LMFDB - Embedded newform 5.10.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,10,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	5.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:	$2.57517918082$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1009}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 252 $ x^2 - x - 252
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-15.3824$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+26.7648 q^{2} +66.4705 q^{3} +204.352 q^{4} +625.000 q^{5} +1779.07 q^{6} -5947.66 q^{7} -8234.11 q^{8} -15264.7 q^{9} +O(q^{10})$	\(q+26.7648 q^{2} +66.4705 q^{3} +204.352 q^{4} +625.000 q^{5} +1779.07 q^{6} -5947.66 q^{7} -8234.11 q^{8} -15264.7 q^{9} +16728.0 q^{10} +72345.0 q^{11} +13583.4 q^{12} +14564.0 q^{13} -159188. q^{14} +41544.0 q^{15} -325013. q^{16} +614778. q^{17} -408555. q^{18} -238472. q^{19} +127720. q^{20} -395344. q^{21} +1.93630e6 q^{22} +91562.8 q^{23} -547326. q^{24} +390625. q^{25} +389803. q^{26} -2.32299e6 q^{27} -1.21542e6 q^{28} -5.23105e6 q^{29} +1.11192e6 q^{30} +5.72058e6 q^{31} -4.48302e6 q^{32} +4.80881e6 q^{33} +1.64544e7 q^{34} -3.71729e6 q^{35} -3.11937e6 q^{36} -4.03979e6 q^{37} -6.38264e6 q^{38} +968079. q^{39} -5.14632e6 q^{40} -1.84276e7 q^{41} -1.05813e7 q^{42} +2.72643e7 q^{43} +1.47839e7 q^{44} -9.54042e6 q^{45} +2.45066e6 q^{46} +1.25825e7 q^{47} -2.16037e7 q^{48} -4.97896e6 q^{49} +1.04550e7 q^{50} +4.08646e7 q^{51} +2.97620e6 q^{52} +1.66132e7 q^{53} -6.21742e7 q^{54} +4.52157e7 q^{55} +4.89737e7 q^{56} -1.58513e7 q^{57} -1.40008e8 q^{58} -7.65654e7 q^{59} +8.48963e6 q^{60} -1.59271e8 q^{61} +1.53110e8 q^{62} +9.07891e7 q^{63} +4.64196e7 q^{64} +9.10253e6 q^{65} +1.28707e8 q^{66} +7.66068e7 q^{67} +1.25631e8 q^{68} +6.08622e6 q^{69} -9.94923e7 q^{70} -2.03001e8 q^{71} +1.25691e8 q^{72} -2.20084e8 q^{73} -1.08124e8 q^{74} +2.59650e7 q^{75} -4.87323e7 q^{76} -4.30284e8 q^{77} +2.59104e7 q^{78} +5.99842e8 q^{79} -2.03133e8 q^{80} +1.46044e8 q^{81} -4.93210e8 q^{82} +6.13872e8 q^{83} -8.07894e7 q^{84} +3.84236e8 q^{85} +7.29723e8 q^{86} -3.47710e8 q^{87} -5.95697e8 q^{88} -1.00215e7 q^{89} -2.55347e8 q^{90} -8.66220e7 q^{91} +1.87111e7 q^{92} +3.80250e8 q^{93} +3.36768e8 q^{94} -1.49045e8 q^{95} -2.97988e8 q^{96} +4.02491e8 q^{97} -1.33261e8 q^{98} -1.10432e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 10 q^{2} + 260 q^{3} + 1044 q^{4} + 1250 q^{5} - 5336 q^{6} + 1700 q^{7} - 20280 q^{8} + 2506 q^{9}+O(q^{10}) $ 2 * q - 10 * q^2 + 260 * q^3 + 1044 * q^4 + 1250 * q^5 - 5336 * q^6 + 1700 * q^7 - 20280 * q^8 + 2506 * q^9	\( 2 q - 10 q^{2} + 260 q^{3} + 1044 q^{4} + 1250 q^{5} - 5336 q^{6} + 1700 q^{7} - 20280 q^{8} + 2506 q^{9} - 6250 q^{10} + 23984 q^{11} + 176080 q^{12} + 115020 q^{13} - 440352 q^{14} + 162500 q^{15} - 312048 q^{16} + 412820 q^{17} - 1061890 q^{18} - 296520 q^{19} + 652500 q^{20} + 1084704 q^{21} + 3714280 q^{22} - 1049220 q^{23} - 2878560 q^{24} + 781250 q^{25} - 3303436 q^{26} - 2693080 q^{27} + 5205920 q^{28} - 3666980 q^{29} - 3335000 q^{30} + 1613144 q^{31} + 1207840 q^{32} - 4550480 q^{33} + 23879308 q^{34} + 1062500 q^{35} + 11801732 q^{36} - 21121940 q^{37} - 4248520 q^{38} + 20409272 q^{39} - 12675000 q^{40} - 26957276 q^{41} - 64994880 q^{42} + 52889700 q^{43} - 25822352 q^{44} + 1566250 q^{45} + 44391264 q^{46} + 58412180 q^{47} - 19094720 q^{48} + 13154114 q^{49} - 3906250 q^{50} + 1779784 q^{51} + 87323800 q^{52} - 39035140 q^{53} - 48567920 q^{54} + 14990000 q^{55} - 43149120 q^{56} - 27085360 q^{57} - 197510380 q^{58} - 54995560 q^{59} + 110050000 q^{60} - 274579716 q^{61} + 304118880 q^{62} + 226693140 q^{63} - 169441216 q^{64} + 71887500 q^{65} + 472798688 q^{66} - 318580 q^{67} - 43942040 q^{68} - 214688928 q^{69} - 275220000 q^{70} - 7130936 q^{71} - 88372440 q^{72} + 120858180 q^{73} + 519897028 q^{74} + 101562500 q^{75} - 97472240 q^{76} - 800132400 q^{77} - 688840400 q^{78} + 6877520 q^{79} - 195030000 q^{80} - 275359358 q^{81} - 179618020 q^{82} + 1402348740 q^{83} + 1161929088 q^{84} + 258012500 q^{85} - 212388136 q^{86} - 45016840 q^{87} - 13145760 q^{88} + 830088660 q^{89} - 663681250 q^{90} + 681630904 q^{91} - 939144480 q^{92} - 414660480 q^{93} - 1348148912 q^{94} - 185325000 q^{95} + 803360384 q^{96} + 638394580 q^{97} - 799918970 q^{98} - 1963732048 q^{99}+O(q^{100}) \) 2 * q - 10 * q^2 + 260 * q^3 + 1044 * q^4 + 1250 * q^5 - 5336 * q^6 + 1700 * q^7 - 20280 * q^8 + 2506 * q^9 - 6250 * q^10 + 23984 * q^11 + 176080 * q^12 + 115020 * q^13 - 440352 * q^14 + 162500 * q^15 - 312048 * q^16 + 412820 * q^17 - 1061890 * q^18 - 296520 * q^19 + 652500 * q^20 + 1084704 * q^21 + 3714280 * q^22 - 1049220 * q^23 - 2878560 * q^24 + 781250 * q^25 - 3303436 * q^26 - 2693080 * q^27 + 5205920 * q^28 - 3666980 * q^29 - 3335000 * q^30 + 1613144 * q^31 + 1207840 * q^32 - 4550480 * q^33 + 23879308 * q^34 + 1062500 * q^35 + 11801732 * q^36 - 21121940 * q^37 - 4248520 * q^38 + 20409272 * q^39 - 12675000 * q^40 - 26957276 * q^41 - 64994880 * q^42 + 52889700 * q^43 - 25822352 * q^44 + 1566250 * q^45 + 44391264 * q^46 + 58412180 * q^47 - 19094720 * q^48 + 13154114 * q^49 - 3906250 * q^50 + 1779784 * q^51 + 87323800 * q^52 - 39035140 * q^53 - 48567920 * q^54 + 14990000 * q^55 - 43149120 * q^56 - 27085360 * q^57 - 197510380 * q^58 - 54995560 * q^59 + 110050000 * q^60 - 274579716 * q^61 + 304118880 * q^62 + 226693140 * q^63 - 169441216 * q^64 + 71887500 * q^65 + 472798688 * q^66 - 318580 * q^67 - 43942040 * q^68 - 214688928 * q^69 - 275220000 * q^70 - 7130936 * q^71 - 88372440 * q^72 + 120858180 * q^73 + 519897028 * q^74 + 101562500 * q^75 - 97472240 * q^76 - 800132400 * q^77 - 688840400 * q^78 + 6877520 * q^79 - 195030000 * q^80 - 275359358 * q^81 - 179618020 * q^82 + 1402348740 * q^83 + 1161929088 * q^84 + 258012500 * q^85 - 212388136 * q^86 - 45016840 * q^87 - 13145760 * q^88 + 830088660 * q^89 - 663681250 * q^90 + 681630904 * q^91 - 939144480 * q^92 - 414660480 * q^93 - 1348148912 * q^94 - 185325000 * q^95 + 803360384 * q^96 + 638394580 * q^97 - 799918970 * q^98 - 1963732048 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	26.7648	1.18285	0.591423	−	0.806361i	$-0.298566\pi$
$2$	26.7648	1.18285	0.591423	+	0.806361i	$0.298566\pi$
$3$	66.4705	0.473787	0.236894	−	0.971536i	$-0.423871\pi$
$3$	66.4705	0.473787	0.236894	+	0.971536i	$0.423871\pi$
$4$	204.352	0.399126
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	1779.07	0.560417
$7$	−5947.66	−0.936278	−0.468139	−	0.883655i	$-0.655075\pi$
$7$	−5947.66	−0.936278	−0.468139	+	0.883655i	$0.655075\pi$
$8$	−8234.11	−0.710742
$9$	−15264.7	−0.775526
$10$	16728.0	0.528985
$11$	72345.0	1.48985	0.744924	−	0.667150i	$-0.232486\pi$
$11$	72345.0	1.48985	0.744924	+	0.667150i	$0.232486\pi$
$12$	13583.4	0.189101
$13$	14564.0	0.141428	0.0707142	−	0.997497i	$-0.477472\pi$
$13$	14564.0	0.141428	0.0707142	+	0.997497i	$0.477472\pi$
$14$	−159188.	−1.10747
$15$	41544.0	0.211884
$16$	−325013.	−1.23982
$17$	614778.	1.78525	0.892623	−	0.450804i	$-0.148863\pi$
$17$	614778.	1.78525	0.892623	+	0.450804i	$0.148863\pi$
$18$	−408555.	−0.917328
$19$	−238472.	−0.419803	−0.209902	−	0.977722i	$-0.567314\pi$
$19$	−238472.	−0.419803	−0.209902	+	0.977722i	$0.567314\pi$
$20$	127720.	0.178494
$21$	−395344.	−0.443596
$22$	1.93630e6	1.76226
$23$	91562.8	0.0682251	0.0341125	−	0.999418i	$-0.489140\pi$
$23$	91562.8	0.0682251	0.0341125	+	0.999418i	$0.489140\pi$
$24$	−547326.	−0.336740
$25$	390625.	0.200000
$26$	389803.	0.167288
$27$	−2.32299e6	−0.841221
$28$	−1.21542e6	−0.373693
$29$	−5.23105e6	−1.37340	−0.686701	−	0.726940i	$-0.740942\pi$
$29$	−5.23105e6	−1.37340	−0.686701	+	0.726940i	$0.740942\pi$
$30$	1.11192e6	0.250626
$31$	5.72058e6	1.11253	0.556266	−	0.831004i	$-0.312234\pi$
$31$	5.72058e6	1.11253	0.556266	+	0.831004i	$0.312234\pi$
$32$	−4.48302e6	−0.755780
$33$	4.80881e6	0.705870
$34$	1.64544e7	2.11167
$35$	−3.71729e6	−0.418716
$36$	−3.11937e6	−0.309532
$37$	−4.03979e6	−0.354365	−0.177183	−	0.984178i	$-0.556698\pi$
$37$	−4.03979e6	−0.354365	−0.177183	+	0.984178i	$0.556698\pi$
$38$	−6.38264e6	−0.496563
$39$	968079.	0.0670070
$40$	−5.14632e6	−0.317853
$41$	−1.84276e7	−1.01845	−0.509227	−	0.860632i	$-0.670069\pi$
$41$	−1.84276e7	−1.01845	−0.509227	+	0.860632i	$0.670069\pi$
$42$	−1.05813e7	−0.524706
$43$	2.72643e7	1.21615	0.608074	−	0.793880i	$-0.291942\pi$
$43$	2.72643e7	1.21615	0.608074	+	0.793880i	$0.291942\pi$
$44$	1.47839e7	0.594636
$45$	−9.54042e6	−0.346826
$46$	2.45066e6	0.0806998
$47$	1.25825e7	0.376120	0.188060	−	0.982157i	$-0.439780\pi$
$47$	1.25825e7	0.376120	0.188060	+	0.982157i	$0.439780\pi$
$48$	−2.16037e7	−0.587413
$49$	−4.97896e6	−0.123383
$50$	1.04550e7	0.236569
$51$	4.08646e7	0.845826
$52$	2.97620e6	0.0564478
$53$	1.66132e7	0.289209	0.144604	−	0.989490i	$-0.453809\pi$
$53$	1.66132e7	0.289209	0.144604	+	0.989490i	$0.453809\pi$
$54$	−6.21742e7	−0.995035
$55$	4.52157e7	0.666280
$56$	4.89737e7	0.665452
$57$	−1.58513e7	−0.198897
$58$	−1.40008e8	−1.62452
$59$	−7.65654e7	−0.822619	−0.411309	−	0.911496i	$-0.634928\pi$
$59$	−7.65654e7	−0.822619	−0.411309	+	0.911496i	$0.634928\pi$
$60$	8.48963e6	0.0845684
$61$	−1.59271e8	−1.47283	−0.736415	−	0.676530i	$-0.763483\pi$
$61$	−1.59271e8	−1.47283	−0.736415	+	0.676530i	$0.763483\pi$
$62$	1.53110e8	1.31595
$63$	9.07891e7	0.726108
$64$	4.64196e7	0.345853
$65$	9.10253e6	0.0632487
$66$	1.28707e8	0.834936
$67$	7.66068e7	0.464441	0.232221	−	0.972663i	$-0.425401\pi$
$67$	7.66068e7	0.464441	0.232221	+	0.972663i	$0.425401\pi$
$68$	1.25631e8	0.712538
$69$	6.08622e6	0.0323241
$70$	−9.94923e7	−0.495277
$71$	−2.03001e8	−0.948057	−0.474029	−	0.880509i	$-0.657201\pi$
$71$	−2.03001e8	−0.948057	−0.474029	+	0.880509i	$0.657201\pi$
$72$	1.25691e8	0.551199
$73$	−2.20084e8	−0.907059	−0.453530	−	0.891241i	$-0.649835\pi$
$73$	−2.20084e8	−0.907059	−0.453530	+	0.891241i	$0.649835\pi$
$74$	−1.08124e8	−0.419160
$75$	2.59650e7	0.0947574
$76$	−4.87323e7	−0.167554
$77$	−4.30284e8	−1.39491
$78$	2.59104e7	0.0792590
$79$	5.99842e8	1.73267	0.866334	−	0.499465i	$-0.166470\pi$
$79$	5.99842e8	1.73267	0.866334	+	0.499465i	$0.166470\pi$
$80$	−2.03133e8	−0.554466
$81$	1.46044e8	0.376966
$82$	−4.93210e8	−1.20467
$83$	6.13872e8	1.41980	0.709899	−	0.704304i	$-0.248741\pi$
$83$	6.13872e8	1.41980	0.709899	+	0.704304i	$0.248741\pi$
$84$	−8.07894e7	−0.177051
$85$	3.84236e8	0.798386
$86$	7.29723e8	1.43852
$87$	−3.47710e8	−0.650700
$88$	−5.95697e8	−1.05890
$89$	−1.00215e7	−0.0169309	−0.00846543	−	0.999964i	$-0.502695\pi$
$89$	−1.00215e7	−0.0169309	−0.00846543	+	0.999964i	$0.502695\pi$
$90$	−2.55347e8	−0.410242
$91$	−8.66220e7	−0.132416
$92$	1.87111e7	0.0272304
$93$	3.80250e8	0.527103
$94$	3.36768e8	0.444893
$95$	−1.49045e8	−0.187742
$96$	−2.97988e8	−0.358079
$97$	4.02491e8	0.461619	0.230810	−	0.972999i	$-0.425863\pi$
$97$	4.02491e8	0.461619	0.230810	+	0.972999i	$0.425863\pi$
$98$	−1.33261e8	−0.145944
$99$	−1.10432e9	−1.15541
$100$	7.98252e7	0.0798252
$101$	−1.30103e9	−1.24406	−0.622032	−	0.782992i	$-0.713693\pi$
$101$	−1.30103e9	−1.24406	−0.622032	+	0.782992i	$0.713693\pi$
$102$	1.09373e9	1.00048
$103$	−2.45156e8	−0.214622	−0.107311	−	0.994225i	$-0.534224\pi$
$103$	−2.45156e8	−0.214622	−0.107311	+	0.994225i	$0.534224\pi$
$104$	−1.19922e8	−0.100519
$105$	−2.47090e8	−0.198382
$106$	4.44648e8	0.342090
$107$	1.00765e9	0.743163	0.371581	−	0.928400i	$-0.378816\pi$
$107$	1.00765e9	0.743163	0.371581	+	0.928400i	$0.378816\pi$
$108$	−4.74708e8	−0.335753
$109$	7.68000e8	0.521125	0.260562	−	0.965457i	$-0.416092\pi$
$109$	7.68000e8	0.521125	0.260562	+	0.965457i	$0.416092\pi$
$110$	1.21019e9	0.788107
$111$	−2.68527e8	−0.167894
$112$	1.93306e9	1.16082
$113$	9.01969e8	0.520402	0.260201	−	0.965555i	$-0.416211\pi$
$113$	9.01969e8	0.520402	0.260201	+	0.965555i	$0.416211\pi$
$114$	−4.24257e8	−0.235265
$115$	5.72268e7	0.0305112
$116$	−1.06898e9	−0.548160
$117$	−2.22315e8	−0.109681
$118$	−2.04926e9	−0.973032
$119$	−3.65649e9	−1.67149
$120$	−3.42078e8	−0.150595
$121$	2.87586e9	1.21964
$122$	−4.26285e9	−1.74213
$123$	−1.22489e9	−0.482530
$124$	1.16901e9	0.444040
$125$	2.44141e8	0.0894427
$126$	2.42995e9	0.858874
$127$	−1.27265e9	−0.434103	−0.217052	−	0.976160i	$-0.569644\pi$
$127$	−1.27265e9	−0.434103	−0.217052	+	0.976160i	$0.569644\pi$
$128$	3.53771e9	1.16487
$129$	1.81227e9	0.576195
$130$	2.43627e8	0.0748136
$131$	4.89056e8	0.145090	0.0725451	−	0.997365i	$-0.476888\pi$
$131$	4.89056e8	0.145090	0.0725451	+	0.997365i	$0.476888\pi$
$132$	9.82692e8	0.281731
$133$	1.41835e9	0.393053
$134$	2.05036e9	0.549363
$135$	−1.45187e9	−0.376206
$136$	−5.06215e9	−1.26885
$137$	1.04222e9	0.252766	0.126383	−	0.991982i	$-0.459663\pi$
$137$	1.04222e9	0.252766	0.126383	+	0.991982i	$0.459663\pi$
$138$	1.62896e8	0.0382345
$139$	1.44082e9	0.327372	0.163686	−	0.986512i	$-0.447662\pi$
$139$	1.44082e9	0.327372	0.163686	+	0.986512i	$0.447662\pi$
$140$	−7.59636e8	−0.167120
$141$	8.36366e8	0.178201
$142$	−5.43326e9	−1.12141
$143$	1.05364e9	0.210707
$144$	4.96121e9	0.961516
$145$	−3.26941e9	−0.614204
$146$	−5.89050e9	−1.07291
$147$	−3.30954e8	−0.0584574
$148$	−8.25541e8	−0.141436
$149$	5.29574e9	0.880214	0.440107	−	0.897945i	$-0.354941\pi$
$149$	5.29574e9	0.880214	0.440107	+	0.897945i	$0.354941\pi$
$150$	6.94948e8	0.112083
$151$	3.60123e9	0.563708	0.281854	−	0.959457i	$-0.409051\pi$
$151$	3.60123e9	0.563708	0.281854	+	0.959457i	$0.409051\pi$
$152$	1.96361e9	0.298372
$153$	−9.38438e9	−1.38450
$154$	−1.15164e10	−1.64997
$155$	3.57536e9	0.497539
$156$	1.97829e8	0.0267442
$157$	3.01791e9	0.396423	0.198211	−	0.980159i	$-0.436487\pi$
$157$	3.01791e9	0.396423	0.198211	+	0.980159i	$0.436487\pi$
$158$	1.60546e10	2.04948
$159$	1.10429e9	0.137023
$160$	−2.80188e9	−0.337995
$161$	−5.44584e8	−0.0638776
$162$	3.90884e9	0.445893
$163$	−9.02201e9	−1.00106	−0.500529	−	0.865720i	$-0.666861\pi$
$163$	−9.02201e9	−1.00106	−0.500529	+	0.865720i	$0.666861\pi$
$164$	−3.76572e9	−0.406491
$165$	3.00551e9	0.315675
$166$	1.64301e10	1.67940
$167$	−2.52141e9	−0.250853	−0.125426	−	0.992103i	$-0.540030\pi$
$167$	−2.52141e9	−0.250853	−0.125426	+	0.992103i	$0.540030\pi$
$168$	3.25531e9	0.315283
$169$	−1.03924e10	−0.979998
$170$	1.02840e10	0.944368
$171$	3.64020e9	0.325568
$172$	5.57153e9	0.485396
$173$	−1.09608e10	−0.930329	−0.465164	−	0.885224i	$-0.654005\pi$
$173$	−1.09608e10	−0.930329	−0.465164	+	0.885224i	$0.654005\pi$
$174$	−9.30638e9	−0.769678
$175$	−2.32330e9	−0.187256
$176$	−2.35130e10	−1.84715
$177$	−5.08934e9	−0.389746
$178$	−2.68224e8	−0.0200266
$179$	6.46578e9	0.470742	0.235371	−	0.971906i	$-0.424370\pi$
$179$	6.46578e9	0.470742	0.235371	+	0.971906i	$0.424370\pi$
$180$	−1.94961e9	−0.138427
$181$	−1.45339e8	−0.0100653	−0.00503267	−	0.999987i	$-0.501602\pi$
$181$	−1.45339e8	−0.0100653	−0.00503267	+	0.999987i	$0.501602\pi$
$182$	−2.31842e9	−0.156628
$183$	−1.05868e10	−0.697808
$184$	−7.53939e8	−0.0484904
$185$	−2.52487e9	−0.158477
$186$	1.01773e10	0.623482
$187$	4.44761e10	2.65974
$188$	2.57127e9	0.150119
$189$	1.38163e10	0.787617
$190$	−3.98915e9	−0.222070
$191$	−1.80577e10	−0.981775	−0.490888	−	0.871223i	$-0.663327\pi$
$191$	−1.80577e10	−0.981775	−0.490888	+	0.871223i	$0.663327\pi$
$192$	3.08553e9	0.163861
$193$	3.63652e10	1.88659	0.943295	−	0.331956i	$-0.107708\pi$
$193$	3.63652e10	1.88659	0.943295	+	0.331956i	$0.107708\pi$
$194$	1.07726e10	0.546024
$195$	6.05049e8	0.0299664
$196$	−1.01746e9	−0.0492455
$197$	−3.85969e10	−1.82580	−0.912902	−	0.408179i	$-0.866164\pi$
$197$	−3.85969e10	−1.82580	−0.912902	+	0.408179i	$0.866164\pi$
$198$	−2.95570e10	−1.36668
$199$	2.78151e8	0.0125731	0.00628653	−	0.999980i	$-0.497999\pi$
$199$	2.78151e8	0.0125731	0.00628653	+	0.999980i	$0.497999\pi$
$200$	−3.21645e9	−0.142148
$201$	5.09209e9	0.220046
$202$	−3.48219e10	−1.47154
$203$	3.11125e10	1.28589
$204$	8.35077e9	0.337591
$205$	−1.15172e10	−0.455466
$206$	−6.56154e9	−0.253865
$207$	−1.39768e9	−0.0529103
$208$	−4.73350e9	−0.175346
$209$	−1.72523e10	−0.625443
$210$	−6.61330e9	−0.234656
$211$	2.36984e10	0.823091	0.411546	−	0.911389i	$-0.364989\pi$
$211$	2.36984e10	0.823091	0.411546	+	0.911389i	$0.364989\pi$
$212$	3.39495e9	0.115431
$213$	−1.34935e10	−0.449177
$214$	2.69696e10	0.879047
$215$	1.70402e10	0.543878
$216$	1.91278e10	0.597891
$217$	−3.40241e10	−1.04164
$218$	2.05553e10	0.616411
$219$	−1.46291e10	−0.429753
$220$	9.23993e9	0.265929
$221$	8.95365e9	0.252485
$222$	−7.18706e9	−0.198592
$223$	−3.57686e10	−0.968567	−0.484284	−	0.874911i	$-0.660920\pi$
$223$	−3.57686e10	−0.968567	−0.484284	+	0.874911i	$0.660920\pi$
$224$	2.66634e10	0.707620
$225$	−5.96276e9	−0.155105
$226$	2.41410e10	0.615555
$227$	−5.92891e9	−0.148203	−0.0741017	−	0.997251i	$-0.523609\pi$
$227$	−5.92891e9	−0.148203	−0.0741017	+	0.997251i	$0.523609\pi$
$228$	−3.23926e9	−0.0793851
$229$	4.15396e9	0.0998165	0.0499082	−	0.998754i	$-0.484107\pi$
$229$	4.15396e9	0.0998165	0.0499082	+	0.998754i	$0.484107\pi$
$230$	1.53166e9	0.0360900
$231$	−2.86012e10	−0.660891
$232$	4.30731e10	0.976135
$233$	7.00301e10	1.55662	0.778310	−	0.627880i	$-0.216077\pi$
$233$	7.00301e10	1.55662	0.778310	+	0.627880i	$0.216077\pi$
$234$	−5.95022e9	−0.129736
$235$	7.86407e9	0.168206
$236$	−1.56463e10	−0.328328
$237$	3.98718e10	0.820916
$238$	−9.78650e10	−1.97711
$239$	−8.12068e10	−1.60991	−0.804955	−	0.593336i	$-0.797811\pi$
$239$	−8.12068e10	−1.60991	−0.804955	+	0.593336i	$0.797811\pi$
$240$	−1.35023e10	−0.262699
$241$	−7.73932e10	−1.47784	−0.738918	−	0.673795i	$-0.764663\pi$
$241$	−7.73932e10	−1.47784	−0.738918	+	0.673795i	$0.764663\pi$
$242$	7.69716e10	1.44265
$243$	5.54310e10	1.01982
$244$	−3.25474e10	−0.587844
$245$	−3.11185e9	−0.0551787
$246$	−3.27839e10	−0.570759
$247$	−3.47312e9	−0.0593722
$248$	−4.71039e10	−0.790723
$249$	4.08044e10	0.672682
$250$	6.53437e9	0.105797
$251$	−6.34869e9	−0.100961	−0.0504804	−	0.998725i	$-0.516075\pi$
$251$	−6.34869e9	−0.100961	−0.0504804	+	0.998725i	$0.516075\pi$
$252$	1.85530e10	0.289808
$253$	6.62412e9	0.101645
$254$	−3.40623e10	−0.513478
$255$	2.55404e10	0.378265
$256$	7.09192e10	1.03201
$257$	3.47169e10	0.496411	0.248206	−	0.968707i	$-0.420159\pi$
$257$	3.47169e10	0.496411	0.248206	+	0.968707i	$0.420159\pi$
$258$	4.85050e10	0.681551
$259$	2.40273e10	0.331784
$260$	1.86012e9	0.0252442
$261$	7.98503e10	1.06511
$262$	1.30895e10	0.171619
$263$	−7.47644e10	−0.963593	−0.481797	−	0.876283i	$-0.660016\pi$
$263$	−7.47644e10	−0.963593	−0.481797	+	0.876283i	$0.660016\pi$
$264$	−3.95963e10	−0.501692
$265$	1.03832e10	0.129338
$266$	3.79618e10	0.464921
$267$	−6.66136e8	−0.00802162
$268$	1.56548e10	0.185370
$269$	7.94021e10	0.924585	0.462293	−	0.886727i	$-0.347027\pi$
$269$	7.94021e10	0.924585	0.462293	+	0.886727i	$0.347027\pi$
$270$	−3.88589e10	−0.444993
$271$	−1.07816e11	−1.21428	−0.607142	−	0.794593i	$-0.707684\pi$
$271$	−1.07816e11	−1.21428	−0.607142	+	0.794593i	$0.707684\pi$
$272$	−1.99810e11	−2.21339
$273$	−5.75780e9	−0.0627372
$274$	2.78949e10	0.298983
$275$	2.82598e10	0.297969
$276$	1.24373e9	0.0129014
$277$	−1.47804e11	−1.50844	−0.754221	−	0.656621i	$-0.771985\pi$
$277$	−1.47804e11	−1.50844	−0.754221	+	0.656621i	$0.771985\pi$
$278$	3.85631e10	0.387231
$279$	−8.73228e10	−0.862797
$280$	3.06086e10	0.297599
$281$	7.71094e10	0.737783	0.368892	−	0.929472i	$-0.379737\pi$
$281$	7.71094e10	0.737783	0.368892	+	0.929472i	$0.379737\pi$
$282$	2.23851e10	0.210784
$283$	−5.20411e10	−0.482289	−0.241145	−	0.970489i	$-0.577523\pi$
$283$	−5.20411e10	−0.482289	−0.241145	+	0.970489i	$0.577523\pi$
$284$	−4.14836e10	−0.378394
$285$	−9.90709e9	−0.0889496
$286$	2.82003e10	0.249234
$287$	1.09601e11	0.953556
$288$	6.84318e10	0.586127
$289$	2.59364e11	2.18710
$290$	−8.75049e10	−0.726509
$291$	2.67538e10	0.218709
$292$	−4.49747e10	−0.362031
$293$	8.61823e10	0.683146	0.341573	−	0.939855i	$-0.389040\pi$
$293$	8.61823e10	0.683146	0.341573	+	0.939855i	$0.389040\pi$
$294$	−8.85791e9	−0.0691462
$295$	−4.78534e10	−0.367886
$296$	3.32641e10	0.251862
$297$	−1.68057e11	−1.25329
$298$	1.41739e11	1.04116
$299$	1.33352e9	0.00964897
$300$	5.30602e9	0.0378201
$301$	−1.62159e11	−1.13865
$302$	9.63860e10	0.666780
$303$	−8.64804e10	−0.589421
$304$	7.75064e10	0.520483
$305$	−9.95444e10	−0.658670
$306$	−2.51171e11	−1.63766
$307$	2.85807e11	1.83633	0.918163	−	0.396203i	$-0.129672\pi$
$307$	2.85807e11	1.83633	0.918163	+	0.396203i	$0.129672\pi$
$308$	−8.79295e10	−0.556745
$309$	−1.62956e10	−0.101685
$310$	9.56937e10	0.588513
$311$	9.10066e10	0.551634	0.275817	−	0.961210i	$-0.411052\pi$
$311$	9.10066e10	0.551634	0.275817	+	0.961210i	$0.411052\pi$
$312$	−7.97127e9	−0.0476247
$313$	−1.10469e11	−0.650565	−0.325283	−	0.945617i	$-0.605459\pi$
$313$	−1.10469e11	−0.650565	−0.325283	+	0.945617i	$0.605459\pi$
$314$	8.07737e10	0.468907
$315$	5.67432e10	0.324725
$316$	1.22579e11	0.691552
$317$	−1.41331e11	−0.786087	−0.393043	−	0.919520i	$-0.628578\pi$
$317$	−1.41331e11	−0.786087	−0.393043	+	0.919520i	$0.628578\pi$
$318$	2.95560e10	0.162078
$319$	−3.78440e11	−2.04616
$320$	2.90122e10	0.154670
$321$	6.69792e10	0.352101
$322$	−1.45757e10	−0.0755574
$323$	−1.46607e11	−0.749452
$324$	2.98445e10	0.150457
$325$	5.68908e9	0.0282857
$326$	−2.41472e11	−1.18410
$327$	5.10493e10	0.246902
$328$	1.51735e11	0.723858
$329$	−7.48365e10	−0.352153
$330$	8.04417e10	0.373395
$331$	1.97402e11	0.903911	0.451956	−	0.892040i	$-0.350727\pi$
$331$	1.97402e11	0.903911	0.451956	+	0.892040i	$0.350727\pi$
$332$	1.25446e11	0.566678
$333$	6.16661e10	0.274819
$334$	−6.74849e10	−0.296721
$335$	4.78792e10	0.207704
$336$	1.28492e11	0.549982
$337$	2.73223e10	0.115394	0.0576969	−	0.998334i	$-0.481624\pi$
$337$	2.73223e10	0.115394	0.0576969	+	0.998334i	$0.481624\pi$
$338$	−2.78150e11	−1.15919
$339$	5.99543e10	0.246560
$340$	7.85196e10	0.318656
$341$	4.13856e11	1.65750
$342$	9.74290e10	0.385098
$343$	2.69623e11	1.05180
$344$	−2.24498e11	−0.864368
$345$	3.80389e9	0.0144558
$346$	−2.93364e11	−1.10044
$347$	3.10713e11	1.15047	0.575236	−	0.817987i	$-0.304910\pi$
$347$	3.10713e11	1.15047	0.575236	+	0.817987i	$0.304910\pi$
$348$	−7.10554e10	−0.259711
$349$	−3.20017e10	−0.115467	−0.0577336	−	0.998332i	$-0.518387\pi$
$349$	−3.20017e10	−0.115467	−0.0577336	+	0.998332i	$0.518387\pi$
$350$	−6.21827e10	−0.221495
$351$	−3.38321e10	−0.118973
$352$	−3.24324e11	−1.12600
$353$	−3.87463e11	−1.32814	−0.664070	−	0.747671i	$-0.731172\pi$
$353$	−3.87463e11	−1.32814	−0.664070	+	0.747671i	$0.731172\pi$
$354$	−1.36215e11	−0.461010
$355$	−1.26875e11	−0.423984
$356$	−2.04792e9	−0.00675754
$357$	−2.43049e11	−0.791929
$358$	1.73055e11	0.556815
$359$	1.07798e11	0.342520	0.171260	−	0.985226i	$-0.445216\pi$
$359$	1.07798e11	0.342520	0.171260	+	0.985226i	$0.445216\pi$
$360$	7.85569e10	0.246504
$361$	−2.65819e11	−0.823765
$362$	−3.88996e9	−0.0119058
$363$	1.91160e11	0.577852
$364$	−1.77014e10	−0.0528508
$365$	−1.37552e11	−0.405649
$366$	−2.83354e11	−0.825399
$367$	3.11151e11	0.895310	0.447655	−	0.894206i	$-0.352259\pi$
$367$	3.11151e11	0.895310	0.447655	+	0.894206i	$0.352259\pi$
$368$	−2.97591e10	−0.0845871
$369$	2.81291e11	0.789837
$370$	−6.75775e10	−0.187454
$371$	−9.88096e10	−0.270780
$372$	7.77049e10	0.210380
$373$	2.69498e11	0.720884	0.360442	−	0.932782i	$-0.382626\pi$
$373$	2.69498e11	0.720884	0.360442	+	0.932782i	$0.382626\pi$
$374$	1.19039e12	3.14607
$375$	1.62281e10	0.0423768
$376$	−1.03606e11	−0.267325
$377$	−7.61852e10	−0.194238
$378$	3.69791e11	0.931630
$379$	−2.99148e11	−0.744749	−0.372375	−	0.928083i	$-0.621456\pi$
$379$	−2.99148e11	−0.744749	−0.372375	+	0.928083i	$0.621456\pi$
$380$	−3.04577e10	−0.0749326
$381$	−8.45939e10	−0.205673
$382$	−4.83310e11	−1.16129
$383$	−4.87824e11	−1.15843	−0.579214	−	0.815176i	$-0.696640\pi$
$383$	−4.87824e11	−1.15843	−0.579214	+	0.815176i	$0.696640\pi$
$384$	2.35153e11	0.551901
$385$	−2.68927e11	−0.623823
$386$	9.73305e11	2.23155
$387$	−4.16181e11	−0.943155
$388$	8.22501e10	0.184244
$389$	−1.05812e10	−0.0234295	−0.0117147	−	0.999931i	$-0.503729\pi$
$389$	−1.05812e10	−0.0234295	−0.0117147	+	0.999931i	$0.503729\pi$
$390$	1.61940e10	0.0354457
$391$	5.62908e10	0.121798
$392$	4.09973e10	0.0876937
$393$	3.25078e10	0.0687418
$394$	−1.03304e12	−2.15965
$395$	3.74902e11	0.774873
$396$	−2.25671e11	−0.461156
$397$	−3.15739e11	−0.637928	−0.318964	−	0.947767i	$-0.603335\pi$
$397$	−3.15739e11	−0.637928	−0.318964	+	0.947767i	$0.603335\pi$
$398$	7.44464e9	0.0148720
$399$	9.42784e10	0.186223
$400$	−1.26958e11	−0.247965
$401$	−2.96087e11	−0.571834	−0.285917	−	0.958254i	$-0.592298\pi$
$401$	−2.96087e11	−0.571834	−0.285917	+	0.958254i	$0.592298\pi$
$402$	1.36289e11	0.260281
$403$	8.33148e10	0.157344
$404$	−2.65869e11	−0.496538
$405$	9.12778e10	0.168584
$406$	8.32718e11	1.52101
$407$	−2.92259e11	−0.527950
$408$	−3.36484e11	−0.601164
$409$	7.70694e11	1.36184	0.680922	−	0.732356i	$-0.261579\pi$
$409$	7.70694e11	1.36184	0.680922	+	0.732356i	$0.261579\pi$
$410$	−3.08256e11	−0.538747
$411$	6.92771e10	0.119757
$412$	−5.00982e10	−0.0856613
$413$	4.55385e11	0.770200
$414$	−3.74085e10	−0.0625848
$415$	3.83670e11	0.634953
$416$	−6.52908e10	−0.106889
$417$	9.57717e10	0.155105
$418$	−4.61753e11	−0.739803
$419$	−7.08818e11	−1.12350	−0.561748	−	0.827308i	$-0.689871\pi$
$419$	−7.08818e11	−1.12350	−0.561748	+	0.827308i	$0.689871\pi$
$420$	−5.04934e10	−0.0791795
$421$	−2.53189e11	−0.392803	−0.196401	−	0.980524i	$-0.562926\pi$
$421$	−2.53189e11	−0.392803	−0.196401	+	0.980524i	$0.562926\pi$
$422$	6.34282e11	0.973590
$423$	−1.92068e11	−0.291691
$424$	−1.36795e11	−0.205553
$425$	2.40148e11	0.357049
$426$	−3.61151e11	−0.531308
$427$	9.47290e11	1.37898
$428$	2.05916e11	0.296615
$429$	7.00357e10	0.0998302
$430$	4.56077e11	0.643324
$431$	−3.58426e11	−0.500325	−0.250162	−	0.968204i	$-0.580484\pi$
$431$	−3.58426e11	−0.500325	−0.250162	+	0.968204i	$0.580484\pi$
$432$	7.55000e11	1.04297
$433$	5.71936e11	0.781901	0.390951	−	0.920412i	$-0.372146\pi$
$433$	5.71936e11	0.781901	0.390951	+	0.920412i	$0.372146\pi$
$434$	−9.10646e11	−1.23210
$435$	−2.17319e11	−0.291002
$436$	1.56943e11	0.207994
$437$	−2.18352e10	−0.0286411
$438$	−3.91544e11	−0.508332
$439$	1.16407e12	1.49585	0.747924	−	0.663784i	$-0.231051\pi$
$439$	1.16407e12	1.49585	0.747924	+	0.663784i	$0.231051\pi$
$440$	−3.72311e11	−0.473553
$441$	7.60023e10	0.0956870
$442$	2.39642e11	0.298651
$443$	−1.24504e12	−1.53592	−0.767958	−	0.640500i	$-0.778727\pi$
$443$	−1.24504e12	−1.53592	−0.767958	+	0.640500i	$0.778727\pi$
$444$	−5.48741e10	−0.0670107
$445$	−6.26346e9	−0.00757171
$446$	−9.57337e11	−1.14567
$447$	3.52010e11	0.417034
$448$	−2.76088e11	−0.323814
$449$	−3.98352e11	−0.462549	−0.231275	−	0.972888i	$-0.574290\pi$
$449$	−3.98352e11	−0.462549	−0.231275	+	0.972888i	$0.574290\pi$
$450$	−1.59592e11	−0.183466
$451$	−1.33314e12	−1.51734
$452$	1.84320e11	0.207706
$453$	2.39375e11	0.267078
$454$	−1.58686e11	−0.175302
$455$	−5.41387e10	−0.0592184
$456$	1.30522e11	0.141365
$457$	−2.64155e11	−0.283293	−0.141647	−	0.989917i	$-0.545240\pi$
$457$	−2.64155e11	−0.283293	−0.141647	+	0.989917i	$0.545240\pi$
$458$	1.11180e11	0.118068
$459$	−1.42812e12	−1.50179
$460$	1.16944e10	0.0121778
$461$	1.54801e12	1.59632	0.798161	−	0.602444i	$-0.205806\pi$
$461$	1.54801e12	1.59632	0.798161	+	0.602444i	$0.205806\pi$
$462$	−7.65503e11	−0.781732
$463$	1.39894e12	1.41477	0.707385	−	0.706829i	$-0.249875\pi$
$463$	1.39894e12	1.41477	0.707385	+	0.706829i	$0.249875\pi$
$464$	1.70016e12	1.70278
$465$	2.37656e11	0.235728
$466$	1.87434e12	1.84124
$467$	−1.13856e12	−1.10772	−0.553858	−	0.832611i	$-0.686845\pi$
$467$	−1.13856e12	−1.10772	−0.553858	+	0.832611i	$0.686845\pi$
$468$	−4.54307e10	−0.0437767
$469$	−4.55631e11	−0.434846
$470$	2.10480e11	0.198962
$471$	2.00602e11	0.187820
$472$	6.30449e11	0.584670
$473$	1.97244e12	1.81188
$474$	1.06716e12	0.971017
$475$	−9.31531e10	−0.0839607
$476$	−7.47212e11	−0.667133
$477$	−2.53595e11	−0.224289
$478$	−2.17348e12	−1.90428
$479$	−1.31802e10	−0.0114396	−0.00571980	−	0.999984i	$-0.501821\pi$
$479$	−1.31802e10	−0.0114396	−0.00571980	+	0.999984i	$0.501821\pi$
$480$	−1.86243e11	−0.160138
$481$	−5.88357e10	−0.0501174
$482$	−2.07141e12	−1.74805
$483$	−3.61988e10	−0.0302644
$484$	5.87688e11	0.486792
$485$	2.51557e11	0.206442
$486$	1.48360e12	1.20629
$487$	−1.39614e12	−1.12473	−0.562367	−	0.826888i	$-0.690109\pi$
$487$	−1.39614e12	−1.12473	−0.562367	+	0.826888i	$0.690109\pi$
$488$	1.31146e12	1.04680
$489$	−5.99697e11	−0.474288
$490$	−8.32880e10	−0.0652679
$491$	−4.13493e11	−0.321071	−0.160536	−	0.987030i	$-0.551322\pi$
$491$	−4.13493e11	−0.321071	−0.160536	+	0.987030i	$0.551322\pi$
$492$	−2.50309e11	−0.192590
$493$	−3.21593e12	−2.45186
$494$	−9.29571e10	−0.0702282
$495$	−6.90202e11	−0.516717
$496$	−1.85926e12	−1.37934
$497$	1.20738e12	0.887645
$498$	1.09212e12	0.795679
$499$	2.65850e12	1.91948	0.959740	−	0.280890i	$-0.0906297\pi$
$499$	2.65850e12	1.91948	0.959740	+	0.280890i	$0.0906297\pi$
$500$	4.98907e10	0.0356989
$501$	−1.67599e11	−0.118851
$502$	−1.69921e11	−0.119421
$503$	1.55866e12	1.08567	0.542834	−	0.839840i	$-0.317351\pi$
$503$	1.55866e12	1.08567	0.542834	+	0.839840i	$0.317351\pi$
$504$	−7.47568e11	−0.516075
$505$	−8.13146e11	−0.556362
$506$	1.77293e11	0.120230
$507$	−6.90787e11	−0.464310
$508$	−2.60070e11	−0.173262
$509$	−4.51109e11	−0.297887	−0.148943	−	0.988846i	$-0.547587\pi$
$509$	−4.51109e11	−0.297887	−0.148943	+	0.988846i	$0.547587\pi$
$510$	6.83582e11	0.447429
$511$	1.30898e12	0.849260
$512$	8.68268e10	0.0558392
$513$	5.53968e11	0.353148
$514$	9.29189e11	0.587178
$515$	−1.53223e11	−0.0959821
$516$	3.70342e11	0.229974
$517$	9.10282e11	0.560362
$518$	6.43085e11	0.392450
$519$	−7.28573e11	−0.440778
$520$	−7.49513e10	−0.0449535
$521$	−2.47767e12	−1.47324	−0.736620	−	0.676307i	$-0.763579\pi$
$521$	−2.47767e12	−1.47324	−0.736620	+	0.676307i	$0.763579\pi$
$522$	2.13717e12	1.25986
$523$	−6.07290e11	−0.354926	−0.177463	−	0.984127i	$-0.556789\pi$
$523$	−6.07290e11	−0.354926	−0.177463	+	0.984127i	$0.556789\pi$
$524$	9.99398e10	0.0579092
$525$	−1.54431e11	−0.0887193
$526$	−2.00105e12	−1.13978
$527$	3.51689e12	1.98614
$528$	−1.56292e12	−0.875155
$529$	−1.79277e12	−0.995345
$530$	2.77905e11	0.152987
$531$	1.16875e12	0.637962
$532$	2.89843e11	0.156878
$533$	−2.68380e11	−0.144038
$534$	−1.78290e10	−0.00948835
$535$	6.29783e11	0.332352
$536$	−6.30789e11	−0.330098
$537$	4.29784e11	0.223031
$538$	2.12518e12	1.09364
$539$	−3.60203e11	−0.183822
$540$	−2.96693e11	−0.150153
$541$	1.12334e12	0.563798	0.281899	−	0.959444i	$-0.409036\pi$
$541$	1.12334e12	0.563798	0.281899	+	0.959444i	$0.409036\pi$
$542$	−2.88566e12	−1.43631
$543$	−9.66075e9	−0.00476883
$544$	−2.75606e12	−1.34925
$545$	4.80000e11	0.233054
$546$	−1.54106e11	−0.0742084
$547$	−1.03643e12	−0.494991	−0.247496	−	0.968889i	$-0.579608\pi$
$547$	−1.03643e12	−0.494991	−0.247496	+	0.968889i	$0.579608\pi$
$548$	2.12981e11	0.100885
$549$	2.43122e12	1.14222
$550$	7.56366e11	0.352452
$551$	1.24746e12	0.576559
$552$	−5.01147e10	−0.0229741
$553$	−3.56766e12	−1.62226
$554$	−3.95595e12	−1.78426
$555$	−1.67829e11	−0.0750843
$556$	2.94434e11	0.130663
$557$	6.38453e11	0.281048	0.140524	−	0.990077i	$-0.455121\pi$
$557$	6.38453e11	0.281048	0.140524	+	0.990077i	$0.455121\pi$
$558$	−2.33717e12	−1.02056
$559$	3.97079e11	0.171998
$560$	1.20816e12	0.519135
$561$	2.95635e12	1.26015
$562$	2.06381e12	0.872684
$563$	−1.22208e12	−0.512639	−0.256319	−	0.966592i	$-0.582510\pi$
$563$	−1.22208e12	−0.512639	−0.256319	+	0.966592i	$0.582510\pi$
$564$	1.70913e11	0.0711246
$565$	5.63731e11	0.232731
$566$	−1.39287e12	−0.570474
$567$	−8.68622e11	−0.352945
$568$	1.67153e12	0.673824
$569$	−1.03020e12	−0.412018	−0.206009	−	0.978550i	$-0.566048\pi$
$569$	−1.03020e12	−0.412018	−0.206009	+	0.978550i	$0.566048\pi$
$570$	−2.65161e11	−0.105214
$571$	2.35639e12	0.927651	0.463826	−	0.885927i	$-0.346476\pi$
$571$	2.35639e12	0.927651	0.463826	+	0.885927i	$0.346476\pi$
$572$	2.15313e11	0.0840985
$573$	−1.20030e12	−0.465152
$574$	2.93344e12	1.12791
$575$	3.57667e10	0.0136450
$576$	−7.08580e11	−0.268218
$577$	−6.23831e11	−0.234302	−0.117151	−	0.993114i	$-0.537376\pi$
$577$	−6.23831e11	−0.234302	−0.117151	+	0.993114i	$0.537376\pi$
$578$	6.94181e12	2.58701
$579$	2.41721e12	0.893842
$580$	−6.68111e11	−0.245145
$581$	−3.65110e12	−1.32933
$582$	7.16059e11	0.258699
$583$	1.20188e12	0.430877
$584$	1.81220e12	0.644685
$585$	−1.38947e11	−0.0490510
$586$	2.30665e12	0.808057
$587$	−2.84599e12	−0.989378	−0.494689	−	0.869070i	$-0.664718\pi$
$587$	−2.84599e12	−0.989378	−0.494689	+	0.869070i	$0.664718\pi$
$588$	−6.76313e10	−0.0233319
$589$	−1.36420e12	−0.467045
$590$	−1.28078e12	−0.435153
$591$	−2.56555e12	−0.865042
$592$	1.31298e12	0.439351
$593$	−2.71615e12	−0.902002	−0.451001	−	0.892523i	$-0.648933\pi$
$593$	−2.71615e12	−0.902002	−0.451001	+	0.892523i	$0.648933\pi$
$594$	−4.49800e12	−1.48245
$595$	−2.28531e12	−0.747511
$596$	1.08220e12	0.351316
$597$	1.84888e10	0.00595696
$598$	3.56915e10	0.0114132
$599$	2.62092e12	0.831827	0.415914	−	0.909404i	$-0.363462\pi$
$599$	2.62092e12	0.831827	0.415914	+	0.909404i	$0.363462\pi$
$600$	−2.13799e11	−0.0673481
$601$	−3.04608e12	−0.952371	−0.476186	−	0.879345i	$-0.657981\pi$
$601$	−3.04608e12	−0.952371	−0.476186	+	0.879345i	$0.657981\pi$
$602$	−4.34014e12	−1.34685
$603$	−1.16938e12	−0.360186
$604$	7.35919e11	0.224990
$605$	1.79741e12	0.545442
$606$	−2.31463e12	−0.697195
$607$	−2.30741e12	−0.689883	−0.344942	−	0.938624i	$-0.612101\pi$
$607$	−2.30741e12	−0.689883	−0.344942	+	0.938624i	$0.612101\pi$
$608$	1.06907e12	0.317279
$609$	2.06806e12	0.609236
$610$	−2.66428e12	−0.779105
$611$	1.83252e11	0.0531941
$612$	−1.91772e12	−0.552591
$613$	3.11665e12	0.891488	0.445744	−	0.895160i	$-0.352939\pi$
$613$	3.11665e12	0.891488	0.445744	+	0.895160i	$0.352939\pi$
$614$	7.64955e12	2.17209
$615$	−7.65557e11	−0.215794
$616$	3.54300e12	0.991422
$617$	6.81198e12	1.89230	0.946151	−	0.323726i	$-0.104936\pi$
$617$	6.81198e12	1.89230	0.946151	+	0.323726i	$0.104936\pi$
$618$	−4.36149e11	−0.120278
$619$	−4.84144e11	−0.132546	−0.0662730	−	0.997802i	$-0.521111\pi$
$619$	−4.84144e11	−0.132546	−0.0662730	+	0.997802i	$0.521111\pi$
$620$	7.30634e11	0.198581
$621$	−2.12699e11	−0.0573924
$622$	2.43577e12	0.652499
$623$	5.96046e10	0.0158520
$624$	−3.14638e11	−0.0830769
$625$	1.52588e11	0.0400000
$626$	−2.95668e12	−0.769519
$627$	−1.14677e12	−0.296327
$628$	6.16718e11	0.158222
$629$	−2.48357e12	−0.632629
$630$	1.51872e12	0.384100
$631$	4.81541e12	1.20921	0.604604	−	0.796526i	$-0.293331\pi$
$631$	4.81541e12	1.20921	0.604604	+	0.796526i	$0.293331\pi$
$632$	−4.93917e12	−1.23148
$633$	1.57524e12	0.389970
$634$	−3.78269e12	−0.929820
$635$	−7.95408e11	−0.194137
$636$	2.25664e11	0.0546896
$637$	−7.25138e10	−0.0174499
$638$	−1.01289e13	−2.42029
$639$	3.09874e12	0.735243
$640$	2.21107e12	0.520946
$641$	5.97949e12	1.39895	0.699476	−	0.714656i	$-0.253417\pi$
$641$	5.97949e12	1.39895	0.699476	+	0.714656i	$0.253417\pi$
$642$	1.79268e12	0.416481
$643$	6.83223e12	1.57621	0.788104	−	0.615542i	$-0.211063\pi$
$643$	6.83223e12	1.57621	0.788104	+	0.615542i	$0.211063\pi$
$644$	−1.11287e11	−0.0254952
$645$	1.13267e12	0.257682
$646$	−3.92391e12	−0.886487
$647$	−5.65905e12	−1.26962	−0.634811	−	0.772667i	$-0.718922\pi$
$647$	−5.65905e12	−1.26962	−0.634811	+	0.772667i	$0.718922\pi$
$648$	−1.20255e12	−0.267926
$649$	−5.53913e12	−1.22558
$650$	1.52267e11	0.0334576
$651$	−2.26160e12	−0.493515
$652$	−1.84367e12	−0.399548
$653$	−1.01707e12	−0.218898	−0.109449	−	0.993992i	$-0.534909\pi$
$653$	−1.01707e12	−0.218898	−0.109449	+	0.993992i	$0.534909\pi$
$654$	1.36632e12	0.292047
$655$	3.05660e11	0.0648863
$656$	5.98920e12	1.26270
$657$	3.35951e12	0.703448
$658$	−2.00298e12	−0.416543
$659$	−3.72612e12	−0.769614	−0.384807	−	0.922997i	$-0.625732\pi$
$659$	−3.72612e12	−0.769614	−0.384807	+	0.922997i	$0.625732\pi$
$660$	6.14182e11	0.125994
$661$	2.45746e11	0.0500704	0.0250352	−	0.999687i	$-0.492030\pi$
$661$	2.45746e11	0.0500704	0.0250352	+	0.999687i	$0.492030\pi$
$662$	5.28342e12	1.06919
$663$	5.95153e11	0.119624
$664$	−5.05469e12	−1.00911
$665$	8.86468e11	0.175779
$666$	1.65048e12	0.325069
$667$	−4.78970e11	−0.0937005
$668$	−5.15256e11	−0.100122
$669$	−2.37755e12	−0.458895
$670$	1.28148e12	0.245682
$671$	−1.15225e13	−2.19429
$672$	1.77233e12	0.335261
$673$	−2.74599e11	−0.0515979	−0.0257989	−	0.999667i	$-0.508213\pi$
$673$	−2.74599e11	−0.0515979	−0.0257989	+	0.999667i	$0.508213\pi$
$674$	7.31274e11	0.136493
$675$	−9.07417e11	−0.168244
$676$	−2.12371e12	−0.391142
$677$	9.25777e12	1.69378	0.846890	−	0.531767i	$-0.178472\pi$
$677$	9.25777e12	1.69378	0.846890	+	0.531767i	$0.178472\pi$
$678$	1.60466e12	0.291642
$679$	−2.39388e12	−0.432204
$680$	−3.16384e12	−0.567447
$681$	−3.94097e11	−0.0702169
$682$	1.10767e13	1.96057
$683$	1.60300e12	0.281865	0.140932	−	0.990019i	$-0.454990\pi$
$683$	1.60300e12	0.281865	0.140932	+	0.990019i	$0.454990\pi$
$684$	7.43883e11	0.129943
$685$	6.51390e11	0.113040
$686$	7.21639e12	1.24412
$687$	2.76115e11	0.0472918
$688$	−8.86124e12	−1.50781
$689$	2.41955e11	0.0409024
$690$	1.01810e11	0.0170990
$691$	−1.63810e12	−0.273331	−0.136665	−	0.990617i	$-0.543638\pi$
$691$	−1.63810e12	−0.273331	−0.136665	+	0.990617i	$0.543638\pi$
$692$	−2.23987e12	−0.371318
$693$	6.56814e12	1.08179
$694$	8.31615e12	1.36083
$695$	9.00509e11	0.146405
$696$	2.86309e12	0.462480
$697$	−1.13289e13	−1.81819
$698$	−8.56518e11	−0.136580
$699$	4.65493e12	0.737507
$700$	−4.74773e11	−0.0747385
$701$	−3.87066e11	−0.0605416	−0.0302708	−	0.999542i	$-0.509637\pi$
$701$	−3.87066e11	−0.0605416	−0.0302708	+	0.999542i	$0.509637\pi$
$702$	−9.05508e11	−0.140726
$703$	9.63377e11	0.148764
$704$	3.35823e12	0.515268
$705$	5.22728e11	0.0796939
$706$	−1.03703e13	−1.57098
$707$	7.73811e12	1.16479
$708$	−1.04002e12	−0.155558
$709$	6.64111e11	0.0987035	0.0493518	−	0.998781i	$-0.484284\pi$
$709$	6.64111e11	0.0987035	0.0493518	+	0.998781i	$0.484284\pi$
$710$	−3.39579e12	−0.501508
$711$	−9.15640e12	−1.34373
$712$	8.25184e10	0.0120335
$713$	5.23792e11	0.0759026
$714$	−6.50514e12	−0.936730
$715$	6.58523e11	0.0942310
$716$	1.32130e12	0.187885
$717$	−5.39785e12	−0.762755
$718$	2.88519e12	0.405149
$719$	−5.51431e12	−0.769505	−0.384752	−	0.923020i	$-0.625713\pi$
$719$	−5.51431e12	−0.769505	−0.384752	+	0.923020i	$0.625713\pi$
$720$	3.10076e12	0.430003
$721$	1.45810e12	0.200946
$722$	−7.11458e12	−0.974388
$723$	−5.14437e12	−0.700180
$724$	−2.97004e10	−0.00401734
$725$	−2.04338e12	−0.274680
$726$	5.11634e12	0.683510
$727$	−1.24897e13	−1.65824	−0.829121	−	0.559070i	$-0.811158\pi$
$727$	−1.24897e13	−1.65824	−0.829121	+	0.559070i	$0.811158\pi$
$728$	7.13255e11	0.0941139
$729$	8.09935e11	0.106213
$730$	−3.68156e12	−0.479821
$731$	1.67615e13	2.17112
$732$	−2.16344e12	−0.278513
$733$	1.43648e12	0.183794	0.0918970	−	0.995769i	$-0.470707\pi$
$733$	1.43648e12	0.183794	0.0918970	+	0.995769i	$0.470707\pi$
$734$	8.32787e12	1.05901
$735$	−2.06846e11	−0.0261430
$736$	−4.10478e11	−0.0515631
$737$	5.54212e12	0.691946
$738$	7.52869e12	0.934256
$739$	1.36179e13	1.67962	0.839810	−	0.542881i	$-0.182667\pi$
$739$	1.36179e13	1.67962	0.839810	+	0.542881i	$0.182667\pi$
$740$	−5.15963e11	−0.0632523
$741$	−2.30860e11	−0.0281298
$742$	−2.64462e12	−0.320291
$743$	−1.01703e10	−0.00122429	−0.000612145	−	1.00000i	$-0.500195\pi$
$743$	−1.01703e10	−0.00122429	−0.000612145		1.00000i	$0.500195\pi$
$744$	−3.13102e12	−0.374634
$745$	3.30984e12	0.393644
$746$	7.21304e12	0.852695
$747$	−9.37056e12	−1.10109
$748$	9.08880e12	1.06157
$749$	−5.99317e12	−0.695807
$750$	4.34342e11	0.0501252
$751$	9.04893e12	1.03805	0.519024	−	0.854760i	$-0.326295\pi$
$751$	9.04893e12	1.03805	0.519024	+	0.854760i	$0.326295\pi$
$752$	−4.08947e12	−0.466323
$753$	−4.22001e11	−0.0478339
$754$	−2.03908e12	−0.229754
$755$	2.25077e12	0.252098
$756$	2.82340e12	0.314358
$757$	3.89773e12	0.431400	0.215700	−	0.976460i	$-0.430797\pi$
$757$	3.89773e12	0.431400	0.215700	+	0.976460i	$0.430797\pi$
$758$	−8.00663e12	−0.880924
$759$	4.40308e11	0.0481580
$760$	1.22725e12	0.133436
$761$	−9.90923e12	−1.07105	−0.535524	−	0.844520i	$-0.679886\pi$
$761$	−9.90923e12	−1.07105	−0.535524	+	0.844520i	$0.679886\pi$
$762$	−2.26413e12	−0.243279
$763$	−4.56780e12	−0.487918
$764$	−3.69013e12	−0.391852
$765$	−5.86524e12	−0.619169
$766$	−1.30565e13	−1.37024
$767$	−1.11510e12	−0.116342
$768$	4.71403e12	0.488953
$769$	1.15295e13	1.18889	0.594444	−	0.804137i	$-0.297372\pi$
$769$	1.15295e13	1.18889	0.594444	+	0.804137i	$0.297372\pi$
$770$	−7.19777e12	−0.737887
$771$	2.30765e12	0.235193
$772$	7.43131e12	0.752987
$773$	−9.67555e12	−0.974693	−0.487347	−	0.873209i	$-0.662035\pi$
$773$	−9.67555e12	−0.974693	−0.487347	+	0.873209i	$0.662035\pi$
$774$	−1.11390e13	−1.11561
$775$	2.23460e12	0.222506
$776$	−3.31416e12	−0.328092
$777$	1.59711e12	0.157195
$778$	−2.83204e11	−0.0277134
$779$	4.39446e12	0.427550
$780$	1.23643e11	0.0119604
$781$	−1.46861e13	−1.41246
$782$	1.50661e12	0.144069
$783$	1.21517e13	1.15534
$784$	1.61823e12	0.152974
$785$	1.88620e12	0.177286
$786$	8.70064e11	0.0813111
$787$	2.10996e13	1.96060	0.980298	−	0.197525i	$-0.0632903\pi$
$787$	2.10996e13	1.96060	0.980298	+	0.197525i	$0.0632903\pi$
$788$	−7.88736e12	−0.728725
$789$	−4.96962e12	−0.456538
$790$	1.00341e13	0.916555
$791$	−5.36460e12	−0.487241
$792$	9.09313e12	0.821202
$793$	−2.31963e12	−0.208300
$794$	−8.45069e12	−0.754571
$795$	6.90179e11	0.0612787
$796$	5.68408e10	0.00501824
$797$	6.35783e12	0.558144	0.279072	−	0.960270i	$-0.409973\pi$
$797$	6.35783e12	0.558144	0.279072	+	0.960270i	$0.409973\pi$
$798$	2.52334e12	0.220274
$799$	7.73545e12	0.671467
$800$	−1.75118e12	−0.151156
$801$	1.52975e11	0.0131303
$802$	−7.92471e12	−0.676392
$803$	−1.59220e13	−1.35138
$804$	1.04058e12	0.0878261
$805$	−3.40365e11	−0.0285669
$806$	2.22990e12	0.186113
$807$	5.27790e12	0.438056
$808$	1.07129e13	0.884208
$809$	−8.03990e12	−0.659906	−0.329953	−	0.943997i	$-0.607033\pi$
$809$	−8.03990e12	−0.659906	−0.329953	+	0.943997i	$0.607033\pi$
$810$	2.44303e12	0.199409
$811$	8.17244e12	0.663373	0.331687	−	0.943390i	$-0.392382\pi$
$811$	8.17244e12	0.663373	0.331687	+	0.943390i	$0.392382\pi$
$812$	6.35791e12	0.513230
$813$	−7.16656e12	−0.575312
$814$	−7.82224e12	−0.624484
$815$	−5.63876e12	−0.447687
$816$	−1.32815e13	−1.04868
$817$	−6.50177e12	−0.510543
$818$	2.06274e13	1.61085
$819$	1.32226e12	0.102692
$820$	−2.35358e12	−0.181788
$821$	2.18882e13	1.68138	0.840688	−	0.541519i	$-0.182151\pi$
$821$	2.18882e13	1.68138	0.840688	+	0.541519i	$0.182151\pi$
$822$	1.85418e12	0.141654
$823$	−7.90628e12	−0.600721	−0.300360	−	0.953826i	$-0.597107\pi$
$823$	−7.90628e12	−0.600721	−0.300360	+	0.953826i	$0.597107\pi$
$824$	2.01864e12	0.152541
$825$	1.87844e12	0.141174
$826$	1.21883e13	0.911029
$827$	1.23397e13	0.917340	0.458670	−	0.888607i	$-0.348326\pi$
$827$	1.23397e13	0.917340	0.458670	+	0.888607i	$0.348326\pi$
$828$	−2.85619e11	−0.0211179
$829$	−1.05174e13	−0.773415	−0.386707	−	0.922203i	$-0.626388\pi$
$829$	−1.05174e13	−0.773415	−0.386707	+	0.922203i	$0.626388\pi$
$830$	1.02688e13	0.751052
$831$	−9.82463e12	−0.714680
$832$	6.76057e11	0.0489134
$833$	−3.06096e12	−0.220270
$834$	2.56331e12	0.183465
$835$	−1.57588e12	−0.112185
$836$	−3.52554e12	−0.249630
$837$	−1.32888e13	−0.935885
$838$	−1.89713e13	−1.32892
$839$	−2.42354e13	−1.68858	−0.844288	−	0.535889i	$-0.819976\pi$
$839$	−2.42354e13	−1.68858	−0.844288	+	0.535889i	$0.819976\pi$
$840$	2.03457e12	0.140999
$841$	1.28567e13	0.886234
$842$	−6.77653e12	−0.464625
$843$	5.12550e12	0.349552
$844$	4.84282e12	0.328517
$845$	−6.49524e12	−0.438268
$846$	−5.14065e12	−0.345026
$847$	−1.71046e13	−1.14193
$848$	−5.39950e12	−0.358568
$849$	−3.45920e12	−0.228502
$850$	6.42749e12	0.422334
$851$	−3.69895e11	−0.0241766
$852$	−2.75744e12	−0.179278
$853$	1.18654e13	0.767381	0.383690	−	0.923462i	$-0.374653\pi$
$853$	1.18654e13	0.767381	0.383690	+	0.923462i	$0.374653\pi$
$854$	2.53540e13	1.63112
$855$	2.27512e12	0.145599
$856$	−8.29713e12	−0.528197
$857$	−2.22495e13	−1.40899	−0.704494	−	0.709710i	$-0.748826\pi$
$857$	−2.22495e13	−1.40899	−0.704494	+	0.709710i	$0.748826\pi$
$858$	1.87449e12	0.118084
$859$	−1.23035e13	−0.771006	−0.385503	−	0.922707i	$-0.625972\pi$
$859$	−1.23035e13	−0.771006	−0.385503	+	0.922707i	$0.625972\pi$
$860$	3.48221e12	0.217076
$861$	7.28523e12	0.451782
$862$	−9.59319e12	−0.591807
$863$	1.67121e13	1.02561	0.512806	−	0.858505i	$-0.328606\pi$
$863$	1.67121e13	1.02561	0.512806	+	0.858505i	$0.328606\pi$
$864$	1.04140e13	0.635778
$865$	−6.85053e12	−0.416056
$866$	1.53077e13	0.924869
$867$	1.72400e13	1.03622
$868$	−6.95290e12	−0.415745
$869$	4.33956e13	2.58141
$870$	−5.81649e12	−0.344211
$871$	1.11570e12	0.0656852
$872$	−6.32380e12	−0.370385
$873$	−6.14390e12	−0.357998
$874$	−5.84413e11	−0.0338780
$875$	−1.45207e12	−0.0837433
$876$	−2.98949e12	−0.171525
$877$	1.11566e13	0.636845	0.318423	−	0.947949i	$-0.396847\pi$
$877$	1.11566e13	0.636845	0.318423	+	0.947949i	$0.396847\pi$
$878$	3.11560e13	1.76936
$879$	5.72858e12	0.323666
$880$	−1.46957e13	−0.826070
$881$	−6.45233e12	−0.360848	−0.180424	−	0.983589i	$-0.557747\pi$
$881$	−6.45233e12	−0.360848	−0.180424	+	0.983589i	$0.557747\pi$
$882$	2.03418e12	0.113183
$883$	−1.06381e13	−0.588898	−0.294449	−	0.955667i	$-0.595136\pi$
$883$	−1.06381e13	−0.588898	−0.294449	+	0.955667i	$0.595136\pi$
$884$	1.82970e12	0.100773
$885$	−3.18084e12	−0.174300
$886$	−3.33233e13	−1.81675
$887$	2.10257e13	1.14050	0.570250	−	0.821471i	$-0.306846\pi$
$887$	2.10257e13	1.14050	0.570250	+	0.821471i	$0.306846\pi$
$888$	2.21108e12	0.119329
$889$	7.56931e12	0.406442
$890$	−1.67640e11	−0.00895617
$891$	1.05656e13	0.561622
$892$	−7.30940e12	−0.386580
$893$	−3.00058e12	−0.157897
$894$	9.42147e12	0.493287
$895$	4.04111e12	0.210522
$896$	−2.10411e13	−1.09064
$897$	8.86400e10	0.00457156
$898$	−1.06618e13	−0.547125
$899$	−2.99246e13	−1.52795
$900$	−1.21851e12	−0.0619065
$901$	1.02134e13	0.516309
$902$	−3.56813e13	−1.79478
$903$	−1.07788e13	−0.539479
$904$	−7.42692e12	−0.369871
$905$	−9.08369e10	−0.00450136
$906$	6.40682e12	0.315912
$907$	−8.98297e12	−0.440745	−0.220372	−	0.975416i	$-0.570727\pi$
$907$	−8.98297e12	−0.440745	−0.220372	+	0.975416i	$0.570727\pi$
$908$	−1.21159e12	−0.0591518
$909$	1.98599e13	0.964803
$910$	−1.44901e12	−0.0700463
$911$	−2.32715e13	−1.11942	−0.559709	−	0.828689i	$-0.689087\pi$
$911$	−2.32715e13	−1.11942	−0.559709	+	0.828689i	$0.689087\pi$
$912$	5.15188e12	0.246598
$913$	4.44106e13	2.11528
$914$	−7.07006e12	−0.335093
$915$	−6.61677e12	−0.312069
$916$	8.48871e11	0.0398393
$917$	−2.90874e12	−0.135845
$918$	−3.82233e13	−1.77638
$919$	−1.25073e13	−0.578420	−0.289210	−	0.957266i	$-0.593393\pi$
$919$	−1.25073e13	−0.578420	−0.289210	+	0.957266i	$0.593393\pi$
$920$	−4.71212e11	−0.0216856
$921$	1.89977e13	0.870027
$922$	4.14322e13	1.88820
$923$	−2.95651e12	−0.134082
$924$	−5.84472e12	−0.263779
$925$	−1.57804e12	−0.0708731
$926$	3.74424e13	1.67346
$927$	3.74223e12	0.166445
$928$	2.34509e13	1.03799
$929$	7.76069e12	0.341845	0.170923	−	0.985284i	$-0.445325\pi$
$929$	7.76069e12	0.341845	0.170923	+	0.985284i	$0.445325\pi$
$930$	6.36081e12	0.278830
$931$	1.18734e12	0.0517968
$932$	1.43108e13	0.621288
$933$	6.04925e12	0.261357
$934$	−3.04732e13	−1.31026
$935$	2.77976e13	1.18947
$936$	1.83057e12	0.0779552
$937$	−3.00977e13	−1.27557	−0.637786	−	0.770214i	$-0.720149\pi$
$937$	−3.00977e13	−1.27557	−0.637786	+	0.770214i	$0.720149\pi$
$938$	−1.21949e13	−0.514356
$939$	−7.34293e12	−0.308229
$940$	1.60704e12	0.0671354
$941$	−4.73101e13	−1.96698	−0.983492	−	0.180950i	$-0.942083\pi$
$941$	−4.73101e13	−1.96698	−0.983492	+	0.180950i	$0.942083\pi$
$942$	5.36907e12	0.222162
$943$	−1.68728e12	−0.0694840
$944$	2.48847e13	1.01990
$945$	8.63522e12	0.352233
$946$	5.27918e13	2.14317
$947$	−5.15925e12	−0.208455	−0.104227	−	0.994553i	$-0.533237\pi$
$947$	−5.15925e12	−0.208455	−0.104227	+	0.994553i	$0.533237\pi$
$948$	8.14790e12	0.327649
$949$	−3.20531e12	−0.128284
$950$	−2.49322e12	−0.0993126
$951$	−9.39433e12	−0.372438
$952$	3.01079e13	1.18800
$953$	−2.89086e13	−1.13530	−0.567648	−	0.823272i	$-0.692146\pi$
$953$	−2.89086e13	−1.13530	−0.567648	+	0.823272i	$0.692146\pi$
$954$	−6.78741e12	−0.265299
$955$	−1.12861e13	−0.439063
$956$	−1.65948e13	−0.642557
$957$	−2.51551e13	−0.969444
$958$	−3.52764e11	−0.0135313
$959$	−6.19879e12	−0.236659
$960$	1.92846e12	0.0732807
$961$	6.28542e12	0.237727
$962$	−1.57472e12	−0.0592811
$963$	−1.53815e13	−0.576342
$964$	−1.58155e13	−0.589843
$965$	2.27282e13	0.843709
$966$	−9.68852e11	−0.0357981
$967$	2.34982e13	0.864204	0.432102	−	0.901825i	$-0.357772\pi$
$967$	2.34982e13	0.864204	0.432102	+	0.901825i	$0.357772\pi$
$968$	−2.36801e13	−0.866852
$969$	−9.74505e12	−0.355081
$970$	6.73287e12	0.244190
$971$	2.08721e13	0.753493	0.376747	−	0.926316i	$-0.377043\pi$
$971$	2.08721e13	0.753493	0.376747	+	0.926316i	$0.377043\pi$
$972$	1.13275e13	0.407038
$973$	−8.56948e12	−0.306511
$974$	−3.73675e13	−1.33039
$975$	3.78156e11	0.0134014
$976$	5.17651e13	1.82605
$977$	3.84347e13	1.34958	0.674789	−	0.738011i	$-0.264235\pi$
$977$	3.84347e13	1.34958	0.674789	+	0.738011i	$0.264235\pi$
$978$	−1.60508e13	−0.561010
$979$	−7.25008e11	−0.0252244
$980$	−6.35914e11	−0.0220232
$981$	−1.17233e13	−0.404146
$982$	−1.10670e13	−0.379778
$983$	3.82774e13	1.30753	0.653764	−	0.756698i	$-0.273189\pi$
$983$	3.82774e13	1.30753	0.653764	+	0.756698i	$0.273189\pi$
$984$	1.00859e13	0.342954
$985$	−2.41230e13	−0.816524
$986$	−8.60737e13	−2.90017
$987$	−4.97442e12	−0.166846
$988$	−7.09739e11	−0.0236970
$989$	2.49640e12	0.0829718
$990$	−1.84731e13	−0.611197
$991$	−5.18610e13	−1.70808	−0.854042	−	0.520204i	$-0.825856\pi$
$991$	−5.18610e13	−1.70808	−0.854042	+	0.520204i	$0.825856\pi$
$992$	−2.56455e13	−0.840829
$993$	1.31214e13	0.428261
$994$	3.23152e13	1.04995
$995$	1.73844e11	0.00562285
$996$	8.33847e12	0.268485
$997$	2.46318e13	0.789529	0.394765	−	0.918782i	$-0.370826\pi$
$997$	2.46318e13	0.789529	0.394765	+	0.918782i	$0.370826\pi$
$998$	7.11540e13	2.27045
$999$	9.38439e12	0.298100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.10.a.b.1.2	✓	2
3.2	odd	2		45.10.a.f.1.1		2
4.3	odd	2		80.10.a.f.1.2		2
5.2	odd	4		25.10.b.b.24.3		4
5.3	odd	4		25.10.b.b.24.2		4
5.4	even	2		25.10.a.b.1.1		2
7.6	odd	2		245.10.a.d.1.2		2
8.3	odd	2		320.10.a.s.1.1		2
8.5	even	2		320.10.a.k.1.2		2
15.2	even	4		225.10.b.h.199.2		4
15.8	even	4		225.10.b.h.199.3		4
15.14	odd	2		225.10.a.h.1.2		2
20.3	even	4		400.10.c.p.49.2		4
20.7	even	4		400.10.c.p.49.3		4
20.19	odd	2		400.10.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.a.b.1.2	✓	2	1.1	even	1	trivial
25.10.a.b.1.1		2	5.4	even	2
25.10.b.b.24.2		4	5.3	odd	4
25.10.b.b.24.3		4	5.2	odd	4
45.10.a.f.1.1		2	3.2	odd	2
80.10.a.f.1.2		2	4.3	odd	2
225.10.a.h.1.2		2	15.14	odd	2
225.10.b.h.199.2		4	15.2	even	4
225.10.b.h.199.3		4	15.8	even	4
245.10.a.d.1.2		2	7.6	odd	2
320.10.a.k.1.2		2	8.5	even	2
320.10.a.s.1.1		2	8.3	odd	2
400.10.a.t.1.1		2	20.19	odd	2
400.10.c.p.49.2		4	20.3	even	4
400.10.c.p.49.3		4	20.7	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+26.7648 q^{2} +66.4705 q^{3} +204.352 q^{4} +625.000 q^{5} +1779.07 q^{6} -5947.66 q^{7} -8234.11 q^{8} -15264.7 q^{9} +O(q^{10})\)	\(q+26.7648 q^{2} +66.4705 q^{3} +204.352 q^{4} +625.000 q^{5} +1779.07 q^{6} -5947.66 q^{7} -8234.11 q^{8} -15264.7 q^{9} +16728.0 q^{10} +72345.0 q^{11} +13583.4 q^{12} +14564.0 q^{13} -159188. q^{14} +41544.0 q^{15} -325013. q^{16} +614778. q^{17} -408555. q^{18} -238472. q^{19} +127720. q^{20} -395344. q^{21} +1.93630e6 q^{22} +91562.8 q^{23} -547326. q^{24} +390625. q^{25} +389803. q^{26} -2.32299e6 q^{27} -1.21542e6 q^{28} -5.23105e6 q^{29} +1.11192e6 q^{30} +5.72058e6 q^{31} -4.48302e6 q^{32} +4.80881e6 q^{33} +1.64544e7 q^{34} -3.71729e6 q^{35} -3.11937e6 q^{36} -4.03979e6 q^{37} -6.38264e6 q^{38} +968079. q^{39} -5.14632e6 q^{40} -1.84276e7 q^{41} -1.05813e7 q^{42} +2.72643e7 q^{43} +1.47839e7 q^{44} -9.54042e6 q^{45} +2.45066e6 q^{46} +1.25825e7 q^{47} -2.16037e7 q^{48} -4.97896e6 q^{49} +1.04550e7 q^{50} +4.08646e7 q^{51} +2.97620e6 q^{52} +1.66132e7 q^{53} -6.21742e7 q^{54} +4.52157e7 q^{55} +4.89737e7 q^{56} -1.58513e7 q^{57} -1.40008e8 q^{58} -7.65654e7 q^{59} +8.48963e6 q^{60} -1.59271e8 q^{61} +1.53110e8 q^{62} +9.07891e7 q^{63} +4.64196e7 q^{64} +9.10253e6 q^{65} +1.28707e8 q^{66} +7.66068e7 q^{67} +1.25631e8 q^{68} +6.08622e6 q^{69} -9.94923e7 q^{70} -2.03001e8 q^{71} +1.25691e8 q^{72} -2.20084e8 q^{73} -1.08124e8 q^{74} +2.59650e7 q^{75} -4.87323e7 q^{76} -4.30284e8 q^{77} +2.59104e7 q^{78} +5.99842e8 q^{79} -2.03133e8 q^{80} +1.46044e8 q^{81} -4.93210e8 q^{82} +6.13872e8 q^{83} -8.07894e7 q^{84} +3.84236e8 q^{85} +7.29723e8 q^{86} -3.47710e8 q^{87} -5.95697e8 q^{88} -1.00215e7 q^{89} -2.55347e8 q^{90} -8.66220e7 q^{91} +1.87111e7 q^{92} +3.80250e8 q^{93} +3.36768e8 q^{94} -1.49045e8 q^{95} -2.97988e8 q^{96} +4.02491e8 q^{97} -1.33261e8 q^{98} -1.10432e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 10 q^{2} + 260 q^{3} + 1044 q^{4} + 1250 q^{5} - 5336 q^{6} + 1700 q^{7} - 20280 q^{8} + 2506 q^{9}+O(q^{10}) \) 2 * q - 10 * q^2 + 260 * q^3 + 1044 * q^4 + 1250 * q^5 - 5336 * q^6 + 1700 * q^7 - 20280 * q^8 + 2506 * q^9	\( 2 q - 10 q^{2} + 260 q^{3} + 1044 q^{4} + 1250 q^{5} - 5336 q^{6} + 1700 q^{7} - 20280 q^{8} + 2506 q^{9} - 6250 q^{10} + 23984 q^{11} + 176080 q^{12} + 115020 q^{13} - 440352 q^{14} + 162500 q^{15} - 312048 q^{16} + 412820 q^{17} - 1061890 q^{18} - 296520 q^{19} + 652500 q^{20} + 1084704 q^{21} + 3714280 q^{22} - 1049220 q^{23} - 2878560 q^{24} + 781250 q^{25} - 3303436 q^{26} - 2693080 q^{27} + 5205920 q^{28} - 3666980 q^{29} - 3335000 q^{30} + 1613144 q^{31} + 1207840 q^{32} - 4550480 q^{33} + 23879308 q^{34} + 1062500 q^{35} + 11801732 q^{36} - 21121940 q^{37} - 4248520 q^{38} + 20409272 q^{39} - 12675000 q^{40} - 26957276 q^{41} - 64994880 q^{42} + 52889700 q^{43} - 25822352 q^{44} + 1566250 q^{45} + 44391264 q^{46} + 58412180 q^{47} - 19094720 q^{48} + 13154114 q^{49} - 3906250 q^{50} + 1779784 q^{51} + 87323800 q^{52} - 39035140 q^{53} - 48567920 q^{54} + 14990000 q^{55} - 43149120 q^{56} - 27085360 q^{57} - 197510380 q^{58} - 54995560 q^{59} + 110050000 q^{60} - 274579716 q^{61} + 304118880 q^{62} + 226693140 q^{63} - 169441216 q^{64} + 71887500 q^{65} + 472798688 q^{66} - 318580 q^{67} - 43942040 q^{68} - 214688928 q^{69} - 275220000 q^{70} - 7130936 q^{71} - 88372440 q^{72} + 120858180 q^{73} + 519897028 q^{74} + 101562500 q^{75} - 97472240 q^{76} - 800132400 q^{77} - 688840400 q^{78} + 6877520 q^{79} - 195030000 q^{80} - 275359358 q^{81} - 179618020 q^{82} + 1402348740 q^{83} + 1161929088 q^{84} + 258012500 q^{85} - 212388136 q^{86} - 45016840 q^{87} - 13145760 q^{88} + 830088660 q^{89} - 663681250 q^{90} + 681630904 q^{91} - 939144480 q^{92} - 414660480 q^{93} - 1348148912 q^{94} - 185325000 q^{95} + 803360384 q^{96} + 638394580 q^{97} - 799918970 q^{98} - 1963732048 q^{99}+O(q^{100}) \) 2 * q - 10 * q^2 + 260 * q^3 + 1044 * q^4 + 1250 * q^5 - 5336 * q^6 + 1700 * q^7 - 20280 * q^8 + 2506 * q^9 - 6250 * q^10 + 23984 * q^11 + 176080 * q^12 + 115020 * q^13 - 440352 * q^14 + 162500 * q^15 - 312048 * q^16 + 412820 * q^17 - 1061890 * q^18 - 296520 * q^19 + 652500 * q^20 + 1084704 * q^21 + 3714280 * q^22 - 1049220 * q^23 - 2878560 * q^24 + 781250 * q^25 - 3303436 * q^26 - 2693080 * q^27 + 5205920 * q^28 - 3666980 * q^29 - 3335000 * q^30 + 1613144 * q^31 + 1207840 * q^32 - 4550480 * q^33 + 23879308 * q^34 + 1062500 * q^35 + 11801732 * q^36 - 21121940 * q^37 - 4248520 * q^38 + 20409272 * q^39 - 12675000 * q^40 - 26957276 * q^41 - 64994880 * q^42 + 52889700 * q^43 - 25822352 * q^44 + 1566250 * q^45 + 44391264 * q^46 + 58412180 * q^47 - 19094720 * q^48 + 13154114 * q^49 - 3906250 * q^50 + 1779784 * q^51 + 87323800 * q^52 - 39035140 * q^53 - 48567920 * q^54 + 14990000 * q^55 - 43149120 * q^56 - 27085360 * q^57 - 197510380 * q^58 - 54995560 * q^59 + 110050000 * q^60 - 274579716 * q^61 + 304118880 * q^62 + 226693140 * q^63 - 169441216 * q^64 + 71887500 * q^65 + 472798688 * q^66 - 318580 * q^67 - 43942040 * q^68 - 214688928 * q^69 - 275220000 * q^70 - 7130936 * q^71 - 88372440 * q^72 + 120858180 * q^73 + 519897028 * q^74 + 101562500 * q^75 - 97472240 * q^76 - 800132400 * q^77 - 688840400 * q^78 + 6877520 * q^79 - 195030000 * q^80 - 275359358 * q^81 - 179618020 * q^82 + 1402348740 * q^83 + 1161929088 * q^84 + 258012500 * q^85 - 212388136 * q^86 - 45016840 * q^87 - 13145760 * q^88 + 830088660 * q^89 - 663681250 * q^90 + 681630904 * q^91 - 939144480 * q^92 - 414660480 * q^93 - 1348148912 * q^94 - 185325000 * q^95 + 803360384 * q^96 + 638394580 * q^97 - 799918970 * q^98 - 1963732048 * q^99

Introduction

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