LMFDB - Embedded newform 177.8.a.c.1.4

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			1.4
Root			$-13.8304$ 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)

$f(q)$	$=$	$q-13.8304 q^{2} -27.0000 q^{3} +63.2803 q^{4} -149.469 q^{5} +373.421 q^{6} +14.2725 q^{7} +895.100 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-13.8304 q^{2} -27.0000 q^{3} +63.2803 q^{4} -149.469 q^{5} +373.421 q^{6} +14.2725 q^{7} +895.100 q^{8} +729.000 q^{9} +2067.22 q^{10} +531.760 q^{11} -1708.57 q^{12} +4168.02 q^{13} -197.395 q^{14} +4035.66 q^{15} -20479.5 q^{16} +4562.28 q^{17} -10082.4 q^{18} +31839.8 q^{19} -9458.44 q^{20} -385.358 q^{21} -7354.45 q^{22} -56030.4 q^{23} -24167.7 q^{24} -55784.0 q^{25} -57645.4 q^{26} -19683.0 q^{27} +903.168 q^{28} +52043.8 q^{29} -55814.9 q^{30} -44036.0 q^{31} +168667. q^{32} -14357.5 q^{33} -63098.2 q^{34} -2133.30 q^{35} +46131.3 q^{36} +11309.5 q^{37} -440358. q^{38} -112536. q^{39} -133790. q^{40} -455543. q^{41} +5329.65 q^{42} +177174. q^{43} +33649.9 q^{44} -108963. q^{45} +774923. q^{46} -1.27260e6 q^{47} +552946. q^{48} -823339. q^{49} +771516. q^{50} -123182. q^{51} +263753. q^{52} +274388. q^{53} +272224. q^{54} -79481.6 q^{55} +12775.3 q^{56} -859675. q^{57} -719787. q^{58} -205379. q^{59} +255378. q^{60} -152764. q^{61} +609036. q^{62} +10404.7 q^{63} +288642. q^{64} -622989. q^{65} +198570. q^{66} +2.06545e6 q^{67} +288702. q^{68} +1.51282e6 q^{69} +29504.4 q^{70} -1.79110e6 q^{71} +652528. q^{72} +3.32985e6 q^{73} -156414. q^{74} +1.50617e6 q^{75} +2.01483e6 q^{76} +7589.54 q^{77} +1.55643e6 q^{78} +6.43667e6 q^{79} +3.06105e6 q^{80} +531441. q^{81} +6.30035e6 q^{82} -1.15501e6 q^{83} -24385.5 q^{84} -681919. q^{85} -2.45039e6 q^{86} -1.40518e6 q^{87} +475978. q^{88} +3.69123e6 q^{89} +1.50700e6 q^{90} +59488.0 q^{91} -3.54562e6 q^{92} +1.18897e6 q^{93} +1.76005e7 q^{94} -4.75907e6 q^{95} -4.55400e6 q^{96} +6.33530e6 q^{97} +1.13871e7 q^{98} +387653. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.8304	−1.22245	−0.611224	−	0.791458i	$-0.709322\pi$
$2$	−13.8304	−1.22245	−0.611224	+	0.791458i	$0.709322\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	63.2803	0.494377
$5$	−149.469	−0.534757	−0.267378	−	0.963592i	$-0.586157\pi$
$5$	−149.469	−0.534757	−0.267378	+	0.963592i	$0.586157\pi$
$6$	373.421	0.705780
$7$	14.2725	0.0157274	0.00786370	−	0.999969i	$-0.497497\pi$
$7$	14.2725	0.0157274	0.00786370	+	0.999969i	$0.497497\pi$
$8$	895.100	0.618097
$9$	729.000	0.333333
$10$	2067.22	0.653712
$11$	531.760	0.120459	0.0602297	−	0.998185i	$-0.480817\pi$
$11$	531.760	0.120459	0.0602297	+	0.998185i	$0.480817\pi$
$12$	−1708.57	−0.285429
$13$	4168.02	0.526172	0.263086	−	0.964772i	$-0.415260\pi$
$13$	4168.02	0.526172	0.263086	+	0.964772i	$0.415260\pi$
$14$	−197.395	−0.0192259
$15$	4035.66	0.308742
$16$	−20479.5	−1.24997
$17$	4562.28	0.225222	0.112611	−	0.993639i	$-0.464079\pi$
$17$	4562.28	0.225222	0.112611	+	0.993639i	$0.464079\pi$
$18$	−10082.4	−0.407482
$19$	31839.8	1.06496	0.532480	−	0.846443i	$-0.321260\pi$
$19$	31839.8	1.06496	0.532480	+	0.846443i	$0.321260\pi$
$20$	−9458.44	−0.264372
$21$	−385.358	−0.00908022
$22$	−7354.45	−0.147255
$23$	−56030.4	−0.960231	−0.480116	−	0.877205i	$-0.659405\pi$
$23$	−56030.4	−0.960231	−0.480116	+	0.877205i	$0.659405\pi$
$24$	−24167.7	−0.356859
$25$	−55784.0	−0.714035
$26$	−57645.4	−0.643217
$27$	−19683.0	−0.192450
$28$	903.168	0.00777527
$29$	52043.8	0.396256	0.198128	−	0.980176i	$-0.436514\pi$
$29$	52043.8	0.396256	0.198128	+	0.980176i	$0.436514\pi$
$30$	−55814.9	−0.377421
$31$	−44036.0	−0.265486	−0.132743	−	0.991150i	$-0.542379\pi$
$31$	−44036.0	−0.265486	−0.132743	+	0.991150i	$0.542379\pi$
$32$	168667.	0.909923
$33$	−14357.5	−0.0695473
$34$	−63098.2	−0.275322
$35$	−2133.30	−0.00841033
$36$	46131.3	0.164792
$37$	11309.5	0.0367059	0.0183529	−	0.999832i	$-0.494158\pi$
$37$	11309.5	0.0367059	0.0183529	+	0.999832i	$0.494158\pi$
$38$	−440358.	−1.30186
$39$	−112536.	−0.303785
$40$	−133790.	−0.330531
$41$	−455543.	−1.03225	−0.516126	−	0.856513i	$-0.672626\pi$
$41$	−455543.	−1.03225	−0.516126	+	0.856513i	$0.672626\pi$
$42$	5329.65	0.0111001
$43$	177174.	0.339829	0.169915	−	0.985459i	$-0.445651\pi$
$43$	177174.	0.339829	0.169915	+	0.985459i	$0.445651\pi$
$44$	33649.9	0.0595524
$45$	−108963.	−0.178252
$46$	774923.	1.17383
$47$	−1.27260e6	−1.78792	−0.893960	−	0.448147i	$-0.852084\pi$
$47$	−1.27260e6	−1.78792	−0.893960	+	0.448147i	$0.852084\pi$
$48$	552946.	0.721670
$49$	−823339.	−0.999753
$50$	771516.	0.872871
$51$	−123182.	−0.130032
$52$	263753.	0.260127
$53$	274388.	0.253162	0.126581	−	0.991956i	$-0.459600\pi$
$53$	274388.	0.253162	0.126581	+	0.991956i	$0.459600\pi$
$54$	272224.	0.235260
$55$	−79481.6	−0.0644165
$56$	12775.3	0.00972106
$57$	−859675.	−0.614854
$58$	−719787.	−0.484402
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	255378.	0.152635
$61$	−152764.	−0.0861719	−0.0430860	−	0.999071i	$-0.513719\pi$
$61$	−152764.	−0.0861719	−0.0430860	+	0.999071i	$0.513719\pi$
$62$	609036.	0.324543
$63$	10404.7	0.00524247
$64$	288642.	0.137635
$65$	−622989.	−0.281374
$66$	198570.	0.0850179
$67$	2.06545e6	0.838984	0.419492	−	0.907759i	$-0.362208\pi$
$67$	2.06545e6	0.838984	0.419492	+	0.907759i	$0.362208\pi$
$68$	288702.	0.111345
$69$	1.51282e6	0.554390
$70$	29504.4	0.0102812
$71$	−1.79110e6	−0.593904	−0.296952	−	0.954892i	$-0.595970\pi$
$71$	−1.79110e6	−0.593904	−0.296952	+	0.954892i	$0.595970\pi$
$72$	652528.	0.206032
$73$	3.32985e6	1.00183	0.500916	−	0.865496i	$-0.332996\pi$
$73$	3.32985e6	1.00183	0.500916	+	0.865496i	$0.332996\pi$
$74$	−156414.	−0.0448710
$75$	1.50617e6	0.412249
$76$	2.01483e6	0.526492
$77$	7589.54	0.00189451
$78$	1.55643e6	0.371362
$79$	6.43667e6	1.46881	0.734406	−	0.678710i	$-0.237461\pi$
$79$	6.43667e6	1.46881	0.734406	+	0.678710i	$0.237461\pi$
$80$	3.06105e6	0.668429
$81$	531441.	0.111111
$82$	6.30035e6	1.26187
$83$	−1.15501e6	−0.221724	−0.110862	−	0.993836i	$-0.535361\pi$
$83$	−1.15501e6	−0.221724	−0.110862	+	0.993836i	$0.535361\pi$
$84$	−24385.5	−0.00448905
$85$	−681919.	−0.120439
$86$	−2.45039e6	−0.415423
$87$	−1.40518e6	−0.228778
$88$	475978.	0.0744556
$89$	3.69123e6	0.555016	0.277508	−	0.960723i	$-0.410491\pi$
$89$	3.69123e6	0.555016	0.277508	+	0.960723i	$0.410491\pi$
$90$	1.50700e6	0.217904
$91$	59488.0	0.00827532
$92$	−3.54562e6	−0.474717
$93$	1.18897e6	0.153279
$94$	1.76005e7	2.18564
$95$	−4.75907e6	−0.569494
$96$	−4.55400e6	−0.525344
$97$	6.33530e6	0.704800	0.352400	−	0.935849i	$-0.385366\pi$
$97$	6.33530e6	0.704800	0.352400	+	0.935849i	$0.385366\pi$
$98$	1.13871e7	1.22214
$99$	387653.	0.0401531
$100$	−3.53003e6	−0.353003
$101$	8.28710e6	0.800346	0.400173	−	0.916440i	$-0.368950\pi$
$101$	8.28710e6	0.800346	0.400173	+	0.916440i	$0.368950\pi$
$102$	1.70365e6	0.158957
$103$	1.33969e7	1.20802	0.604008	−	0.796979i	$-0.293570\pi$
$103$	1.33969e7	1.20802	0.604008	+	0.796979i	$0.293570\pi$
$104$	3.73079e6	0.325225
$105$	57599.0	0.00485571
$106$	−3.79490e6	−0.309478
$107$	7.64708e6	0.603466	0.301733	−	0.953393i	$-0.402435\pi$
$107$	7.64708e6	0.603466	0.301733	+	0.953393i	$0.402435\pi$
$108$	−1.24555e6	−0.0951430
$109$	8.75164e6	0.647287	0.323644	−	0.946179i	$-0.395092\pi$
$109$	8.75164e6	0.647287	0.323644	+	0.946179i	$0.395092\pi$
$110$	1.09926e6	0.0787458
$111$	−305355.	−0.0211922
$112$	−292293.	−0.0196588
$113$	−1.76375e7	−1.14990	−0.574952	−	0.818187i	$-0.694979\pi$
$113$	−1.76375e7	−1.14990	−0.574952	+	0.818187i	$0.694979\pi$
$114$	1.18897e7	0.751627
$115$	8.37480e6	0.513490
$116$	3.29335e6	0.195900
$117$	3.03848e6	0.175391
$118$	2.84048e6	0.159149
$119$	65115.1	0.00354215
$120$	3.61232e6	0.190832
$121$	−1.92044e7	−0.985490
$122$	2.11278e6	0.105341
$123$	1.22997e7	0.595971
$124$	−2.78661e6	−0.131250
$125$	2.00152e7	0.916592
$126$	−143901.	−0.00640864
$127$	−3.15626e7	−1.36729	−0.683643	−	0.729817i	$-0.739605\pi$
$127$	−3.15626e7	−1.36729	−0.683643	+	0.729817i	$0.739605\pi$
$128$	−2.55814e7	−1.07817
$129$	−4.78370e6	−0.196201
$130$	8.61620e6	0.343965
$131$	−1.54251e7	−0.599485	−0.299742	−	0.954020i	$-0.596901\pi$
$131$	−1.54251e7	−0.599485	−0.299742	+	0.954020i	$0.596901\pi$
$132$	−908547.	−0.0343826
$133$	454434.	0.0167490
$134$	−2.85661e7	−1.02561
$135$	2.94200e6	0.102914
$136$	4.08370e6	0.139209
$137$	2.73563e6	0.0908940	0.0454470	−	0.998967i	$-0.485529\pi$
$137$	2.73563e6	0.0908940	0.0454470	+	0.998967i	$0.485529\pi$
$138$	−2.09229e7	−0.677712
$139$	2.21140e7	0.698418	0.349209	−	0.937045i	$-0.386450\pi$
$139$	2.21140e7	0.698418	0.349209	+	0.937045i	$0.386450\pi$
$140$	−134996.	−0.00415788
$141$	3.43601e7	1.03226
$142$	2.47717e7	0.726016
$143$	2.21638e6	0.0633824
$144$	−1.49295e7	−0.416656
$145$	−7.77893e6	−0.211900
$146$	−4.60532e7	−1.22469
$147$	2.22302e7	0.577207
$148$	715666.	0.0181466
$149$	4.34797e6	0.107680	0.0538399	−	0.998550i	$-0.482854\pi$
$149$	4.34797e6	0.107680	0.0538399	+	0.998550i	$0.482854\pi$
$150$	−2.08309e7	−0.503952
$151$	642629.	0.0151894	0.00759470	−	0.999971i	$-0.497583\pi$
$151$	642629.	0.0151894	0.00759470	+	0.999971i	$0.497583\pi$
$152$	2.84998e7	0.658248
$153$	3.32590e6	0.0750739
$154$	−104966.	−0.00231594
$155$	6.58202e6	0.141970
$156$	−7.12134e6	−0.150185
$157$	4.54519e7	0.937354	0.468677	−	0.883370i	$-0.344731\pi$
$157$	4.54519e7	0.937354	0.468677	+	0.883370i	$0.344731\pi$
$158$	−8.90218e7	−1.79555
$159$	−7.40847e6	−0.146163
$160$	−2.52105e7	−0.486587
$161$	−799693.	−0.0151019
$162$	−7.35005e6	−0.135827
$163$	9.12208e7	1.64982	0.824911	−	0.565262i	$-0.191225\pi$
$163$	9.12208e7	1.64982	0.824911	+	0.565262i	$0.191225\pi$
$164$	−2.88269e7	−0.510322
$165$	2.14600e6	0.0371909
$166$	1.59743e7	0.271045
$167$	−6.56493e7	−1.09074	−0.545371	−	0.838194i	$-0.683611\pi$
$167$	−6.56493e7	−1.09074	−0.545371	+	0.838194i	$0.683611\pi$
$168$	−344934.	−0.00561246
$169$	−4.53762e7	−0.723143
$170$	9.43122e6	0.147230
$171$	2.32112e7	0.354986
$172$	1.12116e7	0.168004
$173$	−1.20346e8	−1.76714	−0.883568	−	0.468303i	$-0.844866\pi$
$173$	−1.20346e8	−1.76714	−0.883568	+	0.468303i	$0.844866\pi$
$174$	1.94342e7	0.279670
$175$	−796177.	−0.0112299
$176$	−1.08902e7	−0.150571
$177$	5.54523e6	0.0751646
$178$	−5.10512e7	−0.678478
$179$	−1.33167e7	−0.173544	−0.0867722	−	0.996228i	$-0.527655\pi$
$179$	−1.33167e7	−0.173544	−0.0867722	+	0.996228i	$0.527655\pi$
$180$	−6.89520e6	−0.0881238
$181$	1.20262e7	0.150748	0.0753741	−	0.997155i	$-0.475985\pi$
$181$	1.20262e7	0.150748	0.0753741	+	0.997155i	$0.475985\pi$
$182$	−822744.	−0.0101161
$183$	4.12462e6	0.0497514
$184$	−5.01528e7	−0.593516
$185$	−1.69041e6	−0.0196287
$186$	−1.64440e7	−0.187375
$187$	2.42603e6	0.0271301
$188$	−8.05302e7	−0.883907
$189$	−280926.	−0.00302674
$190$	6.58198e7	0.696176
$191$	−2.96173e6	−0.0307559	−0.0153780	−	0.999882i	$-0.504895\pi$
$191$	−2.96173e6	−0.0307559	−0.0153780	+	0.999882i	$0.504895\pi$
$192$	−7.79333e6	−0.0794636
$193$	−8.88812e6	−0.0889937	−0.0444968	−	0.999010i	$-0.514168\pi$
$193$	−8.88812e6	−0.0889937	−0.0444968	+	0.999010i	$0.514168\pi$
$194$	−8.76198e7	−0.861581
$195$	1.68207e7	0.162451
$196$	−5.21012e7	−0.494255
$197$	5.08009e7	0.473412	0.236706	−	0.971581i	$-0.423932\pi$
$197$	5.08009e7	0.473412	0.236706	+	0.971581i	$0.423932\pi$
$198$	−5.36140e6	−0.0490851
$199$	3.98854e7	0.358780	0.179390	−	0.983778i	$-0.442588\pi$
$199$	3.98854e7	0.358780	0.179390	+	0.983778i	$0.442588\pi$
$200$	−4.99323e7	−0.441343
$201$	−5.57673e7	−0.484388
$202$	−1.14614e8	−0.978381
$203$	742795.	0.00623208
$204$	−7.79496e6	−0.0642848
$205$	6.80896e7	0.552004
$206$	−1.85284e8	−1.47674
$207$	−4.08461e7	−0.320077
$208$	−8.53588e7	−0.657698
$209$	1.69311e7	0.128284
$210$	−796618.	−0.00593585
$211$	7.97162e7	0.584195	0.292098	−	0.956389i	$-0.405647\pi$
$211$	7.97162e7	0.584195	0.292098	+	0.956389i	$0.405647\pi$
$212$	1.73633e7	0.125158
$213$	4.83597e7	0.342890
$214$	−1.05762e8	−0.737705
$215$	−2.64820e7	−0.181726
$216$	−1.76183e7	−0.118953
$217$	−628504.	−0.00417541
$218$	−1.21039e8	−0.791274
$219$	−8.99061e7	−0.578408
$220$	−5.02962e6	−0.0318460
$221$	1.90156e7	0.118505
$222$	4.22319e6	0.0259063
$223$	1.35288e8	0.816947	0.408473	−	0.912770i	$-0.366061\pi$
$223$	1.35288e8	0.816947	0.408473	+	0.912770i	$0.366061\pi$
$224$	2.40730e6	0.0143107
$225$	−4.06665e7	−0.238012
$226$	2.43934e8	1.40570
$227$	−1.97246e8	−1.11923	−0.559613	−	0.828754i	$-0.689050\pi$
$227$	−1.97246e8	−1.11923	−0.559613	+	0.828754i	$0.689050\pi$
$228$	−5.44005e7	−0.303970
$229$	1.35002e8	0.742875	0.371438	−	0.928458i	$-0.378865\pi$
$229$	1.35002e8	0.742875	0.371438	+	0.928458i	$0.378865\pi$
$230$	−1.15827e8	−0.627715
$231$	−204918.	−0.00109380
$232$	4.65844e7	0.244925
$233$	1.36315e8	0.705988	0.352994	−	0.935626i	$-0.385164\pi$
$233$	1.36315e8	0.705988	0.352994	+	0.935626i	$0.385164\pi$
$234$	−4.20235e7	−0.214406
$235$	1.90214e8	0.956102
$236$	−1.29964e7	−0.0643624
$237$	−1.73790e8	−0.848019
$238$	−900569.	−0.00433010
$239$	1.31494e8	0.623038	0.311519	−	0.950240i	$-0.399162\pi$
$239$	1.31494e8	0.623038	0.311519	+	0.950240i	$0.399162\pi$
$240$	−8.26483e7	−0.385918
$241$	2.49648e8	1.14887	0.574433	−	0.818552i	$-0.305223\pi$
$241$	2.49648e8	1.14887	0.574433	+	0.818552i	$0.305223\pi$
$242$	2.65605e8	1.20471
$243$	−1.43489e7	−0.0641500
$244$	−9.66693e6	−0.0426014
$245$	1.23064e8	0.534624
$246$	−1.70109e8	−0.728543
$247$	1.32709e8	0.560351
$248$	−3.94166e7	−0.164096
$249$	3.11852e7	0.128012
$250$	−2.76819e8	−1.12048
$251$	3.53873e7	0.141250	0.0706252	−	0.997503i	$-0.477501\pi$
$251$	3.53873e7	0.141250	0.0706252	+	0.997503i	$0.477501\pi$
$252$	658410.	0.00259176
$253$	−2.97947e7	−0.115669
$254$	4.36523e8	1.67143
$255$	1.84118e7	0.0695354
$256$	3.16855e8	1.18038
$257$	4.79092e7	0.176057	0.0880285	−	0.996118i	$-0.471943\pi$
$257$	4.79092e7	0.176057	0.0880285	+	0.996118i	$0.471943\pi$
$258$	6.61606e7	0.239845
$259$	161414.	0.000577288 0
$260$	−3.94229e7	−0.139105
$261$	3.79399e7	0.132085
$262$	2.13335e8	0.732838
$263$	4.03661e8	1.36827	0.684135	−	0.729355i	$-0.260180\pi$
$263$	4.03661e8	1.36827	0.684135	+	0.729355i	$0.260180\pi$
$264$	−1.28514e7	−0.0429870
$265$	−4.10125e7	−0.135380
$266$	−6.28501e6	−0.0204748
$267$	−9.96631e7	−0.320439
$268$	1.30703e8	0.414775
$269$	1.59050e8	0.498196	0.249098	−	0.968478i	$-0.419866\pi$
$269$	1.59050e8	0.498196	0.249098	+	0.968478i	$0.419866\pi$
$270$	−4.06890e7	−0.125807
$271$	−2.63878e8	−0.805399	−0.402700	−	0.915332i	$-0.631928\pi$
$271$	−2.63878e8	−0.805399	−0.402700	+	0.915332i	$0.631928\pi$
$272$	−9.34331e7	−0.281520
$273$	−1.60618e6	−0.00477776
$274$	−3.78349e7	−0.111113
$275$	−2.96637e7	−0.0860123
$276$	9.57317e7	0.274078
$277$	5.07781e8	1.43548	0.717740	−	0.696311i	$-0.245177\pi$
$277$	5.07781e8	1.43548	0.717740	+	0.696311i	$0.245177\pi$
$278$	−3.05846e8	−0.853779
$279$	−3.21022e7	−0.0884954
$280$	−1.90951e6	−0.00519840
$281$	4.01914e8	1.08059	0.540295	−	0.841476i	$-0.318313\pi$
$281$	4.01914e8	1.08059	0.540295	+	0.841476i	$0.318313\pi$
$282$	−4.75214e8	−1.26188
$283$	−1.41538e7	−0.0371210	−0.0185605	−	0.999828i	$-0.505908\pi$
$283$	−1.41538e7	−0.0371210	−0.0185605	+	0.999828i	$0.505908\pi$
$284$	−1.13341e8	−0.293612
$285$	1.28495e8	0.328797
$286$	−3.06535e7	−0.0774816
$287$	−6.50174e6	−0.0162346
$288$	1.22958e8	0.303308
$289$	−3.89524e8	−0.949275
$290$	1.07586e8	0.259037
$291$	−1.71053e8	−0.406917
$292$	2.10714e8	0.495283
$293$	−5.93471e7	−0.137836	−0.0689180	−	0.997622i	$-0.521955\pi$
$293$	−5.93471e7	−0.137836	−0.0689180	+	0.997622i	$0.521955\pi$
$294$	−3.07452e8	−0.705606
$295$	3.06978e7	0.0696194
$296$	1.01231e7	0.0226878
$297$	−1.04666e7	−0.0231824
$298$	−6.01342e7	−0.131633
$299$	−2.33535e8	−0.505247
$300$	9.53108e7	0.203806
$301$	2.52872e6	0.00534463
$302$	−8.88782e6	−0.0185682
$303$	−2.23752e8	−0.462080
$304$	−6.52063e8	−1.33117
$305$	2.28334e7	0.0460810
$306$	−4.59986e7	−0.0917739
$307$	2.64952e8	0.522617	0.261308	−	0.965255i	$-0.415846\pi$
$307$	2.64952e8	0.522617	0.261308	+	0.965255i	$0.415846\pi$
$308$	480268.	0.000936605 0
$309$	−3.61715e8	−0.697448
$310$	−9.10320e7	−0.173551
$311$	2.51765e8	0.474607	0.237304	−	0.971436i	$-0.423736\pi$
$311$	2.51765e8	0.474607	0.237304	+	0.971436i	$0.423736\pi$
$312$	−1.00731e8	−0.187769
$313$	1.78674e8	0.329348	0.164674	−	0.986348i	$-0.447343\pi$
$313$	1.78674e8	0.329348	0.164674	+	0.986348i	$0.447343\pi$
$314$	−6.28619e8	−1.14587
$315$	−1.55517e6	−0.00280344
$316$	4.07314e8	0.726147
$317$	7.62555e8	1.34451	0.672254	−	0.740320i	$-0.265326\pi$
$317$	7.62555e8	1.34451	0.672254	+	0.740320i	$0.265326\pi$
$318$	1.02462e8	0.178677
$319$	2.76748e7	0.0477328
$320$	−4.31430e7	−0.0736013
$321$	−2.06471e8	−0.348411
$322$	1.10601e7	0.0184613
$323$	1.45262e8	0.239852
$324$	3.36297e7	0.0549308
$325$	−2.32509e8	−0.375705
$326$	−1.26162e9	−2.01682
$327$	−2.36294e8	−0.373711
$328$	−4.07757e8	−0.638032
$329$	−1.81631e7	−0.0281193
$330$	−2.96801e7	−0.0454639
$331$	3.94113e8	0.597342	0.298671	−	0.954356i	$-0.403457\pi$
$331$	3.94113e8	0.597342	0.298671	+	0.954356i	$0.403457\pi$
$332$	−7.30893e7	−0.109615
$333$	8.24459e6	0.0122353
$334$	9.07957e8	1.33338
$335$	−3.08721e8	−0.448652
$336$	7.89192e6	0.0113500
$337$	1.50464e8	0.214155	0.107077	−	0.994251i	$-0.465851\pi$
$337$	1.50464e8	0.214155	0.107077	+	0.994251i	$0.465851\pi$
$338$	6.27571e8	0.884004
$339$	4.76212e8	0.663898
$340$	−4.31520e7	−0.0595422
$341$	−2.34166e7	−0.0319803
$342$	−3.21021e8	−0.433952
$343$	−2.35051e7	−0.0314509
$344$	1.58589e8	0.210047
$345$	−2.26120e8	−0.296464
$346$	1.66443e9	2.16023
$347$	1.12645e9	1.44730	0.723651	−	0.690166i	$-0.242462\pi$
$347$	1.12645e9	1.44730	0.723651	+	0.690166i	$0.242462\pi$
$348$	−8.89203e7	−0.113103
$349$	−2.40653e8	−0.303042	−0.151521	−	0.988454i	$-0.548417\pi$
$349$	−2.40653e8	−0.303042	−0.151521	+	0.988454i	$0.548417\pi$
$350$	1.10115e7	0.0137280
$351$	−8.20391e7	−0.101262
$352$	8.96902e7	0.109609
$353$	−2.62604e8	−0.317754	−0.158877	−	0.987298i	$-0.550787\pi$
$353$	−2.62604e8	−0.317754	−0.158877	+	0.987298i	$0.550787\pi$
$354$	−7.66929e7	−0.0918848
$355$	2.67714e8	0.317594
$356$	2.33582e8	0.274387
$357$	−1.75811e6	−0.00204506
$358$	1.84175e8	0.212149
$359$	1.31180e7	0.0149636	0.00748179	−	0.999972i	$-0.497618\pi$
$359$	1.31180e7	0.0149636	0.00748179	+	0.999972i	$0.497618\pi$
$360$	−9.75327e7	−0.110177
$361$	1.19902e8	0.134138
$362$	−1.66327e8	−0.184282
$363$	5.18519e8	0.568973
$364$	3.76442e6	0.00409113
$365$	−4.97710e8	−0.535737
$366$	−5.70452e7	−0.0608184
$367$	2.85308e8	0.301288	0.150644	−	0.988588i	$-0.451865\pi$
$367$	2.85308e8	0.301288	0.150644	+	0.988588i	$0.451865\pi$
$368$	1.14747e9	1.20026
$369$	−3.32091e8	−0.344084
$370$	2.33791e7	0.0239951
$371$	3.91620e6	0.00398159
$372$	7.52385e7	0.0757774
$373$	−1.76282e8	−0.175884	−0.0879420	−	0.996126i	$-0.528029\pi$
$373$	−1.76282e8	−0.175884	−0.0879420	+	0.996126i	$0.528029\pi$
$374$	−3.35531e7	−0.0331651
$375$	−5.40412e8	−0.529194
$376$	−1.13910e9	−1.10511
$377$	2.16919e8	0.208499
$378$	3.88532e6	0.00370003
$379$	−1.69178e9	−1.59627	−0.798137	−	0.602477i	$-0.794181\pi$
$379$	−1.69178e9	−1.59627	−0.798137	+	0.602477i	$0.794181\pi$
$380$	−3.01155e8	−0.281545
$381$	8.52189e8	0.789402
$382$	4.09620e7	0.0375975
$383$	2.05814e9	1.87189	0.935944	−	0.352149i	$-0.114549\pi$
$383$	2.05814e9	1.87189	0.935944	+	0.352149i	$0.114549\pi$
$384$	6.90698e8	0.622485
$385$	−1.13440e6	−0.00101310
$386$	1.22926e8	0.108790
$387$	1.29160e8	0.113276
$388$	4.00900e8	0.348437
$389$	1.26822e9	1.09237	0.546187	−	0.837663i	$-0.316079\pi$
$389$	1.26822e9	1.09237	0.546187	+	0.837663i	$0.316079\pi$
$390$	−2.32637e8	−0.198588
$391$	−2.55626e8	−0.216265
$392$	−7.36971e8	−0.617944
$393$	4.16477e8	0.346113
$394$	−7.02597e8	−0.578722
$395$	−9.62082e8	−0.785457
$396$	2.45308e7	0.0198508
$397$	1.90127e9	1.52502	0.762512	−	0.646975i	$-0.223966\pi$
$397$	1.90127e9	1.52502	0.762512	+	0.646975i	$0.223966\pi$
$398$	−5.51632e8	−0.438590
$399$	−1.22697e7	−0.00967006
$400$	1.14243e9	0.892522
$401$	−1.68338e9	−1.30370	−0.651849	−	0.758349i	$-0.726007\pi$
$401$	−1.68338e9	−1.30370	−0.651849	+	0.758349i	$0.726007\pi$
$402$	7.71284e8	0.592138
$403$	−1.83543e8	−0.139691
$404$	5.24410e8	0.395673
$405$	−7.94340e7	−0.0594174
$406$	−1.02732e7	−0.00761838
$407$	6.01391e6	0.00442157
$408$	−1.10260e8	−0.0803723
$409$	1.07416e8	0.0776317	0.0388159	−	0.999246i	$-0.487641\pi$
$409$	1.07416e8	0.0776317	0.0388159	+	0.999246i	$0.487641\pi$
$410$	−9.41707e8	−0.674795
$411$	−7.38619e7	−0.0524776
$412$	8.47757e8	0.597215
$413$	−2.93127e6	−0.00204753
$414$	5.64919e8	0.391277
$415$	1.72638e8	0.118568
$416$	7.03006e8	0.478776
$417$	−5.97078e8	−0.403232
$418$	−2.34164e8	−0.156821
$419$	2.36422e8	0.157014	0.0785071	−	0.996914i	$-0.474985\pi$
$419$	2.36422e8	0.157014	0.0785071	+	0.996914i	$0.474985\pi$
$420$	3.64488e6	0.00240055
$421$	−1.71085e9	−1.11744	−0.558722	−	0.829355i	$-0.688708\pi$
$421$	−1.71085e9	−1.11744	−0.558722	+	0.829355i	$0.688708\pi$
$422$	−1.10251e9	−0.714148
$423$	−9.27722e8	−0.595973
$424$	2.45605e8	0.156479
$425$	−2.54502e8	−0.160816
$426$	−6.68835e8	−0.419165
$427$	−2.18032e6	−0.00135526
$428$	4.83910e8	0.298340
$429$	−5.98423e7	−0.0365938
$430$	3.66258e8	0.222150
$431$	6.46052e8	0.388685	0.194342	−	0.980934i	$-0.437743\pi$
$431$	6.46052e8	0.388685	0.194342	+	0.980934i	$0.437743\pi$
$432$	4.03098e8	0.240557
$433$	2.52351e9	1.49382	0.746908	−	0.664927i	$-0.231537\pi$
$433$	2.52351e9	1.49382	0.746908	+	0.664927i	$0.231537\pi$
$434$	8.69247e6	0.00510422
$435$	2.10031e8	0.122341
$436$	5.53807e8	0.320004
$437$	−1.78400e9	−1.02261
$438$	1.24344e9	0.707074
$439$	−1.77473e8	−0.100117	−0.0500584	−	0.998746i	$-0.515941\pi$
$439$	−1.77473e8	−0.100117	−0.0500584	+	0.998746i	$0.515941\pi$
$440$	−7.11440e7	−0.0398156
$441$	−6.00214e8	−0.333251
$442$	−2.62994e8	−0.144867
$443$	1.83781e9	1.00436	0.502178	−	0.864764i	$-0.332532\pi$
$443$	1.83781e9	1.00436	0.502178	+	0.864764i	$0.332532\pi$
$444$	−1.93230e7	−0.0104769
$445$	−5.51724e8	−0.296798
$446$	−1.87110e9	−0.998674
$447$	−1.17395e8	−0.0621690
$448$	4.11964e6	0.00216464
$449$	−8.93570e8	−0.465872	−0.232936	−	0.972492i	$-0.574833\pi$
$449$	−8.93570e8	−0.465872	−0.232936	+	0.972492i	$0.574833\pi$
$450$	5.62435e8	0.290957
$451$	−2.42239e8	−0.124345
$452$	−1.11610e9	−0.568487
$453$	−1.73510e7	−0.00876961
$454$	2.72800e9	1.36820
$455$	−8.89161e6	−0.00442528
$456$	−7.69495e8	−0.380040
$457$	−5.88094e8	−0.288231	−0.144115	−	0.989561i	$-0.546034\pi$
$457$	−5.88094e8	−0.288231	−0.144115	+	0.989561i	$0.546034\pi$
$458$	−1.86713e9	−0.908126
$459$	−8.97993e7	−0.0433440
$460$	5.29960e8	0.253858
$461$	−2.65315e9	−1.26127	−0.630636	−	0.776079i	$-0.717206\pi$
$461$	−2.65315e9	−1.26127	−0.630636	+	0.776079i	$0.717206\pi$
$462$	2.83409e6	0.00133711
$463$	1.10539e9	0.517587	0.258793	−	0.965933i	$-0.416675\pi$
$463$	1.10539e9	0.517587	0.258793	+	0.965933i	$0.416675\pi$
$464$	−1.06583e9	−0.495307
$465$	−1.77714e8	−0.0819667
$466$	−1.88529e9	−0.863033
$467$	6.70125e8	0.304472	0.152236	−	0.988344i	$-0.451353\pi$
$467$	6.70125e8	0.304472	0.152236	+	0.988344i	$0.451353\pi$
$468$	1.92276e8	0.0867091
$469$	2.94792e7	0.0131950
$470$	−2.63073e9	−1.16878
$471$	−1.22720e9	−0.541182
$472$	−1.83835e8	−0.0804694
$473$	9.42140e7	0.0409356
$474$	2.40359e9	1.03666
$475$	−1.77615e9	−0.760418
$476$	4.12050e6	0.00175116
$477$	2.00029e8	0.0843875
$478$	−1.81862e9	−0.761631
$479$	−9.38891e7	−0.0390338	−0.0195169	−	0.999810i	$-0.506213\pi$
$479$	−9.38891e7	−0.0390338	−0.0195169	+	0.999810i	$0.506213\pi$
$480$	6.80683e8	0.280931
$481$	4.71380e7	0.0193136
$482$	−3.45274e9	−1.40443
$483$	2.15917e7	0.00871911
$484$	−1.21526e9	−0.487204
$485$	−9.46931e8	−0.376896
$486$	1.98451e8	0.0784200
$487$	1.37204e9	0.538288	0.269144	−	0.963100i	$-0.413259\pi$
$487$	1.37204e9	0.538288	0.269144	+	0.963100i	$0.413259\pi$
$488$	−1.36739e8	−0.0532626
$489$	−2.46296e9	−0.952525
$490$	−1.70202e9	−0.653550
$491$	3.03791e9	1.15822	0.579108	−	0.815251i	$-0.303401\pi$
$491$	3.03791e9	1.15822	0.579108	+	0.815251i	$0.303401\pi$
$492$	7.78326e8	0.294635
$493$	2.37438e8	0.0892455
$494$	−1.83542e9	−0.685000
$495$	−5.79421e7	−0.0214722
$496$	9.01834e8	0.331849
$497$	−2.55635e7	−0.00934056
$498$	−4.31305e8	−0.156488
$499$	−3.44240e9	−1.24025	−0.620126	−	0.784502i	$-0.712919\pi$
$499$	−3.44240e9	−1.24025	−0.620126	+	0.784502i	$0.712919\pi$
$500$	1.26657e9	0.453142
$501$	1.77253e9	0.629741
$502$	−4.89421e8	−0.172671
$503$	1.03977e8	0.0364291	0.0182146	−	0.999834i	$-0.494202\pi$
$503$	1.03977e8	0.0364291	0.0182146	+	0.999834i	$0.494202\pi$
$504$	9.31321e6	0.00324035
$505$	−1.23866e9	−0.427990
$506$	4.12073e8	0.141399
$507$	1.22516e9	0.417507
$508$	−1.99729e9	−0.675955
$509$	−9.41820e8	−0.316560	−0.158280	−	0.987394i	$-0.550595\pi$
$509$	−9.41820e8	−0.316560	−0.158280	+	0.987394i	$0.550595\pi$
$510$	−2.54643e8	−0.0850034
$511$	4.75253e7	0.0157562
$512$	−1.10782e9	−0.364774
$513$	−6.26703e8	−0.204951
$514$	−6.62604e8	−0.215220
$515$	−2.00241e9	−0.645994
$516$	−3.02714e8	−0.0969971
$517$	−6.76715e8	−0.215372
$518$	−2.23243e6	−0.000705704 0
$519$	3.24934e9	1.02026
$520$	−5.57638e8	−0.173916
$521$	9.49236e8	0.294064	0.147032	−	0.989132i	$-0.453028\pi$
$521$	9.49236e8	0.294064	0.147032	+	0.989132i	$0.453028\pi$
$522$	−5.24725e8	−0.161467
$523$	−3.88735e9	−1.18822	−0.594111	−	0.804383i	$-0.702496\pi$
$523$	−3.88735e9	−1.18822	−0.594111	+	0.804383i	$0.702496\pi$
$524$	−9.76104e8	−0.296372
$525$	2.14968e7	0.00648360
$526$	−5.58280e9	−1.67264
$527$	−2.00904e8	−0.0597933
$528$	2.94034e8	0.0869319
$529$	−2.65425e8	−0.0779555
$530$	5.67220e8	0.165495
$531$	−1.49721e8	−0.0433963
$532$	2.87567e7	0.00828034
$533$	−1.89871e9	−0.543142
$534$	1.37838e9	0.391719
$535$	−1.14300e9	−0.322707
$536$	1.84879e9	0.518574
$537$	3.59550e8	0.100196
$538$	−2.19972e9	−0.609018
$539$	−4.37819e8	−0.120430
$540$	1.86171e8	0.0508783
$541$	−2.42183e9	−0.657588	−0.328794	−	0.944402i	$-0.606642\pi$
$541$	−2.42183e9	−0.657588	−0.328794	+	0.944402i	$0.606642\pi$
$542$	3.64955e9	0.984558
$543$	−3.24707e8	−0.0870345
$544$	7.69505e8	0.204935
$545$	−1.30810e9	−0.346141
$546$	2.22141e7	0.00584055
$547$	5.83350e9	1.52396	0.761980	−	0.647600i	$-0.224227\pi$
$547$	5.83350e9	1.52396	0.761980	+	0.647600i	$0.224227\pi$
$548$	1.73111e8	0.0449359
$549$	−1.11365e8	−0.0287240
$550$	4.10261e8	0.105146
$551$	1.65706e9	0.421996
$552$	1.35413e9	0.342667
$553$	9.18674e7	0.0231006
$554$	−7.02282e9	−1.75480
$555$	4.56412e7	0.0113326
$556$	1.39938e9	0.345282
$557$	2.32049e9	0.568967	0.284484	−	0.958681i	$-0.408178\pi$
$557$	2.32049e9	0.568967	0.284484	+	0.958681i	$0.408178\pi$
$558$	4.43987e8	0.108181
$559$	7.38465e8	0.178809
$560$	4.36888e7	0.0105126
$561$	−6.55029e7	−0.0156636
$562$	−5.55863e9	−1.32096
$563$	−4.30898e9	−1.01764	−0.508821	−	0.860873i	$-0.669918\pi$
$563$	−4.30898e9	−1.01764	−0.508821	+	0.860873i	$0.669918\pi$
$564$	2.17432e9	0.510324
$565$	2.63626e9	0.614919
$566$	1.95753e8	0.0453785
$567$	7.58499e6	0.00174749
$568$	−1.60322e9	−0.367090
$569$	5.58255e9	1.27040	0.635198	−	0.772349i	$-0.280918\pi$
$569$	5.58255e9	1.27040	0.635198	+	0.772349i	$0.280918\pi$
$570$	−1.77714e9	−0.401938
$571$	5.36498e9	1.20598	0.602992	−	0.797747i	$-0.293975\pi$
$571$	5.36498e9	1.20598	0.602992	+	0.797747i	$0.293975\pi$
$572$	1.40253e8	0.0313348
$573$	7.99668e7	0.0177570
$574$	8.99217e7	0.0198460
$575$	3.12560e9	0.685639
$576$	2.10420e8	0.0458784
$577$	4.50669e9	0.976658	0.488329	−	0.872660i	$-0.337607\pi$
$577$	4.50669e9	0.976658	0.488329	+	0.872660i	$0.337607\pi$
$578$	5.38728e9	1.16044
$579$	2.39979e8	0.0513805
$580$	−4.92253e8	−0.104759
$581$	−1.64849e7	−0.00348714
$582$	2.36573e9	0.497434
$583$	1.45908e8	0.0304958
$584$	2.98055e9	0.619230
$585$	−4.54159e8	−0.0937913
$586$	8.20794e8	0.168497
$587$	4.94446e9	1.00899	0.504494	−	0.863415i	$-0.331679\pi$
$587$	4.94446e9	1.00899	0.504494	+	0.863415i	$0.331679\pi$
$588$	1.40673e9	0.285358
$589$	−1.40210e9	−0.282732
$590$	−4.24563e8	−0.0851060
$591$	−1.37162e9	−0.273325
$592$	−2.31612e8	−0.0458812
$593$	7.08369e9	1.39498	0.697490	−	0.716594i	$-0.254300\pi$
$593$	7.08369e9	1.39498	0.697490	+	0.716594i	$0.254300\pi$
$594$	1.44758e8	0.0283393
$595$	−9.73269e6	−0.00189419
$596$	2.75141e8	0.0532345
$597$	−1.07691e9	−0.207142
$598$	3.22989e9	0.617638
$599$	6.53780e9	1.24290	0.621452	−	0.783452i	$-0.286543\pi$
$599$	6.53780e9	1.24290	0.621452	+	0.783452i	$0.286543\pi$
$600$	1.34817e9	0.254810
$601$	−5.66921e9	−1.06528	−0.532638	−	0.846343i	$-0.678799\pi$
$601$	−5.66921e9	−1.06528	−0.532638	+	0.846343i	$0.678799\pi$
$602$	−3.49732e7	−0.00653353
$603$	1.50572e9	0.279661
$604$	4.06657e7	0.00750930
$605$	2.87046e9	0.526997
$606$	3.09458e9	0.564868
$607$	−3.43054e8	−0.0622590	−0.0311295	−	0.999515i	$-0.509910\pi$
$607$	−3.43054e8	−0.0622590	−0.0311295	+	0.999515i	$0.509910\pi$
$608$	5.37032e9	0.969031
$609$	−2.00555e7	−0.00359809
$610$	−3.15796e8	−0.0563316
$611$	−5.30420e9	−0.940753
$612$	2.10464e8	0.0371149
$613$	−1.95826e9	−0.343367	−0.171683	−	0.985152i	$-0.554921\pi$
$613$	−1.95826e9	−0.343367	−0.171683	+	0.985152i	$0.554921\pi$
$614$	−3.66440e9	−0.638872
$615$	−1.83842e9	−0.318699
$616$	6.79340e6	0.00117099
$617$	−1.99932e9	−0.342676	−0.171338	−	0.985212i	$-0.554809\pi$
$617$	−1.99932e9	−0.342676	−0.171338	+	0.985212i	$0.554809\pi$
$618$	5.00267e9	0.852593
$619$	1.57292e9	0.266556	0.133278	−	0.991079i	$-0.457450\pi$
$619$	1.57292e9	0.266556	0.133278	+	0.991079i	$0.457450\pi$
$620$	4.16512e8	0.0701870
$621$	1.10285e9	0.184797
$622$	−3.48202e9	−0.580182
$623$	5.26830e7	0.00872896
$624$	2.30469e9	0.379722
$625$	1.36647e9	0.223882
$626$	−2.47113e9	−0.402611
$627$	−4.57140e8	−0.0740650
$628$	2.87621e9	0.463406
$629$	5.15969e7	0.00826697
$630$	2.15087e7	0.00342706
$631$	3.48635e9	0.552419	0.276209	−	0.961097i	$-0.410922\pi$
$631$	3.48635e9	0.552419	0.276209	+	0.961097i	$0.410922\pi$
$632$	5.76146e9	0.907869
$633$	−2.15234e9	−0.337285
$634$	−1.05464e10	−1.64359
$635$	4.71762e9	0.731165
$636$	−4.68810e8	−0.0722599
$637$	−3.43169e9	−0.526042
$638$	−3.82753e8	−0.0583508
$639$	−1.30571e9	−0.197968
$640$	3.82362e9	0.576561
$641$	3.27300e9	0.490843	0.245422	−	0.969416i	$-0.421074\pi$
$641$	3.27300e9	0.490843	0.245422	+	0.969416i	$0.421074\pi$
$642$	2.85558e9	0.425914
$643$	1.07236e10	1.59075	0.795373	−	0.606120i	$-0.207275\pi$
$643$	1.07236e10	1.59075	0.795373	+	0.606120i	$0.207275\pi$
$644$	−5.06048e7	−0.00746606
$645$	7.15015e8	0.104920
$646$	−2.00903e9	−0.293206
$647$	1.13384e10	1.64584	0.822919	−	0.568159i	$-0.192344\pi$
$647$	1.13384e10	1.64584	0.822919	+	0.568159i	$0.192344\pi$
$648$	4.75693e8	0.0686775
$649$	−1.09212e8	−0.0156825
$650$	3.21569e9	0.459280
$651$	1.69696e7	0.00241067
$652$	5.77248e9	0.815635
$653$	2.78140e9	0.390901	0.195451	−	0.980714i	$-0.437383\pi$
$653$	2.78140e9	0.390901	0.195451	+	0.980714i	$0.437383\pi$
$654$	3.26805e9	0.456842
$655$	2.30557e9	0.320578
$656$	9.32928e9	1.29028
$657$	2.42746e9	0.333944
$658$	2.51204e8	0.0343744
$659$	8.83123e9	1.20205	0.601025	−	0.799230i	$-0.294759\pi$
$659$	8.83123e9	1.20205	0.601025	+	0.799230i	$0.294759\pi$
$660$	1.35800e8	0.0183863
$661$	−5.82485e9	−0.784476	−0.392238	−	0.919864i	$-0.628299\pi$
$661$	−5.82485e9	−0.784476	−0.392238	+	0.919864i	$0.628299\pi$
$662$	−5.45075e9	−0.730219
$663$	−5.13422e8	−0.0684191
$664$	−1.03385e9	−0.137047
$665$	−6.79238e7	−0.00895666
$666$	−1.14026e8	−0.0149570
$667$	−2.91603e9	−0.380497
$668$	−4.15431e9	−0.539239
$669$	−3.65279e9	−0.471664
$670$	4.26974e9	0.548454
$671$	−8.12335e7	−0.0103802
$672$	−6.49970e7	−0.00826230
$673$	3.42844e9	0.433554	0.216777	−	0.976221i	$-0.430446\pi$
$673$	3.42844e9	0.433554	0.216777	+	0.976221i	$0.430446\pi$
$674$	−2.08098e9	−0.261793
$675$	1.09800e9	0.137416
$676$	−2.87142e9	−0.357506
$677$	8.10222e9	1.00356	0.501781	−	0.864995i	$-0.332678\pi$
$677$	8.10222e9	1.00356	0.501781	+	0.864995i	$0.332678\pi$
$678$	−6.58621e9	−0.811580
$679$	9.04206e7	0.0110847
$680$	−6.10386e8	−0.0744429
$681$	5.32565e9	0.646186
$682$	3.23861e8	0.0390943
$683$	1.95901e9	0.235269	0.117634	−	0.993057i	$-0.462469\pi$
$683$	1.95901e9	0.235269	0.117634	+	0.993057i	$0.462469\pi$
$684$	1.46881e9	0.175497
$685$	−4.08892e8	−0.0486061
$686$	3.25086e8	0.0384471
$687$	−3.64505e9	−0.428899
$688$	−3.62844e9	−0.424776
$689$	1.14365e9	0.133207
$690$	3.12733e9	0.362411
$691$	−7.12139e9	−0.821091	−0.410546	−	0.911840i	$-0.634662\pi$
$691$	−7.12139e9	−0.821091	−0.410546	+	0.911840i	$0.634662\pi$
$692$	−7.61552e9	−0.873632
$693$	5.53277e6	0.000631505 0
$694$	−1.55793e10	−1.76925
$695$	−3.30536e9	−0.373484
$696$	−1.25778e9	−0.141407
$697$	−2.07831e9	−0.232486
$698$	3.32833e9	0.370453
$699$	−3.68050e9	−0.407602
$700$	−5.03823e7	−0.00555182
$701$	−9.01916e9	−0.988902	−0.494451	−	0.869206i	$-0.664631\pi$
$701$	−9.01916e9	−0.988902	−0.494451	+	0.869206i	$0.664631\pi$
$702$	1.13463e9	0.123787
$703$	3.60091e8	0.0390903
$704$	1.53488e8	0.0165794
$705$	−5.13577e9	−0.552006
$706$	3.63193e9	0.388437
$707$	1.18278e8	0.0125874
$708$	3.50904e8	0.0371597
$709$	−1.63143e10	−1.71912	−0.859560	−	0.511034i	$-0.829263\pi$
$709$	−1.63143e10	−1.71912	−0.859560	+	0.511034i	$0.829263\pi$
$710$	−3.70260e9	−0.388242
$711$	4.69233e9	0.489604
$712$	3.30402e9	0.343054
$713$	2.46735e9	0.254928
$714$	2.43154e7	0.00249998
$715$	−3.31280e8	−0.0338941
$716$	−8.42684e8	−0.0857964
$717$	−3.55035e9	−0.359711
$718$	−1.81427e8	−0.0182922
$719$	6.12136e9	0.614181	0.307091	−	0.951680i	$-0.400645\pi$
$719$	6.12136e9	0.614181	0.307091	+	0.951680i	$0.400645\pi$
$720$	2.23150e9	0.222810
$721$	1.91207e8	0.0189989
$722$	−1.65829e9	−0.163976
$723$	−6.74051e9	−0.663298
$724$	7.61019e8	0.0745265
$725$	−2.90321e9	−0.282941
$726$	−7.17133e9	−0.695539
$727$	1.56648e9	0.151201	0.0756003	−	0.997138i	$-0.475913\pi$
$727$	1.56648e9	0.151201	0.0756003	+	0.997138i	$0.475913\pi$
$728$	5.32477e7	0.00511495
$729$	3.87420e8	0.0370370
$730$	6.88353e9	0.654910
$731$	8.08318e8	0.0765370
$732$	2.61007e8	0.0245959
$733$	−4.77128e9	−0.447477	−0.223739	−	0.974649i	$-0.571826\pi$
$733$	−4.77128e9	−0.447477	−0.223739	+	0.974649i	$0.571826\pi$
$734$	−3.94592e9	−0.368309
$735$	−3.32272e9	−0.308665
$736$	−9.45046e9	−0.873737
$737$	1.09833e9	0.101064
$738$	4.59295e9	0.420625
$739$	8.82555e8	0.0804427	0.0402213	−	0.999191i	$-0.487194\pi$
$739$	8.82555e8	0.0804427	0.0402213	+	0.999191i	$0.487194\pi$
$740$	−1.06970e8	−0.00970399
$741$	−3.58314e9	−0.323519
$742$	−5.41627e7	−0.00486728
$743$	1.56677e9	0.140134	0.0700672	−	0.997542i	$-0.477679\pi$
$743$	1.56677e9	0.140134	0.0700672	+	0.997542i	$0.477679\pi$
$744$	1.06425e9	0.0947410
$745$	−6.49886e8	−0.0575825
$746$	2.43805e9	0.215009
$747$	−8.42002e8	−0.0739079
$748$	1.53520e8	0.0134125
$749$	1.09143e8	0.00949095
$750$	7.47412e9	0.646912
$751$	5.02135e9	0.432594	0.216297	−	0.976328i	$-0.430602\pi$
$751$	5.02135e9	0.432594	0.216297	+	0.976328i	$0.430602\pi$
$752$	2.60621e10	2.23484
$753$	−9.55458e8	−0.0815510
$754$	−3.00008e9	−0.254879
$755$	−9.60531e7	−0.00812263
$756$	−1.77771e7	−0.00149635
$757$	−2.94352e9	−0.246622	−0.123311	−	0.992368i	$-0.539351\pi$
$757$	−2.94352e9	−0.246622	−0.123311	+	0.992368i	$0.539351\pi$
$758$	2.33980e10	1.95136
$759$	8.04456e8	0.0667815
$760$	−4.25984e9	−0.352002
$761$	−1.87159e10	−1.53945	−0.769724	−	0.638376i	$-0.779606\pi$
$761$	−1.87159e10	−1.53945	−0.769724	+	0.638376i	$0.779606\pi$
$762$	−1.17861e10	−0.965003
$763$	1.24908e8	0.0101801
$764$	−1.87419e8	−0.0152050
$765$	−4.97119e8	−0.0401463
$766$	−2.84650e10	−2.28828
$767$	−8.56023e8	−0.0685017
$768$	−8.55509e9	−0.681491
$769$	−1.08476e10	−0.860187	−0.430093	−	0.902784i	$-0.641519\pi$
$769$	−1.08476e10	−0.860187	−0.430093	+	0.902784i	$0.641519\pi$
$770$	1.56892e7	0.00123847
$771$	−1.29355e9	−0.101647
$772$	−5.62443e8	−0.0439965
$773$	−2.59403e9	−0.201998	−0.100999	−	0.994887i	$-0.532204\pi$
$773$	−2.59403e9	−0.201998	−0.100999	+	0.994887i	$0.532204\pi$
$774$	−1.78634e9	−0.138474
$775$	2.45651e9	0.189567
$776$	5.67073e9	0.435635
$777$	−4.35818e6	−0.000333297 0
$778$	−1.75400e10	−1.33537
$779$	−1.45044e10	−1.09931
$780$	1.06442e9	0.0803122
$781$	−9.52435e8	−0.0715413
$782$	3.53541e9	0.264373
$783$	−1.02438e9	−0.0762595
$784$	1.68616e10	1.24966
$785$	−6.79366e9	−0.501256
$786$	−5.76005e9	−0.423104
$787$	−2.06990e10	−1.51369	−0.756846	−	0.653593i	$-0.773261\pi$
$787$	−2.06990e10	−1.51369	−0.756846	+	0.653593i	$0.773261\pi$
$788$	3.21470e9	0.234044
$789$	−1.08989e10	−0.789971
$790$	1.33060e10	0.960180
$791$	−2.51731e8	−0.0180850
$792$	3.46988e8	0.0248185
$793$	−6.36721e8	−0.0453412
$794$	−2.62953e10	−1.86426
$795$	1.10734e9	0.0781619
$796$	2.52396e9	0.177373
$797$	−6.06784e9	−0.424551	−0.212275	−	0.977210i	$-0.568087\pi$
$797$	−6.06784e9	−0.424551	−0.212275	+	0.977210i	$0.568087\pi$
$798$	1.69695e8	0.0118211
$799$	−5.80594e9	−0.402679
$800$	−9.40891e9	−0.649718
$801$	2.69090e9	0.185005
$802$	2.32819e10	1.59370
$803$	1.77068e9	0.120680
$804$	−3.52897e9	−0.239470
$805$	1.19529e8	0.00807586
$806$	2.53847e9	0.170765
$807$	−4.29434e9	−0.287633
$808$	7.41778e9	0.494691
$809$	−2.20534e10	−1.46438	−0.732192	−	0.681098i	$-0.761503\pi$
$809$	−2.20534e10	−1.46438	−0.732192	+	0.681098i	$0.761503\pi$
$810$	1.09860e9	0.0726346
$811$	9.91610e9	0.652782	0.326391	−	0.945235i	$-0.394167\pi$
$811$	9.91610e9	0.652782	0.326391	+	0.945235i	$0.394167\pi$
$812$	4.70043e7	0.00308100
$813$	7.12472e9	0.464998
$814$	−8.31749e7	−0.00540514
$815$	−1.36347e10	−0.882253
$816$	2.52269e9	0.162536
$817$	5.64119e9	0.361904
$818$	−1.48561e9	−0.0949007
$819$	4.33668e7	0.00275844
$820$	4.30873e9	0.272898
$821$	−4.09876e9	−0.258495	−0.129247	−	0.991612i	$-0.541256\pi$
$821$	−4.09876e9	−0.258495	−0.129247	+	0.991612i	$0.541256\pi$
$822$	1.02154e9	0.0641512
$823$	−6.76087e9	−0.422769	−0.211384	−	0.977403i	$-0.567797\pi$
$823$	−6.76087e9	−0.422769	−0.211384	+	0.977403i	$0.567797\pi$
$824$	1.19915e10	0.746671
$825$	8.00919e8	0.0496592
$826$	4.05407e7	0.00250300
$827$	9.41705e8	0.0578956	0.0289478	−	0.999581i	$-0.490784\pi$
$827$	9.41705e8	0.0578956	0.0289478	+	0.999581i	$0.490784\pi$
$828$	−2.58476e9	−0.158239
$829$	1.36525e10	0.832284	0.416142	−	0.909300i	$-0.363382\pi$
$829$	1.36525e10	0.832284	0.416142	+	0.909300i	$0.363382\pi$
$830$	−2.38766e9	−0.144943
$831$	−1.37101e10	−0.828775
$832$	1.20306e9	0.0724197
$833$	−3.75630e9	−0.225166
$834$	8.25783e9	0.492930
$835$	9.81253e9	0.583282
$836$	1.07141e9	0.0634209
$837$	8.66761e8	0.0510928
$838$	−3.26981e9	−0.191942
$839$	−2.04480e10	−1.19532	−0.597660	−	0.801750i	$-0.703903\pi$
$839$	−2.04480e10	−1.19532	−0.597660	+	0.801750i	$0.703903\pi$
$840$	5.15569e7	0.00300130
$841$	−1.45413e10	−0.842981
$842$	2.36618e10	1.36602
$843$	−1.08517e10	−0.623878
$844$	5.04446e9	0.288813
$845$	6.78233e9	0.386706
$846$	1.28308e10	0.728546
$847$	−2.74095e8	−0.0154992
$848$	−5.61932e9	−0.316445
$849$	3.82152e8	0.0214318
$850$	3.51987e9	0.196590
$851$	−6.33673e8	−0.0352461
$852$	3.06022e9	0.169517
$853$	9.28799e9	0.512389	0.256195	−	0.966625i	$-0.417531\pi$
$853$	9.28799e9	0.512389	0.256195	+	0.966625i	$0.417531\pi$
$854$	3.01547e7	0.00165673
$855$	−3.46936e9	−0.189831
$856$	6.84490e9	0.373000
$857$	−7.57637e9	−0.411177	−0.205588	−	0.978639i	$-0.565911\pi$
$857$	−7.57637e9	−0.411177	−0.205588	+	0.978639i	$0.565911\pi$
$858$	8.27644e8	0.0447340
$859$	5.27186e9	0.283784	0.141892	−	0.989882i	$-0.454681\pi$
$859$	5.27186e9	0.283784	0.141892	+	0.989882i	$0.454681\pi$
$860$	−1.67579e9	−0.0898412
$861$	1.75547e8	0.00937308
$862$	−8.93517e9	−0.475146
$863$	2.11332e10	1.11925	0.559625	−	0.828746i	$-0.310945\pi$
$863$	2.11332e10	1.11925	0.559625	+	0.828746i	$0.310945\pi$
$864$	−3.31987e9	−0.175115
$865$	1.79880e10	0.944988
$866$	−3.49012e10	−1.82611
$867$	1.05172e10	0.548064
$868$	−3.97719e7	−0.00206423
$869$	3.42276e9	0.176932
$870$	−2.90482e9	−0.149555
$871$	8.60885e9	0.441450
$872$	7.83360e9	0.400086
$873$	4.61843e9	0.234933
$874$	2.46734e10	1.25008
$875$	2.85668e8	0.0144156
$876$	−5.68928e9	−0.285952
$877$	1.67780e10	0.839928	0.419964	−	0.907541i	$-0.362043\pi$
$877$	1.67780e10	0.839928	0.419964	+	0.907541i	$0.362043\pi$
$878$	2.45453e9	0.122387
$879$	1.60237e9	0.0795796
$880$	1.62774e9	0.0805186
$881$	4.60252e9	0.226767	0.113384	−	0.993551i	$-0.463831\pi$
$881$	4.60252e9	0.226767	0.113384	+	0.993551i	$0.463831\pi$
$882$	8.30121e9	0.407382
$883$	−1.60291e10	−0.783515	−0.391758	−	0.920068i	$-0.628133\pi$
$883$	−1.60291e10	−0.783515	−0.391758	+	0.920068i	$0.628133\pi$
$884$	1.20332e9	0.0585864
$885$	−8.28840e8	−0.0401948
$886$	−2.54177e10	−1.22777
$887$	−3.53761e10	−1.70207	−0.851034	−	0.525111i	$-0.824024\pi$
$887$	−3.53761e10	−1.70207	−0.851034	+	0.525111i	$0.824024\pi$
$888$	−2.73324e8	−0.0130988
$889$	−4.50477e8	−0.0215038
$890$	7.63057e9	0.362820
$891$	2.82599e8	0.0133844
$892$	8.56109e9	0.403880
$893$	−4.05192e10	−1.90406
$894$	1.62362e9	0.0759983
$895$	1.99043e9	0.0928040
$896$	−3.65110e8	−0.0169569
$897$	6.30546e9	0.291704
$898$	1.23584e10	0.569504
$899$	−2.29180e9	−0.105200
$900$	−2.57339e9	−0.117668
$901$	1.25183e9	0.0570177
$902$	3.35027e9	0.152005
$903$	−6.82754e7	−0.00308572
$904$	−1.57873e10	−0.710753
$905$	−1.79754e9	−0.0806136
$906$	2.39971e8	0.0107204
$907$	−6.61497e9	−0.294376	−0.147188	−	0.989109i	$-0.547022\pi$
$907$	−6.61497e9	−0.294376	−0.147188	+	0.989109i	$0.547022\pi$
$908$	−1.24818e10	−0.553320
$909$	6.04130e9	0.266782
$910$	1.22975e8	0.00540967
$911$	1.46424e10	0.641651	0.320826	−	0.947138i	$-0.396040\pi$
$911$	1.46424e10	0.641651	0.320826	+	0.947138i	$0.396040\pi$
$912$	1.76057e10	0.768549
$913$	−6.14187e8	−0.0267087
$914$	8.13359e9	0.352347
$915$	−6.16503e8	−0.0266049
$916$	8.54297e9	0.367261
$917$	−2.20155e8	−0.00942834
$918$	1.24196e9	0.0529857
$919$	4.03688e10	1.71570	0.857850	−	0.513901i	$-0.171800\pi$
$919$	4.03688e10	1.71570	0.857850	+	0.513901i	$0.171800\pi$
$920$	7.49629e9	0.317387
$921$	−7.15371e9	−0.301733
$922$	3.66942e10	1.54184
$923$	−7.46534e9	−0.312495
$924$	−1.29672e7	−0.000540749 0
$925$	−6.30887e8	−0.0262093
$926$	−1.52880e10	−0.632723
$927$	9.76630e9	0.402672
$928$	8.77806e9	0.360563
$929$	−2.36038e10	−0.965889	−0.482945	−	0.875651i	$-0.660433\pi$
$929$	−2.36038e10	−0.965889	−0.482945	+	0.875651i	$0.660433\pi$
$930$	2.45786e9	0.100200
$931$	−2.62150e10	−1.06470
$932$	8.62604e9	0.349024
$933$	−6.79766e9	−0.274015
$934$	−9.26811e9	−0.372200
$935$	−3.62617e8	−0.0145080
$936$	2.71975e9	0.108408
$937$	2.58838e10	1.02787	0.513937	−	0.857828i	$-0.328186\pi$
$937$	2.58838e10	1.02787	0.513937	+	0.857828i	$0.328186\pi$
$938$	−4.07709e8	−0.0161302
$939$	−4.82419e9	−0.190149
$940$	1.20368e10	0.472675
$941$	1.53080e10	0.598902	0.299451	−	0.954112i	$-0.403196\pi$
$941$	1.53080e10	0.598902	0.299451	+	0.954112i	$0.403196\pi$
$942$	1.69727e10	0.661566
$943$	2.55242e10	0.991201
$944$	4.20606e9	0.162732
$945$	4.19897e7	0.00161857
$946$	−1.30302e9	−0.0500417
$947$	9.43008e9	0.360820	0.180410	−	0.983592i	$-0.442258\pi$
$947$	9.43008e9	0.360820	0.180410	+	0.983592i	$0.442258\pi$
$948$	−1.09975e10	−0.419241
$949$	1.38789e10	0.527136
$950$	2.45649e10	0.929571
$951$	−2.05890e10	−0.776253
$952$	5.82846e7	0.00218940
$953$	−2.53714e10	−0.949555	−0.474777	−	0.880106i	$-0.657471\pi$
$953$	−2.53714e10	−0.949555	−0.474777	+	0.880106i	$0.657471\pi$
$954$	−2.76648e9	−0.103159
$955$	4.42687e8	0.0164469
$956$	8.32100e9	0.308016
$957$	−7.47219e8	−0.0275585
$958$	1.29853e9	0.0477168
$959$	3.90442e7	0.00142953
$960$	1.16486e9	0.0424937
$961$	−2.55734e10	−0.929517
$962$	−6.51938e8	−0.0236099
$963$	5.57472e9	0.201155
$964$	1.57978e10	0.567973
$965$	1.32850e9	0.0475900
$966$	−2.98622e8	−0.0106587
$967$	−2.23509e10	−0.794883	−0.397442	−	0.917627i	$-0.630102\pi$
$967$	−2.23509e10	−0.794883	−0.397442	+	0.917627i	$0.630102\pi$
$968$	−1.71899e10	−0.609128
$969$	−3.92208e9	−0.138479
$970$	1.30964e10	0.460736
$971$	−2.51106e10	−0.880217	−0.440108	−	0.897945i	$-0.645060\pi$
$971$	−2.51106e10	−0.880217	−0.440108	+	0.897945i	$0.645060\pi$
$972$	−9.08003e8	−0.0317143
$973$	3.15622e8	0.0109843
$974$	−1.89758e10	−0.658028
$975$	6.27773e9	0.216914
$976$	3.12852e9	0.107712
$977$	−1.40783e10	−0.482970	−0.241485	−	0.970405i	$-0.577634\pi$
$977$	−1.40783e10	−0.482970	−0.241485	+	0.970405i	$0.577634\pi$
$978$	3.40638e10	1.16441
$979$	1.96284e9	0.0668569
$980$	7.78751e9	0.264306
$981$	6.37995e9	0.215762
$982$	−4.20155e10	−1.41586
$983$	−4.03081e10	−1.35349	−0.676744	−	0.736218i	$-0.736610\pi$
$983$	−4.03081e10	−1.35349	−0.676744	+	0.736218i	$0.736610\pi$
$984$	1.10094e10	0.368368
$985$	−7.59316e9	−0.253160
$986$	−3.28387e9	−0.109098
$987$	4.90404e8	0.0162347
$988$	8.39785e9	0.277025
$989$	−9.92713e9	−0.326315
$990$	8.01363e8	0.0262486
$991$	5.94799e10	1.94139	0.970694	−	0.240318i	$-0.0772517\pi$
$991$	5.94799e10	1.94139	0.970694	+	0.240318i	$0.0772517\pi$
$992$	−7.42741e9	−0.241572
$993$	−1.06411e10	−0.344876
$994$	3.53554e8	0.0114183
$995$	−5.96163e9	−0.191860
$996$	1.97341e9	0.0632863
$997$	1.24113e10	0.396630	0.198315	−	0.980138i	$-0.436453\pi$
$997$	1.24113e10	0.396630	0.198315	+	0.980138i	$0.436453\pi$
$998$	4.76099e10	1.51614
$999$	−2.22604e8	−0.00706405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.c.1.4	✓	17
3.2	odd	2		531.8.a.c.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.4	✓	17	1.1	even	1	trivial
531.8.a.c.1.14		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)

\(f(q)\)	\(=\)	\(q-13.8304 q^{2} -27.0000 q^{3} +63.2803 q^{4} -149.469 q^{5} +373.421 q^{6} +14.2725 q^{7} +895.100 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-13.8304 q^{2} -27.0000 q^{3} +63.2803 q^{4} -149.469 q^{5} +373.421 q^{6} +14.2725 q^{7} +895.100 q^{8} +729.000 q^{9} +2067.22 q^{10} +531.760 q^{11} -1708.57 q^{12} +4168.02 q^{13} -197.395 q^{14} +4035.66 q^{15} -20479.5 q^{16} +4562.28 q^{17} -10082.4 q^{18} +31839.8 q^{19} -9458.44 q^{20} -385.358 q^{21} -7354.45 q^{22} -56030.4 q^{23} -24167.7 q^{24} -55784.0 q^{25} -57645.4 q^{26} -19683.0 q^{27} +903.168 q^{28} +52043.8 q^{29} -55814.9 q^{30} -44036.0 q^{31} +168667. q^{32} -14357.5 q^{33} -63098.2 q^{34} -2133.30 q^{35} +46131.3 q^{36} +11309.5 q^{37} -440358. q^{38} -112536. q^{39} -133790. q^{40} -455543. q^{41} +5329.65 q^{42} +177174. q^{43} +33649.9 q^{44} -108963. q^{45} +774923. q^{46} -1.27260e6 q^{47} +552946. q^{48} -823339. q^{49} +771516. q^{50} -123182. q^{51} +263753. q^{52} +274388. q^{53} +272224. q^{54} -79481.6 q^{55} +12775.3 q^{56} -859675. q^{57} -719787. q^{58} -205379. q^{59} +255378. q^{60} -152764. q^{61} +609036. q^{62} +10404.7 q^{63} +288642. q^{64} -622989. q^{65} +198570. q^{66} +2.06545e6 q^{67} +288702. q^{68} +1.51282e6 q^{69} +29504.4 q^{70} -1.79110e6 q^{71} +652528. q^{72} +3.32985e6 q^{73} -156414. q^{74} +1.50617e6 q^{75} +2.01483e6 q^{76} +7589.54 q^{77} +1.55643e6 q^{78} +6.43667e6 q^{79} +3.06105e6 q^{80} +531441. q^{81} +6.30035e6 q^{82} -1.15501e6 q^{83} -24385.5 q^{84} -681919. q^{85} -2.45039e6 q^{86} -1.40518e6 q^{87} +475978. q^{88} +3.69123e6 q^{89} +1.50700e6 q^{90} +59488.0 q^{91} -3.54562e6 q^{92} +1.18897e6 q^{93} +1.76005e7 q^{94} -4.75907e6 q^{95} -4.55400e6 q^{96} +6.33530e6 q^{97} +1.13871e7 q^{98} +387653. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 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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