LMFDB - Embedded newform 354.8.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 260588 x^{7} - 2627755 x^{6} + 16696953355 x^{5} + 808091684078 x^{4} + \cdots + 15\!\cdots\!00 $ x^9 - 4x^8 - 260588x^7 - 2627755x^6 + 16696953355x^5 + 808091684078x^4 - 191825159847522x^3 - 12153827093891319x^2 + 237398587398357570x + 15300107670464479800
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-93.7830$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -297.331 q^{5} +216.000 q^{6} +367.966 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -297.331 q^{5} +216.000 q^{6} +367.966 q^{7} -512.000 q^{8} +729.000 q^{9} +2378.65 q^{10} -4737.42 q^{11} -1728.00 q^{12} +450.103 q^{13} -2943.73 q^{14} +8027.93 q^{15} +4096.00 q^{16} -12022.4 q^{17} -5832.00 q^{18} +42015.4 q^{19} -19029.2 q^{20} -9935.09 q^{21} +37899.3 q^{22} -12104.2 q^{23} +13824.0 q^{24} +10280.6 q^{25} -3600.82 q^{26} -19683.0 q^{27} +23549.8 q^{28} -178458. q^{29} -64223.5 q^{30} +163004. q^{31} -32768.0 q^{32} +127910. q^{33} +96179.4 q^{34} -109408. q^{35} +46656.0 q^{36} -208059. q^{37} -336123. q^{38} -12152.8 q^{39} +152233. q^{40} +646363. q^{41} +79480.7 q^{42} +884500. q^{43} -303195. q^{44} -216754. q^{45} +96834.0 q^{46} +634804. q^{47} -110592. q^{48} -688144. q^{49} -82244.9 q^{50} +324606. q^{51} +28806.6 q^{52} -25617.8 q^{53} +157464. q^{54} +1.40858e6 q^{55} -188399. q^{56} -1.13442e6 q^{57} +1.42766e6 q^{58} +205379. q^{59} +513788. q^{60} +2.86552e6 q^{61} -1.30403e6 q^{62} +268247. q^{63} +262144. q^{64} -133829. q^{65} -1.02328e6 q^{66} -2.76077e6 q^{67} -769435. q^{68} +326815. q^{69} +875262. q^{70} -1.05383e6 q^{71} -373248. q^{72} +1.30917e6 q^{73} +1.66447e6 q^{74} -277576. q^{75} +2.68899e6 q^{76} -1.74321e6 q^{77} +97222.2 q^{78} -815613. q^{79} -1.21787e6 q^{80} +531441. q^{81} -5.17091e6 q^{82} +8.72597e6 q^{83} -635846. q^{84} +3.57464e6 q^{85} -7.07600e6 q^{86} +4.81836e6 q^{87} +2.42556e6 q^{88} -3.26054e6 q^{89} +1.73403e6 q^{90} +165623. q^{91} -774672. q^{92} -4.40110e6 q^{93} -5.07843e6 q^{94} -1.24925e7 q^{95} +884736. q^{96} +4.06095e6 q^{97} +5.50515e6 q^{98} -3.45358e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) $ 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * 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
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	−297.331	−1.06376	−0.531882	−	0.846819i	$-0.678515\pi$
$5$	−297.331	−1.06376	−0.531882	+	0.846819i	$0.678515\pi$
$6$	216.000	0.408248
$7$	367.966	0.405476	0.202738	−	0.979233i	$-0.435016\pi$
$7$	367.966	0.405476	0.202738	+	0.979233i	$0.435016\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	2378.65	0.752194
$11$	−4737.42	−1.07317	−0.536583	−	0.843847i	$-0.680285\pi$
$11$	−4737.42	−1.07317	−0.536583	+	0.843847i	$0.680285\pi$
$12$	−1728.00	−0.288675
$13$	450.103	0.0568211	0.0284106	−	0.999596i	$-0.490955\pi$
$13$	450.103	0.0568211	0.0284106	+	0.999596i	$0.490955\pi$
$14$	−2943.73	−0.286715
$15$	8027.93	0.614164
$16$	4096.00	0.250000
$17$	−12022.4	−0.593500	−0.296750	−	0.954955i	$-0.595903\pi$
$17$	−12022.4	−0.593500	−0.296750	+	0.954955i	$0.595903\pi$
$18$	−5832.00	−0.235702
$19$	42015.4	1.40531	0.702653	−	0.711532i	$-0.251999\pi$
$19$	42015.4	1.40531	0.702653	+	0.711532i	$0.251999\pi$
$20$	−19029.2	−0.531882
$21$	−9935.09	−0.234102
$22$	37899.3	0.758843
$23$	−12104.2	−0.207439	−0.103719	−	0.994607i	$-0.533074\pi$
$23$	−12104.2	−0.207439	−0.103719	+	0.994607i	$0.533074\pi$
$24$	13824.0	0.204124
$25$	10280.6	0.131592
$26$	−3600.82	−0.0401786
$27$	−19683.0	−0.192450
$28$	23549.8	0.202738
$29$	−178458.	−1.35876	−0.679380	−	0.733787i	$-0.737751\pi$
$29$	−178458.	−1.35876	−0.679380	+	0.733787i	$0.737751\pi$
$30$	−64223.5	−0.434279
$31$	163004.	0.982724	0.491362	−	0.870955i	$-0.336499\pi$
$31$	163004.	0.982724	0.491362	+	0.870955i	$0.336499\pi$
$32$	−32768.0	−0.176777
$33$	127910.	0.619593
$34$	96179.4	0.419668
$35$	−109408.	−0.431330
$36$	46656.0	0.166667
$37$	−208059.	−0.675275	−0.337637	−	0.941276i	$-0.609628\pi$
$37$	−208059.	−0.675275	−0.337637	+	0.941276i	$0.609628\pi$
$38$	−336123.	−0.993702
$39$	−12152.8	−0.0328057
$40$	152233.	0.376097
$41$	646363.	1.46465	0.732324	−	0.680957i	$-0.238436\pi$
$41$	646363.	1.46465	0.732324	+	0.680957i	$0.238436\pi$
$42$	79480.7	0.165535
$43$	884500.	1.69652	0.848259	−	0.529582i	$-0.177651\pi$
$43$	884500.	1.69652	0.848259	+	0.529582i	$0.177651\pi$
$44$	−303195.	−0.536583
$45$	−216754.	−0.354588
$46$	96834.0	0.146681
$47$	634804.	0.891861	0.445930	−	0.895068i	$-0.352873\pi$
$47$	634804.	0.891861	0.445930	+	0.895068i	$0.352873\pi$
$48$	−110592.	−0.144338
$49$	−688144.	−0.835589
$50$	−82244.9	−0.0930494
$51$	324606.	0.342658
$52$	28806.6	0.0284106
$53$	−25617.8	−0.0236361	−0.0118181	−	0.999930i	$-0.503762\pi$
$53$	−25617.8	−0.0236361	−0.0118181	+	0.999930i	$0.503762\pi$
$54$	157464.	0.136083
$55$	1.40858e6	1.14159
$56$	−188399.	−0.143357
$57$	−1.13442e6	−0.811354
$58$	1.42766e6	0.960788
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	513788.	0.307082
$61$	2.86552e6	1.61640	0.808201	−	0.588906i	$-0.200441\pi$
$61$	2.86552e6	1.61640	0.808201	+	0.588906i	$0.200441\pi$
$62$	−1.30403e6	−0.694891
$63$	268247.	0.135159
$64$	262144.	0.125000
$65$	−133829.	−0.0604442
$66$	−1.02328e6	−0.438118
$67$	−2.76077e6	−1.12142	−0.560709	−	0.828013i	$-0.689471\pi$
$67$	−2.76077e6	−1.12142	−0.560709	+	0.828013i	$0.689471\pi$
$68$	−769435.	−0.296750
$69$	326815.	0.119765
$70$	875262.	0.304996
$71$	−1.05383e6	−0.349434	−0.174717	−	0.984619i	$-0.555901\pi$
$71$	−1.05383e6	−0.349434	−0.174717	+	0.984619i	$0.555901\pi$
$72$	−373248.	−0.117851
$73$	1.30917e6	0.393882	0.196941	−	0.980415i	$-0.436899\pi$
$73$	1.30917e6	0.393882	0.196941	+	0.980415i	$0.436899\pi$
$74$	1.66447e6	0.477491
$75$	−277576.	−0.0759745
$76$	2.68899e6	0.702653
$77$	−1.74321e6	−0.435143
$78$	97222.2	0.0231971
$79$	−815613.	−0.186118	−0.0930592	−	0.995661i	$-0.529665\pi$
$79$	−815613.	−0.186118	−0.0930592	+	0.995661i	$0.529665\pi$
$80$	−1.21787e6	−0.265941
$81$	531441.	0.111111
$82$	−5.17091e6	−1.03566
$83$	8.72597e6	1.67510	0.837549	−	0.546362i	$-0.183988\pi$
$83$	8.72597e6	1.67510	0.837549	+	0.546362i	$0.183988\pi$
$84$	−635846.	−0.117051
$85$	3.57464e6	0.631344
$86$	−7.07600e6	−1.19962
$87$	4.81836e6	0.784480
$88$	2.42556e6	0.379422
$89$	−3.26054e6	−0.490257	−0.245129	−	0.969491i	$-0.578830\pi$
$89$	−3.26054e6	−0.490257	−0.245129	+	0.969491i	$0.578830\pi$
$90$	1.73403e6	0.250731
$91$	165623.	0.0230396
$92$	−774672.	−0.103719
$93$	−4.40110e6	−0.567376
$94$	−5.07843e6	−0.630641
$95$	−1.24925e7	−1.49491
$96$	884736.	0.102062
$97$	4.06095e6	0.451779	0.225890	−	0.974153i	$-0.427471\pi$
$97$	4.06095e6	0.451779	0.225890	+	0.974153i	$0.427471\pi$
$98$	5.50515e6	0.590851
$99$	−3.45358e6	−0.357722
$100$	657959.	0.0657959
$101$	−9.46521e6	−0.914124	−0.457062	−	0.889435i	$-0.651098\pi$
$101$	−9.46521e6	−0.914124	−0.457062	+	0.889435i	$0.651098\pi$
$102$	−2.59684e6	−0.242295
$103$	2.03266e7	1.83288	0.916442	−	0.400168i	$-0.131048\pi$
$103$	2.03266e7	1.83288	0.916442	+	0.400168i	$0.131048\pi$
$104$	−230453.	−0.0200893
$105$	2.95401e6	0.249029
$106$	204942.	0.0167133
$107$	2.46909e7	1.94847	0.974233	−	0.225543i	$-0.0724155\pi$
$107$	2.46909e7	1.94847	0.974233	+	0.225543i	$0.0724155\pi$
$108$	−1.25971e6	−0.0962250
$109$	4.34330e6	0.321238	0.160619	−	0.987016i	$-0.448651\pi$
$109$	4.34330e6	0.321238	0.160619	+	0.987016i	$0.448651\pi$
$110$	−1.12686e7	−0.807229
$111$	5.61760e6	0.389870
$112$	1.50719e6	0.101369
$113$	3.65153e6	0.238068	0.119034	−	0.992890i	$-0.462020\pi$
$113$	3.65153e6	0.238068	0.119034	+	0.992890i	$0.462020\pi$
$114$	9.07533e6	0.573714
$115$	3.59897e6	0.220666
$116$	−1.14213e7	−0.679380
$117$	328125.	0.0189404
$118$	−1.64303e6	−0.0920575
$119$	−4.42385e6	−0.240650
$120$	−4.11030e6	−0.217140
$121$	2.95594e6	0.151686
$122$	−2.29242e7	−1.14297
$123$	−1.74518e7	−0.845615
$124$	1.04322e7	0.491362
$125$	2.01722e7	0.923781
$126$	−2.14598e6	−0.0955716
$127$	−4.18753e7	−1.81403	−0.907016	−	0.421096i	$-0.861646\pi$
$127$	−4.18753e7	−1.81403	−0.907016	+	0.421096i	$0.861646\pi$
$128$	−2.09715e6	−0.0883883
$129$	−2.38815e7	−0.979485
$130$	1.07064e6	0.0427405
$131$	1.95833e6	0.0761092	0.0380546	−	0.999276i	$-0.487884\pi$
$131$	1.95833e6	0.0761092	0.0380546	+	0.999276i	$0.487884\pi$
$132$	8.18625e6	0.309796
$133$	1.54603e7	0.569818
$134$	2.20861e7	0.792962
$135$	5.85236e6	0.204721
$136$	6.15548e6	0.209834
$137$	−5.55931e7	−1.84714	−0.923568	−	0.383434i	$-0.874741\pi$
$137$	−5.55931e7	−1.84714	−0.923568	+	0.383434i	$0.874741\pi$
$138$	−2.61452e6	−0.0846866
$139$	−4.78552e7	−1.51139	−0.755696	−	0.654922i	$-0.772701\pi$
$139$	−4.78552e7	−1.51139	−0.755696	+	0.654922i	$0.772701\pi$
$140$	−7.00209e6	−0.215665
$141$	−1.71397e7	−0.514916
$142$	8.43062e6	0.247087
$143$	−2.13232e6	−0.0609785
$144$	2.98598e6	0.0833333
$145$	5.30610e7	1.44540
$146$	−1.04733e7	−0.278516
$147$	1.85799e7	0.482428
$148$	−1.33158e7	−0.337637
$149$	2.51433e7	0.622687	0.311344	−	0.950297i	$-0.399221\pi$
$149$	2.51433e7	0.622687	0.311344	+	0.950297i	$0.399221\pi$
$150$	2.22061e6	0.0537221
$151$	−4.60759e7	−1.08907	−0.544533	−	0.838739i	$-0.683293\pi$
$151$	−4.60759e7	−1.08907	−0.544533	+	0.838739i	$0.683293\pi$
$152$	−2.15119e7	−0.496851
$153$	−8.76435e6	−0.197833
$154$	1.39457e7	0.307693
$155$	−4.84660e7	−1.04539
$156$	−777777.	−0.0164028
$157$	1.87924e7	0.387555	0.193778	−	0.981045i	$-0.437926\pi$
$157$	1.87924e7	0.387555	0.193778	+	0.981045i	$0.437926\pi$
$158$	6.52491e6	0.131606
$159$	691680.	0.0136463
$160$	9.74294e6	0.188049
$161$	−4.45396e6	−0.0841115
$162$	−4.25153e6	−0.0785674
$163$	−5.83869e7	−1.05599	−0.527993	−	0.849248i	$-0.677055\pi$
$163$	−5.83869e7	−1.05599	−0.527993	+	0.849248i	$0.677055\pi$
$164$	4.13672e7	0.732324
$165$	−3.80317e7	−0.659100
$166$	−6.98077e7	−1.18447
$167$	−1.06998e8	−1.77773	−0.888865	−	0.458168i	$-0.848506\pi$
$167$	−1.06998e8	−1.77773	−0.888865	+	0.458168i	$0.848506\pi$
$168$	5.08677e6	0.0827674
$169$	−6.25459e7	−0.996771
$170$	−2.85971e7	−0.446427
$171$	3.06292e7	0.468436
$172$	5.66080e7	0.848259
$173$	−1.09421e8	−1.60671	−0.803357	−	0.595498i	$-0.796955\pi$
$173$	−1.09421e8	−1.60671	−0.803357	+	0.595498i	$0.796955\pi$
$174$	−3.85469e7	−0.554711
$175$	3.78292e6	0.0533573
$176$	−1.94045e7	−0.268292
$177$	−5.54523e6	−0.0751646
$178$	2.60843e7	0.346664
$179$	5.63339e7	0.734150	0.367075	−	0.930191i	$-0.380359\pi$
$179$	5.63339e7	0.734150	0.367075	+	0.930191i	$0.380359\pi$
$180$	−1.38723e7	−0.177294
$181$	3.87188e7	0.485341	0.242670	−	0.970109i	$-0.421977\pi$
$181$	3.87188e7	0.485341	0.242670	+	0.970109i	$0.421977\pi$
$182$	−1.32498e6	−0.0162915
$183$	−7.73691e7	−0.933230
$184$	6.19737e6	0.0733407
$185$	6.18624e7	0.718333
$186$	3.52088e7	0.401195
$187$	5.69552e7	0.636925
$188$	4.06275e7	0.445930
$189$	−7.24268e6	−0.0780339
$190$	9.99398e7	1.05706
$191$	−1.33241e8	−1.38363	−0.691816	−	0.722074i	$-0.743189\pi$
$191$	−1.33241e8	−1.38363	−0.691816	+	0.722074i	$0.743189\pi$
$192$	−7.07789e6	−0.0721688
$193$	−1.93073e8	−1.93317	−0.966585	−	0.256345i	$-0.917482\pi$
$193$	−1.93073e8	−1.93317	−0.966585	+	0.256345i	$0.917482\pi$
$194$	−3.24876e7	−0.319456
$195$	3.61339e6	0.0348975
$196$	−4.40412e7	−0.417795
$197$	−1.34782e8	−1.25603	−0.628014	−	0.778202i	$-0.716132\pi$
$197$	−1.34782e8	−1.25603	−0.628014	+	0.778202i	$0.716132\pi$
$198$	2.76286e7	0.252948
$199$	−1.02545e8	−0.922419	−0.461210	−	0.887291i	$-0.652584\pi$
$199$	−1.02545e8	−0.922419	−0.461210	+	0.887291i	$0.652584\pi$
$200$	−5.26367e6	−0.0465247
$201$	7.45407e7	0.647451
$202$	7.57217e7	0.646384
$203$	−6.56665e7	−0.550944
$204$	2.07748e7	0.171329
$205$	−1.92184e8	−1.55804
$206$	−1.62613e8	−1.29604
$207$	−8.82400e6	−0.0691463
$208$	1.84362e6	0.0142053
$209$	−1.99044e8	−1.50813
$210$	−2.36321e7	−0.176090
$211$	1.75890e8	1.28900	0.644501	−	0.764603i	$-0.277065\pi$
$211$	1.75890e8	1.28900	0.644501	+	0.764603i	$0.277065\pi$
$212$	−1.63954e6	−0.0118181
$213$	2.84533e7	0.201746
$214$	−1.97527e8	−1.37777
$215$	−2.62989e8	−1.80469
$216$	1.00777e7	0.0680414
$217$	5.99799e7	0.398471
$218$	−3.47464e7	−0.227150
$219$	−3.53476e7	−0.227408
$220$	9.01491e7	0.570797
$221$	−5.41133e6	−0.0337234
$222$	−4.49408e7	−0.275680
$223$	1.46527e8	0.884811	0.442406	−	0.896815i	$-0.354125\pi$
$223$	1.46527e8	0.884811	0.442406	+	0.896815i	$0.354125\pi$
$224$	−1.20575e7	−0.0716787
$225$	7.49456e6	0.0438639
$226$	−2.92123e7	−0.168339
$227$	2.72799e8	1.54794	0.773968	−	0.633225i	$-0.218269\pi$
$227$	2.72799e8	1.54794	0.773968	+	0.633225i	$0.218269\pi$
$228$	−7.26026e7	−0.405677
$229$	−1.24276e8	−0.683853	−0.341926	−	0.939727i	$-0.611079\pi$
$229$	−1.24276e8	−0.683853	−0.341926	+	0.939727i	$0.611079\pi$
$230$	−2.87917e7	−0.156034
$231$	4.70667e7	0.251230
$232$	9.13704e7	0.480394
$233$	2.72200e8	1.40975	0.704874	−	0.709332i	$-0.251003\pi$
$233$	2.72200e8	1.40975	0.704874	+	0.709332i	$0.251003\pi$
$234$	−2.62500e6	−0.0133929
$235$	−1.88747e8	−0.948729
$236$	1.31443e7	0.0650945
$237$	2.20216e7	0.107456
$238$	3.53908e7	0.170165
$239$	3.36795e7	0.159578	0.0797891	−	0.996812i	$-0.474575\pi$
$239$	3.36795e7	0.159578	0.0797891	+	0.996812i	$0.474575\pi$
$240$	3.28824e7	0.153541
$241$	−9.89808e7	−0.455503	−0.227752	−	0.973719i	$-0.573137\pi$
$241$	−9.89808e7	−0.455503	−0.227752	+	0.973719i	$0.573137\pi$
$242$	−2.36475e7	−0.107258
$243$	−1.43489e7	−0.0641500
$244$	1.83393e8	0.808201
$245$	2.04606e8	0.888869
$246$	1.39614e8	0.597940
$247$	1.89112e7	0.0798511
$248$	−8.34579e7	−0.347445
$249$	−2.35601e8	−0.967118
$250$	−1.61378e8	−0.653211
$251$	3.11803e8	1.24458	0.622289	−	0.782788i	$-0.286203\pi$
$251$	3.11803e8	1.24458	0.622289	+	0.782788i	$0.286203\pi$
$252$	1.71678e7	0.0675793
$253$	5.73428e7	0.222617
$254$	3.35003e8	1.28271
$255$	−9.65152e7	−0.364506
$256$	1.67772e7	0.0625000
$257$	3.56481e8	1.31000	0.654999	−	0.755630i	$-0.272669\pi$
$257$	3.56481e8	1.31000	0.654999	+	0.755630i	$0.272669\pi$
$258$	1.91052e8	0.692600
$259$	−7.65587e7	−0.273808
$260$	−8.56508e6	−0.0302221
$261$	−1.30096e8	−0.452920
$262$	−1.56667e7	−0.0538173
$263$	−1.60828e8	−0.545151	−0.272576	−	0.962134i	$-0.587875\pi$
$263$	−1.60828e8	−0.545151	−0.272576	+	0.962134i	$0.587875\pi$
$264$	−6.54900e7	−0.219059
$265$	7.61696e6	0.0251432
$266$	−1.23682e8	−0.402922
$267$	8.80344e7	0.283050
$268$	−1.76689e8	−0.560709
$269$	−3.01427e8	−0.944167	−0.472084	−	0.881554i	$-0.656498\pi$
$269$	−3.01427e8	−0.944167	−0.472084	+	0.881554i	$0.656498\pi$
$270$	−4.68189e7	−0.144760
$271$	1.04570e8	0.319164	0.159582	−	0.987185i	$-0.448985\pi$
$271$	1.04570e8	0.319164	0.159582	+	0.987185i	$0.448985\pi$
$272$	−4.92439e7	−0.148375
$273$	−4.47181e6	−0.0133019
$274$	4.44745e8	1.30612
$275$	−4.87035e7	−0.141220
$276$	2.09161e7	0.0598825
$277$	2.70986e8	0.766069	0.383034	−	0.923734i	$-0.374879\pi$
$277$	2.70986e8	0.766069	0.383034	+	0.923734i	$0.374879\pi$
$278$	3.82841e8	1.06872
$279$	1.18830e8	0.327575
$280$	5.60168e7	0.152498
$281$	−5.68170e8	−1.52759	−0.763794	−	0.645460i	$-0.776666\pi$
$281$	−5.68170e8	−1.52759	−0.763794	+	0.645460i	$0.776666\pi$
$282$	1.37118e8	0.364101
$283$	−9.62209e7	−0.252358	−0.126179	−	0.992007i	$-0.540271\pi$
$283$	−9.62209e7	−0.252358	−0.126179	+	0.992007i	$0.540271\pi$
$284$	−6.74450e7	−0.174717
$285$	3.37297e8	0.863088
$286$	1.70586e7	0.0431183
$287$	2.37840e8	0.593879
$288$	−2.38879e7	−0.0589256
$289$	−2.65800e8	−0.647757
$290$	−4.24488e8	−1.02205
$291$	−1.09646e8	−0.260835
$292$	8.37868e7	0.196941
$293$	−6.10721e8	−1.41843	−0.709213	−	0.704995i	$-0.750949\pi$
$293$	−6.10721e8	−1.41843	−0.709213	+	0.704995i	$0.750949\pi$
$294$	−1.48639e8	−0.341128
$295$	−6.10655e7	−0.138490
$296$	1.06526e8	0.238746
$297$	9.32466e7	0.206531
$298$	−2.01146e8	−0.440306
$299$	−5.44815e6	−0.0117869
$300$	−1.77649e7	−0.0379873
$301$	3.25466e8	0.687897
$302$	3.68607e8	0.770086
$303$	2.55561e8	0.527770
$304$	1.72095e8	0.351327
$305$	−8.52008e8	−1.71947
$306$	7.01148e7	0.139889
$307$	−8.06367e7	−0.159055	−0.0795277	−	0.996833i	$-0.525341\pi$
$307$	−8.06367e7	−0.159055	−0.0795277	+	0.996833i	$0.525341\pi$
$308$	−1.11565e8	−0.217572
$309$	−5.48819e8	−1.05822
$310$	3.87728e8	0.739199
$311$	5.46690e8	1.03058	0.515288	−	0.857017i	$-0.327685\pi$
$311$	5.46690e8	1.03058	0.515288	+	0.857017i	$0.327685\pi$
$312$	6.22222e6	0.0115986
$313$	−8.43342e8	−1.55453	−0.777264	−	0.629175i	$-0.783393\pi$
$313$	−8.43342e8	−1.55453	−0.777264	+	0.629175i	$0.783393\pi$
$314$	−1.50339e8	−0.274043
$315$	−7.97582e7	−0.143777
$316$	−5.21993e7	−0.0930592
$317$	−8.26207e8	−1.45674	−0.728369	−	0.685185i	$-0.759721\pi$
$317$	−8.26207e8	−1.45674	−0.728369	+	0.685185i	$0.759721\pi$
$318$	−5.53344e6	−0.00964940
$319$	8.45429e8	1.45818
$320$	−7.79435e7	−0.132970
$321$	−6.66653e8	−1.12495
$322$	3.56316e7	0.0594758
$323$	−5.05127e8	−0.834050
$324$	3.40122e7	0.0555556
$325$	4.62733e6	0.00747719
$326$	4.67095e8	0.746696
$327$	−1.17269e8	−0.185467
$328$	−3.30938e8	−0.517831
$329$	2.33586e8	0.361628
$330$	3.04253e8	0.466054
$331$	4.23842e7	0.0642400	0.0321200	−	0.999484i	$-0.489774\pi$
$331$	4.23842e7	0.0642400	0.0321200	+	0.999484i	$0.489774\pi$
$332$	5.58462e8	0.837549
$333$	−1.51675e8	−0.225092
$334$	8.55980e8	1.25705
$335$	8.20860e8	1.19292
$336$	−4.06941e7	−0.0585254
$337$	2.19071e8	0.311803	0.155901	−	0.987773i	$-0.450172\pi$
$337$	2.19071e8	0.311803	0.155901	+	0.987773i	$0.450172\pi$
$338$	5.00367e8	0.704824
$339$	−9.85914e7	−0.137449
$340$	2.28777e8	0.315672
$341$	−7.72217e8	−1.05463
$342$	−2.45034e8	−0.331234
$343$	−5.56250e8	−0.744287
$344$	−4.52864e8	−0.599810
$345$	−9.71721e7	−0.127402
$346$	8.75366e8	1.13612
$347$	−1.38509e9	−1.77961	−0.889803	−	0.456344i	$-0.849159\pi$
$347$	−1.38509e9	−1.77961	−0.889803	+	0.456344i	$0.849159\pi$
$348$	3.08375e8	0.392240
$349$	7.23913e8	0.911585	0.455793	−	0.890086i	$-0.349356\pi$
$349$	7.23913e8	0.911585	0.455793	+	0.890086i	$0.349356\pi$
$350$	−3.02633e7	−0.0377293
$351$	−8.85937e6	−0.0109352
$352$	1.55236e8	0.189711
$353$	1.02557e9	1.24095	0.620475	−	0.784226i	$-0.286940\pi$
$353$	1.02557e9	1.24095	0.620475	+	0.784226i	$0.286940\pi$
$354$	4.43619e7	0.0531494
$355$	3.13335e8	0.371715
$356$	−2.08674e8	−0.245129
$357$	1.19444e8	0.138939
$358$	−4.50672e8	−0.519122
$359$	3.71954e8	0.424286	0.212143	−	0.977239i	$-0.431956\pi$
$359$	3.71954e8	0.424286	0.212143	+	0.977239i	$0.431956\pi$
$360$	1.10978e8	0.125366
$361$	8.71423e8	0.974886
$362$	−3.09750e8	−0.343188
$363$	−7.98104e7	−0.0875762
$364$	1.05998e7	0.0115198
$365$	−3.89256e8	−0.418997
$366$	6.18953e8	0.659894
$367$	9.64872e8	1.01892	0.509458	−	0.860495i	$-0.329846\pi$
$367$	9.64872e8	1.01892	0.509458	+	0.860495i	$0.329846\pi$
$368$	−4.95790e7	−0.0518597
$369$	4.71199e8	0.488216
$370$	−4.94899e8	−0.507938
$371$	−9.42648e6	−0.00958387
$372$	−2.81670e8	−0.283688
$373$	1.05908e9	1.05669	0.528344	−	0.849030i	$-0.322813\pi$
$373$	1.05908e9	1.05669	0.528344	+	0.849030i	$0.322813\pi$
$374$	−4.55642e8	−0.450374
$375$	−5.44650e8	−0.533345
$376$	−3.25020e8	−0.315320
$377$	−8.03243e7	−0.0772063
$378$	5.79415e7	0.0551783
$379$	6.05960e8	0.571750	0.285875	−	0.958267i	$-0.407716\pi$
$379$	6.05960e8	0.571750	0.285875	+	0.958267i	$0.407716\pi$
$380$	−7.99519e8	−0.747457
$381$	1.13063e9	1.04733
$382$	1.06593e9	0.978375
$383$	7.73770e8	0.703746	0.351873	−	0.936048i	$-0.385545\pi$
$383$	7.73770e8	0.703746	0.351873	+	0.936048i	$0.385545\pi$
$384$	5.66231e7	0.0510310
$385$	5.18310e8	0.462889
$386$	1.54458e9	1.36696
$387$	6.44801e8	0.565506
$388$	2.59901e8	0.225890
$389$	6.39625e8	0.550937	0.275468	−	0.961310i	$-0.411167\pi$
$389$	6.39625e8	0.550937	0.275468	+	0.961310i	$0.411167\pi$
$390$	−2.89071e7	−0.0246762
$391$	1.45522e8	0.123115
$392$	3.52330e8	0.295425
$393$	−5.28750e7	−0.0439416
$394$	1.07825e9	0.888146
$395$	2.42507e8	0.197986
$396$	−2.21029e8	−0.178861
$397$	1.62460e9	1.30310	0.651551	−	0.758605i	$-0.274119\pi$
$397$	1.62460e9	1.30310	0.651551	+	0.758605i	$0.274119\pi$
$398$	8.20359e8	0.652249
$399$	−4.17427e8	−0.328984
$400$	4.21094e7	0.0328979
$401$	−1.05502e9	−0.817061	−0.408531	−	0.912745i	$-0.633959\pi$
$401$	−1.05502e9	−0.817061	−0.408531	+	0.912745i	$0.633959\pi$
$402$	−5.96325e8	−0.457817
$403$	7.33684e7	0.0558395
$404$	−6.05773e8	−0.457062
$405$	−1.58014e8	−0.118196
$406$	5.25332e8	0.389576
$407$	9.85662e8	0.724682
$408$	−1.66198e8	−0.121148
$409$	−1.22547e9	−0.885670	−0.442835	−	0.896603i	$-0.646027\pi$
$409$	−1.22547e9	−0.885670	−0.442835	+	0.896603i	$0.646027\pi$
$410$	1.53747e9	1.10170
$411$	1.50101e9	1.06644
$412$	1.30090e9	0.916442
$413$	7.55726e7	0.0527885
$414$	7.05920e7	0.0488938
$415$	−2.59450e9	−1.78191
$416$	−1.47490e7	−0.0100447
$417$	1.29209e9	0.872603
$418$	1.59236e9	1.06641
$419$	−2.03994e9	−1.35478	−0.677389	−	0.735625i	$-0.736888\pi$
$419$	−2.03994e9	−1.35478	−0.677389	+	0.735625i	$0.736888\pi$
$420$	1.89057e8	0.124514
$421$	−2.96830e8	−0.193875	−0.0969373	−	0.995290i	$-0.530905\pi$
$421$	−2.96830e8	−0.193875	−0.0969373	+	0.995290i	$0.530905\pi$
$422$	−1.40712e9	−0.911462
$423$	4.62772e8	0.297287
$424$	1.31163e7	0.00835663
$425$	−1.23598e8	−0.0780998
$426$	−2.27627e8	−0.142656
$427$	1.05442e9	0.655412
$428$	1.58021e9	0.974233
$429$	5.75727e7	0.0352060
$430$	2.10391e9	1.27611
$431$	−4.60641e8	−0.277135	−0.138568	−	0.990353i	$-0.544250\pi$
$431$	−4.60641e8	−0.277135	−0.138568	+	0.990353i	$0.544250\pi$
$432$	−8.06216e7	−0.0481125
$433$	1.70306e9	1.00814	0.504071	−	0.863662i	$-0.331835\pi$
$433$	1.70306e9	1.00814	0.504071	+	0.863662i	$0.331835\pi$
$434$	−4.79839e8	−0.281761
$435$	−1.43265e9	−0.834501
$436$	2.77971e8	0.160619
$437$	−5.08565e8	−0.291515
$438$	2.82780e8	0.160801
$439$	7.53078e8	0.424829	0.212415	−	0.977180i	$-0.431867\pi$
$439$	7.53078e8	0.424829	0.212415	+	0.977180i	$0.431867\pi$
$440$	−7.21193e8	−0.403615
$441$	−5.01657e8	−0.278530
$442$	4.32906e7	0.0238460
$443$	−2.50954e9	−1.37145	−0.685727	−	0.727859i	$-0.740516\pi$
$443$	−2.50954e9	−1.37145	−0.685727	+	0.727859i	$0.740516\pi$
$444$	3.59526e8	0.194935
$445$	9.69457e8	0.521517
$446$	−1.17222e9	−0.625656
$447$	−6.78869e8	−0.359509
$448$	9.64602e7	0.0506845
$449$	2.74644e9	1.43189	0.715943	−	0.698159i	$-0.245997\pi$
$449$	2.74644e9	1.43189	0.715943	+	0.698159i	$0.245997\pi$
$450$	−5.99565e7	−0.0310165
$451$	−3.06209e9	−1.57181
$452$	2.33698e8	0.119034
$453$	1.24405e9	0.628773
$454$	−2.18240e9	−1.09456
$455$	−4.92447e7	−0.0245087
$456$	5.80821e8	0.286857
$457$	1.24252e9	0.608971	0.304485	−	0.952517i	$-0.401515\pi$
$457$	1.24252e9	0.608971	0.304485	+	0.952517i	$0.401515\pi$
$458$	9.94207e8	0.483557
$459$	2.36637e8	0.114219
$460$	2.30334e8	0.110333
$461$	1.55364e9	0.738579	0.369290	−	0.929314i	$-0.379601\pi$
$461$	1.55364e9	0.738579	0.369290	+	0.929314i	$0.379601\pi$
$462$	−3.76533e8	−0.177646
$463$	−3.18248e9	−1.49016	−0.745078	−	0.666977i	$-0.767588\pi$
$463$	−3.18248e9	−1.49016	−0.745078	+	0.666977i	$0.767588\pi$
$464$	−7.30963e8	−0.339690
$465$	1.30858e9	0.603554
$466$	−2.17760e9	−0.996843
$467$	−2.74505e9	−1.24721	−0.623607	−	0.781738i	$-0.714333\pi$
$467$	−2.74505e9	−1.24721	−0.623607	+	0.781738i	$0.714333\pi$
$468$	2.10000e7	0.00947019
$469$	−1.01587e9	−0.454708
$470$	1.50997e9	0.670852
$471$	−5.07395e8	−0.223755
$472$	−1.05154e8	−0.0460287
$473$	−4.19025e9	−1.82065
$474$	−1.76172e8	−0.0759825
$475$	4.31944e8	0.184927
$476$	−2.83126e8	−0.120325
$477$	−1.86754e7	−0.00787870
$478$	−2.69436e8	−0.112839
$479$	−3.84777e9	−1.59969	−0.799843	−	0.600209i	$-0.795084\pi$
$479$	−3.84777e9	−1.59969	−0.799843	+	0.600209i	$0.795084\pi$
$480$	−2.63059e8	−0.108570
$481$	−9.36479e7	−0.0383699
$482$	7.91846e8	0.322089
$483$	1.20257e8	0.0485618
$484$	1.89180e8	0.0758432
$485$	−1.20745e9	−0.480586
$486$	1.14791e8	0.0453609
$487$	2.34198e9	0.918821	0.459411	−	0.888224i	$-0.348061\pi$
$487$	2.34198e9	0.918821	0.459411	+	0.888224i	$0.348061\pi$
$488$	−1.46715e9	−0.571485
$489$	1.57645e9	0.609674
$490$	−1.63685e9	−0.628525
$491$	2.58508e9	0.985574	0.492787	−	0.870150i	$-0.335978\pi$
$491$	2.58508e9	0.985574	0.492787	+	0.870150i	$0.335978\pi$
$492$	−1.11692e9	−0.422807
$493$	2.14550e9	0.806424
$494$	−1.51290e8	−0.0564633
$495$	1.02685e9	0.380532
$496$	6.67663e8	0.245681
$497$	−3.87773e8	−0.141687
$498$	1.88481e9	0.683856
$499$	5.24306e9	1.88900	0.944501	−	0.328508i	$-0.106546\pi$
$499$	5.24306e9	1.88900	0.944501	+	0.328508i	$0.106546\pi$
$500$	1.29102e9	0.461890
$501$	2.88893e9	1.02637
$502$	−2.49442e9	−0.880049
$503$	4.85158e8	0.169979	0.0849895	−	0.996382i	$-0.472914\pi$
$503$	4.85158e8	0.169979	0.0849895	+	0.996382i	$0.472914\pi$
$504$	−1.37343e8	−0.0477858
$505$	2.81430e9	0.972412
$506$	−4.58743e8	−0.157414
$507$	1.68874e9	0.575486
$508$	−2.68002e9	−0.907016
$509$	−1.70048e9	−0.571555	−0.285778	−	0.958296i	$-0.592252\pi$
$509$	−1.70048e9	−0.571555	−0.285778	+	0.958296i	$0.592252\pi$
$510$	7.72122e8	0.257745
$511$	4.81730e8	0.159709
$512$	−1.34218e8	−0.0441942
$513$	−8.26989e8	−0.270451
$514$	−2.85185e9	−0.926308
$515$	−6.04373e9	−1.94975
$516$	−1.52842e9	−0.489742
$517$	−3.00733e9	−0.957115
$518$	6.12470e8	0.193611
$519$	2.95436e9	0.927636
$520$	6.85206e7	0.0213703
$521$	1.43661e9	0.445048	0.222524	−	0.974927i	$-0.428570\pi$
$521$	1.43661e9	0.445048	0.222524	+	0.974927i	$0.428570\pi$
$522$	1.04077e9	0.320263
$523$	1.08465e9	0.331537	0.165769	−	0.986165i	$-0.446990\pi$
$523$	1.08465e9	0.331537	0.165769	+	0.986165i	$0.446990\pi$
$524$	1.25333e8	0.0380546
$525$	−1.02139e8	−0.0308058
$526$	1.28663e9	0.385480
$527$	−1.95970e9	−0.583247
$528$	5.23920e8	0.154898
$529$	−3.25831e9	−0.956969
$530$	−6.09356e7	−0.0177789
$531$	1.49721e8	0.0433963
$532$	9.89457e8	0.284909
$533$	2.90930e8	0.0832229
$534$	−7.04276e8	−0.200147
$535$	−7.34135e9	−2.07271
$536$	1.41351e9	0.396481
$537$	−1.52102e9	−0.423861
$538$	2.41141e9	0.667627
$539$	3.26002e9	0.896727
$540$	3.74551e8	0.102361
$541$	−5.03843e9	−1.36806	−0.684029	−	0.729455i	$-0.739774\pi$
$541$	−5.03843e9	−1.36806	−0.684029	+	0.729455i	$0.739774\pi$
$542$	−8.36558e8	−0.225683
$543$	−1.04541e9	−0.280212
$544$	3.93951e8	0.104917
$545$	−1.29140e9	−0.341721
$546$	3.57745e7	0.00940587
$547$	−2.57479e9	−0.672646	−0.336323	−	0.941747i	$-0.609183\pi$
$547$	−2.57479e9	−0.672646	−0.336323	+	0.941747i	$0.609183\pi$
$548$	−3.55796e9	−0.923568
$549$	2.08897e9	0.538801
$550$	3.89628e8	0.0998575
$551$	−7.49798e9	−1.90947
$552$	−1.67329e8	−0.0423433
$553$	−3.00118e8	−0.0754665
$554$	−2.16789e9	−0.541693
$555$	−1.67028e9	−0.414729
$556$	−3.06273e9	−0.755696
$557$	7.82140e8	0.191775	0.0958874	−	0.995392i	$-0.469431\pi$
$557$	7.82140e8	0.191775	0.0958874	+	0.995392i	$0.469431\pi$
$558$	−9.50638e8	−0.231630
$559$	3.98116e8	0.0963980
$560$	−4.48134e8	−0.107833
$561$	−1.53779e9	−0.367729
$562$	4.54536e9	1.08017
$563$	−3.55198e9	−0.838864	−0.419432	−	0.907787i	$-0.637771\pi$
$563$	−3.55198e9	−0.838864	−0.419432	+	0.907787i	$0.637771\pi$
$564$	−1.09694e9	−0.257458
$565$	−1.08571e9	−0.253248
$566$	7.69767e8	0.178444
$567$	1.95552e8	0.0450529
$568$	5.39560e8	0.123544
$569$	−2.81782e9	−0.641239	−0.320620	−	0.947208i	$-0.603891\pi$
$569$	−2.81782e9	−0.641239	−0.320620	+	0.947208i	$0.603891\pi$
$570$	−2.69838e9	−0.610296
$571$	6.79119e8	0.152658	0.0763290	−	0.997083i	$-0.475680\pi$
$571$	6.79119e8	0.152658	0.0763290	+	0.997083i	$0.475680\pi$
$572$	−1.36469e8	−0.0304893
$573$	3.59750e9	0.798840
$574$	−1.90272e9	−0.419936
$575$	−1.24439e8	−0.0272973
$576$	1.91103e8	0.0416667
$577$	−4.37359e9	−0.947813	−0.473906	−	0.880575i	$-0.657156\pi$
$577$	−4.37359e9	−0.947813	−0.473906	+	0.880575i	$0.657156\pi$
$578$	2.12640e9	0.458034
$579$	5.21296e9	1.11612
$580$	3.39591e9	0.722699
$581$	3.21086e9	0.679212
$582$	8.77165e8	0.184438
$583$	1.21362e8	0.0253655
$584$	−6.70294e8	−0.139258
$585$	−9.75616e7	−0.0201481
$586$	4.88577e9	1.00298
$587$	−3.35251e9	−0.684127	−0.342064	−	0.939677i	$-0.611126\pi$
$587$	−3.35251e9	−0.684127	−0.342064	+	0.939677i	$0.611126\pi$
$588$	1.18911e9	0.241214
$589$	6.84867e9	1.38103
$590$	4.88524e8	0.0979273
$591$	3.63911e9	0.725169
$592$	−8.52210e8	−0.168819
$593$	−2.39856e9	−0.472344	−0.236172	−	0.971711i	$-0.575893\pi$
$593$	−2.39856e9	−0.472344	−0.236172	+	0.971711i	$0.575893\pi$
$594$	−7.45972e8	−0.146039
$595$	1.31535e9	0.255995
$596$	1.60917e9	0.311344
$597$	2.76871e9	0.532559
$598$	4.35852e7	0.00833461
$599$	−2.01158e9	−0.382422	−0.191211	−	0.981549i	$-0.561241\pi$
$599$	−2.01158e9	−0.382422	−0.191211	+	0.981549i	$0.561241\pi$
$600$	1.42119e8	0.0268611
$601$	−2.43097e9	−0.456793	−0.228396	−	0.973568i	$-0.573348\pi$
$601$	−2.43097e9	−0.456793	−0.228396	+	0.973568i	$0.573348\pi$
$602$	−2.60373e9	−0.486417
$603$	−2.01260e9	−0.373806
$604$	−2.94886e9	−0.544533
$605$	−8.78892e8	−0.161358
$606$	−2.04448e9	−0.373190
$607$	−5.83996e9	−1.05986	−0.529931	−	0.848041i	$-0.677782\pi$
$607$	−5.83996e9	−1.05986	−0.529931	+	0.848041i	$0.677782\pi$
$608$	−1.37676e9	−0.248425
$609$	1.77300e9	0.318088
$610$	6.81607e9	1.21585
$611$	2.85727e8	0.0506765
$612$	−5.60918e8	−0.0989167
$613$	8.03549e9	1.40897	0.704483	−	0.709721i	$-0.251179\pi$
$613$	8.03549e9	1.40897	0.704483	+	0.709721i	$0.251179\pi$
$614$	6.45094e8	0.112469
$615$	5.18896e9	0.899534
$616$	8.92523e8	0.153846
$617$	8.34577e9	1.43044	0.715218	−	0.698901i	$-0.246327\pi$
$617$	8.34577e9	1.43044	0.715218	+	0.698901i	$0.246327\pi$
$618$	4.39055e9	0.748271
$619$	4.50686e9	0.763759	0.381880	−	0.924212i	$-0.375277\pi$
$619$	4.50686e9	0.763759	0.381880	+	0.924212i	$0.375277\pi$
$620$	−3.10183e9	−0.522693
$621$	2.38248e8	0.0399216
$622$	−4.37352e9	−0.728727
$623$	−1.19977e9	−0.198787
$624$	−4.97777e7	−0.00820142
$625$	−6.80100e9	−1.11428
$626$	6.74673e9	1.09922
$627$	5.37420e9	0.870718
$628$	1.20271e9	0.193778
$629$	2.50138e9	0.400776
$630$	6.38066e8	0.101665
$631$	−1.05858e10	−1.67734	−0.838669	−	0.544641i	$-0.816666\pi$
$631$	−1.05858e10	−1.67734	−0.838669	+	0.544641i	$0.816666\pi$
$632$	4.17594e8	0.0658028
$633$	−4.74904e9	−0.744206
$634$	6.60966e9	1.03007
$635$	1.24508e10	1.92970
$636$	4.42675e7	0.00682316
$637$	−3.09735e8	−0.0474791
$638$	−6.76343e9	−1.03109
$639$	−7.68240e8	−0.116478
$640$	6.23548e8	0.0940243
$641$	−1.67709e9	−0.251509	−0.125755	−	0.992061i	$-0.540135\pi$
$641$	−1.67709e9	−0.251509	−0.125755	+	0.992061i	$0.540135\pi$
$642$	5.33323e9	0.795458
$643$	−8.26645e9	−1.22625	−0.613127	−	0.789984i	$-0.710089\pi$
$643$	−8.26645e9	−1.22625	−0.613127	+	0.789984i	$0.710089\pi$
$644$	−2.85053e8	−0.0420557
$645$	7.10071e9	1.04194
$646$	4.04102e9	0.589762
$647$	−6.57456e9	−0.954337	−0.477169	−	0.878812i	$-0.658337\pi$
$647$	−6.57456e9	−0.954337	−0.477169	+	0.878812i	$0.658337\pi$
$648$	−2.72098e8	−0.0392837
$649$	−9.72966e8	−0.139714
$650$	−3.70186e7	−0.00528717
$651$	−1.61946e9	−0.230057
$652$	−3.73676e9	−0.527993
$653$	3.42554e9	0.481430	0.240715	−	0.970596i	$-0.422618\pi$
$653$	3.42554e9	0.481430	0.240715	+	0.970596i	$0.422618\pi$
$654$	9.38153e8	0.131145
$655$	−5.82273e8	−0.0809621
$656$	2.64750e9	0.366162
$657$	9.54384e8	0.131294
$658$	−1.86869e9	−0.255710
$659$	6.85763e9	0.933416	0.466708	−	0.884411i	$-0.345440\pi$
$659$	6.85763e9	0.933416	0.466708	+	0.884411i	$0.345440\pi$
$660$	−2.43403e9	−0.329550
$661$	1.72747e9	0.232652	0.116326	−	0.993211i	$-0.462888\pi$
$661$	1.72747e9	0.232652	0.116326	+	0.993211i	$0.462888\pi$
$662$	−3.39073e8	−0.0454246
$663$	1.46106e8	0.0194702
$664$	−4.46770e9	−0.592237
$665$	−4.59681e9	−0.606151
$666$	1.21340e9	0.159164
$667$	2.16010e9	0.281860
$668$	−6.84784e9	−0.888865
$669$	−3.95623e9	−0.510846
$670$	−6.56688e9	−0.843524
$671$	−1.35752e10	−1.73467
$672$	3.25553e8	0.0413837
$673$	−3.93926e9	−0.498152	−0.249076	−	0.968484i	$-0.580127\pi$
$673$	−3.93926e9	−0.498152	−0.249076	+	0.968484i	$0.580127\pi$
$674$	−1.75257e9	−0.220478
$675$	−2.02353e8	−0.0253248
$676$	−4.00294e9	−0.498386
$677$	8.81086e9	1.09134	0.545668	−	0.838002i	$-0.316276\pi$
$677$	8.81086e9	1.09134	0.545668	+	0.838002i	$0.316276\pi$
$678$	7.88731e8	0.0971908
$679$	1.49429e9	0.183186
$680$	−1.83021e9	−0.223214
$681$	−7.36558e9	−0.893701
$682$	6.17773e9	0.745734
$683$	−1.43580e10	−1.72433	−0.862165	−	0.506627i	$-0.830892\pi$
$683$	−1.43580e10	−1.72433	−0.862165	+	0.506627i	$0.830892\pi$
$684$	1.96027e9	0.234218
$685$	1.65295e10	1.96492
$686$	4.45000e9	0.526290
$687$	3.35545e9	0.394822
$688$	3.62291e9	0.424129
$689$	−1.15306e7	−0.00134303
$690$	7.77376e8	0.0900865
$691$	−1.10795e10	−1.27746	−0.638732	−	0.769429i	$-0.720541\pi$
$691$	−1.10795e10	−1.27746	−0.638732	+	0.769429i	$0.720541\pi$
$692$	−7.00293e9	−0.803357
$693$	−1.27080e9	−0.145048
$694$	1.10807e10	1.25837
$695$	1.42288e10	1.60776
$696$	−2.46700e9	−0.277356
$697$	−7.77086e9	−0.869269
$698$	−5.79130e9	−0.644588
$699$	−7.34939e9	−0.813919
$700$	2.42107e8	0.0266786
$701$	−1.10468e9	−0.121122	−0.0605610	−	0.998164i	$-0.519289\pi$
$701$	−1.10468e9	−0.121122	−0.0605610	+	0.998164i	$0.519289\pi$
$702$	7.08750e7	0.00773238
$703$	−8.74169e9	−0.948968
$704$	−1.24189e9	−0.134146
$705$	5.09616e9	0.547749
$706$	−8.20456e9	−0.877484
$707$	−3.48288e9	−0.370655
$708$	−3.54895e8	−0.0375823
$709$	−1.28857e10	−1.35783	−0.678917	−	0.734215i	$-0.737550\pi$
$709$	−1.28857e10	−1.35783	−0.678917	+	0.734215i	$0.737550\pi$
$710$	−2.50668e9	−0.262842
$711$	−5.94582e8	−0.0620395
$712$	1.66939e9	0.173332
$713$	−1.97304e9	−0.203855
$714$	−9.55551e8	−0.0982450
$715$	6.34005e8	0.0648667
$716$	3.60537e9	0.367075
$717$	−9.09347e8	−0.0921325
$718$	−2.97563e9	−0.300016
$719$	3.12237e9	0.313280	0.156640	−	0.987656i	$-0.449934\pi$
$719$	3.12237e9	0.313280	0.156640	+	0.987656i	$0.449934\pi$
$720$	−8.87825e8	−0.0886469
$721$	7.47951e9	0.743190
$722$	−6.97139e9	−0.689349
$723$	2.67248e9	0.262985
$724$	2.47800e9	0.242670
$725$	−1.83466e9	−0.178802
$726$	6.38483e8	0.0619257
$727$	9.24829e9	0.892670	0.446335	−	0.894866i	$-0.352729\pi$
$727$	9.24829e9	0.892670	0.446335	+	0.894866i	$0.352729\pi$
$728$	−8.47988e7	−0.00814573
$729$	3.87420e8	0.0370370
$730$	3.11405e9	0.296275
$731$	−1.06338e10	−1.00688
$732$	−4.95162e9	−0.466615
$733$	1.74943e10	1.64071	0.820356	−	0.571853i	$-0.193775\pi$
$733$	1.74943e10	1.64071	0.820356	+	0.571853i	$0.193775\pi$
$734$	−7.71898e9	−0.720483
$735$	−5.52437e9	−0.513189
$736$	3.96632e8	0.0366704
$737$	1.30789e10	1.20347
$738$	−3.76959e9	−0.345221
$739$	−5.05636e9	−0.460875	−0.230437	−	0.973087i	$-0.574016\pi$
$739$	−5.05636e9	−0.460875	−0.230437	+	0.973087i	$0.574016\pi$
$740$	3.95919e9	0.359166
$741$	−5.10604e8	−0.0461021
$742$	7.54118e7	0.00677682
$743$	−1.16349e10	−1.04064	−0.520319	−	0.853972i	$-0.674187\pi$
$743$	−1.16349e10	−1.04064	−0.520319	+	0.853972i	$0.674187\pi$
$744$	2.25336e9	0.200598
$745$	−7.47587e9	−0.662392
$746$	−8.47263e9	−0.747192
$747$	6.36123e9	0.558366
$748$	3.64514e9	0.318462
$749$	9.08540e9	0.790056
$750$	4.35720e9	0.377132
$751$	3.08288e9	0.265593	0.132797	−	0.991143i	$-0.457604\pi$
$751$	3.08288e9	0.265593	0.132797	+	0.991143i	$0.457604\pi$
$752$	2.60016e9	0.222965
$753$	−8.41867e9	−0.718557
$754$	6.42595e8	0.0545931
$755$	1.36998e10	1.15851
$756$	−4.63532e8	−0.0390169
$757$	−1.17409e10	−0.983711	−0.491856	−	0.870677i	$-0.663681\pi$
$757$	−1.17409e10	−0.983711	−0.491856	+	0.870677i	$0.663681\pi$
$758$	−4.84768e9	−0.404289
$759$	−1.54826e9	−0.128528
$760$	6.39615e9	0.528532
$761$	−3.64874e9	−0.300121	−0.150061	−	0.988677i	$-0.547947\pi$
$761$	−3.64874e9	−0.300121	−0.150061	+	0.988677i	$0.547947\pi$
$762$	−9.04507e9	−0.740576
$763$	1.59819e9	0.130254
$764$	−8.52741e9	−0.691816
$765$	2.60591e9	0.210448
$766$	−6.19016e9	−0.497624
$767$	9.24416e7	0.00739748
$768$	−4.52985e8	−0.0360844
$769$	−2.42558e9	−0.192342	−0.0961709	−	0.995365i	$-0.530660\pi$
$769$	−2.42558e9	−0.192342	−0.0961709	+	0.995365i	$0.530660\pi$
$770$	−4.14648e9	−0.327312
$771$	−9.62499e9	−0.756328
$772$	−1.23566e10	−0.966585
$773$	4.79943e9	0.373733	0.186867	−	0.982385i	$-0.440167\pi$
$773$	4.79943e9	0.373733	0.186867	+	0.982385i	$0.440167\pi$
$774$	−5.15841e9	−0.399873
$775$	1.67578e9	0.129318
$776$	−2.07921e9	−0.159728
$777$	2.06709e9	0.158083
$778$	−5.11700e9	−0.389571
$779$	2.71572e10	2.05828
$780$	2.31257e8	0.0174487
$781$	4.99242e9	0.375001
$782$	−1.16418e9	−0.0870555
$783$	3.51259e9	0.261493
$784$	−2.81864e9	−0.208897
$785$	−5.58756e9	−0.412267
$786$	4.23000e8	0.0310714
$787$	1.33767e10	0.978219	0.489110	−	0.872222i	$-0.337322\pi$
$787$	1.33767e10	0.978219	0.489110	+	0.872222i	$0.337322\pi$
$788$	−8.62604e9	−0.628014
$789$	4.34236e9	0.314743
$790$	−1.94006e9	−0.139997
$791$	1.34364e9	0.0965308
$792$	1.76823e9	0.126474
$793$	1.28978e9	0.0918458
$794$	−1.29968e10	−0.921432
$795$	−2.05658e8	−0.0145164
$796$	−6.56288e9	−0.461210
$797$	−1.64702e8	−0.0115238	−0.00576189	−	0.999983i	$-0.501834\pi$
$797$	−1.64702e8	−0.0115238	−0.00576189	+	0.999983i	$0.501834\pi$
$798$	3.33942e9	0.232627
$799$	−7.63188e9	−0.529320
$800$	−3.36875e8	−0.0232624
$801$	−2.37693e9	−0.163419
$802$	8.44015e9	0.577750
$803$	−6.20208e9	−0.422700
$804$	4.77060e9	0.323726
$805$	1.32430e9	0.0894747
$806$	−5.86947e8	−0.0394845
$807$	8.13852e9	0.545115
$808$	4.84619e9	0.323192
$809$	−1.95301e10	−1.29683	−0.648417	−	0.761286i	$-0.724568\pi$
$809$	−1.95301e10	−1.29683	−0.648417	+	0.761286i	$0.724568\pi$
$810$	1.26411e9	0.0835771
$811$	−1.44675e10	−0.952405	−0.476202	−	0.879336i	$-0.657987\pi$
$811$	−1.44675e10	−0.952405	−0.476202	+	0.879336i	$0.657987\pi$
$812$	−4.20265e9	−0.275472
$813$	−2.82338e9	−0.184269
$814$	−7.88530e9	−0.512428
$815$	1.73602e10	1.12332
$816$	1.32958e9	0.0856644
$817$	3.71626e10	2.38413
$818$	9.80377e9	0.626263
$819$	1.20739e8	0.00767986
$820$	−1.22998e10	−0.779019
$821$	−7.69143e9	−0.485072	−0.242536	−	0.970142i	$-0.577979\pi$
$821$	−7.69143e9	−0.485072	−0.242536	+	0.970142i	$0.577979\pi$
$822$	−1.20081e10	−0.754090
$823$	1.65905e10	1.03743	0.518717	−	0.854946i	$-0.326410\pi$
$823$	1.65905e10	1.03743	0.518717	+	0.854946i	$0.326410\pi$
$824$	−1.04072e10	−0.648022
$825$	1.31499e9	0.0815333
$826$	−6.04580e8	−0.0373271
$827$	−3.41587e9	−0.210006	−0.105003	−	0.994472i	$-0.533485\pi$
$827$	−3.41587e9	−0.210006	−0.105003	+	0.994472i	$0.533485\pi$
$828$	−5.64736e8	−0.0345732
$829$	−2.50228e10	−1.52544	−0.762720	−	0.646729i	$-0.776137\pi$
$829$	−2.50228e10	−1.52544	−0.762720	+	0.646729i	$0.776137\pi$
$830$	2.07560e10	1.26000
$831$	−7.31662e9	−0.442290
$832$	1.17992e8	0.00710264
$833$	8.27316e9	0.495923
$834$	−1.03367e10	−0.617023
$835$	3.18137e10	1.89108
$836$	−1.27388e10	−0.754064
$837$	−3.20840e9	−0.189125
$838$	1.63195e10	0.957972
$839$	−1.86198e10	−1.08845	−0.544224	−	0.838940i	$-0.683176\pi$
$839$	−1.86198e10	−1.08845	−0.544224	+	0.838940i	$0.683176\pi$
$840$	−1.51245e9	−0.0880449
$841$	1.45973e10	0.846228
$842$	2.37464e9	0.137090
$843$	1.53406e10	0.881954
$844$	1.12570e10	0.644501
$845$	1.85968e10	1.06033
$846$	−3.70218e9	−0.210214
$847$	1.08769e9	0.0615052
$848$	−1.04930e8	−0.00590903
$849$	2.59796e9	0.145699
$850$	9.88783e8	0.0552249
$851$	2.51840e9	0.140078
$852$	1.82101e9	0.100873
$853$	1.54208e10	0.850717	0.425359	−	0.905025i	$-0.360148\pi$
$853$	1.54208e10	0.850717	0.425359	+	0.905025i	$0.360148\pi$
$854$	−8.43533e9	−0.463446
$855$	−9.10702e9	−0.498304
$856$	−1.26417e10	−0.688887
$857$	1.35231e10	0.733910	0.366955	−	0.930239i	$-0.380400\pi$
$857$	1.35231e10	0.733910	0.366955	+	0.930239i	$0.380400\pi$
$858$	−4.60582e8	−0.0248944
$859$	7.10787e9	0.382616	0.191308	−	0.981530i	$-0.438727\pi$
$859$	7.10787e9	0.382616	0.191308	+	0.981530i	$0.438727\pi$
$860$	−1.68313e10	−0.902346
$861$	−6.42168e9	−0.342876
$862$	3.68513e9	0.195964
$863$	−1.67977e10	−0.889635	−0.444817	−	0.895621i	$-0.646731\pi$
$863$	−1.67977e10	−0.889635	−0.444817	+	0.895621i	$0.646731\pi$
$864$	6.44973e8	0.0340207
$865$	3.25342e10	1.70916
$866$	−1.36245e10	−0.712864
$867$	7.17660e9	0.373983
$868$	3.83871e9	0.199235
$869$	3.86390e9	0.199736
$870$	1.14612e10	0.590081
$871$	−1.24263e9	−0.0637202
$872$	−2.22377e9	−0.113575
$873$	2.96043e9	0.150593
$874$	4.06852e9	0.206132
$875$	7.42270e9	0.374571
$876$	−2.26224e9	−0.113704
$877$	−1.11655e10	−0.558958	−0.279479	−	0.960152i	$-0.590162\pi$
$877$	−1.11655e10	−0.558958	−0.279479	+	0.960152i	$0.590162\pi$
$878$	−6.02463e9	−0.300400
$879$	1.64895e10	0.818928
$880$	5.76954e9	0.285399
$881$	2.50816e9	0.123577	0.0617887	−	0.998089i	$-0.480320\pi$
$881$	2.50816e9	0.123577	0.0617887	+	0.998089i	$0.480320\pi$
$882$	4.01325e9	0.196950
$883$	2.13087e10	1.04158	0.520792	−	0.853684i	$-0.325637\pi$
$883$	2.13087e10	1.04158	0.520792	+	0.853684i	$0.325637\pi$
$884$	−3.46325e8	−0.0168617
$885$	1.64877e9	0.0799573
$886$	2.00763e10	0.969765
$887$	4.43629e9	0.213445	0.106723	−	0.994289i	$-0.465964\pi$
$887$	4.43629e9	0.213445	0.106723	+	0.994289i	$0.465964\pi$
$888$	−2.87621e9	−0.137840
$889$	−1.54087e10	−0.735546
$890$	−7.75566e9	−0.368768
$891$	−2.51766e9	−0.119241
$892$	9.37773e9	0.442406
$893$	2.66716e10	1.25334
$894$	5.43095e9	0.254211
$895$	−1.67498e10	−0.780961
$896$	−7.71681e8	−0.0358393
$897$	1.47100e8	0.00680518
$898$	−2.19716e10	−1.01250
$899$	−2.90893e10	−1.33529
$900$	4.79652e8	0.0219320
$901$	3.07988e8	0.0140280
$902$	2.44967e10	1.11144
$903$	−8.78759e9	−0.397157
$904$	−1.86959e9	−0.0841697
$905$	−1.15123e10	−0.516288
$906$	−9.95239e9	−0.444609
$907$	1.62450e10	0.722925	0.361462	−	0.932387i	$-0.382278\pi$
$907$	1.62450e10	0.722925	0.361462	+	0.932387i	$0.382278\pi$
$908$	1.74592e10	0.773968
$909$	−6.90014e9	−0.304708
$910$	3.93958e8	0.0173302
$911$	−6.24808e9	−0.273799	−0.136900	−	0.990585i	$-0.543714\pi$
$911$	−6.24808e9	−0.273799	−0.136900	+	0.990585i	$0.543714\pi$
$912$	−4.64657e9	−0.202839
$913$	−4.13385e10	−1.79766
$914$	−9.94016e9	−0.430607
$915$	2.30042e10	0.992736
$916$	−7.95365e9	−0.341926
$917$	7.20600e8	0.0308604
$918$	−1.89310e9	−0.0807652
$919$	−2.83652e10	−1.20554	−0.602771	−	0.797915i	$-0.705937\pi$
$919$	−2.83652e10	−1.20554	−0.602771	+	0.797915i	$0.705937\pi$
$920$	−1.84267e9	−0.0780172
$921$	2.17719e9	0.0918307
$922$	−1.24291e10	−0.522254
$923$	−4.74330e8	−0.0198552
$924$	3.01227e9	0.125615
$925$	−2.13897e9	−0.0888606
$926$	2.54598e10	1.05370
$927$	1.48181e10	0.610961
$928$	5.84771e9	0.240197
$929$	2.45322e10	1.00388	0.501939	−	0.864903i	$-0.332620\pi$
$929$	2.45322e10	1.00388	0.501939	+	0.864903i	$0.332620\pi$
$930$	−1.04687e10	−0.426777
$931$	−2.89126e10	−1.17426
$932$	1.74208e10	0.704874
$933$	−1.47606e10	−0.595003
$934$	2.19604e10	0.881913
$935$	−1.69345e10	−0.677537
$936$	−1.68000e8	−0.00669643
$937$	3.05782e10	1.21429	0.607147	−	0.794590i	$-0.292314\pi$
$937$	3.05782e10	1.21429	0.607147	+	0.794590i	$0.292314\pi$
$938$	8.12695e9	0.321527
$939$	2.27702e10	0.897507
$940$	−1.20798e10	−0.474364
$941$	7.60477e9	0.297524	0.148762	−	0.988873i	$-0.452471\pi$
$941$	7.60477e9	0.297524	0.148762	+	0.988873i	$0.452471\pi$
$942$	4.05916e9	0.158219
$943$	−7.82374e9	−0.303825
$944$	8.41232e8	0.0325472
$945$	2.15347e9	0.0830095
$946$	3.35220e10	1.28739
$947$	−3.34821e9	−0.128112	−0.0640558	−	0.997946i	$-0.520404\pi$
$947$	−3.34821e9	−0.128112	−0.0640558	+	0.997946i	$0.520404\pi$
$948$	1.40938e9	0.0537278
$949$	5.89260e8	0.0223808
$950$	−3.45555e9	−0.130763
$951$	2.23076e10	0.841048
$952$	2.26501e9	0.0850826
$953$	8.71140e9	0.326034	0.163017	−	0.986623i	$-0.447877\pi$
$953$	8.71140e9	0.326034	0.163017	+	0.986623i	$0.447877\pi$
$954$	1.49403e8	0.00557108
$955$	3.96166e10	1.47186
$956$	2.15549e9	0.0797891
$957$	−2.28266e10	−0.841878
$958$	3.07822e10	1.13115
$959$	−2.04564e10	−0.748969
$960$	2.10447e9	0.0767705
$961$	−9.42392e8	−0.0342531
$962$	7.49184e8	0.0271316
$963$	1.79996e10	0.649489
$964$	−6.33477e9	−0.227752
$965$	5.74064e10	2.05644
$966$	−9.62054e8	−0.0343384
$967$	−1.39733e10	−0.496942	−0.248471	−	0.968639i	$-0.579928\pi$
$967$	−1.39733e10	−0.496942	−0.248471	+	0.968639i	$0.579928\pi$
$968$	−1.51344e9	−0.0536292
$969$	1.36384e10	0.481539
$970$	9.65956e9	0.339826
$971$	−2.58630e10	−0.906590	−0.453295	−	0.891360i	$-0.649752\pi$
$971$	−2.58630e10	−0.906590	−0.453295	+	0.891360i	$0.649752\pi$
$972$	−9.18330e8	−0.0320750
$973$	−1.76091e10	−0.612833
$974$	−1.87358e10	−0.649705
$975$	−1.24938e8	−0.00431696
$976$	1.17372e10	0.404101
$977$	4.01435e10	1.37716	0.688579	−	0.725161i	$-0.258235\pi$
$977$	4.01435e10	1.37716	0.688579	+	0.725161i	$0.258235\pi$
$978$	−1.26116e10	−0.431105
$979$	1.54465e10	0.526127
$980$	1.30948e10	0.444435
$981$	3.16627e9	0.107079
$982$	−2.06807e10	−0.696906
$983$	5.71339e10	1.91848	0.959238	−	0.282601i	$-0.0911972\pi$
$983$	5.71339e10	1.91848	0.959238	+	0.282601i	$0.0911972\pi$
$984$	8.93533e9	0.298970
$985$	4.00748e10	1.33612
$986$	−1.71640e10	−0.570228
$987$	−6.30683e9	−0.208786
$988$	1.21032e9	0.0399255
$989$	−1.07062e10	−0.351924
$990$	−8.21484e9	−0.269076
$991$	−2.07385e10	−0.676891	−0.338445	−	0.940986i	$-0.609901\pi$
$991$	−2.07385e10	−0.676891	−0.338445	+	0.940986i	$0.609901\pi$
$992$	−5.34131e9	−0.173723
$993$	−1.14437e9	−0.0370890
$994$	3.10218e9	0.100188
$995$	3.04898e10	0.981236
$996$	−1.50785e10	−0.483559
$997$	−4.91940e10	−1.57210	−0.786049	−	0.618165i	$-0.787877\pi$
$997$	−4.91940e10	−1.57210	−0.786049	+	0.618165i	$0.787877\pi$
$998$	−4.19444e10	−1.33573
$999$	4.09523e9	0.129957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.e.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.e.1.2	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -297.331 q^{5} +216.000 q^{6} +367.966 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -297.331 q^{5} +216.000 q^{6} +367.966 q^{7} -512.000 q^{8} +729.000 q^{9} +2378.65 q^{10} -4737.42 q^{11} -1728.00 q^{12} +450.103 q^{13} -2943.73 q^{14} +8027.93 q^{15} +4096.00 q^{16} -12022.4 q^{17} -5832.00 q^{18} +42015.4 q^{19} -19029.2 q^{20} -9935.09 q^{21} +37899.3 q^{22} -12104.2 q^{23} +13824.0 q^{24} +10280.6 q^{25} -3600.82 q^{26} -19683.0 q^{27} +23549.8 q^{28} -178458. q^{29} -64223.5 q^{30} +163004. q^{31} -32768.0 q^{32} +127910. q^{33} +96179.4 q^{34} -109408. q^{35} +46656.0 q^{36} -208059. q^{37} -336123. q^{38} -12152.8 q^{39} +152233. q^{40} +646363. q^{41} +79480.7 q^{42} +884500. q^{43} -303195. q^{44} -216754. q^{45} +96834.0 q^{46} +634804. q^{47} -110592. q^{48} -688144. q^{49} -82244.9 q^{50} +324606. q^{51} +28806.6 q^{52} -25617.8 q^{53} +157464. q^{54} +1.40858e6 q^{55} -188399. q^{56} -1.13442e6 q^{57} +1.42766e6 q^{58} +205379. q^{59} +513788. q^{60} +2.86552e6 q^{61} -1.30403e6 q^{62} +268247. q^{63} +262144. q^{64} -133829. q^{65} -1.02328e6 q^{66} -2.76077e6 q^{67} -769435. q^{68} +326815. q^{69} +875262. q^{70} -1.05383e6 q^{71} -373248. q^{72} +1.30917e6 q^{73} +1.66447e6 q^{74} -277576. q^{75} +2.68899e6 q^{76} -1.74321e6 q^{77} +97222.2 q^{78} -815613. q^{79} -1.21787e6 q^{80} +531441. q^{81} -5.17091e6 q^{82} +8.72597e6 q^{83} -635846. q^{84} +3.57464e6 q^{85} -7.07600e6 q^{86} +4.81836e6 q^{87} +2.42556e6 q^{88} -3.26054e6 q^{89} +1.73403e6 q^{90} +165623. q^{91} -774672. q^{92} -4.40110e6 q^{93} -5.07843e6 q^{94} -1.24925e7 q^{95} +884736. q^{96} +4.06095e6 q^{97} +5.50515e6 q^{98} -3.45358e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Introduction

L-functions

Modular forms

Varieties

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