LMFDB - Embedded newform 79.8.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [79,8,Mod(1,79)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(79, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("79.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 79 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	79.a (trivial)

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:	yes
Analytic conductor:	$24.6784170132$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.0433 q^{2} +34.4011 q^{3} +162.475 q^{4} -177.928 q^{5} -586.310 q^{6} +87.6173 q^{7} -587.576 q^{8} -1003.56 q^{9} +O(q^{10})$	\(q-17.0433 q^{2} +34.4011 q^{3} +162.475 q^{4} -177.928 q^{5} -586.310 q^{6} +87.6173 q^{7} -587.576 q^{8} -1003.56 q^{9} +3032.49 q^{10} +394.955 q^{11} +5589.33 q^{12} +10922.4 q^{13} -1493.29 q^{14} -6120.94 q^{15} -10782.6 q^{16} -2940.75 q^{17} +17104.1 q^{18} -53553.2 q^{19} -28909.0 q^{20} +3014.13 q^{21} -6731.35 q^{22} +49770.5 q^{23} -20213.3 q^{24} -46466.5 q^{25} -186154. q^{26} -109759. q^{27} +14235.7 q^{28} +237937. q^{29} +104321. q^{30} -182470. q^{31} +258981. q^{32} +13586.9 q^{33} +50120.2 q^{34} -15589.6 q^{35} -163054. q^{36} +438318. q^{37} +912726. q^{38} +375743. q^{39} +104546. q^{40} +371956. q^{41} -51370.9 q^{42} +991561. q^{43} +64170.5 q^{44} +178562. q^{45} -848256. q^{46} +363036. q^{47} -370933. q^{48} -815866. q^{49} +791944. q^{50} -101165. q^{51} +1.77462e6 q^{52} +783514. q^{53} +1.87066e6 q^{54} -70273.7 q^{55} -51481.8 q^{56} -1.84229e6 q^{57} -4.05525e6 q^{58} -1.03221e6 q^{59} -994501. q^{60} +3.09088e6 q^{61} +3.10990e6 q^{62} -87929.5 q^{63} -3.03373e6 q^{64} -1.94341e6 q^{65} -231566. q^{66} +927930. q^{67} -477799. q^{68} +1.71216e6 q^{69} +265699. q^{70} +1.40154e6 q^{71} +589669. q^{72} +3.37699e6 q^{73} -7.47040e6 q^{74} -1.59850e6 q^{75} -8.70108e6 q^{76} +34604.9 q^{77} -6.40392e6 q^{78} -493039. q^{79} +1.91853e6 q^{80} -1.58104e6 q^{81} -6.33938e6 q^{82} +6.06016e6 q^{83} +489722. q^{84} +523243. q^{85} -1.68995e7 q^{86} +8.18532e6 q^{87} -232066. q^{88} +4.23818e6 q^{89} -3.04330e6 q^{90} +956992. q^{91} +8.08648e6 q^{92} -6.27718e6 q^{93} -6.18734e6 q^{94} +9.52864e6 q^{95} +8.90924e6 q^{96} -1.20334e7 q^{97} +1.39051e7 q^{98} -396362. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 8 q^{2} + 107 q^{3} + 1728 q^{4} + 999 q^{5} + 1113 q^{6} + 883 q^{7} + 2334 q^{8} + 24630 q^{9}+O(q^{10}) $ 25 * q + 8 * q^2 + 107 * q^3 + 1728 * q^4 + 999 * q^5 + 1113 * q^6 + 883 * q^7 + 2334 * q^8 + 24630 * q^9	\( 25 q + 8 q^{2} + 107 q^{3} + 1728 q^{4} + 999 q^{5} + 1113 q^{6} + 883 q^{7} + 2334 q^{8} + 24630 q^{9} + 9125 q^{10} + 7750 q^{11} + 15367 q^{12} + 2889 q^{13} + 19333 q^{14} + 33191 q^{15} + 142884 q^{16} + 78798 q^{17} - 3299 q^{18} + 30540 q^{19} - 12216 q^{20} - 132083 q^{21} - 284791 q^{22} + 164186 q^{23} + 128679 q^{24} + 508126 q^{25} + 505560 q^{26} + 607295 q^{27} + 536123 q^{28} + 638580 q^{29} + 2043027 q^{30} + 910298 q^{31} + 1629475 q^{32} + 598836 q^{33} + 1077090 q^{34} + 1581093 q^{35} + 4005767 q^{36} + 1211146 q^{37} + 1478978 q^{38} + 1344825 q^{39} + 3812582 q^{40} + 2816906 q^{41} + 4045603 q^{42} - 137148 q^{43} + 2136404 q^{44} + 2911464 q^{45} + 1092854 q^{46} + 2190469 q^{47} + 5884593 q^{48} + 6517102 q^{49} + 1975400 q^{50} + 751758 q^{51} - 201731 q^{52} + 4108064 q^{53} + 4068807 q^{54} + 868206 q^{55} + 1949841 q^{56} + 1601962 q^{57} - 2185482 q^{58} + 4346931 q^{59} - 4960425 q^{60} + 4437224 q^{61} - 1283135 q^{62} - 2298764 q^{63} + 6180676 q^{64} + 3307347 q^{65} - 13646860 q^{66} - 4982464 q^{67} + 5261328 q^{68} + 4906500 q^{69} - 20329017 q^{70} + 9728355 q^{71} - 32705097 q^{72} + 1445696 q^{73} - 1636246 q^{74} - 4906804 q^{75} - 9170621 q^{76} + 4420424 q^{77} - 9115731 q^{78} - 12325975 q^{79} - 18733905 q^{80} + 509769 q^{81} - 34706430 q^{82} - 22164078 q^{83} - 98610835 q^{84} - 43977968 q^{85} - 29164330 q^{86} - 57086618 q^{87} - 66593968 q^{88} + 20252339 q^{89} - 34814996 q^{90} - 25616983 q^{91} - 12368519 q^{92} - 35295820 q^{93} - 53030651 q^{94} - 18689280 q^{95} - 35962515 q^{96} + 15021627 q^{97} - 46370127 q^{98} + 5324944 q^{99}+O(q^{100}) \) 25 * q + 8 * q^2 + 107 * q^3 + 1728 * q^4 + 999 * q^5 + 1113 * q^6 + 883 * q^7 + 2334 * q^8 + 24630 * q^9 + 9125 * q^10 + 7750 * q^11 + 15367 * q^12 + 2889 * q^13 + 19333 * q^14 + 33191 * q^15 + 142884 * q^16 + 78798 * q^17 - 3299 * q^18 + 30540 * q^19 - 12216 * q^20 - 132083 * q^21 - 284791 * q^22 + 164186 * q^23 + 128679 * q^24 + 508126 * q^25 + 505560 * q^26 + 607295 * q^27 + 536123 * q^28 + 638580 * q^29 + 2043027 * q^30 + 910298 * q^31 + 1629475 * q^32 + 598836 * q^33 + 1077090 * q^34 + 1581093 * q^35 + 4005767 * q^36 + 1211146 * q^37 + 1478978 * q^38 + 1344825 * q^39 + 3812582 * q^40 + 2816906 * q^41 + 4045603 * q^42 - 137148 * q^43 + 2136404 * q^44 + 2911464 * q^45 + 1092854 * q^46 + 2190469 * q^47 + 5884593 * q^48 + 6517102 * q^49 + 1975400 * q^50 + 751758 * q^51 - 201731 * q^52 + 4108064 * q^53 + 4068807 * q^54 + 868206 * q^55 + 1949841 * q^56 + 1601962 * q^57 - 2185482 * q^58 + 4346931 * q^59 - 4960425 * q^60 + 4437224 * q^61 - 1283135 * q^62 - 2298764 * q^63 + 6180676 * q^64 + 3307347 * q^65 - 13646860 * q^66 - 4982464 * q^67 + 5261328 * q^68 + 4906500 * q^69 - 20329017 * q^70 + 9728355 * q^71 - 32705097 * q^72 + 1445696 * q^73 - 1636246 * q^74 - 4906804 * q^75 - 9170621 * q^76 + 4420424 * q^77 - 9115731 * q^78 - 12325975 * q^79 - 18733905 * q^80 + 509769 * q^81 - 34706430 * q^82 - 22164078 * q^83 - 98610835 * q^84 - 43977968 * q^85 - 29164330 * q^86 - 57086618 * q^87 - 66593968 * q^88 + 20252339 * q^89 - 34814996 * q^90 - 25616983 * q^91 - 12368519 * q^92 - 35295820 * q^93 - 53030651 * q^94 - 18689280 * q^95 - 35962515 * q^96 + 15021627 * q^97 - 46370127 * q^98 + 5324944 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−17.0433	−1.50643	−0.753216	−	0.657773i	$-0.771499\pi$
$2$	−17.0433	−1.50643	−0.753216	+	0.657773i	$0.771499\pi$
$3$	34.4011	0.735611	0.367805	−	0.929903i	$-0.380109\pi$
$3$	34.4011	0.735611	0.367805	+	0.929903i	$0.380109\pi$
$4$	162.475	1.26934
$5$	−177.928	−0.636576	−0.318288	−	0.947994i	$-0.603108\pi$
$5$	−177.928	−0.636576	−0.318288	+	0.947994i	$0.603108\pi$
$6$	−586.310	−1.10815
$7$	87.6173	0.0965487	0.0482744	−	0.998834i	$-0.484628\pi$
$7$	87.6173	0.0965487	0.0482744	+	0.998834i	$0.484628\pi$
$8$	−587.576	−0.405741
$9$	−1003.56	−0.458877
$10$	3032.49	0.958959
$11$	394.955	0.0894692	0.0447346	−	0.998999i	$-0.485756\pi$
$11$	394.955	0.0894692	0.0447346	+	0.998999i	$0.485756\pi$
$12$	5589.33	0.933740
$13$	10922.4	1.37885	0.689424	−	0.724358i	$-0.257864\pi$
$13$	10922.4	1.37885	0.689424	+	0.724358i	$0.257864\pi$
$14$	−1493.29	−0.145444
$15$	−6120.94	−0.468272
$16$	−10782.6	−0.658118
$17$	−2940.75	−0.145173	−0.0725866	−	0.997362i	$-0.523125\pi$
$17$	−2940.75	−0.145173	−0.0725866	+	0.997362i	$0.523125\pi$
$18$	17104.1	0.691267
$19$	−53553.2	−1.79122	−0.895608	−	0.444843i	$-0.853259\pi$
$19$	−53553.2	−1.79122	−0.895608	+	0.444843i	$0.853259\pi$
$20$	−28909.0	−0.808031
$21$	3014.13	0.0710223
$22$	−6731.35	−0.134779
$23$	49770.5	0.852952	0.426476	−	0.904499i	$-0.359755\pi$
$23$	49770.5	0.852952	0.426476	+	0.904499i	$0.359755\pi$
$24$	−20213.3	−0.298467
$25$	−46466.5	−0.594771
$26$	−186154.	−2.07714
$27$	−109759.	−1.07317
$28$	14235.7	0.122553
$29$	237937.	1.81163	0.905816	−	0.423672i	$-0.139259\pi$
$29$	237937.	1.81163	0.905816	+	0.423672i	$0.139259\pi$
$30$	104321.	0.705421
$31$	−182470.	−1.10008	−0.550042	−	0.835137i	$-0.685388\pi$
$31$	−182470.	−1.10008	−0.550042	+	0.835137i	$0.685388\pi$
$32$	258981.	1.39715
$33$	13586.9	0.0658145
$34$	50120.2	0.218694
$35$	−15589.6	−0.0614606
$36$	−163054.	−0.582470
$37$	438318.	1.42260	0.711300	−	0.702888i	$-0.248107\pi$
$37$	438318.	1.42260	0.711300	+	0.702888i	$0.248107\pi$
$38$	912726.	2.69835
$39$	375743.	1.01430
$40$	104546.	0.258285
$41$	371956.	0.842847	0.421423	−	0.906864i	$-0.361531\pi$
$41$	371956.	0.842847	0.421423	+	0.906864i	$0.361531\pi$
$42$	−51370.9	−0.106990
$43$	991561.	1.90187	0.950933	−	0.309396i	$-0.100127\pi$
$43$	991561.	1.90187	0.950933	+	0.309396i	$0.100127\pi$
$44$	64170.5	0.113567
$45$	178562.	0.292110
$46$	−848256.	−1.28491
$47$	363036.	0.510043	0.255022	−	0.966935i	$-0.417917\pi$
$47$	363036.	0.510043	0.255022	+	0.966935i	$0.417917\pi$
$48$	−370933.	−0.484118
$49$	−815866.	−0.990678
$50$	791944.	0.895982
$51$	−101165.	−0.106791
$52$	1.77462e6	1.75023
$53$	783514.	0.722905	0.361453	−	0.932390i	$-0.382281\pi$
$53$	783514.	0.722905	0.361453	+	0.932390i	$0.382281\pi$
$54$	1.87066e6	1.61665
$55$	−70273.7	−0.0569539
$56$	−51481.8	−0.0391738
$57$	−1.84229e6	−1.31764
$58$	−4.05525e6	−2.72910
$59$	−1.03221e6	−0.654316	−0.327158	−	0.944970i	$-0.606091\pi$
$59$	−1.03221e6	−0.654316	−0.327158	+	0.944970i	$0.606091\pi$
$60$	−994501.	−0.594396
$61$	3.09088e6	1.74352	0.871761	−	0.489932i	$-0.162978\pi$
$61$	3.09088e6	1.74352	0.871761	+	0.489932i	$0.162978\pi$
$62$	3.10990e6	1.65720
$63$	−87929.5	−0.0443040
$64$	−3.03373e6	−1.44660
$65$	−1.94341e6	−0.877742
$66$	−231566.	−0.0991451
$67$	927930.	0.376924	0.188462	−	0.982081i	$-0.439650\pi$
$67$	927930.	0.376924	0.188462	+	0.982081i	$0.439650\pi$
$68$	−477799.	−0.184274
$69$	1.71216e6	0.627441
$70$	265699.	0.0925863
$71$	1.40154e6	0.464732	0.232366	−	0.972628i	$-0.425353\pi$
$71$	1.40154e6	0.464732	0.232366	+	0.972628i	$0.425353\pi$
$72$	589669.	0.186185
$73$	3.37699e6	1.01602	0.508008	−	0.861353i	$-0.330382\pi$
$73$	3.37699e6	1.01602	0.508008	+	0.861353i	$0.330382\pi$
$74$	−7.47040e6	−2.14305
$75$	−1.59850e6	−0.437520
$76$	−8.70108e6	−2.27366
$77$	34604.9	0.00863814
$78$	−6.40392e6	−1.52797
$79$	−493039.	−0.112509
$79$	−493039.	−0.112509
$80$	1.91853e6	0.418942
$81$	−1.58104e6	−0.330556
$82$	−6.33938e6	−1.26969
$83$	6.06016e6	1.16335	0.581675	−	0.813421i	$-0.302397\pi$
$83$	6.06016e6	1.16335	0.581675	+	0.813421i	$0.302397\pi$
$84$	489722.	0.0901514
$85$	523243.	0.0924138
$86$	−1.68995e7	−2.86503
$87$	8.18532e6	1.33266
$88$	−232066.	−0.0363013
$89$	4.23818e6	0.637257	0.318629	−	0.947880i	$-0.396778\pi$
$89$	4.23818e6	0.637257	0.318629	+	0.947880i	$0.396778\pi$
$90$	−3.04330e6	−0.440044
$91$	956992.	0.133126
$92$	8.08648e6	1.08269
$93$	−6.27718e6	−0.809234
$94$	−6.18734e6	−0.768346
$95$	9.52864e6	1.14025
$96$	8.90924e6	1.02776
$97$	−1.20334e7	−1.33871	−0.669356	−	0.742941i	$-0.733430\pi$
$97$	−1.20334e7	−1.33871	−0.669356	+	0.742941i	$0.733430\pi$
$98$	1.39051e7	1.49239
$99$	−396362.	−0.0410553
$100$	−7.54966e6	−0.754966
$101$	1.02051e7	0.985581	0.492791	−	0.870148i	$-0.335977\pi$
$101$	1.02051e7	0.985581	0.492791	+	0.870148i	$0.335977\pi$
$102$	1.72419e6	0.160874
$103$	1.49984e7	1.35243	0.676213	−	0.736706i	$-0.263620\pi$
$103$	1.49984e7	1.35243	0.676213	+	0.736706i	$0.263620\pi$
$104$	−6.41774e6	−0.559455
$105$	−536300.	−0.0452111
$106$	−1.33537e7	−1.08901
$107$	5.72506e6	0.451790	0.225895	−	0.974152i	$-0.427469\pi$
$107$	5.72506e6	0.451790	0.225895	+	0.974152i	$0.427469\pi$
$108$	−1.78331e7	−1.36221
$109$	−7.62698e6	−0.564105	−0.282053	−	0.959399i	$-0.591015\pi$
$109$	−7.62698e6	−0.564105	−0.282053	+	0.959399i	$0.591015\pi$
$110$	1.19770e6	0.0857972
$111$	1.50786e7	1.04648
$112$	−944742.	−0.0635404
$113$	−768361.	−0.0500946	−0.0250473	−	0.999686i	$-0.507974\pi$
$113$	−768361.	−0.0500946	−0.0250473	+	0.999686i	$0.507974\pi$
$114$	3.13988e7	1.98493
$115$	−8.85559e6	−0.542969
$116$	3.86590e7	2.29957
$117$	−1.09613e7	−0.632721
$118$	1.75924e7	0.985682
$119$	−257660.	−0.0140163
$120$	3.59651e6	0.189997
$121$	−1.93312e7	−0.991995
$122$	−5.26789e7	−2.62650
$123$	1.27957e7	0.620007
$124$	−2.96469e7	−1.39638
$125$	2.21684e7	1.01519
$126$	1.49861e6	0.0667409
$127$	−1.71314e7	−0.742131	−0.371065	−	0.928607i	$-0.621007\pi$
$127$	−1.71314e7	−0.742131	−0.371065	+	0.928607i	$0.621007\pi$
$128$	1.85553e7	0.782048
$129$	3.41108e7	1.39903
$130$	3.31221e7	1.32226
$131$	−2.12223e7	−0.824790	−0.412395	−	0.911005i	$-0.635308\pi$
$131$	−2.12223e7	−0.824790	−0.412395	+	0.911005i	$0.635308\pi$
$132$	2.20754e6	0.0835409
$133$	−4.69219e6	−0.172940
$134$	−1.58150e7	−0.567810
$135$	1.95292e7	0.683151
$136$	1.72791e6	0.0589028
$137$	−3.46511e7	−1.15132	−0.575659	−	0.817690i	$-0.695254\pi$
$137$	−3.46511e7	−1.15132	−0.575659	+	0.817690i	$0.695254\pi$
$138$	−2.91809e7	−0.945197
$139$	−2.49396e7	−0.787656	−0.393828	−	0.919184i	$-0.628850\pi$
$139$	−2.49396e7	−0.787656	−0.393828	+	0.919184i	$0.628850\pi$
$140$	−2.53293e6	−0.0780144
$141$	1.24888e7	0.375193
$142$	−2.38870e7	−0.700088
$143$	4.31386e6	0.123364
$144$	1.08210e7	0.301995
$145$	−4.23358e7	−1.15324
$146$	−5.75552e7	−1.53056
$147$	−2.80667e7	−0.728754
$148$	7.12158e7	1.80576
$149$	6.45220e7	1.59792	0.798961	−	0.601382i	$-0.205383\pi$
$149$	6.45220e7	1.59792	0.798961	+	0.601382i	$0.205383\pi$
$150$	2.72438e7	0.659094
$151$	−2.95483e7	−0.698416	−0.349208	−	0.937045i	$-0.613549\pi$
$151$	−2.95483e7	−0.698416	−0.349208	+	0.937045i	$0.613549\pi$
$152$	3.14666e7	0.726770
$153$	2.95123e6	0.0666166
$154$	−589783.	−0.0130128
$155$	3.24666e7	0.700287
$156$	6.10490e7	1.28749
$157$	8.15737e6	0.168229	0.0841146	−	0.996456i	$-0.473194\pi$
$157$	8.15737e6	0.168229	0.0841146	+	0.996456i	$0.473194\pi$
$158$	8.40303e6	0.169487
$159$	2.69538e7	0.531777
$160$	−4.60801e7	−0.889393
$161$	4.36076e6	0.0823515
$162$	2.69462e7	0.497960
$163$	−3.14921e7	−0.569567	−0.284784	−	0.958592i	$-0.591922\pi$
$163$	−3.14921e7	−0.569567	−0.284784	+	0.958592i	$0.591922\pi$
$164$	6.04338e7	1.06986
$165$	−2.41750e6	−0.0418959
$166$	−1.03285e8	−1.75251
$167$	1.11264e8	1.84861	0.924307	−	0.381649i	$-0.124644\pi$
$167$	1.11264e8	1.84861	0.924307	+	0.381649i	$0.124644\pi$
$168$	−1.77103e6	−0.0288167
$169$	5.65505e7	0.901224
$170$	−8.91780e6	−0.139215
$171$	5.37441e7	0.821947
$172$	1.61104e8	2.41411
$173$	−5.80756e7	−0.852770	−0.426385	−	0.904542i	$-0.640213\pi$
$173$	−5.80756e7	−0.852770	−0.426385	+	0.904542i	$0.640213\pi$
$174$	−1.39505e8	−2.00756
$175$	−4.07127e6	−0.0574244
$176$	−4.25864e6	−0.0588812
$177$	−3.55093e7	−0.481322
$178$	−7.22328e7	−0.959985
$179$	3.11858e7	0.406416	0.203208	−	0.979136i	$-0.434863\pi$
$179$	3.11858e7	0.406416	0.203208	+	0.979136i	$0.434863\pi$
$180$	2.90120e7	0.370786
$181$	1.32041e8	1.65514	0.827568	−	0.561366i	$-0.189724\pi$
$181$	1.32041e8	1.65514	0.827568	+	0.561366i	$0.189724\pi$
$182$	−1.63103e7	−0.200546
$183$	1.06330e8	1.28255
$184$	−2.92439e7	−0.346078
$185$	−7.79892e7	−0.905593
$186$	1.06984e8	1.21906
$187$	−1.16146e6	−0.0129885
$188$	5.89844e7	0.647418
$189$	−9.61678e6	−0.103613
$190$	−1.62400e8	−1.71770
$191$	−1.15247e8	−1.19677	−0.598387	−	0.801207i	$-0.704192\pi$
$191$	−1.15247e8	−1.19677	−0.598387	+	0.801207i	$0.704192\pi$
$192$	−1.04364e8	−1.06413
$193$	−2.62278e7	−0.262610	−0.131305	−	0.991342i	$-0.541917\pi$
$193$	−2.62278e7	−0.262610	−0.131305	+	0.991342i	$0.541917\pi$
$194$	2.05089e8	2.01668
$195$	−6.68554e7	−0.645677
$196$	−1.32558e8	−1.25751
$197$	−1.07417e8	−1.00102	−0.500508	−	0.865732i	$-0.666853\pi$
$197$	−1.07417e8	−1.00102	−0.500508	+	0.865732i	$0.666853\pi$
$198$	6.75534e6	0.0618470
$199$	9.60910e6	0.0864364	0.0432182	−	0.999066i	$-0.486239\pi$
$199$	9.60910e6	0.0864364	0.0432182	+	0.999066i	$0.486239\pi$
$200$	2.73026e7	0.241323
$201$	3.19218e7	0.277269
$202$	−1.73929e8	−1.48471
$203$	2.08474e7	0.174911
$204$	−1.64368e7	−0.135554
$205$	−6.61816e7	−0.536536
$206$	−2.55622e8	−2.03734
$207$	−4.99478e7	−0.391400
$208$	−1.17772e8	−0.907445
$209$	−2.11511e7	−0.160259
$210$	9.14034e6	0.0681075
$211$	1.74122e8	1.27604	0.638020	−	0.770020i	$-0.279754\pi$
$211$	1.74122e8	1.27604	0.638020	+	0.770020i	$0.279754\pi$
$212$	1.27302e8	0.917612
$213$	4.82147e7	0.341862
$214$	−9.75742e7	−0.680592
$215$	−1.76427e8	−1.21068
$216$	6.44917e7	0.435427
$217$	−1.59875e7	−0.106212
$218$	1.29989e8	0.849786
$219$	1.16172e8	0.747392
$220$	−1.14178e7	−0.0722938
$221$	−3.21201e7	−0.200172
$222$	−2.56990e8	−1.57645
$223$	2.47964e8	1.49734	0.748672	−	0.662941i	$-0.230692\pi$
$223$	2.47964e8	1.49734	0.748672	+	0.662941i	$0.230692\pi$
$224$	2.26912e7	0.134893
$225$	4.66320e7	0.272926
$226$	1.30954e7	0.0754641
$227$	1.72751e7	0.0980233	0.0490116	−	0.998798i	$-0.484393\pi$
$227$	1.72751e7	0.0980233	0.0490116	+	0.998798i	$0.484393\pi$
$228$	−2.99327e8	−1.67253
$229$	−1.67344e8	−0.920846	−0.460423	−	0.887700i	$-0.652302\pi$
$229$	−1.67344e8	−0.920846	−0.460423	+	0.887700i	$0.652302\pi$
$230$	1.50929e8	0.817946
$231$	1.19045e6	0.00635431
$232$	−1.39806e8	−0.735053
$233$	3.13859e8	1.62551	0.812755	−	0.582606i	$-0.197967\pi$
$233$	3.13859e8	1.62551	0.812755	+	0.582606i	$0.197967\pi$
$234$	1.86818e8	0.953152
$235$	−6.45944e7	−0.324681
$236$	−1.67709e8	−0.830548
$237$	−1.69611e7	−0.0827627
$238$	4.39139e6	0.0211146
$239$	−1.77516e8	−0.841095	−0.420548	−	0.907270i	$-0.638162\pi$
$239$	−1.77516e8	−0.841095	−0.420548	+	0.907270i	$0.638162\pi$
$240$	6.59996e7	0.308178
$241$	−3.37578e8	−1.55351	−0.776755	−	0.629803i	$-0.783136\pi$
$241$	−3.37578e8	−1.55351	−0.776755	+	0.629803i	$0.783136\pi$
$242$	3.29468e8	1.49437
$243$	1.85653e8	0.830005
$244$	5.02191e8	2.21312
$245$	1.45166e8	0.630642
$246$	−2.18082e8	−0.933999
$247$	−5.84930e8	−2.46982
$248$	1.07215e8	0.446349
$249$	2.08476e8	0.855774
$250$	−3.77823e8	−1.52932
$251$	−9.15970e7	−0.365614	−0.182807	−	0.983149i	$-0.558518\pi$
$251$	−9.15970e7	−0.365614	−0.182807	+	0.983149i	$0.558518\pi$
$252$	−1.42864e7	−0.0562367
$253$	1.96571e7	0.0763129
$254$	2.91977e8	1.11797
$255$	1.80001e7	0.0679806
$256$	7.20730e7	0.268493
$257$	−1.28198e8	−0.471101	−0.235550	−	0.971862i	$-0.575689\pi$
$257$	−1.28198e8	−0.471101	−0.235550	+	0.971862i	$0.575689\pi$
$258$	−5.81362e8	−2.10755
$259$	3.84042e7	0.137350
$260$	−3.15756e8	−1.11415
$261$	−2.38785e8	−0.831315
$262$	3.61699e8	1.24249
$263$	4.02860e7	0.136555	0.0682777	−	0.997666i	$-0.478250\pi$
$263$	4.02860e7	0.136555	0.0682777	+	0.997666i	$0.478250\pi$
$264$	−7.98333e6	−0.0267036
$265$	−1.39409e8	−0.460184
$266$	7.99706e7	0.260522
$267$	1.45798e8	0.468773
$268$	1.50766e8	0.478444
$269$	4.86177e8	1.52286	0.761432	−	0.648244i	$-0.224496\pi$
$269$	4.86177e8	1.52286	0.761432	+	0.648244i	$0.224496\pi$
$270$	−3.32843e8	−1.02912
$271$	2.13841e8	0.652677	0.326339	−	0.945253i	$-0.394185\pi$
$271$	2.13841e8	0.652677	0.326339	+	0.945253i	$0.394185\pi$
$272$	3.17089e7	0.0955411
$273$	3.29216e7	0.0979290
$274$	5.90571e8	1.73438
$275$	−1.83522e7	−0.0532137
$276$	2.78184e8	0.796435
$277$	−1.83772e8	−0.519519	−0.259759	−	0.965673i	$-0.583643\pi$
$277$	−1.83772e8	−0.519519	−0.259759	+	0.965673i	$0.583643\pi$
$278$	4.25053e8	1.18655
$279$	1.83120e8	0.504803
$280$	9.16007e6	0.0249371
$281$	3.57561e8	0.961342	0.480671	−	0.876901i	$-0.340393\pi$
$281$	3.57561e8	0.961342	0.480671	+	0.876901i	$0.340393\pi$
$282$	−2.12851e8	−0.565203
$283$	4.85857e8	1.27425	0.637127	−	0.770758i	$-0.280122\pi$
$283$	4.85857e8	1.27425	0.637127	+	0.770758i	$0.280122\pi$
$284$	2.27717e8	0.589903
$285$	3.27796e8	0.838777
$286$	−7.35226e7	−0.185840
$287$	3.25898e7	0.0813758
$288$	−2.59904e8	−0.641120
$289$	−4.01691e8	−0.978925
$290$	7.21544e8	1.73728
$291$	−4.13963e8	−0.984772
$292$	5.48678e8	1.28967
$293$	5.92374e8	1.37581	0.687907	−	0.725799i	$-0.258530\pi$
$293$	5.92374e8	1.37581	0.687907	+	0.725799i	$0.258530\pi$
$294$	4.78350e8	1.09782
$295$	1.83660e8	0.416522
$296$	−2.57545e8	−0.577207
$297$	−4.33499e7	−0.0960152
$298$	−1.09967e9	−2.40716
$299$	5.43614e8	1.17609
$300$	−2.59717e8	−0.555361
$301$	8.68779e7	0.183623
$302$	5.03603e8	1.05212
$303$	3.51067e8	0.725004
$304$	5.77443e8	1.17883
$305$	−5.49955e8	−1.10988
$306$	−5.02988e7	−0.100353
$307$	2.46849e8	0.486908	0.243454	−	0.969912i	$-0.421720\pi$
$307$	2.46849e8	0.486908	0.243454	+	0.969912i	$0.421720\pi$
$308$	5.62244e6	0.0109647
$309$	5.15960e8	0.994859
$310$	−5.53340e8	−1.05494
$311$	−4.44995e8	−0.838868	−0.419434	−	0.907786i	$-0.637772\pi$
$311$	−4.44995e8	−0.838868	−0.419434	+	0.907786i	$0.637772\pi$
$312$	−2.20777e8	−0.411542
$313$	−7.97339e8	−1.46973	−0.734866	−	0.678213i	$-0.762755\pi$
$313$	−7.97339e8	−1.46973	−0.734866	+	0.678213i	$0.762755\pi$
$314$	−1.39029e8	−0.253426
$315$	1.56452e7	0.0282028
$316$	−8.01067e7	−0.142812
$317$	3.26253e8	0.575237	0.287619	−	0.957745i	$-0.407136\pi$
$317$	3.26253e8	0.575237	0.287619	+	0.957745i	$0.407136\pi$
$318$	−4.59382e8	−0.801086
$319$	9.39746e7	0.162085
$320$	5.39787e8	0.920868
$321$	1.96949e8	0.332342
$322$	−7.43219e7	−0.124057
$323$	1.57487e8	0.260037
$324$	−2.56880e8	−0.419587
$325$	−5.07526e8	−0.820099
$326$	5.36731e8	0.858015
$327$	−2.62377e8	−0.414962
$328$	−2.18553e8	−0.341977
$329$	3.18082e7	0.0492440
$330$	4.12022e7	0.0631134
$331$	−1.07670e9	−1.63191	−0.815956	−	0.578114i	$-0.803789\pi$
$331$	−1.07670e9	−1.63191	−0.815956	+	0.578114i	$0.803789\pi$
$332$	9.84627e8	1.47669
$333$	−4.39880e8	−0.652798
$334$	−1.89631e9	−2.78481
$335$	−1.65105e8	−0.239940
$336$	−3.25002e7	−0.0467410
$337$	4.76446e8	0.678124	0.339062	−	0.940764i	$-0.389890\pi$
$337$	4.76446e8	0.678124	0.339062	+	0.940764i	$0.389890\pi$
$338$	−9.63809e8	−1.35763
$339$	−2.64325e7	−0.0368501
$340$	8.50141e7	0.117304
$341$	−7.20675e7	−0.0984236
$342$	−9.15978e8	−1.23821
$343$	−1.43641e8	−0.192197
$344$	−5.82617e8	−0.771665
$345$	−3.04642e8	−0.399414
$346$	9.89801e8	1.28464
$347$	−1.07071e9	−1.37569	−0.687844	−	0.725858i	$-0.741443\pi$
$347$	−1.07071e9	−1.37569	−0.687844	+	0.725858i	$0.741443\pi$
$348$	1.32991e9	1.69159
$349$	−4.70103e6	−0.00591976	−0.00295988	−	0.999996i	$-0.500942\pi$
$349$	−4.70103e6	−0.00591976	−0.00295988	+	0.999996i	$0.500942\pi$
$350$	6.93880e7	0.0865060
$351$	−1.19883e9	−1.47973
$352$	1.02286e8	0.125002
$353$	−5.19091e8	−0.628105	−0.314052	−	0.949406i	$-0.601687\pi$
$353$	−5.19091e8	−0.628105	−0.314052	+	0.949406i	$0.601687\pi$
$354$	6.05197e8	0.725079
$355$	−2.49375e8	−0.295837
$356$	6.88601e8	0.808896
$357$	−8.86381e6	−0.0103105
$358$	−5.31510e8	−0.612238
$359$	−1.51944e9	−1.73321	−0.866607	−	0.498991i	$-0.833704\pi$
$359$	−1.51944e9	−1.73321	−0.866607	+	0.498991i	$0.833704\pi$
$360$	−1.04919e8	−0.118521
$361$	1.97408e9	2.20846
$362$	−2.25042e9	−2.49335
$363$	−6.65014e8	−0.729723
$364$	1.55488e8	0.168982
$365$	−6.00863e8	−0.646771
$366$	−1.81221e9	−1.93208
$367$	9.82115e8	1.03713	0.518563	−	0.855040i	$-0.326467\pi$
$367$	9.82115e8	1.03713	0.518563	+	0.855040i	$0.326467\pi$
$368$	−5.36655e8	−0.561343
$369$	−3.73282e8	−0.386763
$370$	1.32920e9	1.36422
$371$	6.86494e7	0.0697956
$372$	−1.01989e9	−1.02719
$373$	−4.81541e8	−0.480455	−0.240227	−	0.970717i	$-0.577222\pi$
$373$	−4.81541e8	−0.480455	−0.240227	+	0.970717i	$0.577222\pi$
$374$	1.97952e7	0.0195664
$375$	7.62616e8	0.746787
$376$	−2.13311e8	−0.206945
$377$	2.59885e9	2.49797
$378$	1.63902e8	0.156086
$379$	7.97951e8	0.752903	0.376452	−	0.926436i	$-0.377144\pi$
$379$	7.97951e8	0.752903	0.376452	+	0.926436i	$0.377144\pi$
$380$	1.54817e9	1.44736
$381$	−5.89340e8	−0.545919
$382$	1.96419e9	1.80286
$383$	−1.60426e9	−1.45908	−0.729539	−	0.683939i	$-0.760265\pi$
$383$	−1.60426e9	−1.45908	−0.729539	+	0.683939i	$0.760265\pi$
$384$	6.38324e8	0.575283
$385$	−6.15719e6	−0.00549883
$386$	4.47009e8	0.395604
$387$	−9.95094e8	−0.872722
$388$	−1.95513e9	−1.69928
$389$	1.98599e9	1.71062	0.855309	−	0.518119i	$-0.173367\pi$
$389$	1.98599e9	1.71062	0.855309	+	0.518119i	$0.173367\pi$
$390$	1.13944e9	0.972668
$391$	−1.46363e8	−0.123826
$392$	4.79383e8	0.401959
$393$	−7.30072e8	−0.606725
$394$	1.83074e9	1.50796
$395$	8.77256e7	0.0716204
$396$	−6.43991e7	−0.0521131
$397$	−1.36649e9	−1.09607	−0.548037	−	0.836454i	$-0.684625\pi$
$397$	−1.36649e9	−1.09607	−0.548037	+	0.836454i	$0.684625\pi$
$398$	−1.63771e8	−0.130211
$399$	−1.61417e8	−0.127216
$400$	5.01029e8	0.391429
$401$	3.31556e8	0.256775	0.128387	−	0.991724i	$-0.459020\pi$
$401$	3.31556e8	0.256775	0.128387	+	0.991724i	$0.459020\pi$
$402$	−5.44054e8	−0.417687
$403$	−1.99301e9	−1.51685
$404$	1.65808e9	1.25104
$405$	2.81312e8	0.210424
$406$	−3.55310e8	−0.263491
$407$	1.73116e8	0.127279
$408$	5.94421e7	0.0433295
$409$	1.19571e9	0.864163	0.432082	−	0.901834i	$-0.357779\pi$
$409$	1.19571e9	0.864163	0.432082	+	0.901834i	$0.357779\pi$
$410$	1.12796e9	0.808255
$411$	−1.19204e9	−0.846922
$412$	2.43686e9	1.71669
$413$	−9.04397e7	−0.0631733
$414$	8.51278e8	0.589617
$415$	−1.07827e9	−0.740561
$416$	2.82870e9	1.92646
$417$	−8.57948e8	−0.579409
$418$	3.60486e8	0.241419
$419$	9.50089e8	0.630980	0.315490	−	0.948929i	$-0.397831\pi$
$419$	9.50089e8	0.630980	0.315490	+	0.948929i	$0.397831\pi$
$420$	−8.71355e7	−0.0573882
$421$	−1.60362e8	−0.104741	−0.0523703	−	0.998628i	$-0.516678\pi$
$421$	−1.60362e8	−0.104741	−0.0523703	+	0.998628i	$0.516678\pi$
$422$	−2.96761e9	−1.92227
$423$	−3.64329e8	−0.234047
$424$	−4.60374e8	−0.293312
$425$	1.36646e8	0.0863449
$426$	−8.21740e8	−0.514992
$427$	2.70814e8	0.168335
$428$	9.30182e8	0.573475
$429$	1.48402e8	0.0907482
$430$	3.00690e9	1.82381
$431$	1.67995e9	1.01071	0.505354	−	0.862912i	$-0.331362\pi$
$431$	1.67995e9	1.01071	0.505354	+	0.862912i	$0.331362\pi$
$432$	1.18349e9	0.706269
$433$	5.77673e8	0.341959	0.170980	−	0.985275i	$-0.445307\pi$
$433$	5.77673e8	0.341959	0.170980	+	0.985275i	$0.445307\pi$
$434$	2.72481e8	0.160001
$435$	−1.45640e9	−0.848337
$436$	−1.23920e9	−0.716041
$437$	−2.66537e9	−1.52782
$438$	−1.97996e9	−1.12590
$439$	2.97197e9	1.67656	0.838280	−	0.545240i	$-0.183562\pi$
$439$	2.97197e9	1.67656	0.838280	+	0.545240i	$0.183562\pi$
$440$	4.12911e7	0.0231085
$441$	8.18773e8	0.454599
$442$	5.47433e8	0.301546
$443$	1.48222e8	0.0810030	0.0405015	−	0.999179i	$-0.487104\pi$
$443$	1.48222e8	0.0810030	0.0405015	+	0.999179i	$0.487104\pi$
$444$	2.44990e9	1.32834
$445$	−7.54093e8	−0.405663
$446$	−4.22613e9	−2.25565
$447$	2.21963e9	1.17545
$448$	−2.65807e8	−0.139667
$449$	−2.72638e9	−1.42142	−0.710712	−	0.703483i	$-0.751627\pi$
$449$	−2.72638e9	−1.42142	−0.710712	+	0.703483i	$0.751627\pi$
$450$	−7.94766e8	−0.411145
$451$	1.46906e8	0.0754088
$452$	−1.24840e8	−0.0635870
$453$	−1.01650e9	−0.513762
$454$	−2.94425e8	−0.147665
$455$	−1.70276e8	−0.0847449
$456$	1.08249e9	0.534620
$457$	9.70563e8	0.475682	0.237841	−	0.971304i	$-0.423560\pi$
$457$	9.70563e8	0.475682	0.237841	+	0.971304i	$0.423560\pi$
$458$	2.85211e9	1.38719
$459$	3.22773e8	0.155795
$460$	−1.43882e9	−0.689212
$461$	−3.29361e9	−1.56574	−0.782869	−	0.622186i	$-0.786245\pi$
$461$	−3.29361e9	−1.56574	−0.782869	+	0.622186i	$0.786245\pi$
$462$	−2.02892e7	−0.00957233
$463$	−1.68939e9	−0.791038	−0.395519	−	0.918458i	$-0.629435\pi$
$463$	−1.68939e9	−0.791038	−0.395519	+	0.918458i	$0.629435\pi$
$464$	−2.56558e9	−1.19227
$465$	1.11689e9	0.515139
$466$	−5.34921e9	−2.44872
$467$	−1.66072e9	−0.754547	−0.377273	−	0.926102i	$-0.623138\pi$
$467$	−1.66072e9	−0.754547	−0.377273	+	0.926102i	$0.623138\pi$
$468$	−1.78095e9	−0.803138
$469$	8.13027e7	0.0363915
$470$	1.10090e9	0.489110
$471$	2.80623e8	0.123751
$472$	6.06503e8	0.265483
$473$	3.91622e8	0.170158
$474$	2.89074e8	0.124676
$475$	2.48843e9	1.06536
$476$	−4.18635e7	−0.0177914
$477$	−7.86306e8	−0.331724
$478$	3.02547e9	1.26705
$479$	−5.43476e8	−0.225947	−0.112973	−	0.993598i	$-0.536037\pi$
$479$	−5.43476e8	−0.225947	−0.112973	+	0.993598i	$0.536037\pi$
$480$	−1.58521e9	−0.654247
$481$	4.78748e9	1.96155
$482$	5.75345e9	2.34026
$483$	1.50015e8	0.0605786
$484$	−3.14084e9	−1.25918
$485$	2.14108e9	0.852192
$486$	−3.16415e9	−1.25035
$487$	7.54020e7	0.0295823	0.0147911	−	0.999891i	$-0.495292\pi$
$487$	7.54020e7	0.0295823	0.0147911	+	0.999891i	$0.495292\pi$
$488$	−1.81612e9	−0.707418
$489$	−1.08336e9	−0.418980
$490$	−2.47411e9	−0.950020
$491$	−1.27325e9	−0.485434	−0.242717	−	0.970097i	$-0.578039\pi$
$491$	−1.27325e9	−0.485434	−0.242717	+	0.970097i	$0.578039\pi$
$492$	2.07899e9	0.786999
$493$	−6.99714e8	−0.263001
$494$	9.96916e9	3.72061
$495$	7.05241e7	0.0261348
$496$	1.96750e9	0.723985
$497$	1.22800e8	0.0448693
$498$	−3.55313e9	−1.28917
$499$	−1.64913e8	−0.0594158	−0.0297079	−	0.999559i	$-0.509458\pi$
$499$	−1.64913e8	−0.0594158	−0.0297079	+	0.999559i	$0.509458\pi$
$500$	3.60181e9	1.28862
$501$	3.82760e9	1.35986
$502$	1.56112e9	0.550773
$503$	−5.48219e9	−1.92073	−0.960364	−	0.278748i	$-0.910080\pi$
$503$	−5.48219e9	−1.92073	−0.960364	+	0.278748i	$0.910080\pi$
$504$	5.16652e7	0.0179759
$505$	−1.81578e9	−0.627398
$506$	−3.35023e8	−0.114960
$507$	1.94540e9	0.662950
$508$	−2.78343e9	−0.942015
$509$	6.37824e8	0.214382	0.107191	−	0.994238i	$-0.465814\pi$
$509$	6.37824e8	0.214382	0.107191	+	0.994238i	$0.465814\pi$
$510$	−3.06782e8	−0.102408
$511$	2.95883e8	0.0980950
$512$	−3.60345e9	−1.18651
$513$	5.87795e9	1.92227
$514$	2.18492e9	0.709682
$515$	−2.66863e9	−0.860922
$516$	5.54217e9	1.77585
$517$	1.43383e8	0.0456331
$518$	−6.54536e8	−0.206909
$519$	−1.99786e9	−0.627307
$520$	1.14190e9	0.356136
$521$	3.49109e9	1.08151	0.540753	−	0.841182i	$-0.318139\pi$
$521$	3.49109e9	1.08151	0.540753	+	0.841182i	$0.318139\pi$
$522$	4.06970e9	1.25232
$523$	−2.43142e9	−0.743197	−0.371598	−	0.928394i	$-0.621190\pi$
$523$	−2.43142e9	−0.743197	−0.371598	+	0.928394i	$0.621190\pi$
$524$	−3.44811e9	−1.04694
$525$	−1.40056e8	−0.0422420
$526$	−6.86607e8	−0.205711
$527$	5.36599e8	0.159703
$528$	−1.46502e8	−0.0433137
$529$	−9.27722e8	−0.272473
$530$	2.37600e9	0.693236
$531$	1.03589e9	0.300250
$532$	−7.62365e8	−0.219519
$533$	4.06266e9	1.16216
$534$	−2.48489e9	−0.706176
$535$	−1.01865e9	−0.287599
$536$	−5.45229e8	−0.152933
$537$	1.07283e9	0.298964
$538$	−8.28608e9	−2.29409
$539$	−3.22231e8	−0.0886352
$540$	3.17302e9	0.867151
$541$	3.11720e9	0.846398	0.423199	−	0.906037i	$-0.360907\pi$
$541$	3.11720e9	0.846398	0.423199	+	0.906037i	$0.360907\pi$
$542$	−3.64456e9	−0.983214
$543$	4.54236e9	1.21754
$544$	−7.61599e8	−0.202829
$545$	1.35706e9	0.359096
$546$	−5.61094e8	−0.147523
$547$	−4.15156e9	−1.08457	−0.542283	−	0.840196i	$-0.682440\pi$
$547$	−4.15156e9	−1.08457	−0.542283	+	0.840196i	$0.682440\pi$
$548$	−5.62995e9	−1.46141
$549$	−3.10189e9	−0.800061
$550$	3.12782e8	0.0801628
$551$	−1.27423e10	−3.24502
$552$	−1.00602e9	−0.254578
$553$	−4.31987e7	−0.0108626
$554$	3.13210e9	0.782620
$555$	−2.68291e9	−0.666164
$556$	−4.05206e9	−0.999803
$557$	4.70969e9	1.15478	0.577390	−	0.816469i	$-0.304071\pi$
$557$	4.70969e9	1.15478	0.577390	+	0.816469i	$0.304071\pi$
$558$	−3.12098e9	−0.760451
$559$	1.08302e10	2.62239
$560$	1.68096e8	0.0404483
$561$	−3.99557e7	−0.00955451
$562$	−6.09403e9	−1.44820
$563$	4.82406e9	1.13929	0.569644	−	0.821891i	$-0.307081\pi$
$563$	4.82406e9	1.13929	0.569644	+	0.821891i	$0.307081\pi$
$564$	2.02913e9	0.476247
$565$	1.36713e8	0.0318890
$566$	−8.28063e9	−1.91958
$567$	−1.38526e8	−0.0319147
$568$	−8.23514e8	−0.188561
$569$	5.26007e9	1.19701	0.598507	−	0.801118i	$-0.295761\pi$
$569$	5.26007e9	1.19701	0.598507	+	0.801118i	$0.295761\pi$
$570$	−5.58674e9	−1.26356
$571$	1.39661e9	0.313942	0.156971	−	0.987603i	$-0.449827\pi$
$571$	1.39661e9	0.313942	0.156971	+	0.987603i	$0.449827\pi$
$572$	7.00896e8	0.156591
$573$	−3.96462e9	−0.880360
$574$	−5.55439e8	−0.122587
$575$	−2.31266e9	−0.507311
$576$	3.04454e9	0.663809
$577$	2.04139e9	0.442394	0.221197	−	0.975229i	$-0.429004\pi$
$577$	2.04139e9	0.442394	0.221197	+	0.975229i	$0.429004\pi$
$578$	6.84615e9	1.47468
$579$	−9.02265e8	−0.193179
$580$	−6.87853e9	−1.46385
$581$	5.30975e8	0.112320
$582$	7.05530e9	1.48349
$583$	3.09453e8	0.0646777
$584$	−1.98424e9	−0.412239
$585$	1.95033e9	0.402775
$586$	−1.00960e10	−2.07257
$587$	8.97188e9	1.83084	0.915420	−	0.402501i	$-0.131859\pi$
$587$	8.97188e9	1.83084	0.915420	+	0.402501i	$0.131859\pi$
$588$	−4.56015e9	−0.925036
$589$	9.77187e9	1.97049
$590$	−3.13018e9	−0.627462
$591$	−3.69526e9	−0.736358
$592$	−4.72620e9	−0.936239
$593$	−6.73460e8	−0.132623	−0.0663117	−	0.997799i	$-0.521123\pi$
$593$	−6.73460e8	−0.132623	−0.0663117	+	0.997799i	$0.521123\pi$
$594$	7.38826e8	0.144640
$595$	4.58451e7	0.00892244
$596$	1.04832e10	2.02831
$597$	3.30564e8	0.0635836
$598$	−9.26499e9	−1.77170
$599$	−3.14228e9	−0.597381	−0.298691	−	0.954350i	$-0.596550\pi$
$599$	−3.14228e9	−0.597381	−0.298691	+	0.954350i	$0.596550\pi$
$600$	9.39239e8	0.177520
$601$	7.12109e9	1.33809	0.669046	−	0.743221i	$-0.266703\pi$
$601$	7.12109e9	1.33809	0.669046	+	0.743221i	$0.266703\pi$
$602$	−1.48069e9	−0.276615
$603$	−9.31236e8	−0.172961
$604$	−4.80088e9	−0.886526
$605$	3.43957e9	0.631480
$606$	−5.98335e9	−1.09217
$607$	−4.64220e8	−0.0842487	−0.0421243	−	0.999112i	$-0.513413\pi$
$607$	−4.64220e8	−0.0842487	−0.0421243	+	0.999112i	$0.513413\pi$
$608$	−1.38693e10	−2.50260
$609$	7.17175e8	0.128666
$610$	9.37307e9	1.67197
$611$	3.96522e9	0.703272
$612$	4.79502e8	0.0845591
$613$	3.06412e9	0.537271	0.268636	−	0.963242i	$-0.413427\pi$
$613$	3.06412e9	0.537271	0.268636	+	0.963242i	$0.413427\pi$
$614$	−4.20713e9	−0.733494
$615$	−2.27672e9	−0.394682
$616$	−2.03330e7	−0.00350485
$617$	−4.37597e8	−0.0750026	−0.0375013	−	0.999297i	$-0.511940\pi$
$617$	−4.37597e8	−0.0750026	−0.0375013	+	0.999297i	$0.511940\pi$
$618$	−8.79369e9	−1.49869
$619$	−4.19184e9	−0.710374	−0.355187	−	0.934795i	$-0.615583\pi$
$619$	−4.19184e9	−0.710374	−0.355187	+	0.934795i	$0.615583\pi$
$620$	5.27503e9	0.888902
$621$	−5.46276e9	−0.915359
$622$	7.58420e9	1.26370
$623$	3.71338e8	0.0615264
$624$	−4.05149e9	−0.667526
$625$	−3.14188e8	−0.0514765
$626$	1.35893e10	2.21405
$627$	−7.27622e8	−0.117888
$628$	1.32537e9	0.213540
$629$	−1.28898e9	−0.206524
$630$	−2.66646e8	−0.0424857
$631$	−7.87167e9	−1.24728	−0.623640	−	0.781712i	$-0.714347\pi$
$631$	−7.87167e9	−1.24728	−0.623640	+	0.781712i	$0.714347\pi$
$632$	2.89698e8	0.0456494
$633$	5.98998e9	0.938669
$634$	−5.56044e9	−0.866556
$635$	3.04817e9	0.472423
$636$	4.37932e9	0.675005
$637$	−8.91122e9	−1.36600
$638$	−1.60164e9	−0.244170
$639$	−1.40654e9	−0.213255
$640$	−3.30152e9	−0.497833
$641$	−5.44876e9	−0.817137	−0.408568	−	0.912728i	$-0.633972\pi$
$641$	−5.44876e9	−0.817137	−0.408568	+	0.912728i	$0.633972\pi$
$642$	−3.35666e9	−0.500651
$643$	5.34618e9	0.793059	0.396529	−	0.918022i	$-0.370214\pi$
$643$	5.34618e9	0.793059	0.396529	+	0.918022i	$0.370214\pi$
$644$	7.08516e8	0.104532
$645$	−6.06928e9	−0.890591
$646$	−2.68410e9	−0.391728
$647$	−1.72911e9	−0.250991	−0.125496	−	0.992094i	$-0.540052\pi$
$647$	−1.72911e9	−0.250991	−0.125496	+	0.992094i	$0.540052\pi$
$648$	9.28979e8	0.134120
$649$	−4.07678e8	−0.0585411
$650$	8.64993e9	1.23542
$651$	−5.49989e8	−0.0781305
$652$	−5.11669e9	−0.722974
$653$	7.81789e9	1.09874	0.549368	−	0.835581i	$-0.314869\pi$
$653$	7.81789e9	1.09874	0.549368	+	0.835581i	$0.314869\pi$
$654$	4.47178e9	0.625112
$655$	3.77606e9	0.525042
$656$	−4.01066e9	−0.554692
$657$	−3.38903e9	−0.466226
$658$	−5.42118e8	−0.0741828
$659$	7.14165e7	0.00972075	0.00486037	−	0.999988i	$-0.498453\pi$
$659$	7.14165e7	0.00972075	0.00486037	+	0.999988i	$0.498453\pi$
$660$	−3.92783e8	−0.0531801
$661$	2.83757e9	0.382156	0.191078	−	0.981575i	$-0.438802\pi$
$661$	2.83757e9	0.382156	0.191078	+	0.981575i	$0.438802\pi$
$662$	1.83506e10	2.45836
$663$	−1.10497e9	−0.147249
$664$	−3.56080e9	−0.472019
$665$	8.34874e8	0.110089
$666$	7.49702e9	0.983396
$667$	1.18423e10	1.54524
$668$	1.80776e10	2.34652
$669$	8.53023e9	1.10146
$670$	2.81394e9	0.361454
$671$	1.22076e9	0.155991
$672$	7.80604e8	0.0992289
$673$	−3.05534e9	−0.386373	−0.193187	−	0.981162i	$-0.561882\pi$
$673$	−3.05534e9	−0.386373	−0.193187	+	0.981162i	$0.561882\pi$
$674$	−8.12024e9	−1.02155
$675$	5.10011e9	0.638288
$676$	9.18806e9	1.14396
$677$	−5.17256e8	−0.0640686	−0.0320343	−	0.999487i	$-0.510199\pi$
$677$	−5.17256e8	−0.0640686	−0.0320343	+	0.999487i	$0.510199\pi$
$678$	4.50498e8	0.0555122
$679$	−1.05433e9	−0.129251
$680$	−3.07445e8	−0.0374961
$681$	5.94282e8	0.0721070
$682$	1.22827e9	0.148269
$683$	−6.94431e9	−0.833981	−0.416991	−	0.908911i	$-0.636915\pi$
$683$	−6.94431e9	−0.833981	−0.416991	+	0.908911i	$0.636915\pi$
$684$	8.73209e9	1.04333
$685$	6.16542e9	0.732901
$686$	2.44812e9	0.289533
$687$	−5.75683e9	−0.677384
$688$	−1.06916e10	−1.25165
$689$	8.55786e9	0.996777
$690$	5.19212e9	0.601690
$691$	−8.07666e9	−0.931234	−0.465617	−	0.884986i	$-0.654167\pi$
$691$	−8.07666e9	−0.931234	−0.465617	+	0.884986i	$0.654167\pi$
$692$	−9.43585e9	−1.08245
$693$	−3.47282e7	−0.00396384
$694$	1.82485e10	2.07238
$695$	4.43745e9	0.501403
$696$	−4.80949e9	−0.540713
$697$	−1.09383e9	−0.122359
$698$	8.01213e7	0.00891772
$699$	1.07971e10	1.19574
$700$	−6.61481e8	−0.0728910
$701$	1.07625e10	1.18005	0.590027	−	0.807384i	$-0.299117\pi$
$701$	1.07625e10	1.18005	0.590027	+	0.807384i	$0.299117\pi$
$702$	2.04321e10	2.22912
$703$	−2.34733e10	−2.54819
$704$	−1.19819e9	−0.129426
$705$	−2.22212e9	−0.238839
$706$	8.84704e9	0.946197
$707$	8.94143e8	0.0951567
$708$	−5.76938e9	−0.610960
$709$	9.05454e9	0.954123	0.477062	−	0.878870i	$-0.341702\pi$
$709$	9.05454e9	0.954123	0.477062	+	0.878870i	$0.341702\pi$
$710$	4.25018e9	0.445659
$711$	4.94796e8	0.0516276
$712$	−2.49025e9	−0.258561
$713$	−9.08163e9	−0.938319
$714$	1.51069e8	0.0155321
$715$	−7.67558e8	−0.0785308
$716$	5.06692e9	0.515880
$717$	−6.10675e9	−0.618719
$718$	2.58963e10	2.61097
$719$	−6.04159e8	−0.0606178	−0.0303089	−	0.999541i	$-0.509649\pi$
$719$	−6.04159e8	−0.0606178	−0.0303089	+	0.999541i	$0.509649\pi$
$720$	−1.92537e9	−0.192243
$721$	1.31412e9	0.130575
$722$	−3.36449e10	−3.32689
$723$	−1.16130e10	−1.14278
$724$	2.14534e10	2.10093
$725$	−1.10561e10	−1.07751
$726$	1.13341e10	1.09928
$727$	−8.44306e9	−0.814948	−0.407474	−	0.913217i	$-0.633590\pi$
$727$	−8.44306e9	−0.814948	−0.407474	+	0.913217i	$0.633590\pi$
$728$	−5.62305e8	−0.0540147
$729$	9.84441e9	0.941117
$730$	1.02407e10	0.974317
$731$	−2.91593e9	−0.276100
$732$	1.72759e10	1.62799
$733$	−5.43934e8	−0.0510132	−0.0255066	−	0.999675i	$-0.508120\pi$
$733$	−5.43934e8	−0.0510132	−0.0255066	+	0.999675i	$0.508120\pi$
$734$	−1.67385e10	−1.56236
$735$	4.99386e9	0.463907
$736$	1.28896e10	1.19170
$737$	3.66491e8	0.0337230
$738$	6.36197e9	0.582632
$739$	−1.32403e10	−1.20682	−0.603409	−	0.797432i	$-0.706191\pi$
$739$	−1.32403e10	−1.20682	−0.603409	+	0.797432i	$0.706191\pi$
$740$	−1.26713e10	−1.14951
$741$	−2.01223e10	−1.81682
$742$	−1.17001e9	−0.105142
$743$	−5.16926e9	−0.462346	−0.231173	−	0.972913i	$-0.574256\pi$
$743$	−5.16926e9	−0.462346	−0.231173	+	0.972913i	$0.574256\pi$
$744$	3.68832e9	0.328339
$745$	−1.14803e10	−1.01720
$746$	8.20707e9	0.723773
$747$	−6.08175e9	−0.533834
$748$	−1.88709e8	−0.0164869
$749$	5.01614e8	0.0436198
$750$	−1.29975e10	−1.12498
$751$	3.55698e9	0.306437	0.153219	−	0.988192i	$-0.451036\pi$
$751$	3.55698e9	0.306437	0.153219	+	0.988192i	$0.451036\pi$
$752$	−3.91447e9	−0.335668
$753$	−3.15104e9	−0.268950
$754$	−4.42931e10	−3.76302
$755$	5.25749e9	0.444595
$756$	−1.56249e9	−0.131520
$757$	−1.49991e10	−1.25670	−0.628348	−	0.777932i	$-0.716269\pi$
$757$	−1.49991e10	−1.25670	−0.628348	+	0.777932i	$0.716269\pi$
$758$	−1.35998e10	−1.13420
$759$	6.76227e8	0.0561366
$760$	−5.59880e9	−0.462644
$761$	−1.43656e10	−1.18162	−0.590810	−	0.806811i	$-0.701192\pi$
$761$	−1.43656e10	−1.18162	−0.590810	+	0.806811i	$0.701192\pi$
$762$	1.00443e10	0.822391
$763$	−6.68256e8	−0.0544636
$764$	−1.87248e10	−1.51911
$765$	−5.25107e8	−0.0424065
$766$	2.73419e10	2.19800
$767$	−1.12742e10	−0.902202
$768$	2.47939e9	0.197506
$769$	1.36167e10	1.07977	0.539885	−	0.841739i	$-0.318468\pi$
$769$	1.36167e10	1.07977	0.539885	+	0.841739i	$0.318468\pi$
$770$	1.04939e8	0.00828362
$771$	−4.41014e9	−0.346547
$772$	−4.26137e9	−0.333341
$773$	1.31303e9	0.102246	0.0511229	−	0.998692i	$-0.483720\pi$
$773$	1.31303e9	0.102246	0.0511229	+	0.998692i	$0.483720\pi$
$774$	1.69597e10	1.31470
$775$	8.47875e9	0.654298
$776$	7.07054e9	0.543171
$777$	1.32115e9	0.101036
$778$	−3.38479e10	−2.57693
$779$	−1.99195e10	−1.50972
$780$	−1.08623e10	−0.819582
$781$	5.53547e8	0.0415792
$782$	2.49451e9	0.186535
$783$	−2.61158e10	−1.94418
$784$	8.79716e9	0.651983
$785$	−1.45143e9	−0.107091
$786$	1.24429e10	0.913990
$787$	1.40166e10	1.02502	0.512508	−	0.858683i	$-0.328717\pi$
$787$	1.40166e10	1.02502	0.512508	+	0.858683i	$0.328717\pi$
$788$	−1.74526e10	−1.27063
$789$	1.38588e9	0.100452
$790$	−1.49514e9	−0.107891
$791$	−6.73217e7	−0.00483657
$792$	2.32893e8	0.0166578
$793$	3.37598e10	2.40405
$794$	2.32896e10	1.65116
$795$	−4.79584e9	−0.338516
$796$	1.56124e9	0.109717
$797$	1.14390e10	0.800356	0.400178	−	0.916437i	$-0.368948\pi$
$797$	1.14390e10	0.800356	0.400178	+	0.916437i	$0.368948\pi$
$798$	2.75108e9	0.191643
$799$	−1.06760e9	−0.0740446
$800$	−1.20339e10	−0.830985
$801$	−4.25329e9	−0.292422
$802$	−5.65083e9	−0.386814
$803$	1.33376e9	0.0909020
$804$	5.18651e9	0.351948
$805$	−7.75903e8	−0.0524230
$806$	3.39676e10	2.28503
$807$	1.67250e10	1.12024
$808$	−5.99627e9	−0.399891
$809$	−2.73022e10	−1.81292	−0.906459	−	0.422293i	$-0.861225\pi$
$809$	−2.73022e10	−1.81292	−0.906459	+	0.422293i	$0.861225\pi$
$810$	−4.79449e9	−0.316989
$811$	−6.86122e9	−0.451677	−0.225839	−	0.974165i	$-0.572512\pi$
$811$	−6.86122e9	−0.451677	−0.225839	+	0.974165i	$0.572512\pi$
$812$	3.38720e9	0.222021
$813$	7.35637e9	0.480116
$814$	−2.95047e9	−0.191737
$815$	5.60334e9	0.362573
$816$	1.09082e9	0.0702811
$817$	−5.31013e10	−3.40665
$818$	−2.03790e10	−1.30180
$819$	−9.60401e8	−0.0610885
$820$	−1.07529e10	−0.681046
$821$	−2.17320e10	−1.37056	−0.685280	−	0.728280i	$-0.740320\pi$
$821$	−2.17320e10	−1.37056	−0.685280	+	0.728280i	$0.740320\pi$
$822$	2.03163e10	1.27583
$823$	−2.19182e9	−0.137058	−0.0685291	−	0.997649i	$-0.521831\pi$
$823$	−2.19182e9	−0.137058	−0.0685291	+	0.997649i	$0.521831\pi$
$824$	−8.81267e9	−0.548735
$825$	−6.31335e8	−0.0391446
$826$	1.54139e9	0.0951664
$827$	3.37939e9	0.207763	0.103882	−	0.994590i	$-0.466874\pi$
$827$	3.37939e9	0.207763	0.103882	+	0.994590i	$0.466874\pi$
$828$	−8.11530e9	−0.496819
$829$	2.63158e10	1.60426	0.802132	−	0.597147i	$-0.203699\pi$
$829$	2.63158e10	1.60426	0.802132	+	0.597147i	$0.203699\pi$
$830$	1.83774e10	1.11561
$831$	−6.32198e9	−0.382164
$832$	−3.31356e10	−1.99464
$833$	2.39926e9	0.143820
$834$	1.46223e10	0.872840
$835$	−1.97970e10	−1.17678
$836$	−3.43654e9	−0.203423
$837$	2.00277e10	1.18057
$838$	−1.61927e10	−0.950528
$839$	−6.58575e9	−0.384980	−0.192490	−	0.981299i	$-0.561656\pi$
$839$	−6.58575e9	−0.384980	−0.192490	+	0.981299i	$0.561656\pi$
$840$	3.15117e8	0.0183440
$841$	3.93644e10	2.28201
$842$	2.73311e9	0.157785
$843$	1.23005e10	0.707174
$844$	2.82905e10	1.61973
$845$	−1.00619e10	−0.573697
$846$	6.20939e9	0.352576
$847$	−1.69375e9	−0.0957759
$848$	−8.44832e9	−0.475757
$849$	1.67140e10	0.937356
$850$	−2.32891e9	−0.130073
$851$	2.18153e10	1.21341
$852$	7.83370e9	0.433939
$853$	9.21489e8	0.0508357	0.0254178	−	0.999677i	$-0.491908\pi$
$853$	9.21489e8	0.0508357	0.0254178	+	0.999677i	$0.491908\pi$
$854$	−4.61558e9	−0.253585
$855$	−9.56259e9	−0.523232
$856$	−3.36391e9	−0.183310
$857$	2.11864e10	1.14980	0.574902	−	0.818222i	$-0.305040\pi$
$857$	2.11864e10	1.14980	0.574902	+	0.818222i	$0.305040\pi$
$858$	−2.52926e9	−0.136706
$859$	2.97776e10	1.60292	0.801462	−	0.598046i	$-0.204056\pi$
$859$	2.97776e10	1.60292	0.801462	+	0.598046i	$0.204056\pi$
$860$	−2.86650e10	−1.53677
$861$	1.12113e9	0.0598609
$862$	−2.86319e10	−1.52256
$863$	6.28278e9	0.332747	0.166373	−	0.986063i	$-0.446794\pi$
$863$	6.28278e9	0.332747	0.166373	+	0.986063i	$0.446794\pi$
$864$	−2.84255e10	−1.49937
$865$	1.03333e10	0.542853
$866$	−9.84547e9	−0.515138
$867$	−1.38186e10	−0.720108
$868$	−2.59758e9	−0.134819
$869$	−1.94728e8	−0.0100661
$870$	2.48219e10	1.27796
$871$	1.01352e10	0.519721
$872$	4.48143e9	0.228881
$873$	1.20763e10	0.614304
$874$	4.54268e10	2.30156
$875$	1.94233e9	0.0980156
$876$	1.88751e10	0.948694
$877$	−5.71755e9	−0.286228	−0.143114	−	0.989706i	$-0.545712\pi$
$877$	−5.71755e9	−0.286228	−0.143114	+	0.989706i	$0.545712\pi$
$878$	−5.06523e10	−2.52562
$879$	2.03783e10	1.01206
$880$	7.57734e8	0.0374824
$881$	−8.93586e8	−0.0440272	−0.0220136	−	0.999758i	$-0.507008\pi$
$881$	−8.93586e8	−0.0440272	−0.0220136	+	0.999758i	$0.507008\pi$
$882$	−1.39546e10	−0.684823
$883$	1.46119e10	0.714242	0.357121	−	0.934058i	$-0.383758\pi$
$883$	1.46119e10	0.714242	0.357121	+	0.934058i	$0.383758\pi$
$884$	−5.21872e9	−0.254086
$885$	6.31811e9	0.306398
$886$	−2.52621e9	−0.122026
$887$	−7.64790e9	−0.367967	−0.183984	−	0.982929i	$-0.558899\pi$
$887$	−7.64790e9	−0.367967	−0.183984	+	0.982929i	$0.558899\pi$
$888$	−8.85983e9	−0.424600
$889$	−1.50101e9	−0.0716518
$890$	1.28523e10	0.611104
$891$	−6.24439e8	−0.0295745
$892$	4.02880e10	1.90064
$893$	−1.94417e10	−0.913598
$894$	−3.78299e10	−1.77073
$895$	−5.54883e9	−0.258715
$896$	1.62577e9	0.0755058
$897$	1.87009e10	0.865146
$898$	4.64666e10	2.14128
$899$	−4.34165e10	−1.99295
$900$	7.57656e9	0.346436
$901$	−2.30412e9	−0.104947
$902$	−2.50377e9	−0.113598
$903$	2.98870e9	0.135075
$904$	4.51470e8	0.0203254
$905$	−2.34938e10	−1.05362
$906$	1.73245e10	0.773948
$907$	1.16798e10	0.519769	0.259884	−	0.965640i	$-0.416316\pi$
$907$	1.16798e10	0.519769	0.259884	+	0.965640i	$0.416316\pi$
$908$	2.80677e9	0.124425
$909$	−1.02415e10	−0.452260
$910$	2.90207e9	0.127662
$911$	3.55665e10	1.55857	0.779286	−	0.626668i	$-0.215582\pi$
$911$	3.55665e10	1.55857	0.779286	+	0.626668i	$0.215582\pi$
$912$	1.98647e10	0.867161
$913$	2.39349e9	0.104084
$914$	−1.65416e10	−0.716583
$915$	−1.89191e10	−0.816443
$916$	−2.71893e10	−1.16887
$917$	−1.85944e9	−0.0796325
$918$	−5.50114e9	−0.234695
$919$	−2.15908e10	−0.917624	−0.458812	−	0.888533i	$-0.651725\pi$
$919$	−2.15908e10	−0.917624	−0.458812	+	0.888533i	$0.651725\pi$
$920$	5.20333e9	0.220305
$921$	8.49188e9	0.358175
$922$	5.61342e10	2.35868
$923$	1.53082e10	0.640795
$924$	1.93418e8	0.00806577
$925$	−2.03671e10	−0.846122
$926$	2.87929e10	1.19165
$927$	−1.50518e10	−0.620597
$928$	6.16213e10	2.53112
$929$	−3.19568e10	−1.30770	−0.653851	−	0.756623i	$-0.726848\pi$
$929$	−3.19568e10	−1.30770	−0.653851	+	0.756623i	$0.726848\pi$
$930$	−1.90355e10	−0.776022
$931$	4.36923e10	1.77452
$932$	5.09944e10	2.06332
$933$	−1.53083e10	−0.617081
$934$	2.83041e10	1.13667
$935$	2.06657e8	0.00826819
$936$	6.44061e9	0.256721
$937$	−2.07456e10	−0.823829	−0.411915	−	0.911222i	$-0.635140\pi$
$937$	−2.07456e10	−0.823829	−0.411915	+	0.911222i	$0.635140\pi$
$938$	−1.38567e9	−0.0548213
$939$	−2.74294e10	−1.08115
$940$	−1.04950e10	−0.412131
$941$	−1.49427e10	−0.584608	−0.292304	−	0.956326i	$-0.594422\pi$
$941$	−1.49427e10	−0.584608	−0.292304	+	0.956326i	$0.594422\pi$
$942$	−4.78275e9	−0.186423
$943$	1.85125e10	0.718908
$944$	1.11299e10	0.430617
$945$	1.71110e9	0.0659574
$946$	−6.67455e9	−0.256332
$947$	4.14659e10	1.58660	0.793298	−	0.608834i	$-0.208362\pi$
$947$	4.14659e10	1.58660	0.793298	+	0.608834i	$0.208362\pi$
$948$	−2.75576e9	−0.105054
$949$	3.68849e10	1.40093
$950$	−4.24112e10	−1.60490
$951$	1.12235e10	0.423151
$952$	1.51395e8	0.00568699
$953$	−3.41449e9	−0.127791	−0.0638957	−	0.997957i	$-0.520352\pi$
$953$	−3.41449e9	−0.127791	−0.0638957	+	0.997957i	$0.520352\pi$
$954$	1.34013e10	0.499720
$955$	2.05057e10	0.761838
$956$	−2.88420e10	−1.06764
$957$	3.23283e9	0.119232
$958$	9.26265e9	0.340374
$959$	−3.03604e9	−0.111158
$960$	1.85693e10	0.677401
$961$	5.78274e9	0.210185
$962$	−8.15947e10	−2.95494
$963$	−5.74546e9	−0.207316
$964$	−5.48481e10	−1.97193
$965$	4.66667e9	0.167171
$966$	−2.55675e9	−0.0912576
$967$	−2.97048e9	−0.105641	−0.0528207	−	0.998604i	$-0.516821\pi$
$967$	−2.97048e9	−0.105641	−0.0528207	+	0.998604i	$0.516821\pi$
$968$	1.13585e10	0.402493
$969$	5.41772e9	0.191286
$970$	−3.64912e10	−1.28377
$971$	1.35430e10	0.474732	0.237366	−	0.971420i	$-0.423716\pi$
$971$	1.35430e10	0.474732	0.237366	+	0.971420i	$0.423716\pi$
$972$	3.01641e10	1.05356
$973$	−2.18514e9	−0.0760472
$974$	−1.28510e9	−0.0445637
$975$	−1.74595e10	−0.603274
$976$	−3.33277e10	−1.14744
$977$	3.62073e10	1.24212	0.621062	−	0.783762i	$-0.286702\pi$
$977$	3.62073e10	1.24212	0.621062	+	0.783762i	$0.286702\pi$
$978$	1.84641e10	0.631165
$979$	1.67389e9	0.0570149
$980$	2.35859e10	0.800499
$981$	7.65416e9	0.258855
$982$	2.17005e10	0.731273
$983$	−4.55846e10	−1.53067	−0.765334	−	0.643633i	$-0.777426\pi$
$983$	−4.55846e10	−1.53067	−0.765334	+	0.643633i	$0.777426\pi$
$984$	−7.51845e9	−0.251562
$985$	1.91125e10	0.637223
$986$	1.19255e10	0.396193
$987$	1.09424e9	0.0362244
$988$	−9.50368e10	−3.13503
$989$	4.93505e10	1.62220
$990$	−1.20197e9	−0.0393703
$991$	−2.42462e10	−0.791383	−0.395691	−	0.918384i	$-0.629495\pi$
$991$	−2.42462e10	−0.791383	−0.395691	+	0.918384i	$0.629495\pi$
$992$	−4.72563e10	−1.53698
$993$	−3.70397e10	−1.20045
$994$	−2.09291e9	−0.0675926
$995$	−1.70973e9	−0.0550234
$996$	3.38723e10	1.08627
$997$	3.03621e9	0.0970284	0.0485142	−	0.998822i	$-0.484551\pi$
$997$	3.03621e9	0.0970284	0.0485142	+	0.998822i	$0.484551\pi$
$998$	2.81066e9	0.0895059
$999$	−4.81093e10	−1.52669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	79.8.a.b.1.5	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
79.8.a.b.1.5	✓	25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	79.a (trivial)

\(f(q)\)	\(=\)	\(q-17.0433 q^{2} +34.4011 q^{3} +162.475 q^{4} -177.928 q^{5} -586.310 q^{6} +87.6173 q^{7} -587.576 q^{8} -1003.56 q^{9} +O(q^{10})\)	\(q-17.0433 q^{2} +34.4011 q^{3} +162.475 q^{4} -177.928 q^{5} -586.310 q^{6} +87.6173 q^{7} -587.576 q^{8} -1003.56 q^{9} +3032.49 q^{10} +394.955 q^{11} +5589.33 q^{12} +10922.4 q^{13} -1493.29 q^{14} -6120.94 q^{15} -10782.6 q^{16} -2940.75 q^{17} +17104.1 q^{18} -53553.2 q^{19} -28909.0 q^{20} +3014.13 q^{21} -6731.35 q^{22} +49770.5 q^{23} -20213.3 q^{24} -46466.5 q^{25} -186154. q^{26} -109759. q^{27} +14235.7 q^{28} +237937. q^{29} +104321. q^{30} -182470. q^{31} +258981. q^{32} +13586.9 q^{33} +50120.2 q^{34} -15589.6 q^{35} -163054. q^{36} +438318. q^{37} +912726. q^{38} +375743. q^{39} +104546. q^{40} +371956. q^{41} -51370.9 q^{42} +991561. q^{43} +64170.5 q^{44} +178562. q^{45} -848256. q^{46} +363036. q^{47} -370933. q^{48} -815866. q^{49} +791944. q^{50} -101165. q^{51} +1.77462e6 q^{52} +783514. q^{53} +1.87066e6 q^{54} -70273.7 q^{55} -51481.8 q^{56} -1.84229e6 q^{57} -4.05525e6 q^{58} -1.03221e6 q^{59} -994501. q^{60} +3.09088e6 q^{61} +3.10990e6 q^{62} -87929.5 q^{63} -3.03373e6 q^{64} -1.94341e6 q^{65} -231566. q^{66} +927930. q^{67} -477799. q^{68} +1.71216e6 q^{69} +265699. q^{70} +1.40154e6 q^{71} +589669. q^{72} +3.37699e6 q^{73} -7.47040e6 q^{74} -1.59850e6 q^{75} -8.70108e6 q^{76} +34604.9 q^{77} -6.40392e6 q^{78} -493039. q^{79} +1.91853e6 q^{80} -1.58104e6 q^{81} -6.33938e6 q^{82} +6.06016e6 q^{83} +489722. q^{84} +523243. q^{85} -1.68995e7 q^{86} +8.18532e6 q^{87} -232066. q^{88} +4.23818e6 q^{89} -3.04330e6 q^{90} +956992. q^{91} +8.08648e6 q^{92} -6.27718e6 q^{93} -6.18734e6 q^{94} +9.52864e6 q^{95} +8.90924e6 q^{96} -1.20334e7 q^{97} +1.39051e7 q^{98} -396362. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 8 q^{2} + 107 q^{3} + 1728 q^{4} + 999 q^{5} + 1113 q^{6} + 883 q^{7} + 2334 q^{8} + 24630 q^{9}+O(q^{10}) \) 25 * q + 8 * q^2 + 107 * q^3 + 1728 * q^4 + 999 * q^5 + 1113 * q^6 + 883 * q^7 + 2334 * q^8 + 24630 * q^9	\( 25 q + 8 q^{2} + 107 q^{3} + 1728 q^{4} + 999 q^{5} + 1113 q^{6} + 883 q^{7} + 2334 q^{8} + 24630 q^{9} + 9125 q^{10} + 7750 q^{11} + 15367 q^{12} + 2889 q^{13} + 19333 q^{14} + 33191 q^{15} + 142884 q^{16} + 78798 q^{17} - 3299 q^{18} + 30540 q^{19} - 12216 q^{20} - 132083 q^{21} - 284791 q^{22} + 164186 q^{23} + 128679 q^{24} + 508126 q^{25} + 505560 q^{26} + 607295 q^{27} + 536123 q^{28} + 638580 q^{29} + 2043027 q^{30} + 910298 q^{31} + 1629475 q^{32} + 598836 q^{33} + 1077090 q^{34} + 1581093 q^{35} + 4005767 q^{36} + 1211146 q^{37} + 1478978 q^{38} + 1344825 q^{39} + 3812582 q^{40} + 2816906 q^{41} + 4045603 q^{42} - 137148 q^{43} + 2136404 q^{44} + 2911464 q^{45} + 1092854 q^{46} + 2190469 q^{47} + 5884593 q^{48} + 6517102 q^{49} + 1975400 q^{50} + 751758 q^{51} - 201731 q^{52} + 4108064 q^{53} + 4068807 q^{54} + 868206 q^{55} + 1949841 q^{56} + 1601962 q^{57} - 2185482 q^{58} + 4346931 q^{59} - 4960425 q^{60} + 4437224 q^{61} - 1283135 q^{62} - 2298764 q^{63} + 6180676 q^{64} + 3307347 q^{65} - 13646860 q^{66} - 4982464 q^{67} + 5261328 q^{68} + 4906500 q^{69} - 20329017 q^{70} + 9728355 q^{71} - 32705097 q^{72} + 1445696 q^{73} - 1636246 q^{74} - 4906804 q^{75} - 9170621 q^{76} + 4420424 q^{77} - 9115731 q^{78} - 12325975 q^{79} - 18733905 q^{80} + 509769 q^{81} - 34706430 q^{82} - 22164078 q^{83} - 98610835 q^{84} - 43977968 q^{85} - 29164330 q^{86} - 57086618 q^{87} - 66593968 q^{88} + 20252339 q^{89} - 34814996 q^{90} - 25616983 q^{91} - 12368519 q^{92} - 35295820 q^{93} - 53030651 q^{94} - 18689280 q^{95} - 35962515 q^{96} + 15021627 q^{97} - 46370127 q^{98} + 5324944 q^{99}+O(q^{100}) \) 25 * q + 8 * q^2 + 107 * q^3 + 1728 * q^4 + 999 * q^5 + 1113 * q^6 + 883 * q^7 + 2334 * q^8 + 24630 * q^9 + 9125 * q^10 + 7750 * q^11 + 15367 * q^12 + 2889 * q^13 + 19333 * q^14 + 33191 * q^15 + 142884 * q^16 + 78798 * q^17 - 3299 * q^18 + 30540 * q^19 - 12216 * q^20 - 132083 * q^21 - 284791 * q^22 + 164186 * q^23 + 128679 * q^24 + 508126 * q^25 + 505560 * q^26 + 607295 * q^27 + 536123 * q^28 + 638580 * q^29 + 2043027 * q^30 + 910298 * q^31 + 1629475 * q^32 + 598836 * q^33 + 1077090 * q^34 + 1581093 * q^35 + 4005767 * q^36 + 1211146 * q^37 + 1478978 * q^38 + 1344825 * q^39 + 3812582 * q^40 + 2816906 * q^41 + 4045603 * q^42 - 137148 * q^43 + 2136404 * q^44 + 2911464 * q^45 + 1092854 * q^46 + 2190469 * q^47 + 5884593 * q^48 + 6517102 * q^49 + 1975400 * q^50 + 751758 * q^51 - 201731 * q^52 + 4108064 * q^53 + 4068807 * q^54 + 868206 * q^55 + 1949841 * q^56 + 1601962 * q^57 - 2185482 * q^58 + 4346931 * q^59 - 4960425 * q^60 + 4437224 * q^61 - 1283135 * q^62 - 2298764 * q^63 + 6180676 * q^64 + 3307347 * q^65 - 13646860 * q^66 - 4982464 * q^67 + 5261328 * q^68 + 4906500 * q^69 - 20329017 * q^70 + 9728355 * q^71 - 32705097 * q^72 + 1445696 * q^73 - 1636246 * q^74 - 4906804 * q^75 - 9170621 * q^76 + 4420424 * q^77 - 9115731 * q^78 - 12325975 * q^79 - 18733905 * q^80 + 509769 * q^81 - 34706430 * q^82 - 22164078 * q^83 - 98610835 * q^84 - 43977968 * q^85 - 29164330 * q^86 - 57086618 * q^87 - 66593968 * q^88 + 20252339 * q^89 - 34814996 * q^90 - 25616983 * q^91 - 12368519 * q^92 - 35295820 * q^93 - 53030651 * q^94 - 18689280 * q^95 - 35962515 * q^96 + 15021627 * q^97 - 46370127 * q^98 + 5324944 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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