LMFDB - Embedded newform 16.7.f.a.11.3

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			11.3
Character	$\chi$	$=$	16.11
Dual form			16.7.f.a.3.3

$q$-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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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	−0.978836	−	0.204647i	$-0.934396\pi$
$3$	−31.9540	−	31.9540i	−1.18348	−	1.18348i	−0.204647	−	0.978836i	$-0.565604\pi$
$4$	15.7866	+	62.0224i	0.246666	+	0.969101i
$5$	95.0213	+	95.0213i	0.760171	+	0.760171i	0.976353	−	0.216182i	$-0.0693606\pi$
$5$	95.0213	+	95.0213i	0.760171	+	0.760171i	−0.216182	+	0.976353i	$0.569361\pi$
$6$	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	−0.990375	−	0.138409i	$-0.955801\pi$
$11$	−1133.97	+	1133.97i	−0.851966	+	0.851966i	0.138409	+	0.990375i	$0.455801\pi$
$12$	1477.42	−	2486.31i	0.854989	−	1.43884i
$13$	300.531	−	300.531i	0.136792	−	0.136792i	−0.635395	−	0.772187i	$-0.719163\pi$
$13$	300.531	−	300.531i	0.136792	−	0.136792i	0.772187	+	0.635395i	$0.219163\pi$
$14$	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	0.966684	−	0.255974i	$-0.0823960\pi$
$19$	4874.76	+	4874.76i	0.710710	+	0.710710i	−0.255974	+	0.966684i	$0.582396\pi$
$20$	−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	−0.967818	−	0.251652i	$-0.919026\pi$
$29$	−17466.6	+	17466.6i	−0.716165	+	0.716165i	0.251652	+	0.967818i	$0.419026\pi$
$30$	−29815.7	+	38355.4i	−1.10429	+	1.42057i
$31$		−	39593.1i		−	1.32903i	−0.747275	−	0.664515i	$-0.768638\pi$
$31$		−	39593.1i		−	1.32903i	0.747275	−	0.664515i	$-0.231362\pi$
$32$	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	0.721202	−	0.692725i	$-0.243590\pi$
$37$	1442.43	+	1442.43i	0.0284768	+	0.0284768i	−0.692725	+	0.721202i	$0.743590\pi$
$38$	−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	$-0.853629\pi$
$41$		−	61174.6i		−	0.887605i	0.896125	−	0.443803i	$-0.146371\pi$
$42$	−13192.3	−	105312.i	−0.178062	−	1.42145i
$43$	4004.05	−	4004.05i	0.0503610	−	0.0503610i	−0.681478	−	0.731839i	$-0.738662\pi$
$43$	4004.05	−	4004.05i	0.0503610	−	0.0503610i	0.731839	+	0.681478i	$0.238662\pi$
$44$	−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	$0.246196\pi$
$47$			145063.i			1.39721i	−0.715506	+	0.698607i	$0.753804\pi$
$48$	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	0.435985	−	0.899954i	$-0.356400\pi$
$53$	−69074.3	−	69074.3i	−0.463969	−	0.463969i	−0.899954	+	0.435985i	$0.856400\pi$
$54$	−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	−0.846203	−	0.532861i	$-0.821117\pi$
$59$	−64353.7	+	64353.7i	−0.313341	+	0.313341i	0.532861	+	0.846203i	$0.321117\pi$
$60$	376639.	−	95866.2i	1.74370	−	0.443825i
$61$	61625.6	−	61625.6i	0.271501	−	0.271501i	−0.558203	−	0.829704i	$-0.688509\pi$
$61$	61625.6	−	61625.6i	0.271501	−	0.271501i	0.829704	+	0.558203i	$0.188509\pi$
$62$	−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	0.950735	−	0.310005i	$-0.100331\pi$
$67$	192708.	+	192708.i	0.640731	+	0.640731i	−0.310005	+	0.950735i	$0.600331\pi$
$68$	−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	$-0.979248\pi$
$73$		−	50686.9i		−	0.130295i	0.997876	−	0.0651474i	$-0.0207518\pi$
$74$	−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	$-0.975831\pi$
$79$		−	74798.9i		−	0.151710i	0.997119	−	0.0758549i	$-0.0241686\pi$
$80$	−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	0.669008	−	0.743256i	$-0.266719\pi$
$83$	−42454.0	−	42454.0i	−0.0742480	−	0.0742480i	−0.743256	+	0.669008i	$0.766719\pi$
$84$	−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	$0.0886033\pi$
$89$			387415.i			0.549550i	−0.961509	+	0.274775i	$0.911397\pi$
$90$	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	0.958706	−	0.284399i	$-0.0917941\pi$
$101$	694739.	+	694739.i	0.674307	+	0.674307i	−0.284399	+	0.958706i	$0.591794\pi$
$102$	−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	−0.114421	−	0.993432i	$-0.536501\pi$
$107$	1.07683e6	−	1.07683e6i	0.879011	−	0.879011i	0.993432	+	0.114421i	$0.0365013\pi$
$108$	1.45230e6	+	862991.i	1.15289	+	0.685070i
$109$	1.12656e6	−	1.12656e6i	0.869908	−	0.869908i	−0.122554	−	0.992462i	$-0.539109\pi$
$109$	1.12656e6	−	1.12656e6i	0.869908	−	0.869908i	0.992462	+	0.122554i	$0.0391086\pi$
$110$	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	$-0.933737\pi$
$127$		−	846677.i		−	0.413339i	0.978411	−	0.206670i	$-0.0662626\pi$
$128$	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	0.990420	−	0.138090i	$-0.0440964\pi$
$131$	1.91611e6	+	1.91611e6i	0.852329	+	0.852329i	−0.138090	+	0.990420i	$0.544096\pi$
$132$	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	$0.291080\pi$
$137$			4.07420e6i			1.58446i	−0.610224	+	0.792229i	$0.708920\pi$
$138$	−473691.	−	3.78142e6i	−0.180243	−	1.43886i
$139$	−1.34384e6	+	1.34384e6i	−0.500384	+	0.500384i	−0.911557	−	0.411173i	$-0.865119\pi$
$139$	−1.34384e6	+	1.34384e6i	−0.500384	+	0.500384i	0.411173	+	0.911557i	$0.365119\pi$
$140$	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	0.0315212	−	0.999503i	$-0.489965\pi$
$149$	−3.20203e6	−	3.20203e6i	−0.967982	−	0.967982i	−0.999503	+	0.0315212i	$0.989965\pi$
$150$	−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	−0.995862	−	0.0908791i	$-0.971032\pi$
$157$	−3.50219e6	+	3.50219e6i	−0.904983	+	0.904983i	0.0908791	+	0.995862i	$0.471032\pi$
$158$	−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	0.428620	−	0.903485i	$-0.359000\pi$
$163$	−2.05652e6	−	2.05652e6i	−0.474865	−	0.474865i	−0.903485	+	0.428620i	$0.859000\pi$
$164$	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	−0.285162	+	0.958479i	$0.592047\pi$
$173$	−6.43922e6	+	6.43922e6i	−1.24364	+	1.24364i	−0.958479	+	0.285162i	$0.907953\pi$
$174$	−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	0.853864	−	0.520496i	$-0.174253\pi$
$179$	1.91198e6	+	1.91198e6i	0.333368	+	0.333368i	−0.520496	+	0.853864i	$0.674253\pi$
$180$	−9.70857e6	−	5.76905e6i	−1.66471	−	0.989206i
$181$	−3.35022e6	−	3.35022e6i	−0.564986	−	0.564986i	0.365734	−	0.930720i	$-0.380818\pi$
$181$	−3.35022e6	−	3.35022e6i	−0.564986	−	0.564986i	−0.930720	+	0.365734i	$0.880818\pi$
$182$	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	$-0.938998\pi$
$191$		−	2.65439e6i		−	0.380948i	0.981692	−	0.190474i	$-0.0610024\pi$
$192$	−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	0.475567	−	0.879679i	$-0.342243\pi$
$197$	−3.08959e6	−	3.08959e6i	−0.404112	−	0.404112i	−0.879679	+	0.475567i	$0.842243\pi$
$198$	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	0.967863	−	0.251477i	$-0.0809163\pi$
$211$	6.72968e6	+	6.72968e6i	0.716386	+	0.716386i	−0.251477	+	0.967863i	$0.580916\pi$
$212$	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	$-0.906723\pi$
$223$		−	6.40671e6i		−	0.577724i	0.957371	−	0.288862i	$-0.0932769\pi$
$224$	−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	0.965359	−	0.260925i	$-0.0840277\pi$
$227$	8.23982e6	+	8.23982e6i	0.704434	+	0.704434i	−0.260925	+	0.965359i	$0.584028\pi$
$228$	1.93223e7	−	4.91810e6i	1.63025	−	0.414947i
$229$	1.19449e7	+	1.19449e7i	0.994662	+	0.994662i	0.999986	−	0.00532420i	$-0.00169475\pi$
$229$	1.19449e7	+	1.19449e7i	0.994662	+	0.994662i	−0.00532420	+	0.999986i	$0.501695\pi$
$230$	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	$-0.947162\pi$
$233$		−	4.18022e6i		−	0.330469i	0.986254	−	0.165235i	$-0.0528382\pi$
$234$	−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	$-0.829128\pi$
$239$		−	1.39631e7i		−	1.02280i	0.859344	−	0.511398i	$-0.170872\pi$
$240$	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	−0.605862	−	0.795570i	$-0.707171\pi$
$251$	2.99991e6	−	2.99991e6i	0.189709	−	0.189709i	0.795570	+	0.605862i	$0.207171\pi$
$252$	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	−0.981828	−	0.189773i	$-0.939225\pi$
$269$	−1.54174e7	+	1.54174e7i	−0.792055	+	0.792055i	0.189773	+	0.981828i	$0.439225\pi$
$270$	−2.24041e7	−	1.74160e7i	−1.13825	−	0.884822i
$271$			2.86452e7i			1.43927i	0.694351	+	0.719637i	$0.255692\pi$
$271$			2.86452e7i			1.43927i	−0.694351	+	0.719637i	$0.744308\pi$
$272$	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	0.310596	−	0.950542i	$-0.399471\pi$
$277$	−1.36014e7	−	1.36014e7i	−0.639946	−	0.639946i	−0.950542	+	0.310596i	$0.899471\pi$
$278$	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	$-0.972309\pi$
$281$		−	3.85563e6i		−	0.173771i	0.996218	−	0.0868853i	$-0.0276914\pi$
$282$	−5.20363e7	+	6.51849e6i	−2.32038	+	0.290670i
$283$	−2.19377e7	+	2.19377e7i	−0.967905	+	0.967905i	−0.999501	−	0.0315958i	$-0.989941\pi$
$283$	−2.19377e7	+	2.19377e7i	−0.967905	+	0.967905i	0.0315958	+	0.999501i	$0.489941\pi$
$284$	−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	0.397712	−	0.917510i	$-0.369804\pi$
$293$	−1.30749e7	−	1.30749e7i	−0.519799	−	0.519799i	−0.917510	+	0.397712i	$0.869804\pi$
$294$	−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	0.888591	−	0.458700i	$-0.151685\pi$
$307$	1.24387e7	+	1.24387e7i	0.429892	+	0.429892i	−0.458700	+	0.888591i	$0.651685\pi$
$308$	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	$0.128332\pi$
$313$			2.40612e7i			0.784666i	−0.919823	+	0.392333i	$0.871668\pi$
$314$	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	−0.256920	−	0.966433i	$-0.582708\pi$
$317$	2.26015e7	−	2.26015e7i	0.709513	−	0.709513i	0.966433	+	0.256920i	$0.0827076\pi$
$318$	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	−0.999540	−	0.0303298i	$-0.990344\pi$
$331$	−3.51481e7	+	3.51481e7i	−0.969210	+	0.969210i	0.0303298	+	0.999540i	$0.490344\pi$
$332$	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	−0.234966	−	0.972003i	$-0.575498\pi$
$347$	3.07948e7	−	3.07948e7i	0.737037	−	0.737037i	0.972003	+	0.234966i	$0.0754980\pi$
$348$	1.76219e7	+	6.92328e7i	0.418132	+	1.64276i
$349$	−3.28683e7	+	3.28683e7i	−0.773215	+	0.773215i	−0.978667	−	0.205452i	$-0.934134\pi$
$349$	−3.28683e7	+	3.28683e7i	−0.773215	+	0.773215i	0.205452	+	0.978667i	$0.434134\pi$
$350$	−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	$-0.598195\pi$
$367$		−	9.41948e7i		−	1.90559i	0.303620	−	0.952793i	$-0.401805\pi$
$368$	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	0.517754	−	0.855529i	$-0.326768\pi$
$373$	−1.75289e7	−	1.75289e7i	−0.337775	−	0.337775i	−0.855529	+	0.517754i	$0.826768\pi$
$374$	−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	−0.900977	−	0.433867i	$-0.857149\pi$
$379$	−2.54295e7	+	2.54295e7i	−0.467110	+	0.467110i	0.433867	+	0.900977i	$0.357149\pi$
$380$	−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	$0.211283\pi$
$383$			6.92259e7i			1.23218i	−0.787678	+	0.616088i	$0.788717\pi$
$384$	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	0.907502	+	0.420047i	$0.137986\pi$
$389$	7.81447e7	+	7.81447e7i	1.32755	+	1.32755i	0.420047	+	0.907502i	$0.362014\pi$
$390$	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	−0.988426	−	0.151706i	$-0.951523\pi$
$397$	−5.23542e7	+	5.23542e7i	−0.836720	+	0.836720i	0.151706	+	0.988426i	$0.451523\pi$
$398$	−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	$-0.634356\pi$
$409$		−	1.24826e8i		−	1.82447i	0.409671	−	0.912233i	$-0.365644\pi$
$410$	−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	0.738145	−	0.674642i	$-0.235702\pi$
$419$	4.67128e6	+	4.67128e6i	0.0635030	+	0.0635030i	−0.674642	+	0.738145i	$0.735702\pi$
$420$	−1.10574e8	+	2.81445e7i	−1.49247	+	0.379880i
$421$	−5.69604e7	−	5.69604e7i	−0.763355	−	0.763355i	0.213572	−	0.976927i	$-0.431490\pi$
$421$	−5.69604e7	−	5.69604e7i	−0.763355	−	0.763355i	−0.976927	+	0.213572i	$0.931490\pi$
$422$	−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	$-0.648891\pi$
$431$		−	1.42926e8i		−	1.78516i	0.450884	−	0.892582i	$-0.351109\pi$
$432$	−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	−0.933485	−	0.358617i	$-0.883249\pi$
$443$	−4.99781e7	+	4.99781e7i	−0.574868	+	0.574868i	0.358617	+	0.933485i	$0.383249\pi$
$444$	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	$0.314682\pi$
$457$			1.59441e8i			1.67052i	−0.549857	+	0.835259i	$0.685318\pi$
$458$	−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	−0.882237	−	0.470805i	$-0.843964\pi$
$461$	−4.03090e7	+	4.03090e7i	−0.411433	+	0.411433i	0.470805	+	0.882237i	$0.343964\pi$
$462$	1.34380e8	+	1.04461e8i	1.36273	+	1.05932i
$463$		−	1.49317e8i		−	1.50441i	−0.658927	−	0.752207i	$-0.728989\pi$
$463$		−	1.49317e8i		−	1.50441i	0.658927	−	0.752207i	$-0.271011\pi$
$464$	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	0.660686	−	0.750663i	$-0.270266\pi$
$467$	−9.16391e6	−	9.16391e6i	−0.0899768	−	0.0899768i	−0.750663	+	0.660686i	$0.770266\pi$
$468$	−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	$0.0494511\pi$
$479$			3.40105e7i			0.309462i	−0.987957	+	0.154731i	$0.950549\pi$
$480$	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	−0.436609	−	0.899651i	$-0.643821\pi$
$491$	5.48107e7	−	5.48107e7i	0.463043	−	0.463043i	0.899651	+	0.436609i	$0.143821\pi$
$492$	−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	0.0513344	−	0.998682i	$-0.483653\pi$
$499$	−1.17709e8	−	1.17709e8i	−0.947347	−	0.947347i	−0.998682	+	0.0513344i	$0.983653\pi$
$500$	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	−0.840919	−	0.541162i	$-0.817985\pi$
$509$	−3.95296e7	+	3.95296e7i	−0.299757	+	0.299757i	0.541162	+	0.840919i	$0.317985\pi$
$510$	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	$0.0659188\pi$
$521$			5.81559e7i			0.411226i	−0.978633	+	0.205613i	$0.934081\pi$
$522$	3.22535e7	+	2.57475e8i	0.226759	+	1.81019i
$523$	−5.92630e7	+	5.92630e7i	−0.414265	+	0.414265i	−0.883221	−	0.468956i	$-0.844630\pi$
$523$	−5.92630e7	+	5.92630e7i	−0.414265	+	0.414265i	0.468956	+	0.883221i	$0.344630\pi$
$524$	−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	−0.999202	−	0.0399372i	$-0.987284\pi$
$541$	−1.51890e8	+	1.51890e8i	−0.959265	+	0.959265i	0.0399372	+	0.999202i	$0.487284\pi$
$542$	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	0.975454	−	0.220204i	$-0.0706722\pi$
$547$	1.23610e8	+	1.23610e8i	0.755250	+	0.755250i	−0.220204	+	0.975454i	$0.570672\pi$
$548$	−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	0.355018	−	0.934860i	$-0.384475\pi$
$557$	2.22902e8	−	2.22902e8i	1.28988	−	1.28988i	0.934860	−	0.355018i	$-0.115525\pi$
$558$	−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	0.885488	−	0.464663i	$-0.153825\pi$
$563$	7.50976e7	+	7.50976e7i	0.420824	+	0.420824i	−0.464663	+	0.885488i	$0.653825\pi$
$564$	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	$-0.812554\pi$
$569$		−	2.04643e8i		−	1.11086i	0.831564	−	0.555430i	$-0.187446\pi$
$570$	−3.32318e8	+	4.16289e7i	−1.79444	+	0.224786i
$571$	6.76421e7	−	6.76421e7i	0.363336	−	0.363336i	−0.501704	−	0.865040i	$-0.667293\pi$
$571$	6.76421e7	−	6.76421e7i	0.363336	−	0.363336i	0.865040	+	0.501704i	$0.167293\pi$
$572$	−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	−0.971304	−	0.237840i	$-0.923561\pi$
$587$	−1.48352e8	+	1.48352e8i	−0.733464	+	0.733464i	0.237840	+	0.971304i	$0.423561\pi$
$588$	−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	$0.182486\pi$
$601$			2.35493e8i			1.08481i	−0.840117	+	0.542405i	$0.817514\pi$
$602$	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	$-0.790417\pi$
$607$		−	2.73689e8i		−	1.22374i	0.790957	−	0.611872i	$-0.209583\pi$
$608$	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	0.975227	−	0.221206i	$-0.0709993\pi$
$613$	1.73686e8	+	1.73686e8i	0.754021	+	0.754021i	−0.221206	+	0.975227i	$0.570999\pi$
$614$	−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	$0.0979403\pi$
$617$			1.42273e8i			0.605713i	−0.953036	+	0.302857i	$0.902060\pi$
$618$	−6.18922e7	−	4.94077e8i	−0.262223	−	2.09329i
$619$	−1.72079e8	+	1.72079e8i	−0.725530	+	0.725530i	−0.969726	−	0.244196i	$-0.921476\pi$
$619$	−1.72079e8	+	1.72079e8i	−0.725530	+	0.725530i	0.244196	+	0.969726i	$0.421476\pi$
$620$	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	0.846087	−	0.533045i	$-0.178953\pi$
$643$	8.32213e7	+	8.32213e7i	0.313041	+	0.313041i	−0.533045	+	0.846087i	$0.678953\pi$
$644$	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	−0.481656	−	0.876360i	$-0.659965\pi$
$653$	1.09903e8	−	1.09903e8i	0.394704	−	0.394704i	0.876360	+	0.481656i	$0.159965\pi$
$654$	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	0.881596	−	0.472004i	$-0.156469\pi$
$659$	1.17222e8	+	1.17222e8i	0.409592	+	0.409592i	−0.472004	+	0.881596i	$0.656469\pi$
$660$	−3.18387e8	+	5.35805e8i	−1.10745	+	1.86370i
$661$	6.26215e7	+	6.26215e7i	0.216830	+	0.216830i	0.807161	−	0.590331i	$-0.201003\pi$
$661$	6.26215e7	+	6.26215e7i	0.216830	+	0.216830i	−0.590331	+	0.807161i	$0.701003\pi$
$662$	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	0.761894	−	0.647702i	$-0.224270\pi$
$677$	3.54325e7	+	3.54325e7i	0.114192	+	0.114192i	−0.647702	+	0.761894i	$0.724270\pi$
$678$	−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	−0.316773	−	0.948501i	$-0.602599\pi$
$683$	2.01276e8	−	2.01276e8i	0.631728	−	0.631728i	0.948501	+	0.316773i	$0.102599\pi$
$684$	−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	0.331108	−	0.943593i	$-0.392578\pi$
$691$	−2.02083e8	−	2.02083e8i	−0.612485	−	0.612485i	−0.943593	+	0.331108i	$0.892578\pi$
$692$	−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	−0.470117	−	0.882604i	$-0.655788\pi$
$701$	1.42090e8	−	1.42090e8i	0.412487	−	0.412487i	0.882604	+	0.470117i	$0.155788\pi$
$702$	−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	−0.956767	−	0.290855i	$-0.906060\pi$
$709$	−4.44653e8	−	4.44653e8i	−1.24762	−	1.24762i	−0.290855	−	0.956767i	$-0.593940\pi$
$710$	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	$0.0210005\pi$
$719$			4.90096e7i			0.131854i	−0.997824	+	0.0659271i	$0.979000\pi$
$720$	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	−0.803355	−	0.595500i	$-0.796954\pi$
$733$	−8.18602e7	+	8.18602e7i	−0.207855	+	0.207855i	0.595500	+	0.803355i	$0.296954\pi$
$734$	−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	0.911737	−	0.410775i	$-0.134742\pi$
$739$	2.02180e8	+	2.02180e8i	0.500962	+	0.500962i	−0.410775	+	0.911737i	$0.634742\pi$
$740$	−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	$0.100471\pi$
$751$			2.62969e8i			0.620847i	−0.950598	+	0.310424i	$0.899529\pi$
$752$	−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	0.999996	−	0.00277321i	$-0.000882742\pi$
$757$	4.32593e8	+	4.32593e8i	0.997223	+	0.997223i	−0.00277321	+	0.999996i	$0.500883\pi$
$758$	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	$0.106439\pi$
$761$			2.89274e8i			0.656380i	−0.944612	+	0.328190i	$0.893561\pi$
$762$	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	0.623678	−	0.781682i	$-0.285638\pi$
$773$	−7.29804e7	−	7.29804e7i	−0.158004	−	0.158004i	−0.781682	+	0.623678i	$0.785638\pi$
$774$	−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	0.785238	−	0.619194i	$-0.212540\pi$
$787$	8.09374e7	+	8.09374e7i	0.166045	+	0.166045i	−0.619194	+	0.785238i	$0.712540\pi$
$788$	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	−0.883937	−	0.467606i	$-0.845117\pi$
$797$	−2.10772e8	+	2.10772e8i	−0.416331	+	0.416331i	0.467606	+	0.883937i	$0.345117\pi$
$798$	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	$-0.736569\pi$
$809$		−	7.79710e8i		−	1.47261i	0.676650	−	0.736304i	$-0.263431\pi$
$810$	3.14790e7	+	2.51293e8i	0.0592332	+	0.472851i
$811$	1.31065e7	−	1.31065e7i	0.0245710	−	0.0245710i	−0.694715	−	0.719286i	$-0.744469\pi$
$811$	1.31065e7	−	1.31065e7i	0.0245710	−	0.0245710i	0.719286	+	0.694715i	$0.244469\pi$
$812$	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	0.686733	−	0.726910i	$-0.259044\pi$
$821$	−2.22336e7	−	2.22336e7i	−0.0401772	−	0.0401772i	−0.726910	+	0.686733i	$0.759044\pi$
$822$	−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	−0.894962	−	0.446142i	$-0.852798\pi$
$827$	−2.53857e8	+	2.53857e8i	−0.448821	+	0.448821i	0.446142	+	0.894962i	$0.352798\pi$
$828$	8.58535e8	−	2.18523e8i	1.51240	−	0.384952i
$829$	5.10963e8	−	5.10963e8i	0.896863	−	0.896863i	−0.0982941	−	0.995157i	$-0.531339\pi$
$829$	5.10963e8	−	5.10963e8i	0.896863	−	0.896863i	0.995157	+	0.0982941i	$0.0313386\pi$
$830$	−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	0.670010	−	0.742352i	$-0.266290\pi$
$853$	−4.48995e7	−	4.48995e7i	−0.0723426	−	0.0723426i	−0.742352	+	0.670010i	$0.766290\pi$
$854$	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	$0.167292\pi$
$857$			6.31563e8i			1.00340i	−0.865041	+	0.501700i	$0.832708\pi$
$858$	−2.44495e8	+	3.06274e7i	−0.387086	+	0.0484895i
$859$	7.22836e8	−	7.22836e8i	1.14041	−	1.14041i	0.152032	−	0.988376i	$-0.451418\pi$
$859$	7.22836e8	−	7.22836e8i	1.14041	−	1.14041i	0.988376	−	0.152032i	$-0.0485816\pi$
$860$	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	$0.0499945\pi$
$863$			2.01070e8i			0.312834i	−0.987691	+	0.156417i	$0.950006\pi$
$864$	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	−0.907608	−	0.419818i	$-0.862094\pi$
$877$	−3.29027e8	+	3.29027e8i	−0.487790	+	0.487790i	0.419818	+	0.907608i	$0.362094\pi$
$878$	−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	−0.953278	−	0.302095i	$-0.902314\pi$
$883$	−8.64281e8	−	8.64281e8i	−1.25537	−	1.25537i	−0.302095	−	0.953278i	$-0.597686\pi$
$884$	−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	−0.975748	−	0.218898i	$-0.929754\pi$
$907$	−5.64718e8	+	5.64718e8i	−0.756850	+	0.756850i	0.218898	+	0.975748i	$0.429754\pi$
$908$	−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	$-0.976316\pi$
$911$		−	1.12404e8i		−	0.148671i	0.997233	−	0.0743356i	$-0.0236836\pi$
$912$	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	$-0.748459\pi$
$937$		−	1.16903e9i		−	1.42104i	0.703675	−	0.710522i	$-0.251541\pi$
$938$	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	−0.0641548	−	0.997940i	$-0.520435\pi$
$941$	7.78065e8	−	7.78065e8i	0.933785	−	0.933785i	0.997940	+	0.0641548i	$0.0204351\pi$
$942$	−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	0.984524	−	0.175253i	$-0.0560742\pi$
$947$	6.87296e8	+	6.87296e8i	0.809271	+	0.809271i	−0.175253	+	0.984524i	$0.556074\pi$
$948$	−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	$0.0567197\pi$
$953$			3.06826e8i			0.354498i	−0.984166	+	0.177249i	$0.943280\pi$
$954$	−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	0.255827	−	0.966723i	$-0.417652\pi$
$971$	1.11924e9	−	1.11924e9i	1.22255	−	1.22255i	0.966723	−	0.255827i	$-0.0823477\pi$
$972$	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	$0.0686852\pi$
$991$			4.16762e8i			0.428221i	−0.976809	+	0.214110i	$0.931315\pi$
$992$	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	0.999089	−	0.0426800i	$-0.0135896\pi$
$997$	9.47827e8	+	9.47827e8i	0.956409	+	0.956409i	−0.0426800	+	0.999089i	$0.513590\pi$
$998$	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.11.3	yes	22
4.3	odd	2		64.7.f.a.15.10		22
8.3	odd	2		128.7.f.a.31.2		22
8.5	even	2		128.7.f.b.31.10		22
16.3	odd	4	inner	16.7.f.a.3.3	✓	22
16.5	even	4		128.7.f.a.95.2		22
16.11	odd	4		128.7.f.b.95.10		22
16.13	even	4		64.7.f.a.47.10		22

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

\(f(q)\)	\(=\)	\(q+(-6.31611 - 4.90986i) q^{2} +(-31.9540 - 31.9540i) q^{3} +(15.7866 + 62.0224i) q^{4} +(95.0213 + 95.0213i) q^{5} +(44.9356 + 358.715i) q^{6} -293.582 q^{7} +(204.811 - 469.251i) q^{8} +1313.12i q^{9} +O(q^{10})\)	\(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

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