LMFDB - Embedded newform 354.8.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 260588 x^{7} - 2627755 x^{6} + 16696953355 x^{5} + 808091684078 x^{4} + \cdots + 15\!\cdots\!00 $ x^9 - 4x^8 - 260588x^7 - 2627755x^6 + 16696953355x^5 + 808091684078x^4 - 191825159847522x^3 - 12153827093891319x^2 + 237398587398357570x + 15300107670464479800
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$315.149$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +253.154 q^{5} +216.000 q^{6} -755.716 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +253.154 q^{5} +216.000 q^{6} -755.716 q^{7} -512.000 q^{8} +729.000 q^{9} -2025.23 q^{10} -866.310 q^{11} -1728.00 q^{12} +7079.97 q^{13} +6045.73 q^{14} -6835.16 q^{15} +4096.00 q^{16} +13297.2 q^{17} -5832.00 q^{18} -50493.1 q^{19} +16201.9 q^{20} +20404.3 q^{21} +6930.48 q^{22} +40770.3 q^{23} +13824.0 q^{24} -14038.1 q^{25} -56639.7 q^{26} -19683.0 q^{27} -48365.8 q^{28} +25194.2 q^{29} +54681.3 q^{30} +158796. q^{31} -32768.0 q^{32} +23390.4 q^{33} -106377. q^{34} -191313. q^{35} +46656.0 q^{36} -341516. q^{37} +403945. q^{38} -191159. q^{39} -129615. q^{40} +50945.1 q^{41} -163235. q^{42} -133763. q^{43} -55443.9 q^{44} +184549. q^{45} -326163. q^{46} -271486. q^{47} -110592. q^{48} -252436. q^{49} +112305. q^{50} -359023. q^{51} +453118. q^{52} -771928. q^{53} +157464. q^{54} -219310. q^{55} +386927. q^{56} +1.36331e6 q^{57} -201554. q^{58} +205379. q^{59} -437450. q^{60} +1.80789e6 q^{61} -1.27037e6 q^{62} -550917. q^{63} +262144. q^{64} +1.79232e6 q^{65} -187123. q^{66} +2.02767e6 q^{67} +851018. q^{68} -1.10080e6 q^{69} +1.53050e6 q^{70} +1.14163e6 q^{71} -373248. q^{72} +6.48023e6 q^{73} +2.73212e6 q^{74} +379028. q^{75} -3.23156e6 q^{76} +654685. q^{77} +1.52927e6 q^{78} -3.37195e6 q^{79} +1.03692e6 q^{80} +531441. q^{81} -407561. q^{82} +3.34783e6 q^{83} +1.30588e6 q^{84} +3.36623e6 q^{85} +1.07011e6 q^{86} -680244. q^{87} +443551. q^{88} +9.38127e6 q^{89} -1.47639e6 q^{90} -5.35044e6 q^{91} +2.60930e6 q^{92} -4.28748e6 q^{93} +2.17189e6 q^{94} -1.27825e7 q^{95} +884736. q^{96} -1.22105e7 q^{97} +2.01949e6 q^{98} -631540. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) $ 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	253.154	0.905711	0.452856	−	0.891584i	$-0.350405\pi$
$5$	253.154	0.905711	0.452856	+	0.891584i	$0.350405\pi$
$6$	216.000	0.408248
$7$	−755.716	−0.832752	−0.416376	−	0.909193i	$-0.636700\pi$
$7$	−755.716	−0.832752	−0.416376	+	0.909193i	$0.636700\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−2025.23	−0.640434
$11$	−866.310	−0.196245	−0.0981226	−	0.995174i	$-0.531284\pi$
$11$	−866.310	−0.196245	−0.0981226	+	0.995174i	$0.531284\pi$
$12$	−1728.00	−0.288675
$13$	7079.97	0.893777	0.446889	−	0.894590i	$-0.352532\pi$
$13$	7079.97	0.893777	0.446889	+	0.894590i	$0.352532\pi$
$14$	6045.73	0.588844
$15$	−6835.16	−0.522913
$16$	4096.00	0.250000
$17$	13297.2	0.656428	0.328214	−	0.944603i	$-0.393553\pi$
$17$	13297.2	0.656428	0.328214	+	0.944603i	$0.393553\pi$
$18$	−5832.00	−0.235702
$19$	−50493.1	−1.68886	−0.844431	−	0.535664i	$-0.820061\pi$
$19$	−50493.1	−1.68886	−0.844431	+	0.535664i	$0.820061\pi$
$20$	16201.9	0.452856
$21$	20404.3	0.480789
$22$	6930.48	0.138766
$23$	40770.3	0.698709	0.349355	−	0.936991i	$-0.386401\pi$
$23$	40770.3	0.698709	0.349355	+	0.936991i	$0.386401\pi$
$24$	13824.0	0.204124
$25$	−14038.1	−0.179687
$26$	−56639.7	−0.631996
$27$	−19683.0	−0.192450
$28$	−48365.8	−0.416376
$29$	25194.2	0.191826	0.0959131	−	0.995390i	$-0.469423\pi$
$29$	25194.2	0.191826	0.0959131	+	0.995390i	$0.469423\pi$
$30$	54681.3	0.369755
$31$	158796.	0.957354	0.478677	−	0.877991i	$-0.341116\pi$
$31$	158796.	0.957354	0.478677	+	0.877991i	$0.341116\pi$
$32$	−32768.0	−0.176777
$33$	23390.4	0.113302
$34$	−106377.	−0.464165
$35$	−191313.	−0.754233
$36$	46656.0	0.166667
$37$	−341516.	−1.10842	−0.554210	−	0.832377i	$-0.686980\pi$
$37$	−341516.	−1.10842	−0.554210	+	0.832377i	$0.686980\pi$
$38$	403945.	1.19421
$39$	−191159.	−0.516023
$40$	−129615.	−0.320217
$41$	50945.1	0.115441	0.0577204	−	0.998333i	$-0.481617\pi$
$41$	50945.1	0.115441	0.0577204	+	0.998333i	$0.481617\pi$
$42$	−163235.	−0.339969
$43$	−133763.	−0.256565	−0.128282	−	0.991738i	$-0.540946\pi$
$43$	−133763.	−0.256565	−0.128282	+	0.991738i	$0.540946\pi$
$44$	−55443.9	−0.0981226
$45$	184549.	0.301904
$46$	−326163.	−0.494062
$47$	−271486.	−0.381422	−0.190711	−	0.981646i	$-0.561079\pi$
$47$	−271486.	−0.381422	−0.190711	+	0.981646i	$0.561079\pi$
$48$	−110592.	−0.144338
$49$	−252436.	−0.306524
$50$	112305.	0.127058
$51$	−359023.	−0.378989
$52$	453118.	0.446889
$53$	−771928.	−0.712215	−0.356108	−	0.934445i	$-0.615896\pi$
$53$	−771928.	−0.712215	−0.356108	+	0.934445i	$0.615896\pi$
$54$	157464.	0.136083
$55$	−219310.	−0.177741
$56$	386927.	0.294422
$57$	1.36331e6	0.975065
$58$	−201554.	−0.135642
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−437450.	−0.261456
$61$	1.80789e6	1.01980	0.509902	−	0.860233i	$-0.329682\pi$
$61$	1.80789e6	1.01980	0.509902	+	0.860233i	$0.329682\pi$
$62$	−1.27037e6	−0.676952
$63$	−550917.	−0.277584
$64$	262144.	0.125000
$65$	1.79232e6	0.809504
$66$	−187123.	−0.0801168
$67$	2.02767e6	0.823637	0.411819	−	0.911266i	$-0.364894\pi$
$67$	2.02767e6	0.823637	0.411819	+	0.911266i	$0.364894\pi$
$68$	851018.	0.328214
$69$	−1.10080e6	−0.403400
$70$	1.53050e6	0.533323
$71$	1.14163e6	0.378547	0.189273	−	0.981924i	$-0.439387\pi$
$71$	1.14163e6	0.378547	0.189273	+	0.981924i	$0.439387\pi$
$72$	−373248.	−0.117851
$73$	6.48023e6	1.94967	0.974834	−	0.222931i	$-0.0715626\pi$
$73$	6.48023e6	1.94967	0.974834	+	0.222931i	$0.0715626\pi$
$74$	2.73212e6	0.783771
$75$	379028.	0.103743
$76$	−3.23156e6	−0.844431
$77$	654685.	0.163424
$78$	1.52927e6	0.364883
$79$	−3.37195e6	−0.769461	−0.384730	−	0.923029i	$-0.625706\pi$
$79$	−3.37195e6	−0.769461	−0.384730	+	0.923029i	$0.625706\pi$
$80$	1.03692e6	0.226428
$81$	531441.	0.111111
$82$	−407561.	−0.0816289
$83$	3.34783e6	0.642673	0.321336	−	0.946965i	$-0.395868\pi$
$83$	3.34783e6	0.642673	0.321336	+	0.946965i	$0.395868\pi$
$84$	1.30588e6	0.240395
$85$	3.36623e6	0.594535
$86$	1.07011e6	0.181419
$87$	−680244.	−0.110751
$88$	443551.	0.0693832
$89$	9.38127e6	1.41058	0.705288	−	0.708921i	$-0.250818\pi$
$89$	9.38127e6	1.41058	0.705288	+	0.708921i	$0.250818\pi$
$90$	−1.47639e6	−0.213478
$91$	−5.35044e6	−0.744295
$92$	2.60930e6	0.349355
$93$	−4.28748e6	−0.552729
$94$	2.17189e6	0.269706
$95$	−1.27825e7	−1.52962
$96$	884736.	0.102062
$97$	−1.22105e7	−1.35842	−0.679209	−	0.733945i	$-0.737677\pi$
$97$	−1.22105e7	−1.35842	−0.679209	+	0.733945i	$0.737677\pi$
$98$	2.01949e6	0.216746
$99$	−631540.	−0.0654151
$100$	−898437.	−0.0898437
$101$	1.80585e7	1.74405	0.872023	−	0.489465i	$-0.162808\pi$
$101$	1.80585e7	1.74405	0.872023	+	0.489465i	$0.162808\pi$
$102$	2.87218e6	0.267986
$103$	−1.60184e7	−1.44440	−0.722201	−	0.691684i	$-0.756869\pi$
$103$	−1.60184e7	−1.44440	−0.722201	+	0.691684i	$0.756869\pi$
$104$	−3.62494e6	−0.315998
$105$	5.16544e6	0.435456
$106$	6.17542e6	0.503612
$107$	363732.	0.0287037	0.0143519	−	0.999897i	$-0.495431\pi$
$107$	363732.	0.0287037	0.0143519	+	0.999897i	$0.495431\pi$
$108$	−1.25971e6	−0.0962250
$109$	1.22229e7	0.904028	0.452014	−	0.892011i	$-0.350706\pi$
$109$	1.22229e7	0.904028	0.452014	+	0.892011i	$0.350706\pi$
$110$	1.75448e6	0.125682
$111$	9.22092e6	0.639947
$112$	−3.09541e6	−0.208188
$113$	5.90105e6	0.384729	0.192365	−	0.981324i	$-0.438384\pi$
$113$	5.90105e6	0.384729	0.192365	+	0.981324i	$0.438384\pi$
$114$	−1.09065e7	−0.689475
$115$	1.03212e7	0.632829
$116$	1.61243e6	0.0959131
$117$	5.16129e6	0.297926
$118$	−1.64303e6	−0.0920575
$119$	−1.00489e7	−0.546642
$120$	3.49960e6	0.184878
$121$	−1.87367e7	−0.961488
$122$	−1.44631e7	−0.721110
$123$	−1.37552e6	−0.0666497
$124$	1.01629e7	0.478677
$125$	−2.33314e7	−1.06846
$126$	4.40734e6	0.196281
$127$	−3.41097e7	−1.47763	−0.738813	−	0.673911i	$-0.764613\pi$
$127$	−3.41097e7	−1.47763	−0.738813	+	0.673911i	$0.764613\pi$
$128$	−2.09715e6	−0.0883883
$129$	3.61161e6	0.148128
$130$	−1.43386e7	−0.572406
$131$	−3.27169e7	−1.27152	−0.635760	−	0.771887i	$-0.719313\pi$
$131$	−3.27169e7	−1.27152	−0.635760	+	0.771887i	$0.719313\pi$
$132$	1.49698e6	0.0566511
$133$	3.81584e7	1.40640
$134$	−1.62214e7	−0.582399
$135$	−4.98283e6	−0.174304
$136$	−6.80814e6	−0.232082
$137$	−4.78777e7	−1.59078	−0.795392	−	0.606095i	$-0.792735\pi$
$137$	−4.78777e7	−1.59078	−0.795392	+	0.606095i	$0.792735\pi$
$138$	8.80639e6	0.285247
$139$	−5.43976e7	−1.71802	−0.859009	−	0.511961i	$-0.828919\pi$
$139$	−5.43976e7	−1.71802	−0.859009	+	0.511961i	$0.828919\pi$
$140$	−1.22440e7	−0.377116
$141$	7.33013e6	0.220214
$142$	−9.13301e6	−0.267673
$143$	−6.13345e6	−0.175400
$144$	2.98598e6	0.0833333
$145$	6.37802e6	0.173739
$146$	−5.18419e7	−1.37862
$147$	6.81577e6	0.176972
$148$	−2.18570e7	−0.554210
$149$	−5.37963e7	−1.33230	−0.666148	−	0.745820i	$-0.732058\pi$
$149$	−5.37963e7	−1.33230	−0.666148	+	0.745820i	$0.732058\pi$
$150$	−3.03222e6	−0.0733570
$151$	1.38365e7	0.327044	0.163522	−	0.986540i	$-0.447715\pi$
$151$	1.38365e7	0.327044	0.163522	+	0.986540i	$0.447715\pi$
$152$	2.58525e7	0.597103
$153$	9.69362e6	0.218809
$154$	−5.23748e6	−0.115558
$155$	4.01997e7	0.867086
$156$	−1.22342e7	−0.258011
$157$	1.26342e7	0.260555	0.130277	−	0.991478i	$-0.458413\pi$
$157$	1.26342e7	0.260555	0.130277	+	0.991478i	$0.458413\pi$
$158$	2.69756e7	0.544091
$159$	2.08421e7	0.411198
$160$	−8.29535e6	−0.160109
$161$	−3.08108e7	−0.581852
$162$	−4.25153e6	−0.0785674
$163$	3.50919e7	0.634674	0.317337	−	0.948313i	$-0.397211\pi$
$163$	3.50919e7	0.634674	0.317337	+	0.948313i	$0.397211\pi$
$164$	3.26049e6	0.0577204
$165$	5.92137e6	0.102619
$166$	−2.67826e7	−0.454438
$167$	−4.40161e7	−0.731314	−0.365657	−	0.930750i	$-0.619156\pi$
$167$	−4.40161e7	−0.731314	−0.365657	+	0.930750i	$0.619156\pi$
$168$	−1.04470e7	−0.169985
$169$	−1.26226e7	−0.201162
$170$	−2.69298e7	−0.420399
$171$	−3.68095e7	−0.562954
$172$	−8.56085e6	−0.128282
$173$	2.57181e7	0.377639	0.188819	−	0.982012i	$-0.439534\pi$
$173$	2.57181e7	0.377639	0.188819	+	0.982012i	$0.439534\pi$
$174$	5.44195e6	0.0783127
$175$	1.06088e7	0.149635
$176$	−3.54841e6	−0.0490613
$177$	−5.54523e6	−0.0751646
$178$	−7.50501e7	−0.997428
$179$	−1.33000e8	−1.73327	−0.866637	−	0.498940i	$-0.833723\pi$
$179$	−1.33000e8	−1.73327	−0.866637	+	0.498940i	$0.833723\pi$
$180$	1.18112e7	0.150952
$181$	9.74398e7	1.22141	0.610705	−	0.791858i	$-0.290886\pi$
$181$	9.74398e7	1.22141	0.610705	+	0.791858i	$0.290886\pi$
$182$	4.28036e7	0.526296
$183$	−4.88129e7	−0.588784
$184$	−2.08744e7	−0.247031
$185$	−8.64560e7	−1.00391
$186$	3.42999e7	0.390838
$187$	−1.15195e7	−0.128821
$188$	−1.73751e7	−0.190711
$189$	1.48748e7	0.160263
$190$	1.02260e8	1.08161
$191$	−6.17246e7	−0.640976	−0.320488	−	0.947253i	$-0.603847\pi$
$191$	−6.17246e7	−0.640976	−0.320488	+	0.947253i	$0.603847\pi$
$192$	−7.07789e6	−0.0721688
$193$	−8.84986e7	−0.886106	−0.443053	−	0.896495i	$-0.646105\pi$
$193$	−8.84986e7	−0.886106	−0.443053	+	0.896495i	$0.646105\pi$
$194$	9.76842e7	0.960546
$195$	−4.83927e7	−0.467367
$196$	−1.61559e7	−0.153262
$197$	−6.00511e7	−0.559615	−0.279808	−	0.960056i	$-0.590271\pi$
$197$	−6.00511e7	−0.559615	−0.279808	+	0.960056i	$0.590271\pi$
$198$	5.05232e6	0.0462554
$199$	1.86220e8	1.67510	0.837548	−	0.546364i	$-0.183988\pi$
$199$	1.86220e8	1.67510	0.837548	+	0.546364i	$0.183988\pi$
$200$	7.18749e6	0.0635291
$201$	−5.47471e7	−0.475527
$202$	−1.44468e8	−1.23323
$203$	−1.90397e7	−0.159744
$204$	−2.29775e7	−0.189495
$205$	1.28970e7	0.104556
$206$	1.28147e8	1.02135
$207$	2.97216e7	0.232903
$208$	2.89995e7	0.223444
$209$	4.37427e7	0.331431
$210$	−4.13235e7	−0.307914
$211$	1.59228e8	1.16689	0.583447	−	0.812151i	$-0.301703\pi$
$211$	1.59228e8	1.16689	0.583447	+	0.812151i	$0.301703\pi$
$212$	−4.94034e7	−0.356108
$213$	−3.08239e7	−0.218554
$214$	−2.90986e6	−0.0202966
$215$	−3.38627e7	−0.232374
$216$	1.00777e7	0.0680414
$217$	−1.20004e8	−0.797238
$218$	−9.77833e7	−0.639244
$219$	−1.74966e8	−1.12564
$220$	−1.40358e7	−0.0888707
$221$	9.41434e7	0.586701
$222$	−7.37674e7	−0.452511
$223$	1.69787e7	0.102527	0.0512635	−	0.998685i	$-0.483675\pi$
$223$	1.69787e7	0.102527	0.0512635	+	0.998685i	$0.483675\pi$
$224$	2.47633e7	0.147211
$225$	−1.02338e7	−0.0598958
$226$	−4.72084e7	−0.272045
$227$	−3.21851e8	−1.82627	−0.913134	−	0.407659i	$-0.866345\pi$
$227$	−3.21851e8	−1.82627	−0.913134	+	0.407659i	$0.866345\pi$
$228$	8.72521e7	0.487533
$229$	−1.46705e8	−0.807274	−0.403637	−	0.914919i	$-0.632254\pi$
$229$	−1.46705e8	−0.807274	−0.403637	+	0.914919i	$0.632254\pi$
$230$	−8.25693e7	−0.447478
$231$	−1.76765e7	−0.0943526
$232$	−1.28994e7	−0.0678208
$233$	−1.16666e8	−0.604227	−0.302113	−	0.953272i	$-0.597692\pi$
$233$	−1.16666e8	−0.604227	−0.302113	+	0.953272i	$0.597692\pi$
$234$	−4.12904e7	−0.210665
$235$	−6.87278e7	−0.345458
$236$	1.31443e7	0.0650945
$237$	9.10427e7	0.444248
$238$	8.03910e7	0.386534
$239$	−3.33190e8	−1.57870	−0.789348	−	0.613946i	$-0.789581\pi$
$239$	−3.33190e8	−1.57870	−0.789348	+	0.613946i	$0.789581\pi$
$240$	−2.79968e7	−0.130728
$241$	5.07684e7	0.233633	0.116816	−	0.993154i	$-0.462731\pi$
$241$	5.07684e7	0.233633	0.116816	+	0.993154i	$0.462731\pi$
$242$	1.49893e8	0.679875
$243$	−1.43489e7	−0.0641500
$244$	1.15705e8	0.509902
$245$	−6.39052e7	−0.277623
$246$	1.10041e7	0.0471285
$247$	−3.57489e8	−1.50947
$248$	−8.13034e7	−0.338476
$249$	−9.03914e7	−0.371047
$250$	1.86652e8	0.755512
$251$	−3.20287e8	−1.27844	−0.639222	−	0.769022i	$-0.720743\pi$
$251$	−3.20287e8	−1.27844	−0.639222	+	0.769022i	$0.720743\pi$
$252$	−3.52587e7	−0.138792
$253$	−3.53197e7	−0.137118
$254$	2.72877e8	1.04484
$255$	−9.08881e7	−0.343255
$256$	1.67772e7	0.0625000
$257$	2.59992e8	0.955421	0.477711	−	0.878517i	$-0.341467\pi$
$257$	2.59992e8	0.955421	0.477711	+	0.878517i	$0.341467\pi$
$258$	−2.88929e7	−0.104742
$259$	2.58089e8	0.923039
$260$	1.14709e8	0.404752
$261$	1.83666e7	0.0639421
$262$	2.61735e8	0.899100
$263$	−3.02770e8	−1.02628	−0.513142	−	0.858304i	$-0.671518\pi$
$263$	−3.02770e8	−1.02628	−0.513142	+	0.858304i	$0.671518\pi$
$264$	−1.19759e7	−0.0400584
$265$	−1.95417e8	−0.645061
$266$	−3.05268e8	−0.994477
$267$	−2.53294e8	−0.814396
$268$	1.29771e8	0.411819
$269$	9.40138e7	0.294482	0.147241	−	0.989101i	$-0.452961\pi$
$269$	9.40138e7	0.294482	0.147241	+	0.989101i	$0.452961\pi$
$270$	3.98626e7	0.123252
$271$	5.49860e6	0.0167826	0.00839131	−	0.999965i	$-0.497329\pi$
$271$	5.49860e6	0.0167826	0.00839131	+	0.999965i	$0.497329\pi$
$272$	5.44651e7	0.164107
$273$	1.44462e8	0.429719
$274$	3.83022e8	1.12485
$275$	1.21613e7	0.0352628
$276$	−7.04511e7	−0.201700
$277$	4.28997e8	1.21276	0.606380	−	0.795175i	$-0.292621\pi$
$277$	4.28997e8	1.21276	0.606380	+	0.795175i	$0.292621\pi$
$278$	4.35181e8	1.21482
$279$	1.15762e8	0.319118
$280$	9.79520e7	0.266661
$281$	−6.65336e8	−1.78883	−0.894415	−	0.447238i	$-0.852408\pi$
$281$	−6.65336e8	−1.78883	−0.894415	+	0.447238i	$0.852408\pi$
$282$	−5.86411e7	−0.155715
$283$	−3.16053e6	−0.00828911	−0.00414456	−	0.999991i	$-0.501319\pi$
$283$	−3.16053e6	−0.00828911	−0.00414456	+	0.999991i	$0.501319\pi$
$284$	7.30641e7	0.189273
$285$	3.45128e8	0.883128
$286$	4.90676e7	0.124026
$287$	−3.85000e7	−0.0961335
$288$	−2.38879e7	−0.0589256
$289$	−2.33524e8	−0.569102
$290$	−5.10241e7	−0.122852
$291$	3.29684e8	0.784283
$292$	4.14735e8	0.974834
$293$	−3.48429e8	−0.809239	−0.404620	−	0.914485i	$-0.632596\pi$
$293$	−3.48429e8	−0.809239	−0.404620	+	0.914485i	$0.632596\pi$
$294$	−5.45262e7	−0.125138
$295$	5.19925e7	0.117914
$296$	1.74856e8	0.391886
$297$	1.70516e7	0.0377674
$298$	4.30370e8	0.942075
$299$	2.88652e8	0.624491
$300$	2.42578e7	0.0518713
$301$	1.01087e8	0.213655
$302$	−1.10692e8	−0.231255
$303$	−4.87581e8	−1.00693
$304$	−2.06820e8	−0.422216
$305$	4.57673e8	0.923647
$306$	−7.75490e7	−0.154722
$307$	−4.69123e8	−0.925342	−0.462671	−	0.886530i	$-0.653109\pi$
$307$	−4.69123e8	−0.925342	−0.462671	+	0.886530i	$0.653109\pi$
$308$	4.18998e7	0.0817118
$309$	4.32496e8	0.833926
$310$	−3.21598e8	−0.613123
$311$	−2.74250e8	−0.516993	−0.258497	−	0.966012i	$-0.583227\pi$
$311$	−2.74250e8	−0.516993	−0.258497	+	0.966012i	$0.583227\pi$
$312$	9.78734e7	0.182442
$313$	4.90782e8	0.904657	0.452328	−	0.891851i	$-0.350594\pi$
$313$	4.90782e8	0.904657	0.452328	+	0.891851i	$0.350594\pi$
$314$	−1.01074e8	−0.184240
$315$	−1.39467e8	−0.251411
$316$	−2.15805e8	−0.384730
$317$	7.74333e8	1.36528	0.682638	−	0.730757i	$-0.260833\pi$
$317$	7.74333e8	1.36528	0.682638	+	0.730757i	$0.260833\pi$
$318$	−1.66736e8	−0.290761
$319$	−2.18260e7	−0.0376450
$320$	6.63628e7	0.113214
$321$	−9.82077e6	−0.0165721
$322$	2.46486e8	0.411431
$323$	−6.71414e8	−1.10862
$324$	3.40122e7	0.0555556
$325$	−9.93891e7	−0.160600
$326$	−2.80735e8	−0.448782
$327$	−3.30019e8	−0.521941
$328$	−2.60839e7	−0.0408145
$329$	2.05167e8	0.317630
$330$	−4.73709e7	−0.0725627
$331$	−3.10120e8	−0.470037	−0.235019	−	0.971991i	$-0.575515\pi$
$331$	−3.10120e8	−0.470037	−0.235019	+	0.971991i	$0.575515\pi$
$332$	2.14261e8	0.321336
$333$	−2.48965e8	−0.369473
$334$	3.52129e8	0.517117
$335$	5.13313e8	0.745977
$336$	8.35762e7	0.120197
$337$	−7.09077e8	−1.00923	−0.504613	−	0.863346i	$-0.668365\pi$
$337$	−7.09077e8	−1.00923	−0.504613	+	0.863346i	$0.668365\pi$
$338$	1.00981e8	0.142243
$339$	−1.59328e8	−0.222123
$340$	2.15438e8	0.297267
$341$	−1.37566e8	−0.187876
$342$	2.94476e8	0.398069
$343$	8.13135e8	1.08801
$344$	6.84868e7	0.0907094
$345$	−2.78671e8	−0.365364
$346$	−2.05744e8	−0.267031
$347$	−3.27511e8	−0.420797	−0.210399	−	0.977616i	$-0.567476\pi$
$347$	−3.27511e8	−0.420797	−0.210399	+	0.977616i	$0.567476\pi$
$348$	−4.35356e7	−0.0553755
$349$	−8.03280e8	−1.01153	−0.505764	−	0.862672i	$-0.668789\pi$
$349$	−8.03280e8	−1.01153	−0.505764	+	0.862672i	$0.668789\pi$
$350$	−8.48704e7	−0.105808
$351$	−1.39355e8	−0.172008
$352$	2.83873e7	0.0346916
$353$	−2.87785e8	−0.348223	−0.174111	−	0.984726i	$-0.555705\pi$
$353$	−2.87785e8	−0.348223	−0.174111	+	0.984726i	$0.555705\pi$
$354$	4.43619e7	0.0531494
$355$	2.89007e8	0.342854
$356$	6.00401e8	0.705288
$357$	2.71320e8	0.315604
$358$	1.06400e9	1.22561
$359$	3.92043e8	0.447202	0.223601	−	0.974681i	$-0.428219\pi$
$359$	3.92043e8	0.447202	0.223601	+	0.974681i	$0.428219\pi$
$360$	−9.44892e7	−0.106739
$361$	1.65568e9	1.85226
$362$	−7.79518e8	−0.863667
$363$	5.05890e8	0.555115
$364$	−3.42428e8	−0.372147
$365$	1.64050e9	1.76584
$366$	3.90503e8	0.416333
$367$	1.01664e9	1.07359	0.536795	−	0.843713i	$-0.319635\pi$
$367$	1.01664e9	1.07359	0.536795	+	0.843713i	$0.319635\pi$
$368$	1.66995e8	0.174677
$369$	3.71390e7	0.0384802
$370$	6.91648e8	0.709871
$371$	5.83358e8	0.593099
$372$	−2.74399e8	−0.276364
$373$	−5.54252e8	−0.553001	−0.276501	−	0.961014i	$-0.589175\pi$
$373$	−5.54252e8	−0.553001	−0.276501	+	0.961014i	$0.589175\pi$
$374$	9.21557e7	0.0910902
$375$	6.29949e8	0.616873
$376$	1.39001e8	0.134853
$377$	1.78374e8	0.171450
$378$	−1.18998e8	−0.113323
$379$	−9.06611e8	−0.855429	−0.427714	−	0.903914i	$-0.640681\pi$
$379$	−9.06611e8	−0.855429	−0.427714	+	0.903914i	$0.640681\pi$
$380$	−8.18082e8	−0.764811
$381$	9.20961e8	0.853107
$382$	4.93797e8	0.453238
$383$	−3.16079e8	−0.287475	−0.143738	−	0.989616i	$-0.545912\pi$
$383$	−3.16079e8	−0.287475	−0.143738	+	0.989616i	$0.545912\pi$
$384$	5.66231e7	0.0510310
$385$	1.65736e8	0.148015
$386$	7.07989e8	0.626572
$387$	−9.75134e7	−0.0855216
$388$	−7.81473e8	−0.679209
$389$	−2.13872e9	−1.84217	−0.921084	−	0.389363i	$-0.872695\pi$
$389$	−2.13872e9	−1.84217	−0.921084	+	0.389363i	$0.872695\pi$
$390$	3.87141e8	0.330479
$391$	5.42129e8	0.458653
$392$	1.29247e8	0.108373
$393$	8.83357e8	0.734112
$394$	4.80409e8	0.395708
$395$	−8.53623e8	−0.696909
$396$	−4.04186e7	−0.0327075
$397$	1.43566e9	1.15156	0.575779	−	0.817605i	$-0.304699\pi$
$397$	1.43566e9	1.15156	0.575779	+	0.817605i	$0.304699\pi$
$398$	−1.48976e9	−1.18447
$399$	−1.03028e9	−0.811987
$400$	−5.74999e7	−0.0449218
$401$	6.98695e8	0.541106	0.270553	−	0.962705i	$-0.412793\pi$
$401$	6.98695e8	0.541106	0.270553	+	0.962705i	$0.412793\pi$
$402$	4.37977e8	0.336248
$403$	1.12427e9	0.855662
$404$	1.15575e9	0.872023
$405$	1.34536e8	0.100635
$406$	1.52317e8	0.112956
$407$	2.95858e8	0.217522
$408$	1.83820e8	0.133993
$409$	−3.85083e8	−0.278306	−0.139153	−	0.990271i	$-0.544438\pi$
$409$	−3.85083e8	−0.278306	−0.139153	+	0.990271i	$0.544438\pi$
$410$	−1.03176e8	−0.0739322
$411$	1.29270e9	0.918440
$412$	−1.02518e9	−0.722201
$413$	−1.55208e8	−0.108415
$414$	−2.37772e8	−0.164687
$415$	8.47516e8	0.582076
$416$	−2.31996e8	−0.157999
$417$	1.46873e9	0.991898
$418$	−3.49941e8	−0.234357
$419$	−9.04398e8	−0.600635	−0.300317	−	0.953839i	$-0.597093\pi$
$419$	−9.04398e8	−0.600635	−0.300317	+	0.953839i	$0.597093\pi$
$420$	3.30588e8	0.217728
$421$	−3.48965e8	−0.227926	−0.113963	−	0.993485i	$-0.536355\pi$
$421$	−3.48965e8	−0.227926	−0.113963	+	0.993485i	$0.536355\pi$
$422$	−1.27383e9	−0.825119
$423$	−1.97914e8	−0.127141
$424$	3.95227e8	0.251806
$425$	−1.86666e8	−0.117952
$426$	2.46591e8	0.154541
$427$	−1.36625e9	−0.849243
$428$	2.32789e7	0.0143519
$429$	1.65603e8	0.101267
$430$	2.70901e8	0.164313
$431$	1.07370e9	0.645969	0.322984	−	0.946404i	$-0.395314\pi$
$431$	1.07370e9	0.645969	0.322984	+	0.946404i	$0.395314\pi$
$432$	−8.06216e7	−0.0481125
$433$	6.33602e8	0.375067	0.187534	−	0.982258i	$-0.439951\pi$
$433$	6.33602e8	0.375067	0.187534	+	0.982258i	$0.439951\pi$
$434$	9.60035e8	0.563733
$435$	−1.72206e8	−0.100308
$436$	7.82266e8	0.452014
$437$	−2.05862e9	−1.18002
$438$	1.39973e9	0.795949
$439$	−2.13152e9	−1.20244	−0.601220	−	0.799083i	$-0.705319\pi$
$439$	−2.13152e9	−1.20244	−0.601220	+	0.799083i	$0.705319\pi$
$440$	1.12287e8	0.0628411
$441$	−1.84026e8	−0.102175
$442$	−7.53147e8	−0.414860
$443$	1.77263e9	0.968735	0.484368	−	0.874865i	$-0.339050\pi$
$443$	1.77263e9	0.968735	0.484368	+	0.874865i	$0.339050\pi$
$444$	5.90139e8	0.319973
$445$	2.37490e9	1.27757
$446$	−1.35830e8	−0.0724975
$447$	1.45250e9	0.769201
$448$	−1.98106e8	−0.104094
$449$	−1.49630e9	−0.780109	−0.390054	−	0.920792i	$-0.627544\pi$
$449$	−1.49630e9	−0.780109	−0.390054	+	0.920792i	$0.627544\pi$
$450$	8.18700e7	0.0423527
$451$	−4.41343e7	−0.0226547
$452$	3.77668e8	0.192365
$453$	−3.73585e8	−0.188819
$454$	2.57481e9	1.29137
$455$	−1.35449e9	−0.674116
$456$	−6.98017e8	−0.344738
$457$	6.95481e8	0.340862	0.170431	−	0.985370i	$-0.445484\pi$
$457$	6.95481e8	0.340862	0.170431	+	0.985370i	$0.445484\pi$
$458$	1.17364e9	0.570829
$459$	−2.61728e8	−0.126330
$460$	6.60555e8	0.316414
$461$	4.04860e8	0.192465	0.0962325	−	0.995359i	$-0.469321\pi$
$461$	4.04860e8	0.192465	0.0962325	+	0.995359i	$0.469321\pi$
$462$	1.41412e8	0.0667174
$463$	1.56475e9	0.732677	0.366339	−	0.930482i	$-0.380611\pi$
$463$	1.56475e9	0.732677	0.366339	+	0.930482i	$0.380611\pi$
$464$	1.03196e8	0.0479565
$465$	−1.08539e9	−0.500613
$466$	9.33331e8	0.427253
$467$	2.09557e8	0.0952124	0.0476062	−	0.998866i	$-0.484841\pi$
$467$	2.09557e8	0.0952124	0.0476062	+	0.998866i	$0.484841\pi$
$468$	3.30323e8	0.148963
$469$	−1.53234e9	−0.685885
$470$	5.49823e8	0.244276
$471$	−3.41124e8	−0.150431
$472$	−1.05154e8	−0.0460287
$473$	1.15880e8	0.0503496
$474$	−7.28341e8	−0.314131
$475$	7.08826e8	0.303467
$476$	−6.43128e8	−0.273321
$477$	−5.62736e8	−0.237405
$478$	2.66552e9	1.11631
$479$	4.34360e7	0.0180582	0.00902911	−	0.999959i	$-0.497126\pi$
$479$	4.34360e7	0.0180582	0.00902911	+	0.999959i	$0.497126\pi$
$480$	2.23974e8	0.0924388
$481$	−2.41792e9	−0.990681
$482$	−4.06147e8	−0.165203
$483$	8.31891e8	0.335932
$484$	−1.19915e9	−0.480744
$485$	−3.09114e9	−1.23033
$486$	1.14791e8	0.0453609
$487$	6.39694e8	0.250970	0.125485	−	0.992096i	$-0.459951\pi$
$487$	6.39694e8	0.250970	0.125485	+	0.992096i	$0.459951\pi$
$488$	−9.25637e8	−0.360555
$489$	−9.47482e8	−0.366429
$490$	5.11242e8	0.196309
$491$	−2.39867e9	−0.914502	−0.457251	−	0.889338i	$-0.651166\pi$
$491$	−2.39867e9	−0.914502	−0.457251	+	0.889338i	$0.651166\pi$
$492$	−8.80332e7	−0.0333249
$493$	3.35011e8	0.125920
$494$	2.85991e9	1.06735
$495$	−1.59877e8	−0.0592472
$496$	6.50427e8	0.239339
$497$	−8.62745e8	−0.315236
$498$	7.23131e8	0.262370
$499$	−4.81468e9	−1.73466	−0.867332	−	0.497730i	$-0.834167\pi$
$499$	−4.81468e9	−1.73466	−0.867332	+	0.497730i	$0.834167\pi$
$500$	−1.49321e9	−0.534228
$501$	1.18843e9	0.422224
$502$	2.56230e9	0.903996
$503$	−2.62350e9	−0.919164	−0.459582	−	0.888135i	$-0.652001\pi$
$503$	−2.62350e9	−0.919164	−0.459582	+	0.888135i	$0.652001\pi$
$504$	2.82070e8	0.0981407
$505$	4.57159e9	1.57960
$506$	2.82558e8	0.0969573
$507$	3.40810e8	0.116141
$508$	−2.18302e9	−0.738813
$509$	−4.18317e9	−1.40603	−0.703013	−	0.711177i	$-0.748162\pi$
$509$	−4.18317e9	−1.40603	−0.703013	+	0.711177i	$0.748162\pi$
$510$	7.27105e8	0.242718
$511$	−4.89722e9	−1.62359
$512$	−1.34218e8	−0.0441942
$513$	9.93856e8	0.325022
$514$	−2.07994e9	−0.675585
$515$	−4.05511e9	−1.30821
$516$	2.31143e8	0.0740639
$517$	2.35191e8	0.0748522
$518$	−2.06471e9	−0.652687
$519$	−6.94388e8	−0.218030
$520$	−9.17668e8	−0.286203
$521$	−5.37919e9	−1.66642	−0.833211	−	0.552955i	$-0.813500\pi$
$521$	−5.37919e9	−1.66642	−0.833211	+	0.552955i	$0.813500\pi$
$522$	−1.46933e8	−0.0452139
$523$	3.46554e9	1.05929	0.529646	−	0.848219i	$-0.322325\pi$
$523$	3.46554e9	1.05929	0.529646	+	0.848219i	$0.322325\pi$
$524$	−2.09388e9	−0.635760
$525$	−2.86438e8	−0.0863918
$526$	2.42216e9	0.725692
$527$	2.11153e9	0.628434
$528$	9.58070e7	0.0283256
$529$	−1.74261e9	−0.511805
$530$	1.56333e9	0.456127
$531$	1.49721e8	0.0433963
$532$	2.44214e9	0.703202
$533$	3.60690e8	0.103178
$534$	2.02635e9	0.575865
$535$	9.20803e7	0.0259973
$536$	−1.03817e9	−0.291200
$537$	3.59101e9	1.00071
$538$	−7.52110e8	−0.208230
$539$	2.18688e8	0.0601540
$540$	−3.18901e8	−0.0871521
$541$	−3.32927e9	−0.903979	−0.451990	−	0.892023i	$-0.649286\pi$
$541$	−3.32927e9	−0.903979	−0.451990	+	0.892023i	$0.649286\pi$
$542$	−4.39888e7	−0.0118671
$543$	−2.63087e9	−0.705181
$544$	−4.35721e8	−0.116041
$545$	3.09428e9	0.818788
$546$	−1.15570e9	−0.303857
$547$	−1.52310e9	−0.397900	−0.198950	−	0.980010i	$-0.563753\pi$
$547$	−1.52310e9	−0.397900	−0.198950	+	0.980010i	$0.563753\pi$
$548$	−3.06417e9	−0.795392
$549$	1.31795e9	0.339934
$550$	−9.72906e7	−0.0249346
$551$	−1.27213e9	−0.323968
$552$	5.63609e8	0.142623
$553$	2.54824e9	0.640770
$554$	−3.43198e9	−0.857551
$555$	2.33431e9	0.579607
$556$	−3.48144e9	−0.859009
$557$	6.94780e9	1.70355	0.851774	−	0.523910i	$-0.175527\pi$
$557$	6.94780e9	1.70355	0.851774	+	0.523910i	$0.175527\pi$
$558$	−9.26096e8	−0.225651
$559$	−9.47039e8	−0.229312
$560$	−7.83616e8	−0.188558
$561$	3.11025e8	0.0743748
$562$	5.32269e9	1.26489
$563$	2.65931e7	0.00628043	0.00314022	−	0.999995i	$-0.499000\pi$
$563$	2.65931e7	0.00628043	0.00314022	+	0.999995i	$0.499000\pi$
$564$	4.69128e8	0.110107
$565$	1.49388e9	0.348453
$566$	2.52843e7	0.00586129
$567$	−4.01619e8	−0.0925280
$568$	−5.84512e8	−0.133837
$569$	6.18268e9	1.40697	0.703484	−	0.710711i	$-0.251627\pi$
$569$	6.18268e9	1.40697	0.703484	+	0.710711i	$0.251627\pi$
$570$	−2.76103e9	−0.624466
$571$	6.14558e8	0.138145	0.0690727	−	0.997612i	$-0.477996\pi$
$571$	6.14558e8	0.138145	0.0690727	+	0.997612i	$0.477996\pi$
$572$	−3.92541e8	−0.0876998
$573$	1.66656e9	0.370067
$574$	3.08000e8	0.0679766
$575$	−5.72337e8	−0.125549
$576$	1.91103e8	0.0416667
$577$	−2.76416e9	−0.599030	−0.299515	−	0.954092i	$-0.596825\pi$
$577$	−2.76416e9	−0.599030	−0.299515	+	0.954092i	$0.596825\pi$
$578$	1.86820e9	0.402416
$579$	2.38946e9	0.511594
$580$	4.08193e8	0.0868696
$581$	−2.53001e9	−0.535187
$582$	−2.63747e9	−0.554572
$583$	6.68729e8	0.139769
$584$	−3.31788e9	−0.689312
$585$	1.30660e9	0.269835
$586$	2.78743e9	0.572219
$587$	3.59318e9	0.733238	0.366619	−	0.930371i	$-0.380515\pi$
$587$	3.59318e9	0.733238	0.366619	+	0.930371i	$0.380515\pi$
$588$	4.36210e8	0.0884860
$589$	−8.01808e9	−1.61684
$590$	−4.15940e8	−0.0833775
$591$	1.62138e9	0.323094
$592$	−1.39885e9	−0.277105
$593$	−3.57268e8	−0.0703563	−0.0351781	−	0.999381i	$-0.511200\pi$
$593$	−3.57268e8	−0.0703563	−0.0351781	+	0.999381i	$0.511200\pi$
$594$	−1.36413e8	−0.0267056
$595$	−2.54391e9	−0.495100
$596$	−3.44296e9	−0.666148
$597$	−5.02793e9	−0.967117
$598$	−2.30922e9	−0.441582
$599$	−3.17396e9	−0.603403	−0.301701	−	0.953402i	$-0.597555\pi$
$599$	−3.17396e9	−0.603403	−0.301701	+	0.953402i	$0.597555\pi$
$600$	−1.94062e8	−0.0366785
$601$	7.29280e9	1.37036	0.685178	−	0.728376i	$-0.259724\pi$
$601$	7.29280e9	1.37036	0.685178	+	0.728376i	$0.259724\pi$
$602$	−8.08696e8	−0.151077
$603$	1.47817e9	0.274546
$604$	8.85534e8	0.163522
$605$	−4.74326e9	−0.870830
$606$	3.90065e9	0.712004
$607$	3.50523e9	0.636145	0.318073	−	0.948066i	$-0.396964\pi$
$607$	3.50523e9	0.636145	0.318073	+	0.948066i	$0.396964\pi$
$608$	1.65456e9	0.298552
$609$	5.14071e8	0.0922280
$610$	−3.66139e9	−0.653117
$611$	−1.92211e9	−0.340906
$612$	6.20392e8	0.109405
$613$	5.69823e9	0.999144	0.499572	−	0.866272i	$-0.333491\pi$
$613$	5.69823e9	0.999144	0.499572	+	0.866272i	$0.333491\pi$
$614$	3.75298e9	0.654316
$615$	−3.48218e8	−0.0603654
$616$	−3.35199e8	−0.0577790
$617$	2.91661e8	0.0499897	0.0249948	−	0.999688i	$-0.492043\pi$
$617$	2.91661e8	0.0499897	0.0249948	+	0.999688i	$0.492043\pi$
$618$	−3.45997e9	−0.589674
$619$	−3.98489e9	−0.675303	−0.337651	−	0.941271i	$-0.609633\pi$
$619$	−3.98489e9	−0.675303	−0.337651	+	0.941271i	$0.609633\pi$
$620$	2.57278e9	0.433543
$621$	−8.02482e8	−0.134467
$622$	2.19400e9	0.365569
$623$	−7.08957e9	−1.17466
$624$	−7.82988e8	−0.129006
$625$	−4.80972e9	−0.788025
$626$	−3.92626e9	−0.639689
$627$	−1.18105e9	−0.191352
$628$	8.08589e8	0.130277
$629$	−4.54118e9	−0.727598
$630$	1.11573e9	0.177774
$631$	6.60792e9	1.04704	0.523518	−	0.852014i	$-0.324619\pi$
$631$	6.60792e9	1.04704	0.523518	+	0.852014i	$0.324619\pi$
$632$	1.72644e9	0.272045
$633$	−4.29916e9	−0.673707
$634$	−6.19466e9	−0.965395
$635$	−8.63499e9	−1.33830
$636$	1.33389e9	0.205599
$637$	−1.78724e9	−0.273965
$638$	1.74608e8	0.0266190
$639$	8.32245e8	0.126182
$640$	−5.30902e8	−0.0800543
$641$	−6.96140e9	−1.04398	−0.521991	−	0.852951i	$-0.674811\pi$
$641$	−6.96140e9	−1.04398	−0.521991	+	0.852951i	$0.674811\pi$
$642$	7.85662e7	0.0117183
$643$	−5.14278e9	−0.762886	−0.381443	−	0.924392i	$-0.624573\pi$
$643$	−5.14278e9	−0.762886	−0.381443	+	0.924392i	$0.624573\pi$
$644$	−1.97189e9	−0.290926
$645$	9.14293e8	0.134161
$646$	5.37131e9	0.783911
$647$	7.43963e9	1.07991	0.539953	−	0.841695i	$-0.318442\pi$
$647$	7.43963e9	1.07991	0.539953	+	0.841695i	$0.318442\pi$
$648$	−2.72098e8	−0.0392837
$649$	−1.77922e8	−0.0255490
$650$	7.95113e8	0.113562
$651$	3.24012e9	0.460286
$652$	2.24588e9	0.317337
$653$	6.15273e9	0.864712	0.432356	−	0.901703i	$-0.357682\pi$
$653$	6.15273e9	0.864712	0.432356	+	0.901703i	$0.357682\pi$
$654$	2.64015e9	0.369068
$655$	−8.28242e9	−1.15163
$656$	2.08671e8	0.0288602
$657$	4.72409e9	0.649889
$658$	−1.64133e9	−0.224598
$659$	8.40166e9	1.14358	0.571790	−	0.820400i	$-0.306249\pi$
$659$	8.40166e9	1.14358	0.571790	+	0.820400i	$0.306249\pi$
$660$	3.78967e8	0.0513095
$661$	1.12410e9	0.151391	0.0756956	−	0.997131i	$-0.475882\pi$
$661$	1.12410e9	0.151391	0.0756956	+	0.997131i	$0.475882\pi$
$662$	2.48096e9	0.332367
$663$	−2.54187e9	−0.338732
$664$	−1.71409e9	−0.227219
$665$	9.65996e9	1.27380
$666$	1.99172e9	0.261257
$667$	1.02718e9	0.134031
$668$	−2.81703e9	−0.365657
$669$	−4.58426e8	−0.0591940
$670$	−4.10651e9	−0.527486
$671$	−1.56619e9	−0.200132
$672$	−6.68609e8	−0.0849924
$673$	−1.28087e10	−1.61976	−0.809882	−	0.586593i	$-0.800469\pi$
$673$	−1.28087e10	−1.61976	−0.809882	+	0.586593i	$0.800469\pi$
$674$	5.67261e9	0.713631
$675$	2.76311e8	0.0345808
$676$	−8.07847e8	−0.100581
$677$	8.20134e9	1.01584	0.507919	−	0.861405i	$-0.330415\pi$
$677$	8.20134e9	1.01584	0.507919	+	0.861405i	$0.330415\pi$
$678$	1.27463e9	0.157065
$679$	9.22769e9	1.13122
$680$	−1.72351e9	−0.210200
$681$	8.68998e9	1.05440
$682$	1.10053e9	0.132849
$683$	5.30275e9	0.636837	0.318419	−	0.947950i	$-0.396848\pi$
$683$	5.30275e9	0.636837	0.318419	+	0.947950i	$0.396848\pi$
$684$	−2.35581e9	−0.281477
$685$	−1.21204e10	−1.44079
$686$	−6.50508e9	−0.769340
$687$	3.96104e9	0.466080
$688$	−5.47894e8	−0.0641412
$689$	−5.46522e9	−0.636562
$690$	2.22937e9	0.258351
$691$	5.05029e9	0.582295	0.291148	−	0.956678i	$-0.405963\pi$
$691$	5.05029e9	0.582295	0.291148	+	0.956678i	$0.405963\pi$
$692$	1.64596e9	0.188819
$693$	4.77265e8	0.0544745
$694$	2.62009e9	0.297549
$695$	−1.37710e10	−1.55603
$696$	3.48285e8	0.0391564
$697$	6.77425e8	0.0757786
$698$	6.42624e9	0.715258
$699$	3.14999e9	0.348851
$700$	6.78963e8	0.0748175
$701$	−1.37437e10	−1.50692	−0.753462	−	0.657491i	$-0.771618\pi$
$701$	−1.37437e10	−1.50692	−0.753462	+	0.657491i	$0.771618\pi$
$702$	1.11484e9	0.121628
$703$	1.72442e10	1.87197
$704$	−2.27098e8	−0.0245307
$705$	1.85565e9	0.199450
$706$	2.30228e9	0.246231
$707$	−1.36471e10	−1.45236
$708$	−3.54895e8	−0.0375823
$709$	2.13109e9	0.224564	0.112282	−	0.993676i	$-0.464184\pi$
$709$	2.13109e9	0.224564	0.112282	+	0.993676i	$0.464184\pi$
$710$	−2.31206e9	−0.242434
$711$	−2.45815e9	−0.256487
$712$	−4.80321e9	−0.498714
$713$	6.47415e9	0.668912
$714$	−2.17056e9	−0.223166
$715$	−1.55271e9	−0.158861
$716$	−8.51202e9	−0.866637
$717$	8.99612e9	0.911461
$718$	−3.13635e9	−0.316219
$719$	8.49804e9	0.852644	0.426322	−	0.904572i	$-0.359809\pi$
$719$	8.49804e9	0.852644	0.426322	+	0.904572i	$0.359809\pi$
$720$	7.55914e8	0.0754759
$721$	1.21053e10	1.20283
$722$	−1.32454e10	−1.30974
$723$	−1.37075e9	−0.134888
$724$	6.23615e9	0.610705
$725$	−3.53678e8	−0.0344687
$726$	−4.04712e9	−0.392526
$727$	1.20637e9	0.116442	0.0582210	−	0.998304i	$-0.481457\pi$
$727$	1.20637e9	0.116442	0.0582210	+	0.998304i	$0.481457\pi$
$728$	2.73943e9	0.263148
$729$	3.87420e8	0.0370370
$730$	−1.31240e10	−1.24863
$731$	−1.77867e9	−0.168416
$732$	−3.12403e9	−0.294392
$733$	1.20288e10	1.12812	0.564062	−	0.825732i	$-0.309238\pi$
$733$	1.20288e10	1.12812	0.564062	+	0.825732i	$0.309238\pi$
$734$	−8.13316e9	−0.759142
$735$	1.72544e9	0.160285
$736$	−1.33596e9	−0.123516
$737$	−1.75659e9	−0.161635
$738$	−2.97112e8	−0.0272096
$739$	−1.61908e10	−1.47575	−0.737876	−	0.674936i	$-0.764171\pi$
$739$	−1.61908e10	−1.47575	−0.737876	+	0.674936i	$0.764171\pi$
$740$	−5.53318e9	−0.501954
$741$	9.65221e9	0.871491
$742$	−4.66687e9	−0.419384
$743$	5.71647e9	0.511290	0.255645	−	0.966771i	$-0.417712\pi$
$743$	5.71647e9	0.511290	0.255645	+	0.966771i	$0.417712\pi$
$744$	2.19519e9	0.195419
$745$	−1.36187e10	−1.20667
$746$	4.43401e9	0.391031
$747$	2.44057e9	0.214224
$748$	−7.37245e8	−0.0644105
$749$	−2.74878e8	−0.0239031
$750$	−5.03959e9	−0.436195
$751$	−8.01965e9	−0.690900	−0.345450	−	0.938437i	$-0.612274\pi$
$751$	−8.01965e9	−0.690900	−0.345450	+	0.938437i	$0.612274\pi$
$752$	−1.11201e9	−0.0953554
$753$	8.64775e9	0.738110
$754$	−1.42699e9	−0.121233
$755$	3.50276e9	0.296207
$756$	9.51985e8	0.0801316
$757$	−5.78867e9	−0.485002	−0.242501	−	0.970151i	$-0.577968\pi$
$757$	−5.78867e9	−0.485002	−0.242501	+	0.970151i	$0.577968\pi$
$758$	7.25289e9	0.604880
$759$	9.53633e8	0.0791653
$760$	6.54465e9	0.540803
$761$	−1.02039e10	−0.839303	−0.419652	−	0.907685i	$-0.637848\pi$
$761$	−1.02039e10	−0.839303	−0.419652	+	0.907685i	$0.637848\pi$
$762$	−7.36769e9	−0.603238
$763$	−9.23705e9	−0.752831
$764$	−3.95037e9	−0.320488
$765$	2.45398e9	0.198178
$766$	2.52864e9	0.203276
$767$	1.45408e9	0.116360
$768$	−4.52985e8	−0.0360844
$769$	1.67148e10	1.32544	0.662719	−	0.748868i	$-0.269402\pi$
$769$	1.67148e10	1.32544	0.662719	+	0.748868i	$0.269402\pi$
$770$	−1.32589e9	−0.104662
$771$	−7.01980e9	−0.551613
$772$	−5.66391e9	−0.443053
$773$	−8.58093e9	−0.668199	−0.334100	−	0.942538i	$-0.608432\pi$
$773$	−8.58093e9	−0.668199	−0.334100	+	0.942538i	$0.608432\pi$
$774$	7.80107e8	0.0604729
$775$	−2.22918e9	−0.172024
$776$	6.25179e9	0.480273
$777$	−6.96840e9	−0.532917
$778$	1.71097e10	1.30261
$779$	−2.57238e9	−0.194964
$780$	−3.09713e9	−0.233684
$781$	−9.89002e8	−0.0742880
$782$	−4.33703e9	−0.324316
$783$	−4.95898e8	−0.0369170
$784$	−1.03398e9	−0.0766311
$785$	3.19840e9	0.235987
$786$	−7.06686e9	−0.519096
$787$	3.40447e9	0.248965	0.124482	−	0.992222i	$-0.460273\pi$
$787$	3.40447e9	0.248965	0.124482	+	0.992222i	$0.460273\pi$
$788$	−3.84327e9	−0.279808
$789$	8.17478e9	0.592525
$790$	6.82898e9	0.492789
$791$	−4.45952e9	−0.320384
$792$	3.23349e8	0.0231277
$793$	1.27998e10	0.911477
$794$	−1.14853e10	−0.814275
$795$	5.27625e9	0.372426
$796$	1.19181e10	0.837548
$797$	5.54877e9	0.388233	0.194117	−	0.980978i	$-0.437816\pi$
$797$	5.54877e9	0.388233	0.194117	+	0.980978i	$0.437816\pi$
$798$	8.24222e9	0.574162
$799$	−3.60999e9	−0.250376
$800$	4.60000e8	0.0317645
$801$	6.83894e9	0.470192
$802$	−5.58956e9	−0.382620
$803$	−5.61389e9	−0.382613
$804$	−3.50382e9	−0.237764
$805$	−7.79987e9	−0.526989
$806$	−8.99414e9	−0.605044
$807$	−2.53837e9	−0.170019
$808$	−9.24598e9	−0.616614
$809$	−1.32770e10	−0.881620	−0.440810	−	0.897600i	$-0.645309\pi$
$809$	−1.32770e10	−0.881620	−0.440810	+	0.897600i	$0.645309\pi$
$810$	−1.07629e9	−0.0711594
$811$	−7.03627e8	−0.0463201	−0.0231601	−	0.999732i	$-0.507373\pi$
$811$	−7.03627e8	−0.0463201	−0.0231601	+	0.999732i	$0.507373\pi$
$812$	−1.21854e9	−0.0798718
$813$	−1.48462e8	−0.00968945
$814$	−2.36687e9	−0.153811
$815$	8.88366e9	0.574831
$816$	−1.47056e9	−0.0947473
$817$	6.75412e9	0.433303
$818$	3.08066e9	0.196792
$819$	−3.90047e9	−0.248098
$820$	8.25405e8	0.0522780
$821$	6.63712e9	0.418580	0.209290	−	0.977854i	$-0.432885\pi$
$821$	6.63712e9	0.418580	0.209290	+	0.977854i	$0.432885\pi$
$822$	−1.03416e10	−0.649435
$823$	−1.16655e10	−0.729463	−0.364731	−	0.931113i	$-0.618839\pi$
$823$	−1.16655e10	−0.729463	−0.364731	+	0.931113i	$0.618839\pi$
$824$	8.20140e9	0.510673
$825$	−3.28356e8	−0.0203590
$826$	1.24167e9	0.0766610
$827$	1.10156e10	0.677235	0.338618	−	0.940924i	$-0.390041\pi$
$827$	1.10156e10	0.677235	0.338618	+	0.940924i	$0.390041\pi$
$828$	1.90218e9	0.116452
$829$	−1.54870e10	−0.944121	−0.472060	−	0.881566i	$-0.656490\pi$
$829$	−1.54870e10	−0.944121	−0.472060	+	0.881566i	$0.656490\pi$
$830$	−6.78013e9	−0.411590
$831$	−1.15829e10	−0.700188
$832$	1.85597e9	0.111722
$833$	−3.35668e9	−0.201211
$834$	−1.17499e10	−0.701378
$835$	−1.11428e10	−0.662359
$836$	2.79953e9	0.165716
$837$	−3.12557e9	−0.184243
$838$	7.23519e9	0.424713
$839$	1.30677e9	0.0763895	0.0381947	−	0.999270i	$-0.487839\pi$
$839$	1.30677e9	0.0763895	0.0381947	+	0.999270i	$0.487839\pi$
$840$	−2.64470e9	−0.153957
$841$	−1.66151e10	−0.963203
$842$	2.79172e9	0.161168
$843$	1.79641e10	1.03278
$844$	1.01906e10	0.583447
$845$	−3.19546e9	−0.182195
$846$	1.58331e9	0.0899020
$847$	1.41596e10	0.800681
$848$	−3.16182e9	−0.178054
$849$	8.53344e7	0.00478572
$850$	1.49333e9	0.0834046
$851$	−1.39237e10	−0.774464
$852$	−1.97273e9	−0.109277
$853$	1.12443e10	0.620311	0.310155	−	0.950686i	$-0.399619\pi$
$853$	1.12443e10	0.620311	0.310155	+	0.950686i	$0.399619\pi$
$854$	1.09300e10	0.600506
$855$	−9.31846e9	−0.509874
$856$	−1.86231e8	−0.0101483
$857$	2.04215e10	1.10829	0.554147	−	0.832419i	$-0.313045\pi$
$857$	2.04215e10	1.10829	0.554147	+	0.832419i	$0.313045\pi$
$858$	−1.32482e9	−0.0716066
$859$	−2.80629e10	−1.51063	−0.755313	−	0.655364i	$-0.772515\pi$
$859$	−2.80629e10	−1.51063	−0.755313	+	0.655364i	$0.772515\pi$
$860$	−2.16721e9	−0.116187
$861$	1.03950e9	0.0555027
$862$	−8.58958e9	−0.456769
$863$	1.29653e10	0.686667	0.343334	−	0.939214i	$-0.388444\pi$
$863$	1.29653e10	0.686667	0.343334	+	0.939214i	$0.388444\pi$
$864$	6.44973e8	0.0340207
$865$	6.51063e9	0.342032
$866$	−5.06882e9	−0.265213
$867$	6.30516e9	0.328571
$868$	−7.68028e9	−0.398619
$869$	2.92116e9	0.151003
$870$	1.37765e9	0.0709287
$871$	1.43558e10	0.736148
$872$	−6.25813e9	−0.319622
$873$	−8.90147e9	−0.452806
$874$	1.64690e10	0.834403
$875$	1.76320e10	0.889759
$876$	−1.11978e10	−0.562821
$877$	8.83447e9	0.442264	0.221132	−	0.975244i	$-0.429025\pi$
$877$	8.83447e9	0.442264	0.221132	+	0.975244i	$0.429025\pi$
$878$	1.70522e10	0.850254
$879$	9.40757e9	0.467215
$880$	−8.98293e8	−0.0444354
$881$	2.30540e10	1.13587	0.567937	−	0.823072i	$-0.307742\pi$
$881$	2.30540e10	1.13587	0.567937	+	0.823072i	$0.307742\pi$
$882$	1.47221e9	0.0722485
$883$	1.28149e10	0.626403	0.313201	−	0.949687i	$-0.398599\pi$
$883$	1.28149e10	0.626403	0.313201	+	0.949687i	$0.398599\pi$
$884$	6.02518e9	0.293350
$885$	−1.40380e9	−0.0680774
$886$	−1.41810e10	−0.684999
$887$	−1.03479e10	−0.497875	−0.248937	−	0.968520i	$-0.580081\pi$
$887$	−1.03479e10	−0.497875	−0.248937	+	0.968520i	$0.580081\pi$
$888$	−4.72111e9	−0.226255
$889$	2.57772e10	1.23050
$890$	−1.89992e10	−0.903381
$891$	−4.60393e8	−0.0218050
$892$	1.08664e9	0.0512635
$893$	1.37082e10	0.644169
$894$	−1.16200e10	−0.543907
$895$	−3.36696e10	−1.56985
$896$	1.58485e9	0.0736056
$897$	−7.79361e9	−0.360550
$898$	1.19704e10	0.551620
$899$	4.00073e9	0.183646
$900$	−6.54960e8	−0.0299479
$901$	−1.02644e10	−0.467518
$902$	3.53074e8	0.0160193
$903$	−2.72935e9	−0.123354
$904$	−3.02134e9	−0.136022
$905$	2.46673e10	1.10624
$906$	2.98868e9	0.133515
$907$	2.52627e10	1.12423	0.562115	−	0.827059i	$-0.309988\pi$
$907$	2.52627e10	1.12423	0.562115	+	0.827059i	$0.309988\pi$
$908$	−2.05985e10	−0.913134
$909$	1.31647e10	0.581349
$910$	1.08359e10	0.476672
$911$	1.76518e10	0.773527	0.386764	−	0.922179i	$-0.373593\pi$
$911$	1.76518e10	0.773527	0.386764	+	0.922179i	$0.373593\pi$
$912$	5.58413e9	0.243766
$913$	−2.90026e9	−0.126121
$914$	−5.56385e9	−0.241026
$915$	−1.23572e10	−0.533268
$916$	−9.38913e9	−0.403637
$917$	2.47247e10	1.05886
$918$	2.09382e9	0.0893286
$919$	2.54976e10	1.08366	0.541832	−	0.840487i	$-0.317731\pi$
$919$	2.54976e10	1.08366	0.541832	+	0.840487i	$0.317731\pi$
$920$	−5.28444e9	−0.223739
$921$	1.26663e10	0.534247
$922$	−3.23888e9	−0.136093
$923$	8.08267e9	0.338337
$924$	−1.13130e9	−0.0471763
$925$	4.79422e9	0.199169
$926$	−1.25180e10	−0.518081
$927$	−1.16774e10	−0.481467
$928$	−8.25564e8	−0.0339104
$929$	4.43801e10	1.81607	0.908037	−	0.418890i	$-0.137581\pi$
$929$	4.43801e10	1.81607	0.908037	+	0.418890i	$0.137581\pi$
$930$	8.68315e9	0.353987
$931$	1.27463e10	0.517678
$932$	−7.46665e9	−0.302113
$933$	7.40474e9	0.298486
$934$	−1.67646e9	−0.0673253
$935$	−2.91620e9	−0.116675
$936$	−2.64258e9	−0.105333
$937$	−1.88085e10	−0.746907	−0.373454	−	0.927649i	$-0.621827\pi$
$937$	−1.88085e10	−0.746907	−0.373454	+	0.927649i	$0.621827\pi$
$938$	1.22588e10	0.484994
$939$	−1.32511e10	−0.522304
$940$	−4.39858e9	−0.172729
$941$	−1.38495e10	−0.541840	−0.270920	−	0.962602i	$-0.587328\pi$
$941$	−1.38495e10	−0.541840	−0.270920	+	0.962602i	$0.587328\pi$
$942$	2.72899e9	0.106371
$943$	2.07705e9	0.0806595
$944$	8.41232e8	0.0325472
$945$	3.76560e9	0.145152
$946$	−9.27044e8	−0.0356026
$947$	−4.14177e10	−1.58475	−0.792376	−	0.610032i	$-0.791156\pi$
$947$	−4.14177e10	−1.58475	−0.792376	+	0.610032i	$0.791156\pi$
$948$	5.82673e9	0.222124
$949$	4.58798e10	1.74257
$950$	−5.67061e9	−0.214584
$951$	−2.09070e10	−0.788242
$952$	5.14502e9	0.193267
$953$	4.78373e9	0.179036	0.0895182	−	0.995985i	$-0.471467\pi$
$953$	4.78373e9	0.179036	0.0895182	+	0.995985i	$0.471467\pi$
$954$	4.50188e9	0.167871
$955$	−1.56258e10	−0.580539
$956$	−2.13241e10	−0.789348
$957$	5.89302e8	0.0217343
$958$	−3.47488e8	−0.0127691
$959$	3.61819e10	1.32473
$960$	−1.79180e9	−0.0653641
$961$	−2.29656e9	−0.0834729
$962$	1.93433e10	0.700517
$963$	2.65161e8	0.00956792
$964$	3.24918e9	0.116816
$965$	−2.24038e10	−0.802556
$966$	−6.65513e9	−0.237540
$967$	4.17328e10	1.48417	0.742086	−	0.670304i	$-0.233836\pi$
$967$	4.17328e10	1.48417	0.742086	+	0.670304i	$0.233836\pi$
$968$	9.59318e9	0.339937
$969$	1.81282e10	0.640061
$970$	2.47291e10	0.869977
$971$	−5.34074e9	−0.187212	−0.0936060	−	0.995609i	$-0.529839\pi$
$971$	−5.34074e9	−0.187212	−0.0936060	+	0.995609i	$0.529839\pi$
$972$	−9.18330e8	−0.0320750
$973$	4.11091e10	1.43068
$974$	−5.11755e9	−0.177462
$975$	2.68350e9	0.0927227
$976$	7.40510e9	0.254951
$977$	−5.59401e10	−1.91908	−0.959538	−	0.281580i	$-0.909141\pi$
$977$	−5.59401e10	−1.91908	−0.959538	+	0.281580i	$0.909141\pi$
$978$	7.57985e9	0.259104
$979$	−8.12709e9	−0.276819
$980$	−4.08993e9	−0.138811
$981$	8.91050e9	0.301343
$982$	1.91893e10	0.646650
$983$	2.80057e10	0.940393	0.470196	−	0.882562i	$-0.344183\pi$
$983$	2.80057e10	0.940393	0.470196	+	0.882562i	$0.344183\pi$
$984$	7.04265e8	0.0235642
$985$	−1.52022e10	−0.506850
$986$	−2.68009e9	−0.0890390
$987$	−5.53950e9	−0.183384
$988$	−2.28793e10	−0.754734
$989$	−5.45357e9	−0.179264
$990$	1.27902e9	0.0418941
$991$	7.29793e9	0.238200	0.119100	−	0.992882i	$-0.461999\pi$
$991$	7.29793e9	0.238200	0.119100	+	0.992882i	$0.461999\pi$
$992$	−5.20342e9	−0.169238
$993$	8.37325e9	0.271376
$994$	6.90196e9	0.222905
$995$	4.71422e10	1.51715
$996$	−5.78505e9	−0.185524
$997$	3.79003e10	1.21118	0.605591	−	0.795776i	$-0.292937\pi$
$997$	3.79003e10	1.21118	0.605591	+	0.795776i	$0.292937\pi$
$998$	3.85174e10	1.22659
$999$	6.72205e9	0.213316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.e.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.e.1.7	✓	9	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +253.154 q^{5} +216.000 q^{6} -755.716 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +253.154 q^{5} +216.000 q^{6} -755.716 q^{7} -512.000 q^{8} +729.000 q^{9} -2025.23 q^{10} -866.310 q^{11} -1728.00 q^{12} +7079.97 q^{13} +6045.73 q^{14} -6835.16 q^{15} +4096.00 q^{16} +13297.2 q^{17} -5832.00 q^{18} -50493.1 q^{19} +16201.9 q^{20} +20404.3 q^{21} +6930.48 q^{22} +40770.3 q^{23} +13824.0 q^{24} -14038.1 q^{25} -56639.7 q^{26} -19683.0 q^{27} -48365.8 q^{28} +25194.2 q^{29} +54681.3 q^{30} +158796. q^{31} -32768.0 q^{32} +23390.4 q^{33} -106377. q^{34} -191313. q^{35} +46656.0 q^{36} -341516. q^{37} +403945. q^{38} -191159. q^{39} -129615. q^{40} +50945.1 q^{41} -163235. q^{42} -133763. q^{43} -55443.9 q^{44} +184549. q^{45} -326163. q^{46} -271486. q^{47} -110592. q^{48} -252436. q^{49} +112305. q^{50} -359023. q^{51} +453118. q^{52} -771928. q^{53} +157464. q^{54} -219310. q^{55} +386927. q^{56} +1.36331e6 q^{57} -201554. q^{58} +205379. q^{59} -437450. q^{60} +1.80789e6 q^{61} -1.27037e6 q^{62} -550917. q^{63} +262144. q^{64} +1.79232e6 q^{65} -187123. q^{66} +2.02767e6 q^{67} +851018. q^{68} -1.10080e6 q^{69} +1.53050e6 q^{70} +1.14163e6 q^{71} -373248. q^{72} +6.48023e6 q^{73} +2.73212e6 q^{74} +379028. q^{75} -3.23156e6 q^{76} +654685. q^{77} +1.52927e6 q^{78} -3.37195e6 q^{79} +1.03692e6 q^{80} +531441. q^{81} -407561. q^{82} +3.34783e6 q^{83} +1.30588e6 q^{84} +3.36623e6 q^{85} +1.07011e6 q^{86} -680244. q^{87} +443551. q^{88} +9.38127e6 q^{89} -1.47639e6 q^{90} -5.35044e6 q^{91} +2.60930e6 q^{92} -4.28748e6 q^{93} +2.17189e6 q^{94} -1.27825e7 q^{95} +884736. q^{96} -1.22105e7 q^{97} +2.01949e6 q^{98} -631540. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Introduction

L-functions

Modular forms

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