LMFDB - Embedded newform 390.10.a.e.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [390,10,Mod(1,390)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("390.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(390, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	390.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-64,324,1024,2500] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$200.863976104$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 103194x^{2} + 6753414x - 65794500 $ x^4 - x^3 - 103194x^2 + 6753414x - 65794500
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$283.710$ of defining polynomial
Character	$\chi$	$=$	390.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} +625.000 q^{5} -1296.00 q^{6} +8281.12 q^{7} -4096.00 q^{8} +6561.00 q^{9} -10000.0 q^{10} -49538.4 q^{11} +20736.0 q^{12} -28561.0 q^{13} -132498. q^{14} +50625.0 q^{15} +65536.0 q^{16} -329640. q^{17} -104976. q^{18} +36208.1 q^{19} +160000. q^{20} +670771. q^{21} +792615. q^{22} +2.51963e6 q^{23} -331776. q^{24} +390625. q^{25} +456976. q^{26} +531441. q^{27} +2.11997e6 q^{28} -3.51653e6 q^{29} -810000. q^{30} -888912. q^{31} -1.04858e6 q^{32} -4.01261e6 q^{33} +5.27425e6 q^{34} +5.17570e6 q^{35} +1.67962e6 q^{36} -1.44301e7 q^{37} -579329. q^{38} -2.31344e6 q^{39} -2.56000e6 q^{40} +1.01908e6 q^{41} -1.07323e7 q^{42} -4.20289e7 q^{43} -1.26818e7 q^{44} +4.10062e6 q^{45} -4.03140e7 q^{46} +1.60359e7 q^{47} +5.30842e6 q^{48} +2.82233e7 q^{49} -6.25000e6 q^{50} -2.67009e7 q^{51} -7.31162e6 q^{52} +1.40657e7 q^{53} -8.50306e6 q^{54} -3.09615e7 q^{55} -3.39195e7 q^{56} +2.93286e6 q^{57} +5.62645e7 q^{58} +2.63443e7 q^{59} +1.29600e7 q^{60} -4.43687e7 q^{61} +1.42226e7 q^{62} +5.43324e7 q^{63} +1.67772e7 q^{64} -1.78506e7 q^{65} +6.42018e7 q^{66} -1.54850e8 q^{67} -8.43880e7 q^{68} +2.04090e8 q^{69} -8.28112e7 q^{70} -1.78522e8 q^{71} -2.68739e7 q^{72} -3.02736e8 q^{73} +2.30882e8 q^{74} +3.16406e7 q^{75} +9.26927e6 q^{76} -4.10234e8 q^{77} +3.70151e7 q^{78} -4.12405e8 q^{79} +4.09600e7 q^{80} +4.30467e7 q^{81} -1.63052e7 q^{82} +9.57570e6 q^{83} +1.71717e8 q^{84} -2.06025e8 q^{85} +6.72462e8 q^{86} -2.84839e8 q^{87} +2.02909e8 q^{88} +7.95208e8 q^{89} -6.56100e7 q^{90} -2.36517e8 q^{91} +6.45024e8 q^{92} -7.20019e7 q^{93} -2.56574e8 q^{94} +2.26301e7 q^{95} -8.49347e7 q^{96} +1.08678e9 q^{97} -4.51573e8 q^{98} -3.25022e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 324 q^{3} + 1024 q^{4} + 2500 q^{5} - 5184 q^{6} - 2318 q^{7} - 16384 q^{8} + 26244 q^{9} - 40000 q^{10} - 10508 q^{11} + 82944 q^{12} - 114244 q^{13} + 37088 q^{14} + 202500 q^{15} + 262144 q^{16}+ \cdots - 68942988 q^{99}+O(q^{100}) $ 4 * q - 64 * q^2 + 324 * q^3 + 1024 * q^4 + 2500 * q^5 - 5184 * q^6 - 2318 * q^7 - 16384 * q^8 + 26244 * q^9 - 40000 * q^10 - 10508 * q^11 + 82944 * q^12 - 114244 * q^13 + 37088 * q^14 + 202500 * q^15 + 262144 * q^16 - 386792 * q^17 - 419904 * q^18 - 228476 * q^19 + 640000 * q^20 - 187758 * q^21 + 168128 * q^22 + 361088 * q^23 - 1327104 * q^24 + 1562500 * q^25 + 1827904 * q^26 + 2125764 * q^27 - 593408 * q^28 + 1053374 * q^29 - 3240000 * q^30 + 12118 * q^31 - 4194304 * q^32 - 851148 * q^33 + 6188672 * q^34 - 1448750 * q^35 + 6718464 * q^36 + 983622 * q^37 + 3655616 * q^38 - 9253764 * q^39 - 10240000 * q^40 - 5900234 * q^41 + 3004128 * q^42 - 7525148 * q^43 - 2690048 * q^44 + 16402500 * q^45 - 5777408 * q^46 + 52858086 * q^47 + 21233664 * q^48 + 54480414 * q^49 - 25000000 * q^50 - 31330152 * q^51 - 29246464 * q^52 - 39944454 * q^53 - 34012224 * q^54 - 6567500 * q^55 + 9494528 * q^56 - 18506556 * q^57 - 16853984 * q^58 - 221262654 * q^59 + 51840000 * q^60 - 301613618 * q^61 - 193888 * q^62 - 15208398 * q^63 + 67108864 * q^64 - 71402500 * q^65 + 13618368 * q^66 + 107925130 * q^67 - 99018752 * q^68 + 29248128 * q^69 + 23180000 * q^70 - 407933556 * q^71 - 107495424 * q^72 - 649353258 * q^73 - 15737952 * q^74 + 126562500 * q^75 - 58489856 * q^76 - 815342786 * q^77 + 148060224 * q^78 - 1126263686 * q^79 + 163840000 * q^80 + 172186884 * q^81 + 94403744 * q^82 - 334595286 * q^83 - 48066048 * q^84 - 241745000 * q^85 + 120402368 * q^86 + 85323294 * q^87 + 43040768 * q^88 + 110458574 * q^89 - 262440000 * q^90 + 66204398 * q^91 + 92438528 * q^92 + 981558 * q^93 - 845729376 * q^94 - 142797500 * q^95 - 339738624 * q^96 + 1740509692 * q^97 - 871686624 * q^98 - 68942988 * q^99

Coefficient data

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

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

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

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	256.000	0.500000
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−1296.00	−0.408248
$7$	8281.12	1.30361	0.651805	−	0.758386i	$-0.274012\pi$
$7$	8281.12	1.30361	0.651805	+	0.758386i	$0.274012\pi$
$8$	−4096.00	−0.353553
$9$	6561.00	0.333333
$10$	−10000.0	−0.316228
$11$	−49538.4	−1.02018	−0.510088	−	0.860122i	$-0.670387\pi$
$11$	−49538.4	−1.02018	−0.510088	+	0.860122i	$0.670387\pi$
$12$	20736.0	0.288675
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−132498.	−0.921792
$15$	50625.0	0.258199
$16$	65536.0	0.250000
$17$	−329640.	−0.957239	−0.478619	−	0.878022i	$-0.658863\pi$
$17$	−329640.	−0.957239	−0.478619	+	0.878022i	$0.658863\pi$
$18$	−104976.	−0.235702
$19$	36208.1	0.0637403	0.0318702	−	0.999492i	$-0.489854\pi$
$19$	36208.1	0.0637403	0.0318702	+	0.999492i	$0.489854\pi$
$20$	160000.	0.223607
$21$	670771.	0.752640
$22$	792615.	0.721374
$23$	2.51963e6	1.87742	0.938708	−	0.344712i	$-0.112024\pi$
$23$	2.51963e6	1.87742	0.938708	+	0.344712i	$0.112024\pi$
$24$	−331776.	−0.204124
$25$	390625.	0.200000
$26$	456976.	0.196116
$27$	531441.	0.192450
$28$	2.11997e6	0.651805
$29$	−3.51653e6	−0.923258	−0.461629	−	0.887073i	$-0.652735\pi$
$29$	−3.51653e6	−0.923258	−0.461629	+	0.887073i	$0.652735\pi$
$30$	−810000.	−0.182574
$31$	−888912.	−0.172875	−0.0864373	−	0.996257i	$-0.527548\pi$
$31$	−888912.	−0.172875	−0.0864373	+	0.996257i	$0.527548\pi$
$32$	−1.04858e6	−0.176777
$33$	−4.01261e6	−0.588999
$34$	5.27425e6	0.676870
$35$	5.17570e6	0.582992
$36$	1.67962e6	0.166667
$37$	−1.44301e7	−1.26579	−0.632897	−	0.774236i	$-0.718134\pi$
$37$	−1.44301e7	−1.26579	−0.632897	+	0.774236i	$0.718134\pi$
$38$	−579329.	−0.0450712
$39$	−2.31344e6	−0.160128
$40$	−2.56000e6	−0.158114
$41$	1.01908e6	0.0563222	0.0281611	−	0.999603i	$-0.491035\pi$
$41$	1.01908e6	0.0563222	0.0281611	+	0.999603i	$0.491035\pi$
$42$	−1.07323e7	−0.532197
$43$	−4.20289e7	−1.87473	−0.937367	−	0.348343i	$-0.886744\pi$
$43$	−4.20289e7	−1.87473	−0.937367	+	0.348343i	$0.886744\pi$
$44$	−1.26818e7	−0.510088
$45$	4.10062e6	0.149071
$46$	−4.03140e7	−1.32753
$47$	1.60359e7	0.479350	0.239675	−	0.970853i	$-0.422959\pi$
$47$	1.60359e7	0.479350	0.239675	+	0.970853i	$0.422959\pi$
$48$	5.30842e6	0.144338
$49$	2.82233e7	0.699400
$50$	−6.25000e6	−0.141421
$51$	−2.67009e7	−0.552662
$52$	−7.31162e6	−0.138675
$53$	1.40657e7	0.244860	0.122430	−	0.992477i	$-0.460931\pi$
$53$	1.40657e7	0.244860	0.122430	+	0.992477i	$0.460931\pi$
$54$	−8.50306e6	−0.136083
$55$	−3.09615e7	−0.456237
$56$	−3.39195e7	−0.460896
$57$	2.93286e6	0.0368005
$58$	5.62645e7	0.652842
$59$	2.63443e7	0.283043	0.141522	−	0.989935i	$-0.454800\pi$
$59$	2.63443e7	0.283043	0.141522	+	0.989935i	$0.454800\pi$
$60$	1.29600e7	0.129099
$61$	−4.43687e7	−0.410291	−0.205146	−	0.978731i	$-0.565767\pi$
$61$	−4.43687e7	−0.410291	−0.205146	+	0.978731i	$0.565767\pi$
$62$	1.42226e7	0.122241
$63$	5.43324e7	0.434537
$64$	1.67772e7	0.125000
$65$	−1.78506e7	−0.124035
$66$	6.42018e7	0.416485
$67$	−1.54850e8	−0.938802	−0.469401	−	0.882985i	$-0.655530\pi$
$67$	−1.54850e8	−0.938802	−0.469401	+	0.882985i	$0.655530\pi$
$68$	−8.43880e7	−0.478619
$69$	2.04090e8	1.08393
$70$	−8.28112e7	−0.412238
$71$	−1.78522e8	−0.833739	−0.416869	−	0.908966i	$-0.636873\pi$
$71$	−1.78522e8	−0.833739	−0.416869	+	0.908966i	$0.636873\pi$
$72$	−2.68739e7	−0.117851
$73$	−3.02736e8	−1.24770	−0.623851	−	0.781544i	$-0.714433\pi$
$73$	−3.02736e8	−1.24770	−0.623851	+	0.781544i	$0.714433\pi$
$74$	2.30882e8	0.895051
$75$	3.16406e7	0.115470
$76$	9.26927e6	0.0318702
$77$	−4.10234e8	−1.32991
$78$	3.70151e7	0.113228
$79$	−4.12405e8	−1.19125	−0.595624	−	0.803263i	$-0.703095\pi$
$79$	−4.12405e8	−1.19125	−0.595624	+	0.803263i	$0.703095\pi$
$80$	4.09600e7	0.111803
$81$	4.30467e7	0.111111
$82$	−1.63052e7	−0.0398258
$83$	9.57570e6	0.0221472	0.0110736	−	0.999939i	$-0.496475\pi$
$83$	9.57570e6	0.0221472	0.0110736	+	0.999939i	$0.496475\pi$
$84$	1.71717e8	0.376320
$85$	−2.06025e8	−0.428090
$86$	6.72462e8	1.32564
$87$	−2.84839e8	−0.533043
$88$	2.02909e8	0.360687
$89$	7.95208e8	1.34346	0.671732	−	0.740794i	$-0.265551\pi$
$89$	7.95208e8	1.34346	0.671732	+	0.740794i	$0.265551\pi$
$90$	−6.56100e7	−0.105409
$91$	−2.36517e8	−0.361556
$92$	6.45024e8	0.938708
$93$	−7.20019e7	−0.0998092
$94$	−2.56574e8	−0.338952
$95$	2.26301e7	0.0285055
$96$	−8.49347e7	−0.102062
$97$	1.08678e9	1.24643	0.623217	−	0.782049i	$-0.285825\pi$
$97$	1.08678e9	1.24643	0.623217	+	0.782049i	$0.285825\pi$
$98$	−4.51573e8	−0.494550
$99$	−3.25022e8	−0.340059
$100$	1.00000e8	0.100000
$101$	8.94198e8	0.855042	0.427521	−	0.904005i	$-0.359387\pi$
$101$	8.94198e8	0.855042	0.427521	+	0.904005i	$0.359387\pi$
$102$	4.27214e8	0.390791
$103$	−1.25207e9	−1.09612	−0.548062	−	0.836438i	$-0.684634\pi$
$103$	−1.25207e9	−1.09612	−0.548062	+	0.836438i	$0.684634\pi$
$104$	1.16986e8	0.0980581
$105$	4.19232e8	0.336591
$106$	−2.25051e8	−0.173143
$107$	−2.23799e9	−1.65056	−0.825281	−	0.564723i	$-0.808983\pi$
$107$	−2.23799e9	−1.65056	−0.825281	+	0.564723i	$0.808983\pi$
$108$	1.36049e8	0.0962250
$109$	−1.79015e9	−1.21471	−0.607353	−	0.794432i	$-0.707769\pi$
$109$	−1.79015e9	−1.21471	−0.607353	+	0.794432i	$0.707769\pi$
$110$	4.95384e8	0.322608
$111$	−1.16884e9	−0.730806
$112$	5.42711e8	0.325903
$113$	1.36821e9	0.789407	0.394703	−	0.918809i	$-0.370847\pi$
$113$	1.36821e9	0.789407	0.394703	+	0.918809i	$0.370847\pi$
$114$	−4.69257e7	−0.0260219
$115$	1.57477e9	0.839606
$116$	−9.00231e8	−0.461629
$117$	−1.87389e8	−0.0924500
$118$	−4.21509e8	−0.200142
$119$	−2.72979e9	−1.24787
$120$	−2.07360e8	−0.0912871
$121$	9.61093e7	0.0407597
$122$	7.09899e8	0.290120
$123$	8.25453e7	0.0325177
$124$	−2.27562e8	−0.0864373
$125$	2.44141e8	0.0894427
$126$	−8.69319e8	−0.307264
$127$	4.36568e9	1.48914	0.744569	−	0.667545i	$-0.232655\pi$
$127$	4.36568e9	1.48914	0.744569	+	0.667545i	$0.232655\pi$
$128$	−2.68435e8	−0.0883883
$129$	−3.40434e9	−1.08238
$130$	2.85610e8	0.0877058
$131$	1.81953e9	0.539808	0.269904	−	0.962887i	$-0.413008\pi$
$131$	1.81953e9	0.539808	0.269904	+	0.962887i	$0.413008\pi$
$132$	−1.02723e9	−0.294500
$133$	2.99843e8	0.0830926
$134$	2.47760e9	0.663833
$135$	3.32151e8	0.0860663
$136$	1.35021e9	0.338435
$137$	−2.78946e9	−0.676516	−0.338258	−	0.941053i	$-0.609838\pi$
$137$	−2.78946e9	−0.676516	−0.338258	+	0.941053i	$0.609838\pi$
$138$	−3.26543e9	−0.766452
$139$	−2.24854e9	−0.510897	−0.255449	−	0.966823i	$-0.582223\pi$
$139$	−2.24854e9	−0.510897	−0.255449	+	0.966823i	$0.582223\pi$
$140$	1.32498e9	0.291496
$141$	1.29891e9	0.276753
$142$	2.85636e9	0.589542
$143$	1.41487e9	0.282946
$144$	4.29982e8	0.0833333
$145$	−2.19783e9	−0.412894
$146$	4.84377e9	0.882258
$147$	2.28609e9	0.403799
$148$	−3.69412e9	−0.632897
$149$	2.41914e9	0.402089	0.201045	−	0.979582i	$-0.435566\pi$
$149$	2.41914e9	0.402089	0.201045	+	0.979582i	$0.435566\pi$
$150$	−5.06250e8	−0.0816497
$151$	5.38655e9	0.843168	0.421584	−	0.906789i	$-0.361474\pi$
$151$	5.38655e9	0.843168	0.421584	+	0.906789i	$0.361474\pi$
$152$	−1.48308e8	−0.0225356
$153$	−2.16277e9	−0.319080
$154$	6.56374e9	0.940390
$155$	−5.55570e8	−0.0773119
$156$	−5.92241e8	−0.0800641
$157$	−5.59233e9	−0.734589	−0.367295	−	0.930105i	$-0.619716\pi$
$157$	−5.59233e9	−0.734589	−0.367295	+	0.930105i	$0.619716\pi$
$158$	6.59849e9	0.842340
$159$	1.13932e9	0.141370
$160$	−6.55360e8	−0.0790569
$161$	2.08653e10	2.44742
$162$	−6.88748e8	−0.0785674
$163$	−1.73725e9	−0.192760	−0.0963802	−	0.995345i	$-0.530726\pi$
$163$	−1.73725e9	−0.192760	−0.0963802	+	0.995345i	$0.530726\pi$
$164$	2.60884e8	0.0281611
$165$	−2.50788e9	−0.263408
$166$	−1.53211e8	−0.0156604
$167$	−7.21585e8	−0.0717899	−0.0358949	−	0.999356i	$-0.511428\pi$
$167$	−7.21585e8	−0.0717899	−0.0358949	+	0.999356i	$0.511428\pi$
$168$	−2.74748e9	−0.266098
$169$	8.15731e8	0.0769231
$170$	3.29640e9	0.302706
$171$	2.37561e8	0.0212468
$172$	−1.07594e10	−0.937367
$173$	−5.90812e9	−0.501467	−0.250733	−	0.968056i	$-0.580672\pi$
$173$	−5.90812e9	−0.501467	−0.250733	+	0.968056i	$0.580672\pi$
$174$	4.55742e9	0.376919
$175$	3.23481e9	0.260722
$176$	−3.24655e9	−0.255044
$177$	2.13389e9	0.163415
$178$	−1.27233e10	−0.949972
$179$	−2.39638e9	−0.174469	−0.0872343	−	0.996188i	$-0.527803\pi$
$179$	−2.39638e9	−0.174469	−0.0872343	+	0.996188i	$0.527803\pi$
$180$	1.04976e9	0.0745356
$181$	1.38875e10	0.961770	0.480885	−	0.876784i	$-0.340315\pi$
$181$	1.38875e10	0.961770	0.480885	+	0.876784i	$0.340315\pi$
$182$	3.78427e9	0.255659
$183$	−3.59386e9	−0.236882
$184$	−1.03204e10	−0.663767
$185$	−9.01884e9	−0.566080
$186$	1.15203e9	0.0705758
$187$	1.63299e10	0.976553
$188$	4.10519e9	0.239675
$189$	4.40093e9	0.250880
$190$	−3.62081e8	−0.0201565
$191$	3.37062e10	1.83256	0.916282	−	0.400534i	$-0.131175\pi$
$191$	3.37062e10	1.83256	0.916282	+	0.400534i	$0.131175\pi$
$192$	1.35895e9	0.0721688
$193$	−2.98580e9	−0.154900	−0.0774502	−	0.996996i	$-0.524678\pi$
$193$	−2.98580e9	−0.154900	−0.0774502	+	0.996996i	$0.524678\pi$
$194$	−1.73885e10	−0.881362
$195$	−1.44590e9	−0.0716115
$196$	7.22516e9	0.349700
$197$	2.02654e9	0.0958643	0.0479321	−	0.998851i	$-0.484737\pi$
$197$	2.02654e9	0.0958643	0.0479321	+	0.998851i	$0.484737\pi$
$198$	5.20035e9	0.240458
$199$	−1.90479e9	−0.0861011	−0.0430505	−	0.999073i	$-0.513708\pi$
$199$	−1.90479e9	−0.0861011	−0.0430505	+	0.999073i	$0.513708\pi$
$200$	−1.60000e9	−0.0707107
$201$	−1.25428e10	−0.542017
$202$	−1.43072e10	−0.604606
$203$	−2.91208e10	−1.20357
$204$	−6.83542e9	−0.276331
$205$	6.36924e8	0.0251881
$206$	2.00331e10	0.775077
$207$	1.65313e10	0.625806
$208$	−1.87177e9	−0.0693375
$209$	−1.79369e9	−0.0650264
$210$	−6.70771e9	−0.238006
$211$	−6.94235e9	−0.241121	−0.120561	−	0.992706i	$-0.538469\pi$
$211$	−6.94235e9	−0.241121	−0.120561	+	0.992706i	$0.538469\pi$
$212$	3.60081e9	0.122430
$213$	−1.44603e10	−0.481359
$214$	3.58079e10	1.16712
$215$	−2.62680e10	−0.838407
$216$	−2.17678e9	−0.0680414
$217$	−7.36119e9	−0.225361
$218$	2.86425e10	0.858927
$219$	−2.45216e10	−0.720361
$220$	−7.92615e9	−0.228118
$221$	9.41486e9	0.265490
$222$	1.87015e10	0.516758
$223$	1.33484e10	0.361457	0.180729	−	0.983533i	$-0.442154\pi$
$223$	1.33484e10	0.361457	0.180729	+	0.983533i	$0.442154\pi$
$224$	−8.68338e9	−0.230448
$225$	2.56289e9	0.0666667
$226$	−2.18914e10	−0.558195
$227$	−6.43112e10	−1.60757	−0.803785	−	0.594919i	$-0.797184\pi$
$227$	−6.43112e10	−1.60757	−0.803785	+	0.594919i	$0.797184\pi$
$228$	7.50811e8	0.0184003
$229$	−1.90507e8	−0.00457774	−0.00228887	−	0.999997i	$-0.500729\pi$
$229$	−1.90507e8	−0.00457774	−0.00228887	+	0.999997i	$0.500729\pi$
$230$	−2.51963e10	−0.593691
$231$	−3.32289e10	−0.767825
$232$	1.44037e10	0.326421
$233$	−3.34339e10	−0.743165	−0.371583	−	0.928400i	$-0.621185\pi$
$233$	−3.34339e10	−0.743165	−0.371583	+	0.928400i	$0.621185\pi$
$234$	2.99822e9	0.0653720
$235$	1.00224e10	0.214372
$236$	6.74415e9	0.141522
$237$	−3.34048e10	−0.687768
$238$	4.36767e10	0.882375
$239$	−4.09559e10	−0.811943	−0.405971	−	0.913886i	$-0.633067\pi$
$239$	−4.09559e10	−0.811943	−0.405971	+	0.913886i	$0.633067\pi$
$240$	3.31776e9	0.0645497
$241$	−4.20239e10	−0.802452	−0.401226	−	0.915979i	$-0.631416\pi$
$241$	−4.20239e10	−0.802452	−0.401226	+	0.915979i	$0.631416\pi$
$242$	−1.53775e9	−0.0288215
$243$	3.48678e9	0.0641500
$244$	−1.13584e10	−0.205146
$245$	1.76396e10	0.312781
$246$	−1.32072e9	−0.0229935
$247$	−1.03414e9	−0.0176784
$248$	3.64098e9	0.0611204
$249$	7.75631e8	0.0127867
$250$	−3.90625e9	−0.0632456
$251$	−3.96698e10	−0.630853	−0.315426	−	0.948950i	$-0.602148\pi$
$251$	−3.96698e10	−0.630853	−0.315426	+	0.948950i	$0.602148\pi$
$252$	1.39091e10	0.217268
$253$	−1.24818e11	−1.91530
$254$	−6.98509e10	−1.05298
$255$	−1.66880e10	−0.247158
$256$	4.29497e9	0.0625000
$257$	−8.50279e8	−0.0121580	−0.00607900	−	0.999982i	$-0.501935\pi$
$257$	−8.50279e8	−0.0121580	−0.00607900	+	0.999982i	$0.501935\pi$
$258$	5.44694e10	0.765357
$259$	−1.19498e11	−1.65010
$260$	−4.56976e9	−0.0620174
$261$	−2.30719e10	−0.307753
$262$	−2.91125e10	−0.381702
$263$	1.74825e10	0.225321	0.112661	−	0.993634i	$-0.464063\pi$
$263$	1.74825e10	0.225321	0.112661	+	0.993634i	$0.464063\pi$
$264$	1.64357e10	0.208243
$265$	8.79104e9	0.109505
$266$	−4.79749e9	−0.0587553
$267$	6.44119e10	0.775649
$268$	−3.96415e10	−0.469401
$269$	−3.63692e10	−0.423495	−0.211747	−	0.977324i	$-0.567915\pi$
$269$	−3.63692e10	−0.423495	−0.211747	+	0.977324i	$0.567915\pi$
$270$	−5.31441e9	−0.0608581
$271$	1.85293e10	0.208688	0.104344	−	0.994541i	$-0.466726\pi$
$271$	1.85293e10	0.208688	0.104344	+	0.994541i	$0.466726\pi$
$272$	−2.16033e10	−0.239310
$273$	−1.91579e10	−0.208745
$274$	4.46314e10	0.478369
$275$	−1.93510e10	−0.204035
$276$	5.22469e10	0.541964
$277$	7.12972e10	0.727635	0.363817	−	0.931470i	$-0.381473\pi$
$277$	7.12972e10	0.727635	0.363817	+	0.931470i	$0.381473\pi$
$278$	3.59766e10	0.361259
$279$	−5.83215e9	−0.0576249
$280$	−2.11997e10	−0.206119
$281$	4.55473e10	0.435797	0.217898	−	0.975971i	$-0.430080\pi$
$281$	4.55473e10	0.435797	0.217898	+	0.975971i	$0.430080\pi$
$282$	−2.07825e10	−0.195694
$283$	−9.23008e10	−0.855395	−0.427697	−	0.903922i	$-0.640675\pi$
$283$	−9.23008e10	−0.855395	−0.427697	+	0.903922i	$0.640675\pi$
$284$	−4.57017e10	−0.416869
$285$	1.83303e9	0.0164577
$286$	−2.26379e10	−0.200073
$287$	8.43910e9	0.0734223
$288$	−6.87971e9	−0.0589256
$289$	−9.92504e9	−0.0836936
$290$	3.51653e10	0.291960
$291$	8.80293e10	0.719629
$292$	−7.75003e10	−0.623851
$293$	−7.63388e10	−0.605120	−0.302560	−	0.953130i	$-0.597841\pi$
$293$	−7.63388e10	−0.605120	−0.302560	+	0.953130i	$0.597841\pi$
$294$	−3.65774e10	−0.285529
$295$	1.64652e10	0.126581
$296$	5.91059e10	0.447526
$297$	−2.63268e10	−0.196333
$298$	−3.87062e10	−0.284320
$299$	−7.19630e10	−0.520702
$300$	8.10000e9	0.0577350
$301$	−3.48046e11	−2.44392
$302$	−8.61847e10	−0.596210
$303$	7.24300e10	0.493659
$304$	2.37293e9	0.0159351
$305$	−2.77304e10	−0.183488
$306$	3.46043e10	0.225623
$307$	−7.35495e10	−0.472560	−0.236280	−	0.971685i	$-0.575928\pi$
$307$	−7.35495e10	−0.472560	−0.236280	+	0.971685i	$0.575928\pi$
$308$	−1.05020e11	−0.664956
$309$	−1.01417e11	−0.632847
$310$	8.88912e9	0.0546678
$311$	−1.68470e11	−1.02118	−0.510588	−	0.859826i	$-0.670572\pi$
$311$	−1.68470e11	−1.02118	−0.510588	+	0.859826i	$0.670572\pi$
$312$	9.47585e9	0.0566139
$313$	−5.08633e10	−0.299540	−0.149770	−	0.988721i	$-0.547853\pi$
$313$	−5.08633e10	−0.299540	−0.149770	+	0.988721i	$0.547853\pi$
$314$	8.94773e10	0.519433
$315$	3.39578e10	0.194331
$316$	−1.05576e11	−0.595624
$317$	1.66288e10	0.0924898	0.0462449	−	0.998930i	$-0.485275\pi$
$317$	1.66288e10	0.0924898	0.0462449	+	0.998930i	$0.485275\pi$
$318$	−1.82291e10	−0.0999639
$319$	1.74203e11	0.941886
$320$	1.04858e10	0.0559017
$321$	−1.81277e11	−0.952952
$322$	−3.33845e11	−1.73059
$323$	−1.19357e10	−0.0610147
$324$	1.10200e10	0.0555556
$325$	−1.11566e10	−0.0554700
$326$	2.77960e10	0.136302
$327$	−1.45003e11	−0.701311
$328$	−4.17414e9	−0.0199129
$329$	1.32795e11	0.624886
$330$	4.01261e10	0.186258
$331$	−1.21761e11	−0.557546	−0.278773	−	0.960357i	$-0.589928\pi$
$331$	−1.21761e11	−0.557546	−0.278773	+	0.960357i	$0.589928\pi$
$332$	2.45138e9	0.0110736
$333$	−9.46761e10	−0.421931
$334$	1.15454e10	0.0507631
$335$	−9.67811e10	−0.419845
$336$	4.39596e10	0.188160
$337$	3.49189e11	1.47477	0.737387	−	0.675470i	$-0.236059\pi$
$337$	3.49189e11	1.47477	0.737387	+	0.675470i	$0.236059\pi$
$338$	−1.30517e10	−0.0543928
$339$	1.10825e11	0.455764
$340$	−5.27425e10	−0.214045
$341$	4.40353e10	0.176363
$342$	−3.80098e9	−0.0150237
$343$	−1.00452e11	−0.391866
$344$	1.72150e11	0.662819
$345$	1.27556e11	0.484747
$346$	9.45300e10	0.354590
$347$	−2.97630e11	−1.10203	−0.551016	−	0.834495i	$-0.685760\pi$
$347$	−2.97630e11	−1.10203	−0.551016	+	0.834495i	$0.685760\pi$
$348$	−7.29187e10	−0.266522
$349$	−2.22052e11	−0.801199	−0.400599	−	0.916253i	$-0.631198\pi$
$349$	−2.22052e11	−0.801199	−0.400599	+	0.916253i	$0.631198\pi$
$350$	−5.17570e10	−0.184358
$351$	−1.51785e10	−0.0533761
$352$	5.19448e10	0.180343
$353$	−7.40921e10	−0.253972	−0.126986	−	0.991905i	$-0.540530\pi$
$353$	−7.40921e10	−0.253972	−0.126986	+	0.991905i	$0.540530\pi$
$354$	−3.41423e10	−0.115552
$355$	−1.11576e11	−0.372859
$356$	2.03573e11	0.671732
$357$	−2.21113e11	−0.720456
$358$	3.83421e10	0.123368
$359$	−2.29579e11	−0.729469	−0.364735	−	0.931111i	$-0.618840\pi$
$359$	−2.29579e11	−0.729469	−0.364735	+	0.931111i	$0.618840\pi$
$360$	−1.67962e10	−0.0527046
$361$	−3.21377e11	−0.995937
$362$	−2.22200e11	−0.680074
$363$	7.78486e9	0.0235326
$364$	−6.05484e10	−0.180778
$365$	−1.89210e11	−0.557989
$366$	5.75018e10	0.167501
$367$	−3.82139e11	−1.09957	−0.549787	−	0.835305i	$-0.685291\pi$
$367$	−3.82139e11	−1.09957	−0.549787	+	0.835305i	$0.685291\pi$
$368$	1.65126e11	0.469354
$369$	6.68617e9	0.0187741
$370$	1.44301e11	0.400279
$371$	1.16479e11	0.319203
$372$	−1.84325e10	−0.0499046
$373$	3.17543e11	0.849402	0.424701	−	0.905334i	$-0.360379\pi$
$373$	3.17543e11	0.849402	0.424701	+	0.905334i	$0.360379\pi$
$374$	−2.61278e11	−0.690527
$375$	1.97754e10	0.0516398
$376$	−6.56830e10	−0.169476
$377$	1.00436e11	0.256066
$378$	−7.04148e10	−0.177399
$379$	−3.98518e11	−0.992136	−0.496068	−	0.868284i	$-0.665223\pi$
$379$	−3.98518e11	−0.992136	−0.496068	+	0.868284i	$0.665223\pi$
$380$	5.79329e9	0.0142528
$381$	3.53620e11	0.859755
$382$	−5.39299e11	−1.29582
$383$	3.31940e11	0.788253	0.394126	−	0.919056i	$-0.371047\pi$
$383$	3.31940e11	0.788253	0.394126	+	0.919056i	$0.371047\pi$
$384$	−2.17433e10	−0.0510310
$385$	−2.56396e11	−0.594755
$386$	4.77728e10	0.109531
$387$	−2.75751e11	−0.624911
$388$	2.78216e11	0.623217
$389$	7.10223e11	1.57261	0.786306	−	0.617837i	$-0.211991\pi$
$389$	7.10223e11	1.57261	0.786306	+	0.617837i	$0.211991\pi$
$390$	2.31344e10	0.0506370
$391$	−8.30570e11	−1.79714
$392$	−1.15603e11	−0.247275
$393$	1.47382e11	0.311658
$394$	−3.24246e10	−0.0677863
$395$	−2.57753e11	−0.532743
$396$	−8.32056e10	−0.170029
$397$	−1.94348e11	−0.392665	−0.196332	−	0.980537i	$-0.562903\pi$
$397$	−1.94348e11	−0.392665	−0.196332	+	0.980537i	$0.562903\pi$
$398$	3.04767e10	0.0608827
$399$	2.42873e10	0.0479735
$400$	2.56000e10	0.0500000
$401$	−7.04900e10	−0.136137	−0.0680687	−	0.997681i	$-0.521684\pi$
$401$	−7.04900e10	−0.136137	−0.0680687	+	0.997681i	$0.521684\pi$
$402$	2.00685e11	0.383264
$403$	2.53882e10	0.0479468
$404$	2.28915e11	0.427521
$405$	2.69042e10	0.0496904
$406$	4.65933e11	0.851052
$407$	7.14847e11	1.29133
$408$	1.09367e11	0.195396
$409$	−6.69143e11	−1.18240	−0.591199	−	0.806526i	$-0.701345\pi$
$409$	−6.69143e11	−1.18240	−0.591199	+	0.806526i	$0.701345\pi$
$410$	−1.01908e10	−0.0178107
$411$	−2.25946e11	−0.390586
$412$	−3.20529e11	−0.548062
$413$	2.18160e11	0.368978
$414$	−2.64500e11	−0.442511
$415$	5.98481e9	0.00990453
$416$	2.99484e10	0.0490290
$417$	−1.82132e11	−0.294967
$418$	2.86991e10	0.0459806
$419$	−9.18824e10	−0.145636	−0.0728181	−	0.997345i	$-0.523199\pi$
$419$	−9.18824e10	−0.145636	−0.0728181	+	0.997345i	$0.523199\pi$
$420$	1.07323e11	0.168295
$421$	1.03742e12	1.60949	0.804743	−	0.593624i	$-0.202303\pi$
$421$	1.03742e12	1.60949	0.804743	+	0.593624i	$0.202303\pi$
$422$	1.11078e11	0.170499
$423$	1.05211e11	0.159783
$424$	−5.76129e10	−0.0865713
$425$	−1.28766e11	−0.191448
$426$	2.31365e11	0.340372
$427$	−3.67422e11	−0.534860
$428$	−5.72926e11	−0.825281
$429$	1.14604e11	0.163359
$430$	4.20289e11	0.592843
$431$	−5.94936e11	−0.830468	−0.415234	−	0.909715i	$-0.636300\pi$
$431$	−5.94936e11	−0.830468	−0.415234	+	0.909715i	$0.636300\pi$
$432$	3.48285e10	0.0481125
$433$	−1.07947e12	−1.47575	−0.737876	−	0.674936i	$-0.764171\pi$
$433$	−1.07947e12	−1.47575	−0.737876	+	0.674936i	$0.764171\pi$
$434$	1.17779e11	0.159354
$435$	−1.78024e11	−0.238384
$436$	−4.58280e11	−0.607353
$437$	9.12308e10	0.119667
$438$	3.92345e11	0.509372
$439$	−5.14665e11	−0.661354	−0.330677	−	0.943744i	$-0.607277\pi$
$439$	−5.14665e11	−0.661354	−0.330677	+	0.943744i	$0.607277\pi$
$440$	1.26818e11	0.161304
$441$	1.85173e11	0.233133
$442$	−1.50638e11	−0.187730
$443$	7.59528e11	0.936973	0.468487	−	0.883471i	$-0.344799\pi$
$443$	7.59528e11	0.936973	0.468487	+	0.883471i	$0.344799\pi$
$444$	−2.99223e11	−0.365403
$445$	4.97005e11	0.600815
$446$	−2.13574e11	−0.255589
$447$	1.95950e11	0.232146
$448$	1.38934e11	0.162951
$449$	7.62298e11	0.885149	0.442574	−	0.896732i	$-0.354065\pi$
$449$	7.62298e11	0.885149	0.442574	+	0.896732i	$0.354065\pi$
$450$	−4.10062e10	−0.0471405
$451$	−5.04835e10	−0.0574586
$452$	3.50263e11	0.394703
$453$	4.36310e11	0.486803
$454$	1.02898e12	1.13672
$455$	−1.47823e11	−0.161693
$456$	−1.20130e10	−0.0130109
$457$	−8.56426e11	−0.918474	−0.459237	−	0.888314i	$-0.651877\pi$
$457$	−8.56426e11	−0.918474	−0.459237	+	0.888314i	$0.651877\pi$
$458$	3.04811e9	0.00323695
$459$	−1.75184e11	−0.184221
$460$	4.03140e11	0.419803
$461$	1.07100e12	1.10443	0.552213	−	0.833703i	$-0.313784\pi$
$461$	1.07100e12	1.10443	0.552213	+	0.833703i	$0.313784\pi$
$462$	5.31663e11	0.542934
$463$	1.67431e12	1.69325	0.846626	−	0.532188i	$-0.178630\pi$
$463$	1.67431e12	1.69325	0.846626	+	0.532188i	$0.178630\pi$
$464$	−2.30459e11	−0.230815
$465$	−4.50012e10	−0.0446360
$466$	5.34942e11	0.525497
$467$	2.41867e11	0.235315	0.117658	−	0.993054i	$-0.462461\pi$
$467$	2.41867e11	0.235315	0.117658	+	0.993054i	$0.462461\pi$
$468$	−4.79715e10	−0.0462250
$469$	−1.28233e12	−1.22383
$470$	−1.60359e11	−0.151584
$471$	−4.52979e11	−0.424115
$472$	−1.07906e11	−0.100071
$473$	2.08205e12	1.91256
$474$	5.34477e11	0.486325
$475$	1.41438e10	0.0127481
$476$	−6.98827e11	−0.623933
$477$	9.22848e10	0.0816202
$478$	6.55294e11	0.574130
$479$	8.06204e11	0.699738	0.349869	−	0.936799i	$-0.386226\pi$
$479$	8.06204e11	0.699738	0.349869	+	0.936799i	$0.386226\pi$
$480$	−5.30842e10	−0.0456435
$481$	4.12139e11	0.351068
$482$	6.72382e11	0.567420
$483$	1.69009e12	1.41302
$484$	2.46040e10	0.0203799
$485$	6.79238e11	0.557422
$486$	−5.57886e10	−0.0453609
$487$	1.20604e12	0.971585	0.485793	−	0.874074i	$-0.338531\pi$
$487$	1.20604e12	0.971585	0.485793	+	0.874074i	$0.338531\pi$
$488$	1.81734e11	0.145060
$489$	−1.40717e11	−0.111290
$490$	−2.82233e11	−0.221170
$491$	−1.37912e12	−1.07087	−0.535434	−	0.844577i	$-0.679852\pi$
$491$	−1.37912e12	−1.07087	−0.535434	+	0.844577i	$0.679852\pi$
$492$	2.11316e10	0.0162588
$493$	1.15919e12	0.883779
$494$	1.65462e10	0.0125005
$495$	−2.03139e11	−0.152079
$496$	−5.82557e10	−0.0432187
$497$	−1.47836e12	−1.08687
$498$	−1.24101e10	−0.00904156
$499$	3.13593e11	0.226419	0.113210	−	0.993571i	$-0.463887\pi$
$499$	3.13593e11	0.226419	0.113210	+	0.993571i	$0.463887\pi$
$500$	6.25000e10	0.0447214
$501$	−5.84484e10	−0.0414479
$502$	6.34717e11	0.446080
$503$	1.23508e12	0.860281	0.430141	−	0.902762i	$-0.358464\pi$
$503$	1.23508e12	0.860281	0.430141	+	0.902762i	$0.358464\pi$
$504$	−2.22546e11	−0.153632
$505$	5.58874e11	0.382386
$506$	1.99709e12	1.35432
$507$	6.60742e10	0.0444116
$508$	1.11761e12	0.744569
$509$	3.88359e11	0.256450	0.128225	−	0.991745i	$-0.459072\pi$
$509$	3.88359e11	0.256450	0.128225	+	0.991745i	$0.459072\pi$
$510$	2.67009e11	0.174767
$511$	−2.50699e12	−1.62652
$512$	−6.87195e10	−0.0441942
$513$	1.92425e10	0.0122668
$514$	1.36045e10	0.00859700
$515$	−7.82541e11	−0.490202
$516$	−8.71511e11	−0.541189
$517$	−7.94393e11	−0.489022
$518$	1.91196e12	1.16680
$519$	−4.78558e11	−0.289522
$520$	7.31162e10	0.0438529
$521$	−1.44737e12	−0.860619	−0.430309	−	0.902681i	$-0.641596\pi$
$521$	−1.44737e12	−0.860619	−0.430309	+	0.902681i	$0.641596\pi$
$522$	3.69151e11	0.217614
$523$	−1.26856e12	−0.741400	−0.370700	−	0.928753i	$-0.620882\pi$
$523$	−1.26856e12	−0.741400	−0.370700	+	0.928753i	$0.620882\pi$
$524$	4.65801e11	0.269904
$525$	2.62020e11	0.150528
$526$	−2.79720e11	−0.159326
$527$	2.93021e11	0.165482
$528$	−2.62971e11	−0.147250
$529$	4.54736e12	2.52469
$530$	−1.40657e11	−0.0774317
$531$	1.72845e11	0.0943478
$532$	7.67599e10	0.0415463
$533$	−2.91059e10	−0.0156210
$534$	−1.03059e12	−0.548467
$535$	−1.39875e12	−0.738153
$536$	6.34264e11	0.331916
$537$	−1.94107e11	−0.100730
$538$	5.81907e11	0.299456
$539$	−1.39814e12	−0.713511
$540$	8.50306e10	0.0430331
$541$	−2.20856e12	−1.10846	−0.554232	−	0.832362i	$-0.686988\pi$
$541$	−2.20856e12	−1.10846	−0.554232	+	0.832362i	$0.686988\pi$
$542$	−2.96469e11	−0.147565
$543$	1.12489e12	0.555278
$544$	3.45653e11	0.169218
$545$	−1.11885e12	−0.543233
$546$	3.06526e11	0.147605
$547$	−3.20992e12	−1.53303	−0.766516	−	0.642225i	$-0.778012\pi$
$547$	−3.20992e12	−1.53303	−0.766516	+	0.642225i	$0.778012\pi$
$548$	−7.14102e11	−0.338258
$549$	−2.91103e11	−0.136764
$550$	3.09615e11	0.144275
$551$	−1.27327e11	−0.0588488
$552$	−8.35951e11	−0.383226
$553$	−3.41518e12	−1.55292
$554$	−1.14076e12	−0.514516
$555$	−7.30526e11	−0.326826
$556$	−5.75626e11	−0.255449
$557$	−2.88331e12	−1.26924	−0.634618	−	0.772826i	$-0.718843\pi$
$557$	−2.88331e12	−1.26924	−0.634618	+	0.772826i	$0.718843\pi$
$558$	9.33144e10	0.0407469
$559$	1.20039e12	0.519958
$560$	3.39195e11	0.145748
$561$	1.32272e12	0.563813
$562$	−7.28757e11	−0.308155
$563$	−3.40237e11	−0.142723	−0.0713615	−	0.997451i	$-0.522734\pi$
$563$	−3.40237e11	−0.142723	−0.0713615	+	0.997451i	$0.522734\pi$
$564$	3.32520e11	0.138376
$565$	8.55133e11	0.353033
$566$	1.47681e12	0.604855
$567$	3.56475e11	0.144846
$568$	7.31227e11	0.294771
$569$	−4.43850e12	−1.77513	−0.887567	−	0.460678i	$-0.847606\pi$
$569$	−4.43850e12	−1.77513	−0.887567	+	0.460678i	$0.847606\pi$
$570$	−2.93286e10	−0.0116373
$571$	−3.88184e12	−1.52818	−0.764091	−	0.645109i	$-0.776812\pi$
$571$	−3.88184e12	−1.52818	−0.764091	+	0.645109i	$0.776812\pi$
$572$	3.62206e11	0.141473
$573$	2.73020e12	1.05803
$574$	−1.35026e11	−0.0519174
$575$	9.84229e11	0.375483
$576$	1.10075e11	0.0416667
$577$	3.36545e12	1.26401	0.632007	−	0.774963i	$-0.282231\pi$
$577$	3.36545e12	1.26401	0.632007	+	0.774963i	$0.282231\pi$
$578$	1.58801e11	0.0591803
$579$	−2.41850e11	−0.0894318
$580$	−5.62645e11	−0.206447
$581$	7.92975e10	0.0288713
$582$	−1.40847e12	−0.508854
$583$	−6.96791e11	−0.249801
$584$	1.24000e12	0.441129
$585$	−1.17118e11	−0.0413449
$586$	1.22142e12	0.427884
$587$	4.57992e11	0.159216	0.0796080	−	0.996826i	$-0.474633\pi$
$587$	4.57992e11	0.159216	0.0796080	+	0.996826i	$0.474633\pi$
$588$	5.85238e11	0.201899
$589$	−3.21858e10	−0.0110191
$590$	−2.63443e11	−0.0895062
$591$	1.64150e11	0.0553473
$592$	−9.45694e11	−0.316448
$593$	−3.18932e12	−1.05914	−0.529569	−	0.848267i	$-0.677646\pi$
$593$	−3.18932e12	−1.05914	−0.529569	+	0.848267i	$0.677646\pi$
$594$	4.21228e11	0.138828
$595$	−1.70612e12	−0.558063
$596$	6.19299e11	0.201045
$597$	−1.54288e11	−0.0497105
$598$	1.15141e12	0.368192
$599$	4.90163e12	1.55568	0.777839	−	0.628463i	$-0.216316\pi$
$599$	4.90163e12	1.55568	0.777839	+	0.628463i	$0.216316\pi$
$600$	−1.29600e11	−0.0408248
$601$	3.34904e12	1.04709	0.523546	−	0.851997i	$-0.324609\pi$
$601$	3.34904e12	1.04709	0.523546	+	0.851997i	$0.324609\pi$
$602$	5.56874e12	1.72811
$603$	−1.01597e12	−0.312934
$604$	1.37896e12	0.421584
$605$	6.00683e10	0.0182283
$606$	−1.15888e12	−0.349069
$607$	6.04390e12	1.80704	0.903520	−	0.428546i	$-0.140974\pi$
$607$	6.04390e12	1.80704	0.903520	+	0.428546i	$0.140974\pi$
$608$	−3.79669e10	−0.0112678
$609$	−2.35878e12	−0.694881
$610$	4.43687e11	0.129745
$611$	−4.58001e11	−0.132948
$612$	−5.53669e11	−0.159540
$613$	−1.22849e12	−0.351397	−0.175698	−	0.984444i	$-0.556218\pi$
$613$	−1.22849e12	−0.351397	−0.175698	+	0.984444i	$0.556218\pi$
$614$	1.17679e12	0.334150
$615$	5.15908e10	0.0145423
$616$	1.68032e12	0.470195
$617$	1.47331e12	0.409271	0.204635	−	0.978838i	$-0.434399\pi$
$617$	1.47331e12	0.409271	0.204635	+	0.978838i	$0.434399\pi$
$618$	1.62268e12	0.447491
$619$	6.79566e12	1.86047	0.930237	−	0.366958i	$-0.119601\pi$
$619$	6.79566e12	1.86047	0.930237	+	0.366958i	$0.119601\pi$
$620$	−1.42226e11	−0.0386559
$621$	1.33903e12	0.361309
$622$	2.69552e12	0.722080
$623$	6.58521e12	1.75135
$624$	−1.51614e11	−0.0400320
$625$	1.52588e11	0.0400000
$626$	8.13812e11	0.211807
$627$	−1.45289e11	−0.0375430
$628$	−1.43164e12	−0.367295
$629$	4.75676e12	1.21167
$630$	−5.43324e11	−0.137413
$631$	−7.14295e12	−1.79368	−0.896842	−	0.442352i	$-0.854144\pi$
$631$	−7.14295e12	−1.79368	−0.896842	+	0.442352i	$0.854144\pi$
$632$	1.68921e12	0.421170
$633$	−5.62331e11	−0.139211
$634$	−2.66061e11	−0.0654002
$635$	2.72855e12	0.665963
$636$	2.91666e11	0.0706851
$637$	−8.06086e11	−0.193979
$638$	−2.78725e12	−0.666014
$639$	−1.17128e12	−0.277913
$640$	−1.67772e11	−0.0395285
$641$	−2.65068e12	−0.620149	−0.310075	−	0.950712i	$-0.600354\pi$
$641$	−2.65068e12	−0.620149	−0.310075	+	0.950712i	$0.600354\pi$
$642$	2.90044e12	0.673839
$643$	−4.68493e12	−1.08082	−0.540411	−	0.841401i	$-0.681731\pi$
$643$	−4.68493e12	−1.08082	−0.540411	+	0.841401i	$0.681731\pi$
$644$	5.34152e12	1.22371
$645$	−2.12771e12	−0.484054
$646$	1.90970e11	0.0431439
$647$	−3.58806e9	−0.000804990 0	−0.000402495	−	1.00000i	$-0.500128\pi$
$647$	−3.58806e9	−0.000804990 0	−0.000402495		1.00000i	$0.500128\pi$
$648$	−1.76319e11	−0.0392837
$649$	−1.30506e12	−0.288754
$650$	1.78506e11	0.0392232
$651$	−5.96256e11	−0.130112
$652$	−4.44736e11	−0.0963802
$653$	−2.11573e12	−0.455355	−0.227678	−	0.973737i	$-0.573113\pi$
$653$	−2.11573e12	−0.455355	−0.227678	+	0.973737i	$0.573113\pi$
$654$	2.32004e12	0.495902
$655$	1.13721e12	0.241409
$656$	6.67863e10	0.0140806
$657$	−1.98625e12	−0.415900
$658$	−2.12472e12	−0.441861
$659$	2.69360e12	0.556352	0.278176	−	0.960530i	$-0.410270\pi$
$659$	2.69360e12	0.556352	0.278176	+	0.960530i	$0.410270\pi$
$660$	−6.42018e11	−0.131704
$661$	3.73186e12	0.760360	0.380180	−	0.924913i	$-0.375862\pi$
$661$	3.73186e12	0.760360	0.380180	+	0.924913i	$0.375862\pi$
$662$	1.94817e12	0.394245
$663$	7.62604e11	0.153281
$664$	−3.92221e10	−0.00783022
$665$	1.87402e11	0.0371601
$666$	1.51482e12	0.298350
$667$	−8.86033e12	−1.73334
$668$	−1.84726e11	−0.0358949
$669$	1.08122e12	0.208688
$670$	1.54850e12	0.296875
$671$	2.19796e12	0.418569
$672$	−7.03354e11	−0.133049
$673$	−6.76030e11	−0.127028	−0.0635138	−	0.997981i	$-0.520231\pi$
$673$	−6.76030e11	−0.127028	−0.0635138	+	0.997981i	$0.520231\pi$
$674$	−5.58702e12	−1.04282
$675$	2.07594e11	0.0384900
$676$	2.08827e11	0.0384615
$677$	−5.01995e11	−0.0918440	−0.0459220	−	0.998945i	$-0.514623\pi$
$677$	−5.01995e11	−0.0918440	−0.0459220	+	0.998945i	$0.514623\pi$
$678$	−1.77320e12	−0.322274
$679$	8.99976e12	1.62486
$680$	8.43880e11	0.151353
$681$	−5.20920e12	−0.928131
$682$	−7.04565e11	−0.124707
$683$	7.04293e12	1.23840	0.619199	−	0.785234i	$-0.287458\pi$
$683$	7.04293e12	1.23840	0.619199	+	0.785234i	$0.287458\pi$
$684$	6.08157e10	0.0106234
$685$	−1.74341e12	−0.302547
$686$	1.60724e12	0.277091
$687$	−1.54311e10	−0.00264296
$688$	−2.75440e12	−0.468684
$689$	−4.01729e11	−0.0679121
$690$	−2.04090e12	−0.342768
$691$	−3.48508e12	−0.581517	−0.290758	−	0.956797i	$-0.593908\pi$
$691$	−3.48508e12	−0.581517	−0.290758	+	0.956797i	$0.593908\pi$
$692$	−1.51248e12	−0.250733
$693$	−2.69154e12	−0.443304
$694$	4.76208e12	0.779254
$695$	−1.40534e12	−0.228480
$696$	1.16670e12	0.188459
$697$	−3.35929e11	−0.0539138
$698$	3.55283e12	0.566533
$699$	−2.70815e12	−0.429067
$700$	8.28112e11	0.130361
$701$	8.64945e12	1.35287	0.676437	−	0.736500i	$-0.263523\pi$
$701$	8.64945e12	1.35287	0.676437	+	0.736500i	$0.263523\pi$
$702$	2.42856e11	0.0377426
$703$	−5.22488e11	−0.0806821
$704$	−8.31117e11	−0.127522
$705$	8.11817e11	0.123768
$706$	1.18547e12	0.179585
$707$	7.40496e12	1.11464
$708$	5.46276e11	0.0817076
$709$	−9.51182e12	−1.41369	−0.706847	−	0.707366i	$-0.749883\pi$
$709$	−9.51182e12	−1.41369	−0.706847	+	0.707366i	$0.749883\pi$
$710$	1.78522e12	0.263651
$711$	−2.70579e12	−0.397083
$712$	−3.25717e12	−0.474986
$713$	−2.23973e12	−0.324558
$714$	3.53781e12	0.509439
$715$	8.84292e11	0.126537
$716$	−6.13474e11	−0.0872343
$717$	−3.31742e12	−0.468775
$718$	3.67326e12	0.515813
$719$	−9.70581e12	−1.35441	−0.677207	−	0.735792i	$-0.736810\pi$
$719$	−9.70581e12	−1.35441	−0.677207	+	0.735792i	$0.736810\pi$
$720$	2.68739e11	0.0372678
$721$	−1.03685e13	−1.42892
$722$	5.14203e12	0.704234
$723$	−3.40393e12	−0.463296
$724$	3.55521e12	0.480885
$725$	−1.37364e12	−0.184652
$726$	−1.24558e11	−0.0166401
$727$	−5.39248e12	−0.715952	−0.357976	−	0.933731i	$-0.616533\pi$
$727$	−5.39248e12	−0.715952	−0.357976	+	0.933731i	$0.616533\pi$
$728$	9.68774e11	0.127830
$729$	2.82430e11	0.0370370
$730$	3.02736e12	0.394558
$731$	1.38544e13	1.79457
$732$	−9.20029e11	−0.118441
$733$	−1.74066e12	−0.222713	−0.111356	−	0.993781i	$-0.535519\pi$
$733$	−1.74066e12	−0.222713	−0.111356	+	0.993781i	$0.535519\pi$
$734$	6.11423e12	0.777516
$735$	1.42880e12	0.180584
$736$	−2.64202e12	−0.331884
$737$	7.67101e12	0.957743
$738$	−1.06979e11	−0.0132753
$739$	−1.23665e13	−1.52527	−0.762634	−	0.646830i	$-0.776094\pi$
$739$	−1.23665e13	−1.52527	−0.762634	+	0.646830i	$0.776094\pi$
$740$	−2.30882e12	−0.283040
$741$	−8.37653e10	−0.0102066
$742$	−1.86367e12	−0.225710
$743$	1.46418e13	1.76257	0.881283	−	0.472588i	$-0.156680\pi$
$743$	1.46418e13	1.76257	0.881283	+	0.472588i	$0.156680\pi$
$744$	2.94920e11	0.0352879
$745$	1.51196e12	0.179820
$746$	−5.08069e12	−0.600618
$747$	6.28261e10	0.00738240
$748$	4.18045e12	0.488276
$749$	−1.85331e13	−2.15169
$750$	−3.16406e11	−0.0365148
$751$	3.89123e12	0.446382	0.223191	−	0.974775i	$-0.428353\pi$
$751$	3.89123e12	0.446382	0.223191	+	0.974775i	$0.428353\pi$
$752$	1.05093e12	0.119838
$753$	−3.21325e12	−0.364223
$754$	−1.60697e12	−0.181066
$755$	3.36659e12	0.377076
$756$	1.12664e12	0.125440
$757$	−1.24174e13	−1.37436	−0.687180	−	0.726487i	$-0.741152\pi$
$757$	−1.24174e13	−1.37436	−0.687180	+	0.726487i	$0.741152\pi$
$758$	6.37629e12	0.701546
$759$	−1.01103e13	−1.10580
$760$	−9.26927e10	−0.0100782
$761$	−9.16764e12	−0.990892	−0.495446	−	0.868639i	$-0.664995\pi$
$761$	−9.16764e12	−0.990892	−0.495446	+	0.868639i	$0.664995\pi$
$762$	−5.65792e12	−0.607938
$763$	−1.48245e13	−1.58350
$764$	8.62878e12	0.916282
$765$	−1.35173e12	−0.142697
$766$	−5.31104e12	−0.557379
$767$	−7.52420e11	−0.0785021
$768$	3.47892e11	0.0360844
$769$	1.23370e13	1.27216	0.636078	−	0.771625i	$-0.280556\pi$
$769$	1.23370e13	1.27216	0.636078	+	0.771625i	$0.280556\pi$
$770$	4.10234e12	0.420555
$771$	−6.88726e10	−0.00701942
$772$	−7.64365e11	−0.0774502
$773$	1.04157e13	1.04925	0.524627	−	0.851332i	$-0.324205\pi$
$773$	1.04157e13	1.04925	0.524627	+	0.851332i	$0.324205\pi$
$774$	4.41202e12	0.441879
$775$	−3.47231e11	−0.0345749
$776$	−4.45145e12	−0.440681
$777$	−9.67931e12	−0.952686
$778$	−1.13636e13	−1.11200
$779$	3.68989e10	0.00359000
$780$	−3.70151e11	−0.0358057
$781$	8.84372e12	0.850560
$782$	1.32891e13	1.27077
$783$	−1.86883e12	−0.177681
$784$	1.84964e12	0.174850
$785$	−3.49521e12	−0.328518
$786$	−2.35812e12	−0.220376
$787$	1.20846e13	1.12291	0.561454	−	0.827508i	$-0.310242\pi$
$787$	1.20846e13	1.12291	0.561454	+	0.827508i	$0.310242\pi$
$788$	5.18794e11	0.0479321
$789$	1.41608e12	0.130089
$790$	4.12405e12	0.376706
$791$	1.13303e13	1.02908
$792$	1.33129e12	0.120229
$793$	1.26721e12	0.113794
$794$	3.10956e12	0.277656
$795$	7.12074e11	0.0632227
$796$	−4.87627e11	−0.0430505
$797$	−4.84006e12	−0.424901	−0.212451	−	0.977172i	$-0.568145\pi$
$797$	−4.84006e12	−0.424901	−0.212451	+	0.977172i	$0.568145\pi$
$798$	−3.88597e11	−0.0339224
$799$	−5.28608e12	−0.458853
$800$	−4.09600e11	−0.0353553
$801$	5.21736e12	0.447821
$802$	1.12784e12	0.0962637
$803$	1.49970e13	1.27288
$804$	−3.21096e12	−0.271009
$805$	1.30408e13	1.09452
$806$	−4.06212e11	−0.0339035
$807$	−2.94590e12	−0.244505
$808$	−3.66263e12	−0.302303
$809$	2.24825e13	1.84534	0.922671	−	0.385589i	$-0.126002\pi$
$809$	2.24825e13	1.84534	0.922671	+	0.385589i	$0.126002\pi$
$810$	−4.30467e11	−0.0351364
$811$	−9.66490e12	−0.784519	−0.392260	−	0.919855i	$-0.628307\pi$
$811$	−9.66490e12	−0.784519	−0.392260	+	0.919855i	$0.628307\pi$
$812$	−7.45492e12	−0.601784
$813$	1.50087e12	0.120486
$814$	−1.14375e13	−0.913110
$815$	−1.08578e12	−0.0862051
$816$	−1.74987e12	−0.138166
$817$	−1.52179e12	−0.119496
$818$	1.07063e13	0.836082
$819$	−1.55179e12	−0.120519
$820$	1.63052e11	0.0125940
$821$	−2.57042e13	−1.97451	−0.987257	−	0.159133i	$-0.949130\pi$
$821$	−2.57042e13	−1.97451	−0.987257	+	0.159133i	$0.949130\pi$
$822$	3.61514e12	0.276186
$823$	1.95771e13	1.48747	0.743737	−	0.668472i	$-0.233051\pi$
$823$	1.95771e13	1.48747	0.743737	+	0.668472i	$0.233051\pi$
$824$	5.12846e12	0.387538
$825$	−1.56743e12	−0.117800
$826$	−3.49057e12	−0.260907
$827$	−1.30998e13	−0.973846	−0.486923	−	0.873445i	$-0.661881\pi$
$827$	−1.30998e13	−0.973846	−0.486923	+	0.873445i	$0.661881\pi$
$828$	4.23200e12	0.312903
$829$	1.64795e13	1.21185	0.605923	−	0.795523i	$-0.292804\pi$
$829$	1.64795e13	1.21185	0.605923	+	0.795523i	$0.292804\pi$
$830$	−9.57570e10	−0.00700356
$831$	5.77507e12	0.420100
$832$	−4.79174e11	−0.0346688
$833$	−9.30354e12	−0.669493
$834$	2.91411e12	0.208573
$835$	−4.50990e11	−0.0321054
$836$	−4.59185e11	−0.0325132
$837$	−4.72404e11	−0.0332697
$838$	1.47012e12	0.102980
$839$	−2.07057e13	−1.44265	−0.721326	−	0.692595i	$-0.756467\pi$
$839$	−2.07057e13	−1.44265	−0.721326	+	0.692595i	$0.756467\pi$
$840$	−1.71717e12	−0.119003
$841$	−2.14117e12	−0.147594
$842$	−1.65988e13	−1.13808
$843$	3.68933e12	0.251607
$844$	−1.77724e12	−0.120561
$845$	5.09832e11	0.0344010
$846$	−1.68338e12	−0.112984
$847$	7.95893e11	0.0531348
$848$	9.21807e11	0.0612151
$849$	−7.47637e12	−0.493862
$850$	2.06025e12	0.135374
$851$	−3.63585e13	−2.37642
$852$	−3.70184e12	−0.240680
$853$	1.27933e13	0.827393	0.413696	−	0.910415i	$-0.364237\pi$
$853$	1.27933e13	0.827393	0.413696	+	0.910415i	$0.364237\pi$
$854$	5.87876e12	0.378203
$855$	1.48476e11	0.00950185
$856$	9.16682e12	0.583561
$857$	6.17404e12	0.390981	0.195490	−	0.980706i	$-0.437370\pi$
$857$	6.17404e12	0.390981	0.195490	+	0.980706i	$0.437370\pi$
$858$	−1.83367e12	−0.115512
$859$	−8.60456e12	−0.539212	−0.269606	−	0.962971i	$-0.586893\pi$
$859$	−8.60456e12	−0.539212	−0.269606	+	0.962971i	$0.586893\pi$
$860$	−6.72462e12	−0.419203
$861$	6.83567e11	0.0423904
$862$	9.51898e12	0.587229
$863$	2.30286e13	1.41325	0.706624	−	0.707589i	$-0.250217\pi$
$863$	2.30286e13	1.41325	0.706624	+	0.707589i	$0.250217\pi$
$864$	−5.57256e11	−0.0340207
$865$	−3.69258e12	−0.224263
$866$	1.72715e13	1.04351
$867$	−8.03928e11	−0.0483205
$868$	−1.88446e12	−0.112681
$869$	2.04299e13	1.21528
$870$	2.84839e12	0.168563
$871$	4.42266e12	0.260377
$872$	7.33247e12	0.429464
$873$	7.13037e12	0.415478
$874$	−1.45969e12	−0.0846175
$875$	2.02176e12	0.116598
$876$	−6.27752e12	−0.360180
$877$	1.30376e13	0.744217	0.372109	−	0.928189i	$-0.378635\pi$
$877$	1.30376e13	0.744217	0.372109	+	0.928189i	$0.378635\pi$
$878$	8.23464e12	0.467648
$879$	−6.18344e12	−0.349366
$880$	−2.02909e12	−0.114059
$881$	1.25438e13	0.701515	0.350758	−	0.936466i	$-0.385924\pi$
$881$	1.25438e13	0.701515	0.350758	+	0.936466i	$0.385924\pi$
$882$	−2.96277e12	−0.164850
$883$	−7.07621e12	−0.391722	−0.195861	−	0.980632i	$-0.562750\pi$
$883$	−7.07621e12	−0.391722	−0.195861	+	0.980632i	$0.562750\pi$
$884$	2.41020e12	0.132745
$885$	1.33368e12	0.0730815
$886$	−1.21525e13	−0.662540
$887$	−2.29362e13	−1.24413	−0.622064	−	0.782967i	$-0.713706\pi$
$887$	−2.29362e13	−1.24413	−0.622064	+	0.782967i	$0.713706\pi$
$888$	4.78757e12	0.258379
$889$	3.61527e13	1.94126
$890$	−7.95208e12	−0.424841
$891$	−2.13247e12	−0.113353
$892$	3.41719e12	0.180729
$893$	5.80629e11	0.0305539
$894$	−3.13520e12	−0.164152
$895$	−1.49774e12	−0.0780248
$896$	−2.22295e12	−0.115224
$897$	−5.82900e12	−0.300627
$898$	−1.21968e13	−0.625895
$899$	3.12589e12	0.159608
$900$	6.56100e11	0.0333333
$901$	−4.63661e12	−0.234390
$902$	8.07736e11	0.0406294
$903$	−2.81917e13	−1.41100
$904$	−5.60420e12	−0.279097
$905$	8.67970e12	0.430117
$906$	−6.98096e12	−0.344222
$907$	8.50011e11	0.0417054	0.0208527	−	0.999783i	$-0.493362\pi$
$907$	8.50011e11	0.0417054	0.0208527	+	0.999783i	$0.493362\pi$
$908$	−1.64637e13	−0.803785
$909$	5.86683e12	0.285014
$910$	2.36517e12	0.114334
$911$	−3.10008e13	−1.49121	−0.745606	−	0.666387i	$-0.767840\pi$
$911$	−3.10008e13	−1.49121	−0.745606	+	0.666387i	$0.767840\pi$
$912$	1.92208e11	0.00920013
$913$	−4.74365e11	−0.0225941
$914$	1.37028e13	0.649459
$915$	−2.24616e12	−0.105937
$916$	−4.87697e10	−0.00228887
$917$	1.50678e13	0.703699
$918$	2.80295e12	0.130264
$919$	−1.64339e13	−0.760014	−0.380007	−	0.924984i	$-0.624078\pi$
$919$	−1.64339e13	−0.760014	−0.380007	+	0.924984i	$0.624078\pi$
$920$	−6.45024e12	−0.296846
$921$	−5.95751e12	−0.272833
$922$	−1.71360e13	−0.780947
$923$	5.09878e12	0.231238
$924$	−8.50660e12	−0.383913
$925$	−5.63677e12	−0.253159
$926$	−2.67890e13	−1.19731
$927$	−8.21480e12	−0.365375
$928$	3.68735e12	0.163211
$929$	7.42321e12	0.326980	0.163490	−	0.986545i	$-0.447725\pi$
$929$	7.42321e12	0.326980	0.163490	+	0.986545i	$0.447725\pi$
$930$	7.20019e11	0.0315624
$931$	1.02191e12	0.0445800
$932$	−8.55908e12	−0.371583
$933$	−1.36461e13	−0.589576
$934$	−3.86987e12	−0.166393
$935$	1.02062e13	0.436728
$936$	7.67544e11	0.0326860
$937$	−1.99236e13	−0.844382	−0.422191	−	0.906507i	$-0.638739\pi$
$937$	−1.99236e13	−0.844382	−0.422191	+	0.906507i	$0.638739\pi$
$938$	2.05173e13	0.865379
$939$	−4.11992e12	−0.172939
$940$	2.56574e12	0.107186
$941$	−1.05676e13	−0.439361	−0.219681	−	0.975572i	$-0.570502\pi$
$941$	−1.05676e13	−0.439361	−0.219681	+	0.975572i	$0.570502\pi$
$942$	7.24766e12	0.299895
$943$	2.56769e12	0.105740
$944$	1.72650e12	0.0707609
$945$	2.75058e12	0.112197
$946$	−3.33127e13	−1.35238
$947$	−3.32359e12	−0.134286	−0.0671432	−	0.997743i	$-0.521388\pi$
$947$	−3.32359e12	−0.134286	−0.0671432	+	0.997743i	$0.521388\pi$
$948$	−8.55164e12	−0.343884
$949$	8.64643e12	0.346050
$950$	−2.26301e11	−0.00901425
$951$	1.34693e12	0.0533990
$952$	1.11812e13	0.441187
$953$	2.19837e13	0.863342	0.431671	−	0.902031i	$-0.357924\pi$
$953$	2.19837e13	0.863342	0.431671	+	0.902031i	$0.357924\pi$
$954$	−1.47656e12	−0.0577142
$955$	2.10663e13	0.819547
$956$	−1.04847e13	−0.405971
$957$	1.41105e13	0.543798
$958$	−1.28993e13	−0.494789
$959$	−2.30999e13	−0.881913
$960$	8.49347e11	0.0322749
$961$	−2.56495e13	−0.970114
$962$	−6.59423e12	−0.248242
$963$	−1.46835e13	−0.550187
$964$	−1.07581e13	−0.401226
$965$	−1.86612e12	−0.0692736
$966$	−2.70414e13	−0.999155
$967$	3.11713e13	1.14640	0.573200	−	0.819416i	$-0.305702\pi$
$967$	3.11713e13	1.14640	0.573200	+	0.819416i	$0.305702\pi$
$968$	−3.93664e11	−0.0144107
$969$	−9.66788e11	−0.0352269
$970$	−1.08678e13	−0.394157
$971$	−4.82856e13	−1.74313	−0.871567	−	0.490276i	$-0.836896\pi$
$971$	−4.82856e13	−1.74313	−0.871567	+	0.490276i	$0.836896\pi$
$972$	8.92617e11	0.0320750
$973$	−1.86204e13	−0.666011
$974$	−1.92966e13	−0.687015
$975$	−9.03688e11	−0.0320256
$976$	−2.90775e12	−0.102573
$977$	1.58992e13	0.558276	0.279138	−	0.960251i	$-0.409951\pi$
$977$	1.58992e13	0.558276	0.279138	+	0.960251i	$0.409951\pi$
$978$	2.25148e12	0.0786941
$979$	−3.93934e13	−1.37057
$980$	4.51573e12	0.156391
$981$	−1.17452e13	−0.404902
$982$	2.20659e13	0.757218
$983$	4.89700e13	1.67278	0.836391	−	0.548133i	$-0.184661\pi$
$983$	4.89700e13	1.67278	0.836391	+	0.548133i	$0.184661\pi$
$984$	−3.38106e11	−0.0114967
$985$	1.26659e12	0.0428718
$986$	−1.85470e13	−0.624926
$987$	1.07564e13	0.360778
$988$	−2.64740e11	−0.00883920
$989$	−1.05897e14	−3.51966
$990$	3.25022e12	0.107536
$991$	−3.20643e13	−1.05606	−0.528032	−	0.849224i	$-0.677070\pi$
$991$	−3.20643e13	−1.05606	−0.528032	+	0.849224i	$0.677070\pi$
$992$	9.32092e11	0.0305602
$993$	−9.86261e12	−0.321900
$994$	2.36538e13	0.768533
$995$	−1.19049e12	−0.0385056
$996$	1.98562e11	0.00639335
$997$	5.33293e13	1.70938	0.854689	−	0.519141i	$-0.173748\pi$
$997$	5.33293e13	1.70938	0.854689	+	0.519141i	$0.173748\pi$
$998$	−5.01748e12	−0.160103
$999$	−7.66877e12	−0.243602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.10.a.e.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.10.a.e.1.4	✓	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	390.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} +625.000 q^{5} -1296.00 q^{6} +8281.12 q^{7} -4096.00 q^{8} +6561.00 q^{9} -10000.0 q^{10} -49538.4 q^{11} +20736.0 q^{12} -28561.0 q^{13} -132498. q^{14} +50625.0 q^{15} +65536.0 q^{16} -329640. q^{17} -104976. q^{18} +36208.1 q^{19} +160000. q^{20} +670771. q^{21} +792615. q^{22} +2.51963e6 q^{23} -331776. q^{24} +390625. q^{25} +456976. q^{26} +531441. q^{27} +2.11997e6 q^{28} -3.51653e6 q^{29} -810000. q^{30} -888912. q^{31} -1.04858e6 q^{32} -4.01261e6 q^{33} +5.27425e6 q^{34} +5.17570e6 q^{35} +1.67962e6 q^{36} -1.44301e7 q^{37} -579329. q^{38} -2.31344e6 q^{39} -2.56000e6 q^{40} +1.01908e6 q^{41} -1.07323e7 q^{42} -4.20289e7 q^{43} -1.26818e7 q^{44} +4.10062e6 q^{45} -4.03140e7 q^{46} +1.60359e7 q^{47} +5.30842e6 q^{48} +2.82233e7 q^{49} -6.25000e6 q^{50} -2.67009e7 q^{51} -7.31162e6 q^{52} +1.40657e7 q^{53} -8.50306e6 q^{54} -3.09615e7 q^{55} -3.39195e7 q^{56} +2.93286e6 q^{57} +5.62645e7 q^{58} +2.63443e7 q^{59} +1.29600e7 q^{60} -4.43687e7 q^{61} +1.42226e7 q^{62} +5.43324e7 q^{63} +1.67772e7 q^{64} -1.78506e7 q^{65} +6.42018e7 q^{66} -1.54850e8 q^{67} -8.43880e7 q^{68} +2.04090e8 q^{69} -8.28112e7 q^{70} -1.78522e8 q^{71} -2.68739e7 q^{72} -3.02736e8 q^{73} +2.30882e8 q^{74} +3.16406e7 q^{75} +9.26927e6 q^{76} -4.10234e8 q^{77} +3.70151e7 q^{78} -4.12405e8 q^{79} +4.09600e7 q^{80} +4.30467e7 q^{81} -1.63052e7 q^{82} +9.57570e6 q^{83} +1.71717e8 q^{84} -2.06025e8 q^{85} +6.72462e8 q^{86} -2.84839e8 q^{87} +2.02909e8 q^{88} +7.95208e8 q^{89} -6.56100e7 q^{90} -2.36517e8 q^{91} +6.45024e8 q^{92} -7.20019e7 q^{93} -2.56574e8 q^{94} +2.26301e7 q^{95} -8.49347e7 q^{96} +1.08678e9 q^{97} -4.51573e8 q^{98} -3.25022e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 324 q^{3} + 1024 q^{4} + 2500 q^{5} - 5184 q^{6} - 2318 q^{7} - 16384 q^{8} + 26244 q^{9} - 40000 q^{10} - 10508 q^{11} + 82944 q^{12} - 114244 q^{13} + 37088 q^{14} + 202500 q^{15} + 262144 q^{16}+ \cdots - 68942988 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 324 * q^3 + 1024 * q^4 + 2500 * q^5 - 5184 * q^6 - 2318 * q^7 - 16384 * q^8 + 26244 * q^9 - 40000 * q^10 - 10508 * q^11 + 82944 * q^12 - 114244 * q^13 + 37088 * q^14 + 202500 * q^15 + 262144 * q^16 - 386792 * q^17 - 419904 * q^18 - 228476 * q^19 + 640000 * q^20 - 187758 * q^21 + 168128 * q^22 + 361088 * q^23 - 1327104 * q^24 + 1562500 * q^25 + 1827904 * q^26 + 2125764 * q^27 - 593408 * q^28 + 1053374 * q^29 - 3240000 * q^30 + 12118 * q^31 - 4194304 * q^32 - 851148 * q^33 + 6188672 * q^34 - 1448750 * q^35 + 6718464 * q^36 + 983622 * q^37 + 3655616 * q^38 - 9253764 * q^39 - 10240000 * q^40 - 5900234 * q^41 + 3004128 * q^42 - 7525148 * q^43 - 2690048 * q^44 + 16402500 * q^45 - 5777408 * q^46 + 52858086 * q^47 + 21233664 * q^48 + 54480414 * q^49 - 25000000 * q^50 - 31330152 * q^51 - 29246464 * q^52 - 39944454 * q^53 - 34012224 * q^54 - 6567500 * q^55 + 9494528 * q^56 - 18506556 * q^57 - 16853984 * q^58 - 221262654 * q^59 + 51840000 * q^60 - 301613618 * q^61 - 193888 * q^62 - 15208398 * q^63 + 67108864 * q^64 - 71402500 * q^65 + 13618368 * q^66 + 107925130 * q^67 - 99018752 * q^68 + 29248128 * q^69 + 23180000 * q^70 - 407933556 * q^71 - 107495424 * q^72 - 649353258 * q^73 - 15737952 * q^74 + 126562500 * q^75 - 58489856 * q^76 - 815342786 * q^77 + 148060224 * q^78 - 1126263686 * q^79 + 163840000 * q^80 + 172186884 * q^81 + 94403744 * q^82 - 334595286 * q^83 - 48066048 * q^84 - 241745000 * q^85 + 120402368 * q^86 + 85323294 * q^87 + 43040768 * q^88 + 110458574 * q^89 - 262440000 * q^90 + 66204398 * q^91 + 92438528 * q^92 + 981558 * q^93 - 845729376 * q^94 - 142797500 * q^95 - 339738624 * q^96 + 1740509692 * q^97 - 871686624 * q^98 - 68942988 * q^99

Introduction

L-functions

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