LMFDB - Embedded newform 230.6.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("230.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.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:	$36.8882785570$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.27980.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 47x - 106 $ x^3 - 47*x - 106
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-5.13326$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +6.88339 q^{3} +16.0000 q^{4} +25.0000 q^{5} -27.5336 q^{6} -45.2649 q^{7} -64.0000 q^{8} -195.619 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +6.88339 q^{3} +16.0000 q^{4} +25.0000 q^{5} -27.5336 q^{6} -45.2649 q^{7} -64.0000 q^{8} -195.619 q^{9} -100.000 q^{10} +460.780 q^{11} +110.134 q^{12} +403.836 q^{13} +181.060 q^{14} +172.085 q^{15} +256.000 q^{16} -2065.15 q^{17} +782.476 q^{18} -2213.13 q^{19} +400.000 q^{20} -311.576 q^{21} -1843.12 q^{22} +529.000 q^{23} -440.537 q^{24} +625.000 q^{25} -1615.34 q^{26} -3019.19 q^{27} -724.238 q^{28} -375.020 q^{29} -688.339 q^{30} +2976.27 q^{31} -1024.00 q^{32} +3171.72 q^{33} +8260.59 q^{34} -1131.62 q^{35} -3129.90 q^{36} +10952.5 q^{37} +8852.52 q^{38} +2779.76 q^{39} -1600.00 q^{40} +6680.63 q^{41} +1246.30 q^{42} -16704.2 q^{43} +7372.47 q^{44} -4890.47 q^{45} -2116.00 q^{46} -6384.74 q^{47} +1762.15 q^{48} -14758.1 q^{49} -2500.00 q^{50} -14215.2 q^{51} +6461.37 q^{52} -16909.6 q^{53} +12076.7 q^{54} +11519.5 q^{55} +2896.95 q^{56} -15233.8 q^{57} +1500.08 q^{58} -44888.9 q^{59} +2753.36 q^{60} +5702.08 q^{61} -11905.1 q^{62} +8854.67 q^{63} +4096.00 q^{64} +10095.9 q^{65} -12686.9 q^{66} -10092.7 q^{67} -33042.4 q^{68} +3641.31 q^{69} +4526.49 q^{70} +6938.65 q^{71} +12519.6 q^{72} -36232.5 q^{73} -43810.0 q^{74} +4302.12 q^{75} -35410.1 q^{76} -20857.1 q^{77} -11119.0 q^{78} -32568.0 q^{79} +6400.00 q^{80} +26753.2 q^{81} -26722.5 q^{82} -11151.4 q^{83} -4985.21 q^{84} -51628.7 q^{85} +66817.0 q^{86} -2581.41 q^{87} -29489.9 q^{88} -122616. q^{89} +19561.9 q^{90} -18279.6 q^{91} +8464.00 q^{92} +20486.8 q^{93} +25539.0 q^{94} -55328.2 q^{95} -7048.59 q^{96} -121861. q^{97} +59032.4 q^{98} -90137.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 12 q^{2} - 26 q^{3} + 48 q^{4} + 75 q^{5} + 104 q^{6} + q^{7} - 192 q^{8} - 71 q^{9}+O(q^{10}) $ 3 * q - 12 * q^2 - 26 * q^3 + 48 * q^4 + 75 * q^5 + 104 * q^6 + q^7 - 192 * q^8 - 71 * q^9	\( 3 q - 12 q^{2} - 26 q^{3} + 48 q^{4} + 75 q^{5} + 104 q^{6} + q^{7} - 192 q^{8} - 71 q^{9} - 300 q^{10} + 178 q^{11} - 416 q^{12} - 236 q^{13} - 4 q^{14} - 650 q^{15} + 768 q^{16} - 1683 q^{17} + 284 q^{18} - 194 q^{19} + 1200 q^{20} + 504 q^{21} - 712 q^{22} + 1587 q^{23} + 1664 q^{24} + 1875 q^{25} + 944 q^{26} + 622 q^{27} + 16 q^{28} + 6901 q^{29} + 2600 q^{30} + 6119 q^{31} - 3072 q^{32} + 4792 q^{33} + 6732 q^{34} + 25 q^{35} - 1136 q^{36} + 5185 q^{37} + 776 q^{38} + 16234 q^{39} - 4800 q^{40} + 6727 q^{41} - 2016 q^{42} - 22988 q^{43} + 2848 q^{44} - 1775 q^{45} - 6348 q^{46} - 13730 q^{47} - 6656 q^{48} - 11788 q^{49} - 7500 q^{50} - 20140 q^{51} - 3776 q^{52} - 38027 q^{53} - 2488 q^{54} + 4450 q^{55} - 64 q^{56} - 62424 q^{57} - 27604 q^{58} - 43715 q^{59} - 10400 q^{60} - 51364 q^{61} - 24476 q^{62} - 40095 q^{63} + 12288 q^{64} - 5900 q^{65} - 19168 q^{66} - 51891 q^{67} - 26928 q^{68} - 13754 q^{69} - 100 q^{70} - 25667 q^{71} + 4544 q^{72} - 108532 q^{73} - 20740 q^{74} - 16250 q^{75} - 3104 q^{76} - 95646 q^{77} - 64936 q^{78} - 224 q^{79} + 19200 q^{80} - 38213 q^{81} - 26908 q^{82} - 61071 q^{83} + 8064 q^{84} - 42075 q^{85} + 91952 q^{86} - 82842 q^{87} - 11392 q^{88} - 93372 q^{89} + 7100 q^{90} + 33030 q^{91} + 25392 q^{92} - 73542 q^{93} + 54920 q^{94} - 4850 q^{95} + 26624 q^{96} - 260238 q^{97} + 47152 q^{98} - 8150 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 - 26 * q^3 + 48 * q^4 + 75 * q^5 + 104 * q^6 + q^7 - 192 * q^8 - 71 * q^9 - 300 * q^10 + 178 * q^11 - 416 * q^12 - 236 * q^13 - 4 * q^14 - 650 * q^15 + 768 * q^16 - 1683 * q^17 + 284 * q^18 - 194 * q^19 + 1200 * q^20 + 504 * q^21 - 712 * q^22 + 1587 * q^23 + 1664 * q^24 + 1875 * q^25 + 944 * q^26 + 622 * q^27 + 16 * q^28 + 6901 * q^29 + 2600 * q^30 + 6119 * q^31 - 3072 * q^32 + 4792 * q^33 + 6732 * q^34 + 25 * q^35 - 1136 * q^36 + 5185 * q^37 + 776 * q^38 + 16234 * q^39 - 4800 * q^40 + 6727 * q^41 - 2016 * q^42 - 22988 * q^43 + 2848 * q^44 - 1775 * q^45 - 6348 * q^46 - 13730 * q^47 - 6656 * q^48 - 11788 * q^49 - 7500 * q^50 - 20140 * q^51 - 3776 * q^52 - 38027 * q^53 - 2488 * q^54 + 4450 * q^55 - 64 * q^56 - 62424 * q^57 - 27604 * q^58 - 43715 * q^59 - 10400 * q^60 - 51364 * q^61 - 24476 * q^62 - 40095 * q^63 + 12288 * q^64 - 5900 * q^65 - 19168 * q^66 - 51891 * q^67 - 26928 * q^68 - 13754 * q^69 - 100 * q^70 - 25667 * q^71 + 4544 * q^72 - 108532 * q^73 - 20740 * q^74 - 16250 * q^75 - 3104 * q^76 - 95646 * q^77 - 64936 * q^78 - 224 * q^79 + 19200 * q^80 - 38213 * q^81 - 26908 * q^82 - 61071 * q^83 + 8064 * q^84 - 42075 * q^85 + 91952 * q^86 - 82842 * q^87 - 11392 * q^88 - 93372 * q^89 + 7100 * q^90 + 33030 * q^91 + 25392 * q^92 - 73542 * q^93 + 54920 * q^94 - 4850 * q^95 + 26624 * q^96 - 260238 * q^97 + 47152 * q^98 - 8150 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	6.88339	0.441570	0.220785	−	0.975323i	$-0.429138\pi$
$3$	6.88339	0.441570	0.220785	+	0.975323i	$0.429138\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−27.5336	−0.312237
$7$	−45.2649	−0.349153	−0.174577	−	0.984644i	$-0.555856\pi$
$7$	−45.2649	−0.349153	−0.174577	+	0.984644i	$0.555856\pi$
$8$	−64.0000	−0.353553
$9$	−195.619	−0.805016
$10$	−100.000	−0.316228
$11$	460.780	1.14818	0.574092	−	0.818791i	$-0.305355\pi$
$11$	460.780	1.14818	0.574092	+	0.818791i	$0.305355\pi$
$12$	110.134	0.220785
$13$	403.836	0.662745	0.331373	−	0.943500i	$-0.392488\pi$
$13$	403.836	0.662745	0.331373	+	0.943500i	$0.392488\pi$
$14$	181.060	0.246889
$15$	172.085	0.197476
$16$	256.000	0.250000
$17$	−2065.15	−1.73312	−0.866560	−	0.499072i	$-0.833674\pi$
$17$	−2065.15	−1.73312	−0.866560	+	0.499072i	$0.833674\pi$
$18$	782.476	0.569232
$19$	−2213.13	−1.40644	−0.703222	−	0.710970i	$-0.748256\pi$
$19$	−2213.13	−1.40644	−0.703222	+	0.710970i	$0.748256\pi$
$20$	400.000	0.223607
$21$	−311.576	−0.154176
$22$	−1843.12	−0.811889
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−440.537	−0.156118
$25$	625.000	0.200000
$26$	−1615.34	−0.468632
$27$	−3019.19	−0.797040
$28$	−724.238	−0.174577
$29$	−375.020	−0.0828056	−0.0414028	−	0.999143i	$-0.513183\pi$
$29$	−375.020	−0.0828056	−0.0414028	+	0.999143i	$0.513183\pi$
$30$	−688.339	−0.139637
$31$	2976.27	0.556247	0.278124	−	0.960545i	$-0.410287\pi$
$31$	2976.27	0.556247	0.278124	+	0.960545i	$0.410287\pi$
$32$	−1024.00	−0.176777
$33$	3171.72	0.507003
$34$	8260.59	1.22550
$35$	−1131.62	−0.156146
$36$	−3129.90	−0.402508
$37$	10952.5	1.31525	0.657626	−	0.753345i	$-0.271561\pi$
$37$	10952.5	1.31525	0.657626	+	0.753345i	$0.271561\pi$
$38$	8852.52	0.994507
$39$	2779.76	0.292648
$40$	−1600.00	−0.158114
$41$	6680.63	0.620666	0.310333	−	0.950628i	$-0.399559\pi$
$41$	6680.63	0.620666	0.310333	+	0.950628i	$0.399559\pi$
$42$	1246.30	0.109019
$43$	−16704.2	−1.37770	−0.688852	−	0.724902i	$-0.741885\pi$
$43$	−16704.2	−1.37770	−0.688852	+	0.724902i	$0.741885\pi$
$44$	7372.47	0.574092
$45$	−4890.47	−0.360014
$46$	−2116.00	−0.147442
$47$	−6384.74	−0.421598	−0.210799	−	0.977529i	$-0.567607\pi$
$47$	−6384.74	−0.421598	−0.210799	+	0.977529i	$0.567607\pi$
$48$	1762.15	0.110392
$49$	−14758.1	−0.878092
$50$	−2500.00	−0.141421
$51$	−14215.2	−0.765293
$52$	6461.37	0.331373
$53$	−16909.6	−0.826880	−0.413440	−	0.910531i	$-0.635673\pi$
$53$	−16909.6	−0.826880	−0.413440	+	0.910531i	$0.635673\pi$
$54$	12076.7	0.563593
$55$	11519.5	0.513483
$56$	2896.95	0.123444
$57$	−15233.8	−0.621043
$58$	1500.08	0.0585524
$59$	−44888.9	−1.67884	−0.839419	−	0.543485i	$-0.817105\pi$
$59$	−44888.9	−1.67884	−0.839419	+	0.543485i	$0.817105\pi$
$60$	2753.36	0.0987380
$61$	5702.08	0.196204	0.0981021	−	0.995176i	$-0.468723\pi$
$61$	5702.08	0.196204	0.0981021	+	0.995176i	$0.468723\pi$
$62$	−11905.1	−0.393326
$63$	8854.67	0.281074
$64$	4096.00	0.125000
$65$	10095.9	0.296389
$66$	−12686.9	−0.358505
$67$	−10092.7	−0.274675	−0.137338	−	0.990524i	$-0.543855\pi$
$67$	−10092.7	−0.274675	−0.137338	+	0.990524i	$0.543855\pi$
$68$	−33042.4	−0.866560
$69$	3641.31	0.0920736
$70$	4526.49	0.110412
$71$	6938.65	0.163354	0.0816769	−	0.996659i	$-0.473972\pi$
$71$	6938.65	0.163354	0.0816769	+	0.996659i	$0.473972\pi$
$72$	12519.6	0.284616
$73$	−36232.5	−0.795776	−0.397888	−	0.917434i	$-0.630257\pi$
$73$	−36232.5	−0.795776	−0.397888	+	0.917434i	$0.630257\pi$
$74$	−43810.0	−0.930024
$75$	4302.12	0.0883139
$76$	−35410.1	−0.703222
$77$	−20857.1	−0.400892
$78$	−11119.0	−0.206933
$79$	−32568.0	−0.587115	−0.293558	−	0.955941i	$-0.594839\pi$
$79$	−32568.0	−0.587115	−0.293558	+	0.955941i	$0.594839\pi$
$80$	6400.00	0.111803
$81$	26753.2	0.453067
$82$	−26722.5	−0.438877
$83$	−11151.4	−0.177679	−0.0888394	−	0.996046i	$-0.528316\pi$
$83$	−11151.4	−0.177679	−0.0888394	+	0.996046i	$0.528316\pi$
$84$	−4985.21	−0.0770878
$85$	−51628.7	−0.775075
$86$	66817.0	0.974184
$87$	−2581.41	−0.0365644
$88$	−29489.9	−0.405944
$89$	−122616.	−1.64087	−0.820434	−	0.571742i	$-0.806268\pi$
$89$	−122616.	−1.64087	−0.820434	+	0.571742i	$0.806268\pi$
$90$	19561.9	0.254568
$91$	−18279.6	−0.231400
$92$	8464.00	0.104257
$93$	20486.8	0.245622
$94$	25539.0	0.298115
$95$	−55328.2	−0.628981
$96$	−7048.59	−0.0780592
$97$	−121861.	−1.31503	−0.657514	−	0.753443i	$-0.728392\pi$
$97$	−121861.	−1.31503	−0.657514	+	0.753443i	$0.728392\pi$
$98$	59032.4	0.620905
$99$	−90137.2	−0.924307
$100$	10000.0	0.100000
$101$	59521.4	0.580590	0.290295	−	0.956937i	$-0.406247\pi$
$101$	59521.4	0.580590	0.290295	+	0.956937i	$0.406247\pi$
$102$	56860.9	0.541144
$103$	−115404.	−1.07184	−0.535919	−	0.844269i	$-0.680035\pi$
$103$	−115404.	−1.07184	−0.535919	+	0.844269i	$0.680035\pi$
$104$	−25845.5	−0.234316
$105$	−7789.40	−0.0689494
$106$	67638.2	0.584692
$107$	14298.4	0.120733	0.0603667	−	0.998176i	$-0.480773\pi$
$107$	14298.4	0.120733	0.0603667	+	0.998176i	$0.480773\pi$
$108$	−48307.0	−0.398520
$109$	48768.3	0.393162	0.196581	−	0.980488i	$-0.437016\pi$
$109$	48768.3	0.393162	0.196581	+	0.980488i	$0.437016\pi$
$110$	−46078.0	−0.363088
$111$	75390.3	0.580775
$112$	−11587.8	−0.0872884
$113$	−132182.	−0.973816	−0.486908	−	0.873453i	$-0.661875\pi$
$113$	−132182.	−0.973816	−0.486908	+	0.873453i	$0.661875\pi$
$114$	60935.3	0.439144
$115$	13225.0	0.0932505
$116$	−6000.32	−0.0414028
$117$	−78998.0	−0.533521
$118$	179556.	1.18712
$119$	93478.7	0.605125
$120$	−11013.4	−0.0698183
$121$	51266.8	0.318326
$122$	−22808.3	−0.138737
$123$	45985.4	0.274067
$124$	47620.3	0.278124
$125$	15625.0	0.0894427
$126$	−35418.7	−0.198749
$127$	84117.5	0.462783	0.231391	−	0.972861i	$-0.425672\pi$
$127$	84117.5	0.462783	0.231391	+	0.972861i	$0.425672\pi$
$128$	−16384.0	−0.0883883
$129$	−114982.	−0.608352
$130$	−40383.6	−0.209578
$131$	99362.4	0.505876	0.252938	−	0.967482i	$-0.418603\pi$
$131$	99362.4	0.505876	0.252938	+	0.967482i	$0.418603\pi$
$132$	50747.6	0.253502
$133$	100177.	0.491065
$134$	40370.7	0.194225
$135$	−75479.6	−0.356447
$136$	132169.	0.612751
$137$	−167560.	−0.762728	−0.381364	−	0.924425i	$-0.624546\pi$
$137$	−167560.	−0.762728	−0.381364	+	0.924425i	$0.624546\pi$
$138$	−14565.3	−0.0651059
$139$	255866.	1.12325	0.561624	−	0.827393i	$-0.310177\pi$
$139$	255866.	1.12325	0.561624	+	0.827393i	$0.310177\pi$
$140$	−18106.0	−0.0780731
$141$	−43948.7	−0.186165
$142$	−27754.6	−0.115509
$143$	186079.	0.760953
$144$	−50078.5	−0.201254
$145$	−9375.51	−0.0370318
$146$	144930.	0.562699
$147$	−101586.	−0.387739
$148$	175240.	0.657626
$149$	144918.	0.534757	0.267379	−	0.963592i	$-0.413843\pi$
$149$	144918.	0.534757	0.267379	+	0.963592i	$0.413843\pi$
$150$	−17208.5	−0.0624474
$151$	−248043.	−0.885287	−0.442643	−	0.896698i	$-0.645959\pi$
$151$	−248043.	−0.885287	−0.442643	+	0.896698i	$0.645959\pi$
$152$	141640.	0.497253
$153$	403982.	1.39519
$154$	83428.5	0.283474
$155$	74406.7	0.248761
$156$	44476.2	0.146324
$157$	−135320.	−0.438141	−0.219070	−	0.975709i	$-0.570302\pi$
$157$	−135320.	−0.438141	−0.219070	+	0.975709i	$0.570302\pi$
$158$	130272.	0.415153
$159$	−116395.	−0.365125
$160$	−25600.0	−0.0790569
$161$	−23945.1	−0.0728035
$162$	−107013.	−0.320367
$163$	−413259.	−1.21830	−0.609149	−	0.793056i	$-0.708489\pi$
$163$	−413259.	−1.21830	−0.609149	+	0.793056i	$0.708489\pi$
$164$	106890.	0.310333
$165$	79293.1	0.226739
$166$	44605.7	0.125638
$167$	288503.	0.800497	0.400249	−	0.916407i	$-0.368924\pi$
$167$	288503.	0.800497	0.400249	+	0.916407i	$0.368924\pi$
$168$	19940.9	0.0545093
$169$	−208210.	−0.560769
$170$	206515.	0.548061
$171$	432930.	1.13221
$172$	−267268.	−0.688852
$173$	661033.	1.67922	0.839611	−	0.543188i	$-0.182783\pi$
$173$	661033.	1.67922	0.839611	+	0.543188i	$0.182783\pi$
$174$	10325.6	0.0258550
$175$	−28290.6	−0.0698307
$176$	117960.	0.287046
$177$	−308988.	−0.741324
$178$	490466.	1.16027
$179$	701044.	1.63536	0.817679	−	0.575674i	$-0.195260\pi$
$179$	701044.	1.63536	0.817679	+	0.575674i	$0.195260\pi$
$180$	−78247.6	−0.180007
$181$	664717.	1.50814	0.754068	−	0.656797i	$-0.228089\pi$
$181$	664717.	1.50814	0.754068	+	0.656797i	$0.228089\pi$
$182$	73118.4	0.163624
$183$	39249.6	0.0866378
$184$	−33856.0	−0.0737210
$185$	273812.	0.588199
$186$	−81947.3	−0.173681
$187$	−951578.	−1.98994
$188$	−102156.	−0.210799
$189$	136663.	0.278289
$190$	221313.	0.444757
$191$	76330.7	0.151396	0.0756982	−	0.997131i	$-0.475881\pi$
$191$	76330.7	0.151396	0.0756982	+	0.997131i	$0.475881\pi$
$192$	28194.4	0.0551962
$193$	−503966.	−0.973885	−0.486942	−	0.873434i	$-0.661888\pi$
$193$	−503966.	−0.973885	−0.486942	+	0.873434i	$0.661888\pi$
$194$	487443.	0.929865
$195$	69494.0	0.130876
$196$	−236129.	−0.439046
$197$	−171037.	−0.313996	−0.156998	−	0.987599i	$-0.550182\pi$
$197$	−171037.	−0.313996	−0.156998	+	0.987599i	$0.550182\pi$
$198$	360549.	0.653584
$199$	80900.1	0.144816	0.0724080	−	0.997375i	$-0.476932\pi$
$199$	80900.1	0.144816	0.0724080	+	0.997375i	$0.476932\pi$
$200$	−40000.0	−0.0707107
$201$	−69471.8	−0.121288
$202$	−238085.	−0.410539
$203$	16975.3	0.0289119
$204$	−227443.	−0.382647
$205$	167016.	0.277570
$206$	461617.	0.757904
$207$	−103482.	−0.167857
$208$	103382.	0.165686
$209$	−1.01976e6	−1.61486
$210$	31157.6	0.0487546
$211$	174165.	0.269312	0.134656	−	0.990892i	$-0.457007\pi$
$211$	174165.	0.269312	0.134656	+	0.990892i	$0.457007\pi$
$212$	−270553.	−0.413440
$213$	47761.4	0.0721321
$214$	−57193.6	−0.0853715
$215$	−417606.	−0.616128
$216$	193228.	0.281796
$217$	−134721.	−0.194216
$218$	−195073.	−0.278007
$219$	−249402.	−0.351391
$220$	184312.	0.256742
$221$	−833981.	−1.14862
$222$	−301561.	−0.410670
$223$	−1.41349e6	−1.90340	−0.951701	−	0.307027i	$-0.900666\pi$
$223$	−1.41349e6	−1.90340	−0.951701	+	0.307027i	$0.900666\pi$
$224$	46351.2	0.0617222
$225$	−122262.	−0.161003
$226$	528729.	0.688592
$227$	1.31499e6	1.69378	0.846889	−	0.531770i	$-0.178473\pi$
$227$	1.31499e6	1.69378	0.846889	+	0.531770i	$0.178473\pi$
$228$	−243741.	−0.310522
$229$	759082.	0.956533	0.478266	−	0.878215i	$-0.341265\pi$
$229$	759082.	0.956533	0.478266	+	0.878215i	$0.341265\pi$
$230$	−52900.0	−0.0659380
$231$	−143568.	−0.177022
$232$	24001.3	0.0292762
$233$	117520.	0.141815	0.0709076	−	0.997483i	$-0.477410\pi$
$233$	117520.	0.141815	0.0709076	+	0.997483i	$0.477410\pi$
$234$	315992.	0.377256
$235$	−159619.	−0.188545
$236$	−718222.	−0.839419
$237$	−224178.	−0.259252
$238$	−373915.	−0.427888
$239$	−272029.	−0.308050	−0.154025	−	0.988067i	$-0.549224\pi$
$239$	−272029.	−0.308050	−0.154025	+	0.988067i	$0.549224\pi$
$240$	44053.7	0.0493690
$241$	893164.	0.990578	0.495289	−	0.868728i	$-0.335062\pi$
$241$	893164.	0.990578	0.495289	+	0.868728i	$0.335062\pi$
$242$	−205067.	−0.225091
$243$	917815.	0.997101
$244$	91233.2	0.0981021
$245$	−368952.	−0.392695
$246$	−183942.	−0.193795
$247$	−893741.	−0.932115
$248$	−190481.	−0.196663
$249$	−76759.7	−0.0784576
$250$	−62500.0	−0.0632456
$251$	394196.	0.394937	0.197469	−	0.980309i	$-0.436728\pi$
$251$	394196.	0.394937	0.197469	+	0.980309i	$0.436728\pi$
$252$	141675.	0.140537
$253$	243752.	0.239413
$254$	−336470.	−0.327237
$255$	−355380.	−0.342250
$256$	65536.0	0.0625000
$257$	−201431.	−0.190237	−0.0951183	−	0.995466i	$-0.530323\pi$
$257$	−201431.	−0.190237	−0.0951183	+	0.995466i	$0.530323\pi$
$258$	459927.	0.430170
$259$	−495764.	−0.459225
$260$	161534.	0.148194
$261$	73361.1	0.0666599
$262$	−397450.	−0.357708
$263$	−32183.0	−0.0286905	−0.0143452	−	0.999897i	$-0.504566\pi$
$263$	−32183.0	−0.0286905	−0.0143452	+	0.999897i	$0.504566\pi$
$264$	−202990.	−0.179253
$265$	−422739.	−0.369792
$266$	−400708.	−0.347235
$267$	−844016.	−0.724557
$268$	−161483.	−0.137338
$269$	2.21833e6	1.86916	0.934578	−	0.355759i	$-0.115777\pi$
$269$	2.21833e6	1.86916	0.934578	+	0.355759i	$0.115777\pi$
$270$	301919.	0.252046
$271$	−50711.3	−0.0419452	−0.0209726	−	0.999780i	$-0.506676\pi$
$271$	−50711.3	−0.0419452	−0.0209726	+	0.999780i	$0.506676\pi$
$272$	−528678.	−0.433280
$273$	−125826.	−0.102179
$274$	670242.	0.539330
$275$	287987.	0.229637
$276$	58261.0	0.0460368
$277$	−2.11823e6	−1.65872	−0.829360	−	0.558715i	$-0.811294\pi$
$277$	−2.11823e6	−1.65872	−0.829360	+	0.558715i	$0.811294\pi$
$278$	−1.02346e6	−0.794256
$279$	−582215.	−0.447788
$280$	72423.8	0.0552060
$281$	−338126.	−0.255454	−0.127727	−	0.991809i	$-0.540768\pi$
$281$	−338126.	−0.255454	−0.127727	+	0.991809i	$0.540768\pi$
$282$	175795.	0.131639
$283$	844155.	0.626550	0.313275	−	0.949662i	$-0.398574\pi$
$283$	844155.	0.626550	0.313275	+	0.949662i	$0.398574\pi$
$284$	111018.	0.0816769
$285$	−380846.	−0.277739
$286$	−744317.	−0.538075
$287$	−302398.	−0.216708
$288$	200314.	0.142308
$289$	2.84498e6	2.00371
$290$	37502.0	0.0261854
$291$	−838816.	−0.580676
$292$	−579720.	−0.397888
$293$	1.75108e6	1.19162	0.595809	−	0.803126i	$-0.296832\pi$
$293$	1.75108e6	1.19162	0.595809	+	0.803126i	$0.296832\pi$
$294$	406343.	0.274173
$295$	−1.12222e6	−0.750799
$296$	−700960.	−0.465012
$297$	−1.39118e6	−0.915149
$298$	−579672.	−0.378131
$299$	213629.	0.138192
$300$	68833.9	0.0441570
$301$	756116.	0.481030
$302$	992170.	0.625992
$303$	409709.	0.256371
$304$	−566561.	−0.351611
$305$	142552.	0.0877452
$306$	−1.61593e6	−0.986549
$307$	141361.	0.0856019	0.0428009	−	0.999084i	$-0.486372\pi$
$307$	141361.	0.0856019	0.0428009	+	0.999084i	$0.486372\pi$
$308$	−333714.	−0.200446
$309$	−794373.	−0.473291
$310$	−297627.	−0.175901
$311$	1.45900e6	0.855371	0.427686	−	0.903928i	$-0.359329\pi$
$311$	1.45900e6	0.855371	0.427686	+	0.903928i	$0.359329\pi$
$312$	−177905.	−0.103467
$313$	−2.42277e6	−1.39782	−0.698910	−	0.715209i	$-0.746331\pi$
$313$	−2.42277e6	−1.39782	−0.698910	+	0.715209i	$0.746331\pi$
$314$	541281.	0.309812
$315$	221367.	0.125700
$316$	−521088.	−0.293558
$317$	−3.14717e6	−1.75902	−0.879511	−	0.475878i	$-0.842130\pi$
$317$	−3.14717e6	−1.75902	−0.879511	+	0.475878i	$0.842130\pi$
$318$	465580.	0.258182
$319$	−172802.	−0.0950761
$320$	102400.	0.0559017
$321$	98421.4	0.0533122
$322$	95780.5	0.0514799
$323$	4.57044e6	2.43754
$324$	428051.	0.226534
$325$	252397.	0.132549
$326$	1.65304e6	0.861466
$327$	335691.	0.173608
$328$	−427560.	−0.219439
$329$	289005.	0.147203
$330$	−317172.	−0.160328
$331$	493646.	0.247654	0.123827	−	0.992304i	$-0.460483\pi$
$331$	493646.	0.247654	0.123827	+	0.992304i	$0.460483\pi$
$332$	−178423.	−0.0888394
$333$	−2.14252e6	−1.05880
$334$	−1.15401e6	−0.566037
$335$	−252317.	−0.122839
$336$	−79763.4	−0.0385439
$337$	2.12057e6	1.01713	0.508566	−	0.861023i	$-0.330176\pi$
$337$	2.12057e6	1.01713	0.508566	+	0.861023i	$0.330176\pi$
$338$	832838.	0.396523
$339$	−909862.	−0.430008
$340$	−826059.	−0.387538
$341$	1.37140e6	0.638674
$342$	−1.73172e6	−0.800594
$343$	1.42879e6	0.655742
$344$	1.06907e6	0.487092
$345$	91032.8	0.0411766
$346$	−2.64413e6	−1.18739
$347$	−1.02396e6	−0.456518	−0.228259	−	0.973600i	$-0.573303\pi$
$347$	−1.02396e6	−0.456518	−0.228259	+	0.973600i	$0.573303\pi$
$348$	−41302.6	−0.0182822
$349$	2.89897e6	1.27403	0.637016	−	0.770851i	$-0.280169\pi$
$349$	2.89897e6	1.27403	0.637016	+	0.770851i	$0.280169\pi$
$350$	113162.	0.0493778
$351$	−1.21926e6	−0.528235
$352$	−471838.	−0.202972
$353$	−1.69107e6	−0.722311	−0.361156	−	0.932506i	$-0.617618\pi$
$353$	−1.69107e6	−0.722311	−0.361156	+	0.932506i	$0.617618\pi$
$354$	1.23595e6	0.524195
$355$	173466.	0.0730540
$356$	−1.96186e6	−0.820434
$357$	643450.	0.267205
$358$	−2.80418e6	−1.15637
$359$	3.98436e6	1.63163	0.815817	−	0.578310i	$-0.196287\pi$
$359$	3.98436e6	1.63163	0.815817	+	0.578310i	$0.196287\pi$
$360$	312990.	0.127284
$361$	2.42184e6	0.978088
$362$	−2.65887e6	−1.06641
$363$	352889.	0.140563
$364$	−292473.	−0.115700
$365$	−905812.	−0.355882
$366$	−156998.	−0.0612622
$367$	−1.85471e6	−0.718805	−0.359403	−	0.933183i	$-0.617020\pi$
$367$	−1.85471e6	−0.718805	−0.359403	+	0.933183i	$0.617020\pi$
$368$	135424.	0.0521286
$369$	−1.30686e6	−0.499646
$370$	−1.09525e6	−0.415919
$371$	765409.	0.288708
$372$	327789.	0.122811
$373$	−4.45635e6	−1.65847	−0.829234	−	0.558902i	$-0.811223\pi$
$373$	−4.45635e6	−1.65847	−0.829234	+	0.558902i	$0.811223\pi$
$374$	3.80631e6	1.40710
$375$	107553.	0.0394952
$376$	408624.	0.149058
$377$	−151447.	−0.0548790
$378$	−546652.	−0.196780
$379$	926813.	0.331432	0.165716	−	0.986174i	$-0.447007\pi$
$379$	926813.	0.331432	0.165716	+	0.986174i	$0.447007\pi$
$380$	−885252.	−0.314491
$381$	579014.	0.204351
$382$	−305323.	−0.107053
$383$	4.49238e6	1.56487	0.782437	−	0.622730i	$-0.213977\pi$
$383$	4.49238e6	1.56487	0.782437	+	0.622730i	$0.213977\pi$
$384$	−112777.	−0.0390296
$385$	−521428.	−0.179285
$386$	2.01586e6	0.688640
$387$	3.26767e6	1.10907
$388$	−1.94977e6	−0.657514
$389$	−643202.	−0.215513	−0.107756	−	0.994177i	$-0.534367\pi$
$389$	−643202.	−0.215513	−0.107756	+	0.994177i	$0.534367\pi$
$390$	−277976.	−0.0925435
$391$	−1.09246e6	−0.361381
$392$	944518.	0.310452
$393$	683950.	0.223379
$394$	684146.	0.222028
$395$	−814200.	−0.262566
$396$	−1.44220e6	−0.462153
$397$	−3.12429e6	−0.994889	−0.497444	−	0.867496i	$-0.665728\pi$
$397$	−3.12429e6	−0.994889	−0.497444	+	0.867496i	$0.665728\pi$
$398$	−323600.	−0.102400
$399$	689558.	0.216839
$400$	160000.	0.0500000
$401$	−3.57022e6	−1.10875	−0.554375	−	0.832267i	$-0.687043\pi$
$401$	−3.57022e6	−1.10875	−0.554375	+	0.832267i	$0.687043\pi$
$402$	277887.	0.0857637
$403$	1.20192e6	0.368650
$404$	952342.	0.290295
$405$	668829.	0.202618
$406$	−67901.0	−0.0204438
$407$	5.04669e6	1.51015
$408$	909774.	0.270572
$409$	−5.67217e6	−1.67664	−0.838322	−	0.545176i	$-0.816463\pi$
$409$	−5.67217e6	−1.67664	−0.838322	+	0.545176i	$0.816463\pi$
$410$	−668063.	−0.196272
$411$	−1.15338e6	−0.336798
$412$	−1.84647e6	−0.535919
$413$	2.03189e6	0.586172
$414$	413930.	0.118693
$415$	−278786.	−0.0794604
$416$	−413528.	−0.117158
$417$	1.76123e6	0.495992
$418$	4.07906e6	1.14188
$419$	2.82239e6	0.785384	0.392692	−	0.919670i	$-0.371544\pi$
$419$	2.82239e6	0.785384	0.392692	+	0.919670i	$0.371544\pi$
$420$	−124630.	−0.0344747
$421$	−5.42319e6	−1.49125	−0.745623	−	0.666368i	$-0.767848\pi$
$421$	−5.42319e6	−1.49125	−0.745623	+	0.666368i	$0.767848\pi$
$422$	−696662.	−0.190432
$423$	1.24898e6	0.339394
$424$	1.08221e6	0.292346
$425$	−1.29072e6	−0.346624
$426$	−191046.	−0.0510051
$427$	−258104.	−0.0685054
$428$	228774.	0.0603667
$429$	1.28086e6	0.336014
$430$	1.67042e6	0.435668
$431$	−1.92799e6	−0.499932	−0.249966	−	0.968255i	$-0.580419\pi$
$431$	−1.92799e6	−0.499932	−0.249966	+	0.968255i	$0.580419\pi$
$432$	−772911.	−0.199260
$433$	2.24911e6	0.576488	0.288244	−	0.957557i	$-0.406929\pi$
$433$	2.24911e6	0.576488	0.288244	+	0.957557i	$0.406929\pi$
$434$	538882.	0.137331
$435$	−64535.3	−0.0163521
$436$	780293.	0.196581
$437$	−1.17075e6	−0.293264
$438$	997609.	0.248471
$439$	−1.97530e6	−0.489185	−0.244592	−	0.969626i	$-0.578654\pi$
$439$	−1.97530e6	−0.489185	−0.244592	+	0.969626i	$0.578654\pi$
$440$	−737247.	−0.181544
$441$	2.88696e6	0.706878
$442$	3.33592e6	0.812195
$443$	2.02443e6	0.490110	0.245055	−	0.969509i	$-0.421194\pi$
$443$	2.02443e6	0.490110	0.245055	+	0.969509i	$0.421194\pi$
$444$	1.20625e6	0.290388
$445$	−3.06541e6	−0.733818
$446$	5.65396e6	1.34591
$447$	997527.	0.236133
$448$	−185405.	−0.0436442
$449$	2.04095e6	0.477768	0.238884	−	0.971048i	$-0.423218\pi$
$449$	2.04095e6	0.477768	0.238884	+	0.971048i	$0.423218\pi$
$450$	489047.	0.113846
$451$	3.07830e6	0.712639
$452$	−2.11492e6	−0.486908
$453$	−1.70737e6	−0.390916
$454$	−5.25994e6	−1.19768
$455$	−456990.	−0.103485
$456$	974965.	0.219572
$457$	1.68821e6	0.378126	0.189063	−	0.981965i	$-0.439455\pi$
$457$	1.68821e6	0.378126	0.189063	+	0.981965i	$0.439455\pi$
$458$	−3.03633e6	−0.676371
$459$	6.23506e6	1.38137
$460$	211600.	0.0466252
$461$	−1.13364e6	−0.248441	−0.124220	−	0.992255i	$-0.539643\pi$
$461$	−1.13364e6	−0.248441	−0.124220	+	0.992255i	$0.539643\pi$
$462$	574271.	0.125173
$463$	4.29330e6	0.930762	0.465381	−	0.885110i	$-0.345917\pi$
$463$	4.29330e6	0.930762	0.465381	+	0.885110i	$0.345917\pi$
$464$	−96005.2	−0.0207014
$465$	512171.	0.109845
$466$	−470081.	−0.100279
$467$	−8.22958e6	−1.74617	−0.873083	−	0.487572i	$-0.837883\pi$
$467$	−8.22958e6	−1.74617	−0.873083	+	0.487572i	$0.837883\pi$
$468$	−1.26397e6	−0.266760
$469$	456844.	0.0959038
$470$	638474.	0.133321
$471$	−931462.	−0.193470
$472$	2.87289e6	0.593559
$473$	−7.69698e6	−1.58186
$474$	896713.	0.183319
$475$	−1.38321e6	−0.281289
$476$	1.49566e6	0.302563
$477$	3.30783e6	0.665652
$478$	1.08812e6	0.217824
$479$	6.87649e6	1.36939	0.684697	−	0.728828i	$-0.259935\pi$
$479$	6.87649e6	1.36939	0.684697	+	0.728828i	$0.259935\pi$
$480$	−176215.	−0.0349091
$481$	4.42301e6	0.871677
$482$	−3.57266e6	−0.700444
$483$	−164824.	−0.0321478
$484$	820268.	0.159163
$485$	−3.04652e6	−0.588098
$486$	−3.67126e6	−0.705057
$487$	−769227.	−0.146971	−0.0734856	−	0.997296i	$-0.523412\pi$
$487$	−769227.	−0.146971	−0.0734856	+	0.997296i	$0.523412\pi$
$488$	−364933.	−0.0693687
$489$	−2.84462e6	−0.537963
$490$	1.47581e6	0.277677
$491$	8.16816e6	1.52905	0.764523	−	0.644597i	$-0.222975\pi$
$491$	8.16816e6	1.52905	0.764523	+	0.644597i	$0.222975\pi$
$492$	735766.	0.137034
$493$	774472.	0.143512
$494$	3.57496e6	0.659105
$495$	−2.25343e6	−0.413363
$496$	761925.	0.139062
$497$	−314077.	−0.0570355
$498$	307039.	0.0554779
$499$	−6.66287e6	−1.19787	−0.598935	−	0.800797i	$-0.704409\pi$
$499$	−6.66287e6	−1.19787	−0.598935	+	0.800797i	$0.704409\pi$
$500$	250000.	0.0447214
$501$	1.98588e6	0.353475
$502$	−1.57679e6	−0.279263
$503$	8.72497e6	1.53760	0.768801	−	0.639489i	$-0.220854\pi$
$503$	8.72497e6	1.53760	0.768801	+	0.639489i	$0.220854\pi$
$504$	−566699.	−0.0993747
$505$	1.48803e6	0.259648
$506$	−975009.	−0.169290
$507$	−1.43319e6	−0.247619
$508$	1.34588e6	0.231391
$509$	4.72025e6	0.807552	0.403776	−	0.914858i	$-0.367697\pi$
$509$	4.72025e6	0.807552	0.403776	+	0.914858i	$0.367697\pi$
$510$	1.42152e6	0.242007
$511$	1.64006e6	0.277848
$512$	−262144.	−0.0441942
$513$	6.68185e6	1.12099
$514$	805725.	0.134518
$515$	−2.88511e6	−0.479340
$516$	−1.83971e6	−0.304176
$517$	−2.94196e6	−0.484072
$518$	1.98305e6	0.324721
$519$	4.55015e6	0.741493
$520$	−646137.	−0.104789
$521$	−1.09945e7	−1.77452	−0.887259	−	0.461271i	$-0.847394\pi$
$521$	−1.09945e7	−1.77452	−0.887259	+	0.461271i	$0.847394\pi$
$522$	−293444.	−0.0471356
$523$	8.83137e6	1.41180	0.705901	−	0.708311i	$-0.250542\pi$
$523$	8.83137e6	1.41180	0.705901	+	0.708311i	$0.250542\pi$
$524$	1.58980e6	0.252938
$525$	−194735.	−0.0308351
$526$	128732.	0.0202872
$527$	−6.14644e6	−0.964044
$528$	811962.	0.126751
$529$	279841.	0.0434783
$530$	1.69096e6	0.261482
$531$	8.78112e6	1.35149
$532$	1.60283e6	0.245533
$533$	2.69788e6	0.411343
$534$	3.37607e6	0.512339
$535$	357460.	0.0539937
$536$	645932.	0.0971124
$537$	4.82556e6	0.722125
$538$	−8.87332e6	−1.32169
$539$	−6.80023e6	−1.00821
$540$	−1.20767e6	−0.178224
$541$	4.97989e6	0.731521	0.365760	−	0.930709i	$-0.380809\pi$
$541$	4.97989e6	0.731521	0.365760	+	0.930709i	$0.380809\pi$
$542$	202845.	0.0296597
$543$	4.57551e6	0.665947
$544$	2.11471e6	0.306375
$545$	1.21921e6	0.175827
$546$	503302.	0.0722515
$547$	1.63280e6	0.233327	0.116664	−	0.993171i	$-0.462780\pi$
$547$	1.63280e6	0.233327	0.116664	+	0.993171i	$0.462780\pi$
$548$	−2.68097e6	−0.381364
$549$	−1.11543e6	−0.157948
$550$	−1.15195e6	−0.162378
$551$	829968.	0.116462
$552$	−233044.	−0.0325529
$553$	1.47419e6	0.204993
$554$	8.47290e6	1.17289
$555$	1.88476e6	0.259731
$556$	4.09386e6	0.561624
$557$	7.59106e6	1.03673	0.518364	−	0.855160i	$-0.326541\pi$
$557$	7.59106e6	1.03673	0.518364	+	0.855160i	$0.326541\pi$
$558$	2.32886e6	0.316634
$559$	−6.74578e6	−0.913066
$560$	−289695.	−0.0390365
$561$	−6.55008e6	−0.878698
$562$	1.35251e6	0.180633
$563$	−9.48022e6	−1.26051	−0.630257	−	0.776387i	$-0.717050\pi$
$563$	−9.48022e6	−1.26051	−0.630257	+	0.776387i	$0.717050\pi$
$564$	−703179.	−0.0930825
$565$	−3.30456e6	−0.435504
$566$	−3.37662e6	−0.443038
$567$	−1.21098e6	−0.158190
$568$	−444074.	−0.0577543
$569$	−1.29931e7	−1.68241	−0.841206	−	0.540714i	$-0.818154\pi$
$569$	−1.29931e7	−1.68241	−0.841206	+	0.540714i	$0.818154\pi$
$570$	1.52338e6	0.196391
$571$	−1.39451e7	−1.78992	−0.894958	−	0.446151i	$-0.852794\pi$
$571$	−1.39451e7	−1.78992	−0.894958	+	0.446151i	$0.852794\pi$
$572$	2.97727e6	0.380477
$573$	525414.	0.0668521
$574$	1.20959e6	0.153235
$575$	330625.	0.0417029
$576$	−801255.	−0.100627
$577$	−1.26617e7	−1.58326	−0.791629	−	0.611002i	$-0.790767\pi$
$577$	−1.26617e7	−1.58326	−0.791629	+	0.611002i	$0.790767\pi$
$578$	−1.13799e7	−1.41684
$579$	−3.46899e6	−0.430038
$580$	−150008.	−0.0185159
$581$	504769.	0.0620372
$582$	3.35526e6	0.410600
$583$	−7.79158e6	−0.949410
$584$	2.31888e6	0.281349
$585$	−1.97495e6	−0.238598
$586$	−7.00432e6	−0.842601
$587$	9.70862e6	1.16295	0.581476	−	0.813563i	$-0.302475\pi$
$587$	9.70862e6	1.16295	0.581476	+	0.813563i	$0.302475\pi$
$588$	−1.62537e6	−0.193869
$589$	−6.58687e6	−0.782331
$590$	4.48889e6	0.530895
$591$	−1.17731e6	−0.138651
$592$	2.80384e6	0.328813
$593$	5.98538e6	0.698964	0.349482	−	0.936943i	$-0.386358\pi$
$593$	5.98538e6	0.698964	0.349482	+	0.936943i	$0.386358\pi$
$594$	5.56471e6	0.647108
$595$	2.33697e6	0.270620
$596$	2.31869e6	0.267379
$597$	556867.	0.0639463
$598$	−854517.	−0.0977164
$599$	8.53936e6	0.972430	0.486215	−	0.873839i	$-0.338377\pi$
$599$	8.53936e6	0.972430	0.486215	+	0.873839i	$0.338377\pi$
$600$	−275336.	−0.0312237
$601$	−1.48231e7	−1.67399	−0.836993	−	0.547214i	$-0.815688\pi$
$601$	−1.48231e7	−1.67399	−0.836993	+	0.547214i	$0.815688\pi$
$602$	−3.02446e6	−0.340140
$603$	1.97432e6	0.221118
$604$	−3.96868e6	−0.442643
$605$	1.28167e6	0.142360
$606$	−1.63884e6	−0.181282
$607$	−4.87597e6	−0.537142	−0.268571	−	0.963260i	$-0.586551\pi$
$607$	−4.87597e6	−0.537142	−0.268571	+	0.963260i	$0.586551\pi$
$608$	2.26624e6	0.248627
$609$	116847.	0.0127666
$610$	−570208.	−0.0620452
$611$	−2.57839e6	−0.279412
$612$	6.46371e6	0.697595
$613$	4.23173e6	0.454848	0.227424	−	0.973796i	$-0.426970\pi$
$613$	4.23173e6	0.454848	0.227424	+	0.973796i	$0.426970\pi$
$614$	−565444.	−0.0605297
$615$	1.14963e6	0.122567
$616$	1.33486e6	0.141737
$617$	9.97619e6	1.05500	0.527499	−	0.849556i	$-0.323130\pi$
$617$	9.97619e6	1.05500	0.527499	+	0.849556i	$0.323130\pi$
$618$	3.17749e6	0.334667
$619$	−8.95919e6	−0.939815	−0.469907	−	0.882716i	$-0.655713\pi$
$619$	−8.95919e6	−0.939815	−0.469907	+	0.882716i	$0.655713\pi$
$620$	1.19051e6	0.124381
$621$	−1.59715e6	−0.166194
$622$	−5.83600e6	−0.604839
$623$	5.55022e6	0.572915
$624$	711619.	0.0731620
$625$	390625.	0.0400000
$626$	9.69108e6	0.988409
$627$	−7.01944e6	−0.713072
$628$	−2.16512e6	−0.219070
$629$	−2.26185e7	−2.27949
$630$	−885467.	−0.0888835
$631$	6.79477e6	0.679362	0.339681	−	0.940541i	$-0.389681\pi$
$631$	6.79477e6	0.679362	0.339681	+	0.940541i	$0.389681\pi$
$632$	2.08435e6	0.207577
$633$	1.19885e6	0.118920
$634$	1.25887e7	1.24382
$635$	2.10294e6	0.206963
$636$	−1.86232e6	−0.182563
$637$	−5.95985e6	−0.581951
$638$	691207.	0.0672289
$639$	−1.35733e6	−0.131502
$640$	−409600.	−0.0395285
$641$	−4.05271e6	−0.389584	−0.194792	−	0.980845i	$-0.562403\pi$
$641$	−4.05271e6	−0.389584	−0.194792	+	0.980845i	$0.562403\pi$
$642$	−393686.	−0.0376974
$643$	1.31980e7	1.25887	0.629434	−	0.777054i	$-0.283287\pi$
$643$	1.31980e7	1.25887	0.629434	+	0.777054i	$0.283287\pi$
$644$	−383122.	−0.0364018
$645$	−2.87455e6	−0.272063
$646$	−1.82818e7	−1.72360
$647$	−7.75045e6	−0.727891	−0.363945	−	0.931420i	$-0.618571\pi$
$647$	−7.75045e6	−0.727891	−0.363945	+	0.931420i	$0.618571\pi$
$648$	−1.71220e6	−0.160184
$649$	−2.06839e7	−1.92761
$650$	−1.00959e6	−0.0937263
$651$	−927334.	−0.0857598
$652$	−6.61214e6	−0.609149
$653$	−3.77035e6	−0.346018	−0.173009	−	0.984920i	$-0.555349\pi$
$653$	−3.77035e6	−0.346018	−0.173009	+	0.984920i	$0.555349\pi$
$654$	−1.34276e6	−0.122760
$655$	2.48406e6	0.226235
$656$	1.71024e6	0.155166
$657$	7.08776e6	0.640613
$658$	−1.15602e6	−0.104088
$659$	−2.41000e6	−0.216174	−0.108087	−	0.994141i	$-0.534472\pi$
$659$	−2.41000e6	−0.216174	−0.108087	+	0.994141i	$0.534472\pi$
$660$	1.26869e6	0.113369
$661$	−1.17936e7	−1.04989	−0.524944	−	0.851137i	$-0.675914\pi$
$661$	−1.17936e7	−1.04989	−0.524944	+	0.851137i	$0.675914\pi$
$662$	−1.97458e6	−0.175118
$663$	−5.74061e6	−0.507195
$664$	713692.	0.0628189
$665$	2.50443e6	0.219611
$666$	8.57007e6	0.748684
$667$	−198386.	−0.0172662
$668$	4.61606e6	0.400249
$669$	−9.72960e6	−0.840484
$670$	1.00927e6	0.0868599
$671$	2.62740e6	0.225279
$672$	319054.	0.0272546
$673$	−4.39020e6	−0.373634	−0.186817	−	0.982395i	$-0.559817\pi$
$673$	−4.39020e6	−0.373634	−0.186817	+	0.982395i	$0.559817\pi$
$674$	−8.48227e6	−0.719221
$675$	−1.88699e6	−0.159408
$676$	−3.33135e6	−0.280384
$677$	−8.60044e6	−0.721189	−0.360594	−	0.932723i	$-0.617426\pi$
$677$	−8.60044e6	−0.721189	−0.360594	+	0.932723i	$0.617426\pi$
$678$	3.63945e6	0.304061
$679$	5.51602e6	0.459146
$680$	3.30424e6	0.274030
$681$	9.05156e6	0.747921
$682$	−5.48562e6	−0.451611
$683$	−5.33828e6	−0.437875	−0.218937	−	0.975739i	$-0.570259\pi$
$683$	−5.33828e6	−0.437875	−0.218937	+	0.975739i	$0.570259\pi$
$684$	6.92688e6	0.566106
$685$	−4.18901e6	−0.341103
$686$	−5.71516e6	−0.463680
$687$	5.22506e6	0.422376
$688$	−4.27629e6	−0.344426
$689$	−6.82868e6	−0.548011
$690$	−364131.	−0.0291162
$691$	2.08639e7	1.66227	0.831133	−	0.556073i	$-0.187693\pi$
$691$	2.08639e7	1.66227	0.831133	+	0.556073i	$0.187693\pi$
$692$	1.05765e7	0.839611
$693$	4.08005e6	0.322725
$694$	4.09583e6	0.322807
$695$	6.39665e6	0.502332
$696$	165210.	0.0129275
$697$	−1.37965e7	−1.07569
$698$	−1.15959e7	−0.900876
$699$	808938.	0.0626213
$700$	−452649.	−0.0349153
$701$	−7.90294e6	−0.607427	−0.303713	−	0.952763i	$-0.598227\pi$
$701$	−7.90294e6	−0.607427	−0.303713	+	0.952763i	$0.598227\pi$
$702$	4.87702e6	0.373518
$703$	−2.42393e7	−1.84983
$704$	1.88735e6	0.143523
$705$	−1.09872e6	−0.0832555
$706$	6.76427e6	0.510751
$707$	−2.69423e6	−0.202715
$708$	−4.94380e6	−0.370662
$709$	1.05967e7	0.791690	0.395845	−	0.918317i	$-0.370452\pi$
$709$	1.05967e7	0.791690	0.395845	+	0.918317i	$0.370452\pi$
$710$	−693865.	−0.0516570
$711$	6.37092e6	0.472637
$712$	7.84745e6	0.580134
$713$	1.57445e6	0.115986
$714$	−2.57380e6	−0.188942
$715$	4.65198e6	0.340309
$716$	1.12167e7	0.817679
$717$	−1.87248e6	−0.136026
$718$	−1.59375e7	−1.15374
$719$	−464773.	−0.0335289	−0.0167644	−	0.999859i	$-0.505337\pi$
$719$	−464773.	−0.0335289	−0.0167644	+	0.999859i	$0.505337\pi$
$720$	−1.25196e6	−0.0900036
$721$	5.22377e6	0.374236
$722$	−9.68737e6	−0.691612
$723$	6.14799e6	0.437409
$724$	1.06355e7	0.754068
$725$	−234388.	−0.0165611
$726$	−1.41156e6	−0.0993932
$727$	2.11980e7	1.48751	0.743755	−	0.668453i	$-0.233043\pi$
$727$	2.11980e7	1.48751	0.743755	+	0.668453i	$0.233043\pi$
$728$	1.16989e6	0.0818122
$729$	−183348.	−0.0127778
$730$	3.62325e6	0.251647
$731$	3.44967e7	2.38773
$732$	627994.	0.0433189
$733$	−5.35702e6	−0.368268	−0.184134	−	0.982901i	$-0.558948\pi$
$733$	−5.35702e6	−0.368268	−0.184134	+	0.982901i	$0.558948\pi$
$734$	7.41885e6	0.508272
$735$	−2.53964e6	−0.173402
$736$	−541696.	−0.0368605
$737$	−4.65050e6	−0.315378
$738$	5.22743e6	0.353303
$739$	1.08732e7	0.732395	0.366197	−	0.930537i	$-0.380660\pi$
$739$	1.08732e7	0.732395	0.366197	+	0.930537i	$0.380660\pi$
$740$	4.38100e6	0.294099
$741$	−6.15197e6	−0.411593
$742$	−3.06164e6	−0.204147
$743$	−2.49116e7	−1.65550	−0.827749	−	0.561098i	$-0.810379\pi$
$743$	−2.49116e7	−1.65550	−0.827749	+	0.561098i	$0.810379\pi$
$744$	−1.31116e6	−0.0868405
$745$	3.62295e6	0.239151
$746$	1.78254e7	1.17271
$747$	2.18143e6	0.143034
$748$	−1.52252e7	−0.994971
$749$	−647215.	−0.0421545
$750$	−430212.	−0.0279273
$751$	−2.84172e7	−1.83858	−0.919288	−	0.393586i	$-0.871234\pi$
$751$	−2.84172e7	−1.83858	−0.919288	+	0.393586i	$0.871234\pi$
$752$	−1.63449e6	−0.105400
$753$	2.71341e6	0.174392
$754$	605787.	0.0388053
$755$	−6.20106e6	−0.395912
$756$	2.18661e6	0.139145
$757$	−3.78962e6	−0.240357	−0.120178	−	0.992752i	$-0.538347\pi$
$757$	−3.78962e6	−0.240357	−0.120178	+	0.992752i	$0.538347\pi$
$758$	−3.70725e6	−0.234358
$759$	1.67784e6	0.105717
$760$	3.54101e6	0.222378
$761$	1.39008e6	0.0870117	0.0435059	−	0.999053i	$-0.486147\pi$
$761$	1.39008e6	0.0870117	0.0435059	+	0.999053i	$0.486147\pi$
$762$	−2.31605e6	−0.144498
$763$	−2.20749e6	−0.137274
$764$	1.22129e6	0.0756982
$765$	1.00996e7	0.623948
$766$	−1.79695e7	−1.10653
$767$	−1.81277e7	−1.11264
$768$	451110.	0.0275981
$769$	−1.70740e7	−1.04117	−0.520583	−	0.853811i	$-0.674285\pi$
$769$	−1.70740e7	−1.04117	−0.520583	+	0.853811i	$0.674285\pi$
$770$	2.08571e6	0.126773
$771$	−1.38653e6	−0.0840027
$772$	−8.06345e6	−0.486942
$773$	4.00548e6	0.241105	0.120552	−	0.992707i	$-0.461533\pi$
$773$	4.00548e6	0.241105	0.120552	+	0.992707i	$0.461533\pi$
$774$	−1.30707e7	−0.784234
$775$	1.86017e6	0.111249
$776$	7.79909e6	0.464932
$777$	−3.41253e6	−0.202780
$778$	2.57281e6	0.152391
$779$	−1.47851e7	−0.872933
$780$	1.11190e6	0.0654381
$781$	3.19719e6	0.187560
$782$	4.36985e6	0.255535
$783$	1.13226e6	0.0659994
$784$	−3.77807e6	−0.219523
$785$	−3.38300e6	−0.195942
$786$	−2.73580e6	−0.157953
$787$	−1.17196e7	−0.674489	−0.337245	−	0.941417i	$-0.609495\pi$
$787$	−1.17196e7	−0.674489	−0.337245	+	0.941417i	$0.609495\pi$
$788$	−2.73659e6	−0.156998
$789$	−221528.	−0.0126688
$790$	3.25680e6	0.185662
$791$	5.98321e6	0.340011
$792$	5.76878e6	0.326792
$793$	2.30270e6	0.130033
$794$	1.24971e7	0.703493
$795$	−2.90988e6	−0.163289
$796$	1.29440e6	0.0724080
$797$	2.55231e7	1.42327	0.711634	−	0.702550i	$-0.247955\pi$
$797$	2.55231e7	1.42327	0.711634	+	0.702550i	$0.247955\pi$
$798$	−2.75823e6	−0.153329
$799$	1.31854e7	0.730681
$800$	−640000.	−0.0353553
$801$	2.39861e7	1.32092
$802$	1.42809e7	0.784005
$803$	−1.66952e7	−0.913698
$804$	−1.11155e6	−0.0606441
$805$	−598628.	−0.0325587
$806$	−4.80770e6	−0.260675
$807$	1.52696e7	0.825362
$808$	−3.80937e6	−0.205270
$809$	1.39728e7	0.750605	0.375302	−	0.926902i	$-0.377539\pi$
$809$	1.39728e7	0.750605	0.375302	+	0.926902i	$0.377539\pi$
$810$	−2.67532e6	−0.143273
$811$	2.73284e7	1.45902	0.729511	−	0.683969i	$-0.239748\pi$
$811$	2.73284e7	1.45902	0.729511	+	0.683969i	$0.239748\pi$
$812$	271604.	0.0144559
$813$	−349066.	−0.0185217
$814$	−2.01868e7	−1.06784
$815$	−1.03315e7	−0.544839
$816$	−3.63910e6	−0.191323
$817$	3.69687e7	1.93766
$818$	2.26887e7	1.18557
$819$	3.57583e6	0.186281
$820$	2.67225e6	0.138785
$821$	1.77637e7	0.919765	0.459882	−	0.887980i	$-0.347892\pi$
$821$	1.77637e7	0.919765	0.459882	+	0.887980i	$0.347892\pi$
$822$	4.61353e6	0.238152
$823$	1.46426e7	0.753563	0.376782	−	0.926302i	$-0.377031\pi$
$823$	1.46426e7	0.753563	0.376782	+	0.926302i	$0.377031\pi$
$824$	7.38588e6	0.378952
$825$	1.98233e6	0.101401
$826$	−8.12756e6	−0.414486
$827$	−1.20498e7	−0.612655	−0.306328	−	0.951926i	$-0.599100\pi$
$827$	−1.20498e7	−0.612655	−0.306328	+	0.951926i	$0.599100\pi$
$828$	−1.65572e6	−0.0839287
$829$	586716.	0.0296512	0.0148256	−	0.999890i	$-0.495281\pi$
$829$	586716.	0.0296512	0.0148256	+	0.999890i	$0.495281\pi$
$830$	1.11514e6	0.0561870
$831$	−1.45806e7	−0.732440
$832$	1.65411e6	0.0828431
$833$	3.04776e7	1.52184
$834$	−7.04490e6	−0.350719
$835$	7.21259e6	0.357993
$836$	−1.63162e7	−0.807429
$837$	−8.98591e6	−0.443352
$838$	−1.12896e7	−0.555351
$839$	−2.09118e7	−1.02562	−0.512809	−	0.858503i	$-0.671395\pi$
$839$	−2.09118e7	−1.02562	−0.512809	+	0.858503i	$0.671395\pi$
$840$	498521.	0.0243773
$841$	−2.03705e7	−0.993143
$842$	2.16927e7	1.05447
$843$	−2.32746e6	−0.112801
$844$	2.78665e6	0.134656
$845$	−5.20524e6	−0.250783
$846$	−4.99591e6	−0.239987
$847$	−2.32058e6	−0.111145
$848$	−4.32885e6	−0.206720
$849$	5.81065e6	0.276666
$850$	5.16287e6	0.245100
$851$	5.79387e6	0.274249
$852$	764183.	0.0360660
$853$	−2.65160e7	−1.24777	−0.623887	−	0.781515i	$-0.714447\pi$
$853$	−2.65160e7	−1.24777	−0.623887	+	0.781515i	$0.714447\pi$
$854$	1.03242e6	0.0484406
$855$	1.08232e7	0.506340
$856$	−915097.	−0.0426857
$857$	4.05691e7	1.88688	0.943439	−	0.331547i	$-0.107571\pi$
$857$	4.05691e7	1.88688	0.943439	+	0.331547i	$0.107571\pi$
$858$	−5.12343e6	−0.237598
$859$	445484.	0.0205992	0.0102996	−	0.999947i	$-0.496721\pi$
$859$	445484.	0.0205992	0.0102996	+	0.999947i	$0.496721\pi$
$860$	−6.68170e6	−0.308064
$861$	−2.08152e6	−0.0956915
$862$	7.71195e6	0.353505
$863$	6.00674e6	0.274544	0.137272	−	0.990533i	$-0.456167\pi$
$863$	6.00674e6	0.274544	0.137272	+	0.990533i	$0.456167\pi$
$864$	3.09165e6	0.140898
$865$	1.65258e7	0.750971
$866$	−8.99643e6	−0.407639
$867$	1.95831e7	0.884776
$868$	−2.15553e6	−0.0971079
$869$	−1.50067e7	−0.674116
$870$	258141.	0.0115627
$871$	−4.07579e6	−0.182040
$872$	−3.12117e6	−0.139004
$873$	2.38383e7	1.05862
$874$	4.68298e6	0.207369
$875$	−707264.	−0.0312292
$876$	−3.99044e6	−0.175695
$877$	3.55021e7	1.55867	0.779337	−	0.626605i	$-0.215556\pi$
$877$	3.55021e7	1.55867	0.779337	+	0.626605i	$0.215556\pi$
$878$	7.90122e6	0.345906
$879$	1.20534e7	0.526182
$880$	2.94899e6	0.128371
$881$	3.19458e7	1.38667	0.693337	−	0.720613i	$-0.256140\pi$
$881$	3.19458e7	1.38667	0.693337	+	0.720613i	$0.256140\pi$
$882$	−1.15478e7	−0.499838
$883$	2.10585e7	0.908919	0.454459	−	0.890767i	$-0.349832\pi$
$883$	2.10585e7	0.908919	0.454459	+	0.890767i	$0.349832\pi$
$884$	−1.33437e7	−0.574309
$885$	−7.72469e6	−0.331530
$886$	−8.09773e6	−0.346560
$887$	1.85709e7	0.792546	0.396273	−	0.918133i	$-0.370303\pi$
$887$	1.85709e7	0.792546	0.396273	+	0.918133i	$0.370303\pi$
$888$	−4.82498e6	−0.205335
$889$	−3.80757e6	−0.161582
$890$	1.22616e7	0.518888
$891$	1.23273e7	0.520205
$892$	−2.26158e7	−0.951701
$893$	1.41303e7	0.592955
$894$	−3.99011e6	−0.166971
$895$	1.75261e7	0.731354
$896$	741620.	0.0308611
$897$	1.47049e6	0.0610214
$898$	−8.16381e6	−0.337833
$899$	−1.11616e6	−0.0460604
$900$	−1.95619e6	−0.0805016
$901$	3.49207e7	1.43308
$902$	−1.23132e7	−0.503912
$903$	5.20464e6	0.212408
$904$	8.45966e6	0.344296
$905$	1.66179e7	0.674459
$906$	6.82950e6	0.276419
$907$	2.39972e7	0.968597	0.484299	−	0.874903i	$-0.339075\pi$
$907$	2.39972e7	0.968597	0.484299	+	0.874903i	$0.339075\pi$
$908$	2.10398e7	0.846889
$909$	−1.16435e7	−0.467384
$910$	1.82796e6	0.0731750
$911$	4.31004e7	1.72062	0.860311	−	0.509770i	$-0.170270\pi$
$911$	4.31004e7	1.72062	0.860311	+	0.509770i	$0.170270\pi$
$912$	−3.89986e6	−0.155261
$913$	−5.13835e6	−0.204008
$914$	−6.75284e6	−0.267375
$915$	981240.	0.0387456
$916$	1.21453e7	0.478266
$917$	−4.49763e6	−0.176628
$918$	−2.49403e7	−0.976774
$919$	−5.03125e7	−1.96511	−0.982555	−	0.185974i	$-0.940456\pi$
$919$	−5.03125e7	−1.96511	−0.982555	+	0.185974i	$0.940456\pi$
$920$	−846400.	−0.0329690
$921$	973042.	0.0377992
$922$	4.53456e6	0.175674
$923$	2.80208e6	0.108262
$924$	−2.29708e6	−0.0885110
$925$	6.84531e6	0.263050
$926$	−1.71732e7	−0.658148
$927$	2.25753e7	0.862847
$928$	384021.	0.0146381
$929$	−4.20715e7	−1.59937	−0.799684	−	0.600421i	$-0.795000\pi$
$929$	−4.20715e7	−1.59937	−0.799684	+	0.600421i	$0.795000\pi$
$930$	−2.04868e6	−0.0776725
$931$	3.26616e7	1.23499
$932$	1.88032e6	0.0709076
$933$	1.00429e7	0.377706
$934$	3.29183e7	1.23473
$935$	−2.37894e7	−0.889929
$936$	5.05587e6	0.188628
$937$	−2.15766e7	−0.802850	−0.401425	−	0.915892i	$-0.631485\pi$
$937$	−2.15766e7	−0.802850	−0.401425	+	0.915892i	$0.631485\pi$
$938$	−1.82738e6	−0.0678142
$939$	−1.66769e7	−0.617235
$940$	−2.55390e6	−0.0942723
$941$	−1.91249e7	−0.704084	−0.352042	−	0.935984i	$-0.614513\pi$
$941$	−1.91249e7	−0.704084	−0.352042	+	0.935984i	$0.614513\pi$
$942$	3.72585e6	0.136804
$943$	3.53405e6	0.129418
$944$	−1.14916e7	−0.419710
$945$	3.41658e6	0.124455
$946$	3.07879e7	1.11854
$947$	3.10515e7	1.12514	0.562571	−	0.826749i	$-0.309812\pi$
$947$	3.10515e7	1.12514	0.562571	+	0.826749i	$0.309812\pi$
$948$	−3.58685e6	−0.129626
$949$	−1.46320e7	−0.527397
$950$	5.53282e6	0.198901
$951$	−2.16632e7	−0.776731
$952$	−5.98264e6	−0.213944
$953$	−4.80997e7	−1.71558	−0.857788	−	0.514003i	$-0.828162\pi$
$953$	−4.80997e7	−1.71558	−0.857788	+	0.514003i	$0.828162\pi$
$954$	−1.32313e7	−0.470687
$955$	1.90827e6	0.0677066
$956$	−4.35247e6	−0.154025
$957$	−1.18946e6	−0.0419827
$958$	−2.75060e7	−0.968307
$959$	7.58460e6	0.266309
$960$	704859.	0.0246845
$961$	−1.97710e7	−0.690589
$962$	−1.76921e7	−0.616369
$963$	−2.79704e6	−0.0971924
$964$	1.42906e7	0.495289
$965$	−1.25991e7	−0.435534
$966$	659295.	0.0227319
$967$	1.23596e7	0.425048	0.212524	−	0.977156i	$-0.431832\pi$
$967$	1.23596e7	0.425048	0.212524	+	0.977156i	$0.431832\pi$
$968$	−3.28107e6	−0.112545
$969$	3.14601e7	1.07634
$970$	1.21861e7	0.415848
$971$	−3.17693e7	−1.08133	−0.540666	−	0.841237i	$-0.681828\pi$
$971$	−3.17693e7	−1.08133	−0.540666	+	0.841237i	$0.681828\pi$
$972$	1.46850e7	0.498551
$973$	−1.15817e7	−0.392186
$974$	3.07691e6	0.103924
$975$	1.73735e6	0.0585296
$976$	1.45973e6	0.0490511
$977$	−5.61670e6	−0.188254	−0.0941272	−	0.995560i	$-0.530006\pi$
$977$	−5.61670e6	−0.188254	−0.0941272	+	0.995560i	$0.530006\pi$
$978$	1.13785e7	0.380397
$979$	−5.64991e7	−1.88402
$980$	−5.90324e6	−0.196347
$981$	−9.54000e6	−0.316502
$982$	−3.26726e7	−1.08120
$983$	−1.64312e7	−0.542359	−0.271179	−	0.962529i	$-0.587414\pi$
$983$	−1.64312e7	−0.542359	−0.271179	+	0.962529i	$0.587414\pi$
$984$	−2.94307e6	−0.0968974
$985$	−4.27592e6	−0.140423
$986$	−3.09789e6	−0.101478
$987$	1.98933e6	0.0650002
$988$	−1.42999e7	−0.466057
$989$	−8.83655e6	−0.287271
$990$	9.01372e6	0.292291
$991$	−3.08869e7	−0.999056	−0.499528	−	0.866298i	$-0.666493\pi$
$991$	−3.08869e7	−0.999056	−0.499528	+	0.866298i	$0.666493\pi$
$992$	−3.04770e6	−0.0983316
$993$	3.39796e6	0.109357
$994$	1.25631e6	0.0403302
$995$	2.02250e6	0.0647636
$996$	−1.22815e6	−0.0392288
$997$	1.19045e7	0.379293	0.189646	−	0.981852i	$-0.439266\pi$
$997$	1.19045e7	0.379293	0.189646	+	0.981852i	$0.439266\pi$
$998$	2.66515e7	0.847023
$999$	−3.30676e7	−1.04831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.c.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.c.1.3	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +6.88339 q^{3} +16.0000 q^{4} +25.0000 q^{5} -27.5336 q^{6} -45.2649 q^{7} -64.0000 q^{8} -195.619 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +6.88339 q^{3} +16.0000 q^{4} +25.0000 q^{5} -27.5336 q^{6} -45.2649 q^{7} -64.0000 q^{8} -195.619 q^{9} -100.000 q^{10} +460.780 q^{11} +110.134 q^{12} +403.836 q^{13} +181.060 q^{14} +172.085 q^{15} +256.000 q^{16} -2065.15 q^{17} +782.476 q^{18} -2213.13 q^{19} +400.000 q^{20} -311.576 q^{21} -1843.12 q^{22} +529.000 q^{23} -440.537 q^{24} +625.000 q^{25} -1615.34 q^{26} -3019.19 q^{27} -724.238 q^{28} -375.020 q^{29} -688.339 q^{30} +2976.27 q^{31} -1024.00 q^{32} +3171.72 q^{33} +8260.59 q^{34} -1131.62 q^{35} -3129.90 q^{36} +10952.5 q^{37} +8852.52 q^{38} +2779.76 q^{39} -1600.00 q^{40} +6680.63 q^{41} +1246.30 q^{42} -16704.2 q^{43} +7372.47 q^{44} -4890.47 q^{45} -2116.00 q^{46} -6384.74 q^{47} +1762.15 q^{48} -14758.1 q^{49} -2500.00 q^{50} -14215.2 q^{51} +6461.37 q^{52} -16909.6 q^{53} +12076.7 q^{54} +11519.5 q^{55} +2896.95 q^{56} -15233.8 q^{57} +1500.08 q^{58} -44888.9 q^{59} +2753.36 q^{60} +5702.08 q^{61} -11905.1 q^{62} +8854.67 q^{63} +4096.00 q^{64} +10095.9 q^{65} -12686.9 q^{66} -10092.7 q^{67} -33042.4 q^{68} +3641.31 q^{69} +4526.49 q^{70} +6938.65 q^{71} +12519.6 q^{72} -36232.5 q^{73} -43810.0 q^{74} +4302.12 q^{75} -35410.1 q^{76} -20857.1 q^{77} -11119.0 q^{78} -32568.0 q^{79} +6400.00 q^{80} +26753.2 q^{81} -26722.5 q^{82} -11151.4 q^{83} -4985.21 q^{84} -51628.7 q^{85} +66817.0 q^{86} -2581.41 q^{87} -29489.9 q^{88} -122616. q^{89} +19561.9 q^{90} -18279.6 q^{91} +8464.00 q^{92} +20486.8 q^{93} +25539.0 q^{94} -55328.2 q^{95} -7048.59 q^{96} -121861. q^{97} +59032.4 q^{98} -90137.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} - 26 q^{3} + 48 q^{4} + 75 q^{5} + 104 q^{6} + q^{7} - 192 q^{8} - 71 q^{9}+O(q^{10}) \) 3 * q - 12 * q^2 - 26 * q^3 + 48 * q^4 + 75 * q^5 + 104 * q^6 + q^7 - 192 * q^8 - 71 * q^9	\( 3 q - 12 q^{2} - 26 q^{3} + 48 q^{4} + 75 q^{5} + 104 q^{6} + q^{7} - 192 q^{8} - 71 q^{9} - 300 q^{10} + 178 q^{11} - 416 q^{12} - 236 q^{13} - 4 q^{14} - 650 q^{15} + 768 q^{16} - 1683 q^{17} + 284 q^{18} - 194 q^{19} + 1200 q^{20} + 504 q^{21} - 712 q^{22} + 1587 q^{23} + 1664 q^{24} + 1875 q^{25} + 944 q^{26} + 622 q^{27} + 16 q^{28} + 6901 q^{29} + 2600 q^{30} + 6119 q^{31} - 3072 q^{32} + 4792 q^{33} + 6732 q^{34} + 25 q^{35} - 1136 q^{36} + 5185 q^{37} + 776 q^{38} + 16234 q^{39} - 4800 q^{40} + 6727 q^{41} - 2016 q^{42} - 22988 q^{43} + 2848 q^{44} - 1775 q^{45} - 6348 q^{46} - 13730 q^{47} - 6656 q^{48} - 11788 q^{49} - 7500 q^{50} - 20140 q^{51} - 3776 q^{52} - 38027 q^{53} - 2488 q^{54} + 4450 q^{55} - 64 q^{56} - 62424 q^{57} - 27604 q^{58} - 43715 q^{59} - 10400 q^{60} - 51364 q^{61} - 24476 q^{62} - 40095 q^{63} + 12288 q^{64} - 5900 q^{65} - 19168 q^{66} - 51891 q^{67} - 26928 q^{68} - 13754 q^{69} - 100 q^{70} - 25667 q^{71} + 4544 q^{72} - 108532 q^{73} - 20740 q^{74} - 16250 q^{75} - 3104 q^{76} - 95646 q^{77} - 64936 q^{78} - 224 q^{79} + 19200 q^{80} - 38213 q^{81} - 26908 q^{82} - 61071 q^{83} + 8064 q^{84} - 42075 q^{85} + 91952 q^{86} - 82842 q^{87} - 11392 q^{88} - 93372 q^{89} + 7100 q^{90} + 33030 q^{91} + 25392 q^{92} - 73542 q^{93} + 54920 q^{94} - 4850 q^{95} + 26624 q^{96} - 260238 q^{97} + 47152 q^{98} - 8150 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 - 26 * q^3 + 48 * q^4 + 75 * q^5 + 104 * q^6 + q^7 - 192 * q^8 - 71 * q^9 - 300 * q^10 + 178 * q^11 - 416 * q^12 - 236 * q^13 - 4 * q^14 - 650 * q^15 + 768 * q^16 - 1683 * q^17 + 284 * q^18 - 194 * q^19 + 1200 * q^20 + 504 * q^21 - 712 * q^22 + 1587 * q^23 + 1664 * q^24 + 1875 * q^25 + 944 * q^26 + 622 * q^27 + 16 * q^28 + 6901 * q^29 + 2600 * q^30 + 6119 * q^31 - 3072 * q^32 + 4792 * q^33 + 6732 * q^34 + 25 * q^35 - 1136 * q^36 + 5185 * q^37 + 776 * q^38 + 16234 * q^39 - 4800 * q^40 + 6727 * q^41 - 2016 * q^42 - 22988 * q^43 + 2848 * q^44 - 1775 * q^45 - 6348 * q^46 - 13730 * q^47 - 6656 * q^48 - 11788 * q^49 - 7500 * q^50 - 20140 * q^51 - 3776 * q^52 - 38027 * q^53 - 2488 * q^54 + 4450 * q^55 - 64 * q^56 - 62424 * q^57 - 27604 * q^58 - 43715 * q^59 - 10400 * q^60 - 51364 * q^61 - 24476 * q^62 - 40095 * q^63 + 12288 * q^64 - 5900 * q^65 - 19168 * q^66 - 51891 * q^67 - 26928 * q^68 - 13754 * q^69 - 100 * q^70 - 25667 * q^71 + 4544 * q^72 - 108532 * q^73 - 20740 * q^74 - 16250 * q^75 - 3104 * q^76 - 95646 * q^77 - 64936 * q^78 - 224 * q^79 + 19200 * q^80 - 38213 * q^81 - 26908 * q^82 - 61071 * q^83 + 8064 * q^84 - 42075 * q^85 + 91952 * q^86 - 82842 * q^87 - 11392 * q^88 - 93372 * q^89 + 7100 * q^90 + 33030 * q^91 + 25392 * q^92 - 73542 * q^93 + 54920 * q^94 - 4850 * q^95 + 26624 * q^96 - 260238 * q^97 + 47152 * q^98 - 8150 * q^99

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