LMFDB - Embedded newform 197.14.a.b.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,14,Mod(1,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

comment:select newform

sage:traces = [109] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$211.244930035$
Analytic rank:	$0$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	\(q-168.643 q^{2} +977.710 q^{3} +20248.6 q^{4} +23282.0 q^{5} -164884. q^{6} -126937. q^{7} -2.03327e6 q^{8} -638407. q^{9} -3.92635e6 q^{10} -8.23416e6 q^{11} +1.97973e7 q^{12} +1.69965e7 q^{13} +2.14071e7 q^{14} +2.27630e7 q^{15} +1.77021e8 q^{16} -8.40289e7 q^{17} +1.07663e8 q^{18} +2.16492e8 q^{19} +4.71428e8 q^{20} -1.24107e8 q^{21} +1.38864e9 q^{22} -6.93845e8 q^{23} -1.98795e9 q^{24} -6.78653e8 q^{25} -2.86635e9 q^{26} -2.18296e9 q^{27} -2.57029e9 q^{28} -1.45113e9 q^{29} -3.83883e9 q^{30} -2.27203e9 q^{31} -1.31969e10 q^{32} -8.05062e9 q^{33} +1.41709e10 q^{34} -2.95534e9 q^{35} -1.29268e10 q^{36} +1.70009e10 q^{37} -3.65099e10 q^{38} +1.66177e10 q^{39} -4.73385e10 q^{40} -4.86955e9 q^{41} +2.09299e10 q^{42} +2.01234e10 q^{43} -1.66730e11 q^{44} -1.48634e10 q^{45} +1.17012e11 q^{46} -1.42493e11 q^{47} +1.73075e11 q^{48} -8.07761e10 q^{49} +1.14450e11 q^{50} -8.21559e10 q^{51} +3.44156e11 q^{52} +3.00267e10 q^{53} +3.68142e11 q^{54} -1.91707e11 q^{55} +2.58097e11 q^{56} +2.11666e11 q^{57} +2.44724e11 q^{58} -3.86530e11 q^{59} +4.60919e11 q^{60} +4.31426e11 q^{61} +3.83163e11 q^{62} +8.10373e10 q^{63} +7.75410e11 q^{64} +3.95712e11 q^{65} +1.35768e12 q^{66} +1.10450e12 q^{67} -1.70147e12 q^{68} -6.78379e11 q^{69} +4.98398e11 q^{70} +1.43288e11 q^{71} +1.29805e12 q^{72} -1.28575e12 q^{73} -2.86709e12 q^{74} -6.63526e11 q^{75} +4.38365e12 q^{76} +1.04522e12 q^{77} -2.80246e12 q^{78} +4.04290e12 q^{79} +4.12139e12 q^{80} -1.11648e12 q^{81} +8.21218e11 q^{82} +4.40239e12 q^{83} -2.51300e12 q^{84} -1.95636e12 q^{85} -3.39368e12 q^{86} -1.41879e12 q^{87} +1.67423e13 q^{88} +2.64544e12 q^{89} +2.50661e12 q^{90} -2.15748e12 q^{91} -1.40494e13 q^{92} -2.22139e12 q^{93} +2.40306e13 q^{94} +5.04035e12 q^{95} -1.29027e13 q^{96} -1.19515e13 q^{97} +1.36224e13 q^{98} +5.25674e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14}+ \cdots + 12084396239183 q^{99}+O(q^{100}) $ 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9 + 16373653 * q^10 + 21199298 * q^11 + 63225856 * q^12 + 59695238 * q^13 + 37888529 * q^14 + 87246239 * q^15 + 2130706432 * q^16 + 228353715 * q^17 + 400647337 * q^18 + 1139301305 * q^19 + 1109969259 * q^20 + 539982398 * q^21 + 1613315649 * q^22 + 920306804 * q^23 + 5542439613 * q^24 + 31241700999 * q^25 + 1864366110 * q^26 + 17825460755 * q^27 + 20413389070 * q^28 + 7185436621 * q^29 + 2050251883 * q^30 + 28475592572 * q^31 + 8334714660 * q^32 + 19623425846 * q^33 + 37845014194 * q^34 + 25255003636 * q^35 + 287968706746 * q^36 + 71523920490 * q^37 + 67778214914 * q^38 + 44951568463 * q^39 + 169184871486 * q^40 + 69139231052 * q^41 + 58715177635 * q^42 + 247544146139 * q^43 + 63861560722 * q^44 + 257443045479 * q^45 + 160530477869 * q^46 + 308496573061 * q^47 + 412228130018 * q^48 + 1736616239908 * q^49 + 1680360028531 * q^50 + 756579032995 * q^51 + 928015404666 * q^52 + 342783723680 * q^53 - 597894730601 * q^54 + 59276330527 * q^55 - 3822929869144 * q^56 - 562905761941 * q^57 + 62740419347 * q^58 + 827401964151 * q^59 - 2247133283907 * q^60 + 988213134514 * q^61 + 1937380192071 * q^62 + 1788190111357 * q^63 + 11682175668457 * q^64 + 2494670804291 * q^65 + 11819807890512 * q^66 + 8038740399790 * q^67 + 10126245189885 * q^68 + 5225665164579 * q^69 + 11464042631319 * q^70 + 4867145119603 * q^71 + 18133468947055 * q^72 + 9684156738615 * q^73 + 16996786880941 * q^74 + 16718732018262 * q^75 + 21454522032798 * q^76 + 6593100920650 * q^77 + 33749579076633 * q^78 + 7591753073823 * q^79 + 24349241260570 * q^80 + 38778649605417 * q^81 + 25555033184251 * q^82 + 16945724819556 * q^83 + 21855489402730 * q^84 + 15544906794766 * q^85 + 18664144286914 * q^86 + 19049540636401 * q^87 + 17318749473003 * q^88 + 11289674998576 * q^89 + 20983303956671 * q^90 + 47242561944227 * q^91 - 25046698097386 * q^92 - 5411884145985 * q^93 + 18338784709341 * q^94 + 6784117894603 * q^95 - 36827486682955 * q^96 + 45969533477736 * q^97 - 42983409526150 * q^98 + 12084396239183 * 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 $

$2$	−168.643	−1.86326	−0.931632	−	0.363403i	$-0.881615\pi$
$2$	−168.643	−1.86326	−0.931632	+	0.363403i	$0.881615\pi$
$3$	977.710	0.774322	0.387161	−	0.922012i	$-0.373456\pi$
$3$	977.710	0.774322	0.387161	+	0.922012i	$0.373456\pi$
$4$	20248.6	2.47175
$5$	23282.0	0.666369	0.333184	−	0.942862i	$-0.391877\pi$
$5$	23282.0	0.666369	0.333184	+	0.942862i	$0.391877\pi$
$6$	−164884.	−1.44277
$7$	−126937.	−0.407803	−0.203901	−	0.978991i	$-0.565362\pi$
$7$	−126937.	−0.407803	−0.203901	+	0.978991i	$0.565362\pi$
$8$	−2.03327e6	−2.74227
$9$	−638407.	−0.400425
$10$	−3.92635e6	−1.24162
$11$	−8.23416e6	−1.40142	−0.700708	−	0.713448i	$-0.747132\pi$
$11$	−8.23416e6	−1.40142	−0.700708	+	0.713448i	$0.747132\pi$
$12$	1.97973e7	1.91393
$13$	1.69965e7	0.976626	0.488313	−	0.872669i	$-0.337612\pi$
$13$	1.69965e7	0.976626	0.488313	+	0.872669i	$0.337612\pi$
$14$	2.14071e7	0.759845
$15$	2.27630e7	0.515984
$16$	1.77021e8	2.63782
$17$	−8.40289e7	−0.844327	−0.422163	−	0.906520i	$-0.638729\pi$
$17$	−8.40289e7	−0.844327	−0.422163	+	0.906520i	$0.638729\pi$
$18$	1.07663e8	0.746097
$19$	2.16492e8	1.05570	0.527852	−	0.849336i	$-0.322997\pi$
$19$	2.16492e8	1.05570	0.527852	+	0.849336i	$0.322997\pi$
$20$	4.71428e8	1.64710
$21$	−1.24107e8	−0.315771
$22$	1.38864e9	2.61121
$23$	−6.93845e8	−0.977308	−0.488654	−	0.872478i	$-0.662512\pi$
$23$	−6.93845e8	−0.977308	−0.488654	+	0.872478i	$0.662512\pi$
$24$	−1.98795e9	−2.12340
$25$	−6.78653e8	−0.555953
$26$	−2.86635e9	−1.81971
$27$	−2.18296e9	−1.08438
$28$	−2.57029e9	−1.00799
$29$	−1.45113e9	−0.453022	−0.226511	−	0.974009i	$-0.572732\pi$
$29$	−1.45113e9	−0.453022	−0.226511	+	0.974009i	$0.572732\pi$
$30$	−3.83883e9	−0.961415
$31$	−2.27203e9	−0.459794	−0.229897	−	0.973215i	$-0.573839\pi$
$31$	−2.27203e9	−0.459794	−0.229897	+	0.973215i	$0.573839\pi$
$32$	−1.31969e10	−2.17268
$33$	−8.05062e9	−1.08515
$34$	1.41709e10	1.57320
$35$	−2.95534e9	−0.271747
$36$	−1.29268e10	−0.989752
$37$	1.70009e10	1.08933	0.544667	−	0.838653i	$-0.316656\pi$
$37$	1.70009e10	1.08933	0.544667	+	0.838653i	$0.316656\pi$
$38$	−3.65099e10	−1.96706
$39$	1.66177e10	0.756223
$40$	−4.73385e10	−1.82736
$41$	−4.86955e9	−0.160101	−0.0800505	−	0.996791i	$-0.525508\pi$
$41$	−4.86955e9	−0.160101	−0.0800505	+	0.996791i	$0.525508\pi$
$42$	2.09299e10	0.588365
$43$	2.01234e10	0.485463	0.242731	−	0.970094i	$-0.421957\pi$
$43$	2.01234e10	0.485463	0.242731	+	0.970094i	$0.421957\pi$
$44$	−1.66730e11	−3.46395
$45$	−1.48634e10	−0.266831
$46$	1.17012e11	1.82098
$47$	−1.42493e11	−1.92823	−0.964114	−	0.265487i	$-0.914467\pi$
$47$	−1.42493e11	−1.92823	−0.964114	+	0.265487i	$0.914467\pi$
$48$	1.73075e11	2.04252
$49$	−8.07761e10	−0.833697
$50$	1.14450e11	1.03589
$51$	−8.21559e10	−0.653781
$52$	3.44156e11	2.41398
$53$	3.00267e10	0.186086	0.0930432	−	0.995662i	$-0.470341\pi$
$53$	3.00267e10	0.186086	0.0930432	+	0.995662i	$0.470341\pi$
$54$	3.68142e11	2.02049
$55$	−1.91707e11	−0.933859
$56$	2.58097e11	1.11830
$57$	2.11666e11	0.817456
$58$	2.44724e11	0.844100
$59$	−3.86530e11	−1.19301	−0.596507	−	0.802608i	$-0.703445\pi$
$59$	−3.86530e11	−1.19301	−0.596507	+	0.802608i	$0.703445\pi$
$60$	4.60919e11	1.27539
$61$	4.31426e11	1.07217	0.536084	−	0.844165i	$-0.319903\pi$
$61$	4.31426e11	1.07217	0.536084	+	0.844165i	$0.319903\pi$
$62$	3.83163e11	0.856717
$63$	8.10373e10	0.163294
$64$	7.75410e11	1.41046
$65$	3.95712e11	0.650793
$66$	1.35768e12	2.02192
$67$	1.10450e12	1.49169	0.745846	−	0.666118i	$-0.232045\pi$
$67$	1.10450e12	1.49169	0.745846	+	0.666118i	$0.232045\pi$
$68$	−1.70147e12	−2.08697
$69$	−6.78379e11	−0.756751
$70$	4.98398e11	0.506337
$71$	1.43288e11	0.132749	0.0663743	−	0.997795i	$-0.478857\pi$
$71$	1.43288e11	0.132749	0.0663743	+	0.997795i	$0.478857\pi$
$72$	1.29805e12	1.09807
$73$	−1.28575e12	−0.994395	−0.497198	−	0.867637i	$-0.665638\pi$
$73$	−1.28575e12	−0.994395	−0.497198	+	0.867637i	$0.665638\pi$
$74$	−2.86709e12	−2.02972
$75$	−6.63526e11	−0.430487
$76$	4.38365e12	2.60944
$77$	1.04522e12	0.571501
$78$	−2.80246e12	−1.40904
$79$	4.04290e12	1.87119	0.935594	−	0.353078i	$-0.114865\pi$
$79$	4.04290e12	1.87119	0.935594	+	0.353078i	$0.114865\pi$
$80$	4.12139e12	1.75776
$81$	−1.11648e12	−0.439235
$82$	8.21218e11	0.298310
$83$	4.40239e12	1.47802	0.739010	−	0.673694i	$-0.235294\pi$
$83$	4.40239e12	1.47802	0.739010	+	0.673694i	$0.235294\pi$
$84$	−2.51300e12	−0.780508
$85$	−1.95636e12	−0.562633
$86$	−3.39368e12	−0.904545
$87$	−1.41879e12	−0.350785
$88$	1.67423e13	3.84306
$89$	2.64544e12	0.564240	0.282120	−	0.959379i	$-0.408962\pi$
$89$	2.64544e12	0.564240	0.282120	+	0.959379i	$0.408962\pi$
$90$	2.50661e12	0.497176
$91$	−2.15748e12	−0.398271
$92$	−1.40494e13	−2.41567
$93$	−2.22139e12	−0.356028
$94$	2.40306e13	3.59280
$95$	5.04035e12	0.703489
$96$	−1.29027e13	−1.68236
$97$	−1.19515e13	−1.45682	−0.728411	−	0.685140i	$-0.759741\pi$
$97$	−1.19515e13	−1.45682	−0.728411	+	0.685140i	$0.759741\pi$
$98$	1.36224e13	1.55340
$99$	5.25674e12	0.561162
$100$	−1.37418e13	−1.37418
$101$	−8.86561e12	−0.831036	−0.415518	−	0.909585i	$-0.636400\pi$
$101$	−8.86561e12	−0.831036	−0.415518	+	0.909585i	$0.636400\pi$
$102$	1.38550e13	1.21817
$103$	−8.84075e12	−0.729537	−0.364769	−	0.931098i	$-0.618852\pi$
$103$	−8.84075e12	−0.729537	−0.364769	+	0.931098i	$0.618852\pi$
$104$	−3.45585e13	−2.67817
$105$	−2.88946e12	−0.210420
$106$	−5.06381e12	−0.346728
$107$	−2.31071e12	−0.148851	−0.0744253	−	0.997227i	$-0.523712\pi$
$107$	−2.31071e12	−0.148851	−0.0744253	+	0.997227i	$0.523712\pi$
$108$	−4.42019e13	−2.68032
$109$	8.23338e12	0.470225	0.235113	−	0.971968i	$-0.424454\pi$
$109$	8.23338e12	0.470225	0.235113	+	0.971968i	$0.424454\pi$
$110$	3.23302e13	1.74003
$111$	1.66220e13	0.843495
$112$	−2.24705e13	−1.07571
$113$	2.01925e13	0.912388	0.456194	−	0.889880i	$-0.349212\pi$
$113$	2.01925e13	0.912388	0.456194	+	0.889880i	$0.349212\pi$
$114$	−3.56961e13	−1.52314
$115$	−1.61541e13	−0.651248
$116$	−2.93834e13	−1.11976
$117$	−1.08507e13	−0.391065
$118$	6.51858e13	2.22290
$119$	1.06664e13	0.344319
$120$	−4.62833e13	−1.41497
$121$	3.32787e13	0.963965
$122$	−7.27572e13	−1.99773
$123$	−4.76101e12	−0.123970
$124$	−4.60054e13	−1.13650
$125$	−4.42207e13	−1.03684
$126$	−1.36664e13	−0.304261
$127$	7.03521e12	0.148783	0.0743914	−	0.997229i	$-0.476299\pi$
$127$	7.03521e12	0.148783	0.0743914	+	0.997229i	$0.476299\pi$
$128$	−2.26591e13	−0.455384
$129$	1.96748e13	0.375905
$130$	−6.67343e13	−1.21260
$131$	6.10944e13	1.05618	0.528090	−	0.849188i	$-0.322908\pi$
$131$	6.10944e13	1.05618	0.528090	+	0.849188i	$0.322908\pi$
$132$	−1.63014e14	−2.68222
$133$	−2.74807e13	−0.430520
$134$	−1.86267e14	−2.77942
$135$	−5.08236e13	−0.722597
$136$	1.70853e14	2.31537
$137$	−2.39957e12	−0.0310062	−0.0155031	−	0.999880i	$-0.504935\pi$
$137$	−2.39957e12	−0.0310062	−0.0155031	+	0.999880i	$0.504935\pi$
$138$	1.14404e14	1.41003
$139$	−1.35358e14	−1.59180	−0.795898	−	0.605431i	$-0.793001\pi$
$139$	−1.35358e14	−1.59180	−0.795898	+	0.605431i	$0.793001\pi$
$140$	−5.98415e13	−0.671692
$141$	−1.39317e14	−1.49307
$142$	−2.41645e13	−0.247346
$143$	−1.39952e14	−1.36866
$144$	−1.13011e14	−1.05625
$145$	−3.37852e13	−0.301880
$146$	2.16834e14	1.85282
$147$	−7.89755e13	−0.645550
$148$	3.44245e14	2.69256
$149$	2.20203e14	1.64859	0.824296	−	0.566159i	$-0.191571\pi$
$149$	2.20203e14	1.64859	0.824296	+	0.566159i	$0.191571\pi$
$150$	1.11899e14	0.802110
$151$	−1.04073e14	−0.714479	−0.357240	−	0.934013i	$-0.616282\pi$
$151$	−1.04073e14	−0.714479	−0.357240	+	0.934013i	$0.616282\pi$
$152$	−4.40186e14	−2.89503
$153$	5.36446e13	0.338089
$154$	−1.76269e14	−1.06486
$155$	−5.28973e13	−0.306392
$156$	3.36485e14	1.86920
$157$	3.51596e14	1.87368	0.936842	−	0.349753i	$-0.113735\pi$
$157$	3.51596e14	1.87368	0.936842	+	0.349753i	$0.113735\pi$
$158$	−6.81809e14	−3.48652
$159$	2.93574e13	0.144091
$160$	−3.07249e14	−1.44781
$161$	8.80745e13	0.398549
$162$	1.88286e14	0.818411
$163$	4.20751e14	1.75714	0.878568	−	0.477617i	$-0.158499\pi$
$163$	4.20751e14	1.75714	0.878568	+	0.477617i	$0.158499\pi$
$164$	−9.86017e13	−0.395730
$165$	−1.87434e14	−0.723108
$166$	−7.42433e14	−2.75394
$167$	−3.34789e14	−1.19430	−0.597152	−	0.802128i	$-0.703701\pi$
$167$	−3.34789e14	−1.19430	−0.597152	+	0.802128i	$0.703701\pi$
$168$	2.52344e14	0.865928
$169$	−1.39934e13	−0.0462018
$170$	3.29927e14	1.04833
$171$	−1.38210e14	−0.422731
$172$	4.07470e14	1.19994
$173$	2.84525e13	0.0806903	0.0403452	−	0.999186i	$-0.487154\pi$
$173$	2.84525e13	0.0806903	0.0403452	+	0.999186i	$0.487154\pi$
$174$	2.39269e14	0.653606
$175$	8.61461e13	0.226719
$176$	−1.45762e15	−3.69668
$177$	−3.77914e14	−0.923777
$178$	−4.46137e14	−1.05133
$179$	6.60949e14	1.50184	0.750920	−	0.660393i	$-0.229610\pi$
$179$	6.60949e14	1.50184	0.750920	+	0.660393i	$0.229610\pi$
$180$	−3.00962e14	−0.659540
$181$	6.24507e14	1.32016	0.660080	−	0.751196i	$-0.270523\pi$
$181$	6.24507e14	1.32016	0.660080	+	0.751196i	$0.270523\pi$
$182$	3.63846e14	0.742084
$183$	4.21810e14	0.830204
$184$	1.41077e15	2.68004
$185$	3.95814e14	0.725898
$186$	3.74622e14	0.663375
$187$	6.91907e14	1.18325
$188$	−2.88529e15	−4.76611
$189$	2.77098e14	0.442213
$190$	−8.50022e14	−1.31079
$191$	4.85135e14	0.723012	0.361506	−	0.932370i	$-0.382263\pi$
$191$	4.85135e14	0.723012	0.361506	+	0.932370i	$0.382263\pi$
$192$	7.58126e14	1.09215
$193$	−6.81300e14	−0.948890	−0.474445	−	0.880285i	$-0.657351\pi$
$193$	−6.81300e14	−0.948890	−0.474445	+	0.880285i	$0.657351\pi$
$194$	2.01554e15	2.71444
$195$	3.86892e14	0.503924
$196$	−1.63560e15	−2.06069
$197$	5.84517e13	0.0712470
$197$	5.84517e13	0.0712470
$198$	−8.86515e14	−1.04559
$199$	−6.99058e14	−0.797937	−0.398968	−	0.916965i	$-0.630632\pi$
$199$	−6.99058e14	−0.797937	−0.398968	+	0.916965i	$0.630632\pi$
$200$	1.37988e15	1.52457
$201$	1.07988e15	1.15505
$202$	1.49513e15	1.54844
$203$	1.84202e14	0.184744
$204$	−1.66354e15	−1.61599
$205$	−1.13373e14	−0.106686
$206$	1.49094e15	1.35932
$207$	4.42955e14	0.391338
$208$	3.00874e15	2.57616
$209$	−1.78263e15	−1.47948
$210$	4.87289e14	0.392068
$211$	−1.16834e14	−0.0911450	−0.0455725	−	0.998961i	$-0.514511\pi$
$211$	−1.16834e14	−0.0911450	−0.0455725	+	0.998961i	$0.514511\pi$
$212$	6.07999e14	0.459960
$213$	1.40094e14	0.102790
$214$	3.89686e14	0.277348
$215$	4.68512e14	0.323497
$216$	4.43855e15	2.97366
$217$	2.88404e14	0.187505
$218$	−1.38851e15	−0.876154
$219$	−1.25709e15	−0.769982
$220$	−3.88181e15	−2.30827
$221$	−1.42820e15	−0.824592
$222$	−2.80318e15	−1.57165
$223$	1.83327e15	0.998261	0.499130	−	0.866527i	$-0.333653\pi$
$223$	1.83327e15	0.998261	0.499130	+	0.866527i	$0.333653\pi$
$224$	1.67517e15	0.886025
$225$	4.33257e14	0.222617
$226$	−3.40533e15	−1.70002
$227$	−2.16336e15	−1.04945	−0.524724	−	0.851272i	$-0.675831\pi$
$227$	−2.16336e15	−1.04945	−0.524724	+	0.851272i	$0.675831\pi$
$228$	4.28594e15	2.02055
$229$	−2.13339e15	−0.977550	−0.488775	−	0.872410i	$-0.662556\pi$
$229$	−2.13339e15	−0.977550	−0.488775	+	0.872410i	$0.662556\pi$
$230$	2.72428e15	1.21345
$231$	1.02192e15	0.442526
$232$	2.95054e15	1.24231
$233$	−1.87987e14	−0.0769688	−0.0384844	−	0.999259i	$-0.512253\pi$
$233$	−1.87987e14	−0.0769688	−0.0384844	+	0.999259i	$0.512253\pi$
$234$	1.82990e15	0.728658
$235$	−3.31753e15	−1.28491
$236$	−7.82670e15	−2.94884
$237$	3.95279e15	1.44890
$238$	−1.79881e15	−0.641557
$239$	−4.75777e15	−1.65127	−0.825633	−	0.564208i	$-0.809182\pi$
$239$	−4.75777e15	−1.65127	−0.825633	+	0.564208i	$0.809182\pi$
$240$	4.02953e15	1.36107
$241$	−1.43440e15	−0.471586	−0.235793	−	0.971803i	$-0.575769\pi$
$241$	−1.43440e15	−0.471586	−0.235793	+	0.971803i	$0.575769\pi$
$242$	−5.61223e15	−1.79612
$243$	2.38876e15	0.744271
$244$	8.73579e15	2.65014
$245$	−1.88063e15	−0.555550
$246$	8.02913e14	0.230988
$247$	3.67960e15	1.03103
$248$	4.61965e15	1.26088
$249$	4.30425e15	1.14446
$250$	7.45754e15	1.93190
$251$	1.42140e15	0.358787	0.179393	−	0.983777i	$-0.442587\pi$
$251$	1.42140e15	0.358787	0.179393	+	0.983777i	$0.442587\pi$
$252$	1.64089e15	0.403624
$253$	5.71323e15	1.36961
$254$	−1.18644e15	−0.277222
$255$	−1.91275e15	−0.435659
$256$	−2.53085e15	−0.561961
$257$	4.96896e15	1.07572	0.537861	−	0.843034i	$-0.319233\pi$
$257$	4.96896e15	1.07572	0.537861	+	0.843034i	$0.319233\pi$
$258$	−3.31803e15	−0.700410
$259$	−2.15804e15	−0.444233
$260$	8.01263e15	1.60860
$261$	9.26412e14	0.181401
$262$	−1.03032e16	−1.96794
$263$	6.85544e15	1.27739	0.638694	−	0.769461i	$-0.279475\pi$
$263$	6.85544e15	1.27739	0.638694	+	0.769461i	$0.279475\pi$
$264$	1.63691e16	2.97576
$265$	6.99081e14	0.124002
$266$	4.63445e15	0.802172
$267$	2.58648e15	0.436903
$268$	2.23646e16	3.68710
$269$	2.11302e15	0.340028	0.170014	−	0.985442i	$-0.445619\pi$
$269$	2.11302e15	0.340028	0.170014	+	0.985442i	$0.445619\pi$
$270$	8.57107e15	1.34639
$271$	3.88890e15	0.596385	0.298192	−	0.954506i	$-0.403616\pi$
$271$	3.88890e15	0.596385	0.298192	+	0.954506i	$0.403616\pi$
$272$	−1.48749e16	−2.22718
$273$	−2.10939e15	−0.308390
$274$	4.04671e14	0.0577728
$275$	5.58814e15	0.779121
$276$	−1.37362e16	−1.87050
$277$	−4.65652e15	−0.619360	−0.309680	−	0.950841i	$-0.600222\pi$
$277$	−4.65652e15	−0.619360	−0.309680	+	0.950841i	$0.600222\pi$
$278$	2.28272e16	2.96594
$279$	1.45048e15	0.184113
$280$	6.00900e15	0.745203
$281$	8.50499e15	1.03058	0.515291	−	0.857015i	$-0.327684\pi$
$281$	8.50499e15	1.03058	0.515291	+	0.857015i	$0.327684\pi$
$282$	2.34949e16	2.78199
$283$	−5.02144e15	−0.581054	−0.290527	−	0.956867i	$-0.593831\pi$
$283$	−5.02144e15	−0.581054	−0.290527	+	0.956867i	$0.593831\pi$
$284$	2.90138e15	0.328122
$285$	4.92800e15	0.544727
$286$	2.36020e16	2.55017
$287$	6.18125e14	0.0652896
$288$	8.42496e15	0.869995
$289$	−2.84372e15	−0.287112
$290$	5.69765e15	0.562482
$291$	−1.16851e16	−1.12805
$292$	−2.60347e16	−2.45790
$293$	−1.47381e15	−0.136082	−0.0680412	−	0.997683i	$-0.521675\pi$
$293$	−1.47381e15	−0.136082	−0.0680412	+	0.997683i	$0.521675\pi$
$294$	1.33187e16	1.20283
$295$	−8.99919e15	−0.794987
$296$	−3.45674e16	−2.98724
$297$	1.79749e16	1.51967
$298$	−3.71358e16	−3.07176
$299$	−1.17929e16	−0.954464
$300$	−1.34355e16	−1.06406
$301$	−2.55440e15	−0.197973
$302$	1.75513e16	1.33126
$303$	−8.66800e15	−0.643490
$304$	3.83235e16	2.78476
$305$	1.00445e16	0.714459
$306$	−9.04681e15	−0.629950
$307$	−1.24139e16	−0.846269	−0.423134	−	0.906067i	$-0.639070\pi$
$307$	−1.24139e16	−0.846269	−0.423134	+	0.906067i	$0.639070\pi$
$308$	2.11642e16	1.41261
$309$	−8.64369e15	−0.564897
$310$	8.92078e15	0.570889
$311$	4.99006e15	0.312726	0.156363	−	0.987700i	$-0.450023\pi$
$311$	4.99006e15	0.312726	0.156363	+	0.987700i	$0.450023\pi$
$312$	−3.37882e16	−2.07377
$313$	1.01680e14	0.00611218	0.00305609	−	0.999995i	$-0.499027\pi$
$313$	1.01680e14	0.00611218	0.00305609	+	0.999995i	$0.499027\pi$
$314$	−5.92944e16	−3.49117
$315$	1.88671e15	0.108814
$316$	8.18632e16	4.62512
$317$	−1.22078e16	−0.675700	−0.337850	−	0.941200i	$-0.609700\pi$
$317$	−1.22078e16	−0.675700	−0.337850	+	0.941200i	$0.609700\pi$
$318$	−4.95093e15	−0.268479
$319$	1.19488e16	0.634873
$320$	1.80531e16	0.939888
$321$	−2.25920e15	−0.115258
$322$	−1.48532e16	−0.742602
$323$	−1.81915e16	−0.891360
$324$	−2.26071e16	−1.08568
$325$	−1.15347e16	−0.542958
$326$	−7.09569e16	−3.27401
$327$	8.04986e15	0.364106
$328$	9.90111e15	0.439040
$329$	1.80877e16	0.786337
$330$	3.16096e16	1.34734
$331$	2.84055e16	1.18719	0.593595	−	0.804764i	$-0.297708\pi$
$331$	2.84055e16	1.18719	0.593595	+	0.804764i	$0.297708\pi$
$332$	8.91422e16	3.65330
$333$	−1.08535e16	−0.436196
$334$	5.64601e16	2.22530
$335$	2.57149e16	0.994017
$336$	−2.19696e16	−0.832945
$337$	−4.27689e16	−1.59050	−0.795250	−	0.606282i	$-0.792660\pi$
$337$	−4.27689e16	−1.59050	−0.795250	+	0.606282i	$0.792660\pi$
$338$	2.35989e15	0.0860862
$339$	1.97424e16	0.706482
$340$	−3.96135e16	−1.39069
$341$	1.87083e16	0.644362
$342$	2.33081e16	0.787659
$343$	2.25522e16	0.747787
$344$	−4.09162e16	−1.33127
$345$	−1.57940e16	−0.504276
$346$	−4.79834e15	−0.150347
$347$	1.49991e16	0.461238	0.230619	−	0.973044i	$-0.425925\pi$
$347$	1.49991e16	0.461238	0.230619	+	0.973044i	$0.425925\pi$
$348$	−2.87284e16	−0.867055
$349$	8.84743e15	0.262091	0.131045	−	0.991376i	$-0.458167\pi$
$349$	8.84743e15	0.262091	0.131045	+	0.991376i	$0.458167\pi$
$350$	−1.45280e16	−0.422438
$351$	−3.71028e16	−1.05903
$352$	1.08665e17	3.04483
$353$	−4.66735e16	−1.28391	−0.641955	−	0.766742i	$-0.721877\pi$
$353$	−4.66735e16	−1.28391	−0.641955	+	0.766742i	$0.721877\pi$
$354$	6.37328e16	1.72124
$355$	3.33602e15	0.0884595
$356$	5.35666e16	1.39466
$357$	1.04286e16	0.266614
$358$	−1.11465e17	−2.79832
$359$	5.38973e16	1.32878	0.664390	−	0.747386i	$-0.268691\pi$
$359$	5.38973e16	1.32878	0.664390	+	0.747386i	$0.268691\pi$
$360$	3.02212e16	0.731721
$361$	4.81561e15	0.114513
$362$	−1.05319e17	−2.45981
$363$	3.25369e16	0.746420
$364$	−4.36861e16	−0.984428
$365$	−2.99349e16	−0.662634
$366$	−7.11355e16	−1.54689
$367$	−4.87652e16	−1.04179	−0.520895	−	0.853621i	$-0.674402\pi$
$367$	−4.87652e16	−1.04179	−0.520895	+	0.853621i	$0.674402\pi$
$368$	−1.22825e17	−2.57796
$369$	3.10875e15	0.0641084
$370$	−6.67515e16	−1.35254
$371$	−3.81149e15	−0.0758866
$372$	−4.49800e16	−0.880015
$373$	5.97019e16	1.14784	0.573920	−	0.818912i	$-0.305422\pi$
$373$	5.97019e16	1.14784	0.573920	+	0.818912i	$0.305422\pi$
$374$	−1.16686e17	−2.20471
$375$	−4.32351e16	−0.802847
$376$	2.89727e17	5.28772
$377$	−2.46642e16	−0.442433
$378$	−4.67308e16	−0.823961
$379$	4.52310e16	0.783937	0.391969	−	0.919979i	$-0.371794\pi$
$379$	4.52310e16	0.783937	0.391969	+	0.919979i	$0.371794\pi$
$380$	1.02060e17	1.73885
$381$	6.87839e15	0.115206
$382$	−8.18148e16	−1.34716
$383$	6.60843e15	0.106981	0.0534904	−	0.998568i	$-0.482965\pi$
$383$	6.60843e15	0.106981	0.0534904	+	0.998568i	$0.482965\pi$
$384$	−2.21540e16	−0.352614
$385$	2.43347e16	0.380831
$386$	1.14897e17	1.76803
$387$	−1.28469e16	−0.194391
$388$	−2.42001e17	−3.60091
$389$	−9.26328e16	−1.35548	−0.677739	−	0.735303i	$-0.737040\pi$
$389$	−9.26328e16	−1.35548	−0.677739	+	0.735303i	$0.737040\pi$
$390$	−6.52468e16	−0.938943
$391$	5.83030e16	0.825167
$392$	1.64239e17	2.28622
$393$	5.97326e16	0.817824
$394$	−9.85750e15	−0.132752
$395$	9.41268e16	1.24690
$396$	1.06442e17	1.38705
$397$	−2.77565e16	−0.355817	−0.177908	−	0.984047i	$-0.556933\pi$
$397$	−2.77565e16	−0.355817	−0.177908	+	0.984047i	$0.556933\pi$
$398$	1.17892e17	1.48677
$399$	−2.68682e16	−0.333361
$400$	−1.20136e17	−1.46650
$401$	−4.95716e16	−0.595380	−0.297690	−	0.954663i	$-0.596216\pi$
$401$	−4.95716e16	−0.595380	−0.297690	+	0.954663i	$0.596216\pi$
$402$	−1.82115e17	−2.15216
$403$	−3.86166e16	−0.449046
$404$	−1.79516e17	−2.05412
$405$	−2.59938e16	−0.292693
$406$	−3.10644e16	−0.344227
$407$	−1.39988e17	−1.52661
$408$	1.67045e17	1.79284
$409$	1.31500e16	0.138907	0.0694534	−	0.997585i	$-0.477874\pi$
$409$	1.31500e16	0.138907	0.0694534	+	0.997585i	$0.477874\pi$
$410$	1.91196e16	0.198785
$411$	−2.34608e15	−0.0240088
$412$	−1.79013e17	−1.80324
$413$	4.90649e16	0.486515
$414$	−7.47015e16	−0.729167
$415$	1.02496e17	0.984907
$416$	−2.24301e17	−2.12190
$417$	−1.32341e17	−1.23256
$418$	3.00628e17	2.75666
$419$	−1.50811e17	−1.36157	−0.680786	−	0.732482i	$-0.738362\pi$
$419$	−1.50811e17	−1.36157	−0.680786	+	0.732482i	$0.738362\pi$
$420$	−5.85076e16	−0.520106
$421$	8.33826e15	0.0729864	0.0364932	−	0.999334i	$-0.488381\pi$
$421$	8.33826e15	0.0729864	0.0364932	+	0.999334i	$0.488381\pi$
$422$	1.97033e16	0.169827
$423$	9.09687e16	0.772111
$424$	−6.10524e16	−0.510299
$425$	5.70265e16	0.469406
$426$	−2.36259e16	−0.191525
$427$	−5.47639e16	−0.437233
$428$	−4.67886e16	−0.367922
$429$	−1.36833e17	−1.05978
$430$	−7.90114e16	−0.602761
$431$	3.93492e16	0.295688	0.147844	−	0.989011i	$-0.452767\pi$
$431$	3.93492e16	0.295688	0.147844	+	0.989011i	$0.452767\pi$
$432$	−3.86430e17	−2.86040
$433$	1.27757e17	0.931566	0.465783	−	0.884899i	$-0.345773\pi$
$433$	1.27757e17	0.931566	0.465783	+	0.884899i	$0.345773\pi$
$434$	−4.86375e16	−0.349372
$435$	−3.30321e16	−0.233752
$436$	1.66715e17	1.16228
$437$	−1.50212e17	−1.03175
$438$	2.12001e17	1.43468
$439$	2.68659e17	1.79135	0.895677	−	0.444705i	$-0.146692\pi$
$439$	2.68659e17	1.79135	0.895677	+	0.444705i	$0.146692\pi$
$440$	3.89793e17	2.56089
$441$	5.15680e16	0.333833
$442$	2.40856e17	1.53643
$443$	2.46386e17	1.54879	0.774393	−	0.632705i	$-0.218055\pi$
$443$	2.46386e17	1.54879	0.774393	+	0.632705i	$0.218055\pi$
$444$	3.36571e17	2.08491
$445$	6.15911e16	0.375992
$446$	−3.09168e17	−1.86002
$447$	2.15295e17	1.27654
$448$	−9.84281e16	−0.575191
$449$	2.00826e17	1.15670	0.578349	−	0.815790i	$-0.303697\pi$
$449$	2.00826e17	1.15670	0.578349	+	0.815790i	$0.303697\pi$
$450$	−7.30659e16	−0.414795
$451$	4.00967e16	0.224368
$452$	4.08869e17	2.25520
$453$	−1.01754e17	−0.553237
$454$	3.64837e17	1.95540
$455$	−5.02305e16	−0.265395
$456$	−4.30374e17	−2.24168
$457$	−2.20923e17	−1.13445	−0.567227	−	0.823562i	$-0.691984\pi$
$457$	−2.20923e17	−1.13445	−0.567227	+	0.823562i	$0.691984\pi$
$458$	3.59782e17	1.82143
$459$	1.83432e17	0.915571
$460$	−3.27098e17	−1.60972
$461$	2.66171e17	1.29153	0.645765	−	0.763536i	$-0.276539\pi$
$461$	2.66171e17	1.29153	0.645765	+	0.763536i	$0.276539\pi$
$462$	−1.72340e17	−0.824543
$463$	1.86059e17	0.877757	0.438878	−	0.898547i	$-0.355376\pi$
$463$	1.86059e17	0.877757	0.438878	+	0.898547i	$0.355376\pi$
$464$	−2.56880e17	−1.19499
$465$	−5.17182e16	−0.237246
$466$	3.17028e16	0.143413
$467$	4.17029e16	0.186040	0.0930200	−	0.995664i	$-0.470348\pi$
$467$	4.17029e16	0.186040	0.0930200	+	0.995664i	$0.470348\pi$
$468$	−2.19711e17	−0.966617
$469$	−1.40202e17	−0.608316
$470$	5.59479e17	2.39413
$471$	3.43759e17	1.45084
$472$	7.85920e17	3.27156
$473$	−1.65699e17	−0.680335
$474$	−6.66612e17	−2.69969
$475$	−1.46923e17	−0.586922
$476$	2.15979e17	0.851072
$477$	−1.91692e16	−0.0745136
$478$	8.02366e17	3.07674
$479$	9.96294e16	0.376883	0.188442	−	0.982084i	$-0.439656\pi$
$479$	9.96294e16	0.376883	0.188442	+	0.982084i	$0.439656\pi$
$480$	−3.00400e17	−1.12107
$481$	2.88956e17	1.06387
$482$	2.41903e17	0.878689
$483$	8.61113e16	0.308605
$484$	6.73847e17	2.38269
$485$	−2.78255e17	−0.970781
$486$	−4.02848e17	−1.38677
$487$	4.08953e17	1.38911	0.694553	−	0.719441i	$-0.255602\pi$
$487$	4.08953e17	1.38911	0.694553	+	0.719441i	$0.255602\pi$
$488$	−8.77206e17	−2.94017
$489$	4.11372e17	1.36059
$490$	3.17155e17	1.03514
$491$	2.83532e17	0.913215	0.456607	−	0.889668i	$-0.349064\pi$
$491$	2.83532e17	0.913215	0.456607	+	0.889668i	$0.349064\pi$
$492$	−9.64038e16	−0.306423
$493$	1.21937e17	0.382499
$494$	−6.20541e17	−1.92108
$495$	1.22387e17	0.373941
$496$	−4.02196e17	−1.21285
$497$	−1.81885e16	−0.0541353
$498$	−7.25884e17	−2.13244
$499$	−2.26848e17	−0.657781	−0.328891	−	0.944368i	$-0.606675\pi$
$499$	−2.26848e17	−0.657781	−0.328891	+	0.944368i	$0.606675\pi$
$500$	−8.95409e17	−2.56281
$501$	−3.27327e17	−0.924776
$502$	−2.39709e17	−0.668514
$503$	2.79315e17	0.768958	0.384479	−	0.923134i	$-0.374381\pi$
$503$	2.79315e17	0.768958	0.384479	+	0.923134i	$0.374381\pi$
$504$	−1.64771e17	−0.447797
$505$	−2.06409e17	−0.553776
$506$	−9.63499e17	−2.55195
$507$	−1.36815e16	−0.0357751
$508$	1.42453e17	0.367754
$509$	2.57680e17	0.656772	0.328386	−	0.944544i	$-0.393495\pi$
$509$	2.57680e17	0.656772	0.328386	+	0.944544i	$0.393495\pi$
$510$	3.22573e17	0.811749
$511$	1.63209e17	0.405517
$512$	6.12434e17	1.50247
$513$	−4.72593e17	−1.14479
$514$	−8.37982e17	−2.00435
$515$	−2.05830e17	−0.486141
$516$	3.98388e17	0.929144
$517$	1.17331e18	2.70225
$518$	3.63939e17	0.827724
$519$	2.78183e16	0.0624803
$520$	−8.04590e17	−1.78465
$521$	2.39796e17	0.525287	0.262643	−	0.964893i	$-0.415406\pi$
$521$	2.39796e17	0.525287	0.262643	+	0.964893i	$0.415406\pi$
$522$	−1.56233e17	−0.337999
$523$	4.83508e17	1.03310	0.516551	−	0.856257i	$-0.327216\pi$
$523$	4.83508e17	1.03310	0.516551	+	0.856257i	$0.327216\pi$
$524$	1.23708e18	2.61062
$525$	8.42259e16	0.175554
$526$	−1.15612e18	−2.38011
$527$	1.90916e17	0.388216
$528$	−1.42513e18	−2.86242
$529$	−2.26156e16	−0.0448690
$530$	−1.17895e17	−0.231049
$531$	2.46763e17	0.477712
$532$	−5.56447e17	−1.06414
$533$	−8.27654e16	−0.156359
$534$	−4.36192e17	−0.814067
$535$	−5.37978e16	−0.0991893
$536$	−2.24574e18	−4.09062
$537$	6.46217e17	1.16291
$538$	−3.56347e17	−0.633561
$539$	6.65123e17	1.16836
$540$	−1.02911e18	−1.78608
$541$	1.04736e17	0.179603	0.0898016	−	0.995960i	$-0.471377\pi$
$541$	1.04736e17	0.179603	0.0898016	+	0.995960i	$0.471377\pi$
$542$	−6.55838e17	−1.11122
$543$	6.10586e17	1.02223
$544$	1.10892e18	1.83445
$545$	1.91689e17	0.313343
$546$	3.55735e17	0.574612
$547$	−6.03348e17	−0.963054	−0.481527	−	0.876431i	$-0.659918\pi$
$547$	−6.03348e17	−0.963054	−0.481527	+	0.876431i	$0.659918\pi$
$548$	−4.85879e16	−0.0766398
$549$	−2.75425e17	−0.429323
$550$	−9.42403e17	−1.45171
$551$	−3.14158e17	−0.478258
$552$	1.37933e18	2.07522
$553$	−5.13193e17	−0.763076
$554$	7.85292e17	1.15403
$555$	3.86992e17	0.562079
$556$	−2.74081e18	−3.93453
$557$	1.94030e16	0.0275302	0.0137651	−	0.999905i	$-0.495618\pi$
$557$	1.94030e16	0.0275302	0.0137651	+	0.999905i	$0.495618\pi$
$558$	−2.44614e17	−0.343051
$559$	3.42027e17	0.474115
$560$	−5.23156e17	−0.716819
$561$	6.76485e17	0.916219
$562$	−1.43431e18	−1.92025
$563$	7.77947e17	1.02955	0.514773	−	0.857327i	$-0.327876\pi$
$563$	7.77947e17	1.02955	0.514773	+	0.857327i	$0.327876\pi$
$564$	−2.82098e18	−3.69050
$565$	4.70120e17	0.607987
$566$	8.46833e17	1.08266
$567$	1.41722e17	0.179121
$568$	−2.91343e17	−0.364032
$569$	−9.09128e17	−1.12304	−0.561520	−	0.827463i	$-0.689783\pi$
$569$	−9.09128e17	−1.12304	−0.561520	+	0.827463i	$0.689783\pi$
$570$	−8.31075e17	−1.01497
$571$	−1.52398e18	−1.84011	−0.920057	−	0.391784i	$-0.871858\pi$
$571$	−1.52398e18	−1.84011	−0.920057	+	0.391784i	$0.871858\pi$
$572$	−2.83384e18	−3.38299
$573$	4.74321e17	0.559844
$574$	−1.04243e17	−0.121652
$575$	4.70880e17	0.543337
$576$	−4.95027e17	−0.564784
$577$	1.21715e18	1.37309	0.686546	−	0.727086i	$-0.259126\pi$
$577$	1.21715e18	1.37309	0.686546	+	0.727086i	$0.259126\pi$
$578$	4.79575e17	0.534966
$579$	−6.66113e17	−0.734746
$580$	−6.84103e17	−0.746173
$581$	−5.58825e17	−0.602741
$582$	1.97062e18	2.10186
$583$	−2.47245e17	−0.260784
$584$	2.61428e18	2.72690
$585$	−2.52625e17	−0.260594
$586$	2.48549e17	0.253558
$587$	8.69734e17	0.877483	0.438742	−	0.898613i	$-0.355424\pi$
$587$	8.69734e17	0.877483	0.438742	+	0.898613i	$0.355424\pi$
$588$	−1.59915e18	−1.59564
$589$	−4.91875e17	−0.485406
$590$	1.51765e18	1.48127
$591$	5.71488e16	0.0551682
$592$	3.00951e18	2.87346
$593$	−5.90997e17	−0.558123	−0.279061	−	0.960273i	$-0.590023\pi$
$593$	−5.90997e17	−0.558123	−0.279061	+	0.960273i	$0.590023\pi$
$594$	−3.03134e18	−2.83154
$595$	2.48334e17	0.229443
$596$	4.45881e18	4.07491
$597$	−6.83476e17	−0.617860
$598$	1.98880e18	1.77842
$599$	9.71699e17	0.859523	0.429762	−	0.902942i	$-0.358598\pi$
$599$	9.71699e17	0.859523	0.429762	+	0.902942i	$0.358598\pi$
$600$	1.34913e18	1.18051
$601$	1.40573e18	1.21680	0.608399	−	0.793631i	$-0.291812\pi$
$601$	1.40573e18	1.21680	0.608399	+	0.793631i	$0.291812\pi$
$602$	4.30782e17	0.368876
$603$	−7.05120e17	−0.597311
$604$	−2.10734e18	−1.76602
$605$	7.74793e17	0.642356
$606$	1.46180e18	1.19899
$607$	−2.00311e18	−1.62547	−0.812734	−	0.582635i	$-0.802022\pi$
$607$	−2.00311e18	−1.62547	−0.812734	+	0.582635i	$0.802022\pi$
$608$	−2.85701e18	−2.29371
$609$	1.80096e17	0.143051
$610$	−1.69393e18	−1.33123
$611$	−2.42189e18	−1.88316
$612$	1.08623e18	0.835674
$613$	1.42761e18	1.08672	0.543360	−	0.839500i	$-0.317152\pi$
$613$	1.42761e18	1.08672	0.543360	+	0.839500i	$0.317152\pi$
$614$	2.09352e18	1.57682
$615$	−1.10846e17	−0.0826096
$616$	−2.12521e18	−1.56721
$617$	−6.56052e17	−0.478724	−0.239362	−	0.970930i	$-0.576938\pi$
$617$	−6.56052e17	−0.478724	−0.239362	+	0.970930i	$0.576938\pi$
$618$	1.45770e18	1.05255
$619$	2.07305e18	1.48123	0.740613	−	0.671932i	$-0.234535\pi$
$619$	2.07305e18	1.48123	0.740613	+	0.671932i	$0.234535\pi$
$620$	−1.07110e18	−0.757326
$621$	1.51464e18	1.05977
$622$	−8.41541e17	−0.582690
$623$	−3.35804e17	−0.230099
$624$	2.94167e18	1.99478
$625$	−2.01112e17	−0.134964
$626$	−1.71476e16	−0.0113886
$627$	−1.74289e18	−1.14560
$628$	7.11933e18	4.63129
$629$	−1.42857e18	−0.919754
$630$	−3.18181e17	−0.202750
$631$	−5.78882e17	−0.365089	−0.182545	−	0.983198i	$-0.558433\pi$
$631$	−5.78882e17	−0.365089	−0.182545	+	0.983198i	$0.558433\pi$
$632$	−8.22031e18	−5.13130
$633$	−1.14230e17	−0.0705756
$634$	2.05877e18	1.25901
$635$	1.63793e17	0.0991442
$636$	5.94447e17	0.356157
$637$	−1.37291e18	−0.814210
$638$	−2.01509e18	−1.18294
$639$	−9.14759e16	−0.0531558
$640$	−5.27549e17	−0.303454
$641$	−1.85697e18	−1.05737	−0.528687	−	0.848817i	$-0.677315\pi$
$641$	−1.85697e18	−1.05737	−0.528687	+	0.848817i	$0.677315\pi$
$642$	3.80999e17	0.214757
$643$	−9.29050e17	−0.518403	−0.259202	−	0.965823i	$-0.583459\pi$
$643$	−9.29050e17	−0.518403	−0.259202	+	0.965823i	$0.583459\pi$
$644$	1.78339e18	0.985115
$645$	4.58069e17	0.250491
$646$	3.06788e18	1.66084
$647$	2.68373e18	1.43834	0.719170	−	0.694834i	$-0.244522\pi$
$647$	2.68373e18	1.43834	0.719170	+	0.694834i	$0.244522\pi$
$648$	2.27010e18	1.20450
$649$	3.18275e18	1.67191
$650$	1.94526e18	1.01167
$651$	2.81976e17	0.145189
$652$	8.51962e18	4.34321
$653$	9.76106e17	0.492676	0.246338	−	0.969184i	$-0.420773\pi$
$653$	9.76106e17	0.492676	0.246338	+	0.969184i	$0.420773\pi$
$654$	−1.35756e18	−0.678426
$655$	1.42240e18	0.703805
$656$	−8.62012e17	−0.422317
$657$	8.20833e17	0.398181
$658$	−3.05036e18	−1.46515
$659$	−3.05827e18	−1.45452	−0.727261	−	0.686361i	$-0.759207\pi$
$659$	−3.05827e18	−1.45452	−0.727261	+	0.686361i	$0.759207\pi$
$660$	−3.79528e18	−1.78735
$661$	4.02652e18	1.87768	0.938838	−	0.344359i	$-0.111904\pi$
$661$	4.02652e18	1.87768	0.938838	+	0.344359i	$0.111904\pi$
$662$	−4.79040e18	−2.21205
$663$	−1.39636e18	−0.638500
$664$	−8.95123e18	−4.05313
$665$	−6.39806e17	−0.286885
$666$	1.83037e18	0.812749
$667$	1.00686e18	0.442742
$668$	−6.77902e18	−2.95203
$669$	1.79240e18	0.772976
$670$	−4.33665e18	−1.85212
$671$	−3.55243e18	−1.50255
$672$	1.63783e18	0.686069
$673$	2.53323e18	1.05094	0.525468	−	0.850814i	$-0.323890\pi$
$673$	2.53323e18	1.05094	0.525468	+	0.850814i	$0.323890\pi$
$674$	7.21269e18	2.96352
$675$	1.48147e18	0.602864
$676$	−2.83347e17	−0.114200
$677$	1.77456e18	0.708379	0.354189	−	0.935174i	$-0.384757\pi$
$677$	1.77456e18	0.708379	0.354189	+	0.935174i	$0.384757\pi$
$678$	−3.32942e18	−1.31636
$679$	1.51709e18	0.594096
$680$	3.97780e18	1.54289
$681$	−2.11514e18	−0.812611
$682$	−3.15502e18	−1.20062
$683$	3.40712e18	1.28426	0.642130	−	0.766596i	$-0.278051\pi$
$683$	3.40712e18	1.28426	0.642130	+	0.766596i	$0.278051\pi$
$684$	−2.79855e18	−1.04489
$685$	−5.58666e16	−0.0206616
$686$	−3.80329e18	−1.39332
$687$	−2.08583e18	−0.756939
$688$	3.56226e18	1.28056
$689$	5.10350e17	0.181737
$690$	2.66355e18	0.939599
$691$	2.47368e18	0.864443	0.432221	−	0.901768i	$-0.357730\pi$
$691$	2.47368e18	0.864443	0.432221	+	0.901768i	$0.357730\pi$
$692$	5.76125e17	0.199447
$693$	−6.67274e17	−0.228843
$694$	−2.52951e18	−0.859408
$695$	−3.15140e18	−1.06072
$696$	2.88477e18	0.961947
$697$	4.09183e17	0.135178
$698$	−1.49206e18	−0.488345
$699$	−1.83797e17	−0.0595987
$700$	1.74434e18	0.560394
$701$	−5.59856e18	−1.78201	−0.891003	−	0.453998i	$-0.849997\pi$
$701$	−5.59856e18	−1.78201	−0.891003	+	0.453998i	$0.849997\pi$
$702$	6.25714e18	1.97326
$703$	3.68055e18	1.15001
$704$	−6.38485e18	−1.97664
$705$	−3.24358e18	−0.994936
$706$	7.87118e18	2.39226
$707$	1.12537e18	0.338899
$708$	−7.65224e18	−2.28335
$709$	4.84633e18	1.43289	0.716444	−	0.697644i	$-0.245768\pi$
$709$	4.84633e18	1.43289	0.716444	+	0.697644i	$0.245768\pi$
$710$	−5.62598e17	−0.164823
$711$	−2.58102e18	−0.749270
$712$	−5.37890e18	−1.54730
$713$	1.57644e18	0.449360
$714$	−1.75872e18	−0.496772
$715$	−3.25836e18	−0.912031
$716$	1.33833e19	3.71218
$717$	−4.65172e18	−1.27861
$718$	−9.08943e18	−2.47587
$719$	4.13840e18	1.11711	0.558554	−	0.829468i	$-0.311356\pi$
$719$	4.13840e18	1.11711	0.558554	+	0.829468i	$0.311356\pi$
$720$	−2.63112e18	−0.703850
$721$	1.12222e18	0.297507
$722$	−8.12121e17	−0.213368
$723$	−1.40243e18	−0.365159
$724$	1.26454e19	3.26311
$725$	9.84815e17	0.251859
$726$	−5.48714e18	−1.39078
$727$	2.30819e18	0.579827	0.289914	−	0.957053i	$-0.406373\pi$
$727$	2.30819e18	0.579827	0.289914	+	0.957053i	$0.406373\pi$
$728$	4.38674e18	1.09217
$729$	4.11553e18	1.01554
$730$	5.04832e18	1.23466
$731$	−1.69095e18	−0.409889
$732$	8.54106e18	2.05206
$733$	9.74851e17	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$733$	9.74851e17	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$734$	8.22392e18	1.94113
$735$	−1.83871e18	−0.430174
$736$	9.15658e18	2.12338
$737$	−9.09462e18	−2.09048
$738$	−5.24271e17	−0.119451
$739$	−1.83041e18	−0.413390	−0.206695	−	0.978405i	$-0.566271\pi$
$739$	−1.83041e18	−0.413390	−0.206695	+	0.978405i	$0.566271\pi$
$740$	8.01469e18	1.79424
$741$	3.59758e18	0.798349
$742$	6.42784e17	0.141397
$743$	9.61873e17	0.209745	0.104872	−	0.994486i	$-0.466557\pi$
$743$	9.61873e17	0.209745	0.104872	+	0.994486i	$0.466557\pi$
$744$	4.51667e18	0.976325
$745$	5.12677e18	1.09857
$746$	−1.00683e19	−2.13873
$747$	−2.81051e18	−0.591836
$748$	1.40102e19	2.92471
$749$	2.93314e17	0.0607017
$750$	7.29131e18	1.49592
$751$	−2.27503e16	−0.00462731	−0.00231365	−	0.999997i	$-0.500736\pi$
$751$	−2.27503e16	−0.00462731	−0.00231365	+	0.999997i	$0.500736\pi$
$752$	−2.52243e19	−5.08631
$753$	1.38971e18	0.277817
$754$	4.15945e18	0.824370
$755$	−2.42303e18	−0.476107
$756$	5.61085e18	1.09304
$757$	1.33460e16	0.00257768	0.00128884	−	0.999999i	$-0.499590\pi$
$757$	1.33460e16	0.00257768	0.00128884	+	0.999999i	$0.499590\pi$
$758$	−7.62791e18	−1.46068
$759$	5.58588e18	1.06052
$760$	−1.02484e19	−1.92915
$761$	−7.44101e18	−1.38877	−0.694387	−	0.719602i	$-0.744324\pi$
$761$	−7.44101e18	−1.38877	−0.694387	+	0.719602i	$0.744324\pi$
$762$	−1.16000e18	−0.214659
$763$	−1.04512e18	−0.191759
$764$	9.82330e18	1.78711
$765$	1.24895e18	0.225292
$766$	−1.11447e18	−0.199334
$767$	−6.56967e18	−1.16513
$768$	−2.47443e18	−0.435139
$769$	−5.10767e18	−0.890638	−0.445319	−	0.895372i	$-0.646910\pi$
$769$	−5.10767e18	−0.890638	−0.445319	+	0.895372i	$0.646910\pi$
$770$	−4.10389e18	−0.709588
$771$	4.85820e18	0.832955
$772$	−1.37954e19	−2.34542
$773$	−5.37726e18	−0.906555	−0.453278	−	0.891369i	$-0.649745\pi$
$773$	−5.37726e18	−0.906555	−0.453278	+	0.891369i	$0.649745\pi$
$774$	2.16654e18	0.362202
$775$	1.54192e18	0.255623
$776$	2.43006e19	3.99500
$777$	−2.10994e18	−0.343980
$778$	1.56219e19	2.52561
$779$	−1.05422e18	−0.169019
$780$	7.83402e18	1.24558
$781$	−1.17985e18	−0.186036
$782$	−9.83242e18	−1.53751
$783$	3.16776e18	0.491249
$784$	−1.42990e19	−2.19914
$785$	8.18585e18	1.24856
$786$	−1.00735e19	−1.52382
$787$	−7.93261e18	−1.19009	−0.595045	−	0.803692i	$-0.702866\pi$
$787$	−7.93261e18	−1.19009	−0.595045	+	0.803692i	$0.702866\pi$
$788$	1.18357e18	0.176105
$789$	6.70263e18	0.989110
$790$	−1.58739e19	−2.32331
$791$	−2.56317e18	−0.372074
$792$	−1.06884e19	−1.53886
$793$	7.33275e18	1.04711
$794$	4.68095e18	0.662981
$795$	6.83498e17	0.0960176
$796$	−1.41550e19	−1.97230
$797$	−4.94222e18	−0.683035	−0.341517	−	0.939875i	$-0.610941\pi$
$797$	−4.94222e18	−0.683035	−0.341517	+	0.939875i	$0.610941\pi$
$798$	4.53115e18	0.621140
$799$	1.19736e19	1.62806
$800$	8.95609e18	1.20791
$801$	−1.68887e18	−0.225936
$802$	8.35992e18	1.10935
$803$	1.05871e19	1.39356
$804$	2.18661e19	2.85500
$805$	2.05055e18	0.265581
$806$	6.51244e18	0.836692
$807$	2.06592e18	0.263291
$808$	1.80262e19	2.27892
$809$	9.58960e18	1.20264	0.601319	−	0.799009i	$-0.294642\pi$
$809$	9.58960e18	1.20264	0.601319	+	0.799009i	$0.294642\pi$
$810$	4.38368e18	0.545364
$811$	1.48266e19	1.82981	0.914905	−	0.403670i	$-0.132266\pi$
$811$	1.48266e19	1.82981	0.914905	+	0.403670i	$0.132266\pi$
$812$	3.72983e18	0.456641
$813$	3.80222e18	0.461794
$814$	2.36081e19	2.84448
$815$	9.79591e18	1.17090
$816$	−1.45433e19	−1.72455
$817$	4.35654e18	0.512505
$818$	−2.21766e18	−0.258820
$819$	1.37735e18	0.159478
$820$	−2.29564e18	−0.263702
$821$	−9.00025e18	−1.02571	−0.512854	−	0.858476i	$-0.671412\pi$
$821$	−9.00025e18	−1.02571	−0.512854	+	0.858476i	$0.671412\pi$
$822$	3.95651e17	0.0447348
$823$	5.63543e18	0.632162	0.316081	−	0.948732i	$-0.397633\pi$
$823$	5.63543e18	0.632162	0.316081	+	0.948732i	$0.397633\pi$
$824$	1.79756e19	2.00059
$825$	5.46358e18	0.603291
$826$	−8.27448e18	−0.906505
$827$	4.31129e18	0.468620	0.234310	−	0.972162i	$-0.424717\pi$
$827$	4.31129e18	0.468620	0.234310	+	0.972162i	$0.424717\pi$
$828$	8.96923e18	0.967292
$829$	5.67661e17	0.0607413	0.0303707	−	0.999539i	$-0.490331\pi$
$829$	5.67661e17	0.0607413	0.0303707	+	0.999539i	$0.490331\pi$
$830$	−1.72853e19	−1.83514
$831$	−4.55273e18	−0.479585
$832$	1.31793e19	1.37749
$833$	6.78752e18	0.703913
$834$	2.23184e19	2.29659
$835$	−7.79456e18	−0.795847
$836$	−3.60957e19	−3.65691
$837$	4.95975e18	0.498591
$838$	2.54332e19	2.53697
$839$	−4.18939e18	−0.414666	−0.207333	−	0.978270i	$-0.566478\pi$
$839$	−4.18939e18	−0.414666	−0.207333	+	0.978270i	$0.566478\pi$
$840$	5.87506e18	0.577028
$841$	−8.15485e18	−0.794771
$842$	−1.40619e18	−0.135993
$843$	8.31541e18	0.798003
$844$	−2.36572e18	−0.225288
$845$	−3.25794e17	−0.0307875
$846$	−1.53413e19	−1.43865
$847$	−4.22429e18	−0.393108
$848$	5.31535e18	0.490862
$849$	−4.90951e18	−0.449923
$850$	−9.61714e18	−0.874627
$851$	−1.17960e19	−1.06461
$852$	2.83671e18	0.254072
$853$	8.68784e18	0.772224	0.386112	−	0.922452i	$-0.373818\pi$
$853$	8.68784e18	0.772224	0.386112	+	0.922452i	$0.373818\pi$
$854$	9.23557e18	0.814681
$855$	−3.21779e18	−0.281694
$856$	4.69829e18	0.408188
$857$	−2.31006e18	−0.199181	−0.0995906	−	0.995029i	$-0.531753\pi$
$857$	−2.31006e18	−0.199181	−0.0995906	+	0.995029i	$0.531753\pi$
$858$	2.30759e19	1.97466
$859$	9.12762e18	0.775179	0.387589	−	0.921832i	$-0.373308\pi$
$859$	9.12762e18	0.775179	0.387589	+	0.921832i	$0.373308\pi$
$860$	9.48671e18	0.799606
$861$	6.04347e17	0.0505552
$862$	−6.63599e18	−0.550945
$863$	−8.94008e18	−0.736667	−0.368333	−	0.929694i	$-0.620072\pi$
$863$	−8.94008e18	−0.736667	−0.368333	+	0.929694i	$0.620072\pi$
$864$	2.88082e19	2.35601
$865$	6.62431e17	0.0537695
$866$	−2.15454e19	−1.73575
$867$	−2.78034e18	−0.222317
$868$	5.83978e18	0.463467
$869$	−3.32899e19	−2.62231
$870$	5.57065e18	0.435543
$871$	1.87726e19	1.45683
$872$	−1.67407e19	−1.28948
$873$	7.62992e18	0.583348
$874$	2.53322e19	1.92242
$875$	5.61324e18	0.422826
$876$	−2.54544e19	−1.90321
$877$	−1.53523e18	−0.113940	−0.0569699	−	0.998376i	$-0.518144\pi$
$877$	−1.53523e18	−0.113940	−0.0569699	+	0.998376i	$0.518144\pi$
$878$	−4.53075e19	−3.33777
$879$	−1.44096e18	−0.105372
$880$	−3.39362e19	−2.46335
$881$	−4.06751e18	−0.293080	−0.146540	−	0.989205i	$-0.546814\pi$
$881$	−4.06751e18	−0.293080	−0.146540	+	0.989205i	$0.546814\pi$
$882$	−8.69660e18	−0.622019
$883$	1.66406e18	0.118148	0.0590739	−	0.998254i	$-0.481185\pi$
$883$	1.66406e18	0.118148	0.0590739	+	0.998254i	$0.481185\pi$
$884$	−2.89190e19	−2.03819
$885$	−8.79859e18	−0.615576
$886$	−4.15514e19	−2.88580
$887$	−1.40781e19	−0.970598	−0.485299	−	0.874348i	$-0.661289\pi$
$887$	−1.40781e19	−0.970598	−0.485299	+	0.874348i	$0.661289\pi$
$888$	−3.37969e19	−2.31309
$889$	−8.93027e17	−0.0606740
$890$	−1.03869e19	−0.700572
$891$	9.19325e18	0.615551
$892$	3.71211e19	2.46746
$893$	−3.08486e19	−2.03564
$894$	−3.63081e19	−2.37853
$895$	1.53882e19	1.00078
$896$	2.87628e18	0.185707
$897$	−1.15301e19	−0.739063
$898$	−3.38681e19	−2.15523
$899$	3.29701e18	0.208297
$900$	8.77285e18	0.550255
$901$	−2.52311e18	−0.157118
$902$	−6.76204e18	−0.418057
$903$	−2.49746e18	−0.153295
$904$	−4.10567e19	−2.50201
$905$	1.45397e19	0.879713
$906$	1.71601e19	1.03083
$907$	1.07645e19	0.642018	0.321009	−	0.947076i	$-0.395978\pi$
$907$	1.07645e19	0.642018	0.321009	+	0.947076i	$0.395978\pi$
$908$	−4.38050e19	−2.59398
$909$	5.65986e18	0.332767
$910$	8.47104e18	0.494502
$911$	−5.38036e18	−0.311847	−0.155924	−	0.987769i	$-0.549835\pi$
$911$	−5.38036e18	−0.311847	−0.155924	+	0.987769i	$0.549835\pi$
$912$	3.74693e19	2.15630
$913$	−3.62499e19	−2.07132
$914$	3.72573e19	2.11379
$915$	9.82056e18	0.553222
$916$	−4.31981e19	−2.41626
$917$	−7.75513e18	−0.430713
$918$	−3.09346e19	−1.70595
$919$	−3.08489e18	−0.168923	−0.0844614	−	0.996427i	$-0.526917\pi$
$919$	−3.08489e18	−0.168923	−0.0844614	+	0.996427i	$0.526917\pi$
$920$	3.28456e19	1.78590
$921$	−1.21372e19	−0.655285
$922$	−4.48880e19	−2.40646
$923$	2.43539e18	0.129646
$924$	2.06925e19	1.09382
$925$	−1.15377e19	−0.605618
$926$	−3.13776e19	−1.63549
$927$	5.64400e18	0.292125
$928$	1.91504e19	0.984273
$929$	4.76854e18	0.243379	0.121690	−	0.992568i	$-0.461169\pi$
$929$	4.76854e18	0.243379	0.121690	+	0.992568i	$0.461169\pi$
$930$	8.72194e18	0.442052
$931$	−1.74873e19	−0.880138
$932$	−3.80648e18	−0.190248
$933$	4.87883e18	0.242150
$934$	−7.03292e18	−0.346642
$935$	1.61090e19	0.788483
$936$	2.20624e19	1.07241
$937$	1.56454e19	0.755232	0.377616	−	0.925962i	$-0.376744\pi$
$937$	1.56454e19	0.755232	0.377616	+	0.925962i	$0.376744\pi$
$938$	2.36441e19	1.13345
$939$	9.94133e16	0.00473280
$940$	−6.71753e19	−3.17599
$941$	1.99139e19	0.935024	0.467512	−	0.883987i	$-0.345150\pi$
$941$	1.99139e19	0.935024	0.467512	+	0.883987i	$0.345150\pi$
$942$	−5.79727e19	−2.70329
$943$	3.37871e18	0.156468
$944$	−6.84239e19	−3.14695
$945$	6.45139e18	0.294677
$946$	2.79441e19	1.26764
$947$	9.90709e18	0.446346	0.223173	−	0.974779i	$-0.428359\pi$
$947$	9.90709e18	0.446346	0.223173	+	0.974779i	$0.428359\pi$
$948$	8.00385e19	3.58133
$949$	−2.18533e19	−0.971152
$950$	2.47775e19	1.09359
$951$	−1.19357e19	−0.523210
$952$	−2.16876e19	−0.944215
$953$	8.48243e18	0.366789	0.183395	−	0.983039i	$-0.441291\pi$
$953$	8.48243e18	0.366789	0.183395	+	0.983039i	$0.441291\pi$
$954$	3.23277e18	0.138839
$955$	1.12949e19	0.481792
$956$	−9.63382e19	−4.08152
$957$	1.16825e19	0.491596
$958$	−1.68018e19	−0.702233
$959$	3.04593e17	0.0126444
$960$	1.76507e19	0.727776
$961$	−1.92554e19	−0.788590
$962$	−4.87306e19	−1.98227
$963$	1.47517e18	0.0596034
$964$	−2.90447e19	−1.16564
$965$	−1.58620e19	−0.632310
$966$	−1.45221e19	−0.575014
$967$	1.71826e19	0.675797	0.337898	−	0.941183i	$-0.390284\pi$
$967$	1.71826e19	0.675797	0.337898	+	0.941183i	$0.390284\pi$
$968$	−6.76645e19	−2.64345
$969$	−1.77861e19	−0.690200
$970$	4.69258e19	1.80882
$971$	−4.44228e19	−1.70091	−0.850454	−	0.526050i	$-0.823673\pi$
$971$	−4.44228e19	−1.70091	−0.850454	+	0.526050i	$0.823673\pi$
$972$	4.83690e19	1.83965
$973$	1.71819e19	0.649139
$974$	−6.89673e19	−2.58827
$975$	−1.12776e19	−0.420424
$976$	7.63715e19	2.82818
$977$	1.89917e19	0.698635	0.349317	−	0.937004i	$-0.386413\pi$
$977$	1.89917e19	0.698635	0.349317	+	0.937004i	$0.386413\pi$
$978$	−6.93752e19	−2.53514
$979$	−2.17830e19	−0.790734
$980$	−3.80801e19	−1.37318
$981$	−5.25625e18	−0.188290
$982$	−4.78159e19	−1.70156
$983$	−1.07021e19	−0.378331	−0.189165	−	0.981945i	$-0.560578\pi$
$983$	−1.07021e19	−0.378331	−0.189165	+	0.981945i	$0.560578\pi$
$984$	9.68041e18	0.339958
$985$	1.36087e18	0.0474768
$986$	−2.05639e19	−0.712697
$987$	1.76845e19	0.608879
$988$	7.45069e19	2.54845
$989$	−1.39625e19	−0.474447
$990$	−2.06398e19	−0.696750
$991$	−5.41492e18	−0.181599	−0.0907995	−	0.995869i	$-0.528942\pi$
$991$	−5.41492e18	−0.181599	−0.0907995	+	0.995869i	$0.528942\pi$
$992$	2.99837e19	0.998985
$993$	2.77723e19	0.919268
$994$	3.06737e18	0.100868
$995$	−1.62754e19	−0.531720
$996$	8.71552e19	2.82883
$997$	2.11859e19	0.683169	0.341584	−	0.939851i	$-0.389037\pi$
$997$	2.11859e19	0.683169	0.341584	+	0.939851i	$0.389037\pi$
$998$	3.82564e19	1.22562
$999$	−3.71123e19	−1.18125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.14.a.b.1.6	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.14.a.b.1.6	✓	109	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-168.643 q^{2} +977.710 q^{3} +20248.6 q^{4} +23282.0 q^{5} -164884. q^{6} -126937. q^{7} -2.03327e6 q^{8} -638407. q^{9} -3.92635e6 q^{10} -8.23416e6 q^{11} +1.97973e7 q^{12} +1.69965e7 q^{13} +2.14071e7 q^{14} +2.27630e7 q^{15} +1.77021e8 q^{16} -8.40289e7 q^{17} +1.07663e8 q^{18} +2.16492e8 q^{19} +4.71428e8 q^{20} -1.24107e8 q^{21} +1.38864e9 q^{22} -6.93845e8 q^{23} -1.98795e9 q^{24} -6.78653e8 q^{25} -2.86635e9 q^{26} -2.18296e9 q^{27} -2.57029e9 q^{28} -1.45113e9 q^{29} -3.83883e9 q^{30} -2.27203e9 q^{31} -1.31969e10 q^{32} -8.05062e9 q^{33} +1.41709e10 q^{34} -2.95534e9 q^{35} -1.29268e10 q^{36} +1.70009e10 q^{37} -3.65099e10 q^{38} +1.66177e10 q^{39} -4.73385e10 q^{40} -4.86955e9 q^{41} +2.09299e10 q^{42} +2.01234e10 q^{43} -1.66730e11 q^{44} -1.48634e10 q^{45} +1.17012e11 q^{46} -1.42493e11 q^{47} +1.73075e11 q^{48} -8.07761e10 q^{49} +1.14450e11 q^{50} -8.21559e10 q^{51} +3.44156e11 q^{52} +3.00267e10 q^{53} +3.68142e11 q^{54} -1.91707e11 q^{55} +2.58097e11 q^{56} +2.11666e11 q^{57} +2.44724e11 q^{58} -3.86530e11 q^{59} +4.60919e11 q^{60} +4.31426e11 q^{61} +3.83163e11 q^{62} +8.10373e10 q^{63} +7.75410e11 q^{64} +3.95712e11 q^{65} +1.35768e12 q^{66} +1.10450e12 q^{67} -1.70147e12 q^{68} -6.78379e11 q^{69} +4.98398e11 q^{70} +1.43288e11 q^{71} +1.29805e12 q^{72} -1.28575e12 q^{73} -2.86709e12 q^{74} -6.63526e11 q^{75} +4.38365e12 q^{76} +1.04522e12 q^{77} -2.80246e12 q^{78} +4.04290e12 q^{79} +4.12139e12 q^{80} -1.11648e12 q^{81} +8.21218e11 q^{82} +4.40239e12 q^{83} -2.51300e12 q^{84} -1.95636e12 q^{85} -3.39368e12 q^{86} -1.41879e12 q^{87} +1.67423e13 q^{88} +2.64544e12 q^{89} +2.50661e12 q^{90} -2.15748e12 q^{91} -1.40494e13 q^{92} -2.22139e12 q^{93} +2.40306e13 q^{94} +5.04035e12 q^{95} -1.29027e13 q^{96} -1.19515e13 q^{97} +1.36224e13 q^{98} +5.25674e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14}+ \cdots + 12084396239183 q^{99}+O(q^{100}) \) 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9 + 16373653 * q^10 + 21199298 * q^11 + 63225856 * q^12 + 59695238 * q^13 + 37888529 * q^14 + 87246239 * q^15 + 2130706432 * q^16 + 228353715 * q^17 + 400647337 * q^18 + 1139301305 * q^19 + 1109969259 * q^20 + 539982398 * q^21 + 1613315649 * q^22 + 920306804 * q^23 + 5542439613 * q^24 + 31241700999 * q^25 + 1864366110 * q^26 + 17825460755 * q^27 + 20413389070 * q^28 + 7185436621 * q^29 + 2050251883 * q^30 + 28475592572 * q^31 + 8334714660 * q^32 + 19623425846 * q^33 + 37845014194 * q^34 + 25255003636 * q^35 + 287968706746 * q^36 + 71523920490 * q^37 + 67778214914 * q^38 + 44951568463 * q^39 + 169184871486 * q^40 + 69139231052 * q^41 + 58715177635 * q^42 + 247544146139 * q^43 + 63861560722 * q^44 + 257443045479 * q^45 + 160530477869 * q^46 + 308496573061 * q^47 + 412228130018 * q^48 + 1736616239908 * q^49 + 1680360028531 * q^50 + 756579032995 * q^51 + 928015404666 * q^52 + 342783723680 * q^53 - 597894730601 * q^54 + 59276330527 * q^55 - 3822929869144 * q^56 - 562905761941 * q^57 + 62740419347 * q^58 + 827401964151 * q^59 - 2247133283907 * q^60 + 988213134514 * q^61 + 1937380192071 * q^62 + 1788190111357 * q^63 + 11682175668457 * q^64 + 2494670804291 * q^65 + 11819807890512 * q^66 + 8038740399790 * q^67 + 10126245189885 * q^68 + 5225665164579 * q^69 + 11464042631319 * q^70 + 4867145119603 * q^71 + 18133468947055 * q^72 + 9684156738615 * q^73 + 16996786880941 * q^74 + 16718732018262 * q^75 + 21454522032798 * q^76 + 6593100920650 * q^77 + 33749579076633 * q^78 + 7591753073823 * q^79 + 24349241260570 * q^80 + 38778649605417 * q^81 + 25555033184251 * q^82 + 16945724819556 * q^83 + 21855489402730 * q^84 + 15544906794766 * q^85 + 18664144286914 * q^86 + 19049540636401 * q^87 + 17318749473003 * q^88 + 11289674998576 * q^89 + 20983303956671 * q^90 + 47242561944227 * q^91 - 25046698097386 * q^92 - 5411884145985 * q^93 + 18338784709341 * q^94 + 6784117894603 * q^95 - 36827486682955 * q^96 + 45969533477736 * q^97 - 42983409526150 * q^98 + 12084396239183 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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