.443452	−	0.261771i
$223$			9.46544e6i			0.853544i	0.904359	+	0.426772i	$0.140349\pi$
$223$			9.46544e6i			0.853544i	−0.904359	+	0.426772i	$0.859651\pi$
$224$	−5.79041e6	+	1.12512e7i	−0.515187	+	1.00105i
$225$	3.55425e6			0.312033
$226$	−908033.	−	1.53825e6i	−0.0786641	−	0.133260i
$227$	−1.08665e6	−	1.08665e6i	−0.0928991	−	0.0928991i	0.659130	−	0.752029i	$-0.270925\pi$
$227$	−1.08665e6	−	1.08665e6i	−0.0928991	−	0.0928991i	−0.752029	+	0.659130i	$0.770925\pi$
$228$	1.87217e7	+	1.03319e7i	1.57957	+	0.871720i
$229$	−2.31924e6	−	2.31924e6i	−0.193125	−	0.193125i	0.603920	−	0.797045i	$-0.293605\pi$
$229$	−2.31924e6	−	2.31924e6i	−0.193125	−	0.193125i	−0.797045	+	0.603920i	$0.793605\pi$
$230$	−2.26958e6	+	8.80973e6i	−0.186535	+	0.724068i
$231$	−3.77878e6			−0.306560
$232$	−2.24098e6	+	2.37479e6i	−0.179463	+	0.190179i
$233$			1.14491e7i			0.905113i	0.891736	+	0.452556i	$0.149488\pi$
$233$			1.14491e7i			0.905113i	−0.891736	+	0.452556i	$0.850512\pi$
$234$	−2.08228e6	+	8.08269e6i	−0.162514	+	0.630824i
$235$	−2.75147e6	+	2.75147e6i	−0.212012	+	0.212012i
$236$	2.59307e6	+	8.97980e6i	0.197278	+	0.683173i
$237$	2.87264e6	−	2.87264e6i	0.215792	−	0.215792i
$238$	−1.35194e7	−	2.29025e7i	−1.00283	−	1.69884i
$239$			4.00255e6i			0.293186i	0.989197	+	0.146593i	$0.0468308\pi$
$239$			4.00255e6i			0.293186i	−0.989197	+	0.146593i	$0.953169\pi$
$240$	9.00226e6	−	5.67209e6i	0.651205	−	0.410308i
$241$	1.10093e7			0.786519			0.393260	−	0.919427i	$-0.371347\pi$
$241$	1.10093e7			0.786519			0.393260	+	0.919427i	$0.371347\pi$
$242$	1.16066e7	−	6.85140e6i	0.818950	−	0.483429i
$243$	9.51825e6	+	9.51825e6i	0.663343	+	0.663343i
$244$	−6.57392e6	−	2.27654e7i	−0.452538	−	1.56714i
$245$	1.74080e6	+	1.74080e6i	0.118372	+	0.118372i
$246$	−4.12210e6	−	1.06194e6i	−0.276894	−	0.0713338i
$247$	2.80752e7			1.86308
$248$	−664133.	−	2.29096e7i	−0.0435412	−	1.50198i
$249$		−	3.78036e6i		−	0.244870i
$250$	−1.52292e7	−	3.92338e6i	−0.974672	−	0.251097i
$251$	8.62903e6	−	8.62903e6i	0.545684	−	0.545684i	−0.379506	−	0.925189i	$-0.623906\pi$
$251$	8.62903e6	−	8.62903e6i	0.545684	−	0.545684i	0.925189	+	0.379506i	$0.123906\pi$
$252$	−8.09001e6	−	4.46464e6i	−0.505530	−	0.278987i
$253$	3.02903e6	−	3.02903e6i	0.187043	−	0.187043i
$254$	5.68381e6	−	3.35517e6i	0.346847	−	0.204745i
$255$			2.23629e7i			1.34868i
$256$	−7.24180e6	+	1.51338e7i	−0.431645	+	0.902044i
$257$	−2.52254e7			−1.48607			−0.743033	−	0.669254i	$-0.766614\pi$
$257$	−2.52254e7			−1.48607			−0.743033	+	0.669254i	$0.766614\pi$
$258$	−3.44020e6	−	5.82785e6i	−0.200320	−	0.339351i
$259$	5.79063e6	+	5.79063e6i	0.333293	+	0.333293i
$260$	6.74993e6	−	1.22310e7i	0.384042	−	0.695893i
$261$	−1.68600e6	−	1.68600e6i	−0.0948278	−	0.0948278i
$262$	−5.81986e6	+	2.25907e7i	−0.323600	+	1.25611i
$263$	−1.39519e7			−0.766947			−0.383474	−	0.923552i	$-0.625272\pi$
$263$	−1.39519e7			−0.766947			−0.383474	+	0.923552i	$0.625272\pi$
$264$	−5.00804e6	+	145179.i	−0.272180	+	0.00789029i
$265$			1.14712e7i			0.616412i
$266$	−7.75394e6	+	3.00982e7i	−0.411982	+	1.59917i
$267$	−2.89479e7	+	2.89479e7i	−1.52084	+	1.52084i
$268$	7.18323e6	−	2.07428e6i	0.373177	−	0.107761i
$269$	1.57599e7	−	1.57599e7i	0.809649	−	0.809649i	−0.174932	−	0.984581i	$-0.555971\pi$
$269$	1.57599e7	−	1.57599e7i	0.809649	−	0.809649i	0.984581	+	0.174932i	$0.0559706\pi$
$270$	−3.75157e6	−	6.35532e6i	−0.190599	−	0.322884i
$271$		−	3.02929e7i		−	1.52207i	−0.648713	−	0.761033i	$-0.724692\pi$
$271$		−	3.02929e7i		−	1.52207i	0.648713	−	0.761033i	$-0.275308\pi$
$272$	−1.87973e7	−	2.98334e7i	−0.934089	−	1.48250i
$273$	−3.57869e7			−1.75888
$274$	−2.82377e7	+	1.66688e7i	−1.37270	+	0.810312i
$275$	1.98070e6	+	1.98070e6i	0.0952404	+	0.0952404i
$276$	2.96861e7	−	8.57239e6i	1.41197	−	0.407732i
$277$	−2.13249e7	−	2.13249e7i	−1.00334	−	1.00334i	−0.999994	−	0.00334306i	$-0.998936\pi$
$277$	−2.13249e7	−	2.13249e7i	−1.00334	−	1.00334i	−0.00334306	−	0.999994i	$-0.501064\pi$
$278$	3.10386e7	+	7.99621e6i	1.44467	+	0.372177i
$279$	1.67364e7			0.770634
$280$	1.12481e7	+	1.06143e7i	0.512395	+	0.483524i
$281$			2.07522e7i			0.935288i	0.883917	+	0.467644i	$0.154897\pi$
$281$			2.07522e7i			0.935288i	−0.883917	+	0.467644i	$0.845103\pi$
$282$	1.27984e7	+	3.29714e6i	0.570700	+	0.147025i
$283$	−9.35874e6	+	9.35874e6i	−0.412913	+	0.412913i	−0.882752	−	0.469839i	$-0.844312\pi$
$283$	−9.35874e6	+	9.35874e6i	−0.412913	+	0.412913i	0.469839	+	0.882752i	$0.344312\pi$
$284$	−667130.	+	1.20885e6i	−0.0291243	+	0.0527738i
$285$	1.84802e7	−	1.84802e7i	0.798311	−	0.798311i
$286$	−5.66471e6	+	3.34389e6i	−0.242147	+	0.142940i
$287$		−	6.18713e6i		−	0.261724i
$288$	−1.08933e7	−	5.60620e6i	−0.456017	−	0.234688i
$289$	4.99730e7			2.07034
$290$	2.02868e6	+	3.43667e6i	0.0831801	+	0.140911i
$291$	−1.85209e7	−	1.85209e7i	−0.751595	−	0.751595i
$292$	2.42023e7	+	1.33566e7i	0.972095	+	0.536471i
$293$	−4.57465e6	−	4.57465e6i	−0.181868	−	0.181868i	0.610302	−	0.792169i	$-0.291048\pi$
$293$	−4.57465e6	−	4.57465e6i	−0.181868	−	0.181868i	−0.792169	+	0.610302i	$0.791048\pi$
$294$	2.08603e6	−	8.09727e6i	0.0820878	−	0.318637i
$295$	1.14236e7			0.444977
$296$	7.89684e6	+	7.45189e6i	0.304494	+	0.287337i
$297$			3.47502e6i			0.132644i
$298$	2.33605e6	−	9.06775e6i	0.0882740	−	0.342650i
$299$	2.86864e7	−	2.86864e7i	1.07315	−	1.07315i
$300$	5.60554e6	+	1.94120e7i	0.207613	+	0.718962i
$301$	6.95552e6	−	6.95552e6i	0.255053	−	0.255053i
$302$	−1.73213e6	−	2.93431e6i	−0.0628869	−	0.106533i
$303$			1.77768e7i			0.639036i
$304$	−9.12000e6	+	4.01873e7i	−0.324619	+	1.43043i
$305$	−2.89609e7			−1.02074
$306$	2.21739e7	−	1.30893e7i	0.773886	−	0.456828i
$307$	1.06310e7	+	1.06310e7i	0.367416	+	0.367416i	0.866534	−	0.499118i	$-0.166343\pi$
$307$	1.06310e7	+	1.06310e7i	0.367416	+	0.367416i	−0.499118	+	0.866534i	$0.666343\pi$
$308$	−2.02034e6	−	6.99642e6i	−0.0691468	−	0.239455i
$309$	−1.28107e7	−	1.28107e7i	−0.434208	−	0.434208i
$310$	−2.71264e7	−	6.98834e6i	−0.910556	−	0.234579i
$311$	3.33806e7			1.10972			0.554859	−	0.831944i	$-0.312772\pi$
$311$	3.33806e7			1.10972			0.554859	+	0.831944i	$0.312772\pi$
$312$	−4.74287e7	+	1.37492e6i	−1.56163	+	0.0452704i
$313$			4.36207e6i			0.142252i	0.997467	+	0.0711261i	$0.0226593\pi$
$313$			4.36207e6i			0.142252i	−0.997467	+	0.0711261i	$0.977341\pi$
$314$	−1.42749e7	−	3.67753e6i	−0.461089	−	0.118786i
$315$	−7.98566e6	+	7.98566e6i	−0.255493	+	0.255493i
$316$	6.85457e6	+	3.78283e6i	0.217230	+	0.119883i
$317$	−1.81053e7	+	1.81053e7i	−0.568364	+	0.568364i	−0.931670	−	0.363306i	$-0.881648\pi$
$317$	−1.81053e7	+	1.81053e7i	−0.568364	+	0.568364i	0.363306	+	0.931670i	$0.381648\pi$
$318$	3.35520e7	−	1.98059e7i	1.04337	−	0.615904i
$319$		−	1.87914e6i		−	0.0578877i
$320$	1.53150e7	+	1.36351e7i	0.467376	+	0.416110i
$321$	2.13108e6			0.0644296
$322$	2.28307e7	+	3.86762e7i	0.683835	+	1.15845i
$323$	−6.12432e7	−	6.12432e7i	−1.81740	−	1.81740i
$324$	−2.05396e7	+	3.72182e7i	−0.603889	+	1.09426i
$325$	1.87582e7	+	1.87582e7i	0.546439	+	0.546439i
$326$	1.26981e7	−	4.92898e7i	0.366511	−	1.42267i
$327$	−2.07600e7			−0.593725
$328$	−237708.	−	8.19985e6i	−0.00673630	−	0.232372i
$329$			1.92099e7i			0.539434i
$330$	−1.52765e6	+	5.92982e6i	−0.0425091	+	0.165006i
$331$	−1.95271e7	+	1.95271e7i	−0.538460	+	0.538460i	−0.923076	−	0.384616i	$-0.874334\pi$
$331$	−1.95271e7	+	1.95271e7i	−0.538460	+	0.538460i	0.384616	+	0.923076i	$0.374334\pi$
$332$	6.99934e6	−	2.02118e6i	0.191268	−	0.0552321i
$333$	−5.60642e6	+	5.60642e6i	−0.151828	+	0.151828i
$334$	−7.42765e6	−	1.25828e7i	−0.199348	−	0.337704i
$335$		−	9.13811e6i		−	0.243065i
$336$	1.16251e7	−	5.12259e7i	0.306463	−	1.35043i
$337$	2.14808e7			0.561255			0.280628	−	0.959817i	$-0.409457\pi$
$337$	2.14808e7			0.561255			0.280628	+	0.959817i	$0.409457\pi$
$338$	−2.03946e7	+	1.20390e7i	−0.528158	+	0.311774i
$339$	5.24329e6	+	5.24329e6i	0.134588	+	0.134588i
$340$	−4.14050e7	+	1.19564e7i	−1.05346	+	0.304204i
$341$	9.32679e6	+	9.32679e6i	0.235217	+	0.235217i
$342$	−2.91407e7	−	7.50727e6i	−0.728486	−	0.187674i
$343$	−3.32780e7			−0.824660
$344$	8.95097e6	−	9.48543e6i	0.219885	−	0.233014i
$345$		−	3.77651e7i		−	0.919672i
$346$	4.62297e7	+	1.19098e7i	1.11607	+	0.287525i
$347$	1.50651e7	−	1.50651e7i	0.360565	−	0.360565i	−0.503456	−	0.864021i	$-0.667938\pi$
$347$	1.50651e7	−	1.50651e7i	0.360565	−	0.360565i	0.864021	+	0.503456i	$0.167938\pi$
$348$	6.54924e6	−	1.18673e7i	0.155401	−	0.281589i
$349$	−1.32060e7	+	1.32060e7i	−0.310666	+	0.310666i	−0.845168	−	0.534501i	$-0.820499\pi$
$349$	−1.32060e7	+	1.32060e7i	−0.310666	+	0.310666i	0.534501	+	0.845168i	$0.320499\pi$
$350$	−2.52906e7	+	1.49291e7i	−0.589869	+	0.348202i
$351$			3.29102e7i			0.761043i
$352$	−2.94637e6	−	9.19478e6i	−0.0675553	−	0.210821i
$353$	5.94273e7			1.35102			0.675511	−	0.737350i	$-0.263923\pi$
$353$	5.94273e7			1.35102			0.675511	+	0.737350i	$0.263923\pi$
$354$	−1.97237e7	−	3.34128e7i	−0.444610	−	0.753188i
$355$	1.19326e6	+	1.19326e6i	0.0266717	+	0.0266717i
$356$	−6.90742e7	−	3.81200e7i	−1.53097	−	0.844895i
$357$	7.80656e7	+	7.80656e7i	1.71575	+	1.71575i
$358$	1.32367e7	−	5.13804e7i	0.288490	−	1.11982i
$359$	−1.77687e7			−0.384037			−0.192018	−	0.981391i	$-0.561503\pi$
$359$	−1.77687e7			−0.384037			−0.192018	+	0.981391i	$0.561503\pi$
$360$	−1.02767e7	+	1.08903e7i	−0.220264	+	0.233416i
$361$			5.41741e7i			1.15152i
$362$	1.56121e7	−	6.06010e7i	0.329107	−	1.27748i
$363$	−3.95623e7	+	3.95623e7i	−0.827106	+	0.827106i
$364$	−1.91336e7	−	6.62596e7i	−0.396728	−	1.37387i
$365$	2.38902e7	−	2.38902e7i	0.491293	−	0.491293i
$366$	5.00032e7	+	8.47077e7i	1.01989	+	1.72774i
$367$		−	3.80906e7i		−	0.770584i	−0.922795	−	0.385292i	$-0.874101\pi$
$367$		−	3.80906e7i		−	0.770584i	0.922795	−	0.385292i	$-0.125899\pi$
$368$	3.17436e7	+	5.03807e7i	0.636961	+	1.01093i
$369$	5.99030e6			0.119226
$370$	1.14279e7	−	6.74593e6i	0.225611	−	0.133179i
$371$	4.00442e7	+	4.00442e7i	0.784184	+	0.784184i
$372$	2.63956e7	+	9.14077e7i	0.512746	+	1.77564i
$373$	−6.08976e7	−	6.08976e7i	−1.17348	−	1.17348i	−0.981375	−	0.192100i	$-0.938470\pi$
$373$	−6.08976e7	−	6.08976e7i	−1.17348	−	1.17348i	−0.192100	−	0.981375i	$-0.561530\pi$
$374$	1.96514e7	+	5.06262e6i	0.375645	+	0.0967744i
$375$	6.52839e7			1.23798
$376$	738039.	+	2.54591e7i	0.0138840	+	0.478938i
$377$		−	1.77964e7i		−	0.332130i
$378$	−3.52816e7	−	9.08930e6i	−0.653240	−	0.168289i
$379$	5.38289e7	−	5.38289e7i	0.988776	−	0.988776i	−0.0111620	−	0.999938i	$-0.503553\pi$
$379$	5.38289e7	−	5.38289e7i	0.988776	−	0.988776i	0.999938	+	0.0111620i	$0.00355306\pi$
$380$	4.40967e7	+	2.43356e7i	0.803628	+	0.443498i
$381$	−1.93739e7	+	1.93739e7i	−0.350302	+	0.350302i
$382$	−4.83602e7	+	2.85472e7i	−0.867557	+	0.512122i
$383$			5.85426e7i			1.04202i	0.853551	+	0.521009i	$0.174444\pi$
$383$			5.85426e7i			1.04202i	−0.853551	+	0.521009i	$0.825556\pi$
$384$	1.34387e7	−	6.83367e7i	0.237337	−	1.20687i
$385$	−8.90046e6			−0.155966
$386$	−8.47859e6	−	1.43631e7i	−0.147422	−	0.249739i
$387$	6.73424e6	+	6.73424e6i	0.116187	+	0.116187i
$388$	2.43893e7	−	4.41939e7i	0.417545	−	0.756601i
$389$	−2.77973e7	−	2.77973e7i	−0.472231	−	0.472231i	0.430405	−	0.902636i	$-0.358371\pi$
$389$	−2.77973e7	−	2.77973e7i	−0.472231	−	0.472231i	−0.902636	+	0.430405i	$0.858371\pi$
$390$	−1.44676e7	+	5.61584e7i	−0.243895	+	0.946718i
$391$	−1.25153e8			−2.09368
$392$	1.61074e7	−	466942.i	0.267404	−	0.00775184i
$393$		−	9.68406e7i		−	1.59544i
$394$	9.90293e6	−	3.84398e7i	0.161910	−	0.628482i
$395$	6.76616e6	−	6.76616e6i	0.109787	−	0.109787i
$396$	6.77384e6	−	1.95607e6i	0.109081	−	0.0314991i
$397$	−5.27910e7	+	5.27910e7i	−0.843701	+	0.843701i	−0.989338	−	0.145637i	$-0.953477\pi$
$397$	−5.27910e7	+	5.27910e7i	−0.843701	+	0.843701i	0.145637	+	0.989338i	$0.453477\pi$
$398$	3.75096e7	+	6.35429e7i	0.594967	+	1.00790i
$399$		−	1.29023e8i		−	2.03118i
$400$	−3.29443e7	+	2.07574e7i	−0.514755	+	0.324334i
$401$	−1.15903e8			−1.79747			−0.898734	−	0.438495i	$-0.855512\pi$
$401$	−1.15903e8			−1.79747			−0.898734	+	0.438495i	$0.855512\pi$
$402$	−2.67280e7	+	1.57776e7i	−0.411423	+	0.242864i
$403$	8.83294e7	+	8.83294e7i	1.34955	+	1.34955i
$404$	−3.29138e7	+	9.50442e6i	−0.499153	+	0.144139i
$405$	3.67382e7	+	3.67382e7i	0.553035	+	0.553035i
$406$	1.90787e7	+	4.91509e6i	0.285083	+	0.0734435i
$407$	−6.24866e6			−0.0926837
$408$	1.06460e8	+	1.00462e8i	1.56750	+	1.47918i
$409$		−	2.93710e7i		−	0.429289i	−0.976692	−	0.214644i	$-0.931141\pi$
$409$		−	2.93710e7i		−	0.429289i	0.976692	−	0.214644i	$-0.0688592\pi$
$410$	−9.70911e6	−	2.50128e6i	−0.140873	−	0.0362920i
$411$	9.62512e7	−	9.62512e7i	1.38638	−	1.38638i
$412$	1.68698e7	−	3.05684e7i	0.241222	−	0.437100i
$413$	3.98781e7	−	3.98781e7i	0.566088	−	0.566088i
$414$	−3.74458e7	+	2.21044e7i	−0.527718	+	0.311514i
$415$		−	8.90418e6i		−	0.124580i
$416$	−2.79036e7	−	8.70792e7i	−0.387597	−	1.20958i
$417$	−1.33054e8			−1.83494
$418$	−1.20558e7	−	2.04231e7i	−0.165070	−	0.279635i
$419$	2.44463e7	+	2.44463e7i	0.332331	+	0.332331i	0.853471	−	0.521140i	$-0.174493\pi$
$419$	2.44463e7	+	2.44463e7i	0.332331	+	0.332331i	−0.521140	+	0.853471i	$0.674493\pi$
$420$	−5.62092e7	−	3.10202e7i	−0.758682	−	0.418694i
$421$	−7.52382e7	−	7.52382e7i	−1.00831	−	1.00831i	−0.999965	−	0.00833990i	$-0.997345\pi$
$421$	−7.52382e7	−	7.52382e7i	−1.00831	−	1.00831i	−0.00833990	−	0.999965i	$-0.502655\pi$
$422$	−1.28847e7	+	5.00139e7i	−0.171449	+	0.665508i
$423$	−1.85988e7			−0.245733
$424$	5.46094e7	+	5.15324e7i	0.716423	+	0.676056i
$425$		−	8.18385e7i		−	1.06608i
$426$	1.42991e6	−	5.55042e6i	0.0184961	−	0.0717954i
$427$	−1.01098e8	+	1.01098e8i	−1.29855	+	1.29855i
$428$	1.13939e6	+	3.94571e6i	0.0145325	+	0.0503261i
$429$	1.93088e7	−	1.93088e7i	0.244559	−	0.244559i
$430$	−8.10299e6	−	1.37268e7i	−0.101915	−	0.172649i
$431$			1.07916e8i			1.34789i	0.738782	+	0.673944i	$0.235401\pi$
$431$			1.07916e8i			1.34789i	−0.738782	+	0.673944i	$0.764599\pi$
$432$	−4.71082e7	−	1.06906e7i	−0.584312	−	0.132602i
$433$	1.18414e8			1.45861			0.729304	−	0.684190i	$-0.239844\pi$
$433$	1.18414e8			1.45861			0.729304	+	0.684190i	$0.239844\pi$
$434$	−1.19089e8	+	7.02988e7i	−1.45681	+	0.859961i
$435$	−1.17143e7	−	1.17143e7i	−0.142314	−	0.142314i
$436$	−1.10994e7	−	3.84373e7i	−0.133919	−	0.463760i
$437$	1.03424e8	+	1.03424e8i	1.23930	+	1.23930i
$438$	−1.11124e8	−	2.86281e7i	−1.32247	−	0.340698i
$439$	5.24716e7			0.620198			0.310099	−	0.950704i	$-0.399638\pi$
$439$	5.24716e7			0.620198			0.310099	+	0.950704i	$0.399638\pi$
$440$	−1.17958e7	+	341953.i	−0.138475	+	0.00401428i
$441$			1.17671e7i			0.137200i
$442$	1.86108e8	+	4.79455e7i	2.15526	+	0.555241i
$443$	5.66174e6	−	5.66174e6i	0.0651236	−	0.0651236i	−0.673795	−	0.738918i	$-0.735337\pi$
$443$	5.66174e6	−	5.66174e6i	0.0651236	−	0.0651236i	0.738918	+	0.673795i	$0.235337\pi$
$444$	−3.94622e7	−	2.17780e7i	−0.450851	−	0.248811i
$445$	−6.81833e7	+	6.81833e7i	−0.773745	+	0.773745i
$446$	6.52097e7	−	3.84935e7i	0.735034	−	0.433893i
$447$			3.88711e7i			0.435215i
$448$	1.01060e8	−	5.86426e6i	1.12395	−	0.0652197i
$449$	9.51702e7			1.05139			0.525693	−	0.850674i	$-0.323806\pi$
$449$	9.51702e7			1.05139			0.525693	+	0.850674i	$0.323806\pi$
$450$	−1.44542e7	−	2.44861e7i	−0.158620	−	0.268709i
$451$	3.33826e6	+	3.33826e6i	0.0363907	+	0.0363907i
$452$	−6.90463e6	+	1.25113e7i	−0.0747696	+	0.135484i
$453$	1.00019e7	+	1.00019e7i	0.107594	+	0.107594i
$454$	−3.06706e6	+	1.19053e7i	−0.0327759	+	0.127225i
$455$	−8.42918e7			−0.894852
$456$	−4.95703e6	−	1.70995e8i	−0.0522790	−	1.80339i
$457$			1.40537e7i			0.147246i	0.997286	+	0.0736230i	$0.0234562\pi$
$457$			1.40537e7i			0.147246i	−0.997286	+	0.0736230i	$0.976544\pi$
$458$	−6.54604e6	+	2.54095e7i	−0.0681369	+	0.264484i
$459$	7.17904e7	−	7.17904e7i	0.742383	−	0.742383i
$460$	6.99221e7	−	2.01912e7i	0.718358	−	0.207438i
$461$	−4.60642e6	+	4.60642e6i	−0.0470177	+	0.0470177i	−0.730225	−	0.683207i	$-0.760585\pi$
$461$	−4.60642e6	+	4.60642e6i	−0.0470177	+	0.0470177i	0.683207	+	0.730225i	$0.260585\pi$
$462$	1.53673e7	+	2.60329e7i	0.155837	+	0.263996i
$463$		−	1.03035e8i		−	1.03810i	−0.854743	−	0.519052i	$-0.826285\pi$
$463$		−	1.03035e8i		−	1.03810i	0.854743	−	0.519052i	$-0.173715\pi$
$464$	2.54740e7	+	5.78101e6i	0.255002	+	0.0578695i
$465$	1.16284e8			1.15654
$466$	7.88754e7	−	4.65604e7i	0.779442	−	0.460107i
$467$	−2.12548e7	−	2.12548e7i	−0.208693	−	0.208693i	0.595019	−	0.803712i	$-0.297145\pi$
$467$	−2.12548e7	−	2.12548e7i	−0.208693	−	0.208693i	−0.803712	+	0.595019i	$0.797145\pi$
$468$	6.41517e7	−	1.85249e7i	0.625850	−	0.180725i
$469$	−3.18997e7	−	3.18997e7i	−0.309221	−	0.309221i
$470$	3.01450e7	+	7.76602e6i	0.290350	+	0.0748005i
$471$	6.11929e7			0.585650
$472$	5.13186e7	−	5.43828e7i	0.488033	−	0.517173i
$473$			7.50568e6i			0.0709262i
$474$	−3.14726e7	−	8.10802e6i	−0.295527	−	0.0761342i
$475$	−6.76294e7	+	6.76294e7i	−0.631037	+	0.631037i
$476$	−1.02801e8	+	1.86277e8i	−0.953180	+	1.72718i
$477$	−3.87703e7	+	3.87703e7i	−0.357227	+	0.357227i
$478$	2.75745e7	−	1.62773e7i	0.252479	−	0.149039i
$479$			2.14666e8i			1.95325i	0.214961	+	0.976623i	$0.431038\pi$
$479$			2.14666e8i			1.95325i	−0.214961	+	0.976623i	$0.568962\pi$
$480$	−7.56863e7	−	3.89517e7i	−0.684374	−	0.352211i
$481$	−5.91779e7			−0.531771
$482$	−4.47720e7	−	7.58458e7i	−0.399821	−	0.677315i
$483$	−1.31832e8	−	1.31832e8i	−1.16998	−	1.16998i
$484$	−9.44018e7	−	5.20975e7i	−0.832615	−	0.459495i
$485$	−4.36239e7	−	4.36239e7i	−0.382383	−	0.382383i
$486$	2.68652e7	−	1.04282e8i	0.234036	−	0.908447i
$487$	2.09525e8			1.81405			0.907026	−	0.421076i	$-0.138347\pi$
$487$	2.09525e8			1.81405			0.907026	+	0.421076i	$0.138347\pi$
$488$	−1.30102e8	+	1.37870e8i	−1.11950	+	1.18635i
$489$			2.11293e8i			1.80700i
$490$	4.91340e6	−	1.90721e7i	0.0417632	−	0.162111i
$491$	−5.12994e7	+	5.12994e7i	−0.433379	+	0.433379i	−0.889776	−	0.456397i	$-0.849140\pi$
$491$	−5.12994e7	+	5.12994e7i	−0.433379	+	0.433379i	0.456397	+	0.889776i	$0.349140\pi$
$492$	9.44754e6	+	3.27168e7i	0.0793274	+	0.274710i
$493$	−3.88210e7	+	3.88210e7i	−0.323986	+	0.323986i
$494$	−1.14175e8	−	1.93417e8i	−0.947084	−	1.60440i
$495$		−	8.61731e6i		−	0.0710487i
$496$	−1.55129e8	+	9.77429e7i	−1.27130	+	0.801014i
$497$	8.33099e6			0.0678621
$498$	−2.60438e7	+	1.53737e7i	−0.210871	+	0.124478i
$499$	−4.42564e7	−	4.42564e7i	−0.356184	−	0.356184i	0.506220	−	0.862404i	$-0.331042\pi$
$499$	−4.42564e7	−	4.42564e7i	−0.356184	−	0.356184i	−0.862404	+	0.506220i	$0.831042\pi$
$500$	3.49043e7	+	1.20873e8i	0.279234	+	0.966986i
$501$	4.28898e7	+	4.28898e7i	0.341068	+	0.341068i
$502$	−9.45395e7	−	2.43554e7i	−0.747312	−	0.192524i
$503$	−1.54078e7			−0.121070			−0.0605349	−	0.998166i	$-0.519281\pi$
$503$	−1.54078e7			−0.121070			−0.0605349	+	0.998166i	$0.519281\pi$
$504$	2.14203e6	+	7.38905e7i	0.0167315	+	0.577161i
$505$			4.18711e7i			0.325117i
$506$	−3.31859e7	−	8.54942e6i	−0.256155	−	0.0659911i
$507$	6.95171e7	−	6.95171e7i	0.533418	−	0.533418i
$508$	−4.62292e7	−	2.55125e7i	−0.352635	−	0.194609i
$509$	1.73530e8	−	1.73530e8i	1.31590	−	1.31590i	0.398904	−	0.916993i	$-0.369391\pi$
$509$	1.73530e8	−	1.73530e8i	1.31590	−	1.31590i	0.916993	−	0.398904i	$-0.130609\pi$
$510$	1.54064e8	−	9.09443e7i	1.16142	−	0.685591i
$511$		−	1.66794e8i		−	1.25002i
$512$	1.33711e8	−	1.16546e7i	0.996223	−	0.0868339i
$513$	−1.18652e8			−0.878865
$514$	1.02585e8	+	1.73784e8i	0.755431	+	1.27973i
$515$	−3.01741e7	−	3.01741e7i	−0.220909	−	0.220909i
$516$	−2.61591e7	+	4.74008e7i	−0.190403	+	0.345014i
$517$	−1.03647e7	−	1.03647e7i	−0.0750041	−	0.0750041i
$518$	1.63440e7	−	6.34421e7i	0.117590	−	0.456444i
$519$	−1.98175e8			−1.41758
$520$	−1.11713e8	+	3.23846e6i	−0.794496	+	0.0230319i
$521$		−	8.55521e7i		−	0.604947i	−0.953158	−	0.302473i	$-0.902188\pi$
$521$		−	8.55521e7i		−	0.604947i	0.953158	−	0.302473i	$-0.0978124\pi$
$522$	−4.75873e6	+	1.84718e7i	−0.0334564	+	0.129866i
$523$	−1.18905e8	+	1.18905e8i	−0.831181	+	0.831181i	−0.987678	−	0.156497i	$-0.949980\pi$
$523$	−1.18905e8	+	1.18905e8i	−0.831181	+	0.831181i	0.156497	+	0.987678i	$0.449980\pi$
$524$	1.79301e8	−	5.17762e7i	1.24620	−	0.359862i
$525$	8.62059e7	−	8.62059e7i	0.595743	−	0.595743i
$526$	5.67387e7	+	9.61178e7i	0.389872	+	0.660460i
$527$		−	3.85364e8i		−	2.63293i
$528$	2.13666e7	+	3.39112e7i	0.145155	+	0.230378i
$529$	6.33144e7			0.427696
$530$	7.90278e7	−	4.66504e7i	0.530826	−	0.313348i
$531$	3.86095e7	+	3.86095e7i	0.257875	+	0.257875i
$532$	2.38887e8	−	6.89828e7i	1.58656	−	0.458148i
$533$	3.16150e7	+	3.16150e7i	0.208791	+	0.208791i
$534$	3.17152e8	+	8.17053e7i	2.08278	+	0.536570i
$535$	5.01951e6			0.0327793
$536$	−4.35025e7	−	4.10514e7i	−0.282501	−	0.266584i
$537$			2.20255e8i			1.42234i
$538$	−1.72665e8	−	4.44823e7i	−1.10881	−	0.285654i
$539$	−6.55753e6	+	6.55753e6i	−0.0418768	+	0.0418768i
$540$	−2.85267e7	+	5.16909e7i	−0.181163	+	0.328271i
$541$	8.65388e7	−	8.65388e7i	0.546537	−	0.546537i	−0.378901	−	0.925437i	$-0.623698\pi$
$541$	8.65388e7	−	8.65388e7i	0.546537	−	0.546537i	0.925437	+	0.378901i	$0.123698\pi$
$542$	−2.08695e8	+	1.23194e8i	−1.31074	+	0.773731i
$543$			2.59781e8i			1.62259i
$544$	−1.29086e8	+	2.50824e8i	−0.801829	+	1.55802i
$545$	−4.88978e7			−0.302065
$546$	1.45536e8	+	2.46545e8i	0.894114	+	1.51467i
$547$	−1.15768e8	−	1.15768e8i	−0.707340	−	0.707340i	0.258635	−	0.965975i	$-0.416727\pi$
$547$	−1.15768e8	−	1.15768e8i	−0.707340	−	0.707340i	−0.965975	+	0.258635i	$0.916727\pi$
$548$	2.29671e8	+	1.26748e8i	1.39561	+	0.770195i
$549$	−9.78820e7	−	9.78820e7i	−0.591542	−	0.591542i
$550$	5.59053e6	−	2.17005e7i	0.0336020	−	0.130431i
$551$	6.41616e7			0.383549
$552$	−1.79783e8	−	1.69653e8i	−1.06889	−	1.00866i
$553$		−	4.72393e7i		−	0.279337i
$554$	−6.01894e7	+	2.33635e8i	−0.353990	+	1.37407i
$555$	−3.89533e7	+	3.89533e7i	−0.227858	+	0.227858i
$556$	−7.11381e7	−	2.46351e8i	−0.413883	−	1.43327i
$557$	2.34847e7	−	2.34847e7i	0.135900	−	0.135900i	−0.635884	−	0.771784i	$-0.719365\pi$
$557$	2.34847e7	−	2.34847e7i	0.135900	−	0.135900i	0.771784	+	0.635884i	$0.219365\pi$
$558$	−6.80624e7	−	1.15301e8i	−0.391746	−	0.663635i
$559$			7.10826e7i			0.406937i
$560$	2.73815e7	−	1.20657e8i	0.155917	−	0.687048i
$561$	−8.42404e7			−0.477125
$562$	1.42967e8	−	8.43939e7i	0.805428	−	0.475447i
$563$	5.12771e7	+	5.12771e7i	0.287342	+	0.287342i	0.836028	−	0.548686i	$-0.184872\pi$
$563$	5.12771e7	+	5.12771e7i	0.287342	+	0.287342i	−0.548686	+	0.836028i	$0.684872\pi$
$564$	−2.93329e7	−	1.01580e8i	−0.163500	−	0.566200i
$565$	1.23499e7	+	1.23499e7i	0.0684731	+	0.0684731i
$566$	1.02534e8	+	2.64150e7i	0.565483	+	0.145681i
$567$	2.56495e8			1.40711
$568$	1.10411e7	−	320074.i	0.0602515	−	0.00174665i
$569$			1.13674e8i			0.617057i	0.951215	+	0.308529i	$0.0998366\pi$
$569$			1.13674e8i			0.617057i	−0.951215	+	0.308529i	$0.900163\pi$
$570$	−2.02469e8	−	5.21603e7i	−1.09329	−	0.281654i
$571$	1.04037e8	−	1.04037e8i	0.558830	−	0.558830i	−0.370144	−	0.928974i	$-0.620692\pi$
$571$	1.04037e8	−	1.04037e8i	0.558830	−	0.558830i	0.928974	+	0.370144i	$0.120692\pi$
$572$	4.60738e7	+	2.54268e7i	0.246187	+	0.135864i
$573$	1.64841e8	−	1.64841e8i	0.876197	−	0.876197i
$574$	−4.26246e7	+	2.51615e7i	−0.225385	+	0.133046i
$575$			1.38203e8i			0.726968i
$576$	5.67770e6	+	9.78454e7i	0.0297102	+	0.512003i
$577$	3.48853e7			0.181600			0.0907998	−	0.995869i	$-0.471058\pi$
$577$	3.48853e7			0.181600			0.0907998	+	0.995869i	$0.471058\pi$
$578$	−2.03227e8	−	3.44276e8i	−1.05244	−	1.78288i
$579$	4.89582e7	+	4.89582e7i	0.252226	+	0.252226i
$580$	1.54259e7	−	2.79521e7i	0.0790620	−	0.143262i
$581$	−3.10831e7	−	3.10831e7i	−0.158488	−	0.158488i
$582$	−5.22753e7	+	2.02915e8i	−0.265172	+	1.02931i
$583$	−4.32116e7			−0.218069
$584$	−6.40817e6	−	2.21053e8i	−0.0321733	−	1.10984i
$585$		−	8.16102e7i		−	0.407640i
$586$	−1.29119e7	+	5.01198e7i	−0.0641651	+	0.249067i
$587$	−9.88213e7	+	9.88213e7i	−0.488581	+	0.488581i	−0.907858	−	0.419277i	$-0.862283\pi$
$587$	−9.88213e7	+	9.88213e7i	−0.488581	+	0.488581i	0.419277	+	0.907858i	$0.362283\pi$
$588$	−6.42674e7	+	1.85583e7i	−0.316125	+	0.0912865i
$589$	−3.18456e8	+	3.18456e8i	−1.55849	+	1.55849i
$590$	−4.64569e7	−	7.87000e7i	−0.226201	−	0.383194i
$591$			1.64782e8i			0.798264i
$592$	1.92235e7	−	8.47082e7i	0.0926545	−	0.408282i
$593$	1.14889e7			0.0550951			0.0275475	−	0.999620i	$-0.491230\pi$
$593$	1.14889e7			0.0550951			0.0275475	+	0.999620i	$0.491230\pi$
$594$	2.39403e7	−	1.41320e7i	0.114227	−	0.0674287i
$595$	1.83874e8	+	1.83874e8i	0.872911	+	0.872911i
$596$	−7.19700e7	+	2.07826e7i	−0.339948	+	0.0981659i
$597$	−2.16593e8	−	2.16593e8i	−1.01794	−	1.01794i
$598$	−3.14288e8	−	8.09673e7i	−1.46968	−	0.378622i
$599$	5.16591e7			0.240363			0.120181	−	0.992752i	$-0.461652\pi$
$599$	5.16591e7			0.240363			0.120181	+	0.992752i	$0.461652\pi$
$600$	1.10937e8	−	1.17561e8i	0.513599	−	0.544266i
$601$			1.54384e8i			0.711178i	0.934642	+	0.355589i	$0.115720\pi$
$601$			1.54384e8i			0.711178i	−0.934642	+	0.355589i	$0.884280\pi$
$602$	−7.62045e7	−	1.96319e7i	−0.349294	−	0.0899857i
$603$	3.08849e7	−	3.08849e7i	0.140862	−	0.140862i
$604$	−1.31710e7	+	2.38661e7i	−0.0597734	+	0.108311i
$605$	−9.31842e7	+	9.31842e7i	−0.420800	+	0.420800i
$606$	1.22468e8	−	7.22936e7i	0.550309	−	0.324849i
$607$		−	3.61044e8i		−	1.61434i	−0.590321	−	0.807168i	$-0.700999\pi$
$607$		−	3.61044e8i		−	1.61434i	0.590321	−	0.807168i	$-0.299001\pi$
$608$	3.13948e8	−	1.00601e8i	1.39684	−	0.447603i
$609$	−8.17856e7			−0.362097
$610$	1.17777e8	+	1.99519e8i	0.518883	+	0.879011i
$611$	−9.81588e7	−	9.81588e7i	−0.430334	−	0.430334i
$612$	−1.80351e8	−	9.95303e7i	−0.786799	−	0.434211i
$613$	4.62153e7	+	4.62153e7i	0.200634	+	0.200634i	0.800272	−	0.599638i	$-0.204689\pi$
$613$	4.62153e7	+	4.62153e7i	0.200634	+	0.200634i	−0.599638	+	0.800272i	$0.704689\pi$
$614$	3.00059e7	−	1.16473e8i	0.129629	−	0.503175i
$615$	4.16205e7			0.178929
$616$	−3.99838e7	+	4.23712e7i	−0.171057	+	0.181271i
$617$		−	4.16120e8i		−	1.77159i	−0.464076	−	0.885795i	$-0.653614\pi$
$617$		−	4.16120e8i		−	1.77159i	0.464076	−	0.885795i	$-0.346386\pi$
$618$	−3.61582e7	+	1.40354e8i	−0.153194	+	0.594647i
$619$	−3.03129e7	+	3.03129e7i	−0.127807	+	0.127807i	−0.768117	−	0.640310i	$-0.778806\pi$
$619$	−3.03129e7	+	3.03129e7i	−0.127807	+	0.127807i	0.640310	+	0.768117i	$0.278806\pi$
$620$	6.21716e7	+	2.15300e8i	0.260866	+	0.903376i
$621$	−1.21235e8	+	1.21235e8i	−0.506236	+	0.506236i
$622$	−1.35750e8	−	2.29967e8i	−0.564117	−	0.955639i
$623$			4.76035e8i			1.96868i
$624$	2.02352e8	+	3.21156e8i	0.832826	+	1.32179i
$625$	5.23039e6			0.0214237
$626$	3.00513e7	−	1.77394e7i	0.122501	−	0.0723129i
$627$	6.96143e7	+	6.96143e7i	0.282420	+	0.282420i
$628$	3.27170e7	+	1.13299e8i	0.132098	+	0.457453i
$629$	1.29091e8	+	1.29091e8i	0.518732	+	0.518732i
$630$	8.74908e7	+	2.25395e7i	0.349897	+	0.0901411i
$631$	4.03573e8			1.60633			0.803164	−	0.595758i	$-0.203148\pi$
$631$	4.03573e8			1.60633			0.803164	+	0.595758i	$0.203148\pi$
$632$	−1.81492e6	−	6.26066e7i	−0.00718961	−	0.248010i
$633$		−	2.14397e8i		−	0.845293i
$634$	1.98361e8	+	5.11020e7i	0.778374	+	0.200526i
$635$	−4.56329e7	+	4.56329e7i	−0.178220	+	0.178220i
$636$	−2.72895e8	−	1.50603e8i	−1.06078	−	0.585411i
$637$	−6.21031e7	+	6.21031e7i	−0.240267	+	0.240267i
$638$	−1.29458e7	+	7.64197e6i	−0.0498503	+	0.0294268i
$639$			8.06596e6i			0.0309139i
$640$	3.16533e7	−	1.60959e8i	0.120748	−	0.614010i
$641$	−3.07358e7			−0.116700			−0.0583500	−	0.998296i	$-0.518584\pi$
$641$	−3.07358e7			−0.116700			−0.0583500	+	0.998296i	$0.518584\pi$
$642$	−8.66656e6	−	1.46815e7i	−0.0327523	−	0.0554838i
$643$	1.85399e8	+	1.85399e8i	0.697388	+	0.697388i	0.963846	−	0.266459i	$-0.0858536\pi$
$643$	1.85399e8	+	1.85399e8i	0.697388	+	0.697388i	−0.266459	+	0.963846i	$0.585854\pi$
$644$	1.73603e8	−	3.14572e8i	0.649979	−	1.17778i
$645$	4.67894e7	+	4.67894e7i	0.174369	+	0.174369i
$646$	−1.72859e8	+	6.70980e8i	−0.641201	+	2.48893i
$647$	−2.80213e8			−1.03461			−0.517304	−	0.855802i	$-0.673064\pi$
$647$	−2.80213e8			−1.03461			−0.517304	+	0.855802i	$0.673064\pi$
$648$	3.39934e8	−	9.85444e6i	1.24931	−	0.0362165i
$649$			4.30323e7i			0.157420i
$650$	5.29451e7	−	2.05515e8i	0.192790	−	0.748347i
$651$	4.05929e8	−	4.05929e8i	1.47132	−	1.47132i
$652$	−3.91209e8	+	1.12968e8i	−1.41145	+	0.407582i
$653$	1.82737e8	−	1.82737e8i	0.656276	−	0.656276i	−0.298221	−	0.954497i	$-0.596393\pi$
$653$	1.82737e8	−	1.82737e8i	0.656276	−	0.656276i	0.954497	+	0.298221i	$0.0963932\pi$
$654$	8.44257e7	+	1.43021e8i	0.301816	+	0.511289i
$655$		−	2.28096e8i		−	0.811698i
$656$	−5.55240e7	+	3.49843e7i	−0.196684	+	0.123926i
$657$	1.61488e8			0.569434
$658$	1.32342e8	−	7.81218e7i	0.464536	−	0.274217i
$659$	−1.96008e8	−	1.96008e8i	−0.684886	−	0.684886i	0.276211	−	0.961097i	$-0.410921\pi$
$659$	−1.96008e8	−	1.96008e8i	−0.684886	−	0.684886i	−0.961097	+	0.276211i	$0.910921\pi$
$660$	4.70645e7	−	1.35907e7i	0.163705	−	0.0472727i
$661$	1.17998e8	+	1.17998e8i	0.408575	+	0.408575i	0.881241	−	0.472666i	$-0.156708\pi$
$661$	1.17998e8	+	1.17998e8i	0.408575	+	0.408575i	−0.472666	+	0.881241i	$0.656708\pi$
$662$	2.13938e8	+	5.51152e7i	0.737420	+	0.189975i
$663$	−7.97799e8			−2.73749
$664$	−4.23889e7	−	4.00005e7i	−0.144793	−	0.136635i
$665$		−	3.03899e8i		−	1.03339i
$666$	6.14238e7	+	1.58241e7i	0.207928	+	0.0535669i
$667$	6.55584e7	−	6.55584e7i	0.220928	−	0.220928i
$668$	−5.64794e7	+	1.02342e8i	−0.189479	+	0.343339i
$669$	−2.22274e8	+	2.22274e8i	−0.742354	+	0.742354i
$670$	−6.29546e7	+	3.71623e7i	−0.209316	+	0.123560i
$671$		−	1.09095e8i		−	0.361108i
$672$	−4.00184e8	+	1.28235e8i	−1.31872	+	0.422569i
$673$	5.51633e8			1.80969			0.904847	−	0.425738i	$-0.139985\pi$
$673$	5.51633e8			1.80969			0.904847	+	0.425738i	$0.139985\pi$
$674$	−8.73568e7	−	1.47986e8i	−0.285310	−	0.483328i
$675$	−7.92763e7	−	7.92763e7i	−0.257770	−	0.257770i
$676$	1.65879e8	+	9.15436e7i	0.536971	+	0.296338i
$677$	2.07052e8	+	2.07052e8i	0.667289	+	0.667289i	0.957088	−	0.289798i	$-0.0935882\pi$
$677$	2.07052e8	+	2.07052e8i	0.667289	+	0.667289i	−0.289798	+	0.957088i	$0.593588\pi$
$678$	1.47992e7	−	5.74454e7i	0.0474841	−	0.184317i
$679$	−3.04569e8			−0.972917
$680$	2.50754e8	+	2.36626e8i	0.797483	+	0.752549i
$681$		−	5.10350e7i		−	0.161595i
$682$	2.63248e7	−	1.02184e8i	0.0829875	−	0.322129i
$683$	−1.72690e7	+	1.72690e7i	−0.0542006	+	0.0542006i	−0.733688	−	0.679487i	$-0.762202\pi$
$683$	−1.72690e7	+	1.72690e7i	−0.0542006	+	0.0542006i	0.679487	+	0.733688i	$0.262202\pi$
$684$	6.67882e7	+	2.31287e8i	0.208704	+	0.722742i
$685$	2.26708e8	−	2.26708e8i	0.705336	−	0.705336i
$686$	1.35333e8	+	2.29260e8i	0.419210	+	0.710160i
$687$		−	1.08924e8i		−	0.335934i
$688$	−1.01749e8	−	2.30906e7i	−0.312438	−	0.0709039i
$689$	−4.09235e8			−1.25117
$690$	−2.60172e8	+	1.53581e8i	−0.791980	+	0.467508i
$691$	−6.52581e7	−	6.52581e7i	−0.197788	−	0.197788i	0.601263	−	0.799051i	$-0.294664\pi$
$691$	−6.52581e7	−	6.52581e7i	−0.197788	−	0.197788i	−0.799051	+	0.601263i	$0.794664\pi$
$692$	−1.05955e8	−	3.66921e8i	−0.319744	−	1.10727i
$693$	−3.00817e7	−	3.00817e7i	−0.0903864	−	0.0903864i
$694$	−1.65053e8	−	4.25212e7i	−0.493793	−	0.127212i
$695$	−3.13394e8			−0.933547
$696$	−1.08391e8	+	3.14218e6i	−0.321489	+	0.00931972i
$697$		−	1.37930e8i		−	0.407343i
$698$	1.44684e8	+	3.72738e7i	0.425457	+	0.109607i
$699$	−2.68856e8	+	2.68856e8i	−0.787205	+	0.787205i
$700$	2.05701e8	+	1.13520e8i	0.599711	+	0.330963i
$701$	−2.07646e8	+	2.07646e8i	−0.602795	+	0.602795i	−0.941053	−	0.338258i	$-0.890162\pi$
$701$	−2.07646e8	+	2.07646e8i	−0.602795	+	0.602795i	0.338258	+	0.941053i	$0.390162\pi$
$702$	2.26726e8	−	1.33837e8i	0.655376	−	0.386871i
$703$		−	2.13355e8i		−	0.614097i
$704$	−5.13629e7	+	5.76910e7i	−0.147208	+	0.165345i
$705$	−1.29224e8			−0.368787
$706$	−2.41676e8	−	4.09409e8i	−0.686782	−	1.16344i
$707$	1.46166e8	+	1.46166e8i	0.413606	+	0.413606i
$708$	−1.49978e8	+	2.71763e8i	−0.422598	+	0.765756i
$709$	−1.18405e8	−	1.18405e8i	−0.332224	−	0.332224i	0.521206	−	0.853431i	$-0.325482\pi$
$709$	−1.18405e8	−	1.18405e8i	−0.332224	−	0.332224i	−0.853431	+	0.521206i	$0.825482\pi$
$710$	3.36798e6	−	1.30733e7i	0.00941010	−	0.0365268i
$711$	4.57365e7			0.127249
$712$	1.82891e7	+	6.30893e8i	0.0506702	+	1.74790i
$713$			6.50777e8i			1.79541i
$714$	2.20340e8	−	8.55285e8i	0.605339	−	2.34972i
$715$	4.54795e7	−	4.54795e7i	0.124422	−	0.124422i
$716$	−4.07802e8	+	1.17760e8i	−1.11099	+	0.320818i
$717$	−9.39909e7	+	9.39909e7i	−0.254993	+	0.254993i
$718$	7.22608e7	+	1.22413e8i	0.195222	+	0.330715i
$719$		−	5.05829e8i		−	1.36087i	−0.732808	−	0.680435i	$-0.761791\pi$
$719$		−	5.05829e8i		−	1.36087i	0.732808	−	0.680435i	$-0.238209\pi$
$720$	1.16818e8	+	2.65104e7i	0.312977	+	0.0710263i
$721$	−2.10666e8			−0.562069
$722$	3.73218e8	−	2.20312e8i	0.991634	−	0.585365i
$723$	2.58529e8	+	2.58529e8i	0.684060	+	0.684060i
$724$	−4.80985e8	+	1.38893e8i	−1.26741	+	0.365986i
$725$	4.28691e7	+	4.28691e7i	0.112494	+	0.112494i
$726$	4.33444e8	+	1.11664e8i	1.13272	+	0.291813i
$727$	9.70112e7			0.252475			0.126238	−	0.992000i	$-0.459710\pi$
$727$	9.70112e7			0.252475			0.126238	+	0.992000i	$0.459710\pi$
$728$	−3.78667e8	+	4.01277e8i	−0.981438	+	1.04004i
$729$		−	3.71823e7i		−	0.0959741i
$730$	−2.61740e8	−	6.74300e7i	−0.672825	−	0.173334i
$731$	1.55060e8	−	1.55060e8i	0.396960	−	0.396960i
$732$	3.80221e8	−	6.88968e8i	0.969400	−	1.75657i
$733$	3.21888e8	−	3.21888e8i	0.817322	−	0.817322i	−0.168397	−	0.985719i	$-0.553859\pi$
$733$	3.21888e8	−	3.21888e8i	0.817322	−	0.817322i	0.985719	+	0.168397i	$0.0538591\pi$
$734$	−2.62415e8	+	1.54905e8i	−0.663592	+	0.391721i
$735$			8.17574e7i			0.205904i
$736$	2.17992e8	−	4.23574e8i	0.546772	−	1.06242i
$737$	3.44229e7			0.0859895
$738$	−2.43610e7	−	4.12686e7i	−0.0606075	−	0.102672i
$739$	3.50446e8	+	3.50446e8i	0.868336	+	0.868336i	0.992288	−	0.123952i	$-0.0395570\pi$
$739$	3.50446e8	+	3.50446e8i	0.868336	+	0.868336i	−0.123952	+	0.992288i	$0.539557\pi$
$740$	−9.29486e7	−	5.12956e7i	−0.229376	−	0.126586i
$741$	6.59282e8	+	6.59282e8i	1.62038	+	1.62038i
$742$	1.13025e8	−	4.38723e8i	0.276670	−	1.07394i
$743$	6.34461e8			1.54682			0.773408	−	0.633909i	$-0.218551\pi$
$743$	6.34461e8			1.54682			0.773408	+	0.633909i	$0.218551\pi$
$744$	5.22385e8	−	5.53577e8i	1.26845	−	1.34418i
$745$			9.15563e7i			0.221421i
$746$	−1.71883e8	+	6.67193e8i	−0.414016	+	1.60707i
$747$	3.00943e7	−	3.00943e7i	0.0721976	−	0.0721976i
$748$	−4.50395e7	−	1.55971e8i	−0.107619	−	0.372683i
$749$	1.75224e7	−	1.75224e7i	0.0417010	−	0.0417010i
$750$	−2.65493e8	−	4.49756e8i	−0.629316	−	1.06609i
$751$			4.04971e8i			0.956102i	0.878332	+	0.478051i	$0.158657\pi$
$751$			4.04971e8i			0.956102i	−0.878332	+	0.478051i	$0.841343\pi$
$752$	1.72392e8	−	1.08620e8i	0.405382	−	0.255421i
$753$	4.05267e8			0.949196
$754$	−1.22603e8	+	7.23733e7i	−0.286015	+	0.168836i
$755$	2.35583e7	+	2.35583e7i	0.0547398	+	0.0547398i
$756$	8.08627e7	+	2.80027e8i	0.187147	+	0.648089i
$757$	−1.23538e8	−	1.23538e8i	−0.284781	−	0.284781i	0.550231	−	0.835012i	$-0.314540\pi$
$757$	−1.23538e8	−	1.23538e8i	−0.284781	−	0.284781i	−0.835012	+	0.550231i	$0.814540\pi$
$758$	−5.89748e8	−	1.51932e8i	−1.35413	−	0.348852i
$759$	1.42260e8			0.325354
$760$	−1.16757e7	−	4.02759e8i	−0.0265976	−	0.917497i
$761$			1.51516e8i			0.343800i	0.985114	+	0.171900i	$0.0549906\pi$
$761$			1.51516e8i			0.343800i	−0.985114	+	0.171900i	$0.945009\pi$
$762$	2.12260e8	+	5.46828e7i	0.479737	+	0.123591i
$763$	−1.70695e8	+	1.70695e8i	−0.384279	+	0.384279i
$764$	3.93337e8	+	2.17071e8i	0.882033	+	0.486768i
$765$	−1.78025e8	+	1.78025e8i	−0.397645	+	0.397645i
$766$	4.03314e8	−	2.38077e8i	0.897339	−	0.529702i
$767$			4.07538e8i			0.903196i
$768$	−5.25440e8	+	1.85325e8i	−1.15995	+	0.409120i
$769$	1.26836e8			0.278909			0.139454	−	0.990229i	$-0.455465\pi$
$769$	1.26836e8			0.278909			0.139454	+	0.990229i	$0.455465\pi$
$770$	3.61959e7	+	6.13174e7i	0.0792842	+	0.134311i
$771$	−5.92361e8	−	5.92361e8i	−1.29248	−	1.29248i
$772$	−6.44706e7	+	1.16822e8i	−0.140123	+	0.253906i
$773$	−4.03242e8	−	4.03242e8i	−0.873026	−	0.873026i	0.119775	−	0.992801i	$-0.461783\pi$
$773$	−4.03242e8	−	4.03242e8i	−0.873026	−	0.873026i	−0.992801	+	0.119775i	$0.961783\pi$
$774$	1.90074e7	−	7.37802e7i	0.0409920	−	0.159117i
$775$	−4.25548e8			−0.914204
$776$	−4.03647e8	+	1.17014e7i	−0.863807	+	0.0250411i
$777$			2.71960e8i			0.579751i
$778$	−7.84579e7	+	3.04547e8i	−0.166609	+	0.646719i
$779$	−1.13982e8	+	1.13982e8i	−0.241115	+	0.241115i
$780$	4.45724e8	−	1.28711e8i	0.939253	−	0.271226i
$781$	−4.49497e6	+	4.49497e6i	−0.00943570	+	0.00943570i
$782$	5.08965e8	+	8.62209e8i	1.06431	+	1.80299i
$783$			7.52113e7i			0.156674i
$784$	−6.87216e7	−	1.09069e8i	−0.142608	−	0.226336i
$785$	1.44133e8			0.297957
$786$	−6.67158e8	+	3.93826e8i	−1.37392	+	0.811029i
$787$	−4.27653e8	−	4.27653e8i	−0.877338	−	0.877338i	0.115920	−	0.993259i	$-0.463018\pi$
$787$	−4.27653e8	−	4.27653e8i	−0.877338	−	0.877338i	−0.993259	+	0.115920i	$0.963018\pi$
$788$	−3.05094e8	+	8.81011e7i	−0.623526	+	0.180054i
$789$	−3.27628e8	−	3.27628e8i	−0.667038	−	0.667038i
$790$	−7.41299e7	−	1.90975e7i	−0.150353	−	0.0387342i
$791$	8.62236e7			0.174219
$792$	−4.10233e7	−	3.87118e7i	−0.0825762	−	0.0779234i
$793$		−	1.03318e9i		−	2.07185i
$794$	5.78377e8	+	1.49002e8i	1.15545	+	0.297668i
$795$	−2.69375e8	+	2.69375e8i	−0.536113	+	0.536113i
$796$	2.85220e8	−	5.16825e8i	0.565511	−	1.02472i
$797$	−3.44445e8	+	3.44445e8i	−0.680369	+	0.680369i	−0.960083	−	0.279714i	$-0.909760\pi$
$797$	−3.44445e8	+	3.44445e8i	−0.680369	+	0.680369i	0.279714	+	0.960083i	$0.409760\pi$
$798$	−8.88872e8	+	5.24704e8i	−1.74916	+	1.03254i
$799$			4.28248e8i			0.839565i
$800$	2.76978e8	+	1.42546e8i	0.540973	+	0.278411i
$801$	−4.60891e8			−0.896810
$802$	4.71347e8	+	7.98482e8i	0.913729	+	1.54790i
$803$	8.99935e7	+	8.99935e7i	0.173806	+	0.173806i
$804$	2.17392e8	+	1.19972e8i	0.418287	+	0.230840i
$805$	−3.10515e8	−	3.10515e8i	−0.595243	−	0.595243i
$806$	2.49309e8	−	9.67735e8i	0.476139	−	1.84821i
$807$	7.40171e8			1.40835
$808$	1.99330e8	+	1.88099e8i	0.377867	+	0.356576i
$809$			8.15463e6i			0.0154013i	0.999970	+	0.00770067i	$0.00245122\pi$
$809$			8.15463e6i			0.0154013i	−0.999970	+	0.00770067i	$0.997549\pi$
$810$	1.03693e8	−	4.02503e8i	0.195117	−	0.757380i
$811$	4.15719e8	−	4.15719e8i	0.779359	−	0.779359i	−0.200363	−	0.979722i	$-0.564212\pi$
$811$	4.15719e8	−	4.15719e8i	0.779359	−	0.779359i	0.979722	+	0.200363i	$0.0642120\pi$
$812$	−4.37270e7	−	1.51426e8i	−0.0816735	−	0.282835i
$813$	7.11361e8	−	7.11361e8i	1.32379	−	1.32379i
$814$	2.54117e7	+	4.30485e7i	0.0471151	+	0.0798150i
$815$			4.97675e8i			0.919333i
$816$	2.59158e8	−	1.14198e9i	0.476974	−	2.10179i
$817$	−2.56275e8			−0.469938
$818$	−2.02344e8	+	1.19444e8i	−0.369684	+	0.218226i
$819$	−2.84889e8	−	2.84889e8i	−0.518590	−	0.518590i
$820$	2.22526e7	+	7.70605e7i	0.0403588	+	0.139762i
$821$	−1.00684e8	−	1.00684e8i	−0.181942	−	0.181942i	0.610260	−	0.792201i	$-0.291065\pi$
$821$	−1.00684e8	−	1.00684e8i	−0.181942	−	0.181942i	−0.792201	+	0.610260i	$0.791065\pi$
$822$	−1.05453e9	−	2.71669e8i	−1.89864	−	0.489130i
$823$	1.78585e8			0.320365			0.160182	−	0.987087i	$-0.448792\pi$
$823$	1.78585e8			0.320365			0.160182	+	0.987087i	$0.448792\pi$
$824$	−2.79198e8	+	8.09373e6i	−0.499034	+	0.0144666i
$825$			9.30246e7i			0.165667i
$826$	−4.36904e8	−	1.12556e8i	−0.775256	−	0.199723i
$827$	2.00812e8	−	2.00812e8i	0.355037	−	0.355037i	−0.506943	−	0.861980i	$-0.669224\pi$
$827$	2.00812e8	−	2.00812e8i	0.355037	−	0.355037i	0.861980	+	0.506943i	$0.169224\pi$
$828$	3.04565e8	+	1.68080e8i	0.536523	+	0.296091i
$829$	−1.76037e8	+	1.76037e8i	−0.308987	+	0.308987i	−0.844517	−	0.535529i	$-0.820112\pi$
$829$	−1.76037e8	+	1.76037e8i	−0.308987	+	0.308987i	0.535529	+	0.844517i	$0.320112\pi$
$830$	−6.13430e7	+	3.62110e7i	−0.107283	+	0.0633295i
$831$		−	1.00153e9i		−	1.74527i
$832$	−4.86433e8	+	5.46363e8i	−0.844603	+	0.948662i
$833$	2.70943e8			0.468752
$834$	5.41098e8	+	9.16644e8i	0.932777	+	1.58016i
$835$	1.01022e8	+	1.01022e8i	0.173522	+	0.173522i
$836$	−9.16715e7	+	1.66111e8i	−0.156897	+	0.284301i
$837$	−3.73299e8	−	3.73299e8i	−0.636620	−	0.636620i
$838$	6.89996e7	−	2.67833e8i	0.117250	−	0.455126i
$839$	9.30167e8			1.57498			0.787490	−	0.616327i	$-0.211380\pi$
$839$	9.30167e8			1.57498			0.787490	+	0.616327i	$0.211380\pi$
$840$	1.48828e7	+	5.13390e8i	0.0251100	+	0.866182i
$841$			5.54152e8i			0.931625i
$842$	−2.12360e8	+	8.24308e8i	−0.355742	+	1.38087i
$843$	−4.87319e8	+	4.87319e8i	−0.813449	+	0.813449i
$844$	3.96956e8	−	1.14628e8i	0.660261	−	0.190662i
$845$	1.63739e8	−	1.63739e8i	0.271383	−	0.271383i
$846$	7.56365e7	+	1.28132e8i	0.124917	+	0.211614i
$847$			6.50584e8i			1.07066i
$848$	1.32937e8	−	5.85786e8i	0.218001	−	0.960619i
$849$	−4.39538e8			−0.718246
$850$	−5.63805e8	+	3.32816e8i	−0.918062	+	0.541935i
$851$	−2.18000e8	−	2.18000e8i	−0.353727	−	0.353727i
$852$	−4.40532e7	+	1.27211e7i	−0.0712293	+	0.0205687i
$853$	−1.76160e8	−	1.76160e8i	−0.283831	−	0.283831i	0.550804	−	0.834635i	$-0.314321\pi$
$853$	−1.76160e8	−	1.76160e8i	−0.283831	−	0.283831i	−0.834635	+	0.550804i	$0.814321\pi$
$854$	1.10763e9	+	2.85350e8i	1.77837	+	0.458146i
$855$	2.94231e8			0.470750
$856$	2.25493e7	−	2.38957e7i	0.0359511	−	0.0380977i
$857$			7.52013e8i			1.19477i	0.801956	+	0.597383i	$0.203793\pi$
$857$			7.52013e8i			1.19477i	−0.801956	+	0.597383i	$0.796207\pi$
$858$	−2.11547e8	−	5.44990e7i	−0.334922	−	0.0862833i
$859$	−5.09238e8	+	5.09238e8i	−0.803417	+	0.803417i	−0.983628	−	0.180211i	$-0.942322\pi$
$859$	−5.09238e8	+	5.09238e8i	−0.803417	+	0.803417i	0.180211	+	0.983628i	$0.442322\pi$
$860$	−6.16146e7	+	1.11647e8i	−0.0968697	+	0.175530i
$861$	1.45291e8	−	1.45291e8i	0.227630	−	0.227630i
$862$	7.43459e8	−	4.38866e8i	1.16074	−	0.685189i
$863$		−	1.02464e9i		−	1.59419i	−0.603853	−	0.797096i	$-0.706369\pi$
$863$		−	1.02464e9i		−	1.59419i	0.603853	−	0.797096i	$-0.293631\pi$
$864$	1.17927e8	+	3.68015e8i	0.182840	+	0.570591i
$865$	−4.66777e8			−0.721209
$866$	−4.81558e8	−	8.15781e8i	−0.741473	−	1.25609i
$867$	1.17350e9	+	1.17350e9i	1.80064	+	1.80064i
$868$	9.68611e8	+	5.34548e8i	1.48112	+	0.817386i
$869$	2.54879e7	+	2.54879e7i	0.0388396	+	0.0388396i
$870$	−3.30635e7	+	1.28341e8i	−0.0502102	+	0.194899i
$871$	3.26002e8			0.493363
$872$	−2.19665e8	+	2.32781e8i	−0.331293	+	0.351074i
$873$		−	2.94879e8i		−	0.443202i
$874$	2.91913e8	−	1.13311e9i	0.437239	−	1.69721i
$875$	5.36782e8	−	5.36782e8i	0.801261	−	0.801261i
$876$	2.54689e8	+	8.81986e8i	0.378876	+	1.31205i
$877$	3.10264e8	−	3.10264e8i	0.459973	−	0.459973i	−0.438674	−	0.898646i	$-0.644552\pi$
$877$	3.10264e8	−	3.10264e8i	0.459973	−	0.459973i	0.898646	+	0.438674i	$0.144552\pi$
$878$	−2.13388e8	−	3.61489e8i	−0.315273	−	0.534087i
$879$		−	2.14851e8i		−	0.316352i
$880$	5.03264e7	+	7.98738e7i	0.0738496	+	0.117208i
$881$	−7.60229e8			−1.11177			−0.555887	−	0.831258i	$-0.687621\pi$
$881$	−7.60229e8			−1.11177			−0.555887	+	0.831258i	$0.687621\pi$
$882$	8.10662e7	−	4.78537e7i	0.118150	−	0.0697444i
$883$	−6.33257e8	−	6.33257e8i	−0.919810	−	0.919810i	0.0772050	−	0.997015i	$-0.475400\pi$
$883$	−6.33257e8	−	6.33257e8i	−0.919810	−	0.919810i	−0.997015	+	0.0772050i	$0.975400\pi$
$884$	−4.26546e8	−	1.47713e9i	−0.617461	−	2.13826i
$885$	2.68258e8	+	2.68258e8i	0.387010	+	0.387010i
$886$	−6.20299e7	−	1.59802e7i	−0.0891866	−	0.0229764i
$887$	−1.24123e9			−1.77862			−0.889309	−	0.457308i	$-0.848814\pi$
$887$	−1.24123e9			−1.77862			−0.889309	+	0.457308i	$0.848814\pi$
$888$	1.04486e7	+	3.60430e8i	0.0149217	+	0.514734i
$889$			3.18595e8i			0.453455i
$890$	7.47015e8	+	1.92447e8i	1.05964	+	0.272987i
$891$	−1.38391e8	+	1.38391e8i	−0.195648	+	0.195648i
$892$	−5.30382e8	−	2.92702e8i	−0.747298	−	0.412412i
$893$	3.53894e8	−	3.53894e8i	0.496957	−	0.496957i
$894$	2.67792e8	−	1.58079e8i	0.374788	−	0.221239i
$895$			5.18783e8i			0.723630i
$896$	−4.51387e8	−	6.72381e8i	−0.627516	−	0.934741i
$897$	1.34727e9			1.86671
$898$	−3.87033e8	−	6.55650e8i	−0.534464	−	0.905406i
$899$	2.01863e8	+	2.01863e8i	0.277830	+	0.277830i
$900$	−1.09909e8	+	1.99157e8i	−0.150767	+	0.273192i
$901$	8.92707e8	+	8.92707e8i	1.22049	+	1.22049i
$902$	9.42223e6	−	3.65739e7i	0.0128391	−	0.0498370i
$903$	3.26669e8			0.443655
$904$	1.14273e8	−	3.31268e6i	0.154681	−	0.00448409i
$905$			6.11883e8i			0.825511i
$906$	2.82304e7	−	1.09581e8i	0.0379605	−	0.147350i
$907$	−3.81167e8	+	3.81167e8i	−0.510850	+	0.510850i	−0.914787	−	0.403937i	$-0.867642\pi$
$907$	−3.81167e8	+	3.81167e8i	−0.510850	+	0.510850i	0.403937	+	0.914787i	$0.367642\pi$
$908$	9.44914e7	−	2.72860e7i	0.126222	−	0.0364488i
$909$	−1.41516e8	+	1.41516e8i	−0.188414	+	0.188414i
$910$	3.42793e8	+	5.80706e8i	0.454891	+	0.770606i
$911$			2.25093e8i			0.297719i	0.988858	+	0.148860i	$0.0475602\pi$
$911$			2.25093e8i			0.297719i	−0.988858	+	0.148860i	$0.952440\pi$
$912$	−1.15787e9	+	7.29544e8i	−1.52642	+	0.961761i
$913$	3.35417e7			0.0440731
$914$	9.68196e7	−	5.71530e7i	0.126802	−	0.0748514i
$915$	−6.80082e8	−	6.80082e8i	−0.887765	−	0.887765i
$916$	2.01673e8	−	5.82367e7i	0.262399	−	0.0757723i
$917$	−7.96250e8	−	7.96250e8i	−1.03262	−	1.03262i
$918$	−7.86534e8	−	2.02628e8i	−1.01669	−	0.261922i
$919$	−1.21160e9			−1.56104			−0.780518	−	0.625133i	$-0.785045\pi$
$919$	−1.21160e9			−1.56104			−0.780518	+	0.625133i	$0.785045\pi$
$920$	−4.23457e8	−	3.99598e8i	−0.543809	−	0.513168i
$921$			4.99288e8i			0.639106i
$922$	5.04679e7	+	1.30016e7i	0.0643906	+	0.0165884i
$923$	−4.25697e7	+	4.25697e7i	−0.0541371	+	0.0541371i
$924$	1.16852e8	−	2.11738e8i	0.148122	−	0.268400i
$925$	1.42552e8	−	1.42552e8i	0.180114	−	0.180114i
$926$	−7.09831e8	+	4.19016e8i	−0.893969	+	0.527713i
$927$		−	2.03964e8i		−	0.256044i
$928$	−6.37694e7	−	1.99006e8i	−0.0797937	−	0.249014i
$929$	9.12609e8			1.13825			0.569125	−	0.822251i	$-0.307282\pi$
$929$	9.12609e8			1.13825			0.569125	+	0.822251i	$0.307282\pi$
$930$	−4.72896e8	−	8.01107e8i	−0.587918	−	0.995960i
$931$	−2.23901e8	−	2.23901e8i	−0.277465	−	0.277465i
$932$	−6.41532e8	−	3.54042e8i	−0.792448	−	0.437328i
$933$	7.83867e8	+	7.83867e8i	0.965156	+	0.965156i
$934$	−5.99917e7	+	2.32868e8i	−0.0736293	+	0.285804i
$935$	−1.98418e8			−0.242743
$936$	−3.88511e8	−	3.66620e8i	−0.473779	−	0.447084i
$937$			5.15006e8i			0.626027i	0.949749	+	0.313014i	$0.101339\pi$
$937$			5.15006e8i			0.626027i	−0.949749	+	0.313014i	$0.898661\pi$
$938$	−9.00369e7	+	3.49493e8i	−0.109097	+	0.423477i
$939$	−1.02433e8	+	1.02433e8i	−0.123721	+	0.123721i
$940$	−6.90902e7	−	2.39259e8i	−0.0831826	−	0.288061i
$941$	−5.76344e8	+	5.76344e8i	−0.691692	+	0.691692i	−0.962604	−	0.270912i	$-0.912675\pi$
$941$	−5.76344e8	+	5.76344e8i	−0.691692	+	0.691692i	0.270912	+	0.962604i	$0.412675\pi$
$942$	−2.48856e8	−	4.21573e8i	−0.297711	−	0.504336i
$943$			2.32927e8i			0.277770i
$944$	−5.83356e8	−	1.32385e8i	−0.693454	−	0.157371i
$945$	3.56235e8			0.422125
$946$	5.17084e7	−	3.05237e7i	0.0610785	−	0.0360548i
$947$	7.52969e8	+	7.52969e8i	0.886598	+	0.886598i	0.994195	−	0.107596i	$-0.0343154\pi$
$947$	7.52969e8	+	7.52969e8i	0.886598	+	0.886598i	−0.107596	+	0.994195i	$0.534315\pi$
$948$	7.21328e7	+	2.49795e8i	0.0846657	+	0.293197i
$949$	8.52284e8	+	8.52284e8i	0.997207	+	0.997207i
$950$	7.40947e8	+	1.90884e8i	0.864204	+	0.222638i
$951$	−8.50322e8			−0.988648
$952$	1.70137e9	−	4.93214e7i	1.97191	−	0.0571643i
$953$		−	9.03533e8i		−	1.04392i	−0.852971	−	0.521958i	$-0.825202\pi$
$953$		−	9.03533e8i		−	1.04392i	0.852971	−	0.521958i	$-0.174798\pi$
$954$	4.24766e8	+	1.09429e8i	0.489221	+	0.126034i
$955$	3.88264e8	−	3.88264e8i	0.445776	−	0.445776i
$956$	−2.24277e8	−	1.23772e8i	−0.256691	−	0.141660i
$957$	4.41273e7	−	4.41273e7i	0.0503468	−	0.0503468i
$958$	1.47889e9	−	8.72991e8i	1.68205	−	0.992918i
$959$		−	1.58281e9i		−	1.79462i
$960$	3.94485e7	+	6.79827e8i	0.0445879	+	0.768396i
$961$	−1.11633e9			−1.25783
$962$	2.40661e8	+	4.07691e8i	0.270322	+	0.457937i
$963$	1.69649e7	+	1.69649e7i	0.0189965	+	0.0189965i
$964$	−3.40444e8	+	6.16891e8i	−0.380027	+	0.688616i
$965$	1.15315e8	+	1.15315e8i	0.128323	+	0.128323i
$966$	−3.72096e8	+	1.44435e9i	−0.412784	+	1.60229i
$967$	−2.38766e8			−0.264054			−0.132027	−	0.991246i	$-0.542149\pi$
$967$	−2.38766e8			−0.264054			−0.132027	+	0.991246i	$0.542149\pi$
$968$	2.49952e7	+	8.62224e8i	0.0275569	+	0.950592i
$969$		−	2.87632e9i		−	3.16130i
$970$	−1.23128e8	+	4.77942e8i	−0.134909	+	0.523673i
$971$	1.16289e9	−	1.16289e9i	1.27023	−	1.27023i	0.324259	−	0.945968i	$-0.394885\pi$
$971$	1.16289e9	−	1.16289e9i	1.27023	−	1.27023i	0.945968	−	0.324259i	$-0.105115\pi$
$972$	−8.27676e8	+	2.39006e8i	−0.901284	+	0.260261i
$973$	−1.09401e9	+	1.09401e9i	−1.18763	+	1.18763i
$974$	−8.52085e8	−	1.44347e9i	−0.922160	−	1.56218i
$975$			8.80990e8i			0.950511i
$976$	1.47891e9	+	3.35621e8i	1.59072	+	0.360994i
$977$	1.21182e9			1.29944			0.649719	−	0.760174i	$-0.274887\pi$
$977$	1.21182e9			1.29944			0.649719	+	0.760174i	$0.274887\pi$
$978$	1.45565e9	−	8.59273e8i	1.55611	−	0.918575i
$979$	−2.56844e8	−	2.56844e8i	−0.273729	−	0.273729i
$980$	−1.51374e8	+	4.37119e7i	−0.160832	+	0.0464431i
$981$	−1.65265e8	−	1.65265e8i	−0.175054	−	0.175054i
$982$	5.62036e8	+	1.44793e8i	0.593512	+	0.152901i
$983$	7.50036e8			0.789626			0.394813	−	0.918761i	$-0.370809\pi$
$983$	7.50036e8			0.789626			0.394813	+	0.918761i	$0.370809\pi$
$984$	1.86973e8	−	1.98137e8i	0.196243	−	0.207960i
$985$			3.88123e8i			0.406126i
$986$	4.25323e8	+	1.09572e8i	0.443698	+	0.114306i
$987$	−4.51102e8	+	4.51102e8i	−0.469162	+	0.469162i
$988$	−8.68175e8	+	1.57315e9i	−0.900195	+	1.63117i
$989$	−2.61855e8	+	2.61855e8i	−0.270689	+	0.270689i
$990$	−5.93667e7	+	3.50444e7i	−0.0611839	+	0.0361171i
$991$			9.13847e8i			0.938971i	0.882940	+	0.469486i	$0.155561\pi$
$991$			9.13847e8i			0.938971i	−0.882940	+	0.469486i	$0.844439\pi$
$992$	1.30424e9	+	6.71226e8i	1.33605	+	0.687597i
$993$	−9.17099e8			−0.936631
$994$	−3.38800e7	−	5.73942e7i	−0.0344972	−	0.0584398i
$995$	−5.10159e8	−	5.10159e8i	−0.517888	−	0.517888i
$996$	2.11827e8	+	1.16901e8i	0.214389	+	0.118315i
$997$	−1.08316e9	−	1.08316e9i	−1.09297	−	1.09297i	−0.995210	−	0.0977566i	$-0.968833\pi$
$997$	−1.08316e9	−	1.08316e9i	−1.09297	−	1.09297i	−0.0977566	−	0.995210i	$-0.531167\pi$
$998$	−1.24914e8	+	4.84872e8i	−0.125666	+	0.487793i
$999$	2.50099e8			0.250850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.11.4	yes	22
4.3	odd	2		64.7.f.a.15.3		22
8.3	odd	2		128.7.f.a.31.9		22
8.5	even	2		128.7.f.b.31.3		22
16.3	odd	4	inner	16.7.f.a.3.4	✓	22
16.5	even	4		128.7.f.a.95.9		22
16.11	odd	4		128.7.f.b.95.3		22
16.13	even	4		64.7.f.a.47.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.4	✓	22	16.3	odd	4	inner
16.7.f.a.11.4	yes	22	1.1	even	1	trivial
64.7.f.a.15.3		22	4.3	odd	2
64.7.f.a.47.3		22	16.13	even	4
128.7.f.a.31.9		22	8.3	odd	2
128.7.f.a.95.9		22	16.5	even	4
128.7.f.b.31.3		22	8.5	even	2
128.7.f.b.95.3		22	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.06674 - 6.88924i) q^{2} +(23.4827 + 23.4827i) q^{3} +(-30.9232 + 56.0335i) q^{4} +(55.3108 + 55.3108i) q^{5} +(66.2800 - 257.276i) q^{6} +386.163 q^{7} +(511.785 - 14.8363i) q^{8} +373.878i q^{9} +O(q^{10})\)	\(q+(-4.06674 - 6.88924i) q^{2} +(23.4827 + 23.4827i) q^{3} +(-30.9232 + 56.0335i) q^{4} +(55.3108 + 55.3108i) q^{5} +(66.2800 - 257.276i) q^{6} +386.163 q^{7} +(511.785 - 14.8363i) q^{8} +373.878i q^{9} +(156.115 - 605.984i) q^{10} +(-208.354 + 208.354i) q^{11} +(-2041.98 + 589.658i) q^{12} +(-1973.22 + 1973.22i) q^{13} +(-1570.43 - 2660.37i) q^{14} +2597.70i q^{15} +(-2183.51 - 3465.47i) q^{16} +8608.75 q^{17} +(2575.74 - 1520.47i) q^{18} +(-7114.07 - 7114.07i) q^{19} +(-4809.65 + 1388.87i) q^{20} +(9068.17 + 9068.17i) q^{21} +(2282.72 + 588.078i) q^{22} -14537.9 q^{23} +(12366.5 + 11669.7i) q^{24} -9506.43i q^{25} +(21618.5 + 5569.40i) q^{26} +(8339.23 - 8339.23i) q^{27} +(-11941.4 + 21638.1i) q^{28} +(-4509.49 + 4509.49i) q^{29} +(17896.2 - 10564.2i) q^{30} -44764.2i q^{31} +(-14994.7 + 29135.9i) q^{32} -9785.44 q^{33} +(-35009.6 - 59307.7i) q^{34} +(21359.0 + 21359.0i) q^{35} +(-20949.7 - 11561.5i) q^{36} +(14995.3 + 14995.3i) q^{37} +(-20079.4 + 77941.6i) q^{38} -92673.0 q^{39} +(29127.8 + 27486.6i) q^{40} -16022.1i q^{41} +(25594.9 - 99350.7i) q^{42} +(18011.9 - 18011.9i) q^{43} +(-5231.82 - 18117.8i) q^{44} +(-20679.5 + 20679.5i) q^{45} +(59121.8 + 100155. i) q^{46} +49745.6i q^{47} +(30104.1 - 132654. i) q^{48} +31473.0 q^{49} +(-65492.1 + 38660.2i) q^{50} +(202157. + 202157. i) q^{51} +(-49548.0 - 171584. i) q^{52} +(103698. + 103698. i) q^{53} +(-91364.5 - 23537.5i) q^{54} -23048.4 q^{55} +(197633. - 5729.22i) q^{56} -334116. i q^{57} +(49405.8 + 12728.0i) q^{58} +(103267. - 103267. i) q^{59} +(-145558. - 80329.2i) q^{60} +(-261802. + 261802. i) q^{61} +(-308391. + 182044. i) q^{62} +144378. i q^{63} +(261704. - 15186.0i) q^{64} -218280. q^{65} +(39794.9 + 67414.2i) q^{66} +(-82606.9 - 82606.9i) q^{67} +(-266210. + 482378. i) q^{68} +(-341390. - 341390. i) q^{69} +(60285.7 - 234009. i) q^{70} +21573.8 q^{71} +(5546.96 + 191345. i) q^{72} -431926. i q^{73} +(42324.2 - 164288. i) q^{74} +(223237. - 223237. i) q^{75} +(618616. - 178636. i) q^{76} +(-80458.6 + 80458.6i) q^{77} +(376877. + 638447. i) q^{78} -122330. i q^{79} +(70906.6 - 312450. i) q^{80} +664213. q^{81} +(-110380. + 65157.6i) q^{82} +(-80492.3 - 80492.3i) q^{83} +(-788539. + 227704. i) q^{84} +(476157. + 476157. i) q^{85} +(-197338. - 50838.4i) q^{86} -211790. q^{87} +(-103541. + 109724. i) q^{88} +1.23273e6i q^{89} +(226564. + 58367.9i) q^{90} +(-761983. + 761983. i) q^{91} +(449559. - 814609. i) q^{92} +(1.05119e6 - 1.05119e6i) q^{93} +(342709. - 202303. i) q^{94} -786970. i q^{95} +(-1.03631e6 + 332074. i) q^{96} -788704. q^{97} +(-127993. - 216825. i) q^{98} +(-77899.0 - 77899.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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