LMFDB - Embedded newform 76.6.d.a.75.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.6
Character	$\chi$	$=$	76.75
Dual form			76.6.d.a.75.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.30781 + 1.95631i) q^{2} -7.37371 q^{3} +(24.3457 - 20.7674i) q^{4} +74.1521 q^{5} +(39.1383 - 14.4252i) q^{6} -80.5452i q^{7} +(-88.5950 + 157.857i) q^{8} -188.628 q^{9} +O(q^{10})$	\(q+(-5.30781 + 1.95631i) q^{2} -7.37371 q^{3} +(24.3457 - 20.7674i) q^{4} +74.1521 q^{5} +(39.1383 - 14.4252i) q^{6} -80.5452i q^{7} +(-88.5950 + 157.857i) q^{8} -188.628 q^{9} +(-393.585 + 145.064i) q^{10} +299.840i q^{11} +(-179.518 + 153.133i) q^{12} -472.618i q^{13} +(157.571 + 427.519i) q^{14} -546.776 q^{15} +(161.428 - 1011.20i) q^{16} +861.194 q^{17} +(1001.20 - 369.015i) q^{18} +(115.343 - 1569.33i) q^{19} +(1805.29 - 1539.95i) q^{20} +593.917i q^{21} +(-586.579 - 1591.49i) q^{22} -840.760i q^{23} +(653.274 - 1163.99i) q^{24} +2373.54 q^{25} +(924.586 + 2508.57i) q^{26} +3182.70 q^{27} +(-1672.72 - 1960.93i) q^{28} -5159.61i q^{29} +(2902.19 - 1069.66i) q^{30} +3421.14 q^{31} +(1121.38 + 5683.04i) q^{32} -2210.93i q^{33} +(-4571.05 + 1684.76i) q^{34} -5972.59i q^{35} +(-4592.29 + 3917.32i) q^{36} -4136.40i q^{37} +(2457.87 + 8555.35i) q^{38} +3484.95i q^{39} +(-6569.51 + 11705.4i) q^{40} -19653.0i q^{41} +(-1161.88 - 3152.40i) q^{42} -11970.7i q^{43} +(6226.90 + 7299.82i) q^{44} -13987.2 q^{45} +(1644.79 + 4462.60i) q^{46} +15826.8i q^{47} +(-1190.33 + 7456.27i) q^{48} +10319.5 q^{49} +(-12598.3 + 4643.36i) q^{50} -6350.19 q^{51} +(-9815.06 - 11506.2i) q^{52} -4883.58i q^{53} +(-16893.2 + 6226.35i) q^{54} +22233.8i q^{55} +(12714.6 + 7135.90i) q^{56} +(-850.510 + 11571.8i) q^{57} +(10093.8 + 27386.3i) q^{58} +31449.1 q^{59} +(-13311.7 + 11355.1i) q^{60} -29401.7 q^{61} +(-18158.8 + 6692.81i) q^{62} +15193.1i q^{63} +(-17069.8 - 27970.7i) q^{64} -35045.6i q^{65} +(4325.26 + 11735.2i) q^{66} -21728.8 q^{67} +(20966.4 - 17884.8i) q^{68} +6199.52i q^{69} +(11684.2 + 31701.4i) q^{70} +2651.65 q^{71} +(16711.5 - 29776.4i) q^{72} -46243.7 q^{73} +(8092.07 + 21955.2i) q^{74} -17501.8 q^{75} +(-29782.8 - 40601.8i) q^{76} +24150.7 q^{77} +(-6817.63 - 18497.5i) q^{78} +75929.5 q^{79} +(11970.3 - 74982.3i) q^{80} +22368.4 q^{81} +(38447.2 + 104314. i) q^{82} -35053.8i q^{83} +(12334.1 + 14459.3i) q^{84} +63859.3 q^{85} +(23418.5 + 63538.4i) q^{86} +38045.5i q^{87} +(-47331.9 - 26564.3i) q^{88} -61381.1i q^{89} +(74241.4 - 27363.2i) q^{90} -38067.1 q^{91} +(-17460.4 - 20468.9i) q^{92} -25226.5 q^{93} +(-30962.0 - 84005.5i) q^{94} +(8552.96 - 116369. i) q^{95} +(-8268.72 - 41905.1i) q^{96} +90996.6i q^{97} +(-54773.8 + 20188.1i) q^{98} -56558.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−5.30781	+	1.95631i	−0.938297	+	0.345830i
$2$	−5.30781	+	1.95631i	−0.938297	+	0.345830i
$3$	−7.37371			−0.473024			−0.236512	−	0.971629i	$-0.576004\pi$
$3$	−7.37371			−0.473024			−0.236512	+	0.971629i	$0.576004\pi$
$4$	24.3457	−	20.7674i	0.760804	−	0.648982i
$5$	74.1521			1.32647			0.663237	−	0.748410i	$-0.269182\pi$
$5$	74.1521			1.32647			0.663237	+	0.748410i	$0.269182\pi$
$6$	39.1383	−	14.4252i	0.443837	−	0.163586i
$7$		−	80.5452i		−	0.621290i	−0.950526	−	0.310645i	$-0.899455\pi$
$7$		−	80.5452i		−	0.621290i	0.950526	−	0.310645i	$-0.100545\pi$
$8$	−88.5950	+	157.857i	−0.489423	+	0.872046i
$9$	−188.628			−0.776248
$10$	−393.585	+	145.064i	−1.24463	+	0.458734i
$11$			299.840i			0.747150i	0.927600	+	0.373575i	$0.121868\pi$
$11$			299.840i			0.747150i	−0.927600	+	0.373575i	$0.878132\pi$
$12$	−179.518	+	153.133i	−0.359878	+	0.306984i
$13$		−	472.618i		−	0.775625i	−0.921738	−	0.387813i	$-0.873231\pi$
$13$		−	472.618i		−	0.775625i	0.921738	−	0.387813i	$-0.126769\pi$
$14$	157.571	+	427.519i	0.214860	+	0.582955i
$15$	−546.776			−0.627453
$16$	161.428	−	1011.20i	0.157645	−	0.987496i
$17$	861.194			0.722734			0.361367	−	0.932424i	$-0.382310\pi$
$17$	861.194			0.722734			0.361367	+	0.932424i	$0.382310\pi$
$18$	1001.20	−	369.015i	0.728352	−	0.268450i
$19$	115.343	−	1569.33i	0.0733009	−	0.997310i
$19$	115.343	−	1569.33i	0.0733009	−	0.997310i
$20$	1805.29	−	1539.95i	1.00919	−	0.860857i
$21$			593.917i			0.293885i
$22$	−586.579	−	1591.49i	−0.258387	−	0.701049i
$23$		−	840.760i		−	0.331400i	−0.986176	−	0.165700i	$-0.947012\pi$
$23$		−	840.760i		−	0.331400i	0.986176	−	0.165700i	$-0.0529883\pi$
$24$	653.274	−	1163.99i	0.231509	−	0.412499i
$25$	2373.54			0.759531
$26$	924.586	+	2508.57i	0.268234	+	0.727767i
$27$	3182.70			0.840208
$28$	−1672.72	−	1960.93i	−0.403206	−	0.472680i
$29$		−	5159.61i		−	1.13926i	−0.821902	−	0.569629i	$-0.807087\pi$
$29$		−	5159.61i		−	1.13926i	0.821902	−	0.569629i	$-0.192913\pi$
$30$	2902.19	−	1069.66i	0.588738	−	0.216992i
$31$	3421.14			0.639392			0.319696	−	0.947520i	$-0.396419\pi$
$31$	3421.14			0.639392			0.319696	+	0.947520i	$0.396419\pi$
$32$	1121.38	+	5683.04i	0.193587	+	0.981083i
$33$		−	2210.93i		−	0.353420i
$34$	−4571.05	+	1684.76i	−0.678140	+	0.249943i
$35$		−	5972.59i		−	0.824125i
$36$	−4592.29	+	3917.32i	−0.590573	+	0.503771i
$37$		−	4136.40i		−	0.496727i	−0.968667	−	0.248364i	$-0.920107\pi$
$37$		−	4136.40i		−	0.496727i	0.968667	−	0.248364i	$-0.0798928\pi$
$38$	2457.87	+	8555.35i	0.276121	+	0.961123i
$39$			3484.95i			0.366889i
$40$	−6569.51	+	11705.4i	−0.649207	+	1.15675i
$41$		−	19653.0i		−	1.82586i	−0.408112	−	0.912932i	$-0.633813\pi$
$41$		−	19653.0i		−	1.82586i	0.408112	−	0.912932i	$-0.366187\pi$
$42$	−1161.88	−	3152.40i	−0.101634	−	0.275752i
$43$		−	11970.7i		−	0.987302i	−0.869660	−	0.493651i	$-0.835662\pi$
$43$		−	11970.7i		−	0.987302i	0.869660	−	0.493651i	$-0.164338\pi$
$44$	6226.90	+	7299.82i	0.484887	+	0.568434i
$45$	−13987.2			−1.02967
$46$	1644.79	+	4462.60i	0.114608	+	0.310952i
$47$			15826.8i			1.04508i	0.852616	+	0.522538i	$0.175015\pi$
$47$			15826.8i			1.04508i	−0.852616	+	0.522538i	$0.824985\pi$
$48$	−1190.33	+	7456.27i	−0.0745698	+	0.467109i
$49$	10319.5			0.613999
$50$	−12598.3	+	4643.36i	−0.712666	+	0.262668i
$51$	−6350.19			−0.341870
$52$	−9815.06	−	11506.2i	−0.503367	−	0.590099i
$53$		−	4883.58i		−	0.238808i	−0.992846	−	0.119404i	$-0.961902\pi$
$53$		−	4883.58i		−	0.238808i	0.992846	−	0.119404i	$-0.0380984\pi$
$54$	−16893.2	+	6226.35i	−0.788365	+	0.290569i
$55$			22233.8i			0.991074i
$56$	12714.6	+	7135.90i	0.541794	+	0.304074i
$57$	−850.510	+	11571.8i	−0.0346731	+	0.471751i
$58$	10093.8	+	27386.3i	0.393989	+	1.06896i
$59$	31449.1			1.17619			0.588097	−	0.808790i	$-0.299877\pi$
$59$	31449.1			1.17619			0.588097	+	0.808790i	$0.299877\pi$
$60$	−13311.7	+	11355.1i	−0.477369	+	0.407206i
$61$	−29401.7			−1.01169			−0.505845	−	0.862625i	$-0.668819\pi$
$61$	−29401.7			−1.01169			−0.505845	+	0.862625i	$0.668819\pi$
$62$	−18158.8	+	6692.81i	−0.599940	+	0.221121i
$63$			15193.1i			0.482275i
$64$	−17069.8	−	27970.7i	−0.520930	−	0.853599i
$65$		−	35045.6i		−	1.02885i
$66$	4325.26	+	11735.2i	0.122223	+	0.331613i
$67$	−21728.8			−0.591355			−0.295677	−	0.955288i	$-0.595545\pi$
$67$	−21728.8			−0.591355			−0.295677	+	0.955288i	$0.595545\pi$
$68$	20966.4	−	17884.8i	0.549859	−	0.469041i
$69$			6199.52i			0.156760i
$70$	11684.2	+	31701.4i	0.285007	+	0.773274i
$71$	2651.65			0.0624266			0.0312133	−	0.999513i	$-0.490063\pi$
$71$	2651.65			0.0624266			0.0312133	+	0.999513i	$0.490063\pi$
$72$	16711.5	−	29776.4i	0.379914	−	0.676925i
$73$	−46243.7			−1.01565			−0.507826	−	0.861460i	$-0.669551\pi$
$73$	−46243.7			−1.01565			−0.507826	+	0.861460i	$0.669551\pi$
$74$	8092.07	+	21955.2i	0.171783	+	0.466078i
$75$	−17501.8			−0.359276
$76$	−29782.8	−	40601.8i	−0.591469	−	0.806328i
$77$	24150.7			0.464197
$78$	−6817.63	−	18497.5i	−0.126881	−	0.344251i
$79$	75929.5			1.36881			0.684404	−	0.729103i	$-0.260062\pi$
$79$	75929.5			1.36881			0.684404	+	0.729103i	$0.260062\pi$
$80$	11970.3	−	74982.3i	0.209112	−	1.30989i
$81$	22368.4			0.378810
$82$	38447.2	+	104314.i	0.631438	+	1.71320i
$83$		−	35053.8i		−	0.558522i	−0.960215	−	0.279261i	$-0.909911\pi$
$83$		−	35053.8i		−	0.558522i	0.960215	−	0.279261i	$-0.0900895\pi$
$84$	12334.1	+	14459.3i	0.190726	+	0.223589i
$85$	63859.3			0.958687
$86$	23418.5	+	63538.4i	0.341438	+	0.926383i
$87$			38045.5i			0.538896i
$88$	−47331.9	−	26564.3i	−0.651549	−	0.365672i
$89$		−	61381.1i		−	0.821409i	−0.911768	−	0.410705i	$-0.865283\pi$
$89$		−	61381.1i		−	0.821409i	0.911768	−	0.410705i	$-0.134717\pi$
$90$	74241.4	−	27363.2i	0.966139	−	0.356091i
$91$	−38067.1			−0.481888
$92$	−17460.4	−	20468.9i	−0.215073	−	0.252130i
$93$	−25226.5			−0.302448
$94$	−30962.0	−	84005.5i	−0.361418	−	0.980591i
$95$	8552.96	−	116369.i	0.0972316	−	1.32290i
$96$	−8268.72	−	41905.1i	−0.0915715	−	0.464076i
$97$			90996.6i			0.981965i	0.871169	+	0.490983i	$0.163362\pi$
$97$			90996.6i			0.981965i	−0.871169	+	0.490983i	$0.836638\pi$
$98$	−54773.8	+	20188.1i	−0.576113	+	0.212339i
$99$		−	56558.3i		−	0.579974i
$100$	57785.4	−	49292.2i	0.577854	−	0.492922i
$101$	105909.			1.03307			0.516536	−	0.856265i	$-0.327221\pi$
$101$	105909.			1.03307			0.516536	+	0.856265i	$0.327221\pi$
$102$	33705.6	−	12422.9i	0.320776	−	0.118229i
$103$	−200157.			−1.85899			−0.929497	−	0.368829i	$-0.879759\pi$
$103$	−200157.			−1.85899			−0.929497	+	0.368829i	$0.879759\pi$
$104$	74606.2	+	41871.6i	0.676381	+	0.379609i
$105$			44040.2i			0.389831i
$106$	9553.79	+	25921.1i	0.0825869	+	0.224073i
$107$	36092.6			0.304761			0.152380	−	0.988322i	$-0.451306\pi$
$107$	36092.6			0.304761			0.152380	+	0.988322i	$0.451306\pi$
$108$	77485.2	−	66096.5i	0.639233	−	0.545280i
$109$			239339.i			1.92951i	0.263145	+	0.964756i	$0.415240\pi$
$109$			239339.i			1.92951i	−0.263145	+	0.964756i	$0.584760\pi$
$110$	−43496.1	−	118013.i	−0.342743	−	0.929922i
$111$			30500.6i			0.234964i
$112$	−81446.9	−	13002.3i	−0.613521	−	0.0979432i
$113$			94952.4i			0.699535i	0.936836	+	0.349768i	$0.113739\pi$
$113$			94952.4i			0.699535i	−0.936836	+	0.349768i	$0.886261\pi$
$114$	−18123.6	−	63084.7i	−0.130612	−	0.454634i
$115$		−	62344.1i		−	0.439593i
$116$	−107152.	−	125615.i	−0.739358	−	0.866752i
$117$			89149.2i			0.602078i
$118$	−166926.	+	61524.2i	−1.10362	+	0.406763i
$119$		−	69365.0i		−	0.449028i
$120$	48441.7	−	86312.6i	0.307090	−	0.547169i
$121$	71147.0			0.441767
$122$	156058.	−	57518.7i	0.949266	−	0.349872i
$123$			144915.i			0.863677i
$124$	83290.2	−	71048.3i	0.486452	−	0.414954i
$125$	−55722.7			−0.318975
$126$	−29722.4	−	80642.1i	−0.166785	−	0.452518i
$127$	−287732.			−1.58299			−0.791496	−	0.611174i	$-0.790698\pi$
$127$	−287732.			−1.58299			−0.791496	+	0.611174i	$0.790698\pi$
$128$	145323.	+	115070.i	0.783987	+	0.620777i
$129$			88268.8i			0.467017i
$130$	68560.0	+	186016.i	0.355805	+	0.965364i
$131$			321.169i			0.00163514i	1.00000		0.000817572i	$0.000260241\pi$
$131$			321.169i			0.00163514i	−1.00000		0.000817572i	$0.999740\pi$
$132$	−45915.4	−	53826.8i	−0.229363	−	0.268883i
$133$	−126402.	−	9290.36i	−0.619619	−	0.0455411i
$134$	115332.	−	42508.2i	0.554867	−	0.204508i
$135$	236004.			1.11451
$136$	−76297.5	+	135946.i	−0.353723	+	0.630258i
$137$	−44552.3			−0.202800			−0.101400	−	0.994846i	$-0.532332\pi$
$137$	−44552.3			−0.202800			−0.101400	+	0.994846i	$0.532332\pi$
$138$	−12128.2	−	32905.9i	−0.0542123	−	0.147088i
$139$			364472.i			1.60002i	0.599984	+	0.800012i	$0.295174\pi$
$139$			364472.i			1.60002i	−0.599984	+	0.800012i	$0.704826\pi$
$140$	−124035.	−	145407.i	−0.534842	−	0.626997i
$141$		−	116702.i		−	0.494346i
$142$	−14074.4	+	5187.43i	−0.0585747	+	0.0215890i
$143$	141710.			0.579508
$144$	−30450.0	+	190740.i	−0.122372	+	0.766542i
$145$		−	382596.i		−	1.51120i
$146$	245453.	−	90466.8i	0.952984	−	0.351243i
$147$	−76092.8			−0.290436
$148$	−85902.3	−	100704.i	−0.322367	−	0.377912i
$149$	40734.1			0.150312			0.0751558	−	0.997172i	$-0.476055\pi$
$149$	40734.1			0.150312			0.0751558	+	0.997172i	$0.476055\pi$
$150$	92896.1	−	34238.8i	0.337108	−	0.124248i
$151$	311478.			1.11169			0.555846	−	0.831285i	$-0.312394\pi$
$151$	311478.			1.11169			0.555846	+	0.831285i	$0.312394\pi$
$152$	237511.	+	157243.i	0.833825	+	0.552028i
$153$	−162446.			−0.561021
$154$	−128187.	+	47246.1i	−0.435555	+	0.160533i
$155$	253685.			0.848136
$156$	72373.4	+	84843.6i	0.238104	+	0.279131i
$157$	−113376.			−0.367090			−0.183545	−	0.983011i	$-0.558757\pi$
$157$	−113376.			−0.367090			−0.183545	+	0.983011i	$0.558757\pi$
$158$	−403019.	+	148541.i	−1.28435	+	0.473374i
$159$			36010.1i			0.112962i
$160$	83152.6	+	421409.i	0.256789	+	1.30138i
$161$	−67719.2			−0.205896
$162$	−118727.	+	43759.4i	−0.355436	+	0.131004i
$163$		−	90072.7i		−	0.265536i	−0.991147	−	0.132768i	$-0.957613\pi$
$163$		−	90072.7i		−	0.265536i	0.991147	−	0.132768i	$-0.0423866\pi$
$164$	−408141.	−	478465.i	−1.18495	−	1.38912i
$165$		−	163945.i		−	0.468802i
$166$	68576.1	+	186059.i	0.193153	+	0.524060i
$167$	−513808.			−1.42564			−0.712820	−	0.701347i	$-0.752582\pi$
$167$	−513808.			−1.42564			−0.712820	+	0.701347i	$0.752582\pi$
$168$	−93754.1	−	52618.1i	−0.256281	−	0.143834i
$169$	147925.			0.398406
$170$	−338953.	+	124928.i	−0.899534	+	0.331542i
$171$	−21757.1	+	296020.i	−0.0568997	+	0.774160i
$172$	−248601.	−	291436.i	−0.640741	−	0.751143i
$173$			677354.i			1.72068i	0.509719	+	0.860341i	$0.329749\pi$
$173$			677354.i			1.72068i	−0.509719	+	0.860341i	$0.670251\pi$
$174$	−74428.7	−	201938.i	−0.186366	−	0.505645i
$175$		−	191177.i		−	0.471889i
$176$	303197.	+	48402.7i	0.737807	+	0.117784i
$177$	−231897.			−0.556368
$178$	120080.	+	325799.i	0.284068	+	0.770726i
$179$	−389094.			−0.907657			−0.453828	−	0.891089i	$-0.649942\pi$
$179$	−389094.			−0.907657			−0.453828	+	0.891089i	$0.649942\pi$
$180$	−340528.	+	290478.i	−0.783379	+	0.668239i
$181$			112470.i			0.255176i	0.991827	+	0.127588i	$0.0407235\pi$
$181$			112470.i			0.255176i	−0.991827	+	0.127588i	$0.959276\pi$
$182$	202053.	−	74471.0i	0.452154	−	0.166651i
$183$	216799.			0.478553
$184$	132720.	+	74487.2i	0.288996	+	0.162195i
$185$		−	306723.i		−	0.658896i
$186$	133898.	−	49350.8i	0.283786	−	0.104595i
$187$			258220.i			0.539991i
$188$	328681.	+	385314.i	0.678235	+	0.795097i
$189$		−	256351.i		−	0.522013i
$190$	182256.	+	634397.i	0.366267	+	1.27490i
$191$		−	579910.i		−	1.15021i	−0.818080	−	0.575105i	$-0.804961\pi$
$191$		−	579910.i		−	1.15021i	0.818080	−	0.575105i	$-0.195039\pi$
$192$	125868.	+	206248.i	0.246412	+	0.403773i
$193$		−	214903.i		−	0.415287i	−0.978205	−	0.207644i	$-0.933421\pi$
$193$		−	214903.i		−	0.415287i	0.978205	−	0.207644i	$-0.0665794\pi$
$194$	−178017.	−	482993.i	−0.339593	−	0.921375i
$195$			258416.i			0.486669i
$196$	251235.	−	214309.i	0.467133	−	0.398474i
$197$	753104.			1.38258			0.691288	−	0.722579i	$-0.257043\pi$
$197$	753104.			1.38258			0.691288	+	0.722579i	$0.257043\pi$
$198$	110645.	+	300201.i	0.200572	+	0.544188i
$199$		−	848329.i		−	1.51856i	−0.650765	−	0.759279i	$-0.725552\pi$
$199$		−	848329.i		−	1.51856i	0.650765	−	0.759279i	$-0.274448\pi$
$200$	−210283.	+	374680.i	−0.371732	+	0.662347i
$201$	160222.			0.279725
$202$	−562147.	+	207191.i	−0.969330	+	0.357267i
$203$	−415582.			−0.707810
$204$	−154600.	+	131877.i	−0.260096	+	0.221868i
$205$		−	1.45731e6i		−	2.42196i
$206$	1.06240e6	−	391569.i	1.74429	−	0.642895i
$207$			158591.i			0.257249i
$208$	−477909.	−	76294.0i	−0.765927	−	0.122273i
$209$	470548.	+	34584.6i	0.745140	+	0.0547667i
$210$	−86156.2	−	233757.i	−0.134815	−	0.365777i
$211$	1.02977e6			1.59233			0.796165	−	0.605080i	$-0.206859\pi$
$211$	1.02977e6			1.59233			0.796165	+	0.605080i	$0.206859\pi$
$212$	−101419.	−	118894.i	−0.154982	−	0.181686i
$213$	−19552.5			−0.0295293
$214$	−191573.	+	70608.2i	−0.285956	+	0.105395i
$215$		−	887656.i		−	1.30963i
$216$	−281972.	+	502413.i	−0.411217	+	0.732700i
$217$		−	275557.i		−	0.397248i
$218$	−468221.	−	1.27037e6i	−0.667283	−	1.81046i
$219$	340987.			0.480428
$220$	461738.	+	541297.i	0.643189	+	0.754013i
$221$		−	407016.i		−	0.560571i
$222$	−59668.6	−	161891.i	−0.0812575	−	0.220466i
$223$	953172.			1.28354			0.641769	−	0.766898i	$-0.278201\pi$
$223$	953172.			1.28354			0.641769	+	0.766898i	$0.278201\pi$
$224$	457741.	−	90321.6i	0.609537	−	0.120274i
$225$	−447716.			−0.589585
$226$	−185756.	−	503989.i	−0.241920	−	0.656372i
$227$	644020.			0.829535			0.414767	−	0.909927i	$-0.363863\pi$
$227$	644020.			0.829535			0.414767	+	0.909927i	$0.363863\pi$
$228$	219610.	+	299386.i	0.279779	+	0.381412i
$229$	−1.08188e6			−1.36330			−0.681648	−	0.731680i	$-0.738737\pi$
$229$	−1.08188e6			−1.36330			−0.681648	+	0.731680i	$0.738737\pi$
$230$	121964.	+	330911.i	0.152024	+	0.412469i
$231$	−178080.			−0.219576
$232$	814483.	+	457116.i	0.993486	+	0.557579i
$233$	554996.			0.669731			0.334865	−	0.942266i	$-0.391309\pi$
$233$	554996.			0.669731			0.334865	+	0.942266i	$0.391309\pi$
$234$	−174403.	−	473187.i	−0.208216	−	0.564928i
$235$			1.17359e6i			1.38626i
$236$	765652.	−	653118.i	0.894853	−	0.763329i
$237$	−559882.			−0.647479
$238$	135699.	+	368176.i	0.155287	+	0.421321i
$239$			131718.i			0.149159i	0.997215	+	0.0745795i	$0.0237614\pi$
$239$			131718.i			0.149159i	−0.997215	+	0.0745795i	$0.976239\pi$
$240$	−88265.2	+	552898.i	−0.0989148	+	0.619608i
$241$		−	635781.i		−	0.705123i	−0.935789	−	0.352562i	$-0.885311\pi$
$241$		−	635781.i		−	0.705123i	0.935789	−	0.352562i	$-0.114689\pi$
$242$	−377635.	+	139185.i	−0.414509	+	0.152776i
$243$	−938335.			−1.01939
$244$	−715805.	+	610597.i	−0.769697	+	0.656568i
$245$	765211.			0.814453
$246$	−283499.	−	769183.i	−0.298685	−	0.810386i
$247$	−741693.	−	54513.4i	−0.773539	−	0.0568540i
$248$	−303096.	+	540052.i	−0.312933	+	0.557579i
$249$			258477.i			0.264194i
$250$	295766.	−	109011.i	0.299294	−	0.110311i
$251$			450280.i			0.451126i	0.974229	+	0.225563i	$0.0724222\pi$
$251$			450280.i			0.451126i	−0.974229	+	0.225563i	$0.927578\pi$
$252$	315522.	+	369887.i	0.312988	+	0.366917i
$253$	252093.			0.247605
$254$	1.52723e6	−	562892.i	1.48532	−	0.547446i
$255$	−470880.			−0.453482
$256$	−996458.	−	326471.i	−0.950296	−	0.311347i
$257$			2.04006e6i			1.92668i	0.268285	+	0.963340i	$0.413543\pi$
$257$			2.04006e6i			1.92668i	−0.268285	+	0.963340i	$0.586457\pi$
$258$	−172681.	−	468514.i	−0.161508	−	0.438201i
$259$	−333167.			−0.308612
$260$	−727807.	−	853211.i	−0.667703	−	0.782750i
$261$			973250.i			0.884348i
$262$	−628.306	−	1704.71i	−0.000565481	−	0.00153425i
$263$		−	1.56262e6i		−	1.39304i	−0.717539	−	0.696518i	$-0.754731\pi$
$263$		−	1.56262e6i		−	1.39304i	0.717539	−	0.696518i	$-0.245269\pi$
$264$	349012.	+	195878.i	0.308198	+	0.172972i
$265$		−	362128.i		−	0.316772i
$266$	689092.	−	197970.i	0.597136	−	0.171551i
$267$			452606.i			0.388546i
$268$	−529003.	+	451251.i	−0.449905	+	0.383779i
$269$			688832.i			0.580407i	0.956965	+	0.290203i	$0.0937230\pi$
$269$			688832.i			0.580407i	−0.956965	+	0.290203i	$0.906277\pi$
$270$	−1.25267e6	+	461697.i	−1.04574	+	0.385432i
$271$			1.09484e6i			0.905580i	0.891617	+	0.452790i	$0.149571\pi$
$271$			1.09484e6i			0.905580i	−0.891617	+	0.452790i	$0.850429\pi$
$272$	139021.	−	870835.i	0.113935	−	0.713697i
$273$	280696.			0.227945
$274$	236475.	−	87157.9i	0.190287	−	0.0701343i
$275$			711680.i			0.567484i
$276$	128748.	+	150932.i	0.101734	+	0.119264i
$277$	−855408.			−0.669844			−0.334922	−	0.942246i	$-0.608710\pi$
$277$	−855408.			−0.669844			−0.334922	+	0.942246i	$0.608710\pi$
$278$	−713018.	−	1.93455e6i	−0.553336	−	1.50130i
$279$	−645325.			−0.496327
$280$	942817.	+	529142.i	0.718675	+	0.403346i
$281$			672672.i			0.508204i	0.967177	+	0.254102i	$0.0817798\pi$
$281$			672672.i			0.508204i	−0.967177	+	0.254102i	$0.918220\pi$
$282$	228305.	+	619432.i	0.170959	+	0.463843i
$283$			530064.i			0.393425i	0.980461	+	0.196713i	$0.0630266\pi$
$283$			530064.i			0.393425i	−0.980461	+	0.196713i	$0.936973\pi$
$284$	64556.2	−	55067.8i	0.0474944	−	0.0405137i
$285$	−63067.1	+	858072.i	−0.0459929	+	0.625766i
$286$	−752169.	+	277228.i	−0.543751	+	0.200411i
$287$	−1.58295e6			−1.13439
$288$	−211524.	−	1.07198e6i	−0.150272	−	0.761564i
$289$	−678202.			−0.477655
$290$	748476.	+	2.03075e6i	0.522616	+	1.41795i
$291$		−	670983.i		−	0.464493i
$292$	−1.12584e6	+	960361.i	−0.772712	+	0.659140i
$293$			345695.i			0.235247i	0.993058	+	0.117623i	$0.0375276\pi$
$293$			345695.i			0.235247i	−0.993058	+	0.117623i	$0.962472\pi$
$294$	403886.	−	148861.i	0.272515	−	0.100441i
$295$	2.33202e6			1.56019
$296$	652961.	+	366464.i	0.433169	+	0.243110i
$297$			954301.i			0.627761i
$298$	−216209.	+	79688.4i	−0.141037	+	0.0519822i
$299$	−397358.			−0.257042
$300$	−426093.	+	363467.i	−0.273339	+	0.233164i
$301$	−964186.			−0.613401
$302$	−1.65327e6	+	609346.i	−1.04310	+	0.384456i
$303$	−780945.			−0.488668
$304$	−1.56828e6	−	369969.i	−0.973284	−	0.229605i
$305$	−2.18020e6			−1.34198
$306$	862230.	−	317793.i	0.526405	−	0.194018i
$307$	120422.			0.0729225			0.0364612	−	0.999335i	$-0.488391\pi$
$307$	120422.			0.0729225			0.0364612	+	0.999335i	$0.488391\pi$
$308$	587965.	−	501547.i	0.353163	−	0.301255i
$309$	1.47590e6			0.879349
$310$	−1.34651e6	+	496286.i	−0.795804	+	0.293311i
$311$			932903.i			0.546935i	0.961881	+	0.273467i	$0.0881705\pi$
$311$			932903.i			0.546935i	−0.961881	+	0.273467i	$0.911829\pi$
$312$	−550125.	−	308749.i	−0.319944	−	0.179564i
$313$	1.41695e6			0.817509			0.408754	−	0.912644i	$-0.365963\pi$
$313$	1.41695e6			0.817509			0.408754	+	0.912644i	$0.365963\pi$
$314$	601779.	−	221799.i	0.344440	−	0.126951i
$315$			1.12660e6i			0.639725i
$316$	1.84856e6	−	1.57686e6i	1.04139	−	0.888332i
$317$		−	1.50073e6i		−	0.838790i	−0.907804	−	0.419395i	$-0.862242\pi$
$317$		−	1.50073e6i		−	0.838790i	0.907804	−	0.419395i	$-0.137758\pi$
$318$	−70446.9	−	191135.i	−0.0390656	−	0.105992i
$319$	1.54706e6			0.851197
$320$	−1.26576e6	−	2.07409e6i	−0.691000	−	1.13228i
$321$	−266137.			−0.144159
$322$	359441.	−	132480.i	0.193191	−	0.0712048i
$323$	99333.1	−	1.35150e6i	0.0529770	−	0.720790i
$324$	544574.	−	464533.i	0.288200	−	0.245841i
$325$		−	1.12178e6i		−	0.589112i
$326$	176210.	+	478089.i	0.0918303	+	0.249152i
$327$		−	1.76482e6i		−	0.912706i
$328$	3.10236e6	+	1.74115e6i	1.59224	+	0.893620i
$329$	1.27477e6			0.649295
$330$	320728.	+	870191.i	0.162126	+	0.439875i
$331$	566817.			0.284363			0.142181	−	0.989841i	$-0.454588\pi$
$331$	566817.			0.284363			0.142181	+	0.989841i	$0.454588\pi$
$332$	−727978.	−	853411.i	−0.362471	−	0.424926i
$333$			780242.i			0.385584i
$334$	2.72720e6	−	1.00517e6i	1.33767	−	0.493029i
$335$	−1.61123e6			−0.784416
$336$	600566.	+	95875.0i	0.290210	+	0.0463295i
$337$			682903.i			0.327555i	0.986497	+	0.163778i	$0.0523680\pi$
$337$			682903.i			0.327555i	−0.986497	+	0.163778i	$0.947632\pi$
$338$	−785159.	+	289387.i	−0.373823	+	0.137780i
$339$		−	700151.i		−	0.330897i
$340$	1.55470e6	−	1.32619e6i	0.729373	−	0.622171i
$341$			1.02580e6i			0.477721i
$342$	−463624.	−	1.61378e6i	−0.214339	−	0.746070i
$343$		−	2.18491e6i		−	1.00276i
$344$	1.88967e6	+	1.06055e6i	0.860973	+	0.483208i
$345$			459708.i			0.207938i
$346$	−1.32511e6	−	3.59527e6i	−0.595063	−	1.61451i
$347$			2.93498e6i			1.30852i	0.756268	+	0.654262i	$0.227021\pi$
$347$			2.93498e6i			1.30852i	−0.756268	+	0.654262i	$0.772979\pi$
$348$	790107.	+	926246.i	0.349734	+	0.409994i
$349$	3.80401e6			1.67178			0.835888	−	0.548900i	$-0.184953\pi$
$349$	3.80401e6			1.67178			0.835888	+	0.548900i	$0.184953\pi$
$350$	374001.	+	1.01473e6i	0.163193	+	0.442772i
$351$		−	1.50420e6i		−	0.651686i
$352$	−1.70400e6	+	336234.i	−0.733016	+	0.144639i
$353$	2.67782e6			1.14378			0.571892	−	0.820329i	$-0.306210\pi$
$353$	2.67782e6			1.14378			0.571892	+	0.820329i	$0.306210\pi$
$354$	1.23087e6	−	453662.i	0.522038	−	0.192408i
$355$	196625.			0.0828072
$356$	−1.27473e6	−	1.49437e6i	−0.533080	−	0.624931i
$357$			511478.i			0.212401i
$358$	2.06524e6	−	761187.i	0.851652	−	0.313895i
$359$		−	1.10297e6i		−	0.451675i	−0.974165	−	0.225838i	$-0.927488\pi$
$359$		−	1.10297e6i		−	0.451675i	0.974165	−	0.225838i	$-0.0725119\pi$
$360$	1.23920e6	−	2.20798e6i	0.503946	−	0.897923i
$361$	−2.44949e6	−	362024.i	−0.989254	−	0.146207i
$362$	−220026.	−	596969.i	−0.0882475	−	0.239431i
$363$	−524618.			−0.208966
$364$	−926771.	+	790556.i	−0.366622	+	0.312737i
$365$	−3.42906e6			−1.34724
$366$	−1.15073e6	+	424126.i	−0.449025	+	0.165498i
$367$			1.68764e6i			0.654055i	0.945015	+	0.327028i	$0.106047\pi$
$367$			1.68764e6i			0.654055i	−0.945015	+	0.327028i	$0.893953\pi$
$368$	−850173.	−	135723.i	−0.327256	−	0.0522435i
$369$			3.70711e6i			1.41732i
$370$	600044.	+	1.62803e6i	0.227866	+	0.618240i
$371$	−393349.			−0.148369
$372$	−614158.	+	523890.i	−0.230103	+	0.196283i
$373$		−	2.23384e6i		−	0.831343i	−0.909515	−	0.415671i	$-0.863547\pi$
$373$		−	2.23384e6i		−	0.831343i	0.909515	−	0.415671i	$-0.136453\pi$
$374$	−505158.	−	1.37058e6i	−0.186745	−	0.506672i
$375$	410883.			0.150883
$376$	−2.49837e6	−	1.40217e6i	−0.911354	−	0.511484i
$377$	−2.43853e6			−0.883638
$378$	501502.	+	1.36066e6i	0.180527	+	0.489803i
$379$	−5.05682e6			−1.80834			−0.904170	−	0.427174i	$-0.859509\pi$
$379$	−5.05682e6			−1.80834			−0.904170	+	0.427174i	$0.859509\pi$
$380$	−2.20846e6	−	3.01071e6i	−0.784567	−	1.06957i
$381$	2.12165e6			0.748793
$382$	1.13448e6	+	3.07805e6i	0.397777	+	1.07924i
$383$	147080.			0.0512339			0.0256169	−	0.999672i	$-0.491845\pi$
$383$	147080.			0.0512339			0.0256169	+	0.999672i	$0.491845\pi$
$384$	−1.07157e6	−	848490.i	−0.370845	−	0.293642i
$385$	1.79082e6			0.615745
$386$	420416.	+	1.14066e6i	0.143619	+	0.389663i
$387$			2.25802e6i			0.766392i
$388$	1.88977e6	+	2.21538e6i	0.637278	+	0.747083i
$389$	−1.65969e6			−0.556102			−0.278051	−	0.960566i	$-0.589688\pi$
$389$	−1.65969e6			−0.556102			−0.278051	+	0.960566i	$0.589688\pi$
$390$	−505542.	−	1.37163e6i	−0.168304	−	0.456640i
$391$		−	724057.i		−	0.239514i
$392$	−914254.	+	1.62900e6i	−0.300505	+	0.535435i
$393$		−	2368.21i		−	0.000773462i
$394$	−3.99733e6	+	1.47330e6i	−1.29727	+	0.478136i
$395$	5.63033e6			1.81569
$396$	−1.17457e6	−	1.37695e6i	−0.376393	−	0.441246i
$397$	380495.			0.121164			0.0605819	−	0.998163i	$-0.480704\pi$
$397$	380495.			0.121164			0.0605819	+	0.998163i	$0.480704\pi$
$398$	1.65959e6	+	4.50277e6i	0.525162	+	1.42486i
$399$	932051.	+	68504.5i	0.293094	+	0.0215420i
$400$	383156.	−	2.40011e6i	0.119736	−	0.750034i
$401$		−	3.81805e6i		−	1.18572i	−0.805307	−	0.592859i	$-0.797999\pi$
$401$		−	3.81805e6i		−	1.18572i	0.805307	−	0.592859i	$-0.202001\pi$
$402$	−850427.	+	313443.i	−0.262465	+	0.0967372i
$403$		−	1.61689e6i		−	0.495928i
$404$	2.57844e6	−	2.19946e6i	0.785966	−	0.670446i
$405$	1.65866e6			0.502481
$406$	2.20583e6	−	813006.i	0.664136	−	0.244782i
$407$	1.24026e6			0.371130
$408$	562596.	−	1.00242e6i	0.167319	−	0.298127i
$409$		−	6.20250e6i		−	1.83341i	−0.399569	−	0.916703i	$-0.630840\pi$
$409$		−	6.20250e6i		−	1.83341i	0.399569	−	0.916703i	$-0.369160\pi$
$410$	2.85094e6	+	7.73512e6i	0.837585	+	2.27252i
$411$	328515.			0.0959293
$412$	−4.87297e6	+	4.15675e6i	−1.41433	+	1.20645i
$413$		−	2.53308e6i		−	0.730758i
$414$	−310253.	−	841772.i	−0.0889642	−	0.241376i
$415$		−	2.59932e6i		−	0.740865i
$416$	2.68591e6	−	529984.i	0.760953	−	0.150151i
$417$		−	2.68751e6i		−	0.756850i
$418$	−2.56524e6	+	736967.i	−0.718103	+	0.206304i
$419$		−	1.54034e6i		−	0.428629i	−0.976765	−	0.214314i	$-0.931248\pi$
$419$		−	1.54034e6i		−	0.428629i	0.976765	−	0.214314i	$-0.0687517\pi$
$420$	914601.	+	1.07219e6i	0.252993	+	0.296585i
$421$		−	1.41317e6i		−	0.388588i	−0.980943	−	0.194294i	$-0.937758\pi$
$421$		−	1.41317e6i		−	0.388588i	0.980943	−	0.194294i	$-0.0622416\pi$
$422$	−5.46581e6	+	2.01454e6i	−1.49408	+	0.550675i
$423$		−	2.98538e6i		−	0.811238i
$424$	770909.	+	432661.i	0.208252	+	0.116878i
$425$	2.04407e6			0.548939
$426$	103781.	−	38250.6i	0.0277072	−	0.0102121i
$427$			2.36816e6i			0.628553i
$428$	878701.	−	749550.i	0.231863	−	0.197784i
$429$	−1.04493e6			−0.274121
$430$	1.73653e6	+	4.71151e6i	0.452909	+	1.22882i
$431$	3.79553e6			0.984192			0.492096	−	0.870541i	$-0.336231\pi$
$431$	3.79553e6			0.984192			0.492096	+	0.870541i	$0.336231\pi$
$432$	513779.	−	3.21834e6i	0.132454	−	0.829702i
$433$			113030.i			0.0289717i	0.999895	+	0.0144858i	$0.00461115\pi$
$433$			113030.i			0.0289717i	−0.999895	+	0.0144858i	$0.995389\pi$
$434$	539073.	+	1.46260e6i	0.137380	+	0.372737i
$435$			2.82116e6i			0.714832i
$436$	4.97046e6	+	5.82689e6i	1.25222	+	1.46798i
$437$	−1.31943e6	−	96976.2i	−0.330509	−	0.0242919i
$438$	−1.80990e6	+	667076.i	−0.450784	+	0.166146i
$439$	−5.89472e6			−1.45983			−0.729914	−	0.683539i	$-0.760440\pi$
$439$	−5.89472e6			−1.45983			−0.729914	+	0.683539i	$0.760440\pi$
$440$	−3.50976e6	−	1.96980e6i	−0.864263	−	0.485055i
$441$	−1.94655e6			−0.476615
$442$	796248.	+	2.16036e6i	0.193862	+	0.525982i
$443$			6.87826e6i			1.66521i	0.553866	+	0.832606i	$0.313152\pi$
$443$			6.87826e6i			1.66521i	−0.553866	+	0.832606i	$0.686848\pi$
$444$	633419.	+	742559.i	0.152487	+	0.178761i
$445$		−	4.55154e6i		−	1.08958i
$446$	−5.05926e6	+	1.86470e6i	−1.20434	+	0.443886i
$447$	−300362.			−0.0711010
$448$	−2.25291e6	+	1.37489e6i	−0.530333	+	0.323649i
$449$			3.64357e6i			0.852926i	0.904505	+	0.426463i	$0.140241\pi$
$449$			3.64357e6i			0.852926i	−0.904505	+	0.426463i	$0.859759\pi$
$450$	2.37639e6	−	875870.i	0.553206	−	0.203896i
$451$	5.89274e6			1.36419
$452$	1.97192e6	+	2.31168e6i	0.453986	+	0.532209i
$453$	−2.29675e6			−0.525857
$454$	−3.41834e6	+	1.25990e6i	−0.778350	+	0.286878i
$455$	−2.82276e6			−0.639212
$456$	−1.75134e6	−	1.15946e6i	−0.394419	−	0.261123i
$457$	−6.59770e6			−1.47775			−0.738876	−	0.673841i	$-0.764643\pi$
$457$	−6.59770e6			−1.47775			−0.738876	+	0.673841i	$0.764643\pi$
$458$	5.74241e6	−	2.11649e6i	1.27918	−	0.471468i
$459$	2.74092e6			0.607247
$460$	−1.29473e6	−	1.51781e6i	−0.285288	−	0.334444i
$461$	989844.			0.216927			0.108464	−	0.994100i	$-0.465407\pi$
$461$	989844.			0.216927			0.108464	+	0.994100i	$0.465407\pi$
$462$	945215.	−	348379.i	0.206028	−	0.0759359i
$463$		−	1.18817e6i		−	0.257589i	−0.991671	−	0.128795i	$-0.958889\pi$
$463$		−	1.18817e6i		−	0.257589i	0.991671	−	0.128795i	$-0.0411108\pi$
$464$	−5.21738e6	−	832908.i	−1.12501	−	0.179598i
$465$	−1.87060e6			−0.401189
$466$	−2.94581e6	+	1.08574e6i	−0.628407	+	0.231613i
$467$			7.10061e6i			1.50662i	0.657666	+	0.753310i	$0.271544\pi$
$467$			7.10061e6i			1.50662i	−0.657666	+	0.753310i	$0.728456\pi$
$468$	1.85140e6	+	2.17040e6i	0.390738	+	0.458063i
$469$			1.75015e6i			0.367403i
$470$	−2.29590e6	−	6.22919e6i	−0.479411	−	1.30073i
$471$	836003.			0.173642
$472$	−2.78624e6	+	4.96448e6i	−0.575656	+	1.02570i
$473$	3.58931e6			0.737662
$474$	2.97175e6	−	1.09530e6i	0.607528	−	0.223917i
$475$	273772.	−	3.72486e6i	0.0556743	−	0.757488i
$476$	−1.44053e6	−	1.68874e6i	−0.291411	−	0.341622i
$477$			921182.i			0.185374i
$478$	−257680.	−	699132.i	−0.0515836	−	0.139955i
$479$		−	8.66400e6i		−	1.72536i	−0.505750	−	0.862680i	$-0.668784\pi$
$479$		−	8.66400e6i		−	1.72536i	0.505750	−	0.862680i	$-0.331216\pi$
$480$	−613143.	−	3.10735e6i	−0.121467	−	0.615584i
$481$	−1.95494e6			−0.385274
$482$	1.24378e6	+	3.37461e6i	0.243853	+	0.661615i
$483$	499342.			0.0973935
$484$	1.73213e6	−	1.47754e6i	0.336098	−	0.286699i
$485$			6.74759e6i			1.30255i
$486$	4.98050e6	−	1.83567e6i	0.956495	−	0.352537i
$487$	1.53710e6			0.293684			0.146842	−	0.989160i	$-0.453089\pi$
$487$	1.53710e6			0.293684			0.146842	+	0.989160i	$0.453089\pi$
$488$	2.60484e6	−	4.64127e6i	0.495144	−	0.882240i
$489$			664170.i			0.125605i
$490$	−4.06159e6	+	1.49699e6i	−0.764199	+	0.281662i
$491$			9.45899e6i			1.77068i	0.464941	+	0.885342i	$0.346075\pi$
$491$			9.45899e6i			1.77068i	−0.464941	+	0.885342i	$0.653925\pi$
$492$	3.00952e6	+	3.52807e6i	0.560511	+	0.657089i
$493$		−	4.44343e6i		−	0.823381i
$494$	4.04341e6	−	1.16163e6i	0.745471	−	0.214167i
$495$		−	4.19392e6i		−	0.769320i
$496$	552270.	−	3.45945e6i	0.100797	−	0.631397i
$497$		−	213577.i		−	0.0387850i
$498$	−505660.	−	1.37195e6i	−0.0913662	−	0.247893i
$499$			6.86012e6i			1.23333i	0.787224	+	0.616667i	$0.211517\pi$
$499$			6.86012e6i			1.23333i	−0.787224	+	0.616667i	$0.788483\pi$
$500$	−1.35661e6	+	1.15722e6i	−0.242678	+	0.207009i
$501$	3.78867e6			0.674362
$502$	−880886.	−	2.39000e6i	−0.156013	−	0.423291i
$503$		−	7.79162e6i		−	1.37312i	−0.727075	−	0.686558i	$-0.759121\pi$
$503$		−	7.79162e6i		−	1.37312i	0.727075	−	0.686558i	$-0.240879\pi$
$504$	−2.39834e6	−	1.34603e6i	−0.420567	−	0.236037i
$505$	7.85340e6			1.37034
$506$	−1.33806e6	+	493172.i	−0.232328	+	0.0856293i
$507$	−1.09076e6			−0.188455
$508$	−7.00504e6	+	5.97545e6i	−1.20435	+	1.02733i
$509$			9.60795e6i			1.64375i	0.569667	+	0.821876i	$0.307072\pi$
$509$			9.60795e6i			1.64375i	−0.569667	+	0.821876i	$0.692928\pi$
$510$	2.49934e6	−	921187.i	0.425501	−	0.156828i
$511$			3.72470e6i			0.631015i
$512$	5.92769e6	−	216529.i	0.999334	−	0.0365041i
$513$	367104.	−	4.99471e6i	0.0615880	−	0.837948i
$514$	−3.99098e6	−	1.08282e7i	−0.666303	−	1.80780i
$515$	−1.48421e7			−2.46591
$516$	1.83312e6	+	2.14897e6i	0.303086	+	0.355309i
$517$	−4.74550e6			−0.780828
$518$	1.76839e6	−	651777.i	0.289570	−	0.106727i
$519$		−	4.99461e6i		−	0.813924i
$520$	5.53221e6	+	3.10487e6i	0.897202	+	0.503541i
$521$		−	6.64194e6i		−	1.07202i	−0.844213	−	0.536008i	$-0.819932\pi$
$521$		−	6.64194e6i		−	1.07202i	0.844213	−	0.536008i	$-0.180068\pi$
$522$	−1.90398e6	−	5.16583e6i	−0.305834	−	0.829781i
$523$	3.32969e6			0.532292			0.266146	−	0.963933i	$-0.414250\pi$
$523$	3.32969e6			0.532292			0.266146	+	0.963933i	$0.414250\pi$
$524$	6669.86	+	7819.10i	0.00106118	+	0.00124402i
$525$			1.40968e6i			0.223215i
$526$	3.05696e6	+	8.29407e6i	0.481753	+	1.30708i
$527$	2.94627e6			0.462110
$528$	−2.23569e6	−	356907.i	−0.349000	−	0.0557148i
$529$	5.72947e6			0.890174
$530$	708434.	+	1.92211e6i	0.109549	+	0.297227i
$531$	−5.93220e6			−0.913019
$532$	−3.27028e6	+	2.39886e6i	−0.500964	+	0.367474i
$533$	−9.28834e6			−1.41619
$534$	−885437.	−	2.40235e6i	−0.134371	−	0.364572i
$535$	2.67634e6			0.404257
$536$	1.92506e6	−	3.43005e6i	0.289423	−	0.515689i
$537$	2.86906e6			0.429343
$538$	−1.34757e6	−	3.65619e6i	−0.200722	−	0.544594i
$539$			3.09419e6i			0.458749i
$540$	5.74569e6	−	4.90120e6i	0.847926	−	0.723299i
$541$	1.36743e6			0.200868			0.100434	−	0.994944i	$-0.467977\pi$
$541$	1.36743e6			0.200868			0.100434	+	0.994944i	$0.467977\pi$
$542$	−2.14184e6	−	5.81119e6i	−0.313176	−	0.849703i
$543$		−	829321.i		−	0.120704i
$544$	965724.	+	4.89420e6i	0.139912	+	0.709062i
$545$			1.77475e7i			2.55945i
$546$	−1.48988e6	+	549127.i	−0.213880	+	0.0788300i
$547$	5.44793e6			0.778509			0.389254	−	0.921130i	$-0.372733\pi$
$547$	5.44793e6			0.778509			0.389254	+	0.921130i	$0.372733\pi$
$548$	−1.08466e6	+	925235.i	−0.154291	+	0.131614i
$549$	5.54599e6			0.785322
$550$	−1.39227e6	−	3.77747e6i	−0.196253	−	0.532468i
$551$	−8.09714e6	−	595128.i	−1.13619	−	0.0835086i
$552$	−978640.	−	549247.i	−0.136702	−	0.0767220i
$553$		−	6.11575e6i		−	0.850427i
$554$	4.54034e6	−	1.67344e6i	0.628513	−	0.231652i
$555$			2.26168e6i			0.311673i
$556$	7.56913e6	+	8.87332e6i	1.03839	+	1.21730i
$557$	−313832.			−0.0428608			−0.0214304	−	0.999770i	$-0.506822\pi$
$557$	−313832.			−0.0428608			−0.0214304	+	0.999770i	$0.506822\pi$
$558$	3.42526e6	−	1.26245e6i	0.465702	−	0.171645i
$559$	−5.65759e6			−0.765776
$560$	−6.03946e6	−	964146.i	−0.813820	−	0.129919i
$561$		−	1.90404e6i		−	0.255428i
$562$	−1.31595e6	−	3.57042e6i	−0.175752	−	0.476846i
$563$	2.48402e6			0.330282			0.165141	−	0.986270i	$-0.447192\pi$
$563$	2.48402e6			0.330282			0.165141	+	0.986270i	$0.447192\pi$
$564$	−2.42360e6	−	2.84120e6i	−0.320821	−	0.376100i
$565$			7.04092e6i			0.927915i
$566$	−1.03697e6	−	2.81348e6i	−0.136058	−	0.369150i
$567$		−	1.80166e6i		−	0.235351i
$568$	−234923.	+	418582.i	−0.0305530	+	0.0544389i
$569$			3.30528e6i			0.427985i	0.976835	+	0.213992i	$0.0686468\pi$
$569$			3.30528e6i			0.427985i	−0.976835	+	0.213992i	$0.931353\pi$
$570$	−1.34390e6	−	4.67786e6i	−0.173253	−	0.603060i
$571$		−	1.51598e7i		−	1.94582i	−0.231174	−	0.972912i	$-0.574257\pi$
$571$		−	1.51598e7i		−	1.94582i	0.231174	−	0.972912i	$-0.425743\pi$
$572$	3.45003e6	−	2.94295e6i	0.440892	−	0.376090i
$573$			4.27609e6i			0.544077i
$574$	8.40200e6	−	3.09674e6i	1.06440	−	0.392306i
$575$		−	1.99557e6i		−	0.251709i
$576$	3.21986e6	+	5.27608e6i	0.404371	+	0.662605i
$577$	−818742.			−0.102378			−0.0511891	−	0.998689i	$-0.516301\pi$
$577$	−818742.			−0.102378			−0.0511891	+	0.998689i	$0.516301\pi$
$578$	3.59977e6	−	1.32677e6i	0.448183	−	0.165187i
$579$			1.58463e6i			0.196441i
$580$	−7.94554e6	−	9.31458e6i	−0.980739	−	1.14972i
$581$	−2.82342e6			−0.347004
$582$	1.31265e6	+	3.56145e6i	0.160635	+	0.435832i
$583$	1.46429e6			0.178425
$584$	4.09696e6	−	7.29990e6i	0.497084	−	0.885696i
$585$			6.61060e6i			0.798640i
$586$	−676285.	−	1.83488e6i	−0.0813553	−	0.220732i
$587$			2.05576e6i			0.246251i	0.992391	+	0.123126i	$0.0392918\pi$
$587$			2.05576e6i			0.246251i	−0.992391	+	0.123126i	$0.960708\pi$
$588$	−1.85254e6	+	1.58025e6i	−0.220965	+	0.188488i
$589$	394607.	−	5.36890e6i	0.0468680	−	0.637672i
$590$	−1.23779e7	+	4.56215e6i	−1.46392	+	0.539560i
$591$	−5.55317e6			−0.653992
$592$	−4.18271e6	−	667732.i	−0.490516	−	0.0783065i
$593$	8.30825e6			0.970226			0.485113	−	0.874451i	$-0.338778\pi$
$593$	8.30825e6			0.970226			0.485113	+	0.874451i	$0.338778\pi$
$594$	−1.86691e6	−	5.06525e6i	−0.217098	−	0.589027i
$595$		−	5.14356e6i		−	0.595623i
$596$	991701.	−	845942.i	0.114358	−	0.0975495i
$597$			6.25533e6i			0.718314i
$598$	2.10910e6	−	777355.i	0.241182	−	0.0888928i
$599$	1.13233e7			1.28945			0.644727	−	0.764413i	$-0.276971\pi$
$599$	1.13233e7			1.28945			0.644727	+	0.764413i	$0.276971\pi$
$600$	1.55057e6	−	2.76278e6i	0.175838	−	0.313306i
$601$			2.35047e6i			0.265442i	0.991153	+	0.132721i	$0.0423714\pi$
$601$			2.35047e6i			0.265442i	−0.991153	+	0.132721i	$0.957629\pi$
$602$	5.11771e6	−	1.88624e6i	0.575552	−	0.212132i
$603$	4.09866e6			0.459038
$604$	7.58315e6	−	6.46859e6i	0.845780	−	0.721469i
$605$	5.27570e6			0.585992
$606$	4.14511e6	−	1.52777e6i	0.458516	−	0.168996i
$607$	3.76789e6			0.415075			0.207537	−	0.978227i	$-0.433455\pi$
$607$	3.76789e6			0.415075			0.207537	+	0.978227i	$0.433455\pi$
$608$	9.04791e6	−	1.10431e6i	0.992634	−	0.121152i
$609$	3.06438e6			0.334811
$610$	1.15721e7	−	4.26513e6i	1.25918	−	0.464096i
$611$	7.48002e6			0.810587
$612$	−3.95485e6	+	3.37358e6i	−0.426827	+	0.364093i
$613$	1.48787e7			1.59924			0.799618	−	0.600509i	$-0.205035\pi$
$613$	1.48787e7			1.59924			0.799618	+	0.600509i	$0.205035\pi$
$614$	−639180.	+	235583.i	−0.0684230	+	0.0252188i
$615$			1.07458e7i			1.14564i
$616$	−2.13963e6	+	3.81236e6i	−0.227189	+	0.404801i
$617$	−1.58901e7			−1.68040			−0.840200	−	0.542276i	$-0.817563\pi$
$617$	−1.58901e7			−1.68040			−0.840200	+	0.542276i	$0.817563\pi$
$618$	−7.83381e6	+	2.88732e6i	−0.825091	+	0.304105i
$619$		−	9.96333e6i		−	1.04515i	−0.852594	−	0.522574i	$-0.824972\pi$
$619$		−	9.96333e6i		−	1.04515i	0.852594	−	0.522574i	$-0.175028\pi$
$620$	6.17614e6	−	5.26838e6i	0.645265	−	0.550425i
$621$		−	2.67589e6i		−	0.278445i
$622$	−1.82504e6	−	4.95167e6i	−0.189146	−	0.513187i
$623$	−4.94395e6			−0.510333
$624$	3.52397e6	+	562570.i	0.362302	+	0.0578382i
$625$	−1.15493e7			−1.18264
$626$	−7.52088e6	+	2.77198e6i	−0.767066	+	0.282719i
$627$	−3.46968e6	−	255017.i	−0.352469	−	0.0259060i
$628$	−2.76022e6	+	2.35453e6i	−0.279283	+	0.238235i
$629$		−	3.56224e6i		−	0.359002i
$630$	−2.20398e6	−	5.97978e6i	−0.221236	−	0.600253i
$631$			1.50560e7i			1.50535i	0.658394	+	0.752674i	$0.271236\pi$
$631$			1.50560e7i			1.50535i	−0.658394	+	0.752674i	$0.728764\pi$
$632$	−6.72697e6	+	1.19860e7i	−0.669926	+	1.19366i
$633$	−7.59321e6			−0.753210
$634$	2.93588e6	+	7.96557e6i	0.290078	+	0.787035i
$635$	−2.13359e7			−2.09980
$636$	747838.	+	876693.i	0.0733102	+	0.0859418i
$637$		−	4.87717e6i		−	0.476233i
$638$	−8.21149e6	+	3.02652e6i	−0.798676	+	0.294369i
$639$	−500176.			−0.0484585
$640$	1.07760e7	+	8.53265e6i	1.03994	+	0.823444i
$641$		−	1.52722e6i		−	0.146810i	−0.997302	−	0.0734051i	$-0.976613\pi$
$641$		−	1.52722e6i		−	0.146810i	0.997302	−	0.0734051i	$-0.0233866\pi$
$642$	1.41260e6	−	520645.i	0.135264	−	0.0498545i
$643$		−	4.88237e6i		−	0.465696i	−0.972513	−	0.232848i	$-0.925195\pi$
$643$		−	4.88237e6i		−	0.465696i	0.972513	−	0.232848i	$-0.0748045\pi$
$644$	−1.64867e6	+	1.40635e6i	−0.156646	+	0.133622i
$645$			6.54532e6i			0.619486i
$646$	2.11670e6	+	7.36782e6i	0.199562	+	0.694636i
$647$			1.57872e7i			1.48267i	0.671136	+	0.741334i	$0.265807\pi$
$647$			1.57872e7i			1.48267i	−0.671136	+	0.741334i	$0.734193\pi$
$648$	−1.98173e6	+	3.53101e6i	−0.185398	+	0.330340i
$649$			9.42971e6i			0.878793i
$650$	2.19454e6	+	5.95417e6i	0.203732	+	0.552762i
$651$			2.03188e6i			0.187908i
$652$	−1.87058e6	−	2.19288e6i	−0.172328	−	0.202021i
$653$	−3.17397e6			−0.291286			−0.145643	−	0.989337i	$-0.546525\pi$
$653$	−3.17397e6			−0.291286			−0.145643	+	0.989337i	$0.546525\pi$
$654$	3.45253e6	+	9.36732e6i	0.315641	+	0.856389i
$655$			23815.4i			0.00216897i
$656$	−1.98730e7	−	3.17254e6i	−1.80303	−	0.287838i
$657$	8.72287e6			0.788398
$658$	−6.76624e6	+	2.49384e6i	−0.609232	+	0.224545i
$659$	1.10241e6			0.0988852			0.0494426	−	0.998777i	$-0.484256\pi$
$659$	1.10241e6			0.0988852			0.0494426	+	0.998777i	$0.484256\pi$
$660$	−3.40472e6	−	3.99137e6i	−0.304244	−	0.356666i
$661$		−	1.07049e7i		−	0.952971i	−0.879182	−	0.476486i	$-0.841910\pi$
$661$		−	1.07049e7i		−	0.952971i	0.879182	−	0.476486i	$-0.158090\pi$
$662$	−3.00856e6	+	1.10887e6i	−0.266817	+	0.0983411i
$663$			3.00122e6i			0.265163i
$664$	5.53350e6	+	3.10560e6i	0.487057	+	0.273354i
$665$	−9.37297e6	−	688900.i	−0.821908	−	0.0604091i
$666$	−1.52639e6	−	4.14138e6i	−0.133346	−	0.361792i
$667$	−4.33800e6			−0.377550
$668$	−1.25090e7	+	1.06705e7i	−1.08463	+	0.925215i
$669$	−7.02842e6			−0.607145
$670$	8.55213e6	−	3.15207e6i	0.736016	−	0.271274i
$671$		−	8.81579e6i		−	0.755884i
$672$	−3.37525e6	+	666006.i	−0.288326	+	0.0568925i
$673$		−	1.71375e7i		−	1.45851i	−0.684241	−	0.729256i	$-0.739866\pi$
$673$		−	1.71375e7i		−	1.45851i	0.684241	−	0.729256i	$-0.260134\pi$
$674$	−1.33597e6	−	3.62472e6i	−0.113278	−	0.307344i
$675$	7.55426e6			0.638164
$676$	3.60135e6	−	3.07202e6i	0.303108	−	0.258558i
$677$			1.53359e6i			0.128599i	0.997931	+	0.0642995i	$0.0204813\pi$
$677$			1.53359e6i			0.128599i	−0.997931	+	0.0642995i	$0.979519\pi$
$678$	1.36971e6	+	3.71627e6i	0.114434	+	0.310480i
$679$	7.32934e6			0.610085
$680$	−5.65762e6	+	1.00807e7i	−0.469204	+	0.836020i
$681$	−4.74882e6			−0.392390
$682$	−2.00677e6	−	5.44473e6i	−0.165210	−	0.448245i
$683$	1.26404e7			1.03683			0.518415	−	0.855129i	$-0.326522\pi$
$683$	1.26404e7			1.03683			0.518415	+	0.855129i	$0.326522\pi$
$684$	5.61788e6	+	7.65866e6i	0.459127	+	0.625911i
$685$	−3.30364e6			−0.269009
$686$	4.27435e6	+	1.15971e7i	0.346785	+	0.940888i
$687$	7.97747e6			0.644872
$688$	−1.21048e7	−	1.93242e6i	−0.974956	−	0.155643i
$689$	−2.30807e6			−0.185225
$690$	−899330.	−	2.44004e6i	−0.0719111	−	0.195108i
$691$		−	3.64221e6i		−	0.290181i	−0.989418	−	0.145091i	$-0.953653\pi$
$691$		−	3.64221e6i		−	0.290181i	0.989418	−	0.145091i	$-0.0463474\pi$
$692$	1.40669e7	+	1.64907e7i	1.11669	+	1.30910i
$693$	−4.55550e6			−0.360332
$694$	−5.74173e6	−	1.55783e7i	−0.452527	−	1.22779i
$695$			2.70263e7i			2.12239i
$696$	−6.00576e6	−	3.37064e6i	−0.469943	−	0.263748i
$697$		−	1.69250e7i		−	1.31961i
$698$	−2.01910e7	+	7.44182e6i	−1.56862	+	0.578150i
$699$	−4.09238e6			−0.316799
$700$	−3.97025e6	−	4.65434e6i	−0.306248	−	0.359015i
$701$	8.50256e6			0.653514			0.326757	−	0.945108i	$-0.394044\pi$
$701$	8.50256e6			0.653514			0.326757	+	0.945108i	$0.394044\pi$
$702$	2.94268e6	+	7.98403e6i	0.225372	+	0.611476i
$703$	−6.49137e6	−	477107.i	−0.495391	−	0.0364105i
$704$	8.38674e6	−	5.11822e6i	0.637767	−	0.389213i
$705$		−	8.65370e6i		−	0.655736i
$706$	−1.42133e7	+	5.23863e6i	−1.07321	+	0.395554i
$707$		−	8.53049e6i		−	0.641838i
$708$	−5.64570e6	+	4.81590e6i	−0.423287	+	0.361073i
$709$	9.45835e6			0.706642			0.353321	−	0.935502i	$-0.385052\pi$
$709$	9.45835e6			0.706642			0.353321	+	0.935502i	$0.385052\pi$
$710$	−1.04365e6	+	384659.i	−0.0776978	+	0.0286372i
$711$	−1.43224e7			−1.06254
$712$	9.68945e6	+	5.43806e6i	0.716307	+	0.402017i
$713$		−	2.87636e6i		−	0.211894i
$714$	−1.00061e6	−	2.71483e6i	−0.0734545	−	0.199295i
$715$	1.05081e7			0.768702
$716$	−9.47277e6	+	8.08047e6i	−0.690549	+	0.589053i
$717$		−	971248.i		−	0.0705557i
$718$	2.15774e6	+	5.85434e6i	0.156203	+	0.423806i
$719$		−	1.31194e7i		−	0.946436i	−0.880945	−	0.473218i	$-0.843092\pi$
$719$		−	1.31194e7i		−	0.946436i	0.880945	−	0.473218i	$-0.156908\pi$
$720$	−2.25793e6	+	1.41438e7i	−0.162323	+	1.01680i
$721$			1.61217e7i			1.15498i
$722$	1.37097e7	−	2.87040e6i	0.978777	−	0.204927i
$723$			4.68807e6i			0.333540i
$724$	2.33571e6	+	2.73816e6i	0.165605	+	0.194139i
$725$		−	1.22465e7i		−	0.865302i
$726$	2.78457e6	−	1.02631e6i	0.196073	−	0.0722668i
$727$			2.23602e7i			1.56906i	0.620092	+	0.784529i	$0.287095\pi$
$727$			2.23602e7i			1.56906i	−0.620092	+	0.784529i	$0.712905\pi$
$728$	3.37256e6	−	6.00917e6i	0.235847	−	0.420229i
$729$	1.48350e6			0.103388
$730$	1.82008e7	−	6.70830e6i	1.26411	−	0.465914i
$731$		−	1.03091e7i		−	0.713557i
$732$	5.27814e6	−	4.50236e6i	0.364085	−	0.310572i
$733$	−9.88432e6			−0.679496			−0.339748	−	0.940517i	$-0.610342\pi$
$733$	−9.88432e6			−0.679496			−0.339748	+	0.940517i	$0.610342\pi$
$734$	−3.30154e6	−	8.95767e6i	−0.226192	−	0.613698i
$735$	−5.64244e6			−0.385256
$736$	4.77807e6	−	942810.i	0.325131	−	0.0641549i
$737$		−	6.51515e6i		−	0.441831i
$738$	−7.25224e6	−	1.96766e7i	−0.490152	−	1.32987i
$739$		−	1.99370e7i		−	1.34292i	−0.741042	−	0.671459i	$-0.765668\pi$
$739$		−	1.99370e7i		−	1.34292i	0.741042	−	0.671459i	$-0.234332\pi$
$740$	−6.36984e6	−	7.46738e6i	−0.427611	−	0.501290i
$741$	5.46903e6	+	401966.i	0.365902	+	0.0268933i
$742$	2.08782e6	−	769512.i	0.139214	−	0.0513104i
$743$	1.15065e6			0.0764663			0.0382331	−	0.999269i	$-0.487827\pi$
$743$	1.15065e6			0.0764663			0.0382331	+	0.999269i	$0.487827\pi$
$744$	2.23495e6	−	3.98219e6i	0.148025	−	0.263748i
$745$	3.02052e6			0.199384
$746$	4.37008e6	+	1.18568e7i	0.287503	+	0.780047i
$747$			6.61215e6i			0.433552i
$748$	5.36257e6	+	6.28656e6i	0.350444	+	0.410827i
$749$		−	2.90709e6i		−	0.189345i
$750$	−2.18089e6	+	803814.i	−0.141573	+	0.0521798i
$751$	1.63685e7			1.05903			0.529517	−	0.848299i	$-0.322373\pi$
$751$	1.63685e7			1.05903			0.529517	+	0.848299i	$0.322373\pi$
$752$	1.60040e7	+	2.55489e6i	1.03201	+	0.164751i
$753$		−	3.32023e6i		−	0.213394i
$754$	1.29432e7	−	4.77051e6i	0.829115	−	0.305588i
$755$	2.30967e7			1.47463
$756$	−5.32376e6	−	6.24106e6i	−0.338777	−	0.397149i
$757$	230669.			0.0146302			0.00731509	−	0.999973i	$-0.497672\pi$
$757$	230669.			0.0146302			0.00731509	+	0.999973i	$0.497672\pi$
$758$	2.68407e7	−	9.89270e6i	1.69676	−	0.625377i
$759$	−1.85886e6			−0.117123
$760$	1.76120e7	+	1.16599e7i	1.10605	+	0.732251i
$761$	2.58078e7			1.61544			0.807719	−	0.589568i	$-0.200702\pi$
$761$	2.58078e7			1.61544			0.807719	+	0.589568i	$0.200702\pi$
$762$	−1.12613e7	+	4.15061e6i	−0.702591	+	0.258955i
$763$	1.92776e7			1.19879
$764$	−1.20432e7	−	1.41183e7i	−0.746466	−	0.875084i
$765$	−1.20457e7			−0.744180
$766$	−780674.	+	287734.i	−0.0480726	+	0.0177182i
$767$		−	1.48634e7i		−	0.912286i
$768$	7.34759e6	+	2.40731e6i	0.449513	+	0.147275i
$769$	1.21242e7			0.739329			0.369664	−	0.929165i	$-0.379473\pi$
$769$	1.21242e7			0.739329			0.369664	+	0.929165i	$0.379473\pi$
$770$	−9.50535e6	+	3.50340e6i	−0.577752	+	0.212943i
$771$		−	1.50428e7i		−	0.911365i
$772$	−4.46297e6	−	5.23196e6i	−0.269514	−	0.315952i
$773$		−	1.38975e7i		−	0.836541i	−0.908323	−	0.418270i	$-0.862636\pi$
$773$		−	1.38975e7i		−	0.836541i	0.908323	−	0.418270i	$-0.137364\pi$
$774$	−4.41738e6	−	1.19852e7i	−0.265041	−	0.719103i
$775$	8.12020e6			0.485638
$776$	−1.43645e7	−	8.06185e6i	−0.856319	−	0.480596i
$777$	2.45668e6			0.145981
$778$	8.80934e6	−	3.24687e6i	0.521789	−	0.192316i
$779$	−3.08420e7	−	2.26684e6i	−1.82095	−	0.133837i
$780$	5.36664e6	+	6.29133e6i	0.315839	+	0.370259i
$781$			795069.i			0.0466420i
$782$	1.41648e6	+	3.84316e6i	0.0828311	+	0.224735i
$783$		−	1.64215e7i		−	0.957214i
$784$	1.66586e6	−	1.04350e7i	0.0967937	−	0.606321i
$785$	−8.40708e6			−0.486935
$786$	4632.95	+	12570.0i	0.000267486	+	0.000725737i
$787$	−2.18558e7			−1.25786			−0.628928	−	0.777464i	$-0.716506\pi$
$787$	−2.18558e7			−1.25786			−0.628928	+	0.777464i	$0.716506\pi$
$788$	1.83349e7	−	1.56400e7i	1.05187	−	0.897267i
$789$			1.15223e7i			0.658940i
$790$	−2.98847e7	+	1.10147e7i	−1.70365	+	0.627918i
$791$	7.64795e6			0.434614
$792$	8.92814e6	+	5.01079e6i	0.505764	+	0.283853i
$793$			1.38958e7i			0.784692i
$794$	−2.01960e6	+	744366.i	−0.113688	+	0.0419020i
$795$			2.67023e6i			0.149841i
$796$	−1.76176e7	−	2.06532e7i	−0.985517	−	1.15532i
$797$		−	3.40246e7i		−	1.89735i	−0.316253	−	0.948675i	$-0.602425\pi$
$797$		−	3.40246e7i		−	1.89735i	0.316253	−	0.948675i	$-0.397575\pi$
$798$	−5.08117e6	+	1.45977e6i	−0.282460	+	0.0811479i
$799$			1.36299e7i			0.755312i
$800$	2.66163e6	+	1.34889e7i	0.147036	+	0.745163i
$801$			1.15782e7i			0.637618i
$802$	7.46929e6	+	2.02655e7i	0.410056	+	1.11256i
$803$		−	1.38657e7i		−	0.758844i
$804$	3.90071e6	−	3.32739e6i	0.212816	−	0.181536i
$805$	−5.02152e6			−0.273115
$806$	3.16314e6	+	8.58217e6i	0.171507	+	0.465328i
$807$		−	5.07925e6i		−	0.274546i
$808$	−9.38305e6	+	1.67186e7i	−0.505610	+	0.900888i
$809$	2.78329e7			1.49516			0.747578	−	0.664174i	$-0.231216\pi$
$809$	2.78329e7			1.49516			0.747578	+	0.664174i	$0.231216\pi$
$810$	−8.80386e6	+	3.24485e6i	−0.471477	+	0.173773i
$811$	−3.12418e7			−1.66796			−0.833978	−	0.551798i	$-0.813942\pi$
$811$	−3.12418e7			−1.66796			−0.833978	+	0.551798i	$0.813942\pi$
$812$	−1.01176e7	+	8.63057e6i	−0.538505	+	0.459356i
$813$		−	8.07302e6i		−	0.428361i
$814$	−6.58305e6	+	2.42632e6i	−0.348230	+	0.128348i
$815$		−	6.67908e6i		−	0.352227i
$816$	−1.02510e6	+	6.42129e6i	−0.0538941	+	0.337596i
$817$	−1.87860e7	−	1.38075e6i	−0.984646	−	0.0723701i
$818$	1.21340e7	+	3.29217e7i	0.634046	+	1.72028i
$819$	7.18054e6			0.374065
$820$	−3.02645e7	−	3.54792e7i	−1.57181	−	1.84264i
$821$	−9.21704e6			−0.477236			−0.238618	−	0.971113i	$-0.576694\pi$
$821$	−9.21704e6			−0.477236			−0.238618	+	0.971113i	$0.576694\pi$
$822$	−1.74370e6	+	642677.i	−0.0900102	+	0.0331752i
$823$			1.61444e7i			0.830848i	0.909628	+	0.415424i	$0.136367\pi$
$823$			1.61444e7i			0.830848i	−0.909628	+	0.415424i	$0.863633\pi$
$824$	1.77329e7	−	3.15963e7i	0.909835	−	1.62113i
$825$		−	5.24773e6i		−	0.268433i
$826$	4.95548e6	+	1.34451e7i	0.252718	+	0.685668i
$827$	3.64283e7			1.85214			0.926072	−	0.377346i	$-0.123163\pi$
$827$	3.64283e7			1.85214			0.926072	+	0.377346i	$0.123163\pi$
$828$	3.29353e6	+	3.86102e6i	0.166950	+	0.195716i
$829$			1.47504e7i			0.745447i	0.927942	+	0.372724i	$0.121576\pi$
$829$			1.47504e7i			0.745447i	−0.927942	+	0.372724i	$0.878424\pi$
$830$	5.08506e6	+	1.37967e7i	0.256213	+	0.695151i
$831$	6.30753e6			0.316852
$832$	−1.32195e7	+	8.06751e6i	−0.662073	+	0.404047i
$833$	8.88707e6			0.443758
$834$	5.25759e6	+	1.42648e7i	0.261741	+	0.710150i
$835$	−3.81000e7			−1.89107
$836$	1.21741e7	−	8.93007e6i	0.602448	−	0.441916i
$837$	1.08885e7			0.537222
$838$	3.01338e6	+	8.17583e6i	0.148232	+	0.402181i
$839$	1.94790e7			0.955349			0.477675	−	0.878537i	$-0.341480\pi$
$839$	1.94790e7			0.955349			0.477675	+	0.878537i	$0.341480\pi$
$840$	−6.95206e6	−	3.90174e6i	−0.339950	−	0.190792i
$841$	−6.11048e6			−0.297910
$842$	2.76460e6	+	7.50085e6i	0.134385	+	0.364611i
$843$		−	4.96009e6i		−	0.240392i
$844$	2.50704e7	−	2.13856e7i	1.21145	−	1.03339i
$845$	1.09690e7			0.528474
$846$	5.84032e6	+	1.58458e7i	0.280550	+	0.761183i
$847$		−	5.73055e6i		−	0.274466i
$848$	−4.93826e6	−	788349.i	−0.235822	−	0.0376469i
$849$		−	3.90854e6i		−	0.186100i
$850$	−1.08496e7	+	3.99884e6i	−0.515068	+	0.189839i
$851$	−3.47772e6			−0.164615
$852$	−476019.	+	406054.i	−0.0224660	+	0.0191640i
$853$	−2.48591e7			−1.16980			−0.584901	−	0.811105i	$-0.698867\pi$
$853$	−2.48591e7			−1.16980			−0.584901	+	0.811105i	$0.698867\pi$
$854$	−4.63285e6	−	1.25698e7i	−0.217372	−	0.589769i
$855$	−1.61333e6	+	2.19505e7i	−0.0754759	+	1.02690i
$856$	−3.19763e6	+	5.69748e6i	−0.149157	+	0.265765i
$857$			2.33074e6i			0.108403i	0.998530	+	0.0542015i	$0.0172613\pi$
$857$			2.33074e6i			0.108403i	−0.998530	+	0.0542015i	$0.982739\pi$
$858$	5.54627e6	−	2.04420e6i	0.257207	−	0.0947992i
$859$			7.46055e6i			0.344975i	0.985012	+	0.172488i	$0.0551805\pi$
$859$			7.46055e6i			0.344975i	−0.985012	+	0.172488i	$0.944820\pi$
$860$	−1.84343e7	−	2.16106e7i	−0.849926	−	0.996371i
$861$	1.16722e7			0.536594
$862$	−2.01460e7	+	7.42523e6i	−0.923465	+	0.340363i
$863$	−2.11346e7			−0.965977			−0.482989	−	0.875627i	$-0.660449\pi$
$863$	−2.11346e7			−0.965977			−0.482989	+	0.875627i	$0.660449\pi$
$864$	3.56902e6	+	1.80874e7i	0.162654	+	0.824314i
$865$			5.02272e7i			2.28244i
$866$	−221121.	−	599942.i	−0.0100193	−	0.0271841i
$867$	5.00087e6			0.225942
$868$	−5.72260e6	−	6.70862e6i	−0.257807	−	0.302228i
$869$			2.27667e7i			1.02270i
$870$	−5.51905e6	−	1.49742e7i	−0.247210	−	0.670725i
$871$			1.02694e7i			0.458670i
$872$	−3.77814e7	−	2.12043e7i	−1.68262	−	0.944348i
$873$		−	1.71645e7i		−	0.762249i
$874$	7.19300e6	−	2.06648e6i	0.318516	−	0.0915066i
$875$			4.48820e6i			0.198176i
$876$	8.30158e6	−	7.08143e6i	0.365511	−	0.311789i
$877$			3.31426e7i			1.45508i	0.686064	+	0.727541i	$0.259337\pi$
$877$			3.31426e7i			1.45508i	−0.686064	+	0.727541i	$0.740663\pi$
$878$	3.12881e7	−	1.15319e7i	1.36975	−	0.504852i
$879$		−	2.54905e6i		−	0.111277i
$880$	2.24827e7	+	3.58916e6i	0.978682	+	0.156238i
$881$	−2.52197e7			−1.09471			−0.547357	−	0.836899i	$-0.684366\pi$
$881$	−2.52197e7			−1.09471			−0.547357	+	0.836899i	$0.684366\pi$
$882$	1.03319e7	−	3.80804e6i	0.447207	−	0.164828i
$883$			3.20322e7i			1.38256i	0.722586	+	0.691282i	$0.242954\pi$
$883$			3.20322e7i			1.38256i	−0.722586	+	0.691282i	$0.757046\pi$
$884$	−8.45267e6	−	9.90909e6i	−0.363800	−	0.426484i
$885$	−1.71956e7			−0.738007
$886$	−1.34560e7	−	3.65085e7i	−0.575880	−	1.56246i
$887$	−2.94824e7			−1.25821			−0.629107	−	0.777319i	$-0.716579\pi$
$887$	−2.94824e7			−1.25821			−0.629107	+	0.777319i	$0.716579\pi$
$888$	−4.81474e6	−	2.70220e6i	−0.204899	−	0.114997i
$889$			2.31754e7i			0.983498i
$890$	8.90421e6	+	2.41587e7i	0.376808	+	1.02235i
$891$			6.70693e6i			0.283028i
$892$	2.32057e7	−	1.97949e7i	0.976521	−	0.832994i
$893$	2.48374e7	+	1.82551e6i	1.04226	+	0.0766049i
$894$	1.59426e6	−	587600.i	0.0667139	−	0.0245888i
$895$	−2.88521e7			−1.20398
$896$	9.26830e6	−	1.17051e7i	0.385683	−	0.487084i
$897$	2.93001e6			0.121587
$898$	−7.12794e6	−	1.93394e7i	−0.294967	−	0.800298i
$899$		−	1.76518e7i		−	0.728433i
$900$	−1.09000e7	+	9.29791e6i	−0.448558	+	0.382630i
$901$		−	4.20571e6i		−	0.172595i
$902$	−3.12776e7	+	1.15280e7i	−1.28002	+	0.471778i
$903$	7.10963e6			0.290153
$904$	−1.49889e7	−	8.41231e6i	−0.610027	−	0.342369i
$905$			8.33988e6i			0.338484i
$906$	1.21907e7	−	4.49315e6i	0.493410	−	0.181857i
$907$	2.64541e7			1.06776			0.533882	−	0.845559i	$-0.320733\pi$
$907$	2.64541e7			1.06776			0.533882	+	0.845559i	$0.320733\pi$
$908$	1.56791e7	−	1.33746e7i	0.631113	−	0.538353i
$909$	−1.99775e7			−0.801921
$910$	1.49827e7	−	5.52218e6i	0.599771	−	0.221058i
$911$	−1.36140e7			−0.543487			−0.271744	−	0.962370i	$-0.587600\pi$
$911$	−1.36140e7			−0.543487			−0.271744	+	0.962370i	$0.587600\pi$
$912$	1.15640e7	+	2.72805e6i	0.460386	+	0.108609i
$913$	1.05105e7			0.417300
$914$	3.50193e7	−	1.29071e7i	1.38657	−	0.511051i
$915$	1.60761e7			0.634788
$916$	−2.63391e7	+	2.24679e7i	−1.03720	+	0.884755i
$917$	25868.6			0.00101590
$918$	−1.45483e7	+	5.36209e6i	−0.569778	+	0.210004i
$919$			1.83366e7i			0.716193i	0.933685	+	0.358097i	$0.116574\pi$
$919$			1.83366e7i			0.716193i	−0.933685	+	0.358097i	$0.883426\pi$
$920$	9.84148e6	+	5.52338e6i	0.383346	+	0.215147i
$921$	−887960.			−0.0344941
$922$	−5.25391e6	+	1.93644e6i	−0.203542	+	0.0750199i
$923$		−	1.25322e6i		−	0.0484196i
$924$	−4.33549e6	+	3.69826e6i	−0.167054	+	0.142501i
$925$		−	9.81789e6i		−	0.377280i
$926$	2.32444e6	+	6.30661e6i	0.0890820	+	0.241695i
$927$	3.77553e7			1.44304
$928$	2.93223e7	−	5.78588e6i	1.11771	−	0.220546i
$929$	−7.07716e6			−0.269042			−0.134521	−	0.990911i	$-0.542950\pi$
$929$	−7.07716e6			−0.269042			−0.134521	+	0.990911i	$0.542950\pi$
$930$	9.92879e6	−	3.65947e6i	0.376434	−	0.138743i
$931$	1.19028e6	−	1.61947e7i	0.0450066	−	0.612347i
$932$	1.35118e7	−	1.15258e7i	0.509534	−	0.434643i
$933$		−	6.87896e6i		−	0.258713i
$934$	−1.38910e7	−	3.76887e7i	−0.521034	−	1.41366i
$935$			1.91476e7i			0.716283i
$936$	−1.40728e7	−	7.89817e6i	−0.525040	−	0.294671i
$937$	−3.32962e7			−1.23893			−0.619463	−	0.785025i	$-0.712650\pi$
$937$	−3.32962e7			−1.23893			−0.619463	+	0.785025i	$0.712650\pi$
$938$	−3.42383e6	−	9.28945e6i	−0.127059	−	0.344733i
$939$	−1.04482e7			−0.386701
$940$	2.43724e7	+	2.85719e7i	0.899661	+	1.05468i
$941$			3.92170e7i			1.44378i	0.692009	+	0.721889i	$0.256726\pi$
$941$			3.92170e7i			1.44378i	−0.692009	+	0.721889i	$0.743274\pi$
$942$	−4.43735e6	+	1.63548e6i	−0.162928	+	0.0600506i
$943$	−1.65234e7			−0.605091
$944$	5.07678e6	−	3.18012e7i	0.185421	−	1.16149i
$945$		−	1.90090e7i		−	0.692436i
$946$	−1.90514e7	+	7.02179e6i	−0.692147	+	0.255105i
$947$			3.14175e7i			1.13840i	0.822198	+	0.569202i	$0.192748\pi$
$947$			3.14175e7i			1.13840i	−0.822198	+	0.569202i	$0.807252\pi$
$948$	−1.36307e7	+	1.16273e7i	−0.492604	+	0.420202i
$949$			2.18556e7i			0.787765i
$950$	5.83384e6	+	2.03064e7i	0.209723	+	0.730003i
$951$			1.10659e7i			0.396768i
$952$	1.09498e7	+	6.14539e6i	0.391573	+	0.219764i
$953$		−	1.13168e7i		−	0.403638i	−0.979423	−	0.201819i	$-0.935315\pi$
$953$		−	1.13168e7i		−	0.403638i	0.979423	−	0.201819i	$-0.0646852\pi$
$954$	−1.80212e6	−	4.88946e6i	−0.0641079	−	0.173936i
$955$		−	4.30016e7i		−	1.52572i
$956$	2.73544e6	+	3.20676e6i	0.0968015	+	0.113481i
$957$	−1.14076e7			−0.402636
$958$	1.69495e7	+	4.59869e7i	0.596681	+	1.61890i
$959$			3.58847e6i			0.125998i
$960$	9.33338e6	+	1.52937e7i	0.326859	+	0.535594i
$961$	−1.69249e7			−0.591178
$962$	1.03764e7	−	3.82446e6i	0.361502	−	0.133239i
$963$	−6.80809e6			−0.236570
$964$	−1.32035e7	−	1.54786e7i	−0.457612	−	0.536461i
$965$		−	1.59355e7i		−	0.550867i
$966$	−2.65041e6	+	976866.i	−0.0913841	+	0.0336816i
$967$			9.67290e6i			0.332652i	0.986071	+	0.166326i	$0.0531905\pi$
$967$			9.67290e6i			0.332652i	−0.986071	+	0.166326i	$0.946810\pi$
$968$	−6.30327e6	+	1.12311e7i	−0.216211	+	0.385241i
$969$	−732454.	+	9.96555e6i	−0.0250594	+	0.340951i
$970$	−1.32004e7	−	3.58150e7i	−0.450460	−	1.22218i
$971$	−2.30392e7			−0.784186			−0.392093	−	0.919926i	$-0.628249\pi$
$971$	−2.30392e7			−0.784186			−0.392093	+	0.919926i	$0.628249\pi$
$972$	−2.28444e7	+	1.94868e7i	−0.775559	+	0.661568i
$973$	2.93564e7			0.994079
$974$	−8.15864e6	+	3.00704e6i	−0.275563	+	0.101565i
$975$			8.27165e6i			0.278664i
$976$	−4.74626e6	+	2.97308e7i	−0.159488	+	0.999039i
$977$			1.94595e7i			0.652220i	0.945332	+	0.326110i	$0.105738\pi$
$977$			1.94595e7i			0.652220i	−0.945332	+	0.326110i	$0.894262\pi$
$978$	−1.29932e6	−	3.52529e6i	−0.0434379	−	0.117855i
$979$	1.84045e7			0.613716
$980$	1.86296e7	−	1.58915e7i	0.619639	−	0.528565i
$981$		−	4.51462e7i		−	1.49778i
$982$	−1.85047e7	−	5.02065e7i	−0.612355	−	1.66143i
$983$	4.54651e7			1.50070			0.750351	−	0.661039i	$-0.229884\pi$
$983$	4.54651e7			1.50070			0.750351	+	0.661039i	$0.229884\pi$
$984$	−2.28759e7	−	1.28388e7i	−0.753166	−	0.422703i
$985$	5.58442e7			1.83395
$986$	8.69271e6	+	2.35849e7i	0.284750	+	0.772576i
$987$	−9.39979e6			−0.307132
$988$	−1.91892e7	+	1.40759e7i	−0.625408	+	0.458758i
$989$	−1.00645e7			−0.327192
$990$	8.20459e6	+	2.22605e7i	0.266054	+	0.721851i
$991$	7.45194e6			0.241038			0.120519	−	0.992711i	$-0.461544\pi$
$991$	7.45194e6			0.241038			0.120519	+	0.992711i	$0.461544\pi$
$992$	3.83640e6	+	1.94425e7i	0.123778	+	0.627296i
$993$	−4.17955e6			−0.134510
$994$	417823.	+	1.13363e6i	0.0134130	+	0.0363919i
$995$		−	6.29054e7i		−	2.01433i
$996$	5.36790e6	+	6.29281e6i	0.171457	+	0.201000i
$997$	2.53403e7			0.807371			0.403685	−	0.914898i	$-0.367729\pi$
$997$	2.53403e7			0.807371			0.403685	+	0.914898i	$0.367729\pi$
$998$	−1.34205e7	−	3.64122e7i	−0.426523	−	1.15723i
$999$		−	1.31649e7i		−	0.417354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.d.a.75.6	yes	48
4.3	odd	2	inner	76.6.d.a.75.44	yes	48
19.18	odd	2	inner	76.6.d.a.75.43	yes	48
76.75	even	2	inner	76.6.d.a.75.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.d.a.75.5	✓	48	76.75	even	2	inner
76.6.d.a.75.6	yes	48	1.1	even	1	trivial
76.6.d.a.75.43	yes	48	19.18	odd	2	inner
76.6.d.a.75.44	yes	48	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.30781 + 1.95631i) q^{2} -7.37371 q^{3} +(24.3457 - 20.7674i) q^{4} +74.1521 q^{5} +(39.1383 - 14.4252i) q^{6} -80.5452i q^{7} +(-88.5950 + 157.857i) q^{8} -188.628 q^{9} +O(q^{10})\)	\(q+(-5.30781 + 1.95631i) q^{2} -7.37371 q^{3} +(24.3457 - 20.7674i) q^{4} +74.1521 q^{5} +(39.1383 - 14.4252i) q^{6} -80.5452i q^{7} +(-88.5950 + 157.857i) q^{8} -188.628 q^{9} +(-393.585 + 145.064i) q^{10} +299.840i q^{11} +(-179.518 + 153.133i) q^{12} -472.618i q^{13} +(157.571 + 427.519i) q^{14} -546.776 q^{15} +(161.428 - 1011.20i) q^{16} +861.194 q^{17} +(1001.20 - 369.015i) q^{18} +(115.343 - 1569.33i) q^{19} +(1805.29 - 1539.95i) q^{20} +593.917i q^{21} +(-586.579 - 1591.49i) q^{22} -840.760i q^{23} +(653.274 - 1163.99i) q^{24} +2373.54 q^{25} +(924.586 + 2508.57i) q^{26} +3182.70 q^{27} +(-1672.72 - 1960.93i) q^{28} -5159.61i q^{29} +(2902.19 - 1069.66i) q^{30} +3421.14 q^{31} +(1121.38 + 5683.04i) q^{32} -2210.93i q^{33} +(-4571.05 + 1684.76i) q^{34} -5972.59i q^{35} +(-4592.29 + 3917.32i) q^{36} -4136.40i q^{37} +(2457.87 + 8555.35i) q^{38} +3484.95i q^{39} +(-6569.51 + 11705.4i) q^{40} -19653.0i q^{41} +(-1161.88 - 3152.40i) q^{42} -11970.7i q^{43} +(6226.90 + 7299.82i) q^{44} -13987.2 q^{45} +(1644.79 + 4462.60i) q^{46} +15826.8i q^{47} +(-1190.33 + 7456.27i) q^{48} +10319.5 q^{49} +(-12598.3 + 4643.36i) q^{50} -6350.19 q^{51} +(-9815.06 - 11506.2i) q^{52} -4883.58i q^{53} +(-16893.2 + 6226.35i) q^{54} +22233.8i q^{55} +(12714.6 + 7135.90i) q^{56} +(-850.510 + 11571.8i) q^{57} +(10093.8 + 27386.3i) q^{58} +31449.1 q^{59} +(-13311.7 + 11355.1i) q^{60} -29401.7 q^{61} +(-18158.8 + 6692.81i) q^{62} +15193.1i q^{63} +(-17069.8 - 27970.7i) q^{64} -35045.6i q^{65} +(4325.26 + 11735.2i) q^{66} -21728.8 q^{67} +(20966.4 - 17884.8i) q^{68} +6199.52i q^{69} +(11684.2 + 31701.4i) q^{70} +2651.65 q^{71} +(16711.5 - 29776.4i) q^{72} -46243.7 q^{73} +(8092.07 + 21955.2i) q^{74} -17501.8 q^{75} +(-29782.8 - 40601.8i) q^{76} +24150.7 q^{77} +(-6817.63 - 18497.5i) q^{78} +75929.5 q^{79} +(11970.3 - 74982.3i) q^{80} +22368.4 q^{81} +(38447.2 + 104314. i) q^{82} -35053.8i q^{83} +(12334.1 + 14459.3i) q^{84} +63859.3 q^{85} +(23418.5 + 63538.4i) q^{86} +38045.5i q^{87} +(-47331.9 - 26564.3i) q^{88} -61381.1i q^{89} +(74241.4 - 27363.2i) q^{90} -38067.1 q^{91} +(-17460.4 - 20468.9i) q^{92} -25226.5 q^{93} +(-30962.0 - 84005.5i) q^{94} +(8552.96 - 116369. i) q^{95} +(-8268.72 - 41905.1i) q^{96} +90996.6i q^{97} +(-54773.8 + 20188.1i) q^{98} -56558.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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