LMFDB - Embedded newform 177.8.a.c.1.14

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			1.14
Root			$15.1891$ 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)

$f(q)$	$=$	$q+15.1891 q^{2} -27.0000 q^{3} +102.710 q^{4} -418.807 q^{5} -410.107 q^{6} -814.653 q^{7} -384.131 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+15.1891 q^{2} -27.0000 q^{3} +102.710 q^{4} -418.807 q^{5} -410.107 q^{6} -814.653 q^{7} -384.131 q^{8} +729.000 q^{9} -6361.32 q^{10} -2422.96 q^{11} -2773.17 q^{12} +10673.2 q^{13} -12373.9 q^{14} +11307.8 q^{15} -18981.5 q^{16} -26705.4 q^{17} +11072.9 q^{18} +33854.6 q^{19} -43015.7 q^{20} +21995.6 q^{21} -36802.7 q^{22} +15069.2 q^{23} +10371.5 q^{24} +97274.0 q^{25} +162116. q^{26} -19683.0 q^{27} -83673.1 q^{28} +32501.7 q^{29} +171756. q^{30} +26459.3 q^{31} -239144. q^{32} +65420.0 q^{33} -405632. q^{34} +341182. q^{35} +74875.7 q^{36} +497796. q^{37} +514222. q^{38} -288176. q^{39} +160877. q^{40} +366715. q^{41} +334095. q^{42} +493861. q^{43} -248863. q^{44} -305310. q^{45} +228889. q^{46} -825019. q^{47} +512501. q^{48} -159884. q^{49} +1.47751e6 q^{50} +721046. q^{51} +1.09624e6 q^{52} -1.78313e6 q^{53} -298968. q^{54} +1.01475e6 q^{55} +312933. q^{56} -914074. q^{57} +493673. q^{58} -205379. q^{59} +1.16142e6 q^{60} +628605. q^{61} +401894. q^{62} -593882. q^{63} -1.20276e6 q^{64} -4.46999e6 q^{65} +993674. q^{66} +1.85849e6 q^{67} -2.74292e6 q^{68} -406870. q^{69} +5.18226e6 q^{70} +3.64832e6 q^{71} -280032. q^{72} +5.50965e6 q^{73} +7.56110e6 q^{74} -2.62640e6 q^{75} +3.47721e6 q^{76} +1.97387e6 q^{77} -4.37714e6 q^{78} -6.04365e6 q^{79} +7.94959e6 q^{80} +531441. q^{81} +5.57009e6 q^{82} -4.72119e6 q^{83} +2.25917e6 q^{84} +1.11844e7 q^{85} +7.50133e6 q^{86} -877545. q^{87} +930735. q^{88} -875348. q^{89} -4.63740e6 q^{90} -8.69493e6 q^{91} +1.54776e6 q^{92} -714401. q^{93} -1.25313e7 q^{94} -1.41785e7 q^{95} +6.45690e6 q^{96} -1.26140e7 q^{97} -2.42850e6 q^{98} -1.76634e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	15.1891	1.34254	0.671272	−	0.741211i	$-0.265748\pi$
$2$	15.1891	1.34254	0.671272	+	0.741211i	$0.265748\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	102.710	0.802423
$5$	−418.807	−1.49837	−0.749184	−	0.662362i	$-0.769554\pi$
$5$	−418.807	−1.49837	−0.749184	+	0.662362i	$0.769554\pi$
$6$	−410.107	−0.775118
$7$	−814.653	−0.897696	−0.448848	−	0.893608i	$-0.648166\pi$
$7$	−814.653	−0.897696	−0.448848	+	0.893608i	$0.648166\pi$
$8$	−384.131	−0.265256
$9$	729.000	0.333333
$10$	−6361.32	−2.01162
$11$	−2422.96	−0.548874	−0.274437	−	0.961605i	$-0.588491\pi$
$11$	−2422.96	−0.548874	−0.274437	+	0.961605i	$0.588491\pi$
$12$	−2773.17	−0.463279
$13$	10673.2	1.34738	0.673692	−	0.739012i	$-0.264707\pi$
$13$	10673.2	1.34738	0.673692	+	0.739012i	$0.264707\pi$
$14$	−12373.9	−1.20520
$15$	11307.8	0.865083
$16$	−18981.5	−1.15854
$17$	−26705.4	−1.31834	−0.659171	−	0.751993i	$-0.729093\pi$
$17$	−26705.4	−1.31834	−0.659171	+	0.751993i	$0.729093\pi$
$18$	11072.9	0.447515
$19$	33854.6	1.13235	0.566174	−	0.824286i	$-0.308423\pi$
$19$	33854.6	1.13235	0.566174	+	0.824286i	$0.308423\pi$
$20$	−43015.7	−1.20233
$21$	21995.6	0.518285
$22$	−36802.7	−0.736887
$23$	15069.2	0.258252	0.129126	−	0.991628i	$-0.458783\pi$
$23$	15069.2	0.258252	0.129126	+	0.991628i	$0.458783\pi$
$24$	10371.5	0.153145
$25$	97274.0	1.24511
$26$	162116.	1.80892
$27$	−19683.0	−0.192450
$28$	−83673.1	−0.720332
$29$	32501.7	0.247464	0.123732	−	0.992316i	$-0.460514\pi$
$29$	32501.7	0.247464	0.123732	+	0.992316i	$0.460514\pi$
$30$	171756.	1.16141
$31$	26459.3	0.159519	0.0797594	−	0.996814i	$-0.474585\pi$
$31$	26459.3	0.159519	0.0797594	+	0.996814i	$0.474585\pi$
$32$	−239144.	−1.29014
$33$	65420.0	0.316892
$34$	−405632.	−1.76993
$35$	341182.	1.34508
$36$	74875.7	0.267474
$37$	497796.	1.61564	0.807822	−	0.589427i	$-0.200646\pi$
$37$	497796.	1.61564	0.807822	+	0.589427i	$0.200646\pi$
$38$	514222.	1.52023
$39$	−288176.	−0.777913
$40$	160877.	0.397451
$41$	366715.	0.830970	0.415485	−	0.909600i	$-0.363612\pi$
$41$	366715.	0.830970	0.415485	+	0.909600i	$0.363612\pi$
$42$	334095.	0.695820
$43$	493861.	0.947251	0.473626	−	0.880726i	$-0.342945\pi$
$43$	493861.	0.947251	0.473626	+	0.880726i	$0.342945\pi$
$44$	−248863.	−0.440429
$45$	−305310.	−0.499456
$46$	228889.	0.346715
$47$	−825019.	−1.15910	−0.579550	−	0.814936i	$-0.696772\pi$
$47$	−825019.	−1.15910	−0.579550	+	0.814936i	$0.696772\pi$
$48$	512501.	0.668884
$49$	−159884.	−0.194142
$50$	1.47751e6	1.67161
$51$	721046.	0.761145
$52$	1.09624e6	1.08117
$53$	−1.78313e6	−1.64520	−0.822598	−	0.568624i	$-0.807476\pi$
$53$	−1.78313e6	−1.64520	−0.822598	+	0.568624i	$0.807476\pi$
$54$	−298968.	−0.258373
$55$	1.01475e6	0.822415
$56$	312933.	0.238119
$57$	−914074.	−0.653761
$58$	493673.	0.332232
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	1.16142e6	0.694163
$61$	628605.	0.354587	0.177294	−	0.984158i	$-0.443266\pi$
$61$	628605.	0.354587	0.177294	+	0.984158i	$0.443266\pi$
$62$	401894.	0.214161
$63$	−593882.	−0.299232
$64$	−1.20276e6	−0.573522
$65$	−4.46999e6	−2.01888
$66$	993674.	0.425442
$67$	1.85849e6	0.754915	0.377458	−	0.926027i	$-0.376798\pi$
$67$	1.85849e6	0.754915	0.377458	+	0.926027i	$0.376798\pi$
$68$	−2.74292e6	−1.05787
$69$	−406870.	−0.149102
$70$	5.18226e6	1.80583
$71$	3.64832e6	1.20973	0.604865	−	0.796328i	$-0.293227\pi$
$71$	3.64832e6	1.20973	0.604865	+	0.796328i	$0.293227\pi$
$72$	−280032.	−0.0884185
$73$	5.50965e6	1.65765	0.828827	−	0.559505i	$-0.189009\pi$
$73$	5.50965e6	1.65765	0.828827	+	0.559505i	$0.189009\pi$
$74$	7.56110e6	2.16907
$75$	−2.62640e6	−0.718863
$76$	3.47721e6	0.908622
$77$	1.97387e6	0.492722
$78$	−4.37714e6	−1.04438
$79$	−6.04365e6	−1.37913	−0.689564	−	0.724224i	$-0.742198\pi$
$79$	−6.04365e6	−1.37913	−0.689564	+	0.724224i	$0.742198\pi$
$80$	7.94959e6	1.73592
$81$	531441.	0.111111
$82$	5.57009e6	1.11561
$83$	−4.72119e6	−0.906313	−0.453156	−	0.891431i	$-0.649702\pi$
$83$	−4.72119e6	−0.906313	−0.453156	+	0.891431i	$0.649702\pi$
$84$	2.25917e6	0.415884
$85$	1.11844e7	1.97536
$86$	7.50133e6	1.27173
$87$	−877545.	−0.142874
$88$	930735.	0.145592
$89$	−875348.	−0.131618	−0.0658091	−	0.997832i	$-0.520963\pi$
$89$	−875348.	−0.131618	−0.0658091	+	0.997832i	$0.520963\pi$
$90$	−4.63740e6	−0.670541
$91$	−8.69493e6	−1.20954
$92$	1.54776e6	0.207228
$93$	−714401.	−0.0920983
$94$	−1.25313e7	−1.55614
$95$	−1.41785e7	−1.69667
$96$	6.45690e6	0.744860
$97$	−1.26140e7	−1.40331	−0.701653	−	0.712519i	$-0.747554\pi$
$97$	−1.26140e7	−1.40331	−0.701653	+	0.712519i	$0.747554\pi$
$98$	−2.42850e6	−0.260644
$99$	−1.76634e6	−0.182958
$100$	9.99103e6	0.999103
$101$	1.43083e6	0.138185	0.0690926	−	0.997610i	$-0.477990\pi$
$101$	1.43083e6	0.138185	0.0690926	+	0.997610i	$0.477990\pi$
$102$	1.09521e7	1.02187
$103$	5.60899e6	0.505772	0.252886	−	0.967496i	$-0.418620\pi$
$103$	5.60899e6	0.505772	0.252886	+	0.967496i	$0.418620\pi$
$104$	−4.09990e6	−0.357401
$105$	−9.21191e6	−0.776582
$106$	−2.70842e7	−2.20875
$107$	2.17512e7	1.71648	0.858241	−	0.513247i	$-0.171558\pi$
$107$	2.17512e7	1.71648	0.858241	+	0.513247i	$0.171558\pi$
$108$	−2.02164e6	−0.154426
$109$	−9.32545e6	−0.689727	−0.344863	−	0.938653i	$-0.612075\pi$
$109$	−9.32545e6	−0.689727	−0.344863	+	0.938653i	$0.612075\pi$
$110$	1.54132e7	1.10413
$111$	−1.34405e7	−0.932792
$112$	1.54634e7	1.04002
$113$	1.50397e7	0.980537	0.490268	−	0.871572i	$-0.336899\pi$
$113$	1.50397e7	0.980537	0.490268	+	0.871572i	$0.336899\pi$
$114$	−1.38840e7	−0.877703
$115$	−6.31110e6	−0.386957
$116$	3.33825e6	0.198571
$117$	7.78074e6	0.449128
$118$	−3.11953e6	−0.174784
$119$	2.17556e7	1.18347
$120$	−4.34367e6	−0.229468
$121$	−1.36164e7	−0.698738
$122$	9.54797e6	0.476049
$123$	−9.90131e6	−0.479761
$124$	2.71764e6	0.128002
$125$	−8.01973e6	−0.367261
$126$	−9.02056e6	−0.401732
$127$	1.78413e7	0.772883	0.386441	−	0.922314i	$-0.373704\pi$
$127$	1.78413e7	0.772883	0.386441	+	0.922314i	$0.373704\pi$
$128$	1.23415e7	0.520156
$129$	−1.33342e7	−0.546896
$130$	−6.78954e7	−2.71043
$131$	3.78349e6	0.147043	0.0735214	−	0.997294i	$-0.476576\pi$
$131$	3.78349e6	0.147043	0.0735214	+	0.997294i	$0.476576\pi$
$132$	6.71930e6	0.254282
$133$	−2.75797e7	−1.01650
$134$	2.82289e7	1.01351
$135$	8.24337e6	0.288361
$136$	1.02584e7	0.349697
$137$	−2.85640e7	−0.949069	−0.474534	−	0.880237i	$-0.657384\pi$
$137$	−2.85640e7	−0.949069	−0.474534	+	0.880237i	$0.657384\pi$
$138$	−6.18000e6	−0.200176
$139$	3.44323e7	1.08746	0.543731	−	0.839260i	$-0.317011\pi$
$139$	3.44323e7	1.08746	0.543731	+	0.839260i	$0.317011\pi$
$140$	3.50429e7	1.07932
$141$	2.22755e7	0.669207
$142$	5.54148e7	1.62412
$143$	−2.58607e7	−0.739544
$144$	−1.38375e7	−0.386180
$145$	−1.36119e7	−0.370793
$146$	8.36868e7	2.22547
$147$	4.31687e6	0.112088
$148$	5.11287e7	1.29643
$149$	4.80665e6	0.119039	0.0595196	−	0.998227i	$-0.481043\pi$
$149$	4.80665e6	0.119039	0.0595196	+	0.998227i	$0.481043\pi$
$150$	−3.98927e7	−0.965105
$151$	−5.09354e6	−0.120393	−0.0601964	−	0.998187i	$-0.519173\pi$
$151$	−5.09354e6	−0.120393	−0.0601964	+	0.998187i	$0.519173\pi$
$152$	−1.30046e7	−0.300362
$153$	−1.94682e7	−0.439447
$154$	2.99815e7	0.661500
$155$	−1.10813e7	−0.239018
$156$	−2.95986e7	−0.624215
$157$	2.01246e7	0.415028	0.207514	−	0.978232i	$-0.433463\pi$
$157$	2.01246e7	0.415028	0.207514	+	0.978232i	$0.433463\pi$
$158$	−9.17980e7	−1.85154
$159$	4.81445e7	0.949854
$160$	1.00155e8	1.93310
$161$	−1.22762e7	−0.231832
$162$	8.07213e6	0.149172
$163$	−6.76023e7	−1.22266	−0.611328	−	0.791377i	$-0.709365\pi$
$163$	−6.76023e7	−1.22266	−0.611328	+	0.791377i	$0.709365\pi$
$164$	3.76654e7	0.666790
$165$	−2.73983e7	−0.474821
$166$	−7.17108e7	−1.21676
$167$	1.10791e8	1.84076	0.920382	−	0.391020i	$-0.127878\pi$
$167$	1.10791e8	1.84076	0.920382	+	0.391020i	$0.127878\pi$
$168$	−8.44920e6	−0.137478
$169$	5.11680e7	0.815446
$170$	1.69881e8	2.65201
$171$	2.46800e7	0.377449
$172$	5.07245e7	0.760096
$173$	1.14352e8	1.67912	0.839559	−	0.543269i	$-0.182814\pi$
$173$	1.14352e8	1.67912	0.839559	+	0.543269i	$0.182814\pi$
$174$	−1.33292e7	−0.191814
$175$	−7.92445e7	−1.11773
$176$	4.59915e7	0.635892
$177$	5.54523e6	0.0751646
$178$	−1.32958e7	−0.176703
$179$	−1.89246e7	−0.246627	−0.123313	−	0.992368i	$-0.539352\pi$
$179$	−1.89246e7	−0.246627	−0.123313	+	0.992368i	$0.539352\pi$
$180$	−3.13584e7	−0.400775
$181$	9.30564e7	1.16646	0.583232	−	0.812306i	$-0.301788\pi$
$181$	9.30564e7	1.16646	0.583232	+	0.812306i	$0.301788\pi$
$182$	−1.32069e8	−1.62386
$183$	−1.69723e7	−0.204721
$184$	−5.78857e6	−0.0685029
$185$	−2.08480e8	−2.42083
$186$	−1.08511e7	−0.123646
$187$	6.47062e7	0.723603
$188$	−8.47378e7	−0.930089
$189$	1.60348e7	0.172762
$190$	−2.15360e8	−2.27786
$191$	1.28269e8	1.33200	0.666001	−	0.745951i	$-0.268005\pi$
$191$	1.28269e8	1.33200	0.666001	+	0.745951i	$0.268005\pi$
$192$	3.24746e7	0.331123
$193$	−7.49379e7	−0.750327	−0.375164	−	0.926959i	$-0.622413\pi$
$193$	−7.49379e7	−0.750327	−0.375164	+	0.926959i	$0.622413\pi$
$194$	−1.91596e8	−1.88400
$195$	1.20690e8	1.16560
$196$	−1.64217e7	−0.155784
$197$	−1.42886e8	−1.33155	−0.665775	−	0.746152i	$-0.731899\pi$
$197$	−1.42886e8	−1.33155	−0.665775	+	0.746152i	$0.731899\pi$
$198$	−2.68292e7	−0.245629
$199$	−7.59209e7	−0.682929	−0.341465	−	0.939895i	$-0.610923\pi$
$199$	−7.59209e7	−0.682929	−0.341465	+	0.939895i	$0.610923\pi$
$200$	−3.73660e7	−0.330272
$201$	−5.01792e7	−0.435851
$202$	2.17330e7	0.185520
$203$	−2.64776e7	−0.222148
$204$	7.40587e7	0.610760
$205$	−1.53583e8	−1.24510
$206$	8.51958e7	0.679021
$207$	1.09855e7	0.0860841
$208$	−2.02593e8	−1.56100
$209$	−8.20284e7	−0.621516
$210$	−1.39921e8	−1.04260
$211$	−6.90924e7	−0.506339	−0.253170	−	0.967422i	$-0.581473\pi$
$211$	−6.90924e7	−0.506339	−0.253170	+	0.967422i	$0.581473\pi$
$212$	−1.83146e8	−1.32014
$213$	−9.85046e7	−0.698438
$214$	3.30381e8	2.30445
$215$	−2.06832e8	−1.41933
$216$	7.56085e6	0.0510485
$217$	−2.15551e7	−0.143199
$218$	−1.41646e8	−0.925988
$219$	−1.48760e8	−0.957047
$220$	1.04225e8	0.659925
$221$	−2.85031e8	−1.77631
$222$	−2.04150e8	−1.25231
$223$	−2.23657e8	−1.35057	−0.675284	−	0.737558i	$-0.735979\pi$
$223$	−2.23657e8	−1.35057	−0.675284	+	0.737558i	$0.735979\pi$
$224$	1.94820e8	1.15815
$225$	7.09127e7	0.415036
$226$	2.28440e8	1.31641
$227$	−2.62570e7	−0.148989	−0.0744945	−	0.997221i	$-0.523734\pi$
$227$	−2.62570e7	−0.148989	−0.0744945	+	0.997221i	$0.523734\pi$
$228$	−9.38847e7	−0.524593
$229$	2.78378e8	1.53183	0.765916	−	0.642940i	$-0.222286\pi$
$229$	2.78378e8	1.53183	0.765916	+	0.642940i	$0.222286\pi$
$230$	−9.58602e7	−0.519507
$231$	−5.32946e7	−0.284473
$232$	−1.24849e7	−0.0656413
$233$	4.33659e7	0.224596	0.112298	−	0.993675i	$-0.464179\pi$
$233$	4.33659e7	0.224596	0.112298	+	0.993675i	$0.464179\pi$
$234$	1.18183e8	0.602974
$235$	3.45523e8	1.73676
$236$	−2.10945e7	−0.104467
$237$	1.63179e8	0.796240
$238$	3.30449e8	1.58886
$239$	−3.28872e8	−1.55824	−0.779120	−	0.626875i	$-0.784334\pi$
$239$	−3.28872e8	−1.55824	−0.779120	+	0.626875i	$0.784334\pi$
$240$	−2.14639e8	−1.00223
$241$	3.31564e7	0.152583	0.0762917	−	0.997086i	$-0.475692\pi$
$241$	3.31564e7	0.152583	0.0762917	+	0.997086i	$0.475692\pi$
$242$	−2.06822e8	−0.938086
$243$	−1.43489e7	−0.0641500
$244$	6.45641e7	0.284529
$245$	6.69604e7	0.290896
$246$	−1.50392e8	−0.644100
$247$	3.61336e8	1.52571
$248$	−1.01638e7	−0.0423133
$249$	1.27472e8	0.523260
$250$	−1.21813e8	−0.493063
$251$	2.94819e8	1.17679	0.588394	−	0.808574i	$-0.299760\pi$
$251$	2.94819e8	1.17679	0.588394	+	0.808574i	$0.299760\pi$
$252$	−6.09977e7	−0.240111
$253$	−3.65122e7	−0.141748
$254$	2.70994e8	1.03763
$255$	−3.01979e8	−1.14047
$256$	3.41411e8	1.27186
$257$	−2.56922e8	−0.944139	−0.472069	−	0.881561i	$-0.656493\pi$
$257$	−2.56922e8	−0.944139	−0.472069	+	0.881561i	$0.656493\pi$
$258$	−2.02536e8	−0.734231
$259$	−4.05531e8	−1.45036
$260$	−4.59114e8	−1.61999
$261$	2.36937e7	0.0824881
$262$	5.74680e7	0.197411
$263$	3.01656e8	1.02251	0.511255	−	0.859429i	$-0.329181\pi$
$263$	3.01656e8	1.02251	0.511255	+	0.859429i	$0.329181\pi$
$264$	−2.51299e7	−0.0840575
$265$	7.46787e8	2.46511
$266$	−4.18913e8	−1.36470
$267$	2.36344e7	0.0759898
$268$	1.90886e8	0.605762
$269$	−2.61569e8	−0.819318	−0.409659	−	0.912239i	$-0.634352\pi$
$269$	−2.61569e8	−0.819318	−0.409659	+	0.912239i	$0.634352\pi$
$270$	1.25210e8	0.387137
$271$	−1.44509e8	−0.441064	−0.220532	−	0.975380i	$-0.570779\pi$
$271$	−1.44509e8	−0.441064	−0.220532	+	0.975380i	$0.570779\pi$
$272$	5.06909e8	1.52735
$273$	2.34763e8	0.698330
$274$	−4.33863e8	−1.27417
$275$	−2.35691e8	−0.683406
$276$	−4.17897e7	−0.119643
$277$	−4.66473e7	−0.131870	−0.0659352	−	0.997824i	$-0.521003\pi$
$277$	−4.66473e7	−0.131870	−0.0659352	+	0.997824i	$0.521003\pi$
$278$	5.22997e8	1.45996
$279$	1.92888e7	0.0531730
$280$	−1.31059e8	−0.356790
$281$	6.78292e8	1.82366	0.911832	−	0.410564i	$-0.134668\pi$
$281$	6.78292e8	1.82366	0.911832	+	0.410564i	$0.134668\pi$
$282$	3.38346e8	0.898440
$283$	2.33845e8	0.613305	0.306652	−	0.951822i	$-0.400791\pi$
$283$	2.33845e8	0.613305	0.306652	+	0.951822i	$0.400791\pi$
$284$	3.74719e8	0.970715
$285$	3.82820e8	0.979575
$286$	−3.92802e8	−0.992870
$287$	−2.98746e8	−0.745959
$288$	−1.74336e8	−0.430045
$289$	3.02840e8	0.738024
$290$	−2.06753e8	−0.497805
$291$	3.40579e8	0.810199
$292$	5.65897e8	1.33014
$293$	3.28205e8	0.762270	0.381135	−	0.924519i	$-0.375533\pi$
$293$	3.28205e8	0.762270	0.381135	+	0.924519i	$0.375533\pi$
$294$	6.55695e7	0.150483
$295$	8.60141e7	0.195071
$296$	−1.91219e8	−0.428559
$297$	4.76912e7	0.105631
$298$	7.30089e7	0.159815
$299$	1.60837e8	0.347965
$300$	−2.69758e8	−0.576832
$301$	−4.02325e8	−0.850344
$302$	−7.73665e7	−0.161632
$303$	−3.86323e7	−0.0797813
$304$	−6.42612e8	−1.31187
$305$	−2.63264e8	−0.531302
$306$	−2.95706e8	−0.589977
$307$	1.82586e8	0.360150	0.180075	−	0.983653i	$-0.442366\pi$
$307$	1.82586e8	0.360150	0.180075	+	0.983653i	$0.442366\pi$
$308$	2.02737e8	0.395371
$309$	−1.51443e8	−0.292007
$310$	−1.68316e8	−0.320892
$311$	−5.84419e8	−1.10170	−0.550850	−	0.834605i	$-0.685696\pi$
$311$	−5.84419e8	−1.10170	−0.550850	+	0.834605i	$0.685696\pi$
$312$	1.10697e8	0.206346
$313$	9.32347e8	1.71859	0.859295	−	0.511480i	$-0.170903\pi$
$313$	9.32347e8	1.71859	0.859295	+	0.511480i	$0.170903\pi$
$314$	3.05675e8	0.557194
$315$	2.48722e8	0.448360
$316$	−6.20745e8	−1.10664
$317$	8.93740e8	1.57581	0.787905	−	0.615797i	$-0.211166\pi$
$317$	8.93740e8	1.57581	0.787905	+	0.615797i	$0.211166\pi$
$318$	7.31274e8	1.27522
$319$	−7.87503e7	−0.135827
$320$	5.03725e8	0.859348
$321$	−5.87281e8	−0.991011
$322$	−1.86465e8	−0.311245
$323$	−9.04100e8	−1.49282
$324$	5.45844e7	0.0891581
$325$	1.03822e9	1.67764
$326$	−1.02682e9	−1.64147
$327$	2.51787e8	0.398214
$328$	−1.40867e8	−0.220419
$329$	6.72104e8	1.04052
$330$	−4.16157e8	−0.637468
$331$	9.07658e8	1.37570	0.687851	−	0.725852i	$-0.258554\pi$
$331$	9.07658e8	1.37570	0.687851	+	0.725852i	$0.258554\pi$
$332$	−4.84914e8	−0.727246
$333$	3.62893e8	0.538548
$334$	1.68283e9	2.47131
$335$	−7.78348e8	−1.13114
$336$	−4.17510e8	−0.600454
$337$	7.89412e8	1.12357	0.561784	−	0.827284i	$-0.310115\pi$
$337$	7.89412e8	1.12357	0.561784	+	0.827284i	$0.310115\pi$
$338$	7.77198e8	1.09477
$339$	−4.06071e8	−0.566113
$340$	1.14875e9	1.58507
$341$	−6.41099e7	−0.0875557
$342$	3.74868e8	0.506742
$343$	8.01151e8	1.07198
$344$	−1.89707e8	−0.251264
$345$	1.70400e8	0.223410
$346$	1.73690e9	2.25429
$347$	−5.28902e8	−0.679551	−0.339775	−	0.940507i	$-0.610351\pi$
$347$	−5.28902e8	−0.679551	−0.339775	+	0.940507i	$0.610351\pi$
$348$	−9.01328e7	−0.114645
$349$	2.00046e8	0.251908	0.125954	−	0.992036i	$-0.459801\pi$
$349$	2.00046e8	0.251908	0.125954	+	0.992036i	$0.459801\pi$
$350$	−1.20366e9	−1.50060
$351$	−2.10080e8	−0.259304
$352$	5.79438e8	0.708121
$353$	2.52531e8	0.305565	0.152782	−	0.988260i	$-0.451177\pi$
$353$	2.52531e8	0.305565	0.152782	+	0.988260i	$0.451177\pi$
$354$	8.42274e7	0.100912
$355$	−1.52794e9	−1.81262
$356$	−8.99072e7	−0.105613
$357$	−5.87402e8	−0.683277
$358$	−2.87448e8	−0.331107
$359$	−6.83126e8	−0.779238	−0.389619	−	0.920976i	$-0.627393\pi$
$359$	−6.83126e8	−0.779238	−0.389619	+	0.920976i	$0.627393\pi$
$360$	1.17279e8	0.132484
$361$	2.52261e8	0.282212
$362$	1.41345e9	1.56603
$363$	3.67643e8	0.403416
$364$	−8.93057e8	−0.970565
$365$	−2.30748e9	−2.48378
$366$	−2.57795e8	−0.274847
$367$	5.09383e8	0.537914	0.268957	−	0.963152i	$-0.413321\pi$
$367$	5.09383e8	0.537914	0.268957	+	0.963152i	$0.413321\pi$
$368$	−2.86037e8	−0.299196
$369$	2.67335e8	0.276990
$370$	−3.16664e9	−3.25007
$371$	1.45263e9	1.47689
$372$	−7.33762e7	−0.0739018
$373$	7.78305e8	0.776549	0.388274	−	0.921544i	$-0.373071\pi$
$373$	7.78305e8	0.776549	0.388274	+	0.921544i	$0.373071\pi$
$374$	9.82832e8	0.971468
$375$	2.16533e8	0.212038
$376$	3.16915e8	0.307458
$377$	3.46896e8	0.333430
$378$	2.43555e8	0.231940
$379$	1.51777e9	1.43209	0.716043	−	0.698056i	$-0.245951\pi$
$379$	1.51777e9	1.43209	0.716043	+	0.698056i	$0.245951\pi$
$380$	−1.45628e9	−1.36145
$381$	−4.81715e8	−0.446224
$382$	1.94830e9	1.78827
$383$	1.35344e9	1.23096	0.615481	−	0.788152i	$-0.288962\pi$
$383$	1.35344e9	1.23096	0.615481	+	0.788152i	$0.288962\pi$
$384$	−3.33221e8	−0.300312
$385$	−8.26671e8	−0.738279
$386$	−1.13824e9	−1.00735
$387$	3.60025e8	0.315750
$388$	−1.29559e9	−1.12605
$389$	−2.16650e7	−0.0186610	−0.00933052	−	0.999956i	$-0.502970\pi$
$389$	−2.16650e7	−0.0186610	−0.00933052	+	0.999956i	$0.502970\pi$
$390$	1.83318e9	1.56487
$391$	−4.02430e8	−0.340465
$392$	6.14164e7	0.0514971
$393$	−1.02154e8	−0.0848951
$394$	−2.17031e9	−1.78766
$395$	2.53112e9	2.06644
$396$	−1.81421e8	−0.146810
$397$	9.27708e8	0.744123	0.372061	−	0.928208i	$-0.378651\pi$
$397$	9.27708e8	0.744123	0.372061	+	0.928208i	$0.378651\pi$
$398$	−1.15317e9	−0.916862
$399$	7.44653e8	0.586879
$400$	−1.84641e9	−1.44251
$401$	−2.89379e8	−0.224110	−0.112055	−	0.993702i	$-0.535743\pi$
$401$	−2.89379e8	−0.224110	−0.112055	+	0.993702i	$0.535743\pi$
$402$	−7.62179e8	−0.585148
$403$	2.82404e8	0.214933
$404$	1.46960e8	0.110883
$405$	−2.22571e8	−0.166485
$406$	−4.02172e8	−0.298243
$407$	−1.20614e9	−0.886784
$408$	−2.76976e8	−0.201898
$409$	1.85339e9	1.33947	0.669737	−	0.742598i	$-0.266407\pi$
$409$	1.85339e9	1.33947	0.669737	+	0.742598i	$0.266407\pi$
$410$	−2.33279e9	−1.67160
$411$	7.71229e8	0.547945
$412$	5.76100e8	0.405843
$413$	1.67313e8	0.116870
$414$	1.66860e8	0.115572
$415$	1.97727e9	1.35799
$416$	−2.55243e9	−1.73831
$417$	−9.29671e8	−0.627846
$418$	−1.24594e9	−0.834412
$419$	2.29514e9	1.52427	0.762133	−	0.647420i	$-0.224152\pi$
$419$	2.29514e9	1.52427	0.762133	+	0.647420i	$0.224152\pi$
$420$	−9.46157e8	−0.623147
$421$	1.32746e9	0.867028	0.433514	−	0.901147i	$-0.357273\pi$
$421$	1.32746e9	0.867028	0.433514	+	0.901147i	$0.357273\pi$
$422$	−1.04945e9	−0.679782
$423$	−6.01439e8	−0.386367
$424$	6.84956e8	0.436397
$425$	−2.59774e9	−1.64148
$426$	−1.49620e9	−0.937683
$427$	−5.12094e8	−0.318312
$428$	2.23406e9	1.37734
$429$	6.98239e8	0.426976
$430$	−3.14161e9	−1.90551
$431$	4.95028e8	0.297823	0.148912	−	0.988850i	$-0.452423\pi$
$431$	4.95028e8	0.297823	0.148912	+	0.988850i	$0.452423\pi$
$432$	3.73613e8	0.222961
$433$	−1.81935e9	−1.07698	−0.538491	−	0.842631i	$-0.681005\pi$
$433$	−1.81935e9	−1.07698	−0.538491	+	0.842631i	$0.681005\pi$
$434$	−3.27404e8	−0.192252
$435$	3.67522e8	0.214077
$436$	−9.57818e8	−0.553453
$437$	5.10163e8	0.292431
$438$	−2.25954e9	−1.28488
$439$	−3.28149e9	−1.85117	−0.925583	−	0.378546i	$-0.876424\pi$
$439$	−3.28149e9	−1.85117	−0.925583	+	0.378546i	$0.876424\pi$
$440$	−3.89798e8	−0.218150
$441$	−1.16555e8	−0.0647139
$442$	−4.32938e9	−2.38478
$443$	−2.09880e9	−1.14699	−0.573493	−	0.819210i	$-0.694412\pi$
$443$	−2.09880e9	−1.14699	−0.573493	+	0.819210i	$0.694412\pi$
$444$	−1.38048e9	−0.748494
$445$	3.66602e8	0.197212
$446$	−3.39716e9	−1.81320
$447$	−1.29779e8	−0.0687274
$448$	9.79835e8	0.514849
$449$	8.92700e7	0.0465418	0.0232709	−	0.999729i	$-0.492592\pi$
$449$	8.92700e7	0.0465418	0.0232709	+	0.999729i	$0.492592\pi$
$450$	1.07710e9	0.557203
$451$	−8.88537e8	−0.456098
$452$	1.54473e9	0.786805
$453$	1.37526e8	0.0695088
$454$	−3.98821e8	−0.200024
$455$	3.64149e9	1.81234
$456$	3.51124e8	0.173414
$457$	−1.68348e9	−0.825092	−0.412546	−	0.910937i	$-0.635360\pi$
$457$	−1.68348e9	−0.825092	−0.412546	+	0.910937i	$0.635360\pi$
$458$	4.22833e9	2.05655
$459$	5.25642e8	0.253715
$460$	−6.48214e8	−0.310503
$461$	−1.92435e9	−0.914811	−0.457406	−	0.889258i	$-0.651221\pi$
$461$	−1.92435e9	−0.914811	−0.457406	+	0.889258i	$0.651221\pi$
$462$	−8.09499e8	−0.381917
$463$	−1.42542e9	−0.667437	−0.333718	−	0.942673i	$-0.608303\pi$
$463$	−1.42542e9	−0.667437	−0.333718	+	0.942673i	$0.608303\pi$
$464$	−6.16931e8	−0.286697
$465$	2.99196e8	0.137997
$466$	6.58691e8	0.301530
$467$	1.67879e9	0.762759	0.381380	−	0.924418i	$-0.375449\pi$
$467$	1.67879e9	0.762759	0.381380	+	0.924418i	$0.375449\pi$
$468$	7.99161e8	0.360391
$469$	−1.51402e9	−0.677685
$470$	5.24820e9	2.33168
$471$	−5.43363e8	−0.239617
$472$	7.88925e7	0.0345333
$473$	−1.19661e9	−0.519921
$474$	2.47854e9	1.06899
$475$	3.29317e9	1.40989
$476$	2.23452e9	0.949644
$477$	−1.29990e9	−0.548398
$478$	−4.99528e9	−2.09200
$479$	2.45408e9	1.02027	0.510135	−	0.860094i	$-0.329595\pi$
$479$	2.45408e9	1.02027	0.510135	+	0.860094i	$0.329595\pi$
$480$	−2.70419e9	−1.11607
$481$	5.31306e9	2.17689
$482$	5.03617e8	0.204850
$483$	3.31458e8	0.133848
$484$	−1.39854e9	−0.560683
$485$	5.28283e9	2.10267
$486$	−2.17948e8	−0.0861242
$487$	1.22859e9	0.482008	0.241004	−	0.970524i	$-0.422523\pi$
$487$	1.22859e9	0.482008	0.241004	+	0.970524i	$0.422523\pi$
$488$	−2.41467e8	−0.0940563
$489$	1.82526e9	0.705901
$490$	1.01707e9	0.390540
$491$	−4.00300e9	−1.52616	−0.763081	−	0.646303i	$-0.776314\pi$
$491$	−4.00300e9	−1.52616	−0.763081	+	0.646303i	$0.776314\pi$
$492$	−1.01697e9	−0.384971
$493$	−8.67970e8	−0.326242
$494$	5.48838e9	2.04833
$495$	7.39755e8	0.274138
$496$	−5.02237e8	−0.184809
$497$	−2.97211e9	−1.08597
$498$	1.93619e9	0.702499
$499$	−6.37493e8	−0.229680	−0.114840	−	0.993384i	$-0.536636\pi$
$499$	−6.37493e8	−0.229680	−0.114840	+	0.993384i	$0.536636\pi$
$500$	−8.23707e8	−0.294698
$501$	−2.99137e9	−1.06277
$502$	4.47806e9	1.57989
$503$	3.52591e9	1.23533	0.617666	−	0.786440i	$-0.288078\pi$
$503$	3.52591e9	1.23533	0.617666	+	0.786440i	$0.288078\pi$
$504$	2.28128e8	0.0793730
$505$	−5.99239e8	−0.207052
$506$	−5.54590e8	−0.190303
$507$	−1.38154e9	−0.470798
$508$	1.83248e9	0.620179
$509$	−1.03941e9	−0.349360	−0.174680	−	0.984625i	$-0.555889\pi$
$509$	−1.03941e9	−0.349360	−0.174680	+	0.984625i	$0.555889\pi$
$510$	−4.58680e9	−1.53114
$511$	−4.48845e9	−1.48807
$512$	3.60603e9	1.18736
$513$	−6.66360e8	−0.217920
$514$	−3.90243e9	−1.26755
$515$	−2.34908e9	−0.757832
$516$	−1.36956e9	−0.438842
$517$	1.99899e9	0.636200
$518$	−6.15967e9	−1.94717
$519$	−3.08749e9	−0.969439
$520$	1.71706e9	0.535519
$521$	−1.04135e9	−0.322600	−0.161300	−	0.986905i	$-0.551569\pi$
$521$	−1.04135e9	−0.322600	−0.161300	+	0.986905i	$0.551569\pi$
$522$	3.59887e8	0.110744
$523$	4.18130e9	1.27807	0.639036	−	0.769177i	$-0.279334\pi$
$523$	4.18130e9	1.27807	0.639036	+	0.769177i	$0.279334\pi$
$524$	3.88603e8	0.117990
$525$	2.13960e9	0.645320
$526$	4.58190e9	1.37276
$527$	−7.06606e8	−0.210300
$528$	−1.24177e9	−0.367133
$529$	−3.17774e9	−0.933306
$530$	1.13431e10	3.30952
$531$	−1.49721e8	−0.0433963
$532$	−2.83272e9	−0.815667
$533$	3.91401e9	1.11964
$534$	3.58986e8	0.102020
$535$	−9.10953e9	−2.57192
$536$	−7.13904e8	−0.200246
$537$	5.10964e8	0.142390
$538$	−3.97300e9	−1.09997
$539$	3.87393e8	0.106559
$540$	8.46678e8	0.231388
$541$	−5.65879e9	−1.53650	−0.768251	−	0.640149i	$-0.778873\pi$
$541$	−5.65879e9	−1.53650	−0.768251	+	0.640149i	$0.778873\pi$
$542$	−2.19497e9	−0.592148
$543$	−2.51252e9	−0.673458
$544$	6.38645e9	1.70084
$545$	3.90556e9	1.03346
$546$	3.56585e9	0.937538
$547$	5.02175e8	0.131190	0.0655948	−	0.997846i	$-0.479106\pi$
$547$	5.02175e8	0.131190	0.0655948	+	0.997846i	$0.479106\pi$
$548$	−2.93382e9	−0.761555
$549$	4.58253e8	0.118196
$550$	−3.57995e9	−0.917503
$551$	1.10033e9	0.280216
$552$	1.56291e8	0.0395501
$553$	4.92348e9	1.23804
$554$	−7.08533e8	−0.177042
$555$	5.62897e9	1.39767
$556$	3.53654e9	0.872604
$557$	−2.86842e9	−0.703314	−0.351657	−	0.936129i	$-0.614382\pi$
$557$	−2.86842e9	−0.703314	−0.351657	+	0.936129i	$0.614382\pi$
$558$	2.92981e8	0.0713870
$559$	5.27106e9	1.27631
$560$	−6.47615e9	−1.55833
$561$	−1.74707e9	−0.417772
$562$	1.03027e10	2.44835
$563$	3.72076e9	0.878723	0.439361	−	0.898310i	$-0.355205\pi$
$563$	3.72076e9	0.878723	0.439361	+	0.898310i	$0.355205\pi$
$564$	2.28792e9	0.536987
$565$	−6.29871e9	−1.46920
$566$	3.55191e9	0.823388
$567$	−4.32940e8	−0.0997440
$568$	−1.40143e9	−0.320888
$569$	−5.12299e9	−1.16582	−0.582909	−	0.812538i	$-0.698085\pi$
$569$	−5.12299e9	−1.16582	−0.582909	+	0.812538i	$0.698085\pi$
$570$	5.81471e9	1.31512
$571$	−3.51571e9	−0.790289	−0.395145	−	0.918619i	$-0.629306\pi$
$571$	−3.51571e9	−0.790289	−0.395145	+	0.918619i	$0.629306\pi$
$572$	−2.65616e9	−0.593427
$573$	−3.46326e9	−0.769031
$574$	−4.53769e9	−1.00148
$575$	1.46585e9	0.321552
$576$	−8.76815e8	−0.191174
$577$	−9.70425e8	−0.210304	−0.105152	−	0.994456i	$-0.533533\pi$
$577$	−9.70425e8	−0.210304	−0.105152	+	0.994456i	$0.533533\pi$
$578$	4.59988e9	0.990829
$579$	2.02332e9	0.433202
$580$	−1.39808e9	−0.297533
$581$	3.84613e9	0.813593
$582$	5.17310e9	1.08773
$583$	4.32046e9	0.903004
$584$	−2.11643e9	−0.439702
$585$	−3.25863e9	−0.672959
$586$	4.98516e9	1.02338
$587$	5.54244e9	1.13101	0.565506	−	0.824744i	$-0.308681\pi$
$587$	5.54244e9	1.13101	0.565506	+	0.824744i	$0.308681\pi$
$588$	4.43386e8	0.0899418
$589$	8.95768e8	0.180631
$590$	1.30648e9	0.261891
$591$	3.85792e9	0.768771
$592$	−9.44893e9	−1.87179
$593$	−5.71802e8	−0.112604	−0.0563021	−	0.998414i	$-0.517931\pi$
$593$	−5.71802e8	−0.112604	−0.0563021	+	0.998414i	$0.517931\pi$
$594$	7.24388e8	0.141814
$595$	−9.11140e9	−1.77327
$596$	4.93691e8	0.0955199
$597$	2.04986e9	0.394289
$598$	2.44297e9	0.467158
$599$	1.65083e9	0.313840	0.156920	−	0.987611i	$-0.449843\pi$
$599$	1.65083e9	0.313840	0.156920	+	0.987611i	$0.449843\pi$
$600$	1.00888e9	0.190682
$601$	4.29026e9	0.806163	0.403081	−	0.915164i	$-0.367939\pi$
$601$	4.29026e9	0.806163	0.403081	+	0.915164i	$0.367939\pi$
$602$	−6.11098e9	−1.14162
$603$	1.35484e9	0.251638
$604$	−5.23158e8	−0.0966059
$605$	5.70265e9	1.04697
$606$	−5.86791e8	−0.107110
$607$	8.68657e8	0.157648	0.0788239	−	0.996889i	$-0.474884\pi$
$607$	8.68657e8	0.157648	0.0788239	+	0.996889i	$0.474884\pi$
$608$	−8.09613e9	−1.46088
$609$	7.14894e8	0.128257
$610$	−3.99875e9	−0.713296
$611$	−8.80556e9	−1.56175
$612$	−1.99959e9	−0.352623
$613$	2.12755e9	0.373050	0.186525	−	0.982450i	$-0.440277\pi$
$613$	2.12755e9	0.373050	0.186525	+	0.982450i	$0.440277\pi$
$614$	2.77333e9	0.483517
$615$	4.14673e9	0.718858
$616$	−7.58226e8	−0.130697
$617$	−8.95889e9	−1.53552	−0.767761	−	0.640736i	$-0.778629\pi$
$617$	−8.95889e9	−1.53552	−0.767761	+	0.640736i	$0.778629\pi$
$618$	−2.30029e9	−0.392033
$619$	−5.17081e9	−0.876277	−0.438138	−	0.898908i	$-0.644362\pi$
$619$	−5.17081e9	−0.876277	−0.438138	+	0.898908i	$0.644362\pi$
$620$	−1.13816e9	−0.191794
$621$	−2.96608e8	−0.0497007
$622$	−8.87683e9	−1.47908
$623$	7.13105e8	0.118153
$624$	5.47001e9	0.901244
$625$	−4.24082e9	−0.694815
$626$	1.41616e10	2.30728
$627$	2.21477e9	0.358832
$628$	2.06700e9	0.333028
$629$	−1.32938e10	−2.12997
$630$	3.77787e9	0.601943
$631$	−2.71332e9	−0.429931	−0.214965	−	0.976622i	$-0.568964\pi$
$631$	−2.71332e9	−0.429931	−0.214965	+	0.976622i	$0.568964\pi$
$632$	2.32156e9	0.365822
$633$	1.86549e9	0.292335
$634$	1.35751e10	2.11559
$635$	−7.47206e9	−1.15806
$636$	4.94493e9	0.762185
$637$	−1.70647e9	−0.261583
$638$	−1.19615e9	−0.182353
$639$	2.65962e9	0.403243
$640$	−5.16871e9	−0.779386
$641$	3.35162e9	0.502634	0.251317	−	0.967905i	$-0.419136\pi$
$641$	3.35162e9	0.502634	0.251317	+	0.967905i	$0.419136\pi$
$642$	−8.92030e9	−1.33048
$643$	7.57020e9	1.12297	0.561486	−	0.827486i	$-0.310230\pi$
$643$	7.57020e9	1.12297	0.561486	+	0.827486i	$0.310230\pi$
$644$	−1.26089e9	−0.186027
$645$	5.58447e9	0.819451
$646$	−1.37325e10	−2.00418
$647$	−3.82356e9	−0.555013	−0.277507	−	0.960724i	$-0.589508\pi$
$647$	−3.82356e9	−0.555013	−0.277507	+	0.960724i	$0.589508\pi$
$648$	−2.04143e8	−0.0294728
$649$	4.97626e8	0.0714573
$650$	1.57697e10	2.25230
$651$	5.81988e8	0.0826763
$652$	−6.94344e9	−0.981088
$653$	−9.84140e9	−1.38312	−0.691561	−	0.722318i	$-0.743077\pi$
$653$	−9.84140e9	−1.38312	−0.691561	+	0.722318i	$0.743077\pi$
$654$	3.82443e9	0.534619
$655$	−1.58455e9	−0.220324
$656$	−6.96081e9	−0.962712
$657$	4.01653e9	0.552551
$658$	1.02087e10	1.39694
$659$	1.04889e10	1.42768	0.713842	−	0.700307i	$-0.246954\pi$
$659$	1.04889e10	1.42768	0.713842	+	0.700307i	$0.246954\pi$
$660$	−2.81409e9	−0.381008
$661$	−5.13152e8	−0.0691100	−0.0345550	−	0.999403i	$-0.511001\pi$
$661$	−5.13152e8	−0.0691100	−0.0345550	+	0.999403i	$0.511001\pi$
$662$	1.37866e10	1.84694
$663$	7.69584e9	1.02555
$664$	1.81356e9	0.240404
$665$	1.15506e10	1.52310
$666$	5.51204e9	0.723024
$667$	4.89776e8	0.0639082
$668$	1.13794e10	1.47707
$669$	6.03875e9	0.779750
$670$	−1.18224e10	−1.51861
$671$	−1.52309e9	−0.194624
$672$	−5.26013e9	−0.668658
$673$	4.59671e8	0.0581292	0.0290646	−	0.999578i	$-0.490747\pi$
$673$	4.59671e8	0.0581292	0.0290646	+	0.999578i	$0.490747\pi$
$674$	1.19905e10	1.50844
$675$	−1.91464e9	−0.239621
$676$	5.25547e9	0.654333
$677$	−1.30244e10	−1.61324	−0.806619	−	0.591072i	$-0.798705\pi$
$677$	−1.30244e10	−1.61324	−0.806619	+	0.591072i	$0.798705\pi$
$678$	−6.16787e9	−0.760031
$679$	1.02760e10	1.25974
$680$	−4.29628e9	−0.523975
$681$	7.08939e8	0.0860189
$682$	−9.73774e8	−0.117547
$683$	−1.27703e9	−0.153366	−0.0766830	−	0.997056i	$-0.524433\pi$
$683$	−1.27703e9	−0.153366	−0.0766830	+	0.997056i	$0.524433\pi$
$684$	2.53489e9	0.302874
$685$	1.19628e10	1.42205
$686$	1.21688e10	1.43917
$687$	−7.51622e9	−0.884404
$688$	−9.37423e9	−1.09743
$689$	−1.90316e10	−2.21671
$690$	2.58823e9	0.299937
$691$	1.46413e10	1.68813	0.844063	−	0.536243i	$-0.180157\pi$
$691$	1.46413e10	1.68813	0.844063	+	0.536243i	$0.180157\pi$
$692$	1.17451e10	1.34736
$693$	1.43895e9	0.164241
$694$	−8.03356e9	−0.912326
$695$	−1.44205e10	−1.62942
$696$	3.37092e8	0.0378980
$697$	−9.79328e9	−1.09550
$698$	3.03853e9	0.338197
$699$	−1.17088e9	−0.129671
$700$	−8.13922e9	−0.896891
$701$	−1.79391e10	−1.96692	−0.983460	−	0.181127i	$-0.942026\pi$
$701$	−1.79391e10	−1.96692	−0.983460	+	0.181127i	$0.942026\pi$
$702$	−3.19094e9	−0.348127
$703$	1.68527e10	1.82947
$704$	2.91425e9	0.314791
$705$	−9.32913e9	−1.00272
$706$	3.83573e9	0.410234
$707$	−1.16563e9	−0.124048
$708$	5.69552e8	0.0603138
$709$	−1.11761e10	−1.17769	−0.588843	−	0.808248i	$-0.700416\pi$
$709$	−1.11761e10	−1.17769	−0.588843	+	0.808248i	$0.700416\pi$
$710$	−2.32081e10	−2.43352
$711$	−4.40582e9	−0.459710
$712$	3.36248e8	0.0349125
$713$	3.98721e8	0.0411961
$714$	−8.92213e9	−0.917329
$715$	1.08306e10	1.10811
$716$	−1.94375e9	−0.197899
$717$	8.87954e9	0.899650
$718$	−1.03761e10	−1.04616
$719$	9.74647e9	0.977904	0.488952	−	0.872311i	$-0.337379\pi$
$719$	9.74647e9	0.977904	0.488952	+	0.872311i	$0.337379\pi$
$720$	5.79525e9	0.578640
$721$	−4.56938e9	−0.454029
$722$	3.83163e9	0.378881
$723$	−8.95222e8	−0.0880940
$724$	9.55784e9	0.935997
$725$	3.16157e9	0.308120
$726$	5.58419e9	0.541604
$727$	1.00742e10	0.972389	0.486195	−	0.873851i	$-0.338385\pi$
$727$	1.00742e10	0.972389	0.486195	+	0.873851i	$0.338385\pi$
$728$	3.33999e9	0.320838
$729$	3.87420e8	0.0370370
$730$	−3.50486e10	−3.33458
$731$	−1.31888e10	−1.24880
$732$	−1.74323e9	−0.164273
$733$	1.97006e10	1.84763	0.923814	−	0.382841i	$-0.125054\pi$
$733$	1.97006e10	1.84763	0.923814	+	0.382841i	$0.125054\pi$
$734$	7.73709e9	0.722173
$735$	−1.80793e9	−0.167949
$736$	−3.60373e9	−0.333180
$737$	−4.50305e9	−0.414353
$738$	4.06060e9	0.371871
$739$	−9.78856e9	−0.892202	−0.446101	−	0.894983i	$-0.647188\pi$
$739$	−9.78856e9	−0.892202	−0.446101	+	0.894983i	$0.647188\pi$
$740$	−2.14131e10	−1.94253
$741$	−9.75606e9	−0.880868
$742$	2.20642e10	1.98278
$743$	7.25852e9	0.649213	0.324607	−	0.945849i	$-0.394768\pi$
$743$	7.25852e9	0.649213	0.324607	+	0.945849i	$0.394768\pi$
$744$	2.74423e8	0.0244296
$745$	−2.01306e9	−0.178365
$746$	1.18218e10	1.04255
$747$	−3.44175e9	−0.302104
$748$	6.64598e9	0.580636
$749$	−1.77196e10	−1.54088
$750$	3.28894e9	0.284670
$751$	1.17654e10	1.01360	0.506799	−	0.862064i	$-0.330829\pi$
$751$	1.17654e10	1.01360	0.506799	+	0.862064i	$0.330829\pi$
$752$	1.56601e10	1.34287
$753$	−7.96013e9	−0.679419
$754$	5.26905e9	0.447644
$755$	2.13321e9	0.180393
$756$	1.64694e9	0.138628
$757$	−1.11582e10	−0.934886	−0.467443	−	0.884023i	$-0.654825\pi$
$757$	−1.11582e10	−0.934886	−0.467443	+	0.884023i	$0.654825\pi$
$758$	2.30537e10	1.92264
$759$	9.85830e8	0.0818382
$760$	5.44641e9	0.450052
$761$	−5.87504e9	−0.483242	−0.241621	−	0.970371i	$-0.577679\pi$
$761$	−5.87504e9	−0.483242	−0.241621	+	0.970371i	$0.577679\pi$
$762$	−7.31684e9	−0.599075
$763$	7.59700e9	0.619165
$764$	1.31745e10	1.06883
$765$	8.15343e9	0.658454
$766$	2.05577e10	1.65262
$767$	−2.19204e9	−0.175415
$768$	−9.21810e9	−0.734306
$769$	1.13603e10	0.900841	0.450420	−	0.892817i	$-0.351274\pi$
$769$	1.13603e10	0.900841	0.450420	+	0.892817i	$0.351274\pi$
$770$	−1.25564e10	−0.991171
$771$	6.93690e9	0.545099
$772$	−7.69688e9	−0.602080
$773$	−1.76385e10	−1.37352	−0.686759	−	0.726885i	$-0.740967\pi$
$773$	−1.76385e10	−1.37352	−0.686759	+	0.726885i	$0.740967\pi$
$774$	5.46847e9	0.423909
$775$	2.57380e9	0.198618
$776$	4.84544e9	0.372235
$777$	1.09493e10	0.837364
$778$	−3.29074e8	−0.0250533
$779$	1.24150e10	0.940947
$780$	1.23961e10	0.935304
$781$	−8.83974e9	−0.663989
$782$	−6.11257e9	−0.457089
$783$	−6.39730e8	−0.0476245
$784$	3.03484e9	0.224921
$785$	−8.42830e9	−0.621865
$786$	−1.55164e9	−0.113975
$787$	−2.46188e10	−1.80034	−0.900172	−	0.435534i	$-0.856560\pi$
$787$	−2.46188e10	−1.80034	−0.900172	+	0.435534i	$0.856560\pi$
$788$	−1.46758e10	−1.06847
$789$	−8.14472e9	−0.590346
$790$	3.84456e10	2.77429
$791$	−1.22521e10	−0.880224
$792$	6.78506e8	0.0485306
$793$	6.70920e9	0.477766
$794$	1.40911e10	0.999017
$795$	−2.01632e10	−1.42323
$796$	−7.79785e9	−0.547998
$797$	−1.36580e10	−0.955612	−0.477806	−	0.878465i	$-0.658568\pi$
$797$	−1.36580e10	−0.955612	−0.477806	+	0.878465i	$0.658568\pi$
$798$	1.13106e10	0.787911
$799$	2.20325e10	1.52809
$800$	−2.32625e10	−1.60636
$801$	−6.38129e8	−0.0438727
$802$	−4.39542e9	−0.300878
$803$	−1.33497e10	−0.909843
$804$	−5.15392e9	−0.349737
$805$	5.14136e9	0.347370
$806$	4.28948e9	0.288557
$807$	7.06235e9	0.473034
$808$	−5.49624e8	−0.0366544
$809$	−4.59136e9	−0.304875	−0.152438	−	0.988313i	$-0.548712\pi$
$809$	−4.59136e9	−0.304875	−0.152438	+	0.988313i	$0.548712\pi$
$810$	−3.38066e9	−0.223514
$811$	−2.86469e10	−1.88584	−0.942919	−	0.333022i	$-0.891931\pi$
$811$	−2.86469e10	−1.88584	−0.942919	+	0.333022i	$0.891931\pi$
$812$	−2.71952e9	−0.178257
$813$	3.90174e9	0.254649
$814$	−1.83203e10	−1.19055
$815$	2.83123e10	1.83199
$816$	−1.36865e10	−0.881817
$817$	1.67195e10	1.07262
$818$	2.81513e10	1.79830
$819$	−6.33860e9	−0.403181
$820$	−1.57745e10	−0.999096
$821$	−1.33387e10	−0.841225	−0.420613	−	0.907240i	$-0.638185\pi$
$821$	−1.33387e10	−0.841225	−0.420613	+	0.907240i	$0.638185\pi$
$822$	1.17143e10	0.735640
$823$	1.33719e10	0.836171	0.418085	−	0.908408i	$-0.362701\pi$
$823$	1.33719e10	0.836171	0.418085	+	0.908408i	$0.362701\pi$
$824$	−2.15459e9	−0.134159
$825$	6.36366e9	0.394565
$826$	2.54133e9	0.156903
$827$	−1.27792e10	−0.785658	−0.392829	−	0.919612i	$-0.628503\pi$
$827$	−1.27792e10	−0.785658	−0.392829	+	0.919612i	$0.628503\pi$
$828$	1.12832e9	0.0690759
$829$	3.01708e10	1.83927	0.919635	−	0.392775i	$-0.128485\pi$
$829$	3.01708e10	1.83927	0.919635	+	0.392775i	$0.128485\pi$
$830$	3.00330e10	1.82316
$831$	1.25948e9	0.0761354
$832$	−1.28373e10	−0.772755
$833$	4.26976e9	0.255945
$834$	−1.41209e10	−0.842911
$835$	−4.64002e10	−2.75814
$836$	−8.42515e9	−0.498719
$837$	−5.20798e8	−0.0306994
$838$	3.48613e10	2.04639
$839$	1.99280e10	1.16492	0.582460	−	0.812859i	$-0.302090\pi$
$839$	1.99280e10	1.16492	0.582460	+	0.812859i	$0.302090\pi$
$840$	3.53858e9	0.205993
$841$	−1.61935e10	−0.938761
$842$	2.01629e10	1.16402
$843$	−1.83139e10	−1.05289
$844$	−7.09649e9	−0.406298
$845$	−2.14295e10	−1.22184
$846$	−9.13534e9	−0.518714
$847$	1.10927e10	0.627254
$848$	3.38465e10	1.90603
$849$	−6.31383e9	−0.354092
$850$	−3.94575e10	−2.20375
$851$	7.50142e9	0.417244
$852$	−1.01174e10	−0.560443
$853$	−2.14201e10	−1.18168	−0.590840	−	0.806789i	$-0.701204\pi$
$853$	−2.14201e10	−1.18168	−0.590840	+	0.806789i	$0.701204\pi$
$854$	−7.77828e9	−0.427347
$855$	−1.03361e10	−0.565558
$856$	−8.35529e9	−0.455306
$857$	3.13832e10	1.70320	0.851599	−	0.524195i	$-0.175634\pi$
$857$	3.13832e10	1.70320	0.851599	+	0.524195i	$0.175634\pi$
$858$	1.06056e10	0.573234
$859$	−1.10229e10	−0.593362	−0.296681	−	0.954977i	$-0.595880\pi$
$859$	−1.10229e10	−0.593362	−0.296681	+	0.954977i	$0.595880\pi$
$860$	−2.12438e10	−1.13890
$861$	8.06613e9	0.430679
$862$	7.51905e9	0.399841
$863$	2.63685e10	1.39652	0.698260	−	0.715844i	$-0.253958\pi$
$863$	2.63685e10	1.39652	0.698260	+	0.715844i	$0.253958\pi$
$864$	4.70708e9	0.248287
$865$	−4.78912e10	−2.51594
$866$	−2.76344e10	−1.44590
$867$	−8.17667e9	−0.426098
$868$	−2.21393e9	−0.114907
$869$	1.46436e10	0.756967
$870$	5.58234e9	0.287408
$871$	1.98360e10	1.01716
$872$	3.58220e9	0.182954
$873$	−9.19562e9	−0.467769
$874$	7.74894e9	0.392602
$875$	6.53329e9	0.329689
$876$	−1.52792e10	−0.767957
$877$	−9.58767e9	−0.479970	−0.239985	−	0.970777i	$-0.577143\pi$
$877$	−9.58767e9	−0.479970	−0.239985	+	0.970777i	$0.577143\pi$
$878$	−4.98430e10	−2.48527
$879$	−8.86154e9	−0.440097
$880$	−1.92616e10	−0.952801
$881$	−2.62769e10	−1.29467	−0.647334	−	0.762206i	$-0.724116\pi$
$881$	−2.62769e10	−1.29467	−0.647334	+	0.762206i	$0.724116\pi$
$882$	−1.77038e9	−0.0868812
$883$	−9.16067e9	−0.447780	−0.223890	−	0.974614i	$-0.571876\pi$
$883$	−9.16067e9	−0.447780	−0.223890	+	0.974614i	$0.571876\pi$
$884$	−2.92756e10	−1.42535
$885$	−2.32238e9	−0.112624
$886$	−3.18790e10	−1.53988
$887$	−2.61104e10	−1.25626	−0.628132	−	0.778107i	$-0.716180\pi$
$887$	−2.61104e10	−1.25626	−0.628132	+	0.778107i	$0.716180\pi$
$888$	5.16291e9	0.247428
$889$	−1.45345e10	−0.693814
$890$	5.56837e9	0.264766
$891$	−1.28766e9	−0.0609860
$892$	−2.29719e10	−1.08373
$893$	−2.79307e10	−1.31251
$894$	−1.97124e9	−0.0922695
$895$	7.92574e9	0.369538
$896$	−1.00541e10	−0.466942
$897$	−4.34259e9	−0.200898
$898$	1.35593e9	0.0624844
$899$	8.59971e8	0.0394752
$900$	7.28346e9	0.333034
$901$	4.76192e10	2.16893
$902$	−1.34961e10	−0.612331
$903$	1.08628e10	0.490946
$904$	−5.77721e9	−0.260093
$905$	−3.89726e10	−1.74779
$906$	2.08890e9	0.0933185
$907$	7.07125e9	0.314681	0.157340	−	0.987544i	$-0.449708\pi$
$907$	7.07125e9	0.314681	0.157340	+	0.987544i	$0.449708\pi$
$908$	−2.69686e9	−0.119552
$909$	1.04307e9	0.0460618
$910$	5.53112e10	2.43314
$911$	2.11411e10	0.926432	0.463216	−	0.886245i	$-0.346695\pi$
$911$	2.11411e10	0.926432	0.463216	+	0.886245i	$0.346695\pi$
$912$	1.73505e10	0.757409
$913$	1.14393e10	0.497451
$914$	−2.55707e10	−1.10772
$915$	7.10812e9	0.306748
$916$	2.85923e10	1.22918
$917$	−3.08223e9	−0.132000
$918$	7.98406e9	0.340623
$919$	3.00700e9	0.127799	0.0638997	−	0.997956i	$-0.479646\pi$
$919$	3.00700e9	0.127799	0.0638997	+	0.997956i	$0.479646\pi$
$920$	2.42429e9	0.102642
$921$	−4.92983e9	−0.207933
$922$	−2.92293e10	−1.22817
$923$	3.89391e10	1.62997
$924$	−5.47390e9	−0.228268
$925$	4.84226e10	2.01165
$926$	−2.16509e10	−0.896063
$927$	4.08895e9	0.168591
$928$	−7.77259e9	−0.319262
$929$	−2.87222e9	−0.117534	−0.0587668	−	0.998272i	$-0.518717\pi$
$929$	−2.87222e9	−0.117534	−0.0587668	+	0.998272i	$0.518717\pi$
$930$	4.54453e9	0.185267
$931$	−5.41280e9	−0.219836
$932$	4.45412e9	0.180221
$933$	1.57793e10	0.636066
$934$	2.54994e10	1.02404
$935$	−2.70994e10	−1.08422
$936$	−2.98882e9	−0.119134
$937$	−2.25687e10	−0.896227	−0.448114	−	0.893977i	$-0.647904\pi$
$937$	−2.25687e10	−0.896227	−0.448114	+	0.893977i	$0.647904\pi$
$938$	−2.29967e10	−0.909821
$939$	−2.51734e10	−0.992228
$940$	3.54887e10	1.39362
$941$	1.01256e10	0.396149	0.198075	−	0.980187i	$-0.436531\pi$
$941$	1.01256e10	0.396149	0.198075	+	0.980187i	$0.436531\pi$
$942$	−8.25323e9	−0.321696
$943$	5.52612e9	0.214600
$944$	3.89841e9	0.150829
$945$	−6.71548e9	−0.258861
$946$	−1.81754e10	−0.698017
$947$	−6.73699e9	−0.257775	−0.128888	−	0.991659i	$-0.541141\pi$
$947$	−6.73699e9	−0.257775	−0.128888	+	0.991659i	$0.541141\pi$
$948$	1.67601e10	0.638922
$949$	5.88054e10	2.23350
$950$	5.00204e10	1.89284
$951$	−2.41310e10	−0.909794
$952$	−8.35701e9	−0.313922
$953$	2.23147e10	0.835153	0.417577	−	0.908642i	$-0.362880\pi$
$953$	2.23147e10	0.835153	0.417577	+	0.908642i	$0.362880\pi$
$954$	−1.97444e10	−0.736249
$955$	−5.37199e10	−1.99583
$956$	−3.37785e10	−1.25037
$957$	2.12626e9	0.0784196
$958$	3.72754e10	1.36976
$959$	2.32698e10	0.851975
$960$	−1.36006e10	−0.496145
$961$	−2.68125e10	−0.974554
$962$	8.07009e10	2.92257
$963$	1.58566e10	0.572160
$964$	3.40549e9	0.122436
$965$	3.13845e10	1.12427
$966$	5.03456e9	0.179697
$967$	−2.22573e9	−0.0791554	−0.0395777	−	0.999216i	$-0.512601\pi$
$967$	−2.22573e9	−0.0791554	−0.0395777	+	0.999216i	$0.512601\pi$
$968$	5.23049e9	0.185344
$969$	2.44107e10	0.861881
$970$	8.02417e10	2.82292
$971$	−3.19447e9	−0.111978	−0.0559888	−	0.998431i	$-0.517831\pi$
$971$	−3.19447e9	−0.111978	−0.0559888	+	0.998431i	$0.517831\pi$
$972$	−1.47378e9	−0.0514755
$973$	−2.80503e10	−0.976210
$974$	1.86612e10	0.647116
$975$	−2.80320e10	−0.968585
$976$	−1.19319e10	−0.410804
$977$	−1.60496e10	−0.550598	−0.275299	−	0.961359i	$-0.588777\pi$
$977$	−1.60496e10	−0.550598	−0.275299	+	0.961359i	$0.588777\pi$
$978$	2.77242e10	0.947703
$979$	2.12094e9	0.0722417
$980$	6.87752e9	0.233421
$981$	−6.79825e9	−0.229909
$982$	−6.08022e10	−2.04894
$983$	3.86768e10	1.29871	0.649357	−	0.760484i	$-0.275038\pi$
$983$	3.86768e10	1.29871	0.649357	+	0.760484i	$0.275038\pi$
$984$	3.80340e9	0.127259
$985$	5.98416e10	1.99515
$986$	−1.31837e10	−0.437995
$987$	−1.81468e10	−0.600745
$988$	3.71128e10	1.22426
$989$	7.44211e9	0.244630
$990$	1.12362e10	0.368043
$991$	1.63094e10	0.532328	0.266164	−	0.963928i	$-0.414244\pi$
$991$	1.63094e10	0.532328	0.266164	+	0.963928i	$0.414244\pi$
$992$	−6.32759e9	−0.205801
$993$	−2.45068e10	−0.794262
$994$	−4.51438e10	−1.45796
$995$	3.17962e10	1.02328
$996$	1.30927e10	0.419876
$997$	2.35819e10	0.753608	0.376804	−	0.926293i	$-0.377023\pi$
$997$	2.35819e10	0.753608	0.376804	+	0.926293i	$0.377023\pi$
$998$	−9.68298e9	−0.308356
$999$	−9.79812e9	−0.310931

Twists

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

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

\(f(q)\)	\(=\)	\(q+15.1891 q^{2} -27.0000 q^{3} +102.710 q^{4} -418.807 q^{5} -410.107 q^{6} -814.653 q^{7} -384.131 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+15.1891 q^{2} -27.0000 q^{3} +102.710 q^{4} -418.807 q^{5} -410.107 q^{6} -814.653 q^{7} -384.131 q^{8} +729.000 q^{9} -6361.32 q^{10} -2422.96 q^{11} -2773.17 q^{12} +10673.2 q^{13} -12373.9 q^{14} +11307.8 q^{15} -18981.5 q^{16} -26705.4 q^{17} +11072.9 q^{18} +33854.6 q^{19} -43015.7 q^{20} +21995.6 q^{21} -36802.7 q^{22} +15069.2 q^{23} +10371.5 q^{24} +97274.0 q^{25} +162116. q^{26} -19683.0 q^{27} -83673.1 q^{28} +32501.7 q^{29} +171756. q^{30} +26459.3 q^{31} -239144. q^{32} +65420.0 q^{33} -405632. q^{34} +341182. q^{35} +74875.7 q^{36} +497796. q^{37} +514222. q^{38} -288176. q^{39} +160877. q^{40} +366715. q^{41} +334095. q^{42} +493861. q^{43} -248863. q^{44} -305310. q^{45} +228889. q^{46} -825019. q^{47} +512501. q^{48} -159884. q^{49} +1.47751e6 q^{50} +721046. q^{51} +1.09624e6 q^{52} -1.78313e6 q^{53} -298968. q^{54} +1.01475e6 q^{55} +312933. q^{56} -914074. q^{57} +493673. q^{58} -205379. q^{59} +1.16142e6 q^{60} +628605. q^{61} +401894. q^{62} -593882. q^{63} -1.20276e6 q^{64} -4.46999e6 q^{65} +993674. q^{66} +1.85849e6 q^{67} -2.74292e6 q^{68} -406870. q^{69} +5.18226e6 q^{70} +3.64832e6 q^{71} -280032. q^{72} +5.50965e6 q^{73} +7.56110e6 q^{74} -2.62640e6 q^{75} +3.47721e6 q^{76} +1.97387e6 q^{77} -4.37714e6 q^{78} -6.04365e6 q^{79} +7.94959e6 q^{80} +531441. q^{81} +5.57009e6 q^{82} -4.72119e6 q^{83} +2.25917e6 q^{84} +1.11844e7 q^{85} +7.50133e6 q^{86} -877545. q^{87} +930735. q^{88} -875348. q^{89} -4.63740e6 q^{90} -8.69493e6 q^{91} +1.54776e6 q^{92} -714401. q^{93} -1.25313e7 q^{94} -1.41785e7 q^{95} +6.45690e6 q^{96} -1.26140e7 q^{97} -2.42850e6 q^{98} -1.76634e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9	\( 17 q + 2 q^{2} - 459 q^{3} + 1166 q^{4} - 318 q^{5} - 54 q^{6} + 3145 q^{7} + 2355 q^{8} + 12393 q^{9} + 6521 q^{10} - 1764 q^{11} - 31482 q^{12} + 18192 q^{13} - 7827 q^{14} + 8586 q^{15} + 139226 q^{16} - 15507 q^{17} + 1458 q^{18} + 52083 q^{19} + 721 q^{20} - 84915 q^{21} - 234434 q^{22} + 63823 q^{23} - 63585 q^{24} + 202153 q^{25} - 367956 q^{26} - 334611 q^{27} + 182306 q^{28} - 502955 q^{29} - 176067 q^{30} + 347531 q^{31} - 243908 q^{32} + 47628 q^{33} - 330872 q^{34} + 92641 q^{35} + 850014 q^{36} + 447615 q^{37} + 775669 q^{38} - 491184 q^{39} + 2203270 q^{40} + 940335 q^{41} + 211329 q^{42} + 478562 q^{43} - 596924 q^{44} - 231822 q^{45} - 3078663 q^{46} + 703121 q^{47} - 3759102 q^{48} + 1895082 q^{49} - 876967 q^{50} + 418689 q^{51} + 6278296 q^{52} - 1005974 q^{53} - 39366 q^{54} + 5212846 q^{55} + 3425294 q^{56} - 1406241 q^{57} + 6710166 q^{58} - 3491443 q^{59} - 19467 q^{60} + 11510749 q^{61} + 5996234 q^{62} + 2292705 q^{63} + 29496941 q^{64} + 11094180 q^{65} + 6329718 q^{66} + 14007144 q^{67} + 19688159 q^{68} - 1723221 q^{69} + 30909708 q^{70} + 5229074 q^{71} + 1716795 q^{72} + 5452211 q^{73} + 12819662 q^{74} - 5458131 q^{75} + 41929340 q^{76} + 9930777 q^{77} + 9934812 q^{78} + 15275654 q^{79} + 36576105 q^{80} + 9034497 q^{81} + 32025935 q^{82} + 7826609 q^{83} - 4922262 q^{84} + 11836945 q^{85} + 51649136 q^{86} + 13579785 q^{87} + 30223741 q^{88} - 6436185 q^{89} + 4753809 q^{90} + 11633535 q^{91} + 43357972 q^{92} - 9383337 q^{93} - 4494252 q^{94} + 23741055 q^{95} + 6585516 q^{96} + 26377540 q^{97} + 26517816 q^{98} - 1285956 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 459 * q^3 + 1166 * q^4 - 318 * q^5 - 54 * q^6 + 3145 * q^7 + 2355 * q^8 + 12393 * q^9 + 6521 * q^10 - 1764 * q^11 - 31482 * q^12 + 18192 * q^13 - 7827 * q^14 + 8586 * q^15 + 139226 * q^16 - 15507 * q^17 + 1458 * q^18 + 52083 * q^19 + 721 * q^20 - 84915 * q^21 - 234434 * q^22 + 63823 * q^23 - 63585 * q^24 + 202153 * q^25 - 367956 * q^26 - 334611 * q^27 + 182306 * q^28 - 502955 * q^29 - 176067 * q^30 + 347531 * q^31 - 243908 * q^32 + 47628 * q^33 - 330872 * q^34 + 92641 * q^35 + 850014 * q^36 + 447615 * q^37 + 775669 * q^38 - 491184 * q^39 + 2203270 * q^40 + 940335 * q^41 + 211329 * q^42 + 478562 * q^43 - 596924 * q^44 - 231822 * q^45 - 3078663 * q^46 + 703121 * q^47 - 3759102 * q^48 + 1895082 * q^49 - 876967 * q^50 + 418689 * q^51 + 6278296 * q^52 - 1005974 * q^53 - 39366 * q^54 + 5212846 * q^55 + 3425294 * q^56 - 1406241 * q^57 + 6710166 * q^58 - 3491443 * q^59 - 19467 * q^60 + 11510749 * q^61 + 5996234 * q^62 + 2292705 * q^63 + 29496941 * q^64 + 11094180 * q^65 + 6329718 * q^66 + 14007144 * q^67 + 19688159 * q^68 - 1723221 * q^69 + 30909708 * q^70 + 5229074 * q^71 + 1716795 * q^72 + 5452211 * q^73 + 12819662 * q^74 - 5458131 * q^75 + 41929340 * q^76 + 9930777 * q^77 + 9934812 * q^78 + 15275654 * q^79 + 36576105 * q^80 + 9034497 * q^81 + 32025935 * q^82 + 7826609 * q^83 - 4922262 * q^84 + 11836945 * q^85 + 51649136 * q^86 + 13579785 * q^87 + 30223741 * q^88 - 6436185 * q^89 + 4753809 * q^90 + 11633535 * q^91 + 43357972 * q^92 - 9383337 * q^93 - 4494252 * q^94 + 23741055 * q^95 + 6585516 * q^96 + 26377540 * q^97 + 26517816 * q^98 - 1285956 * q^99

Introduction

L-functions

Modular forms

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