LMFDB - Embedded newform 177.8.a.b.1.6

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:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-10.1391$ 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)

$f(q)$	$=$	$q-12.1391 q^{2} +27.0000 q^{3} +19.3578 q^{4} +236.334 q^{5} -327.756 q^{6} +1426.66 q^{7} +1318.82 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-12.1391 q^{2} +27.0000 q^{3} +19.3578 q^{4} +236.334 q^{5} -327.756 q^{6} +1426.66 q^{7} +1318.82 q^{8} +729.000 q^{9} -2868.89 q^{10} -5472.58 q^{11} +522.660 q^{12} -8451.67 q^{13} -17318.4 q^{14} +6381.03 q^{15} -18487.1 q^{16} -6087.08 q^{17} -8849.40 q^{18} -12974.5 q^{19} +4574.91 q^{20} +38519.8 q^{21} +66432.2 q^{22} -53979.7 q^{23} +35608.1 q^{24} -22271.1 q^{25} +102596. q^{26} +19683.0 q^{27} +27617.0 q^{28} -14368.8 q^{29} -77459.9 q^{30} -48485.8 q^{31} +55607.6 q^{32} -147760. q^{33} +73891.7 q^{34} +337169. q^{35} +14111.8 q^{36} +82881.8 q^{37} +157499. q^{38} -228195. q^{39} +311682. q^{40} -782250. q^{41} -467596. q^{42} -369462. q^{43} -105937. q^{44} +172288. q^{45} +655265. q^{46} +368463. q^{47} -499151. q^{48} +1.21182e6 q^{49} +270351. q^{50} -164351. q^{51} -163605. q^{52} +836648. q^{53} -238934. q^{54} -1.29336e6 q^{55} +1.88151e6 q^{56} -350312. q^{57} +174424. q^{58} -205379. q^{59} +123522. q^{60} +37349.1 q^{61} +588573. q^{62} +1.04004e6 q^{63} +1.69132e6 q^{64} -1.99742e6 q^{65} +1.79367e6 q^{66} +2.64158e6 q^{67} -117832. q^{68} -1.45745e6 q^{69} -4.09293e6 q^{70} -2.03139e6 q^{71} +961419. q^{72} -3.64005e6 q^{73} -1.00611e6 q^{74} -601319. q^{75} -251158. q^{76} -7.80751e6 q^{77} +2.77008e6 q^{78} -7.63186e6 q^{79} -4.36913e6 q^{80} +531441. q^{81} +9.49581e6 q^{82} -6.69291e6 q^{83} +745658. q^{84} -1.43859e6 q^{85} +4.48494e6 q^{86} -387957. q^{87} -7.21734e6 q^{88} +717966. q^{89} -2.09142e6 q^{90} -1.20577e7 q^{91} -1.04493e6 q^{92} -1.30912e6 q^{93} -4.47281e6 q^{94} -3.06632e6 q^{95} +1.50141e6 q^{96} +1.06996e7 q^{97} -1.47104e7 q^{98} -3.98951e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * 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 $

$2$	−12.1391	−1.07296	−0.536478	−	0.843915i	$-0.680245\pi$
$2$	−12.1391	−1.07296	−0.536478	+	0.843915i	$0.680245\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	19.3578	0.151233
$5$	236.334	0.845536	0.422768	−	0.906238i	$-0.361059\pi$
$5$	236.334	0.845536	0.422768	+	0.906238i	$0.361059\pi$
$6$	−327.756	−0.619471
$7$	1426.66	1.57209	0.786045	−	0.618169i	$-0.212125\pi$
$7$	1426.66	1.57209	0.786045	+	0.618169i	$0.212125\pi$
$8$	1318.82	0.910689
$9$	729.000	0.333333
$10$	−2868.89	−0.907222
$11$	−5472.58	−1.23970	−0.619851	−	0.784719i	$-0.712807\pi$
$11$	−5472.58	−1.23970	−0.619851	+	0.784719i	$0.712807\pi$
$12$	522.660	0.0873142
$13$	−8451.67	−1.06694	−0.533471	−	0.845819i	$-0.679113\pi$
$13$	−8451.67	−1.06694	−0.533471	+	0.845819i	$0.679113\pi$
$14$	−17318.4	−1.68678
$15$	6381.03	0.488170
$16$	−18487.1	−1.12836
$17$	−6087.08	−0.300495	−0.150248	−	0.988648i	$-0.548007\pi$
$17$	−6087.08	−0.300495	−0.150248	+	0.988648i	$0.548007\pi$
$18$	−8849.40	−0.357652
$19$	−12974.5	−0.433964	−0.216982	−	0.976176i	$-0.569621\pi$
$19$	−12974.5	−0.433964	−0.216982	+	0.976176i	$0.569621\pi$
$20$	4574.91	0.127873
$21$	38519.8	0.907647
$22$	66432.2	1.33015
$23$	−53979.7	−0.925087	−0.462544	−	0.886597i	$-0.653063\pi$
$23$	−53979.7	−0.925087	−0.462544	+	0.886597i	$0.653063\pi$
$24$	35608.1	0.525787
$25$	−22271.1	−0.285070
$26$	102596.	1.14478
$27$	19683.0	0.192450
$28$	27617.0	0.237751
$29$	−14368.8	−0.109402	−0.0547011	−	0.998503i	$-0.517421\pi$
$29$	−14368.8	−0.109402	−0.0547011	+	0.998503i	$0.517421\pi$
$30$	−77459.9	−0.523785
$31$	−48485.8	−0.292313	−0.146157	−	0.989261i	$-0.546690\pi$
$31$	−48485.8	−0.292313	−0.146157	+	0.989261i	$0.546690\pi$
$32$	55607.6	0.299992
$33$	−147760.	−0.715743
$34$	73891.7	0.322418
$35$	337169.	1.32926
$36$	14111.8	0.0504109
$37$	82881.8	0.269001	0.134500	−	0.990914i	$-0.457057\pi$
$37$	82881.8	0.269001	0.134500	+	0.990914i	$0.457057\pi$
$38$	157499.	0.465624
$39$	−228195.	−0.615999
$40$	311682.	0.770020
$41$	−782250.	−1.77256	−0.886282	−	0.463146i	$-0.846720\pi$
$41$	−782250.	−1.77256	−0.886282	+	0.463146i	$0.846720\pi$
$42$	−467596.	−0.973864
$43$	−369462.	−0.708647	−0.354324	−	0.935123i	$-0.615289\pi$
$43$	−369462.	−0.708647	−0.354324	+	0.935123i	$0.615289\pi$
$44$	−105937.	−0.187483
$45$	172288.	0.281845
$46$	655265.	0.992577
$47$	368463.	0.517668	0.258834	−	0.965922i	$-0.416662\pi$
$47$	368463.	0.517668	0.258834	+	0.965922i	$0.416662\pi$
$48$	−499151.	−0.651460
$49$	1.21182e6	1.47147
$50$	270351.	0.305867
$51$	−164351.	−0.173491
$52$	−163605.	−0.161356
$53$	836648.	0.771929	0.385964	−	0.922514i	$-0.373869\pi$
$53$	836648.	0.771929	0.385964	+	0.922514i	$0.373869\pi$
$54$	−238934.	−0.206490
$55$	−1.29336e6	−1.04821
$56$	1.88151e6	1.43169
$57$	−350312.	−0.250549
$58$	174424.	0.117384
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	123522.	0.0738272
$61$	37349.1	0.0210681	0.0105341	−	0.999945i	$-0.496647\pi$
$61$	37349.1	0.0210681	0.0105341	+	0.999945i	$0.496647\pi$
$62$	588573.	0.313639
$63$	1.04004e6	0.524030
$64$	1.69132e6	0.806484
$65$	−1.99742e6	−0.902137
$66$	1.79367e6	0.767960
$67$	2.64158e6	1.07300	0.536502	−	0.843899i	$-0.319745\pi$
$67$	2.64158e6	1.07300	0.536502	+	0.843899i	$0.319745\pi$
$68$	−117832.	−0.0454447
$69$	−1.45745e6	−0.534099
$70$	−4.09293e6	−1.42623
$71$	−2.03139e6	−0.673579	−0.336790	−	0.941580i	$-0.609341\pi$
$71$	−2.03139e6	−0.673579	−0.336790	+	0.941580i	$0.609341\pi$
$72$	961419.	0.303563
$73$	−3.64005e6	−1.09516	−0.547580	−	0.836753i	$-0.684451\pi$
$73$	−3.64005e6	−1.09516	−0.547580	+	0.836753i	$0.684451\pi$
$74$	−1.00611e6	−0.288625
$75$	−601319.	−0.164585
$76$	−251158.	−0.0656295
$77$	−7.80751e6	−1.94892
$78$	2.77008e6	0.660939
$79$	−7.63186e6	−1.74155	−0.870774	−	0.491683i	$-0.836382\pi$
$79$	−7.63186e6	−1.74155	−0.870774	+	0.491683i	$0.836382\pi$
$80$	−4.36913e6	−0.954070
$81$	531441.	0.111111
$82$	9.49581e6	1.90188
$83$	−6.69291e6	−1.28482	−0.642409	−	0.766362i	$-0.722065\pi$
$83$	−6.69291e6	−1.28482	−0.642409	+	0.766362i	$0.722065\pi$
$84$	745658.	0.137266
$85$	−1.43859e6	−0.254079
$86$	4.48494e6	0.760347
$87$	−387957.	−0.0631634
$88$	−7.21734e6	−1.12898
$89$	717966.	0.107954	0.0539770	−	0.998542i	$-0.482810\pi$
$89$	717966.	0.107954	0.0539770	+	0.998542i	$0.482810\pi$
$90$	−2.09142e6	−0.302407
$91$	−1.20577e7	−1.67733
$92$	−1.04493e6	−0.139903
$93$	−1.30912e6	−0.168767
$94$	−4.47281e6	−0.555435
$95$	−3.06632e6	−0.366932
$96$	1.50141e6	0.173200
$97$	1.06996e7	1.19033	0.595165	−	0.803604i	$-0.297087\pi$
$97$	1.06996e7	1.19033	0.595165	+	0.803604i	$0.297087\pi$
$98$	−1.47104e7	−1.57882
$99$	−3.98951e6	−0.413234
$100$	−431118.	−0.0431118
$101$	−1.14739e7	−1.10812	−0.554058	−	0.832478i	$-0.686921\pi$
$101$	−1.14739e7	−1.10812	−0.554058	+	0.832478i	$0.686921\pi$
$102$	1.99507e6	0.186148
$103$	7.95531e6	0.717343	0.358671	−	0.933464i	$-0.383230\pi$
$103$	7.95531e6	0.717343	0.358671	+	0.933464i	$0.383230\pi$
$104$	−1.11462e7	−0.971652
$105$	9.10356e6	0.767448
$106$	−1.01562e7	−0.828245
$107$	1.10513e7	0.872107	0.436054	−	0.899921i	$-0.356376\pi$
$107$	1.10513e7	0.872107	0.436054	+	0.899921i	$0.356376\pi$
$108$	381019.	0.0291047
$109$	8.08293e6	0.597828	0.298914	−	0.954280i	$-0.403376\pi$
$109$	8.08293e6	0.597828	0.298914	+	0.954280i	$0.403376\pi$
$110$	1.57002e7	1.12469
$111$	2.23781e6	0.155308
$112$	−2.63748e7	−1.77389
$113$	−9.96488e6	−0.649677	−0.324839	−	0.945769i	$-0.605310\pi$
$113$	−9.96488e6	−0.649677	−0.324839	+	0.945769i	$0.605310\pi$
$114$	4.25247e6	0.268828
$115$	−1.27572e7	−0.782194
$116$	−278147.	−0.0165452
$117$	−6.16126e6	−0.355647
$118$	2.49312e6	0.139687
$119$	−8.68420e6	−0.472406
$120$	8.41542e6	0.444571
$121$	1.04619e7	0.536863
$122$	−453384.	−0.0226051
$123$	−2.11207e7	−1.02339
$124$	−938576.	−0.0442073
$125$	−2.37270e7	−1.08657
$126$	−1.26251e7	−0.562261
$127$	3.01471e7	1.30597	0.652984	−	0.757372i	$-0.273517\pi$
$127$	3.01471e7	1.30597	0.652984	+	0.757372i	$0.273517\pi$
$128$	−2.76489e7	−1.16531
$129$	−9.97547e6	−0.409138
$130$	2.42469e7	0.967952
$131$	−4.85605e7	−1.88727	−0.943634	−	0.330990i	$-0.892617\pi$
$131$	−4.85605e7	−1.88727	−0.943634	+	0.330990i	$0.892617\pi$
$132$	−2.86030e6	−0.108244
$133$	−1.85102e7	−0.682231
$134$	−3.20664e7	−1.15129
$135$	4.65177e6	0.162723
$136$	−8.02775e6	−0.273658
$137$	−1.46792e7	−0.487732	−0.243866	−	0.969809i	$-0.578416\pi$
$137$	−1.46792e7	−0.487732	−0.243866	+	0.969809i	$0.578416\pi$
$138$	1.76921e7	0.573065
$139$	3.93077e7	1.24144	0.620721	−	0.784032i	$-0.286840\pi$
$139$	3.93077e7	1.24144	0.620721	+	0.784032i	$0.286840\pi$
$140$	6.52684e6	0.201027
$141$	9.94850e6	0.298876
$142$	2.46592e7	0.722720
$143$	4.62524e7	1.32269
$144$	−1.34771e7	−0.376120
$145$	−3.39583e6	−0.0925035
$146$	4.41870e7	1.17506
$147$	3.27191e7	0.849553
$148$	1.60441e6	0.0406817
$149$	−6.99960e7	−1.73349	−0.866745	−	0.498752i	$-0.833792\pi$
$149$	−6.99960e7	−1.73349	−0.866745	+	0.498752i	$0.833792\pi$
$150$	7.29947e6	0.176592
$151$	5.84052e7	1.38049	0.690243	−	0.723577i	$-0.257503\pi$
$151$	5.84052e7	1.38049	0.690243	+	0.723577i	$0.257503\pi$
$152$	−1.71110e7	−0.395206
$153$	−4.43748e6	−0.100165
$154$	9.47762e7	2.09111
$155$	−1.14588e7	−0.247161
$156$	−4.41735e6	−0.0931591
$157$	5.09364e7	1.05046	0.525230	−	0.850960i	$-0.323979\pi$
$157$	5.09364e7	1.05046	0.525230	+	0.850960i	$0.323979\pi$
$158$	9.26439e7	1.86860
$159$	2.25895e7	0.445673
$160$	1.31420e7	0.253654
$161$	−7.70107e7	−1.45432
$162$	−6.45122e6	−0.119217
$163$	−2.83386e7	−0.512532	−0.256266	−	0.966606i	$-0.582492\pi$
$163$	−2.83386e7	−0.512532	−0.256266	+	0.966606i	$0.582492\pi$
$164$	−1.51426e7	−0.268069
$165$	−3.49207e7	−0.605186
$166$	8.12459e7	1.37855
$167$	9.62396e6	0.159899	0.0799496	−	0.996799i	$-0.474524\pi$
$167$	9.62396e6	0.159899	0.0799496	+	0.996799i	$0.474524\pi$
$168$	5.08007e7	0.826584
$169$	8.68213e6	0.138364
$170$	1.74631e7	0.272616
$171$	−9.45842e6	−0.144655
$172$	−7.15196e6	−0.107171
$173$	7.21139e7	1.05891	0.529454	−	0.848339i	$-0.322397\pi$
$173$	7.21139e7	1.05891	0.529454	+	0.848339i	$0.322397\pi$
$174$	4.70944e6	0.0677715
$175$	−3.17733e7	−0.448155
$176$	1.01172e8	1.39883
$177$	−5.54523e6	−0.0751646
$178$	−8.71546e6	−0.115830
$179$	−2.09311e7	−0.272777	−0.136388	−	0.990655i	$-0.543549\pi$
$179$	−2.09311e7	−0.272777	−0.136388	+	0.990655i	$0.543549\pi$
$180$	3.33511e6	0.0426242
$181$	4.58129e7	0.574266	0.287133	−	0.957891i	$-0.407298\pi$
$181$	4.58129e7	0.574266	0.287133	+	0.957891i	$0.407298\pi$
$182$	1.46369e8	1.79970
$183$	1.00843e6	0.0121637
$184$	−7.11894e7	−0.842467
$185$	1.95878e7	0.227450
$186$	1.58915e7	0.181079
$187$	3.33120e7	0.372525
$188$	7.13262e6	0.0782883
$189$	2.80810e7	0.302549
$190$	3.72224e7	0.393701
$191$	−1.58678e8	−1.64779	−0.823893	−	0.566746i	$-0.808202\pi$
$191$	−1.58678e8	−1.64779	−0.823893	+	0.566746i	$0.808202\pi$
$192$	4.56656e7	0.465624
$193$	6.81944e7	0.682807	0.341404	−	0.939917i	$-0.389098\pi$
$193$	6.81944e7	0.682807	0.341404	+	0.939917i	$0.389098\pi$
$194$	−1.29884e8	−1.27717
$195$	−5.39303e7	−0.520849
$196$	2.34581e7	0.222534
$197$	8.04764e7	0.749957	0.374979	−	0.927033i	$-0.377650\pi$
$197$	8.04764e7	0.749957	0.374979	+	0.927033i	$0.377650\pi$
$198$	4.84291e7	0.443382
$199$	−6.86011e7	−0.617085	−0.308543	−	0.951211i	$-0.599841\pi$
$199$	−6.86011e7	−0.617085	−0.308543	+	0.951211i	$0.599841\pi$
$200$	−2.93715e7	−0.259610
$201$	7.13226e7	0.619499
$202$	1.39283e8	1.18896
$203$	−2.04993e7	−0.171990
$204$	−3.18147e6	−0.0262375
$205$	−1.84872e8	−1.49877
$206$	−9.65703e7	−0.769677
$207$	−3.93512e7	−0.308362
$208$	1.56247e8	1.20390
$209$	7.10040e7	0.537986
$210$	−1.10509e8	−0.823437
$211$	2.88847e7	0.211679	0.105840	−	0.994383i	$-0.466247\pi$
$211$	2.88847e7	0.211679	0.105840	+	0.994383i	$0.466247\pi$
$212$	1.61956e7	0.116741
$213$	−5.48475e7	−0.388891
$214$	−1.34153e8	−0.935732
$215$	−8.73166e7	−0.599187
$216$	2.59583e7	0.175262
$217$	−6.91727e7	−0.459543
$218$	−9.81195e7	−0.641442
$219$	−9.82815e7	−0.632291
$220$	−2.50365e7	−0.158524
$221$	5.14459e7	0.320611
$222$	−2.71650e7	−0.166638
$223$	2.59394e8	1.56637	0.783184	−	0.621790i	$-0.213594\pi$
$223$	2.59394e8	1.56637	0.783184	+	0.621790i	$0.213594\pi$
$224$	7.93332e7	0.471614
$225$	−1.62356e7	−0.0950232
$226$	1.20965e8	0.697074
$227$	−2.03673e8	−1.15570	−0.577848	−	0.816144i	$-0.696107\pi$
$227$	−2.03673e8	−1.15570	−0.577848	+	0.816144i	$0.696107\pi$
$228$	−6.78126e6	−0.0378912
$229$	−3.48601e8	−1.91825	−0.959124	−	0.282986i	$-0.908675\pi$
$229$	−3.48601e8	−1.91825	−0.959124	+	0.282986i	$0.908675\pi$
$230$	1.54862e8	0.839259
$231$	−2.10803e8	−1.12521
$232$	−1.89498e7	−0.0996315
$233$	1.56687e8	0.811495	0.405748	−	0.913985i	$-0.367011\pi$
$233$	1.56687e8	0.811495	0.405748	+	0.913985i	$0.367011\pi$
$234$	7.47922e7	0.381593
$235$	8.70805e7	0.437707
$236$	−3.97568e6	−0.0196888
$237$	−2.06060e8	−1.00548
$238$	1.05418e8	0.506870
$239$	2.08708e8	0.988885	0.494443	−	0.869210i	$-0.335372\pi$
$239$	2.08708e8	0.988885	0.494443	+	0.869210i	$0.335372\pi$
$240$	−1.17967e8	−0.550832
$241$	−3.80494e8	−1.75101	−0.875505	−	0.483209i	$-0.839471\pi$
$241$	−3.80494e8	−1.75101	−0.875505	+	0.483209i	$0.839471\pi$
$242$	−1.26998e8	−0.576029
$243$	1.43489e7	0.0641500
$244$	722995.	0.00318619
$245$	2.86394e8	1.24418
$246$	2.56387e8	1.09805
$247$	1.09656e8	0.463014
$248$	−6.39439e7	−0.266206
$249$	−1.80708e8	−0.741790
$250$	2.88025e8	1.16584
$251$	−1.88517e8	−0.752474	−0.376237	−	0.926523i	$-0.622782\pi$
$251$	−1.88517e8	−0.752474	−0.376237	+	0.926523i	$0.622782\pi$
$252$	2.01328e7	0.0792505
$253$	2.95408e8	1.14683
$254$	−3.65959e8	−1.40125
$255$	−3.88418e7	−0.146693
$256$	1.19144e8	0.443844
$257$	3.79943e8	1.39621	0.698107	−	0.715993i	$-0.254026\pi$
$257$	3.79943e8	1.39621	0.698107	+	0.715993i	$0.254026\pi$
$258$	1.21093e8	0.438986
$259$	1.18244e8	0.422893
$260$	−3.86656e7	−0.136433
$261$	−1.04748e7	−0.0364674
$262$	5.89481e8	2.02495
$263$	1.63239e8	0.553322	0.276661	−	0.960968i	$-0.410772\pi$
$263$	1.63239e8	0.553322	0.276661	+	0.960968i	$0.410772\pi$
$264$	−1.94868e8	−0.651819
$265$	1.97729e8	0.652693
$266$	2.24698e8	0.732003
$267$	1.93851e7	0.0623272
$268$	5.11350e7	0.162273
$269$	−5.26713e8	−1.64984	−0.824918	−	0.565252i	$-0.808779\pi$
$269$	−5.26713e8	−1.64984	−0.824918	+	0.565252i	$0.808779\pi$
$270$	−5.64683e7	−0.174595
$271$	1.21168e8	0.369824	0.184912	−	0.982755i	$-0.440800\pi$
$271$	1.21168e8	0.369824	0.184912	+	0.982755i	$0.440800\pi$
$272$	1.12532e8	0.339067
$273$	−3.25557e8	−0.968406
$274$	1.78193e8	0.523315
$275$	1.21880e8	0.353402
$276$	−2.82130e7	−0.0807732
$277$	3.39227e8	0.958985	0.479492	−	0.877546i	$-0.340821\pi$
$277$	3.39227e8	0.958985	0.479492	+	0.877546i	$0.340821\pi$
$278$	−4.77161e8	−1.33201
$279$	−3.53461e7	−0.0974377
$280$	4.44665e8	1.21054
$281$	−2.48935e8	−0.669289	−0.334644	−	0.942344i	$-0.608616\pi$
$281$	−2.48935e8	−0.669289	−0.334644	+	0.942344i	$0.608616\pi$
$282$	−1.20766e8	−0.320680
$283$	−6.01535e8	−1.57764	−0.788821	−	0.614623i	$-0.789308\pi$
$283$	−6.01535e8	−1.57764	−0.788821	+	0.614623i	$0.789308\pi$
$284$	−3.93232e7	−0.101867
$285$	−8.27908e7	−0.211848
$286$	−5.61462e8	−1.41919
$287$	−1.11600e9	−2.78663
$288$	4.05379e7	0.0999972
$289$	−3.73286e8	−0.909703
$290$	4.12224e7	0.0992521
$291$	2.88890e8	0.687237
$292$	−7.04633e7	−0.165624
$293$	2.39333e8	0.555860	0.277930	−	0.960601i	$-0.410352\pi$
$293$	2.39333e8	0.555860	0.277930	+	0.960601i	$0.410352\pi$
$294$	−3.97180e8	−0.911532
$295$	−4.85381e7	−0.110079
$296$	1.09306e8	0.244976
$297$	−1.07717e8	−0.238581
$298$	8.49688e8	1.85996
$299$	4.56218e8	0.987014
$300$	−1.16402e7	−0.0248906
$301$	−5.27097e8	−1.11406
$302$	−7.08987e8	−1.48120
$303$	−3.09795e8	−0.639771
$304$	2.39861e8	0.489668
$305$	8.82687e6	0.0178138
$306$	5.38670e7	0.107473
$307$	1.00262e8	0.197767	0.0988833	−	0.995099i	$-0.468473\pi$
$307$	1.00262e8	0.197767	0.0988833	+	0.995099i	$0.468473\pi$
$308$	−1.51136e8	−0.294741
$309$	2.14793e8	0.414158
$310$	1.39100e8	0.265193
$311$	7.10291e8	1.33898	0.669491	−	0.742820i	$-0.266512\pi$
$311$	7.10291e8	1.33898	0.669491	+	0.742820i	$0.266512\pi$
$312$	−3.00948e8	−0.560984
$313$	−6.55081e8	−1.20751	−0.603753	−	0.797171i	$-0.706329\pi$
$313$	−6.55081e8	−1.20751	−0.603753	+	0.797171i	$0.706329\pi$
$314$	−6.18322e8	−1.12710
$315$	2.45796e8	0.443086
$316$	−1.47736e8	−0.263379
$317$	−1.70031e8	−0.299793	−0.149896	−	0.988702i	$-0.547894\pi$
$317$	−1.70031e8	−0.299793	−0.149896	+	0.988702i	$0.547894\pi$
$318$	−2.74216e8	−0.478187
$319$	7.86342e7	0.135626
$320$	3.99717e8	0.681911
$321$	2.98385e8	0.503511
$322$	9.34840e8	1.56042
$323$	7.89769e7	0.130404
$324$	1.02875e7	0.0168036
$325$	1.88228e8	0.304153
$326$	3.44005e8	0.549924
$327$	2.18239e8	0.345156
$328$	−1.03165e9	−1.61425
$329$	5.25672e8	0.813821
$330$	4.23906e8	0.649337
$331$	1.29730e8	0.196626	0.0983131	−	0.995156i	$-0.468655\pi$
$331$	1.29730e8	0.196626	0.0983131	+	0.995156i	$0.468655\pi$
$332$	−1.29560e8	−0.194306
$333$	6.04208e7	0.0896668
$334$	−1.16826e8	−0.171565
$335$	6.24295e8	0.907263
$336$	−7.12119e8	−1.02415
$337$	9.55271e7	0.135963	0.0679817	−	0.997687i	$-0.478344\pi$
$337$	9.55271e7	0.135963	0.0679817	+	0.997687i	$0.478344\pi$
$338$	−1.05393e8	−0.148458
$339$	−2.69052e8	−0.375091
$340$	−2.78478e7	−0.0384251
$341$	2.65342e8	0.362381
$342$	1.14817e8	0.155208
$343$	5.53936e8	0.741191
$344$	−4.87254e8	−0.645358
$345$	−3.44446e8	−0.451600
$346$	−8.75398e8	−1.13616
$347$	−1.13393e8	−0.145690	−0.0728452	−	0.997343i	$-0.523208\pi$
$347$	−1.13393e8	−0.145690	−0.0728452	+	0.997343i	$0.523208\pi$
$348$	−7.50998e6	−0.00955237
$349$	−3.72221e8	−0.468719	−0.234359	−	0.972150i	$-0.575299\pi$
$349$	−3.72221e8	−0.468719	−0.234359	+	0.972150i	$0.575299\pi$
$350$	3.85699e8	0.480850
$351$	−1.66354e8	−0.205333
$352$	−3.04317e8	−0.371901
$353$	5.74672e8	0.695358	0.347679	−	0.937614i	$-0.386970\pi$
$353$	5.74672e8	0.695358	0.347679	+	0.937614i	$0.386970\pi$
$354$	6.73141e7	0.0806482
$355$	−4.80087e8	−0.569535
$356$	1.38982e7	0.0163262
$357$	−2.34473e8	−0.272744
$358$	2.54085e8	0.292677
$359$	−5.65130e7	−0.0644640	−0.0322320	−	0.999480i	$-0.510262\pi$
$359$	−5.65130e7	−0.0644640	−0.0322320	+	0.999480i	$0.510262\pi$
$360$	2.27216e8	0.256673
$361$	−7.25534e8	−0.811675
$362$	−5.56127e8	−0.616161
$363$	2.82472e8	0.309958
$364$	−2.33409e8	−0.253667
$365$	−8.60270e8	−0.925997
$366$	−1.22414e7	−0.0130511
$367$	−2.25564e8	−0.238198	−0.119099	−	0.992882i	$-0.538001\pi$
$367$	−2.25564e8	−0.238198	−0.119099	+	0.992882i	$0.538001\pi$
$368$	9.97926e8	1.04383
$369$	−5.70260e8	−0.590855
$370$	−2.37779e8	−0.244043
$371$	1.19361e9	1.21354
$372$	−2.53416e7	−0.0255231
$373$	5.86159e8	0.584837	0.292418	−	0.956290i	$-0.405540\pi$
$373$	5.86159e8	0.584837	0.292418	+	0.956290i	$0.405540\pi$
$374$	−4.04378e8	−0.399702
$375$	−6.40630e8	−0.627333
$376$	4.85936e8	0.471435
$377$	1.21440e8	0.116726
$378$	−3.40878e8	−0.324621
$379$	4.01728e8	0.379048	0.189524	−	0.981876i	$-0.439305\pi$
$379$	4.01728e8	0.379048	0.189524	+	0.981876i	$0.439305\pi$
$380$	−5.93572e7	−0.0554921
$381$	8.13972e8	0.754001
$382$	1.92621e9	1.76800
$383$	−9.90140e8	−0.900536	−0.450268	−	0.892894i	$-0.648671\pi$
$383$	−9.90140e8	−0.900536	−0.450268	+	0.892894i	$0.648671\pi$
$384$	−7.46519e8	−0.672793
$385$	−1.84518e9	−1.64789
$386$	−8.27819e8	−0.732622
$387$	−2.69338e8	−0.236216
$388$	2.07121e8	0.180017
$389$	9.31063e8	0.801965	0.400982	−	0.916086i	$-0.368669\pi$
$389$	9.31063e8	0.801965	0.400982	+	0.916086i	$0.368669\pi$
$390$	6.54666e8	0.558848
$391$	3.28578e8	0.277984
$392$	1.59817e9	1.34005
$393$	−1.31113e9	−1.08962
$394$	−9.76911e8	−0.804671
$395$	−1.80367e9	−1.47254
$396$	−7.72280e7	−0.0624945
$397$	4.18272e8	0.335500	0.167750	−	0.985830i	$-0.446350\pi$
$397$	4.18272e8	0.335500	0.167750	+	0.985830i	$0.446350\pi$
$398$	8.32755e8	0.662105
$399$	−4.99776e8	−0.393886
$400$	4.11727e8	0.321662
$401$	−1.89613e9	−1.46846	−0.734230	−	0.678900i	$-0.762457\pi$
$401$	−1.89613e9	−1.46846	−0.734230	+	0.678900i	$0.762457\pi$
$402$	−8.65792e8	−0.664695
$403$	4.09785e8	0.311881
$404$	−2.22109e8	−0.167583
$405$	1.25598e8	0.0939484
$406$	2.48844e8	0.184538
$407$	−4.53577e8	−0.333481
$408$	−2.16749e8	−0.157996
$409$	−2.41716e9	−1.74693	−0.873463	−	0.486890i	$-0.838131\pi$
$409$	−2.41716e9	−1.74693	−0.873463	+	0.486890i	$0.838131\pi$
$410$	2.24419e9	1.60811
$411$	−3.96340e8	−0.281592
$412$	1.53997e8	0.108486
$413$	−2.93006e8	−0.204669
$414$	4.77688e8	0.330859
$415$	−1.58176e9	−1.08636
$416$	−4.69977e8	−0.320074
$417$	1.06131e9	0.716747
$418$	−8.61925e8	−0.577235
$419$	−1.73070e9	−1.14941	−0.574703	−	0.818362i	$-0.694882\pi$
$419$	−1.73070e9	−1.14941	−0.574703	+	0.818362i	$0.694882\pi$
$420$	1.76225e8	0.116063
$421$	2.38954e9	1.56073	0.780363	−	0.625327i	$-0.215034\pi$
$421$	2.38954e9	1.56073	0.780363	+	0.625327i	$0.215034\pi$
$422$	−3.50634e8	−0.227123
$423$	2.68610e8	0.172556
$424$	1.10339e9	0.702987
$425$	1.35566e8	0.0856621
$426$	6.65799e8	0.417263
$427$	5.32845e7	0.0331210
$428$	2.13928e8	0.131891
$429$	1.24881e9	0.763655
$430$	1.05994e9	0.642900
$431$	−1.06409e9	−0.640188	−0.320094	−	0.947386i	$-0.603714\pi$
$431$	−1.06409e9	−0.640188	−0.320094	+	0.947386i	$0.603714\pi$
$432$	−3.63881e8	−0.217153
$433$	−8.34289e8	−0.493866	−0.246933	−	0.969033i	$-0.579423\pi$
$433$	−8.34289e8	−0.493866	−0.246933	+	0.969033i	$0.579423\pi$
$434$	8.39695e8	0.493069
$435$	−9.16875e7	−0.0534069
$436$	1.56467e8	0.0904110
$437$	7.00360e8	0.401454
$438$	1.19305e9	0.678420
$439$	1.91632e9	1.08104	0.540521	−	0.841331i	$-0.318227\pi$
$439$	1.91632e9	1.08104	0.540521	+	0.841331i	$0.318227\pi$
$440$	−1.70571e9	−0.954596
$441$	8.83415e8	0.490490
$442$	−6.24508e8	−0.344001
$443$	1.43118e9	0.782136	0.391068	−	0.920362i	$-0.372106\pi$
$443$	1.43118e9	0.782136	0.391068	+	0.920362i	$0.372106\pi$
$444$	4.33190e7	0.0234876
$445$	1.69680e8	0.0912789
$446$	−3.14882e9	−1.68064
$447$	−1.88989e9	−1.00083
$448$	2.41294e9	1.26787
$449$	−1.00483e9	−0.523877	−0.261938	−	0.965085i	$-0.584362\pi$
$449$	−1.00483e9	−0.523877	−0.261938	+	0.965085i	$0.584362\pi$
$450$	1.97086e8	0.101956
$451$	4.28092e9	2.19745
$452$	−1.92898e8	−0.0982524
$453$	1.57694e9	0.797024
$454$	2.47241e9	1.24001
$455$	−2.84964e9	−1.41824
$456$	−4.61998e8	−0.228172
$457$	3.31474e9	1.62459	0.812293	−	0.583250i	$-0.198219\pi$
$457$	3.31474e9	1.62459	0.812293	+	0.583250i	$0.198219\pi$
$458$	4.23171e9	2.05819
$459$	−1.19812e8	−0.0578303
$460$	−2.46952e8	−0.118293
$461$	2.98497e7	0.0141901	0.00709507	−	0.999975i	$-0.497742\pi$
$461$	2.98497e7	0.0141901	0.00709507	+	0.999975i	$0.497742\pi$
$462$	2.55896e9	1.20730
$463$	5.11925e8	0.239702	0.119851	−	0.992792i	$-0.461758\pi$
$463$	5.11925e8	0.239702	0.119851	+	0.992792i	$0.461758\pi$
$464$	2.65636e8	0.123445
$465$	−3.09389e8	−0.142699
$466$	−1.90203e9	−0.870698
$467$	−3.33639e9	−1.51589	−0.757946	−	0.652317i	$-0.773797\pi$
$467$	−3.33639e9	−1.51589	−0.757946	+	0.652317i	$0.773797\pi$
$468$	−1.19268e8	−0.0537854
$469$	3.76863e9	1.68686
$470$	−1.05708e9	−0.469640
$471$	1.37528e9	0.606483
$472$	−2.70858e8	−0.118562
$473$	2.02191e9	0.878512
$474$	2.50139e9	1.07884
$475$	2.88956e8	0.123710
$476$	−1.68107e8	−0.0714432
$477$	6.09916e8	0.257310
$478$	−2.53352e9	−1.06103
$479$	−2.42772e8	−0.100931	−0.0504655	−	0.998726i	$-0.516070\pi$
$479$	−2.42772e8	−0.100931	−0.0504655	+	0.998726i	$0.516070\pi$
$480$	3.54834e8	0.146447
$481$	−7.00489e8	−0.287008
$482$	4.61886e9	1.87875
$483$	−2.07929e9	−0.839653
$484$	2.02520e8	0.0811911
$485$	2.52869e9	1.00647
$486$	−1.74183e8	−0.0688301
$487$	−1.18746e9	−0.465872	−0.232936	−	0.972492i	$-0.574833\pi$
$487$	−1.18746e9	−0.465872	−0.232936	+	0.972492i	$0.574833\pi$
$488$	4.92567e7	0.0191865
$489$	−7.65141e8	−0.295911
$490$	−3.47657e9	−1.33495
$491$	1.93067e9	0.736077	0.368039	−	0.929811i	$-0.380029\pi$
$491$	1.93067e9	0.736077	0.368039	+	0.929811i	$0.380029\pi$
$492$	−4.08850e8	−0.154770
$493$	8.74638e7	0.0328749
$494$	−1.33113e9	−0.496793
$495$	−9.42858e8	−0.349404
$496$	8.96360e8	0.329835
$497$	−2.89810e9	−1.05893
$498$	2.19364e9	0.795907
$499$	3.11720e9	1.12308	0.561542	−	0.827448i	$-0.310208\pi$
$499$	3.11720e9	1.12308	0.561542	+	0.827448i	$0.310208\pi$
$500$	−4.59303e8	−0.164325
$501$	2.59847e8	0.0923179
$502$	2.28842e9	0.807371
$503$	−3.19404e8	−0.111906	−0.0559529	−	0.998433i	$-0.517820\pi$
$503$	−3.19404e8	−0.111906	−0.0559529	+	0.998433i	$0.517820\pi$
$504$	1.37162e9	0.477229
$505$	−2.71167e9	−0.936952
$506$	−3.58599e9	−1.23050
$507$	2.34418e8	0.0798845
$508$	5.83581e8	0.197505
$509$	2.35968e9	0.793124	0.396562	−	0.918008i	$-0.370203\pi$
$509$	2.35968e9	0.793124	0.396562	+	0.918008i	$0.370203\pi$
$510$	4.71505e8	0.157395
$511$	−5.19312e9	−1.72169
$512$	2.09276e9	0.689088
$513$	−2.55377e8	−0.0835164
$514$	−4.61216e9	−1.49808
$515$	1.88011e9	0.606539
$516$	−1.93103e8	−0.0618750
$517$	−2.01644e9	−0.641754
$518$	−1.43538e9	−0.453745
$519$	1.94708e9	0.611360
$520$	−2.63423e9	−0.821566
$521$	6.10979e9	1.89276	0.946378	−	0.323062i	$-0.104712\pi$
$521$	6.10979e9	1.89276	0.946378	+	0.323062i	$0.104712\pi$
$522$	1.27155e8	0.0391279
$523$	3.79857e8	0.116109	0.0580543	−	0.998313i	$-0.481510\pi$
$523$	3.79857e8	0.116109	0.0580543	+	0.998313i	$0.481510\pi$
$524$	−9.40023e8	−0.285417
$525$	−8.57878e8	−0.258743
$526$	−1.98157e9	−0.593690
$527$	2.95137e8	0.0878387
$528$	2.73164e9	0.807616
$529$	−4.91022e8	−0.144214
$530$	−2.40025e9	−0.700310
$531$	−1.49721e8	−0.0433963
$532$	−3.58317e8	−0.103176
$533$	6.61131e9	1.89122
$534$	−2.35317e8	−0.0668743
$535$	2.61180e9	0.737398
$536$	3.48376e9	0.977173
$537$	−5.65140e8	−0.157488
$538$	6.39382e9	1.77020
$539$	−6.63177e9	−1.82418
$540$	9.00479e7	0.0246091
$541$	−1.86189e8	−0.0505549	−0.0252774	−	0.999680i	$-0.508047\pi$
$541$	−1.86189e8	−0.0505549	−0.0252774	+	0.999680i	$0.508047\pi$
$542$	−1.47087e9	−0.396805
$543$	1.23695e9	0.331552
$544$	−3.38488e8	−0.0901461
$545$	1.91027e9	0.505484
$546$	3.95197e9	1.03906
$547$	2.56203e8	0.0669311	0.0334656	−	0.999440i	$-0.489346\pi$
$547$	2.56203e8	0.0669311	0.0334656	+	0.999440i	$0.489346\pi$
$548$	−2.84157e8	−0.0737611
$549$	2.72275e7	0.00702270
$550$	−1.47952e9	−0.379184
$551$	1.86428e8	0.0474766
$552$	−1.92211e9	−0.486399
$553$	−1.08881e10	−2.73787
$554$	−4.11792e9	−1.02895
$555$	5.28871e8	0.131318
$556$	7.60911e8	0.187746
$557$	3.54346e9	0.868829	0.434415	−	0.900713i	$-0.356955\pi$
$557$	3.54346e9	0.868829	0.434415	+	0.900713i	$0.356955\pi$
$558$	4.29070e8	0.104546
$559$	3.12257e9	0.756085
$560$	−6.23327e9	−1.49988
$561$	8.99424e8	0.215077
$562$	3.02184e9	0.718117
$563$	−5.23102e9	−1.23540	−0.617699	−	0.786414i	$-0.711935\pi$
$563$	−5.23102e9	−1.23540	−0.617699	+	0.786414i	$0.711935\pi$
$564$	1.92581e8	0.0451998
$565$	−2.35504e9	−0.549325
$566$	7.30209e9	1.69274
$567$	7.58186e8	0.174677
$568$	−2.67903e9	−0.613421
$569$	−2.02667e8	−0.0461200	−0.0230600	−	0.999734i	$-0.507341\pi$
$569$	−2.02667e8	−0.0461200	−0.0230600	+	0.999734i	$0.507341\pi$
$570$	1.00501e9	0.227304
$571$	1.61917e9	0.363969	0.181985	−	0.983301i	$-0.441748\pi$
$571$	1.61917e9	0.363969	0.181985	+	0.983301i	$0.441748\pi$
$572$	8.95343e8	0.200034
$573$	−4.28431e9	−0.951350
$574$	1.35473e10	2.98993
$575$	1.20218e9	0.263714
$576$	1.23297e9	0.268828
$577$	−8.09171e8	−0.175358	−0.0876789	−	0.996149i	$-0.527945\pi$
$577$	−8.09171e8	−0.175358	−0.0876789	+	0.996149i	$0.527945\pi$
$578$	4.53136e9	0.976070
$579$	1.84125e9	0.394219
$580$	−6.57358e7	−0.0139895
$581$	−9.54851e9	−2.01985
$582$	−3.50686e9	−0.737374
$583$	−4.57862e9	−0.956962
$584$	−4.80057e9	−0.997351
$585$	−1.45612e9	−0.300712
$586$	−2.90528e9	−0.596413
$587$	−3.34084e9	−0.681746	−0.340873	−	0.940109i	$-0.610723\pi$
$587$	−3.34084e9	−0.681746	−0.340873	+	0.940109i	$0.610723\pi$
$588$	6.33369e8	0.128480
$589$	6.29079e8	0.126853
$590$	5.89209e8	0.118110
$591$	2.17286e9	0.432988
$592$	−1.53224e9	−0.303530
$593$	4.75989e9	0.937358	0.468679	−	0.883369i	$-0.344730\pi$
$593$	4.75989e9	0.937358	0.468679	+	0.883369i	$0.344730\pi$
$594$	1.30758e9	0.255987
$595$	−2.05237e9	−0.399436
$596$	−1.35497e9	−0.262160
$597$	−1.85223e9	−0.356274
$598$	−5.53808e9	−1.05902
$599$	5.11303e9	0.972041	0.486020	−	0.873947i	$-0.338448\pi$
$599$	5.11303e9	0.972041	0.486020	+	0.873947i	$0.338448\pi$
$600$	−7.93031e8	−0.149886
$601$	−6.88520e9	−1.29377	−0.646883	−	0.762589i	$-0.723928\pi$
$601$	−6.88520e9	−1.29377	−0.646883	+	0.762589i	$0.723928\pi$
$602$	6.39848e9	1.19533
$603$	1.92571e9	0.357668
$604$	1.13059e9	0.208775
$605$	2.47251e9	0.453936
$606$	3.76063e9	0.686446
$607$	−9.35321e9	−1.69746	−0.848732	−	0.528824i	$-0.822633\pi$
$607$	−9.35321e9	−1.69746	−0.848732	+	0.528824i	$0.822633\pi$
$608$	−7.21482e8	−0.130186
$609$	−5.53482e8	−0.0992986
$610$	−1.07150e8	−0.0191134
$611$	−3.11413e9	−0.552321
$612$	−8.58997e7	−0.0151482
$613$	5.18941e9	0.909927	0.454963	−	0.890510i	$-0.349652\pi$
$613$	5.18941e9	0.909927	0.454963	+	0.890510i	$0.349652\pi$
$614$	−1.21709e9	−0.212195
$615$	−4.99156e9	−0.865313
$616$	−1.02967e10	−1.77486
$617$	6.12264e9	1.04940	0.524700	−	0.851287i	$-0.324178\pi$
$617$	6.12264e9	1.04940	0.524700	+	0.851287i	$0.324178\pi$
$618$	−2.60740e9	−0.444373
$619$	2.63490e9	0.446527	0.223263	−	0.974758i	$-0.428329\pi$
$619$	2.63490e9	0.446527	0.223263	+	0.974758i	$0.428329\pi$
$620$	−2.21818e8	−0.0373788
$621$	−1.06248e9	−0.178033
$622$	−8.62230e9	−1.43667
$623$	1.02429e9	0.169713
$624$	4.21866e9	0.695069
$625$	−3.86759e9	−0.633666
$626$	7.95209e9	1.29560
$627$	1.91711e9	0.310606
$628$	9.86016e8	0.158864
$629$	−5.04508e8	−0.0808334
$630$	−2.98374e9	−0.475412
$631$	2.67647e9	0.424092	0.212046	−	0.977260i	$-0.431987\pi$
$631$	2.67647e9	0.424092	0.212046	+	0.977260i	$0.431987\pi$
$632$	−1.00650e10	−1.58601
$633$	7.79886e8	0.122213
$634$	2.06403e9	0.321664
$635$	7.12480e9	1.10424
$636$	4.37282e8	0.0674003
$637$	−1.02419e10	−1.56997
$638$	−9.54548e8	−0.145521
$639$	−1.48088e9	−0.224526
$640$	−6.53438e9	−0.985313
$641$	−1.12657e10	−1.68949	−0.844747	−	0.535166i	$-0.820249\pi$
$641$	−1.12657e10	−1.68949	−0.844747	+	0.535166i	$0.820249\pi$
$642$	−3.62212e9	−0.540245
$643$	5.64942e9	0.838041	0.419021	−	0.907977i	$-0.362373\pi$
$643$	5.64942e9	0.838041	0.419021	+	0.907977i	$0.362373\pi$
$644$	−1.49075e9	−0.219941
$645$	−2.35755e9	−0.345941
$646$	−9.58709e8	−0.139918
$647$	8.48556e9	1.23173	0.615865	−	0.787852i	$-0.288807\pi$
$647$	8.48556e9	1.23173	0.615865	+	0.787852i	$0.288807\pi$
$648$	7.00874e8	0.101188
$649$	1.12395e9	0.161396
$650$	−2.28491e9	−0.326342
$651$	−1.86766e9	−0.265317
$652$	−5.48572e8	−0.0775116
$653$	−5.48317e9	−0.770611	−0.385306	−	0.922789i	$-0.625904\pi$
$653$	−5.48317e9	−0.770611	−0.385306	+	0.922789i	$0.625904\pi$
$654$	−2.64923e9	−0.370337
$655$	−1.14765e10	−1.59575
$656$	1.44615e10	2.00009
$657$	−2.65360e9	−0.365054
$658$	−6.38118e9	−0.873193
$659$	−5.95072e9	−0.809974	−0.404987	−	0.914323i	$-0.632724\pi$
$659$	−5.95072e9	−0.809974	−0.404987	+	0.914323i	$0.632724\pi$
$660$	−6.75986e8	−0.0915238
$661$	−8.08136e9	−1.08838	−0.544188	−	0.838963i	$-0.683162\pi$
$661$	−8.08136e9	−1.08838	−0.544188	+	0.838963i	$0.683162\pi$
$662$	−1.57480e9	−0.210971
$663$	1.38904e9	0.185105
$664$	−8.82673e9	−1.17007
$665$	−4.37460e9	−0.576850
$666$	−7.33455e8	−0.0962085
$667$	7.75621e8	0.101207
$668$	1.86299e8	0.0241820
$669$	7.00365e9	0.904343
$670$	−7.57838e9	−0.973453
$671$	−2.04396e8	−0.0261182
$672$	2.14200e9	0.272287
$673$	−9.07433e9	−1.14752	−0.573762	−	0.819022i	$-0.694517\pi$
$673$	−9.07433e9	−1.14752	−0.573762	+	0.819022i	$0.694517\pi$
$674$	−1.15961e9	−0.145883
$675$	−4.38361e8	−0.0548617
$676$	1.68067e8	0.0209251
$677$	1.13075e10	1.40057	0.700286	−	0.713862i	$-0.253056\pi$
$677$	1.13075e10	1.40057	0.700286	+	0.713862i	$0.253056\pi$
$678$	3.26605e9	0.402456
$679$	1.52647e10	1.87131
$680$	−1.89723e9	−0.231387
$681$	−5.49918e9	−0.667241
$682$	−3.22101e9	−0.388819
$683$	1.42517e10	1.71157	0.855783	−	0.517336i	$-0.173076\pi$
$683$	1.42517e10	1.71157	0.855783	+	0.517336i	$0.173076\pi$
$684$	−1.83094e8	−0.0218765
$685$	−3.46921e9	−0.412395
$686$	−6.72429e9	−0.795265
$687$	−9.41224e9	−1.10750
$688$	6.83027e9	0.799610
$689$	−7.07107e9	−0.823603
$690$	4.18126e9	0.484547
$691$	1.15882e10	1.33612	0.668058	−	0.744109i	$-0.267126\pi$
$691$	1.15882e10	1.33612	0.668058	+	0.744109i	$0.267126\pi$
$692$	1.39597e9	0.160141
$693$	−5.69168e9	−0.649642
$694$	1.37648e9	0.156319
$695$	9.28977e9	1.04968
$696$	−5.11644e8	−0.0575223
$697$	4.76161e9	0.532647
$698$	4.51843e9	0.502914
$699$	4.23054e9	0.468517
$700$	−6.15059e8	−0.0677757
$701$	3.16850e9	0.347408	0.173704	−	0.984798i	$-0.444426\pi$
$701$	3.16850e9	0.347408	0.173704	+	0.984798i	$0.444426\pi$
$702$	2.01939e9	0.220313
$703$	−1.07535e9	−0.116737
$704$	−9.25587e9	−0.999800
$705$	2.35117e9	0.252710
$706$	−6.97600e9	−0.746088
$707$	−1.63693e10	−1.74206
$708$	−1.07343e8	−0.0113673
$709$	7.17426e9	0.755988	0.377994	−	0.925808i	$-0.376614\pi$
$709$	7.17426e9	0.755988	0.377994	+	0.925808i	$0.376614\pi$
$710$	5.82782e9	0.611086
$711$	−5.56363e9	−0.580516
$712$	9.46867e8	0.0983125
$713$	2.61724e9	0.270415
$714$	2.84629e9	0.292642
$715$	1.09310e10	1.11838
$716$	−4.05180e8	−0.0412527
$717$	5.63511e9	0.570933
$718$	6.86017e8	0.0691670
$719$	3.09019e9	0.310052	0.155026	−	0.987910i	$-0.450454\pi$
$719$	3.09019e9	0.310052	0.155026	+	0.987910i	$0.450454\pi$
$720$	−3.18510e9	−0.318023
$721$	1.13495e10	1.12773
$722$	8.80733e9	0.870891
$723$	−1.02733e10	−1.01095
$724$	8.86836e8	0.0868477
$725$	3.20008e8	0.0311873
$726$	−3.42896e9	−0.332571
$727$	1.26127e9	0.121741	0.0608707	−	0.998146i	$-0.480612\pi$
$727$	1.26127e9	0.121741	0.0608707	+	0.998146i	$0.480612\pi$
$728$	−1.59019e10	−1.52753
$729$	3.87420e8	0.0370370
$730$	1.04429e10	0.993553
$731$	2.24894e9	0.212945
$732$	1.95209e7	0.00183954
$733$	−1.05469e10	−0.989146	−0.494573	−	0.869136i	$-0.664676\pi$
$733$	−1.05469e10	−0.989146	−0.494573	+	0.869136i	$0.664676\pi$
$734$	2.73815e9	0.255576
$735$	7.73264e9	0.718327
$736$	−3.00168e9	−0.277519
$737$	−1.44562e10	−1.33021
$738$	6.92244e9	0.633960
$739$	7.89796e9	0.719879	0.359940	−	0.932976i	$-0.382797\pi$
$739$	7.89796e9	0.719879	0.359940	+	0.932976i	$0.382797\pi$
$740$	3.79177e8	0.0343978
$741$	2.96072e9	0.267321
$742$	−1.44894e10	−1.30208
$743$	−7.69335e8	−0.0688105	−0.0344053	−	0.999408i	$-0.510954\pi$
$743$	−7.69335e8	−0.0688105	−0.0344053	+	0.999408i	$0.510954\pi$
$744$	−1.72649e9	−0.153694
$745$	−1.65425e10	−1.46573
$746$	−7.11545e9	−0.627504
$747$	−4.87913e9	−0.428272
$748$	6.44846e8	0.0563379
$749$	1.57664e10	1.37103
$750$	7.77667e9	0.673100
$751$	1.79359e10	1.54519	0.772596	−	0.634898i	$-0.218958\pi$
$751$	1.79359e10	1.54519	0.772596	+	0.634898i	$0.218958\pi$
$752$	−6.81180e9	−0.584117
$753$	−5.08995e9	−0.434441
$754$	−1.47417e9	−0.125242
$755$	1.38032e10	1.16725
$756$	5.43585e8	0.0457553
$757$	4.00304e9	0.335394	0.167697	−	0.985839i	$-0.446367\pi$
$757$	4.00304e9	0.335394	0.167697	+	0.985839i	$0.446367\pi$
$758$	−4.87661e9	−0.406702
$759$	7.97601e9	0.662124
$760$	−4.04393e9	−0.334161
$761$	3.91126e9	0.321714	0.160857	−	0.986978i	$-0.448574\pi$
$761$	3.91126e9	0.321714	0.160857	+	0.986978i	$0.448574\pi$
$762$	−9.88089e9	−0.809009
$763$	1.15316e10	0.939839
$764$	−3.07166e9	−0.249199
$765$	−1.04873e9	−0.0846932
$766$	1.20194e10	0.966234
$767$	1.73579e9	0.138904
$768$	3.21688e9	0.256254
$769$	1.77498e10	1.40751	0.703756	−	0.710441i	$-0.251505\pi$
$769$	1.77498e10	1.40751	0.703756	+	0.710441i	$0.251505\pi$
$770$	2.23989e10	1.76811
$771$	1.02585e10	0.806105
$772$	1.32009e9	0.103263
$773$	2.00177e10	1.55879	0.779393	−	0.626536i	$-0.215528\pi$
$773$	2.00177e10	1.55879	0.779393	+	0.626536i	$0.215528\pi$
$774$	3.26952e9	0.253449
$775$	1.07983e9	0.0833296
$776$	1.41109e10	1.08402
$777$	3.19259e9	0.244158
$778$	−1.13023e10	−0.860472
$779$	1.01493e10	0.769229
$780$	−1.04397e9	−0.0787693
$781$	1.11169e10	0.835038
$782$	−3.98865e9	−0.298265
$783$	−2.82820e8	−0.0210545
$784$	−2.24030e10	−1.66035
$785$	1.20380e10	0.888201
$786$	1.59160e10	1.16911
$787$	−1.57588e10	−1.15242	−0.576212	−	0.817300i	$-0.695470\pi$
$787$	−1.57588e10	−1.15242	−0.576212	+	0.817300i	$0.695470\pi$
$788$	1.55784e9	0.113418
$789$	4.40745e9	0.319461
$790$	2.18949e10	1.57997
$791$	−1.42165e10	−1.02135
$792$	−5.26144e9	−0.376328
$793$	−3.15662e8	−0.0224784
$794$	−5.07745e9	−0.359976
$795$	5.33867e9	0.376833
$796$	−1.32796e9	−0.0933234
$797$	−9.19325e9	−0.643228	−0.321614	−	0.946871i	$-0.604225\pi$
$797$	−9.19325e9	−0.643228	−0.321614	+	0.946871i	$0.604225\pi$
$798$	6.06684e9	0.422622
$799$	−2.24286e9	−0.155557
$800$	−1.23844e9	−0.0855185
$801$	5.23397e8	0.0359847
$802$	2.30173e10	1.57559
$803$	1.99205e10	1.35767
$804$	1.38065e9	0.0936885
$805$	−1.82003e10	−1.22968
$806$	−4.97443e9	−0.334634
$807$	−1.42212e10	−0.952534
$808$	−1.51320e10	−1.00915
$809$	−1.69661e10	−1.12658	−0.563290	−	0.826259i	$-0.690465\pi$
$809$	−1.69661e10	−1.12658	−0.563290	+	0.826259i	$0.690465\pi$
$810$	−1.52464e9	−0.100802
$811$	−2.19205e10	−1.44303	−0.721517	−	0.692397i	$-0.756555\pi$
$811$	−2.19205e10	−1.44303	−0.721517	+	0.692397i	$0.756555\pi$
$812$	−3.96822e8	−0.0260105
$813$	3.27154e9	0.213518
$814$	5.50602e9	0.357810
$815$	−6.69738e9	−0.433364
$816$	3.03837e9	0.195761
$817$	4.79359e9	0.307527
$818$	2.93422e10	1.87437
$819$	−8.79003e9	−0.559109
$820$	−3.57872e9	−0.226662
$821$	1.97496e10	1.24554	0.622770	−	0.782405i	$-0.286007\pi$
$821$	1.97496e10	1.24554	0.622770	+	0.782405i	$0.286007\pi$
$822$	4.81121e9	0.302136
$823$	3.26341e9	0.204067	0.102033	−	0.994781i	$-0.467465\pi$
$823$	3.26341e9	0.204067	0.102033	+	0.994781i	$0.467465\pi$
$824$	1.04916e10	0.653276
$825$	3.29076e9	0.204036
$826$	3.55683e9	0.219600
$827$	7.08713e9	0.435713	0.217857	−	0.975981i	$-0.430093\pi$
$827$	7.08713e9	0.435713	0.217857	+	0.975981i	$0.430093\pi$
$828$	−7.61751e8	−0.0466345
$829$	3.03587e10	1.85073	0.925365	−	0.379078i	$-0.123759\pi$
$829$	3.03587e10	1.85073	0.925365	+	0.379078i	$0.123759\pi$
$830$	1.92012e10	1.16561
$831$	9.15914e9	0.553670
$832$	−1.42945e10	−0.860471
$833$	−7.37643e9	−0.442169
$834$	−1.28833e10	−0.769037
$835$	2.27447e9	0.135200
$836$	1.37448e9	0.0813611
$837$	−9.54345e8	−0.0562557
$838$	2.10092e10	1.23326
$839$	1.35904e10	0.794448	0.397224	−	0.917722i	$-0.369974\pi$
$839$	1.35904e10	0.794448	0.397224	+	0.917722i	$0.369974\pi$
$840$	1.20060e10	0.698906
$841$	−1.70434e10	−0.988031
$842$	−2.90069e10	−1.67459
$843$	−6.72124e9	−0.386414
$844$	5.59143e8	0.0320128
$845$	2.05189e9	0.116992
$846$	−3.26068e9	−0.185145
$847$	1.49256e10	0.843997
$848$	−1.54672e10	−0.871014
$849$	−1.62414e10	−0.910852
$850$	−1.64565e9	−0.0919116
$851$	−4.47393e9	−0.248849
$852$	−1.06173e9	−0.0588130
$853$	1.23490e10	0.681255	0.340628	−	0.940198i	$-0.389361\pi$
$853$	1.23490e10	0.681255	0.340628	+	0.940198i	$0.389361\pi$
$854$	−6.46826e8	−0.0355373
$855$	−2.23535e9	−0.122311
$856$	1.45747e10	0.794219
$857$	−1.91652e10	−1.04011	−0.520057	−	0.854132i	$-0.674089\pi$
$857$	−1.91652e10	−1.04011	−0.520057	+	0.854132i	$0.674089\pi$
$858$	−1.51595e10	−0.819368
$859$	−2.69718e10	−1.45189	−0.725946	−	0.687751i	$-0.758598\pi$
$859$	−2.69718e10	−1.45189	−0.725946	+	0.687751i	$0.758598\pi$
$860$	−1.69025e9	−0.0906166
$861$	−3.01321e10	−1.60886
$862$	1.29171e10	0.686893
$863$	−1.15124e9	−0.0609715	−0.0304858	−	0.999535i	$-0.509705\pi$
$863$	−1.15124e9	−0.0609715	−0.0304858	+	0.999535i	$0.509705\pi$
$864$	1.09452e9	0.0577334
$865$	1.70430e10	0.895344
$866$	1.01275e10	0.529896
$867$	−1.00787e10	−0.525217
$868$	−1.33903e9	−0.0694978
$869$	4.17659e10	2.15900
$870$	1.11300e9	0.0573032
$871$	−2.23257e10	−1.14483
$872$	1.06599e10	0.544435
$873$	7.80002e9	0.396776
$874$	−8.50174e9	−0.430743
$875$	−3.38504e10	−1.70819
$876$	−1.90251e9	−0.0956231
$877$	−2.50007e9	−0.125157	−0.0625784	−	0.998040i	$-0.519932\pi$
$877$	−2.50007e9	−0.125157	−0.0625784	+	0.998040i	$0.519932\pi$
$878$	−2.32624e10	−1.15991
$879$	6.46198e9	0.320926
$880$	2.39104e10	1.18276
$881$	1.84978e10	0.911392	0.455696	−	0.890136i	$-0.349390\pi$
$881$	1.84978e10	0.911392	0.455696	+	0.890136i	$0.349390\pi$
$882$	−1.07239e10	−0.526273
$883$	3.27036e10	1.59857	0.799287	−	0.600950i	$-0.205211\pi$
$883$	3.27036e10	1.59857	0.799287	+	0.600950i	$0.205211\pi$
$884$	9.95879e8	0.0484868
$885$	−1.31053e9	−0.0635543
$886$	−1.73733e10	−0.839196
$887$	−2.66571e10	−1.28257	−0.641285	−	0.767303i	$-0.721598\pi$
$887$	−2.66571e10	−1.28257	−0.641285	+	0.767303i	$0.721598\pi$
$888$	2.95126e9	0.141437
$889$	4.30097e10	2.05310
$890$	−2.05976e9	−0.0979382
$891$	−2.90835e9	−0.137745
$892$	5.02130e9	0.236886
$893$	−4.78063e9	−0.224649
$894$	2.29416e10	1.07385
$895$	−4.94674e9	−0.230642
$896$	−3.94455e10	−1.83198
$897$	1.23179e10	0.569853
$898$	1.21977e10	0.562096
$899$	6.96680e8	0.0319797
$900$	−3.14285e8	−0.0143706
$901$	−5.09274e9	−0.231961
$902$	−5.19665e10	−2.35777
$903$	−1.42316e10	−0.643202
$904$	−1.31419e10	−0.591654
$905$	1.08272e10	0.485562
$906$	−1.91426e10	−0.855171
$907$	−2.98097e10	−1.32658	−0.663289	−	0.748364i	$-0.730840\pi$
$907$	−2.98097e10	−1.32658	−0.663289	+	0.748364i	$0.730840\pi$
$908$	−3.94266e9	−0.174779
$909$	−8.36446e9	−0.369372
$910$	3.45921e10	1.52171
$911$	−1.60230e10	−0.702149	−0.351074	−	0.936348i	$-0.614184\pi$
$911$	−1.60230e10	−0.702149	−0.351074	+	0.936348i	$0.614184\pi$
$912$	6.47624e9	0.282710
$913$	3.66274e10	1.59279
$914$	−4.02379e10	−1.74311
$915$	2.38326e8	0.0102848
$916$	−6.74815e9	−0.290102
$917$	−6.92794e10	−2.96696
$918$	1.45441e9	0.0620494
$919$	2.67157e10	1.13543	0.567717	−	0.823224i	$-0.307827\pi$
$919$	2.67157e10	1.13543	0.567717	+	0.823224i	$0.307827\pi$
$920$	−1.68245e10	−0.712336
$921$	2.70708e9	0.114181
$922$	−3.62349e8	−0.0152254
$923$	1.71686e10	0.718670
$924$	−4.08067e9	−0.170169
$925$	−1.84587e9	−0.0766839
$926$	−6.21430e9	−0.257190
$927$	5.79942e9	0.239114
$928$	−7.99012e8	−0.0328198
$929$	−1.01936e10	−0.417130	−0.208565	−	0.978009i	$-0.566879\pi$
$929$	−1.01936e10	−0.417130	−0.208565	+	0.978009i	$0.566879\pi$
$930$	3.75570e9	0.153109
$931$	−1.57228e10	−0.638564
$932$	3.03310e9	0.122725
$933$	1.91779e10	0.773062
$934$	4.05008e10	1.62648
$935$	7.87277e9	0.314983
$936$	−8.12559e9	−0.323884
$937$	−2.50793e10	−0.995923	−0.497962	−	0.867199i	$-0.665918\pi$
$937$	−2.50793e10	−0.995923	−0.497962	+	0.867199i	$0.665918\pi$
$938$	−4.57478e10	−1.80992
$939$	−1.76872e10	−0.697154
$940$	1.68568e9	0.0661955
$941$	−5.38850e9	−0.210816	−0.105408	−	0.994429i	$-0.533615\pi$
$941$	−5.38850e9	−0.210816	−0.105408	+	0.994429i	$0.533615\pi$
$942$	−1.66947e10	−0.650730
$943$	4.22256e10	1.63978
$944$	3.79686e9	0.146900
$945$	6.63650e9	0.255816
$946$	−2.45442e10	−0.942604
$947$	−1.51551e10	−0.579876	−0.289938	−	0.957045i	$-0.593635\pi$
$947$	−1.51551e10	−0.579876	−0.289938	+	0.957045i	$0.593635\pi$
$948$	−3.98887e9	−0.152062
$949$	3.07645e10	1.16847
$950$	−3.50767e9	−0.132735
$951$	−4.59084e9	−0.173085
$952$	−1.14529e10	−0.430215
$953$	4.14430e9	0.155105	0.0775526	−	0.996988i	$-0.475289\pi$
$953$	4.14430e9	0.155105	0.0775526	+	0.996988i	$0.475289\pi$
$954$	−7.40383e9	−0.276082
$955$	−3.75011e10	−1.39326
$956$	4.04012e9	0.149552
$957$	2.12312e9	0.0783039
$958$	2.94703e9	0.108294
$959$	−2.09423e10	−0.766760
$960$	1.07924e10	0.393701
$961$	−2.51617e10	−0.914553
$962$	8.50331e9	0.307946
$963$	8.05639e9	0.290702
$964$	−7.36552e9	−0.264810
$965$	1.61167e10	0.577338
$966$	2.52407e10	0.900910
$967$	−7.19424e9	−0.255854	−0.127927	−	0.991784i	$-0.540832\pi$
$967$	−7.19424e9	−0.255854	−0.127927	+	0.991784i	$0.540832\pi$
$968$	1.37974e10	0.488915
$969$	2.13238e9	0.0752888
$970$	−3.06960e10	−1.07989
$971$	−3.04216e10	−1.06639	−0.533193	−	0.845993i	$-0.679008\pi$
$971$	−3.04216e10	−1.06639	−0.533193	+	0.845993i	$0.679008\pi$
$972$	2.77763e8	0.00970158
$973$	5.60788e10	1.95166
$974$	1.44147e10	0.499860
$975$	5.08214e9	0.175603
$976$	−6.90475e8	−0.0237724
$977$	−1.19680e9	−0.0410572	−0.0205286	−	0.999789i	$-0.506535\pi$
$977$	−1.19680e9	−0.0410572	−0.0205286	+	0.999789i	$0.506535\pi$
$978$	9.28813e9	0.317499
$979$	−3.92912e9	−0.133831
$980$	5.54395e9	0.188160
$981$	5.89245e9	0.199276
$982$	−2.34366e10	−0.789778
$983$	5.01551e10	1.68414	0.842069	−	0.539370i	$-0.181337\pi$
$983$	5.01551e10	1.68414	0.842069	+	0.539370i	$0.181337\pi$
$984$	−2.78544e10	−0.931990
$985$	1.90193e10	0.634116
$986$	−1.06173e9	−0.0352733
$987$	1.41931e10	0.469860
$988$	2.12270e9	0.0700228
$989$	1.99434e10	0.655561
$990$	1.14454e10	0.374895
$991$	2.70432e10	0.882674	0.441337	−	0.897341i	$-0.354504\pi$
$991$	2.70432e10	0.882674	0.441337	+	0.897341i	$0.354504\pi$
$992$	−2.69618e9	−0.0876915
$993$	3.50270e9	0.113522
$994$	3.51803e10	1.13618
$995$	−1.62128e10	−0.521767
$996$	−3.49811e9	−0.112183
$997$	1.18645e10	0.379154	0.189577	−	0.981866i	$-0.439288\pi$
$997$	1.18645e10	0.379154	0.189577	+	0.981866i	$0.439288\pi$
$998$	−3.78400e10	−1.20502
$999$	1.63136e9	0.0517692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.6	✓	17
3.2	odd	2		531.8.a.d.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.6	✓	17	1.1	even	1	trivial
531.8.a.d.1.12		17	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)

\(f(q)\)	\(=\)	\(q-12.1391 q^{2} +27.0000 q^{3} +19.3578 q^{4} +236.334 q^{5} -327.756 q^{6} +1426.66 q^{7} +1318.82 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-12.1391 q^{2} +27.0000 q^{3} +19.3578 q^{4} +236.334 q^{5} -327.756 q^{6} +1426.66 q^{7} +1318.82 q^{8} +729.000 q^{9} -2868.89 q^{10} -5472.58 q^{11} +522.660 q^{12} -8451.67 q^{13} -17318.4 q^{14} +6381.03 q^{15} -18487.1 q^{16} -6087.08 q^{17} -8849.40 q^{18} -12974.5 q^{19} +4574.91 q^{20} +38519.8 q^{21} +66432.2 q^{22} -53979.7 q^{23} +35608.1 q^{24} -22271.1 q^{25} +102596. q^{26} +19683.0 q^{27} +27617.0 q^{28} -14368.8 q^{29} -77459.9 q^{30} -48485.8 q^{31} +55607.6 q^{32} -147760. q^{33} +73891.7 q^{34} +337169. q^{35} +14111.8 q^{36} +82881.8 q^{37} +157499. q^{38} -228195. q^{39} +311682. q^{40} -782250. q^{41} -467596. q^{42} -369462. q^{43} -105937. q^{44} +172288. q^{45} +655265. q^{46} +368463. q^{47} -499151. q^{48} +1.21182e6 q^{49} +270351. q^{50} -164351. q^{51} -163605. q^{52} +836648. q^{53} -238934. q^{54} -1.29336e6 q^{55} +1.88151e6 q^{56} -350312. q^{57} +174424. q^{58} -205379. q^{59} +123522. q^{60} +37349.1 q^{61} +588573. q^{62} +1.04004e6 q^{63} +1.69132e6 q^{64} -1.99742e6 q^{65} +1.79367e6 q^{66} +2.64158e6 q^{67} -117832. q^{68} -1.45745e6 q^{69} -4.09293e6 q^{70} -2.03139e6 q^{71} +961419. q^{72} -3.64005e6 q^{73} -1.00611e6 q^{74} -601319. q^{75} -251158. q^{76} -7.80751e6 q^{77} +2.77008e6 q^{78} -7.63186e6 q^{79} -4.36913e6 q^{80} +531441. q^{81} +9.49581e6 q^{82} -6.69291e6 q^{83} +745658. q^{84} -1.43859e6 q^{85} +4.48494e6 q^{86} -387957. q^{87} -7.21734e6 q^{88} +717966. q^{89} -2.09142e6 q^{90} -1.20577e7 q^{91} -1.04493e6 q^{92} -1.30912e6 q^{93} -4.47281e6 q^{94} -3.06632e6 q^{95} +1.50141e6 q^{96} +1.06996e7 q^{97} -1.47104e7 q^{98} -3.98951e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more