LMFDB - Embedded newform 197.10.a.b.1.67

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,10,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, 10, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
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:	$101.462059724$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.67
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)

$f(q)$	$=$	\(q+37.7446 q^{2} -12.6356 q^{3} +912.651 q^{4} +2090.01 q^{5} -476.926 q^{6} +6297.82 q^{7} +15122.4 q^{8} -19523.3 q^{9} +78886.6 q^{10} -54815.7 q^{11} -11531.9 q^{12} +117280. q^{13} +237708. q^{14} -26408.7 q^{15} +103511. q^{16} +461690. q^{17} -736900. q^{18} +412792. q^{19} +1.90745e6 q^{20} -79577.0 q^{21} -2.06899e6 q^{22} +722499. q^{23} -191081. q^{24} +2.41503e6 q^{25} +4.42669e6 q^{26} +495397. q^{27} +5.74772e6 q^{28} -3.63767e6 q^{29} -996783. q^{30} +4.00992e6 q^{31} -3.83569e6 q^{32} +692631. q^{33} +1.74263e7 q^{34} +1.31625e7 q^{35} -1.78180e7 q^{36} +1.23268e7 q^{37} +1.55806e7 q^{38} -1.48191e6 q^{39} +3.16060e7 q^{40} -2.81025e7 q^{41} -3.00360e6 q^{42} +2.45488e7 q^{43} -5.00276e7 q^{44} -4.08041e7 q^{45} +2.72704e7 q^{46} +2.99944e7 q^{47} -1.30793e6 q^{48} -691047. q^{49} +9.11543e7 q^{50} -5.83375e6 q^{51} +1.07036e8 q^{52} +5.31424e7 q^{53} +1.86985e7 q^{54} -1.14565e8 q^{55} +9.52382e7 q^{56} -5.21589e6 q^{57} -1.37302e8 q^{58} -7.64651e7 q^{59} -2.41019e7 q^{60} +1.32844e8 q^{61} +1.51353e8 q^{62} -1.22955e8 q^{63} -1.97774e8 q^{64} +2.45117e8 q^{65} +2.61430e7 q^{66} -2.39094e8 q^{67} +4.21362e8 q^{68} -9.12923e6 q^{69} +4.96814e8 q^{70} -2.23327e8 q^{71} -2.95240e8 q^{72} -2.76322e8 q^{73} +4.65271e8 q^{74} -3.05155e7 q^{75} +3.76735e8 q^{76} -3.45219e8 q^{77} -5.59341e7 q^{78} -3.47595e8 q^{79} +2.16340e8 q^{80} +3.78018e8 q^{81} -1.06072e9 q^{82} -2.64163e7 q^{83} -7.26261e7 q^{84} +9.64938e8 q^{85} +9.26584e8 q^{86} +4.59643e7 q^{87} -8.28945e8 q^{88} +5.53802e8 q^{89} -1.54013e9 q^{90} +7.38611e8 q^{91} +6.59389e8 q^{92} -5.06679e7 q^{93} +1.13213e9 q^{94} +8.62741e8 q^{95} +4.84664e7 q^{96} +1.30594e9 q^{97} -2.60833e7 q^{98} +1.07018e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15}+ \cdots + 8731109606 q^{99}+O(q^{100}) $ 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * 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 $

$2$	37.7446	1.66809	0.834045	−	0.551697i	$-0.186019\pi$
$2$	37.7446	1.66809	0.834045	+	0.551697i	$0.186019\pi$
$3$	−12.6356	−0.0900641	−0.0450320	−	0.998986i	$-0.514339\pi$
$3$	−12.6356	−0.0900641	−0.0450320	+	0.998986i	$0.514339\pi$
$4$	912.651	1.78252
$5$	2090.01	1.49549	0.747746	−	0.663985i	$-0.231136\pi$
$5$	2090.01	1.49549	0.747746	+	0.663985i	$0.231136\pi$
$6$	−476.926	−0.150235
$7$	6297.82	0.991401	0.495700	−	0.868494i	$-0.334911\pi$
$7$	6297.82	0.991401	0.495700	+	0.868494i	$0.334911\pi$
$8$	15122.4	1.30532
$9$	−19523.3	−0.991888
$10$	78886.6	2.49461
$11$	−54815.7	−1.12885	−0.564427	−	0.825483i	$-0.690903\pi$
$11$	−54815.7	−1.12885	−0.564427	+	0.825483i	$0.690903\pi$
$12$	−11531.9	−0.160541
$13$	117280.	1.13889	0.569443	−	0.822031i	$-0.307159\pi$
$13$	117280.	1.13889	0.569443	+	0.822031i	$0.307159\pi$
$14$	237708.	1.65374
$15$	−26408.7	−0.134690
$16$	103511.	0.394864
$17$	461690.	1.34070	0.670348	−	0.742047i	$-0.266145\pi$
$17$	461690.	1.34070	0.670348	+	0.742047i	$0.266145\pi$
$18$	−736900.	−1.65456
$19$	412792.	0.726675	0.363337	−	0.931658i	$-0.381637\pi$
$19$	412792.	0.726675	0.363337	+	0.931658i	$0.381637\pi$
$20$	1.90745e6	2.66575
$21$	−79577.0	−0.0892896
$22$	−2.06899e6	−1.88303
$23$	722499.	0.538346	0.269173	−	0.963092i	$-0.413250\pi$
$23$	722499.	0.538346	0.269173	+	0.963092i	$0.413250\pi$
$24$	−191081.	−0.117562
$25$	2.41503e6	1.23650
$26$	4.42669e6	1.89976
$27$	495397.	0.179398
$28$	5.74772e6	1.76719
$29$	−3.63767e6	−0.955064	−0.477532	−	0.878614i	$-0.658468\pi$
$29$	−3.63767e6	−0.955064	−0.477532	+	0.878614i	$0.658468\pi$
$30$	−996783.	−0.224675
$31$	4.00992e6	0.779845	0.389923	−	0.920848i	$-0.372502\pi$
$31$	4.00992e6	0.779845	0.389923	+	0.920848i	$0.372502\pi$
$32$	−3.83569e6	−0.646649
$33$	692631.	0.101669
$34$	1.74263e7	2.23640
$35$	1.31625e7	1.48263
$36$	−1.78180e7	−1.76806
$37$	1.23268e7	1.08129	0.540647	−	0.841250i	$-0.318180\pi$
$37$	1.23268e7	1.08129	0.540647	+	0.841250i	$0.318180\pi$
$38$	1.55806e7	1.21216
$39$	−1.48191e6	−0.102573
$40$	3.16060e7	1.95209
$41$	−2.81025e7	−1.55316	−0.776582	−	0.630016i	$-0.783048\pi$
$41$	−2.81025e7	−1.55316	−0.776582	+	0.630016i	$0.783048\pi$
$42$	−3.00360e6	−0.148943
$43$	2.45488e7	1.09502	0.547510	−	0.836799i	$-0.315576\pi$
$43$	2.45488e7	1.09502	0.547510	+	0.836799i	$0.315576\pi$
$44$	−5.00276e7	−2.01221
$45$	−4.08041e7	−1.48336
$46$	2.72704e7	0.898010
$47$	2.99944e7	0.896603	0.448301	−	0.893883i	$-0.352029\pi$
$47$	2.99944e7	0.896603	0.448301	+	0.893883i	$0.352029\pi$
$48$	−1.30793e6	−0.0355630
$49$	−691047.	−0.0171248
$50$	9.11543e7	2.06259
$51$	−5.83375e6	−0.120748
$52$	1.07036e8	2.03009
$53$	5.31424e7	0.925124	0.462562	−	0.886587i	$-0.346930\pi$
$53$	5.31424e7	0.925124	0.462562	+	0.886587i	$0.346930\pi$
$54$	1.86985e7	0.299251
$55$	−1.14565e8	−1.68819
$56$	9.52382e7	1.29409
$57$	−5.21589e6	−0.0654473
$58$	−1.37302e8	−1.59313
$59$	−7.64651e7	−0.821541	−0.410770	−	0.911739i	$-0.634740\pi$
$59$	−7.64651e7	−0.821541	−0.410770	+	0.911739i	$0.634740\pi$
$60$	−2.41019e7	−0.240088
$61$	1.32844e8	1.22845	0.614225	−	0.789131i	$-0.289469\pi$
$61$	1.32844e8	1.22845	0.614225	+	0.789131i	$0.289469\pi$
$62$	1.51353e8	1.30085
$63$	−1.22955e8	−0.983359
$64$	−1.97774e8	−1.47353
$65$	2.45117e8	1.70319
$66$	2.61430e7	0.169593
$67$	−2.39094e8	−1.44955	−0.724774	−	0.688987i	$-0.758056\pi$
$67$	−2.39094e8	−1.44955	−0.724774	+	0.688987i	$0.758056\pi$
$68$	4.21362e8	2.38982
$69$	−9.12923e6	−0.0484857
$70$	4.96814e8	2.47316
$71$	−2.23327e8	−1.04299	−0.521493	−	0.853256i	$-0.674625\pi$
$71$	−2.23327e8	−1.04299	−0.521493	+	0.853256i	$0.674625\pi$
$72$	−2.95240e8	−1.29473
$73$	−2.76322e8	−1.13884	−0.569420	−	0.822047i	$-0.692832\pi$
$73$	−2.76322e8	−1.13884	−0.569420	+	0.822047i	$0.692832\pi$
$74$	4.65271e8	1.80369
$75$	−3.05155e7	−0.111364
$76$	3.76735e8	1.29531
$77$	−3.45219e8	−1.11915
$78$	−5.59341e7	−0.171100
$79$	−3.47595e8	−1.00404	−0.502021	−	0.864855i	$-0.667410\pi$
$79$	−3.47595e8	−1.00404	−0.502021	+	0.864855i	$0.667410\pi$
$80$	2.16340e8	0.590515
$81$	3.78018e8	0.975731
$82$	−1.06072e9	−2.59082
$83$	−2.64163e7	−0.0610970	−0.0305485	−	0.999533i	$-0.509725\pi$
$83$	−2.64163e7	−0.0610970	−0.0305485	+	0.999533i	$0.509725\pi$
$84$	−7.26261e7	−0.159161
$85$	9.64938e8	2.00500
$86$	9.26584e8	1.82659
$87$	4.59643e7	0.0860169
$88$	−8.28945e8	−1.47351
$89$	5.53802e8	0.935620	0.467810	−	0.883829i	$-0.345043\pi$
$89$	5.53802e8	0.935620	0.467810	+	0.883829i	$0.345043\pi$
$90$	−1.54013e9	−2.47438
$91$	7.38611e8	1.12909
$92$	6.59389e8	0.959614
$93$	−5.06679e7	−0.0702360
$94$	1.13213e9	1.49561
$95$	8.62741e8	1.08674
$96$	4.84664e7	0.0582399
$97$	1.30594e9	1.49779	0.748893	−	0.662691i	$-0.230586\pi$
$97$	1.30594e9	1.49779	0.748893	+	0.662691i	$0.230586\pi$
$98$	−2.60833e7	−0.0285657
$99$	1.07018e9	1.11970
$100$	2.20408e9	2.20408
$101$	−1.40262e9	−1.34120	−0.670601	−	0.741818i	$-0.733964\pi$
$101$	−1.40262e9	−1.34120	−0.670601	+	0.741818i	$0.733964\pi$
$102$	−2.20192e8	−0.201419
$103$	1.46620e9	1.28359	0.641796	−	0.766875i	$-0.278190\pi$
$103$	1.46620e9	1.28359	0.641796	+	0.766875i	$0.278190\pi$
$104$	1.77356e9	1.48661
$105$	−1.66317e8	−0.133532
$106$	2.00584e9	1.54319
$107$	1.32200e9	0.975003	0.487501	−	0.873122i	$-0.337908\pi$
$107$	1.32200e9	0.975003	0.487501	+	0.873122i	$0.337908\pi$
$108$	4.52125e8	0.319780
$109$	2.11858e8	0.143756	0.0718780	−	0.997413i	$-0.477101\pi$
$109$	2.11858e8	0.143756	0.0718780	+	0.997413i	$0.477101\pi$
$110$	−4.32422e9	−2.81605
$111$	−1.55757e8	−0.0973857
$112$	6.51895e8	0.391468
$113$	−4.22674e8	−0.243867	−0.121933	−	0.992538i	$-0.538909\pi$
$113$	−4.22674e8	−0.243867	−0.121933	+	0.992538i	$0.538909\pi$
$114$	−1.96871e8	−0.109172
$115$	1.51003e9	0.805093
$116$	−3.31992e9	−1.70242
$117$	−2.28970e9	−1.12965
$118$	−2.88614e9	−1.37040
$119$	2.90764e9	1.32917
$120$	−3.99363e8	−0.175813
$121$	6.46810e8	0.274310
$122$	5.01414e9	2.04917
$123$	3.55093e8	0.139884
$124$	3.65966e9	1.39009
$125$	9.65393e8	0.353679
$126$	−4.64086e9	−1.64033
$127$	3.84861e9	1.31277	0.656383	−	0.754428i	$-0.272085\pi$
$127$	3.84861e9	1.31277	0.656383	+	0.754428i	$0.272085\pi$
$128$	−5.50103e9	−1.81133
$129$	−3.10190e8	−0.0986220
$130$	9.25185e9	2.84108
$131$	3.22370e9	0.956388	0.478194	−	0.878254i	$-0.341292\pi$
$131$	3.22370e9	0.956388	0.478194	+	0.878254i	$0.341292\pi$
$132$	6.32131e8	0.181227
$133$	2.59969e9	0.720426
$134$	−9.02451e9	−2.41798
$135$	1.03539e9	0.268288
$136$	6.98186e9	1.75003
$137$	2.44880e8	0.0593895	0.0296948	−	0.999559i	$-0.490546\pi$
$137$	2.44880e8	0.0593895	0.0296948	+	0.999559i	$0.490546\pi$
$138$	−3.44579e8	−0.0808784
$139$	−6.14746e9	−1.39678	−0.698392	−	0.715716i	$-0.746101\pi$
$139$	−6.14746e9	−1.39678	−0.698392	+	0.715716i	$0.746101\pi$
$140$	1.20128e10	2.64282
$141$	−3.78998e8	−0.0807517
$142$	−8.42937e9	−1.73979
$143$	−6.42880e9	−1.28563
$144$	−2.02088e9	−0.391661
$145$	−7.60278e9	−1.42829
$146$	−1.04296e10	−1.89969
$147$	8.73182e6	0.00154233
$148$	1.12501e10	1.92743
$149$	−9.03290e9	−1.50138	−0.750688	−	0.660657i	$-0.770278\pi$
$149$	−9.03290e9	−1.50138	−0.750688	+	0.660657i	$0.770278\pi$
$150$	−1.15179e9	−0.185765
$151$	−1.16113e9	−0.181754	−0.0908768	−	0.995862i	$-0.528967\pi$
$151$	−1.16113e9	−0.181754	−0.0908768	+	0.995862i	$0.528967\pi$
$152$	6.24241e9	0.948541
$153$	−9.01373e9	−1.32982
$154$	−1.30301e10	−1.86684
$155$	8.38079e9	1.16625
$156$	−1.35247e9	−0.182838
$157$	6.75243e9	0.886976	0.443488	−	0.896280i	$-0.353741\pi$
$157$	6.75243e9	0.886976	0.443488	+	0.896280i	$0.353741\pi$
$158$	−1.31198e10	−1.67483
$159$	−6.71489e8	−0.0833205
$160$	−8.01665e9	−0.967059
$161$	4.55017e9	0.533717
$162$	1.42681e10	1.62761
$163$	1.17625e10	1.30513	0.652566	−	0.757732i	$-0.273693\pi$
$163$	1.17625e10	1.30513	0.652566	+	0.757732i	$0.273693\pi$
$164$	−2.56478e10	−2.76855
$165$	1.44761e9	0.152045
$166$	−9.97070e8	−0.101915
$167$	−1.75316e10	−1.74421	−0.872104	−	0.489320i	$-0.837245\pi$
$167$	−1.75316e10	−1.74421	−0.872104	+	0.489320i	$0.837245\pi$
$168$	−1.20340e9	−0.116551
$169$	3.15017e9	0.297060
$170$	3.64212e10	3.34452
$171$	−8.05908e9	−0.720780
$172$	2.24045e10	1.95190
$173$	−2.27827e10	−1.93373	−0.966867	−	0.255280i	$-0.917832\pi$
$173$	−2.27827e10	−1.93373	−0.966867	+	0.255280i	$0.917832\pi$
$174$	1.73490e9	0.143484
$175$	1.52094e10	1.22586
$176$	−5.67403e9	−0.445743
$177$	9.66185e8	0.0739913
$178$	2.09030e10	1.56070
$179$	−1.10734e10	−0.806200	−0.403100	−	0.915156i	$-0.632067\pi$
$179$	−1.10734e10	−0.806200	−0.403100	+	0.915156i	$0.632067\pi$
$180$	−3.72399e10	−2.64412
$181$	−1.25275e10	−0.867583	−0.433792	−	0.901013i	$-0.642825\pi$
$181$	−1.25275e10	−0.867583	−0.433792	+	0.901013i	$0.642825\pi$
$182$	2.78785e10	1.88343
$183$	−1.67857e9	−0.110639
$184$	1.09259e10	0.702713
$185$	2.57632e10	1.61707
$186$	−1.91244e9	−0.117160
$187$	−2.53078e10	−1.51345
$188$	2.73744e10	1.59821
$189$	3.11992e9	0.177855
$190$	3.25638e10	1.81277
$191$	−2.08512e10	−1.13365	−0.566827	−	0.823837i	$-0.691829\pi$
$191$	−2.08512e10	−1.13365	−0.566827	+	0.823837i	$0.691829\pi$
$192$	2.49900e9	0.132712
$193$	1.53909e9	0.0798464	0.0399232	−	0.999203i	$-0.487289\pi$
$193$	1.53909e9	0.0798464	0.0399232	+	0.999203i	$0.487289\pi$
$194$	4.92920e10	2.49844
$195$	−3.09722e9	−0.153397
$196$	−6.30685e8	−0.0305253
$197$	1.50614e9	0.0712470
$197$	1.50614e9	0.0712470
$198$	4.03937e10	1.86775
$199$	2.67718e10	1.21015	0.605074	−	0.796169i	$-0.293143\pi$
$199$	2.67718e10	1.21015	0.605074	+	0.796169i	$0.293143\pi$
$200$	3.65211e10	1.61402
$201$	3.02111e9	0.130552
$202$	−5.29413e10	−2.23724
$203$	−2.29094e10	−0.946851
$204$	−5.32418e9	−0.215237
$205$	−5.87346e10	−2.32274
$206$	5.53412e10	2.14115
$207$	−1.41056e10	−0.533980
$208$	1.21398e10	0.449704
$209$	−2.26275e10	−0.820309
$210$	−6.27756e9	−0.222743
$211$	8.59049e9	0.298364	0.149182	−	0.988810i	$-0.452336\pi$
$211$	8.59049e9	0.298364	0.149182	+	0.988810i	$0.452336\pi$
$212$	4.85005e10	1.64905
$213$	2.82188e9	0.0939355
$214$	4.98985e10	1.62639
$215$	5.13074e10	1.63760
$216$	7.49160e9	0.234171
$217$	2.52538e10	0.773139
$218$	7.99649e9	0.239798
$219$	3.49150e9	0.102568
$220$	−1.04558e11	−3.00924
$221$	5.41471e10	1.52690
$222$	−5.87899e9	−0.162448
$223$	5.26722e10	1.42630	0.713148	−	0.701013i	$-0.247269\pi$
$223$	5.26722e10	1.42630	0.713148	+	0.701013i	$0.247269\pi$
$224$	−2.41565e10	−0.641089
$225$	−4.71495e10	−1.22647
$226$	−1.59537e10	−0.406792
$227$	−6.70043e10	−1.67489	−0.837445	−	0.546521i	$-0.815952\pi$
$227$	−6.70043e10	−1.67489	−0.837445	+	0.546521i	$0.815952\pi$
$228$	−4.76029e9	−0.116661
$229$	−6.07620e10	−1.46007	−0.730033	−	0.683412i	$-0.760495\pi$
$229$	−6.07620e10	−1.46007	−0.730033	+	0.683412i	$0.760495\pi$
$230$	5.69955e10	1.34297
$231$	4.36207e9	0.100795
$232$	−5.50103e10	−1.24666
$233$	−2.16175e10	−0.480512	−0.240256	−	0.970710i	$-0.577231\pi$
$233$	−2.16175e10	−0.480512	−0.240256	+	0.970710i	$0.577231\pi$
$234$	−8.64238e10	−1.88435
$235$	6.26887e10	1.34086
$236$	−6.97860e10	−1.46441
$237$	4.39209e9	0.0904281
$238$	1.09748e11	2.21717
$239$	−2.06119e10	−0.408628	−0.204314	−	0.978905i	$-0.565496\pi$
$239$	−2.06119e10	−0.408628	−0.204314	+	0.978905i	$0.565496\pi$
$240$	−2.73359e9	−0.0531842
$241$	−7.32722e10	−1.39914	−0.699572	−	0.714562i	$-0.746626\pi$
$241$	−7.32722e10	−1.39914	−0.699572	+	0.714562i	$0.746626\pi$
$242$	2.44135e10	0.457574
$243$	−1.45274e10	−0.267276
$244$	1.21240e11	2.18974
$245$	−1.44430e9	−0.0256100
$246$	1.34028e10	0.233339
$247$	4.84124e10	0.827599
$248$	6.06397e10	1.01795
$249$	3.33786e8	0.00550264
$250$	3.64383e10	0.589968
$251$	4.69506e10	0.746637	0.373318	−	0.927703i	$-0.378220\pi$
$251$	4.69506e10	0.746637	0.373318	+	0.927703i	$0.378220\pi$
$252$	−1.12215e11	−1.75286
$253$	−3.96042e10	−0.607714
$254$	1.45264e11	2.18981
$255$	−1.21926e10	−0.180578
$256$	−1.06373e11	−1.54794
$257$	1.51148e10	0.216125	0.108062	−	0.994144i	$-0.465535\pi$
$257$	1.51148e10	0.216125	0.108062	+	0.994144i	$0.465535\pi$
$258$	−1.17080e10	−0.164510
$259$	7.76322e10	1.07199
$260$	2.23707e11	3.03598
$261$	7.10195e10	0.947317
$262$	1.21677e11	1.59534
$263$	2.98007e10	0.384083	0.192042	−	0.981387i	$-0.438489\pi$
$263$	2.98007e10	0.384083	0.192042	+	0.981387i	$0.438489\pi$
$264$	1.04742e10	0.132710
$265$	1.11068e11	1.38352
$266$	9.81241e10	1.20173
$267$	−6.99764e9	−0.0842657
$268$	−2.18210e11	−2.58385
$269$	3.91298e10	0.455640	0.227820	−	0.973703i	$-0.426840\pi$
$269$	3.91298e10	0.455640	0.227820	+	0.973703i	$0.426840\pi$
$270$	3.90802e10	0.447528
$271$	−1.63268e11	−1.83883	−0.919413	−	0.393294i	$-0.871335\pi$
$271$	−1.63268e11	−1.83883	−0.919413	+	0.393294i	$0.871335\pi$
$272$	4.77900e10	0.529392
$273$	−9.33281e9	−0.101691
$274$	9.24287e9	0.0990670
$275$	−1.32382e11	−1.39582
$276$	−8.33180e9	−0.0864268
$277$	5.84781e10	0.596808	0.298404	−	0.954440i	$-0.403546\pi$
$277$	5.84781e10	0.596808	0.298404	+	0.954440i	$0.403546\pi$
$278$	−2.32033e11	−2.32996
$279$	−7.82871e10	−0.773519
$280$	1.99049e11	1.93530
$281$	−1.96178e11	−1.87703	−0.938516	−	0.345236i	$-0.887799\pi$
$281$	−1.96178e11	−1.87703	−0.938516	+	0.345236i	$0.887799\pi$
$282$	−1.43051e10	−0.134701
$283$	4.54091e10	0.420827	0.210413	−	0.977612i	$-0.432519\pi$
$283$	4.54091e10	0.420827	0.210413	+	0.977612i	$0.432519\pi$
$284$	−2.03819e11	−1.85914
$285$	−1.09013e10	−0.0978759
$286$	−2.42652e11	−2.14455
$287$	−1.76984e11	−1.53981
$288$	7.48855e10	0.641404
$289$	9.45696e10	0.797465
$290$	−2.86964e11	−2.38252
$291$	−1.65014e10	−0.134897
$292$	−2.52186e11	−2.03001
$293$	−1.88944e11	−1.49771	−0.748856	−	0.662733i	$-0.769397\pi$
$293$	−1.88944e11	−1.49771	−0.748856	+	0.662733i	$0.769397\pi$
$294$	3.29579e8	0.00257274
$295$	−1.59813e11	−1.22861
$296$	1.86411e11	1.41143
$297$	−2.71555e10	−0.202514
$298$	−3.40943e11	−2.50443
$299$	8.47349e10	0.613115
$300$	−2.78500e10	−0.198509
$301$	1.54604e11	1.08560
$302$	−4.38262e10	−0.303181
$303$	1.77230e10	0.120794
$304$	4.27286e10	0.286937
$305$	2.77646e11	1.83714
$306$	−3.40219e11	−2.21826
$307$	−8.54216e10	−0.548839	−0.274420	−	0.961610i	$-0.588486\pi$
$307$	−8.54216e10	−0.548839	−0.274420	+	0.961610i	$0.588486\pi$
$308$	−3.15065e11	−1.99490
$309$	−1.85264e10	−0.115606
$310$	3.16329e11	1.94541
$311$	−1.01593e11	−0.615805	−0.307903	−	0.951418i	$-0.599627\pi$
$311$	−1.01593e11	−0.615805	−0.307903	+	0.951418i	$0.599627\pi$
$312$	−2.24101e10	−0.133890
$313$	−1.14373e11	−0.673554	−0.336777	−	0.941584i	$-0.609337\pi$
$313$	−1.14373e11	−0.673554	−0.336777	+	0.941584i	$0.609337\pi$
$314$	2.54868e11	1.47956
$315$	−2.56977e11	−1.47061
$316$	−3.17233e11	−1.78973
$317$	1.76694e10	0.0982779	0.0491389	−	0.998792i	$-0.484352\pi$
$317$	1.76694e10	0.0982779	0.0491389	+	0.998792i	$0.484352\pi$
$318$	−2.53450e10	−0.138986
$319$	1.99401e11	1.07813
$320$	−4.13351e11	−2.20366
$321$	−1.67044e10	−0.0878127
$322$	1.71744e11	0.890287
$323$	1.90582e11	0.974249
$324$	3.44999e11	1.73926
$325$	2.83236e11	1.40823
$326$	4.43969e11	2.17708
$327$	−2.67696e9	−0.0129472
$328$	−4.24977e11	−2.02737
$329$	1.88899e11	0.888892
$330$	5.46393e10	0.253625
$331$	1.98398e11	0.908474	0.454237	−	0.890881i	$-0.349912\pi$
$331$	1.98398e11	0.908474	0.454237	+	0.890881i	$0.349912\pi$
$332$	−2.41088e10	−0.108907
$333$	−2.40661e11	−1.07252
$334$	−6.61724e11	−2.90950
$335$	−4.99710e11	−2.16779
$336$	−8.23710e9	−0.0352572
$337$	2.37269e11	1.00209	0.501044	−	0.865422i	$-0.332950\pi$
$337$	2.37269e11	1.00209	0.501044	+	0.865422i	$0.332950\pi$
$338$	1.18902e11	0.495523
$339$	5.34076e9	0.0219636
$340$	8.80652e11	3.57396
$341$	−2.19807e11	−0.880331
$342$	−3.04186e11	−1.20233
$343$	−2.58492e11	−1.00838
$344$	3.71237e11	1.42935
$345$	−1.90802e10	−0.0725099
$346$	−8.59921e11	−3.22564
$347$	1.21002e11	0.448033	0.224017	−	0.974585i	$-0.428083\pi$
$347$	1.21002e11	0.448033	0.224017	+	0.974585i	$0.428083\pi$
$348$	4.19494e10	0.153327
$349$	−2.76202e11	−0.996582	−0.498291	−	0.867010i	$-0.666039\pi$
$349$	−2.76202e11	−0.996582	−0.498291	+	0.867010i	$0.666039\pi$
$350$	5.74074e11	2.04485
$351$	5.81003e10	0.204313
$352$	2.10256e11	0.729973
$353$	−1.20335e11	−0.412483	−0.206241	−	0.978501i	$-0.566123\pi$
$353$	−1.20335e11	−0.412483	−0.206241	+	0.978501i	$0.566123\pi$
$354$	3.64682e10	0.123424
$355$	−4.66756e11	−1.55978
$356$	5.05428e11	1.66776
$357$	−3.67399e10	−0.119710
$358$	−4.17961e11	−1.34481
$359$	−4.13453e10	−0.131371	−0.0656857	−	0.997840i	$-0.520923\pi$
$359$	−4.13453e10	−0.131371	−0.0656857	+	0.997840i	$0.520923\pi$
$360$	−6.17056e11	−1.93626
$361$	−1.52291e11	−0.471944
$362$	−4.72845e11	−1.44721
$363$	−8.17285e9	−0.0247055
$364$	6.74094e11	2.01263
$365$	−5.77517e11	−1.70312
$366$	−6.33568e10	−0.184556
$367$	3.01595e11	0.867814	0.433907	−	0.900958i	$-0.357135\pi$
$367$	3.01595e11	0.867814	0.433907	+	0.900958i	$0.357135\pi$
$368$	7.47866e10	0.212573
$369$	5.48654e11	1.54057
$370$	9.72422e11	2.69741
$371$	3.34682e11	0.917169
$372$	−4.62422e10	−0.125197
$373$	−5.18919e10	−0.138806	−0.0694032	−	0.997589i	$-0.522110\pi$
$373$	−5.18919e10	−0.138806	−0.0694032	+	0.997589i	$0.522110\pi$
$374$	−9.55233e11	−2.52457
$375$	−1.21984e10	−0.0318537
$376$	4.53588e11	1.17035
$377$	−4.26627e11	−1.08771
$378$	1.17760e11	0.296678
$379$	2.36437e11	0.588624	0.294312	−	0.955709i	$-0.404909\pi$
$379$	2.36437e11	0.588624	0.294312	+	0.955709i	$0.404909\pi$
$380$	7.87382e11	1.93713
$381$	−4.86297e10	−0.118233
$382$	−7.87019e11	−1.89104
$383$	−1.09688e11	−0.260474	−0.130237	−	0.991483i	$-0.541574\pi$
$383$	−1.09688e11	−0.260474	−0.130237	+	0.991483i	$0.541574\pi$
$384$	6.95090e10	0.163136
$385$	−7.21513e11	−1.67367
$386$	5.80921e10	0.133191
$387$	−4.79275e11	−1.08614
$388$	1.19187e12	2.66984
$389$	3.78253e11	0.837547	0.418774	−	0.908091i	$-0.362460\pi$
$389$	3.78253e11	0.837547	0.418774	+	0.908091i	$0.362460\pi$
$390$	−1.16903e11	−0.255879
$391$	3.33570e11	0.721759
$392$	−1.04503e10	−0.0223533
$393$	−4.07335e10	−0.0861361
$394$	5.68485e10	0.118846
$395$	−7.26479e11	−1.50154
$396$	9.76706e11	1.99588
$397$	2.27028e11	0.458693	0.229347	−	0.973345i	$-0.426341\pi$
$397$	2.27028e11	0.458693	0.229347	+	0.973345i	$0.426341\pi$
$398$	1.01049e12	2.01864
$399$	−3.28487e10	−0.0648845
$400$	2.49983e11	0.488248
$401$	6.76102e10	0.130576	0.0652878	−	0.997866i	$-0.479203\pi$
$401$	6.76102e10	0.130576	0.0652878	+	0.997866i	$0.479203\pi$
$402$	1.14030e11	0.217773
$403$	4.70285e11	0.888154
$404$	−1.28010e12	−2.39072
$405$	7.90063e11	1.45920
$406$	−8.64705e11	−1.57943
$407$	−6.75703e11	−1.22062
$408$	−8.82203e10	−0.157615
$409$	−6.26708e11	−1.10742	−0.553708	−	0.832711i	$-0.686788\pi$
$409$	−6.26708e11	−1.10742	−0.553708	+	0.832711i	$0.686788\pi$
$410$	−2.21691e12	−3.87455
$411$	−3.09421e9	−0.00534886
$412$	1.33813e12	2.28803
$413$	−4.81564e11	−0.814476
$414$	−5.32409e11	−0.890726
$415$	−5.52104e10	−0.0913701
$416$	−4.49851e11	−0.736460
$417$	7.76771e10	0.125800
$418$	−8.54064e11	−1.36835
$419$	3.01445e11	0.477798	0.238899	−	0.971044i	$-0.423213\pi$
$419$	3.01445e11	0.477798	0.238899	+	0.971044i	$0.423213\pi$
$420$	−1.51789e11	−0.238023
$421$	1.19046e12	1.84691	0.923456	−	0.383705i	$-0.125352\pi$
$421$	1.19046e12	1.84691	0.923456	+	0.383705i	$0.125352\pi$
$422$	3.24244e11	0.497698
$423$	−5.85591e11	−0.889330
$424$	8.03642e11	1.20758
$425$	1.11500e12	1.65777
$426$	1.06510e11	0.156693
$427$	8.36628e11	1.21789
$428$	1.20653e12	1.73796
$429$	8.12320e10	0.115789
$430$	1.93657e12	2.73166
$431$	8.84672e11	1.23491	0.617454	−	0.786607i	$-0.288164\pi$
$431$	8.84672e11	1.23491	0.617454	+	0.786607i	$0.288164\pi$
$432$	5.12791e10	0.0708376
$433$	3.46888e11	0.474235	0.237118	−	0.971481i	$-0.423797\pi$
$433$	3.46888e11	0.474235	0.237118	+	0.971481i	$0.423797\pi$
$434$	9.53193e11	1.28967
$435$	9.60660e10	0.128638
$436$	1.93353e11	0.256248
$437$	2.98242e11	0.391203
$438$	1.31785e11	0.171093
$439$	2.93904e11	0.377673	0.188836	−	0.982009i	$-0.439528\pi$
$439$	2.93904e11	0.377673	0.188836	+	0.982009i	$0.439528\pi$
$440$	−1.73251e12	−2.20363
$441$	1.34916e10	0.0169859
$442$	2.04376e12	2.54700
$443$	−8.19078e11	−1.01044	−0.505218	−	0.862992i	$-0.668588\pi$
$443$	−8.19078e11	−1.01044	−0.505218	+	0.862992i	$0.668588\pi$
$444$	−1.42152e11	−0.173592
$445$	1.15745e12	1.39921
$446$	1.98809e12	2.37919
$447$	1.14136e11	0.135220
$448$	−1.24555e12	−1.46086
$449$	1.12447e12	1.30568	0.652841	−	0.757495i	$-0.273577\pi$
$449$	1.12447e12	1.30568	0.652841	+	0.757495i	$0.273577\pi$
$450$	−1.77964e12	−2.04586
$451$	1.54046e12	1.75329
$452$	−3.85754e11	−0.434698
$453$	1.46716e10	0.0163695
$454$	−2.52905e12	−2.79387
$455$	1.54371e12	1.68855
$456$	−7.88768e10	−0.0854294
$457$	−2.25481e11	−0.241818	−0.120909	−	0.992664i	$-0.538581\pi$
$457$	−2.25481e11	−0.241818	−0.120909	+	0.992664i	$0.538581\pi$
$458$	−2.29343e12	−2.43552
$459$	2.28720e11	0.240517
$460$	1.37813e12	1.43510
$461$	1.15063e12	1.18654	0.593269	−	0.805004i	$-0.297837\pi$
$461$	1.15063e12	1.18654	0.593269	+	0.805004i	$0.297837\pi$
$462$	1.64644e11	0.168135
$463$	−1.14452e12	−1.15747	−0.578734	−	0.815516i	$-0.696453\pi$
$463$	−1.14452e12	−1.15747	−0.578734	+	0.815516i	$0.696453\pi$
$464$	−3.76539e11	−0.377120
$465$	−1.05897e11	−0.105037
$466$	−8.15943e11	−0.801537
$467$	1.10959e12	1.07954	0.539769	−	0.841813i	$-0.318511\pi$
$467$	1.10959e12	1.07954	0.539769	+	0.841813i	$0.318511\pi$
$468$	−2.08970e12	−2.01362
$469$	−1.50577e12	−1.43708
$470$	2.36616e12	2.23668
$471$	−8.53213e10	−0.0798846
$472$	−1.15634e12	−1.07237
$473$	−1.34566e12	−1.23612
$474$	1.65777e11	0.150842
$475$	9.96906e11	0.898531
$476$	2.65366e12	2.36927
$477$	−1.03752e12	−0.917620
$478$	−7.77988e11	−0.681628
$479$	−1.29638e12	−1.12518	−0.562591	−	0.826735i	$-0.690196\pi$
$479$	−1.29638e12	−1.12518	−0.562591	+	0.826735i	$0.690196\pi$
$480$	1.01295e11	0.0870973
$481$	1.44569e12	1.23147
$482$	−2.76563e12	−2.33390
$483$	−5.74943e10	−0.0480687
$484$	5.90312e11	0.488965
$485$	2.72943e12	2.23993
$486$	−5.48330e11	−0.445840
$487$	−1.18971e12	−0.958429	−0.479215	−	0.877698i	$-0.659078\pi$
$487$	−1.18971e12	−0.958429	−0.479215	+	0.877698i	$0.659078\pi$
$488$	2.00892e12	1.60352
$489$	−1.48626e11	−0.117545
$490$	−5.45144e10	−0.0427198
$491$	9.50708e11	0.738211	0.369105	−	0.929388i	$-0.379664\pi$
$491$	9.50708e11	0.738211	0.369105	+	0.929388i	$0.379664\pi$
$492$	3.24076e11	0.249347
$493$	−1.67948e12	−1.28045
$494$	1.82730e12	1.38051
$495$	2.23670e12	1.67450
$496$	4.15072e11	0.307932
$497$	−1.40647e12	−1.03402
$498$	1.25986e10	0.00917890
$499$	1.26939e12	0.916524	0.458262	−	0.888817i	$-0.348472\pi$
$499$	1.26939e12	0.916524	0.458262	+	0.888817i	$0.348472\pi$
$500$	8.81067e11	0.630440
$501$	2.21523e11	0.157091
$502$	1.77213e12	1.24546
$503$	−1.78501e12	−1.24332	−0.621662	−	0.783286i	$-0.713542\pi$
$503$	−1.78501e12	−1.24332	−0.621662	+	0.783286i	$0.713542\pi$
$504$	−1.85937e12	−1.28360
$505$	−2.93150e12	−2.00576
$506$	−1.49484e12	−1.01372
$507$	−3.98045e10	−0.0267544
$508$	3.51244e12	2.34004
$509$	2.17337e11	0.143517	0.0717584	−	0.997422i	$-0.477139\pi$
$509$	2.17337e11	0.143517	0.0717584	+	0.997422i	$0.477139\pi$
$510$	−4.60205e11	−0.301221
$511$	−1.74023e12	−1.12905
$512$	−1.19849e12	−0.770761
$513$	2.04496e11	0.130364
$514$	5.70503e11	0.360516
$515$	3.06439e12	1.91960
$516$	−2.83095e11	−0.175796
$517$	−1.64416e12	−1.01213
$518$	2.93019e12	1.78818
$519$	2.87873e11	0.174160
$520$	3.70677e12	2.22321
$521$	2.02228e11	0.120247	0.0601233	−	0.998191i	$-0.480851\pi$
$521$	2.02228e11	0.120247	0.0601233	+	0.998191i	$0.480851\pi$
$522$	2.68060e12	1.58021
$523$	−1.02904e12	−0.601416	−0.300708	−	0.953716i	$-0.597223\pi$
$523$	−1.02904e12	−0.601416	−0.300708	+	0.953716i	$0.597223\pi$
$524$	2.94212e12	1.70478
$525$	−1.92181e11	−0.110406
$526$	1.12481e12	0.640685
$527$	1.85134e12	1.04554
$528$	7.16950e10	0.0401454
$529$	−1.27915e12	−0.710183
$530$	4.19223e12	2.30783
$531$	1.49285e12	0.814877
$532$	2.37261e12	1.28417
$533$	−3.29587e12	−1.76888
$534$	−2.64123e11	−0.140563
$535$	2.76301e12	1.45811
$536$	−3.61568e12	−1.89212
$537$	1.39920e11	0.0726096
$538$	1.47694e12	0.760049
$539$	3.78802e10	0.0193314
$540$	9.44947e11	0.478229
$541$	1.41641e12	0.710888	0.355444	−	0.934698i	$-0.384330\pi$
$541$	1.41641e12	0.710888	0.355444	+	0.934698i	$0.384330\pi$
$542$	−6.16249e12	−3.06732
$543$	1.58293e11	0.0781381
$544$	−1.77090e12	−0.866960
$545$	4.42787e11	0.214986
$546$	−3.52263e11	−0.169629
$547$	−2.94469e12	−1.40636	−0.703180	−	0.711012i	$-0.748237\pi$
$547$	−2.94469e12	−1.40636	−0.703180	+	0.711012i	$0.748237\pi$
$548$	2.23490e11	0.105863
$549$	−2.59356e12	−1.21849
$550$	−4.99669e12	−2.32836
$551$	−1.50160e12	−0.694020
$552$	−1.38056e11	−0.0632892
$553$	−2.18909e12	−0.995408
$554$	2.20723e12	0.995529
$555$	−3.25535e11	−0.145639
$556$	−5.61049e12	−2.48980
$557$	−1.25037e11	−0.0550413	−0.0275207	−	0.999621i	$-0.508761\pi$
$557$	−1.25037e11	−0.0550413	−0.0275207	+	0.999621i	$0.508761\pi$
$558$	−2.95491e12	−1.29030
$559$	2.87909e12	1.24710
$560$	1.36247e12	0.585437
$561$	3.19781e11	0.136307
$562$	−7.40465e12	−3.13106
$563$	−2.65624e12	−1.11424	−0.557121	−	0.830431i	$-0.688094\pi$
$563$	−2.65624e12	−1.11424	−0.557121	+	0.830431i	$0.688094\pi$
$564$	−3.45894e11	−0.143942
$565$	−8.83395e11	−0.364701
$566$	1.71394e12	0.701977
$567$	2.38069e12	0.967341
$568$	−3.37724e12	−1.36143
$569$	2.28987e12	0.915809	0.457904	−	0.889001i	$-0.348600\pi$
$569$	2.28987e12	0.915809	0.457904	+	0.889001i	$0.348600\pi$
$570$	−4.11464e11	−0.163266
$571$	−1.03100e12	−0.405878	−0.202939	−	0.979191i	$-0.565049\pi$
$571$	−1.03100e12	−0.405878	−0.202939	+	0.979191i	$0.565049\pi$
$572$	−5.86725e12	−2.29167
$573$	2.63468e11	0.102102
$574$	−6.68020e12	−2.56854
$575$	1.74486e12	0.665663
$576$	3.86121e12	1.46158
$577$	2.39754e12	0.900482	0.450241	−	0.892907i	$-0.351338\pi$
$577$	2.39754e12	0.900482	0.450241	+	0.892907i	$0.351338\pi$
$578$	3.56949e12	1.33024
$579$	−1.94473e10	−0.00719129
$580$	−6.93869e12	−2.54596
$581$	−1.66365e11	−0.0605716
$582$	−6.22836e11	−0.225020
$583$	−2.91304e12	−1.04433
$584$	−4.17865e12	−1.48655
$585$	−4.78551e12	−1.68938
$586$	−7.13160e12	−2.49832
$587$	1.65092e12	0.573925	0.286962	−	0.957942i	$-0.407355\pi$
$587$	1.65092e12	0.573925	0.286962	+	0.957942i	$0.407355\pi$
$588$	7.96911e9	0.00274924
$589$	1.65526e12	0.566694
$590$	−6.03207e12	−2.04943
$591$	−1.90310e10	−0.00641680
$592$	1.27596e12	0.426963
$593$	2.06402e12	0.685438	0.342719	−	0.939438i	$-0.388652\pi$
$593$	2.06402e12	0.685438	0.342719	+	0.939438i	$0.388652\pi$
$594$	−1.02497e12	−0.337811
$595$	6.07701e12	1.98776
$596$	−8.24389e12	−2.67623
$597$	−3.38279e11	−0.108991
$598$	3.19828e12	1.02273
$599$	8.93661e11	0.283630	0.141815	−	0.989893i	$-0.454706\pi$
$599$	8.93661e11	0.283630	0.141815	+	0.989893i	$0.454706\pi$
$600$	−4.61468e11	−0.145365
$601$	−5.36661e12	−1.67789	−0.838947	−	0.544213i	$-0.816828\pi$
$601$	−5.36661e12	−1.67789	−0.838947	+	0.544213i	$0.816828\pi$
$602$	5.83546e12	1.81089
$603$	4.66792e12	1.43779
$604$	−1.05970e12	−0.323980
$605$	1.35184e12	0.410229
$606$	6.68947e11	0.201495
$607$	6.31098e12	1.88690	0.943448	−	0.331521i	$-0.107562\pi$
$607$	6.31098e12	1.88690	0.943448	+	0.331521i	$0.107562\pi$
$608$	−1.58334e12	−0.469904
$609$	2.89475e11	0.0852772
$610$	1.04796e13	3.06451
$611$	3.51775e12	1.02113
$612$	−8.22639e12	−2.37043
$613$	−4.30294e12	−1.23082	−0.615408	−	0.788209i	$-0.711009\pi$
$613$	−4.30294e12	−1.23082	−0.615408	+	0.788209i	$0.711009\pi$
$614$	−3.22420e12	−0.915513
$615$	7.42149e11	0.209196
$616$	−5.22055e12	−1.46084
$617$	−3.56214e12	−0.989527	−0.494764	−	0.869028i	$-0.664745\pi$
$617$	−3.56214e12	−0.989527	−0.494764	+	0.869028i	$0.664745\pi$
$618$	−6.99272e11	−0.192840
$619$	1.20507e12	0.329918	0.164959	−	0.986300i	$-0.447251\pi$
$619$	1.20507e12	0.329918	0.164959	+	0.986300i	$0.447251\pi$
$620$	7.64874e12	2.07887
$621$	3.57924e11	0.0965780
$622$	−3.83459e12	−1.02722
$623$	3.48774e12	0.927574
$624$	−1.53394e11	−0.0405022
$625$	−2.69918e12	−0.707573
$626$	−4.31694e12	−1.12355
$627$	2.85912e11	0.0738804
$628$	6.16262e12	1.58105
$629$	5.69117e12	1.44969
$630$	−9.69947e12	−2.45310
$631$	−6.09945e11	−0.153165	−0.0765823	−	0.997063i	$-0.524401\pi$
$631$	−6.09945e11	−0.153165	−0.0765823	+	0.997063i	$0.524401\pi$
$632$	−5.25648e12	−1.31059
$633$	−1.08546e11	−0.0268719
$634$	6.66925e11	0.163936
$635$	8.04365e12	1.96323
$636$	−6.12835e11	−0.148521
$637$	−8.10462e10	−0.0195032
$638$	7.52631e12	1.79841
$639$	4.36008e12	1.03452
$640$	−1.14972e13	−2.70884
$641$	3.83813e12	0.897964	0.448982	−	0.893541i	$-0.351787\pi$
$641$	3.83813e12	0.897964	0.448982	+	0.893541i	$0.351787\pi$
$642$	−6.30499e11	−0.146479
$643$	−1.40801e12	−0.324830	−0.162415	−	0.986723i	$-0.551928\pi$
$643$	−1.40801e12	−0.324830	−0.162415	+	0.986723i	$0.551928\pi$
$644$	4.15272e12	0.951362
$645$	−6.48301e11	−0.147488
$646$	7.19343e12	1.62514
$647$	6.97386e12	1.56460	0.782301	−	0.622900i	$-0.214046\pi$
$647$	6.97386e12	1.56460	0.782301	+	0.622900i	$0.214046\pi$
$648$	5.71655e12	1.27364
$649$	4.19148e12	0.927399
$650$	1.06906e13	2.34905
$651$	−3.19098e11	−0.0696320
$652$	1.07350e13	2.32643
$653$	−6.98633e11	−0.150363	−0.0751813	−	0.997170i	$-0.523954\pi$
$653$	−6.98633e11	−0.150363	−0.0751813	+	0.997170i	$0.523954\pi$
$654$	−1.01041e11	−0.0215972
$655$	6.73758e12	1.43027
$656$	−2.90892e12	−0.613288
$657$	5.39473e12	1.12960
$658$	7.12993e12	1.48275
$659$	−3.69601e12	−0.763395	−0.381697	−	0.924287i	$-0.624660\pi$
$659$	−3.69601e12	−0.763395	−0.381697	+	0.924287i	$0.624660\pi$
$660$	1.32116e12	0.271024
$661$	4.47465e11	0.0911702	0.0455851	−	0.998960i	$-0.485485\pi$
$661$	4.47465e11	0.0911702	0.0455851	+	0.998960i	$0.485485\pi$
$662$	7.48846e12	1.51542
$663$	−6.84183e11	−0.137519
$664$	−3.99478e11	−0.0797510
$665$	5.43339e12	1.07739
$666$	−9.08364e12	−1.78906
$667$	−2.62821e12	−0.514155
$668$	−1.60003e13	−3.10909
$669$	−6.65547e11	−0.128458
$670$	−1.88613e13	−3.61606
$671$	−7.28193e12	−1.38674
$672$	3.05233e11	0.0577390
$673$	−3.81682e11	−0.0717189	−0.0358595	−	0.999357i	$-0.511417\pi$
$673$	−3.81682e11	−0.0717189	−0.0358595	+	0.999357i	$0.511417\pi$
$674$	8.95560e12	1.67157
$675$	1.19640e12	0.221824
$676$	2.87501e12	0.529516
$677$	8.70178e12	1.59206	0.796030	−	0.605257i	$-0.206930\pi$
$677$	8.70178e12	1.59206	0.796030	+	0.605257i	$0.206930\pi$
$678$	2.01585e11	0.0366373
$679$	8.22456e12	1.48491
$680$	1.45922e13	2.61716
$681$	8.46642e11	0.150847
$682$	−8.29650e12	−1.46847
$683$	7.76587e12	1.36552	0.682758	−	0.730644i	$-0.260780\pi$
$683$	7.76587e12	1.36552	0.682758	+	0.730644i	$0.260780\pi$
$684$	−7.35513e12	−1.28481
$685$	5.11802e11	0.0888166
$686$	−9.75666e12	−1.68206
$687$	7.67766e11	0.131499
$688$	2.54108e12	0.432384
$689$	6.23256e12	1.05361
$690$	−7.20174e11	−0.120953
$691$	−9.69765e12	−1.61814	−0.809068	−	0.587715i	$-0.800028\pi$
$691$	−9.69765e12	−1.61814	−0.809068	+	0.587715i	$0.800028\pi$
$692$	−2.07926e13	−3.44692
$693$	6.73983e12	1.11007
$694$	4.56717e12	0.747360
$695$	−1.28483e13	−2.08888
$696$	6.95091e11	0.112279
$697$	−1.29746e13	−2.08232
$698$	−1.04251e13	−1.66239
$699$	2.73151e11	0.0432768
$700$	1.38809e13	2.18513
$701$	−4.37598e12	−0.684454	−0.342227	−	0.939617i	$-0.611181\pi$
$701$	−4.37598e12	−0.684454	−0.342227	+	0.939617i	$0.611181\pi$
$702$	2.19297e12	0.340813
$703$	5.08842e12	0.785749
$704$	1.08411e13	1.66340
$705$	−7.92112e11	−0.120763
$706$	−4.54199e12	−0.688058
$707$	−8.83346e12	−1.32967
$708$	8.81790e11	0.131891
$709$	1.25705e13	1.86829	0.934144	−	0.356895i	$-0.116165\pi$
$709$	1.25705e13	1.86829	0.934144	+	0.356895i	$0.116165\pi$
$710$	−1.76175e13	−2.60185
$711$	6.78622e12	0.995898
$712$	8.37482e12	1.22128
$713$	2.89716e12	0.419827
$714$	−1.38673e12	−0.199687
$715$	−1.34363e13	−1.92266
$716$	−1.01062e13	−1.43707
$717$	2.60445e11	0.0368027
$718$	−1.56056e12	−0.219139
$719$	2.15235e12	0.300354	0.150177	−	0.988659i	$-0.452016\pi$
$719$	2.15235e12	0.300354	0.150177	+	0.988659i	$0.452016\pi$
$720$	−4.22367e12	−0.585725
$721$	9.23389e12	1.27255
$722$	−5.74814e12	−0.787245
$723$	9.25841e11	0.126013
$724$	−1.14333e13	−1.54649
$725$	−8.78509e12	−1.18093
$726$	−3.08481e11	−0.0412110
$727$	9.51298e12	1.26302	0.631512	−	0.775366i	$-0.282435\pi$
$727$	9.51298e12	1.26302	0.631512	+	0.775366i	$0.282435\pi$
$728$	1.11696e13	1.47382
$729$	−7.25697e12	−0.951659
$730$	−2.17981e13	−2.84096
$731$	1.13339e13	1.46809
$732$	−1.53195e12	−0.197217
$733$	1.51345e13	1.93642	0.968211	−	0.250134i	$-0.0804748\pi$
$733$	1.51345e13	1.93642	0.968211	+	0.250134i	$0.0804748\pi$
$734$	1.13836e13	1.44759
$735$	1.82496e10	0.00230654
$736$	−2.77128e12	−0.348121
$737$	1.31061e13	1.63633
$738$	2.07087e13	2.56980
$739$	−3.27729e12	−0.404217	−0.202109	−	0.979363i	$-0.564779\pi$
$739$	−3.27729e12	−0.404217	−0.202109	+	0.979363i	$0.564779\pi$
$740$	2.35129e13	2.88246
$741$	−6.11721e11	−0.0745369
$742$	1.26324e13	1.52992
$743$	−1.44664e13	−1.74145	−0.870723	−	0.491775i	$-0.836348\pi$
$743$	−1.44664e13	−1.74145	−0.870723	+	0.491775i	$0.836348\pi$
$744$	−7.66221e11	−0.0916803
$745$	−1.88789e13	−2.24529
$746$	−1.95864e12	−0.231542
$747$	5.15734e11	0.0606014
$748$	−2.30972e13	−2.69776
$749$	8.32575e12	0.966618
$750$	−4.60421e11	−0.0531349
$751$	9.62879e12	1.10457	0.552283	−	0.833656i	$-0.313757\pi$
$751$	9.62879e12	1.10457	0.552283	+	0.833656i	$0.313757\pi$
$752$	3.10476e12	0.354036
$753$	−5.93251e11	−0.0672451
$754$	−1.61028e13	−1.81439
$755$	−2.42677e12	−0.271811
$756$	2.84740e12	0.317030
$757$	−1.66900e13	−1.84725	−0.923623	−	0.383302i	$-0.874787\pi$
$757$	−1.66900e13	−1.84725	−0.923623	+	0.383302i	$0.874787\pi$
$758$	8.92419e12	0.981878
$759$	5.00425e11	0.0547332
$760$	1.30467e13	1.41854
$761$	−1.68484e12	−0.182108	−0.0910538	−	0.995846i	$-0.529024\pi$
$761$	−1.68484e12	−0.182108	−0.0910538	+	0.995846i	$0.529024\pi$
$762$	−1.83551e12	−0.197223
$763$	1.33425e12	0.142520
$764$	−1.90299e13	−2.02077
$765$	−1.88388e13	−1.98874
$766$	−4.14013e12	−0.434494
$767$	−8.96785e12	−0.935641
$768$	1.34409e12	0.139413
$769$	−5.38645e12	−0.555436	−0.277718	−	0.960663i	$-0.589578\pi$
$769$	−5.38645e12	−0.555436	−0.277718	+	0.960663i	$0.589578\pi$
$770$	−2.72332e13	−2.79184
$771$	−1.90986e11	−0.0194651
$772$	1.40465e12	0.142328
$773$	2.71716e12	0.273720	0.136860	−	0.990590i	$-0.456299\pi$
$773$	2.71716e12	0.273720	0.136860	+	0.990590i	$0.456299\pi$
$774$	−1.80900e13	−1.81178
$775$	9.68409e12	0.964276
$776$	1.97489e13	1.95509
$777$	−9.80932e11	−0.0965482
$778$	1.42770e13	1.39710
$779$	−1.16005e13	−1.12864
$780$	−2.82668e12	−0.273433
$781$	1.22418e13	1.17738
$782$	1.25905e13	1.20396
$783$	−1.80209e12	−0.171336
$784$	−7.15311e10	−0.00676196
$785$	1.41127e13	1.32647
$786$	−1.53747e12	−0.143683
$787$	−7.14537e12	−0.663954	−0.331977	−	0.943287i	$-0.607716\pi$
$787$	−7.14537e12	−0.663954	−0.331977	+	0.943287i	$0.607716\pi$
$788$	1.37458e12	0.126999
$789$	−3.76551e11	−0.0345921
$790$	−2.74206e13	−2.50470
$791$	−2.66193e12	−0.241770
$792$	1.61838e13	1.46156
$793$	1.55800e13	1.39906
$794$	8.56908e12	0.765142
$795$	−1.40342e12	−0.124605
$796$	2.44333e13	2.15712
$797$	−1.34979e13	−1.18496	−0.592482	−	0.805584i	$-0.701852\pi$
$797$	−1.34979e13	−1.18496	−0.592482	+	0.805584i	$0.701852\pi$
$798$	−1.23986e12	−0.108233
$799$	1.38481e13	1.20207
$800$	−9.26332e12	−0.799580
$801$	−1.08121e13	−0.928030
$802$	2.55192e12	0.217812
$803$	1.51468e13	1.28558
$804$	2.75722e12	0.232712
$805$	9.50991e12	0.798169
$806$	1.77507e13	1.48152
$807$	−4.94430e11	−0.0410368
$808$	−2.12110e13	−1.75069
$809$	−4.56990e12	−0.375092	−0.187546	−	0.982256i	$-0.560053\pi$
$809$	−4.56990e12	−0.375092	−0.187546	+	0.982256i	$0.560053\pi$
$810$	2.98206e13	2.43407
$811$	−2.23553e12	−0.181462	−0.0907311	−	0.995875i	$-0.528920\pi$
$811$	−2.23553e12	−0.181462	−0.0907311	+	0.995875i	$0.528920\pi$
$812$	−2.09083e13	−1.68778
$813$	2.06300e12	0.165612
$814$	−2.55041e13	−2.03611
$815$	2.45837e13	1.95181
$816$	−6.03858e11	−0.0476792
$817$	1.01336e13	0.795724
$818$	−2.36548e13	−1.84727
$819$	−1.44201e13	−1.11993
$820$	−5.36042e13	−4.14034
$821$	−1.00661e13	−0.773246	−0.386623	−	0.922238i	$-0.626359\pi$
$821$	−1.00661e13	−0.773246	−0.386623	+	0.922238i	$0.626359\pi$
$822$	−1.16790e11	−0.00892238
$823$	1.79418e13	1.36323	0.681613	−	0.731713i	$-0.261279\pi$
$823$	1.79418e13	1.36323	0.681613	+	0.731713i	$0.261279\pi$
$824$	2.21725e13	1.67550
$825$	1.67273e12	0.125714
$826$	−1.81764e13	−1.35862
$827$	1.53344e12	0.113997	0.0569984	−	0.998374i	$-0.481847\pi$
$827$	1.53344e12	0.113997	0.0569984	+	0.998374i	$0.481847\pi$
$828$	−1.28735e13	−0.951830
$829$	−1.99317e13	−1.46571	−0.732857	−	0.680383i	$-0.761813\pi$
$829$	−1.99317e13	−1.46571	−0.732857	+	0.680383i	$0.761813\pi$
$830$	−2.08389e12	−0.152413
$831$	−7.38908e11	−0.0537509
$832$	−2.31950e13	−1.67819
$833$	−3.19050e11	−0.0229591
$834$	2.93189e12	0.209846
$835$	−3.66414e13	−2.60845
$836$	−2.06510e13	−1.46222
$837$	1.98650e12	0.139902
$838$	1.13779e13	0.797010
$839$	3.30735e12	0.230437	0.115218	−	0.993340i	$-0.463243\pi$
$839$	3.30735e12	0.230437	0.115218	+	0.993340i	$0.463243\pi$
$840$	−2.51511e12	−0.174301
$841$	−1.27450e12	−0.0878536
$842$	4.49335e13	3.08081
$843$	2.47883e12	0.169053
$844$	7.84012e12	0.531841
$845$	6.58391e12	0.444251
$846$	−2.21029e13	−1.48348
$847$	4.07349e12	0.271952
$848$	5.50083e12	0.365298
$849$	−5.73772e11	−0.0379014
$850$	4.20850e13	2.76530
$851$	8.90612e12	0.582110
$852$	2.57539e12	0.167442
$853$	−1.64413e13	−1.06332	−0.531662	−	0.846957i	$-0.678432\pi$
$853$	−1.64413e13	−1.06332	−0.531662	+	0.846957i	$0.678432\pi$
$854$	3.15781e13	2.03154
$855$	−1.68436e13	−1.07792
$856$	1.99919e13	1.27269
$857$	8.18562e12	0.518368	0.259184	−	0.965828i	$-0.416546\pi$
$857$	8.18562e12	0.518368	0.259184	+	0.965828i	$0.416546\pi$
$858$	3.06606e12	0.193147
$859$	2.72058e13	1.70487	0.852436	−	0.522831i	$-0.175124\pi$
$859$	2.72058e13	1.70487	0.852436	+	0.522831i	$0.175124\pi$
$860$	4.68257e13	2.91905
$861$	2.23631e12	0.138681
$862$	3.33915e13	2.05994
$863$	1.73975e13	1.06767	0.533835	−	0.845589i	$-0.320750\pi$
$863$	1.73975e13	1.06767	0.533835	+	0.845589i	$0.320750\pi$
$864$	−1.90019e12	−0.116007
$865$	−4.76161e13	−2.89188
$866$	1.30931e13	0.791067
$867$	−1.19495e12	−0.0718229
$868$	2.30479e13	1.37814
$869$	1.90537e13	1.13342
$870$	3.62597e12	0.214579
$871$	−2.80411e13	−1.65087
$872$	3.20381e12	0.187647
$873$	−2.54963e13	−1.48564
$874$	1.12570e13	0.652561
$875$	6.07987e12	0.350637
$876$	3.18653e12	0.182831
$877$	−1.12698e13	−0.643305	−0.321653	−	0.946858i	$-0.604238\pi$
$877$	−1.12698e13	−0.643305	−0.321653	+	0.946858i	$0.604238\pi$
$878$	1.10933e13	0.629992
$879$	2.38742e12	0.134890
$880$	−1.18588e13	−0.666605
$881$	−7.04811e12	−0.394167	−0.197084	−	0.980387i	$-0.563147\pi$
$881$	−7.04811e12	−0.394167	−0.197084	+	0.980387i	$0.563147\pi$
$882$	5.09233e11	0.0283340
$883$	−2.02190e13	−1.11927	−0.559636	−	0.828738i	$-0.689059\pi$
$883$	−2.02190e13	−1.11927	−0.559636	+	0.828738i	$0.689059\pi$
$884$	4.94175e13	2.72173
$885$	2.01934e12	0.110653
$886$	−3.09157e13	−1.68550
$887$	2.47730e13	1.34376	0.671882	−	0.740658i	$-0.265486\pi$
$887$	2.47730e13	1.34376	0.671882	+	0.740658i	$0.265486\pi$
$888$	−2.35543e12	−0.127119
$889$	2.42379e13	1.30148
$890$	4.36876e13	2.33401
$891$	−2.07213e13	−1.10146
$892$	4.80714e13	2.54240
$893$	1.23815e13	0.651538
$894$	4.30803e12	0.225559
$895$	−2.31436e13	−1.20567
$896$	−3.46445e13	−1.79576
$897$	−1.07068e12	−0.0552196
$898$	4.24424e13	2.17799
$899$	−1.45868e13	−0.744802
$900$	−4.30311e13	−2.18620
$901$	2.45353e13	1.24031
$902$	5.81438e13	2.92465
$903$	−1.95352e12	−0.0977739
$904$	−6.39185e12	−0.318324
$905$	−2.61827e13	−1.29746
$906$	5.53772e11	0.0273057
$907$	−3.25103e13	−1.59510	−0.797551	−	0.603251i	$-0.793872\pi$
$907$	−3.25103e13	−1.59510	−0.797551	+	0.603251i	$0.793872\pi$
$908$	−6.11516e13	−2.98553
$909$	2.73838e13	1.33032
$910$	5.82665e13	2.81665
$911$	−1.03382e11	−0.00497292	−0.00248646	−	0.999997i	$-0.500791\pi$
$911$	−1.03382e11	−0.00497292	−0.00248646	+	0.999997i	$0.500791\pi$
$912$	−5.39903e11	−0.0258427
$913$	1.44803e12	0.0689696
$914$	−8.51069e12	−0.403373
$915$	−3.50823e12	−0.165460
$916$	−5.54545e13	−2.60260
$917$	2.03023e13	0.948163
$918$	8.63293e12	0.401205
$919$	3.52155e13	1.62860	0.814298	−	0.580446i	$-0.197122\pi$
$919$	3.52155e13	1.62860	0.814298	+	0.580446i	$0.197122\pi$
$920$	2.28353e13	1.05090
$921$	1.07936e12	0.0494307
$922$	4.34301e13	1.97925
$923$	−2.61918e13	−1.18784
$924$	3.98105e12	0.179669
$925$	2.97697e13	1.33702
$926$	−4.31994e13	−1.93076
$927$	−2.86252e13	−1.27318
$928$	1.39530e13	0.617591
$929$	2.63485e13	1.16061	0.580304	−	0.814400i	$-0.302934\pi$
$929$	2.63485e13	1.16061	0.580304	+	0.814400i	$0.302934\pi$
$930$	−3.99702e12	−0.175212
$931$	−2.85259e11	−0.0124442
$932$	−1.97292e13	−0.856523
$933$	1.28370e12	0.0554619
$934$	4.18811e13	1.80077
$935$	−5.28937e13	−2.26335
$936$	−3.46258e13	−1.47455
$937$	−1.91087e12	−0.0809847	−0.0404923	−	0.999180i	$-0.512893\pi$
$937$	−1.91087e12	−0.0809847	−0.0404923	+	0.999180i	$0.512893\pi$
$938$	−5.68347e13	−2.39718
$939$	1.44517e12	0.0606630
$940$	5.72130e13	2.39012
$941$	3.81321e13	1.58539	0.792697	−	0.609616i	$-0.208676\pi$
$941$	3.81321e13	1.58539	0.792697	+	0.609616i	$0.208676\pi$
$942$	−3.22041e12	−0.133255
$943$	−2.03040e13	−0.836140
$944$	−7.91499e12	−0.324397
$945$	6.52068e12	0.265981
$946$	−5.07913e13	−2.06196
$947$	−8.41980e12	−0.340194	−0.170097	−	0.985427i	$-0.554408\pi$
$947$	−8.41980e12	−0.340194	−0.170097	+	0.985427i	$0.554408\pi$
$948$	4.00844e12	0.161190
$949$	−3.24071e13	−1.29701
$950$	3.76278e13	1.49883
$951$	−2.23264e11	−0.00885131
$952$	4.39705e13	1.73498
$953$	1.15938e13	0.455310	0.227655	−	0.973742i	$-0.426894\pi$
$953$	1.15938e13	0.455310	0.227655	+	0.973742i	$0.426894\pi$
$954$	−3.91607e13	−1.53067
$955$	−4.35793e13	−1.69537
$956$	−1.88115e13	−0.728388
$957$	−2.51956e12	−0.0971005
$958$	−4.89314e13	−1.87691
$959$	1.54221e12	0.0588788
$960$	5.22295e12	0.198470
$961$	−1.03601e13	−0.391841
$962$	5.45671e13	2.05420
$963$	−2.58099e13	−0.967094
$964$	−6.68720e13	−2.49401
$965$	3.21671e12	0.119410
$966$	−2.17010e12	−0.0801829
$967$	5.28976e12	0.194543	0.0972717	−	0.995258i	$-0.468988\pi$
$967$	5.28976e12	0.194543	0.0972717	+	0.995258i	$0.468988\pi$
$968$	9.78132e12	0.358062
$969$	−2.40812e12	−0.0877449
$970$	1.03021e14	3.73640
$971$	1.71219e13	0.618108	0.309054	−	0.951045i	$-0.399988\pi$
$971$	1.71219e13	0.618108	0.309054	+	0.951045i	$0.399988\pi$
$972$	−1.32585e13	−0.476425
$973$	−3.87156e13	−1.38477
$974$	−4.49050e13	−1.59875
$975$	−3.57886e12	−0.126831
$976$	1.37508e13	0.485070
$977$	1.06777e13	0.374932	0.187466	−	0.982271i	$-0.439973\pi$
$977$	1.06777e13	0.374932	0.187466	+	0.982271i	$0.439973\pi$
$978$	−5.60983e12	−0.196076
$979$	−3.03570e13	−1.05618
$980$	−1.31814e12	−0.0456504
$981$	−4.13618e12	−0.142590
$982$	3.58840e13	1.23140
$983$	4.51168e13	1.54116	0.770579	−	0.637344i	$-0.219967\pi$
$983$	4.51168e13	1.54116	0.770579	+	0.637344i	$0.219967\pi$
$984$	5.36986e12	0.182593
$985$	3.14785e12	0.106549
$986$	−6.33910e13	−2.13590
$987$	−2.38686e12	−0.0800572
$988$	4.41836e13	1.47521
$989$	1.77365e13	0.589500
$990$	8.44233e13	2.79321
$991$	1.01742e13	0.335095	0.167548	−	0.985864i	$-0.446415\pi$
$991$	1.01742e13	0.335095	0.167548	+	0.985864i	$0.446415\pi$
$992$	−1.53808e13	−0.504286
$993$	−2.50689e12	−0.0818208
$994$	−5.30867e13	−1.72483
$995$	5.59534e13	1.80977
$996$	3.04631e11	0.00980859
$997$	2.59997e13	0.833376	0.416688	−	0.909050i	$-0.363191\pi$
$997$	2.59997e13	0.833376	0.416688	+	0.909050i	$0.363191\pi$
$998$	4.79127e13	1.52884
$999$	6.10667e12	0.193981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.b.1.67	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.b.1.67	✓	76	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q+37.7446 q^{2} -12.6356 q^{3} +912.651 q^{4} +2090.01 q^{5} -476.926 q^{6} +6297.82 q^{7} +15122.4 q^{8} -19523.3 q^{9} +78886.6 q^{10} -54815.7 q^{11} -11531.9 q^{12} +117280. q^{13} +237708. q^{14} -26408.7 q^{15} +103511. q^{16} +461690. q^{17} -736900. q^{18} +412792. q^{19} +1.90745e6 q^{20} -79577.0 q^{21} -2.06899e6 q^{22} +722499. q^{23} -191081. q^{24} +2.41503e6 q^{25} +4.42669e6 q^{26} +495397. q^{27} +5.74772e6 q^{28} -3.63767e6 q^{29} -996783. q^{30} +4.00992e6 q^{31} -3.83569e6 q^{32} +692631. q^{33} +1.74263e7 q^{34} +1.31625e7 q^{35} -1.78180e7 q^{36} +1.23268e7 q^{37} +1.55806e7 q^{38} -1.48191e6 q^{39} +3.16060e7 q^{40} -2.81025e7 q^{41} -3.00360e6 q^{42} +2.45488e7 q^{43} -5.00276e7 q^{44} -4.08041e7 q^{45} +2.72704e7 q^{46} +2.99944e7 q^{47} -1.30793e6 q^{48} -691047. q^{49} +9.11543e7 q^{50} -5.83375e6 q^{51} +1.07036e8 q^{52} +5.31424e7 q^{53} +1.86985e7 q^{54} -1.14565e8 q^{55} +9.52382e7 q^{56} -5.21589e6 q^{57} -1.37302e8 q^{58} -7.64651e7 q^{59} -2.41019e7 q^{60} +1.32844e8 q^{61} +1.51353e8 q^{62} -1.22955e8 q^{63} -1.97774e8 q^{64} +2.45117e8 q^{65} +2.61430e7 q^{66} -2.39094e8 q^{67} +4.21362e8 q^{68} -9.12923e6 q^{69} +4.96814e8 q^{70} -2.23327e8 q^{71} -2.95240e8 q^{72} -2.76322e8 q^{73} +4.65271e8 q^{74} -3.05155e7 q^{75} +3.76735e8 q^{76} -3.45219e8 q^{77} -5.59341e7 q^{78} -3.47595e8 q^{79} +2.16340e8 q^{80} +3.78018e8 q^{81} -1.06072e9 q^{82} -2.64163e7 q^{83} -7.26261e7 q^{84} +9.64938e8 q^{85} +9.26584e8 q^{86} +4.59643e7 q^{87} -8.28945e8 q^{88} +5.53802e8 q^{89} -1.54013e9 q^{90} +7.38611e8 q^{91} +6.59389e8 q^{92} -5.06679e7 q^{93} +1.13213e9 q^{94} +8.62741e8 q^{95} +4.84664e7 q^{96} +1.30594e9 q^{97} -2.60833e7 q^{98} +1.07018e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15}+ \cdots + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * q^99

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