LMFDB - Embedded newform 10.18.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,18,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	10.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:	$18.3222087345$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{36061}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 9015 $ x^2 - x - 9015
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$95.4487$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-256.000 q^{2} -18345.8 q^{3} +65536.0 q^{4} -390625. q^{5} +4.69652e6 q^{6} +1.60786e7 q^{7} -1.67772e7 q^{8} +2.07428e8 q^{9} +1.00000e8 q^{10} +7.88217e8 q^{11} -1.20231e9 q^{12} -2.87409e9 q^{13} -4.11612e9 q^{14} +7.16632e9 q^{15} +4.29497e9 q^{16} +2.01570e10 q^{17} -5.31015e10 q^{18} -2.28657e10 q^{19} -2.56000e10 q^{20} -2.94975e11 q^{21} -2.01784e11 q^{22} -6.65718e11 q^{23} +3.07791e11 q^{24} +1.52588e11 q^{25} +7.35766e11 q^{26} -1.43625e12 q^{27} +1.05373e12 q^{28} -2.42182e12 q^{29} -1.83458e12 q^{30} +8.75874e12 q^{31} -1.09951e12 q^{32} -1.44605e13 q^{33} -5.16020e12 q^{34} -6.28070e12 q^{35} +1.35940e13 q^{36} +2.75298e13 q^{37} +5.85361e12 q^{38} +5.27274e13 q^{39} +6.55360e12 q^{40} +3.91759e13 q^{41} +7.55135e13 q^{42} -1.29981e14 q^{43} +5.16566e13 q^{44} -8.10265e13 q^{45} +1.70424e14 q^{46} -3.00620e14 q^{47} -7.87946e13 q^{48} +2.58908e13 q^{49} -3.90625e13 q^{50} -3.69796e14 q^{51} -1.88356e14 q^{52} +1.01926e14 q^{53} +3.67679e14 q^{54} -3.07897e14 q^{55} -2.69754e14 q^{56} +4.19488e14 q^{57} +6.19987e14 q^{58} -9.67154e14 q^{59} +4.69652e14 q^{60} -1.14011e15 q^{61} -2.24224e15 q^{62} +3.33515e15 q^{63} +2.81475e14 q^{64} +1.12269e15 q^{65} +3.70188e15 q^{66} -4.04577e15 q^{67} +1.32101e15 q^{68} +1.22131e16 q^{69} +1.60786e15 q^{70} -7.35604e15 q^{71} -3.48006e15 q^{72} +6.99946e14 q^{73} -7.04762e15 q^{74} -2.79934e15 q^{75} -1.49852e15 q^{76} +1.26734e16 q^{77} -1.34982e16 q^{78} +1.08787e16 q^{79} -1.67772e15 q^{80} -4.38165e14 q^{81} -1.00290e16 q^{82} -1.23277e16 q^{83} -1.93315e16 q^{84} -7.87384e15 q^{85} +3.32752e16 q^{86} +4.44303e16 q^{87} -1.32241e16 q^{88} -2.21332e16 q^{89} +2.07428e16 q^{90} -4.62113e16 q^{91} -4.36285e16 q^{92} -1.60686e17 q^{93} +7.69588e16 q^{94} +8.93190e15 q^{95} +2.01714e16 q^{96} +9.41354e16 q^{97} -6.62805e15 q^{98} +1.63498e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 512 q^{2} - 6308 q^{3} + 131072 q^{4} - 781250 q^{5} + 1614848 q^{6} + 6543844 q^{7} - 33554432 q^{8} + 223195906 q^{9} + 200000000 q^{10} + 1189408704 q^{11} - 413401088 q^{12} - 2017919228 q^{13}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 512 * q^2 - 6308 * q^3 + 131072 * q^4 - 781250 * q^5 + 1614848 * q^6 + 6543844 * q^7 - 33554432 * q^8 + 223195906 * q^9 + 200000000 * q^10 + 1189408704 * q^11 - 413401088 * q^12 - 2017919228 * q^13 - 1675224064 * q^14 + 2464062500 * q^15 + 8589934592 * q^16 - 18755639436 * q^17 - 57138151936 * q^18 - 136704830600 * q^19 - 51200000000 * q^20 - 409751898376 * q^21 - 304488628224 * q^22 - 649234170708 * q^23 + 105830678528 * q^24 + 305175781250 * q^25 + 516587322368 * q^26 - 2800995425720 * q^27 + 428857360384 * q^28 - 4696543420020 * q^29 - 630800000000 * q^30 + 7120867378744 * q^31 - 2199023255552 * q^32 - 9631011282816 * q^33 + 4801443695616 * q^34 - 2556189062500 * q^35 + 14627366895616 * q^36 + 9933114637444 * q^37 + 34996436633600 * q^38 + 63033715222712 * q^39 + 13107200000000 * q^40 + 9622711880844 * q^41 + 104896485984256 * q^42 + 7708436011852 * q^43 + 77949088825344 * q^44 - 87185900781250 * q^45 + 166203947701248 * q^46 - 466072575837996 * q^47 - 27092653703168 * q^48 - 115828146887046 * q^49 - 78125000000000 * q^50 - 838218717084456 * q^51 - 132246354526208 * q^52 - 623333120284428 * q^53 + 717054828984320 * q^54 - 464612775000000 * q^55 - 109787484258304 * q^56 - 950883425062000 * q^57 + 1202315115525120 * q^58 + 654616071995160 * q^59 + 161484800000000 * q^60 + 1329040385162884 * q^61 - 1822942048958464 * q^62 + 3184801966786532 * q^63 + 562949953421312 * q^64 + 788249698437500 * q^65 + 2465538888400896 * q^66 - 4249016411877596 * q^67 - 1229169586077696 * q^68 + 12411535659353832 * q^69 + 654384400000000 * q^70 + 2035131949347624 * q^71 - 3744605925277696 * q^72 + 2248593461347972 * q^73 - 2542877347185664 * q^74 - 962524414062500 * q^75 - 8959087778201600 * q^76 + 8848168987836288 * q^77 - 16136631097014272 * q^78 + 19188427678495120 * q^79 - 3355443200000000 * q^80 - 18903014015714198 * q^81 - 2463414241496064 * q^82 - 18474649086611988 * q^83 - 26853500411969536 * q^84 + 7326421654687500 * q^85 - 1973359619034112 * q^86 + 17047661699498280 * q^87 - 19954966739288064 * q^88 - 17458912916395020 * q^89 + 22319590600000000 * q^90 - 54374608211433016 * q^91 - 42548210611519488 * q^92 - 180402465813627376 * q^93 + 119314579414526976 * q^94 + 53400324453125000 * q^95 + 6935719348011008 * q^96 + 195934325822490244 * q^97 + 29652005603083776 * q^98 + 169824195828146112 * 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 $

$2$	−256.000	−0.707107
$2$	−256.000	−0.707107
$3$	−18345.8	−1.61438	−0.807190	−	0.590292i	$-0.799013\pi$
$3$	−18345.8	−1.61438	−0.807190	+	0.590292i	$0.799013\pi$
$4$	65536.0	0.500000
$5$	−390625.	−0.447214
$5$	−390625.	−0.447214
$6$	4.69652e6	1.14154
$7$	1.60786e7	1.05418	0.527090	−	0.849809i	$-0.323283\pi$
$7$	1.60786e7	1.05418	0.527090	+	0.849809i	$0.323283\pi$
$8$	−1.67772e7	−0.353553
$9$	2.07428e8	1.60622
$10$	1.00000e8	0.316228
$11$	7.88217e8	1.10868	0.554342	−	0.832289i	$-0.312970\pi$
$11$	7.88217e8	1.10868	0.554342	+	0.832289i	$0.312970\pi$
$12$	−1.20231e9	−0.807190
$13$	−2.87409e9	−0.977195	−0.488597	−	0.872509i	$-0.662491\pi$
$13$	−2.87409e9	−0.977195	−0.488597	+	0.872509i	$0.662491\pi$
$14$	−4.11612e9	−0.745418
$15$	7.16632e9	0.721973
$16$	4.29497e9	0.250000
$17$	2.01570e10	0.700826	0.350413	−	0.936595i	$-0.386041\pi$
$17$	2.01570e10	0.700826	0.350413	+	0.936595i	$0.386041\pi$
$18$	−5.31015e10	−1.13577
$19$	−2.28657e10	−0.308872	−0.154436	−	0.988003i	$-0.549356\pi$
$19$	−2.28657e10	−0.308872	−0.154436	+	0.988003i	$0.549356\pi$
$20$	−2.56000e10	−0.223607
$21$	−2.94975e11	−1.70185
$22$	−2.01784e11	−0.783959
$23$	−6.65718e11	−1.77257	−0.886285	−	0.463140i	$-0.846723\pi$
$23$	−6.65718e11	−1.77257	−0.886285	+	0.463140i	$0.846723\pi$
$24$	3.07791e11	0.570769
$25$	1.52588e11	0.200000
$26$	7.35766e11	0.690981
$27$	−1.43625e12	−0.978672
$28$	1.05373e12	0.527090
$29$	−2.42182e12	−0.899000	−0.449500	−	0.893280i	$-0.648398\pi$
$29$	−2.42182e12	−0.899000	−0.449500	+	0.893280i	$0.648398\pi$
$30$	−1.83458e12	−0.510512
$31$	8.75874e12	1.84445	0.922226	−	0.386651i	$-0.126368\pi$
$31$	8.75874e12	1.84445	0.922226	+	0.386651i	$0.126368\pi$
$32$	−1.09951e12	−0.176777
$33$	−1.44605e13	−1.78984
$34$	−5.16020e12	−0.495559
$35$	−6.28070e12	−0.471444
$36$	1.35940e13	0.803111
$37$	2.75298e13	1.28851	0.644255	−	0.764810i	$-0.277167\pi$
$37$	2.75298e13	1.28851	0.644255	+	0.764810i	$0.277167\pi$
$38$	5.85361e12	0.218405
$39$	5.27274e13	1.57756
$40$	6.55360e12	0.158114
$41$	3.91759e13	0.766225	0.383112	−	0.923702i	$-0.374852\pi$
$41$	3.91759e13	0.766225	0.383112	+	0.923702i	$0.374852\pi$
$42$	7.55135e13	1.20339
$43$	−1.29981e14	−1.69589	−0.847947	−	0.530082i	$-0.822161\pi$
$43$	−1.29981e14	−1.69589	−0.847947	+	0.530082i	$0.822161\pi$
$44$	5.16566e13	0.554342
$45$	−8.10265e13	−0.718324
$46$	1.70424e14	1.25340
$47$	−3.00620e14	−1.84156	−0.920781	−	0.390079i	$-0.872448\pi$
$47$	−3.00620e14	−1.84156	−0.920781	+	0.390079i	$0.872448\pi$
$48$	−7.87946e13	−0.403595
$49$	2.58908e13	0.111296
$50$	−3.90625e13	−0.141421
$51$	−3.69796e14	−1.13140
$52$	−1.88356e14	−0.488597
$53$	1.01926e14	0.224874	0.112437	−	0.993659i	$-0.464134\pi$
$53$	1.01926e14	0.224874	0.112437	+	0.993659i	$0.464134\pi$
$54$	3.67679e14	0.692026
$55$	−3.07897e14	−0.495819
$56$	−2.69754e14	−0.372709
$57$	4.19488e14	0.498636
$58$	6.19987e14	0.635689
$59$	−9.67154e14	−0.857538	−0.428769	−	0.903414i	$-0.641053\pi$
$59$	−9.67154e14	−0.857538	−0.428769	+	0.903414i	$0.641053\pi$
$60$	4.69652e14	0.360986
$61$	−1.14011e15	−0.761455	−0.380727	−	0.924687i	$-0.624326\pi$
$61$	−1.14011e15	−0.761455	−0.380727	+	0.924687i	$0.624326\pi$
$62$	−2.24224e15	−1.30422
$63$	3.33515e15	1.69325
$64$	2.81475e14	0.125000
$65$	1.12269e15	0.437015
$66$	3.70188e15	1.26561
$67$	−4.04577e15	−1.21721	−0.608605	−	0.793473i	$-0.708271\pi$
$67$	−4.04577e15	−1.21721	−0.608605	+	0.793473i	$0.708271\pi$
$68$	1.32101e15	0.350413
$69$	1.22131e16	2.86160
$70$	1.60786e15	0.333361
$71$	−7.35604e15	−1.35191	−0.675955	−	0.736943i	$-0.736269\pi$
$71$	−7.35604e15	−1.35191	−0.675955	+	0.736943i	$0.736269\pi$
$72$	−3.48006e15	−0.567885
$73$	6.99946e14	0.101583	0.0507914	−	0.998709i	$-0.483826\pi$
$73$	6.99946e14	0.101583	0.0507914	+	0.998709i	$0.483826\pi$
$74$	−7.04762e15	−0.911115
$75$	−2.79934e15	−0.322876
$76$	−1.49852e15	−0.154436
$77$	1.26734e16	1.16875
$78$	−1.34982e16	−1.11551
$79$	1.08787e16	0.806761	0.403381	−	0.915032i	$-0.367835\pi$
$79$	1.08787e16	0.806761	0.403381	+	0.915032i	$0.367835\pi$
$80$	−1.67772e15	−0.111803
$81$	−4.38165e14	−0.0262733
$82$	−1.00290e16	−0.541803
$83$	−1.23277e16	−0.600783	−0.300391	−	0.953816i	$-0.597117\pi$
$83$	−1.23277e16	−0.600783	−0.300391	+	0.953816i	$0.597117\pi$
$84$	−1.93315e16	−0.850924
$85$	−7.87384e15	−0.313419
$86$	3.32752e16	1.19918
$87$	4.44303e16	1.45133
$88$	−1.32241e16	−0.391979
$89$	−2.21332e16	−0.595976	−0.297988	−	0.954570i	$-0.596316\pi$
$89$	−2.21332e16	−0.595976	−0.297988	+	0.954570i	$0.596316\pi$
$90$	2.07428e16	0.507932
$91$	−4.62113e16	−1.03014
$92$	−4.36285e16	−0.886285
$93$	−1.60686e17	−2.97765
$94$	7.69588e16	1.30218
$95$	8.93190e15	0.138132
$96$	2.01714e16	0.285385
$97$	9.41354e16	1.21953	0.609766	−	0.792581i	$-0.291263\pi$
$97$	9.41354e16	1.21953	0.609766	+	0.792581i	$0.291263\pi$
$98$	−6.62805e15	−0.0786981
$99$	1.63498e17	1.78079
$100$	1.00000e16	0.100000
$101$	3.77746e16	0.347111	0.173556	−	0.984824i	$-0.444474\pi$
$101$	3.77746e16	0.347111	0.173556	+	0.984824i	$0.444474\pi$
$102$	9.46679e16	0.800021
$103$	1.63051e17	1.26826	0.634130	−	0.773226i	$-0.281358\pi$
$103$	1.63051e17	1.26826	0.634130	+	0.773226i	$0.281358\pi$
$104$	4.82192e16	0.345491
$105$	1.15224e17	0.761089
$106$	−2.60930e16	−0.159010
$107$	−2.33848e17	−1.31574	−0.657871	−	0.753131i	$-0.728543\pi$
$107$	−2.33848e17	−1.31574	−0.657871	+	0.753131i	$0.728543\pi$
$108$	−9.41259e16	−0.489336
$109$	−4.47257e16	−0.214997	−0.107498	−	0.994205i	$-0.534284\pi$
$109$	−4.47257e16	−0.214997	−0.107498	+	0.994205i	$0.534284\pi$
$110$	7.88217e16	0.350597
$111$	−5.05055e17	−2.08015
$112$	6.90571e16	0.263545
$113$	−2.41764e17	−0.855510	−0.427755	−	0.903895i	$-0.640695\pi$
$113$	−2.41764e17	−0.855510	−0.427755	+	0.903895i	$0.640695\pi$
$114$	−1.07389e17	−0.352589
$115$	2.60046e17	0.792717
$116$	−1.58717e17	−0.449500
$117$	−5.96165e17	−1.56959
$118$	2.47591e17	0.606371
$119$	3.24097e17	0.738797
$120$	−1.20231e17	−0.255256
$121$	1.15840e17	0.229182
$122$	2.91869e17	0.538430
$123$	−7.18713e17	−1.23698
$124$	5.74013e17	0.922226
$125$	−5.96046e16	−0.0894427
$126$	−8.53798e17	−1.19731
$127$	1.14453e17	0.150070	0.0750352	−	0.997181i	$-0.476093\pi$
$127$	1.14453e17	0.150070	0.0750352	+	0.997181i	$0.476093\pi$
$128$	−7.20576e16	−0.0883883
$129$	2.38461e18	2.73782
$130$	−2.87409e17	−0.309016
$131$	4.93656e16	0.0497300	0.0248650	−	0.999691i	$-0.492084\pi$
$131$	4.93656e16	0.0497300	0.0248650	+	0.999691i	$0.492084\pi$
$132$	−9.47681e17	−0.894919
$133$	−3.67648e17	−0.325606
$134$	1.03572e18	0.860698
$135$	5.61034e17	0.437676
$136$	−3.38179e17	−0.247780
$137$	−4.16706e17	−0.286883	−0.143442	−	0.989659i	$-0.545817\pi$
$137$	−4.16706e17	−0.286883	−0.143442	+	0.989659i	$0.545817\pi$
$138$	−3.12656e18	−2.02346
$139$	5.01647e17	0.305332	0.152666	−	0.988278i	$-0.451214\pi$
$139$	5.01647e17	0.305332	0.152666	+	0.988278i	$0.451214\pi$
$140$	−4.11612e17	−0.235722
$141$	5.51512e18	2.97298
$142$	1.88315e18	0.955945
$143$	−2.26540e18	−1.08340
$144$	8.90895e17	0.401555
$145$	9.46025e17	0.402045
$146$	−1.79186e17	−0.0718298
$147$	−4.74987e17	−0.179674
$148$	1.80419e18	0.644255
$149$	−1.16146e18	−0.391670	−0.195835	−	0.980637i	$-0.562742\pi$
$149$	−1.16146e18	−0.391670	−0.195835	+	0.980637i	$0.562742\pi$
$150$	7.16632e17	0.228308
$151$	−5.58219e18	−1.68074	−0.840371	−	0.542012i	$-0.817663\pi$
$151$	−5.58219e18	−1.68074	−0.840371	+	0.542012i	$0.817663\pi$
$152$	3.83622e17	0.109203
$153$	4.18113e18	1.12568
$154$	−3.24440e18	−0.826434
$155$	−3.42138e18	−0.824864
$156$	3.45554e18	0.788782
$157$	−2.25949e18	−0.488499	−0.244249	−	0.969712i	$-0.578542\pi$
$157$	−2.25949e18	−0.488499	−0.244249	+	0.969712i	$0.578542\pi$
$158$	−2.78494e18	−0.570466
$159$	−1.86991e18	−0.363033
$160$	4.29497e17	0.0790569
$161$	−1.07038e19	−1.86861
$162$	1.12170e17	0.0185780
$163$	−2.17080e18	−0.341212	−0.170606	−	0.985339i	$-0.554573\pi$
$163$	−2.17080e18	−0.341212	−0.170606	+	0.985339i	$0.554573\pi$
$164$	2.56743e18	0.383112
$165$	5.64862e18	0.800440
$166$	3.15589e18	0.424818
$167$	2.02306e18	0.258772	0.129386	−	0.991594i	$-0.458699\pi$
$167$	2.02306e18	0.258772	0.129386	+	0.991594i	$0.458699\pi$
$168$	4.94885e18	0.601694
$169$	−3.90047e17	−0.0450900
$170$	2.01570e18	0.221621
$171$	−4.74297e18	−0.496116
$172$	−8.51844e18	−0.847947
$173$	1.22669e19	1.16237	0.581183	−	0.813773i	$-0.302590\pi$
$173$	1.22669e19	1.16237	0.581183	+	0.813773i	$0.302590\pi$
$174$	−1.13741e19	−1.02624
$175$	2.45340e18	0.210836
$176$	3.38537e18	0.277171
$177$	1.77432e19	1.38439
$178$	5.66610e18	0.421419
$179$	−1.77359e19	−1.25778	−0.628888	−	0.777496i	$-0.716490\pi$
$179$	−1.77359e19	−1.25778	−0.628888	+	0.777496i	$0.716490\pi$
$180$	−5.31015e18	−0.359162
$181$	−1.40303e19	−0.905315	−0.452657	−	0.891684i	$-0.649524\pi$
$181$	−1.40303e19	−0.905315	−0.452657	+	0.891684i	$0.649524\pi$
$182$	1.18301e19	0.728419
$183$	2.09163e19	1.22928
$184$	1.11689e19	0.626698
$185$	−1.07538e19	−0.576239
$186$	4.11356e19	2.10551
$187$	1.58881e19	0.776996
$188$	−1.97015e19	−0.920781
$189$	−2.30928e19	−1.03170
$190$	−2.28657e18	−0.0976738
$191$	1.22487e19	0.500387	0.250194	−	0.968196i	$-0.419506\pi$
$191$	1.22487e19	0.500387	0.250194	+	0.968196i	$0.419506\pi$
$192$	−5.16388e18	−0.201797
$193$	3.98799e19	1.49114	0.745568	−	0.666430i	$-0.232179\pi$
$193$	3.98799e19	1.49114	0.745568	+	0.666430i	$0.232179\pi$
$194$	−2.40987e19	−0.862340
$195$	−2.05966e19	−0.705508
$196$	1.69678e18	0.0556479
$197$	−1.32923e19	−0.417481	−0.208740	−	0.977971i	$-0.566936\pi$
$197$	−1.32923e19	−0.417481	−0.208740	+	0.977971i	$0.566936\pi$
$198$	−4.18555e19	−1.25921
$199$	6.95301e18	0.200411	0.100206	−	0.994967i	$-0.468050\pi$
$199$	6.95301e18	0.200411	0.100206	+	0.994967i	$0.468050\pi$
$200$	−2.56000e18	−0.0707107
$201$	7.42229e19	1.96504
$202$	−9.67031e18	−0.245445
$203$	−3.89395e19	−0.947708
$204$	−2.42350e19	−0.565700
$205$	−1.53031e19	−0.342666
$206$	−4.17412e19	−0.896795
$207$	−1.38088e20	−2.84714
$208$	−1.23441e19	−0.244299
$209$	−1.80231e19	−0.342441
$210$	−2.94975e19	−0.538171
$211$	−1.70414e19	−0.298611	−0.149305	−	0.988791i	$-0.547704\pi$
$211$	−1.70414e19	−0.298611	−0.149305	+	0.988791i	$0.547704\pi$
$212$	6.67982e18	0.112437
$213$	1.34952e20	2.18250
$214$	5.98650e19	0.930370
$215$	5.07739e19	0.758426
$216$	2.40962e19	0.346013
$217$	1.40828e20	1.94439
$218$	1.14498e19	0.152026
$219$	−1.28411e19	−0.163993
$220$	−2.01784e19	−0.247909
$221$	−5.79330e19	−0.684844
$222$	1.29294e20	1.47088
$223$	2.89177e19	0.316645	0.158322	−	0.987387i	$-0.449391\pi$
$223$	2.89177e19	0.316645	0.158322	+	0.987387i	$0.449391\pi$
$224$	−1.76786e19	−0.186354
$225$	3.16510e19	0.321244
$226$	6.18916e19	0.604937
$227$	−1.32244e20	−1.24496	−0.622481	−	0.782635i	$-0.713875\pi$
$227$	−1.32244e20	−1.24496	−0.622481	+	0.782635i	$0.713875\pi$
$228$	2.74916e19	0.249318
$229$	−1.21349e19	−0.106031	−0.0530157	−	0.998594i	$-0.516883\pi$
$229$	−1.21349e19	−0.106031	−0.0530157	+	0.998594i	$0.516883\pi$
$230$	−6.65718e19	−0.560536
$231$	−2.32504e20	−1.88681
$232$	4.06315e19	0.317844
$233$	1.12741e20	0.850271	0.425135	−	0.905130i	$-0.360227\pi$
$233$	1.12741e20	0.850271	0.425135	+	0.905130i	$0.360227\pi$
$234$	1.52618e20	1.10987
$235$	1.17430e20	0.823572
$236$	−6.33834e19	−0.428769
$237$	−1.99578e20	−1.30242
$238$	−8.29687e19	−0.522409
$239$	−1.64296e20	−0.998261	−0.499131	−	0.866527i	$-0.666347\pi$
$239$	−1.64296e20	−0.998261	−0.499131	+	0.866527i	$0.666347\pi$
$240$	3.07791e19	0.180493
$241$	1.25647e20	0.711223	0.355612	−	0.934634i	$-0.384273\pi$
$241$	1.25647e20	0.711223	0.355612	+	0.934634i	$0.384273\pi$
$242$	−2.96549e19	−0.162056
$243$	1.93516e20	1.02109
$244$	−7.47184e19	−0.380727
$245$	−1.01136e19	−0.0497730
$246$	1.83990e20	0.874675
$247$	6.57178e19	0.301828
$248$	−1.46947e20	−0.652112
$249$	2.26161e20	0.969892
$250$	1.52588e19	0.0632456
$251$	−1.37960e20	−0.552746	−0.276373	−	0.961050i	$-0.589133\pi$
$251$	−1.37960e20	−0.552746	−0.276373	+	0.961050i	$0.589133\pi$
$252$	2.18572e20	0.846624
$253$	−5.24730e20	−1.96522
$254$	−2.92999e19	−0.106116
$255$	1.44452e20	0.505977
$256$	1.84467e19	0.0625000
$257$	−1.08129e19	−0.0354414	−0.0177207	−	0.999843i	$-0.505641\pi$
$257$	−1.08129e19	−0.0354414	−0.0177207	+	0.999843i	$0.505641\pi$
$258$	−6.10459e20	−1.93593
$259$	4.42640e20	1.35832
$260$	7.35766e19	0.218507
$261$	−5.02353e20	−1.44399
$262$	−1.26376e19	−0.0351644
$263$	−7.17651e20	−1.93326	−0.966628	−	0.256185i	$-0.917534\pi$
$263$	−7.17651e20	−1.93326	−0.966628	+	0.256185i	$0.917534\pi$
$264$	2.42606e20	0.632803
$265$	−3.98148e19	−0.100567
$266$	9.41178e19	0.230238
$267$	4.06051e20	0.962132
$268$	−2.65144e20	−0.608605
$269$	−5.80280e20	−1.29046	−0.645228	−	0.763990i	$-0.723238\pi$
$269$	−5.80280e20	−1.29046	−0.645228	+	0.763990i	$0.723238\pi$
$270$	−1.43625e20	−0.309483
$271$	1.64836e20	0.344201	0.172101	−	0.985079i	$-0.444945\pi$
$271$	1.64836e20	0.344201	0.172101	+	0.985079i	$0.444945\pi$
$272$	8.65737e19	0.175207
$273$	8.47782e20	1.66304
$274$	1.06677e20	0.202857
$275$	1.20272e20	0.221737
$276$	8.00399e20	1.43080
$277$	1.52391e20	0.264168	0.132084	−	0.991239i	$-0.457833\pi$
$277$	1.52391e20	0.264168	0.132084	+	0.991239i	$0.457833\pi$
$278$	−1.28422e20	−0.215902
$279$	1.81681e21	2.96260
$280$	1.05373e20	0.166681
$281$	1.60032e20	0.245586	0.122793	−	0.992432i	$-0.460815\pi$
$281$	1.60032e20	0.245586	0.122793	+	0.992432i	$0.460815\pi$
$282$	−1.41187e21	−2.10222
$283$	2.34430e20	0.338711	0.169356	−	0.985555i	$-0.445831\pi$
$283$	2.34430e20	0.338711	0.169356	+	0.985555i	$0.445831\pi$
$284$	−4.82085e20	−0.675955
$285$	−1.63863e20	−0.222997
$286$	5.79943e20	0.766080
$287$	6.29894e20	0.807739
$288$	−2.28069e20	−0.283943
$289$	−4.20935e20	−0.508842
$290$	−2.42182e20	−0.284289
$291$	−1.72699e21	−1.96879
$292$	4.58716e19	0.0507914
$293$	1.57885e21	1.69811	0.849056	−	0.528303i	$-0.177172\pi$
$293$	1.57885e21	1.69811	0.849056	+	0.528303i	$0.177172\pi$
$294$	1.21597e20	0.127049
$295$	3.77795e20	0.383503
$296$	−4.61873e20	−0.455557
$297$	−1.13208e21	−1.08504
$298$	2.97333e20	0.276952
$299$	1.91333e21	1.73215
$300$	−1.83458e20	−0.161438
$301$	−2.08991e21	−1.78778
$302$	1.42904e21	1.18846
$303$	−6.93005e20	−0.560369
$304$	−9.82072e19	−0.0772179
$305$	4.45356e20	0.340533
$306$	−1.07037e21	−0.795978
$307$	−2.38391e21	−1.72430	−0.862152	−	0.506650i	$-0.830884\pi$
$307$	−2.38391e21	−1.72430	−0.862152	+	0.506650i	$0.830884\pi$
$308$	8.30566e20	0.584377
$309$	−2.99131e21	−2.04745
$310$	8.75874e20	0.583267
$311$	1.58302e21	1.02570	0.512852	−	0.858477i	$-0.328589\pi$
$311$	1.58302e21	1.02570	0.512852	+	0.858477i	$0.328589\pi$
$312$	−8.84618e20	−0.557753
$313$	−2.98369e20	−0.183074	−0.0915370	−	0.995802i	$-0.529178\pi$
$313$	−2.98369e20	−0.183074	−0.0915370	+	0.995802i	$0.529178\pi$
$314$	5.78430e20	0.345421
$315$	−1.30279e21	−0.757243
$316$	7.12944e20	0.403381
$317$	−1.01873e21	−0.561117	−0.280559	−	0.959837i	$-0.590520\pi$
$317$	−1.01873e21	−0.561117	−0.280559	+	0.959837i	$0.590520\pi$
$318$	4.78697e20	0.256703
$319$	−1.90892e21	−0.996707
$320$	−1.09951e20	−0.0559017
$321$	4.29012e21	2.12411
$322$	2.74017e21	1.32131
$323$	−4.60903e20	−0.216465
$324$	−2.87156e19	−0.0131366
$325$	−4.38551e20	−0.195439
$326$	5.55724e20	0.241273
$327$	8.20527e20	0.347086
$328$	−6.57263e20	−0.270901
$329$	−4.83355e21	−1.94134
$330$	−1.44605e21	−0.565997
$331$	−6.27305e20	−0.239299	−0.119649	−	0.992816i	$-0.538177\pi$
$331$	−6.27305e20	−0.239299	−0.119649	+	0.992816i	$0.538177\pi$
$332$	−8.07907e20	−0.300391
$333$	5.71044e21	2.06963
$334$	−5.17903e20	−0.182980
$335$	1.58038e21	0.544353
$336$	−1.26691e21	−0.425462
$337$	3.61857e21	1.18490	0.592451	−	0.805606i	$-0.298160\pi$
$337$	3.61857e21	1.18490	0.592451	+	0.805606i	$0.298160\pi$
$338$	9.98521e19	0.0318834
$339$	4.43535e21	1.38112
$340$	−5.16020e20	−0.156710
$341$	6.90379e21	2.04492
$342$	1.21420e21	0.350807
$343$	−3.32408e21	−0.936854
$344$	2.18072e21	0.599589
$345$	−4.77075e21	−1.27975
$346$	−3.14033e21	−0.821917
$347$	7.74896e21	1.97899	0.989493	−	0.144579i	$-0.0461827\pi$
$347$	7.74896e21	1.97899	0.989493	+	0.144579i	$0.0461827\pi$
$348$	2.91178e21	0.725663
$349$	−7.13117e21	−1.73438	−0.867191	−	0.497976i	$-0.834077\pi$
$349$	−7.13117e21	−1.73438	−0.867191	+	0.497976i	$0.834077\pi$
$350$	−6.28070e20	−0.149084
$351$	4.12790e21	0.956354
$352$	−8.66654e20	−0.195990
$353$	−7.70298e21	−1.70049	−0.850244	−	0.526388i	$-0.823546\pi$
$353$	−7.70298e21	−1.70049	−0.850244	+	0.526388i	$0.823546\pi$
$354$	−4.54226e21	−0.978913
$355$	2.87345e21	0.604593
$356$	−1.45052e21	−0.297988
$357$	−5.94581e21	−1.19270
$358$	4.54040e21	0.889382
$359$	−4.55697e21	−0.871712	−0.435856	−	0.900016i	$-0.643554\pi$
$359$	−4.55697e21	−0.871712	−0.435856	+	0.900016i	$0.643554\pi$
$360$	1.35940e21	0.253966
$361$	−4.95755e21	−0.904598
$362$	3.59176e21	0.640154
$363$	−2.12517e21	−0.369987
$364$	−3.02850e21	−0.515070
$365$	−2.73416e20	−0.0454292
$366$	−5.35456e21	−0.869230
$367$	−6.69643e19	−0.0106214	−0.00531070	−	0.999986i	$-0.501690\pi$
$367$	−6.69643e19	−0.0106214	−0.00531070	+	0.999986i	$0.501690\pi$
$368$	−2.85924e21	−0.443142
$369$	8.12617e21	1.23073
$370$	2.75298e21	0.407463
$371$	1.63883e21	0.237058
$372$	−1.05307e22	−1.48882
$373$	5.61068e21	0.775336	0.387668	−	0.921799i	$-0.373281\pi$
$373$	5.61068e21	0.775336	0.387668	+	0.921799i	$0.373281\pi$
$374$	−4.06736e21	−0.549419
$375$	1.09349e21	0.144395
$376$	5.04357e21	0.651091
$377$	6.96053e21	0.878498
$378$	5.91177e21	0.729520
$379$	6.43379e21	0.776307	0.388153	−	0.921595i	$-0.373113\pi$
$379$	6.43379e21	0.776307	0.388153	+	0.921595i	$0.373113\pi$
$380$	5.85361e20	0.0690658
$381$	−2.09973e21	−0.242271
$382$	−3.13567e21	−0.353827
$383$	1.11213e22	1.22735	0.613674	−	0.789560i	$-0.289691\pi$
$383$	1.11213e22	1.22735	0.613674	+	0.789560i	$0.289691\pi$
$384$	1.32195e21	0.142692
$385$	−4.95056e21	−0.522683
$386$	−1.02093e22	−1.05439
$387$	−2.69617e22	−2.72398
$388$	6.16926e21	0.609766
$389$	6.91791e21	0.668965	0.334483	−	0.942402i	$-0.391438\pi$
$389$	6.91791e21	0.668965	0.334483	+	0.942402i	$0.391438\pi$
$390$	5.27274e21	0.498869
$391$	−1.34189e22	−1.24226
$392$	−4.34376e20	−0.0393490
$393$	−9.05651e20	−0.0802831
$394$	3.40282e21	0.295204
$395$	−4.24948e21	−0.360795
$396$	1.07150e22	0.890397
$397$	2.17800e22	1.77149	0.885746	−	0.464171i	$-0.153648\pi$
$397$	2.17800e22	1.77149	0.885746	+	0.464171i	$0.153648\pi$
$398$	−1.77997e21	−0.141712
$399$	6.74479e21	0.525652
$400$	6.55360e20	0.0500000
$401$	4.05717e21	0.303037	0.151519	−	0.988454i	$-0.451584\pi$
$401$	4.05717e21	0.303037	0.151519	+	0.988454i	$0.451584\pi$
$402$	−1.90011e22	−1.38949
$403$	−2.51734e22	−1.80239
$404$	2.47560e21	0.173556
$405$	1.71158e20	0.0117498
$406$	9.96852e21	0.670130
$407$	2.16994e22	1.42855
$408$	6.20415e21	0.400010
$409$	−6.48833e21	−0.409717	−0.204859	−	0.978792i	$-0.565673\pi$
$409$	−6.48833e21	−0.409717	−0.204859	+	0.978792i	$0.565673\pi$
$410$	3.91759e21	0.242302
$411$	7.64480e21	0.463138
$412$	1.06857e22	0.634130
$413$	−1.55505e22	−0.904000
$414$	3.53506e22	2.01323
$415$	4.81550e21	0.268678
$416$	3.16009e21	0.172745
$417$	−9.20310e21	−0.492922
$418$	4.61391e21	0.242143
$419$	2.17453e22	1.11827	0.559135	−	0.829077i	$-0.311133\pi$
$419$	2.17453e22	1.11827	0.559135	+	0.829077i	$0.311133\pi$
$420$	7.55135e21	0.380545
$421$	1.45920e22	0.720638	0.360319	−	0.932829i	$-0.382668\pi$
$421$	1.45920e22	0.720638	0.360319	+	0.932829i	$0.382668\pi$
$422$	4.36261e21	0.211150
$423$	−6.23570e22	−2.95796
$424$	−1.71003e21	−0.0795051
$425$	3.07572e21	0.140165
$426$	−3.45478e22	−1.54326
$427$	−1.83314e22	−0.802710
$428$	−1.53254e22	−0.657871
$429$	4.15606e22	1.74902
$430$	−1.29981e22	−0.536288
$431$	−2.61293e22	−1.05699	−0.528495	−	0.848937i	$-0.677243\pi$
$431$	−2.61293e22	−1.05699	−0.528495	+	0.848937i	$0.677243\pi$
$432$	−6.16864e21	−0.244668
$433$	−1.27697e22	−0.496632	−0.248316	−	0.968679i	$-0.579877\pi$
$433$	−1.27697e22	−0.496632	−0.248316	+	0.968679i	$0.579877\pi$
$434$	−3.60521e22	−1.37489
$435$	−1.73556e22	−0.649053
$436$	−2.93114e21	−0.107498
$437$	1.52221e22	0.547497
$438$	3.28731e21	0.115961
$439$	−2.83409e22	−0.980540	−0.490270	−	0.871571i	$-0.663102\pi$
$439$	−2.83409e22	−0.980540	−0.490270	+	0.871571i	$0.663102\pi$
$440$	5.16566e21	0.175298
$441$	5.37047e21	0.178766
$442$	1.48308e22	0.484258
$443$	−1.45222e22	−0.465158	−0.232579	−	0.972578i	$-0.574716\pi$
$443$	−1.45222e22	−0.465158	−0.232579	+	0.972578i	$0.574716\pi$
$444$	−3.30993e22	−1.04007
$445$	8.64578e21	0.266529
$446$	−7.40293e21	−0.223902
$447$	2.13078e22	0.632303
$448$	4.52572e21	0.131773
$449$	1.38898e22	0.396828	0.198414	−	0.980118i	$-0.436421\pi$
$449$	1.38898e22	0.396828	0.198414	+	0.980118i	$0.436421\pi$
$450$	−8.10265e21	−0.227154
$451$	3.08791e22	0.849502
$452$	−1.58443e22	−0.427755
$453$	1.02410e23	2.71335
$454$	3.38544e22	0.880321
$455$	1.80513e22	0.460692
$456$	−7.03785e21	−0.176294
$457$	−3.72555e22	−0.916016	−0.458008	−	0.888948i	$-0.651437\pi$
$457$	−3.72555e22	−0.916016	−0.458008	+	0.888948i	$0.651437\pi$
$458$	3.10653e21	0.0749755
$459$	−2.89505e22	−0.685879
$460$	1.70424e22	0.396359
$461$	1.60242e22	0.365864	0.182932	−	0.983126i	$-0.441441\pi$
$461$	1.60242e22	0.365864	0.182932	+	0.983126i	$0.441441\pi$
$462$	5.95210e22	1.33418
$463$	6.01797e22	1.32438	0.662189	−	0.749337i	$-0.269628\pi$
$463$	6.01797e22	1.32438	0.662189	+	0.749337i	$0.269628\pi$
$464$	−1.04017e22	−0.224750
$465$	6.27680e22	1.33164
$466$	−2.88617e22	−0.601232
$467$	−4.21105e22	−0.861384	−0.430692	−	0.902499i	$-0.641730\pi$
$467$	−4.21105e22	−0.861384	−0.430692	+	0.902499i	$0.641730\pi$
$468$	−3.90703e22	−0.784796
$469$	−6.50504e22	−1.28316
$470$	−3.00620e22	−0.582353
$471$	4.14521e22	0.788622
$472$	1.62262e22	0.303186
$473$	−1.02453e23	−1.88021
$474$	5.10919e22	0.920949
$475$	−3.48902e21	−0.0617743
$476$	2.12400e22	0.369399
$477$	2.11423e22	0.361198
$478$	4.20597e22	0.705877
$479$	−4.13412e22	−0.681603	−0.340801	−	0.940135i	$-0.610698\pi$
$479$	−4.13412e22	−0.681603	−0.340801	+	0.940135i	$0.610698\pi$
$480$	−7.87946e21	−0.127628
$481$	−7.91229e22	−1.25913
$482$	−3.21655e22	−0.502911
$483$	1.96370e23	3.01664
$484$	7.59166e21	0.114591
$485$	−3.67716e22	−0.545391
$486$	−4.95400e22	−0.722018
$487$	9.82373e22	1.40696	0.703478	−	0.710717i	$-0.251630\pi$
$487$	9.82373e22	1.40696	0.703478	+	0.710717i	$0.251630\pi$
$488$	1.91279e22	0.269215
$489$	3.98250e22	0.550846
$490$	2.58908e21	0.0351949
$491$	−2.86911e21	−0.0383314	−0.0191657	−	0.999816i	$-0.506101\pi$
$491$	−2.86911e21	−0.0383314	−0.0191657	+	0.999816i	$0.506101\pi$
$492$	−4.71016e22	−0.618489
$493$	−4.88167e22	−0.630043
$494$	−1.68238e22	−0.213424
$495$	−6.38665e22	−0.796395
$496$	3.76185e22	0.461113
$497$	−1.18275e23	−1.42516
$498$	−5.78972e22	−0.685817
$499$	−8.68275e22	−1.01112	−0.505560	−	0.862791i	$-0.668714\pi$
$499$	−8.68275e22	−1.01112	−0.505560	+	0.862791i	$0.668714\pi$
$500$	−3.90625e21	−0.0447214
$501$	−3.71146e22	−0.417757
$502$	3.53177e22	0.390851
$503$	2.63166e22	0.286353	0.143177	−	0.989697i	$-0.454268\pi$
$503$	2.63166e22	0.286353	0.143177	+	0.989697i	$0.454268\pi$
$504$	−5.59545e22	−0.598653
$505$	−1.47557e22	−0.155233
$506$	1.34331e23	1.38962
$507$	7.15572e21	0.0727924
$508$	7.50078e21	0.0750352
$509$	2.52122e22	0.248033	0.124017	−	0.992280i	$-0.460422\pi$
$509$	2.52122e22	0.248033	0.124017	+	0.992280i	$0.460422\pi$
$510$	−3.69796e22	−0.357780
$511$	1.12541e22	0.107087
$512$	−4.72237e21	−0.0441942
$513$	3.28407e22	0.302284
$514$	2.76810e21	0.0250608
$515$	−6.36920e22	−0.567183
$516$	1.56278e23	1.36891
$517$	−2.36954e23	−2.04171
$518$	−1.13316e23	−0.960479
$519$	−2.25046e23	−1.87650
$520$	−1.88356e22	−0.154508
$521$	8.93522e22	0.721082	0.360541	−	0.932743i	$-0.382592\pi$
$521$	8.93522e22	0.721082	0.360541	+	0.932743i	$0.382592\pi$
$522$	1.28602e23	1.02106
$523$	9.62048e22	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$523$	9.62048e22	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$524$	3.23523e21	0.0248650
$525$	−4.50095e22	−0.340369
$526$	1.83719e23	1.36702
$527$	1.76550e23	1.29264
$528$	−6.21072e22	−0.447460
$529$	3.02130e23	2.14200
$530$	1.01926e22	0.0711115
$531$	−2.00615e23	−1.37740
$532$	−2.40942e22	−0.162803
$533$	−1.12595e23	−0.748751
$534$	−1.03949e23	−0.680330
$535$	9.13467e22	0.588418
$536$	6.78768e22	0.430349
$537$	3.25380e23	2.03053
$538$	1.48552e23	0.912490
$539$	2.04076e22	0.123392
$540$	3.67679e22	0.218838
$541$	−1.09224e23	−0.639944	−0.319972	−	0.947427i	$-0.603673\pi$
$541$	−1.09224e23	−0.639944	−0.319972	+	0.947427i	$0.603673\pi$
$542$	−4.21979e22	−0.243387
$543$	2.57397e23	1.46152
$544$	−2.21629e22	−0.123890
$545$	1.74710e22	0.0961494
$546$	−2.17032e23	−1.17594
$547$	−2.52518e23	−1.34710	−0.673551	−	0.739140i	$-0.735232\pi$
$547$	−2.52518e23	−1.34710	−0.673551	+	0.739140i	$0.735232\pi$
$548$	−2.73092e22	−0.143442
$549$	−2.36491e23	−1.22307
$550$	−3.07897e22	−0.156792
$551$	5.53766e22	0.277675
$552$	−2.04902e23	−1.01173
$553$	1.74914e23	0.850472
$554$	−3.90120e22	−0.186795
$555$	1.97287e23	0.930269
$556$	3.28759e22	0.152666
$557$	1.44437e23	0.660554	0.330277	−	0.943884i	$-0.392858\pi$
$557$	1.44437e23	0.660554	0.330277	+	0.943884i	$0.392858\pi$
$558$	−4.65102e23	−2.09487
$559$	3.73577e23	1.65722
$560$	−2.69754e22	−0.117861
$561$	−2.91480e23	−1.25437
$562$	−4.09682e22	−0.173655
$563$	7.42080e22	0.309834	0.154917	−	0.987927i	$-0.450489\pi$
$563$	7.42080e22	0.309834	0.154917	+	0.987927i	$0.450489\pi$
$564$	3.61439e23	1.48649
$565$	9.44391e22	0.382596
$566$	−6.00142e22	−0.239505
$567$	−7.04507e21	−0.0276968
$568$	1.23414e23	0.477972
$569$	1.99386e23	0.760747	0.380373	−	0.924833i	$-0.375795\pi$
$569$	1.99386e23	0.760747	0.380373	+	0.924833i	$0.375795\pi$
$570$	4.19488e22	0.157683
$571$	5.76243e22	0.213402	0.106701	−	0.994291i	$-0.465971\pi$
$571$	5.76243e22	0.213402	0.106701	+	0.994291i	$0.465971\pi$
$572$	−1.48466e23	−0.541701
$573$	−2.24712e23	−0.807815
$574$	−1.61253e23	−0.571158
$575$	−1.01580e23	−0.354514
$576$	5.83857e22	0.200778
$577$	−2.51358e23	−0.851722	−0.425861	−	0.904789i	$-0.640029\pi$
$577$	−2.51358e23	−0.851722	−0.425861	+	0.904789i	$0.640029\pi$
$578$	1.07759e23	0.359806
$579$	−7.31628e23	−2.40726
$580$	6.19987e22	0.201022
$581$	−1.98212e23	−0.633333
$582$	4.42109e23	1.39214
$583$	8.03398e22	0.249315
$584$	−1.17431e22	−0.0359149
$585$	2.32877e23	0.701943
$586$	−4.04186e23	−1.20075
$587$	2.04262e23	0.598087	0.299043	−	0.954240i	$-0.403332\pi$
$587$	2.04262e23	0.598087	0.299043	+	0.954240i	$0.403332\pi$
$588$	−3.11288e22	−0.0898369
$589$	−2.00274e23	−0.569699
$590$	−9.67154e22	−0.271177
$591$	2.43857e23	0.673973
$592$	1.18239e23	0.322128
$593$	−2.40118e23	−0.644851	−0.322425	−	0.946595i	$-0.604498\pi$
$593$	−2.40118e23	−0.644851	−0.322425	+	0.946595i	$0.604498\pi$
$594$	2.89811e23	0.767239
$595$	−1.26600e23	−0.330400
$596$	−7.61172e22	−0.195835
$597$	−1.27558e23	−0.323539
$598$	−4.89812e23	−1.22481
$599$	6.64163e23	1.63737	0.818684	−	0.574244i	$-0.194704\pi$
$599$	6.64163e23	1.63737	0.818684	+	0.574244i	$0.194704\pi$
$600$	4.69652e22	0.114154
$601$	−5.64984e23	−1.35395	−0.676975	−	0.736006i	$-0.736710\pi$
$601$	−5.64984e23	−1.35395	−0.676975	+	0.736006i	$0.736710\pi$
$602$	5.35018e23	1.26415
$603$	−8.39206e23	−1.95511
$604$	−3.65835e23	−0.840371
$605$	−4.52498e22	−0.102493
$606$	1.77409e23	0.396241
$607$	−2.77451e23	−0.611057	−0.305529	−	0.952183i	$-0.598833\pi$
$607$	−2.77451e23	−0.611057	−0.305529	+	0.952183i	$0.598833\pi$
$608$	2.51411e22	0.0546013
$609$	7.14376e23	1.52996
$610$	−1.14011e23	−0.240793
$611$	8.64009e23	1.79957
$612$	2.74014e23	0.562841
$613$	−3.66032e23	−0.741491	−0.370745	−	0.928735i	$-0.620898\pi$
$613$	−3.66032e23	−0.741491	−0.370745	+	0.928735i	$0.620898\pi$
$614$	6.10281e23	1.21927
$615$	2.80747e23	0.553193
$616$	−2.12625e23	−0.413217
$617$	−5.54311e23	−1.06250	−0.531251	−	0.847215i	$-0.678278\pi$
$617$	−5.54311e23	−1.06250	−0.531251	+	0.847215i	$0.678278\pi$
$618$	7.65775e23	1.44777
$619$	7.96802e23	1.48587	0.742934	−	0.669365i	$-0.233434\pi$
$619$	7.96802e23	1.48587	0.742934	+	0.669365i	$0.233434\pi$
$620$	−2.24224e23	−0.412432
$621$	9.56135e23	1.73476
$622$	−4.05252e23	−0.725282
$623$	−3.55871e23	−0.628266
$624$	2.26462e23	0.394391
$625$	2.32831e22	0.0400000
$626$	7.63825e22	0.129453
$627$	3.30648e23	0.552830
$628$	−1.48078e23	−0.244249
$629$	5.54918e23	0.903022
$630$	3.33515e23	0.535452
$631$	4.62634e23	0.732804	0.366402	−	0.930457i	$-0.380590\pi$
$631$	4.62634e23	0.732804	0.366402	+	0.930457i	$0.380590\pi$
$632$	−1.82514e23	−0.285233
$633$	3.12639e23	0.482071
$634$	2.60794e23	0.396770
$635$	−4.47081e22	−0.0671135
$636$	−1.22547e23	−0.181516
$637$	−7.44124e22	−0.108758
$638$	4.88684e23	0.704779
$639$	−1.52585e24	−2.17147
$640$	2.81475e22	0.0395285
$641$	2.38553e23	0.330592	0.165296	−	0.986244i	$-0.447142\pi$
$641$	2.38553e23	0.330592	0.165296	+	0.986244i	$0.447142\pi$
$642$	−1.09827e24	−1.50197
$643$	−1.39064e24	−1.87681	−0.938405	−	0.345536i	$-0.887697\pi$
$643$	−1.39064e24	−1.87681	−0.938405	+	0.345536i	$0.887697\pi$
$644$	−7.01485e23	−0.934304
$645$	−9.31487e23	−1.22439
$646$	1.17991e23	0.153064
$647$	−1.93162e23	−0.247306	−0.123653	−	0.992325i	$-0.539461\pi$
$647$	−1.93162e23	−0.247306	−0.123653	+	0.992325i	$0.539461\pi$
$648$	7.35118e21	0.00928901
$649$	−7.62328e23	−0.950740
$650$	1.12269e23	0.138196
$651$	−2.58361e24	−3.13898
$652$	−1.42265e23	−0.170606
$653$	1.41423e24	1.67401	0.837007	−	0.547192i	$-0.184303\pi$
$653$	1.41423e24	1.67401	0.837007	+	0.547192i	$0.184303\pi$
$654$	−2.10055e23	−0.245427
$655$	−1.92835e22	−0.0222399
$656$	1.68259e23	0.191556
$657$	1.45188e23	0.163164
$658$	1.23739e24	1.37273
$659$	−3.77712e23	−0.413651	−0.206826	−	0.978378i	$-0.566313\pi$
$659$	−3.77712e23	−0.413651	−0.206826	+	0.978378i	$0.566313\pi$
$660$	3.70188e23	0.400220
$661$	6.30952e23	0.673416	0.336708	−	0.941609i	$-0.390686\pi$
$661$	6.30952e23	0.673416	0.336708	+	0.941609i	$0.390686\pi$
$662$	1.60590e23	0.169210
$663$	1.06283e24	1.10560
$664$	2.06824e23	0.212409
$665$	1.43612e23	0.145616
$666$	−1.46187e24	−1.46345
$667$	1.61225e24	1.59354
$668$	1.32583e23	0.129386
$669$	−5.30518e23	−0.511185
$670$	−4.04577e23	−0.384916
$671$	−8.98656e23	−0.844213
$672$	3.24328e23	0.300847
$673$	1.46706e24	1.34375	0.671876	−	0.740663i	$-0.265489\pi$
$673$	1.46706e24	1.34375	0.671876	+	0.740663i	$0.265489\pi$
$674$	−9.26353e23	−0.837852
$675$	−2.19154e23	−0.195734
$676$	−2.55621e22	−0.0225450
$677$	8.89634e22	0.0774832	0.0387416	−	0.999249i	$-0.487665\pi$
$677$	8.89634e22	0.0774832	0.0387416	+	0.999249i	$0.487665\pi$
$678$	−1.13545e24	−0.976598
$679$	1.51357e24	1.28561
$680$	1.32101e23	0.110810
$681$	2.42612e24	2.00984
$682$	−1.76737e24	−1.44597
$683$	−8.93594e23	−0.722045	−0.361022	−	0.932557i	$-0.617572\pi$
$683$	−8.93594e23	−0.722045	−0.361022	+	0.932557i	$0.617572\pi$
$684$	−3.10835e23	−0.248058
$685$	1.62776e23	0.128298
$686$	8.50966e23	0.662456
$687$	2.22624e23	0.171175
$688$	−5.58265e23	−0.423973
$689$	−2.92944e23	−0.219746
$690$	1.22131e24	0.904918
$691$	−7.89975e23	−0.578162	−0.289081	−	0.957305i	$-0.593350\pi$
$691$	−7.89975e23	−0.578162	−0.289081	+	0.957305i	$0.593350\pi$
$692$	8.03924e23	0.581183
$693$	2.62882e24	1.87728
$694$	−1.98373e24	−1.39935
$695$	−1.95956e23	−0.136549
$696$	−7.45416e23	−0.513121
$697$	7.89669e23	0.536991
$698$	1.82558e24	1.22639
$699$	−2.06833e24	−1.37266
$700$	1.60786e23	0.105418
$701$	3.61705e23	0.234288	0.117144	−	0.993115i	$-0.462626\pi$
$701$	3.61705e23	0.234288	0.117144	+	0.993115i	$0.462626\pi$
$702$	−1.05674e24	−0.676244
$703$	−6.29486e23	−0.397984
$704$	2.21863e23	0.138586
$705$	−2.15434e24	−1.32956
$706$	1.97196e24	1.20243
$707$	6.07363e23	0.365918
$708$	1.16282e24	0.692196
$709$	4.46298e23	0.262501	0.131251	−	0.991349i	$-0.458101\pi$
$709$	4.46298e23	0.262501	0.131251	+	0.991349i	$0.458101\pi$
$710$	−7.35604e23	−0.427512
$711$	2.25654e24	1.29584
$712$	3.71333e23	0.210709
$713$	−5.83085e24	−3.26942
$714$	1.52213e24	0.843366
$715$	8.84924e23	0.484512
$716$	−1.16234e24	−0.628888
$717$	3.01414e24	1.61157
$718$	1.16658e24	0.616393
$719$	1.55258e24	0.810698	0.405349	−	0.914162i	$-0.367150\pi$
$719$	1.55258e24	0.810698	0.405349	+	0.914162i	$0.367150\pi$
$720$	−3.48006e23	−0.179581
$721$	2.62164e24	1.33697
$722$	1.26913e24	0.639648
$723$	−2.30509e24	−1.14818
$724$	−9.19491e23	−0.452657
$725$	−3.69541e23	−0.179800
$726$	5.44043e23	0.261621
$727$	1.38114e23	0.0656439	0.0328219	−	0.999461i	$-0.489551\pi$
$727$	1.38114e23	0.0656439	0.0328219	+	0.999461i	$0.489551\pi$
$728$	7.75296e23	0.364209
$729$	−3.49361e24	−1.62215
$730$	6.99946e22	0.0321233
$731$	−2.62003e24	−1.18853
$732$	1.37077e24	0.614639
$733$	1.51067e24	0.669555	0.334778	−	0.942297i	$-0.391339\pi$
$733$	1.51067e24	0.669555	0.334778	+	0.942297i	$0.391339\pi$
$734$	1.71428e22	0.00751046
$735$	1.85542e23	0.0803526
$736$	7.31964e23	0.313349
$737$	−3.18895e24	−1.34950
$738$	−2.08030e24	−0.870255
$739$	−3.13836e24	−1.29785	−0.648926	−	0.760851i	$-0.724782\pi$
$739$	−3.13836e24	−1.29785	−0.648926	+	0.760851i	$0.724782\pi$
$740$	−7.04762e23	−0.288120
$741$	−1.20565e24	−0.487265
$742$	−4.19540e23	−0.167625
$743$	−4.99845e23	−0.197438	−0.0987190	−	0.995115i	$-0.531474\pi$
$743$	−4.99845e23	−0.197438	−0.0987190	+	0.995115i	$0.531474\pi$
$744$	2.69586e24	1.05276
$745$	4.53694e23	0.175160
$746$	−1.43633e24	−0.548246
$747$	−2.55710e24	−0.964991
$748$	1.04124e24	0.388498
$749$	−3.75994e24	−1.38703
$750$	−2.79934e23	−0.102102
$751$	4.01494e24	1.44790	0.723952	−	0.689851i	$-0.242324\pi$
$751$	4.01494e24	1.44790	0.723952	+	0.689851i	$0.242324\pi$
$752$	−1.29115e24	−0.460391
$753$	2.53098e24	0.892342
$754$	−1.78190e24	−0.621192
$755$	2.18054e24	0.751650
$756$	−1.51341e24	−0.515848
$757$	−3.79032e24	−1.27750	−0.638750	−	0.769414i	$-0.720548\pi$
$757$	−3.79032e24	−1.27750	−0.638750	+	0.769414i	$0.720548\pi$
$758$	−1.64705e24	−0.548932
$759$	9.62659e24	3.17261
$760$	−1.49852e23	−0.0488369
$761$	−1.23826e24	−0.399065	−0.199532	−	0.979891i	$-0.563942\pi$
$761$	−1.23826e24	−0.399065	−0.199532	+	0.979891i	$0.563942\pi$
$762$	5.37530e23	0.171311
$763$	−7.19126e23	−0.226645
$764$	8.02731e23	0.250194
$765$	−1.63325e24	−0.503421
$766$	−2.84706e24	−0.867866
$767$	2.77968e24	0.837982
$768$	−3.38420e23	−0.100899
$769$	3.58282e24	1.05646	0.528228	−	0.849102i	$-0.322857\pi$
$769$	3.58282e24	1.05646	0.528228	+	0.849102i	$0.322857\pi$
$770$	1.26734e24	0.369592
$771$	1.98371e23	0.0572158
$772$	2.61357e24	0.745568
$773$	1.21994e24	0.344203	0.172101	−	0.985079i	$-0.444944\pi$
$773$	1.21994e24	0.344203	0.172101	+	0.985079i	$0.444944\pi$
$774$	6.90219e24	1.92615
$775$	1.33648e24	0.368890
$776$	−1.57933e24	−0.431170
$777$	−8.12058e24	−2.19285
$778$	−1.77099e24	−0.473030
$779$	−8.95783e23	−0.236665
$780$	−1.34982e24	−0.352754
$781$	−5.79815e24	−1.49884
$782$	3.43523e24	0.878413
$783$	3.47834e24	0.879826
$784$	1.11200e23	0.0278240
$785$	8.82613e23	0.218463
$786$	2.31847e23	0.0567688
$787$	−1.07097e24	−0.259414	−0.129707	−	0.991552i	$-0.541404\pi$
$787$	−1.07097e24	−0.259414	−0.129707	+	0.991552i	$0.541404\pi$
$788$	−8.71123e23	−0.208740
$789$	1.31659e25	3.12101
$790$	1.08787e24	0.255120
$791$	−3.88723e24	−0.901862
$792$	−2.74304e24	−0.629606
$793$	3.27678e24	0.744090
$794$	−5.57569e24	−1.25263
$795$	7.30434e23	0.162353
$796$	4.55672e23	0.100206
$797$	5.86608e22	0.0127630	0.00638149	−	0.999980i	$-0.497969\pi$
$797$	5.86608e22	0.0127630	0.00638149	+	0.999980i	$0.497969\pi$
$798$	−1.72667e24	−0.371692
$799$	−6.05961e24	−1.29062
$800$	−1.67772e23	−0.0353553
$801$	−4.59104e24	−0.957270
$802$	−1.03864e24	−0.214280
$803$	5.51709e23	0.112623
$804$	4.86427e24	0.982520
$805$	4.18117e24	0.835667
$806$	6.44439e24	1.27448
$807$	1.06457e25	2.08329
$808$	−6.33753e23	−0.122722
$809$	2.47056e24	0.473406	0.236703	−	0.971582i	$-0.423933\pi$
$809$	2.47056e24	0.473406	0.236703	+	0.971582i	$0.423933\pi$
$810$	−4.38165e22	−0.00830835
$811$	9.80457e24	1.83972	0.919859	−	0.392249i	$-0.128303\pi$
$811$	9.80457e24	1.83972	0.919859	+	0.392249i	$0.128303\pi$
$812$	−2.55194e24	−0.473854
$813$	−3.02404e24	−0.555671
$814$	−5.55506e24	−1.01014
$815$	8.47967e23	0.152595
$816$	−1.58826e24	−0.282850
$817$	2.97210e24	0.523813
$818$	1.66101e24	0.289714
$819$	−9.58550e24	−1.65463
$820$	−1.00290e24	−0.171333
$821$	3.65428e23	0.0617853	0.0308927	−	0.999523i	$-0.490165\pi$
$821$	3.65428e23	0.0617853	0.0308927	+	0.999523i	$0.490165\pi$
$822$	−1.95707e24	−0.327488
$823$	−9.20886e24	−1.52513	−0.762565	−	0.646911i	$-0.776060\pi$
$823$	−9.20886e24	−1.52513	−0.762565	+	0.646911i	$0.776060\pi$
$824$	−2.73555e24	−0.448398
$825$	−2.20649e24	−0.357968
$826$	3.98092e24	0.639224
$827$	2.05375e24	0.326400	0.163200	−	0.986593i	$-0.447818\pi$
$827$	2.05375e24	0.326400	0.163200	+	0.986593i	$0.447818\pi$
$828$	−9.04975e24	−1.42357
$829$	2.35707e24	0.366994	0.183497	−	0.983020i	$-0.441258\pi$
$829$	2.35707e24	0.366994	0.183497	+	0.983020i	$0.441258\pi$
$830$	−1.23277e24	−0.189984
$831$	−2.79573e24	−0.426468
$832$	−8.08983e23	−0.122149
$833$	5.21882e23	0.0779991
$834$	2.35599e24	0.348548
$835$	−7.90257e23	−0.115727
$836$	−1.18116e24	−0.171221
$837$	−1.25797e25	−1.80511
$838$	−5.56680e24	−0.790736
$839$	4.69193e24	0.659743	0.329872	−	0.944026i	$-0.392994\pi$
$839$	4.69193e24	0.659743	0.329872	+	0.944026i	$0.392994\pi$
$840$	−1.93315e24	−0.269086
$841$	−1.39192e24	−0.191800
$842$	−3.73555e24	−0.509568
$843$	−2.93591e24	−0.396469
$844$	−1.11683e24	−0.149305
$845$	1.52362e23	0.0201649
$846$	1.59634e25	2.09159
$847$	1.86254e24	0.241600
$848$	4.37769e23	0.0562186
$849$	−4.30081e24	−0.546808
$850$	−7.87384e23	−0.0991118
$851$	−1.83271e25	−2.28398
$852$	8.84423e24	1.09125
$853$	−8.89565e24	−1.08670	−0.543352	−	0.839505i	$-0.682845\pi$
$853$	−8.89565e24	−1.08670	−0.543352	+	0.839505i	$0.682845\pi$
$854$	4.69284e24	0.567602
$855$	1.85272e24	0.221870
$856$	3.92331e24	0.465185
$857$	1.23863e25	1.45413	0.727066	−	0.686567i	$-0.240883\pi$
$857$	1.23863e25	1.45413	0.727066	+	0.686567i	$0.240883\pi$
$858$	−1.06395e25	−1.23674
$859$	3.17743e24	0.365708	0.182854	−	0.983140i	$-0.441466\pi$
$859$	3.17743e24	0.365708	0.182854	+	0.983140i	$0.441466\pi$
$860$	3.32752e24	0.379213
$861$	−1.15559e25	−1.30400
$862$	6.68909e24	0.747404
$863$	1.42021e25	1.57130	0.785652	−	0.618669i	$-0.212328\pi$
$863$	1.42021e25	1.57130	0.785652	+	0.618669i	$0.212328\pi$
$864$	1.57917e24	0.173006
$865$	−4.79176e24	−0.519826
$866$	3.26905e24	0.351172
$867$	7.72238e24	0.821465
$868$	9.22933e24	0.972193
$869$	8.57475e24	0.894444
$870$	4.44303e24	0.458950
$871$	1.16279e25	1.18945
$872$	7.50372e23	0.0760128
$873$	1.95263e25	1.95884
$874$	−3.89685e24	−0.387139
$875$	−9.58359e23	−0.0942887
$876$	−8.41551e23	−0.0819966
$877$	−8.28800e24	−0.799748	−0.399874	−	0.916570i	$-0.630946\pi$
$877$	−8.28800e24	−0.799748	−0.399874	+	0.916570i	$0.630946\pi$
$878$	7.25527e24	0.693347
$879$	−2.89653e25	−2.74140
$880$	−1.32241e24	−0.123955
$881$	7.02937e24	0.652561	0.326281	−	0.945273i	$-0.394205\pi$
$881$	7.02937e24	0.652561	0.326281	+	0.945273i	$0.394205\pi$
$882$	−1.37484e24	−0.126407
$883$	−3.64222e23	−0.0331665	−0.0165833	−	0.999862i	$-0.505279\pi$
$883$	−3.64222e23	−0.0331665	−0.0165833	+	0.999862i	$0.505279\pi$
$884$	−3.79670e24	−0.342422
$885$	−6.93094e24	−0.619119
$886$	3.71768e24	0.328916
$887$	1.85309e25	1.62385	0.811923	−	0.583765i	$-0.198421\pi$
$887$	1.85309e25	1.62385	0.811923	+	0.583765i	$0.198421\pi$
$888$	8.47342e24	0.735442
$889$	1.84024e24	0.158201
$890$	−2.21332e24	−0.188464
$891$	−3.45369e23	−0.0291288
$892$	1.89515e24	0.158322
$893$	6.87388e24	0.568807
$894$	−5.45481e24	−0.447106
$895$	6.92810e24	0.562495
$896$	−1.15859e24	−0.0931772
$897$	−3.51015e25	−2.79634
$898$	−3.55579e24	−0.280600
$899$	−2.12121e25	−1.65816
$900$	2.07428e24	0.160622
$901$	2.05452e24	0.157598
$902$	−7.90506e24	−0.600689
$903$	3.83411e25	2.88615
$904$	4.05613e24	0.302469
$905$	5.48059e24	0.404869
$906$	−2.62169e25	−1.91863
$907$	−1.87024e25	−1.35592	−0.677962	−	0.735097i	$-0.737137\pi$
$907$	−1.87024e25	−1.35592	−0.677962	+	0.735097i	$0.737137\pi$
$908$	−8.66674e24	−0.622481
$909$	7.83551e24	0.557538
$910$	−4.62113e24	−0.325759
$911$	−1.41129e25	−0.985620	−0.492810	−	0.870137i	$-0.664030\pi$
$911$	−1.41129e25	−0.985620	−0.492810	+	0.870137i	$0.664030\pi$
$912$	1.80169e24	0.124659
$913$	−9.71689e24	−0.666079
$914$	9.53741e24	0.647721
$915$	−8.17041e24	−0.549749
$916$	−7.95273e23	−0.0530157
$917$	7.93730e23	0.0524244
$918$	7.41132e24	0.484990
$919$	−2.33638e25	−1.51482	−0.757411	−	0.652938i	$-0.773536\pi$
$919$	−2.33638e25	−1.51482	−0.757411	+	0.652938i	$0.773536\pi$
$920$	−4.36285e24	−0.280268
$921$	4.37347e25	2.78368
$922$	−4.10221e24	−0.258705
$923$	2.11419e25	1.32108
$924$	−1.52374e25	−0.943406
$925$	4.20071e24	0.257702
$926$	−1.54060e25	−0.936476
$927$	3.38214e25	2.03711
$928$	2.66282e24	0.158922
$929$	2.98004e25	1.76234	0.881169	−	0.472802i	$-0.156757\pi$
$929$	2.98004e25	1.76234	0.881169	+	0.472802i	$0.156757\pi$
$930$	−1.60686e25	−0.941614
$931$	−5.92010e23	−0.0343761
$932$	7.38860e24	0.425135
$933$	−2.90417e25	−1.65588
$934$	1.07803e25	0.609090
$935$	−6.20629e24	−0.347483
$936$	1.00020e25	0.554935
$937$	−2.48730e25	−1.36755	−0.683774	−	0.729694i	$-0.739663\pi$
$937$	−2.48730e25	−1.36755	−0.683774	+	0.729694i	$0.739663\pi$
$938$	1.66529e25	0.907331
$939$	5.47381e24	0.295551
$940$	7.69588e24	0.411786
$941$	−3.05795e25	−1.62150	−0.810752	−	0.585390i	$-0.800941\pi$
$941$	−3.05795e25	−1.62150	−0.810752	+	0.585390i	$0.800941\pi$
$942$	−1.06117e25	−0.557640
$943$	−2.60801e25	−1.35819
$944$	−4.15389e24	−0.214385
$945$	9.02064e24	0.461389
$946$	2.62281e25	1.32951
$947$	−3.09044e25	−1.55255	−0.776276	−	0.630393i	$-0.782894\pi$
$947$	−3.09044e25	−1.55255	−0.776276	+	0.630393i	$0.782894\pi$
$948$	−1.30795e25	−0.651210
$949$	−2.01170e24	−0.0992661
$950$	8.93190e23	0.0436810
$951$	1.86893e25	0.905856
$952$	−5.43744e24	−0.261204
$953$	2.50647e24	0.119337	0.0596683	−	0.998218i	$-0.480996\pi$
$953$	2.50647e24	0.119337	0.0596683	+	0.998218i	$0.480996\pi$
$954$	−5.41242e24	−0.255406
$955$	−4.78465e24	−0.223780
$956$	−1.07673e25	−0.499131
$957$	3.50207e25	1.60906
$958$	1.05834e25	0.481966
$959$	−6.70005e24	−0.302426
$960$	2.01714e24	0.0902466
$961$	5.41655e25	2.40200
$962$	2.02555e25	0.890337
$963$	−4.85065e25	−2.11337
$964$	8.23438e24	0.355612
$965$	−1.55781e25	−0.666856
$966$	−5.02707e25	−2.13309
$967$	−1.13278e25	−0.476455	−0.238228	−	0.971209i	$-0.576566\pi$
$967$	−1.13278e25	−0.476455	−0.238228	+	0.971209i	$0.576566\pi$
$968$	−1.94347e24	−0.0810282
$969$	8.45564e24	0.349457
$970$	9.41354e24	0.385650
$971$	4.00712e25	1.62731	0.813653	−	0.581351i	$-0.197476\pi$
$971$	4.00712e25	1.62731	0.813653	+	0.581351i	$0.197476\pi$
$972$	1.26822e25	0.510544
$973$	8.06578e24	0.321875
$974$	−2.51488e25	−0.994868
$975$	8.04556e24	0.315513
$976$	−4.89675e24	−0.190364
$977$	8.86356e24	0.341589	0.170795	−	0.985307i	$-0.445367\pi$
$977$	8.86356e24	0.341589	0.170795	+	0.985307i	$0.445367\pi$
$978$	−1.01952e25	−0.389507
$979$	−1.74458e25	−0.660750
$980$	−6.62805e23	−0.0248865
$981$	−9.27734e24	−0.345332
$982$	7.34492e23	0.0271044
$983$	−1.56885e25	−0.573954	−0.286977	−	0.957938i	$-0.592650\pi$
$983$	−1.56885e25	−0.573954	−0.286977	+	0.957938i	$0.592650\pi$
$984$	1.20580e25	0.437338
$985$	5.19230e24	0.186703
$986$	1.24971e25	0.445507
$987$	8.86754e25	3.13406
$988$	4.30688e24	0.150914
$989$	8.65307e25	3.00609
$990$	1.63498e25	0.563137
$991$	−2.85830e25	−0.976073	−0.488037	−	0.872823i	$-0.662287\pi$
$991$	−2.85830e25	−0.976073	−0.488037	+	0.872823i	$0.662287\pi$
$992$	−9.63034e24	−0.326056
$993$	1.15084e25	0.386319
$994$	3.02783e25	1.00774
$995$	−2.71602e24	−0.0896265
$996$	1.48217e25	0.484946
$997$	−6.58977e24	−0.213777	−0.106889	−	0.994271i	$-0.534089\pi$
$997$	−6.58977e24	−0.213777	−0.106889	+	0.994271i	$0.534089\pi$
$998$	2.22278e25	0.714970
$999$	−3.95396e25	−1.26103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.18.a.b.1.1	✓	2
3.2	odd	2		90.18.a.n.1.2		2
4.3	odd	2		80.18.a.e.1.2		2
5.2	odd	4		50.18.b.e.49.2		4
5.3	odd	4		50.18.b.e.49.3		4
5.4	even	2		50.18.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.b.1.1	✓	2	1.1	even	1	trivial
50.18.a.g.1.2		2	5.4	even	2
50.18.b.e.49.2		4	5.2	odd	4
50.18.b.e.49.3		4	5.3	odd	4
80.18.a.e.1.2		2	4.3	odd	2
90.18.a.n.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-256.000 q^{2} -18345.8 q^{3} +65536.0 q^{4} -390625. q^{5} +4.69652e6 q^{6} +1.60786e7 q^{7} -1.67772e7 q^{8} +2.07428e8 q^{9} +1.00000e8 q^{10} +7.88217e8 q^{11} -1.20231e9 q^{12} -2.87409e9 q^{13} -4.11612e9 q^{14} +7.16632e9 q^{15} +4.29497e9 q^{16} +2.01570e10 q^{17} -5.31015e10 q^{18} -2.28657e10 q^{19} -2.56000e10 q^{20} -2.94975e11 q^{21} -2.01784e11 q^{22} -6.65718e11 q^{23} +3.07791e11 q^{24} +1.52588e11 q^{25} +7.35766e11 q^{26} -1.43625e12 q^{27} +1.05373e12 q^{28} -2.42182e12 q^{29} -1.83458e12 q^{30} +8.75874e12 q^{31} -1.09951e12 q^{32} -1.44605e13 q^{33} -5.16020e12 q^{34} -6.28070e12 q^{35} +1.35940e13 q^{36} +2.75298e13 q^{37} +5.85361e12 q^{38} +5.27274e13 q^{39} +6.55360e12 q^{40} +3.91759e13 q^{41} +7.55135e13 q^{42} -1.29981e14 q^{43} +5.16566e13 q^{44} -8.10265e13 q^{45} +1.70424e14 q^{46} -3.00620e14 q^{47} -7.87946e13 q^{48} +2.58908e13 q^{49} -3.90625e13 q^{50} -3.69796e14 q^{51} -1.88356e14 q^{52} +1.01926e14 q^{53} +3.67679e14 q^{54} -3.07897e14 q^{55} -2.69754e14 q^{56} +4.19488e14 q^{57} +6.19987e14 q^{58} -9.67154e14 q^{59} +4.69652e14 q^{60} -1.14011e15 q^{61} -2.24224e15 q^{62} +3.33515e15 q^{63} +2.81475e14 q^{64} +1.12269e15 q^{65} +3.70188e15 q^{66} -4.04577e15 q^{67} +1.32101e15 q^{68} +1.22131e16 q^{69} +1.60786e15 q^{70} -7.35604e15 q^{71} -3.48006e15 q^{72} +6.99946e14 q^{73} -7.04762e15 q^{74} -2.79934e15 q^{75} -1.49852e15 q^{76} +1.26734e16 q^{77} -1.34982e16 q^{78} +1.08787e16 q^{79} -1.67772e15 q^{80} -4.38165e14 q^{81} -1.00290e16 q^{82} -1.23277e16 q^{83} -1.93315e16 q^{84} -7.87384e15 q^{85} +3.32752e16 q^{86} +4.44303e16 q^{87} -1.32241e16 q^{88} -2.21332e16 q^{89} +2.07428e16 q^{90} -4.62113e16 q^{91} -4.36285e16 q^{92} -1.60686e17 q^{93} +7.69588e16 q^{94} +8.93190e15 q^{95} +2.01714e16 q^{96} +9.41354e16 q^{97} -6.62805e15 q^{98} +1.63498e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 512 q^{2} - 6308 q^{3} + 131072 q^{4} - 781250 q^{5} + 1614848 q^{6} + 6543844 q^{7} - 33554432 q^{8} + 223195906 q^{9} + 200000000 q^{10} + 1189408704 q^{11} - 413401088 q^{12} - 2017919228 q^{13}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 512 * q^2 - 6308 * q^3 + 131072 * q^4 - 781250 * q^5 + 1614848 * q^6 + 6543844 * q^7 - 33554432 * q^8 + 223195906 * q^9 + 200000000 * q^10 + 1189408704 * q^11 - 413401088 * q^12 - 2017919228 * q^13 - 1675224064 * q^14 + 2464062500 * q^15 + 8589934592 * q^16 - 18755639436 * q^17 - 57138151936 * q^18 - 136704830600 * q^19 - 51200000000 * q^20 - 409751898376 * q^21 - 304488628224 * q^22 - 649234170708 * q^23 + 105830678528 * q^24 + 305175781250 * q^25 + 516587322368 * q^26 - 2800995425720 * q^27 + 428857360384 * q^28 - 4696543420020 * q^29 - 630800000000 * q^30 + 7120867378744 * q^31 - 2199023255552 * q^32 - 9631011282816 * q^33 + 4801443695616 * q^34 - 2556189062500 * q^35 + 14627366895616 * q^36 + 9933114637444 * q^37 + 34996436633600 * q^38 + 63033715222712 * q^39 + 13107200000000 * q^40 + 9622711880844 * q^41 + 104896485984256 * q^42 + 7708436011852 * q^43 + 77949088825344 * q^44 - 87185900781250 * q^45 + 166203947701248 * q^46 - 466072575837996 * q^47 - 27092653703168 * q^48 - 115828146887046 * q^49 - 78125000000000 * q^50 - 838218717084456 * q^51 - 132246354526208 * q^52 - 623333120284428 * q^53 + 717054828984320 * q^54 - 464612775000000 * q^55 - 109787484258304 * q^56 - 950883425062000 * q^57 + 1202315115525120 * q^58 + 654616071995160 * q^59 + 161484800000000 * q^60 + 1329040385162884 * q^61 - 1822942048958464 * q^62 + 3184801966786532 * q^63 + 562949953421312 * q^64 + 788249698437500 * q^65 + 2465538888400896 * q^66 - 4249016411877596 * q^67 - 1229169586077696 * q^68 + 12411535659353832 * q^69 + 654384400000000 * q^70 + 2035131949347624 * q^71 - 3744605925277696 * q^72 + 2248593461347972 * q^73 - 2542877347185664 * q^74 - 962524414062500 * q^75 - 8959087778201600 * q^76 + 8848168987836288 * q^77 - 16136631097014272 * q^78 + 19188427678495120 * q^79 - 3355443200000000 * q^80 - 18903014015714198 * q^81 - 2463414241496064 * q^82 - 18474649086611988 * q^83 - 26853500411969536 * q^84 + 7326421654687500 * q^85 - 1973359619034112 * q^86 + 17047661699498280 * q^87 - 19954966739288064 * q^88 - 17458912916395020 * q^89 + 22319590600000000 * q^90 - 54374608211433016 * q^91 - 42548210611519488 * q^92 - 180402465813627376 * q^93 + 119314579414526976 * q^94 + 53400324453125000 * q^95 + 6935719348011008 * q^96 + 195934325822490244 * q^97 + 29652005603083776 * q^98 + 169824195828146112 * q^99

Introduction

L-functions

Modular forms

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Database

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