LMFDB - Embedded newform 88.6.c.a.45.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,6,Mod(45,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("88.45");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	88.c (of order $2$, degree $1$, 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:	$14.1137761435$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			45.12
Character	$\chi$	$=$	88.45
Dual form			88.6.c.a.45.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.04438 + 3.95512i) q^{2} -30.7355i q^{3} +(0.713979 - 31.9920i) q^{4} +80.1293i q^{5} +(121.563 + 124.306i) q^{6} +31.2790 q^{7} +(123.645 + 132.212i) q^{8} -701.671 q^{9} +O(q^{10})$	\(q+(-4.04438 + 3.95512i) q^{2} -30.7355i q^{3} +(0.713979 - 31.9920i) q^{4} +80.1293i q^{5} +(121.563 + 124.306i) q^{6} +31.2790 q^{7} +(123.645 + 132.212i) q^{8} -701.671 q^{9} +(-316.921 - 324.073i) q^{10} +121.000i q^{11} +(-983.291 - 21.9445i) q^{12} +282.450i q^{13} +(-126.504 + 123.712i) q^{14} +2462.81 q^{15} +(-1022.98 - 45.6833i) q^{16} +1398.50 q^{17} +(2837.82 - 2775.20i) q^{18} +1846.24i q^{19} +(2563.50 + 57.2106i) q^{20} -961.376i q^{21} +(-478.570 - 489.370i) q^{22} +765.079 q^{23} +(4063.59 - 3800.29i) q^{24} -3295.70 q^{25} +(-1117.13 - 1142.34i) q^{26} +14097.5i q^{27} +(22.3326 - 1000.68i) q^{28} -5486.62i q^{29} +(-9960.54 + 9740.73i) q^{30} +7931.38 q^{31} +(4318.00 - 3861.25i) q^{32} +3719.00 q^{33} +(-5656.08 + 5531.26i) q^{34} +2506.36i q^{35} +(-500.978 + 22447.9i) q^{36} +10924.7i q^{37} +(-7302.12 - 7466.90i) q^{38} +8681.26 q^{39} +(-10594.0 + 9907.57i) q^{40} +7889.88 q^{41} +(3802.36 + 3888.17i) q^{42} -1876.90i q^{43} +(3871.04 + 86.3915i) q^{44} -56224.4i q^{45} +(-3094.27 + 3025.98i) q^{46} +8759.36 q^{47} +(-1404.10 + 31441.8i) q^{48} -15828.6 q^{49} +(13329.0 - 13034.9i) q^{50} -42983.7i q^{51} +(9036.17 + 201.664i) q^{52} +18211.8i q^{53} +(-55757.3 - 57015.5i) q^{54} -9695.64 q^{55} +(3867.49 + 4135.45i) q^{56} +56745.2 q^{57} +(21700.2 + 22189.9i) q^{58} -531.019i q^{59} +(1758.40 - 78790.4i) q^{60} +23908.4i q^{61} +(-32077.5 + 31369.6i) q^{62} -21947.6 q^{63} +(-2191.89 + 32694.6i) q^{64} -22632.5 q^{65} +(-15041.0 + 14709.1i) q^{66} +3145.18i q^{67} +(998.503 - 44741.0i) q^{68} -23515.1i q^{69} +(-9912.98 - 10136.7i) q^{70} +39892.0 q^{71} +(-86758.0 - 92769.1i) q^{72} -7768.54 q^{73} +(-43208.6 - 44183.6i) q^{74} +101295. i q^{75} +(59065.0 + 1318.18i) q^{76} +3784.76i q^{77} +(-35110.3 + 34335.4i) q^{78} -50559.4 q^{79} +(3660.57 - 81970.7i) q^{80} +262787. q^{81} +(-31909.6 + 31205.4i) q^{82} +84631.7i q^{83} +(-30756.4 - 686.402i) q^{84} +112061. i q^{85} +(7423.38 + 7590.90i) q^{86} -168634. q^{87} +(-15997.6 + 14961.0i) q^{88} -95779.1 q^{89} +(222374. + 227393. i) q^{90} +8834.77i q^{91} +(546.251 - 24476.4i) q^{92} -243775. i q^{93} +(-35426.1 + 34644.4i) q^{94} -147938. q^{95} +(-118678. - 132716. i) q^{96} -51932.3 q^{97} +(64016.9 - 62604.2i) q^{98} -84902.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 20 q^{4} + 294 q^{6} + 672 q^{8} - 4050 q^{9}+O(q^{10}) $ 50 * q - 20 * q^4 + 294 * q^6 + 672 * q^8 - 4050 * q^9	\( 50 q - 20 q^{4} + 294 q^{6} + 672 q^{8} - 4050 q^{9} - 634 q^{10} - 1876 q^{12} + 3004 q^{14} + 1800 q^{15} + 1600 q^{16} - 404 q^{17} - 8278 q^{18} - 1892 q^{20} - 6348 q^{23} + 8096 q^{24} - 34366 q^{25} - 8524 q^{26} - 13372 q^{28} - 2042 q^{30} + 25852 q^{31} + 780 q^{32} - 13184 q^{34} - 3776 q^{36} - 53352 q^{38} - 44904 q^{39} + 11956 q^{40} - 2476 q^{41} + 58380 q^{42} + 2420 q^{44} - 76170 q^{46} + 109436 q^{47} - 44576 q^{48} + 90786 q^{49} + 85734 q^{50} + 29756 q^{52} - 113778 q^{54} - 24200 q^{55} + 22648 q^{56} - 25776 q^{57} - 67268 q^{58} + 85100 q^{60} + 70514 q^{62} + 161240 q^{63} + 60208 q^{64} + 51536 q^{65} - 49610 q^{66} + 75796 q^{68} + 187924 q^{70} - 213068 q^{71} - 8836 q^{72} - 79956 q^{73} - 34530 q^{74} + 7004 q^{76} + 500776 q^{78} + 177680 q^{79} + 148360 q^{80} + 238370 q^{81} - 83516 q^{82} - 304740 q^{84} - 53436 q^{86} - 433120 q^{87} + 114708 q^{88} + 169260 q^{89} + 4 q^{90} - 182068 q^{92} + 6656 q^{94} + 38424 q^{95} - 259748 q^{96} + 66972 q^{97} + 541672 q^{98}+O(q^{100}) \) 50 * q - 20 * q^4 + 294 * q^6 + 672 * q^8 - 4050 * q^9 - 634 * q^10 - 1876 * q^12 + 3004 * q^14 + 1800 * q^15 + 1600 * q^16 - 404 * q^17 - 8278 * q^18 - 1892 * q^20 - 6348 * q^23 + 8096 * q^24 - 34366 * q^25 - 8524 * q^26 - 13372 * q^28 - 2042 * q^30 + 25852 * q^31 + 780 * q^32 - 13184 * q^34 - 3776 * q^36 - 53352 * q^38 - 44904 * q^39 + 11956 * q^40 - 2476 * q^41 + 58380 * q^42 + 2420 * q^44 - 76170 * q^46 + 109436 * q^47 - 44576 * q^48 + 90786 * q^49 + 85734 * q^50 + 29756 * q^52 - 113778 * q^54 - 24200 * q^55 + 22648 * q^56 - 25776 * q^57 - 67268 * q^58 + 85100 * q^60 + 70514 * q^62 + 161240 * q^63 + 60208 * q^64 + 51536 * q^65 - 49610 * q^66 + 75796 * q^68 + 187924 * q^70 - 213068 * q^71 - 8836 * q^72 - 79956 * q^73 - 34530 * q^74 + 7004 * q^76 + 500776 * q^78 + 177680 * q^79 + 148360 * q^80 + 238370 * q^81 - 83516 * q^82 - 304740 * q^84 - 53436 * q^86 - 433120 * q^87 + 114708 * q^88 + 169260 * q^89 + 4 * q^90 - 182068 * q^92 + 6656 * q^94 + 38424 * q^95 - 259748 * q^96 + 66972 * q^97 + 541672 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−4.04438	+	3.95512i	−0.714952	+	0.699174i
$2$	−4.04438	+	3.95512i	−0.714952	+	0.699174i
$3$		−	30.7355i		−	1.97168i	−0.167680	−	0.985841i	$-0.553628\pi$
$3$		−	30.7355i		−	1.97168i	0.167680	−	0.985841i	$-0.446372\pi$
$4$	0.713979	−	31.9920i	0.0223118	−	0.999751i
$5$			80.1293i			1.43340i	0.697384	+	0.716698i	$0.254347\pi$
$5$			80.1293i			1.43340i	−0.697384	+	0.716698i	$0.745653\pi$
$6$	121.563	+	124.306i	1.37855	+	1.40966i
$7$	31.2790			0.241272			0.120636	−	0.992697i	$-0.461507\pi$
$7$	31.2790			0.241272			0.120636	+	0.992697i	$0.461507\pi$
$8$	123.645	+	132.212i	0.683048	+	0.730374i
$9$	−701.671			−2.88753
$10$	−316.921	−	324.073i	−1.00219	−	1.02481i
$11$			121.000i			0.301511i
$11$			121.000i			0.301511i
$12$	−983.291	−	21.9445i	−1.97119	−	0.0439919i
$13$			282.450i			0.463537i	0.972771	+	0.231768i	$0.0744511\pi$
$13$			282.450i			0.463537i	−0.972771	+	0.231768i	$0.925549\pi$
$14$	−126.504	+	123.712i	−0.172498	+	0.168691i
$15$	2462.81			2.82620
$16$	−1022.98	−	45.6833i	−0.999004	−	0.0446126i
$17$	1398.50			1.17366			0.586829	−	0.809711i	$-0.300376\pi$
$17$	1398.50			1.17366			0.586829	+	0.809711i	$0.300376\pi$
$18$	2837.82	−	2775.20i	2.06445	−	2.01889i
$19$			1846.24i			1.17329i	0.809845	+	0.586644i	$0.199551\pi$
$19$			1846.24i			1.17329i	−0.809845	+	0.586644i	$0.800449\pi$
$20$	2563.50	+	57.2106i	1.43304	+	0.0319817i
$21$		−	961.376i		−	0.475713i
$22$	−478.570	−	489.370i	−0.210809	−	0.215566i
$23$	765.079			0.301569			0.150785	−	0.988567i	$-0.451820\pi$
$23$	765.079			0.301569			0.150785	+	0.988567i	$0.451820\pi$
$24$	4063.59	−	3800.29i	1.44007	−	1.34675i
$25$	−3295.70			−1.05462
$26$	−1117.13	−	1142.34i	−0.324093	−	0.331406i
$27$			14097.5i			3.72162i
$28$	22.3326	−	1000.68i	0.00538323	−	0.241212i
$29$		−	5486.62i		−	1.21146i	−0.795670	−	0.605731i	$-0.792881\pi$
$29$		−	5486.62i		−	1.21146i	0.795670	−	0.605731i	$-0.207119\pi$
$30$	−9960.54	+	9740.73i	−2.02060	+	1.97601i
$31$	7931.38			1.48233			0.741164	−	0.671324i	$-0.234274\pi$
$31$	7931.38			1.48233			0.741164	+	0.671324i	$0.234274\pi$
$32$	4318.00	−	3861.25i	0.745432	−	0.666582i
$33$	3719.00			0.594485
$34$	−5656.08	+	5531.26i	−0.839109	+	0.820591i
$35$			2506.36i			0.345839i
$36$	−500.978	+	22447.9i	−0.0644262	+	2.88681i
$37$			10924.7i			1.31191i	0.754798	+	0.655957i	$0.227735\pi$
$37$			10924.7i			1.31191i	−0.754798	+	0.655957i	$0.772265\pi$
$38$	−7302.12	−	7466.90i	−0.820332	−	0.838844i
$39$	8681.26			0.913947
$40$	−10594.0	+	9907.57i	−1.04691	+	0.979078i
$41$	7889.88			0.733011			0.366506	−	0.930416i	$-0.380554\pi$
$41$	7889.88			0.733011			0.366506	+	0.930416i	$0.380554\pi$
$42$	3802.36	+	3888.17i	0.332606	+	0.340112i
$43$		−	1876.90i		−	0.154800i	−0.997000	−	0.0773999i	$-0.975338\pi$
$43$		−	1876.90i		−	0.154800i	0.997000	−	0.0773999i	$-0.0246618\pi$
$44$	3871.04	+	86.3915i	0.301436	+	0.00672727i
$45$		−	56224.4i		−	4.13898i
$46$	−3094.27	+	3025.98i	−0.215607	+	0.210849i
$47$	8759.36			0.578399			0.289200	−	0.957269i	$-0.406611\pi$
$47$	8759.36			0.578399			0.289200	+	0.957269i	$0.406611\pi$
$48$	−1404.10	+	31441.8i	−0.0879619	+	1.96972i
$49$	−15828.6			−0.941788
$50$	13329.0	−	13034.9i	0.754005	−	0.737365i
$51$		−	42983.7i		−	2.31408i
$52$	9036.17	+	201.664i	0.463421	+	0.0103424i
$53$			18211.8i			0.890560i	0.895391	+	0.445280i	$0.146896\pi$
$53$			18211.8i			0.890560i	−0.895391	+	0.445280i	$0.853104\pi$
$54$	−55757.3	−	57015.5i	−2.60206	−	2.66078i
$55$	−9695.64			−0.432185
$56$	3867.49	+	4135.45i	0.164801	+	0.176219i
$57$	56745.2			2.31335
$58$	21700.2	+	22189.9i	0.847022	+	0.866136i
$59$		−	531.019i		−	0.0198601i	−0.999951	−	0.00993003i	$-0.996839\pi$
$59$		−	531.019i		−	0.0198601i	0.999951	−	0.00993003i	$-0.00316088\pi$
$60$	1758.40	−	78790.4i	0.0630578	−	2.82550i
$61$			23908.4i			0.822670i	0.911484	+	0.411335i	$0.134937\pi$
$61$			23908.4i			0.822670i	−0.911484	+	0.411335i	$0.865063\pi$
$62$	−32077.5	+	31369.6i	−1.05979	+	1.03641i
$63$	−21947.6			−0.696682
$64$	−2191.89	+	32694.6i	−0.0668911	+	0.997760i
$65$	−22632.5			−0.664431
$66$	−15041.0	+	14709.1i	−0.425028	+	0.415648i
$67$			3145.18i			0.0855969i	0.999084	+	0.0427984i	$0.0136273\pi$
$67$			3145.18i			0.0855969i	−0.999084	+	0.0427984i	$0.986373\pi$
$68$	998.503	−	44741.0i	0.0261865	−	1.17337i
$69$		−	23515.1i		−	0.594599i
$70$	−9912.98	−	10136.7i	−0.241802	−	0.247258i
$71$	39892.0			0.939160			0.469580	−	0.882890i	$-0.344405\pi$
$71$	39892.0			0.939160			0.469580	+	0.882890i	$0.344405\pi$
$72$	−86758.0	−	92769.1i	−1.97232	−	2.10898i
$73$	−7768.54			−0.170621			−0.0853105	−	0.996354i	$-0.527188\pi$
$73$	−7768.54			−0.170621			−0.0853105	+	0.996354i	$0.527188\pi$
$74$	−43208.6	−	44183.6i	−0.917256	−	0.937955i
$75$			101295.i			2.07938i
$76$	59065.0	+	1318.18i	1.17300	+	0.0261782i
$77$			3784.76i			0.0727464i
$78$	−35110.3	+	34335.4i	−0.653428	+	0.639008i
$79$	−50559.4			−0.911453			−0.455727	−	0.890120i	$-0.650621\pi$
$79$	−50559.4			−0.911453			−0.455727	+	0.890120i	$0.650621\pi$
$80$	3660.57	−	81970.7i	0.0639475	−	1.43197i
$81$	262787.			4.45032
$82$	−31909.6	+	31205.4i	−0.524068	+	0.512502i
$83$			84631.7i			1.34846i	0.738522	+	0.674230i	$0.235524\pi$
$83$			84631.7i			1.34846i	−0.738522	+	0.674230i	$0.764476\pi$
$84$	−30756.4	−	686.402i	−0.475594	−	0.0106140i
$85$			112061.i			1.68232i
$86$	7423.38	+	7590.90i	0.108232	+	0.110674i
$87$	−168634.			−2.38862
$88$	−15997.6	+	14961.0i	−0.220216	+	0.205947i
$89$	−95779.1			−1.28173			−0.640864	−	0.767654i	$-0.721424\pi$
$89$	−95779.1			−1.28173			−0.640864	+	0.767654i	$0.721424\pi$
$90$	222374.	+	227393.i	2.89387	+	2.95917i
$91$			8834.77i			0.111839i
$92$	546.251	−	24476.4i	0.00672856	−	0.301494i
$93$		−	243775.i		−	2.92268i
$94$	−35426.1	+	34644.4i	−0.413527	+	0.404402i
$95$	−147938.			−1.68179
$96$	−118678.	−	132716.i	−1.31429	−	1.46976i
$97$	−51932.3			−0.560413			−0.280206	−	0.959940i	$-0.590403\pi$
$97$	−51932.3			−0.560413			−0.280206	+	0.959940i	$0.590403\pi$
$98$	64016.9	−	62604.2i	0.673333	−	0.658473i
$99$		−	84902.2i		−	0.870624i
$100$	−2353.06	+	105436.i	−0.0235306	+	1.05436i
$101$			170096.i			1.65917i	0.558381	+	0.829585i	$0.311423\pi$
$101$			170096.i			1.65917i	−0.558381	+	0.829585i	$0.688577\pi$
$102$	170006.	+	173842.i	1.61795	+	1.65446i
$103$	34939.1			0.324503			0.162251	−	0.986749i	$-0.448124\pi$
$103$	34939.1			0.324503			0.162251	+	0.986749i	$0.448124\pi$
$104$	−37343.3	+	34923.6i	−0.338555	+	0.316618i
$105$	77034.3			0.681885
$106$	−72029.9	−	73655.4i	−0.622656	−	0.636707i
$107$		−	116898.i		−	0.987067i	−0.869727	−	0.493533i	$-0.835705\pi$
$107$		−	116898.i		−	0.987067i	0.869727	−	0.493533i	$-0.164295\pi$
$108$	451007.	+	10065.3i	3.72069	+	0.0830362i
$109$		−	54443.9i		−	0.438918i	−0.975622	−	0.219459i	$-0.929571\pi$
$109$		−	54443.9i		−	0.438918i	0.975622	−	0.219459i	$-0.0704291\pi$
$110$	39212.8	−	38347.5i	0.308991	−	0.302173i
$111$	335776.			2.58668
$112$	−31997.8	−	1428.93i	−0.241032	−	0.0107638i
$113$	36882.1			0.271719			0.135859	−	0.990728i	$-0.456620\pi$
$113$	36882.1			0.271719			0.135859	+	0.990728i	$0.456620\pi$
$114$	−229499.	+	224434.i	−1.65394	+	1.61744i
$115$			61305.2i			0.432268i
$116$	−175528.	−	3917.33i	−1.21116	−	0.0270299i
$117$		−	198187.i		−	1.33848i
$118$	2100.25	+	2147.64i	0.0138856	+	0.0141990i
$119$	43743.8			0.283171
$120$	304514.	+	325613.i	1.93043	+	2.06418i
$121$	−14641.0			−0.0909091
$122$	−94560.7	−	96694.6i	−0.575190	−	0.588169i
$123$		−	242499.i		−	1.44527i
$124$	5662.84	−	253741.i	0.0330735	−	1.48196i
$125$		−	13677.9i		−	0.0782969i
$126$	88764.2	−	86805.3i	0.498094	−	0.487102i
$127$	−25454.8			−0.140043			−0.0700213	−	0.997545i	$-0.522307\pi$
$127$	−25454.8			−0.140043			−0.0700213	+	0.997545i	$0.522307\pi$
$128$	−120446.	−	140899.i	−0.649784	−	0.760119i
$129$	−57687.5			−0.305216
$130$	91534.6	−	89514.5i	0.475036	−	0.464553i
$131$			257383.i			1.31039i	0.755459	+	0.655195i	$0.227414\pi$
$131$			257383.i			1.31039i	−0.755459	+	0.655195i	$0.772586\pi$
$132$	2655.28	−	118978.i	0.0132641	−	0.594337i
$133$			57748.6i			0.283082i
$134$	−12439.6	−	12720.3i	−0.0598471	−	0.0611976i
$135$	−1.12962e6			−5.33455
$136$	172918.	+	184899.i	0.801665	+	0.857209i
$137$	41401.7			0.188459			0.0942295	−	0.995551i	$-0.469961\pi$
$137$	41401.7			0.188459			0.0942295	+	0.995551i	$0.469961\pi$
$138$	93005.1	+	95103.9i	0.415728	+	0.425109i
$139$			283887.i			1.24626i	0.782118	+	0.623131i	$0.214140\pi$
$139$			283887.i			1.24626i	−0.782118	+	0.623131i	$0.785860\pi$
$140$	80183.7	+	1789.49i	0.345753	+	0.00771631i
$141$		−	269223.i		−	1.14042i
$142$	−161338.	+	157778.i	−0.671454	+	0.656636i
$143$	−34176.5			−0.139762
$144$	717795.	+	32054.6i	2.88466	+	0.128820i
$145$	439638.			1.73650
$146$	31418.9	−	30725.6i	0.121986	−	0.119294i
$147$			486501.i			1.85691i
$148$	349503.	+	7800.01i	1.31159	+	0.0292712i
$149$		−	196555.i		−	0.725301i	−0.931925	−	0.362650i	$-0.881872\pi$
$149$		−	196555.i		−	0.725301i	0.931925	−	0.362650i	$-0.118128\pi$
$150$	−400634.	−	409675.i	−1.45385	−	1.48666i
$151$	93004.7			0.331942			0.165971	−	0.986131i	$-0.446924\pi$
$151$	93004.7			0.331942			0.165971	+	0.986131i	$0.446924\pi$
$152$	−244095.	+	228278.i	−0.856939	+	0.801412i
$153$	−981290.			−3.38898
$154$	−14969.2	−	15307.0i	−0.0508624	−	0.0520102i
$155$			635535.i			2.12476i
$156$	6198.23	−	277731.i	0.0203918	−	0.913720i
$157$			121386.i			0.393024i	0.980501	+	0.196512i	$0.0629615\pi$
$157$			121386.i			0.393024i	−0.980501	+	0.196512i	$0.937039\pi$
$158$	204481.	−	199969.i	0.651645	−	0.637264i
$159$	559748.			1.75590
$160$	309399.	+	345998.i	0.955476	+	1.06850i
$161$	23930.9			0.0727603
$162$	−1.06281e6	+	1.03935e6i	−3.18176	+	3.11155i
$163$			195481.i			0.576283i	0.957588	+	0.288142i	$0.0930374\pi$
$163$			195481.i			0.576283i	−0.957588	+	0.288142i	$0.906963\pi$
$164$	5633.21	−	252413.i	0.0163548	−	0.732829i
$165$			298000.i			0.852132i
$166$	−334729.	−	342283.i	−0.942807	−	0.964083i
$167$	−73572.6			−0.204139			−0.102069	−	0.994777i	$-0.532546\pi$
$167$	−73572.6			−0.204139			−0.102069	+	0.994777i	$0.532546\pi$
$168$	127105.	−	118869.i	0.347448	−	0.324935i
$169$	291515.			0.785134
$170$	−443216.	−	453217.i	−1.17623	−	1.20277i
$171$		−	1.29545e6i		−	3.38791i
$172$	−60045.9	−	1340.07i	−0.154761	−	0.00345387i
$173$		−	460999.i		−	1.17107i	−0.810646	−	0.585537i	$-0.800884\pi$
$173$		−	460999.i		−	1.17107i	0.810646	−	0.585537i	$-0.199116\pi$
$174$	682019.	−	666968.i	1.70775	−	1.67006i
$175$	−103086.			−0.254452
$176$	5527.68	−	123781.i	0.0134512	−	0.301211i
$177$	−16321.1			−0.0391577
$178$	387367.	−	378818.i	0.916374	−	0.896151i
$179$		−	301103.i		−	0.702397i	−0.936301	−	0.351199i	$-0.885774\pi$
$179$		−	301103.i		−	0.702397i	0.936301	−	0.351199i	$-0.114226\pi$
$180$	−1.79873e6	−	40143.0i	−4.13795	−	0.0923483i
$181$			17213.7i			0.0390552i	0.999809	+	0.0195276i	$0.00621622\pi$
$181$			17213.7i			0.0390552i	−0.999809	+	0.0195276i	$0.993784\pi$
$182$	−34942.6	−	35731.1i	−0.0781946	−	0.0799592i
$183$	734836.			1.62204
$184$	94598.1	+	101152.i	0.205986	+	0.220258i
$185$	−875388.			−1.88049
$186$	964160.	+	985917.i	2.04346	+	2.08958i
$187$			169219.i			0.353871i
$188$	6254.00	−	280230.i	0.0129052	−	0.578255i
$189$			440955.i			0.897924i
$190$	598317.	−	585113.i	1.20240	−	1.17586i
$191$	600847.			1.19174			0.595868	−	0.803082i	$-0.296808\pi$
$191$	600847.			1.19174			0.595868	+	0.803082i	$0.296808\pi$
$192$	1.00489e6	+	67368.8i	1.96727	+	0.131888i
$193$	−86429.0			−0.167019			−0.0835095	−	0.996507i	$-0.526613\pi$
$193$	−86429.0			−0.167019			−0.0835095	+	0.996507i	$0.526613\pi$
$194$	210034.	−	205399.i	0.400668	−	0.391826i
$195$			695623.i			1.31005i
$196$	−11301.3	+	506390.i	−0.0210130	+	0.941553i
$197$		−	786417.i		−	1.44373i	−0.692032	−	0.721867i	$-0.743284\pi$
$197$		−	786417.i		−	1.44373i	0.692032	−	0.721867i	$-0.256716\pi$
$198$	335799.	+	343376.i	0.608718	+	0.622454i
$199$	−76630.8			−0.137174			−0.0685868	−	0.997645i	$-0.521849\pi$
$199$	−76630.8			−0.137174			−0.0685868	+	0.997645i	$0.521849\pi$
$200$	−407496.	−	435730.i	−0.720358	−	0.770269i
$201$	96668.6			0.168770
$202$	−672751.	−	687933.i	−1.16005	−	1.18623i
$203$		−	171616.i		−	0.292292i
$204$	−1.37514e6	−	30689.5i	−2.31351	−	0.0516314i
$205$			632210.i			1.05070i
$206$	−141307.	+	138189.i	−0.232004	+	0.226884i
$207$	−536834.			−0.870791
$208$	12903.3	−	288941.i	0.0206796	−	0.463075i
$209$	−223395.			−0.353760
$210$	−311556.	+	304680.i	−0.487515	+	0.476756i
$211$		−	955972.i		−	1.47822i	−0.673585	−	0.739110i	$-0.735246\pi$
$211$		−	955972.i		−	1.47822i	0.673585	−	0.739110i	$-0.264754\pi$
$212$	582632.	+	13002.8i	0.890338	+	0.0198700i
$213$		−	1.22610e6i		−	1.85173i
$214$	462345.	+	472778.i	0.690131	+	0.705705i
$215$	150395.			0.221889
$216$	−1.86385e6	+	1.74308e6i	−2.71817	+	2.54204i
$217$	248086.			0.357645
$218$	215332.	+	220192.i	0.306880	+	0.313805i
$219$			238770.i			0.336411i
$220$	−6922.48	+	310183.i	−0.00964285	+	0.432077i
$221$			395008.i			0.544033i
$222$	−1.35801e6	+	1.32804e6i	−1.84935	+	1.80854i
$223$	−1.10014e6			−1.48144			−0.740721	−	0.671813i	$-0.765516\pi$
$223$	−1.10014e6			−1.48144			−0.740721	+	0.671813i	$0.765516\pi$
$224$	135063.	−	120776.i	0.179852	−	0.160828i
$225$	2.31249e6			3.04526
$226$	−149165.	+	145873.i	−0.194266	+	0.189978i
$227$			114158.i			0.147042i	0.997294	+	0.0735212i	$0.0234237\pi$
$227$			114158.i			0.147042i	−0.997294	+	0.0735212i	$0.976576\pi$
$228$	40514.9	−	1.81539e6i	0.0516152	−	2.31278i
$229$			1.47966e6i			1.86455i	0.361752	+	0.932274i	$0.382179\pi$
$229$			1.47966e6i			1.86455i	−0.361752	+	0.932274i	$0.617821\pi$
$230$	−242470.	−	247942.i	−0.302230	−	0.309051i
$231$	116326.			0.143433
$232$	725395.	−	678392.i	0.884819	−	0.827486i
$233$	225652.			0.272301			0.136151	−	0.990688i	$-0.456527\pi$
$233$	225652.			0.272301			0.136151	+	0.990688i	$0.456527\pi$
$234$	783855.	+	801544.i	0.935828	+	0.956947i
$235$			701881.i			0.829075i
$236$	−16988.4	−	379.137i	−0.0198551	−	0.000443114i
$237$			1.55397e6i			1.79710i
$238$	−176917.	+	173012.i	−0.202454	+	0.197986i
$239$	1.41341e6			1.60056			0.800280	−	0.599626i	$-0.204684\pi$
$239$	1.41341e6			1.60056			0.800280	+	0.599626i	$0.204684\pi$
$240$	−2.51941e6	−	112509.i	−2.82339	−	0.126084i
$241$	−647007.			−0.717573			−0.358787	−	0.933420i	$-0.616809\pi$
$241$	−647007.			−0.717573			−0.358787	+	0.933420i	$0.616809\pi$
$242$	59213.7	−	57907.0i	0.0649956	−	0.0635613i
$243$		−	4.65120e6i		−	5.05300i
$244$	764878.	+	17070.1i	0.822465	+	0.0183553i
$245$		−	1.26834e6i		−	1.34995i
$246$	959115.	+	980759.i	1.01049	+	1.03330i
$247$	−521472.			−0.543862
$248$	980674.	+	1.04862e6i	1.01250	+	1.08265i
$249$	2.60120e6			2.65873
$250$	54097.8	+	55318.6i	0.0547431	+	0.0559785i
$251$		−	1.12944e6i		−	1.13156i	−0.824555	−	0.565782i	$-0.808574\pi$
$251$		−	1.12944e6i		−	1.13156i	0.824555	−	0.565782i	$-0.191426\pi$
$252$	−15670.1	+	702147.i	−0.0155443	+	0.696509i
$253$			92574.6i			0.0909265i
$254$	102949.	−	100677.i	0.100124	−	0.0979142i
$255$	3.44425e6			3.31699
$256$	1.04440e6	+	93466.2i	0.996019	+	0.0891363i
$257$	324981.			0.306920			0.153460	−	0.988155i	$-0.450958\pi$
$257$	324981.			0.306920			0.153460	+	0.988155i	$0.450958\pi$
$258$	233310.	−	228161.i	0.218215	−	0.213399i
$259$			341714.i			0.316529i
$260$	−16159.2	+	724061.i	−0.0148247	+	0.664266i
$261$			3.84980e6i			3.49814i
$262$	−1.01798e6	−	1.04095e6i	−0.916191	−	0.936866i
$263$	−987719.			−0.880530			−0.440265	−	0.897868i	$-0.645115\pi$
$263$	−987719.			−0.880530			−0.440265	+	0.897868i	$0.645115\pi$
$264$	459835.	+	491695.i	0.406062	+	0.434196i
$265$	−1.45930e6			−1.27652
$266$	−228403.	−	233557.i	−0.197924	−	0.202390i
$267$			2.94382e6i			2.52716i
$268$	100621.	+	2245.59i	0.0855756	+	0.00190982i
$269$		−	514538.i		−	0.433547i	−0.976222	−	0.216774i	$-0.930447\pi$
$269$		−	514538.i		−	0.433547i	0.976222	−	0.216774i	$-0.0695534\pi$
$270$	4.56861e6	−	4.46779e6i	3.81395	−	3.72978i
$271$	2.21062e6			1.82848			0.914241	−	0.405171i	$-0.132788\pi$
$271$	2.21062e6			1.82848			0.914241	+	0.405171i	$0.132788\pi$
$272$	−1.43064e6	−	63888.3i	−1.17249	−	0.0523599i
$273$	271541.			0.220510
$274$	−167444.	+	163749.i	−0.134739	+	0.131766i
$275$		−	398779.i		−	0.317981i
$276$	−752296.	−	16789.3i	−0.594451	−	0.0132666i
$277$		−	1.66116e6i		−	1.30081i	−0.759589	−	0.650404i	$-0.774600\pi$
$277$		−	1.66116e6i		−	1.30081i	0.759589	−	0.650404i	$-0.225400\pi$
$278$	−1.12281e6	−	1.14815e6i	−0.871353	−	0.891017i
$279$	−5.56521e6			−4.28027
$280$	−331371.	+	309899.i	−0.252592	+	0.236225i
$281$	−2.36508e6			−1.78682			−0.893409	−	0.449244i	$-0.851694\pi$
$281$	−2.36508e6			−1.78682			−0.893409	+	0.449244i	$0.851694\pi$
$282$	1.06481e6	+	1.08884e6i	0.797352	+	0.815345i
$283$		−	314297.i		−	0.233278i	−0.993174	−	0.116639i	$-0.962788\pi$
$283$		−	314297.i		−	0.233278i	0.993174	−	0.116639i	$-0.0372121\pi$
$284$	28482.0	−	1.27623e6i	0.0209544	−	0.938926i
$285$			4.54695e6i			3.31595i
$286$	138223.	−	135172.i	0.0999227	−	0.0977176i
$287$	246787.			0.176855
$288$	−3.02982e6	+	2.70933e6i	−2.15246	+	1.92478i
$289$	535958.			0.377473
$290$	−1.77806e6	+	1.73882e6i	−1.24152	+	1.21412i
$291$			1.59616e6i			1.10496i
$292$	−5546.58	+	248532.i	−0.00380687	+	0.170579i
$293$			13575.7i			0.00923835i	0.999989	+	0.00461917i	$0.00147033\pi$
$293$			13575.7i			0.00923835i	−0.999989	+	0.00461917i	$0.998530\pi$
$294$	−1.92417e6	−	1.96759e6i	−1.29830	−	1.32760i
$295$	42550.2			0.0284673
$296$	−1.44437e6	+	1.35078e6i	−0.958187	+	0.896100i
$297$	−1.70579e6			−1.12211
$298$	777399.	+	794942.i	0.507111	+	0.518555i
$299$			216097.i			0.139788i
$300$	3.24063e6	+	72322.4i	2.07887	+	0.0463949i
$301$		−	58707.6i		−	0.0373489i
$302$	−376146.	+	367845.i	−0.237323	+	0.232085i
$303$	5.22799e6			3.27136
$304$	84342.4	−	1.88867e6i	0.0523434	−	1.17212i
$305$	−1.91576e6			−1.17921
$306$	3.96871e6	−	3.88112e6i	2.42295	−	2.36948i
$307$		−	190035.i		−	0.115077i	−0.998343	−	0.0575383i	$-0.981675\pi$
$307$		−	190035.i		−	0.115077i	0.998343	−	0.0575383i	$-0.0183251\pi$
$308$	121082.	+	2702.24i	0.0727283	+	0.00162311i
$309$		−	1.07387e6i		−	0.639817i
$310$	−2.51362e6	−	2.57034e6i	−1.48558	−	1.51910i
$311$	1.27422e6			0.747038			0.373519	−	0.927623i	$-0.378151\pi$
$311$	1.27422e6			0.747038			0.373519	+	0.927623i	$0.378151\pi$
$312$	1.07339e6	+	1.14776e6i	0.624270	+	0.667523i
$313$	−882411.			−0.509108			−0.254554	−	0.967059i	$-0.581929\pi$
$313$	−882411.			−0.509108			−0.254554	+	0.967059i	$0.581929\pi$
$314$	−480096.	−	490930.i	−0.274792	−	0.280993i
$315$		−	1.75864e6i		−	0.998622i
$316$	−36098.4	+	1.61750e6i	−0.0203362	+	0.911226i
$317$		−	640555.i		−	0.358021i	−0.983847	−	0.179010i	$-0.942710\pi$
$317$		−	640555.i		−	0.358021i	0.983847	−	0.179010i	$-0.0572895\pi$
$318$	−2.26383e6	+	2.21387e6i	−1.25538	+	1.22768i
$319$	663880.			0.365269
$320$	−2.61979e6	−	175634.i	−1.43019	−	0.0958814i
$321$	−3.59291e6			−1.94618
$322$	−96785.7	+	94649.8i	−0.0520201	+	0.0508721i
$323$			2.58198e6i			1.37704i
$324$	187624.	−	8.40708e6i	0.0992948	−	4.44921i
$325$		−	930871.i		−	0.488856i
$326$	−773153.	−	790600.i	−0.402922	−	0.412015i
$327$	−1.67336e6			−0.865406
$328$	975543.	+	1.04313e6i	0.500682	+	0.535372i
$329$	273984.			0.139552
$330$	−1.17863e6	−	1.20523e6i	−0.595788	−	0.609233i
$331$		−	1.20990e6i		−	0.606987i	−0.952833	−	0.303494i	$-0.901847\pi$
$331$		−	1.20990e6i		−	0.606987i	0.952833	−	0.303494i	$-0.0981531\pi$
$332$	2.70754e6	+	60425.3i	1.34812	+	0.0300866i
$333$		−	7.66554e6i		−	3.78819i
$334$	297556.	−	290989.i	0.145949	−	0.142728i
$335$	−252021.			−0.122694
$336$	−43918.8	+	983469.i	−0.0212228	+	0.475239i
$337$	−2.80864e6			−1.34716			−0.673582	−	0.739112i	$-0.735245\pi$
$337$	−2.80864e6			−1.34716			−0.673582	+	0.739112i	$0.735245\pi$
$338$	−1.17900e6	+	1.15298e6i	−0.561333	+	0.548945i
$339$		−	1.13359e6i		−	0.535743i
$340$	3.58506e6	+	80009.3i	1.68190	+	0.0375356i
$341$			959697.i			0.446939i
$342$	5.12368e6	+	5.23931e6i	2.36874	+	2.42219i
$343$	−1.02081e6			−0.468500
$344$	248148.	−	232069.i	0.113062	−	0.105736i
$345$	1.88425e6			0.852295
$346$	1.82331e6	+	1.86445e6i	0.818785	+	0.837262i
$347$		−	2.45618e6i		−	1.09506i	−0.836787	−	0.547529i	$-0.815569\pi$
$347$		−	2.45618e6i		−	1.09506i	0.836787	−	0.547529i	$-0.184431\pi$
$348$	−120401.	+	5.39494e6i	−0.0532945	+	2.38802i
$349$		−	4.45397e6i		−	1.95742i	−0.205248	−	0.978710i	$-0.565800\pi$
$349$		−	4.45397e6i		−	1.95742i	0.205248	−	0.978710i	$-0.434200\pi$
$350$	416919.	−	407719.i	0.181921	−	0.177906i
$351$	−3.98184e6			−1.72511
$352$	467212.	+	522478.i	0.200982	+	0.224756i
$353$	1.32337e6			0.565253			0.282627	−	0.959230i	$-0.408794\pi$
$353$	1.32337e6			0.565253			0.282627	+	0.959230i	$0.408794\pi$
$354$	66008.9	−	64552.2i	0.0279959	−	0.0273781i
$355$			3.19651e6i			1.34619i
$356$	−68384.3	+	3.06417e6i	−0.0285977	+	1.28141i
$357$		−	1.34449e6i		−	0.558324i
$358$	1.19090e6	+	1.21777e6i	0.491098	+	0.502180i
$359$	−501781.			−0.205484			−0.102742	−	0.994708i	$-0.532762\pi$
$359$	−501781.			−0.205484			−0.102742	+	0.994708i	$0.532762\pi$
$360$	7.43352e6	−	6.95185e6i	3.02300	−	2.82712i
$361$	−932511.			−0.376605
$362$	−68082.4	−	69618.8i	−0.0273063	−	0.0279225i
$363$			449998.i			0.179244i
$364$	282642.	+	6307.84i	0.111811	+	0.00249533i
$365$		−	622488.i		−	0.244567i
$366$	−2.97196e6	+	2.90637e6i	−1.15968	+	1.13409i
$367$	−1.14834e6			−0.445047			−0.222523	−	0.974927i	$-0.571429\pi$
$367$	−1.14834e6			−0.445047			−0.222523	+	0.974927i	$0.571429\pi$
$368$	−782661.	−	34951.3i	−0.301269	−	0.0134538i
$369$	−5.53610e6			−2.11659
$370$	3.54040e6	−	3.46227e6i	1.34446	−	1.31479i
$371$			569647.i			0.214868i
$372$	−7.79885e6	−	174050.i	−2.92195	−	0.0652104i
$373$		−	4.42243e6i		−	1.64585i	−0.568153	−	0.822923i	$-0.692342\pi$
$373$		−	4.42243e6i		−	1.64585i	0.568153	−	0.822923i	$-0.307658\pi$
$374$	−669282.	−	684386.i	−0.247417	−	0.253001i
$375$	−420397.			−0.154377
$376$	1.08305e6	+	1.15809e6i	0.395074	+	0.422447i
$377$	1.54970e6			0.561556
$378$	−1.74403e6	−	1.78339e6i	−0.627805	−	0.641972i
$379$			1.11132e6i			0.397411i	0.980059	+	0.198705i	$0.0636737\pi$
$379$			1.11132e6i			0.397411i	−0.980059	+	0.198705i	$0.936326\pi$
$380$	−105625.	+	4.73284e6i	−0.0375238	+	1.68137i
$381$			782366.i			0.276120i
$382$	−2.43005e6	+	2.37642e6i	−0.852034	+	0.833231i
$383$	4.82550e6			1.68091			0.840457	−	0.541878i	$-0.182286\pi$
$383$	4.82550e6			1.68091			0.840457	+	0.541878i	$0.182286\pi$
$384$	−4.33059e6	+	3.70198e6i	−1.49871	+	1.28117i
$385$	−303270.			−0.104274
$386$	349551.	−	341837.i	0.119411	−	0.116775i
$387$			1.31697e6i			0.446990i
$388$	−37078.5	+	1.66142e6i	−0.0125038	+	0.560273i
$389$			4.60356e6i			1.54248i	0.636544	+	0.771240i	$0.280363\pi$
$389$			4.60356e6i			1.54248i	−0.636544	+	0.771240i	$0.719637\pi$
$390$	−2.75127e6	−	2.81336e6i	−0.915951	−	0.936621i
$391$	1.06997e6			0.353939
$392$	−1.95713e6	−	2.09273e6i	−0.643286	−	0.687857i
$393$	7.91078e6			2.58368
$394$	3.11038e6	+	3.18057e6i	1.00942	+	1.03220i
$395$		−	4.05129e6i		−	1.30647i
$396$	−2.71619e6	−	60618.4i	−0.870407	−	0.0194252i
$397$			2.63880e6i			0.840292i	0.907456	+	0.420146i	$0.138021\pi$
$397$			2.63880e6i			0.840292i	−0.907456	+	0.420146i	$0.861979\pi$
$398$	309924.	−	303084.i	0.0980725	−	0.0959082i
$399$	1.77493e6			0.558148
$400$	3.37143e6	+	150558.i	1.05357	+	0.0470495i
$401$	−1.01591e6			−0.315497			−0.157748	−	0.987479i	$-0.550423\pi$
$401$	−1.01591e6			−0.315497			−0.157748	+	0.987479i	$0.550423\pi$
$402$	−390964.	+	382336.i	−0.120662	+	0.118000i
$403$			2.24022e6i			0.687113i
$404$	5.44172e6	+	121445.i	1.65876	+	0.0370191i
$405$			2.10569e7i			6.37907i
$406$	678762.	+	694079.i	0.204363	+	0.208975i
$407$	−1.32189e6			−0.395557
$408$	5.68295e6	−	5.31472e6i	1.69014	−	1.58063i
$409$	−1.29630e6			−0.383176			−0.191588	−	0.981475i	$-0.561364\pi$
$409$	−1.29630e6			−0.383176			−0.191588	+	0.981475i	$0.561364\pi$
$410$	−2.50047e6	−	2.55690e6i	−0.734619	−	0.751196i
$411$		−	1.27250e6i		−	0.371581i
$412$	24945.8	−	1.11777e6i	0.00724026	−	0.324422i
$413$		−	16609.8i		−	0.00479168i
$414$	2.17116e6	−	2.12324e6i	0.622573	−	0.608834i
$415$	−6.78147e6			−1.93288
$416$	1.09061e6	+	1.21962e6i	0.308985	+	0.345535i
$417$	8.72542e6			2.45723
$418$	903495.	−	883556.i	0.252921	−	0.247340i
$419$			6.48495e6i			1.80456i	0.431150	+	0.902280i	$0.358108\pi$
$419$			6.48495e6i			1.80456i	−0.431150	+	0.902280i	$0.641892\pi$
$420$	55000.9	−	2.46448e6i	0.0152141	−	0.681715i
$421$			715414.i			0.196722i	0.995151	+	0.0983608i	$0.0313599\pi$
$421$			715414.i			0.196722i	−0.995151	+	0.0983608i	$0.968640\pi$
$422$	3.78099e6	+	3.86631e6i	1.03353	+	1.05686i
$423$	−6.14618e6			−1.67015
$424$	−2.40781e6	+	2.25179e6i	−0.650441	+	0.608295i
$425$	−4.60905e6			−1.23777
$426$	4.84938e6	+	4.95881e6i	1.29468	+	1.32389i
$427$			747831.i			0.198488i
$428$	−3.73979e6	−	83462.5i	−0.986821	−	0.0220233i
$429$			1.05043e6i			0.275565i
$430$	−608253.	+	594830.i	−0.158640	+	0.155139i
$431$	−1.67232e6			−0.433636			−0.216818	−	0.976212i	$-0.569568\pi$
$431$	−1.67232e6			−0.433636			−0.216818	+	0.976212i	$0.569568\pi$
$432$	644019.	−	1.44214e7i	0.166031	−	3.71791i
$433$	−3.99876e6			−1.02496			−0.512479	−	0.858700i	$-0.671273\pi$
$433$	−3.99876e6			−1.02496			−0.512479	+	0.858700i	$0.671273\pi$
$434$	−1.00335e6	+	981209.i	−0.255699	+	0.250056i
$435$		−	1.35125e7i		−	3.42383i
$436$	−1.74177e6	−	38871.8i	−0.438808	−	0.00979306i
$437$			1.41252e6i			0.353827i
$438$	−944365.	−	965676.i	−0.235209	−	0.240517i
$439$	1.93027e6			0.478031			0.239015	−	0.971016i	$-0.423175\pi$
$439$	1.93027e6			0.478031			0.239015	+	0.971016i	$0.423175\pi$
$440$	−1.19882e6	−	1.28188e6i	−0.295203	−	0.315657i
$441$	1.11065e7			2.71944
$442$	−1.56231e6	−	1.59756e6i	−0.380374	−	0.388958i
$443$			2.23966e6i			0.542217i	0.962549	+	0.271108i	$0.0873902\pi$
$443$			2.23966e6i			0.542217i	−0.962549	+	0.271108i	$0.912610\pi$
$444$	239737.	−	1.07422e7i	0.0577136	−	2.58603i
$445$		−	7.67471e6i		−	1.83722i
$446$	4.44937e6	−	4.35118e6i	1.05916	−	1.03579i
$447$	−6.04121e6			−1.43006
$448$	−68560.1	+	1.02265e6i	−0.0161390	+	0.240732i
$449$	3.08094e6			0.721219			0.360609	−	0.932717i	$-0.382569\pi$
$449$	3.08094e6			0.721219			0.360609	+	0.932717i	$0.382569\pi$
$450$	−9.35260e6	+	9.14620e6i	−2.17721	+	2.12917i
$451$			954675.i			0.221011i
$452$	26333.0	−	1.17993e6i	0.00606254	−	0.271651i
$453$		−	2.85854e6i		−	0.654485i
$454$	−451510.	−	461699.i	−0.102808	−	0.105128i
$455$	−707924.			−0.160309
$456$	7.01625e6	+	7.50238e6i	1.58013	+	1.68961i
$457$	6.09982e6			1.36624			0.683119	−	0.730307i	$-0.260623\pi$
$457$	6.09982e6			1.36624			0.683119	+	0.730307i	$0.260623\pi$
$458$	−5.85225e6	−	5.98431e6i	−1.30364	−	1.33306i
$459$			1.97154e7i			4.36791i
$460$	1.96128e6	+	43770.7i	0.432160	+	0.00964469i
$461$		−	7.03671e6i		−	1.54212i	−0.636764	−	0.771059i	$-0.719727\pi$
$461$		−	7.03671e6i		−	1.54212i	0.636764	−	0.771059i	$-0.280273\pi$
$462$	−470468.	+	460086.i	−0.102548	+	0.100284i
$463$	213094.			0.0461974			0.0230987	−	0.999733i	$-0.492647\pi$
$463$	213094.			0.0461974			0.0230987	+	0.999733i	$0.492647\pi$
$464$	−250647.	+	5.61270e6i	−0.0540464	+	1.21025i
$465$	1.95335e7			4.18936
$466$	−912623.	+	892483.i	−0.194682	+	0.190386i
$467$		−	4.35509e6i		−	0.924071i	−0.886861	−	0.462036i	$-0.847119\pi$
$467$		−	4.35509e6i		−	0.924071i	0.886861	−	0.462036i	$-0.152881\pi$
$468$	−6.34041e6	−	141502.i	−1.33814	−	0.0298639i
$469$			98378.0i			0.0206522i
$470$	−2.77603e6	−	2.83867e6i	−0.579667	−	0.592748i
$471$	3.73086e6			0.774919
$472$	70207.0	−	65657.8i	0.0145053	−	0.0135654i
$473$	227105.			0.0466739
$474$	−6.14614e6	−	6.28484e6i	−1.25648	−	1.28484i
$475$		−	6.08466e6i		−	1.23738i
$476$	31232.2	−	1.39945e6i	0.00631808	−	0.283101i
$477$		−	1.27787e7i		−	2.57152i
$478$	−5.71635e6	+	5.59020e6i	−1.14432	+	1.11907i
$479$	3.88291e6			0.773248			0.386624	−	0.922237i	$-0.373641\pi$
$479$	3.88291e6			0.773248			0.386624	+	0.922237i	$0.373641\pi$
$480$	1.06344e7	−	9.50955e6i	2.10674	−	1.88390i
$481$	−3.08569e6			−0.608120
$482$	2.61674e6	−	2.55899e6i	0.513030	−	0.501709i
$483$		−	735529.i		−	0.143460i
$484$	−10453.4	+	468395.i	−0.00202835	+	0.0908865i
$485$		−	4.16129e6i		−	0.803293i
$486$	1.83961e7	+	1.88112e7i	3.53292	+	3.61265i
$487$	−5.90233e6			−1.12772			−0.563860	−	0.825870i	$-0.690684\pi$
$487$	−5.90233e6			−1.12772			−0.563860	+	0.825870i	$0.690684\pi$
$488$	−3.16097e6	+	2.95615e6i	−0.600857	+	0.561923i
$489$	6.00821e6			1.13625
$490$	5.01643e6	+	5.12963e6i	0.943853	+	0.965152i
$491$		−	2.88333e6i		−	0.539747i	−0.962896	−	0.269874i	$-0.913018\pi$
$491$		−	2.88333e6i		−	0.539747i	0.962896	−	0.269874i	$-0.0869819\pi$
$492$	−7.75805e6	−	173139.i	−1.44491	−	0.0322465i
$493$		−	7.67306e6i		−	1.42184i
$494$	2.10903e6	−	2.06249e6i	0.388835	−	0.380254i
$495$	6.80315e6			1.24795
$496$	−8.11364e6	−	362331.i	−1.48085	−	0.0661305i
$497$	1.24778e6			0.226593
$498$	−1.05202e7	+	1.02881e7i	−1.90087	+	1.85892i
$499$			7.34897e6i			1.32122i	0.750729	+	0.660610i	$0.229702\pi$
$499$			7.34897e6i			1.32122i	−0.750729	+	0.660610i	$0.770298\pi$
$500$	−437584.	−	9765.74i	−0.0782774	−	0.00174695i
$501$			2.26129e6i			0.402497i
$502$	4.46708e6	+	4.56789e6i	0.791160	+	0.809014i
$503$	3.08274e6			0.543271			0.271636	−	0.962400i	$-0.412435\pi$
$503$	3.08274e6			0.543271			0.271636	+	0.962400i	$0.412435\pi$
$504$	−2.71370e6	−	2.90173e6i	−0.475867	−	0.508838i
$505$	−1.36297e7			−2.37825
$506$	−366144.	−	374407.i	−0.0635734	−	0.0650081i
$507$		−	8.95985e6i		−	1.54804i
$508$	−18174.2	+	814351.i	−0.00312461	+	0.140008i
$509$			6.42791e6i			1.09970i	0.835263	+	0.549851i	$0.185316\pi$
$509$			6.42791e6i			1.09970i	−0.835263	+	0.549851i	$0.814684\pi$
$510$	−1.39299e7	+	1.36225e7i	−2.37149	+	2.31916i
$511$	−242992.			−0.0411662
$512$	−4.59363e6	+	3.75273e6i	−0.774428	+	0.632663i
$513$	−2.60273e7			−4.36653
$514$	−1.31435e6	+	1.28534e6i	−0.219433	+	0.214591i
$515$			2.79964e6i			0.465141i
$516$	−41187.7	+	1.84554e6i	−0.00680993	+	0.305140i
$517$			1.05988e6i			0.174394i
$518$	−1.35152e6	−	1.38202e6i	−0.221309	−	0.226303i
$519$	−1.41690e7			−2.30899
$520$	−2.79840e6	−	2.99229e6i	−0.453838	−	0.485283i
$521$	6.72376e6			1.08522			0.542610	−	0.839985i	$-0.317436\pi$
$521$	6.72376e6			1.08522			0.542610	+	0.839985i	$0.317436\pi$
$522$	−1.52264e7	−	1.55700e7i	−2.44580	−	2.50100i
$523$		−	2.41223e6i		−	0.385624i	−0.981236	−	0.192812i	$-0.938239\pi$
$523$		−	2.41223e6i		−	0.385624i	0.981236	−	0.192812i	$-0.0617607\pi$
$524$	8.23419e6	+	183766.i	1.31006	+	0.0292372i
$525$			3.16840e6i			0.501698i
$526$	3.99471e6	−	3.90655e6i	0.629536	−	0.615643i
$527$	1.10921e7			1.73975
$528$	−3.80446e6	−	169896.i	−0.593893	−	0.0265215i
$529$	−5.85100e6			−0.909056
$530$	5.90195e6	−	5.77170e6i	0.912653	−	0.892512i
$531$			372601.i			0.0573466i
$532$	1.84750e6	+	41231.3i	0.283012	+	0.00631608i
$533$			2.22850e6i			0.339777i
$534$	−1.16432e7	−	1.19059e7i	−1.76693	−	1.80680i
$535$	9.36692e6			1.41486
$536$	−415829.	+	388885.i	−0.0625177	+	0.0584668i
$537$	−9.25456e6			−1.38490
$538$	2.03506e6	+	2.08099e6i	0.303125	+	0.309965i
$539$		−	1.91526e6i		−	0.283960i
$540$	−806525.	+	3.61388e7i	−0.119024	+	5.33322i
$541$			5.87270e6i			0.862670i	0.902192	+	0.431335i	$0.141957\pi$
$541$			5.87270e6i			0.862670i	−0.902192	+	0.431335i	$0.858043\pi$
$542$	−8.94058e6	+	8.74327e6i	−1.30728	+	1.27843i
$543$	529072.			0.0770044
$544$	6.03875e6	−	5.39998e6i	0.874882	−	0.782339i
$545$	4.36255e6			0.629143
$546$	−1.09821e6	+	1.07398e6i	−0.157654	+	0.154175i
$547$		−	727632.i		−	0.103978i	−0.998648	−	0.0519892i	$-0.983444\pi$
$547$		−	727632.i		−	0.103978i	0.998648	−	0.0519892i	$-0.0165561\pi$
$548$	29560.0	−	1.32452e6i	0.00420487	−	0.188412i
$549$		−	1.67758e7i		−	2.37549i
$550$	1.57722e6	+	1.61281e6i	0.222324	+	0.227341i
$551$	1.01296e7			1.42139
$552$	3.10897e6	−	2.90752e6i	0.434279	−	0.406139i
$553$	−1.58145e6			−0.219909
$554$	6.57011e6	+	6.71837e6i	0.909490	+	0.930014i
$555$			2.69055e7i			3.70773i
$556$	9.08213e6	+	202690.i	1.24595	+	0.0278064i
$557$		−	2.61530e6i		−	0.357177i	−0.983924	−	0.178588i	$-0.942847\pi$
$557$		−	2.61530e6i		−	0.357177i	0.983924	−	0.178588i	$-0.0571531\pi$
$558$	2.25078e7	−	2.20111e7i	3.06019	−	2.99265i
$559$	530132.			0.0717553
$560$	114499.	−	2.56396e6i	0.0154288	−	0.345495i
$561$	5.20103e6			0.697722
$562$	9.56529e6	−	9.35420e6i	1.27749	−	1.24930i
$563$		−	1.12525e7i		−	1.49615i	−0.663612	−	0.748077i	$-0.730977\pi$
$563$		−	1.12525e7i		−	1.49615i	0.663612	−	0.748077i	$-0.269023\pi$
$564$	−8.61300e6	−	192220.i	−1.14014	−	0.0254449i
$565$			2.95533e6i			0.389480i
$566$	1.24309e6	+	1.27114e6i	0.163102	+	0.166783i
$567$	8.21971e6			1.07374
$568$	4.93244e6	+	5.27419e6i	0.641491	+	0.685938i
$569$	1.49064e6			0.193015			0.0965076	−	0.995332i	$-0.469233\pi$
$569$	1.49064e6			0.193015			0.0965076	+	0.995332i	$0.469233\pi$
$570$	−1.79837e7	−	1.83896e7i	−2.31842	−	2.37074i
$571$			1.11512e7i			1.43130i	0.698460	+	0.715649i	$0.253869\pi$
$571$			1.11512e7i			1.43130i	−0.698460	+	0.715649i	$0.746131\pi$
$572$	−24401.3	+	1.09338e6i	−0.00311834	+	0.139727i
$573$		−	1.84673e7i		−	2.34973i
$574$	−998102.	+	976075.i	−0.126443	+	0.123653i
$575$	−2.52147e6			−0.318042
$576$	1.53798e6	−	2.29408e7i	0.193150	−	2.88107i
$577$	−1.68822e6			−0.211101			−0.105551	−	0.994414i	$-0.533660\pi$
$577$	−1.68822e6			−0.211101			−0.105551	+	0.994414i	$0.533660\pi$
$578$	−2.16761e6	+	2.11978e6i	−0.269875	+	0.263919i
$579$			2.65644e6i			0.329309i
$580$	313893.	−	1.40649e7i	0.0387446	−	1.73607i
$581$			2.64719e6i			0.325346i
$582$	−6.31303e6	−	6.45549e6i	−0.772556	−	0.789990i
$583$	−2.20363e6			−0.268514
$584$	−960541.	−	1.02709e6i	−0.116542	−	0.124617i
$585$	1.58806e7			1.91857
$586$	−53693.7	−	54905.4i	−0.00645921	−	0.00660497i
$587$		−	6.92624e6i		−	0.829664i	−0.909898	−	0.414832i	$-0.863840\pi$
$587$		−	6.92624e6i		−	0.829664i	0.909898	−	0.414832i	$-0.136160\pi$
$588$	1.55641e7	+	347351.i	1.85644	+	0.0414310i
$589$			1.46432e7i			1.73920i
$590$	−172089.	+	168291.i	−0.0203528	+	0.0199036i
$591$	−2.41709e7			−2.84658
$592$	499076.	−	1.11758e7i	0.0585279	−	1.31061i
$593$	5.82868e6			0.680665			0.340332	−	0.940305i	$-0.389460\pi$
$593$	5.82868e6			0.680665			0.340332	+	0.940305i	$0.389460\pi$
$594$	6.89888e6	−	6.74663e6i	0.802255	−	0.784550i
$595$			3.50516e6i			0.405897i
$596$	−6.28819e6	−	140336.i	−0.725120	−	0.0161828i
$597$			2.35529e6i			0.270463i
$598$	−854691.	−	873978.i	−0.0977363	−	0.0999419i
$599$	1.56394e6			0.178096			0.0890480	−	0.996027i	$-0.471618\pi$
$599$	1.56394e6			0.178096			0.0890480	+	0.996027i	$0.471618\pi$
$600$	−1.33924e7	+	1.25246e7i	−1.51873	+	1.42032i
$601$	1.24787e7			1.40923			0.704615	−	0.709590i	$-0.251120\pi$
$601$	1.24787e7			1.40923			0.704615	+	0.709590i	$0.251120\pi$
$602$	232196.	+	237436.i	0.0261134	+	0.0267027i
$603$		−	2.20688e6i		−	0.247164i
$604$	66403.4	−	2.97541e6i	0.00740624	−	0.331860i
$605$		−	1.17317e6i		−	0.130309i
$606$	−2.11439e7	+	2.06773e7i	−2.33886	+	2.28725i
$607$	−4.94516e6			−0.544765			−0.272382	−	0.962189i	$-0.587812\pi$
$607$	−4.94516e6			−0.544765			−0.272382	+	0.962189i	$0.587812\pi$
$608$	7.12881e6	+	7.97208e6i	0.782093	+	0.874606i
$609$	−5.27470e6			−0.576308
$610$	7.74806e6	−	7.57708e6i	0.843080	−	0.824474i
$611$			2.47408e6i			0.268109i
$612$	−700620.	+	3.13934e7i	−0.0756143	+	3.38813i
$613$		−	4.81997e6i		−	0.518076i	−0.965867	−	0.259038i	$-0.916595\pi$
$613$		−	4.81997e6i		−	0.518076i	0.965867	−	0.259038i	$-0.0834055\pi$
$614$	751611.	+	768572.i	0.0804585	+	0.0822742i
$615$	1.94313e7			2.07164
$616$	−500390.	+	467966.i	−0.0531320	+	0.0496893i
$617$	−1.62297e7			−1.71632			−0.858160	−	0.513382i	$-0.828392\pi$
$617$	−1.62297e7			−1.71632			−0.858160	+	0.513382i	$0.828392\pi$
$618$	4.24729e6	+	4.34314e6i	0.447343	+	0.457438i
$619$		−	1.56984e7i		−	1.64675i	−0.567498	−	0.823375i	$-0.692089\pi$
$619$		−	1.56984e7i		−	1.64675i	0.567498	−	0.823375i	$-0.307911\pi$
$620$	2.03321e7	+	453759.i	2.12423	+	0.0474074i
$621$			1.07857e7i			1.12233i
$622$	−5.15342e6	+	5.03969e6i	−0.534096	+	0.522309i
$623$	−2.99588e6			−0.309246
$624$	−8.88075e6	−	396588.i	−0.913037	−	0.0407735i
$625$	−9.20306e6			−0.942393
$626$	3.56880e6	−	3.49005e6i	0.363988	−	0.355955i
$627$			6.86617e6i			0.697502i
$628$	3.88338e6	+	86667.0i	0.392926	+	0.00876909i
$629$			1.52782e7i			1.53974i
$630$	6.95565e6	+	7.11261e6i	0.698210	+	0.713966i
$631$	1.30217e6			0.130195			0.0650976	−	0.997879i	$-0.479264\pi$
$631$	1.30217e6			0.130195			0.0650976	+	0.997879i	$0.479264\pi$
$632$	−6.25141e6	−	6.68455e6i	−0.622566	−	0.665701i
$633$	−2.93823e7			−2.91458
$634$	2.53347e6	+	2.59064e6i	0.250319	+	0.255967i
$635$		−	2.03967e6i		−	0.200737i
$636$	399649.	−	1.79075e7i	0.0391774	−	1.75546i
$637$		−	4.47080e6i		−	0.436553i
$638$	−2.68498e6	+	2.62573e6i	−0.261150	+	0.255387i
$639$	−2.79910e7			−2.71186
$640$	1.12901e7	−	9.65128e6i	1.08955	−	0.931398i
$641$	1.04343e7			1.00304			0.501522	−	0.865145i	$-0.332774\pi$
$641$	1.04343e7			1.00304			0.501522	+	0.865145i	$0.332774\pi$
$642$	1.45311e7	−	1.42104e7i	1.39143	−	1.36072i
$643$			1.66164e7i			1.58493i	0.609916	+	0.792466i	$0.291203\pi$
$643$			1.66164e7i			1.58493i	−0.609916	+	0.792466i	$0.708797\pi$
$644$	17086.2	−	765599.i	0.00162342	−	0.0727422i
$645$		−	4.62246e6i		−	0.437495i
$646$	−1.02120e7	−	1.04425e7i	−0.962790	−	0.984516i
$647$	1.26273e7			1.18591			0.592955	−	0.805236i	$-0.297961\pi$
$647$	1.26273e7			1.18591			0.592955	+	0.805236i	$0.297961\pi$
$648$	3.24922e7	+	3.47435e7i	3.03978	+	3.25039i
$649$	64253.3			0.00598803
$650$	3.68171e6	+	3.76480e6i	0.341796	+	0.349509i
$651$		−	7.62503e6i		−	0.705163i
$652$	6.25384e6	+	139569.i	0.576140	+	0.0128579i
$653$			1.55400e7i			1.42616i	0.701084	+	0.713078i	$0.252700\pi$
$653$			1.55400e7i			1.42616i	−0.701084	+	0.713078i	$0.747300\pi$
$654$	6.76770e6	−	6.61835e6i	0.618724	−	0.605069i
$655$	−2.06239e7			−1.87831
$656$	−8.07119e6	−	360435.i	−0.732281	−	0.0327015i
$657$	5.45096e6			0.492674
$658$	−1.10809e6	+	1.08364e6i	−0.0997728	+	0.0975710i
$659$		−	4.17957e6i		−	0.374903i	−0.982274	−	0.187451i	$-0.939977\pi$
$659$		−	4.17957e6i		−	0.374903i	0.982274	−	0.187451i	$-0.0600227\pi$
$660$	9.53364e6	+	212766.i	0.851920	+	0.0190126i
$661$		−	7.14229e6i		−	0.635819i	−0.948121	−	0.317910i	$-0.897019\pi$
$661$		−	7.14229e6i		−	0.635819i	0.948121	−	0.317910i	$-0.102981\pi$
$662$	4.78531e6	+	4.89329e6i	0.424390	+	0.433967i
$663$	1.21408e7			1.07266
$664$	−1.11893e7	+	1.04643e7i	−0.984879	+	0.921062i
$665$	−4.62735e6			−0.405769
$666$	3.03182e7	+	3.10023e7i	2.64861	+	2.70838i
$667$		−	4.19770e6i		−	0.365339i
$668$	−52529.3	+	2.35374e6i	−0.00455471	+	0.204088i
$669$			3.38132e7i			2.92093i
$670$	1.01927e6	−	996773.i	0.0877204	−	0.0857846i
$671$	−2.89292e6			−0.248044
$672$	−3.71212e6	−	4.15122e6i	−0.317102	−	0.354611i
$673$	−3.17630e6			−0.270323			−0.135162	−	0.990824i	$-0.543155\pi$
$673$	−3.17630e6			−0.270323			−0.135162	+	0.990824i	$0.543155\pi$
$674$	1.13592e7	−	1.11085e7i	0.963158	−	0.941902i
$675$		−	4.64610e7i		−	3.92491i
$676$	208135.	−	9.32615e6i	0.0175178	−	0.784938i
$677$			1.14176e7i			0.957420i	0.877973	+	0.478710i	$0.158896\pi$
$677$			1.14176e7i			0.957420i	−0.877973	+	0.478710i	$0.841104\pi$
$678$	4.48349e6	+	4.58466e6i	0.374577	+	0.383030i
$679$	−1.62439e6			−0.135212
$680$	−1.48158e7	+	1.38558e7i	−1.22872	+	1.14910i
$681$	3.50871e6			0.289921
$682$	−3.79572e6	−	3.88138e6i	−0.312488	−	0.319540i
$683$		−	2.06531e6i		−	0.169408i	−0.996406	−	0.0847041i	$-0.973006\pi$
$683$		−	2.06531e6i		−	0.169408i	0.996406	−	0.0847041i	$-0.0269945\pi$
$684$	−4.14442e7	−	924927.i	−3.38707	−	0.0755905i
$685$			3.31749e6i			0.270136i
$686$	4.12854e6	−	4.03743e6i	0.334955	−	0.327563i
$687$	4.54781e7			3.67630
$688$	−85743.0	+	1.92003e6i	−0.00690602	+	0.154646i
$689$	−5.14393e6			−0.412807
$690$	−7.62061e6	+	7.45243e6i	−0.609350	+	0.595903i
$691$		−	86652.2i		−	0.00690374i	−0.999994	−	0.00345187i	$-0.998901\pi$
$691$		−	86652.2i		−	0.00690374i	0.999994	−	0.00345187i	$-0.00109877\pi$
$692$	−1.47483e7	−	329143.i	−1.17078	−	0.0261288i
$693$		−	2.65565e6i		−	0.210058i
$694$	9.71451e6	+	9.93373e6i	0.765636	+	0.782913i
$695$	−2.27477e7			−1.78639
$696$	−2.08507e7	−	2.22954e7i	−1.63154	−	1.74458i
$697$	1.10340e7			0.860304
$698$	1.76160e7	+	1.80135e7i	1.36858	+	1.39946i
$699$		−	6.93553e6i		−	0.536892i
$700$	−73601.3	+	3.29794e6i	−0.00567728	+	0.254388i
$701$		−	331264.i		−	0.0254612i	−0.999919	−	0.0127306i	$-0.995948\pi$
$701$		−	331264.i		−	0.0254612i	0.999919	−	0.0127306i	$-0.00405239\pi$
$702$	1.61041e7	−	1.57487e7i	1.23337	−	1.20615i
$703$	−2.01696e7			−1.53925
$704$	−3.95605e6	−	265218.i	−0.300836	−	0.0201684i
$705$	2.15727e7			1.63467
$706$	−5.35219e6	+	5.23407e6i	−0.404129	+	0.395210i
$707$			5.32043e6i			0.400312i
$708$	−11653.0	+	522147.i	−0.000873681	+	0.0391480i
$709$		−	5.10919e6i		−	0.381713i	−0.981618	−	0.190856i	$-0.938874\pi$
$709$		−	5.10919e6i		−	0.381713i	0.981618	−	0.190856i	$-0.0611265\pi$
$710$	−1.26426e7	−	1.29279e7i	−0.941219	−	0.962459i
$711$	3.54761e7			2.63185
$712$	−1.18426e7	−	1.26631e7i	−0.875482	−	0.936140i
$713$	6.06813e6			0.447024
$714$	5.31762e6	+	5.43762e6i	0.390366	+	0.399175i
$715$		−	2.73854e6i		−	0.200334i
$716$	−9.63290e6	−	214981.i	−0.702222	−	0.0156718i
$717$		−	4.34417e7i		−	3.15580i
$718$	2.02939e6	−	1.98461e6i	0.146911	−	0.143669i
$719$	1.15427e7			0.832690			0.416345	−	0.909207i	$-0.363311\pi$
$719$	1.15427e7			0.832690			0.416345	+	0.909207i	$0.363311\pi$
$720$	−2.56851e6	+	5.75164e7i	−0.184651	+	4.13486i
$721$	1.09286e6			0.0782936
$722$	3.77143e6	−	3.68820e6i	0.269254	−	0.263312i
$723$			1.98861e7i			1.41483i
$724$	550702.	+	12290.2i	0.0390454	+	0.000871392i
$725$			1.80822e7i			1.27764i
$726$	−1.77980e6	−	1.81996e6i	−0.125323	−	0.128151i
$727$	−3.17073e6			−0.222496			−0.111248	−	0.993793i	$-0.535485\pi$
$727$	−3.17073e6			−0.222496			−0.111248	+	0.993793i	$0.535485\pi$
$728$	−1.16806e6	+	1.09237e6i	−0.0816840	+	0.0763911i
$729$	−7.90997e7			−5.51259
$730$	2.46202e6	+	2.51758e6i	0.170995	+	0.174854i
$731$		−	2.62485e6i		−	0.181682i
$732$	524658.	−	2.35089e7i	0.0361908	−	1.62164i
$733$			2.53373e7i			1.74181i	0.491451	+	0.870905i	$0.336467\pi$
$733$			2.53373e7i			1.74181i	−0.491451	+	0.870905i	$0.663533\pi$
$734$	4.64433e6	−	4.54183e6i	0.318187	−	0.311165i
$735$	−3.89829e7			−2.66168
$736$	3.30361e6	−	2.95417e6i	0.224799	−	0.201021i
$737$	−380566.			−0.0258084
$738$	2.23901e7	−	2.18959e7i	1.51326	−	1.47987i
$739$		−	7.64513e6i		−	0.514960i	−0.966284	−	0.257480i	$-0.917108\pi$
$739$		−	7.64513e6i		−	0.514960i	0.966284	−	0.257480i	$-0.0828922\pi$
$740$	−625009.	+	2.80054e7i	−0.0419572	+	1.88002i
$741$			1.60277e7i			1.07232i
$742$	−2.25302e6	−	2.30387e6i	−0.150230	−	0.153620i
$743$	1.53737e7			1.02166			0.510831	−	0.859681i	$-0.329338\pi$
$743$	1.53737e7			1.02166			0.510831	+	0.859681i	$0.329338\pi$
$744$	3.22299e7	−	3.01415e7i	2.13465	−	1.99633i
$745$	1.57498e7			1.03964
$746$	1.74913e7	+	1.78860e7i	1.15073	+	1.17670i
$747$		−	5.93836e7i		−	3.89372i
$748$	5.41366e6	+	120819.i	0.353783	+	0.00789552i
$749$		−	3.65644e6i		−	0.238152i
$750$	1.70024e6	−	1.66272e6i	0.110372	−	0.107936i
$751$	−2.40235e7			−1.55431			−0.777154	−	0.629310i	$-0.783338\pi$
$751$	−2.40235e7			−1.55431			−0.777154	+	0.629310i	$0.783338\pi$
$752$	−8.96065e6	−	400156.i	−0.577823	−	0.0258039i
$753$	−3.47139e7			−2.23109
$754$	−6.26756e6	+	6.12924e6i	−0.401486	+	0.392626i
$755$			7.45240e6i			0.475805i
$756$	1.41070e7	+	314833.i	0.897701	+	0.0200343i
$757$			4.07382e6i			0.258382i	0.991620	+	0.129191i	$0.0412380\pi$
$757$			4.07382e6i			0.258382i	−0.991620	+	0.129191i	$0.958762\pi$
$758$	−4.39539e6	−	4.49458e6i	−0.277859	−	0.284130i
$759$	2.84533e6			0.179278
$760$	−1.82918e7	−	1.95591e7i	−1.14874	−	1.22833i
$761$	1.00638e7			0.629944			0.314972	−	0.949101i	$-0.398005\pi$
$761$	1.00638e7			0.629944			0.314972	+	0.949101i	$0.398005\pi$
$762$	−3.09435e6	−	3.16418e6i	−0.193056	−	0.197412i
$763$		−	1.70295e6i		−	0.105899i
$764$	428992.	−	1.92223e7i	0.0265898	−	1.19144i
$765$		−	7.86300e7i		−	4.85774i
$766$	−1.95162e7	+	1.90855e7i	−1.20177	+	1.17525i
$767$	149987.			0.00920586
$768$	2.87273e6	−	3.21002e7i	0.175749	−	1.96383i
$769$	2.04279e7			1.24569			0.622843	−	0.782347i	$-0.285977\pi$
$769$	2.04279e7			1.24569			0.622843	+	0.782347i	$0.285977\pi$
$770$	1.22654e6	−	1.19947e6i	0.0745511	−	0.0729059i
$771$		−	9.98846e6i		−	0.605150i
$772$	−61708.5	+	2.76504e6i	−0.00372650	+	0.166977i
$773$			1.78550e7i			1.07476i	0.843340	+	0.537380i	$0.180586\pi$
$773$			1.78550e7i			1.07476i	−0.843340	+	0.537380i	$0.819414\pi$
$774$	−5.20877e6	−	5.32631e6i	−0.312523	−	0.319576i
$775$	−2.61394e7			−1.56330
$776$	−6.42116e6	−	6.86605e6i	−0.382789	−	0.409311i
$777$	1.05027e7			0.624094
$778$	−1.82077e7	−	1.86185e7i	−1.07846	−	1.10280i
$779$			1.45666e7i			0.860033i
$780$	2.22544e7	+	496660.i	1.30972	+	0.0292296i
$781$			4.82693e6i			0.283167i
$782$	−4.32735e6	+	4.23185e6i	−0.253049	+	0.247465i
$783$	7.73474e7			4.50860
$784$	1.61924e7	+	723104.i	0.940850	+	0.0420156i
$785$	−9.72656e6			−0.563359
$786$	−3.19942e7	+	3.12881e7i	−1.84720	+	1.80644i
$787$			3.00472e7i			1.72929i	0.502388	+	0.864643i	$0.332455\pi$
$787$			3.00472e7i			1.72929i	−0.502388	+	0.864643i	$0.667545\pi$
$788$	−2.51591e7	−	561485.i	−1.44337	−	0.0322124i
$789$			3.03580e7i			1.73613i
$790$	1.60234e7	+	1.63849e7i	0.913452	+	0.934065i
$791$	1.15363e6			0.0655582
$792$	1.12251e7	−	1.04977e7i	0.635881	−	0.594678i
$793$	−6.75294e6			−0.381338
$794$	−1.04368e7	−	1.06723e7i	−0.587510	−	0.600768i
$795$			4.48522e7i			2.51690i
$796$	−54712.8	+	2.45157e6i	−0.00306060	+	0.137139i
$797$			1.01681e7i			0.567016i	0.958970	+	0.283508i	$0.0914982\pi$
$797$			1.01681e7i			0.567016i	−0.958970	+	0.283508i	$0.908502\pi$
$798$	−7.17850e6	+	7.02008e6i	−0.399049	+	0.390243i
$799$	1.22500e7			0.678843
$800$	−1.42308e7	+	1.27255e7i	−0.786150	+	0.702993i
$801$	6.72054e7			3.70103
$802$	4.10873e6	−	4.01806e6i	0.225565	−	0.220587i
$803$		−	939994.i		−	0.0514442i
$804$	69019.3	−	3.09262e6i	0.00376557	−	0.168728i
$805$			1.91757e6i			0.104294i
$806$	−8.86035e6	−	9.06030e6i	−0.480412	−	0.491253i
$807$	−1.58146e7			−0.854818
$808$	−2.24887e7	+	2.10315e7i	−1.21181	+	1.13329i
$809$	6.85880e6			0.368449			0.184224	−	0.982884i	$-0.441023\pi$
$809$	6.85880e6			0.368449			0.184224	+	0.982884i	$0.441023\pi$
$810$	−8.32827e7	−	8.51621e7i	−4.46008	−	4.56072i
$811$		−	1.60091e7i		−	0.854703i	−0.904086	−	0.427352i	$-0.859447\pi$
$811$		−	1.60091e7i		−	0.854703i	0.904086	−	0.427352i	$-0.140553\pi$
$812$	−5.49034e6	−	122530.i	−0.292219	−	0.00652158i
$813$		−	6.79445e7i		−	3.60519i
$814$	5.34622e6	−	5.22824e6i	0.282804	−	0.276563i
$815$	−1.56638e7			−0.826042
$816$	−1.96364e6	+	4.39715e7i	−0.103237	+	2.31178i
$817$	3.46521e6			0.181625
$818$	5.24273e6	−	5.12704e6i	0.273952	−	0.267906i
$819$		−	6.19910e6i		−	0.322938i
$820$	2.02257e7	+	451385.i	1.05043	+	0.0234429i
$821$		−	1.76770e7i		−	0.915271i	−0.889140	−	0.457636i	$-0.848696\pi$
$821$		−	1.76770e7i		−	0.915271i	0.889140	−	0.457636i	$-0.151304\pi$
$822$	5.03290e6	+	5.14648e6i	0.259800	+	0.265663i
$823$	−8.13813e6			−0.418818			−0.209409	−	0.977828i	$-0.567154\pi$
$823$	−8.13813e6			−0.418818			−0.209409	+	0.977828i	$0.567154\pi$
$824$	4.32004e6	+	4.61936e6i	0.221651	+	0.237008i
$825$	−1.22567e7			−0.626958
$826$	65693.7	+	67176.1i	0.00335022	+	0.00342582i
$827$		−	5.16893e6i		−	0.262807i	−0.991329	−	0.131404i	$-0.958052\pi$
$827$		−	5.16893e6i		−	0.262807i	0.991329	−	0.131404i	$-0.0419484\pi$
$828$	−383288.	+	1.71744e7i	−0.0194290	+	0.870574i
$829$		−	2.85004e7i		−	1.44034i	−0.693798	−	0.720170i	$-0.744064\pi$
$829$		−	2.85004e7i		−	1.44034i	0.693798	−	0.720170i	$-0.255936\pi$
$830$	2.74268e7	−	2.68216e7i	1.38191	−	1.35142i
$831$	−5.10567e7			−2.56478
$832$	−9.23461e6	−	619100.i	−0.462498	−	0.0310065i
$833$	−2.21364e7			−1.10534
$834$	−3.52889e7	+	3.45101e7i	−1.75680	+	1.71803i
$835$		−	5.89532e6i		−	0.292611i
$836$	−159500.	+	7.14687e6i	−0.00789303	+	0.353672i
$837$			1.11812e8i			5.51666i
$838$	−2.56488e7	−	2.62276e7i	−1.26170	−	1.29017i
$839$	3.22566e7			1.58203			0.791013	−	0.611800i	$-0.209554\pi$
$839$	3.22566e7			1.58203			0.791013	+	0.611800i	$0.209554\pi$
$840$	9.52490e6	+	1.01848e7i	0.465760	+	0.498031i
$841$	−9.59180e6			−0.467638
$842$	−2.82955e6	−	2.89340e6i	−0.137543	−	0.140646i
$843$			7.26920e7i			3.52304i
$844$	−3.05835e7	−	682544.i	−1.47785	−	0.0329818i
$845$			2.33589e7i			1.12541i
$846$	2.48575e7	−	2.43089e7i	1.19407	−	1.16772i
$847$	−457956.			−0.0219339
$848$	831974.	−	1.86303e7i	0.0397302	−	0.889673i
$849$	−9.66008e6			−0.459951
$850$	1.86407e7	−	1.82294e7i	0.884944	−	0.865414i
$851$			8.35826e6i			0.395633i
$852$	−3.92254e7	−	875409.i	−1.85126	−	0.0413154i
$853$		−	2.81907e6i		−	0.132658i	−0.997798	−	0.0663290i	$-0.978871\pi$
$853$		−	2.81907e6i		−	0.132658i	0.997798	−	0.0663290i	$-0.0211287\pi$
$854$	−2.95776e6	−	3.02451e6i	−0.138777	−	0.141909i
$855$	1.03804e8			4.85621
$856$	1.54552e7	−	1.44538e7i	0.720927	−	0.674214i
$857$	−3.21173e7			−1.49378			−0.746891	−	0.664947i	$-0.768454\pi$
$857$	−3.21173e7			−1.49378			−0.746891	+	0.664947i	$0.768454\pi$
$858$	−4.15459e6	−	4.24834e6i	−0.192668	−	0.197016i
$859$		−	5.13775e6i		−	0.237569i	−0.992920	−	0.118785i	$-0.962100\pi$
$859$		−	5.13775e6i		−	0.237569i	0.992920	−	0.118785i	$-0.0378998\pi$
$860$	107379.	−	4.81143e6i	0.00495076	−	0.221834i
$861$		−	7.58514e6i		−	0.348703i
$862$	6.76347e6	−	6.61421e6i	0.310029	−	0.303187i
$863$	7.32418e6			0.334759			0.167379	−	0.985893i	$-0.446469\pi$
$863$	7.32418e6			0.334759			0.167379	+	0.985893i	$0.446469\pi$
$864$	5.44339e7	+	6.08729e7i	2.48076	+	2.77421i
$865$	3.69395e7			1.67861
$866$	1.61725e7	−	1.58156e7i	0.732795	−	0.716624i
$867$		−	1.64729e7i		−	0.744257i
$868$	177128.	−	7.93676e6i	0.00797972	−	0.357556i
$869$		−	6.11769e6i		−	0.274814i
$870$	5.34436e7	+	5.46497e7i	2.39386	+	2.44788i
$871$	−888357.			−0.0396773
$872$	7.19812e6	−	6.73171e6i	0.320574	−	0.299802i
$873$	3.64393e7			1.61821
$874$	−5.58670e6	−	5.71277e6i	−0.247387	−	0.252970i
$875$		−	427831.i		−	0.0188909i
$876$	7.63874e6	+	170477.i	0.336327	+	0.00750594i
$877$			1.44797e7i			0.635713i	0.948139	+	0.317856i	$0.102963\pi$
$877$			1.44797e7i			0.635713i	−0.948139	+	0.317856i	$0.897037\pi$
$878$	−7.80673e6	+	7.63444e6i	−0.341769	+	0.334227i
$879$	417257.			0.0182151
$880$	9.91845e6	+	442929.i	0.431755	+	0.0192809i
$881$	−2.70289e6			−0.117324			−0.0586622	−	0.998278i	$-0.518683\pi$
$881$	−2.70289e6			−0.117324			−0.0586622	+	0.998278i	$0.518683\pi$
$882$	−4.49188e7	+	4.39275e7i	−1.94427	+	1.90136i
$883$		−	3.57718e7i		−	1.54397i	−0.635641	−	0.771985i	$-0.719264\pi$
$883$		−	3.57718e7i		−	1.54397i	0.635641	−	0.771985i	$-0.280736\pi$
$884$	1.26371e7	+	282028.i	0.543898	+	0.0121384i
$885$		−	1.30780e6i		−	0.0561285i
$886$	−8.85814e6	−	9.05804e6i	−0.379104	−	0.387659i
$887$	5.18030e6			0.221078			0.110539	−	0.993872i	$-0.464742\pi$
$887$	5.18030e6			0.221078			0.110539	+	0.993872i	$0.464742\pi$
$888$	4.15170e7	+	4.43935e7i	1.76682	+	1.88924i
$889$	−796201.			−0.0337884
$890$	3.03544e7	+	3.10394e7i	1.28454	+	1.31353i
$891$			3.17972e7i			1.34182i
$892$	−785474.	+	3.51956e7i	−0.0330537	+	1.48107i
$893$			1.61719e7i			0.678629i
$894$	2.44329e7	−	2.38937e7i	1.02243	−	0.999863i
$895$	2.41272e7			1.00681
$896$	−3.76744e6	−	4.40717e6i	−0.156775	−	0.183396i
$897$	6.64185e6			0.275618
$898$	−1.24605e7	+	1.21855e7i	−0.515637	+	0.504257i
$899$		−	4.35164e7i		−	1.79578i
$900$	1.65107e6	−	7.39814e7i	0.0679454	−	3.04450i
$901$			2.54693e7i			1.04521i
$902$	−3.77586e6	−	3.86107e6i	−0.154525	−	0.158012i
$903$	−1.80441e6			−0.0736402
$904$	4.56028e6	+	4.87624e6i	0.185597	+	0.198456i
$905$	−1.37932e6			−0.0559815
$906$	1.13059e7	+	1.15610e7i	0.457599	+	0.467925i
$907$		−	1.75997e7i		−	0.710376i	−0.934795	−	0.355188i	$-0.884417\pi$
$907$		−	1.75997e7i		−	0.710376i	0.934795	−	0.355188i	$-0.115583\pi$
$908$	3.65216e6	+	81506.6i	0.147006	+	0.00328079i
$909$		−	1.19351e8i		−	4.79091i
$910$	2.86311e6	−	2.79993e6i	0.114613	−	0.112084i
$911$	−2.26132e7			−0.902747			−0.451373	−	0.892335i	$-0.649066\pi$
$911$	−2.26132e7			−0.902747			−0.451373	+	0.892335i	$0.649066\pi$
$912$	−5.80492e7	−	2.59231e6i	−2.31105	−	0.103205i
$913$	−1.02404e7			−0.406576
$914$	−2.46700e7	+	2.41255e7i	−0.976794	+	0.955238i
$915$			5.88819e7i			2.32503i
$916$	4.73374e7	+	1.05645e6i	1.86408	+	0.0416015i
$917$			8.05067e6i			0.316161i
$918$	−7.79768e7	−	7.97364e7i	−3.05393	−	3.12284i
$919$	2.19042e7			0.855538			0.427769	−	0.903888i	$-0.359300\pi$
$919$	2.19042e7			0.855538			0.427769	+	0.903888i	$0.359300\pi$
$920$	−8.10527e6	+	7.58008e6i	−0.315717	+	0.295260i
$921$	−5.84081e6			−0.226895
$922$	2.78311e7	+	2.84591e7i	1.07821	+	1.10254i
$923$			1.12675e7i			0.435335i
$924$	83054.7	−	3.72152e6i	0.00320025	−	0.143397i
$925$		−	3.60045e7i		−	1.38357i
$926$	−861831.	+	842811.i	−0.0330289	+	0.0323000i
$927$	−2.45157e7			−0.937013
$928$	−2.11852e7	−	2.36912e7i	−0.807538	−	0.903062i
$929$	−1.10548e7			−0.420255			−0.210128	−	0.977674i	$-0.567388\pi$
$929$	−1.10548e7			−0.420255			−0.210128	+	0.977674i	$0.567388\pi$
$930$	−7.90008e7	+	7.72574e7i	−2.99519	+	2.92909i
$931$		−	2.92235e7i		−	1.10499i
$932$	161111.	−	7.21908e6i	0.00607555	−	0.272234i
$933$		−	3.91637e7i		−	1.47292i
$934$	1.72249e7	+	1.76136e7i	0.646086	+	0.660666i
$935$	−1.35594e7			−0.507237
$936$	2.62027e7	−	2.45048e7i	0.977588	−	0.914244i
$937$	4.09721e7			1.52454			0.762271	−	0.647258i	$-0.224084\pi$
$937$	4.09721e7			1.52454			0.762271	+	0.647258i	$0.224084\pi$
$938$	−389097.	−	397878.i	−0.0144395	−	0.0147653i
$939$			2.71213e7i			1.00380i
$940$	2.24546e7	+	501128.i	0.828868	+	0.0184982i
$941$		−	1.38036e7i		−	0.508183i	−0.967180	−	0.254091i	$-0.918224\pi$
$941$		−	1.38036e7i		−	0.508183i	0.967180	−	0.254091i	$-0.0817764\pi$
$942$	−1.50890e7	+	1.47560e7i	−0.554029	+	0.541803i
$943$	6.03638e6			0.221054
$944$	−24258.7	+	543222.i	−0.000886008	+	0.0198403i
$945$	−3.53334e7			−1.28708
$946$	−918499.	+	898229.i	−0.0333696	+	0.0326332i
$947$		−	4.54695e7i		−	1.64757i	−0.566899	−	0.823787i	$-0.691857\pi$
$947$		−	4.54695e7i		−	1.64757i	0.566899	−	0.823787i	$-0.308143\pi$
$948$	4.97146e7	+	1.10950e6i	1.79665	+	0.0400965i
$949$		−	2.19423e6i		−	0.0790891i
$950$	2.40656e7	+	2.46086e7i	0.865142	+	0.884665i
$951$	−1.96878e7			−0.705903
$952$	5.40870e6	+	5.78345e6i	0.193420	+	0.206821i
$953$	−2.12384e7			−0.757511			−0.378756	−	0.925497i	$-0.623648\pi$
$953$	−2.12384e7			−0.757511			−0.378756	+	0.925497i	$0.623648\pi$
$954$	5.05413e7	+	5.16818e7i	1.79794	+	1.83851i
$955$			4.81454e7i			1.70823i
$956$	1.00914e6	−	4.52177e7i	0.0357115	−	1.60016i
$957$		−	2.04047e7i		−	0.720195i
$958$	−1.57040e7	+	1.53574e7i	−0.552835	+	0.540635i
$959$	1.29500e6			0.0454700
$960$	−5.39821e6	+	8.05207e7i	−0.189048	+	2.81987i
$961$	3.42776e7			1.19730
$962$	1.24797e7	−	1.22043e7i	0.434776	−	0.425182i
$963$			8.20237e7i			2.85019i
$964$	−461949.	+	2.06991e7i	−0.0160104	+	0.717395i
$965$		−	6.92549e6i		−	0.239404i
$966$	2.90911e6	+	2.97476e6i	0.100304	+	0.102567i
$967$	−4.37086e7			−1.50315			−0.751573	−	0.659650i	$-0.770704\pi$
$967$	−4.37086e7			−1.50315			−0.751573	+	0.659650i	$0.770704\pi$
$968$	−1.81028e6	−	1.93571e6i	−0.0620953	−	0.0663976i
$969$	7.93584e7			2.71508
$970$	1.64584e7	+	1.68298e7i	0.561642	+	0.574316i
$971$		−	3.57521e7i		−	1.21690i	−0.793593	−	0.608448i	$-0.791792\pi$
$971$		−	3.57521e7i		−	1.21690i	0.793593	−	0.608448i	$-0.208208\pi$
$972$	−1.48801e8	−	3.32086e6i	−5.05174	−	0.112742i
$973$			8.87971e6i			0.300689i
$974$	2.38713e7	−	2.33445e7i	0.806265	−	0.788472i
$975$	−2.86108e7			−0.963870
$976$	1.09221e6	−	2.44578e7i	0.0367014	−	0.821851i
$977$	1.89186e7			0.634094			0.317047	−	0.948410i	$-0.397309\pi$
$977$	1.89186e7			0.634094			0.317047	+	0.948410i	$0.397309\pi$
$978$	−2.42995e7	+	2.37632e7i	−0.812362	+	0.794435i
$979$		−	1.15893e7i		−	0.386456i
$980$	−4.05766e7	−	905565.i	−1.34962	−	0.0301200i
$981$			3.82017e7i			1.26739i
$982$	1.14039e7	+	1.16613e7i	0.377377	+	0.385893i
$983$	7.71344e6			0.254603			0.127302	−	0.991864i	$-0.459368\pi$
$983$	7.71344e6			0.254603			0.127302	+	0.991864i	$0.459368\pi$
$984$	3.20613e7	−	2.99838e7i	1.05558	−	0.987186i
$985$	6.30150e7			2.06944
$986$	3.03479e7	+	3.10327e7i	0.994114	+	1.01655i
$987$		−	8.42103e6i		−	0.275152i
$988$	−372320.	+	1.66829e7i	−0.0121346	+	0.543726i
$989$		−	1.43598e6i		−	0.0466828i
$990$	−2.75145e7	+	2.69073e7i	−0.892223	+	0.872533i
$991$	−2.25881e7			−0.730627			−0.365313	−	0.930885i	$-0.619038\pi$
$991$	−2.25881e7			−0.730627			−0.365313	+	0.930885i	$0.619038\pi$
$992$	3.42477e7	−	3.06251e7i	1.10497	−	0.988093i
$993$	−3.71869e7			−1.19679
$994$	−5.04650e6	+	4.93513e6i	−0.162003	+	0.158428i
$995$		−	6.14037e6i		−	0.196624i
$996$	1.85720e6	−	8.32176e7i	0.0593213	−	2.65807i
$997$		−	2.28647e7i		−	0.728496i	−0.931302	−	0.364248i	$-0.881326\pi$
$997$		−	2.28647e7i		−	0.728496i	0.931302	−	0.364248i	$-0.118674\pi$
$998$	−2.90661e7	−	2.97220e7i	−0.923763	−	0.944609i
$999$	−1.54011e8			−4.88244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.6.c.a.45.12	yes	50
4.3	odd	2		352.6.c.a.177.50		50
8.3	odd	2		352.6.c.a.177.1		50
8.5	even	2	inner	88.6.c.a.45.11	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.6.c.a.45.11	✓	50	8.5	even	2	inner
88.6.c.a.45.12	yes	50	1.1	even	1	trivial
352.6.c.a.177.1		50	8.3	odd	2
352.6.c.a.177.50		50	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	88.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.04438 + 3.95512i) q^{2} -30.7355i q^{3} +(0.713979 - 31.9920i) q^{4} +80.1293i q^{5} +(121.563 + 124.306i) q^{6} +31.2790 q^{7} +(123.645 + 132.212i) q^{8} -701.671 q^{9} +O(q^{10})\)	\(q+(-4.04438 + 3.95512i) q^{2} -30.7355i q^{3} +(0.713979 - 31.9920i) q^{4} +80.1293i q^{5} +(121.563 + 124.306i) q^{6} +31.2790 q^{7} +(123.645 + 132.212i) q^{8} -701.671 q^{9} +(-316.921 - 324.073i) q^{10} +121.000i q^{11} +(-983.291 - 21.9445i) q^{12} +282.450i q^{13} +(-126.504 + 123.712i) q^{14} +2462.81 q^{15} +(-1022.98 - 45.6833i) q^{16} +1398.50 q^{17} +(2837.82 - 2775.20i) q^{18} +1846.24i q^{19} +(2563.50 + 57.2106i) q^{20} -961.376i q^{21} +(-478.570 - 489.370i) q^{22} +765.079 q^{23} +(4063.59 - 3800.29i) q^{24} -3295.70 q^{25} +(-1117.13 - 1142.34i) q^{26} +14097.5i q^{27} +(22.3326 - 1000.68i) q^{28} -5486.62i q^{29} +(-9960.54 + 9740.73i) q^{30} +7931.38 q^{31} +(4318.00 - 3861.25i) q^{32} +3719.00 q^{33} +(-5656.08 + 5531.26i) q^{34} +2506.36i q^{35} +(-500.978 + 22447.9i) q^{36} +10924.7i q^{37} +(-7302.12 - 7466.90i) q^{38} +8681.26 q^{39} +(-10594.0 + 9907.57i) q^{40} +7889.88 q^{41} +(3802.36 + 3888.17i) q^{42} -1876.90i q^{43} +(3871.04 + 86.3915i) q^{44} -56224.4i q^{45} +(-3094.27 + 3025.98i) q^{46} +8759.36 q^{47} +(-1404.10 + 31441.8i) q^{48} -15828.6 q^{49} +(13329.0 - 13034.9i) q^{50} -42983.7i q^{51} +(9036.17 + 201.664i) q^{52} +18211.8i q^{53} +(-55757.3 - 57015.5i) q^{54} -9695.64 q^{55} +(3867.49 + 4135.45i) q^{56} +56745.2 q^{57} +(21700.2 + 22189.9i) q^{58} -531.019i q^{59} +(1758.40 - 78790.4i) q^{60} +23908.4i q^{61} +(-32077.5 + 31369.6i) q^{62} -21947.6 q^{63} +(-2191.89 + 32694.6i) q^{64} -22632.5 q^{65} +(-15041.0 + 14709.1i) q^{66} +3145.18i q^{67} +(998.503 - 44741.0i) q^{68} -23515.1i q^{69} +(-9912.98 - 10136.7i) q^{70} +39892.0 q^{71} +(-86758.0 - 92769.1i) q^{72} -7768.54 q^{73} +(-43208.6 - 44183.6i) q^{74} +101295. i q^{75} +(59065.0 + 1318.18i) q^{76} +3784.76i q^{77} +(-35110.3 + 34335.4i) q^{78} -50559.4 q^{79} +(3660.57 - 81970.7i) q^{80} +262787. q^{81} +(-31909.6 + 31205.4i) q^{82} +84631.7i q^{83} +(-30756.4 - 686.402i) q^{84} +112061. i q^{85} +(7423.38 + 7590.90i) q^{86} -168634. q^{87} +(-15997.6 + 14961.0i) q^{88} -95779.1 q^{89} +(222374. + 227393. i) q^{90} +8834.77i q^{91} +(546.251 - 24476.4i) q^{92} -243775. i q^{93} +(-35426.1 + 34644.4i) q^{94} -147938. q^{95} +(-118678. - 132716. i) q^{96} -51932.3 q^{97} +(64016.9 - 62604.2i) q^{98} -84902.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 20 q^{4} + 294 q^{6} + 672 q^{8} - 4050 q^{9}+O(q^{10}) \) 50 * q - 20 * q^4 + 294 * q^6 + 672 * q^8 - 4050 * q^9	\( 50 q - 20 q^{4} + 294 q^{6} + 672 q^{8} - 4050 q^{9} - 634 q^{10} - 1876 q^{12} + 3004 q^{14} + 1800 q^{15} + 1600 q^{16} - 404 q^{17} - 8278 q^{18} - 1892 q^{20} - 6348 q^{23} + 8096 q^{24} - 34366 q^{25} - 8524 q^{26} - 13372 q^{28} - 2042 q^{30} + 25852 q^{31} + 780 q^{32} - 13184 q^{34} - 3776 q^{36} - 53352 q^{38} - 44904 q^{39} + 11956 q^{40} - 2476 q^{41} + 58380 q^{42} + 2420 q^{44} - 76170 q^{46} + 109436 q^{47} - 44576 q^{48} + 90786 q^{49} + 85734 q^{50} + 29756 q^{52} - 113778 q^{54} - 24200 q^{55} + 22648 q^{56} - 25776 q^{57} - 67268 q^{58} + 85100 q^{60} + 70514 q^{62} + 161240 q^{63} + 60208 q^{64} + 51536 q^{65} - 49610 q^{66} + 75796 q^{68} + 187924 q^{70} - 213068 q^{71} - 8836 q^{72} - 79956 q^{73} - 34530 q^{74} + 7004 q^{76} + 500776 q^{78} + 177680 q^{79} + 148360 q^{80} + 238370 q^{81} - 83516 q^{82} - 304740 q^{84} - 53436 q^{86} - 433120 q^{87} + 114708 q^{88} + 169260 q^{89} + 4 q^{90} - 182068 q^{92} + 6656 q^{94} + 38424 q^{95} - 259748 q^{96} + 66972 q^{97} + 541672 q^{98}+O(q^{100}) \) 50 * q - 20 * q^4 + 294 * q^6 + 672 * q^8 - 4050 * q^9 - 634 * q^10 - 1876 * q^12 + 3004 * q^14 + 1800 * q^15 + 1600 * q^16 - 404 * q^17 - 8278 * q^18 - 1892 * q^20 - 6348 * q^23 + 8096 * q^24 - 34366 * q^25 - 8524 * q^26 - 13372 * q^28 - 2042 * q^30 + 25852 * q^31 + 780 * q^32 - 13184 * q^34 - 3776 * q^36 - 53352 * q^38 - 44904 * q^39 + 11956 * q^40 - 2476 * q^41 + 58380 * q^42 + 2420 * q^44 - 76170 * q^46 + 109436 * q^47 - 44576 * q^48 + 90786 * q^49 + 85734 * q^50 + 29756 * q^52 - 113778 * q^54 - 24200 * q^55 + 22648 * q^56 - 25776 * q^57 - 67268 * q^58 + 85100 * q^60 + 70514 * q^62 + 161240 * q^63 + 60208 * q^64 + 51536 * q^65 - 49610 * q^66 + 75796 * q^68 + 187924 * q^70 - 213068 * q^71 - 8836 * q^72 - 79956 * q^73 - 34530 * q^74 + 7004 * q^76 + 500776 * q^78 + 177680 * q^79 + 148360 * q^80 + 238370 * q^81 - 83516 * q^82 - 304740 * q^84 - 53436 * q^86 - 433120 * q^87 + 114708 * q^88 + 169260 * q^89 + 4 * q^90 - 182068 * q^92 + 6656 * q^94 + 38424 * q^95 - 259748 * q^96 + 66972 * q^97 + 541672 * q^98

Introduction

L-functions

Modular forms

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