LMFDB - Embedded newform 177.8.a.c.1.12

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			1.12
Root			$9.14085$ 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)

$f(q)$	$=$	$q+9.14085 q^{2} -27.0000 q^{3} -44.4448 q^{4} -27.9722 q^{5} -246.803 q^{6} -1415.76 q^{7} -1576.29 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+9.14085 q^{2} -27.0000 q^{3} -44.4448 q^{4} -27.9722 q^{5} -246.803 q^{6} -1415.76 q^{7} -1576.29 q^{8} +729.000 q^{9} -255.690 q^{10} -4887.09 q^{11} +1200.01 q^{12} -5210.02 q^{13} -12941.3 q^{14} +755.249 q^{15} -8719.72 q^{16} +5796.28 q^{17} +6663.68 q^{18} +24940.5 q^{19} +1243.22 q^{20} +38225.5 q^{21} -44672.2 q^{22} -63003.2 q^{23} +42559.9 q^{24} -77342.6 q^{25} -47624.1 q^{26} -19683.0 q^{27} +62923.2 q^{28} +86556.7 q^{29} +6903.62 q^{30} +268352. q^{31} +122060. q^{32} +131951. q^{33} +52983.0 q^{34} +39601.9 q^{35} -32400.3 q^{36} -235277. q^{37} +227977. q^{38} +140671. q^{39} +44092.3 q^{40} -585710. q^{41} +349414. q^{42} -806765. q^{43} +217206. q^{44} -20391.7 q^{45} -575903. q^{46} +557072. q^{47} +235432. q^{48} +1.18083e6 q^{49} -706977. q^{50} -156500. q^{51} +231559. q^{52} +2.07376e6 q^{53} -179919. q^{54} +136703. q^{55} +2.23165e6 q^{56} -673393. q^{57} +791202. q^{58} -205379. q^{59} -33566.9 q^{60} -1.17120e6 q^{61} +2.45297e6 q^{62} -1.03209e6 q^{63} +2.23185e6 q^{64} +145736. q^{65} +1.20615e6 q^{66} +4.57510e6 q^{67} -257615. q^{68} +1.70109e6 q^{69} +361995. q^{70} +798821. q^{71} -1.14912e6 q^{72} -2.35826e6 q^{73} -2.15063e6 q^{74} +2.08825e6 q^{75} -1.10847e6 q^{76} +6.91895e6 q^{77} +1.28585e6 q^{78} +117864. q^{79} +243910. q^{80} +531441. q^{81} -5.35389e6 q^{82} +2.44537e6 q^{83} -1.69893e6 q^{84} -162135. q^{85} -7.37452e6 q^{86} -2.33703e6 q^{87} +7.70349e6 q^{88} -5.83686e6 q^{89} -186398. q^{90} +7.37614e6 q^{91} +2.80017e6 q^{92} -7.24551e6 q^{93} +5.09211e6 q^{94} -697640. q^{95} -3.29561e6 q^{96} -6.38002e6 q^{97} +1.07938e7 q^{98} -3.56269e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.14085	0.807945	0.403972	−	0.914771i	$-0.367629\pi$
$2$	9.14085	0.807945	0.403972	+	0.914771i	$0.367629\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−44.4448	−0.347225
$5$	−27.9722	−0.100076	−0.0500382	−	0.998747i	$-0.515934\pi$
$5$	−27.9722	−0.100076	−0.0500382	+	0.998747i	$0.515934\pi$
$6$	−246.803	−0.466467
$7$	−1415.76	−1.56008	−0.780040	−	0.625730i	$-0.784801\pi$
$7$	−1415.76	−1.56008	−0.780040	+	0.625730i	$0.784801\pi$
$8$	−1576.29	−1.08848
$9$	729.000	0.333333
$10$	−255.690	−0.0808562
$11$	−4887.09	−1.10707	−0.553536	−	0.832825i	$-0.686722\pi$
$11$	−4887.09	−1.10707	−0.553536	+	0.832825i	$0.686722\pi$
$12$	1200.01	0.200471
$13$	−5210.02	−0.657715	−0.328858	−	0.944380i	$-0.606664\pi$
$13$	−5210.02	−0.657715	−0.328858	+	0.944380i	$0.606664\pi$
$14$	−12941.3	−1.26046
$15$	755.249	0.0577791
$16$	−8719.72	−0.532210
$17$	5796.28	0.286140	0.143070	−	0.989713i	$-0.454303\pi$
$17$	5796.28	0.286140	0.143070	+	0.989713i	$0.454303\pi$
$18$	6663.68	0.269315
$19$	24940.5	0.834194	0.417097	−	0.908862i	$-0.363048\pi$
$19$	24940.5	0.834194	0.417097	+	0.908862i	$0.363048\pi$
$20$	1243.22	0.0347490
$21$	38225.5	0.900712
$22$	−44672.2	−0.894454
$23$	−63003.2	−1.07973	−0.539865	−	0.841751i	$-0.681525\pi$
$23$	−63003.2	−1.07973	−0.539865	+	0.841751i	$0.681525\pi$
$24$	42559.9	0.628436
$25$	−77342.6	−0.989985
$26$	−47624.1	−0.531398
$27$	−19683.0	−0.192450
$28$	62923.2	0.541699
$29$	86556.7	0.659034	0.329517	−	0.944150i	$-0.393114\pi$
$29$	86556.7	0.659034	0.329517	+	0.944150i	$0.393114\pi$
$30$	6903.62	0.0466823
$31$	268352.	1.61785	0.808927	−	0.587909i	$-0.200049\pi$
$31$	268352.	1.61785	0.808927	+	0.587909i	$0.200049\pi$
$32$	122060.	0.658488
$33$	131951.	0.639169
$34$	52983.0	0.231185
$35$	39601.9	0.156127
$36$	−32400.3	−0.115742
$37$	−235277.	−0.763614	−0.381807	−	0.924242i	$-0.624698\pi$
$37$	−235277.	−0.763614	−0.381807	+	0.924242i	$0.624698\pi$
$38$	227977.	0.673983
$39$	140671.	0.379732
$40$	44092.3	0.108931
$41$	−585710.	−1.32721	−0.663605	−	0.748083i	$-0.730974\pi$
$41$	−585710.	−1.32721	−0.663605	+	0.748083i	$0.730974\pi$
$42$	349414.	0.727726
$43$	−806765.	−1.54742	−0.773709	−	0.633541i	$-0.781601\pi$
$43$	−806765.	−1.54742	−0.773709	+	0.633541i	$0.781601\pi$
$44$	217206.	0.384403
$45$	−20391.7	−0.0333588
$46$	−575903.	−0.872363
$47$	557072.	0.782652	0.391326	−	0.920252i	$-0.372016\pi$
$47$	557072.	0.782652	0.391326	+	0.920252i	$0.372016\pi$
$48$	235432.	0.307271
$49$	1.18083e6	1.43385
$50$	−706977.	−0.799853
$51$	−156500.	−0.165203
$52$	231559.	0.228375
$53$	2.07376e6	1.91334	0.956671	−	0.291170i	$-0.0940446\pi$
$53$	2.07376e6	1.91334	0.956671	+	0.291170i	$0.0940446\pi$
$54$	−179919.	−0.155489
$55$	136703.	0.110792
$56$	2.23165e6	1.69812
$57$	−673393.	−0.481622
$58$	791202.	0.532463
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−33566.9	−0.0200624
$61$	−1.17120e6	−0.660656	−0.330328	−	0.943866i	$-0.607159\pi$
$61$	−1.17120e6	−0.660656	−0.330328	+	0.943866i	$0.607159\pi$
$62$	2.45297e6	1.30714
$63$	−1.03209e6	−0.520026
$64$	2.23185e6	1.06423
$65$	145736.	0.0658217
$66$	1.20615e6	0.516413
$67$	4.57510e6	1.85840	0.929199	−	0.369579i	$-0.120498\pi$
$67$	4.57510e6	1.85840	0.929199	+	0.369579i	$0.120498\pi$
$68$	−257615.	−0.0993549
$69$	1.70109e6	0.623383
$70$	361995.	0.126142
$71$	798821.	0.264878	0.132439	−	0.991191i	$-0.457719\pi$
$71$	798821.	0.264878	0.132439	+	0.991191i	$0.457719\pi$
$72$	−1.14912e6	−0.362828
$73$	−2.35826e6	−0.709516	−0.354758	−	0.934958i	$-0.615437\pi$
$73$	−2.35826e6	−0.709516	−0.354758	+	0.934958i	$0.615437\pi$
$74$	−2.15063e6	−0.616958
$75$	2.08825e6	0.571568
$76$	−1.10847e6	−0.289653
$77$	6.91895e6	1.72712
$78$	1.28585e6	0.306803
$79$	117864.	0.0268958	0.0134479	−	0.999910i	$-0.495719\pi$
$79$	117864.	0.0268958	0.0134479	+	0.999910i	$0.495719\pi$
$80$	243910.	0.0532616
$81$	531441.	0.111111
$82$	−5.35389e6	−1.07231
$83$	2.44537e6	0.469431	0.234715	−	0.972064i	$-0.424584\pi$
$83$	2.44537e6	0.469431	0.234715	+	0.972064i	$0.424584\pi$
$84$	−1.69893e6	−0.312750
$85$	−162135.	−0.0286358
$86$	−7.37452e6	−1.25023
$87$	−2.33703e6	−0.380493
$88$	7.70349e6	1.20503
$89$	−5.83686e6	−0.877636	−0.438818	−	0.898576i	$-0.644603\pi$
$89$	−5.83686e6	−0.877636	−0.438818	+	0.898576i	$0.644603\pi$
$90$	−186398.	−0.0269521
$91$	7.37614e6	1.02609
$92$	2.80017e6	0.374910
$93$	−7.24551e6	−0.934069
$94$	5.09211e6	0.632340
$95$	−697640.	−0.0834831
$96$	−3.29561e6	−0.380178
$97$	−6.38002e6	−0.709776	−0.354888	−	0.934909i	$-0.615481\pi$
$97$	−6.38002e6	−0.709776	−0.354888	+	0.934909i	$0.615481\pi$
$98$	1.07938e7	1.15847
$99$	−3.56269e6	−0.369024
$100$	3.43748e6	0.343748
$101$	−1.63929e7	−1.58319	−0.791593	−	0.611048i	$-0.790748\pi$
$101$	−1.63929e7	−1.58319	−0.791593	+	0.611048i	$0.790748\pi$
$102$	−1.43054e6	−0.133475
$103$	−1.41494e7	−1.27587	−0.637935	−	0.770090i	$-0.720211\pi$
$103$	−1.41494e7	−1.27587	−0.637935	+	0.770090i	$0.720211\pi$
$104$	8.21252e6	0.715912
$105$	−1.06925e6	−0.0901400
$106$	1.89559e7	1.54588
$107$	1.58657e7	1.25204	0.626019	−	0.779808i	$-0.284683\pi$
$107$	1.58657e7	1.25204	0.626019	+	0.779808i	$0.284683\pi$
$108$	874807.	0.0668235
$109$	−8.25579e6	−0.610613	−0.305307	−	0.952254i	$-0.598759\pi$
$109$	−8.25579e6	−0.610613	−0.305307	+	0.952254i	$0.598759\pi$
$110$	1.24958e6	0.0895136
$111$	6.35249e6	0.440873
$112$	1.23450e7	0.830289
$113$	2.60775e7	1.70016	0.850082	−	0.526651i	$-0.176552\pi$
$113$	2.60775e7	1.70016	0.850082	+	0.526651i	$0.176552\pi$
$114$	−6.15538e6	−0.389124
$115$	1.76234e6	0.108055
$116$	−3.84700e6	−0.228833
$117$	−3.79811e6	−0.219238
$118$	−1.87734e6	−0.105185
$119$	−8.20615e6	−0.446401
$120$	−1.19049e6	−0.0628916
$121$	4.39649e6	0.225610
$122$	−1.07057e7	−0.533774
$123$	1.58142e7	0.766265
$124$	−1.19269e7	−0.561760
$125$	4.34877e6	0.199150
$126$	−9.43418e6	−0.420153
$127$	1.28036e7	0.554649	0.277325	−	0.960776i	$-0.410552\pi$
$127$	1.28036e7	0.554649	0.277325	+	0.960776i	$0.410552\pi$
$128$	4.77741e6	0.201353
$129$	2.17827e7	0.893402
$130$	1.33215e6	0.0531803
$131$	2.45517e6	0.0954184	0.0477092	−	0.998861i	$-0.484808\pi$
$131$	2.45517e6	0.0954184	0.0477092	+	0.998861i	$0.484808\pi$
$132$	−5.86456e6	−0.221935
$133$	−3.53097e7	−1.30141
$134$	4.18203e7	1.50148
$135$	550577.	0.0192597
$136$	−9.13664e6	−0.311459
$137$	−1.15632e7	−0.384198	−0.192099	−	0.981376i	$-0.561529\pi$
$137$	−1.15632e7	−0.384198	−0.192099	+	0.981376i	$0.561529\pi$
$138$	1.55494e7	0.503659
$139$	−1.38898e7	−0.438678	−0.219339	−	0.975649i	$-0.570390\pi$
$139$	−1.38898e7	−0.438678	−0.219339	+	0.975649i	$0.570390\pi$
$140$	−1.76010e6	−0.0542112
$141$	−1.50409e7	−0.451865
$142$	7.30191e6	0.214007
$143$	2.54619e7	0.728139
$144$	−6.35668e6	−0.177403
$145$	−2.42118e6	−0.0659537
$146$	−2.15565e7	−0.573250
$147$	−3.18825e7	−0.827832
$148$	1.04569e7	0.265146
$149$	6.33739e6	0.156949	0.0784745	−	0.996916i	$-0.474995\pi$
$149$	6.33739e6	0.156949	0.0784745	+	0.996916i	$0.474995\pi$
$150$	1.90884e7	0.461795
$151$	−6.02966e6	−0.142519	−0.0712596	−	0.997458i	$-0.522702\pi$
$151$	−6.02966e6	−0.142519	−0.0712596	+	0.997458i	$0.522702\pi$
$152$	−3.93135e7	−0.908007
$153$	4.22549e6	0.0953799
$154$	6.32451e7	1.39542
$155$	−7.50640e6	−0.161909
$156$	−6.25208e6	−0.131853
$157$	3.30649e6	0.0681896	0.0340948	−	0.999419i	$-0.489145\pi$
$157$	3.30649e6	0.0681896	0.0340948	+	0.999419i	$0.489145\pi$
$158$	1.07737e6	0.0217303
$159$	−5.59915e7	−1.10467
$160$	−3.41428e6	−0.0658990
$161$	8.91975e7	1.68447
$162$	4.85782e6	0.0897717
$163$	3.35536e7	0.606851	0.303425	−	0.952855i	$-0.401870\pi$
$163$	3.35536e7	0.606851	0.303425	+	0.952855i	$0.401870\pi$
$164$	2.60318e7	0.460840
$165$	−3.69097e6	−0.0639657
$166$	2.23528e7	0.379274
$167$	4.17102e7	0.693002	0.346501	−	0.938050i	$-0.387370\pi$
$167$	4.17102e7	0.693002	0.346501	+	0.938050i	$0.387370\pi$
$168$	−6.02546e7	−0.980410
$169$	−3.56042e7	−0.567411
$170$	−1.48205e6	−0.0231362
$171$	1.81816e7	0.278065
$172$	3.58565e7	0.537302
$173$	−9.03552e7	−1.32676	−0.663379	−	0.748284i	$-0.730878\pi$
$173$	−9.03552e7	−1.32676	−0.663379	+	0.748284i	$0.730878\pi$
$174$	−2.13625e7	−0.307418
$175$	1.09499e8	1.54445
$176$	4.26141e7	0.589195
$177$	5.54523e6	0.0751646
$178$	−5.33539e7	−0.709081
$179$	−2.78323e6	−0.0362713	−0.0181357	−	0.999836i	$-0.505773\pi$
$179$	−2.78323e6	−0.0362713	−0.0181357	+	0.999836i	$0.505773\pi$
$180$	906306.	0.0115830
$181$	−1.28005e8	−1.60455	−0.802274	−	0.596955i	$-0.796377\pi$
$181$	−1.28005e8	−1.60455	−0.802274	+	0.596955i	$0.796377\pi$
$182$	6.74243e7	0.829022
$183$	3.16223e7	0.381430
$184$	9.93115e7	1.17527
$185$	6.58122e6	0.0764197
$186$	−6.62302e7	−0.754676
$187$	−2.83270e7	−0.316778
$188$	−2.47590e7	−0.271757
$189$	2.78664e7	0.300237
$190$	−6.37702e6	−0.0674497
$191$	−1.75929e8	−1.82693	−0.913464	−	0.406920i	$-0.866603\pi$
$191$	−1.75929e8	−1.82693	−0.913464	+	0.406920i	$0.866603\pi$
$192$	−6.02601e7	−0.614434
$193$	−9.04189e7	−0.905333	−0.452667	−	0.891680i	$-0.649527\pi$
$193$	−9.04189e7	−0.905333	−0.452667	+	0.891680i	$0.649527\pi$
$194$	−5.83188e7	−0.573460
$195$	−3.93486e6	−0.0380022
$196$	−5.24820e7	−0.497868
$197$	−7.90918e7	−0.737055	−0.368527	−	0.929617i	$-0.620138\pi$
$197$	−7.90918e7	−0.737055	−0.368527	+	0.929617i	$0.620138\pi$
$198$	−3.25660e7	−0.298151
$199$	1.80077e8	1.61985	0.809923	−	0.586537i	$-0.199509\pi$
$199$	1.80077e8	1.61985	0.809923	+	0.586537i	$0.199509\pi$
$200$	1.21915e8	1.07758
$201$	−1.23528e8	−1.07295
$202$	−1.49845e8	−1.27913
$203$	−1.22544e8	−1.02814
$204$	6.95560e6	0.0573626
$205$	1.63836e7	0.132822
$206$	−1.29337e8	−1.03083
$207$	−4.59294e7	−0.359910
$208$	4.54300e7	0.350042
$209$	−1.21886e8	−0.923513
$210$	−9.77387e6	−0.0728281
$211$	2.21867e8	1.62594	0.812968	−	0.582308i	$-0.197850\pi$
$211$	2.21867e8	1.62594	0.812968	+	0.582308i	$0.197850\pi$
$212$	−9.21678e7	−0.664361
$213$	−2.15682e7	−0.152927
$214$	1.45026e8	1.01158
$215$	2.25670e7	0.154860
$216$	3.10262e7	0.209479
$217$	−3.79923e8	−2.52398
$218$	−7.54650e7	−0.493342
$219$	6.36731e7	0.409639
$220$	−6.07572e6	−0.0384697
$221$	−3.01988e7	−0.188199
$222$	5.80671e7	0.356201
$223$	2.20216e8	1.32978	0.664892	−	0.746940i	$-0.268478\pi$
$223$	2.20216e8	1.32978	0.664892	+	0.746940i	$0.268478\pi$
$224$	−1.72807e8	−1.02729
$225$	−5.63827e7	−0.329995
$226$	2.38370e8	1.37364
$227$	1.55341e8	0.881444	0.440722	−	0.897644i	$-0.354723\pi$
$227$	1.55341e8	0.881444	0.440722	+	0.897644i	$0.354723\pi$
$228$	2.99288e7	0.167231
$229$	−2.23695e8	−1.23093	−0.615464	−	0.788165i	$-0.711031\pi$
$229$	−2.23695e8	−1.23093	−0.615464	+	0.788165i	$0.711031\pi$
$230$	1.61093e7	0.0873029
$231$	−1.86812e8	−0.997154
$232$	−1.36439e8	−0.717347
$233$	1.96538e8	1.01789	0.508946	−	0.860798i	$-0.330035\pi$
$233$	1.96538e8	1.01789	0.508946	+	0.860798i	$0.330035\pi$
$234$	−3.47179e7	−0.177133
$235$	−1.55825e7	−0.0783250
$236$	9.12803e6	0.0452049
$237$	−3.18231e6	−0.0155283
$238$	−7.50112e7	−0.360667
$239$	−3.22046e8	−1.52589	−0.762947	−	0.646461i	$-0.776248\pi$
$239$	−3.22046e8	−1.52589	−0.762947	+	0.646461i	$0.776248\pi$
$240$	−6.58556e6	−0.0307506
$241$	1.17931e8	0.542711	0.271355	−	0.962479i	$-0.412528\pi$
$241$	1.17931e8	0.542711	0.271355	+	0.962479i	$0.412528\pi$
$242$	4.01877e7	0.182280
$243$	−1.43489e7	−0.0641500
$244$	5.20536e7	0.229396
$245$	−3.30305e7	−0.143494
$246$	1.44555e8	0.619100
$247$	−1.29940e8	−0.548662
$248$	−4.23002e8	−1.76101
$249$	−6.60250e7	−0.271026
$250$	3.97514e7	0.160903
$251$	−4.16401e8	−1.66209	−0.831043	−	0.556208i	$-0.812256\pi$
$251$	−4.16401e8	−1.66209	−0.831043	+	0.556208i	$0.812256\pi$
$252$	4.58710e7	0.180566
$253$	3.07903e8	1.19534
$254$	1.17036e8	0.448126
$255$	4.37764e6	0.0165329
$256$	−2.42008e8	−0.901549
$257$	3.87165e8	1.42276	0.711378	−	0.702810i	$-0.248072\pi$
$257$	3.87165e8	1.42276	0.711378	+	0.702810i	$0.248072\pi$
$258$	1.99112e8	0.721820
$259$	3.33096e8	1.19130
$260$	−6.47720e6	−0.0228550
$261$	6.30998e7	0.219678
$262$	2.24424e7	0.0770928
$263$	−1.55540e8	−0.527227	−0.263613	−	0.964628i	$-0.584914\pi$
$263$	−1.55540e8	−0.527227	−0.263613	+	0.964628i	$0.584914\pi$
$264$	−2.07994e8	−0.695725
$265$	−5.80076e7	−0.191480
$266$	−3.22761e8	−1.05147
$267$	1.57595e8	0.506703
$268$	−2.03339e8	−0.645283
$269$	2.06155e8	0.645743	0.322872	−	0.946443i	$-0.395352\pi$
$269$	2.06155e8	0.645743	0.322872	+	0.946443i	$0.395352\pi$
$270$	5.03274e6	0.0155608
$271$	2.53618e8	0.774082	0.387041	−	0.922062i	$-0.373497\pi$
$271$	2.53618e8	0.774082	0.387041	+	0.922062i	$0.373497\pi$
$272$	−5.05420e7	−0.152286
$273$	−1.99156e8	−0.592412
$274$	−1.05697e8	−0.310410
$275$	3.77980e8	1.09598
$276$	−7.56045e7	−0.216454
$277$	5.09014e8	1.43896	0.719482	−	0.694511i	$-0.244379\pi$
$277$	5.09014e8	1.43896	0.719482	+	0.694511i	$0.244379\pi$
$278$	−1.26965e8	−0.354427
$279$	1.95629e8	0.539285
$280$	−6.24242e7	−0.169942
$281$	−1.26418e8	−0.339888	−0.169944	−	0.985454i	$-0.554359\pi$
$281$	−1.26418e8	−0.339888	−0.169944	+	0.985454i	$0.554359\pi$
$282$	−1.37487e8	−0.365082
$283$	2.56537e8	0.672819	0.336409	−	0.941716i	$-0.390787\pi$
$283$	2.56537e8	0.672819	0.336409	+	0.941716i	$0.390787\pi$
$284$	−3.55035e7	−0.0919722
$285$	1.88363e7	0.0481990
$286$	2.32743e8	0.588296
$287$	8.29226e8	2.07055
$288$	8.89816e7	0.219496
$289$	−3.76742e8	−0.918124
$290$	−2.21316e7	−0.0532869
$291$	1.72261e8	0.409789
$292$	1.04813e8	0.246362
$293$	9.81288e7	0.227908	0.113954	−	0.993486i	$-0.463648\pi$
$293$	9.81288e7	0.227908	0.113954	+	0.993486i	$0.463648\pi$
$294$	−2.91434e8	−0.668843
$295$	5.74490e6	0.0130288
$296$	3.70866e8	0.831181
$297$	9.61926e7	0.213056
$298$	5.79292e7	0.126806
$299$	3.28248e8	0.710155
$300$	−9.28118e7	−0.198463
$301$	1.14219e9	2.41409
$302$	−5.51162e7	−0.115148
$303$	4.42609e8	0.914053
$304$	−2.17474e8	−0.443966
$305$	3.27609e7	0.0661160
$306$	3.86246e7	0.0770617
$307$	4.01381e8	0.791722	0.395861	−	0.918311i	$-0.370446\pi$
$307$	4.01381e8	0.791722	0.395861	+	0.918311i	$0.370446\pi$
$308$	−3.07512e8	−0.599700
$309$	3.82032e8	0.736624
$310$	−6.86149e7	−0.130813
$311$	−9.27378e8	−1.74822	−0.874109	−	0.485730i	$-0.838554\pi$
$311$	−9.27378e8	−1.74822	−0.874109	+	0.485730i	$0.838554\pi$
$312$	−2.21738e8	−0.413332
$313$	8.01269e8	1.47697	0.738487	−	0.674268i	$-0.235541\pi$
$313$	8.01269e8	1.47697	0.738487	+	0.674268i	$0.235541\pi$
$314$	3.02241e7	0.0550934
$315$	2.88698e7	0.0520423
$316$	−5.23842e6	−0.00933890
$317$	−2.96984e8	−0.523632	−0.261816	−	0.965118i	$-0.584321\pi$
$317$	−2.96984e8	−0.523632	−0.261816	+	0.965118i	$0.584321\pi$
$318$	−5.11810e8	−0.892512
$319$	−4.23011e8	−0.729598
$320$	−6.24299e7	−0.106504
$321$	−4.28375e8	−0.722864
$322$	8.15341e8	1.36095
$323$	1.44562e8	0.238696
$324$	−2.36198e7	−0.0385806
$325$	4.02957e8	0.651128
$326$	3.06708e8	0.490302
$327$	2.22906e8	0.352538
$328$	9.23251e8	1.44465
$329$	−7.88681e8	−1.22100
$330$	−3.37386e7	−0.0516807
$331$	4.65841e8	0.706057	0.353029	−	0.935612i	$-0.385152\pi$
$331$	4.65841e8	0.706057	0.353029	+	0.935612i	$0.385152\pi$
$332$	−1.08684e8	−0.162998
$333$	−1.71517e8	−0.254538
$334$	3.81267e8	0.559908
$335$	−1.27976e8	−0.185982
$336$	−3.33316e8	−0.479368
$337$	9.05809e8	1.28924	0.644618	−	0.764505i	$-0.277017\pi$
$337$	9.05809e8	1.28924	0.644618	+	0.764505i	$0.277017\pi$
$338$	−3.25453e8	−0.458436
$339$	−7.04091e8	−0.981590
$340$	7.20605e6	0.00994308
$341$	−1.31146e9	−1.79108
$342$	1.66195e8	0.224661
$343$	−5.05839e8	−0.676836
$344$	1.27170e9	1.68434
$345$	−4.75831e7	−0.0623859
$346$	−8.25923e8	−1.07195
$347$	8.14436e8	1.04642	0.523208	−	0.852205i	$-0.324735\pi$
$347$	8.14436e8	1.04642	0.523208	+	0.852205i	$0.324735\pi$
$348$	1.03869e8	0.132117
$349$	1.34997e9	1.69994	0.849972	−	0.526827i	$-0.176619\pi$
$349$	1.34997e9	1.69994	0.849972	+	0.526827i	$0.176619\pi$
$350$	1.00091e9	1.24783
$351$	1.02549e8	0.126577
$352$	−5.96517e8	−0.728994
$353$	6.77178e8	0.819391	0.409695	−	0.912222i	$-0.365635\pi$
$353$	6.77178e8	0.819391	0.409695	+	0.912222i	$0.365635\pi$
$354$	5.06882e7	0.0607289
$355$	−2.23448e7	−0.0265080
$356$	2.59418e8	0.304737
$357$	2.21566e8	0.257730
$358$	−2.54411e7	−0.0293052
$359$	7.72908e8	0.881652	0.440826	−	0.897592i	$-0.354685\pi$
$359$	7.72908e8	0.881652	0.440826	+	0.897592i	$0.354685\pi$
$360$	3.21433e7	0.0363105
$361$	−2.71844e8	−0.304120
$362$	−1.17008e9	−1.29639
$363$	−1.18705e8	−0.130256
$364$	−3.27831e8	−0.356283
$365$	6.59658e7	0.0710058
$366$	2.89055e8	0.308174
$367$	1.86496e9	1.96942	0.984712	−	0.174192i	$-0.0557312\pi$
$367$	1.86496e9	1.96942	0.984712	+	0.174192i	$0.0557312\pi$
$368$	5.49371e8	0.574643
$369$	−4.26983e8	−0.442403
$370$	6.01580e7	0.0617429
$371$	−2.93595e9	−2.98497
$372$	3.22025e8	0.324332
$373$	1.15094e9	1.14834	0.574171	−	0.818735i	$-0.305324\pi$
$373$	1.15094e9	1.14834	0.574171	+	0.818735i	$0.305324\pi$
$374$	−2.58933e8	−0.255939
$375$	−1.17417e8	−0.114980
$376$	−8.78109e8	−0.851904
$377$	−4.50962e8	−0.433457
$378$	2.54723e8	0.242575
$379$	8.25715e7	0.0779100	0.0389550	−	0.999241i	$-0.487597\pi$
$379$	8.25715e7	0.0779100	0.0389550	+	0.999241i	$0.487597\pi$
$380$	3.10065e7	0.0289874
$381$	−3.45697e8	−0.320227
$382$	−1.60814e9	−1.47606
$383$	−6.72581e8	−0.611714	−0.305857	−	0.952077i	$-0.598943\pi$
$383$	−6.72581e8	−0.611714	−0.305857	+	0.952077i	$0.598943\pi$
$384$	−1.28990e8	−0.116251
$385$	−1.93538e8	−0.172844
$386$	−8.26505e8	−0.731459
$387$	−5.88132e8	−0.515806
$388$	2.83559e8	0.246452
$389$	−9.07409e8	−0.781591	−0.390795	−	0.920478i	$-0.627800\pi$
$389$	−9.07409e8	−0.781591	−0.390795	+	0.920478i	$0.627800\pi$
$390$	−3.59680e7	−0.0307037
$391$	−3.65185e8	−0.308954
$392$	−1.86134e9	−1.56072
$393$	−6.62896e7	−0.0550899
$394$	−7.22967e8	−0.595500
$395$	−3.29690e6	−0.00269163
$396$	1.58343e8	0.128134
$397$	2.34468e9	1.88069	0.940345	−	0.340223i	$-0.110503\pi$
$397$	2.34468e9	1.88069	0.940345	+	0.340223i	$0.110503\pi$
$398$	1.64606e9	1.30875
$399$	9.53363e8	0.751369
$400$	6.74406e8	0.526879
$401$	1.03275e9	0.799819	0.399910	−	0.916555i	$-0.369042\pi$
$401$	1.03275e9	0.799819	0.399910	+	0.916555i	$0.369042\pi$
$402$	−1.12915e9	−0.866882
$403$	−1.39812e9	−1.06409
$404$	7.28581e8	0.549722
$405$	−1.48656e7	−0.0111196
$406$	−1.12015e9	−0.830684
$407$	1.14982e9	0.845376
$408$	2.46689e8	0.179821
$409$	−4.25915e8	−0.307816	−0.153908	−	0.988085i	$-0.549186\pi$
$409$	−4.25915e8	−0.307816	−0.153908	+	0.988085i	$0.549186\pi$
$410$	1.49760e8	0.107313
$411$	3.12205e8	0.221817
$412$	6.28865e8	0.443014
$413$	2.90767e8	0.203105
$414$	−4.19833e8	−0.290788
$415$	−6.84024e7	−0.0469789
$416$	−6.35934e8	−0.433097
$417$	3.75026e8	0.253271
$418$	−1.11415e9	−0.746148
$419$	−9.70564e8	−0.644577	−0.322289	−	0.946641i	$-0.604452\pi$
$419$	−9.70564e8	−0.644577	−0.322289	+	0.946641i	$0.604452\pi$
$420$	4.75227e7	0.0312989
$421$	3.26959e6	0.00213553	0.00106777	−	0.999999i	$-0.499660\pi$
$421$	3.26959e6	0.00213553	0.00106777	+	0.999999i	$0.499660\pi$
$422$	2.02805e9	1.31367
$423$	4.06106e8	0.260884
$424$	−3.26885e9	−2.08264
$425$	−4.48299e8	−0.283274
$426$	−1.97152e8	−0.123557
$427$	1.65813e9	1.03068
$428$	−7.05150e8	−0.434739
$429$	−6.87470e8	−0.420391
$430$	2.06281e8	0.125118
$431$	9.95591e8	0.598978	0.299489	−	0.954100i	$-0.403184\pi$
$431$	9.95591e8	0.598978	0.299489	+	0.954100i	$0.403184\pi$
$432$	1.71630e8	0.102424
$433$	−1.28699e9	−0.761847	−0.380924	−	0.924606i	$-0.624394\pi$
$433$	−1.28699e9	−0.761847	−0.380924	+	0.924606i	$0.624394\pi$
$434$	−3.47282e9	−2.03924
$435$	6.53719e7	0.0380784
$436$	3.66927e8	0.212020
$437$	−1.57133e9	−0.900705
$438$	5.82027e8	0.330966
$439$	5.89758e8	0.332697	0.166348	−	0.986067i	$-0.446802\pi$
$439$	5.89758e8	0.332697	0.166348	+	0.986067i	$0.446802\pi$
$440$	−2.15483e8	−0.120595
$441$	8.60828e8	0.477949
$442$	−2.76042e8	−0.152054
$443$	3.59302e8	0.196357	0.0981786	−	0.995169i	$-0.468698\pi$
$443$	3.59302e8	0.196357	0.0981786	+	0.995169i	$0.468698\pi$
$444$	−2.82335e8	−0.153082
$445$	1.63270e8	0.0878306
$446$	2.01296e9	1.07439
$447$	−1.71110e8	−0.0906146
$448$	−3.15977e9	−1.66028
$449$	2.56647e9	1.33806	0.669028	−	0.743237i	$-0.266710\pi$
$449$	2.56647e9	1.33806	0.669028	+	0.743237i	$0.266710\pi$
$450$	−5.15386e8	−0.266618
$451$	2.86242e9	1.46932
$452$	−1.15901e9	−0.590340
$453$	1.62801e8	0.0822835
$454$	1.41995e9	0.712158
$455$	−2.06327e8	−0.102687
$456$	1.06146e9	0.524238
$457$	−1.46001e9	−0.715565	−0.357782	−	0.933805i	$-0.616467\pi$
$457$	−1.46001e9	−0.715565	−0.357782	+	0.933805i	$0.616467\pi$
$458$	−2.04477e9	−0.994522
$459$	−1.14088e8	−0.0550676
$460$	−7.83268e7	−0.0375196
$461$	−4.94351e7	−0.0235008	−0.0117504	−	0.999931i	$-0.503740\pi$
$461$	−4.94351e7	−0.0235008	−0.0117504	+	0.999931i	$0.503740\pi$
$462$	−1.70762e9	−0.805645
$463$	−2.80354e9	−1.31272	−0.656361	−	0.754447i	$-0.727905\pi$
$463$	−2.80354e9	−1.31272	−0.656361	+	0.754447i	$0.727905\pi$
$464$	−7.54750e8	−0.350744
$465$	2.02673e8	0.0934782
$466$	1.79653e9	0.822401
$467$	2.95995e9	1.34485	0.672426	−	0.740164i	$-0.265252\pi$
$467$	2.95995e9	1.34485	0.672426	+	0.740164i	$0.265252\pi$
$468$	1.68806e8	0.0761251
$469$	−6.47725e9	−2.89925
$470$	−1.42438e8	−0.0632823
$471$	−8.92752e7	−0.0393693
$472$	3.23737e8	0.141708
$473$	3.94274e9	1.71310
$474$	−2.90891e7	−0.0125460
$475$	−1.92896e9	−0.825839
$476$	3.64721e8	0.155002
$477$	1.51177e9	0.637781
$478$	−2.94377e9	−1.23284
$479$	2.16259e9	0.899084	0.449542	−	0.893259i	$-0.351587\pi$
$479$	2.16259e9	0.899084	0.449542	+	0.893259i	$0.351587\pi$
$480$	9.21855e7	0.0380468
$481$	1.22580e9	0.502241
$482$	1.07799e9	0.438480
$483$	−2.40833e9	−0.972526
$484$	−1.95401e8	−0.0783374
$485$	1.78463e8	0.0710317
$486$	−1.31161e8	−0.0518297
$487$	−2.92186e9	−1.14633	−0.573163	−	0.819441i	$-0.694284\pi$
$487$	−2.92186e9	−1.14633	−0.573163	+	0.819441i	$0.694284\pi$
$488$	1.84615e9	0.719113
$489$	−9.05946e8	−0.350366
$490$	−3.01927e8	−0.115935
$491$	1.26732e9	0.483171	0.241585	−	0.970380i	$-0.422333\pi$
$491$	1.26732e9	0.483171	0.241585	+	0.970380i	$0.422333\pi$
$492$	−7.02858e8	−0.266066
$493$	5.01707e8	0.188576
$494$	−1.18777e9	−0.443289
$495$	9.96562e7	0.0369306
$496$	−2.33996e9	−0.861038
$497$	−1.13094e9	−0.413230
$498$	−6.03525e8	−0.218974
$499$	−2.05947e9	−0.742000	−0.371000	−	0.928633i	$-0.620985\pi$
$499$	−2.05947e9	−0.742000	−0.371000	+	0.928633i	$0.620985\pi$
$500$	−1.93280e8	−0.0691500
$501$	−1.12618e9	−0.400105
$502$	−3.80626e9	−1.34287
$503$	1.28852e9	0.451443	0.225721	−	0.974192i	$-0.427526\pi$
$503$	1.28852e9	0.451443	0.225721	+	0.974192i	$0.427526\pi$
$504$	1.62687e9	0.566040
$505$	4.58546e8	0.158440
$506$	2.81449e9	0.965769
$507$	9.61313e8	0.327595
$508$	−5.69053e8	−0.192588
$509$	7.14570e7	0.0240177	0.0120089	−	0.999928i	$-0.496177\pi$
$509$	7.14570e7	0.0240177	0.0120089	+	0.999928i	$0.496177\pi$
$510$	4.00153e7	0.0133577
$511$	3.33874e9	1.10690
$512$	−2.82367e9	−0.929755
$513$	−4.90903e8	−0.160541
$514$	3.53902e9	1.14951
$515$	3.95788e8	0.127684
$516$	−9.68126e8	−0.310212
$517$	−2.72246e9	−0.866453
$518$	3.04478e9	0.962503
$519$	2.43959e9	0.766004
$520$	−2.29722e8	−0.0716459
$521$	−1.07670e8	−0.0333551	−0.0166776	−	0.999861i	$-0.505309\pi$
$521$	−1.07670e8	−0.0333551	−0.0166776	+	0.999861i	$0.505309\pi$
$522$	5.76786e8	0.177488
$523$	1.67231e9	0.511165	0.255582	−	0.966787i	$-0.417733\pi$
$523$	1.67231e9	0.511165	0.255582	+	0.966787i	$0.417733\pi$
$524$	−1.09120e8	−0.0331317
$525$	−2.95646e9	−0.891691
$526$	−1.42177e9	−0.425970
$527$	1.55545e9	0.462933
$528$	−1.15058e9	−0.340172
$529$	5.64582e8	0.165818
$530$	−5.30239e8	−0.154706
$531$	−1.49721e8	−0.0433963
$532$	1.56933e9	0.451882
$533$	3.05156e9	0.872926
$534$	1.44055e9	0.409388
$535$	−4.43800e8	−0.125299
$536$	−7.21170e9	−2.02284
$537$	7.51472e7	0.0209412
$538$	1.88443e9	0.521725
$539$	−5.77085e9	−1.58737
$540$	−2.44703e7	−0.00668745
$541$	1.37337e9	0.372903	0.186452	−	0.982464i	$-0.440301\pi$
$541$	1.37337e9	0.372903	0.186452	+	0.982464i	$0.440301\pi$
$542$	2.31828e9	0.625416
$543$	3.45614e9	0.926387
$544$	7.07493e8	0.188420
$545$	2.30933e8	0.0611079
$546$	−1.82045e9	−0.478636
$547$	−3.99898e9	−1.04470	−0.522352	−	0.852730i	$-0.674945\pi$
$547$	−3.99898e9	−1.04470	−0.522352	+	0.852730i	$0.674945\pi$
$548$	5.13923e8	0.133403
$549$	−8.53803e8	−0.220219
$550$	3.45506e9	0.885495
$551$	2.15877e9	0.549762
$552$	−2.68141e9	−0.678542
$553$	−1.66867e8	−0.0419596
$554$	4.65282e9	1.16260
$555$	−1.77693e8	−0.0441209
$556$	6.17331e8	0.152320
$557$	−2.15460e9	−0.528291	−0.264146	−	0.964483i	$-0.585090\pi$
$557$	−2.15460e9	−0.528291	−0.264146	+	0.964483i	$0.585090\pi$
$558$	1.78821e9	0.435712
$559$	4.20327e9	1.01776
$560$	−3.45318e8	−0.0830923
$561$	7.64828e8	0.182892
$562$	−1.15557e9	−0.274611
$563$	−5.78892e9	−1.36716	−0.683578	−	0.729878i	$-0.739577\pi$
$563$	−5.78892e9	−1.36716	−0.683578	+	0.729878i	$0.739577\pi$
$564$	6.68492e8	0.156899
$565$	−7.29444e8	−0.170146
$566$	2.34497e9	0.543600
$567$	−7.52393e8	−0.173342
$568$	−1.25918e9	−0.288315
$569$	−2.74050e9	−0.623643	−0.311822	−	0.950141i	$-0.600939\pi$
$569$	−2.74050e9	−0.623643	−0.311822	+	0.950141i	$0.600939\pi$
$570$	1.72180e8	0.0389421
$571$	8.65695e9	1.94598	0.972991	−	0.230844i	$-0.0741488\pi$
$571$	8.65695e9	1.94598	0.972991	+	0.230844i	$0.0741488\pi$
$572$	−1.13165e9	−0.252828
$573$	4.75009e9	1.05478
$574$	7.57983e9	1.67289
$575$	4.87283e9	1.06892
$576$	1.62702e9	0.354744
$577$	−5.33758e9	−1.15672	−0.578361	−	0.815781i	$-0.696308\pi$
$577$	−5.33758e9	−1.15672	−0.578361	+	0.815781i	$0.696308\pi$
$578$	−3.44374e9	−0.741794
$579$	2.44131e9	0.522694
$580$	1.07609e8	0.0229008
$581$	−3.46206e9	−0.732349
$582$	1.57461e9	0.331087
$583$	−1.01347e10	−2.11821
$584$	3.71731e9	0.772297
$585$	1.06241e8	0.0219406
$586$	8.96981e8	0.184137
$587$	−7.46525e9	−1.52339	−0.761695	−	0.647936i	$-0.775633\pi$
$587$	−7.46525e9	−1.52339	−0.761695	+	0.647936i	$0.775633\pi$
$588$	1.41701e9	0.287444
$589$	6.69283e9	1.34960
$590$	5.25133e7	0.0105266
$591$	2.13548e9	0.425539
$592$	2.05155e9	0.406403
$593$	3.09092e9	0.608690	0.304345	−	0.952562i	$-0.401562\pi$
$593$	3.09092e9	0.608690	0.304345	+	0.952562i	$0.401562\pi$
$594$	8.79283e8	0.172138
$595$	2.29544e8	0.0446742
$596$	−2.81664e8	−0.0544966
$597$	−4.86209e9	−0.935218
$598$	3.00047e9	0.573766
$599$	2.66060e9	0.505809	0.252904	−	0.967491i	$-0.418614\pi$
$599$	2.66060e9	0.505809	0.252904	+	0.967491i	$0.418614\pi$
$600$	−3.29169e9	−0.622142
$601$	4.24214e8	0.0797122	0.0398561	−	0.999205i	$-0.487310\pi$
$601$	4.24214e8	0.0797122	0.0398561	+	0.999205i	$0.487310\pi$
$602$	1.04406e10	1.95045
$603$	3.33525e9	0.619466
$604$	2.67987e8	0.0494862
$605$	−1.22980e8	−0.0225782
$606$	4.04583e9	0.738505
$607$	1.13859e9	0.206637	0.103318	−	0.994648i	$-0.467054\pi$
$607$	1.13859e9	0.206637	0.103318	+	0.994648i	$0.467054\pi$
$608$	3.04423e9	0.549306
$609$	3.30868e9	0.593600
$610$	2.99463e8	0.0534181
$611$	−2.90236e9	−0.514762
$612$	−1.87801e8	−0.0331183
$613$	−1.59219e9	−0.279179	−0.139590	−	0.990209i	$-0.544578\pi$
$613$	−1.59219e9	−0.279179	−0.139590	+	0.990209i	$0.544578\pi$
$614$	3.66896e9	0.639667
$615$	−4.42357e8	−0.0766849
$616$	−1.09063e10	−1.87994
$617$	−5.01588e9	−0.859705	−0.429853	−	0.902899i	$-0.641434\pi$
$617$	−5.01588e9	−0.859705	−0.429853	+	0.902899i	$0.641434\pi$
$618$	3.49210e9	0.595151
$619$	−1.05539e10	−1.78854	−0.894268	−	0.447532i	$-0.852303\pi$
$619$	−1.05539e10	−1.78854	−0.894268	+	0.447532i	$0.852303\pi$
$620$	3.33621e8	0.0562188
$621$	1.24009e9	0.207794
$622$	−8.47703e9	−1.41246
$623$	8.26360e9	1.36918
$624$	−1.22661e9	−0.202097
$625$	5.92074e9	0.970054
$626$	7.32428e9	1.19331
$627$	3.29093e9	0.533191
$628$	−1.46956e8	−0.0236771
$629$	−1.36373e9	−0.218500
$630$	2.63895e8	0.0420473
$631$	−5.24953e9	−0.831797	−0.415899	−	0.909411i	$-0.636533\pi$
$631$	−5.24953e9	−0.831797	−0.415899	+	0.909411i	$0.636533\pi$
$632$	−1.85787e8	−0.0292756
$633$	−5.99040e9	−0.938735
$634$	−2.71469e9	−0.423066
$635$	−3.58144e8	−0.0555073
$636$	2.48853e9	0.383569
$637$	−6.15218e9	−0.943063
$638$	−3.86668e9	−0.589475
$639$	5.82341e8	0.0882926
$640$	−1.33634e8	−0.0201506
$641$	−4.54601e9	−0.681753	−0.340876	−	0.940108i	$-0.610724\pi$
$641$	−4.54601e9	−0.681753	−0.340876	+	0.940108i	$0.610724\pi$
$642$	−3.91571e9	−0.584034
$643$	3.12857e9	0.464095	0.232048	−	0.972704i	$-0.425458\pi$
$643$	3.12857e9	0.464095	0.232048	+	0.972704i	$0.425458\pi$
$644$	−3.96437e9	−0.584889
$645$	−6.09309e8	−0.0894084
$646$	1.32142e9	0.192853
$647$	−5.99209e9	−0.869788	−0.434894	−	0.900482i	$-0.643214\pi$
$647$	−5.99209e9	−0.869788	−0.434894	+	0.900482i	$0.643214\pi$
$648$	−8.37707e8	−0.120943
$649$	1.00371e9	0.144129
$650$	3.68337e9	0.526076
$651$	1.02579e10	1.45722
$652$	−1.49128e9	−0.210714
$653$	1.00926e10	1.41842	0.709210	−	0.704997i	$-0.249052\pi$
$653$	1.00926e10	1.41842	0.709210	+	0.704997i	$0.249052\pi$
$654$	2.03755e9	0.284831
$655$	−6.86765e7	−0.00954913
$656$	5.10723e9	0.706353
$657$	−1.71917e9	−0.236505
$658$	−7.20921e9	−0.986500
$659$	1.22466e10	1.66693	0.833465	−	0.552573i	$-0.186354\pi$
$659$	1.22466e10	1.66693	0.833465	+	0.552573i	$0.186354\pi$
$660$	1.64045e8	0.0222105
$661$	−6.31287e8	−0.0850201	−0.0425101	−	0.999096i	$-0.513535\pi$
$661$	−6.31287e8	−0.0850201	−0.0425101	+	0.999096i	$0.513535\pi$
$662$	4.25819e9	0.570455
$663$	8.15367e8	0.108656
$664$	−3.85462e9	−0.510968
$665$	9.87690e8	0.130240
$666$	−1.56781e9	−0.205653
$667$	−5.45335e9	−0.711579
$668$	−1.85380e9	−0.240628
$669$	−5.94582e9	−0.767751
$670$	−1.16981e9	−0.150263
$671$	5.72375e9	0.731394
$672$	4.66580e9	0.593108
$673$	1.33894e10	1.69320	0.846599	−	0.532232i	$-0.178647\pi$
$673$	1.33894e10	1.69320	0.846599	+	0.532232i	$0.178647\pi$
$674$	8.27987e9	1.04163
$675$	1.52233e9	0.190523
$676$	1.58242e9	0.197019
$677$	−1.86123e9	−0.230536	−0.115268	−	0.993334i	$-0.536773\pi$
$677$	−1.86123e9	−0.230536	−0.115268	+	0.993334i	$0.536773\pi$
$678$	−6.43600e9	−0.793071
$679$	9.03258e9	1.10731
$680$	2.55572e8	0.0311696
$681$	−4.19420e9	−0.508902
$682$	−1.19879e10	−1.44710
$683$	−1.29941e10	−1.56054	−0.780268	−	0.625445i	$-0.784918\pi$
$683$	−1.29941e10	−1.56054	−0.780268	+	0.625445i	$0.784918\pi$
$684$	−8.08078e8	−0.0965510
$685$	3.23447e8	0.0384491
$686$	−4.62380e9	−0.546846
$687$	6.03977e9	0.710677
$688$	7.03477e9	0.823550
$689$	−1.08043e10	−1.25843
$690$	−4.34950e8	−0.0504043
$691$	−9.85622e9	−1.13642	−0.568208	−	0.822885i	$-0.692363\pi$
$691$	−9.85622e9	−1.13642	−0.568208	+	0.822885i	$0.692363\pi$
$692$	4.01582e9	0.460684
$693$	5.04392e9	0.575707
$694$	7.44464e9	0.845446
$695$	3.88529e8	0.0439012
$696$	3.68384e9	0.414161
$697$	−3.39494e9	−0.379767
$698$	1.23399e10	1.37346
$699$	−5.30654e9	−0.587680
$700$	−4.86664e9	−0.536273
$701$	−9.35979e9	−1.02625	−0.513125	−	0.858314i	$-0.671512\pi$
$701$	−9.35979e9	−1.02625	−0.513125	+	0.858314i	$0.671512\pi$
$702$	9.37384e8	0.102268
$703$	−5.86793e9	−0.637002
$704$	−1.09073e10	−1.17818
$705$	4.20728e8	0.0452209
$706$	6.18998e9	0.662023
$707$	2.32085e10	2.46990
$708$	−2.46457e8	−0.0260990
$709$	−9.52210e9	−1.00339	−0.501696	−	0.865044i	$-0.667290\pi$
$709$	−9.52210e9	−1.00339	−0.501696	+	0.865044i	$0.667290\pi$
$710$	−2.04250e8	−0.0214170
$711$	8.59225e7	0.00896527
$712$	9.20060e9	0.955292
$713$	−1.69071e10	−1.74685
$714$	2.02530e9	0.208231
$715$	−7.12224e8	−0.0728694
$716$	1.23700e8	0.0125943
$717$	8.69523e9	0.880976
$718$	7.06504e9	0.712327
$719$	−6.22106e9	−0.624185	−0.312092	−	0.950052i	$-0.601030\pi$
$719$	−6.22106e9	−0.624185	−0.312092	+	0.950052i	$0.601030\pi$
$720$	1.77810e8	0.0177539
$721$	2.00321e10	1.99046
$722$	−2.48489e9	−0.245712
$723$	−3.18414e9	−0.313334
$724$	5.68917e9	0.557140
$725$	−6.69452e9	−0.652433
$726$	−1.08507e9	−0.105240
$727$	4.54280e9	0.438483	0.219242	−	0.975671i	$-0.429642\pi$
$727$	4.54280e9	0.438483	0.219242	+	0.975671i	$0.429642\pi$
$728$	−1.16270e10	−1.11688
$729$	3.87420e8	0.0370370
$730$	6.02984e8	0.0573688
$731$	−4.67624e9	−0.442778
$732$	−1.40545e9	−0.132442
$733$	9.84479e9	0.923299	0.461649	−	0.887062i	$-0.347258\pi$
$733$	9.84479e9	0.923299	0.461649	+	0.887062i	$0.347258\pi$
$734$	1.70474e10	1.59119
$735$	8.91824e8	0.0828464
$736$	−7.69016e9	−0.710989
$737$	−2.23589e10	−2.05738
$738$	−3.90299e9	−0.357437
$739$	8.69557e9	0.792579	0.396289	−	0.918126i	$-0.370298\pi$
$739$	8.69557e9	0.792579	0.396289	+	0.918126i	$0.370298\pi$
$740$	−2.92501e8	−0.0265348
$741$	3.50839e9	0.316770
$742$	−2.68370e10	−2.41169
$743$	1.41962e10	1.26973	0.634864	−	0.772624i	$-0.281056\pi$
$743$	1.41962e10	1.26973	0.634864	+	0.772624i	$0.281056\pi$
$744$	1.14210e10	1.01672
$745$	−1.77271e8	−0.0157069
$746$	1.05206e10	0.927797
$747$	1.78268e9	0.156477
$748$	1.25899e9	0.109993
$749$	−2.24621e10	−1.95328
$750$	−1.07329e9	−0.0928971
$751$	1.57390e10	1.35593	0.677967	−	0.735092i	$-0.262861\pi$
$751$	1.57390e10	1.35593	0.677967	+	0.735092i	$0.262861\pi$
$752$	−4.85751e9	−0.416535
$753$	1.12428e10	0.959606
$754$	−4.12218e9	−0.350209
$755$	1.68663e8	0.0142628
$756$	−1.23852e9	−0.104250
$757$	2.58251e9	0.216374	0.108187	−	0.994131i	$-0.465495\pi$
$757$	2.58251e9	0.216374	0.108187	+	0.994131i	$0.465495\pi$
$758$	7.54774e8	0.0629470
$759$	−8.31337e9	−0.690130
$760$	1.09968e9	0.0908700
$761$	−1.11863e9	−0.0920114	−0.0460057	−	0.998941i	$-0.514649\pi$
$761$	−1.11863e9	−0.0920114	−0.0460057	+	0.998941i	$0.514649\pi$
$762$	−3.15996e9	−0.258726
$763$	1.16882e10	0.952605
$764$	7.81914e9	0.634355
$765$	−1.18196e8	−0.00954528
$766$	−6.14796e9	−0.494231
$767$	1.07003e9	0.0856272
$768$	6.53421e9	0.520510
$769$	4.81105e9	0.381503	0.190751	−	0.981638i	$-0.438908\pi$
$769$	4.81105e9	0.381503	0.190751	+	0.981638i	$0.438908\pi$
$770$	−1.76910e9	−0.139648
$771$	−1.04535e10	−0.821428
$772$	4.01865e9	0.314354
$773$	−9.07363e9	−0.706566	−0.353283	−	0.935516i	$-0.614935\pi$
$773$	−9.07363e9	−0.706566	−0.353283	+	0.935516i	$0.614935\pi$
$774$	−5.37603e9	−0.416743
$775$	−2.07551e10	−1.60165
$776$	1.00568e10	0.772579
$777$	−8.99360e9	−0.687796
$778$	−8.29449e9	−0.631482
$779$	−1.46079e10	−1.10715
$780$	1.74884e8	0.0131953
$781$	−3.90391e9	−0.293239
$782$	−3.33810e9	−0.249618
$783$	−1.70370e9	−0.126831
$784$	−1.02965e10	−0.763107
$785$	−9.24897e7	−0.00682417
$786$	−6.05944e8	−0.0445096
$787$	−9.67486e9	−0.707511	−0.353755	−	0.935338i	$-0.615095\pi$
$787$	−9.67486e9	−0.707511	−0.353755	+	0.935338i	$0.615095\pi$
$788$	3.51522e9	0.255924
$789$	4.19958e9	0.304395
$790$	−3.01365e7	−0.00217469
$791$	−3.69194e10	−2.65239
$792$	5.61584e9	0.401677
$793$	6.10196e9	0.434524
$794$	2.14324e10	1.51949
$795$	1.56620e9	0.110551
$796$	−8.00351e9	−0.562451
$797$	5.79578e9	0.405516	0.202758	−	0.979229i	$-0.435010\pi$
$797$	5.79578e9	0.405516	0.202758	+	0.979229i	$0.435010\pi$
$798$	8.71455e9	0.607064
$799$	3.22895e9	0.223948
$800$	−9.44041e9	−0.651893
$801$	−4.25507e9	−0.292545
$802$	9.44026e9	0.646210
$803$	1.15251e10	0.785486
$804$	5.49017e9	0.372554
$805$	−2.49505e9	−0.168575
$806$	−1.27800e10	−0.859724
$807$	−5.56617e9	−0.372820
$808$	2.58401e10	1.72327
$809$	−5.99978e9	−0.398396	−0.199198	−	0.979959i	$-0.563834\pi$
$809$	−5.99978e9	−0.398396	−0.199198	+	0.979959i	$0.563834\pi$
$810$	−1.35884e8	−0.00898402
$811$	2.58658e10	1.70275	0.851377	−	0.524553i	$-0.175768\pi$
$811$	2.58658e10	1.70275	0.851377	+	0.524553i	$0.175768\pi$
$812$	5.44643e9	0.356998
$813$	−6.84768e9	−0.446917
$814$	1.05103e10	0.683017
$815$	−9.38566e8	−0.0607314
$816$	1.36463e9	0.0879226
$817$	−2.01211e10	−1.29085
$818$	−3.89323e9	−0.248699
$819$	5.37721e9	0.342029
$820$	−7.28166e8	−0.0461192
$821$	6.65337e9	0.419605	0.209802	−	0.977744i	$-0.432718\pi$
$821$	6.65337e9	0.419605	0.209802	+	0.977744i	$0.432718\pi$
$822$	2.85382e9	0.179216
$823$	2.32319e10	1.45273	0.726366	−	0.687308i	$-0.241208\pi$
$823$	2.32319e10	1.45273	0.726366	+	0.687308i	$0.241208\pi$
$824$	2.23035e10	1.38876
$825$	−1.02055e10	−0.632767
$826$	2.65786e9	0.164098
$827$	4.17843e9	0.256888	0.128444	−	0.991717i	$-0.459002\pi$
$827$	4.17843e9	0.256888	0.128444	+	0.991717i	$0.459002\pi$
$828$	2.04132e9	0.124970
$829$	1.91468e10	1.16722	0.583612	−	0.812033i	$-0.301639\pi$
$829$	1.91468e10	1.16722	0.583612	+	0.812033i	$0.301639\pi$
$830$	−6.25256e8	−0.0379564
$831$	−1.37434e10	−0.830787
$832$	−1.16280e10	−0.699961
$833$	6.84445e9	0.410281
$834$	3.42805e9	0.204629
$835$	−1.16673e9	−0.0693531
$836$	5.41722e9	0.320667
$837$	−5.28198e9	−0.311356
$838$	−8.87178e9	−0.520783
$839$	8.57931e9	0.501517	0.250758	−	0.968050i	$-0.419320\pi$
$839$	8.57931e9	0.501517	0.250758	+	0.968050i	$0.419320\pi$
$840$	1.68545e9	0.0981159
$841$	−9.75781e9	−0.565674
$842$	2.98869e7	0.00172539
$843$	3.41328e9	0.196234
$844$	−9.86082e9	−0.564566
$845$	9.95927e8	0.0567844
$846$	3.71215e9	0.210780
$847$	−6.22438e9	−0.351969
$848$	−1.80826e10	−1.01830
$849$	−6.92651e9	−0.388452
$850$	−4.09784e9	−0.228870
$851$	1.48232e10	0.824497
$852$	9.58594e8	0.0531002
$853$	1.55006e10	0.855118	0.427559	−	0.903987i	$-0.359374\pi$
$853$	1.55006e10	0.855118	0.427559	+	0.903987i	$0.359374\pi$
$854$	1.51568e10	0.832729
$855$	−5.08579e8	−0.0278277
$856$	−2.50091e10	−1.36282
$857$	−2.35700e10	−1.27916	−0.639582	−	0.768723i	$-0.720893\pi$
$857$	−2.35700e10	−1.27916	−0.639582	+	0.768723i	$0.720893\pi$
$858$	−6.28406e9	−0.339653
$859$	−1.55175e10	−0.835307	−0.417654	−	0.908606i	$-0.637147\pi$
$859$	−1.55175e10	−0.835307	−0.417654	+	0.908606i	$0.637147\pi$
$860$	−1.00299e9	−0.0537712
$861$	−2.23891e10	−1.19543
$862$	9.10055e9	0.483941
$863$	−1.31058e10	−0.694104	−0.347052	−	0.937846i	$-0.612817\pi$
$863$	−1.31058e10	−0.694104	−0.347052	+	0.937846i	$0.612817\pi$
$864$	−2.40250e9	−0.126726
$865$	2.52743e9	0.132777
$866$	−1.17642e10	−0.615531
$867$	1.01720e10	0.530079
$868$	1.68856e10	0.876390
$869$	−5.76010e8	−0.0297756
$870$	5.97555e8	0.0307652
$871$	−2.38364e10	−1.22230
$872$	1.30135e10	0.664642
$873$	−4.65104e9	−0.236592
$874$	−1.43633e10	−0.727720
$875$	−6.15681e9	−0.310690
$876$	−2.82994e9	−0.142237
$877$	−3.93591e10	−1.97037	−0.985183	−	0.171509i	$-0.945136\pi$
$877$	−3.93591e10	−1.97037	−0.985183	+	0.171509i	$0.945136\pi$
$878$	5.39089e9	0.268800
$879$	−2.64948e9	−0.131583
$880$	−1.19201e9	−0.0589644
$881$	−2.83704e10	−1.39781	−0.698907	−	0.715213i	$-0.746330\pi$
$881$	−2.83704e10	−1.39781	−0.698907	+	0.715213i	$0.746330\pi$
$882$	7.86871e9	0.386156
$883$	−2.71601e10	−1.32760	−0.663802	−	0.747908i	$-0.731058\pi$
$883$	−2.71601e10	−1.32760	−0.663802	+	0.747908i	$0.731058\pi$
$884$	1.34218e9	0.0653473
$885$	−1.55112e8	−0.00752220
$886$	3.28433e9	0.158646
$887$	−2.72456e10	−1.31088	−0.655441	−	0.755246i	$-0.727517\pi$
$887$	−2.72456e10	−1.31088	−0.655441	+	0.755246i	$0.727517\pi$
$888$	−1.00134e10	−0.479883
$889$	−1.81268e10	−0.865297
$890$	1.49242e9	0.0709622
$891$	−2.59720e9	−0.123008
$892$	−9.78744e9	−0.461734
$893$	1.38936e10	0.652884
$894$	−1.56409e9	−0.0732116
$895$	7.78530e7	0.00362990
$896$	−6.76366e9	−0.314126
$897$	−8.86270e9	−0.410008
$898$	2.34597e10	1.08108
$899$	2.32277e10	1.06622
$900$	2.50592e9	0.114583
$901$	1.20201e10	0.547484
$902$	2.61650e10	1.18713
$903$	−3.08390e10	−1.39378
$904$	−4.11057e10	−1.85060
$905$	3.58059e9	0.160577
$906$	1.48814e9	0.0664805
$907$	−2.89542e10	−1.28850	−0.644251	−	0.764814i	$-0.722831\pi$
$907$	−2.89542e10	−1.28850	−0.644251	+	0.764814i	$0.722831\pi$
$908$	−6.90409e9	−0.306059
$909$	−1.19505e10	−0.527729
$910$	−1.88600e9	−0.0829655
$911$	4.90888e9	0.215114	0.107557	−	0.994199i	$-0.465697\pi$
$911$	4.90888e9	0.215114	0.107557	+	0.994199i	$0.465697\pi$
$912$	5.87180e9	0.256324
$913$	−1.19508e10	−0.519694
$914$	−1.33457e10	−0.578137
$915$	−8.84545e8	−0.0381721
$916$	9.94210e9	0.427409
$917$	−3.47593e9	−0.148860
$918$	−1.04286e9	−0.0444916
$919$	−8.65519e8	−0.0367851	−0.0183926	−	0.999831i	$-0.505855\pi$
$919$	−8.65519e8	−0.0367851	−0.0183926	+	0.999831i	$0.505855\pi$
$920$	−2.77796e9	−0.117617
$921$	−1.08373e10	−0.457101
$922$	−4.51879e8	−0.0189873
$923$	−4.16188e9	−0.174214
$924$	8.30281e9	0.346237
$925$	1.81969e10	0.755966
$926$	−2.56267e10	−1.06061
$927$	−1.03149e10	−0.425290
$928$	1.05651e10	0.433966
$929$	1.75729e10	0.719100	0.359550	−	0.933126i	$-0.382930\pi$
$929$	1.75729e10	0.719100	0.359550	+	0.933126i	$0.382930\pi$
$930$	1.85260e9	0.0755252
$931$	2.94506e10	1.19611
$932$	−8.73512e9	−0.353438
$933$	2.50392e10	1.00933
$934$	2.70564e10	1.08657
$935$	7.92367e8	0.0317019
$936$	5.98693e9	0.238637
$937$	−1.98729e9	−0.0789174	−0.0394587	−	0.999221i	$-0.512563\pi$
$937$	−1.98729e9	−0.0789174	−0.0394587	+	0.999221i	$0.512563\pi$
$938$	−5.92076e10	−2.34243
$939$	−2.16343e10	−0.852731
$940$	6.92562e8	0.0271964
$941$	9.16263e9	0.358473	0.179237	−	0.983806i	$-0.442637\pi$
$941$	9.16263e9	0.358473	0.179237	+	0.983806i	$0.442637\pi$
$942$	−8.16051e8	−0.0318082
$943$	3.69016e10	1.43303
$944$	1.79085e9	0.0692878
$945$	−7.79484e8	−0.0300467
$946$	3.60400e10	1.38409
$947$	−8.66497e9	−0.331545	−0.165772	−	0.986164i	$-0.553012\pi$
$947$	−8.66497e9	−0.331545	−0.165772	+	0.986164i	$0.553012\pi$
$948$	1.41437e8	0.00539182
$949$	1.22866e10	0.466660
$950$	−1.76323e10	−0.667233
$951$	8.01858e9	0.302319
$952$	1.29353e10	0.485900
$953$	4.09329e10	1.53196	0.765979	−	0.642866i	$-0.222255\pi$
$953$	4.09329e10	1.53196	0.765979	+	0.642866i	$0.222255\pi$
$954$	1.38189e10	0.515292
$955$	4.92113e9	0.182832
$956$	1.43133e10	0.529829
$957$	1.14213e10	0.421234
$958$	1.97679e10	0.726411
$959$	1.63707e10	0.599379
$960$	1.68561e9	0.0614903
$961$	4.45004e10	1.61745
$962$	1.12049e10	0.405783
$963$	1.15661e10	0.417346
$964$	−5.24142e9	−0.188443
$965$	2.52921e9	0.0906024
$966$	−2.20142e10	−0.785748
$967$	4.75373e10	1.69060	0.845302	−	0.534289i	$-0.179421\pi$
$967$	4.75373e10	1.69060	0.845302	+	0.534289i	$0.179421\pi$
$968$	−6.93016e9	−0.245572
$969$	−3.90318e9	−0.137811
$970$	1.63131e9	0.0573897
$971$	4.18209e10	1.46597	0.732986	−	0.680244i	$-0.238126\pi$
$971$	4.18209e10	1.46597	0.732986	+	0.680244i	$0.238126\pi$
$972$	6.37735e8	0.0222745
$973$	1.96647e10	0.684372
$974$	−2.67083e10	−0.926168
$975$	−1.08798e10	−0.375929
$976$	1.02125e10	0.351608
$977$	−3.63532e10	−1.24713	−0.623565	−	0.781771i	$-0.714316\pi$
$977$	−3.63532e10	−1.24713	−0.623565	+	0.781771i	$0.714316\pi$
$978$	−8.28112e9	−0.283076
$979$	2.85253e10	0.971606
$980$	1.46804e9	0.0498248
$981$	−6.01847e9	−0.203538
$982$	1.15844e10	0.390375
$983$	1.22719e10	0.412072	0.206036	−	0.978544i	$-0.433944\pi$
$983$	1.22719e10	0.412072	0.206036	+	0.978544i	$0.433944\pi$
$984$	−2.49278e10	−0.834066
$985$	2.21237e9	0.0737617
$986$	4.58603e9	0.152359
$987$	2.12944e10	0.704944
$988$	5.77518e9	0.190509
$989$	5.08288e10	1.67079
$990$	9.10943e8	0.0298379
$991$	−3.42031e10	−1.11637	−0.558185	−	0.829717i	$-0.688502\pi$
$991$	−3.42031e10	−1.11637	−0.558185	+	0.829717i	$0.688502\pi$
$992$	3.27550e10	1.06534
$993$	−1.25777e10	−0.407642
$994$	−1.03378e10	−0.333867
$995$	−5.03716e9	−0.162108
$996$	2.93447e9	0.0941070
$997$	6.42072e9	0.205187	0.102594	−	0.994723i	$-0.467286\pi$
$997$	6.42072e9	0.205187	0.102594	+	0.994723i	$0.467286\pi$
$998$	−1.88253e10	−0.599495
$999$	4.63096e9	0.146958

Twists

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

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

\(f(q)\)	\(=\)	\(q+9.14085 q^{2} -27.0000 q^{3} -44.4448 q^{4} -27.9722 q^{5} -246.803 q^{6} -1415.76 q^{7} -1576.29 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+9.14085 q^{2} -27.0000 q^{3} -44.4448 q^{4} -27.9722 q^{5} -246.803 q^{6} -1415.76 q^{7} -1576.29 q^{8} +729.000 q^{9} -255.690 q^{10} -4887.09 q^{11} +1200.01 q^{12} -5210.02 q^{13} -12941.3 q^{14} +755.249 q^{15} -8719.72 q^{16} +5796.28 q^{17} +6663.68 q^{18} +24940.5 q^{19} +1243.22 q^{20} +38225.5 q^{21} -44672.2 q^{22} -63003.2 q^{23} +42559.9 q^{24} -77342.6 q^{25} -47624.1 q^{26} -19683.0 q^{27} +62923.2 q^{28} +86556.7 q^{29} +6903.62 q^{30} +268352. q^{31} +122060. q^{32} +131951. q^{33} +52983.0 q^{34} +39601.9 q^{35} -32400.3 q^{36} -235277. q^{37} +227977. q^{38} +140671. q^{39} +44092.3 q^{40} -585710. q^{41} +349414. q^{42} -806765. q^{43} +217206. q^{44} -20391.7 q^{45} -575903. q^{46} +557072. q^{47} +235432. q^{48} +1.18083e6 q^{49} -706977. q^{50} -156500. q^{51} +231559. q^{52} +2.07376e6 q^{53} -179919. q^{54} +136703. q^{55} +2.23165e6 q^{56} -673393. q^{57} +791202. q^{58} -205379. q^{59} -33566.9 q^{60} -1.17120e6 q^{61} +2.45297e6 q^{62} -1.03209e6 q^{63} +2.23185e6 q^{64} +145736. q^{65} +1.20615e6 q^{66} +4.57510e6 q^{67} -257615. q^{68} +1.70109e6 q^{69} +361995. q^{70} +798821. q^{71} -1.14912e6 q^{72} -2.35826e6 q^{73} -2.15063e6 q^{74} +2.08825e6 q^{75} -1.10847e6 q^{76} +6.91895e6 q^{77} +1.28585e6 q^{78} +117864. q^{79} +243910. q^{80} +531441. q^{81} -5.35389e6 q^{82} +2.44537e6 q^{83} -1.69893e6 q^{84} -162135. q^{85} -7.37452e6 q^{86} -2.33703e6 q^{87} +7.70349e6 q^{88} -5.83686e6 q^{89} -186398. q^{90} +7.37614e6 q^{91} +2.80017e6 q^{92} -7.24551e6 q^{93} +5.09211e6 q^{94} -697640. q^{95} -3.29561e6 q^{96} -6.38002e6 q^{97} +1.07938e7 q^{98} -3.56269e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 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

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