LMFDB - Embedded newform 7.7.d.b.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.61037858534$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	7.5
Dual form			7.7.d.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.121320 - 0.210133i) q^{2} +(32.0772 - 18.5198i) q^{3} +(31.9706 + 55.3746i) q^{4} +(-143.566 - 82.8879i) q^{5} -8.98729i q^{6} +(-197.286 + 280.583i) q^{7} +31.0437 q^{8} +(321.463 - 556.790i) q^{9} +O(q^{10})$	\(q+(0.121320 - 0.210133i) q^{2} +(32.0772 - 18.5198i) q^{3} +(31.9706 + 55.3746i) q^{4} +(-143.566 - 82.8879i) q^{5} -8.98729i q^{6} +(-197.286 + 280.583i) q^{7} +31.0437 q^{8} +(321.463 - 556.790i) q^{9} +(-34.8350 + 20.1120i) q^{10} +(86.5410 + 149.893i) q^{11} +(2051.05 + 1184.17i) q^{12} -1963.14i q^{13} +(35.0250 + 75.4969i) q^{14} -6140.25 q^{15} +(-2042.35 + 3537.45i) q^{16} +(3199.04 - 1846.96i) q^{17} +(-78.0000 - 135.100i) q^{18} +(3953.11 + 2282.33i) q^{19} -10599.9i q^{20} +(-1132.05 + 12654.0i) q^{21} +41.9967 q^{22} +(7895.75 - 13675.8i) q^{23} +(995.795 - 574.922i) q^{24} +(5928.30 + 10268.1i) q^{25} +(-412.520 - 238.168i) q^{26} +3188.14i q^{27} +(-21844.6 - 1954.25i) q^{28} -23782.2 q^{29} +(-744.938 + 1290.27i) q^{30} +(1785.57 - 1030.90i) q^{31} +(1488.96 + 2578.95i) q^{32} +(5551.98 + 3205.44i) q^{33} -896.298i q^{34} +(51580.6 - 23929.6i) q^{35} +41109.4 q^{36} +(-24255.5 + 42011.7i) q^{37} +(959.185 - 553.786i) q^{38} +(-36356.8 - 62971.8i) q^{39} +(-4456.82 - 2573.15i) q^{40} +26437.9i q^{41} +(2521.69 + 1773.07i) q^{42} +68471.6 q^{43} +(-5533.53 + 9584.36i) q^{44} +(-92302.3 + 53290.8i) q^{45} +(-1915.83 - 3318.32i) q^{46} +(-121557. - 70180.9i) q^{47} +151295. i q^{48} +(-39805.2 - 110711. i) q^{49} +2876.89 q^{50} +(68410.7 - 118491. i) q^{51} +(108708. - 62762.6i) q^{52} +(127065. + 220083. i) q^{53} +(669.934 + 386.786i) q^{54} -28692.8i q^{55} +(-6124.50 + 8710.36i) q^{56} +169073. q^{57} +(-2885.27 + 4997.43i) q^{58} +(-84178.0 + 48600.2i) q^{59} +(-196307. - 340014. i) q^{60} +(15062.4 + 8696.26i) q^{61} -500.276i q^{62} +(92805.9 + 200044. i) q^{63} -260698. q^{64} +(-162720. + 281840. i) q^{65} +(1347.14 - 777.770i) q^{66} +(60340.8 + 104513. i) q^{67} +(204550. + 118097. i) q^{68} -584910. i q^{69} +(1229.37 - 13741.9i) q^{70} -339555. q^{71} +(9979.41 - 17284.8i) q^{72} +(96432.8 - 55675.5i) q^{73} +(5885.36 + 10193.7i) q^{74} +(380326. + 219581. i) q^{75} +291869. i q^{76} +(-59131.0 - 5289.95i) q^{77} -17643.3 q^{78} +(307919. - 533332. i) q^{79} +(586424. - 338572. i) q^{80} +(293390. + 508167. i) q^{81} +(5555.47 + 3207.45i) q^{82} -383668. i q^{83} +(-736904. + 341869. i) q^{84} -612364. q^{85} +(8307.00 - 14388.1i) q^{86} +(-762866. + 440441. i) q^{87} +(2686.56 + 4653.25i) q^{88} +(-668299. - 385843. i) q^{89} +25861.0i q^{90} +(550824. + 387300. i) q^{91} +1.00973e6 q^{92} +(38184.0 - 66136.6i) q^{93} +(-29494.6 + 17028.7i) q^{94} +(-378355. - 655329. i) q^{95} +(95523.0 + 55150.2i) q^{96} +292263. i q^{97} +(-28093.1 - 5067.06i) q^{98} +111279. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9	\( 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9} - 1200 q^{10} + 1882 q^{11} + 4284 q^{12} - 1820 q^{14} - 16500 q^{15} + 248 q^{16} + 13458 q^{17} - 312 q^{18} + 18078 q^{19} - 16170 q^{21} - 28088 q^{22} + 2470 q^{23} + 24840 q^{24} + 2500 q^{25} + 43848 q^{26} - 45444 q^{28} - 34544 q^{29} + 15900 q^{30} - 17202 q^{31} + 7008 q^{32} - 67770 q^{33} + 154350 q^{35} + 82368 q^{36} - 43870 q^{37} - 81924 q^{38} + 10668 q^{39} - 76800 q^{40} - 22344 q^{42} + 320216 q^{43} - 4332 q^{44} - 187200 q^{45} - 113636 q^{46} - 354714 q^{47} + 140140 q^{49} + 160000 q^{50} + 28206 q^{51} + 196056 q^{52} + 104530 q^{53} + 285876 q^{54} - 346192 q^{56} + 25164 q^{57} - 59432 q^{58} - 62646 q^{59} - 384300 q^{60} - 140682 q^{61} + 181272 q^{63} - 33248 q^{64} - 77700 q^{65} + 652824 q^{66} + 432494 q^{67} + 381276 q^{68} - 338100 q^{70} - 1481528 q^{71} + 29328 q^{72} - 971778 q^{73} + 50024 q^{74} + 1192500 q^{75} + 642670 q^{77} - 1409856 q^{78} + 935990 q^{79} + 1767000 q^{80} + 1104066 q^{81} + 286776 q^{82} - 1405908 q^{84} - 579300 q^{85} - 738712 q^{86} - 1826208 q^{87} - 840616 q^{88} - 679290 q^{89} + 711480 q^{91} + 2124456 q^{92} + 395958 q^{93} + 860892 q^{94} - 291750 q^{95} + 5040 q^{96} - 361424 q^{98} + 157872 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9 - 1200 * q^10 + 1882 * q^11 + 4284 * q^12 - 1820 * q^14 - 16500 * q^15 + 248 * q^16 + 13458 * q^17 - 312 * q^18 + 18078 * q^19 - 16170 * q^21 - 28088 * q^22 + 2470 * q^23 + 24840 * q^24 + 2500 * q^25 + 43848 * q^26 - 45444 * q^28 - 34544 * q^29 + 15900 * q^30 - 17202 * q^31 + 7008 * q^32 - 67770 * q^33 + 154350 * q^35 + 82368 * q^36 - 43870 * q^37 - 81924 * q^38 + 10668 * q^39 - 76800 * q^40 - 22344 * q^42 + 320216 * q^43 - 4332 * q^44 - 187200 * q^45 - 113636 * q^46 - 354714 * q^47 + 140140 * q^49 + 160000 * q^50 + 28206 * q^51 + 196056 * q^52 + 104530 * q^53 + 285876 * q^54 - 346192 * q^56 + 25164 * q^57 - 59432 * q^58 - 62646 * q^59 - 384300 * q^60 - 140682 * q^61 + 181272 * q^63 - 33248 * q^64 - 77700 * q^65 + 652824 * q^66 + 432494 * q^67 + 381276 * q^68 - 338100 * q^70 - 1481528 * q^71 + 29328 * q^72 - 971778 * q^73 + 50024 * q^74 + 1192500 * q^75 + 642670 * q^77 - 1409856 * q^78 + 935990 * q^79 + 1767000 * q^80 + 1104066 * q^81 + 286776 * q^82 - 1405908 * q^84 - 579300 * q^85 - 738712 * q^86 - 1826208 * q^87 - 840616 * q^88 - 679290 * q^89 + 711480 * q^91 + 2124456 * q^92 + 395958 * q^93 + 860892 * q^94 - 291750 * q^95 + 5040 * q^96 - 361424 * q^98 + 157872 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.121320	−	0.210133i	0.0151650	−	0.0262666i	−0.858343	−	0.513076i	$-0.828506\pi$
$2$	0.121320	−	0.210133i	0.0151650	−	0.0262666i	0.873508	+	0.486809i	$0.161839\pi$
$3$	32.0772	−	18.5198i	1.18804	−	0.685917i	0.230182	−	0.973148i	$-0.426068\pi$
$3$	32.0772	−	18.5198i	1.18804	−	0.685917i	0.957861	+	0.287231i	$0.0927346\pi$
$4$	31.9706	+	55.3746i	0.499540	+	0.865229i
$5$	−143.566	−	82.8879i	−1.14853	−	0.663103i	−0.200000	−	0.979796i	$-0.564094\pi$
$5$	−143.566	−	82.8879i	−1.14853	−	0.663103i	−0.948528	+	0.316693i	$0.897428\pi$
$6$		−	8.98729i		−	0.0416078i
$7$	−197.286	+	280.583i	−0.575179	+	0.818028i
$7$	−197.286	+	280.583i	−0.575179	+	0.818028i
$8$	31.0437			0.0606323
$9$	321.463	−	556.790i	0.440964	−	0.763773i
$10$	−34.8350	+	20.1120i	−0.0348350	+	0.0201120i
$11$	86.5410	+	149.893i	0.0650195	+	0.112617i	0.896703	−	0.442633i	$-0.145956\pi$
$11$	86.5410	+	149.893i	0.0650195	+	0.112617i	−0.831683	+	0.555251i	$0.812622\pi$
$12$	2051.05	+	1184.17i	1.18695	+	0.685286i
$13$		−	1963.14i		−	0.893553i	−0.894646	−	0.446777i	$-0.852572\pi$
$13$		−	1963.14i		−	0.893553i	0.894646	−	0.446777i	$-0.147428\pi$
$14$	35.0250	+	75.4969i	0.0127642	+	0.0275134i
$15$	−6140.25			−1.81933
$16$	−2042.35	+	3537.45i	−0.498621	+	0.863636i
$17$	3199.04	−	1846.96i	0.651137	−	0.375934i	−0.137755	−	0.990466i	$-0.543989\pi$
$17$	3199.04	−	1846.96i	0.651137	−	0.375934i	0.788892	+	0.614532i	$0.210655\pi$
$18$	−78.0000	−	135.100i	−0.0133745	−	0.0231653i
$19$	3953.11	+	2282.33i	0.576339	+	0.332749i	0.759677	−	0.650301i	$-0.225357\pi$
$19$	3953.11	+	2282.33i	0.576339	+	0.332749i	−0.183338	+	0.983050i	$0.558690\pi$
$20$		−	10599.9i		−	1.32499i
$21$	−1132.05	+	12654.0i	−0.122238	+	1.36638i
$22$	41.9967			0.00394410
$23$	7895.75	−	13675.8i	0.648948	−	1.12401i	−0.334427	−	0.942422i	$-0.608543\pi$
$23$	7895.75	−	13675.8i	0.648948	−	1.12401i	0.983375	−	0.181589i	$-0.0581241\pi$
$24$	995.795	−	574.922i	0.0720338	−	0.0415887i
$25$	5928.30	+	10268.1i	0.379411	+	0.657160i
$26$	−412.520	−	238.168i	−0.0234706	−	0.0135508i
$27$			3188.14i			0.161974i
$28$	−21844.6	−	1954.25i	−0.995106	−	0.0890237i
$29$	−23782.2			−0.975121			−0.487561	−	0.873089i	$-0.662113\pi$
$29$	−23782.2			−0.975121			−0.487561	+	0.873089i	$0.662113\pi$
$30$	−744.938	+	1290.27i	−0.0275903	+	0.0477878i
$31$	1785.57	−	1030.90i	0.0599365	−	0.0346044i	−0.469732	−	0.882809i	$-0.655650\pi$
$31$	1785.57	−	1030.90i	0.0599365	−	0.0346044i	0.529669	+	0.848205i	$0.322316\pi$
$32$	1488.96	+	2578.95i	0.0454393	+	0.0787032i
$33$	5551.98	+	3205.44i	0.154492	+	0.0891960i
$34$		−	896.298i		−	0.0228042i
$35$	51580.6	−	23929.6i	1.20305	−	0.558125i
$36$	41109.4			0.881117
$37$	−24255.5	+	42011.7i	−0.478855	+	0.829401i	−0.999706	−	0.0242462i	$-0.992281\pi$
$37$	−24255.5	+	42011.7i	−0.478855	+	0.829401i	0.520851	+	0.853648i	$0.325615\pi$
$38$	959.185	−	553.786i	0.0174804	−	0.0100923i
$39$	−36356.8	−	62971.8i	−0.612903	−	1.06158i
$40$	−4456.82	−	2573.15i	−0.0696379	−	0.0402054i
$41$			26437.9i			0.383597i	0.981434	+	0.191799i	$0.0614320\pi$
$41$			26437.9i			0.383597i	−0.981434	+	0.191799i	$0.938568\pi$
$42$	2521.69	+	1773.07i	0.0340364	+	0.0239320i
$43$	68471.6			0.861202			0.430601	−	0.902542i	$-0.358302\pi$
$43$	68471.6			0.861202			0.430601	+	0.902542i	$0.358302\pi$
$44$	−5533.53	+	9584.36i	−0.0649597	+	0.112514i
$45$	−92302.3	+	53290.8i	−1.01292	+	0.584810i
$46$	−1915.83	−	3318.32i	−0.0196826	−	0.0340913i
$47$	−121557.	−	70180.9i	−1.17081	−	0.675967i	−0.216938	−	0.976185i	$-0.569607\pi$
$47$	−121557.	−	70180.9i	−1.17081	−	0.675967i	−0.953870	+	0.300219i	$0.902940\pi$
$48$			151295.i			1.36805i
$49$	−39805.2	−	110711.i	−0.338338	−	0.941024i
$50$	2876.89			0.0230152
$51$	68410.7	−	118491.i	0.515719	−	0.893252i
$52$	108708.	−	62762.6i	0.773128	−	0.446366i
$53$	127065.	+	220083.i	0.853489	+	1.47829i	0.878039	+	0.478588i	$0.158851\pi$
$53$	127065.	+	220083.i	0.853489	+	1.47829i	−0.0245502	+	0.999699i	$0.507815\pi$
$54$	669.934	+	386.786i	0.00425452	+	0.00245635i
$55$		−	28692.8i		−	0.172459i
$56$	−6124.50	+	8710.36i	−0.0348744	+	0.0495989i
$57$	169073.			0.912954
$58$	−2885.27	+	4997.43i	−0.0147878	+	0.0256131i
$59$	−84178.0	+	48600.2i	−0.409867	+	0.236637i	−0.690732	−	0.723110i	$-0.742712\pi$
$59$	−84178.0	+	48600.2i	−0.409867	+	0.236637i	0.280866	+	0.959747i	$0.409378\pi$
$60$	−196307.	−	340014.i	−0.908830	−	1.57414i
$61$	15062.4	+	8696.26i	0.0663596	+	0.0383127i	0.532813	−	0.846233i	$-0.321135\pi$
$61$	15062.4	+	8696.26i	0.0663596	+	0.0383127i	−0.466453	+	0.884546i	$0.654468\pi$
$62$		−	500.276i		−	0.00209911i
$63$	92805.9	+	200044.i	0.371154	+	0.800027i
$64$	−260698.			−0.994485
$65$	−162720.	+	281840.i	−0.592518	+	1.02627i
$66$	1347.14	−	777.770i	0.00468576	−	0.00270532i
$67$	60340.8	+	104513.i	0.200626	+	0.347494i	0.948730	−	0.316087i	$-0.102369\pi$
$67$	60340.8	+	104513.i	0.200626	+	0.347494i	−0.748105	+	0.663581i	$0.769036\pi$
$68$	204550.	+	118097.i	0.650538	+	0.375588i
$69$		−	584910.i		−	1.78050i
$70$	1229.37	−	13741.9i	0.00358418	−	0.0400639i
$71$	−339555.			−0.948713			−0.474357	−	0.880333i	$-0.657319\pi$
$71$	−339555.			−0.948713			−0.474357	+	0.880333i	$0.657319\pi$
$72$	9979.41	−	17284.8i	0.0267367	−	0.0463093i
$73$	96432.8	−	55675.5i	0.247888	−	0.143118i	−0.370909	−	0.928669i	$-0.620954\pi$
$73$	96432.8	−	55675.5i	0.247888	−	0.143118i	0.618797	+	0.785551i	$0.287620\pi$
$74$	5885.36	+	10193.7i	0.0145237	+	0.0251558i
$75$	380326.	+	219581.i	0.901514	+	0.520489i
$76$			291869.i			0.664886i
$77$	−59131.0	−	5289.95i	−0.129522	−	0.0115872i
$78$	−17643.3			−0.0371788
$79$	307919.	−	533332.i	0.624533	−	1.08172i	−0.364098	−	0.931361i	$-0.618623\pi$
$79$	307919.	−	533332.i	0.624533	−	1.08172i	0.988631	−	0.150362i	$-0.0480440\pi$
$80$	586424.	−	338572.i	1.14536	−	0.661274i
$81$	293390.	+	508167.i	0.552065	+	0.956205i
$82$	5555.47	+	3207.45i	0.0100758	+	0.00581727i
$83$		−	383668.i		−	0.670999i	−0.942040	−	0.335499i	$-0.891095\pi$
$83$		−	383668.i		−	0.670999i	0.942040	−	0.335499i	$-0.108905\pi$
$84$	−736904.	+	341869.i	−1.24329	+	0.576796i
$85$	−612364.			−0.997133
$86$	8307.00	−	14388.1i	0.0130602	−	0.0226209i
$87$	−762866.	+	440441.i	−1.15849	+	0.668852i
$88$	2686.56	+	4653.25i	0.00394228	+	0.00682823i
$89$	−668299.	−	385843.i	−0.947983	−	0.547318i	−0.0555294	−	0.998457i	$-0.517685\pi$
$89$	−668299.	−	385843.i	−0.947983	−	0.547318i	−0.892454	+	0.451139i	$0.851018\pi$
$90$			25861.0i			0.0354746i
$91$	550824.	+	387300.i	0.730951	+	0.513953i
$92$	1.00973e6			1.29670
$93$	38184.0	−	66136.6i	0.0474714	−	0.0822229i
$94$	−29494.6	+	17028.7i	−0.0355107	+	0.0205021i
$95$	−378355.	−	655329.i	−0.441294	−	0.764344i
$96$	95523.0	+	55150.2i	0.107968	+	0.0623352i
$97$			292263.i			0.320227i	0.987099	+	0.160113i	$0.0511860\pi$
$97$			292263.i			0.320227i	−0.987099	+	0.160113i	$0.948814\pi$
$98$	−28093.1	−	5067.06i	−0.0298485	−	0.00538367i
$99$	111279.			0.114685
$100$	−379062.	+	656555.i	−0.379062	+	0.656555i
$101$	779310.	−	449935.i	0.756391	−	0.436703i	−0.0716075	−	0.997433i	$-0.522813\pi$
$101$	779310.	−	449935.i	0.756391	−	0.436703i	0.827998	+	0.560730i	$0.189480\pi$
$102$	−16599.2	−	28750.7i	−0.0156418	−	0.0270924i
$103$	235773.	+	136123.i	0.215765	+	0.124572i	0.603988	−	0.796993i	$-0.293578\pi$
$103$	235773.	+	136123.i	0.215765	+	0.124572i	−0.388223	+	0.921566i	$0.626911\pi$
$104$		−	60943.1i		−	0.0541782i
$105$	1.21139e6	−	1.72285e6i	1.04644	−	1.48827i
$106$	61662.2			0.0517728
$107$	−406596.	+	704245.i	−0.331904	+	0.574874i	−0.982885	−	0.184220i	$-0.941024\pi$
$107$	−406596.	+	704245.i	−0.331904	+	0.574874i	0.650982	+	0.759094i	$0.274358\pi$
$108$	−176542.	+	101927.i	−0.140145	+	0.0809127i
$109$	192645.	+	333672.i	0.148758	+	0.257656i	0.930769	−	0.365609i	$-0.119139\pi$
$109$	192645.	+	333672.i	0.148758	+	0.257656i	−0.782011	+	0.623265i	$0.785806\pi$
$110$	−6029.31	−	3481.02i	−0.00452991	−	0.00261534i
$111$			1.79682e6i			1.31382i
$112$	−589623.	−	1.27094e6i	−0.419682	−	0.904631i
$113$	498078.			0.345193			0.172596	−	0.984993i	$-0.444784\pi$
$113$	498078.			0.345193			0.172596	+	0.984993i	$0.444784\pi$
$114$	20512.0	−	35527.7i	0.0138450	−	0.0239802i
$115$	−2.26712e6	+	1.30892e6i	−1.49067	+	0.860639i
$116$	−760331.	−	1.31693e6i	−0.487112	−	0.843703i
$117$	−1.09306e6	−	631076.i	−0.682471	−	0.394025i
$118$			23584.8i			0.0143544i
$119$	−112899.	+	1.26198e6i	−0.0669958	+	0.748878i
$120$	−190616.			−0.110310
$121$	870802.	−	1.50827e6i	0.491545	−	0.851381i
$122$	3654.74	−	2110.07i	0.00201269	−	0.00116203i
$123$	489623.	+	848053.i	0.263116	+	0.455730i
$124$	114171.	+	65916.8i	0.0598814	+	0.0345725i
$125$			624709.i			0.319851i
$126$	53295.2	+	4767.87i	0.0266426	+	0.00238349i
$127$	3.60632e6			1.76057			0.880285	−	0.474445i	$-0.157351\pi$
$127$	3.60632e6			1.76057			0.880285	+	0.474445i	$0.157351\pi$
$128$	−126921.	+	219834.i	−0.0605207	+	0.104825i
$129$	2.19637e6	−	1.26808e6i	1.02315	−	0.590713i
$130$	39482.5	+	68385.8i	0.0179711	+	0.0311269i
$131$	−1.81180e6	−	1.04604e6i	−0.805926	−	0.465302i	0.0396129	−	0.999215i	$-0.487388\pi$
$131$	−1.81180e6	−	1.04604e6i	−0.805926	−	0.465302i	−0.845539	+	0.533913i	$0.820721\pi$
$132$			409919.i			0.178228i
$133$	−1.42028e6	+	658905.i	−0.603696	+	0.280071i
$134$	29282.2			0.0121700
$135$	264258.	−	457709.i	0.107406	−	0.186032i
$136$	99310.0	−	57336.7i	0.0394799	−	0.0227937i
$137$	230246.	+	398797.i	0.0895426	+	0.155092i	0.907318	−	0.420445i	$-0.138126\pi$
$137$	230246.	+	398797.i	0.0895426	+	0.155092i	−0.817775	+	0.575538i	$0.804793\pi$
$138$	−122909.	−	70961.4i	−0.0467677	−	0.0270013i
$139$		−	3.07473e6i		−	1.14489i	−0.819944	−	0.572444i	$-0.805996\pi$
$139$		−	3.07473e6i		−	1.14489i	0.819944	−	0.572444i	$-0.194004\pi$
$140$	2.97415e6	+	2.09121e6i	1.08388	+	0.762104i
$141$	−5.19893e6			−1.85463
$142$	−41194.9	+	71351.7i	−0.0143873	+	0.0249195i
$143$	294261.	−	169892.i	0.100629	−	0.0580984i
$144$	1.31308e6	+	2.27432e6i	0.439748	+	0.761665i
$145$	3.41432e6	+	1.97126e6i	1.11995	+	0.646606i
$146$		−	27018.3i		−	0.00868159i
$147$	−3.32717e6	−	2.81410e6i	−1.04743	−	0.885906i
$148$	−3.10184e6			−0.956829
$149$	−2.70712e6	+	4.68886e6i	−0.818367	+	1.41745i	0.0885184	+	0.996075i	$0.471787\pi$
$149$	−2.70712e6	+	4.68886e6i	−0.818367	+	1.41745i	−0.906885	+	0.421378i	$0.861547\pi$
$150$	92282.6	−	53279.4i	0.0273430	−	0.0157865i
$151$	−1.77457e6	−	3.07364e6i	−0.515420	−	0.892734i	−0.999840	−	0.0178985i	$-0.994302\pi$
$151$	−1.77457e6	−	3.07364e6i	−0.515420	−	0.892734i	0.484419	−	0.874836i	$-0.339031\pi$
$152$	122719.	+	70851.9i	0.0349447	+	0.0201753i
$153$		−	2.37492e6i		−	0.663094i
$154$	−8285.38	+	11783.6i	−0.00226856	+	0.00322638i
$155$	−341796.			−0.0917850
$156$	2.32470e6	−	4.02649e6i	0.612339	−	1.06060i
$157$	−364829.	+	210634.i	−0.0942737	+	0.0544290i	−0.546396	−	0.837527i	$-0.684001\pi$
$157$	−364829.	+	210634.i	−0.0942737	+	0.0544290i	0.452122	+	0.891956i	$0.350667\pi$
$158$	−74713.7	−	129408.i	−0.0189421	−	0.0328088i
$159$	8.15176e6	+	4.70642e6i	2.02796	+	1.17085i
$160$		−	493666.i		−	0.120524i
$161$	2.27949e6	+	4.91347e6i	0.546211	+	1.17736i
$162$	142377.			0.0334884
$163$	1.48705e6	−	2.57564e6i	0.343370	−	0.594734i	−0.641686	−	0.766967i	$-0.721765\pi$
$163$	1.48705e6	−	2.57564e6i	0.343370	−	0.594734i	0.985056	+	0.172233i	$0.0550981\pi$
$164$	−1.46399e6	+	845234.i	−0.331899	+	0.191622i
$165$	−531384.	−	920384.i	−0.118292	−	0.204888i
$166$	−80621.4	−	46546.8i	−0.0176249	−	0.0101757i
$167$		−	4.29683e6i		−	0.922568i	−0.887253	−	0.461284i	$-0.847389\pi$
$167$		−	4.29683e6i		−	0.922568i	0.887253	−	0.461284i	$-0.152611\pi$
$168$	−35143.0	+	392828.i	−0.00741158	+	0.0828465i
$169$	972906.			0.201563
$170$	−74292.2	+	128678.i	−0.0151216	+	0.0261913i
$171$	2.54156e6	−	1.46737e6i	0.508290	−	0.293461i
$172$	2.18908e6	+	3.79159e6i	0.430205	+	0.745137i
$173$	−8.05265e6	−	4.64920e6i	−1.55525	−	0.897925i	−0.997700	−	0.0677829i	$-0.978407\pi$
$173$	−8.05265e6	−	4.64920e6i	−1.55525	−	0.897925i	−0.557552	−	0.830142i	$-0.688259\pi$
$174$			213738.i			0.0405727i
$175$	−4.05064e6	−	362376.i	−0.755804	−	0.0676154i
$176$	−706988.			−0.129680
$177$	−1.80013e6	+	3.11791e6i	−0.324626	+	0.562269i
$178$	−162156.	+	93621.1i	−0.0287524	+	0.0166002i
$179$	1.33295e6	+	2.30874e6i	0.232410	+	0.402546i	0.958517	−	0.285036i	$-0.0920056\pi$
$179$	1.33295e6	+	2.30874e6i	0.232410	+	0.402546i	−0.726107	+	0.687582i	$0.758672\pi$
$180$	−5.90191e6	−	3.40747e6i	−1.01199	−	0.584272i
$181$			1.11842e7i			1.88612i	0.332627	+	0.943058i	$0.392065\pi$
$181$			1.11842e7i			1.88612i	−0.332627	+	0.943058i	$0.607935\pi$
$182$	148211.	−	68758.8i	0.0245847	−	0.0114055i
$183$	644211.			0.105117
$184$	245113.	−	424549.i	0.0393472	−	0.0681513i
$185$	6.96452e6	−	4.02097e6i	1.09996	−	0.635061i
$186$	−9264.99	−	16047.4i	−0.00143981	−	0.00249383i
$187$	553696.	+	319676.i	0.0846733	+	0.0488861i
$188$		−	8.97489e6i		−	1.35069i
$189$	−894540.	−	628977.i	−0.132499	−	0.0931642i
$190$	−183608.			−0.0267690
$191$	666098.	−	1.15372e6i	0.0955956	−	0.165576i	−0.814261	−	0.580498i	$-0.802858\pi$
$191$	666098.	−	1.15372e6i	0.0955956	−	0.165576i	0.909857	+	0.414922i	$0.136191\pi$
$192$	−8.36246e6	+	4.82807e6i	−1.18149	+	0.682134i
$193$	−2.27796e6	−	3.94554e6i	−0.316864	−	0.548825i	0.662968	−	0.748648i	$-0.269297\pi$
$193$	−2.27796e6	−	3.94554e6i	−0.316864	−	0.548825i	−0.979832	+	0.199823i	$0.935963\pi$
$194$	61414.0	+	35457.4i	0.00841128	+	0.00485626i
$195$			1.20542e7i			1.62567i
$196$	4.85796e6	−	5.74368e6i	0.645188	−	0.762820i
$197$	1.12847e7			1.47602			0.738009	−	0.674791i	$-0.235766\pi$
$197$	1.12847e7			1.47602			0.738009	+	0.674791i	$0.235766\pi$
$198$	13500.4	−	23383.4i	0.00173921	−	0.00301239i
$199$	−3.34434e6	+	1.93086e6i	−0.424377	+	0.245014i	−0.696948	−	0.717121i	$-0.745459\pi$
$199$	−3.34434e6	+	1.93086e6i	−0.424377	+	0.245014i	0.272571	+	0.962136i	$0.412126\pi$
$200$	184037.	+	318761.i	0.0230046	+	0.0398451i
$201$	3.87112e6	+	2.23499e6i	0.476704	+	0.275225i
$202$		−	218345.i		−	0.0264905i
$203$	4.69191e6	−	6.67290e6i	0.560869	−	0.797676i
$204$	8.74851e6			1.03049
$205$	2.19138e6	−	3.79558e6i	0.254364	−	0.440572i
$206$	57208.0	−	33029.1i	0.00654418	−	0.00377828i
$207$	−5.07638e6	−	8.79255e6i	−0.572326	−	0.991297i
$208$	6.94450e6	+	4.00941e6i	0.771705	+	0.445544i
$209$			790060.i			0.0865408i
$210$	−215062.	−	463570.i	−0.0232224	−	0.0500561i
$211$	−1.21891e7			−1.29755			−0.648777	−	0.760978i	$-0.724719\pi$
$211$	−1.21891e7			−1.29755			−0.648777	+	0.760978i	$0.724719\pi$
$212$	−8.12467e6	+	1.40723e7i	−0.852704	+	1.47693i
$213$	−1.08920e7	+	6.28848e6i	−1.12711	+	0.650739i
$214$	98656.8	+	170879.i	0.0100667	+	0.0174360i
$215$	−9.83019e6	−	5.67546e6i	−0.989115	−	0.571066i
$216$			98971.8i			0.00982087i
$217$	−63015.2	+	704383.i	−0.00616689	+	0.0689334i
$218$	93487.2			0.00902366
$219$	2.06219e6	−	3.57183e6i	0.196335	−	0.340062i
$220$	1.58885e6	−	917325.i	0.149216	−	0.0861500i
$221$	−3.62584e6	−	6.28015e6i	−0.335917	−	0.581826i
$222$	377571.	+	217991.i	0.0345096	+	0.0199241i
$223$			8.39432e6i			0.756956i	0.925610	+	0.378478i	$0.123552\pi$
$223$			8.39432e6i			0.756956i	−0.925610	+	0.378478i	$0.876448\pi$
$224$	−1.01736e6	−	91014.7i	−0.0905172	−	0.00809781i
$225$	7.62292e6			0.669227
$226$	60426.9	−	104663.i	0.00523486	−	0.00906705i
$227$	1.76855e7	−	1.02108e7i	1.51196	−	0.872931i	0.512059	−	0.858950i	$-0.328883\pi$
$227$	1.76855e7	−	1.02108e7i	1.51196	−	0.872931i	0.999902	−	0.0139813i	$-0.00445053\pi$
$228$	5.40535e6	+	9.36234e6i	0.456057	+	0.789914i
$229$	−1.11730e7	−	6.45075e6i	−0.930389	−	0.537160i	−0.0434543	−	0.999055i	$-0.513836\pi$
$229$	−1.11730e7	−	6.45075e6i	−0.930389	−	0.537160i	−0.886935	+	0.461895i	$0.847170\pi$
$230$			635196.i			0.0522065i
$231$	−1.99472e6	+	925405.i	−0.161825	+	0.0750751i
$232$	−738289.			−0.0591238
$233$	−4.62592e6	+	8.01233e6i	−0.365705	+	0.633419i	−0.988889	−	0.148656i	$-0.952505\pi$
$233$	−4.62592e6	+	8.01233e6i	−0.365705	+	0.633419i	0.623184	+	0.782075i	$0.285839\pi$
$234$	−265220.	+	153125.i	−0.0206994	+	0.0119508i
$235$	1.16343e7	+	2.01512e7i	0.896471	+	1.55273i
$236$	−5.38244e6	−	3.10755e6i	−0.409490	−	0.236419i
$237$		−	2.28104e7i		−	1.71351i
$238$	251486.	+	176827.i	0.0186545	+	0.0131165i
$239$	−8.08505e6			−0.592228			−0.296114	−	0.955153i	$-0.595691\pi$
$239$	−8.08505e6			−0.592228			−0.296114	+	0.955153i	$0.595691\pi$
$240$	1.25405e7	−	2.17209e7i	0.907158	−	1.57124i
$241$	4.18250e6	−	2.41477e6i	0.298803	−	0.172514i	−0.343102	−	0.939298i	$-0.611478\pi$
$241$	4.18250e6	−	2.41477e6i	0.298803	−	0.172514i	0.641905	+	0.766784i	$0.278144\pi$
$242$	−211292.	−	365968.i	−0.0149086	−	0.0258225i
$243$	1.68095e7	+	9.70495e6i	1.17148	+	0.676355i
$244$			1.11210e6i			0.0765550i
$245$	−3.46189e6	+	1.91936e7i	−0.235405	+	1.30515i
$246$	237605.			0.0159606
$247$	4.48052e6	−	7.76049e6i	0.297329	−	0.514989i
$248$	55430.7	−	32002.9i	0.00363409	−	0.00209814i
$249$	−7.10545e6	−	1.23070e7i	−0.460249	−	0.797175i
$250$	131272.	+	75789.9i	0.00840141	+	0.00485055i
$251$			8.54870e6i			0.540604i	0.962776	+	0.270302i	$0.0871235\pi$
$251$			8.54870e6i			0.540604i	−0.962776	+	0.270302i	$0.912877\pi$
$252$	−8.11033e6	+	1.15346e7i	−0.506800	+	0.720778i
$253$	2.73322e6			0.168777
$254$	437520.	−	757807.i	0.0266991	−	0.0462442i
$255$	−1.96429e7	+	1.13408e7i	−1.18464	+	0.683950i
$256$	−8.31155e6	−	1.43960e7i	−0.495407	−	0.858070i
$257$	1.66231e7	+	9.59736e6i	0.979294	+	0.565396i	0.902057	−	0.431617i	$-0.142057\pi$
$257$	1.66231e7	+	9.59736e6i	0.979294	+	0.565396i	0.0772369	+	0.997013i	$0.475390\pi$
$258$		−	615374.i		−	0.0358328i
$259$	−7.00251e6	−	1.50940e7i	−0.403046	−	0.868771i
$260$	−2.08090e7			−1.18395
$261$	−7.64511e6	+	1.32417e7i	−0.429994	+	0.744771i
$262$	−439615.	+	253812.i	−0.0244438	+	0.0141126i
$263$	8.69310e6	+	1.50569e7i	0.477868	+	0.827691i	0.999678	−	0.0253706i	$-0.00807657\pi$
$263$	8.69310e6	+	1.50569e7i	0.477868	+	0.827691i	−0.521811	+	0.853061i	$0.674743\pi$
$264$	172354.	+	99508.7i	0.00936720	+	0.00540816i
$265$		−	4.21286e7i		−	2.26381i
$266$	−33851.0	+	378386.i	−0.00179857	+	0.0201043i
$267$	−2.85828e7			−1.50166
$268$	−3.85826e6	+	6.68270e6i	−0.200441	+	0.347174i
$269$	6.35243e6	−	3.66757e6i	0.326349	−	0.188418i	−0.327870	−	0.944723i	$-0.606331\pi$
$269$	6.35243e6	−	3.66757e6i	0.326349	−	0.188418i	0.654219	+	0.756305i	$0.272997\pi$
$270$	−64119.8	−	111059.i	−0.00325762	−	0.00564237i
$271$	2.20318e7	+	1.27201e7i	1.10699	+	0.639118i	0.938047	−	0.346508i	$-0.112633\pi$
$271$	2.20318e7	+	1.27201e7i	1.10699	+	0.639118i	0.168938	+	0.985627i	$0.445966\pi$
$272$			1.50886e7i			0.749794i
$273$	2.48416e7	+	2.22237e6i	1.22093	+	0.109226i
$274$	111734.			0.00543167
$275$	−1.02608e6	+	1.77723e6i	−0.0493383	+	0.0854564i
$276$	3.23892e7	−	1.86999e7i	1.54054	−	0.889430i
$277$	5.46009e6	+	9.45715e6i	0.256898	+	0.444960i	0.965409	−	0.260739i	$-0.0839663\pi$
$277$	5.46009e6	+	9.45715e6i	0.256898	+	0.444960i	−0.708512	+	0.705699i	$0.750633\pi$
$278$	−646102.	−	373027.i	−0.0300723	−	0.0173623i
$279$		−	1.32558e6i		−	0.0610371i
$280$	1.60125e6	−	742864.i	0.0729434	−	0.0338404i
$281$	2.11105e7			0.951438			0.475719	−	0.879597i	$-0.342188\pi$
$281$	2.11105e7			0.951438			0.475719	+	0.879597i	$0.342188\pi$
$282$	−630736.	+	1.09247e6i	−0.0281255	+	0.0487148i
$283$	−9.26912e6	+	5.35153e6i	−0.408958	+	0.236112i	−0.690342	−	0.723483i	$-0.742540\pi$
$283$	−9.26912e6	+	5.35153e6i	−0.408958	+	0.236112i	0.281384	+	0.959595i	$0.409207\pi$
$284$	−1.08558e7	−	1.88027e7i	−0.473920	−	0.820854i
$285$	−2.42731e7	−	1.40141e7i	−1.04855	−	0.605382i
$286$		−	82445.3i		−	0.00352426i
$287$	−7.41804e6	−	5.21584e6i	−0.313793	−	0.220637i
$288$	1.91458e6			0.0801485
$289$	−5.24623e6	+	9.08673e6i	−0.217347	+	0.376456i
$290$	828453.	−	478307.i	0.0339683	−	0.0196116i
$291$	5.41263e6	+	9.37495e6i	0.219649	+	0.380443i
$292$	6.16602e6	+	3.55995e6i	0.247660	+	0.142987i
$293$		−	4.43426e6i		−	0.176286i	−0.996108	−	0.0881430i	$-0.971907\pi$
$293$		−	4.43426e6i		−	0.176286i	0.996108	−	0.0881430i	$-0.0280932\pi$
$294$	−994989.	+	357741.i	−0.0391540	+	0.0140775i
$295$	1.61135e7			0.627658
$296$	−752979.	+	1.30420e6i	−0.0290341	+	0.0502885i
$297$	−477881.	+	275905.i	−0.0182411	+	0.0105315i
$298$	656856.	+	1.13771e6i	0.0248211	+	0.0429915i
$299$	−2.68475e7	−	1.55004e7i	−1.00436	−	0.579869i
$300$			2.80806e7i			1.04002i
$301$	−1.35085e7	+	1.92120e7i	−0.495345	+	0.704487i
$302$	−861165.			−0.0312655
$303$	1.66654e7	−	2.88653e7i	0.599083	−	1.03764i
$304$	−1.61473e7	+	9.32262e6i	−0.574749	+	0.331831i
$305$	−1.44163e6	−	2.49698e6i	−0.0508106	−	0.0880065i
$306$	−499050.	−	288127.i	−0.0174172	−	0.0100559i
$307$			2.26980e7i			0.784463i	0.919866	+	0.392232i	$0.128297\pi$
$307$			2.26980e7i			0.784463i	−0.919866	+	0.392232i	$0.871703\pi$
$308$	−1.59752e6	−	3.44348e6i	−0.0546757	−	0.117854i
$309$	1.00839e7			0.341785
$310$	−41466.8	+	71822.6i	−0.00139192	+	0.00241088i
$311$	−4.38151e7	+	2.52966e7i	−1.45661	+	0.840972i	−0.998842	−	0.0481018i	$-0.984683\pi$
$311$	−4.38151e7	+	2.52966e7i	−1.45661	+	0.840972i	−0.457764	+	0.889074i	$0.651349\pi$
$312$	−1.12865e6	−	1.95488e6i	−0.0371617	−	0.0643660i
$313$	−4.90034e7	−	2.82921e7i	−1.59806	−	0.922641i	−0.991860	−	0.127329i	$-0.959359\pi$
$313$	−4.90034e7	−	2.82921e7i	−1.59806	−	0.922641i	−0.606201	−	0.795312i	$-0.707307\pi$
$314$			102217.i			0.00330167i
$315$	3.25748e6	−	3.64120e7i	0.104220	−	1.16497i
$316$	3.93774e7			1.24792
$317$	1.92615e7	−	3.33619e7i	0.604662	−	1.04730i	−0.387443	−	0.921894i	$-0.626642\pi$
$317$	1.92615e7	−	3.33619e7i	0.604662	−	1.04730i	0.992105	−	0.125411i	$-0.0400250\pi$
$318$	1.97795e6	−	1.14197e6i	0.0615083	−	0.0355118i
$319$	−2.05814e6	−	3.56480e6i	−0.0634019	−	0.109815i
$320$	3.74274e7	+	2.16087e7i	1.14219	+	0.659446i
$321$			3.01202e7i			0.910633i
$322$	1.30903e6	+	117108.i	0.0392087	+	0.00350767i
$323$	1.68615e7			0.500367
$324$	−1.87597e7	+	3.24927e7i	−0.551557	+	0.955325i
$325$	2.01577e7	−	1.16381e7i	0.587207	−	0.339024i
$326$	−360819.	−	624956.i	−0.0104144	−	0.0180383i
$327$	1.23590e7	+	7.13549e6i	0.353461	+	0.204071i
$328$			820731.i			0.0232584i
$329$	4.36731e7	−	2.02611e7i	1.22638	−	0.568952i
$330$	−257871.			−0.00717563
$331$	−5.58708e6	+	9.67710e6i	−0.154064	+	0.266846i	−0.932718	−	0.360607i	$-0.882569\pi$
$331$	−5.58708e6	+	9.67710e6i	−0.154064	+	0.266846i	0.778654	+	0.627454i	$0.215903\pi$
$332$	2.12455e7	−	1.22661e7i	0.580567	−	0.335191i
$333$	1.55945e7	+	2.70104e7i	0.422316	+	0.731473i
$334$	−902905.	−	521292.i	−0.0242327	−	0.0139908i
$335$		−	2.00061e7i		−	0.532142i
$336$	−4.24510e7	−	2.98485e7i	−1.11910	−	0.786873i
$337$	−4.35415e7			−1.13766			−0.568832	−	0.822454i	$-0.692604\pi$
$337$	−4.35415e7			−1.13766			−0.568832	+	0.822454i	$0.692604\pi$
$338$	118033.	−	204440.i	0.00305671	−	0.00529438i
$339$	1.59769e7	−	9.22428e6i	0.410104	−	0.236774i
$340$	−1.95776e7	−	3.39094e7i	−0.498108	−	0.862748i
$341$	309050.	+	178430.i	0.00779409	+	0.00449992i
$342$		−	712086.i		−	0.0178014i
$343$	3.89166e7	+	1.06730e7i	0.964389	+	0.264487i
$344$	2.12561e6			0.0522166
$345$	−4.84819e7	+	8.39731e7i	−1.18065	+	2.04495i
$346$	−1.95390e6	+	1.12809e6i	−0.0471709	+	0.0272341i
$347$	−1.59976e7	−	2.77086e7i	−0.382883	−	0.663173i	0.608590	−	0.793485i	$-0.291735\pi$
$347$	−1.59976e7	−	2.77086e7i	−0.382883	−	0.663173i	−0.991473	+	0.130312i	$0.958402\pi$
$348$	−4.87785e7	−	2.81623e7i	−1.15742	−	0.668237i
$349$			4.40810e7i			1.03699i	0.855080	+	0.518495i	$0.173508\pi$
$349$			4.40810e7i			1.03699i	−0.855080	+	0.518495i	$0.826492\pi$
$350$	−567572.	+	807209.i	−0.0132378	+	0.0188270i
$351$	6.25875e6			0.144733
$352$	−257712.	+	446370.i	−0.00590889	+	0.0102345i
$353$	−5.81948e7	+	3.35988e7i	−1.32300	+	0.763834i	−0.984206	−	0.177026i	$-0.943352\pi$
$353$	−5.81948e7	+	3.35988e7i	−1.32300	+	0.763834i	−0.338794	+	0.940861i	$0.610019\pi$
$354$	436784.	+	756533.i	0.00984594	+	0.0170537i
$355$	4.87486e7	+	2.81450e7i	1.08962	+	0.629095i
$356$		−	4.93424e7i		−	1.09363i
$357$	1.97501e7	+	4.25715e7i	0.434074	+	0.935653i
$358$	646855.			0.0140980
$359$	3.81356e7	−	6.60528e7i	0.824228	−	1.42761i	−0.0782796	−	0.996931i	$-0.524943\pi$
$359$	3.81356e7	−	6.60528e7i	0.824228	−	1.42761i	0.902508	−	0.430674i	$-0.141724\pi$
$360$	−2.86541e6	+	1.65434e6i	−0.0614156	+	0.0354583i
$361$	−1.31049e7	−	2.26984e7i	−0.278556	−	0.482473i
$362$	2.35017e6	+	1.35687e6i	0.0495419	+	0.0286030i
$363$		−	6.45082e7i		−	1.34864i
$364$	−3.83646e6	+	4.28839e7i	−0.0795474	+	0.889180i
$365$	−1.84593e7			−0.379609
$366$	78155.9	−	135370.i	0.00159411	−	0.00276108i
$367$	1.78005e7	−	1.02772e7i	0.360110	−	0.207910i	−0.309019	−	0.951056i	$-0.600001\pi$
$367$	1.78005e7	−	1.02772e7i	0.360110	−	0.207910i	0.669129	+	0.743146i	$0.266667\pi$
$368$	3.22518e7	+	5.58617e7i	0.647158	+	1.12091i
$369$	1.47204e7	+	8.49880e6i	0.292981	+	0.169153i
$370$		−	1.95130e6i		−	0.0385229i
$371$	−8.68198e7	−	7.76704e6i	−1.70019	−	0.152102i
$372$	4.88305e6			0.0948555
$373$	1.49659e7	−	2.59216e7i	0.288386	−	0.499500i	−0.685038	−	0.728507i	$-0.740215\pi$
$373$	1.49659e7	−	2.59216e7i	0.288386	−	0.499500i	0.973425	+	0.229007i	$0.0735479\pi$
$374$	134349.	−	77566.5i	0.00256815	−	0.00148272i
$375$	1.15695e7	+	2.00389e7i	0.219391	+	0.379997i
$376$	−3.77358e6	−	2.17868e6i	−0.0709888	−	0.0409854i
$377$			4.66877e7i			0.871322i
$378$	−240695.	+	111665.i	−0.00445647	+	0.00206747i
$379$	−1.35836e7			−0.249515			−0.124757	−	0.992187i	$-0.539815\pi$
$379$	−1.35836e7			−0.249515			−0.124757	+	0.992187i	$0.539815\pi$
$380$	2.41924e7	−	4.19025e7i	0.440888	−	0.763641i
$381$	1.15681e8	−	6.67882e7i	2.09163	−	1.20761i
$382$	−161622.	−	279938.i	−0.00289942	−	0.00502195i
$383$	4.77451e7	+	2.75657e7i	0.849831	+	0.490650i	0.860594	−	0.509292i	$-0.170093\pi$
$383$	4.77451e7	+	2.75657e7i	0.849831	+	0.490650i	−0.0107626	+	0.999942i	$0.503426\pi$
$384$			9.40220e6i			0.166049i
$385$	8.05073e6	+	5.66070e6i	0.141076	+	0.0991946i
$386$	−1.10545e6			−0.0192211
$387$	2.20111e7	−	3.81243e7i	0.379759	−	0.657763i
$388$	−1.61839e7	+	9.34380e6i	−0.277070	+	0.159966i
$389$	3.09731e7	+	5.36470e7i	0.526182	+	0.911373i	0.999535	+	0.0305006i	$0.00971015\pi$
$389$	3.09731e7	+	5.36470e7i	0.526182	+	0.911373i	−0.473353	+	0.880873i	$0.656957\pi$
$390$	2.53298e6	+	1.46241e6i	0.0427009	+	0.0246534i
$391$		−	5.83327e7i		−	0.975847i
$392$	−1.23570e6	−	3.43687e6i	−0.0205142	−	0.0570565i
$393$	−7.74897e7			−1.27663
$394$	1.36906e6	−	2.37129e6i	0.0223839	−	0.0387700i
$395$	−8.84135e7	+	5.10455e7i	−1.43459	+	0.828260i
$396$	3.55765e6	+	6.16203e6i	0.0572899	+	0.0992289i
$397$	−7.35421e7	−	4.24595e7i	−1.17534	−	0.678584i	−0.220410	−	0.975407i	$-0.570739\pi$
$397$	−7.35421e7	−	4.24595e7i	−1.17534	−	0.678584i	−0.954932	+	0.296823i	$0.904073\pi$
$398$			937010.i			0.0148626i
$399$	−3.33557e7	+	4.74390e7i	−0.525112	+	0.746821i
$400$	−4.84307e7			−0.756729
$401$	−5.13168e7	+	8.88833e7i	−0.795841	+	1.37844i	0.126463	+	0.991971i	$0.459638\pi$
$401$	−5.13168e7	+	8.88833e7i	−0.795841	+	1.37844i	−0.922304	+	0.386466i	$0.873696\pi$
$402$	939291.	−	542300.i	0.0144585	−	0.00834760i
$403$	−2.02379e6	−	3.50531e6i	−0.0309208	−	0.0535564i
$404$	4.98300e7	+	2.87694e7i	0.755695	+	0.436301i
$405$		−	9.72739e7i		−	1.46430i
$406$	−832972.	−	1.79548e6i	−0.0124467	−	0.0268289i
$407$	−8.39637e6			−0.124540
$408$	2.12372e6	−	3.67840e6i	0.0312692	−	0.0541599i
$409$	8.42787e7	−	4.86583e7i	1.23182	−	0.711193i	0.264413	−	0.964410i	$-0.414822\pi$
$409$	8.42787e7	−	4.86583e7i	1.23182	−	0.711193i	0.967410	+	0.253217i	$0.0814886\pi$
$410$	−531718.	−	920963.i	−0.00771489	−	0.0133626i
$411$	1.47713e7	+	8.52819e6i	0.212761	+	0.122838i
$412$			1.74078e7i			0.248915i
$413$	2.97076e6	−	3.32071e7i	0.0421714	−	0.471391i
$414$	−2.46347e6			−0.0347174
$415$	−3.18015e7	+	5.50817e7i	−0.444941	+	0.770661i
$416$	5.06283e6	−	2.92302e6i	0.0703255	−	0.0406025i
$417$	−5.69433e7	−	9.86286e7i	−0.785298	−	1.36018i
$418$	166018.	+	95850.3i	0.00227314	+	0.00131240i
$419$			8.57907e7i			1.16627i	0.812376	+	0.583134i	$0.198174\pi$
$419$			8.57907e7i			1.16627i	−0.812376	+	0.583134i	$0.801826\pi$
$420$	1.34131e8	+	1.19996e7i	1.81043	+	0.161964i
$421$	1.03761e8			1.39055			0.695275	−	0.718743i	$-0.255282\pi$
$421$	1.03761e8			1.39055			0.695275	+	0.718743i	$0.255282\pi$
$422$	−1.47879e6	+	2.56134e6i	−0.0196775	+	0.0340824i
$423$	−7.81521e7	+	4.51211e7i	−1.03257	+	0.596154i
$424$	3.94457e6	+	6.83219e6i	0.0517490	+	0.0896319i
$425$	3.79297e7	+	2.18987e7i	0.494098	+	0.285267i
$426$			3.05168e6i			0.0394739i
$427$	−5.41163e6	+	2.51060e6i	−0.0695095	+	0.0322473i
$428$	−5.19964e7			−0.663196
$429$	6.29271e6	−	1.08993e7i	0.0797014	−	0.138047i
$430$	−2.38520e6	+	1.37710e6i	−0.0299999	+	0.0173205i
$431$	−4.93663e7	−	8.55049e7i	−0.616593	−	1.06797i	−0.990103	−	0.140344i	$-0.955179\pi$
$431$	−4.93663e7	−	8.55049e7i	−0.616593	−	1.06797i	0.373510	−	0.927626i	$-0.378154\pi$
$432$	−1.12779e7	−	6.51130e6i	−0.139887	−	0.0807637i
$433$		−	9.55356e7i		−	1.17680i	−0.808571	−	0.588399i	$-0.799759\pi$
$433$		−	9.55356e7i		−	1.17680i	0.808571	−	0.588399i	$-0.200241\pi$
$434$	140369.	+	98697.6i	0.00171713	+	0.00120736i
$435$	1.46029e8			1.77407
$436$	−1.23180e7	+	2.13353e7i	−0.148621	+	0.257419i
$437$	6.24255e7	−	3.60414e7i	0.748028	−	0.431874i
$438$	−500372.	−	866670.i	−0.00595485	−	0.0103141i
$439$	1.42457e7	+	8.22477e6i	0.168380	+	0.0972143i	0.581822	−	0.813316i	$-0.302340\pi$
$439$	1.42457e7	+	8.22477e6i	0.168380	+	0.0972143i	−0.413442	+	0.910531i	$0.635673\pi$
$440$		−	890731.i		−	0.0104566i
$441$	−7.44385e7	−	1.34262e7i	−0.867924	−	0.156545i
$442$	−1.75955e6			−0.0203768
$443$	4.15949e7	−	7.20445e7i	0.478442	−	0.828685i	−0.521253	−	0.853402i	$-0.674535\pi$
$443$	4.15949e7	−	7.20445e7i	0.478442	−	0.828685i	0.999694	+	0.0247172i	$0.00786853\pi$
$444$	−9.94983e7	+	5.74454e7i	−1.13675	+	0.656306i
$445$	6.39633e7	+	1.10788e8i	0.725857	+	1.25722i
$446$	1.76392e6	+	1.01840e6i	0.0198827	+	0.0114793i
$447$			2.00540e8i			2.24533i
$448$	5.14322e7	−	7.31476e7i	0.572007	−	0.813516i
$449$	−3.16448e7			−0.349593			−0.174796	−	0.984605i	$-0.555927\pi$
$449$	−3.16448e7			−0.349593			−0.174796	+	0.984605i	$0.555927\pi$
$450$	924815.	−	1.60183e6i	0.0101489	−	0.0175783i
$451$	−3.96287e6	+	2.28796e6i	−0.0431996	+	0.0249413i
$452$	1.59238e7	+	2.75809e7i	0.172438	+	0.298671i
$453$	−1.13846e8	−	6.57291e7i	−1.22468	−	0.707071i
$454$		−	4.95509e6i		−	0.0529522i
$455$	−4.69771e7	−	1.01260e8i	−0.498714	−	1.07499i
$456$	5.24864e6			0.0553545
$457$	−2.73326e7	+	4.73414e7i	−0.286373	+	0.496012i	−0.972941	−	0.231053i	$-0.925783\pi$
$457$	−2.73326e7	+	4.73414e7i	−0.286373	+	0.496012i	0.686568	+	0.727065i	$0.259116\pi$
$458$	−2.71103e6	+	1.56521e6i	−0.0282188	+	0.0162921i
$459$	5.88838e6	+	1.01990e7i	0.0608917	+	0.105468i
$460$	−1.44962e8	−	8.36941e7i	−1.48930	−	0.859847i
$461$			1.65878e8i			1.69311i	0.532299	+	0.846556i	$0.321328\pi$
$461$			1.65878e8i			1.69311i	−0.532299	+	0.846556i	$0.678672\pi$
$462$	−47542.4	+	531428.i	−0.000482120	+	0.00538912i
$463$	−1.44466e7			−0.145553			−0.0727767	−	0.997348i	$-0.523186\pi$
$463$	−1.44466e7			−0.145553			−0.0727767	+	0.997348i	$0.523186\pi$
$464$	4.85716e7	−	8.41285e7i	0.486215	−	0.842150i
$465$	−1.09638e7	+	6.32998e6i	−0.109045	+	0.0629569i
$466$	1.12244e6	+	1.94412e6i	0.0110919	+	0.0192117i
$467$	−9.01506e6	−	5.20485e6i	−0.0885152	−	0.0511043i	0.455089	−	0.890446i	$-0.349607\pi$
$467$	−9.01506e6	−	5.20485e6i	−0.0885152	−	0.0511043i	−0.543604	+	0.839342i	$0.682941\pi$
$468$		−	8.07034e7i		−	0.787325i
$469$	−4.12291e7	−	3.68842e6i	−0.399655	−	0.0357538i
$470$	5.64590e6			0.0543801
$471$	−7.80179e6	+	1.35131e7i	−0.0746675	+	0.129328i
$472$	−2.61320e6	+	1.50873e6i	−0.0248512	+	0.0143478i
$473$	5.92560e6	+	1.02634e7i	0.0559950	+	0.0969861i
$474$	−4.79321e6	−	2.76736e6i	−0.0450082	−	0.0259855i
$475$			5.41213e7i			0.504995i
$476$	−7.34910e7	+	3.40944e7i	−0.681418	+	0.316128i
$477$	1.63387e8			1.50543
$478$	−980881.	+	1.69894e6i	−0.00898117	+	0.0155558i
$479$	8.51582e7	−	4.91661e7i	0.774855	−	0.447362i	−0.0597491	−	0.998213i	$-0.519030\pi$
$479$	8.51582e7	−	4.91661e7i	0.774855	−	0.447362i	0.834604	+	0.550851i	$0.185697\pi$
$480$	−9.14257e6	−	1.58354e7i	−0.0826694	−	0.143188i
$481$	8.24746e7	+	4.76168e7i	0.741114	+	0.427883i
$482$		−	1.17184e6i		−	0.0104647i
$483$	1.64116e8	+	1.15395e8i	1.45650	+	1.02410i
$484$	1.11360e8			0.982185
$485$	2.42250e7	−	4.19590e7i	0.212343	−	0.367790i
$486$	4.07866e6	−	2.35482e6i	0.0355311	−	0.0205139i
$487$	−5.56651e7	−	9.64147e7i	−0.481943	−	0.834750i	0.517842	−	0.855476i	$-0.326735\pi$
$487$	−5.56651e7	−	9.64147e7i	−0.481943	−	0.834750i	−0.999785	+	0.0207263i	$0.993402\pi$
$488$	467592.	+	269964.i	0.00402353	+	0.00232299i
$489$		−	1.10159e8i		−	0.942094i
$490$	3.61322e6	+	3.05604e6i	0.0307119	+	0.0259759i
$491$	−2.97699e7			−0.251497			−0.125748	−	0.992062i	$-0.540133\pi$
$491$	−2.97699e7			−0.251497			−0.125748	+	0.992062i	$0.540133\pi$
$492$	−3.13071e7	+	5.42254e7i	−0.262874	+	0.455311i
$493$	−7.60802e7	+	4.39249e7i	−0.634938	+	0.366581i
$494$	−1.08716e6	−	1.88301e6i	−0.00901802	−	0.0156197i
$495$	−1.59759e7	−	9.22367e6i	−0.131719	−	0.0760481i
$496$			8.42182e6i			0.0690178i
$497$	6.69896e7	−	9.52735e7i	0.545680	−	0.776074i
$498$	−3.44814e6			−0.0279188
$499$	−6.72883e7	+	1.16547e8i	−0.541549	+	0.937991i	0.457266	+	0.889330i	$0.348829\pi$
$499$	−6.72883e7	+	1.16547e8i	−0.541549	+	0.937991i	−0.998815	+	0.0486607i	$0.984505\pi$
$500$	−3.45930e7	+	1.99723e7i	−0.276744	+	0.159778i
$501$	−7.95762e7	−	1.37830e8i	−0.632805	−	1.09605i
$502$	1.79636e6	+	1.03713e6i	0.0141998	+	0.00819828i
$503$		−	7.92858e7i		−	0.623005i	−0.950245	−	0.311502i	$-0.899168\pi$
$503$		−	7.92858e7i		−	0.623005i	0.950245	−	0.311502i	$-0.100832\pi$
$504$	2.88104e6	+	6.21012e6i	0.0225039	+	0.0485074i
$505$	−1.49177e8			−1.15832
$506$	331596.	−	574341.i	0.00255951	−	0.00443321i
$507$	3.12081e7	−	1.80180e7i	0.239465	−	0.138255i
$508$	1.15296e8	+	1.99699e8i	0.879475	+	1.52330i
$509$	5.45385e7	+	3.14878e7i	0.413570	+	0.238775i	0.692323	−	0.721588i	$-0.256587\pi$
$509$	5.45385e7	+	3.14878e7i	0.413570	+	0.238775i	−0.278752	+	0.960363i	$0.589921\pi$
$510$			5.50350e6i			0.0414885i
$511$	−3.40325e6	+	3.80415e7i	−0.0255053	+	0.285098i
$512$	−2.02794e7			−0.151093
$513$	−7.27638e6	+	1.26031e7i	−0.0538968	+	0.0933521i
$514$	4.03344e6	−	2.32871e6i	0.0297021	−	0.0171485i
$515$	−2.25659e7	−	3.90854e7i	−0.165208	−	0.286149i
$516$	1.40439e8	+	8.10823e7i	1.02220	+	0.590170i
$517$		−	2.42941e7i		−	0.175804i
$518$	−4.02130e6	−	359752.i	−0.0289319	−	0.00258829i
$519$	−3.44408e8			−2.46361
$520$	−5.05144e6	+	8.74935e6i	−0.0359257	+	0.0622251i
$521$	2.63217e7	−	1.51968e7i	0.186123	−	0.107458i	−0.404043	−	0.914740i	$-0.632395\pi$
$521$	2.63217e7	−	1.51968e7i	0.186123	−	0.107458i	0.590166	+	0.807282i	$0.299062\pi$
$522$	1.85501e6	+	3.21298e6i	0.0130417	+	0.0225890i
$523$	5.21989e7	+	3.01371e7i	0.364885	+	0.210667i	0.671222	−	0.741257i	$-0.265770\pi$
$523$	5.21989e7	+	3.01371e7i	0.364885	+	0.210667i	−0.306336	+	0.951923i	$0.599103\pi$
$524$		−	1.33770e8i		−	0.929747i
$525$	−1.36644e8	+	6.33928e7i	−0.944306	+	0.438089i
$526$	4.21860e6			0.0289875
$527$	3.80807e6	−	6.59576e6i	0.0260179	−	0.0450644i
$528$	−2.26782e7	+	1.30932e7i	−0.154066	+	0.0889499i
$529$	−5.06678e7	−	8.77592e7i	−0.342267	−	0.592824i
$530$	−8.85260e6	−	5.11105e6i	−0.0594625	−	0.0343307i
$531$			6.24927e7i			0.417393i
$532$	−8.18937e7	−	5.75818e7i	−0.543896	−	0.382429i
$533$	5.19012e7			0.342764
$534$	−3.46768e6	+	6.00620e6i	−0.0227727	+	0.0394435i
$535$	1.16747e8	−	6.74038e7i	0.762401	−	0.440172i
$536$	1.87320e6	+	3.24448e6i	0.0121644	+	0.0210693i
$537$	8.55144e7	+	4.93718e7i	0.552226	+	0.318828i
$538$		−	1.77981e6i		−	0.0114295i
$539$	1.31500e7	−	1.55475e7i	0.0839769	−	0.0992877i
$540$	3.37939e7			0.214614
$541$	1.20240e8	−	2.08262e8i	0.759377	−	1.31528i	−0.183792	−	0.982965i	$-0.558837\pi$
$541$	1.20240e8	−	2.08262e8i	0.759377	−	1.31528i	0.943169	−	0.332314i	$-0.107829\pi$
$542$	5.34581e6	−	3.08640e6i	0.0335750	−	0.0193845i
$543$	2.07128e8	+	3.58757e8i	1.29372	+	2.24079i
$544$	9.52645e6	+	5.50010e6i	0.0591745	+	0.0341644i
$545$		−	6.38719e7i		−	0.394566i
$546$	3.48078e6	−	4.95041e6i	0.0213845	−	0.0304133i
$547$	−5.01977e7			−0.306705			−0.153353	−	0.988172i	$-0.549007\pi$
$547$	−5.01977e7			−0.306705			−0.153353	+	0.988172i	$0.549007\pi$
$548$	−1.47222e7	+	2.54995e7i	−0.0894602	+	0.154950i
$549$	9.68399e6	−	5.59105e6i	0.0585244	−	0.0337891i
$550$	248969.	+	431228.i	0.00149643	+	0.00259190i
$551$	−9.40137e7	−	5.42788e7i	−0.562000	−	0.324471i
$552$		−	1.81578e7i		−	0.107956i
$553$	8.88958e7	+	1.91616e8i	0.525661	+	1.13307i
$554$	2.64968e6			0.0155835
$555$	1.48935e8	−	2.57962e8i	0.871198	−	1.50896i
$556$	1.70262e8	−	9.83009e7i	0.990589	−	0.571917i
$557$	6.78104e7	+	1.17451e8i	0.392402	+	0.679659i	0.992766	−	0.120067i	$-0.0383110\pi$
$557$	6.78104e7	+	1.17451e8i	0.392402	+	0.679659i	−0.600364	+	0.799727i	$0.704978\pi$
$558$	−278549.	−	160820.i	−0.00160324	−	0.000925631i
$559$		−	1.34419e8i		−	0.769530i
$560$	−2.06957e7	+	2.31337e8i	−0.117847	+	1.31729i
$561$	2.36813e7			0.134127
$562$	2.56114e6	−	4.43602e6i	0.0144286	−	0.0249911i
$563$	−1.43141e8	+	8.26425e7i	−0.802119	+	0.463104i	−0.844212	−	0.536010i	$-0.819931\pi$
$563$	−1.43141e8	+	8.26425e7i	−0.802119	+	0.463104i	0.0420925	+	0.999114i	$0.486598\pi$
$564$	−1.66213e8	−	2.87889e8i	−0.926461	−	1.60468i
$565$	−7.15070e7	−	4.12846e7i	−0.396464	−	0.228898i
$566$			2.59700e6i			0.0143226i
$567$	−2.00465e8	−	1.79339e7i	−1.09974	−	0.0983843i
$568$	−1.05411e7			−0.0575226
$569$	−1.13638e8	+	1.96826e8i	−0.616858	+	1.06843i	0.373198	+	0.927752i	$0.378261\pi$
$569$	−1.13638e8	+	1.96826e8i	−0.616858	+	1.06843i	−0.990055	+	0.140677i	$0.955072\pi$
$570$	−5.88964e6	+	3.40038e6i	−0.0318027	+	0.0183613i
$571$	−8.26649e7	−	1.43180e8i	−0.444031	−	0.769084i	0.553953	−	0.832548i	$-0.313119\pi$
$571$	−8.26649e7	−	1.43180e8i	−0.444031	−	0.769084i	−0.997984	+	0.0634640i	$0.979785\pi$
$572$	1.88154e7	+	1.08631e7i	0.100537	+	0.0580450i
$573$		−	4.93439e7i		−	0.262283i
$574$	−1.99598e6	+	925987.i	−0.0105541	+	0.00489631i
$575$	1.87234e8			0.984873
$576$	−8.38048e7	+	1.45154e8i	−0.438532	+	0.759560i
$577$	−2.33390e8	+	1.34748e8i	−1.21494	+	0.701446i	−0.963831	−	0.266512i	$-0.914129\pi$
$577$	−2.33390e8	+	1.34748e8i	−1.21494	+	0.701446i	−0.251109	+	0.967959i	$0.580795\pi$
$578$	1.27295e6	+	2.20481e6i	0.00659215	+	0.0114179i
$579$	−1.46141e8	−	8.43744e7i	−0.752897	−	0.434686i
$580$			2.52089e8i			1.29202i
$581$	1.07651e8	+	7.56925e7i	0.548895	+	0.385944i
$582$	2.62665e6			0.0133240
$583$	−2.19927e7	+	3.80924e7i	−0.110987	+	0.192235i
$584$	2.99363e6	−	1.72838e6i	0.0150300	−	0.00867760i
$585$	1.04617e8	+	1.81202e8i	0.522558	+	0.905098i
$586$	−931783.	−	537965.i	−0.00463044	−	0.00267338i
$587$		−	1.07673e8i		−	0.532344i	−0.963926	−	0.266172i	$-0.914241\pi$
$587$		−	1.07673e8i		−	0.532344i	0.963926	−	0.266172i	$-0.0857589\pi$
$588$	4.94582e7	−	2.74209e8i	0.243280	−	1.34881i
$589$	9.41139e6			0.0460583
$590$	1.95489e6	−	3.38597e6i	0.00951846	−	0.0164865i
$591$	3.61981e8	−	2.08990e8i	1.75357	−	1.01243i
$592$	−9.90762e7	−	1.71605e8i	−0.477534	−	0.827113i
$593$	4.29092e7	+	2.47737e7i	0.205772	+	0.118803i	0.599345	−	0.800491i	$-0.295428\pi$
$593$	4.29092e7	+	2.47737e7i	0.205772	+	0.118803i	−0.393573	+	0.919293i	$0.628761\pi$
$594$			133892.i			0.000638842i
$595$	1.20811e8	−	1.71819e8i	0.573530	−	0.815682i
$596$	−3.46192e8			−1.63523
$597$	−7.15181e7	+	1.23873e8i	−0.336119	+	0.582175i
$598$	−6.51430e6	+	3.76104e6i	−0.0304624	+	0.0175875i
$599$	6.50352e7	+	1.12644e8i	0.302600	+	0.524118i	0.976724	−	0.214500i	$-0.0688122\pi$
$599$	6.50352e7	+	1.12644e8i	0.302600	+	0.524118i	−0.674124	+	0.738618i	$0.735479\pi$
$600$	1.18067e7	+	6.81662e6i	0.0546608	+	0.0315584i
$601$			3.05422e8i			1.40695i	0.710722	+	0.703473i	$0.248368\pi$
$601$			3.05422e8i			1.40695i	−0.710722	+	0.703473i	$0.751632\pi$
$602$	2.39822e6	+	5.16939e6i	0.0109926	+	0.0236946i
$603$	7.75893e7			0.353875
$604$	1.13468e8	−	1.96532e8i	0.514946	−	0.891913i
$605$	−2.50035e8	+	1.44358e8i	−1.12911	+	0.651890i
$606$	−4.04370e6	−	7.00389e6i	−0.0181703	−	0.0314718i
$607$	2.13143e8	+	1.23058e8i	0.953026	+	0.550230i	0.894020	−	0.448028i	$-0.147874\pi$
$607$	2.13143e8	+	1.23058e8i	0.953026	+	0.550230i	0.0590061	+	0.998258i	$0.481207\pi$
$608$			1.35931e7i			0.0604796i
$609$	2.69226e7	−	3.00941e8i	0.119197	−	1.33238i
$610$	−699596.			−0.00308218
$611$	−1.37775e8	+	2.38633e8i	−0.604012	+	1.04618i
$612$	1.31511e8	−	7.59276e7i	0.573728	−	0.331242i
$613$	−5.82157e7	−	1.00833e8i	−0.252731	−	0.437743i	0.711546	−	0.702640i	$-0.247996\pi$
$613$	−5.82157e7	−	1.00833e8i	−0.252731	−	0.437743i	−0.964277	+	0.264897i	$0.914662\pi$
$614$	4.76960e6	+	2.75373e6i	0.0206052	+	0.0118964i
$615$		−	1.62335e8i		−	0.697891i
$616$	−1.83565e6	−	164220.i	−0.00785320	−	0.000702560i
$617$	3.80306e8			1.61912			0.809558	−	0.587041i	$-0.199707\pi$
$617$	3.80306e8			1.61912			0.809558	+	0.587041i	$0.199707\pi$
$618$	1.22338e6	−	2.11896e6i	0.00518318	−	0.00897753i
$619$	−1.69319e8	+	9.77566e7i	−0.713896	+	0.412168i	−0.812502	−	0.582959i	$-0.801895\pi$
$619$	−1.69319e8	+	9.77566e7i	−0.713896	+	0.412168i	0.0986061	+	0.995127i	$0.468562\pi$
$620$	−1.09274e7	−	1.89268e7i	−0.0458503	−	0.0794150i
$621$	4.36005e7	+	2.51728e7i	0.182061	+	0.105113i
$622$			1.22760e7i			0.0510135i
$623$	2.40107e8	−	1.11392e8i	0.992982	−	0.460671i
$624$	2.97013e8			1.22242
$625$	1.44411e8	−	2.50126e8i	0.591505	−	1.02452i
$626$	−1.18902e7	+	6.86482e6i	−0.0484693	+	0.0279838i
$627$	1.46317e7	+	2.53429e7i	0.0593598	+	0.102814i
$628$	−2.33276e7	−	1.34682e7i	−0.0941870	−	0.0543789i
$629$			1.79196e8i			0.720072i
$630$	−7.25617e6	−	5.10203e6i	−0.0290192	−	0.0204043i
$631$	6.19380e7			0.246529			0.123265	−	0.992374i	$-0.460664\pi$
$631$	6.19380e7			0.246529			0.123265	+	0.992374i	$0.460664\pi$
$632$	9.55896e6	−	1.65566e7i	0.0378669	−	0.0655873i
$633$	−3.90993e8	+	2.25740e8i	−1.54155	+	0.890015i
$634$	−4.67362e6	−	8.09496e6i	−0.0183394	−	0.0317648i
$635$	−5.17745e8	−	2.98920e8i	−2.02206	−	1.16744i
$636$			6.01868e8i			2.33954i
$637$	−2.17340e8	+	7.81430e7i	−0.840855	+	0.302323i
$638$	−998776.			−0.00384597
$639$	−1.09154e8	+	1.89061e8i	−0.418349	+	0.724601i
$640$	3.64431e7	−	2.10405e7i	0.139020	−	0.0802630i
$641$	−1.90907e8	−	3.30661e8i	−0.724850	−	1.25548i	−0.959036	−	0.283285i	$-0.908576\pi$
$641$	−1.90907e8	−	3.30661e8i	−0.724850	−	1.25548i	0.234186	−	0.972192i	$-0.424758\pi$
$642$	6.32926e6	+	3.65420e6i	0.0239193	+	0.0138098i
$643$		−	3.52624e8i		−	1.32641i	−0.748436	−	0.663207i	$-0.769195\pi$
$643$		−	3.52624e8i		−	1.32641i	0.748436	−	0.663207i	$-0.230805\pi$
$644$	−1.99205e8	+	2.83313e8i	−0.745836	+	1.06074i
$645$	−4.20433e8			−1.56681
$646$	2.04564e6	−	3.54316e6i	0.00758809	−	0.0131430i
$647$	2.66973e8	−	1.54137e8i	0.985721	−	0.569106i	0.0817283	−	0.996655i	$-0.473956\pi$
$647$	2.66973e8	−	1.54137e8i	0.985721	−	0.569106i	0.903992	+	0.427549i	$0.140623\pi$
$648$	9.10792e6	+	1.57754e7i	0.0334730	+	0.0579769i
$649$	−1.45697e7	−	8.41182e6i	−0.0532987	−	0.0307720i
$650$		−	5.64773e6i		−	0.0205653i
$651$	1.10237e7	+	2.37616e7i	0.0399561	+	0.0861258i
$652$	1.90167e8			0.686108
$653$	1.29181e8	−	2.23748e8i	0.463937	−	0.803562i	−0.535216	−	0.844715i	$-0.679770\pi$
$653$	1.29181e8	−	2.23748e8i	0.463937	−	0.803562i	0.999153	+	0.0411534i	$0.0131032\pi$
$654$	2.99880e6	−	1.73136e6i	0.0107205	−	0.00618948i
$655$	1.73408e8	+	3.00352e8i	0.617086	+	1.06882i
$656$	−9.35228e7	−	5.39954e7i	−0.331288	−	0.191269i
$657$		−	7.15905e7i		−	0.252441i
$658$	1.04091e6	−	1.16352e7i	0.00365371	−	0.0408411i
$659$	3.93903e8			1.37636			0.688182	−	0.725538i	$-0.258409\pi$
$659$	3.93903e8			1.37636			0.688182	+	0.725538i	$0.258409\pi$
$660$	3.39773e7	−	5.88504e7i	0.118183	−	0.204700i
$661$	−7.75908e7	+	4.47971e7i	−0.268662	+	0.155112i	−0.628279	−	0.777988i	$-0.716240\pi$
$661$	−7.75908e7	+	4.47971e7i	−0.268662	+	0.155112i	0.359618	+	0.933100i	$0.382907\pi$
$662$	1.35565e6	+	2.34806e6i	0.00467277	+	0.00809347i
$663$	−2.32614e8	−	1.34299e8i	−0.798168	−	0.460823i
$664$		−	1.19105e7i		−	0.0406842i
$665$	2.58519e8	+	2.31275e7i	0.879078	+	0.0786437i
$666$	7.56770e6			0.0256178
$667$	−1.87779e8	+	3.25242e8i	−0.632803	+	1.09605i
$668$	2.37935e8	−	1.37372e8i	0.798232	−	0.460860i
$669$	1.55461e8	+	2.69266e8i	0.519209	+	0.899296i
$670$	−4.20394e6	−	2.42714e6i	−0.0139776	−	0.00806995i
$671$			3.01033e6i			0.00996430i
$672$	−3.43196e7	+	1.59218e7i	−0.113093	+	0.0524667i
$673$	−6.05778e7			−0.198732			−0.0993661	−	0.995051i	$-0.531681\pi$
$673$	−6.05778e7			−0.198732			−0.0993661	+	0.995051i	$0.531681\pi$
$674$	−5.28247e6	+	9.14951e6i	−0.0172527	+	0.0298826i
$675$	−3.27362e7	+	1.89003e7i	−0.106443	+	0.0614549i
$676$	3.11043e7	+	5.38743e7i	0.100689	+	0.174398i
$677$	9.22382e7	+	5.32538e7i	0.297266	+	0.171626i	0.641214	−	0.767362i	$-0.278431\pi$
$677$	9.22382e7	+	5.32538e7i	0.297266	+	0.171626i	−0.343948	+	0.938989i	$0.611764\pi$
$678$		−	4.47637e6i		−	0.0143627i
$679$	−8.20040e7	−	5.76594e7i	−0.261955	−	0.184188i
$680$	−1.90101e7			−0.0604584
$681$	3.78201e8	−	6.55064e8i	1.19752	−	2.07416i
$682$	74988.0	−	43294.4i	0.000236395	−	0.000136483i
$683$	−8.18781e7	−	1.41817e8i	−0.256984	−	0.445109i	0.708449	−	0.705762i	$-0.249395\pi$
$683$	−8.18781e7	−	1.41817e8i	−0.256984	−	0.445109i	−0.965432	+	0.260653i	$0.916062\pi$
$684$	1.62510e8	+	9.38251e7i	0.507822	+	0.293191i
$685$		−	7.63383e7i		−	0.237504i
$686$	6.96413e6	−	6.88280e6i	0.0215722	−	0.0213203i
$687$	−4.77865e8			−1.47379
$688$	−1.39843e8	+	2.42215e8i	−0.429413	+	0.743765i
$689$	4.32053e8	−	2.49446e8i	1.32093	−	0.762638i
$690$	1.17637e7	+	2.03753e7i	0.0358093	+	0.0620236i
$691$	3.67054e8	+	2.11919e8i	1.11249	+	0.642296i	0.939473	−	0.342622i	$-0.111315\pi$
$691$	3.67054e8	+	2.11919e8i	1.11249	+	0.642296i	0.173017	+	0.984919i	$0.444648\pi$
$692$		−	5.94550e8i		−	1.79420i
$693$	−2.19538e7	+	3.12230e7i	−0.0659645	+	0.0938157i
$694$	−7.76334e6			−0.0232258
$695$	−2.54858e8	+	4.41427e8i	−0.759178	+	1.31494i
$696$	−2.36822e7	+	1.36729e7i	−0.0702416	+	0.0405540i
$697$	4.88299e7	+	8.45758e7i	0.144207	+	0.249774i
$698$	9.26287e6	+	5.34792e6i	0.0272382	+	0.0157260i
$699$			3.42684e8i			1.00337i
$700$	−1.09435e8	−	2.35888e8i	−0.319052	−	0.687720i
$701$	−5.46701e8			−1.58707			−0.793535	−	0.608525i	$-0.791762\pi$
$701$	−5.46701e8			−1.58707			−0.793535	+	0.608525i	$0.791762\pi$
$702$	759314.	−	1.31517e6i	0.00219488	−	0.00380164i
$703$	−1.91769e8	+	1.10718e8i	−0.551966	+	0.318677i
$704$	−2.25611e7	−	3.90770e7i	−0.0646609	−	0.111996i
$705$	7.46390e8	+	4.30928e8i	2.13009	+	1.22981i
$706$			1.63049e7i			0.0463343i
$707$	−2.75030e7	+	3.07428e8i	−0.0778254	+	0.869931i
$708$	−2.30204e8			−0.648655
$709$	1.11801e8	−	1.93645e8i	0.313695	−	0.543335i	−0.665464	−	0.746430i	$-0.731766\pi$
$709$	1.11801e8	−	1.93645e8i	0.313695	−	0.543335i	0.979159	+	0.203094i	$0.0650998\pi$
$710$	1.18284e7	−	6.82912e6i	0.0330484	−	0.0190805i
$711$	−1.97969e8	−	3.42893e8i	−0.550794	−	0.954002i
$712$	−2.07465e7	−	1.19780e7i	−0.0574784	−	0.0331852i
$713$		−	3.25589e7i		−	0.0898257i
$714$	1.13418e7	+	1.01465e6i	0.0311592	+	0.00278755i
$715$	−5.63279e7			−0.154101
$716$	−8.52303e7	+	1.47623e8i	−0.232196	+	0.402175i
$717$	−2.59346e8	+	1.49733e8i	−0.703593	+	0.406219i
$718$	−9.25325e6	−	1.60271e7i	−0.0249989	−	0.0432994i
$719$	−1.75116e8	−	1.01103e8i	−0.471129	−	0.272007i	0.245583	−	0.969376i	$-0.421021\pi$
$719$	−1.75116e8	−	1.01103e8i	−0.471129	−	0.272007i	−0.716712	+	0.697369i	$0.754354\pi$
$720$		−	4.35354e8i		−	1.16639i
$721$	−8.47087e7	+	3.92986e7i	−0.226007	+	0.104851i
$722$	−6.35956e6			−0.0168972
$723$	8.94419e7	−	1.54918e8i	0.236661	−	0.409908i
$724$	−6.19320e8	+	3.57565e8i	−1.63192	+	0.942191i
$725$	−1.40988e8	−	2.44199e8i	−0.369972	−	0.640810i
$726$	−1.35553e7	−	7.82615e6i	−0.0354241	−	0.0204521i
$727$		−	2.28025e8i		−	0.593444i	−0.954964	−	0.296722i	$-0.904106\pi$
$727$		−	2.28025e8i		−	0.593444i	0.954964	−	0.296722i	$-0.0958935\pi$
$728$	1.70996e7	+	1.20232e7i	0.0443192	+	0.0311621i
$729$	2.91171e8			0.751562
$730$	−2.23949e6	+	3.87891e6i	−0.00575679	+	0.00997105i
$731$	2.19043e8	−	1.26465e8i	0.560761	−	0.323755i
$732$	2.05958e7	+	3.56729e7i	0.0525104	+	0.0909506i
$733$	−7.52957e7	−	4.34720e7i	−0.191187	−	0.110382i	0.401351	−	0.915924i	$-0.368541\pi$
$733$	−7.52957e7	−	4.34720e7i	−0.191187	−	0.110382i	−0.592538	+	0.805542i	$0.701874\pi$
$734$		−	4.98731e6i		−	0.0126118i
$735$	2.44414e8	+	6.79791e8i	0.615551	+	1.71204i
$736$	4.70257e7			0.117951
$737$	−1.04439e7	+	1.80894e7i	−0.0260892	+	0.0451878i
$738$	3.57176e6	−	2.06216e6i	0.00888614	−	0.00513041i
$739$	2.67835e8	+	4.63904e8i	0.663643	+	1.14946i	0.979651	+	0.200707i	$0.0643239\pi$
$739$	2.67835e8	+	4.63904e8i	0.663643	+	1.14946i	−0.316008	+	0.948756i	$0.602343\pi$
$740$	4.45319e8	+	2.57105e8i	1.09895	+	0.634476i
$741$		−	3.31913e8i		−	0.815773i
$742$	−1.21651e7	+	1.73014e7i	−0.0297786	+	0.0423516i
$743$	1.33928e7			0.0326517			0.0163259	−	0.999867i	$-0.494803\pi$
$743$	1.33928e7			0.0326517			0.0163259	+	0.999867i	$0.494803\pi$
$744$	1.18537e6	−	2.05313e6i	0.00287830	−	0.00498536i
$745$	7.77299e8	−	4.48774e8i	1.87983	−	1.08532i
$746$	−3.63132e6	−	6.28964e6i	−0.00874679	−	0.0151499i
$747$	−2.13623e8	−	1.23335e8i	−0.512490	−	0.295886i
$748$			4.08809e7i			0.0976824i
$749$	−1.17384e8	−	2.53022e8i	−0.279359	−	0.602162i
$750$	5.61444e6			0.0133083
$751$	1.89533e8	−	3.28281e8i	0.447472	−	0.775043i	−0.550749	−	0.834671i	$-0.685658\pi$
$751$	1.89533e8	−	3.28281e8i	0.447472	−	0.775043i	0.998221	+	0.0596274i	$0.0189912\pi$
$752$	4.96523e8	−	2.86668e8i	1.16758	−	0.674102i
$753$	1.58320e8	+	2.74218e8i	0.370809	+	0.642261i
$754$	9.81064e6	+	5.66417e6i	0.0228867	+	0.0132136i
$755$			5.88361e8i			1.36711i
$756$	6.23042e6	−	6.96435e7i	0.0144196	−	0.161182i
$757$	−3.70184e8			−0.853356			−0.426678	−	0.904404i	$-0.640316\pi$
$757$	−3.70184e8			−0.853356			−0.426678	+	0.904404i	$0.640316\pi$
$758$	−1.64796e6	+	2.85435e6i	−0.00378390	+	0.00655391i
$759$	8.76741e7	−	5.06187e7i	0.200515	−	0.115767i
$760$	−1.17455e7	−	2.03439e7i	−0.0267567	−	0.0463439i
$761$	−7.53848e8	−	4.35234e8i	−1.71053	−	0.987572i	−0.933845	−	0.357677i	$-0.883569\pi$
$761$	−7.53848e8	−	4.35234e8i	−1.71053	−	0.987572i	−0.776680	−	0.629895i	$-0.783098\pi$
$762$		−	3.24111e7i		−	0.0732535i
$763$	−1.31629e8	−	1.17757e7i	−0.296332	−	0.0265103i
$764$	8.51821e7			0.191015
$765$	−1.96852e8	+	3.40958e8i	−0.439700	+	0.761582i
$766$	1.15849e7	−	6.68855e6i	0.0257755	−	0.0148815i
$767$	9.54088e7	+	1.65253e8i	0.211447	+	0.366238i
$768$	−5.33222e8	−	3.07856e8i	−1.17713	−	0.679616i
$769$			3.17023e8i			0.697126i	0.937285	+	0.348563i	$0.113330\pi$
$769$			3.17023e8i			0.697126i	−0.937285	+	0.348563i	$0.886670\pi$
$770$	2.16622e6	−	1.00497e6i	0.00474493	−	0.00220130i
$771$	7.10963e8			1.55126
$772$	1.45655e8	−	2.52282e8i	0.316573	−	0.548321i
$773$	−3.00058e8	+	1.73238e8i	−0.649630	+	0.375064i	−0.788315	−	0.615272i	$-0.789046\pi$
$773$	−3.00058e8	+	1.73238e8i	−0.649630	+	0.375064i	0.138684	+	0.990337i	$0.455713\pi$
$774$	−5.34078e6	−	9.25051e6i	−0.0115181	−	0.0199500i
$775$	2.11708e7	+	1.22229e7i	0.0454812	+	0.0262586i
$776$			9.07292e6i			0.0194161i
$777$	−5.04158e8	−	3.54488e8i	−1.07474	−	0.755681i
$778$	1.50307e7			0.0319183
$779$	−6.03399e7	+	1.04512e8i	−0.127642	+	0.221082i
$780$	−6.67494e8	+	3.85378e8i	−1.40658	+	0.812088i
$781$	−2.93854e7	−	5.08971e7i	−0.0616849	−	0.106841i
$782$	−1.22576e7	−	7.07694e6i	−0.0256322	−	0.0147988i
$783$		−	7.58211e7i		−	0.157945i
$784$	4.72930e8	+	8.53008e7i	0.981405	+	0.177013i
$785$	6.98361e7			0.144368
$786$	−9.40108e6	+	1.62831e7i	−0.0193602	+	0.0335329i
$787$	4.06239e7	−	2.34542e7i	0.0833408	−	0.0481168i	−0.457750	−	0.889081i	$-0.651345\pi$
$787$	4.06239e7	−	2.34542e7i	0.0833408	−	0.0481168i	0.541091	+	0.840964i	$0.318011\pi$
$788$	3.60779e8	+	6.24887e8i	0.737330	+	1.27709i
$789$	5.57700e8	+	3.21988e8i	1.13545	+	0.655555i
$790$			2.47714e7i			0.0502424i
$791$	−9.82639e7	+	1.39752e8i	−0.198548	+	0.282377i
$792$	3.45451e6			0.00695362
$793$	1.70719e7	−	2.95695e7i	0.0342345	−	0.0592958i
$794$	−1.78443e7	+	1.03024e7i	−0.0356482	+	0.0205815i
$795$	−7.80211e8	−	1.35136e9i	−1.55278	−	2.68950i
$796$	−2.13841e8	−	1.23461e8i	−0.423987	−	0.244789i
$797$			4.62223e8i			0.913013i	0.889720	+	0.456506i	$0.150899\pi$
$797$			4.62223e8i			0.913013i	−0.889720	+	0.456506i	$0.849101\pi$
$798$	5.92177e6	+	1.27645e7i	0.0116531	+	0.0251185i
$799$	−5.18486e8			−1.01648
$800$	−1.76540e7	+	3.05776e7i	−0.0344804	+	0.0597218i
$801$	−4.29667e8	+	2.48068e8i	−0.836054	+	0.482696i
$802$	1.24515e7	+	2.15667e7i	0.0241379	+	0.0418081i
$803$	1.66908e7	+	9.63643e6i	0.0322352	+	0.0186110i
$804$			2.85816e8i			0.549944i
$805$	8.00100e7	−	8.94350e8i	0.153376	−	1.71443i
$806$	−982109.			−0.00187566
$807$	1.35845e8	−	2.35291e8i	0.258478	−	0.447697i
$808$	2.41927e7	−	1.39677e7i	0.0458617	−	0.0264783i
$809$	−7.75409e7	−	1.34305e8i	−0.146449	−	0.253657i	0.783464	−	0.621437i	$-0.213451\pi$
$809$	−7.75409e7	−	1.34305e8i	−0.146449	−	0.253657i	−0.929912	+	0.367781i	$0.880118\pi$
$810$	−2.04405e7	−	1.18013e7i	−0.0384623	−	0.0222062i
$811$		−	4.07999e7i		−	0.0764887i	−0.999268	−	0.0382443i	$-0.987823\pi$
$811$		−	4.07999e7i		−	0.0764887i	0.999268	−	0.0382443i	$-0.0121765\pi$
$812$	5.19512e8	+	4.64764e7i	0.970349	+	0.0868089i
$813$	9.42290e8			1.75353
$814$	−1.01865e6	+	1.76435e6i	−0.00188865	+	0.00327124i
$815$	−4.26979e8	+	2.46517e8i	−0.788740	+	0.455380i
$816$	2.79437e8	+	4.83999e8i	0.514297	+	0.890788i
$817$	2.70676e8	+	1.56275e8i	0.496344	+	0.286564i
$818$		−	2.36130e7i		−	0.0431411i
$819$	3.92714e8	−	1.82191e8i	0.714866	−	0.331646i
$820$	2.80239e8			0.508261
$821$	−4.33422e8	+	7.50709e8i	−0.783216	+	1.35657i	0.146843	+	0.989160i	$0.453089\pi$
$821$	−4.33422e8	+	7.50709e8i	−0.783216	+	1.35657i	−0.930059	+	0.367410i	$0.880245\pi$
$822$	3.58411e6	−	2.06929e6i	0.00645306	−	0.00372567i
$823$	−4.20034e8	−	7.27521e8i	−0.753504	−	1.30511i	−0.946115	−	0.323832i	$-0.895029\pi$
$823$	−4.20034e8	−	7.27521e8i	−0.753504	−	1.30511i	0.192611	−	0.981275i	$-0.438304\pi$
$824$	7.31926e6	+	4.22577e6i	0.0130823	+	0.00755309i
$825$			7.60112e7i			0.135368i
$826$	−6.61750e6	−	4.65295e6i	−0.0117423	−	0.00825636i
$827$	7.77404e8			1.37445			0.687227	−	0.726443i	$-0.258828\pi$
$827$	7.77404e8			1.37445			0.687227	+	0.726443i	$0.258828\pi$
$828$	3.24590e8	−	5.62206e8i	0.571799	−	0.990385i
$829$	3.73641e8	−	2.15722e8i	0.655829	−	0.378643i	−0.134857	−	0.990865i	$-0.543057\pi$
$829$	3.73641e8	−	2.15722e8i	0.655829	−	0.378643i	0.790686	+	0.612222i	$0.209724\pi$
$830$	7.71633e6	+	1.33651e7i	0.0134951	+	0.0233742i
$831$	3.50288e8	+	2.02239e8i	0.610411	+	0.352421i
$832$			5.11786e8i			0.888625i
$833$	−3.31817e8	−	2.80649e8i	−0.574068	−	0.485543i
$834$	−2.76335e7			−0.0476363
$835$	−3.56155e8	+	6.16878e8i	−0.611758	+	1.05960i
$836$	−4.37493e7	+	2.52587e7i	−0.0748776	+	0.0432306i
$837$	3.28665e6	+	5.69264e6i	0.00560502	+	0.00970817i
$838$	1.80275e7	+	1.04082e7i	0.0306339	+	0.0176865i
$839$		−	5.88080e8i		−	0.995751i	−0.867249	−	0.497875i	$-0.834114\pi$
$839$		−	5.88080e8i		−	0.995751i	0.867249	−	0.497875i	$-0.165886\pi$
$840$	3.76060e7	−	5.34838e7i	0.0634482	−	0.0902369i
$841$	−2.92290e7			−0.0491389
$842$	1.25883e7	−	2.18036e7i	0.0210878	−	0.0365251i
$843$	6.77166e8	−	3.90962e8i	1.13035	−	0.652607i
$844$	−3.89694e8	−	6.74969e8i	−0.648180	−	1.12268i
$845$	−1.39676e8	−	8.06421e7i	−0.231501	−	0.133657i
$846$			2.18964e7i			0.0361628i
$847$	2.51399e8	+	5.41894e8i	0.413727	+	0.891794i
$848$	−1.03804e9			−1.70227
$849$	−1.98218e8	+	3.43324e8i	−0.323907	+	0.561023i
$850$	9.20329e6	−	5.31352e6i	0.0149860	−	0.00865218i
$851$	3.83030e8	+	6.63427e8i	0.621504	+	1.07648i
$852$	−6.96444e8	−	4.02092e8i	−1.12608	−	0.650140i
$853$			5.38320e8i			0.867347i	0.901070	+	0.433674i	$0.142783\pi$
$853$			5.38320e8i			0.867347i	−0.901070	+	0.433674i	$0.857217\pi$
$854$	−128981.	+	1.44175e6i	−0.000207087	+	0.00231481i
$855$	−4.86508e8			−0.778380
$856$	−1.26223e7	+	2.18624e7i	−0.0201241	+	0.0348559i
$857$	−3.82550e8	+	2.20865e8i	−0.607779	+	0.350901i	−0.772096	−	0.635506i	$-0.780791\pi$
$857$	−3.82550e8	+	2.20865e8i	−0.607779	+	0.350901i	0.164317	+	0.986408i	$0.447458\pi$
$858$	−1.52687e6	−	2.64461e6i	−0.00241735	−	0.00418697i
$859$	−9.83416e8	−	5.67776e8i	−1.55152	−	0.895772i	−0.998018	−	0.0629248i	$-0.979957\pi$
$859$	−9.83416e8	−	5.67776e8i	−1.55152	−	0.895772i	−0.553504	−	0.832847i	$-0.686709\pi$
$860$		−	7.25791e8i		−	1.14108i
$861$	−3.34546e8	−	2.99290e7i	−0.524138	−	0.0468902i
$862$	−2.39565e7			−0.0374026
$863$	3.27409e7	−	5.67089e7i	0.0509399	−	0.0882306i	−0.839431	−	0.543466i	$-0.817112\pi$
$863$	3.27409e7	−	5.67089e7i	0.0509399	−	0.0882306i	0.890371	+	0.455236i	$0.150445\pi$
$864$	−8.22205e6	+	4.74700e6i	−0.0127479	+	0.00736001i
$865$	7.70725e8	+	1.33493e9i	1.19083	+	2.06258i
$866$	−2.00752e7	−	1.15904e7i	−0.0309105	−	0.0178462i
$867$			3.88635e8i			0.596328i
$868$	−4.10196e7	+	1.90301e7i	−0.0627238	+	0.0290992i
$869$	1.06591e8			0.162427
$870$	1.77163e7	−	3.06855e7i	0.0269039	−	0.0465989i
$871$	2.05174e8	−	1.18457e8i	0.310504	−	0.179270i
$872$	5.98043e6	+	1.03584e7i	0.00901951	+	0.0156223i
$873$	1.62729e8	+	9.39516e7i	0.244581	+	0.141209i
$874$		−	1.74902e7i		−	0.0261976i
$875$	−1.75283e8	−	1.23247e8i	−0.261647	−	0.183972i
$876$	2.63718e8			0.392308
$877$	3.86987e8	−	6.70282e8i	0.573718	−	0.993708i	−0.422462	−	0.906381i	$-0.638834\pi$
$877$	3.86987e8	−	6.70282e8i	0.573718	−	0.993708i	0.996180	−	0.0873273i	$-0.0278326\pi$
$878$	3.45659e6	−	1.99566e6i	0.00510698	−	0.00294852i
$879$	−8.21213e7	−	1.42238e8i	−0.120918	−	0.209435i
$880$	1.01499e8	+	5.86007e7i	0.148942	+	0.0859914i
$881$		−	2.81948e8i		−	0.412326i	−0.978518	−	0.206163i	$-0.933902\pi$
$881$		−	2.81948e8i		−	0.412326i	0.978518	−	0.206163i	$-0.0660977\pi$
$882$	−1.18522e7	+	1.40131e7i	−0.0172740	+	0.0204234i
$883$	5.28378e8			0.767472			0.383736	−	0.923443i	$-0.374637\pi$
$883$	5.28378e8			0.767472			0.383736	+	0.923443i	$0.374637\pi$
$884$	2.31841e8	−	4.01560e8i	0.335608	−	0.581290i
$885$	5.16874e8	−	2.98418e8i	0.745685	−	0.430521i
$886$	−1.00926e7	−	1.74809e7i	−0.0145112	−	0.0251341i
$887$	4.38960e8	+	2.53433e8i	0.629004	+	0.363156i	0.780366	−	0.625323i	$-0.215033\pi$
$887$	4.38960e8	+	2.53433e8i	0.629004	+	0.363156i	−0.151362	+	0.988478i	$0.548366\pi$
$888$			5.57800e7i			0.0796599i
$889$	−7.11478e8	+	1.01187e9i	−1.01264	+	1.44020i
$890$	3.10402e7			0.0440306
$891$	−5.07806e7	+	8.79545e7i	−0.0717901	+	0.124344i
$892$	−4.64832e8	+	2.68371e8i	−0.654940	+	0.378130i
$893$	−3.20352e8	−	5.54865e8i	−0.449855	−	0.779171i
$894$	4.21402e7	+	2.43296e7i	0.0589771	+	0.0340505i
$895$		−	4.41941e8i		−	0.616447i
$896$	−3.66420e7	−	7.89822e7i	−0.0509395	−	0.109801i
$897$	−1.14826e9			−1.59097
$898$	−3.83915e6	+	6.64961e6i	−0.00530159	+	0.00918263i
$899$	−4.24648e7	+	2.45171e7i	−0.0584453	+	0.0337434i
$900$	2.43709e8	+	4.22116e8i	0.334306	+	0.579035i
$901$	8.12971e8	+	4.69369e8i	1.11148	+	0.641712i
$902$			1.11031e6i			0.00151294i
$903$	−7.75132e7	+	8.66441e8i	−0.105272	+	1.17673i
$904$	1.54622e7			0.0209298
$905$	9.27033e8	−	1.60567e9i	1.25069	−	2.16626i
$906$	−2.76237e7	+	1.59486e7i	−0.0371448	+	0.0214455i
$907$	−3.68441e8	−	6.38159e8i	−0.493795	−	0.855278i	0.506180	−	0.862428i	$-0.331057\pi$
$907$	−3.68441e8	−	6.38159e8i	−0.493795	−	0.855278i	−0.999974	+	0.00715027i	$0.997724\pi$
$908$	1.13083e9	+	6.52887e8i	1.51057	+	0.872128i
$909$		−	5.78550e8i		−	0.770281i
$910$	−2.69773e7	−	2.41343e6i	−0.0357993	−	0.00320266i
$911$	5.49771e8			0.727154			0.363577	−	0.931564i	$-0.381555\pi$
$911$	5.49771e8			0.727154			0.363577	+	0.931564i	$0.381555\pi$
$912$	−3.45305e8	+	5.98087e8i	−0.455217	+	0.788460i
$913$	5.75094e7	−	3.32030e7i	0.0755660	−	0.0436280i
$914$	6.63199e6	+	1.14869e7i	0.00868571	+	0.0150441i
$915$	−9.24868e7	−	5.33973e7i	−0.120730	−	0.0697037i
$916$		−	8.24937e8i		−	1.07333i
$917$	6.50944e8	−	3.01990e8i	0.844182	−	0.391638i
$918$	2.85752e6			0.00369370
$919$	1.34727e8	−	2.33354e8i	0.173583	−	0.300655i	−0.766087	−	0.642737i	$-0.777799\pi$
$919$	1.34727e8	−	2.33354e8i	0.173583	−	0.300655i	0.939670	+	0.342082i	$0.111132\pi$
$920$	−7.03799e7	+	4.06339e7i	−0.0903827	+	0.0521825i
$921$	4.20362e8	+	7.28088e8i	0.538077	+	0.931976i
$922$	3.48564e7	+	2.01244e7i	0.0444723	+	0.0256761i
$923$			6.66593e8i			0.847726i
$924$	−1.15016e8	−	8.08713e7i	−0.145795	−	0.102513i
$925$	−5.75174e8			−0.726732
$926$	−1.75267e6	+	3.03571e6i	−0.00220732	+	0.00382320i
$927$	1.51584e8	−	8.75172e7i	0.190290	−	0.109864i
$928$	−3.54107e7	−	6.13331e7i	−0.0443089	−	0.0767452i
$929$	−3.75878e8	−	2.17013e8i	−0.468813	−	0.270669i	0.246930	−	0.969033i	$-0.420578\pi$
$929$	−3.75878e8	−	2.17013e8i	−0.468813	−	0.270669i	−0.715742	+	0.698364i	$0.753912\pi$
$930$			3.07182e6i			0.00381898i
$931$	9.53237e7	−	5.28499e8i	0.118128	−	0.654931i
$932$	−5.91573e8			−0.730736
$933$	−9.36975e8	+	1.62289e9i	−1.15367	+	1.99822i
$934$	−2.18742e6	+	1.26291e6i	−0.00268467	+	0.00155000i
$935$	−5.29946e7	−	9.17893e7i	−0.0648331	−	0.112294i
$936$	−3.39325e7	−	1.95909e7i	−0.0413798	−	0.0238906i
$937$		−	7.33456e7i		−	0.0891569i	−0.999006	−	0.0445785i	$-0.985806\pi$
$937$		−	7.33456e7i		−	0.0891569i	0.999006	−	0.0445785i	$-0.0141945\pi$
$938$	−5.77699e6	+	8.21611e6i	−0.00699992	+	0.00995538i
$939$	−2.09585e9			−2.53142
$940$	−7.43909e8	+	1.28849e9i	−0.895646	+	1.55130i
$941$	−5.63455e8	+	3.25311e8i	−0.676224	+	0.390418i	−0.798431	−	0.602087i	$-0.794336\pi$
$941$	−5.63455e8	+	3.25311e8i	−0.676224	+	0.390418i	0.122207	+	0.992505i	$0.461003\pi$
$942$	1.89303e6	+	3.27883e6i	0.00226467	+	0.00392253i
$943$	3.61560e8	+	2.08747e8i	0.431167	+	0.248935i
$944$		−	3.97034e8i		−	0.471968i
$945$	7.62909e7	+	1.64446e8i	0.0904019	+	0.194863i
$946$	2.87558e6			0.00339666
$947$	4.51604e8	−	7.82201e8i	0.531750	−	0.921018i	−0.467563	−	0.883960i	$-0.654868\pi$
$947$	4.51604e8	−	7.82201e8i	0.531750	−	0.921018i	0.999313	−	0.0370584i	$-0.0117988\pi$
$948$	1.26312e9	−	7.29260e8i	1.48258	−	0.855968i
$949$	−1.09299e8	−	1.89311e8i	−0.127884	−	0.221501i
$950$	1.13727e7	+	6.56601e6i	0.0132645	+	0.00765828i
$951$		−	1.42687e9i		−	1.65899i
$952$	−3.50479e6	+	3.91765e7i	−0.00406211	+	0.0454062i
$953$	−6.19910e8			−0.716226			−0.358113	−	0.933678i	$-0.616580\pi$
$953$	−6.19910e8			−0.716226			−0.358113	+	0.933678i	$0.616580\pi$
$954$	1.98221e7	−	3.43329e7i	0.0228300	−	0.0395427i
$955$	−1.91258e8	+	1.10423e8i	−0.219588	+	0.126779i
$956$	−2.58484e8	−	4.47707e8i	−0.295842	−	0.512413i
$957$	−1.32038e8	−	7.62324e7i	−0.150648	−	0.0869769i
$958$		−	2.38594e7i		−	0.0271371i
$959$	−1.57320e8	−	1.40741e7i	−0.178373	−	0.0159575i
$960$	1.60075e9			1.80930
$961$	−4.41626e8	+	7.64919e8i	−0.497605	+	0.861877i
$962$	2.00117e7	−	1.15538e7i	0.0224781	−	0.0129777i
$963$	2.61411e8	+	4.52777e8i	0.292715	+	0.506998i
$964$	2.67434e8	+	1.54403e8i	0.298528	+	0.172355i
$965$			7.55260e8i			0.840455i
$966$	4.41588e7	−	2.04865e7i	0.0489876	−	0.0227267i
$967$	9.96095e8			1.10159			0.550797	−	0.834639i	$-0.314324\pi$
$967$	9.96095e8			1.10159			0.550797	+	0.834639i	$0.314324\pi$
$968$	2.70329e7	−	4.68224e7i	0.0298035	−	0.0516211i
$969$	5.40870e8	−	3.12271e8i	0.594458	−	0.343211i
$970$	−5.87798e6	−	1.01810e7i	−0.00644040	−	0.0111551i
$971$	5.54338e7	+	3.20047e7i	0.0605504	+	0.0349588i	0.529970	−	0.848017i	$-0.322203\pi$
$971$	5.54338e7	+	3.20047e7i	0.0605504	+	0.0349588i	−0.469419	+	0.882975i	$0.655537\pi$
$972$			1.24109e9i			1.35147i
$973$	8.62719e8	+	6.06602e8i	0.936549	+	0.658515i
$974$	−2.70132e7			−0.0292348
$975$	4.31068e8	−	7.46632e8i	0.465085	−	0.805550i
$976$	−6.15252e7	+	3.55216e7i	−0.0661765	+	0.0382070i
$977$	−2.82631e8	−	4.89532e8i	−0.303065	−	0.524925i	0.673763	−	0.738947i	$-0.264677\pi$
$977$	−2.82631e8	−	4.89532e8i	−0.303065	−	0.524925i	−0.976829	+	0.214023i	$0.931343\pi$
$978$	−2.31481e7	−	1.33645e7i	−0.0247456	−	0.0142869i
$979$		−	1.33565e8i		−	0.142346i
$980$	−1.17352e9	+	4.21930e8i	−1.24684	+	0.448294i
$981$	2.47713e8			0.262387
$982$	−3.61169e6	+	6.25563e6i	−0.00381396	+	0.00660597i
$983$	−1.61269e8	+	9.31085e7i	−0.169781	+	0.0980232i	−0.582483	−	0.812843i	$-0.697919\pi$
$983$	−1.61269e8	+	9.31085e7i	−0.169781	+	0.0980232i	0.412701	+	0.910866i	$0.364585\pi$
$984$	1.51997e7	+	2.63267e7i	0.0159533	+	0.0276319i
$985$	−1.62010e9	−	9.35366e8i	−1.69525	−	0.978752i
$986$			2.13160e7i			0.0222369i
$987$	1.02568e9	−	1.45873e9i	1.06674	−	1.51714i
$988$	5.72979e8			0.594111
$989$	5.40635e8	−	9.36407e8i	0.558875	−	0.968000i
$990$	−3.87640e6	+	2.23804e6i	−0.00399505	+	0.00230655i
$991$	4.04187e8	+	7.00072e8i	0.415299	+	0.719320i	0.995460	−	0.0951825i	$-0.0303435\pi$
$991$	4.04187e8	+	7.00072e8i	0.415299	+	0.719320i	−0.580160	+	0.814502i	$0.697010\pi$
$992$	5.31727e6	+	3.06992e6i	0.00544695	+	0.00314480i
$993$			4.13885e8i			0.422700i
$994$	−1.18929e7	−	2.56353e7i	−0.0121096	−	0.0261024i
$995$	6.40179e8			0.649879
$996$	4.54330e8	−	7.86923e8i	0.459826	−	0.796442i
$997$	−3.48053e8	+	2.00949e8i	−0.351205	+	0.202768i	−0.665216	−	0.746651i	$-0.731660\pi$
$997$	−3.48053e8	+	2.00949e8i	−0.351205	+	0.202768i	0.314011	+	0.949419i	$0.398327\pi$
$998$	1.63269e7	+	2.82790e7i	0.0164252	+	0.0284493i
$999$	−1.33939e8	−	7.73298e7i	−0.134342	−	0.0775622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.7.d.b.5.2	yes	4
3.2	odd	2		63.7.m.b.19.1		4
4.3	odd	2		112.7.s.b.33.1		4
7.2	even	3		49.7.b.b.48.2		4
7.3	odd	6	inner	7.7.d.b.3.2	✓	4
7.4	even	3		49.7.d.c.31.2		4
7.5	odd	6		49.7.b.b.48.1		4
7.6	odd	2		49.7.d.c.19.2		4
21.2	odd	6		441.7.d.b.244.3		4
21.5	even	6		441.7.d.b.244.4		4
21.17	even	6		63.7.m.b.10.1		4
28.3	even	6		112.7.s.b.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.7.d.b.3.2	✓	4	7.3	odd	6	inner
7.7.d.b.5.2	yes	4	1.1	even	1	trivial
49.7.b.b.48.1		4	7.5	odd	6
49.7.b.b.48.2		4	7.2	even	3
49.7.d.c.19.2		4	7.6	odd	2
49.7.d.c.31.2		4	7.4	even	3
63.7.m.b.10.1		4	21.17	even	6
63.7.m.b.19.1		4	3.2	odd	2
112.7.s.b.17.1		4	28.3	even	6
112.7.s.b.33.1		4	4.3	odd	2
441.7.d.b.244.3		4	21.2	odd	6
441.7.d.b.244.4		4	21.5	even	6

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.121320 - 0.210133i) q^{2} +(32.0772 - 18.5198i) q^{3} +(31.9706 + 55.3746i) q^{4} +(-143.566 - 82.8879i) q^{5} -8.98729i q^{6} +(-197.286 + 280.583i) q^{7} +31.0437 q^{8} +(321.463 - 556.790i) q^{9} +O(q^{10})\)	\(q+(0.121320 - 0.210133i) q^{2} +(32.0772 - 18.5198i) q^{3} +(31.9706 + 55.3746i) q^{4} +(-143.566 - 82.8879i) q^{5} -8.98729i q^{6} +(-197.286 + 280.583i) q^{7} +31.0437 q^{8} +(321.463 - 556.790i) q^{9} +(-34.8350 + 20.1120i) q^{10} +(86.5410 + 149.893i) q^{11} +(2051.05 + 1184.17i) q^{12} -1963.14i q^{13} +(35.0250 + 75.4969i) q^{14} -6140.25 q^{15} +(-2042.35 + 3537.45i) q^{16} +(3199.04 - 1846.96i) q^{17} +(-78.0000 - 135.100i) q^{18} +(3953.11 + 2282.33i) q^{19} -10599.9i q^{20} +(-1132.05 + 12654.0i) q^{21} +41.9967 q^{22} +(7895.75 - 13675.8i) q^{23} +(995.795 - 574.922i) q^{24} +(5928.30 + 10268.1i) q^{25} +(-412.520 - 238.168i) q^{26} +3188.14i q^{27} +(-21844.6 - 1954.25i) q^{28} -23782.2 q^{29} +(-744.938 + 1290.27i) q^{30} +(1785.57 - 1030.90i) q^{31} +(1488.96 + 2578.95i) q^{32} +(5551.98 + 3205.44i) q^{33} -896.298i q^{34} +(51580.6 - 23929.6i) q^{35} +41109.4 q^{36} +(-24255.5 + 42011.7i) q^{37} +(959.185 - 553.786i) q^{38} +(-36356.8 - 62971.8i) q^{39} +(-4456.82 - 2573.15i) q^{40} +26437.9i q^{41} +(2521.69 + 1773.07i) q^{42} +68471.6 q^{43} +(-5533.53 + 9584.36i) q^{44} +(-92302.3 + 53290.8i) q^{45} +(-1915.83 - 3318.32i) q^{46} +(-121557. - 70180.9i) q^{47} +151295. i q^{48} +(-39805.2 - 110711. i) q^{49} +2876.89 q^{50} +(68410.7 - 118491. i) q^{51} +(108708. - 62762.6i) q^{52} +(127065. + 220083. i) q^{53} +(669.934 + 386.786i) q^{54} -28692.8i q^{55} +(-6124.50 + 8710.36i) q^{56} +169073. q^{57} +(-2885.27 + 4997.43i) q^{58} +(-84178.0 + 48600.2i) q^{59} +(-196307. - 340014. i) q^{60} +(15062.4 + 8696.26i) q^{61} -500.276i q^{62} +(92805.9 + 200044. i) q^{63} -260698. q^{64} +(-162720. + 281840. i) q^{65} +(1347.14 - 777.770i) q^{66} +(60340.8 + 104513. i) q^{67} +(204550. + 118097. i) q^{68} -584910. i q^{69} +(1229.37 - 13741.9i) q^{70} -339555. q^{71} +(9979.41 - 17284.8i) q^{72} +(96432.8 - 55675.5i) q^{73} +(5885.36 + 10193.7i) q^{74} +(380326. + 219581. i) q^{75} +291869. i q^{76} +(-59131.0 - 5289.95i) q^{77} -17643.3 q^{78} +(307919. - 533332. i) q^{79} +(586424. - 338572. i) q^{80} +(293390. + 508167. i) q^{81} +(5555.47 + 3207.45i) q^{82} -383668. i q^{83} +(-736904. + 341869. i) q^{84} -612364. q^{85} +(8307.00 - 14388.1i) q^{86} +(-762866. + 440441. i) q^{87} +(2686.56 + 4653.25i) q^{88} +(-668299. - 385843. i) q^{89} +25861.0i q^{90} +(550824. + 387300. i) q^{91} +1.00973e6 q^{92} +(38184.0 - 66136.6i) q^{93} +(-29494.6 + 17028.7i) q^{94} +(-378355. - 655329. i) q^{95} +(95523.0 + 55150.2i) q^{96} +292263. i q^{97} +(-28093.1 - 5067.06i) q^{98} +111279. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9	\( 4 q - 8 q^{2} + 18 q^{3} + 60 q^{4} - 150 q^{5} + 280 q^{7} - 928 q^{8} + 624 q^{9} - 1200 q^{10} + 1882 q^{11} + 4284 q^{12} - 1820 q^{14} - 16500 q^{15} + 248 q^{16} + 13458 q^{17} - 312 q^{18} + 18078 q^{19} - 16170 q^{21} - 28088 q^{22} + 2470 q^{23} + 24840 q^{24} + 2500 q^{25} + 43848 q^{26} - 45444 q^{28} - 34544 q^{29} + 15900 q^{30} - 17202 q^{31} + 7008 q^{32} - 67770 q^{33} + 154350 q^{35} + 82368 q^{36} - 43870 q^{37} - 81924 q^{38} + 10668 q^{39} - 76800 q^{40} - 22344 q^{42} + 320216 q^{43} - 4332 q^{44} - 187200 q^{45} - 113636 q^{46} - 354714 q^{47} + 140140 q^{49} + 160000 q^{50} + 28206 q^{51} + 196056 q^{52} + 104530 q^{53} + 285876 q^{54} - 346192 q^{56} + 25164 q^{57} - 59432 q^{58} - 62646 q^{59} - 384300 q^{60} - 140682 q^{61} + 181272 q^{63} - 33248 q^{64} - 77700 q^{65} + 652824 q^{66} + 432494 q^{67} + 381276 q^{68} - 338100 q^{70} - 1481528 q^{71} + 29328 q^{72} - 971778 q^{73} + 50024 q^{74} + 1192500 q^{75} + 642670 q^{77} - 1409856 q^{78} + 935990 q^{79} + 1767000 q^{80} + 1104066 q^{81} + 286776 q^{82} - 1405908 q^{84} - 579300 q^{85} - 738712 q^{86} - 1826208 q^{87} - 840616 q^{88} - 679290 q^{89} + 711480 q^{91} + 2124456 q^{92} + 395958 q^{93} + 860892 q^{94} - 291750 q^{95} + 5040 q^{96} - 361424 q^{98} + 157872 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 18 * q^3 + 60 * q^4 - 150 * q^5 + 280 * q^7 - 928 * q^8 + 624 * q^9 - 1200 * q^10 + 1882 * q^11 + 4284 * q^12 - 1820 * q^14 - 16500 * q^15 + 248 * q^16 + 13458 * q^17 - 312 * q^18 + 18078 * q^19 - 16170 * q^21 - 28088 * q^22 + 2470 * q^23 + 24840 * q^24 + 2500 * q^25 + 43848 * q^26 - 45444 * q^28 - 34544 * q^29 + 15900 * q^30 - 17202 * q^31 + 7008 * q^32 - 67770 * q^33 + 154350 * q^35 + 82368 * q^36 - 43870 * q^37 - 81924 * q^38 + 10668 * q^39 - 76800 * q^40 - 22344 * q^42 + 320216 * q^43 - 4332 * q^44 - 187200 * q^45 - 113636 * q^46 - 354714 * q^47 + 140140 * q^49 + 160000 * q^50 + 28206 * q^51 + 196056 * q^52 + 104530 * q^53 + 285876 * q^54 - 346192 * q^56 + 25164 * q^57 - 59432 * q^58 - 62646 * q^59 - 384300 * q^60 - 140682 * q^61 + 181272 * q^63 - 33248 * q^64 - 77700 * q^65 + 652824 * q^66 + 432494 * q^67 + 381276 * q^68 - 338100 * q^70 - 1481528 * q^71 + 29328 * q^72 - 971778 * q^73 + 50024 * q^74 + 1192500 * q^75 + 642670 * q^77 - 1409856 * q^78 + 935990 * q^79 + 1767000 * q^80 + 1104066 * q^81 + 286776 * q^82 - 1405908 * q^84 - 579300 * q^85 - 738712 * q^86 - 1826208 * q^87 - 840616 * q^88 - 679290 * q^89 + 711480 * q^91 + 2124456 * q^92 + 395958 * q^93 + 860892 * q^94 - 291750 * q^95 + 5040 * q^96 - 361424 * q^98 + 157872 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more