LMFDB - Embedded newform 177.14.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-41.9317 q^{2} +729.000 q^{3} -6433.74 q^{4} -10428.5 q^{5} -30568.2 q^{6} -484911. q^{7} +613281. q^{8} +531441. q^{9} +O(q^{10})$	\(q-41.9317 q^{2} +729.000 q^{3} -6433.74 q^{4} -10428.5 q^{5} -30568.2 q^{6} -484911. q^{7} +613281. q^{8} +531441. q^{9} +437283. q^{10} -5.22450e6 q^{11} -4.69019e6 q^{12} -2.63123e7 q^{13} +2.03331e7 q^{14} -7.60235e6 q^{15} +2.69892e7 q^{16} +5.55106e7 q^{17} -2.22842e7 q^{18} +2.91313e8 q^{19} +6.70939e7 q^{20} -3.53500e8 q^{21} +2.19072e8 q^{22} +4.45190e8 q^{23} +4.47082e8 q^{24} -1.11195e9 q^{25} +1.10332e9 q^{26} +3.87420e8 q^{27} +3.11979e9 q^{28} +1.14421e9 q^{29} +3.18779e8 q^{30} +1.75609e9 q^{31} -6.15571e9 q^{32} -3.80866e9 q^{33} -2.32765e9 q^{34} +5.05687e9 q^{35} -3.41915e9 q^{36} +1.94584e10 q^{37} -1.22152e10 q^{38} -1.91817e10 q^{39} -6.39558e9 q^{40} +4.10675e10 q^{41} +1.48228e10 q^{42} -6.68796e10 q^{43} +3.36130e10 q^{44} -5.54211e9 q^{45} -1.86676e10 q^{46} +1.07923e11 q^{47} +1.96752e10 q^{48} +1.38250e11 q^{49} +4.66259e10 q^{50} +4.04673e10 q^{51} +1.69287e11 q^{52} +1.14657e11 q^{53} -1.62452e10 q^{54} +5.44834e10 q^{55} -2.97387e11 q^{56} +2.12367e11 q^{57} -4.79788e10 q^{58} +4.21805e10 q^{59} +4.89115e10 q^{60} -3.36859e11 q^{61} -7.36359e10 q^{62} -2.57702e11 q^{63} +3.70231e10 q^{64} +2.74397e11 q^{65} +1.59703e11 q^{66} -2.42464e11 q^{67} -3.57141e11 q^{68} +3.24544e11 q^{69} -2.12043e11 q^{70} +4.15485e11 q^{71} +3.25923e11 q^{72} -1.88437e12 q^{73} -8.15925e11 q^{74} -8.10612e11 q^{75} -1.87423e12 q^{76} +2.53342e12 q^{77} +8.04320e11 q^{78} -1.69099e12 q^{79} -2.81456e11 q^{80} +2.82430e11 q^{81} -1.72203e12 q^{82} -1.99354e12 q^{83} +2.27433e12 q^{84} -5.78890e11 q^{85} +2.80437e12 q^{86} +8.34133e11 q^{87} -3.20409e12 q^{88} +2.92261e12 q^{89} +2.32390e11 q^{90} +1.27591e13 q^{91} -2.86423e12 q^{92} +1.28019e12 q^{93} -4.52538e12 q^{94} -3.03794e12 q^{95} -4.48751e12 q^{96} +1.31868e13 q^{97} -5.79704e12 q^{98} -2.77651e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) $ 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * 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 $

$2$	−41.9317	−0.463284	−0.231642	−	0.972801i	$-0.574410\pi$
$2$	−41.9317	−0.463284	−0.231642	+	0.972801i	$0.574410\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−6433.74	−0.785368
$5$	−10428.5	−0.298480	−0.149240	−	0.988801i	$-0.547683\pi$
$5$	−10428.5	−0.298480	−0.149240	+	0.988801i	$0.547683\pi$
$6$	−30568.2	−0.267477
$7$	−484911.	−1.55785	−0.778923	−	0.627119i	$-0.784234\pi$
$7$	−484911.	−1.55785	−0.778923	+	0.627119i	$0.784234\pi$
$8$	613281.	0.827132
$9$	531441.	0.333333
$10$	437283.	0.138281
$11$	−5.22450e6	−0.889184	−0.444592	−	0.895733i	$-0.646651\pi$
$11$	−5.22450e6	−0.889184	−0.444592	+	0.895733i	$0.646651\pi$
$12$	−4.69019e6	−0.453432
$13$	−2.63123e7	−1.51192	−0.755958	−	0.654620i	$-0.772829\pi$
$13$	−2.63123e7	−1.51192	−0.755958	+	0.654620i	$0.772829\pi$
$14$	2.03331e7	0.721725
$15$	−7.60235e6	−0.172327
$16$	2.69892e7	0.402171
$17$	5.55106e7	0.557774	0.278887	−	0.960324i	$-0.410035\pi$
$17$	5.55106e7	0.557774	0.278887	+	0.960324i	$0.410035\pi$
$18$	−2.22842e7	−0.154428
$19$	2.91313e8	1.42057	0.710283	−	0.703917i	$-0.248567\pi$
$19$	2.91313e8	1.42057	0.710283	+	0.703917i	$0.248567\pi$
$20$	6.70939e7	0.234417
$21$	−3.53500e8	−0.899423
$22$	2.19072e8	0.411945
$23$	4.45190e8	0.627068	0.313534	−	0.949577i	$-0.398487\pi$
$23$	4.45190e8	0.627068	0.313534	+	0.949577i	$0.398487\pi$
$24$	4.47082e8	0.477545
$25$	−1.11195e9	−0.910910
$26$	1.10332e9	0.700446
$27$	3.87420e8	0.192450
$28$	3.11979e9	1.22348
$29$	1.14421e9	0.357207	0.178604	−	0.983921i	$-0.442842\pi$
$29$	1.14421e9	0.357207	0.178604	+	0.983921i	$0.442842\pi$
$30$	3.18779e8	0.0798365
$31$	1.75609e9	0.355383	0.177691	−	0.984086i	$-0.443137\pi$
$31$	1.75609e9	0.355383	0.177691	+	0.984086i	$0.443137\pi$
$32$	−6.15571e9	−1.01345
$33$	−3.80866e9	−0.513371
$34$	−2.32765e9	−0.258408
$35$	5.05687e9	0.464986
$36$	−3.41915e9	−0.261789
$37$	1.94584e10	1.24680	0.623400	−	0.781903i	$-0.285751\pi$
$37$	1.94584e10	1.24680	0.623400	+	0.781903i	$0.285751\pi$
$38$	−1.22152e10	−0.658125
$39$	−1.91817e10	−0.872905
$40$	−6.39558e9	−0.246882
$41$	4.10675e10	1.35022	0.675108	−	0.737719i	$-0.264097\pi$
$41$	4.10675e10	1.35022	0.675108	+	0.737719i	$0.264097\pi$
$42$	1.48228e10	0.416688
$43$	−6.68796e10	−1.61342	−0.806712	−	0.590945i	$-0.798755\pi$
$43$	−6.68796e10	−1.61342	−0.806712	+	0.590945i	$0.798755\pi$
$44$	3.36130e10	0.698337
$45$	−5.54211e9	−0.0994933
$46$	−1.86676e10	−0.290510
$47$	1.07923e11	1.46042	0.730209	−	0.683224i	$-0.239423\pi$
$47$	1.07923e11	1.46042	0.730209	+	0.683224i	$0.239423\pi$
$48$	1.96752e10	0.232194
$49$	1.38250e11	1.42689
$50$	4.66259e10	0.422010
$51$	4.04673e10	0.322031
$52$	1.69287e11	1.18741
$53$	1.14657e11	0.710573	0.355286	−	0.934758i	$-0.384383\pi$
$53$	1.14657e11	0.710573	0.355286	+	0.934758i	$0.384383\pi$
$54$	−1.62452e10	−0.0891590
$55$	5.44834e10	0.265404
$56$	−2.97387e11	−1.28855
$57$	2.12367e11	0.820164
$58$	−4.79788e10	−0.165488
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	4.89115e10	0.135340
$61$	−3.36859e11	−0.837152	−0.418576	−	0.908182i	$-0.637471\pi$
$61$	−3.36859e11	−0.837152	−0.418576	+	0.908182i	$0.637471\pi$
$62$	−7.36359e10	−0.164643
$63$	−2.57702e11	−0.519282
$64$	3.70231e10	0.0673446
$65$	2.74397e11	0.451276
$66$	1.59703e11	0.237836
$67$	−2.42464e11	−0.327461	−0.163731	−	0.986505i	$-0.552353\pi$
$67$	−2.42464e11	−0.327461	−0.163731	+	0.986505i	$0.552353\pi$
$68$	−3.57141e11	−0.438058
$69$	3.24544e11	0.362038
$70$	−2.12043e11	−0.215420
$71$	4.15485e11	0.384925	0.192463	−	0.981304i	$-0.438353\pi$
$71$	4.15485e11	0.384925	0.192463	+	0.981304i	$0.438353\pi$
$72$	3.25923e11	0.275711
$73$	−1.88437e12	−1.45736	−0.728682	−	0.684852i	$-0.759867\pi$
$73$	−1.88437e12	−1.45736	−0.728682	+	0.684852i	$0.759867\pi$
$74$	−8.15925e11	−0.577623
$75$	−8.10612e11	−0.525914
$76$	−1.87423e12	−1.11567
$77$	2.53342e12	1.38521
$78$	8.04320e11	0.404403
$79$	−1.69099e12	−0.782647	−0.391324	−	0.920253i	$-0.627983\pi$
$79$	−1.69099e12	−0.782647	−0.391324	+	0.920253i	$0.627983\pi$
$80$	−2.81456e11	−0.120040
$81$	2.82430e11	0.111111
$82$	−1.72203e12	−0.625533
$83$	−1.99354e12	−0.669293	−0.334647	−	0.942344i	$-0.608617\pi$
$83$	−1.99354e12	−0.669293	−0.334647	+	0.942344i	$0.608617\pi$
$84$	2.27433e12	0.706378
$85$	−5.78890e11	−0.166484
$86$	2.80437e12	0.747473
$87$	8.34133e11	0.206234
$88$	−3.20409e12	−0.735473
$89$	2.92261e12	0.623356	0.311678	−	0.950188i	$-0.399109\pi$
$89$	2.92261e12	0.623356	0.311678	+	0.950188i	$0.399109\pi$
$90$	2.32390e11	0.0460936
$91$	1.27591e13	2.35533
$92$	−2.86423e12	−0.492479
$93$	1.28019e12	0.205180
$94$	−4.52538e12	−0.676588
$95$	−3.03794e12	−0.424010
$96$	−4.48751e12	−0.585117
$97$	1.31868e13	1.60739	0.803697	−	0.595038i	$-0.202863\pi$
$97$	1.31868e13	1.60739	0.803697	+	0.595038i	$0.202863\pi$
$98$	−5.79704e12	−0.661054
$99$	−2.77651e12	−0.296395
$100$	7.15399e12	0.715399
$101$	1.44784e13	1.35716	0.678582	−	0.734524i	$-0.262595\pi$
$101$	1.44784e13	1.35716	0.678582	+	0.734524i	$0.262595\pi$
$102$	−1.69686e12	−0.149192
$103$	−1.26142e13	−1.04092	−0.520462	−	0.853885i	$-0.674240\pi$
$103$	−1.26142e13	−1.04092	−0.520462	+	0.853885i	$0.674240\pi$
$104$	−1.61369e13	−1.25055
$105$	3.68646e12	0.268460
$106$	−4.80777e12	−0.329197
$107$	1.85559e13	1.19533	0.597665	−	0.801746i	$-0.296095\pi$
$107$	1.85559e13	1.19533	0.597665	+	0.801746i	$0.296095\pi$
$108$	−2.49256e12	−0.151144
$109$	−1.64035e13	−0.936839	−0.468420	−	0.883506i	$-0.655176\pi$
$109$	−1.64035e13	−0.936839	−0.468420	+	0.883506i	$0.655176\pi$
$110$	−2.28458e12	−0.122957
$111$	1.41852e13	0.719841
$112$	−1.30874e13	−0.626521
$113$	1.96811e13	0.889283	0.444642	−	0.895709i	$-0.353331\pi$
$113$	1.96811e13	0.889283	0.444642	+	0.895709i	$0.353331\pi$
$114$	−8.90490e12	−0.379969
$115$	−4.64265e12	−0.187167
$116$	−7.36157e12	−0.280539
$117$	−1.39835e13	−0.503972
$118$	−1.76870e12	−0.0603144
$119$	−2.69177e13	−0.868926
$120$	−4.66238e12	−0.142538
$121$	−7.22736e12	−0.209351
$122$	1.41251e13	0.387839
$123$	2.99382e13	0.779548
$124$	−1.12982e13	−0.279106
$125$	2.43260e13	0.570368
$126$	1.08059e13	0.240575
$127$	−4.59428e13	−0.971612	−0.485806	−	0.874067i	$-0.661474\pi$
$127$	−4.59428e13	−0.971612	−0.485806	+	0.874067i	$0.661474\pi$
$128$	4.88751e13	0.982252
$129$	−4.87552e13	−0.931511
$130$	−1.15059e13	−0.209069
$131$	−7.21311e13	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$131$	−7.21311e13	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$132$	2.45039e13	0.403185
$133$	−1.41261e14	−2.21302
$134$	1.01669e13	0.151708
$135$	−4.04020e12	−0.0574425
$136$	3.40436e13	0.461353
$137$	1.19310e14	1.54168	0.770841	−	0.637028i	$-0.219836\pi$
$137$	1.19310e14	1.54168	0.770841	+	0.637028i	$0.219836\pi$
$138$	−1.36086e13	−0.167726
$139$	1.11346e14	1.30942	0.654710	−	0.755880i	$-0.272791\pi$
$139$	1.11346e14	1.30942	0.654710	+	0.755880i	$0.272791\pi$
$140$	−3.25346e13	−0.365185
$141$	7.86757e13	0.843173
$142$	−1.74220e13	−0.178330
$143$	1.37469e14	1.34437
$144$	1.43432e13	0.134057
$145$	−1.19324e13	−0.106619
$146$	7.90149e13	0.675174
$147$	1.00784e14	0.823814
$148$	−1.25191e14	−0.979197
$149$	−7.98647e13	−0.597922	−0.298961	−	0.954265i	$-0.596640\pi$
$149$	−7.98647e13	−0.597922	−0.298961	+	0.954265i	$0.596640\pi$
$150$	3.39903e13	0.243647
$151$	2.22450e13	0.152715	0.0763575	−	0.997081i	$-0.475671\pi$
$151$	2.22450e13	0.152715	0.0763575	+	0.997081i	$0.475671\pi$
$152$	1.78657e14	1.17500
$153$	2.95006e13	0.185925
$154$	−1.06230e14	−0.641747
$155$	−1.83133e13	−0.106075
$156$	1.23410e14	0.685552
$157$	−1.49092e14	−0.794525	−0.397262	−	0.917705i	$-0.630040\pi$
$157$	−1.49092e14	−0.794525	−0.397262	+	0.917705i	$0.630040\pi$
$158$	7.09062e13	0.362588
$159$	8.35852e13	0.410249
$160$	6.41945e13	0.302495
$161$	−2.15878e14	−0.976876
$162$	−1.18427e13	−0.0514760
$163$	1.43831e14	0.600665	0.300333	−	0.953835i	$-0.402902\pi$
$163$	1.43831e14	0.600665	0.300333	+	0.953835i	$0.402902\pi$
$164$	−2.64218e14	−1.06042
$165$	3.97184e13	0.153231
$166$	8.35923e13	0.310073
$167$	1.10771e14	0.395156	0.197578	−	0.980287i	$-0.436692\pi$
$167$	1.10771e14	0.395156	0.197578	+	0.980287i	$0.436692\pi$
$168$	−2.16795e14	−0.743942
$169$	3.89464e14	1.28589
$170$	2.42738e13	0.0771295
$171$	1.54816e14	0.473522
$172$	4.30285e14	1.26713
$173$	−4.81517e14	−1.36556	−0.682782	−	0.730622i	$-0.739230\pi$
$173$	−4.81517e14	−1.36556	−0.682782	+	0.730622i	$0.739230\pi$
$174$	−3.49766e13	−0.0955448
$175$	5.39197e14	1.41906
$176$	−1.41005e14	−0.357604
$177$	3.07496e13	0.0751646
$178$	−1.22550e14	−0.288791
$179$	7.45116e14	1.69309	0.846544	−	0.532320i	$-0.178680\pi$
$179$	7.45116e14	1.69309	0.846544	+	0.532320i	$0.178680\pi$
$180$	3.56565e13	0.0781389
$181$	−1.39421e14	−0.294725	−0.147362	−	0.989083i	$-0.547078\pi$
$181$	−1.39421e14	−0.294725	−0.147362	+	0.989083i	$0.547078\pi$
$182$	−5.35012e14	−1.09119
$183$	−2.45570e14	−0.483330
$184$	2.73027e14	0.518668
$185$	−2.02922e14	−0.372145
$186$	−5.36806e13	−0.0950568
$187$	−2.90015e14	−0.495964
$188$	−6.94347e14	−1.14697
$189$	−1.87864e14	−0.299808
$190$	1.27386e14	0.196437
$191$	−3.13121e14	−0.466654	−0.233327	−	0.972398i	$-0.574961\pi$
$191$	−3.13121e14	−0.466654	−0.233327	+	0.972398i	$0.574961\pi$
$192$	2.69898e13	0.0388814
$193$	−8.97607e14	−1.25016	−0.625078	−	0.780563i	$-0.714933\pi$
$193$	−8.97607e14	−1.25016	−0.625078	+	0.780563i	$0.714933\pi$
$194$	−5.52944e14	−0.744680
$195$	2.00035e14	0.260545
$196$	−8.89462e14	−1.12063
$197$	−3.94105e14	−0.480377	−0.240188	−	0.970726i	$-0.577209\pi$
$197$	−3.94105e14	−0.480377	−0.240188	+	0.970726i	$0.577209\pi$
$198$	1.16424e14	0.137315
$199$	5.70291e13	0.0650956	0.0325478	−	0.999470i	$-0.489638\pi$
$199$	5.70291e13	0.0650956	0.0325478	+	0.999470i	$0.489638\pi$
$200$	−6.81939e14	−0.753443
$201$	−1.76756e14	−0.189060
$202$	−6.07105e14	−0.628752
$203$	−5.54842e14	−0.556475
$204$	−2.60356e14	−0.252913
$205$	−4.28271e14	−0.403012
$206$	5.28936e14	0.482243
$207$	2.36592e14	0.209023
$208$	−7.10150e14	−0.608049
$209$	−1.52196e15	−1.26314
$210$	−1.54579e14	−0.124373
$211$	1.73039e14	0.134992	0.0674961	−	0.997720i	$-0.478499\pi$
$211$	1.73039e14	0.134992	0.0674961	+	0.997720i	$0.478499\pi$
$212$	−7.37675e14	−0.558061
$213$	3.02889e14	0.222237
$214$	−7.78080e14	−0.553777
$215$	6.97451e14	0.481575
$216$	2.37598e14	0.159182
$217$	−8.51549e14	−0.553632
$218$	6.87827e14	0.434022
$219$	−1.37371e15	−0.841410
$220$	−3.50532e14	−0.208440
$221$	−1.46061e15	−0.843307
$222$	−5.94809e14	−0.333491
$223$	7.48625e14	0.407646	0.203823	−	0.979008i	$-0.434663\pi$
$223$	7.48625e14	0.407646	0.203823	+	0.979008i	$0.434663\pi$
$224$	2.98497e15	1.57880
$225$	−5.90936e14	−0.303637
$226$	−8.25263e14	−0.411991
$227$	−2.46575e15	−1.19614	−0.598068	−	0.801445i	$-0.704065\pi$
$227$	−2.46575e15	−1.19614	−0.598068	+	0.801445i	$0.704065\pi$
$228$	−1.36631e15	−0.644130
$229$	8.33539e13	0.0381940	0.0190970	−	0.999818i	$-0.493921\pi$
$229$	8.33539e13	0.0381940	0.0190970	+	0.999818i	$0.493921\pi$
$230$	1.94674e14	0.0867115
$231$	1.84686e15	0.799753
$232$	7.01726e14	0.295458
$233$	1.25130e15	0.512326	0.256163	−	0.966634i	$-0.417542\pi$
$233$	1.25130e15	0.512326	0.256163	+	0.966634i	$0.417542\pi$
$234$	5.86349e14	0.233482
$235$	−1.12547e15	−0.435905
$236$	−2.71378e14	−0.102246
$237$	−1.23274e15	−0.451862
$238$	1.12870e15	0.402560
$239$	−2.29876e15	−0.797823	−0.398912	−	0.916989i	$-0.630612\pi$
$239$	−2.29876e15	−0.797823	−0.398912	+	0.916989i	$0.630612\pi$
$240$	−2.05182e14	−0.0693051
$241$	−3.05920e15	−1.00577	−0.502883	−	0.864355i	$-0.667727\pi$
$241$	−3.05920e15	−1.00577	−0.502883	+	0.864355i	$0.667727\pi$
$242$	3.03055e14	0.0969889
$243$	2.05891e14	0.0641500
$244$	2.16726e15	0.657473
$245$	−1.44173e15	−0.425897
$246$	−1.25536e15	−0.361152
$247$	−7.66512e15	−2.14777
$248$	1.07698e15	0.293949
$249$	−1.45329e15	−0.386417
$250$	−1.02003e15	−0.264242
$251$	6.63415e14	0.167458	0.0837290	−	0.996489i	$-0.473317\pi$
$251$	6.63415e14	0.167458	0.0837290	+	0.996489i	$0.473317\pi$
$252$	1.65798e15	0.407828
$253$	−2.32589e15	−0.557579
$254$	1.92646e15	0.450132
$255$	−4.22011e14	−0.0961197
$256$	−2.35271e15	−0.522406
$257$	−2.29163e15	−0.496111	−0.248056	−	0.968746i	$-0.579792\pi$
$257$	−2.29163e15	−0.496111	−0.248056	+	0.968746i	$0.579792\pi$
$258$	2.04439e15	0.431554
$259$	−9.43562e15	−1.94232
$260$	−1.76540e15	−0.354418
$261$	6.08083e14	0.119069
$262$	3.02458e15	0.577706
$263$	1.59259e15	0.296750	0.148375	−	0.988931i	$-0.452596\pi$
$263$	1.59259e15	0.296750	0.148375	+	0.988931i	$0.452596\pi$
$264$	−2.33578e15	−0.424626
$265$	−1.19570e15	−0.212092
$266$	5.92330e15	1.02526
$267$	2.13058e15	0.359895
$268$	1.55995e15	0.257178
$269$	5.54351e15	0.892063	0.446031	−	0.895017i	$-0.352837\pi$
$269$	5.54351e15	0.892063	0.446031	+	0.895017i	$0.352837\pi$
$270$	1.69412e14	0.0266122
$271$	−8.05173e15	−1.23478	−0.617389	−	0.786658i	$-0.711810\pi$
$271$	−8.05173e15	−1.23478	−0.617389	+	0.786658i	$0.711810\pi$
$272$	1.49819e15	0.224321
$273$	9.30141e15	1.35985
$274$	−5.00289e15	−0.714236
$275$	5.80938e15	0.809967
$276$	−2.08803e15	−0.284333
$277$	−3.58336e15	−0.476620	−0.238310	−	0.971189i	$-0.576593\pi$
$277$	−3.58336e15	−0.476620	−0.238310	+	0.971189i	$0.576593\pi$
$278$	−4.66893e15	−0.606633
$279$	9.33260e14	0.118461
$280$	3.10129e15	0.384605
$281$	−1.62922e16	−1.97419	−0.987096	−	0.160127i	$-0.948810\pi$
$281$	−1.62922e16	−1.97419	−0.987096	+	0.160127i	$0.948810\pi$
$282$	−3.29900e15	−0.390628
$283$	−4.04402e15	−0.467953	−0.233976	−	0.972242i	$-0.575174\pi$
$283$	−4.04402e15	−0.467953	−0.233976	+	0.972242i	$0.575174\pi$
$284$	−2.67312e15	−0.302308
$285$	−2.21466e15	−0.244802
$286$	−5.76429e15	−0.622826
$287$	−1.99141e16	−2.10343
$288$	−3.27139e15	−0.337817
$289$	−6.82315e15	−0.688888
$290$	5.00345e14	0.0493950
$291$	9.61316e15	0.928030
$292$	1.21236e16	1.14457
$293$	−2.80853e15	−0.259322	−0.129661	−	0.991558i	$-0.541389\pi$
$293$	−2.80853e15	−0.259322	−0.129661	+	0.991558i	$0.541389\pi$
$294$	−4.22604e15	−0.381660
$295$	−4.39878e14	−0.0388588
$296$	1.19335e16	1.03127
$297$	−2.02408e15	−0.171124
$298$	3.34886e15	0.277007
$299$	−1.17140e16	−0.948074
$300$	5.21526e15	0.413036
$301$	3.24306e16	2.51347
$302$	−9.32769e14	−0.0707504
$303$	1.05548e16	0.783559
$304$	7.86231e15	0.571310
$305$	3.51292e15	0.249873
$306$	−1.23701e15	−0.0861359
$307$	−1.24621e16	−0.849554	−0.424777	−	0.905298i	$-0.639647\pi$
$307$	−1.24621e16	−0.849554	−0.424777	+	0.905298i	$0.639647\pi$
$308$	−1.62993e16	−1.08790
$309$	−9.19577e15	−0.600977
$310$	7.67909e14	0.0491427
$311$	1.54773e16	0.969959	0.484979	−	0.874526i	$-0.338827\pi$
$311$	1.54773e16	0.969959	0.484979	+	0.874526i	$0.338827\pi$
$312$	−1.17638e16	−0.722008
$313$	−3.84420e15	−0.231083	−0.115541	−	0.993303i	$-0.536860\pi$
$313$	−3.84420e15	−0.231083	−0.115541	+	0.993303i	$0.536860\pi$
$314$	6.25169e15	0.368090
$315$	2.68743e15	0.154995
$316$	1.08794e16	0.614666
$317$	−1.20939e16	−0.669395	−0.334697	−	0.942326i	$-0.608634\pi$
$317$	−1.20939e16	−0.669395	−0.334697	+	0.942326i	$0.608634\pi$
$318$	−3.50487e15	−0.190062
$319$	−5.97794e15	−0.317623
$320$	−3.86093e14	−0.0201010
$321$	1.35273e16	0.690124
$322$	9.05210e15	0.452571
$323$	1.61710e16	0.792354
$324$	−1.81708e15	−0.0872631
$325$	2.92580e16	1.37722
$326$	−6.03106e15	−0.278278
$327$	−1.19582e16	−0.540884
$328$	2.51859e16	1.11681
$329$	−5.23329e16	−2.27511
$330$	−1.66546e15	−0.0709894
$331$	−1.26292e16	−0.527829	−0.263915	−	0.964546i	$-0.585014\pi$
$331$	−1.26292e16	−0.527829	−0.263915	+	0.964546i	$0.585014\pi$
$332$	1.28259e16	0.525641
$333$	1.03410e16	0.415600
$334$	−4.64481e15	−0.183069
$335$	2.52852e15	0.0977407
$336$	−9.54070e15	−0.361722
$337$	−3.65154e16	−1.35794	−0.678972	−	0.734165i	$-0.737574\pi$
$337$	−3.65154e16	−1.35794	−0.678972	+	0.734165i	$0.737574\pi$
$338$	−1.63309e16	−0.595732
$339$	1.43475e16	0.513428
$340$	3.72443e15	0.130751
$341$	−9.17470e15	−0.316001
$342$	−6.49167e15	−0.219375
$343$	−2.00562e16	−0.665025
$344$	−4.10160e16	−1.33451
$345$	−3.38449e15	−0.108061
$346$	2.01908e16	0.632644
$347$	7.54050e15	0.231877	0.115939	−	0.993256i	$-0.463012\pi$
$347$	7.54050e15	0.231877	0.115939	+	0.993256i	$0.463012\pi$
$348$	−5.36659e15	−0.161969
$349$	4.18243e16	1.23898	0.619488	−	0.785006i	$-0.287340\pi$
$349$	4.18243e16	1.23898	0.619488	+	0.785006i	$0.287340\pi$
$350$	−2.26094e16	−0.657427
$351$	−1.01939e16	−0.290968
$352$	3.21605e16	0.901145
$353$	5.81122e16	1.59857	0.799285	−	0.600952i	$-0.205212\pi$
$353$	5.81122e16	1.59857	0.799285	+	0.600952i	$0.205212\pi$
$354$	−1.28938e15	−0.0348225
$355$	−4.33287e15	−0.114892
$356$	−1.88033e16	−0.489564
$357$	−1.96230e16	−0.501675
$358$	−3.12440e16	−0.784380
$359$	−5.56531e16	−1.37207	−0.686034	−	0.727570i	$-0.740650\pi$
$359$	−5.56531e16	−1.37207	−0.686034	+	0.727570i	$0.740650\pi$
$360$	−3.39887e15	−0.0822941
$361$	4.28102e16	1.01801
$362$	5.84615e15	0.136541
$363$	−5.26875e15	−0.120869
$364$	−8.20889e16	−1.84980
$365$	1.96511e16	0.434994
$366$	1.02972e16	0.223919
$367$	6.40933e16	1.36925	0.684625	−	0.728895i	$-0.259966\pi$
$367$	6.40933e16	1.36925	0.684625	+	0.728895i	$0.259966\pi$
$368$	1.20153e16	0.252189
$369$	2.18250e16	0.450072
$370$	8.50884e15	0.172409
$371$	−5.55986e16	−1.10696
$372$	−8.23642e15	−0.161142
$373$	−8.30832e16	−1.59737	−0.798685	−	0.601749i	$-0.794471\pi$
$373$	−8.30832e16	−1.59737	−0.798685	+	0.601749i	$0.794471\pi$
$374$	1.21608e16	0.229772
$375$	1.77336e16	0.329302
$376$	6.61870e16	1.20796
$377$	−3.01070e16	−0.540068
$378$	7.87747e15	0.138896
$379$	7.40374e16	1.28320	0.641602	−	0.767037i	$-0.278270\pi$
$379$	7.40374e16	1.28320	0.641602	+	0.767037i	$0.278270\pi$
$380$	1.95453e16	0.333004
$381$	−3.34923e16	−0.560960
$382$	1.31297e16	0.216193
$383$	−1.15582e17	−1.87110	−0.935552	−	0.353190i	$-0.885097\pi$
$383$	−1.15582e17	−1.87110	−0.935552	+	0.353190i	$0.885097\pi$
$384$	3.56299e16	0.567103
$385$	−2.64196e16	−0.413458
$386$	3.76382e16	0.579177
$387$	−3.55425e16	−0.537808
$388$	−8.48403e16	−1.26240
$389$	−1.06005e16	−0.155115	−0.0775576	−	0.996988i	$-0.524712\pi$
$389$	−1.06005e16	−0.155115	−0.0775576	+	0.996988i	$0.524712\pi$
$390$	−8.38782e15	−0.120706
$391$	2.47128e16	0.349762
$392$	8.47860e16	1.18022
$393$	−5.25836e16	−0.719944
$394$	1.65255e16	0.222551
$395$	1.76345e16	0.233605
$396$	1.78633e16	0.232779
$397$	2.54679e16	0.326479	0.163239	−	0.986586i	$-0.447806\pi$
$397$	2.54679e16	0.326479	0.163239	+	0.986586i	$0.447806\pi$
$398$	−2.39133e15	−0.0301578
$399$	−1.02979e17	−1.27769
$400$	−3.00107e16	−0.366342
$401$	1.11895e17	1.34392	0.671960	−	0.740588i	$-0.265453\pi$
$401$	1.11895e17	1.34392	0.671960	+	0.740588i	$0.265453\pi$
$402$	7.41167e15	0.0875884
$403$	−4.62069e16	−0.537309
$404$	−9.31504e16	−1.06587
$405$	−2.94530e15	−0.0331644
$406$	2.32655e16	0.257806
$407$	−1.01661e17	−1.10864
$408$	2.48178e16	0.266362
$409$	8.23815e15	0.0870218	0.0435109	−	0.999053i	$-0.486146\pi$
$409$	8.23815e15	0.0870218	0.0435109	+	0.999053i	$0.486146\pi$
$410$	1.79581e16	0.186709
$411$	8.69773e16	0.890090
$412$	8.11566e16	0.817508
$413$	−2.04538e16	−0.202814
$414$	−9.92071e15	−0.0968368
$415$	2.07895e16	0.199771
$416$	1.61971e17	1.53225
$417$	8.11713e16	0.755994
$418$	6.38184e16	0.585194
$419$	1.24414e17	1.12325	0.561626	−	0.827391i	$-0.310176\pi$
$419$	1.24414e17	1.12325	0.561626	+	0.827391i	$0.310176\pi$
$420$	−2.37177e16	−0.210840
$421$	1.47476e17	1.29088	0.645442	−	0.763809i	$-0.276673\pi$
$421$	1.47476e17	1.29088	0.645442	+	0.763809i	$0.276673\pi$
$422$	−7.25582e15	−0.0625397
$423$	5.73546e16	0.486806
$424$	7.03172e16	0.587738
$425$	−6.17251e16	−0.508082
$426$	−1.27006e16	−0.102959
$427$	1.63347e17	1.30416
$428$	−1.19384e17	−0.938774
$429$	1.00215e17	0.776173
$430$	−2.92453e16	−0.223106
$431$	1.59550e17	1.19893	0.599465	−	0.800401i	$-0.295380\pi$
$431$	1.59550e17	1.19893	0.599465	+	0.800401i	$0.295380\pi$
$432$	1.04562e16	0.0773979
$433$	6.91743e16	0.504398	0.252199	−	0.967675i	$-0.418846\pi$
$433$	6.91743e16	0.504398	0.252199	+	0.967675i	$0.418846\pi$
$434$	3.57069e16	0.256489
$435$	−8.69872e15	−0.0615567
$436$	1.05536e17	0.735763
$437$	1.29690e17	0.890791
$438$	5.76019e16	0.389812
$439$	8.97220e16	0.598246	0.299123	−	0.954215i	$-0.403306\pi$
$439$	8.97220e16	0.598246	0.299123	+	0.954215i	$0.403306\pi$
$440$	3.34137e16	0.219524
$441$	7.34716e16	0.475629
$442$	6.12460e16	0.390691
$443$	−1.47931e17	−0.929896	−0.464948	−	0.885338i	$-0.653927\pi$
$443$	−1.47931e17	−0.929896	−0.464948	+	0.885338i	$0.653927\pi$
$444$	−9.12639e16	−0.565340
$445$	−3.04783e16	−0.186059
$446$	−3.13911e16	−0.188856
$447$	−5.82214e16	−0.345210
$448$	−1.79529e16	−0.104913
$449$	1.58665e17	0.913860	0.456930	−	0.889503i	$-0.348949\pi$
$449$	1.58665e17	0.913860	0.456930	+	0.889503i	$0.348949\pi$
$450$	2.47789e16	0.140670
$451$	−2.14557e17	−1.20059
$452$	−1.26623e17	−0.698415
$453$	1.62166e16	0.0881700
$454$	1.03393e17	0.554151
$455$	−1.33058e17	−0.703020
$456$	1.30241e17	0.678384
$457$	−9.53833e16	−0.489798	−0.244899	−	0.969549i	$-0.578755\pi$
$457$	−9.53833e16	−0.489798	−0.244899	+	0.969549i	$0.578755\pi$
$458$	−3.49517e15	−0.0176947
$459$	2.15060e16	0.107344
$460$	2.98696e16	0.146995
$461$	−7.63684e16	−0.370559	−0.185280	−	0.982686i	$-0.559319\pi$
$461$	−7.63684e16	−0.370559	−0.185280	+	0.982686i	$0.559319\pi$
$462$	−7.74419e16	−0.370513
$463$	−1.08628e17	−0.512464	−0.256232	−	0.966615i	$-0.582481\pi$
$463$	−1.08628e17	−0.512464	−0.256232	+	0.966615i	$0.582481\pi$
$464$	3.08815e16	0.143659
$465$	−1.33504e16	−0.0612422
$466$	−5.24689e16	−0.237352
$467$	−3.17982e17	−1.41854	−0.709272	−	0.704935i	$-0.750976\pi$
$467$	−3.17982e17	−1.41854	−0.709272	+	0.704935i	$0.750976\pi$
$468$	8.99658e16	0.395803
$469$	1.17573e17	0.510135
$470$	4.71928e16	0.201948
$471$	−1.08688e17	−0.458719
$472$	2.58685e16	0.107683
$473$	3.49412e17	1.43463
$474$	5.16906e16	0.209340
$475$	−3.23925e17	−1.29401
$476$	1.73181e17	0.682427
$477$	6.09336e16	0.236858
$478$	9.63907e16	0.369619
$479$	−4.89415e17	−1.85138	−0.925692	−	0.378277i	$-0.876517\pi$
$479$	−4.89415e17	−1.85138	−0.925692	+	0.378277i	$0.876517\pi$
$480$	4.67978e16	0.174646
$481$	−5.11997e17	−1.88506
$482$	1.28277e17	0.465955
$483$	−1.57375e17	−0.563999
$484$	4.64989e16	0.164418
$485$	−1.37518e17	−0.479775
$486$	−8.63336e15	−0.0297197
$487$	2.63271e17	0.894261	0.447131	−	0.894469i	$-0.352446\pi$
$487$	2.63271e17	0.894261	0.447131	+	0.894469i	$0.352446\pi$
$488$	−2.06590e17	−0.692436
$489$	1.04853e17	0.346794
$490$	6.04542e16	0.197311
$491$	3.20068e17	1.03089	0.515445	−	0.856923i	$-0.327627\pi$
$491$	3.20068e17	1.03089	0.515445	+	0.856923i	$0.327627\pi$
$492$	−1.92615e17	−0.612232
$493$	6.35161e16	0.199241
$494$	3.21411e17	0.995029
$495$	2.89547e16	0.0884679
$496$	4.73956e16	0.142925
$497$	−2.01473e17	−0.599654
$498$	6.09388e16	0.179021
$499$	−4.56082e17	−1.32248	−0.661241	−	0.750174i	$-0.729970\pi$
$499$	−4.56082e17	−1.32248	−0.661241	+	0.750174i	$0.729970\pi$
$500$	−1.56507e17	−0.447949
$501$	8.07520e16	0.228143
$502$	−2.78181e16	−0.0775806
$503$	5.91424e17	1.62820	0.814099	−	0.580726i	$-0.197231\pi$
$503$	5.91424e17	1.62820	0.814099	+	0.580726i	$0.197231\pi$
$504$	−1.58044e17	−0.429515
$505$	−1.50988e17	−0.405086
$506$	9.75286e16	0.258317
$507$	2.83919e17	0.742408
$508$	2.95584e17	0.763073
$509$	7.16767e17	1.82689	0.913445	−	0.406963i	$-0.133412\pi$
$509$	7.16767e17	1.82689	0.913445	+	0.406963i	$0.133412\pi$
$510$	1.76956e16	0.0445307
$511$	9.13753e17	2.27035
$512$	−3.01732e17	−0.740230
$513$	1.12861e17	0.273388
$514$	9.60918e16	0.229840
$515$	1.31547e17	0.310695
$516$	3.13678e17	0.731579
$517$	−5.63842e17	−1.29858
$518$	3.95651e17	0.899848
$519$	−3.51026e17	−0.788409
$520$	1.68283e17	0.373265
$521$	6.37395e16	0.139625	0.0698126	−	0.997560i	$-0.477760\pi$
$521$	6.37395e16	0.139625	0.0698126	+	0.997560i	$0.477760\pi$
$522$	−2.54979e16	−0.0551628
$523$	3.40594e17	0.727739	0.363869	−	0.931450i	$-0.381455\pi$
$523$	3.40594e17	0.727739	0.363869	+	0.931450i	$0.381455\pi$
$524$	4.64073e17	0.979338
$525$	3.93075e17	0.819294
$526$	−6.67799e16	−0.137480
$527$	9.74819e16	0.198223
$528$	−1.02793e17	−0.206463
$529$	−3.05842e17	−0.606786
$530$	5.01376e16	0.0982586
$531$	2.24165e16	0.0433963
$532$	9.08835e17	1.73804
$533$	−1.08058e18	−2.04141
$534$	−8.93390e16	−0.166733
$535$	−1.93510e17	−0.356782
$536$	−1.48698e17	−0.270854
$537$	5.43190e17	0.977504
$538$	−2.32449e17	−0.413278
$539$	−7.22285e17	−1.26877
$540$	2.59936e16	0.0451135
$541$	3.19418e16	0.0547743	0.0273872	−	0.999625i	$-0.491281\pi$
$541$	3.19418e16	0.0547743	0.0273872	+	0.999625i	$0.491281\pi$
$542$	3.37622e17	0.572053
$543$	−1.01638e17	−0.170160
$544$	−3.41707e17	−0.565277
$545$	1.71063e17	0.279628
$546$	−3.90024e17	−0.629998
$547$	−6.84332e17	−1.09232	−0.546159	−	0.837682i	$-0.683911\pi$
$547$	−6.84332e17	−1.09232	−0.546159	+	0.837682i	$0.683911\pi$
$548$	−7.67612e17	−1.21079
$549$	−1.79021e17	−0.279051
$550$	−2.43597e17	−0.375245
$551$	3.33324e17	0.507437
$552$	1.99037e17	0.299453
$553$	8.19982e17	1.21924
$554$	1.50256e17	0.220810
$555$	−1.47930e17	−0.214858
$556$	−7.16371e17	−1.02838
$557$	−1.24182e16	−0.0176198	−0.00880990	−	0.999961i	$-0.502804\pi$
$557$	−1.24182e16	−0.0176198	−0.00880990	+	0.999961i	$0.502804\pi$
$558$	−3.91331e16	−0.0548811
$559$	1.75976e18	2.43936
$560$	1.36481e17	0.187004
$561$	−2.11421e17	−0.286345
$562$	6.83161e17	0.914612
$563$	2.43031e17	0.321630	0.160815	−	0.986985i	$-0.448588\pi$
$563$	2.43031e17	0.321630	0.160815	+	0.986985i	$0.448588\pi$
$564$	−5.06179e17	−0.662201
$565$	−2.05244e17	−0.265433
$566$	1.69573e17	0.216795
$567$	−1.36953e17	−0.173094
$568$	2.54809e17	0.318384
$569$	4.46432e17	0.551475	0.275737	−	0.961233i	$-0.411078\pi$
$569$	4.46432e17	0.551475	0.275737	+	0.961233i	$0.411078\pi$
$570$	9.28644e16	0.113413
$571$	−1.45138e16	−0.0175245	−0.00876224	−	0.999962i	$-0.502789\pi$
$571$	−1.45138e16	−0.0175245	−0.00876224	+	0.999962i	$0.502789\pi$
$572$	−8.84437e17	−1.05583
$573$	−2.28265e17	−0.269423
$574$	8.35031e17	0.974485
$575$	−4.95029e17	−0.571202
$576$	1.96756e16	0.0224482
$577$	−1.03181e18	−1.16401	−0.582004	−	0.813186i	$-0.697731\pi$
$577$	−1.03181e18	−1.16401	−0.582004	+	0.813186i	$0.697731\pi$
$578$	2.86106e17	0.319151
$579$	−6.54356e17	−0.721777
$580$	7.67699e16	0.0837354
$581$	9.66687e17	1.04266
$582$	−4.03096e17	−0.429941
$583$	−5.99026e17	−0.631830
$584$	−1.15565e18	−1.20543
$585$	1.45826e17	0.150425
$586$	1.17766e17	0.120140
$587$	−1.61946e18	−1.63389	−0.816945	−	0.576716i	$-0.804334\pi$
$587$	−1.61946e18	−1.63389	−0.816945	+	0.576716i	$0.804334\pi$
$588$	−6.48418e17	−0.646997
$589$	5.11572e17	0.504845
$590$	1.84448e16	0.0180026
$591$	−2.87303e17	−0.277346
$592$	5.25169e17	0.501427
$593$	1.83507e18	1.73300	0.866498	−	0.499181i	$-0.166366\pi$
$593$	1.83507e18	1.73300	0.866498	+	0.499181i	$0.166366\pi$
$594$	8.48729e16	0.0792788
$595$	2.80710e17	0.259357
$596$	5.13828e17	0.469589
$597$	4.15742e16	0.0375830
$598$	4.91187e17	0.439227
$599$	−5.61954e17	−0.497080	−0.248540	−	0.968622i	$-0.579951\pi$
$599$	−5.61954e17	−0.497080	−0.248540	+	0.968622i	$0.579951\pi$
$600$	−4.97133e17	−0.435000
$601$	9.46428e17	0.819226	0.409613	−	0.912259i	$-0.365664\pi$
$601$	9.46428e17	0.819226	0.409613	+	0.912259i	$0.365664\pi$
$602$	−1.35987e18	−1.16445
$603$	−1.28855e17	−0.109154
$604$	−1.43118e17	−0.119937
$605$	7.53703e16	0.0624871
$606$	−4.42579e17	−0.363010
$607$	1.56184e18	1.26739	0.633696	−	0.773582i	$-0.281537\pi$
$607$	1.56184e18	1.26739	0.633696	+	0.773582i	$0.281537\pi$
$608$	−1.79324e18	−1.43967
$609$	−4.04480e17	−0.321281
$610$	−1.47303e17	−0.115762
$611$	−2.83970e18	−2.20803
$612$	−1.89799e17	−0.146019
$613$	1.54590e18	1.17676	0.588379	−	0.808585i	$-0.299766\pi$
$613$	1.54590e18	1.17676	0.588379	+	0.808585i	$0.299766\pi$
$614$	5.22555e17	0.393584
$615$	−3.12209e17	−0.232679
$616$	1.55370e18	1.14575
$617$	−1.38383e17	−0.100979	−0.0504895	−	0.998725i	$-0.516078\pi$
$617$	−1.38383e17	−0.100979	−0.0504895	+	0.998725i	$0.516078\pi$
$618$	3.85594e17	0.278423
$619$	1.99704e18	1.42691	0.713456	−	0.700700i	$-0.247129\pi$
$619$	1.99704e18	1.42691	0.713456	+	0.700700i	$0.247129\pi$
$620$	1.17823e17	0.0833077
$621$	1.72476e17	0.120679
$622$	−6.48990e17	−0.449366
$623$	−1.41721e18	−0.971093
$624$	−5.17699e17	−0.351057
$625$	1.10368e18	0.740666
$626$	1.61194e17	0.107057
$627$	−1.10951e18	−0.729277
$628$	9.59220e17	0.623994
$629$	1.08015e18	0.695433
$630$	−1.12688e17	−0.0718068
$631$	−1.78543e18	−1.12603	−0.563017	−	0.826445i	$-0.690360\pi$
$631$	−1.78543e18	−1.12603	−0.563017	+	0.826445i	$0.690360\pi$
$632$	−1.03706e18	−0.647353
$633$	1.26146e17	0.0779377
$634$	5.07119e17	0.310120
$635$	4.79112e17	0.290007
$636$	−5.37765e17	−0.322197
$637$	−3.63767e18	−2.15733
$638$	2.50665e17	0.147150
$639$	2.20806e17	0.128308
$640$	−5.09692e17	−0.293182
$641$	−4.96522e17	−0.282723	−0.141362	−	0.989958i	$-0.545148\pi$
$641$	−4.96522e17	−0.282723	−0.141362	+	0.989958i	$0.545148\pi$
$642$	−5.67220e17	−0.319723
$643$	−3.55250e18	−1.98227	−0.991134	−	0.132863i	$-0.957583\pi$
$643$	−3.55250e18	−1.98227	−0.991134	+	0.132863i	$0.957583\pi$
$644$	1.38890e18	0.767207
$645$	5.08442e17	0.278037
$646$	−6.78075e17	−0.367085
$647$	−1.84037e18	−0.986340	−0.493170	−	0.869933i	$-0.664162\pi$
$647$	−1.84037e18	−0.986340	−0.493170	+	0.869933i	$0.664162\pi$
$648$	1.73209e17	0.0919036
$649$	−2.20372e17	−0.115762
$650$	−1.22684e18	−0.638043
$651$	−6.20779e17	−0.319640
$652$	−9.25369e17	−0.471743
$653$	−1.07637e18	−0.543283	−0.271641	−	0.962399i	$-0.587566\pi$
$653$	−1.07637e18	−0.543283	−0.271641	+	0.962399i	$0.587566\pi$
$654$	5.01426e17	0.250583
$655$	7.52217e17	0.372198
$656$	1.10838e18	0.543018
$657$	−1.00143e18	−0.485788
$658$	2.19441e18	1.05402
$659$	1.13582e18	0.540201	0.270100	−	0.962832i	$-0.412943\pi$
$659$	1.13582e18	0.540201	0.270100	+	0.962832i	$0.412943\pi$
$660$	−2.55538e17	−0.120343
$661$	1.99757e18	0.931522	0.465761	−	0.884911i	$-0.345781\pi$
$661$	1.99757e18	0.931522	0.465761	+	0.884911i	$0.345781\pi$
$662$	5.29563e17	0.244535
$663$	−1.06479e18	−0.486884
$664$	−1.22260e18	−0.553594
$665$	1.47313e18	0.660543
$666$	−4.33616e17	−0.192541
$667$	5.09393e17	0.223993
$668$	−7.12671e17	−0.310343
$669$	5.45748e17	0.235354
$670$	−1.06025e17	−0.0452817
$671$	1.75992e18	0.744383
$672$	2.17604e18	0.911522
$673$	1.38797e17	0.0575814	0.0287907	−	0.999585i	$-0.490834\pi$
$673$	1.38797e17	0.0575814	0.0287907	+	0.999585i	$0.490834\pi$
$674$	1.53115e18	0.629113
$675$	−4.30792e17	−0.175305
$676$	−2.50571e18	−1.00990
$677$	−6.61948e17	−0.264239	−0.132120	−	0.991234i	$-0.542178\pi$
$677$	−6.61948e17	−0.264239	−0.132120	+	0.991234i	$0.542178\pi$
$678$	−6.01616e17	−0.237863
$679$	−6.39441e18	−2.50407
$680$	−3.55023e17	−0.137705
$681$	−1.79753e18	−0.690590
$682$	3.84710e17	0.146398
$683$	2.19099e18	0.825857	0.412929	−	0.910763i	$-0.364506\pi$
$683$	2.19099e18	0.825857	0.412929	+	0.910763i	$0.364506\pi$
$684$	−9.96042e17	−0.371889
$685$	−1.24422e18	−0.460161
$686$	8.40992e17	0.308095
$687$	6.07650e16	0.0220513
$688$	−1.80503e18	−0.648873
$689$	−3.01690e18	−1.07433
$690$	1.41917e17	0.0500629
$691$	2.88496e18	1.00817	0.504084	−	0.863655i	$-0.331830\pi$
$691$	2.88496e18	1.00817	0.504084	+	0.863655i	$0.331830\pi$
$692$	3.09795e18	1.07247
$693$	1.34636e18	0.461738
$694$	−3.16186e17	−0.107425
$695$	−1.16117e18	−0.390835
$696$	5.11558e17	0.170583
$697$	2.27968e18	0.753116
$698$	−1.75376e18	−0.573998
$699$	9.12194e17	0.295792
$700$	−3.46905e18	−1.11448
$701$	−3.57673e18	−1.13846	−0.569232	−	0.822177i	$-0.692759\pi$
$701$	−3.57673e18	−1.13846	−0.569232	+	0.822177i	$0.692759\pi$
$702$	4.27449e17	0.134801
$703$	5.66850e18	1.77116
$704$	−1.93427e17	−0.0598817
$705$	−8.20466e17	−0.251670
$706$	−2.43674e18	−0.740592
$707$	−7.02075e18	−2.11425
$708$	−1.97835e17	−0.0590319
$709$	−3.26567e18	−0.965542	−0.482771	−	0.875747i	$-0.660370\pi$
$709$	−3.26567e18	−0.965542	−0.482771	+	0.875747i	$0.660370\pi$
$710$	1.81684e17	0.0532278
$711$	−8.98664e17	−0.260882
$712$	1.79238e18	0.515598
$713$	7.81795e17	0.222849
$714$	8.22826e17	0.232418
$715$	−1.43359e18	−0.401268
$716$	−4.79388e18	−1.32970
$717$	−1.67579e18	−0.460624
$718$	2.33363e18	0.635657
$719$	−3.22106e18	−0.869484	−0.434742	−	0.900555i	$-0.643160\pi$
$719$	−3.22106e18	−0.869484	−0.434742	+	0.900555i	$0.643160\pi$
$720$	−1.49577e17	−0.0400133
$721$	6.11678e18	1.62160
$722$	−1.79510e18	−0.471625
$723$	−2.23016e18	−0.580679
$724$	8.96997e17	0.231468
$725$	−1.27231e18	−0.325384
$726$	2.20927e17	0.0559966
$727$	3.16803e18	0.795821	0.397911	−	0.917424i	$-0.369735\pi$
$727$	3.16803e18	0.795821	0.397911	+	0.917424i	$0.369735\pi$
$728$	7.82494e18	1.94817
$729$	1.50095e17	0.0370370
$730$	−8.24004e17	−0.201526
$731$	−3.71253e18	−0.899926
$732$	1.57993e18	0.379592
$733$	4.06683e18	0.968458	0.484229	−	0.874941i	$-0.339100\pi$
$733$	4.06683e18	0.968458	0.484229	+	0.874941i	$0.339100\pi$
$734$	−2.68754e18	−0.634352
$735$	−1.05102e18	−0.245892
$736$	−2.74046e18	−0.635503
$737$	1.26675e18	0.291174
$738$	−9.15157e17	−0.208511
$739$	3.29847e18	0.744944	0.372472	−	0.928044i	$-0.378510\pi$
$739$	3.29847e18	0.744944	0.372472	+	0.928044i	$0.378510\pi$
$740$	1.30554e18	0.292271
$741$	−5.58787e18	−1.24002
$742$	2.33134e18	0.512838
$743$	−2.79284e18	−0.609002	−0.304501	−	0.952512i	$-0.598490\pi$
$743$	−2.79284e18	−0.609002	−0.304501	+	0.952512i	$0.598490\pi$
$744$	7.85118e17	0.169711
$745$	8.32866e17	0.178468
$746$	3.48382e18	0.740036
$747$	−1.05945e18	−0.223098
$748$	1.86588e18	0.389514
$749$	−8.99796e18	−1.86214
$750$	−7.43601e17	−0.152560
$751$	−6.31465e18	−1.28437	−0.642184	−	0.766550i	$-0.721972\pi$
$751$	−6.31465e18	−1.28437	−0.642184	+	0.766550i	$0.721972\pi$
$752$	2.91276e18	0.587338
$753$	4.83629e17	0.0966819
$754$	1.26243e18	0.250205
$755$	−2.31981e17	−0.0455824
$756$	1.20867e18	0.235459
$757$	−2.12986e18	−0.411365	−0.205683	−	0.978619i	$-0.565941\pi$
$757$	−2.12986e18	−0.411365	−0.205683	+	0.978619i	$0.565941\pi$
$758$	−3.10451e18	−0.594488
$759$	−1.69558e18	−0.321918
$760$	−1.86311e18	−0.350712
$761$	−1.07384e18	−0.200419	−0.100210	−	0.994966i	$-0.531951\pi$
$761$	−1.07384e18	−0.200419	−0.100210	+	0.994966i	$0.531951\pi$
$762$	1.40439e18	0.259884
$763$	7.95425e18	1.45945
$764$	2.01454e18	0.366495
$765$	−3.07646e17	−0.0554948
$766$	4.84654e18	0.866852
$767$	−1.10987e18	−0.196835
$768$	−1.71512e18	−0.301611
$769$	−9.62435e18	−1.67823	−0.839113	−	0.543957i	$-0.816925\pi$
$769$	−9.62435e18	−1.67823	−0.839113	+	0.543957i	$0.816925\pi$
$770$	1.10782e18	0.191549
$771$	−1.67060e18	−0.286430
$772$	5.77497e18	0.981832
$773$	6.61677e18	1.11553	0.557763	−	0.830001i	$-0.311660\pi$
$773$	6.61677e18	1.11553	0.557763	+	0.830001i	$0.311660\pi$
$774$	1.49036e18	0.249158
$775$	−1.95269e18	−0.323722
$776$	8.08721e18	1.32953
$777$	−6.87856e18	−1.12140
$778$	4.44497e17	0.0718623
$779$	1.19635e19	1.91807
$780$	−1.28698e18	−0.204623
$781$	−2.17070e18	−0.342269
$782$	−1.03625e18	−0.162039
$783$	4.43292e17	0.0687446
$784$	3.73126e18	0.573853
$785$	1.55480e18	0.237150
$786$	2.20492e18	0.333538
$787$	8.44091e18	1.26635	0.633175	−	0.774009i	$-0.281751\pi$
$787$	8.44091e18	1.26635	0.633175	+	0.774009i	$0.281751\pi$
$788$	2.53557e18	0.377272
$789$	1.16100e18	0.171329
$790$	−7.39443e17	−0.108225
$791$	−9.54360e18	−1.38537
$792$	−1.70278e18	−0.245158
$793$	8.86355e18	1.26570
$794$	−1.06791e18	−0.151252
$795$	−8.71664e17	−0.122451
$796$	−3.66910e17	−0.0511240
$797$	−7.37903e18	−1.01981	−0.509906	−	0.860230i	$-0.670320\pi$
$797$	−7.37903e18	−1.01981	−0.509906	+	0.860230i	$0.670320\pi$
$798$	4.31809e18	0.591933
$799$	5.99086e18	0.814583
$800$	6.84484e18	0.923163
$801$	1.55320e18	0.207785
$802$	−4.69195e18	−0.622616
$803$	9.84490e18	1.29587
$804$	1.13720e18	0.148482
$805$	2.25127e18	0.291578
$806$	1.93753e18	0.248927
$807$	4.04122e18	0.515033
$808$	8.87935e18	1.12255
$809$	−5.15112e18	−0.646006	−0.323003	−	0.946398i	$-0.604692\pi$
$809$	−5.15112e18	−0.646006	−0.323003	+	0.946398i	$0.604692\pi$
$810$	1.23502e17	0.0153645
$811$	1.50635e19	1.85905	0.929524	−	0.368761i	$-0.120218\pi$
$811$	1.50635e19	1.85905	0.929524	+	0.368761i	$0.120218\pi$
$812$	3.56971e18	0.437037
$813$	−5.86971e18	−0.712899
$814$	4.26280e18	0.513613
$815$	−1.49993e18	−0.179286
$816$	1.09218e18	0.129512
$817$	−1.94829e19	−2.29197
$818$	−3.45439e17	−0.0403158
$819$	6.78073e18	0.785111
$820$	2.75538e18	0.316513
$821$	−2.51846e18	−0.287015	−0.143508	−	0.989649i	$-0.545838\pi$
$821$	−2.51846e18	−0.287015	−0.143508	+	0.989649i	$0.545838\pi$
$822$	−3.64710e18	−0.412365
$823$	8.82032e18	0.989431	0.494715	−	0.869055i	$-0.335272\pi$
$823$	8.82032e18	0.989431	0.494715	+	0.869055i	$0.335272\pi$
$824$	−7.73607e18	−0.860981
$825$	4.23504e18	0.467635
$826$	8.57662e17	0.0939606
$827$	3.27336e18	0.355802	0.177901	−	0.984048i	$-0.443069\pi$
$827$	3.27336e18	0.355802	0.177901	+	0.984048i	$0.443069\pi$
$828$	−1.52217e18	−0.164160
$829$	6.05713e18	0.648131	0.324065	−	0.946035i	$-0.394950\pi$
$829$	6.05713e18	0.648131	0.324065	+	0.946035i	$0.394950\pi$
$830$	−8.71738e17	−0.0925505
$831$	−2.61227e18	−0.275177
$832$	−9.74163e17	−0.101819
$833$	7.67433e18	0.795880
$834$	−3.40365e18	−0.350240
$835$	−1.15517e18	−0.117946
$836$	9.79190e18	0.992033
$837$	6.80347e17	0.0683935
$838$	−5.21688e18	−0.520385
$839$	3.44143e18	0.340632	0.170316	−	0.985389i	$-0.445521\pi$
$839$	3.44143e18	0.340632	0.170316	+	0.985389i	$0.445521\pi$
$840$	2.26084e18	0.222052
$841$	−8.95140e18	−0.872403
$842$	−6.18391e18	−0.598046
$843$	−1.18770e19	−1.13980
$844$	−1.11329e18	−0.106018
$845$	−4.06151e18	−0.383812
$846$	−2.40497e18	−0.225529
$847$	3.50463e18	0.326137
$848$	3.09451e18	0.285772
$849$	−2.94809e18	−0.270173
$850$	2.58823e18	0.235386
$851$	8.66271e18	0.781828
$852$	−1.94871e18	−0.174538
$853$	−9.61437e18	−0.854579	−0.427289	−	0.904115i	$-0.640531\pi$
$853$	−9.61437e18	−0.854579	−0.427289	+	0.904115i	$0.640531\pi$
$854$	−6.84940e18	−0.604194
$855$	−1.61449e18	−0.141337
$856$	1.13800e19	0.988696
$857$	−1.78667e19	−1.54053	−0.770263	−	0.637726i	$-0.779875\pi$
$857$	−1.78667e19	−1.54053	−0.770263	+	0.637726i	$0.779875\pi$
$858$	−4.20217e18	−0.359589
$859$	1.24841e19	1.06023	0.530116	−	0.847925i	$-0.322148\pi$
$859$	1.24841e19	1.06023	0.530116	+	0.847925i	$0.322148\pi$
$860$	−4.48721e18	−0.378213
$861$	−1.45174e19	−1.21442
$862$	−6.69019e18	−0.555445
$863$	1.05396e18	0.0868472	0.0434236	−	0.999057i	$-0.486173\pi$
$863$	1.05396e18	0.0868472	0.0434236	+	0.999057i	$0.486173\pi$
$864$	−2.38485e18	−0.195039
$865$	5.02148e18	0.407593
$866$	−2.90059e18	−0.233679
$867$	−4.97407e18	−0.397730
$868$	5.47864e18	0.434805
$869$	8.83459e18	0.695918
$870$	3.64752e17	0.0285182
$871$	6.37978e18	0.495094
$872$	−1.00600e19	−0.774890
$873$	7.00800e18	0.535798
$874$	−5.43810e18	−0.412689
$875$	−1.17959e19	−0.888546
$876$	8.83807e18	0.660817
$877$	1.28385e19	0.952834	0.476417	−	0.879220i	$-0.341935\pi$
$877$	1.28385e19	0.952834	0.476417	+	0.879220i	$0.341935\pi$
$878$	−3.76219e18	−0.277158
$879$	−2.04742e18	−0.149719
$880$	1.47047e18	0.106738
$881$	2.18015e19	1.57088	0.785439	−	0.618939i	$-0.212437\pi$
$881$	2.18015e19	1.57088	0.785439	+	0.618939i	$0.212437\pi$
$882$	−3.08078e18	−0.220351
$883$	1.33672e19	0.949063	0.474532	−	0.880238i	$-0.342617\pi$
$883$	1.33672e19	0.949063	0.474532	+	0.880238i	$0.342617\pi$
$884$	9.39721e18	0.662306
$885$	−3.20671e17	−0.0224351
$886$	6.20298e18	0.430806
$887$	−1.95495e19	−1.34782	−0.673912	−	0.738812i	$-0.735387\pi$
$887$	−1.95495e19	−1.34782	−0.673912	+	0.738812i	$0.735387\pi$
$888$	8.69953e18	0.595403
$889$	2.22781e19	1.51362
$890$	1.27801e18	0.0861982
$891$	−1.47555e18	−0.0987983
$892$	−4.81646e18	−0.320152
$893$	3.14393e19	2.07462
$894$	2.44132e18	0.159930
$895$	−7.77041e18	−0.505352
$896$	−2.37001e19	−1.53020
$897$	−8.53950e18	−0.547371
$898$	−6.65308e18	−0.423376
$899$	2.00935e18	0.126945
$900$	3.80193e18	0.238466
$901$	6.36470e18	0.396339
$902$	8.99673e18	0.556215
$903$	2.36419e19	1.45115
$904$	1.20701e19	0.735555
$905$	1.45394e18	0.0879695
$906$	−6.79988e17	−0.0408478
$907$	−8.49574e18	−0.506703	−0.253352	−	0.967374i	$-0.581533\pi$
$907$	−8.49574e18	−0.506703	−0.253352	+	0.967374i	$0.581533\pi$
$908$	1.58640e19	0.939408
$909$	7.69443e18	0.452388
$910$	5.57935e18	0.325698
$911$	−2.21168e18	−0.128190	−0.0640949	−	0.997944i	$-0.520416\pi$
$911$	−2.21168e18	−0.128190	−0.0640949	+	0.997944i	$0.520416\pi$
$912$	5.73163e18	0.329846
$913$	1.04152e19	0.595125
$914$	3.99958e18	0.226915
$915$	2.56092e18	0.144264
$916$	−5.36277e17	−0.0299964
$917$	3.49772e19	1.94260
$918$	−9.01781e17	−0.0497306
$919$	−3.31535e18	−0.181542	−0.0907712	−	0.995872i	$-0.528933\pi$
$919$	−3.31535e18	−0.181542	−0.0907712	+	0.995872i	$0.528933\pi$
$920$	−2.84725e18	−0.154812
$921$	−9.08485e18	−0.490490
$922$	3.20225e18	0.171674
$923$	−1.09324e19	−0.581974
$924$	−1.18822e19	−0.628101
$925$	−2.16368e19	−1.13572
$926$	4.55493e18	0.237416
$927$	−6.70372e18	−0.346975
$928$	−7.04345e18	−0.362012
$929$	−4.98587e18	−0.254472	−0.127236	−	0.991873i	$-0.540610\pi$
$929$	−4.98587e18	−0.254472	−0.127236	+	0.991873i	$0.540610\pi$
$930$	5.59806e17	0.0283725
$931$	4.02739e19	2.02699
$932$	−8.05050e18	−0.402365
$933$	1.12830e19	0.560006
$934$	1.33335e19	0.657189
$935$	3.02441e18	0.148035
$936$	−8.57579e18	−0.416851
$937$	−1.45978e19	−0.704660	−0.352330	−	0.935876i	$-0.614610\pi$
$937$	−1.45978e19	−0.704660	−0.352330	+	0.935876i	$0.614610\pi$
$938$	−4.93004e18	−0.236337
$939$	−2.80242e18	−0.133416
$940$	7.24097e18	0.342346
$941$	−2.94295e19	−1.38182	−0.690908	−	0.722942i	$-0.742789\pi$
$941$	−2.94295e19	−1.38182	−0.690908	+	0.722942i	$0.742789\pi$
$942$	4.55748e18	0.212517
$943$	1.82828e19	0.846677
$944$	1.13842e18	0.0523582
$945$	1.95914e18	0.0894866
$946$	−1.46514e19	−0.664642
$947$	1.32549e19	0.597173	0.298587	−	0.954383i	$-0.403485\pi$
$947$	1.32549e19	0.597173	0.298587	+	0.954383i	$0.403485\pi$
$948$	7.93109e18	0.354878
$949$	4.95822e19	2.20341
$950$	1.35827e19	0.599492
$951$	−8.81648e18	−0.386475
$952$	−1.65081e19	−0.718717
$953$	−2.18343e19	−0.944139	−0.472069	−	0.881561i	$-0.656493\pi$
$953$	−2.18343e19	−0.944139	−0.472069	+	0.881561i	$0.656493\pi$
$954$	−2.55505e18	−0.109732
$955$	3.26537e18	0.139287
$956$	1.47896e19	0.626585
$957$	−4.35792e18	−0.183380
$958$	2.05220e19	0.857717
$959$	−5.78550e19	−2.40170
$960$	−2.81462e17	−0.0116053
$961$	−2.13337e19	−0.873703
$962$	2.14689e19	0.873317
$963$	9.86137e18	0.398443
$964$	1.96821e19	0.789896
$965$	9.36066e18	0.373146
$966$	6.59898e18	0.261292
$967$	2.52961e19	0.994906	0.497453	−	0.867491i	$-0.334269\pi$
$967$	2.52961e19	0.994906	0.497453	+	0.867491i	$0.334269\pi$
$968$	−4.43241e18	−0.173161
$969$	1.17886e19	0.457466
$970$	5.76635e18	0.222272
$971$	6.40939e18	0.245410	0.122705	−	0.992443i	$-0.460843\pi$
$971$	6.40939e18	0.245410	0.122705	+	0.992443i	$0.460843\pi$
$972$	−1.32465e18	−0.0503814
$973$	−5.39930e19	−2.03988
$974$	−1.10394e19	−0.414297
$975$	2.13291e19	0.795138
$976$	−9.09158e18	−0.336679
$977$	−1.73549e19	−0.638423	−0.319211	−	0.947684i	$-0.603418\pi$
$977$	−1.73549e19	−0.638423	−0.319211	+	0.947684i	$0.603418\pi$
$978$	−4.39665e18	−0.160664
$979$	−1.52692e19	−0.554279
$980$	9.27572e18	0.334486
$981$	−8.71751e18	−0.312280
$982$	−1.34210e19	−0.477594
$983$	−4.87986e19	−1.72508	−0.862541	−	0.505988i	$-0.831128\pi$
$983$	−4.87986e19	−1.72508	−0.862541	+	0.505988i	$0.831128\pi$
$984$	1.83606e19	0.644789
$985$	4.10991e18	0.143383
$986$	−2.66334e18	−0.0923051
$987$	−3.81507e19	−1.31353
$988$	4.93154e19	1.68679
$989$	−2.97741e19	−1.01173
$990$	−1.21412e18	−0.0409857
$991$	−1.35291e19	−0.453722	−0.226861	−	0.973927i	$-0.572846\pi$
$991$	−1.35291e19	−0.453722	−0.226861	+	0.973927i	$0.572846\pi$
$992$	−1.08100e19	−0.360163
$993$	−9.20667e18	−0.304742
$994$	8.44811e18	0.277810
$995$	−5.94726e17	−0.0194297
$996$	9.35007e18	0.303479
$997$	−5.49885e19	−1.77318	−0.886591	−	0.462555i	$-0.846933\pi$
$997$	−5.49885e19	−1.77318	−0.886591	+	0.462555i	$0.846933\pi$
$998$	1.91243e19	0.612684
$999$	7.53860e18	0.239947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.13	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.13	✓	30	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-41.9317 q^{2} +729.000 q^{3} -6433.74 q^{4} -10428.5 q^{5} -30568.2 q^{6} -484911. q^{7} +613281. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-41.9317 q^{2} +729.000 q^{3} -6433.74 q^{4} -10428.5 q^{5} -30568.2 q^{6} -484911. q^{7} +613281. q^{8} +531441. q^{9} +437283. q^{10} -5.22450e6 q^{11} -4.69019e6 q^{12} -2.63123e7 q^{13} +2.03331e7 q^{14} -7.60235e6 q^{15} +2.69892e7 q^{16} +5.55106e7 q^{17} -2.22842e7 q^{18} +2.91313e8 q^{19} +6.70939e7 q^{20} -3.53500e8 q^{21} +2.19072e8 q^{22} +4.45190e8 q^{23} +4.47082e8 q^{24} -1.11195e9 q^{25} +1.10332e9 q^{26} +3.87420e8 q^{27} +3.11979e9 q^{28} +1.14421e9 q^{29} +3.18779e8 q^{30} +1.75609e9 q^{31} -6.15571e9 q^{32} -3.80866e9 q^{33} -2.32765e9 q^{34} +5.05687e9 q^{35} -3.41915e9 q^{36} +1.94584e10 q^{37} -1.22152e10 q^{38} -1.91817e10 q^{39} -6.39558e9 q^{40} +4.10675e10 q^{41} +1.48228e10 q^{42} -6.68796e10 q^{43} +3.36130e10 q^{44} -5.54211e9 q^{45} -1.86676e10 q^{46} +1.07923e11 q^{47} +1.96752e10 q^{48} +1.38250e11 q^{49} +4.66259e10 q^{50} +4.04673e10 q^{51} +1.69287e11 q^{52} +1.14657e11 q^{53} -1.62452e10 q^{54} +5.44834e10 q^{55} -2.97387e11 q^{56} +2.12367e11 q^{57} -4.79788e10 q^{58} +4.21805e10 q^{59} +4.89115e10 q^{60} -3.36859e11 q^{61} -7.36359e10 q^{62} -2.57702e11 q^{63} +3.70231e10 q^{64} +2.74397e11 q^{65} +1.59703e11 q^{66} -2.42464e11 q^{67} -3.57141e11 q^{68} +3.24544e11 q^{69} -2.12043e11 q^{70} +4.15485e11 q^{71} +3.25923e11 q^{72} -1.88437e12 q^{73} -8.15925e11 q^{74} -8.10612e11 q^{75} -1.87423e12 q^{76} +2.53342e12 q^{77} +8.04320e11 q^{78} -1.69099e12 q^{79} -2.81456e11 q^{80} +2.82430e11 q^{81} -1.72203e12 q^{82} -1.99354e12 q^{83} +2.27433e12 q^{84} -5.78890e11 q^{85} +2.80437e12 q^{86} +8.34133e11 q^{87} -3.20409e12 q^{88} +2.92261e12 q^{89} +2.32390e11 q^{90} +1.27591e13 q^{91} -2.86423e12 q^{92} +1.28019e12 q^{93} -4.52538e12 q^{94} -3.03794e12 q^{95} -4.48751e12 q^{96} +1.31868e13 q^{97} -5.79704e12 q^{98} -2.77651e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more