LMFDB - Embedded newform 38.8.c.b.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, 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:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 9740 x^{12} + 37173 x^{11} + 71393485 x^{10} + 196352446 x^{9} + 218671355941 x^{8} + \cdots + 66\!\cdots\!81 $ x^14 - x^13 + 9740x^12 + 37173x^11 + 71393485x^10 + 196352446x^9 + 218671355941x^8 - 33116965187x^7 + 501909199155445x^6 + 488917878843726x^5 + 115037439673768301x^4 + 1132246613431747493x^3 + 24536677825193566084x^2 + 126800218755690130647x + 666410398757822143881
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.5
Root			$-5.55281 - 9.61775i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.8.c.b.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 - 6.92820i) q^{2} +(9.55281 - 16.5459i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(226.101 - 391.619i) q^{5} +(-76.4225 - 132.368i) q^{6} -488.812 q^{7} -512.000 q^{8} +(910.988 + 1577.88i) q^{9} +O(q^{10})$	\(q+(4.00000 - 6.92820i) q^{2} +(9.55281 - 16.5459i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(226.101 - 391.619i) q^{5} +(-76.4225 - 132.368i) q^{6} -488.812 q^{7} -512.000 q^{8} +(910.988 + 1577.88i) q^{9} +(-1808.81 - 3132.95i) q^{10} +1811.05 q^{11} -1222.76 q^{12} +(-7654.71 - 13258.3i) q^{13} +(-1955.25 + 3386.59i) q^{14} +(-4319.80 - 7482.12i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-2174.85 + 3766.96i) q^{17} +14575.8 q^{18} +(-28198.8 + 9934.64i) q^{19} -28941.0 q^{20} +(-4669.52 + 8087.85i) q^{21} +(7244.21 - 12547.3i) q^{22} +(7980.59 + 13822.8i) q^{23} +(-4891.04 + 8471.53i) q^{24} +(-63181.0 - 109433. i) q^{25} -122475. q^{26} +76593.9 q^{27} +(15642.0 + 27092.7i) q^{28} +(-39147.2 - 67805.0i) q^{29} -69116.8 q^{30} +236947. q^{31} +(16384.0 + 28377.9i) q^{32} +(17300.6 - 29965.6i) q^{33} +(17398.8 + 30135.7i) q^{34} +(-110521. + 191428. i) q^{35} +(58303.2 - 100984. i) q^{36} +468275. q^{37} +(-43966.2 + 235106. i) q^{38} -292496. q^{39} +(-115764. + 200509. i) q^{40} +(171438. - 296939. i) q^{41} +(37356.2 + 64702.8i) q^{42} +(222864. - 386011. i) q^{43} +(-57953.6 - 100379. i) q^{44} +823902. q^{45} +127689. q^{46} +(507732. + 879418. i) q^{47} +(39128.3 + 67772.2i) q^{48} -584606. q^{49} -1.01090e6 q^{50} +(41551.9 + 71970.1i) q^{51} +(-489901. + 848534. i) q^{52} +(871309. + 1.50915e6i) q^{53} +(306376. - 530658. i) q^{54} +(409481. - 709242. i) q^{55} +250272. q^{56} +(-105000. + 561480. i) q^{57} -626356. q^{58} +(824646. - 1.42833e6i) q^{59} +(-276467. + 478856. i) q^{60} +(-84660.8 - 146637. i) q^{61} +(947787. - 1.64162e6i) q^{62} +(-445301. - 771285. i) q^{63} +262144. q^{64} -6.92295e6 q^{65} +(-138405. - 239725. i) q^{66} +(-1.52385e6 - 2.63939e6i) q^{67} +278381. q^{68} +304948. q^{69} +(884167. + 1.53142e6i) q^{70} +(953730. - 1.65191e6i) q^{71} +(-466426. - 807873. i) q^{72} +(1.00436e6 - 1.73961e6i) q^{73} +(1.87310e6 - 3.24431e6i) q^{74} -2.41422e6 q^{75} +(1.45300e6 + 1.24503e6i) q^{76} -885263. q^{77} +(-1.16998e6 + 2.02647e6i) q^{78} +(-2.92848e6 + 5.07228e6i) q^{79} +(926111. + 1.60407e6i) q^{80} +(-1.26064e6 + 2.18350e6i) q^{81} +(-1.37150e6 - 2.37551e6i) q^{82} +4.58253e6 q^{83} +597699. q^{84} +(983474. + 1.70343e6i) q^{85} +(-1.78291e6 - 3.08809e6i) q^{86} -1.49586e6 q^{87} -927258. q^{88} +(1.61129e6 + 2.79083e6i) q^{89} +(3.29561e6 - 5.70816e6i) q^{90} +(3.74171e6 + 6.48083e6i) q^{91} +(510758. - 884659. i) q^{92} +(2.26351e6 - 3.92051e6i) q^{93} +8.12372e6 q^{94} +(-2.48520e6 + 1.32894e7i) q^{95} +626053. q^{96} +(-37472.1 + 64903.6i) q^{97} +(-2.33842e6 + 4.05027e6i) q^{98} +(1.64985e6 + 2.85762e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9}+O(q^{10}) $ 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9} + 1008 q^{10} + 646 q^{11} - 7040 q^{12} - 1308 q^{13} + 7712 q^{14} + 8740 q^{15} - 28672 q^{16} + 10528 q^{17} - 73632 q^{18} - 87463 q^{19} + 16128 q^{20} - 30584 q^{21} + 2584 q^{22} - 113822 q^{23} - 28160 q^{24} - 50143 q^{25} - 20928 q^{26} - 319898 q^{27} - 61696 q^{28} + 167706 q^{29} + 139840 q^{30} + 201780 q^{31} + 229376 q^{32} + 377473 q^{33} - 84224 q^{34} - 33168 q^{35} - 294528 q^{36} + 380924 q^{37} - 384064 q^{38} + 1379564 q^{39} + 64512 q^{40} + 66301 q^{41} + 244672 q^{42} + 726564 q^{43} - 20672 q^{44} + 428936 q^{45} - 1821152 q^{46} - 2373788 q^{47} + 225280 q^{48} + 5898846 q^{49} - 802288 q^{50} + 3264054 q^{51} - 83712 q^{52} + 161792 q^{53} - 1279592 q^{54} - 53424 q^{55} - 987136 q^{56} - 4487994 q^{57} + 2683296 q^{58} - 1845767 q^{59} + 559360 q^{60} - 1600418 q^{61} + 807120 q^{62} - 3064040 q^{63} + 3670016 q^{64} + 6534852 q^{65} - 3019784 q^{66} - 8911929 q^{67} - 1347584 q^{68} - 8860208 q^{69} + 265344 q^{70} + 517154 q^{71} + 2356224 q^{72} - 9558049 q^{73} + 1523696 q^{74} - 24621450 q^{75} + 2525120 q^{76} - 9188192 q^{77} + 5518256 q^{78} + 7963520 q^{79} - 516096 q^{80} - 4125855 q^{81} - 530408 q^{82} + 30616886 q^{83} + 3914752 q^{84} + 6973266 q^{85} - 5812512 q^{86} + 25084136 q^{87} - 330752 q^{88} + 11829436 q^{89} + 1715744 q^{90} + 4017336 q^{91} - 7284608 q^{92} + 396810 q^{93} - 37980608 q^{94} + 7058892 q^{95} + 3604480 q^{96} - 8033723 q^{97} + 23595384 q^{98} + 24812606 q^{99}+O(q^{100}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9 + 1008 * q^10 + 646 * q^11 - 7040 * q^12 - 1308 * q^13 + 7712 * q^14 + 8740 * q^15 - 28672 * q^16 + 10528 * q^17 - 73632 * q^18 - 87463 * q^19 + 16128 * q^20 - 30584 * q^21 + 2584 * q^22 - 113822 * q^23 - 28160 * q^24 - 50143 * q^25 - 20928 * q^26 - 319898 * q^27 - 61696 * q^28 + 167706 * q^29 + 139840 * q^30 + 201780 * q^31 + 229376 * q^32 + 377473 * q^33 - 84224 * q^34 - 33168 * q^35 - 294528 * q^36 + 380924 * q^37 - 384064 * q^38 + 1379564 * q^39 + 64512 * q^40 + 66301 * q^41 + 244672 * q^42 + 726564 * q^43 - 20672 * q^44 + 428936 * q^45 - 1821152 * q^46 - 2373788 * q^47 + 225280 * q^48 + 5898846 * q^49 - 802288 * q^50 + 3264054 * q^51 - 83712 * q^52 + 161792 * q^53 - 1279592 * q^54 - 53424 * q^55 - 987136 * q^56 - 4487994 * q^57 + 2683296 * q^58 - 1845767 * q^59 + 559360 * q^60 - 1600418 * q^61 + 807120 * q^62 - 3064040 * q^63 + 3670016 * q^64 + 6534852 * q^65 - 3019784 * q^66 - 8911929 * q^67 - 1347584 * q^68 - 8860208 * q^69 + 265344 * q^70 + 517154 * q^71 + 2356224 * q^72 - 9558049 * q^73 + 1523696 * q^74 - 24621450 * q^75 + 2525120 * q^76 - 9188192 * q^77 + 5518256 * q^78 + 7963520 * q^79 - 516096 * q^80 - 4125855 * q^81 - 530408 * q^82 + 30616886 * q^83 + 3914752 * q^84 + 6973266 * q^85 - 5812512 * q^86 + 25084136 * q^87 - 330752 * q^88 + 11829436 * q^89 + 1715744 * q^90 + 4017336 * q^91 - 7284608 * q^92 + 396810 * q^93 - 37980608 * q^94 + 7058892 * q^95 + 3604480 * q^96 - 8033723 * q^97 + 23595384 * q^98 + 24812606 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$	9.55281	−	16.5459i	0.204271	−	0.353808i	−0.745629	−	0.666361i	$-0.767851\pi$
$3$	9.55281	−	16.5459i	0.204271	−	0.353808i	0.949900	+	0.312553i	$0.101184\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	226.101	−	391.619i	0.808924	−	1.40110i	−0.104685	−	0.994505i	$-0.533384\pi$
$5$	226.101	−	391.619i	0.808924	−	1.40110i	0.913610	−	0.406593i	$-0.133283\pi$
$6$	−76.4225	−	132.368i	−0.144441	−	0.250180i
$7$	−488.812			−0.538640			−0.269320	−	0.963051i	$-0.586799\pi$
$7$	−488.812			−0.538640			−0.269320	+	0.963051i	$0.586799\pi$
$8$	−512.000			−0.353553
$9$	910.988	+	1577.88i	0.416547	+	0.721480i
$10$	−1808.81	−	3132.95i	−0.571996	−	0.990726i
$11$	1811.05			0.410257			0.205129	−	0.978735i	$-0.434239\pi$
$11$	1811.05			0.410257			0.205129	+	0.978735i	$0.434239\pi$
$12$	−1222.76			−0.204271
$13$	−7654.71	−	13258.3i	−0.966333	−	1.67374i	−0.705991	−	0.708221i	$-0.749498\pi$
$13$	−7654.71	−	13258.3i	−0.966333	−	1.67374i	−0.260342	−	0.965516i	$-0.583835\pi$
$14$	−1955.25	+	3386.59i	−0.190438	+	0.329848i
$15$	−4319.80	−	7482.12i	−0.330480	−	0.572407i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−2174.85	+	3766.96i	−0.107364	+	0.185960i	−0.914702	−	0.404130i	$-0.867574\pi$
$17$	−2174.85	+	3766.96i	−0.107364	+	0.185960i	0.807338	+	0.590090i	$0.200908\pi$
$18$	14575.8			0.589086
$19$	−28198.8	+	9934.64i	−0.943178	+	0.332288i
$19$	−28198.8	+	9934.64i	−0.943178	+	0.332288i
$20$	−28941.0			−0.808924
$21$	−4669.52	+	8087.85i	−0.110028	+	0.190575i
$22$	7244.21	−	12547.3i	0.145048	−	0.251230i
$23$	7980.59	+	13822.8i	0.136769	+	0.236891i	0.926272	−	0.376856i	$-0.122995\pi$
$23$	7980.59	+	13822.8i	0.136769	+	0.236891i	−0.789503	+	0.613747i	$0.789662\pi$
$24$	−4891.04	+	8471.53i	−0.0722207	+	0.125090i
$25$	−63181.0	−	109433.i	−0.808717	−	1.40074i
$26$	−122475.			−1.36660
$27$	76593.9			0.748896
$28$	15642.0	+	27092.7i	0.134660	+	0.233238i
$29$	−39147.2	−	67805.0i	−0.298063	−	0.516260i	0.677630	−	0.735403i	$-0.263007\pi$
$29$	−39147.2	−	67805.0i	−0.298063	−	0.516260i	−0.975693	+	0.219143i	$0.929674\pi$
$30$	−69116.8			−0.467369
$31$	236947.			1.42852			0.714258	−	0.699883i	$-0.246765\pi$
$31$	236947.			1.42852			0.714258	+	0.699883i	$0.246765\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$	17300.6	−	29965.6i	0.0838037	−	0.145152i
$34$	17398.8	+	30135.7i	0.0759179	+	0.131494i
$35$	−110521.	+	191428.i	−0.435719	+	0.754687i
$36$	58303.2	−	100984.i	0.208273	−	0.360740i
$37$	468275.			1.51983			0.759916	−	0.650022i	$-0.225240\pi$
$37$	468275.			1.51983			0.759916	+	0.650022i	$0.225240\pi$
$38$	−43966.2	+	235106.i	−0.129980	+	0.695058i
$39$	−292496.			−0.789575
$40$	−115764.	+	200509.i	−0.285998	+	0.495363i
$41$	171438.	−	296939.i	0.388475	−	0.672858i	−0.603770	−	0.797159i	$-0.706335\pi$
$41$	171438.	−	296939.i	0.388475	−	0.672858i	0.992245	+	0.124301i	$0.0396688\pi$
$42$	37356.2	+	64702.8i	0.0778019	+	0.134757i
$43$	222864.	−	386011.i	0.427464	−	0.740390i	−0.569183	−	0.822211i	$-0.692740\pi$
$43$	222864.	−	386011.i	0.427464	−	0.740390i	0.996647	+	0.0818213i	$0.0260737\pi$
$44$	−57953.6	−	100379.i	−0.102564	−	0.177647i
$45$	823902.			1.34782
$46$	127689.			0.193421
$47$	507732.	+	879418.i	0.713333	+	1.23553i	0.963599	+	0.267352i	$0.0861486\pi$
$47$	507732.	+	879418.i	0.713333	+	1.23553i	−0.250266	+	0.968177i	$0.580518\pi$
$48$	39128.3	+	67772.2i	0.0510677	+	0.0884519i
$49$	−584606.			−0.709867
$50$	−1.01090e6			−1.14370
$51$	41551.9	+	71970.1i	0.0438627	+	0.0759725i
$52$	−489901.	+	848534.i	−0.483166	+	0.836869i
$53$	871309.	+	1.50915e6i	0.803908	+	1.39241i	0.917026	+	0.398828i	$0.130583\pi$
$53$	871309.	+	1.50915e6i	0.803908	+	1.39241i	−0.113117	+	0.993582i	$0.536084\pi$
$54$	306376.	−	530658.i	0.264775	−	0.458603i
$55$	409481.	−	709242.i	0.331867	−	0.574811i
$56$	250272.			0.190438
$57$	−105000.	+	561480.i	−0.0750979	+	0.401580i
$58$	−626356.			−0.421525
$59$	824646.	−	1.42833e6i	0.522740	−	0.905412i	−0.476910	−	0.878952i	$-0.658243\pi$
$59$	824646.	−	1.42833e6i	0.522740	−	0.905412i	0.999650	−	0.0264599i	$-0.00842343\pi$
$60$	−276467.	+	478856.i	−0.165240	+	0.286204i
$61$	−84660.8	−	146637.i	−0.0477560	−	0.0827158i	0.841159	−	0.540787i	$-0.181874\pi$
$61$	−84660.8	−	146637.i	−0.0477560	−	0.0827158i	−0.888915	+	0.458072i	$0.848540\pi$
$62$	947787.	−	1.64162e6i	0.505056	−	0.874783i
$63$	−445301.	−	771285.i	−0.224369	−	0.388618i
$64$	262144.			0.125000
$65$	−6.92295e6			−3.12676
$66$	−138405.	−	239725.i	−0.0592581	−	0.102638i
$67$	−1.52385e6	−	2.63939e6i	−0.618987	−	1.07212i	−0.989671	−	0.143358i	$-0.954210\pi$
$67$	−1.52385e6	−	2.63939e6i	−0.618987	−	1.07212i	0.370683	−	0.928759i	$-0.379123\pi$
$68$	278381.			0.107364
$69$	304948.			0.111752
$70$	884167.	+	1.53142e6i	0.308100	+	0.533644i
$71$	953730.	−	1.65191e6i	0.316243	−	0.547749i	−0.663458	−	0.748214i	$-0.730912\pi$
$71$	953730.	−	1.65191e6i	0.316243	−	0.547749i	0.979701	+	0.200464i	$0.0642451\pi$
$72$	−466426.	−	807873.i	−0.147272	−	0.255082i
$73$	1.00436e6	−	1.73961e6i	0.302176	−	0.523385i	−0.674452	−	0.738318i	$-0.735620\pi$
$73$	1.00436e6	−	1.73961e6i	0.302176	−	0.523385i	0.976629	+	0.214934i	$0.0689535\pi$
$74$	1.87310e6	−	3.24431e6i	0.537341	−	0.930703i
$75$	−2.41422e6			−0.660790
$76$	1.45300e6	+	1.24503e6i	0.379679	+	0.325336i
$77$	−885263.			−0.220981
$78$	−1.16998e6	+	2.02647e6i	−0.279157	+	0.483514i
$79$	−2.92848e6	+	5.07228e6i	−0.668263	+	1.15747i	0.310127	+	0.950695i	$0.399629\pi$
$79$	−2.92848e6	+	5.07228e6i	−0.668263	+	1.15747i	−0.978390	+	0.206770i	$0.933705\pi$
$80$	926111.	+	1.60407e6i	0.202231	+	0.350274i
$81$	−1.26064e6	+	2.18350e6i	−0.263569	+	0.456515i
$82$	−1.37150e6	−	2.37551e6i	−0.274693	−	0.475782i
$83$	4.58253e6			0.879695			0.439848	−	0.898072i	$-0.355032\pi$
$83$	4.58253e6			0.879695			0.439848	+	0.898072i	$0.355032\pi$
$84$	597699.			0.110028
$85$	983474.	+	1.70343e6i	0.173699	+	0.300855i
$86$	−1.78291e6	−	3.08809e6i	−0.302263	−	0.523535i
$87$	−1.49586e6			−0.243542
$88$	−927258.			−0.145048
$89$	1.61129e6	+	2.79083e6i	0.242275	+	0.419632i	0.961362	−	0.275288i	$-0.0887731\pi$
$89$	1.61129e6	+	2.79083e6i	0.242275	+	0.419632i	−0.719087	+	0.694920i	$0.755440\pi$
$90$	3.29561e6	−	5.70816e6i	0.476526	−	0.825367i
$91$	3.74171e6	+	6.48083e6i	0.520505	+	0.901542i
$92$	510758.	−	884659.i	0.0683845	−	0.118445i
$93$	2.26351e6	−	3.92051e6i	0.291804	−	0.505420i
$94$	8.12372e6			1.00881
$95$	−2.48520e6	+	1.32894e7i	−0.297392	+	1.59028i
$96$	626053.			0.0722207
$97$	−37472.1	+	64903.6i	−0.00416876	+	0.00722051i	−0.868102	−	0.496385i	$-0.834660\pi$
$97$	−37472.1	+	64903.6i	−0.00416876	+	0.00722051i	0.863933	+	0.503606i	$0.167994\pi$
$98$	−2.33842e6	+	4.05027e6i	−0.250976	+	0.434703i
$99$	1.64985e6	+	2.85762e6i	0.170891	+	0.295993i
$100$	−4.04358e6	+	7.00369e6i	−0.404358	+	0.700369i
$101$	−7.71101e6	−	1.33559e7i	−0.744709	−	1.28987i	−0.950331	−	0.311243i	$-0.899255\pi$
$101$	−7.71101e6	−	1.33559e7i	−0.744709	−	1.28987i	0.205621	−	0.978632i	$-0.434078\pi$
$102$	664831.			0.0620313
$103$	5.29887e6			0.477807			0.238904	−	0.971043i	$-0.423212\pi$
$103$	5.29887e6			0.477807			0.238904	+	0.971043i	$0.423212\pi$
$104$	3.91921e6	+	6.78827e6i	0.341650	+	0.591756i
$105$	2.11157e6	+	3.65735e6i	0.178009	+	0.308321i
$106$	1.39409e7			1.13690
$107$	5.67296e6			0.447679			0.223840	−	0.974626i	$-0.428141\pi$
$107$	5.67296e6			0.447679			0.223840	+	0.974626i	$0.428141\pi$
$108$	−2.45101e6	−	4.24527e6i	−0.187224	−	0.324281i
$109$	846780.	−	1.46667e6i	0.0626294	−	0.108477i	−0.833011	−	0.553257i	$-0.813385\pi$
$109$	846780.	−	1.46667e6i	0.0626294	−	0.108477i	0.895640	+	0.444780i	$0.146718\pi$
$110$	−3.27585e6	−	5.67393e6i	−0.234666	−	0.406453i
$111$	4.47335e6	−	7.74806e6i	0.310457	−	0.537728i
$112$	1.00109e6	−	1.73393e6i	0.0673300	−	0.116619i
$113$	−1.43585e7			−0.936125			−0.468062	−	0.883695i	$-0.655048\pi$
$113$	−1.43585e7			−0.936125			−0.468062	+	0.883695i	$0.655048\pi$
$114$	3.47005e6	+	2.97338e6i	0.219366	+	0.187968i
$115$	7.21769e6			0.442543
$116$	−2.50542e6	+	4.33952e6i	−0.149032	+	0.258130i
$117$	1.39467e7	−	2.41564e7i	0.805046	−	1.39438i
$118$	−6.59717e6	−	1.14266e7i	−0.369633	−	0.640223i
$119$	1.06309e6	−	1.84133e6i	0.0578306	−	0.100165i
$120$	2.21174e6	+	3.83084e6i	0.116842	+	0.202377i
$121$	−1.62073e7			−0.831689
$122$	−1.35457e6			−0.0675371
$123$	−3.27542e6	−	5.67320e6i	−0.158708	−	0.274891i
$124$	−7.58230e6	−	1.31329e7i	−0.357129	−	0.618565i
$125$	−2.18129e7			−0.998915
$126$	−7.12482e6			−0.317305
$127$	2.14498e7	+	3.71521e7i	0.929202	+	1.60942i	0.784661	+	0.619926i	$0.212837\pi$
$127$	2.14498e7	+	3.71521e7i	0.929202	+	1.60942i	0.144541	+	0.989499i	$0.453829\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$	−4.25795e6	−	7.37498e6i	−0.174637	−	0.302480i
$130$	−2.76918e7	+	4.79636e7i	−1.10548	+	1.91474i
$131$	−1.52005e7	+	2.63281e7i	−0.590757	+	1.02322i	0.403373	+	0.915036i	$0.367838\pi$
$131$	−1.52005e7	+	2.63281e7i	−0.590757	+	1.02322i	−0.994131	+	0.108186i	$0.965496\pi$
$132$	−2.21448e6			−0.0838037
$133$	1.37839e7	−	4.85617e6i	0.508033	−	0.178983i
$134$	−2.43817e7			−0.875380
$135$	1.73180e7	−	2.99956e7i	0.605800	−	1.04928i
$136$	1.11353e6	−	1.92868e6i	0.0379589	−	0.0657468i
$137$	−8.38716e6	−	1.45270e7i	−0.278672	−	0.482673i	0.692383	−	0.721530i	$-0.256561\pi$
$137$	−8.38716e6	−	1.45270e7i	−0.278672	−	0.482673i	−0.971055	+	0.238857i	$0.923227\pi$
$138$	1.21979e6	−	2.11274e6i	0.0395102	−	0.0684337i
$139$	1.52944e7	+	2.64906e7i	0.483036	+	0.836643i	0.999810	−	0.0194790i	$-0.00620074\pi$
$139$	1.52944e7	+	2.64906e7i	0.483036	+	0.836643i	−0.516774	+	0.856122i	$0.672867\pi$
$140$	1.41467e7			0.435719
$141$	1.94011e7			0.582853
$142$	−7.62984e6	−	1.32153e7i	−0.223618	−	0.387317i
$143$	−1.38631e7	−	2.40115e7i	−0.396445	−	0.686663i
$144$	−7.46281e6			−0.208273
$145$	−3.54049e7			−0.964442
$146$	−8.03490e6	−	1.39169e7i	−0.213671	−	0.370089i
$147$	−5.58463e6	+	9.67286e6i	−0.145005	+	0.251156i
$148$	−1.49848e7	−	2.59545e7i	−0.379958	−	0.658106i
$149$	2.05724e7	−	3.56325e7i	0.509487	−	0.882457i	−0.490453	−	0.871468i	$-0.663169\pi$
$149$	2.05724e7	−	3.56325e7i	0.509487	−	0.882457i	0.999940	−	0.0109895i	$-0.00349814\pi$
$150$	−9.65690e6	+	1.67262e7i	−0.233624	+	0.404649i
$151$	−3.68984e7			−0.872143			−0.436071	−	0.899912i	$-0.643631\pi$
$151$	−3.68984e7			−0.872143			−0.436071	+	0.899912i	$0.643631\pi$
$152$	1.44378e7	−	5.08653e6i	0.333464	−	0.117481i
$153$	−7.92506e6			−0.178889
$154$	−3.54105e6	+	6.13328e6i	−0.0781286	+	0.135323i
$155$	5.35739e7	−	9.27928e7i	1.15556	−	2.00149i
$156$	9.35986e6	+	1.62118e7i	0.197394	+	0.341896i
$157$	−7.78779e6	+	1.34888e7i	−0.160607	+	0.278180i	−0.935087	−	0.354419i	$-0.884679\pi$
$157$	−7.78779e6	+	1.34888e7i	−0.160607	+	0.278180i	0.774479	+	0.632599i	$0.218012\pi$
$158$	2.34278e7	+	4.05782e7i	0.472533	+	0.818452i
$159$	3.32938e7			0.656860
$160$	1.48178e7			0.285998
$161$	−3.90101e6	−	6.75674e6i	−0.0736692	−	0.127599i
$162$	1.00851e7	+	1.74680e7i	0.186371	+	0.322805i
$163$	6.18256e7			1.11818			0.559090	−	0.829107i	$-0.311151\pi$
$163$	6.18256e7			1.11818			0.559090	+	0.829107i	$0.311151\pi$
$164$	−2.19440e7			−0.388475
$165$	−7.82339e6	−	1.35505e7i	−0.135582	−	0.234834i
$166$	1.83301e7	−	3.17487e7i	0.311019	−	0.538701i
$167$	3.74092e7	+	6.47946e7i	0.621542	+	1.07654i	0.989199	+	0.146580i	$0.0468267\pi$
$167$	3.74092e7	+	6.47946e7i	0.621542	+	1.07654i	−0.367657	+	0.929961i	$0.619840\pi$
$168$	2.39080e6	−	4.14098e6i	0.0389009	−	0.0673784i
$169$	−8.58148e7	+	1.48636e8i	−1.36760	+	2.36875i
$170$	1.57356e7			0.245647
$171$	−4.13644e7	−	3.54440e7i	−0.632617	−	0.542071i
$172$	−2.85266e7			−0.427464
$173$	−1.91782e7	+	3.32177e7i	−0.281610	+	0.487762i	−0.971781	−	0.235883i	$-0.924202\pi$
$173$	−1.91782e7	+	3.32177e7i	−0.281610	+	0.487762i	0.690172	+	0.723646i	$0.257535\pi$
$174$	−5.98346e6	+	1.03637e7i	−0.0861053	+	0.149139i
$175$	3.08836e7	+	5.34920e7i	0.435607	+	0.754494i
$176$	−3.70903e6	+	6.42423e6i	−0.0512822	+	0.0888233i
$177$	−1.57554e7	−	2.72891e7i	−0.213561	−	0.369899i
$178$	2.57806e7			0.342628
$179$	1.08105e8			1.40884			0.704421	−	0.709783i	$-0.251207\pi$
$179$	1.08105e8			1.40884			0.704421	+	0.709783i	$0.251207\pi$
$180$	−2.63649e7	−	4.56653e7i	−0.336955	−	0.583623i
$181$	3.95962e7	+	6.85827e7i	0.496340	+	0.859685i	0.999991	−	0.00422163i	$-0.00134379\pi$
$181$	3.95962e7	+	6.85827e7i	0.496340	+	0.859685i	−0.503652	+	0.863907i	$0.668010\pi$
$182$	5.98674e7			0.736106
$183$	−3.23499e6			−0.0390206
$184$	−4.08606e6	−	7.07727e6i	−0.0483551	−	0.0837536i
$185$	1.05878e8	−	1.83385e8i	1.22943	−	2.12943i
$186$	−1.81081e7	−	3.13641e7i	−0.206337	−	0.357386i
$187$	−3.93877e6	+	6.82216e6i	−0.0440469	+	0.0762915i
$188$	3.24949e7	−	5.62828e7i	0.356666	−	0.617764i
$189$	−3.74400e7			−0.403385
$190$	8.21311e7	+	7.03757e7i	0.868700	+	0.744364i
$191$	−5.08051e7			−0.527582			−0.263791	−	0.964580i	$-0.584973\pi$
$191$	−5.08051e7			−0.527582			−0.263791	+	0.964580i	$0.584973\pi$
$192$	2.50421e6	−	4.33742e6i	0.0255339	−	0.0442260i
$193$	−3.33939e7	+	5.78399e7i	−0.334361	+	0.579131i	−0.983362	−	0.181657i	$-0.941854\pi$
$193$	−3.33939e7	+	5.78399e7i	−0.334361	+	0.579131i	0.649001	+	0.760788i	$0.275187\pi$
$194$	299777.	+	519229.i	0.00294776	+	0.00510567i
$195$	−6.61336e7	+	1.14547e8i	−0.638706	+	1.10627i
$196$	1.87074e7	+	3.24022e7i	0.177467	+	0.307381i
$197$	−5.95897e7			−0.555315			−0.277658	−	0.960680i	$-0.589558\pi$
$197$	−5.95897e7			−0.555315			−0.277658	+	0.960680i	$0.589558\pi$
$198$	2.63975e7			0.241677
$199$	9.85751e6	+	1.70737e7i	0.0886710	+	0.153583i	0.906950	−	0.421239i	$-0.138405\pi$
$199$	9.85751e6	+	1.70737e7i	0.0886710	+	0.153583i	−0.818279	+	0.574822i	$0.805071\pi$
$200$	3.23487e7	+	5.60296e7i	0.285925	+	0.495236i
$201$	−5.82284e7			−0.505765
$202$	−1.23376e8			−1.05318
$203$	1.91356e7	+	3.31439e7i	0.160549	+	0.278078i
$204$	2.65932e6	−	4.60608e6i	0.0219314	−	0.0379862i
$205$	−7.75245e7	−	1.34276e8i	−0.628493	−	1.08858i
$206$	2.11955e7	−	3.67116e7i	0.168930	−	0.292596i
$207$	−1.45404e7	+	2.51848e7i	−0.113941	+	0.197352i
$208$	6.27073e7			0.483166
$209$	−5.10696e7	+	1.79921e7i	−0.386946	+	0.136324i
$210$	3.37851e7			0.251743
$211$	−8.30557e7	+	1.43857e8i	−0.608668	+	1.05424i	0.382792	+	0.923835i	$0.374963\pi$
$211$	−8.30557e7	+	1.43857e8i	−0.608668	+	1.05424i	−0.991460	+	0.130410i	$0.958371\pi$
$212$	5.57638e7	−	9.65857e7i	0.401954	−	0.696205i
$213$	−1.82216e7	−	3.15607e7i	−0.129199	−	0.223779i
$214$	2.26919e7	−	3.93034e7i	0.158278	−	0.274146i
$215$	−1.00780e8	−	1.74555e8i	−0.691572	−	1.19784i
$216$	−3.92161e7			−0.264775
$217$	−1.15822e8			−0.769455
$218$	−6.77424e6	−	1.17333e7i	−0.0442856	−	0.0767050i
$219$	−1.91890e7	−	3.32363e7i	−0.123452	−	0.213825i
$220$	−5.24136e7			−0.331867
$221$	6.65915e7			0.414998
$222$	−3.57868e7	−	6.19845e7i	−0.219527	−	0.380231i
$223$	3.28601e7	−	5.69154e7i	0.198428	−	0.343687i	−0.749591	−	0.661901i	$-0.769750\pi$
$223$	3.28601e7	−	5.69154e7i	0.198428	−	0.343687i	0.948019	+	0.318214i	$0.103083\pi$
$224$	−8.00869e6	−	1.38715e7i	−0.0476095	−	0.0824621i
$225$	1.15114e8	−	1.99384e8i	0.673737	−	1.16695i
$226$	−5.74339e7	+	9.94784e7i	−0.330970	+	0.573257i
$227$	−5.54258e7			−0.314501			−0.157250	−	0.987559i	$-0.550263\pi$
$227$	−5.54258e7			−0.314501			−0.157250	+	0.987559i	$0.550263\pi$
$228$	3.44804e7	−	1.21477e7i	0.192664	−	0.0678768i
$229$	−1.43327e8			−0.788687			−0.394344	−	0.918963i	$-0.629028\pi$
$229$	−1.43327e8			−0.788687			−0.394344	+	0.918963i	$0.629028\pi$
$230$	2.88707e7	−	5.00056e7i	0.156463	−	0.271001i
$231$	−8.45675e6	+	1.46475e7i	−0.0451400	+	0.0781848i
$232$	2.00434e7	+	3.47162e7i	0.105381	+	0.182526i
$233$	5.90564e7	−	1.02289e8i	0.305859	−	0.529764i	−0.671593	−	0.740920i	$-0.734390\pi$
$233$	5.90564e7	−	1.02289e8i	0.305859	−	0.529764i	0.977452	+	0.211157i	$0.0677230\pi$
$234$	−1.11573e8	−	1.93251e8i	−0.569253	−	0.985975i
$235$	4.59196e8			2.30813
$236$	−1.05555e8			−0.522740
$237$	5.59504e7	+	9.69090e7i	0.273013	+	0.472873i
$238$	−8.50476e6	−	1.47307e7i	−0.0408924	−	0.0708277i
$239$	−3.17615e8			−1.50490			−0.752450	−	0.658649i	$-0.771128\pi$
$239$	−3.17615e8			−1.50490			−0.752450	+	0.658649i	$0.771128\pi$
$240$	3.53878e7			0.165240
$241$	−4.83921e7	−	8.38176e7i	−0.222697	−	0.385723i	0.732929	−	0.680305i	$-0.238153\pi$
$241$	−4.83921e7	−	8.38176e7i	−0.222697	−	0.385723i	−0.955626	+	0.294582i	$0.904820\pi$
$242$	−6.48291e7	+	1.12287e8i	−0.294046	+	0.509303i
$243$	1.07841e8	+	1.86786e8i	0.482127	+	0.835068i
$244$	−5.41829e6	+	9.38475e6i	−0.0238780	+	0.0413579i
$245$	−1.32180e8	+	2.28943e8i	−0.574229	+	0.994593i
$246$	−5.24067e7			−0.224447
$247$	3.47571e8	+	2.97823e8i	1.46759	+	1.25753i
$248$	−1.21317e8			−0.505056
$249$	4.37761e7	−	7.58224e7i	0.179696	−	0.311243i
$250$	−8.72516e7	+	1.51124e8i	−0.353170	+	0.611708i
$251$	−1.75369e8	−	3.03747e8i	−0.699993	−	1.21242i	−0.968468	−	0.249137i	$-0.919853\pi$
$251$	−1.75369e8	−	3.03747e8i	−0.699993	−	1.21242i	0.268475	−	0.963287i	$-0.413480\pi$
$252$	−2.84993e7	+	4.93622e7i	−0.112184	+	0.194309i
$253$	1.44533e7	+	2.50338e7i	0.0561105	+	0.0971862i
$254$	3.43197e8			1.31409
$255$	3.75798e7			0.141927
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	1.03386e6	+	1.79070e6i	0.00379924	+	0.00658047i	0.867919	−	0.496706i	$-0.165457\pi$
$257$	1.03386e6	+	1.79070e6i	0.00379924	+	0.00658047i	−0.864120	+	0.503287i	$0.832124\pi$
$258$	−6.81272e7			−0.246974
$259$	−2.28899e8			−0.818642
$260$	2.21534e8	+	3.83709e8i	0.781690	+	1.35393i
$261$	7.13253e7	−	1.23539e8i	0.248314	−	0.430093i
$262$	1.21604e8	+	2.10625e8i	0.417729	+	0.723527i
$263$	−6.15102e7	+	1.06539e8i	−0.208498	+	0.361129i	−0.951242	−	0.308447i	$-0.900191\pi$
$263$	−6.15102e7	+	1.06539e8i	−0.208498	+	0.361129i	0.742744	+	0.669576i	$0.233524\pi$
$264$	−8.85792e6	+	1.53424e7i	−0.0296291	+	0.0513191i
$265$	7.88016e8			2.60120
$266$	2.14912e7	−	1.14923e8i	0.0700124	−	0.374386i
$267$	6.15693e7			0.197959
$268$	−9.75267e7	+	1.68921e8i	−0.309494	+	0.536059i
$269$	−1.05544e8	+	1.82808e8i	−0.330600	+	0.572615i	−0.982630	−	0.185578i	$-0.940584\pi$
$269$	−1.05544e8	+	1.82808e8i	−0.330600	+	0.572615i	0.652030	+	0.758193i	$0.273918\pi$
$270$	−1.38544e8	−	2.39965e8i	−0.428365	−	0.741950i
$271$	1.79726e8	−	3.11294e8i	0.548553	−	0.950121i	−0.449821	−	0.893119i	$-0.648512\pi$
$271$	1.79726e8	−	3.11294e8i	0.548553	−	0.950121i	0.998374	−	0.0570025i	$-0.0181543\pi$
$272$	−8.90820e6	−	1.54295e7i	−0.0268410	−	0.0464900i
$273$	1.42975e8			0.425297
$274$	−1.34195e8			−0.394101
$275$	−1.14424e8	−	1.98188e8i	−0.331782	−	0.574663i
$276$	−9.75835e6	−	1.69019e7i	−0.0279379	−	0.0483899i
$277$	−5.22774e8			−1.47787			−0.738933	−	0.673779i	$-0.764670\pi$
$277$	−5.22774e8			−1.47787			−0.738933	+	0.673779i	$0.764670\pi$
$278$	2.44710e8			0.683116
$279$	2.15856e8	+	3.73873e8i	0.595043	+	1.03065i
$280$	5.65867e7	−	9.80111e7i	0.154050	−	0.266822i
$281$	1.32817e8	+	2.30045e8i	0.357093	+	0.618503i	0.987474	−	0.157783i	$-0.0504347\pi$
$281$	1.32817e8	+	2.30045e8i	0.357093	+	0.618503i	−0.630381	+	0.776286i	$0.717101\pi$
$282$	7.76043e7	−	1.34415e8i	0.206070	−	0.356923i
$283$	2.25867e8	−	3.91212e8i	0.592379	−	1.02603i	−0.401532	−	0.915845i	$-0.631522\pi$
$283$	2.25867e8	−	3.91212e8i	0.592379	−	1.02603i	0.993911	−	0.110185i	$-0.0351444\pi$
$284$	−1.22077e8			−0.316243
$285$	1.96146e8	+	1.68071e8i	0.501905	+	0.430068i
$286$	−2.21809e8			−0.560658
$287$	−8.38007e7	+	1.45147e8i	−0.209248	+	0.362428i
$288$	−2.98512e7	+	5.17039e7i	−0.0736358	+	0.127541i
$289$	1.95709e8	+	3.38979e8i	0.476946	+	0.826095i
$290$	−1.41620e8	+	2.45293e8i	−0.340982	+	0.590597i
$291$	715928.	+	1.24002e6i	0.00170311	+	0.00294988i
$292$	−1.28558e8			−0.302176
$293$	6.49085e8			1.50753			0.753763	−	0.657146i	$-0.228237\pi$
$293$	6.49085e8			1.50753			0.753763	+	0.657146i	$0.228237\pi$
$294$	4.46770e7	+	7.73829e7i	0.102534	+	0.177594i
$295$	−3.72907e8	−	6.45894e8i	−0.845714	−	1.46482i
$296$	−2.39757e8			−0.537341
$297$	1.38716e8			0.307240
$298$	−1.64579e8	−	2.85060e8i	−0.360262	−	0.623992i
$299$	1.22178e8	−	2.11619e8i	0.264329	−	0.457831i
$300$	7.72552e7	+	1.33810e8i	0.165197	+	0.286130i
$301$	−1.08938e8	+	1.88687e8i	−0.230249	+	0.398803i
$302$	−1.47593e8	+	2.55639e8i	−0.308349	+	0.534076i
$303$	−2.94647e8			−0.608490
$304$	2.25107e7	−	1.20374e8i	0.0459548	−	0.245740i
$305$	−7.65676e7			−0.154524
$306$	−3.17003e7	+	5.49064e7i	−0.0632467	+	0.109546i
$307$	−3.17819e7	+	5.50478e7i	−0.0626895	+	0.108581i	−0.895667	−	0.444726i	$-0.853301\pi$
$307$	−3.17819e7	+	5.50478e7i	−0.0626895	+	0.108581i	0.832977	+	0.553307i	$0.186634\pi$
$308$	2.83284e7	+	4.90663e7i	0.0552452	+	0.0956876i
$309$	5.06191e7	−	8.76748e7i	0.0976022	−	0.169052i
$310$	−4.28592e8	−	7.42342e8i	−0.817105	−	1.41527i
$311$	1.51523e8			0.285640			0.142820	−	0.989749i	$-0.454383\pi$
$311$	1.51523e8			0.285640			0.142820	+	0.989749i	$0.454383\pi$
$312$	1.49758e8			0.279157
$313$	−4.59614e8	−	7.96075e8i	−0.847204	−	1.46740i	−0.883693	−	0.468067i	$-0.844951\pi$
$313$	−4.59614e8	−	7.96075e8i	−0.847204	−	1.46740i	0.0364887	−	0.999334i	$-0.488383\pi$
$314$	6.23023e7	+	1.07911e8i	0.113567	+	0.196703i
$315$	−4.02733e8			−0.725989
$316$	3.74845e8			0.668263
$317$	−2.46198e8	−	4.26427e8i	−0.434087	−	0.751861i	0.563134	−	0.826366i	$-0.309596\pi$
$317$	−2.46198e8	−	4.26427e8i	−0.434087	−	0.751861i	−0.997221	+	0.0745051i	$0.976262\pi$
$318$	1.33175e8	−	2.30666e8i	0.232235	−	0.402243i
$319$	−7.08977e7	−	1.22798e8i	−0.122283	−	0.211800i
$320$	5.92711e7	−	1.02661e8i	0.101116	−	0.175137i
$321$	5.41927e7	−	9.38646e7i	0.0914478	−	0.158392i
$322$	−6.24161e7			−0.104184
$323$	2.39050e7	−	1.27830e8i	0.0394712	−	0.211069i
$324$	1.61362e8			0.263569
$325$	−9.67264e8	+	1.67535e9i	−1.56298	+	2.70716i
$326$	2.47302e8	−	4.28340e8i	0.395336	−	0.684742i
$327$	−1.61783e7	−	2.80216e7i	−0.0255867	−	0.0443175i
$328$	−8.77760e7	+	1.52033e8i	−0.137346	+	0.237891i
$329$	−2.48185e8	−	4.29870e8i	−0.384230	−	0.665505i
$330$	−1.25174e8			−0.191741
$331$	−4.71635e8			−0.714839			−0.357420	−	0.933944i	$-0.616343\pi$
$331$	−4.71635e8			−0.714839			−0.357420	+	0.933944i	$0.616343\pi$
$332$	−1.46641e8	−	2.53990e8i	−0.219924	−	0.380919i
$333$	4.26593e8	+	7.38881e8i	0.633081	+	1.09653i
$334$	5.98546e8			0.878993
$335$	−1.37818e9			−2.00286
$336$	−1.91264e7	−	3.31279e7i	−0.0275071	−	0.0476437i
$337$	1.75480e8	−	3.03941e8i	0.249760	−	0.432598i	−0.713699	−	0.700453i	$-0.752981\pi$
$337$	1.75480e8	−	3.03941e8i	0.249760	−	0.432598i	0.963459	+	0.267855i	$0.0863148\pi$
$338$	6.86518e8	+	1.18908e9i	0.967038	+	1.67496i
$339$	−1.37164e8	+	2.37575e8i	−0.191223	+	0.331208i
$340$	6.29424e7	−	1.09019e8i	0.0868494	−	0.150428i
$341$	4.29123e8			0.586059
$342$	−4.11021e8	+	1.44805e8i	−0.555613	+	0.195746i
$343$	6.88320e8			0.921003
$344$	−1.14106e8	+	1.97638e8i	−0.151131	+	0.261767i
$345$	6.89492e7	−	1.19423e8i	0.0903987	−	0.156575i
$346$	1.53426e8	+	2.65742e8i	0.199128	+	0.344900i
$347$	−6.08203e8	+	1.05344e9i	−0.781439	+	1.35349i	0.149664	+	0.988737i	$0.452181\pi$
$347$	−6.08203e8	+	1.05344e9i	−0.781439	+	1.35349i	−0.931103	+	0.364756i	$0.881152\pi$
$348$	4.78677e7	+	8.29092e7i	0.0608856	+	0.105457i
$349$	1.12027e9			1.41069			0.705346	−	0.708864i	$-0.250792\pi$
$349$	1.12027e9			1.41069			0.705346	+	0.708864i	$0.250792\pi$
$350$	4.94138e8			0.616042
$351$	−5.86304e8	−	1.01551e9i	−0.723682	−	1.25345i
$352$	2.96723e7	+	5.13939e7i	0.0362620	+	0.0628076i
$353$	−2.44078e8			−0.295337			−0.147668	−	0.989037i	$-0.547177\pi$
$353$	−2.44078e8			−0.295337			−0.147668	+	0.989037i	$0.547177\pi$
$354$	−2.52086e8			−0.302021
$355$	−4.31279e8	−	7.46997e8i	−0.511634	−	0.886175i
$356$	1.03122e8	−	1.78613e8i	0.121137	−	0.209816i
$357$	−2.03111e7	−	3.51798e7i	−0.0236262	−	0.0409218i
$358$	4.32422e8	−	7.48977e8i	0.498101	−	0.862736i
$359$	−6.13168e8	+	1.06204e9i	−0.699437	+	1.21146i	0.269225	+	0.963077i	$0.413232\pi$
$359$	−6.13168e8	+	1.06204e9i	−0.699437	+	1.21146i	−0.968662	+	0.248383i	$0.920101\pi$
$360$	−4.21838e8			−0.476526
$361$	6.96478e8	−	5.60291e8i	0.779170	−	0.626813i
$362$	6.33540e8			0.701930
$363$	−1.54825e8	+	2.68165e8i	−0.169890	+	0.294258i
$364$	2.39469e8	−	4.14773e8i	0.260253	−	0.450771i
$365$	−4.54175e8	−	7.86655e8i	−0.488876	−	0.846758i
$366$	−1.29400e7	+	2.24127e7i	−0.0137959	+	0.0238952i
$367$	8.10433e8	+	1.40371e9i	0.855827	+	1.48234i	0.875876	+	0.482537i	$0.160285\pi$
$367$	8.10433e8	+	1.40371e9i	0.855827	+	1.48234i	−0.0200484	+	0.999799i	$0.506382\pi$
$368$	−6.53770e7			−0.0683845
$369$	6.24710e8			0.647271
$370$	−8.47021e8	−	1.46708e9i	−0.869337	−	1.50574i
$371$	−4.25906e8	−	7.37691e8i	−0.433017	−	0.750007i
$372$	−2.89729e8			−0.291804
$373$	5.47853e8			0.546617			0.273308	−	0.961926i	$-0.411882\pi$
$373$	5.47853e8			0.546617			0.273308	+	0.961926i	$0.411882\pi$
$374$	3.15102e7	+	5.45772e7i	0.0311459	+	0.0539462i
$375$	−2.08374e8	+	3.60915e8i	−0.204049	+	0.353424i
$376$	−2.59959e8	−	4.50262e8i	−0.252201	−	0.436825i
$377$	−5.99321e8	+	1.03805e9i	−0.576056	+	0.997759i
$378$	−1.49760e8	+	2.59392e8i	−0.142618	+	0.247022i
$379$	1.14655e9			1.08182			0.540911	−	0.841080i	$-0.318080\pi$
$379$	1.14655e9			1.08182			0.540911	+	0.841080i	$0.318080\pi$
$380$	8.16101e8	−	2.87518e8i	0.762960	−	0.268796i
$381$	8.19623e8			0.759236
$382$	−2.03220e8	+	3.51988e8i	−0.186529	+	0.323077i
$383$	8.31973e8	−	1.44102e9i	0.756682	−	1.31061i	−0.187851	−	0.982197i	$-0.560152\pi$
$383$	8.31973e8	−	1.44102e9i	0.756682	−	1.31061i	0.944534	−	0.328415i	$-0.106514\pi$
$384$	−2.00337e7	−	3.46994e7i	−0.0180552	−	0.0312725i
$385$	−2.00159e8	+	3.46686e8i	−0.178757	+	0.309616i
$386$	2.67151e8	+	4.62719e8i	0.236429	+	0.409507i
$387$	8.12104e8			0.712235
$388$	4.79643e6			0.00416876
$389$	−3.05804e8	−	5.29669e8i	−0.263403	−	0.456227i	0.703741	−	0.710456i	$-0.251511\pi$
$389$	−3.05804e8	−	5.29669e8i	−0.263403	−	0.456227i	−0.967144	+	0.254230i	$0.918178\pi$
$390$	5.29069e8	+	9.16375e8i	0.451634	+	0.782252i
$391$	−6.94265e7			−0.0587363
$392$	2.99318e8			0.250976
$393$	2.90416e8	+	5.03014e8i	0.241349	+	0.418029i
$394$	−2.38359e8	+	4.12850e8i	−0.196334	+	0.340060i
$395$	1.32427e9	+	2.29370e9i	1.08115	+	1.87260i
$396$	1.05590e8	−	1.82887e8i	0.0854457	−	0.147996i
$397$	−6.05633e8	+	1.04899e9i	−0.485783	+	0.841401i	−0.999867	−	0.0163392i	$-0.994799\pi$
$397$	−6.05633e8	+	1.04899e9i	−0.485783	+	0.841401i	0.514083	+	0.857740i	$0.328132\pi$
$398$	1.57720e8			0.125400
$399$	5.13253e7	−	2.74458e8i	0.0404507	−	0.216307i
$400$	5.17579e8			0.404358
$401$	−5.98312e8	+	1.03631e9i	−0.463364	+	0.802570i	−0.999126	−	0.0417987i	$-0.986691\pi$
$401$	−5.98312e8	+	1.03631e9i	−0.463364	+	0.802570i	0.535762	+	0.844369i	$0.320025\pi$
$402$	−2.32913e8	+	4.03418e8i	−0.178815	+	0.309716i
$403$	−1.81376e9	−	3.14152e9i	−1.38042	−	2.39096i
$404$	−4.93505e8	+	8.54776e8i	−0.372355	+	0.644937i
$405$	5.70066e8	+	9.87383e8i	0.426415	+	0.738572i
$406$	3.06170e8			0.227050
$407$	8.48071e8			0.623522
$408$	−2.12746e7	−	3.68487e7i	−0.0155078	−	0.0268603i
$409$	−3.46536e8	−	6.00218e8i	−0.250448	−	0.433788i	0.713202	−	0.700959i	$-0.247244\pi$
$409$	−3.46536e8	−	6.00218e8i	−0.250448	−	0.433788i	−0.963649	+	0.267171i	$0.913911\pi$
$410$	−1.24039e9			−0.888823
$411$	−3.20484e8			−0.227698
$412$	−1.69564e8	−	2.93693e8i	−0.119452	−	0.206897i
$413$	−4.03097e8	+	6.98184e8i	−0.281569	+	0.487691i
$414$	1.16324e8	+	2.01478e8i	0.0805687	+	0.139549i
$415$	1.03612e9	−	1.79461e9i	0.711607	−	1.23254i
$416$	2.50829e8	−	4.34449e8i	0.170825	−	0.295878i
$417$	5.84416e8			0.394681
$418$	−7.96250e7	+	4.25789e8i	−0.0533252	+	0.285153i
$419$	−4.33109e8			−0.287639			−0.143820	−	0.989604i	$-0.545939\pi$
$419$	−4.33109e8			−0.287639			−0.143820	+	0.989604i	$0.545939\pi$
$420$	1.35141e8	−	2.34070e8i	0.0890047	−	0.154161i
$421$	4.64713e8	−	8.04907e8i	0.303527	−	0.525725i	−0.673405	−	0.739274i	$-0.735169\pi$
$421$	4.64713e8	−	8.04907e8i	0.303527	−	0.525725i	0.976932	+	0.213549i	$0.0685023\pi$
$422$	6.64445e8	+	1.15085e9i	0.430394	+	0.745463i
$423$	−9.25076e8	+	1.60228e9i	−0.594273	+	1.02931i
$424$	−4.46110e8	−	7.72685e8i	−0.284224	−	0.492291i
$425$	5.49638e8			0.347309
$426$	−2.91546e8			−0.182714
$427$	4.13832e7	+	7.16778e7i	0.0257233	+	0.0445540i
$428$	−1.81535e8	−	3.14428e8i	−0.111920	−	0.193851i
$429$	−5.29725e8			−0.323929
$430$	−1.61247e9			−0.978031
$431$	−1.46600e9	−	2.53918e9i	−0.881989	−	1.52765i	−0.849126	−	0.528190i	$-0.822871\pi$
$431$	−1.46600e9	−	2.53918e9i	−0.881989	−	1.52765i	−0.0328623	−	0.999460i	$-0.510462\pi$
$432$	−1.56864e8	+	2.71697e8i	−0.0936119	+	0.162141i
$433$	4.50492e8	+	7.80275e8i	0.266673	+	0.461891i	0.968001	−	0.250948i	$-0.0807423\pi$
$433$	4.50492e8	+	7.80275e8i	0.266673	+	0.461891i	−0.701328	+	0.712839i	$0.747409\pi$
$434$	−4.63289e8	+	8.02441e8i	−0.272043	+	0.471193i
$435$	−3.38217e8	+	5.85808e8i	−0.197007	+	0.341227i
$436$	−1.08388e8			−0.0626294
$437$	−3.62368e8	−	3.10502e8i	−0.207713	−	0.177984i
$438$	−3.07024e8			−0.174587
$439$	−1.68837e8	+	2.92435e8i	−0.0952450	+	0.164969i	−0.909711	−	0.415242i	$-0.863697\pi$
$439$	−1.68837e8	+	2.92435e8i	−0.0952450	+	0.164969i	0.814466	+	0.580212i	$0.197030\pi$
$440$	−2.09654e8	+	3.63132e8i	−0.117333	+	0.203226i
$441$	−5.32569e8	−	9.22436e8i	−0.295693	−	0.512155i
$442$	2.66366e8	−	4.61359e8i	0.146724	−	0.254133i
$443$	−2.82302e8	−	4.88962e8i	−0.154277	−	0.267216i	0.778518	−	0.627622i	$-0.215972\pi$
$443$	−2.82302e8	−	4.88962e8i	−0.154277	−	0.267216i	−0.932796	+	0.360406i	$0.882638\pi$
$444$	−5.72588e8			−0.310457
$445$	1.45726e9			0.783928
$446$	−2.62881e8	−	4.55323e8i	−0.140310	−	0.243023i
$447$	−3.93048e8	−	6.80780e8i	−0.208147	−	0.360521i
$448$	−1.28139e8			−0.0673300
$449$	−3.50852e8			−0.182920			−0.0914600	−	0.995809i	$-0.529153\pi$
$449$	−3.50852e8			−0.182920			−0.0914600	+	0.995809i	$0.529153\pi$
$450$	−9.20914e8	−	1.59507e9i	−0.476404	−	0.825156i
$451$	3.10482e8	−	5.37771e8i	0.159375	−	0.276045i
$452$	4.59471e8	+	7.95827e8i	0.234031	+	0.405354i
$453$	−3.52483e8	+	6.10518e8i	−0.178153	+	0.308571i
$454$	−2.21703e8	+	3.84001e8i	−0.111193	+	0.192592i
$455$	3.38402e9			1.68420
$456$	5.37601e7	−	2.87478e8i	0.0265511	−	0.141980i
$457$	9.05089e8			0.443593			0.221796	−	0.975093i	$-0.428808\pi$
$457$	9.05089e8			0.443593			0.221796	+	0.975093i	$0.428808\pi$
$458$	−5.73309e8	+	9.93001e8i	−0.278843	+	0.482970i
$459$	−1.66581e8	+	2.88526e8i	−0.0804045	+	0.139265i
$460$	−2.30966e8	−	4.00045e8i	−0.110636	−	0.191627i
$461$	1.94612e9	−	3.37077e9i	0.925157	−	1.60242i	0.133848	−	0.991002i	$-0.457267\pi$
$461$	1.94612e9	−	3.37077e9i	0.925157	−	1.60242i	0.791309	−	0.611417i	$-0.209400\pi$
$462$	6.76540e7	+	1.17180e8i	0.0319188	+	0.0552850i
$463$	−3.64439e9			−1.70644			−0.853220	−	0.521551i	$-0.825354\pi$
$463$	−3.64439e9			−1.70644			−0.853220	+	0.521551i	$0.825354\pi$
$464$	3.20694e8			0.149032
$465$	−1.02356e9	−	1.77286e9i	−0.472095	−	0.817692i
$466$	−4.72452e8	−	8.18310e8i	−0.216275	−	0.374600i
$467$	−2.69332e9			−1.22371			−0.611855	−	0.790970i	$-0.709577\pi$
$467$	−2.69332e9			−1.22371			−0.611855	+	0.790970i	$0.709577\pi$
$468$	−1.78518e9			−0.805046
$469$	7.44878e8	+	1.29017e9i	0.333411	+	0.577485i
$470$	1.83678e9	−	3.18140e9i	0.816047	−	1.41343i
$471$	1.48790e8	+	2.57713e8i	0.0656148	+	0.113648i
$472$	−4.22219e8	+	7.31305e8i	−0.184816	+	0.320111i
$473$	4.03618e8	−	6.99086e8i	0.175370	−	0.303750i
$474$	8.95207e8			0.386099
$475$	2.86881e9	+	2.45820e9i	1.22821	+	1.05242i
$476$	−1.36076e8			−0.0578306
$477$	−1.58750e9	+	2.74964e9i	−0.669731	+	1.16001i
$478$	−1.27046e9	+	2.20050e9i	−0.532063	+	0.921559i
$479$	4.29135e8	+	7.43283e8i	0.178410	+	0.309015i	0.941336	−	0.337470i	$-0.109571\pi$
$479$	4.29135e8	+	7.43283e8i	0.178410	+	0.309015i	−0.762926	+	0.646486i	$0.776238\pi$
$480$	1.41551e8	−	2.45174e8i	0.0584211	−	0.101188i
$481$	−3.58451e9	−	6.20855e9i	−1.46866	−	2.54380i
$482$	−7.74274e8			−0.314942
$483$	−1.49062e8			−0.0601940
$484$	5.18632e8	+	8.98298e8i	0.207922	+	0.360132i
$485$	1.69450e7	+	2.93496e7i	0.00674443	+	0.0116817i
$486$	1.72545e9			0.681830
$487$	3.56700e9			1.39943			0.699715	−	0.714422i	$-0.253310\pi$
$487$	3.56700e9			1.39943			0.699715	+	0.714422i	$0.253310\pi$
$488$	4.33463e7	+	7.50780e7i	0.0168843	+	0.0292444i
$489$	5.90608e8	−	1.02296e9i	0.228412	−	0.395620i
$490$	1.05744e9	+	1.83154e9i	0.406041	+	0.703284i
$491$	1.07379e9	−	1.85986e9i	0.409387	−	0.709079i	−0.585434	−	0.810720i	$-0.699076\pi$
$491$	1.07379e9	−	1.85986e9i	0.409387	−	0.709079i	0.994821	+	0.101641i	$0.0324092\pi$
$492$	−2.09627e8	+	3.63084e8i	−0.0793541	+	0.137445i
$493$	3.40558e8			0.128005
$494$	3.45366e9	−	1.21675e9i	1.28895	−	0.454105i
$495$	1.49213e9			0.552953
$496$	−4.85267e8	+	8.40507e8i	−0.178564	+	0.309283i
$497$	−4.66194e8	+	8.07472e8i	−0.170341	+	0.295040i
$498$	−3.50209e8	−	6.06579e8i	−0.127064	−	0.220082i
$499$	−2.26178e9	+	3.91752e9i	−0.814889	+	1.41143i	0.0945183	+	0.995523i	$0.469869\pi$
$499$	−2.26178e9	+	3.91752e9i	−0.814889	+	1.41143i	−0.909407	+	0.415906i	$0.863464\pi$
$500$	6.98013e8	+	1.20899e9i	0.249729	+	0.432543i
$501$	1.42945e9			0.507852
$502$	−2.80590e9			−0.989940
$503$	1.85763e9	+	3.21750e9i	0.650834	+	1.12728i	0.982921	+	0.184028i	$0.0589139\pi$
$503$	1.85763e9	+	3.21750e9i	0.650834	+	1.12728i	−0.332087	+	0.943249i	$0.607753\pi$
$504$	2.27994e8	+	3.94898e8i	0.0793263	+	0.137397i
$505$	−6.97388e9			−2.40965
$506$	2.31252e8			0.0793522
$507$	1.63954e9	+	2.83977e9i	0.558721	+	0.967734i
$508$	1.37279e9	−	2.37774e9i	0.464601	−	0.804712i
$509$	2.49920e9	+	4.32874e9i	0.840019	+	1.45496i	0.889878	+	0.456199i	$0.150790\pi$
$509$	2.49920e9	+	4.32874e9i	0.840019	+	1.45496i	−0.0498588	+	0.998756i	$0.515877\pi$
$510$	1.50319e8	−	2.60360e8i	0.0501786	−	0.0869119i
$511$	−4.90944e8	+	8.50340e8i	−0.162764	+	0.281916i
$512$	−1.34218e8			−0.0441942
$513$	−2.15986e9	+	7.60933e8i	−0.706342	+	0.248849i
$514$	1.65418e7			0.00537293
$515$	1.19808e9	−	2.07514e9i	0.386510	−	0.669455i
$516$	−2.72509e8	+	4.71999e8i	−0.0873185	+	0.151240i
$517$	9.19529e8	+	1.59267e9i	0.292650	+	0.506885i
$518$	−9.15594e8	+	1.58586e9i	−0.289434	+	0.501314i
$519$	3.66412e8	+	6.34644e8i	0.115049	+	0.199271i
$520$	3.54455e9			1.10548
$521$	−4.60959e8			−0.142801			−0.0714004	−	0.997448i	$-0.522747\pi$
$521$	−4.60959e8			−0.142801			−0.0714004	+	0.997448i	$0.522747\pi$
$522$	−5.70602e8	−	9.88312e8i	−0.175585	−	0.304122i
$523$	2.13138e9	+	3.69167e9i	0.651487	+	1.12841i	0.982762	+	0.184874i	$0.0591878\pi$
$523$	2.13138e9	+	3.69167e9i	0.651487	+	1.12841i	−0.331275	+	0.943534i	$0.607479\pi$
$524$	1.94567e9			0.590757
$525$	1.18010e9			0.355928
$526$	4.92082e8	+	8.52310e8i	0.147430	+	0.255357i
$527$	−5.15325e8	+	8.92569e8i	−0.153371	+	0.265647i
$528$	7.08634e7	+	1.22739e8i	0.0209509	+	0.0362881i
$529$	1.57503e9	−	2.72804e9i	0.462588	−	0.801227i
$530$	3.15206e9	−	5.45953e9i	0.919664	−	1.59291i
$531$	3.00497e9			0.870982
$532$	−7.10242e8	−	6.08585e8i	−0.204510	−	0.175239i
$533$	−5.24922e9			−1.50158
$534$	2.46277e8	−	4.26565e8i	0.0699890	−	0.121225i
$535$	1.28266e9	−	2.22164e9i	0.362138	−	0.627242i
$536$	7.80214e8	+	1.35137e9i	0.218845	+	0.379051i
$537$	1.03271e9	−	1.78871e9i	0.287785	−	0.498459i
$538$	8.44355e8	+	1.46247e9i	0.233769	+	0.404900i
$539$	−1.05875e9			−0.291228
$540$	−2.21670e9			−0.605800
$541$	−1.29602e9	−	2.24477e9i	−0.351901	−	0.609510i	0.634682	−	0.772773i	$-0.281131\pi$
$541$	−1.29602e9	−	2.24477e9i	−0.351901	−	0.609510i	−0.986582	+	0.163264i	$0.947798\pi$
$542$	−1.43781e9	−	2.49036e9i	−0.387885	−	0.671837i
$543$	1.51302e9			0.405551
$544$	−1.42531e8			−0.0379589
$545$	−3.82916e8	−	6.63230e8i	−0.101325	−	0.175500i
$546$	5.71901e8	−	9.90562e8i	0.150365	−	0.260440i
$547$	6.33539e8	+	1.09732e9i	0.165507	+	0.286667i	0.936835	−	0.349771i	$-0.113740\pi$
$547$	6.33539e8	+	1.09732e9i	0.165507	+	0.286667i	−0.771328	+	0.636438i	$0.780407\pi$
$548$	−5.36778e8	+	9.29727e8i	−0.139336	+	0.241337i
$549$	1.54250e8	−	2.67169e8i	0.0397852	−	0.0689100i
$550$	−1.83079e9			−0.469211
$551$	1.77752e9	+	1.52311e9i	0.452673	+	0.387883i
$552$	−1.56134e8			−0.0395102
$553$	1.43148e9	−	2.47939e9i	0.359953	−	0.623457i
$554$	−2.09110e9	+	3.62189e9i	−0.522505	+	0.905004i
$555$	−2.02286e9	−	3.50369e9i	−0.502273	−	0.869963i
$556$	9.78839e8	−	1.69540e9i	0.241518	−	0.418321i
$557$	−2.68155e8	−	4.64459e8i	−0.0657496	−	0.113882i	0.831277	−	0.555859i	$-0.187611\pi$
$557$	−2.68155e8	−	4.64459e8i	−0.0657496	−	0.113882i	−0.897026	+	0.441977i	$0.854277\pi$
$558$	3.45369e9			0.841518
$559$	−6.82382e9			−1.65229
$560$	−4.52694e8	−	7.84089e8i	−0.108930	−	0.188672i
$561$	7.52527e7	+	1.30341e8i	0.0179950	+	0.0311683i
$562$	2.12507e9			0.505005
$563$	−6.63529e9			−1.56704			−0.783520	−	0.621366i	$-0.786578\pi$
$563$	−6.63529e9			−1.56704			−0.783520	+	0.621366i	$0.786578\pi$
$564$	−6.20834e8	−	1.07532e9i	−0.145713	−	0.252383i
$565$	−3.24647e9	+	5.62305e9i	−0.757254	+	1.31160i
$566$	−1.80693e9	−	3.12970e9i	−0.418875	−	0.725513i
$567$	6.16217e8	−	1.06732e9i	0.141969	−	0.245897i
$568$	−4.88310e8	+	8.45777e8i	−0.111809	+	0.193659i
$569$	−3.21694e9			−0.732066			−0.366033	−	0.930602i	$-0.619284\pi$
$569$	−3.21694e9			−0.732066			−0.366033	+	0.930602i	$0.619284\pi$
$570$	1.94902e9	−	6.86651e8i	0.440812	−	0.155301i
$571$	1.39052e9			0.312572			0.156286	−	0.987712i	$-0.450048\pi$
$571$	1.39052e9			0.312572			0.156286	+	0.987712i	$0.450048\pi$
$572$	−8.87236e8	+	1.53674e9i	−0.198223	+	0.343332i
$573$	−4.85331e8	+	8.40618e8i	−0.107770	+	0.186663i
$574$	6.70406e8	+	1.16118e9i	0.147961	+	0.256275i
$575$	1.00844e9	−	1.74668e9i	0.221215	−	0.383155i
$576$	2.38810e8	+	4.13631e8i	0.0520683	+	0.0901850i
$577$	8.33092e9			1.80542			0.902708	−	0.430253i	$-0.141576\pi$
$577$	8.33092e9			1.80542			0.902708	+	0.430253i	$0.141576\pi$
$578$	3.13135e9			0.674503
$579$	6.38010e8	+	1.10507e9i	0.136601	+	0.236599i
$580$	1.13296e9	+	1.96234e9i	0.241110	+	0.417615i
$581$	−2.24000e9			−0.473839
$582$	1.14548e7			0.00240857
$583$	1.57798e9	+	2.73315e9i	0.329809	+	0.571246i
$584$	−5.14234e8	+	8.90679e8i	−0.106836	+	0.185045i
$585$	−6.30672e9	−	1.09236e10i	−1.30244	−	2.25590i
$586$	2.59634e9	−	4.49699e9i	0.532991	−	0.923168i
$587$	−3.41662e9	+	5.91775e9i	−0.697209	+	1.20760i	0.272221	+	0.962235i	$0.412242\pi$
$587$	−3.41662e9	+	5.91775e9i	−0.697209	+	1.20760i	−0.969430	+	0.245367i	$0.921092\pi$
$588$	7.14833e8			0.145005
$589$	−6.68162e9	+	2.35398e9i	−1.34734	+	0.474678i
$590$	−5.96651e9			−1.19602
$591$	−5.69249e8	+	9.85968e8i	−0.113435	+	0.196475i
$592$	−9.59028e8	+	1.66109e9i	−0.189979	+	0.329053i
$593$	−2.05999e9	−	3.56800e9i	−0.405670	−	0.702642i	0.588729	−	0.808331i	$-0.299629\pi$
$593$	−2.05999e9	−	3.56800e9i	−0.405670	−	0.702642i	−0.994399	+	0.105689i	$0.966295\pi$
$594$	5.54862e8	−	9.61050e8i	0.108626	−	0.188145i
$595$	−4.80734e8	−	8.32656e8i	−0.0935611	−	0.162053i
$596$	−2.63327e9			−0.509487
$597$	3.76668e8			0.0724517
$598$	−9.77425e8	−	1.69295e9i	−0.186909	−	0.323735i
$599$	−3.67139e9	−	6.35903e9i	−0.697969	−	1.20892i	−0.969169	−	0.246395i	$-0.920754\pi$
$599$	−3.67139e9	−	6.35903e9i	−0.697969	−	1.20892i	0.271200	−	0.962523i	$-0.412579\pi$
$600$	1.23608e9			0.233624
$601$	1.04548e10			1.96450			0.982252	−	0.187563i	$-0.0600590\pi$
$601$	1.04548e10			1.96450			0.982252	+	0.187563i	$0.0600590\pi$
$602$	8.71507e8	+	1.50949e9i	0.162811	+	0.281997i
$603$	2.77643e9	−	4.80891e9i	0.515674	−	0.893174i
$604$	1.18075e9	+	2.04511e9i	0.218036	+	0.377649i
$605$	−3.66448e9	+	6.34707e9i	−0.672773	+	1.16528i
$606$	−1.17859e9	+	2.04138e9i	−0.215134	+	0.372622i
$607$	1.68889e9			0.306508			0.153254	−	0.988187i	$-0.451025\pi$
$607$	1.68889e9			0.306508			0.153254	+	0.988187i	$0.451025\pi$
$608$	−7.43934e8	−	6.37455e8i	−0.134237	−	0.115024i
$609$	7.31196e8			0.131182
$610$	−3.06270e8	+	5.30476e8i	−0.0546324	+	0.0946262i
$611$	7.77308e9	−	1.34634e10i	1.37863	−	2.38786i
$612$	2.53602e8	+	4.39252e8i	0.0447222	+	0.0774610i
$613$	−2.41088e9	+	4.17576e9i	−0.422730	+	0.732191i	−0.996205	−	0.0870324i	$-0.972262\pi$
$613$	−2.41088e9	+	4.17576e9i	−0.422730	+	0.732191i	0.573475	+	0.819223i	$0.305595\pi$
$614$	2.54255e8	+	4.40382e8i	0.0443282	+	0.0767787i
$615$	−2.96231e9			−0.513531
$616$	4.53255e8			0.0781286
$617$	1.12400e9	+	1.94683e9i	0.192650	+	0.333680i	0.946128	−	0.323794i	$-0.104958\pi$
$617$	1.12400e9	+	1.94683e9i	0.192650	+	0.333680i	−0.753478	+	0.657474i	$0.771625\pi$
$618$	−4.04952e8	−	7.01398e8i	−0.0690151	−	0.119538i
$619$	−1.17787e9			−0.199609			−0.0998043	−	0.995007i	$-0.531822\pi$
$619$	−1.17787e9			−0.199609			−0.0998043	+	0.995007i	$0.531822\pi$
$620$	−6.85747e9			−1.15556
$621$	6.11265e8	+	1.05874e9i	0.102426	+	0.177407i
$622$	6.06094e8	−	1.04979e9i	0.100989	−	0.174918i
$623$	−7.87616e8	−	1.36419e9i	−0.130499	−	0.226031i
$624$	5.99031e8	−	1.03755e9i	0.0986969	−	0.170948i
$625$	4.09320e6	−	7.08964e6i	0.000670631	−	0.00116157i
$626$	−7.35383e9			−1.19813
$627$	−1.90161e8	+	1.01687e9i	−0.0308095	+	0.164751i
$628$	9.96837e8			0.160607
$629$	−1.01843e9	+	1.76397e9i	−0.163175	+	0.282628i
$630$	−1.61093e9	+	2.79021e9i	−0.256676	+	0.444576i
$631$	8.76710e8	+	1.51851e9i	0.138916	+	0.240610i	0.927087	−	0.374847i	$-0.122305\pi$
$631$	8.76710e8	+	1.51851e9i	0.138916	+	0.240610i	−0.788170	+	0.615457i	$0.788971\pi$
$632$	1.49938e9	−	2.59701e9i	0.236267	−	0.409226i
$633$	1.58683e9	+	2.74847e9i	0.248667	+	0.430703i
$634$	−3.93917e9			−0.613892
$635$	1.93993e10			3.00662
$636$	−1.06540e9	−	1.84533e9i	−0.164215	−	0.284429i
$637$	4.47499e9	+	7.75091e9i	0.685968	+	1.18813i
$638$	−1.13436e9			−0.172934
$639$	3.47535e9			0.526920
$640$	−4.74169e8	−	8.21284e8i	−0.0714995	−	0.123841i
$641$	−2.65279e9	+	4.59476e9i	−0.397831	+	0.689064i	−0.993458	−	0.114197i	$-0.963570\pi$
$641$	−2.65279e9	+	4.59476e9i	−0.397831	+	0.689064i	0.595627	+	0.803261i	$0.296904\pi$
$642$	−4.33542e8	−	7.50917e8i	−0.0646634	−	0.112000i
$643$	−3.92792e9	+	6.80335e9i	−0.582672	+	1.00922i	0.412489	+	0.910962i	$0.364659\pi$
$643$	−3.92792e9	+	6.80335e9i	−0.582672	+	1.00922i	−0.995161	+	0.0982549i	$0.968674\pi$
$644$	−2.49664e8	+	4.32432e8i	−0.0368346	+	0.0637994i
$645$	−3.85091e9			−0.565073
$646$	−7.90014e8	−	6.76940e8i	−0.115298	−	0.0987953i
$647$	1.49826e9			0.217481			0.108741	−	0.994070i	$-0.465318\pi$
$647$	1.49826e9			0.217481			0.108741	+	0.994070i	$0.465318\pi$
$648$	6.45449e8	−	1.11795e9i	0.0931857	−	0.161402i
$649$	1.49348e9	−	2.58678e9i	0.214458	−	0.371452i
$650$	7.73811e9	+	1.34028e10i	1.10519	+	1.91425i
$651$	−1.10643e9	+	1.91639e9i	−0.157177	+	0.272239i
$652$	−1.97842e9	−	3.42672e9i	−0.279545	−	0.484186i
$653$	5.91866e9			0.831816			0.415908	−	0.909407i	$-0.363464\pi$
$653$	5.91866e9			0.831816			0.415908	+	0.909407i	$0.363464\pi$
$654$	−2.58852e8			−0.0361851
$655$	6.87372e9	+	1.19056e10i	0.955756	+	1.65542i
$656$	7.02208e8	+	1.21626e9i	0.0971186	+	0.168214i
$657$	3.65985e9			0.503482
$658$	−3.97097e9			−0.543383
$659$	−2.04413e9	−	3.54053e9i	−0.278233	−	0.481914i	0.692712	−	0.721214i	$-0.256416\pi$
$659$	−2.04413e9	−	3.54053e9i	−0.278233	−	0.481914i	−0.970946	+	0.239300i	$0.923082\pi$
$660$	−5.00697e8	+	8.67232e8i	−0.0677908	+	0.117417i
$661$	−7.21499e9	−	1.24967e10i	−0.971696	−	1.68303i	−0.690433	−	0.723396i	$-0.742580\pi$
$661$	−7.21499e9	−	1.24967e10i	−0.971696	−	1.68303i	−0.281263	−	0.959631i	$-0.590753\pi$
$662$	−1.88654e9	+	3.26759e9i	−0.252734	+	0.437748i
$663$	6.36136e8	−	1.10182e9i	0.0847720	−	0.146829i
$664$	−2.34626e9			−0.311019
$665$	1.21480e9	−	6.49603e9i	0.160187	−	0.856588i
$666$	6.82549e9			0.895311
$667$	6.24836e8	−	1.08225e9i	0.0815316	−	0.141217i
$668$	2.39419e9	−	4.14685e9i	0.310771	−	0.538271i
$669$	−6.27813e8	−	1.08740e9i	−0.0810660	−	0.140411i
$670$	−5.51273e9	+	9.54832e9i	−0.708116	+	1.22649i
$671$	−1.53325e8	−	2.65567e8i	−0.0195922	−	0.0339348i
$672$	−3.06022e8			−0.0389009
$673$	8.30247e9			1.04992			0.524958	−	0.851128i	$-0.324081\pi$
$673$	8.30247e9			1.04992			0.524958	+	0.851128i	$0.324081\pi$
$674$	−1.40384e9	−	2.43153e9i	−0.176607	−	0.305893i
$675$	−4.83928e9	−	8.38188e9i	−0.605645	−	1.04901i
$676$	1.09843e10			1.36760
$677$	2.71206e9			0.335922			0.167961	−	0.985794i	$-0.446282\pi$
$677$	2.71206e9			0.335922			0.167961	+	0.985794i	$0.446282\pi$
$678$	1.09731e9	+	1.90060e9i	0.135215	+	0.234200i
$679$	1.83168e7	−	3.17257e7i	0.00224546	−	0.00388925i
$680$	−5.03539e8	−	8.72155e8i	−0.0614118	−	0.106368i
$681$	−5.29472e8	+	9.17073e8i	−0.0642434	+	0.111273i
$682$	1.71649e9	−	2.97305e9i	0.207203	−	0.358886i
$683$	−4.42929e9			−0.531938			−0.265969	−	0.963982i	$-0.585692\pi$
$683$	−4.42929e9			−0.531938			−0.265969	+	0.963982i	$0.585692\pi$
$684$	−6.40843e8	+	3.42686e9i	−0.0765694	+	0.409449i
$685$	−7.58538e9			−0.901697
$686$	2.75328e9	−	4.76882e9i	0.325624	−	0.563997i
$687$	−1.36918e9	+	2.37149e9i	−0.161106	+	0.279044i
$688$	9.12850e8	+	1.58110e9i	0.106866	+	0.185097i
$689$	1.33392e10	−	2.31042e10i	1.55369	−	2.69106i
$690$	−5.51593e8	−	9.55388e8i	−0.0639215	−	0.110715i
$691$	8.50985e8			0.0981180			0.0490590	−	0.998796i	$-0.484378\pi$
$691$	8.50985e8			0.0981180			0.0490590	+	0.998796i	$0.484378\pi$
$692$	2.45482e9			0.281610
$693$	−8.06464e8	−	1.39684e9i	−0.0920489	−	0.159433i
$694$	4.86562e9	+	8.42751e9i	0.552561	+	0.957064i
$695$	1.38323e10			1.56296
$696$	7.65882e8			0.0861053
$697$	7.45704e8	+	1.29160e9i	0.0834164	+	0.144481i
$698$	4.48106e9	−	7.76143e9i	0.498755	−	0.863868i
$699$	−1.12831e9	−	1.95429e9i	−0.124956	−	0.216431i
$700$	1.97655e9	−	3.42349e9i	0.217804	−	0.377247i
$701$	−6.10982e9	+	1.05825e10i	−0.669908	+	1.16031i	0.308022	+	0.951379i	$0.400333\pi$
$701$	−6.10982e9	+	1.05825e10i	−0.669908	+	1.16031i	−0.977929	+	0.208935i	$0.933000\pi$
$702$	−9.38087e9			−1.02344
$703$	−1.32048e10	+	4.65215e9i	−1.43347	+	0.505021i
$704$	4.74756e8			0.0512822
$705$	4.38661e9	−	7.59783e9i	0.471484	−	0.816634i
$706$	−9.76312e8	+	1.69102e9i	−0.104417	+	0.180856i
$707$	3.76923e9	+	6.52851e9i	0.401130	+	0.694778i
$708$	−1.00834e9	+	1.74650e9i	−0.106781	+	0.184949i
$709$	6.76937e9	+	1.17249e10i	0.713324	+	1.23551i	0.963603	+	0.267339i	$0.0861443\pi$
$709$	6.76937e9	+	1.17249e10i	0.713324	+	1.23551i	−0.250279	+	0.968174i	$0.580522\pi$
$710$	−6.90046e9			−0.723559
$711$	−1.06712e10			−1.11345
$712$	−8.24979e8	−	1.42891e9i	−0.0856571	−	0.148362i
$713$	1.89098e9	+	3.27527e9i	0.195377	+	0.338402i
$714$	−3.24977e8			−0.0334125
$715$	−1.25378e10			−1.28278
$716$	−3.45938e9	−	5.99181e9i	−0.352210	−	0.610046i
$717$	−3.03411e9	+	5.25523e9i	−0.307407	+	0.532445i
$718$	4.90534e9	+	8.49630e9i	0.494577	+	0.856632i
$719$	−7.78035e9	+	1.34760e10i	−0.780635	+	1.35210i	0.150937	+	0.988543i	$0.451771\pi$
$719$	−7.78035e9	+	1.34760e10i	−0.780635	+	1.35210i	−0.931572	+	0.363557i	$0.881562\pi$
$720$	−1.68735e9	+	2.92258e9i	−0.168477	+	0.291811i
$721$	−2.59015e9			−0.257366
$722$	−1.09590e9	−	7.06650e9i	−0.108365	−	0.698754i
$723$	−1.84912e9			−0.181962
$724$	2.53416e9	−	4.38929e9i	0.248170	−	0.429843i
$725$	−4.94672e9	+	8.56798e9i	−0.482097	+	0.835017i
$726$	1.23860e9	+	2.14532e9i	0.120130	+	0.208072i
$727$	−1.26916e9	+	2.19826e9i	−0.122503	+	0.212182i	−0.920754	−	0.390143i	$-0.872426\pi$
$727$	−1.26916e9	+	2.19826e9i	−0.122503	+	0.212182i	0.798251	+	0.602325i	$0.205759\pi$
$728$	−1.91576e9	−	3.31819e9i	−0.184026	−	0.318743i
$729$	−1.39332e9			−0.133200
$730$	−7.26680e9			−0.691375
$731$	9.69392e8	+	1.67904e9i	0.0917886	+	0.158983i
$732$	1.03520e8	+	1.79301e8i	0.00975516	+	0.0168964i
$733$	4.84535e9			0.454424			0.227212	−	0.973845i	$-0.427039\pi$
$733$	4.84535e9			0.454424			0.227212	+	0.973845i	$0.427039\pi$
$734$	1.29669e10			1.21032
$735$	2.52538e9	+	4.37409e9i	0.234597	+	0.406333i
$736$	−2.61508e8	+	4.52945e8i	−0.0241776	+	0.0418768i
$737$	−2.75978e9	−	4.78008e9i	−0.253944	−	0.439844i
$738$	2.49884e9	−	4.32812e9i	0.228845	−	0.396371i
$739$	4.54541e9	−	7.87288e9i	0.414303	−	0.717593i	−0.581052	−	0.813866i	$-0.697359\pi$
$739$	4.54541e9	−	7.87288e9i	0.414303	−	0.717593i	0.995355	+	0.0962731i	$0.0306922\pi$
$740$	−1.35523e10			−1.22943
$741$	8.24804e9	−	2.90584e9i	0.744710	−	0.262366i
$742$	−6.81449e9			−0.612379
$743$	1.04801e10	−	1.81521e10i	0.937358	−	1.62355i	0.166984	−	0.985960i	$-0.446597\pi$
$743$	1.04801e10	−	1.81521e10i	0.937358	−	1.62355i	0.770374	−	0.637592i	$-0.220070\pi$
$744$	−1.15892e9	+	2.00730e9i	−0.103168	+	0.178693i
$745$	−9.30289e9	−	1.61131e10i	−0.824273	−	1.42768i
$746$	2.19141e9	−	3.79564e9i	0.193258	−	0.334733i
$747$	4.17463e9	+	7.23067e9i	0.366434	+	0.634683i
$748$	5.04163e8			0.0440469
$749$	−2.77301e9			−0.241138
$750$	1.66700e9	+	2.88732e9i	0.144285	+	0.249908i
$751$	−4.27713e9	−	7.40820e9i	−0.368479	−	0.638224i	0.620849	−	0.783930i	$-0.286788\pi$
$751$	−4.27713e9	−	7.40820e9i	−0.368479	−	0.638224i	−0.989328	+	0.145706i	$0.953455\pi$
$752$	−4.15934e9			−0.356666
$753$	−6.70105e9			−0.571953
$754$	4.79457e9	+	8.30444e9i	0.407333	+	0.705522i
$755$	−8.34276e9	+	1.44501e10i	−0.705498	+	1.22196i
$756$	1.19808e9	+	2.07514e9i	0.100846	+	0.174671i
$757$	3.63045e9	−	6.28813e9i	0.304176	−	0.526849i	−0.672901	−	0.739732i	$-0.734952\pi$
$757$	3.63045e9	−	6.28813e9i	0.304176	−	0.526849i	0.977078	+	0.212884i	$0.0682855\pi$
$758$	4.58620e9	−	7.94353e9i	0.382482	−	0.662478i
$759$	5.52277e8			0.0458470
$760$	1.27242e9	−	6.80419e9i	0.105144	−	0.562249i
$761$	−6.39599e9			−0.526092			−0.263046	−	0.964783i	$-0.584727\pi$
$761$	−6.39599e9			−0.526092			−0.263046	+	0.964783i	$0.584727\pi$
$762$	3.27849e9	−	5.67851e9i	0.268430	−	0.464935i
$763$	−4.13916e8	+	7.16924e8i	−0.0337347	+	0.0584302i
$764$	1.62576e9	+	2.81590e9i	0.131896	+	0.228450i
$765$	−1.79187e9	+	3.10360e9i	−0.144707	+	0.250640i
$766$	−6.65579e9	−	1.15282e10i	−0.535055	−	0.926743i
$767$	−2.52497e10			−2.02056
$768$	−3.20539e8			−0.0255339
$769$	2.33962e9	+	4.05233e9i	0.185525	+	0.321339i	0.943753	−	0.330650i	$-0.107268\pi$
$769$	2.33962e9	+	4.05233e9i	0.185525	+	0.321339i	−0.758228	+	0.651989i	$0.773935\pi$
$770$	1.60127e9	+	2.77349e9i	0.126400	+	0.218932i
$771$	3.95051e7			0.00310429
$772$	4.27442e9			0.334361
$773$	9.45486e9	+	1.63763e10i	0.736253	+	1.27523i	0.954171	+	0.299261i	$0.0967400\pi$
$773$	9.45486e9	+	1.63763e10i	0.736253	+	1.27523i	−0.217919	+	0.975967i	$0.569927\pi$
$774$	3.24842e9	−	5.62642e9i	0.251813	−	0.436153i
$775$	−1.49705e10	−	2.59297e10i	−1.15526	−	2.00098i
$776$	1.91857e7	−	3.32307e7i	0.00147388	−	0.00255284i
$777$	−2.18662e9	+	3.78734e9i	−0.167225	+	0.289642i
$778$	−4.89287e9			−0.372508
$779$	−1.88436e9	+	1.00765e10i	−0.142818	+	0.763710i
$780$	8.46511e9			0.638706
$781$	1.72725e9	−	2.99169e9i	0.129741	−	0.224718i
$782$	−2.77706e8	+	4.81001e8i	−0.0207664	+	0.0359685i
$783$	−2.99844e9	−	5.19345e9i	−0.223218	−	0.386625i
$784$	1.19727e9	−	2.07374e9i	0.0887334	−	0.153691i
$785$	3.52166e9	+	6.09969e9i	0.259838	+	0.450053i
$786$	4.64665e9			0.341319
$787$	−1.68660e10			−1.23339			−0.616696	−	0.787201i	$-0.711529\pi$
$787$	−1.68660e10			−1.23339			−0.616696	+	0.787201i	$0.711529\pi$
$788$	1.90687e9	+	3.30280e9i	0.138829	+	0.240458i
$789$	1.17519e9	+	2.03549e9i	0.0851802	+	0.147536i
$790$	2.11883e10			1.52897
$791$	7.01859e9			0.504234
$792$	−8.44721e8	−	1.46310e9i	−0.0604192	−	0.104649i
$793$	−1.29611e9	+	2.24492e9i	−0.0922963	+	0.159862i
$794$	4.84506e9	+	8.39189e9i	0.343501	+	0.594960i
$795$	7.52776e9	−	1.30385e10i	0.531350	−	0.920326i
$796$	6.30881e8	−	1.09272e9i	0.0443355	−	0.0767913i
$797$	2.61596e10			1.83032			0.915160	−	0.403091i	$-0.132064\pi$
$797$	2.61596e10			1.83032			0.915160	+	0.403091i	$0.132064\pi$
$798$	−1.69620e9	−	1.45342e9i	−0.118159	−	0.101247i
$799$	−4.41698e9			−0.306345
$800$	2.07032e9	−	3.58589e9i	0.142962	−	0.247618i
$801$	−2.93573e9	+	5.08483e9i	−0.201837	+	0.349593i
$802$	4.78650e9	+	8.29046e9i	0.327648	+	0.567503i
$803$	1.81895e9	−	3.15052e9i	0.123970	−	0.214723i
$804$	1.86331e9	+	3.22734e9i	0.126441	+	0.219003i
$805$	−3.52809e9			−0.238371
$806$	−2.90201e10			−1.95221
$807$	2.01649e9	+	3.49267e9i	0.135064	+	0.233937i
$808$	3.94804e9	+	6.83821e9i	0.263294	+	0.456039i
$809$	−1.79429e10			−1.19144			−0.595721	−	0.803192i	$-0.703133\pi$
$809$	−1.79429e10			−1.19144			−0.595721	+	0.803192i	$0.703133\pi$
$810$	9.12105e9			0.603042
$811$	−1.94315e9	−	3.36563e9i	−0.127918	−	0.221561i	0.794952	−	0.606673i	$-0.207496\pi$
$811$	−1.94315e9	−	3.36563e9i	−0.127918	−	0.221561i	−0.922870	+	0.385112i	$0.874163\pi$
$812$	1.22468e9	−	2.12121e9i	0.0802743	−	0.139039i
$813$	−3.43378e9	−	5.94747e9i	−0.224107	−	0.388164i
$814$	3.39228e9	−	5.87561e9i	0.220448	−	0.381828i
$815$	1.39788e10	−	2.42120e10i	0.904522	−	1.56668i
$816$	−3.40393e8			−0.0219314
$817$	−2.44962e9	+	1.30991e10i	−0.157152	+	0.840360i
$818$	−5.54458e9			−0.354186
$819$	−6.81730e9	+	1.18079e10i	−0.433630	+	0.751069i
$820$	−4.96157e9	+	8.59369e9i	−0.314246	+	0.544291i
$821$	1.04545e10	+	1.81078e10i	0.659331	+	1.14199i	0.980789	+	0.195071i	$0.0624937\pi$
$821$	1.04545e10	+	1.81078e10i	0.659331	+	1.14199i	−0.321458	+	0.946924i	$0.604173\pi$
$822$	−1.28193e9	+	2.22038e9i	−0.0805034	+	0.139436i
$823$	3.38094e9	+	5.85596e9i	0.211416	+	0.366183i	0.952158	−	0.305606i	$-0.0988592\pi$
$823$	3.38094e9	+	5.85596e9i	0.211416	+	0.366183i	−0.740742	+	0.671790i	$0.765526\pi$
$824$	−2.71302e9			−0.168930
$825$	−4.37228e9			−0.271094
$826$	3.22477e9	+	5.58547e9i	0.199099	+	0.344850i
$827$	−1.39529e10	−	2.41672e10i	−0.857820	−	1.48579i	−0.874004	−	0.485918i	$-0.838485\pi$
$827$	−1.39529e10	−	2.41672e10i	−0.857820	−	1.48579i	0.0161847	−	0.999869i	$-0.494848\pi$
$828$	1.86118e9			0.113941
$829$	3.35286e9			0.204397			0.102199	−	0.994764i	$-0.467412\pi$
$829$	3.35286e9			0.204397			0.102199	+	0.994764i	$0.467412\pi$
$830$	−8.28893e9	−	1.43568e10i	−0.503182	−	0.871537i
$831$	−4.99396e9	+	8.64980e9i	−0.301885	+	0.522880i
$832$	−2.00664e9	−	3.47559e9i	−0.120792	−	0.209217i
$833$	1.27143e9	−	2.20219e9i	0.0762142	−	0.132007i
$834$	2.33766e9	−	4.04895e9i	0.139541	−	0.241692i
$835$	3.38330e10			2.01112
$836$	2.63145e9	+	2.25481e9i	0.155766	+	0.133472i
$837$	1.81487e10			1.06981
$838$	−1.73244e9	+	3.00067e9i	−0.101696	+	0.176142i
$839$	3.95867e9	−	6.85661e9i	0.231410	−	0.400814i	−0.726813	−	0.686835i	$-0.758999\pi$
$839$	3.95867e9	−	6.85661e9i	0.231410	−	0.400814i	0.958223	+	0.286021i	$0.0923328\pi$
$840$	−1.08112e9	−	1.87256e9i	−0.0629358	−	0.109008i
$841$	5.55993e9	−	9.63007e9i	0.322317	−	0.558269i
$842$	−3.71771e9	−	6.43926e9i	−0.214626	−	0.371743i
$843$	5.07509e9			0.291775
$844$	1.06311e10			0.608668
$845$	3.88056e10	+	6.72134e10i	2.21257	+	3.83228i
$846$	7.40061e9	+	1.28182e10i	0.420214	+	0.727833i
$847$	7.92230e9			0.447981
$848$	−7.13776e9			−0.401954
$849$	−4.31532e9	−	7.47435e9i	−0.242012	−	0.419176i
$850$	2.19855e9	−	3.80800e9i	0.122792	−	0.212682i
$851$	3.73712e9	+	6.47287e9i	0.207866	+	0.360034i
$852$	−1.16618e9	+	2.01989e9i	−0.0645993	+	0.111889i
$853$	1.47690e10	−	2.55807e10i	0.814759	−	1.41120i	−0.0947412	−	0.995502i	$-0.530202\pi$
$853$	1.47690e10	−	2.55807e10i	0.814759	−	1.41120i	0.909501	−	0.415703i	$-0.136464\pi$
$854$	6.62131e8			0.0363782
$855$	−2.32331e10	+	8.18516e9i	−1.27123	+	0.447864i
$856$	−2.90456e9			−0.158278
$857$	7.97066e8	−	1.38056e9i	0.0432575	−	0.0749242i	−0.843586	−	0.536994i	$-0.819560\pi$
$857$	7.97066e8	−	1.38056e9i	0.0432575	−	0.0749242i	0.886844	+	0.462070i	$0.152893\pi$
$858$	−2.11890e9	+	3.67004e9i	−0.114526	+	0.198365i
$859$	−7.29492e9	−	1.26352e10i	−0.392685	−	0.680151i	0.600118	−	0.799912i	$-0.295120\pi$
$859$	−7.29492e9	−	1.26352e10i	−0.392685	−	0.680151i	−0.992803	+	0.119761i	$0.961787\pi$
$860$	−6.44989e9	+	1.11715e10i	−0.345786	+	0.598919i
$861$	1.60106e9	+	2.77312e9i	0.0854865	+	0.148067i
$862$	−2.34560e10			−1.24732
$863$	1.10966e10			0.587693			0.293847	−	0.955853i	$-0.405064\pi$
$863$	1.10966e10			0.587693			0.293847	+	0.955853i	$0.405064\pi$
$864$	1.25492e9	+	2.17358e9i	0.0661936	+	0.114651i
$865$	8.67245e9	+	1.50211e10i	0.455602	+	0.789125i
$866$	7.20787e9			0.377133
$867$	7.47830e9			0.389705
$868$	3.70632e9	+	6.41953e9i	0.192364	+	0.333184i
$869$	−5.30363e9	+	9.18615e9i	−0.274160	+	0.474859i
$870$	2.70573e9	+	4.68647e9i	0.139305	+	0.241284i
$871$	−2.33293e10	+	4.04076e10i	−1.19630	+	2.07204i
$872$	−4.33552e8	+	7.50933e8i	−0.0221428	+	0.0383525i
$873$	−1.36547e8			−0.00694594
$874$	−3.60070e9	+	1.26855e9i	−0.182430	+	0.0642713i
$875$	1.06624e10			0.538055
$876$	−1.22809e9	+	2.12712e9i	−0.0617259	+	0.106912i
$877$	−1.85977e9	+	3.22122e9i	−0.0931025	+	0.161258i	−0.908815	−	0.417199i	$-0.863012\pi$
$877$	−1.85977e9	+	3.22122e9i	−0.0931025	+	0.161258i	0.815713	+	0.578457i	$0.196345\pi$
$878$	1.35070e9	+	2.33948e9i	0.0673484	+	0.116651i
$879$	6.20059e9	−	1.07397e10i	0.307944	−	0.533375i
$880$	1.67723e9	+	2.90505e9i	0.0829668	+	0.143703i
$881$	−2.58272e10			−1.27251			−0.636255	−	0.771479i	$-0.719517\pi$
$881$	−2.58272e10			−1.27251			−0.636255	+	0.771479i	$0.719517\pi$
$882$	−8.52110e9			−0.418173
$883$	−2.85268e9	−	4.94099e9i	−0.139441	−	0.241519i	0.787844	−	0.615875i	$-0.211197\pi$
$883$	−2.85268e9	−	4.94099e9i	−0.139441	−	0.241519i	−0.927285	+	0.374356i	$0.877864\pi$
$884$	−2.13093e9	−	3.69087e9i	−0.103749	−	0.179699i
$885$	−1.42492e10			−0.691019
$886$	−4.51684e9			−0.218181
$887$	6.09829e9	+	1.05626e10i	0.293411	+	0.508202i	0.974614	−	0.223892i	$-0.0718764\pi$
$887$	6.09829e9	+	1.05626e10i	0.293411	+	0.508202i	−0.681203	+	0.732094i	$0.738543\pi$
$888$	−2.29035e9	+	3.96701e9i	−0.109763	+	0.190116i
$889$	−1.04849e10	−	1.81604e10i	−0.500505	−	0.866900i
$890$	5.82903e9	−	1.00962e10i	0.277160	−	0.480056i
$891$	−2.28309e9	+	3.95443e9i	−0.108131	+	0.187289i
$892$	−4.20610e9			−0.198428
$893$	−2.30542e10	−	1.97544e10i	−1.08335	−	0.928292i
$894$	−6.28878e9			−0.294364
$895$	2.44428e10	−	4.23361e10i	1.13965	−	1.97392i
$896$	−5.12556e8	+	8.87773e8i	−0.0238047	+	0.0412310i
$897$	−2.33429e9	−	4.04311e9i	−0.107989	−	0.187043i
$898$	−1.40341e9	+	2.43077e9i	−0.0646720	+	0.112015i
$899$	−9.27581e9	−	1.60662e10i	−0.425788	−	0.737486i
$900$	−1.47346e10			−0.673737
$901$	−7.57988e9			−0.345243
$902$	−2.48386e9	−	4.30217e9i	−0.112695	−	0.195193i
$903$	2.08134e9	+	3.60498e9i	0.0940665	+	0.162928i
$904$	7.35154e9			0.330970
$905$	3.58110e10			1.60600
$906$	2.81986e9	+	4.88415e9i	0.125974	+	0.218193i
$907$	5.61488e9	−	9.72525e9i	0.249870	−	0.432788i	−0.713619	−	0.700534i	$-0.752945\pi$
$907$	5.61488e9	−	9.72525e9i	0.249870	−	0.432788i	0.963490	+	0.267746i	$0.0862787\pi$
$908$	1.77363e9	+	3.07201e9i	0.0786252	+	0.136183i
$909$	1.40493e10	−	2.43341e10i	0.620412	−	1.07459i
$910$	1.35361e10	−	2.34452e10i	0.595454	−	1.03136i
$911$	−7.61252e9			−0.333591			−0.166795	−	0.985992i	$-0.553342\pi$
$911$	−7.61252e9			−0.333591			−0.166795	+	0.985992i	$0.553342\pi$
$912$	−1.77667e9	−	1.52237e9i	−0.0775575	−	0.0664567i
$913$	8.29920e9			0.360902
$914$	3.62035e9	−	6.27064e9i	0.156834	−	0.271644i
$915$	−7.31436e8	+	1.26688e9i	−0.0315647	+	0.0546717i
$916$	4.58648e9	+	7.94401e9i	0.197172	+	0.341512i
$917$	7.43020e9	−	1.28695e10i	0.318206	−	0.551148i
$918$	1.33265e9	+	2.30821e9i	0.0568546	+	0.0984750i
$919$	−1.14376e10			−0.486106			−0.243053	−	0.970013i	$-0.578149\pi$
$919$	−1.14376e10			−0.486106			−0.243053	+	0.970013i	$0.578149\pi$
$920$	−3.69546e9			−0.156463
$921$	6.07212e8	+	1.05172e9i	0.0256113	+	0.0443601i
$922$	−1.55689e10	−	2.69662e10i	−0.654185	−	1.13308i
$923$	−2.92021e10			−1.22238
$924$	1.08246e9			0.0451400
$925$	−2.95861e10	−	5.12447e10i	−1.22911	−	2.12889i
$926$	−1.45776e10	+	2.52491e10i	−0.603318	+	1.04498i
$927$	4.82720e9	+	8.36096e9i	0.199029	+	0.344728i
$928$	1.28278e9	−	2.22183e9i	0.0526906	−	0.0912628i
$929$	1.53447e9	−	2.65777e9i	0.0627917	−	0.108758i	−0.832921	−	0.553393i	$-0.813333\pi$
$929$	1.53447e9	−	2.65777e9i	0.0627917	−	0.108758i	0.895712	+	0.444634i	$0.146666\pi$
$930$	−1.63770e10			−0.667643
$931$	1.64852e10	−	5.80785e9i	0.669531	−	0.235880i
$932$	−7.55922e9			−0.305859
$933$	1.44747e9	−	2.50710e9i	0.0583479	−	0.101061i
$934$	−1.07733e10	+	1.86599e10i	−0.432647	+	0.749367i
$935$	1.78112e9	+	3.08500e9i	0.0712612	+	0.123428i
$936$	−7.14070e9	+	1.23681e10i	−0.284627	+	0.492988i
$937$	1.33014e10	+	2.30388e10i	0.528214	+	0.914894i	0.999459	+	0.0328913i	$0.0104715\pi$
$937$	1.33014e10	+	2.30388e10i	0.528214	+	0.914894i	−0.471245	+	0.882002i	$0.656195\pi$
$938$	1.19181e10			0.471515
$939$	−1.75624e10			−0.692237
$940$	−1.46943e10	−	2.54512e10i	−0.577032	−	0.999449i
$941$	−6.98734e9	−	1.21024e10i	−0.273368	−	0.473488i	0.696354	−	0.717699i	$-0.254804\pi$
$941$	−6.98734e9	−	1.21024e10i	−0.273368	−	0.473488i	−0.969722	+	0.244211i	$0.921471\pi$
$942$	2.38065e9			0.0927934
$943$	5.47269e9			0.212525
$944$	3.37775e9	+	5.85044e9i	0.130685	+	0.226353i
$945$	−8.46523e9	+	1.46622e10i	−0.326308	+	0.565182i
$946$	−3.22894e9	−	5.59269e9i	−0.124006	−	0.214784i
$947$	2.12484e8	−	3.68033e8i	0.00813020	−	0.0140819i	−0.861932	−	0.507024i	$-0.830745\pi$
$947$	2.12484e8	−	3.68033e8i	0.00813020	−	0.0140819i	0.870062	+	0.492943i	$0.164079\pi$
$948$	3.58083e9	−	6.20217e9i	0.136507	−	0.236437i
$949$	−3.07524e10			−1.16801
$950$	2.85061e10	−	1.00429e10i	1.07871	−	0.380037i
$951$	−9.40752e9			−0.354686
$952$	−5.44304e8	+	9.42763e8i	−0.0204462	+	0.0354138i
$953$	9.81820e9	−	1.70056e10i	0.367457	−	0.636454i	−0.621710	−	0.783247i	$-0.713562\pi$
$953$	9.81820e9	−	1.70056e10i	0.367457	−	0.636454i	0.989167	+	0.146793i	$0.0468951\pi$
$954$	1.27000e10	+	2.19971e10i	0.473571	+	0.820249i
$955$	−1.14871e10	+	1.98962e10i	−0.426774	+	0.739194i
$956$	1.01637e10	+	1.76040e10i	0.376225	+	0.651641i
$957$	−2.70909e9			−0.0999151
$958$	6.86616e9			0.252310
$959$	4.09974e9	+	7.10096e9i	0.150104	+	0.259987i
$960$	−1.13241e9	−	1.96139e9i	−0.0413099	−	0.0715509i
$961$	2.86311e10			1.04066
$962$	−5.73522e10			−2.07700
$963$	5.16800e9	+	8.95124e9i	0.186479	+	0.322992i
$964$	−3.09710e9	+	5.36433e9i	−0.111349	+	0.192862i
$965$	1.51008e10	+	2.61553e10i	0.540946	+	0.936946i
$966$	−5.96249e8	+	1.03273e9i	−0.0212818	+	0.0368611i
$967$	−7.62195e9	+	1.32016e10i	−0.271065	+	0.469498i	−0.969135	−	0.246531i	$-0.920709\pi$
$967$	−7.62195e9	+	1.32016e10i	−0.271065	+	0.469498i	0.698070	+	0.716030i	$0.254042\pi$
$968$	8.29812e9			0.294046
$969$	−1.88671e9	−	1.61667e9i	−0.0666151	−	0.0570805i
$970$	2.71120e8			0.00953806
$971$	−1.81028e10	+	3.13549e10i	−0.634568	+	1.09910i	0.352039	+	0.935985i	$0.385489\pi$
$971$	−1.81028e10	+	3.13549e10i	−0.634568	+	1.09910i	−0.986607	+	0.163118i	$0.947845\pi$
$972$	6.90181e9	−	1.19543e10i	0.241063	−	0.417534i
$973$	−7.47606e9	−	1.29489e10i	−0.260182	−	0.450649i
$974$	1.42680e10	−	2.47129e10i	0.494773	−	0.856973i
$975$	1.84802e10	+	3.20086e10i	0.638543	+	1.10599i
$976$	6.93541e8			0.0238780
$977$	1.42751e10			0.489721			0.244861	−	0.969558i	$-0.421258\pi$
$977$	1.42751e10			0.489721			0.244861	+	0.969558i	$0.421258\pi$
$978$	−4.72486e9	−	8.18370e9i	−0.161511	−	0.279746i
$979$	2.91813e9	+	5.05434e9i	0.0993950	+	0.172157i
$980$	1.69191e10			0.574229
$981$	3.08563e9			0.104352
$982$	−8.59032e9	−	1.48789e10i	−0.289480	−	0.501395i
$983$	−8.55767e9	+	1.48223e10i	−0.287355	+	0.497713i	−0.973177	−	0.230056i	$-0.926109\pi$
$983$	−8.55767e9	+	1.48223e10i	−0.287355	+	0.497713i	0.685823	+	0.727769i	$0.259443\pi$
$984$	1.67702e9	+	2.90468e9i	0.0561118	+	0.0971885i
$985$	−1.34733e10	+	2.33364e10i	−0.449208	+	0.778051i
$986$	1.36223e9	−	2.35946e9i	0.0452566	−	0.0783868i
$987$	−9.48347e9			−0.313948
$988$	5.38477e9	−	2.87947e10i	0.177631	−	0.949867i
$989$	7.11434e9			0.233855
$990$	5.96851e9	−	1.03378e10i	0.195498	−	0.338613i
$991$	1.14184e10	−	1.97773e10i	0.372691	−	0.645520i	−0.617288	−	0.786738i	$-0.711769\pi$
$991$	1.14184e10	−	1.97773e10i	0.372691	−	0.645520i	0.989979	+	0.141218i	$0.0451018\pi$
$992$	3.88214e9	+	6.72406e9i	0.126264	+	0.218696i
$993$	−4.50544e9	+	7.80366e9i	−0.146021	+	0.252916i
$994$	3.72956e9	+	6.45978e9i	0.120449	+	0.208625i
$995$	8.91518e9			0.286913
$996$	−5.60334e9			−0.179696
$997$	−2.42185e10	−	4.19476e10i	−0.773951	−	1.34052i	−0.935382	−	0.353638i	$-0.884944\pi$
$997$	−2.42185e10	−	4.19476e10i	−0.773951	−	1.34052i	0.161432	−	0.986884i	$-0.448389\pi$
$998$	1.80942e10	+	3.13402e10i	0.576214	+	0.998031i
$999$	3.58671e10			1.13819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.c.b.11.5	yes	14
19.7	even	3	inner	38.8.c.b.7.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.c.b.7.5	✓	14	19.7	even	3	inner
38.8.c.b.11.5	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(9.55281 - 16.5459i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(226.101 - 391.619i) q^{5} +(-76.4225 - 132.368i) q^{6} -488.812 q^{7} -512.000 q^{8} +(910.988 + 1577.88i) q^{9} +O(q^{10})\)	\(q+(4.00000 - 6.92820i) q^{2} +(9.55281 - 16.5459i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(226.101 - 391.619i) q^{5} +(-76.4225 - 132.368i) q^{6} -488.812 q^{7} -512.000 q^{8} +(910.988 + 1577.88i) q^{9} +(-1808.81 - 3132.95i) q^{10} +1811.05 q^{11} -1222.76 q^{12} +(-7654.71 - 13258.3i) q^{13} +(-1955.25 + 3386.59i) q^{14} +(-4319.80 - 7482.12i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-2174.85 + 3766.96i) q^{17} +14575.8 q^{18} +(-28198.8 + 9934.64i) q^{19} -28941.0 q^{20} +(-4669.52 + 8087.85i) q^{21} +(7244.21 - 12547.3i) q^{22} +(7980.59 + 13822.8i) q^{23} +(-4891.04 + 8471.53i) q^{24} +(-63181.0 - 109433. i) q^{25} -122475. q^{26} +76593.9 q^{27} +(15642.0 + 27092.7i) q^{28} +(-39147.2 - 67805.0i) q^{29} -69116.8 q^{30} +236947. q^{31} +(16384.0 + 28377.9i) q^{32} +(17300.6 - 29965.6i) q^{33} +(17398.8 + 30135.7i) q^{34} +(-110521. + 191428. i) q^{35} +(58303.2 - 100984. i) q^{36} +468275. q^{37} +(-43966.2 + 235106. i) q^{38} -292496. q^{39} +(-115764. + 200509. i) q^{40} +(171438. - 296939. i) q^{41} +(37356.2 + 64702.8i) q^{42} +(222864. - 386011. i) q^{43} +(-57953.6 - 100379. i) q^{44} +823902. q^{45} +127689. q^{46} +(507732. + 879418. i) q^{47} +(39128.3 + 67772.2i) q^{48} -584606. q^{49} -1.01090e6 q^{50} +(41551.9 + 71970.1i) q^{51} +(-489901. + 848534. i) q^{52} +(871309. + 1.50915e6i) q^{53} +(306376. - 530658. i) q^{54} +(409481. - 709242. i) q^{55} +250272. q^{56} +(-105000. + 561480. i) q^{57} -626356. q^{58} +(824646. - 1.42833e6i) q^{59} +(-276467. + 478856. i) q^{60} +(-84660.8 - 146637. i) q^{61} +(947787. - 1.64162e6i) q^{62} +(-445301. - 771285. i) q^{63} +262144. q^{64} -6.92295e6 q^{65} +(-138405. - 239725. i) q^{66} +(-1.52385e6 - 2.63939e6i) q^{67} +278381. q^{68} +304948. q^{69} +(884167. + 1.53142e6i) q^{70} +(953730. - 1.65191e6i) q^{71} +(-466426. - 807873. i) q^{72} +(1.00436e6 - 1.73961e6i) q^{73} +(1.87310e6 - 3.24431e6i) q^{74} -2.41422e6 q^{75} +(1.45300e6 + 1.24503e6i) q^{76} -885263. q^{77} +(-1.16998e6 + 2.02647e6i) q^{78} +(-2.92848e6 + 5.07228e6i) q^{79} +(926111. + 1.60407e6i) q^{80} +(-1.26064e6 + 2.18350e6i) q^{81} +(-1.37150e6 - 2.37551e6i) q^{82} +4.58253e6 q^{83} +597699. q^{84} +(983474. + 1.70343e6i) q^{85} +(-1.78291e6 - 3.08809e6i) q^{86} -1.49586e6 q^{87} -927258. q^{88} +(1.61129e6 + 2.79083e6i) q^{89} +(3.29561e6 - 5.70816e6i) q^{90} +(3.74171e6 + 6.48083e6i) q^{91} +(510758. - 884659. i) q^{92} +(2.26351e6 - 3.92051e6i) q^{93} +8.12372e6 q^{94} +(-2.48520e6 + 1.32894e7i) q^{95} +626053. q^{96} +(-37472.1 + 64903.6i) q^{97} +(-2.33842e6 + 4.05027e6i) q^{98} +(1.64985e6 + 2.85762e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9}+O(q^{10}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9} + 1008 q^{10} + 646 q^{11} - 7040 q^{12} - 1308 q^{13} + 7712 q^{14} + 8740 q^{15} - 28672 q^{16} + 10528 q^{17} - 73632 q^{18} - 87463 q^{19} + 16128 q^{20} - 30584 q^{21} + 2584 q^{22} - 113822 q^{23} - 28160 q^{24} - 50143 q^{25} - 20928 q^{26} - 319898 q^{27} - 61696 q^{28} + 167706 q^{29} + 139840 q^{30} + 201780 q^{31} + 229376 q^{32} + 377473 q^{33} - 84224 q^{34} - 33168 q^{35} - 294528 q^{36} + 380924 q^{37} - 384064 q^{38} + 1379564 q^{39} + 64512 q^{40} + 66301 q^{41} + 244672 q^{42} + 726564 q^{43} - 20672 q^{44} + 428936 q^{45} - 1821152 q^{46} - 2373788 q^{47} + 225280 q^{48} + 5898846 q^{49} - 802288 q^{50} + 3264054 q^{51} - 83712 q^{52} + 161792 q^{53} - 1279592 q^{54} - 53424 q^{55} - 987136 q^{56} - 4487994 q^{57} + 2683296 q^{58} - 1845767 q^{59} + 559360 q^{60} - 1600418 q^{61} + 807120 q^{62} - 3064040 q^{63} + 3670016 q^{64} + 6534852 q^{65} - 3019784 q^{66} - 8911929 q^{67} - 1347584 q^{68} - 8860208 q^{69} + 265344 q^{70} + 517154 q^{71} + 2356224 q^{72} - 9558049 q^{73} + 1523696 q^{74} - 24621450 q^{75} + 2525120 q^{76} - 9188192 q^{77} + 5518256 q^{78} + 7963520 q^{79} - 516096 q^{80} - 4125855 q^{81} - 530408 q^{82} + 30616886 q^{83} + 3914752 q^{84} + 6973266 q^{85} - 5812512 q^{86} + 25084136 q^{87} - 330752 q^{88} + 11829436 q^{89} + 1715744 q^{90} + 4017336 q^{91} - 7284608 q^{92} + 396810 q^{93} - 37980608 q^{94} + 7058892 q^{95} + 3604480 q^{96} - 8033723 q^{97} + 23595384 q^{98} + 24812606 q^{99}+O(q^{100}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9 + 1008 * q^10 + 646 * q^11 - 7040 * q^12 - 1308 * q^13 + 7712 * q^14 + 8740 * q^15 - 28672 * q^16 + 10528 * q^17 - 73632 * q^18 - 87463 * q^19 + 16128 * q^20 - 30584 * q^21 + 2584 * q^22 - 113822 * q^23 - 28160 * q^24 - 50143 * q^25 - 20928 * q^26 - 319898 * q^27 - 61696 * q^28 + 167706 * q^29 + 139840 * q^30 + 201780 * q^31 + 229376 * q^32 + 377473 * q^33 - 84224 * q^34 - 33168 * q^35 - 294528 * q^36 + 380924 * q^37 - 384064 * q^38 + 1379564 * q^39 + 64512 * q^40 + 66301 * q^41 + 244672 * q^42 + 726564 * q^43 - 20672 * q^44 + 428936 * q^45 - 1821152 * q^46 - 2373788 * q^47 + 225280 * q^48 + 5898846 * q^49 - 802288 * q^50 + 3264054 * q^51 - 83712 * q^52 + 161792 * q^53 - 1279592 * q^54 - 53424 * q^55 - 987136 * q^56 - 4487994 * q^57 + 2683296 * q^58 - 1845767 * q^59 + 559360 * q^60 - 1600418 * q^61 + 807120 * q^62 - 3064040 * q^63 + 3670016 * q^64 + 6534852 * q^65 - 3019784 * q^66 - 8911929 * q^67 - 1347584 * q^68 - 8860208 * q^69 + 265344 * q^70 + 517154 * q^71 + 2356224 * q^72 - 9558049 * q^73 + 1523696 * q^74 - 24621450 * q^75 + 2525120 * q^76 - 9188192 * q^77 + 5518256 * q^78 + 7963520 * q^79 - 516096 * q^80 - 4125855 * q^81 - 530408 * q^82 + 30616886 * q^83 + 3914752 * q^84 + 6973266 * q^85 - 5812512 * q^86 + 25084136 * q^87 - 330752 * q^88 + 11829436 * q^89 + 1715744 * q^90 + 4017336 * q^91 - 7284608 * q^92 + 396810 * q^93 - 37980608 * q^94 + 7058892 * q^95 + 3604480 * q^96 - 8033723 * q^97 + 23595384 * q^98 + 24812606 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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