LMFDB - Embedded newform 361.10.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,10,Mod(1,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, 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("361.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	361.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:	$185.927936855$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.1701 q^{2} +248.674 q^{3} +1022.30 q^{4} -1256.48 q^{5} -9740.57 q^{6} -166.160 q^{7} -19988.3 q^{8} +42155.6 q^{9} +O(q^{10})$	\(q-39.1701 q^{2} +248.674 q^{3} +1022.30 q^{4} -1256.48 q^{5} -9740.57 q^{6} -166.160 q^{7} -19988.3 q^{8} +42155.6 q^{9} +49216.5 q^{10} -85800.6 q^{11} +254218. q^{12} -75769.3 q^{13} +6508.49 q^{14} -312454. q^{15} +259529. q^{16} +396124. q^{17} -1.65124e6 q^{18} -1.28450e6 q^{20} -41319.5 q^{21} +3.36082e6 q^{22} +2.21066e6 q^{23} -4.97057e6 q^{24} -374376. q^{25} +2.96789e6 q^{26} +5.58834e6 q^{27} -169864. q^{28} -1.71899e6 q^{29} +1.22389e7 q^{30} +152647. q^{31} +68258.7 q^{32} -2.13363e7 q^{33} -1.55162e7 q^{34} +208777. q^{35} +4.30954e7 q^{36} -7.71043e6 q^{37} -1.88418e7 q^{39} +2.51150e7 q^{40} -8.29977e6 q^{41} +1.61849e6 q^{42} +9.63083e6 q^{43} -8.77135e7 q^{44} -5.29678e7 q^{45} -8.65916e7 q^{46} -4.28370e7 q^{47} +6.45379e7 q^{48} -4.03260e7 q^{49} +1.46643e7 q^{50} +9.85056e7 q^{51} -7.74586e7 q^{52} -7.75078e6 q^{53} -2.18896e8 q^{54} +1.07807e8 q^{55} +3.32125e6 q^{56} +6.73329e7 q^{58} -3.34998e6 q^{59} -3.19420e8 q^{60} +1.31588e8 q^{61} -5.97919e6 q^{62} -7.00456e6 q^{63} -1.35552e8 q^{64} +9.52028e7 q^{65} +8.35746e8 q^{66} -1.25132e8 q^{67} +4.04956e8 q^{68} +5.49732e8 q^{69} -8.17780e6 q^{70} +1.92466e8 q^{71} -8.42619e8 q^{72} +1.87816e7 q^{73} +3.02018e8 q^{74} -9.30975e7 q^{75} +1.42566e7 q^{77} +7.38036e8 q^{78} -1.20061e8 q^{79} -3.26093e8 q^{80} +5.59924e8 q^{81} +3.25103e8 q^{82} +8.00434e7 q^{83} -4.22408e7 q^{84} -4.97723e8 q^{85} -3.77240e8 q^{86} -4.27467e8 q^{87} +1.71501e9 q^{88} +3.86415e8 q^{89} +2.07475e9 q^{90} +1.25898e7 q^{91} +2.25994e9 q^{92} +3.79593e7 q^{93} +1.67793e9 q^{94} +1.69741e7 q^{96} +1.27771e9 q^{97} +1.57957e9 q^{98} -3.61697e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 48 q^{2} + 486 q^{3} + 9984 q^{4} + 852 q^{5} + 1536 q^{6} - 5715 q^{7} + 36861 q^{8} + 236196 q^{9}+O(q^{10}) $ 42 * q + 48 * q^2 + 486 * q^3 + 9984 * q^4 + 852 * q^5 + 1536 * q^6 - 5715 * q^7 + 36861 * q^8 + 236196 * q^9	\( 42 q + 48 q^{2} + 486 q^{3} + 9984 q^{4} + 852 q^{5} + 1536 q^{6} - 5715 q^{7} + 36861 q^{8} + 236196 q^{9} + 58464 q^{10} - 11295 q^{11} + 373245 q^{12} + 117150 q^{13} + 642912 q^{14} + 548451 q^{15} + 2162688 q^{16} + 997809 q^{17} + 1359318 q^{18} + 2160357 q^{20} + 1367568 q^{21} + 5031171 q^{22} + 2213706 q^{23} - 6545730 q^{24} + 13853862 q^{25} + 9164091 q^{26} + 9159258 q^{27} - 14025501 q^{28} + 9949038 q^{29} + 31527234 q^{30} + 14008185 q^{31} + 10978065 q^{32} + 14330319 q^{33} - 585930 q^{34} - 48129252 q^{35} + 7475208 q^{36} + 34869216 q^{37} + 15720432 q^{39} + 103478568 q^{40} + 86266776 q^{41} + 69259017 q^{42} - 12988605 q^{43} - 203224311 q^{44} + 61014765 q^{45} - 63830328 q^{46} + 17328918 q^{47} + 213121044 q^{48} + 163636377 q^{49} + 314983974 q^{50} + 96577575 q^{51} + 75305472 q^{52} + 103187364 q^{53} - 272434584 q^{54} - 56373354 q^{55} + 372695601 q^{56} + 287431734 q^{58} + 660784728 q^{59} + 368982060 q^{60} + 169972728 q^{61} + 300679941 q^{62} - 1173015477 q^{63} + 866999625 q^{64} - 153878493 q^{65} + 853102866 q^{66} + 189790482 q^{67} + 821601474 q^{68} + 1193576865 q^{69} - 629548281 q^{70} + 920008254 q^{71} - 118366770 q^{72} - 976066764 q^{73} - 782973429 q^{74} + 2015364294 q^{75} - 479229111 q^{77} + 2285947218 q^{78} + 2003560392 q^{79} + 3171353712 q^{80} + 1356085014 q^{81} - 1540624044 q^{82} + 1226988585 q^{83} + 1236853875 q^{84} - 372049179 q^{85} + 1472174664 q^{86} + 601158705 q^{87} + 2100827301 q^{88} + 853591443 q^{89} + 5492348259 q^{90} + 3495862842 q^{91} - 536774244 q^{92} - 1750089960 q^{93} + 7410646467 q^{94} + 4632812853 q^{96} + 1807268862 q^{97} + 5836044465 q^{98} + 777469992 q^{99}+O(q^{100}) \) 42 * q + 48 * q^2 + 486 * q^3 + 9984 * q^4 + 852 * q^5 + 1536 * q^6 - 5715 * q^7 + 36861 * q^8 + 236196 * q^9 + 58464 * q^10 - 11295 * q^11 + 373245 * q^12 + 117150 * q^13 + 642912 * q^14 + 548451 * q^15 + 2162688 * q^16 + 997809 * q^17 + 1359318 * q^18 + 2160357 * q^20 + 1367568 * q^21 + 5031171 * q^22 + 2213706 * q^23 - 6545730 * q^24 + 13853862 * q^25 + 9164091 * q^26 + 9159258 * q^27 - 14025501 * q^28 + 9949038 * q^29 + 31527234 * q^30 + 14008185 * q^31 + 10978065 * q^32 + 14330319 * q^33 - 585930 * q^34 - 48129252 * q^35 + 7475208 * q^36 + 34869216 * q^37 + 15720432 * q^39 + 103478568 * q^40 + 86266776 * q^41 + 69259017 * q^42 - 12988605 * q^43 - 203224311 * q^44 + 61014765 * q^45 - 63830328 * q^46 + 17328918 * q^47 + 213121044 * q^48 + 163636377 * q^49 + 314983974 * q^50 + 96577575 * q^51 + 75305472 * q^52 + 103187364 * q^53 - 272434584 * q^54 - 56373354 * q^55 + 372695601 * q^56 + 287431734 * q^58 + 660784728 * q^59 + 368982060 * q^60 + 169972728 * q^61 + 300679941 * q^62 - 1173015477 * q^63 + 866999625 * q^64 - 153878493 * q^65 + 853102866 * q^66 + 189790482 * q^67 + 821601474 * q^68 + 1193576865 * q^69 - 629548281 * q^70 + 920008254 * q^71 - 118366770 * q^72 - 976066764 * q^73 - 782973429 * q^74 + 2015364294 * q^75 - 479229111 * q^77 + 2285947218 * q^78 + 2003560392 * q^79 + 3171353712 * q^80 + 1356085014 * q^81 - 1540624044 * q^82 + 1226988585 * q^83 + 1236853875 * q^84 - 372049179 * q^85 + 1472174664 * q^86 + 601158705 * q^87 + 2100827301 * q^88 + 853591443 * q^89 + 5492348259 * q^90 + 3495862842 * q^91 - 536774244 * q^92 - 1750089960 * q^93 + 7410646467 * q^94 + 4632812853 * q^96 + 1807268862 * q^97 + 5836044465 * q^98 + 777469992 * 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 $

$2$	−39.1701	−1.73109	−0.865545	−	0.500832i	$-0.833028\pi$
$2$	−39.1701	−1.73109	−0.865545	+	0.500832i	$0.833028\pi$
$3$	248.674	1.77249	0.886246	−	0.463216i	$-0.153304\pi$
$3$	248.674	1.77249	0.886246	+	0.463216i	$0.153304\pi$
$4$	1022.30	1.99667
$5$	−1256.48	−0.899066	−0.449533	−	0.893264i	$-0.648410\pi$
$5$	−1256.48	−0.899066	−0.449533	+	0.893264i	$0.648410\pi$
$6$	−9740.57	−3.06834
$7$	−166.160	−0.0261568	−0.0130784	−	0.999914i	$-0.504163\pi$
$7$	−166.160	−0.0261568	−0.0130784	+	0.999914i	$0.504163\pi$
$8$	−19988.3	−1.72533
$9$	42155.6	2.14173
$10$	49216.5	1.55636
$11$	−85800.6	−1.76695	−0.883473	−	0.468483i	$-0.844801\pi$
$11$	−85800.6	−1.76695	−0.883473	+	0.468483i	$0.844801\pi$
$12$	254218.	3.53908
$13$	−75769.3	−0.735781	−0.367890	−	0.929869i	$-0.619920\pi$
$13$	−75769.3	−0.735781	−0.367890	+	0.929869i	$0.619920\pi$
$14$	6508.49	0.0452797
$15$	−312454.	−1.59359
$16$	259529.	0.990023
$17$	396124.	1.15030	0.575150	−	0.818048i	$-0.304944\pi$
$17$	396124.	1.15030	0.575150	+	0.818048i	$0.304944\pi$
$18$	−1.65124e6	−3.70752
$19$	0	0
$19$	0	0
$20$	−1.28450e6	−1.79514
$21$	−41319.5	−0.0463627
$22$	3.36082e6	3.05874
$23$	2.21066e6	1.64720	0.823600	−	0.567172i	$-0.191962\pi$
$23$	2.21066e6	1.64720	0.823600	+	0.567172i	$0.191962\pi$
$24$	−4.97057e6	−3.05813
$25$	−374376.	−0.191681
$26$	2.96789e6	1.27370
$27$	5.58834e6	2.02370
$28$	−169864.	−0.0522265
$29$	−1.71899e6	−0.451317	−0.225659	−	0.974206i	$-0.572453\pi$
$29$	−1.71899e6	−0.451317	−0.225659	+	0.974206i	$0.572453\pi$
$30$	1.22389e7	2.75864
$31$	152647.	0.0296866	0.0148433	−	0.999890i	$-0.495275\pi$
$31$	152647.	0.0296866	0.0148433	+	0.999890i	$0.495275\pi$
$32$	68258.7	0.0115076
$33$	−2.13363e7	−3.13190
$34$	−1.55162e7	−1.99127
$35$	208777.	0.0235167
$36$	4.30954e7	4.27632
$37$	−7.71043e6	−0.676349	−0.338174	−	0.941084i	$-0.609809\pi$
$37$	−7.71043e6	−0.676349	−0.338174	+	0.941084i	$0.609809\pi$
$38$	0	0
$39$	−1.88418e7	−1.30416
$40$	2.51150e7	1.55118
$41$	−8.29977e6	−0.458710	−0.229355	−	0.973343i	$-0.573662\pi$
$41$	−8.29977e6	−0.458710	−0.229355	+	0.973343i	$0.573662\pi$
$42$	1.61849e6	0.0802580
$43$	9.63083e6	0.429592	0.214796	−	0.976659i	$-0.431091\pi$
$43$	9.63083e6	0.429592	0.214796	+	0.976659i	$0.431091\pi$
$44$	−8.77135e7	−3.52801
$45$	−5.29678e7	−1.92555
$46$	−8.65916e7	−2.85145
$47$	−4.28370e7	−1.28050	−0.640248	−	0.768168i	$-0.721168\pi$
$47$	−4.28370e7	−1.28050	−0.640248	+	0.768168i	$0.721168\pi$
$48$	6.45379e7	1.75481
$49$	−4.03260e7	−0.999316
$50$	1.46643e7	0.331816
$51$	9.85056e7	2.03890
$52$	−7.74586e7	−1.46911
$53$	−7.75078e6	−0.134929	−0.0674643	−	0.997722i	$-0.521491\pi$
$53$	−7.75078e6	−0.134929	−0.0674643	+	0.997722i	$0.521491\pi$
$54$	−2.18896e8	−3.50320
$55$	1.07807e8	1.58860
$56$	3.32125e6	0.0451290
$57$	0	0
$58$	6.73329e7	0.781270
$59$	−3.34998e6	−0.0359922	−0.0179961	−	0.999838i	$-0.505729\pi$
$59$	−3.34998e6	−0.0359922	−0.0179961	+	0.999838i	$0.505729\pi$
$60$	−3.19420e8	−3.18187
$61$	1.31588e8	1.21684	0.608418	−	0.793617i	$-0.291804\pi$
$61$	1.31588e8	1.21684	0.608418	+	0.793617i	$0.291804\pi$
$62$	−5.97919e6	−0.0513902
$63$	−7.00456e6	−0.0560207
$64$	−1.35552e8	−1.00994
$65$	9.52028e7	0.661515
$66$	8.35746e8	5.42159
$67$	−1.25132e8	−0.758634	−0.379317	−	0.925267i	$-0.623841\pi$
$67$	−1.25132e8	−0.758634	−0.379317	+	0.925267i	$0.623841\pi$
$68$	4.04956e8	2.29677
$69$	5.49732e8	2.91965
$70$	−8.17780e6	−0.0407095
$71$	1.92466e8	0.898860	0.449430	−	0.893316i	$-0.351627\pi$
$71$	1.92466e8	0.898860	0.449430	+	0.893316i	$0.351627\pi$
$72$	−8.42619e8	−3.69517
$73$	1.87816e7	0.0774069	0.0387035	−	0.999251i	$-0.487677\pi$
$73$	1.87816e7	0.0774069	0.0387035	+	0.999251i	$0.487677\pi$
$74$	3.02018e8	1.17082
$75$	−9.30975e7	−0.339752
$76$	0	0
$77$	1.42566e7	0.0462176
$78$	7.38036e8	2.25763
$79$	−1.20061e8	−0.346801	−0.173400	−	0.984851i	$-0.555475\pi$
$79$	−1.20061e8	−0.346801	−0.173400	+	0.984851i	$0.555475\pi$
$80$	−3.26093e8	−0.890096
$81$	5.59924e8	1.44526
$82$	3.25103e8	0.794069
$83$	8.00434e7	0.185129	0.0925644	−	0.995707i	$-0.470494\pi$
$83$	8.00434e7	0.185129	0.0925644	+	0.995707i	$0.470494\pi$
$84$	−4.22408e7	−0.0925710
$85$	−4.97723e8	−1.03420
$86$	−3.77240e8	−0.743661
$87$	−4.27467e8	−0.799956
$88$	1.71501e9	3.04856
$89$	3.86415e8	0.652828	0.326414	−	0.945227i	$-0.394160\pi$
$89$	3.86415e8	0.652828	0.326414	+	0.945227i	$0.394160\pi$
$90$	2.07475e9	3.33330
$91$	1.25898e7	0.0192457
$92$	2.25994e9	3.28891
$93$	3.79593e7	0.0526193
$94$	1.67793e9	2.21665
$95$	0	0
$96$	1.69741e7	0.0203970
$97$	1.27771e9	1.46541	0.732706	−	0.680545i	$-0.238257\pi$
$97$	1.27771e9	1.46541	0.732706	+	0.680545i	$0.238257\pi$
$98$	1.57957e9	1.72991
$99$	−3.61697e9	−3.78431
$100$	−3.82723e8	−0.382723
$101$	−5.50672e8	−0.526559	−0.263279	−	0.964720i	$-0.584804\pi$
$101$	−5.50672e8	−0.526559	−0.263279	+	0.964720i	$0.584804\pi$
$102$	−3.85847e9	−3.52951
$103$	6.13369e8	0.536975	0.268487	−	0.963283i	$-0.413476\pi$
$103$	6.13369e8	0.536975	0.268487	+	0.963283i	$0.413476\pi$
$104$	1.51450e9	1.26946
$105$	5.19173e7	0.0416831
$106$	3.03599e8	0.233574
$107$	−1.94540e8	−0.143477	−0.0717383	−	0.997423i	$-0.522855\pi$
$107$	−1.94540e8	−0.143477	−0.0717383	+	0.997423i	$0.522855\pi$
$108$	5.71293e9	4.04066
$109$	−2.01302e9	−1.36593	−0.682966	−	0.730450i	$-0.739310\pi$
$109$	−2.01302e9	−1.36593	−0.682966	+	0.730450i	$0.739310\pi$
$110$	−4.22281e9	−2.75001
$111$	−1.91738e9	−1.19882
$112$	−4.31232e7	−0.0258958
$113$	3.26655e9	1.88468	0.942338	−	0.334663i	$-0.108622\pi$
$113$	3.26655e9	1.88468	0.942338	+	0.334663i	$0.108622\pi$
$114$	0	0
$115$	−2.77765e9	−1.48094
$116$	−1.75731e9	−0.901132
$117$	−3.19410e9	−1.57584
$118$	1.31219e8	0.0623057
$119$	−6.58198e7	−0.0300882
$120$	6.24543e9	2.74946
$121$	5.00379e9	2.12210
$122$	−5.15432e9	−2.10645
$123$	−2.06393e9	−0.813060
$124$	1.56050e8	0.0592744
$125$	2.92447e9	1.07140
$126$	2.74369e8	0.0969768
$127$	2.92825e9	0.998830	0.499415	−	0.866363i	$-0.333548\pi$
$127$	2.92825e9	0.998830	0.499415	+	0.866363i	$0.333548\pi$
$128$	5.27465e9	1.73680
$129$	2.39493e9	0.761447
$130$	−3.72910e9	−1.14514
$131$	−4.06160e9	−1.20497	−0.602485	−	0.798130i	$-0.705823\pi$
$131$	−4.06160e9	−1.20497	−0.602485	+	0.798130i	$0.705823\pi$
$132$	−2.18120e10	−6.25336
$133$	0	0
$134$	4.90144e9	1.31326
$135$	−7.02165e9	−1.81944
$136$	−7.91785e9	−1.98464
$137$	3.34247e7	0.00810633	0.00405317	−	0.999992i	$-0.498710\pi$
$137$	3.34247e7	0.00810633	0.00405317	+	0.999992i	$0.498710\pi$
$138$	−2.15331e10	−5.05417
$139$	−2.32291e9	−0.527796	−0.263898	−	0.964551i	$-0.585008\pi$
$139$	−2.32291e9	−0.527796	−0.263898	+	0.964551i	$0.585008\pi$
$140$	2.13432e8	0.0469551
$141$	−1.06524e10	−2.26967
$142$	−7.53892e9	−1.55601
$143$	6.50105e9	1.30008
$144$	1.09406e10	2.12036
$145$	2.15988e9	0.405764
$146$	−7.35677e8	−0.133998
$147$	−1.00280e10	−1.77128
$148$	−7.88233e9	−1.35045
$149$	−1.12270e9	−0.186606	−0.0933031	−	0.995638i	$-0.529743\pi$
$149$	−1.12270e9	−0.186606	−0.0933031	+	0.995638i	$0.529743\pi$
$150$	3.64664e9	0.588141
$151$	3.96225e9	0.620220	0.310110	−	0.950701i	$-0.399634\pi$
$151$	3.96225e9	0.620220	0.310110	+	0.950701i	$0.399634\pi$
$152$	0	0
$153$	1.66988e10	2.46363
$154$	−5.58432e8	−0.0800068
$155$	−1.91798e8	−0.0266902
$156$	−1.92619e10	−2.60399
$157$	−9.21903e9	−1.21098	−0.605490	−	0.795853i	$-0.707023\pi$
$157$	−9.21903e9	−1.21098	−0.605490	+	0.795853i	$0.707023\pi$
$158$	4.70280e9	0.600343
$159$	−1.92742e9	−0.239160
$160$	−8.57658e7	−0.0103460
$161$	−3.67322e8	−0.0430854
$162$	−2.19323e10	−2.50188
$163$	−3.40888e9	−0.378240	−0.189120	−	0.981954i	$-0.560564\pi$
$163$	−3.40888e9	−0.378240	−0.189120	+	0.981954i	$0.560564\pi$
$164$	−8.48481e9	−0.915894
$165$	2.68087e10	2.81578
$166$	−3.13531e9	−0.320475
$167$	1.32434e10	1.31758	0.658790	−	0.752327i	$-0.271069\pi$
$167$	1.32434e10	1.31758	0.658790	+	0.752327i	$0.271069\pi$
$168$	8.25908e8	0.0799907
$169$	−4.86351e9	−0.458627
$170$	1.94958e10	1.79028
$171$	0	0
$172$	9.84555e9	0.857753
$173$	1.16232e10	0.986552	0.493276	−	0.869873i	$-0.335799\pi$
$173$	1.16232e10	0.986552	0.493276	+	0.869873i	$0.335799\pi$
$174$	1.67439e10	1.38479
$175$	6.22062e7	0.00501375
$176$	−2.22677e10	−1.74932
$177$	−8.33052e8	−0.0637958
$178$	−1.51359e10	−1.13010
$179$	1.52760e10	1.11217	0.556086	−	0.831125i	$-0.312303\pi$
$179$	1.52760e10	1.11217	0.556086	+	0.831125i	$0.312303\pi$
$180$	−5.41487e10	−3.84469
$181$	−7.29176e9	−0.504985	−0.252493	−	0.967599i	$-0.581250\pi$
$181$	−7.29176e9	−0.504985	−0.252493	+	0.967599i	$0.581250\pi$
$182$	−4.93144e8	−0.0333160
$183$	3.27225e10	2.15683
$184$	−4.41873e10	−2.84196
$185$	9.68802e9	0.608082
$186$	−1.48687e9	−0.0910886
$187$	−3.39877e10	−2.03252
$188$	−4.37920e10	−2.55673
$189$	−9.28556e8	−0.0529334
$190$	0	0
$191$	5.07416e9	0.275876	0.137938	−	0.990441i	$-0.455953\pi$
$191$	5.07416e9	0.275876	0.137938	+	0.990441i	$0.455953\pi$
$192$	−3.37083e10	−1.79012
$193$	4.53240e9	0.235137	0.117568	−	0.993065i	$-0.462490\pi$
$193$	4.53240e9	0.235137	0.117568	+	0.993065i	$0.462490\pi$
$194$	−5.00480e10	−2.53676
$195$	2.36744e10	1.17253
$196$	−4.12251e10	−1.99530
$197$	3.08213e10	1.45799	0.728993	−	0.684521i	$-0.239988\pi$
$197$	3.08213e10	1.45799	0.728993	+	0.684521i	$0.239988\pi$
$198$	1.41677e11	6.55098
$199$	1.46887e9	0.0663966	0.0331983	−	0.999449i	$-0.489431\pi$
$199$	1.46887e9	0.0663966	0.0331983	+	0.999449i	$0.489431\pi$
$200$	7.48315e9	0.330712
$201$	−3.11171e10	−1.34467
$202$	2.15699e10	0.911520
$203$	2.85626e8	0.0118050
$204$	1.00702e11	4.07100
$205$	1.04285e10	0.412411
$206$	−2.40257e10	−0.929552
$207$	9.31915e10	3.52785
$208$	−1.96643e10	−0.728440
$209$	0	0
$210$	−2.03360e9	−0.0721572
$211$	−1.37385e10	−0.477165	−0.238583	−	0.971122i	$-0.576683\pi$
$211$	−1.37385e10	−0.477165	−0.238583	+	0.971122i	$0.576683\pi$
$212$	−7.92359e9	−0.269408
$213$	4.78613e10	1.59322
$214$	7.62013e9	0.248371
$215$	−1.21010e10	−0.386231
$216$	−1.11701e11	−3.49154
$217$	−2.53638e7	−0.000776506 0
$218$	7.88502e10	2.36455
$219$	4.67049e9	0.137203
$220$	1.10211e11	3.17191
$221$	−3.00140e10	−0.846368
$222$	7.51039e10	2.07527
$223$	2.94831e10	0.798366	0.399183	−	0.916871i	$-0.369294\pi$
$223$	2.94831e10	0.798366	0.399183	+	0.916871i	$0.369294\pi$
$224$	−1.13418e7	−0.000301001 0
$225$	−1.57820e10	−0.410527
$226$	−1.27951e11	−3.26254
$227$	2.91124e10	0.727717	0.363858	−	0.931454i	$-0.381459\pi$
$227$	2.91124e10	0.727717	0.363858	+	0.931454i	$0.381459\pi$
$228$	0	0
$229$	2.98659e10	0.717655	0.358828	−	0.933404i	$-0.383177\pi$
$229$	2.98659e10	0.717655	0.358828	+	0.933404i	$0.383177\pi$
$230$	1.08801e11	2.56364
$231$	3.54524e9	0.0819203
$232$	3.43597e10	0.778669
$233$	3.66106e10	0.813777	0.406888	−	0.913478i	$-0.366614\pi$
$233$	3.66106e10	0.813777	0.406888	+	0.913478i	$0.366614\pi$
$234$	1.25113e11	2.72792
$235$	5.38239e10	1.15125
$236$	−3.42467e9	−0.0718645
$237$	−2.98560e10	−0.614701
$238$	2.57817e9	0.0520853
$239$	1.69879e10	0.336782	0.168391	−	0.985720i	$-0.446143\pi$
$239$	1.69879e10	0.336782	0.168391	+	0.985720i	$0.446143\pi$
$240$	−8.10908e10	−1.57769
$241$	−4.35518e10	−0.831630	−0.415815	−	0.909449i	$-0.636504\pi$
$241$	−4.35518e10	−0.831630	−0.415815	+	0.909449i	$0.636504\pi$
$242$	−1.95999e11	−3.67354
$243$	2.92431e10	0.538015
$244$	1.34522e11	2.42962
$245$	5.06689e10	0.898451
$246$	8.08444e10	1.40748
$247$	0	0
$248$	−3.05116e9	−0.0512191
$249$	1.99047e10	0.328139
$250$	−1.14552e11	−1.85469
$251$	2.95004e10	0.469133	0.234567	−	0.972100i	$-0.424633\pi$
$251$	2.95004e10	0.469133	0.234567	+	0.972100i	$0.424633\pi$
$252$	−7.16073e9	−0.111855
$253$	−1.89676e11	−2.91051
$254$	−1.14700e11	−1.72906
$255$	−1.23771e11	−1.83310
$256$	−1.37206e11	−1.99660
$257$	1.03292e11	1.47695	0.738475	−	0.674281i	$-0.235546\pi$
$257$	1.03292e11	1.47695	0.738475	+	0.674281i	$0.235546\pi$
$258$	−9.38098e10	−1.31813
$259$	1.28116e9	0.0176911
$260$	9.73254e10	1.32083
$261$	−7.24649e10	−0.966597
$262$	1.59093e11	2.08591
$263$	−3.32982e10	−0.429160	−0.214580	−	0.976706i	$-0.568838\pi$
$263$	−3.32982e10	−0.429160	−0.214580	+	0.976706i	$0.568838\pi$
$264$	4.26477e11	5.40354
$265$	9.73873e9	0.121310
$266$	0	0
$267$	9.60911e10	1.15713
$268$	−1.27922e11	−1.51474
$269$	−4.52611e10	−0.527035	−0.263518	−	0.964655i	$-0.584883\pi$
$269$	−4.52611e10	−0.527035	−0.263518	+	0.964655i	$0.584883\pi$
$270$	2.75039e11	3.14961
$271$	−1.53622e11	−1.73018	−0.865091	−	0.501616i	$-0.832739\pi$
$271$	−1.53622e11	−1.73018	−0.865091	+	0.501616i	$0.832739\pi$
$272$	1.02806e11	1.13882
$273$	3.13075e9	0.0341128
$274$	−1.30925e9	−0.0140328
$275$	3.21217e10	0.338689
$276$	5.61989e11	5.82957
$277$	5.97558e10	0.609847	0.304924	−	0.952377i	$-0.401369\pi$
$277$	5.97558e10	0.609847	0.304924	+	0.952377i	$0.401369\pi$
$278$	9.09886e10	0.913662
$279$	6.43492e9	0.0635806
$280$	−4.17310e9	−0.0405739
$281$	−9.14330e10	−0.874832	−0.437416	−	0.899259i	$-0.644106\pi$
$281$	−9.14330e10	−0.874832	−0.437416	+	0.899259i	$0.644106\pi$
$282$	4.17256e11	3.92900
$283$	3.86853e10	0.358515	0.179257	−	0.983802i	$-0.442631\pi$
$283$	3.86853e10	0.358515	0.179257	+	0.983802i	$0.442631\pi$
$284$	1.96757e11	1.79473
$285$	0	0
$286$	−2.54647e11	−2.25056
$287$	1.37909e9	0.0119984
$288$	2.87748e9	0.0246460
$289$	3.83263e10	0.323189
$290$	−8.46026e10	−0.702413
$291$	3.17733e11	2.59743
$292$	1.92003e10	0.154556
$293$	9.10211e10	0.721502	0.360751	−	0.932662i	$-0.382520\pi$
$293$	9.10211e10	0.721502	0.360751	+	0.932662i	$0.382520\pi$
$294$	3.92798e11	3.06624
$295$	4.20919e9	0.0323593
$296$	1.54118e11	1.16692
$297$	−4.79483e11	−3.57576
$298$	4.39763e10	0.323032
$299$	−1.67500e11	−1.21198
$300$	−9.51731e10	−0.678373
$301$	−1.60026e9	−0.0112367
$302$	−1.55202e11	−1.07366
$303$	−1.36938e11	−0.933320
$304$	0	0
$305$	−1.65338e11	−1.09402
$306$	−6.54095e11	−4.26476
$307$	9.84090e10	0.632284	0.316142	−	0.948712i	$-0.397612\pi$
$307$	9.84090e10	0.632284	0.316142	+	0.948712i	$0.397612\pi$
$308$	1.45745e10	0.0922814
$309$	1.52529e11	0.951783
$310$	7.51276e9	0.0462032
$311$	1.55510e11	0.942622	0.471311	−	0.881967i	$-0.343781\pi$
$311$	1.55510e11	0.942622	0.471311	+	0.881967i	$0.343781\pi$
$312$	3.76616e11	2.25011
$313$	−5.52888e10	−0.325602	−0.162801	−	0.986659i	$-0.552053\pi$
$313$	−5.52888e10	−0.325602	−0.162801	+	0.986659i	$0.552053\pi$
$314$	3.61110e11	2.09631
$315$	8.80111e9	0.0503663
$316$	−1.22738e11	−0.692447
$317$	−1.87333e11	−1.04195	−0.520976	−	0.853571i	$-0.674432\pi$
$317$	−1.87333e11	−1.04195	−0.520976	+	0.853571i	$0.674432\pi$
$318$	7.54970e10	0.414007
$319$	1.47490e11	0.797453
$320$	1.70319e11	0.908006
$321$	−4.83769e10	−0.254311
$322$	1.43880e10	0.0745848
$323$	0	0
$324$	5.72408e11	2.88571
$325$	2.83662e10	0.141035
$326$	1.33526e11	0.654767
$327$	−5.00585e11	−2.42110
$328$	1.65898e11	0.791425
$329$	7.11778e9	0.0334937
$330$	−1.05010e12	−4.87437
$331$	2.78385e11	1.27473	0.637367	−	0.770560i	$-0.280023\pi$
$331$	2.78385e11	1.27473	0.637367	+	0.770560i	$0.280023\pi$
$332$	8.18280e10	0.369641
$333$	−3.25037e11	−1.44855
$334$	−5.18747e11	−2.28085
$335$	1.57226e11	0.682062
$336$	−1.07236e10	−0.0459001
$337$	1.06585e11	0.450153	0.225076	−	0.974341i	$-0.427737\pi$
$337$	1.06585e11	0.450153	0.225076	+	0.974341i	$0.427737\pi$
$338$	1.90504e11	0.793924
$339$	8.12306e11	3.34057
$340$	−5.08820e11	−2.06495
$341$	−1.30972e10	−0.0524546
$342$	0	0
$343$	1.34057e10	0.0522957
$344$	−1.92504e11	−0.741185
$345$	−6.90729e11	−2.62495
$346$	−4.55283e11	−1.70781
$347$	5.26826e11	1.95067	0.975337	−	0.220720i	$-0.0708407\pi$
$347$	5.26826e11	1.95067	0.975337	+	0.220720i	$0.0708407\pi$
$348$	−4.36998e11	−1.59725
$349$	5.99488e10	0.216305	0.108152	−	0.994134i	$-0.465507\pi$
$349$	5.99488e10	0.216305	0.108152	+	0.994134i	$0.465507\pi$
$350$	−2.43662e9	−0.00867925
$351$	−4.23424e11	−1.48900
$352$	−5.85663e9	−0.0203332
$353$	4.13682e11	1.41801	0.709006	−	0.705202i	$-0.249144\pi$
$353$	4.13682e11	1.41801	0.709006	+	0.705202i	$0.249144\pi$
$354$	3.26307e10	0.110436
$355$	−2.41830e11	−0.808134
$356$	3.95030e11	1.30348
$357$	−1.63677e10	−0.0533310
$358$	−5.98363e11	−1.92527
$359$	6.08188e11	1.93247	0.966234	−	0.257665i	$-0.0829530\pi$
$359$	6.08188e11	1.93247	0.966234	+	0.257665i	$0.0829530\pi$
$360$	1.05874e12	3.32220
$361$	0	0
$362$	2.85619e11	0.874175
$363$	1.24431e12	3.76140
$364$	1.28705e10	0.0384272
$365$	−2.35988e10	−0.0695939
$366$	−1.28174e12	−3.73367
$367$	4.67856e11	1.34622	0.673109	−	0.739543i	$-0.264959\pi$
$367$	4.67856e11	1.34622	0.673109	+	0.739543i	$0.264959\pi$
$368$	5.73729e11	1.63077
$369$	−3.49881e11	−0.982431
$370$	−3.79480e11	−1.05264
$371$	1.28787e9	0.00352930
$372$	3.88056e10	0.105063
$373$	3.94359e11	1.05488	0.527439	−	0.849593i	$-0.323152\pi$
$373$	3.94359e11	1.05488	0.527439	+	0.849593i	$0.323152\pi$
$374$	1.33130e12	3.51847
$375$	7.27237e11	1.89905
$376$	8.56239e11	2.20927
$377$	1.30247e11	0.332070
$378$	3.63716e10	0.0916325
$379$	−6.60774e11	−1.64504	−0.822520	−	0.568736i	$-0.807433\pi$
$379$	−6.60774e11	−1.64504	−0.822520	+	0.568736i	$0.807433\pi$
$380$	0	0
$381$	7.28179e11	1.77042
$382$	−1.98755e11	−0.477566
$383$	4.01433e11	0.953276	0.476638	−	0.879100i	$-0.341855\pi$
$383$	4.01433e11	0.953276	0.476638	+	0.879100i	$0.341855\pi$
$384$	1.31167e12	3.07845
$385$	−1.79132e10	−0.0415527
$386$	−1.77535e11	−0.407043
$387$	4.05993e11	0.920067
$388$	1.30620e12	2.92595
$389$	4.06345e11	0.899749	0.449874	−	0.893092i	$-0.351469\pi$
$389$	4.06345e11	0.899749	0.449874	+	0.893092i	$0.351469\pi$
$390$	−9.27330e11	−2.02975
$391$	8.75694e11	1.89477
$392$	8.06049e11	1.72415
$393$	−1.01001e12	−2.13580
$394$	−1.20727e12	−2.52391
$395$	1.50855e11	0.311797
$396$	−3.69761e12	−7.55602
$397$	−1.23288e11	−0.249095	−0.124547	−	0.992214i	$-0.539748\pi$
$397$	−1.23288e11	−0.249095	−0.124547	+	0.992214i	$0.539748\pi$
$398$	−5.75359e10	−0.114938
$399$	0	0
$400$	−9.71613e10	−0.189768
$401$	−8.70915e10	−0.168200	−0.0841000	−	0.996457i	$-0.526802\pi$
$401$	−8.70915e10	−0.168200	−0.0841000	+	0.996457i	$0.526802\pi$
$402$	1.21886e12	2.32775
$403$	−1.15660e10	−0.0218428
$404$	−5.62949e11	−1.05136
$405$	−7.03535e11	−1.29939
$406$	−1.11880e10	−0.0204355
$407$	6.61559e11	1.19507
$408$	−1.96896e12	−3.51776
$409$	3.15595e10	0.0557668	0.0278834	−	0.999611i	$-0.491123\pi$
$409$	3.15595e10	0.0557668	0.0278834	+	0.999611i	$0.491123\pi$
$410$	−4.08486e11	−0.713920
$411$	8.31183e9	0.0143684
$412$	6.27044e11	1.07216
$413$	5.56632e8	0.000941440 0
$414$	−3.65032e12	−6.10702
$415$	−1.00573e11	−0.166443
$416$	−5.17191e9	−0.00846703
$417$	−5.77647e11	−0.935514
$418$	0	0
$419$	−1.25178e12	−1.98411	−0.992056	−	0.125799i	$-0.959851\pi$
$419$	−1.25178e12	−1.98411	−0.992056	+	0.125799i	$0.959851\pi$
$420$	5.30748e10	0.0832274
$421$	−9.46527e11	−1.46847	−0.734233	−	0.678898i	$-0.762458\pi$
$421$	−9.46527e11	−1.46847	−0.734233	+	0.678898i	$0.762458\pi$
$422$	5.38139e11	0.826016
$423$	−1.80582e12	−2.74247
$424$	1.54925e11	0.232796
$425$	−1.48299e11	−0.220490
$426$	−1.87473e12	−2.75801
$427$	−2.18646e10	−0.0318285
$428$	−1.98877e11	−0.286475
$429$	1.61664e12	2.30439
$430$	4.73996e11	0.668601
$431$	1.13227e12	1.58053	0.790265	−	0.612765i	$-0.209943\pi$
$431$	1.13227e12	1.58053	0.790265	+	0.612765i	$0.209943\pi$
$432$	1.45033e12	2.00351
$433$	9.91068e11	1.35490	0.677451	−	0.735568i	$-0.263084\pi$
$433$	9.91068e11	1.35490	0.677451	+	0.735568i	$0.263084\pi$
$434$	9.93501e8	0.00134420
$435$	5.37105e11	0.719213
$436$	−2.05790e12	−2.72732
$437$	0	0
$438$	−1.82943e11	−0.237511
$439$	1.19607e12	1.53698	0.768489	−	0.639863i	$-0.221009\pi$
$439$	1.19607e12	1.53698	0.768489	+	0.639863i	$0.221009\pi$
$440$	−2.15488e12	−2.74085
$441$	−1.69997e12	−2.14026
$442$	1.17565e12	1.46514
$443$	−1.13278e12	−1.39742	−0.698712	−	0.715403i	$-0.746243\pi$
$443$	−1.13278e12	−1.39742	−0.698712	+	0.715403i	$0.746243\pi$
$444$	−1.96013e12	−2.39365
$445$	−4.85523e11	−0.586935
$446$	−1.15486e12	−1.38204
$447$	−2.79186e11	−0.330758
$448$	2.25233e10	0.0264169
$449$	4.44260e11	0.515856	0.257928	−	0.966164i	$-0.416960\pi$
$449$	4.44260e11	0.515856	0.257928	+	0.966164i	$0.416960\pi$
$450$	6.18184e11	0.710659
$451$	7.12125e11	0.810516
$452$	3.33938e12	3.76308
$453$	9.85308e11	1.09933
$454$	−1.14034e12	−1.25974
$455$	−1.58189e10	−0.0173031
$456$	0	0
$457$	7.56053e11	0.810829	0.405414	−	0.914133i	$-0.367127\pi$
$457$	7.56053e11	0.810829	0.405414	+	0.914133i	$0.367127\pi$
$458$	−1.16985e12	−1.24233
$459$	2.21367e12	2.32786
$460$	−2.83958e12	−2.95695
$461$	7.32096e11	0.754942	0.377471	−	0.926021i	$-0.376794\pi$
$461$	7.32096e11	0.754942	0.377471	+	0.926021i	$0.376794\pi$
$462$	−1.38867e11	−0.141811
$463$	4.54429e11	0.459570	0.229785	−	0.973241i	$-0.426198\pi$
$463$	4.54429e11	0.459570	0.229785	+	0.973241i	$0.426198\pi$
$464$	−4.46127e11	−0.446814
$465$	−4.76952e10	−0.0473082
$466$	−1.43404e12	−1.40872
$467$	−1.74229e12	−1.69510	−0.847551	−	0.530714i	$-0.821924\pi$
$467$	−1.74229e12	−1.69510	−0.847551	+	0.530714i	$0.821924\pi$
$468$	−3.26531e12	−3.14643
$469$	2.07919e10	0.0198434
$470$	−2.10829e12	−1.99292
$471$	−2.29253e12	−2.14645
$472$	6.69604e10	0.0620982
$473$	−8.26331e11	−0.759065
$474$	1.16946e12	1.06410
$475$	0	0
$476$	−6.72873e10	−0.0600761
$477$	−3.26739e11	−0.288980
$478$	−6.65418e11	−0.583000
$479$	−1.95175e12	−1.69400	−0.847002	−	0.531589i	$-0.821595\pi$
$479$	−1.95175e12	−1.69400	−0.847002	+	0.531589i	$0.821595\pi$
$480$	−2.13277e10	−0.0183383
$481$	5.84214e11	0.497644
$482$	1.70593e12	1.43963
$483$	−9.13433e10	−0.0763686
$484$	5.11535e12	4.23713
$485$	−1.60542e12	−1.31750
$486$	−1.14545e12	−0.931352
$487$	−1.08246e12	−0.872028	−0.436014	−	0.899940i	$-0.643610\pi$
$487$	−1.08246e12	−0.872028	−0.436014	+	0.899940i	$0.643610\pi$
$488$	−2.63022e12	−2.09944
$489$	−8.47698e11	−0.670427
$490$	−1.98471e12	−1.55530
$491$	−2.51019e11	−0.194913	−0.0974564	−	0.995240i	$-0.531071\pi$
$491$	−2.51019e11	−0.194913	−0.0974564	+	0.995240i	$0.531071\pi$
$492$	−2.10995e12	−1.62341
$493$	−6.80932e11	−0.519150
$494$	0	0
$495$	4.54466e12	3.40235
$496$	3.96163e10	0.0293904
$497$	−3.19801e10	−0.0235113
$498$	−7.79668e11	−0.568038
$499$	2.53207e11	0.182820	0.0914100	−	0.995813i	$-0.470863\pi$
$499$	2.53207e11	0.182820	0.0914100	+	0.995813i	$0.470863\pi$
$500$	2.98967e12	2.13923
$501$	3.29330e12	2.33540
$502$	−1.15553e12	−0.812112
$503$	−3.90840e11	−0.272234	−0.136117	−	0.990693i	$-0.543462\pi$
$503$	−3.90840e11	−0.272234	−0.136117	+	0.990693i	$0.543462\pi$
$504$	1.40009e11	0.0966539
$505$	6.91910e11	0.473411
$506$	7.42961e12	5.03835
$507$	−1.20943e12	−0.812912
$508$	2.99354e12	1.99433
$509$	2.84927e12	1.88149	0.940747	−	0.339108i	$-0.110125\pi$
$509$	2.84927e12	1.88149	0.940747	+	0.339108i	$0.110125\pi$
$510$	4.84810e12	3.17326
$511$	−3.12075e9	−0.00202472
$512$	2.67374e12	1.71951
$513$	0	0
$514$	−4.04594e12	−2.55673
$515$	−7.70687e11	−0.482776
$516$	2.44833e12	1.52036
$517$	3.67544e12	2.26257
$518$	−5.01832e10	−0.0306249
$519$	2.89039e12	1.74865
$520$	−1.90294e12	−1.14133
$521$	8.40314e11	0.499657	0.249828	−	0.968290i	$-0.419626\pi$
$521$	8.40314e11	0.499657	0.249828	+	0.968290i	$0.419626\pi$
$522$	2.83846e12	1.67327
$523$	2.69693e12	1.57621	0.788103	−	0.615544i	$-0.211064\pi$
$523$	2.69693e12	1.57621	0.788103	+	0.615544i	$0.211064\pi$
$524$	−4.15216e12	−2.40593
$525$	1.54690e10	0.00888683
$526$	1.30429e12	0.742915
$527$	6.04671e10	0.0341485
$528$	−5.53739e12	−3.10065
$529$	3.08585e12	1.71326
$530$	−3.81467e11	−0.209998
$531$	−1.41220e11	−0.0770853
$532$	0	0
$533$	6.28868e11	0.337510
$534$	−3.76390e12	−2.00310
$535$	2.44436e11	0.128995
$536$	2.50118e12	1.30889
$537$	3.79874e12	1.97131
$538$	1.77288e12	0.912346
$539$	3.45999e12	1.76574
$540$	−7.17820e12	−3.63282
$541$	−5.66704e11	−0.284426	−0.142213	−	0.989836i	$-0.545422\pi$
$541$	−5.66704e11	−0.284426	−0.142213	+	0.989836i	$0.545422\pi$
$542$	6.01739e12	2.99510
$543$	−1.81327e12	−0.895082
$544$	2.70389e10	0.0132371
$545$	2.52933e12	1.22806
$546$	−1.22632e11	−0.0590522
$547$	6.37520e11	0.304474	0.152237	−	0.988344i	$-0.451352\pi$
$547$	6.37520e11	0.304474	0.152237	+	0.988344i	$0.451352\pi$
$548$	3.41699e10	0.0161857
$549$	5.54717e12	2.60613
$550$	−1.25821e12	−0.586301
$551$	0	0
$552$	−1.09882e13	−5.03734
$553$	1.99493e10	0.00907120
$554$	−2.34064e12	−1.05570
$555$	2.40915e12	1.07782
$556$	−2.37470e12	−1.05383
$557$	−3.41601e12	−1.50373	−0.751867	−	0.659315i	$-0.770846\pi$
$557$	−3.41601e12	−1.50373	−0.751867	+	0.659315i	$0.770846\pi$
$558$	−2.52056e11	−0.110064
$559$	−7.29722e11	−0.316085
$560$	5.41835e10	0.0232821
$561$	−8.45184e12	−3.60262
$562$	3.58144e12	1.51441
$563$	−2.86043e12	−1.19989	−0.599947	−	0.800040i	$-0.704812\pi$
$563$	−2.86043e12	−1.19989	−0.599947	+	0.800040i	$0.704812\pi$
$564$	−1.08899e13	−4.53178
$565$	−4.10437e12	−1.69445
$566$	−1.51531e12	−0.620621
$567$	−9.30368e10	−0.0378034
$568$	−3.84707e12	−1.55083
$569$	4.58210e12	1.83257	0.916283	−	0.400532i	$-0.131175\pi$
$569$	4.58210e12	1.83257	0.916283	+	0.400532i	$0.131175\pi$
$570$	0	0
$571$	1.22148e12	0.480865	0.240432	−	0.970666i	$-0.422711\pi$
$571$	1.22148e12	0.480865	0.240432	+	0.970666i	$0.422711\pi$
$572$	6.64599e12	2.59584
$573$	1.26181e12	0.488987
$574$	−5.40189e10	−0.0207703
$575$	−8.27617e11	−0.315736
$576$	−5.71429e12	−2.16302
$577$	−4.03984e12	−1.51731	−0.758653	−	0.651495i	$-0.774142\pi$
$577$	−4.03984e12	−1.51731	−0.758653	+	0.651495i	$0.774142\pi$
$578$	−1.50125e12	−0.559470
$579$	1.12709e12	0.416778
$580$	2.20803e12	0.810177
$581$	−1.33000e10	−0.00484238
$582$	−1.24456e13	−4.49638
$583$	6.65022e11	0.238412
$584$	−3.75413e11	−0.133552
$585$	4.01333e12	1.41678
$586$	−3.56530e12	−1.24898
$587$	4.69795e12	1.63319	0.816595	−	0.577210i	$-0.195859\pi$
$587$	4.69795e12	1.63319	0.816595	+	0.577210i	$0.195859\pi$
$588$	−1.02516e13	−3.53666
$589$	0	0
$590$	−1.64874e11	−0.0560169
$591$	7.66446e12	2.58427
$592$	−2.00108e12	−0.669601
$593$	−1.23653e12	−0.410638	−0.205319	−	0.978695i	$-0.565823\pi$
$593$	−1.23653e12	−0.410638	−0.205319	+	0.978695i	$0.565823\pi$
$594$	1.87814e13	6.18997
$595$	8.27015e10	0.0270512
$596$	−1.14773e12	−0.372591
$597$	3.65270e11	0.117687
$598$	6.56099e12	2.09804
$599$	2.23370e12	0.708932	0.354466	−	0.935069i	$-0.384663\pi$
$599$	2.23370e12	0.708932	0.354466	+	0.935069i	$0.384663\pi$
$600$	1.86086e12	0.586183
$601$	2.26049e12	0.706753	0.353376	−	0.935481i	$-0.385034\pi$
$601$	2.26049e12	0.706753	0.353376	+	0.935481i	$0.385034\pi$
$602$	6.26822e10	0.0194518
$603$	−5.27502e12	−1.62479
$604$	4.05059e12	1.23838
$605$	−6.28718e12	−1.90790
$606$	5.36386e12	1.61566
$607$	1.81733e12	0.543356	0.271678	−	0.962388i	$-0.412421\pi$
$607$	1.81733e12	0.543356	0.271678	+	0.962388i	$0.412421\pi$
$608$	0	0
$609$	7.10278e10	0.0209243
$610$	6.47631e12	1.89384
$611$	3.24573e12	0.942164
$612$	1.70711e13	4.91905
$613$	−1.11651e12	−0.319366	−0.159683	−	0.987168i	$-0.551047\pi$
$613$	−1.11651e12	−0.319366	−0.159683	+	0.987168i	$0.551047\pi$
$614$	−3.85469e12	−1.09454
$615$	2.59330e12	0.730995
$616$	−2.84965e11	−0.0797405
$617$	−5.42926e12	−1.50820	−0.754098	−	0.656762i	$-0.771925\pi$
$617$	−5.42926e12	−1.50820	−0.754098	+	0.656762i	$0.771925\pi$
$618$	−5.97456e12	−1.64762
$619$	−3.62860e12	−0.993415	−0.496708	−	0.867918i	$-0.665458\pi$
$619$	−3.62860e12	−0.993415	−0.496708	+	0.867918i	$0.665458\pi$
$620$	−1.96075e11	−0.0532916
$621$	1.23539e13	3.33343
$622$	−6.09136e12	−1.63176
$623$	−6.42065e10	−0.0170759
$624$	−4.88999e12	−1.29115
$625$	−2.94334e12	−0.771578
$626$	2.16567e12	0.563647
$627$	0	0
$628$	−9.42457e12	−2.41793
$629$	−3.05428e12	−0.778004
$630$	−3.44740e11	−0.0871885
$631$	−6.04290e12	−1.51745	−0.758723	−	0.651413i	$-0.774177\pi$
$631$	−6.04290e12	−1.51745	−0.758723	+	0.651413i	$0.774177\pi$
$632$	2.39982e12	0.598344
$633$	−3.41641e12	−0.845771
$634$	7.33785e12	1.80371
$635$	−3.67930e12	−0.898014
$636$	−1.97039e12	−0.477523
$637$	3.05547e12	0.735277
$638$	−5.77720e12	−1.38046
$639$	8.11352e12	1.92511
$640$	−6.62750e12	−1.56149
$641$	−4.99876e12	−1.16950	−0.584752	−	0.811212i	$-0.698808\pi$
$641$	−4.99876e12	−1.16950	−0.584752	+	0.811212i	$0.698808\pi$
$642$	1.89493e12	0.440235
$643$	8.15075e12	1.88039	0.940195	−	0.340636i	$-0.110642\pi$
$643$	8.15075e12	1.88039	0.940195	+	0.340636i	$0.110642\pi$
$644$	−3.75512e11	−0.0860274
$645$	−3.00919e12	−0.684591
$646$	0	0
$647$	1.50807e12	0.338338	0.169169	−	0.985587i	$-0.445892\pi$
$647$	1.50807e12	0.338338	0.169169	+	0.985587i	$0.445892\pi$
$648$	−1.11919e13	−2.49355
$649$	2.87430e11	0.0635962
$650$	−1.11111e12	−0.244144
$651$	−6.30730e9	−0.00137635
$652$	−3.48488e12	−0.755221
$653$	6.54313e12	1.40824	0.704119	−	0.710082i	$-0.251342\pi$
$653$	6.54313e12	1.40824	0.704119	+	0.710082i	$0.251342\pi$
$654$	1.96080e13	4.19114
$655$	5.10333e12	1.08335
$656$	−2.15403e12	−0.454134
$657$	7.91749e11	0.165784
$658$	−2.78804e11	−0.0579805
$659$	−3.98727e12	−0.823553	−0.411777	−	0.911285i	$-0.635092\pi$
$659$	−3.98727e12	−0.823553	−0.411777	+	0.911285i	$0.635092\pi$
$660$	2.74065e13	5.62219
$661$	−4.43183e12	−0.902977	−0.451489	−	0.892277i	$-0.649107\pi$
$661$	−4.43183e12	−0.902977	−0.451489	+	0.892277i	$0.649107\pi$
$662$	−1.09044e13	−2.20668
$663$	−7.46370e12	−1.50018
$664$	−1.59993e12	−0.319408
$665$	0	0
$666$	1.27317e13	2.50757
$667$	−3.80009e12	−0.743409
$668$	1.35387e13	2.63077
$669$	7.33168e12	1.41510
$670$	−6.15857e12	−1.18071
$671$	−1.12903e13	−2.15008
$672$	−2.82042e9	−0.000533521 0
$673$	−4.03747e12	−0.758650	−0.379325	−	0.925263i	$-0.623844\pi$
$673$	−4.03747e12	−0.758650	−0.379325	+	0.925263i	$0.623844\pi$
$674$	−4.17493e12	−0.779255
$675$	−2.09214e12	−0.387904
$676$	−4.97194e12	−0.915727
$677$	5.81979e11	0.106478	0.0532388	−	0.998582i	$-0.483046\pi$
$677$	5.81979e11	0.106478	0.0532388	+	0.998582i	$0.483046\pi$
$678$	−3.18181e13	−5.78283
$679$	−2.12304e11	−0.0383305
$680$	9.94864e12	1.78432
$681$	7.23950e12	1.28987
$682$	5.13018e11	0.0908036
$683$	5.12188e12	0.900609	0.450304	−	0.892875i	$-0.351315\pi$
$683$	5.12188e12	0.900609	0.450304	+	0.892875i	$0.351315\pi$
$684$	0	0
$685$	−4.19975e10	−0.00728813
$686$	−5.25102e11	−0.0905285
$687$	7.42686e12	1.27204
$688$	2.49948e12	0.425306
$689$	5.87272e11	0.0992779
$690$	2.70559e13	4.54403
$691$	−7.40637e12	−1.23582	−0.617909	−	0.786250i	$-0.712020\pi$
$691$	−7.40637e12	−1.23582	−0.617909	+	0.786250i	$0.712020\pi$
$692$	1.18824e13	1.96982
$693$	6.00995e11	0.0989854
$694$	−2.06358e13	−3.37679
$695$	2.91870e12	0.474523
$696$	8.54434e12	1.38018
$697$	−3.28774e12	−0.527654
$698$	−2.34820e12	−0.374443
$699$	9.10409e12	1.44241
$700$	6.35931e10	0.0100108
$701$	−1.00592e13	−1.57338	−0.786689	−	0.617350i	$-0.788206\pi$
$701$	−1.00592e13	−1.57338	−0.786689	+	0.617350i	$0.788206\pi$
$702$	1.65856e13	2.57759
$703$	0	0
$704$	1.16305e13	1.78452
$705$	1.33846e13	2.04058
$706$	−1.62039e13	−2.45471
$707$	9.14995e10	0.0137731
$708$	−8.51625e11	−0.127379
$709$	6.93175e12	1.03023	0.515116	−	0.857120i	$-0.327749\pi$
$709$	6.93175e12	1.03023	0.515116	+	0.857120i	$0.327749\pi$
$710$	9.47252e12	1.39895
$711$	−5.06124e12	−0.742752
$712$	−7.72378e12	−1.12634
$713$	3.37450e11	0.0488998
$714$	6.41123e11	0.0923207
$715$	−8.16846e12	−1.16886
$716$	1.56166e13	2.22064
$717$	4.22444e12	0.596944
$718$	−2.38228e13	−3.34528
$719$	1.78797e10	0.00249506	0.00124753	−	0.999999i	$-0.499603\pi$
$719$	1.78797e10	0.00249506	0.00124753	+	0.999999i	$0.499603\pi$
$720$	−1.37466e13	−1.90634
$721$	−1.01917e11	−0.0140455
$722$	0	0
$723$	−1.08302e13	−1.47406
$724$	−7.45433e12	−1.00829
$725$	6.43548e11	0.0865087
$726$	−4.87398e13	−6.51131
$727$	−1.72504e12	−0.229031	−0.114515	−	0.993421i	$-0.536532\pi$
$727$	−1.72504e12	−0.229031	−0.114515	+	0.993421i	$0.536532\pi$
$728$	−2.51649e11	−0.0332050
$729$	−3.74900e12	−0.491634
$730$	9.24365e11	0.120473
$731$	3.81500e12	0.494159
$732$	3.34520e13	4.30648
$733$	1.49525e12	0.191313	0.0956567	−	0.995414i	$-0.469505\pi$
$733$	1.49525e12	0.191313	0.0956567	+	0.995414i	$0.469505\pi$
$734$	−1.83260e13	−2.33042
$735$	1.26000e13	1.59250
$736$	1.50896e11	0.0189552
$737$	1.07364e13	1.34046
$738$	1.37049e13	1.70068
$739$	−5.18620e12	−0.639660	−0.319830	−	0.947475i	$-0.603626\pi$
$739$	−5.18620e12	−0.639660	−0.319830	+	0.947475i	$0.603626\pi$
$740$	9.90401e12	1.21414
$741$	0	0
$742$	−5.04459e10	−0.00610954
$743$	5.16695e12	0.621991	0.310996	−	0.950411i	$-0.399338\pi$
$743$	5.16695e12	0.621991	0.310996	+	0.950411i	$0.399338\pi$
$744$	−7.58742e11	−0.0907854
$745$	1.41065e12	0.167771
$746$	−1.54471e13	−1.82609
$747$	3.37428e12	0.396495
$748$	−3.47454e13	−4.05827
$749$	3.23246e10	0.00375289
$750$	−2.84859e13	−3.28742
$751$	−9.96310e12	−1.14292	−0.571459	−	0.820631i	$-0.693622\pi$
$751$	−9.96310e12	−1.14292	−0.571459	+	0.820631i	$0.693622\pi$
$752$	−1.11174e13	−1.26772
$753$	7.33598e12	0.831535
$754$	−5.10177e12	−0.574844
$755$	−4.97850e12	−0.557619
$756$	−9.49259e11	−0.105691
$757$	1.22320e13	1.35384	0.676918	−	0.736059i	$-0.263315\pi$
$757$	1.22320e13	1.35384	0.676918	+	0.736059i	$0.263315\pi$
$758$	2.58826e13	2.84771
$759$	−4.71673e13	−5.15885
$760$	0	0
$761$	6.25535e12	0.676116	0.338058	−	0.941125i	$-0.390230\pi$
$761$	6.25535e12	0.676116	0.338058	+	0.941125i	$0.390230\pi$
$762$	−2.85228e13	−3.06475
$763$	3.34483e11	0.0357284
$764$	5.18729e12	0.550833
$765$	−2.09818e13	−2.21496
$766$	−1.57242e13	−1.65021
$767$	2.53826e11	0.0264823
$768$	−3.41194e13	−3.53896
$769$	−3.55889e11	−0.0366983	−0.0183491	−	0.999832i	$-0.505841\pi$
$769$	−3.55889e11	−0.0366983	−0.0183491	+	0.999832i	$0.505841\pi$
$770$	7.01660e11	0.0719314
$771$	2.56859e13	2.61788
$772$	4.63345e12	0.469491
$773$	1.89169e12	0.190565	0.0952823	−	0.995450i	$-0.469625\pi$
$773$	1.89169e12	0.190565	0.0952823	+	0.995450i	$0.469625\pi$
$774$	−1.59028e13	−1.59272
$775$	−5.71474e10	−0.00569035
$776$	−2.55393e13	−2.52831
$777$	3.18591e11	0.0313573
$778$	−1.59166e13	−1.55755
$779$	0	0
$780$	2.42023e13	2.34116
$781$	−1.65137e13	−1.58824
$782$	−3.43010e13	−3.28002
$783$	−9.60628e12	−0.913329
$784$	−1.04658e13	−0.989346
$785$	1.15835e13	1.08875
$786$	3.95623e13	3.69726
$787$	5.80060e12	0.538997	0.269498	−	0.963001i	$-0.413142\pi$
$787$	5.80060e12	0.538997	0.269498	+	0.963001i	$0.413142\pi$
$788$	3.15085e13	2.91112
$789$	−8.28038e12	−0.760683
$790$	−5.90899e12	−0.539748
$791$	−5.42769e11	−0.0492971
$792$	7.22972e13	6.52917
$793$	−9.97034e12	−0.895325
$794$	4.82921e12	0.431205
$795$	2.42176e12	0.215020
$796$	1.50162e12	0.132572
$797$	1.86624e12	0.163834	0.0819171	−	0.996639i	$-0.473896\pi$
$797$	1.86624e12	0.163834	0.0819171	+	0.996639i	$0.473896\pi$
$798$	0	0
$799$	−1.69687e13	−1.47295
$800$	−2.55544e10	−0.00220577
$801$	1.62895e13	1.39818
$802$	3.41138e12	0.291169
$803$	−1.61147e12	−0.136774
$804$	−3.18108e13	−2.68487
$805$	4.61534e11	0.0387367
$806$	4.53040e11	0.0378119
$807$	−1.12552e13	−0.934166
$808$	1.10070e13	0.908485
$809$	−7.64949e12	−0.627862	−0.313931	−	0.949446i	$-0.601646\pi$
$809$	−7.64949e12	−0.627862	−0.313931	+	0.949446i	$0.601646\pi$
$810$	2.75575e13	2.24935
$811$	1.42490e13	1.15662	0.578309	−	0.815818i	$-0.303713\pi$
$811$	1.42490e13	1.15662	0.578309	+	0.815818i	$0.303713\pi$
$812$	2.91995e11	0.0235707
$813$	−3.82017e13	−3.06673
$814$	−2.59133e13	−2.06877
$815$	4.28320e12	0.340063
$816$	2.55650e13	2.01855
$817$	0	0
$818$	−1.23619e12	−0.0965373
$819$	5.30731e11	0.0412189
$820$	1.06610e13	0.823449
$821$	2.28752e13	1.75719	0.878597	−	0.477563i	$-0.158480\pi$
$821$	2.28752e13	1.75719	0.878597	+	0.477563i	$0.158480\pi$
$822$	−3.25575e11	−0.0248730
$823$	1.71786e13	1.30524	0.652618	−	0.757687i	$-0.273671\pi$
$823$	1.71786e13	1.30524	0.652618	+	0.757687i	$0.273671\pi$
$824$	−1.22602e13	−0.926457
$825$	7.98782e12	0.600324
$826$	−2.18033e10	−0.00162972
$827$	−6.85184e12	−0.509369	−0.254685	−	0.967024i	$-0.581972\pi$
$827$	−6.85184e12	−0.509369	−0.254685	+	0.967024i	$0.581972\pi$
$828$	9.52693e13	7.04395
$829$	−9.78197e12	−0.719334	−0.359667	−	0.933081i	$-0.617110\pi$
$829$	−9.78197e12	−0.719334	−0.359667	+	0.933081i	$0.617110\pi$
$830$	3.93946e12	0.288128
$831$	1.48597e13	1.08095
$832$	1.02707e13	0.743097
$833$	−1.59741e13	−1.14951
$834$	2.26265e13	1.61946
$835$	−1.66402e13	−1.18459
$836$	0	0
$837$	8.53043e11	0.0600767
$838$	4.90325e13	3.43467
$839$	−6.29291e12	−0.438453	−0.219226	−	0.975674i	$-0.570353\pi$
$839$	−6.29291e12	−0.438453	−0.219226	+	0.975674i	$0.570353\pi$
$840$	−1.03774e12	−0.0719170
$841$	−1.15522e13	−0.796313
$842$	3.70755e13	2.54204
$843$	−2.27370e13	−1.55063
$844$	−1.40448e13	−0.952742
$845$	6.11092e12	0.412336
$846$	7.07340e13	4.74746
$847$	−8.31428e11	−0.0555072
$848$	−2.01155e12	−0.133582
$849$	9.62001e12	0.635464
$850$	5.80890e12	0.381688
$851$	−1.70451e13	−1.11408
$852$	4.89283e13	3.18114
$853$	6.18652e12	0.400107	0.200053	−	0.979785i	$-0.435888\pi$
$853$	6.18652e12	0.400107	0.200053	+	0.979785i	$0.435888\pi$
$854$	8.56439e11	0.0550980
$855$	0	0
$856$	3.88852e12	0.247544
$857$	2.53771e13	1.60705	0.803523	−	0.595273i	$-0.202956\pi$
$857$	2.53771e13	1.60705	0.803523	+	0.595273i	$0.202956\pi$
$858$	−6.33239e13	−3.98910
$859$	1.37438e13	0.861268	0.430634	−	0.902527i	$-0.358290\pi$
$859$	1.37438e13	0.861268	0.430634	+	0.902527i	$0.358290\pi$
$860$	−1.23708e13	−0.771176
$861$	3.42942e11	0.0212670
$862$	−4.43512e13	−2.73604
$863$	−1.40495e13	−0.862206	−0.431103	−	0.902303i	$-0.641875\pi$
$863$	−1.40495e13	−0.862206	−0.431103	+	0.902303i	$0.641875\pi$
$864$	3.81452e11	0.0232878
$865$	−1.46044e13	−0.886975
$866$	−3.88202e13	−2.34546
$867$	9.53075e12	0.572850
$868$	−2.59293e10	−0.00155043
$869$	1.03013e13	0.612778
$870$	−2.10384e13	−1.24502
$871$	9.48118e12	0.558188
$872$	4.02369e13	2.35668
$873$	5.38626e13	3.13851
$874$	0	0
$875$	−4.85928e11	−0.0280244
$876$	4.77462e12	0.273949
$877$	3.24938e13	1.85482	0.927410	−	0.374046i	$-0.122030\pi$
$877$	3.24938e13	1.85482	0.927410	+	0.374046i	$0.122030\pi$
$878$	−4.68503e13	−2.66065
$879$	2.26345e13	1.27886
$880$	2.79790e13	1.57275
$881$	−9.55601e12	−0.534423	−0.267211	−	0.963638i	$-0.586102\pi$
$881$	−9.55601e12	−0.534423	−0.267211	+	0.963638i	$0.586102\pi$
$882$	6.65878e13	3.70498
$883$	−2.26150e13	−1.25191	−0.625955	−	0.779860i	$-0.715290\pi$
$883$	−2.26150e13	−1.25191	−0.625955	+	0.779860i	$0.715290\pi$
$884$	−3.06832e13	−1.68992
$885$	1.04671e12	0.0573566
$886$	4.43710e13	2.41907
$887$	−2.21949e13	−1.20392	−0.601960	−	0.798526i	$-0.705613\pi$
$887$	−2.21949e13	−1.20392	−0.601960	+	0.798526i	$0.705613\pi$
$888$	3.83252e13	2.06836
$889$	−4.86557e11	−0.0261262
$890$	1.90180e13	1.01604
$891$	−4.80418e13	−2.55370
$892$	3.01405e13	1.59407
$893$	0	0
$894$	1.09357e13	0.572571
$895$	−1.91941e13	−0.999915
$896$	−8.76434e11	−0.0454290
$897$	−4.16528e13	−2.14822
$898$	−1.74017e13	−0.892994
$899$	−2.62398e11	−0.0133981
$900$	−1.61339e13	−0.819687
$901$	−3.07027e12	−0.155208
$902$	−2.78940e13	−1.40308
$903$	−3.97941e11	−0.0199170
$904$	−6.52929e13	−3.25168
$905$	9.16197e12	0.454015
$906$	−3.85946e13	−1.90305
$907$	3.18574e13	1.56307	0.781533	−	0.623864i	$-0.214438\pi$
$907$	3.18574e13	1.56307	0.781533	+	0.623864i	$0.214438\pi$
$908$	2.97615e13	1.45301
$909$	−2.32139e13	−1.12774
$910$	6.19627e11	0.0299532
$911$	3.09513e13	1.48883	0.744416	−	0.667716i	$-0.232728\pi$
$911$	3.09513e13	1.48883	0.744416	+	0.667716i	$0.232728\pi$
$912$	0	0
$913$	−6.86777e12	−0.327113
$914$	−2.96146e13	−1.40362
$915$	−4.11152e13	−1.93913
$916$	3.05318e13	1.43292
$917$	6.74874e11	0.0315182
$918$	−8.67098e13	−4.02973
$919$	−4.25786e12	−0.196912	−0.0984558	−	0.995141i	$-0.531390\pi$
$919$	−4.25786e12	−0.196912	−0.0984558	+	0.995141i	$0.531390\pi$
$920$	5.55206e13	2.55511
$921$	2.44717e13	1.12072
$922$	−2.86762e13	−1.30687
$923$	−1.45830e13	−0.661363
$924$	3.62428e12	0.163568
$925$	2.88660e12	0.129643
$926$	−1.78000e13	−0.795557
$927$	2.58569e13	1.15005
$928$	−1.17336e11	−0.00519356
$929$	−7.71107e12	−0.339660	−0.169830	−	0.985473i	$-0.554322\pi$
$929$	−7.71107e12	−0.339660	−0.169830	+	0.985473i	$0.554322\pi$
$930$	1.86822e12	0.0818947
$931$	0	0
$932$	3.74269e13	1.62484
$933$	3.86713e13	1.67079
$934$	6.82458e13	2.93437
$935$	4.27049e13	1.82737
$936$	6.38447e13	2.71884
$937$	−7.03477e11	−0.0298141	−0.0149071	−	0.999889i	$-0.504745\pi$
$937$	−7.03477e11	−0.0298141	−0.0149071	+	0.999889i	$0.504745\pi$
$938$	−8.14421e11	−0.0343508
$939$	−1.37489e13	−0.577127
$940$	5.50239e13	2.29867
$941$	2.19580e13	0.912936	0.456468	−	0.889740i	$-0.349114\pi$
$941$	2.19580e13	0.912936	0.456468	+	0.889740i	$0.349114\pi$
$942$	8.97985e13	3.71570
$943$	−1.83479e13	−0.755587
$944$	−8.69415e11	−0.0356331
$945$	1.16671e12	0.0475906
$946$	3.23674e13	1.31401
$947$	1.35177e13	0.546169	0.273084	−	0.961990i	$-0.411956\pi$
$947$	1.35177e13	0.546169	0.273084	+	0.961990i	$0.411956\pi$
$948$	−3.05217e13	−1.22736
$949$	−1.42307e12	−0.0569545
$950$	0	0
$951$	−4.65848e13	−1.84685
$952$	1.31563e12	0.0519119
$953$	2.44274e13	0.959312	0.479656	−	0.877457i	$-0.340762\pi$
$953$	2.44274e13	0.959312	0.479656	+	0.877457i	$0.340762\pi$
$954$	1.27984e13	0.500250
$955$	−6.37559e12	−0.248030
$956$	1.73667e13	0.672443
$957$	3.66769e13	1.41348
$958$	7.64503e13	2.93247
$959$	−5.55383e9	−0.000212036 0
$960$	4.23539e13	1.60943
$961$	−2.64163e13	−0.999119
$962$	−2.28837e13	−0.861466
$963$	−8.20093e12	−0.307287
$964$	−4.45229e13	−1.66049
$965$	−5.69489e12	−0.211403
$966$	3.57792e12	0.132201
$967$	1.24705e13	0.458631	0.229315	−	0.973352i	$-0.426351\pi$
$967$	1.24705e13	0.458631	0.229315	+	0.973352i	$0.426351\pi$
$968$	−1.00017e14	−3.66131
$969$	0	0
$970$	6.28845e13	2.28071
$971$	−1.68307e13	−0.607597	−0.303799	−	0.952736i	$-0.598255\pi$
$971$	−1.68307e13	−0.607597	−0.303799	+	0.952736i	$0.598255\pi$
$972$	2.98950e13	1.07424
$973$	3.85974e11	0.0138054
$974$	4.23999e13	1.50956
$975$	7.05393e12	0.249983
$976$	3.41509e13	1.20470
$977$	2.39254e13	0.840105	0.420052	−	0.907500i	$-0.362012\pi$
$977$	2.39254e13	0.840105	0.420052	+	0.907500i	$0.362012\pi$
$978$	3.32044e13	1.16057
$979$	−3.31546e13	−1.15351
$980$	5.17986e13	1.79391
$981$	−8.48600e13	−2.92545
$982$	9.83244e12	0.337411
$983$	2.88360e13	0.985017	0.492508	−	0.870308i	$-0.336080\pi$
$983$	2.88360e13	0.985017	0.492508	+	0.870308i	$0.336080\pi$
$984$	4.12545e13	1.40279
$985$	−3.87265e13	−1.31083
$986$	2.66722e13	0.898695
$987$	1.77000e12	0.0593672
$988$	0	0
$989$	2.12905e13	0.707623
$990$	−1.78015e14	−5.88976
$991$	−3.47149e13	−1.14336	−0.571682	−	0.820475i	$-0.693709\pi$
$991$	−3.47149e13	−1.14336	−0.571682	+	0.820475i	$0.693709\pi$
$992$	1.04195e10	0.000341620 0
$993$	6.92270e13	2.25946
$994$	1.25266e12	0.0407001
$995$	−1.84562e12	−0.0596949
$996$	2.03485e13	0.655186
$997$	−3.60467e13	−1.15541	−0.577707	−	0.816244i	$-0.696052\pi$
$997$	−3.60467e13	−1.15541	−0.577707	+	0.816244i	$0.696052\pi$
$998$	−9.91815e12	−0.316478
$999$	−4.30885e13	−1.36872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.10.a.j.1.4		42
19.2	odd	18		19.10.e.a.4.2	✓	84
19.10	odd	18		19.10.e.a.5.2	yes	84
19.18	odd	2		361.10.a.i.1.39		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.e.a.4.2	✓	84	19.2	odd	18
19.10.e.a.5.2	yes	84	19.10	odd	18
361.10.a.i.1.39		42	19.18	odd	2
361.10.a.j.1.4		42	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	361.a (trivial)

\(f(q)\)	\(=\)	\(q-39.1701 q^{2} +248.674 q^{3} +1022.30 q^{4} -1256.48 q^{5} -9740.57 q^{6} -166.160 q^{7} -19988.3 q^{8} +42155.6 q^{9} +O(q^{10})\)	\(q-39.1701 q^{2} +248.674 q^{3} +1022.30 q^{4} -1256.48 q^{5} -9740.57 q^{6} -166.160 q^{7} -19988.3 q^{8} +42155.6 q^{9} +49216.5 q^{10} -85800.6 q^{11} +254218. q^{12} -75769.3 q^{13} +6508.49 q^{14} -312454. q^{15} +259529. q^{16} +396124. q^{17} -1.65124e6 q^{18} -1.28450e6 q^{20} -41319.5 q^{21} +3.36082e6 q^{22} +2.21066e6 q^{23} -4.97057e6 q^{24} -374376. q^{25} +2.96789e6 q^{26} +5.58834e6 q^{27} -169864. q^{28} -1.71899e6 q^{29} +1.22389e7 q^{30} +152647. q^{31} +68258.7 q^{32} -2.13363e7 q^{33} -1.55162e7 q^{34} +208777. q^{35} +4.30954e7 q^{36} -7.71043e6 q^{37} -1.88418e7 q^{39} +2.51150e7 q^{40} -8.29977e6 q^{41} +1.61849e6 q^{42} +9.63083e6 q^{43} -8.77135e7 q^{44} -5.29678e7 q^{45} -8.65916e7 q^{46} -4.28370e7 q^{47} +6.45379e7 q^{48} -4.03260e7 q^{49} +1.46643e7 q^{50} +9.85056e7 q^{51} -7.74586e7 q^{52} -7.75078e6 q^{53} -2.18896e8 q^{54} +1.07807e8 q^{55} +3.32125e6 q^{56} +6.73329e7 q^{58} -3.34998e6 q^{59} -3.19420e8 q^{60} +1.31588e8 q^{61} -5.97919e6 q^{62} -7.00456e6 q^{63} -1.35552e8 q^{64} +9.52028e7 q^{65} +8.35746e8 q^{66} -1.25132e8 q^{67} +4.04956e8 q^{68} +5.49732e8 q^{69} -8.17780e6 q^{70} +1.92466e8 q^{71} -8.42619e8 q^{72} +1.87816e7 q^{73} +3.02018e8 q^{74} -9.30975e7 q^{75} +1.42566e7 q^{77} +7.38036e8 q^{78} -1.20061e8 q^{79} -3.26093e8 q^{80} +5.59924e8 q^{81} +3.25103e8 q^{82} +8.00434e7 q^{83} -4.22408e7 q^{84} -4.97723e8 q^{85} -3.77240e8 q^{86} -4.27467e8 q^{87} +1.71501e9 q^{88} +3.86415e8 q^{89} +2.07475e9 q^{90} +1.25898e7 q^{91} +2.25994e9 q^{92} +3.79593e7 q^{93} +1.67793e9 q^{94} +1.69741e7 q^{96} +1.27771e9 q^{97} +1.57957e9 q^{98} -3.61697e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 48 q^{2} + 486 q^{3} + 9984 q^{4} + 852 q^{5} + 1536 q^{6} - 5715 q^{7} + 36861 q^{8} + 236196 q^{9}+O(q^{10}) \) 42 * q + 48 * q^2 + 486 * q^3 + 9984 * q^4 + 852 * q^5 + 1536 * q^6 - 5715 * q^7 + 36861 * q^8 + 236196 * q^9	\( 42 q + 48 q^{2} + 486 q^{3} + 9984 q^{4} + 852 q^{5} + 1536 q^{6} - 5715 q^{7} + 36861 q^{8} + 236196 q^{9} + 58464 q^{10} - 11295 q^{11} + 373245 q^{12} + 117150 q^{13} + 642912 q^{14} + 548451 q^{15} + 2162688 q^{16} + 997809 q^{17} + 1359318 q^{18} + 2160357 q^{20} + 1367568 q^{21} + 5031171 q^{22} + 2213706 q^{23} - 6545730 q^{24} + 13853862 q^{25} + 9164091 q^{26} + 9159258 q^{27} - 14025501 q^{28} + 9949038 q^{29} + 31527234 q^{30} + 14008185 q^{31} + 10978065 q^{32} + 14330319 q^{33} - 585930 q^{34} - 48129252 q^{35} + 7475208 q^{36} + 34869216 q^{37} + 15720432 q^{39} + 103478568 q^{40} + 86266776 q^{41} + 69259017 q^{42} - 12988605 q^{43} - 203224311 q^{44} + 61014765 q^{45} - 63830328 q^{46} + 17328918 q^{47} + 213121044 q^{48} + 163636377 q^{49} + 314983974 q^{50} + 96577575 q^{51} + 75305472 q^{52} + 103187364 q^{53} - 272434584 q^{54} - 56373354 q^{55} + 372695601 q^{56} + 287431734 q^{58} + 660784728 q^{59} + 368982060 q^{60} + 169972728 q^{61} + 300679941 q^{62} - 1173015477 q^{63} + 866999625 q^{64} - 153878493 q^{65} + 853102866 q^{66} + 189790482 q^{67} + 821601474 q^{68} + 1193576865 q^{69} - 629548281 q^{70} + 920008254 q^{71} - 118366770 q^{72} - 976066764 q^{73} - 782973429 q^{74} + 2015364294 q^{75} - 479229111 q^{77} + 2285947218 q^{78} + 2003560392 q^{79} + 3171353712 q^{80} + 1356085014 q^{81} - 1540624044 q^{82} + 1226988585 q^{83} + 1236853875 q^{84} - 372049179 q^{85} + 1472174664 q^{86} + 601158705 q^{87} + 2100827301 q^{88} + 853591443 q^{89} + 5492348259 q^{90} + 3495862842 q^{91} - 536774244 q^{92} - 1750089960 q^{93} + 7410646467 q^{94} + 4632812853 q^{96} + 1807268862 q^{97} + 5836044465 q^{98} + 777469992 q^{99}+O(q^{100}) \) 42 * q + 48 * q^2 + 486 * q^3 + 9984 * q^4 + 852 * q^5 + 1536 * q^6 - 5715 * q^7 + 36861 * q^8 + 236196 * q^9 + 58464 * q^10 - 11295 * q^11 + 373245 * q^12 + 117150 * q^13 + 642912 * q^14 + 548451 * q^15 + 2162688 * q^16 + 997809 * q^17 + 1359318 * q^18 + 2160357 * q^20 + 1367568 * q^21 + 5031171 * q^22 + 2213706 * q^23 - 6545730 * q^24 + 13853862 * q^25 + 9164091 * q^26 + 9159258 * q^27 - 14025501 * q^28 + 9949038 * q^29 + 31527234 * q^30 + 14008185 * q^31 + 10978065 * q^32 + 14330319 * q^33 - 585930 * q^34 - 48129252 * q^35 + 7475208 * q^36 + 34869216 * q^37 + 15720432 * q^39 + 103478568 * q^40 + 86266776 * q^41 + 69259017 * q^42 - 12988605 * q^43 - 203224311 * q^44 + 61014765 * q^45 - 63830328 * q^46 + 17328918 * q^47 + 213121044 * q^48 + 163636377 * q^49 + 314983974 * q^50 + 96577575 * q^51 + 75305472 * q^52 + 103187364 * q^53 - 272434584 * q^54 - 56373354 * q^55 + 372695601 * q^56 + 287431734 * q^58 + 660784728 * q^59 + 368982060 * q^60 + 169972728 * q^61 + 300679941 * q^62 - 1173015477 * q^63 + 866999625 * q^64 - 153878493 * q^65 + 853102866 * q^66 + 189790482 * q^67 + 821601474 * q^68 + 1193576865 * q^69 - 629548281 * q^70 + 920008254 * q^71 - 118366770 * q^72 - 976066764 * q^73 - 782973429 * q^74 + 2015364294 * q^75 - 479229111 * q^77 + 2285947218 * q^78 + 2003560392 * q^79 + 3171353712 * q^80 + 1356085014 * q^81 - 1540624044 * q^82 + 1226988585 * q^83 + 1236853875 * q^84 - 372049179 * q^85 + 1472174664 * q^86 + 601158705 * q^87 + 2100827301 * q^88 + 853591443 * q^89 + 5492348259 * q^90 + 3495862842 * q^91 - 536774244 * q^92 - 1750089960 * q^93 + 7410646467 * q^94 + 4632812853 * q^96 + 1807268862 * q^97 + 5836044465 * q^98 + 777469992 * q^99

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