LMFDB - Embedded newform 105.10.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,10,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, 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("105.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	105.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:	$54.0787627972$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 988x^{2} - 844x + 192256 $ x^4 - x^3 - 988x^2 - 844x + 192256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$15.2587$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.08732 q^{2} -81.0000 q^{3} -446.595 q^{4} +625.000 q^{5} -655.073 q^{6} +2401.00 q^{7} -7752.47 q^{8} +6561.00 q^{9} +5054.57 q^{10} +30872.0 q^{11} +36174.2 q^{12} -166715. q^{13} +19417.7 q^{14} -50625.0 q^{15} +165960. q^{16} +201152. q^{17} +53060.9 q^{18} +1.00462e6 q^{19} -279122. q^{20} -194481. q^{21} +249672. q^{22} -915554. q^{23} +627950. q^{24} +390625. q^{25} -1.34828e6 q^{26} -531441. q^{27} -1.07228e6 q^{28} +3.99190e6 q^{29} -409421. q^{30} +3.23344e6 q^{31} +5.31144e6 q^{32} -2.50063e6 q^{33} +1.62678e6 q^{34} +1.50062e6 q^{35} -2.93011e6 q^{36} -1.89353e7 q^{37} +8.12470e6 q^{38} +1.35039e7 q^{39} -4.84529e6 q^{40} -3.41736e7 q^{41} -1.57283e6 q^{42} -2.75623e7 q^{43} -1.37873e7 q^{44} +4.10062e6 q^{45} -7.40438e6 q^{46} -2.71691e7 q^{47} -1.34428e7 q^{48} +5.76480e6 q^{49} +3.15911e6 q^{50} -1.62933e7 q^{51} +7.44542e7 q^{52} -3.86079e7 q^{53} -4.29793e6 q^{54} +1.92950e7 q^{55} -1.86137e7 q^{56} -8.13744e7 q^{57} +3.22838e7 q^{58} -1.34261e8 q^{59} +2.26089e7 q^{60} +4.51183e7 q^{61} +2.61499e7 q^{62} +1.57530e7 q^{63} -4.20163e7 q^{64} -1.04197e8 q^{65} -2.02234e7 q^{66} +4.21823e7 q^{67} -8.98335e7 q^{68} +7.41599e7 q^{69} +1.21360e7 q^{70} -2.86299e7 q^{71} -5.08639e7 q^{72} +2.85608e7 q^{73} -1.53136e8 q^{74} -3.16406e7 q^{75} -4.48659e8 q^{76} +7.41237e7 q^{77} +1.09211e8 q^{78} +3.50870e8 q^{79} +1.03725e8 q^{80} +4.30467e7 q^{81} -2.76373e8 q^{82} +1.96427e8 q^{83} +8.68543e7 q^{84} +1.25720e8 q^{85} -2.22905e8 q^{86} -3.23344e8 q^{87} -2.39334e8 q^{88} -9.91592e8 q^{89} +3.31631e7 q^{90} -4.00283e8 q^{91} +4.08882e8 q^{92} -2.61909e8 q^{93} -2.19725e8 q^{94} +6.27889e8 q^{95} -4.30226e8 q^{96} -1.03335e9 q^{97} +4.66218e7 q^{98} +2.02551e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) $ 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * 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 $

$2$	8.08732	0.357412	0.178706	−	0.983902i	$-0.442809\pi$
$2$	8.08732	0.357412	0.178706	+	0.983902i	$0.442809\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−446.595	−0.872256
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−655.073	−0.206352
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−7752.47	−0.669168
$9$	6561.00	0.333333
$10$	5054.57	0.159840
$11$	30872.0	0.635767	0.317883	−	0.948130i	$-0.397028\pi$
$11$	30872.0	0.635767	0.317883	+	0.948130i	$0.397028\pi$
$12$	36174.2	0.503597
$13$	−166715.	−1.61894	−0.809469	−	0.587163i	$-0.800245\pi$
$13$	−166715.	−1.61894	−0.809469	+	0.587163i	$0.800245\pi$
$14$	19417.7	0.135089
$15$	−50625.0	−0.258199
$16$	165960.	0.633088
$17$	201152.	0.584122	0.292061	−	0.956400i	$-0.405659\pi$
$17$	201152.	0.584122	0.292061	+	0.956400i	$0.405659\pi$
$18$	53060.9	0.119137
$19$	1.00462e6	1.76853	0.884263	−	0.466990i	$-0.154661\pi$
$19$	1.00462e6	1.76853	0.884263	+	0.466990i	$0.154661\pi$
$20$	−279122.	−0.390085
$21$	−194481.	−0.218218
$22$	249672.	0.227231
$23$	−915554.	−0.682195	−0.341098	−	0.940028i	$-0.610799\pi$
$23$	−915554.	−0.682195	−0.341098	+	0.940028i	$0.610799\pi$
$24$	627950.	0.386344
$25$	390625.	0.200000
$26$	−1.34828e6	−0.578628
$27$	−531441.	−0.192450
$28$	−1.07228e6	−0.329682
$29$	3.99190e6	1.04807	0.524034	−	0.851698i	$-0.324427\pi$
$29$	3.99190e6	1.04807	0.524034	+	0.851698i	$0.324427\pi$
$30$	−409421.	−0.0922835
$31$	3.23344e6	0.628836	0.314418	−	0.949285i	$-0.398191\pi$
$31$	3.23344e6	0.628836	0.314418	+	0.949285i	$0.398191\pi$
$32$	5.31144e6	0.895441
$33$	−2.50063e6	−0.367060
$34$	1.62678e6	0.208773
$35$	1.50062e6	0.169031
$36$	−2.93011e6	−0.290752
$37$	−1.89353e7	−1.66098	−0.830490	−	0.557033i	$-0.811940\pi$
$37$	−1.89353e7	−1.66098	−0.830490	+	0.557033i	$0.811940\pi$
$38$	8.12470e6	0.632093
$39$	1.35039e7	0.934694
$40$	−4.84529e6	−0.299261
$41$	−3.41736e7	−1.88870	−0.944351	−	0.328940i	$-0.893309\pi$
$41$	−3.41736e7	−1.88870	−0.944351	+	0.328940i	$0.893309\pi$
$42$	−1.57283e6	−0.0779938
$43$	−2.75623e7	−1.22944	−0.614721	−	0.788745i	$-0.710731\pi$
$43$	−2.75623e7	−1.22944	−0.614721	+	0.788745i	$0.710731\pi$
$44$	−1.37873e7	−0.554552
$45$	4.10062e6	0.149071
$46$	−7.40438e6	−0.243825
$47$	−2.71691e7	−0.812148	−0.406074	−	0.913840i	$-0.633103\pi$
$47$	−2.71691e7	−0.812148	−0.406074	+	0.913840i	$0.633103\pi$
$48$	−1.34428e7	−0.365513
$49$	5.76480e6	0.142857
$50$	3.15911e6	0.0714825
$51$	−1.62933e7	−0.337243
$52$	7.44542e7	1.41213
$53$	−3.86079e7	−0.672102	−0.336051	−	0.941844i	$-0.609091\pi$
$53$	−3.86079e7	−0.672102	−0.336051	+	0.941844i	$0.609091\pi$
$54$	−4.29793e6	−0.0687840
$55$	1.92950e7	0.284324
$56$	−1.86137e7	−0.252922
$57$	−8.13744e7	−1.02106
$58$	3.22838e7	0.374592
$59$	−1.34261e8	−1.44250	−0.721250	−	0.692675i	$-0.756432\pi$
$59$	−1.34261e8	−1.44250	−0.721250	+	0.692675i	$0.756432\pi$
$60$	2.26089e7	0.225216
$61$	4.51183e7	0.417223	0.208612	−	0.977999i	$-0.433106\pi$
$61$	4.51183e7	0.417223	0.208612	+	0.977999i	$0.433106\pi$
$62$	2.61499e7	0.224754
$63$	1.57530e7	0.125988
$64$	−4.20163e7	−0.313046
$65$	−1.04197e8	−0.724011
$66$	−2.02234e7	−0.131192
$67$	4.21823e7	0.255737	0.127868	−	0.991791i	$-0.459186\pi$
$67$	4.21823e7	0.255737	0.127868	+	0.991791i	$0.459186\pi$
$68$	−8.98335e7	−0.509504
$69$	7.41599e7	0.393866
$70$	1.21360e7	0.0604137
$71$	−2.86299e7	−0.133708	−0.0668539	−	0.997763i	$-0.521296\pi$
$71$	−2.86299e7	−0.133708	−0.0668539	+	0.997763i	$0.521296\pi$
$72$	−5.08639e7	−0.223056
$73$	2.85608e7	0.117711	0.0588556	−	0.998267i	$-0.481255\pi$
$73$	2.85608e7	0.117711	0.0588556	+	0.998267i	$0.481255\pi$
$74$	−1.53136e8	−0.593655
$75$	−3.16406e7	−0.115470
$76$	−4.48659e8	−1.54261
$77$	7.41237e7	0.240297
$78$	1.09211e8	0.334071
$79$	3.50870e8	1.01350	0.506751	−	0.862092i	$-0.330846\pi$
$79$	3.50870e8	1.01350	0.506751	+	0.862092i	$0.330846\pi$
$80$	1.03725e8	0.283125
$81$	4.30467e7	0.111111
$82$	−2.76373e8	−0.675045
$83$	1.96427e8	0.454306	0.227153	−	0.973859i	$-0.427058\pi$
$83$	1.96427e8	0.454306	0.227153	+	0.973859i	$0.427058\pi$
$84$	8.68543e7	0.190342
$85$	1.25720e8	0.261227
$86$	−2.22905e8	−0.439418
$87$	−3.23344e8	−0.605102
$88$	−2.39334e8	−0.425434
$89$	−9.91592e8	−1.67524	−0.837622	−	0.546250i	$-0.816055\pi$
$89$	−9.91592e8	−1.67524	−0.837622	+	0.546250i	$0.816055\pi$
$90$	3.31631e7	0.0532799
$91$	−4.00283e8	−0.611901
$92$	4.08882e8	0.595049
$93$	−2.61909e8	−0.363059
$94$	−2.19725e8	−0.290272
$95$	6.27889e8	0.790909
$96$	−4.30226e8	−0.516983
$97$	−1.03335e9	−1.18515	−0.592575	−	0.805515i	$-0.701889\pi$
$97$	−1.03335e9	−1.18515	−0.592575	+	0.805515i	$0.701889\pi$
$98$	4.66218e7	0.0510589
$99$	2.02551e8	0.211922
$100$	−1.74451e8	−0.174451
$101$	−1.43234e9	−1.36962	−0.684809	−	0.728723i	$-0.740114\pi$
$101$	−1.43234e9	−1.36962	−0.684809	+	0.728723i	$0.740114\pi$
$102$	−1.31769e8	−0.120535
$103$	2.74489e8	0.240302	0.120151	−	0.992756i	$-0.461662\pi$
$103$	2.74489e8	0.240302	0.120151	+	0.992756i	$0.461662\pi$
$104$	1.29245e9	1.08334
$105$	−1.21551e8	−0.0975900
$106$	−3.12235e8	−0.240218
$107$	−8.38858e8	−0.618674	−0.309337	−	0.950953i	$-0.600107\pi$
$107$	−8.38858e8	−0.618674	−0.309337	+	0.950953i	$0.600107\pi$
$108$	2.37339e8	0.167866
$109$	4.21471e8	0.285988	0.142994	−	0.989724i	$-0.454327\pi$
$109$	4.21471e8	0.285988	0.142994	+	0.989724i	$0.454327\pi$
$110$	1.56045e8	0.101621
$111$	1.53376e9	0.958968
$112$	3.98470e8	0.239285
$113$	1.88360e8	0.108677	0.0543384	−	0.998523i	$-0.482695\pi$
$113$	1.88360e8	0.108677	0.0543384	+	0.998523i	$0.482695\pi$
$114$	−6.58100e8	−0.364939
$115$	−5.72221e8	−0.305087
$116$	−1.78277e9	−0.914183
$117$	−1.09382e9	−0.539646
$118$	−1.08581e9	−0.515567
$119$	4.82966e8	0.220778
$120$	3.92469e8	0.172778
$121$	−1.40487e9	−0.595801
$122$	3.64886e8	0.149121
$123$	2.76806e9	1.09044
$124$	−1.44404e9	−0.548506
$125$	2.44141e8	0.0894427
$126$	1.27399e8	0.0450297
$127$	5.47639e8	0.186800	0.0934002	−	0.995629i	$-0.470226\pi$
$127$	5.47639e8	0.186800	0.0934002	+	0.995629i	$0.470226\pi$
$128$	−3.05925e9	−1.00733
$129$	2.23255e9	0.709819
$130$	−8.42675e8	−0.258771
$131$	5.05351e9	1.49924	0.749621	−	0.661867i	$-0.230236\pi$
$131$	5.05351e9	1.49924	0.749621	+	0.661867i	$0.230236\pi$
$132$	1.11677e9	0.320170
$133$	2.41210e9	0.668440
$134$	3.41142e8	0.0914035
$135$	−3.32151e8	−0.0860663
$136$	−1.55942e9	−0.390876
$137$	−7.09276e8	−0.172017	−0.0860087	−	0.996294i	$-0.527411\pi$
$137$	−7.09276e8	−0.172017	−0.0860087	+	0.996294i	$0.527411\pi$
$138$	5.99755e8	0.140772
$139$	−3.63040e9	−0.824874	−0.412437	−	0.910986i	$-0.635322\pi$
$139$	−3.63040e9	−0.824874	−0.412437	+	0.910986i	$0.635322\pi$
$140$	−6.70172e8	−0.147438
$141$	2.20070e9	0.468894
$142$	−2.31539e8	−0.0477888
$143$	−5.14683e9	−1.02927
$144$	1.08886e9	0.211029
$145$	2.49494e9	0.468710
$146$	2.30980e8	0.0420714
$147$	−4.66949e8	−0.0824786
$148$	8.45642e9	1.44880
$149$	7.02310e9	1.16732	0.583661	−	0.811997i	$-0.301620\pi$
$149$	7.02310e9	1.16732	0.583661	+	0.811997i	$0.301620\pi$
$150$	−2.55888e8	−0.0412704
$151$	−6.78483e9	−1.06204	−0.531022	−	0.847358i	$-0.678192\pi$
$151$	−6.78483e9	−1.06204	−0.531022	+	0.847358i	$0.678192\pi$
$152$	−7.78830e9	−1.18344
$153$	1.31976e9	0.194707
$154$	5.99462e8	0.0858852
$155$	2.02090e9	0.281224
$156$	−6.03079e9	−0.815293
$157$	3.30278e9	0.433841	0.216920	−	0.976189i	$-0.430399\pi$
$157$	3.30278e9	0.433841	0.216920	+	0.976189i	$0.430399\pi$
$158$	2.83760e9	0.362238
$159$	3.12724e9	0.388038
$160$	3.31965e9	0.400453
$161$	−2.19825e9	−0.257846
$162$	3.48133e8	0.0397125
$163$	−1.14249e10	−1.26768	−0.633840	−	0.773464i	$-0.718522\pi$
$163$	−1.14249e10	−1.26768	−0.633840	+	0.773464i	$0.718522\pi$
$164$	1.52618e10	1.64743
$165$	−1.56290e9	−0.164154
$166$	1.58856e9	0.162375
$167$	1.71120e10	1.70246	0.851229	−	0.524794i	$-0.175858\pi$
$167$	1.71120e10	1.70246	0.851229	+	0.524794i	$0.175858\pi$
$168$	1.50771e9	0.146024
$169$	1.71895e10	1.62096
$170$	1.01674e9	0.0933659
$171$	6.59132e9	0.589509
$172$	1.23092e10	1.07239
$173$	−1.26212e9	−0.107126	−0.0535628	−	0.998564i	$-0.517058\pi$
$173$	−1.26212e9	−0.107126	−0.0535628	+	0.998564i	$0.517058\pi$
$174$	−2.61499e9	−0.216271
$175$	9.37891e8	0.0755929
$176$	5.12352e9	0.402496
$177$	1.08751e10	0.832828
$178$	−8.01932e9	−0.598753
$179$	8.75642e9	0.637512	0.318756	−	0.947837i	$-0.396735\pi$
$179$	8.75642e9	0.637512	0.318756	+	0.947837i	$0.396735\pi$
$180$	−1.83132e9	−0.130028
$181$	9.63283e9	0.667115	0.333557	−	0.942730i	$-0.391751\pi$
$181$	9.63283e9	0.667115	0.333557	+	0.942730i	$0.391751\pi$
$182$	−3.23722e9	−0.218701
$183$	−3.65458e9	−0.240884
$184$	7.09780e9	0.456503
$185$	−1.18346e10	−0.742813
$186$	−2.11814e9	−0.129762
$187$	6.20996e9	0.371366
$188$	1.21336e10	0.708402
$189$	−1.27599e9	−0.0727393
$190$	5.07794e9	0.282681
$191$	1.12793e10	0.613244	0.306622	−	0.951831i	$-0.400801\pi$
$191$	1.12793e10	0.613244	0.306622	+	0.951831i	$0.400801\pi$
$192$	3.40332e9	0.180737
$193$	−1.64930e10	−0.855641	−0.427820	−	0.903864i	$-0.640718\pi$
$193$	−1.64930e10	−0.855641	−0.427820	+	0.903864i	$0.640718\pi$
$194$	−8.35700e9	−0.423587
$195$	8.43996e9	0.418008
$196$	−2.57453e9	−0.124608
$197$	−2.83993e10	−1.34341	−0.671706	−	0.740818i	$-0.734438\pi$
$197$	−2.83993e10	−1.34341	−0.671706	+	0.740818i	$0.734438\pi$
$198$	1.63810e9	0.0757436
$199$	−3.58092e10	−1.61866	−0.809331	−	0.587353i	$-0.800170\pi$
$199$	−3.58092e10	−1.61866	−0.809331	+	0.587353i	$0.800170\pi$
$200$	−3.02831e9	−0.133834
$201$	−3.41676e9	−0.147650
$202$	−1.15838e10	−0.489518
$203$	9.58456e9	0.396132
$204$	7.27651e9	0.294163
$205$	−2.13585e10	−0.844653
$206$	2.21988e9	0.0858870
$207$	−6.00695e9	−0.227398
$208$	−2.76681e10	−1.02493
$209$	3.10147e10	1.12437
$210$	−9.83019e8	−0.0348799
$211$	−5.10235e10	−1.77215	−0.886073	−	0.463547i	$-0.846577\pi$
$211$	−5.10235e10	−1.77215	−0.886073	+	0.463547i	$0.846577\pi$
$212$	1.72421e10	0.586245
$213$	2.31902e9	0.0771962
$214$	−6.78412e9	−0.221122
$215$	−1.72265e10	−0.549823
$216$	4.11998e9	0.128781
$217$	7.76349e9	0.237678
$218$	3.40857e9	0.102216
$219$	−2.31343e9	−0.0679606
$220$	−8.61706e9	−0.248003
$221$	−3.35351e10	−0.945658
$222$	1.24040e10	0.342747
$223$	3.95921e10	1.07210	0.536052	−	0.844185i	$-0.319915\pi$
$223$	3.95921e10	1.07210	0.536052	+	0.844185i	$0.319915\pi$
$224$	1.27528e10	0.338445
$225$	2.56289e9	0.0666667
$226$	1.52333e9	0.0388424
$227$	1.01342e10	0.253323	0.126662	−	0.991946i	$-0.459574\pi$
$227$	1.01342e10	0.253323	0.126662	+	0.991946i	$0.459574\pi$
$228$	3.63414e10	0.890625
$229$	−4.58102e10	−1.10078	−0.550392	−	0.834906i	$-0.685522\pi$
$229$	−4.58102e10	−1.10078	−0.550392	+	0.834906i	$0.685522\pi$
$230$	−4.62774e9	−0.109042
$231$	−6.00402e9	−0.138736
$232$	−3.09471e10	−0.701333
$233$	−9.29624e9	−0.206636	−0.103318	−	0.994648i	$-0.532946\pi$
$233$	−9.29624e9	−0.206636	−0.103318	+	0.994648i	$0.532946\pi$
$234$	−8.84606e9	−0.192876
$235$	−1.69807e10	−0.363204
$236$	5.99603e10	1.25823
$237$	−2.84205e10	−0.585146
$238$	3.90590e9	0.0789086
$239$	−9.60319e9	−0.190382	−0.0951908	−	0.995459i	$-0.530346\pi$
$239$	−9.60319e9	−0.190382	−0.0951908	+	0.995459i	$0.530346\pi$
$240$	−8.40173e9	−0.163463
$241$	9.03494e10	1.72524	0.862618	−	0.505856i	$-0.168823\pi$
$241$	9.03494e10	1.72524	0.862618	+	0.505856i	$0.168823\pi$
$242$	−1.13616e10	−0.212947
$243$	−3.48678e9	−0.0641500
$244$	−2.01496e10	−0.363926
$245$	3.60300e9	0.0638877
$246$	2.23862e10	0.389738
$247$	−1.67486e11	−2.86313
$248$	−2.50671e10	−0.420797
$249$	−1.59106e10	−0.262294
$250$	1.97444e9	0.0319679
$251$	−6.79439e10	−1.08049	−0.540243	−	0.841509i	$-0.681668\pi$
$251$	−6.79439e10	−1.08049	−0.540243	+	0.841509i	$0.681668\pi$
$252$	−7.03520e9	−0.109894
$253$	−2.82650e10	−0.433717
$254$	4.42894e9	0.0667648
$255$	−1.01833e10	−0.150820
$256$	−3.22882e9	−0.0469855
$257$	8.84842e10	1.26522	0.632611	−	0.774470i	$-0.281983\pi$
$257$	8.84842e10	1.26522	0.632611	+	0.774470i	$0.281983\pi$
$258$	1.80553e10	0.253698
$259$	−4.54637e10	−0.627792
$260$	4.65339e10	0.631523
$261$	2.61909e10	0.349356
$262$	4.08693e10	0.535848
$263$	−4.53152e10	−0.584041	−0.292020	−	0.956412i	$-0.594328\pi$
$263$	−4.53152e10	−0.584041	−0.292020	+	0.956412i	$0.594328\pi$
$264$	1.93861e10	0.245625
$265$	−2.41300e10	−0.300573
$266$	1.95074e10	0.238909
$267$	8.03190e10	0.967203
$268$	−1.88384e10	−0.223068
$269$	1.28110e11	1.49175	0.745875	−	0.666086i	$-0.232032\pi$
$269$	1.28110e11	1.49175	0.745875	+	0.666086i	$0.232032\pi$
$270$	−2.68621e9	−0.0307612
$271$	−9.78643e10	−1.10221	−0.551103	−	0.834438i	$-0.685793\pi$
$271$	−9.78643e10	−1.10221	−0.551103	+	0.834438i	$0.685793\pi$
$272$	3.33832e10	0.369801
$273$	3.24229e10	0.353281
$274$	−5.73614e9	−0.0614812
$275$	1.20594e10	0.127153
$276$	−3.31194e10	−0.343552
$277$	−1.74054e11	−1.77634	−0.888170	−	0.459514i	$-0.848024\pi$
$277$	−1.74054e11	−1.77634	−0.888170	+	0.459514i	$0.848024\pi$
$278$	−2.93602e10	−0.294820
$279$	2.12146e10	0.209612
$280$	−1.16335e10	−0.113110
$281$	−1.42337e11	−1.36188	−0.680942	−	0.732337i	$-0.738429\pi$
$281$	−1.42337e11	−1.36188	−0.680942	+	0.732337i	$0.738429\pi$
$282$	1.77978e10	0.167589
$283$	−7.64989e10	−0.708951	−0.354476	−	0.935065i	$-0.615341\pi$
$283$	−7.64989e10	−0.708951	−0.354476	+	0.935065i	$0.615341\pi$
$284$	1.27860e10	0.116627
$285$	−5.08590e10	−0.456631
$286$	−4.16241e10	−0.367873
$287$	−8.20508e10	−0.713862
$288$	3.48483e10	0.298480
$289$	−7.81258e10	−0.658801
$290$	2.01774e10	0.167523
$291$	8.37011e10	0.684246
$292$	−1.27551e10	−0.102674
$293$	4.93207e10	0.390953	0.195477	−	0.980708i	$-0.437375\pi$
$293$	4.93207e10	0.390953	0.195477	+	0.980708i	$0.437375\pi$
$294$	−3.77636e9	−0.0294789
$295$	−8.39131e10	−0.645105
$296$	1.46795e11	1.11147
$297$	−1.64066e10	−0.122353
$298$	5.67981e10	0.417216
$299$	1.52637e11	1.10443
$300$	1.41306e10	0.100719
$301$	−6.61772e10	−0.464685
$302$	−5.48711e10	−0.379588
$303$	1.16019e11	0.790749
$304$	1.66727e11	1.11963
$305$	2.81989e10	0.186588
$306$	1.06733e10	0.0695909
$307$	−7.32812e10	−0.470836	−0.235418	−	0.971894i	$-0.575646\pi$
$307$	−7.32812e10	−0.470836	−0.235418	+	0.971894i	$0.575646\pi$
$308$	−3.31033e10	−0.209601
$309$	−2.22336e10	−0.138739
$310$	1.63437e10	0.100513
$311$	−9.73556e10	−0.590119	−0.295059	−	0.955479i	$-0.595339\pi$
$311$	−9.73556e10	−0.590119	−0.295059	+	0.955479i	$0.595339\pi$
$312$	−1.04689e11	−0.625467
$313$	3.33884e11	1.96628	0.983141	−	0.182848i	$-0.0585317\pi$
$313$	3.33884e11	1.96628	0.983141	+	0.182848i	$0.0585317\pi$
$314$	2.67106e10	0.155060
$315$	9.84560e9	0.0563436
$316$	−1.56697e11	−0.884034
$317$	−1.74313e11	−0.969534	−0.484767	−	0.874643i	$-0.661096\pi$
$317$	−1.74313e11	−0.969534	−0.484767	+	0.874643i	$0.661096\pi$
$318$	2.52910e10	0.138690
$319$	1.23238e11	0.666326
$320$	−2.62602e10	−0.139998
$321$	6.79475e10	0.357191
$322$	−1.77779e10	−0.0921572
$323$	2.02082e11	1.03304
$324$	−1.92245e10	−0.0969174
$325$	−6.51231e10	−0.323788
$326$	−9.23972e10	−0.453085
$327$	−3.41392e10	−0.165116
$328$	2.64930e11	1.26386
$329$	−6.52331e10	−0.306963
$330$	−1.26396e10	−0.0586708
$331$	2.45584e10	0.112454	0.0562269	−	0.998418i	$-0.482093\pi$
$331$	2.45584e10	0.112454	0.0562269	+	0.998418i	$0.482093\pi$
$332$	−8.77232e10	−0.396272
$333$	−1.24235e11	−0.553660
$334$	1.38390e11	0.608480
$335$	2.63639e10	0.114369
$336$	−3.22761e10	−0.138151
$337$	3.54043e10	0.149528	0.0747639	−	0.997201i	$-0.476180\pi$
$337$	3.54043e10	0.149528	0.0747639	+	0.997201i	$0.476180\pi$
$338$	1.39017e11	0.579351
$339$	−1.52572e10	−0.0627445
$340$	−5.61459e10	−0.227857
$341$	9.98228e10	0.399793
$342$	5.33061e10	0.210698
$343$	1.38413e10	0.0539949
$344$	2.13676e11	0.822703
$345$	4.63499e10	0.176142
$346$	−1.02072e10	−0.0382880
$347$	6.28148e10	0.232584	0.116292	−	0.993215i	$-0.462899\pi$
$347$	6.28148e10	0.232584	0.116292	+	0.993215i	$0.462899\pi$
$348$	1.44404e11	0.527804
$349$	−8.06407e10	−0.290964	−0.145482	−	0.989361i	$-0.546473\pi$
$349$	−8.06407e10	−0.290964	−0.145482	+	0.989361i	$0.546473\pi$
$350$	7.58502e9	0.0270178
$351$	8.85993e10	0.311565
$352$	1.63975e11	0.569292
$353$	4.35194e11	1.49175	0.745877	−	0.666084i	$-0.232031\pi$
$353$	4.35194e11	1.49175	0.745877	+	0.666084i	$0.232031\pi$
$354$	8.79507e10	0.297663
$355$	−1.78937e10	−0.0597959
$356$	4.42840e11	1.46124
$357$	−3.91202e10	−0.127466
$358$	7.08160e10	0.227855
$359$	−1.55998e11	−0.495673	−0.247836	−	0.968802i	$-0.579720\pi$
$359$	−1.55998e11	−0.495673	−0.247836	+	0.968802i	$0.579720\pi$
$360$	−3.17900e10	−0.0997536
$361$	6.86577e11	2.12768
$362$	7.79038e10	0.238435
$363$	1.13794e11	0.343986
$364$	1.78765e11	0.533735
$365$	1.78505e10	0.0526420
$366$	−2.95558e10	−0.0860949
$367$	−6.27647e11	−1.80600	−0.903000	−	0.429640i	$-0.858641\pi$
$367$	−6.27647e11	−1.80600	−0.903000	+	0.429640i	$0.858641\pi$
$368$	−1.51945e11	−0.431889
$369$	−2.24213e11	−0.629567
$370$	−9.57099e10	−0.265491
$371$	−9.26977e10	−0.254031
$372$	1.16967e11	0.316680
$373$	−6.67271e11	−1.78489	−0.892447	−	0.451152i	$-0.851013\pi$
$373$	−6.67271e11	−1.78489	−0.892447	+	0.451152i	$0.851013\pi$
$374$	5.02219e10	0.132731
$375$	−1.97754e10	−0.0516398
$376$	2.10628e11	0.543463
$377$	−6.65511e11	−1.69676
$378$	−1.03193e10	−0.0259979
$379$	5.31202e11	1.32246	0.661231	−	0.750182i	$-0.270034\pi$
$379$	5.31202e11	1.32246	0.661231	+	0.750182i	$0.270034\pi$
$380$	−2.80412e11	−0.689875
$381$	−4.43588e10	−0.107849
$382$	9.12196e10	0.219181
$383$	−4.26936e11	−1.01384	−0.506919	−	0.861994i	$-0.669216\pi$
$383$	−4.26936e11	−1.01384	−0.506919	+	0.861994i	$0.669216\pi$
$384$	2.47800e11	0.581581
$385$	4.63273e10	0.107464
$386$	−1.33384e11	−0.305817
$387$	−1.80836e11	−0.409814
$388$	4.61488e11	1.03375
$389$	5.62759e11	1.24609	0.623045	−	0.782186i	$-0.285895\pi$
$389$	5.62759e11	1.24609	0.623045	+	0.782186i	$0.285895\pi$
$390$	6.82566e10	0.149401
$391$	−1.84165e11	−0.398486
$392$	−4.46914e10	−0.0955954
$393$	−4.09334e11	−0.865588
$394$	−2.29674e11	−0.480152
$395$	2.19294e11	0.453252
$396$	−9.04584e10	−0.184851
$397$	5.96192e10	0.120456	0.0602281	−	0.998185i	$-0.480817\pi$
$397$	5.96192e10	0.120456	0.0602281	+	0.998185i	$0.480817\pi$
$398$	−2.89601e11	−0.578530
$399$	−1.95380e11	−0.385924
$400$	6.48282e10	0.126618
$401$	−2.89485e10	−0.0559084	−0.0279542	−	0.999609i	$-0.508899\pi$
$401$	−2.89485e10	−0.0559084	−0.0279542	+	0.999609i	$0.508899\pi$
$402$	−2.76325e10	−0.0527719
$403$	−5.39064e11	−1.01805
$404$	6.39675e11	1.19466
$405$	2.69042e10	0.0496904
$406$	7.75134e10	0.141583
$407$	−5.84571e11	−1.05600
$408$	1.26313e11	0.225672
$409$	−2.36907e11	−0.418622	−0.209311	−	0.977849i	$-0.567122\pi$
$409$	−2.36907e11	−0.418622	−0.209311	+	0.977849i	$0.567122\pi$
$410$	−1.72733e11	−0.301890
$411$	5.74513e10	0.0993143
$412$	−1.22586e11	−0.209605
$413$	−3.22361e11	−0.545214
$414$	−4.85801e10	−0.0812750
$415$	1.22767e11	0.203172
$416$	−8.85497e11	−1.44966
$417$	2.94062e11	0.476241
$418$	2.50826e11	0.401864
$419$	5.10589e11	0.809297	0.404649	−	0.914472i	$-0.367394\pi$
$419$	5.10589e11	0.809297	0.404649	+	0.914472i	$0.367394\pi$
$420$	5.42839e10	0.0851235
$421$	1.18375e12	1.83650	0.918252	−	0.395997i	$-0.129601\pi$
$421$	1.18375e12	1.83650	0.918252	+	0.395997i	$0.129601\pi$
$422$	−4.12643e11	−0.633387
$423$	−1.78257e11	−0.270716
$424$	2.99307e11	0.449749
$425$	7.85749e10	0.116824
$426$	1.87546e10	0.0275909
$427$	1.08329e11	0.157696
$428$	3.74630e11	0.539642
$429$	4.16894e11	0.594247
$430$	−1.39316e11	−0.196514
$431$	−4.12273e11	−0.575489	−0.287744	−	0.957707i	$-0.592905\pi$
$431$	−4.12273e11	−0.575489	−0.287744	+	0.957707i	$0.592905\pi$
$432$	−8.81980e10	−0.121838
$433$	−2.47912e11	−0.338924	−0.169462	−	0.985537i	$-0.554203\pi$
$433$	−2.47912e11	−0.338924	−0.169462	+	0.985537i	$0.554203\pi$
$434$	6.27859e10	0.0849490
$435$	−2.02090e11	−0.270610
$436$	−1.88227e11	−0.249455
$437$	−9.19785e11	−1.20648
$438$	−1.87094e10	−0.0242900
$439$	6.04082e11	0.776257	0.388129	−	0.921605i	$-0.373122\pi$
$439$	6.04082e11	0.776257	0.388129	+	0.921605i	$0.373122\pi$
$440$	−1.49584e11	−0.190260
$441$	3.78229e10	0.0476190
$442$	−2.71209e11	−0.337990
$443$	8.25313e11	1.01813	0.509063	−	0.860729i	$-0.329992\pi$
$443$	8.25313e11	1.01813	0.509063	+	0.860729i	$0.329992\pi$
$444$	−6.84970e11	−0.836466
$445$	−6.19745e11	−0.749192
$446$	3.20194e11	0.383183
$447$	−5.68871e11	−0.673954
$448$	−1.00881e11	−0.118320
$449$	6.44201e11	0.748020	0.374010	−	0.927425i	$-0.377983\pi$
$449$	6.44201e11	0.748020	0.374010	+	0.927425i	$0.377983\pi$
$450$	2.07269e10	0.0238275
$451$	−1.05501e12	−1.20077
$452$	−8.41209e10	−0.0947940
$453$	5.49571e11	0.613171
$454$	8.19588e10	0.0905408
$455$	−2.50177e11	−0.273650
$456$	6.30852e11	0.683259
$457$	−1.18172e12	−1.26733	−0.633666	−	0.773607i	$-0.718451\pi$
$457$	−1.18172e12	−1.26733	−0.633666	+	0.773607i	$0.718451\pi$
$458$	−3.70482e11	−0.393434
$459$	−1.06900e11	−0.112414
$460$	2.55551e11	0.266114
$461$	1.43006e12	1.47469	0.737346	−	0.675515i	$-0.236079\pi$
$461$	1.43006e12	1.47469	0.737346	+	0.675515i	$0.236079\pi$
$462$	−4.85564e10	−0.0495858
$463$	−7.31340e11	−0.739614	−0.369807	−	0.929109i	$-0.620576\pi$
$463$	−7.31340e11	−0.739614	−0.369807	+	0.929109i	$0.620576\pi$
$464$	6.62497e11	0.663518
$465$	−1.63693e11	−0.162365
$466$	−7.51817e10	−0.0738542
$467$	−1.76786e12	−1.71997	−0.859986	−	0.510318i	$-0.829528\pi$
$467$	−1.76786e12	−1.71997	−0.859986	+	0.510318i	$0.829528\pi$
$468$	4.88494e11	0.470710
$469$	1.01280e11	0.0966595
$470$	−1.37328e11	−0.129814
$471$	−2.67525e11	−0.250478
$472$	1.04085e12	0.965274
$473$	−8.50905e11	−0.781638
$474$	−2.29846e11	−0.209138
$475$	3.92430e11	0.353705
$476$	−2.15690e11	−0.192575
$477$	−2.53307e11	−0.224034
$478$	−7.76641e10	−0.0680447
$479$	−4.33455e11	−0.376213	−0.188107	−	0.982149i	$-0.560235\pi$
$479$	−4.33455e11	−0.376213	−0.188107	+	0.982149i	$0.560235\pi$
$480$	−2.68891e11	−0.231202
$481$	3.15680e12	2.68902
$482$	7.30684e11	0.616621
$483$	1.78058e11	0.148867
$484$	6.27407e11	0.519691
$485$	−6.45842e11	−0.530015
$486$	−2.81987e10	−0.0229280
$487$	−3.20625e11	−0.258295	−0.129148	−	0.991625i	$-0.541224\pi$
$487$	−3.20625e11	−0.258295	−0.129148	+	0.991625i	$0.541224\pi$
$488$	−3.49778e11	−0.279192
$489$	9.25420e11	0.731896
$490$	2.91386e10	0.0228342
$491$	−1.17787e12	−0.914598	−0.457299	−	0.889313i	$-0.651183\pi$
$491$	−1.17787e12	−0.914598	−0.457299	+	0.889313i	$0.651183\pi$
$492$	−1.23620e12	−0.951145
$493$	8.02979e11	0.612200
$494$	−1.35451e12	−1.02332
$495$	1.26595e11	0.0947745
$496$	5.36622e11	0.398108
$497$	−6.87403e10	−0.0505368
$498$	−1.28674e11	−0.0937471
$499$	−5.19297e11	−0.374941	−0.187471	−	0.982270i	$-0.560029\pi$
$499$	−5.19297e11	−0.374941	−0.187471	+	0.982270i	$0.560029\pi$
$500$	−1.09032e11	−0.0780170
$501$	−1.38607e12	−0.982915
$502$	−5.49484e11	−0.386179
$503$	−2.13815e12	−1.48930	−0.744650	−	0.667455i	$-0.767384\pi$
$503$	−2.13815e12	−1.48930	−0.744650	+	0.667455i	$0.767384\pi$
$504$	−1.22124e11	−0.0843072
$505$	−8.95211e11	−0.612511
$506$	−2.28588e11	−0.155016
$507$	−1.39235e12	−0.935862
$508$	−2.44573e11	−0.162938
$509$	2.59692e12	1.71486	0.857429	−	0.514602i	$-0.172060\pi$
$509$	2.59692e12	1.71486	0.857429	+	0.514602i	$0.172060\pi$
$510$	−8.23557e10	−0.0539048
$511$	6.85745e10	0.0444906
$512$	1.54023e12	0.990534
$513$	−5.33897e11	−0.340353
$514$	7.15600e11	0.452206
$515$	1.71556e11	0.107466
$516$	−9.97046e11	−0.619144
$517$	−8.38766e11	−0.516337
$518$	−3.67679e11	−0.224381
$519$	1.02232e11	0.0618490
$520$	8.07784e11	0.484485
$521$	−2.04991e12	−1.21889	−0.609447	−	0.792827i	$-0.708608\pi$
$521$	−2.04991e12	−1.21889	−0.609447	+	0.792827i	$0.708608\pi$
$522$	2.11814e11	0.124864
$523$	2.87343e12	1.67936	0.839680	−	0.543082i	$-0.182743\pi$
$523$	2.87343e12	1.67936	0.839680	+	0.543082i	$0.182743\pi$
$524$	−2.25687e12	−1.30772
$525$	−7.59691e10	−0.0436436
$526$	−3.66479e11	−0.208743
$527$	6.50413e11	0.367317
$528$	−4.15005e11	−0.232381
$529$	−9.62914e11	−0.534610
$530$	−1.95147e11	−0.107429
$531$	−8.80886e11	−0.480833
$532$	−1.07723e12	−0.583051
$533$	5.69726e12	3.05769
$534$	6.49565e11	0.345690
$535$	−5.24286e11	−0.276679
$536$	−3.27017e11	−0.171131
$537$	−7.09270e11	−0.368068
$538$	1.03606e12	0.533170
$539$	1.77971e11	0.0908238
$540$	1.48337e11	0.0750719
$541$	−3.39659e12	−1.70473	−0.852364	−	0.522950i	$-0.824832\pi$
$541$	−3.39659e12	−1.70473	−0.852364	+	0.522950i	$0.824832\pi$
$542$	−7.91460e11	−0.393942
$543$	−7.80259e11	−0.385159
$544$	1.06840e12	0.523047
$545$	2.63419e11	0.127898
$546$	2.62215e11	0.126267
$547$	2.09648e12	1.00126	0.500630	−	0.865661i	$-0.333102\pi$
$547$	2.09648e12	1.00126	0.500630	+	0.865661i	$0.333102\pi$
$548$	3.16759e11	0.150043
$549$	2.96021e11	0.139074
$550$	9.75280e10	0.0454462
$551$	4.01035e12	1.85353
$552$	−5.74922e11	−0.263562
$553$	8.42440e11	0.383068
$554$	−1.40763e12	−0.634886
$555$	9.58600e11	0.428863
$556$	1.62132e12	0.719502
$557$	−1.76027e12	−0.774874	−0.387437	−	0.921896i	$-0.626639\pi$
$557$	−1.76027e12	−0.774874	−0.387437	+	0.921896i	$0.626639\pi$
$558$	1.71569e11	0.0749179
$559$	4.59506e12	1.99039
$560$	2.49044e11	0.107011
$561$	−5.03007e11	−0.214408
$562$	−1.15113e12	−0.486754
$563$	1.17448e12	0.492673	0.246336	−	0.969184i	$-0.420773\pi$
$563$	1.17448e12	0.492673	0.246336	+	0.969184i	$0.420773\pi$
$564$	−9.82822e11	−0.408996
$565$	1.17725e11	0.0486017
$566$	−6.18671e11	−0.253388
$567$	1.03355e11	0.0419961
$568$	2.21952e11	0.0894729
$569$	−4.64171e12	−1.85641	−0.928203	−	0.372074i	$-0.878647\pi$
$569$	−4.64171e12	−1.85641	−0.928203	+	0.372074i	$0.878647\pi$
$570$	−4.11313e11	−0.163206
$571$	1.18993e12	0.468447	0.234224	−	0.972183i	$-0.424745\pi$
$571$	1.18993e12	0.468447	0.234224	+	0.972183i	$0.424745\pi$
$572$	2.29855e12	0.897785
$573$	−9.13627e11	−0.354057
$574$	−6.63571e11	−0.255143
$575$	−3.57638e11	−0.136439
$576$	−2.75669e11	−0.104349
$577$	4.03535e12	1.51562	0.757809	−	0.652476i	$-0.226270\pi$
$577$	4.03535e12	1.51562	0.757809	+	0.652476i	$0.226270\pi$
$578$	−6.31828e11	−0.235464
$579$	1.33593e12	0.494004
$580$	−1.11423e12	−0.408835
$581$	4.71620e11	0.171712
$582$	6.76917e11	0.244558
$583$	−1.19190e12	−0.427300
$584$	−2.21417e11	−0.0787685
$585$	−6.83637e11	−0.241337
$586$	3.98872e11	0.139732
$587$	3.43062e12	1.19262	0.596308	−	0.802756i	$-0.296634\pi$
$587$	3.43062e12	1.19262	0.596308	+	0.802756i	$0.296634\pi$
$588$	2.08537e11	0.0719425
$589$	3.24839e12	1.11211
$590$	−6.78632e11	−0.230569
$591$	2.30034e12	0.775619
$592$	−3.14251e12	−1.05155
$593$	4.44094e12	1.47479	0.737393	−	0.675464i	$-0.236057\pi$
$593$	4.44094e12	1.47479	0.737393	+	0.675464i	$0.236057\pi$
$594$	−1.32686e11	−0.0437306
$595$	3.01853e11	0.0987347
$596$	−3.13649e12	−1.01820
$597$	2.90055e12	0.934535
$598$	1.23442e12	0.394738
$599$	1.61842e12	0.513652	0.256826	−	0.966458i	$-0.417323\pi$
$599$	1.61842e12	0.513652	0.256826	+	0.966458i	$0.417323\pi$
$600$	2.45293e11	0.0772688
$601$	2.09693e12	0.655616	0.327808	−	0.944744i	$-0.393690\pi$
$601$	2.09693e12	0.655616	0.327808	+	0.944744i	$0.393690\pi$
$602$	−5.35196e11	−0.166084
$603$	2.76758e11	0.0852456
$604$	3.03007e12	0.926374
$605$	−8.78042e11	−0.266450
$606$	9.38285e11	0.282623
$607$	2.12609e12	0.635671	0.317835	−	0.948146i	$-0.397044\pi$
$607$	2.12609e12	0.635671	0.317835	+	0.948146i	$0.397044\pi$
$608$	5.33598e12	1.58361
$609$	−7.76350e11	−0.228707
$610$	2.28054e11	0.0666888
$611$	4.52951e12	1.31482
$612$	−5.89397e11	−0.169835
$613$	−2.11173e11	−0.0604041	−0.0302021	−	0.999544i	$-0.509615\pi$
$613$	−2.11173e11	−0.0604041	−0.0302021	+	0.999544i	$0.509615\pi$
$614$	−5.92649e11	−0.168283
$615$	1.73004e12	0.487661
$616$	−5.74641e11	−0.160799
$617$	−4.18810e10	−0.0116341	−0.00581706	−	0.999983i	$-0.501852\pi$
$617$	−4.18810e10	−0.0116341	−0.00581706	+	0.999983i	$0.501852\pi$
$618$	−1.79810e11	−0.0495869
$619$	−2.83282e12	−0.775551	−0.387775	−	0.921754i	$-0.626756\pi$
$619$	−2.83282e12	−0.775551	−0.387775	+	0.921754i	$0.626756\pi$
$620$	−9.02525e11	−0.245299
$621$	4.86563e11	0.131289
$622$	−7.87346e11	−0.210916
$623$	−2.38081e12	−0.633183
$624$	2.24111e12	0.591743
$625$	1.52588e11	0.0400000
$626$	2.70023e12	0.702774
$627$	−2.51219e12	−0.649155
$628$	−1.47500e12	−0.378421
$629$	−3.80887e12	−0.970216
$630$	7.96245e10	0.0201379
$631$	−2.00967e12	−0.504653	−0.252327	−	0.967642i	$-0.581196\pi$
$631$	−2.00967e12	−0.504653	−0.252327	+	0.967642i	$0.581196\pi$
$632$	−2.72011e12	−0.678203
$633$	4.13290e12	1.02315
$634$	−1.40972e12	−0.346523
$635$	3.42275e11	0.0835397
$636$	−1.39661e12	−0.338469
$637$	−9.61080e11	−0.231277
$638$	9.96666e11	0.238153
$639$	−1.87840e11	−0.0445692
$640$	−1.91203e12	−0.450491
$641$	−6.97881e12	−1.63275	−0.816377	−	0.577520i	$-0.804021\pi$
$641$	−6.97881e12	−1.63275	−0.816377	+	0.577520i	$0.804021\pi$
$642$	5.49513e11	0.127665
$643$	−7.24045e12	−1.67038	−0.835192	−	0.549959i	$-0.814643\pi$
$643$	−7.24045e12	−1.67038	−0.835192	+	0.549959i	$0.814643\pi$
$644$	9.81726e11	0.224907
$645$	1.39534e12	0.317441
$646$	1.63430e12	0.369220
$647$	1.29428e12	0.290374	0.145187	−	0.989404i	$-0.453622\pi$
$647$	1.29428e12	0.290374	0.145187	+	0.989404i	$0.453622\pi$
$648$	−3.33718e11	−0.0743520
$649$	−4.14491e12	−0.917093
$650$	−5.26672e11	−0.115726
$651$	−6.28843e11	−0.137223
$652$	5.10233e12	1.10574
$653$	2.84700e12	0.612742	0.306371	−	0.951912i	$-0.400885\pi$
$653$	2.84700e12	0.612742	0.306371	+	0.951912i	$0.400885\pi$
$654$	−2.76094e11	−0.0590143
$655$	3.15844e12	0.670482
$656$	−5.67145e12	−1.19571
$657$	1.87388e11	0.0392371
$658$	−5.27561e11	−0.109712
$659$	2.82991e12	0.584504	0.292252	−	0.956341i	$-0.405595\pi$
$659$	2.82991e12	0.584504	0.292252	+	0.956341i	$0.405595\pi$
$660$	6.97982e11	0.143185
$661$	1.81499e12	0.369801	0.184900	−	0.982757i	$-0.440804\pi$
$661$	1.81499e12	0.369801	0.184900	+	0.982757i	$0.440804\pi$
$662$	1.98612e11	0.0401924
$663$	2.71634e12	0.545976
$664$	−1.52279e12	−0.304007
$665$	1.50756e12	0.298935
$666$	−1.00472e12	−0.197885
$667$	−3.65480e12	−0.714987
$668$	−7.64214e12	−1.48498
$669$	−3.20696e12	−0.618979
$670$	2.13213e11	0.0408769
$671$	1.39289e12	0.265257
$672$	−1.03297e12	−0.195401
$673$	4.85309e12	0.911907	0.455954	−	0.890004i	$-0.349298\pi$
$673$	4.85309e12	0.911907	0.455954	+	0.890004i	$0.349298\pi$
$674$	2.86326e11	0.0534431
$675$	−2.07594e11	−0.0384900
$676$	−7.67674e12	−1.41389
$677$	5.14066e12	0.940523	0.470262	−	0.882527i	$-0.344160\pi$
$677$	5.14066e12	0.940523	0.470262	+	0.882527i	$0.344160\pi$
$678$	−1.23390e11	−0.0224257
$679$	−2.48106e12	−0.447944
$680$	−9.74639e11	−0.174805
$681$	−8.20874e11	−0.146256
$682$	8.07299e11	0.142891
$683$	5.45466e11	0.0959124	0.0479562	−	0.998849i	$-0.484729\pi$
$683$	5.45466e11	0.0959124	0.0479562	+	0.998849i	$0.484729\pi$
$684$	−2.94365e12	−0.514203
$685$	−4.43297e11	−0.0769285
$686$	1.11939e11	0.0192985
$687$	3.71062e12	0.635538
$688$	−4.57425e12	−0.778344
$689$	6.43653e12	1.08809
$690$	3.74847e11	0.0629554
$691$	1.40764e12	0.234876	0.117438	−	0.993080i	$-0.462532\pi$
$691$	1.40764e12	0.234876	0.117438	+	0.993080i	$0.462532\pi$
$692$	5.63657e11	0.0934410
$693$	4.86326e11	0.0800991
$694$	5.08003e11	0.0831283
$695$	−2.26900e12	−0.368895
$696$	2.50672e12	0.404915
$697$	−6.87408e12	−1.10323
$698$	−6.52167e11	−0.103994
$699$	7.52995e11	0.119301
$700$	−4.18858e11	−0.0659364
$701$	−3.89404e12	−0.609072	−0.304536	−	0.952501i	$-0.598501\pi$
$701$	−3.89404e12	−0.609072	−0.304536	+	0.952501i	$0.598501\pi$
$702$	7.16531e11	0.111357
$703$	−1.90228e13	−2.93749
$704$	−1.29713e12	−0.199024
$705$	1.37544e12	0.209696
$706$	3.51956e12	0.533171
$707$	−3.43904e12	−0.517667
$708$	−4.85679e12	−0.726439
$709$	−1.58070e12	−0.234931	−0.117465	−	0.993077i	$-0.537477\pi$
$709$	−1.58070e12	−0.234931	−0.117465	+	0.993077i	$0.537477\pi$
$710$	−1.44712e11	−0.0213718
$711$	2.30206e12	0.337834
$712$	7.68729e12	1.12102
$713$	−2.96039e12	−0.428989
$714$	−3.16378e11	−0.0455579
$715$	−3.21677e12	−0.460302
$716$	−3.91058e12	−0.556074
$717$	7.77858e11	0.109917
$718$	−1.26161e12	−0.177160
$719$	1.17529e13	1.64008	0.820040	−	0.572307i	$-0.193951\pi$
$719$	1.17529e13	1.64008	0.820040	+	0.572307i	$0.193951\pi$
$720$	6.80540e11	0.0943751
$721$	6.59049e11	0.0908257
$722$	5.55257e12	0.760460
$723$	−7.31830e12	−0.996065
$724$	−4.30198e12	−0.581895
$725$	1.55934e12	0.209613
$726$	9.20290e11	0.122945
$727$	−6.34431e12	−0.842325	−0.421162	−	0.906985i	$-0.638378\pi$
$727$	−6.34431e12	−0.842325	−0.421162	+	0.906985i	$0.638378\pi$
$728$	3.10318e12	0.409464
$729$	2.82430e11	0.0370370
$730$	1.44363e11	0.0188149
$731$	−5.54421e12	−0.718145
$732$	1.63212e12	0.210112
$733$	−1.64666e11	−0.0210686	−0.0105343	−	0.999945i	$-0.503353\pi$
$733$	−1.64666e11	−0.0210686	−0.0105343	+	0.999945i	$0.503353\pi$
$734$	−5.07598e12	−0.645487
$735$	−2.91843e11	−0.0368856
$736$	−4.86291e12	−0.610866
$737$	1.30225e12	0.162589
$738$	−1.81328e12	−0.225015
$739$	−4.23588e12	−0.522449	−0.261224	−	0.965278i	$-0.584126\pi$
$739$	−4.23588e12	−0.522449	−0.261224	+	0.965278i	$0.584126\pi$
$740$	5.28526e12	0.647923
$741$	1.35663e13	1.65303
$742$	−7.49676e11	−0.0907937
$743$	−5.11220e12	−0.615402	−0.307701	−	0.951483i	$-0.599560\pi$
$743$	−5.11220e12	−0.615402	−0.307701	+	0.951483i	$0.599560\pi$
$744$	2.03044e12	0.242947
$745$	4.38944e12	0.522043
$746$	−5.39643e12	−0.637943
$747$	1.28875e12	0.151435
$748$	−2.77334e12	−0.323926
$749$	−2.01410e12	−0.233837
$750$	−1.59930e11	−0.0184567
$751$	−1.32282e10	−0.00151747	−0.000758734	−	1.00000i	$-0.500242\pi$
$751$	−1.32282e10	−0.00151747	−0.000758734		1.00000i	$0.500242\pi$
$752$	−4.50899e12	−0.514161
$753$	5.50346e12	0.623818
$754$	−5.38220e12	−0.606442
$755$	−4.24052e12	−0.474960
$756$	5.69851e11	0.0634473
$757$	7.19785e12	0.796657	0.398328	−	0.917243i	$-0.369590\pi$
$757$	7.19785e12	0.796657	0.398328	+	0.917243i	$0.369590\pi$
$758$	4.29600e12	0.472665
$759$	2.28946e12	0.250407
$760$	−4.86768e12	−0.529251
$761$	6.27551e12	0.678294	0.339147	−	0.940733i	$-0.389862\pi$
$761$	6.27551e12	0.678294	0.339147	+	0.940733i	$0.389862\pi$
$762$	−3.58744e11	−0.0385467
$763$	1.01195e12	0.108093
$764$	−5.03730e12	−0.534906
$765$	8.24848e11	0.0870758
$766$	−3.45277e12	−0.362358
$767$	2.23833e13	2.33532
$768$	2.61534e11	0.0271271
$769$	−6.16669e11	−0.0635892	−0.0317946	−	0.999494i	$-0.510122\pi$
$769$	−6.16669e11	−0.0635892	−0.0317946	+	0.999494i	$0.510122\pi$
$770$	3.74664e11	0.0384090
$771$	−7.16722e12	−0.730476
$772$	7.36569e12	0.746338
$773$	−1.63508e13	−1.64715	−0.823573	−	0.567211i	$-0.808022\pi$
$773$	−1.63508e13	−1.64715	−0.823573	+	0.567211i	$0.808022\pi$
$774$	−1.46248e12	−0.146473
$775$	1.26306e12	0.125767
$776$	8.01098e12	0.793064
$777$	3.68256e12	0.362456
$778$	4.55121e12	0.445368
$779$	−3.43315e13	−3.34022
$780$	−3.76925e12	−0.364610
$781$	−8.83861e11	−0.0850069
$782$	−1.48940e12	−0.142424
$783$	−2.12146e12	−0.201701
$784$	9.56727e11	0.0904411
$785$	2.06423e12	0.194020
$786$	−3.31041e12	−0.309372
$787$	6.63488e12	0.616520	0.308260	−	0.951302i	$-0.400253\pi$
$787$	6.63488e12	0.616520	0.308260	+	0.951302i	$0.400253\pi$
$788$	1.26830e13	1.17180
$789$	3.67053e12	0.337196
$790$	1.77350e12	0.161998
$791$	4.52253e11	0.0410759
$792$	−1.57027e12	−0.141811
$793$	−7.52191e12	−0.675458
$794$	4.82160e11	0.0430525
$795$	1.95453e12	0.173536
$796$	1.59922e13	1.41189
$797$	1.46563e13	1.28666	0.643328	−	0.765591i	$-0.277553\pi$
$797$	1.46563e13	1.28666	0.643328	+	0.765591i	$0.277553\pi$
$798$	−1.58010e12	−0.137934
$799$	−5.46512e12	−0.474394
$800$	2.07478e12	0.179088
$801$	−6.50584e12	−0.558415
$802$	−2.34116e11	−0.0199823
$803$	8.81730e11	0.0748369
$804$	1.52591e12	0.128788
$805$	−1.37390e12	−0.115312
$806$	−4.35958e12	−0.363862
$807$	−1.03769e13	−0.861262
$808$	1.11041e13	0.916503
$809$	1.33356e13	1.09457	0.547287	−	0.836945i	$-0.315661\pi$
$809$	1.33356e13	1.09457	0.547287	+	0.836945i	$0.315661\pi$
$810$	2.17583e11	0.0177600
$811$	9.82036e12	0.797138	0.398569	−	0.917138i	$-0.369507\pi$
$811$	9.82036e12	0.797138	0.398569	+	0.917138i	$0.369507\pi$
$812$	−4.28042e12	−0.345529
$813$	7.92701e12	0.636358
$814$	−4.72761e12	−0.377426
$815$	−7.14059e12	−0.566924
$816$	−2.70404e12	−0.213504
$817$	−2.76897e13	−2.17430
$818$	−1.91594e12	−0.149621
$819$	−2.62626e12	−0.203967
$820$	9.53861e12	0.736754
$821$	−9.12388e12	−0.700867	−0.350433	−	0.936588i	$-0.613966\pi$
$821$	−9.12388e12	−0.700867	−0.350433	+	0.936588i	$0.613966\pi$
$822$	4.64627e11	0.0354962
$823$	−2.40628e13	−1.82829	−0.914147	−	0.405382i	$-0.867139\pi$
$823$	−2.40628e13	−1.82829	−0.914147	+	0.405382i	$0.867139\pi$
$824$	−2.12797e12	−0.160802
$825$	−9.76810e11	−0.0734120
$826$	−2.60703e12	−0.194866
$827$	2.05090e13	1.52465	0.762324	−	0.647196i	$-0.224058\pi$
$827$	2.05090e13	1.52465	0.762324	+	0.647196i	$0.224058\pi$
$828$	2.68268e12	0.198350
$829$	−3.02576e12	−0.222505	−0.111252	−	0.993792i	$-0.535486\pi$
$829$	−3.02576e12	−0.222505	−0.111252	+	0.993792i	$0.535486\pi$
$830$	9.92853e11	0.0726162
$831$	1.40984e13	1.02557
$832$	7.00476e12	0.506802
$833$	1.15960e12	0.0834461
$834$	2.37818e12	0.170215
$835$	1.06950e13	0.761363
$836$	−1.38510e13	−0.980739
$837$	−1.71838e12	−0.121020
$838$	4.12929e12	0.289253
$839$	5.54166e12	0.386110	0.193055	−	0.981188i	$-0.438160\pi$
$839$	5.54166e12	0.386110	0.193055	+	0.981188i	$0.438160\pi$
$840$	9.42317e11	0.0653041
$841$	1.42816e12	0.0984452
$842$	9.57339e12	0.656389
$843$	1.15293e13	0.786284
$844$	2.27869e13	1.54576
$845$	1.07434e13	0.724915
$846$	−1.44162e12	−0.0967573
$847$	−3.37309e12	−0.225192
$848$	−6.40738e12	−0.425499
$849$	6.19641e12	0.409313
$850$	6.35461e11	0.0417545
$851$	1.73363e13	1.13311
$852$	−1.03566e12	−0.0673349
$853$	−8.32787e12	−0.538596	−0.269298	−	0.963057i	$-0.586792\pi$
$853$	−8.32787e12	−0.538596	−0.269298	+	0.963057i	$0.586792\pi$
$854$	8.76091e11	0.0563623
$855$	4.11958e12	0.263636
$856$	6.50322e12	0.413996
$857$	1.94279e13	1.23030	0.615152	−	0.788409i	$-0.289095\pi$
$857$	1.94279e13	1.23030	0.615152	+	0.788409i	$0.289095\pi$
$858$	3.37155e12	0.212391
$859$	−2.74463e13	−1.71994	−0.859971	−	0.510343i	$-0.829519\pi$
$859$	−2.74463e13	−1.71994	−0.859971	+	0.510343i	$0.829519\pi$
$860$	7.69326e12	0.479587
$861$	6.64612e12	0.412149
$862$	−3.33418e12	−0.205687
$863$	2.92651e13	1.79598	0.897989	−	0.440018i	$-0.145028\pi$
$863$	2.92651e13	1.79598	0.897989	+	0.440018i	$0.145028\pi$
$864$	−2.82271e12	−0.172328
$865$	−7.88826e11	−0.0479080
$866$	−2.00495e12	−0.121136
$867$	6.32819e12	0.380359
$868$	−3.46714e12	−0.207316
$869$	1.08321e13	0.644351
$870$	−1.63437e12	−0.0967193
$871$	−7.03243e12	−0.414022
$872$	−3.26744e12	−0.191374
$873$	−6.77979e12	−0.395050
$874$	−7.43860e12	−0.431211
$875$	5.86182e11	0.0338062
$876$	1.03317e12	0.0592791
$877$	1.49560e13	0.853722	0.426861	−	0.904317i	$-0.359619\pi$
$877$	1.49560e13	0.853722	0.426861	+	0.904317i	$0.359619\pi$
$878$	4.88541e12	0.277444
$879$	−3.99498e12	−0.225717
$880$	3.20220e12	0.180002
$881$	−1.07277e13	−0.599949	−0.299974	−	0.953947i	$-0.596978\pi$
$881$	−1.07277e13	−0.599949	−0.299974	+	0.953947i	$0.596978\pi$
$882$	3.05886e11	0.0170196
$883$	−1.02173e13	−0.565602	−0.282801	−	0.959179i	$-0.591264\pi$
$883$	−1.02173e13	−0.565602	−0.282801	+	0.959179i	$0.591264\pi$
$884$	1.49766e13	0.824856
$885$	6.79696e12	0.372452
$886$	6.67457e12	0.363891
$887$	−8.09599e12	−0.439151	−0.219575	−	0.975596i	$-0.570467\pi$
$887$	−8.09599e12	−0.439151	−0.219575	+	0.975596i	$0.570467\pi$
$888$	−1.18904e13	−0.641710
$889$	1.31488e12	0.0706039
$890$	−5.01208e12	−0.267771
$891$	1.32894e12	0.0706407
$892$	−1.76816e13	−0.935149
$893$	−2.72947e13	−1.43631
$894$	−4.60065e12	−0.240880
$895$	5.47276e12	0.285104
$896$	−7.34527e12	−0.380734
$897$	−1.23636e13	−0.637644
$898$	5.20986e12	0.267352
$899$	1.29076e13	0.659063
$900$	−1.14457e12	−0.0581504
$901$	−7.76606e12	−0.392590
$902$	−8.53218e12	−0.429171
$903$	5.36035e12	0.268286
$904$	−1.46026e12	−0.0727230
$905$	6.02052e12	0.298343
$906$	4.44456e12	0.219155
$907$	2.65951e13	1.30487	0.652437	−	0.757843i	$-0.273747\pi$
$907$	2.65951e13	1.30487	0.652437	+	0.757843i	$0.273747\pi$
$908$	−4.52590e12	−0.220963
$909$	−9.39757e12	−0.456539
$910$	−2.02326e12	−0.0978061
$911$	−1.23987e13	−0.596410	−0.298205	−	0.954502i	$-0.596388\pi$
$911$	−1.23987e13	−0.596410	−0.298205	+	0.954502i	$0.596388\pi$
$912$	−1.35049e13	−0.646420
$913$	6.06408e12	0.288833
$914$	−9.55692e12	−0.452960
$915$	−2.28411e12	−0.107727
$916$	2.04586e13	0.960166
$917$	1.21335e13	0.566661
$918$	−8.64537e11	−0.0401783
$919$	−1.70103e13	−0.786668	−0.393334	−	0.919396i	$-0.628678\pi$
$919$	−1.70103e13	−0.786668	−0.393334	+	0.919396i	$0.628678\pi$
$920$	4.43613e12	0.204154
$921$	5.93578e12	0.271838
$922$	1.15654e13	0.527073
$923$	4.77303e12	0.216465
$924$	2.68137e12	0.121013
$925$	−7.39660e12	−0.332196
$926$	−5.91458e12	−0.264347
$927$	1.80092e12	0.0801007
$928$	2.12027e13	0.938482
$929$	2.02298e13	0.891091	0.445545	−	0.895259i	$-0.353010\pi$
$929$	2.02298e13	0.891091	0.445545	+	0.895259i	$0.353010\pi$
$930$	−1.32384e12	−0.0580312
$931$	5.79144e12	0.252647
$932$	4.15166e12	0.180239
$933$	7.88581e12	0.340705
$934$	−1.42972e13	−0.614739
$935$	3.88123e12	0.166080
$936$	8.47979e12	0.361114
$937$	3.63130e13	1.53898	0.769491	−	0.638658i	$-0.220510\pi$
$937$	3.63130e13	1.53898	0.769491	+	0.638658i	$0.220510\pi$
$938$	8.19081e11	0.0345473
$939$	−2.70446e13	−1.13523
$940$	7.58350e12	0.316807
$941$	−1.43638e13	−0.597194	−0.298597	−	0.954379i	$-0.596519\pi$
$941$	−1.43638e13	−0.597194	−0.298597	+	0.954379i	$0.596519\pi$
$942$	−2.16356e12	−0.0895240
$943$	3.12878e13	1.28846
$944$	−2.22820e13	−0.913229
$945$	−7.97494e11	−0.0325300
$946$	−6.88154e12	−0.279367
$947$	−1.61530e13	−0.652646	−0.326323	−	0.945258i	$-0.605810\pi$
$947$	−1.61530e13	−0.652646	−0.326323	+	0.945258i	$0.605810\pi$
$948$	1.26925e13	0.510397
$949$	−4.76152e12	−0.190567
$950$	3.17371e12	0.126419
$951$	1.41194e13	0.559761
$952$	−3.74417e12	−0.147737
$953$	−3.41342e13	−1.34052	−0.670258	−	0.742128i	$-0.733816\pi$
$953$	−3.41342e13	−1.34052	−0.670258	+	0.742128i	$0.733816\pi$
$954$	−2.04857e12	−0.0800725
$955$	7.04959e12	0.274251
$956$	4.28874e12	0.166062
$957$	−9.98229e12	−0.384704
$958$	−3.50549e12	−0.134463
$959$	−1.70297e12	−0.0650165
$960$	2.12708e12	0.0808281
$961$	−1.59845e13	−0.604565
$962$	2.55301e13	0.961091
$963$	−5.50375e12	−0.206225
$964$	−4.03496e13	−1.50485
$965$	−1.03081e13	−0.382654
$966$	1.44001e12	0.0532070
$967$	−1.67489e13	−0.615980	−0.307990	−	0.951390i	$-0.599656\pi$
$967$	−1.67489e13	−0.615980	−0.307990	+	0.951390i	$0.599656\pi$
$968$	1.08912e13	0.398691
$969$	−1.63686e13	−0.596423
$970$	−5.22313e12	−0.189434
$971$	−4.31403e13	−1.55739	−0.778693	−	0.627405i	$-0.784117\pi$
$971$	−4.31403e13	−1.55739	−0.778693	+	0.627405i	$0.784117\pi$
$972$	1.55718e12	0.0559553
$973$	−8.71659e12	−0.311773
$974$	−2.59299e12	−0.0923180
$975$	5.27497e12	0.186939
$976$	7.48784e12	0.264139
$977$	2.69967e13	0.947950	0.473975	−	0.880538i	$-0.342819\pi$
$977$	2.69967e13	0.947950	0.473975	+	0.880538i	$0.342819\pi$
$978$	7.48417e12	0.261589
$979$	−3.06124e13	−1.06506
$980$	−1.60908e12	−0.0557264
$981$	2.76527e12	0.0953295
$982$	−9.52581e12	−0.326889
$983$	2.10717e13	0.719795	0.359898	−	0.932992i	$-0.382812\pi$
$983$	2.10717e13	0.719795	0.359898	+	0.932992i	$0.382812\pi$
$984$	−2.14593e13	−0.729689
$985$	−1.77495e13	−0.600792
$986$	6.49395e12	0.218808
$987$	5.28388e12	0.177225
$988$	7.47983e13	2.49739
$989$	2.52348e13	0.838719
$990$	1.02381e12	0.0338736
$991$	1.02559e13	0.337787	0.168893	−	0.985634i	$-0.445981\pi$
$991$	1.02559e13	0.337787	0.168893	+	0.985634i	$0.445981\pi$
$992$	1.71742e13	0.563086
$993$	−1.98923e12	−0.0649253
$994$	−5.55925e11	−0.0180625
$995$	−2.23808e13	−0.723888
$996$	7.10558e12	0.228788
$997$	1.85777e13	0.595474	0.297737	−	0.954648i	$-0.403768\pi$
$997$	1.85777e13	0.595474	0.297737	+	0.954648i	$0.403768\pi$
$998$	−4.19972e12	−0.134009
$999$	1.00630e13	0.319656

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.10.a.a.1.3	✓	4
3.2	odd	2		315.10.a.i.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.10.a.a.1.3	✓	4	1.1	even	1	trivial
315.10.a.i.1.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q+8.08732 q^{2} -81.0000 q^{3} -446.595 q^{4} +625.000 q^{5} -655.073 q^{6} +2401.00 q^{7} -7752.47 q^{8} +6561.00 q^{9} +5054.57 q^{10} +30872.0 q^{11} +36174.2 q^{12} -166715. q^{13} +19417.7 q^{14} -50625.0 q^{15} +165960. q^{16} +201152. q^{17} +53060.9 q^{18} +1.00462e6 q^{19} -279122. q^{20} -194481. q^{21} +249672. q^{22} -915554. q^{23} +627950. q^{24} +390625. q^{25} -1.34828e6 q^{26} -531441. q^{27} -1.07228e6 q^{28} +3.99190e6 q^{29} -409421. q^{30} +3.23344e6 q^{31} +5.31144e6 q^{32} -2.50063e6 q^{33} +1.62678e6 q^{34} +1.50062e6 q^{35} -2.93011e6 q^{36} -1.89353e7 q^{37} +8.12470e6 q^{38} +1.35039e7 q^{39} -4.84529e6 q^{40} -3.41736e7 q^{41} -1.57283e6 q^{42} -2.75623e7 q^{43} -1.37873e7 q^{44} +4.10062e6 q^{45} -7.40438e6 q^{46} -2.71691e7 q^{47} -1.34428e7 q^{48} +5.76480e6 q^{49} +3.15911e6 q^{50} -1.62933e7 q^{51} +7.44542e7 q^{52} -3.86079e7 q^{53} -4.29793e6 q^{54} +1.92950e7 q^{55} -1.86137e7 q^{56} -8.13744e7 q^{57} +3.22838e7 q^{58} -1.34261e8 q^{59} +2.26089e7 q^{60} +4.51183e7 q^{61} +2.61499e7 q^{62} +1.57530e7 q^{63} -4.20163e7 q^{64} -1.04197e8 q^{65} -2.02234e7 q^{66} +4.21823e7 q^{67} -8.98335e7 q^{68} +7.41599e7 q^{69} +1.21360e7 q^{70} -2.86299e7 q^{71} -5.08639e7 q^{72} +2.85608e7 q^{73} -1.53136e8 q^{74} -3.16406e7 q^{75} -4.48659e8 q^{76} +7.41237e7 q^{77} +1.09211e8 q^{78} +3.50870e8 q^{79} +1.03725e8 q^{80} +4.30467e7 q^{81} -2.76373e8 q^{82} +1.96427e8 q^{83} +8.68543e7 q^{84} +1.25720e8 q^{85} -2.22905e8 q^{86} -3.23344e8 q^{87} -2.39334e8 q^{88} -9.91592e8 q^{89} +3.31631e7 q^{90} -4.00283e8 q^{91} +4.08882e8 q^{92} -2.61909e8 q^{93} -2.19725e8 q^{94} +6.27889e8 q^{95} -4.30226e8 q^{96} -1.03335e9 q^{97} +4.66218e7 q^{98} +2.02551e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) \) 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * q^99

Introduction

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