LMFDB - Embedded newform 38.6.e.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	38.17
Dual form			38.6.e.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.694593 + 3.93923i) q^{2} +(15.2107 + 12.7633i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-77.4900 + 28.2040i) q^{5} +(-60.8427 + 51.0531i) q^{6} +(31.0980 + 53.8633i) q^{7} +(32.0000 - 55.4256i) q^{8} +(26.2669 + 148.967i) q^{9} +O(q^{10})$	\(q+(-0.694593 + 3.93923i) q^{2} +(15.2107 + 12.7633i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-77.4900 + 28.2040i) q^{5} +(-60.8427 + 51.0531i) q^{6} +(31.0980 + 53.8633i) q^{7} +(32.0000 - 55.4256i) q^{8} +(26.2669 + 148.967i) q^{9} +(-57.2783 - 324.841i) q^{10} +(23.0319 - 39.8924i) q^{11} +(-158.849 - 275.134i) q^{12} +(-470.595 + 394.876i) q^{13} +(-233.780 + 85.0891i) q^{14} +(-1538.65 - 560.023i) q^{15} +(196.107 + 164.554i) q^{16} +(-265.830 + 1507.60i) q^{17} -605.061 q^{18} +(1059.07 - 1163.81i) q^{19} +1319.41 q^{20} +(-214.450 + 1216.21i) q^{21} +(141.148 + 118.437i) q^{22} +(1547.62 + 563.288i) q^{23} +(1194.15 - 434.636i) q^{24} +(2815.34 - 2362.35i) q^{25} +(-1228.64 - 2128.06i) q^{26} +(910.748 - 1577.46i) q^{27} +(-172.803 - 980.017i) q^{28} +(1410.66 + 8000.26i) q^{29} +(3274.79 - 5672.11i) q^{30} +(3137.20 + 5433.79i) q^{31} +(-784.430 + 658.215i) q^{32} +(859.487 - 312.828i) q^{33} +(-5754.13 - 2094.33i) q^{34} +(-3928.94 - 3296.77i) q^{35} +(420.271 - 2383.47i) q^{36} +7660.34 q^{37} +(3848.91 + 4980.31i) q^{38} -12198.0 q^{39} +(-916.452 + 5197.46i) q^{40} +(-3980.33 - 3339.89i) q^{41} +(-4641.97 - 1689.54i) q^{42} +(7859.62 - 2860.67i) q^{43} +(-564.590 + 473.747i) q^{44} +(-6236.90 - 10802.6i) q^{45} +(-3293.89 + 5705.18i) q^{46} +(-1318.75 - 7478.98i) q^{47} +(882.682 + 5005.94i) q^{48} +(6469.33 - 11205.2i) q^{49} +(7350.32 + 12731.1i) q^{50} +(-23285.3 + 19538.7i) q^{51} +(9236.32 - 3361.75i) q^{52} +(-24672.2 - 8979.94i) q^{53} +(5581.39 + 4683.34i) q^{54} +(-659.613 + 3740.85i) q^{55} +3980.54 q^{56} +(30963.3 - 4185.14i) q^{57} -32494.7 q^{58} +(-8904.62 + 50500.6i) q^{59} +(20069.1 + 16840.0i) q^{60} +(-18443.2 - 6712.78i) q^{61} +(-23584.0 + 8583.88i) q^{62} +(-7207.01 + 6047.40i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(25329.3 - 43871.6i) q^{65} +(635.307 + 3603.01i) q^{66} +(-10679.6 - 60566.9i) q^{67} +(12246.8 - 21212.2i) q^{68} +(16350.9 + 28320.7i) q^{69} +(15715.8 - 13187.1i) q^{70} +(44421.6 - 16168.1i) q^{71} +(9097.14 + 3311.09i) q^{72} +(-35504.7 - 29792.0i) q^{73} +(-5320.82 + 30175.9i) q^{74} +72974.4 q^{75} +(-22292.0 + 11702.4i) q^{76} +2864.98 q^{77} +(8472.62 - 48050.6i) q^{78} +(41904.4 + 35162.0i) q^{79} +(-19837.4 - 7220.23i) q^{80} +(68527.4 - 24941.9i) q^{81} +(15921.3 - 13359.6i) q^{82} +(22493.9 + 38960.5i) q^{83} +(9879.76 - 17112.2i) q^{84} +(-21921.2 - 124321. i) q^{85} +(5809.60 + 32947.9i) q^{86} +(-80652.4 + 139694. i) q^{87} +(-1474.04 - 2553.11i) q^{88} +(-87568.0 + 73478.3i) q^{89} +(46886.1 - 17065.2i) q^{90} +(-35903.9 - 13067.9i) q^{91} +(-20186.1 - 16938.2i) q^{92} +(-21634.0 + 122692. i) q^{93} +30377.4 q^{94} +(-49243.3 + 120054. i) q^{95} -20332.7 q^{96} +(22813.0 - 129379. i) q^{97} +(39646.4 + 33267.2i) q^{98} +(6547.63 + 2383.14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9}+O(q^{10}) $ 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9	\( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22} - 1170 q^{23} - 1152 q^{24} + 5940 q^{25} - 1776 q^{26} - 5130 q^{27} + 768 q^{28} - 7554 q^{29} + 294 q^{31} - 45912 q^{33} + 1584 q^{34} + 22116 q^{35} + 6048 q^{36} + 28608 q^{37} - 9528 q^{38} - 38868 q^{39} + 37278 q^{41} - 9720 q^{42} + 13212 q^{43} + 20640 q^{44} - 34344 q^{45} - 29856 q^{46} - 3054 q^{47} - 9216 q^{48} + 1422 q^{49} + 16584 q^{50} + 2352 q^{51} - 1824 q^{52} + 73806 q^{53} + 136944 q^{54} - 41598 q^{55} + 56064 q^{56} + 178248 q^{57} - 52848 q^{58} + 123528 q^{59} + 46944 q^{60} - 149172 q^{61} + 58344 q^{62} - 170124 q^{63} - 49152 q^{64} - 202674 q^{65} - 84840 q^{66} - 313212 q^{67} + 35520 q^{68} - 19938 q^{69} - 88464 q^{70} + 75810 q^{71} + 48384 q^{72} + 172872 q^{73} + 4872 q^{74} + 174960 q^{75} + 31008 q^{76} - 115056 q^{77} + 101304 q^{78} + 158058 q^{79} - 47250 q^{81} - 149112 q^{82} - 148440 q^{83} - 176736 q^{84} - 226752 q^{85} - 57528 q^{86} + 182874 q^{87} - 38400 q^{88} - 322464 q^{89} + 48816 q^{90} - 27264 q^{91} + 88992 q^{92} + 779424 q^{93} + 143712 q^{94} + 634752 q^{95} - 108552 q^{97} - 173544 q^{98} + 656436 q^{99}+O(q^{100}) \) 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9 + 600 * q^11 - 1662 * q^13 - 1776 * q^14 - 1206 * q^15 + 4194 * q^17 - 4368 * q^18 + 9570 * q^19 - 1344 * q^20 + 2430 * q^21 - 5160 * q^22 - 1170 * q^23 - 1152 * q^24 + 5940 * q^25 - 1776 * q^26 - 5130 * q^27 + 768 * q^28 - 7554 * q^29 + 294 * q^31 - 45912 * q^33 + 1584 * q^34 + 22116 * q^35 + 6048 * q^36 + 28608 * q^37 - 9528 * q^38 - 38868 * q^39 + 37278 * q^41 - 9720 * q^42 + 13212 * q^43 + 20640 * q^44 - 34344 * q^45 - 29856 * q^46 - 3054 * q^47 - 9216 * q^48 + 1422 * q^49 + 16584 * q^50 + 2352 * q^51 - 1824 * q^52 + 73806 * q^53 + 136944 * q^54 - 41598 * q^55 + 56064 * q^56 + 178248 * q^57 - 52848 * q^58 + 123528 * q^59 + 46944 * q^60 - 149172 * q^61 + 58344 * q^62 - 170124 * q^63 - 49152 * q^64 - 202674 * q^65 - 84840 * q^66 - 313212 * q^67 + 35520 * q^68 - 19938 * q^69 - 88464 * q^70 + 75810 * q^71 + 48384 * q^72 + 172872 * q^73 + 4872 * q^74 + 174960 * q^75 + 31008 * q^76 - 115056 * q^77 + 101304 * q^78 + 158058 * q^79 - 47250 * q^81 - 149112 * q^82 - 148440 * q^83 - 176736 * q^84 - 226752 * q^85 - 57528 * q^86 + 182874 * q^87 - 38400 * q^88 - 322464 * q^89 + 48816 * q^90 - 27264 * q^91 + 88992 * q^92 + 779424 * q^93 + 143712 * q^94 + 634752 * q^95 - 108552 * q^97 - 173544 * q^98 + 656436 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.694593	+	3.93923i	−0.122788	+	0.696364i
$2$	−0.694593	+	3.93923i	−0.122788	+	0.696364i
$3$	15.2107	+	12.7633i	0.975765	+	0.818764i	0.983445	−	0.181207i	$-0.0580003\pi$
$3$	15.2107	+	12.7633i	0.975765	+	0.818764i	−0.00768044	+	0.999971i	$0.502445\pi$
$4$	−15.0351	−	5.47232i	−0.469846	−	0.171010i
$5$	−77.4900	+	28.2040i	−1.38618	+	0.504529i	−0.924047	−	0.382280i	$-0.875139\pi$
$5$	−77.4900	+	28.2040i	−1.38618	+	0.504529i	−0.462136	+	0.886809i	$0.652917\pi$
$6$	−60.8427	+	51.0531i	−0.689970	+	0.578953i
$7$	31.0980	+	53.8633i	0.239876	+	0.415478i	0.960679	−	0.277663i	$-0.0895598\pi$
$7$	31.0980	+	53.8633i	0.239876	+	0.415478i	−0.720802	+	0.693141i	$0.756226\pi$
$8$	32.0000	−	55.4256i	0.176777	−	0.306186i
$9$	26.2669	+	148.967i	0.108094	+	0.613033i
$10$	−57.2783	−	324.841i	−0.181130	−	1.02724i
$11$	23.0319	−	39.8924i	0.0573915	−	0.0994050i	−0.835902	−	0.548878i	$-0.815055\pi$
$11$	23.0319	−	39.8924i	0.0573915	−	0.0994050i	0.893294	+	0.449473i	$0.148388\pi$
$12$	−158.849	−	275.134i	−0.318443	−	0.551559i
$13$	−470.595	+	394.876i	−0.772305	+	0.648041i	−0.941298	−	0.337576i	$-0.890393\pi$
$13$	−470.595	+	394.876i	−0.772305	+	0.648041i	0.168993	+	0.985617i	$0.445948\pi$
$14$	−233.780	+	85.0891i	−0.318778	+	0.116026i
$15$	−1538.65	−	560.023i	−1.76568	−	0.642654i
$16$	196.107	+	164.554i	0.191511	+	0.160697i
$17$	−265.830	+	1507.60i	−0.223091	+	1.26521i	0.643210	+	0.765690i	$0.277602\pi$
$17$	−265.830	+	1507.60i	−0.223091	+	1.26521i	−0.866301	+	0.499522i	$0.833509\pi$
$18$	−605.061			−0.440167
$19$	1059.07	−	1163.81i	0.673042	−	0.739604i
$19$	1059.07	−	1163.81i	0.673042	−	0.739604i
$20$	1319.41			0.737572
$21$	−214.450	+	1216.21i	−0.106115	+	0.601810i
$22$	141.148	+	118.437i	0.0621751	+	0.0521711i
$23$	1547.62	+	563.288i	0.610021	+	0.222030i	0.628513	−	0.777799i	$-0.283664\pi$
$23$	1547.62	+	563.288i	0.610021	+	0.222030i	−0.0184913	+	0.999829i	$0.505886\pi$
$24$	1194.15	−	434.636i	0.423187	−	0.154027i
$25$	2815.34	−	2362.35i	0.900908	−	0.755951i
$26$	−1228.64	−	2128.06i	−0.356443	−	0.617377i
$27$	910.748	−	1577.46i	0.240430	−	0.416437i
$28$	−172.803	−	980.017i	−0.0416541	−	0.236232i
$29$	1410.66	+	8000.26i	0.311478	+	1.76648i	0.591321	+	0.806436i	$0.298607\pi$
$29$	1410.66	+	8000.26i	0.311478	+	1.76648i	−0.279842	+	0.960046i	$0.590282\pi$
$30$	3274.79	−	5672.11i	0.664325	−	1.15064i
$31$	3137.20	+	5433.79i	0.586324	+	1.01554i	0.994709	+	0.102734i	$0.0327589\pi$
$31$	3137.20	+	5433.79i	0.586324	+	1.01554i	−0.408384	+	0.912810i	$0.633908\pi$
$32$	−784.430	+	658.215i	−0.135419	+	0.113630i
$33$	859.487	−	312.828i	0.137390	−	0.0500058i
$34$	−5754.13	−	2094.33i	−0.853655	−	0.310705i
$35$	−3928.94	−	3296.77i	−0.542133	−	0.454903i
$36$	420.271	−	2383.47i	0.0540472	−	0.306517i
$37$	7660.34			0.919907			0.459953	−	0.887943i	$-0.347866\pi$
$37$	7660.34			0.919907			0.459953	+	0.887943i	$0.347866\pi$
$38$	3848.91	+	4980.31i	0.432393	+	0.559497i
$39$	−12198.0			−1.28418
$40$	−916.452	+	5197.46i	−0.0905649	+	0.513619i
$41$	−3980.33	−	3339.89i	−0.369793	−	0.310293i	0.438886	−	0.898543i	$-0.355373\pi$
$41$	−3980.33	−	3339.89i	−0.369793	−	0.310293i	−0.808680	+	0.588249i	$0.799817\pi$
$42$	−4641.97	−	1689.54i	−0.406049	−	0.147790i
$43$	7859.62	−	2860.67i	0.648232	−	0.235937i	0.00308448	−	0.999995i	$-0.499018\pi$
$43$	7859.62	−	2860.67i	0.648232	−	0.235937i	0.645147	+	0.764058i	$0.276796\pi$
$44$	−564.590	+	473.747i	−0.0439645	+	0.0368906i
$45$	−6236.90	−	10802.6i	−0.459132	−	0.795239i
$46$	−3293.89	+	5705.18i	−0.229517	+	0.397534i
$47$	−1318.75	−	7478.98i	−0.0870797	−	0.493853i	−0.996888	−	0.0788256i	$-0.974883\pi$
$47$	−1318.75	−	7478.98i	−0.0870797	−	0.493853i	0.909809	−	0.415028i	$-0.136228\pi$
$48$	882.682	+	5005.94i	0.0552970	+	0.313605i
$49$	6469.33	−	11205.2i	0.384919	−	0.666699i
$50$	7350.32	+	12731.1i	0.415797	+	0.720182i
$51$	−23285.3	+	19538.7i	−1.25359	+	1.05189i
$52$	9236.32	−	3361.75i	0.473686	−	0.172408i
$53$	−24672.2	−	8979.94i	−1.20647	−	0.439121i	−0.340995	−	0.940065i	$-0.610764\pi$
$53$	−24672.2	−	8979.94i	−1.20647	−	0.439121i	−0.865479	+	0.500945i	$0.832986\pi$
$54$	5581.39	+	4683.34i	0.260470	+	0.218560i
$55$	−659.613	+	3740.85i	−0.0294024	+	0.166749i
$56$	3980.54			0.169618
$57$	30963.3	−	4185.14i	1.26229	−	0.170617i
$58$	−32494.7			−1.26836
$59$	−8904.62	+	50500.6i	−0.333031	+	1.88872i	0.112831	+	0.993614i	$0.464008\pi$
$59$	−8904.62	+	50500.6i	−0.333031	+	1.88872i	−0.445863	+	0.895101i	$0.647103\pi$
$60$	20069.1	+	16840.0i	0.719697	+	0.603897i
$61$	−18443.2	−	6712.78i	−0.634617	−	0.230982i	0.00462260	−	0.999989i	$-0.498529\pi$
$61$	−18443.2	−	6712.78i	−0.634617	−	0.230982i	−0.639240	+	0.769008i	$0.720751\pi$
$62$	−23584.0	+	8583.88i	−0.779182	+	0.283599i
$63$	−7207.01	+	6047.40i	−0.228772	+	0.191963i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	25329.3	−	43871.6i	0.743600	−	1.28795i
$66$	635.307	+	3603.01i	0.0179525	+	0.101813i
$67$	−10679.6	−	60566.9i	−0.290648	−	1.64835i	−0.684383	−	0.729123i	$-0.739928\pi$
$67$	−10679.6	−	60566.9i	−0.290648	−	1.64835i	0.393735	−	0.919224i	$-0.371183\pi$
$68$	12246.8	−	21212.2i	0.321182	−	0.556304i
$69$	16350.9	+	28320.7i	0.413447	+	0.716112i
$70$	15715.8	−	13187.1i	0.383346	−	0.321665i
$71$	44421.6	−	16168.1i	1.04580	−	0.380639i	0.238723	−	0.971088i	$-0.423271\pi$
$71$	44421.6	−	16168.1i	1.04580	−	0.380639i	0.807075	+	0.590448i	$0.201049\pi$
$72$	9097.14	+	3311.09i	0.206811	+	0.0752730i
$73$	−35504.7	−	29792.0i	−0.779792	−	0.654323i	0.163404	−	0.986559i	$-0.447753\pi$
$73$	−35504.7	−	29792.0i	−0.779792	−	0.654323i	−0.943196	+	0.332236i	$0.892197\pi$
$74$	−5320.82	+	30175.9i	−0.112953	+	0.640590i
$75$	72974.4			1.49802
$76$	−22292.0	+	11702.4i	−0.442706	+	0.232403i
$77$	2864.98			0.0550674
$78$	8472.62	−	48050.6i	0.157682	−	0.894257i
$79$	41904.4	+	35162.0i	0.755427	+	0.633878i	0.936932	−	0.349512i	$-0.113653\pi$
$79$	41904.4	+	35162.0i	0.755427	+	0.633878i	−0.181505	+	0.983390i	$0.558097\pi$
$80$	−19837.4	−	7220.23i	−0.346546	−	0.126132i
$81$	68527.4	−	24941.9i	1.16052	−	0.422394i
$82$	15921.3	−	13359.6i	0.261483	−	0.219411i
$83$	22493.9	+	38960.5i	0.358401	+	0.620768i	0.987694	−	0.156400i	$-0.0499889\pi$
$83$	22493.9	+	38960.5i	0.358401	+	0.620768i	−0.629293	+	0.777168i	$0.716656\pi$
$84$	9879.76	−	17112.2i	0.152774	−	0.264612i
$85$	−21921.2	−	124321.i	−0.329091	−	1.86637i
$86$	5809.60	+	32947.9i	0.0847032	+	0.480376i
$87$	−80652.4	+	139694.i	−1.14240	+	1.97870i
$88$	−1474.04	−	2553.11i	−0.0202910	−	0.0351450i
$89$	−87568.0	+	73478.3i	−1.17185	+	0.983295i	−0.999998	−	0.00182840i	$-0.999418\pi$
$89$	−87568.0	+	73478.3i	−1.17185	+	0.983295i	−0.171847	+	0.985124i	$0.554974\pi$
$90$	46886.1	−	17065.2i	0.610152	−	0.222077i
$91$	−35903.9	−	13067.9i	−0.454504	−	0.165426i
$92$	−20186.1	−	16938.2i	−0.248647	−	0.208640i
$93$	−21634.0	+	122692.i	−0.259376	+	1.47099i
$94$	30377.4			0.354594
$95$	−49243.3	+	120054.i	−0.559807	+	1.36480i
$96$	−20332.7			−0.225173
$97$	22813.0	−	129379.i	0.246180	−	1.39615i	−0.571557	−	0.820562i	$-0.693660\pi$
$97$	22813.0	−	129379.i	0.246180	−	1.39615i	0.817737	−	0.575592i	$-0.195229\pi$
$98$	39646.4	+	33267.2i	0.417002	+	0.349906i
$99$	6547.63	+	2383.14i	0.0671423	+	0.0244378i
$100$	−55256.3	+	20111.7i	−0.552563	+	0.201117i
$101$	32070.1	−	26910.0i	0.312822	−	0.262489i	−0.472835	−	0.881151i	$-0.656769\pi$
$101$	32070.1	−	26910.0i	0.312822	−	0.262489i	0.785657	+	0.618662i	$0.212325\pi$
$102$	−60793.7	−	105298.i	−0.578573	−	1.00212i
$103$	−19560.4	+	33879.5i	−0.181670	+	0.314662i	−0.942449	−	0.334349i	$-0.891484\pi$
$103$	−19560.4	+	33879.5i	−0.181670	+	0.314662i	0.760779	+	0.649011i	$0.224817\pi$
$104$	6827.21	+	38719.1i	0.0618957	+	0.351028i
$105$	−17684.2	−	100292.i	−0.156536	−	0.887757i
$106$	52511.2	−	90952.0i	0.453928	−	0.786227i
$107$	−56869.7	−	98501.2i	−0.480199	−	0.831729i	0.519543	−	0.854444i	$-0.326102\pi$
$107$	−56869.7	−	98501.2i	−0.480199	−	0.831729i	−0.999742	+	0.0227151i	$0.992769\pi$
$108$	−22325.6	+	18733.4i	−0.184180	+	0.154546i
$109$	−74835.2	+	27237.8i	−0.603309	+	0.219586i	−0.625573	−	0.780166i	$-0.715135\pi$
$109$	−74835.2	+	27237.8i	−0.603309	+	0.219586i	0.0222642	+	0.999752i	$0.492912\pi$
$110$	−14277.9	−	5196.74i	−0.112508	−	0.0409495i
$111$	116519.	+	97771.0i	0.897613	+	0.753186i
$112$	−2764.85	+	15680.3i	−0.0208270	+	0.118116i
$113$	153808.			1.13313			0.566567	−	0.824015i	$-0.308271\pi$
$113$	153808.			1.13313			0.566567	+	0.824015i	$0.308271\pi$
$114$	−5020.64	+	124878.i	−0.0361823	+	0.899964i
$115$	−135812.			−0.957621
$116$	22570.6	−	128004.i	0.155739	−	0.883241i
$117$	−71184.6	−	59731.0i	−0.480753	−	0.403399i
$118$	−192748.	−	70154.7i	−1.27434	−	0.463822i
$119$	−89471.0	+	32564.8i	−0.579181	+	0.210805i
$120$	−80276.4	+	67359.9i	−0.508903	+	0.427020i
$121$	79464.6	+	137637.i	0.493412	+	0.854615i
$122$	39253.7	−	67989.4i	0.238771	−	0.413563i
$123$	−17915.5	−	101604.i	−0.106774	−	0.605547i
$124$	−17432.6	−	98865.2i	−0.101814	−	0.577417i
$125$	−22684.0	+	39289.8i	−0.129851	+	0.224908i
$126$	−18816.2	−	32590.6i	−0.105586	−	0.182880i
$127$	−92220.2	+	77381.9i	−0.507361	+	0.425726i	−0.860199	−	0.509958i	$-0.829661\pi$
$127$	−92220.2	+	77381.9i	−0.507361	+	0.425726i	0.352839	+	0.935684i	$0.385216\pi$
$128$	15395.9	−	5603.66i	0.0830579	−	0.0302306i
$129$	156061.	+	56801.7i	0.825698	+	0.300530i
$130$	155227.	+	130251.i	0.805580	+	0.675962i
$131$	20010.7	−	113487.i	0.101879	−	0.577785i	−0.890542	−	0.454901i	$-0.849675\pi$
$131$	20010.7	−	113487.i	0.101879	−	0.577785i	0.992421	−	0.122884i	$-0.0392142\pi$
$132$	−14634.4			−0.0731036
$133$	95621.9	+	20852.9i	0.468736	+	0.102221i
$134$	246005.			1.18354
$135$	−26083.0	+	147924.i	−0.123175	+	0.698562i
$136$	75053.0	+	62976.9i	0.347953	+	0.291967i
$137$	390343.	+	142073.i	1.77683	+	0.646712i	0.999852	+	0.0171817i	$0.00546936\pi$
$137$	390343.	+	142073.i	1.77683	+	0.646712i	0.776976	+	0.629531i	$0.216753\pi$
$138$	−122919.	+	44738.8i	−0.549441	+	0.199980i
$139$	−3198.03	+	2683.47i	−0.0140393	+	0.0117804i	−0.649780	−	0.760122i	$-0.725139\pi$
$139$	−3198.03	+	2683.47i	−0.0140393	+	0.0117804i	0.635741	+	0.771902i	$0.280695\pi$
$140$	41031.0	+	71067.7i	0.176926	+	0.306445i
$141$	75397.2	−	130592.i	0.319380	−	0.553182i
$142$	32835.1	+	186217.i	0.136652	+	0.774994i
$143$	4913.86	+	27867.9i	0.0200948	+	0.113963i
$144$	−19361.9	+	33535.9i	−0.0778113	+	0.134773i
$145$	−334952.	−	580154.i	−1.32301	−	2.29152i
$146$	142019.	−	119168.i	0.551396	−	0.462676i
$147$	241418.	−	87868.9i	0.921459	−	0.335384i
$148$	−115174.	−	41919.9i	−0.432215	−	0.157313i
$149$	7696.00	+	6457.71i	0.0283988	+	0.0238294i	0.656877	−	0.753998i	$-0.271877\pi$
$149$	7696.00	+	6457.71i	0.0283988	+	0.0238294i	−0.628478	+	0.777828i	$0.716322\pi$
$150$	−50687.5	+	287463.i	−0.183939	+	1.04317i
$151$	478763.			1.70875			0.854374	−	0.519658i	$-0.173941\pi$
$151$	478763.			1.70875			0.854374	+	0.519658i	$0.173941\pi$
$152$	−30614.7	−	95941.9i	−0.107478	−	0.336821i
$153$	−231565.			−0.799732
$154$	−1989.99	+	11285.8i	−0.00676161	+	0.0383470i
$155$	−396356.	−	332582.i	−1.32512	−	1.11191i
$156$	183397.	+	66751.2i	0.603367	+	0.219608i
$157$	28635.2	−	10422.4i	0.0927153	−	0.0337456i	−0.295246	−	0.955421i	$-0.595402\pi$
$157$	28635.2	−	10422.4i	0.0927153	−	0.0337456i	0.387961	+	0.921676i	$0.373179\pi$
$158$	−167618.	+	140648.i	−0.534167	+	0.448220i
$159$	−260667.	−	451488.i	−0.817699	−	1.41630i
$160$	42221.1	−	73129.1i	0.130386	−	0.225834i
$161$	17787.3	+	100877.i	0.0540812	+	0.306710i
$162$	50653.4	+	287270.i	0.151642	+	0.860007i
$163$	109005.	−	188803.i	0.321350	−	0.556595i	−0.659417	−	0.751778i	$-0.729197\pi$
$163$	109005.	−	188803.i	0.321350	−	0.556595i	0.980767	+	0.195183i	$0.0625301\pi$
$164$	41567.6	+	71997.2i	0.120683	+	0.209029i
$165$	−57778.6	+	48482.0i	−0.165218	+	0.138634i
$166$	−169098.	+	61546.8i	−0.476288	+	0.173355i
$167$	51032.4	+	18574.3i	0.141597	+	0.0515372i	0.411847	−	0.911253i	$-0.364884\pi$
$167$	51032.4	+	18574.3i	0.141597	+	0.0515372i	−0.270249	+	0.962790i	$0.587106\pi$
$168$	60546.7	+	50804.7i	0.165507	+	0.138877i
$169$	1058.18	−	6001.23i	0.00284999	−	0.0161631i
$170$	504956.			1.34008
$171$	201189.	+	127197.i	0.526154	+	0.332650i
$172$	−133825.			−0.344917
$173$	−4756.12	+	26973.3i	−0.0120820	+	0.0685202i	−0.990253	−	0.139283i	$-0.955520\pi$
$173$	−4756.12	+	26973.3i	−0.0120820	+	0.0685202i	0.978171	+	0.207803i	$0.0666314\pi$
$174$	−494266.	−	414739.i	−1.23762	−	1.03849i
$175$	214795.	+	78179.0i	0.530187	+	0.192972i
$176$	11081.2	−	4033.21i	0.0269652	−	0.00981453i
$177$	−779998.	+	654496.i	−1.87137	+	1.57027i
$178$	−228624.	−	395988.i	−0.540843	−	0.936768i
$179$	−311054.	+	538761.i	−0.725609	+	1.25679i	0.233113	+	0.972450i	$0.425109\pi$
$179$	−311054.	+	538761.i	−0.725609	+	1.25679i	−0.958723	+	0.284343i	$0.908225\pi$
$180$	34656.8	+	196549.i	0.0797274	+	0.452156i
$181$	69821.7	+	395978.i	0.158414	+	0.898411i	0.955598	+	0.294674i	$0.0952111\pi$
$181$	69821.7	+	395978.i	0.158414	+	0.898411i	−0.797184	+	0.603737i	$0.793678\pi$
$182$	76416.2	−	132357.i	0.171004	−	0.296188i
$183$	−194856.	−	337501.i	−0.430117	−	0.744985i
$184$	80744.4	−	67752.6i	0.175820	−	0.147530i
$185$	−593600.	+	216053.i	−1.27516	+	0.464120i
$186$	−468287.	−	170443.i	−0.992499	−	0.361240i
$187$	54019.1	+	45327.4i	0.112965	+	0.0947888i
$188$	−21099.9	+	119664.i	−0.0435398	+	0.246927i
$189$	113290.			0.230694
$190$	−438716.	−	277370.i	−0.881657	−	0.557410i
$191$	−167577.			−0.332376			−0.166188	−	0.986094i	$-0.553146\pi$
$191$	−167577.			−0.332376			−0.166188	+	0.986094i	$0.553146\pi$
$192$	14122.9	−	80095.0i	0.0276485	−	0.156802i
$193$	−47176.4	−	39585.7i	−0.0911657	−	0.0764971i	0.596066	−	0.802936i	$-0.296730\pi$
$193$	−47176.4	−	39585.7i	−0.0911657	−	0.0764971i	−0.687231	+	0.726438i	$0.741174\pi$
$194$	493807.	+	179731.i	0.942004	+	0.342862i
$195$	945220.	−	344032.i	1.78011	−	0.647906i
$196$	−158585.	+	133069.i	−0.294865	+	0.247421i
$197$	36133.1	+	62584.3i	0.0663345	+	0.114895i	0.897285	−	0.441451i	$-0.145536\pi$
$197$	36133.1	+	62584.3i	0.0663345	+	0.114895i	−0.830951	+	0.556346i	$0.812203\pi$
$198$	−13935.7	+	24137.3i	−0.0252619	+	0.0437548i
$199$	114815.	+	651150.i	0.205526	+	1.16560i	0.896609	+	0.442822i	$0.146023\pi$
$199$	114815.	+	651150.i	0.205526	+	1.16560i	−0.691083	+	0.722775i	$0.742866\pi$
$200$	−40843.8	−	231637.i	−0.0722024	−	0.409480i
$201$	610588.	−	1.05757e6i	1.06600	−	1.84637i
$202$	83729.1	+	145023.i	0.144377	+	0.250068i
$203$	−387052.	+	324775.i	−0.659218	+	0.553149i
$204$	457019.	−	166341.i	0.768880	−	0.279850i
$205$	402634.	+	146547.i	0.669153	+	0.243552i
$206$	−119873.	−	100585.i	−0.196813	−	0.165145i
$207$	−43260.1	+	245340.i	−0.0701717	+	0.397964i
$208$	−157265.			−0.252043
$209$	−22034.8	−	69053.8i	−0.0348935	−	0.109351i
$210$	407358.			0.637423
$211$	47954.8	−	271965.i	0.0741526	−	0.420540i	−0.925022	−	0.379914i	$-0.875954\pi$
$211$	47954.8	−	271965.i	0.0741526	−	0.420540i	0.999174	−	0.0406262i	$-0.0129353\pi$
$212$	321807.	+	270028.i	0.491763	+	0.412638i
$213$	882039.	+	321036.i	1.33211	+	0.484847i
$214$	427520.	−	155605.i	0.638149	−	0.232267i
$215$	−528359.	+	443346.i	−0.779531	+	0.654104i
$216$	−58287.9	−	100958.i	−0.0850049	−	0.147233i
$217$	−195121.	+	337960.i	−0.281290	+	0.487209i
$218$	−55315.9	−	313712.i	−0.0788332	−	0.447085i
$219$	−159807.	−	906312.i	−0.225157	−	1.27693i
$220$	30388.5	−	52634.4i	0.0423304	−	0.0733184i
$221$	−470216.	−	814438.i	−0.647615	−	1.12170i
$222$	−466076.	+	391084.i	−0.634708	+	0.532583i
$223$	322671.	−	117443.i	0.434508	−	0.158148i	−0.115500	−	0.993307i	$-0.536847\pi$
$223$	322671.	−	117443.i	0.434508	−	0.158148i	0.550008	+	0.835160i	$0.314625\pi$
$224$	−59847.8	−	21782.8i	−0.0796944	−	0.0290064i
$225$	425862.	+	357341.i	0.560806	+	0.470573i
$226$	−106834.	+	605883.i	−0.139135	+	0.789074i
$227$	−313556.			−0.403878			−0.201939	−	0.979398i	$-0.564724\pi$
$227$	−313556.			−0.403878			−0.201939	+	0.979398i	$0.564724\pi$
$228$	−488438.	−	106517.i	−0.622260	−	0.135701i
$229$	−1.30256e6			−1.64139			−0.820693	−	0.571370i	$-0.806412\pi$
$229$	−1.30256e6			−1.64139			−0.820693	+	0.571370i	$0.806412\pi$
$230$	94334.1	−	534995.i	0.117584	−	0.666853i
$231$	43578.2	+	36566.5i	0.0537328	+	0.0450872i
$232$	488561.	+	177822.i	0.595935	+	0.216902i
$233$	−417802.	+	152067.i	−0.504174	+	0.183504i	−0.581570	−	0.813496i	$-0.697562\pi$
$233$	−417802.	+	152067.i	−0.504174	+	0.183504i	0.0773963	+	0.997000i	$0.475339\pi$
$234$	284739.	−	238924.i	0.339943	−	0.285246i
$235$	313127.	+	542352.i	0.369872	+	0.640637i
$236$	410237.	−	710552.i	0.479463	−	0.830454i
$237$	188613.	+	1.06967e6i	0.218122	+	1.23703i
$238$	−66134.3	−	375066.i	−0.0756805	−	0.429206i
$239$	790728.	−	1.36958e6i	0.895431	−	1.55093i	0.0621614	−	0.998066i	$-0.480201\pi$
$239$	790728.	−	1.36958e6i	0.895431	−	1.55093i	0.833270	−	0.552866i	$-0.186466\pi$
$240$	−209587.	−	363015.i	−0.234874	−	0.406814i
$241$	1.15944e6	−	972888.i	1.28590	−	1.07900i	0.293497	−	0.955960i	$-0.405181\pi$
$241$	1.15944e6	−	972888.i	1.28590	−	1.07900i	0.992402	−	0.123037i	$-0.0392634\pi$
$242$	−597378.	+	217428.i	−0.655709	+	0.238658i
$243$	944757.	+	343863.i	1.02637	+	0.373568i
$244$	240561.	+	201854.i	0.258672	+	0.217052i
$245$	−185276.	+	1.05075e6i	−0.197199	+	1.11837i
$246$	412685.			0.434792
$247$	−38832.7	+	965888.i	−0.0405001	+	1.00736i
$248$	401562.			0.414594
$249$	−155117.	+	879710.i	−0.158548	+	0.899169i
$250$	−139016.	−	116648.i	−0.140674	−	0.118039i
$251$	−11559.2	−	4207.21i	−0.0115810	−	0.00421512i	0.336223	−	0.941782i	$-0.390850\pi$
$251$	−11559.2	−	4207.21i	−0.0115810	−	0.00421512i	−0.347804	+	0.937567i	$0.613073\pi$
$252$	141451.	−	51484.1i	0.140315	−	0.0510707i
$253$	58115.5	−	48764.7i	0.0570809	−	0.0478966i
$254$	−240770.	−	417026.i	−0.234163	−	0.405582i
$255$	1.25331e6	−	2.17079e6i	1.20700	−	2.09059i
$256$	11380.2	+	64540.4i	0.0108530	+	0.0615505i
$257$	−81883.0	−	464382.i	−0.0773323	−	0.438573i	−0.998749	−	0.0499982i	$-0.984078\pi$
$257$	−81883.0	−	464382.i	−0.0773323	−	0.438573i	0.921417	−	0.388575i	$-0.127033\pi$
$258$	−332154.	+	575308.i	−0.310664	+	0.538085i
$259$	238221.	+	412611.i	0.220664	+	0.382201i
$260$	−620908.	+	521003.i	−0.569631	+	0.477977i
$261$	−1.15472e6	+	420285.i	−1.04924	+	0.381893i
$262$	433150.	+	157654.i	0.389839	+	0.141890i
$263$	−1.39351e6	−	1.16929e6i	−1.24228	−	1.04240i	−0.997342	−	0.0728618i	$-0.976787\pi$
$263$	−1.39351e6	−	1.16929e6i	−1.24228	−	1.04240i	−0.244942	−	0.969538i	$-0.578769\pi$
$264$	10164.9	−	57648.1i	0.00897623	−	0.0509067i
$265$	2.16512e6			1.89394
$266$	−148563.	+	362192.i	−0.128738	+	0.313859i
$267$	−2.26979e6			−1.94853
$268$	−170873.	+	969071.i	−0.145324	+	0.824173i
$269$	−751526.	−	630605.i	−0.633232	−	0.531345i	0.268699	−	0.963224i	$-0.413406\pi$
$269$	−751526.	−	630605.i	−0.633232	−	0.531345i	−0.901931	+	0.431879i	$0.857851\pi$
$270$	−564591.	−	205494.i	−0.471329	−	0.171550i
$271$	13481.8	−	4906.99i	0.0111513	−	0.00405875i	−0.336438	−	0.941705i	$-0.609222\pi$
$271$	13481.8	−	4906.99i	0.0111513	−	0.00405875i	0.347590	+	0.937647i	$0.387000\pi$
$272$	−300212.	+	251908.i	−0.246040	+	0.206452i
$273$	−379332.	−	657023.i	−0.308044	−	0.533548i
$274$	−830789.	+	1.43897e6i	−0.668520	+	1.15791i
$275$	−29397.2	−	166720.i	−0.0234409	−	0.132940i
$276$	−90858.0	−	515281.i	−0.0717944	−	0.407166i
$277$	−1.04857e6	+	1.81617e6i	−0.821100	+	1.42219i	0.0837641	+	0.996486i	$0.473306\pi$
$277$	−1.04857e6	+	1.81617e6i	−0.821100	+	1.42219i	−0.904864	+	0.425701i	$0.860028\pi$
$278$	−8349.47	−	14461.7i	−0.00647958	−	0.0112230i
$279$	−727051.	+	610069.i	−0.559184	+	0.469211i
$280$	−308452.	+	112267.i	−0.235122	+	0.0855773i
$281$	1.43958e6	+	523965.i	1.08760	+	0.395856i	0.822733	−	0.568428i	$-0.192448\pi$
$281$	1.43958e6	+	523965.i	1.08760	+	0.395856i	0.264871	+	0.964284i	$0.414671\pi$
$282$	462061.	+	387715.i	0.346000	+	0.290329i
$283$	−209267.	+	1.18681e6i	−0.155323	+	0.880879i	0.803167	+	0.595753i	$0.203146\pi$
$283$	−209267.	+	1.18681e6i	−0.155323	+	0.880879i	−0.958490	+	0.285126i	$0.907965\pi$
$284$	−756359.			−0.556458
$285$	−2.28130e6	+	1.19760e6i	−1.66369	+	0.873369i
$286$	−113191.			−0.0818272
$287$	56117.3	−	318257.i	0.0402154	−	0.228073i
$288$	−118657.	−	99564.9i	−0.0842969	−	0.0707335i
$289$	−867957.	−	315910.i	−0.611299	−	0.222495i
$290$	2.51801e6	−	916482.i	1.75818	−	0.639925i
$291$	1.99830e6	−	1.67677e6i	1.38333	−	1.16076i
$292$	370785.	+	642218.i	0.254487	+	0.440784i
$293$	285621.	−	494710.i	0.194366	−	0.336652i	−0.752326	−	0.658791i	$-0.771068\pi$
$293$	285621.	−	494710.i	0.194366	−	0.336652i	0.946693	+	0.322138i	$0.104402\pi$
$294$	178449.	+	1.01203e6i	0.120405	+	0.682852i
$295$	−734302.	−	4.16444e6i	−0.491270	−	2.78613i
$296$	245131.	−	424579.i	0.162618	−	0.281663i
$297$	−41952.5	−	72663.9i	−0.0275973	−	0.0477999i
$298$	−30784.0	+	25830.8i	−0.0200809	+	0.0168499i
$299$	−950732.	+	346038.i	−0.615007	+	0.223844i
$300$	−1.09718e6	−	399339.i	−0.703839	−	0.256176i
$301$	398503.	+	334384.i	0.253522	+	0.212730i
$302$	−332545.	+	1.88596e6i	−0.209813	+	1.18991i
$303$	831267.			0.520157
$304$	399202.	−	53958.0i	0.247747	−	0.0334866i
$305$	1.61849e6			0.996232
$306$	160843.	−	912188.i	0.0981973	−	0.556905i
$307$	−33717.0	−	28291.9i	−0.0204175	−	0.0171323i	0.632522	−	0.774543i	$-0.282020\pi$
$307$	−33717.0	−	28291.9i	−0.0204175	−	0.0171323i	−0.652939	+	0.757410i	$0.726464\pi$
$308$	−43075.2	−	15678.1i	−0.0258732	−	0.00941708i
$309$	−729939.	+	265676.i	−0.434901	+	0.158291i
$310$	1.58543e6	−	1.33033e6i	0.937004	−	0.786240i
$311$	−1.06298e6	−	1.84113e6i	−0.623194	−	1.07940i	−0.988887	−	0.148669i	$-0.952501\pi$
$311$	−1.06298e6	−	1.84113e6i	−0.623194	−	1.07940i	0.365693	−	0.930736i	$-0.380832\pi$
$312$	−390335.	+	676080.i	−0.227013	+	0.393198i
$313$	100129.	+	567857.i	0.0577693	+	0.327626i	0.999973	−	0.00741598i	$-0.00236060\pi$
$313$	100129.	+	567857.i	0.0577693	+	0.327626i	−0.942203	+	0.335042i	$0.891249\pi$
$314$	21166.3	+	120040.i	0.0121149	+	0.0687072i
$315$	387910.	−	671879.i	0.220269	−	0.381518i
$316$	−437619.	−	757978.i	−0.246535	−	0.427011i
$317$	682202.	−	572436.i	0.381298	−	0.319947i	−0.431913	−	0.901915i	$-0.642161\pi$
$317$	682202.	−	572436.i	0.381298	−	0.319947i	0.813212	+	0.581968i	$0.197717\pi$
$318$	1.95957e6	−	713227.i	1.08666	−	0.395512i
$319$	351640.	+	127986.i	0.193473	+	0.0704186i
$320$	258746.	+	217114.i	0.141253	+	0.118526i
$321$	392171.	−	2.22411e6i	0.212428	−	1.20474i
$322$	−409733.			−0.220222
$323$	1.47303e6	+	1.90603e6i	0.785606	+	1.01654i
$324$	−1.16680e6			−0.617498
$325$	−392049.	+	2.22342e6i	−0.205888	+	1.16765i
$326$	668023.	+	560538.i	0.348135	+	0.292120i
$327$	−1.48594e6	−	540836.i	−0.768477	−	0.279703i
$328$	−312486.	+	113736.i	−0.160378	+	0.0583730i
$329$	361832.	−	303613.i	0.184297	−	0.154643i
$330$	−150849.	−	261279.i	−0.0762533	−	0.132075i
$331$	258499.	−	447734.i	0.129685	−	0.224621i	−0.793870	−	0.608088i	$-0.791937\pi$
$331$	258499.	−	447734.i	0.129685	−	0.224621i	0.923555	+	0.383467i	$0.125270\pi$
$332$	−124993.	−	708868.i	−0.0622356	−	0.352956i
$333$	201214.	+	1.14114e6i	0.0994367	+	0.563934i
$334$	−108615.	+	188127.i	−0.0532751	+	0.0922752i
$335$	2.53579e6	+	4.39212e6i	1.23453	+	2.13827i
$336$	−242187.	+	203219.i	−0.117031	+	0.0982009i
$337$	3.17862e6	−	1.15692e6i	1.52463	−	0.554919i	0.562329	−	0.826913i	$-0.309905\pi$
$337$	3.17862e6	−	1.15692e6i	1.52463	−	0.554919i	0.962299	+	0.271994i	$0.0876831\pi$
$338$	22905.2	+	8336.83i	0.0109054	+	0.00396926i
$339$	2.33951e6	+	1.96309e6i	1.10567	+	0.927770i
$340$	−350739.	+	1.98914e6i	−0.164546	+	0.933185i
$341$	289022.			0.134600
$342$	−640804.	+	704178.i	−0.296251	+	0.325550i
$343$	1.85006e6			0.849084
$344$	92953.5	−	527166.i	0.0423516	−	0.240188i
$345$	−2.06579e6	−	1.73341e6i	−0.934413	−	0.784065i
$346$	−102950.	−	37470.9i	−0.0462315	−	0.0168269i
$347$	−2.68279e6	+	976455.i	−1.19609	+	0.435340i	−0.861857	−	0.507151i	$-0.830699\pi$
$347$	−2.68279e6	+	976455.i	−1.19609	+	0.435340i	−0.334230	+	0.942491i	$0.608476\pi$
$348$	1.97707e6	−	1.65895e6i	0.875131	−	0.734322i
$349$	255333.	+	442249.i	0.112213	+	0.194358i	0.916662	−	0.399663i	$-0.130873\pi$
$349$	255333.	+	442249.i	0.112213	+	0.194358i	−0.804449	+	0.594021i	$0.797539\pi$
$350$	−457160.	+	791825.i	−0.199480	+	0.345509i
$351$	194309.	+	1.10198e6i	0.0841830	+	0.477425i
$352$	8190.86	+	46452.7i	0.00352349	+	0.0199827i
$353$	1.51661e6	−	2.62684e6i	0.647794	−	1.12201i	−0.335855	−	0.941914i	$-0.609025\pi$
$353$	1.51661e6	−	2.62684e6i	0.647794	−	1.12201i	0.983649	−	0.180098i	$-0.0576416\pi$
$354$	−2.03643e6	−	3.52720e6i	−0.863696	−	1.49597i
$355$	−2.98622e6	+	2.50573e6i	−1.25762	+	1.05527i
$356$	1.71869e6	−	625552.i	0.718741	−	0.261600i
$357$	−1.77655e6	−	646610.i	−0.737744	−	0.268517i
$358$	−1.90625e6	−	1.59953e6i	−0.786089	−	0.659607i
$359$	−472458.	+	2.67944e6i	−0.193476	+	1.09726i	0.721097	+	0.692835i	$0.243638\pi$
$359$	−472458.	+	2.67944e6i	−0.193476	+	1.09726i	−0.914573	+	0.404422i	$0.867473\pi$
$360$	−798323.			−0.324655
$361$	−232824.	−	2.46513e6i	−0.0940287	−	0.995569i
$362$	−1.60835e6			−0.645073
$363$	−547984.	+	3.10777e6i	−0.218274	+	1.23789i
$364$	468306.	+	392955.i	0.185258	+	0.155450i
$365$	3.59151e6	+	1.30720e6i	1.41106	+	0.513584i
$366$	1.46484e6	−	533159.i	0.571594	−	0.208043i
$367$	−1.44942e6	+	1.21621e6i	−0.561731	+	0.471348i	−0.878890	−	0.477024i	$-0.841715\pi$
$367$	−1.44942e6	+	1.21621e6i	−0.561731	+	0.471348i	0.317159	+	0.948372i	$0.397271\pi$
$368$	210809.	+	365132.i	0.0811464	+	0.140550i
$369$	392983.	−	680667.i	0.150248	−	0.260237i
$370$	−438771.	−	2.48839e6i	−0.166623	−	0.944963i
$371$	−283566.	−	1.60818e6i	−0.106960	−	0.606598i
$372$	996682.	−	1.72630e6i	0.373421	−	0.646785i
$373$	−452418.	−	783611.i	−0.168371	−	0.291627i	0.769476	−	0.638675i	$-0.220517\pi$
$373$	−452418.	−	783611.i	−0.168371	−	0.291627i	−0.937847	+	0.347048i	$0.887184\pi$
$374$	−216076.	+	181310.i	−0.0798782	+	0.0670258i
$375$	−846505.	+	308103.i	−0.310850	+	0.113140i
$376$	−456727.	−	166235.i	−0.166605	−	0.0606392i
$377$	−3.82296e6	−	3.20785e6i	−1.38531	−	1.16241i
$378$	−78690.2	+	446274.i	−0.0283264	+	0.160647i
$379$	2.29403e6			0.820352			0.410176	−	0.912006i	$-0.365467\pi$
$379$	2.29403e6			0.820352			0.410176	+	0.912006i	$0.365467\pi$
$380$	1.39735e6	−	1.53555e6i	0.496417	−	0.545512i
$381$	−2.39038e6			−0.843634
$382$	116398.	−	660123.i	0.0408118	−	0.231455i
$383$	−207144.	−	173815.i	−0.0721567	−	0.0605466i	0.605996	−	0.795468i	$-0.292775\pi$
$383$	−207144.	−	173815.i	−0.0721567	−	0.0605466i	−0.678153	+	0.734921i	$0.737219\pi$
$384$	305703.	+	111267.i	0.105797	+	0.0385068i
$385$	−222007.	+	80804.0i	−0.0763335	+	0.0277831i
$386$	188706.	−	158343.i	0.0644639	−	0.0540916i
$387$	632593.	+	1.09568e6i	0.214708	+	0.371884i
$388$	−1.05100e6	+	1.82038e6i	−0.354423	+	0.613879i
$389$	260072.	+	1.47494e6i	0.0871405	+	0.494198i	0.996874	+	0.0790059i	$0.0251746\pi$
$389$	260072.	+	1.47494e6i	0.0871405	+	0.494198i	−0.909734	+	0.415192i	$0.863714\pi$
$390$	698679.	+	3.96240e6i	0.232603	+	1.31916i
$391$	−1.26062e6	+	2.18345e6i	−0.417005	+	0.722273i
$392$	−414037.	−	717133.i	−0.136089	−	0.235714i
$393$	1.75283e6	−	1.47080e6i	0.572479	−	0.480367i
$394$	−271632.	+	98865.9i	−0.0881536	+	0.0320853i
$395$	−4.23888e6	−	1.54283e6i	−1.36697	−	0.497536i
$396$	−85402.8	−	71661.5i	−0.0273675	−	0.0229640i
$397$	669395.	−	3.79633e6i	0.213160	−	1.20889i	−0.670910	−	0.741539i	$-0.734096\pi$
$397$	669395.	−	3.79633e6i	0.213160	−	1.20889i	0.884070	−	0.467354i	$-0.154793\pi$
$398$	−2.64478e6			−0.836917
$399$	1.18832e6	+	1.53763e6i	0.373681	+	0.483527i
$400$	940841.			0.294013
$401$	1.04365e6	−	5.91882e6i	0.324111	−	1.83812i	−0.191742	−	0.981445i	$-0.561414\pi$
$401$	1.04365e6	−	5.91882e6i	0.324111	−	1.83812i	0.515853	−	0.856677i	$-0.327475\pi$
$402$	3.74190e6	+	3.13983e6i	1.15485	+	0.969038i
$403$	−3.62202e6	−	1.31831e6i	−1.11094	−	0.404347i
$404$	−629437.	+	229096.i	−0.191866	+	0.0698336i
$405$	−4.60672e6	+	3.86550e6i	−1.39558	+	1.17103i
$406$	−1.01052e6	−	1.75027e6i	−0.304250	−	0.526976i
$407$	176432.	−	305589.i	0.0527949	−	0.0914434i
$408$	337815.	+	1.91584e6i	0.100468	+	0.569783i
$409$	669101.	+	3.79466e6i	0.197781	+	1.12167i	0.908403	+	0.418096i	$0.137302\pi$
$409$	669101.	+	3.79466e6i	0.197781	+	1.12167i	−0.710622	+	0.703574i	$0.751587\pi$
$410$	−856948.	+	1.48428e6i	−0.251765	+	0.436069i
$411$	4.12406e6	+	7.14308e6i	1.20426	+	2.08584i
$412$	479491.	−	402341.i	0.139167	−	0.116775i
$413$	−2.99704e6	+	1.09083e6i	−0.864605	+	0.314691i
$414$	−936405.	−	340823.i	−0.268511	−	0.0977301i
$415$	−2.84189e6	−	2.38463e6i	−0.810004	−	0.679674i
$416$	109235.	−	619505.i	0.0309478	−	0.175514i
$417$	−82894.0			−0.0233444
$418$	287324.	−	38836.0i	0.0804325	−	0.0108716i
$419$	3.35885e6			0.934664			0.467332	−	0.884082i	$-0.345215\pi$
$419$	3.35885e6			0.934664			0.467332	+	0.884082i	$0.345215\pi$
$420$	−282948.	+	1.60468e6i	−0.0782678	+	0.443879i
$421$	−3.44633e6	−	2.89181e6i	−0.947657	−	0.795179i	0.0312440	−	0.999512i	$-0.490053\pi$
$421$	−3.44633e6	−	2.89181e6i	−0.947657	−	0.795179i	−0.978901	+	0.204333i	$0.934498\pi$
$422$	1.03803e6	+	377810.i	0.283744	+	0.103274i
$423$	1.07948e6	−	392900.i	0.293336	−	0.106765i
$424$	−1.28723e6	+	1.08011e6i	−0.347729	+	0.291779i
$425$	2.81307e6	+	4.87238e6i	0.755454	+	1.30849i
$426$	−1.87729e6	+	3.25157e6i	−0.501197	+	0.868098i
$427$	−211974.	−	1.20217e6i	−0.0562617	−	0.319076i
$428$	316010.	+	1.79218e6i	0.0833857	+	0.472904i
$429$	−280942.	+	486606.i	−0.0737011	+	0.127654i
$430$	−1.37945e6	−	2.38927e6i	−0.359778	−	0.623153i
$431$	2.38043e6	−	1.99741e6i	0.617250	−	0.517935i	−0.279687	−	0.960091i	$-0.590231\pi$
$431$	2.38043e6	−	1.99741e6i	0.617250	−	0.517935i	0.896938	+	0.442156i	$0.145786\pi$
$432$	438182.	−	159485.i	0.112965	−	0.0411160i
$433$	4.60118e6	+	1.67469e6i	1.17937	+	0.429255i	0.855979	−	0.517011i	$-0.172955\pi$
$433$	4.60118e6	+	1.67469e6i	1.17937	+	0.429255i	0.323389	+	0.946266i	$0.395178\pi$
$434$	−1.19577e6	−	1.00337e6i	−0.304736	−	0.255704i
$435$	2.30981e6	−	1.30996e7i	0.585267	−	3.31921i
$436$	1.27421e6			0.321014
$437$	2.29461e6	−	1.20458e6i	0.574784	−	0.301739i
$438$	3.68117e6			0.916856
$439$	−816103.	+	4.62835e6i	−0.202108	+	1.14621i	0.699818	+	0.714321i	$0.253264\pi$
$439$	−816103.	+	4.62835e6i	−0.202108	+	1.14621i	−0.901926	+	0.431891i	$0.857847\pi$
$440$	186231.	+	156267.i	0.0458587	+	0.0384800i
$441$	1.83914e6	+	669391.i	0.450316	+	0.163902i
$442$	3.53487e6	−	1.28659e6i	0.860632	−	0.313245i
$443$	−2.18434e6	+	1.83288e6i	−0.528825	+	0.443736i	−0.867695	−	0.497096i	$-0.834400\pi$
$443$	−2.18434e6	+	1.83288e6i	−0.528825	+	0.443736i	0.338871	+	0.940833i	$0.389955\pi$
$444$	−1.21684e6	−	2.10762e6i	−0.292938	−	0.507383i
$445$	4.71326e6	−	8.16360e6i	1.12829	−	1.95426i
$446$	238509.	+	1.35265e6i	0.0567763	+	0.321994i
$447$	34639.8	+	196452.i	0.00819986	+	0.0465037i
$448$	127377.	−	220624.i	0.0299845	−	0.0519347i
$449$	−88427.7	−	153161.i	−0.0207001	−	0.0358536i	0.855490	−	0.517820i	$-0.173256\pi$
$449$	−88427.7	−	153161.i	−0.0207001	−	0.0358536i	−0.876190	+	0.481966i	$0.839923\pi$
$450$	−1.70345e6	+	1.42936e6i	−0.396550	+	0.332745i
$451$	−224911.	+	81860.8i	−0.0520677	+	0.0189511i
$452$	−2.31251e6	−	841684.i	−0.532399	−	0.193777i
$453$	7.28230e6	+	6.11058e6i	1.66734	+	1.39906i
$454$	217794.	−	1.23517e6i	0.0495913	−	0.281246i
$455$	3.15076e6			0.713488
$456$	758861.	−	1.85008e6i	0.170903	−	0.416657i
$457$	−2.26578e6			−0.507490			−0.253745	−	0.967271i	$-0.581662\pi$
$457$	−2.26578e6			−0.507490			−0.253745	+	0.967271i	$0.581662\pi$
$458$	904752.	−	5.13110e6i	0.201542	−	1.14300i
$459$	2.13607e6	+	1.79238e6i	0.473244	+	0.397099i
$460$	2.04195e6	+	743207.i	0.449935	+	0.163763i
$461$	−7.33241e6	+	2.66878e6i	−1.60692	+	0.584871i	−0.980828	−	0.194877i	$-0.937569\pi$
$461$	−7.33241e6	+	2.66878e6i	−1.60692	+	0.584871i	−0.626093	+	0.779748i	$0.715347\pi$
$462$	−174313.	+	146266.i	−0.0379949	+	0.0318815i
$463$	−96262.4	−	166731.i	−0.0208691	−	0.0361464i	0.855402	−	0.517964i	$-0.173310\pi$
$463$	−96262.4	−	166731.i	−0.0208691	−	0.0361464i	−0.876271	+	0.481818i	$0.839977\pi$
$464$	−1.03983e6	+	1.80104e6i	−0.224217	+	0.388355i
$465$	−1.78401e6	−	1.01176e7i	−0.382617	−	2.16993i
$466$	−308827.	−	1.75144e6i	−0.0658795	−	0.373621i
$467$	−1.21551e6	+	2.10533e6i	−0.257910	+	0.446713i	−0.965682	−	0.259728i	$-0.916367\pi$
$467$	−1.21551e6	+	2.10533e6i	−0.257910	+	0.446713i	0.707772	+	0.706441i	$0.249700\pi$
$468$	743400.	+	1.28761e6i	0.156894	+	0.271749i
$469$	2.93022e6	−	2.45875e6i	0.615132	−	0.516157i
$470$	−2.35395e6	+	856766.i	−0.491532	+	0.178903i
$471$	568584.	+	206948.i	0.118098	+	0.0429842i
$472$	2.51408e6	+	2.10956e6i	0.519426	+	0.435851i
$473$	66903.0	−	379426.i	0.0137497	−	0.0779783i
$474$	−4.34471e6			−0.888208
$475$	232317.	−	5.77843e6i	0.0472440	−	1.17510i
$476$	1.52341e6			0.308176
$477$	689654.	−	3.91122e6i	0.138783	−	0.787075i
$478$	4.84586e6	+	4.06616e6i	0.970066	+	0.813982i
$479$	−1.57839e6	−	574488.i	−0.314323	−	0.114404i	0.180041	−	0.983659i	$-0.442377\pi$
$479$	−1.57839e6	−	574488.i	−0.314323	−	0.114404i	−0.494364	+	0.869255i	$0.664599\pi$
$480$	1.57558e6	−	573463.i	0.312131	−	0.113606i
$481$	−3.60492e6	+	3.02489e6i	−0.710449	+	0.596137i
$482$	3.02709e6	+	5.24307e6i	0.593482	+	1.02794i
$483$	−1.01696e6	+	1.76143e6i	−0.198352	+	0.343556i
$484$	−441564.	−	2.50423e6i	−0.0856802	−	0.485916i
$485$	1.88123e6	+	1.06690e7i	0.363151	+	2.05953i
$486$	−2.01078e6	+	3.48277e6i	−0.386165	+	0.668858i
$487$	−4.94190e6	−	8.55962e6i	−0.944216	−	1.63543i	−0.757314	−	0.653051i	$-0.773489\pi$
$487$	−4.94190e6	−	8.55962e6i	−0.944216	−	1.63543i	−0.186902	−	0.982379i	$-0.559845\pi$
$488$	−962242.	+	807417.i	−0.182909	+	0.153479i
$489$	4.06778e6	−	1.48055e6i	0.769281	−	0.279996i
$490$	−4.01047e6	−	1.45969e6i	−0.754579	−	0.274644i
$491$	1.16585e6	+	978260.i	0.218241	+	0.183126i	0.745353	−	0.666670i	$-0.232281\pi$
$491$	1.16585e6	+	978260.i	0.218241	+	0.183126i	−0.527112	+	0.849796i	$0.676725\pi$
$492$	−286648.	+	1.62566e6i	−0.0533871	+	0.302773i
$493$	−1.24362e7			−2.30446
$494$	−3.77788e6	−	823870.i	−0.696516	−	0.151894i
$495$	−574590.			−0.105401
$496$	−278922.	+	1.58184e6i	−0.0509071	+	0.288708i
$497$	2.25229e6	+	1.88989e6i	0.409009	+	0.343199i
$498$	−3.35764e6	−	1.22208e6i	−0.606681	−	0.220814i
$499$	−1.81064e6	+	659019.i	−0.325522	+	0.118480i	−0.499612	−	0.866249i	$-0.666524\pi$
$499$	−1.81064e6	+	659019.i	−0.325522	+	0.118480i	0.174089	+	0.984730i	$0.444302\pi$
$500$	556062.	−	466592.i	0.0994715	−	0.0834665i
$501$	539169.	+	933868.i	0.0959689	+	0.166223i
$502$	24602.1	−	42612.1i	0.00435726	−	0.00754699i
$503$	45607.9	+	258655.i	0.00803748	+	0.0455828i	0.988563	−	0.150810i	$-0.0481882\pi$
$503$	45607.9	+	258655.i	0.00803748	+	0.0455828i	−0.980525	+	0.196393i	$0.937077\pi$
$504$	104557.	+	592970.i	0.0183347	+	0.103982i
$505$	−1.72614e6	+	2.98976e6i	−0.301195	+	0.521685i
$506$	151729.	+	262802.i	0.0263446	+	0.0456302i
$507$	92691.0	−	77776.9i	0.0160147	−	0.0134379i
$508$	1.81000e6	−	658785.i	0.311185	−	0.113262i
$509$	8.59192e6	+	3.12720e6i	1.46993	+	0.535010i	0.948081	−	0.318030i	$-0.103021\pi$
$509$	8.59192e6	+	3.12720e6i	1.46993	+	0.535010i	0.521847	+	0.853039i	$0.325243\pi$
$510$	7.68072e6	+	6.44489e6i	1.30760	+	1.09721i
$511$	500570.	−	2.83887e6i	0.0848032	−	0.480943i
$512$	−262144.			−0.0441942
$513$	−871322.	−	2.73059e6i	−0.146179	−	0.458103i
$514$	1.88618e6			0.314902
$515$	560192.	−	3.17700e6i	0.0930719	−	0.527837i
$516$	−2.03556e6	−	1.70804e6i	−0.336558	−	0.282405i
$517$	−328728.	−	119647.i	−0.0540891	−	0.0196868i
$518$	−1.79084e6	+	651812.i	−0.293246	+	0.106733i
$519$	−416611.	+	349578.i	−0.0678910	+	0.0569673i
$520$	−1.62107e6	−	2.80778e6i	−0.262902	−	0.455360i
$521$	−2.44776e6	+	4.23965e6i	−0.395071	+	0.684283i	−0.993110	−	0.117184i	$-0.962613\pi$
$521$	−2.44776e6	+	4.23965e6i	−0.395071	+	0.684283i	0.598039	+	0.801467i	$0.295947\pi$
$522$	−853536.	−	4.84065e6i	−0.137103	−	0.777548i
$523$	10460.9	+	59326.5i	0.00167230	+	0.00948406i	0.985632	−	0.168904i	$-0.0540228\pi$
$523$	10460.9	+	59326.5i	0.00167230	+	0.00948406i	−0.983960	+	0.178388i	$0.942912\pi$
$524$	−921898.	+	1.59677e6i	−0.146674	+	0.254048i
$525$	2.26936e6	+	3.93064e6i	0.359339	+	0.622394i
$526$	5.57404e6	−	4.67718e6i	0.878427	−	0.737088i
$527$	−9.02593e6	+	3.28517e6i	−1.41568	+	0.515266i
$528$	220029.	+	80083.9i	0.0343475	+	0.0125015i
$529$	−2.85269e6	−	2.39369e6i	−0.443216	−	0.371902i
$530$	−1.50387e6	+	8.52890e6i	−0.232553	+	1.31887i
$531$	−7.75683e6			−1.19384
$532$	−1.32357e6	−	836799.i	−0.202753	−	0.128186i
$533$	3.19197e6			0.486676
$534$	1.57658e6	−	8.94123e6i	0.239256	−	1.35689i
$535$	7.18496e6	+	6.02890e6i	1.08528	+	0.910654i
$536$	−3.69871e6	−	1.34622e6i	−0.556081	−	0.202397i
$537$	−1.16077e7	+	4.22485e6i	−1.73704	+	0.632231i
$538$	3.00610e6	−	2.52242e6i	0.447763	−	0.375718i
$539$	−298002.	−	516154.i	−0.0441822	−	0.0765257i
$540$	1.20165e6	−	2.08132e6i	0.177335	−	0.307153i
$541$	−272123.	−	1.54329e6i	−0.0399735	−	0.226701i	0.958276	−	0.285845i	$-0.0922742\pi$
$541$	−272123.	−	1.54329e6i	−0.0399735	−	0.226701i	−0.998249	+	0.0591435i	$0.981163\pi$
$542$	9965.37	+	56516.4i	0.00145712	+	0.00826374i
$543$	−3.99194e6	+	6.91425e6i	−0.581012	+	1.00634i
$544$	−783798.	−	1.35758e6i	−0.113555	−	0.196683i
$545$	5.03076e6	−	4.22131e6i	0.725508	−	0.608774i
$546$	2.85165e6	−	1.03791e6i	0.409368	−	0.148998i
$547$	4.93857e6	+	1.79749e6i	0.705721	+	0.256861i	0.669852	−	0.742495i	$-0.266358\pi$
$547$	4.93857e6	+	1.79749e6i	0.705721	+	0.256861i	0.0358694	+	0.999356i	$0.488580\pi$
$548$	−5.09137e6	−	4.27217e6i	−0.724242	−	0.607711i
$549$	515537.	−	2.92375e6i	0.0730010	−	0.414009i
$550$	677167.			0.0954529
$551$	1.08048e7	+	6.83112e6i	1.51614	+	0.958546i
$552$	2.09292e6			0.292351
$553$	−590797.	+	3.35058e6i	−0.0821534	+	0.465915i
$554$	−6.42598e6	−	5.39204e6i	−0.889539	−	0.746412i
$555$	−1.17866e7	−	4.28996e6i	−1.62426	−	0.591182i
$556$	62767.5	−	22845.5i	0.00861088	−	0.00313410i
$557$	9.48141e6	−	7.95585e6i	1.29490	−	1.08655i	0.303894	−	0.952706i	$-0.401713\pi$
$557$	9.48141e6	−	7.95585e6i	1.29490	−	1.08655i	0.991003	−	0.133841i	$-0.0427313\pi$
$558$	−1.89820e6	−	3.28777e6i	−0.258081	−	0.447009i
$559$	−2.56909e6	+	4.44979e6i	−0.347736	+	0.602296i
$560$	−227998.	−	1.29304e6i	−0.0307229	−	0.174238i
$561$	243141.	+	1.37892e6i	0.0326175	+	0.184983i
$562$	−3.06394e6	+	5.30691e6i	−0.409204	+	0.708762i
$563$	−293820.	−	508912.i	−0.0390671	−	0.0676662i	0.845831	−	0.533451i	$-0.179105\pi$
$563$	−293820.	−	508912.i	−0.0390671	−	0.0676662i	−0.884898	+	0.465785i	$0.845772\pi$
$564$	−1.84824e6	+	1.55086e6i	−0.244659	+	0.205293i
$565$	−1.19185e7	+	4.33799e6i	−1.57073	+	0.571699i
$566$	−4.52978e6	−	1.64870e6i	−0.594341	−	0.216322i
$567$	3.47452e6	+	2.91546e6i	0.453875	+	0.380847i
$568$	525361.	−	2.97947e6i	0.0683262	−	0.387497i
$569$	6.31516e6			0.817718			0.408859	−	0.912598i	$-0.365927\pi$
$569$	6.31516e6			0.817718			0.408859	+	0.912598i	$0.365927\pi$
$570$	−3.13303e6	−	9.81843e6i	−0.403903	−	1.26577i
$571$	9.16749e6			1.17668			0.588342	−	0.808612i	$-0.299781\pi$
$571$	9.16749e6			1.17668			0.588342	+	0.808612i	$0.299781\pi$
$572$	78621.8	−	445886.i	0.0100474	−	0.0569815i
$573$	−2.54895e6	−	2.13883e6i	−0.324321	−	0.272138i
$574$	1.21471e6	+	442118.i	0.153884	+	0.0560091i
$575$	5.68776e6	−	2.07017e6i	0.717416	−	0.261118i
$576$	474627.	−	398260.i	0.0596069	−	0.0500161i
$577$	3.10147e6	+	5.37190e6i	0.387818	+	0.671720i	0.992156	−	0.125008i	$-0.0398957\pi$
$577$	3.10147e6	+	5.37190e6i	0.387818	+	0.671720i	−0.604338	+	0.796728i	$0.706562\pi$
$578$	1.84732e6	−	3.19965e6i	0.229997	−	0.398367i
$579$	−212342.	−	1.20425e6i	−0.0263232	−	0.149286i
$580$	1.86124e6	+	1.05556e7i	0.229738	+	1.30291i
$581$	−1.39903e6	+	2.42319e6i	−0.171943	+	0.297815i
$582$	5.21718e6	+	9.03642e6i	0.638452	+	1.10583i
$583$	−926478.	+	777408.i	−0.112892	+	0.0947278i
$584$	−2.78739e6	+	1.01453e6i	−0.338194	+	0.123092i
$585$	7.20075e6	+	2.62086e6i	0.869938	+	0.316631i
$586$	1.75039e6	+	1.46875e6i	0.210567	+	0.176686i
$587$	2.41915e6	−	1.37197e7i	0.289779	−	1.64342i	−0.397917	−	0.917421i	$-0.630267\pi$
$587$	2.41915e6	−	1.37197e7i	0.289779	−	1.64342i	0.687697	−	0.725998i	$-0.258622\pi$
$588$	−4.11058e6			−0.490298
$589$	9.64644e6	+	2.10367e6i	1.14572	+	0.249856i
$590$	1.69147e7			2.00048
$591$	−249172.	+	1.41312e6i	−0.0293448	+	0.166422i
$592$	1.50225e6	+	1.26054e6i	0.176172	+	0.147826i
$593$	−4.75341e6	−	1.73010e6i	−0.555097	−	0.202039i	0.0492128	−	0.998788i	$-0.484329\pi$
$593$	−4.75341e6	−	1.73010e6i	−0.555097	−	0.202039i	−0.604310	+	0.796750i	$0.706551\pi$
$594$	315380.	−	114789.i	0.0366748	−	0.0133485i
$595$	6.01464e6	−	5.04688e6i	0.696494	−	0.584428i
$596$	−80371.3	−	139207.i	−0.00926798	−	0.0160526i
$597$	−6.56439e6	+	1.13698e7i	−0.753804	+	1.30563i
$598$	−702752.	−	3.98551e6i	−0.0803617	−	0.455754i
$599$	−2.48336e6	−	1.40838e7i	−0.282795	−	1.60381i	−0.713057	−	0.701106i	$-0.752690\pi$
$599$	−2.48336e6	−	1.40838e7i	−0.282795	−	1.60381i	0.430262	−	0.902704i	$-0.358421\pi$
$600$	2.33518e6	−	4.04465e6i	0.264815	−	0.458673i
$601$	2.15122e6	+	3.72602e6i	0.242940	+	0.420784i	0.961550	−	0.274629i	$-0.0885549\pi$
$601$	2.15122e6	+	3.72602e6i	0.242940	+	0.420784i	−0.718611	+	0.695413i	$0.755222\pi$
$602$	−1.59401e6	+	1.33754e6i	−0.179267	+	0.150423i
$603$	8.74196e6	−	3.18181e6i	0.979074	−	0.356354i
$604$	−7.19824e6	−	2.61994e6i	−0.802849	−	0.292213i
$605$	−1.00396e7	−	8.42424e6i	−1.11514	−	0.935712i
$606$	−577392.	+	3.27455e6i	−0.0638689	+	0.362218i
$607$	4.42774e6			0.487764			0.243882	−	0.969805i	$-0.421579\pi$
$607$	4.42774e6			0.487764			0.243882	+	0.969805i	$0.421579\pi$
$608$	−64729.8	+	1.61003e6i	−0.00710143	+	0.176634i
$609$	−1.00325e7			−1.09614
$610$	−1.12419e6	+	6.37561e6i	−0.122325	+	0.693740i
$611$	3.57387e6	+	2.99883e6i	0.387289	+	0.324974i
$612$	3.48160e6	+	1.26720e6i	0.375751	+	0.136762i
$613$	−1.13452e6	+	412930.i	−0.121944	+	0.0443839i	−0.402271	−	0.915521i	$-0.631779\pi$
$613$	−1.13452e6	+	412930.i	−0.121944	+	0.0443839i	0.280328	+	0.959904i	$0.409557\pi$
$614$	134868.	−	113168.i	0.0144374	−	0.0121144i
$615$	4.25391e6	+	7.36799e6i	0.453525	+	0.785528i
$616$	91679.4	−	158793.i	0.00973464	−	0.0168609i
$617$	−2.17035e6	−	1.23087e7i	−0.229518	−	1.30166i	−0.853856	−	0.520509i	$-0.825742\pi$
$617$	−2.17035e6	−	1.23087e7i	−0.229518	−	1.30166i	0.624338	−	0.781154i	$-0.285369\pi$
$618$	−539549.	−	3.05994e6i	−0.0568277	−	0.322286i
$619$	4.27444e6	−	7.40355e6i	0.448387	−	0.776629i	−0.549894	−	0.835234i	$-0.685332\pi$
$619$	4.27444e6	−	7.40355e6i	0.448387	−	0.776629i	0.998281	+	0.0586054i	$0.0186654\pi$
$620$	4.13925e6	+	7.16939e6i	0.432457	+	0.749037i
$621$	2.29806e6	−	1.92830e6i	0.239129	−	0.200653i
$622$	7.99098e6	−	2.90848e6i	0.828179	−	0.301433i
$623$	−6.68097e6	−	2.43167e6i	−0.689635	−	0.251007i
$624$	−2.39211e6	−	2.00722e6i	−0.245935	−	0.206364i
$625$	−1.34468e6	+	7.62605e6i	−0.137695	+	0.780908i
$626$	−2.30647e6			−0.235240
$627$	546187.	−	1.33159e6i	0.0554846	−	0.135270i
$628$	−487568.			−0.0493328
$629$	−2.03635e6	+	1.15487e7i	−0.205223	+	1.16388i
$630$	2.37725e6	+	1.99475e6i	0.238629	+	0.200234i
$631$	−1.08961e6	−	396585.i	−0.108942	−	0.0396518i	0.286974	−	0.957938i	$-0.407351\pi$
$631$	−1.08961e6	−	396585.i	−0.108942	−	0.0396518i	−0.395916	+	0.918287i	$0.629573\pi$
$632$	3.28982e6	−	1.19740e6i	0.327627	−	0.119246i
$633$	4.20059e6	−	3.52471e6i	0.416678	−	0.349635i
$634$	1.78110e6	+	3.08496e6i	0.175981	+	0.304808i
$635$	4.96366e6	−	8.59730e6i	0.488503	−	0.846112i
$636$	1.44846e6	+	8.21462e6i	0.141992	+	0.805276i
$637$	1.38023e6	+	7.82770e6i	0.134773	+	0.764338i
$638$	−748415.	+	1.29629e6i	−0.0727932	+	0.126081i
$639$	3.57534e6	+	6.19266e6i	0.346390	+	0.599964i
$640$	−1.03498e6	+	868454.i	−0.0998812	+	0.0838102i
$641$	5.63000e6	−	2.04915e6i	0.541207	−	0.196983i	−0.0569283	−	0.998378i	$-0.518131\pi$
$641$	5.63000e6	−	2.04915e6i	0.541207	−	0.196983i	0.598136	+	0.801395i	$0.295908\pi$
$642$	8.48889e6	+	3.08970e6i	0.812855	+	0.295855i
$643$	−8.08176e6	−	6.78140e6i	−0.770865	−	0.646833i	0.170065	−	0.985433i	$-0.445602\pi$
$643$	−8.08176e6	−	6.78140e6i	−0.770865	−	0.646833i	−0.940930	+	0.338600i	$0.890047\pi$
$644$	284598.	−	1.61403e6i	0.0270406	−	0.153355i
$645$	−1.36952e7			−1.29619
$646$	−8.53146e6	+	4.47868e6i	−0.804345	+	0.422249i
$647$	−3.26509e6			−0.306644			−0.153322	−	0.988176i	$-0.548997\pi$
$647$	−3.26509e6			−0.306644			−0.153322	+	0.988176i	$0.548997\pi$
$648$	810454.	−	4.59631e6i	0.0758212	−	0.430004i
$649$	1.80950e6	+	1.51835e6i	0.168635	+	0.141501i
$650$	−8.48624e6	−	3.08874e6i	−0.787829	−	0.286746i
$651$	−7.28139e6	+	2.65021e6i	−0.673383	+	0.245091i
$652$	−2.67209e6	+	2.24215e6i	−0.246168	+	0.206560i
$653$	−1.06385e6	−	1.84264e6i	−0.0976329	−	0.169105i	0.813072	−	0.582164i	$-0.197794\pi$
$653$	−1.06385e6	−	1.84264e6i	−0.0976329	−	0.169105i	−0.910704	+	0.413059i	$0.864460\pi$
$654$	3.16260e6	−	5.47778e6i	0.289134	−	0.500796i
$655$	1.65015e6	+	9.35845e6i	0.150286	+	0.852316i
$656$	−230980.	−	1.30995e6i	−0.0209563	−	0.118849i
$657$	3.50543e6	−	6.07158e6i	0.316831	−	0.548767i
$658$	944677.	+	1.63623e6i	0.0850587	+	0.147326i
$659$	−5.03649e6	+	4.22612e6i	−0.451767	+	0.379077i	−0.840091	−	0.542445i	$-0.817499\pi$
$659$	−5.03649e6	+	4.22612e6i	−0.451767	+	0.379077i	0.388324	+	0.921523i	$0.373054\pi$
$660$	1.13402e6	−	412748.i	0.101335	−	0.0368829i
$661$	−7.87859e6	−	2.86757e6i	−0.701366	−	0.255276i	−0.0333722	−	0.999443i	$-0.510625\pi$
$661$	−7.87859e6	−	2.86757e6i	−0.701366	−	0.255276i	−0.667994	+	0.744166i	$0.732847\pi$
$662$	1.58418e6	+	1.32928e6i	0.140494	+	0.117889i
$663$	3.24259e6	−	1.83896e7i	0.286489	−	1.62476i
$664$	2.87921e6			0.253427
$665$	−7.99787e6	+	1.08103e6i	−0.701327	+	0.0947945i
$666$	−4.63497e6			−0.404913
$667$	−2.32328e6	+	1.31760e7i	−0.202203	+	1.14675i
$668$	−665632.	−	558532.i	−0.0577156	−	0.0484291i
$669$	6.40699e6	+	2.33195e6i	0.553463	+	0.201444i
$670$	−1.90629e7	+	6.93834e6i	−1.64060	+	0.597129i
$671$	−692570.	+	581136.i	−0.0593824	+	0.0498277i
$672$	−632305.	−	1.09518e6i	−0.0540136	−	0.0935543i
$673$	2.20692e6	−	3.82249e6i	0.187823	−	0.325319i	−0.756701	−	0.653761i	$-0.773190\pi$
$673$	2.20692e6	−	3.82249e6i	0.187823	−	0.325319i	0.944524	+	0.328442i	$0.106524\pi$
$674$	2.34954e6	+	1.33249e7i	0.199220	+	1.12983i
$675$	−1.16245e6	−	6.59259e6i	−0.0982009	−	0.556925i
$676$	−48750.5	+	84438.4i	−0.00410310	+	0.00710678i
$677$	4.56820e6	+	7.91236e6i	0.383066	+	0.663490i	0.991499	−	0.130115i	$-0.0415348\pi$
$677$	4.56820e6	+	7.91236e6i	0.383066	+	0.663490i	−0.608433	+	0.793606i	$0.708201\pi$
$678$	−9.35806e6	+	7.85234e6i	−0.781829	+	0.656032i
$679$	7.67820e6	−	2.79464e6i	0.639124	−	0.232622i
$680$	−7.59206e6	−	2.76328e6i	−0.629633	−	0.229168i
$681$	−4.76940e6	−	4.00200e6i	−0.394090	−	0.330681i
$682$	−200753.	+	1.13853e6i	−0.0165273	+	0.0937308i
$683$	−1.36162e7			−1.11687			−0.558437	−	0.829547i	$-0.688599\pi$
$683$	−1.36162e7			−1.11687			−0.558437	+	0.829547i	$0.688599\pi$
$684$	−2.32882e6	−	3.01339e6i	−0.190325	−	0.246272i
$685$	−3.42547e7			−2.78929
$686$	−1.28504e6	+	7.28781e6i	−0.104257	+	0.591272i
$687$	−1.98129e7	−	1.66250e7i	−1.60161	−	1.34391i
$688$	2.01206e6	+	732331.i	0.162058	+	0.0589843i
$689$	1.51566e7	−	5.51654e6i	1.21633	−	0.442709i
$690$	8.26317e6	−	6.93362e6i	0.660730	−	0.554418i
$691$	8.24663e6	+	1.42836e7i	0.657024	+	1.13800i	0.981382	+	0.192065i	$0.0615185\pi$
$691$	8.24663e6	+	1.42836e7i	0.657024	+	1.13800i	−0.324358	+	0.945934i	$0.605148\pi$
$692$	219115.	−	379519.i	0.0173943	−	0.0301278i
$693$	75254.2	+	426788.i	0.00595248	+	0.0337582i
$694$	−1.98304e6	−	1.12464e7i	−0.156290	−	0.886367i
$695$	172131.	−	298139.i	0.0135175	−	0.0234130i
$696$	5.16175e6	+	8.94041e6i	0.403900	+	0.699575i
$697$	6.09330e6	−	5.11289e6i	0.475085	−	0.398643i
$698$	−1.91947e6	+	698631.i	−0.149123	+	0.0542762i
$699$	−8.29592e6	−	3.01947e6i	−0.642202	−	0.233742i
$700$	−2.80164e6	−	2.35086e6i	−0.216106	−	0.181335i
$701$	1.10665e6	−	6.27614e6i	0.0850582	−	0.482389i	−0.912286	−	0.409554i	$-0.865684\pi$
$701$	1.10665e6	−	6.27614e6i	0.0850582	−	0.482389i	0.997344	−	0.0728349i	$-0.0232046\pi$
$702$	−4.47591e6			−0.342799
$703$	8.11287e6	−	8.91521e6i	0.619136	−	0.680367i
$704$	−188677.			−0.0143479
$705$	−2.15931e6	+	1.22461e7i	−0.163622	+	0.927948i
$706$	9.29432e6	+	7.79886e6i	0.701788	+	0.588870i
$707$	2.44678e6	+	890554.i	0.184097	+	0.0670057i
$708$	1.53089e7	−	5.57200e6i	1.14779	−	0.417761i
$709$	1.41440e7	−	1.18682e7i	1.05671	−	0.886684i	0.0629262	−	0.998018i	$-0.479957\pi$
$709$	1.41440e7	−	1.18682e7i	1.05671	−	0.886684i	0.993783	+	0.111334i	$0.0355123\pi$
$710$	−7.79646e6	−	1.35039e7i	−0.580432	−	1.00534i
$711$	−4.13728e6	+	7.16598e6i	−0.306931	+	0.531620i
$712$	1.27040e6	+	7.20482e6i	0.0939164	+	0.532627i
$713$	1.79441e6	+	1.01766e7i	0.132190	+	0.749685i
$714$	3.78112e6	−	6.54909e6i	0.277572	−	0.480768i
$715$	−1.16676e6	−	2.02089e6i	−0.0853527	−	0.147835i
$716$	7.62499e6	−	6.39813e6i	0.555849	−	0.466413i
$717$	2.95078e7	−	1.07400e7i	2.14358	−	0.780198i
$718$	−1.02268e7	−	3.72224e6i	−0.740334	−	0.269459i
$719$	−1.06003e7	−	8.89475e6i	−0.764712	−	0.641669i	0.174637	−	0.984633i	$-0.444125\pi$
$719$	−1.06003e7	−	8.89475e6i	−0.764712	−	0.641669i	−0.939349	+	0.342963i	$0.888569\pi$
$720$	554509.	−	3.14478e6i	0.0398637	−	0.226078i
$721$	−2.43315e6			−0.174313
$722$	9.87243e6	+	795111.i	0.704825	+	0.0567656i
$723$	3.00531e7			2.13818
$724$	1.11715e6	−	6.33566e6i	0.0792071	−	0.449206i
$725$	2.28709e7	+	1.91910e7i	1.61599	+	1.35598i
$726$	−1.18616e7	−	4.31727e6i	−0.835222	−	0.303996i
$727$	2.01216e7	−	7.32366e6i	1.41197	−	0.513916i	0.480264	−	0.877124i	$-0.340541\pi$
$727$	2.01216e7	−	7.32366e6i	1.41197	−	0.513916i	0.931708	+	0.363208i	$0.118319\pi$
$728$	−1.87322e6	+	1.57182e6i	−0.130997	+	0.109919i
$729$	1.12114e6	+	1.94186e6i	0.0781338	+	0.135332i
$730$	−7.64402e6	+	1.32398e7i	−0.530902	+	0.919549i
$731$	2.22341e6	+	1.26096e7i	0.153896	+	0.872786i
$732$	1.08277e6	+	6.14068e6i	0.0746891	+	0.423583i
$733$	−5.62123e6	+	9.73626e6i	−0.386431	+	0.669317i	−0.991967	−	0.126501i	$-0.959625\pi$
$733$	−5.62123e6	+	9.73626e6i	−0.386431	+	0.669317i	0.605536	+	0.795818i	$0.292959\pi$
$734$	−3.78416e6	−	6.55436e6i	−0.259256	−	0.449045i
$735$	−1.62292e7	+	1.36179e7i	−1.10810	+	0.929806i
$736$	−1.58476e6	+	576807.i	−0.107838	+	0.0392497i
$737$	−2.66213e6	−	968936.i	−0.180535	−	0.0657092i
$738$	2.40834e6	+	2.02084e6i	0.162771	+	0.136581i
$739$	−3.04145e6	+	1.72489e7i	−0.204866	+	1.16185i	0.692784	+	0.721145i	$0.256384\pi$
$739$	−3.04145e6	+	1.72489e7i	−0.204866	+	1.16185i	−0.897650	+	0.440709i	$0.854727\pi$
$740$	1.01071e7			0.678498
$741$	−1.29186e7	+	1.41962e7i	−0.864307	+	0.949785i
$742$	6.53197e6			0.435546
$743$	2.20293e6	−	1.24935e7i	0.146396	−	0.830253i	−0.819840	−	0.572593i	$-0.805937\pi$
$743$	2.20293e6	−	1.24935e7i	0.146396	−	0.830253i	0.966236	−	0.257660i	$-0.0829515\pi$
$744$	6.10802e6	+	5.12524e6i	0.404546	+	0.339454i
$745$	−778496.	−	283349.i	−0.0513885	−	0.0187039i
$746$	3.40107e6	−	1.23789e6i	0.223753	−	0.0814393i
$747$	−5.21299e6	+	4.37422e6i	−0.341810	+	0.286813i
$748$	−564136.	−	977112.i	−0.0368663	−	0.0638543i
$749$	3.53706e6	−	6.12638e6i	0.230377	−	0.399024i
$750$	−625711.	−	3.54858e6i	−0.0406182	−	0.230357i
$751$	1.04161e6	+	5.90729e6i	0.0673918	+	0.382198i	0.999785	+	0.0207515i	$0.00660589\pi$
$751$	1.04161e6	+	5.90729e6i	0.0673918	+	0.382198i	−0.932393	+	0.361447i	$0.882283\pi$
$752$	972078.	−	1.68369e6i	0.0626840	−	0.108572i
$753$	−122126.	−	211528.i	−0.00784909	−	0.0135950i
$754$	1.52919e7	−	1.28314e7i	0.979562	−	0.821950i
$755$	−3.70993e7	+	1.35030e7i	−2.36864	+	0.862113i
$756$	−1.70332e6	−	619958.i	−0.108391	−	0.0394510i
$757$	−1.42437e7	−	1.19519e7i	−0.903405	−	0.758046i	0.0674482	−	0.997723i	$-0.478514\pi$
$757$	−1.42437e7	−	1.19519e7i	−0.903405	−	0.758046i	−0.970853	+	0.239676i	$0.922959\pi$
$758$	−1.59341e6	+	9.03670e6i	−0.100729	+	0.571264i
$759$	1.50637e6			0.0949135
$760$	5.07828e6	+	6.57107e6i	0.318921	+	0.412669i
$761$	−6.40685e6			−0.401036			−0.200518	−	0.979690i	$-0.564262\pi$
$761$	−6.40685e6			−0.401036			−0.200518	+	0.979690i	$0.564262\pi$
$762$	1.66034e6	−	9.41624e6i	0.103588	−	0.587476i
$763$	−3.79434e6	−	3.18383e6i	−0.235953	−	0.197988i
$764$	2.51953e6	+	917034.i	0.156166	+	0.0568397i
$765$	1.79440e7	−	6.53107e6i	1.10857	−	0.403488i
$766$	828578.	−	695259.i	0.0510225	−	0.0428129i
$767$	−1.57510e7	−	2.72816e7i	−0.966763	−	1.67448i
$768$	−650645.	+	1.12695e6i	−0.0398053	+	0.0689448i
$769$	3.36785e6	+	1.91000e7i	0.205370	+	1.16471i	0.896856	+	0.442322i	$0.145845\pi$
$769$	3.36785e6	+	1.91000e7i	0.205370	+	1.16471i	−0.691486	+	0.722390i	$0.743044\pi$
$770$	−164101.	−	930663.i	−0.00997435	−	0.0565673i
$771$	4.68153e6	−	8.10865e6i	0.283630	−	0.491261i
$772$	492675.	+	853339.i	0.0297521	+	0.0515321i
$773$	8.53151e6	−	7.15879e6i	0.513543	−	0.430914i	−0.348831	−	0.937186i	$-0.613421\pi$
$773$	8.53151e6	−	7.15879e6i	0.513543	−	0.430914i	0.862374	+	0.506272i	$0.168977\pi$
$774$	−4.75555e6	+	1.73088e6i	−0.285330	+	0.103852i
$775$	2.16688e7	+	7.88679e6i	1.29593	+	0.471678i
$776$	−6.44088e6	−	5.40454e6i	−0.383965	−	0.322185i
$777$	−1.64276e6	+	9.31657e6i	−0.0976163	+	0.553609i
$778$	−5.99078e6			−0.354842
$779$	−8.10247e6	+	1.09517e6i	−0.478381	+	0.0646602i
$780$	−1.60941e7			−0.947176
$781$	378127.	−	2.14446e6i	0.0221825	−	0.125803i
$782$	−7.72550e6	−	6.48247e6i	−0.451762	−	0.379074i
$783$	1.39049e7	+	5.06096e6i	0.810518	+	0.295004i
$784$	3.11254e6	−	1.13287e6i	0.180853	−	0.0658250i
$785$	−1.92499e6	+	1.61526e6i	−0.111495	+	0.0935552i
$786$	4.57633e6	+	7.92643e6i	0.264217	+	0.457637i
$787$	6.64945e6	−	1.15172e7i	0.382692	−	0.662841i	−0.608754	−	0.793359i	$-0.708331\pi$
$787$	6.64945e6	−	1.15172e7i	0.382692	−	0.662841i	0.991446	+	0.130517i	$0.0416638\pi$
$788$	−200782.	−	1.13869e6i	−0.0115189	−	0.0653267i
$789$	−6.27221e6	−	3.55715e7i	−0.358697	−	2.03427i
$790$	9.02185e6	−	1.56263e7i	0.514314	−	0.890817i
$791$	4.78310e6	+	8.28458e6i	0.271812	+	0.470792i
$792$	341611.	−	286646.i	0.0193517	−	0.0162380i
$793$	1.13300e7	−	4.12378e6i	0.639804	−	0.232869i
$794$	1.44897e7	+	5.27381e6i	0.815656	+	0.296874i
$795$	3.29329e7	+	2.76340e7i	1.84804	+	1.55069i
$796$	1.83705e6	−	1.04184e7i	0.102763	−	0.582799i
$797$	2.09776e7			1.16979			0.584897	−	0.811108i	$-0.301135\pi$
$797$	2.09776e7			1.16979			0.584897	+	0.811108i	$0.301135\pi$
$798$	−6.88249e6	+	3.61304e6i	−0.382594	+	0.200847i
$799$	1.16259e7			0.644256
$800$	−653501.	+	3.70619e6i	−0.0361012	+	0.204740i
$801$	−1.32460e7	−	1.11147e7i	−0.729463	−	0.612092i
$802$	2.25907e7	+	8.22234e6i	1.24021	+	0.451398i
$803$	−2.00621e6	+	730202.i	−0.109796	+	0.0399626i
$804$	−1.49676e7	+	1.25593e7i	−0.816605	+	0.685213i
$805$	−4.22348e6	−	7.31528e6i	−0.229710	−	0.397870i
$806$	7.70896e6	−	1.33523e7i	0.417982	−	0.723967i
$807$	−3.38263e6	−	1.91838e7i	−0.182840	−	1.03694i
$808$	−465261.	−	2.63863e6i	−0.0250708	−	0.142184i
$809$	−1.32196e7	+	2.28970e7i	−0.710145	+	1.23001i	0.254657	+	0.967031i	$0.418037\pi$
$809$	−1.32196e7	+	2.28970e7i	−0.710145	+	1.23001i	−0.964802	+	0.262976i	$0.915296\pi$
$810$	−1.20273e7	−	2.08319e7i	−0.644103	−	1.11562i
$811$	−1.44518e7	+	1.21265e7i	−0.771563	+	0.647418i	−0.941109	−	0.338104i	$-0.890214\pi$
$811$	−1.44518e7	+	1.21265e7i	−0.771563	+	0.647418i	0.169546	+	0.985522i	$0.445770\pi$
$812$	7.59663e6	−	2.76495e6i	0.404325	−	0.147162i
$813$	267697.	+	97433.7i	0.0142042	+	0.00516991i
$814$	1.08124e6	+	907267.i	0.0571953	+	0.0479926i
$815$	−3.12181e6	+	1.77047e7i	−0.164632	+	0.933672i
$816$	−7.78159e6			−0.409113
$817$	4.99463e6	−	1.21768e7i	0.261787	−	0.638231i
$818$	−1.54128e7			−0.805375
$819$	1.00361e6	−	5.69175e6i	0.0522823	−	0.296508i
$820$	−5.25168e6	−	4.40668e6i	−0.272749	−	0.228864i
$821$	−1.97833e6	−	720053.i	−0.102433	−	0.0372826i	0.290295	−	0.956937i	$-0.406247\pi$
$821$	−1.97833e6	−	720053.i	−0.102433	−	0.0372826i	−0.392728	+	0.919655i	$0.628469\pi$
$822$	−3.10028e7	+	1.12841e7i	−1.60037	+	0.582488i
$823$	−8.28138e6	+	6.94890e6i	−0.426190	+	0.357616i	−0.830512	−	0.557001i	$-0.811952\pi$
$823$	−8.28138e6	+	6.94890e6i	−0.426190	+	0.357616i	0.404322	+	0.914617i	$0.367508\pi$
$824$	1.25186e6	+	2.16829e6i	0.0642301	+	0.111250i
$825$	1.68074e6	−	2.91112e6i	0.0859736	−	0.148911i
$826$	−2.21533e6	−	1.25637e7i	−0.112976	−	0.640720i
$827$	−2.34700e6	−	1.33105e7i	−0.119330	−	0.676753i	−0.984515	−	0.175300i	$-0.943910\pi$
$827$	−2.34700e6	−	1.33105e7i	−0.119330	−	0.676753i	0.865185	−	0.501453i	$-0.167201\pi$
$828$	1.99300e6	−	3.45198e6i	0.101026	−	0.174982i
$829$	−7.91112e6	−	1.37025e7i	−0.399808	−	0.692488i	0.593894	−	0.804543i	$-0.297590\pi$
$829$	−7.91112e6	−	1.37025e7i	−0.399808	−	0.692488i	−0.993702	+	0.112055i	$0.964257\pi$
$830$	1.13676e7	−	9.53852e6i	0.572759	−	0.480602i
$831$	−3.91296e7	+	1.42420e7i	−1.96563	+	0.715433i
$832$	2.36450e6	+	860607.i	0.118422	+	0.0431019i
$833$	1.51732e7	+	1.27318e7i	0.757644	+	0.635738i
$834$	57577.6	−	326539.i	0.00286641	−	0.0162562i
$835$	−4.47837e6			−0.222282
$836$	−46589.1	+	1.15881e6i	−0.00230552	+	0.0573452i
$837$	1.14288e7			0.563880
$838$	−2.33303e6	+	1.32313e7i	−0.114765	+	0.650866i
$839$	−1.94290e7	−	1.63029e7i	−0.952898	−	0.799577i	0.0268849	−	0.999639i	$-0.491441\pi$
$839$	−1.94290e7	−	1.63029e7i	−0.952898	−	0.799577i	−0.979783	+	0.200062i	$0.935886\pi$
$840$	−6.12466e6	−	2.22919e6i	−0.299491	−	0.109006i
$841$	−4.27401e7	+	1.55561e7i	−2.08375	+	0.758422i
$842$	1.37853e7	−	1.15673e7i	0.670095	−	0.562277i
$843$	1.52095e7	+	2.63436e7i	0.737134	+	1.27675i
$844$	−2.20929e6	+	3.82660e6i	−0.106757	+	0.184908i
$845$	87260.8	+	494880.i	0.00420414	+	0.0238429i
$846$	797922.	+	4.52524e6i	0.0383296	+	0.217378i
$847$	−4.94237e6	+	8.56044e6i	−0.236716	+	0.410004i
$848$	−3.36072e6	−	5.82093e6i	−0.160488	−	0.277973i
$849$	−1.83307e7	+	1.53813e7i	−0.872790	+	0.732358i
$850$	−2.11474e7	+	7.69701e6i	−1.00394	+	0.365405i
$851$	1.18553e7	+	4.31498e6i	0.561163	+	0.204247i
$852$	−1.15047e7	−	9.65361e6i	−0.542972	−	0.455607i
$853$	−4.99387e6	+	2.83216e7i	−0.234998	+	1.33274i	0.607619	+	0.794228i	$0.292125\pi$
$853$	−4.99387e6	+	2.83216e7i	−0.234998	+	1.33274i	−0.842618	+	0.538512i	$0.818986\pi$
$854$	4.88284e6			0.229102
$855$	−1.91776e7	−	4.18219e6i	−0.897177	−	0.195654i
$856$	−7.27932e6			−0.339552
$857$	−1.58795e6	+	9.00570e6i	−0.0738558	+	0.418857i	0.925354	+	0.379105i	$0.123768\pi$
$857$	−1.58795e6	+	9.00570e6i	−0.0738558	+	0.418857i	−0.999210	+	0.0397522i	$0.987343\pi$
$858$	−1.72171e6	−	1.44469e6i	−0.0798441	−	0.0669971i
$859$	3.39161e7	+	1.23445e7i	1.56828	+	0.570807i	0.972614	−	0.232425i	$-0.0746661\pi$
$859$	3.39161e7	+	1.23445e7i	1.56828	+	0.570807i	0.595666	+	0.803232i	$0.296888\pi$
$860$	1.03701e7	−	3.77439e6i	0.478118	−	0.174021i
$861$	4.91558e6	−	4.12466e6i	0.225979	−	0.189619i
$862$	6.21485e6	+	1.07644e7i	0.284880	+	0.493427i
$863$	−1.85522e7	+	3.21334e7i	−0.847949	+	1.46869i	0.0350870	+	0.999384i	$0.488829\pi$
$863$	−1.85522e7	+	3.21334e7i	−0.847949	+	1.46869i	−0.883036	+	0.469306i	$0.844504\pi$
$864$	323891.	+	1.83688e6i	0.0147609	+	0.0837135i
$865$	−392204.	−	2.22430e6i	−0.0178226	−	0.101077i
$866$	−9.79294e6	+	1.69619e7i	−0.443730	+	0.768562i
$867$	−9.17015e6	−	1.58832e7i	−0.414313	−	0.717612i
$868$	4.78309e6	−	4.01349e6i	0.215481	−	0.180810i
$869$	2.36783e6	−	861821.i	0.106366	−	0.0387140i
$870$	4.99980e7	+	1.81978e7i	2.23952	+	0.815117i
$871$	2.89422e7	+	2.42854e7i	1.29266	+	1.08467i
$872$	−885055.	+	5.01940e6i	−0.0394166	+	0.223543i
$873$	1.98724e7			0.882500
$874$	3.15130e6	+	9.87568e6i	0.139544	+	0.437309i
$875$	−2.82171e6			−0.124592
$876$	−2.55692e6	+	1.45010e7i	−0.112579	+	0.638465i
$877$	−2.73010e7	−	2.29083e7i	−1.19861	−	1.00576i	−0.999669	−	0.0257465i	$-0.991804\pi$
$877$	−2.73010e7	−	2.29083e7i	−1.19861	−	1.00576i	−0.198946	−	0.980010i	$-0.563752\pi$
$878$	−1.76653e7	−	6.42964e6i	−0.773364	−	0.281482i
$879$	1.06586e7	−	3.87941e6i	0.465294	−	0.169353i
$880$	−744926.	+	625067.i	−0.0324270	+	0.0272095i
$881$	−1.43601e7	−	2.48724e7i	−0.623329	−	1.07964i	−0.988861	−	0.148839i	$-0.952446\pi$
$881$	−1.43601e7	−	2.48724e7i	−0.623329	−	1.07964i	0.365532	−	0.930799i	$-0.380887\pi$
$882$	−3.91434e6	+	6.77983e6i	−0.169429	+	0.293459i
$883$	−256376.	−	1.45398e6i	−0.0110656	−	0.0627563i	0.978775	−	0.204938i	$-0.0656993\pi$
$883$	−256376.	−	1.45398e6i	−0.0110656	−	0.0627563i	−0.989841	+	0.142182i	$0.954588\pi$
$884$	2.61287e6	+	1.48183e7i	0.112457	+	0.637776i
$885$	4.19826e7	−	7.27159e7i	1.80182	−	3.12084i
$886$	−5.70292e6	−	9.87774e6i	−0.244069	−	0.422740i
$887$	1.73439e7	−	1.45532e7i	0.740179	−	0.621084i	−0.192707	−	0.981256i	$-0.561727\pi$
$887$	1.73439e7	−	1.45532e7i	0.740179	−	0.621084i	0.932886	+	0.360173i	$0.117282\pi$
$888$	9.14762e6	−	3.32946e6i	0.389292	−	0.141691i
$889$	−7.03591e6	−	2.56086e6i	−0.298583	−	0.108675i
$890$	2.88845e7	+	2.42370e7i	1.22233	+	1.02566i
$891$	583321.	−	3.30818e6i	0.0246158	−	0.139603i
$892$	−5.49407e6			−0.231197
$893$	−1.01008e7	−	6.38602e6i	−0.423864	−	0.267980i
$894$	−797931.			−0.0333904
$895$	8.90831e6	−	5.05215e7i	0.371739	−	2.10823i
$896$	780613.	+	655012.i	0.0324837	+	0.0272571i
$897$	−1.88778e7	−	6.87097e6i	−0.783377	−	0.285126i
$898$	664759.	−	241952.i	0.0275089	−	0.0100124i
$899$	−3.90462e7	+	3.27637e7i	−1.61131	+	1.35205i
$900$	−4.44739e6	−	7.70311e6i	−0.183020	−	0.317000i
$901$	2.00968e7	−	3.48086e7i	0.824734	−	1.42848i
$902$	−166247.	−	942835.i	−0.00680359	−	0.0385851i
$903$	1.79367e6	+	1.01724e7i	0.0732020	+	0.415149i
$904$	4.92184e6	−	8.52488e6i	0.200312	−	0.346950i
$905$	−1.65787e7	−	2.87151e7i	−0.672866	−	1.16544i
$906$	−2.91292e7	+	2.44423e7i	−1.17898	+	0.989286i
$907$	−3.44915e6	+	1.25539e6i	−0.139218	+	0.0506711i	−0.410689	−	0.911775i	$-0.634712\pi$
$907$	−3.44915e6	+	1.25539e6i	−0.139218	+	0.0506711i	0.271472	+	0.962446i	$0.412490\pi$
$908$	4.71434e6	+	1.71588e6i	0.189761	+	0.0690673i
$909$	4.85109e6	+	4.07055e6i	0.194729	+	0.163397i
$910$	−2.18849e6	+	1.24116e7i	−0.0876076	+	0.496847i
$911$	3.84905e7			1.53659			0.768294	−	0.640097i	$-0.221106\pi$
$911$	3.84905e7			1.53659			0.768294	+	0.640097i	$0.221106\pi$
$912$	6.76081e6	+	4.27438e6i	0.269161	+	0.170171i
$913$	2.07230e6			0.0822766
$914$	1.57379e6	−	8.92543e6i	0.0623135	−	0.353398i
$915$	2.46183e7	+	2.06572e7i	0.972088	+	0.815679i
$916$	1.95842e7	+	7.12805e6i	0.771199	+	0.280693i
$917$	6.73505e6	−	2.45136e6i	0.264495	−	0.0962683i
$918$	−8.54430e6	+	7.16952e6i	−0.334634	+	0.280791i
$919$	−1.58983e7	−	2.75367e7i	−0.620959	−	1.07553i	−0.989307	−	0.145845i	$-0.953410\pi$
$919$	−1.58983e7	−	2.75367e7i	−0.620959	−	1.07553i	0.368349	−	0.929688i	$-0.379923\pi$
$920$	−4.34599e6	+	7.52747e6i	−0.169285	+	0.293210i
$921$	−151761.	−	860678.i	−0.00589536	−	0.0334343i
$922$	−5.41990e6	−	3.07378e7i	−0.209973	−	1.19082i
$923$	−1.45202e7	+	2.51496e7i	−0.561005	+	0.971690i
$924$	−455099.	−	788254.i	−0.0175358	−	0.0303729i
$925$	2.15664e7	−	1.80964e7i	0.828751	−	0.695405i
$926$	723657.	−	263390.i	0.0277335	−	0.0100942i
$927$	−5.56073e6	−	2.02394e6i	−0.212536	−	0.0773567i
$928$	−6.37245e6	−	5.34712e6i	−0.242905	−	0.203822i
$929$	−12266.9	+	69569.0i	−0.000466332	+	0.00264470i	−0.985040	−	0.172326i	$-0.944872\pi$
$929$	−12266.9	+	69569.0i	−0.000466332	+	0.00264470i	0.984574	+	0.174970i	$0.0559830\pi$
$930$	4.10947e7			1.55804
$931$	−6.18928e6	−	1.93962e7i	−0.234027	−	0.733404i
$932$	7.11385e6			0.268265
$933$	7.33025e6	−	4.15719e7i	0.275686	−	1.56349i
$934$	−7.44910e6	−	6.25054e6i	−0.279407	−	0.234450i
$935$	−5.46436e6	−	1.98886e6i	−0.204414	−	0.0744005i
$936$	−5.58854e6	+	2.03406e6i	−0.208501	+	0.0758882i
$937$	−2.10124e6	+	1.76315e6i	−0.0781855	+	0.0656054i	−0.681043	−	0.732244i	$-0.738473\pi$
$937$	−2.10124e6	+	1.76315e6i	−0.0781855	+	0.0656054i	0.602857	+	0.797849i	$0.294029\pi$
$938$	7.65026e6	+	1.32506e7i	0.283902	+	0.491733i
$939$	−5.72469e6	+	9.91545e6i	−0.211879	+	0.366985i
$940$	−1.73997e6	−	9.86784e6i	−0.0642275	−	0.364253i
$941$	3.87199e6	+	2.19592e7i	0.142548	+	0.808428i	0.969303	+	0.245867i	$0.0790728\pi$
$941$	3.87199e6	+	2.19592e7i	0.142548	+	0.808428i	−0.826756	+	0.562561i	$0.809816\pi$
$942$	−1.21015e6	+	2.09604e6i	−0.0444336	+	0.0769613i
$943$	−4.27872e6	−	7.41095e6i	−0.156687	−	0.271391i
$944$	−1.00563e7	+	8.43825e6i	−0.367290	+	0.308193i
$945$	−8.77882e6	+	3.19523e6i	−0.319784	+	0.116392i
$946$	1.44817e6	+	527092.i	0.0526130	+	0.0191496i
$947$	1.01610e6	+	852607.i	0.0368180	+	0.0308940i	0.661011	−	0.750376i	$-0.270128\pi$
$947$	1.01610e6	+	852607.i	0.0368180	+	0.0308940i	−0.624193	+	0.781270i	$0.714572\pi$
$948$	3.01780e6	−	1.71148e7i	0.109061	−	0.618516i
$949$	2.84725e7			1.02627
$950$	2.26012e7	+	4.92880e6i	0.812498	+	0.177187i
$951$	1.76829e7			0.634019
$952$	−1.05815e6	+	6.00106e6i	−0.0378403	+	0.214603i
$953$	2.36073e7	+	1.98088e7i	0.842002	+	0.706524i	0.958013	−	0.286724i	$-0.0925663\pi$
$953$	2.36073e7	+	1.98088e7i	0.842002	+	0.706524i	−0.116011	+	0.993248i	$0.537011\pi$
$954$	1.49282e7	+	5.43341e6i	0.531050	+	0.193287i
$955$	1.29855e7	−	4.72634e6i	0.460734	−	0.167694i
$956$	−1.93834e7	+	1.62646e7i	−0.685940	+	0.575572i
$957$	3.71515e6	+	6.43483e6i	0.131128	+	0.227121i
$958$	3.35938e6	−	5.81862e6i	0.118262	−	0.204836i
$959$	4.48635e6	+	2.54434e7i	0.157524	+	0.893363i
$960$	1.16462e6	+	6.60488e6i	0.0407855	+	0.231306i
$961$	−5.36947e6	+	9.30020e6i	−0.187553	+	0.324851i
$962$	−9.41178e6	−	1.63017e7i	−0.327894	−	0.567930i
$963$	1.31796e7	−	1.10590e7i	0.457971	−	0.384283i
$964$	−2.27563e7	+	8.28261e6i	−0.788694	+	0.287061i
$965$	4.77217e6	+	1.73693e6i	0.164967	+	0.0600432i
$966$	−6.23231e6	−	5.22953e6i	−0.214885	−	0.180310i
$967$	−4.06916e6	+	2.30773e7i	−0.139939	+	0.793633i	0.831353	+	0.555744i	$0.187567\pi$
$967$	−4.06916e6	+	2.30773e7i	−0.139939	+	0.793633i	−0.971292	+	0.237889i	$0.923545\pi$
$968$	1.01715e7			0.348895
$969$	−1.92147e6	+	4.77927e7i	−0.0657391	+	1.63513i
$970$	−4.33342e7			−1.47877
$971$	−6.00889e6	+	3.40781e7i	−0.204525	+	1.15992i	0.693661	+	0.720302i	$0.255997\pi$
$971$	−6.00889e6	+	3.40781e7i	−0.204525	+	1.15992i	−0.898186	+	0.439616i	$0.855114\pi$
$972$	−1.23228e7	−	1.03400e7i	−0.418352	−	0.351039i
$973$	−243993.	−	88806.1i	−0.00826218	−	0.00300719i
$974$	3.71509e7	−	1.35218e7i	1.25479	−	0.456707i
$975$	−3.43414e7	+	2.88159e7i	−1.15693	+	0.970778i
$976$	−2.51224e6	−	4.35132e6i	−0.0844182	−	0.146217i
$977$	−9.51915e6	+	1.64877e7i	−0.319052	+	0.552615i	−0.980291	−	0.197561i	$-0.936698\pi$
$977$	−9.51915e6	+	1.64877e7i	−0.319052	+	0.552615i	0.661238	+	0.750176i	$0.270031\pi$
$978$	3.00678e6	+	1.70523e7i	0.100520	+	0.570080i
$979$	914368.	+	5.18564e6i	0.0304905	+	0.172920i
$980$	8.53570e6	−	1.47843e7i	0.283905	−	0.491739i
$981$	−6.02322e6	−	1.04325e7i	−0.199828	−	0.346112i
$982$	−4.66338e6	+	3.91304e6i	−0.154320	+	0.129490i
$983$	3.24544e7	−	1.18124e7i	1.07125	−	0.389902i	0.254604	−	0.967045i	$-0.418055\pi$
$983$	3.24544e7	−	1.18124e7i	1.07125	−	0.389902i	0.816643	+	0.577144i	$0.195833\pi$
$984$	−6.20476e6	−	2.25835e6i	−0.204285	−	0.0743538i
$985$	−4.56508e6	−	3.83056e6i	−0.149919	−	0.125797i
$986$	8.63808e6	−	4.89890e7i	0.282960	−	1.60475i
$987$	9.37881e6			0.306446
$988$	5.86950e6	−	1.43097e7i	0.191297	−	0.466378i
$989$	1.37751e7			0.447820
$990$	399106.	−	2.26344e6i	0.0129420	−	0.0733975i
$991$	−1.44343e7	−	1.21118e7i	−0.466887	−	0.391765i	0.378770	−	0.925491i	$-0.376347\pi$
$991$	−1.44343e7	−	1.21118e7i	−0.466887	−	0.391765i	−0.845658	+	0.533726i	$0.820791\pi$
$992$	−6.03751e6	−	2.19747e6i	−0.194795	−	0.0708997i
$993$	9.64650e6	−	3.51104e6i	0.310453	−	0.112996i
$994$	−9.00915e6	+	7.55958e6i	−0.289213	+	0.242679i
$995$	−2.72621e7	−	4.72194e7i	−0.872975	−	1.51204i
$996$	7.14625e6	−	1.23777e7i	0.228260	−	0.395358i
$997$	1.14859e6	+	6.51399e6i	0.0365955	+	0.207544i	0.997623	−	0.0689097i	$-0.0219520\pi$
$997$	1.14859e6	+	6.51399e6i	0.0365955	+	0.207544i	−0.961027	+	0.276453i	$0.910841\pi$
$998$	−1.33837e6	−	7.59028e6i	−0.0425354	−	0.241230i
$999$	6.97664e6	−	1.20839e7i	0.221173	−	0.383084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.a.17.4	yes	24
19.3	odd	18		722.6.a.p.1.3		12
19.9	even	9	inner	38.6.e.a.9.4	✓	24
19.16	even	9		722.6.a.o.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.a.9.4	✓	24	19.9	even	9	inner
38.6.e.a.17.4	yes	24	1.1	even	1	trivial
722.6.a.o.1.10		12	19.16	even	9
722.6.a.p.1.3		12	19.3	odd	18

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.694593 + 3.93923i) q^{2} +(15.2107 + 12.7633i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-77.4900 + 28.2040i) q^{5} +(-60.8427 + 51.0531i) q^{6} +(31.0980 + 53.8633i) q^{7} +(32.0000 - 55.4256i) q^{8} +(26.2669 + 148.967i) q^{9} +O(q^{10})\)	\(q+(-0.694593 + 3.93923i) q^{2} +(15.2107 + 12.7633i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-77.4900 + 28.2040i) q^{5} +(-60.8427 + 51.0531i) q^{6} +(31.0980 + 53.8633i) q^{7} +(32.0000 - 55.4256i) q^{8} +(26.2669 + 148.967i) q^{9} +(-57.2783 - 324.841i) q^{10} +(23.0319 - 39.8924i) q^{11} +(-158.849 - 275.134i) q^{12} +(-470.595 + 394.876i) q^{13} +(-233.780 + 85.0891i) q^{14} +(-1538.65 - 560.023i) q^{15} +(196.107 + 164.554i) q^{16} +(-265.830 + 1507.60i) q^{17} -605.061 q^{18} +(1059.07 - 1163.81i) q^{19} +1319.41 q^{20} +(-214.450 + 1216.21i) q^{21} +(141.148 + 118.437i) q^{22} +(1547.62 + 563.288i) q^{23} +(1194.15 - 434.636i) q^{24} +(2815.34 - 2362.35i) q^{25} +(-1228.64 - 2128.06i) q^{26} +(910.748 - 1577.46i) q^{27} +(-172.803 - 980.017i) q^{28} +(1410.66 + 8000.26i) q^{29} +(3274.79 - 5672.11i) q^{30} +(3137.20 + 5433.79i) q^{31} +(-784.430 + 658.215i) q^{32} +(859.487 - 312.828i) q^{33} +(-5754.13 - 2094.33i) q^{34} +(-3928.94 - 3296.77i) q^{35} +(420.271 - 2383.47i) q^{36} +7660.34 q^{37} +(3848.91 + 4980.31i) q^{38} -12198.0 q^{39} +(-916.452 + 5197.46i) q^{40} +(-3980.33 - 3339.89i) q^{41} +(-4641.97 - 1689.54i) q^{42} +(7859.62 - 2860.67i) q^{43} +(-564.590 + 473.747i) q^{44} +(-6236.90 - 10802.6i) q^{45} +(-3293.89 + 5705.18i) q^{46} +(-1318.75 - 7478.98i) q^{47} +(882.682 + 5005.94i) q^{48} +(6469.33 - 11205.2i) q^{49} +(7350.32 + 12731.1i) q^{50} +(-23285.3 + 19538.7i) q^{51} +(9236.32 - 3361.75i) q^{52} +(-24672.2 - 8979.94i) q^{53} +(5581.39 + 4683.34i) q^{54} +(-659.613 + 3740.85i) q^{55} +3980.54 q^{56} +(30963.3 - 4185.14i) q^{57} -32494.7 q^{58} +(-8904.62 + 50500.6i) q^{59} +(20069.1 + 16840.0i) q^{60} +(-18443.2 - 6712.78i) q^{61} +(-23584.0 + 8583.88i) q^{62} +(-7207.01 + 6047.40i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(25329.3 - 43871.6i) q^{65} +(635.307 + 3603.01i) q^{66} +(-10679.6 - 60566.9i) q^{67} +(12246.8 - 21212.2i) q^{68} +(16350.9 + 28320.7i) q^{69} +(15715.8 - 13187.1i) q^{70} +(44421.6 - 16168.1i) q^{71} +(9097.14 + 3311.09i) q^{72} +(-35504.7 - 29792.0i) q^{73} +(-5320.82 + 30175.9i) q^{74} +72974.4 q^{75} +(-22292.0 + 11702.4i) q^{76} +2864.98 q^{77} +(8472.62 - 48050.6i) q^{78} +(41904.4 + 35162.0i) q^{79} +(-19837.4 - 7220.23i) q^{80} +(68527.4 - 24941.9i) q^{81} +(15921.3 - 13359.6i) q^{82} +(22493.9 + 38960.5i) q^{83} +(9879.76 - 17112.2i) q^{84} +(-21921.2 - 124321. i) q^{85} +(5809.60 + 32947.9i) q^{86} +(-80652.4 + 139694. i) q^{87} +(-1474.04 - 2553.11i) q^{88} +(-87568.0 + 73478.3i) q^{89} +(46886.1 - 17065.2i) q^{90} +(-35903.9 - 13067.9i) q^{91} +(-20186.1 - 16938.2i) q^{92} +(-21634.0 + 122692. i) q^{93} +30377.4 q^{94} +(-49243.3 + 120054. i) q^{95} -20332.7 q^{96} +(22813.0 - 129379. i) q^{97} +(39646.4 + 33267.2i) q^{98} +(6547.63 + 2383.14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9}+O(q^{10}) \) 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9	\( 24 q + 18 q^{3} - 72 q^{6} + 438 q^{7} + 768 q^{8} + 378 q^{9} + 600 q^{11} - 1662 q^{13} - 1776 q^{14} - 1206 q^{15} + 4194 q^{17} - 4368 q^{18} + 9570 q^{19} - 1344 q^{20} + 2430 q^{21} - 5160 q^{22} - 1170 q^{23} - 1152 q^{24} + 5940 q^{25} - 1776 q^{26} - 5130 q^{27} + 768 q^{28} - 7554 q^{29} + 294 q^{31} - 45912 q^{33} + 1584 q^{34} + 22116 q^{35} + 6048 q^{36} + 28608 q^{37} - 9528 q^{38} - 38868 q^{39} + 37278 q^{41} - 9720 q^{42} + 13212 q^{43} + 20640 q^{44} - 34344 q^{45} - 29856 q^{46} - 3054 q^{47} - 9216 q^{48} + 1422 q^{49} + 16584 q^{50} + 2352 q^{51} - 1824 q^{52} + 73806 q^{53} + 136944 q^{54} - 41598 q^{55} + 56064 q^{56} + 178248 q^{57} - 52848 q^{58} + 123528 q^{59} + 46944 q^{60} - 149172 q^{61} + 58344 q^{62} - 170124 q^{63} - 49152 q^{64} - 202674 q^{65} - 84840 q^{66} - 313212 q^{67} + 35520 q^{68} - 19938 q^{69} - 88464 q^{70} + 75810 q^{71} + 48384 q^{72} + 172872 q^{73} + 4872 q^{74} + 174960 q^{75} + 31008 q^{76} - 115056 q^{77} + 101304 q^{78} + 158058 q^{79} - 47250 q^{81} - 149112 q^{82} - 148440 q^{83} - 176736 q^{84} - 226752 q^{85} - 57528 q^{86} + 182874 q^{87} - 38400 q^{88} - 322464 q^{89} + 48816 q^{90} - 27264 q^{91} + 88992 q^{92} + 779424 q^{93} + 143712 q^{94} + 634752 q^{95} - 108552 q^{97} - 173544 q^{98} + 656436 q^{99}+O(q^{100}) \) 24 * q + 18 * q^3 - 72 * q^6 + 438 * q^7 + 768 * q^8 + 378 * q^9 + 600 * q^11 - 1662 * q^13 - 1776 * q^14 - 1206 * q^15 + 4194 * q^17 - 4368 * q^18 + 9570 * q^19 - 1344 * q^20 + 2430 * q^21 - 5160 * q^22 - 1170 * q^23 - 1152 * q^24 + 5940 * q^25 - 1776 * q^26 - 5130 * q^27 + 768 * q^28 - 7554 * q^29 + 294 * q^31 - 45912 * q^33 + 1584 * q^34 + 22116 * q^35 + 6048 * q^36 + 28608 * q^37 - 9528 * q^38 - 38868 * q^39 + 37278 * q^41 - 9720 * q^42 + 13212 * q^43 + 20640 * q^44 - 34344 * q^45 - 29856 * q^46 - 3054 * q^47 - 9216 * q^48 + 1422 * q^49 + 16584 * q^50 + 2352 * q^51 - 1824 * q^52 + 73806 * q^53 + 136944 * q^54 - 41598 * q^55 + 56064 * q^56 + 178248 * q^57 - 52848 * q^58 + 123528 * q^59 + 46944 * q^60 - 149172 * q^61 + 58344 * q^62 - 170124 * q^63 - 49152 * q^64 - 202674 * q^65 - 84840 * q^66 - 313212 * q^67 + 35520 * q^68 - 19938 * q^69 - 88464 * q^70 + 75810 * q^71 + 48384 * q^72 + 172872 * q^73 + 4872 * q^74 + 174960 * q^75 + 31008 * q^76 - 115056 * q^77 + 101304 * q^78 + 158058 * q^79 - 47250 * q^81 - 149112 * q^82 - 148440 * q^83 - 176736 * q^84 - 226752 * q^85 - 57528 * q^86 + 182874 * q^87 - 38400 * q^88 - 322464 * q^89 + 48816 * q^90 - 27264 * q^91 + 88992 * q^92 + 779424 * q^93 + 143712 * q^94 + 634752 * q^95 - 108552 * q^97 - 173544 * q^98 + 656436 * q^99

Introduction

L-functions

Modular forms

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Database

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