LMFDB - Embedded newform 16.7.f.a.3.3

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			3.3
Character	$\chi$	$=$	16.3
Dual form			16.7.f.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.31611 + 4.90986i) q^{2} +(-31.9540 + 31.9540i) q^{3} +(15.7866 - 62.0224i) q^{4} +(95.0213 - 95.0213i) q^{5} +(44.9356 - 358.715i) q^{6} -293.582 q^{7} +(204.811 + 469.251i) q^{8} -1313.12i q^{9} +O(q^{10})$	\(q+(-6.31611 + 4.90986i) q^{2} +(-31.9540 + 31.9540i) q^{3} +(15.7866 - 62.0224i) q^{4} +(95.0213 - 95.0213i) q^{5} +(44.9356 - 358.715i) q^{6} -293.582 q^{7} +(204.811 + 469.251i) q^{8} -1313.12i q^{9} +(-133.624 + 1066.71i) q^{10} +(-1133.97 - 1133.97i) q^{11} +(1477.42 + 2486.31i) q^{12} +(300.531 + 300.531i) q^{13} +(1854.30 - 1441.44i) q^{14} +6072.63i q^{15} +(-3597.57 - 1958.25i) q^{16} -7159.68 q^{17} +(6447.23 + 8293.81i) q^{18} +(4874.76 - 4874.76i) q^{19} +(-4393.39 - 7393.52i) q^{20} +(9381.12 - 9381.12i) q^{21} +(12729.9 + 1594.65i) q^{22} -10541.6 q^{23} +(-21539.0 - 8449.90i) q^{24} -2433.11i q^{25} +(-3373.75 - 422.624i) q^{26} +(18665.0 + 18665.0i) q^{27} +(-4634.66 + 18208.6i) q^{28} +(-17466.6 - 17466.6i) q^{29} +(-29815.7 - 38355.4i) q^{30} +39593.1i q^{31} +(32337.4 - 5295.03i) q^{32} +72469.6 q^{33} +(45221.3 - 35153.0i) q^{34} +(-27896.5 + 27896.5i) q^{35} +(-81442.9 - 20729.7i) q^{36} +(1442.43 - 1442.43i) q^{37} +(-6855.17 + 54723.9i) q^{38} -19206.4 q^{39} +(64050.3 + 25127.4i) q^{40} +61174.6i q^{41} +(-13192.3 + 105312. i) q^{42} +(4004.05 + 4004.05i) q^{43} +(-88232.9 + 52429.9i) q^{44} +(-124774. - 124774. i) q^{45} +(66581.7 - 51757.6i) q^{46} -145063. i q^{47} +(177531. - 52382.9i) q^{48} -31458.8 q^{49} +(11946.2 + 15367.8i) q^{50} +(228781. - 228781. i) q^{51} +(23384.0 - 13895.3i) q^{52} +(-69074.3 + 69074.3i) q^{53} +(-209532. - 26247.7i) q^{54} -215502. q^{55} +(-60128.9 - 137763. i) q^{56} +311536. i q^{57} +(196079. + 24562.5i) q^{58} +(-64353.7 - 64353.7i) q^{59} +(376639. + 95866.2i) q^{60} +(61625.6 + 61625.6i) q^{61} +(-194397. - 250075. i) q^{62} +385508. i q^{63} +(-178249. + 192216. i) q^{64} +57113.7 q^{65} +(-457726. + 355815. i) q^{66} +(192708. - 192708. i) q^{67} +(-113027. + 444061. i) q^{68} +(336845. - 336845. i) q^{69} +(39229.7 - 313166. i) q^{70} -231273. q^{71} +(616182. - 268942. i) q^{72} +50686.9i q^{73} +(-2028.43 + 16192.7i) q^{74} +(77747.6 + 77747.6i) q^{75} +(-225389. - 379300. i) q^{76} +(332912. + 332912. i) q^{77} +(121310. - 94300.5i) q^{78} +74798.9i q^{79} +(-527921. + 155770. i) q^{80} -235578. q^{81} +(-300359. - 386386. i) q^{82} +(-42454.0 + 42454.0i) q^{83} +(-433744. - 729936. i) q^{84} +(-680322. + 680322. i) q^{85} +(-44949.4 - 5630.72i) q^{86} +1.11625e6 q^{87} +(299865. - 764364. i) q^{88} -387415. i q^{89} +(1.40071e6 + 175465. i) q^{90} +(-88230.4 - 88230.4i) q^{91} +(-166415. + 653813. i) q^{92} +(-1.26516e6 - 1.26516e6i) q^{93} +(712239. + 916234. i) q^{94} -926413. i q^{95} +(-864111. + 1.20251e6i) q^{96} +1.13627e6 q^{97} +(198698. - 154458. i) q^{98} +(-1.48903e6 + 1.48903e6i) 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−6.31611	+	4.90986i	−0.789514	+	0.613732i
$2$	−6.31611	+	4.90986i	−0.789514	+	0.613732i
$3$	−31.9540	+	31.9540i	−1.18348	+	1.18348i	−0.204647	+	0.978836i	$0.565604\pi$
$3$	−31.9540	+	31.9540i	−1.18348	+	1.18348i	−0.978836	+	0.204647i	$0.934396\pi$
$4$	15.7866	−	62.0224i	0.246666	−	0.969101i
$5$	95.0213	−	95.0213i	0.760171	−	0.760171i	−0.216182	−	0.976353i	$-0.569361\pi$
$5$	95.0213	−	95.0213i	0.760171	−	0.760171i	0.976353	+	0.216182i	$0.0693606\pi$
$6$	44.9356	−	358.715i	0.208035	−	1.66072i
$7$	−293.582			−0.855923			−0.427962	−	0.903797i	$-0.640768\pi$
$7$	−293.582			−0.855923			−0.427962	+	0.903797i	$0.640768\pi$
$8$	204.811	+	469.251i	0.400022	+	0.916505i
$9$		−	1313.12i		−	1.80126i
$10$	−133.624	+	1066.71i	−0.133624	+	1.06671i
$11$	−1133.97	−	1133.97i	−0.851966	−	0.851966i	0.138409	−	0.990375i	$-0.455801\pi$
$11$	−1133.97	−	1133.97i	−0.851966	−	0.851966i	−0.990375	+	0.138409i	$0.955801\pi$
$12$	1477.42	+	2486.31i	0.854989	+	1.43884i
$13$	300.531	+	300.531i	0.136792	+	0.136792i	0.772187	−	0.635395i	$-0.219163\pi$
$13$	300.531	+	300.531i	0.136792	+	0.136792i	−0.635395	+	0.772187i	$0.719163\pi$
$14$	1854.30	−	1441.44i	0.675764	−	0.525308i
$15$			6072.63i			1.79930i
$16$	−3597.57	−	1958.25i	−0.878312	−	0.478088i
$17$	−7159.68			−1.45729			−0.728646	−	0.684890i	$-0.759850\pi$
$17$	−7159.68			−1.45729			−0.728646	+	0.684890i	$0.759850\pi$
$18$	6447.23	+	8293.81i	1.10549	+	1.42212i
$19$	4874.76	−	4874.76i	0.710710	−	0.710710i	−0.255974	−	0.966684i	$-0.582396\pi$
$19$	4874.76	−	4874.76i	0.710710	−	0.710710i	0.966684	+	0.255974i	$0.0823960\pi$
$20$	−4393.39	−	7393.52i	−0.549174	−	0.924190i
$21$	9381.12	−	9381.12i	1.01297	−	1.01297i
$22$	12729.9	+	1594.65i	1.19552	+	0.149760i
$23$	−10541.6			−0.866406			−0.433203	−	0.901296i	$-0.642617\pi$
$23$	−10541.6			−0.866406			−0.433203	+	0.901296i	$0.642617\pi$
$24$	−21539.0	−	8449.90i	−1.55809	−	0.611249i
$25$		−	2433.11i		−	0.155719i
$26$	−3373.75	−	422.624i	−0.191952	−	0.0240455i
$27$	18665.0	+	18665.0i	0.948279	+	0.948279i
$28$	−4634.66	+	18208.6i	−0.211127	+	0.829476i
$29$	−17466.6	−	17466.6i	−0.716165	−	0.716165i	0.251652	−	0.967818i	$-0.419026\pi$
$29$	−17466.6	−	17466.6i	−0.716165	−	0.716165i	−0.967818	+	0.251652i	$0.919026\pi$
$30$	−29815.7	−	38355.4i	−1.10429	−	1.42057i
$31$			39593.1i			1.32903i	0.747275	+	0.664515i	$0.231362\pi$
$31$			39593.1i			1.32903i	−0.747275	+	0.664515i	$0.768638\pi$
$32$	32337.4	−	5295.03i	0.986858	−	0.161591i
$33$	72469.6			2.01657
$34$	45221.3	−	35153.0i	1.15055	−	0.894387i
$35$	−27896.5	+	27896.5i	−0.650648	+	0.650648i
$36$	−81442.9	−	20729.7i	−1.74560	−	0.444309i
$37$	1442.43	−	1442.43i	0.0284768	−	0.0284768i	−0.692725	−	0.721202i	$-0.743590\pi$
$37$	1442.43	−	1442.43i	0.0284768	−	0.0284768i	0.721202	+	0.692725i	$0.243590\pi$
$38$	−6855.17	+	54723.9i	−0.124930	+	0.997301i
$39$	−19206.4			−0.323781
$40$	64050.3	+	25127.4i	1.00079	+	0.392615i
$41$			61174.6i			0.887605i	0.896125	+	0.443803i	$0.146371\pi$
$41$			61174.6i			0.887605i	−0.896125	+	0.443803i	$0.853629\pi$
$42$	−13192.3	+	105312.i	−0.178062	+	1.42145i
$43$	4004.05	+	4004.05i	0.0503610	+	0.0503610i	0.731839	−	0.681478i	$-0.238662\pi$
$43$	4004.05	+	4004.05i	0.0503610	+	0.0503610i	−0.681478	+	0.731839i	$0.738662\pi$
$44$	−88232.9	+	52429.9i	−1.03579	+	0.615490i
$45$	−124774.	−	124774.i	−1.36927	−	1.36927i
$46$	66581.7	−	51757.6i	0.684040	−	0.531741i
$47$		−	145063.i		−	1.39721i	−0.715506	−	0.698607i	$-0.753804\pi$
$47$		−	145063.i		−	1.39721i	0.715506	−	0.698607i	$-0.246196\pi$
$48$	177531.	−	52382.9i	1.60528	−	0.473659i
$49$	−31458.8			−0.267396
$50$	11946.2	+	15367.8i	0.0955698	+	0.122942i
$51$	228781.	−	228781.i	1.72468	−	1.72468i
$52$	23384.0	−	13895.3i	0.166307	−	0.0988230i
$53$	−69074.3	+	69074.3i	−0.463969	+	0.463969i	−0.899954	−	0.435985i	$-0.856400\pi$
$53$	−69074.3	+	69074.3i	−0.463969	+	0.463969i	0.435985	+	0.899954i	$0.356400\pi$
$54$	−209532.	−	26247.7i	−1.33067	−	0.166690i
$55$	−215502.			−1.29528
$56$	−60128.9	−	137763.i	−0.342388	−	0.784458i
$57$			311536.i			1.68223i
$58$	196079.	+	24562.5i	1.00496	+	0.125889i
$59$	−64353.7	−	64353.7i	−0.313341	−	0.313341i	0.532861	−	0.846203i	$-0.321117\pi$
$59$	−64353.7	−	64353.7i	−0.313341	−	0.313341i	−0.846203	+	0.532861i	$0.821117\pi$
$60$	376639.	+	95866.2i	1.74370	+	0.443825i
$61$	61625.6	+	61625.6i	0.271501	+	0.271501i	0.829704	−	0.558203i	$-0.188509\pi$
$61$	61625.6	+	61625.6i	0.271501	+	0.271501i	−0.558203	+	0.829704i	$0.688509\pi$
$62$	−194397.	−	250075.i	−0.815668	−	1.04929i
$63$			385508.i			1.54174i
$64$	−178249.	+	192216.i	−0.679964	+	0.733245i
$65$	57113.7			0.207970
$66$	−457726.	+	355815.i	−1.59211	+	1.23764i
$67$	192708.	−	192708.i	0.640731	−	0.640731i	−0.310005	−	0.950735i	$-0.600331\pi$
$67$	192708.	−	192708.i	0.640731	−	0.640731i	0.950735	+	0.310005i	$0.100331\pi$
$68$	−113027.	+	444061.i	−0.359464	+	1.41226i
$69$	336845.	−	336845.i	1.02538	−	1.02538i
$70$	39229.7	−	313166.i	0.114372	−	0.913019i
$71$	−231273.			−0.646175			−0.323087	−	0.946369i	$-0.604721\pi$
$71$	−231273.			−0.646175			−0.323087	+	0.946369i	$0.604721\pi$
$72$	616182.	−	268942.i	1.65087	−	0.720545i
$73$			50686.9i			0.130295i	0.997876	+	0.0651474i	$0.0207518\pi$
$73$			50686.9i			0.130295i	−0.997876	+	0.0651474i	$0.979248\pi$
$74$	−2028.43	+	16192.7i	−0.00500571	+	0.0399599i
$75$	77747.6	+	77747.6i	0.184291	+	0.184291i
$76$	−225389.	−	379300.i	−0.513442	−	0.864057i
$77$	332912.	+	332912.i	0.729217	+	0.729217i
$78$	121310.	−	94300.5i	0.255630	−	0.198715i
$79$			74798.9i			0.151710i	0.997119	+	0.0758549i	$0.0241686\pi$
$79$			74798.9i			0.151710i	−0.997119	+	0.0758549i	$0.975831\pi$
$80$	−527921.	+	155770.i	−1.03110	+	0.304239i
$81$	−235578.			−0.443281
$82$	−300359.	−	386386.i	−0.544752	−	0.700777i
$83$	−42454.0	+	42454.0i	−0.0742480	+	0.0742480i	−0.743256	−	0.669008i	$-0.766719\pi$
$83$	−42454.0	+	42454.0i	−0.0742480	+	0.0742480i	0.669008	+	0.743256i	$0.266719\pi$
$84$	−433744.	−	729936.i	−0.731805	−	1.23153i
$85$	−680322.	+	680322.i	−1.10779	+	1.10779i
$86$	−44949.4	−	5630.72i	−0.0706689	−	0.00885256i
$87$	1.11625e6			1.69514
$88$	299865.	−	764364.i	0.440026	−	1.12164i
$89$		−	387415.i		−	0.549550i	−0.961509	−	0.274775i	$-0.911397\pi$
$89$		−	387415.i		−	0.549550i	0.961509	−	0.274775i	$-0.0886033\pi$
$90$	1.40071e6	+	175465.i	1.92142	+	0.240692i
$91$	−88230.4	−	88230.4i	−0.117083	−	0.117083i
$92$	−166415.	+	653813.i	−0.213713	+	0.839635i
$93$	−1.26516e6	−	1.26516e6i	−1.57288	−	1.57288i
$94$	712239.	+	916234.i	0.857515	+	1.10312i
$95$		−	926413.i		−	1.08052i
$96$	−864111.	+	1.20251e6i	−0.976688	+	1.35917i
$97$	1.13627e6			1.24499			0.622497	−	0.782623i	$-0.286118\pi$
$97$	1.13627e6			1.24499			0.622497	+	0.782623i	$0.286118\pi$
$98$	198698.	−	154458.i	0.211113	−	0.164109i
$99$	−1.48903e6	+	1.48903e6i	−1.53461	+	1.53461i
$100$	−150907.	−	38410.5i	−0.150907	−	0.0384105i
$101$	694739.	−	694739.i	0.674307	−	0.674307i	−0.284399	−	0.958706i	$-0.591794\pi$
$101$	694739.	−	694739.i	0.674307	−	0.674307i	0.958706	+	0.284399i	$0.0917941\pi$
$102$	−321724.	+	2.56828e6i	−0.303168	+	2.42015i
$103$	−1.37735e6			−1.26047			−0.630237	−	0.776403i	$-0.717042\pi$
$103$	−1.37735e6			−1.26047			−0.630237	+	0.776403i	$0.717042\pi$
$104$	−79472.2	+	202577.i	−0.0706505	+	0.180090i
$105$		−	1.78281e6i		−	1.54006i
$106$	97136.3	−	775427.i	0.0815575	−	0.651063i
$107$	1.07683e6	+	1.07683e6i	0.879011	+	0.879011i	0.993432	−	0.114421i	$-0.0365013\pi$
$107$	1.07683e6	+	1.07683e6i	0.879011	+	0.879011i	−0.114421	+	0.993432i	$0.536501\pi$
$108$	1.45230e6	−	862991.i	1.15289	−	0.685070i
$109$	1.12656e6	+	1.12656e6i	0.869908	+	0.869908i	0.992462	−	0.122554i	$-0.0391086\pi$
$109$	1.12656e6	+	1.12656e6i	0.869908	+	0.869908i	−0.122554	+	0.992462i	$0.539109\pi$
$110$	1.36114e6	−	1.05808e6i	1.02264	−	0.794955i
$111$			92183.1i			0.0674035i
$112$	1.05618e6	+	574905.i	0.751768	+	0.409206i
$113$	−1.87079e6			−1.29655			−0.648276	−	0.761405i	$-0.724510\pi$
$113$	−1.87079e6			−1.29655			−0.648276	+	0.761405i	$0.724510\pi$
$114$	−1.52960e6	−	1.96770e6i	−1.03244	−	1.32814i
$115$	−1.00167e6	+	1.00167e6i	−0.658616	+	0.658616i
$116$	−1.35906e6	+	807581.i	−0.870690	+	0.517383i
$117$	394633.	−	394633.i	0.246397	−	0.246397i
$118$	722433.	+	90497.8i	0.439695	+	0.0550798i
$119$	2.10195e6			1.24733
$120$	−2.84959e6	+	1.24374e6i	−1.64907	+	0.719759i
$121$			800200.i			0.451692i
$122$	−691807.	−	86661.4i	−0.380983	−	0.0477251i
$123$	−1.95478e6	−	1.95478e6i	−1.05047	−	1.05047i
$124$	2.45566e6	+	625041.i	1.28796	+	0.327826i
$125$	1.25351e6	+	1.25351e6i	0.641798	+	0.641798i
$126$	−1.89279e6	−	2.43491e6i	−0.946216	−	1.21723i
$127$			846677.i			0.413339i	0.978411	+	0.206670i	$0.0662626\pi$
$127$			846677.i			0.413339i	−0.978411	+	0.206670i	$0.933737\pi$
$128$	182086.	−	2.08923e6i	0.0868255	−	0.996224i
$129$	−255891.			−0.119203
$130$	−360737.	+	280420.i	−0.164195	+	0.127638i
$131$	1.91611e6	−	1.91611e6i	0.852329	−	0.852329i	−0.138090	−	0.990420i	$-0.544096\pi$
$131$	1.91611e6	−	1.91611e6i	0.852329	−	0.852329i	0.990420	+	0.138090i	$0.0440964\pi$
$132$	1.14405e6	−	4.49474e6i	0.497419	−	1.95426i
$133$	−1.43114e6	+	1.43114e6i	−0.608313	+	0.608313i
$134$	−270997.	+	2.16333e6i	−0.112629	+	0.899103i
$135$	3.54714e6			1.44171
$136$	−1.46638e6	−	3.35968e6i	−0.582949	−	1.33562i
$137$		−	4.07420e6i		−	1.58446i	−0.610224	−	0.792229i	$-0.708920\pi$
$137$		−	4.07420e6i		−	1.58446i	0.610224	−	0.792229i	$-0.291080\pi$
$138$	−473691.	+	3.78142e6i	−0.180243	+	1.43886i
$139$	−1.34384e6	−	1.34384e6i	−0.500384	−	0.500384i	0.411173	−	0.911557i	$-0.365119\pi$
$139$	−1.34384e6	−	1.34384e6i	−0.500384	−	0.500384i	−0.911557	+	0.411173i	$0.865119\pi$
$140$	1.28982e6	+	2.17060e6i	0.470051	+	0.791036i
$141$	4.63535e6	+	4.63535e6i	1.65358	+	1.65358i
$142$	1.46075e6	−	1.13552e6i	0.510164	−	0.396578i
$143$		−	681584.i		−	0.233084i
$144$	−2.57141e6	+	4.72404e6i	−0.861161	+	1.58207i
$145$	−3.31939e6			−1.08882
$146$	−248865.	−	320144.i	−0.0799661	−	0.102870i
$147$	1.00524e6	−	1.00524e6i	0.316458	−	0.316458i
$148$	−66692.1	−	112234.i	−0.0205726	−	0.0346211i
$149$	−3.20203e6	+	3.20203e6i	−0.967982	+	0.967982i	−0.999503	−	0.0315212i	$-0.989965\pi$
$149$	−3.20203e6	+	3.20203e6i	−0.967982	+	0.967982i	0.0315212	+	0.999503i	$0.489965\pi$
$150$	−872793.	−	109333.i	−0.258605	−	0.0323950i
$151$	−3.52525e6			−1.02390			−0.511951	−	0.859015i	$-0.671077\pi$
$151$	−3.52525e6			−1.02390			−0.511951	+	0.859015i	$0.671077\pi$
$152$	3.28589e6	+	1.28908e6i	0.935669	+	0.367070i
$153$			9.40151e6i			2.62497i
$154$	−3.73726e6	−	468160.i	−1.02327	−	0.128183i
$155$	3.76219e6	+	3.76219e6i	1.01029	+	1.01029i
$156$	−303203.	+	1.19122e6i	−0.0798656	+	0.313776i
$157$	−3.50219e6	−	3.50219e6i	−0.904983	−	0.904983i	0.0908791	−	0.995862i	$-0.471032\pi$
$157$	−3.50219e6	−	3.50219e6i	−0.904983	−	0.904983i	−0.995862	+	0.0908791i	$0.971032\pi$
$158$	−367252.	−	472438.i	−0.0931092	−	0.119777i
$159$		−	4.41441e6i		−	1.09820i
$160$	2.56960e6	−	3.57588e6i	0.627343	−	0.873017i
$161$	3.09481e6			0.741577
$162$	1.48794e6	−	1.15665e6i	0.349977	−	0.272056i
$163$	−2.05652e6	+	2.05652e6i	−0.474865	+	0.474865i	−0.903485	−	0.428620i	$-0.859000\pi$
$163$	−2.05652e6	+	2.05652e6i	−0.474865	+	0.474865i	0.428620	+	0.903485i	$0.359000\pi$
$164$	3.79420e6	+	965739.i	0.860179	+	0.218942i
$165$	6.88616e6	−	6.88616e6i	1.53294	−	1.53294i
$166$	59701.2	−	476588.i	0.0130515	−	0.104188i
$167$	−2.27703e6			−0.488900			−0.244450	−	0.969662i	$-0.578607\pi$
$167$	−2.27703e6			−0.488900			−0.244450	+	0.969662i	$0.578607\pi$
$168$	6.32345e6	+	2.48074e6i	1.33360	+	0.523182i
$169$		−	4.64617e6i		−	0.962576i
$170$	956708.	−	7.63728e6i	0.194730	−	1.55450i
$171$	−6.40114e6	−	6.40114e6i	−1.28017	−	1.28017i
$172$	311551.	−	185131.i	0.0612272	−	0.0363825i
$173$	−6.43922e6	−	6.43922e6i	−1.24364	−	1.24364i	−0.958479	−	0.285162i	$-0.907953\pi$
$173$	−6.43922e6	−	6.43922e6i	−1.24364	−	1.24364i	−0.285162	−	0.958479i	$-0.592047\pi$
$174$	−7.05039e6	+	5.48065e6i	−1.33834	+	1.04036i
$175$			714316.i			0.133284i
$176$	1.85893e6	+	6.30011e6i	0.340978	+	1.15561i
$177$	4.11272e6			0.741668
$178$	1.90215e6	+	2.44696e6i	0.337276	+	0.433877i
$179$	1.91198e6	−	1.91198e6i	0.333368	−	0.333368i	−0.520496	−	0.853864i	$-0.674253\pi$
$179$	1.91198e6	−	1.91198e6i	0.333368	−	0.333368i	0.853864	+	0.520496i	$0.174253\pi$
$180$	−9.70857e6	+	5.76905e6i	−1.66471	+	0.989206i
$181$	−3.35022e6	+	3.35022e6i	−0.564986	+	0.564986i	−0.930720	−	0.365734i	$-0.880818\pi$
$181$	−3.35022e6	+	3.35022e6i	−0.564986	+	0.564986i	0.365734	+	0.930720i	$0.380818\pi$
$182$	990472.	+	124075.i	0.164296	+	0.0205811i
$183$	−3.93837e6			−0.642634
$184$	−2.15903e6	−	4.94664e6i	−0.346582	−	0.794066i
$185$		−	274124.i		−	0.0432944i
$186$	1.42026e7	+	1.77914e6i	2.20714	+	0.276485i
$187$	8.11884e6	+	8.11884e6i	1.24156	+	1.24156i
$188$	−8.99716e6	−	2.29005e6i	−1.35404	−	0.344645i
$189$	−5.47969e6	−	5.47969e6i	−0.811654	−	0.811654i
$190$	4.54855e6	+	5.85133e6i	0.663151	+	0.853088i
$191$			2.65439e6i			0.380948i	0.981692	+	0.190474i	$0.0610024\pi$
$191$			2.65439e6i			0.380948i	−0.981692	+	0.190474i	$0.938998\pi$
$192$	−446308.	−	1.18378e7i	−0.0630567	−	1.67251i
$193$	9.75895e6			1.35747			0.678736	−	0.734382i	$-0.262528\pi$
$193$	9.75895e6			1.35747			0.678736	+	0.734382i	$0.262528\pi$
$194$	−7.17682e6	+	5.57893e6i	−0.982940	+	0.764092i
$195$	−1.82501e6	+	1.82501e6i	−0.246129	+	0.246129i
$196$	−496628.	+	1.95115e6i	−0.0659573	+	0.259133i
$197$	−3.08959e6	+	3.08959e6i	−0.404112	+	0.404112i	−0.879679	−	0.475567i	$-0.842243\pi$
$197$	−3.08959e6	+	3.08959e6i	−0.404112	+	0.404112i	0.475567	+	0.879679i	$0.342243\pi$
$198$	2.09396e6	−	1.67159e7i	0.269758	−	2.15344i
$199$	2.32175e6			0.294615			0.147308	−	0.989091i	$-0.452939\pi$
$199$	2.32175e6			0.294615			0.147308	+	0.989091i	$0.452939\pi$
$200$	1.14174e6	−	498329.i	0.142717	−	0.0622911i
$201$			1.23156e7i			1.51659i
$202$	−976981.	+	7.79912e6i	−0.118531	+	0.946218i
$203$	5.12786e6	+	5.12786e6i	0.612983	+	0.612983i
$204$	−1.05779e7	−	1.78012e7i	−1.24597	−	2.09681i
$205$	5.81290e6	+	5.81290e6i	0.674731	+	0.674731i
$206$	8.69952e6	−	6.76261e6i	0.995162	−	0.773593i
$207$			1.38423e7i			1.56062i
$208$	−492666.	−	1.66969e6i	−0.0547473	−	0.185544i
$209$	−1.10556e7			−1.21100
$210$	8.75335e6	+	1.12604e7i	0.945185	+	1.21590i
$211$	6.72968e6	−	6.72968e6i	0.716386	−	0.716386i	−0.251477	−	0.967863i	$-0.580916\pi$
$211$	6.72968e6	−	6.72968e6i	0.716386	−	0.716386i	0.967863	+	0.251477i	$0.0809163\pi$
$212$	3.19371e6	+	5.37461e6i	0.335188	+	0.564078i
$213$	7.39011e6	−	7.39011e6i	0.764737	−	0.764737i
$214$	−1.20884e7	−	1.51429e6i	−1.23347	−	0.154514i
$215$	760941.			0.0765659
$216$	−4.93575e6	+	1.25814e7i	−0.489770	+	1.24844i
$217$		−	1.16238e7i		−	1.13755i
$218$	−1.26467e7	−	1.58423e6i	−1.22069	−	0.152914i
$219$	−1.61965e6	−	1.61965e6i	−0.154202	−	0.154202i
$220$	−3.40205e6	+	1.33660e7i	−0.319501	+	1.25526i
$221$	−2.15171e6	−	2.15171e6i	−0.199345	−	0.199345i
$222$	−452606.	−	582239.i	−0.0413677	−	0.0532160i
$223$			6.40671e6i			0.577724i	0.957371	+	0.288862i	$0.0932769\pi$
$223$			6.40671e6i			0.577724i	−0.957371	+	0.288862i	$0.906723\pi$
$224$	−9.49365e6	+	1.55452e6i	−0.844674	+	0.138310i
$225$	−3.19496e6			−0.280491
$226$	1.18161e7	−	9.18532e6i	1.02365	−	0.795736i
$227$	8.23982e6	−	8.23982e6i	0.704434	−	0.704434i	−0.260925	−	0.965359i	$-0.584028\pi$
$227$	8.23982e6	−	8.23982e6i	0.704434	−	0.704434i	0.965359	+	0.260925i	$0.0840277\pi$
$228$	1.93223e7	+	4.91810e6i	1.63025	+	0.414947i
$229$	1.19449e7	−	1.19449e7i	0.994662	−	0.994662i	−0.00532420	−	0.999986i	$-0.501695\pi$
$229$	1.19449e7	−	1.19449e7i	0.994662	−	0.994662i	0.999986	+	0.00532420i	$0.00169475\pi$
$230$	1.40861e6	−	1.12448e7i	0.115773	−	0.924201i
$231$	−2.12757e7			−1.72603
$232$	4.61885e6	−	1.17735e7i	0.369887	−	0.942852i
$233$			4.18022e6i			0.330469i	0.986254	+	0.165235i	$0.0528382\pi$
$233$			4.18022e6i			0.330469i	−0.986254	+	0.165235i	$0.947162\pi$
$234$	−554956.	+	4.43014e6i	−0.0433122	+	0.345756i
$235$	−1.37841e7	−	1.37841e7i	−1.06212	−	1.06212i
$236$	−5.00730e6	+	2.97545e6i	−0.380950	+	0.226369i
$237$	−2.39012e6	−	2.39012e6i	−0.179546	−	0.179546i
$238$	−1.32762e7	+	1.03203e7i	−0.984785	+	0.765527i
$239$			1.39631e7i			1.02280i	0.859344	+	0.511398i	$0.170872\pi$
$239$			1.39631e7i			1.02280i	−0.859344	+	0.511398i	$0.829128\pi$
$240$	1.18917e7	−	2.18467e7i	0.860222	−	1.58034i
$241$	1.25874e7			0.899259			0.449629	−	0.893215i	$-0.351556\pi$
$241$	1.25874e7			0.899259			0.449629	+	0.893215i	$0.351556\pi$
$242$	−3.92887e6	−	5.05416e6i	−0.277218	−	0.356617i
$243$	−6.07910e6	+	6.07910e6i	−0.423663	+	0.423663i
$244$	4.79503e6	−	2.84931e6i	0.330082	−	0.196142i
$245$	−2.98926e6	+	2.98926e6i	−0.203266	+	0.203266i
$246$	2.19443e7	+	2.74892e6i	1.47406	+	0.184653i
$247$	2.93003e6			0.194438
$248$	−1.85791e7	+	8.10912e6i	−1.21806	+	0.531641i
$249$		−	2.71315e6i		−	0.175742i
$250$	−1.40719e7	−	1.76276e6i	−0.900600	−	0.112817i
$251$	2.99991e6	+	2.99991e6i	0.189709	+	0.189709i	0.795570	−	0.605862i	$-0.207171\pi$
$251$	2.99991e6	+	2.99991e6i	0.189709	+	0.189709i	−0.605862	+	0.795570i	$0.707171\pi$
$252$	2.39101e7	+	6.08586e6i	1.49410	+	0.380295i
$253$	1.19538e7	+	1.19538e7i	0.738148	+	0.738148i
$254$	−4.15707e6	−	5.34771e6i	−0.253680	−	0.326337i
$255$		−	4.34781e7i		−	2.62210i
$256$	9.10775e6	+	1.40898e7i	0.542864	+	0.839820i
$257$	−2.65835e7			−1.56608			−0.783039	−	0.621973i	$-0.786331\pi$
$257$	−2.65835e7			−1.56608			−0.783039	+	0.621973i	$0.786331\pi$
$258$	1.61624e6	−	1.25639e6i	0.0941122	−	0.0731585i
$259$	−423472.	+	423472.i	−0.0243739	+	0.0243739i
$260$	901631.	−	3.54233e6i	0.0512990	−	0.201544i
$261$	−2.29357e7	+	2.29357e7i	−1.29000	+	1.29000i
$262$	−2.69455e6	+	2.15102e7i	−0.149824	+	1.19603i
$263$	1.18815e7			0.653136			0.326568	−	0.945174i	$-0.394108\pi$
$263$	1.18815e7			0.653136			0.326568	+	0.945174i	$0.394108\pi$
$264$	1.48426e7	+	3.40064e7i	0.806674	+	1.84820i
$265$			1.31271e7i			0.705392i
$266$	2.01255e6	−	1.60659e7i	0.106931	−	0.853613i
$267$	1.23795e7	+	1.23795e7i	0.650382	+	0.650382i
$268$	−8.91002e6	−	1.49944e7i	−0.462886	−	0.778979i
$269$	−1.54174e7	−	1.54174e7i	−0.792055	−	0.792055i	0.189773	−	0.981828i	$-0.439225\pi$
$269$	−1.54174e7	−	1.54174e7i	−0.792055	−	0.792055i	−0.981828	+	0.189773i	$0.939225\pi$
$270$	−2.24041e7	+	1.74160e7i	−1.13825	+	0.884822i
$271$		−	2.86452e7i		−	1.43927i	−0.694351	−	0.719637i	$-0.744308\pi$
$271$		−	2.86452e7i		−	1.43927i	0.694351	−	0.719637i	$-0.255692\pi$
$272$	2.57574e7	+	1.40204e7i	1.27996	+	0.696714i
$273$	5.63863e6			0.277131
$274$	2.00037e7	+	2.57331e7i	0.972433	+	1.25095i
$275$	−2.75907e6	+	2.75907e6i	−0.132667	+	0.132667i
$276$	−1.55743e7	−	2.62096e7i	−0.740768	−	1.24662i
$277$	−1.36014e7	+	1.36014e7i	−0.639946	+	0.639946i	−0.950542	−	0.310596i	$-0.899471\pi$
$277$	−1.36014e7	+	1.36014e7i	−0.639946	+	0.639946i	0.310596	+	0.950542i	$0.399471\pi$
$278$	1.50859e7	+	1.88978e6i	0.702162	+	0.0879585i
$279$	5.19905e7			2.39393
$280$	−1.88040e7	−	7.37694e6i	−0.856596	−	0.336049i
$281$			3.85563e6i			0.173771i	0.996218	+	0.0868853i	$0.0276914\pi$
$281$			3.85563e6i			0.173771i	−0.996218	+	0.0868853i	$0.972309\pi$
$282$	−5.20363e7	−	6.51849e6i	−2.32038	−	0.290670i
$283$	−2.19377e7	−	2.19377e7i	−0.967905	−	0.967905i	0.0315958	−	0.999501i	$-0.489941\pi$
$283$	−2.19377e7	−	2.19377e7i	−0.967905	−	0.967905i	−0.999501	+	0.0315958i	$0.989941\pi$
$284$	−3.65102e6	+	1.43441e7i	−0.159389	+	0.626208i
$285$	2.96026e7	+	2.96026e7i	1.27878	+	1.27878i
$286$	3.34648e6	+	4.30497e6i	0.143051	+	0.184023i
$287$		−	1.79597e7i		−	0.759722i
$288$	−6.95300e6	−	4.24628e7i	−0.291068	−	1.77759i
$289$	2.71234e7			1.12370
$290$	2.09657e7	−	1.62977e7i	0.859636	−	0.668241i
$291$	−3.63085e7	+	3.63085e7i	−1.47343	+	1.47343i
$292$	3.14373e6	+	800174.i	0.126269	+	0.0321393i
$293$	−1.30749e7	+	1.30749e7i	−0.519799	+	0.519799i	−0.917510	−	0.397712i	$-0.869804\pi$
$293$	−1.30749e7	+	1.30749e7i	−0.519799	+	0.519799i	0.397712	+	0.917510i	$0.369804\pi$
$294$	−1.41362e6	+	1.12848e7i	−0.0556276	+	0.444069i
$295$	−1.22300e7			−0.476386
$296$	972290.	+	381436.i	0.0374904	+	0.0147078i
$297$		−	4.23309e7i		−	1.61580i
$298$	4.50288e6	−	3.59460e7i	0.170154	−	1.35832i
$299$	−3.16807e6	−	3.16807e6i	−0.118517	−	0.118517i
$300$	6.04947e6	−	3.59473e6i	0.224054	−	0.133138i
$301$	−1.17552e6	−	1.17552e6i	−0.0431051	−	0.0431051i
$302$	2.22659e7	−	1.73085e7i	0.808386	−	0.628402i
$303$			4.43994e7i			1.59606i
$304$	−2.70833e7	+	7.99129e6i	−0.964007	+	0.284444i
$305$	1.17115e7			0.412775
$306$	−4.61601e7	−	5.93810e7i	−1.61103	−	2.07245i
$307$	1.24387e7	−	1.24387e7i	0.429892	−	0.429892i	−0.458700	−	0.888591i	$-0.651685\pi$
$307$	1.24387e7	−	1.24387e7i	0.429892	−	0.429892i	0.888591	+	0.458700i	$0.151685\pi$
$308$	2.59035e7	−	1.53925e7i	0.886558	−	0.526812i
$309$	4.40120e7	−	4.40120e7i	1.49175	−	1.49175i
$310$	−4.22342e7	−	5.29061e6i	−1.41768	−	0.177591i
$311$	2.22422e7			0.739430			0.369715	−	0.929145i	$-0.379455\pi$
$311$	2.22422e7			0.739430			0.369715	+	0.929145i	$0.379455\pi$
$312$	−3.93368e6	−	9.01260e6i	−0.129520	−	0.296747i
$313$		−	2.40612e7i		−	0.784666i	−0.919823	−	0.392333i	$-0.871668\pi$
$313$		−	2.40612e7i		−	0.784666i	0.919823	−	0.392333i	$-0.128332\pi$
$314$	3.93154e7	+	4.92497e6i	1.26991	+	0.159080i
$315$	3.66315e7	+	3.66315e7i	1.17199	+	1.17199i
$316$	4.63921e6	+	1.18082e6i	0.147022	+	0.0374216i
$317$	2.26015e7	+	2.26015e7i	0.709513	+	0.709513i	0.966433	−	0.256920i	$-0.0827076\pi$
$317$	2.26015e7	+	2.26015e7i	0.709513	+	0.709513i	−0.256920	+	0.966433i	$0.582708\pi$
$318$	2.16741e7	+	2.78819e7i	0.674000	+	0.867044i
$319$			3.96130e7i			1.22030i
$320$	1.32718e6	+	3.52020e7i	0.0405024	+	1.07428i
$321$	−6.88179e7			−2.08059
$322$	−1.95472e7	+	1.51951e7i	−0.585486	+	0.455130i
$323$	−3.49017e7	+	3.49017e7i	−1.03571	+	1.03571i
$324$	−3.71897e6	+	1.46111e7i	−0.109342	+	0.429584i
$325$	731225.	−	731225.i	0.0213010	−	0.0213010i
$326$	2.89199e6	−	2.30864e7i	0.0834727	−	0.666352i
$327$	−7.19960e7			−2.05904
$328$	−2.87062e7	+	1.25293e7i	−0.813495	+	0.355062i
$329$			4.25878e7i			1.19591i
$330$	−9.68371e6	+	7.73038e7i	−0.269463	+	2.15109i
$331$	−3.51481e7	−	3.51481e7i	−0.969210	−	0.969210i	0.0303298	−	0.999540i	$-0.490344\pi$
$331$	−3.51481e7	−	3.51481e7i	−0.969210	−	0.969210i	−0.999540	+	0.0303298i	$0.990344\pi$
$332$	1.96290e6	+	3.30331e6i	0.0536393	+	0.0902682i
$333$	−1.89409e6	−	1.89409e6i	−0.0512941	−	0.0512941i
$334$	1.43820e7	−	1.11799e7i	0.385993	−	0.300054i
$335$		−	3.66228e7i		−	0.974129i
$336$	−5.21197e7	+	1.53786e7i	−1.37399	+	0.405415i
$337$	3.86296e6			0.100932			0.0504662	−	0.998726i	$-0.483929\pi$
$337$	3.86296e6			0.100932			0.0504662	+	0.998726i	$0.483929\pi$
$338$	2.28120e7	+	2.93457e7i	0.590764	+	0.759968i
$339$	5.97793e7	−	5.97793e7i	1.53445	−	1.53445i
$340$	3.14553e7	+	5.29352e7i	0.800307	+	1.34682i
$341$	4.48973e7	−	4.48973e7i	1.13229	−	1.13229i
$342$	7.18591e7	+	9.00165e6i	1.79640	+	0.225032i
$343$	4.37753e7			1.08479
$344$	−1.05883e6	+	2.69898e6i	−0.0260106	+	0.0663016i
$345$		−	6.40150e7i		−	1.55892i
$346$	7.22865e7	+	9.05520e6i	1.74514	+	0.218610i
$347$	3.07948e7	+	3.07948e7i	0.737037	+	0.737037i	0.972003	−	0.234966i	$-0.0754980\pi$
$347$	3.07948e7	+	3.07948e7i	0.737037	+	0.737037i	−0.234966	+	0.972003i	$0.575498\pi$
$348$	1.76219e7	−	6.92328e7i	0.418132	−	1.64276i
$349$	−3.28683e7	−	3.28683e7i	−0.773215	−	0.773215i	0.205452	−	0.978667i	$-0.434134\pi$
$349$	−3.28683e7	−	3.28683e7i	−0.773215	−	0.773215i	−0.978667	+	0.205452i	$0.934134\pi$
$350$	−3.50719e6	−	4.51170e6i	−0.0818004	−	0.105229i
$351$			1.12188e7i			0.259433i
$352$	−4.26739e7	−	3.06651e7i	−0.978440	−	0.703099i
$353$	−5.74827e7			−1.30681			−0.653406	−	0.757008i	$-0.726661\pi$
$353$	−5.74827e7			−1.30681			−0.653406	+	0.757008i	$0.726661\pi$
$354$	−2.59764e7	+	2.01929e7i	−0.585557	+	0.455185i
$355$	−2.19759e7	+	2.19759e7i	−0.491203	+	0.491203i
$356$	−2.40284e7	−	6.11597e6i	−0.532569	−	0.135555i
$357$	−6.71658e7	+	6.71658e7i	−1.47619	+	1.47619i
$358$	−2.68873e6	+	2.14638e7i	−0.0586001	+	0.467797i
$359$	1.22478e6			0.0264714			0.0132357	−	0.999912i	$-0.495787\pi$
$359$	1.22478e6			0.0264714			0.0132357	+	0.999912i	$0.495787\pi$
$360$	3.29953e7	−	8.41057e7i	0.707203	−	1.80268i
$361$		−	480699.i		−	0.0102177i
$362$	4.71127e6	−	3.76095e7i	0.0993144	−	0.792814i
$363$	−2.55696e7	−	2.55696e7i	−0.534570	−	0.534570i
$364$	−6.86512e6	+	4.07941e6i	−0.142346	+	0.0845849i
$365$	4.81634e6	+	4.81634e6i	0.0990463	+	0.0990463i
$366$	2.48752e7	−	1.93369e7i	0.507369	−	0.394405i
$367$			9.41948e7i			1.90559i	0.303620	+	0.952793i	$0.401805\pi$
$367$			9.41948e7i			1.90559i	−0.303620	+	0.952793i	$0.598195\pi$
$368$	3.79240e7	+	2.06430e7i	0.760975	+	0.414218i
$369$	8.03296e7			1.59881
$370$	1.34591e6	+	1.73140e6i	0.0265712	+	0.0341816i
$371$	2.02790e7	−	2.02790e7i	0.397122	−	0.397122i
$372$	−9.84408e7	+	5.84957e7i	−1.91226	+	1.13631i
$373$	−1.75289e7	+	1.75289e7i	−0.337775	+	0.337775i	−0.855529	−	0.517754i	$-0.826768\pi$
$373$	−1.75289e7	+	1.75289e7i	−0.337775	+	0.337775i	0.517754	+	0.855529i	$0.326768\pi$
$374$	−9.11418e7	−	1.14172e7i	−1.74222	−	0.218245i
$375$	−8.01095e7			−1.51911
$376$	6.80709e7	−	2.97105e7i	1.28055	−	0.558917i
$377$		−	1.04985e7i		−	0.195931i
$378$	6.15149e7	+	7.70586e6i	1.13895	+	0.142674i
$379$	−2.54295e7	−	2.54295e7i	−0.467110	−	0.467110i	0.433867	−	0.900977i	$-0.357149\pi$
$379$	−2.54295e7	−	2.54295e7i	−0.467110	−	0.467110i	−0.900977	+	0.433867i	$0.857149\pi$
$380$	−5.74584e7	−	1.46249e7i	−1.04713	−	0.266528i
$381$	−2.70548e7	−	2.70548e7i	−0.489180	−	0.489180i
$382$	−1.30327e7	−	1.67655e7i	−0.233800	−	0.300764i
$383$		−	6.92259e7i		−	1.23218i	−0.787678	−	0.616088i	$-0.788717\pi$
$383$		−	6.92259e7i		−	1.23218i	0.787678	−	0.616088i	$-0.211283\pi$
$384$	6.09410e7	+	7.25778e7i	1.07626	+	1.28177i
$385$	6.32675e7			1.10866
$386$	−6.16386e7	+	4.79151e7i	−1.07174	+	0.833125i
$387$	5.25780e6	−	5.25780e6i	0.0907133	−	0.0907133i
$388$	1.79379e7	−	7.04743e7i	0.307097	−	1.20652i
$389$	7.81447e7	−	7.81447e7i	1.32755	−	1.32755i	0.420047	−	0.907502i	$-0.362014\pi$
$389$	7.81447e7	−	7.81447e7i	1.32755	−	1.32755i	0.907502	−	0.420047i	$-0.137986\pi$
$390$	2.56644e6	−	2.04875e7i	0.0432650	−	0.345379i
$391$	7.54742e7			1.26261
$392$	−6.44312e6	−	1.47621e7i	−0.106964	−	0.245070i
$393$			1.22455e8i			2.01743i
$394$	4.34476e6	−	3.46837e7i	0.0710357	−	0.567069i
$395$	7.10749e6	+	7.10749e6i	0.115325	+	0.115325i
$396$	6.88467e7	+	1.15860e8i	1.10866	+	1.86573i
$397$	−5.23542e7	−	5.23542e7i	−0.836720	−	0.836720i	0.151706	−	0.988426i	$-0.451523\pi$
$397$	−5.23542e7	−	5.23542e7i	−0.836720	−	0.836720i	−0.988426	+	0.151706i	$0.951523\pi$
$398$	−1.46644e7	+	1.13994e7i	−0.232603	+	0.180815i
$399$		−	9.14614e7i		−	1.43986i
$400$	−4.76463e6	+	8.75327e6i	−0.0744473	+	0.136770i
$401$	2.59321e6			0.0402165			0.0201082	−	0.999798i	$-0.493599\pi$
$401$	2.59321e6			0.0402165			0.0201082	+	0.999798i	$0.493599\pi$
$402$	−6.04678e7	−	7.77867e7i	−0.930778	−	1.19737i
$403$	−1.18990e7	+	1.18990e7i	−0.181800	+	0.181800i
$404$	−3.21218e7	−	5.40570e7i	−0.487143	−	0.819799i
$405$	−2.23849e7	+	2.23849e7i	−0.336969	+	0.336969i
$406$	−5.75652e7	−	7.21109e6i	−0.860166	−	0.107751i
$407$	−3.27134e6			−0.0485225
$408$	1.54212e8	+	6.04986e7i	2.27059	+	0.890768i
$409$			1.24826e8i			1.82447i	0.409671	+	0.912233i	$0.365644\pi$
$409$			1.24826e8i			1.82447i	−0.409671	+	0.912233i	$0.634356\pi$
$410$	−6.52554e7	−	8.17442e6i	−0.946814	−	0.118606i
$411$	1.30187e8	+	1.30187e8i	1.87518	+	1.87518i
$412$	−2.17437e7	+	8.54268e7i	−0.310915	+	1.22153i
$413$	1.88931e7	+	1.88931e7i	0.268196	+	0.268196i
$414$	−6.79639e7	−	8.74297e7i	−0.957805	−	1.23213i
$415$			8.06807e6i			0.112882i
$416$	1.13097e7	+	8.12706e6i	0.157098	+	0.112889i
$417$	8.58822e7			1.18439
$418$	6.98286e7	−	5.42816e7i	0.956103	−	0.743231i
$419$	4.67128e6	−	4.67128e6i	0.0635030	−	0.0635030i	−0.674642	−	0.738145i	$-0.735702\pi$
$419$	4.67128e6	−	4.67128e6i	0.0635030	−	0.0635030i	0.738145	+	0.674642i	$0.235702\pi$
$420$	−1.10574e8	−	2.81445e7i	−1.49247	−	0.379880i
$421$	−5.69604e7	+	5.69604e7i	−0.763355	+	0.763355i	−0.976927	−	0.213572i	$-0.931490\pi$
$421$	−5.69604e7	+	5.69604e7i	−0.763355	+	0.763355i	0.213572	+	0.976927i	$0.431490\pi$
$422$	−9.46366e6	+	7.55472e7i	−0.125928	+	1.00527i
$423$	−1.90485e8			−2.51675
$424$	−4.65604e7	−	1.82660e7i	−0.610828	−	0.239632i
$425$			1.74203e7i			0.226928i
$426$	−1.03924e7	+	8.29611e7i	−0.134427	+	1.07311i
$427$	−1.80921e7	−	1.80921e7i	−0.232384	−	0.232384i
$428$	8.37868e7	−	4.97880e7i	1.06867	−	0.635029i
$429$	2.17794e7	+	2.17794e7i	0.275850	+	0.275850i
$430$	−4.80619e6	+	3.73611e6i	−0.0604499	+	0.0469909i
$431$			1.42926e8i			1.78516i	0.450884	+	0.892582i	$0.351109\pi$
$431$			1.42926e8i			1.78516i	−0.450884	+	0.892582i	$0.648891\pi$
$432$	−3.05979e7	−	1.03699e8i	−0.379524	−	1.28625i
$433$	1.06589e6			0.0131295			0.00656475	−	0.999978i	$-0.497910\pi$
$433$	1.06589e6			0.0131295			0.00656475	+	0.999978i	$0.497910\pi$
$434$	5.70712e7	+	7.34173e7i	0.698149	+	0.898109i
$435$	1.06068e8	−	1.06068e8i	1.28859	−	1.28859i
$436$	8.76562e7	−	5.20872e7i	1.05760	−	0.628452i
$437$	−5.13876e7	+	5.13876e7i	−0.615763	+	0.615763i
$438$	1.81822e7	+	2.27765e6i	0.216383	+	0.0271059i
$439$	7.97200e7			0.942266			0.471133	−	0.882062i	$-0.343845\pi$
$439$	7.97200e7			0.942266			0.471133	+	0.882062i	$0.343845\pi$
$440$	−4.41373e7	−	1.01125e8i	−0.518140	−	1.18713i
$441$			4.13092e7i			0.481649i
$442$	2.41550e7	+	3.02585e6i	0.279731	+	0.0350413i
$443$	−4.99781e7	−	4.99781e7i	−0.574868	−	0.574868i	0.358617	−	0.933485i	$-0.383249\pi$
$443$	−4.99781e7	−	4.99781e7i	−0.574868	−	0.574868i	−0.933485	+	0.358617i	$0.883249\pi$
$444$	5.71742e6	+	1.45526e6i	0.0653208	+	0.0166261i
$445$	−3.68127e7	−	3.68127e7i	−0.417751	−	0.417751i
$446$	−3.14560e7	−	4.04655e7i	−0.354568	−	0.456122i
$447$		−	2.04636e8i		−	2.29118i
$448$	5.23305e7	−	5.64310e7i	0.581997	−	0.627601i
$449$	−6.19013e7			−0.683850			−0.341925	−	0.939727i	$-0.611079\pi$
$449$	−6.19013e7			−0.683850			−0.341925	+	0.939727i	$0.611079\pi$
$450$	2.01798e7	−	1.56868e7i	0.221451	−	0.172146i
$451$	6.93700e7	−	6.93700e7i	0.756209	−	0.756209i
$452$	−2.95334e7	+	1.16031e8i	−0.319815	+	1.25649i
$453$	1.12646e8	−	1.12646e8i	1.21177	−	1.21177i
$454$	−1.15873e7	+	9.25000e7i	−0.123827	+	0.988494i
$455$	−1.67675e7			−0.178006
$456$	−1.46189e8	+	6.38062e7i	−1.54177	+	0.672928i
$457$		−	1.59441e8i		−	1.67052i	−0.549857	−	0.835259i	$-0.685318\pi$
$457$		−	1.59441e8i		−	1.67052i	0.549857	−	0.835259i	$-0.314682\pi$
$458$	−1.67976e7	+	1.34093e8i	−0.174844	+	1.39576i
$459$	−1.33635e8	−	1.33635e8i	−1.38192	−	1.38192i
$460$	4.63132e7	+	7.79392e7i	0.475808	+	0.800724i
$461$	−4.03090e7	−	4.03090e7i	−0.411433	−	0.411433i	0.470805	−	0.882237i	$-0.343964\pi$
$461$	−4.03090e7	−	4.03090e7i	−0.411433	−	0.411433i	−0.882237	+	0.470805i	$0.843964\pi$
$462$	1.34380e8	−	1.04461e8i	1.36273	−	1.05932i
$463$			1.49317e8i			1.50441i	0.658927	+	0.752207i	$0.271011\pi$
$463$			1.49317e8i			1.50441i	−0.658927	+	0.752207i	$0.728989\pi$
$464$	2.86333e7	+	9.70409e7i	0.286627	+	0.971407i
$465$	−2.40434e8			−2.39132
$466$	−2.05243e7	−	2.64027e7i	−0.202820	−	0.260910i
$467$	−9.16391e6	+	9.16391e6i	−0.0899768	+	0.0899768i	−0.750663	−	0.660686i	$-0.770266\pi$
$467$	−9.16391e6	+	9.16391e6i	−0.0899768	+	0.0899768i	0.660686	+	0.750663i	$0.270266\pi$
$468$	−1.82462e7	−	3.07060e7i	−0.178006	−	0.299562i
$469$	−5.65755e7	+	5.65755e7i	−0.548416	+	0.548416i
$470$	1.54740e8	+	1.93840e7i	1.49042	+	0.186702i
$471$	2.23818e8			2.14206
$472$	1.70177e7	−	4.33784e7i	0.161835	−	0.412522i
$473$		−	9.08092e6i		−	0.0858117i
$474$	2.68315e7	+	3.36113e6i	0.251947	+	0.0315610i
$475$	−1.18608e7	−	1.18608e7i	−0.110671	−	0.110671i
$476$	3.31826e7	−	1.30368e8i	0.307674	−	1.20879i
$477$	9.07029e7	+	9.07029e7i	0.835730	+	0.835730i
$478$	−6.85570e7	−	8.81927e7i	−0.627723	−	0.807512i
$479$		−	3.40105e7i		−	0.309462i	−0.987957	−	0.154731i	$-0.950549\pi$
$479$		−	3.40105e7i		−	0.309462i	0.987957	−	0.154731i	$-0.0494511\pi$
$480$	3.21547e7	+	1.96373e8i	0.290751	+	1.77565i
$481$	866992.			0.00779076
$482$	−7.95034e7	+	6.18023e7i	−0.709978	+	0.551904i
$483$	−9.88916e7	+	9.88916e7i	−0.877643	+	0.877643i
$484$	4.96304e7	+	1.26324e7i	0.437735	+	0.111417i
$485$	1.07970e8	−	1.07970e8i	0.946407	−	0.946407i
$486$	8.54878e6	−	6.82438e7i	0.0744724	−	0.594504i
$487$	−2.20294e8			−1.90729			−0.953644	−	0.300937i	$-0.902700\pi$
$487$	−2.20294e8			−1.90729			−0.953644	+	0.300937i	$0.902700\pi$
$488$	−1.62962e7	+	4.15395e7i	−0.140226	+	0.357439i
$489$		−	1.31428e8i		−	1.12399i
$490$	4.20367e6	−	3.35573e7i	0.0357306	−	0.285233i
$491$	5.48107e7	+	5.48107e7i	0.463043	+	0.463043i	0.899651	−	0.436609i	$-0.143821\pi$
$491$	5.48107e7	+	5.48107e7i	0.463043	+	0.463043i	−0.436609	+	0.899651i	$0.643821\pi$
$492$	−1.52099e8	+	9.03807e7i	−1.27712	+	0.758893i
$493$	1.25055e8	+	1.25055e8i	1.04366	+	1.04366i
$494$	−1.85064e7	+	1.43860e7i	−0.153512	+	0.119333i
$495$			2.82980e8i			2.33314i
$496$	7.75331e7	−	1.42439e8i	0.635392	−	1.16730i
$497$	6.78975e7			0.553076
$498$	1.33212e7	+	1.71366e7i	0.107859	+	0.138751i
$499$	−1.17709e8	+	1.17709e8i	−0.947347	+	0.947347i	−0.998682	−	0.0513344i	$-0.983653\pi$
$499$	−1.17709e8	+	1.17709e8i	−0.947347	+	0.947347i	0.0513344	+	0.998682i	$0.483653\pi$
$500$	9.75345e7	−	5.79571e7i	0.780276	−	0.463657i
$501$	7.27604e7	−	7.27604e7i	0.578604	−	0.578604i
$502$	−3.36769e7	−	4.21864e6i	−0.266208	−	0.0333474i
$503$	−1.75259e8			−1.37713			−0.688567	−	0.725173i	$-0.741760\pi$
$503$	−1.75259e8			−1.37713			−0.688567	+	0.725173i	$0.741760\pi$
$504$	−1.80900e8	+	7.89564e7i	−1.41301	+	0.616731i
$505$		−	1.32030e8i		−	1.02518i
$506$	−1.34193e8	−	1.68101e7i	−1.03580	−	0.129753i
$507$	1.48464e8	+	1.48464e8i	1.13919	+	1.13919i
$508$	5.25130e7	+	1.33662e7i	0.400567	+	0.101957i
$509$	−3.95296e7	−	3.95296e7i	−0.299757	−	0.299757i	0.541162	−	0.840919i	$-0.317985\pi$
$509$	−3.95296e7	−	3.95296e7i	−0.299757	−	0.299757i	−0.840919	+	0.541162i	$0.817985\pi$
$510$	2.13471e8	+	2.74612e8i	1.60927	+	2.07019i
$511$		−	1.48807e7i		−	0.111522i
$512$	−1.26705e8	−	4.42753e7i	−0.944024	−	0.329877i
$513$	1.81975e8			1.34790
$514$	1.67905e8	−	1.30521e8i	1.23644	−	0.961152i
$515$	−1.30878e8	+	1.30878e8i	−0.958175	+	0.958175i
$516$	−4.03965e6	+	1.58710e7i	−0.0294032	+	0.115519i
$517$	−1.64497e8	+	1.64497e8i	−1.19038	+	1.19038i
$518$	595510.	−	4.75388e6i	0.00428450	−	0.0342026i
$519$	4.11518e8			2.94366
$520$	1.16975e7	+	2.68007e7i	0.0831926	+	0.190606i
$521$		−	5.81559e7i		−	0.411226i	−0.978633	−	0.205613i	$-0.934081\pi$
$521$		−	5.81559e7i		−	0.411226i	0.978633	−	0.205613i	$-0.0659188\pi$
$522$	3.22535e7	−	2.57475e8i	0.226759	−	1.81019i
$523$	−5.92630e7	−	5.92630e7i	−0.414265	−	0.414265i	0.468956	−	0.883221i	$-0.344630\pi$
$523$	−5.92630e7	−	5.92630e7i	−0.414265	−	0.414265i	−0.883221	+	0.468956i	$0.844630\pi$
$524$	−8.85931e7	−	1.49091e8i	−0.615753	−	1.03623i
$525$	−2.28253e7	−	2.28253e7i	−0.157739	−	0.157739i
$526$	−7.50448e7	+	5.83364e7i	−0.515660	+	0.400850i
$527$		−	2.83474e8i		−	1.93678i
$528$	−2.60714e8	−	1.41913e8i	−1.77118	−	0.964099i
$529$	−3.69114e7			−0.249341
$530$	−6.44521e7	−	8.29121e7i	−0.432921	−	0.556917i
$531$	−8.45041e7	+	8.45041e7i	−0.564409	+	0.564409i
$532$	6.61700e7	+	1.11356e8i	0.439467	+	0.739567i
$533$	−1.83849e7	+	1.83849e7i	−0.121417	+	0.121417i
$534$	−1.38972e8	−	1.74087e7i	−0.912647	−	0.114326i
$535$	2.04643e8			1.33640
$536$	1.29897e8	+	5.09596e7i	0.843539	+	0.330927i
$537$			1.22191e8i			0.789070i
$538$	1.73076e8	+	2.16809e7i	1.11145	+	0.139229i
$539$	3.56733e7	+	3.56733e7i	0.227812	+	0.227812i
$540$	5.59973e7	−	2.20002e8i	0.355620	−	1.39716i
$541$	−1.51890e8	−	1.51890e8i	−0.959265	−	0.959265i	0.0399372	−	0.999202i	$-0.487284\pi$
$541$	−1.51890e8	−	1.51890e8i	−0.959265	−	0.959265i	−0.999202	+	0.0399372i	$0.987284\pi$
$542$	1.40644e8	+	1.80926e8i	0.883328	+	1.13633i
$543$		−	2.14106e8i		−	1.33730i
$544$	−2.31525e8	+	3.79107e7i	−1.43814	+	0.235486i
$545$	2.14094e8			1.32256
$546$	−3.56142e7	+	2.76849e7i	−0.218799	+	0.170085i
$547$	1.23610e8	−	1.23610e8i	0.755250	−	0.755250i	−0.220204	−	0.975454i	$-0.570672\pi$
$547$	1.23610e8	−	1.23610e8i	0.755250	−	0.755250i	0.975454	+	0.220204i	$0.0706722\pi$
$548$	−2.52692e8	−	6.43178e7i	−1.53550	−	0.390831i
$549$	8.09218e7	−	8.09218e7i	0.489045	−	0.489045i
$550$	3.87995e6	−	3.09732e7i	0.0233205	−	0.186165i
$551$	−1.70291e8			−1.01797
$552$	2.27055e8	+	8.90752e7i	1.34994	+	0.529590i
$553$		−	2.19596e7i		−	0.129852i
$554$	1.91270e7	−	1.52689e8i	0.112491	−	0.898002i
$555$	8.75936e6	+	8.75936e6i	0.0512382	+	0.0512382i
$556$	−1.04563e8	+	6.21336e7i	−0.608350	+	0.361495i
$557$	2.22902e8	+	2.22902e8i	1.28988	+	1.28988i	0.934860	+	0.355018i	$0.115525\pi$
$557$	2.22902e8	+	2.22902e8i	1.28988	+	1.28988i	0.355018	+	0.934860i	$0.384475\pi$
$558$	−3.28378e8	+	2.55266e8i	−1.89004	+	1.46923i
$559$			2.40668e6i			0.0137779i
$560$	1.54988e8	−	4.57313e7i	0.882538	−	0.260405i
$561$	−5.18859e8			−2.93874
$562$	−1.89306e7	−	2.43526e7i	−0.106649	−	0.137194i
$563$	7.50976e7	−	7.50976e7i	0.420824	−	0.420824i	−0.464663	−	0.885488i	$-0.653825\pi$
$563$	7.50976e7	−	7.50976e7i	0.420824	−	0.420824i	0.885488	+	0.464663i	$0.153825\pi$
$564$	3.60672e8	−	2.14319e8i	2.01036	−	1.19460i
$565$	−1.77765e8	+	1.77765e8i	−0.985601	+	0.985601i
$566$	2.46273e8	+	3.08501e7i	1.35821	+	0.170140i
$567$	6.91613e7			0.379415
$568$	−4.73674e7	−	1.08525e8i	−0.258484	−	0.592223i
$569$			2.04643e8i			1.11086i	0.831564	+	0.555430i	$0.187446\pi$
$569$			2.04643e8i			1.11086i	−0.831564	+	0.555430i	$0.812554\pi$
$570$	−3.32318e8	−	4.16289e7i	−1.79444	−	0.224786i
$571$	6.76421e7	+	6.76421e7i	0.363336	+	0.363336i	0.865040	−	0.501704i	$-0.167293\pi$
$571$	6.76421e7	+	6.76421e7i	0.363336	+	0.363336i	−0.501704	+	0.865040i	$0.667293\pi$
$572$	−4.22735e7	−	1.07599e7i	−0.225881	−	0.0574937i
$573$	−8.48185e7	−	8.48185e7i	−0.450845	−	0.450845i
$574$	8.81798e7	+	1.13436e8i	0.466266	+	0.599811i
$575$			2.56488e7i			0.134916i
$576$	2.52402e8	+	2.34062e8i	1.32077	+	1.22479i
$577$	9.01774e6			0.0469429			0.0234715	−	0.999725i	$-0.492528\pi$
$577$	9.01774e6			0.0469429			0.0234715	+	0.999725i	$0.492528\pi$
$578$	−1.71315e8	+	1.33172e8i	−0.887179	+	0.689652i
$579$	−3.11838e8	+	3.11838e8i	−1.60655	+	1.60655i
$580$	−5.24019e7	+	2.05877e8i	−0.268573	+	1.05517i
$581$	1.24637e7	−	1.24637e7i	0.0635505	−	0.0635505i
$582$	5.10590e7	−	4.07598e8i	0.259002	−	2.06758i
$583$	1.56656e8			0.790572
$584$	−2.37849e7	+	1.03813e7i	−0.119416	+	0.0521208i
$585$		−	7.49971e7i		−	0.374608i
$586$	1.83867e7	−	1.46778e8i	0.0913713	−	0.729406i
$587$	−1.48352e8	−	1.48352e8i	−0.733464	−	0.733464i	0.237840	−	0.971304i	$-0.423561\pi$
$587$	−1.48352e8	−	1.48352e8i	−0.733464	−	0.733464i	−0.971304	+	0.237840i	$0.923561\pi$
$588$	−4.64779e7	−	7.82165e7i	−0.228620	−	0.384739i
$589$	1.93007e8	+	1.93007e8i	0.944554	+	0.944554i
$590$	7.72458e7	−	6.00473e7i	0.376113	−	0.292373i
$591$		−	1.97450e8i		−	0.956520i
$592$	−8.01389e6	+	2.36461e6i	−0.0386259	+	0.0113971i
$593$	3.63513e8			1.74324			0.871618	−	0.490185i	$-0.163071\pi$
$593$	3.63513e8			1.74324			0.871618	+	0.490185i	$0.163071\pi$
$594$	2.07839e8	+	2.67367e8i	0.991670	+	1.27570i
$595$	1.99730e8	−	1.99730e8i	0.948184	−	0.948184i
$596$	1.48049e8	+	2.49147e8i	0.699304	+	1.17684i
$597$	−7.41891e7	+	7.41891e7i	−0.348672	+	0.348672i
$598$	3.55646e7	+	4.45511e6i	0.166309	+	0.0208332i
$599$	−1.39710e8			−0.650052			−0.325026	−	0.945705i	$-0.605373\pi$
$599$	−1.39710e8			−0.650052			−0.325026	+	0.945705i	$0.605373\pi$
$600$	−2.05595e7	+	5.24067e7i	−0.0951831	+	0.242624i
$601$		−	2.35493e8i		−	1.08481i	−0.840117	−	0.542405i	$-0.817514\pi$
$601$		−	2.35493e8i		−	1.08481i	0.840117	−	0.542405i	$-0.182486\pi$
$602$	1.31963e7	+	1.65308e6i	0.0604871	+	0.00757711i
$603$	−2.53049e8	−	2.53049e8i	−1.15412	−	1.15412i
$604$	−5.56516e7	+	2.18644e8i	−0.252562	+	0.992265i
$605$	7.60361e7	+	7.60361e7i	0.343363	+	0.343363i
$606$	−2.17995e8	−	2.80432e8i	−0.979553	−	1.26011i
$607$			2.73689e8i			1.22374i	0.790957	+	0.611872i	$0.209583\pi$
$607$			2.73689e8i			1.22374i	−0.790957	+	0.611872i	$0.790417\pi$
$608$	1.31825e8	−	1.83449e8i	0.586525	−	0.816214i
$609$	−3.27712e8			−1.45091
$610$	−7.39712e7	+	5.75018e7i	−0.325891	+	0.253333i
$611$	4.35959e7	−	4.35959e7i	0.191127	−	0.191127i
$612$	5.83105e8	+	1.48418e8i	2.54386	+	0.647489i
$613$	1.73686e8	−	1.73686e8i	0.754021	−	0.754021i	−0.221206	−	0.975227i	$-0.570999\pi$
$613$	1.73686e8	−	1.73686e8i	0.754021	−	0.754021i	0.975227	+	0.221206i	$0.0709993\pi$
$614$	−1.74920e7	+	1.39636e8i	−0.0755673	+	0.603244i
$615$	−3.71491e8			−1.59707
$616$	−8.80350e7	+	2.24403e8i	−0.376629	+	0.960035i
$617$		−	1.42273e8i		−	0.605713i	−0.953036	−	0.302857i	$-0.902060\pi$
$617$		−	1.42273e8i		−	0.605713i	0.953036	−	0.302857i	$-0.0979403\pi$
$618$	−6.18922e7	+	4.94077e8i	−0.262223	+	2.09329i
$619$	−1.72079e8	−	1.72079e8i	−0.725530	−	0.725530i	0.244196	−	0.969726i	$-0.421476\pi$
$619$	−1.72079e8	−	1.72079e8i	−0.725530	−	0.725530i	−0.969726	+	0.244196i	$0.921476\pi$
$620$	2.92732e8	−	1.73948e8i	1.22828	−	0.729868i
$621$	−1.96758e8	−	1.96758e8i	−0.821594	−	0.821594i
$622$	−1.40484e8	+	1.09206e8i	−0.583791	+	0.453812i
$623$			1.13738e8i			0.470372i
$624$	6.90961e7	+	3.76108e7i	0.284381	+	0.154796i
$625$	2.76238e8			1.13147
$626$	1.18137e8	+	1.51973e8i	0.481575	+	0.619505i
$627$	3.53272e8	−	3.53272e8i	1.43320	−	1.43320i
$628$	−2.72502e8	+	1.61927e8i	−1.10025	+	0.653791i
$629$	−1.03274e7	+	1.03274e7i	−0.0414990	+	0.0414990i
$630$	−4.11224e8	−	5.15133e7i	−1.64459	−	0.206014i
$631$	−1.51806e7			−0.0604229			−0.0302114	−	0.999544i	$-0.509618\pi$
$631$	−1.51806e7			−0.0604229			−0.0302114	+	0.999544i	$0.509618\pi$
$632$	−3.50994e7	+	1.53197e7i	−0.139043	+	0.0606873i
$633$			4.30081e8i			1.69566i
$634$	−2.53724e8	−	3.17836e7i	−0.995621	−	0.124720i
$635$	8.04524e7	+	8.04524e7i	0.314209	+	0.314209i
$636$	−2.73792e8	−	6.96885e7i	−1.06427	−	0.270888i
$637$	−9.45435e6	−	9.45435e6i	−0.0365775	−	0.0365775i
$638$	−1.94494e8	−	2.50200e8i	−0.748936	−	0.963442i
$639$			3.03689e8i			1.16393i
$640$	−1.81220e8	−	2.15824e8i	−0.691298	−	0.823302i
$641$	−4.47660e8			−1.69971			−0.849853	−	0.527020i	$-0.823309\pi$
$641$	−4.47660e8			−1.69971			−0.849853	+	0.527020i	$0.823309\pi$
$642$	4.34662e8	−	3.37886e8i	1.64265	−	1.27692i
$643$	8.32213e7	−	8.32213e7i	0.313041	−	0.313041i	−0.533045	−	0.846087i	$-0.678953\pi$
$643$	8.32213e7	−	8.32213e7i	0.313041	−	0.313041i	0.846087	+	0.533045i	$0.178953\pi$
$644$	4.88565e7	−	1.91948e8i	0.182922	−	0.718663i
$645$	−2.43151e7	+	2.43151e7i	−0.0906144	+	0.0906144i
$646$	4.90808e7	−	3.91806e8i	0.182060	−	1.45336i
$647$	3.14403e7			0.116085			0.0580423	−	0.998314i	$-0.481514\pi$
$647$	3.14403e7			0.116085			0.0580423	+	0.998314i	$0.481514\pi$
$648$	−4.82490e7	−	1.10545e8i	−0.177322	−	0.406270i
$649$			1.45950e8i			0.533912i
$650$	−1.02829e6	+	8.20871e6i	−0.00374434	+	0.0298906i
$651$	3.71428e8	+	3.71428e8i	1.34627	+	1.34627i
$652$	9.50849e7	+	1.60016e8i	0.343059	+	0.577324i
$653$	1.09903e8	+	1.09903e8i	0.394704	+	0.394704i	0.876360	−	0.481656i	$-0.159965\pi$
$653$	1.09903e8	+	1.09903e8i	0.394704	+	0.394704i	−0.481656	+	0.876360i	$0.659965\pi$
$654$	4.54735e8	−	3.53490e8i	1.62564	−	1.26370i
$655$		−	3.64143e8i		−	1.29583i
$656$	1.19795e8	−	2.20080e8i	0.424353	−	0.779594i
$657$	6.65580e7			0.234695
$658$	−2.09100e8	−	2.68990e8i	−0.733967	−	0.944186i
$659$	1.17222e8	−	1.17222e8i	0.409592	−	0.409592i	−0.472004	−	0.881596i	$-0.656469\pi$
$659$	1.17222e8	−	1.17222e8i	0.409592	−	0.409592i	0.881596	+	0.472004i	$0.156469\pi$
$660$	−3.18387e8	−	5.35805e8i	−1.10745	−	1.86370i
$661$	6.26215e7	−	6.26215e7i	0.216830	−	0.216830i	−0.590331	−	0.807161i	$-0.701003\pi$
$661$	6.26215e7	−	6.26215e7i	0.216830	−	0.216830i	0.807161	+	0.590331i	$0.201003\pi$
$662$	3.94572e8	+	4.94273e7i	1.36004	+	0.170370i
$663$	1.37511e8			0.471843
$664$	−2.86166e7	−	1.12265e7i	−0.0977495	−	0.0383478i
$665$			2.71978e8i			0.924844i
$666$	2.12630e7	+	2.66357e6i	0.0719783	+	0.00901658i
$667$	1.84125e8	+	1.84125e8i	0.620490	+	0.620490i
$668$	−3.59466e7	+	1.41227e8i	−0.120595	+	0.473793i
$669$	−2.04720e8	−	2.04720e8i	−0.683727	−	0.683727i
$670$	1.79812e8	+	2.31313e8i	0.597854	+	0.769089i
$671$		−	1.39763e8i		−	0.462620i
$672$	2.53687e8	−	3.53034e8i	0.835970	−	1.16334i
$673$	2.69706e8			0.884800			0.442400	−	0.896818i	$-0.354127\pi$
$673$	2.69706e8			0.884800			0.442400	+	0.896818i	$0.354127\pi$
$674$	−2.43989e7	+	1.89666e7i	−0.0796876	+	0.0619455i
$675$	4.54139e7	−	4.54139e7i	0.147665	−	0.147665i
$676$	−2.88167e8	−	7.33472e7i	−0.932833	−	0.237434i
$677$	3.54325e7	−	3.54325e7i	0.114192	−	0.114192i	−0.647702	−	0.761894i	$-0.724270\pi$
$677$	3.54325e7	−	3.54325e7i	0.114192	−	0.114192i	0.761894	+	0.647702i	$0.224270\pi$
$678$	−8.40651e7	+	6.71081e8i	−0.269728	+	2.15321i
$679$	−3.33588e8			−1.06562
$680$	−4.58579e8	−	1.79904e8i	−1.45844	−	0.572156i
$681$			5.26591e8i			1.66737i
$682$	−6.31371e7	+	5.04015e8i	−0.199036	+	1.58888i
$683$	2.01276e8	+	2.01276e8i	0.631728	+	0.631728i	0.948501	−	0.316773i	$-0.102599\pi$
$683$	2.01276e8	+	2.01276e8i	0.631728	+	0.631728i	−0.316773	+	0.948501i	$0.602599\pi$
$684$	−4.98067e8	+	2.95962e8i	−1.55639	+	0.924843i
$685$	−3.87136e8	−	3.87136e8i	−1.20446	−	1.20446i
$686$	−2.76490e8	+	2.14931e8i	−0.856460	+	0.665772i
$687$			7.63374e8i			2.35433i
$688$	−6.56392e6	−	2.22458e7i	−0.0201557	−	0.0683096i
$689$	−4.15180e7			−0.126934
$690$	3.14304e8	+	4.04326e8i	0.956761	+	1.23079i
$691$	−2.02083e8	+	2.02083e8i	−0.612485	+	0.612485i	−0.943593	−	0.331108i	$-0.892578\pi$
$691$	−2.02083e8	+	2.02083e8i	−0.612485	+	0.612485i	0.331108	+	0.943593i	$0.392578\pi$
$692$	−5.01030e8	+	2.97723e8i	−1.51198	+	0.898450i
$693$	4.37153e8	−	4.37153e8i	1.31351	−	1.31351i
$694$	−3.45702e8	−	4.33054e7i	−1.03424	−	0.129558i
$695$	−2.55387e8			−0.760754
$696$	2.28621e8	+	5.23803e8i	0.678093	+	1.55360i
$697$		−	4.37991e8i		−	1.29350i
$698$	3.68978e8	+	4.62212e7i	1.08501	+	0.135917i
$699$	−1.33575e8	−	1.33575e8i	−0.391105	−	0.391105i
$700$	4.43036e7	+	1.12766e7i	0.129165	+	0.0328765i
$701$	1.42090e8	+	1.42090e8i	0.412487	+	0.412487i	0.882604	−	0.470117i	$-0.155788\pi$
$701$	1.42090e8	+	1.42090e8i	0.412487	+	0.412487i	−0.470117	+	0.882604i	$0.655788\pi$
$702$	−5.50827e7	−	7.08593e7i	−0.159222	−	0.204826i
$703$		−	1.40630e7i		−	0.0404774i
$704$	4.20094e8	−	1.58383e7i	1.20401	−	0.0453933i
$705$	8.80914e8			2.51400
$706$	3.63067e8	−	2.82232e8i	1.03175	−	0.802033i
$707$	−2.03963e8	+	2.03963e8i	−0.577155	+	0.577155i
$708$	6.49259e7	−	2.55081e8i	0.182944	−	0.718751i
$709$	−4.44653e8	+	4.44653e8i	−1.24762	+	1.24762i	−0.290855	+	0.956767i	$0.593940\pi$
$709$	−4.44653e8	+	4.44653e8i	−1.24762	+	1.24762i	−0.956767	+	0.290855i	$0.906060\pi$
$710$	3.09037e7	−	2.46701e8i	0.0863447	−	0.689279i
$711$	9.82198e7			0.273269
$712$	1.81795e8	−	7.93471e7i	0.503665	−	0.219832i
$713$		−	4.17373e8i		−	1.15148i
$714$	9.44523e7	−	7.54001e8i	0.259488	−	2.07146i
$715$	−6.47651e7	−	6.47651e7i	−0.177183	−	0.177183i
$716$	−8.84019e7	−	1.48769e8i	−0.240837	−	0.405297i
$717$	−4.46178e8	−	4.46178e8i	−1.21046	−	1.21046i
$718$	−7.73588e6	+	6.01352e6i	−0.0208995	+	0.0162463i
$719$		−	4.90096e7i		−	0.131854i	−0.997824	−	0.0659271i	$-0.979000\pi$
$719$		−	4.90096e7i		−	0.131854i	0.997824	−	0.0659271i	$-0.0210005\pi$
$720$	2.04545e8	+	6.93223e8i	0.548014	+	1.85727i
$721$	4.04366e8			1.07887
$722$	2.36016e6	+	3.03615e6i	0.00627090	+	0.00806698i
$723$	−4.02218e8	+	4.02218e8i	−1.06426	+	1.06426i
$724$	1.54900e8	+	2.60677e8i	0.408166	+	0.686891i
$725$	−4.24981e7	+	4.24981e7i	−0.111521	+	0.111521i
$726$	2.87044e8	+	3.59575e7i	0.750133	+	0.0939678i
$727$	4.83441e8			1.25817			0.629086	−	0.777335i	$-0.283429\pi$
$727$	4.83441e8			1.25817			0.629086	+	0.777335i	$0.283429\pi$
$728$	2.33316e7	−	5.94728e7i	0.0604714	−	0.154143i
$729$		−	5.60240e8i		−	1.44608i
$730$	−5.40681e7	−	6.77301e6i	−0.138986	−	0.0174106i
$731$	−2.86677e7	−	2.86677e7i	−0.0733907	−	0.0733907i
$732$	−6.21735e7	+	2.44268e8i	−0.158516	+	0.622777i
$733$	−8.18602e7	−	8.18602e7i	−0.207855	−	0.207855i	0.595500	−	0.803355i	$-0.296954\pi$
$733$	−8.18602e7	−	8.18602e7i	−0.207855	−	0.207855i	−0.803355	+	0.595500i	$0.796954\pi$
$734$	−4.62483e8	−	5.94945e8i	−1.16952	−	1.50449i
$735$		−	1.91038e8i		−	0.481124i
$736$	−3.40886e8	+	5.58179e7i	−0.855019	+	0.140004i
$737$	−4.37049e8			−1.09176
$738$	−5.07371e8	+	3.94407e8i	−1.26228	+	0.981240i
$739$	2.02180e8	−	2.02180e8i	0.500962	−	0.500962i	−0.410775	−	0.911737i	$-0.634742\pi$
$739$	2.02180e8	−	2.02180e8i	0.500962	−	0.500962i	0.911737	+	0.410775i	$0.134742\pi$
$740$	−1.70018e7	−	4.32748e6i	−0.0419566	−	0.0106792i
$741$	−9.36264e7	+	9.36264e7i	−0.230114	+	0.230114i
$742$	−2.85174e7	+	2.27651e8i	−0.0698069	+	0.557260i
$743$	−1.51708e8			−0.369864			−0.184932	−	0.982751i	$-0.559207\pi$
$743$	−1.51708e8			−0.369864			−0.184932	+	0.982751i	$0.559207\pi$
$744$	3.34558e8	−	8.52796e8i	0.812368	−	2.07074i
$745$			6.08523e8i			1.47166i
$746$	2.46501e7	−	1.96779e8i	0.0593748	−	0.473982i
$747$	5.57472e7	+	5.57472e7i	0.133740	+	0.133740i
$748$	6.31719e8	−	3.75381e8i	1.50945	−	0.896949i
$749$	−3.16137e8	−	3.16137e8i	−0.752366	−	0.752366i
$750$	5.05980e8	−	3.93326e8i	1.19936	−	0.932328i
$751$		−	2.62969e8i		−	0.620847i	−0.950598	−	0.310424i	$-0.899529\pi$
$751$		−	2.62969e8i		−	0.620847i	0.950598	−	0.310424i	$-0.100471\pi$
$752$	−2.84069e8	+	5.21874e8i	−0.667991	+	1.22719i
$753$	−1.91718e8			−0.449033
$754$	5.15461e7	+	6.63096e7i	0.120249	+	0.154690i
$755$	−3.34974e8	+	3.34974e8i	−0.778341	+	0.778341i
$756$	−4.26370e8	+	2.53358e8i	−0.986781	+	0.586367i
$757$	4.32593e8	−	4.32593e8i	0.997223	−	0.997223i	−0.00277321	−	0.999996i	$-0.500883\pi$
$757$	4.32593e8	−	4.32593e8i	0.997223	−	0.997223i	0.999996	+	0.00277321i	$0.000882742\pi$
$758$	2.85470e8	+	3.57603e7i	0.655471	+	0.0821096i
$759$	−7.63943e8			−1.74717
$760$	4.34720e8	−	1.89740e8i	0.990304	−	0.432233i
$761$		−	2.89274e8i		−	0.656380i	−0.944612	−	0.328190i	$-0.893561\pi$
$761$		−	2.89274e8i		−	0.656380i	0.944612	−	0.328190i	$-0.106439\pi$
$762$	3.03716e8	+	3.80459e7i	0.686440	+	0.0859891i
$763$	−3.30736e8	−	3.30736e8i	−0.744574	−	0.744574i
$764$	1.64632e8	+	4.19038e7i	0.369176	+	0.0939667i
$765$	8.93344e8	+	8.93344e8i	1.99542	+	1.99542i
$766$	3.39889e8	+	4.37239e8i	0.756226	+	0.972820i
$767$		−	3.86806e7i		−	0.0857249i
$768$	−7.41257e8	−	1.59198e8i	−1.63638	−	0.351442i
$769$	−4.70018e8			−1.03356			−0.516779	−	0.856119i	$-0.672869\pi$
$769$	−4.70018e8			−1.03356			−0.516779	+	0.856119i	$0.672869\pi$
$770$	−3.99604e8	+	3.10634e8i	−0.875302	+	0.680420i
$771$	8.49451e8	−	8.49451e8i	1.85343	−	1.85343i
$772$	1.54061e8	−	6.05274e8i	0.334842	−	1.31553i
$773$	−7.29804e7	+	7.29804e7i	−0.158004	+	0.158004i	−0.781682	−	0.623678i	$-0.785638\pi$
$773$	−7.29804e7	+	7.29804e7i	−0.158004	+	0.158004i	0.623678	+	0.781682i	$0.285638\pi$
$774$	−7.39381e6	+	5.90239e7i	−0.0159458	+	0.127293i
$775$	9.63344e7			0.206955
$776$	2.32721e8	+	5.33196e8i	0.498025	+	1.14104i
$777$		−	2.70633e7i		−	0.0576922i
$778$	−1.09892e8	+	8.77250e8i	−0.233359	+	1.86288i
$779$	2.98212e8	+	2.98212e8i	0.630830	+	0.630830i
$780$	8.43810e7	+	1.42003e8i	0.177812	+	0.299235i
$781$	2.62256e8	+	2.62256e8i	0.550519	+	0.550519i
$782$	−4.76704e8	+	3.70567e8i	−0.996846	+	0.774903i
$783$		−	6.52026e8i		−	1.35825i
$784$	1.13175e8	+	6.16041e7i	0.234857	+	0.127839i
$785$	−6.65565e8			−1.37588
$786$	−6.01237e8	−	7.73440e8i	−1.23816	−	1.59279i
$787$	8.09374e7	−	8.09374e7i	0.166045	−	0.166045i	−0.619194	−	0.785238i	$-0.712540\pi$
$787$	8.09374e7	−	8.09374e7i	0.166045	−	0.166045i	0.785238	+	0.619194i	$0.212540\pi$
$788$	1.42850e8	+	2.40398e8i	0.291945	+	0.491306i
$789$	−3.79661e8	+	3.79661e8i	−0.772975	+	0.772975i
$790$	−7.97885e7	−	9.99495e6i	−0.161830	−	0.0202721i
$791$	5.49230e8			1.10975
$792$	−1.00370e9	−	3.93759e8i	−2.02036	−	0.792602i
$793$			3.70408e7i			0.0742781i
$794$	5.87727e8	+	7.36234e7i	1.17412	+	0.147080i
$795$	−4.19463e8	−	4.19463e8i	−0.834818	−	0.834818i
$796$	3.66525e7	−	1.44000e8i	0.0726715	−	0.285512i
$797$	−2.10772e8	−	2.10772e8i	−0.416331	−	0.416331i	0.467606	−	0.883937i	$-0.345117\pi$
$797$	−2.10772e8	−	2.10772e8i	−0.416331	−	0.416331i	−0.883937	+	0.467606i	$0.845117\pi$
$798$	4.49062e8	+	5.77681e8i	0.883686	+	1.13679i
$799$			1.03860e9i			2.03615i
$800$	−1.28834e7	−	7.86803e7i	−0.0251629	−	0.153673i
$801$	−5.08723e8			−0.989882
$802$	−1.63790e7	+	1.27323e7i	−0.0317515	+	0.0246822i
$803$	5.74773e7	−	5.74773e7i	0.111007	−	0.111007i
$804$	7.63843e8	+	1.94421e8i	1.46973	+	0.374090i
$805$	2.94073e8	−	2.94073e8i	0.563725	−	0.563725i
$806$	1.67330e7	−	1.33577e8i	0.0319572	−	0.255110i
$807$	9.85299e8			1.87477
$808$	4.68297e8	+	1.83716e8i	0.887743	+	0.348268i
$809$			7.79710e8i			1.47261i	0.676650	+	0.736304i	$0.263431\pi$
$809$			7.79710e8i			1.47261i	−0.676650	+	0.736304i	$0.736569\pi$
$810$	3.14790e7	−	2.51293e8i	0.0592332	−	0.472851i
$811$	1.31065e7	+	1.31065e7i	0.0245710	+	0.0245710i	0.719286	−	0.694715i	$-0.244469\pi$
$811$	1.31065e7	+	1.31065e7i	0.0245710	+	0.0245710i	−0.694715	+	0.719286i	$0.744469\pi$
$812$	3.98994e8	−	2.37091e8i	0.745244	−	0.442840i
$813$	9.15328e8	+	9.15328e8i	1.70335	+	1.70335i
$814$	2.06622e7	−	1.60618e7i	0.0383092	−	0.0297798i
$815$			3.90826e8i			0.721956i
$816$	−1.27106e9	+	3.75044e8i	−2.33936	+	0.690259i
$817$	3.90376e7			0.0715841
$818$	−6.12879e8	−	7.88417e8i	−1.11973	−	1.44044i
$819$	−1.15857e8	+	1.15857e8i	−0.210897	+	0.210897i
$820$	4.52296e8	−	2.68764e8i	0.820316	−	0.487450i
$821$	−2.22336e7	+	2.22336e7i	−0.0401772	+	0.0401772i	−0.726910	−	0.686733i	$-0.759044\pi$
$821$	−2.22336e7	+	2.22336e7i	−0.0401772	+	0.0401772i	0.686733	+	0.726910i	$0.259044\pi$
$822$	−1.46148e9	−	1.83077e8i	−2.63134	−	0.329623i
$823$	−3.32061e8			−0.595687			−0.297844	−	0.954615i	$-0.596267\pi$
$823$	−3.32061e8			−0.595687			−0.297844	+	0.954615i	$0.596267\pi$
$824$	−2.82098e8	−	6.46324e8i	−0.504217	−	1.15523i
$825$		−	1.76326e8i		−	0.314019i
$826$	−2.12093e8	−	2.65685e7i	−0.376345	−	0.0471441i
$827$	−2.53857e8	−	2.53857e8i	−0.448821	−	0.448821i	0.446142	−	0.894962i	$-0.352798\pi$
$827$	−2.53857e8	−	2.53857e8i	−0.448821	−	0.448821i	−0.894962	+	0.446142i	$0.852798\pi$
$828$	8.58535e8	+	2.18523e8i	1.51240	+	0.384952i
$829$	5.10963e8	+	5.10963e8i	0.896863	+	0.896863i	0.995157	−	0.0982941i	$-0.0313386\pi$
$829$	5.10963e8	+	5.10963e8i	0.896863	+	0.896863i	−0.0982941	+	0.995157i	$0.531339\pi$
$830$	−3.96131e7	−	5.09589e7i	−0.0692795	−	0.0891221i
$831$		−	8.69237e8i		−	1.51473i
$832$	−1.11336e8	+	4.19758e6i	−0.193315	+	0.00728834i
$833$	2.25235e8			0.389674
$834$	−5.42442e8	+	4.21669e8i	−0.935094	+	0.726899i
$835$	−2.16367e8	+	2.16367e8i	−0.371647	+	0.371647i
$836$	−1.74531e8	+	6.85697e8i	−0.298712	+	1.17358i
$837$	−7.39004e8	+	7.39004e8i	−1.26029	+	1.26029i
$838$	−6.56902e6	+	5.24397e7i	−0.0111627	+	0.0891103i
$839$	9.58003e8			1.62211			0.811056	−	0.584968i	$-0.198893\pi$
$839$	9.58003e8			1.62211			0.811056	+	0.584968i	$0.198893\pi$
$840$	8.36586e8	−	3.65140e8i	1.41147	−	0.616058i
$841$			1.53380e7i			0.0257859i
$842$	8.01009e7	−	6.39435e8i	0.134184	−	1.07117i
$843$	−1.23203e8	−	1.23203e8i	−0.205654	−	0.205654i
$844$	−3.11153e8	−	5.23630e8i	−0.517542	−	0.870958i
$845$	−4.41485e8	−	4.41485e8i	−0.731722	−	0.731722i
$846$	1.20313e9	−	9.35254e8i	1.98701	−	1.54461i
$847$		−	2.34924e8i		−	0.386614i
$848$	3.83764e8	−	1.13235e8i	0.629328	−	0.185692i
$849$	1.40200e9			2.29100
$850$	−8.55311e7	−	1.10028e8i	−0.139273	−	0.179163i
$851$	−1.52055e7	+	1.52055e7i	−0.0246724	+	0.0246724i
$852$	−3.41688e8	−	5.75017e8i	−0.552473	−	0.929741i
$853$	−4.48995e7	+	4.48995e7i	−0.0723426	+	0.0723426i	−0.742352	−	0.670010i	$-0.766290\pi$
$853$	−4.48995e7	+	4.48995e7i	−0.0723426	+	0.0723426i	0.670010	+	0.742352i	$0.266290\pi$
$854$	2.03102e8	+	2.54422e7i	0.326092	+	0.0408490i
$855$	−1.21649e9			−1.94630
$856$	−2.84755e8	+	7.25848e8i	−0.453995	+	1.15724i
$857$		−	6.31563e8i		−	1.00340i	−0.865041	−	0.501700i	$-0.832708\pi$
$857$		−	6.31563e8i		−	1.00340i	0.865041	−	0.501700i	$-0.167292\pi$
$858$	−2.44495e8	−	3.06274e7i	−0.387086	−	0.0484895i
$859$	7.22836e8	+	7.22836e8i	1.14041	+	1.14041i	0.988376	+	0.152032i	$0.0485816\pi$
$859$	7.22836e8	+	7.22836e8i	1.14041	+	1.14041i	0.152032	+	0.988376i	$0.451418\pi$
$860$	1.20127e7	−	4.71954e7i	0.0188862	−	0.0742001i
$861$	5.73886e8	+	5.73886e8i	0.899117	+	0.899117i
$862$	−7.01744e8	−	9.02735e8i	−1.09561	−	1.40941i
$863$		−	2.01070e8i		−	0.312834i	−0.987691	−	0.156417i	$-0.950006\pi$
$863$		−	2.01070e8i		−	0.312834i	0.987691	−	0.156417i	$-0.0499945\pi$
$864$	7.02407e8	+	5.04744e8i	1.08905	+	0.782583i
$865$	−1.22373e9			−1.89076
$866$	−6.73228e6	+	5.23336e6i	−0.0103659	+	0.00805800i
$867$	−8.66703e8	+	8.66703e8i	−1.32988	+	1.32988i
$868$	−7.20937e8	−	1.83500e8i	−1.10240	−	0.280594i
$869$	8.48194e7	−	8.48194e7i	0.129252	−	0.129252i
$870$	−1.49159e8	+	1.19072e9i	−0.226512	+	1.80822i
$871$	1.15829e8			0.175293
$872$	−2.97906e8	+	7.59368e8i	−0.449293	+	1.14526i
$873$		−	1.49206e9i		−	2.24256i
$874$	7.22641e7	−	5.76876e8i	0.108240	−	0.864068i
$875$	−3.68008e8	−	3.68008e8i	−0.549329	−	0.549329i
$876$	−1.26023e8	+	7.48859e7i	−0.187473	+	0.111401i
$877$	−3.29027e8	−	3.29027e8i	−0.487790	−	0.487790i	0.419818	−	0.907608i	$-0.362094\pi$
$877$	−3.29027e8	−	3.29027e8i	−0.487790	−	0.487790i	−0.907608	+	0.419818i	$0.862094\pi$
$878$	−5.03521e8	+	3.91414e8i	−0.743933	+	0.578299i
$879$		−	8.35591e8i		−	1.23035i
$880$	7.75283e8	+	4.22006e8i	1.13766	+	0.619257i
$881$	4.56021e8			0.666895			0.333447	−	0.942769i	$-0.391788\pi$
$881$	4.56021e8			0.666895			0.333447	+	0.942769i	$0.391788\pi$
$882$	−2.02822e8	−	2.60914e8i	−0.295604	−	0.380269i
$883$	−8.64281e8	+	8.64281e8i	−1.25537	+	1.25537i	−0.302095	+	0.953278i	$0.597686\pi$
$883$	−8.64281e8	+	8.64281e8i	−1.25537	+	1.25537i	−0.953278	+	0.302095i	$0.902314\pi$
$884$	−1.67422e8	+	9.94859e7i	−0.242357	+	0.144014i
$885$	3.90796e8	−	3.90796e8i	0.563794	−	0.563794i
$886$	5.61053e8	+	7.02820e7i	0.806682	+	0.101052i
$887$	1.02674e9			1.47126			0.735629	−	0.677385i	$-0.236887\pi$
$887$	1.02674e9			1.47126			0.735629	+	0.677385i	$0.236887\pi$
$888$	−4.32570e7	+	1.88802e7i	−0.0617757	+	0.0269629i
$889$		−	2.48569e8i		−	0.353787i
$890$	4.13259e8	+	5.17682e7i	0.586208	+	0.0734332i
$891$	2.67137e8	+	2.67137e8i	0.377661	+	0.377661i
$892$	3.97360e8	+	1.01140e8i	0.559873	+	0.142505i
$893$	−7.07147e8	−	7.07147e8i	−0.993014	−	0.993014i
$894$	1.00473e9	+	1.29250e9i	1.40617	+	1.80892i
$895$		−	3.63357e8i		−	0.506833i
$896$	−5.34572e7	+	6.13360e8i	−0.0743160	+	0.852691i
$897$	2.02465e8			0.280526
$898$	3.90976e8	−	3.03927e8i	0.539909	−	0.419701i
$899$	6.91555e8	−	6.91555e8i	0.951805	−	0.951805i
$900$	−5.04376e7	+	1.98159e8i	−0.0691874	+	0.271824i
$901$	4.94550e8	−	4.94550e8i	0.676139	−	0.676139i
$902$	−9.75520e7	+	7.78746e8i	−0.132928	+	1.06115i
$903$	7.51249e7			0.102028
$904$	−3.83159e8	−	8.77870e8i	−0.518650	−	1.18830i
$905$			6.36685e8i			0.858971i
$906$	−1.58409e8	+	1.26456e9i	−0.213008	+	1.70041i
$907$	−5.64718e8	−	5.64718e8i	−0.756850	−	0.756850i	0.218898	−	0.975748i	$-0.429754\pi$
$907$	−5.64718e8	−	5.64718e8i	−0.756850	−	0.756850i	−0.975748	+	0.218898i	$0.929754\pi$
$908$	−3.80975e8	−	6.41132e8i	−0.508907	−	0.856427i
$909$	−9.12275e8	−	9.12275e8i	−1.21460	−	1.21460i
$910$	1.05906e8	−	8.23262e7i	0.140538	−	0.109248i
$911$			1.12404e8i			0.148671i	0.997233	+	0.0743356i	$0.0236836\pi$
$911$			1.12404e8i			0.148671i	−0.997233	+	0.0743356i	$0.976316\pi$
$912$	6.10065e8	−	1.12077e9i	0.804251	−	1.47752i
$913$	9.62829e7			0.126513
$914$	7.82832e8	+	1.00705e9i	1.02525	+	1.31890i
$915$	−3.74229e8	+	3.74229e8i	−0.488511	+	0.488511i
$916$	−5.52282e8	−	9.29420e8i	−0.718578	−	1.20928i
$917$	−5.62536e8	+	5.62536e8i	−0.729528	+	0.729528i
$918$	1.50019e9	+	1.87925e8i	1.93917	+	0.242917i
$919$	−1.03635e9			−1.33524			−0.667620	−	0.744502i	$-0.732687\pi$
$919$	−1.03635e9			−1.33524			−0.667620	+	0.744502i	$0.732687\pi$
$920$	−6.75190e8	−	2.64882e8i	−0.867087	−	0.340164i
$921$			7.94931e8i			1.01754i
$922$	4.52507e8	+	5.66848e7i	0.577342	+	0.0723225i
$923$	−6.95047e7	−	6.95047e7i	−0.0883913	−	0.0883913i
$924$	−3.35872e8	+	1.31957e9i	−0.425753	+	1.67270i
$925$	−3.50960e6	−	3.50960e6i	−0.00443437	−	0.00443437i
$926$	−7.33127e8	−	9.43105e8i	−0.923307	−	1.18776i
$927$			1.80863e9i			2.27044i
$928$	−6.57308e8	−	4.72336e8i	−0.822480	−	0.591027i
$929$	5.60817e8			0.699478			0.349739	−	0.936847i	$-0.386270\pi$
$929$	5.60817e8			0.699478			0.349739	+	0.936847i	$0.386270\pi$
$930$	1.51861e9	−	1.18050e9i	1.88798	−	1.46763i
$931$	−1.53354e8	+	1.53354e8i	−0.190041	+	0.190041i
$932$	2.59267e8	+	6.59914e7i	0.320258	+	0.0815154i
$933$	−7.10729e8	+	7.10729e8i	−0.875103	+	0.875103i
$934$	1.28868e7	−	1.02874e8i	0.0158163	−	0.126260i
$935$	1.54293e9			1.88760
$936$	2.66007e8	+	1.04357e8i	0.324389	+	0.127260i
$937$			1.16903e9i			1.42104i	0.703675	+	0.710522i	$0.251541\pi$
$937$			1.16903e9i			1.42104i	−0.703675	+	0.710522i	$0.748459\pi$
$938$	7.95597e7	−	6.35115e8i	0.0964017	−	0.769563i
$939$	7.68853e8	+	7.68853e8i	0.928638	+	0.928638i
$940$	−1.07253e9	+	6.37318e8i	−1.29129	+	0.767314i
$941$	7.78065e8	+	7.78065e8i	0.933785	+	0.933785i	0.997940	−	0.0641548i	$-0.0204351\pi$
$941$	7.78065e8	+	7.78065e8i	0.933785	+	0.933785i	−0.0641548	+	0.997940i	$0.520435\pi$
$942$	−1.41366e9	+	1.09891e9i	−1.69119	+	1.31465i
$943$		−	6.44876e8i		−	0.769026i
$944$	1.05496e8	+	3.57537e8i	0.125407	+	0.425016i
$945$	−1.04138e9			−1.23399
$946$	4.45860e7	+	5.73561e7i	0.0526654	+	0.0677496i
$947$	6.87296e8	−	6.87296e8i	0.809271	−	0.809271i	−0.175253	−	0.984524i	$-0.556074\pi$
$947$	6.87296e8	−	6.87296e8i	0.809271	−	0.809271i	0.984524	+	0.175253i	$0.0560742\pi$
$948$	−1.85973e8	+	1.10509e8i	−0.218286	+	0.129710i
$949$	−1.52330e7	+	1.52330e7i	−0.0178232	+	0.0178232i
$950$	1.33149e8	+	1.66794e7i	0.155299	+	0.0194540i
$951$	−1.44442e9			−1.67939
$952$	4.30503e8	+	9.86342e8i	0.498960	+	1.14319i
$953$		−	3.06826e8i		−	0.354498i	−0.984166	−	0.177249i	$-0.943280\pi$
$953$		−	3.06826e8i		−	0.354498i	0.984166	−	0.177249i	$-0.0567197\pi$
$954$	−1.01823e9	−	1.27552e8i	−1.17273	−	0.146906i
$955$	2.52224e8	+	2.52224e8i	0.289585	+	0.289585i
$956$	8.66027e8	+	2.20430e8i	0.991192	+	0.252289i
$957$	−1.26579e9	−	1.26579e9i	−1.44420	−	1.44420i
$958$	1.66987e8	+	2.14815e8i	0.189927	+	0.244325i
$959$			1.19611e9i			1.35617i
$960$	−1.16726e9	−	1.08244e9i	−1.31933	−	1.22346i
$961$	−6.80111e8			−0.766319
$962$	−5.47602e6	+	4.25681e6i	−0.00615092	+	0.00478144i
$963$	1.41400e9	−	1.41400e9i	1.58333	−	1.58333i
$964$	1.98712e8	−	7.80701e8i	0.221816	−	0.871472i
$965$	9.27309e8	−	9.27309e8i	1.03191	−	1.03191i
$966$	1.39067e8	−	1.11015e9i	0.154274	−	1.23155i
$967$	−9.01285e8			−0.996742			−0.498371	−	0.866964i	$-0.666068\pi$
$967$	−9.01285e8			−0.996742			−0.498371	+	0.866964i	$0.666068\pi$
$968$	−3.75495e8	+	1.63890e8i	−0.413978	+	0.180687i
$969$		−	2.23050e9i		−	2.45150i
$970$	−1.51834e8	+	1.21207e9i	−0.166361	+	1.32804i
$971$	1.11924e9	+	1.11924e9i	1.22255	+	1.22255i	0.966723	+	0.255827i	$0.0823477\pi$
$971$	1.11924e9	+	1.11924e9i	1.22255	+	1.22255i	0.255827	+	0.966723i	$0.417652\pi$
$972$	2.81072e8	+	4.73009e8i	0.306069	+	0.515075i
$973$	3.94527e8	+	3.94527e8i	0.428290	+	0.428290i
$974$	1.39140e9	−	1.08161e9i	1.50583	−	1.17056i
$975$			4.67312e7i			0.0504188i
$976$	−1.01024e8	−	3.42380e8i	−0.108661	−	0.368264i
$977$	1.17973e8			0.126502			0.0632511	−	0.997998i	$-0.479853\pi$
$977$	1.17973e8			0.126502			0.0632511	+	0.997998i	$0.479853\pi$
$978$	6.45293e8	+	8.30115e8i	0.689827	+	0.887404i
$979$	−4.39316e8	+	4.39316e8i	−0.468198	+	0.468198i
$980$	1.38211e8	+	2.32591e8i	0.146847	+	0.247124i
$981$	1.47930e9	−	1.47930e9i	1.56693	−	1.56693i
$982$	−6.15304e8	−	7.70780e7i	−0.649763	−	0.0813946i
$983$	−1.50005e9			−1.57923			−0.789613	−	0.613605i	$-0.789719\pi$
$983$	−1.50005e9			−1.57923			−0.789613	+	0.613605i	$0.789719\pi$
$984$	5.16920e8	−	1.31764e9i	0.542548	−	1.38297i
$985$			5.87154e8i			0.614389i
$986$	−1.40386e9	−	1.75859e8i	−1.46452	−	0.183457i
$987$	−1.36085e9	−	1.36085e9i	−1.41534	−	1.41534i
$988$	4.62553e7	−	1.81728e8i	0.0479612	−	0.188430i
$989$	−4.22089e7	−	4.22089e7i	−0.0436331	−	0.0436331i
$990$	−1.38939e9	−	1.78733e9i	−1.43192	−	1.84204i
$991$		−	4.16762e8i		−	0.428221i	−0.976809	−	0.214110i	$-0.931315\pi$
$991$		−	4.16762e8i		−	0.428221i	0.976809	−	0.214110i	$-0.0686852\pi$
$992$	2.09647e8	+	1.28034e9i	0.214760	+	1.31156i
$993$	2.24625e9			2.29409
$994$	−4.28849e8	+	3.33367e8i	−0.436661	+	0.339441i
$995$	2.20615e8	−	2.20615e8i	0.223958	−	0.223958i
$996$	−1.68276e8	−	4.28315e7i	−0.170312	−	0.0433496i
$997$	9.47827e8	−	9.47827e8i	0.956409	−	0.956409i	−0.0426800	−	0.999089i	$-0.513590\pi$
$997$	9.47827e8	−	9.47827e8i	0.956409	−	0.956409i	0.999089	+	0.0426800i	$0.0135896\pi$
$998$	1.65530e8	−	1.32140e9i	0.166527	−	1.32936i
$999$	5.38460e7			0.0540078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.3.3	✓	22
4.3	odd	2		64.7.f.a.47.10		22
8.3	odd	2		128.7.f.a.95.2		22
8.5	even	2		128.7.f.b.95.10		22
16.3	odd	4		128.7.f.b.31.10		22
16.5	even	4		64.7.f.a.15.10		22
16.11	odd	4	inner	16.7.f.a.11.3	yes	22
16.13	even	4		128.7.f.a.31.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.3	✓	22	1.1	even	1	trivial
16.7.f.a.11.3	yes	22	16.11	odd	4	inner
64.7.f.a.15.10		22	16.5	even	4
64.7.f.a.47.10		22	4.3	odd	2
128.7.f.a.31.2		22	16.13	even	4
128.7.f.a.95.2		22	8.3	odd	2
128.7.f.b.31.10		22	16.3	odd	4
128.7.f.b.95.10		22	8.5	even	2

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)

\(f(q)\)	\(=\)	\(q+(-6.31611 + 4.90986i) q^{2} +(-31.9540 + 31.9540i) q^{3} +(15.7866 - 62.0224i) q^{4} +(95.0213 - 95.0213i) q^{5} +(44.9356 - 358.715i) q^{6} -293.582 q^{7} +(204.811 + 469.251i) q^{8} -1313.12i q^{9} +O(q^{10})\)	\(q+(-6.31611 + 4.90986i) q^{2} +(-31.9540 + 31.9540i) q^{3} +(15.7866 - 62.0224i) q^{4} +(95.0213 - 95.0213i) q^{5} +(44.9356 - 358.715i) q^{6} -293.582 q^{7} +(204.811 + 469.251i) q^{8} -1313.12i q^{9} +(-133.624 + 1066.71i) q^{10} +(-1133.97 - 1133.97i) q^{11} +(1477.42 + 2486.31i) q^{12} +(300.531 + 300.531i) q^{13} +(1854.30 - 1441.44i) q^{14} +6072.63i q^{15} +(-3597.57 - 1958.25i) q^{16} -7159.68 q^{17} +(6447.23 + 8293.81i) q^{18} +(4874.76 - 4874.76i) q^{19} +(-4393.39 - 7393.52i) q^{20} +(9381.12 - 9381.12i) q^{21} +(12729.9 + 1594.65i) q^{22} -10541.6 q^{23} +(-21539.0 - 8449.90i) q^{24} -2433.11i q^{25} +(-3373.75 - 422.624i) q^{26} +(18665.0 + 18665.0i) q^{27} +(-4634.66 + 18208.6i) q^{28} +(-17466.6 - 17466.6i) q^{29} +(-29815.7 - 38355.4i) q^{30} +39593.1i q^{31} +(32337.4 - 5295.03i) q^{32} +72469.6 q^{33} +(45221.3 - 35153.0i) q^{34} +(-27896.5 + 27896.5i) q^{35} +(-81442.9 - 20729.7i) q^{36} +(1442.43 - 1442.43i) q^{37} +(-6855.17 + 54723.9i) q^{38} -19206.4 q^{39} +(64050.3 + 25127.4i) q^{40} +61174.6i q^{41} +(-13192.3 + 105312. i) q^{42} +(4004.05 + 4004.05i) q^{43} +(-88232.9 + 52429.9i) q^{44} +(-124774. - 124774. i) q^{45} +(66581.7 - 51757.6i) q^{46} -145063. i q^{47} +(177531. - 52382.9i) q^{48} -31458.8 q^{49} +(11946.2 + 15367.8i) q^{50} +(228781. - 228781. i) q^{51} +(23384.0 - 13895.3i) q^{52} +(-69074.3 + 69074.3i) q^{53} +(-209532. - 26247.7i) q^{54} -215502. q^{55} +(-60128.9 - 137763. i) q^{56} +311536. i q^{57} +(196079. + 24562.5i) q^{58} +(-64353.7 - 64353.7i) q^{59} +(376639. + 95866.2i) q^{60} +(61625.6 + 61625.6i) q^{61} +(-194397. - 250075. i) q^{62} +385508. i q^{63} +(-178249. + 192216. i) q^{64} +57113.7 q^{65} +(-457726. + 355815. i) q^{66} +(192708. - 192708. i) q^{67} +(-113027. + 444061. i) q^{68} +(336845. - 336845. i) q^{69} +(39229.7 - 313166. i) q^{70} -231273. q^{71} +(616182. - 268942. i) q^{72} +50686.9i q^{73} +(-2028.43 + 16192.7i) q^{74} +(77747.6 + 77747.6i) q^{75} +(-225389. - 379300. i) q^{76} +(332912. + 332912. i) q^{77} +(121310. - 94300.5i) q^{78} +74798.9i q^{79} +(-527921. + 155770. i) q^{80} -235578. q^{81} +(-300359. - 386386. i) q^{82} +(-42454.0 + 42454.0i) q^{83} +(-433744. - 729936. i) q^{84} +(-680322. + 680322. i) q^{85} +(-44949.4 - 5630.72i) q^{86} +1.11625e6 q^{87} +(299865. - 764364. i) q^{88} -387415. i q^{89} +(1.40071e6 + 175465. i) q^{90} +(-88230.4 - 88230.4i) q^{91} +(-166415. + 653813. i) q^{92} +(-1.26516e6 - 1.26516e6i) q^{93} +(712239. + 916234. i) q^{94} -926413. i q^{95} +(-864111. + 1.20251e6i) q^{96} +1.13627e6 q^{97} +(198698. - 154458. i) q^{98} +(-1.48903e6 + 1.48903e6i) 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

Properties

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