LMFDB - Embedded newform 165.6.c.b.34.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [165,6,Mod(34,165)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("165.34"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(165, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [26,0,0,-418] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.12
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.31741i q^{2} +9.00000i q^{3} +30.2644 q^{4} +(-35.6376 - 43.0693i) q^{5} +11.8567 q^{6} +87.4786i q^{7} -82.0279i q^{8} -81.0000 q^{9} +(-56.7399 + 46.9494i) q^{10} +121.000 q^{11} +272.380i q^{12} +521.292i q^{13} +115.245 q^{14} +(387.623 - 320.739i) q^{15} +860.397 q^{16} +68.1523i q^{17} +106.710i q^{18} +1588.76 q^{19} +(-1078.55 - 1303.47i) q^{20} -787.308 q^{21} -159.407i q^{22} +191.904i q^{23} +738.251 q^{24} +(-584.921 + 3069.77i) q^{25} +686.756 q^{26} -729.000i q^{27} +2647.49i q^{28} +4252.98 q^{29} +(-422.545 - 510.659i) q^{30} -83.6771 q^{31} -3758.39i q^{32} +1089.00i q^{33} +89.7846 q^{34} +(3767.64 - 3117.53i) q^{35} -2451.42 q^{36} +14445.4i q^{37} -2093.06i q^{38} -4691.63 q^{39} +(-3532.88 + 2923.28i) q^{40} +6151.94 q^{41} +1037.21i q^{42} +1408.62i q^{43} +3662.00 q^{44} +(2886.65 + 3488.61i) q^{45} +252.816 q^{46} +14797.5i q^{47} +7743.57i q^{48} +9154.49 q^{49} +(4044.15 + 770.582i) q^{50} -613.371 q^{51} +15776.6i q^{52} +10938.4i q^{53} -960.393 q^{54} +(-4312.15 - 5211.38i) q^{55} +7175.69 q^{56} +14298.9i q^{57} -5602.92i q^{58} +16099.1 q^{59} +(11731.2 - 9706.97i) q^{60} +41095.0 q^{61} +110.237i q^{62} -7085.77i q^{63} +22581.4 q^{64} +(22451.7 - 18577.6i) q^{65} +1434.66 q^{66} +1254.02i q^{67} +2062.59i q^{68} -1727.14 q^{69} +(-4107.07 - 4963.53i) q^{70} +47638.4 q^{71} +6644.26i q^{72} -7358.01i q^{73} +19030.5 q^{74} +(-27627.9 - 5264.29i) q^{75} +48083.1 q^{76} +10584.9i q^{77} +6180.81i q^{78} -90184.5 q^{79} +(-30662.5 - 37056.7i) q^{80} +6561.00 q^{81} -8104.64i q^{82} +10857.0i q^{83} -23827.4 q^{84} +(2935.27 - 2428.79i) q^{85} +1855.73 q^{86} +38276.8i q^{87} -9925.37i q^{88} -112869. q^{89} +(4595.93 - 3802.90i) q^{90} -45601.9 q^{91} +5807.86i q^{92} -753.094i q^{93} +19494.4 q^{94} +(-56619.8 - 68426.9i) q^{95} +33825.5 q^{96} -96993.9i q^{97} -12060.2i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29}+ \cdots - 254826 q^{99}+O(q^{100}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.31741i		−	0.232888i	−0.993197	−	0.116444i	$-0.962851\pi$
$2$		−	1.31741i		−	0.232888i	0.993197	−	0.116444i	$-0.0371495\pi$
$3$			9.00000i			0.577350i
$3$			9.00000i			0.577350i
$4$	30.2644			0.945763
$5$	−35.6376	−	43.0693i	−0.637505	−	0.770446i
$5$	−35.6376	−	43.0693i	−0.637505	−	0.770446i
$6$	11.8567			0.134458
$7$			87.4786i			0.674772i	0.941366	+	0.337386i	$0.109543\pi$
$7$			87.4786i			0.674772i	−0.941366	+	0.337386i	$0.890457\pi$
$8$		−	82.0279i		−	0.453144i
$9$	−81.0000			−0.333333
$10$	−56.7399	+	46.9494i	−0.179427	+	0.148467i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$			272.380i			0.546037i
$13$			521.292i			0.855506i	0.903896	+	0.427753i	$0.140695\pi$
$13$			521.292i			0.855506i	−0.903896	+	0.427753i	$0.859305\pi$
$14$	115.245			0.157146
$15$	387.623	−	320.739i	0.444817	−	0.368064i
$16$	860.397			0.840232
$17$			68.1523i			0.0571950i	0.999591	+	0.0285975i	$0.00910411\pi$
$17$			68.1523i			0.0571950i	−0.999591	+	0.0285975i	$0.990896\pi$
$18$			106.710i			0.0776292i
$19$	1588.76			1.00966			0.504830	−	0.863219i	$-0.331555\pi$
$19$	1588.76			1.00966			0.504830	+	0.863219i	$0.331555\pi$
$20$	−1078.55	−	1303.47i	−0.602929	−	0.728660i
$21$	−787.308			−0.389580
$22$		−	159.407i		−	0.0702183i
$23$			191.904i			0.0756422i	0.999285	+	0.0378211i	$0.0120417\pi$
$23$			191.904i			0.0756422i	−0.999285	+	0.0378211i	$0.987958\pi$
$24$	738.251			0.261623
$25$	−584.921	+	3069.77i	−0.187175	+	0.982327i
$26$	686.756			0.199237
$27$		−	729.000i		−	0.192450i
$28$			2647.49i			0.638174i
$29$	4252.98			0.939071			0.469535	−	0.882914i	$-0.344421\pi$
$29$	4252.98			0.939071			0.469535	+	0.882914i	$0.344421\pi$
$30$	−422.545	−	510.659i	−0.0857175	−	0.103592i
$31$	−83.6771			−0.0156388			−0.00781938	−	0.999969i	$-0.502489\pi$
$31$	−83.6771			−0.0156388			−0.00781938	+	0.999969i	$0.502489\pi$
$32$		−	3758.39i		−	0.648824i
$33$			1089.00i			0.174078i
$34$	89.7846			0.0133200
$35$	3767.64	−	3117.53i	0.519875	−	0.430170i
$36$	−2451.42			−0.315254
$37$			14445.4i			1.73470i	0.497695	+	0.867352i	$0.334180\pi$
$37$			14445.4i			1.73470i	−0.497695	+	0.867352i	$0.665820\pi$
$38$		−	2093.06i		−	0.235138i
$39$	−4691.63			−0.493926
$40$	−3532.88	+	2923.28i	−0.349123	+	0.288882i
$41$	6151.94			0.571548			0.285774	−	0.958297i	$-0.407749\pi$
$41$	6151.94			0.571548			0.285774	+	0.958297i	$0.407749\pi$
$42$			1037.21i			0.0907283i
$43$			1408.62i			0.116177i	0.998311	+	0.0580886i	$0.0185006\pi$
$43$			1408.62i			0.116177i	−0.998311	+	0.0580886i	$0.981499\pi$
$44$	3662.00			0.285158
$45$	2886.65	+	3488.61i	0.212502	+	0.256815i
$46$	252.816			0.0176161
$47$			14797.5i			0.977110i	0.872533	+	0.488555i	$0.162476\pi$
$47$			14797.5i			0.977110i	−0.872533	+	0.488555i	$0.837524\pi$
$48$			7743.57i			0.485108i
$49$	9154.49			0.544683
$50$	4044.15	+	770.582i	0.228772	+	0.0435907i
$51$	−613.371			−0.0330216
$52$			15776.6i			0.809106i
$53$			10938.4i			0.534891i	0.963573	+	0.267445i	$0.0861795\pi$
$53$			10938.4i			0.534891i	−0.963573	+	0.267445i	$0.913820\pi$
$54$	−960.393			−0.0448192
$55$	−4312.15	−	5211.38i	−0.192215	−	0.232298i
$56$	7175.69			0.305769
$57$			14298.9i			0.582928i
$58$		−	5602.92i		−	0.218698i
$59$	16099.1			0.602103			0.301052	−	0.953608i	$-0.402662\pi$
$59$	16099.1			0.602103			0.301052	+	0.953608i	$0.402662\pi$
$60$	11731.2	−	9706.97i	0.420692	−	0.348101i
$61$	41095.0			1.41405			0.707025	−	0.707189i	$-0.250037\pi$
$61$	41095.0			1.41405			0.707025	+	0.707189i	$0.250037\pi$
$62$			110.237i			0.00364208i
$63$		−	7085.77i		−	0.224924i
$64$	22581.4			0.689129
$65$	22451.7	−	18577.6i	0.659121	−	0.545389i
$66$	1434.66			0.0405405
$67$			1254.02i			0.0341286i	0.999854	+	0.0170643i	$0.00543199\pi$
$67$			1254.02i			0.0341286i	−0.999854	+	0.0170643i	$0.994568\pi$
$68$			2062.59i			0.0540930i
$69$	−1727.14			−0.0436721
$70$	−4107.07	−	4963.53i	−0.100181	−	0.121073i
$71$	47638.4			1.12153			0.560765	−	0.827975i	$-0.310507\pi$
$71$	47638.4			1.12153			0.560765	+	0.827975i	$0.310507\pi$
$72$			6644.26i			0.151048i
$73$		−	7358.01i		−	0.161604i	−0.996730	−	0.0808022i	$-0.974252\pi$
$73$		−	7358.01i		−	0.161604i	0.996730	−	0.0808022i	$-0.0257482\pi$
$74$	19030.5			0.403991
$75$	−27627.9	−	5264.29i	−0.567147	−	0.108065i
$76$	48083.1			0.954900
$77$			10584.9i			0.203451i
$78$			6180.81i			0.115029i
$79$	−90184.5			−1.62579			−0.812895	−	0.582411i	$-0.802110\pi$
$79$	−90184.5			−1.62579			−0.812895	+	0.582411i	$0.802110\pi$
$80$	−30662.5	−	37056.7i	−0.535652	−	0.647353i
$81$	6561.00			0.111111
$82$		−	8104.64i		−	0.133106i
$83$			10857.0i			0.172987i	0.996252	+	0.0864935i	$0.0275662\pi$
$83$			10857.0i			0.172987i	−0.996252	+	0.0864935i	$0.972434\pi$
$84$	−23827.4			−0.368450
$85$	2935.27	−	2428.79i	0.0440657	−	0.0364621i
$86$	1855.73			0.0270563
$87$			38276.8i			0.542173i
$88$		−	9925.37i		−	0.136628i
$89$	−112869.			−1.51043			−0.755216	−	0.655476i	$-0.772468\pi$
$89$	−112869.			−1.51043			−0.755216	+	0.655476i	$0.772468\pi$
$90$	4595.93	−	3802.90i	0.0598091	−	0.0494890i
$91$	−45601.9			−0.577271
$92$			5807.86i			0.0715396i
$93$		−	753.094i		−	0.00902905i
$94$	19494.4			0.227557
$95$	−56619.8	−	68426.9i	−0.643664	−	0.777889i
$96$	33825.5			0.374599
$97$		−	96993.9i		−	1.04668i	−0.852123	−	0.523341i	$-0.824685\pi$
$97$		−	96993.9i		−	1.04668i	0.852123	−	0.523341i	$-0.175315\pi$
$98$		−	12060.2i		−	0.126850i
$99$	−9801.00			−0.100504
$100$	−17702.3	+	92904.9i	−0.177023	+	0.929049i
$101$	−55750.8			−0.543810			−0.271905	−	0.962324i	$-0.587654\pi$
$101$	−55750.8			−0.543810			−0.271905	+	0.962324i	$0.587654\pi$
$102$			808.062i			0.00769031i
$103$			107469.i			0.998139i	0.866562	+	0.499069i	$0.166325\pi$
$103$			107469.i			0.998139i	−0.866562	+	0.499069i	$0.833675\pi$
$104$	42760.5			0.387667
$105$	28057.8	+	33908.8i	0.248359	+	0.300150i
$106$	14410.4			0.124569
$107$		−	25673.1i		−	0.216780i	−0.994108	−	0.108390i	$-0.965430\pi$
$107$		−	25673.1i		−	0.216780i	0.994108	−	0.108390i	$-0.0345696\pi$
$108$		−	22062.8i		−	0.182012i
$109$	−98829.6			−0.796748			−0.398374	−	0.917223i	$-0.630425\pi$
$109$	−98829.6			−0.796748			−0.398374	+	0.917223i	$0.630425\pi$
$110$	−6865.53	+	5680.88i	−0.0540994	+	0.0447645i
$111$	−130009.			−1.00153
$112$			75266.4i			0.566965i
$113$		−	12055.0i		−	0.0888120i	−0.999014	−	0.0444060i	$-0.985860\pi$
$113$		−	12055.0i		−	0.0888120i	0.999014	−	0.0444060i	$-0.0141395\pi$
$114$	18837.5			0.135757
$115$	8265.16	−	6839.00i	0.0582783	−	0.0482223i
$116$	128714.			0.888139
$117$		−	42224.7i		−	0.285169i
$118$		−	21209.1i		−	0.140222i
$119$	−5961.87			−0.0385936
$120$	−26309.5	−	31795.9i	−0.166786	−	0.201566i
$121$	14641.0			0.0909091
$122$		−	54139.1i		−	0.329315i
$123$			55367.5i			0.329983i
$124$	−2532.44			−0.0147906
$125$	153058.	−	84207.2i	0.876155	−	0.482030i
$126$	−9334.87			−0.0523820
$127$		−	57953.4i		−	0.318838i	−0.987211	−	0.159419i	$-0.949038\pi$
$127$		−	57953.4i		−	0.318838i	0.987211	−	0.159419i	$-0.0509620\pi$
$128$		−	150017.i		−	0.809313i
$129$	−12677.5			−0.0670750
$130$	−24474.4	−	29578.1i	−0.127014	−	0.153501i
$131$	−124350.			−0.633095			−0.316548	−	0.948577i	$-0.602524\pi$
$131$	−124350.			−0.633095			−0.316548	+	0.948577i	$0.602524\pi$
$132$			32958.0i			0.164636i
$133$			138983.i			0.681291i
$134$	1652.06			0.00794812
$135$	−31397.5	+	25979.8i	−0.148272	+	0.122688i
$136$	5590.39			0.0259176
$137$		−	408683.i		−	1.86031i	−0.367170	−	0.930154i	$-0.619673\pi$
$137$		−	408683.i		−	1.86031i	0.367170	−	0.930154i	$-0.380327\pi$
$138$			2275.35i			0.0101707i
$139$	−378463.			−1.66145			−0.830723	−	0.556686i	$-0.812073\pi$
$139$	−378463.			−1.66145			−0.830723	+	0.556686i	$0.812073\pi$
$140$	114025.	−	94350.2i	0.491679	−	0.406839i
$141$	−133177.			−0.564135
$142$		−	62759.4i		−	0.261191i
$143$			63076.4i			0.257945i
$144$	−69692.2			−0.280077
$145$	−151566.	−	183173.i	−0.598662	−	0.723503i
$146$	−9693.52			−0.0376357
$147$			82390.4i			0.314473i
$148$			437182.i			1.64062i
$149$	271317.			1.00118			0.500588	−	0.865686i	$-0.333117\pi$
$149$	271317.			1.00118			0.500588	+	0.865686i	$0.333117\pi$
$150$	−6935.24	+	36397.4i	−0.0251671	+	0.132081i
$151$	−146748.			−0.523758			−0.261879	−	0.965101i	$-0.584342\pi$
$151$	−146748.			−0.523758			−0.261879	+	0.965101i	$0.584342\pi$
$152$		−	130323.i		−	0.457522i
$153$		−	5520.34i		−	0.0190650i
$154$	13944.7			0.0473813
$155$	2982.05	+	3603.91i	0.00996979	+	0.0120488i
$156$	−141990.			−0.467138
$157$		−	365562.i		−	1.18362i	−0.806077	−	0.591810i	$-0.798414\pi$
$157$		−	365562.i		−	1.18362i	0.806077	−	0.591810i	$-0.201586\pi$
$158$			118810.i			0.378626i
$159$	−98445.8			−0.308819
$160$	−161871.	+	133940.i	−0.499884	+	0.413628i
$161$	−16787.5			−0.0510412
$162$		−	8643.54i		−	0.0258764i
$163$		−	16695.2i		−	0.0492180i	−0.999697	−	0.0246090i	$-0.992166\pi$
$163$		−	16695.2i		−	0.0492180i	0.999697	−	0.0246090i	$-0.00783408\pi$
$164$	186185.			0.540549
$165$	46902.4	−	38809.4i	0.134117	−	0.110975i
$166$	14303.1			0.0402865
$167$		−	568590.i		−	1.57764i	−0.614623	−	0.788821i	$-0.710692\pi$
$167$		−	568590.i		−	1.57764i	0.614623	−	0.788821i	$-0.289308\pi$
$168$			64581.2i			0.176536i
$169$	99547.4			0.268110
$170$	−3199.71	−	3866.96i	−0.00849157	−	0.0102624i
$171$	−128690.			−0.336554
$172$			42630.9i			0.109876i
$173$		−	552203.i		−	1.40276i	−0.712788	−	0.701380i	$-0.752568\pi$
$173$		−	552203.i		−	1.40276i	0.712788	−	0.701380i	$-0.247432\pi$
$174$	50426.3			0.126265
$175$	−268539.	−	51168.1i	−0.662846	−	0.126300i
$176$	104108.			0.253339
$177$			144892.i			0.347624i
$178$			148695.i			0.351761i
$179$	179962.			0.419807			0.209903	−	0.977722i	$-0.432685\pi$
$179$	179962.			0.419807			0.209903	+	0.977722i	$0.432685\pi$
$180$	87362.7	+	105581.i	0.200976	+	0.242887i
$181$	612439.			1.38953			0.694763	−	0.719239i	$-0.255509\pi$
$181$	612439.			1.38953			0.694763	+	0.719239i	$0.255509\pi$
$182$			60076.5i			0.134439i
$183$			369855.i			0.816402i
$184$	15741.5			0.0342768
$185$	622153.	−	514800.i	1.33650	−	1.10588i
$186$	−992.135			−0.00210275
$187$			8246.43i			0.0172449i
$188$			447838.i			0.924115i
$189$	63771.9			0.129860
$190$	−90146.4	+	74591.5i	−0.181161	+	0.149901i
$191$	65407.8			0.129732			0.0648659	−	0.997894i	$-0.479338\pi$
$191$	65407.8			0.129732			0.0648659	+	0.997894i	$0.479338\pi$
$192$			203232.i			0.397869i
$193$			661050.i			1.27744i	0.769439	+	0.638721i	$0.220536\pi$
$193$			661050.i			1.27744i	−0.769439	+	0.638721i	$0.779464\pi$
$194$	−127781.			−0.243759
$195$	167199.	+	202065.i	0.314881	+	0.380544i
$196$	277055.			0.515141
$197$			590186.i			1.08349i	0.840544	+	0.541743i	$0.182235\pi$
$197$			590186.i			1.08349i	−0.840544	+	0.541743i	$0.817765\pi$
$198$			12911.9i			0.0234061i
$199$	342750.			0.613543			0.306771	−	0.951783i	$-0.400751\pi$
$199$	342750.			0.613543			0.306771	+	0.951783i	$0.400751\pi$
$200$	251807.	+	47979.8i	0.445136	+	0.0848172i
$201$	−11286.2			−0.0197041
$202$			73446.7i			0.126647i
$203$			372045.i			0.633658i
$204$	−18563.3			−0.0312306
$205$	−219240.	−	264959.i	−0.364364	−	0.440347i
$206$	141581.			0.232454
$207$		−	15544.2i		−	0.0252141i
$208$			448518.i			0.718823i
$209$	192241.			0.304424
$210$	44671.8	−	36963.6i	0.0699013	−	0.0578397i
$211$	−214655.			−0.331921			−0.165960	−	0.986132i	$-0.553072\pi$
$211$	−214655.			−0.331921			−0.165960	+	0.986132i	$0.553072\pi$
$212$			331045.i			0.505880i
$213$			428746.i			0.647516i
$214$	−33822.1			−0.0504854
$215$	60668.0	−	50199.7i	0.0895083	−	0.0740636i
$216$	−59798.3			−0.0872076
$217$		−	7319.96i		−	0.0105526i
$218$			130199.i			0.185553i
$219$	66222.1			0.0933023
$220$	−130505.	−	157719.i	−0.181790	−	0.219699i
$221$	−35527.3			−0.0489307
$222$			171275.i			0.233244i
$223$		−	118747.i		−	0.159904i	−0.996799	−	0.0799521i	$-0.974523\pi$
$223$		−	118747.i		−	0.159904i	0.996799	−	0.0799521i	$-0.0254767\pi$
$224$	328779.			0.437808
$225$	47378.6	−	248651.i	0.0623916	−	0.327442i
$226$	−15881.4			−0.0206832
$227$		−	2183.16i		−	0.00281204i	−0.999999	−	0.00140602i	$-0.999552\pi$
$227$		−	2183.16i		−	0.00281204i	0.999999	−	0.00140602i	$-0.000447550\pi$
$228$			432747.i			0.551312i
$229$	−123704.			−0.155881			−0.0779407	−	0.996958i	$-0.524834\pi$
$229$	−123704.			−0.155881			−0.0779407	+	0.996958i	$0.524834\pi$
$230$	−9009.77	−	10888.6i	−0.0112304	−	0.0135723i
$231$	−95264.2			−0.117463
$232$		−	348863.i		−	0.425534i
$233$			1.16587e6i			1.40689i	0.710748	+	0.703446i	$0.248356\pi$
$233$			1.16587e6i			1.40689i	−0.710748	+	0.703446i	$0.751644\pi$
$234$	−55627.3			−0.0664122
$235$	637317.	−	527347.i	0.752811	−	0.622912i
$236$	487229.			0.569447
$237$		−	811661.i		−	0.938650i
$238$			7854.24i			0.00898797i
$239$	−770619.			−0.872659			−0.436330	−	0.899787i	$-0.643722\pi$
$239$	−770619.			−0.872659			−0.436330	+	0.899787i	$0.643722\pi$
$240$	333510.	−	275963.i	0.373750	−	0.309259i
$241$	−1.42541e6			−1.58087			−0.790434	−	0.612547i	$-0.790145\pi$
$241$	−1.42541e6			−1.58087			−0.790434	+	0.612547i	$0.790145\pi$
$242$		−	19288.2i		−	0.0211716i
$243$			59049.0i			0.0641500i
$244$	1.24372e6			1.33736
$245$	−326244.	−	394277.i	−0.347238	−	0.419649i
$246$	72941.7			0.0768490
$247$			828211.i			0.863771i
$248$			6863.86i			0.00708662i
$249$	−97712.7			−0.0998741
$250$	−110935.	−	201640.i	−0.112259	−	0.204046i
$251$	−668745.			−0.670002			−0.335001	−	0.942218i	$-0.608737\pi$
$251$	−668745.			−0.670002			−0.335001	+	0.942218i	$0.608737\pi$
$252$		−	214447.i		−	0.212725i
$253$			23220.4i			0.0228070i
$254$	−76348.5			−0.0742534
$255$	21859.1	+	26417.4i	0.0210514	+	0.0254413i
$256$	524969.			0.500650
$257$		−	1.08696e6i		−	1.02655i	−0.858223	−	0.513276i	$-0.828432\pi$
$257$		−	1.08696e6i		−	1.02655i	0.858223	−	0.513276i	$-0.171568\pi$
$258$			16701.5i			0.0156209i
$259$	−1.26366e6			−1.17053
$260$	679487.	−	562241.i	0.623373	−	0.515809i
$261$	−344491.			−0.313024
$262$			163821.i			0.147440i
$263$			865881.i			0.771914i	0.922517	+	0.385957i	$0.126129\pi$
$263$			865881.i			0.771914i	−0.922517	+	0.385957i	$0.873871\pi$
$264$	89328.3			0.0788823
$265$	471110.	−	389819.i	0.412105	−	0.340996i
$266$	183098.			0.158664
$267$		−	1.01582e6i		−	0.872049i
$268$			37952.2i			0.0322775i
$269$	−455847.			−0.384094			−0.192047	−	0.981386i	$-0.561513\pi$
$269$	−455847.			−0.384094			−0.192047	+	0.981386i	$0.561513\pi$
$270$	34226.1	+	41363.4i	0.0285725	+	0.0345308i
$271$	1.93670e6			1.60191			0.800955	−	0.598725i	$-0.204326\pi$
$271$	1.93670e6			1.60191			0.800955	+	0.598725i	$0.204326\pi$
$272$			58638.1i			0.0480571i
$273$		−	410417.i		−	0.333288i
$274$	−538403.			−0.433243
$275$	−70775.5	+	371442.i	−0.0564353	+	0.296183i
$276$	−52270.8			−0.0413034
$277$			1.67891e6i			1.31470i	0.753584	+	0.657352i	$0.228323\pi$
$277$			1.67891e6i			1.31470i	−0.753584	+	0.657352i	$0.771677\pi$
$278$			498591.i			0.386930i
$279$	6777.85			0.00521292
$280$	−255724.	−	309051.i	−0.194929	−	0.235578i
$281$	−1.66433e6			−1.25740			−0.628700	−	0.777648i	$-0.716413\pi$
$281$	−1.66433e6			−1.25740			−0.628700	+	0.777648i	$0.716413\pi$
$282$			175449.i			0.131380i
$283$			529051.i			0.392673i	0.980537	+	0.196337i	$0.0629045\pi$
$283$			529051.i			0.392673i	−0.980537	+	0.196337i	$0.937095\pi$
$284$	1.44175e6			1.06070
$285$	615842.	−	509578.i	0.449115	−	0.371620i
$286$	83097.5			0.0600721
$287$			538163.i			0.385664i
$288$			304430.i			0.216275i
$289$	1.41521e6			0.996729
$290$	−241314.	+	199675.i	−0.168495	+	0.139421i
$291$	872945.			0.604302
$292$		−	222686.i		−	0.152839i
$293$		−	1.17586e6i		−	0.800178i	−0.916476	−	0.400089i	$-0.868979\pi$
$293$		−	1.17586e6i		−	0.800178i	0.916476	−	0.400089i	$-0.131021\pi$
$294$	108542.			0.0732369
$295$	−573733.	−	693375.i	−0.383844	−	0.463888i
$296$	1.18493e6			0.786071
$297$		−	88209.0i		−	0.0580259i
$298$		−	357436.i		−	0.233162i
$299$	−100038.			−0.0647123
$300$	−836144.	−	159321.i	−0.536386	−	0.102204i
$301$	−123224.			−0.0783931
$302$			193328.i			0.121977i
$303$		−	501757.i		−	0.313969i
$304$	1.36697e6			0.848349
$305$	−1.46453e6	−	1.76993e6i	−0.901464	−	1.08945i
$306$	−7272.55			−0.00444000
$307$		−	1.53089e6i		−	0.927037i	−0.886087	−	0.463518i	$-0.846587\pi$
$307$		−	1.53089e6i		−	0.927037i	0.886087	−	0.463518i	$-0.153413\pi$
$308$			320346.i			0.192417i
$309$	−967223.			−0.576276
$310$	4747.83	−	3928.59i	0.00280602	−	0.00232184i
$311$	−1.11621e6			−0.654400			−0.327200	−	0.944955i	$-0.606105\pi$
$311$	−1.11621e6			−0.654400			−0.327200	+	0.944955i	$0.606105\pi$
$312$			384844.i			0.223820i
$313$			864587.i			0.498824i	0.968397	+	0.249412i	$0.0802374\pi$
$313$			864587.i			0.498824i	−0.968397	+	0.249412i	$0.919763\pi$
$314$	−481596.			−0.275651
$315$	−305179.	+	252520.i	−0.173292	+	0.143390i
$316$	−2.72938e6			−1.53761
$317$			1.80604e6i			1.00943i	0.863285	+	0.504717i	$0.168403\pi$
$317$			1.80604e6i			1.00943i	−0.863285	+	0.504717i	$0.831597\pi$
$318$			129694.i			0.0719202i
$319$	514611.			0.283140
$320$	−804746.	−	972563.i	−0.439323	−	0.530937i
$321$	231058.			0.125158
$322$			22116.0i			0.0118869i
$323$			108278.i			0.0577476i
$324$	198565.			0.105085
$325$	−1.60025e6	−	304915.i	−0.840386	−	0.160129i
$326$	−21994.5			−0.0114623
$327$		−	889466.i		−	0.460003i
$328$		−	504630.i		−	0.258994i
$329$	−1.29446e6			−0.659326
$330$	−51127.9	−	61789.8i	−0.0258448	−	0.0312343i
$331$	1.85701e6			0.931634			0.465817	−	0.884881i	$-0.345761\pi$
$331$	1.85701e6			0.931634			0.465817	+	0.884881i	$0.345761\pi$
$332$			328580.i			0.163605i
$333$		−	1.17008e6i		−	0.578235i
$334$	−749068.			−0.367413
$335$	54009.8	−	44690.3i	0.0262942	−	0.0217571i
$336$	−677397.			−0.327337
$337$		−	2.18068e6i		−	1.04597i	−0.852343	−	0.522983i	$-0.824819\pi$
$337$		−	2.18068e6i		−	1.04597i	0.852343	−	0.522983i	$-0.175181\pi$
$338$		−	131145.i		−	0.0624395i
$339$	108495.			0.0512757
$340$	88834.2	−	73505.8i	0.0416757	−	0.0344845i
$341$	−10124.9			−0.00471527
$342$			169538.i			0.0783792i
$343$			2.27108e6i			1.04231i
$344$	115546.			0.0526451
$345$	61551.0	+	74386.4i	0.0278411	+	0.0336470i
$346$	−727478.			−0.326685
$347$		−	2.59930e6i		−	1.15886i	−0.815021	−	0.579432i	$-0.803274\pi$
$347$		−	2.59930e6i		−	1.15886i	0.815021	−	0.579432i	$-0.196726\pi$
$348$			1.15843e6i			0.512767i
$349$	−1.17216e6			−0.515138			−0.257569	−	0.966260i	$-0.582921\pi$
$349$	−1.17216e6			−0.515138			−0.257569	+	0.966260i	$0.582921\pi$
$350$	−67409.5	+	353777.i	−0.0294138	+	0.154369i
$351$	380022.			0.164642
$352$		−	454765.i		−	0.195628i
$353$			1.57881e6i			0.674364i	0.941440	+	0.337182i	$0.109474\pi$
$353$			1.57881e6i			0.674364i	−0.941440	+	0.337182i	$0.890526\pi$
$354$	190882.			0.0809574
$355$	−1.69772e6	−	2.05175e6i	−0.714982	−	0.864079i
$356$	−3.41593e6			−1.42851
$357$		−	53656.8i		−	0.0222820i
$358$		−	237085.i		−	0.0977678i
$359$	−3.19520e6			−1.30847			−0.654233	−	0.756293i	$-0.727008\pi$
$359$	−3.19520e6			−1.30847			−0.654233	+	0.756293i	$0.727008\pi$
$360$	286163.	−	236785.i	0.116374	−	0.0962939i
$361$	48073.9			0.0194152
$362$		−	806834.i		−	0.323603i
$363$			131769.i			0.0524864i
$364$	−1.38012e6			−0.545962
$365$	−316904.	+	262222.i	−0.124507	+	0.103024i
$366$	487252.			0.190130
$367$		−	2.52046e6i		−	0.976819i	−0.872615	−	0.488409i	$-0.837577\pi$
$367$		−	2.52046e6i		−	0.976819i	0.872615	−	0.488409i	$-0.162423\pi$
$368$			165114.i			0.0635570i
$369$	−498307.			−0.190516
$370$	−678203.	−	819631.i	−0.257546	−	0.311253i
$371$	−956879.			−0.360929
$372$		−	22792.0i		−	0.00853934i
$373$			1.66879e6i			0.621053i	0.950565	+	0.310527i	$0.100505\pi$
$373$			1.66879e6i			0.621053i	−0.950565	+	0.310527i	$0.899495\pi$
$374$	10863.9			0.00401614
$375$	757865.	+	1.37752e6i	0.278300	+	0.505848i
$376$	1.21381e6			0.442772
$377$			2.21705e6i			0.803380i
$378$		−	84013.9i		−	0.0302428i
$379$	3.13030e6			1.11941			0.559704	−	0.828692i	$-0.310915\pi$
$379$	3.13030e6			1.11941			0.559704	+	0.828692i	$0.310915\pi$
$380$	−1.71357e6	−	2.07090e6i	−0.608754	−	0.735699i
$381$	521581.			0.184081
$382$		−	86169.0i		−	0.0302129i
$383$			4.30969e6i			1.50124i	0.660737	+	0.750618i	$0.270244\pi$
$383$			4.30969e6i			1.50124i	−0.660737	+	0.750618i	$0.729756\pi$
$384$	1.35016e6			0.467257
$385$	455884.	−	377221.i	0.156748	−	0.129701i
$386$	870875.			0.297500
$387$		−	114098.i		−	0.0387258i
$388$		−	2.93546e6i		−	0.989914i
$389$	2.45755e6			0.823432			0.411716	−	0.911312i	$-0.364929\pi$
$389$	2.45755e6			0.823432			0.411716	+	0.911312i	$0.364929\pi$
$390$	266203.	−	220269.i	0.0886239	−	0.0733318i
$391$	−13078.7			−0.00432636
$392$		−	750923.i		−	0.246820i
$393$		−	1.11915e6i		−	0.365518i
$394$	777518.			0.252330
$395$	3.21396e6	+	3.88418e6i	1.03645	+	1.25258i
$396$	−296622.			−0.0950528
$397$		−	5.93203e6i		−	1.88898i	−0.328544	−	0.944489i	$-0.606558\pi$
$397$		−	5.93203e6i		−	1.88898i	0.328544	−	0.944489i	$-0.393442\pi$
$398$		−	451543.i		−	0.142887i
$399$	−1.25085e6			−0.393343
$400$	−503265.	+	2.64122e6i	−0.157270	+	0.825382i
$401$	4.56758e6			1.41849			0.709243	−	0.704964i	$-0.249037\pi$
$401$	4.56758e6			1.41849			0.709243	+	0.704964i	$0.249037\pi$
$402$			14868.6i			0.00458885i
$403$		−	43620.2i		−	0.0133791i
$404$	−1.68727e6			−0.514316
$405$	−233818.	−	282577.i	−0.0708339	−	0.0856051i
$406$	490136.			0.147571
$407$			1.74789e6i			0.523033i
$408$			50313.5i			0.0149635i
$409$	5.87934e6			1.73788			0.868941	−	0.494915i	$-0.164801\pi$
$409$	5.87934e6			1.73788			0.868941	+	0.494915i	$0.164801\pi$
$410$	−349061.	+	288830.i	−0.102551	+	0.0848560i
$411$	3.67814e6			1.07405
$412$			3.25249e6i			0.944003i
$413$			1.40833e6i			0.406282i
$414$	−20478.1			−0.00587205
$415$	467601.	−	386916.i	0.133277	−	0.110280i
$416$	1.95922e6			0.555072
$417$		−	3.40616e6i		−	0.959236i
$418$		−	253260.i		−	0.0708966i
$419$	−6.12464e6			−1.70430			−0.852149	−	0.523299i	$-0.824701\pi$
$419$	−6.12464e6			−1.70430			−0.852149	+	0.523299i	$0.824701\pi$
$420$	849152.	+	1.02623e6i	0.234889	+	0.283871i
$421$	−2.83114e6			−0.778495			−0.389248	−	0.921133i	$-0.627265\pi$
$421$	−2.83114e6			−0.778495			−0.389248	+	0.921133i	$0.627265\pi$
$422$			282789.i			0.0773003i
$423$		−	1.19860e6i		−	0.325703i
$424$	897256.			0.242383
$425$	−209212.	−	39863.7i	−0.0561842	−	0.0107055i
$426$	564834.			0.150799
$427$			3.59494e6i			0.954161i
$428$		−	776983.i		−	0.205023i
$429$	−567687.			−0.148924
$430$	−66133.6	−	79924.7i	−0.0172485	−	0.0208454i
$431$	6.20538e6			1.60907			0.804536	−	0.593904i	$-0.202414\pi$
$431$	6.20538e6			1.60907			0.804536	+	0.593904i	$0.202414\pi$
$432$		−	627230.i		−	0.161703i
$433$			422736.i			0.108355i	0.998531	+	0.0541775i	$0.0172537\pi$
$433$			422736.i			0.108355i	−0.998531	+	0.0541775i	$0.982746\pi$
$434$	−9643.40			−0.00245757
$435$	1.64855e6	−	1.36409e6i	0.417715	−	0.345638i
$436$	−2.99102e6			−0.753535
$437$			304890.i			0.0763730i
$438$		−	87241.7i		−	0.0217290i
$439$	4.07012e6			1.00797			0.503983	−	0.863713i	$-0.331867\pi$
$439$	4.07012e6			1.00797			0.503983	+	0.863713i	$0.331867\pi$
$440$	−427478.	+	353717.i	−0.105265	+	0.0871011i
$441$	−741514.			−0.181561
$442$			46804.0i			0.0113953i
$443$			4.95245e6i			1.19898i	0.800384	+	0.599488i	$0.204629\pi$
$443$			4.95245e6i			1.19898i	−0.800384	+	0.599488i	$0.795371\pi$
$444$	−3.93464e6			−0.947212
$445$	4.02240e6	+	4.86120e6i	0.962908	+	1.16371i
$446$	−156438.			−0.0372397
$447$			2.44185e6i			0.578029i
$448$			1.97539e6i			0.465004i
$449$	−7.34037e6			−1.71831			−0.859157	−	0.511713i	$-0.829011\pi$
$449$	−7.34037e6			−1.71831			−0.859157	+	0.511713i	$0.829011\pi$
$450$	−327576.	−	62417.1i	−0.0762572	−	0.0145302i
$451$	744385.			0.172328
$452$		−	364838.i		−	0.0839952i
$453$		−	1.32073e6i		−	0.302392i
$454$	−2876.12			−0.000654888
$455$	1.62514e6	+	1.96404e6i	0.368013	+	0.444756i
$456$	1.17291e6			0.264150
$457$		−	2.07655e6i		−	0.465106i	−0.972584	−	0.232553i	$-0.925292\pi$
$457$		−	2.07655e6i		−	0.465106i	0.972584	−	0.232553i	$-0.0747080\pi$
$458$			162969.i			0.0363029i
$459$	49683.0			0.0110072
$460$	250140.	−	206978.i	0.0551174	−	0.0456069i
$461$	−1.68917e6			−0.370186			−0.185093	−	0.982721i	$-0.559259\pi$
$461$	−1.68917e6			−0.370186			−0.185093	+	0.982721i	$0.559259\pi$
$462$			125502.i			0.0273556i
$463$		−	1.35953e6i		−	0.294739i	−0.989082	−	0.147369i	$-0.952919\pi$
$463$		−	1.35953e6i		−	0.294739i	0.989082	−	0.147369i	$-0.0470806\pi$
$464$	3.65925e6			0.789037
$465$	−32435.2	+	26838.5i	−0.00695639	+	0.00575606i
$466$	1.53593e6			0.327648
$467$			8.47580e6i			1.79841i	0.437528	+	0.899205i	$0.355854\pi$
$467$			8.47580e6i			1.79841i	−0.437528	+	0.899205i	$0.644146\pi$
$468$		−	1.27791e6i		−	0.269702i
$469$	−109700.			−0.0230290
$470$	−694733.	−	839608.i	−0.145069	−	0.175320i
$471$	3.29006e6			0.683363
$472$		−	1.32057e6i		−	0.272840i
$473$			170442.i			0.0350288i
$474$	−1.06929e6			−0.218600
$475$	−929302.	+	4.87714e6i	−0.188983	+	0.991817i
$476$	−180433.			−0.0365004
$477$		−	886013.i		−	0.178297i
$478$			1.01522e6i			0.203232i
$479$	3.52896e6			0.702762			0.351381	−	0.936233i	$-0.385712\pi$
$479$	3.52896e6			0.702762			0.351381	+	0.936233i	$0.385712\pi$
$480$	−1.20546e6	−	1.45684e6i	−0.238808	−	0.288608i
$481$	−7.53028e6			−1.48405
$482$			1.87784e6i			0.368165i
$483$		−	151087.i		−	0.0294687i
$484$	443101.			0.0859785
$485$	−4.17745e6	+	3.45663e6i	−0.806413	+	0.667265i
$486$	77791.8			0.0149397
$487$		−	4.66713e6i		−	0.891719i	−0.895103	−	0.445859i	$-0.852898\pi$
$487$		−	4.66713e6i		−	0.891719i	0.895103	−	0.445859i	$-0.147102\pi$
$488$		−	3.37094e6i		−	0.640768i
$489$	150257.			0.0284160
$490$	−519425.	+	429798.i	−0.0977311	+	0.0808675i
$491$	−7.22516e6			−1.35252			−0.676260	−	0.736663i	$-0.736400\pi$
$491$	−7.22516e6			−1.35252			−0.676260	+	0.736663i	$0.736400\pi$
$492$			1.67566e6i			0.312086i
$493$			289850.i			0.0537102i
$494$	1.09109e6			0.201162
$495$	349284.	+	422122.i	0.0640717	+	0.0774328i
$496$	−71995.6			−0.0131402
$497$			4.16734e6i			0.756777i
$498$			128728.i			0.0232594i
$499$	1.04815e7			1.88440			0.942202	−	0.335046i	$-0.108752\pi$
$499$	1.04815e7			1.88440			0.942202	+	0.335046i	$0.108752\pi$
$500$	4.63221e6	−	2.54848e6i	0.828635	−	0.455886i
$501$	5.11731e6			0.910852
$502$			881012.i			0.156035i
$503$		−	8.37701e6i		−	1.47628i	−0.674647	−	0.738140i	$-0.735704\pi$
$503$		−	8.37701e6i		−	1.47628i	0.674647	−	0.738140i	$-0.264296\pi$
$504$	−581230.			−0.101923
$505$	1.98682e6	+	2.40114e6i	0.346682	+	0.418977i
$506$	30590.8			0.00531146
$507$			895926.i			0.154793i
$508$		−	1.75393e6i		−	0.301545i
$509$	−3.17550e6			−0.543272			−0.271636	−	0.962400i	$-0.587565\pi$
$509$	−3.17550e6			−0.543272			−0.271636	+	0.962400i	$0.587565\pi$
$510$	34802.6	−	28797.4i	0.00592497	−	0.00490261i
$511$	643668.			0.109046
$512$		−	5.49216e6i		−	0.925908i
$513$		−	1.15821e6i		−	0.194309i
$514$	−1.43198e6			−0.239071
$515$	4.62862e6	−	3.82995e6i	0.769012	−	0.636318i
$516$	−383678.			−0.0634371
$517$			1.79050e6i			0.294610i
$518$			1.66477e6i			0.272602i
$519$	4.96982e6			0.809884
$520$	−1.52388e6	−	1.84166e6i	−0.247140	−	0.298677i
$521$	3.72507e6			0.601230			0.300615	−	0.953746i	$-0.402808\pi$
$521$	3.72507e6			0.601230			0.300615	+	0.953746i	$0.402808\pi$
$522$			453837.i			0.0728993i
$523$		−	3.77963e6i		−	0.604219i	−0.953273	−	0.302110i	$-0.902309\pi$
$523$		−	3.77963e6i		−	0.604219i	0.953273	−	0.302110i	$-0.0976909\pi$
$524$	−3.76339e6			−0.598758
$525$	460513.	−	2.41685e6i	0.0729195	−	0.382694i
$526$	1.14072e6			0.179769
$527$		−	5702.79i		−	0.000894460i
$528$			936973.i			0.146266i
$529$	6.39952e6			0.994278
$530$	−513553.	−	620646.i	−0.0794137	−	0.0959741i
$531$	−1.30403e6			−0.200701
$532$			4.20624e6i			0.644340i
$533$			3.20696e6i			0.488962i
$534$	−1.33826e6			−0.203089
$535$	−1.10572e6	+	914929.i	−0.167017	+	0.138198i
$536$	102865.			0.0154652
$537$			1.61966e6i			0.242375i
$538$			600538.i			0.0894509i
$539$	1.10769e6			0.164228
$540$	−950227.	+	786264.i	−0.140231	+	0.116034i
$541$	−6.08511e6			−0.893871			−0.446936	−	0.894566i	$-0.647485\pi$
$541$	−6.08511e6			−0.893871			−0.446936	+	0.894566i	$0.647485\pi$
$542$		−	2.55142e6i		−	0.373065i
$543$			5.51195e6i			0.802243i
$544$	256143.			0.0371095
$545$	3.52205e6	+	4.25652e6i	0.507931	+	0.613851i
$546$	−540689.			−0.0776186
$547$			2.49034e6i			0.355870i	0.984042	+	0.177935i	$0.0569416\pi$
$547$			2.49034e6i			0.355870i	−0.984042	+	0.177935i	$0.943058\pi$
$548$		−	1.23685e7i		−	1.75941i
$549$	−3.32870e6			−0.471350
$550$	489342.	+	93240.4i	0.0689773	+	0.0131431i
$551$	6.75698e6			0.948143
$552$			141673.i			0.0197897i
$553$		−	7.88922e6i		−	1.09704i
$554$	2.21181e6			0.306178
$555$	4.63320e6	+	5.59937e6i	0.638481	+	0.771626i
$556$	−1.14540e7			−1.57133
$557$		−	5.36235e6i		−	0.732347i	−0.930547	−	0.366173i	$-0.880668\pi$
$557$		−	5.36235e6i		−	0.732347i	0.930547	−	0.366173i	$-0.119332\pi$
$558$		−	8929.21i		−	0.00121403i
$559$	−734300.			−0.0993903
$560$	3.24167e6	−	2.68231e6i	0.436816	−	0.361443i
$561$	−74217.9			−0.00995638
$562$			2.19261e6i			0.292833i
$563$		−	479316.i		−	0.0637310i	−0.999492	−	0.0318655i	$-0.989855\pi$
$563$		−	479316.i		−	0.0637310i	0.999492	−	0.0318655i	$-0.0101448\pi$
$564$	−4.03054e6			−0.533538
$565$	−519201.	+	429612.i	−0.0684249	+	0.0566181i
$566$	696978.			0.0914488
$567$			573947.i			0.0749746i
$568$		−	3.90768e6i		−	0.508215i
$569$	−3.08333e6			−0.399245			−0.199623	−	0.979873i	$-0.563972\pi$
$569$	−3.08333e6			−0.399245			−0.199623	+	0.979873i	$0.563972\pi$
$570$	−671324.	−	811317.i	−0.0865456	−	0.104593i
$571$	−5.85646e6			−0.751701			−0.375850	−	0.926680i	$-0.622649\pi$
$571$	−5.85646e6			−0.751701			−0.375850	+	0.926680i	$0.622649\pi$
$572$			1.90897e6i			0.243955i
$573$			588670.i			0.0749007i
$574$	708982.			0.0898164
$575$	−589101.	−	112249.i	−0.0743054	−	0.0141583i
$576$	−1.82909e6			−0.229710
$577$			5.66144e6i			0.707925i	0.935260	+	0.353963i	$0.115166\pi$
$577$			5.66144e6i			0.707925i	−0.935260	+	0.353963i	$0.884834\pi$
$578$		−	1.86442e6i		−	0.232126i
$579$	−5.94945e6			−0.737531
$580$	−4.58706e6	−	5.54362e6i	−0.566193	−	0.684263i
$581$	−949753.			−0.116727
$582$		−	1.15003e6i		−	0.140735i
$583$			1.32355e6i			0.161276i
$584$	−603562.			−0.0732301
$585$	−1.81859e6	+	1.50479e6i	−0.219707	+	0.181796i
$586$	−1.54909e6			−0.186352
$587$			1.39978e7i			1.67674i	0.545104	+	0.838368i	$0.316490\pi$
$587$			1.39978e7i			1.67674i	−0.545104	+	0.838368i	$0.683510\pi$
$588$			2.49350e6i			0.297417i
$589$	−132943.			−0.0157899
$590$	−913460.	+	755842.i	−0.108034	+	0.0893925i
$591$	−5.31167e6			−0.625551
$592$			1.24288e7i			1.45755i
$593$		−	1.27936e7i		−	1.49402i	−0.664810	−	0.747012i	$-0.731488\pi$
$593$		−	1.27936e7i		−	1.49402i	0.664810	−	0.747012i	$-0.268512\pi$
$594$	−116208.			−0.0135135
$595$	212467.	+	256773.i	0.0246036	+	0.0297343i
$596$	8.21124e6			0.946876
$597$			3.08475e6i			0.354229i
$598$			131791.i			0.0150707i
$599$	1.21733e7			1.38625			0.693125	−	0.720818i	$-0.256234\pi$
$599$	1.21733e7			1.38625			0.693125	+	0.720818i	$0.256234\pi$
$600$	−431819.	+	2.26626e6i	−0.0489692	+	0.256999i
$601$	−6.74801e6			−0.762060			−0.381030	−	0.924563i	$-0.624431\pi$
$601$	−6.74801e6			−0.762060			−0.381030	+	0.924563i	$0.624431\pi$
$602$			162336.i			0.0182568i
$603$		−	101576.i		−	0.0113762i
$604$	−4.44125e6			−0.495351
$605$	−521770.	−	630577.i	−0.0579550	−	0.0700406i
$606$	−661020.			−0.0731195
$607$		−	1.16658e7i		−	1.28512i	−0.766234	−	0.642561i	$-0.777872\pi$
$607$		−	1.16658e7i		−	1.28512i	0.766234	−	0.642561i	$-0.222128\pi$
$608$		−	5.97120e6i		−	0.655092i
$609$	−3.34840e6			−0.365843
$610$	−2.33173e6	+	1.92939e6i	−0.253719	+	0.209940i
$611$	−7.71382e6			−0.835923
$612$		−	167070.i		−	0.0180310i
$613$		−	1.36615e7i		−	1.46841i	−0.678928	−	0.734204i	$-0.737555\pi$
$613$		−	1.36615e7i		−	1.46841i	0.678928	−	0.734204i	$-0.262445\pi$
$614$	−2.01681e6			−0.215895
$615$	2.38464e6	−	1.97316e6i	0.254234	−	0.210366i
$616$	868258.			0.0921928
$617$		−	1.15742e7i		−	1.22399i	−0.790862	−	0.611995i	$-0.790367\pi$
$617$		−	1.15742e7i		−	1.22399i	0.790862	−	0.611995i	$-0.209633\pi$
$618$			1.27423e6i			0.134207i
$619$	−9.22658e6			−0.967863			−0.483932	−	0.875106i	$-0.660792\pi$
$619$	−9.22658e6			−0.967863			−0.483932	+	0.875106i	$0.660792\pi$
$620$	90250.1	+	109070.i	0.00942906	+	0.0113953i
$621$	139898.			0.0145574
$622$			1.47050e6i			0.152402i
$623$		−	9.87366e6i		−	1.01920i
$624$	−4.03667e6			−0.415013
$625$	−9.08136e6	−	3.59115e6i	−0.929931	−	0.367734i
$626$	1.13902e6			0.116170
$627$			1.73016e6i			0.175759i
$628$		−	1.10635e7i		−	1.11942i
$629$	−984487.			−0.0992164
$630$	332673.	+	402046.i	0.0333938	+	0.0403575i
$631$	1.03002e7			1.02985			0.514923	−	0.857237i	$-0.327821\pi$
$631$	1.03002e7			1.02985			0.514923	+	0.857237i	$0.327821\pi$
$632$			7.39764e6i			0.736717i
$633$		−	1.93189e6i		−	0.191635i
$634$	2.37929e6			0.235085
$635$	−2.49601e6	+	2.06532e6i	−0.245647	+	0.203261i
$636$	−2.97941e6			−0.292070
$637$			4.77217e6i			0.465980i
$638$		−	677954.i		−	0.0659399i
$639$	−3.85871e6			−0.373844
$640$	−6.46114e6	+	5.34626e6i	−0.623532	+	0.515941i
$641$	−3.06165e6			−0.294313			−0.147157	−	0.989113i	$-0.547012\pi$
$641$	−3.06165e6			−0.294313			−0.147157	+	0.989113i	$0.547012\pi$
$642$		−	304399.i		−	0.0291478i
$643$		−	1.62044e6i		−	0.154563i	−0.997009	−	0.0772813i	$-0.975376\pi$
$643$		−	1.62044e6i		−	0.154563i	0.997009	−	0.0772813i	$-0.0246240\pi$
$644$	−508064.			−0.0482729
$645$	451797.	+	546012.i	0.0427606	+	0.0516777i
$646$	142647.			0.0134487
$647$		−	1.57992e6i		−	0.148380i	−0.997244	−	0.0741900i	$-0.976363\pi$
$647$		−	1.57992e6i		−	0.148380i	0.997244	−	0.0741900i	$-0.0236371\pi$
$648$		−	538185.i		−	0.0503494i
$649$	1.94799e6			0.181541
$650$	−401698.	+	2.10818e6i	−0.0372921	+	0.195716i
$651$	65879.6			0.00609254
$652$		−	505272.i		−	0.0465486i
$653$			1.29080e6i			0.118462i	0.998244	+	0.0592308i	$0.0188648\pi$
$653$			1.29080e6i			0.118462i	−0.998244	+	0.0592308i	$0.981135\pi$
$654$	−1.17179e6			−0.107129
$655$	4.43155e6	+	5.35568e6i	0.403601	+	0.487766i
$656$	5.29311e6			0.480232
$657$			595999.i			0.0538681i
$658$			1.70534e6i			0.153549i
$659$	−1.44401e7			−1.29525			−0.647627	−	0.761957i	$-0.724239\pi$
$659$	−1.44401e7			−1.29525			−0.647627	+	0.761957i	$0.724239\pi$
$660$	1.41947e6	−	1.17454e6i	0.126843	−	0.104956i
$661$	8.80403e6			0.783751			0.391875	−	0.920018i	$-0.371826\pi$
$661$	8.80403e6			0.783751			0.391875	+	0.920018i	$0.371826\pi$
$662$		−	2.44645e6i		−	0.216966i
$663$		−	319745.i		−	0.0282501i
$664$	890574.			0.0783880
$665$	5.98589e6	−	4.95302e6i	0.524898	−	0.434326i
$666$	−1.54147e6			−0.134664
$667$			816163.i			0.0710334i
$668$		−	1.72081e7i		−	1.49208i
$669$	1.06872e6			0.0923207
$670$	−58875.5	−	71153.1i	−0.00506697	−	0.00612360i
$671$	4.97250e6			0.426352
$672$			2.95901e6i			0.252769i
$673$			1.43891e7i			1.22461i	0.790623	+	0.612303i	$0.209757\pi$
$673$			1.43891e7i			1.22461i	−0.790623	+	0.612303i	$0.790243\pi$
$674$	−2.87286e6			−0.243593
$675$	2.23786e6	+	426408.i	0.189049	+	0.0360218i
$676$	3.01274e6			0.253569
$677$		−	1.21710e7i		−	1.02060i	−0.859997	−	0.510299i	$-0.829535\pi$
$677$		−	1.21710e7i		−	1.02060i	0.859997	−	0.510299i	$-0.170465\pi$
$678$		−	142933.i		−	0.0119415i
$679$	8.48489e6			0.706272
$680$	−199228.	−	240774.i	−0.0165226	−	0.0199681i
$681$	19648.4			0.00162353
$682$			13338.7i			0.00109813i
$683$		−	5.96383e6i		−	0.489186i	−0.969626	−	0.244593i	$-0.921346\pi$
$683$		−	5.96383e6i		−	0.489186i	0.969626	−	0.244593i	$-0.0786543\pi$
$684$	−3.89473e6			−0.318300
$685$	−1.76017e7	+	1.45645e7i	−1.43327	+	1.18596i
$686$	2.99194e6			0.242741
$687$		−	1.11333e6i		−	0.0899982i
$688$			1.21197e6i			0.0976158i
$689$	−5.70212e6			−0.457602
$690$	97997.5	−	81088.0i	0.00783596	−	0.00648386i
$691$	−1.10524e7			−0.880565			−0.440283	−	0.897859i	$-0.645122\pi$
$691$	−1.10524e7			−0.880565			−0.440283	+	0.897859i	$0.645122\pi$
$692$		−	1.67121e7i		−	1.32668i
$693$		−	857378.i		−	0.0678171i
$694$	−3.42434e6			−0.269885
$695$	1.34875e7	+	1.63001e7i	1.05918	+	1.28005i
$696$	3.13977e6			0.245682
$697$			419269.i			0.0326897i
$698$			1.54422e6i			0.119969i
$699$	−1.04928e7			−0.812270
$700$	−8.12719e6	−	1.54857e6i	−0.626896	−	0.119450i
$701$	−9.86637e6			−0.758337			−0.379168	−	0.925328i	$-0.623790\pi$
$701$	−9.86637e6			−0.758337			−0.379168	+	0.925328i	$0.623790\pi$
$702$		−	500645.i		−	0.0383431i
$703$			2.29503e7i			1.75146i
$704$	2.73235e6			0.207780
$705$	4.74612e6	+	5.73585e6i	0.359639	+	0.434635i
$706$	2.07995e6			0.157051
$707$		−	4.87700e6i		−	0.366948i
$708$			4.38506e6i			0.328770i
$709$	1.65852e7			1.23910			0.619550	−	0.784957i	$-0.287315\pi$
$709$	1.65852e7			1.23910			0.619550	+	0.784957i	$0.287315\pi$
$710$	−2.70300e6	+	2.23659e6i	−0.201233	+	0.166510i
$711$	7.30495e6			0.541930
$712$			9.25844e6i			0.684444i
$713$		−	16058.0i		−	0.00118295i
$714$	−70688.1			−0.00518921
$715$	2.71665e6	−	2.24789e6i	0.198733	−	0.164441i
$716$	5.44646e6			0.397038
$717$		−	6.93557e6i		−	0.503830i
$718$			4.20940e6i			0.304725i
$719$	1.70621e6			0.123086			0.0615430	−	0.998104i	$-0.480398\pi$
$719$	1.70621e6			0.123086			0.0615430	+	0.998104i	$0.480398\pi$
$720$	2.48366e6	+	3.00159e6i	0.178551	+	0.215784i
$721$	−9.40126e6			−0.673516
$722$		−	63333.1i		−	0.00452156i
$723$		−	1.28286e7i		−	0.912715i
$724$	1.85351e7			1.31416
$725$	−2.48766e6	+	1.30557e7i	−0.175770	+	0.922474i
$726$	173594.			0.0122234
$727$		−	4.79877e6i		−	0.336739i	−0.985724	−	0.168370i	$-0.946150\pi$
$727$		−	4.79877e6i		−	0.336739i	0.985724	−	0.168370i	$-0.0538502\pi$
$728$			3.74063e6i			0.261587i
$729$	−531441.			−0.0370370
$730$	345454.	+	417493.i	0.0239929	+	0.0289962i
$731$	−96000.4			−0.00664476
$732$			1.11935e7i			0.772123i
$733$		−	2.10050e7i		−	1.44398i	−0.691902	−	0.721991i	$-0.743227\pi$
$733$		−	2.10050e7i		−	1.44398i	0.691902	−	0.721991i	$-0.256773\pi$
$734$	−3.32048e6			−0.227489
$735$	3.54849e6	−	2.93620e6i	0.242285	−	0.200478i
$736$	721250.			0.0490785
$737$			151737.i			0.0102901i
$738$			656475.i			0.0443688i
$739$	1.45144e7			0.977660			0.488830	−	0.872379i	$-0.337424\pi$
$739$	1.45144e7			0.977660			0.488830	+	0.872379i	$0.337424\pi$
$740$	1.88291e7	−	1.55801e7i	1.26401	−	1.04590i
$741$	−7.45390e6			−0.498698
$742$			1.26060e6i			0.0840560i
$743$			1.33510e7i			0.887245i	0.896214	+	0.443622i	$0.146307\pi$
$743$			1.33510e7i			0.887245i	−0.896214	+	0.443622i	$0.853693\pi$
$744$	−61774.7			−0.00409146
$745$	−9.66907e6	−	1.16854e7i	−0.638255	−	0.771353i
$746$	2.19848e6			0.144636
$747$		−	879414.i		−	0.0576623i
$748$			249573.i			0.0163096i
$749$	2.24585e6			0.146277
$750$	1.81476e6	−	998419.i	0.117806	−	0.0648127i
$751$	1.03902e7			0.672242			0.336121	−	0.941819i	$-0.390885\pi$
$751$	1.03902e7			0.672242			0.336121	+	0.941819i	$0.390885\pi$
$752$			1.27317e7i			0.820999i
$753$		−	6.01870e6i		−	0.386826i
$754$	2.92076e6			0.187097
$755$	5.22976e6	+	6.32034e6i	0.333898	+	0.403527i
$756$	1.93002e6			0.122817
$757$			1.09141e7i			0.692227i	0.938193	+	0.346113i	$0.112499\pi$
$757$			1.09141e7i			0.692227i	−0.938193	+	0.346113i	$0.887501\pi$
$758$		−	4.12390e6i		−	0.260696i
$759$	−208983.			−0.0131676
$760$	−5.61291e6	+	4.64440e6i	−0.352496	+	0.291673i
$761$	1.04145e7			0.651894			0.325947	−	0.945388i	$-0.394317\pi$
$761$	1.04145e7			0.651894			0.325947	+	0.945388i	$0.394317\pi$
$762$		−	687136.i		−	0.0428702i
$763$		−	8.64548e6i		−	0.537623i
$764$	1.97953e6			0.122696
$765$	−237757.	+	196732.i	−0.0146886	+	0.0121540i
$766$	5.67763e6			0.349619
$767$			8.39232e6i			0.515103i
$768$			4.72472e6i			0.289050i
$769$	9.42825e6			0.574930			0.287465	−	0.957791i	$-0.407187\pi$
$769$	9.42825e6			0.574930			0.287465	+	0.957791i	$0.407187\pi$
$770$	−496955.	−	600587.i	−0.0302058	−	0.0365047i
$771$	9.78265e6			0.592681
$772$			2.00063e7i			1.20816i
$773$		−	1.18529e7i		−	0.713469i	−0.934206	−	0.356734i	$-0.883890\pi$
$773$		−	1.18529e7i		−	0.713469i	0.934206	−	0.356734i	$-0.116110\pi$
$774$	−150314.			−0.00901875
$775$	48944.5	−	256870.i	0.00292718	−	0.0153624i
$776$	−7.95620e6			−0.474298
$777$		−	1.13730e7i		−	0.675805i
$778$		−	3.23760e6i		−	0.191767i
$779$	9.77398e6			0.577069
$780$	5.06017e6	+	6.11538e6i	0.297803	+	0.359904i
$781$	5.76425e6			0.338154
$782$			17230.0i			0.00100756i
$783$		−	3.10042e6i		−	0.180724i
$784$	7.87650e6			0.457660
$785$	−1.57445e7	+	1.30278e7i	−0.911916	+	0.754564i
$786$	−1.47439e6			−0.0851246
$787$		−	1.84213e7i		−	1.06019i	−0.847939	−	0.530094i	$-0.822157\pi$
$787$		−	1.84213e7i		−	1.06019i	0.847939	−	0.530094i	$-0.177843\pi$
$788$			1.78616e7i			1.02472i
$789$	−7.79293e6			−0.445664
$790$	5.11706e6	−	4.23411e6i	0.291711	−	0.241376i
$791$	1.05456e6			0.0599279
$792$			803955.i			0.0455427i
$793$			2.14225e7i			1.20973i
$794$	−7.81492e6			−0.439919
$795$	3.50837e6	+	4.23999e6i	0.196874	+	0.237929i
$796$	1.03731e7			0.580266
$797$		−	8.83478e6i		−	0.492663i	−0.969186	−	0.246331i	$-0.920775\pi$
$797$		−	8.83478e6i		−	0.492663i	0.969186	−	0.246331i	$-0.0792252\pi$
$798$			1.64788e6i			0.0916048i
$799$	−1.00848e6			−0.0558858
$800$	1.15374e7	+	2.19836e6i	0.637357	+	0.121443i
$801$	9.14242e6			0.503478
$802$		−	6.01738e6i		−	0.330348i
$803$		−	890319.i		−	0.0487255i
$804$	−341570.			−0.0186354
$805$	598266.	+	723025.i	0.0325390	+	0.0393245i
$806$	−57465.8			−0.00311582
$807$		−	4.10262e6i		−	0.221757i
$808$			4.57312e6i			0.246425i
$809$	−1.51577e7			−0.814259			−0.407129	−	0.913370i	$-0.633470\pi$
$809$	−1.51577e7			−0.814259			−0.407129	+	0.913370i	$0.633470\pi$
$810$	−372271.	+	308035.i	−0.0199364	+	0.0164963i
$811$	−1.02018e7			−0.544658			−0.272329	−	0.962204i	$-0.587794\pi$
$811$	−1.02018e7			−0.544658			−0.272329	+	0.962204i	$0.587794\pi$
$812$			1.12597e7i			0.599291i
$813$			1.74303e7i			0.924863i
$814$	2.30270e6			0.121808
$815$	−719052.	+	594979.i	−0.0379198	+	0.0313767i
$816$	−527742.			−0.0277458
$817$			2.23796e6i			0.117300i
$818$		−	7.74551e6i		−	0.404731i
$819$	3.69376e6			0.192424
$820$	−6.63519e6	−	8.01885e6i	−0.344603	−	0.416464i
$821$	2.60152e7			1.34700			0.673501	−	0.739186i	$-0.264790\pi$
$821$	2.60152e7			1.34700			0.673501	+	0.739186i	$0.264790\pi$
$822$		−	4.84563e6i		−	0.250133i
$823$		−	1.36038e7i		−	0.700103i	−0.936730	−	0.350052i	$-0.886164\pi$
$823$		−	1.36038e7i		−	0.700103i	0.936730	−	0.350052i	$-0.113836\pi$
$824$	8.81547e6			0.452301
$825$	−3.34298e6	−	636979.i	−0.171001	−	0.0325830i
$826$	1.85534e6			0.0946181
$827$		−	6.94229e6i		−	0.352971i	−0.984303	−	0.176486i	$-0.943527\pi$
$827$		−	6.94229e6i		−	0.352971i	0.984303	−	0.176486i	$-0.0564729\pi$
$828$		−	470437.i		−	0.0238465i
$829$	6.04757e6			0.305629			0.152814	−	0.988255i	$-0.451166\pi$
$829$	6.04757e6			0.305629			0.152814	+	0.988255i	$0.451166\pi$
$830$	−509728.	−	616024.i	−0.0256829	−	0.0310386i
$831$	−1.51102e7			−0.759044
$832$			1.17715e7i			0.589553i
$833$			623900.i			0.0311532i
$834$	−4.48732e6			−0.223394
$835$	−2.44888e7	+	2.02632e7i	−1.21549	+	1.00575i
$836$	5.81805e6			0.287913
$837$			61000.6i			0.00300968i
$838$			8.06867e6i			0.396910i
$839$	−4.32449e6			−0.212095			−0.106047	−	0.994361i	$-0.533820\pi$
$839$	−4.32449e6			−0.212095			−0.106047	+	0.994361i	$0.533820\pi$
$840$	2.78146e6	−	2.30152e6i	0.136011	−	0.112542i
$841$	−2.42331e6			−0.118146
$842$			3.72977e6i			0.181302i
$843$		−	1.49790e7i		−	0.725961i
$844$	−6.49641e6			−0.313919
$845$	−3.54763e6	−	4.28743e6i	−0.170921	−	0.206564i
$846$	−1.57904e6			−0.0758523
$847$			1.28077e6i			0.0613429i
$848$			9.41139e6i			0.449432i
$849$	−4.76146e6			−0.226710
$850$	−52516.9	+	275618.i	−0.00249317	+	0.0130846i
$851$	−2.77213e6			−0.131217
$852$			1.29757e7i			0.612397i
$853$		−	4.01062e7i		−	1.88729i	−0.330959	−	0.943645i	$-0.607372\pi$
$853$		−	4.01062e7i		−	1.88729i	0.330959	−	0.943645i	$-0.392628\pi$
$854$	4.73601e6			0.222212
$855$	4.58620e6	+	5.54258e6i	0.214555	+	0.259296i
$856$	−2.10591e6			−0.0982327
$857$		−	1.21434e7i		−	0.564792i	−0.959298	−	0.282396i	$-0.908871\pi$
$857$		−	1.21434e7i		−	0.564792i	0.959298	−	0.282396i	$-0.0911292\pi$
$858$			747878.i			0.0346827i
$859$	1.69726e7			0.784810			0.392405	−	0.919792i	$-0.371643\pi$
$859$	1.69726e7			0.784810			0.392405	+	0.919792i	$0.371643\pi$
$860$	1.83608e6	−	1.51926e6i	0.0846537	−	0.0700466i
$861$	−4.84347e6			−0.222663
$862$		−	8.17504e6i		−	0.374733i
$863$			3.51856e7i			1.60819i	0.594501	+	0.804095i	$0.297350\pi$
$863$			3.51856e7i			1.60819i	−0.594501	+	0.804095i	$0.702650\pi$
$864$	−2.73987e6			−0.124866
$865$	−2.37830e7	+	1.96792e7i	−1.08075	+	0.894266i
$866$	556917.			0.0252346
$867$			1.27369e7i			0.575462i
$868$		−	221534.i		−	0.00998026i
$869$	−1.09123e7			−0.490194
$870$	−1.79707e6	−	2.17182e6i	−0.0804948	−	0.0972806i
$871$	−653712.			−0.0291972
$872$			8.10678e6i			0.361042i
$873$			7.85650e6i			0.348894i
$874$	401666.			0.0177863
$875$	7.36633e6	+	1.33893e7i	0.325260	+	0.591204i
$876$	2.00417e6			0.0882419
$877$		−	3.15265e7i		−	1.38413i	−0.721834	−	0.692066i	$-0.756701\pi$
$877$		−	3.15265e7i		−	1.38413i	0.721834	−	0.692066i	$-0.243299\pi$
$878$		−	5.36203e6i		−	0.234743i
$879$	1.05827e7			0.461983
$880$	−3.71016e6	−	4.48386e6i	−0.161505	−	0.195184i
$881$	−2.96796e7			−1.28831			−0.644153	−	0.764897i	$-0.722790\pi$
$881$	−2.96796e7			−1.28831			−0.644153	+	0.764897i	$0.722790\pi$
$882$			976879.i			0.0422833i
$883$			1.56983e7i			0.677564i	0.940865	+	0.338782i	$0.110015\pi$
$883$			1.56983e7i			0.677564i	−0.940865	+	0.338782i	$0.889985\pi$
$884$	−1.07521e6			−0.0462768
$885$	6.24038e6	−	5.16359e6i	0.267826	−	0.221612i
$886$	6.52441e6			0.279227
$887$		−	532251.i		−	0.0227147i	−0.999936	−	0.0113574i	$-0.996385\pi$
$887$		−	532251.i		−	0.0227147i	0.999936	−	0.0113574i	$-0.00361524\pi$
$888$			1.06643e7i			0.453838i
$889$	5.06969e6			0.215143
$890$	6.40420e6	−	5.29915e6i	0.271013	−	0.224249i
$891$	793881.			0.0335013
$892$		−	3.59381e6i		−	0.151232i
$893$			2.35097e7i			0.986550i
$894$	3.21692e6			0.134616
$895$	−6.41343e6	−	7.75085e6i	−0.267629	−	0.323438i
$896$	1.31233e7			0.546102
$897$		−	900342.i		−	0.0373617i
$898$			9.67029e6i			0.400174i
$899$	−355877.			−0.0146859
$900$	1.43389e6	−	7.52529e6i	0.0590077	−	0.309683i
$901$	−745479.			−0.0305931
$902$		−	980661.i		−	0.0401331i
$903$		−	1.10901e6i		−	0.0452603i
$904$	−988848.			−0.0402447
$905$	−2.18259e7	−	2.63773e7i	−0.885829	−	1.07055i
$906$	−1.73995e6			−0.0704233
$907$			7.46788e6i			0.301425i	0.988578	+	0.150713i	$0.0481568\pi$
$907$			7.46788e6i			0.301425i	−0.988578	+	0.150713i	$0.951843\pi$
$908$		−	66072.1i		−	0.00265952i
$909$	4.51581e6			0.181270
$910$	2.58745e6	−	2.14098e6i	0.103578	−	0.0857057i
$911$	4.14937e6			0.165648			0.0828240	−	0.996564i	$-0.473606\pi$
$911$	4.14937e6			0.165648			0.0828240	+	0.996564i	$0.473606\pi$
$912$			1.23027e7i			0.489795i
$913$			1.31369e6i			0.0521575i
$914$	−2.73567e6			−0.108318
$915$	1.59294e7	−	1.31808e7i	0.628994	−	0.520460i
$916$	−3.74383e6			−0.147427
$917$		−	1.08780e7i		−	0.427195i
$918$		−	65453.0i		−	0.00256344i
$919$	2.25977e7			0.882625			0.441313	−	0.897353i	$-0.354513\pi$
$919$	2.25977e7			0.882625			0.441313	+	0.897353i	$0.354513\pi$
$920$	−560988.	−	677973.i	−0.0218517	−	0.0264085i
$921$	1.37780e7			0.535225
$922$			2.22533e6i			0.0862118i
$923$			2.48335e7i			0.959476i
$924$	−2.88312e6			−0.111092
$925$	−4.43441e7	−	8.44942e6i	−1.70405	−	0.324693i
$926$	−1.79106e6			−0.0686410
$927$		−	8.70500e6i		−	0.332713i
$928$		−	1.59844e7i		−	0.609291i
$929$	−4.69291e7			−1.78403			−0.892017	−	0.452002i	$-0.850710\pi$
$929$	−4.69291e7			−1.78403			−0.892017	+	0.452002i	$0.850710\pi$
$930$	35357.3	+	42730.5i	0.00134052	+	0.00162006i
$931$	1.45443e7			0.549945
$932$			3.52844e7i			1.33059i
$933$		−	1.00458e7i		−	0.377818i
$934$	1.11661e7			0.418827
$935$	355168.	−	293883.i	0.0132863	−	0.0109937i
$936$	−3.46360e6			−0.129222
$937$			5.63886e6i			0.209818i	0.994482	+	0.104909i	$0.0334551\pi$
$937$			5.63886e6i			0.209818i	−0.994482	+	0.104909i	$0.966545\pi$
$938$			144520.i			0.00536317i
$939$	−7.78128e6			−0.287996
$940$	1.92880e7	−	1.59599e7i	0.711981	−	0.589128i
$941$	−2.03249e7			−0.748261			−0.374131	−	0.927376i	$-0.622059\pi$
$941$	−2.03249e7			−0.748261			−0.374131	+	0.927376i	$0.622059\pi$
$942$		−	4.33436e6i		−	0.159147i
$943$			1.18058e6i			0.0432331i
$944$	1.38516e7			0.505906
$945$	−2.27268e6	−	2.74661e6i	−0.0827863	−	0.100050i
$946$	224543.			0.00815777
$947$		−	1.36521e7i		−	0.494681i	−0.968929	−	0.247340i	$-0.920443\pi$
$947$		−	1.36521e7i		−	0.494681i	0.968929	−	0.247340i	$-0.0795566\pi$
$948$		−	2.45644e7i		−	0.887741i
$949$	3.83567e6			0.138253
$950$	6.42520e6	+	1.22427e6i	0.230982	+	0.0440118i
$951$	−1.62543e7			−0.582797
$952$			489039.i			0.0174885i
$953$		−	5.93702e6i		−	0.211756i	−0.994379	−	0.105878i	$-0.966235\pi$
$953$		−	5.93702e6i		−	0.211756i	0.994379	−	0.105878i	$-0.0337654\pi$
$954$	−1.16724e6			−0.0415232
$955$	−2.33098e6	−	2.81707e6i	−0.0827046	−	0.0999514i
$956$	−2.33223e7			−0.825329
$957$			4.63149e6i			0.163471i
$958$		−	4.64909e6i		−	0.163664i
$959$	3.57510e7			1.25528
$960$	8.75306e6	−	7.24271e6i	0.306536	−	0.253643i
$961$	−2.86221e7			−0.999755
$962$			9.92047e6i			0.345617i
$963$			2.07952e6i			0.0722601i
$964$	−4.31391e7			−1.49513
$965$	2.84709e7	−	2.35582e7i	0.984200	−	0.814375i
$966$	−199044.			−0.00686289
$967$		−	4.40436e7i		−	1.51467i	−0.653029	−	0.757333i	$-0.726502\pi$
$967$		−	4.40436e7i		−	1.51467i	0.653029	−	0.757333i	$-0.273498\pi$
$968$		−	1.20097e6i		−	0.0411949i
$969$	−974502.			−0.0333406
$970$	4.55380e6	+	5.50343e6i	0.155398	+	0.187804i
$971$	−1.01824e7			−0.346577			−0.173289	−	0.984871i	$-0.555439\pi$
$971$	−1.01824e7			−0.346577			−0.173289	+	0.984871i	$0.555439\pi$
$972$			1.78708e6i			0.0606707i
$973$		−	3.31074e7i		−	1.12110i
$974$	−6.14854e6			−0.207670
$975$	2.74423e6	−	1.44022e7i	0.0924506	−	0.485197i
$976$	3.53580e7			1.18813
$977$		−	4.43840e7i		−	1.48761i	−0.668395	−	0.743806i	$-0.733018\pi$
$977$		−	4.43840e7i		−	1.48761i	0.668395	−	0.743806i	$-0.266982\pi$
$978$		−	197951.i		−	0.00661774i
$979$	−1.36572e7			−0.455413
$980$	−9.87359e6	−	1.19326e7i	−0.328405	−	0.396889i
$981$	8.00520e6			0.265583
$982$			9.51850e6i			0.314985i
$983$			2.94574e7i			0.972324i	0.873869	+	0.486162i	$0.161604\pi$
$983$			2.94574e7i			0.972324i	−0.873869	+	0.486162i	$0.838396\pi$
$984$	4.54167e6			0.149530
$985$	2.54189e7	−	2.10328e7i	0.834768	−	0.690728i
$986$	381852.			0.0125084
$987$		−	1.16502e7i		−	0.380662i
$988$			2.50653e7i			0.816923i
$989$	−270319.			−0.00878791
$990$	556108.	−	460151.i	0.0180331	−	0.0149215i
$991$	−1.97622e7			−0.639221			−0.319611	−	0.947549i	$-0.603552\pi$
$991$	−1.97622e7			−0.639221			−0.319611	+	0.947549i	$0.603552\pi$
$992$			314491.i			0.0101468i
$993$			1.67131e7i			0.537879i
$994$	5.49010e6			0.176244
$995$	−1.22148e7	−	1.47620e7i	−0.391137	−	0.472702i
$996$	−2.95722e6			−0.0944572
$997$			2.39291e7i			0.762408i	0.924491	+	0.381204i	$0.124491\pi$
$997$			2.39291e7i			0.762408i	−0.924491	+	0.381204i	$0.875509\pi$
$998$		−	1.38085e7i		−	0.438854i
$999$	1.05307e7			0.333844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.b.34.12	✓	26
5.2	odd	4		825.6.a.y.1.7		13
5.3	odd	4		825.6.a.v.1.7		13
5.4	even	2	inner	165.6.c.b.34.15	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.b.34.12	✓	26	1.1	even	1	trivial
165.6.c.b.34.15	yes	26	5.4	even	2	inner
825.6.a.v.1.7		13	5.3	odd	4
825.6.a.y.1.7		13	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.31741i q^{2} +9.00000i q^{3} +30.2644 q^{4} +(-35.6376 - 43.0693i) q^{5} +11.8567 q^{6} +87.4786i q^{7} -82.0279i q^{8} -81.0000 q^{9} +(-56.7399 + 46.9494i) q^{10} +121.000 q^{11} +272.380i q^{12} +521.292i q^{13} +115.245 q^{14} +(387.623 - 320.739i) q^{15} +860.397 q^{16} +68.1523i q^{17} +106.710i q^{18} +1588.76 q^{19} +(-1078.55 - 1303.47i) q^{20} -787.308 q^{21} -159.407i q^{22} +191.904i q^{23} +738.251 q^{24} +(-584.921 + 3069.77i) q^{25} +686.756 q^{26} -729.000i q^{27} +2647.49i q^{28} +4252.98 q^{29} +(-422.545 - 510.659i) q^{30} -83.6771 q^{31} -3758.39i q^{32} +1089.00i q^{33} +89.7846 q^{34} +(3767.64 - 3117.53i) q^{35} -2451.42 q^{36} +14445.4i q^{37} -2093.06i q^{38} -4691.63 q^{39} +(-3532.88 + 2923.28i) q^{40} +6151.94 q^{41} +1037.21i q^{42} +1408.62i q^{43} +3662.00 q^{44} +(2886.65 + 3488.61i) q^{45} +252.816 q^{46} +14797.5i q^{47} +7743.57i q^{48} +9154.49 q^{49} +(4044.15 + 770.582i) q^{50} -613.371 q^{51} +15776.6i q^{52} +10938.4i q^{53} -960.393 q^{54} +(-4312.15 - 5211.38i) q^{55} +7175.69 q^{56} +14298.9i q^{57} -5602.92i q^{58} +16099.1 q^{59} +(11731.2 - 9706.97i) q^{60} +41095.0 q^{61} +110.237i q^{62} -7085.77i q^{63} +22581.4 q^{64} +(22451.7 - 18577.6i) q^{65} +1434.66 q^{66} +1254.02i q^{67} +2062.59i q^{68} -1727.14 q^{69} +(-4107.07 - 4963.53i) q^{70} +47638.4 q^{71} +6644.26i q^{72} -7358.01i q^{73} +19030.5 q^{74} +(-27627.9 - 5264.29i) q^{75} +48083.1 q^{76} +10584.9i q^{77} +6180.81i q^{78} -90184.5 q^{79} +(-30662.5 - 37056.7i) q^{80} +6561.00 q^{81} -8104.64i q^{82} +10857.0i q^{83} -23827.4 q^{84} +(2935.27 - 2428.79i) q^{85} +1855.73 q^{86} +38276.8i q^{87} -9925.37i q^{88} -112869. q^{89} +(4595.93 - 3802.90i) q^{90} -45601.9 q^{91} +5807.86i q^{92} -753.094i q^{93} +19494.4 q^{94} +(-56619.8 - 68426.9i) q^{95} +33825.5 q^{96} -96993.9i q^{97} -12060.2i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29}+ \cdots - 254826 q^{99}+O(q^{100}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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