LMFDB - Embedded newform 197.12.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,12,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$N$	$=$	$197$
Weight:	$k$	$=$	$12$
Character orbit:	$[\chi]$	$=$	197.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:	$151.363606570$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	197.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-87.1440 q^{2} +786.167 q^{3} +5546.07 q^{4} +12634.2 q^{5} -68509.7 q^{6} -52867.9 q^{7} -304836. q^{8} +440912. q^{9} -1.10099e6 q^{10} -243497. q^{11} +4.36014e6 q^{12} +1.64401e6 q^{13} +4.60712e6 q^{14} +9.93256e6 q^{15} +1.52063e7 q^{16} -3.18554e6 q^{17} -3.84228e7 q^{18} -1.13223e6 q^{19} +7.00699e7 q^{20} -4.15630e7 q^{21} +2.12193e7 q^{22} -5.58534e7 q^{23} -2.39652e8 q^{24} +1.10794e8 q^{25} -1.43265e8 q^{26} +2.07363e8 q^{27} -2.93209e8 q^{28} +7.30013e7 q^{29} -8.65562e8 q^{30} +1.66906e8 q^{31} -7.00830e8 q^{32} -1.91429e8 q^{33} +2.77600e8 q^{34} -6.67941e8 q^{35} +2.44533e9 q^{36} -2.24431e8 q^{37} +9.86673e7 q^{38} +1.29246e9 q^{39} -3.85134e9 q^{40} -3.79319e8 q^{41} +3.62197e9 q^{42} +2.22500e8 q^{43} -1.35045e9 q^{44} +5.57055e9 q^{45} +4.86728e9 q^{46} +2.25481e9 q^{47} +1.19547e10 q^{48} +8.17688e8 q^{49} -9.65500e9 q^{50} -2.50437e9 q^{51} +9.11778e9 q^{52} -5.59241e7 q^{53} -1.80705e10 q^{54} -3.07638e9 q^{55} +1.61160e10 q^{56} -8.90124e8 q^{57} -6.36162e9 q^{58} +2.40144e9 q^{59} +5.50867e10 q^{60} -5.86229e9 q^{61} -1.45449e10 q^{62} -2.33101e10 q^{63} +2.99307e10 q^{64} +2.07706e10 q^{65} +1.66819e10 q^{66} +7.91950e9 q^{67} -1.76672e10 q^{68} -4.39101e10 q^{69} +5.82070e10 q^{70} +2.05210e10 q^{71} -1.34406e11 q^{72} +1.74831e10 q^{73} +1.95578e10 q^{74} +8.71024e10 q^{75} -6.27944e9 q^{76} +1.28732e10 q^{77} -1.12630e11 q^{78} +2.82858e10 q^{79} +1.92118e11 q^{80} +8.49161e10 q^{81} +3.30554e10 q^{82} +6.22953e10 q^{83} -2.30511e11 q^{84} -4.02466e10 q^{85} -1.93896e10 q^{86} +5.73912e10 q^{87} +7.42266e10 q^{88} -8.70641e10 q^{89} -4.85440e11 q^{90} -8.69152e10 q^{91} -3.09767e11 q^{92} +1.31216e11 q^{93} -1.96493e11 q^{94} -1.43048e10 q^{95} -5.50969e11 q^{96} +1.00198e11 q^{97} -7.12566e10 q^{98} -1.07361e11 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$92 q + 64 q^{2} + 2420 q^{3} + 98304 q^{4} + 16604 q^{5} + 46656 q^{6} + 305891 q^{7} + 234027 q^{8} + 5900444 q^{9} + 1074277 q^{10} + 595928 q^{11} + 4956160 q^{12} + 7463810 q^{13} + 4915769 q^{14} + 6749159 q^{15}+ \cdots + 9542377031 q^{99}+O(q^{100})$ 92 * q + 64 * q^2 + 2420 * q^3 + 98304 * q^4 + 16604 * q^5 + 46656 * q^6 + 305891 * q^7 + 234027 * q^8 + 5900444 * q^9 + 1074277 * q^10 + 595928 * q^11 + 4956160 * q^12 + 7463810 * q^13 + 4915769 * q^14 + 6749159 * q^15 + 109051904 * q^16 + 9869683 * q^17 + 15324721 * q^18 + 71500013 * q^19 + 79804779 * q^20 + 55741034 * q^21 + 120367289 * q^22 + 38597564 * q^23 + 104015637 * q^24 + 1039976880 * q^25 + 51802726 * q^26 + 665312351 * q^27 + 713160630 * q^28 - 2827541 * q^29 - 43013765 * q^30 + 939775728 * q^31 + 723479980 * q^32 + 978717002 * q^33 + 1063528738 * q^34 + 843197112 * q^35 + 6613742458 * q^36 + 2009031770 * q^37 + 918086794 * q^38 + 2279970607 * q^39 + 3093842646 * q^40 - 30014736 * q^41 + 3159549307 * q^42 + 6320365127 * q^43 + 3019176802 * q^44 + 5538230697 * q^45 + 4344764621 * q^46 + 2853606373 * q^47 + 15616060178 * q^48 + 31617715853 * q^49 - 28784136763 * q^50 - 7216660253 * q^51 + 19141188860 * q^52 + 3389732468 * q^53 + 14059623295 * q^54 + 23123173075 * q^55 + 75592019872 * q^56 + 27508365203 * q^57 + 42079603023 * q^58 + 40032802875 * q^59 + 99482549469 * q^60 + 31816702886 * q^61 + 35401555571 * q^62 + 79170604993 * q^63 + 168463042533 * q^64 + 50313809737 * q^65 + 93218912814 * q^66 + 129966589578 * q^67 + 73640879491 * q^68 - 9850635033 * q^69 + 62387700391 * q^70 + 32189826123 * q^71 + 47439469795 * q^72 + 60612500511 * q^73 - 110473527245 * q^74 + 48823210110 * q^75 + 48170982110 * q^76 - 9381499362 * q^77 - 251751253299 * q^78 + 40812909551 * q^79 - 36932560002 * q^80 + 294126355776 * q^81 + 29914326881 * q^82 + 112077199076 * q^83 - 242466547988 * q^84 - 65194167314 * q^85 - 384596985360 * q^86 + 30701235703 * q^87 + 102229734783 * q^88 - 47595308310 * q^89 - 957657692329 * q^90 + 217575098757 * q^91 - 762245602306 * q^92 - 47762776839 * q^93 - 251435906373 * q^94 - 84935429021 * q^95 - 1089429573223 * q^96 + 432665748880 * q^97 - 404245603446 * q^98 + 9542377031 * q^99

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

)

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

$2$	−87.1440	−1.92563	−0.962814	−	0.270165i	$-0.912922\pi$
$2$	−87.1440	−1.92563	−0.962814	+	0.270165i	$0.912922\pi$
$3$	786.167	1.86788	0.933938	−	0.357435i	$-0.116349\pi$
$3$	786.167	1.86788	0.933938	+	0.357435i	$0.116349\pi$
$4$	5546.07	2.70804
$5$	12634.2	1.80805	0.904026	−	0.427477i	$-0.140597\pi$
$5$	12634.2	1.80805	0.904026	+	0.427477i	$0.140597\pi$
$6$	−68509.7	−3.59683
$7$	−52867.9	−1.18892	−0.594460	−	0.804125i	$-0.702634\pi$
$7$	−52867.9	−1.18892	−0.594460	+	0.804125i	$0.702634\pi$
$8$	−304836.	−3.28906
$9$	440912.	2.48896
$10$	−1.10099e6	−3.48164
$11$	−243497.	−0.455863	−0.227931	−	0.973677i	$-0.573196\pi$
$11$	−243497.	−0.455863	−0.227931	+	0.973677i	$0.573196\pi$
$12$	4.36014e6	5.05829
$13$	1.64401e6	1.22805	0.614024	−	0.789288i	$-0.289550\pi$
$13$	1.64401e6	1.22805	0.614024	+	0.789288i	$0.289550\pi$
$14$	4.60712e6	2.28942
$15$	9.93256e6	3.37722
$16$	1.52063e7	3.62545
$17$	−3.18554e6	−0.544144	−0.272072	−	0.962277i	$-0.587709\pi$
$17$	−3.18554e6	−0.544144	−0.272072	+	0.962277i	$0.587709\pi$
$18$	−3.84228e7	−4.79281
$19$	−1.13223e6	−0.104904	−0.0524519	−	0.998623i	$-0.516704\pi$
$19$	−1.13223e6	−0.104904	−0.0524519	+	0.998623i	$0.516704\pi$
$20$	7.00699e7	4.89628
$21$	−4.15630e7	−2.22076
$22$	2.12193e7	0.877822
$23$	−5.58534e7	−1.80945	−0.904724	−	0.425998i	$-0.859923\pi$
$23$	−5.58534e7	−1.80945	−0.904724	+	0.425998i	$0.859923\pi$
$24$	−2.39652e8	−6.14355
$25$	1.10794e8	2.26905
$26$	−1.43265e8	−2.36476
$27$	2.07363e8	2.78119
$28$	−2.93209e8	−3.21965
$29$	7.30013e7	0.660909	0.330454	−	0.943822i	$-0.392798\pi$
$29$	7.30013e7	0.660909	0.330454	+	0.943822i	$0.392798\pi$
$30$	−8.65562e8	−6.50327
$31$	1.66906e8	1.04709	0.523544	−	0.851999i	$-0.324610\pi$
$31$	1.66906e8	1.04709	0.523544	+	0.851999i	$0.324610\pi$
$32$	−7.00830e8	−3.69222
$33$	−1.91429e8	−0.851495
$34$	2.77600e8	1.04782
$35$	−6.67941e8	−2.14963
$36$	2.44533e9	6.74021
$37$	−2.24431e8	−0.532075	−0.266037	−	0.963963i	$-0.585714\pi$
$37$	−2.24431e8	−0.532075	−0.266037	+	0.963963i	$0.585714\pi$
$38$	9.86673e7	0.202006
$39$	1.29246e9	2.29384
$40$	−3.85134e9	−5.94679
$41$	−3.79319e8	−0.511321	−0.255660	−	0.966767i	$-0.582293\pi$
$41$	−3.79319e8	−0.511321	−0.255660	+	0.966767i	$0.582293\pi$
$42$	3.62197e9	4.27635
$43$	2.22500e8	0.230810	0.115405	−	0.993319i	$-0.463183\pi$
$43$	2.22500e8	0.230810	0.115405	+	0.993319i	$0.463183\pi$
$44$	−1.35045e9	−1.23450
$45$	5.57055e9	4.50017
$46$	4.86728e9	3.48432
$47$	2.25481e9	1.43408	0.717038	−	0.697034i	$-0.245498\pi$
$47$	2.25481e9	1.43408	0.717038	+	0.697034i	$0.245498\pi$
$48$	1.19547e10	6.77190
$49$	8.17688e8	0.413532
$50$	−9.65500e9	−4.36935
$51$	−2.50437e9	−1.01639
$52$	9.11778e9	3.32561
$53$	−5.59241e7	−0.0183689	−0.00918443	−	0.999958i	$-0.502924\pi$
$53$	−5.59241e7	−0.0183689	−0.00918443	+	0.999958i	$0.502924\pi$
$54$	−1.80705e10	−5.35555
$55$	−3.07638e9	−0.824223
$56$	1.61160e10	3.91043
$57$	−8.90124e8	−0.195947
$58$	−6.36162e9	−1.27266
$59$	2.40144e9	0.437307	0.218653	−	0.975803i	$-0.429834\pi$
$59$	2.40144e9	0.437307	0.218653	+	0.975803i	$0.429834\pi$
$60$	5.50867e10	9.14565
$61$	−5.86229e9	−0.888696	−0.444348	−	0.895854i	$-0.646565\pi$
$61$	−5.86229e9	−0.888696	−0.444348	+	0.895854i	$0.646565\pi$
$62$	−1.45449e10	−2.01630
$63$	−2.33101e10	−2.95918
$64$	2.99307e10	3.48439
$65$	2.07706e10	2.22037
$66$	1.66819e10	1.63966
$67$	7.91950e9	0.716616	0.358308	−	0.933603i	$-0.383354\pi$
$67$	7.91950e9	0.716616	0.358308	+	0.933603i	$0.383354\pi$
$68$	−1.76672e10	−1.47357
$69$	−4.39101e10	−3.37983
$70$	5.82070e10	4.13939
$71$	2.05210e10	1.34982	0.674911	−	0.737899i	$-0.264182\pi$
$71$	2.05210e10	1.34982	0.674911	+	0.737899i	$0.264182\pi$
$72$	−1.34406e11	−8.18633
$73$	1.74831e10	0.987060	0.493530	−	0.869729i	$-0.335706\pi$
$73$	1.74831e10	0.987060	0.493530	+	0.869729i	$0.335706\pi$
$74$	1.95578e10	1.02458
$75$	8.71024e10	4.23831
$76$	−6.27944e9	−0.284084
$77$	1.28732e10	0.541984
$78$	−1.12630e11	−4.41708
$79$	2.82858e10	1.03423	0.517117	−	0.855915i	$-0.327005\pi$
$79$	2.82858e10	1.03423	0.517117	+	0.855915i	$0.327005\pi$
$80$	1.92118e11	6.55501
$81$	8.49161e10	2.70597
$82$	3.30554e10	0.984614
$83$	6.22953e10	1.73590	0.867952	−	0.496649i	$-0.165436\pi$
$83$	6.22953e10	1.73590	0.867952	+	0.496649i	$0.165436\pi$
$84$	−2.30511e11	−6.01390
$85$	−4.02466e10	−0.983841
$86$	−1.93896e10	−0.444453
$87$	5.73912e10	1.23450
$88$	7.42266e10	1.49936
$89$	−8.70641e10	−1.65270	−0.826350	−	0.563156i	$-0.809587\pi$
$89$	−8.70641e10	−1.65270	−0.826350	+	0.563156i	$0.809587\pi$
$90$	−4.85440e11	−8.66566
$91$	−8.69152e10	−1.46005
$92$	−3.09767e11	−4.90006
$93$	1.31216e11	1.95583
$94$	−1.96493e11	−2.76150
$95$	−1.43048e10	−0.189671
$96$	−5.50969e11	−6.89661
$97$	1.00198e11	1.18471	0.592356	−	0.805676i	$-0.298198\pi$
$97$	1.00198e11	1.18471	0.592356	+	0.805676i	$0.298198\pi$
$98$	−7.12566e10	−0.796309
$99$	−1.07361e11	−1.13462
$100$	6.14470e11	6.14470
$101$	1.32458e11	1.25404	0.627021	−	0.779002i	$-0.284274\pi$
$101$	1.32458e11	1.25404	0.627021	+	0.779002i	$0.284274\pi$
$102$	2.18240e11	1.95720
$103$	1.10119e11	0.935959	0.467979	−	0.883739i	$-0.344982\pi$
$103$	1.10119e11	0.935959	0.467979	+	0.883739i	$0.344982\pi$
$104$	−5.01152e11	−4.03912
$105$	−5.25113e11	−4.01524
$106$	4.87345e9	0.0353716
$107$	7.80172e10	0.537749	0.268875	−	0.963175i	$-0.413348\pi$
$107$	7.80172e10	0.537749	0.268875	+	0.963175i	$0.413348\pi$
$108$	1.15005e12	7.53160
$109$	−3.81290e10	−0.237361	−0.118681	−	0.992932i	$-0.537866\pi$
$109$	−3.81290e10	−0.237361	−0.118681	+	0.992932i	$0.537866\pi$
$110$	2.68088e11	1.58715
$111$	−1.76440e11	−0.993850
$112$	−8.03923e11	−4.31038
$113$	2.06621e11	1.05498	0.527490	−	0.849561i	$-0.323133\pi$
$113$	2.06621e11	1.05498	0.527490	+	0.849561i	$0.323133\pi$
$114$	7.75690e10	0.377321
$115$	−7.05660e11	−3.27158
$116$	4.04871e11	1.78977
$117$	7.24862e11	3.05656
$118$	−2.09271e11	−0.842090
$119$	1.68413e11	0.646944
$120$	−3.02780e12	−11.1079
$121$	−2.26021e11	−0.792189
$122$	5.10863e11	1.71130
$123$	−2.98208e11	−0.955084
$124$	9.25674e11	2.83556
$125$	7.82882e11	2.29452
$126$	2.03133e12	5.69827
$127$	−5.46793e11	−1.46860	−0.734299	−	0.678826i	$-0.762489\pi$
$127$	−5.46793e11	−1.46860	−0.734299	+	0.678826i	$0.762489\pi$
$128$	−1.17298e12	−3.01742
$129$	1.74922e11	0.431124
$130$	−1.81004e12	−4.27561
$131$	−3.13074e11	−0.709014	−0.354507	−	0.935053i	$-0.615351\pi$
$131$	−3.13074e11	−0.709014	−0.354507	+	0.935053i	$0.615351\pi$
$132$	−1.06168e12	−2.30588
$133$	5.98588e10	0.124722
$134$	−6.90137e11	−1.37994
$135$	2.61986e12	5.02855
$136$	9.71066e11	1.78972
$137$	5.60447e11	0.992136	0.496068	−	0.868284i	$-0.334777\pi$
$137$	5.60447e11	0.992136	0.496068	+	0.868284i	$0.334777\pi$
$138$	3.82650e12	6.50829
$139$	3.59980e11	0.588432	0.294216	−	0.955739i	$-0.404941\pi$
$139$	3.59980e11	0.588432	0.294216	+	0.955739i	$0.404941\pi$
$140$	−3.70445e12	−5.82129
$141$	1.77266e12	2.67868
$142$	−1.78828e12	−2.59926
$143$	−4.00311e11	−0.559821
$144$	6.70462e12	9.02361
$145$	9.22310e11	1.19496
$146$	−1.52355e12	−1.90071
$147$	6.42840e11	0.772427
$148$	−1.24471e12	−1.44088
$149$	−1.32672e12	−1.47998	−0.739990	−	0.672618i	$-0.765170\pi$
$149$	−1.32672e12	−1.47998	−0.739990	+	0.672618i	$0.765170\pi$
$150$	−7.59045e12	−8.16141
$151$	1.54430e12	1.60088	0.800438	−	0.599416i	$-0.204600\pi$
$151$	1.54430e12	1.60088	0.800438	+	0.599416i	$0.204600\pi$
$152$	3.45145e11	0.345034
$153$	−1.40454e12	−1.35435
$154$	−1.12182e12	−1.04366
$155$	2.10872e12	1.89319
$156$	7.16810e12	6.21182
$157$	1.54023e12	1.28865	0.644327	−	0.764750i	$-0.277138\pi$
$157$	1.54023e12	1.28865	0.644327	+	0.764750i	$0.277138\pi$
$158$	−2.46493e12	−1.99155
$159$	−4.39657e10	−0.0343107
$160$	−8.85439e12	−6.67573
$161$	2.95285e12	2.15129
$162$	−7.39993e12	−5.21068
$163$	−2.89330e11	−0.196952	−0.0984762	−	0.995139i	$-0.531397\pi$
$163$	−2.89330e11	−0.196952	−0.0984762	+	0.995139i	$0.531397\pi$
$164$	−2.10373e12	−1.38468
$165$	−2.41855e12	−1.53955
$166$	−5.42866e12	−3.34270
$167$	−2.72326e11	−0.162237	−0.0811183	−	0.996704i	$-0.525849\pi$
$167$	−2.72326e11	−0.162237	−0.0811183	+	0.996704i	$0.525849\pi$
$168$	1.26699e13	7.30419
$169$	9.10598e11	0.508100
$170$	3.50725e12	1.89451
$171$	−4.99215e11	−0.261101
$172$	1.23400e12	0.625042
$173$	−8.95594e11	−0.439397	−0.219699	−	0.975568i	$-0.570507\pi$
$173$	−8.95594e11	−0.439397	−0.219699	+	0.975568i	$0.570507\pi$
$174$	−5.00130e12	−2.37718
$175$	−5.85743e12	−2.69773
$176$	−3.70268e12	−1.65271
$177$	1.88794e12	0.816835
$178$	7.58711e12	3.18249
$179$	−1.68681e12	−0.686081	−0.343041	−	0.939321i	$-0.611457\pi$
$179$	−1.68681e12	−0.686081	−0.343041	+	0.939321i	$0.611457\pi$
$180$	3.08947e13	12.1867
$181$	−1.70026e12	−0.650555	−0.325278	−	0.945619i	$-0.605458\pi$
$181$	−1.70026e12	−0.650555	−0.325278	+	0.945619i	$0.605458\pi$
$182$	7.57413e12	2.81151
$183$	−4.60874e12	−1.65997
$184$	1.70261e13	5.95138
$185$	−2.83549e12	−0.962019
$186$	−1.14347e13	−3.76620
$187$	7.75669e11	0.248055
$188$	1.25053e13	3.88354
$189$	−1.09629e13	−3.30662
$190$	1.24658e12	0.365237
$191$	2.77001e12	0.788493	0.394246	−	0.919005i	$-0.371006\pi$
$191$	2.77001e12	0.788493	0.394246	+	0.919005i	$0.371006\pi$
$192$	2.35305e13	6.50841
$193$	2.80210e11	0.0753214	0.0376607	−	0.999291i	$-0.488009\pi$
$193$	2.80210e11	0.0753214	0.0376607	+	0.999291i	$0.488009\pi$
$194$	−8.73162e12	−2.28132
$195$	1.63292e13	4.14738
$196$	4.53496e12	1.11986
$197$	−2.96709e11	−0.0712470
$197$	−2.96709e11	−0.0712470
$198$	9.35584e12	2.18486
$199$	2.56480e12	0.582588	0.291294	−	0.956634i	$-0.405914\pi$
$199$	2.56480e12	0.582588	0.291294	+	0.956634i	$0.405914\pi$
$200$	−3.37739e13	−7.46304
$201$	6.22606e12	1.33855
$202$	−1.15430e13	−2.41482
$203$	−3.85943e12	−0.785768
$204$	−1.38894e13	−2.75244
$205$	−4.79237e12	−0.924495
$206$	−9.59619e12	−1.80231
$207$	−2.46264e13	−4.50365
$208$	2.49992e13	4.45223
$209$	2.75695e11	0.0478217
$210$	4.57605e13	7.73187
$211$	−6.35815e11	−0.104659	−0.0523295	−	0.998630i	$-0.516665\pi$
$211$	−6.35815e11	−0.104659	−0.0523295	+	0.998630i	$0.516665\pi$
$212$	−3.10159e11	−0.0497436
$213$	1.61329e13	2.52130
$214$	−6.79873e12	−1.03550
$215$	2.81110e12	0.417316
$216$	−6.32118e13	−9.14750
$217$	−8.82398e12	−1.24490
$218$	3.32272e12	0.457070
$219$	1.37447e13	1.84371
$220$	−1.70618e13	−2.23203
$221$	−5.23705e12	−0.668235
$222$	1.53757e13	1.91378
$223$	8.89651e12	1.08030	0.540148	−	0.841570i	$-0.318368\pi$
$223$	8.89651e12	1.08030	0.540148	+	0.841570i	$0.318368\pi$
$224$	3.70514e13	4.38976
$225$	4.88503e13	5.64759
$226$	−1.80058e13	−2.03150
$227$	−7.22778e12	−0.795908	−0.397954	−	0.917405i	$-0.630280\pi$
$227$	−7.22778e12	−0.795908	−0.397954	+	0.917405i	$0.630280\pi$
$228$	−4.93669e12	−0.530633
$229$	−5.30547e12	−0.556709	−0.278355	−	0.960478i	$-0.589789\pi$
$229$	−5.30547e12	−0.556709	−0.278355	+	0.960478i	$0.589789\pi$
$230$	6.14940e13	6.29984
$231$	1.01205e13	1.01236
$232$	−2.22534e13	−2.17377
$233$	−9.75341e11	−0.0930462	−0.0465231	−	0.998917i	$-0.514814\pi$
$233$	−9.75341e11	−0.0930462	−0.0465231	+	0.998917i	$0.514814\pi$
$234$	−6.31674e13	−5.88580
$235$	2.84876e13	2.59288
$236$	1.33186e13	1.18425
$237$	2.22373e13	1.93182
$238$	−1.46762e13	−1.24577
$239$	−1.61817e13	−1.34226	−0.671129	−	0.741341i	$-0.734190\pi$
$239$	−1.61817e13	−1.34226	−0.671129	+	0.741341i	$0.734190\pi$
$240$	1.51037e14	12.2439
$241$	3.10447e10	0.00245976	0.00122988	−	0.999999i	$-0.499609\pi$
$241$	3.10447e10	0.00245976	0.00122988	+	0.999999i	$0.499609\pi$
$242$	1.96964e13	1.52546
$243$	3.00244e13	2.27321
$244$	−3.25127e13	−2.40663
$245$	1.03308e13	0.747688
$246$	2.59871e13	1.83914
$247$	−1.86140e12	−0.128827
$248$	−5.08790e13	−3.44393
$249$	4.89745e13	3.24245
$250$	−6.82234e13	−4.41839
$251$	−9.77956e12	−0.619604	−0.309802	−	0.950801i	$-0.600263\pi$
$251$	−9.77956e12	−0.619604	−0.309802	+	0.950801i	$0.600263\pi$
$252$	−1.29279e14	−8.01358
$253$	1.36001e13	0.824860
$254$	4.76498e13	2.82797
$255$	−3.16405e13	−1.83769
$256$	4.09200e13	2.32603
$257$	−3.13864e13	−1.74626	−0.873132	−	0.487484i	$-0.837915\pi$
$257$	−3.13864e13	−1.74626	−0.873132	+	0.487484i	$0.837915\pi$
$258$	−1.52434e13	−0.830184
$259$	1.18652e13	0.632595
$260$	1.15195e14	6.01287
$261$	3.21872e13	1.64498
$262$	2.72825e13	1.36530
$263$	1.19615e13	0.586177	0.293089	−	0.956085i	$-0.405317\pi$
$263$	1.19615e13	0.586177	0.293089	+	0.956085i	$0.405317\pi$
$264$	5.83546e13	2.80061
$265$	−7.06554e11	−0.0332119
$266$	−5.21633e12	−0.240169
$267$	−6.84470e13	−3.08704
$268$	4.39221e13	1.94063
$269$	−2.88848e13	−1.25035	−0.625175	−	0.780485i	$-0.714972\pi$
$269$	−2.88848e13	−1.25035	−0.625175	+	0.780485i	$0.714972\pi$
$270$	−2.28305e14	−9.68311
$271$	−1.75361e13	−0.728790	−0.364395	−	0.931245i	$-0.618724\pi$
$271$	−1.75361e13	−0.728790	−0.364395	+	0.931245i	$0.618724\pi$
$272$	−4.84401e13	−1.97277
$273$	−6.83299e13	−2.72719
$274$	−4.88396e13	−1.91049
$275$	−2.69779e13	−1.03438
$276$	−2.43528e14	−9.15271
$277$	−4.89346e13	−1.80292	−0.901462	−	0.432859i	$-0.857505\pi$
$277$	−4.89346e13	−1.80292	−0.901462	+	0.432859i	$0.857505\pi$
$278$	−3.13701e13	−1.13310
$279$	7.35909e13	2.60616
$280$	2.03612e14	7.07026
$281$	−6.93651e12	−0.236187	−0.118094	−	0.993002i	$-0.537678\pi$
$281$	−6.93651e12	−0.236187	−0.118094	+	0.993002i	$0.537678\pi$
$282$	−1.54477e14	−5.15813
$283$	5.95228e13	1.94921	0.974604	−	0.223935i	$-0.0718905\pi$
$283$	5.95228e13	1.94921	0.974604	+	0.223935i	$0.0718905\pi$
$284$	1.13811e14	3.65538
$285$	−1.12460e13	−0.354283
$286$	3.48847e13	1.07801
$287$	2.00538e13	0.607920
$288$	−3.09004e14	−9.18979
$289$	−2.41242e13	−0.703907
$290$	−8.03737e13	−2.30104
$291$	7.87721e13	2.21290
$292$	9.69627e13	2.67300
$293$	4.44871e12	0.120355	0.0601773	−	0.998188i	$-0.480833\pi$
$293$	4.44871e12	0.120355	0.0601773	+	0.998188i	$0.480833\pi$
$294$	−5.60196e13	−1.48741
$295$	3.03402e13	0.790673
$296$	6.84145e13	1.75002
$297$	−5.04924e13	−1.26784
$298$	1.15616e14	2.84989
$299$	−9.18233e13	−2.22209
$300$	4.83076e14	11.4775
$301$	−1.17631e13	−0.274414
$302$	−1.34576e14	−3.08269
$303$	1.04134e14	2.34239
$304$	−1.72170e13	−0.380324
$305$	−7.40651e13	−1.60681
$306$	1.22397e14	2.60798
$307$	4.35234e13	0.910881	0.455441	−	0.890266i	$-0.349482\pi$
$307$	4.35234e13	0.910881	0.455441	+	0.890266i	$0.349482\pi$
$308$	7.13956e13	1.46772
$309$	8.65718e13	1.74825
$310$	−1.83762e14	−3.64558
$311$	5.89792e12	0.114952	0.0574761	−	0.998347i	$-0.481695\pi$
$311$	5.89792e12	0.114952	0.0574761	+	0.998347i	$0.481695\pi$
$312$	−3.93990e14	−7.54457
$313$	3.03098e13	0.570281	0.285141	−	0.958486i	$-0.407960\pi$
$313$	3.03098e13	0.570281	0.285141	+	0.958486i	$0.407960\pi$
$314$	−1.34221e14	−2.48147
$315$	−2.94503e14	−5.35035
$316$	1.56875e14	2.80075
$317$	−8.45658e12	−0.148378	−0.0741889	−	0.997244i	$-0.523637\pi$
$317$	−8.45658e12	−0.148378	−0.0741889	+	0.997244i	$0.523637\pi$
$318$	3.83135e12	0.0660697
$319$	−1.77756e13	−0.301284
$320$	3.78149e14	6.29996
$321$	6.13346e13	1.00445
$322$	−2.57323e14	−4.14259
$323$	3.60677e12	0.0570827
$324$	4.70951e14	7.32787
$325$	1.82146e14	2.78651
$326$	2.52133e13	0.379257
$327$	−2.99758e13	−0.443362
$328$	1.15630e14	1.68176
$329$	−1.19207e14	−1.70500
$330$	2.10762e14	2.96460
$331$	−1.08434e14	−1.50007	−0.750037	−	0.661396i	$-0.769964\pi$
$331$	−1.08434e14	−1.50007	−0.750037	+	0.661396i	$0.769964\pi$
$332$	3.45494e14	4.70090
$333$	−9.89541e13	−1.32431
$334$	2.37316e13	0.312408
$335$	1.00056e14	1.29568
$336$	−6.32018e14	−8.05125
$337$	1.08104e14	1.35480	0.677401	−	0.735613i	$-0.263106\pi$
$337$	1.08104e14	1.35480	0.677401	+	0.735613i	$0.263106\pi$
$338$	−7.93531e13	−0.978412
$339$	1.62439e14	1.97057
$340$	−2.23210e14	−2.66428
$341$	−4.06412e13	−0.477328
$342$	4.35036e13	0.502784
$343$	6.13077e13	0.697264
$344$	−6.78261e13	−0.759146
$345$	−5.54767e14	−6.11090
$346$	7.80456e13	0.846116
$347$	−6.13520e13	−0.654661	−0.327331	−	0.944910i	$-0.606149\pi$
$347$	−6.13520e13	−0.654661	−0.327331	+	0.944910i	$0.606149\pi$
$348$	3.18296e14	3.34307
$349$	−6.29685e13	−0.651004	−0.325502	−	0.945541i	$-0.605533\pi$
$349$	−6.29685e13	−0.651004	−0.325502	+	0.945541i	$0.605533\pi$
$350$	5.10440e14	5.19482
$351$	3.40907e14	3.41544
$352$	1.70650e14	1.68314
$353$	3.83303e13	0.372204	0.186102	−	0.982530i	$-0.440415\pi$
$353$	3.83303e13	0.372204	0.186102	+	0.982530i	$0.440415\pi$
$354$	−1.64522e14	−1.57292
$355$	2.59265e14	2.44055
$356$	−4.82864e14	−4.47558
$357$	1.32401e14	1.20841
$358$	1.46996e14	1.32114
$359$	1.77156e14	1.56796	0.783982	−	0.620784i	$-0.213186\pi$
$359$	1.77156e14	1.56796	0.783982	+	0.620784i	$0.213186\pi$
$360$	−1.69810e15	−14.8013
$361$	−1.15208e14	−0.988995
$362$	1.48168e14	1.25273
$363$	−1.77690e14	−1.47971
$364$	−4.82038e14	−3.95388
$365$	2.20884e14	1.78466
$366$	4.01624e14	3.19649
$367$	−5.67164e13	−0.444677	−0.222339	−	0.974969i	$-0.571369\pi$
$367$	−5.67164e13	−0.444677	−0.222339	+	0.974969i	$0.571369\pi$
$368$	−8.49321e14	−6.56007
$369$	−1.67246e14	−1.27266
$370$	2.47096e14	1.85249
$371$	2.95659e12	0.0218391
$372$	7.27734e14	5.29647
$373$	1.04076e14	0.746363	0.373182	−	0.927758i	$-0.378267\pi$
$373$	1.04076e14	0.746363	0.373182	+	0.927758i	$0.378267\pi$
$374$	−6.75949e13	−0.477661
$375$	6.15476e14	4.28587
$376$	−6.87347e14	−4.71675
$377$	1.20015e14	0.811628
$378$	9.55348e14	6.36732
$379$	−9.10659e12	−0.0598191	−0.0299096	−	0.999553i	$-0.509522\pi$
$379$	−9.10659e12	−0.0598191	−0.0299096	+	0.999553i	$0.509522\pi$
$380$	−7.93354e13	−0.513638
$381$	−4.29871e14	−2.74316
$382$	−2.41390e14	−1.51834
$383$	4.60884e13	0.285758	0.142879	−	0.989740i	$-0.454364\pi$
$383$	4.60884e13	0.285758	0.142879	+	0.989740i	$0.454364\pi$
$384$	−9.22157e14	−5.63616
$385$	1.62642e14	0.979936
$386$	−2.44186e13	−0.145041
$387$	9.81030e13	0.574476
$388$	5.55703e14	3.20825
$389$	−2.14867e14	−1.22306	−0.611530	−	0.791221i	$-0.709446\pi$
$389$	−2.14867e14	−1.22306	−0.611530	+	0.791221i	$0.709446\pi$
$390$	−1.42299e15	−7.98632
$391$	1.77923e14	0.984600
$392$	−2.49261e14	−1.36013
$393$	−2.46129e14	−1.32435
$394$	2.58564e13	0.137195
$395$	3.57366e14	1.86995
$396$	−5.95431e14	−3.07261
$397$	−1.39664e14	−0.710783	−0.355392	−	0.934717i	$-0.615653\pi$
$397$	−1.39664e14	−0.710783	−0.355392	+	0.934717i	$0.615653\pi$
$398$	−2.23507e14	−1.12185
$399$	4.70590e13	0.232966
$400$	1.68476e15	8.22635
$401$	−3.58063e14	−1.72451	−0.862255	−	0.506474i	$-0.830949\pi$
$401$	−3.58063e14	−1.72451	−0.862255	+	0.506474i	$0.830949\pi$
$402$	−5.42563e14	−2.57755
$403$	2.74395e14	1.28587
$404$	7.34624e14	3.39600
$405$	1.07284e15	4.89253
$406$	3.36326e14	1.51310
$407$	5.46482e13	0.242553
$408$	7.63421e14	3.34297
$409$	1.52082e14	0.657050	0.328525	−	0.944495i	$-0.393449\pi$
$409$	1.52082e14	0.657050	0.328525	+	0.944495i	$0.393449\pi$
$410$	4.17627e14	1.78023
$411$	4.40605e14	1.85319
$412$	6.10727e14	2.53462
$413$	−1.26959e14	−0.519923
$414$	2.14604e15	8.67235
$415$	7.87048e14	3.13860
$416$	−1.15217e15	−4.53422
$417$	2.83004e14	1.09912
$418$	−2.40252e13	−0.0920868
$419$	−2.33547e14	−0.883480	−0.441740	−	0.897143i	$-0.645639\pi$
$419$	−2.33547e14	−0.883480	−0.441740	+	0.897143i	$0.645639\pi$
$420$	−2.91232e15	−10.8735
$421$	8.00503e13	0.294993	0.147496	−	0.989063i	$-0.452879\pi$
$421$	8.00503e13	0.294993	0.147496	+	0.989063i	$0.452879\pi$
$422$	5.54074e13	0.201534
$423$	9.94173e14	3.56936
$424$	1.70477e13	0.0604162
$425$	−3.52937e14	−1.23469
$426$	−1.40589e15	−4.85509
$427$	3.09927e14	1.05659
$428$	4.32689e14	1.45625
$429$	−3.14711e14	−1.04568
$430$	−2.44971e14	−0.803595
$431$	3.50083e14	1.13383	0.566913	−	0.823777i	$-0.308137\pi$
$431$	3.50083e14	1.13383	0.566913	+	0.823777i	$0.308137\pi$
$432$	3.15322e15	10.0831
$433$	−1.57619e14	−0.497651	−0.248826	−	0.968548i	$-0.580045\pi$
$433$	−1.57619e14	−0.497651	−0.248826	+	0.968548i	$0.580045\pi$
$434$	7.68957e14	2.39722
$435$	7.25090e14	2.23203
$436$	−2.11466e14	−0.642785
$437$	6.32390e13	0.189818
$438$	−1.19776e15	−3.55029
$439$	−5.00298e14	−1.46445	−0.732225	−	0.681063i	$-0.761518\pi$
$439$	−5.00298e14	−1.46445	−0.732225	+	0.681063i	$0.761518\pi$
$440$	9.37791e14	2.71092
$441$	3.60529e14	1.02927
$442$	4.56377e14	1.28677
$443$	2.78354e14	0.775133	0.387567	−	0.921842i	$-0.373316\pi$
$443$	2.78354e14	0.775133	0.387567	+	0.921842i	$0.373316\pi$
$444$	−9.78549e14	−2.69139
$445$	−1.09998e15	−2.98817
$446$	−7.75277e14	−2.08025
$447$	−1.04303e15	−2.76442
$448$	−1.58237e15	−4.14266
$449$	−4.73886e14	−1.22552	−0.612758	−	0.790270i	$-0.709940\pi$
$449$	−4.73886e14	−1.22552	−0.612758	+	0.790270i	$0.709940\pi$
$450$	−4.25701e15	−10.8752
$451$	9.23631e13	0.233092
$452$	1.14594e15	2.85693
$453$	1.21408e15	2.99024
$454$	6.29857e14	1.53262
$455$	−1.09810e15	−2.63985
$456$	2.71342e14	0.644481
$457$	−4.20915e14	−0.987769	−0.493884	−	0.869528i	$-0.664423\pi$
$457$	−4.20915e14	−0.987769	−0.493884	+	0.869528i	$0.664423\pi$
$458$	4.62339e14	1.07201
$459$	−6.60564e14	−1.51337
$460$	−3.91364e15	−8.85957
$461$	5.26897e14	1.17861	0.589306	−	0.807910i	$-0.299401\pi$
$461$	5.26897e14	1.17861	0.589306	+	0.807910i	$0.299401\pi$
$462$	−8.81938e14	−1.94943
$463$	4.35851e14	0.952012	0.476006	−	0.879442i	$-0.342084\pi$
$463$	4.35851e14	0.952012	0.476006	+	0.879442i	$0.342084\pi$
$464$	1.11008e15	2.39610
$465$	1.65781e15	3.53624
$466$	8.49951e13	0.179172
$467$	3.98633e14	0.830483	0.415241	−	0.909711i	$-0.363697\pi$
$467$	3.98633e14	0.830483	0.415241	+	0.909711i	$0.363697\pi$
$468$	4.02014e15	8.27730
$469$	−4.18688e14	−0.852000
$470$	−2.48253e15	−4.99293
$471$	1.21088e15	2.40705
$472$	−7.32046e14	−1.43833
$473$	−5.41781e13	−0.105217
$474$	−1.93785e15	−3.71997
$475$	−1.25444e14	−0.238032
$476$	9.34029e14	1.75195
$477$	−2.46576e13	−0.0457194
$478$	1.41014e15	2.58469
$479$	1.15602e14	0.209468	0.104734	−	0.994500i	$-0.466601\pi$
$479$	1.15602e14	0.209468	0.104734	+	0.994500i	$0.466601\pi$
$480$	−6.96103e15	−12.4694
$481$	−3.68965e14	−0.653413
$482$	−2.70536e12	−0.00473659
$483$	2.32143e15	4.01834
$484$	−1.25353e15	−2.14528
$485$	1.26591e15	2.14202
$486$	−2.61645e15	−4.37737
$487$	4.03307e14	0.667155	0.333577	−	0.942723i	$-0.391744\pi$
$487$	4.03307e14	0.667155	0.333577	+	0.942723i	$0.391744\pi$
$488$	1.78704e15	2.92297
$489$	−2.27461e14	−0.367883
$490$	−9.00267e14	−1.43977
$491$	4.64426e14	0.734461	0.367230	−	0.930130i	$-0.380306\pi$
$491$	4.64426e14	0.734461	0.367230	+	0.930130i	$0.380306\pi$
$492$	−1.65388e15	−2.58641
$493$	−2.32548e14	−0.359630
$494$	1.62210e14	0.248072
$495$	−1.35641e15	−2.05146
$496$	2.53802e15	3.79617
$497$	−1.08490e15	−1.60483
$498$	−4.26783e15	−6.24376
$499$	3.73382e14	0.540257	0.270128	−	0.962824i	$-0.412934\pi$
$499$	3.73382e14	0.540257	0.270128	+	0.962824i	$0.412934\pi$
$500$	4.34192e15	6.21365
$501$	−2.14094e14	−0.303038
$502$	8.52230e14	1.19313
$503$	−9.19697e14	−1.27356	−0.636782	−	0.771044i	$-0.719735\pi$
$503$	−9.19697e14	−1.27356	−0.636782	+	0.771044i	$0.719735\pi$
$504$	7.10575e15	9.73290
$505$	1.67350e15	2.26737
$506$	−1.18517e15	−1.58837
$507$	7.15882e14	0.949069
$508$	−3.03256e15	−3.97703
$509$	−5.01368e14	−0.650442	−0.325221	−	0.945638i	$-0.605439\pi$
$509$	−5.01368e14	−0.650442	−0.325221	+	0.945638i	$0.605439\pi$
$510$	2.75728e15	3.53871
$511$	−9.24296e14	−1.17354
$512$	−1.16367e15	−1.46166
$513$	−2.34784e14	−0.291758
$514$	2.73514e15	3.36266
$515$	1.39126e15	1.69226
$516$	9.70132e14	1.16750
$517$	−5.49040e14	−0.653741
$518$	−1.03398e15	−1.21814
$519$	−7.04086e14	−0.820740
$520$	−6.33163e15	−7.30293
$521$	−8.34015e14	−0.951845	−0.475922	−	0.879487i	$-0.657886\pi$
$521$	−8.34015e14	−0.951845	−0.475922	+	0.879487i	$0.657886\pi$
$522$	−2.80492e15	−3.16761
$523$	−7.13094e14	−0.796870	−0.398435	−	0.917197i	$-0.630447\pi$
$523$	−7.13094e14	−0.796870	−0.398435	+	0.917197i	$0.630447\pi$
$524$	−1.73633e15	−1.92004
$525$	−4.60492e15	−5.03902
$526$	−1.04237e15	−1.12876
$527$	−5.31686e14	−0.569766
$528$	−2.91092e15	−3.08706
$529$	2.16679e15	2.27410
$530$	6.15719e13	0.0639537
$531$	1.05882e15	1.08844
$532$	3.31981e14	0.337753
$533$	−6.23603e14	−0.627926
$534$	5.96474e15	5.94449
$535$	9.85681e14	0.972279
$536$	−2.41415e15	−2.35699
$537$	−1.32612e15	−1.28152
$538$	2.51713e15	2.40771
$539$	−1.99105e14	−0.188514
$540$	1.45299e16	13.6175
$541$	−1.58429e15	−1.46977	−0.734885	−	0.678192i	$-0.762764\pi$
$541$	−1.58429e15	−1.46977	−0.734885	+	0.678192i	$0.762764\pi$
$542$	1.52817e15	1.40338
$543$	−1.33669e15	−1.21516
$544$	2.23252e15	2.00910
$545$	−4.81728e14	−0.429162
$546$	5.95454e15	5.25156
$547$	−2.40211e14	−0.209731	−0.104866	−	0.994486i	$-0.533441\pi$
$547$	−2.40211e14	−0.209731	−0.104866	+	0.994486i	$0.533441\pi$
$548$	3.10828e15	2.68675
$549$	−2.58475e15	−2.21193
$550$	2.35096e15	1.99182
$551$	−8.26545e13	−0.0693318
$552$	1.33854e16	11.1164
$553$	−1.49541e15	−1.22962
$554$	4.26435e15	3.47176
$555$	−2.22917e15	−1.79693
$556$	1.99647e15	1.59350
$557$	4.00785e14	0.316744	0.158372	−	0.987380i	$-0.449375\pi$
$557$	4.00785e14	0.316744	0.158372	+	0.987380i	$0.449375\pi$
$558$	−6.41301e15	−5.01850
$559$	3.65792e14	0.283445
$560$	−1.01569e16	−7.79339
$561$	6.09806e14	0.463336
$562$	6.04475e14	0.454809
$563$	−1.30980e15	−0.975906	−0.487953	−	0.872870i	$-0.662256\pi$
$563$	−1.30980e15	−0.975906	−0.487953	+	0.872870i	$0.662256\pi$
$564$	9.83129e15	7.25397
$565$	2.61049e15	1.90746
$566$	−5.18706e15	−3.75345
$567$	−4.48934e15	−3.21718
$568$	−6.25552e15	−4.43964
$569$	−9.61821e14	−0.676047	−0.338024	−	0.941138i	$-0.609758\pi$
$569$	−9.61821e14	−0.676047	−0.338024	+	0.941138i	$0.609758\pi$
$570$	9.80018e14	0.682217
$571$	2.05240e15	1.41503	0.707513	−	0.706700i	$-0.249817\pi$
$571$	2.05240e15	1.41503	0.707513	+	0.706700i	$0.249817\pi$
$572$	−2.22015e15	−1.51602
$573$	2.17769e15	1.47281
$574$	−1.74757e15	−1.17063
$575$	−6.18820e15	−4.10574
$576$	1.31968e16	8.67251
$577$	5.64715e14	0.367589	0.183794	−	0.982965i	$-0.441162\pi$
$577$	5.64715e14	0.367589	0.183794	+	0.982965i	$0.441162\pi$
$578$	2.10228e15	1.35546
$579$	2.20292e14	0.140691
$580$	5.11520e15	3.23600
$581$	−3.29342e15	−2.06385
$582$	−6.86451e15	−4.26121
$583$	1.36174e13	0.00837367
$584$	−5.32949e15	−3.24649
$585$	9.15802e15	5.52643
$586$	−3.87679e14	−0.231758
$587$	4.21382e14	0.249555	0.124778	−	0.992185i	$-0.460178\pi$
$587$	4.21382e14	0.249555	0.124778	+	0.992185i	$0.460178\pi$
$588$	3.56524e15	2.09177
$589$	−1.88977e14	−0.109843
$590$	−2.64396e15	−1.52254
$591$	−2.33263e14	−0.133081
$592$	−3.41275e15	−1.92901
$593$	−4.78325e14	−0.267869	−0.133934	−	0.990990i	$-0.542761\pi$
$593$	−4.78325e14	−0.267869	−0.133934	+	0.990990i	$0.542761\pi$
$594$	4.40011e15	2.44139
$595$	2.12775e15	1.16971
$596$	−7.35810e15	−4.00785
$597$	2.01636e15	1.08820
$598$	8.00185e15	4.27892
$599$	−5.93499e14	−0.314465	−0.157232	−	0.987562i	$-0.550257\pi$
$599$	−5.93499e14	−0.314465	−0.157232	+	0.987562i	$0.550257\pi$
$600$	−2.65519e16	−13.9400
$601$	3.22160e15	1.67596	0.837978	−	0.545704i	$-0.183738\pi$
$601$	3.22160e15	1.67596	0.837978	+	0.545704i	$0.183738\pi$
$602$	1.02509e15	0.528420
$603$	3.49180e15	1.78363
$604$	8.56478e15	4.33524
$605$	−2.85558e15	−1.43232
$606$	−9.07469e15	−4.51058
$607$	−3.13500e15	−1.54419	−0.772093	−	0.635509i	$-0.780790\pi$
$607$	−3.13500e15	−1.54419	−0.772093	+	0.635509i	$0.780790\pi$
$608$	7.93502e14	0.387328
$609$	−3.03415e15	−1.46772
$610$	6.45432e15	3.09412
$611$	3.70692e15	1.76111
$612$	−7.78969e15	−3.66765
$613$	1.54585e15	0.721332	0.360666	−	0.932695i	$-0.382549\pi$
$613$	1.54585e15	0.721332	0.360666	+	0.932695i	$0.382549\pi$
$614$	−3.79280e15	−1.75402
$615$	−3.76761e15	−1.72684
$616$	−3.92421e15	−1.78262
$617$	−1.75213e15	−0.788855	−0.394428	−	0.918927i	$-0.629057\pi$
$617$	−1.75213e15	−0.788855	−0.394428	+	0.918927i	$0.629057\pi$
$618$	−7.54421e15	−3.36649
$619$	4.13897e15	1.83060	0.915300	−	0.402773i	$-0.131954\pi$
$619$	4.13897e15	1.83060	0.915300	+	0.402773i	$0.131954\pi$
$620$	1.16951e16	5.12684
$621$	−1.15819e16	−5.03243
$622$	−5.13969e14	−0.221355
$623$	4.60290e15	1.96493
$624$	1.96535e16	8.31621
$625$	4.48120e15	1.87955
$626$	−2.64131e15	−1.09815
$627$	2.16743e14	0.0893250
$628$	8.54220e15	3.48973
$629$	7.14932e14	0.289525
$630$	2.56642e16	10.3028
$631$	1.34196e15	0.534046	0.267023	−	0.963690i	$-0.413960\pi$
$631$	1.34196e15	0.534046	0.267023	+	0.963690i	$0.413960\pi$
$632$	−8.62251e15	−3.40165
$633$	−4.99857e14	−0.195490
$634$	7.36940e14	0.285721
$635$	−6.90827e15	−2.65530
$636$	−2.43837e14	−0.0929150
$637$	1.34428e15	0.507837
$638$	1.54904e15	0.580160
$639$	9.04794e15	3.35966
$640$	−1.48196e16	−5.45565
$641$	2.56166e15	0.934978	0.467489	−	0.883999i	$-0.345159\pi$
$641$	2.56166e15	0.934978	0.467489	+	0.883999i	$0.345159\pi$
$642$	−5.34494e15	−1.93419
$643$	1.86299e15	0.668420	0.334210	−	0.942499i	$-0.391531\pi$
$643$	1.86299e15	0.668420	0.334210	+	0.942499i	$0.391531\pi$
$644$	1.63767e16	5.82579
$645$	2.21000e15	0.779495
$646$	−3.14308e14	−0.109920
$647$	−2.31615e15	−0.803144	−0.401572	−	0.915827i	$-0.631536\pi$
$647$	−2.31615e15	−0.803144	−0.401572	+	0.915827i	$0.631536\pi$
$648$	−2.58855e16	−8.90007
$649$	−5.84744e14	−0.199352
$650$	−1.58729e16	−5.36577
$651$	−6.93712e15	−2.32533
$652$	−1.60464e15	−0.533355
$653$	3.45678e15	1.13933	0.569665	−	0.821877i	$-0.307073\pi$
$653$	3.45678e15	1.13933	0.569665	+	0.821877i	$0.307073\pi$
$654$	2.61221e15	0.853749
$655$	−3.95542e15	−1.28193
$656$	−5.76802e15	−1.85377
$657$	7.70852e15	2.45675
$658$	1.03882e16	3.28320
$659$	−1.88198e15	−0.589856	−0.294928	−	0.955519i	$-0.595296\pi$
$659$	−1.88198e15	−0.589856	−0.294928	+	0.955519i	$0.595296\pi$
$660$	−1.34134e16	−4.16916
$661$	1.30744e15	0.403007	0.201504	−	0.979488i	$-0.435417\pi$
$661$	1.30744e15	0.403007	0.201504	+	0.979488i	$0.435417\pi$
$662$	9.44940e15	2.88858
$663$	−4.11719e15	−1.24818
$664$	−1.89898e16	−5.70948
$665$	7.56265e14	0.225504
$666$	8.62326e15	2.55013
$667$	−4.07737e15	−1.19588
$668$	−1.51034e15	−0.439344
$669$	6.99415e15	2.01786
$670$	−8.71930e15	−2.49500
$671$	1.42745e15	0.405123
$672$	2.91286e16	8.19952
$673$	−4.80307e15	−1.34102	−0.670512	−	0.741899i	$-0.733925\pi$
$673$	−4.80307e15	−1.34102	−0.670512	+	0.741899i	$0.733925\pi$
$674$	−9.42059e15	−2.60885
$675$	2.29746e16	6.31068
$676$	5.05024e15	1.37596
$677$	−6.54600e15	−1.76904	−0.884521	−	0.466500i	$-0.845515\pi$
$677$	−6.54600e15	−1.76904	−0.884521	+	0.466500i	$0.845515\pi$
$678$	−1.41556e16	−3.79459
$679$	−5.29724e15	−1.40853
$680$	1.22686e16	3.23591
$681$	−5.68224e15	−1.48666
$682$	3.54163e15	0.919156
$683$	−3.91112e15	−1.00690	−0.503451	−	0.864024i	$-0.667937\pi$
$683$	−3.91112e15	−1.00690	−0.503451	+	0.864024i	$0.667937\pi$
$684$	−2.76868e15	−0.707073
$685$	7.08077e15	1.79383
$686$	−5.34259e15	−1.34267
$687$	−4.17098e15	−1.03986
$688$	3.38340e15	0.836790
$689$	−9.19397e13	−0.0225578
$690$	4.83446e16	11.7673
$691$	6.39806e14	0.154497	0.0772483	−	0.997012i	$-0.475387\pi$
$691$	6.39806e14	0.154497	0.0772483	+	0.997012i	$0.475387\pi$
$692$	−4.96703e15	−1.18991
$693$	5.67594e15	1.34898
$694$	5.34646e15	1.26063
$695$	4.54804e15	1.06392
$696$	−1.74949e16	−4.06033
$697$	1.20834e15	0.278232
$698$	5.48733e15	1.25359
$699$	−7.66781e14	−0.173799
$700$	−3.24857e16	−7.30556
$701$	−6.15819e15	−1.37405	−0.687027	−	0.726631i	$-0.741085\pi$
$701$	−6.15819e15	−1.37405	−0.687027	+	0.726631i	$0.741085\pi$
$702$	−2.97080e16	−6.57687
$703$	2.54108e14	0.0558166
$704$	−7.28803e15	−1.58840
$705$	2.23960e16	4.84319
$706$	−3.34025e15	−0.716726
$707$	−7.00280e15	−1.49096
$708$	1.04706e16	2.21202
$709$	4.62591e15	0.969713	0.484857	−	0.874594i	$-0.338872\pi$
$709$	4.62591e15	0.969713	0.484857	+	0.874594i	$0.338872\pi$
$710$	−2.25934e16	−4.69959
$711$	1.24715e16	2.57417
$712$	2.65403e16	5.43582
$713$	−9.32227e15	−1.89465
$714$	−1.15379e16	−2.32695
$715$	−5.05759e15	−1.01219
$716$	−9.35520e15	−1.85794
$717$	−1.27215e16	−2.50717
$718$	−1.54381e16	−3.01931
$719$	−2.95761e14	−0.0574027	−0.0287013	−	0.999588i	$-0.509137\pi$
$719$	−2.95761e14	−0.0574027	−0.0287013	+	0.999588i	$0.509137\pi$
$720$	8.47072e16	16.3152
$721$	−5.82175e15	−1.11278
$722$	1.00397e16	1.90444
$723$	2.44063e13	0.00459453
$724$	−9.42978e15	−1.76173
$725$	8.08808e15	1.49964
$726$	1.54846e16	2.84937
$727$	−6.30502e15	−1.15146	−0.575728	−	0.817642i	$-0.695281\pi$
$727$	−6.30502e15	−1.15146	−0.575728	+	0.817642i	$0.695281\pi$
$728$	2.64949e16	4.80219
$729$	8.56161e15	1.54012
$730$	−1.92488e16	−3.43658
$731$	−7.08783e14	−0.125594
$732$	−2.55604e16	−4.49528
$733$	5.25600e15	0.917452	0.458726	−	0.888578i	$-0.348306\pi$
$733$	5.25600e15	0.917452	0.458726	+	0.888578i	$0.348306\pi$
$734$	4.94249e15	0.856283
$735$	8.12174e15	1.39659
$736$	3.91437e16	6.68088
$737$	−1.92838e15	−0.326678
$738$	1.45745e16	2.45067
$739$	−9.12100e15	−1.52229	−0.761146	−	0.648580i	$-0.775363\pi$
$739$	−9.12100e15	−1.52229	−0.761146	+	0.648580i	$0.775363\pi$
$740$	−1.57258e16	−2.60519
$741$	−1.46337e15	−0.240632
$742$	−2.57649e14	−0.0420540
$743$	−2.18359e15	−0.353780	−0.176890	−	0.984231i	$-0.556604\pi$
$743$	−2.18359e15	−0.353780	−0.176890	+	0.984231i	$0.556604\pi$
$744$	−3.99994e16	−6.43283
$745$	−1.67620e16	−2.67588
$746$	−9.06956e15	−1.43722
$747$	2.74667e16	4.32060
$748$	4.30192e15	0.671743
$749$	−4.12461e15	−0.639341
$750$	−5.36350e16	−8.25300
$751$	1.00530e16	1.53560	0.767798	−	0.640692i	$-0.221353\pi$
$751$	1.00530e16	1.53560	0.767798	+	0.640692i	$0.221353\pi$
$752$	3.42872e16	5.19917
$753$	−7.68837e15	−1.15734
$754$	−1.04586e16	−1.56289
$755$	1.95109e16	2.89447
$756$	−6.08009e16	−8.95447
$757$	4.05739e15	0.593225	0.296613	−	0.954998i	$-0.404143\pi$
$757$	4.05739e15	0.593225	0.296613	+	0.954998i	$0.404143\pi$
$758$	7.93584e14	0.115189
$759$	1.06920e16	1.54074
$760$	4.36062e15	0.623840
$761$	−2.25831e15	−0.320751	−0.160375	−	0.987056i	$-0.551270\pi$
$761$	−2.25831e15	−0.320751	−0.160375	+	0.987056i	$0.551270\pi$
$762$	3.74607e16	5.28230
$763$	2.01580e15	0.282204
$764$	1.53627e16	2.13527
$765$	−1.77452e16	−2.44874
$766$	−4.01633e15	−0.550264
$767$	3.94799e15	0.537033
$768$	3.21699e16	4.34474
$769$	−3.92462e15	−0.526263	−0.263131	−	0.964760i	$-0.584755\pi$
$769$	−3.92462e15	−0.526263	−0.263131	+	0.964760i	$0.584755\pi$
$770$	−1.41732e16	−1.88699
$771$	−2.46750e16	−3.26181
$772$	1.55406e15	0.203974
$773$	−5.34422e15	−0.696462	−0.348231	−	0.937409i	$-0.613218\pi$
$773$	−5.34422e15	−0.696462	−0.348231	+	0.937409i	$0.613218\pi$
$774$	−8.54909e15	−1.10623
$775$	1.84921e16	2.37590
$776$	−3.05438e16	−3.89658
$777$	9.32801e15	1.18161
$778$	1.87244e16	2.35516
$779$	4.29477e14	0.0536395
$780$	9.05629e16	11.2313
$781$	−4.99679e15	−0.615334
$782$	−1.55049e16	−1.89597
$783$	1.51378e16	1.83812
$784$	1.24340e16	1.49924
$785$	1.94594e16	2.32995
$786$	2.14486e16	2.55021
$787$	9.57063e15	1.13000	0.565002	−	0.825090i	$-0.308876\pi$
$787$	9.57063e15	1.13000	0.565002	+	0.825090i	$0.308876\pi$
$788$	−1.64557e15	−0.192940
$789$	9.40374e15	1.09491
$790$	−3.11423e16	−3.60083
$791$	−1.09236e16	−1.25429
$792$	3.27274e16	3.73184
$793$	−9.63764e15	−1.09136
$794$	1.21709e16	1.36870
$795$	−5.55470e14	−0.0620356
$796$	1.42246e16	1.57767
$797$	2.69107e15	0.296418	0.148209	−	0.988956i	$-0.452649\pi$
$797$	2.69107e15	0.296418	0.148209	+	0.988956i	$0.452649\pi$
$798$	−4.10091e15	−0.448605
$799$	−7.18279e15	−0.780343
$800$	−7.76475e16	−8.37785
$801$	−3.83876e16	−4.11351
$802$	3.12031e16	3.32077
$803$	−4.25709e15	−0.449964
$804$	3.45302e16	3.62485
$805$	3.73068e16	3.88965
$806$	−2.39119e16	−2.47611
$807$	−2.27083e16	−2.33550
$808$	−4.03781e16	−4.12461
$809$	−1.22996e16	−1.24788	−0.623942	−	0.781471i	$-0.714470\pi$
$809$	−1.22996e16	−1.24788	−0.623942	+	0.781471i	$0.714470\pi$
$810$	−9.34918e16	−9.42119
$811$	1.42153e16	1.42279	0.711395	−	0.702792i	$-0.248064\pi$
$811$	1.42153e16	1.42279	0.711395	+	0.702792i	$0.248064\pi$
$812$	−2.14047e16	−2.12789
$813$	−1.37863e16	−1.36129
$814$	−4.76226e15	−0.467067
$815$	−3.65543e15	−0.356100
$816$	−3.80820e16	−3.68489
$817$	−2.51922e14	−0.0242128
$818$	−1.32530e16	−1.26523
$819$	−3.83219e16	−3.63401
$820$	−2.65789e16	−2.50357
$821$	1.42313e16	1.33155	0.665773	−	0.746154i	$-0.268102\pi$
$821$	1.42313e16	1.33155	0.665773	+	0.746154i	$0.268102\pi$
$822$	−3.83961e16	−3.56855
$823$	−3.08929e15	−0.285206	−0.142603	−	0.989780i	$-0.545547\pi$
$823$	−3.08929e15	−0.285206	−0.142603	+	0.989780i	$0.545547\pi$
$824$	−3.35682e16	−3.07842
$825$	−2.12092e16	−1.93209
$826$	1.10637e16	1.00118
$827$	1.91274e16	1.71940	0.859698	−	0.510802i	$-0.170652\pi$
$827$	1.91274e16	1.71940	0.859698	+	0.510802i	$0.170652\pi$
$828$	−1.36580e17	−12.1961
$829$	2.34185e15	0.207735	0.103867	−	0.994591i	$-0.466878\pi$
$829$	2.34185e15	0.207735	0.103867	+	0.994591i	$0.466878\pi$
$830$	−6.85865e16	−6.04378
$831$	−3.84708e16	−3.36764
$832$	4.92062e16	4.27899
$833$	−2.60478e15	−0.225021
$834$	−2.46621e16	−2.11649
$835$	−3.44061e15	−0.293332
$836$	1.52903e15	0.129503
$837$	3.46102e16	2.91216
$838$	2.03522e16	1.70125
$839$	2.07683e16	1.72468	0.862342	−	0.506326i	$-0.168997\pi$
$839$	2.07683e16	1.72468	0.862342	+	0.506326i	$0.168997\pi$
$840$	1.60073e17	13.2064
$841$	−6.87132e15	−0.563199
$842$	−6.97590e15	−0.568047
$843$	−5.45326e15	−0.441168
$844$	−3.52627e15	−0.283421
$845$	1.15046e16	0.918672
$846$	−8.66362e16	−6.87326
$847$	1.19492e16	0.941850
$848$	−8.50397e14	−0.0665954
$849$	4.67949e16	3.64088
$850$	3.07564e16	2.37756
$851$	1.25352e16	0.962762
$852$	8.94742e16	6.82779
$853$	−1.94025e16	−1.47108	−0.735541	−	0.677480i	$-0.763072\pi$
$853$	−1.94025e16	−1.47108	−0.735541	+	0.677480i	$0.763072\pi$
$854$	−2.70083e16	−2.03460
$855$	−6.30716e15	−0.472085
$856$	−2.37825e16	−1.76869
$857$	3.13237e15	0.231462	0.115731	−	0.993281i	$-0.463079\pi$
$857$	3.13237e15	0.231462	0.115731	+	0.993281i	$0.463079\pi$
$858$	2.74252e16	2.01358
$859$	−1.69679e15	−0.123785	−0.0618923	−	0.998083i	$-0.519714\pi$
$859$	−1.69679e15	−0.123785	−0.0618923	+	0.998083i	$0.519714\pi$
$860$	1.55906e16	1.13011
$861$	1.57656e16	1.13552
$862$	−3.05077e16	−2.18333
$863$	−1.62531e16	−1.15578	−0.577891	−	0.816114i	$-0.696124\pi$
$863$	−1.62531e16	−1.15578	−0.577891	+	0.816114i	$0.696124\pi$
$864$	−1.45326e17	−10.2688
$865$	−1.13151e16	−0.794454
$866$	1.37355e16	0.958291
$867$	−1.89657e16	−1.31481
$868$	−4.89384e16	−3.37125
$869$	−6.88750e15	−0.471468
$870$	−6.31872e16	−4.29807
$871$	1.30197e16	0.880039
$872$	1.16231e16	0.780695
$873$	4.41783e16	2.94870
$874$	−5.51090e15	−0.365519
$875$	−4.13893e16	−2.72800
$876$	7.62289e16	4.99283
$877$	8.57996e15	0.558454	0.279227	−	0.960225i	$-0.409922\pi$
$877$	8.57996e15	0.558454	0.279227	+	0.960225i	$0.409922\pi$
$878$	4.35980e16	2.81998
$879$	3.49743e15	0.224807
$880$	−4.67802e16	−2.98818
$881$	1.89430e16	1.20249	0.601246	−	0.799064i	$-0.294671\pi$
$881$	1.89430e16	1.20249	0.601246	+	0.799064i	$0.294671\pi$
$882$	−3.14179e16	−1.98198
$883$	−1.01854e16	−0.638551	−0.319275	−	0.947662i	$-0.603440\pi$
$883$	−1.01854e16	−0.638551	−0.319275	+	0.947662i	$0.603440\pi$
$884$	−2.90450e16	−1.80961
$885$	2.38525e16	1.47688
$886$	−2.42568e16	−1.49262
$887$	3.01644e15	0.184465	0.0922326	−	0.995737i	$-0.470600\pi$
$887$	3.01644e15	0.184465	0.0922326	+	0.995737i	$0.470600\pi$
$888$	5.37852e16	3.26883
$889$	2.89078e16	1.74605
$890$	9.58567e16	5.75410
$891$	−2.06768e16	−1.23355
$892$	4.93407e16	2.92549
$893$	−2.55297e15	−0.150440
$894$	9.08934e16	5.32324
$895$	−2.13115e16	−1.24047
$896$	6.20129e16	3.58747
$897$	−7.21885e16	−4.15059
$898$	4.12963e16	2.35989
$899$	1.21844e16	0.692030
$900$	2.70927e17	15.2939
$901$	1.78148e14	0.00999530
$902$	−8.04889e15	−0.448849
$903$	−9.24778e15	−0.512572
$904$	−6.29856e16	−3.46989
$905$	−2.14814e16	−1.17624
$906$	−1.05799e17	−5.75809
$907$	−5.94995e15	−0.321865	−0.160932	−	0.986965i	$-0.551450\pi$
$907$	−5.94995e15	−0.321865	−0.160932	+	0.986965i	$0.551450\pi$
$908$	−4.00858e16	−2.15535
$909$	5.84025e16	3.12126
$910$	9.56928e16	5.08337
$911$	3.48799e15	0.184172	0.0920861	−	0.995751i	$-0.470647\pi$
$911$	3.48799e15	0.184172	0.0920861	+	0.995751i	$0.470647\pi$
$912$	−1.35355e16	−0.710397
$913$	−1.51687e16	−0.791333
$914$	3.66802e16	1.90208
$915$	−5.82275e16	−3.00132
$916$	−2.94245e16	−1.50759
$917$	1.65516e16	0.842961
$918$	5.75642e16	2.91419
$919$	−9.47651e15	−0.476885	−0.238442	−	0.971157i	$-0.576637\pi$
$919$	−9.47651e15	−0.476885	−0.238442	+	0.971157i	$0.576637\pi$
$920$	2.15110e17	10.7604
$921$	3.42167e16	1.70141
$922$	−4.59159e16	−2.26957
$923$	3.37366e16	1.65765
$924$	5.61289e16	2.74151
$925$	−2.48655e16	−1.20731
$926$	−3.79818e16	−1.83322
$927$	4.85527e16	2.32956
$928$	−5.11615e16	−2.44022
$929$	−1.03025e16	−0.488492	−0.244246	−	0.969713i	$-0.578540\pi$
$929$	−1.03025e16	−0.488492	−0.244246	+	0.969713i	$0.578540\pi$
$930$	−1.44468e17	−6.80949
$931$	−9.25813e14	−0.0433811
$932$	−5.40931e15	−0.251973
$933$	4.63675e15	0.214716
$934$	−3.47385e16	−1.59920
$935$	9.79992e15	0.448496
$936$	−2.20964e17	−10.0532
$937$	2.53627e15	0.114717	0.0573584	−	0.998354i	$-0.481732\pi$
$937$	2.53627e15	0.114717	0.0573584	+	0.998354i	$0.481732\pi$
$938$	3.64861e16	1.64063
$939$	2.38286e16	1.06521
$940$	1.57994e17	7.02164
$941$	3.43149e15	0.151614	0.0758072	−	0.997122i	$-0.475847\pi$
$941$	3.43149e15	0.151614	0.0758072	+	0.997122i	$0.475847\pi$
$942$	−1.05520e17	−4.63508
$943$	2.11862e16	0.925209
$944$	3.65169e16	1.58544
$945$	−1.38507e17	−5.97854
$946$	4.72130e15	0.202610
$947$	1.77905e16	0.759038	0.379519	−	0.925184i	$-0.376090\pi$
$947$	1.77905e16	0.759038	0.379519	+	0.925184i	$0.376090\pi$
$948$	1.23330e17	5.23145
$949$	2.87424e16	1.21216
$950$	1.09317e16	0.458361
$951$	−6.64829e15	−0.277151
$952$	−5.13382e16	−2.12783
$953$	1.39263e16	0.573886	0.286943	−	0.957948i	$-0.407361\pi$
$953$	1.39263e16	0.573886	0.286943	+	0.957948i	$0.407361\pi$
$954$	2.14876e15	0.0880385
$955$	3.49967e16	1.42564
$956$	−8.97449e16	−3.63489
$957$	−1.39746e16	−0.562761
$958$	−1.00740e16	−0.403358
$959$	−2.96297e16	−1.17957
$960$	2.97288e17	11.7675
$961$	2.44920e15	0.0963930
$962$	3.21531e16	1.25823
$963$	3.43987e16	1.33844
$964$	1.72176e14	0.00666115
$965$	3.54021e15	0.136185
$966$	−2.02299e17	−7.73784
$967$	−4.21314e15	−0.160236	−0.0801180	−	0.996785i	$-0.525530\pi$
$967$	−4.21314e15	−0.160236	−0.0801180	+	0.996785i	$0.525530\pi$
$968$	6.88993e16	2.60555
$969$	2.83552e15	0.106623
$970$	−1.10317e17	−4.12474
$971$	−1.89268e16	−0.703674	−0.351837	−	0.936061i	$-0.614443\pi$
$971$	−1.89268e16	−0.703674	−0.351837	+	0.936061i	$0.614443\pi$
$972$	1.66518e17	6.15596
$973$	−1.90314e16	−0.699599
$974$	−3.51458e16	−1.28469
$975$	1.43197e17	5.20485
$976$	−8.91435e16	−3.22193
$977$	1.55524e16	0.558956	0.279478	−	0.960152i	$-0.409839\pi$
$977$	1.55524e16	0.558956	0.279478	+	0.960152i	$0.409839\pi$
$978$	1.98219e16	0.708405
$979$	2.11999e16	0.753404
$980$	5.72953e16	2.02477
$981$	−1.68115e16	−0.590783
$982$	−4.04719e16	−1.41430
$983$	−4.23979e16	−1.47333	−0.736665	−	0.676258i	$-0.763600\pi$
$983$	−4.23979e16	−1.47333	−0.736665	+	0.676258i	$0.763600\pi$
$984$	9.09046e16	3.14132
$985$	−3.74867e15	−0.128818
$986$	2.02652e16	0.692513
$987$	−9.37168e16	−3.18473
$988$	−1.03234e16	−0.348868
$989$	−1.24274e16	−0.417638
$990$	1.18203e17	3.95035
$991$	−1.03132e16	−0.342757	−0.171379	−	0.985205i	$-0.554822\pi$
$991$	−1.03132e16	−0.342757	−0.171379	+	0.985205i	$0.554822\pi$
$992$	−1.16973e17	−3.86608
$993$	−8.52475e16	−2.80195
$994$	9.45425e16	3.09031
$995$	3.24041e16	1.05335
$996$	2.71616e17	8.78070
$997$	2.96304e16	0.952609	0.476304	−	0.879280i	$-0.341976\pi$
$997$	2.96304e16	0.952609	0.476304	+	0.879280i	$0.341976\pi$
$998$	−3.25380e16	−1.04033
$999$	−4.65387e16	−1.47980

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.12.a.b.1.2	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.12.a.b.1.2	✓	92	1.1	even	1	trivial

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	197.12.a.b.1.2

Level	$197$
Weight	$12$
Character	197.1
Self dual	yes
Analytic conductor	$151.364$
Analytic rank	$0$
Dimension	$92$
CM	no
Inner twists	$1$