LMFDB - Embedded newform 289.10.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-31.9341 q^{2} -159.334 q^{3} +507.789 q^{4} +1397.46 q^{5} +5088.20 q^{6} -9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} +O(q^{10})$	\(q-31.9341 q^{2} -159.334 q^{3} +507.789 q^{4} +1397.46 q^{5} +5088.20 q^{6} -9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} -44626.6 q^{10} +50614.6 q^{11} -80908.1 q^{12} -76005.9 q^{13} +318600. q^{14} -222662. q^{15} -264282. q^{16} -182163. q^{18} -650626. q^{19} +709613. q^{20} +1.58964e6 q^{21} -1.61633e6 q^{22} -592123. q^{23} -21427.2 q^{24} -239.413 q^{25} +2.42718e6 q^{26} +2.22728e6 q^{27} -5.06610e6 q^{28} -3.53259e6 q^{29} +7.11053e6 q^{30} +3.41000e6 q^{31} +8.37077e6 q^{32} -8.06462e6 q^{33} -1.39421e7 q^{35} +2.89660e6 q^{36} +6.22732e6 q^{37} +2.07772e7 q^{38} +1.21103e7 q^{39} +187930. q^{40} -16809.2 q^{41} -5.07638e7 q^{42} +3.25305e7 q^{43} +2.57015e7 q^{44} +7.97157e6 q^{45} +1.89089e7 q^{46} -5.02215e7 q^{47} +4.21092e7 q^{48} +5.91825e7 q^{49} +7645.44 q^{50} -3.85949e7 q^{52} +1.56012e7 q^{53} -7.11261e7 q^{54} +7.07317e7 q^{55} -1.34168e6 q^{56} +1.03667e8 q^{57} +1.12810e8 q^{58} +1.62168e8 q^{59} -1.13066e8 q^{60} -1.55917e8 q^{61} -1.08895e8 q^{62} -5.69110e7 q^{63} -1.32001e8 q^{64} -1.06215e8 q^{65} +2.57537e8 q^{66} -2.74298e8 q^{67} +9.43453e7 q^{69} +4.45229e8 q^{70} -2.72244e8 q^{71} +767119. q^{72} +8.57367e6 q^{73} -1.98864e8 q^{74} +38146.6 q^{75} -3.30381e8 q^{76} -5.04970e8 q^{77} -3.86733e8 q^{78} -2.87273e8 q^{79} -3.69323e8 q^{80} -4.67160e8 q^{81} +536788. q^{82} -3.71797e8 q^{83} +8.07202e8 q^{84} -1.03883e9 q^{86} +5.62862e8 q^{87} +6.80664e6 q^{88} -4.29631e8 q^{89} -2.54565e8 q^{90} +7.58294e8 q^{91} -3.00673e8 q^{92} -5.43330e8 q^{93} +1.60378e9 q^{94} -9.09222e8 q^{95} -1.33375e9 q^{96} -1.01912e9 q^{97} -1.88994e9 q^{98} +2.88723e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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 $

$2$	−31.9341	−1.41130	−0.705651	−	0.708559i	$-0.749345\pi$
$2$	−31.9341	−1.41130	−0.705651	+	0.708559i	$0.749345\pi$
$3$	−159.334	−1.13570	−0.567849	−	0.823133i	$-0.692224\pi$
$3$	−159.334	−1.13570	−0.567849	+	0.823133i	$0.692224\pi$
$4$	507.789	0.991775
$5$	1397.46	0.999939	0.499969	−	0.866043i	$-0.333345\pi$
$5$	1397.46	0.999939	0.499969	+	0.866043i	$0.333345\pi$
$6$	5088.20	1.60281
$7$	−9976.78	−1.57054	−0.785270	−	0.619153i	$-0.787476\pi$
$7$	−9976.78	−1.57054	−0.785270	+	0.619153i	$0.787476\pi$
$8$	134.480	0.0116079
$9$	5704.34	0.289811
$10$	−44626.6	−1.41122
$11$	50614.6	1.04234	0.521169	−	0.853454i	$-0.325496\pi$
$11$	50614.6	1.04234	0.521169	+	0.853454i	$0.325496\pi$
$12$	−80908.1	−1.12636
$13$	−76005.9	−0.738078	−0.369039	−	0.929414i	$-0.620313\pi$
$13$	−76005.9	−0.738078	−0.369039	+	0.929414i	$0.620313\pi$
$14$	318600.	2.21651
$15$	−222662.	−1.13563
$16$	−264282.	−1.00816
$17$	0	0
$17$	0	0
$18$	−182163.	−0.409011
$19$	−650626.	−1.14536	−0.572678	−	0.819781i	$-0.694095\pi$
$19$	−650626.	−1.14536	−0.572678	+	0.819781i	$0.694095\pi$
$20$	709613.	0.991714
$21$	1.58964e6	1.78366
$22$	−1.61633e6	−1.47105
$23$	−592123.	−0.441201	−0.220600	−	0.975364i	$-0.570802\pi$
$23$	−592123.	−0.441201	−0.220600	+	0.975364i	$0.570802\pi$
$24$	−21427.2	−0.0131830
$25$	−239.413	−0.000122579 0
$26$	2.42718e6	1.04165
$27$	2.22728e6	0.806561
$28$	−5.06610e6	−1.55762
$29$	−3.53259e6	−0.927475	−0.463737	−	0.885973i	$-0.653492\pi$
$29$	−3.53259e6	−0.927475	−0.463737	+	0.885973i	$0.653492\pi$
$30$	7.11053e6	1.60272
$31$	3.41000e6	0.663173	0.331587	−	0.943425i	$-0.392416\pi$
$31$	3.41000e6	0.663173	0.331587	+	0.943425i	$0.392416\pi$
$32$	8.37077e6	1.41121
$33$	−8.06462e6	−1.18378
$34$	0	0
$35$	−1.39421e7	−1.57044
$36$	2.89660e6	0.287427
$37$	6.22732e6	0.546253	0.273126	−	0.961978i	$-0.411942\pi$
$37$	6.22732e6	0.546253	0.273126	+	0.961978i	$0.411942\pi$
$38$	2.07772e7	1.61644
$39$	1.21103e7	0.838234
$40$	187930.	0.0116072
$41$	−16809.2	−0.000929011 0	−0.000464505	−	1.00000i	$-0.500148\pi$
$41$	−16809.2	−0.000929011 0	−0.000464505		1.00000i	$0.500148\pi$
$42$	−5.07638e7	−2.51728
$43$	3.25305e7	1.45105	0.725525	−	0.688196i	$-0.241597\pi$
$43$	3.25305e7	1.45105	0.725525	+	0.688196i	$0.241597\pi$
$44$	2.57015e7	1.03376
$45$	7.97157e6	0.289793
$46$	1.89089e7	0.622668
$47$	−5.02215e7	−1.50124	−0.750619	−	0.660736i	$-0.770244\pi$
$47$	−5.02215e7	−1.50124	−0.750619	+	0.660736i	$0.770244\pi$
$48$	4.21092e7	1.14496
$49$	5.91825e7	1.46660
$50$	7645.44	0.000172997 0
$51$	0	0
$52$	−3.85949e7	−0.732007
$53$	1.56012e7	0.271592	0.135796	−	0.990737i	$-0.456641\pi$
$53$	1.56012e7	0.271592	0.135796	+	0.990737i	$0.456641\pi$
$54$	−7.11261e7	−1.13830
$55$	7.07317e7	1.04227
$56$	−1.34168e6	−0.0182306
$57$	1.03667e8	1.30078
$58$	1.12810e8	1.30895
$59$	1.62168e8	1.74233	0.871165	−	0.490991i	$-0.163365\pi$
$59$	1.62168e8	1.74233	0.871165	+	0.490991i	$0.163365\pi$
$60$	−1.13066e8	−1.12629
$61$	−1.55917e8	−1.44181	−0.720906	−	0.693033i	$-0.756274\pi$
$61$	−1.55917e8	−1.44181	−0.720906	+	0.693033i	$0.756274\pi$
$62$	−1.08895e8	−0.935938
$63$	−5.69110e7	−0.455159
$64$	−1.32001e8	−0.983483
$65$	−1.06215e8	−0.738033
$66$	2.57537e8	1.67067
$67$	−2.74298e8	−1.66298	−0.831488	−	0.555542i	$-0.812511\pi$
$67$	−2.74298e8	−1.66298	−0.831488	+	0.555542i	$0.812511\pi$
$68$	0	0
$69$	9.43453e7	0.501071
$70$	4.45229e8	2.21637
$71$	−2.72244e8	−1.27144	−0.635721	−	0.771919i	$-0.719297\pi$
$71$	−2.72244e8	−1.27144	−0.635721	+	0.771919i	$0.719297\pi$
$72$	767119.	0.00336408
$73$	8.57367e6	0.0353357	0.0176679	−	0.999844i	$-0.494376\pi$
$73$	8.57367e6	0.0353357	0.0176679	+	0.999844i	$0.494376\pi$
$74$	−1.98864e8	−0.770928
$75$	38146.6	0.000139213 0
$76$	−3.30381e8	−1.13593
$77$	−5.04970e8	−1.63703
$78$	−3.86733e8	−1.18300
$79$	−2.87273e8	−0.829799	−0.414899	−	0.909867i	$-0.636183\pi$
$79$	−2.87273e8	−0.829799	−0.414899	+	0.909867i	$0.636183\pi$
$80$	−3.69323e8	−1.00810
$81$	−4.67160e8	−1.20582
$82$	536788.	0.00131112
$83$	−3.71797e8	−0.859913	−0.429956	−	0.902850i	$-0.641471\pi$
$83$	−3.71797e8	−0.859913	−0.429956	+	0.902850i	$0.641471\pi$
$84$	8.07202e8	1.76899
$85$	0	0
$86$	−1.03883e9	−2.04787
$87$	5.62862e8	1.05333
$88$	6.80664e6	0.0120993
$89$	−4.29631e8	−0.725839	−0.362919	−	0.931821i	$-0.618220\pi$
$89$	−4.29631e8	−0.725839	−0.362919	+	0.931821i	$0.618220\pi$
$90$	−2.54565e8	−0.408986
$91$	7.58294e8	1.15918
$92$	−3.00673e8	−0.437572
$93$	−5.43330e8	−0.753165
$94$	1.60378e9	2.11870
$95$	−9.09222e8	−1.14529
$96$	−1.33375e9	−1.60271
$97$	−1.01912e9	−1.16884	−0.584418	−	0.811453i	$-0.698677\pi$
$97$	−1.01912e9	−1.16884	−0.584418	+	0.811453i	$0.698677\pi$
$98$	−1.88994e9	−2.06981
$99$	2.88723e8	0.302081
$100$	−121571.	−0.000121571 0
$101$	−5.60377e8	−0.535838	−0.267919	−	0.963441i	$-0.586336\pi$
$101$	−5.60377e8	−0.535838	−0.267919	+	0.963441i	$0.586336\pi$
$102$	0	0
$103$	−1.44725e8	−0.126699	−0.0633497	−	0.997991i	$-0.520178\pi$
$103$	−1.44725e8	−0.126699	−0.0633497	+	0.997991i	$0.520178\pi$
$104$	−1.02213e7	−0.00856751
$105$	2.22145e9	1.78355
$106$	−4.98212e8	−0.383299
$107$	−1.91158e9	−1.40983	−0.704914	−	0.709293i	$-0.749014\pi$
$107$	−1.91158e9	−1.40983	−0.704914	+	0.709293i	$0.749014\pi$
$108$	1.13099e9	0.799927
$109$	2.42408e9	1.64485	0.822426	−	0.568872i	$-0.192620\pi$
$109$	2.42408e9	1.64485	0.822426	+	0.568872i	$0.192620\pi$
$110$	−2.25875e9	−1.47096
$111$	−9.92225e8	−0.620379
$112$	2.63669e9	1.58335
$113$	−1.14662e9	−0.661555	−0.330777	−	0.943709i	$-0.607311\pi$
$113$	−1.14662e9	−0.661555	−0.330777	+	0.943709i	$0.607311\pi$
$114$	−3.31051e9	−1.83579
$115$	−8.27466e8	−0.441174
$116$	−1.79381e9	−0.919846
$117$	−4.33564e8	−0.213903
$118$	−5.17869e9	−2.45895
$119$	0	0
$120$	−2.99436e7	−0.0131822
$121$	2.03886e8	0.0864676
$122$	4.97907e9	2.03483
$123$	2.67828e6	0.00105508
$124$	1.73156e9	0.657719
$125$	−2.72974e9	−1.00006
$126$	1.81740e9	0.642368
$127$	2.47510e9	0.844260	0.422130	−	0.906535i	$-0.361283\pi$
$127$	2.47510e9	0.844260	0.422130	+	0.906535i	$0.361283\pi$
$128$	−7.05038e7	−0.0232149
$129$	−5.18321e9	−1.64796
$130$	3.39188e9	1.04159
$131$	2.01408e9	0.597526	0.298763	−	0.954327i	$-0.403426\pi$
$131$	2.01408e9	0.597526	0.298763	+	0.954327i	$0.403426\pi$
$132$	−4.09513e9	−1.17404
$133$	6.49115e9	1.79883
$134$	8.75947e9	2.34696
$135$	3.11252e9	0.806511
$136$	0	0
$137$	2.91545e9	0.707070	0.353535	−	0.935421i	$-0.384979\pi$
$137$	2.91545e9	0.707070	0.353535	+	0.935421i	$0.384979\pi$
$138$	−3.01284e9	−0.707163
$139$	7.52889e9	1.71066	0.855331	−	0.518081i	$-0.173353\pi$
$139$	7.52889e9	1.71066	0.855331	+	0.518081i	$0.173353\pi$
$140$	−7.07965e9	−1.55753
$141$	8.00200e9	1.70495
$142$	8.69389e9	1.79439
$143$	−3.84701e9	−0.769326
$144$	−1.50756e9	−0.292175
$145$	−4.93664e9	−0.927418
$146$	−2.73793e8	−0.0498694
$147$	−9.42979e9	−1.66561
$148$	3.16217e9	0.541760
$149$	−8.08087e9	−1.34314	−0.671568	−	0.740943i	$-0.734379\pi$
$149$	−8.08087e9	−1.34314	−0.671568	+	0.740943i	$0.734379\pi$
$150$	−1.21818e6	−0.000196472 0
$151$	−3.19079e9	−0.499461	−0.249730	−	0.968315i	$-0.580342\pi$
$151$	−3.19079e9	−0.499461	−0.249730	+	0.968315i	$0.580342\pi$
$152$	−8.74961e7	−0.0132951
$153$	0	0
$154$	1.61258e10	2.31035
$155$	4.76533e9	0.663133
$156$	6.14949e9	0.831339
$157$	−2.16958e9	−0.284988	−0.142494	−	0.989796i	$-0.545512\pi$
$157$	−2.16958e9	−0.284988	−0.142494	+	0.989796i	$0.545512\pi$
$158$	9.17381e9	1.17110
$159$	−2.48581e9	−0.308447
$160$	1.16978e10	1.41112
$161$	5.90748e9	0.692924
$162$	1.49183e10	1.70178
$163$	−1.61234e10	−1.78900	−0.894502	−	0.447064i	$-0.852470\pi$
$163$	−1.61234e10	−1.78900	−0.894502	+	0.447064i	$0.852470\pi$
$164$	−8.53554e6	−0.000921370 0
$165$	−1.12700e10	−1.18371
$166$	1.18730e10	1.21360
$167$	−1.11195e10	−1.10627	−0.553133	−	0.833093i	$-0.686568\pi$
$167$	−1.11195e10	−1.10627	−0.553133	+	0.833093i	$0.686568\pi$
$168$	2.13775e8	0.0207045
$169$	−4.82760e9	−0.455241
$170$	0	0
$171$	−3.71139e9	−0.331936
$172$	1.65186e10	1.43912
$173$	−1.48857e10	−1.26346	−0.631729	−	0.775189i	$-0.717654\pi$
$173$	−1.48857e10	−1.26346	−0.631729	+	0.775189i	$0.717654\pi$
$174$	−1.79745e10	−1.48657
$175$	2.38857e6	0.000192516 0
$176$	−1.33765e10	−1.05084
$177$	−2.58388e10	−1.97876
$178$	1.37199e10	1.02438
$179$	1.45764e10	1.06124	0.530618	−	0.847611i	$-0.321960\pi$
$179$	1.45764e10	1.06124	0.530618	+	0.847611i	$0.321960\pi$
$180$	4.04788e9	0.287409
$181$	2.90444e9	0.201145	0.100572	−	0.994930i	$-0.467933\pi$
$181$	2.90444e9	0.201145	0.100572	+	0.994930i	$0.467933\pi$
$182$	−2.42155e10	−1.63596
$183$	2.48429e10	1.63746
$184$	−7.96286e7	−0.00512140
$185$	8.70242e9	0.546219
$186$	1.73508e10	1.06294
$187$	0	0
$188$	−2.55019e10	−1.48889
$189$	−2.22210e10	−1.26674
$190$	2.90352e10	1.61634
$191$	1.67129e10	0.908658	0.454329	−	0.890834i	$-0.349879\pi$
$191$	1.67129e10	0.908658	0.454329	+	0.890834i	$0.349879\pi$
$192$	2.10322e10	1.11694
$193$	−1.00548e10	−0.521635	−0.260818	−	0.965388i	$-0.583992\pi$
$193$	−1.00548e10	−0.521635	−0.260818	+	0.965388i	$0.583992\pi$
$194$	3.25448e10	1.64958
$195$	1.69237e10	0.838182
$196$	3.00522e10	1.45454
$197$	6.48737e9	0.306882	0.153441	−	0.988158i	$-0.450965\pi$
$197$	6.48737e9	0.306882	0.153441	+	0.988158i	$0.450965\pi$
$198$	−9.22011e9	−0.426327
$199$	4.66693e8	0.0210956	0.0105478	−	0.999944i	$-0.496642\pi$
$199$	4.66693e8	0.0210956	0.0105478	+	0.999944i	$0.496642\pi$
$200$	−32196.2	−1.42288e−6 0
$201$	4.37050e10	1.88864
$202$	1.78951e10	0.756230
$203$	3.52439e10	1.45664
$204$	0	0
$205$	−2.34902e7	−0.000928954 0
$206$	4.62165e9	0.178811
$207$	−3.37767e9	−0.127865
$208$	2.00870e10	0.744099
$209$	−3.29312e10	−1.19385
$210$	−7.09402e10	−2.51713
$211$	1.06287e9	0.0369156	0.0184578	−	0.999830i	$-0.494124\pi$
$211$	1.06287e9	0.0369156	0.0184578	+	0.999830i	$0.494124\pi$
$212$	7.92213e9	0.269359
$213$	4.33778e10	1.44397
$214$	6.10447e10	1.98969
$215$	4.54599e10	1.45096
$216$	2.99524e8	0.00936245
$217$	−3.40208e10	−1.04154
$218$	−7.74108e10	−2.32139
$219$	−1.36608e9	−0.0401307
$220$	3.59167e10	1.03370
$221$	0	0
$222$	3.16858e10	0.875542
$223$	−4.79547e10	−1.29855	−0.649276	−	0.760553i	$-0.724928\pi$
$223$	−4.79547e10	−1.29855	−0.649276	+	0.760553i	$0.724928\pi$
$224$	−8.35134e10	−2.21636
$225$	−1.36569e6	−3.55248e−5 0
$226$	3.66163e10	0.933654
$227$	−2.10496e10	−0.526171	−0.263085	−	0.964773i	$-0.584740\pi$
$227$	−2.10496e10	−0.526171	−0.263085	+	0.964773i	$0.584740\pi$
$228$	5.26409e10	1.29008
$229$	−1.60702e10	−0.386156	−0.193078	−	0.981183i	$-0.561847\pi$
$229$	−1.60702e10	−0.386156	−0.193078	+	0.981183i	$0.561847\pi$
$230$	2.64244e10	0.622630
$231$	8.04590e10	1.85918
$232$	−4.75062e8	−0.0107660
$233$	−6.08238e10	−1.35198	−0.675992	−	0.736909i	$-0.736285\pi$
$233$	−6.08238e10	−1.35198	−0.675992	+	0.736909i	$0.736285\pi$
$234$	1.38455e10	0.301882
$235$	−7.01824e10	−1.50115
$236$	8.23470e10	1.72800
$237$	4.57724e10	0.942401
$238$	0	0
$239$	4.66769e10	0.925362	0.462681	−	0.886525i	$-0.346887\pi$
$239$	4.66769e10	0.925362	0.462681	+	0.886525i	$0.346887\pi$
$240$	5.88458e10	1.14489
$241$	9.83868e9	0.187871	0.0939356	−	0.995578i	$-0.470055\pi$
$241$	9.83868e9	0.187871	0.0939356	+	0.995578i	$0.470055\pi$
$242$	−6.51093e9	−0.122032
$243$	3.05950e10	0.562887
$244$	−7.91728e10	−1.42995
$245$	8.27050e10	1.46651
$246$	−8.55287e7	−0.00148903
$247$	4.94514e10	0.845361
$248$	4.58577e8	0.00769803
$249$	5.92399e10	0.976601
$250$	8.71720e10	1.41139
$251$	5.71571e10	0.908947	0.454473	−	0.890760i	$-0.349827\pi$
$251$	5.71571e10	0.908947	0.454473	+	0.890760i	$0.349827\pi$
$252$	−2.88988e10	−0.451416
$253$	−2.99700e10	−0.459880
$254$	−7.90402e10	−1.19151
$255$	0	0
$256$	6.98359e10	1.01625
$257$	8.59864e10	1.22951	0.614753	−	0.788720i	$-0.289256\pi$
$257$	8.59864e10	1.22951	0.614753	+	0.788720i	$0.289256\pi$
$258$	1.65521e11	2.32576
$259$	−6.21286e10	−0.857912
$260$	−5.39348e10	−0.731962
$261$	−2.01511e10	−0.268792
$262$	−6.43181e10	−0.843290
$263$	2.61461e10	0.336982	0.168491	−	0.985703i	$-0.446111\pi$
$263$	2.61461e10	0.336982	0.168491	+	0.985703i	$0.446111\pi$
$264$	−1.08453e9	−0.0137412
$265$	2.18021e10	0.271576
$266$	−2.07289e11	−2.53869
$267$	6.84548e10	0.824334
$268$	−1.39285e11	−1.64930
$269$	2.14758e10	0.250072	0.125036	−	0.992152i	$-0.460095\pi$
$269$	2.14758e10	0.250072	0.125036	+	0.992152i	$0.460095\pi$
$270$	−9.93957e10	−1.13823
$271$	1.61241e11	1.81599	0.907997	−	0.418976i	$-0.137611\pi$
$271$	1.61241e11	1.81599	0.907997	+	0.418976i	$0.137611\pi$
$272$	0	0
$273$	−1.20822e11	−1.31648
$274$	−9.31023e10	−0.997890
$275$	−1.21178e7	−0.000127769 0
$276$	4.79075e10	0.496950
$277$	4.74856e10	0.484622	0.242311	−	0.970199i	$-0.422095\pi$
$277$	4.74856e10	0.484622	0.242311	+	0.970199i	$0.422095\pi$
$278$	−2.40429e11	−2.41426
$279$	1.94518e10	0.192195
$280$	−1.87493e9	−0.0182295
$281$	2.72583e9	0.0260808	0.0130404	−	0.999915i	$-0.495849\pi$
$281$	2.72583e9	0.0260808	0.0130404	+	0.999915i	$0.495849\pi$
$282$	−2.55537e11	−2.40620
$283$	−4.24874e10	−0.393751	−0.196876	−	0.980428i	$-0.563079\pi$
$283$	−4.24874e10	−0.393751	−0.196876	+	0.980428i	$0.563079\pi$
$284$	−1.38243e11	−1.26098
$285$	1.44870e11	1.30070
$286$	1.22851e11	1.08575
$287$	1.67702e8	0.00145905
$288$	4.77498e10	0.408983
$289$	0	0
$290$	1.57647e11	1.30887
$291$	1.62381e11	1.32744
$292$	4.35361e9	0.0350451
$293$	6.93631e9	0.0549825	0.0274912	−	0.999622i	$-0.491248\pi$
$293$	6.93631e9	0.0549825	0.0274912	+	0.999622i	$0.491248\pi$
$294$	3.01132e11	2.35068
$295$	2.26622e11	1.74222
$296$	8.37450e8	0.00634083
$297$	1.12733e11	0.840709
$298$	2.58056e11	1.89557
$299$	4.50048e10	0.325641
$300$	1.93704e7	0.000138068 0
$301$	−3.24549e11	−2.27893
$302$	1.01895e11	0.704891
$303$	8.92871e10	0.608551
$304$	1.71949e11	1.15470
$305$	−2.17887e11	−1.44172
$306$	0	0
$307$	1.64410e10	0.105635	0.0528173	−	0.998604i	$-0.483180\pi$
$307$	1.64410e10	0.105635	0.0528173	+	0.998604i	$0.483180\pi$
$308$	−2.56418e11	−1.62357
$309$	2.30595e10	0.143892
$310$	−1.52177e11	−0.935881
$311$	−1.22476e11	−0.742383	−0.371191	−	0.928556i	$-0.621051\pi$
$311$	−1.22476e11	−0.742383	−0.371191	+	0.928556i	$0.621051\pi$
$312$	1.62860e9	0.00973011
$313$	−2.36493e11	−1.39274	−0.696368	−	0.717685i	$-0.745202\pi$
$313$	−2.36493e11	−1.39274	−0.696368	+	0.717685i	$0.745202\pi$
$314$	6.92836e10	0.402204
$315$	−7.95306e10	−0.455132
$316$	−1.45874e11	−0.822974
$317$	4.33607e10	0.241173	0.120587	−	0.992703i	$-0.461522\pi$
$317$	4.33607e10	0.241173	0.120587	+	0.992703i	$0.461522\pi$
$318$	7.93821e10	0.435312
$319$	−1.78800e11	−0.966742
$320$	−1.84466e11	−0.983423
$321$	3.04580e11	1.60114
$322$	−1.88650e11	−0.977926
$323$	0	0
$324$	−2.37218e11	−1.19590
$325$	1.81968e7	9.04731e−5 0
$326$	5.14885e11	2.52483
$327$	−3.86238e11	−1.86806
$328$	−2.26050e6	−1.07838e−5 0
$329$	5.01049e11	2.35775
$330$	3.59897e11	1.67057
$331$	−1.69990e11	−0.778392	−0.389196	−	0.921155i	$-0.627247\pi$
$331$	−1.69990e11	−0.778392	−0.389196	+	0.921155i	$0.627247\pi$
$332$	−1.88794e11	−0.852840
$333$	3.55228e10	0.158310
$334$	3.55090e11	1.56128
$335$	−3.83320e11	−1.66287
$336$	−4.20114e11	−1.79821
$337$	−1.02637e10	−0.0433478	−0.0216739	−	0.999765i	$-0.506900\pi$
$337$	−1.02637e10	−0.0433478	−0.0216739	+	0.999765i	$0.506900\pi$
$338$	1.54165e11	0.642483
$339$	1.82695e11	0.751327
$340$	0	0
$341$	1.72596e11	0.691251
$342$	1.18520e11	0.468462
$343$	−1.87852e11	−0.732811
$344$	4.37469e9	0.0168436
$345$	1.31844e11	0.501040
$346$	4.75361e11	1.78312
$347$	−1.50419e11	−0.556957	−0.278478	−	0.960443i	$-0.589830\pi$
$347$	−1.50419e11	−0.556957	−0.278478	+	0.960443i	$0.589830\pi$
$348$	2.85815e11	1.04467
$349$	4.38444e11	1.58197	0.790987	−	0.611833i	$-0.209567\pi$
$349$	4.38444e11	1.58197	0.790987	+	0.611833i	$0.209567\pi$
$350$	−7.62769e7	−0.000271698 0
$351$	−1.69286e11	−0.595305
$352$	4.23683e11	1.47095
$353$	3.32465e10	0.113962	0.0569810	−	0.998375i	$-0.481853\pi$
$353$	3.32465e10	0.113962	0.0569810	+	0.998375i	$0.481853\pi$
$354$	8.25141e11	2.79263
$355$	−3.80450e11	−1.27136
$356$	−2.18162e11	−0.719869
$357$	0	0
$358$	−4.65485e11	−1.49773
$359$	2.04791e11	0.650707	0.325354	−	0.945592i	$-0.394517\pi$
$359$	2.04791e11	0.650707	0.325354	+	0.945592i	$0.394517\pi$
$360$	1.07202e9	0.00336388
$361$	1.00627e11	0.311839
$362$	−9.27507e10	−0.283876
$363$	−3.24860e10	−0.0982012
$364$	3.85053e11	1.14965
$365$	1.19813e10	0.0353336
$366$	−7.93335e11	−2.31096
$367$	−3.19895e11	−0.920472	−0.460236	−	0.887797i	$-0.652235\pi$
$367$	−3.19895e11	−0.920472	−0.460236	+	0.887797i	$0.652235\pi$
$368$	1.56488e11	0.444800
$369$	−9.58857e7	−0.000269237 0
$370$	−2.77904e11	−0.770881
$371$	−1.55650e11	−0.426547
$372$	−2.75897e11	−0.746970
$373$	−1.73495e11	−0.464084	−0.232042	−	0.972706i	$-0.574541\pi$
$373$	−1.73495e11	−0.464084	−0.232042	+	0.972706i	$0.574541\pi$
$374$	0	0
$375$	4.34941e11	1.13577
$376$	−6.75378e9	−0.0174262
$377$	2.68498e11	0.684549
$378$	7.09610e11	1.78775
$379$	−1.34082e11	−0.333807	−0.166903	−	0.985973i	$-0.553377\pi$
$379$	−1.34082e11	−0.333807	−0.166903	+	0.985973i	$0.553377\pi$
$380$	−4.61693e11	−1.13587
$381$	−3.94368e11	−0.958824
$382$	−5.33711e11	−1.28239
$383$	−5.78666e11	−1.37415	−0.687074	−	0.726588i	$-0.741105\pi$
$383$	−5.78666e11	−1.37415	−0.687074	+	0.726588i	$0.741105\pi$
$384$	1.12337e10	0.0263652
$385$	−7.05674e11	−1.63693
$386$	3.21092e11	0.736185
$387$	1.85565e11	0.420530
$388$	−5.17499e11	−1.15922
$389$	3.40387e11	0.753702	0.376851	−	0.926274i	$-0.377007\pi$
$389$	3.40387e11	0.753702	0.376851	+	0.926274i	$0.377007\pi$
$390$	−5.40442e11	−1.18293
$391$	0	0
$392$	7.95886e9	0.0170241
$393$	−3.20912e11	−0.678610
$394$	−2.07169e11	−0.433103
$395$	−4.01452e11	−0.829748
$396$	1.46610e11	0.299596
$397$	−3.37985e11	−0.682874	−0.341437	−	0.939905i	$-0.610914\pi$
$397$	−3.37985e11	−0.682874	−0.341437	+	0.939905i	$0.610914\pi$
$398$	−1.49034e10	−0.0297723
$399$	−1.03426e12	−2.04292
$400$	6.32726e7	0.000123579 0
$401$	−6.78361e11	−1.31012	−0.655060	−	0.755577i	$-0.727357\pi$
$401$	−6.78361e11	−1.31012	−0.655060	+	0.755577i	$0.727357\pi$
$402$	−1.39568e12	−2.66544
$403$	−2.59180e11	−0.489474
$404$	−2.84553e11	−0.531431
$405$	−6.52835e11	−1.20575
$406$	−1.12548e12	−2.05576
$407$	3.15193e11	0.569380
$408$	0	0
$409$	3.79922e11	0.671336	0.335668	−	0.941980i	$-0.391038\pi$
$409$	3.79922e11	0.671336	0.335668	+	0.941980i	$0.391038\pi$
$410$	7.50139e8	0.00131103
$411$	−4.64530e11	−0.803018
$412$	−7.34895e10	−0.125657
$413$	−1.61791e12	−2.73640
$414$	1.07863e11	0.180456
$415$	−5.19570e11	−0.859860
$416$	−6.36228e11	−1.04158
$417$	−1.19961e12	−1.94280
$418$	1.05163e12	1.68488
$419$	6.30348e11	0.999118	0.499559	−	0.866280i	$-0.333495\pi$
$419$	6.30348e11	0.999118	0.499559	+	0.866280i	$0.333495\pi$
$420$	1.12803e12	1.76888
$421$	3.36779e11	0.522488	0.261244	−	0.965273i	$-0.415867\pi$
$421$	3.36779e11	0.522488	0.261244	+	0.965273i	$0.415867\pi$
$422$	−3.39419e10	−0.0520990
$423$	−2.86481e11	−0.435075
$424$	2.09805e9	0.00315261
$425$	0	0
$426$	−1.38523e12	−2.03788
$427$	1.55555e12	2.26443
$428$	−9.70680e11	−1.39823
$429$	6.12959e11	0.873723
$430$	−1.45172e12	−2.04775
$431$	2.07449e11	0.289576	0.144788	−	0.989463i	$-0.453750\pi$
$431$	2.07449e11	0.289576	0.144788	+	0.989463i	$0.453750\pi$
$432$	−5.88630e11	−0.813140
$433$	6.52648e11	0.892243	0.446122	−	0.894972i	$-0.352805\pi$
$433$	6.52648e11	0.892243	0.446122	+	0.894972i	$0.352805\pi$
$434$	1.08643e12	1.46993
$435$	7.86575e11	1.05327
$436$	1.23092e12	1.63132
$437$	3.85250e11	0.505332
$438$	4.36245e10	0.0566366
$439$	5.99383e11	0.770218	0.385109	−	0.922871i	$-0.374164\pi$
$439$	5.99383e11	0.770218	0.385109	+	0.922871i	$0.374164\pi$
$440$	9.51199e9	0.0120986
$441$	3.37597e11	0.425036
$442$	0	0
$443$	1.38710e11	0.171117	0.0855583	−	0.996333i	$-0.472733\pi$
$443$	1.38710e11	0.171117	0.0855583	+	0.996333i	$0.472733\pi$
$444$	−5.03841e11	−0.615276
$445$	−6.00390e11	−0.725794
$446$	1.53139e12	1.83265
$447$	1.28756e12	1.52540
$448$	1.31694e12	1.54460
$449$	−1.78071e11	−0.206769	−0.103385	−	0.994641i	$-0.532967\pi$
$449$	−1.78071e11	−0.206769	−0.103385	+	0.994641i	$0.532967\pi$
$450$	4.36122e7	5.01362e−5 0
$451$	−8.50792e8	−0.000968343 0
$452$	−5.82240e11	−0.656114
$453$	5.08401e11	0.567237
$454$	6.72199e11	0.742586
$455$	1.05968e12	1.15911
$456$	1.39411e10	0.0150993
$457$	−1.62766e11	−0.174558	−0.0872790	−	0.996184i	$-0.527817\pi$
$457$	−1.62766e11	−0.174558	−0.0872790	+	0.996184i	$0.527817\pi$
$458$	5.13189e11	0.544983
$459$	0	0
$460$	−4.20178e11	−0.437545
$461$	−1.43453e12	−1.47930	−0.739648	−	0.672994i	$-0.765008\pi$
$461$	−1.43453e12	−1.47930	−0.739648	+	0.672994i	$0.765008\pi$
$462$	−2.56939e12	−2.62386
$463$	8.05823e11	0.814939	0.407470	−	0.913219i	$-0.366411\pi$
$463$	8.05823e11	0.814939	0.407470	+	0.913219i	$0.366411\pi$
$464$	9.33601e11	0.935040
$465$	−7.59280e11	−0.753119
$466$	1.94235e12	1.90806
$467$	9.22766e11	0.897771	0.448886	−	0.893589i	$-0.351821\pi$
$467$	9.22766e11	0.897771	0.448886	+	0.893589i	$0.351821\pi$
$468$	−2.20159e11	−0.212144
$469$	2.73661e12	2.61177
$470$	2.24121e12	2.11857
$471$	3.45688e11	0.323661
$472$	2.18083e10	0.0202247
$473$	1.64652e12	1.51248
$474$	−1.46170e12	−1.33001
$475$	1.55768e8	0.000140397 0
$476$	0	0
$477$	8.89948e10	0.0787104
$478$	−1.49059e12	−1.30597
$479$	4.10737e11	0.356496	0.178248	−	0.983986i	$-0.442957\pi$
$479$	4.10737e11	0.356496	0.178248	+	0.983986i	$0.442957\pi$
$480$	−1.86386e12	−1.60261
$481$	−4.73313e11	−0.403177
$482$	−3.14190e11	−0.265143
$483$	−9.41262e11	−0.786953
$484$	1.03531e11	0.0857565
$485$	−1.42418e12	−1.16876
$486$	−9.77023e11	−0.794405
$487$	7.30098e11	0.588167	0.294083	−	0.955780i	$-0.404986\pi$
$487$	7.30098e11	0.588167	0.294083	+	0.955780i	$0.404986\pi$
$488$	−2.09677e10	−0.0167364
$489$	2.56900e12	2.03177
$490$	−2.64111e12	−2.06969
$491$	2.19308e12	1.70289	0.851446	−	0.524442i	$-0.175726\pi$
$491$	2.19308e12	1.70289	0.851446	+	0.524442i	$0.175726\pi$
$492$	1.36000e9	0.00104640
$493$	0	0
$494$	−1.57919e12	−1.19306
$495$	4.03478e11	0.302062
$496$	−9.01204e11	−0.668583
$497$	2.71612e12	1.99685
$498$	−1.89178e12	−1.37828
$499$	2.10713e12	1.52138	0.760691	−	0.649115i	$-0.224860\pi$
$499$	2.10713e12	1.52138	0.760691	+	0.649115i	$0.224860\pi$
$500$	−1.38613e12	−0.991836
$501$	1.77171e12	1.25638
$502$	−1.82526e12	−1.28280
$503$	−2.92024e11	−0.203406	−0.101703	−	0.994815i	$-0.532429\pi$
$503$	−2.92024e11	−0.203406	−0.101703	+	0.994815i	$0.532429\pi$
$504$	−7.65338e9	−0.00528343
$505$	−7.83102e11	−0.535806
$506$	9.57067e11	0.649030
$507$	7.69202e11	0.517016
$508$	1.25683e12	0.837316
$509$	−3.27240e11	−0.216091	−0.108045	−	0.994146i	$-0.534459\pi$
$509$	−3.27240e11	−0.216091	−0.108045	+	0.994146i	$0.534459\pi$
$510$	0	0
$511$	−8.55376e10	−0.0554962
$512$	−2.19405e12	−1.41102
$513$	−1.44912e12	−0.923799
$514$	−2.74590e12	−1.73521
$515$	−2.02246e11	−0.126692
$516$	−2.63198e12	−1.63440
$517$	−2.54194e12	−1.56480
$518$	1.98402e12	1.21077
$519$	2.37179e12	1.43491
$520$	−1.42838e10	−0.00856698
$521$	4.58716e11	0.272756	0.136378	−	0.990657i	$-0.456454\pi$
$521$	4.58716e11	0.272756	0.136378	+	0.990657i	$0.456454\pi$
$522$	6.43508e11	0.379347
$523$	2.19925e11	0.128534	0.0642669	−	0.997933i	$-0.479529\pi$
$523$	2.19925e11	0.128534	0.0642669	+	0.997933i	$0.479529\pi$
$524$	1.02273e12	0.592612
$525$	−3.80580e8	−0.000218640 0
$526$	−8.34954e11	−0.475583
$527$	0	0
$528$	2.13134e12	1.19344
$529$	−1.45054e12	−0.805342
$530$	−6.96230e11	−0.383276
$531$	9.25060e11	0.504946
$532$	3.29613e12	1.78403
$533$	1.27760e9	0.000685682 0
$534$	−2.18604e12	−1.16338
$535$	−2.67135e12	−1.40974
$536$	−3.68876e10	−0.0193036
$537$	−2.32252e12	−1.20524
$538$	−6.85812e11	−0.352927
$539$	2.99550e12	1.52869
$540$	1.58050e12	0.799878
$541$	1.58562e12	0.795815	0.397907	−	0.917426i	$-0.369737\pi$
$541$	1.58562e12	0.795815	0.397907	+	0.917426i	$0.369737\pi$
$542$	−5.14910e12	−2.56292
$543$	−4.62776e11	−0.228440
$544$	0	0
$545$	3.38754e12	1.64475
$546$	3.85835e12	1.85795
$547$	3.66475e12	1.75025	0.875127	−	0.483893i	$-0.160778\pi$
$547$	3.66475e12	1.75025	0.875127	+	0.483893i	$0.160778\pi$
$548$	1.48043e12	0.701255
$549$	−8.89403e11	−0.417853
$550$	3.86971e8	0.000180321 0
$551$	2.29839e12	1.06229
$552$	1.26875e10	0.00581637
$553$	2.86606e12	1.30323
$554$	−1.51641e12	−0.683948
$555$	−1.38659e12	−0.620340
$556$	3.82309e12	1.69659
$557$	−1.44850e12	−0.637632	−0.318816	−	0.947817i	$-0.603285\pi$
$557$	−1.44850e12	−0.637632	−0.318816	+	0.947817i	$0.603285\pi$
$558$	−6.21177e11	−0.271245
$559$	−2.47251e12	−1.07099
$560$	3.68466e12	1.58326
$561$	0	0
$562$	−8.70470e10	−0.0368079
$563$	3.44734e12	1.44609	0.723046	−	0.690800i	$-0.242742\pi$
$563$	3.44734e12	1.44609	0.723046	+	0.690800i	$0.242742\pi$
$564$	4.06332e12	1.69093
$565$	−1.60235e12	−0.661514
$566$	1.35680e12	0.555702
$567$	4.66075e12	1.89379
$568$	−3.66114e10	−0.0147587
$569$	−2.93321e12	−1.17311	−0.586554	−	0.809910i	$-0.699516\pi$
$569$	−2.93321e12	−1.17311	−0.586554	+	0.809910i	$0.699516\pi$
$570$	−4.62630e12	−1.83568
$571$	4.85517e12	1.91136	0.955678	−	0.294414i	$-0.0951243\pi$
$571$	4.85517e12	1.91136	0.955678	+	0.294414i	$0.0951243\pi$
$572$	−1.95347e12	−0.762999
$573$	−2.66293e12	−1.03196
$574$	−5.35542e9	−0.00205916
$575$	1.41762e8	5.40821e−5 0
$576$	−7.52978e11	−0.285024
$577$	−3.14368e12	−1.18072	−0.590360	−	0.807140i	$-0.701014\pi$
$577$	−3.14368e12	−1.18072	−0.590360	+	0.807140i	$0.701014\pi$
$578$	0	0
$579$	1.60208e12	0.592420
$580$	−2.50677e12	−0.919790
$581$	3.70934e12	1.35053
$582$	−5.18549e12	−1.87343
$583$	7.89650e11	0.283091
$584$	1.15299e9	0.000410172 0
$585$	−6.05887e11	−0.213890
$586$	−2.21505e11	−0.0775969
$587$	5.29849e11	0.184196	0.0920981	−	0.995750i	$-0.470643\pi$
$587$	5.29849e11	0.184196	0.0920981	+	0.995750i	$0.470643\pi$
$588$	−4.78834e12	−1.65191
$589$	−2.21864e12	−0.759569
$590$	−7.23699e12	−2.45880
$591$	−1.03366e12	−0.348525
$592$	−1.64577e12	−0.550709
$593$	1.85102e12	0.614702	0.307351	−	0.951596i	$-0.400557\pi$
$593$	1.85102e12	0.614702	0.307351	+	0.951596i	$0.400557\pi$
$594$	−3.60002e12	−1.18649
$595$	0	0
$596$	−4.10338e12	−1.33209
$597$	−7.43601e10	−0.0239583
$598$	−1.43719e12	−0.459578
$599$	9.54735e11	0.303014	0.151507	−	0.988456i	$-0.451587\pi$
$599$	9.54735e11	0.303014	0.151507	+	0.988456i	$0.451587\pi$
$600$	5.12995e6	1.61597e−6 0
$601$	−5.29994e12	−1.65705	−0.828526	−	0.559951i	$-0.810820\pi$
$601$	−5.29994e12	−1.65705	−0.828526	+	0.559951i	$0.810820\pi$
$602$	1.03642e13	3.21626
$603$	−1.56469e12	−0.481948
$604$	−1.62025e12	−0.495353
$605$	2.84922e11	0.0864623
$606$	−2.85131e12	−0.858849
$607$	2.76852e12	0.827748	0.413874	−	0.910334i	$-0.364175\pi$
$607$	2.76852e12	0.827748	0.413874	+	0.910334i	$0.364175\pi$
$608$	−5.44624e12	−1.61633
$609$	−5.61555e12	−1.65430
$610$	6.95803e12	2.03471
$611$	3.81713e12	1.10803
$612$	0	0
$613$	6.26290e11	0.179144	0.0895722	−	0.995980i	$-0.471450\pi$
$613$	6.26290e11	0.179144	0.0895722	+	0.995980i	$0.471450\pi$
$614$	−5.25030e11	−0.149082
$615$	3.74279e9	0.00105501
$616$	−6.79083e10	−0.0190025
$617$	−3.77388e12	−1.04835	−0.524173	−	0.851612i	$-0.675625\pi$
$617$	−3.77388e12	−1.04835	−0.524173	+	0.851612i	$0.675625\pi$
$618$	−7.36387e11	−0.203076
$619$	−1.48879e12	−0.407592	−0.203796	−	0.979013i	$-0.565328\pi$
$619$	−1.48879e12	−0.407592	−0.203796	+	0.979013i	$0.565328\pi$
$620$	2.41978e12	0.657679
$621$	−1.31882e12	−0.355855
$622$	3.91115e12	1.04773
$623$	4.28633e12	1.13996
$624$	−3.20055e12	−0.845072
$625$	−3.81423e12	−0.999877
$626$	7.55220e12	1.96557
$627$	5.24705e12	1.35585
$628$	−1.10169e12	−0.282644
$629$	0	0
$630$	2.53974e12	0.642328
$631$	−8.19149e10	−0.0205698	−0.0102849	−	0.999947i	$-0.503274\pi$
$631$	−8.19149e10	−0.0205698	−0.0102849	+	0.999947i	$0.503274\pi$
$632$	−3.86324e10	−0.00963219
$633$	−1.69352e11	−0.0419249
$634$	−1.38469e12	−0.340368
$635$	3.45885e12	0.844208
$636$	−1.26227e12	−0.305910
$637$	−4.49822e12	−1.08246
$638$	5.70984e12	1.36437
$639$	−1.55298e12	−0.368477
$640$	−9.85260e10	−0.0232135
$641$	8.71629e11	0.203925	0.101962	−	0.994788i	$-0.467488\pi$
$641$	8.71629e11	0.203925	0.101962	+	0.994788i	$0.467488\pi$
$642$	−9.72650e12	−2.25969
$643$	7.01475e11	0.161831	0.0809157	−	0.996721i	$-0.474216\pi$
$643$	7.01475e11	0.161831	0.0809157	+	0.996721i	$0.474216\pi$
$644$	2.99975e12	0.687225
$645$	−7.24332e12	−1.64785
$646$	0	0
$647$	−6.30742e12	−1.41509	−0.707543	−	0.706671i	$-0.750196\pi$
$647$	−6.30742e12	−1.41509	−0.707543	+	0.706671i	$0.750196\pi$
$648$	−6.28236e10	−0.0139970
$649$	8.20805e12	1.81610
$650$	−5.81098e8	−0.000127685 0
$651$	5.42068e12	1.18288
$652$	−8.18726e12	−1.77429
$653$	−2.08016e12	−0.447701	−0.223850	−	0.974624i	$-0.571863\pi$
$653$	−2.08016e12	−0.447701	−0.223850	+	0.974624i	$0.571863\pi$
$654$	1.23342e13	2.63639
$655$	2.81460e12	0.597490
$656$	4.44239e9	0.000936589 0
$657$	4.89072e10	0.0102407
$658$	−1.60006e13	−3.32751
$659$	−1.77225e12	−0.366051	−0.183025	−	0.983108i	$-0.558589\pi$
$659$	−1.77225e12	−0.366051	−0.183025	+	0.983108i	$0.558589\pi$
$660$	−5.72276e12	−1.17397
$661$	−1.32844e12	−0.270666	−0.135333	−	0.990800i	$-0.543210\pi$
$661$	−1.32844e12	−0.270666	−0.135333	+	0.990800i	$0.543210\pi$
$662$	5.42849e12	1.09855
$663$	0	0
$664$	−4.99992e10	−0.00998175
$665$	9.07111e12	1.79872
$666$	−1.13439e12	−0.223423
$667$	2.09173e12	0.409203
$668$	−5.64634e12	−1.09717
$669$	7.64081e12	1.47476
$670$	1.22410e13	2.34682
$671$	−7.89166e12	−1.50286
$672$	1.33065e13	2.51711
$673$	−7.10413e12	−1.33488	−0.667441	−	0.744662i	$-0.732611\pi$
$673$	−7.10413e12	−1.33488	−0.667441	+	0.744662i	$0.732611\pi$
$674$	3.27761e11	0.0611769
$675$	−5.33238e8	−9.88677e−5 0
$676$	−2.45140e12	−0.451497
$677$	1.12958e11	0.0206665	0.0103333	−	0.999947i	$-0.496711\pi$
$677$	1.12958e11	0.0206665	0.0103333	+	0.999947i	$0.496711\pi$
$678$	−5.83422e12	−1.06035
$679$	1.01676e13	1.83570
$680$	0	0
$681$	3.35391e12	0.597571
$682$	−5.51170e12	−0.975564
$683$	−3.35112e12	−0.589246	−0.294623	−	0.955614i	$-0.595194\pi$
$683$	−3.35112e12	−0.589246	−0.294623	+	0.955614i	$0.595194\pi$
$684$	−1.88460e12	−0.329206
$685$	4.07421e12	0.707027
$686$	5.99889e12	1.03422
$687$	2.56054e12	0.438557
$688$	−8.59723e12	−1.46289
$689$	−1.18579e12	−0.200456
$690$	−4.21031e12	−0.707120
$691$	−7.54720e12	−1.25932	−0.629658	−	0.776873i	$-0.716805\pi$
$691$	−7.54720e12	−1.25932	−0.629658	+	0.776873i	$0.716805\pi$
$692$	−7.55877e12	−1.25307
$693$	−2.88052e12	−0.474430
$694$	4.80351e12	0.786034
$695$	1.05213e13	1.71056
$696$	7.56936e10	0.0122269
$697$	0	0
$698$	−1.40013e13	−2.23264
$699$	9.69130e12	1.53545
$700$	1.21289e9	0.000190932 0
$701$	1.61959e12	0.253323	0.126662	−	0.991946i	$-0.459574\pi$
$701$	1.61959e12	0.253323	0.126662	+	0.991946i	$0.459574\pi$
$702$	5.40601e12	0.840155
$703$	−4.05166e12	−0.625654
$704$	−6.68117e12	−1.02512
$705$	1.11824e13	1.70485
$706$	−1.06170e12	−0.160835
$707$	5.59075e12	0.841556
$708$	−1.31207e13	−1.96249
$709$	1.71850e12	0.255413	0.127706	−	0.991812i	$-0.459239\pi$
$709$	1.71850e12	0.255413	0.127706	+	0.991812i	$0.459239\pi$
$710$	1.21493e13	1.79428
$711$	−1.63870e12	−0.240485
$712$	−5.77767e10	−0.00842544
$713$	−2.01914e12	−0.292593
$714$	0	0
$715$	−5.37602e12	−0.769279
$716$	7.40174e12	1.05251
$717$	−7.43723e12	−1.05093
$718$	−6.53982e12	−0.918345
$719$	1.34411e13	1.87566	0.937832	−	0.347089i	$-0.112830\pi$
$719$	1.34411e13	1.87566	0.937832	+	0.347089i	$0.112830\pi$
$720$	−2.10675e12	−0.292157
$721$	1.44388e12	0.198987
$722$	−3.21342e12	−0.440099
$723$	−1.56764e12	−0.213365
$724$	1.47484e12	0.199490
$725$	8.45747e8	0.000113689 0
$726$	1.03741e12	0.138592
$727$	1.27527e13	1.69316	0.846579	−	0.532263i	$-0.178658\pi$
$727$	1.27527e13	1.69316	0.846579	+	0.532263i	$0.178658\pi$
$728$	1.01975e11	0.0134556
$729$	4.32028e12	0.566550
$730$	−3.82614e11	−0.0498663
$731$	0	0
$732$	1.26149e13	1.62400
$733$	1.14507e13	1.46509	0.732547	−	0.680717i	$-0.238332\pi$
$733$	1.14507e13	1.46509	0.732547	+	0.680717i	$0.238332\pi$
$734$	1.02156e13	1.29906
$735$	−1.31777e13	−1.66551
$736$	−4.95653e12	−0.622626
$737$	−1.38835e13	−1.73338
$738$	3.06203e9	0.000379975 0
$739$	1.27616e13	1.57400	0.787000	−	0.616953i	$-0.211633\pi$
$739$	1.27616e13	1.57400	0.787000	+	0.616953i	$0.211633\pi$
$740$	4.41899e12	0.541727
$741$	−7.87930e12	−0.960076
$742$	4.97055e12	0.601987
$743$	4.54322e12	0.546907	0.273454	−	0.961885i	$-0.411834\pi$
$743$	4.54322e12	0.546907	0.273454	+	0.961885i	$0.411834\pi$
$744$	−7.30669e10	−0.00874264
$745$	−1.12927e13	−1.34305
$746$	5.54041e12	0.654963
$747$	−2.12086e12	−0.249212
$748$	0	0
$749$	1.90714e13	2.21419
$750$	−1.38895e13	−1.60291
$751$	8.88851e12	1.01965	0.509823	−	0.860279i	$-0.329711\pi$
$751$	8.88851e12	1.01965	0.509823	+	0.860279i	$0.329711\pi$
$752$	1.32727e13	1.51348
$753$	−9.10707e12	−1.03229
$754$	−8.57424e12	−0.966105
$755$	−4.45899e12	−0.499430
$756$	−1.12836e13	−1.25632
$757$	6.29935e12	0.697211	0.348605	−	0.937270i	$-0.386655\pi$
$757$	6.29935e12	0.697211	0.348605	+	0.937270i	$0.386655\pi$
$758$	4.28180e12	0.471102
$759$	4.77525e12	0.522285
$760$	−1.22272e11	−0.0132943
$761$	2.40574e12	0.260026	0.130013	−	0.991512i	$-0.458498\pi$
$761$	2.40574e12	0.260026	0.130013	+	0.991512i	$0.458498\pi$
$762$	1.25938e13	1.35319
$763$	−2.41845e13	−2.58331
$764$	8.48660e12	0.901185
$765$	0	0
$766$	1.84792e13	1.93934
$767$	−1.23257e13	−1.28598
$768$	−1.11272e13	−1.15415
$769$	−1.51735e12	−0.156465	−0.0782326	−	0.996935i	$-0.524928\pi$
$769$	−1.51735e12	−0.156465	−0.0782326	+	0.996935i	$0.524928\pi$
$770$	2.25351e13	2.31021
$771$	−1.37006e13	−1.39635
$772$	−5.10573e12	−0.517345
$773$	1.39024e13	1.40050	0.700251	−	0.713897i	$-0.253072\pi$
$773$	1.39024e13	1.40050	0.700251	+	0.713897i	$0.253072\pi$
$774$	−5.92586e12	−0.593495
$775$	−8.16398e8	−8.12914e−5 0
$776$	−1.37051e11	−0.0135677
$777$	9.89921e12	0.974330
$778$	−1.08700e13	−1.06370
$779$	1.09365e10	0.00106405
$780$	8.59365e12	0.831289
$781$	−1.37795e13	−1.32527
$782$	0	0
$783$	−7.86805e12	−0.748065
$784$	−1.56409e13	−1.47856
$785$	−3.03189e12	−0.284971
$786$	1.02481e13	0.957723
$787$	−1.50319e13	−1.39678	−0.698391	−	0.715716i	$-0.746100\pi$
$787$	−1.50319e13	−1.39678	−0.698391	+	0.715716i	$0.746100\pi$
$788$	3.29422e12	0.304358
$789$	−4.16597e12	−0.382710
$790$	1.28200e13	1.17103
$791$	1.14396e13	1.03900
$792$	3.88274e10	0.00350651
$793$	1.18506e13	1.06417
$794$	1.07933e13	0.963741
$795$	−3.47381e12	−0.308428
$796$	2.36982e11	0.0209221
$797$	1.82924e13	1.60586	0.802930	−	0.596073i	$-0.203273\pi$
$797$	1.82924e13	1.60586	0.802930	+	0.596073i	$0.203273\pi$
$798$	3.30283e13	2.88319
$799$	0	0
$800$	−2.00407e9	−0.000172985 0
$801$	−2.45076e12	−0.210356
$802$	2.16629e13	1.84897
$803$	4.33953e11	0.0368317
$804$	2.21929e13	1.87311
$805$	8.25545e12	0.692882
$806$	8.27670e12	0.690796
$807$	−3.42183e12	−0.284006
$808$	−7.53594e10	−0.00621994
$809$	−6.91099e11	−0.0567246	−0.0283623	−	0.999598i	$-0.509029\pi$
$809$	−6.91099e11	−0.0567246	−0.0283623	+	0.999598i	$0.509029\pi$
$810$	2.08477e13	1.70167
$811$	1.42607e13	1.15757	0.578785	−	0.815480i	$-0.303527\pi$
$811$	1.42607e13	1.15757	0.578785	+	0.815480i	$0.303527\pi$
$812$	1.78964e13	1.44466
$813$	−2.56912e13	−2.06242
$814$	−1.00654e13	−0.803567
$815$	−2.25317e13	−1.78889
$816$	0	0
$817$	−2.11652e13	−1.66197
$818$	−1.21325e13	−0.947458
$819$	4.32557e12	0.335943
$820$	−1.19281e10	−0.000921313 0
$821$	−4.35431e12	−0.334484	−0.167242	−	0.985916i	$-0.553486\pi$
$821$	−4.35431e12	−0.334484	−0.167242	+	0.985916i	$0.553486\pi$
$822$	1.48344e13	1.13330
$823$	1.25808e13	0.955892	0.477946	−	0.878389i	$-0.341381\pi$
$823$	1.25808e13	0.955892	0.477946	+	0.878389i	$0.341381\pi$
$824$	−1.94625e10	−0.00147071
$825$	1.93077e9	0.000145107 0
$826$	5.16666e13	3.86189
$827$	1.63352e13	1.21437	0.607183	−	0.794562i	$-0.292300\pi$
$827$	1.63352e13	1.21437	0.607183	+	0.794562i	$0.292300\pi$
$828$	−1.71514e12	−0.126813
$829$	2.48744e13	1.82918	0.914591	−	0.404380i	$-0.132513\pi$
$829$	2.48744e13	1.82918	0.914591	+	0.404380i	$0.132513\pi$
$830$	1.65920e13	1.21352
$831$	−7.56607e12	−0.550384
$832$	1.00328e13	0.725887
$833$	0	0
$834$	3.83085e13	2.74187
$835$	−1.55390e13	−1.10620
$836$	−1.67221e13	−1.18403
$837$	7.59502e12	0.534890
$838$	−2.01296e13	−1.41006
$839$	−1.61316e13	−1.12396	−0.561978	−	0.827152i	$-0.689960\pi$
$839$	−1.61316e13	−1.12396	−0.561978	+	0.827152i	$0.689960\pi$
$840$	2.98741e11	0.0207032
$841$	−2.02796e12	−0.139791
$842$	−1.07548e13	−0.737388
$843$	−4.34318e11	−0.0296199
$844$	5.39714e11	0.0366119
$845$	−6.74637e12	−0.455213
$846$	9.14851e12	0.614022
$847$	−2.03413e12	−0.135801
$848$	−4.12313e12	−0.273808
$849$	6.76970e12	0.447182
$850$	0	0
$851$	−3.68734e12	−0.241007
$852$	2.20268e13	1.43210
$853$	−1.29304e10	−0.000836263 0	−0.000418132	−	1.00000i	$-0.500133\pi$
$853$	−1.29304e10	−0.000836263 0	−0.000418132		1.00000i	$0.500133\pi$
$854$	−4.96751e13	−3.19579
$855$	−5.18651e12	−0.331916
$856$	−2.57069e11	−0.0163651
$857$	−1.42717e12	−0.0903779	−0.0451889	−	0.998978i	$-0.514389\pi$
$857$	−1.42717e12	−0.0903779	−0.0451889	+	0.998978i	$0.514389\pi$
$858$	−1.95743e13	−1.23309
$859$	−9.05087e12	−0.567180	−0.283590	−	0.958946i	$-0.591526\pi$
$859$	−9.05087e12	−0.567180	−0.283590	+	0.958946i	$0.591526\pi$
$860$	2.30840e13	1.43903
$861$	−2.67207e10	−0.00165704
$862$	−6.62469e12	−0.408680
$863$	1.02844e13	0.631148	0.315574	−	0.948901i	$-0.397803\pi$
$863$	1.02844e13	0.631148	0.315574	+	0.948901i	$0.397803\pi$
$864$	1.86440e13	1.13822
$865$	−2.08021e13	−1.26338
$866$	−2.08417e13	−1.25923
$867$	0	0
$868$	−1.72754e13	−1.03297
$869$	−1.45402e13	−0.864931
$870$	−2.51186e13	−1.48648
$871$	2.08483e13	1.22741
$872$	3.25989e11	0.0190932
$873$	−5.81342e12	−0.338741
$874$	−1.23026e13	−0.713176
$875$	2.72340e13	1.57064
$876$	−6.93679e11	−0.0398006
$877$	6.79965e12	0.388140	0.194070	−	0.980988i	$-0.437831\pi$
$877$	6.79965e12	0.388140	0.194070	+	0.980988i	$0.437831\pi$
$878$	−1.91408e13	−1.08701
$879$	−1.10519e12	−0.0624435
$880$	−1.86931e13	−1.05078
$881$	−3.08404e13	−1.72476	−0.862380	−	0.506262i	$-0.831027\pi$
$881$	−3.08404e13	−1.72476	−0.862380	+	0.506262i	$0.831027\pi$
$882$	−1.07809e13	−0.599854
$883$	3.17104e13	1.75541	0.877706	−	0.479200i	$-0.159073\pi$
$883$	3.17104e13	1.75541	0.877706	+	0.479200i	$0.159073\pi$
$884$	0	0
$885$	−3.61087e13	−1.97864
$886$	−4.42960e12	−0.241497
$887$	6.89150e12	0.373816	0.186908	−	0.982377i	$-0.440153\pi$
$887$	6.89150e12	0.373816	0.186908	+	0.982377i	$0.440153\pi$
$888$	−1.33434e11	−0.00720127
$889$	−2.46935e13	−1.32594
$890$	1.91729e13	1.02432
$891$	−2.36451e13	−1.25687
$892$	−2.43508e13	−1.28787
$893$	3.26754e13	1.71945
$894$	−4.11171e13	−2.15280
$895$	2.03699e13	1.06117
$896$	7.03401e11	0.0364600
$897$	−7.17080e12	−0.369830
$898$	5.68656e12	0.291814
$899$	−1.20461e13	−0.615077
$900$	−6.93484e8	−3.52326e−5 0
$901$	0	0
$902$	2.71693e10	0.00136662
$903$	5.17118e13	2.58818
$904$	−1.54197e11	−0.00767924
$905$	4.05883e12	0.201132
$906$	−1.62353e13	−0.800543
$907$	−2.11844e13	−1.03940	−0.519700	−	0.854349i	$-0.673956\pi$
$907$	−2.11844e13	−1.03940	−0.519700	+	0.854349i	$0.673956\pi$
$908$	−1.06887e13	−0.521843
$909$	−3.19658e12	−0.155292
$910$	−3.38401e13	−1.63586
$911$	−3.86760e13	−1.86041	−0.930206	−	0.367039i	$-0.880372\pi$
$911$	−3.86760e13	−1.86041	−0.930206	+	0.367039i	$0.880372\pi$
$912$	−2.73973e13	−1.31139
$913$	−1.88183e13	−0.896319
$914$	5.19778e12	0.246354
$915$	3.47168e13	1.63736
$916$	−8.16029e12	−0.382980
$917$	−2.00941e13	−0.938439
$918$	0	0
$919$	3.05320e11	0.0141200	0.00706000	−	0.999975i	$-0.497753\pi$
$919$	3.05320e11	0.0141200	0.00706000	+	0.999975i	$0.497753\pi$
$920$	−1.11278e11	−0.00512109
$921$	−2.61962e12	−0.119969
$922$	4.58105e13	2.08774
$923$	2.06922e13	0.938423
$924$	4.08562e13	1.84388
$925$	−1.49090e9	−6.69593e−5 0
$926$	−2.57333e13	−1.15013
$927$	−8.25558e11	−0.0367188
$928$	−2.95705e13	−1.30886
$929$	−1.17442e13	−0.517313	−0.258656	−	0.965969i	$-0.583280\pi$
$929$	−1.17442e13	−0.517313	−0.258656	+	0.965969i	$0.583280\pi$
$930$	2.42469e13	1.06288
$931$	−3.85057e13	−1.67978
$932$	−3.08856e13	−1.34086
$933$	1.95145e13	0.843123
$934$	−2.94677e13	−1.26703
$935$	0	0
$936$	−5.83056e10	−0.00248296
$937$	−2.08580e13	−0.883983	−0.441991	−	0.897019i	$-0.645728\pi$
$937$	−2.08580e13	−0.883983	−0.441991	+	0.897019i	$0.645728\pi$
$938$	−8.73913e13	−3.68600
$939$	3.76814e13	1.58173
$940$	−3.56378e13	−1.48880
$941$	3.69821e13	1.53758	0.768791	−	0.639500i	$-0.220859\pi$
$941$	3.69821e13	1.53758	0.768791	+	0.639500i	$0.220859\pi$
$942$	−1.10392e13	−0.456783
$943$	9.95313e9	0.000409880 0
$944$	−4.28581e13	−1.75654
$945$	−3.10529e13	−1.26666
$946$	−5.25801e13	−2.13457
$947$	3.26913e13	1.32086	0.660432	−	0.750886i	$-0.270373\pi$
$947$	3.26913e13	1.32086	0.660432	+	0.750886i	$0.270373\pi$
$948$	2.32427e13	0.934650
$949$	−6.51650e11	−0.0260805
$950$	−4.97432e9	−0.000198143 0
$951$	−6.90883e12	−0.273900
$952$	0	0
$953$	−3.10457e13	−1.21922	−0.609612	−	0.792700i	$-0.708675\pi$
$953$	−3.10457e13	−1.21922	−0.609612	+	0.792700i	$0.708675\pi$
$954$	−2.84197e12	−0.111084
$955$	2.33555e13	0.908603
$956$	2.37020e13	0.917751
$957$	2.84890e13	1.09793
$958$	−1.31165e13	−0.503124
$959$	−2.90868e13	−1.11048
$960$	2.93916e13	1.11687
$961$	−1.48115e13	−0.560201
$962$	1.51149e13	0.569005
$963$	−1.09043e13	−0.408583
$964$	4.99597e12	0.186326
$965$	−1.40512e13	−0.521603
$966$	3.00584e13	1.11063
$967$	1.13694e13	0.418138	0.209069	−	0.977901i	$-0.432957\pi$
$967$	1.13694e13	0.418138	0.209069	+	0.977901i	$0.432957\pi$
$968$	2.74186e10	0.00100370
$969$	0	0
$970$	4.54799e13	1.64948
$971$	2.34437e13	0.846330	0.423165	−	0.906053i	$-0.360919\pi$
$971$	2.34437e13	0.846330	0.423165	+	0.906053i	$0.360919\pi$
$972$	1.55358e13	0.558258
$973$	−7.51141e13	−2.68667
$974$	−2.33150e13	−0.830082
$975$	−2.89937e9	−0.000102750 0
$976$	4.12061e13	1.45357
$977$	−8.22524e11	−0.0288817	−0.0144409	−	0.999896i	$-0.504597\pi$
$977$	−8.22524e11	−0.0288817	−0.0144409	+	0.999896i	$0.504597\pi$
$978$	−8.20388e13	−2.86744
$979$	−2.17456e13	−0.756569
$980$	4.19967e13	1.45445
$981$	1.38278e13	0.476696
$982$	−7.00340e13	−2.40330
$983$	−2.37832e12	−0.0812417	−0.0406209	−	0.999175i	$-0.512934\pi$
$983$	−2.37832e12	−0.0812417	−0.0406209	+	0.999175i	$0.512934\pi$
$984$	3.60175e8	1.22472e−5 0
$985$	9.06583e12	0.306863
$986$	0	0
$987$	−7.98342e13	−2.67770
$988$	2.51109e13	0.838408
$989$	−1.92620e13	−0.640205
$990$	−1.28847e13	−0.426301
$991$	4.31408e11	0.0142088	0.00710439	−	0.999975i	$-0.497739\pi$
$991$	4.31408e11	0.0142088	0.00710439	+	0.999975i	$0.497739\pi$
$992$	2.85444e13	0.935875
$993$	2.70852e13	0.884018
$994$	−8.67370e13	−2.81816
$995$	6.52184e11	0.0210943
$996$	3.00814e13	0.968569
$997$	3.60987e13	1.15708	0.578539	−	0.815655i	$-0.303623\pi$
$997$	3.60987e13	1.15708	0.578539	+	0.815655i	$0.303623\pi$
$998$	−6.72892e13	−2.14713
$999$	1.38700e13	0.440586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.9		52
17.11	odd	16		17.10.d.a.2.3	✓	52
17.14	odd	16		17.10.d.a.9.3	yes	52
17.16	even	2	inner	289.10.a.i.1.10		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.3	✓	52	17.11	odd	16
17.10.d.a.9.3	yes	52	17.14	odd	16
289.10.a.i.1.9		52	1.1	even	1	trivial
289.10.a.i.1.10		52	17.16	even	2	inner

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-31.9341 q^{2} -159.334 q^{3} +507.789 q^{4} +1397.46 q^{5} +5088.20 q^{6} -9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} +O(q^{10})\)	\(q-31.9341 q^{2} -159.334 q^{3} +507.789 q^{4} +1397.46 q^{5} +5088.20 q^{6} -9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} -44626.6 q^{10} +50614.6 q^{11} -80908.1 q^{12} -76005.9 q^{13} +318600. q^{14} -222662. q^{15} -264282. q^{16} -182163. q^{18} -650626. q^{19} +709613. q^{20} +1.58964e6 q^{21} -1.61633e6 q^{22} -592123. q^{23} -21427.2 q^{24} -239.413 q^{25} +2.42718e6 q^{26} +2.22728e6 q^{27} -5.06610e6 q^{28} -3.53259e6 q^{29} +7.11053e6 q^{30} +3.41000e6 q^{31} +8.37077e6 q^{32} -8.06462e6 q^{33} -1.39421e7 q^{35} +2.89660e6 q^{36} +6.22732e6 q^{37} +2.07772e7 q^{38} +1.21103e7 q^{39} +187930. q^{40} -16809.2 q^{41} -5.07638e7 q^{42} +3.25305e7 q^{43} +2.57015e7 q^{44} +7.97157e6 q^{45} +1.89089e7 q^{46} -5.02215e7 q^{47} +4.21092e7 q^{48} +5.91825e7 q^{49} +7645.44 q^{50} -3.85949e7 q^{52} +1.56012e7 q^{53} -7.11261e7 q^{54} +7.07317e7 q^{55} -1.34168e6 q^{56} +1.03667e8 q^{57} +1.12810e8 q^{58} +1.62168e8 q^{59} -1.13066e8 q^{60} -1.55917e8 q^{61} -1.08895e8 q^{62} -5.69110e7 q^{63} -1.32001e8 q^{64} -1.06215e8 q^{65} +2.57537e8 q^{66} -2.74298e8 q^{67} +9.43453e7 q^{69} +4.45229e8 q^{70} -2.72244e8 q^{71} +767119. q^{72} +8.57367e6 q^{73} -1.98864e8 q^{74} +38146.6 q^{75} -3.30381e8 q^{76} -5.04970e8 q^{77} -3.86733e8 q^{78} -2.87273e8 q^{79} -3.69323e8 q^{80} -4.67160e8 q^{81} +536788. q^{82} -3.71797e8 q^{83} +8.07202e8 q^{84} -1.03883e9 q^{86} +5.62862e8 q^{87} +6.80664e6 q^{88} -4.29631e8 q^{89} -2.54565e8 q^{90} +7.58294e8 q^{91} -3.00673e8 q^{92} -5.43330e8 q^{93} +1.60378e9 q^{94} -9.09222e8 q^{95} -1.33375e9 q^{96} -1.01912e9 q^{97} -1.88994e9 q^{98} +2.88723e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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