LMFDB - Embedded newform 177.8.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.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:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-20.9501$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-19.9501 q^{2} +27.0000 q^{3} +270.005 q^{4} +505.865 q^{5} -538.652 q^{6} +222.970 q^{7} -2833.01 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-19.9501 q^{2} +27.0000 q^{3} +270.005 q^{4} +505.865 q^{5} -538.652 q^{6} +222.970 q^{7} -2833.01 q^{8} +729.000 q^{9} -10092.0 q^{10} -1831.62 q^{11} +7290.13 q^{12} +688.848 q^{13} -4448.27 q^{14} +13658.4 q^{15} +21958.1 q^{16} +2843.94 q^{17} -14543.6 q^{18} +34416.2 q^{19} +136586. q^{20} +6020.19 q^{21} +36540.9 q^{22} -3272.29 q^{23} -76491.2 q^{24} +177775. q^{25} -13742.6 q^{26} +19683.0 q^{27} +60203.0 q^{28} +128507. q^{29} -272485. q^{30} -16509.0 q^{31} -75439.5 q^{32} -49453.7 q^{33} -56736.8 q^{34} +112793. q^{35} +196834. q^{36} -424491. q^{37} -686606. q^{38} +18598.9 q^{39} -1.43312e6 q^{40} -12500.6 q^{41} -120103. q^{42} +338393. q^{43} -494546. q^{44} +368776. q^{45} +65282.4 q^{46} +560303. q^{47} +592867. q^{48} -773827. q^{49} -3.54662e6 q^{50} +76786.4 q^{51} +185992. q^{52} +2.04079e6 q^{53} -392677. q^{54} -926551. q^{55} -631676. q^{56} +929239. q^{57} -2.56371e6 q^{58} +205379. q^{59} +3.68783e6 q^{60} -2.42610e6 q^{61} +329355. q^{62} +162545. q^{63} -1.30561e6 q^{64} +348464. q^{65} +986603. q^{66} -2.63298e6 q^{67} +767879. q^{68} -88351.8 q^{69} -2.25022e6 q^{70} +2.62379e6 q^{71} -2.06526e6 q^{72} +3.21761e6 q^{73} +8.46862e6 q^{74} +4.79992e6 q^{75} +9.29256e6 q^{76} -408396. q^{77} -371049. q^{78} +3.42920e6 q^{79} +1.11078e7 q^{80} +531441. q^{81} +249387. q^{82} +1.20365e6 q^{83} +1.62548e6 q^{84} +1.43865e6 q^{85} -6.75097e6 q^{86} +3.46968e6 q^{87} +5.18899e6 q^{88} -2.50843e6 q^{89} -7.35710e6 q^{90} +153592. q^{91} -883534. q^{92} -445743. q^{93} -1.11781e7 q^{94} +1.74100e7 q^{95} -2.03687e6 q^{96} +8.73888e6 q^{97} +1.54379e7 q^{98} -1.33525e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) $ 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * 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 $

$2$	−19.9501	−1.76335	−0.881677	−	0.471854i	$-0.843585\pi$
$2$	−19.9501	−1.76335	−0.881677	+	0.471854i	$0.843585\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	270.005	2.10941
$5$	505.865	1.80984	0.904919	−	0.425583i	$-0.139931\pi$
$5$	505.865	1.80984	0.904919	+	0.425583i	$0.139931\pi$
$6$	−538.652	−1.01807
$7$	222.970	0.245699	0.122849	−	0.992425i	$-0.460797\pi$
$7$	222.970	0.245699	0.122849	+	0.992425i	$0.460797\pi$
$8$	−2833.01	−1.95629
$9$	729.000	0.333333
$10$	−10092.0	−3.19138
$11$	−1831.62	−0.414916	−0.207458	−	0.978244i	$-0.566519\pi$
$11$	−1831.62	−0.414916	−0.207458	+	0.978244i	$0.566519\pi$
$12$	7290.13	1.21787
$13$	688.848	0.0869604	0.0434802	−	0.999054i	$-0.486155\pi$
$13$	688.848	0.0869604	0.0434802	+	0.999054i	$0.486155\pi$
$14$	−4448.27	−0.433254
$15$	13658.4	1.04491
$16$	21958.1	1.34021
$17$	2843.94	0.140394	0.0701972	−	0.997533i	$-0.477637\pi$
$17$	2843.94	0.140394	0.0701972	+	0.997533i	$0.477637\pi$
$18$	−14543.6	−0.587784
$19$	34416.2	1.15113	0.575567	−	0.817755i	$-0.304781\pi$
$19$	34416.2	1.15113	0.575567	+	0.817755i	$0.304781\pi$
$20$	136586.	3.81770
$21$	6020.19	0.141854
$22$	36540.9	0.731643
$23$	−3272.29	−0.0560795	−0.0280398	−	0.999607i	$-0.508927\pi$
$23$	−3272.29	−0.0560795	−0.0280398	+	0.999607i	$0.508927\pi$
$24$	−76491.2	−1.12946
$25$	177775.	2.27552
$26$	−13742.6	−0.153342
$27$	19683.0	0.192450
$28$	60203.0	0.518281
$29$	128507.	0.978436	0.489218	−	0.872162i	$-0.337282\pi$
$29$	128507.	0.978436	0.489218	+	0.872162i	$0.337282\pi$
$30$	−272485.	−1.84255
$31$	−16509.0	−0.0995301	−0.0497651	−	0.998761i	$-0.515847\pi$
$31$	−16509.0	−0.0995301	−0.0497651	+	0.998761i	$0.515847\pi$
$32$	−75439.5	−0.406981
$33$	−49453.7	−0.239552
$34$	−56736.8	−0.247565
$35$	112793.	0.444675
$36$	196834.	0.703138
$37$	−424491.	−1.37772	−0.688862	−	0.724892i	$-0.741889\pi$
$37$	−424491.	−1.37772	−0.688862	+	0.724892i	$0.741889\pi$
$38$	−686606.	−2.02986
$39$	18598.9	0.0502066
$40$	−1.43312e6	−3.54057
$41$	−12500.6	−0.0283261	−0.0141630	−	0.999900i	$-0.504508\pi$
$41$	−12500.6	−0.0283261	−0.0141630	+	0.999900i	$0.504508\pi$
$42$	−120103.	−0.250139
$43$	338393.	0.649056	0.324528	−	0.945876i	$-0.394795\pi$
$43$	338393.	0.649056	0.324528	+	0.945876i	$0.394795\pi$
$44$	−494546.	−0.875230
$45$	368776.	0.603280
$46$	65282.4	0.0988880
$47$	560303.	0.787192	0.393596	−	0.919284i	$-0.371231\pi$
$47$	560303.	0.787192	0.393596	+	0.919284i	$0.371231\pi$
$48$	592867.	0.773772
$49$	−773827.	−0.939632
$50$	−3.54662e6	−4.01254
$51$	76786.4	0.0810567
$52$	185992.	0.183436
$53$	2.04079e6	1.88293	0.941463	−	0.337116i	$-0.109452\pi$
$53$	2.04079e6	1.88293	0.941463	+	0.337116i	$0.109452\pi$
$54$	−392677.	−0.339357
$55$	−926551.	−0.750931
$56$	−631676.	−0.480658
$57$	929239.	0.664608
$58$	−2.56371e6	−1.72533
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	3.68783e6	2.20415
$61$	−2.42610e6	−1.36853	−0.684265	−	0.729233i	$-0.739877\pi$
$61$	−2.42610e6	−1.36853	−0.684265	+	0.729233i	$0.739877\pi$
$62$	329355.	0.175507
$63$	162545.	0.0818997
$64$	−1.30561e6	−0.622563
$65$	348464.	0.157384
$66$	986603.	0.422415
$67$	−2.63298e6	−1.06951	−0.534757	−	0.845006i	$-0.679597\pi$
$67$	−2.63298e6	−1.06951	−0.534757	+	0.845006i	$0.679597\pi$
$68$	767879.	0.296150
$69$	−88351.8	−0.0323775
$70$	−2.25022e6	−0.784120
$71$	2.62379e6	0.870013	0.435006	−	0.900427i	$-0.356746\pi$
$71$	2.62379e6	0.870013	0.435006	+	0.900427i	$0.356746\pi$
$72$	−2.06526e6	−0.652096
$73$	3.21761e6	0.968062	0.484031	−	0.875051i	$-0.339172\pi$
$73$	3.21761e6	0.968062	0.484031	+	0.875051i	$0.339172\pi$
$74$	8.46862e6	2.42941
$75$	4.79992e6	1.31377
$76$	9.29256e6	2.42822
$77$	−408396.	−0.101944
$78$	−371049.	−0.0885320
$79$	3.42920e6	0.782525	0.391263	−	0.920279i	$-0.372038\pi$
$79$	3.42920e6	0.782525	0.391263	+	0.920279i	$0.372038\pi$
$80$	1.11078e7	2.42557
$81$	531441.	0.111111
$82$	249387.	0.0499489
$83$	1.20365e6	0.231060	0.115530	−	0.993304i	$-0.463143\pi$
$83$	1.20365e6	0.231060	0.115530	+	0.993304i	$0.463143\pi$
$84$	1.62548e6	0.299230
$85$	1.43865e6	0.254091
$86$	−6.75097e6	−1.14451
$87$	3.46968e6	0.564900
$88$	5.18899e6	0.811695
$89$	−2.50843e6	−0.377170	−0.188585	−	0.982057i	$-0.560390\pi$
$89$	−2.50843e6	−0.377170	−0.188585	+	0.982057i	$0.560390\pi$
$90$	−7.35710e6	−1.06379
$91$	153592.	0.0213661
$92$	−883534.	−0.118295
$93$	−445743.	−0.0574637
$94$	−1.11781e7	−1.38810
$95$	1.74100e7	2.08337
$96$	−2.03687e6	−0.234970
$97$	8.73888e6	0.972198	0.486099	−	0.873904i	$-0.338420\pi$
$97$	8.73888e6	0.972198	0.486099	+	0.873904i	$0.338420\pi$
$98$	1.54379e7	1.65690
$99$	−1.33525e6	−0.138305
$100$	4.80000e7	4.80000
$101$	−814288.	−0.0786418	−0.0393209	−	0.999227i	$-0.512519\pi$
$101$	−814288.	−0.0786418	−0.0393209	+	0.999227i	$0.512519\pi$
$102$	−1.53189e6	−0.142932
$103$	−1.34032e7	−1.20859	−0.604296	−	0.796760i	$-0.706546\pi$
$103$	−1.34032e7	−1.20859	−0.604296	+	0.796760i	$0.706546\pi$
$104$	−1.95151e6	−0.170120
$105$	3.04541e6	0.256734
$106$	−4.07139e7	−3.32026
$107$	−5.36199e6	−0.423139	−0.211569	−	0.977363i	$-0.567857\pi$
$107$	−5.36199e6	−0.423139	−0.211569	+	0.977363i	$0.567857\pi$
$108$	5.31451e6	0.405957
$109$	2.36393e6	0.174841	0.0874203	−	0.996172i	$-0.472138\pi$
$109$	2.36393e6	0.174841	0.0874203	+	0.996172i	$0.472138\pi$
$110$	1.84848e7	1.32416
$111$	−1.14613e7	−0.795429
$112$	4.89599e6	0.329289
$113$	1.26518e7	0.824855	0.412428	−	0.910990i	$-0.364681\pi$
$113$	1.26518e7	0.824855	0.412428	+	0.910990i	$0.364681\pi$
$114$	−1.85384e7	−1.17194
$115$	−1.65534e6	−0.101495
$116$	3.46974e7	2.06393
$117$	502170.	0.0289868
$118$	−4.09732e6	−0.229569
$119$	634114.	0.0344947
$120$	−3.86943e7	−2.04415
$121$	−1.61324e7	−0.827845
$122$	4.84009e7	2.41320
$123$	−337516.	−0.0163541
$124$	−4.45751e6	−0.209950
$125$	5.04093e7	2.30848
$126$	−3.24279e6	−0.144418
$127$	−2.94888e7	−1.27745	−0.638726	−	0.769434i	$-0.720538\pi$
$127$	−2.94888e7	−1.27745	−0.638726	+	0.769434i	$0.720538\pi$
$128$	3.57032e7	1.50478
$129$	9.13662e6	0.374733
$130$	−6.95188e6	−0.277524
$131$	2.80740e7	1.09107	0.545537	−	0.838087i	$-0.316326\pi$
$131$	2.80740e7	1.09107	0.545537	+	0.838087i	$0.316326\pi$
$132$	−1.33527e7	−0.505314
$133$	7.67379e6	0.282832
$134$	5.25282e7	1.88593
$135$	9.95695e6	0.348304
$136$	−8.05691e6	−0.274652
$137$	−5.12815e7	−1.70388	−0.851939	−	0.523641i	$-0.824573\pi$
$137$	−5.12815e7	−1.70388	−0.851939	+	0.523641i	$0.824573\pi$
$138$	1.76262e6	0.0570930
$139$	3.88050e6	0.122556	0.0612782	−	0.998121i	$-0.480482\pi$
$139$	3.88050e6	0.122556	0.0612782	+	0.998121i	$0.480482\pi$
$140$	3.04546e7	0.938005
$141$	1.51282e7	0.454485
$142$	−5.23449e7	−1.53414
$143$	−1.26171e6	−0.0360813
$144$	1.60074e7	0.446738
$145$	6.50070e7	1.77081
$146$	−6.41915e7	−1.70704
$147$	−2.08933e7	−0.542497
$148$	−1.14615e8	−2.90619
$149$	−3.38987e6	−0.0839520	−0.0419760	−	0.999119i	$-0.513365\pi$
$149$	−3.38987e6	−0.0839520	−0.0419760	+	0.999119i	$0.513365\pi$
$150$	−9.57586e7	−2.31664
$151$	4.99988e7	1.18179	0.590895	−	0.806748i	$-0.298775\pi$
$151$	4.99988e7	1.18179	0.590895	+	0.806748i	$0.298775\pi$
$152$	−9.75015e7	−2.25195
$153$	2.07323e6	0.0467981
$154$	8.14752e6	0.179764
$155$	−8.35132e6	−0.180133
$156$	5.02179e6	0.105907
$157$	−4.76455e7	−0.982591	−0.491295	−	0.870993i	$-0.663476\pi$
$157$	−4.76455e7	−0.982591	−0.491295	+	0.870993i	$0.663476\pi$
$158$	−6.84128e7	−1.37987
$159$	5.51014e7	1.08711
$160$	−3.81622e7	−0.736569
$161$	−729622.	−0.0137787
$162$	−1.06023e7	−0.195928
$163$	7.64073e7	1.38191	0.690953	−	0.722900i	$-0.257191\pi$
$163$	7.64073e7	1.38191	0.690953	+	0.722900i	$0.257191\pi$
$164$	−3.37522e6	−0.0597514
$165$	−2.50169e7	−0.433550
$166$	−2.40128e7	−0.407441
$167$	−6.91463e6	−0.114885	−0.0574423	−	0.998349i	$-0.518295\pi$
$167$	−6.91463e6	−0.114885	−0.0574423	+	0.998349i	$0.518295\pi$
$168$	−1.70552e7	−0.277508
$169$	−6.22740e7	−0.992438
$170$	−2.87012e7	−0.448052
$171$	2.50894e7	0.383711
$172$	9.13679e7	1.36913
$173$	9.54381e7	1.40139	0.700697	−	0.713459i	$-0.252872\pi$
$173$	9.54381e7	1.40139	0.700697	+	0.713459i	$0.252872\pi$
$174$	−6.92203e7	−0.996118
$175$	3.96384e7	0.559092
$176$	−4.02187e7	−0.556076
$177$	5.54523e6	0.0751646
$178$	5.00434e7	0.665085
$179$	3.26295e7	0.425231	0.212616	−	0.977136i	$-0.431802\pi$
$179$	3.26295e7	0.425231	0.212616	+	0.977136i	$0.431802\pi$
$180$	9.95713e7	1.27257
$181$	−8.74090e7	−1.09567	−0.547837	−	0.836585i	$-0.684548\pi$
$181$	−8.74090e7	−1.09567	−0.547837	+	0.836585i	$0.684548\pi$
$182$	−3.06418e6	−0.0376760
$183$	−6.55048e7	−0.790122
$184$	9.27042e6	0.109708
$185$	−2.14735e8	−2.49346
$186$	8.89259e6	0.101329
$187$	−5.20901e6	−0.0582519
$188$	1.51285e8	1.66051
$189$	4.38872e6	0.0472848
$190$	−3.47330e8	−3.67371
$191$	2.62452e7	0.272542	0.136271	−	0.990672i	$-0.456488\pi$
$191$	2.62452e7	0.272542	0.136271	+	0.990672i	$0.456488\pi$
$192$	−3.52514e7	−0.359437
$193$	3.00614e7	0.300995	0.150497	−	0.988610i	$-0.451912\pi$
$193$	3.00614e7	0.300995	0.150497	+	0.988610i	$0.451912\pi$
$194$	−1.74341e8	−1.71433
$195$	9.40853e6	0.0908659
$196$	−2.08937e8	−1.98207
$197$	−6.36038e7	−0.592722	−0.296361	−	0.955076i	$-0.595773\pi$
$197$	−6.36038e7	−0.592722	−0.296361	+	0.955076i	$0.595773\pi$
$198$	2.66383e7	0.243881
$199$	1.34497e8	1.20984	0.604919	−	0.796287i	$-0.293205\pi$
$199$	1.34497e8	1.20984	0.604919	+	0.796287i	$0.293205\pi$
$200$	−5.03637e8	−4.45157
$201$	−7.10906e7	−0.617484
$202$	1.62451e7	0.138673
$203$	2.86531e7	0.240401
$204$	2.07327e7	0.170982
$205$	−6.32361e6	−0.0512656
$206$	2.67396e8	2.13117
$207$	−2.38550e6	−0.0186932
$208$	1.51258e7	0.116545
$209$	−6.30374e7	−0.477624
$210$	−6.07560e7	−0.452712
$211$	1.72469e8	1.26393	0.631965	−	0.774997i	$-0.282249\pi$
$211$	1.72469e8	1.26393	0.631965	+	0.774997i	$0.282249\pi$
$212$	5.51024e8	3.97187
$213$	7.08425e7	0.502302
$214$	1.06972e8	0.746143
$215$	1.71181e8	1.17469
$216$	−5.57621e7	−0.376488
$217$	−3.68101e6	−0.0244544
$218$	−4.71606e7	−0.308306
$219$	8.68754e7	0.558911
$220$	−2.50173e8	−1.58402
$221$	1.95904e6	0.0122088
$222$	2.28653e8	1.40262
$223$	1.98662e8	1.19963	0.599815	−	0.800138i	$-0.295241\pi$
$223$	1.98662e8	1.19963	0.599815	+	0.800138i	$0.295241\pi$
$224$	−1.68207e7	−0.0999947
$225$	1.29598e8	0.758505
$226$	−2.52404e8	−1.45451
$227$	−1.97341e8	−1.11977	−0.559884	−	0.828571i	$-0.689154\pi$
$227$	−1.97341e8	−1.11977	−0.559884	+	0.828571i	$0.689154\pi$
$228$	2.50899e8	1.40193
$229$	2.77784e8	1.52856	0.764281	−	0.644883i	$-0.223094\pi$
$229$	2.77784e8	1.52856	0.764281	+	0.644883i	$0.223094\pi$
$230$	3.30241e7	0.178971
$231$	−1.10267e7	−0.0588576
$232$	−3.64060e8	−1.91410
$233$	3.29662e8	1.70735	0.853677	−	0.520803i	$-0.174367\pi$
$233$	3.29662e8	1.70735	0.853677	+	0.520803i	$0.174367\pi$
$234$	−1.00183e7	−0.0511140
$235$	2.83438e8	1.42469
$236$	5.54534e7	0.274622
$237$	9.25885e7	0.451791
$238$	−1.26506e7	−0.0608264
$239$	3.52106e8	1.66833	0.834163	−	0.551518i	$-0.185951\pi$
$239$	3.52106e8	1.66833	0.834163	+	0.551518i	$0.185951\pi$
$240$	2.99911e8	1.40040
$241$	−1.57129e8	−0.723097	−0.361549	−	0.932353i	$-0.617752\pi$
$241$	−1.57129e8	−0.723097	−0.361549	+	0.932353i	$0.617752\pi$
$242$	3.21841e8	1.45978
$243$	1.43489e7	0.0641500
$244$	−6.55060e8	−2.88680
$245$	−3.91452e8	−1.70058
$246$	6.73346e6	0.0288380
$247$	2.37076e7	0.100103
$248$	4.67701e7	0.194710
$249$	3.24985e7	0.133403
$250$	−1.00567e9	−4.07066
$251$	−2.31577e8	−0.924353	−0.462177	−	0.886788i	$-0.652931\pi$
$251$	−2.31577e8	−0.924353	−0.462177	+	0.886788i	$0.652931\pi$
$252$	4.38880e7	0.172760
$253$	5.99358e6	0.0232683
$254$	5.88304e8	2.25260
$255$	3.88436e7	0.146700
$256$	−5.45164e8	−2.03089
$257$	3.21230e8	1.18046	0.590228	−	0.807237i	$-0.299038\pi$
$257$	3.21230e8	1.18046	0.590228	+	0.807237i	$0.299038\pi$
$258$	−1.82276e8	−0.660786
$259$	−9.46487e7	−0.338505
$260$	9.40871e7	0.331989
$261$	9.36813e7	0.326145
$262$	−5.60078e8	−1.92395
$263$	3.68323e8	1.24849	0.624243	−	0.781230i	$-0.285408\pi$
$263$	3.68323e8	1.24849	0.624243	+	0.781230i	$0.285408\pi$
$264$	1.40103e8	0.468633
$265$	1.03237e9	3.40779
$266$	−1.53093e8	−0.498733
$267$	−6.77277e7	−0.217759
$268$	−7.10919e8	−2.25605
$269$	−2.17400e8	−0.680967	−0.340484	−	0.940250i	$-0.610591\pi$
$269$	−2.17400e8	−0.680967	−0.340484	+	0.940250i	$0.610591\pi$
$270$	−1.98642e8	−0.614182
$271$	1.69294e8	0.516713	0.258356	−	0.966050i	$-0.416819\pi$
$271$	1.69294e8	0.516713	0.258356	+	0.966050i	$0.416819\pi$
$272$	6.24474e7	0.188158
$273$	4.14700e6	0.0123357
$274$	1.02307e9	3.00454
$275$	−3.25615e8	−0.944148
$276$	−2.38554e7	−0.0682976
$277$	5.18960e6	0.0146708	0.00733541	−	0.999973i	$-0.497665\pi$
$277$	5.18960e6	0.0146708	0.00733541	+	0.999973i	$0.497665\pi$
$278$	−7.74162e7	−0.216110
$279$	−1.20351e7	−0.0331767
$280$	−3.19543e8	−0.869913
$281$	−4.92517e8	−1.32419	−0.662093	−	0.749421i	$-0.730332\pi$
$281$	−4.92517e8	−1.32419	−0.662093	+	0.749421i	$0.730332\pi$
$282$	−3.01808e8	−0.801418
$283$	−5.84814e8	−1.53379	−0.766893	−	0.641775i	$-0.778198\pi$
$283$	−5.84814e8	−1.53379	−0.766893	+	0.641775i	$0.778198\pi$
$284$	7.08438e8	1.83522
$285$	4.70070e8	1.20283
$286$	2.51711e7	0.0636240
$287$	−2.78725e6	−0.00695969
$288$	−5.49954e7	−0.135660
$289$	−4.02251e8	−0.980289
$290$	−1.29689e9	−3.12256
$291$	2.35950e8	0.561299
$292$	8.68770e8	2.04204
$293$	6.94020e8	1.61189	0.805945	−	0.591990i	$-0.201658\pi$
$293$	6.94020e8	1.61189	0.805945	+	0.591990i	$0.201658\pi$
$294$	4.16823e8	0.956613
$295$	1.03894e8	0.235621
$296$	1.20259e9	2.69523
$297$	−3.60517e7	−0.0798506
$298$	6.76281e7	0.148037
$299$	−2.25411e6	−0.00487670
$300$	1.29600e9	2.77128
$301$	7.54515e7	0.159472
$302$	−9.97480e8	−2.08391
$303$	−2.19858e7	−0.0454038
$304$	7.55714e8	1.54276
$305$	−1.22728e9	−2.47682
$306$	−4.13611e7	−0.0825216
$307$	6.33917e8	1.25040	0.625199	−	0.780465i	$-0.285018\pi$
$307$	6.33917e8	1.25040	0.625199	+	0.780465i	$0.285018\pi$
$308$	−1.10269e8	−0.215043
$309$	−3.61888e8	−0.697781
$310$	1.66609e8	0.317639
$311$	−2.89601e8	−0.545932	−0.272966	−	0.962024i	$-0.588005\pi$
$311$	−2.89601e8	−0.545932	−0.272966	+	0.962024i	$0.588005\pi$
$312$	−5.26908e7	−0.0982186
$313$	5.90653e8	1.08875	0.544374	−	0.838843i	$-0.316767\pi$
$313$	5.90653e8	1.08875	0.544374	+	0.838843i	$0.316767\pi$
$314$	9.50530e8	1.73265
$315$	8.22259e7	0.148225
$316$	9.25902e8	1.65067
$317$	−9.69791e8	−1.70990	−0.854950	−	0.518710i	$-0.826413\pi$
$317$	−9.69791e8	−1.70990	−0.854950	+	0.518710i	$0.826413\pi$
$318$	−1.09928e9	−1.91695
$319$	−2.35375e8	−0.405969
$320$	−6.60462e8	−1.12674
$321$	−1.44774e8	−0.244299
$322$	1.45560e7	0.0242967
$323$	9.78778e7	0.161613
$324$	1.43492e8	0.234379
$325$	1.22460e8	0.197880
$326$	−1.52433e9	−2.43679
$327$	6.38262e7	0.100944
$328$	3.54142e7	0.0554140
$329$	1.24931e8	0.193412
$330$	4.99088e8	0.764502
$331$	−1.23241e9	−1.86792	−0.933959	−	0.357381i	$-0.883670\pi$
$331$	−1.23241e9	−1.86792	−0.933959	+	0.357381i	$0.883670\pi$
$332$	3.24991e8	0.487402
$333$	−3.09454e8	−0.459241
$334$	1.37947e8	0.202582
$335$	−1.33194e9	−1.93565
$336$	1.32192e8	0.190115
$337$	3.81254e8	0.542638	0.271319	−	0.962490i	$-0.412540\pi$
$337$	3.81254e8	0.542638	0.271319	+	0.962490i	$0.412540\pi$
$338$	1.24237e9	1.75002
$339$	3.41599e8	0.476230
$340$	3.88443e8	0.535983
$341$	3.02381e7	0.0412966
$342$	−5.00536e8	−0.676619
$343$	−3.56166e8	−0.476566
$344$	−9.58671e8	−1.26974
$345$	−4.46941e7	−0.0585981
$346$	−1.90400e9	−2.47115
$347$	−2.23058e7	−0.0286592	−0.0143296	−	0.999897i	$-0.504561\pi$
$347$	−2.23058e7	−0.0286592	−0.0143296	+	0.999897i	$0.504561\pi$
$348$	9.36830e8	1.19161
$349$	−1.22256e9	−1.53951	−0.769755	−	0.638340i	$-0.779622\pi$
$349$	−1.22256e9	−1.53951	−0.769755	+	0.638340i	$0.779622\pi$
$350$	−7.90789e8	−0.985876
$351$	1.35586e7	0.0167355
$352$	1.38176e8	0.168863
$353$	−1.53975e9	−1.86311	−0.931557	−	0.363595i	$-0.881549\pi$
$353$	−1.53975e9	−1.86311	−0.931557	+	0.363595i	$0.881549\pi$
$354$	−1.10628e8	−0.132542
$355$	1.32729e9	1.57458
$356$	−6.77290e8	−0.795609
$357$	1.71211e7	0.0199155
$358$	−6.50961e8	−0.749832
$359$	−6.36027e7	−0.0725513	−0.0362757	−	0.999342i	$-0.511549\pi$
$359$	−6.36027e7	−0.0725513	−0.0362757	+	0.999342i	$0.511549\pi$
$360$	−1.04474e9	−1.18019
$361$	2.90606e8	0.325110
$362$	1.74381e9	1.93206
$363$	−4.35573e8	−0.477956
$364$	4.14707e7	0.0450699
$365$	1.62768e9	1.75204
$366$	1.30682e9	1.39326
$367$	2.43871e8	0.257531	0.128765	−	0.991675i	$-0.458899\pi$
$367$	2.43871e8	0.257531	0.128765	+	0.991675i	$0.458899\pi$
$368$	−7.18531e7	−0.0751585
$369$	−9.11292e6	−0.00944203
$370$	4.28398e9	4.39685
$371$	4.55035e8	0.462633
$372$	−1.20353e8	−0.121215
$373$	−5.36181e8	−0.534972	−0.267486	−	0.963562i	$-0.586193\pi$
$373$	−5.36181e8	−0.534972	−0.267486	+	0.963562i	$0.586193\pi$
$374$	1.03920e8	0.102719
$375$	1.36105e9	1.33280
$376$	−1.58734e9	−1.53997
$377$	8.85215e7	0.0850852
$378$	−8.75552e7	−0.0833798
$379$	−9.43440e8	−0.890178	−0.445089	−	0.895486i	$-0.646828\pi$
$379$	−9.43440e8	−0.890178	−0.445089	+	0.895486i	$0.646828\pi$
$380$	4.70078e9	4.39468
$381$	−7.96198e8	−0.737537
$382$	−5.23593e8	−0.480587
$383$	7.47419e8	0.679780	0.339890	−	0.940465i	$-0.389610\pi$
$383$	7.47419e8	0.679780	0.339890	+	0.940465i	$0.389610\pi$
$384$	9.63987e8	0.868784
$385$	−2.06593e8	−0.184503
$386$	−5.99727e8	−0.530760
$387$	2.46689e8	0.216352
$388$	2.35954e9	2.05077
$389$	5.07334e8	0.436989	0.218494	−	0.975838i	$-0.429885\pi$
$389$	5.07334e8	0.436989	0.218494	+	0.975838i	$0.429885\pi$
$390$	−1.87701e8	−0.160229
$391$	−9.30620e6	−0.00787324
$392$	2.19226e9	1.83819
$393$	7.57997e8	0.629932
$394$	1.26890e9	1.04518
$395$	1.73471e9	1.41624
$396$	−3.60524e8	−0.291743
$397$	3.30439e8	0.265048	0.132524	−	0.991180i	$-0.457692\pi$
$397$	3.30439e8	0.265048	0.132524	+	0.991180i	$0.457692\pi$
$398$	−2.68323e9	−2.13337
$399$	2.07192e8	0.163293
$400$	3.90359e9	3.04968
$401$	−8.76898e8	−0.679116	−0.339558	−	0.940585i	$-0.610277\pi$
$401$	−8.76898e8	−0.679116	−0.339558	+	0.940585i	$0.610277\pi$
$402$	1.41826e9	1.08884
$403$	−1.13722e7	−0.00865518
$404$	−2.19862e8	−0.165888
$405$	2.68838e8	0.201093
$406$	−5.71631e8	−0.423911
$407$	7.77505e8	0.571640
$408$	−2.17537e8	−0.158570
$409$	1.20367e9	0.869915	0.434958	−	0.900451i	$-0.356763\pi$
$409$	1.20367e9	0.869915	0.434958	+	0.900451i	$0.356763\pi$
$410$	1.26156e8	0.0903994
$411$	−1.38460e9	−0.983734
$412$	−3.61894e9	−2.54942
$413$	4.57934e7	0.0319873
$414$	4.75908e7	0.0329627
$415$	6.08883e8	0.418182
$416$	−5.19663e7	−0.0353912
$417$	1.04774e8	0.0707580
$418$	1.25760e9	0.842220
$419$	1.30342e9	0.865638	0.432819	−	0.901481i	$-0.357519\pi$
$419$	1.30342e9	0.865638	0.432819	+	0.901481i	$0.357519\pi$
$420$	8.22275e8	0.541557
$421$	−2.37970e9	−1.55430	−0.777150	−	0.629315i	$-0.783336\pi$
$421$	−2.37970e9	−1.55430	−0.777150	+	0.629315i	$0.783336\pi$
$422$	−3.44077e9	−2.22875
$423$	4.08461e8	0.262397
$424$	−5.78158e9	−3.68355
$425$	5.05581e8	0.319470
$426$	−1.41331e9	−0.885736
$427$	−5.40948e8	−0.336247
$428$	−1.44776e9	−0.892574
$429$	−3.40660e7	−0.0208315
$430$	−3.41508e9	−2.07139
$431$	1.38543e9	0.833515	0.416758	−	0.909018i	$-0.363166\pi$
$431$	1.38543e9	0.833515	0.416758	+	0.909018i	$0.363166\pi$
$432$	4.32200e8	0.257924
$433$	2.85632e9	1.69082	0.845412	−	0.534114i	$-0.179355\pi$
$433$	2.85632e9	1.69082	0.845412	+	0.534114i	$0.179355\pi$
$434$	7.34364e7	0.0431218
$435$	1.75519e9	1.02238
$436$	6.38274e8	0.368811
$437$	−1.12620e8	−0.0645550
$438$	−1.73317e9	−0.985557
$439$	−3.08827e9	−1.74217	−0.871083	−	0.491137i	$-0.836582\pi$
$439$	−3.08827e9	−1.74217	−0.871083	+	0.491137i	$0.836582\pi$
$440$	2.62493e9	1.46904
$441$	−5.64120e8	−0.313211
$442$	−3.90830e7	−0.0215283
$443$	2.10701e9	1.15147	0.575737	−	0.817635i	$-0.304715\pi$
$443$	2.10701e9	1.15147	0.575737	+	0.817635i	$0.304715\pi$
$444$	−3.09460e9	−1.67789
$445$	−1.26893e9	−0.682618
$446$	−3.96332e9	−2.11537
$447$	−9.15264e7	−0.0484697
$448$	−2.91112e8	−0.152963
$449$	−5.27169e8	−0.274845	−0.137422	−	0.990513i	$-0.543882\pi$
$449$	−5.27169e8	−0.274845	−0.137422	+	0.990513i	$0.543882\pi$
$450$	−2.58548e9	−1.33751
$451$	2.28963e7	0.0117529
$452$	3.41605e9	1.73996
$453$	1.34997e9	0.682307
$454$	3.93697e9	1.97454
$455$	7.76971e7	0.0386692
$456$	−2.63254e9	−1.30016
$457$	1.47995e9	0.725337	0.362668	−	0.931918i	$-0.381866\pi$
$457$	1.47995e9	0.725337	0.362668	+	0.931918i	$0.381866\pi$
$458$	−5.54181e9	−2.69540
$459$	5.59773e7	0.0270189
$460$	−4.46949e8	−0.214095
$461$	−3.37266e9	−1.60332	−0.801658	−	0.597783i	$-0.796048\pi$
$461$	−3.37266e9	−1.60332	−0.801658	+	0.597783i	$0.796048\pi$
$462$	2.19983e8	0.103787
$463$	−2.58669e9	−1.21119	−0.605593	−	0.795774i	$-0.707064\pi$
$463$	−2.58669e9	−1.21119	−0.605593	+	0.795774i	$0.707064\pi$
$464$	2.82175e9	1.31131
$465$	−2.25486e8	−0.104000
$466$	−6.57678e9	−3.01067
$467$	−7.12728e8	−0.323828	−0.161914	−	0.986805i	$-0.551767\pi$
$467$	−7.12728e8	−0.323828	−0.161914	+	0.986805i	$0.551767\pi$
$468$	1.35588e8	0.0611452
$469$	−5.87077e8	−0.262778
$470$	−5.65460e9	−2.51223
$471$	−1.28643e9	−0.567299
$472$	−5.81840e8	−0.254687
$473$	−6.19807e8	−0.269304
$474$	−1.84715e9	−0.796667
$475$	6.11834e9	2.61942
$476$	1.71214e8	0.0727637
$477$	1.48774e9	0.627642
$478$	−7.02454e9	−2.94185
$479$	−1.28719e9	−0.535140	−0.267570	−	0.963538i	$-0.586221\pi$
$479$	−1.28719e9	−0.535140	−0.267570	+	0.963538i	$0.586221\pi$
$480$	−1.03038e9	−0.425258
$481$	−2.92410e8	−0.119807
$482$	3.13473e9	1.27508
$483$	−1.96998e7	−0.00795512
$484$	−4.35582e9	−1.74627
$485$	4.42069e9	1.75952
$486$	−2.86262e8	−0.113119
$487$	−4.87502e8	−0.191260	−0.0956301	−	0.995417i	$-0.530487\pi$
$487$	−4.87502e8	−0.191260	−0.0956301	+	0.995417i	$0.530487\pi$
$488$	6.87317e9	2.67724
$489$	2.06300e9	0.797843
$490$	7.80950e9	2.99873
$491$	−5.36881e8	−0.204688	−0.102344	−	0.994749i	$-0.532634\pi$
$491$	−5.36881e8	−0.204688	−0.102344	+	0.994749i	$0.532634\pi$
$492$	−9.11309e7	−0.0344975
$493$	3.65465e8	0.137367
$494$	−4.72967e8	−0.176517
$495$	−6.75456e8	−0.250310
$496$	−3.62505e8	−0.133392
$497$	5.85028e8	0.213761
$498$	−6.48346e8	−0.235236
$499$	−4.34284e8	−0.156467	−0.0782334	−	0.996935i	$-0.524928\pi$
$499$	−4.34284e8	−0.156467	−0.0782334	+	0.996935i	$0.524928\pi$
$500$	1.36108e10	4.86954
$501$	−1.86695e8	−0.0663286
$502$	4.61998e9	1.62996
$503$	−3.59458e9	−1.25939	−0.629696	−	0.776842i	$-0.716820\pi$
$503$	−3.59458e9	−1.25939	−0.629696	+	0.776842i	$0.716820\pi$
$504$	−4.60492e8	−0.160219
$505$	−4.11920e8	−0.142329
$506$	−1.19572e8	−0.0410302
$507$	−1.68140e9	−0.572984
$508$	−7.96213e9	−2.69467
$509$	−3.79038e9	−1.27400	−0.637002	−	0.770862i	$-0.719826\pi$
$509$	−3.79038e9	−1.27400	−0.637002	+	0.770862i	$0.719826\pi$
$510$	−7.74932e8	−0.258683
$511$	7.17430e8	0.237852
$512$	6.30604e9	2.07640
$513$	6.77415e8	0.221536
$514$	−6.40855e9	−2.08156
$515$	−6.78024e9	−2.18736
$516$	2.46693e9	0.790466
$517$	−1.02626e9	−0.326619
$518$	1.88825e9	0.596905
$519$	2.57683e9	0.809096
$520$	−9.87202e8	−0.307889
$521$	2.93658e9	0.909724	0.454862	−	0.890562i	$-0.349688\pi$
$521$	2.93658e9	0.909724	0.454862	+	0.890562i	$0.349688\pi$
$522$	−1.86895e9	−0.575109
$523$	2.13933e8	0.0653917	0.0326959	−	0.999465i	$-0.489591\pi$
$523$	2.13933e8	0.0653917	0.0326959	+	0.999465i	$0.489591\pi$
$524$	7.58011e9	2.30153
$525$	1.07024e9	0.322792
$526$	−7.34806e9	−2.20152
$527$	−4.69506e7	−0.0139735
$528$	−1.08591e9	−0.321051
$529$	−3.39412e9	−0.996855
$530$	−2.05958e10	−6.00914
$531$	1.49721e8	0.0433963
$532$	2.07196e9	0.596611
$533$	−8.61100e6	−0.00246325
$534$	1.35117e9	0.383987
$535$	−2.71244e9	−0.765813
$536$	7.45927e9	2.09228
$537$	8.80997e8	0.245507
$538$	4.33714e9	1.20079
$539$	1.41736e9	0.389868
$540$	2.68843e9	0.734716
$541$	2.06559e9	0.560860	0.280430	−	0.959874i	$-0.409523\pi$
$541$	2.06559e9	0.560860	0.280430	+	0.959874i	$0.409523\pi$
$542$	−3.37743e9	−0.911147
$543$	−2.36004e9	−0.632587
$544$	−2.14545e8	−0.0571378
$545$	1.19583e9	0.316433
$546$	−8.27328e7	−0.0217522
$547$	2.12658e9	0.555555	0.277777	−	0.960645i	$-0.410402\pi$
$547$	2.12658e9	0.555555	0.277777	+	0.960645i	$0.410402\pi$
$548$	−1.38463e10	−3.59418
$549$	−1.76863e9	−0.456177
$550$	6.49604e9	1.66487
$551$	4.42271e9	1.12631
$552$	2.50301e8	0.0633398
$553$	7.64609e8	0.192266
$554$	−1.03533e8	−0.0258698
$555$	−5.79785e9	−1.43960
$556$	1.04775e9	0.258522
$557$	3.52559e9	0.864448	0.432224	−	0.901766i	$-0.357729\pi$
$557$	3.52559e9	0.864448	0.432224	+	0.901766i	$0.357729\pi$
$558$	2.40100e8	0.0585022
$559$	2.33101e8	0.0564422
$560$	2.47671e9	0.595960
$561$	−1.40643e8	−0.0336317
$562$	9.82575e9	2.33501
$563$	3.62920e9	0.857100	0.428550	−	0.903518i	$-0.359025\pi$
$563$	3.62920e9	0.857100	0.428550	+	0.903518i	$0.359025\pi$
$564$	4.08469e9	0.958698
$565$	6.40011e9	1.49285
$566$	1.16671e10	2.70461
$567$	1.18495e8	0.0272999
$568$	−7.43323e9	−1.70200
$569$	−1.16789e9	−0.265772	−0.132886	−	0.991131i	$-0.542424\pi$
$569$	−1.16789e9	−0.265772	−0.132886	+	0.991131i	$0.542424\pi$
$570$	−9.37792e9	−2.12102
$571$	4.02884e8	0.0905635	0.0452818	−	0.998974i	$-0.485581\pi$
$571$	4.02884e8	0.0905635	0.0452818	+	0.998974i	$0.485581\pi$
$572$	−3.40667e8	−0.0761103
$573$	7.08620e8	0.157352
$574$	5.56059e7	0.0122724
$575$	−5.81730e8	−0.127610
$576$	−9.51789e8	−0.207521
$577$	3.29893e9	0.714921	0.357461	−	0.933928i	$-0.383643\pi$
$577$	3.29893e9	0.714921	0.357461	+	0.933928i	$0.383643\pi$
$578$	8.02493e9	1.72860
$579$	8.11658e8	0.173779
$580$	1.75522e10	3.73537
$581$	2.68377e8	0.0567713
$582$	−4.70721e9	−0.989768
$583$	−3.73795e9	−0.781256
$584$	−9.11551e9	−1.89381
$585$	2.54030e8	0.0524614
$586$	−1.38457e10	−2.84233
$587$	4.64184e9	0.947233	0.473617	−	0.880731i	$-0.342948\pi$
$587$	4.64184e9	0.947233	0.473617	+	0.880731i	$0.342948\pi$
$588$	−5.64131e9	−1.14435
$589$	−5.68177e8	−0.114572
$590$	−2.07269e9	−0.415483
$591$	−1.71730e9	−0.342208
$592$	−9.32099e9	−1.84644
$593$	−4.01516e7	−0.00790699	−0.00395349	−	0.999992i	$-0.501258\pi$
$593$	−4.01516e7	−0.00790699	−0.00395349	+	0.999992i	$0.501258\pi$
$594$	7.19234e8	0.140805
$595$	3.20776e8	0.0624299
$596$	−9.15281e8	−0.177089
$597$	3.63142e9	0.698500
$598$	4.49696e7	0.00859934
$599$	6.08823e9	1.15744	0.578719	−	0.815527i	$-0.303553\pi$
$599$	6.08823e9	1.15744	0.578719	+	0.815527i	$0.303553\pi$
$600$	−1.35982e10	−2.57011
$601$	8.96979e9	1.68547	0.842736	−	0.538327i	$-0.180944\pi$
$601$	8.96979e9	1.68547	0.842736	+	0.538327i	$0.180944\pi$
$602$	−1.50526e9	−0.281206
$603$	−1.91945e9	−0.356505
$604$	1.34999e10	2.49289
$605$	−8.16080e9	−1.49827
$606$	4.38618e8	0.0800630
$607$	2.86102e9	0.519230	0.259615	−	0.965712i	$-0.416404\pi$
$607$	2.86102e9	0.519230	0.259615	+	0.965712i	$0.416404\pi$
$608$	−2.59634e9	−0.468489
$609$	7.73634e8	0.138795
$610$	2.44843e10	4.36751
$611$	3.85964e8	0.0684545
$612$	5.59784e8	0.0987166
$613$	−2.84576e9	−0.498984	−0.249492	−	0.968377i	$-0.580264\pi$
$613$	−2.84576e9	−0.498984	−0.249492	+	0.968377i	$0.580264\pi$
$614$	−1.26467e10	−2.20489
$615$	−1.70737e8	−0.0295982
$616$	1.15699e9	0.199433
$617$	−9.53360e9	−1.63403	−0.817013	−	0.576619i	$-0.804372\pi$
$617$	−9.53360e9	−1.63403	−0.817013	+	0.576619i	$0.804372\pi$
$618$	7.21968e9	1.23043
$619$	4.09983e9	0.694783	0.347391	−	0.937720i	$-0.387068\pi$
$619$	4.09983e9	0.694783	0.347391	+	0.937720i	$0.387068\pi$
$620$	−2.25490e9	−0.379976
$621$	−6.44085e7	−0.0107925
$622$	5.77756e9	0.962672
$623$	−5.59306e8	−0.0926704
$624$	4.08395e8	0.0672876
$625$	1.16117e10	1.90246
$626$	−1.17836e10	−1.91985
$627$	−1.70201e9	−0.275756
$628$	−1.28645e10	−2.07269
$629$	−1.20723e9	−0.193425
$630$	−1.64041e9	−0.261373
$631$	−1.39182e9	−0.220536	−0.110268	−	0.993902i	$-0.535171\pi$
$631$	−1.39182e9	−0.220536	−0.110268	+	0.993902i	$0.535171\pi$
$632$	−9.71496e9	−1.53085
$633$	4.65667e9	0.729730
$634$	1.93474e10	3.01516
$635$	−1.49174e10	−2.31198
$636$	1.48777e10	2.29316
$637$	−5.33049e8	−0.0817108
$638$	4.69574e9	0.715866
$639$	1.91275e9	0.290004
$640$	1.80610e10	2.72341
$641$	−5.13220e9	−0.769663	−0.384832	−	0.922987i	$-0.625740\pi$
$641$	−5.13220e9	−0.769663	−0.384832	+	0.922987i	$0.625740\pi$
$642$	2.88824e9	0.430786
$643$	−3.56886e9	−0.529408	−0.264704	−	0.964330i	$-0.585274\pi$
$643$	−3.56886e9	−0.529408	−0.264704	+	0.964330i	$0.585274\pi$
$644$	−1.97002e8	−0.0290649
$645$	4.62190e9	0.678205
$646$	−1.95267e9	−0.284980
$647$	−7.81292e9	−1.13409	−0.567046	−	0.823686i	$-0.691914\pi$
$647$	−7.81292e9	−1.13409	−0.567046	+	0.823686i	$0.691914\pi$
$648$	−1.50558e9	−0.217365
$649$	−3.76176e8	−0.0540175
$650$	−2.44308e9	−0.348932
$651$	−9.93872e7	−0.0141188
$652$	2.06304e10	2.91501
$653$	−8.76103e9	−1.23129	−0.615643	−	0.788025i	$-0.711104\pi$
$653$	−8.76103e9	−1.23129	−0.615643	+	0.788025i	$0.711104\pi$
$654$	−1.27334e9	−0.178000
$655$	1.42016e10	1.97467
$656$	−2.74488e8	−0.0379630
$657$	2.34564e9	0.322687
$658$	−2.49238e9	−0.341054
$659$	−1.26819e10	−1.72618	−0.863089	−	0.505052i	$-0.831473\pi$
$659$	−1.26819e10	−1.72618	−0.863089	+	0.505052i	$0.831473\pi$
$660$	−6.75468e9	−0.914537
$661$	−1.96990e9	−0.265301	−0.132651	−	0.991163i	$-0.542349\pi$
$661$	−1.96990e9	−0.265301	−0.132651	+	0.991163i	$0.542349\pi$
$662$	2.45867e10	3.29380
$663$	5.28942e7	0.00704873
$664$	−3.40994e9	−0.452021
$665$	3.88190e9	0.511881
$666$	6.17362e9	0.809805
$667$	−4.20511e8	−0.0548702
$668$	−1.86699e9	−0.242339
$669$	5.36387e9	0.692607
$670$	2.65722e10	3.41323
$671$	4.44369e9	0.567825
$672$	−4.54160e8	−0.0577320
$673$	8.38158e9	1.05992	0.529960	−	0.848023i	$-0.322207\pi$
$673$	8.38158e9	1.05992	0.529960	+	0.848023i	$0.322207\pi$
$674$	−7.60605e9	−0.956862
$675$	3.49914e9	0.437923
$676$	−1.68143e10	−2.09346
$677$	8.10465e9	1.00386	0.501931	−	0.864908i	$-0.332623\pi$
$677$	8.10465e9	1.00386	0.501931	+	0.864908i	$0.332623\pi$
$678$	−6.81491e9	−0.839762
$679$	1.94851e9	0.238868
$680$	−4.07571e9	−0.497075
$681$	−5.32822e9	−0.646498
$682$	−6.03253e8	−0.0728206
$683$	8.52346e9	1.02363	0.511816	−	0.859095i	$-0.328973\pi$
$683$	8.52346e9	1.02363	0.511816	+	0.859095i	$0.328973\pi$
$684$	6.77427e9	0.809406
$685$	−2.59415e10	−3.08374
$686$	7.10553e9	0.840353
$687$	7.50017e9	0.882516
$688$	7.43046e9	0.869873
$689$	1.40580e9	0.163740
$690$	8.91650e8	0.103329
$691$	−6.80331e9	−0.784417	−0.392208	−	0.919876i	$-0.628289\pi$
$691$	−6.80331e9	−0.784417	−0.392208	+	0.919876i	$0.628289\pi$
$692$	2.57688e10	2.95612
$693$	−2.97720e8	−0.0339815
$694$	4.45001e8	0.0505362
$695$	1.96301e9	0.221807
$696$	−9.82962e9	−1.10511
$697$	−3.55509e7	−0.00397682
$698$	2.43902e10	2.71470
$699$	8.90088e9	0.985741
$700$	1.07026e10	1.17936
$701$	−1.06363e9	−0.116621	−0.0583106	−	0.998298i	$-0.518571\pi$
$701$	−1.06363e9	−0.116621	−0.0583106	+	0.998298i	$0.518571\pi$
$702$	−2.70495e8	−0.0295107
$703$	−1.46094e10	−1.58595
$704$	2.39138e9	0.258311
$705$	7.65282e9	0.822545
$706$	3.07182e10	3.28533
$707$	−1.81562e8	−0.0193222
$708$	1.49724e9	0.158553
$709$	1.77993e10	1.87561	0.937803	−	0.347168i	$-0.112857\pi$
$709$	1.77993e10	1.87561	0.937803	+	0.347168i	$0.112857\pi$
$710$	−2.64794e10	−2.77655
$711$	2.49989e9	0.260842
$712$	7.10641e9	0.737854
$713$	5.40222e7	0.00558160
$714$	−3.41567e8	−0.0351181
$715$	−6.38253e8	−0.0653013
$716$	8.81013e9	0.896988
$717$	9.50686e9	0.963208
$718$	1.26888e9	0.127934
$719$	−1.95303e10	−1.95956	−0.979780	−	0.200078i	$-0.935880\pi$
$719$	−1.95303e10	−1.95956	−0.979780	+	0.200078i	$0.935880\pi$
$720$	8.09760e9	0.808523
$721$	−2.98852e9	−0.296950
$722$	−5.79761e9	−0.573283
$723$	−4.24248e9	−0.417480
$724$	−2.36009e10	−2.31123
$725$	2.28452e10	2.22645
$726$	8.68972e9	0.842806
$727$	−1.51589e10	−1.46317	−0.731587	−	0.681748i	$-0.761220\pi$
$727$	−1.51589e10	−1.46317	−0.731587	+	0.681748i	$0.761220\pi$
$728$	−4.35129e8	−0.0417982
$729$	3.87420e8	0.0370370
$730$	−3.24723e10	−3.08946
$731$	9.62371e8	0.0911238
$732$	−1.76866e10	−1.66669
$733$	1.19810e7	0.00112365	0.000561823	−	1.00000i	$-0.499821\pi$
$733$	1.19810e7	0.00112365	0.000561823		1.00000i	$0.499821\pi$
$734$	−4.86524e9	−0.454118
$735$	−1.05692e10	−0.981832
$736$	2.46860e8	0.0228233
$737$	4.82262e9	0.443758
$738$	1.81803e8	0.0166496
$739$	−1.13380e10	−1.03343	−0.516715	−	0.856158i	$-0.672845\pi$
$739$	−1.13380e10	−1.03343	−0.516715	+	0.856158i	$0.672845\pi$
$740$	−5.79796e10	−5.25974
$741$	6.40104e8	0.0577946
$742$	−9.07799e9	−0.815785
$743$	−2.12227e10	−1.89819	−0.949096	−	0.314987i	$-0.898000\pi$
$743$	−2.12227e10	−1.89819	−0.949096	+	0.314987i	$0.898000\pi$
$744$	1.26279e9	0.112416
$745$	−1.71482e9	−0.151939
$746$	1.06969e10	0.943344
$747$	8.77458e8	0.0770202
$748$	−1.40646e9	−0.122877
$749$	−1.19556e9	−0.103965
$750$	−2.71531e10	−2.35020
$751$	−2.06229e10	−1.77669	−0.888343	−	0.459181i	$-0.848143\pi$
$751$	−2.06229e10	−1.77669	−0.888343	+	0.459181i	$0.848143\pi$
$752$	1.23032e10	1.05500
$753$	−6.25259e9	−0.533676
$754$	−1.76601e9	−0.150035
$755$	2.52927e10	2.13885
$756$	1.18498e9	0.0997432
$757$	−2.12910e10	−1.78386	−0.891929	−	0.452175i	$-0.850648\pi$
$757$	−2.12910e10	−1.78386	−0.891929	+	0.452175i	$0.850648\pi$
$758$	1.88217e10	1.56970
$759$	1.61827e8	0.0134340
$760$	−4.93226e10	−4.07567
$761$	−4.78297e9	−0.393415	−0.196708	−	0.980462i	$-0.563025\pi$
$761$	−4.78297e9	−0.393415	−0.196708	+	0.980462i	$0.563025\pi$
$762$	1.58842e10	1.30054
$763$	5.27086e8	0.0429582
$764$	7.08633e9	0.574903
$765$	1.04878e9	0.0846970
$766$	−1.49111e10	−1.19869
$767$	1.41475e8	0.0113213
$768$	−1.47194e10	−1.17254
$769$	−7.38239e9	−0.585403	−0.292702	−	0.956204i	$-0.594554\pi$
$769$	−7.38239e9	−0.585403	−0.292702	+	0.956204i	$0.594554\pi$
$770$	4.12155e9	0.325344
$771$	8.67320e9	0.681536
$772$	8.11673e9	0.634922
$773$	−1.10993e10	−0.864305	−0.432153	−	0.901801i	$-0.642246\pi$
$773$	−1.10993e10	−0.864305	−0.432153	+	0.901801i	$0.642246\pi$
$774$	−4.92145e9	−0.381505
$775$	−2.93488e9	−0.226482
$776$	−2.47573e10	−1.90190
$777$	−2.55552e9	−0.195436
$778$	−1.01213e10	−0.770566
$779$	−4.30223e8	−0.0326071
$780$	2.54035e9	0.191674
$781$	−4.80579e9	−0.360982
$782$	1.85659e8	0.0138833
$783$	2.52939e9	0.188300
$784$	−1.69917e10	−1.25931
$785$	−2.41022e10	−1.77833
$786$	−1.51221e10	−1.11079
$787$	2.48619e10	1.81812	0.909060	−	0.416666i	$-0.136801\pi$
$787$	2.48619e10	1.81812	0.909060	+	0.416666i	$0.136801\pi$
$788$	−1.71733e10	−1.25030
$789$	9.94472e9	0.720813
$790$	−3.46077e10	−2.49734
$791$	2.82097e9	0.202666
$792$	3.78277e9	0.270565
$793$	−1.67122e9	−0.119008
$794$	−6.59229e9	−0.467374
$795$	2.78739e10	1.96749
$796$	3.63149e10	2.55205
$797$	−9.78058e9	−0.684322	−0.342161	−	0.939641i	$-0.611159\pi$
$797$	−9.78058e9	−0.684322	−0.342161	+	0.939641i	$0.611159\pi$
$798$	−4.13350e9	−0.287944
$799$	1.59347e9	0.110517
$800$	−1.34112e10	−0.926091
$801$	−1.82865e9	−0.125723
$802$	1.74942e10	1.19752
$803$	−5.89343e9	−0.401665
$804$	−1.91948e10	−1.30253
$805$	−3.69091e8	−0.0249372
$806$	2.26876e8	0.0152621
$807$	−5.86980e9	−0.393157
$808$	2.30688e9	0.153846
$809$	−4.39665e9	−0.291945	−0.145973	−	0.989289i	$-0.546631\pi$
$809$	−4.39665e9	−0.291945	−0.145973	+	0.989289i	$0.546631\pi$
$810$	−5.36333e9	−0.354598
$811$	−9.64279e9	−0.634790	−0.317395	−	0.948293i	$-0.602808\pi$
$811$	−9.64279e9	−0.634790	−0.317395	+	0.948293i	$0.602808\pi$
$812$	7.73648e9	0.507104
$813$	4.57094e9	0.298324
$814$	−1.55113e10	−1.00800
$815$	3.86518e10	2.50103
$816$	1.68608e9	0.108633
$817$	1.16462e10	0.747150
$818$	−2.40133e10	−1.53397
$819$	1.11969e8	0.00712203
$820$	−1.70741e9	−0.108140
$821$	−1.47265e10	−0.928750	−0.464375	−	0.885639i	$-0.653721\pi$
$821$	−1.47265e10	−0.928750	−0.464375	+	0.885639i	$0.653721\pi$
$822$	2.76229e10	1.73467
$823$	−1.30056e10	−0.813264	−0.406632	−	0.913592i	$-0.633297\pi$
$823$	−1.30056e10	−0.813264	−0.406632	+	0.913592i	$0.633297\pi$
$824$	3.79715e10	2.36435
$825$	−8.79161e9	−0.545104
$826$	−9.13580e8	−0.0564049
$827$	2.38555e10	1.46662	0.733312	−	0.679892i	$-0.237974\pi$
$827$	2.38555e10	1.46662	0.733312	+	0.679892i	$0.237974\pi$
$828$	−6.44096e8	−0.0394316
$829$	2.02291e10	1.23321	0.616605	−	0.787273i	$-0.288508\pi$
$829$	2.02291e10	1.23321	0.616605	+	0.787273i	$0.288508\pi$
$830$	−1.21473e10	−0.737403
$831$	1.40119e8	0.00847020
$832$	−8.99366e8	−0.0541383
$833$	−2.20072e9	−0.131919
$834$	−2.09024e9	−0.124771
$835$	−3.49787e9	−0.207922
$836$	−1.70204e10	−1.00751
$837$	−3.24946e8	−0.0191546
$838$	−2.60034e10	−1.52643
$839$	−1.07547e10	−0.628684	−0.314342	−	0.949310i	$-0.601784\pi$
$839$	−1.07547e10	−0.628684	−0.314342	+	0.949310i	$0.601784\pi$
$840$	−8.62766e9	−0.502245
$841$	−7.35941e8	−0.0426635
$842$	4.74752e10	2.74078
$843$	−1.32980e10	−0.764519
$844$	4.65675e10	2.66615
$845$	−3.15023e10	−1.79615
$846$	−8.14882e9	−0.462699
$847$	−3.59703e9	−0.203401
$848$	4.48118e10	2.52352
$849$	−1.57900e10	−0.885532
$850$	−1.00864e10	−0.563338
$851$	1.38906e9	0.0772621
$852$	1.91278e10	1.05956
$853$	3.60150e10	1.98683	0.993417	−	0.114556i	$-0.0365445\pi$
$853$	3.60150e10	1.98683	0.993417	+	0.114556i	$0.0365445\pi$
$854$	1.07919e10	0.592922
$855$	1.26919e10	0.694456
$856$	1.51906e10	0.827781
$857$	−7.43401e9	−0.403450	−0.201725	−	0.979442i	$-0.564655\pi$
$857$	−7.43401e9	−0.403450	−0.201725	+	0.979442i	$0.564655\pi$
$858$	6.79620e8	0.0367333
$859$	−2.19350e10	−1.18076	−0.590380	−	0.807125i	$-0.701022\pi$
$859$	−2.19350e10	−1.18076	−0.590380	+	0.807125i	$0.701022\pi$
$860$	4.62198e10	2.47790
$861$	−7.52558e7	−0.00401818
$862$	−2.76394e10	−1.46978
$863$	2.36338e10	1.25169	0.625843	−	0.779949i	$-0.284755\pi$
$863$	2.36338e10	1.25169	0.625843	+	0.779949i	$0.284755\pi$
$864$	−1.48487e9	−0.0783234
$865$	4.82788e10	2.53630
$866$	−5.69837e10	−2.98152
$867$	−1.08608e10	−0.565970
$868$	−9.93891e8	−0.0515845
$869$	−6.28099e9	−0.324682
$870$	−3.50161e10	−1.80281
$871$	−1.81373e9	−0.0930054
$872$	−6.69704e9	−0.342039
$873$	6.37064e9	0.324066
$874$	2.24677e9	0.113833
$875$	1.12398e10	0.567191
$876$	2.34568e10	1.17897
$877$	−6.10352e9	−0.305550	−0.152775	−	0.988261i	$-0.548821\pi$
$877$	−6.10352e9	−0.305550	−0.152775	+	0.988261i	$0.548821\pi$
$878$	6.16112e10	3.07205
$879$	1.87386e10	0.930625
$880$	−2.03453e10	−1.00641
$881$	7.45828e9	0.367471	0.183735	−	0.982976i	$-0.441181\pi$
$881$	7.45828e9	0.367471	0.183735	+	0.982976i	$0.441181\pi$
$882$	1.12542e10	0.552301
$883$	2.44182e10	1.19358	0.596789	−	0.802398i	$-0.296443\pi$
$883$	2.44182e10	1.19358	0.596789	+	0.802398i	$0.296443\pi$
$884$	5.28952e8	0.0257533
$885$	2.80514e9	0.136036
$886$	−4.20350e10	−2.03046
$887$	−1.25593e10	−0.604272	−0.302136	−	0.953265i	$-0.597700\pi$
$887$	−1.25593e10	−0.604272	−0.302136	+	0.953265i	$0.597700\pi$
$888$	3.24698e10	1.55609
$889$	−6.57512e9	−0.313869
$890$	2.53152e10	1.20370
$891$	−9.73396e8	−0.0461018
$892$	5.36397e10	2.53052
$893$	1.92835e10	0.906163
$894$	1.82596e9	0.0854692
$895$	1.65061e10	0.769600
$896$	7.96075e9	0.369723
$897$	−6.08609e7	−0.00281556
$898$	1.05170e10	0.484648
$899$	−2.12151e9	−0.0973838
$900$	3.49920e10	1.60000
$901$	5.80390e9	0.264352
$902$	−4.56782e8	−0.0207246
$903$	2.03719e9	0.0920714
$904$	−3.58426e10	−1.61365
$905$	−4.42172e10	−1.98299
$906$	−2.69320e10	−1.20315
$907$	−1.35865e10	−0.604618	−0.302309	−	0.953210i	$-0.597758\pi$
$907$	−1.35865e10	−0.604618	−0.302309	+	0.953210i	$0.597758\pi$
$908$	−5.32832e10	−2.36205
$909$	−5.93616e8	−0.0262139
$910$	−1.55006e9	−0.0681874
$911$	2.70365e9	0.118478	0.0592389	−	0.998244i	$-0.481133\pi$
$911$	2.70365e9	0.118478	0.0592389	+	0.998244i	$0.481133\pi$
$912$	2.04043e10	0.890716
$913$	−2.20462e9	−0.0958707
$914$	−2.95251e10	−1.27903
$915$	−3.31366e10	−1.42999
$916$	7.50031e10	3.22437
$917$	6.25965e9	0.268076
$918$	−1.11675e9	−0.0476439
$919$	−1.61178e10	−0.685019	−0.342509	−	0.939514i	$-0.611277\pi$
$919$	−1.61178e10	−0.685019	−0.342509	+	0.939514i	$0.611277\pi$
$920$	4.68958e9	0.198553
$921$	1.71158e10	0.721918
$922$	6.72848e10	2.82721
$923$	1.80740e9	0.0756567
$924$	−2.97726e9	−0.124155
$925$	−7.54637e10	−3.13503
$926$	5.16046e10	2.13575
$927$	−9.77097e9	−0.402864
$928$	−9.69446e9	−0.398204
$929$	−4.59174e10	−1.87898	−0.939491	−	0.342573i	$-0.888702\pi$
$929$	−4.59174e10	−1.87898	−0.939491	+	0.342573i	$0.888702\pi$
$930$	4.49845e9	0.183389
$931$	−2.66322e10	−1.08164
$932$	8.90104e10	3.60152
$933$	−7.81923e9	−0.315194
$934$	1.42190e10	0.571023
$935$	−2.63506e9	−0.105426
$936$	−1.42265e9	−0.0567066
$937$	−2.98124e10	−1.18388	−0.591942	−	0.805981i	$-0.701638\pi$
$937$	−2.98124e10	−1.18388	−0.591942	+	0.805981i	$0.701638\pi$
$938$	1.17122e10	0.463371
$939$	1.59476e10	0.628589
$940$	7.65297e10	3.00526
$941$	−3.77260e10	−1.47597	−0.737983	−	0.674819i	$-0.764222\pi$
$941$	−3.77260e10	−1.47597	−0.737983	+	0.674819i	$0.764222\pi$
$942$	2.56643e10	1.00035
$943$	4.09055e7	0.00158851
$944$	4.50972e9	0.174481
$945$	2.22010e9	0.0855778
$946$	1.23652e10	0.474877
$947$	2.08865e10	0.799173	0.399587	−	0.916695i	$-0.369154\pi$
$947$	2.08865e10	0.799173	0.399587	+	0.916695i	$0.369154\pi$
$948$	2.49993e10	0.953015
$949$	2.21644e9	0.0841831
$950$	−1.22061e11	−4.61897
$951$	−2.61844e10	−0.987212
$952$	−1.79645e9	−0.0674817
$953$	3.06639e9	0.114763	0.0573815	−	0.998352i	$-0.481725\pi$
$953$	3.06639e9	0.114763	0.0573815	+	0.998352i	$0.481725\pi$
$954$	−2.96805e10	−1.10675
$955$	1.32765e10	0.493256
$956$	9.50704e10	3.51919
$957$	−6.35512e9	−0.234386
$958$	2.56795e10	0.943641
$959$	−1.14342e10	−0.418641
$960$	−1.78325e10	−0.650523
$961$	−2.72401e10	−0.990094
$962$	5.83359e9	0.211263
$963$	−3.90889e9	−0.141046
$964$	−4.24256e10	−1.52531
$965$	1.52070e10	0.544752
$966$	3.93012e8	0.0140277
$967$	3.45519e10	1.22880	0.614398	−	0.788997i	$-0.289399\pi$
$967$	3.45519e10	1.22880	0.614398	+	0.788997i	$0.289399\pi$
$968$	4.57031e10	1.61950
$969$	2.64270e9	0.0933071
$970$	−8.81931e10	−3.10266
$971$	3.51892e10	1.23351	0.616754	−	0.787156i	$-0.288447\pi$
$971$	3.51892e10	1.23351	0.616754	+	0.787156i	$0.288447\pi$
$972$	3.87428e9	0.135319
$973$	8.65235e8	0.0301120
$974$	9.72569e9	0.337259
$975$	3.30641e9	0.114246
$976$	−5.32725e10	−1.83412
$977$	−6.56102e9	−0.225082	−0.112541	−	0.993647i	$-0.535899\pi$
$977$	−6.56102e9	−0.225082	−0.112541	+	0.993647i	$0.535899\pi$
$978$	−4.11569e10	−1.40688
$979$	4.59449e9	0.156494
$980$	−1.05694e11	−3.58723
$981$	1.72331e9	0.0582802
$982$	1.07108e10	0.360938
$983$	−1.57970e9	−0.0530442	−0.0265221	−	0.999648i	$-0.508443\pi$
$983$	−1.57970e9	−0.0530442	−0.0265221	+	0.999648i	$0.508443\pi$
$984$	9.56184e8	0.0319933
$985$	−3.21749e10	−1.07273
$986$	−7.29105e9	−0.242226
$987$	3.37313e9	0.111667
$988$	6.40116e9	0.211159
$989$	−1.10732e9	−0.0363987
$990$	1.34754e10	0.441386
$991$	−5.75725e10	−1.87913	−0.939566	−	0.342369i	$-0.888771\pi$
$991$	−5.75725e10	−1.87913	−0.939566	+	0.342369i	$0.888771\pi$
$992$	1.24543e9	0.0405068
$993$	−3.32751e10	−1.07844
$994$	−1.16713e10	−0.376937
$995$	6.80374e10	2.18961
$996$	8.77475e9	0.281402
$997$	−3.86631e10	−1.23556	−0.617780	−	0.786351i	$-0.711968\pi$
$997$	−3.86631e10	−1.23556	−0.617780	+	0.786351i	$0.711968\pi$
$998$	8.66400e9	0.275906
$999$	−8.35525e9	−0.265143

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.1	✓	18
3.2	odd	2		531.8.a.e.1.18		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.1	✓	18	1.1	even	1	trivial
531.8.a.e.1.18		18	3.2	odd	2

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-19.9501 q^{2} +27.0000 q^{3} +270.005 q^{4} +505.865 q^{5} -538.652 q^{6} +222.970 q^{7} -2833.01 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-19.9501 q^{2} +27.0000 q^{3} +270.005 q^{4} +505.865 q^{5} -538.652 q^{6} +222.970 q^{7} -2833.01 q^{8} +729.000 q^{9} -10092.0 q^{10} -1831.62 q^{11} +7290.13 q^{12} +688.848 q^{13} -4448.27 q^{14} +13658.4 q^{15} +21958.1 q^{16} +2843.94 q^{17} -14543.6 q^{18} +34416.2 q^{19} +136586. q^{20} +6020.19 q^{21} +36540.9 q^{22} -3272.29 q^{23} -76491.2 q^{24} +177775. q^{25} -13742.6 q^{26} +19683.0 q^{27} +60203.0 q^{28} +128507. q^{29} -272485. q^{30} -16509.0 q^{31} -75439.5 q^{32} -49453.7 q^{33} -56736.8 q^{34} +112793. q^{35} +196834. q^{36} -424491. q^{37} -686606. q^{38} +18598.9 q^{39} -1.43312e6 q^{40} -12500.6 q^{41} -120103. q^{42} +338393. q^{43} -494546. q^{44} +368776. q^{45} +65282.4 q^{46} +560303. q^{47} +592867. q^{48} -773827. q^{49} -3.54662e6 q^{50} +76786.4 q^{51} +185992. q^{52} +2.04079e6 q^{53} -392677. q^{54} -926551. q^{55} -631676. q^{56} +929239. q^{57} -2.56371e6 q^{58} +205379. q^{59} +3.68783e6 q^{60} -2.42610e6 q^{61} +329355. q^{62} +162545. q^{63} -1.30561e6 q^{64} +348464. q^{65} +986603. q^{66} -2.63298e6 q^{67} +767879. q^{68} -88351.8 q^{69} -2.25022e6 q^{70} +2.62379e6 q^{71} -2.06526e6 q^{72} +3.21761e6 q^{73} +8.46862e6 q^{74} +4.79992e6 q^{75} +9.29256e6 q^{76} -408396. q^{77} -371049. q^{78} +3.42920e6 q^{79} +1.11078e7 q^{80} +531441. q^{81} +249387. q^{82} +1.20365e6 q^{83} +1.62548e6 q^{84} +1.43865e6 q^{85} -6.75097e6 q^{86} +3.46968e6 q^{87} +5.18899e6 q^{88} -2.50843e6 q^{89} -7.35710e6 q^{90} +153592. q^{91} -883534. q^{92} -445743. q^{93} -1.11781e7 q^{94} +1.74100e7 q^{95} -2.03687e6 q^{96} +8.73888e6 q^{97} +1.54379e7 q^{98} -1.33525e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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