LMFDB - Embedded newform 285.10.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$N$	$=$	$285 = 3 \cdot 5 \cdot 19$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{14} - x^{13} - 5365 x^{12} + 7107 x^{11} + 10970098 x^{10} - 19024208 x^{9} - 10608934432 x^{8} + \cdots - 480881506516992$ x^14 - x^13 - 5365x^12 + 7107x^11 + 10970098x^10 - 19024208x^9 - 10608934432x^8 + 24552331696x^7 + 4820661863456x^6 - 15731969979520x^5 - 831531966469120x^4 + 3954911489638400x^3 + 12984029397983232x^2 - 9924122935296x - 480881506516992
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$2^{18}\cdot 3^{8}\cdot 5^{2}$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$33.9313$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-33.9313 q^{2} -81.0000 q^{3} +639.331 q^{4} -625.000 q^{5} +2748.43 q^{6} +9880.04 q^{7} -4320.49 q^{8} +6561.00 q^{9} +21207.0 q^{10} -69660.6 q^{11} -51785.8 q^{12} -176048. q^{13} -335242. q^{14} +50625.0 q^{15} -180738. q^{16} -491581. q^{17} -222623. q^{18} +130321. q^{19} -399582. q^{20} -800283. q^{21} +2.36367e6 q^{22} -712914. q^{23} +349960. q^{24} +390625. q^{25} +5.97353e6 q^{26} -531441. q^{27} +6.31661e6 q^{28} -134373. q^{29} -1.71777e6 q^{30} -2.59229e6 q^{31} +8.34475e6 q^{32} +5.64251e6 q^{33} +1.66800e7 q^{34} -6.17502e6 q^{35} +4.19465e6 q^{36} -3.66220e6 q^{37} -4.42196e6 q^{38} +1.42599e7 q^{39} +2.70031e6 q^{40} -9.74654e6 q^{41} +2.71546e7 q^{42} +4.21021e6 q^{43} -4.45362e7 q^{44} -4.10062e6 q^{45} +2.41901e7 q^{46} -6.41652e7 q^{47} +1.46397e7 q^{48} +5.72616e7 q^{49} -1.32544e7 q^{50} +3.98181e7 q^{51} -1.12553e8 q^{52} -2.38522e7 q^{53} +1.80325e7 q^{54} +4.35379e7 q^{55} -4.26866e7 q^{56} -1.05560e7 q^{57} +4.55945e6 q^{58} -1.02156e8 q^{59} +3.23661e7 q^{60} -1.25148e8 q^{61} +8.79596e7 q^{62} +6.48229e7 q^{63} -1.90610e8 q^{64} +1.10030e8 q^{65} -1.91457e8 q^{66} -9.38601e6 q^{67} -3.14283e8 q^{68} +5.77460e7 q^{69} +2.09526e8 q^{70} +1.74680e8 q^{71} -2.83468e7 q^{72} +3.17964e8 q^{73} +1.24263e8 q^{74} -3.16406e7 q^{75} +8.33182e7 q^{76} -6.88250e8 q^{77} -4.83856e8 q^{78} +4.82600e7 q^{79} +1.12961e8 q^{80} +4.30467e7 q^{81} +3.30712e8 q^{82} +3.83115e8 q^{83} -5.11646e8 q^{84} +3.07238e8 q^{85} -1.42858e8 q^{86} +1.08842e7 q^{87} +3.00968e8 q^{88} -1.01770e9 q^{89} +1.39139e8 q^{90} -1.73936e9 q^{91} -4.55788e8 q^{92} +2.09975e8 q^{93} +2.17721e9 q^{94} -8.14506e7 q^{95} -6.75924e8 q^{96} -1.08495e9 q^{97} -1.94296e9 q^{98} -4.57043e8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$14 q - q^{2} - 1134 q^{3} + 3563 q^{4} - 8750 q^{5} + 81 q^{6} + 13054 q^{7} + 6249 q^{8} + 91854 q^{9} + 625 q^{10} + 43520 q^{11} - 288603 q^{12} + 256834 q^{13} + 250610 q^{14} + 708750 q^{15} + 866291 q^{16}+ \cdots + 285534720 q^{99}+O(q^{100})$ 14 * q - q^2 - 1134 * q^3 + 3563 * q^4 - 8750 * q^5 + 81 * q^6 + 13054 * q^7 + 6249 * q^8 + 91854 * q^9 + 625 * q^10 + 43520 * q^11 - 288603 * q^12 + 256834 * q^13 + 250610 * q^14 + 708750 * q^15 + 866291 * q^16 - 91412 * q^17 - 6561 * q^18 + 1824494 * q^19 - 2226875 * q^20 - 1057374 * q^21 + 5028672 * q^22 - 1629286 * q^23 - 506169 * q^24 + 5468750 * q^25 - 5525738 * q^26 - 7440174 * q^27 + 2214066 * q^28 - 3136160 * q^29 - 50625 * q^30 + 216848 * q^31 - 5019923 * q^32 - 3525120 * q^33 + 14499560 * q^34 - 8158750 * q^35 + 23376843 * q^36 + 29450026 * q^37 - 130321 * q^38 - 20803554 * q^39 - 3905625 * q^40 - 18243760 * q^41 - 20299410 * q^42 + 26051662 * q^43 - 66833140 * q^44 - 57408750 * q^45 - 87479176 * q^46 + 15959554 * q^47 - 70169571 * q^48 + 120608310 * q^49 - 390625 * q^50 + 7404372 * q^51 - 76766782 * q^52 + 24009130 * q^53 + 531441 * q^54 - 27200000 * q^55 - 248644798 * q^56 - 147784014 * q^57 - 208603522 * q^58 - 51606384 * q^59 + 180376875 * q^60 - 267404032 * q^61 + 211868546 * q^62 + 85647294 * q^63 - 647618425 * q^64 - 160521250 * q^65 - 407322432 * q^66 + 354061992 * q^67 - 690026380 * q^68 + 131972166 * q^69 - 156631250 * q^70 + 178030792 * q^71 + 40999689 * q^72 + 571450504 * q^73 + 406967766 * q^74 - 442968750 * q^75 + 464333723 * q^76 + 922830092 * q^77 + 447584778 * q^78 + 456688676 * q^79 - 541431875 * q^80 + 602654094 * q^81 + 1477406200 * q^82 + 275098162 * q^83 - 179339346 * q^84 + 57132500 * q^85 - 909539740 * q^86 + 254028960 * q^87 + 1278025456 * q^88 - 2005727664 * q^89 + 4100625 * q^90 - 181709276 * q^91 + 209371504 * q^92 - 17564688 * q^93 - 617421584 * q^94 - 1140308750 * q^95 + 406613763 * q^96 + 1606885598 * q^97 - 3483053209 * q^98 + 285534720 * q^99

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

)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$\alpha_n$			$\theta_n$
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$

$2$	−33.9313	−1.49956	−0.749782	−	0.661685i	$-0.769842\pi$
$2$	−33.9313	−1.49956	−0.749782	+	0.661685i	$0.769842\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	639.331	1.24869
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	2748.43	0.865774
$7$	9880.04	1.55531	0.777656	−	0.628690i	$-0.216409\pi$
$7$	9880.04	1.55531	0.777656	+	0.628690i	$0.216409\pi$
$8$	−4320.49	−0.372931
$9$	6561.00	0.333333
$10$	21207.0	0.670626
$11$	−69660.6	−1.43456	−0.717282	−	0.696782i	$-0.754614\pi$
$11$	−69660.6	−1.43456	−0.717282	+	0.696782i	$0.754614\pi$
$12$	−51785.8	−0.720933
$13$	−176048.	−1.70956	−0.854782	−	0.518987i	$-0.826309\pi$
$13$	−176048.	−1.70956	−0.854782	+	0.518987i	$0.826309\pi$
$14$	−335242.	−2.33229
$15$	50625.0	0.258199
$16$	−180738.	−0.689459
$17$	−491581.	−1.42750	−0.713748	−	0.700402i	$-0.753004\pi$
$17$	−491581.	−1.42750	−0.713748	+	0.700402i	$0.753004\pi$
$18$	−222623.	−0.499855
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	−399582.	−0.558432
$21$	−800283.	−0.897960
$22$	2.36367e6	2.15122
$23$	−712914.	−0.531205	−0.265602	−	0.964083i	$-0.585571\pi$
$23$	−712914.	−0.531205	−0.265602	+	0.964083i	$0.585571\pi$
$24$	349960.	0.215312
$25$	390625.	0.200000
$26$	5.97353e6	2.56360
$27$	−531441.	−0.192450
$28$	6.31661e6	1.94211
$29$	−134373.	−0.0352794	−0.0176397	−	0.999844i	$-0.505615\pi$
$29$	−134373.	−0.0352794	−0.0176397	+	0.999844i	$0.505615\pi$
$30$	−1.71777e6	−0.387186
$31$	−2.59229e6	−0.504145	−0.252073	−	0.967708i	$-0.581112\pi$
$31$	−2.59229e6	−0.504145	−0.252073	+	0.967708i	$0.581112\pi$
$32$	8.34475e6	1.40682
$33$	5.64251e6	0.828246
$34$	1.66800e7	2.14062
$35$	−6.17502e6	−0.695557
$36$	4.19465e6	0.416231
$37$	−3.66220e6	−0.321243	−0.160622	−	0.987016i	$-0.551350\pi$
$37$	−3.66220e6	−0.321243	−0.160622	+	0.987016i	$0.551350\pi$
$38$	−4.42196e6	−0.344024
$39$	1.42599e7	0.987018
$40$	2.70031e6	0.166780
$41$	−9.74654e6	−0.538670	−0.269335	−	0.963047i	$-0.586804\pi$
$41$	−9.74654e6	−0.538670	−0.269335	+	0.963047i	$0.586804\pi$
$42$	2.71546e7	1.34655
$43$	4.21021e6	0.187800	0.0938999	−	0.995582i	$-0.470067\pi$
$43$	4.21021e6	0.187800	0.0938999	+	0.995582i	$0.470067\pi$
$44$	−4.45362e7	−1.79133
$45$	−4.10062e6	−0.149071
$46$	2.41901e7	0.796575
$47$	−6.41652e7	−1.91805	−0.959024	−	0.283325i	$-0.908562\pi$
$47$	−6.41652e7	−1.91805	−0.959024	+	0.283325i	$0.908562\pi$
$48$	1.46397e7	0.398059
$49$	5.72616e7	1.41900
$50$	−1.32544e7	−0.299913
$51$	3.98181e7	0.824166
$52$	−1.12553e8	−2.13472
$53$	−2.38522e7	−0.415228	−0.207614	−	0.978211i	$-0.566570\pi$
$53$	−2.38522e7	−0.415228	−0.207614	+	0.978211i	$0.566570\pi$
$54$	1.80325e7	0.288591
$55$	4.35379e7	0.641557
$56$	−4.26866e7	−0.580024
$57$	−1.05560e7	−0.132453
$58$	4.55945e6	0.0529037
$59$	−1.02156e8	−1.09757	−0.548783	−	0.835965i	$-0.684909\pi$
$59$	−1.02156e8	−1.09757	−0.548783	+	0.835965i	$0.684909\pi$
$60$	3.23661e7	0.322411
$61$	−1.25148e8	−1.15728	−0.578642	−	0.815582i	$-0.696417\pi$
$61$	−1.25148e8	−1.15728	−0.578642	+	0.815582i	$0.696417\pi$
$62$	8.79596e7	0.755998
$63$	6.48229e7	0.518437
$64$	−1.90610e8	−1.42016
$65$	1.10030e8	0.764541
$66$	−1.91457e8	−1.24201
$67$	−9.38601e6	−0.0569042	−0.0284521	−	0.999595i	$-0.509058\pi$
$67$	−9.38601e6	−0.0569042	−0.0284521	+	0.999595i	$0.509058\pi$
$68$	−3.14283e8	−1.78250
$69$	5.77460e7	0.306691
$70$	2.09526e8	1.04303
$71$	1.74680e8	0.815792	0.407896	−	0.913028i	$-0.366263\pi$
$71$	1.74680e8	0.815792	0.407896	+	0.913028i	$0.366263\pi$
$72$	−2.83468e7	−0.124310
$73$	3.17964e8	1.31046	0.655232	−	0.755428i	$-0.272571\pi$
$73$	3.17964e8	1.31046	0.655232	+	0.755428i	$0.272571\pi$
$74$	1.24263e8	0.481725
$75$	−3.16406e7	−0.115470
$76$	8.33182e7	0.286470
$77$	−6.88250e8	−2.23120
$78$	−4.83856e8	−1.48010
$79$	4.82600e7	0.139401	0.0697004	−	0.997568i	$-0.477796\pi$
$79$	4.82600e7	0.139401	0.0697004	+	0.997568i	$0.477796\pi$
$80$	1.12961e8	0.308335
$81$	4.30467e7	0.111111
$82$	3.30712e8	0.807771
$83$	3.83115e8	0.886090	0.443045	−	0.896499i	$-0.353898\pi$
$83$	3.83115e8	0.886090	0.443045	+	0.896499i	$0.353898\pi$
$84$	−5.11646e8	−1.12128
$85$	3.07238e8	0.638396
$86$	−1.42858e8	−0.281618
$87$	1.08842e7	0.0203686
$88$	3.00968e8	0.534994
$89$	−1.01770e9	−1.71936	−0.859678	−	0.510836i	$-0.829336\pi$
$89$	−1.01770e9	−1.71936	−0.859678	+	0.510836i	$0.829336\pi$
$90$	1.39139e8	0.223542
$91$	−1.73936e9	−2.65891
$92$	−4.55788e8	−0.663311
$93$	2.09975e8	0.291068
$94$	2.17721e9	2.87624
$95$	−8.14506e7	−0.102598
$96$	−6.75924e8	−0.812227
$97$	−1.08495e9	−1.24434	−0.622168	−	0.782883i	$-0.713748\pi$
$97$	−1.08495e9	−1.24434	−0.622168	+	0.782883i	$0.713748\pi$
$98$	−1.94296e9	−2.12787
$99$	−4.57043e8	−0.478188
$100$	2.49739e8	0.249739
$101$	−2.54570e8	−0.243423	−0.121711	−	0.992566i	$-0.538838\pi$
$101$	−2.54570e8	−0.243423	−0.121711	+	0.992566i	$0.538838\pi$
$102$	−1.35108e9	−1.23589
$103$	1.61531e6	0.00141413	0.000707063	−	1.00000i	$-0.499775\pi$
$103$	1.61531e6	0.00141413	0.000707063		1.00000i	$0.499775\pi$
$104$	7.60613e8	0.637549
$105$	5.00177e8	0.401580
$106$	8.09335e8	0.622661
$107$	1.89093e9	1.39460	0.697299	−	0.716780i	$-0.254385\pi$
$107$	1.89093e9	1.39460	0.697299	+	0.716780i	$0.254385\pi$
$108$	−3.39767e8	−0.240311
$109$	6.16231e8	0.418142	0.209071	−	0.977900i	$-0.432956\pi$
$109$	6.16231e8	0.418142	0.209071	+	0.977900i	$0.432956\pi$
$110$	−1.47730e9	−0.962056
$111$	2.96638e8	0.185470
$112$	−1.78569e9	−1.07232
$113$	−3.36282e9	−1.94022	−0.970110	−	0.242666i	$-0.921978\pi$
$113$	−3.36282e9	−1.94022	−0.970110	+	0.242666i	$0.921978\pi$
$114$	3.58178e8	0.198622
$115$	4.45571e8	0.237562
$116$	−8.59088e7	−0.0440531
$117$	−1.15505e9	−0.569855
$118$	3.46629e9	1.64587
$119$	−4.85684e9	−2.22020
$120$	−2.18725e8	−0.0962903
$121$	2.49465e9	1.05798
$122$	4.24643e9	1.73542
$123$	7.89470e8	0.311001
$124$	−1.65733e9	−0.629522
$125$	−2.44141e8	−0.0894427
$126$	−2.19952e9	−0.777430
$127$	−2.51900e9	−0.859232	−0.429616	−	0.903012i	$-0.641351\pi$
$127$	−2.51900e9	−0.859232	−0.429616	+	0.903012i	$0.641351\pi$
$128$	2.19513e9	0.722797
$129$	−3.41027e8	−0.108426
$130$	−3.73345e9	−1.14648
$131$	−5.00056e9	−1.48353	−0.741767	−	0.670657i	$-0.766012\pi$
$131$	−5.00056e9	−1.48353	−0.741767	+	0.670657i	$0.766012\pi$
$132$	3.60743e9	1.03423
$133$	1.28758e9	0.356813
$134$	3.18479e8	0.0853315
$135$	3.32151e8	0.0860663
$136$	2.12387e9	0.532358
$137$	−2.10286e9	−0.509998	−0.254999	−	0.966941i	$-0.582075\pi$
$137$	−2.10286e9	−0.509998	−0.254999	+	0.966941i	$0.582075\pi$
$138$	−1.95940e9	−0.459903
$139$	−1.92992e9	−0.438503	−0.219251	−	0.975668i	$-0.570362\pi$
$139$	−1.92992e9	−0.438503	−0.219251	+	0.975668i	$0.570362\pi$
$140$	−3.94788e9	−0.868537
$141$	5.19738e9	1.10739
$142$	−5.92710e9	−1.22333
$143$	1.22636e10	2.45248
$144$	−1.18582e9	−0.229820
$145$	8.39831e7	0.0157774
$146$	−1.07889e10	−1.96512
$147$	−4.63819e9	−0.819257
$148$	−2.34136e9	−0.401134
$149$	7.40405e9	1.23064	0.615320	−	0.788277i	$-0.289027\pi$
$149$	7.40405e9	1.23064	0.615320	+	0.788277i	$0.289027\pi$
$150$	1.07361e9	0.173155
$151$	1.15986e9	0.181555	0.0907776	−	0.995871i	$-0.471065\pi$
$151$	1.15986e9	0.181555	0.0907776	+	0.995871i	$0.471065\pi$
$152$	−5.63051e8	−0.0855562
$153$	−3.22526e9	−0.475832
$154$	2.33532e10	3.34582
$155$	1.62018e9	0.225461
$156$	9.11678e9	1.23248
$157$	−7.39247e9	−0.971049	−0.485525	−	0.874223i	$-0.661371\pi$
$157$	−7.39247e9	−0.971049	−0.485525	+	0.874223i	$0.661371\pi$
$158$	−1.63752e9	−0.209041
$159$	1.93203e9	0.239732
$160$	−5.21547e9	−0.629149
$161$	−7.04362e9	−0.826189
$162$	−1.46063e9	−0.166618
$163$	2.42581e9	0.269162	0.134581	−	0.990903i	$-0.457031\pi$
$163$	2.42581e9	0.269162	0.134581	+	0.990903i	$0.457031\pi$
$164$	−6.23126e9	−0.672634
$165$	−3.52657e9	−0.370403
$166$	−1.29996e10	−1.32875
$167$	−1.27031e10	−1.26382	−0.631911	−	0.775041i	$-0.717729\pi$
$167$	−1.27031e10	−1.26382	−0.631911	+	0.775041i	$0.717729\pi$
$168$	3.45762e9	0.334877
$169$	2.03883e10	1.92261
$170$	−1.04250e10	−0.957316
$171$	8.55036e8	0.0764719
$172$	2.69171e9	0.234504
$173$	1.98216e10	1.68240	0.841202	−	0.540721i	$-0.181849\pi$
$173$	1.98216e10	1.68240	0.841202	+	0.540721i	$0.181849\pi$
$174$	−3.69315e8	−0.0305440
$175$	3.85939e9	0.311062
$176$	1.25903e10	0.989074
$177$	8.27466e9	0.633680
$178$	3.45319e10	2.57828
$179$	1.27221e10	0.926230	0.463115	−	0.886298i	$-0.346732\pi$
$179$	1.27221e10	0.926230	0.463115	+	0.886298i	$0.346732\pi$
$180$	−2.62166e9	−0.186144
$181$	6.13497e9	0.424873	0.212436	−	0.977175i	$-0.431860\pi$
$181$	6.13497e9	0.424873	0.212436	+	0.977175i	$0.431860\pi$
$182$	5.90187e10	3.98720
$183$	1.01370e10	0.668158
$184$	3.08014e9	0.198103
$185$	2.28888e9	0.143664
$186$	−7.12473e9	−0.436476
$187$	3.42438e10	2.04784
$188$	−4.10228e10	−2.39505
$189$	−5.25066e9	−0.299320
$190$	2.76372e9	0.153852
$191$	−3.51221e10	−1.90955	−0.954774	−	0.297331i	$-0.903903\pi$
$191$	−3.51221e10	−1.90955	−0.954774	+	0.297331i	$0.903903\pi$
$192$	1.54394e10	0.819928
$193$	3.31686e10	1.72075	0.860377	−	0.509657i	$-0.170228\pi$
$193$	3.31686e10	1.72075	0.860377	+	0.509657i	$0.170228\pi$
$194$	3.68138e10	1.86596
$195$	−8.91242e9	−0.441408
$196$	3.66091e10	1.77189
$197$	1.17394e10	0.555324	0.277662	−	0.960679i	$-0.410441\pi$
$197$	1.17394e10	0.555324	0.277662	+	0.960679i	$0.410441\pi$
$198$	1.55081e10	0.717074
$199$	−3.84124e10	−1.73633	−0.868166	−	0.496273i	$-0.834701\pi$
$199$	−3.84124e10	−1.73633	−0.868166	+	0.496273i	$0.834701\pi$
$200$	−1.68769e9	−0.0745862
$201$	7.60267e8	0.0328536
$202$	8.63789e9	0.365028
$203$	−1.32761e9	−0.0548705
$204$	2.54569e10	1.02913
$205$	6.09159e9	0.240901
$206$	−5.48095e7	−0.00212057
$207$	−4.67743e9	−0.177068
$208$	3.18185e10	1.17867
$209$	−9.07824e9	−0.329112
$210$	−1.69716e10	−0.602195
$211$	9.53224e9	0.331073	0.165537	−	0.986204i	$-0.447064\pi$
$211$	9.53224e9	0.331073	0.165537	+	0.986204i	$0.447064\pi$
$212$	−1.52494e10	−0.518492
$213$	−1.41490e10	−0.470998
$214$	−6.41618e10	−2.09129
$215$	−2.63138e9	−0.0839867
$216$	2.29609e9	0.0717706
$217$	−2.56119e10	−0.784103
$218$	−2.09095e10	−0.627031
$219$	−2.57551e10	−0.756596
$220$	2.78351e10	0.801108
$221$	8.65418e10	2.44040
$222$	−1.00653e10	−0.278124
$223$	−3.45762e10	−0.936280	−0.468140	−	0.883654i	$-0.655076\pi$
$223$	−3.45762e10	−0.936280	−0.468140	+	0.883654i	$0.655076\pi$
$224$	8.24464e10	2.18804
$225$	2.56289e9	0.0666667
$226$	1.14105e11	2.90948
$227$	2.09866e10	0.524597	0.262299	−	0.964987i	$-0.415519\pi$
$227$	2.09866e10	0.524597	0.262299	+	0.964987i	$0.415519\pi$
$228$	−6.74878e9	−0.165393
$229$	−5.45785e10	−1.31148	−0.655741	−	0.754986i	$-0.727643\pi$
$229$	−5.45785e10	−1.31148	−0.655741	+	0.754986i	$0.727643\pi$
$230$	−1.51188e10	−0.356239
$231$	5.57482e10	1.28818
$232$	5.80558e8	0.0131568
$233$	2.43534e10	0.541324	0.270662	−	0.962674i	$-0.412757\pi$
$233$	2.43534e10	0.541324	0.270662	+	0.962674i	$0.412757\pi$
$234$	3.91923e10	0.854534
$235$	4.01033e10	0.857777
$236$	−6.53116e10	−1.37052
$237$	−3.90906e9	−0.0804831
$238$	1.64799e11	3.32934
$239$	−9.34512e10	−1.85265	−0.926327	−	0.376720i	$-0.877052\pi$
$239$	−9.34512e10	−1.85265	−0.926327	+	0.376720i	$0.877052\pi$
$240$	−9.14984e9	−0.178018
$241$	−7.79516e10	−1.48850	−0.744250	−	0.667902i	$-0.767193\pi$
$241$	−7.79516e10	−1.48850	−0.744250	+	0.667902i	$0.767193\pi$
$242$	−8.46468e10	−1.58650
$243$	−3.48678e9	−0.0641500
$244$	−8.00109e10	−1.44509
$245$	−3.57885e10	−0.634594
$246$	−2.67877e10	−0.466367
$247$	−2.29427e10	−0.392201
$248$	1.12000e10	0.188011
$249$	−3.10323e10	−0.511584
$250$	8.28400e9	0.134125
$251$	−8.60114e10	−1.36781	−0.683903	−	0.729573i	$-0.739719\pi$
$251$	−8.60114e10	−1.36781	−0.683903	+	0.729573i	$0.739719\pi$
$252$	4.14433e10	0.647369
$253$	4.96620e10	0.762048
$254$	8.54727e10	1.28847
$255$	−2.48863e10	−0.368578
$256$	2.31087e10	0.336276
$257$	3.35045e10	0.479076	0.239538	−	0.970887i	$-0.423004\pi$
$257$	3.35045e10	0.479076	0.239538	+	0.970887i	$0.423004\pi$
$258$	1.15715e10	0.162592
$259$	−3.61827e10	−0.499634
$260$	7.03455e10	0.954676
$261$	−8.81621e8	−0.0117598
$262$	1.69675e11	2.22466
$263$	−1.25298e11	−1.61490	−0.807449	−	0.589938i	$-0.799152\pi$
$263$	−1.25298e11	−1.61490	−0.807449	+	0.589938i	$0.799152\pi$
$264$	−2.43784e10	−0.308879
$265$	1.49076e10	0.185696
$266$	−4.36891e10	−0.535064
$267$	8.24339e10	0.992671
$268$	−6.00076e9	−0.0710559
$269$	−3.18538e10	−0.370917	−0.185458	−	0.982652i	$-0.559377\pi$
$269$	−3.18538e10	−0.370917	−0.185458	+	0.982652i	$0.559377\pi$
$270$	−1.12703e10	−0.129062
$271$	−3.80191e10	−0.428193	−0.214097	−	0.976812i	$-0.568681\pi$
$271$	−3.80191e10	−0.428193	−0.214097	+	0.976812i	$0.568681\pi$
$272$	8.88472e10	0.984201
$273$	1.40888e11	1.53512
$274$	7.13529e10	0.764775
$275$	−2.72112e10	−0.286913
$276$	3.69188e10	0.382963
$277$	1.05646e11	1.07819	0.539095	−	0.842245i	$-0.318766\pi$
$277$	1.05646e11	1.07819	0.539095	+	0.842245i	$0.318766\pi$
$278$	6.54846e10	0.657563
$279$	−1.70080e10	−0.168048
$280$	2.66792e10	0.259395
$281$	−4.31314e10	−0.412682	−0.206341	−	0.978480i	$-0.566156\pi$
$281$	−4.31314e10	−0.412682	−0.206341	+	0.978480i	$0.566156\pi$
$282$	−1.76354e11	−1.66060
$283$	1.39197e11	1.29000	0.645002	−	0.764181i	$-0.276857\pi$
$283$	1.39197e11	1.29000	0.645002	+	0.764181i	$0.276857\pi$
$284$	1.11678e11	1.01867
$285$	6.59750e9	0.0592349
$286$	−4.16119e11	−3.67765
$287$	−9.62962e10	−0.837800
$288$	5.47499e10	0.468940
$289$	1.23064e11	1.03775
$290$	−2.84965e9	−0.0236593
$291$	8.78812e10	0.718418
$292$	2.03284e11	1.63637
$293$	1.18645e11	0.940473	0.470236	−	0.882541i	$-0.344169\pi$
$293$	1.18645e11	0.940473	0.470236	+	0.882541i	$0.344169\pi$
$294$	1.57380e11	1.22853
$295$	6.38477e10	0.490847
$296$	1.58225e10	0.119802
$297$	3.70205e10	0.276082
$298$	−2.51229e11	−1.84542
$299$	1.25507e11	0.908129
$300$	−2.02288e10	−0.144187
$301$	4.15970e10	0.292087
$302$	−3.93555e10	−0.272254
$303$	2.06202e10	0.140540
$304$	−2.35539e10	−0.158173
$305$	7.82175e10	0.517553
$306$	1.09437e11	0.713541
$307$	1.54568e11	0.993109	0.496554	−	0.868006i	$-0.334598\pi$
$307$	1.54568e11	0.993109	0.496554	+	0.868006i	$0.334598\pi$
$308$	−4.40019e11	−2.78608
$309$	−1.30840e8	−0.000816446 0
$310$	−5.49747e10	−0.338093
$311$	−5.00657e10	−0.303472	−0.151736	−	0.988421i	$-0.548486\pi$
$311$	−5.00657e10	−0.303472	−0.151736	+	0.988421i	$0.548486\pi$
$312$	−6.16097e10	−0.368089
$313$	1.63498e11	0.962858	0.481429	−	0.876485i	$-0.340118\pi$
$313$	1.63498e11	0.962858	0.481429	+	0.876485i	$0.340118\pi$
$314$	2.50836e11	1.45615
$315$	−4.05143e10	−0.231852
$316$	3.08541e10	0.174069
$317$	1.23719e11	0.688129	0.344064	−	0.938946i	$-0.388196\pi$
$317$	1.23719e11	0.688129	0.344064	+	0.938946i	$0.388196\pi$
$318$	−6.55561e10	−0.359494
$319$	9.36051e9	0.0506106
$320$	1.19131e11	0.635113
$321$	−1.53166e11	−0.805172
$322$	2.38999e11	1.23892
$323$	−6.40634e10	−0.327490
$324$	2.75211e10	0.138744
$325$	−6.87687e10	−0.341913
$326$	−8.23109e10	−0.403625
$327$	−4.99147e10	−0.241415
$328$	4.21098e10	0.200887
$329$	−6.33955e11	−2.98316
$330$	1.19661e11	0.555443
$331$	−3.51714e11	−1.61051	−0.805255	−	0.592929i	$-0.797972\pi$
$331$	−3.51714e11	−1.61051	−0.805255	+	0.592929i	$0.797972\pi$
$332$	2.44937e11	1.10645
$333$	−2.40277e10	−0.107081
$334$	4.31033e11	1.89518
$335$	5.86625e9	0.0254483
$336$	1.44641e11	0.619106
$337$	4.10219e11	1.73253	0.866267	−	0.499582i	$-0.166513\pi$
$337$	4.10219e11	1.73253	0.866267	+	0.499582i	$0.166513\pi$
$338$	−6.91802e11	−2.88308
$339$	2.72389e11	1.12019
$340$	1.96427e11	0.797160
$341$	1.80580e11	0.723229
$342$	−2.90125e10	−0.114675
$343$	1.67051e11	0.651668
$344$	−1.81902e10	−0.0700364
$345$	−3.60913e10	−0.137156
$346$	−6.72570e11	−2.52287
$347$	4.08881e11	1.51396	0.756979	−	0.653439i	$-0.226674\pi$
$347$	4.08881e11	1.51396	0.756979	+	0.653439i	$0.226674\pi$
$348$	6.95861e9	0.0254341
$349$	−4.04337e11	−1.45891	−0.729457	−	0.684027i	$-0.760227\pi$
$349$	−4.04337e11	−1.45891	−0.729457	+	0.684027i	$0.760227\pi$
$350$	−1.30954e11	−0.466458
$351$	9.35590e10	0.329006
$352$	−5.81300e11	−2.01817
$353$	−1.14276e11	−0.391714	−0.195857	−	0.980633i	$-0.562749\pi$
$353$	−1.14276e11	−0.391714	−0.195857	+	0.980633i	$0.562749\pi$
$354$	−2.80770e11	−0.950245
$355$	−1.09175e11	−0.364833
$356$	−6.50649e11	−2.14695
$357$	3.93404e11	1.28183
$358$	−4.31676e11	−1.38894
$359$	2.73301e11	0.868393	0.434197	−	0.900818i	$-0.357032\pi$
$359$	2.73301e11	0.868393	0.434197	+	0.900818i	$0.357032\pi$
$360$	1.77167e10	0.0555933
$361$	1.69836e10	0.0526316
$362$	−2.08167e11	−0.637124
$363$	−2.02067e11	−0.610823
$364$	−1.11203e12	−3.32016
$365$	−1.98727e11	−0.586057
$366$	−3.43961e11	−1.00195
$367$	3.97112e11	1.14266	0.571328	−	0.820722i	$-0.306428\pi$
$367$	3.97112e11	1.14266	0.571328	+	0.820722i	$0.306428\pi$
$368$	1.28850e11	0.366244
$369$	−6.39470e10	−0.179557
$370$	−7.76644e10	−0.215434
$371$	−2.35661e11	−0.645809
$372$	1.34244e11	0.363455
$373$	−2.90603e11	−0.777338	−0.388669	−	0.921378i	$-0.627065\pi$
$373$	−2.90603e11	−0.777338	−0.388669	+	0.921378i	$0.627065\pi$
$374$	−1.16194e12	−3.07086
$375$	1.97754e10	0.0516398
$376$	2.77225e11	0.715299
$377$	2.36561e10	0.0603124
$378$	1.78161e11	0.448849
$379$	3.42610e11	0.852949	0.426474	−	0.904500i	$-0.359755\pi$
$379$	3.42610e11	0.852949	0.426474	+	0.904500i	$0.359755\pi$
$380$	−5.20739e10	−0.128113
$381$	2.04039e11	0.496078
$382$	1.19174e12	2.86349
$383$	−1.05333e11	−0.250133	−0.125066	−	0.992148i	$-0.539914\pi$
$383$	−1.05333e11	−0.250133	−0.125066	+	0.992148i	$0.539914\pi$
$384$	−1.77806e11	−0.417307
$385$	4.30156e11	0.997821
$386$	−1.12545e12	−2.58038
$387$	2.76232e10	0.0626000
$388$	−6.93643e11	−1.55379
$389$	−7.35118e11	−1.62774	−0.813868	−	0.581050i	$-0.802642\pi$
$389$	−7.35118e11	−1.62774	−0.813868	+	0.581050i	$0.802642\pi$
$390$	3.02410e11	0.661919
$391$	3.50455e11	0.758293
$392$	−2.47398e11	−0.529187
$393$	4.05045e11	0.856519
$394$	−3.98331e11	−0.832743
$395$	−3.01625e10	−0.0623420
$396$	−2.92202e11	−0.597110
$397$	−1.30600e11	−0.263868	−0.131934	−	0.991258i	$-0.542119\pi$
$397$	−1.30600e11	−0.263868	−0.131934	+	0.991258i	$0.542119\pi$
$398$	1.30338e12	2.60374
$399$	−1.04294e11	−0.206006
$400$	−7.06006e10	−0.137892
$401$	3.26468e11	0.630509	0.315254	−	0.949007i	$-0.397910\pi$
$401$	3.26468e11	0.630509	0.315254	+	0.949007i	$0.397910\pi$
$402$	−2.57968e10	−0.0492662
$403$	4.56366e11	0.861869
$404$	−1.62755e11	−0.303960
$405$	−2.69042e10	−0.0496904
$406$	4.50475e10	0.0822818
$407$	2.55111e11	0.460845
$408$	−1.72034e11	−0.307357
$409$	9.96939e11	1.76163	0.880813	−	0.473464i	$-0.156997\pi$
$409$	9.96939e11	1.76163	0.880813	+	0.473464i	$0.156997\pi$
$410$	−2.06695e11	−0.361246
$411$	1.70332e11	0.294448
$412$	1.03272e9	0.00176581
$413$	−1.00931e12	−1.70706
$414$	1.58711e11	0.265525
$415$	−2.39447e11	−0.396272
$416$	−1.46907e12	−2.40505
$417$	1.56323e11	0.253170
$418$	3.08036e11	0.493524
$419$	1.41597e11	0.224435	0.112217	−	0.993684i	$-0.464205\pi$
$419$	1.41597e11	0.224435	0.112217	+	0.993684i	$0.464205\pi$
$420$	3.19779e11	0.501450
$421$	7.96738e11	1.23608	0.618039	−	0.786147i	$-0.287927\pi$
$421$	7.96738e11	1.23608	0.618039	+	0.786147i	$0.287927\pi$
$422$	−3.23441e11	−0.496465
$423$	−4.20988e11	−0.639349
$424$	1.03053e11	0.154851
$425$	−1.92024e11	−0.285499
$426$	4.80095e11	0.706291
$427$	−1.23647e12	−1.79994
$428$	1.20893e12	1.74143
$429$	−9.93352e11	−1.41594
$430$	8.92860e10	0.125943
$431$	−4.11727e11	−0.574727	−0.287364	−	0.957822i	$-0.592779\pi$
$431$	−4.11727e11	−0.574727	−0.287364	+	0.957822i	$0.592779\pi$
$432$	9.60513e10	0.132686
$433$	−5.25038e11	−0.717787	−0.358893	−	0.933379i	$-0.616846\pi$
$433$	−5.25038e11	−0.717787	−0.358893	+	0.933379i	$0.616846\pi$
$434$	8.69044e11	1.17581
$435$	−6.80263e9	−0.00910910
$436$	3.93975e11	0.522131
$437$	−9.29077e10	−0.121867
$438$	8.73902e11	1.13456
$439$	5.92349e11	0.761180	0.380590	−	0.924744i	$-0.375721\pi$
$439$	5.92349e11	0.761180	0.380590	+	0.924744i	$0.375721\pi$
$440$	−1.88105e11	−0.239256
$441$	3.75693e11	0.472998
$442$	−2.93647e12	−3.65953
$443$	−3.46221e11	−0.427107	−0.213553	−	0.976931i	$-0.568504\pi$
$443$	−3.46221e11	−0.427107	−0.213553	+	0.976931i	$0.568504\pi$
$444$	1.89650e11	0.231595
$445$	6.36064e11	0.768919
$446$	1.17322e12	1.40401
$447$	−5.99728e11	−0.710511
$448$	−1.88324e12	−2.20879
$449$	−1.90995e11	−0.221775	−0.110888	−	0.993833i	$-0.535369\pi$
$449$	−1.90995e11	−0.221775	−0.110888	+	0.993833i	$0.535369\pi$
$450$	−8.69621e10	−0.0999709
$451$	6.78950e11	0.772758
$452$	−2.14996e12	−2.42274
$453$	−9.39485e10	−0.104821
$454$	−7.12102e11	−0.786667
$455$	1.08710e12	1.18910
$456$	4.56071e10	0.0493959
$457$	−8.99317e11	−0.964472	−0.482236	−	0.876041i	$-0.660175\pi$
$457$	−8.99317e11	−0.964472	−0.482236	+	0.876041i	$0.660175\pi$
$458$	1.85192e12	1.96665
$459$	2.61246e11	0.274722
$460$	2.84867e11	0.296642
$461$	−2.78718e11	−0.287416	−0.143708	−	0.989620i	$-0.545903\pi$
$461$	−2.78718e11	−0.287416	−0.143708	+	0.989620i	$0.545903\pi$
$462$	−1.89161e12	−1.93171
$463$	7.59495e11	0.768087	0.384044	−	0.923315i	$-0.374531\pi$
$463$	7.59495e11	0.768087	0.384044	+	0.923315i	$0.374531\pi$
$464$	2.42863e10	0.0243237
$465$	−1.31235e11	−0.130170
$466$	−8.26341e11	−0.811751
$467$	9.77081e11	0.950615	0.475307	−	0.879820i	$-0.342337\pi$
$467$	9.77081e11	0.950615	0.475307	+	0.879820i	$0.342337\pi$
$468$	−7.38459e11	−0.711574
$469$	−9.27341e10	−0.0885038
$470$	−1.36075e12	−1.28629
$471$	5.98790e11	0.560636
$472$	4.41365e11	0.409317
$473$	−2.93286e11	−0.269411
$474$	1.32639e11	0.120690
$475$	5.09066e10	0.0458831
$476$	−3.10513e12	−2.77235
$477$	−1.56494e11	−0.138409
$478$	3.17092e12	2.77817
$479$	−1.93121e12	−1.67617	−0.838086	−	0.545538i	$-0.816325\pi$
$479$	−1.93121e12	−1.67617	−0.838086	+	0.545538i	$0.816325\pi$
$480$	4.22453e11	0.363239
$481$	6.44722e11	0.549187
$482$	2.64500e12	2.23210
$483$	5.70533e11	0.477000
$484$	1.59491e12	1.32109
$485$	6.78095e11	0.556484
$486$	1.18311e11	0.0961971
$487$	1.99512e12	1.60727	0.803634	−	0.595124i	$-0.202897\pi$
$487$	1.99512e12	1.60727	0.803634	+	0.595124i	$0.202897\pi$
$488$	5.40701e11	0.431587
$489$	−1.96491e11	−0.155401
$490$	1.21435e12	0.951614
$491$	1.79495e12	1.39375	0.696876	−	0.717192i	$-0.254573\pi$
$491$	1.79495e12	1.39375	0.696876	+	0.717192i	$0.254573\pi$
$492$	5.04732e11	0.388345
$493$	6.60553e10	0.0503612
$494$	7.78476e11	0.588131
$495$	2.85652e11	0.213852
$496$	4.68524e11	0.347587
$497$	1.72584e12	1.26881
$498$	1.05297e12	0.767154
$499$	−5.00717e11	−0.361526	−0.180763	−	0.983527i	$-0.557857\pi$
$499$	−5.00717e11	−0.361526	−0.180763	+	0.983527i	$0.557857\pi$
$500$	−1.56087e11	−0.111686
$501$	1.02895e12	0.729669
$502$	2.91848e12	2.05111
$503$	−2.44897e12	−1.70580	−0.852900	−	0.522074i	$-0.825158\pi$
$503$	−2.44897e12	−1.70580	−0.852900	+	0.522074i	$0.825158\pi$
$504$	−2.80067e11	−0.193341
$505$	1.59106e11	0.108862
$506$	−1.68510e12	−1.14274
$507$	−1.65146e12	−1.11002
$508$	−1.61047e12	−1.07292
$509$	1.39357e12	0.920235	0.460117	−	0.887858i	$-0.347807\pi$
$509$	1.39357e12	0.920235	0.460117	+	0.887858i	$0.347807\pi$
$510$	8.44424e11	0.552706
$511$	3.14150e12	2.03818
$512$	−1.90802e12	−1.22706
$513$	−6.92579e10	−0.0441511
$514$	−1.13685e12	−0.718405
$515$	−1.00957e9	−0.000632417 0
$516$	−2.18029e11	−0.135391
$517$	4.46979e12	2.75156
$518$	1.22772e12	0.749233
$519$	−1.60555e12	−0.971336
$520$	−4.75383e11	−0.285121
$521$	1.18713e12	0.705875	0.352937	−	0.935647i	$-0.385183\pi$
$521$	1.18713e12	0.705875	0.352937	+	0.935647i	$0.385183\pi$
$522$	2.99145e10	0.0176346
$523$	7.35893e11	0.430088	0.215044	−	0.976604i	$-0.431011\pi$
$523$	7.35893e11	0.430088	0.215044	+	0.976604i	$0.431011\pi$
$524$	−3.19701e12	−1.85248
$525$	−3.12611e11	−0.179592
$526$	4.25154e12	2.42164
$527$	1.27432e12	0.719665
$528$	−1.01981e12	−0.571042
$529$	−1.29291e12	−0.717822
$530$	−5.05834e11	−0.278463
$531$	−6.70247e11	−0.365856
$532$	8.23187e11	0.445550
$533$	1.71586e12	0.920892
$534$	−2.79709e12	−1.48857
$535$	−1.18183e12	−0.623683
$536$	4.05522e10	0.0212213
$537$	−1.03049e12	−0.534759
$538$	1.08084e12	0.556213
$539$	−3.98888e12	−2.03564
$540$	2.12354e11	0.107470
$541$	3.42601e12	1.71950	0.859748	−	0.510719i	$-0.170621\pi$
$541$	3.42601e12	1.71950	0.859748	+	0.510719i	$0.170621\pi$
$542$	1.29004e12	0.642103
$543$	−4.96932e11	−0.245300
$544$	−4.10212e12	−2.00823
$545$	−3.85144e11	−0.186999
$546$	−4.78051e12	−2.30201
$547$	−2.19990e11	−0.105065	−0.0525327	−	0.998619i	$-0.516729\pi$
$547$	−2.19990e11	−0.105065	−0.0525327	+	0.998619i	$0.516729\pi$
$548$	−1.34443e12	−0.636831
$549$	−8.21096e11	−0.385761
$550$	9.23310e11	0.430244
$551$	−1.75116e10	−0.00809365
$552$	−2.49491e11	−0.114375
$553$	4.76811e11	0.216812
$554$	−3.58471e12	−1.61681
$555$	−1.85399e11	−0.0829447
$556$	−1.23386e12	−0.547556
$557$	−4.44924e11	−0.195856	−0.0979281	−	0.995193i	$-0.531222\pi$
$557$	−4.44924e11	−0.195856	−0.0979281	+	0.995193i	$0.531222\pi$
$558$	5.77103e11	0.251999
$559$	−7.41198e11	−0.321056
$560$	1.11606e12	0.479558
$561$	−2.77375e12	−1.18232
$562$	1.46350e12	0.618843
$563$	−2.85252e12	−1.19658	−0.598289	−	0.801281i	$-0.704152\pi$
$563$	−2.85252e12	−1.19658	−0.598289	+	0.801281i	$0.704152\pi$
$564$	3.32285e12	1.38278
$565$	2.10176e12	0.867693
$566$	−4.72313e12	−1.93444
$567$	4.25303e11	0.172812
$568$	−7.54702e11	−0.304234
$569$	3.03910e12	1.21546	0.607729	−	0.794144i	$-0.292081\pi$
$569$	3.03910e12	1.21546	0.607729	+	0.794144i	$0.292081\pi$
$570$	−2.23862e11	−0.0888265
$571$	8.39653e11	0.330550	0.165275	−	0.986248i	$-0.447149\pi$
$571$	8.39653e11	0.330550	0.165275	+	0.986248i	$0.447149\pi$
$572$	7.84050e12	3.06240
$573$	2.84489e12	1.10248
$574$	3.26745e12	1.25634
$575$	−2.78482e11	−0.106241
$576$	−1.25059e12	−0.473385
$577$	−2.51851e12	−0.945914	−0.472957	−	0.881085i	$-0.656813\pi$
$577$	−2.51851e12	−0.945914	−0.472957	+	0.881085i	$0.656813\pi$
$578$	−4.17572e12	−1.55617
$579$	−2.68666e12	−0.993478
$580$	5.36930e10	0.0197012
$581$	3.78519e12	1.37815
$582$	−2.98192e12	−1.07731
$583$	1.66156e12	0.595672
$584$	−1.37376e12	−0.488712
$585$	7.21906e11	0.254847
$586$	−4.02578e12	−1.41030
$587$	−7.40507e11	−0.257429	−0.128715	−	0.991682i	$-0.541085\pi$
$587$	−7.40507e11	−0.257429	−0.128715	+	0.991682i	$0.541085\pi$
$588$	−2.96534e12	−1.02300
$589$	−3.37829e11	−0.115659
$590$	−2.16643e12	−0.736056
$591$	−9.50887e11	−0.320616
$592$	6.61897e11	0.221484
$593$	1.87921e12	0.624066	0.312033	−	0.950071i	$-0.398990\pi$
$593$	1.87921e12	0.624066	0.312033	+	0.950071i	$0.398990\pi$
$594$	−1.25615e12	−0.414003
$595$	3.03553e12	0.992905
$596$	4.73364e12	1.53669
$597$	3.11141e12	1.00247
$598$	−4.25861e12	−1.36180
$599$	5.78020e11	0.183452	0.0917259	−	0.995784i	$-0.470762\pi$
$599$	5.78020e11	0.183452	0.0917259	+	0.995784i	$0.470762\pi$
$600$	1.36703e11	0.0430623
$601$	−3.96250e12	−1.23889	−0.619447	−	0.785038i	$-0.712643\pi$
$601$	−3.96250e12	−1.23889	−0.619447	+	0.785038i	$0.712643\pi$
$602$	−1.41144e12	−0.438004
$603$	−6.15816e10	−0.0189681
$604$	7.41533e11	0.226707
$605$	−1.55916e12	−0.473142
$606$	−6.99669e11	−0.210749
$607$	−3.06642e12	−0.916817	−0.458408	−	0.888742i	$-0.651580\pi$
$607$	−3.06642e12	−0.916817	−0.458408	+	0.888742i	$0.651580\pi$
$608$	1.08750e12	0.322746
$609$	1.07536e11	0.0316795
$610$	−2.65402e12	−0.776104
$611$	1.12961e13	3.27903
$612$	−2.06201e12	−0.594168
$613$	−4.26173e12	−1.21903	−0.609514	−	0.792775i	$-0.708636\pi$
$613$	−4.26173e12	−1.21903	−0.609514	+	0.792775i	$0.708636\pi$
$614$	−5.24469e12	−1.48923
$615$	−4.93419e11	−0.139084
$616$	2.97358e12	0.832082
$617$	6.21898e12	1.72757	0.863785	−	0.503860i	$-0.168087\pi$
$617$	6.21898e12	1.72757	0.863785	+	0.503860i	$0.168087\pi$
$618$	4.43957e9	0.00122431
$619$	1.11768e12	0.305992	0.152996	−	0.988227i	$-0.451108\pi$
$619$	1.11768e12	0.305992	0.152996	+	0.988227i	$0.451108\pi$
$620$	1.03583e12	0.281531
$621$	3.78872e11	0.102230
$622$	1.69879e12	0.455076
$623$	−1.00549e13	−2.67414
$624$	−2.57729e12	−0.680508
$625$	1.52588e11	0.0400000
$626$	−5.54768e12	−1.44387
$627$	7.35338e11	0.190013
$628$	−4.72624e12	−1.21254
$629$	1.80027e12	0.458574
$630$	1.37470e12	0.347677
$631$	−2.69935e12	−0.677839	−0.338920	−	0.940815i	$-0.610061\pi$
$631$	−2.69935e12	−0.677839	−0.338920	+	0.940815i	$0.610061\pi$
$632$	−2.08507e11	−0.0519869
$633$	−7.72111e11	−0.191145
$634$	−4.19794e12	−1.03189
$635$	1.57437e12	0.384260
$636$	1.23520e12	0.299352
$637$	−1.00808e13	−2.42586
$638$	−3.17614e11	−0.0758938
$639$	1.14607e12	0.271931
$640$	−1.37196e12	−0.323244
$641$	−1.19746e12	−0.280157	−0.140078	−	0.990140i	$-0.544735\pi$
$641$	−1.19746e12	−0.280157	−0.140078	+	0.990140i	$0.544735\pi$
$642$	5.19710e12	1.20741
$643$	−7.98005e11	−0.184101	−0.0920505	−	0.995754i	$-0.529342\pi$
$643$	−7.98005e11	−0.184101	−0.0920505	+	0.995754i	$0.529342\pi$
$644$	−4.50320e12	−1.03166
$645$	2.13142e11	0.0484897
$646$	2.17375e12	0.491093
$647$	2.32481e12	0.521577	0.260788	−	0.965396i	$-0.416017\pi$
$647$	2.32481e12	0.521577	0.260788	+	0.965396i	$0.416017\pi$
$648$	−1.85983e11	−0.0414368
$649$	7.11627e12	1.57453
$650$	2.33341e12	0.512720
$651$	2.07456e12	0.452702
$652$	1.55090e12	0.336100
$653$	−2.42366e12	−0.521630	−0.260815	−	0.965389i	$-0.583991\pi$
$653$	−2.42366e12	−0.521630	−0.260815	+	0.965389i	$0.583991\pi$
$654$	1.69367e12	0.362017
$655$	3.12535e12	0.663457
$656$	1.76157e12	0.371391
$657$	2.08616e12	0.436821
$658$	2.15109e13	4.47344
$659$	2.04543e12	0.422474	0.211237	−	0.977435i	$-0.432251\pi$
$659$	2.04543e12	0.422474	0.211237	+	0.977435i	$0.432251\pi$
$660$	−2.25464e12	−0.462520
$661$	−1.14535e12	−0.233363	−0.116682	−	0.993169i	$-0.537226\pi$
$661$	−1.14535e12	−0.233363	−0.116682	+	0.993169i	$0.537226\pi$
$662$	1.19341e13	2.41506
$663$	−7.00989e12	−1.40896
$664$	−1.65525e12	−0.330450
$665$	−8.04735e11	−0.159572
$666$	8.15290e11	0.160575
$667$	9.57964e10	0.0187406
$668$	−8.12149e12	−1.57813
$669$	2.80067e12	0.540561
$670$	−1.99049e11	−0.0381614
$671$	8.71789e12	1.66020
$672$	−6.67816e12	−1.26327
$673$	4.53266e12	0.851697	0.425848	−	0.904795i	$-0.359976\pi$
$673$	4.53266e12	0.851697	0.425848	+	0.904795i	$0.359976\pi$
$674$	−1.39193e13	−2.59805
$675$	−2.07594e11	−0.0384900
$676$	1.30349e13	2.40075
$677$	3.07988e12	0.563489	0.281744	−	0.959489i	$-0.409087\pi$
$677$	3.07988e12	0.563489	0.281744	+	0.959489i	$0.409087\pi$
$678$	−9.24249e12	−1.67979
$679$	−1.07194e13	−1.93533
$680$	−1.32742e12	−0.238078
$681$	−1.69992e12	−0.302876
$682$	−6.12732e12	−1.08453
$683$	8.81574e12	1.55012	0.775060	−	0.631887i	$-0.217719\pi$
$683$	8.81574e12	1.55012	0.775060	+	0.631887i	$0.217719\pi$
$684$	5.46651e11	0.0954899
$685$	1.31429e12	0.228078
$686$	−5.66827e12	−0.977219
$687$	4.42086e12	0.757184
$688$	−7.60942e11	−0.129480
$689$	4.19912e12	0.709859
$690$	1.22462e12	0.205675
$691$	−1.13198e12	−0.188880	−0.0944401	−	0.995531i	$-0.530106\pi$
$691$	−1.13198e12	−0.188880	−0.0944401	+	0.995531i	$0.530106\pi$
$692$	1.26725e13	2.10081
$693$	−4.51561e12	−0.743732
$694$	−1.38738e13	−2.27028
$695$	1.20620e12	0.196104
$696$	−4.70252e10	−0.00759607
$697$	4.79121e12	0.768950
$698$	1.37197e13	2.18773
$699$	−1.97262e12	−0.312534
$700$	2.46743e12	0.388421
$701$	9.40714e12	1.47138	0.735692	−	0.677316i	$-0.236857\pi$
$701$	9.40714e12	1.47138	0.735692	+	0.677316i	$0.236857\pi$
$702$	−3.17458e12	−0.493365
$703$	−4.77262e11	−0.0736983
$704$	1.32780e13	2.03731
$705$	−3.24836e12	−0.495238
$706$	3.87753e12	0.587400
$707$	−2.51516e12	−0.378598
$708$	5.29024e12	0.791272
$709$	−6.66779e12	−0.991001	−0.495500	−	0.868608i	$-0.665015\pi$
$709$	−6.66779e12	−0.991001	−0.495500	+	0.868608i	$0.665015\pi$
$710$	3.70444e12	0.547091
$711$	3.16634e11	0.0464670
$712$	4.39698e12	0.641201
$713$	1.84808e12	0.267804
$714$	−1.33487e13	−1.92219
$715$	−7.66475e12	−1.09678
$716$	8.13361e12	1.15658
$717$	7.56955e12	1.06963
$718$	−9.27346e12	−1.30221
$719$	2.41689e12	0.337269	0.168635	−	0.985679i	$-0.446064\pi$
$719$	2.41689e12	0.337269	0.168635	+	0.985679i	$0.446064\pi$
$720$	7.41137e11	0.102778
$721$	1.59593e10	0.00219941
$722$	−5.76274e11	−0.0789244
$723$	6.31408e12	0.859385
$724$	3.92227e12	0.530535
$725$	−5.24895e10	−0.00705588
$726$	6.85639e12	0.915968
$727$	−7.53146e12	−0.999941	−0.499970	−	0.866043i	$-0.666656\pi$
$727$	−7.53146e12	−0.999941	−0.499970	+	0.866043i	$0.666656\pi$
$728$	7.51489e12	0.991588
$729$	2.82430e11	0.0370370
$730$	6.74307e12	0.878830
$731$	−2.06966e12	−0.268084
$732$	6.48089e12	0.834324
$733$	−2.65885e11	−0.0340194	−0.0170097	−	0.999855i	$-0.505415\pi$
$733$	−2.65885e11	−0.0340194	−0.0170097	+	0.999855i	$0.505415\pi$
$734$	−1.34745e13	−1.71349
$735$	2.89887e12	0.366383
$736$	−5.94909e12	−0.747309
$737$	6.53835e11	0.0816328
$738$	2.16980e12	0.269257
$739$	−7.54408e12	−0.930478	−0.465239	−	0.885185i	$-0.654032\pi$
$739$	−7.54408e12	−0.930478	−0.465239	+	0.885185i	$0.654032\pi$
$740$	1.46335e12	0.179393
$741$	1.85836e12	0.226437
$742$	7.99626e12	0.968432
$743$	−9.27540e12	−1.11656	−0.558281	−	0.829652i	$-0.688539\pi$
$743$	−9.27540e12	−1.11656	−0.558281	+	0.829652i	$0.688539\pi$
$744$	−9.07197e11	−0.108548
$745$	−4.62753e12	−0.550359
$746$	9.86051e12	1.16567
$747$	2.51362e12	0.295363
$748$	2.18931e13	2.55712
$749$	1.86825e13	2.16904
$750$	−6.71004e11	−0.0774372
$751$	−3.97286e12	−0.455747	−0.227874	−	0.973691i	$-0.573177\pi$
$751$	−3.97286e12	−0.455747	−0.227874	+	0.973691i	$0.573177\pi$
$752$	1.15971e13	1.32242
$753$	6.96693e12	0.789703
$754$	−8.02681e11	−0.0904423
$755$	−7.24912e11	−0.0811940
$756$	−3.35691e12	−0.373759
$757$	−3.95644e12	−0.437899	−0.218949	−	0.975736i	$-0.570263\pi$
$757$	−3.95644e12	−0.437899	−0.218949	+	0.975736i	$0.570263\pi$
$758$	−1.16252e13	−1.27905
$759$	−4.02262e12	−0.439968
$760$	3.51907e11	0.0382619
$761$	4.02381e12	0.434917	0.217458	−	0.976070i	$-0.430223\pi$
$761$	4.02381e12	0.434917	0.217458	+	0.976070i	$0.430223\pi$
$762$	−6.92329e12	−0.743901
$763$	6.08838e12	0.650342
$764$	−2.24547e13	−2.38444
$765$	2.01579e12	0.212799
$766$	3.57409e12	0.375090
$767$	1.79844e13	1.87636
$768$	−1.87181e12	−0.194149
$769$	1.47012e13	1.51595	0.757976	−	0.652283i	$-0.226188\pi$
$769$	1.47012e13	1.51595	0.757976	+	0.652283i	$0.226188\pi$
$770$	−1.45957e13	−1.49630
$771$	−2.71387e12	−0.276595
$772$	2.12057e13	2.14869
$773$	5.27223e12	0.531113	0.265556	−	0.964095i	$-0.414444\pi$
$773$	5.27223e12	0.531113	0.265556	+	0.964095i	$0.414444\pi$
$774$	−9.37289e11	−0.0938727
$775$	−1.01261e12	−0.100829
$776$	4.68753e12	0.464052
$777$	2.93080e12	0.288464
$778$	2.49435e13	2.44090
$779$	−1.27018e12	−0.123579
$780$	−5.69798e12	−0.551183
$781$	−1.21683e13	−1.17031
$782$	−1.18914e13	−1.13711
$783$	7.14113e10	0.00678952
$784$	−1.03493e13	−0.978339
$785$	4.62030e12	0.434267
$786$	−1.37437e13	−1.28441
$787$	1.14758e13	1.06634	0.533169	−	0.846009i	$-0.321001\pi$
$787$	1.14758e13	1.06634	0.533169	+	0.846009i	$0.321001\pi$
$788$	7.50533e12	0.693428
$789$	1.01492e13	0.932362
$790$	1.02345e12	0.0934858
$791$	−3.32248e13	−3.01765
$792$	1.97465e12	0.178331
$793$	2.20320e13	1.97845
$794$	4.43144e12	0.395688
$795$	−1.20752e12	−0.107211
$796$	−2.45582e13	−2.16815
$797$	−8.04453e12	−0.706217	−0.353108	−	0.935582i	$-0.614875\pi$
$797$	−8.04453e12	−0.706217	−0.353108	+	0.935582i	$0.614875\pi$
$798$	3.53882e12	0.308919
$799$	3.15424e13	2.73801
$800$	3.25967e12	0.281364
$801$	−6.67715e12	−0.573119
$802$	−1.10775e13	−0.945489
$803$	−2.21496e13	−1.87995
$804$	4.86062e11	0.0410241
$805$	4.40226e12	0.369483
$806$	−1.54851e13	−1.29243
$807$	2.58016e12	0.214149
$808$	1.09987e12	0.0907799
$809$	−1.46887e13	−1.20563	−0.602814	−	0.797882i	$-0.705954\pi$
$809$	−1.46887e13	−1.20563	−0.602814	+	0.797882i	$0.705954\pi$
$810$	9.12894e11	0.0745139
$811$	5.18047e12	0.420509	0.210255	−	0.977647i	$-0.432571\pi$
$811$	5.18047e12	0.420509	0.210255	+	0.977647i	$0.432571\pi$
$812$	−8.48782e11	−0.0685164
$813$	3.07955e12	0.247218
$814$	−8.65624e12	−0.691066
$815$	−1.51613e12	−0.120373
$816$	−7.19662e12	−0.568228
$817$	5.48678e11	0.0430842
$818$	−3.38274e13	−2.64167
$819$	−1.14119e13	−0.886302
$820$	3.89454e12	0.300811
$821$	2.10676e13	1.61834	0.809172	−	0.587572i	$-0.199916\pi$
$821$	2.10676e13	1.61834	0.809172	+	0.587572i	$0.199916\pi$
$822$	−5.77958e12	−0.441543
$823$	−1.23011e12	−0.0934644	−0.0467322	−	0.998907i	$-0.514881\pi$
$823$	−1.23011e12	−0.0934644	−0.0467322	+	0.998907i	$0.514881\pi$
$824$	−6.97893e9	−0.000527371 0
$825$	2.20411e12	0.165649
$826$	3.42471e13	2.55984
$827$	−1.85555e12	−0.137942	−0.0689712	−	0.997619i	$-0.521972\pi$
$827$	−1.85555e12	−0.137942	−0.0689712	+	0.997619i	$0.521972\pi$
$828$	−2.99042e12	−0.221104
$829$	9.09884e12	0.669099	0.334550	−	0.942378i	$-0.391416\pi$
$829$	9.09884e12	0.669099	0.334550	+	0.942378i	$0.391416\pi$
$830$	8.12474e12	0.594235
$831$	−8.55734e12	−0.622493
$832$	3.35565e13	2.42785
$833$	−2.81487e13	−2.02561
$834$	−5.30425e12	−0.379644
$835$	7.93945e12	0.565199
$836$	−5.80400e12	−0.410960
$837$	1.37765e12	0.0970228
$838$	−4.80455e12	−0.336554
$839$	1.12716e13	0.785341	0.392670	−	0.919679i	$-0.371551\pi$
$839$	1.12716e13	0.785341	0.392670	+	0.919679i	$0.371551\pi$
$840$	−2.16101e12	−0.149762
$841$	−1.44891e13	−0.998755
$842$	−2.70343e13	−1.85358
$843$	3.49364e12	0.238262
$844$	6.09425e12	0.413409
$845$	−1.27427e13	−0.859818
$846$	1.42847e13	0.958745
$847$	2.46473e13	1.64548
$848$	4.31098e12	0.286283
$849$	−1.12750e13	−0.744784
$850$	6.51561e12	0.428125
$851$	2.61083e12	0.170646
$852$	−9.04592e12	−0.588131
$853$	9.70339e12	0.627556	0.313778	−	0.949496i	$-0.398405\pi$
$853$	9.70339e12	0.627556	0.313778	+	0.949496i	$0.398405\pi$
$854$	4.19549e13	2.69912
$855$	−5.34398e11	−0.0341993
$856$	−8.16976e12	−0.520089
$857$	2.75330e13	1.74357	0.871787	−	0.489885i	$-0.162961\pi$
$857$	2.75330e13	1.74357	0.871787	+	0.489885i	$0.162961\pi$
$858$	3.37057e13	2.12329
$859$	−1.21276e13	−0.759989	−0.379994	−	0.924989i	$-0.624074\pi$
$859$	−1.21276e13	−0.759989	−0.379994	+	0.924989i	$0.624074\pi$
$860$	−1.68232e12	−0.104874
$861$	7.79999e12	0.483704
$862$	1.39704e13	0.861841
$863$	1.58553e13	0.973032	0.486516	−	0.873672i	$-0.338268\pi$
$863$	1.58553e13	0.973032	0.486516	+	0.873672i	$0.338268\pi$
$864$	−4.43474e12	−0.270742
$865$	−1.23885e13	−0.752394
$866$	1.78152e13	1.07637
$867$	−9.96820e12	−0.599143
$868$	−1.63745e13	−0.979104
$869$	−3.36182e12	−0.199980
$870$	2.30822e11	0.0136597
$871$	1.65239e12	0.0972814
$872$	−2.66242e12	−0.155938
$873$	−7.11837e12	−0.414779
$874$	3.15247e12	0.182747
$875$	−2.41212e12	−0.139111
$876$	−1.64660e13	−0.944757
$877$	−2.86146e13	−1.63339	−0.816695	−	0.577069i	$-0.804196\pi$
$877$	−2.86146e13	−1.63339	−0.816695	+	0.577069i	$0.804196\pi$
$878$	−2.00992e13	−1.14144
$879$	−9.61027e12	−0.542982
$880$	−7.86893e12	−0.442327
$881$	−1.23867e13	−0.692729	−0.346365	−	0.938100i	$-0.612584\pi$
$881$	−1.23867e13	−0.692729	−0.346365	+	0.938100i	$0.612584\pi$
$882$	−1.27477e13	−0.709292
$883$	−3.23596e12	−0.179135	−0.0895673	−	0.995981i	$-0.528548\pi$
$883$	−3.23596e12	−0.179135	−0.0895673	+	0.995981i	$0.528548\pi$
$884$	5.53288e13	3.04731
$885$	−5.17166e12	−0.283391
$886$	1.17477e13	0.640474
$887$	−2.35148e11	−0.0127551	−0.00637757	−	0.999980i	$-0.502030\pi$
$887$	−2.35148e11	−0.0127551	−0.00637757	+	0.999980i	$0.502030\pi$
$888$	−1.28162e12	−0.0691675
$889$	−2.48878e13	−1.33637
$890$	−2.15825e13	−1.15304
$891$	−2.99866e12	−0.159396
$892$	−2.21056e13	−1.16913
$893$	−8.36208e12	−0.440030
$894$	2.03495e13	1.06546
$895$	−7.95129e12	−0.414223
$896$	2.16880e13	1.12417
$897$	−1.01661e13	−0.524308
$898$	6.48070e12	0.332566
$899$	3.48333e11	0.0177859
$900$	1.63853e12	0.0832462
$901$	1.17253e13	0.592737
$902$	−2.30376e13	−1.15880
$903$	−3.36936e12	−0.168637
$904$	1.45291e13	0.723568
$905$	−3.83435e12	−0.190009
$906$	3.18779e12	0.157186
$907$	3.22682e13	1.58322	0.791611	−	0.611026i	$-0.209243\pi$
$907$	3.22682e13	1.58322	0.791611	+	0.611026i	$0.209243\pi$
$908$	1.34174e13	0.655061
$909$	−1.67023e12	−0.0811409
$910$	−3.68867e13	−1.78313
$911$	2.50945e13	1.20711	0.603553	−	0.797323i	$-0.293751\pi$
$911$	2.50945e13	1.20711	0.603553	+	0.797323i	$0.293751\pi$
$912$	1.90787e12	0.0913211
$913$	−2.66880e13	−1.27115
$914$	3.05149e13	1.44629
$915$	−6.33562e12	−0.298809
$916$	−3.48937e13	−1.63764
$917$	−4.94057e13	−2.30736
$918$	−8.86442e12	−0.411963
$919$	1.22135e13	0.564835	0.282418	−	0.959292i	$-0.408864\pi$
$919$	1.22135e13	0.564835	0.282418	+	0.959292i	$0.408864\pi$
$920$	−1.92509e12	−0.0885942
$921$	−1.25200e13	−0.573372
$922$	9.45727e12	0.430999
$923$	−3.07519e13	−1.39465
$924$	3.56416e13	1.60854
$925$	−1.43055e12	−0.0642487
$926$	−2.57706e13	−1.15180
$927$	1.05980e10	0.000471376 0
$928$	−1.12131e12	−0.0496317
$929$	−2.81613e13	−1.24046	−0.620228	−	0.784422i	$-0.712960\pi$
$929$	−2.81613e13	−1.24046	−0.620228	+	0.784422i	$0.712960\pi$
$930$	4.45295e12	0.195198
$931$	7.46239e12	0.325540
$932$	1.55699e13	0.675948
$933$	4.05532e12	0.175210
$934$	−3.31536e13	−1.42551
$935$	−2.14024e13	−0.915820
$936$	4.99038e12	0.212516
$937$	4.52888e12	0.191939	0.0959695	−	0.995384i	$-0.469405\pi$
$937$	4.52888e12	0.191939	0.0959695	+	0.995384i	$0.469405\pi$
$938$	3.14659e12	0.132717
$939$	−1.32433e13	−0.555906
$940$	2.56393e13	1.07110
$941$	3.51517e13	1.46148	0.730741	−	0.682655i	$-0.239175\pi$
$941$	3.51517e13	1.46148	0.730741	+	0.682655i	$0.239175\pi$
$942$	−2.03177e13	−0.840709
$943$	6.94844e12	0.286144
$944$	1.84635e13	0.756727
$945$	3.28166e12	0.133860
$946$	9.95155e12	0.403999
$947$	−1.47283e13	−0.595083	−0.297541	−	0.954709i	$-0.596167\pi$
$947$	−1.47283e13	−0.595083	−0.297541	+	0.954709i	$0.596167\pi$
$948$	−2.49918e12	−0.100499
$949$	−5.59768e13	−2.24032
$950$	−1.72733e12	−0.0688047
$951$	−1.00212e13	−0.397291
$952$	2.09839e13	0.827982
$953$	7.97246e12	0.313094	0.156547	−	0.987671i	$-0.449964\pi$
$953$	7.97246e12	0.313094	0.156547	+	0.987671i	$0.449964\pi$
$954$	5.31004e12	0.207554
$955$	2.19513e13	0.853976
$956$	−5.97462e13	−2.31340
$957$	−7.58201e11	−0.0292200
$958$	6.55282e13	2.51353
$959$	−2.07764e13	−0.793207
$960$	−9.64964e12	−0.366683
$961$	−1.97197e13	−0.745838
$962$	−2.18762e13	−0.823541
$963$	1.24064e13	0.464866
$964$	−4.98369e13	−1.85868
$965$	−2.07304e13	−0.769545
$966$	−1.93589e13	−0.715293
$967$	−4.87770e13	−1.79389	−0.896945	−	0.442143i	$-0.854218\pi$
$967$	−4.87770e13	−1.79389	−0.896945	+	0.442143i	$0.854218\pi$
$968$	−1.07781e13	−0.394552
$969$	5.18913e12	0.189077
$970$	−2.30086e13	−0.834484
$971$	−4.14096e13	−1.49491	−0.747454	−	0.664314i	$-0.768724\pi$
$971$	−4.14096e13	−1.49491	−0.747454	+	0.664314i	$0.768724\pi$
$972$	−2.22921e12	−0.0801037
$973$	−1.90677e13	−0.682009
$974$	−6.76969e13	−2.41020
$975$	5.57026e12	0.197404
$976$	2.26189e13	0.797899
$977$	−4.15877e13	−1.46029	−0.730145	−	0.683292i	$-0.760547\pi$
$977$	−4.15877e13	−1.46029	−0.730145	+	0.683292i	$0.760547\pi$
$978$	6.66718e12	0.233033
$979$	7.08938e13	2.46653
$980$	−2.28807e13	−0.792413
$981$	4.04309e12	0.139381
$982$	−6.09049e13	−2.09002
$983$	3.82096e13	1.30522	0.652608	−	0.757696i	$-0.273675\pi$
$983$	3.82096e13	1.30522	0.652608	+	0.757696i	$0.273675\pi$
$984$	−3.41090e12	−0.115982
$985$	−7.33709e12	−0.248348
$986$	−2.24134e12	−0.0755199
$987$	5.13504e13	1.72233
$988$	−1.46680e13	−0.489739
$989$	−3.00151e12	−0.0997602
$990$	−9.69254e12	−0.320685
$991$	3.49657e13	1.15163	0.575813	−	0.817582i	$-0.304686\pi$
$991$	3.49657e13	1.15163	0.575813	+	0.817582i	$0.304686\pi$
$992$	−2.16320e13	−0.709241
$993$	2.84888e13	0.929828
$994$	−5.85600e13	−1.90266
$995$	2.40078e13	0.776512
$996$	−1.98399e13	−0.638812
$997$	−2.24998e13	−0.721193	−0.360596	−	0.932722i	$-0.617427\pi$
$997$	−2.24998e13	−0.721193	−0.360596	+	0.932722i	$0.617427\pi$
$998$	1.69900e13	0.542132
$999$	1.94624e12	0.0618233

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.f.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.f.1.3	✓	14	1.1	even	1	trivial

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	285.10.a.f.1.3

Level	$285$
Weight	$10$
Character	285.1
Self dual	yes
Analytic conductor	$146.785$
Analytic rank	$0$
Dimension	$14$
CM	no
Inner twists	$1$