LMFDB - Embedded newform 14.8.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,8,Mod(1,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.37339035678$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1969}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 492 $ x^2 - x - 492
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-21.6867$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.00000 q^{2} +79.3734 q^{3} +64.0000 q^{4} -336.361 q^{5} +634.987 q^{6} +343.000 q^{7} +512.000 q^{8} +4113.14 q^{9} -2690.89 q^{10} -7301.05 q^{11} +5079.90 q^{12} +5187.58 q^{13} +2744.00 q^{14} -26698.1 q^{15} +4096.00 q^{16} -23229.6 q^{17} +32905.1 q^{18} -10896.3 q^{19} -21527.1 q^{20} +27225.1 q^{21} -58408.4 q^{22} +33781.9 q^{23} +40639.2 q^{24} +35013.5 q^{25} +41500.6 q^{26} +152884. q^{27} +21952.0 q^{28} +186018. q^{29} -213585. q^{30} -98163.8 q^{31} +32768.0 q^{32} -579509. q^{33} -185837. q^{34} -115372. q^{35} +263241. q^{36} +283413. q^{37} -87170.1 q^{38} +411756. q^{39} -172217. q^{40} -241537. q^{41} +217801. q^{42} +747209. q^{43} -467267. q^{44} -1.38350e6 q^{45} +270255. q^{46} +1.01668e6 q^{47} +325114. q^{48} +117649. q^{49} +280108. q^{50} -1.84381e6 q^{51} +332005. q^{52} +217877. q^{53} +1.22307e6 q^{54} +2.45579e6 q^{55} +175616. q^{56} -864873. q^{57} +1.48814e6 q^{58} -2.04271e6 q^{59} -1.70868e6 q^{60} -1.16948e6 q^{61} -785310. q^{62} +1.41081e6 q^{63} +262144. q^{64} -1.74490e6 q^{65} -4.63607e6 q^{66} +1.32624e6 q^{67} -1.48669e6 q^{68} +2.68138e6 q^{69} -922974. q^{70} -1.28248e6 q^{71} +2.10593e6 q^{72} +2.59761e6 q^{73} +2.26730e6 q^{74} +2.77914e6 q^{75} -697361. q^{76} -2.50426e6 q^{77} +3.29404e6 q^{78} -2.40172e6 q^{79} -1.37773e6 q^{80} +3.13951e6 q^{81} -1.93230e6 q^{82} -5.37289e6 q^{83} +1.74241e6 q^{84} +7.81353e6 q^{85} +5.97767e6 q^{86} +1.47649e7 q^{87} -3.73814e6 q^{88} -1.19114e7 q^{89} -1.10680e7 q^{90} +1.77934e6 q^{91} +2.16204e6 q^{92} -7.79160e6 q^{93} +8.13343e6 q^{94} +3.66507e6 q^{95} +2.60091e6 q^{96} +1.35717e6 q^{97} +941192. q^{98} -3.00302e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{2} + 70 q^{3} + 128 q^{4} + 126 q^{5} + 560 q^{6} + 686 q^{7} + 1024 q^{8} + 2014 q^{9} + 1008 q^{10} - 3420 q^{11} + 4480 q^{12} - 6398 q^{13} + 5488 q^{14} - 31032 q^{15} + 8192 q^{16} - 38472 q^{17}+ \cdots - 38177100 q^{99}+O(q^{100}) $ 2 * q + 16 * q^2 + 70 * q^3 + 128 * q^4 + 126 * q^5 + 560 * q^6 + 686 * q^7 + 1024 * q^8 + 2014 * q^9 + 1008 * q^10 - 3420 * q^11 + 4480 * q^12 - 6398 * q^13 + 5488 * q^14 - 31032 * q^15 + 8192 * q^16 - 38472 * q^17 + 16112 * q^18 - 43358 * q^19 + 8064 * q^20 + 24010 * q^21 - 27360 * q^22 + 89928 * q^23 + 35840 * q^24 + 170666 * q^25 - 51184 * q^26 + 193060 * q^27 + 43904 * q^28 + 159576 * q^29 - 248256 * q^30 - 143612 * q^31 + 65536 * q^32 - 615888 * q^33 - 307776 * q^34 + 43218 * q^35 + 128896 * q^36 - 271832 * q^37 - 346864 * q^38 + 520352 * q^39 + 64512 * q^40 + 64848 * q^41 + 192080 * q^42 + 1527964 * q^43 - 218880 * q^44 - 2354058 * q^45 + 719424 * q^46 + 485436 * q^47 + 286720 * q^48 + 235298 * q^49 + 1365328 * q^50 - 1700940 * q^51 - 409472 * q^52 - 145716 * q^53 + 1544480 * q^54 + 4250232 * q^55 + 351232 * q^56 - 560596 * q^57 + 1276608 * q^58 - 4183662 * q^59 - 1986048 * q^60 - 280658 * q^61 - 1148896 * q^62 + 690802 * q^63 + 524288 * q^64 - 7101612 * q^65 - 4927104 * q^66 + 5671648 * q^67 - 2462208 * q^68 + 2155104 * q^69 + 345744 * q^70 - 619272 * q^71 + 1031168 * q^72 + 3939628 * q^73 - 2174656 * q^74 + 1507618 * q^75 - 2774912 * q^76 - 1173060 * q^77 + 4162816 * q^78 + 4656616 * q^79 + 516096 * q^80 + 7353742 * q^81 + 518784 * q^82 + 1235850 * q^83 + 1536640 * q^84 + 766044 * q^85 + 12223712 * q^86 + 15012732 * q^87 - 1751040 * q^88 - 17241420 * q^89 - 18832464 * q^90 - 2194514 * q^91 + 5755392 * q^92 - 7365592 * q^93 + 3883488 * q^94 - 11343960 * q^95 + 2293760 * q^96 - 740936 * q^97 + 1882384 * q^98 - 38177100 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	79.3734	1.69727	0.848634	−	0.528980i	$-0.177425\pi$
$3$	79.3734	1.69727	0.848634	+	0.528980i	$0.177425\pi$
$4$	64.0000	0.500000
$5$	−336.361	−1.20340	−0.601700	−	0.798722i	$-0.705510\pi$
$5$	−336.361	−1.20340	−0.601700	+	0.798722i	$0.705510\pi$
$6$	634.987	1.20015
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	4113.14	1.88072
$10$	−2690.89	−0.850933
$11$	−7301.05	−1.65391	−0.826953	−	0.562271i	$-0.809928\pi$
$11$	−7301.05	−1.65391	−0.826953	+	0.562271i	$0.809928\pi$
$12$	5079.90	0.848634
$13$	5187.58	0.654881	0.327441	−	0.944872i	$-0.393814\pi$
$13$	5187.58	0.654881	0.327441	+	0.944872i	$0.393814\pi$
$14$	2744.00	0.267261
$15$	−26698.1	−2.04249
$16$	4096.00	0.250000
$17$	−23229.6	−1.14676	−0.573378	−	0.819291i	$-0.694367\pi$
$17$	−23229.6	−1.14676	−0.573378	+	0.819291i	$0.694367\pi$
$18$	32905.1	1.32987
$19$	−10896.3	−0.364452	−0.182226	−	0.983257i	$-0.558330\pi$
$19$	−10896.3	−0.364452	−0.182226	+	0.983257i	$0.558330\pi$
$20$	−21527.1	−0.601700
$21$	27225.1	0.641507
$22$	−58408.4	−1.16949
$23$	33781.9	0.578944	0.289472	−	0.957186i	$-0.406520\pi$
$23$	33781.9	0.578944	0.289472	+	0.957186i	$0.406520\pi$
$24$	40639.2	0.600075
$25$	35013.5	0.448173
$26$	41500.6	0.463071
$27$	152884.	1.49482
$28$	21952.0	0.188982
$29$	186018.	1.41632	0.708161	−	0.706051i	$-0.249525\pi$
$29$	186018.	1.41632	0.708161	+	0.706051i	$0.249525\pi$
$30$	−213585.	−1.44426
$31$	−98163.8	−0.591814	−0.295907	−	0.955217i	$-0.595622\pi$
$31$	−98163.8	−0.591814	−0.295907	+	0.955217i	$0.595622\pi$
$32$	32768.0	0.176777
$33$	−579509.	−2.80712
$34$	−185837.	−0.810878
$35$	−115372.	−0.454843
$36$	263241.	0.940361
$37$	283413.	0.919842	0.459921	−	0.887960i	$-0.347878\pi$
$37$	283413.	0.919842	0.459921	+	0.887960i	$0.347878\pi$
$38$	−87170.1	−0.257706
$39$	411756.	1.11151
$40$	−172217.	−0.425466
$41$	−241537.	−0.547320	−0.273660	−	0.961827i	$-0.588234\pi$
$41$	−241537.	−0.547320	−0.273660	+	0.961827i	$0.588234\pi$
$42$	217801.	0.453614
$43$	747209.	1.43319	0.716593	−	0.697492i	$-0.245701\pi$
$43$	747209.	1.43319	0.716593	+	0.697492i	$0.245701\pi$
$44$	−467267.	−0.826953
$45$	−1.38350e6	−2.26326
$46$	270255.	0.409375
$47$	1.01668e6	1.42837	0.714186	−	0.699956i	$-0.246797\pi$
$47$	1.01668e6	1.42837	0.714186	+	0.699956i	$0.246797\pi$
$48$	325114.	0.424317
$49$	117649.	0.142857
$50$	280108.	0.316906
$51$	−1.84381e6	−1.94635
$52$	332005.	0.327441
$53$	217877.	0.201023	0.100511	−	0.994936i	$-0.467952\pi$
$53$	217877.	0.201023	0.100511	+	0.994936i	$0.467952\pi$
$54$	1.22307e6	1.05700
$55$	2.45579e6	1.99031
$56$	175616.	0.133631
$57$	−864873.	−0.618572
$58$	1.48814e6	1.00149
$59$	−2.04271e6	−1.29487	−0.647433	−	0.762123i	$-0.724157\pi$
$59$	−2.04271e6	−1.29487	−0.647433	+	0.762123i	$0.724157\pi$
$60$	−1.70868e6	−1.02125
$61$	−1.16948e6	−0.659689	−0.329844	−	0.944035i	$-0.606996\pi$
$61$	−1.16948e6	−0.659689	−0.329844	+	0.944035i	$0.606996\pi$
$62$	−785310.	−0.418476
$63$	1.41081e6	0.710846
$64$	262144.	0.125000
$65$	−1.74490e6	−0.788085
$66$	−4.63607e6	−1.98494
$67$	1.32624e6	0.538717	0.269358	−	0.963040i	$-0.413188\pi$
$67$	1.32624e6	0.538717	0.269358	+	0.963040i	$0.413188\pi$
$68$	−1.48669e6	−0.573378
$69$	2.68138e6	0.982624
$70$	−922974.	−0.321622
$71$	−1.28248e6	−0.425252	−0.212626	−	0.977134i	$-0.568202\pi$
$71$	−1.28248e6	−0.425252	−0.212626	+	0.977134i	$0.568202\pi$
$72$	2.10593e6	0.664936
$73$	2.59761e6	0.781527	0.390763	−	0.920491i	$-0.372211\pi$
$73$	2.59761e6	0.781527	0.390763	+	0.920491i	$0.372211\pi$
$74$	2.26730e6	0.650427
$75$	2.77914e6	0.760671
$76$	−697361.	−0.182226
$77$	−2.50426e6	−0.625118
$78$	3.29404e6	0.785956
$79$	−2.40172e6	−0.548059	−0.274030	−	0.961721i	$-0.588357\pi$
$79$	−2.40172e6	−0.548059	−0.274030	+	0.961721i	$0.588357\pi$
$80$	−1.37773e6	−0.300850
$81$	3.13951e6	0.656393
$82$	−1.93230e6	−0.387013
$83$	−5.37289e6	−1.03142	−0.515708	−	0.856764i	$-0.672471\pi$
$83$	−5.37289e6	−1.03142	−0.515708	+	0.856764i	$0.672471\pi$
$84$	1.74241e6	0.320754
$85$	7.81353e6	1.38001
$86$	5.97767e6	1.01342
$87$	1.47649e7	2.40388
$88$	−3.73814e6	−0.584744
$89$	−1.19114e7	−1.79102	−0.895508	−	0.445046i	$-0.853187\pi$
$89$	−1.19114e7	−1.79102	−0.895508	+	0.445046i	$0.853187\pi$
$90$	−1.10680e7	−1.60037
$91$	1.77934e6	0.247522
$92$	2.16204e6	0.289472
$93$	−7.79160e6	−1.00447
$94$	8.13343e6	1.01001
$95$	3.66507e6	0.438581
$96$	2.60091e6	0.300038
$97$	1.35717e6	0.150984	0.0754922	−	0.997146i	$-0.475947\pi$
$97$	1.35717e6	0.150984	0.0754922	+	0.997146i	$0.475947\pi$
$98$	941192.	0.101015
$99$	−3.00302e7	−3.11054
$100$	2.24087e6	0.224087
$101$	−4.61311e6	−0.445522	−0.222761	−	0.974873i	$-0.571507\pi$
$101$	−4.61311e6	−0.445522	−0.222761	+	0.974873i	$0.571507\pi$
$102$	−1.47505e7	−1.37628
$103$	−1.63304e6	−0.147254	−0.0736270	−	0.997286i	$-0.523457\pi$
$103$	−1.63304e6	−0.147254	−0.0736270	+	0.997286i	$0.523457\pi$
$104$	2.65604e6	0.231536
$105$	−9.15745e6	−0.771990
$106$	1.74301e6	0.142145
$107$	1.91481e7	1.51106	0.755530	−	0.655114i	$-0.227379\pi$
$107$	1.91481e7	1.51106	0.755530	+	0.655114i	$0.227379\pi$
$108$	9.78459e6	0.747411
$109$	−7.47493e6	−0.552859	−0.276430	−	0.961034i	$-0.589151\pi$
$109$	−7.47493e6	−0.552859	−0.276430	+	0.961034i	$0.589151\pi$
$110$	1.96463e7	1.40736
$111$	2.24954e7	1.56122
$112$	1.40493e6	0.0944911
$113$	1.11093e6	0.0724290	0.0362145	−	0.999344i	$-0.488470\pi$
$113$	1.11093e6	0.0724290	0.0362145	+	0.999344i	$0.488470\pi$
$114$	−6.91899e6	−0.437397
$115$	−1.13629e7	−0.696702
$116$	1.19051e7	0.708161
$117$	2.13372e7	1.23165
$118$	−1.63417e7	−0.915608
$119$	−7.96776e6	−0.433433
$120$	−1.36694e7	−0.722131
$121$	3.38182e7	1.73541
$122$	−9.35585e6	−0.466470
$123$	−1.91717e7	−0.928949
$124$	−6.28248e6	−0.295907
$125$	1.45010e7	0.664069
$126$	1.12865e7	0.502644
$127$	−4.20574e7	−1.82192	−0.910959	−	0.412496i	$-0.864657\pi$
$127$	−4.20574e7	−1.82192	−0.910959	+	0.412496i	$0.864657\pi$
$128$	2.09715e6	0.0883883
$129$	5.93085e7	2.43250
$130$	−1.39592e7	−0.557260
$131$	1.24851e7	0.485225	0.242612	−	0.970123i	$-0.421996\pi$
$131$	1.24851e7	0.485225	0.242612	+	0.970123i	$0.421996\pi$
$132$	−3.70886e7	−1.40356
$133$	−3.73742e6	−0.137750
$134$	1.06099e7	0.380930
$135$	−5.14243e7	−1.79887
$136$	−1.18936e7	−0.405439
$137$	−4.47899e6	−0.148819	−0.0744094	−	0.997228i	$-0.523707\pi$
$137$	−4.47899e6	−0.148819	−0.0744094	+	0.997228i	$0.523707\pi$
$138$	2.14511e7	0.694820
$139$	2.24454e7	0.708884	0.354442	−	0.935078i	$-0.384671\pi$
$139$	2.24454e7	0.708884	0.354442	+	0.935078i	$0.384671\pi$
$140$	−7.38379e6	−0.227421
$141$	8.06973e7	2.42433
$142$	−1.02598e7	−0.300698
$143$	−3.78748e7	−1.08311
$144$	1.68474e7	0.470181
$145$	−6.25691e7	−1.70440
$146$	2.07809e7	0.552623
$147$	9.33820e6	0.242467
$148$	1.81384e7	0.459921
$149$	−6.07014e7	−1.50330	−0.751651	−	0.659561i	$-0.770742\pi$
$149$	−6.07014e7	−1.50330	−0.751651	+	0.659561i	$0.770742\pi$
$150$	2.22332e7	0.537875
$151$	−1.88146e7	−0.444709	−0.222354	−	0.974966i	$-0.571374\pi$
$151$	−1.88146e7	−0.444709	−0.222354	+	0.974966i	$0.571374\pi$
$152$	−5.57889e6	−0.128853
$153$	−9.55466e7	−2.15673
$154$	−2.00341e7	−0.442025
$155$	3.30185e7	0.712190
$156$	2.63524e7	0.555755
$157$	−7.64122e6	−0.157585	−0.0787923	−	0.996891i	$-0.525106\pi$
$157$	−7.64122e6	−0.157585	−0.0787923	+	0.996891i	$0.525106\pi$
$158$	−1.92138e7	−0.387537
$159$	1.72936e7	0.341190
$160$	−1.10219e7	−0.212733
$161$	1.15872e7	0.218820
$162$	2.51161e7	0.464140
$163$	9.09986e7	1.64580	0.822902	−	0.568184i	$-0.192354\pi$
$163$	9.09986e7	1.64580	0.822902	+	0.568184i	$0.192354\pi$
$164$	−1.54584e7	−0.273660
$165$	1.94924e8	3.37810
$166$	−4.29831e7	−0.729322
$167$	6.93101e7	1.15157	0.575783	−	0.817603i	$-0.304697\pi$
$167$	6.93101e7	1.15157	0.575783	+	0.817603i	$0.304697\pi$
$168$	1.39392e7	0.226807
$169$	−3.58376e7	−0.571130
$170$	6.25082e7	0.975811
$171$	−4.48178e7	−0.685432
$172$	4.78214e7	0.716593
$173$	−7.73949e7	−1.13645	−0.568226	−	0.822872i	$-0.692370\pi$
$173$	−7.73949e7	−1.13645	−0.568226	+	0.822872i	$0.692370\pi$
$174$	1.18119e8	1.69980
$175$	1.20096e7	0.169394
$176$	−2.99051e7	−0.413477
$177$	−1.62137e8	−2.19773
$178$	−9.52915e7	−1.26644
$179$	−4.95423e7	−0.645640	−0.322820	−	0.946460i	$-0.604631\pi$
$179$	−4.95423e7	−0.645640	−0.322820	+	0.946460i	$0.604631\pi$
$180$	−8.85439e7	−1.13163
$181$	1.39330e7	0.174650	0.0873251	−	0.996180i	$-0.472168\pi$
$181$	1.39330e7	0.174650	0.0873251	+	0.996180i	$0.472168\pi$
$182$	1.42347e7	0.175024
$183$	−9.28258e7	−1.11967
$184$	1.72963e7	0.204688
$185$	−9.53289e7	−1.10694
$186$	−6.23328e7	−0.710266
$187$	1.69601e8	1.89663
$188$	6.50675e7	0.714186
$189$	5.24393e7	0.564990
$190$	2.93206e7	0.310124
$191$	6.78160e7	0.704231	0.352116	−	0.935957i	$-0.385462\pi$
$191$	6.78160e7	0.704231	0.352116	+	0.935957i	$0.385462\pi$
$192$	2.08073e7	0.212159
$193$	−1.09345e8	−1.09484	−0.547419	−	0.836859i	$-0.684390\pi$
$193$	−1.09345e8	−1.09484	−0.547419	+	0.836859i	$0.684390\pi$
$194$	1.08573e7	0.106762
$195$	−1.38498e8	−1.33759
$196$	7.52954e6	0.0714286
$197$	9.14828e7	0.852526	0.426263	−	0.904599i	$-0.359830\pi$
$197$	9.14828e7	0.852526	0.426263	+	0.904599i	$0.359830\pi$
$198$	−2.40242e8	−2.19948
$199$	3.08493e7	0.277498	0.138749	−	0.990328i	$-0.455692\pi$
$199$	3.08493e7	0.277498	0.138749	+	0.990328i	$0.455692\pi$
$200$	1.79269e7	0.158453
$201$	1.05268e8	0.914347
$202$	−3.69049e7	−0.315031
$203$	6.38042e7	0.535319
$204$	−1.18004e8	−0.973176
$205$	8.12437e7	0.658645
$206$	−1.30643e7	−0.104124
$207$	1.38950e8	1.08883
$208$	2.12483e7	0.163720
$209$	7.95541e7	0.602769
$210$	−7.32596e7	−0.545880
$211$	1.24066e8	0.909212	0.454606	−	0.890693i	$-0.349780\pi$
$211$	1.24066e8	0.909212	0.454606	+	0.890693i	$0.349780\pi$
$212$	1.39441e7	0.100511
$213$	−1.01795e8	−0.721766
$214$	1.53185e8	1.06848
$215$	−2.51332e8	−1.72470
$216$	7.82767e7	0.528499
$217$	−3.36702e7	−0.223685
$218$	−5.97995e7	−0.390931
$219$	2.06181e8	1.32646
$220$	1.57170e8	0.995156
$221$	−1.20505e8	−0.750989
$222$	1.79964e8	1.10395
$223$	−8.25681e7	−0.498592	−0.249296	−	0.968427i	$-0.580199\pi$
$223$	−8.25681e7	−0.498592	−0.249296	+	0.968427i	$0.580199\pi$
$224$	1.12394e7	0.0668153
$225$	1.44016e8	0.842890
$226$	8.88744e6	0.0512150
$227$	3.76858e7	0.213839	0.106919	−	0.994268i	$-0.465901\pi$
$227$	3.76858e7	0.213839	0.106919	+	0.994268i	$0.465901\pi$
$228$	−5.53519e7	−0.309286
$229$	1.08195e8	0.595362	0.297681	−	0.954665i	$-0.403787\pi$
$229$	1.08195e8	0.595362	0.297681	+	0.954665i	$0.403787\pi$
$230$	−9.09032e7	−0.492643
$231$	−1.98772e8	−1.06099
$232$	9.52412e7	0.500745
$233$	−1.03320e8	−0.535104	−0.267552	−	0.963543i	$-0.586215\pi$
$233$	−1.03320e8	−0.535104	−0.267552	+	0.963543i	$0.586215\pi$
$234$	1.70698e8	0.870908
$235$	−3.41971e8	−1.71890
$236$	−1.30733e8	−0.647433
$237$	−1.90633e8	−0.930204
$238$	−6.37420e7	−0.306483
$239$	2.95896e8	1.40200	0.700998	−	0.713163i	$-0.252738\pi$
$239$	2.95896e8	1.40200	0.700998	+	0.713163i	$0.252738\pi$
$240$	−1.09355e8	−0.510624
$241$	−6.39349e7	−0.294224	−0.147112	−	0.989120i	$-0.546998\pi$
$241$	−6.39349e7	−0.294224	−0.147112	+	0.989120i	$0.546998\pi$
$242$	2.70545e8	1.22712
$243$	−8.51643e7	−0.380746
$244$	−7.48468e7	−0.329844
$245$	−3.95725e7	−0.171914
$246$	−1.53373e8	−0.656866
$247$	−5.65252e7	−0.238673
$248$	−5.02599e7	−0.209238
$249$	−4.26464e8	−1.75059
$250$	1.16008e8	0.469567
$251$	−1.48417e7	−0.0592414	−0.0296207	−	0.999561i	$-0.509430\pi$
$251$	−1.48417e7	−0.0592414	−0.0296207	+	0.999561i	$0.509430\pi$
$252$	9.02916e7	0.355423
$253$	−2.46643e8	−0.957519
$254$	−3.36459e8	−1.28829
$255$	6.20186e8	2.34224
$256$	1.67772e7	0.0625000
$257$	9.52785e7	0.350130	0.175065	−	0.984557i	$-0.443986\pi$
$257$	9.52785e7	0.350130	0.175065	+	0.984557i	$0.443986\pi$
$258$	4.74468e8	1.72004
$259$	9.72106e7	0.347668
$260$	−1.11673e8	−0.394042
$261$	7.65118e8	2.66371
$262$	9.98809e7	0.343106
$263$	2.25843e8	0.765528	0.382764	−	0.923846i	$-0.374972\pi$
$263$	2.25843e8	0.765528	0.382764	+	0.923846i	$0.374972\pi$
$264$	−2.96709e8	−0.992468
$265$	−7.32851e7	−0.241911
$266$	−2.98993e7	−0.0974038
$267$	−9.45452e8	−3.03984
$268$	8.48794e7	0.269358
$269$	2.37028e7	0.0742450	0.0371225	−	0.999311i	$-0.488181\pi$
$269$	2.37028e7	0.0742450	0.0371225	+	0.999311i	$0.488181\pi$
$270$	−4.11394e8	−1.27199
$271$	2.32187e8	0.708673	0.354337	−	0.935118i	$-0.384707\pi$
$271$	2.32187e8	0.708673	0.354337	+	0.935118i	$0.384707\pi$
$272$	−9.51485e7	−0.286689
$273$	1.41232e8	0.420111
$274$	−3.58319e7	−0.105231
$275$	−2.55636e8	−0.741237
$276$	1.71609e8	0.491312
$277$	5.44889e8	1.54038	0.770192	−	0.637813i	$-0.220161\pi$
$277$	5.44889e8	1.54038	0.770192	+	0.637813i	$0.220161\pi$
$278$	1.79563e8	0.501257
$279$	−4.03761e8	−1.11304
$280$	−5.90703e7	−0.160811
$281$	−2.72204e8	−0.731849	−0.365925	−	0.930644i	$-0.619247\pi$
$281$	−2.72204e8	−0.731849	−0.365925	+	0.930644i	$0.619247\pi$
$282$	6.45578e8	1.71426
$283$	3.81118e8	0.999556	0.499778	−	0.866154i	$-0.333415\pi$
$283$	3.81118e8	0.999556	0.499778	+	0.866154i	$0.333415\pi$
$284$	−8.20786e7	−0.212626
$285$	2.90909e8	0.744390
$286$	−3.02998e8	−0.765876
$287$	−8.28474e7	−0.206867
$288$	1.34779e8	0.332468
$289$	1.29276e8	0.315047
$290$	−5.00553e8	−1.20519
$291$	1.07723e8	0.256261
$292$	1.66247e8	0.390763
$293$	6.97920e8	1.62095	0.810473	−	0.585775i	$-0.199210\pi$
$293$	6.97920e8	1.62095	0.810473	+	0.585775i	$0.199210\pi$
$294$	7.47056e7	0.171450
$295$	6.87087e8	1.55824
$296$	1.45107e8	0.325213
$297$	−1.11622e9	−2.47230
$298$	−4.85611e8	−1.06300
$299$	1.75246e8	0.379140
$300$	1.77865e8	0.380335
$301$	2.56293e8	0.541693
$302$	−1.50517e8	−0.314456
$303$	−3.66158e8	−0.756170
$304$	−4.46311e7	−0.0911129
$305$	3.93368e8	0.793870
$306$	−7.64373e8	−1.52504
$307$	−8.88578e8	−1.75272	−0.876358	−	0.481661i	$-0.840034\pi$
$307$	−8.88578e8	−1.75272	−0.876358	+	0.481661i	$0.840034\pi$
$308$	−1.60273e8	−0.312559
$309$	−1.29620e8	−0.249930
$310$	2.64148e8	0.503594
$311$	6.56861e8	1.23826	0.619130	−	0.785288i	$-0.287485\pi$
$311$	6.56861e8	1.23826	0.619130	+	0.785288i	$0.287485\pi$
$312$	2.10819e8	0.392978
$313$	−1.06434e9	−1.96189	−0.980944	−	0.194292i	$-0.937759\pi$
$313$	−1.06434e9	−1.96189	−0.980944	+	0.194292i	$0.937759\pi$
$314$	−6.11298e7	−0.111429
$315$	−4.74540e8	−0.855433
$316$	−1.53710e8	−0.274030
$317$	−7.45589e8	−1.31459	−0.657297	−	0.753631i	$-0.728300\pi$
$317$	−7.45589e8	−1.31459	−0.657297	+	0.753631i	$0.728300\pi$
$318$	1.38349e8	0.241257
$319$	−1.35813e9	−2.34246
$320$	−8.81749e7	−0.150425
$321$	1.51985e9	2.56468
$322$	9.26975e7	0.154729
$323$	2.53116e8	0.417937
$324$	2.00929e8	0.328197
$325$	1.81635e8	0.293500
$326$	7.27988e8	1.16376
$327$	−5.93311e8	−0.938351
$328$	−1.23667e8	−0.193507
$329$	3.48721e8	0.539874
$330$	1.55939e9	2.38867
$331$	−8.82799e8	−1.33802	−0.669012	−	0.743252i	$-0.733282\pi$
$331$	−8.82799e8	−1.33802	−0.669012	+	0.743252i	$0.733282\pi$
$332$	−3.43865e8	−0.515708
$333$	1.16572e9	1.72997
$334$	5.54480e8	0.814280
$335$	−4.46095e8	−0.648292
$336$	1.11514e8	0.160377
$337$	6.91575e8	0.984317	0.492158	−	0.870506i	$-0.336208\pi$
$337$	6.91575e8	0.984317	0.492158	+	0.870506i	$0.336208\pi$
$338$	−2.86701e8	−0.403850
$339$	8.81783e7	0.122931
$340$	5.00066e8	0.690003
$341$	7.16699e8	0.978806
$342$	−3.58543e8	−0.484674
$343$	4.03536e7	0.0539949
$344$	3.82571e8	0.506708
$345$	−9.01913e8	−1.18249
$346$	−6.19160e8	−0.803593
$347$	9.09153e8	1.16811	0.584055	−	0.811714i	$-0.301465\pi$
$347$	9.09153e8	1.16811	0.584055	+	0.811714i	$0.301465\pi$
$348$	9.44952e8	1.20194
$349$	−2.66615e8	−0.335734	−0.167867	−	0.985810i	$-0.553688\pi$
$349$	−2.66615e8	−0.335734	−0.167867	+	0.985810i	$0.553688\pi$
$350$	9.60772e7	0.119779
$351$	7.93099e8	0.978931
$352$	−2.39241e8	−0.292372
$353$	−5.81098e8	−0.703134	−0.351567	−	0.936163i	$-0.614351\pi$
$353$	−5.81098e8	−0.703134	−0.351567	+	0.936163i	$0.614351\pi$
$354$	−1.29709e9	−1.55403
$355$	4.31376e8	0.511748
$356$	−7.62332e8	−0.895508
$357$	−6.32428e8	−0.735652
$358$	−3.96338e8	−0.456536
$359$	4.07067e8	0.464339	0.232169	−	0.972675i	$-0.425418\pi$
$359$	4.07067e8	0.464339	0.232169	+	0.972675i	$0.425418\pi$
$360$	−7.08351e8	−0.800184
$361$	−7.75143e8	−0.867175
$362$	1.11464e8	0.123496
$363$	2.68426e9	2.94545
$364$	1.13878e8	0.123761
$365$	−8.73734e8	−0.940490
$366$	−7.42606e8	−0.791726
$367$	−1.13161e9	−1.19499	−0.597497	−	0.801871i	$-0.703838\pi$
$367$	−1.13161e9	−1.19499	−0.597497	+	0.801871i	$0.703838\pi$
$368$	1.38371e8	0.144736
$369$	−9.93477e8	−1.02936
$370$	−7.62631e8	−0.782724
$371$	7.47317e7	0.0759794
$372$	−4.98662e8	−0.502234
$373$	4.02614e8	0.401706	0.200853	−	0.979621i	$-0.435629\pi$
$373$	4.02614e8	0.401706	0.200853	+	0.979621i	$0.435629\pi$
$374$	1.35680e9	1.34112
$375$	1.15099e9	1.12710
$376$	5.20540e8	0.505006
$377$	9.64982e8	0.927523
$378$	4.19514e8	0.399508
$379$	−1.10601e9	−1.04358	−0.521788	−	0.853075i	$-0.674735\pi$
$379$	−1.10601e9	−1.04358	−0.521788	+	0.853075i	$0.674735\pi$
$380$	2.34565e8	0.219291
$381$	−3.33824e9	−3.09229
$382$	5.42528e8	0.497967
$383$	−4.53921e8	−0.412843	−0.206421	−	0.978463i	$-0.566182\pi$
$383$	−4.53921e8	−0.412843	−0.206421	+	0.978463i	$0.566182\pi$
$384$	1.66458e8	0.150019
$385$	8.42335e8	0.752267
$386$	−8.74763e8	−0.774167
$387$	3.07337e9	2.69542
$388$	8.68587e7	0.0754922
$389$	−9.60495e8	−0.827316	−0.413658	−	0.910432i	$-0.635749\pi$
$389$	−9.60495e8	−0.827316	−0.413658	+	0.910432i	$0.635749\pi$
$390$	−1.10799e9	−0.945820
$391$	−7.84740e8	−0.663907
$392$	6.02363e7	0.0505076
$393$	9.90986e8	0.823557
$394$	7.31863e8	0.602827
$395$	8.07845e8	0.659535
$396$	−1.92194e9	−1.55527
$397$	1.12291e9	0.900697	0.450348	−	0.892853i	$-0.351300\pi$
$397$	1.12291e9	0.900697	0.450348	+	0.892853i	$0.351300\pi$
$398$	2.46795e8	0.196221
$399$	−2.96652e8	−0.233798
$400$	1.43415e8	0.112043
$401$	−1.76041e9	−1.36336	−0.681678	−	0.731652i	$-0.738750\pi$
$401$	−1.76041e9	−1.36336	−0.681678	+	0.731652i	$0.738750\pi$
$402$	8.42146e8	0.646541
$403$	−5.09232e8	−0.387568
$404$	−2.95239e8	−0.222761
$405$	−1.05601e9	−0.789904
$406$	5.10433e8	0.378528
$407$	−2.06921e9	−1.52133
$408$	−9.44032e8	−0.688139
$409$	2.11281e9	1.52697	0.763484	−	0.645827i	$-0.223487\pi$
$409$	2.11281e9	1.52697	0.763484	+	0.645827i	$0.223487\pi$
$410$	6.49950e8	0.465732
$411$	−3.55513e8	−0.252586
$412$	−1.04515e8	−0.0736270
$413$	−7.00649e8	−0.489413
$414$	1.11160e9	0.769921
$415$	1.80723e9	1.24121
$416$	1.69986e8	0.115768
$417$	1.78157e9	1.20317
$418$	6.36433e8	0.426222
$419$	2.60472e9	1.72987	0.864933	−	0.501888i	$-0.167361\pi$
$419$	2.60472e9	1.72987	0.864933	+	0.501888i	$0.167361\pi$
$420$	−5.86077e8	−0.385995
$421$	2.12220e9	1.38612	0.693058	−	0.720882i	$-0.256263\pi$
$421$	2.12220e9	1.38612	0.693058	+	0.720882i	$0.256263\pi$
$422$	9.92531e8	0.642910
$423$	4.18174e9	2.68637
$424$	1.11553e8	0.0710723
$425$	−8.13351e8	−0.513945
$426$	−8.14358e8	−0.510366
$427$	−4.01132e8	−0.249339
$428$	1.22548e9	0.755530
$429$	−3.00625e9	−1.83833
$430$	−2.01065e9	−1.21954
$431$	−1.95548e9	−1.17647	−0.588237	−	0.808689i	$-0.700178\pi$
$431$	−1.95548e9	−1.17647	−0.588237	+	0.808689i	$0.700178\pi$
$432$	6.26214e8	0.373706
$433$	−2.66286e9	−1.57630	−0.788152	−	0.615480i	$-0.788962\pi$
$433$	−2.66286e9	−1.57630	−0.788152	+	0.615480i	$0.788962\pi$
$434$	−2.69361e8	−0.158169
$435$	−4.96633e9	−2.89283
$436$	−4.78396e8	−0.276430
$437$	−3.68096e8	−0.210997
$438$	1.64945e9	0.937950
$439$	−6.85269e8	−0.386576	−0.193288	−	0.981142i	$-0.561915\pi$
$439$	−6.85269e8	−0.386576	−0.193288	+	0.981142i	$0.561915\pi$
$440$	1.25736e9	0.703682
$441$	4.83907e8	0.268675
$442$	−9.64043e8	−0.531029
$443$	−5.97929e8	−0.326766	−0.163383	−	0.986563i	$-0.552241\pi$
$443$	−5.97929e8	−0.326766	−0.163383	+	0.986563i	$0.552241\pi$
$444$	1.43971e9	0.780610
$445$	4.00654e9	2.15531
$446$	−6.60545e8	−0.352558
$447$	−4.81807e9	−2.55151
$448$	8.99154e7	0.0472456
$449$	1.99499e9	1.04011	0.520054	−	0.854133i	$-0.325912\pi$
$449$	1.99499e9	1.04011	0.520054	+	0.854133i	$0.325912\pi$
$450$	1.15212e9	0.596013
$451$	1.76348e9	0.905215
$452$	7.10995e7	0.0362145
$453$	−1.49338e9	−0.754790
$454$	3.01486e8	0.151207
$455$	−5.98500e8	−0.297868
$456$	−4.42815e8	−0.218698
$457$	1.90956e9	0.935896	0.467948	−	0.883756i	$-0.344994\pi$
$457$	1.90956e9	0.935896	0.467948	+	0.883756i	$0.344994\pi$
$458$	8.65556e8	0.420985
$459$	−3.55144e9	−1.71419
$460$	−7.27226e8	−0.348351
$461$	−2.16216e9	−1.02786	−0.513931	−	0.857832i	$-0.671811\pi$
$461$	−2.16216e9	−1.02786	−0.513931	+	0.857832i	$0.671811\pi$
$462$	−1.59017e9	−0.750235
$463$	2.71501e9	1.27127	0.635634	−	0.771990i	$-0.280739\pi$
$463$	2.71501e9	1.27127	0.635634	+	0.771990i	$0.280739\pi$
$464$	7.61930e8	0.354080
$465$	2.62079e9	1.20878
$466$	−8.26560e8	−0.378376
$467$	2.47856e9	1.12613	0.563067	−	0.826411i	$-0.309621\pi$
$467$	2.47856e9	1.12613	0.563067	+	0.826411i	$0.309621\pi$
$468$	1.36558e9	0.615825
$469$	4.54900e8	0.203616
$470$	−2.73577e9	−1.21545
$471$	−6.06510e8	−0.267464
$472$	−1.04587e9	−0.457804
$473$	−5.45541e9	−2.37035
$474$	−1.52506e9	−0.657754
$475$	−3.81517e8	−0.163338
$476$	−5.09936e8	−0.216716
$477$	8.96157e8	0.378068
$478$	2.36717e9	0.991361
$479$	−1.60708e8	−0.0668135	−0.0334068	−	0.999442i	$-0.510636\pi$
$479$	−1.60708e8	−0.0668135	−0.0334068	+	0.999442i	$0.510636\pi$
$480$	−8.74843e8	−0.361065
$481$	1.47023e9	0.602388
$482$	−5.11479e8	−0.208048
$483$	9.19715e8	0.371397
$484$	2.16436e9	0.867703
$485$	−4.56498e8	−0.181695
$486$	−6.81314e8	−0.269228
$487$	−2.42367e9	−0.950871	−0.475435	−	0.879751i	$-0.657709\pi$
$487$	−2.42367e9	−0.950871	−0.475435	+	0.879751i	$0.657709\pi$
$488$	−5.98775e8	−0.233235
$489$	7.22287e9	2.79337
$490$	−3.16580e8	−0.121562
$491$	−1.20070e9	−0.457772	−0.228886	−	0.973453i	$-0.573508\pi$
$491$	−1.20070e9	−0.457772	−0.228886	+	0.973453i	$0.573508\pi$
$492$	−1.22699e9	−0.464474
$493$	−4.32112e9	−1.62417
$494$	−4.52201e8	−0.168767
$495$	1.01010e10	3.74322
$496$	−4.02079e8	−0.147954
$497$	−4.39890e8	−0.160730
$498$	−3.41171e9	−1.23786
$499$	3.49146e9	1.25793	0.628963	−	0.777435i	$-0.283480\pi$
$499$	3.49146e9	1.25793	0.628963	+	0.777435i	$0.283480\pi$
$500$	9.28064e8	0.332034
$501$	5.50138e9	1.95452
$502$	−1.18733e8	−0.0418900
$503$	3.28614e9	1.15133	0.575663	−	0.817687i	$-0.304744\pi$
$503$	3.28614e9	1.15133	0.575663	+	0.817687i	$0.304744\pi$
$504$	7.22333e8	0.251322
$505$	1.55167e9	0.536141
$506$	−1.97315e9	−0.677068
$507$	−2.84455e9	−0.969362
$508$	−2.69167e9	−0.910959
$509$	−3.22801e9	−1.08498	−0.542492	−	0.840061i	$-0.682519\pi$
$509$	−3.22801e9	−1.08498	−0.542492	+	0.840061i	$0.682519\pi$
$510$	4.96149e9	1.65621
$511$	8.90980e8	0.295389
$512$	1.34218e8	0.0441942
$513$	−1.66587e9	−0.544790
$514$	7.62228e8	0.247579
$515$	5.49292e8	0.177206
$516$	3.79575e9	1.21625
$517$	−7.42283e9	−2.36239
$518$	7.77685e8	0.245838
$519$	−6.14310e9	−1.92887
$520$	−8.93387e8	−0.278630
$521$	4.36929e9	1.35356	0.676782	−	0.736183i	$-0.263374\pi$
$521$	4.36929e9	1.35356	0.676782	+	0.736183i	$0.263374\pi$
$522$	6.12094e9	1.88353
$523$	−1.17386e9	−0.358806	−0.179403	−	0.983776i	$-0.557417\pi$
$523$	−1.17386e9	−0.358806	−0.179403	+	0.983776i	$0.557417\pi$
$524$	7.99047e8	0.242612
$525$	9.53247e8	0.287507
$526$	1.80674e9	0.541310
$527$	2.28031e9	0.678666
$528$	−2.37367e9	−0.701781
$529$	−2.26361e9	−0.664824
$530$	−5.86281e8	−0.171057
$531$	−8.40195e9	−2.43528
$532$	−2.39195e8	−0.0688749
$533$	−1.25299e9	−0.358429
$534$	−7.56361e9	−2.14949
$535$	−6.44066e9	−1.81841
$536$	6.79035e8	0.190465
$537$	−3.93234e9	−1.09582
$538$	1.89623e8	0.0524992
$539$	−8.58961e8	−0.236272
$540$	−3.29115e9	−0.899435
$541$	4.81764e9	1.30811	0.654054	−	0.756448i	$-0.273067\pi$
$541$	4.81764e9	1.30811	0.654054	+	0.756448i	$0.273067\pi$
$542$	1.85750e9	0.501108
$543$	1.10591e9	0.296428
$544$	−7.61188e8	−0.202720
$545$	2.51427e9	0.665311
$546$	1.12986e9	0.297064
$547$	3.75203e9	0.980192	0.490096	−	0.871668i	$-0.336962\pi$
$547$	3.75203e9	0.980192	0.490096	+	0.871668i	$0.336962\pi$
$548$	−2.86655e8	−0.0744094
$549$	−4.81024e9	−1.24069
$550$	−2.04509e9	−0.524134
$551$	−2.02690e9	−0.516181
$552$	1.37287e9	0.347410
$553$	−8.23790e8	−0.207147
$554$	4.35911e9	1.08922
$555$	−7.56658e9	−1.87877
$556$	1.43650e9	0.354442
$557$	7.46410e9	1.83014	0.915070	−	0.403296i	$-0.132135\pi$
$557$	7.46410e9	1.83014	0.915070	+	0.403296i	$0.132135\pi$
$558$	−3.23009e9	−0.787037
$559$	3.87620e9	0.938567
$560$	−4.72563e8	−0.113711
$561$	1.34618e10	3.21908
$562$	−2.17763e9	−0.517496
$563$	2.15093e9	0.507980	0.253990	−	0.967207i	$-0.418257\pi$
$563$	2.15093e9	0.507980	0.253990	+	0.967207i	$0.418257\pi$
$564$	5.16463e9	1.21217
$565$	−3.73673e8	−0.0871611
$566$	3.04895e9	0.706793
$567$	1.07685e9	0.248093
$568$	−6.56629e8	−0.150349
$569$	3.41171e9	0.776390	0.388195	−	0.921577i	$-0.373099\pi$
$569$	3.41171e9	0.776390	0.388195	+	0.921577i	$0.373099\pi$
$570$	2.32728e9	0.526364
$571$	−3.38481e9	−0.760865	−0.380432	−	0.924809i	$-0.624225\pi$
$571$	−3.38481e9	−0.760865	−0.380432	+	0.924809i	$0.624225\pi$
$572$	−2.42398e9	−0.541556
$573$	5.38279e9	1.19527
$574$	−6.62779e8	−0.146277
$575$	1.18282e9	0.259467
$576$	1.07823e9	0.235090
$577$	−7.98376e9	−1.73018	−0.865091	−	0.501614i	$-0.832740\pi$
$577$	−7.98376e9	−1.73018	−0.865091	+	0.501614i	$0.832740\pi$
$578$	1.03421e9	0.222772
$579$	−8.67912e9	−1.85823
$580$	−4.00442e9	−0.852201
$581$	−1.84290e9	−0.389839
$582$	8.61784e8	0.181204
$583$	−1.59073e9	−0.332473
$584$	1.32998e9	0.276311
$585$	−7.17700e9	−1.48217
$586$	5.58336e9	1.14618
$587$	−2.58389e9	−0.527280	−0.263640	−	0.964621i	$-0.584923\pi$
$587$	−2.58389e9	−0.527280	−0.263640	+	0.964621i	$0.584923\pi$
$588$	5.97645e8	0.121233
$589$	1.06962e9	0.215688
$590$	5.49670e9	1.10184
$591$	7.26131e9	1.44697
$592$	1.16086e9	0.229961
$593$	−9.30932e8	−0.183327	−0.0916635	−	0.995790i	$-0.529218\pi$
$593$	−9.30932e8	−0.183327	−0.0916635	+	0.995790i	$0.529218\pi$
$594$	−8.92972e9	−1.74818
$595$	2.68004e9	0.521593
$596$	−3.88489e9	−0.751651
$597$	2.44862e9	0.470989
$598$	1.40197e9	0.268092
$599$	7.05476e9	1.34118	0.670592	−	0.741827i	$-0.266040\pi$
$599$	7.05476e9	1.34118	0.670592	+	0.741827i	$0.266040\pi$
$600$	1.42292e9	0.268938
$601$	−2.65816e8	−0.0499483	−0.0249742	−	0.999688i	$-0.507950\pi$
$601$	−2.65816e8	−0.0499483	−0.0249742	+	0.999688i	$0.507950\pi$
$602$	2.05034e9	0.383035
$603$	5.45501e9	1.01318
$604$	−1.20413e9	−0.222354
$605$	−1.13751e10	−2.08839
$606$	−2.92926e9	−0.534693
$607$	−5.73526e9	−1.04086	−0.520431	−	0.853904i	$-0.674229\pi$
$607$	−5.73526e9	−1.04086	−0.520431	+	0.853904i	$0.674229\pi$
$608$	−3.57049e8	−0.0644265
$609$	5.06435e9	0.908581
$610$	3.14694e9	0.561351
$611$	5.27410e9	0.935415
$612$	−6.11498e9	−1.07836
$613$	3.09475e9	0.542643	0.271321	−	0.962489i	$-0.412539\pi$
$613$	3.09475e9	0.542643	0.271321	+	0.962489i	$0.412539\pi$
$614$	−7.10863e9	−1.23936
$615$	6.44859e9	1.11790
$616$	−1.28218e9	−0.221013
$617$	−4.45734e9	−0.763973	−0.381986	−	0.924168i	$-0.624760\pi$
$617$	−4.45734e9	−0.763973	−0.381986	+	0.924168i	$0.624760\pi$
$618$	−1.03696e9	−0.176727
$619$	6.56511e9	1.11256	0.556282	−	0.830994i	$-0.312227\pi$
$619$	6.56511e9	1.11256	0.556282	+	0.830994i	$0.312227\pi$
$620$	2.11318e9	0.356095
$621$	5.16472e9	0.865418
$622$	5.25489e9	0.875582
$623$	−4.08562e9	−0.676940
$624$	1.68655e9	0.277878
$625$	−7.61300e9	−1.24731
$626$	−8.51470e9	−1.38726
$627$	6.31448e9	1.02306
$628$	−4.89038e8	−0.0787923
$629$	−6.58357e9	−1.05483
$630$	−3.79632e9	−0.604882
$631$	−9.00692e9	−1.42716	−0.713581	−	0.700573i	$-0.752928\pi$
$631$	−9.00692e9	−1.42716	−0.713581	+	0.700573i	$0.752928\pi$
$632$	−1.22968e9	−0.193768
$633$	9.84757e9	1.54318
$634$	−5.96471e9	−0.929559
$635$	1.41464e10	2.19250
$636$	1.10679e9	0.170595
$637$	6.10313e8	0.0935545
$638$	−1.08650e10	−1.65637
$639$	−5.27501e9	−0.799780
$640$	−7.05400e8	−0.106367
$641$	−9.44807e9	−1.41690	−0.708452	−	0.705759i	$-0.750606\pi$
$641$	−9.44807e9	−1.41690	−0.708452	+	0.705759i	$0.750606\pi$
$642$	1.21588e10	1.81350
$643$	−4.93538e9	−0.732120	−0.366060	−	0.930591i	$-0.619293\pi$
$643$	−4.93538e9	−0.732120	−0.366060	+	0.930591i	$0.619293\pi$
$644$	7.41580e8	0.109410
$645$	−1.99491e10	−2.92727
$646$	2.02493e9	0.295526
$647$	3.64554e9	0.529172	0.264586	−	0.964362i	$-0.414765\pi$
$647$	3.64554e9	0.529172	0.264586	+	0.964362i	$0.414765\pi$
$648$	1.60743e9	0.232070
$649$	1.49139e10	2.14159
$650$	1.45308e9	0.207536
$651$	−2.67252e9	−0.379653
$652$	5.82391e9	0.822902
$653$	−1.22716e10	−1.72466	−0.862332	−	0.506344i	$-0.830997\pi$
$653$	−1.22716e10	−1.72466	−0.862332	+	0.506344i	$0.830997\pi$
$654$	−4.74649e9	−0.663514
$655$	−4.19950e9	−0.583920
$656$	−9.89337e8	−0.136830
$657$	1.06843e10	1.46983
$658$	2.78977e9	0.381749
$659$	5.59468e9	0.761511	0.380755	−	0.924676i	$-0.375664\pi$
$659$	5.59468e9	0.761511	0.380755	+	0.924676i	$0.375664\pi$
$660$	1.24751e10	1.68905
$661$	2.59747e8	0.0349821	0.0174910	−	0.999847i	$-0.494432\pi$
$661$	2.59747e8	0.0349821	0.0174910	+	0.999847i	$0.494432\pi$
$662$	−7.06239e9	−0.946126
$663$	−9.56492e9	−1.27463
$664$	−2.75092e9	−0.364661
$665$	1.25712e9	0.165768
$666$	9.32573e9	1.22327
$667$	6.28404e9	0.819971
$668$	4.43584e9	0.575783
$669$	−6.55371e9	−0.846244
$670$	−3.56876e9	−0.458412
$671$	8.53844e9	1.09106
$672$	8.92111e8	0.113404
$673$	−1.35567e10	−1.71436	−0.857179	−	0.515018i	$-0.827785\pi$
$673$	−1.35567e10	−1.71436	−0.857179	+	0.515018i	$0.827785\pi$
$674$	5.53260e9	0.696017
$675$	5.35302e9	0.669940
$676$	−2.29360e9	−0.285565
$677$	1.04549e10	1.29497	0.647485	−	0.762078i	$-0.275821\pi$
$677$	1.04549e10	1.29497	0.647485	+	0.762078i	$0.275821\pi$
$678$	7.05427e8	0.0869257
$679$	4.65508e8	0.0570667
$680$	4.00053e9	0.487906
$681$	2.99125e9	0.362942
$682$	5.73359e9	0.692120
$683$	8.53262e9	1.02473	0.512365	−	0.858768i	$-0.328769\pi$
$683$	8.53262e9	1.02473	0.512365	+	0.858768i	$0.328769\pi$
$684$	−2.86834e9	−0.342716
$685$	1.50656e9	0.179089
$686$	3.22829e8	0.0381802
$687$	8.58777e9	1.01049
$688$	3.06057e9	0.358296
$689$	1.13025e9	0.131646
$690$	−7.21530e9	−0.836147
$691$	−5.91850e9	−0.682400	−0.341200	−	0.939991i	$-0.610833\pi$
$691$	−5.91850e9	−0.682400	−0.341200	+	0.939991i	$0.610833\pi$
$692$	−4.95328e9	−0.568226
$693$	−1.03004e10	−1.17567
$694$	7.27322e9	0.825979
$695$	−7.54975e9	−0.853072
$696$	7.55962e9	0.849899
$697$	5.61082e9	0.627642
$698$	−2.13292e9	−0.237400
$699$	−8.20086e9	−0.908216
$700$	7.68617e8	0.0846968
$701$	3.37718e9	0.370289	0.185145	−	0.982711i	$-0.440725\pi$
$701$	3.37718e9	0.370289	0.185145	+	0.982711i	$0.440725\pi$
$702$	6.34479e9	0.692209
$703$	−3.08814e9	−0.335238
$704$	−1.91393e9	−0.206738
$705$	−2.71434e10	−2.91744
$706$	−4.64879e9	−0.497191
$707$	−1.58230e9	−0.168391
$708$	−1.03768e10	−1.09887
$709$	1.18000e10	1.24343	0.621714	−	0.783244i	$-0.286437\pi$
$709$	1.18000e10	1.24343	0.621714	+	0.783244i	$0.286437\pi$
$710$	3.45100e9	0.361861
$711$	−9.87861e9	−1.03075
$712$	−6.09866e9	−0.633220
$713$	−3.31616e9	−0.342627
$714$	−5.05942e9	−0.520184
$715$	1.27396e10	1.30342
$716$	−3.17071e9	−0.322820
$717$	2.34863e10	2.37956
$718$	3.25653e9	0.328337
$719$	1.33183e10	1.33628	0.668142	−	0.744034i	$-0.267090\pi$
$719$	1.33183e10	1.33628	0.668142	+	0.744034i	$0.267090\pi$
$720$	−5.66681e9	−0.565816
$721$	−5.60134e8	−0.0556568
$722$	−6.20115e9	−0.613185
$723$	−5.07473e9	−0.499377
$724$	8.91711e8	0.0873251
$725$	6.51315e9	0.634758
$726$	2.14741e10	2.08275
$727$	−1.02572e10	−0.990048	−0.495024	−	0.868879i	$-0.664841\pi$
$727$	−1.02572e10	−0.990048	−0.495024	+	0.868879i	$0.664841\pi$
$728$	9.11021e8	0.0875122
$729$	−1.36259e10	−1.30262
$730$	−6.98987e9	−0.665027
$731$	−1.73574e10	−1.64351
$732$	−5.94085e9	−0.559835
$733$	8.94962e9	0.839345	0.419673	−	0.907676i	$-0.362145\pi$
$733$	8.94962e9	0.839345	0.419673	+	0.907676i	$0.362145\pi$
$734$	−9.05288e9	−0.844988
$735$	−3.14100e9	−0.291785
$736$	1.10697e9	0.102344
$737$	−9.68295e9	−0.890987
$738$	−7.94782e9	−0.727865
$739$	8.25850e9	0.752741	0.376370	−	0.926469i	$-0.377172\pi$
$739$	8.25850e9	0.752741	0.376370	+	0.926469i	$0.377172\pi$
$740$	−6.10105e9	−0.553469
$741$	−4.48660e9	−0.405092
$742$	5.97853e8	0.0537256
$743$	6.90080e9	0.617218	0.308609	−	0.951189i	$-0.400136\pi$
$743$	6.90080e9	0.617218	0.308609	+	0.951189i	$0.400136\pi$
$744$	−3.98930e9	−0.355133
$745$	2.04176e10	1.80908
$746$	3.22091e9	0.284049
$747$	−2.20994e10	−1.93981
$748$	1.08544e10	0.948313
$749$	6.56779e9	0.571127
$750$	9.20795e9	0.796982
$751$	4.65872e9	0.401353	0.200677	−	0.979658i	$-0.435686\pi$
$751$	4.65872e9	0.401353	0.200677	+	0.979658i	$0.435686\pi$
$752$	4.16432e9	0.357093
$753$	−1.17803e9	−0.100549
$754$	7.71986e9	0.655858
$755$	6.32849e9	0.535163
$756$	3.35611e9	0.282495
$757$	−1.55423e10	−1.30221	−0.651103	−	0.758990i	$-0.725693\pi$
$757$	−1.55423e10	−1.30221	−0.651103	+	0.758990i	$0.725693\pi$
$758$	−8.84812e9	−0.737919
$759$	−1.95769e10	−1.62517
$760$	1.87652e9	0.155062
$761$	−6.53914e9	−0.537866	−0.268933	−	0.963159i	$-0.586671\pi$
$761$	−6.53914e9	−0.537866	−0.268933	+	0.963159i	$0.586671\pi$
$762$	−2.67059e10	−2.18658
$763$	−2.56390e9	−0.208961
$764$	4.34022e9	0.352116
$765$	3.21381e10	2.59541
$766$	−3.63137e9	−0.291924
$767$	−1.05967e10	−0.847983
$768$	1.33166e9	0.106079
$769$	1.21454e10	0.963099	0.481549	−	0.876419i	$-0.340074\pi$
$769$	1.21454e10	0.963099	0.481549	+	0.876419i	$0.340074\pi$
$770$	6.73868e9	0.531933
$771$	7.56258e9	0.594264
$772$	−6.99811e9	−0.547419
$773$	1.58915e10	1.23748	0.618739	−	0.785596i	$-0.287644\pi$
$773$	1.58915e10	1.23748	0.618739	+	0.785596i	$0.287644\pi$
$774$	2.45870e10	1.90595
$775$	−3.43706e9	−0.265235
$776$	6.94869e8	0.0533810
$777$	7.71594e9	0.590086
$778$	−7.68396e9	−0.585001
$779$	2.63186e9	0.199472
$780$	−8.86390e9	−0.668796
$781$	9.36344e9	0.703326
$782$	−6.27792e9	−0.469453
$783$	2.84392e10	2.11715
$784$	4.81890e8	0.0357143
$785$	2.57021e9	0.189638
$786$	7.92789e9	0.582343
$787$	2.21461e10	1.61952	0.809758	−	0.586763i	$-0.199598\pi$
$787$	2.21461e10	1.61952	0.809758	+	0.586763i	$0.199598\pi$
$788$	5.85490e9	0.426263
$789$	1.79259e10	1.29931
$790$	6.46276e9	0.466362
$791$	3.81049e8	0.0273756
$792$	−1.53755e10	−1.09974
$793$	−6.06677e9	−0.432018
$794$	8.98329e9	0.636889
$795$	−5.81689e9	−0.410588
$796$	1.97436e9	0.138749
$797$	1.99270e10	1.39424	0.697120	−	0.716954i	$-0.254464\pi$
$797$	1.99270e10	1.39424	0.697120	+	0.716954i	$0.254464\pi$
$798$	−2.37321e9	−0.165320
$799$	−2.36171e10	−1.63799
$800$	1.14732e9	0.0792266
$801$	−4.89934e10	−3.36840
$802$	−1.40833e10	−0.964039
$803$	−1.89653e10	−1.29257
$804$	6.73717e9	0.457174
$805$	−3.89748e9	−0.263329
$806$	−4.07386e9	−0.274052
$807$	1.88138e9	0.126014
$808$	−2.36191e9	−0.157516
$809$	−1.55211e10	−1.03063	−0.515313	−	0.857002i	$-0.672324\pi$
$809$	−1.55211e10	−1.03063	−0.515313	+	0.857002i	$0.672324\pi$
$810$	−8.44806e9	−0.558547
$811$	5.22078e9	0.343686	0.171843	−	0.985124i	$-0.445028\pi$
$811$	5.22078e9	0.343686	0.171843	+	0.985124i	$0.445028\pi$
$812$	4.08347e9	0.267660
$813$	1.84295e10	1.20281
$814$	−1.65537e10	−1.07575
$815$	−3.06083e10	−1.98056
$816$	−7.55226e9	−0.486588
$817$	−8.14178e9	−0.522327
$818$	1.69025e10	1.07973
$819$	7.31867e9	0.465520
$820$	5.19960e9	0.329322
$821$	−1.97215e10	−1.24377	−0.621883	−	0.783110i	$-0.713632\pi$
$821$	−1.97215e10	−1.24377	−0.621883	+	0.783110i	$0.713632\pi$
$822$	−2.84410e9	−0.178605
$823$	1.27286e10	0.795944	0.397972	−	0.917398i	$-0.369714\pi$
$823$	1.27286e10	0.795944	0.397972	+	0.917398i	$0.369714\pi$
$824$	−8.36118e8	−0.0520622
$825$	−2.02907e10	−1.25808
$826$	−5.60520e9	−0.346067
$827$	4.32638e9	0.265984	0.132992	−	0.991117i	$-0.457542\pi$
$827$	4.32638e9	0.265984	0.132992	+	0.991117i	$0.457542\pi$
$828$	8.89278e9	0.544416
$829$	−2.39465e10	−1.45982	−0.729912	−	0.683541i	$-0.760439\pi$
$829$	−2.39465e10	−1.45982	−0.729912	+	0.683541i	$0.760439\pi$
$830$	1.44578e10	0.877667
$831$	4.32497e10	2.61444
$832$	1.35989e9	0.0818602
$833$	−2.73294e9	−0.163822
$834$	1.42525e10	0.850767
$835$	−2.33132e10	−1.38579
$836$	5.09147e9	0.301384
$837$	−1.50077e10	−0.884657
$838$	2.08378e10	1.22320
$839$	−2.67007e10	−1.56083	−0.780414	−	0.625263i	$-0.784992\pi$
$839$	−2.67007e10	−1.56083	−0.780414	+	0.625263i	$0.784992\pi$
$840$	−4.68861e9	−0.272940
$841$	1.73528e10	1.00597
$842$	1.69776e10	0.980132
$843$	−2.16057e10	−1.24215
$844$	7.94024e9	0.454606
$845$	1.20544e10	0.687299
$846$	3.34539e10	1.89955
$847$	1.15996e10	0.655922
$848$	8.92423e8	0.0502557
$849$	3.02506e10	1.69652
$850$	−6.50681e9	−0.363414
$851$	9.57422e9	0.532537
$852$	−6.51486e9	−0.360883
$853$	−3.26804e10	−1.80288	−0.901439	−	0.432906i	$-0.857488\pi$
$853$	−3.26804e10	−1.80288	−0.901439	+	0.432906i	$0.857488\pi$
$854$	−3.20906e9	−0.176309
$855$	1.50750e10	0.824850
$856$	9.80381e9	0.534241
$857$	1.36792e10	0.742383	0.371191	−	0.928556i	$-0.378949\pi$
$857$	1.36792e10	0.742383	0.371191	+	0.928556i	$0.378949\pi$
$858$	−2.40500e10	−1.29990
$859$	−3.58563e10	−1.93014	−0.965070	−	0.261991i	$-0.915621\pi$
$859$	−3.58563e10	−1.93014	−0.965070	+	0.261991i	$0.915621\pi$
$860$	−1.60852e10	−0.862348
$861$	−6.57588e9	−0.351110
$862$	−1.56438e10	−0.831892
$863$	−1.19390e10	−0.632309	−0.316154	−	0.948708i	$-0.602392\pi$
$863$	−1.19390e10	−0.632309	−0.316154	+	0.948708i	$0.602392\pi$
$864$	5.00971e9	0.264250
$865$	2.60326e10	1.36761
$866$	−2.13029e10	−1.11462
$867$	1.02611e10	0.534720
$868$	−2.15489e9	−0.111842
$869$	1.75351e10	0.906439
$870$	−3.97306e10	−2.04554
$871$	6.87997e9	0.352796
$872$	−3.82717e9	−0.195465
$873$	5.58221e9	0.283960
$874$	−2.94477e9	−0.149197
$875$	4.97384e9	0.250994
$876$	1.31956e10	0.663230
$877$	−2.49676e10	−1.24991	−0.624953	−	0.780662i	$-0.714882\pi$
$877$	−2.49676e10	−1.24991	−0.624953	+	0.780662i	$0.714882\pi$
$878$	−5.48215e9	−0.273351
$879$	5.53963e10	2.75118
$880$	1.00589e10	0.497578
$881$	−2.30202e10	−1.13421	−0.567106	−	0.823645i	$-0.691937\pi$
$881$	−2.30202e10	−1.13421	−0.567106	+	0.823645i	$0.691937\pi$
$882$	3.87125e9	0.189982
$883$	−3.66045e9	−0.178925	−0.0894627	−	0.995990i	$-0.528515\pi$
$883$	−3.66045e9	−0.178925	−0.0894627	+	0.995990i	$0.528515\pi$
$884$	−7.71234e9	−0.375494
$885$	5.45365e10	2.64476
$886$	−4.78344e9	−0.231058
$887$	1.36071e10	0.654685	0.327342	−	0.944906i	$-0.393847\pi$
$887$	1.36071e10	0.654685	0.327342	+	0.944906i	$0.393847\pi$
$888$	1.15177e10	0.551975
$889$	−1.44257e10	−0.688621
$890$	3.20523e10	1.52403
$891$	−2.29217e10	−1.08561
$892$	−5.28436e9	−0.249296
$893$	−1.10780e10	−0.520573
$894$	−3.85446e10	−1.80419
$895$	1.66641e10	0.776964
$896$	7.19323e8	0.0334077
$897$	1.39099e10	0.643502
$898$	1.59599e10	0.735468
$899$	−1.82602e10	−0.838199
$900$	9.21700e9	0.421445
$901$	−5.06119e9	−0.230524
$902$	1.41078e10	0.640084
$903$	2.03428e10	0.919399
$904$	5.68796e8	0.0256075
$905$	−4.68651e9	−0.210174
$906$	−1.19470e10	−0.533717
$907$	−1.79942e10	−0.800771	−0.400385	−	0.916347i	$-0.631124\pi$
$907$	−1.79942e10	−0.800771	−0.400385	+	0.916347i	$0.631124\pi$
$908$	2.41189e9	0.106919
$909$	−1.89744e10	−0.837902
$910$	−4.78800e9	−0.210625
$911$	2.77433e10	1.21575	0.607875	−	0.794033i	$-0.292022\pi$
$911$	2.77433e10	1.21575	0.607875	+	0.794033i	$0.292022\pi$
$912$	−3.54252e9	−0.154643
$913$	3.92277e10	1.70587
$914$	1.52765e10	0.661778
$915$	3.12229e10	1.34741
$916$	6.92445e9	0.297681
$917$	4.28239e9	0.183398
$918$	−2.84115e10	−1.21212
$919$	8.80141e9	0.374066	0.187033	−	0.982354i	$-0.440113\pi$
$919$	8.80141e9	0.374066	0.187033	+	0.982354i	$0.440113\pi$
$920$	−5.81781e9	−0.246321
$921$	−7.05295e10	−2.97483
$922$	−1.72973e10	−0.726808
$923$	−6.65296e9	−0.278489
$924$	−1.27214e10	−0.530497
$925$	9.92329e9	0.412249
$926$	2.17201e10	0.898923
$927$	−6.71693e9	−0.276944
$928$	6.09544e9	0.250373
$929$	4.45563e10	1.82328	0.911642	−	0.410984i	$-0.134815\pi$
$929$	4.45563e10	1.82328	0.911642	+	0.410984i	$0.134815\pi$
$930$	2.09663e10	0.854735
$931$	−1.28193e9	−0.0520645
$932$	−6.61248e9	−0.267552
$933$	5.21373e10	2.10166
$934$	1.98285e10	0.796298
$935$	−5.70470e10	−2.28240
$936$	1.09247e10	0.435454
$937$	1.31838e10	0.523544	0.261772	−	0.965130i	$-0.415693\pi$
$937$	1.31838e10	0.523544	0.261772	+	0.965130i	$0.415693\pi$
$938$	3.63920e9	0.143978
$939$	−8.44801e10	−3.32985
$940$	−2.18861e10	−0.859452
$941$	−1.06709e10	−0.417481	−0.208741	−	0.977971i	$-0.566936\pi$
$941$	−1.06709e10	−0.417481	−0.208741	+	0.977971i	$0.566936\pi$
$942$	−4.85208e9	−0.189125
$943$	−8.15959e9	−0.316867
$944$	−8.36694e9	−0.323716
$945$	−1.76385e10	−0.679909
$946$	−4.36433e10	−1.67609
$947$	4.13633e10	1.58267	0.791334	−	0.611384i	$-0.209387\pi$
$947$	4.13633e10	1.58267	0.791334	+	0.611384i	$0.209387\pi$
$948$	−1.22005e10	−0.465102
$949$	1.34753e10	0.511807
$950$	−3.05213e9	−0.115497
$951$	−5.91799e10	−2.23122
$952$	−4.07949e9	−0.153242
$953$	−1.95469e10	−0.731564	−0.365782	−	0.930701i	$-0.619198\pi$
$953$	−1.95469e10	−0.731564	−0.365782	+	0.930701i	$0.619198\pi$
$954$	7.16925e9	0.267334
$955$	−2.28106e10	−0.847472
$956$	1.89374e10	0.700998
$957$	−1.07799e11	−3.97579
$958$	−1.28567e9	−0.0472443
$959$	−1.53629e9	−0.0562482
$960$	−6.99875e9	−0.255312
$961$	−1.78765e10	−0.649756
$962$	1.17618e10	0.425952
$963$	7.87587e10	2.84188
$964$	−4.09183e9	−0.147112
$965$	3.67795e10	1.31753
$966$	7.35772e9	0.262617
$967$	1.61106e10	0.572952	0.286476	−	0.958087i	$-0.407516\pi$
$967$	1.61106e10	0.572952	0.286476	+	0.958087i	$0.407516\pi$
$968$	1.73149e10	0.613559
$969$	2.00907e10	0.709351
$970$	−3.65198e9	−0.128478
$971$	3.31578e10	1.16230	0.581151	−	0.813796i	$-0.302603\pi$
$971$	3.31578e10	1.16230	0.581151	+	0.813796i	$0.302603\pi$
$972$	−5.45051e9	−0.190373
$973$	7.69877e9	0.267933
$974$	−1.93893e10	−0.672367
$975$	1.44170e10	0.498149
$976$	−4.79020e9	−0.164922
$977$	1.84221e10	0.631989	0.315994	−	0.948761i	$-0.397662\pi$
$977$	1.84221e10	0.631989	0.315994	+	0.948761i	$0.397662\pi$
$978$	5.77829e10	1.97521
$979$	8.69660e10	2.96217
$980$	−2.53264e9	−0.0859572
$981$	−3.07454e10	−1.03977
$982$	−9.60561e9	−0.323694
$983$	−7.35533e9	−0.246982	−0.123491	−	0.992346i	$-0.539409\pi$
$983$	−7.35533e9	−0.246982	−0.123491	+	0.992346i	$0.539409\pi$
$984$	−9.81589e9	−0.328433
$985$	−3.07712e10	−1.02593
$986$	−3.45690e10	−1.14846
$987$	2.76792e10	0.916311
$988$	−3.61761e9	−0.119336
$989$	2.52421e10	0.829734
$990$	8.08079e10	2.64686
$991$	−4.71378e10	−1.53855	−0.769275	−	0.638918i	$-0.779382\pi$
$991$	−4.71378e10	−1.53855	−0.769275	+	0.638918i	$0.779382\pi$
$992$	−3.21663e9	−0.104619
$993$	−7.00708e10	−2.27099
$994$	−3.51912e9	−0.113653
$995$	−1.03765e10	−0.333941
$996$	−2.72937e10	−0.875296
$997$	4.17584e9	0.133448	0.0667238	−	0.997771i	$-0.478745\pi$
$997$	4.17584e9	0.133448	0.0667238	+	0.997771i	$0.478745\pi$
$998$	2.79317e10	0.889488
$999$	4.33293e10	1.37500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.8.a.c.1.2	✓	2
3.2	odd	2		126.8.a.i.1.2		2
4.3	odd	2		112.8.a.g.1.1		2
5.2	odd	4		350.8.c.k.99.3		4
5.3	odd	4		350.8.c.k.99.2		4
5.4	even	2		350.8.a.j.1.1		2
7.2	even	3		98.8.c.g.67.1		4
7.3	odd	6		98.8.c.k.79.2		4
7.4	even	3		98.8.c.g.79.1		4
7.5	odd	6		98.8.c.k.67.2		4
7.6	odd	2		98.8.a.g.1.1		2
8.3	odd	2		448.8.a.s.1.2		2
8.5	even	2		448.8.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.a.c.1.2	✓	2	1.1	even	1	trivial
98.8.a.g.1.1		2	7.6	odd	2
98.8.c.g.67.1		4	7.2	even	3
98.8.c.g.79.1		4	7.4	even	3
98.8.c.k.67.2		4	7.5	odd	6
98.8.c.k.79.2		4	7.3	odd	6
112.8.a.g.1.1		2	4.3	odd	2
126.8.a.i.1.2		2	3.2	odd	2
350.8.a.j.1.1		2	5.4	even	2
350.8.c.k.99.2		4	5.3	odd	4
350.8.c.k.99.3		4	5.2	odd	4
448.8.a.l.1.1		2	8.5	even	2
448.8.a.s.1.2		2	8.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +79.3734 q^{3} +64.0000 q^{4} -336.361 q^{5} +634.987 q^{6} +343.000 q^{7} +512.000 q^{8} +4113.14 q^{9} -2690.89 q^{10} -7301.05 q^{11} +5079.90 q^{12} +5187.58 q^{13} +2744.00 q^{14} -26698.1 q^{15} +4096.00 q^{16} -23229.6 q^{17} +32905.1 q^{18} -10896.3 q^{19} -21527.1 q^{20} +27225.1 q^{21} -58408.4 q^{22} +33781.9 q^{23} +40639.2 q^{24} +35013.5 q^{25} +41500.6 q^{26} +152884. q^{27} +21952.0 q^{28} +186018. q^{29} -213585. q^{30} -98163.8 q^{31} +32768.0 q^{32} -579509. q^{33} -185837. q^{34} -115372. q^{35} +263241. q^{36} +283413. q^{37} -87170.1 q^{38} +411756. q^{39} -172217. q^{40} -241537. q^{41} +217801. q^{42} +747209. q^{43} -467267. q^{44} -1.38350e6 q^{45} +270255. q^{46} +1.01668e6 q^{47} +325114. q^{48} +117649. q^{49} +280108. q^{50} -1.84381e6 q^{51} +332005. q^{52} +217877. q^{53} +1.22307e6 q^{54} +2.45579e6 q^{55} +175616. q^{56} -864873. q^{57} +1.48814e6 q^{58} -2.04271e6 q^{59} -1.70868e6 q^{60} -1.16948e6 q^{61} -785310. q^{62} +1.41081e6 q^{63} +262144. q^{64} -1.74490e6 q^{65} -4.63607e6 q^{66} +1.32624e6 q^{67} -1.48669e6 q^{68} +2.68138e6 q^{69} -922974. q^{70} -1.28248e6 q^{71} +2.10593e6 q^{72} +2.59761e6 q^{73} +2.26730e6 q^{74} +2.77914e6 q^{75} -697361. q^{76} -2.50426e6 q^{77} +3.29404e6 q^{78} -2.40172e6 q^{79} -1.37773e6 q^{80} +3.13951e6 q^{81} -1.93230e6 q^{82} -5.37289e6 q^{83} +1.74241e6 q^{84} +7.81353e6 q^{85} +5.97767e6 q^{86} +1.47649e7 q^{87} -3.73814e6 q^{88} -1.19114e7 q^{89} -1.10680e7 q^{90} +1.77934e6 q^{91} +2.16204e6 q^{92} -7.79160e6 q^{93} +8.13343e6 q^{94} +3.66507e6 q^{95} +2.60091e6 q^{96} +1.35717e6 q^{97} +941192. q^{98} -3.00302e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{2} + 70 q^{3} + 128 q^{4} + 126 q^{5} + 560 q^{6} + 686 q^{7} + 1024 q^{8} + 2014 q^{9} + 1008 q^{10} - 3420 q^{11} + 4480 q^{12} - 6398 q^{13} + 5488 q^{14} - 31032 q^{15} + 8192 q^{16} - 38472 q^{17}+ \cdots - 38177100 q^{99}+O(q^{100}) \) 2 * q + 16 * q^2 + 70 * q^3 + 128 * q^4 + 126 * q^5 + 560 * q^6 + 686 * q^7 + 1024 * q^8 + 2014 * q^9 + 1008 * q^10 - 3420 * q^11 + 4480 * q^12 - 6398 * q^13 + 5488 * q^14 - 31032 * q^15 + 8192 * q^16 - 38472 * q^17 + 16112 * q^18 - 43358 * q^19 + 8064 * q^20 + 24010 * q^21 - 27360 * q^22 + 89928 * q^23 + 35840 * q^24 + 170666 * q^25 - 51184 * q^26 + 193060 * q^27 + 43904 * q^28 + 159576 * q^29 - 248256 * q^30 - 143612 * q^31 + 65536 * q^32 - 615888 * q^33 - 307776 * q^34 + 43218 * q^35 + 128896 * q^36 - 271832 * q^37 - 346864 * q^38 + 520352 * q^39 + 64512 * q^40 + 64848 * q^41 + 192080 * q^42 + 1527964 * q^43 - 218880 * q^44 - 2354058 * q^45 + 719424 * q^46 + 485436 * q^47 + 286720 * q^48 + 235298 * q^49 + 1365328 * q^50 - 1700940 * q^51 - 409472 * q^52 - 145716 * q^53 + 1544480 * q^54 + 4250232 * q^55 + 351232 * q^56 - 560596 * q^57 + 1276608 * q^58 - 4183662 * q^59 - 1986048 * q^60 - 280658 * q^61 - 1148896 * q^62 + 690802 * q^63 + 524288 * q^64 - 7101612 * q^65 - 4927104 * q^66 + 5671648 * q^67 - 2462208 * q^68 + 2155104 * q^69 + 345744 * q^70 - 619272 * q^71 + 1031168 * q^72 + 3939628 * q^73 - 2174656 * q^74 + 1507618 * q^75 - 2774912 * q^76 - 1173060 * q^77 + 4162816 * q^78 + 4656616 * q^79 + 516096 * q^80 + 7353742 * q^81 + 518784 * q^82 + 1235850 * q^83 + 1536640 * q^84 + 766044 * q^85 + 12223712 * q^86 + 15012732 * q^87 - 1751040 * q^88 - 17241420 * q^89 - 18832464 * q^90 - 2194514 * q^91 + 5755392 * q^92 - 7365592 * q^93 + 3883488 * q^94 - 11343960 * q^95 + 2293760 * q^96 - 740936 * q^97 + 1882384 * q^98 - 38177100 * q^99

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