LMFDB - Embedded newform 197.8.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,8,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, 8, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 8 $
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:	$61.5398500204$
Analytic rank:	$1$
Dimension:	$55$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	\(q-19.8304 q^{2} -24.8621 q^{3} +265.245 q^{4} -146.760 q^{5} +493.027 q^{6} -946.144 q^{7} -2721.63 q^{8} -1568.87 q^{9} +2910.32 q^{10} +5267.06 q^{11} -6594.57 q^{12} +5561.59 q^{13} +18762.4 q^{14} +3648.78 q^{15} +20019.7 q^{16} -26574.1 q^{17} +31111.4 q^{18} -24708.6 q^{19} -38927.5 q^{20} +23523.2 q^{21} -104448. q^{22} +51814.8 q^{23} +67665.7 q^{24} -56586.4 q^{25} -110289. q^{26} +93379.1 q^{27} -250960. q^{28} -226216. q^{29} -72356.8 q^{30} +246250. q^{31} -48630.1 q^{32} -130950. q^{33} +526975. q^{34} +138856. q^{35} -416136. q^{36} +283573. q^{37} +489981. q^{38} -138273. q^{39} +399428. q^{40} +570412. q^{41} -466474. q^{42} +515728. q^{43} +1.39706e6 q^{44} +230248. q^{45} -1.02751e6 q^{46} +1.02847e6 q^{47} -497733. q^{48} +71645.2 q^{49} +1.12213e6 q^{50} +660689. q^{51} +1.47518e6 q^{52} -1.60897e6 q^{53} -1.85175e6 q^{54} -772995. q^{55} +2.57506e6 q^{56} +614308. q^{57} +4.48596e6 q^{58} +1.83722e6 q^{59} +967822. q^{60} +352085. q^{61} -4.88325e6 q^{62} +1.48438e6 q^{63} -1.59817e6 q^{64} -816220. q^{65} +2.59680e6 q^{66} -3.13851e6 q^{67} -7.04866e6 q^{68} -1.28823e6 q^{69} -2.75358e6 q^{70} +2.15957e6 q^{71} +4.26990e6 q^{72} +866346. q^{73} -5.62337e6 q^{74} +1.40686e6 q^{75} -6.55383e6 q^{76} -4.98339e6 q^{77} +2.74201e6 q^{78} +7.48766e6 q^{79} -2.93810e6 q^{80} +1.10952e6 q^{81} -1.13115e7 q^{82} +6.07920e6 q^{83} +6.23941e6 q^{84} +3.90002e6 q^{85} -1.02271e7 q^{86} +5.62422e6 q^{87} -1.43350e7 q^{88} +1.00861e7 q^{89} -4.56592e6 q^{90} -5.26206e6 q^{91} +1.37436e7 q^{92} -6.12231e6 q^{93} -2.03949e7 q^{94} +3.62624e6 q^{95} +1.20905e6 q^{96} -8.98768e6 q^{97} -1.42075e6 q^{98} -8.26335e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 55 q - 24 q^{2} - 298 q^{3} + 3264 q^{4} - 946 q^{5} - 960 q^{6} - 6017 q^{7} - 5109 q^{8} + 36449 q^{9} - 9763 q^{10} - 11506 q^{11} - 37376 q^{12} - 33844 q^{13} - 33495 q^{14} - 25861 q^{15} + 176128 q^{16}+ \cdots - 85438141 q^{99}+O(q^{100}) $ 55 * q - 24 * q^2 - 298 * q^3 + 3264 * q^4 - 946 * q^5 - 960 * q^6 - 6017 * q^7 - 5109 * q^8 + 36449 * q^9 - 9763 * q^10 - 11506 * q^11 - 37376 * q^12 - 33844 * q^13 - 33495 * q^14 - 25861 * q^15 + 176128 * q^16 - 55125 * q^17 - 69815 * q^18 - 205015 * q^19 - 209621 * q^20 - 76786 * q^21 - 184567 * q^22 - 132580 * q^23 - 126075 * q^24 + 703595 * q^25 - 802 * q^26 - 942457 * q^27 - 980794 * q^28 - 180975 * q^29 - 231365 * q^30 - 752200 * q^31 - 458116 * q^32 - 1189462 * q^33 - 534334 * q^34 - 501828 * q^35 + 2216122 * q^36 - 1812550 * q^37 - 1732590 * q^38 - 316133 * q^39 - 2564154 * q^40 + 387642 * q^41 - 1974005 * q^42 - 3120525 * q^43 - 1010046 * q^44 - 4004703 * q^45 - 2804563 * q^46 - 1968319 * q^47 - 5200654 * q^48 + 3219122 * q^49 + 5080367 * q^50 + 4015335 * q^51 - 105242 * q^52 + 793560 * q^53 + 9980039 * q^54 - 2193645 * q^55 + 7180088 * q^56 - 848029 * q^57 - 4318541 * q^58 - 4206985 * q^59 - 3767411 * q^60 - 3233922 * q^61 - 4798113 * q^62 - 16370607 * q^63 - 3153855 * q^64 - 5234873 * q^65 - 27799028 * q^66 - 29330378 * q^67 - 38894327 * q^68 - 12421645 * q^69 - 42976929 * q^70 - 20675277 * q^71 - 57843841 * q^72 - 21269365 * q^73 - 32764695 * q^74 - 51817010 * q^75 - 59377690 * q^76 - 16275190 * q^77 - 85089407 * q^78 - 28033705 * q^79 - 75304702 * q^80 - 923221 * q^81 - 54988201 * q^82 - 35573360 * q^83 - 80450394 * q^84 - 33089314 * q^85 - 71770618 * q^86 - 38591063 * q^87 - 62367981 * q^88 - 22496216 * q^89 - 138633489 * q^90 - 69344213 * q^91 - 112457146 * q^92 - 38701181 * q^93 - 49016719 * q^94 - 35589281 * q^95 - 173964883 * q^96 - 59838870 * q^97 - 95514862 * q^98 - 85438141 * 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 $

$2$	−19.8304	−1.75278	−0.876389	−	0.481604i	$-0.840054\pi$
$2$	−19.8304	−1.75278	−0.876389	+	0.481604i	$0.840054\pi$
$3$	−24.8621	−0.531636	−0.265818	−	0.964023i	$-0.585642\pi$
$3$	−24.8621	−0.531636	−0.265818	+	0.964023i	$0.585642\pi$
$4$	265.245	2.07223
$5$	−146.760	−0.525066	−0.262533	−	0.964923i	$-0.584558\pi$
$5$	−146.760	−0.525066	−0.262533	+	0.964923i	$0.584558\pi$
$6$	493.027	0.931840
$7$	−946.144	−1.04259	−0.521296	−	0.853376i	$-0.674551\pi$
$7$	−946.144	−1.04259	−0.521296	+	0.853376i	$0.674551\pi$
$8$	−2721.63	−1.87938
$9$	−1568.87	−0.717363
$10$	2910.32	0.920324
$11$	5267.06	1.19315	0.596573	−	0.802559i	$-0.296529\pi$
$11$	5267.06	1.19315	0.596573	+	0.802559i	$0.296529\pi$
$12$	−6594.57	−1.10167
$13$	5561.59	0.702097	0.351048	−	0.936357i	$-0.385825\pi$
$13$	5561.59	0.702097	0.351048	+	0.936357i	$0.385825\pi$
$14$	18762.4	1.82743
$15$	3648.78	0.279144
$16$	20019.7	1.22191
$17$	−26574.1	−1.31186	−0.655930	−	0.754822i	$-0.727723\pi$
$17$	−26574.1	−1.31186	−0.655930	+	0.754822i	$0.727723\pi$
$18$	31111.4	1.25738
$19$	−24708.6	−0.826437	−0.413219	−	0.910632i	$-0.635595\pi$
$19$	−24708.6	−0.826437	−0.413219	+	0.910632i	$0.635595\pi$
$20$	−38927.5	−1.08806
$21$	23523.2	0.554279
$22$	−104448.	−2.09132
$23$	51814.8	0.887987	0.443993	−	0.896030i	$-0.353561\pi$
$23$	51814.8	0.887987	0.443993	+	0.896030i	$0.353561\pi$
$24$	67665.7	0.999146
$25$	−56586.4	−0.724306
$26$	−110289.	−1.23062
$27$	93379.1	0.913012
$28$	−250960.	−2.16049
$29$	−226216.	−1.72239	−0.861193	−	0.508278i	$-0.830282\pi$
$29$	−226216.	−1.72239	−0.861193	+	0.508278i	$0.830282\pi$
$30$	−72356.8	−0.489277
$31$	246250.	1.48461	0.742303	−	0.670065i	$-0.233734\pi$
$31$	246250.	1.48461	0.742303	+	0.670065i	$0.233734\pi$
$32$	−48630.1	−0.262349
$33$	−130950.	−0.634319
$34$	526975.	2.29940
$35$	138856.	0.547429
$36$	−416136.	−1.48654
$37$	283573.	0.920363	0.460181	−	0.887825i	$-0.347784\pi$
$37$	283573.	0.920363	0.460181	+	0.887825i	$0.347784\pi$
$38$	489981.	1.44856
$39$	−138273.	−0.373260
$40$	399428.	0.986798
$41$	570412.	1.29254	0.646272	−	0.763107i	$-0.276327\pi$
$41$	570412.	1.29254	0.646272	+	0.763107i	$0.276327\pi$
$42$	−466474.	−0.971528
$43$	515728.	0.989194	0.494597	−	0.869122i	$-0.335316\pi$
$43$	515728.	0.989194	0.494597	+	0.869122i	$0.335316\pi$
$44$	1.39706e6	2.47247
$45$	230248.	0.376663
$46$	−1.02751e6	−1.55644
$47$	1.02847e6	1.44493	0.722466	−	0.691406i	$-0.243009\pi$
$47$	1.02847e6	1.44493	0.722466	+	0.691406i	$0.243009\pi$
$48$	−497733.	−0.649609
$49$	71645.2	0.0869963
$50$	1.12213e6	1.26955
$51$	660689.	0.697431
$52$	1.47518e6	1.45491
$53$	−1.60897e6	−1.48450	−0.742252	−	0.670121i	$-0.766242\pi$
$53$	−1.60897e6	−1.48450	−0.742252	+	0.670121i	$0.766242\pi$
$54$	−1.85175e6	−1.60031
$55$	−772995.	−0.626480
$56$	2.57506e6	1.95943
$57$	614308.	0.439364
$58$	4.48596e6	3.01896
$59$	1.83722e6	1.16461	0.582304	−	0.812971i	$-0.302151\pi$
$59$	1.83722e6	1.16461	0.582304	+	0.812971i	$0.302151\pi$
$60$	967822.	0.578450
$61$	352085.	0.198606	0.0993031	−	0.995057i	$-0.468339\pi$
$61$	352085.	0.198606	0.0993031	+	0.995057i	$0.468339\pi$
$62$	−4.88325e6	−2.60218
$63$	1.48438e6	0.747917
$64$	−1.59817e6	−0.762066
$65$	−816220.	−0.368647
$66$	2.59680e6	1.11182
$67$	−3.13851e6	−1.27486	−0.637428	−	0.770510i	$-0.720002\pi$
$67$	−3.13851e6	−1.27486	−0.637428	+	0.770510i	$0.720002\pi$
$68$	−7.04866e6	−2.71847
$69$	−1.28823e6	−0.472086
$70$	−2.75358e6	−0.959521
$71$	2.15957e6	0.716082	0.358041	−	0.933706i	$-0.383445\pi$
$71$	2.15957e6	0.716082	0.358041	+	0.933706i	$0.383445\pi$
$72$	4.26990e6	1.34820
$73$	866346.	0.260652	0.130326	−	0.991471i	$-0.458398\pi$
$73$	866346.	0.260652	0.130326	+	0.991471i	$0.458398\pi$
$74$	−5.62337e6	−1.61319
$75$	1.40686e6	0.385067
$76$	−6.55383e6	−1.71257
$77$	−4.98339e6	−1.24396
$78$	2.74201e6	0.654241
$79$	7.48766e6	1.70864	0.854321	−	0.519746i	$-0.173973\pi$
$79$	7.48766e6	1.70864	0.854321	+	0.519746i	$0.173973\pi$
$80$	−2.93810e6	−0.641581
$81$	1.10952e6	0.231973
$82$	−1.13115e7	−2.26554
$83$	6.07920e6	1.16701	0.583503	−	0.812111i	$-0.301682\pi$
$83$	6.07920e6	1.16701	0.583503	+	0.812111i	$0.301682\pi$
$84$	6.23941e6	1.14859
$85$	3.90002e6	0.688813
$86$	−1.02271e7	−1.73384
$87$	5.62422e6	0.915683
$88$	−1.43350e7	−2.24238
$89$	1.00861e7	1.51655	0.758276	−	0.651934i	$-0.226042\pi$
$89$	1.00861e7	1.51655	0.758276	+	0.651934i	$0.226042\pi$
$90$	−4.56592e6	−0.660207
$91$	−5.26206e6	−0.732000
$92$	1.37436e7	1.84011
$93$	−6.12231e6	−0.789269
$94$	−2.03949e7	−2.53264
$95$	3.62624e6	0.433934
$96$	1.20905e6	0.139474
$97$	−8.98768e6	−0.999877	−0.499939	−	0.866061i	$-0.666644\pi$
$97$	−8.98768e6	−0.999877	−0.499939	+	0.866061i	$0.666644\pi$
$98$	−1.42075e6	−0.152485
$99$	−8.26335e6	−0.855919
$100$	−1.50093e7	−1.50093
$101$	6.39476e6	0.617588	0.308794	−	0.951129i	$-0.400075\pi$
$101$	6.39476e6	0.617588	0.308794	+	0.951129i	$0.400075\pi$
$102$	−1.31017e7	−1.22244
$103$	−1.53185e7	−1.38130	−0.690648	−	0.723191i	$-0.742674\pi$
$103$	−1.53185e7	−1.38130	−0.690648	+	0.723191i	$0.742674\pi$
$104$	−1.51366e7	−1.31951
$105$	−3.45227e6	−0.291033
$106$	3.19065e7	2.60201
$107$	−1.43854e7	−1.13521	−0.567607	−	0.823299i	$-0.692131\pi$
$107$	−1.43854e7	−1.13521	−0.567607	+	0.823299i	$0.692131\pi$
$108$	2.47684e7	1.89197
$109$	−1.24198e7	−0.918594	−0.459297	−	0.888283i	$-0.651899\pi$
$109$	−1.24198e7	−0.918594	−0.459297	+	0.888283i	$0.651899\pi$
$110$	1.53288e7	1.09808
$111$	−7.05024e6	−0.489298
$112$	−1.89415e7	−1.27395
$113$	−1.66401e7	−1.08488	−0.542441	−	0.840094i	$-0.682500\pi$
$113$	−1.66401e7	−1.08488	−0.542441	+	0.840094i	$0.682500\pi$
$114$	−1.21820e7	−0.770107
$115$	−7.60436e6	−0.466252
$116$	−6.00028e7	−3.56918
$117$	−8.72542e6	−0.503658
$118$	−3.64329e7	−2.04130
$119$	2.51429e7	1.36773
$120$	−9.93064e6	−0.524617
$121$	8.25473e6	0.423598
$122$	−6.98198e6	−0.348112
$123$	−1.41817e7	−0.687163
$124$	6.53168e7	3.07644
$125$	1.97703e7	0.905374
$126$	−2.94359e7	−1.31093
$127$	−4.35617e7	−1.88709	−0.943544	−	0.331248i	$-0.892530\pi$
$127$	−4.35617e7	−1.88709	−0.943544	+	0.331248i	$0.892530\pi$
$128$	3.79170e7	1.59808
$129$	−1.28221e7	−0.525891
$130$	1.61860e7	0.646156
$131$	2.44136e6	0.0948816	0.0474408	−	0.998874i	$-0.484893\pi$
$131$	2.44136e6	0.0948816	0.0474408	+	0.998874i	$0.484893\pi$
$132$	−3.47340e7	−1.31446
$133$	2.33779e7	0.861636
$134$	6.22379e7	2.23454
$135$	−1.37044e7	−0.479391
$136$	7.23249e7	2.46548
$137$	−2.15949e7	−0.717512	−0.358756	−	0.933431i	$-0.616799\pi$
$137$	−2.15949e7	−0.717512	−0.358756	+	0.933431i	$0.616799\pi$
$138$	2.55461e7	0.827461
$139$	3.73248e7	1.17882	0.589408	−	0.807835i	$-0.299361\pi$
$139$	3.73248e7	1.17882	0.589408	+	0.807835i	$0.299361\pi$
$140$	3.68310e7	1.13440
$141$	−2.55699e7	−0.768178
$142$	−4.28252e7	−1.25513
$143$	2.92932e7	0.837704
$144$	−3.14084e7	−0.876551
$145$	3.31996e7	0.904366
$146$	−1.71800e7	−0.456865
$147$	−1.78125e6	−0.0462504
$148$	7.52165e7	1.90720
$149$	3.28978e7	0.814733	0.407366	−	0.913265i	$-0.366447\pi$
$149$	3.28978e7	0.814733	0.407366	+	0.913265i	$0.366447\pi$
$150$	−2.78986e7	−0.674937
$151$	−4.04447e7	−0.955967	−0.477983	−	0.878369i	$-0.658632\pi$
$151$	−4.04447e7	−0.955967	−0.477983	+	0.878369i	$0.658632\pi$
$152$	6.72476e7	1.55319
$153$	4.16914e7	0.941080
$154$	9.88228e7	2.18039
$155$	−3.61398e7	−0.779516
$156$	−3.66763e7	−0.773480
$157$	−8.81312e7	−1.81753	−0.908763	−	0.417312i	$-0.862972\pi$
$157$	−8.81312e7	−1.81753	−0.908763	+	0.417312i	$0.862972\pi$
$158$	−1.48483e8	−2.99487
$159$	4.00024e7	0.789216
$160$	7.13697e6	0.137751
$161$	−4.90243e7	−0.925807
$162$	−2.20023e7	−0.406598
$163$	−9.52747e7	−1.72314	−0.861571	−	0.507637i	$-0.830519\pi$
$163$	−9.52747e7	−1.72314	−0.861571	+	0.507637i	$0.830519\pi$
$164$	1.51299e8	2.67845
$165$	1.92183e7	0.333059
$166$	−1.20553e8	−2.04550
$167$	3.10564e7	0.515992	0.257996	−	0.966146i	$-0.416938\pi$
$167$	3.10564e7	0.515992	0.257996	+	0.966146i	$0.416938\pi$
$168$	−6.40214e7	−1.04170
$169$	−3.18173e7	−0.507060
$170$	−7.73391e7	−1.20734
$171$	3.87646e7	0.592856
$172$	1.36795e8	2.04984
$173$	2.69916e7	0.396339	0.198169	−	0.980168i	$-0.436500\pi$
$173$	2.69916e7	0.396339	0.198169	+	0.980168i	$0.436500\pi$
$174$	−1.11531e8	−1.60499
$175$	5.35389e7	0.755155
$176$	1.05445e8	1.45791
$177$	−4.56773e7	−0.619147
$178$	−2.00011e8	−2.65818
$179$	1.34819e8	1.75697	0.878487	−	0.477767i	$-0.158554\pi$
$179$	1.34819e8	1.75697	0.878487	+	0.477767i	$0.158554\pi$
$180$	6.10723e7	0.780532
$181$	6.24169e7	0.782398	0.391199	−	0.920306i	$-0.372060\pi$
$181$	6.24169e7	0.782398	0.391199	+	0.920306i	$0.372060\pi$
$182$	1.04349e8	1.28303
$183$	−8.75358e6	−0.105586
$184$	−1.41021e8	−1.66886
$185$	−4.16173e7	−0.483251
$186$	1.21408e8	1.38341
$187$	−1.39967e8	−1.56524
$188$	2.72796e8	2.99423
$189$	−8.83501e7	−0.951898
$190$	−7.19098e7	−0.760590
$191$	−1.72014e8	−1.78627	−0.893136	−	0.449788i	$-0.851500\pi$
$191$	−1.72014e8	−1.78627	−0.893136	+	0.449788i	$0.851500\pi$
$192$	3.97339e7	0.405142
$193$	−2.84904e7	−0.285265	−0.142633	−	0.989776i	$-0.545557\pi$
$193$	−2.84904e7	−0.285265	−0.142633	+	0.989776i	$0.545557\pi$
$194$	1.78230e8	1.75256
$195$	2.02930e7	0.195986
$196$	1.90036e7	0.180276
$197$	7.64537e6	0.0712470
$197$	7.64537e6	0.0712470
$198$	1.63866e8	1.50024
$199$	−4.85998e7	−0.437168	−0.218584	−	0.975818i	$-0.570144\pi$
$199$	−4.85998e7	−0.437168	−0.218584	+	0.975818i	$0.570144\pi$
$200$	1.54007e8	1.36125
$201$	7.80301e7	0.677760
$202$	−1.26811e8	−1.08250
$203$	2.14033e8	1.79575
$204$	1.75245e8	1.44524
$205$	−8.37140e7	−0.678671
$206$	3.03773e8	2.42110
$207$	−8.12909e7	−0.637009
$208$	1.11341e8	0.857896
$209$	−1.30141e8	−0.986060
$210$	6.84599e7	0.510116
$211$	1.79861e8	1.31810	0.659048	−	0.752100i	$-0.270959\pi$
$211$	1.79861e8	1.31810	0.659048	+	0.752100i	$0.270959\pi$
$212$	−4.26771e8	−3.07623
$213$	−5.36915e7	−0.380695
$214$	2.85268e8	1.98978
$215$	−7.56885e7	−0.519392
$216$	−2.54144e8	−1.71590
$217$	−2.32988e8	−1.54784
$218$	2.46291e8	1.61009
$219$	−2.15392e7	−0.138572
$220$	−2.05033e8	−1.29821
$221$	−1.47794e8	−0.921052
$222$	1.39809e8	0.857630
$223$	1.01179e8	0.610972	0.305486	−	0.952197i	$-0.401181\pi$
$223$	1.01179e8	0.610972	0.305486	+	0.952197i	$0.401181\pi$
$224$	4.60111e7	0.273523
$225$	8.87769e7	0.519590
$226$	3.29981e8	1.90156
$227$	2.10418e8	1.19397	0.596985	−	0.802253i	$-0.296365\pi$
$227$	2.10418e8	1.19397	0.596985	+	0.802253i	$0.296365\pi$
$228$	1.62942e8	0.910462
$229$	7.67285e6	0.0422214	0.0211107	−	0.999777i	$-0.493280\pi$
$229$	7.67285e6	0.0422214	0.0211107	+	0.999777i	$0.493280\pi$
$230$	1.50798e8	0.817235
$231$	1.23898e8	0.661336
$232$	6.15677e8	3.23702
$233$	−2.19338e8	−1.13597	−0.567987	−	0.823038i	$-0.692278\pi$
$233$	−2.19338e8	−1.13597	−0.567987	+	0.823038i	$0.692278\pi$
$234$	1.73029e8	0.882801
$235$	−1.50938e8	−0.758685
$236$	4.87315e8	2.41333
$237$	−1.86159e8	−0.908375
$238$	−4.98594e8	−2.39733
$239$	−2.15573e8	−1.02141	−0.510707	−	0.859755i	$-0.670616\pi$
$239$	−2.15573e8	−1.02141	−0.510707	+	0.859755i	$0.670616\pi$
$240$	7.30475e7	0.341088
$241$	3.25554e8	1.49818	0.749089	−	0.662469i	$-0.230491\pi$
$241$	3.25554e8	1.49818	0.749089	+	0.662469i	$0.230491\pi$
$242$	−1.63695e8	−0.742473
$243$	−2.31805e8	−1.03634
$244$	9.33888e7	0.411557
$245$	−1.05147e7	−0.0456788
$246$	2.81229e8	1.20444
$247$	−1.37419e8	−0.580239
$248$	−6.70203e8	−2.79014
$249$	−1.51142e8	−0.620423
$250$	−3.92053e8	−1.58692
$251$	8.49859e6	0.0339226	0.0169613	−	0.999856i	$-0.494601\pi$
$251$	8.49859e6	0.0339226	0.0169613	+	0.999856i	$0.494601\pi$
$252$	3.93725e8	1.54985
$253$	2.72912e8	1.05950
$254$	8.63847e8	3.30764
$255$	−9.69630e7	−0.366197
$256$	−5.47344e8	−2.03902
$257$	7.25957e7	0.266775	0.133387	−	0.991064i	$-0.457415\pi$
$257$	7.25957e7	0.266775	0.133387	+	0.991064i	$0.457415\pi$
$258$	2.54268e8	0.921770
$259$	−2.68301e8	−0.959562
$260$	−2.16499e8	−0.763921
$261$	3.54905e8	1.23558
$262$	−4.84132e7	−0.166306
$263$	2.49019e8	0.844088	0.422044	−	0.906575i	$-0.361313\pi$
$263$	2.49019e8	0.844088	0.422044	+	0.906575i	$0.361313\pi$
$264$	3.56399e8	1.19213
$265$	2.36133e8	0.779463
$266$	−4.63593e8	−1.51026
$267$	−2.50762e8	−0.806254
$268$	−8.32475e8	−2.64180
$269$	−5.65234e8	−1.77050	−0.885249	−	0.465117i	$-0.846012\pi$
$269$	−5.65234e8	−1.77050	−0.885249	+	0.465117i	$0.846012\pi$
$270$	2.71763e8	0.840267
$271$	−3.68405e8	−1.12443	−0.562215	−	0.826991i	$-0.690051\pi$
$271$	−3.68405e8	−1.12443	−0.562215	+	0.826991i	$0.690051\pi$
$272$	−5.32006e8	−1.60297
$273$	1.30826e8	0.389157
$274$	4.28236e8	1.25764
$275$	−2.98044e8	−0.864203
$276$	−3.41696e8	−0.978270
$277$	−6.54109e8	−1.84915	−0.924573	−	0.381005i	$-0.875578\pi$
$277$	−6.54109e8	−1.84915	−0.924573	+	0.381005i	$0.875578\pi$
$278$	−7.40167e8	−2.06620
$279$	−3.86336e8	−1.06500
$280$	−3.77916e8	−1.02883
$281$	5.79016e8	1.55675	0.778375	−	0.627800i	$-0.216044\pi$
$281$	5.79016e8	1.55675	0.778375	+	0.627800i	$0.216044\pi$
$282$	5.07061e8	1.34644
$283$	−1.56053e8	−0.409278	−0.204639	−	0.978838i	$-0.565602\pi$
$283$	−1.56053e8	−0.409278	−0.204639	+	0.978838i	$0.565602\pi$
$284$	5.72816e8	1.48389
$285$	−9.01561e7	−0.230695
$286$	−5.80896e8	−1.46831
$287$	−5.39692e8	−1.34760
$288$	7.62945e7	0.188200
$289$	2.95844e8	0.720975
$290$	−6.58361e8	−1.58515
$291$	2.23453e8	0.531571
$292$	2.29794e8	0.540131
$293$	2.55984e8	0.594534	0.297267	−	0.954794i	$-0.403925\pi$
$293$	2.55984e8	0.594534	0.297267	+	0.954794i	$0.403925\pi$
$294$	3.53230e7	0.0810666
$295$	−2.69631e8	−0.611496
$296$	−7.71782e8	−1.72971
$297$	4.91833e8	1.08936
$298$	−6.52377e8	−1.42805
$299$	2.88173e8	0.623453
$300$	3.73163e8	0.797947
$301$	−4.87953e8	−1.03132
$302$	8.02036e8	1.67560
$303$	−1.58987e8	−0.328332
$304$	−4.94658e8	−1.00983
$305$	−5.16721e7	−0.104281
$306$	−8.26758e8	−1.64950
$307$	−6.69019e8	−1.31964	−0.659818	−	0.751426i	$-0.729367\pi$
$307$	−6.69019e8	−1.31964	−0.659818	+	0.751426i	$0.729367\pi$
$308$	−1.32182e9	−2.57778
$309$	3.80851e8	0.734346
$310$	7.16667e8	1.36632
$311$	−3.36398e8	−0.634150	−0.317075	−	0.948400i	$-0.602701\pi$
$311$	−3.36398e8	−0.634150	−0.317075	+	0.948400i	$0.602701\pi$
$312$	3.76328e8	0.701497
$313$	−1.11842e8	−0.206158	−0.103079	−	0.994673i	$-0.532869\pi$
$313$	−1.11842e8	−0.206158	−0.103079	+	0.994673i	$0.532869\pi$
$314$	1.74768e9	3.18572
$315$	−2.17848e8	−0.392706
$316$	1.98607e9	3.54070
$317$	3.07908e8	0.542892	0.271446	−	0.962454i	$-0.412498\pi$
$317$	3.07908e8	0.542892	0.271446	+	0.962454i	$0.412498\pi$
$318$	−7.93264e8	−1.38332
$319$	−1.19149e9	−2.05506
$320$	2.34548e8	0.400135
$321$	3.57651e8	0.603521
$322$	9.72172e8	1.62273
$323$	6.56608e8	1.08417
$324$	2.94295e8	0.480702
$325$	−3.14710e8	−0.508533
$326$	1.88934e9	3.02028
$327$	3.08784e8	0.488357
$328$	−1.55245e9	−2.42918
$329$	−9.73077e8	−1.50647
$330$	−3.81107e8	−0.583779
$331$	1.14781e8	0.173969	0.0869846	−	0.996210i	$-0.472277\pi$
$331$	1.14781e8	0.173969	0.0869846	+	0.996210i	$0.472277\pi$
$332$	1.61248e9	2.41831
$333$	−4.44890e8	−0.660234
$334$	−6.15861e8	−0.904420
$335$	4.60609e8	0.669384
$336$	4.70927e8	0.677277
$337$	−1.61424e7	−0.0229755	−0.0114877	−	0.999934i	$-0.503657\pi$
$337$	−1.61424e7	−0.0229755	−0.0114877	+	0.999934i	$0.503657\pi$
$338$	6.30950e8	0.888764
$339$	4.13709e8	0.576762
$340$	1.03446e9	1.42738
$341$	1.29702e9	1.77135
$342$	−7.68718e8	−1.03914
$343$	7.11403e8	0.951890
$344$	−1.40362e9	−1.85907
$345$	1.89061e8	0.247876
$346$	−5.35254e8	−0.694694
$347$	8.07705e8	1.03777	0.518883	−	0.854845i	$-0.326348\pi$
$347$	8.07705e8	1.03777	0.518883	+	0.854845i	$0.326348\pi$
$348$	1.49180e9	1.89750
$349$	−2.57320e8	−0.324030	−0.162015	−	0.986788i	$-0.551799\pi$
$349$	−2.57320e8	−0.324030	−0.162015	+	0.986788i	$0.551799\pi$
$350$	−1.06170e9	−1.32362
$351$	5.19336e8	0.641023
$352$	−2.56137e8	−0.313021
$353$	−4.25417e8	−0.514758	−0.257379	−	0.966310i	$-0.582859\pi$
$353$	−4.25417e8	−0.514758	−0.257379	+	0.966310i	$0.582859\pi$
$354$	9.05800e8	1.08523
$355$	−3.16939e8	−0.375990
$356$	2.67529e9	3.14264
$357$	−6.25107e8	−0.727136
$358$	−2.67351e9	−3.07958
$359$	−3.21951e6	−0.00367248	−0.00183624	−	0.999998i	$-0.500584\pi$
$359$	−3.21951e6	−0.00367248	−0.00183624	+	0.999998i	$0.500584\pi$
$360$	−6.26652e8	−0.707893
$361$	−2.83359e8	−0.317002
$362$	−1.23775e9	−1.37137
$363$	−2.05230e8	−0.225200
$364$	−1.39574e9	−1.51687
$365$	−1.27145e8	−0.136859
$366$	1.73587e8	0.185069
$367$	8.27968e8	0.874344	0.437172	−	0.899378i	$-0.355980\pi$
$367$	8.27968e8	0.874344	0.437172	+	0.899378i	$0.355980\pi$
$368$	1.03732e9	1.08504
$369$	−8.94905e8	−0.927224
$370$	8.25288e8	0.847032
$371$	1.52231e9	1.54773
$372$	−1.62392e9	−1.63555
$373$	1.58890e9	1.58532	0.792658	−	0.609667i	$-0.208697\pi$
$373$	1.58890e9	1.58532	0.792658	+	0.609667i	$0.208697\pi$
$374$	2.77561e9	2.74352
$375$	−4.91532e8	−0.481329
$376$	−2.79911e9	−2.71558
$377$	−1.25812e9	−1.20928
$378$	1.75202e9	1.66847
$379$	1.29198e9	1.21904	0.609521	−	0.792770i	$-0.291362\pi$
$379$	1.29198e9	1.21904	0.609521	+	0.792770i	$0.291362\pi$
$380$	9.61843e8	0.899211
$381$	1.08304e9	1.00324
$382$	3.41111e9	3.13094
$383$	−1.60359e9	−1.45847	−0.729233	−	0.684265i	$-0.760123\pi$
$383$	−1.60359e9	−1.45847	−0.729233	+	0.684265i	$0.760123\pi$
$384$	−9.42698e8	−0.849597
$385$	7.31365e8	0.653163
$386$	5.64977e8	0.500006
$387$	−8.09113e8	−0.709611
$388$	−2.38394e9	−2.07198
$389$	−2.26821e9	−1.95371	−0.976853	−	0.213912i	$-0.931379\pi$
$389$	−2.26821e9	−1.95371	−0.976853	+	0.213912i	$0.931379\pi$
$390$	−4.02419e8	−0.343520
$391$	−1.37693e9	−1.16491
$392$	−1.94992e8	−0.163499
$393$	−6.06974e7	−0.0504425
$394$	−1.51611e8	−0.124880
$395$	−1.09889e9	−0.897150
$396$	−2.19181e9	−1.77366
$397$	1.49942e9	1.20270	0.601349	−	0.798986i	$-0.294630\pi$
$397$	1.49942e9	1.20270	0.601349	+	0.798986i	$0.294630\pi$
$398$	9.63754e8	0.766259
$399$	−5.81224e8	−0.458077
$400$	−1.13284e9	−0.885034
$401$	1.58869e9	1.23036	0.615182	−	0.788385i	$-0.289083\pi$
$401$	1.58869e9	1.23036	0.615182	+	0.788385i	$0.289083\pi$
$402$	−1.54737e9	−1.18796
$403$	1.36954e9	1.04234
$404$	1.69618e9	1.27979
$405$	−1.62834e8	−0.121801
$406$	−4.24436e9	−3.14754
$407$	1.49360e9	1.09813
$408$	−1.79815e9	−1.31074
$409$	−1.06609e9	−0.770485	−0.385243	−	0.922815i	$-0.625882\pi$
$409$	−1.06609e9	−0.770485	−0.385243	+	0.922815i	$0.625882\pi$
$410$	1.66008e9	1.18956
$411$	5.36896e8	0.381455
$412$	−4.06317e9	−2.86236
$413$	−1.73828e9	−1.21421
$414$	1.61203e9	1.11654
$415$	−8.92186e8	−0.612755
$416$	−2.70460e8	−0.184195
$417$	−9.27976e8	−0.626701
$418$	2.58076e9	1.72834
$419$	9.56044e8	0.634934	0.317467	−	0.948269i	$-0.397168\pi$
$419$	9.56044e8	0.634934	0.317467	+	0.948269i	$0.397168\pi$
$420$	−9.15699e8	−0.603087
$421$	−8.05434e8	−0.526069	−0.263034	−	0.964786i	$-0.584723\pi$
$421$	−8.05434e8	−0.526069	−0.263034	+	0.964786i	$0.584723\pi$
$422$	−3.56671e9	−2.31033
$423$	−1.61353e9	−1.03654
$424$	4.37902e9	2.78995
$425$	1.50373e9	0.950187
$426$	1.06473e9	0.667274
$427$	−3.33123e8	−0.207065
$428$	−3.81565e9	−2.35243
$429$	−7.28292e8	−0.445353
$430$	1.50093e9	0.910379
$431$	−1.47296e9	−0.886180	−0.443090	−	0.896477i	$-0.646118\pi$
$431$	−1.47296e9	−0.886180	−0.443090	+	0.896477i	$0.646118\pi$
$432$	1.86942e9	1.11561
$433$	5.07384e8	0.300351	0.150175	−	0.988659i	$-0.452016\pi$
$433$	5.07384e8	0.300351	0.150175	+	0.988659i	$0.452016\pi$
$434$	4.62026e9	2.71301
$435$	−8.25413e8	−0.480794
$436$	−3.29431e9	−1.90354
$437$	−1.28027e9	−0.733865
$438$	4.27132e8	0.242886
$439$	1.45521e8	0.0820920	0.0410460	−	0.999157i	$-0.486931\pi$
$439$	1.45521e8	0.0820920	0.0410460	+	0.999157i	$0.486931\pi$
$440$	2.10381e9	1.17739
$441$	−1.12402e8	−0.0624080
$442$	2.93082e9	1.61440
$443$	6.69078e7	0.0365649	0.0182824	−	0.999833i	$-0.494180\pi$
$443$	6.69078e7	0.0365649	0.0182824	+	0.999833i	$0.494180\pi$
$444$	−1.87004e9	−1.01394
$445$	−1.48024e9	−0.796290
$446$	−2.00641e9	−1.07090
$447$	−8.17910e8	−0.433141
$448$	1.51210e9	0.794523
$449$	−8.58536e8	−0.447607	−0.223803	−	0.974634i	$-0.571847\pi$
$449$	−8.58536e8	−0.447607	−0.223803	+	0.974634i	$0.571847\pi$
$450$	−1.76048e9	−0.910726
$451$	3.00440e9	1.54219
$452$	−4.41372e9	−2.24812
$453$	1.00554e9	0.508226
$454$	−4.17268e9	−2.09276
$455$	7.72262e8	0.384348
$456$	−1.67192e9	−0.825731
$457$	−1.62722e9	−0.797517	−0.398758	−	0.917056i	$-0.630559\pi$
$457$	−1.62722e9	−0.797517	−0.398758	+	0.917056i	$0.630559\pi$
$458$	−1.52156e8	−0.0740047
$459$	−2.48146e9	−1.19774
$460$	−2.01702e9	−0.966180
$461$	1.25536e9	0.596780	0.298390	−	0.954444i	$-0.403550\pi$
$461$	1.25536e9	0.596780	0.298390	+	0.954444i	$0.403550\pi$
$462$	−2.45695e9	−1.15917
$463$	−7.95344e8	−0.372410	−0.186205	−	0.982511i	$-0.559619\pi$
$463$	−7.95344e8	−0.372410	−0.186205	+	0.982511i	$0.559619\pi$
$464$	−4.52878e9	−2.10459
$465$	8.98513e8	0.414419
$466$	4.34956e9	1.99111
$467$	−2.27900e8	−0.103546	−0.0517732	−	0.998659i	$-0.516487\pi$
$467$	−2.27900e8	−0.103546	−0.0517732	+	0.998659i	$0.516487\pi$
$468$	−2.31438e9	−1.04370
$469$	2.96948e9	1.32915
$470$	2.99316e9	1.32981
$471$	2.19113e9	0.966262
$472$	−5.00024e9	−2.18874
$473$	2.71637e9	1.18025
$474$	3.69161e9	1.59218
$475$	1.39817e9	0.598593
$476$	6.66904e9	2.83426
$477$	2.52427e9	1.06493
$478$	4.27490e9	1.79031
$479$	−2.17914e9	−0.905962	−0.452981	−	0.891520i	$-0.649640\pi$
$479$	−2.17914e9	−0.905962	−0.452981	+	0.891520i	$0.649640\pi$
$480$	−1.77440e8	−0.0732332
$481$	1.57712e9	0.646184
$482$	−6.45588e9	−2.62597
$483$	1.21885e9	0.492192
$484$	2.18953e9	0.877792
$485$	1.31904e9	0.525002
$486$	4.59679e9	1.81647
$487$	2.30264e9	0.903389	0.451695	−	0.892173i	$-0.350820\pi$
$487$	2.30264e9	0.903389	0.451695	+	0.892173i	$0.350820\pi$
$488$	−9.58245e8	−0.373256
$489$	2.36873e9	0.916084
$490$	2.08510e8	0.0800648
$491$	−5.81006e8	−0.221511	−0.110756	−	0.993848i	$-0.535327\pi$
$491$	−5.81006e8	−0.221511	−0.110756	+	0.993848i	$0.535327\pi$
$492$	−3.76163e9	−1.42396
$493$	6.01149e9	2.25953
$494$	2.72507e9	1.01703
$495$	1.21273e9	0.449414
$496$	4.92986e9	1.81405
$497$	−2.04326e9	−0.746581
$498$	2.99721e9	1.08746
$499$	−1.46196e9	−0.526724	−0.263362	−	0.964697i	$-0.584831\pi$
$499$	−1.46196e9	−0.526724	−0.263362	+	0.964697i	$0.584831\pi$
$500$	5.24398e9	1.87614
$501$	−7.72129e8	−0.274320
$502$	−1.68530e8	−0.0594587
$503$	1.51310e9	0.530128	0.265064	−	0.964231i	$-0.414607\pi$
$503$	1.51310e9	0.530128	0.265064	+	0.964231i	$0.414607\pi$
$504$	−4.03994e9	−1.40562
$505$	−9.38497e8	−0.324275
$506$	−5.41195e9	−1.85706
$507$	7.91046e8	0.269571
$508$	−1.15545e10	−3.91048
$509$	−1.27005e8	−0.0426884	−0.0213442	−	0.999772i	$-0.506795\pi$
$509$	−1.27005e8	−0.0426884	−0.0213442	+	0.999772i	$0.506795\pi$
$510$	1.92282e9	0.641863
$511$	−8.19688e8	−0.271754
$512$	6.00069e9	1.97586
$513$	−2.30726e9	−0.754547
$514$	−1.43960e9	−0.467597
$515$	2.24815e9	0.725271
$516$	−3.40101e9	−1.08977
$517$	5.41699e9	1.72402
$518$	5.32052e9	1.68190
$519$	−6.71068e8	−0.210708
$520$	2.22145e9	0.692828
$521$	−4.69577e9	−1.45470	−0.727352	−	0.686264i	$-0.759249\pi$
$521$	−4.69577e9	−1.45470	−0.727352	+	0.686264i	$0.759249\pi$
$522$	−7.03790e9	−2.16569
$523$	−2.33474e9	−0.713644	−0.356822	−	0.934172i	$-0.616140\pi$
$523$	−2.33474e9	−0.713644	−0.356822	+	0.934172i	$0.616140\pi$
$524$	6.47559e8	0.196616
$525$	−1.33109e9	−0.401467
$526$	−4.93815e9	−1.47950
$527$	−6.54388e9	−1.94759
$528$	−2.62159e9	−0.775079
$529$	−7.20051e8	−0.211480
$530$	−4.68261e9	−1.36622
$531$	−2.88237e9	−0.835447
$532$	6.20087e9	1.78551
$533$	3.17240e9	0.907491
$534$	4.97271e9	1.41318
$535$	2.11120e9	0.596062
$536$	8.54187e9	2.39594
$537$	−3.35189e9	−0.934070
$538$	1.12088e10	3.10329
$539$	3.77359e8	0.103799
$540$	−3.63502e9	−0.993409
$541$	−6.28378e9	−1.70620	−0.853102	−	0.521745i	$-0.825281\pi$
$541$	−6.28378e9	−1.70620	−0.853102	+	0.521745i	$0.825281\pi$
$542$	7.30562e9	1.97088
$543$	−1.55182e9	−0.415951
$544$	1.29230e9	0.344166
$545$	1.82274e9	0.482322
$546$	−2.59434e9	−0.682106
$547$	5.48029e9	1.43169	0.715844	−	0.698261i	$-0.246042\pi$
$547$	5.48029e9	1.43169	0.715844	+	0.698261i	$0.246042\pi$
$548$	−5.72795e9	−1.48685
$549$	−5.52376e8	−0.142473
$550$	5.91033e9	1.51476
$551$	5.58948e9	1.42344
$552$	3.50608e9	0.887228
$553$	−7.08440e9	−1.78142
$554$	1.29713e10	3.24114
$555$	1.03470e9	0.256914
$556$	9.90024e9	2.44278
$557$	2.20639e7	0.00540991	0.00270495	−	0.999996i	$-0.499139\pi$
$557$	2.20639e7	0.00540991	0.00270495	+	0.999996i	$0.499139\pi$
$558$	7.66120e9	1.86671
$559$	2.86827e9	0.694510
$560$	2.77987e9	0.668907
$561$	3.47989e9	0.832138
$562$	−1.14821e10	−2.72864
$563$	−4.00497e9	−0.945844	−0.472922	−	0.881104i	$-0.656801\pi$
$563$	−4.00497e9	−0.945844	−0.472922	+	0.881104i	$0.656801\pi$
$564$	−6.78229e9	−1.59184
$565$	2.44211e9	0.569634
$566$	3.09459e9	0.717373
$567$	−1.04977e9	−0.241853
$568$	−5.87756e9	−1.34579
$569$	3.72069e9	0.846702	0.423351	−	0.905966i	$-0.360854\pi$
$569$	3.72069e9	0.846702	0.423351	+	0.905966i	$0.360854\pi$
$570$	1.78783e9	0.404357
$571$	5.42056e9	1.21848	0.609239	−	0.792987i	$-0.291475\pi$
$571$	5.42056e9	1.21848	0.609239	+	0.792987i	$0.291475\pi$
$572$	7.76988e9	1.73592
$573$	4.27664e9	0.949646
$574$	1.07023e10	2.36204
$575$	−2.93201e9	−0.643174
$576$	2.50732e9	0.546678
$577$	−4.58461e9	−0.993543	−0.496772	−	0.867881i	$-0.665481\pi$
$577$	−4.58461e9	−0.993543	−0.496772	+	0.867881i	$0.665481\pi$
$578$	−5.86670e9	−1.26371
$579$	7.08334e8	0.151657
$580$	8.80603e9	1.87406
$581$	−5.75180e9	−1.21671
$582$	−4.43117e9	−0.931725
$583$	−8.47452e9	−1.77123
$584$	−2.35787e9	−0.489864
$585$	1.28055e9	0.264454
$586$	−5.07628e9	−1.04209
$587$	−7.81597e9	−1.59496	−0.797479	−	0.603346i	$-0.793834\pi$
$587$	−7.81597e9	−1.59496	−0.797479	+	0.603346i	$0.793834\pi$
$588$	−4.72469e8	−0.0958414
$589$	−6.08449e9	−1.22693
$590$	5.34690e9	1.07182
$591$	−1.90080e8	−0.0378775
$592$	5.67705e9	1.12460
$593$	−4.55255e9	−0.896526	−0.448263	−	0.893902i	$-0.647957\pi$
$593$	−4.55255e9	−0.896526	−0.448263	+	0.893902i	$0.647957\pi$
$594$	−9.75325e9	−1.90940
$595$	−3.68998e9	−0.718150
$596$	8.72599e9	1.68831
$597$	1.20830e9	0.232414
$598$	−5.71458e9	−1.09277
$599$	−5.05845e8	−0.0961665	−0.0480832	−	0.998843i	$-0.515311\pi$
$599$	−5.05845e8	−0.0961665	−0.0480832	+	0.998843i	$0.515311\pi$
$600$	−3.82896e9	−0.723687
$601$	−4.47492e8	−0.0840861	−0.0420431	−	0.999116i	$-0.513387\pi$
$601$	−4.47492e8	−0.0840861	−0.0420431	+	0.999116i	$0.513387\pi$
$602$	9.67632e9	1.80768
$603$	4.92392e9	0.914536
$604$	−1.07278e10	−1.98098
$605$	−1.21147e9	−0.222417
$606$	3.15279e9	0.575493
$607$	−5.53242e9	−1.00405	−0.502024	−	0.864854i	$-0.667411\pi$
$607$	−5.53242e9	−1.00405	−0.502024	+	0.864854i	$0.667411\pi$
$608$	1.20158e9	0.216815
$609$	−5.32132e9	−0.954683
$610$	1.02468e9	0.182782
$611$	5.71990e9	1.01448
$612$	1.10584e10	1.95013
$613$	4.08588e9	0.716430	0.358215	−	0.933639i	$-0.383385\pi$
$613$	4.08588e9	0.716430	0.358215	+	0.933639i	$0.383385\pi$
$614$	1.32669e10	2.31303
$615$	2.08131e9	0.360806
$616$	1.35630e10	2.33788
$617$	−9.75149e8	−0.167137	−0.0835685	−	0.996502i	$-0.526632\pi$
$617$	−9.75149e8	−0.167137	−0.0835685	+	0.996502i	$0.526632\pi$
$618$	−7.55244e9	−1.28715
$619$	2.13678e8	0.0362112	0.0181056	−	0.999836i	$-0.494237\pi$
$619$	2.13678e8	0.0362112	0.0181056	+	0.999836i	$0.494237\pi$
$620$	−9.58592e9	−1.61534
$621$	4.83842e9	0.810743
$622$	6.67091e9	1.11152
$623$	−9.54288e9	−1.58114
$624$	−2.76818e9	−0.456088
$625$	1.51932e9	0.248925
$626$	2.21788e9	0.361349
$627$	3.23560e9	0.524225
$628$	−2.33764e10	−3.76633
$629$	−7.53570e9	−1.20739
$630$	4.32002e9	0.688325
$631$	2.19481e9	0.347771	0.173886	−	0.984766i	$-0.444368\pi$
$631$	2.19481e9	0.347771	0.173886	+	0.984766i	$0.444368\pi$
$632$	−2.03787e10	−3.21119
$633$	−4.47172e9	−0.700748
$634$	−6.10594e9	−0.951569
$635$	6.39314e9	0.990845
$636$	1.06104e10	1.63544
$637$	3.98461e8	0.0610798
$638$	2.36278e10	3.60206
$639$	−3.38809e9	−0.513691
$640$	−5.56471e9	−0.839098
$641$	3.13994e9	0.470888	0.235444	−	0.971888i	$-0.424346\pi$
$641$	3.13994e9	0.470888	0.235444	+	0.971888i	$0.424346\pi$
$642$	−7.09237e9	−1.05784
$643$	−6.42162e8	−0.0952590	−0.0476295	−	0.998865i	$-0.515167\pi$
$643$	−6.42162e8	−0.0952590	−0.0476295	+	0.998865i	$0.515167\pi$
$644$	−1.30035e10	−1.91848
$645$	1.88178e9	0.276127
$646$	−1.30208e10	−1.90031
$647$	1.02057e10	1.48142	0.740711	−	0.671824i	$-0.234489\pi$
$647$	1.02057e10	1.48142	0.740711	+	0.671824i	$0.234489\pi$
$648$	−3.01971e9	−0.435966
$649$	9.67675e9	1.38955
$650$	6.24083e9	0.891345
$651$	5.79259e9	0.822885
$652$	−2.52712e10	−3.57075
$653$	−3.21641e9	−0.452038	−0.226019	−	0.974123i	$-0.572571\pi$
$653$	−3.21641e9	−0.452038	−0.226019	+	0.974123i	$0.572571\pi$
$654$	−6.12332e9	−0.855982
$655$	−3.58295e8	−0.0498191
$656$	1.14195e10	1.57937
$657$	−1.35919e9	−0.186982
$658$	1.92965e10	2.64051
$659$	−4.62412e8	−0.0629404	−0.0314702	−	0.999505i	$-0.510019\pi$
$659$	−4.62412e8	−0.0629404	−0.0314702	+	0.999505i	$0.510019\pi$
$660$	5.09757e9	0.690176
$661$	5.64983e9	0.760905	0.380453	−	0.924800i	$-0.375768\pi$
$661$	5.64983e9	0.760905	0.380453	+	0.924800i	$0.375768\pi$
$662$	−2.27616e9	−0.304929
$663$	3.67448e9	0.489664
$664$	−1.65454e10	−2.19325
$665$	−3.43094e9	−0.452416
$666$	8.82236e9	1.15724
$667$	−1.17213e10	−1.52946
$668$	8.23756e9	1.06925
$669$	−2.51552e9	−0.324815
$670$	−9.13406e9	−1.17328
$671$	1.85445e9	0.236966
$672$	−1.14393e9	−0.145415
$673$	7.19221e9	0.909514	0.454757	−	0.890615i	$-0.349726\pi$
$673$	7.19221e9	0.909514	0.454757	+	0.890615i	$0.349726\pi$
$674$	3.20111e8	0.0402709
$675$	−5.28399e9	−0.661300
$676$	−8.43939e9	−1.05075
$677$	−5.19276e9	−0.643188	−0.321594	−	0.946878i	$-0.604219\pi$
$677$	−5.19276e9	−0.643188	−0.321594	+	0.946878i	$0.604219\pi$
$678$	−8.20403e9	−1.01094
$679$	8.50364e9	1.04246
$680$	−1.06144e10	−1.29454
$681$	−5.23145e9	−0.634757
$682$	−2.57203e10	−3.10479
$683$	2.64296e9	0.317409	0.158704	−	0.987326i	$-0.449268\pi$
$683$	2.64296e9	0.317409	0.158704	+	0.987326i	$0.449268\pi$
$684$	1.02821e10	1.22853
$685$	3.16928e9	0.376741
$686$	−1.41074e10	−1.66845
$687$	−1.90763e8	−0.0224464
$688$	1.03247e10	1.20870
$689$	−8.94841e9	−1.04227
$690$	−3.74915e9	−0.434472
$691$	−8.31816e9	−0.959079	−0.479539	−	0.877520i	$-0.659196\pi$
$691$	−8.31816e9	−0.959079	−0.479539	+	0.877520i	$0.659196\pi$
$692$	7.15939e9	0.821305
$693$	7.81832e9	0.892374
$694$	−1.60171e10	−1.81897
$695$	−5.47781e9	−0.618956
$696$	−1.53071e10	−1.72092
$697$	−1.51582e10	−1.69564
$698$	5.10277e9	0.567953
$699$	5.45322e9	0.603924
$700$	1.42009e10	1.56485
$701$	−3.37985e9	−0.370583	−0.185291	−	0.982684i	$-0.559323\pi$
$701$	−3.37985e9	−0.370583	−0.185291	+	0.982684i	$0.559323\pi$
$702$	−1.02986e10	−1.12357
$703$	−7.00668e9	−0.760622
$704$	−8.41764e9	−0.909256
$705$	3.75265e9	0.403344
$706$	8.43620e9	0.902257
$707$	−6.05036e9	−0.643892
$708$	−1.21157e10	−1.28301
$709$	9.69289e9	1.02139	0.510695	−	0.859762i	$-0.329388\pi$
$709$	9.69289e9	1.02139	0.510695	+	0.859762i	$0.329388\pi$
$710$	6.28504e9	0.659028
$711$	−1.17472e10	−1.22572
$712$	−2.74506e10	−2.85018
$713$	1.27594e10	1.31831
$714$	1.23961e10	1.27451
$715$	−4.29908e9	−0.439850
$716$	3.57601e10	3.64085
$717$	5.35961e9	0.543020
$718$	6.38442e7	0.00643704
$719$	6.50355e9	0.652528	0.326264	−	0.945279i	$-0.394210\pi$
$719$	6.50355e9	0.652528	0.326264	+	0.945279i	$0.394210\pi$
$720$	4.60951e9	0.460247
$721$	1.44935e10	1.44013
$722$	5.61912e9	0.555633
$723$	−8.09398e9	−0.796486
$724$	1.65558e10	1.62131
$725$	1.28008e10	1.24753
$726$	4.06980e9	0.394725
$727$	−1.74369e10	−1.68305	−0.841527	−	0.540216i	$-0.818343\pi$
$727$	−1.74369e10	−1.68305	−0.841527	+	0.540216i	$0.818343\pi$
$728$	1.43214e10	1.37571
$729$	3.33665e9	0.318981
$730$	2.52134e9	0.239884
$731$	−1.37050e10	−1.29768
$732$	−2.32185e9	−0.218799
$733$	9.23589e9	0.866194	0.433097	−	0.901347i	$-0.357421\pi$
$733$	9.23589e9	0.866194	0.433097	+	0.901347i	$0.357421\pi$
$734$	−1.64189e10	−1.53253
$735$	2.61418e8	0.0242845
$736$	−2.51976e9	−0.232963
$737$	−1.65307e10	−1.52109
$738$	1.77463e10	1.62522
$739$	−5.27852e9	−0.481124	−0.240562	−	0.970634i	$-0.577332\pi$
$739$	−5.27852e9	−0.481124	−0.240562	+	0.970634i	$0.577332\pi$
$740$	−1.10388e10	−1.00141
$741$	3.41653e9	0.308476
$742$	−3.01881e10	−2.71283
$743$	1.30756e10	1.16950	0.584752	−	0.811212i	$-0.301192\pi$
$743$	1.30756e10	1.16950	0.584752	+	0.811212i	$0.301192\pi$
$744$	1.66627e10	1.48334
$745$	−4.82810e9	−0.427788
$746$	−3.15085e10	−2.77870
$747$	−9.53750e9	−0.837168
$748$	−3.71257e10	−3.24354
$749$	1.36106e10	1.18356
$750$	9.74728e9	0.843663
$751$	4.01864e9	0.346210	0.173105	−	0.984903i	$-0.444620\pi$
$751$	4.01864e9	0.346210	0.173105	+	0.984903i	$0.444620\pi$
$752$	2.05896e10	1.76557
$753$	−2.11293e8	−0.0180345
$754$	2.49491e10	2.11960
$755$	5.93569e9	0.501945
$756$	−2.34344e10	−1.97255
$757$	−1.46088e10	−1.22399	−0.611995	−	0.790862i	$-0.709633\pi$
$757$	−1.46088e10	−1.22399	−0.611995	+	0.790862i	$0.709633\pi$
$758$	−2.56205e10	−2.13671
$759$	−6.78517e9	−0.563267
$760$	−9.86929e9	−0.815527
$761$	−1.85272e10	−1.52393	−0.761964	−	0.647619i	$-0.775765\pi$
$761$	−1.85272e10	−1.52393	−0.761964	+	0.647619i	$0.775765\pi$
$762$	−2.14771e10	−1.75846
$763$	1.17510e10	0.957718
$764$	−4.56260e10	−3.70156
$765$	−6.11864e9	−0.494129
$766$	3.17998e10	2.55637
$767$	1.02179e10	0.817667
$768$	1.36082e10	1.08401
$769$	−2.03533e10	−1.61396	−0.806981	−	0.590577i	$-0.798900\pi$
$769$	−2.03533e10	−1.61396	−0.806981	+	0.590577i	$0.798900\pi$
$770$	−1.45033e10	−1.14485
$771$	−1.80489e9	−0.141827
$772$	−7.55696e9	−0.591135
$773$	−2.37821e9	−0.185192	−0.0925959	−	0.995704i	$-0.529516\pi$
$773$	−2.37821e9	−0.185192	−0.0925959	+	0.995704i	$0.529516\pi$
$774$	1.60450e10	1.24379
$775$	−1.39344e10	−1.07531
$776$	2.44612e10	1.87915
$777$	6.67054e9	0.510138
$778$	4.49795e10	3.42441
$779$	−1.40941e10	−1.06821
$780$	5.38262e9	0.406128
$781$	1.13746e10	0.854391
$782$	2.73051e10	2.04183
$783$	−2.11239e10	−1.57256
$784$	1.43432e9	0.106301
$785$	1.29342e10	0.954321
$786$	1.20366e9	0.0884144
$787$	−3.17661e9	−0.232302	−0.116151	−	0.993232i	$-0.537056\pi$
$787$	−3.17661e9	−0.232302	−0.116151	+	0.993232i	$0.537056\pi$
$788$	2.02790e9	0.147640
$789$	−6.19115e9	−0.448747
$790$	2.17915e10	1.57250
$791$	1.57440e10	1.13109
$792$	2.24898e10	1.60860
$793$	1.95815e9	0.139441
$794$	−2.97341e10	−2.10806
$795$	−5.87076e9	−0.414390
$796$	−1.28909e10	−0.905913
$797$	1.53084e10	1.07109	0.535546	−	0.844506i	$-0.320106\pi$
$797$	1.53084e10	1.07109	0.535546	+	0.844506i	$0.320106\pi$
$798$	1.15259e10	0.802907
$799$	−2.73306e10	−1.89555
$800$	2.75180e9	0.190021
$801$	−1.58238e10	−1.08792
$802$	−3.15044e10	−2.15655
$803$	4.56309e9	0.310996
$804$	2.06971e10	1.40447
$805$	7.19482e9	0.486110
$806$	−2.71586e10	−1.82698
$807$	1.40529e10	0.941260
$808$	−1.74042e10	−1.16068
$809$	−1.12375e10	−0.746189	−0.373095	−	0.927793i	$-0.621703\pi$
$809$	−1.12375e10	−0.746189	−0.373095	+	0.927793i	$0.621703\pi$
$810$	3.22906e9	0.213491
$811$	−1.91072e9	−0.125783	−0.0628917	−	0.998020i	$-0.520032\pi$
$811$	−1.91072e9	−0.125783	−0.0628917	+	0.998020i	$0.520032\pi$
$812$	5.67713e10	3.72120
$813$	9.15933e9	0.597787
$814$	−2.96186e10	−1.92477
$815$	1.39826e10	0.904763
$816$	1.32268e10	0.852196
$817$	−1.27429e10	−0.817507
$818$	2.11411e10	1.35049
$819$	8.25551e9	0.525110
$820$	−2.22047e10	−1.40636
$821$	4.16755e9	0.262833	0.131416	−	0.991327i	$-0.458047\pi$
$821$	4.16755e9	0.262833	0.131416	+	0.991327i	$0.458047\pi$
$822$	−1.06469e10	−0.668606
$823$	−1.21381e10	−0.759015	−0.379507	−	0.925189i	$-0.623906\pi$
$823$	−1.21381e10	−0.759015	−0.379507	+	0.925189i	$0.623906\pi$
$824$	4.16914e10	2.59598
$825$	7.41001e9	0.459441
$826$	3.44707e10	2.12824
$827$	2.14027e10	1.31583	0.657913	−	0.753094i	$-0.271439\pi$
$827$	2.14027e10	1.31583	0.657913	+	0.753094i	$0.271439\pi$
$828$	−2.15620e10	−1.32003
$829$	−1.17377e10	−0.715552	−0.357776	−	0.933807i	$-0.616465\pi$
$829$	−1.17377e10	−0.715552	−0.357776	+	0.933807i	$0.616465\pi$
$830$	1.76924e10	1.07402
$831$	1.62626e10	0.983072
$832$	−8.88835e9	−0.535044
$833$	−1.90391e9	−0.114127
$834$	1.84021e10	1.09847
$835$	−4.55785e9	−0.270930
$836$	−3.45194e10	−2.04334
$837$	2.29946e10	1.35546
$838$	−1.89587e10	−1.11290
$839$	2.54177e10	1.48583	0.742916	−	0.669385i	$-0.233442\pi$
$839$	2.54177e10	1.48583	0.742916	+	0.669385i	$0.233442\pi$
$840$	9.39581e9	0.546962
$841$	3.39239e10	1.96662
$842$	1.59721e10	0.922082
$843$	−1.43956e10	−0.827624
$844$	4.77072e10	2.73140
$845$	4.66952e9	0.266240
$846$	3.19970e10	1.81683
$847$	−7.81016e9	−0.441640
$848$	−3.22110e10	−1.81392
$849$	3.87980e9	0.217587
$850$	−2.98196e10	−1.66547
$851$	1.46933e10	0.817270
$852$	−1.42414e10	−0.788888
$853$	1.97148e10	1.08761	0.543803	−	0.839213i	$-0.316984\pi$
$853$	1.97148e10	1.08761	0.543803	+	0.839213i	$0.316984\pi$
$854$	6.60596e9	0.362939
$855$	−5.68911e9	−0.311288
$856$	3.91517e10	2.13350
$857$	−3.03727e8	−0.0164835	−0.00824176	−	0.999966i	$-0.502623\pi$
$857$	−3.03727e8	−0.0164835	−0.00824176	+	0.999966i	$0.502623\pi$
$858$	1.44423e10	0.780606
$859$	−1.03944e10	−0.559529	−0.279765	−	0.960069i	$-0.590256\pi$
$859$	−1.03944e10	−0.559529	−0.279765	+	0.960069i	$0.590256\pi$
$860$	−2.00760e10	−1.07630
$861$	1.34179e10	0.716430
$862$	2.92095e10	1.55328
$863$	1.99530e10	1.05674	0.528372	−	0.849013i	$-0.322803\pi$
$863$	1.99530e10	1.05674	0.528372	+	0.849013i	$0.322803\pi$
$864$	−4.54103e9	−0.239528
$865$	−3.96129e9	−0.208104
$866$	−1.00616e10	−0.526448
$867$	−7.35531e9	−0.383296
$868$	−6.17991e10	−3.20747
$869$	3.94379e10	2.03866
$870$	1.63683e10	0.842724
$871$	−1.74551e10	−0.895073
$872$	3.38023e10	1.72639
$873$	1.41005e10	0.717275
$874$	2.53883e10	1.28630
$875$	−1.87055e10	−0.943935
$876$	−5.71318e9	−0.287153
$877$	−2.43984e9	−0.122142	−0.0610708	−	0.998133i	$-0.519452\pi$
$877$	−2.43984e9	−0.122142	−0.0610708	+	0.998133i	$0.519452\pi$
$878$	−2.88575e9	−0.143889
$879$	−6.36432e9	−0.316076
$880$	−1.54751e10	−0.765500
$881$	1.87983e10	0.926198	0.463099	−	0.886307i	$-0.346737\pi$
$881$	1.87983e10	0.926198	0.463099	+	0.886307i	$0.346737\pi$
$882$	2.22898e9	0.109387
$883$	−1.13291e10	−0.553776	−0.276888	−	0.960902i	$-0.589303\pi$
$883$	−1.13291e10	−0.553776	−0.276888	+	0.960902i	$0.589303\pi$
$884$	−3.92017e10	−1.90863
$885$	6.70362e9	0.325093
$886$	−1.32681e9	−0.0640901
$887$	−8.31285e9	−0.399961	−0.199980	−	0.979800i	$-0.564088\pi$
$887$	−8.31285e9	−0.399961	−0.199980	+	0.979800i	$0.564088\pi$
$888$	1.91882e10	0.919577
$889$	4.12157e10	1.96746
$890$	2.93537e10	1.39572
$891$	5.84391e9	0.276778
$892$	2.68371e10	1.26607
$893$	−2.54119e10	−1.19415
$894$	1.62195e10	0.759200
$895$	−1.97861e10	−0.922527
$896$	−3.58749e10	−1.66615
$897$	−7.16459e9	−0.331450
$898$	1.70251e10	0.784555
$899$	−5.57058e10	−2.55706
$900$	2.35477e10	1.07671
$901$	4.27568e10	1.94746
$902$	−5.95784e10	−2.70312
$903$	1.21316e10	0.548289
$904$	4.52883e10	2.03890
$905$	−9.16034e9	−0.410810
$906$	−1.99403e10	−0.890808
$907$	−2.97090e10	−1.32209	−0.661047	−	0.750345i	$-0.729887\pi$
$907$	−2.97090e10	−1.32209	−0.661047	+	0.750345i	$0.729887\pi$
$908$	5.58125e10	2.47418
$909$	−1.00326e10	−0.443035
$910$	−1.53143e10	−0.673677
$911$	3.20009e10	1.40232	0.701161	−	0.713003i	$-0.252666\pi$
$911$	3.20009e10	1.40232	0.701161	+	0.713003i	$0.252666\pi$
$912$	1.22983e10	0.536861
$913$	3.20195e10	1.39241
$914$	3.22685e10	1.39787
$915$	1.28468e9	0.0554397
$916$	2.03519e9	0.0874924
$917$	−2.30988e9	−0.0989227
$918$	4.92085e10	2.09938
$919$	−3.19694e10	−1.35872	−0.679361	−	0.733805i	$-0.737743\pi$
$919$	−3.19694e10	−1.35872	−0.679361	+	0.733805i	$0.737743\pi$
$920$	2.06963e10	0.876264
$921$	1.66332e10	0.701566
$922$	−2.48943e10	−1.04602
$923$	1.20106e10	0.502759
$924$	3.28633e10	1.37044
$925$	−1.60464e10	−0.666624
$926$	1.57720e10	0.652752
$927$	2.40328e10	0.990891
$928$	1.10009e10	0.451867
$929$	−5.13567e9	−0.210156	−0.105078	−	0.994464i	$-0.533509\pi$
$929$	−5.13567e9	−0.210156	−0.105078	+	0.994464i	$0.533509\pi$
$930$	−1.78179e10	−0.726384
$931$	−1.77025e9	−0.0718970
$932$	−5.81784e10	−2.35400
$933$	8.36358e9	0.337137
$934$	4.51935e9	0.181494
$935$	2.05417e10	0.821854
$936$	2.37474e10	0.946566
$937$	−6.06141e9	−0.240705	−0.120353	−	0.992731i	$-0.538403\pi$
$937$	−6.06141e9	−0.240705	−0.120353	+	0.992731i	$0.538403\pi$
$938$	−5.88860e10	−2.32971
$939$	2.78064e9	0.109601
$940$	−4.00356e10	−1.57217
$941$	−3.61955e10	−1.41609	−0.708044	−	0.706168i	$-0.750422\pi$
$941$	−3.61955e10	−1.41609	−0.708044	+	0.706168i	$0.750422\pi$
$942$	−4.34510e10	−1.69364
$943$	2.95558e10	1.14776
$944$	3.67806e10	1.42304
$945$	1.29663e10	0.499809
$946$	−5.38668e10	−2.06872
$947$	−3.05023e10	−1.16710	−0.583549	−	0.812078i	$-0.698337\pi$
$947$	−3.05023e10	−1.16710	−0.583549	+	0.812078i	$0.698337\pi$
$948$	−4.93779e10	−1.88236
$949$	4.81825e9	0.183003
$950$	−2.77263e10	−1.04920
$951$	−7.65525e9	−0.288621
$952$	−6.84298e10	−2.57049
$953$	−3.70375e10	−1.38617	−0.693085	−	0.720856i	$-0.743749\pi$
$953$	−3.70375e10	−1.38617	−0.693085	+	0.720856i	$0.743749\pi$
$954$	−5.00572e10	−1.86658
$955$	2.52449e10	0.937910
$956$	−5.71798e10	−2.11660
$957$	2.96231e10	1.09254
$958$	4.32132e10	1.58795
$959$	2.04319e10	0.748072
$960$	−5.83136e9	−0.212726
$961$	3.31266e10	1.20405
$962$	−3.12749e10	−1.13262
$963$	2.25688e10	0.814361
$964$	8.63518e10	3.10457
$965$	4.18127e9	0.149783
$966$	−2.41703e10	−0.862704
$967$	2.28479e10	0.812558	0.406279	−	0.913749i	$-0.366826\pi$
$967$	2.28479e10	0.812558	0.406279	+	0.913749i	$0.366826\pi$
$968$	−2.24663e10	−0.796102
$969$	−1.63247e10	−0.576383
$970$	−2.61570e10	−0.920211
$971$	−7.16859e9	−0.251285	−0.125642	−	0.992076i	$-0.540099\pi$
$971$	−7.16859e9	−0.251285	−0.125642	+	0.992076i	$0.540099\pi$
$972$	−6.14853e10	−2.14753
$973$	−3.53147e10	−1.22902
$974$	−4.56623e10	−1.58344
$975$	7.82437e9	0.270354
$976$	7.04863e9	0.242678
$977$	4.37305e9	0.150021	0.0750107	−	0.997183i	$-0.476101\pi$
$977$	4.37305e9	0.150021	0.0750107	+	0.997183i	$0.476101\pi$
$978$	−4.69730e10	−1.60569
$979$	5.31240e10	1.80947
$980$	−2.78897e9	−0.0946570
$981$	1.94852e10	0.658965
$982$	1.15216e10	0.388260
$983$	−3.00251e10	−1.00820	−0.504101	−	0.863645i	$-0.668176\pi$
$983$	−3.00251e10	−1.00820	−0.504101	+	0.863645i	$0.668176\pi$
$984$	3.85973e10	1.29144
$985$	−1.12204e9	−0.0374094
$986$	−1.19210e11	−3.96045
$987$	2.41928e10	0.800895
$988$	−3.64497e10	−1.20239
$989$	2.67224e10	0.878391
$990$	−2.40490e10	−0.787723
$991$	−1.22875e10	−0.401056	−0.200528	−	0.979688i	$-0.564266\pi$
$991$	−1.22875e10	−0.401056	−0.200528	+	0.979688i	$0.564266\pi$
$992$	−1.19752e10	−0.389485
$993$	−2.85370e9	−0.0924882
$994$	4.05188e10	1.30859
$995$	7.13252e9	0.229542
$996$	−4.00897e10	−1.28566
$997$	1.05206e10	0.336207	0.168104	−	0.985769i	$-0.446236\pi$
$997$	1.05206e10	0.336207	0.168104	+	0.985769i	$0.446236\pi$
$998$	2.89913e10	0.923231
$999$	2.64798e10	0.840302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.8.a.a.1.5	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.8.a.a.1.5	✓	55	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-19.8304 q^{2} -24.8621 q^{3} +265.245 q^{4} -146.760 q^{5} +493.027 q^{6} -946.144 q^{7} -2721.63 q^{8} -1568.87 q^{9} +2910.32 q^{10} +5267.06 q^{11} -6594.57 q^{12} +5561.59 q^{13} +18762.4 q^{14} +3648.78 q^{15} +20019.7 q^{16} -26574.1 q^{17} +31111.4 q^{18} -24708.6 q^{19} -38927.5 q^{20} +23523.2 q^{21} -104448. q^{22} +51814.8 q^{23} +67665.7 q^{24} -56586.4 q^{25} -110289. q^{26} +93379.1 q^{27} -250960. q^{28} -226216. q^{29} -72356.8 q^{30} +246250. q^{31} -48630.1 q^{32} -130950. q^{33} +526975. q^{34} +138856. q^{35} -416136. q^{36} +283573. q^{37} +489981. q^{38} -138273. q^{39} +399428. q^{40} +570412. q^{41} -466474. q^{42} +515728. q^{43} +1.39706e6 q^{44} +230248. q^{45} -1.02751e6 q^{46} +1.02847e6 q^{47} -497733. q^{48} +71645.2 q^{49} +1.12213e6 q^{50} +660689. q^{51} +1.47518e6 q^{52} -1.60897e6 q^{53} -1.85175e6 q^{54} -772995. q^{55} +2.57506e6 q^{56} +614308. q^{57} +4.48596e6 q^{58} +1.83722e6 q^{59} +967822. q^{60} +352085. q^{61} -4.88325e6 q^{62} +1.48438e6 q^{63} -1.59817e6 q^{64} -816220. q^{65} +2.59680e6 q^{66} -3.13851e6 q^{67} -7.04866e6 q^{68} -1.28823e6 q^{69} -2.75358e6 q^{70} +2.15957e6 q^{71} +4.26990e6 q^{72} +866346. q^{73} -5.62337e6 q^{74} +1.40686e6 q^{75} -6.55383e6 q^{76} -4.98339e6 q^{77} +2.74201e6 q^{78} +7.48766e6 q^{79} -2.93810e6 q^{80} +1.10952e6 q^{81} -1.13115e7 q^{82} +6.07920e6 q^{83} +6.23941e6 q^{84} +3.90002e6 q^{85} -1.02271e7 q^{86} +5.62422e6 q^{87} -1.43350e7 q^{88} +1.00861e7 q^{89} -4.56592e6 q^{90} -5.26206e6 q^{91} +1.37436e7 q^{92} -6.12231e6 q^{93} -2.03949e7 q^{94} +3.62624e6 q^{95} +1.20905e6 q^{96} -8.98768e6 q^{97} -1.42075e6 q^{98} -8.26335e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 24 q^{2} - 298 q^{3} + 3264 q^{4} - 946 q^{5} - 960 q^{6} - 6017 q^{7} - 5109 q^{8} + 36449 q^{9} - 9763 q^{10} - 11506 q^{11} - 37376 q^{12} - 33844 q^{13} - 33495 q^{14} - 25861 q^{15} + 176128 q^{16}+ \cdots - 85438141 q^{99}+O(q^{100}) \) 55 * q - 24 * q^2 - 298 * q^3 + 3264 * q^4 - 946 * q^5 - 960 * q^6 - 6017 * q^7 - 5109 * q^8 + 36449 * q^9 - 9763 * q^10 - 11506 * q^11 - 37376 * q^12 - 33844 * q^13 - 33495 * q^14 - 25861 * q^15 + 176128 * q^16 - 55125 * q^17 - 69815 * q^18 - 205015 * q^19 - 209621 * q^20 - 76786 * q^21 - 184567 * q^22 - 132580 * q^23 - 126075 * q^24 + 703595 * q^25 - 802 * q^26 - 942457 * q^27 - 980794 * q^28 - 180975 * q^29 - 231365 * q^30 - 752200 * q^31 - 458116 * q^32 - 1189462 * q^33 - 534334 * q^34 - 501828 * q^35 + 2216122 * q^36 - 1812550 * q^37 - 1732590 * q^38 - 316133 * q^39 - 2564154 * q^40 + 387642 * q^41 - 1974005 * q^42 - 3120525 * q^43 - 1010046 * q^44 - 4004703 * q^45 - 2804563 * q^46 - 1968319 * q^47 - 5200654 * q^48 + 3219122 * q^49 + 5080367 * q^50 + 4015335 * q^51 - 105242 * q^52 + 793560 * q^53 + 9980039 * q^54 - 2193645 * q^55 + 7180088 * q^56 - 848029 * q^57 - 4318541 * q^58 - 4206985 * q^59 - 3767411 * q^60 - 3233922 * q^61 - 4798113 * q^62 - 16370607 * q^63 - 3153855 * q^64 - 5234873 * q^65 - 27799028 * q^66 - 29330378 * q^67 - 38894327 * q^68 - 12421645 * q^69 - 42976929 * q^70 - 20675277 * q^71 - 57843841 * q^72 - 21269365 * q^73 - 32764695 * q^74 - 51817010 * q^75 - 59377690 * q^76 - 16275190 * q^77 - 85089407 * q^78 - 28033705 * q^79 - 75304702 * q^80 - 923221 * q^81 - 54988201 * q^82 - 35573360 * q^83 - 80450394 * q^84 - 33089314 * q^85 - 71770618 * q^86 - 38591063 * q^87 - 62367981 * q^88 - 22496216 * q^89 - 138633489 * q^90 - 69344213 * q^91 - 112457146 * q^92 - 38701181 * q^93 - 49016719 * q^94 - 35589281 * q^95 - 173964883 * q^96 - 59838870 * q^97 - 95514862 * q^98 - 85438141 * q^99

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