LMFDB - Embedded newform 115.5.c.c.114.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.12
Character	$\chi$	$=$	115.114
Dual form			115.5.c.c.114.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.94563i q^{2} -6.82837i q^{3} -8.45927 q^{4} +(22.1235 + 11.6426i) q^{5} -33.7706 q^{6} +47.4193 q^{7} -37.2937i q^{8} +34.3734 q^{9} +(57.5800 - 109.415i) q^{10} -121.460i q^{11} +57.7631i q^{12} -25.2927i q^{13} -234.518i q^{14} +(79.4999 - 151.068i) q^{15} -319.789 q^{16} +130.920 q^{17} -169.998i q^{18} +292.655i q^{19} +(-187.149 - 98.4878i) q^{20} -323.797i q^{21} -600.696 q^{22} +(-215.187 + 483.255i) q^{23} -254.655 q^{24} +(353.900 + 515.150i) q^{25} -125.088 q^{26} -787.812i q^{27} -401.133 q^{28} -790.956 q^{29} +(-747.125 - 393.177i) q^{30} +365.318 q^{31} +984.861i q^{32} -829.373 q^{33} -647.481i q^{34} +(1049.08 + 552.083i) q^{35} -290.774 q^{36} -471.550 q^{37} +1447.36 q^{38} -172.708 q^{39} +(434.195 - 825.067i) q^{40} -1821.57 q^{41} -1601.38 q^{42} -7.12217 q^{43} +1027.46i q^{44} +(760.460 + 400.195i) q^{45} +(2390.00 + 1064.24i) q^{46} -2540.24i q^{47} +2183.64i q^{48} -152.410 q^{49} +(2547.74 - 1750.26i) q^{50} -893.969i q^{51} +213.958i q^{52} +2852.07 q^{53} -3896.23 q^{54} +(1414.11 - 2687.12i) q^{55} -1768.44i q^{56} +1998.36 q^{57} +3911.78i q^{58} -4053.87 q^{59} +(-672.512 + 1277.92i) q^{60} +3186.31i q^{61} -1806.73i q^{62} +1629.96 q^{63} -245.867 q^{64} +(294.472 - 559.563i) q^{65} +4101.77i q^{66} +6094.08 q^{67} -1107.49 q^{68} +(3299.84 + 1469.38i) q^{69} +(2730.40 - 5188.37i) q^{70} +4387.94 q^{71} -1281.91i q^{72} +3217.13i q^{73} +2332.11i q^{74} +(3517.64 - 2416.56i) q^{75} -2475.65i q^{76} -5759.54i q^{77} +854.149i q^{78} +8824.58i q^{79} +(-7074.86 - 3723.17i) q^{80} -2595.23 q^{81} +9008.82i q^{82} +12862.0 q^{83} +2739.08i q^{84} +(2896.41 + 1524.24i) q^{85} +35.2236i q^{86} +5400.94i q^{87} -4529.68 q^{88} +5490.66i q^{89} +(1979.22 - 3760.95i) q^{90} -1199.36i q^{91} +(1820.33 - 4087.99i) q^{92} -2494.53i q^{93} -12563.1 q^{94} +(-3407.26 + 6474.56i) q^{95} +6724.99 q^{96} -15520.6 q^{97} +753.765i q^{98} -4174.98i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 360 q^{4} + 160 q^{6} - 1128 q^{9} + 2136 q^{16} - 3940 q^{24} - 2540 q^{25} + 3144 q^{26} - 348 q^{29} - 4480 q^{31} - 1440 q^{35} - 3728 q^{36} - 1800 q^{39} + 7176 q^{41} + 5372 q^{46} + 9580 q^{49}+ \cdots - 39960 q^{96}+O(q^{100}) $ 44 * q - 360 * q^4 + 160 * q^6 - 1128 * q^9 + 2136 * q^16 - 3940 * q^24 - 2540 * q^25 + 3144 * q^26 - 348 * q^29 - 4480 * q^31 - 1440 * q^35 - 3728 * q^36 - 1800 * q^39 + 7176 * q^41 + 5372 * q^46 + 9580 * q^49 + 10920 * q^50 + 2780 * q^54 - 6340 * q^55 + 11100 * q^59 - 37372 * q^64 - 22700 * q^69 - 8340 * q^70 + 26736 * q^71 - 10420 * q^75 + 54644 * q^81 + 12720 * q^85 + 46572 * q^94 + 53640 * q^95 - 39960 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	4.94563i		−	1.23641i	−0.786018	−	0.618204i	$-0.787861\pi$
$2$		−	4.94563i		−	1.23641i	0.786018	−	0.618204i	$-0.212139\pi$
$3$		−	6.82837i		−	0.758708i	−0.925252	−	0.379354i	$-0.876146\pi$
$3$		−	6.82837i		−	0.758708i	0.925252	−	0.379354i	$-0.123854\pi$
$4$	−8.45927			−0.528705
$5$	22.1235	+	11.6426i	0.884941	+	0.465703i
$5$	22.1235	+	11.6426i	0.884941	+	0.465703i
$6$	−33.7706			−0.938072
$7$	47.4193			0.967741			0.483870	−	0.875140i	$-0.339231\pi$
$7$	47.4193			0.967741			0.483870	+	0.875140i	$0.339231\pi$
$8$		−	37.2937i		−	0.582713i
$9$	34.3734			0.424362
$10$	57.5800	−	109.415i	0.575800	−	1.09415i
$11$		−	121.460i		−	1.00380i	−0.864926	−	0.501900i	$-0.832634\pi$
$11$		−	121.460i		−	1.00380i	0.864926	−	0.501900i	$-0.167366\pi$
$12$			57.7631i			0.401132i
$13$		−	25.2927i		−	0.149661i	−0.997196	−	0.0748304i	$-0.976158\pi$
$13$		−	25.2927i		−	0.149661i	0.997196	−	0.0748304i	$-0.0238416\pi$
$14$		−	234.518i		−	1.19652i
$15$	79.4999	−	151.068i	0.353333	−	0.671412i
$16$	−319.789			−1.24918
$17$	130.920			0.453010			0.226505	−	0.974010i	$-0.427270\pi$
$17$	130.920			0.453010			0.226505	+	0.974010i	$0.427270\pi$
$18$		−	169.998i		−	0.524685i
$19$			292.655i			0.810679i	0.914166	+	0.405339i	$0.132847\pi$
$19$			292.655i			0.810679i	−0.914166	+	0.405339i	$0.867153\pi$
$20$	−187.149	−	98.4878i	−0.467872	−	0.246220i
$21$		−	323.797i		−	0.734233i
$22$	−600.696			−1.24111
$23$	−215.187	+	483.255i	−0.406781	+	0.913526i
$23$	−215.187	+	483.255i	−0.406781	+	0.913526i
$24$	−254.655			−0.442109
$25$	353.900	+	515.150i	0.566241	+	0.824240i
$26$	−125.088			−0.185042
$27$		−	787.812i		−	1.08067i
$28$	−401.133			−0.511649
$29$	−790.956			−0.940495			−0.470247	−	0.882535i	$-0.655835\pi$
$29$	−790.956			−0.940495			−0.470247	+	0.882535i	$0.655835\pi$
$30$	−747.125	−	393.177i	−0.830139	−	0.436864i
$31$	365.318			0.380144			0.190072	−	0.981770i	$-0.439128\pi$
$31$	365.318			0.380144			0.190072	+	0.981770i	$0.439128\pi$
$32$			984.861i			0.961778i
$33$	−829.373			−0.761591
$34$		−	647.481i		−	0.560105i
$35$	1049.08	+	552.083i	0.856393	+	0.450680i
$36$	−290.774			−0.224362
$37$	−471.550			−0.344449			−0.172224	−	0.985058i	$-0.555095\pi$
$37$	−471.550			−0.344449			−0.172224	+	0.985058i	$0.555095\pi$
$38$	1447.36			1.00233
$39$	−172.708			−0.113549
$40$	434.195	−	825.067i	0.271372	−	0.515667i
$41$	−1821.57			−1.08362			−0.541812	−	0.840500i	$-0.682261\pi$
$41$	−1821.57			−1.08362			−0.541812	+	0.840500i	$0.682261\pi$
$42$	−1601.38			−0.907811
$43$	−7.12217			−0.00385190			−0.00192595	−	0.999998i	$-0.500613\pi$
$43$	−7.12217			−0.00385190			−0.00192595	+	0.999998i	$0.500613\pi$
$44$			1027.46i			0.530714i
$45$	760.460	+	400.195i	0.375536	+	0.197627i
$46$	2390.00	+	1064.24i	1.12949	+	0.502948i
$47$		−	2540.24i		−	1.14995i	−0.818171	−	0.574975i	$-0.805012\pi$
$47$		−	2540.24i		−	1.14995i	0.818171	−	0.574975i	$-0.194988\pi$
$48$			2183.64i			0.947760i
$49$	−152.410			−0.0634778
$50$	2547.74	−	1750.26i	1.01910	−	0.700104i
$51$		−	893.969i		−	0.343702i
$52$			213.958i			0.0791264i
$53$	2852.07			1.01533			0.507666	−	0.861554i	$-0.330509\pi$
$53$	2852.07			1.01533			0.507666	+	0.861554i	$0.330509\pi$
$54$	−3896.23			−1.33616
$55$	1414.11	−	2687.12i	0.467473	−	0.888304i
$56$		−	1768.44i		−	0.563915i
$57$	1998.36			0.615068
$58$			3911.78i			1.16284i
$59$	−4053.87			−1.16457			−0.582285	−	0.812985i	$-0.697841\pi$
$59$	−4053.87			−1.16457			−0.582285	+	0.812985i	$0.697841\pi$
$60$	−672.512	+	1277.92i	−0.186809	+	0.354978i
$61$			3186.31i			0.856304i	0.903707	+	0.428152i	$0.140835\pi$
$61$			3186.31i			0.856304i	−0.903707	+	0.428152i	$0.859165\pi$
$62$		−	1806.73i		−	0.470013i
$63$	1629.96			0.410673
$64$	−245.867			−0.0600262
$65$	294.472	−	559.563i	0.0696976	−	0.132441i
$66$			4101.77i			0.941638i
$67$	6094.08			1.35756			0.678779	−	0.734342i	$-0.262509\pi$
$67$	6094.08			1.35756			0.678779	+	0.734342i	$0.262509\pi$
$68$	−1107.49			−0.239508
$69$	3299.84	+	1469.38i	0.693099	+	0.308628i
$70$	2730.40	−	5188.37i	0.557225	−	1.05885i
$71$	4387.94			0.870449			0.435225	−	0.900322i	$-0.356669\pi$
$71$	4387.94			0.870449			0.435225	+	0.900322i	$0.356669\pi$
$72$		−	1281.91i		−	0.247282i
$73$			3217.13i			0.603702i	0.953355	+	0.301851i	$0.0976044\pi$
$73$			3217.13i			0.603702i	−0.953355	+	0.301851i	$0.902396\pi$
$74$			2332.11i			0.425879i
$75$	3517.64	−	2416.56i	0.625357	−	0.429611i
$76$		−	2475.65i		−	0.428610i
$77$		−	5759.54i		−	0.971419i
$78$			854.149i			0.140393i
$79$			8824.58i			1.41397i	0.707229	+	0.706984i	$0.249945\pi$
$79$			8824.58i			1.41397i	−0.707229	+	0.706984i	$0.750055\pi$
$80$	−7074.86	−	3723.17i	−1.10545	−	0.581746i
$81$	−2595.23			−0.395554
$82$			9008.82i			1.33980i
$83$	12862.0			1.86704			0.933519	−	0.358527i	$-0.116721\pi$
$83$	12862.0			1.86704			0.933519	+	0.358527i	$0.116721\pi$
$84$			2739.08i			0.388192i
$85$	2896.41	+	1524.24i	0.400887	+	0.210968i
$86$			35.2236i			0.00476252i
$87$			5400.94i			0.713561i
$88$	−4529.68			−0.584928
$89$			5490.66i			0.693178i	0.938017	+	0.346589i	$0.112660\pi$
$89$			5490.66i			0.693178i	−0.938017	+	0.346589i	$0.887340\pi$
$90$	1979.22	−	3760.95i	0.244348	−	0.464315i
$91$		−	1199.36i		−	0.144833i
$92$	1820.33	−	4087.99i	0.215067	−	0.482985i
$93$		−	2494.53i		−	0.288418i
$94$	−12563.1			−1.42181
$95$	−3407.26	+	6474.56i	−0.377536	+	0.717403i
$96$	6724.99			0.729708
$97$	−15520.6			−1.64955			−0.824775	−	0.565461i	$-0.808698\pi$
$97$	−15520.6			−1.64955			−0.824775	+	0.565461i	$0.808698\pi$
$98$			753.765i			0.0784845i
$99$		−	4174.98i		−	0.425975i
$100$	−2993.74	−	4357.80i	−0.299374	−	0.435780i
$101$	3046.74			0.298671			0.149336	−	0.988787i	$-0.452287\pi$
$101$	3046.74			0.298671			0.149336	+	0.988787i	$0.452287\pi$
$102$	−4421.24			−0.424956
$103$	−6210.09			−0.585361			−0.292680	−	0.956210i	$-0.594547\pi$
$103$	−6210.09			−0.585361			−0.292680	+	0.956210i	$0.594547\pi$
$104$	−943.257			−0.0872094
$105$	3769.83	−	7163.52i	0.341935	−	0.649752i
$106$		−	14105.3i		−	1.25536i
$107$	1863.57			0.162771			0.0813857	−	0.996683i	$-0.474065\pi$
$107$	1863.57			0.162771			0.0813857	+	0.996683i	$0.474065\pi$
$108$			6664.32i			0.571358i
$109$		−	3764.74i		−	0.316870i	−0.987369	−	0.158435i	$-0.949355\pi$
$109$		−	3764.74i		−	0.316870i	0.987369	−	0.158435i	$-0.0506449\pi$
$110$	−13289.5	−	6993.65i	−1.09831	−	0.577988i
$111$			3219.92i			0.261336i
$112$	−15164.2			−1.20888
$113$	−10.8182			−0.000847225			−0.000423612	−	1.00000i	$-0.500135\pi$
$113$	−10.8182			−0.000847225			−0.000423612		1.00000i	$0.500135\pi$
$114$		−	9883.14i		−	0.760475i
$115$	−10387.0	+	8185.97i	−0.785409	+	0.618977i
$116$	6690.91			0.497244
$117$		−	869.394i		−	0.0635104i
$118$			20048.9i			1.43988i
$119$	6208.12			0.438396
$120$	−5633.86	−	2964.84i	−0.391240	−	0.205892i
$121$	−111.498			−0.00761547
$122$	15758.3			1.05874
$123$			12438.4i			0.822154i
$124$	−3090.33			−0.200984
$125$	1831.84	+	15517.2i	0.117238	+	0.993104i
$126$		−	8061.18i		−	0.507759i
$127$		−	16809.7i		−	1.04221i	−0.853494	−	0.521103i	$-0.825521\pi$
$127$		−	16809.7i		−	1.04221i	0.853494	−	0.521103i	$-0.174479\pi$
$128$			16973.7i			1.03599i
$129$			48.6328i			0.00292247i
$130$	−2767.39	−	1456.35i	−0.163751	−	0.0861747i
$131$	4191.57			0.244250			0.122125	−	0.992515i	$-0.461029\pi$
$131$	4191.57			0.244250			0.122125	+	0.992515i	$0.461029\pi$
$132$	7015.89			0.402657
$133$			13877.5i			0.784527i
$134$		−	30139.1i		−	1.67850i
$135$	9172.17	−	17429.2i	0.503274	−	0.956333i
$136$		−	4882.48i		−	0.263975i
$137$	8299.84			0.442210			0.221105	−	0.975250i	$-0.429034\pi$
$137$	8299.84			0.442210			0.221105	+	0.975250i	$0.429034\pi$
$138$	7267.00	−	16319.8i	0.381590	−	0.856953i
$139$	24420.7			1.26395			0.631973	−	0.774990i	$-0.282245\pi$
$139$	24420.7			1.26395			0.631973	+	0.774990i	$0.282245\pi$
$140$	−8874.47	−	4670.22i	−0.452779	−	0.238277i
$141$	−17345.7			−0.872476
$142$		−	21701.1i		−	1.07623i
$143$	−3072.05			−0.150230
$144$	−10992.2			−0.530103
$145$	−17498.7	−	9208.77i	−0.832282	−	0.437992i
$146$	15910.7			0.746421
$147$			1040.71i			0.0481611i
$148$	3988.97			0.182112
$149$		−	104.420i		−	0.00470339i	−0.999997	−	0.00235170i	$-0.999251\pi$
$149$		−	104.420i		−	0.00470339i	0.999997	−	0.00235170i	$-0.000748569\pi$
$150$	−11951.4	−	17396.9i	−0.531175	−	0.773197i
$151$	−27841.9			−1.22108			−0.610542	−	0.791984i	$-0.709048\pi$
$151$	−27841.9			−1.22108			−0.610542	+	0.791984i	$0.709048\pi$
$152$	10914.2			0.472393
$153$	4500.15			0.192240
$154$	−28484.6			−1.20107
$155$	8082.13	+	4253.25i	0.336405	+	0.177034i
$156$	1460.98			0.0600338
$157$	−46395.1			−1.88223			−0.941116	−	0.338084i	$-0.890221\pi$
$157$	−46395.1			−1.88223			−0.941116	+	0.338084i	$0.890221\pi$
$158$	43643.1			1.74824
$159$		−	19475.0i		−	0.770340i
$160$	−11466.3	+	21788.6i	−0.447903	+	0.851117i
$161$	−10204.0	+	22915.6i	−0.393659	+	0.884056i
$162$			12835.1i			0.489066i
$163$			29520.0i			1.11107i	0.831493	+	0.555535i	$0.187486\pi$
$163$			29520.0i			1.11107i	−0.831493	+	0.555535i	$0.812514\pi$
$164$	15409.2			0.572917
$165$	−18348.7	−	9656.05i	−0.673963	−	0.354676i
$166$		−	63610.9i		−	2.30842i
$167$		−	37239.6i		−	1.33528i	−0.744485	−	0.667639i	$-0.767305\pi$
$167$		−	37239.6i		−	1.33528i	0.744485	−	0.667639i	$-0.232695\pi$
$168$	−12075.6			−0.427847
$169$	27921.3			0.977602
$170$	7538.35	−	14324.6i	0.260843	−	0.495659i
$171$			10059.5i			0.344022i
$172$	60.2484			0.00203652
$173$			19212.6i			0.641940i	0.947089	+	0.320970i	$0.104009\pi$
$173$			19212.6i			0.641940i	−0.947089	+	0.320970i	$0.895991\pi$
$174$	26711.1			0.882252
$175$	16781.7	+	24428.1i	0.547974	+	0.797651i
$176$			38841.5i			1.25392i
$177$			27681.3i			0.883569i
$178$	27154.8			0.857051
$179$	54673.8			1.70637			0.853185	−	0.521609i	$-0.174668\pi$
$179$	54673.8			1.70637			0.853185	+	0.521609i	$0.174668\pi$
$180$	−6432.94	−	3385.36i	−0.198547	−	0.104486i
$181$			60172.9i			1.83672i	0.395742	+	0.918362i	$0.370488\pi$
$181$			60172.9i			1.83672i	−0.395742	+	0.918362i	$0.629512\pi$
$182$	−5931.60			−0.179073
$183$	21757.3			0.649685
$184$	18022.3	+	8025.12i	0.532324	+	0.237037i
$185$	−10432.3	−	5490.06i	−0.304817	−	0.160411i
$186$	−12337.0			−0.356603
$187$		−	15901.5i		−	0.454731i
$188$			21488.6i			0.607984i
$189$		−	37357.5i		−	1.04581i
$190$	32020.8	+	16851.1i	0.887002	+	0.466788i
$191$			48565.0i			1.33124i	0.746290	+	0.665621i	$0.231833\pi$
$191$			48565.0i			1.33124i	−0.746290	+	0.665621i	$0.768167\pi$
$192$			1678.87i			0.0455424i
$193$			22851.5i			0.613479i	0.951793	+	0.306740i	$0.0992381\pi$
$193$			22851.5i			0.613479i	−0.951793	+	0.306740i	$0.900762\pi$
$194$			76759.3i			2.03952i
$195$	−3820.91	−	2010.77i	−0.100484	−	0.0528801i
$196$	1289.28			0.0335610
$197$		−	14182.4i		−	0.365441i	−0.983165	−	0.182720i	$-0.941510\pi$
$197$		−	14182.4i		−	0.365441i	0.983165	−	0.182720i	$-0.0584903\pi$
$198$	−20647.9			−0.526679
$199$			44550.7i			1.12499i	0.826801	+	0.562495i	$0.190159\pi$
$199$			44550.7i			1.12499i	−0.826801	+	0.562495i	$0.809841\pi$
$200$	19211.8	−	13198.2i	0.480296	−	0.329956i
$201$		−	41612.7i		−	1.02999i
$202$		−	15068.1i		−	0.369279i
$203$	−37506.6			−0.910155
$204$			7562.33i			0.181717i
$205$	−40299.6	−	21207.8i	−0.958943	−	0.504647i
$206$			30712.8i			0.723745i
$207$	−7396.71	+	16611.1i	−0.172623	+	0.387666i
$208$			8088.33i			0.186953i
$209$	35545.8			0.813760
$210$	−35428.1	−	18644.2i	−0.803359	−	0.422771i
$211$	−41236.0			−0.926215			−0.463108	−	0.886302i	$-0.653266\pi$
$211$	−41236.0			−0.926215			−0.463108	+	0.886302i	$0.653266\pi$
$212$	−24126.4			−0.536810
$213$		−	29962.5i		−	0.660417i
$214$		−	9216.53i		−	0.201252i
$215$	−157.567	−	82.9205i	−0.00340871	−	0.00179384i
$216$	−29380.4			−0.629724
$217$	17323.1			0.367881
$218$	−18619.0			−0.391781
$219$	21967.7			0.458033
$220$	−11962.3	+	22731.1i	−0.247155	+	0.469650i
$221$		−	3311.31i		−	0.0677978i
$222$	15924.5			0.323118
$223$		−	15976.4i		−	0.321269i	−0.987014	−	0.160634i	$-0.948646\pi$
$223$		−	15976.4i		−	0.321269i	0.987014	−	0.160634i	$-0.0513540\pi$
$224$			46701.4i			0.930752i
$225$	12164.7	+	17707.4i	0.240291	+	0.349776i
$226$			53.5029i			0.00104752i
$227$	48395.1			0.939181			0.469590	−	0.882884i	$-0.344402\pi$
$227$	48395.1			0.939181			0.469590	+	0.882884i	$0.344402\pi$
$228$	−16904.7			−0.325190
$229$		−	69898.5i		−	1.33290i	−0.745551	−	0.666449i	$-0.767814\pi$
$229$		−	69898.5i		−	1.33290i	0.745551	−	0.666449i	$-0.232186\pi$
$230$	40484.8	+	51370.5i	0.765308	+	0.971086i
$231$	−39328.3			−0.737023
$232$			29497.6i			0.548039i
$233$		−	64869.9i		−	1.19490i	−0.801906	−	0.597450i	$-0.796181\pi$
$233$		−	64869.9i		−	1.19490i	0.801906	−	0.597450i	$-0.203819\pi$
$234$	−4299.70			−0.0785248
$235$	29575.0	−	56199.0i	0.535536	−	1.01764i
$236$	34292.8			0.615714
$237$	60257.5			1.07279
$238$		−	30703.1i		−	0.542036i
$239$	−29088.5			−0.509243			−0.254621	−	0.967041i	$-0.581951\pi$
$239$	−29088.5			−0.509243			−0.254621	+	0.967041i	$0.581951\pi$
$240$	−25423.2	+	48309.8i	−0.441375	+	0.838711i
$241$		−	60948.1i		−	1.04936i	−0.851298	−	0.524682i	$-0.824184\pi$
$241$		−	60948.1i		−	1.04936i	0.851298	−	0.524682i	$-0.175816\pi$
$242$			551.429i			0.00941583i
$243$		−	46091.6i		−	0.780565i
$244$		−	26953.8i		−	0.452732i
$245$	−3371.85	−	1774.45i	−0.0561741	−	0.0295618i
$246$	61515.6			1.01652
$247$	7402.03			0.121327
$248$		−	13624.1i		−	0.221515i
$249$		−	87826.7i		−	1.41654i
$250$	76742.6	−	9059.61i	1.22788	−	0.144954i
$251$		−	21475.3i		−	0.340873i	−0.985369	−	0.170437i	$-0.945482\pi$
$251$		−	21475.3i		−	0.340873i	0.985369	−	0.170437i	$-0.0545178\pi$
$252$	−13788.3			−0.217125
$253$	58696.1	+	26136.6i	0.916997	+	0.408327i
$254$	−83134.8			−1.28859
$255$	10408.1	−	19777.7i	0.160063	−	0.304156i
$256$	80012.0			1.22089
$257$			89616.4i			1.35682i	0.734685	+	0.678409i	$0.237330\pi$
$257$			89616.4i			1.35682i	−0.734685	+	0.678409i	$0.762670\pi$
$258$	240.520			0.00361336
$259$	−22360.6			−0.333337
$260$	−2491.02	+	4733.50i	−0.0368494	+	0.0700222i
$261$	−27187.8			−0.399111
$262$		−	20730.0i		−	0.301992i
$263$	21291.6			0.307820			0.153910	−	0.988085i	$-0.450813\pi$
$263$	21291.6			0.307820			0.153910	+	0.988085i	$0.450813\pi$
$264$			30930.3i			0.443789i
$265$	63097.7	+	33205.4i	0.898508	+	0.472843i
$266$	68633.0			0.969995
$267$	37492.3			0.525919
$268$	−51551.5			−0.717748
$269$	−117290.			−1.62090			−0.810450	−	0.585808i	$-0.800777\pi$
$269$	−117290.			−1.62090			−0.810450	+	0.585808i	$0.800777\pi$
$270$	−86198.3	−	45362.2i	−1.18242	−	0.622252i
$271$	−110364.			−1.50276			−0.751379	−	0.659871i	$-0.770611\pi$
$271$	−110364.			−1.50276			−0.751379	+	0.659871i	$0.770611\pi$
$272$	−41866.7			−0.565889
$273$	−8189.69			−0.109886
$274$		−	41048.0i		−	0.546752i
$275$	62570.1	−	42984.7i	0.827373	−	0.568393i
$276$	−27914.3	−	12429.9i	−0.366445	−	0.163173i
$277$		−	12201.9i		−	0.159025i	−0.996834	−	0.0795127i	$-0.974664\pi$
$277$		−	12201.9i		−	0.159025i	0.996834	−	0.0795127i	$-0.0253364\pi$
$278$		−	120776.i		−	1.56275i
$279$	12557.2			0.161319
$280$	20589.2	−	39124.1i	0.262617	−	0.499032i
$281$		−	138763.i		−	1.75737i	−0.477405	−	0.878683i	$-0.658423\pi$
$281$		−	138763.i		−	1.75737i	0.477405	−	0.878683i	$-0.341577\pi$
$282$			85785.4i			1.07874i
$283$	−2905.51			−0.0362785			−0.0181392	−	0.999835i	$-0.505774\pi$
$283$	−2905.51			−0.0362785			−0.0181392	+	0.999835i	$0.505774\pi$
$284$	−37118.8			−0.460211
$285$	44210.7	+	23266.0i	0.544299	+	0.286439i
$286$			15193.2i			0.185745i
$287$	−86377.6			−1.04867
$288$			33853.0i			0.408142i
$289$	−66381.0			−0.794782
$290$	−45543.2	+	86542.3i	−0.541536	+	1.02904i
$291$			105981.i			1.25153i
$292$		−	27214.5i		−	0.319180i
$293$	−96882.7			−1.12852			−0.564262	−	0.825596i	$-0.690839\pi$
$293$	−96882.7			−1.12852			−0.564262	+	0.825596i	$0.690839\pi$
$294$	5146.99			0.0595468
$295$	−89685.9	−	47197.5i	−1.03058	−	0.542345i
$296$			17585.8i			0.200715i
$297$	−95687.5			−1.08478
$298$	−516.423			−0.00581531
$299$	12222.8	+	5442.66i	0.136719	+	0.0608792i
$300$	−29756.6	+	20442.4i	−0.330629	+	0.227137i
$301$	−337.728			−0.00372764
$302$			137696.i			1.50976i
$303$		−	20804.3i		−	0.226604i
$304$		−	93587.9i		−	1.01268i
$305$	−37096.9	+	70492.3i	−0.398784	+	0.757778i
$306$		−	22256.1i		−	0.237687i
$307$		−	80278.2i		−	0.851767i	−0.904778	−	0.425884i	$-0.859963\pi$
$307$		−	80278.2i		−	0.851767i	0.904778	−	0.425884i	$-0.140037\pi$
$308$			48721.5i			0.513594i
$309$			42404.8i			0.444118i
$310$	21035.0	−	39971.2i	0.218887	−	0.415934i
$311$	99847.5			1.03233			0.516163	−	0.856491i	$-0.327360\pi$
$311$	99847.5			1.03233			0.516163	+	0.856491i	$0.327360\pi$
$312$			6440.91i			0.0661664i
$313$	9836.64			0.100406			0.0502028	−	0.998739i	$-0.484013\pi$
$313$	9836.64			0.100406			0.0502028	+	0.998739i	$0.484013\pi$
$314$			229453.i			2.32721i
$315$	36060.5	+	18977.0i	0.363421	+	0.191252i
$316$		−	74649.5i		−	0.747572i
$317$		−	104833.i		−	1.04323i	−0.853182	−	0.521613i	$-0.825330\pi$
$317$		−	104833.i		−	1.04323i	0.853182	−	0.521613i	$-0.174670\pi$
$318$	−96316.0			−0.952454
$319$			96069.4i			0.944069i
$320$	−5439.45	−	2862.53i	−0.0531196	−	0.0279544i
$321$		−	12725.1i		−	0.123496i
$322$	113332.	+	50465.4i	1.09305	+	0.486723i
$323$			38314.3i			0.367245i
$324$	21953.8			0.209131
$325$	13029.5	−	8951.09i	0.123356	−	0.0847441i
$326$	145995.			1.37374
$327$	−25707.0			−0.240412
$328$			67933.0i			0.631442i
$329$		−	120456.i		−	1.11285i
$330$	−47755.3	+	90745.7i	−0.438524	+	0.833294i
$331$	−38032.9			−0.347139			−0.173569	−	0.984822i	$-0.555530\pi$
$331$	−38032.9			−0.347139			−0.173569	+	0.984822i	$0.555530\pi$
$332$	−108803.			−0.987112
$333$	−16208.8			−0.146171
$334$	−184173.			−1.65095
$335$	134823.	+	70950.9i	1.20136	+	0.632220i
$336$			103547.i			0.917186i
$337$	−33040.3			−0.290927			−0.145463	−	0.989364i	$-0.546467\pi$
$337$	−33040.3			−0.290927			−0.145463	+	0.989364i	$0.546467\pi$
$338$		−	138088.i		−	1.20871i
$339$			73.8708i			0.000642796i
$340$	−24501.5	−	12894.0i	−0.211951	−	0.111540i
$341$		−	44371.5i		−	0.381589i
$342$	49750.8			0.425351
$343$	−121081.			−1.02917
$344$			265.612i			0.00224456i
$345$	55896.8	+	70926.6i	0.469622	+	0.595896i
$346$	95018.6			0.793700
$347$		−	43160.3i		−	0.358448i	−0.983808	−	0.179224i	$-0.942641\pi$
$347$		−	43160.3i		−	0.358448i	0.983808	−	0.179224i	$-0.0573586\pi$
$348$		−	45688.0i		−	0.377263i
$349$	−91666.3			−0.752591			−0.376296	−	0.926500i	$-0.622802\pi$
$349$	−91666.3			−0.752591			−0.376296	+	0.926500i	$0.622802\pi$
$350$	120812.	−	82996.1i	0.986222	−	0.677519i
$351$	−19925.9			−0.161735
$352$	119621.			0.965433
$353$			51870.6i			0.416267i	0.978100	+	0.208133i	$0.0667388\pi$
$353$			51870.6i			0.416267i	−0.978100	+	0.208133i	$0.933261\pi$
$354$	136902.			1.09245
$355$	97076.6	+	51086.9i	0.770296	+	0.405371i
$356$		−	46447.0i		−	0.366486i
$357$		−	42391.4i		−	0.332614i
$358$		−	270396.i		−	2.10977i
$359$			240529.i			1.86629i	0.359499	+	0.933146i	$0.382948\pi$
$359$			240529.i			1.86629i	−0.359499	+	0.933146i	$0.617052\pi$
$360$	14924.7	−	28360.3i	0.115160	−	0.218830i
$361$	44674.0			0.342800
$362$	297593.			2.27094
$363$			761.351i			0.00577792i
$364$			10145.7i			0.0765738i
$365$	−37455.7	+	71174.1i	−0.281146	+	0.534240i
$366$		−	107604.i		−	0.803275i
$367$	−188291.			−1.39797			−0.698983	−	0.715139i	$-0.746363\pi$
$367$	−188291.			−1.39797			−0.698983	+	0.715139i	$0.746363\pi$
$368$	68814.5	−	154540.i	0.508141	−	1.14115i
$369$	−62613.5			−0.459849
$370$	−27151.8	+	51594.5i	−0.198333	+	0.376878i
$371$	135243.			0.982577
$372$			21101.9i			0.152488i
$373$	156696.			1.12626			0.563132	−	0.826367i	$-0.309596\pi$
$373$	156696.			1.12626			0.563132	+	0.826367i	$0.309596\pi$
$374$	−78643.0			−0.562233
$375$	105958.	−	12508.5i	0.753476	−	0.0889493i
$376$	−94734.8			−0.670091
$377$			20005.4i			0.140755i
$378$	−184756.			−1.29305
$379$			148654.i			1.03490i	0.855714	+	0.517449i	$0.173118\pi$
$379$			148654.i			1.03490i	−0.855714	+	0.517449i	$0.826882\pi$
$380$	28823.0	−	54770.1i	0.199605	−	0.379294i
$381$	−114783.			−0.790730
$382$	240185.			1.64596
$383$	122905.			0.837859			0.418929	−	0.908019i	$-0.362405\pi$
$383$	122905.			0.837859			0.418929	+	0.908019i	$0.362405\pi$
$384$	115903.			0.786017
$385$	67056.0	−	127421.i	0.452393	−	0.859648i
$386$	113015.			0.758511
$387$	−244.813			−0.00163460
$388$	131293.			0.872125
$389$		−	122657.i		−	0.810578i	−0.914189	−	0.405289i	$-0.867171\pi$
$389$		−	122657.i		−	0.810578i	0.914189	−	0.405289i	$-0.132829\pi$
$390$	−9944.51	+	18896.8i	−0.0653814	+	0.124239i
$391$	−28172.3	+	63267.6i	−0.184276	+	0.413836i
$392$			5683.94i			0.0369894i
$393$		−	28621.6i		−	0.185314i
$394$	−70140.9			−0.451834
$395$	−102741.	+	195231.i	−0.658490	+	1.25128i
$396$			35317.3i			0.225215i
$397$		−	99402.5i		−	0.630691i	−0.948977	−	0.315345i	$-0.897880\pi$
$397$		−	99402.5i		−	0.630691i	0.948977	−	0.315345i	$-0.102120\pi$
$398$	220332.			1.39095
$399$	94760.7			0.595227
$400$	−113173.	−	164739.i	−0.707334	−	1.02962i
$401$			233065.i			1.44940i	0.689065	+	0.724700i	$0.258021\pi$
$401$			233065.i			1.44940i	−0.689065	+	0.724700i	$0.741979\pi$
$402$	−205801.			−1.27349
$403$		−	9239.88i		−	0.0568927i
$404$	−25773.2			−0.157909
$405$	−57415.7	−	30215.2i	−0.350042	−	0.184211i
$406$			185494.i			1.12532i
$407$			57274.4i			0.345758i
$408$	−33339.4			−0.200280
$409$	92352.0			0.552077			0.276038	−	0.961147i	$-0.410978\pi$
$409$	92352.0			0.552077			0.276038	+	0.961147i	$0.410978\pi$
$410$	−104886.	+	199307.i	−0.623950	+	1.18564i
$411$		−	56674.4i		−	0.335508i
$412$	52532.9			0.309483
$413$	−192232.			−1.12700
$414$	82152.4	+	36581.4i	0.479313	+	0.213432i
$415$	284553.	+	149747.i	1.65222	+	0.869486i
$416$	24909.8			0.143941
$417$		−	166754.i		−	0.958966i
$418$		−	175797.i		−	1.00614i
$419$		−	64162.6i		−	0.365472i	−0.983162	−	0.182736i	$-0.941505\pi$
$419$		−	64162.6i		−	0.365472i	0.983162	−	0.182736i	$-0.0584953\pi$
$420$	−31890.0	+	60598.2i	−0.180782	+	0.343527i
$421$		−	125400.i		−	0.707514i	−0.935337	−	0.353757i	$-0.884904\pi$
$421$		−	125400.i		−	0.707514i	0.935337	−	0.353757i	$-0.115096\pi$
$422$			203938.i			1.14518i
$423$		−	87316.5i		−	0.487995i
$424$		−	106364.i		−	0.591647i
$425$	46332.5	+	67443.3i	0.256512	+	0.373389i
$426$	−148183.			−0.816545
$427$			151092.i			0.828680i
$428$	−15764.4			−0.0860580
$429$			20977.1i			0.113980i
$430$	−410.094	+	779.271i	−0.00221792	+	0.00421455i
$431$		−	202228.i		−	1.08864i	−0.838876	−	0.544322i	$-0.816787\pi$
$431$		−	202228.i		−	1.08864i	0.838876	−	0.544322i	$-0.183213\pi$
$432$			251934.i			1.34995i
$433$	−231136.			−1.23280			−0.616400	−	0.787433i	$-0.711409\pi$
$433$	−231136.			−1.23280			−0.616400	+	0.787433i	$0.711409\pi$
$434$		−	85673.9i		−	0.454851i
$435$	−62880.9	+	119488.i	−0.332308	+	0.631459i
$436$			31847.0i			0.167531i
$437$	−141427.	−	62975.6i	−0.740576	−	0.329769i
$438$		−	108644.i		−	0.566316i
$439$	282237.			1.46449			0.732243	−	0.681044i	$-0.238474\pi$
$439$	282237.			1.46449			0.732243	+	0.681044i	$0.238474\pi$
$440$	−100213.	−	52737.2i	−0.517627	−	0.272403i
$441$	−5238.85			−0.0269376
$442$	−16376.5			−0.0838258
$443$		−	123666.i		−	0.630147i	−0.949067	−	0.315073i	$-0.897971\pi$
$443$		−	123666.i		−	0.630147i	0.949067	−	0.315073i	$-0.102029\pi$
$444$		−	27238.2i		−	0.138169i
$445$	−63925.5	+	121473.i	−0.322815	+	0.613421i
$446$	−79013.2			−0.397219
$447$	−713.019			−0.00356850
$448$	−11658.9			−0.0580898
$449$	−258480.			−1.28214			−0.641069	−	0.767483i	$-0.721509\pi$
$449$	−258480.			−1.28214			−0.641069	+	0.767483i	$0.721509\pi$
$450$	87574.4	−	60162.3i	0.432466	−	0.297098i
$451$			221248.i			1.08774i
$452$	91.5142			0.000447932
$453$			190115.i			0.926445i
$454$		−	239344.i		−	1.16121i
$455$	13963.7	−	26534.1i	0.0674492	−	0.128169i
$456$		−	74526.0i		−	0.358409i
$457$	−184081.			−0.881407			−0.440703	−	0.897653i	$-0.645271\pi$
$457$	−184081.			−0.881407			−0.440703	+	0.897653i	$0.645271\pi$
$458$	−345692.			−1.64800
$459$		−	103140.i		−	0.489556i
$460$	87866.8	−	69247.3i	0.415250	−	0.327256i
$461$	−39428.1			−0.185526			−0.0927628	−	0.995688i	$-0.529570\pi$
$461$	−39428.1			−0.185526			−0.0927628	+	0.995688i	$0.529570\pi$
$462$			194503.i			0.911261i
$463$			157266.i			0.733623i	0.930295	+	0.366812i	$0.119551\pi$
$463$			157266.i			0.733623i	−0.930295	+	0.366812i	$0.880449\pi$
$464$	252939.			1.17484
$465$	29042.8	−	55187.8i	0.134317	−	0.255233i
$466$	−320823.			−1.47738
$467$	397293.			1.82170			0.910851	−	0.412735i	$-0.135426\pi$
$467$	397293.			1.82170			0.910851	+	0.412735i	$0.135426\pi$
$468$			7354.45i			0.0335783i
$469$	288977.			1.31377
$470$	−277940.	−	146267.i	−1.25822	−	0.662140i
$471$			316803.i			1.42806i
$472$			151184.i			0.678611i
$473$			865.058i			0.00386654i
$474$		−	298011.i		−	1.32640i
$475$	−150761.	+	103571.i	−0.668194	+	0.459039i
$476$	−52516.2			−0.231782
$477$	98035.0			0.430868
$478$			143861.i			0.629632i
$479$			137130.i			0.597668i	0.954305	+	0.298834i	$0.0965977\pi$
$479$			137130.i			0.597668i	−0.954305	+	0.298834i	$0.903402\pi$
$480$	148781.	+	78296.3i	0.645749	+	0.339828i
$481$			11926.8i			0.0515505i
$482$	−301427.			−1.29744
$483$	156476.	+	69676.9i	0.670740	+	0.298672i
$484$	943.193			0.00402634
$485$	−343371.	−	180700.i	−1.45975	−	0.768201i
$486$	−227952.			−0.965097
$487$		−	333190.i		−	1.40487i	−0.711750	−	0.702433i	$-0.752097\pi$
$487$		−	333190.i		−	1.40487i	0.711750	−	0.702433i	$-0.247903\pi$
$488$	118829.			0.498980
$489$	201574.			0.842977
$490$	−8775.78	+	16675.9i	−0.0365505	+	0.0694541i
$491$	72764.5			0.301826			0.150913	−	0.988547i	$-0.451779\pi$
$491$	72764.5			0.301826			0.150913	+	0.988547i	$0.451779\pi$
$492$		−	105220.i		−	0.434676i
$493$	−103552.			−0.426053
$494$		−	36607.7i		−	0.150010i
$495$	48607.6	−	92365.3i	0.198378	−	0.376963i
$496$	−116825.			−0.474867
$497$	208073.			0.842369
$498$	−434359.			−1.75142
$499$	−64799.7			−0.260239			−0.130119	−	0.991498i	$-0.541536\pi$
$499$	−64799.7			−0.260239			−0.130119	+	0.991498i	$0.541536\pi$
$500$	−15496.0	−	131265.i	−0.0619842	−	0.525059i
$501$	−254286.			−1.01309
$502$	−106209.			−0.421458
$503$	66136.2			0.261399			0.130699	−	0.991422i	$-0.458278\pi$
$503$	66136.2			0.261399			0.130699	+	0.991422i	$0.458278\pi$
$504$		−	60787.2i		−	0.239304i
$505$	67404.7	+	35472.0i	0.264306	+	0.139092i
$506$	129262.	−	290289.i	0.504859	−	1.13378i
$507$		−	190657.i		−	0.741714i
$508$			142198.i			0.551019i
$509$	−278831.			−1.07623			−0.538115	−	0.842871i	$-0.680864\pi$
$509$	−278831.			−1.07623			−0.538115	+	0.842871i	$0.680864\pi$
$510$	−97813.4	−	51474.7i	−0.376061	−	0.197903i
$511$			152554.i			0.584227i
$512$		−	124130.i		−	0.473518i
$513$	230557.			0.876080
$514$	443210.			1.67758
$515$	−137389.	−	72301.6i	−0.518010	−	0.272605i
$516$		−	411.398i		−	0.00154512i
$517$	−308537.			−1.15432
$518$			110587.i			0.412140i
$519$	131191.			0.487045
$520$	−20868.2	−	10981.9i	−0.0771751	−	0.0406137i
$521$		−	335750.i		−	1.23692i	−0.785817	−	0.618459i	$-0.787757\pi$
$521$		−	335750.i		−	1.23692i	0.785817	−	0.618459i	$-0.212243\pi$
$522$			134461.i			0.493463i
$523$	343493.			1.25578			0.627891	−	0.778301i	$-0.283918\pi$
$523$	343493.			1.25578			0.627891	+	0.778301i	$0.283918\pi$
$524$	−35457.6			−0.129136
$525$	166804.	−	114592.i	0.605184	−	0.415752i
$526$		−	105301.i		−	0.380592i
$527$	47827.4			0.172209
$528$	265224.			0.951362
$529$	−187230.	−	207981.i	−0.669058	−	0.743210i
$530$	164222.	−	312058.i	0.584627	−	1.11092i
$531$	−139345.			−0.494200
$532$		−	117394.i		−	0.414783i
$533$			46072.4i			0.162176i
$534$		−	185423.i		−	0.650251i
$535$	41228.7	+	21696.8i	0.144043	+	0.0758032i
$536$		−	227271.i		−	0.791068i
$537$		−	373333.i		−	1.29464i
$538$			580073.i			2.00409i
$539$			18511.7i			0.0637191i
$540$	−77589.9	+	147438.i	−0.266083	+	0.505618i
$541$	317068.			1.08332			0.541661	−	0.840597i	$-0.317796\pi$
$541$	317068.			1.08332			0.541661	+	0.840597i	$0.317796\pi$
$542$			545820.i			1.85802i
$543$	410883.			1.39354
$544$			128938.i			0.435695i
$545$	43831.3	−	83289.3i	0.147568	−	0.280412i
$546$			40503.2i			0.135864i
$547$			5272.95i			0.0176230i	0.999961	+	0.00881148i	$0.00280482\pi$
$547$			5272.95i			0.0176230i	−0.999961	+	0.00881148i	$0.997195\pi$
$548$	−70210.6			−0.233799
$549$			109524.i			0.363383i
$550$	−212586.	−	309448.i	−0.702765	−	1.02297i
$551$		−	231477.i		−	0.762439i
$552$	54798.5	−	123063.i	0.179842	−	0.403878i
$553$			418455.i			1.36835i
$554$	−60345.9			−0.196620
$555$	−37488.2	+	71235.9i	−0.121705	+	0.231267i
$556$	−206582.			−0.668254
$557$	279435.			0.900679			0.450340	−	0.892857i	$-0.351303\pi$
$557$	279435.			0.900679			0.450340	+	0.892857i	$0.351303\pi$
$558$		−	62103.4i		−	0.199456i
$559$			180.139i			0.000576479i
$560$	−335485.	−	176550.i	−1.06979	−	0.562979i
$561$	−108581.			−0.345008
$562$	−686273.			−2.17282
$563$	−259566.			−0.818902			−0.409451	−	0.912332i	$-0.634280\pi$
$563$	−259566.			−0.818902			−0.409451	+	0.912332i	$0.634280\pi$
$564$	146732.			0.461282
$565$	−239.337	−	125.952i	−0.000749744	−	0.000394556i
$566$			14369.6i			0.0448550i
$567$	−123064.			−0.382794
$568$		−	163642.i		−	0.507223i
$569$		−	298678.i		−	0.922527i	−0.887263	−	0.461264i	$-0.847396\pi$
$569$		−	298678.i		−	0.922527i	0.887263	−	0.461264i	$-0.152604\pi$
$570$	115065.	−	218650.i	0.354156	−	0.672976i
$571$			335764.i			1.02982i	0.857244	+	0.514910i	$0.172175\pi$
$571$			335764.i			1.02982i	−0.857244	+	0.514910i	$0.827825\pi$
$572$	25987.3			0.0794271
$573$	331620.			1.01002
$574$			427192.i			1.29658i
$575$	−325104.	+	60170.4i	−0.983300	+	0.181990i
$576$	−8451.29			−0.0254729
$577$			159733.i			0.479782i	0.970800	+	0.239891i	$0.0771117\pi$
$577$			159733.i			0.479782i	−0.970800	+	0.239891i	$0.922888\pi$
$578$			328296.i			0.982675i
$579$	156038.			0.465452
$580$	148027.	+	77899.5i	0.440031	+	0.231568i
$581$	609908.			1.80681
$582$	524141.			1.54740
$583$		−	346411.i		−	1.01919i
$584$	119978.			0.351785
$585$	10122.0	−	19234.1i	0.0295770	−	0.0562030i
$586$			479146.i			1.39532i
$587$		−	524199.i		−	1.52132i	−0.649151	−	0.760659i	$-0.724876\pi$
$587$		−	524199.i		−	1.52132i	0.649151	−	0.760659i	$-0.275124\pi$
$588$		−	8803.68i		−	0.0254630i
$589$			106912.i			0.308175i
$590$	−233422.	+	443553.i	−0.670559	+	1.27421i
$591$	−96842.7			−0.277263
$592$	150797.			0.430277
$593$		−	272680.i		−	0.775432i	−0.921779	−	0.387716i	$-0.873264\pi$
$593$		−	272680.i		−	0.775432i	0.921779	−	0.387716i	$-0.126736\pi$
$594$			473235.i			1.34123i
$595$	137346.	+	72278.6i	0.387954	+	0.204162i
$596$			883.318i			0.00248671i
$597$	304209.			0.853539
$598$	26917.4	−	60449.6i	0.0752716	−	0.169041i
$599$	−372361.			−1.03779			−0.518896	−	0.854838i	$-0.673657\pi$
$599$	−372361.			−1.03779			−0.518896	+	0.854838i	$0.673657\pi$
$600$	−90122.4	−	131185.i	−0.250340	−	0.364404i
$601$	686200.			1.89977			0.949887	−	0.312594i	$-0.101198\pi$
$601$	686200.			1.89977			0.949887	+	0.312594i	$0.101198\pi$
$602$			1670.28i			0.00460889i
$603$	209474.			0.576097
$604$	235522.			0.645592
$605$	−2466.73	−	1298.13i	−0.00673924	−	0.00354655i
$606$	−102890.			−0.280175
$607$		−	39449.6i		−	0.107069i	−0.998566	−	0.0535346i	$-0.982951\pi$
$607$		−	39449.6i		−	0.107069i	0.998566	−	0.0535346i	$-0.0170488\pi$
$608$	−288224.			−0.779693
$609$			256109.i			0.690542i
$610$	348629.	+	183467.i	0.936923	+	0.493059i
$611$	−64249.5			−0.172102
$612$	−38068.0			−0.101638
$613$	−328168.			−0.873323			−0.436662	−	0.899626i	$-0.643839\pi$
$613$	−328168.			−0.873323			−0.436662	+	0.899626i	$0.643839\pi$
$614$	−397026.			−1.05313
$615$	−144815.	+	275180.i	−0.382880	+	0.727557i
$616$	−214794.			−0.566059
$617$	−676661.			−1.77746			−0.888731	−	0.458428i	$-0.848413\pi$
$617$	−676661.			−1.77746			−0.888731	+	0.458428i	$0.848413\pi$
$618$	209719.			0.549111
$619$			334267.i			0.872394i	0.899851	+	0.436197i	$0.143675\pi$
$619$			334267.i			0.872394i	−0.899851	+	0.436197i	$0.856325\pi$
$620$	−68368.9	−	35979.4i	−0.177859	−	0.0935989i
$621$	380714.	+	169527.i	0.987224	+	0.439598i
$622$		−	493809.i		−	1.27638i
$623$			260363.i			0.670816i
$624$	55230.1			0.141843
$625$	−140134.	+	364624.i	−0.358743	+	0.933436i
$626$		−	48648.4i		−	0.124142i
$627$		−	242720.i		−	0.617406i
$628$	392469.			0.995145
$629$	−61735.2			−0.156038
$630$	93853.0	−	178342.i	0.236465	−	0.449337i
$631$			331904.i			0.833592i	0.909000	+	0.416796i	$0.136847\pi$
$631$			331904.i			0.833592i	−0.909000	+	0.416796i	$0.863153\pi$
$632$	329101.			0.823938
$633$			281575.i			0.702727i
$634$	−518464.			−1.28985
$635$	195709.	−	371891.i	0.485359	−	0.922290i
$636$			164744.i			0.407282i
$637$			3854.87i			0.00950015i
$638$	475124.			1.16725
$639$	150828.			0.369386
$640$	−197618.	+	375519.i	−0.482466	+	0.916794i
$641$		−	802258.i		−	1.95253i	−0.216579	−	0.976265i	$-0.569490\pi$
$641$		−	802258.i		−	1.95253i	0.216579	−	0.976265i	$-0.430510\pi$
$642$	−62933.9			−0.152691
$643$	−143766.			−0.347724			−0.173862	−	0.984770i	$-0.555625\pi$
$643$	−143766.			−0.347724			−0.173862	+	0.984770i	$0.555625\pi$
$644$	86318.7	−	193849.i	0.208129	−	0.467405i
$645$	−566.212	+	1075.93i	−0.00136100	+	0.00258621i
$646$	189489.			0.454065
$647$			756331.i			1.80677i	0.428828	+	0.903386i	$0.358927\pi$
$647$			756331.i			1.80677i	−0.428828	+	0.903386i	$0.641073\pi$
$648$			96785.7i			0.230495i
$649$			492382.i			1.16900i
$650$	−44268.8	−	64439.3i	−0.104778	−	0.152519i
$651$		−	118289.i		−	0.279114i
$652$		−	249718.i		−	0.587428i
$653$			442957.i			1.03881i	0.854529	+	0.519404i	$0.173846\pi$
$653$			442957.i			1.03881i	−0.854529	+	0.519404i	$0.826154\pi$
$654$			127137.i			0.297247i
$655$	92732.3	+	48800.7i	0.216147	+	0.113748i
$656$	582518.			1.35364
$657$			110583.i			0.256188i
$658$	−595733.			−1.37594
$659$		−	654514.i		−	1.50712i	−0.657379	−	0.753560i	$-0.728335\pi$
$659$		−	654514.i		−	1.50712i	0.657379	−	0.753560i	$-0.271665\pi$
$660$	155216.	+	81683.2i	0.356328	+	0.187519i
$661$			175823.i			0.402413i	0.979549	+	0.201206i	$0.0644862\pi$
$661$			175823.i			0.402413i	−0.979549	+	0.201206i	$0.935514\pi$
$662$			188097.i			0.429205i
$663$	−22610.9			−0.0514387
$664$		−	479672.i		−	1.08795i
$665$	−161570.	+	307019.i	−0.365357	+	0.694260i
$666$			80162.5i			0.180727i
$667$	170204.	−	382233.i	0.382576	−	0.859166i
$668$			315020.i			0.705968i
$669$	−109093.			−0.243749
$670$	350897.	−	666783.i	0.781682	−	1.48537i
$671$	387008.			0.859558
$672$	318894.			0.706169
$673$			487162.i			1.07558i	0.843078	+	0.537791i	$0.180741\pi$
$673$			487162.i			1.07558i	−0.843078	+	0.537791i	$0.819259\pi$
$674$			163405.i			0.359704i
$675$	405841.	−	278807.i	0.890736	−	0.611922i
$676$	−236194.			−0.516863
$677$	−372718.			−0.813210			−0.406605	−	0.913604i	$-0.633288\pi$
$677$	−372718.			−0.813210			−0.406605	+	0.913604i	$0.633288\pi$
$678$	365.338			0.000794758
$679$	−735977.			−1.59634
$680$	56844.7	−	108018.i	0.122934	−	0.233602i
$681$		−	330459.i		−	0.712564i
$682$	−219445.			−0.471799
$683$		−	278036.i		−	0.596019i	−0.954563	−	0.298009i	$-0.903677\pi$
$683$		−	278036.i		−	0.596019i	0.954563	−	0.298009i	$-0.0963227\pi$
$684$		−	85096.4i		−	0.181886i
$685$	183622.	+	96631.6i	0.391330	+	0.205939i
$686$			598822.i			1.27248i
$687$	−477293.			−1.01128
$688$	2277.59			0.00481171
$689$		−	72136.4i		−	0.151955i
$690$	350777.	−	276445.i	0.736771	−	0.580645i
$691$	−335596.			−0.702848			−0.351424	−	0.936216i	$-0.614302\pi$
$691$	−335596.			−0.702848			−0.351424	+	0.936216i	$0.614302\pi$
$692$		−	162525.i		−	0.339397i
$693$		−	197975.i		−	0.412234i
$694$	−213455.			−0.443188
$695$	540272.	+	284320.i	1.11852	+	0.588624i
$696$	201421.			0.415801
$697$	−238480.			−0.490892
$698$			453348.i			0.930510i
$699$	−442956.			−0.906580
$700$	−141961.	−	206644.i	−0.289716	−	0.421722i
$701$		−	220951.i		−	0.449635i	−0.974401	−	0.224817i	$-0.927821\pi$
$701$		−	220951.i		−	0.449635i	0.974401	−	0.224817i	$-0.0721785\pi$
$702$			98546.1i			0.199970i
$703$		−	138001.i		−	0.279237i
$704$			29863.0i			0.0602543i
$705$	−383748.	−	201949.i	−0.772090	−	0.406315i
$706$	256533.			0.514675
$707$	144474.			0.289036
$708$		−	234164.i		−	0.467147i
$709$			755284.i			1.50251i	0.660012	+	0.751255i	$0.270551\pi$
$709$			755284.i			1.50251i	−0.660012	+	0.751255i	$0.729449\pi$
$710$	252657.	−	480105.i	0.501204	−	0.952400i
$711$			303330.i			0.600035i
$712$	204767.			0.403924
$713$	−78611.9	+	176542.i	−0.154635	+	0.347271i
$714$	−209652.			−0.411247
$715$	−67964.5	−	35766.6i	−0.132944	−	0.0699625i
$716$	−462501.			−0.902165
$717$			198627.i			0.386367i
$718$	1.18957e6			2.30750
$719$	−68333.1			−0.132182			−0.0660912	−	0.997814i	$-0.521053\pi$
$719$	−68333.1			−0.132182			−0.0660912	+	0.997814i	$0.521053\pi$
$720$	−243187.	−	127978.i	−0.469110	−	0.246871i
$721$	−294478.			−0.566478
$722$		−	220941.i		−	0.423841i
$723$	−416176.			−0.796160
$724$		−	509019.i		−	0.971084i
$725$	−279920.	−	407461.i	−0.532546	−	0.775193i
$726$	3765.36			0.00714387
$727$	−343164.			−0.649281			−0.324640	−	0.945838i	$-0.605243\pi$
$727$	−343164.			−0.649281			−0.324640	+	0.945838i	$0.605243\pi$
$728$	−44728.6			−0.0843961
$729$	−524944.			−0.987775
$730$	352001.	+	185242.i	0.660539	+	0.347611i
$731$	−932.433			−0.00174495
$732$	−184051.			−0.343491
$733$	449850.			0.837259			0.418630	−	0.908157i	$-0.362511\pi$
$733$	449850.			0.837259			0.418630	+	0.908157i	$0.362511\pi$
$734$			931216.i			1.72846i
$735$	−12116.6	+	23024.3i	−0.0224288	+	0.0426197i
$736$	−475939.	−	211929.i	−0.878609	−	0.391233i
$737$		−	740186.i		−	1.36272i
$738$			309663.i			0.568561i
$739$	321903.			0.589435			0.294717	−	0.955584i	$-0.404774\pi$
$739$	321903.			0.589435			0.294717	+	0.955584i	$0.404774\pi$
$740$	88250.1	+	46441.9i	0.161158	+	0.0848100i
$741$		−	50543.8i		−	0.0920517i
$742$		−	668862.i		−	1.21487i
$743$	−725883.			−1.31489			−0.657445	−	0.753503i	$-0.728363\pi$
$743$	−725883.			−1.31489			−0.657445	+	0.753503i	$0.728363\pi$
$744$	−93030.1			−0.168065
$745$	1215.72	−	2310.14i	0.00219039	−	0.00416222i
$746$		−	774960.i		−	1.39252i
$747$	442111.			0.792301
$748$			134515.i			0.240419i
$749$	88369.1			0.157520
$750$	−61862.4	−	524027.i	−0.109978	−	0.931603i
$751$		−	943161.i		−	1.67227i	−0.548525	−	0.836134i	$-0.684810\pi$
$751$		−	943161.i		−	1.67227i	0.548525	−	0.836134i	$-0.315190\pi$
$752$			812341.i			1.43649i
$753$	−146642.			−0.258623
$754$	98939.4			0.174031
$755$	−615961.	−	324152.i	−1.08059	−	0.568663i
$756$			316017.i			0.552926i
$757$	534635.			0.932965			0.466483	−	0.884530i	$-0.345521\pi$
$757$	534635.			0.932965			0.466483	+	0.884530i	$0.345521\pi$
$758$	735187.			1.27956
$759$	178470.	−	400799.i	0.309801	−	0.695733i
$760$	241460.	+	127069.i	0.418040	+	0.219995i
$761$	150078.			0.259148			0.129574	−	0.991570i	$-0.458639\pi$
$761$	150078.			0.259148			0.129574	+	0.991570i	$0.458639\pi$
$762$			567675.i			0.977665i
$763$		−	178521.i		−	0.306648i
$764$		−	410825.i		−	0.703834i
$765$	99559.2	+	52393.4i	0.170121	+	0.0895269i
$766$		−	607841.i		−	1.03594i
$767$			102533.i			0.174291i
$768$		−	546351.i		−	0.926296i
$769$			238646.i			0.403553i	0.979432	+	0.201777i	$0.0646715\pi$
$769$			238646.i			0.403553i	−0.979432	+	0.201777i	$0.935329\pi$
$770$	−630179.	−	331634.i	−1.06288	−	0.559342i
$771$	611934.			1.02943
$772$		−	193307.i		−	0.324349i
$773$	197164.			0.329965			0.164983	−	0.986296i	$-0.447243\pi$
$773$	197164.			0.329965			0.164983	+	0.986296i	$0.447243\pi$
$774$			1210.75i			0.00202104i
$775$	129286.	+	188194.i	0.215253	+	0.313330i
$776$			578821.i			0.961215i
$777$			152686.i			0.252905i
$778$	−606619.			−1.00220
$779$		−	533092.i		−	0.878471i
$780$	32322.1	+	17009.6i	0.0531264	+	0.0279580i
$781$		−	532958.i		−	0.873758i
$782$	312898.	+	139330.i	0.511670	+	0.227840i
$783$			623125.i			1.01637i
$784$	48739.1			0.0792950
$785$	−1.02642e6	−	540159.i	−1.66566	−	0.876562i
$786$	−141552.			−0.229124
$787$	103089.			0.166441			0.0832206	−	0.996531i	$-0.473479\pi$
$787$	103089.			0.166441			0.0832206	+	0.996531i	$0.473479\pi$
$788$			119973.i			0.193210i
$789$		−	145387.i		−	0.233546i
$790$	965539.	+	508119.i	1.54709	+	0.814162i
$791$	−512.992			−0.000819894
$792$	−155700.			−0.248221
$793$	80590.3			0.128155
$794$	−491608.			−0.779791
$795$	226739.	−	430855.i	0.358750	−	0.681705i
$796$		−	376867.i		−	0.594788i
$797$	−1.05340e6			−1.65835			−0.829174	−	0.558990i	$-0.811189\pi$
$797$	−1.05340e6			−1.65835			−0.829174	+	0.558990i	$0.811189\pi$
$798$		−	468651.i		−	0.735943i
$799$		−	332568.i		−	0.520938i
$800$	−507351.	+	348542.i	−0.792736	+	0.544598i
$801$			188732.i			0.294159i
$802$	1.15265e6			1.79205
$803$	390752.			0.605996
$804$			352013.i			0.544561i
$805$	−492546.	+	388173.i	−0.760073	+	0.599009i
$806$	−45697.1			−0.0703426
$807$			800899.i			1.22979i
$808$		−	113624.i		−	0.174040i
$809$	−280562.			−0.428679			−0.214340	−	0.976759i	$-0.568760\pi$
$809$	−280562.			−0.428679			−0.214340	+	0.976759i	$0.568760\pi$
$810$	−149433.	+	283957.i	−0.227760	+	0.432795i
$811$	−977553.			−1.48627			−0.743137	−	0.669140i	$-0.766663\pi$
$811$	−977553.			−1.48627			−0.743137	+	0.669140i	$0.766663\pi$
$812$	317278.			0.481203
$813$			753607.i			1.14015i
$814$	283258.			0.427497
$815$	−343689.	+	653086.i	−0.517429	+	0.983231i
$816$			285881.i			0.429344i
$817$		−	2084.34i		−	0.00312266i
$818$		−	456739.i		−	0.682592i
$819$		−	41226.1i		−	0.0614616i
$820$	340905.	+	179403.i	0.506997	+	0.266809i
$821$	240514.			0.356824			0.178412	−	0.983956i	$-0.442904\pi$
$821$	240514.			0.356824			0.178412	+	0.983956i	$0.442904\pi$
$822$	−280291.			−0.414825
$823$		−	148476.i		−	0.219208i	−0.993975	−	0.109604i	$-0.965042\pi$
$823$		−	148476.i		−	0.219208i	0.993975	−	0.109604i	$-0.0349583\pi$
$824$			231597.i			0.341098i
$825$	−293515.	−	427252.i	−0.431244	−	0.627734i
$826$			950707.i			1.39343i
$827$	−186234.			−0.272301			−0.136150	−	0.990688i	$-0.543473\pi$
$827$	−186234.			−0.272301			−0.136150	+	0.990688i	$0.543473\pi$
$828$	62570.8	−	140518.i	0.0912664	−	0.204961i
$829$	601485.			0.875217			0.437608	−	0.899166i	$-0.355826\pi$
$829$	601485.			0.875217			0.437608	+	0.899166i	$0.355826\pi$
$830$	740595.	−	1.40730e6i	1.07504	−	2.04282i
$831$	−83318.9			−0.120654
$832$			6218.65i			0.00898358i
$833$	−19953.5			−0.0287561
$834$	−824702.			−1.18567
$835$	433565.	−	823871.i	0.621844	−	1.18164i
$836$	−300692.			−0.430239
$837$		−	287802.i		−	0.410812i
$838$	−317325.			−0.451872
$839$		−	335094.i		−	0.476039i	−0.971260	−	0.238020i	$-0.923502\pi$
$839$		−	335094.i		−	0.476039i	0.971260	−	0.238020i	$-0.0764982\pi$
$840$	−267154.	−	140591.i	−0.378619	−	0.199250i
$841$	−81669.6			−0.115470
$842$	−620184.			−0.874775
$843$	−947528.			−1.33333
$844$	348827.			0.489694
$845$	617717.	+	325076.i	0.865120	+	0.455272i
$846$	−431835.			−0.603361
$847$	−5287.16			−0.00736980
$848$	−912059.			−1.26833
$849$			19839.9i			0.0275248i
$850$	333550.	−	229144.i	0.461661	−	0.317154i
$851$	101472.	−	227879.i	0.140115	−	0.314663i
$852$			253461.i			0.349165i
$853$		−	374862.i		−	0.515197i	−0.966252	−	0.257598i	$-0.917069\pi$
$853$		−	374862.i		−	0.515197i	0.966252	−	0.257598i	$-0.0829311\pi$
$854$	747248.			1.02459
$855$	−117119.	+	222552.i	−0.160212	+	0.304439i
$856$		−	69499.3i		−	0.0948490i
$857$		−	141026.i		−	0.192017i	−0.995381	−	0.0960083i	$-0.969392\pi$
$857$		−	141026.i		−	0.192017i	0.995381	−	0.0960083i	$-0.0306075\pi$
$858$	103745.			0.140926
$859$	413213.			0.560000			0.280000	−	0.960000i	$-0.409666\pi$
$859$	413213.			0.560000			0.280000	+	0.960000i	$0.409666\pi$
$860$	1332.91	+	701.447i	0.00180220	+	0.000948414i
$861$			589818.i			0.795632i
$862$	−1.00014e6			−1.34601
$863$		−	166710.i		−	0.223841i	−0.993717	−	0.111920i	$-0.964300\pi$
$863$		−	166710.i		−	0.223841i	0.993717	−	0.111920i	$-0.0357002\pi$
$864$	775885.			1.03937
$865$	−223685.	+	425051.i	−0.298954	+	0.568079i
$866$			1.14312e6i			1.52424i
$867$			453274.i			0.603008i
$868$	−146541.			−0.194500
$869$	1.07183e6			1.41934
$870$	590943.	+	310986.i	0.780741	+	0.410868i
$871$		−	154136.i		−	0.203173i
$872$	−140401.			−0.184645
$873$	−533496.			−0.700007
$874$	−311454.	+	699446.i	−0.407729	+	0.915654i
$875$	86864.6	+	735817.i	0.113456	+	0.961067i
$876$	−185831.			−0.242164
$877$		−	543966.i		−	0.707249i	−0.935387	−	0.353625i	$-0.884949\pi$
$877$		−	543966.i		−	0.707249i	0.935387	−	0.353625i	$-0.115051\pi$
$878$		−	1.39584e6i		−	1.81070i
$879$			661551.i			0.856220i
$880$	−452216.	+	859312.i	−0.583957	+	1.10965i
$881$			173103.i			0.223025i	0.993763	+	0.111512i	$0.0355695\pi$
$881$			173103.i			0.223025i	−0.993763	+	0.111512i	$0.964431\pi$
$882$			25909.4i			0.0333059i
$883$			350410.i			0.449423i	0.974425	+	0.224712i	$0.0721440\pi$
$883$			350410.i			0.449423i	−0.974425	+	0.224712i	$0.927856\pi$
$884$			28011.3i			0.0358450i
$885$	−322282.	+	612408.i	−0.411481	+	0.781906i
$886$	−611605.			−0.779118
$887$			735051.i			0.934266i	0.884187	+	0.467133i	$0.154713\pi$
$887$			735051.i			0.934266i	−0.884187	+	0.467133i	$0.845287\pi$
$888$	120083.			0.152284
$889$		−	797106.i		−	1.00859i
$890$	600760.	+	316152.i	0.758439	+	0.399131i
$891$			315216.i			0.397058i
$892$			135148.i			0.169856i
$893$	743414.			0.932240
$894$			3526.33i			0.00441212i
$895$	1.20958e6	+	636544.i	1.51004	+	0.794662i
$896$			804883.i			1.00257i
$897$	37164.5	−	83461.9i	0.0461896	−	0.103730i
$898$			1.27835e6i			1.58525i
$899$	−288951.			−0.357523
$900$	−102905.	−	149792.i	−0.127043	−	0.184928i
$901$	373392.			0.459955
$902$	1.09421e6			1.34489
$903$			2306.13i			0.00282819i
$904$			403.451i			0.000493689i
$905$	−700568.	+	1.33124e6i	−0.855369	+	1.62539i
$906$	940238.			1.14546
$907$	281974.			0.342763			0.171381	−	0.985205i	$-0.445177\pi$
$907$	281974.			0.342763			0.171381	+	0.985205i	$0.445177\pi$
$908$	−409387.			−0.496549
$909$	104727.			0.126745
$910$	−131228.	−	69059.2i	−0.158469	−	0.0833947i
$911$		−	1.44668e6i		−	1.74315i	−0.490260	−	0.871576i	$-0.663098\pi$
$911$		−	1.44668e6i		−	1.74315i	0.490260	−	0.871576i	$-0.336902\pi$
$912$	−639053.			−0.768329
$913$		−	1.56222e6i		−	1.87413i
$914$			910396.i			1.08978i
$915$	481348.	+	253311.i	0.574932	+	0.302560i
$916$			591290.i			0.704709i
$917$	198761.			0.236370
$918$	−510093.			−0.605291
$919$		−	86628.3i		−	0.102572i	−0.998684	−	0.0512860i	$-0.983668\pi$
$919$		−	86628.3i		−	0.102572i	0.998684	−	0.0512860i	$-0.0163320\pi$
$920$	305285.	+	387371.i	0.360686	+	0.457668i
$921$	−548169.			−0.646243
$922$			194997.i			0.229385i
$923$		−	110983.i		−	0.130272i
$924$	332689.			0.389667
$925$	−166882.	−	242919.i	−0.195041	−	0.283908i
$926$	777780.			0.907058
$927$	−213462.			−0.248405
$928$		−	778981.i		−	0.904547i
$929$	169901.			0.196863			0.0984316	−	0.995144i	$-0.468617\pi$
$929$	169901.			0.196863			0.0984316	+	0.995144i	$0.468617\pi$
$930$	−272938.	−	143635.i	−0.315572	−	0.166071i
$931$		−	44603.6i		−	0.0514601i
$932$			548753.i			0.631749i
$933$		−	681796.i		−	0.783233i
$934$		−	1.96487e6i		−	2.25237i
$935$	185135.	−	351797.i	0.211770	−	0.402410i
$936$	−32422.9			−0.0370084
$937$	1.28498e6			1.46358			0.731792	−	0.681529i	$-0.238684\pi$
$937$	1.28498e6			1.46358			0.731792	+	0.681529i	$0.238684\pi$
$938$		−	1.42917e6i		−	1.62435i
$939$		−	67168.3i		−	0.0761786i
$940$	−250183.	+	475403.i	−0.283140	+	0.538030i
$941$			942315.i			1.06418i	0.846687	+	0.532092i	$0.178594\pi$
$941$			942315.i			1.06418i	−0.846687	+	0.532092i	$0.821406\pi$
$942$	1.56679e6			1.76567
$943$	391979.	−	880283.i	0.440798	−	0.989918i
$944$	1.29638e6			1.45475
$945$	434938.	−	826479.i	0.487039	−	0.925483i
$946$	4278.26			0.00478062
$947$		−	819939.i		−	0.914285i	−0.889394	−	0.457142i	$-0.848873\pi$
$947$		−	819939.i		−	0.914285i	0.889394	−	0.457142i	$-0.151127\pi$
$948$	−509735.			−0.567189
$949$	81369.7			0.0903505
$950$	512223.	+	745610.i	0.567560	+	0.826160i
$951$	−715837.			−0.791504
$952$		−	231524.i		−	0.255459i
$953$	143611.			0.158125			0.0790625	−	0.996870i	$-0.474807\pi$
$953$	143611.			0.158125			0.0790625	+	0.996870i	$0.474807\pi$
$954$		−	484845.i		−	0.532729i
$955$	−565423.	+	1.07443e6i	−0.619964	+	1.17807i
$956$	246067.			0.269239
$957$	655998.			0.716273
$958$	678192.			0.738961
$959$	393573.			0.427945
$960$	−19546.4	+	37142.6i	−0.0212092	+	0.0403023i
$961$	−790063.			−0.855491
$962$	58985.4			0.0637374
$963$	64057.1			0.0690740
$964$			515577.i			0.554803i
$965$	−266050.	+	505555.i	−0.285699	+	0.542893i
$966$	344596.	−	773874.i	0.369280	−	0.829309i
$967$		−	1.68061e6i		−	1.79728i	−0.438691	−	0.898638i	$-0.644558\pi$
$967$		−	1.68061e6i		−	1.79728i	0.438691	−	0.898638i	$-0.355442\pi$
$968$			4158.17i			0.00443764i
$969$	261624.			0.278632
$970$	−893676.	+	1.69819e6i	−0.949810	+	1.80485i
$971$			1.16288e6i			1.23338i	0.787207	+	0.616689i	$0.211526\pi$
$971$			1.16288e6i			1.23338i	−0.787207	+	0.616689i	$0.788474\pi$
$972$			389901.i			0.412688i
$973$	1.15801e6			1.22317
$974$	−1.64784e6			−1.73699
$975$	−61121.4	−	88970.5i	−0.0642960	−	0.0935915i
$976$		−	1.01895e6i		−	1.06967i
$977$	997.036			0.00104453			0.000522266	−	1.00000i	$-0.499834\pi$
$977$	997.036			0.00104453			0.000522266		1.00000i	$0.499834\pi$
$978$		−	996909.i		−	1.04226i
$979$	666895.			0.695812
$980$	28523.4	+	15010.6i	0.0296995	+	0.0156295i
$981$		−	129407.i		−	0.134468i
$982$		−	359866.i		−	0.373180i
$983$	597261.			0.618097			0.309049	−	0.951046i	$-0.399989\pi$
$983$	597261.			0.618097			0.309049	+	0.951046i	$0.399989\pi$
$984$	463872.			0.479080
$985$	165120.	−	313765.i	0.170187	−	0.323394i
$986$			512129.i			0.526775i
$987$	−822521.			−0.844331
$988$	−62615.8			−0.0641461
$989$	1532.60	−	3441.82i	0.00156688	−	0.00351881i
$990$	−456805.	−	240395.i	−0.466080	−	0.245276i
$991$	307119.			0.312722			0.156361	−	0.987700i	$-0.450024\pi$
$991$	307119.			0.312722			0.156361	+	0.987700i	$0.450024\pi$
$992$			359788.i			0.365614i
$993$			259703.i			0.263377i
$994$		−	1.02905e6i		−	1.04151i
$995$	−518686.	+	985619.i	−0.523912	+	0.995550i
$996$			742950.i			0.748930i
$997$		−	1.32569e6i		−	1.33368i	−0.745202	−	0.666839i	$-0.767647\pi$
$997$		−	1.32569e6i		−	1.33368i	0.745202	−	0.666839i	$-0.232353\pi$
$998$			320475.i			0.321761i
$999$			371493.i			0.372237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.c.c.114.12	yes	44
5.4	even	2	inner	115.5.c.c.114.33	yes	44
23.22	odd	2	inner	115.5.c.c.114.11	✓	44
115.114	odd	2	inner	115.5.c.c.114.34	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.c.c.114.11	✓	44	23.22	odd	2	inner
115.5.c.c.114.12	yes	44	1.1	even	1	trivial
115.5.c.c.114.33	yes	44	5.4	even	2	inner
115.5.c.c.114.34	yes	44	115.114	odd	2	inner

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.94563i q^{2} -6.82837i q^{3} -8.45927 q^{4} +(22.1235 + 11.6426i) q^{5} -33.7706 q^{6} +47.4193 q^{7} -37.2937i q^{8} +34.3734 q^{9} +(57.5800 - 109.415i) q^{10} -121.460i q^{11} +57.7631i q^{12} -25.2927i q^{13} -234.518i q^{14} +(79.4999 - 151.068i) q^{15} -319.789 q^{16} +130.920 q^{17} -169.998i q^{18} +292.655i q^{19} +(-187.149 - 98.4878i) q^{20} -323.797i q^{21} -600.696 q^{22} +(-215.187 + 483.255i) q^{23} -254.655 q^{24} +(353.900 + 515.150i) q^{25} -125.088 q^{26} -787.812i q^{27} -401.133 q^{28} -790.956 q^{29} +(-747.125 - 393.177i) q^{30} +365.318 q^{31} +984.861i q^{32} -829.373 q^{33} -647.481i q^{34} +(1049.08 + 552.083i) q^{35} -290.774 q^{36} -471.550 q^{37} +1447.36 q^{38} -172.708 q^{39} +(434.195 - 825.067i) q^{40} -1821.57 q^{41} -1601.38 q^{42} -7.12217 q^{43} +1027.46i q^{44} +(760.460 + 400.195i) q^{45} +(2390.00 + 1064.24i) q^{46} -2540.24i q^{47} +2183.64i q^{48} -152.410 q^{49} +(2547.74 - 1750.26i) q^{50} -893.969i q^{51} +213.958i q^{52} +2852.07 q^{53} -3896.23 q^{54} +(1414.11 - 2687.12i) q^{55} -1768.44i q^{56} +1998.36 q^{57} +3911.78i q^{58} -4053.87 q^{59} +(-672.512 + 1277.92i) q^{60} +3186.31i q^{61} -1806.73i q^{62} +1629.96 q^{63} -245.867 q^{64} +(294.472 - 559.563i) q^{65} +4101.77i q^{66} +6094.08 q^{67} -1107.49 q^{68} +(3299.84 + 1469.38i) q^{69} +(2730.40 - 5188.37i) q^{70} +4387.94 q^{71} -1281.91i q^{72} +3217.13i q^{73} +2332.11i q^{74} +(3517.64 - 2416.56i) q^{75} -2475.65i q^{76} -5759.54i q^{77} +854.149i q^{78} +8824.58i q^{79} +(-7074.86 - 3723.17i) q^{80} -2595.23 q^{81} +9008.82i q^{82} +12862.0 q^{83} +2739.08i q^{84} +(2896.41 + 1524.24i) q^{85} +35.2236i q^{86} +5400.94i q^{87} -4529.68 q^{88} +5490.66i q^{89} +(1979.22 - 3760.95i) q^{90} -1199.36i q^{91} +(1820.33 - 4087.99i) q^{92} -2494.53i q^{93} -12563.1 q^{94} +(-3407.26 + 6474.56i) q^{95} +6724.99 q^{96} -15520.6 q^{97} +753.765i q^{98} -4174.98i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 360 q^{4} + 160 q^{6} - 1128 q^{9} + 2136 q^{16} - 3940 q^{24} - 2540 q^{25} + 3144 q^{26} - 348 q^{29} - 4480 q^{31} - 1440 q^{35} - 3728 q^{36} - 1800 q^{39} + 7176 q^{41} + 5372 q^{46} + 9580 q^{49}+ \cdots - 39960 q^{96}+O(q^{100}) \) 44 * q - 360 * q^4 + 160 * q^6 - 1128 * q^9 + 2136 * q^16 - 3940 * q^24 - 2540 * q^25 + 3144 * q^26 - 348 * q^29 - 4480 * q^31 - 1440 * q^35 - 3728 * q^36 - 1800 * q^39 + 7176 * q^41 + 5372 * q^46 + 9580 * q^49 + 10920 * q^50 + 2780 * q^54 - 6340 * q^55 + 11100 * q^59 - 37372 * q^64 - 22700 * q^69 - 8340 * q^70 + 26736 * q^71 - 10420 * q^75 + 54644 * q^81 + 12720 * q^85 + 46572 * q^94 + 53640 * q^95 - 39960 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more