LMFDB - Embedded newform 22.8.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,8,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	22.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:	$6.87247056065$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14881}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3720 $ x^2 - x - 3720
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$61.4939$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} -72.4939 q^{3} +64.0000 q^{4} +226.494 q^{5} -579.951 q^{6} +1750.91 q^{7} +512.000 q^{8} +3068.36 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -72.4939 q^{3} +64.0000 q^{4} +226.494 q^{5} -579.951 q^{6} +1750.91 q^{7} +512.000 q^{8} +3068.36 q^{9} +1811.95 q^{10} +1331.00 q^{11} -4639.61 q^{12} -9900.27 q^{13} +14007.3 q^{14} -16419.4 q^{15} +4096.00 q^{16} +21910.5 q^{17} +24546.9 q^{18} +37979.0 q^{19} +14495.6 q^{20} -126930. q^{21} +10648.0 q^{22} +8908.01 q^{23} -37116.9 q^{24} -26825.5 q^{25} -79202.2 q^{26} -63893.1 q^{27} +112058. q^{28} -148091. q^{29} -131355. q^{30} +69451.5 q^{31} +32768.0 q^{32} -96489.3 q^{33} +175284. q^{34} +396571. q^{35} +196375. q^{36} -30797.7 q^{37} +303832. q^{38} +717709. q^{39} +115965. q^{40} -426512. q^{41} -1.01544e6 q^{42} -853435. q^{43} +85184.0 q^{44} +694964. q^{45} +71264.1 q^{46} +577393. q^{47} -296935. q^{48} +2.24216e6 q^{49} -214604. q^{50} -1.58838e6 q^{51} -633618. q^{52} -62685.2 q^{53} -511145. q^{54} +301463. q^{55} +896468. q^{56} -2.75325e6 q^{57} -1.18472e6 q^{58} -428866. q^{59} -1.05084e6 q^{60} -1.03808e6 q^{61} +555612. q^{62} +5.37243e6 q^{63} +262144. q^{64} -2.24235e6 q^{65} -771915. q^{66} -698953. q^{67} +1.40228e6 q^{68} -645776. q^{69} +3.17257e6 q^{70} -1.83316e6 q^{71} +1.57100e6 q^{72} -500059. q^{73} -246382. q^{74} +1.94469e6 q^{75} +2.43066e6 q^{76} +2.33047e6 q^{77} +5.74167e6 q^{78} -4.84357e6 q^{79} +927719. q^{80} -2.07864e6 q^{81} -3.41209e6 q^{82} +3.47288e6 q^{83} -8.12355e6 q^{84} +4.96260e6 q^{85} -6.82748e6 q^{86} +1.07357e7 q^{87} +681472. q^{88} +955049. q^{89} +5.55971e6 q^{90} -1.73345e7 q^{91} +570113. q^{92} -5.03481e6 q^{93} +4.61914e6 q^{94} +8.60202e6 q^{95} -2.37548e6 q^{96} -1.39593e7 q^{97} +1.79373e7 q^{98} +4.08399e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{2} - 23 q^{3} + 128 q^{4} + 331 q^{5} - 184 q^{6} + 1794 q^{7} + 1024 q^{8} + 3331 q^{9}+O(q^{10}) $ 2 * q + 16 * q^2 - 23 * q^3 + 128 * q^4 + 331 * q^5 - 184 * q^6 + 1794 * q^7 + 1024 * q^8 + 3331 * q^9	\( 2 q + 16 q^{2} - 23 q^{3} + 128 q^{4} + 331 q^{5} - 184 q^{6} + 1794 q^{7} + 1024 q^{8} + 3331 q^{9} + 2648 q^{10} + 2662 q^{11} - 1472 q^{12} - 5406 q^{13} + 14352 q^{14} - 11247 q^{15} + 8192 q^{16} + 15032 q^{17} + 26648 q^{18} + 16916 q^{19} + 21184 q^{20} - 124798 q^{21} + 21296 q^{22} - 51351 q^{23} - 11776 q^{24} - 94029 q^{25} - 43248 q^{26} - 159137 q^{27} + 114816 q^{28} - 207130 q^{29} - 89976 q^{30} - 19071 q^{31} + 65536 q^{32} - 30613 q^{33} + 120256 q^{34} + 401074 q^{35} + 213184 q^{36} + 351333 q^{37} + 135328 q^{38} + 940148 q^{39} + 169472 q^{40} + 123610 q^{41} - 998384 q^{42} - 159822 q^{43} + 170368 q^{44} + 722412 q^{45} - 410808 q^{46} + 451160 q^{47} - 94208 q^{48} + 1420470 q^{49} - 752232 q^{50} - 1928826 q^{51} - 345984 q^{52} - 1260832 q^{53} - 1273096 q^{54} + 440561 q^{55} + 918528 q^{56} - 3795736 q^{57} - 1657040 q^{58} + 887547 q^{59} - 719808 q^{60} - 597918 q^{61} - 152568 q^{62} + 5383748 q^{63} + 524288 q^{64} - 1772672 q^{65} - 244904 q^{66} + 2864711 q^{67} + 962048 q^{68} - 3628227 q^{69} + 3208592 q^{70} + 1306267 q^{71} + 1705472 q^{72} - 4577530 q^{73} + 2810664 q^{74} - 1381472 q^{75} + 1082624 q^{76} + 2387814 q^{77} + 7521184 q^{78} - 2946342 q^{79} + 1355776 q^{80} - 7367030 q^{81} + 988880 q^{82} + 9965450 q^{83} - 7987072 q^{84} + 4243754 q^{85} - 1278576 q^{86} + 7813560 q^{87} + 1362944 q^{88} + 10185377 q^{89} + 5779296 q^{90} - 17140888 q^{91} - 3286464 q^{92} - 9416131 q^{93} + 3609280 q^{94} + 6400800 q^{95} - 753664 q^{96} - 27765477 q^{97} + 11363760 q^{98} + 4433561 q^{99}+O(q^{100}) \) 2 * q + 16 * q^2 - 23 * q^3 + 128 * q^4 + 331 * q^5 - 184 * q^6 + 1794 * q^7 + 1024 * q^8 + 3331 * q^9 + 2648 * q^10 + 2662 * q^11 - 1472 * q^12 - 5406 * q^13 + 14352 * q^14 - 11247 * q^15 + 8192 * q^16 + 15032 * q^17 + 26648 * q^18 + 16916 * q^19 + 21184 * q^20 - 124798 * q^21 + 21296 * q^22 - 51351 * q^23 - 11776 * q^24 - 94029 * q^25 - 43248 * q^26 - 159137 * q^27 + 114816 * q^28 - 207130 * q^29 - 89976 * q^30 - 19071 * q^31 + 65536 * q^32 - 30613 * q^33 + 120256 * q^34 + 401074 * q^35 + 213184 * q^36 + 351333 * q^37 + 135328 * q^38 + 940148 * q^39 + 169472 * q^40 + 123610 * q^41 - 998384 * q^42 - 159822 * q^43 + 170368 * q^44 + 722412 * q^45 - 410808 * q^46 + 451160 * q^47 - 94208 * q^48 + 1420470 * q^49 - 752232 * q^50 - 1928826 * q^51 - 345984 * q^52 - 1260832 * q^53 - 1273096 * q^54 + 440561 * q^55 + 918528 * q^56 - 3795736 * q^57 - 1657040 * q^58 + 887547 * q^59 - 719808 * q^60 - 597918 * q^61 - 152568 * q^62 + 5383748 * q^63 + 524288 * q^64 - 1772672 * q^65 - 244904 * q^66 + 2864711 * q^67 + 962048 * q^68 - 3628227 * q^69 + 3208592 * q^70 + 1306267 * q^71 + 1705472 * q^72 - 4577530 * q^73 + 2810664 * q^74 - 1381472 * q^75 + 1082624 * q^76 + 2387814 * q^77 + 7521184 * q^78 - 2946342 * q^79 + 1355776 * q^80 - 7367030 * q^81 + 988880 * q^82 + 9965450 * q^83 - 7987072 * q^84 + 4243754 * q^85 - 1278576 * q^86 + 7813560 * q^87 + 1362944 * q^88 + 10185377 * q^89 + 5779296 * q^90 - 17140888 * q^91 - 3286464 * q^92 - 9416131 * q^93 + 3609280 * q^94 + 6400800 * q^95 - 753664 * q^96 - 27765477 * q^97 + 11363760 * q^98 + 4433561 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	−72.4939	−1.55016	−0.775080	−	0.631863i	$-0.782291\pi$
$3$	−72.4939	−1.55016	−0.775080	+	0.631863i	$0.782291\pi$
$4$	64.0000	0.500000
$5$	226.494	0.810329	0.405165	−	0.914244i	$-0.367214\pi$
$5$	226.494	0.810329	0.405165	+	0.914244i	$0.367214\pi$
$6$	−579.951	−1.09613
$7$	1750.91	1.92940	0.964699	−	0.263356i	$-0.0848295\pi$
$7$	1750.91	1.92940	0.964699	+	0.263356i	$0.0848295\pi$
$8$	512.000	0.353553
$9$	3068.36	1.40300
$10$	1811.95	0.572989
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	−4639.61	−0.775080
$13$	−9900.27	−1.24981	−0.624907	−	0.780699i	$-0.714863\pi$
$13$	−9900.27	−1.24981	−0.624907	+	0.780699i	$0.714863\pi$
$14$	14007.3	1.36429
$15$	−16419.4	−1.25614
$16$	4096.00	0.250000
$17$	21910.5	1.08164	0.540819	−	0.841139i	$-0.318114\pi$
$17$	21910.5	1.08164	0.540819	+	0.841139i	$0.318114\pi$
$18$	24546.9	0.992070
$19$	37979.0	1.27030	0.635150	−	0.772389i	$-0.280938\pi$
$19$	37979.0	1.27030	0.635150	+	0.772389i	$0.280938\pi$
$20$	14495.6	0.405165
$21$	−126930.	−2.99088
$22$	10648.0	0.213201
$23$	8908.01	0.152663	0.0763314	−	0.997082i	$-0.475679\pi$
$23$	8908.01	0.152663	0.0763314	+	0.997082i	$0.475679\pi$
$24$	−37116.9	−0.548065
$25$	−26825.5	−0.343367
$26$	−79202.2	−0.883752
$27$	−63893.1	−0.624713
$28$	112058.	0.964699
$29$	−148091.	−1.12755	−0.563773	−	0.825930i	$-0.690651\pi$
$29$	−148091.	−1.12755	−0.563773	+	0.825930i	$0.690651\pi$
$30$	−131355.	−0.888225
$31$	69451.5	0.418713	0.209356	−	0.977839i	$-0.432863\pi$
$31$	69451.5	0.418713	0.209356	+	0.977839i	$0.432863\pi$
$32$	32768.0	0.176777
$33$	−96489.3	−0.467391
$34$	175284.	0.764834
$35$	396571.	1.56345
$36$	196375.	0.701499
$37$	−30797.7	−0.0999567	−0.0499784	−	0.998750i	$-0.515915\pi$
$37$	−30797.7	−0.0999567	−0.0499784	+	0.998750i	$0.515915\pi$
$38$	303832.	0.898238
$39$	717709.	1.93741
$40$	115965.	0.286495
$41$	−426512.	−0.966468	−0.483234	−	0.875491i	$-0.660538\pi$
$41$	−426512.	−0.966468	−0.483234	+	0.875491i	$0.660538\pi$
$42$	−1.01544e6	−2.11487
$43$	−853435.	−1.63693	−0.818466	−	0.574554i	$-0.805175\pi$
$43$	−853435.	−1.63693	−0.818466	+	0.574554i	$0.805175\pi$
$44$	85184.0	0.150756
$45$	694964.	1.13689
$46$	71264.1	0.107949
$47$	577393.	0.811201	0.405601	−	0.914050i	$-0.367062\pi$
$47$	577393.	0.811201	0.405601	+	0.914050i	$0.367062\pi$
$48$	−296935.	−0.387540
$49$	2.24216e6	2.72257
$50$	−214604.	−0.242797
$51$	−1.58838e6	−1.67671
$52$	−633618.	−0.624907
$53$	−62685.2	−0.0578362	−0.0289181	−	0.999582i	$-0.509206\pi$
$53$	−62685.2	−0.0578362	−0.0289181	+	0.999582i	$0.509206\pi$
$54$	−511145.	−0.441739
$55$	301463.	0.244323
$56$	896468.	0.682145
$57$	−2.75325e6	−1.96917
$58$	−1.18472e6	−0.797295
$59$	−428866.	−0.271856	−0.135928	−	0.990719i	$-0.543402\pi$
$59$	−428866.	−0.271856	−0.135928	+	0.990719i	$0.543402\pi$
$60$	−1.05084e6	−0.628070
$61$	−1.03808e6	−0.585568	−0.292784	−	0.956179i	$-0.594582\pi$
$61$	−1.03808e6	−0.585568	−0.292784	+	0.956179i	$0.594582\pi$
$62$	555612.	0.296074
$63$	5.37243e6	2.70694
$64$	262144.	0.125000
$65$	−2.24235e6	−1.01276
$66$	−771915.	−0.330495
$67$	−698953.	−0.283913	−0.141957	−	0.989873i	$-0.545339\pi$
$67$	−698953.	−0.283913	−0.141957	+	0.989873i	$0.545339\pi$
$68$	1.40228e6	0.540819
$69$	−645776.	−0.236652
$70$	3.17257e6	1.10552
$71$	−1.83316e6	−0.607849	−0.303925	−	0.952696i	$-0.598297\pi$
$71$	−1.83316e6	−0.607849	−0.303925	+	0.952696i	$0.598297\pi$
$72$	1.57100e6	0.496035
$73$	−500059.	−0.150450	−0.0752249	−	0.997167i	$-0.523967\pi$
$73$	−500059.	−0.150450	−0.0752249	+	0.997167i	$0.523967\pi$
$74$	−246382.	−0.0706801
$75$	1.94469e6	0.532274
$76$	2.43066e6	0.635150
$77$	2.33047e6	0.581735
$78$	5.74167e6	1.36996
$79$	−4.84357e6	−1.10528	−0.552638	−	0.833421i	$-0.686379\pi$
$79$	−4.84357e6	−1.10528	−0.552638	+	0.833421i	$0.686379\pi$
$80$	927719.	0.202582
$81$	−2.07864e6	−0.434593
$82$	−3.41209e6	−0.683396
$83$	3.47288e6	0.666679	0.333340	−	0.942807i	$-0.391824\pi$
$83$	3.47288e6	0.666679	0.333340	+	0.942807i	$0.391824\pi$
$84$	−8.12355e6	−1.49544
$85$	4.96260e6	0.876483
$86$	−6.82748e6	−1.15749
$87$	1.07357e7	1.74788
$88$	681472.	0.106600
$89$	955049.	0.143602	0.0718010	−	0.997419i	$-0.477125\pi$
$89$	955049.	0.143602	0.0718010	+	0.997419i	$0.477125\pi$
$90$	5.55971e6	0.803903
$91$	−1.73345e7	−2.41139
$92$	570113.	0.0763314
$93$	−5.03481e6	−0.649072
$94$	4.61914e6	0.573606
$95$	8.60202e6	1.02936
$96$	−2.37548e6	−0.274032
$97$	−1.39593e7	−1.55297	−0.776483	−	0.630138i	$-0.782998\pi$
$97$	−1.39593e7	−1.55297	−0.776483	+	0.630138i	$0.782998\pi$
$98$	1.79373e7	1.92515
$99$	4.08399e6	0.423020
$100$	−1.71683e6	−0.171683
$101$	9.16872e6	0.885491	0.442745	−	0.896647i	$-0.354005\pi$
$101$	9.16872e6	0.885491	0.442745	+	0.896647i	$0.354005\pi$
$102$	−1.27070e7	−1.18562
$103$	−1.36882e6	−0.123428	−0.0617142	−	0.998094i	$-0.519657\pi$
$103$	−1.36882e6	−0.123428	−0.0617142	+	0.998094i	$0.519657\pi$
$104$	−5.06894e6	−0.441876
$105$	−2.87490e7	−2.42359
$106$	−501482.	−0.0408964
$107$	2.15337e7	1.69932	0.849659	−	0.527332i	$-0.176807\pi$
$107$	2.15337e7	1.69932	0.849659	+	0.527332i	$0.176807\pi$
$108$	−4.08916e6	−0.312357
$109$	−2.11639e7	−1.56532	−0.782660	−	0.622450i	$-0.786138\pi$
$109$	−2.11639e7	−1.56532	−0.782660	+	0.622450i	$0.786138\pi$
$110$	2.41171e6	0.172763
$111$	2.23264e6	0.154949
$112$	7.17174e6	0.482349
$113$	2.05115e7	1.33728	0.668642	−	0.743584i	$-0.266876\pi$
$113$	2.05115e7	1.33728	0.668642	+	0.743584i	$0.266876\pi$
$114$	−2.20260e7	−1.39241
$115$	2.01761e6	0.123707
$116$	−9.47779e6	−0.563773
$117$	−3.03776e7	−1.75349
$118$	−3.43092e6	−0.192231
$119$	3.83635e7	2.08691
$120$	−8.40674e6	−0.444113
$121$	1.77156e6	0.0909091
$122$	−8.30466e6	−0.414059
$123$	3.09195e7	1.49818
$124$	4.44490e6	0.209356
$125$	−2.37707e7	−1.08857
$126$	4.29795e7	1.91410
$127$	1.78362e7	0.772660	0.386330	−	0.922361i	$-0.373743\pi$
$127$	1.78362e7	0.772660	0.386330	+	0.922361i	$0.373743\pi$
$128$	2.09715e6	0.0883883
$129$	6.18688e7	2.53751
$130$	−1.79388e7	−0.716130
$131$	−7.31001e6	−0.284098	−0.142049	−	0.989860i	$-0.545369\pi$
$131$	−7.31001e6	−0.284098	−0.142049	+	0.989860i	$0.545369\pi$
$132$	−6.17532e6	−0.233696
$133$	6.64980e7	2.45091
$134$	−5.59162e6	−0.200757
$135$	−1.44714e7	−0.506223
$136$	1.12182e7	0.382417
$137$	−1.66829e7	−0.554307	−0.277153	−	0.960826i	$-0.589391\pi$
$137$	−1.66829e7	−0.554307	−0.277153	+	0.960826i	$0.589391\pi$
$138$	−5.16621e6	−0.167338
$139$	−1.29918e7	−0.410316	−0.205158	−	0.978729i	$-0.565771\pi$
$139$	−1.29918e7	−0.410316	−0.205158	+	0.978729i	$0.565771\pi$
$140$	2.53806e7	0.781723
$141$	−4.18574e7	−1.25749
$142$	−1.46653e7	−0.429814
$143$	−1.31773e7	−0.376833
$144$	1.25680e7	0.350750
$145$	−3.35416e7	−0.913683
$146$	−4.00047e6	−0.106384
$147$	−1.62543e8	−4.22043
$148$	−1.97105e6	−0.0499784
$149$	−1.12735e7	−0.279195	−0.139598	−	0.990208i	$-0.544581\pi$
$149$	−1.12735e7	−0.279195	−0.139598	+	0.990208i	$0.544581\pi$
$150$	1.55575e7	0.376374
$151$	−4.16803e7	−0.985171	−0.492586	−	0.870264i	$-0.663948\pi$
$151$	−4.16803e7	−0.985171	−0.492586	+	0.870264i	$0.663948\pi$
$152$	1.94453e7	0.449119
$153$	6.72294e7	1.51754
$154$	1.86437e7	0.411349
$155$	1.57303e7	0.339295
$156$	4.59334e7	0.968707
$157$	3.55935e7	0.734045	0.367022	−	0.930212i	$-0.380377\pi$
$157$	3.55935e7	0.734045	0.367022	+	0.930212i	$0.380377\pi$
$158$	−3.87486e7	−0.781548
$159$	4.54429e6	0.0896554
$160$	7.42175e6	0.143247
$161$	1.55972e7	0.294547
$162$	−1.66292e7	−0.307304
$163$	−9.91643e7	−1.79349	−0.896744	−	0.442549i	$-0.854074\pi$
$163$	−9.91643e7	−1.79349	−0.896744	+	0.442549i	$0.854074\pi$
$164$	−2.72968e7	−0.483234
$165$	−2.18542e7	−0.378741
$166$	2.77831e7	0.471413
$167$	8.13890e7	1.35225	0.676126	−	0.736786i	$-0.263657\pi$
$167$	8.13890e7	1.35225	0.676126	+	0.736786i	$0.263657\pi$
$168$	−6.49884e7	−1.05743
$169$	3.52669e7	0.562036
$170$	3.97008e7	0.619767
$171$	1.16533e8	1.78223
$172$	−5.46198e7	−0.818466
$173$	−2.47680e7	−0.363689	−0.181844	−	0.983327i	$-0.558207\pi$
$173$	−2.47680e7	−0.363689	−0.181844	+	0.983327i	$0.558207\pi$
$174$	8.58852e7	1.23594
$175$	−4.69692e7	−0.662491
$176$	5.45178e6	0.0753778
$177$	3.10901e7	0.421421
$178$	7.64039e6	0.101542
$179$	−1.33876e8	−1.74469	−0.872343	−	0.488894i	$-0.837401\pi$
$179$	−1.33876e8	−1.74469	−0.872343	+	0.488894i	$0.837401\pi$
$180$	4.44777e7	0.568445
$181$	2.75561e7	0.345417	0.172708	−	0.984973i	$-0.444748\pi$
$181$	2.75561e7	0.345417	0.172708	+	0.984973i	$0.444748\pi$
$182$	−1.38676e8	−1.70511
$183$	7.52546e7	0.907725
$184$	4.56090e6	0.0539745
$185$	−6.97549e6	−0.0809979
$186$	−4.02785e7	−0.458963
$187$	2.91629e7	0.326126
$188$	3.69531e7	0.405601
$189$	−1.11871e8	−1.20532
$190$	6.88161e7	0.727868
$191$	1.10570e8	1.14820	0.574102	−	0.818784i	$-0.305351\pi$
$191$	1.10570e8	1.14820	0.574102	+	0.818784i	$0.305351\pi$
$192$	−1.90038e7	−0.193770
$193$	6.81474e7	0.682336	0.341168	−	0.940002i	$-0.389177\pi$
$193$	6.81474e7	0.682336	0.341168	+	0.940002i	$0.389177\pi$
$194$	−1.11674e8	−1.09811
$195$	1.62557e8	1.56994
$196$	1.43498e8	1.36129
$197$	1.58884e8	1.48064	0.740318	−	0.672257i	$-0.234675\pi$
$197$	1.58884e8	1.48064	0.740318	+	0.672257i	$0.234675\pi$
$198$	3.26719e7	0.299120
$199$	−5.17682e7	−0.465669	−0.232834	−	0.972516i	$-0.574800\pi$
$199$	−5.17682e7	−0.465669	−0.232834	+	0.972516i	$0.574800\pi$
$200$	−1.37347e7	−0.121399
$201$	5.06698e7	0.440112
$202$	7.33498e7	0.626136
$203$	−2.59294e8	−2.17548
$204$	−1.01656e8	−0.838357
$205$	−9.66023e7	−0.783157
$206$	−1.09505e7	−0.0872770
$207$	2.73330e7	0.214186
$208$	−4.05515e7	−0.312454
$209$	5.05501e7	0.383010
$210$	−2.29992e8	−1.71374
$211$	−6.61157e7	−0.484525	−0.242263	−	0.970211i	$-0.577890\pi$
$211$	−6.61157e7	−0.484525	−0.242263	+	0.970211i	$0.577890\pi$
$212$	−4.01185e6	−0.0289181
$213$	1.32893e8	0.942264
$214$	1.72269e8	1.20160
$215$	−1.93298e8	−1.32645
$216$	−3.27133e7	−0.220869
$217$	1.21604e8	0.807863
$218$	−1.69311e8	−1.10685
$219$	3.62512e7	0.233221
$220$	1.92937e7	0.122162
$221$	−2.16920e8	−1.35185
$222$	1.78611e7	0.109566
$223$	1.13417e8	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$223$	1.13417e8	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$224$	5.73739e7	0.341072
$225$	−8.23104e7	−0.481743
$226$	1.64092e8	0.945603
$227$	2.69424e8	1.52878	0.764391	−	0.644752i	$-0.223040\pi$
$227$	2.69424e8	1.52878	0.764391	+	0.644752i	$0.223040\pi$
$228$	−1.76208e8	−0.984584
$229$	−2.58093e8	−1.42021	−0.710105	−	0.704096i	$-0.751353\pi$
$229$	−2.58093e8	−1.42021	−0.710105	+	0.704096i	$0.751353\pi$
$230$	1.61409e7	0.0874742
$231$	−1.68944e8	−0.901783
$232$	−7.58223e7	−0.398648
$233$	−1.97294e8	−1.02181	−0.510903	−	0.859638i	$-0.670689\pi$
$233$	−1.97294e8	−1.02181	−0.510903	+	0.859638i	$0.670689\pi$
$234$	−2.43021e8	−1.23990
$235$	1.30776e8	0.657340
$236$	−2.74474e7	−0.135928
$237$	3.51129e8	1.71336
$238$	3.06908e8	1.47567
$239$	−1.76075e8	−0.834265	−0.417133	−	0.908846i	$-0.636965\pi$
$239$	−1.76075e8	−0.834265	−0.417133	+	0.908846i	$0.636965\pi$
$240$	−6.72539e7	−0.314035
$241$	−4.22960e7	−0.194644	−0.0973218	−	0.995253i	$-0.531028\pi$
$241$	−4.22960e7	−0.194644	−0.0973218	+	0.995253i	$0.531028\pi$
$242$	1.41725e7	0.0642824
$243$	2.90423e8	1.29840
$244$	−6.64373e7	−0.292784
$245$	5.07835e8	2.20618
$246$	2.47356e8	1.05937
$247$	−3.76003e8	−1.58764
$248$	3.55592e7	0.148037
$249$	−2.51763e8	−1.03346
$250$	−1.90165e8	−0.769735
$251$	1.00835e8	0.402489	0.201245	−	0.979541i	$-0.435501\pi$
$251$	1.00835e8	0.402489	0.201245	+	0.979541i	$0.435501\pi$
$252$	3.43836e8	1.35347
$253$	1.18566e7	0.0460296
$254$	1.42689e8	0.546353
$255$	−3.59758e8	−1.35869
$256$	1.67772e7	0.0625000
$257$	8.85623e7	0.325449	0.162725	−	0.986672i	$-0.447972\pi$
$257$	8.85623e7	0.325449	0.162725	+	0.986672i	$0.447972\pi$
$258$	4.94950e8	1.79429
$259$	−5.39241e7	−0.192856
$260$	−1.43510e8	−0.506380
$261$	−4.54395e8	−1.58195
$262$	−5.84800e7	−0.200888
$263$	−4.15591e8	−1.40871	−0.704353	−	0.709850i	$-0.748763\pi$
$263$	−4.15591e8	−1.40871	−0.704353	+	0.709850i	$0.748763\pi$
$264$	−4.94025e7	−0.165248
$265$	−1.41978e7	−0.0468663
$266$	5.31984e8	1.73306
$267$	−6.92351e7	−0.222606
$268$	−4.47330e7	−0.141957
$269$	−1.84945e8	−0.579308	−0.289654	−	0.957131i	$-0.593540\pi$
$269$	−1.84945e8	−0.579308	−0.289654	+	0.957131i	$0.593540\pi$
$270$	−1.15771e8	−0.357954
$271$	5.17862e8	1.58060	0.790300	−	0.612721i	$-0.209925\pi$
$271$	5.17862e8	1.58060	0.790300	+	0.612721i	$0.209925\pi$
$272$	8.97456e7	0.270410
$273$	1.25665e9	3.73804
$274$	−1.33463e8	−0.391954
$275$	−3.57048e7	−0.103529
$276$	−4.13297e7	−0.118326
$277$	−3.23904e7	−0.0915667	−0.0457833	−	0.998951i	$-0.514578\pi$
$277$	−3.23904e7	−0.0915667	−0.0457833	+	0.998951i	$0.514578\pi$
$278$	−1.03935e8	−0.290137
$279$	2.13102e8	0.587453
$280$	2.03044e8	0.552762
$281$	3.54172e8	0.952231	0.476115	−	0.879383i	$-0.342044\pi$
$281$	3.54172e8	0.952231	0.476115	+	0.879383i	$0.342044\pi$
$282$	−3.34859e8	−0.889182
$283$	1.82414e8	0.478415	0.239207	−	0.970968i	$-0.423112\pi$
$283$	1.82414e8	0.478415	0.239207	+	0.970968i	$0.423112\pi$
$284$	−1.17322e8	−0.303925
$285$	−6.23593e8	−1.59567
$286$	−1.05418e8	−0.266461
$287$	−7.46785e8	−1.86470
$288$	1.00544e8	0.248018
$289$	6.97335e7	0.169941
$290$	−2.68333e8	−0.646072
$291$	1.01196e9	2.40735
$292$	−3.20038e7	−0.0752249
$293$	4.36215e6	0.0101313	0.00506563	−	0.999987i	$-0.498388\pi$
$293$	4.36215e6	0.0101313	0.00506563	+	0.999987i	$0.498388\pi$
$294$	−1.30034e9	−2.98429
$295$	−9.71354e7	−0.220293
$296$	−1.57684e7	−0.0353400
$297$	−8.50417e7	−0.188358
$298$	−9.01882e7	−0.197421
$299$	−8.81918e7	−0.190800
$300$	1.24460e8	0.266137
$301$	−1.49429e9	−3.15829
$302$	−3.33443e8	−0.696621
$303$	−6.64676e8	−1.37265
$304$	1.55562e8	0.317575
$305$	−2.35119e8	−0.474503
$306$	5.37835e8	1.07306
$307$	−4.08466e8	−0.805697	−0.402849	−	0.915267i	$-0.631980\pi$
$307$	−4.08466e8	−0.805697	−0.402849	+	0.915267i	$0.631980\pi$
$308$	1.49150e8	0.290868
$309$	9.92308e7	0.191334
$310$	1.25843e8	0.239918
$311$	8.06482e8	1.52031	0.760157	−	0.649740i	$-0.225122\pi$
$311$	8.06482e8	1.52031	0.760157	+	0.649740i	$0.225122\pi$
$312$	3.67467e8	0.684979
$313$	2.34539e8	0.432325	0.216162	−	0.976357i	$-0.430646\pi$
$313$	2.34539e8	0.432325	0.216162	+	0.976357i	$0.430646\pi$
$314$	2.84748e8	0.519048
$315$	1.21682e9	2.19351
$316$	−3.09988e8	−0.552638
$317$	2.10448e8	0.371054	0.185527	−	0.982639i	$-0.440601\pi$
$317$	2.10448e8	0.371054	0.185527	+	0.982639i	$0.440601\pi$
$318$	3.63543e7	0.0633959
$319$	−1.97108e8	−0.339968
$320$	5.93740e7	0.101291
$321$	−1.56106e9	−2.63422
$322$	1.24777e8	0.208276
$323$	8.32141e8	1.37400
$324$	−1.33033e8	−0.217296
$325$	2.65580e8	0.429145
$326$	−7.93314e8	−1.26819
$327$	1.53425e9	2.42650
$328$	−2.18374e8	−0.341698
$329$	1.01096e9	1.56513
$330$	−1.74834e8	−0.267810
$331$	−9.04546e8	−1.37099	−0.685493	−	0.728080i	$-0.740413\pi$
$331$	−9.04546e8	−1.37099	−0.685493	+	0.728080i	$0.740413\pi$
$332$	2.22265e8	0.333340
$333$	−9.44984e7	−0.140239
$334$	6.51112e8	0.956187
$335$	−1.58308e8	−0.230063
$336$	−5.19907e8	−0.747719
$337$	6.56273e8	0.934071	0.467036	−	0.884238i	$-0.345322\pi$
$337$	6.56273e8	0.934071	0.467036	+	0.884238i	$0.345322\pi$
$338$	2.82135e8	0.397419
$339$	−1.48696e9	−2.07301
$340$	3.17607e8	0.438241
$341$	9.24400e7	0.126247
$342$	9.32266e8	1.26023
$343$	2.48387e9	3.32353
$344$	−4.36959e8	−0.578743
$345$	−1.46264e8	−0.191766
$346$	−1.98144e8	−0.257167
$347$	8.23306e8	1.05781	0.528906	−	0.848681i	$-0.322603\pi$
$347$	8.23306e8	1.05781	0.528906	+	0.848681i	$0.322603\pi$
$348$	6.87082e8	0.873939
$349$	−5.24128e8	−0.660007	−0.330004	−	0.943980i	$-0.607050\pi$
$349$	−5.24128e8	−0.660007	−0.330004	+	0.943980i	$0.607050\pi$
$350$	−3.75754e8	−0.468452
$351$	6.32559e8	0.780775
$352$	4.36142e7	0.0533002
$353$	−3.31476e8	−0.401089	−0.200544	−	0.979685i	$-0.564271\pi$
$353$	−3.31476e8	−0.401089	−0.200544	+	0.979685i	$0.564271\pi$
$354$	2.48721e8	0.297989
$355$	−4.15199e8	−0.492558
$356$	6.11231e7	0.0718010
$357$	−2.78112e9	−3.23505
$358$	−1.07101e9	−1.23368
$359$	−1.60697e9	−1.83306	−0.916529	−	0.399968i	$-0.869021\pi$
$359$	−1.60697e9	−1.83306	−0.916529	+	0.399968i	$0.869021\pi$
$360$	3.55822e8	0.401952
$361$	5.48535e8	0.613661
$362$	2.20449e8	0.244246
$363$	−1.28427e8	−0.140924
$364$	−1.10941e9	−1.20569
$365$	−1.13260e8	−0.121914
$366$	6.02037e8	0.641858
$367$	−2.48331e7	−0.0262240	−0.0131120	−	0.999914i	$-0.504174\pi$
$367$	−2.48331e7	−0.0262240	−0.0131120	+	0.999914i	$0.504174\pi$
$368$	3.64872e7	0.0381657
$369$	−1.30869e9	−1.35595
$370$	−5.58039e7	−0.0572741
$371$	−1.09756e8	−0.111589
$372$	−3.22228e8	−0.324536
$373$	1.33542e9	1.33241	0.666204	−	0.745770i	$-0.267918\pi$
$373$	1.33542e9	1.33241	0.666204	+	0.745770i	$0.267918\pi$
$374$	2.33304e8	0.230606
$375$	1.72323e9	1.68746
$376$	2.95625e8	0.286803
$377$	1.46614e9	1.40922
$378$	−8.94970e8	−0.852290
$379$	−5.06235e8	−0.477656	−0.238828	−	0.971062i	$-0.576763\pi$
$379$	−5.06235e8	−0.477656	−0.238828	+	0.971062i	$0.576763\pi$
$380$	5.50529e8	0.514680
$381$	−1.29301e9	−1.19775
$382$	8.84556e8	0.811902
$383$	4.48094e8	0.407543	0.203771	−	0.979019i	$-0.434680\pi$
$383$	4.48094e8	0.407543	0.203771	+	0.979019i	$0.434680\pi$
$384$	−1.52031e8	−0.137016
$385$	5.27836e8	0.471397
$386$	5.45179e8	0.482485
$387$	−2.61864e9	−2.29662
$388$	−8.93394e8	−0.776483
$389$	7.22169e8	0.622036	0.311018	−	0.950404i	$-0.399330\pi$
$389$	7.22169e8	0.622036	0.311018	+	0.950404i	$0.399330\pi$
$390$	1.30045e9	1.11012
$391$	1.95179e8	0.165126
$392$	1.14798e9	0.962575
$393$	5.29930e8	0.440398
$394$	1.27107e9	1.04697
$395$	−1.09704e9	−0.895637
$396$	2.61375e8	0.211510
$397$	−9.71374e8	−0.779147	−0.389574	−	0.920995i	$-0.627378\pi$
$397$	−9.71374e8	−0.779147	−0.389574	+	0.920995i	$0.627378\pi$
$398$	−4.14146e8	−0.329278
$399$	−4.82070e9	−3.79931
$400$	−1.09877e8	−0.0858417
$401$	1.22326e9	0.947354	0.473677	−	0.880699i	$-0.342926\pi$
$401$	1.22326e9	0.947354	0.473677	+	0.880699i	$0.342926\pi$
$402$	4.05358e8	0.311206
$403$	−6.87589e8	−0.523313
$404$	5.86798e8	0.442745
$405$	−4.70800e8	−0.352163
$406$	−2.07435e9	−1.53830
$407$	−4.09917e7	−0.0301381
$408$	−8.13251e8	−0.592808
$409$	1.75949e9	1.27161	0.635806	−	0.771849i	$-0.280668\pi$
$409$	1.75949e9	1.27161	0.635806	+	0.771849i	$0.280668\pi$
$410$	−7.72818e8	−0.553776
$411$	1.20941e9	0.859264
$412$	−8.76043e7	−0.0617142
$413$	−7.50907e8	−0.524518
$414$	2.18664e8	0.151452
$415$	7.86587e8	0.540229
$416$	−3.24412e8	−0.220938
$417$	9.41827e8	0.636056
$418$	4.04401e8	0.270829
$419$	1.02214e9	0.678830	0.339415	−	0.940637i	$-0.389771\pi$
$419$	1.02214e9	0.678830	0.339415	+	0.940637i	$0.389771\pi$
$420$	−1.83993e9	−1.21180
$421$	8.07976e8	0.527729	0.263865	−	0.964560i	$-0.415003\pi$
$421$	8.07976e8	0.527729	0.263865	+	0.964560i	$0.415003\pi$
$422$	−5.28926e8	−0.342611
$423$	1.77165e9	1.13811
$424$	−3.20948e7	−0.0204482
$425$	−5.87762e8	−0.371399
$426$	1.06314e9	0.666281
$427$	−1.81759e9	−1.12979
$428$	1.37816e9	0.849659
$429$	9.55271e8	0.584152
$430$	−1.54638e9	−0.937945
$431$	2.11098e9	1.27003	0.635015	−	0.772499i	$-0.280994\pi$
$431$	2.11098e9	1.27003	0.635015	+	0.772499i	$0.280994\pi$
$432$	−2.61706e8	−0.156178
$433$	−2.05374e9	−1.21573	−0.607867	−	0.794039i	$-0.707975\pi$
$433$	−2.05374e9	−1.21573	−0.607867	+	0.794039i	$0.707975\pi$
$434$	9.72829e8	0.571245
$435$	2.43156e9	1.41636
$436$	−1.35449e9	−0.782660
$437$	3.38318e8	0.193928
$438$	2.90010e8	0.164912
$439$	−2.72396e8	−0.153665	−0.0768324	−	0.997044i	$-0.524481\pi$
$439$	−2.72396e8	−0.153665	−0.0768324	+	0.997044i	$0.524481\pi$
$440$	1.54349e8	0.0863814
$441$	6.87974e9	3.81977
$442$	−1.73536e9	−0.955900
$443$	2.53670e8	0.138629	0.0693147	−	0.997595i	$-0.477919\pi$
$443$	2.53670e8	0.138629	0.0693147	+	0.997595i	$0.477919\pi$
$444$	1.42889e8	0.0774745
$445$	2.16313e8	0.116365
$446$	9.07338e8	0.484280
$447$	8.17261e8	0.432797
$448$	4.58992e8	0.241175
$449$	−1.18063e9	−0.615533	−0.307766	−	0.951462i	$-0.599581\pi$
$449$	−1.18063e9	−0.615533	−0.307766	+	0.951462i	$0.599581\pi$
$450$	−6.58483e8	−0.340644
$451$	−5.67687e8	−0.291401
$452$	1.31274e9	0.668642
$453$	3.02157e9	1.52717
$454$	2.15539e9	1.08101
$455$	−3.92616e9	−1.95402
$456$	−1.40966e9	−0.696206
$457$	1.44893e9	0.710133	0.355066	−	0.934841i	$-0.384458\pi$
$457$	1.44893e9	0.710133	0.355066	+	0.934841i	$0.384458\pi$
$458$	−2.06475e9	−1.00424
$459$	−1.39993e9	−0.675714
$460$	1.29127e8	0.0618536
$461$	−2.23879e9	−1.06429	−0.532145	−	0.846653i	$-0.678614\pi$
$461$	−2.23879e9	−1.06429	−0.532145	+	0.846653i	$0.678614\pi$
$462$	−1.35156e9	−0.637657
$463$	2.75405e9	1.28955	0.644776	−	0.764372i	$-0.276951\pi$
$463$	2.75405e9	1.28955	0.644776	+	0.764372i	$0.276951\pi$
$464$	−6.06579e8	−0.281886
$465$	−1.14035e9	−0.525962
$466$	−1.57835e9	−0.722526
$467$	−2.08168e9	−0.945811	−0.472905	−	0.881113i	$-0.656795\pi$
$467$	−2.08168e9	−0.945811	−0.472905	+	0.881113i	$0.656795\pi$
$468$	−1.94417e9	−0.876744
$469$	−1.22381e9	−0.547782
$470$	1.04621e9	0.464810
$471$	−2.58031e9	−1.13789
$472$	−2.19579e8	−0.0961157
$473$	−1.13592e9	−0.493554
$474$	2.80903e9	1.21153
$475$	−1.01881e9	−0.436179
$476$	2.45526e9	1.04345
$477$	−1.92341e8	−0.0811441
$478$	−1.40860e9	−0.589915
$479$	4.51168e8	0.187570	0.0937852	−	0.995592i	$-0.470103\pi$
$479$	4.51168e8	0.187570	0.0937852	+	0.995592i	$0.470103\pi$
$480$	−5.38031e8	−0.222056
$481$	3.04906e8	0.124927
$482$	−3.38368e8	−0.137634
$483$	−1.13070e9	−0.456596
$484$	1.13380e8	0.0454545
$485$	−3.16169e9	−1.25841
$486$	2.32339e9	0.918109
$487$	−1.48099e9	−0.581033	−0.290516	−	0.956870i	$-0.593827\pi$
$487$	−1.48099e9	−0.581033	−0.290516	+	0.956870i	$0.593827\pi$
$488$	−5.31498e8	−0.207030
$489$	7.18880e9	2.78020
$490$	4.06268e9	1.56001
$491$	−6.07557e8	−0.231634	−0.115817	−	0.993271i	$-0.536949\pi$
$491$	−6.07557e8	−0.231634	−0.115817	+	0.993271i	$0.536949\pi$
$492$	1.97885e9	0.749091
$493$	−3.24474e9	−1.21960
$494$	−3.00802e9	−1.12263
$495$	9.24998e8	0.342785
$496$	2.84474e8	0.104678
$497$	−3.20970e9	−1.17278
$498$	−2.01410e9	−0.730767
$499$	4.69266e9	1.69070	0.845351	−	0.534212i	$-0.179391\pi$
$499$	4.69266e9	1.69070	0.845351	+	0.534212i	$0.179391\pi$
$500$	−1.52132e9	−0.544285
$501$	−5.90020e9	−2.09621
$502$	8.06682e8	0.284603
$503$	−2.56555e9	−0.898860	−0.449430	−	0.893315i	$-0.648373\pi$
$503$	−2.56555e9	−0.898860	−0.449430	+	0.893315i	$0.648373\pi$
$504$	2.75069e9	0.957049
$505$	2.07666e9	0.717539
$506$	9.48525e7	0.0325478
$507$	−2.55663e9	−0.871246
$508$	1.14151e9	0.386330
$509$	5.55142e9	1.86591	0.932957	−	0.359987i	$-0.117219\pi$
$509$	5.55142e9	1.86591	0.932957	+	0.359987i	$0.117219\pi$
$510$	−2.87807e9	−0.960739
$511$	−8.75561e8	−0.290277
$512$	1.34218e8	0.0441942
$513$	−2.42660e9	−0.793573
$514$	7.08499e8	0.230127
$515$	−3.10029e8	−0.100018
$516$	3.95960e9	1.26875
$517$	7.68509e8	0.244586
$518$	−4.31393e8	−0.136370
$519$	1.79553e9	0.563776
$520$	−1.14808e9	−0.358065
$521$	−3.93859e9	−1.22014	−0.610069	−	0.792348i	$-0.708858\pi$
$521$	−3.93859e9	−1.22014	−0.610069	+	0.792348i	$0.708858\pi$
$522$	−3.63516e9	−1.11860
$523$	1.28298e9	0.392160	0.196080	−	0.980588i	$-0.437179\pi$
$523$	1.28298e9	0.392160	0.196080	+	0.980588i	$0.437179\pi$
$524$	−4.67840e8	−0.142049
$525$	3.40498e9	1.02697
$526$	−3.32472e9	−0.996106
$527$	1.52172e9	0.452895
$528$	−3.95220e8	−0.116848
$529$	−3.32547e9	−0.976694
$530$	−1.13583e8	−0.0331395
$531$	−1.31591e9	−0.381414
$532$	4.25587e9	1.22546
$533$	4.22258e9	1.20791
$534$	−5.53881e8	−0.157406
$535$	4.87724e9	1.37701
$536$	−3.57864e8	−0.100379
$537$	9.70520e9	2.70455
$538$	−1.47956e9	−0.409633
$539$	2.98431e9	0.820887
$540$	−9.26169e8	−0.253112
$541$	3.43581e9	0.932908	0.466454	−	0.884546i	$-0.345531\pi$
$541$	3.43581e9	0.932908	0.466454	+	0.884546i	$0.345531\pi$
$542$	4.14290e9	1.11765
$543$	−1.99765e9	−0.535451
$544$	7.17965e8	0.191208
$545$	−4.79349e9	−1.26842
$546$	1.00532e10	2.64319
$547$	−1.20501e8	−0.0314800	−0.0157400	−	0.999876i	$-0.505010\pi$
$547$	−1.20501e8	−0.0314800	−0.0157400	+	0.999876i	$0.505010\pi$
$548$	−1.06771e9	−0.277153
$549$	−3.18521e9	−0.821551
$550$	−2.85638e8	−0.0732061
$551$	−5.62433e9	−1.43232
$552$	−3.30637e8	−0.0836691
$553$	−8.48067e9	−2.13252
$554$	−2.59123e8	−0.0647474
$555$	5.05680e8	0.125560
$556$	−8.31477e8	−0.205158
$557$	−1.81976e9	−0.446191	−0.223096	−	0.974797i	$-0.571616\pi$
$557$	−1.81976e9	−0.446191	−0.223096	+	0.974797i	$0.571616\pi$
$558$	1.70482e9	0.415392
$559$	8.44924e9	2.04586
$560$	1.62436e9	0.390862
$561$	−2.11413e9	−0.505548
$562$	2.83338e9	0.673329
$563$	6.87134e9	1.62279	0.811394	−	0.584499i	$-0.198709\pi$
$563$	6.87134e9	1.62279	0.811394	+	0.584499i	$0.198709\pi$
$564$	−2.67887e9	−0.628746
$565$	4.64574e9	1.08364
$566$	1.45931e9	0.338290
$567$	−3.63953e9	−0.838503
$568$	−9.38577e8	−0.214907
$569$	−6.30670e8	−0.143519	−0.0717595	−	0.997422i	$-0.522861\pi$
$569$	−6.30670e8	−0.143519	−0.0717595	+	0.997422i	$0.522861\pi$
$570$	−4.98875e9	−1.12831
$571$	2.00096e9	0.449793	0.224896	−	0.974383i	$-0.427796\pi$
$571$	2.00096e9	0.449793	0.224896	+	0.974383i	$0.427796\pi$
$572$	−8.43345e8	−0.188417
$573$	−8.01561e9	−1.77990
$574$	−5.97428e9	−1.31854
$575$	−2.38962e8	−0.0524194
$576$	8.04352e8	0.175375
$577$	−5.92670e9	−1.28439	−0.642196	−	0.766541i	$-0.721976\pi$
$577$	−5.92670e9	−1.28439	−0.642196	+	0.766541i	$0.721976\pi$
$578$	5.57868e8	0.120167
$579$	−4.94027e9	−1.05773
$580$	−2.14666e9	−0.456842
$581$	6.08072e9	1.28629
$582$	8.09570e9	1.70225
$583$	−8.34340e7	−0.0174383
$584$	−2.56030e8	−0.0531920
$585$	−6.88034e9	−1.42090
$586$	3.48972e7	0.00716388
$587$	−1.54400e9	−0.315075	−0.157538	−	0.987513i	$-0.550356\pi$
$587$	−1.54400e9	−0.315075	−0.157538	+	0.987513i	$0.550356\pi$
$588$	−1.04027e10	−2.11021
$589$	2.63770e9	0.531890
$590$	−7.77083e8	−0.155771
$591$	−1.15181e10	−2.29522
$592$	−1.26147e8	−0.0249892
$593$	6.29215e9	1.23910	0.619552	−	0.784956i	$-0.287314\pi$
$593$	6.29215e9	1.23910	0.619552	+	0.784956i	$0.287314\pi$
$594$	−6.80334e8	−0.133189
$595$	8.68909e9	1.69108
$596$	−7.21505e8	−0.139598
$597$	3.75288e9	0.721862
$598$	−7.05534e8	−0.134916
$599$	−3.20572e9	−0.609441	−0.304721	−	0.952442i	$-0.598563\pi$
$599$	−3.20572e9	−0.609441	−0.304721	+	0.952442i	$0.598563\pi$
$600$	9.95679e8	0.188187
$601$	1.65231e9	0.310477	0.155239	−	0.987877i	$-0.450385\pi$
$601$	1.65231e9	0.310477	0.155239	+	0.987877i	$0.450385\pi$
$602$	−1.19543e10	−2.23325
$603$	−2.14464e9	−0.398330
$604$	−2.66754e9	−0.492586
$605$	4.01248e8	0.0736663
$606$	−5.31741e9	−0.970612
$607$	1.08264e9	0.196482	0.0982410	−	0.995163i	$-0.468678\pi$
$607$	1.08264e9	0.196482	0.0982410	+	0.995163i	$0.468678\pi$
$608$	1.24450e9	0.224559
$609$	1.87972e10	3.37235
$610$	−1.88095e9	−0.335524
$611$	−5.71634e9	−1.01385
$612$	4.30268e9	0.758769
$613$	1.86372e9	0.326790	0.163395	−	0.986561i	$-0.447755\pi$
$613$	1.86372e9	0.326790	0.163395	+	0.986561i	$0.447755\pi$
$614$	−3.26773e9	−0.569714
$615$	7.00307e9	1.21402
$616$	1.19320e9	0.205674
$617$	−4.23169e8	−0.0725297	−0.0362649	−	0.999342i	$-0.511546\pi$
$617$	−4.23169e8	−0.0725297	−0.0362649	+	0.999342i	$0.511546\pi$
$618$	7.93846e8	0.135293
$619$	2.37963e9	0.403266	0.201633	−	0.979461i	$-0.435375\pi$
$619$	2.37963e9	0.403266	0.201633	+	0.979461i	$0.435375\pi$
$620$	1.00674e9	0.169647
$621$	−5.69160e8	−0.0953705
$622$	6.45185e9	1.07502
$623$	1.67221e9	0.277065
$624$	2.93974e9	0.484353
$625$	−3.28816e9	−0.538732
$626$	1.87631e9	0.305700
$627$	−3.66457e9	−0.593727
$628$	2.27799e9	0.367022
$629$	−6.74794e8	−0.108117
$630$	9.73458e9	1.55105
$631$	7.34037e9	1.16309	0.581547	−	0.813513i	$-0.302447\pi$
$631$	7.34037e9	1.16309	0.581547	+	0.813513i	$0.302447\pi$
$632$	−2.47991e9	−0.390774
$633$	4.79299e9	0.751092
$634$	1.68358e9	0.262375
$635$	4.03978e9	0.626109
$636$	2.90835e8	0.0448277
$637$	−2.21980e10	−3.40271
$638$	−1.57687e9	−0.240394
$639$	−5.62479e9	−0.852812
$640$	4.74992e8	0.0716236
$641$	−4.78647e9	−0.717814	−0.358907	−	0.933373i	$-0.616850\pi$
$641$	−4.78647e9	−0.717814	−0.358907	+	0.933373i	$0.616850\pi$
$642$	−1.24885e10	−1.86267
$643$	4.12710e9	0.612219	0.306110	−	0.951996i	$-0.400973\pi$
$643$	4.12710e9	0.612219	0.306110	+	0.951996i	$0.400973\pi$
$644$	9.98219e8	0.147274
$645$	1.40129e10	2.05622
$646$	6.65713e9	0.971568
$647$	2.07770e9	0.301591	0.150796	−	0.988565i	$-0.451816\pi$
$647$	2.07770e9	0.301591	0.150796	+	0.988565i	$0.451816\pi$
$648$	−1.06427e9	−0.153652
$649$	−5.70820e8	−0.0819677
$650$	2.12464e9	0.303451
$651$	−8.81552e9	−1.25232
$652$	−6.34651e9	−0.896744
$653$	−1.03614e10	−1.45621	−0.728104	−	0.685467i	$-0.759598\pi$
$653$	−1.03614e10	−1.45621	−0.728104	+	0.685467i	$0.759598\pi$
$654$	1.22740e10	1.71579
$655$	−1.65567e9	−0.230213
$656$	−1.74699e9	−0.241617
$657$	−1.53436e9	−0.211081
$658$	8.08772e9	1.10671
$659$	6.72335e9	0.915139	0.457569	−	0.889174i	$-0.348720\pi$
$659$	6.72335e9	0.915139	0.457569	+	0.889174i	$0.348720\pi$
$660$	−1.39867e9	−0.189370
$661$	−1.14081e10	−1.53641	−0.768204	−	0.640206i	$-0.778849\pi$
$661$	−1.14081e10	−1.53641	−0.768204	+	0.640206i	$0.778849\pi$
$662$	−7.23637e9	−0.969433
$663$	1.57254e10	2.09558
$664$	1.77812e9	0.235707
$665$	1.50614e10	1.98605
$666$	−7.55987e8	−0.0991641
$667$	−1.31919e9	−0.172134
$668$	5.20889e9	0.676126
$669$	−8.22205e9	−1.06167
$670$	−1.26647e9	−0.162679
$671$	−1.38169e9	−0.176555
$672$	−4.15926e9	−0.528717
$673$	−4.18258e9	−0.528922	−0.264461	−	0.964396i	$-0.585194\pi$
$673$	−4.18258e9	−0.528922	−0.264461	+	0.964396i	$0.585194\pi$
$674$	5.25019e9	0.660488
$675$	1.71397e9	0.214506
$676$	2.25708e9	0.281018
$677$	3.43078e9	0.424945	0.212472	−	0.977167i	$-0.431848\pi$
$677$	3.43078e9	0.424945	0.212472	+	0.977167i	$0.431848\pi$
$678$	−1.18957e10	−1.46584
$679$	−2.44415e10	−2.99629
$680$	2.54085e9	0.309883
$681$	−1.95316e10	−2.36986
$682$	7.39520e8	0.0892698
$683$	1.62297e10	1.94911	0.974556	−	0.224144i	$-0.0719585\pi$
$683$	1.62297e10	1.94911	0.974556	+	0.224144i	$0.0719585\pi$
$684$	7.45813e9	0.891115
$685$	−3.77858e9	−0.449171
$686$	1.98710e10	2.35009
$687$	1.87102e10	2.20155
$688$	−3.49567e9	−0.409233
$689$	6.20601e8	0.0722845
$690$	−1.17011e9	−0.135599
$691$	6.75599e9	0.778962	0.389481	−	0.921035i	$-0.372654\pi$
$691$	6.75599e9	0.778962	0.389481	+	0.921035i	$0.372654\pi$
$692$	−1.58515e9	−0.181844
$693$	7.15071e9	0.816174
$694$	6.58645e9	0.747985
$695$	−2.94257e9	−0.332491
$696$	5.49665e9	0.617968
$697$	−9.34511e9	−1.04537
$698$	−4.19303e9	−0.466696
$699$	1.43026e10	1.58396
$700$	−3.00603e9	−0.331246
$701$	−7.32837e9	−0.803516	−0.401758	−	0.915746i	$-0.631601\pi$
$701$	−7.32837e9	−0.803516	−0.401758	+	0.915746i	$0.631601\pi$
$702$	5.06047e9	0.552092
$703$	−1.16967e9	−0.126975
$704$	3.48914e8	0.0376889
$705$	−9.48045e9	−1.01898
$706$	−2.65181e9	−0.283613
$707$	1.60536e10	1.70846
$708$	1.98977e9	0.210710
$709$	−1.38412e10	−1.45852	−0.729260	−	0.684236i	$-0.760136\pi$
$709$	−1.38412e10	−1.45852	−0.729260	+	0.684236i	$0.760136\pi$
$710$	−3.32159e9	−0.348291
$711$	−1.48618e10	−1.55070
$712$	4.88985e8	0.0507710
$713$	6.18675e8	0.0639219
$714$	−2.22489e10	−2.28752
$715$	−2.98457e9	−0.305359
$716$	−8.56807e9	−0.872343
$717$	1.27643e10	1.29325
$718$	−1.28557e10	−1.29617
$719$	1.31832e9	0.132273	0.0661365	−	0.997811i	$-0.478933\pi$
$719$	1.31832e9	0.132273	0.0661365	+	0.997811i	$0.478933\pi$
$720$	2.84657e9	0.284223
$721$	−2.39668e9	−0.238142
$722$	4.38828e9	0.433924
$723$	3.06620e9	0.301729
$724$	1.76359e9	0.172708
$725$	3.97261e9	0.387162
$726$	−1.02742e9	−0.0996481
$727$	−1.99337e9	−0.192405	−0.0962027	−	0.995362i	$-0.530670\pi$
$727$	−1.99337e9	−0.192405	−0.0962027	+	0.995362i	$0.530670\pi$
$728$	−8.87528e9	−0.852555
$729$	−1.65079e10	−1.57814
$730$	−9.06083e8	−0.0862061
$731$	−1.86992e10	−1.77057
$732$	4.81629e9	0.453862
$733$	8.58436e9	0.805089	0.402545	−	0.915400i	$-0.368126\pi$
$733$	8.58436e9	0.805089	0.402545	+	0.915400i	$0.368126\pi$
$734$	−1.98664e8	−0.0185432
$735$	−3.68149e10	−3.41993
$736$	2.91898e8	0.0269872
$737$	−9.30306e8	−0.0856031
$738$	−1.04695e10	−0.958804
$739$	4.87753e9	0.444575	0.222287	−	0.974981i	$-0.428648\pi$
$739$	4.87753e9	0.444575	0.222287	+	0.974981i	$0.428648\pi$
$740$	−4.46431e8	−0.0404989
$741$	2.72579e10	2.46110
$742$	−8.78051e8	−0.0789053
$743$	−1.46925e9	−0.131412	−0.0657059	−	0.997839i	$-0.520930\pi$
$743$	−1.46925e9	−0.131412	−0.0657059	+	0.997839i	$0.520930\pi$
$744$	−2.57782e9	−0.229482
$745$	−2.55338e9	−0.226240
$746$	1.06834e10	0.942155
$747$	1.06561e10	0.935350
$748$	1.86643e9	0.163063
$749$	3.77036e10	3.27866
$750$	1.37858e10	1.19321
$751$	7.26899e9	0.626230	0.313115	−	0.949715i	$-0.398627\pi$
$751$	7.26899e9	0.626230	0.313115	+	0.949715i	$0.398627\pi$
$752$	2.36500e9	0.202800
$753$	−7.30993e9	−0.623923
$754$	1.17291e10	0.996471
$755$	−9.44034e9	−0.798313
$756$	−7.15976e9	−0.602660
$757$	2.05022e10	1.71777	0.858884	−	0.512170i	$-0.171158\pi$
$757$	2.05022e10	1.71777	0.858884	+	0.512170i	$0.171158\pi$
$758$	−4.04988e9	−0.337754
$759$	−8.59528e8	−0.0713533
$760$	4.40423e9	0.363934
$761$	−1.30953e10	−1.07713	−0.538566	−	0.842583i	$-0.681034\pi$
$761$	−1.30953e10	−1.07713	−0.538566	+	0.842583i	$0.681034\pi$
$762$	−1.03441e10	−0.846935
$763$	−3.70562e10	−3.02012
$764$	7.07645e9	0.574102
$765$	1.52271e10	1.22970
$766$	3.58475e9	0.288176
$767$	4.24589e9	0.339770
$768$	−1.21625e9	−0.0968851
$769$	2.32970e10	1.84739	0.923694	−	0.383131i	$-0.125154\pi$
$769$	2.32970e10	1.84739	0.923694	+	0.383131i	$0.125154\pi$
$770$	4.22269e9	0.333328
$771$	−6.42022e9	−0.504498
$772$	4.36143e9	0.341168
$773$	−7.01207e9	−0.546032	−0.273016	−	0.962009i	$-0.588021\pi$
$773$	−7.01207e9	−0.546032	−0.273016	+	0.962009i	$0.588021\pi$
$774$	−2.09492e10	−1.62395
$775$	−1.86307e9	−0.143772
$776$	−7.14715e9	−0.549057
$777$	3.90917e9	0.298958
$778$	5.77735e9	0.439846
$779$	−1.61985e10	−1.22770
$780$	1.04036e10	0.784971
$781$	−2.43993e9	−0.183273
$782$	1.56144e9	0.116762
$783$	9.46196e9	0.704393
$784$	9.18387e9	0.680643
$785$	8.06172e9	0.594818
$786$	4.23944e9	0.311408
$787$	9.15470e9	0.669472	0.334736	−	0.942312i	$-0.391353\pi$
$787$	9.15470e9	0.669472	0.334736	+	0.942312i	$0.391353\pi$
$788$	1.01686e10	0.740318
$789$	3.01278e10	2.18372
$790$	−8.77631e9	−0.633311
$791$	3.59139e10	2.58015
$792$	2.09100e9	0.149560
$793$	1.02773e10	0.731851
$794$	−7.77099e9	−0.550940
$795$	1.02925e9	0.0726504
$796$	−3.31316e9	−0.232834
$797$	3.58195e9	0.250620	0.125310	−	0.992118i	$-0.460007\pi$
$797$	3.58195e9	0.250620	0.125310	+	0.992118i	$0.460007\pi$
$798$	−3.85656e10	−2.68652
$799$	1.26510e10	0.877426
$800$	−8.79019e8	−0.0606993
$801$	2.93043e9	0.201473
$802$	9.78606e9	0.669881
$803$	−6.65579e8	−0.0453623
$804$	3.24287e9	0.220056
$805$	3.53266e9	0.238680
$806$	−5.50071e9	−0.370038
$807$	1.34074e10	0.898021
$808$	4.69439e9	0.313068
$809$	−1.39506e10	−0.926345	−0.463173	−	0.886268i	$-0.653289\pi$
$809$	−1.39506e10	−0.926345	−0.463173	+	0.886268i	$0.653289\pi$
$810$	−3.76640e9	−0.249017
$811$	3.44260e8	0.0226628	0.0113314	−	0.999936i	$-0.496393\pi$
$811$	3.44260e8	0.0226628	0.0113314	+	0.999936i	$0.496393\pi$
$812$	−1.65948e10	−1.08774
$813$	−3.75418e10	−2.45018
$814$	−3.27934e8	−0.0213108
$815$	−2.24601e10	−1.45332
$816$	−6.50600e9	−0.419178
$817$	−3.24126e10	−2.07940
$818$	1.40759e10	0.899166
$819$	−5.31885e10	−3.38318
$820$	−6.18255e9	−0.391579
$821$	7.16819e9	0.452073	0.226036	−	0.974119i	$-0.427423\pi$
$821$	7.16819e9	0.452073	0.226036	+	0.974119i	$0.427423\pi$
$822$	9.67527e9	0.607592
$823$	9.52943e9	0.595892	0.297946	−	0.954583i	$-0.403698\pi$
$823$	9.52943e9	0.595892	0.297946	+	0.954583i	$0.403698\pi$
$824$	−7.00834e8	−0.0436385
$825$	2.58838e9	0.160487
$826$	−6.00725e9	−0.370891
$827$	−7.58166e9	−0.466117	−0.233059	−	0.972463i	$-0.574873\pi$
$827$	−7.58166e9	−0.466117	−0.233059	+	0.972463i	$0.574873\pi$
$828$	1.74931e9	0.107093
$829$	−1.26823e10	−0.773139	−0.386569	−	0.922260i	$-0.626340\pi$
$829$	−1.26823e10	−0.773139	−0.386569	+	0.922260i	$0.626340\pi$
$830$	6.29269e9	0.382000
$831$	2.34811e9	0.141943
$832$	−2.59530e9	−0.156227
$833$	4.91269e10	2.94484
$834$	7.53462e9	0.449759
$835$	1.84341e10	1.09577
$836$	3.23521e9	0.191505
$837$	−4.43747e9	−0.261575
$838$	8.17712e9	0.480005
$839$	−1.50145e10	−0.877695	−0.438847	−	0.898562i	$-0.644613\pi$
$839$	−1.50145e10	−0.877695	−0.438847	+	0.898562i	$0.644613\pi$
$840$	−1.47195e10	−0.856870
$841$	4.68092e9	0.271360
$842$	6.46381e9	0.373161
$843$	−2.56753e10	−1.47611
$844$	−4.23141e9	−0.242263
$845$	7.98774e9	0.455434
$846$	1.41732e10	0.804769
$847$	3.10185e9	0.175400
$848$	−2.56759e8	−0.0144590
$849$	−1.32239e10	−0.741620
$850$	−4.70210e9	−0.262619
$851$	−2.74346e8	−0.0152597
$852$	8.50514e9	0.471132
$853$	−2.88665e10	−1.59247	−0.796236	−	0.604986i	$-0.793179\pi$
$853$	−2.88665e10	−1.59247	−0.796236	+	0.604986i	$0.793179\pi$
$854$	−1.45407e10	−0.798885
$855$	2.63941e10	1.44419
$856$	1.10252e10	0.600800
$857$	−2.27563e10	−1.23500	−0.617502	−	0.786569i	$-0.711855\pi$
$857$	−2.27563e10	−1.23500	−0.617502	+	0.786569i	$0.711855\pi$
$858$	7.64217e9	0.413058
$859$	7.60631e8	0.0409447	0.0204723	−	0.999790i	$-0.493483\pi$
$859$	7.60631e8	0.0409447	0.0204723	+	0.999790i	$0.493483\pi$
$860$	−1.23711e10	−0.663227
$861$	5.41374e10	2.89059
$862$	1.68879e10	0.898047
$863$	1.03239e10	0.546772	0.273386	−	0.961904i	$-0.411856\pi$
$863$	1.03239e10	0.546772	0.273386	+	0.961904i	$0.411856\pi$
$864$	−2.09365e9	−0.110435
$865$	−5.60981e9	−0.294708
$866$	−1.64300e10	−0.859654
$867$	−5.05525e9	−0.263436
$868$	7.78263e9	0.403931
$869$	−6.44679e9	−0.333253
$870$	1.94525e10	1.00151
$871$	6.91982e9	0.354839
$872$	−1.08359e10	−0.553424
$873$	−4.28321e10	−2.17881
$874$	2.70654e9	0.137128
$875$	−4.16204e10	−2.10028
$876$	2.32008e9	0.116611
$877$	−3.48516e9	−0.174471	−0.0872357	−	0.996188i	$-0.527803\pi$
$877$	−3.48516e9	−0.174471	−0.0872357	+	0.996188i	$0.527803\pi$
$878$	−2.17917e9	−0.108657
$879$	−3.16229e8	−0.0157051
$880$	1.23479e9	0.0610808
$881$	−3.74696e10	−1.84613	−0.923067	−	0.384638i	$-0.874326\pi$
$881$	−3.74696e10	−1.84613	−0.923067	+	0.384638i	$0.874326\pi$
$882$	5.50379e10	2.70098
$883$	−2.65271e10	−1.29667	−0.648333	−	0.761357i	$-0.724533\pi$
$883$	−2.65271e10	−1.29667	−0.648333	+	0.761357i	$0.724533\pi$
$884$	−1.38829e10	−0.675924
$885$	7.04172e9	0.341489
$886$	2.02936e9	0.0980258
$887$	−3.93196e10	−1.89181	−0.945903	−	0.324450i	$-0.894821\pi$
$887$	−3.93196e10	−1.89181	−0.945903	+	0.324450i	$0.894821\pi$
$888$	1.14311e9	0.0547828
$889$	3.12296e10	1.49077
$890$	1.73050e9	0.0822824
$891$	−2.76668e9	−0.131035
$892$	7.25870e9	0.342438
$893$	2.19288e10	1.03047
$894$	6.53809e9	0.306034
$895$	−3.03221e10	−1.41377
$896$	3.67193e9	0.170536
$897$	6.39336e9	0.295771
$898$	−9.44503e9	−0.435247
$899$	−1.02851e10	−0.472118
$900$	−5.26786e9	−0.240872
$901$	−1.37347e9	−0.0625578
$902$	−4.54150e9	−0.206052
$903$	1.08327e11	4.89586
$904$	1.05019e10	0.472801
$905$	6.24130e9	0.279901
$906$	2.41725e10	1.07988
$907$	2.63565e10	1.17290	0.586451	−	0.809984i	$-0.300524\pi$
$907$	2.63565e10	1.17290	0.586451	+	0.809984i	$0.300524\pi$
$908$	1.72431e10	0.764391
$909$	2.81329e10	1.24234
$910$	−3.14093e10	−1.38170
$911$	−2.82134e10	−1.23635	−0.618175	−	0.786041i	$-0.712128\pi$
$911$	−2.82134e10	−1.23635	−0.618175	+	0.786041i	$0.712128\pi$
$912$	−1.12773e10	−0.492292
$913$	4.62241e9	0.201011
$914$	1.15914e10	0.502140
$915$	1.70447e10	0.735556
$916$	−1.65180e10	−0.710105
$917$	−1.27992e10	−0.548138
$918$	−1.11995e10	−0.477802
$919$	3.73720e10	1.58834	0.794168	−	0.607698i	$-0.207907\pi$
$919$	3.73720e10	1.58834	0.794168	+	0.607698i	$0.207907\pi$
$920$	1.03302e9	0.0437371
$921$	2.96113e10	1.24896
$922$	−1.79103e10	−0.752567
$923$	1.81488e10	0.759699
$924$	−1.08124e10	−0.450892
$925$	8.26164e8	0.0343218
$926$	2.20324e10	0.911851
$927$	−4.20002e9	−0.173170
$928$	−4.85263e9	−0.199324
$929$	1.01264e10	0.414380	0.207190	−	0.978301i	$-0.433568\pi$
$929$	1.01264e10	0.414380	0.207190	+	0.978301i	$0.433568\pi$
$930$	−9.12283e9	−0.371911
$931$	8.51549e10	3.45848
$932$	−1.26268e10	−0.510903
$933$	−5.84650e10	−2.35673
$934$	−1.66534e10	−0.668789
$935$	6.60523e9	0.264270
$936$	−1.55533e10	−0.619952
$937$	−1.52255e10	−0.604622	−0.302311	−	0.953209i	$-0.597758\pi$
$937$	−1.52255e10	−0.604622	−0.302311	+	0.953209i	$0.597758\pi$
$938$	−9.79045e9	−0.387340
$939$	−1.70026e10	−0.670173
$940$	8.36966e9	0.328670
$941$	1.50765e10	0.589844	0.294922	−	0.955521i	$-0.404706\pi$
$941$	1.50765e10	0.589844	0.294922	+	0.955521i	$0.404706\pi$
$942$	−2.06425e10	−0.804608
$943$	−3.79937e9	−0.147544
$944$	−1.75663e9	−0.0679640
$945$	−2.53382e10	−0.976706
$946$	−9.08738e9	−0.348995
$947$	−2.57203e10	−0.984125	−0.492063	−	0.870560i	$-0.663757\pi$
$947$	−2.57203e10	−0.984125	−0.492063	+	0.870560i	$0.663757\pi$
$948$	2.24723e10	0.856678
$949$	4.95072e9	0.188034
$950$	−8.15046e9	−0.308425
$951$	−1.52562e10	−0.575193
$952$	1.96421e10	0.737834
$953$	−3.41315e10	−1.27741	−0.638704	−	0.769452i	$-0.720529\pi$
$953$	−3.41315e10	−1.27741	−0.638704	+	0.769452i	$0.720529\pi$
$954$	−1.53873e9	−0.0573775
$955$	2.50433e10	0.930422
$956$	−1.12688e10	−0.417133
$957$	1.42892e10	0.527005
$958$	3.60935e9	0.132632
$959$	−2.92104e10	−1.06948
$960$	−4.30425e9	−0.157018
$961$	−2.26891e10	−0.824680
$962$	2.43924e9	0.0883370
$963$	6.60730e10	2.38414
$964$	−2.70695e9	−0.0973218
$965$	1.54350e10	0.552917
$966$	−9.04559e9	−0.322862
$967$	−3.81102e10	−1.35534	−0.677670	−	0.735366i	$-0.737010\pi$
$967$	−3.81102e10	−1.35534	−0.677670	+	0.735366i	$0.737010\pi$
$968$	9.07039e8	0.0321412
$969$	−6.03251e10	−2.12993
$970$	−2.52935e10	−0.889833
$971$	4.36002e10	1.52835	0.764173	−	0.645011i	$-0.223147\pi$
$971$	4.36002e10	1.52835	0.764173	+	0.645011i	$0.223147\pi$
$972$	1.85871e10	0.649201
$973$	−2.27476e10	−0.791662
$974$	−1.18479e10	−0.410852
$975$	−1.92529e10	−0.665244
$976$	−4.25199e9	−0.146392
$977$	2.46833e10	0.846785	0.423392	−	0.905946i	$-0.360839\pi$
$977$	2.46833e10	0.846785	0.423392	+	0.905946i	$0.360839\pi$
$978$	5.75104e10	1.96590
$979$	1.27117e9	0.0432976
$980$	3.25014e10	1.10309
$981$	−6.49385e10	−2.19614
$982$	−4.86046e9	−0.163790
$983$	1.78371e10	0.598946	0.299473	−	0.954105i	$-0.403189\pi$
$983$	1.78371e10	0.598946	0.299473	+	0.954105i	$0.403189\pi$
$984$	1.58308e10	0.529687
$985$	3.59862e10	1.19980
$986$	−2.59580e10	−0.862385
$987$	−7.32887e10	−2.42620
$988$	−2.40642e10	−0.793819
$989$	−7.60241e9	−0.249899
$990$	7.39998e9	0.242386
$991$	3.07472e10	1.00357	0.501785	−	0.864993i	$-0.332677\pi$
$991$	3.07472e10	1.00357	0.501785	+	0.864993i	$0.332677\pi$
$992$	2.27579e9	0.0740186
$993$	6.55740e10	2.12525
$994$	−2.56776e10	−0.829283
$995$	−1.17252e10	−0.377345
$996$	−1.61128e10	−0.516730
$997$	−4.48450e9	−0.143312	−0.0716558	−	0.997429i	$-0.522828\pi$
$997$	−4.48450e9	−0.143312	−0.0716558	+	0.997429i	$0.522828\pi$
$998$	3.75413e10	1.19551
$999$	1.96776e9	0.0624443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.8.a.d.1.1	✓	2
3.2	odd	2		198.8.a.f.1.1		2
4.3	odd	2		176.8.a.e.1.2		2
5.4	even	2		550.8.a.d.1.2		2
11.10	odd	2		242.8.a.h.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.8.a.d.1.1	✓	2	1.1	even	1	trivial
176.8.a.e.1.2		2	4.3	odd	2
198.8.a.f.1.1		2	3.2	odd	2
242.8.a.h.1.1		2	11.10	odd	2
550.8.a.d.1.2		2	5.4	even	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -72.4939 q^{3} +64.0000 q^{4} +226.494 q^{5} -579.951 q^{6} +1750.91 q^{7} +512.000 q^{8} +3068.36 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -72.4939 q^{3} +64.0000 q^{4} +226.494 q^{5} -579.951 q^{6} +1750.91 q^{7} +512.000 q^{8} +3068.36 q^{9} +1811.95 q^{10} +1331.00 q^{11} -4639.61 q^{12} -9900.27 q^{13} +14007.3 q^{14} -16419.4 q^{15} +4096.00 q^{16} +21910.5 q^{17} +24546.9 q^{18} +37979.0 q^{19} +14495.6 q^{20} -126930. q^{21} +10648.0 q^{22} +8908.01 q^{23} -37116.9 q^{24} -26825.5 q^{25} -79202.2 q^{26} -63893.1 q^{27} +112058. q^{28} -148091. q^{29} -131355. q^{30} +69451.5 q^{31} +32768.0 q^{32} -96489.3 q^{33} +175284. q^{34} +396571. q^{35} +196375. q^{36} -30797.7 q^{37} +303832. q^{38} +717709. q^{39} +115965. q^{40} -426512. q^{41} -1.01544e6 q^{42} -853435. q^{43} +85184.0 q^{44} +694964. q^{45} +71264.1 q^{46} +577393. q^{47} -296935. q^{48} +2.24216e6 q^{49} -214604. q^{50} -1.58838e6 q^{51} -633618. q^{52} -62685.2 q^{53} -511145. q^{54} +301463. q^{55} +896468. q^{56} -2.75325e6 q^{57} -1.18472e6 q^{58} -428866. q^{59} -1.05084e6 q^{60} -1.03808e6 q^{61} +555612. q^{62} +5.37243e6 q^{63} +262144. q^{64} -2.24235e6 q^{65} -771915. q^{66} -698953. q^{67} +1.40228e6 q^{68} -645776. q^{69} +3.17257e6 q^{70} -1.83316e6 q^{71} +1.57100e6 q^{72} -500059. q^{73} -246382. q^{74} +1.94469e6 q^{75} +2.43066e6 q^{76} +2.33047e6 q^{77} +5.74167e6 q^{78} -4.84357e6 q^{79} +927719. q^{80} -2.07864e6 q^{81} -3.41209e6 q^{82} +3.47288e6 q^{83} -8.12355e6 q^{84} +4.96260e6 q^{85} -6.82748e6 q^{86} +1.07357e7 q^{87} +681472. q^{88} +955049. q^{89} +5.55971e6 q^{90} -1.73345e7 q^{91} +570113. q^{92} -5.03481e6 q^{93} +4.61914e6 q^{94} +8.60202e6 q^{95} -2.37548e6 q^{96} -1.39593e7 q^{97} +1.79373e7 q^{98} +4.08399e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{2} - 23 q^{3} + 128 q^{4} + 331 q^{5} - 184 q^{6} + 1794 q^{7} + 1024 q^{8} + 3331 q^{9}+O(q^{10}) \) 2 * q + 16 * q^2 - 23 * q^3 + 128 * q^4 + 331 * q^5 - 184 * q^6 + 1794 * q^7 + 1024 * q^8 + 3331 * q^9	\( 2 q + 16 q^{2} - 23 q^{3} + 128 q^{4} + 331 q^{5} - 184 q^{6} + 1794 q^{7} + 1024 q^{8} + 3331 q^{9} + 2648 q^{10} + 2662 q^{11} - 1472 q^{12} - 5406 q^{13} + 14352 q^{14} - 11247 q^{15} + 8192 q^{16} + 15032 q^{17} + 26648 q^{18} + 16916 q^{19} + 21184 q^{20} - 124798 q^{21} + 21296 q^{22} - 51351 q^{23} - 11776 q^{24} - 94029 q^{25} - 43248 q^{26} - 159137 q^{27} + 114816 q^{28} - 207130 q^{29} - 89976 q^{30} - 19071 q^{31} + 65536 q^{32} - 30613 q^{33} + 120256 q^{34} + 401074 q^{35} + 213184 q^{36} + 351333 q^{37} + 135328 q^{38} + 940148 q^{39} + 169472 q^{40} + 123610 q^{41} - 998384 q^{42} - 159822 q^{43} + 170368 q^{44} + 722412 q^{45} - 410808 q^{46} + 451160 q^{47} - 94208 q^{48} + 1420470 q^{49} - 752232 q^{50} - 1928826 q^{51} - 345984 q^{52} - 1260832 q^{53} - 1273096 q^{54} + 440561 q^{55} + 918528 q^{56} - 3795736 q^{57} - 1657040 q^{58} + 887547 q^{59} - 719808 q^{60} - 597918 q^{61} - 152568 q^{62} + 5383748 q^{63} + 524288 q^{64} - 1772672 q^{65} - 244904 q^{66} + 2864711 q^{67} + 962048 q^{68} - 3628227 q^{69} + 3208592 q^{70} + 1306267 q^{71} + 1705472 q^{72} - 4577530 q^{73} + 2810664 q^{74} - 1381472 q^{75} + 1082624 q^{76} + 2387814 q^{77} + 7521184 q^{78} - 2946342 q^{79} + 1355776 q^{80} - 7367030 q^{81} + 988880 q^{82} + 9965450 q^{83} - 7987072 q^{84} + 4243754 q^{85} - 1278576 q^{86} + 7813560 q^{87} + 1362944 q^{88} + 10185377 q^{89} + 5779296 q^{90} - 17140888 q^{91} - 3286464 q^{92} - 9416131 q^{93} + 3609280 q^{94} + 6400800 q^{95} - 753664 q^{96} - 27765477 q^{97} + 11363760 q^{98} + 4433561 q^{99}+O(q^{100}) \) 2 * q + 16 * q^2 - 23 * q^3 + 128 * q^4 + 331 * q^5 - 184 * q^6 + 1794 * q^7 + 1024 * q^8 + 3331 * q^9 + 2648 * q^10 + 2662 * q^11 - 1472 * q^12 - 5406 * q^13 + 14352 * q^14 - 11247 * q^15 + 8192 * q^16 + 15032 * q^17 + 26648 * q^18 + 16916 * q^19 + 21184 * q^20 - 124798 * q^21 + 21296 * q^22 - 51351 * q^23 - 11776 * q^24 - 94029 * q^25 - 43248 * q^26 - 159137 * q^27 + 114816 * q^28 - 207130 * q^29 - 89976 * q^30 - 19071 * q^31 + 65536 * q^32 - 30613 * q^33 + 120256 * q^34 + 401074 * q^35 + 213184 * q^36 + 351333 * q^37 + 135328 * q^38 + 940148 * q^39 + 169472 * q^40 + 123610 * q^41 - 998384 * q^42 - 159822 * q^43 + 170368 * q^44 + 722412 * q^45 - 410808 * q^46 + 451160 * q^47 - 94208 * q^48 + 1420470 * q^49 - 752232 * q^50 - 1928826 * q^51 - 345984 * q^52 - 1260832 * q^53 - 1273096 * q^54 + 440561 * q^55 + 918528 * q^56 - 3795736 * q^57 - 1657040 * q^58 + 887547 * q^59 - 719808 * q^60 - 597918 * q^61 - 152568 * q^62 + 5383748 * q^63 + 524288 * q^64 - 1772672 * q^65 - 244904 * q^66 + 2864711 * q^67 + 962048 * q^68 - 3628227 * q^69 + 3208592 * q^70 + 1306267 * q^71 + 1705472 * q^72 - 4577530 * q^73 + 2810664 * q^74 - 1381472 * q^75 + 1082624 * q^76 + 2387814 * q^77 + 7521184 * q^78 - 2946342 * q^79 + 1355776 * q^80 - 7367030 * q^81 + 988880 * q^82 + 9965450 * q^83 - 7987072 * q^84 + 4243754 * q^85 - 1278576 * q^86 + 7813560 * q^87 + 1362944 * q^88 + 10185377 * q^89 + 5779296 * q^90 - 17140888 * q^91 - 3286464 * q^92 - 9416131 * q^93 + 3609280 * q^94 + 6400800 * q^95 - 753664 * q^96 - 27765477 * q^97 + 11363760 * q^98 + 4433561 * q^99

Introduction

L-functions

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