LMFDB - Embedded newform 177.8.a.d.1.7

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			1.7
Root			$-6.66616$ 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)

$f(q)$	$=$	$q-5.66616 q^{2} +27.0000 q^{3} -95.8947 q^{4} -15.0142 q^{5} -152.986 q^{6} +499.350 q^{7} +1268.62 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-5.66616 q^{2} +27.0000 q^{3} -95.8947 q^{4} -15.0142 q^{5} -152.986 q^{6} +499.350 q^{7} +1268.62 q^{8} +729.000 q^{9} +85.0729 q^{10} +5251.00 q^{11} -2589.16 q^{12} +114.657 q^{13} -2829.39 q^{14} -405.384 q^{15} +5086.30 q^{16} -16772.2 q^{17} -4130.63 q^{18} +5407.16 q^{19} +1439.78 q^{20} +13482.4 q^{21} -29753.0 q^{22} -74684.5 q^{23} +34252.8 q^{24} -77899.6 q^{25} -649.662 q^{26} +19683.0 q^{27} -47885.0 q^{28} +58710.0 q^{29} +2296.97 q^{30} +194742. q^{31} -191203. q^{32} +141777. q^{33} +95033.9 q^{34} -7497.35 q^{35} -69907.2 q^{36} +319137. q^{37} -30637.8 q^{38} +3095.73 q^{39} -19047.4 q^{40} +172353. q^{41} -76393.7 q^{42} +17400.1 q^{43} -503543. q^{44} -10945.4 q^{45} +423174. q^{46} +701890. q^{47} +137330. q^{48} -574193. q^{49} +441391. q^{50} -452849. q^{51} -10995.0 q^{52} +467762. q^{53} -111527. q^{54} -78839.7 q^{55} +633486. q^{56} +145993. q^{57} -332660. q^{58} +205379. q^{59} +38874.1 q^{60} -878795. q^{61} -1.10344e6 q^{62} +364026. q^{63} +432342. q^{64} -1721.48 q^{65} -803331. q^{66} -301315. q^{67} +1.60836e6 q^{68} -2.01648e6 q^{69} +42481.1 q^{70} +722433. q^{71} +924826. q^{72} +6.53656e6 q^{73} -1.80828e6 q^{74} -2.10329e6 q^{75} -518518. q^{76} +2.62209e6 q^{77} -17540.9 q^{78} +3.78720e6 q^{79} -76366.8 q^{80} +531441. q^{81} -976580. q^{82} -190031. q^{83} -1.29289e6 q^{84} +251821. q^{85} -98591.5 q^{86} +1.58517e6 q^{87} +6.66154e6 q^{88} +2.70581e6 q^{89} +62018.2 q^{90} +57253.7 q^{91} +7.16185e6 q^{92} +5.25803e6 q^{93} -3.97702e6 q^{94} -81184.2 q^{95} -5.16249e6 q^{96} +1.47369e7 q^{97} +3.25347e6 q^{98} +3.82798e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.66616	−0.500822	−0.250411	−	0.968140i	$-0.580566\pi$
$2$	−5.66616	−0.500822	−0.250411	+	0.968140i	$0.580566\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−95.8947	−0.749177
$5$	−15.0142	−0.0537165	−0.0268582	−	0.999639i	$-0.508550\pi$
$5$	−15.0142	−0.0537165	−0.0268582	+	0.999639i	$0.508550\pi$
$6$	−152.986	−0.289150
$7$	499.350	0.550252	0.275126	−	0.961408i	$-0.411280\pi$
$7$	499.350	0.550252	0.275126	+	0.961408i	$0.411280\pi$
$8$	1268.62	0.876027
$9$	729.000	0.333333
$10$	85.0729	0.0269024
$11$	5251.00	1.18951	0.594755	−	0.803907i	$-0.297249\pi$
$11$	5251.00	1.18951	0.594755	+	0.803907i	$0.297249\pi$
$12$	−2589.16	−0.432538
$13$	114.657	0.0144743	0.00723714	−	0.999974i	$-0.497696\pi$
$13$	114.657	0.0144743	0.00723714	+	0.999974i	$0.497696\pi$
$14$	−2829.39	−0.275579
$15$	−405.384	−0.0310132
$16$	5086.30	0.310443
$17$	−16772.2	−0.827977	−0.413989	−	0.910282i	$-0.635865\pi$
$17$	−16772.2	−0.827977	−0.413989	+	0.910282i	$0.635865\pi$
$18$	−4130.63	−0.166941
$19$	5407.16	0.180855	0.0904277	−	0.995903i	$-0.471177\pi$
$19$	5407.16	0.180855	0.0904277	+	0.995903i	$0.471177\pi$
$20$	1439.78	0.0402432
$21$	13482.4	0.317688
$22$	−29753.0	−0.595733
$23$	−74684.5	−1.27992	−0.639961	−	0.768408i	$-0.721049\pi$
$23$	−74684.5	−1.27992	−0.639961	+	0.768408i	$0.721049\pi$
$24$	34252.8	0.505774
$25$	−77899.6	−0.997115
$26$	−649.662	−0.00724905
$27$	19683.0	0.192450
$28$	−47885.0	−0.412236
$29$	58710.0	0.447012	0.223506	−	0.974703i	$-0.428250\pi$
$29$	58710.0	0.447012	0.223506	+	0.974703i	$0.428250\pi$
$30$	2296.97	0.0155321
$31$	194742.	1.17407	0.587034	−	0.809562i	$-0.300296\pi$
$31$	194742.	1.17407	0.587034	+	0.809562i	$0.300296\pi$
$32$	−191203.	−1.03150
$33$	141777.	0.686764
$34$	95033.9	0.414670
$35$	−7497.35	−0.0295576
$36$	−69907.2	−0.249726
$37$	319137.	1.03579	0.517895	−	0.855444i	$-0.326716\pi$
$37$	319137.	1.03579	0.517895	+	0.855444i	$0.326716\pi$
$38$	−30637.8	−0.0905764
$39$	3095.73	0.00835673
$40$	−19047.4	−0.0470571
$41$	172353.	0.390549	0.195275	−	0.980749i	$-0.437440\pi$
$41$	172353.	0.390549	0.195275	+	0.980749i	$0.437440\pi$
$42$	−76393.7	−0.159105
$43$	17400.1	0.0333742	0.0166871	−	0.999861i	$-0.494688\pi$
$43$	17400.1	0.0333742	0.0166871	+	0.999861i	$0.494688\pi$
$44$	−503543.	−0.891153
$45$	−10945.4	−0.0179055
$46$	423174.	0.641013
$47$	701890.	0.986113	0.493057	−	0.869997i	$-0.335880\pi$
$47$	701890.	0.986113	0.493057	+	0.869997i	$0.335880\pi$
$48$	137330.	0.179234
$49$	−574193.	−0.697223
$50$	441391.	0.499377
$51$	−452849.	−0.478033
$52$	−10995.0	−0.0108438
$53$	467762.	0.431578	0.215789	−	0.976440i	$-0.430768\pi$
$53$	467762.	0.431578	0.215789	+	0.976440i	$0.430768\pi$
$54$	−111527.	−0.0963833
$55$	−78839.7	−0.0638963
$56$	633486.	0.482036
$57$	145993.	0.104417
$58$	−332660.	−0.223874
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	38874.1	0.0232344
$61$	−878795.	−0.495716	−0.247858	−	0.968796i	$-0.579727\pi$
$61$	−878795.	−0.495716	−0.247858	+	0.968796i	$0.579727\pi$
$62$	−1.10344e6	−0.587999
$63$	364026.	0.183417
$64$	432342.	0.206157
$65$	−1721.48	−0.000777508 0
$66$	−803331.	−0.343947
$67$	−301315.	−0.122394	−0.0611968	−	0.998126i	$-0.519492\pi$
$67$	−301315.	−0.122394	−0.0611968	+	0.998126i	$0.519492\pi$
$68$	1.60836e6	0.620302
$69$	−2.01648e6	−0.738963
$70$	42481.1	0.0148031
$71$	722433.	0.239548	0.119774	−	0.992801i	$-0.461783\pi$
$71$	722433.	0.239548	0.119774	+	0.992801i	$0.461783\pi$
$72$	924826.	0.292009
$73$	6.53656e6	1.96661	0.983307	−	0.181956i	$-0.0582429\pi$
$73$	6.53656e6	1.96661	0.983307	+	0.181956i	$0.0582429\pi$
$74$	−1.80828e6	−0.518746
$75$	−2.10329e6	−0.575684
$76$	−518518.	−0.135493
$77$	2.62209e6	0.654530
$78$	−17540.9	−0.00418524
$79$	3.78720e6	0.864217	0.432109	−	0.901822i	$-0.357770\pi$
$79$	3.78720e6	0.864217	0.432109	+	0.901822i	$0.357770\pi$
$80$	−76366.8	−0.0166759
$81$	531441.	0.111111
$82$	−976580.	−0.195596
$83$	−190031.	−0.0364797	−0.0182398	−	0.999834i	$-0.505806\pi$
$83$	−190031.	−0.0364797	−0.0182398	+	0.999834i	$0.505806\pi$
$84$	−1.29289e6	−0.238005
$85$	251821.	0.0444760
$86$	−98591.5	−0.0167146
$87$	1.58517e6	0.258083
$88$	6.66154e6	1.04204
$89$	2.70581e6	0.406848	0.203424	−	0.979091i	$-0.434793\pi$
$89$	2.70581e6	0.406848	0.203424	+	0.979091i	$0.434793\pi$
$90$	62018.2	0.00896747
$91$	57253.7	0.00796451
$92$	7.16185e6	0.958888
$93$	5.25803e6	0.677848
$94$	−3.97702e6	−0.493867
$95$	−81184.2	−0.00971492
$96$	−5.16249e6	−0.595539
$97$	1.47369e7	1.63948	0.819738	−	0.572739i	$-0.194119\pi$
$97$	1.47369e7	1.63948	0.819738	+	0.572739i	$0.194119\pi$
$98$	3.25347e6	0.349185
$99$	3.82798e6	0.396503
$100$	7.47015e6	0.747015
$101$	3.16363e6	0.305535	0.152767	−	0.988262i	$-0.451181\pi$
$101$	3.16363e6	0.305535	0.152767	+	0.988262i	$0.451181\pi$
$102$	2.56591e6	0.239410
$103$	−8.88176e6	−0.800883	−0.400441	−	0.916322i	$-0.631143\pi$
$103$	−8.88176e6	−0.800883	−0.400441	+	0.916322i	$0.631143\pi$
$104$	145456.	0.0126799
$105$	−202428.	−0.0170651
$106$	−2.65041e6	−0.216144
$107$	1.68081e7	1.32641	0.663203	−	0.748440i	$-0.269197\pi$
$107$	1.68081e7	1.32641	0.663203	+	0.748440i	$0.269197\pi$
$108$	−1.88749e6	−0.144179
$109$	6.20279e6	0.458769	0.229385	−	0.973336i	$-0.426329\pi$
$109$	6.20279e6	0.458769	0.229385	+	0.973336i	$0.426329\pi$
$110$	446718.	0.0320007
$111$	8.61670e6	0.598013
$112$	2.53984e6	0.170822
$113$	1.00745e7	0.656821	0.328410	−	0.944535i	$-0.393487\pi$
$113$	1.00745e7	0.656821	0.328410	+	0.944535i	$0.393487\pi$
$114$	−827221.	−0.0522943
$115$	1.12133e6	0.0687529
$116$	−5.62998e6	−0.334891
$117$	83584.6	0.00482476
$118$	−1.16371e6	−0.0652015
$119$	−8.37519e6	−0.455596
$120$	−514279.	−0.0271684
$121$	8.08587e6	0.414933
$122$	4.97939e6	0.248266
$123$	4.65354e6	0.225484
$124$	−1.86747e7	−0.879585
$125$	2.34259e6	0.107278
$126$	−2.06263e6	−0.0918595
$127$	8.08324e6	0.350165	0.175082	−	0.984554i	$-0.443981\pi$
$127$	8.08324e6	0.350165	0.175082	+	0.984554i	$0.443981\pi$
$128$	2.20243e7	0.928256
$129$	469802.	0.0192686
$130$	9754.17	0.000389393 0
$131$	4.08601e7	1.58800	0.793999	−	0.607919i	$-0.207995\pi$
$131$	4.08601e7	1.58800	0.793999	+	0.607919i	$0.207995\pi$
$132$	−1.35957e7	−0.514508
$133$	2.70006e6	0.0995161
$134$	1.70730e6	0.0612974
$135$	−295525.	−0.0103377
$136$	−2.12776e7	−0.725331
$137$	4.34315e7	1.44306	0.721528	−	0.692385i	$-0.243440\pi$
$137$	4.34315e7	1.44306	0.721528	+	0.692385i	$0.243440\pi$
$138$	1.14257e7	0.370089
$139$	−3.00038e7	−0.947598	−0.473799	−	0.880633i	$-0.657118\pi$
$139$	−3.00038e7	−0.947598	−0.473799	+	0.880633i	$0.657118\pi$
$140$	718955.	0.0221439
$141$	1.89510e7	0.569333
$142$	−4.09342e6	−0.119971
$143$	602062.	0.0172173
$144$	3.70791e6	0.103481
$145$	−881485.	−0.0240119
$146$	−3.70372e7	−0.984924
$147$	−1.55032e7	−0.402542
$148$	−3.06036e7	−0.775990
$149$	−2.00795e7	−0.497279	−0.248640	−	0.968596i	$-0.579983\pi$
$149$	−2.00795e7	−0.497279	−0.248640	+	0.968596i	$0.579983\pi$
$150$	1.19176e7	0.288316
$151$	−4.42468e7	−1.04583	−0.522917	−	0.852384i	$-0.675156\pi$
$151$	−4.42468e7	−1.04583	−0.522917	+	0.852384i	$0.675156\pi$
$152$	6.85964e6	0.158434
$153$	−1.22269e7	−0.275992
$154$	−1.48572e7	−0.327803
$155$	−2.92390e6	−0.0630668
$156$	−296864.	−0.00626067
$157$	−5.91607e7	−1.22007	−0.610035	−	0.792375i	$-0.708844\pi$
$157$	−5.91607e7	−1.22007	−0.610035	+	0.792375i	$0.708844\pi$
$158$	−2.14588e7	−0.432819
$159$	1.26296e7	0.249172
$160$	2.87077e6	0.0554088
$161$	−3.72937e7	−0.704279
$162$	−3.01123e6	−0.0556469
$163$	−3.45882e7	−0.625564	−0.312782	−	0.949825i	$-0.601261\pi$
$163$	−3.45882e7	−0.625564	−0.312782	+	0.949825i	$0.601261\pi$
$164$	−1.65277e7	−0.292590
$165$	−2.12867e6	−0.0368905
$166$	1.07674e6	0.0182698
$167$	−1.07115e8	−1.77969	−0.889844	−	0.456265i	$-0.849187\pi$
$167$	−1.07115e8	−1.77969	−0.889844	+	0.456265i	$0.849187\pi$
$168$	1.71041e7	0.278303
$169$	−6.27354e7	−0.999790
$170$	−1.42686e6	−0.0222746
$171$	3.94182e6	0.0602851
$172$	−1.66857e6	−0.0250032
$173$	2.97790e7	0.437269	0.218634	−	0.975807i	$-0.429840\pi$
$173$	2.97790e7	0.437269	0.218634	+	0.975807i	$0.429840\pi$
$174$	−8.98183e6	−0.129254
$175$	−3.88991e7	−0.548664
$176$	2.67082e7	0.369275
$177$	5.54523e6	0.0751646
$178$	−1.53315e7	−0.203758
$179$	1.22880e8	1.60139	0.800693	−	0.599075i	$-0.204465\pi$
$179$	1.22880e8	1.60139	0.800693	+	0.599075i	$0.204465\pi$
$180$	1.04960e6	0.0134144
$181$	7.94319e7	0.995680	0.497840	−	0.867269i	$-0.334127\pi$
$181$	7.94319e7	0.995680	0.497840	+	0.867269i	$0.334127\pi$
$182$	−324409.	−0.00398880
$183$	−2.37275e7	−0.286202
$184$	−9.47465e7	−1.12125
$185$	−4.79160e6	−0.0556390
$186$	−2.97928e7	−0.339482
$187$	−8.80708e7	−0.984887
$188$	−6.73075e7	−0.738773
$189$	9.82870e6	0.105896
$190$	460003.	0.00486545
$191$	1.37986e8	1.43291	0.716453	−	0.697635i	$-0.245764\pi$
$191$	1.37986e8	1.43291	0.716453	+	0.697635i	$0.245764\pi$
$192$	1.16732e7	0.119025
$193$	871407.	0.00872510	0.00436255	−	0.999990i	$-0.498611\pi$
$193$	871407.	0.00872510	0.00436255	+	0.999990i	$0.498611\pi$
$194$	−8.35016e7	−0.821086
$195$	−46479.9	−0.000448894 0
$196$	5.50620e7	0.522343
$197$	1.71832e8	1.60130	0.800648	−	0.599135i	$-0.204489\pi$
$197$	1.71832e8	1.60130	0.800648	+	0.599135i	$0.204489\pi$
$198$	−2.16899e7	−0.198578
$199$	−9.52117e7	−0.856455	−0.428227	−	0.903671i	$-0.640862\pi$
$199$	−9.52117e7	−0.856455	−0.428227	+	0.903671i	$0.640862\pi$
$200$	−9.88251e7	−0.873499
$201$	−8.13550e6	−0.0706639
$202$	−1.79256e7	−0.153019
$203$	2.93168e7	0.245969
$204$	4.34258e7	0.358131
$205$	−2.58775e6	−0.0209789
$206$	5.03255e7	0.401100
$207$	−5.44450e7	−0.426640
$208$	583178.	0.00449344
$209$	2.83930e7	0.215129
$210$	1.14699e6	0.00854658
$211$	1.10926e8	0.812917	0.406458	−	0.913669i	$-0.366764\pi$
$211$	1.10926e8	0.812917	0.406458	+	0.913669i	$0.366764\pi$
$212$	−4.48559e7	−0.323328
$213$	1.95057e7	0.138303
$214$	−9.52375e7	−0.664293
$215$	−261248.	−0.00179275
$216$	2.49703e7	0.168591
$217$	9.72443e7	0.646033
$218$	−3.51460e7	−0.229762
$219$	1.76487e8	1.13542
$220$	7.56031e6	0.0478696
$221$	−1.92304e6	−0.0119844
$222$	−4.88236e7	−0.299498
$223$	−1.48718e8	−0.898042	−0.449021	−	0.893521i	$-0.648227\pi$
$223$	−1.48718e8	−0.898042	−0.449021	+	0.893521i	$0.648227\pi$
$224$	−9.54774e7	−0.567587
$225$	−5.67888e7	−0.332372
$226$	−5.70834e7	−0.328951
$227$	4.45860e7	0.252993	0.126496	−	0.991967i	$-0.459627\pi$
$227$	4.45860e7	0.252993	0.126496	+	0.991967i	$0.459627\pi$
$228$	−1.40000e7	−0.0782267
$229$	−9.60064e7	−0.528294	−0.264147	−	0.964482i	$-0.585090\pi$
$229$	−9.60064e7	−0.528294	−0.264147	+	0.964482i	$0.585090\pi$
$230$	−6.35363e6	−0.0344330
$231$	7.07964e7	0.377893
$232$	7.44809e7	0.391595
$233$	−1.49924e8	−0.776470	−0.388235	−	0.921560i	$-0.626915\pi$
$233$	−1.49924e8	−0.776470	−0.388235	+	0.921560i	$0.626915\pi$
$234$	−473604.	−0.00241635
$235$	−1.05383e7	−0.0529705
$236$	−1.96947e7	−0.0975345
$237$	1.02254e8	0.498956
$238$	4.74551e7	0.228173
$239$	−4.99588e7	−0.236712	−0.118356	−	0.992971i	$-0.537762\pi$
$239$	−4.99588e7	−0.236712	−0.118356	+	0.992971i	$0.537762\pi$
$240$	−2.06190e6	−0.00962785
$241$	3.94054e6	0.0181341	0.00906705	−	0.999959i	$-0.497114\pi$
$241$	3.94054e6	0.0181341	0.00906705	+	0.999959i	$0.497114\pi$
$242$	−4.58158e7	−0.207808
$243$	1.43489e7	0.0641500
$244$	8.42717e7	0.371379
$245$	8.62106e6	0.0374524
$246$	−2.63677e7	−0.112927
$247$	619966.	0.00261775
$248$	2.47054e8	1.02851
$249$	−5.13083e6	−0.0210615
$250$	−1.32735e7	−0.0537272
$251$	−6.89865e7	−0.275363	−0.137682	−	0.990477i	$-0.543965\pi$
$251$	−6.89865e7	−0.275363	−0.137682	+	0.990477i	$0.543965\pi$
$252$	−3.49081e7	−0.137412
$253$	−3.92169e8	−1.52248
$254$	−4.58009e7	−0.175370
$255$	6.79917e6	0.0256783
$256$	−1.80133e8	−0.671048
$257$	6.74827e7	0.247986	0.123993	−	0.992283i	$-0.460430\pi$
$257$	6.74827e7	0.247986	0.123993	+	0.992283i	$0.460430\pi$
$258$	−2.66197e6	−0.00965016
$259$	1.59361e8	0.569945
$260$	165081.	0.000582491 0
$261$	4.27996e7	0.149004
$262$	−2.31520e8	−0.795305
$263$	7.91658e7	0.268344	0.134172	−	0.990958i	$-0.457162\pi$
$263$	7.91658e7	0.268344	0.134172	+	0.990958i	$0.457162\pi$
$264$	1.79862e8	0.601623
$265$	−7.02308e6	−0.0231829
$266$	−1.52990e7	−0.0498399
$267$	7.30568e7	0.234894
$268$	2.88945e7	0.0916944
$269$	2.24443e8	0.703030	0.351515	−	0.936182i	$-0.385667\pi$
$269$	2.24443e8	0.703030	0.351515	+	0.936182i	$0.385667\pi$
$270$	1.67449e6	0.00517737
$271$	5.85302e7	0.178644	0.0893218	−	0.996003i	$-0.471530\pi$
$271$	5.85302e7	0.178644	0.0893218	+	0.996003i	$0.471530\pi$
$272$	−8.53084e7	−0.257040
$273$	1.54585e6	0.00459831
$274$	−2.46090e8	−0.722715
$275$	−4.09051e8	−1.18608
$276$	1.93370e8	0.553614
$277$	3.20396e8	0.905749	0.452874	−	0.891574i	$-0.350399\pi$
$277$	3.20396e8	0.905749	0.452874	+	0.891574i	$0.350399\pi$
$278$	1.70006e8	0.474578
$279$	1.41967e8	0.391356
$280$	−9.51130e6	−0.0258933
$281$	−2.95974e8	−0.795758	−0.397879	−	0.917438i	$-0.630254\pi$
$281$	−2.95974e8	−0.795758	−0.397879	+	0.917438i	$0.630254\pi$
$282$	−1.07380e8	−0.285135
$283$	−2.63828e8	−0.691940	−0.345970	−	0.938246i	$-0.612450\pi$
$283$	−2.63828e8	−0.691940	−0.345970	+	0.938246i	$0.612450\pi$
$284$	−6.92775e7	−0.179464
$285$	−2.19197e6	−0.00560891
$286$	−3.41138e6	−0.00862281
$287$	8.60645e7	0.214901
$288$	−1.39387e8	−0.343835
$289$	−1.29032e8	−0.314453
$290$	4.99463e6	0.0120257
$291$	3.97896e8	0.946552
$292$	−6.26821e8	−1.47334
$293$	3.79473e8	0.881342	0.440671	−	0.897669i	$-0.354741\pi$
$293$	3.79473e8	0.881342	0.440671	+	0.897669i	$0.354741\pi$
$294$	8.78436e7	0.201602
$295$	−3.08360e6	−0.00699329
$296$	4.04865e8	0.907379
$297$	1.03356e8	0.228921
$298$	1.13773e8	0.249048
$299$	−8.56307e6	−0.0185260
$300$	2.01694e8	0.431289
$301$	8.68872e6	0.0183642
$302$	2.50709e8	0.523777
$303$	8.54180e7	0.176401
$304$	2.75024e7	0.0561453
$305$	1.31944e7	0.0266281
$306$	6.92797e7	0.138223
$307$	4.67759e8	0.922652	0.461326	−	0.887231i	$-0.347374\pi$
$307$	4.67759e8	0.922652	0.461326	+	0.887231i	$0.347374\pi$
$308$	−2.51444e8	−0.490359
$309$	−2.39808e8	−0.462390
$310$	1.65673e7	0.0315853
$311$	−3.46804e7	−0.0653767	−0.0326883	−	0.999466i	$-0.510407\pi$
$311$	−3.46804e7	−0.0653767	−0.0326883	+	0.999466i	$0.510407\pi$
$312$	3.92731e6	0.00732072
$313$	3.26866e8	0.602511	0.301256	−	0.953543i	$-0.402594\pi$
$313$	3.26866e8	0.602511	0.301256	+	0.953543i	$0.402594\pi$
$314$	3.35214e8	0.611038
$315$	−5.46557e6	−0.00985254
$316$	−3.63172e8	−0.647452
$317$	4.00162e8	0.705552	0.352776	−	0.935708i	$-0.385238\pi$
$317$	4.00162e8	0.705552	0.352776	+	0.935708i	$0.385238\pi$
$318$	−7.15612e7	−0.124791
$319$	3.08287e8	0.531725
$320$	−6.49128e6	−0.0110740
$321$	4.53819e8	0.765800
$322$	2.11312e8	0.352719
$323$	−9.06899e7	−0.149744
$324$	−5.09624e7	−0.0832419
$325$	−8.93170e6	−0.0144325
$326$	1.95982e8	0.313296
$327$	1.67475e8	0.264871
$328$	2.18651e8	0.342132
$329$	3.50489e8	0.542611
$330$	1.20614e7	0.0184756
$331$	−2.08461e8	−0.315957	−0.157978	−	0.987443i	$-0.550498\pi$
$331$	−2.08461e8	−0.315957	−0.157978	+	0.987443i	$0.550498\pi$
$332$	1.82229e7	0.0273297
$333$	2.32651e8	0.345263
$334$	6.06932e8	0.891308
$335$	4.52400e6	0.00657455
$336$	6.85758e7	0.0986242
$337$	−1.17533e9	−1.67284	−0.836422	−	0.548086i	$-0.815357\pi$
$337$	−1.17533e9	−1.67284	−0.836422	+	0.548086i	$0.815357\pi$
$338$	3.55468e8	0.500717
$339$	2.72010e8	0.379216
$340$	−2.41483e7	−0.0333204
$341$	1.02259e9	1.39656
$342$	−2.23350e7	−0.0301921
$343$	−6.97959e8	−0.933900
$344$	2.20741e7	0.0292367
$345$	3.02759e7	0.0396945
$346$	−1.68732e8	−0.218994
$347$	3.03478e8	0.389919	0.194960	−	0.980811i	$-0.437542\pi$
$347$	3.03478e8	0.389919	0.194960	+	0.980811i	$0.437542\pi$
$348$	−1.52009e8	−0.193350
$349$	7.65904e8	0.964463	0.482232	−	0.876044i	$-0.339826\pi$
$349$	7.65904e8	0.964463	0.482232	+	0.876044i	$0.339826\pi$
$350$	2.20409e8	0.274783
$351$	2.25679e6	0.00278558
$352$	−1.00401e9	−1.22698
$353$	1.07514e9	1.30092	0.650462	−	0.759539i	$-0.274575\pi$
$353$	1.07514e9	1.30092	0.650462	+	0.759539i	$0.274575\pi$
$354$	−3.14202e7	−0.0376441
$355$	−1.08468e7	−0.0128677
$356$	−2.59473e8	−0.304801
$357$	−2.26130e8	−0.263039
$358$	−6.96258e8	−0.802010
$359$	−8.01759e8	−0.914562	−0.457281	−	0.889322i	$-0.651177\pi$
$359$	−8.01759e8	−0.914562	−0.457281	+	0.889322i	$0.651177\pi$
$360$	−1.38855e7	−0.0156857
$361$	−8.64634e8	−0.967291
$362$	−4.50074e8	−0.498659
$363$	2.18319e8	0.239562
$364$	−5.49033e6	−0.00596683
$365$	−9.81413e7	−0.105640
$366$	1.34444e8	0.143336
$367$	2.39324e8	0.252729	0.126364	−	0.991984i	$-0.459669\pi$
$367$	2.39324e8	0.252729	0.126364	+	0.991984i	$0.459669\pi$
$368$	−3.79868e8	−0.397343
$369$	1.25645e8	0.130183
$370$	2.71499e7	0.0278652
$371$	2.33577e8	0.237477
$372$	−5.04217e8	−0.507828
$373$	1.44976e9	1.44649	0.723245	−	0.690592i	$-0.242650\pi$
$373$	1.44976e9	1.44649	0.723245	+	0.690592i	$0.242650\pi$
$374$	4.99023e8	0.493253
$375$	6.32498e7	0.0619370
$376$	8.90434e8	0.863862
$377$	6.73149e6	0.00647018
$378$	−5.56910e7	−0.0530351
$379$	5.83143e8	0.550221	0.275111	−	0.961413i	$-0.411285\pi$
$379$	5.83143e8	0.550221	0.275111	+	0.961413i	$0.411285\pi$
$380$	7.78513e6	0.00727819
$381$	2.18247e8	0.202168
$382$	−7.81850e8	−0.717631
$383$	−2.12967e9	−1.93694	−0.968472	−	0.249121i	$-0.919858\pi$
$383$	−2.12967e9	−1.93694	−0.968472	+	0.249121i	$0.919858\pi$
$384$	5.94657e8	0.535929
$385$	−3.93686e7	−0.0351591
$386$	−4.93753e6	−0.00436973
$387$	1.26847e7	0.0111247
$388$	−1.41319e9	−1.22826
$389$	1.02632e9	0.884017	0.442008	−	0.897011i	$-0.354266\pi$
$389$	1.02632e9	0.884017	0.442008	+	0.897011i	$0.354266\pi$
$390$	263363.	0.000224816 0
$391$	1.25262e9	1.05975
$392$	−7.28434e8	−0.610786
$393$	1.10322e9	0.916831
$394$	−9.73626e8	−0.801965
$395$	−5.68618e7	−0.0464227
$396$	−3.67083e8	−0.297051
$397$	8.48731e8	0.680775	0.340387	−	0.940285i	$-0.389442\pi$
$397$	8.48731e8	0.680775	0.340387	+	0.940285i	$0.389442\pi$
$398$	5.39484e8	0.428932
$399$	7.29017e7	0.0574556
$400$	−3.96221e8	−0.309547
$401$	−1.05558e9	−0.817498	−0.408749	−	0.912647i	$-0.634035\pi$
$401$	−1.05558e9	−0.817498	−0.408749	+	0.912647i	$0.634035\pi$
$402$	4.60970e7	0.0353901
$403$	2.23284e7	0.0169938
$404$	−3.03375e8	−0.228900
$405$	−7.97917e6	−0.00596850
$406$	−1.66114e8	−0.123187
$407$	1.67579e9	1.23208
$408$	−5.74495e8	−0.418770
$409$	3.62710e7	0.0262137	0.0131068	−	0.999914i	$-0.495828\pi$
$409$	3.62710e7	0.0262137	0.0131068	+	0.999914i	$0.495828\pi$
$410$	1.46626e7	0.0105067
$411$	1.17265e9	0.833149
$412$	8.51714e8	0.600003
$413$	1.02556e8	0.0716367
$414$	3.08494e8	0.213671
$415$	2.85316e6	0.00195956
$416$	−2.19227e7	−0.0149303
$417$	−8.10102e8	−0.547096
$418$	−1.60879e8	−0.107742
$419$	−2.92602e8	−0.194325	−0.0971623	−	0.995269i	$-0.530977\pi$
$419$	−2.92602e8	−0.194325	−0.0971623	+	0.995269i	$0.530977\pi$
$420$	1.94118e7	0.0127848
$421$	−1.22412e9	−0.799534	−0.399767	−	0.916617i	$-0.630909\pi$
$421$	−1.22412e9	−0.799534	−0.399767	+	0.916617i	$0.630909\pi$
$422$	−6.28526e8	−0.407127
$423$	5.11678e8	0.328704
$424$	5.93413e8	0.378074
$425$	1.30655e9	0.825588
$426$	−1.10522e8	−0.0692654
$427$	−4.38826e8	−0.272769
$428$	−1.61181e9	−0.993712
$429$	1.62557e7	0.00994042
$430$	1.48027e6	0.000897848 0
$431$	−6.26512e8	−0.376929	−0.188464	−	0.982080i	$-0.560351\pi$
$431$	−6.26512e8	−0.376929	−0.188464	+	0.982080i	$0.560351\pi$
$432$	1.00114e8	0.0597448
$433$	−2.79784e9	−1.65621	−0.828106	−	0.560571i	$-0.810582\pi$
$433$	−2.79784e9	−1.65621	−0.828106	+	0.560571i	$0.810582\pi$
$434$	−5.51001e8	−0.323548
$435$	−2.38001e7	−0.0138633
$436$	−5.94814e8	−0.343699
$437$	−4.03831e8	−0.231481
$438$	−1.00000e9	−0.568646
$439$	−6.09498e8	−0.343832	−0.171916	−	0.985112i	$-0.554996\pi$
$439$	−6.09498e8	−0.343832	−0.171916	+	0.985112i	$0.554996\pi$
$440$	−1.00018e8	−0.0559749
$441$	−4.18587e8	−0.232408
$442$	1.08963e7	0.00600205
$443$	−1.80771e9	−0.987905	−0.493953	−	0.869489i	$-0.664448\pi$
$443$	−1.80771e9	−0.987905	−0.493953	+	0.869489i	$0.664448\pi$
$444$	−8.26296e8	−0.448018
$445$	−4.06256e7	−0.0218544
$446$	8.42660e8	0.449760
$447$	−5.42146e8	−0.287104
$448$	2.15890e8	0.113438
$449$	6.32760e8	0.329896	0.164948	−	0.986302i	$-0.447254\pi$
$449$	6.32760e8	0.329896	0.164948	+	0.986302i	$0.447254\pi$
$450$	3.21774e8	0.166459
$451$	9.05027e8	0.464562
$452$	−9.66086e8	−0.492075
$453$	−1.19466e9	−0.603812
$454$	−2.52631e8	−0.126704
$455$	−859620.	−0.000427825 0
$456$	1.85210e8	0.0914720
$457$	−3.19962e8	−0.156816	−0.0784082	−	0.996921i	$-0.524984\pi$
$457$	−3.19962e8	−0.156816	−0.0784082	+	0.996921i	$0.524984\pi$
$458$	5.43987e8	0.264582
$459$	−3.30127e8	−0.159344
$460$	−1.07530e8	−0.0515081
$461$	−9.55318e8	−0.454145	−0.227073	−	0.973878i	$-0.572915\pi$
$461$	−9.55318e8	−0.454145	−0.227073	+	0.973878i	$0.572915\pi$
$462$	−4.01143e8	−0.189257
$463$	3.55134e9	1.66287	0.831437	−	0.555619i	$-0.187519\pi$
$463$	3.55134e9	1.66287	0.831437	+	0.555619i	$0.187519\pi$
$464$	2.98617e8	0.138772
$465$	−7.89452e7	−0.0364116
$466$	8.49491e8	0.388873
$467$	4.08842e9	1.85758	0.928788	−	0.370613i	$-0.120852\pi$
$467$	4.08842e9	1.85758	0.928788	+	0.370613i	$0.120852\pi$
$468$	−8.01532e6	−0.00361460
$469$	−1.50461e8	−0.0673473
$470$	5.97119e7	0.0265288
$471$	−1.59734e9	−0.704407
$472$	2.60548e8	0.114049
$473$	9.13679e7	0.0396990
$474$	−5.79389e8	−0.249888
$475$	−4.21215e8	−0.180334
$476$	8.03136e8	0.341322
$477$	3.40999e8	0.143859
$478$	2.83075e8	0.118550
$479$	2.21317e9	0.920112	0.460056	−	0.887890i	$-0.347829\pi$
$479$	2.21317e9	0.920112	0.460056	+	0.887890i	$0.347829\pi$
$480$	7.75108e7	0.0319903
$481$	3.65912e7	0.0149923
$482$	−2.23277e7	−0.00908196
$483$	−1.00693e9	−0.406616
$484$	−7.75392e8	−0.310858
$485$	−2.21263e8	−0.0880669
$486$	−8.13032e7	−0.0321278
$487$	−4.68349e9	−1.83746	−0.918731	−	0.394883i	$-0.870785\pi$
$487$	−4.68349e9	−1.83746	−0.918731	+	0.394883i	$0.870785\pi$
$488$	−1.11486e9	−0.434261
$489$	−9.33882e8	−0.361170
$490$	−4.88483e7	−0.0187570
$491$	−1.79902e9	−0.685885	−0.342942	−	0.939356i	$-0.611424\pi$
$491$	−1.79902e9	−0.685885	−0.342942	+	0.939356i	$0.611424\pi$
$492$	−4.46249e8	−0.168927
$493$	−9.84696e8	−0.370116
$494$	−3.51283e6	−0.00131103
$495$	−5.74742e7	−0.0212988
$496$	9.90515e8	0.364481
$497$	3.60747e8	0.131812
$498$	2.90721e7	0.0105481
$499$	−8.51942e8	−0.306943	−0.153472	−	0.988153i	$-0.549045\pi$
$499$	−8.51942e8	−0.306943	−0.153472	+	0.988153i	$0.549045\pi$
$500$	−2.24642e8	−0.0803702
$501$	−2.89211e9	−1.02750
$502$	3.90888e8	0.137908
$503$	−3.29333e9	−1.15385	−0.576923	−	0.816798i	$-0.695747\pi$
$503$	−3.29333e9	−1.15385	−0.576923	+	0.816798i	$0.695747\pi$
$504$	4.61812e8	0.160679
$505$	−4.74994e7	−0.0164123
$506$	2.22209e9	0.762491
$507$	−1.69386e9	−0.577229
$508$	−7.75139e8	−0.262335
$509$	−1.92293e9	−0.646325	−0.323162	−	0.946344i	$-0.604746\pi$
$509$	−1.92293e9	−0.646325	−0.323162	+	0.946344i	$0.604746\pi$
$510$	−3.85252e7	−0.0128602
$511$	3.26403e9	1.08213
$512$	−1.79845e9	−0.592180
$513$	1.06429e8	0.0348056
$514$	−3.82367e8	−0.124197
$515$	1.33353e8	0.0430206
$516$	−4.50515e7	−0.0144356
$517$	3.68563e9	1.17299
$518$	−9.02965e8	−0.285441
$519$	8.04032e8	0.252457
$520$	−2.18391e6	−0.000681118 0
$521$	5.43560e9	1.68390	0.841949	−	0.539558i	$-0.181409\pi$
$521$	5.43560e9	1.68390	0.841949	+	0.539558i	$0.181409\pi$
$522$	−2.42509e8	−0.0746246
$523$	−3.26406e9	−0.997705	−0.498853	−	0.866687i	$-0.666245\pi$
$523$	−3.26406e9	−0.997705	−0.498853	+	0.866687i	$0.666245\pi$
$524$	−3.91827e9	−1.18969
$525$	−1.05028e9	−0.316772
$526$	−4.48566e8	−0.134393
$527$	−3.26625e9	−0.972102
$528$	7.21121e8	0.213201
$529$	2.17296e9	0.638199
$530$	3.97939e7	0.0116105
$531$	1.49721e8	0.0433963
$532$	−2.58922e8	−0.0745551
$533$	1.97614e7	0.00565292
$534$	−4.13951e8	−0.117640
$535$	−2.52361e8	−0.0712498
$536$	−3.82255e8	−0.107220
$537$	3.31776e9	0.924561
$538$	−1.27173e9	−0.352093
$539$	−3.01509e9	−0.829353
$540$	2.83393e7	0.00774480
$541$	6.87940e9	1.86793	0.933964	−	0.357367i	$-0.116325\pi$
$541$	6.87940e9	1.86793	0.933964	+	0.357367i	$0.116325\pi$
$542$	−3.31641e8	−0.0894687
$543$	2.14466e9	0.574856
$544$	3.20690e9	0.854062
$545$	−9.31300e7	−0.0246435
$546$	−8.75903e6	−0.00230294
$547$	−3.21914e9	−0.840977	−0.420489	−	0.907298i	$-0.638141\pi$
$547$	−3.21914e9	−0.840977	−0.420489	+	0.907298i	$0.638141\pi$
$548$	−4.16485e9	−1.08110
$549$	−6.40641e8	−0.165239
$550$	2.31775e9	0.594014
$551$	3.17454e8	0.0808446
$552$	−2.55816e9	−0.647351
$553$	1.89114e9	0.475537
$554$	−1.81541e9	−0.453619
$555$	−1.29373e8	−0.0321232
$556$	2.87720e9	0.709918
$557$	−2.80717e9	−0.688295	−0.344148	−	0.938916i	$-0.611832\pi$
$557$	−2.80717e9	−0.688295	−0.344148	+	0.938916i	$0.611832\pi$
$558$	−8.04406e8	−0.196000
$559$	1.99503e6	0.000483068 0
$560$	−3.81338e7	−0.00917596
$561$	−2.37791e9	−0.568625
$562$	1.67703e9	0.398533
$563$	6.17910e8	0.145930	0.0729652	−	0.997334i	$-0.476754\pi$
$563$	6.17910e8	0.145930	0.0729652	+	0.997334i	$0.476754\pi$
$564$	−1.81730e9	−0.426531
$565$	−1.51260e8	−0.0352821
$566$	1.49489e9	0.346539
$567$	2.65375e8	0.0611391
$568$	9.16495e8	0.209851
$569$	−4.23484e9	−0.963705	−0.481852	−	0.876252i	$-0.660036\pi$
$569$	−4.23484e9	−0.963705	−0.481852	+	0.876252i	$0.660036\pi$
$570$	1.24201e7	0.00280907
$571$	6.61606e8	0.148721	0.0743607	−	0.997231i	$-0.476308\pi$
$571$	6.61606e8	0.148721	0.0743607	+	0.997231i	$0.476308\pi$
$572$	−5.77345e7	−0.0128988
$573$	3.72562e9	0.827289
$574$	−4.87655e8	−0.107627
$575$	5.81789e9	1.27623
$576$	3.15178e8	0.0687190
$577$	9.05424e8	0.196217	0.0981085	−	0.995176i	$-0.468721\pi$
$577$	9.05424e8	0.196217	0.0981085	+	0.995176i	$0.468721\pi$
$578$	7.31118e8	0.157485
$579$	2.35280e7	0.00503744
$580$	8.45297e7	0.0179892
$581$	−9.48919e7	−0.0200730
$582$	−2.25454e9	−0.474054
$583$	2.45622e9	0.513366
$584$	8.29242e9	1.72281
$585$	−1.25496e6	−0.000259169 0
$586$	−2.15016e9	−0.441396
$587$	5.48391e9	1.11907	0.559534	−	0.828807i	$-0.310980\pi$
$587$	5.48391e9	1.11907	0.559534	+	0.828807i	$0.310980\pi$
$588$	1.48667e9	0.301575
$589$	1.05300e9	0.212336
$590$	1.74722e7	0.00350240
$591$	4.63946e9	0.924509
$592$	1.62323e9	0.321554
$593$	−6.47258e9	−1.27464	−0.637318	−	0.770601i	$-0.719956\pi$
$593$	−6.47258e9	−1.27464	−0.637318	+	0.770601i	$0.719956\pi$
$594$	−5.85629e8	−0.114649
$595$	1.25747e8	0.0244730
$596$	1.92551e9	0.372550
$597$	−2.57072e9	−0.494474
$598$	4.85197e7	0.00927821
$599$	2.50605e8	0.0476426	0.0238213	−	0.999716i	$-0.492417\pi$
$599$	2.50605e8	0.0476426	0.0238213	+	0.999716i	$0.492417\pi$
$600$	−2.66828e9	−0.504315
$601$	−4.78670e9	−0.899447	−0.449724	−	0.893168i	$-0.648477\pi$
$601$	−4.78670e9	−0.899447	−0.449724	+	0.893168i	$0.648477\pi$
$602$	−4.92317e7	−0.00919723
$603$	−2.19658e8	−0.0407978
$604$	4.24303e9	0.783514
$605$	−1.21403e8	−0.0222888
$606$	−4.83992e8	−0.0883453
$607$	−2.08136e9	−0.377735	−0.188868	−	0.982003i	$-0.560482\pi$
$607$	−2.08136e9	−0.377735	−0.188868	+	0.982003i	$0.560482\pi$
$608$	−1.03387e9	−0.186553
$609$	7.91555e8	0.142011
$610$	−7.47616e7	−0.0133360
$611$	8.04763e7	0.0142733
$612$	1.17250e9	0.206767
$613$	9.25255e9	1.62237	0.811185	−	0.584790i	$-0.198823\pi$
$613$	9.25255e9	1.62237	0.811185	+	0.584790i	$0.198823\pi$
$614$	−2.65040e9	−0.462085
$615$	−6.98692e7	−0.0121122
$616$	3.32644e9	0.573386
$617$	4.36405e9	0.747982	0.373991	−	0.927432i	$-0.377989\pi$
$617$	4.36405e9	0.747982	0.373991	+	0.927432i	$0.377989\pi$
$618$	1.35879e9	0.231575
$619$	−5.18190e9	−0.878156	−0.439078	−	0.898449i	$-0.644695\pi$
$619$	−5.18190e9	−0.878156	−0.439078	+	0.898449i	$0.644695\pi$
$620$	2.80386e8	0.0472482
$621$	−1.47002e9	−0.246321
$622$	1.96505e8	0.0327421
$623$	1.35114e9	0.223869
$624$	1.57458e7	0.00259429
$625$	6.05073e9	0.991352
$626$	−1.85208e9	−0.301751
$627$	7.66611e8	0.124205
$628$	5.67319e9	0.914048
$629$	−5.35263e9	−0.857610
$630$	3.09688e7	0.00493437
$631$	5.15467e9	0.816767	0.408383	−	0.912810i	$-0.366093\pi$
$631$	5.15467e9	0.816767	0.408383	+	0.912810i	$0.366093\pi$
$632$	4.80452e9	0.757077
$633$	2.99501e9	0.469338
$634$	−2.26738e9	−0.353356
$635$	−1.21363e8	−0.0188096
$636$	−1.21111e9	−0.186674
$637$	−6.58350e7	−0.0100918
$638$	−1.74680e9	−0.266300
$639$	5.26654e8	0.0798495
$640$	−3.30678e8	−0.0498626
$641$	−4.91786e9	−0.737518	−0.368759	−	0.929525i	$-0.620217\pi$
$641$	−4.91786e9	−0.737518	−0.368759	+	0.929525i	$0.620217\pi$
$642$	−2.57141e9	−0.383530
$643$	−1.42616e9	−0.211558	−0.105779	−	0.994390i	$-0.533734\pi$
$643$	−1.42616e9	−0.211558	−0.105779	+	0.994390i	$0.533734\pi$
$644$	3.57627e9	0.527630
$645$	−7.05371e6	−0.00103504
$646$	5.13863e8	0.0749952
$647$	6.26814e9	0.909858	0.454929	−	0.890528i	$-0.349665\pi$
$647$	6.26814e9	0.909858	0.454929	+	0.890528i	$0.349665\pi$
$648$	6.74198e8	0.0973363
$649$	1.07845e9	0.154861
$650$	5.06084e7	0.00722813
$651$	2.62559e9	0.372987
$652$	3.31683e9	0.468658
$653$	1.00126e10	1.40719	0.703593	−	0.710603i	$-0.251578\pi$
$653$	1.00126e10	1.40719	0.703593	+	0.710603i	$0.251578\pi$
$654$	−9.48941e8	−0.132653
$655$	−6.13483e8	−0.0853017
$656$	8.76640e8	0.121243
$657$	4.76515e9	0.655538
$658$	−1.98592e9	−0.271752
$659$	3.69501e9	0.502941	0.251470	−	0.967865i	$-0.419086\pi$
$659$	3.69501e9	0.502941	0.251470	+	0.967865i	$0.419086\pi$
$660$	2.04128e8	0.0276375
$661$	2.49829e9	0.336464	0.168232	−	0.985747i	$-0.446194\pi$
$661$	2.49829e9	0.336464	0.168232	+	0.985747i	$0.446194\pi$
$662$	1.18117e9	0.158238
$663$	−5.19221e7	−0.00691919
$664$	−2.41077e8	−0.0319572
$665$	−4.05393e7	−0.00534565
$666$	−1.31824e9	−0.172915
$667$	−4.38473e9	−0.572140
$668$	1.02718e10	1.33330
$669$	−4.01539e9	−0.518485
$670$	−2.56337e7	−0.00329268
$671$	−4.61455e9	−0.589659
$672$	−2.57789e9	−0.327697
$673$	3.99102e9	0.504698	0.252349	−	0.967636i	$-0.418797\pi$
$673$	3.99102e9	0.504698	0.252349	+	0.967636i	$0.418797\pi$
$674$	6.65961e9	0.837798
$675$	−1.53330e9	−0.191895
$676$	6.01599e9	0.749020
$677$	−3.69552e9	−0.457737	−0.228868	−	0.973457i	$-0.573503\pi$
$677$	−3.69552e9	−0.457737	−0.228868	+	0.973457i	$0.573503\pi$
$678$	−1.54125e9	−0.189920
$679$	7.35887e9	0.902125
$680$	3.19466e8	0.0389622
$681$	1.20382e9	0.146065
$682$	−5.79416e9	−0.699431
$683$	−6.33943e9	−0.761338	−0.380669	−	0.924711i	$-0.624306\pi$
$683$	−6.33943e9	−0.761338	−0.380669	+	0.924711i	$0.624306\pi$
$684$	−3.77999e8	−0.0451642
$685$	−6.52091e8	−0.0775159
$686$	3.95475e9	0.467718
$687$	−2.59217e9	−0.305011
$688$	8.85020e7	0.0103608
$689$	5.36320e7	0.00624679
$690$	−1.71548e8	−0.0198799
$691$	9.02991e9	1.04114	0.520572	−	0.853818i	$-0.325719\pi$
$691$	9.02991e9	1.04114	0.520572	+	0.853818i	$0.325719\pi$
$692$	−2.85564e9	−0.327592
$693$	1.91150e9	0.218177
$694$	−1.71956e9	−0.195280
$695$	4.50483e8	0.0509016
$696$	2.01098e9	0.226087
$697$	−2.89074e9	−0.323366
$698$	−4.33974e9	−0.483025
$699$	−4.04794e9	−0.448295
$700$	3.73022e9	0.411047
$701$	−4.09079e9	−0.448533	−0.224267	−	0.974528i	$-0.571999\pi$
$701$	−4.09079e9	−0.448533	−0.224267	+	0.974528i	$0.571999\pi$
$702$	−1.27873e7	−0.00139508
$703$	1.72563e9	0.187328
$704$	2.27023e9	0.245226
$705$	−2.84535e8	−0.0305826
$706$	−6.09189e9	−0.651532
$707$	1.57976e9	0.168121
$708$	−5.31758e8	−0.0563116
$709$	−1.70129e10	−1.79273	−0.896366	−	0.443315i	$-0.853802\pi$
$709$	−1.70129e10	−1.79273	−0.896366	+	0.443315i	$0.853802\pi$
$710$	6.14595e7	0.00644443
$711$	2.76087e9	0.288072
$712$	3.43265e9	0.356410
$713$	−1.45442e10	−1.50271
$714$	1.28129e9	0.131736
$715$	−9.03949e6	−0.000924853 0
$716$	−1.17835e10	−1.19972
$717$	−1.34889e9	−0.136666
$718$	4.54289e9	0.458033
$719$	−1.05938e10	−1.06292	−0.531460	−	0.847083i	$-0.678357\pi$
$719$	−1.05938e10	−1.06292	−0.531460	+	0.847083i	$0.678357\pi$
$720$	−5.56714e7	−0.00555864
$721$	−4.43511e9	−0.440687
$722$	4.89915e9	0.484441
$723$	1.06395e8	0.0104697
$724$	−7.61709e9	−0.745941
$725$	−4.57349e9	−0.445722
$726$	−1.23703e9	−0.119978
$727$	6.96354e9	0.672140	0.336070	−	0.941837i	$-0.390902\pi$
$727$	6.96354e9	0.672140	0.336070	+	0.941837i	$0.390902\pi$
$728$	7.26334e7	0.00697712
$729$	3.87420e8	0.0370370
$730$	5.56084e8	0.0529067
$731$	−2.91837e8	−0.0276331
$732$	2.27534e9	0.214416
$733$	−2.65861e9	−0.249340	−0.124670	−	0.992198i	$-0.539787\pi$
$733$	−2.65861e9	−0.249340	−0.124670	+	0.992198i	$0.539787\pi$
$734$	−1.35605e9	−0.126572
$735$	2.32768e8	0.0216231
$736$	1.42799e10	1.32024
$737$	−1.58220e9	−0.145588
$738$	−7.11927e8	−0.0651986
$739$	−4.87522e8	−0.0444364	−0.0222182	−	0.999753i	$-0.507073\pi$
$739$	−4.87522e8	−0.0444364	−0.0222182	+	0.999753i	$0.507073\pi$
$740$	4.59488e8	0.0416834
$741$	1.67391e7	0.00151136
$742$	−1.32348e9	−0.118934
$743$	−1.88059e10	−1.68202	−0.841012	−	0.541016i	$-0.818040\pi$
$743$	−1.88059e10	−1.68202	−0.841012	+	0.541016i	$0.818040\pi$
$744$	6.67045e9	0.593813
$745$	3.01477e8	0.0267121
$746$	−8.21457e9	−0.724434
$747$	−1.38532e8	−0.0121599
$748$	8.44552e9	0.737855
$749$	8.39314e9	0.729857
$750$	−3.58384e8	−0.0310194
$751$	2.25057e10	1.93889	0.969444	−	0.245315i	$-0.0788912\pi$
$751$	2.25057e10	1.93889	0.969444	+	0.245315i	$0.0788912\pi$
$752$	3.57003e9	0.306132
$753$	−1.86264e9	−0.158981
$754$	−3.81417e7	−0.00324041
$755$	6.64331e8	0.0561785
$756$	−9.42520e8	−0.0793349
$757$	9.35131e8	0.0783496	0.0391748	−	0.999232i	$-0.487527\pi$
$757$	9.35131e8	0.0783496	0.0391748	+	0.999232i	$0.487527\pi$
$758$	−3.30418e9	−0.275563
$759$	−1.05886e10	−0.879004
$760$	−1.02992e8	−0.00851053
$761$	−8.03138e9	−0.660608	−0.330304	−	0.943875i	$-0.607151\pi$
$761$	−8.03138e9	−0.660608	−0.330304	+	0.943875i	$0.607151\pi$
$762$	−1.23662e9	−0.101250
$763$	3.09736e9	0.252439
$764$	−1.32321e10	−1.07350
$765$	1.83578e8	0.0148253
$766$	1.20671e10	0.970065
$767$	2.35481e7	0.00188439
$768$	−4.86359e9	−0.387430
$769$	−2.58797e9	−0.205219	−0.102610	−	0.994722i	$-0.532719\pi$
$769$	−2.58797e9	−0.205219	−0.102610	+	0.994722i	$0.532719\pi$
$770$	2.23069e8	0.0176084
$771$	1.82203e9	0.143175
$772$	−8.35633e7	−0.00653665
$773$	−1.46523e10	−1.14098	−0.570489	−	0.821306i	$-0.693246\pi$
$773$	−1.46523e10	−1.14098	−0.570489	+	0.821306i	$0.693246\pi$
$774$	−7.18732e7	−0.00557152
$775$	−1.51703e10	−1.17068
$776$	1.86956e10	1.43622
$777$	4.30275e9	0.329058
$778$	−5.81531e9	−0.442735
$779$	9.31941e8	0.0706329
$780$	4.45718e6	0.000336301 0
$781$	3.79350e9	0.284945
$782$	−7.09756e9	−0.530744
$783$	1.15559e9	0.0860275
$784$	−2.92052e9	−0.216448
$785$	8.88251e8	0.0655378
$786$	−6.25104e9	−0.459170
$787$	−7.14096e9	−0.522210	−0.261105	−	0.965310i	$-0.584087\pi$
$787$	−7.14096e9	−0.522210	−0.261105	+	0.965310i	$0.584087\pi$
$788$	−1.64777e10	−1.19965
$789$	2.13748e9	0.154929
$790$	3.22188e8	0.0232495
$791$	5.03068e9	0.361417
$792$	4.85626e9	0.347347
$793$	−1.00760e8	−0.00717514
$794$	−4.80904e9	−0.340947
$795$	−1.89623e8	−0.0133846
$796$	9.13029e9	0.641636
$797$	1.01959e10	0.713379	0.356689	−	0.934223i	$-0.383905\pi$
$797$	1.01959e10	0.713379	0.356689	+	0.934223i	$0.383905\pi$
$798$	−4.13073e8	−0.0287751
$799$	−1.17722e10	−0.816480
$800$	1.48947e10	1.02853
$801$	1.97253e9	0.135616
$802$	5.98110e9	0.409421
$803$	3.43235e10	2.33931
$804$	7.80151e8	0.0529398
$805$	5.59936e8	0.0378314
$806$	−1.26516e8	−0.00851087
$807$	6.05997e9	0.405894
$808$	4.01345e9	0.267657
$809$	−1.75531e10	−1.16556	−0.582780	−	0.812630i	$-0.698035\pi$
$809$	−1.75531e10	−1.16556	−0.582780	+	0.812630i	$0.698035\pi$
$810$	4.52112e7	0.00298916
$811$	−2.83520e10	−1.86643	−0.933214	−	0.359321i	$-0.883008\pi$
$811$	−2.83520e10	−1.86643	−0.933214	+	0.359321i	$0.883008\pi$
$812$	−2.81133e9	−0.184275
$813$	1.58032e9	0.103140
$814$	−9.49529e9	−0.617054
$815$	5.19315e8	0.0336031
$816$	−2.30333e9	−0.148402
$817$	9.40849e7	0.00603591
$818$	−2.05517e8	−0.0131284
$819$	4.17380e7	0.00265484
$820$	2.48151e8	0.0157169
$821$	−2.80476e10	−1.76886	−0.884432	−	0.466669i	$-0.845454\pi$
$821$	−2.80476e10	−1.76886	−0.884432	+	0.466669i	$0.845454\pi$
$822$	−6.64443e9	−0.417260
$823$	−2.23504e10	−1.39761	−0.698806	−	0.715311i	$-0.746285\pi$
$823$	−2.23504e10	−1.39761	−0.698806	+	0.715311i	$0.746285\pi$
$824$	−1.12676e10	−0.701595
$825$	−1.10444e10	−0.684782
$826$	−5.81098e8	−0.0358773
$827$	1.26693e10	0.778900	0.389450	−	0.921048i	$-0.372665\pi$
$827$	1.26693e10	0.778900	0.389450	+	0.921048i	$0.372665\pi$
$828$	5.22099e9	0.319629
$829$	−2.22306e10	−1.35522	−0.677610	−	0.735421i	$-0.736984\pi$
$829$	−2.22306e10	−1.35522	−0.677610	+	0.735421i	$0.736984\pi$
$830$	−1.61665e7	−0.000981391 0
$831$	8.65069e9	0.522934
$832$	4.95709e7	0.00298397
$833$	9.63047e9	0.577285
$834$	4.59016e9	0.273998
$835$	1.60825e9	0.0955986
$836$	−2.72274e9	−0.161170
$837$	3.83310e9	0.225949
$838$	1.65793e9	0.0973221
$839$	−2.27124e10	−1.32769	−0.663845	−	0.747870i	$-0.731077\pi$
$839$	−2.27124e10	−1.32769	−0.663845	+	0.747870i	$0.731077\pi$
$840$	−2.56805e8	−0.0149495
$841$	−1.38030e10	−0.800180
$842$	6.93606e9	0.400425
$843$	−7.99129e9	−0.459431
$844$	−1.06372e10	−0.609019
$845$	9.41922e8	0.0537052
$846$	−2.89925e9	−0.164622
$847$	4.03768e9	0.228318
$848$	2.37918e9	0.133981
$849$	−7.12336e9	−0.399492
$850$	−7.40310e9	−0.413473
$851$	−2.38346e10	−1.32573
$852$	−1.87049e9	−0.103614
$853$	−2.92944e10	−1.61608	−0.808041	−	0.589127i	$-0.799472\pi$
$853$	−2.92944e10	−1.61608	−0.808041	+	0.589127i	$0.799472\pi$
$854$	2.48646e9	0.136609
$855$	−5.91833e7	−0.00323831
$856$	2.13232e10	1.16197
$857$	−2.01612e9	−0.109417	−0.0547084	−	0.998502i	$-0.517423\pi$
$857$	−2.01612e9	−0.109417	−0.0547084	+	0.998502i	$0.517423\pi$
$858$	−9.21072e7	−0.00497838
$859$	−1.62001e10	−0.872052	−0.436026	−	0.899934i	$-0.643614\pi$
$859$	−1.62001e10	−0.872052	−0.436026	+	0.899934i	$0.643614\pi$
$860$	2.50523e7	0.00134309
$861$	2.32374e9	0.124073
$862$	3.54992e9	0.188774
$863$	4.82303e9	0.255436	0.127718	−	0.991811i	$-0.459235\pi$
$863$	4.82303e9	0.255436	0.127718	+	0.991811i	$0.459235\pi$
$864$	−3.76346e9	−0.198513
$865$	−4.47108e8	−0.0234885
$866$	1.58530e10	0.829468
$867$	−3.48387e9	−0.181550
$868$	−9.32521e9	−0.483993
$869$	1.98866e10	1.02799
$870$	1.34855e8	0.00694305
$871$	−3.45477e7	−0.00177156
$872$	7.86900e9	0.401894
$873$	1.07432e10	0.546492
$874$	2.28817e9	0.115931
$875$	1.16977e9	0.0590299
$876$	−1.69242e10	−0.850634
$877$	4.98280e9	0.249445	0.124723	−	0.992192i	$-0.460196\pi$
$877$	4.98280e9	0.249445	0.124723	+	0.992192i	$0.460196\pi$
$878$	3.45351e9	0.172199
$879$	1.02458e10	0.508843
$880$	−4.01003e8	−0.0198362
$881$	1.27067e10	0.626061	0.313031	−	0.949743i	$-0.398656\pi$
$881$	1.27067e10	0.626061	0.313031	+	0.949743i	$0.398656\pi$
$882$	2.37178e9	0.116395
$883$	−1.01601e9	−0.0496633	−0.0248316	−	0.999692i	$-0.507905\pi$
$883$	−1.01601e9	−0.0496633	−0.0248316	+	0.999692i	$0.507905\pi$
$884$	1.84409e8	0.00897843
$885$	−8.32573e7	−0.00403758
$886$	1.02428e10	0.494765
$887$	1.10442e10	0.531376	0.265688	−	0.964059i	$-0.414401\pi$
$887$	1.10442e10	0.531376	0.265688	+	0.964059i	$0.414401\pi$
$888$	1.09313e10	0.523876
$889$	4.03636e9	0.192679
$890$	2.30191e8	0.0109452
$891$	2.79060e9	0.132168
$892$	1.42613e10	0.672793
$893$	3.79523e9	0.178344
$894$	3.07188e9	0.143788
$895$	−1.84495e9	−0.0860208
$896$	1.09978e10	0.510775
$897$	−2.31203e8	−0.0106960
$898$	−3.58532e9	−0.165219
$899$	1.14333e10	0.524823
$900$	5.44574e9	0.249005
$901$	−7.84539e9	−0.357337
$902$	−5.12803e9	−0.232663
$903$	2.34595e8	0.0106026
$904$	1.27807e10	0.575393
$905$	−1.19261e9	−0.0534844
$906$	6.76915e9	0.302403
$907$	−2.36818e10	−1.05388	−0.526938	−	0.849904i	$-0.676660\pi$
$907$	−2.36818e10	−1.05388	−0.526938	+	0.849904i	$0.676660\pi$
$908$	−4.27556e9	−0.189536
$909$	2.30628e9	0.101845
$910$	4.87074e6	0.000214265 0
$911$	1.78985e10	0.784338	0.392169	−	0.919893i	$-0.371725\pi$
$911$	1.78985e10	0.784338	0.392169	+	0.919893i	$0.371725\pi$
$912$	7.42566e8	0.0324155
$913$	−9.97853e8	−0.0433929
$914$	1.81295e9	0.0785371
$915$	3.56249e8	0.0153738
$916$	9.20650e9	0.395786
$917$	2.04035e10	0.873799
$918$	1.87055e9	0.0798032
$919$	−5.16659e9	−0.219584	−0.109792	−	0.993955i	$-0.535018\pi$
$919$	−5.16659e9	−0.219584	−0.109792	+	0.993955i	$0.535018\pi$
$920$	1.42254e9	0.0602294
$921$	1.26295e10	0.532694
$922$	5.41298e9	0.227446
$923$	8.28317e7	0.00346729
$924$	−6.78899e9	−0.283109
$925$	−2.48607e10	−1.03280
$926$	−2.01225e10	−0.832804
$927$	−6.47481e9	−0.266961
$928$	−1.12256e10	−0.461095
$929$	2.17904e10	0.891681	0.445840	−	0.895112i	$-0.352905\pi$
$929$	2.17904e10	0.891681	0.445840	+	0.895112i	$0.352905\pi$
$930$	4.47316e8	0.0182358
$931$	−3.10475e9	−0.126096
$932$	1.43769e10	0.581713
$933$	−9.36371e8	−0.0377452
$934$	−2.31656e10	−0.930315
$935$	1.32231e9	0.0529047
$936$	1.06037e8	0.00422662
$937$	−2.40380e10	−0.954575	−0.477287	−	0.878747i	$-0.658380\pi$
$937$	−2.40380e10	−0.954575	−0.477287	+	0.878747i	$0.658380\pi$
$938$	8.52538e8	0.0337290
$939$	8.82539e9	0.347860
$940$	1.01057e9	0.0396843
$941$	4.36782e10	1.70884	0.854419	−	0.519585i	$-0.173913\pi$
$941$	4.36782e10	1.70884	0.854419	+	0.519585i	$0.173913\pi$
$942$	9.05077e9	0.352783
$943$	−1.28721e10	−0.499872
$944$	1.04462e9	0.0404163
$945$	−1.47570e8	−0.00568837
$946$	−5.17705e8	−0.0198821
$947$	1.94958e10	0.745961	0.372980	−	0.927839i	$-0.378336\pi$
$947$	1.94958e10	0.745961	0.372980	+	0.927839i	$0.378336\pi$
$948$	−9.80564e9	−0.373806
$949$	7.49459e8	0.0284653
$950$	2.38667e9	0.0903151
$951$	1.08044e10	0.407350
$952$	−1.06250e10	−0.399115
$953$	1.31470e10	0.492040	0.246020	−	0.969265i	$-0.420877\pi$
$953$	1.31470e10	0.492040	0.246020	+	0.969265i	$0.420877\pi$
$954$	−1.93215e9	−0.0720480
$955$	−2.07175e9	−0.0769707
$956$	4.79079e9	0.177339
$957$	8.32374e9	0.306992
$958$	−1.25402e10	−0.460813
$959$	2.16875e10	0.794045
$960$	−1.75265e8	−0.00639359
$961$	1.04117e10	0.378435
$962$	−2.07331e8	−0.00750848
$963$	1.22531e10	0.442135
$964$	−3.77877e8	−0.0135857
$965$	−1.30835e7	−0.000468682 0
$966$	5.70542e9	0.203642
$967$	4.78218e10	1.70072	0.850361	−	0.526200i	$-0.176384\pi$
$967$	4.78218e10	1.70072	0.850361	+	0.526200i	$0.176384\pi$
$968$	1.02579e10	0.363493
$969$	−2.44863e9	−0.0864548
$970$	1.25371e9	0.0441059
$971$	2.03563e10	0.713560	0.356780	−	0.934188i	$-0.383875\pi$
$971$	2.03563e10	0.713560	0.356780	+	0.934188i	$0.383875\pi$
$972$	−1.37598e9	−0.0480597
$973$	−1.49824e10	−0.521418
$974$	2.65374e10	0.920242
$975$	−2.41156e8	−0.00833262
$976$	−4.46982e9	−0.153892
$977$	−4.11493e10	−1.41166	−0.705832	−	0.708379i	$-0.749427\pi$
$977$	−4.11493e10	−1.41166	−0.705832	+	0.708379i	$0.749427\pi$
$978$	5.29152e9	0.180882
$979$	1.42082e10	0.483949
$980$	−8.26713e8	−0.0280584
$981$	4.52183e9	0.152923
$982$	1.01935e10	0.343506
$983$	−2.78989e10	−0.936805	−0.468402	−	0.883515i	$-0.655170\pi$
$983$	−2.78989e10	−0.936805	−0.468402	+	0.883515i	$0.655170\pi$
$984$	5.90358e9	0.197530
$985$	−2.57992e9	−0.0860160
$986$	5.57944e9	0.185362
$987$	9.46320e9	0.313277
$988$	−5.94514e7	−0.00196116
$989$	−1.29952e9	−0.0427164
$990$	3.25658e8	0.0106669
$991$	−5.57475e10	−1.81957	−0.909783	−	0.415084i	$-0.863752\pi$
$991$	−5.57475e10	−1.81957	−0.909783	+	0.415084i	$0.863752\pi$
$992$	−3.72353e10	−1.21106
$993$	−5.62846e9	−0.182418
$994$	−2.04405e9	−0.0660144
$995$	1.42953e9	0.0460058
$996$	4.92019e8	0.0157788
$997$	1.05869e10	0.338326	0.169163	−	0.985588i	$-0.445894\pi$
$997$	1.05869e10	0.338326	0.169163	+	0.985588i	$0.445894\pi$
$998$	4.82724e9	0.153724
$999$	6.28158e9	0.199338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.7	✓	18
3.2	odd	2		531.8.a.e.1.12		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.7	✓	18	1.1	even	1	trivial
531.8.a.e.1.12		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)

\(f(q)\)	\(=\)	\(q-5.66616 q^{2} +27.0000 q^{3} -95.8947 q^{4} -15.0142 q^{5} -152.986 q^{6} +499.350 q^{7} +1268.62 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-5.66616 q^{2} +27.0000 q^{3} -95.8947 q^{4} -15.0142 q^{5} -152.986 q^{6} +499.350 q^{7} +1268.62 q^{8} +729.000 q^{9} +85.0729 q^{10} +5251.00 q^{11} -2589.16 q^{12} +114.657 q^{13} -2829.39 q^{14} -405.384 q^{15} +5086.30 q^{16} -16772.2 q^{17} -4130.63 q^{18} +5407.16 q^{19} +1439.78 q^{20} +13482.4 q^{21} -29753.0 q^{22} -74684.5 q^{23} +34252.8 q^{24} -77899.6 q^{25} -649.662 q^{26} +19683.0 q^{27} -47885.0 q^{28} +58710.0 q^{29} +2296.97 q^{30} +194742. q^{31} -191203. q^{32} +141777. q^{33} +95033.9 q^{34} -7497.35 q^{35} -69907.2 q^{36} +319137. q^{37} -30637.8 q^{38} +3095.73 q^{39} -19047.4 q^{40} +172353. q^{41} -76393.7 q^{42} +17400.1 q^{43} -503543. q^{44} -10945.4 q^{45} +423174. q^{46} +701890. q^{47} +137330. q^{48} -574193. q^{49} +441391. q^{50} -452849. q^{51} -10995.0 q^{52} +467762. q^{53} -111527. q^{54} -78839.7 q^{55} +633486. q^{56} +145993. q^{57} -332660. q^{58} +205379. q^{59} +38874.1 q^{60} -878795. q^{61} -1.10344e6 q^{62} +364026. q^{63} +432342. q^{64} -1721.48 q^{65} -803331. q^{66} -301315. q^{67} +1.60836e6 q^{68} -2.01648e6 q^{69} +42481.1 q^{70} +722433. q^{71} +924826. q^{72} +6.53656e6 q^{73} -1.80828e6 q^{74} -2.10329e6 q^{75} -518518. q^{76} +2.62209e6 q^{77} -17540.9 q^{78} +3.78720e6 q^{79} -76366.8 q^{80} +531441. q^{81} -976580. q^{82} -190031. q^{83} -1.29289e6 q^{84} +251821. q^{85} -98591.5 q^{86} +1.58517e6 q^{87} +6.66154e6 q^{88} +2.70581e6 q^{89} +62018.2 q^{90} +57253.7 q^{91} +7.16185e6 q^{92} +5.25803e6 q^{93} -3.97702e6 q^{94} -81184.2 q^{95} -5.16249e6 q^{96} +1.47369e7 q^{97} +3.25347e6 q^{98} +3.82798e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 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

Properties

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