LMFDB - Embedded newform 177.12.a.a.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
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)

$f(q)$	$=$	$q+60.5708 q^{2} -243.000 q^{3} +1620.82 q^{4} +3733.47 q^{5} -14718.7 q^{6} +51542.9 q^{7} -25874.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+60.5708 q^{2} -243.000 q^{3} +1620.82 q^{4} +3733.47 q^{5} -14718.7 q^{6} +51542.9 q^{7} -25874.6 q^{8} +59049.0 q^{9} +226139. q^{10} +8197.47 q^{11} -393859. q^{12} -2.10127e6 q^{13} +3.12200e6 q^{14} -907234. q^{15} -4.88669e6 q^{16} +4.38795e6 q^{17} +3.57664e6 q^{18} -3.78954e6 q^{19} +6.05129e6 q^{20} -1.25249e7 q^{21} +496527. q^{22} +2.08704e7 q^{23} +6.28753e6 q^{24} -3.48893e7 q^{25} -1.27276e8 q^{26} -1.43489e7 q^{27} +8.35419e7 q^{28} -1.72215e8 q^{29} -5.49519e7 q^{30} +2.05932e8 q^{31} -2.42999e8 q^{32} -1.99198e6 q^{33} +2.65781e8 q^{34} +1.92434e8 q^{35} +9.57078e7 q^{36} -4.55455e7 q^{37} -2.29535e8 q^{38} +5.10609e8 q^{39} -9.66021e7 q^{40} -1.14598e9 q^{41} -7.58645e8 q^{42} +6.27327e8 q^{43} +1.32866e7 q^{44} +2.20458e8 q^{45} +1.26413e9 q^{46} -1.39069e9 q^{47} +1.18746e9 q^{48} +6.79348e8 q^{49} -2.11327e9 q^{50} -1.06627e9 q^{51} -3.40578e9 q^{52} +5.76515e9 q^{53} -8.69125e8 q^{54} +3.06050e7 q^{55} -1.33365e9 q^{56} +9.20857e8 q^{57} -1.04312e10 q^{58} +7.14924e8 q^{59} -1.47046e9 q^{60} -9.92538e9 q^{61} +1.24735e10 q^{62} +3.04356e9 q^{63} -4.71072e9 q^{64} -7.84504e9 q^{65} -1.20656e8 q^{66} +2.96887e9 q^{67} +7.11208e9 q^{68} -5.07150e9 q^{69} +1.16559e10 q^{70} -3.75907e9 q^{71} -1.52787e9 q^{72} -1.30199e10 q^{73} -2.75873e9 q^{74} +8.47810e9 q^{75} -6.14216e9 q^{76} +4.22522e8 q^{77} +3.09280e10 q^{78} +1.07884e10 q^{79} -1.82443e10 q^{80} +3.48678e9 q^{81} -6.94128e10 q^{82} +3.38622e10 q^{83} -2.03007e10 q^{84} +1.63823e10 q^{85} +3.79977e10 q^{86} +4.18484e10 q^{87} -2.12106e8 q^{88} -7.13197e10 q^{89} +1.33533e10 q^{90} -1.08306e11 q^{91} +3.38271e10 q^{92} -5.00416e10 q^{93} -8.42354e10 q^{94} -1.41481e10 q^{95} +5.90488e10 q^{96} -5.74773e10 q^{97} +4.11486e10 q^{98} +4.84052e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	60.5708	1.33844	0.669219	−	0.743065i	$-0.266629\pi$
$2$	60.5708	1.33844	0.669219	+	0.743065i	$0.266629\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	1620.82	0.791416
$5$	3733.47	0.534291	0.267146	−	0.963656i	$-0.413920\pi$
$5$	3733.47	0.534291	0.267146	+	0.963656i	$0.413920\pi$
$6$	−14718.7	−0.772748
$7$	51542.9	1.15912	0.579562	−	0.814928i	$-0.303224\pi$
$7$	51542.9	1.15912	0.579562	+	0.814928i	$0.303224\pi$
$8$	−25874.6	−0.279176
$9$	59049.0	0.333333
$10$	226139.	0.715116
$11$	8197.47	0.0153469	0.00767344	−	0.999971i	$-0.497557\pi$
$11$	8197.47	0.0153469	0.00767344	+	0.999971i	$0.497557\pi$
$12$	−393859.	−0.456924
$13$	−2.10127e6	−1.56962	−0.784808	−	0.619739i	$-0.787239\pi$
$13$	−2.10127e6	−1.56962	−0.784808	+	0.619739i	$0.787239\pi$
$14$	3.12200e6	1.55142
$15$	−907234.	−0.308473
$16$	−4.88669e6	−1.16508
$17$	4.38795e6	0.749536	0.374768	−	0.927119i	$-0.377722\pi$
$17$	4.38795e6	0.749536	0.374768	+	0.927119i	$0.377722\pi$
$18$	3.57664e6	0.446146
$19$	−3.78954e6	−0.351108	−0.175554	−	0.984470i	$-0.556172\pi$
$19$	−3.78954e6	−0.351108	−0.175554	+	0.984470i	$0.556172\pi$
$20$	6.05129e6	0.422847
$21$	−1.25249e7	−0.669221
$22$	496527.	0.0205408
$23$	2.08704e7	0.676125	0.338062	−	0.941124i	$-0.390228\pi$
$23$	2.08704e7	0.676125	0.338062	+	0.941124i	$0.390228\pi$
$24$	6.28753e6	0.161183
$25$	−3.48893e7	−0.714533
$26$	−1.27276e8	−2.10083
$27$	−1.43489e7	−0.192450
$28$	8.35419e7	0.917350
$29$	−1.72215e8	−1.55913	−0.779566	−	0.626320i	$-0.784561\pi$
$29$	−1.72215e8	−1.55913	−0.779566	+	0.626320i	$0.784561\pi$
$30$	−5.49519e7	−0.412872
$31$	2.05932e8	1.29192	0.645960	−	0.763372i	$-0.276457\pi$
$31$	2.05932e8	1.29192	0.645960	+	0.763372i	$0.276457\pi$
$32$	−2.42999e8	−1.28021
$33$	−1.99198e6	−0.00886052
$34$	2.65781e8	1.00321
$35$	1.92434e8	0.619310
$36$	9.57078e7	0.263805
$37$	−4.55455e7	−0.107978	−0.0539891	−	0.998542i	$-0.517194\pi$
$37$	−4.55455e7	−0.107978	−0.0539891	+	0.998542i	$0.517194\pi$
$38$	−2.29535e8	−0.469937
$39$	5.10609e8	0.906218
$40$	−9.66021e7	−0.149161
$41$	−1.14598e9	−1.54477	−0.772387	−	0.635152i	$-0.780938\pi$
$41$	−1.14598e9	−1.54477	−0.772387	+	0.635152i	$0.780938\pi$
$42$	−7.58645e8	−0.895710
$43$	6.27327e8	0.650755	0.325378	−	0.945584i	$-0.394509\pi$
$43$	6.27327e8	0.650755	0.325378	+	0.945584i	$0.394509\pi$
$44$	1.32866e7	0.0121458
$45$	2.20458e8	0.178097
$46$	1.26413e9	0.904951
$47$	−1.39069e9	−0.884490	−0.442245	−	0.896894i	$-0.645818\pi$
$47$	−1.39069e9	−0.884490	−0.442245	+	0.896894i	$0.645818\pi$
$48$	1.18746e9	0.672657
$49$	6.79348e8	0.343569
$50$	−2.11327e9	−0.956358
$51$	−1.06627e9	−0.432745
$52$	−3.40578e9	−1.24222
$53$	5.76515e9	1.89362	0.946810	−	0.321792i	$-0.104285\pi$
$53$	5.76515e9	1.89362	0.946810	+	0.321792i	$0.104285\pi$
$54$	−8.69125e8	−0.257583
$55$	3.06050e7	0.00819970
$56$	−1.33365e9	−0.323600
$57$	9.20857e8	0.202713
$58$	−1.04312e10	−2.08680
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−1.47046e9	−0.244131
$61$	−9.92538e9	−1.50464	−0.752321	−	0.658797i	$-0.771066\pi$
$61$	−9.92538e9	−1.50464	−0.752321	+	0.658797i	$0.771066\pi$
$62$	1.24735e10	1.72915
$63$	3.04356e9	0.386375
$64$	−4.71072e9	−0.548400
$65$	−7.84504e9	−0.838632
$66$	−1.20656e8	−0.0118593
$67$	2.96887e9	0.268645	0.134323	−	0.990938i	$-0.457114\pi$
$67$	2.96887e9	0.268645	0.134323	+	0.990938i	$0.457114\pi$
$68$	7.11208e9	0.593195
$69$	−5.07150e9	−0.390361
$70$	1.16559e10	0.828908
$71$	−3.75907e9	−0.247263	−0.123632	−	0.992328i	$-0.539454\pi$
$71$	−3.75907e9	−0.247263	−0.123632	+	0.992328i	$0.539454\pi$
$72$	−1.52787e9	−0.0930588
$73$	−1.30199e10	−0.735078	−0.367539	−	0.930008i	$-0.619799\pi$
$73$	−1.30199e10	−0.735078	−0.367539	+	0.930008i	$0.619799\pi$
$74$	−2.75873e9	−0.144522
$75$	8.47810e9	0.412536
$76$	−6.14216e9	−0.277873
$77$	4.22522e8	0.0177889
$78$	3.09280e10	1.21292
$79$	1.07884e10	0.394463	0.197232	−	0.980357i	$-0.436805\pi$
$79$	1.07884e10	0.394463	0.197232	+	0.980357i	$0.436805\pi$
$80$	−1.82443e10	−0.622490
$81$	3.48678e9	0.111111
$82$	−6.94128e10	−2.06759
$83$	3.38622e10	0.943595	0.471798	−	0.881707i	$-0.343605\pi$
$83$	3.38622e10	0.943595	0.471798	+	0.881707i	$0.343605\pi$
$84$	−2.03007e10	−0.529632
$85$	1.63823e10	0.400470
$86$	3.79977e10	0.870996
$87$	4.18484e10	0.900166
$88$	−2.12106e8	−0.00428448
$89$	−7.13197e10	−1.35383	−0.676915	−	0.736061i	$-0.736684\pi$
$89$	−7.13197e10	−1.35383	−0.676915	+	0.736061i	$0.736684\pi$
$90$	1.33533e10	0.238372
$91$	−1.08306e11	−1.81938
$92$	3.38271e10	0.535096
$93$	−5.00416e10	−0.745890
$94$	−8.42354e10	−1.18384
$95$	−1.41481e10	−0.187594
$96$	5.90488e10	0.739128
$97$	−5.74773e10	−0.679598	−0.339799	−	0.940498i	$-0.610359\pi$
$97$	−5.74773e10	−0.679598	−0.339799	+	0.940498i	$0.610359\pi$
$98$	4.11486e10	0.459846
$99$	4.84052e8	0.00511562
$100$	−5.65493e10	−0.565493
$101$	−9.01764e10	−0.853740	−0.426870	−	0.904313i	$-0.640384\pi$
$101$	−9.01764e10	−0.853740	−0.426870	+	0.904313i	$0.640384\pi$
$102$	−6.45849e10	−0.579202
$103$	1.00632e11	0.855321	0.427661	−	0.903939i	$-0.359338\pi$
$103$	1.00632e11	0.855321	0.427661	+	0.903939i	$0.359338\pi$
$104$	5.43695e10	0.438200
$105$	−4.67615e10	−0.357559
$106$	3.49199e11	2.53449
$107$	−2.50318e11	−1.72537	−0.862684	−	0.505743i	$-0.831218\pi$
$107$	−2.50318e11	−1.72537	−0.862684	+	0.505743i	$0.831218\pi$
$108$	−2.32570e10	−0.152308
$109$	−2.34333e11	−1.45877	−0.729385	−	0.684103i	$-0.760194\pi$
$109$	−2.34333e11	−1.45877	−0.729385	+	0.684103i	$0.760194\pi$
$110$	1.85377e9	0.0109748
$111$	1.10676e10	0.0623412
$112$	−2.51874e11	−1.35047
$113$	−3.10993e11	−1.58789	−0.793944	−	0.607991i	$-0.791975\pi$
$113$	−3.10993e11	−1.58789	−0.793944	+	0.607991i	$0.791975\pi$
$114$	5.57771e10	0.271318
$115$	7.79190e10	0.361248
$116$	−2.79130e11	−1.23392
$117$	−1.24078e11	−0.523205
$118$	4.33035e10	0.174250
$119$	2.26168e11	0.868805
$120$	2.34743e10	0.0861184
$121$	−2.85244e11	−0.999764
$122$	−6.01188e11	−2.01387
$123$	2.78473e11	0.891876
$124$	3.33779e11	1.02245
$125$	−3.12557e11	−0.916060
$126$	1.84351e11	0.517139
$127$	−2.28256e10	−0.0613059	−0.0306530	−	0.999530i	$-0.509759\pi$
$127$	−2.28256e10	−0.0613059	−0.0306530	+	0.999530i	$0.509759\pi$
$128$	2.12330e11	0.546206
$129$	−1.52441e11	−0.375714
$130$	−4.75180e11	−1.12246
$131$	−4.71963e11	−1.06885	−0.534424	−	0.845217i	$-0.679471\pi$
$131$	−4.71963e11	−1.06885	−0.534424	+	0.845217i	$0.679471\pi$
$132$	−3.22865e9	−0.00701236
$133$	−1.95324e11	−0.406978
$134$	1.79827e11	0.359565
$135$	−5.35713e10	−0.102824
$136$	−1.13536e11	−0.209253
$137$	−9.83893e11	−1.74175	−0.870873	−	0.491508i	$-0.836446\pi$
$137$	−9.83893e11	−1.74175	−0.870873	+	0.491508i	$0.836446\pi$
$138$	−3.07185e11	−0.522474
$139$	−6.09086e11	−0.995628	−0.497814	−	0.867284i	$-0.665864\pi$
$139$	−6.09086e11	−0.995628	−0.497814	+	0.867284i	$0.665864\pi$
$140$	3.11901e11	0.490132
$141$	3.37938e11	0.510661
$142$	−2.27690e11	−0.330947
$143$	−1.72251e10	−0.0240887
$144$	−2.88554e11	−0.388359
$145$	−6.42962e11	−0.833031
$146$	−7.88628e11	−0.983856
$147$	−1.65082e11	−0.198360
$148$	−7.38211e10	−0.0854557
$149$	9.98841e11	1.11422	0.557111	−	0.830438i	$-0.311910\pi$
$149$	9.98841e11	1.11422	0.557111	+	0.830438i	$0.311910\pi$
$150$	5.13525e11	0.552154
$151$	−1.54795e12	−1.60466	−0.802332	−	0.596878i	$-0.796408\pi$
$151$	−1.54795e12	−1.60466	−0.802332	+	0.596878i	$0.796408\pi$
$152$	9.80527e10	0.0980212
$153$	2.59104e11	0.249845
$154$	2.55925e10	0.0238094
$155$	7.68843e11	0.690261
$156$	8.27605e11	0.717196
$157$	2.09764e12	1.75502	0.877510	−	0.479558i	$-0.159203\pi$
$157$	2.09764e12	1.75502	0.877510	+	0.479558i	$0.159203\pi$
$158$	6.53460e11	0.527965
$159$	−1.40093e12	−1.09328
$160$	−9.07231e11	−0.684003
$161$	1.07572e12	0.783713
$162$	2.11197e11	0.148715
$163$	2.42348e12	1.64971	0.824854	−	0.565346i	$-0.191257\pi$
$163$	2.42348e12	1.64971	0.824854	+	0.565346i	$0.191257\pi$
$164$	−1.85743e12	−1.22256
$165$	−7.43702e9	−0.00473410
$166$	2.05106e12	1.26294
$167$	2.21723e12	1.32090	0.660450	−	0.750870i	$-0.270365\pi$
$167$	2.21723e12	1.32090	0.660450	+	0.750870i	$0.270365\pi$
$168$	3.24078e11	0.186831
$169$	2.62318e12	1.46370
$170$	9.92288e11	0.536005
$171$	−2.23768e11	−0.117036
$172$	1.01679e12	0.515018
$173$	3.06408e12	1.50330	0.751651	−	0.659561i	$-0.229258\pi$
$173$	3.06408e12	1.50330	0.751651	+	0.659561i	$0.229258\pi$
$174$	2.53479e12	1.20482
$175$	−1.79830e12	−0.828232
$176$	−4.00584e10	−0.0178803
$177$	−1.73727e11	−0.0751646
$178$	−4.31989e12	−1.81202
$179$	−2.18794e12	−0.889906	−0.444953	−	0.895554i	$-0.646780\pi$
$179$	−2.18794e12	−0.889906	−0.444953	+	0.895554i	$0.646780\pi$
$180$	3.57323e11	0.140949
$181$	−2.33641e12	−0.893959	−0.446980	−	0.894544i	$-0.647500\pi$
$181$	−2.33641e12	−0.893959	−0.446980	+	0.894544i	$0.647500\pi$
$182$	−6.56016e12	−2.43513
$183$	2.41187e12	0.868705
$184$	−5.40012e11	−0.188758
$185$	−1.70043e11	−0.0576918
$186$	−3.03106e12	−0.998327
$187$	3.59701e10	0.0115030
$188$	−2.25406e12	−0.700000
$189$	−7.39585e11	−0.223074
$190$	−8.56964e11	−0.251083
$191$	3.50468e12	0.997618	0.498809	−	0.866712i	$-0.333771\pi$
$191$	3.50468e12	0.997618	0.498809	+	0.866712i	$0.333771\pi$
$192$	1.14471e12	0.316619
$193$	4.71015e12	1.26611	0.633053	−	0.774109i	$-0.281802\pi$
$193$	4.71015e12	1.26611	0.633053	+	0.774109i	$0.281802\pi$
$194$	−3.48145e12	−0.909599
$195$	1.90634e12	0.484185
$196$	1.10110e12	0.271906
$197$	−2.38674e12	−0.573114	−0.286557	−	0.958063i	$-0.592511\pi$
$197$	−2.38674e12	−0.573114	−0.286557	+	0.958063i	$0.592511\pi$
$198$	2.93194e10	0.00684695
$199$	−2.18916e12	−0.497262	−0.248631	−	0.968598i	$-0.579981\pi$
$199$	−2.18916e12	−0.497262	−0.248631	+	0.968598i	$0.579981\pi$
$200$	9.02746e11	0.199481
$201$	−7.21434e11	−0.155102
$202$	−5.46206e12	−1.14268
$203$	−8.87649e12	−1.80723
$204$	−1.72823e12	−0.342481
$205$	−4.27848e12	−0.825360
$206$	6.09533e12	1.14479
$207$	1.23237e12	0.225375
$208$	1.02682e13	1.82872
$209$	−3.10646e10	−0.00538842
$210$	−2.83238e12	−0.478570
$211$	1.32116e12	0.217471	0.108735	−	0.994071i	$-0.465320\pi$
$211$	1.32116e12	0.217471	0.108735	+	0.994071i	$0.465320\pi$
$212$	9.34427e12	1.49864
$213$	9.13455e11	0.142758
$214$	−1.51620e13	−2.30930
$215$	2.34211e12	0.347693
$216$	3.71272e11	0.0537275
$217$	1.06144e13	1.49749
$218$	−1.41937e13	−1.95247
$219$	3.16384e12	0.424397
$220$	4.96053e10	0.00648938
$221$	−9.22027e12	−1.17648
$222$	6.70370e11	0.0834399
$223$	4.97159e12	0.603697	0.301848	−	0.953356i	$-0.402396\pi$
$223$	4.97159e12	0.603697	0.301848	+	0.953356i	$0.402396\pi$
$224$	−1.25249e13	−1.48392
$225$	−2.06018e12	−0.238178
$226$	−1.88371e13	−2.12529
$227$	8.10911e12	0.892958	0.446479	−	0.894794i	$-0.352678\pi$
$227$	8.10911e12	0.892958	0.446479	+	0.894794i	$0.352678\pi$
$228$	1.49254e12	0.160430
$229$	−1.05022e12	−0.110201	−0.0551006	−	0.998481i	$-0.517548\pi$
$229$	−1.05022e12	−0.110201	−0.0551006	+	0.998481i	$0.517548\pi$
$230$	4.71961e12	0.483508
$231$	−1.02673e11	−0.0102704
$232$	4.45600e12	0.435273
$233$	−9.21077e12	−0.878696	−0.439348	−	0.898317i	$-0.644790\pi$
$233$	−9.21077e12	−0.878696	−0.439348	+	0.898317i	$0.644790\pi$
$234$	−7.51550e12	−0.700278
$235$	−5.19211e12	−0.472575
$236$	1.15876e12	0.103034
$237$	−2.62157e12	−0.227744
$238$	1.36992e13	1.16284
$239$	4.53953e12	0.376550	0.188275	−	0.982116i	$-0.439710\pi$
$239$	4.53953e12	0.376550	0.188275	+	0.982116i	$0.439710\pi$
$240$	4.43337e12	0.359395
$241$	−1.03270e13	−0.818241	−0.409121	−	0.912480i	$-0.634164\pi$
$241$	−1.03270e13	−0.818241	−0.409121	+	0.912480i	$0.634164\pi$
$242$	−1.72775e13	−1.33812
$243$	−8.47289e11	−0.0641500
$244$	−1.60873e13	−1.19080
$245$	2.53633e12	0.183566
$246$	1.68673e13	1.19372
$247$	7.96284e12	0.551106
$248$	−5.32842e12	−0.360673
$249$	−8.22851e12	−0.544785
$250$	−1.89318e13	−1.22609
$251$	−2.40666e13	−1.52479	−0.762395	−	0.647112i	$-0.775976\pi$
$251$	−2.40666e13	−1.52479	−0.762395	+	0.647112i	$0.775976\pi$
$252$	4.93306e12	0.305783
$253$	1.71084e11	0.0103764
$254$	−1.38257e12	−0.0820541
$255$	−3.98090e12	−0.231212
$256$	2.25086e13	1.27946
$257$	−7.34188e12	−0.408484	−0.204242	−	0.978920i	$-0.565473\pi$
$257$	−7.34188e12	−0.408484	−0.204242	+	0.978920i	$0.565473\pi$
$258$	−9.23344e12	−0.502870
$259$	−2.34755e12	−0.125160
$260$	−1.27154e13	−0.663707
$261$	−1.01692e13	−0.519711
$262$	−2.85872e13	−1.43059
$263$	1.31064e13	0.642284	0.321142	−	0.947031i	$-0.395933\pi$
$263$	1.31064e13	0.642284	0.321142	+	0.947031i	$0.395933\pi$
$264$	5.15418e10	0.00247365
$265$	2.15240e13	1.01175
$266$	−1.18309e13	−0.544715
$267$	1.73307e13	0.781635
$268$	4.81200e12	0.212610
$269$	3.48998e12	0.151072	0.0755362	−	0.997143i	$-0.475933\pi$
$269$	3.48998e12	0.151072	0.0755362	+	0.997143i	$0.475933\pi$
$270$	−3.24485e12	−0.137624
$271$	2.74166e13	1.13942	0.569709	−	0.821847i	$-0.307056\pi$
$271$	2.74166e13	1.13942	0.569709	+	0.821847i	$0.307056\pi$
$272$	−2.14425e13	−0.873267
$273$	2.63183e13	1.05042
$274$	−5.95952e13	−2.33122
$275$	−2.86004e11	−0.0109658
$276$	−8.21999e12	−0.308938
$277$	−4.43374e12	−0.163354	−0.0816772	−	0.996659i	$-0.526028\pi$
$277$	−4.43374e12	−0.163354	−0.0816772	+	0.996659i	$0.526028\pi$
$278$	−3.68928e13	−1.33259
$279$	1.21601e13	0.430640
$280$	−4.97916e12	−0.172897
$281$	1.81627e13	0.618436	0.309218	−	0.950991i	$-0.399933\pi$
$281$	1.81627e13	0.618436	0.309218	+	0.950991i	$0.399933\pi$
$282$	2.04692e13	0.683488
$283$	2.15554e13	0.705881	0.352940	−	0.935646i	$-0.385182\pi$
$283$	2.15554e13	0.705881	0.352940	+	0.935646i	$0.385182\pi$
$284$	−6.09278e12	−0.195688
$285$	3.43800e12	0.108308
$286$	−1.04334e12	−0.0322412
$287$	−5.90671e13	−1.79059
$288$	−1.43489e13	−0.426735
$289$	−1.50178e13	−0.438196
$290$	−3.89447e13	−1.11496
$291$	1.39670e13	0.392366
$292$	−2.11030e13	−0.581752
$293$	3.18276e13	0.861058	0.430529	−	0.902577i	$-0.358327\pi$
$293$	3.18276e13	0.861058	0.430529	+	0.902577i	$0.358327\pi$
$294$	−9.99912e12	−0.265492
$295$	2.66915e12	0.0695588
$296$	1.17847e12	0.0301449
$297$	−1.17625e11	−0.00295351
$298$	6.05006e13	1.49132
$299$	−4.38543e13	−1.06126
$300$	1.37415e13	0.326488
$301$	3.23343e13	0.754306
$302$	−9.37607e13	−2.14774
$303$	2.19129e13	0.492907
$304$	1.85183e13	0.409068
$305$	−3.70561e13	−0.803917
$306$	1.56941e13	0.334402
$307$	6.29154e13	1.31673	0.658364	−	0.752700i	$-0.271249\pi$
$307$	6.29154e13	1.31673	0.658364	+	0.752700i	$0.271249\pi$
$308$	6.84832e11	0.0140785
$309$	−2.44535e13	−0.493820
$310$	4.65694e13	0.923872
$311$	−2.26249e13	−0.440966	−0.220483	−	0.975391i	$-0.570763\pi$
$311$	−2.26249e13	−0.440966	−0.220483	+	0.975391i	$0.570763\pi$
$312$	−1.32118e13	−0.252995
$313$	−7.46918e13	−1.40533	−0.702666	−	0.711520i	$-0.748007\pi$
$313$	−7.46918e13	−1.40533	−0.702666	+	0.711520i	$0.748007\pi$
$314$	1.27055e14	2.34899
$315$	1.13630e13	0.206437
$316$	1.74860e13	0.312185
$317$	5.89358e13	1.03408	0.517039	−	0.855962i	$-0.327034\pi$
$317$	5.89358e13	1.03408	0.517039	+	0.855962i	$0.327034\pi$
$318$	−8.48555e13	−1.46329
$319$	−1.41173e12	−0.0239278
$320$	−1.75874e13	−0.293006
$321$	6.08274e13	0.996142
$322$	6.51572e13	1.04895
$323$	−1.66283e13	−0.263168
$324$	5.65145e12	0.0879351
$325$	7.33119e13	1.12154
$326$	1.46792e14	2.20803
$327$	5.69428e13	0.842221
$328$	2.96517e13	0.431265
$329$	−7.16804e13	−1.02523
$330$	−4.50466e11	−0.00633630
$331$	1.27988e14	1.77058	0.885290	−	0.465039i	$-0.153960\pi$
$331$	1.27988e14	1.77058	0.885290	+	0.465039i	$0.153960\pi$
$332$	5.48846e13	0.746777
$333$	−2.68942e12	−0.0359927
$334$	1.34299e14	1.76794
$335$	1.10842e13	0.143535
$336$	6.12054e13	0.779693
$337$	3.81105e13	0.477617	0.238809	−	0.971067i	$-0.423243\pi$
$337$	3.81105e13	0.477617	0.238809	+	0.971067i	$0.423243\pi$
$338$	1.58888e14	1.95907
$339$	7.55714e13	0.916767
$340$	2.65528e13	0.316939
$341$	1.68812e12	0.0198269
$342$	−1.35538e13	−0.156646
$343$	−6.69016e13	−0.760885
$344$	−1.62318e13	−0.181675
$345$	−1.89343e13	−0.208566
$346$	1.85594e14	2.01208
$347$	−3.43199e13	−0.366213	−0.183106	−	0.983093i	$-0.558615\pi$
$347$	−3.43199e13	−0.366213	−0.183106	+	0.983093i	$0.558615\pi$
$348$	6.78287e13	0.712406
$349$	3.07555e13	0.317967	0.158984	−	0.987281i	$-0.449178\pi$
$349$	3.07555e13	0.317967	0.158984	+	0.987281i	$0.449178\pi$
$350$	−1.08924e14	−1.10854
$351$	3.01509e13	0.302073
$352$	−1.99198e12	−0.0196472
$353$	−1.51838e14	−1.47442	−0.737208	−	0.675666i	$-0.763856\pi$
$353$	−1.51838e14	−1.47442	−0.737208	+	0.675666i	$0.763856\pi$
$354$	−1.05228e13	−0.100603
$355$	−1.40344e13	−0.132111
$356$	−1.15596e14	−1.07144
$357$	−5.49588e13	−0.501605
$358$	−1.32525e14	−1.19108
$359$	5.11655e13	0.452853	0.226427	−	0.974028i	$-0.427296\pi$
$359$	5.11655e13	0.452853	0.226427	+	0.974028i	$0.427296\pi$
$360$	−5.70426e12	−0.0497205
$361$	−1.02130e14	−0.876723
$362$	−1.41518e14	−1.19651
$363$	6.93144e13	0.577214
$364$	−1.75544e14	−1.43989
$365$	−4.86096e13	−0.392745
$366$	1.46089e14	1.16271
$367$	1.12307e14	0.880530	0.440265	−	0.897868i	$-0.354884\pi$
$367$	1.12307e14	0.880530	0.440265	+	0.897868i	$0.354884\pi$
$368$	−1.01987e14	−0.787737
$369$	−6.76689e13	−0.514925
$370$	−1.02996e13	−0.0772169
$371$	2.97153e14	2.19494
$372$	−8.11084e13	−0.590309
$373$	−1.89088e14	−1.35602	−0.678008	−	0.735055i	$-0.737156\pi$
$373$	−1.89088e14	−1.35602	−0.678008	+	0.735055i	$0.737156\pi$
$374$	2.17874e12	0.0153961
$375$	7.59513e13	0.528887
$376$	3.59836e13	0.246929
$377$	3.61871e14	2.44724
$378$	−4.47972e13	−0.298570
$379$	−2.69273e14	−1.76879	−0.884397	−	0.466735i	$-0.845430\pi$
$379$	−2.69273e14	−1.76879	−0.884397	+	0.466735i	$0.845430\pi$
$380$	−2.29316e13	−0.148465
$381$	5.54663e12	0.0353950
$382$	2.12281e14	1.33525
$383$	1.65685e14	1.02728	0.513641	−	0.858005i	$-0.328297\pi$
$383$	1.65685e14	1.02728	0.513641	+	0.858005i	$0.328297\pi$
$384$	−5.15962e13	−0.315352
$385$	1.57747e12	0.00950447
$386$	2.85298e14	1.69460
$387$	3.70431e13	0.216918
$388$	−9.31604e13	−0.537845
$389$	2.95800e14	1.68374	0.841870	−	0.539680i	$-0.181455\pi$
$389$	2.95800e14	1.68374	0.841870	+	0.539680i	$0.181455\pi$
$390$	1.15469e14	0.648051
$391$	9.15781e13	0.506780
$392$	−1.75779e13	−0.0959163
$393$	1.14687e14	0.617100
$394$	−1.44567e14	−0.767077
$395$	4.02781e13	0.210758
$396$	7.84562e11	0.00404859
$397$	2.47790e13	0.126106	0.0630530	−	0.998010i	$-0.479916\pi$
$397$	2.47790e13	0.126106	0.0630530	+	0.998010i	$0.479916\pi$
$398$	−1.32599e14	−0.665555
$399$	4.74637e13	0.234969
$400$	1.70493e14	0.832485
$401$	−1.21810e14	−0.586664	−0.293332	−	0.956011i	$-0.594764\pi$
$401$	−1.21810e14	−0.586664	−0.293332	+	0.956011i	$0.594764\pi$
$402$	−4.36978e13	−0.207595
$403$	−4.32720e14	−2.02782
$404$	−1.46160e14	−0.675664
$405$	1.30178e13	0.0593657
$406$	−5.37656e14	−2.41886
$407$	−3.73358e11	−0.00165713
$408$	2.75893e13	0.120812
$409$	6.26630e13	0.270728	0.135364	−	0.990796i	$-0.456780\pi$
$409$	6.26630e13	0.270728	0.135364	+	0.990796i	$0.456780\pi$
$410$	−2.59151e14	−1.10469
$411$	2.39086e14	1.00560
$412$	1.63106e14	0.676915
$413$	3.68493e13	0.150905
$414$	7.46459e13	0.301650
$415$	1.26424e14	0.504155
$416$	5.10607e14	2.00943
$417$	1.48008e14	0.574826
$418$	−1.88161e12	−0.00721206
$419$	3.19512e14	1.20868	0.604338	−	0.796728i	$-0.293438\pi$
$419$	3.19512e14	1.20868	0.604338	+	0.796728i	$0.293438\pi$
$420$	−7.57920e13	−0.282978
$421$	4.81196e14	1.77325	0.886627	−	0.462486i	$-0.153042\pi$
$421$	4.81196e14	1.77325	0.886627	+	0.462486i	$0.153042\pi$
$422$	8.00235e13	0.291071
$423$	−8.21190e13	−0.294830
$424$	−1.49171e14	−0.528654
$425$	−1.53092e14	−0.535568
$426$	5.53287e13	0.191072
$427$	−5.11583e14	−1.74407
$428$	−4.05721e14	−1.36548
$429$	4.18570e12	0.0139076
$430$	1.41863e14	0.465365
$431$	−3.69293e14	−1.19604	−0.598020	−	0.801481i	$-0.704046\pi$
$431$	−3.69293e14	−1.19604	−0.598020	+	0.801481i	$0.704046\pi$
$432$	7.01186e13	0.224219
$433$	3.30299e14	1.04286	0.521428	−	0.853295i	$-0.325400\pi$
$433$	3.30299e14	1.04286	0.521428	+	0.853295i	$0.325400\pi$
$434$	6.42920e14	2.00430
$435$	1.56240e14	0.480951
$436$	−3.79811e14	−1.15449
$437$	−7.90890e13	−0.237393
$438$	1.91637e14	0.568029
$439$	8.70926e13	0.254933	0.127467	−	0.991843i	$-0.459315\pi$
$439$	8.70926e13	0.254933	0.127467	+	0.991843i	$0.459315\pi$
$440$	−7.91893e11	−0.00228916
$441$	4.01148e13	0.114523
$442$	−5.58479e14	−1.57465
$443$	3.65477e14	1.01775	0.508873	−	0.860842i	$-0.330062\pi$
$443$	3.65477e14	1.01775	0.508873	+	0.860842i	$0.330062\pi$
$444$	1.79385e13	0.0493379
$445$	−2.66270e14	−0.723340
$446$	3.01133e14	0.808011
$447$	−2.42718e14	−0.643297
$448$	−2.42805e14	−0.635664
$449$	−1.67608e14	−0.433452	−0.216726	−	0.976232i	$-0.569538\pi$
$449$	−1.67608e14	−0.433452	−0.216726	+	0.976232i	$0.569538\pi$
$450$	−1.24787e14	−0.318786
$451$	−9.39412e12	−0.0237075
$452$	−5.04064e14	−1.25668
$453$	3.76152e14	0.926454
$454$	4.91175e14	1.19517
$455$	−4.04356e14	−0.972079
$456$	−2.38268e13	−0.0565926
$457$	−1.34461e14	−0.315543	−0.157772	−	0.987476i	$-0.550431\pi$
$457$	−1.34461e14	−0.315543	−0.157772	+	0.987476i	$0.550431\pi$
$458$	−6.36128e13	−0.147497
$459$	−6.29623e13	−0.144248
$460$	1.26293e14	0.285897
$461$	5.77377e14	1.29153	0.645765	−	0.763537i	$-0.276539\pi$
$461$	5.77377e14	1.29153	0.645765	+	0.763537i	$0.276539\pi$
$462$	−6.21897e12	−0.0137464
$463$	−4.97910e14	−1.08757	−0.543783	−	0.839226i	$-0.683008\pi$
$463$	−4.97910e14	−1.08757	−0.543783	+	0.839226i	$0.683008\pi$
$464$	8.41563e14	1.81651
$465$	−1.86829e14	−0.398522
$466$	−5.57904e14	−1.17608
$467$	1.38512e14	0.288566	0.144283	−	0.989536i	$-0.453912\pi$
$467$	1.38512e14	0.288566	0.144283	+	0.989536i	$0.453912\pi$
$468$	−2.01108e14	−0.414073
$469$	1.53024e14	0.311393
$470$	−3.14491e14	−0.632513
$471$	−5.09726e14	−1.01326
$472$	−1.84984e13	−0.0363457
$473$	5.14250e12	0.00998706
$474$	−1.58791e14	−0.304821
$475$	1.32214e14	0.250879
$476$	3.66577e14	0.687587
$477$	3.40426e14	0.631207
$478$	2.74963e14	0.503989
$479$	−5.67127e14	−1.02763	−0.513813	−	0.857902i	$-0.671767\pi$
$479$	−5.67127e14	−1.02763	−0.513813	+	0.857902i	$0.671767\pi$
$480$	2.20457e14	0.394909
$481$	9.57034e13	0.169484
$482$	−6.25516e14	−1.09516
$483$	−2.61400e14	−0.452477
$484$	−4.62330e14	−0.791230
$485$	−2.14590e14	−0.363103
$486$	−5.13209e13	−0.0858608
$487$	9.12154e10	0.000150889 0	7.54447e−5	−	1.00000i	$-0.499976\pi$
$487$	9.12154e10	0.000150889 0	7.54447e−5		1.00000i	$0.499976\pi$
$488$	2.56815e14	0.420060
$489$	−5.88905e14	−0.952460
$490$	1.53627e14	0.245692
$491$	1.20600e14	0.190722	0.0953608	−	0.995443i	$-0.469600\pi$
$491$	1.20600e14	0.190722	0.0953608	+	0.995443i	$0.469600\pi$
$492$	4.51354e14	0.705845
$493$	−7.55672e14	−1.16863
$494$	4.82316e14	0.737621
$495$	1.80720e12	0.00273323
$496$	−1.00633e15	−1.50518
$497$	−1.93754e14	−0.286609
$498$	−4.98408e14	−0.729161
$499$	6.81501e14	0.986082	0.493041	−	0.870006i	$-0.335885\pi$
$499$	6.81501e14	0.986082	0.493041	+	0.870006i	$0.335885\pi$
$500$	−5.06599e14	−0.724985
$501$	−5.38787e14	−0.762622
$502$	−1.45774e15	−2.04084
$503$	−3.20766e14	−0.444186	−0.222093	−	0.975025i	$-0.571289\pi$
$503$	−3.20766e14	−0.444186	−0.222093	+	0.975025i	$0.571289\pi$
$504$	−7.87508e13	−0.107867
$505$	−3.36671e14	−0.456146
$506$	1.03627e13	0.0138882
$507$	−6.37432e14	−0.845065
$508$	−3.69962e13	−0.0485185
$509$	−9.98074e14	−1.29484	−0.647418	−	0.762135i	$-0.724151\pi$
$509$	−9.98074e14	−1.29484	−0.647418	+	0.762135i	$0.724151\pi$
$510$	−2.41126e14	−0.309463
$511$	−6.71086e14	−0.852046
$512$	9.28510e14	1.16628
$513$	5.43757e13	0.0675709
$514$	−4.44704e14	−0.546731
$515$	3.75705e14	0.456991
$516$	−2.47079e14	−0.297346
$517$	−1.14002e13	−0.0135742
$518$	−1.42193e14	−0.167519
$519$	−7.44571e14	−0.867932
$520$	2.02987e14	0.234126
$521$	−1.66176e15	−1.89653	−0.948266	−	0.317477i	$-0.897164\pi$
$521$	−1.66176e15	−1.89653	−0.948266	+	0.317477i	$0.897164\pi$
$522$	−6.15953e14	−0.695601
$523$	−4.06295e14	−0.454027	−0.227014	−	0.973892i	$-0.572896\pi$
$523$	−4.06295e14	−0.454027	−0.227014	+	0.973892i	$0.572896\pi$
$524$	−7.64968e14	−0.845904
$525$	4.36986e14	0.478180
$526$	7.93866e14	0.859658
$527$	9.03621e14	0.968340
$528$	9.73420e12	0.0103232
$529$	−5.17238e14	−0.542855
$530$	1.30373e15	1.35416
$531$	4.22156e13	0.0433963
$532$	−3.16585e14	−0.322089
$533$	2.40801e15	2.42470
$534$	1.04973e15	1.04617
$535$	−9.34557e14	−0.921849
$536$	−7.68182e13	−0.0749994
$537$	5.31670e14	0.513787
$538$	2.11391e14	0.202201
$539$	5.56893e12	0.00527271
$540$	−8.68294e13	−0.0813769
$541$	−6.01417e13	−0.0557944	−0.0278972	−	0.999611i	$-0.508881\pi$
$541$	−6.01417e13	−0.0557944	−0.0278972	+	0.999611i	$0.508881\pi$
$542$	1.66065e15	1.52504
$543$	5.67749e14	0.516128
$544$	−1.06627e15	−0.959561
$545$	−8.74874e14	−0.779408
$546$	1.59412e15	1.40592
$547$	1.27342e15	1.11184	0.555919	−	0.831236i	$-0.312366\pi$
$547$	1.27342e15	1.11184	0.555919	+	0.831236i	$0.312366\pi$
$548$	−1.59471e15	−1.37845
$549$	−5.86084e14	−0.501547
$550$	−1.73235e13	−0.0146771
$551$	6.52617e14	0.547425
$552$	1.31223e14	0.108980
$553$	5.56064e14	0.457232
$554$	−2.68555e14	−0.218640
$555$	4.13204e13	0.0333084
$556$	−9.87218e14	−0.787956
$557$	−1.28386e14	−0.101464	−0.0507322	−	0.998712i	$-0.516155\pi$
$557$	−1.28386e14	−0.101464	−0.0507322	+	0.998712i	$0.516155\pi$
$558$	7.36547e14	0.576385
$559$	−1.31818e15	−1.02144
$560$	−9.40365e14	−0.721543
$561$	−8.74072e12	−0.00664128
$562$	1.10013e15	0.827738
$563$	1.70059e15	1.26708	0.633539	−	0.773711i	$-0.281602\pi$
$563$	1.70059e15	1.26708	0.633539	+	0.773711i	$0.281602\pi$
$564$	5.47737e14	0.404145
$565$	−1.16109e15	−0.848394
$566$	1.30563e15	0.944777
$567$	1.79719e14	0.128792
$568$	9.72645e13	0.0690301
$569$	1.15025e15	0.808487	0.404244	−	0.914651i	$-0.367535\pi$
$569$	1.15025e15	0.808487	0.404244	+	0.914651i	$0.367535\pi$
$570$	2.08242e14	0.144963
$571$	1.20109e15	0.828092	0.414046	−	0.910256i	$-0.364115\pi$
$571$	1.20109e15	0.828092	0.414046	+	0.910256i	$0.364115\pi$
$572$	−2.79188e13	−0.0190642
$573$	−8.51636e14	−0.575975
$574$	−3.57774e15	−2.39659
$575$	−7.28152e14	−0.483114
$576$	−2.78164e14	−0.182800
$577$	2.48103e15	1.61497	0.807487	−	0.589885i	$-0.200827\pi$
$577$	2.48103e15	1.61497	0.807487	+	0.589885i	$0.200827\pi$
$578$	−9.09640e14	−0.586498
$579$	−1.14457e15	−0.730986
$580$	−1.04213e15	−0.659274
$581$	1.74536e15	1.09374
$582$	8.45991e14	0.525157
$583$	4.72596e13	0.0290612
$584$	3.36886e14	0.205216
$585$	−4.63242e14	−0.279544
$586$	1.92783e15	1.15247
$587$	7.42648e14	0.439818	0.219909	−	0.975520i	$-0.429424\pi$
$587$	7.42648e14	0.439818	0.219909	+	0.975520i	$0.429424\pi$
$588$	−2.67568e14	−0.156985
$589$	−7.80388e14	−0.453604
$590$	1.61673e14	0.0931001
$591$	5.79978e14	0.330887
$592$	2.22566e14	0.125803
$593$	1.20478e15	0.674696	0.337348	−	0.941380i	$-0.390470\pi$
$593$	1.20478e15	0.674696	0.337348	+	0.941380i	$0.390470\pi$
$594$	−7.12462e12	−0.00395309
$595$	8.44391e14	0.464195
$596$	1.61894e15	0.881814
$597$	5.31966e14	0.287095
$598$	−2.65629e15	−1.42043
$599$	−3.55760e13	−0.0188499	−0.00942497	−	0.999956i	$-0.503000\pi$
$599$	−3.55760e13	−0.0188499	−0.00942497	+	0.999956i	$0.503000\pi$
$600$	−2.19367e14	−0.115170
$601$	−2.68678e15	−1.39773	−0.698864	−	0.715255i	$-0.746311\pi$
$601$	−2.68678e15	−1.39773	−0.698864	+	0.715255i	$0.746311\pi$
$602$	1.95851e15	1.00959
$603$	1.75309e14	0.0895484
$604$	−2.50895e15	−1.26996
$605$	−1.06495e15	−0.534165
$606$	1.32728e15	0.659725
$607$	−3.06560e15	−1.51000	−0.755001	−	0.655724i	$-0.772364\pi$
$607$	−3.06560e15	−1.51000	−0.755001	+	0.655724i	$0.772364\pi$
$608$	9.20854e14	0.449491
$609$	2.15699e15	1.04340
$610$	−2.24452e15	−1.07599
$611$	2.92222e15	1.38831
$612$	4.19961e14	0.197732
$613$	3.78497e15	1.76616	0.883080	−	0.469223i	$-0.155466\pi$
$613$	3.78497e15	1.76616	0.883080	+	0.469223i	$0.155466\pi$
$614$	3.81084e15	1.76236
$615$	1.03967e15	0.476522
$616$	−1.09326e13	−0.00496625
$617$	−4.24211e15	−1.90991	−0.954957	−	0.296744i	$-0.904099\pi$
$617$	−4.24211e15	−1.90991	−0.954957	+	0.296744i	$0.904099\pi$
$618$	−1.48117e15	−0.660948
$619$	−1.01866e15	−0.450535	−0.225268	−	0.974297i	$-0.572326\pi$
$619$	−1.01866e15	−0.450535	−0.225268	+	0.974297i	$0.572326\pi$
$620$	1.24616e15	0.546284
$621$	−2.99467e14	−0.130120
$622$	−1.37041e15	−0.590206
$623$	−3.67603e15	−1.56926
$624$	−2.49518e15	−1.05581
$625$	5.36657e14	0.225090
$626$	−4.52414e15	−1.88095
$627$	7.54870e12	0.00311100
$628$	3.39989e15	1.38895
$629$	−1.99851e14	−0.0809335
$630$	6.88269e14	0.276303
$631$	1.06023e15	0.421928	0.210964	−	0.977494i	$-0.432340\pi$
$631$	1.06023e15	0.421928	0.210964	+	0.977494i	$0.432340\pi$
$632$	−2.79145e14	−0.110125
$633$	−3.21041e14	−0.125557
$634$	3.56979e15	1.38405
$635$	−8.52189e13	−0.0327552
$636$	−2.27066e15	−0.865242
$637$	−1.42749e15	−0.539271
$638$	−8.55096e13	−0.0320259
$639$	−2.21970e14	−0.0824211
$640$	7.92729e14	0.291833
$641$	−1.60975e15	−0.587543	−0.293772	−	0.955876i	$-0.594911\pi$
$641$	−1.60975e15	−0.587543	−0.293772	+	0.955876i	$0.594911\pi$
$642$	3.68436e15	1.33327
$643$	−4.78205e15	−1.71575	−0.857875	−	0.513858i	$-0.828216\pi$
$643$	−4.78205e15	−1.71575	−0.857875	+	0.513858i	$0.828216\pi$
$644$	1.74355e15	0.620243
$645$	−5.69133e14	−0.200741
$646$	−1.00719e15	−0.352235
$647$	−1.07304e15	−0.372084	−0.186042	−	0.982542i	$-0.559566\pi$
$647$	−1.07304e15	−0.372084	−0.186042	+	0.982542i	$0.559566\pi$
$648$	−9.02191e13	−0.0310196
$649$	5.86057e12	0.00199799
$650$	4.44056e15	1.50112
$651$	−2.57929e15	−0.864579
$652$	3.92802e15	1.30561
$653$	2.59599e15	0.855620	0.427810	−	0.903869i	$-0.359285\pi$
$653$	2.59599e15	0.855620	0.427810	+	0.903869i	$0.359285\pi$
$654$	3.44907e15	1.12726
$655$	−1.76206e15	−0.571076
$656$	5.60003e15	1.79978
$657$	−7.68814e14	−0.245026
$658$	−4.34174e15	−1.37221
$659$	1.47229e15	0.461450	0.230725	−	0.973019i	$-0.425890\pi$
$659$	1.47229e15	0.461450	0.230725	+	0.973019i	$0.425890\pi$
$660$	−1.20541e13	−0.00374664
$661$	3.18725e14	0.0982446	0.0491223	−	0.998793i	$-0.484358\pi$
$661$	3.18725e14	0.0982446	0.0491223	+	0.998793i	$0.484358\pi$
$662$	7.75234e15	2.36981
$663$	2.24052e15	0.679243
$664$	−8.76171e14	−0.263429
$665$	−7.29237e14	−0.217445
$666$	−1.62900e14	−0.0481740
$667$	−3.59420e15	−1.05417
$668$	3.59373e15	1.04538
$669$	−1.20810e15	−0.348545
$670$	6.71378e14	0.192112
$671$	−8.13630e13	−0.0230915
$672$	3.04355e15	0.856741
$673$	1.03994e15	0.290353	0.145177	−	0.989406i	$-0.453625\pi$
$673$	1.03994e15	0.290353	0.145177	+	0.989406i	$0.453625\pi$
$674$	2.30838e15	0.639261
$675$	5.00623e14	0.137512
$676$	4.25170e15	1.15839
$677$	−4.99687e15	−1.35039	−0.675197	−	0.737637i	$-0.735942\pi$
$677$	−4.99687e15	−1.35039	−0.675197	+	0.737637i	$0.735942\pi$
$678$	4.57742e15	1.22704
$679$	−2.96255e15	−0.787738
$680$	−4.23885e14	−0.111802
$681$	−1.97051e15	−0.515550
$682$	1.02251e14	0.0265371
$683$	−4.94894e13	−0.0127409	−0.00637043	−	0.999980i	$-0.502028\pi$
$683$	−4.94894e13	−0.0127409	−0.00637043	+	0.999980i	$0.502028\pi$
$684$	−3.62688e14	−0.0926243
$685$	−3.67334e15	−0.930599
$686$	−4.05229e15	−1.01840
$687$	2.55204e14	0.0636247
$688$	−3.06555e15	−0.758180
$689$	−1.21141e16	−2.97226
$690$	−1.14687e15	−0.279153
$691$	3.02572e15	0.730634	0.365317	−	0.930883i	$-0.380961\pi$
$691$	3.02572e15	0.730634	0.365317	+	0.930883i	$0.380961\pi$
$692$	4.96632e15	1.18974
$693$	2.49495e13	0.00592964
$694$	−2.07878e15	−0.490153
$695$	−2.27400e15	−0.531955
$696$	−1.08281e15	−0.251305
$697$	−5.02849e15	−1.15786
$698$	1.86288e15	0.425579
$699$	2.23822e15	0.507315
$700$	−2.91472e15	−0.655477
$701$	4.61337e15	1.02936	0.514682	−	0.857381i	$-0.327910\pi$
$701$	4.61337e15	1.02936	0.514682	+	0.857381i	$0.327910\pi$
$702$	1.82627e15	0.404306
$703$	1.72596e14	0.0379120
$704$	−3.86160e13	−0.00841623
$705$	1.26168e15	0.272841
$706$	−9.19695e15	−1.97341
$707$	−4.64796e15	−0.989590
$708$	−2.81580e14	−0.0594865
$709$	1.54686e15	0.324263	0.162131	−	0.986769i	$-0.448163\pi$
$709$	1.54686e15	0.324263	0.162131	+	0.986769i	$0.448163\pi$
$710$	−8.50075e14	−0.176822
$711$	6.37042e14	0.131488
$712$	1.84537e15	0.377957
$713$	4.29788e15	0.873499
$714$	−3.32890e15	−0.671367
$715$	−6.43094e13	−0.0128704
$716$	−3.54626e15	−0.704286
$717$	−1.10311e15	−0.217401
$718$	3.09913e15	0.606116
$719$	5.57795e15	1.08259	0.541297	−	0.840831i	$-0.317933\pi$
$719$	5.57795e15	1.08259	0.541297	+	0.840831i	$0.317933\pi$
$720$	−1.07731e15	−0.207497
$721$	5.18685e15	0.991424
$722$	−6.18607e15	−1.17344
$723$	2.50947e15	0.472412
$724$	−3.78691e15	−0.707494
$725$	6.00848e15	1.11405
$726$	4.19843e15	0.772566
$727$	8.15436e15	1.48919	0.744596	−	0.667516i	$-0.232642\pi$
$727$	8.15436e15	1.48919	0.744596	+	0.667516i	$0.232642\pi$
$728$	2.80236e15	0.507928
$729$	2.05891e14	0.0370370
$730$	−2.94432e15	−0.525665
$731$	2.75268e15	0.487764
$732$	3.90920e15	0.687507
$733$	−3.90202e15	−0.681111	−0.340555	−	0.940224i	$-0.610615\pi$
$733$	−3.90202e15	−0.681111	−0.340555	+	0.940224i	$0.610615\pi$
$734$	6.80253e15	1.17853
$735$	−6.16328e14	−0.105982
$736$	−5.07148e15	−0.865579
$737$	2.43372e13	0.00412286
$738$	−4.09876e15	−0.689195
$739$	−1.56435e15	−0.261090	−0.130545	−	0.991442i	$-0.541673\pi$
$739$	−1.56435e15	−0.261090	−0.130545	+	0.991442i	$0.541673\pi$
$740$	−2.75609e14	−0.0456582
$741$	−1.93497e15	−0.318181
$742$	1.79988e16	2.93779
$743$	−1.35429e15	−0.219419	−0.109710	−	0.993964i	$-0.534992\pi$
$743$	−1.35429e15	−0.219419	−0.109710	+	0.993964i	$0.534992\pi$
$744$	1.29481e15	0.208235
$745$	3.72915e15	0.595319
$746$	−1.14532e16	−1.81494
$747$	1.99953e15	0.314532
$748$	5.83010e13	0.00910369
$749$	−1.29021e16	−1.99992
$750$	4.60043e15	0.707883
$751$	−1.24477e16	−1.90139	−0.950694	−	0.310131i	$-0.899627\pi$
$751$	−1.24477e16	−1.90139	−0.950694	+	0.310131i	$0.899627\pi$
$752$	6.79588e15	1.03050
$753$	5.84819e15	0.880338
$754$	2.19188e16	3.27548
$755$	−5.77924e15	−0.857358
$756$	−1.19873e15	−0.176544
$757$	−8.01462e15	−1.17181	−0.585903	−	0.810381i	$-0.699260\pi$
$757$	−8.01462e15	−1.17181	−0.585903	+	0.810381i	$0.699260\pi$
$758$	−1.63101e16	−2.36742
$759$	−4.15734e13	−0.00599082
$760$	3.66077e14	0.0523719
$761$	6.72624e15	0.955338	0.477669	−	0.878540i	$-0.341482\pi$
$761$	6.72624e15	0.955338	0.477669	+	0.878540i	$0.341482\pi$
$762$	3.35964e14	0.0473740
$763$	−1.20782e16	−1.69090
$764$	5.68045e15	0.789531
$765$	9.67358e14	0.133490
$766$	1.00357e16	1.37495
$767$	−1.50225e15	−0.204347
$768$	−5.46958e15	−0.738699
$769$	−7.80657e15	−1.04680	−0.523402	−	0.852086i	$-0.675337\pi$
$769$	−7.80657e15	−1.04680	−0.523402	+	0.852086i	$0.675337\pi$
$770$	9.55488e13	0.0127211
$771$	1.78408e15	0.235838
$772$	7.63431e15	1.00202
$773$	1.77765e15	0.231664	0.115832	−	0.993269i	$-0.463047\pi$
$773$	1.77765e15	0.231664	0.115832	+	0.993269i	$0.463047\pi$
$774$	2.24373e15	0.290332
$775$	−7.18484e15	−0.923119
$776$	1.48720e15	0.189728
$777$	5.70454e14	0.0722612
$778$	1.79168e16	2.25358
$779$	4.34273e15	0.542384
$780$	3.08984e15	0.383192
$781$	−3.08149e13	−0.00379472
$782$	5.54696e15	0.678293
$783$	2.47110e15	0.300055
$784$	−3.31976e15	−0.400284
$785$	7.83147e15	0.937692
$786$	6.94668e15	0.825950
$787$	1.99708e15	0.235795	0.117898	−	0.993026i	$-0.462385\pi$
$787$	1.99708e15	0.235795	0.117898	+	0.993026i	$0.462385\pi$
$788$	−3.86848e15	−0.453571
$789$	−3.18486e15	−0.370823
$790$	2.43968e15	0.282087
$791$	−1.60295e16	−1.84056
$792$	−1.25247e13	−0.00142816
$793$	2.08559e16	2.36171
$794$	1.50088e15	0.168785
$795$	−5.23034e15	−0.584131
$796$	−3.54824e15	−0.393542
$797$	2.09836e15	0.231132	0.115566	−	0.993300i	$-0.463132\pi$
$797$	2.09836e15	0.231132	0.115566	+	0.993300i	$0.463132\pi$
$798$	2.87491e15	0.314492
$799$	−6.10229e15	−0.662957
$800$	8.47807e15	0.914750
$801$	−4.21136e15	−0.451277
$802$	−7.37814e15	−0.785213
$803$	−1.06731e14	−0.0112811
$804$	−1.16932e15	−0.122751
$805$	4.01617e15	0.418731
$806$	−2.62102e16	−2.71411
$807$	−8.48064e14	−0.0872217
$808$	2.33328e15	0.238344
$809$	−3.11783e15	−0.316327	−0.158163	−	0.987413i	$-0.550557\pi$
$809$	−3.11783e15	−0.316327	−0.158163	+	0.987413i	$0.550557\pi$
$810$	7.88499e14	0.0794573
$811$	4.39769e15	0.440159	0.220079	−	0.975482i	$-0.429368\pi$
$811$	4.39769e15	0.440159	0.220079	+	0.975482i	$0.429368\pi$
$812$	−1.43872e16	−1.43027
$813$	−6.66224e15	−0.657843
$814$	−2.26146e13	−0.00221796
$815$	9.04799e15	0.881425
$816$	5.21053e15	0.504181
$817$	−2.37728e15	−0.228486
$818$	3.79555e15	0.362353
$819$	−6.39534e15	−0.606460
$820$	−6.93465e15	−0.653203
$821$	3.55120e15	0.332267	0.166134	−	0.986103i	$-0.446872\pi$
$821$	3.55120e15	0.332267	0.166134	+	0.986103i	$0.446872\pi$
$822$	1.44816e16	1.34593
$823$	−1.04761e16	−0.967169	−0.483584	−	0.875298i	$-0.660665\pi$
$823$	−1.04761e16	−0.967169	−0.483584	+	0.875298i	$0.660665\pi$
$824$	−2.60380e15	−0.238785
$825$	6.94989e13	0.00633113
$826$	2.23199e15	0.201977
$827$	1.66969e16	1.50091	0.750454	−	0.660922i	$-0.229835\pi$
$827$	1.66969e16	1.50091	0.750454	+	0.660922i	$0.229835\pi$
$828$	1.99746e15	0.178365
$829$	−1.74540e16	−1.54826	−0.774132	−	0.633024i	$-0.781813\pi$
$829$	−1.74540e16	−1.54826	−0.774132	+	0.633024i	$0.781813\pi$
$830$	7.65758e15	0.674780
$831$	1.07740e15	0.0943128
$832$	9.89850e15	0.860778
$833$	2.98094e15	0.257517
$834$	8.96495e15	0.769369
$835$	8.27797e15	0.705745
$836$	−5.03502e13	−0.00426448
$837$	−2.95490e15	−0.248630
$838$	1.93531e16	1.61774
$839$	−7.19255e15	−0.597299	−0.298650	−	0.954363i	$-0.596536\pi$
$839$	−7.19255e15	−0.597299	−0.298650	+	0.954363i	$0.596536\pi$
$840$	1.20993e15	0.0998219
$841$	1.74577e16	1.43090
$842$	2.91464e16	2.37339
$843$	−4.41353e15	−0.357054
$844$	2.14136e15	0.172110
$845$	9.79356e15	0.782040
$846$	−4.97401e15	−0.394612
$847$	−1.47023e16	−1.15885
$848$	−2.81725e16	−2.20621
$849$	−5.23797e15	−0.407540
$850$	−9.27293e15	−0.716825
$851$	−9.50551e14	−0.0730067
$852$	1.48055e15	0.112981
$853$	1.57811e16	1.19651	0.598256	−	0.801305i	$-0.295861\pi$
$853$	1.57811e16	1.19651	0.598256	+	0.801305i	$0.295861\pi$
$854$	−3.09870e16	−2.33432
$855$	−8.35433e14	−0.0625314
$856$	6.47688e15	0.481682
$857$	−1.65746e16	−1.22475	−0.612377	−	0.790566i	$-0.709786\pi$
$857$	−1.65746e16	−1.22475	−0.612377	+	0.790566i	$0.709786\pi$
$858$	2.53531e14	0.0186145
$859$	−2.23815e16	−1.63278	−0.816388	−	0.577504i	$-0.804027\pi$
$859$	−2.23815e16	−1.63278	−0.816388	+	0.577504i	$0.804027\pi$
$860$	3.79614e15	0.275170
$861$	1.43533e16	1.03380
$862$	−2.23684e16	−1.60083
$863$	1.71069e16	1.21650	0.608251	−	0.793745i	$-0.291872\pi$
$863$	1.71069e16	1.21650	0.608251	+	0.793745i	$0.291872\pi$
$864$	3.48677e15	0.246376
$865$	1.14397e16	0.803201
$866$	2.00065e16	1.39580
$867$	3.64933e15	0.252993
$868$	1.72040e16	1.18514
$869$	8.84373e13	0.00605378
$870$	9.46356e15	0.643723
$871$	−6.23839e15	−0.421670
$872$	6.06326e15	0.407254
$873$	−3.39398e15	−0.226533
$874$	−4.79048e15	−0.317736
$875$	−1.61101e16	−1.06183
$876$	5.12802e15	0.335875
$877$	7.48315e15	0.487065	0.243533	−	0.969893i	$-0.421694\pi$
$877$	7.48315e15	0.487065	0.243533	+	0.969893i	$0.421694\pi$
$878$	5.27527e15	0.341212
$879$	−7.73412e15	−0.497132
$880$	−1.49557e14	−0.00955328
$881$	1.91607e16	1.21631	0.608154	−	0.793819i	$-0.291910\pi$
$881$	1.91607e16	1.21631	0.608154	+	0.793819i	$0.291910\pi$
$882$	2.42979e15	0.153282
$883$	−2.56429e16	−1.60762	−0.803810	−	0.594886i	$-0.797197\pi$
$883$	−2.56429e16	−1.60762	−0.803810	+	0.594886i	$0.797197\pi$
$884$	−1.49444e16	−0.931088
$885$	−6.48604e14	−0.0401598
$886$	2.21372e16	1.36219
$887$	−3.22334e16	−1.97118	−0.985590	−	0.169153i	$-0.945897\pi$
$887$	−3.22334e16	−1.97118	−0.985590	+	0.169153i	$0.945897\pi$
$888$	−2.86368e14	−0.0174042
$889$	−1.17650e15	−0.0710612
$890$	−1.61282e16	−0.968146
$891$	2.85828e13	0.00170521
$892$	8.05806e15	0.477776
$893$	5.27008e15	0.310552
$894$	−1.47016e16	−0.861013
$895$	−8.16862e15	−0.475469
$896$	1.09441e16	0.633121
$897$	1.06566e16	0.612717
$898$	−1.01522e16	−0.580149
$899$	−3.54647e16	−2.01427
$900$	−3.33918e15	−0.188498
$901$	2.52972e16	1.41934
$902$	−5.69009e14	−0.0317310
$903$	−7.85723e15	−0.435499
$904$	8.04683e15	0.443300
$905$	−8.72294e15	−0.477635
$906$	2.27838e16	1.24000
$907$	2.41652e15	0.130722	0.0653612	−	0.997862i	$-0.479180\pi$
$907$	2.41652e15	0.130722	0.0653612	+	0.997862i	$0.479180\pi$
$908$	1.31434e16	0.706702
$909$	−5.32483e15	−0.284580
$910$	−2.44922e16	−1.30107
$911$	9.85203e15	0.520205	0.260103	−	0.965581i	$-0.416244\pi$
$911$	9.85203e15	0.520205	0.260103	+	0.965581i	$0.416244\pi$
$912$	−4.49994e15	−0.236176
$913$	2.77584e14	0.0144812
$914$	−8.14444e15	−0.422335
$915$	9.00464e15	0.464141
$916$	−1.70222e15	−0.0872150
$917$	−2.43264e16	−1.23893
$918$	−3.81367e15	−0.193067
$919$	−2.49680e16	−1.25646	−0.628230	−	0.778028i	$-0.716220\pi$
$919$	−2.49680e16	−1.25646	−0.628230	+	0.778028i	$0.716220\pi$
$920$	−2.01612e15	−0.100852
$921$	−1.52885e16	−0.760213
$922$	3.49722e16	1.72863
$923$	7.89883e15	0.388109
$924$	−1.66414e14	−0.00812820
$925$	1.58905e15	0.0771539
$926$	−3.01588e16	−1.45564
$927$	5.94219e15	0.285107
$928$	4.18482e16	1.99601
$929$	−1.59336e16	−0.755488	−0.377744	−	0.925910i	$-0.623300\pi$
$929$	−1.59336e16	−0.755488	−0.377744	+	0.925910i	$0.623300\pi$
$930$	−1.13164e16	−0.533398
$931$	−2.57441e15	−0.120630
$932$	−1.49290e16	−0.695414
$933$	5.49786e15	0.254592
$934$	8.38979e15	0.386227
$935$	1.34293e14	0.00614597
$936$	3.21047e15	0.146067
$937$	2.77710e16	1.25610	0.628050	−	0.778173i	$-0.283853\pi$
$937$	2.77710e16	1.25610	0.628050	+	0.778173i	$0.283853\pi$
$938$	9.26879e15	0.416780
$939$	1.81501e16	0.811369
$940$	−8.41549e15	−0.374004
$941$	8.94751e15	0.395329	0.197665	−	0.980270i	$-0.436664\pi$
$941$	8.94751e15	0.395329	0.197665	+	0.980270i	$0.436664\pi$
$942$	−3.08745e16	−1.35619
$943$	−2.39170e16	−1.04446
$944$	−3.49361e15	−0.151680
$945$	−2.76122e15	−0.119186
$946$	3.11485e14	0.0133671
$947$	1.99952e16	0.853100	0.426550	−	0.904464i	$-0.359729\pi$
$947$	1.99952e16	0.853100	0.426550	+	0.904464i	$0.359729\pi$
$948$	−4.24910e15	−0.180240
$949$	2.73584e16	1.15379
$950$	8.00832e15	0.335785
$951$	−1.43214e16	−0.597025
$952$	−5.85200e15	−0.242550
$953$	−4.43727e16	−1.82854	−0.914272	−	0.405101i	$-0.867236\pi$
$953$	−4.43727e16	−1.82854	−0.914272	+	0.405101i	$0.867236\pi$
$954$	2.06199e16	0.844831
$955$	1.30846e16	0.533019
$956$	7.35776e15	0.298008
$957$	3.43051e14	0.0138147
$958$	−3.43513e16	−1.37541
$959$	−5.07127e16	−2.01890
$960$	4.27373e15	0.169167
$961$	1.69997e16	0.669055
$962$	5.79683e15	0.226844
$963$	−1.47810e16	−0.575123
$964$	−1.67382e16	−0.647569
$965$	1.75852e16	0.676469
$966$	−1.58332e16	−0.605612
$967$	−1.35151e15	−0.0514012	−0.0257006	−	0.999670i	$-0.508182\pi$
$967$	−1.35151e15	−0.0514012	−0.0257006	+	0.999670i	$0.508182\pi$
$968$	7.38058e15	0.279111
$969$	4.04067e15	0.151940
$970$	−1.29979e16	−0.485991
$971$	2.35458e16	0.875403	0.437701	−	0.899120i	$-0.355793\pi$
$971$	2.35458e16	0.875403	0.437701	+	0.899120i	$0.355793\pi$
$972$	−1.37330e15	−0.0507694
$973$	−3.13941e16	−1.15406
$974$	5.52499e12	0.000201956 0
$975$	−1.78148e16	−0.647523
$976$	4.85022e16	1.75302
$977$	1.95540e16	0.702775	0.351388	−	0.936230i	$-0.385710\pi$
$977$	1.95540e16	0.702775	0.351388	+	0.936230i	$0.385710\pi$
$978$	−3.56704e16	−1.27481
$979$	−5.84641e14	−0.0207771
$980$	4.11093e15	0.145277
$981$	−1.38371e16	−0.486257
$982$	7.30485e15	0.255269
$983$	3.28169e16	1.14039	0.570194	−	0.821510i	$-0.306868\pi$
$983$	3.28169e16	1.14039	0.570194	+	0.821510i	$0.306868\pi$
$984$	−7.20537e15	−0.248991
$985$	−8.91083e15	−0.306210
$986$	−4.57717e16	−1.56413
$987$	1.74183e16	0.591919
$988$	1.29063e16	0.436154
$989$	1.30926e16	0.439992
$990$	1.09463e14	0.00365826
$991$	3.26920e16	1.08652	0.543258	−	0.839566i	$-0.317191\pi$
$991$	3.26920e16	1.08652	0.543258	+	0.839566i	$0.317191\pi$
$992$	−5.00414e16	−1.65392
$993$	−3.11011e16	−1.02225
$994$	−1.17358e16	−0.383608
$995$	−8.17317e15	−0.265683
$996$	−1.33369e16	−0.431152
$997$	−4.28863e16	−1.37878	−0.689390	−	0.724391i	$-0.742121\pi$
$997$	−4.28863e16	−1.37878	−0.689390	+	0.724391i	$0.742121\pi$
$998$	4.12790e16	1.31981
$999$	6.53528e14	0.0207804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.23	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.23	✓	26	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+60.5708 q^{2} -243.000 q^{3} +1620.82 q^{4} +3733.47 q^{5} -14718.7 q^{6} +51542.9 q^{7} -25874.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+60.5708 q^{2} -243.000 q^{3} +1620.82 q^{4} +3733.47 q^{5} -14718.7 q^{6} +51542.9 q^{7} -25874.6 q^{8} +59049.0 q^{9} +226139. q^{10} +8197.47 q^{11} -393859. q^{12} -2.10127e6 q^{13} +3.12200e6 q^{14} -907234. q^{15} -4.88669e6 q^{16} +4.38795e6 q^{17} +3.57664e6 q^{18} -3.78954e6 q^{19} +6.05129e6 q^{20} -1.25249e7 q^{21} +496527. q^{22} +2.08704e7 q^{23} +6.28753e6 q^{24} -3.48893e7 q^{25} -1.27276e8 q^{26} -1.43489e7 q^{27} +8.35419e7 q^{28} -1.72215e8 q^{29} -5.49519e7 q^{30} +2.05932e8 q^{31} -2.42999e8 q^{32} -1.99198e6 q^{33} +2.65781e8 q^{34} +1.92434e8 q^{35} +9.57078e7 q^{36} -4.55455e7 q^{37} -2.29535e8 q^{38} +5.10609e8 q^{39} -9.66021e7 q^{40} -1.14598e9 q^{41} -7.58645e8 q^{42} +6.27327e8 q^{43} +1.32866e7 q^{44} +2.20458e8 q^{45} +1.26413e9 q^{46} -1.39069e9 q^{47} +1.18746e9 q^{48} +6.79348e8 q^{49} -2.11327e9 q^{50} -1.06627e9 q^{51} -3.40578e9 q^{52} +5.76515e9 q^{53} -8.69125e8 q^{54} +3.06050e7 q^{55} -1.33365e9 q^{56} +9.20857e8 q^{57} -1.04312e10 q^{58} +7.14924e8 q^{59} -1.47046e9 q^{60} -9.92538e9 q^{61} +1.24735e10 q^{62} +3.04356e9 q^{63} -4.71072e9 q^{64} -7.84504e9 q^{65} -1.20656e8 q^{66} +2.96887e9 q^{67} +7.11208e9 q^{68} -5.07150e9 q^{69} +1.16559e10 q^{70} -3.75907e9 q^{71} -1.52787e9 q^{72} -1.30199e10 q^{73} -2.75873e9 q^{74} +8.47810e9 q^{75} -6.14216e9 q^{76} +4.22522e8 q^{77} +3.09280e10 q^{78} +1.07884e10 q^{79} -1.82443e10 q^{80} +3.48678e9 q^{81} -6.94128e10 q^{82} +3.38622e10 q^{83} -2.03007e10 q^{84} +1.63823e10 q^{85} +3.79977e10 q^{86} +4.18484e10 q^{87} -2.12106e8 q^{88} -7.13197e10 q^{89} +1.33533e10 q^{90} -1.08306e11 q^{91} +3.38271e10 q^{92} -5.00416e10 q^{93} -8.42354e10 q^{94} -1.41481e10 q^{95} +5.90488e10 q^{96} -5.74773e10 q^{97} +4.11486e10 q^{98} +4.84052e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

Modular forms

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