LMFDB - Embedded newform 177.8.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$0$
Dimension:	$17$
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} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
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			1.1
Root			$-22.1687$ 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)

$f(q)$	$=$	$q-22.1687 q^{2} -27.0000 q^{3} +363.451 q^{4} +258.765 q^{5} +598.555 q^{6} +411.003 q^{7} -5219.64 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-22.1687 q^{2} -27.0000 q^{3} +363.451 q^{4} +258.765 q^{5} +598.555 q^{6} +411.003 q^{7} -5219.64 q^{8} +729.000 q^{9} -5736.49 q^{10} +437.879 q^{11} -9813.17 q^{12} +13224.5 q^{13} -9111.39 q^{14} -6986.67 q^{15} +69190.8 q^{16} +24930.4 q^{17} -16161.0 q^{18} +38005.6 q^{19} +94048.5 q^{20} -11097.1 q^{21} -9707.20 q^{22} +79710.8 q^{23} +140930. q^{24} -11165.5 q^{25} -293169. q^{26} -19683.0 q^{27} +149379. q^{28} -64355.4 q^{29} +154885. q^{30} +241791. q^{31} -865756. q^{32} -11822.7 q^{33} -552675. q^{34} +106353. q^{35} +264956. q^{36} +353659. q^{37} -842535. q^{38} -357060. q^{39} -1.35066e6 q^{40} +246146. q^{41} +246008. q^{42} -151362. q^{43} +159147. q^{44} +188640. q^{45} -1.76708e6 q^{46} -512816. q^{47} -1.86815e6 q^{48} -654620. q^{49} +247524. q^{50} -673122. q^{51} +4.80644e6 q^{52} -141087. q^{53} +436346. q^{54} +113308. q^{55} -2.14528e6 q^{56} -1.02615e6 q^{57} +1.42668e6 q^{58} -205379. q^{59} -2.53931e6 q^{60} +846302. q^{61} -5.36020e6 q^{62} +299621. q^{63} +1.03362e7 q^{64} +3.42203e6 q^{65} +262095. q^{66} +3.36339e6 q^{67} +9.06099e6 q^{68} -2.15219e6 q^{69} -2.35771e6 q^{70} -4.07342e6 q^{71} -3.80511e6 q^{72} -4.42831e6 q^{73} -7.84015e6 q^{74} +301467. q^{75} +1.38132e7 q^{76} +179969. q^{77} +7.91556e6 q^{78} -4.19495e6 q^{79} +1.79042e7 q^{80} +531441. q^{81} -5.45672e6 q^{82} -6.96295e6 q^{83} -4.03324e6 q^{84} +6.45114e6 q^{85} +3.35550e6 q^{86} +1.73760e6 q^{87} -2.28557e6 q^{88} -2.48793e6 q^{89} -4.18190e6 q^{90} +5.43529e6 q^{91} +2.89710e7 q^{92} -6.52837e6 q^{93} +1.13685e7 q^{94} +9.83454e6 q^{95} +2.33754e7 q^{96} +8.97300e6 q^{97} +1.45121e7 q^{98} +319214. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9} + 6521 q^{10} - 1764 q^{11} - 31482 q^{12} + 18192 q^{13} - 7827 q^{14} + 8586 q^{15} + 139226 q^{16} - 15507 q^{17} + 1458 q^{18} + 52083 q^{19} + 721 q^{20} - 84915 q^{21} - 234434 q^{22} + 63823 q^{23} - 63585 q^{24} + 202153 q^{25} - 367956 q^{26} - 334611 q^{27} + 182306 q^{28} - 502955 q^{29} - 176067 q^{30} + 347531 q^{31} - 243908 q^{32} + 47628 q^{33} - 330872 q^{34} + 92641 q^{35} + 850014 q^{36} + 447615 q^{37} + 775669 q^{38} - 491184 q^{39} + 2203270 q^{40} + 940335 q^{41} + 211329 q^{42} + 478562 q^{43} - 596924 q^{44} - 231822 q^{45} - 3078663 q^{46} + 703121 q^{47} - 3759102 q^{48} + 1895082 q^{49} - 876967 q^{50} + 418689 q^{51} + 6278296 q^{52} - 1005974 q^{53} - 39366 q^{54} + 5212846 q^{55} + 3425294 q^{56} - 1406241 q^{57} + 6710166 q^{58} - 3491443 q^{59} - 19467 q^{60} + 11510749 q^{61} + 5996234 q^{62} + 2292705 q^{63} + 29496941 q^{64} + 11094180 q^{65} + 6329718 q^{66} + 14007144 q^{67} + 19688159 q^{68} - 1723221 q^{69} + 30909708 q^{70} + 5229074 q^{71} + 1716795 q^{72} + 5452211 q^{73} + 12819662 q^{74} - 5458131 q^{75} + 41929340 q^{76} + 9930777 q^{77} + 9934812 q^{78} + 15275654 q^{79} + 36576105 q^{80} + 9034497 q^{81} + 32025935 q^{82} + 7826609 q^{83} - 4922262 q^{84} + 11836945 q^{85} + 51649136 q^{86} + 13579785 q^{87} + 30223741 q^{88} - 6436185 q^{89} + 4753809 q^{90} + 11633535 q^{91} + 43357972 q^{92} - 9383337 q^{93} - 4494252 q^{94} + 23741055 q^{95} + 6585516 q^{96} + 26377540 q^{97} + 26517816 q^{98} - 1285956 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9 + 6521 * q^10 - 1764 * q^11 - 31482 * q^12 + 18192 * q^13 - 7827 * q^14 + 8586 * q^15 + 139226 * q^16 - 15507 * q^17 + 1458 * q^18 + 52083 * q^19 + 721 * q^20 - 84915 * q^21 - 234434 * q^22 + 63823 * q^23 - 63585 * q^24 + 202153 * q^25 - 367956 * q^26 - 334611 * q^27 + 182306 * q^28 - 502955 * q^29 - 176067 * q^30 + 347531 * q^31 - 243908 * q^32 + 47628 * q^33 - 330872 * q^34 + 92641 * q^35 + 850014 * q^36 + 447615 * q^37 + 775669 * q^38 - 491184 * q^39 + 2203270 * q^40 + 940335 * q^41 + 211329 * q^42 + 478562 * q^43 - 596924 * q^44 - 231822 * q^45 - 3078663 * q^46 + 703121 * q^47 - 3759102 * q^48 + 1895082 * q^49 - 876967 * q^50 + 418689 * q^51 + 6278296 * q^52 - 1005974 * q^53 - 39366 * q^54 + 5212846 * q^55 + 3425294 * q^56 - 1406241 * q^57 + 6710166 * q^58 - 3491443 * q^59 - 19467 * q^60 + 11510749 * q^61 + 5996234 * q^62 + 2292705 * q^63 + 29496941 * q^64 + 11094180 * q^65 + 6329718 * q^66 + 14007144 * q^67 + 19688159 * q^68 - 1723221 * q^69 + 30909708 * q^70 + 5229074 * q^71 + 1716795 * q^72 + 5452211 * q^73 + 12819662 * q^74 - 5458131 * q^75 + 41929340 * q^76 + 9930777 * q^77 + 9934812 * q^78 + 15275654 * q^79 + 36576105 * q^80 + 9034497 * q^81 + 32025935 * q^82 + 7826609 * q^83 - 4922262 * q^84 + 11836945 * q^85 + 51649136 * q^86 + 13579785 * q^87 + 30223741 * q^88 - 6436185 * q^89 + 4753809 * q^90 + 11633535 * q^91 + 43357972 * q^92 - 9383337 * q^93 - 4494252 * q^94 + 23741055 * q^95 + 6585516 * q^96 + 26377540 * q^97 + 26517816 * q^98 - 1285956 * 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 $

$2$	−22.1687	−1.95945	−0.979727	−	0.200338i	$-0.935796\pi$
$2$	−22.1687	−1.95945	−0.979727	+	0.200338i	$0.935796\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	363.451	2.83946
$5$	258.765	0.925787	0.462894	−	0.886414i	$-0.346811\pi$
$5$	258.765	0.925787	0.462894	+	0.886414i	$0.346811\pi$
$6$	598.555	1.13129
$7$	411.003	0.452899	0.226450	−	0.974023i	$-0.427288\pi$
$7$	411.003	0.452899	0.226450	+	0.974023i	$0.427288\pi$
$8$	−5219.64	−3.60434
$9$	729.000	0.333333
$10$	−5736.49	−1.81404
$11$	437.879	0.0991927	0.0495964	−	0.998769i	$-0.484207\pi$
$11$	437.879	0.0991927	0.0495964	+	0.998769i	$0.484207\pi$
$12$	−9813.17	−1.63936
$13$	13224.5	1.66946	0.834730	−	0.550659i	$-0.185624\pi$
$13$	13224.5	1.66946	0.834730	+	0.550659i	$0.185624\pi$
$14$	−9111.39	−0.887435
$15$	−6986.67	−0.534504
$16$	69190.8	4.22307
$17$	24930.4	1.23072	0.615359	−	0.788247i	$-0.289011\pi$
$17$	24930.4	1.23072	0.615359	+	0.788247i	$0.289011\pi$
$18$	−16161.0	−0.653151
$19$	38005.6	1.27119	0.635595	−	0.772023i	$-0.280755\pi$
$19$	38005.6	1.27119	0.635595	+	0.772023i	$0.280755\pi$
$20$	94048.5	2.62874
$21$	−11097.1	−0.261481
$22$	−9707.20	−0.194364
$23$	79710.8	1.36606	0.683030	−	0.730390i	$-0.260662\pi$
$23$	79710.8	1.36606	0.683030	+	0.730390i	$0.260662\pi$
$24$	140930.	2.08096
$25$	−11165.5	−0.142918
$26$	−293169.	−3.27123
$27$	−19683.0	−0.192450
$28$	149379.	1.28599
$29$	−64355.4	−0.489996	−0.244998	−	0.969524i	$-0.578787\pi$
$29$	−64355.4	−0.489996	−0.244998	+	0.969524i	$0.578787\pi$
$30$	154885.	1.04734
$31$	241791.	1.45772	0.728862	−	0.684661i	$-0.240050\pi$
$31$	241791.	1.45772	0.728862	+	0.684661i	$0.240050\pi$
$32$	−865756.	−4.67058
$33$	−11822.7	−0.0572689
$34$	−552675.	−2.41154
$35$	106353.	0.419288
$36$	264956.	0.946486
$37$	353659.	1.14783	0.573916	−	0.818914i	$-0.305424\pi$
$37$	353659.	1.14783	0.573916	+	0.818914i	$0.305424\pi$
$38$	−842535.	−2.49084
$39$	−357060.	−0.963863
$40$	−1.35066e6	−3.33685
$41$	246146.	0.557761	0.278881	−	0.960326i	$-0.410037\pi$
$41$	246146.	0.557761	0.278881	+	0.960326i	$0.410037\pi$
$42$	246008.	0.512361
$43$	−151362.	−0.290321	−0.145160	−	0.989408i	$-0.546370\pi$
$43$	−151362.	−0.290321	−0.145160	+	0.989408i	$0.546370\pi$
$44$	159147.	0.281654
$45$	188640.	0.308596
$46$	−1.76708e6	−2.67673
$47$	−512816.	−0.720475	−0.360238	−	0.932861i	$-0.617304\pi$
$47$	−512816.	−0.720475	−0.360238	+	0.932861i	$0.617304\pi$
$48$	−1.86815e6	−2.43819
$49$	−654620.	−0.794882
$50$	247524.	0.280041
$51$	−673122.	−0.710556
$52$	4.80644e6	4.74036
$53$	−141087.	−0.130173	−0.0650867	−	0.997880i	$-0.520732\pi$
$53$	−141087.	−0.130173	−0.0650867	+	0.997880i	$0.520732\pi$
$54$	436346.	0.377097
$55$	113308.	0.0918314
$56$	−2.14528e6	−1.63240
$57$	−1.02615e6	−0.733922
$58$	1.42668e6	0.960124
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−2.53931e6	−1.51770
$61$	846302.	0.477388	0.238694	−	0.971095i	$-0.423281\pi$
$61$	846302.	0.477388	0.238694	+	0.971095i	$0.423281\pi$
$62$	−5.36020e6	−2.85634
$63$	299621.	0.150966
$64$	1.03362e7	4.92871
$65$	3.42203e6	1.54556
$66$	262095.	0.112216
$67$	3.36339e6	1.36620	0.683101	−	0.730324i	$-0.260631\pi$
$67$	3.36339e6	1.36620	0.683101	+	0.730324i	$0.260631\pi$
$68$	9.06099e6	3.49458
$69$	−2.15219e6	−0.788695
$70$	−2.35771e6	−0.821576
$71$	−4.07342e6	−1.35069	−0.675344	−	0.737503i	$-0.736005\pi$
$71$	−4.07342e6	−1.35069	−0.675344	+	0.737503i	$0.736005\pi$
$72$	−3.80511e6	−1.20145
$73$	−4.42831e6	−1.33232	−0.666159	−	0.745810i	$-0.732063\pi$
$73$	−4.42831e6	−1.33232	−0.666159	+	0.745810i	$0.732063\pi$
$74$	−7.84015e6	−2.24912
$75$	301467.	0.0825137
$76$	1.38132e7	3.60949
$77$	179969.	0.0449243
$78$	7.91556e6	1.88865
$79$	−4.19495e6	−0.957265	−0.478633	−	0.878015i	$-0.658867\pi$
$79$	−4.19495e6	−0.957265	−0.478633	+	0.878015i	$0.658867\pi$
$80$	1.79042e7	3.90967
$81$	531441.	0.111111
$82$	−5.45672e6	−1.09291
$83$	−6.96295e6	−1.33666	−0.668329	−	0.743866i	$-0.732990\pi$
$83$	−6.96295e6	−1.33666	−0.668329	+	0.743866i	$0.732990\pi$
$84$	−4.03324e6	−0.742466
$85$	6.45114e6	1.13938
$86$	3.35550e6	0.568870
$87$	1.73760e6	0.282899
$88$	−2.28557e6	−0.357524
$89$	−2.48793e6	−0.374088	−0.187044	−	0.982352i	$-0.559891\pi$
$89$	−2.48793e6	−0.374088	−0.187044	+	0.982352i	$0.559891\pi$
$90$	−4.18190e6	−0.604679
$91$	5.43529e6	0.756097
$92$	2.89710e7	3.87887
$93$	−6.52837e6	−0.841617
$94$	1.13685e7	1.41174
$95$	9.83454e6	1.17685
$96$	2.33754e7	2.69656
$97$	8.97300e6	0.998244	0.499122	−	0.866532i	$-0.333656\pi$
$97$	8.97300e6	0.998244	0.499122	+	0.866532i	$0.333656\pi$
$98$	1.45121e7	1.55754
$99$	319214.	0.0330642
$100$	−4.05810e6	−0.405810
$101$	−1.29861e6	−0.125417	−0.0627084	−	0.998032i	$-0.519974\pi$
$101$	−1.29861e6	−0.125417	−0.0627084	+	0.998032i	$0.519974\pi$
$102$	1.49222e7	1.39230
$103$	1.51079e7	1.36230	0.681150	−	0.732144i	$-0.261480\pi$
$103$	1.51079e7	1.36230	0.681150	+	0.732144i	$0.261480\pi$
$104$	−6.90268e7	−6.01729
$105$	−2.87154e6	−0.242076
$106$	3.12772e6	0.255069
$107$	6.86606e6	0.541832	0.270916	−	0.962603i	$-0.412673\pi$
$107$	6.86606e6	0.541832	0.270916	+	0.962603i	$0.412673\pi$
$108$	−7.15380e6	−0.546454
$109$	−1.26929e7	−0.938790	−0.469395	−	0.882988i	$-0.655528\pi$
$109$	−1.26929e7	−0.938790	−0.469395	+	0.882988i	$0.655528\pi$
$110$	−2.51189e6	−0.179939
$111$	−9.54879e6	−0.662701
$112$	2.84376e7	1.91262
$113$	−1.90547e7	−1.24230	−0.621151	−	0.783691i	$-0.713335\pi$
$113$	−1.90547e7	−1.24230	−0.621151	+	0.783691i	$0.713335\pi$
$114$	2.27485e7	1.43809
$115$	2.06264e7	1.26468
$116$	−2.33900e7	−1.39132
$117$	9.64063e6	0.556487
$118$	4.55298e6	0.255099
$119$	1.02465e7	0.557391
$120$	3.64679e7	1.92653
$121$	−1.92954e7	−0.990161
$122$	−1.87614e7	−0.935419
$123$	−6.64593e6	−0.322024
$124$	8.78793e7	4.13915
$125$	−2.31053e7	−1.05810
$126$	−6.64220e6	−0.295812
$127$	3.81929e7	1.65451	0.827254	−	0.561828i	$-0.189902\pi$
$127$	3.81929e7	1.65451	0.827254	+	0.561828i	$0.189902\pi$
$128$	−1.18324e8	−4.98700
$129$	4.08678e6	0.167617
$130$	−7.58620e7	−3.02846
$131$	4.40577e7	1.71227	0.856135	−	0.516752i	$-0.172859\pi$
$131$	4.40577e7	1.71227	0.856135	+	0.516752i	$0.172859\pi$
$132$	−4.29698e6	−0.162613
$133$	1.56204e7	0.575721
$134$	−7.45619e7	−2.67701
$135$	−5.09328e6	−0.178168
$136$	−1.30128e8	−4.43592
$137$	−2.64599e7	−0.879156	−0.439578	−	0.898204i	$-0.644872\pi$
$137$	−2.64599e7	−0.879156	−0.439578	+	0.898204i	$0.644872\pi$
$138$	4.77113e7	1.54541
$139$	−2.17850e7	−0.688029	−0.344014	−	0.938964i	$-0.611787\pi$
$139$	−2.17850e7	−0.688029	−0.344014	+	0.938964i	$0.611787\pi$
$140$	3.86542e7	1.19055
$141$	1.38460e7	0.415967
$142$	9.03024e7	2.64661
$143$	5.79071e6	0.165598
$144$	5.04401e7	1.40769
$145$	−1.66530e7	−0.453632
$146$	9.81698e7	2.61061
$147$	1.76747e7	0.458926
$148$	1.28538e8	3.25922
$149$	5.57470e6	0.138061	0.0690303	−	0.997615i	$-0.478009\pi$
$149$	5.57470e6	0.138061	0.0690303	+	0.997615i	$0.478009\pi$
$150$	−6.68314e6	−0.161682
$151$	−3.98105e7	−0.940975	−0.470487	−	0.882407i	$-0.655922\pi$
$151$	−3.98105e7	−0.940975	−0.470487	+	0.882407i	$0.655922\pi$
$152$	−1.98376e8	−4.58180
$153$	1.81743e7	0.410240
$154$	−3.98969e6	−0.0880271
$155$	6.25673e7	1.34954
$156$	−1.29774e8	−2.73685
$157$	−2.43241e7	−0.501635	−0.250818	−	0.968034i	$-0.580699\pi$
$157$	−2.43241e7	−0.501635	−0.250818	+	0.968034i	$0.580699\pi$
$158$	9.29966e7	1.87572
$159$	3.80936e6	0.0751556
$160$	−2.24028e8	−4.32396
$161$	3.27614e7	0.618687
$162$	−1.17814e7	−0.217717
$163$	1.62611e7	0.294098	0.147049	−	0.989129i	$-0.453022\pi$
$163$	1.62611e7	0.294098	0.147049	+	0.989129i	$0.453022\pi$
$164$	8.94618e7	1.58374
$165$	−3.05931e6	−0.0530189
$166$	1.54360e8	2.61912
$167$	2.00507e7	0.333136	0.166568	−	0.986030i	$-0.446732\pi$
$167$	2.00507e7	0.333136	0.166568	+	0.986030i	$0.446732\pi$
$168$	5.79227e7	0.942467
$169$	1.12138e8	1.78710
$170$	−1.43013e8	−2.23257
$171$	2.77061e7	0.423730
$172$	−5.50128e7	−0.824354
$173$	1.22817e8	1.80342	0.901712	−	0.432338i	$-0.142311\pi$
$173$	1.22817e8	1.80342	0.901712	+	0.432338i	$0.142311\pi$
$174$	−3.85202e7	−0.554328
$175$	−4.58903e6	−0.0647274
$176$	3.02972e7	0.418898
$177$	5.54523e6	0.0751646
$178$	5.51542e7	0.733008
$179$	−4.55080e7	−0.593065	−0.296532	−	0.955023i	$-0.595830\pi$
$179$	−4.55080e7	−0.593065	−0.296532	+	0.955023i	$0.595830\pi$
$180$	6.85614e7	0.876245
$181$	−1.43158e8	−1.79448	−0.897241	−	0.441541i	$-0.854432\pi$
$181$	−1.43158e8	−1.79448	−0.897241	+	0.441541i	$0.854432\pi$
$182$	−1.20493e8	−1.48154
$183$	−2.28502e7	−0.275620
$184$	−4.16061e8	−4.92374
$185$	9.15147e7	1.06265
$186$	1.44725e8	1.64911
$187$	1.09165e7	0.122078
$188$	−1.86383e8	−2.04576
$189$	−8.08976e6	−0.0871605
$190$	−2.18019e8	−2.30599
$191$	5.12128e7	0.531817	0.265908	−	0.963998i	$-0.414328\pi$
$191$	5.12128e7	0.531817	0.265908	+	0.963998i	$0.414328\pi$
$192$	−2.79079e8	−2.84559
$193$	9.92991e7	0.994248	0.497124	−	0.867680i	$-0.334389\pi$
$193$	9.92991e7	0.994248	0.497124	+	0.867680i	$0.334389\pi$
$194$	−1.98920e8	−1.95601
$195$	−9.23948e7	−0.892332
$196$	−2.37922e8	−2.25704
$197$	−1.34248e8	−1.25105	−0.625527	−	0.780202i	$-0.715116\pi$
$197$	−1.34248e8	−1.25105	−0.625527	+	0.780202i	$0.715116\pi$
$198$	−7.07655e6	−0.0647878
$199$	−6.47369e7	−0.582326	−0.291163	−	0.956674i	$-0.594042\pi$
$199$	−6.47369e7	−0.582326	−0.291163	+	0.956674i	$0.594042\pi$
$200$	5.82796e7	0.515124
$201$	−9.08115e7	−0.788777
$202$	2.87886e7	0.245748
$203$	−2.64502e7	−0.221919
$204$	−2.44647e8	−2.01759
$205$	6.36940e7	0.516368
$206$	−3.34922e8	−2.66936
$207$	5.81092e7	0.455353
$208$	9.15010e8	7.05025
$209$	1.66419e7	0.126093
$210$	6.36582e7	0.474337
$211$	−3.50321e7	−0.256731	−0.128365	−	0.991727i	$-0.540973\pi$
$211$	−3.50321e7	−0.256731	−0.128365	+	0.991727i	$0.540973\pi$
$212$	−5.12783e7	−0.369622
$213$	1.09982e8	0.779820
$214$	−1.52212e8	−1.06169
$215$	−3.91673e7	−0.268775
$216$	1.02738e8	0.693655
$217$	9.93769e7	0.660201
$218$	2.81385e8	1.83952
$219$	1.19564e8	0.769214
$220$	4.11819e7	0.260751
$221$	3.29692e8	2.05464
$222$	2.11684e8	1.29853
$223$	2.00970e8	1.21357	0.606783	−	0.794867i	$-0.292460\pi$
$223$	2.00970e8	1.21357	0.606783	+	0.794867i	$0.292460\pi$
$224$	−3.55828e8	−2.11530
$225$	−8.13962e6	−0.0476393
$226$	4.22417e8	2.43423
$227$	2.01923e8	1.14577	0.572883	−	0.819637i	$-0.305825\pi$
$227$	2.01923e8	1.14577	0.572883	+	0.819637i	$0.305825\pi$
$228$	−3.72956e8	−2.08394
$229$	−8.98434e7	−0.494381	−0.247191	−	0.968967i	$-0.579507\pi$
$229$	−8.98434e7	−0.494381	−0.247191	+	0.968967i	$0.579507\pi$
$230$	−4.57260e8	−2.47808
$231$	−4.85917e6	−0.0259370
$232$	3.35912e8	1.76611
$233$	2.22230e8	1.15095	0.575476	−	0.817819i	$-0.304817\pi$
$233$	2.22230e8	1.15095	0.575476	+	0.817819i	$0.304817\pi$
$234$	−2.13720e8	−1.09041
$235$	−1.32699e8	−0.667007
$236$	−7.46452e7	−0.369666
$237$	1.13264e8	0.552677
$238$	−2.27151e8	−1.09218
$239$	1.33230e8	0.631262	0.315631	−	0.948882i	$-0.397784\pi$
$239$	1.33230e8	0.631262	0.315631	+	0.948882i	$0.397784\pi$
$240$	−4.83413e8	−2.25725
$241$	5.22856e7	0.240615	0.120307	−	0.992737i	$-0.461612\pi$
$241$	5.22856e7	0.240615	0.120307	+	0.992737i	$0.461612\pi$
$242$	4.27754e8	1.94017
$243$	−1.43489e7	−0.0641500
$244$	3.07589e8	1.35552
$245$	−1.69393e8	−0.735892
$246$	1.47332e8	0.630991
$247$	5.02604e8	2.12220
$248$	−1.26206e9	−5.25412
$249$	1.88000e8	0.771720
$250$	5.12214e8	2.07330
$251$	−2.01583e8	−0.804629	−0.402314	−	0.915502i	$-0.631794\pi$
$251$	−2.01583e8	−0.804629	−0.402314	+	0.915502i	$0.631794\pi$
$252$	1.08897e8	0.428663
$253$	3.49037e7	0.135503
$254$	−8.46686e8	−3.24193
$255$	−1.74181e8	−0.657823
$256$	1.30006e9	4.84309
$257$	2.23672e7	0.0821949	0.0410975	−	0.999155i	$-0.486915\pi$
$257$	2.23672e7	0.0821949	0.0410975	+	0.999155i	$0.486915\pi$
$258$	−9.05986e7	−0.328437
$259$	1.45355e8	0.519852
$260$	1.24374e9	4.38857
$261$	−4.69151e7	−0.163332
$262$	−9.76702e8	−3.35512
$263$	2.02431e8	0.686170	0.343085	−	0.939304i	$-0.388528\pi$
$263$	2.02431e8	0.686170	0.343085	+	0.939304i	$0.388528\pi$
$264$	6.17104e7	0.206416
$265$	−3.65085e7	−0.120513
$266$	−3.46284e8	−1.12810
$267$	6.71742e7	0.215980
$268$	1.22243e9	3.87928
$269$	6.24827e8	1.95716	0.978581	−	0.205862i	$-0.0659997\pi$
$269$	6.24827e8	1.95716	0.978581	+	0.205862i	$0.0659997\pi$
$270$	1.12911e8	0.349112
$271$	−3.54191e8	−1.08105	−0.540525	−	0.841328i	$-0.681774\pi$
$271$	−3.54191e8	−1.08105	−0.540525	+	0.841328i	$0.681774\pi$
$272$	1.72496e9	5.19741
$273$	−1.46753e8	−0.436533
$274$	5.86581e8	1.72267
$275$	−4.88912e6	−0.0141764
$276$	−7.82216e8	−2.23947
$277$	−6.00748e8	−1.69829	−0.849147	−	0.528156i	$-0.822884\pi$
$277$	−6.00748e8	−1.69829	−0.849147	+	0.528156i	$0.822884\pi$
$278$	4.82946e8	1.34816
$279$	1.76266e8	0.485908
$280$	−5.55125e8	−1.51126
$281$	−5.54600e8	−1.49110	−0.745551	−	0.666448i	$-0.767814\pi$
$281$	−5.54600e8	−1.49110	−0.745551	+	0.666448i	$0.767814\pi$
$282$	−3.06948e8	−0.815067
$283$	1.85734e8	0.487124	0.243562	−	0.969885i	$-0.421684\pi$
$283$	1.85734e8	0.487124	0.243562	+	0.969885i	$0.421684\pi$
$284$	−1.48049e9	−3.83522
$285$	−2.65533e8	−0.679456
$286$	−1.28372e8	−0.324482
$287$	1.01166e8	0.252610
$288$	−6.31136e8	−1.55686
$289$	2.11188e8	0.514668
$290$	3.69174e8	0.888870
$291$	−2.42271e8	−0.576336
$292$	−1.60947e9	−3.78306
$293$	8.06147e8	1.87231	0.936154	−	0.351590i	$-0.114359\pi$
$293$	8.06147e8	1.87231	0.936154	+	0.351590i	$0.114359\pi$
$294$	−3.91826e8	−0.899244
$295$	−5.31450e7	−0.120527
$296$	−1.84597e9	−4.13717
$297$	−8.61877e6	−0.0190896
$298$	−1.23584e8	−0.270523
$299$	1.05413e9	2.28058
$300$	1.09569e8	0.234294
$301$	−6.22103e7	−0.131486
$302$	8.82546e8	1.84380
$303$	3.50626e7	0.0724094
$304$	2.62964e9	5.36832
$305$	2.18994e8	0.441959
$306$	−4.02900e8	−0.803845
$307$	−5.41975e8	−1.06904	−0.534522	−	0.845155i	$-0.679508\pi$
$307$	−5.41975e8	−1.06904	−0.534522	+	0.845155i	$0.679508\pi$
$308$	6.54100e7	0.127561
$309$	−4.07912e8	−0.786525
$310$	−1.38703e9	−2.64436
$311$	−2.23407e8	−0.421149	−0.210575	−	0.977578i	$-0.567534\pi$
$311$	−2.23407e8	−0.421149	−0.210575	+	0.977578i	$0.567534\pi$
$312$	1.86372e9	3.47409
$313$	−6.53332e8	−1.20428	−0.602142	−	0.798389i	$-0.705686\pi$
$313$	−6.53332e8	−1.20428	−0.602142	+	0.798389i	$0.705686\pi$
$314$	5.39234e8	0.982932
$315$	7.75315e7	0.139763
$316$	−1.52466e9	−2.71812
$317$	3.82141e8	0.673777	0.336889	−	0.941544i	$-0.390625\pi$
$317$	3.82141e8	0.673777	0.336889	+	0.941544i	$0.390625\pi$
$318$	−8.44484e7	−0.147264
$319$	−2.81799e7	−0.0486040
$320$	2.67466e9	4.56293
$321$	−1.85384e8	−0.312827
$322$	−7.26276e8	−1.21229
$323$	9.47497e8	1.56448
$324$	1.93153e8	0.315495
$325$	−1.47657e8	−0.238596
$326$	−3.60486e8	−0.576272
$327$	3.42709e8	0.542011
$328$	−1.28479e9	−2.01036
$329$	−2.10769e8	−0.326303
$330$	6.78210e7	0.103888
$331$	−1.19439e8	−0.181030	−0.0905148	−	0.995895i	$-0.528851\pi$
$331$	−1.19439e8	−0.181030	−0.0905148	+	0.995895i	$0.528851\pi$
$332$	−2.53069e9	−3.79539
$333$	2.57817e8	0.382611
$334$	−4.44497e8	−0.652764
$335$	8.70328e8	1.26481
$336$	−7.67815e8	−1.10425
$337$	6.48790e8	0.923421	0.461710	−	0.887031i	$-0.347236\pi$
$337$	6.48790e8	0.923421	0.461710	+	0.887031i	$0.347236\pi$
$338$	−2.48595e9	−3.50173
$339$	5.14477e8	0.717244
$340$	2.34467e9	3.23523
$341$	1.05875e8	0.144596
$342$	−6.14208e8	−0.830279
$343$	−6.07529e8	−0.812901
$344$	7.90056e8	1.04641
$345$	−5.56913e8	−0.730164
$346$	−2.72270e9	−3.53372
$347$	−1.32744e9	−1.70553	−0.852766	−	0.522292i	$-0.825077\pi$
$347$	−1.32744e9	−1.70553	−0.852766	+	0.522292i	$0.825077\pi$
$348$	6.31531e8	0.803280
$349$	−2.41076e7	−0.0303575	−0.0151787	−	0.999885i	$-0.504832\pi$
$349$	−2.41076e7	−0.0303575	−0.0151787	+	0.999885i	$0.504832\pi$
$350$	1.01733e8	0.126830
$351$	−2.60297e8	−0.321288
$352$	−3.79096e8	−0.463287
$353$	−1.15393e9	−1.39626	−0.698132	−	0.715969i	$-0.745985\pi$
$353$	−1.15393e9	−1.39626	−0.698132	+	0.715969i	$0.745985\pi$
$354$	−1.22931e8	−0.147282
$355$	−1.05406e9	−1.25045
$356$	−9.04241e8	−1.06221
$357$	−2.76655e8	−0.321810
$358$	1.00885e9	1.16208
$359$	−1.33636e8	−0.152438	−0.0762190	−	0.997091i	$-0.524285\pi$
$359$	−1.33636e8	−0.152438	−0.0762190	+	0.997091i	$0.524285\pi$
$360$	−9.84632e8	−1.11228
$361$	5.50557e8	0.615924
$362$	3.17361e9	3.51621
$363$	5.20977e8	0.571670
$364$	1.97546e9	2.14691
$365$	−1.14589e9	−1.23344
$366$	5.06558e8	0.540064
$367$	6.96923e8	0.735959	0.367980	−	0.929834i	$-0.380050\pi$
$367$	6.96923e8	0.735959	0.367980	+	0.929834i	$0.380050\pi$
$368$	5.51525e9	5.76897
$369$	1.79440e8	0.185920
$370$	−2.02876e9	−2.08221
$371$	−5.79872e7	−0.0589554
$372$	−2.37274e9	−2.38974
$373$	−2.37598e7	−0.0237062	−0.0118531	−	0.999930i	$-0.503773\pi$
$373$	−2.37598e7	−0.0237062	−0.0118531	+	0.999930i	$0.503773\pi$
$374$	−2.42005e8	−0.239207
$375$	6.23843e8	0.610894
$376$	2.67671e9	2.59684
$377$	−8.51065e8	−0.818028
$378$	1.79339e8	0.170787
$379$	6.51339e8	0.614568	0.307284	−	0.951618i	$-0.400580\pi$
$379$	6.51339e8	0.614568	0.307284	+	0.951618i	$0.400580\pi$
$380$	3.57437e9	3.34162
$381$	−1.03121e9	−0.955231
$382$	−1.13532e9	−1.04207
$383$	7.66231e8	0.696889	0.348445	−	0.937329i	$-0.386710\pi$
$383$	7.66231e8	0.696889	0.348445	+	0.937329i	$0.386710\pi$
$384$	3.19476e9	2.87925
$385$	4.65699e7	0.0415903
$386$	−2.20133e9	−1.94818
$387$	−1.10343e8	−0.0967736
$388$	3.26124e9	2.83447
$389$	−9.02040e8	−0.776966	−0.388483	−	0.921456i	$-0.627001\pi$
$389$	−9.02040e8	−0.776966	−0.388483	+	0.921456i	$0.627001\pi$
$390$	2.04827e9	1.74848
$391$	1.98723e9	1.68124
$392$	3.41688e9	2.86502
$393$	−1.18956e9	−0.988580
$394$	2.97610e9	2.45138
$395$	−1.08551e9	−0.886224
$396$	1.16019e8	0.0938846
$397$	−4.92346e8	−0.394915	−0.197458	−	0.980311i	$-0.563268\pi$
$397$	−4.92346e8	−0.394915	−0.197458	+	0.980311i	$0.563268\pi$
$398$	1.43513e9	1.14104
$399$	−4.21751e8	−0.332393
$400$	−7.72547e8	−0.603552
$401$	−8.45019e8	−0.654427	−0.327213	−	0.944950i	$-0.606110\pi$
$401$	−8.45019e8	−0.654427	−0.327213	+	0.944950i	$0.606110\pi$
$402$	2.01317e9	1.54557
$403$	3.19756e9	2.43361
$404$	−4.71983e8	−0.356116
$405$	1.37519e8	0.102865
$406$	5.86367e8	0.434839
$407$	1.54860e8	0.113857
$408$	3.51345e9	2.56108
$409$	−1.44863e9	−1.04695	−0.523474	−	0.852042i	$-0.675364\pi$
$409$	−1.44863e9	−1.04695	−0.523474	+	0.852042i	$0.675364\pi$
$410$	−1.41201e9	−1.01180
$411$	7.14417e8	0.507581
$412$	5.49097e9	3.86820
$413$	−8.44113e7	−0.0589624
$414$	−1.28820e9	−0.892244
$415$	−1.80177e9	−1.23746
$416$	−1.14491e10	−7.79734
$417$	5.88196e8	0.397233
$418$	−3.68929e8	−0.247073
$419$	−1.06290e9	−0.705902	−0.352951	−	0.935642i	$-0.614822\pi$
$419$	−1.06290e9	−0.705902	−0.352951	+	0.935642i	$0.614822\pi$
$420$	−1.04366e9	−0.687365
$421$	−1.46411e9	−0.956282	−0.478141	−	0.878283i	$-0.658689\pi$
$421$	−1.46411e9	−0.956282	−0.478141	+	0.878283i	$0.658689\pi$
$422$	7.76617e8	0.503052
$423$	−3.73843e8	−0.240158
$424$	7.36424e8	0.469189
$425$	−2.78360e8	−0.175892
$426$	−2.43817e9	−1.52802
$427$	3.47832e8	0.216208
$428$	2.49548e9	1.53851
$429$	−1.56349e8	−0.0956082
$430$	8.68289e8	0.526653
$431$	9.71394e8	0.584420	0.292210	−	0.956354i	$-0.405609\pi$
$431$	9.71394e8	0.584420	0.292210	+	0.956354i	$0.405609\pi$
$432$	−1.36188e9	−0.812730
$433$	−1.99519e9	−1.18107	−0.590535	−	0.807012i	$-0.701083\pi$
$433$	−1.99519e9	−1.18107	−0.590535	+	0.807012i	$0.701083\pi$
$434$	−2.20306e9	−1.29363
$435$	4.49630e8	0.261904
$436$	−4.61325e9	−2.66566
$437$	3.02946e9	1.73652
$438$	−2.65058e9	−1.50724
$439$	−3.32793e9	−1.87737	−0.938683	−	0.344782i	$-0.887953\pi$
$439$	−3.32793e9	−1.87737	−0.938683	+	0.344782i	$0.887953\pi$
$440$	−5.91426e8	−0.330991
$441$	−4.77218e8	−0.264961
$442$	−7.30883e9	−4.02596
$443$	6.61628e8	0.361577	0.180789	−	0.983522i	$-0.442135\pi$
$443$	6.61628e8	0.361577	0.180789	+	0.983522i	$0.442135\pi$
$444$	−3.47052e9	−1.88171
$445$	−6.43791e8	−0.346326
$446$	−4.45523e9	−2.37793
$447$	−1.50517e8	−0.0797094
$448$	4.24823e9	2.23221
$449$	2.39627e9	1.24932	0.624661	−	0.780896i	$-0.285237\pi$
$449$	2.39627e9	1.24932	0.624661	+	0.780896i	$0.285237\pi$
$450$	1.80445e8	0.0933470
$451$	1.07782e8	0.0553259
$452$	−6.92544e9	−3.52747
$453$	1.07488e9	0.543272
$454$	−4.47637e9	−2.24507
$455$	1.40646e9	0.699985
$456$	5.35614e9	2.64530
$457$	5.13759e8	0.251798	0.125899	−	0.992043i	$-0.459818\pi$
$457$	5.13759e8	0.251798	0.125899	+	0.992043i	$0.459818\pi$
$458$	1.99171e9	0.968717
$459$	−4.90706e8	−0.236852
$460$	7.49668e9	3.59101
$461$	1.60015e9	0.760687	0.380344	−	0.924845i	$-0.375806\pi$
$461$	1.60015e9	0.760687	0.380344	+	0.924845i	$0.375806\pi$
$462$	1.07722e8	0.0508225
$463$	7.65148e8	0.358271	0.179136	−	0.983824i	$-0.442670\pi$
$463$	7.65148e8	0.358271	0.179136	+	0.983824i	$0.442670\pi$
$464$	−4.45280e9	−2.06929
$465$	−1.68932e9	−0.779158
$466$	−4.92655e9	−2.25524
$467$	2.99058e9	1.35877	0.679386	−	0.733782i	$-0.262246\pi$
$467$	2.99058e9	1.35877	0.679386	+	0.733782i	$0.262246\pi$
$468$	3.50389e9	1.58012
$469$	1.38236e9	0.618752
$470$	2.94176e9	1.30697
$471$	6.56751e8	0.289619
$472$	1.07200e9	0.469245
$473$	−6.62784e7	−0.0287977
$474$	−2.51091e9	−1.08295
$475$	−4.24350e8	−0.181676
$476$	3.72409e9	1.58269
$477$	−1.02853e8	−0.0433911
$478$	−2.95354e9	−1.23693
$479$	−1.96100e9	−0.815275	−0.407637	−	0.913144i	$-0.633647\pi$
$479$	−1.96100e9	−0.815275	−0.407637	+	0.913144i	$0.633647\pi$
$480$	6.04875e9	2.49644
$481$	4.67695e9	1.91626
$482$	−1.15910e9	−0.471473
$483$	−8.84557e8	−0.357199
$484$	−7.01294e9	−2.81152
$485$	2.32190e9	0.924161
$486$	3.18096e8	0.125699
$487$	−4.21150e9	−1.65229	−0.826143	−	0.563460i	$-0.809470\pi$
$487$	−4.21150e9	−1.65229	−0.826143	+	0.563460i	$0.809470\pi$
$488$	−4.41739e9	−1.72066
$489$	−4.39049e8	−0.169798
$490$	3.75522e9	1.44195
$491$	1.16149e9	0.442824	0.221412	−	0.975180i	$-0.428934\pi$
$491$	1.16149e9	0.442824	0.221412	+	0.975180i	$0.428934\pi$
$492$	−2.41547e9	−0.914373
$493$	−1.60441e9	−0.603047
$494$	−1.11421e10	−4.15835
$495$	8.26015e7	0.0306105
$496$	1.67297e10	6.15607
$497$	−1.67419e9	−0.611725
$498$	−4.16771e9	−1.51215
$499$	2.79801e9	1.00808	0.504042	−	0.863679i	$-0.331846\pi$
$499$	2.79801e9	1.00808	0.504042	+	0.863679i	$0.331846\pi$
$500$	−8.39763e9	−3.00443
$501$	−5.41368e8	−0.192336
$502$	4.46883e9	1.57663
$503$	−2.19333e9	−0.768452	−0.384226	−	0.923239i	$-0.625532\pi$
$503$	−2.19333e9	−0.768452	−0.384226	+	0.923239i	$0.625532\pi$
$504$	−1.56391e9	−0.544133
$505$	−3.36037e8	−0.116109
$506$	−7.73769e8	−0.265512
$507$	−3.02772e9	−1.03178
$508$	1.38812e10	4.69791
$509$	−1.63668e9	−0.550112	−0.275056	−	0.961428i	$-0.588696\pi$
$509$	−1.63668e9	−0.550112	−0.275056	+	0.961428i	$0.588696\pi$
$510$	3.86136e9	1.28897
$511$	−1.82005e9	−0.603405
$512$	−1.36750e10	−4.50281
$513$	−7.48065e8	−0.244641
$514$	−4.95851e8	−0.161057
$515$	3.90939e9	1.26120
$516$	1.48534e9	0.475941
$517$	−2.24551e8	−0.0714659
$518$	−3.22232e9	−1.01863
$519$	−3.31606e9	−1.04121
$520$	−1.78618e10	−5.57074
$521$	−8.21908e8	−0.254619	−0.127310	−	0.991863i	$-0.540634\pi$
$521$	−8.21908e8	−0.254619	−0.127310	+	0.991863i	$0.540634\pi$
$522$	1.04005e9	0.320041
$523$	8.10572e8	0.247763	0.123881	−	0.992297i	$-0.460466\pi$
$523$	8.10572e8	0.247763	0.123881	+	0.992297i	$0.460466\pi$
$524$	1.60128e10	4.86192
$525$	1.23904e8	0.0373704
$526$	−4.48763e9	−1.34452
$527$	6.02797e9	1.79405
$528$	−8.18024e8	−0.241851
$529$	2.94899e9	0.866120
$530$	8.09346e8	0.236139
$531$	−1.49721e8	−0.0433963
$532$	5.67725e9	1.63474
$533$	3.25514e9	0.931160
$534$	−1.48916e9	−0.423202
$535$	1.77670e9	0.501621
$536$	−1.75557e10	−4.92425
$537$	1.22872e9	0.342406
$538$	−1.38516e10	−3.83497
$539$	−2.86644e8	−0.0788465
$540$	−1.85116e9	−0.505900
$541$	5.84572e9	1.58726	0.793629	−	0.608402i	$-0.208189\pi$
$541$	5.84572e9	1.58726	0.793629	+	0.608402i	$0.208189\pi$
$542$	7.85196e9	2.11827
$543$	3.86525e9	1.03604
$544$	−2.15837e10	−5.74816
$545$	−3.28449e9	−0.869120
$546$	3.25332e9	0.855366
$547$	−7.90478e8	−0.206507	−0.103253	−	0.994655i	$-0.532925\pi$
$547$	−7.90478e8	−0.206507	−0.103253	+	0.994655i	$0.532925\pi$
$548$	−9.61686e9	−2.49633
$549$	6.16954e8	0.159129
$550$	1.08385e8	0.0277780
$551$	−2.44587e9	−0.622877
$552$	1.12337e10	2.84272
$553$	−1.72414e9	−0.433544
$554$	1.33178e10	3.32773
$555$	−2.47090e9	−0.613521
$556$	−7.91779e9	−1.95363
$557$	4.59101e9	1.12568	0.562840	−	0.826566i	$-0.309709\pi$
$557$	4.59101e9	1.12568	0.562840	+	0.826566i	$0.309709\pi$
$558$	−3.90759e9	−0.952114
$559$	−2.00168e9	−0.484679
$560$	7.35867e9	1.77068
$561$	−2.94746e8	−0.0704820
$562$	1.22947e10	2.92175
$563$	−1.87013e9	−0.441663	−0.220832	−	0.975312i	$-0.570877\pi$
$563$	−1.87013e9	−0.441663	−0.220832	+	0.975312i	$0.570877\pi$
$564$	5.03235e9	1.18112
$565$	−4.93069e9	−1.15011
$566$	−4.11749e9	−0.954497
$567$	2.18424e8	0.0503221
$568$	2.12618e10	4.86833
$569$	−3.29999e8	−0.0750965	−0.0375482	−	0.999295i	$-0.511955\pi$
$569$	−3.29999e8	−0.0750965	−0.0375482	+	0.999295i	$0.511955\pi$
$570$	5.88651e9	1.33136
$571$	8.31103e9	1.86822	0.934111	−	0.356982i	$-0.116194\pi$
$571$	8.31103e9	1.86822	0.934111	+	0.356982i	$0.116194\pi$
$572$	2.10464e9	0.470210
$573$	−1.38275e9	−0.307045
$574$	−2.24273e9	−0.494977
$575$	−8.90008e8	−0.195234
$576$	7.53513e9	1.64290
$577$	−3.65097e9	−0.791212	−0.395606	−	0.918420i	$-0.629465\pi$
$577$	−3.65097e9	−0.791212	−0.395606	+	0.918420i	$0.629465\pi$
$578$	−4.68177e9	−1.00847
$579$	−2.68108e9	−0.574029
$580$	−6.05253e9	−1.28807
$581$	−2.86179e9	−0.605371
$582$	5.37083e9	1.12930
$583$	−6.17792e7	−0.0129123
$584$	2.31142e10	4.80212
$585$	2.49466e9	0.515188
$586$	−1.78712e10	−3.66870
$587$	3.05418e9	0.623248	0.311624	−	0.950206i	$-0.399127\pi$
$587$	3.05418e9	0.623248	0.311624	+	0.950206i	$0.399127\pi$
$588$	6.42390e9	1.30310
$589$	9.18944e9	1.85304
$590$	1.17815e9	0.236168
$591$	3.62470e9	0.722297
$592$	2.44699e10	4.84738
$593$	−4.80493e9	−0.946227	−0.473113	−	0.881002i	$-0.656870\pi$
$593$	−4.80493e9	−0.946227	−0.473113	+	0.881002i	$0.656870\pi$
$594$	1.91067e8	0.0374053
$595$	2.65143e9	0.516026
$596$	2.02613e9	0.392018
$597$	1.74790e9	0.336206
$598$	−2.33687e10	−4.46870
$599$	3.86139e9	0.734090	0.367045	−	0.930203i	$-0.380369\pi$
$599$	3.86139e9	0.734090	0.367045	+	0.930203i	$0.380369\pi$
$600$	−1.57355e9	−0.297407
$601$	1.96007e9	0.368308	0.184154	−	0.982897i	$-0.441045\pi$
$601$	1.96007e9	0.368308	0.184154	+	0.982897i	$0.441045\pi$
$602$	1.37912e9	0.257641
$603$	2.45191e9	0.455401
$604$	−1.44691e10	−2.67186
$605$	−4.99299e9	−0.916678
$606$	−7.77292e8	−0.141883
$607$	−4.97911e9	−0.903632	−0.451816	−	0.892111i	$-0.649224\pi$
$607$	−4.97911e9	−0.903632	−0.451816	+	0.892111i	$0.649224\pi$
$608$	−3.29036e10	−5.93719
$609$	7.14157e8	0.128125
$610$	−4.85480e9	−0.865999
$611$	−6.78171e9	−1.20280
$612$	6.60546e9	1.16486
$613$	2.72401e9	0.477636	0.238818	−	0.971064i	$-0.423240\pi$
$613$	2.72401e9	0.477636	0.238818	+	0.971064i	$0.423240\pi$
$614$	1.20149e10	2.09474
$615$	−1.71974e9	−0.298125
$616$	−9.39375e8	−0.161922
$617$	7.00273e9	1.20024	0.600122	−	0.799909i	$-0.295119\pi$
$617$	7.00273e9	1.20024	0.600122	+	0.799909i	$0.295119\pi$
$618$	9.04288e9	1.54116
$619$	8.54432e9	1.44797	0.723986	−	0.689815i	$-0.242308\pi$
$619$	8.54432e9	1.44797	0.723986	+	0.689815i	$0.242308\pi$
$620$	2.27401e10	3.83197
$621$	−1.56895e9	−0.262898
$622$	4.95265e9	0.825223
$623$	−1.02255e9	−0.169424
$624$	−2.47053e10	−4.07046
$625$	−5.10655e9	−0.836657
$626$	1.44835e10	2.35974
$627$	−4.49331e8	−0.0727997
$628$	−8.84062e9	−1.42437
$629$	8.81687e9	1.41266
$630$	−1.71877e9	−0.273859
$631$	9.15178e9	1.45012	0.725058	−	0.688688i	$-0.241813\pi$
$631$	9.15178e9	1.45012	0.725058	+	0.688688i	$0.241813\pi$
$632$	2.18961e10	3.45030
$633$	9.45868e8	0.148224
$634$	−8.47157e9	−1.32024
$635$	9.88299e9	1.53172
$636$	1.38451e9	0.213401
$637$	−8.65699e9	−1.32702
$638$	6.24711e8	0.0952373
$639$	−2.96952e9	−0.450229
$640$	−3.06183e10	−4.61690
$641$	7.04336e9	1.05627	0.528137	−	0.849159i	$-0.322891\pi$
$641$	7.04336e9	1.05627	0.528137	+	0.849159i	$0.322891\pi$
$642$	4.10971e9	0.612969
$643$	−6.27887e9	−0.931415	−0.465708	−	0.884939i	$-0.654200\pi$
$643$	−6.27887e9	−0.931415	−0.465708	+	0.884939i	$0.654200\pi$
$644$	1.19071e10	1.75674
$645$	1.05752e9	0.155178
$646$	−2.10048e10	−3.06552
$647$	−4.23121e9	−0.614185	−0.307093	−	0.951680i	$-0.599356\pi$
$647$	−4.23121e9	−0.614185	−0.307093	+	0.951680i	$0.599356\pi$
$648$	−2.77393e9	−0.400482
$649$	−8.99312e7	−0.0129138
$650$	3.27337e9	0.467517
$651$	−2.68318e9	−0.381167
$652$	5.91009e9	0.835080
$653$	3.22584e9	0.453364	0.226682	−	0.973969i	$-0.427212\pi$
$653$	3.22584e9	0.453364	0.226682	+	0.973969i	$0.427212\pi$
$654$	−7.59740e9	−1.06205
$655$	1.14006e10	1.58520
$656$	1.70310e10	2.35547
$657$	−3.22824e9	−0.444106
$658$	4.67247e9	0.639375
$659$	1.14067e10	1.55261	0.776303	−	0.630360i	$-0.217093\pi$
$659$	1.14067e10	1.55261	0.776303	+	0.630360i	$0.217093\pi$
$660$	−1.11191e9	−0.150545
$661$	−5.33531e9	−0.718546	−0.359273	−	0.933233i	$-0.616975\pi$
$661$	−5.33531e9	−0.718546	−0.359273	+	0.933233i	$0.616975\pi$
$662$	2.64782e9	0.354719
$663$	−8.90167e9	−1.18624
$664$	3.63441e10	4.81776
$665$	4.04202e9	0.532995
$666$	−5.71547e9	−0.749708
$667$	−5.12982e9	−0.669363
$668$	7.28743e9	0.945926
$669$	−5.42618e9	−0.700653
$670$	−1.92940e10	−2.47834
$671$	3.70578e8	0.0473534
$672$	9.60735e9	1.22127
$673$	−4.70152e9	−0.594547	−0.297273	−	0.954792i	$-0.596077\pi$
$673$	−4.70152e9	−0.594547	−0.297273	+	0.954792i	$0.596077\pi$
$674$	−1.43828e10	−1.80940
$675$	2.19770e8	0.0275046
$676$	4.07565e10	5.07439
$677$	−1.06147e10	−1.31477	−0.657384	−	0.753555i	$-0.728337\pi$
$677$	−1.06147e10	−1.31477	−0.657384	+	0.753555i	$0.728337\pi$
$678$	−1.14053e10	−1.40541
$679$	3.68793e9	0.452104
$680$	−3.36726e10	−4.10672
$681$	−5.45192e9	−0.661508
$682$	−2.34712e9	−0.283328
$683$	1.13835e10	1.36711	0.683556	−	0.729898i	$-0.260432\pi$
$683$	1.13835e10	1.36711	0.683556	+	0.729898i	$0.260432\pi$
$684$	1.00698e10	1.20316
$685$	−6.84690e9	−0.813911
$686$	1.34681e10	1.59284
$687$	2.42577e9	0.285431
$688$	−1.04729e10	−1.22605
$689$	−1.86580e9	−0.217319
$690$	1.23460e10	1.43072
$691$	−1.20923e10	−1.39423	−0.697117	−	0.716958i	$-0.745534\pi$
$691$	−1.20923e10	−1.39423	−0.697117	+	0.716958i	$0.745534\pi$
$692$	4.46380e10	5.12075
$693$	1.31198e8	0.0149748
$694$	2.94275e10	3.34191
$695$	−5.63721e9	−0.636968
$696$	−9.06962e9	−1.01966
$697$	6.13652e9	0.686447
$698$	5.34435e8	0.0594841
$699$	−6.00021e9	−0.664502
$700$	−1.66789e9	−0.183791
$701$	−7.42546e9	−0.814161	−0.407080	−	0.913392i	$-0.633453\pi$
$701$	−7.42546e9	−0.814161	−0.407080	+	0.913392i	$0.633453\pi$
$702$	5.77044e9	0.629549
$703$	1.34410e10	1.45911
$704$	4.52603e9	0.488892
$705$	3.58287e9	0.385097
$706$	2.55811e10	2.73592
$707$	−5.33734e8	−0.0568011
$708$	2.01542e9	0.213427
$709$	−1.74012e10	−1.83366	−0.916828	−	0.399283i	$-0.869259\pi$
$709$	−1.74012e10	−1.83366	−0.916828	+	0.399283i	$0.869259\pi$
$710$	2.33671e10	2.45020
$711$	−3.05812e9	−0.319088
$712$	1.29861e10	1.34834
$713$	1.92734e10	1.99134
$714$	6.13308e9	0.630572
$715$	1.49844e9	0.153309
$716$	−1.65399e10	−1.68398
$717$	−3.59721e9	−0.364459
$718$	2.96254e9	0.298695
$719$	−1.32945e10	−1.33389	−0.666947	−	0.745105i	$-0.732399\pi$
$719$	−1.32945e10	−1.33389	−0.666947	+	0.745105i	$0.732399\pi$
$720$	1.30521e10	1.30322
$721$	6.20937e9	0.616985
$722$	−1.22051e10	−1.20687
$723$	−1.41171e9	−0.138919
$724$	−5.20307e10	−5.09536
$725$	7.18558e8	0.0700291
$726$	−1.15494e10	−1.12016
$727$	−1.92881e9	−0.186174	−0.0930870	−	0.995658i	$-0.529673\pi$
$727$	−1.92881e9	−0.186174	−0.0930870	+	0.995658i	$0.529673\pi$
$728$	−2.83702e10	−2.72523
$729$	3.87420e8	0.0370370
$730$	2.54029e10	2.41687
$731$	−3.77353e9	−0.357303
$732$	−8.30491e9	−0.782611
$733$	−1.50113e10	−1.40785	−0.703924	−	0.710276i	$-0.748570\pi$
$733$	−1.50113e10	−1.40785	−0.703924	+	0.710276i	$0.748570\pi$
$734$	−1.54499e10	−1.44208
$735$	4.57361e9	0.424867
$736$	−6.90101e10	−6.38029
$737$	1.47276e9	0.135517
$738$	−3.97795e9	−0.364303
$739$	1.34293e9	0.122404	0.0612022	−	0.998125i	$-0.480507\pi$
$739$	1.34293e9	0.122404	0.0612022	+	0.998125i	$0.480507\pi$
$740$	3.32611e10	3.01735
$741$	−1.35703e10	−1.22525
$742$	1.28550e9	0.115520
$743$	−2.17047e10	−1.94130	−0.970650	−	0.240497i	$-0.922690\pi$
$743$	−2.17047e10	−1.94130	−0.970650	+	0.240497i	$0.922690\pi$
$744$	3.40757e10	3.03347
$745$	1.44254e9	0.127815
$746$	5.26723e8	0.0464511
$747$	−5.07599e9	−0.445553
$748$	3.96762e9	0.346636
$749$	2.82197e9	0.245395
$750$	−1.38298e10	−1.19702
$751$	2.45348e9	0.211370	0.105685	−	0.994400i	$-0.466297\pi$
$751$	2.45348e9	0.211370	0.105685	+	0.994400i	$0.466297\pi$
$752$	−3.54821e10	−3.04262
$753$	5.44274e9	0.464553
$754$	1.88670e10	1.60289
$755$	−1.03016e10	−0.871143
$756$	−2.94023e9	−0.247489
$757$	9.08326e9	0.761038	0.380519	−	0.924773i	$-0.375745\pi$
$757$	9.08326e9	0.761038	0.380519	+	0.924773i	$0.375745\pi$
$758$	−1.44393e10	−1.20422
$759$	−9.42400e8	−0.0782328
$760$	−5.13327e10	−4.24177
$761$	2.38536e10	1.96204	0.981021	−	0.193902i	$-0.0621145\pi$
$761$	2.38536e10	1.96204	0.981021	+	0.193902i	$0.0621145\pi$
$762$	2.28605e10	1.87173
$763$	−5.21682e9	−0.425177
$764$	1.86133e10	1.51007
$765$	4.70288e9	0.379795
$766$	−1.69863e10	−1.36552
$767$	−2.71603e9	−0.217345
$768$	−3.51015e10	−2.79616
$769$	1.44982e10	1.14967	0.574834	−	0.818270i	$-0.305067\pi$
$769$	1.44982e10	1.14967	0.574834	+	0.818270i	$0.305067\pi$
$770$	−1.03239e9	−0.0814943
$771$	−6.03913e8	−0.0474553
$772$	3.60903e10	2.82313
$773$	−1.48061e10	−1.15296	−0.576479	−	0.817112i	$-0.695574\pi$
$773$	−1.48061e10	−1.15296	−0.576479	+	0.817112i	$0.695574\pi$
$774$	2.44616e9	0.189623
$775$	−2.69971e9	−0.208335
$776$	−4.68358e10	−3.59801
$777$	−3.92458e9	−0.300137
$778$	1.99970e10	1.52243
$779$	9.35492e9	0.709021
$780$	−3.35810e10	−2.53374
$781$	−1.78367e9	−0.133978
$782$	−4.40542e10	−3.29430
$783$	1.26671e9	0.0942997
$784$	−4.52937e10	−3.35684
$785$	−6.29424e9	−0.464408
$786$	2.63709e10	1.93708
$787$	1.47489e10	1.07857	0.539286	−	0.842122i	$-0.318694\pi$
$787$	1.47489e10	1.07857	0.539286	+	0.842122i	$0.318694\pi$
$788$	−4.87926e10	−3.55232
$789$	−5.46564e9	−0.396161
$790$	2.40643e10	1.73651
$791$	−7.83153e9	−0.562638
$792$	−1.66618e9	−0.119175
$793$	1.11919e10	0.796979
$794$	1.09147e10	0.773818
$795$	9.85730e8	0.0695781
$796$	−2.35287e10	−1.65349
$797$	1.53056e10	1.07090	0.535448	−	0.844568i	$-0.320143\pi$
$797$	1.53056e10	1.07090	0.535448	+	0.844568i	$0.320143\pi$
$798$	9.34967e9	0.651308
$799$	−1.27847e10	−0.886702
$800$	9.66656e9	0.667509
$801$	−1.81370e9	−0.124696
$802$	1.87330e10	1.28232
$803$	−1.93906e9	−0.132156
$804$	−3.30055e10	−2.23970
$805$	8.47751e9	0.572773
$806$	−7.08857e10	−4.76855
$807$	−1.68703e10	−1.12997
$808$	6.77830e9	0.452044
$809$	2.54329e8	0.0168879	0.00844396	−	0.999964i	$-0.497312\pi$
$809$	2.54329e8	0.0168879	0.00844396	+	0.999964i	$0.497312\pi$
$810$	−3.04861e9	−0.201560
$811$	1.23140e10	0.810637	0.405318	−	0.914176i	$-0.367161\pi$
$811$	1.23140e10	0.810637	0.405318	+	0.914176i	$0.367161\pi$
$812$	−9.61336e9	−0.630129
$813$	9.56317e9	0.624144
$814$	−3.43304e9	−0.223097
$815$	4.20780e9	0.272272
$816$	−4.65738e10	−3.00073
$817$	−5.75262e9	−0.369053
$818$	3.21141e10	2.05144
$819$	3.96232e9	0.252032
$820$	2.31496e10	1.46621
$821$	5.18812e9	0.327197	0.163598	−	0.986527i	$-0.447690\pi$
$821$	5.18812e9	0.327197	0.163598	+	0.986527i	$0.447690\pi$
$822$	−1.58377e10	−0.994581
$823$	−4.12489e9	−0.257937	−0.128968	−	0.991649i	$-0.541167\pi$
$823$	−4.12489e9	−0.257937	−0.128968	+	0.991649i	$0.541167\pi$
$824$	−7.88576e10	−4.91019
$825$	1.32006e8	0.00818476
$826$	1.87129e9	0.115534
$827$	5.89785e9	0.362597	0.181298	−	0.983428i	$-0.441970\pi$
$827$	5.89785e9	0.362597	0.181298	+	0.983428i	$0.441970\pi$
$828$	2.11198e10	1.29296
$829$	−2.77208e10	−1.68991	−0.844957	−	0.534835i	$-0.820374\pi$
$829$	−2.77208e10	−1.68991	−0.844957	+	0.534835i	$0.820374\pi$
$830$	3.99429e10	2.42475
$831$	1.62202e10	0.980511
$832$	1.36691e11	8.22828
$833$	−1.63200e10	−0.978277
$834$	−1.30395e10	−0.778361
$835$	5.18842e9	0.308413
$836$	6.04850e9	0.358035
$837$	−4.75918e9	−0.280539
$838$	2.35632e10	1.38318
$839$	1.84332e10	1.07754	0.538771	−	0.842452i	$-0.318889\pi$
$839$	1.84332e10	1.07754	0.538771	+	0.842452i	$0.318889\pi$
$840$	1.49884e10	0.872524
$841$	−1.31083e10	−0.759904
$842$	3.24574e10	1.87379
$843$	1.49742e10	0.860888
$844$	−1.27325e10	−0.728977
$845$	2.90174e10	1.65447
$846$	8.28761e9	0.470579
$847$	−7.93047e9	−0.448443
$848$	−9.76194e9	−0.549731
$849$	−5.01483e9	−0.281241
$850$	6.17087e9	0.344652
$851$	2.81904e10	1.56801
$852$	3.99732e10	2.21427
$853$	−3.15892e10	−1.74268	−0.871339	−	0.490682i	$-0.836748\pi$
$853$	−3.15892e10	−1.74268	−0.871339	+	0.490682i	$0.836748\pi$
$854$	−7.71099e9	−0.423650
$855$	7.16938e9	0.392284
$856$	−3.58383e10	−1.95294
$857$	−1.55096e10	−0.841722	−0.420861	−	0.907125i	$-0.638272\pi$
$857$	−1.55096e10	−0.841722	−0.420861	+	0.907125i	$0.638272\pi$
$858$	3.46606e9	0.187340
$859$	−2.86456e10	−1.54199	−0.770997	−	0.636839i	$-0.780241\pi$
$859$	−2.86456e10	−1.54199	−0.770997	+	0.636839i	$0.780241\pi$
$860$	−1.42354e10	−0.763177
$861$	−2.73149e9	−0.145844
$862$	−2.15345e10	−1.14514
$863$	−3.05356e10	−1.61722	−0.808609	−	0.588346i	$-0.799779\pi$
$863$	−3.05356e10	−1.61722	−0.808609	+	0.588346i	$0.799779\pi$
$864$	1.70407e10	0.898853
$865$	3.17808e10	1.66959
$866$	4.42307e10	2.31425
$867$	−5.70208e9	−0.297144
$868$	3.61186e10	1.87462
$869$	−1.83688e9	−0.0949537
$870$	−9.96770e9	−0.513189
$871$	4.44790e10	2.28082
$872$	6.62524e10	3.38372
$873$	6.54132e9	0.332748
$874$	−6.71592e10	−3.40263
$875$	−9.49633e9	−0.479212
$876$	4.34557e10	2.18415
$877$	−1.42738e10	−0.714562	−0.357281	−	0.933997i	$-0.616296\pi$
$877$	−1.42738e10	−0.714562	−0.357281	+	0.933997i	$0.616296\pi$
$878$	7.37759e10	3.67861
$879$	−2.17660e10	−1.08098
$880$	7.83987e9	0.387810
$881$	−5.85758e9	−0.288604	−0.144302	−	0.989534i	$-0.546094\pi$
$881$	−5.85758e9	−0.288604	−0.144302	+	0.989534i	$0.546094\pi$
$882$	1.05793e10	0.519178
$883$	3.15376e10	1.54158	0.770790	−	0.637089i	$-0.219862\pi$
$883$	3.15376e10	1.54158	0.770790	+	0.637089i	$0.219862\pi$
$884$	1.19827e11	5.83405
$885$	1.43491e9	0.0695864
$886$	−1.46674e10	−0.708494
$887$	1.06379e10	0.511829	0.255914	−	0.966699i	$-0.417624\pi$
$887$	1.06379e10	0.511829	0.255914	+	0.966699i	$0.417624\pi$
$888$	4.98412e10	2.38860
$889$	1.56974e10	0.749325
$890$	1.42720e10	0.678609
$891$	2.32707e8	0.0110214
$892$	7.30426e10	3.44587
$893$	−1.94899e10	−0.915861
$894$	3.33677e9	0.156187
$895$	−1.17759e10	−0.549052
$896$	−4.86316e10	−2.25861
$897$	−2.84616e10	−1.31670
$898$	−5.31222e10	−2.44799
$899$	−1.55606e10	−0.714278
$900$	−2.95835e9	−0.135270
$901$	−3.51737e9	−0.160207
$902$	−2.38939e9	−0.108408
$903$	1.67968e9	0.0759135
$904$	9.94585e10	4.47767
$905$	−3.70442e10	−1.66131
$906$	−2.38287e10	−1.06452
$907$	−1.21567e10	−0.540993	−0.270497	−	0.962721i	$-0.587188\pi$
$907$	−1.21567e10	−0.540993	−0.270497	+	0.962721i	$0.587188\pi$
$908$	7.33891e10	3.25335
$909$	−9.46690e8	−0.0418056
$910$	−3.11795e10	−1.37159
$911$	−1.79794e10	−0.787881	−0.393941	−	0.919136i	$-0.628888\pi$
$911$	−1.79794e10	−0.787881	−0.393941	+	0.919136i	$0.628888\pi$
$912$	−7.10003e10	−3.09940
$913$	−3.04893e9	−0.132587
$914$	−1.13894e10	−0.493387
$915$	−5.91283e9	−0.255165
$916$	−3.26537e10	−1.40378
$917$	1.81078e10	0.775486
$918$	1.08783e10	0.464100
$919$	3.12747e10	1.32919	0.664597	−	0.747202i	$-0.268603\pi$
$919$	3.12747e10	1.32919	0.664597	+	0.747202i	$0.268603\pi$
$920$	−1.07662e11	−4.55834
$921$	1.46333e10	0.617212
$922$	−3.54731e10	−1.49053
$923$	−5.38688e10	−2.25492
$924$	−1.76607e9	−0.0736472
$925$	−3.94876e9	−0.164046
$926$	−1.69623e10	−0.702016
$927$	1.10136e10	0.454100
$928$	5.57161e10	2.28856
$929$	−4.19833e9	−0.171799	−0.0858997	−	0.996304i	$-0.527376\pi$
$929$	−4.19833e9	−0.171799	−0.0858997	+	0.996304i	$0.527376\pi$
$930$	3.74499e10	1.52672
$931$	−2.48792e10	−1.01045
$932$	8.07697e10	3.26808
$933$	6.03200e9	0.243151
$934$	−6.62972e10	−2.66245
$935$	2.82482e9	0.113019
$936$	−5.03206e10	−2.00576
$937$	−4.93627e10	−1.96024	−0.980122	−	0.198393i	$-0.936428\pi$
$937$	−4.93627e10	−1.96024	−0.980122	+	0.198393i	$0.936428\pi$
$938$	−3.06451e10	−1.21242
$939$	1.76400e10	0.695294
$940$	−4.82296e10	−1.89394
$941$	5.81164e9	0.227371	0.113685	−	0.993517i	$-0.463734\pi$
$941$	5.81164e9	0.227371	0.113685	+	0.993517i	$0.463734\pi$
$942$	−1.45593e10	−0.567496
$943$	1.96205e10	0.761936
$944$	−1.42103e10	−0.549797
$945$	−2.09335e9	−0.0806921
$946$	1.46931e9	0.0564278
$947$	−3.48866e10	−1.33485	−0.667427	−	0.744676i	$-0.732604\pi$
$947$	−3.48866e10	−1.33485	−0.667427	+	0.744676i	$0.732604\pi$
$948$	4.11658e10	1.56930
$949$	−5.85619e10	−2.22425
$950$	9.40729e9	0.355985
$951$	−1.03178e10	−0.389006
$952$	−5.34829e10	−2.00903
$953$	8.20632e9	0.307131	0.153565	−	0.988138i	$-0.450924\pi$
$953$	8.20632e9	0.307131	0.153565	+	0.988138i	$0.450924\pi$
$954$	2.28011e9	0.0850229
$955$	1.32521e10	0.492349
$956$	4.84226e10	1.79244
$957$	7.60857e8	0.0280615
$958$	4.34729e10	1.59749
$959$	−1.08751e10	−0.398169
$960$	−7.22159e10	−2.63441
$961$	3.09505e10	1.12496
$962$	−1.03682e11	−3.75482
$963$	5.00536e9	0.180611
$964$	1.90032e10	0.683216
$965$	2.56952e10	0.920462
$966$	1.96095e10	0.699916
$967$	1.16190e10	0.413213	0.206607	−	0.978424i	$-0.433758\pi$
$967$	1.16190e10	0.413213	0.206607	+	0.978424i	$0.433758\pi$
$968$	1.00715e11	3.56887
$969$	−2.55824e10	−0.903251
$970$	−5.14735e10	−1.81085
$971$	−4.87190e9	−0.170778	−0.0853889	−	0.996348i	$-0.527213\pi$
$971$	−4.87190e9	−0.170778	−0.0853889	+	0.996348i	$0.527213\pi$
$972$	−5.21512e9	−0.182151
$973$	−8.95371e9	−0.311607
$974$	9.33634e10	3.23758
$975$	3.98674e9	0.137753
$976$	5.85563e10	2.01604
$977$	−2.06779e10	−0.709375	−0.354688	−	0.934985i	$-0.615413\pi$
$977$	−2.06779e10	−0.709375	−0.354688	+	0.934985i	$0.615413\pi$
$978$	9.73313e9	0.332711
$979$	−1.08941e9	−0.0371068
$980$	−6.15660e10	−2.08954
$981$	−9.25314e9	−0.312930
$982$	−2.57487e10	−0.867692
$983$	−1.54356e8	−0.00518306	−0.00259153	−	0.999997i	$-0.500825\pi$
$983$	−1.54356e8	−0.00518306	−0.00259153	+	0.999997i	$0.500825\pi$
$984$	3.46893e10	1.16068
$985$	−3.47388e10	−1.15821
$986$	3.55676e10	1.18164
$987$	5.69076e9	0.188391
$988$	1.82672e11	6.02590
$989$	−1.20652e10	−0.396596
$990$	−1.83117e9	−0.0599798
$991$	−2.23061e10	−0.728057	−0.364029	−	0.931388i	$-0.618599\pi$
$991$	−2.23061e10	−0.728057	−0.364029	+	0.931388i	$0.618599\pi$
$992$	−2.09332e11	−6.80841
$993$	3.22487e9	0.104518
$994$	3.71145e10	1.19865
$995$	−1.67517e10	−0.539110
$996$	6.83287e10	2.19127
$997$	3.27229e10	1.04573	0.522865	−	0.852416i	$-0.324863\pi$
$997$	3.27229e10	1.04573	0.522865	+	0.852416i	$0.324863\pi$
$998$	−6.20281e10	−1.97529
$999$	−6.96107e9	−0.220900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.1	✓	17
3.2	odd	2		531.8.a.c.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.1	✓	17	1.1	even	1	trivial
531.8.a.c.1.17		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)

\(f(q)\)	\(=\)	\(q-22.1687 q^{2} -27.0000 q^{3} +363.451 q^{4} +258.765 q^{5} +598.555 q^{6} +411.003 q^{7} -5219.64 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-22.1687 q^{2} -27.0000 q^{3} +363.451 q^{4} +258.765 q^{5} +598.555 q^{6} +411.003 q^{7} -5219.64 q^{8} +729.000 q^{9} -5736.49 q^{10} +437.879 q^{11} -9813.17 q^{12} +13224.5 q^{13} -9111.39 q^{14} -6986.67 q^{15} +69190.8 q^{16} +24930.4 q^{17} -16161.0 q^{18} +38005.6 q^{19} +94048.5 q^{20} -11097.1 q^{21} -9707.20 q^{22} +79710.8 q^{23} +140930. q^{24} -11165.5 q^{25} -293169. q^{26} -19683.0 q^{27} +149379. q^{28} -64355.4 q^{29} +154885. q^{30} +241791. q^{31} -865756. q^{32} -11822.7 q^{33} -552675. q^{34} +106353. q^{35} +264956. q^{36} +353659. q^{37} -842535. q^{38} -357060. q^{39} -1.35066e6 q^{40} +246146. q^{41} +246008. q^{42} -151362. q^{43} +159147. q^{44} +188640. q^{45} -1.76708e6 q^{46} -512816. q^{47} -1.86815e6 q^{48} -654620. q^{49} +247524. q^{50} -673122. q^{51} +4.80644e6 q^{52} -141087. q^{53} +436346. q^{54} +113308. q^{55} -2.14528e6 q^{56} -1.02615e6 q^{57} +1.42668e6 q^{58} -205379. q^{59} -2.53931e6 q^{60} +846302. q^{61} -5.36020e6 q^{62} +299621. q^{63} +1.03362e7 q^{64} +3.42203e6 q^{65} +262095. q^{66} +3.36339e6 q^{67} +9.06099e6 q^{68} -2.15219e6 q^{69} -2.35771e6 q^{70} -4.07342e6 q^{71} -3.80511e6 q^{72} -4.42831e6 q^{73} -7.84015e6 q^{74} +301467. q^{75} +1.38132e7 q^{76} +179969. q^{77} +7.91556e6 q^{78} -4.19495e6 q^{79} +1.79042e7 q^{80} +531441. q^{81} -5.45672e6 q^{82} -6.96295e6 q^{83} -4.03324e6 q^{84} +6.45114e6 q^{85} +3.35550e6 q^{86} +1.73760e6 q^{87} -2.28557e6 q^{88} -2.48793e6 q^{89} -4.18190e6 q^{90} +5.43529e6 q^{91} +2.89710e7 q^{92} -6.52837e6 q^{93} +1.13685e7 q^{94} +9.83454e6 q^{95} +2.33754e7 q^{96} +8.97300e6 q^{97} +1.45121e7 q^{98} +319214. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9} + 6521 q^{10} - 1764 q^{11} - 31482 q^{12} + 18192 q^{13} - 7827 q^{14} + 8586 q^{15} + 139226 q^{16} - 15507 q^{17} + 1458 q^{18} + 52083 q^{19} + 721 q^{20} - 84915 q^{21} - 234434 q^{22} + 63823 q^{23} - 63585 q^{24} + 202153 q^{25} - 367956 q^{26} - 334611 q^{27} + 182306 q^{28} - 502955 q^{29} - 176067 q^{30} + 347531 q^{31} - 243908 q^{32} + 47628 q^{33} - 330872 q^{34} + 92641 q^{35} + 850014 q^{36} + 447615 q^{37} + 775669 q^{38} - 491184 q^{39} + 2203270 q^{40} + 940335 q^{41} + 211329 q^{42} + 478562 q^{43} - 596924 q^{44} - 231822 q^{45} - 3078663 q^{46} + 703121 q^{47} - 3759102 q^{48} + 1895082 q^{49} - 876967 q^{50} + 418689 q^{51} + 6278296 q^{52} - 1005974 q^{53} - 39366 q^{54} + 5212846 q^{55} + 3425294 q^{56} - 1406241 q^{57} + 6710166 q^{58} - 3491443 q^{59} - 19467 q^{60} + 11510749 q^{61} + 5996234 q^{62} + 2292705 q^{63} + 29496941 q^{64} + 11094180 q^{65} + 6329718 q^{66} + 14007144 q^{67} + 19688159 q^{68} - 1723221 q^{69} + 30909708 q^{70} + 5229074 q^{71} + 1716795 q^{72} + 5452211 q^{73} + 12819662 q^{74} - 5458131 q^{75} + 41929340 q^{76} + 9930777 q^{77} + 9934812 q^{78} + 15275654 q^{79} + 36576105 q^{80} + 9034497 q^{81} + 32025935 q^{82} + 7826609 q^{83} - 4922262 q^{84} + 11836945 q^{85} + 51649136 q^{86} + 13579785 q^{87} + 30223741 q^{88} - 6436185 q^{89} + 4753809 q^{90} + 11633535 q^{91} + 43357972 q^{92} - 9383337 q^{93} - 4494252 q^{94} + 23741055 q^{95} + 6585516 q^{96} + 26377540 q^{97} + 26517816 q^{98} - 1285956 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9 + 6521 * q^10 - 1764 * q^11 - 31482 * q^12 + 18192 * q^13 - 7827 * q^14 + 8586 * q^15 + 139226 * q^16 - 15507 * q^17 + 1458 * q^18 + 52083 * q^19 + 721 * q^20 - 84915 * q^21 - 234434 * q^22 + 63823 * q^23 - 63585 * q^24 + 202153 * q^25 - 367956 * q^26 - 334611 * q^27 + 182306 * q^28 - 502955 * q^29 - 176067 * q^30 + 347531 * q^31 - 243908 * q^32 + 47628 * q^33 - 330872 * q^34 + 92641 * q^35 + 850014 * q^36 + 447615 * q^37 + 775669 * q^38 - 491184 * q^39 + 2203270 * q^40 + 940335 * q^41 + 211329 * q^42 + 478562 * q^43 - 596924 * q^44 - 231822 * q^45 - 3078663 * q^46 + 703121 * q^47 - 3759102 * q^48 + 1895082 * q^49 - 876967 * q^50 + 418689 * q^51 + 6278296 * q^52 - 1005974 * q^53 - 39366 * q^54 + 5212846 * q^55 + 3425294 * q^56 - 1406241 * q^57 + 6710166 * q^58 - 3491443 * q^59 - 19467 * q^60 + 11510749 * q^61 + 5996234 * q^62 + 2292705 * q^63 + 29496941 * q^64 + 11094180 * q^65 + 6329718 * q^66 + 14007144 * q^67 + 19688159 * q^68 - 1723221 * q^69 + 30909708 * q^70 + 5229074 * q^71 + 1716795 * q^72 + 5452211 * q^73 + 12819662 * q^74 - 5458131 * q^75 + 41929340 * q^76 + 9930777 * q^77 + 9934812 * q^78 + 15275654 * q^79 + 36576105 * q^80 + 9034497 * q^81 + 32025935 * q^82 + 7826609 * q^83 - 4922262 * q^84 + 11836945 * q^85 + 51649136 * q^86 + 13579785 * q^87 + 30223741 * q^88 - 6436185 * q^89 + 4753809 * q^90 + 11633535 * q^91 + 43357972 * q^92 - 9383337 * q^93 - 4494252 * q^94 + 23741055 * q^95 + 6585516 * q^96 + 26377540 * q^97 + 26517816 * q^98 - 1285956 * q^99

Introduction

L-functions

Modular forms

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