LMFDB - Embedded newform 50.6.d.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, 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:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	50.31
Dual form			50.6.d.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 + 3.80423i) q^{2} +(-16.6068 + 12.0655i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(2.13641 + 55.8609i) q^{5} +(-66.4272 - 48.2622i) q^{6} +12.6460 q^{7} +(-51.7771 - 37.6183i) q^{8} +(55.1171 - 169.633i) q^{9} +O(q^{10})$	\(q+(1.23607 + 3.80423i) q^{2} +(-16.6068 + 12.0655i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(2.13641 + 55.8609i) q^{5} +(-66.4272 - 48.2622i) q^{6} +12.6460 q^{7} +(-51.7771 - 37.6183i) q^{8} +(55.1171 - 169.633i) q^{9} +(-209.867 + 77.1752i) q^{10} +(-169.549 - 521.819i) q^{11} +(101.492 - 312.359i) q^{12} +(-13.3485 + 41.0825i) q^{13} +(15.6313 + 48.1082i) q^{14} +(-709.470 - 901.893i) q^{15} +(79.1084 - 243.470i) q^{16} +(-175.126 - 127.237i) q^{17} +713.451 q^{18} +(135.594 + 98.5151i) q^{19} +(-553.001 - 702.986i) q^{20} +(-210.009 + 152.581i) q^{21} +(1775.54 - 1290.01i) q^{22} +(1127.84 + 3471.12i) q^{23} +1313.74 q^{24} +(-3115.87 + 238.684i) q^{25} -172.787 q^{26} +(-410.009 - 1261.88i) q^{27} +(-163.693 + 118.930i) q^{28} +(-5133.12 + 3729.43i) q^{29} +(2554.05 - 3813.79i) q^{30} +(-5353.87 - 3889.81i) q^{31} +1024.00 q^{32} +(9111.69 + 6620.03i) q^{33} +(267.569 - 823.494i) q^{34} +(27.0170 + 706.416i) q^{35} +(881.874 + 2714.13i) q^{36} +(-1481.06 + 4558.22i) q^{37} +(-207.170 + 637.603i) q^{38} +(-274.006 - 843.305i) q^{39} +(1990.77 - 2972.68i) q^{40} +(-2673.77 + 8229.01i) q^{41} +(-840.037 - 610.322i) q^{42} +17907.8 q^{43} +(7102.17 + 5160.03i) q^{44} +(9593.60 + 2716.48i) q^{45} +(-11810.9 + 8581.09i) q^{46} +(-6217.25 + 4517.09i) q^{47} +(1623.87 + 4997.75i) q^{48} -16647.1 q^{49} +(-4759.44 - 11558.5i) q^{50} +4443.47 q^{51} +(-213.576 - 657.319i) q^{52} +(-11166.5 + 8112.94i) q^{53} +(4293.67 - 3119.54i) q^{54} +(28787.0 - 10586.0i) q^{55} +(-654.772 - 475.720i) q^{56} -3440.43 q^{57} +(-20532.5 - 14917.7i) q^{58} +(14900.7 - 45859.6i) q^{59} +(17665.5 + 5002.08i) q^{60} +(-639.145 - 1967.09i) q^{61} +(8179.99 - 25175.4i) q^{62} +(697.010 - 2145.18i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-2323.42 - 657.890i) q^{65} +(-13921.4 + 42845.7i) q^{66} +(-42820.3 - 31110.7i) q^{67} +3463.49 q^{68} +(-60610.7 - 44036.3i) q^{69} +(-2653.97 + 975.957i) q^{70} +(-27296.0 + 19831.7i) q^{71} +(-9235.10 + 6709.69i) q^{72} +(-1209.13 - 3721.31i) q^{73} -19171.2 q^{74} +(48864.8 - 41558.4i) q^{75} -2681.66 q^{76} +(-2144.12 - 6598.91i) q^{77} +(2869.43 - 2084.76i) q^{78} +(-58732.3 + 42671.5i) q^{79} +(13769.5 + 3898.91i) q^{80} +(57098.7 + 41484.6i) q^{81} -34610.0 q^{82} +(73832.9 + 53642.8i) q^{83} +(1283.46 - 3950.09i) q^{84} +(6733.42 - 10054.5i) q^{85} +(22135.2 + 68125.3i) q^{86} +(40247.1 - 123868. i) q^{87} +(-10851.1 + 33396.4i) q^{88} +(34090.0 + 104918. i) q^{89} +(1524.22 + 39854.0i) q^{90} +(-168.805 + 519.528i) q^{91} +(-47243.4 - 34324.4i) q^{92} +135843. q^{93} +(-24869.0 - 18068.4i) q^{94} +(-5213.45 + 7784.89i) q^{95} +(-17005.4 + 12355.1i) q^{96} +(82727.6 - 60105.1i) q^{97} +(-20576.9 - 63329.3i) q^{98} -97862.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9	\( 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9} + 320 q^{10} - 327 q^{11} - 96 q^{12} - 1161 q^{13} - 948 q^{14} + 760 q^{15} - 1536 q^{16} + 83 q^{17} + 7368 q^{18} - 6250 q^{19} + 2320 q^{20} + 6193 q^{21} + 852 q^{22} + 2069 q^{23} + 2176 q^{24} - 14380 q^{25} + 15976 q^{26} - 18935 q^{27} - 592 q^{28} - 11775 q^{29} - 9840 q^{30} + 2103 q^{31} + 24576 q^{32} - 11747 q^{33} + 972 q^{34} + 33235 q^{35} - 14288 q^{36} + 4148 q^{37} + 14260 q^{38} - 12576 q^{39} + 1600 q^{40} - 26427 q^{41} + 24772 q^{42} + 13024 q^{43} + 3408 q^{44} - 65535 q^{45} - 16964 q^{46} + 29803 q^{47} - 1536 q^{48} + 38368 q^{49} - 14020 q^{50} + 194058 q^{51} - 18576 q^{52} - 29011 q^{53} + 11820 q^{54} - 4185 q^{55} - 2368 q^{56} - 78040 q^{57} - 47100 q^{58} + 31430 q^{59} + 28160 q^{60} - 18362 q^{61} - 15828 q^{62} - 95886 q^{63} - 24576 q^{64} - 193280 q^{65} + 28992 q^{66} - 71657 q^{67} - 10432 q^{68} + 245919 q^{69} - 107460 q^{70} - 153827 q^{71} - 1792 q^{72} + 108264 q^{73} - 27648 q^{74} + 126020 q^{75} + 85920 q^{76} + 96141 q^{77} - 55724 q^{78} + 66670 q^{79} - 33280 q^{80} + 17709 q^{81} - 42408 q^{82} - 30621 q^{83} - 140352 q^{84} - 64895 q^{85} - 94444 q^{86} - 265360 q^{87} - 20928 q^{88} + 351835 q^{89} - 101720 q^{90} + 19323 q^{91} - 67856 q^{92} + 707998 q^{93} + 119212 q^{94} + 158570 q^{95} - 11264 q^{96} + 11058 q^{97} + 18532 q^{98} - 455966 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9 + 320 * q^10 - 327 * q^11 - 96 * q^12 - 1161 * q^13 - 948 * q^14 + 760 * q^15 - 1536 * q^16 + 83 * q^17 + 7368 * q^18 - 6250 * q^19 + 2320 * q^20 + 6193 * q^21 + 852 * q^22 + 2069 * q^23 + 2176 * q^24 - 14380 * q^25 + 15976 * q^26 - 18935 * q^27 - 592 * q^28 - 11775 * q^29 - 9840 * q^30 + 2103 * q^31 + 24576 * q^32 - 11747 * q^33 + 972 * q^34 + 33235 * q^35 - 14288 * q^36 + 4148 * q^37 + 14260 * q^38 - 12576 * q^39 + 1600 * q^40 - 26427 * q^41 + 24772 * q^42 + 13024 * q^43 + 3408 * q^44 - 65535 * q^45 - 16964 * q^46 + 29803 * q^47 - 1536 * q^48 + 38368 * q^49 - 14020 * q^50 + 194058 * q^51 - 18576 * q^52 - 29011 * q^53 + 11820 * q^54 - 4185 * q^55 - 2368 * q^56 - 78040 * q^57 - 47100 * q^58 + 31430 * q^59 + 28160 * q^60 - 18362 * q^61 - 15828 * q^62 - 95886 * q^63 - 24576 * q^64 - 193280 * q^65 + 28992 * q^66 - 71657 * q^67 - 10432 * q^68 + 245919 * q^69 - 107460 * q^70 - 153827 * q^71 - 1792 * q^72 + 108264 * q^73 - 27648 * q^74 + 126020 * q^75 + 85920 * q^76 + 96141 * q^77 - 55724 * q^78 + 66670 * q^79 - 33280 * q^80 + 17709 * q^81 - 42408 * q^82 - 30621 * q^83 - 140352 * q^84 - 64895 * q^85 - 94444 * q^86 - 265360 * q^87 - 20928 * q^88 + 351835 * q^89 - 101720 * q^90 + 19323 * q^91 - 67856 * q^92 + 707998 * q^93 + 119212 * q^94 + 158570 * q^95 - 11264 * q^96 + 11058 * q^97 + 18532 * q^98 - 455966 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$3$	−16.6068	+	12.0655i	−1.06533	+	0.774005i	−0.975066	−	0.221914i	$-0.928770\pi$
$3$	−16.6068	+	12.0655i	−1.06533	+	0.774005i	−0.0902597	+	0.995918i	$0.528770\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	2.13641	+	55.8609i	0.0382173	+	0.999269i
$5$	2.13641	+	55.8609i	0.0382173	+	0.999269i
$6$	−66.4272	−	48.2622i	−0.753299	−	0.547304i
$7$	12.6460			0.0975456			0.0487728	−	0.998810i	$-0.484469\pi$
$7$	12.6460			0.0975456			0.0487728	+	0.998810i	$0.484469\pi$
$8$	−51.7771	−	37.6183i	−0.286031	−	0.207813i
$9$	55.1171	−	169.633i	0.226819	−	0.698078i
$10$	−209.867	+	77.1752i	−0.663656	+	0.244049i
$11$	−169.549	−	521.819i	−0.422488	−	1.30028i	−0.905380	−	0.424603i	$-0.860414\pi$
$11$	−169.549	−	521.819i	−0.422488	−	1.30028i	0.482892	−	0.875680i	$-0.339586\pi$
$12$	101.492	−	312.359i	0.203459	−	0.626183i
$13$	−13.3485	+	41.0825i	−0.0219066	+	0.0674215i	−0.961412	−	0.275112i	$-0.911285\pi$
$13$	−13.3485	+	41.0825i	−0.0219066	+	0.0674215i	0.939506	+	0.342534i	$0.111285\pi$
$14$	15.6313	+	48.1082i	0.0213145	+	0.0655993i
$15$	−709.470	−	901.893i	−0.814153	−	1.03497i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−175.126	−	127.237i	−0.146970	−	0.106780i	0.511870	−	0.859063i	$-0.328953\pi$
$17$	−175.126	−	127.237i	−0.146970	−	0.106780i	−0.658841	+	0.752283i	$0.728953\pi$
$18$	713.451			0.519018
$19$	135.594	+	98.5151i	0.0861703	+	0.0626064i	0.630036	−	0.776566i	$-0.283040\pi$
$19$	135.594	+	98.5151i	0.0861703	+	0.0626064i	−0.543866	+	0.839172i	$0.683040\pi$
$20$	−553.001	−	702.986i	−0.309137	−	0.392981i
$21$	−210.009	+	152.581i	−0.103918	+	0.0755007i
$22$	1775.54	−	1290.01i	0.782121	−	0.568244i
$23$	1127.84	+	3471.12i	0.444556	+	1.36820i	0.882970	+	0.469429i	$0.155540\pi$
$23$	1127.84	+	3471.12i	0.444556	+	1.36820i	−0.438414	+	0.898773i	$0.644460\pi$
$24$	1313.74			0.465565
$25$	−3115.87	+	238.684i	−0.997079	+	0.0763787i
$26$	−172.787			−0.0501276
$27$	−410.009	−	1261.88i	−0.108239	−	0.333126i
$28$	−163.693	+	118.930i	−0.0394580	+	0.0286679i
$29$	−5133.12	+	3729.43i	−1.13341	+	0.823470i	−0.986187	−	0.165634i	$-0.947033\pi$
$29$	−5133.12	+	3729.43i	−1.13341	+	0.823470i	−0.147221	+	0.989104i	$0.547033\pi$
$30$	2554.05	−	3813.79i	0.518115	−	0.773665i
$31$	−5353.87	−	3889.81i	−1.00061	−	0.726984i	−0.0383889	−	0.999263i	$-0.512223\pi$
$31$	−5353.87	−	3889.81i	−1.00061	−	0.726984i	−0.962218	+	0.272279i	$0.912223\pi$
$32$	1024.00			0.176777
$33$	9111.69	+	6620.03i	1.45651	+	1.05822i
$34$	267.569	−	823.494i	0.0396953	−	0.122170i
$35$	27.0170	+	706.416i	0.00372793	+	0.0974743i
$36$	881.874	+	2714.13i	0.113410	+	0.349039i
$37$	−1481.06	+	4558.22i	−0.177855	+	0.547383i	−0.999752	−	0.0222535i	$-0.992916\pi$
$37$	−1481.06	+	4558.22i	−0.177855	+	0.547383i	0.821897	+	0.569636i	$0.192916\pi$
$38$	−207.170	+	637.603i	−0.0232738	+	0.0716294i
$39$	−274.006	−	843.305i	−0.0288469	−	0.0887816i
$40$	1990.77	−	2972.68i	0.196730	−	0.293764i
$41$	−2673.77	+	8229.01i	−0.248407	+	0.764518i	0.746650	+	0.665217i	$0.231661\pi$
$41$	−2673.77	+	8229.01i	−0.248407	+	0.764518i	−0.995057	+	0.0993015i	$0.968339\pi$
$42$	−840.037	−	610.322i	−0.0734810	−	0.0533871i
$43$	17907.8			1.47697			0.738483	−	0.674272i	$-0.235542\pi$
$43$	17907.8			1.47697			0.738483	+	0.674272i	$0.235542\pi$
$44$	7102.17	+	5160.03i	0.553043	+	0.401810i
$45$	9593.60	+	2716.48i	0.706237	+	0.199975i
$46$	−11810.9	+	8581.09i	−0.822975	+	0.597926i
$47$	−6217.25	+	4517.09i	−0.410538	+	0.298273i	−0.773820	−	0.633406i	$-0.781656\pi$
$47$	−6217.25	+	4517.09i	−0.410538	+	0.298273i	0.363282	+	0.931679i	$0.381656\pi$
$48$	1623.87	+	4997.75i	0.101730	+	0.313091i
$49$	−16647.1			−0.990485
$50$	−4759.44	−	11558.5i	−0.269234	−	0.653845i
$51$	4443.47			0.239220
$52$	−213.576	−	657.319i	−0.0109533	−	0.0337107i
$53$	−11166.5	+	8112.94i	−0.546044	+	0.396724i	−0.826325	−	0.563194i	$-0.809572\pi$
$53$	−11166.5	+	8112.94i	−0.546044	+	0.396724i	0.280281	+	0.959918i	$0.409572\pi$
$54$	4293.67	−	3119.54i	0.200375	−	0.145581i
$55$	28787.0	−	10586.0i	1.28319	−	0.471872i
$56$	−654.772	−	475.720i	−0.0279010	−	0.0202713i
$57$	−3440.43			−0.140257
$58$	−20532.5	−	14917.7i	−0.801441	−	0.582281i
$59$	14900.7	−	45859.6i	0.557284	−	1.71514i	−0.132549	−	0.991176i	$-0.542316\pi$
$59$	14900.7	−	45859.6i	0.557284	−	1.71514i	0.689834	−	0.723968i	$-0.257684\pi$
$60$	17665.5	+	5002.08i	0.633501	+	0.179380i
$61$	−639.145	−	1967.09i	−0.0219925	−	0.0676860i	0.939458	−	0.342664i	$-0.111329\pi$
$61$	−639.145	−	1967.09i	−0.0219925	−	0.0676860i	−0.961450	+	0.274978i	$0.911329\pi$
$62$	8179.99	−	25175.4i	0.270255	−	0.831759i
$63$	697.010	−	2145.18i	0.0221252	−	0.0680944i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−2323.42	−	657.890i	−0.0682094	−	0.0193139i
$66$	−13921.4	+	42845.7i	−0.393390	+	1.21073i
$67$	−42820.3	−	31110.7i	−1.16537	−	0.846688i	−0.174919	−	0.984583i	$-0.555966\pi$
$67$	−42820.3	−	31110.7i	−1.16537	−	0.846688i	−0.990447	+	0.137895i	$0.955966\pi$
$68$	3463.49			0.0908326
$69$	−60610.7	−	44036.3i	−1.53259	−	1.11349i
$70$	−2653.97	+	975.957i	−0.0647367	+	0.0238059i
$71$	−27296.0	+	19831.7i	−0.642617	+	0.466889i	−0.860748	−	0.509031i	$-0.830004\pi$
$71$	−27296.0	+	19831.7i	−0.642617	+	0.466889i	0.218131	+	0.975919i	$0.430004\pi$
$72$	−9235.10	+	6709.69i	−0.209947	+	0.152536i
$73$	−1209.13	−	3721.31i	−0.0265561	−	0.0817314i	0.936900	−	0.349597i	$-0.113682\pi$
$73$	−1209.13	−	3721.31i	−0.0265561	−	0.0817314i	−0.963456	+	0.267866i	$0.913682\pi$
$74$	−19171.2			−0.406977
$75$	48864.8	−	41558.4i	1.00310	−	0.853112i
$76$	−2681.66			−0.0532562
$77$	−2144.12	−	6598.91i	−0.0412118	−	0.126837i
$78$	2869.43	−	2084.76i	0.0534022	−	0.0387990i
$79$	−58732.3	+	42671.5i	−1.05879	+	0.769256i	−0.973864	−	0.227132i	$-0.927065\pi$
$79$	−58732.3	+	42671.5i	−1.05879	+	0.769256i	−0.0849254	+	0.996387i	$0.527065\pi$
$80$	13769.5	+	3898.91i	0.240543	+	0.0681111i
$81$	57098.7	+	41484.6i	0.966972	+	0.702546i
$82$	−34610.0			−0.568416
$83$	73832.9	+	53642.8i	1.17640	+	0.854704i	0.991761	−	0.128102i	$-0.0408885\pi$
$83$	73832.9	+	53642.8i	1.17640	+	0.854704i	0.184639	+	0.982806i	$0.440889\pi$
$84$	1283.46	−	3950.09i	0.0198465	−	0.0610814i
$85$	6733.42	−	10054.5i	0.101085	−	0.150944i
$86$	22135.2	+	68125.3i	0.322729	+	0.993258i
$87$	40247.1	−	123868.i	0.570080	−	1.75453i
$88$	−10851.1	+	33396.4i	−0.149372	+	0.459719i
$89$	34090.0	+	104918.i	0.456196	+	1.40403i	0.869725	+	0.493536i	$0.164296\pi$
$89$	34090.0	+	104918.i	0.456196	+	1.40403i	−0.413529	+	0.910491i	$0.635704\pi$
$90$	1524.22	+	39854.0i	0.0198355	+	0.518639i
$91$	−168.805	+	519.528i	−0.00213689	+	0.00657666i
$92$	−47243.4	−	34324.4i	−0.581931	−	0.422798i
$93$	135843.			1.62866
$94$	−24869.0	−	18068.4i	−0.290294	−	0.210911i
$95$	−5213.45	+	7784.89i	−0.0592675	+	0.0885000i
$96$	−17005.4	+	12355.1i	−0.188325	+	0.136826i
$97$	82727.6	−	60105.1i	0.892732	−	0.648608i	−0.0438571	−	0.999038i	$-0.513965\pi$
$97$	82727.6	−	60105.1i	0.892732	−	0.648608i	0.936589	+	0.350430i	$0.113965\pi$
$98$	−20576.9	−	63329.3i	−0.216429	−	0.666100i
$99$	−97862.7			−1.00353
$100$	38088.0	−	32393.0i	0.380880	−	0.323930i
$101$	62107.7			0.605817			0.302909	−	0.953020i	$-0.402042\pi$
$101$	62107.7			0.605817			0.302909	+	0.953020i	$0.402042\pi$
$102$	5492.43	+	16904.0i	0.0522714	+	0.160875i
$103$	−134438.	+	97674.8i	−1.24861	+	0.907172i	−0.998141	−	0.0609514i	$-0.980587\pi$
$103$	−134438.	+	97674.8i	−1.24861	+	0.907172i	−0.250474	+	0.968123i	$0.580587\pi$
$104$	2236.60	−	1624.98i	0.0202770	−	0.0147321i
$105$	−8971.95	−	11405.3i	−0.0794170	−	0.100956i
$106$	−44666.0	−	32451.8i	−0.386111	−	0.280526i
$107$	184486.			1.55777			0.778885	−	0.627167i	$-0.215786\pi$
$107$	184486.			1.55777			0.778885	+	0.627167i	$0.215786\pi$
$108$	17174.7	+	12478.1i	0.141687	+	0.102942i
$109$	−26826.2	+	82562.7i	−0.216269	+	0.665607i	0.782792	+	0.622283i	$0.213795\pi$
$109$	−26826.2	+	82562.7i	−0.216269	+	0.665607i	−0.999061	+	0.0433237i	$0.986205\pi$
$110$	75854.2	+	96427.3i	0.597720	+	0.759833i
$111$	−30401.8	−	93567.1i	−0.234203	−	0.720802i
$112$	1000.40	−	3078.92i	0.00753581	−	0.0231928i
$113$	−58788.2	+	180931.i	−0.433106	+	1.33296i	0.461909	+	0.886927i	$0.347165\pi$
$113$	−58788.2	+	180931.i	−0.433106	+	1.33296i	−0.895015	+	0.446036i	$0.852835\pi$
$114$	−4252.60	−	13088.2i	−0.0306473	−	0.0943227i
$115$	−191490.	+	70417.6i	−1.35021	+	0.496520i
$116$	31370.8	−	96549.5i	0.216462	−	0.666201i
$117$	6233.21	+	4528.69i	0.0420966	+	0.0305850i
$118$	192879.			1.27520
$119$	−2214.65	−	1609.03i	−0.0143363	−	0.0104159i
$120$	2806.68	+	73386.4i	0.0177926	+	0.465224i
$121$	−113255.	+	82284.4i	−0.703223	+	0.510921i
$122$	6693.21	−	4862.90i	0.0407132	−	0.0295798i
$123$	−54884.7	−	168918.i	−0.327106	−	1.00673i
$124$	105884.			0.618409
$125$	−19989.9	−	173545.i	−0.114429	−	0.993431i
$126$	9022.29			0.0506279
$127$	13272.5	+	40848.5i	0.0730203	+	0.224733i	0.980905	−	0.194486i	$-0.0623039\pi$
$127$	13272.5	+	40848.5i	0.0730203	+	0.224733i	−0.907885	+	0.419219i	$0.862304\pi$
$128$	−13254.9	+	9630.27i	−0.0715077	+	0.0519534i
$129$	−297391.	+	216067.i	−1.57345	+	1.14318i
$130$	−369.143	−	9652.01i	−0.00191574	−	0.0500910i
$131$	−88601.4	−	64372.7i	−0.451089	−	0.327735i	0.338937	−	0.940809i	$-0.389933\pi$
$131$	−88601.4	−	64372.7i	−0.451089	−	0.327735i	−0.790026	+	0.613074i	$0.789933\pi$
$132$	−180203.			−0.900174
$133$	1714.72	+	1245.82i	0.00840553	+	0.00610698i
$134$	65423.5	−	201353.i	0.314755	−	0.968715i
$135$	69613.7	−	25599.4i	0.328746	−	0.120891i
$136$	4281.11	+	13175.9i	0.0198477	+	0.0610848i
$137$	−88497.7	+	272368.i	−0.402838	+	1.23981i	0.519849	+	0.854258i	$0.325988\pi$
$137$	−88497.7	+	272368.i	−0.402838	+	1.23981i	−0.922687	+	0.385550i	$0.874012\pi$
$138$	92604.9	−	285009.i	0.413939	−	1.27397i
$139$	−42113.0	−	129610.i	−0.184875	−	0.568987i	0.815071	−	0.579361i	$-0.196698\pi$
$139$	−42113.0	−	129610.i	−0.184875	−	0.568987i	−0.999946	+	0.0103737i	$0.996698\pi$
$140$	−6993.25	−	8889.95i	−0.0301550	−	0.0383336i
$141$	48747.3	−	150029.i	0.206492	−	0.635517i
$142$	−109184.	−	79326.7i	−0.454399	−	0.330140i
$143$	23700.8			0.0969222
$144$	−36940.4	−	26838.8i	−0.148455	−	0.107859i
$145$	−219296.	−	278773.i	−0.866184	−	1.10111i
$146$	12662.1	−	9199.58i	0.0491615	−	0.0357179i
$147$	276455.	−	200856.i	1.05519	−	0.766640i
$148$	−23696.9	−	72931.5i	−0.0889277	−	0.273691i
$149$	520409.			1.92034			0.960172	−	0.279410i	$-0.0901387\pi$
$149$	520409.			1.92034			0.960172	+	0.279410i	$0.0901387\pi$
$150$	218498.	+	134524.i	0.792901	+	0.488169i
$151$	121606.			0.434024			0.217012	−	0.976169i	$-0.430369\pi$
$151$	121606.			0.434024			0.217012	+	0.976169i	$0.430369\pi$
$152$	−3314.72	−	10201.6i	−0.0116369	−	0.0358147i
$153$	−31236.0	+	22694.3i	−0.107877	+	0.0783769i
$154$	22453.5	−	16313.4i	0.0762925	−	0.0554297i
$155$	205850.	−	307382.i	0.688212	−	1.02766i
$156$	11477.7	+	8339.06i	0.0377611	+	0.0274350i
$157$	−354670.			−1.14835			−0.574177	−	0.818731i	$-0.694678\pi$
$157$	−354670.			−1.14835			−0.574177	+	0.818731i	$0.694678\pi$
$158$	−234929.	−	170686.i	−0.748677	−	0.543946i
$159$	87552.8	−	269460.i	0.274648	−	0.845281i
$160$	2187.69	+	57201.5i	0.00675593	+	0.176648i
$161$	14262.6	+	43895.8i	0.0433645	+	0.133462i
$162$	−87239.1	+	268494.i	−0.261170	+	0.803799i
$163$	−138400.	+	425950.i	−0.408005	+	1.25571i	0.510354	+	0.859964i	$0.329514\pi$
$163$	−138400.	+	425950.i	−0.408005	+	1.25571i	−0.918360	+	0.395747i	$0.870486\pi$
$164$	−42780.3	−	131664.i	−0.124204	−	0.382259i
$165$	−350334.	+	523130.i	−1.00178	+	1.49589i
$166$	−112807.	+	347183.i	−0.317735	+	0.977887i
$167$	64958.9	+	47195.4i	0.180239	+	0.130951i	0.674246	−	0.738506i	$-0.264469\pi$
$167$	64958.9	+	47195.4i	0.180239	+	0.130951i	−0.494008	+	0.869457i	$0.664469\pi$
$168$	16613.5			0.0454138
$169$	298873.	+	217144.i	0.804951	+	0.584831i
$170$	46572.7	+	13187.3i	0.123597	+	0.0349973i
$171$	24185.0	−	17571.4i	0.0632493	−	0.0459533i
$172$	−231803.	+	168415.i	−0.597446	+	0.434070i
$173$	−109842.	−	338059.i	−0.279032	−	0.858772i	−0.988124	−	0.153656i	$-0.950895\pi$
$173$	−109842.	−	338059.i	−0.279032	−	0.858772i	0.709093	−	0.705115i	$-0.249105\pi$
$174$	520969.			1.30448
$175$	−39403.3	+	3018.39i	−0.0972606	+	0.00745041i
$176$	−140460.			−0.341800
$177$	305869.	+	941366.i	0.733840	+	2.25853i
$178$	−356995.	+	259372.i	−0.844524	+	0.613582i
$179$	129580.	−	94145.5i	0.302278	−	0.219618i	−0.426298	−	0.904583i	$-0.640183\pi$
$179$	129580.	−	94145.5i	0.302278	−	0.219618i	0.728576	+	0.684965i	$0.240183\pi$
$180$	−149729.	+	55060.7i	−0.344450	+	0.126666i
$181$	−142553.	−	103570.i	−0.323429	−	0.234985i	0.414208	−	0.910182i	$-0.364058\pi$
$181$	−142553.	−	103570.i	−0.323429	−	0.234985i	−0.737637	+	0.675197i	$0.764058\pi$
$182$	−2185.06			−0.00488972
$183$	34348.1	+	24955.3i	0.0758184	+	0.0550853i
$184$	72181.5	−	222152.i	0.157174	−	0.483733i
$185$	−257790.	−	72994.8i	−0.553780	−	0.156806i
$186$	167912.	+	516779.i	0.355876	+	1.09527i
$187$	−36702.0	+	112957.i	−0.0767513	+	0.236216i
$188$	37996.4	−	116941.i	0.0784058	−	0.241308i
$189$	−5184.97	−	15957.7i	−0.0105582	−	0.0324949i
$190$	−36059.7	−	10210.5i	−0.0724666	−	0.0205193i
$191$	226280.	−	696418.i	0.448810	−	1.38130i	−0.429440	−	0.903095i	$-0.641289\pi$
$191$	226280.	−	696418.i	0.448810	−	1.38130i	0.878251	−	0.478201i	$-0.158711\pi$
$192$	−68021.4	−	49420.4i	−0.133166	−	0.0967506i
$193$	24412.7			0.0471761			0.0235880	−	0.999722i	$-0.492491\pi$
$193$	24412.7			0.0471761			0.0235880	+	0.999722i	$0.492491\pi$
$194$	330910.	+	240420.i	0.631257	+	0.458635i
$195$	46522.3	−	17107.9i	0.0876143	−	0.0322188i
$196$	215484.	−	156559.i	0.400660	−	0.291096i
$197$	−178863.	+	129951.i	−0.328363	+	0.238570i	−0.739736	−	0.672897i	$-0.765049\pi$
$197$	−178863.	+	129951.i	−0.328363	+	0.238570i	0.411373	+	0.911467i	$0.365049\pi$
$198$	−120965.	−	372292.i	−0.219279	−	0.674871i
$199$	−171225.			−0.306504			−0.153252	−	0.988187i	$-0.548975\pi$
$199$	−171225.			−0.306504			−0.153252	+	0.988187i	$0.548975\pi$
$200$	170310.	+	104855.i	0.301068	+	0.185360i
$201$	1.08647e6			1.89683
$202$	76769.3	+	236272.i	0.132376	+	0.407411i
$203$	−64913.4	+	47162.3i	−0.110559	+	0.0803258i
$204$	−57517.5	+	41788.9i	−0.0967663	+	0.0703049i
$205$	−465392.	−	131778.i	−0.773453	−	0.219008i
$206$	−537751.	−	390699.i	−0.882904	−	0.641467i
$207$	650980.			1.05595
$208$	8946.39	+	6499.93i	0.0143380	+	0.0104172i
$209$	28417.1	−	87458.8i	0.0450002	−	0.138496i
$210$	32298.5	−	48229.1i	0.0505398	−	0.0754676i
$211$	−369974.	−	1.13866e6i	−0.572091	−	1.76071i	−0.645878	−	0.763440i	$-0.723509\pi$
$211$	−369974.	−	1.13866e6i	−0.572091	−	1.76071i	0.0737874	−	0.997274i	$-0.476491\pi$
$212$	68243.6	−	210032.i	0.104285	−	0.320957i
$213$	214018.	−	658681.i	0.323223	−	0.994778i
$214$	228037.	+	701825.i	0.340385	+	1.04760i
$215$	38258.4	+	1.00034e6i	0.0564457	+	1.47589i
$216$	−26240.6	+	80760.2i	−0.0382683	+	0.117778i
$217$	−67705.0	−	49190.5i	−0.0976048	−	0.0709140i
$218$	−347246.			−0.494876
$219$	64979.3	+	47210.2i	0.0915514	+	0.0665160i
$220$	−273070.	+	407757.i	−0.380380	+	0.567995i
$221$	7564.88	−	5496.20i	0.0104189	−	0.00756976i
$222$	318372.	−	231311.i	0.433563	−	0.315002i
$223$	102240.	+	314662.i	0.137676	+	0.423724i	0.995997	−	0.0893903i	$-0.0284918\pi$
$223$	102240.	+	314662.i	0.137676	+	0.423724i	−0.858321	+	0.513114i	$0.828492\pi$
$224$	12949.5			0.0172438
$225$	−131249.	+	541710.i	−0.172838	+	0.713363i
$226$	−760970.			−0.991053
$227$	197523.	+	607914.i	0.254421	+	0.783028i	0.993943	+	0.109895i	$0.0350516\pi$
$227$	197523.	+	607914.i	0.254421	+	0.783028i	−0.739522	+	0.673132i	$0.764948\pi$
$228$	44533.8	−	32355.7i	0.0567352	−	0.0412205i
$229$	−479297.	+	348230.i	−0.603971	+	0.438811i	−0.847286	−	0.531137i	$-0.821765\pi$
$229$	−479297.	+	348230.i	−0.603971	+	0.438811i	0.243315	+	0.969947i	$0.421765\pi$
$230$	−504580.	−	641432.i	−0.628941	−	0.799523i
$231$	115226.	+	83716.8i	0.142076	+	0.103224i
$232$	406073.			0.495318
$233$	307600.	+	223484.i	0.371190	+	0.269685i	0.757704	−	0.652598i	$-0.226321\pi$
$233$	307600.	+	223484.i	0.371190	+	0.269685i	−0.386514	+	0.922283i	$0.626321\pi$
$234$	−9523.50	+	29310.3i	−0.0113699	+	0.0349930i
$235$	−265611.	−	337650.i	−0.313745	−	0.398839i
$236$	238411.	+	733754.i	0.278642	+	0.857572i
$237$	460500.	−	1.41727e6i	0.532549	−	1.63902i
$238$	3383.68	−	10413.9i	0.00387210	−	0.0119171i
$239$	12743.3	+	39219.9i	0.0144307	+	0.0444131i	0.958013	−	0.286726i	$-0.0925670\pi$
$239$	12743.3	+	39219.9i	0.0144307	+	0.0444131i	−0.943582	+	0.331139i	$0.892567\pi$
$240$	−275709.	+	101388.i	−0.308975	+	0.113621i
$241$	495360.	−	1.52456e6i	0.549387	−	1.69084i	−0.160938	−	0.986964i	$-0.551452\pi$
$241$	495360.	−	1.52456e6i	0.549387	−	1.69084i	0.710325	−	0.703874i	$-0.248548\pi$
$242$	−453019.	−	329138.i	−0.497254	−	0.361276i
$243$	−1.12634e6			−1.22364
$244$	26772.8	+	19451.6i	0.0287886	+	0.0209161i
$245$	−35565.0	−	929920.i	−0.0378536	−	0.989761i
$246$	574760.	−	417588.i	0.605549	−	0.439957i
$247$	−5857.22	+	4255.52i	−0.00610871	+	0.00443824i
$248$	130880.	+	402807.i	0.135127	+	0.415879i
$249$	−1.87336e6			−1.91479
$250$	635497.	−	290560.i	0.643078	−	0.294026i
$251$	−853480.			−0.855084			−0.427542	−	0.903995i	$-0.640620\pi$
$251$	−853480.			−0.855084			−0.427542	+	0.903995i	$0.640620\pi$
$252$	11152.2	+	34322.8i	0.0110626	+	0.0340472i
$253$	1.62007e6	−	1.17705e6i	1.59123	−	1.15610i
$254$	−138991.	+	100983.i	−0.135177	+	0.0982120i
$255$	9493.08	+	248216.i	0.00914232	+	0.239045i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	97803.9			0.0923684			0.0461842	−	0.998933i	$-0.485294\pi$
$257$	97803.9			0.0923684			0.0461842	+	0.998933i	$0.485294\pi$
$258$	−1.18956e6	−	864268.i	−1.11260	−	0.808350i
$259$	−18729.4	+	57643.2i	−0.0173490	+	0.0533948i
$260$	36262.1	−	13334.8i	0.0332675	−	0.0122336i
$261$	349712.	+	1.07630e6i	0.317767	+	0.977987i
$262$	135371.	−	416629.i	0.121835	−	0.374969i
$263$	−347566.	+	1.06970e6i	−0.309847	+	0.953612i	0.667976	+	0.744182i	$0.267161\pi$
$263$	−347566.	+	1.06970e6i	−0.309847	+	0.953612i	−0.977824	+	0.209430i	$0.932839\pi$
$264$	−222743.	−	685532.i	−0.196695	−	0.605366i
$265$	−477052.	−	606438.i	−0.417303	−	0.530483i
$266$	−2619.87	+	8063.12i	−0.00227026	+	0.00698713i
$267$	−1.83202e6	−	1.33104e6i	−1.57272	−	1.14265i
$268$	846860.			0.720236
$269$	1.58913e6	+	1.15457e6i	1.33899	+	0.972834i	0.999480	+	0.0322319i	$0.0102615\pi$
$269$	1.58913e6	+	1.15457e6i	1.33899	+	0.972834i	0.339511	+	0.940602i	$0.389738\pi$
$270$	183433.	+	233184.i	0.153133	+	0.194665i
$271$	−793760.	+	576701.i	−0.656547	+	0.477010i	−0.865495	−	0.500917i	$-0.832996\pi$
$271$	−793760.	+	576701.i	−0.656547	+	0.477010i	0.208948	+	0.977927i	$0.432996\pi$
$272$	−44832.4	+	32572.6i	−0.0367426	+	0.0266950i
$273$	−3465.08	−	10664.4i	−0.00281389	−	0.00866025i
$274$	−1.14554e6			−0.921792
$275$	652843.	+	1.58545e6i	0.520567	+	1.26422i
$276$	1.19870e6			0.947194
$277$	327774.	+	1.00878e6i	0.256670	+	0.789949i	0.993496	+	0.113867i	$0.0363236\pi$
$277$	327774.	+	1.00878e6i	0.256670	+	0.789949i	−0.736826	+	0.676082i	$0.763676\pi$
$278$	441013.	−	320414.i	0.342247	−	0.248657i
$279$	−954931.	+	693798.i	−0.734449	+	0.533608i
$280$	25175.3	−	37592.5i	0.0191902	−	0.0286554i
$281$	829492.	+	602662.i	0.626681	+	0.455310i	0.855249	−	0.518218i	$-0.173404\pi$
$281$	829492.	+	602662.i	0.626681	+	0.455310i	−0.228568	+	0.973528i	$0.573404\pi$
$282$	630999.			0.472504
$283$	1.21373e6	+	881829.i	0.900860	+	0.654513i	0.938687	−	0.344771i	$-0.112043\pi$
$283$	1.21373e6	+	881829.i	0.900860	+	0.654513i	−0.0378267	+	0.999284i	$0.512043\pi$
$284$	166818.	−	513413.i	0.122729	−	0.377721i
$285$	−7350.16	−	192185.i	−0.00536025	−	0.140155i
$286$	29295.8	+	90163.3i	0.0211783	+	0.0651800i
$287$	−33812.4	+	104064.i	−0.0242310	+	0.0745754i
$288$	56439.9	−	173704.i	0.0400964	−	0.123404i
$289$	−424280.	−	1.30580e6i	−0.298819	−	0.919670i
$290$	789451.	−	1.17883e6i	0.551227	−	0.823109i
$291$	−648639.	+	1.99631e6i	−0.449025	+	1.38196i
$292$	50648.6	+	36798.3i	0.0347624	+	0.0252564i
$293$	−2.55296e6			−1.73730			−0.868649	−	0.495428i	$-0.835011\pi$
$293$	−2.55296e6			−1.73730			−0.868649	+	0.495428i	$0.835011\pi$
$294$	1.10582e6	+	803424.i	0.746132	+	0.542096i
$295$	2.59359e6	+	734391.i	1.73519	+	0.491329i
$296$	248157.	−	180297.i	0.164626	−	0.119607i
$297$	−588955.	+	427901.i	−0.387428	+	0.281483i
$298$	643261.	+	1.97975e6i	0.419611	+	1.29143i
$299$	−157657.			−0.101985
$300$	−241680.	+	997496.i	−0.155038	+	0.639894i
$301$	226462.			0.144072
$302$	150314.	+	462618.i	0.0948377	+	0.291881i
$303$	−1.03141e6	+	749362.i	−0.645393	+	0.468906i
$304$	34712.2	−	25219.9i	0.0215426	−	0.0156516i
$305$	108518.	−	39905.7i	0.0667960	−	0.0245632i
$306$	−124944.	−	90777.2i	−0.0762803	−	0.0554209i
$307$	767182.			0.464571			0.232286	−	0.972648i	$-0.425380\pi$
$307$	767182.			0.464571			0.232286	+	0.972648i	$0.425380\pi$
$308$	89813.9	+	65253.6i	0.0539469	+	0.0391947i
$309$	1.05408e6	−	3.24413e6i	0.628027	−	1.93287i
$310$	1.42380e6	+	403156.i	0.841479	+	0.238270i
$311$	499899.	+	1.53853e6i	0.293077	+	0.901997i	0.983861	+	0.178936i	$0.0572655\pi$
$311$	499899.	+	1.53853e6i	0.293077	+	0.901997i	−0.690784	+	0.723061i	$0.742734\pi$
$312$	−17536.4	+	53971.5i	−0.0101989	+	0.0313890i
$313$	432868.	−	1.33223e6i	0.249744	−	0.768633i	−0.745076	−	0.666980i	$-0.767587\pi$
$313$	432868.	−	1.33223e6i	0.249744	−	0.768633i	0.994820	−	0.101653i	$-0.0324133\pi$
$314$	−438397.	−	1.34925e6i	−0.250924	−	0.772266i
$315$	121320.	+	34352.6i	0.0688903	+	0.0195067i
$316$	358940.	−	1.10470e6i	0.202211	−	0.622341i
$317$	−942198.	−	684547.i	−0.526616	−	0.382609i	0.292474	−	0.956273i	$-0.405521\pi$
$317$	−942198.	−	684547.i	−0.526616	−	0.382609i	−0.819090	+	0.573664i	$0.805521\pi$
$318$	1.13331e6			0.628463
$319$	2.81640e6	+	2.04624e6i	1.54959	+	1.12585i
$320$	−214903.	+	79027.4i	−0.117319	+	0.0431423i
$321$	−3.06371e6	+	2.22592e6i	−1.65953	+	1.20572i
$322$	−149360.	+	108516.i	−0.0802776	+	0.0583251i
$323$	−11211.4	−	34505.2i	−0.00597935	−	0.0184026i
$324$	−1.12925e6			−0.597621
$325$	31786.5	−	131194.i	0.0166930	−	0.0688977i
$326$	−1.79148e6			−0.933616
$327$	−550666.	−	1.69477e6i	−0.284786	−	0.876481i
$328$	448001.	−	325492.i	0.229929	−	0.167053i
$329$	−78623.2	+	57123.1i	−0.0400462	+	0.0290952i
$330$	−2.42314e6	−	686127.i	−1.22488	−	0.346832i
$331$	705184.	+	512346.i	0.353779	+	0.257036i	0.750453	−	0.660924i	$-0.229835\pi$
$331$	705184.	+	512346.i	0.353779	+	0.257036i	−0.396673	+	0.917960i	$0.629835\pi$
$332$	−1.46020e6			−0.727055
$333$	691593.	+	502472.i	0.341775	+	0.248314i
$334$	−99248.4	+	305455.i	−0.0486808	+	0.149824i
$335$	1.64639e6	−	2.45844e6i	0.801532	−	1.19687i
$336$	20535.4	+	63201.4i	0.00992327	+	0.0305407i
$337$	349028.	−	1.07420e6i	0.167411	−	0.515239i	−0.831795	−	0.555084i	$-0.812686\pi$
$337$	349028.	−	1.07420e6i	0.167411	−	0.515239i	0.999206	+	0.0398445i	$0.0126862\pi$
$338$	−456637.	+	1.40538e6i	−0.217410	+	0.669119i
$339$	−1.20675e6	−	3.71400e6i	−0.570320	−	1.75527i
$340$	7399.44	+	193474.i	0.00347138	+	0.0907662i
$341$	−1.12203e6	+	3.45326e6i	−0.522540	+	1.60821i
$342$	96739.9	+	70285.7i	0.0447240	+	0.0324939i
$343$	−423060.			−0.194163
$344$	−927213.	−	673660.i	−0.422458	−	0.306934i
$345$	2.33041e6	−	3.47985e6i	1.05411	−	1.57403i
$346$	1.15028e6	−	835729.i	0.516552	−	0.375297i
$347$	−1.33146e6	+	967365.i	−0.593616	+	0.431287i	−0.843607	−	0.536961i	$-0.819572\pi$
$347$	−1.33146e6	+	967365.i	−0.593616	+	0.431287i	0.249991	+	0.968248i	$0.419572\pi$
$348$	643953.	+	1.98188e6i	0.285040	+	0.877264i
$349$	−960097.			−0.421941			−0.210970	−	0.977492i	$-0.567662\pi$
$349$	−960097.			−0.421941			−0.210970	+	0.977492i	$0.567662\pi$
$350$	−60187.7	−	146168.i	−0.0262626	−	0.0637797i
$351$	57314.1			0.0248310
$352$	−173618.	−	534342.i	−0.0746859	−	0.229860i
$353$	2.22942e6	−	1.61977e6i	0.952260	−	0.691857i	0.000919674	−	1.00000i	$-0.499707\pi$
$353$	2.22942e6	−	1.61977e6i	0.952260	−	0.691857i	0.951340	+	0.308142i	$0.0997073\pi$
$354$	−3.20310e6	+	2.32719e6i	−1.35851	+	0.987013i
$355$	−1.16613e6	−	1.48241e6i	−0.491107	−	0.624305i
$356$	−1.42798e6	−	1.03749e6i	−0.597168	−	0.433868i
$357$	56192.0			0.0233348
$358$	518321.	+	376582.i	0.213743	+	0.155293i
$359$	−816431.	+	2.51272e6i	−0.334336	+	1.02898i	0.632712	+	0.774387i	$0.281942\pi$
$359$	−816431.	+	2.51272e6i	−0.334336	+	1.02898i	−0.967048	+	0.254594i	$0.918058\pi$
$360$	−394539.	−	501546.i	−0.160448	−	0.203964i
$361$	−756476.	−	2.32819e6i	−0.305511	−	0.940267i
$362$	217801.	−	670322.i	0.0873551	−	0.268851i
$363$	887992.	−	2.73296e6i	0.353706	−	1.08860i
$364$	−2700.88	−	8312.45i	−0.00106844	−	0.00328833i
$365$	205292.	−	75493.1i	0.0806567	−	0.0296603i
$366$	−52479.2	+	161514.i	−0.0204779	+	0.0630244i
$367$	−1.68175e6	−	1.22186e6i	−0.651772	−	0.473540i	0.212102	−	0.977247i	$-0.431969\pi$
$367$	−1.68175e6	−	1.22186e6i	−0.651772	−	0.473540i	−0.863874	+	0.503707i	$0.831969\pi$
$368$	934337.			0.359653
$369$	1.24854e6	+	907118.i	0.477350	+	0.346815i
$370$	−40957.5	−	1.07092e6i	−0.0155536	−	0.406680i
$371$	−141211.	+	102596.i	−0.0532642	+	0.0386987i
$372$	−1.75839e6	+	1.27755e6i	−0.658808	+	0.478652i
$373$	1.24898e6	+	3.84397e6i	0.464819	+	1.43057i	0.859210	+	0.511623i	$0.170956\pi$
$373$	1.24898e6	+	3.84397e6i	0.464819	+	1.43057i	−0.394391	+	0.918943i	$0.629044\pi$
$374$	−475081.			−0.175626
$375$	2.42589e6	+	2.64084e6i	0.890824	+	0.969760i
$376$	491836.			0.179412
$377$	−84694.7	−	260664.i	−0.0306904	−	0.0944554i
$378$	54297.7	−	39449.6i	0.0195457	−	0.0142008i
$379$	−675054.	+	490456.i	−0.241402	+	0.175389i	−0.701908	−	0.712268i	$-0.747668\pi$
$379$	−675054.	+	490456.i	−0.241402	+	0.175389i	0.460506	+	0.887657i	$0.347668\pi$
$380$	−5729.13	−	149800.i	−0.00203531	−	0.0532173i
$381$	−713273.	−	518223.i	−0.251735	−	0.182896i
$382$	2.92903e6			1.02699
$383$	−734384.	−	533561.i	−0.255815	−	0.185861i	0.452485	−	0.891772i	$-0.350538\pi$
$383$	−734384.	−	533561.i	−0.255815	−	0.185861i	−0.708300	+	0.705911i	$0.750538\pi$
$384$	103927.	−	319856.i	0.0359668	−	0.110695i
$385$	364040.	−	133870.i	0.125169	−	0.0460290i
$386$	30175.7	+	92871.3i	0.0103084	+	0.0317258i
$387$	987025.	−	3.03775e6i	0.335005	−	1.03104i
$388$	−505586.	+	1.55603e6i	−0.170497	+	0.524735i
$389$	−364901.	−	1.12305e6i	−0.122265	−	0.376292i	0.871128	−	0.491056i	$-0.163389\pi$
$389$	−364901.	−	1.12305e6i	−0.122265	−	0.376292i	−0.993393	+	0.114764i	$0.963389\pi$
$390$	122587.	+	155835.i	0.0408115	+	0.0518804i
$391$	244141.	−	751388.i	0.0807604	−	0.248555i
$392$	861937.	+	626234.i	0.283309	+	0.205836i
$393$	2.24808e6			0.734225
$394$	−715451.	−	519806.i	−0.232188	−	0.168694i
$395$	−2.50915e6	−	3.18968e6i	−0.809158	−	1.02862i
$396$	1.26676e6	−	920356.i	0.405935	−	0.294929i
$397$	−605066.	+	439606.i	−0.192676	+	0.139987i	−0.679941	−	0.733267i	$-0.737995\pi$
$397$	−605066.	+	439606.i	−0.192676	+	0.139987i	0.487265	+	0.873254i	$0.337995\pi$
$398$	−211646.	−	651380.i	−0.0669735	−	0.206123i
$399$	−43507.6			−0.0136815
$400$	−188379.	+	777505.i	−0.0588685	+	0.242970i
$401$	−3.17136e6			−0.984884			−0.492442	−	0.870345i	$-0.663896\pi$
$401$	−3.17136e6			−0.984884			−0.492442	+	0.870345i	$0.663896\pi$
$402$	1.34296e6	+	4.13320e6i	0.414474	+	1.27562i
$403$	231269.	−	168027.i	0.0709342	−	0.0515367i
$404$	−803939.	+	584096.i	−0.245058	+	0.178045i
$405$	−2.19538e6	+	3.27821e6i	−0.665078	+	0.993115i
$406$	−259653.	−	188649.i	−0.0781770	−	0.0567989i
$407$	2.62968e6			0.786894
$408$	−230070.	−	167156.i	−0.0684241	−	0.0497130i
$409$	896740.	−	2.75988e6i	0.265069	−	0.815798i	−0.726609	−	0.687051i	$-0.758905\pi$
$409$	896740.	−	2.75988e6i	0.265069	−	0.815798i	0.991678	−	0.128746i	$-0.0410953\pi$
$410$	−73941.1	−	1.93334e6i	−0.0217233	−	0.568001i
$411$	−1.81660e6	−	5.59093e6i	−0.530463	−	1.63260i
$412$	821611.	−	2.52866e6i	0.238464	−	0.733917i
$413$	188434.	−	579940.i	0.0543606	−	0.167305i
$414$	804656.	+	2.47648e6i	0.230733	+	0.710122i
$415$	−2.83879e6	+	4.23897e6i	−0.809121	+	1.20820i
$416$	−13668.9	+	42068.4i	−0.00387257	+	0.0119185i
$417$	2.26318e6	+	1.64430e6i	0.637351	+	0.463063i
$418$	367839.			0.102971
$419$	4.30662e6	+	3.12894e6i	1.19840	+	0.870687i	0.994126	−	0.108227i	$-0.0345172\pi$
$419$	4.30662e6	+	3.12894e6i	1.19840	+	0.870687i	0.204272	+	0.978914i	$0.434517\pi$
$420$	223397.	+	63256.3i	0.0617952	+	0.0174977i
$421$	1.17109e6	−	850848.i	0.322022	−	0.233963i	−0.415016	−	0.909814i	$-0.636224\pi$
$421$	1.17109e6	−	850848.i	0.322022	−	0.233963i	0.737038	+	0.675852i	$0.236224\pi$
$422$	3.87442e6	−	2.81493e6i	1.05907	−	0.769460i
$423$	423572.	+	1.30362e6i	0.115100	+	0.354242i
$424$	883364.			0.238630
$425$	576041.	+	354654.i	0.154697	+	0.0952428i
$426$	2.77031e6			0.739613
$427$	−8082.61	−	24875.7i	−0.00214527	−	0.00660247i
$428$	−2.38803e6	+	1.73501e6i	−0.630131	+	0.457817i
$429$	−393595.	+	285963.i	−0.103254	+	0.0750182i
$430$	−3.75825e6	+	1.38204e6i	−0.980199	+	0.360453i
$431$	3.77356e6	+	2.74165e6i	0.978495	+	0.710918i	0.957372	−	0.288859i	$-0.0932758\pi$
$431$	3.77356e6	+	2.74165e6i	0.978495	+	0.710918i	0.0211230	+	0.999777i	$0.493276\pi$
$432$	−339665.			−0.0875673
$433$	−1.10685e6	−	804173.i	−0.283706	−	0.206125i	0.436826	−	0.899546i	$-0.356102\pi$
$433$	−1.10685e6	−	804173.i	−0.283706	−	0.206125i	−0.720532	+	0.693421i	$0.756102\pi$
$434$	103444.	−	318368.i	0.0263622	−	0.0811344i
$435$	7.00534e6	+	1.98360e6i	1.77503	+	0.502611i
$436$	−429220.	−	1.32100e6i	−0.108134	−	0.332803i
$437$	−189030.	+	581774.i	−0.0473507	+	0.145731i
$438$	−99279.6	+	305551.i	−0.0247272	+	0.0761024i
$439$	363008.	+	1.11722e6i	0.0898991	+	0.276681i	0.985891	−	0.167390i	$-0.0535339\pi$
$439$	363008.	+	1.11722e6i	0.0898991	+	0.276681i	−0.895992	+	0.444071i	$0.853534\pi$
$440$	−1.88873e6	−	534806.i	−0.465092	−	0.131694i
$441$	−917539.	+	2.82389e6i	−0.224661	+	0.691436i
$442$	30259.5	+	21984.8i	0.00736726	+	0.00535263i
$443$	−4.83494e6			−1.17053			−0.585264	−	0.810843i	$-0.699009\pi$
$443$	−4.83494e6			−1.17053			−0.585264	+	0.810843i	$0.699009\pi$
$444$	1.27349e6	+	925243.i	0.306575	+	0.222740i
$445$	−5.78799e6	+	2.12844e6i	−1.38557	+	0.509521i
$446$	−1.07067e6	+	777888.i	−0.254870	+	0.185174i
$447$	−8.64232e6	+	6.27901e6i	−2.04579	+	1.48636i
$448$	16006.4	+	49262.8i	0.00376790	+	0.0115964i
$449$	1.14345e6			0.267670			0.133835	−	0.991004i	$-0.457271\pi$
$449$	1.14345e6			0.267670			0.133835	+	0.991004i	$0.457271\pi$
$450$	−2.22302e6	+	170289.i	−0.517502	+	0.0396420i
$451$	4.74738e6			1.09904
$452$	−940611.	−	2.89490e6i	−0.216553	−	0.666481i
$453$	−2.01949e6	+	1.46725e6i	−0.462377	+	0.335937i
$454$	−2.06849e6	+	1.50285e6i	−0.470992	+	0.342196i
$455$	−29381.9	−	8319.66i	−0.00665353	−	0.00188398i
$456$	178135.	+	129423.i	0.0401179	+	0.0291473i
$457$	3.32830e6			0.745473			0.372736	−	0.927937i	$-0.378420\pi$
$457$	3.32830e6			0.745473			0.372736	+	0.927937i	$0.378420\pi$
$458$	−1.91719e6	−	1.39292e6i	−0.427072	−	0.310286i
$459$	−88754.0	+	273157.i	−0.0196633	+	0.0605174i
$460$	1.81646e6	−	2.71239e6i	0.400249	−	0.597664i
$461$	1.75638e6	+	5.40558e6i	0.384916	+	1.18465i	0.936541	+	0.350557i	$0.114008\pi$
$461$	1.75638e6	+	5.40558e6i	0.384916	+	1.18465i	−0.551625	+	0.834092i	$0.685992\pi$
$462$	−176050.	+	541826.i	−0.0383735	+	0.118101i
$463$	1.10345e6	−	3.39608e6i	0.239223	−	0.736251i	−0.757311	−	0.653055i	$-0.773487\pi$
$463$	1.10345e6	−	3.39608e6i	0.239223	−	0.736251i	0.996533	−	0.0831964i	$-0.0265129\pi$
$464$	501934.	+	1.54479e6i	0.108231	+	0.333100i
$465$	290217.	+	7.58832e6i	0.0622430	+	1.62747i
$466$	−469971.	+	1.44642e6i	−0.100255	+	0.308553i
$467$	−3.05641e6	−	2.22061e6i	−0.648514	−	0.471173i	0.214251	−	0.976779i	$-0.431269\pi$
$467$	−3.05641e6	−	2.22061e6i	−0.648514	−	0.471173i	−0.862765	+	0.505606i	$0.831269\pi$
$468$	−123275.			−0.0260171
$469$	−541504.	−	393426.i	−0.113676	−	0.0825906i
$470$	956185.	−	1.42780e6i	0.199663	−	0.298143i
$471$	5.88993e6	−	4.27929e6i	1.22337	−	0.888831i
$472$	−2.49667e6	+	1.81394e6i	−0.515830	+	0.374773i
$473$	−3.03625e6	−	9.34462e6i	−0.624000	−	1.92047i
$474$	5.96084e6			1.21860
$475$	−446009.	−	274596.i	−0.0907004	−	0.0558419i
$476$	43799.3			0.00886032
$477$	760757.	+	2.34137e6i	0.153091	+	0.471166i
$478$	−133450.	+	96956.8i	−0.0267145	+	0.0194092i
$479$	−1.26523e6	+	919240.i	−0.251959	+	0.183059i	−0.706594	−	0.707619i	$-0.749769\pi$
$479$	−1.26523e6	+	919240.i	−0.251959	+	0.183059i	0.454636	+	0.890677i	$0.349769\pi$
$480$	−726498.	−	923538.i	−0.143923	−	0.182958i
$481$	−167493.	−	121691.i	−0.0330091	−	0.0239825i
$482$	6.41207e6			1.25713
$483$	−766482.	−	556882.i	−0.149498	−	0.108616i
$484$	692151.	−	2.13022e6i	0.134304	−	0.413344i
$485$	3.53426e6	+	4.49282e6i	0.682252	+	0.867292i
$486$	−1.39224e6	−	4.28487e6i	−0.267376	−	0.822899i
$487$	−615643.	+	1.89475e6i	−0.117627	+	0.362018i	−0.992486	−	0.122359i	$-0.960954\pi$
$487$	−615643.	+	1.89475e6i	−0.117627	+	0.362018i	0.874859	+	0.484378i	$0.160954\pi$
$488$	−40905.3	+	125893.i	−0.00777552	+	0.0239306i
$489$	−2.84094e6	−	8.74353e6i	−0.537268	−	1.65354i
$490$	3.49367e6	−	1.28474e6i	0.657342	−	0.241727i
$491$	1.89715e6	−	5.83883e6i	0.355139	−	1.09300i	−0.600791	−	0.799406i	$-0.705147\pi$
$491$	1.89715e6	−	5.83883e6i	0.355139	−	1.09300i	0.955929	−	0.293598i	$-0.0948525\pi$
$492$	2.29904e6	+	1.67035e6i	0.428188	+	0.311096i
$493$	1.37347e6			0.254508
$494$	−23428.9	−	17022.1i	−0.00431951	−	0.00313831i
$495$	−209075.	−	5.46670e6i	−0.0383521	−	1.00279i
$496$	−1.37059e6	+	995793.i	−0.250152	+	0.181746i
$497$	−345184.	+	250791.i	−0.0626845	+	0.0455429i
$498$	−2.31560e6	−	7.12667e6i	−0.418398	−	1.28770i
$499$	−537138.			−0.0965684			−0.0482842	−	0.998834i	$-0.515375\pi$
$499$	−537138.			−0.0965684			−0.0482842	+	0.998834i	$0.515375\pi$
$500$	1.89087e6	+	2.05842e6i	0.338250	+	0.368222i
$501$	−1.64820e6			−0.293370
$502$	−1.05496e6	−	3.24683e6i	−0.186843	−	0.575043i
$503$	−5.95682e6	+	4.32788e6i	−1.04977	+	0.762703i	−0.972169	−	0.234282i	$-0.924726\pi$
$503$	−5.95682e6	+	4.32788e6i	−1.04977	+	0.762703i	−0.0776017	+	0.996984i	$0.524726\pi$
$504$	−116787.	+	84850.7i	−0.0204794	+	0.0148792i
$505$	132688.	+	3.46939e6i	0.0231527	+	0.605375i
$506$	6.48029e6	+	4.70821e6i	1.12517	+	0.817484i
$507$	−7.58327e6			−1.31020
$508$	−555966.	−	403933.i	−0.0955848	−	0.0694464i
$509$	3.27346e6	−	1.00747e7i	0.560032	−	1.72360i	−0.122238	−	0.992501i	$-0.539007\pi$
$509$	3.27346e6	−	1.00747e7i	0.560032	−	1.72360i	0.682270	−	0.731100i	$-0.260993\pi$
$510$	−932536.	+	342926.i	−0.158760	+	0.0583814i
$511$	−15290.6	−	47059.6i	−0.00259043	−	0.00797253i
$512$	81007.0	−	249314.i	0.0136568	−	0.0420312i
$513$	68719.2	−	211496.i	0.0115288	−	0.0354820i
$514$	120892.	+	372068.i	0.0201832	+	0.0621176i
$515$	−5.74341e6	−	7.30114e6i	−0.954228	−	1.21303i
$516$	1.81749e6	−	5.59366e6i	0.300502	−	0.924851i
$517$	3.41123e6	+	2.47841e6i	0.561287	+	0.407799i
$518$	−242439.			−0.0396988
$519$	5.90299e6	+	4.28878e6i	0.961953	+	0.698900i
$520$	95551.2	+	121467.i	0.0154963	+	0.0196992i
$521$	−2.09379e6	+	1.52122e6i	−0.337939	+	0.245527i	−0.743792	−	0.668412i	$-0.766975\pi$
$521$	−2.09379e6	+	1.52122e6i	−0.337939	+	0.245527i	0.405853	+	0.913938i	$0.366975\pi$
$522$	−3.66223e6	+	2.66077e6i	−0.588260	+	0.427396i
$523$	−3.50247e6	−	1.07795e7i	−0.559913	−	1.72324i	−0.682602	−	0.730790i	$-0.739152\pi$
$523$	−3.50247e6	−	1.07795e7i	−0.559913	−	1.72324i	0.122689	−	0.992445i	$-0.460848\pi$
$524$	1.75228e6			0.278788
$525$	617943.	−	525547.i	0.0978476	−	0.0832173i
$526$	−4.49899e6			−0.709007
$527$	442677.	+	1.36242e6i	0.0694321	+	0.213690i
$528$	2.33259e6	−	1.69473e6i	0.364128	−	0.264554i
$529$	−5.56957e6	+	4.04653e6i	−0.865331	+	0.628700i
$530$	1.71736e6	−	2.56441e6i	0.265565	−	0.396550i
$531$	−6.95803e6	−	5.05530e6i	−1.07090	−	0.778056i
$532$	−33912.3			−0.00519491
$533$	−302377.	−	219690.i	−0.0461032	−	0.0334959i
$534$	2.79908e6	−	8.61467e6i	0.424777	−	1.30733i
$535$	394137.	+	1.03055e7i	0.0595337	+	1.55663i
$536$	1.04678e6	+	3.22165e6i	0.157377	+	0.484357i
$537$	−1.01599e6	+	3.12691e6i	−0.152039	+	0.467929i
$538$	−2.42797e6	+	7.47252e6i	−0.361649	+	1.11304i
$539$	2.82250e6	+	8.68676e6i	0.418467	+	1.28791i
$540$	−660348.	+	986052.i	−0.0974514	+	0.145517i
$541$	242295.	−	745706.i	0.0355919	−	0.109540i	−0.931682	−	0.363274i	$-0.881659\pi$
$541$	242295.	−	745706.i	0.0355919	−	0.109540i	0.967274	+	0.253734i	$0.0816588\pi$
$542$	−3.17504e6	−	2.30680e6i	−0.464249	−	0.337297i
$543$	3.61697e6			0.526436
$544$	−179329.	−	130290.i	−0.0259809	−	0.0188762i
$545$	−4.66934e6	−	1.32215e6i	−0.673386	−	0.190673i
$546$	36286.8	−	26363.9i	0.00520915	−	0.00378467i
$547$	−2.73445e6	+	1.98669e6i	−0.390752	+	0.283898i	−0.765764	−	0.643122i	$-0.777639\pi$
$547$	−2.73445e6	+	1.98669e6i	−0.390752	+	0.283898i	0.375011	+	0.927020i	$0.377639\pi$
$548$	−1.41596e6	−	4.35789e6i	−0.201419	−	0.619904i
$549$	−368910.			−0.0522384
$550$	−5.22446e6	+	4.44329e6i	−0.736435	+	0.626322i
$551$	−1.06343e6			−0.149221
$552$	1.48168e6	+	4.56014e6i	0.206969	+	0.636987i
$553$	−742728.	+	539624.i	−0.103280	+	0.0750375i
$554$	−3.43249e6	+	2.49385e6i	−0.475155	+	0.345220i
$555$	5.16179e6	−	1.89817e6i	0.711325	−	0.261579i
$556$	1.76405e6	+	1.28166e6i	0.242005	+	0.175827i
$557$	1.34951e7			1.84305			0.921527	−	0.388315i	$-0.126943\pi$
$557$	1.34951e7			1.84305			0.921527	+	0.388315i	$0.126943\pi$
$558$	−3.81972e6	−	2.77519e6i	−0.519334	−	0.377318i
$559$	−239042.	+	735696.i	−0.0323553	+	0.0995792i
$560$	174129.	+	49305.5i	0.0234639	+	0.00664394i
$561$	−753386.	−	2.31868e6i	−0.101067	−	0.311053i
$562$	−1.26735e6	+	3.90051e6i	−0.169261	+	0.520931i
$563$	30866.9	−	94998.6i	0.00410414	−	0.0126312i	−0.948983	−	0.315326i	$-0.897886\pi$
$563$	30866.9	−	94998.6i	0.00410414	−	0.0126312i	0.953088	+	0.302695i	$0.0978862\pi$
$564$	779957.	+	2.40046e6i	0.103246	+	0.317758i
$565$	−1.02326e7	−	2.89742e6i	−1.34854	−	0.381847i
$566$	−1.85442e6	+	5.70732e6i	−0.243314	+	0.748843i
$567$	722069.	+	524614.i	0.0943238	+	0.0685303i
$568$	2.15934e6			0.280834
$569$	7.72473e6	+	5.61235e6i	1.00024	+	0.726714i	0.962139	−	0.272560i	$-0.0878702\pi$
$569$	7.72473e6	+	5.61235e6i	1.00024	+	0.726714i	0.0380976	+	0.999274i	$0.487870\pi$
$570$	722030.	−	265516.i	0.0930826	−	0.0342297i
$571$	9.33605e6	−	6.78304e6i	1.19832	−	0.870630i	0.204202	−	0.978929i	$-0.434540\pi$
$571$	9.33605e6	−	6.78304e6i	1.19832	−	0.870630i	0.994118	+	0.108298i	$0.0345402\pi$
$572$	−306790.	+	222896.i	−0.0392059	+	0.0284847i
$573$	4.64488e6	+	1.42955e7i	0.591000	+	1.81891i
$574$	−437677.			−0.0554465
$575$	−4.34269e6	−	1.05464e7i	−0.547759	−	1.33025i
$576$	730574.			0.0917504
$577$	2.00532e6	+	6.17174e6i	0.250752	+	0.771734i	0.994637	+	0.103427i	$0.0329808\pi$
$577$	2.00532e6	+	6.17174e6i	0.250752	+	0.771734i	−0.743885	+	0.668307i	$0.767019\pi$
$578$	4.44312e6	−	3.22811e6i	0.553182	−	0.401910i
$579$	−405416.	+	294552.i	−0.0502579	+	0.0365145i
$580$	5.46036e6	+	1.54613e6i	0.673987	+	0.190843i
$581$	933690.	+	678366.i	0.114753	+	0.0833726i
$582$	−8.39616e6			−1.02748
$583$	6.12675e6	+	4.45135e6i	0.746550	+	0.542401i
$584$	−77384.1	+	238164.i	−0.00938901	+	0.0288964i
$585$	−239660.	+	357868.i	−0.0289538	+	0.0432347i
$586$	−3.15563e6	−	9.71203e6i	−0.379614	−	1.16833i
$587$	4.89155e6	−	1.50547e7i	0.585938	−	1.80333i	−0.00953275	−	0.999955i	$-0.503034\pi$
$587$	4.89155e6	−	1.50547e7i	0.585938	−	1.80333i	0.595471	−	0.803377i	$-0.296966\pi$
$588$	−1.68954e6	+	5.19987e6i	−0.201523	+	0.620225i
$589$	−342749.	−	1.05487e6i	−0.0407088	−	0.125289i
$590$	412068.	+	1.07744e7i	0.0487348	+	1.27427i
$591$	1.40240e6	−	4.31615e6i	0.165160	−	0.508309i
$592$	992628.	+	721187.i	0.116408	+	0.0845753i
$593$	3.54667e6			0.414176			0.207088	−	0.978322i	$-0.433601\pi$
$593$	3.54667e6			0.414176			0.207088	+	0.978322i	$0.433601\pi$
$594$	−2.35582e6	−	1.71160e6i	−0.273953	−	0.199039i
$595$	85150.7	−	127150.i	0.00986043	−	0.0147239i
$596$	−6.73631e6	+	4.89422e6i	−0.776795	+	0.564375i
$597$	2.84351e6	−	2.06593e6i	0.326526	−	0.237235i
$598$	−194875.	−	599764.i	−0.0222845	−	0.0685847i
$599$	8.52188e6			0.970439			0.485220	−	0.874392i	$-0.338740\pi$
$599$	8.52188e6			0.970439			0.485220	+	0.874392i	$0.338740\pi$
$600$	−4.09343e6	+	313567.i	−0.464205	+	0.0355592i
$601$	−1.27056e7			−1.43486			−0.717429	−	0.696632i	$-0.754681\pi$
$601$	−1.27056e7			−1.43486			−0.717429	+	0.696632i	$0.754681\pi$
$602$	279922.	+	861511.i	0.0314808	+	0.0968879i
$603$	−7.63754e6	+	5.54900e6i	−0.855382	+	0.621471i
$604$	−1.57411e6	+	1.14365e6i	−0.175566	+	0.127556i
$605$	−4.83844e6	−	6.15071e6i	−0.537423	−	0.683183i
$606$	−4.12564e6	−	2.99745e6i	−0.456362	−	0.331566i
$607$	3.39692e6			0.374208			0.187104	−	0.982340i	$-0.440090\pi$
$607$	3.39692e6			0.374208			0.187104	+	0.982340i	$0.440090\pi$
$608$	138849.	+	100879.i	0.0152329	+	0.0110674i
$609$	508964.	−	1.56643e6i	0.0556088	−	0.171146i
$610$	285945.	+	363499.i	0.0311142	+	0.0395530i
$611$	−102582.	−	315716.i	−0.0111165	−	0.0342132i
$612$	190898.	−	587522.i	0.0206026	−	0.0634083i
$613$	813997.	−	2.50523e6i	0.0874927	−	0.269275i	−0.897732	−	0.440542i	$-0.854786\pi$
$613$	813997.	−	2.50523e6i	0.0874927	−	0.269275i	0.985225	+	0.171267i	$0.0547862\pi$
$614$	948289.	+	2.91853e6i	0.101513	+	0.312423i
$615$	9.31864e6	−	3.42679e6i	0.993493	−	0.365342i
$616$	−137223.	+	422330.i	−0.0145706	+	0.0448436i
$617$	1.17139e7	+	8.51062e6i	1.23876	+	0.900012i	0.997515	−	0.0704524i	$-0.0224443\pi$
$617$	1.17139e7	+	8.51062e6i	1.23876	+	0.900012i	0.241245	+	0.970464i	$0.422444\pi$
$618$	1.36443e7			1.43708
$619$	−5.87776e6	−	4.27044e6i	−0.616574	−	0.447967i	0.235149	−	0.971959i	$-0.424442\pi$
$619$	−5.87776e6	−	4.27044e6i	−0.616574	−	0.447967i	−0.851723	+	0.523992i	$0.824442\pi$
$620$	226212.	+	5.91477e6i	0.0236339	+	0.617958i
$621$	3.91771e6	−	2.84639e6i	0.407665	−	0.296186i
$622$	−5.23501e6	+	3.80346e6i	−0.542552	+	0.394187i
$623$	431101.	+	1.32679e6i	0.0444999	+	0.136957i
$624$	−226996.			−0.0233376
$625$	9.65169e6	−	1.48741e6i	0.988333	−	0.152311i
$626$	5.60317e6			0.571476
$627$	583321.	+	1.79528e6i	0.0592569	+	0.182374i
$628$	4.59095e6	−	3.33552e6i	0.464519	−	0.337493i
$629$	839345.	−	609820.i	0.0845890	−	0.0614575i
$630$	19275.3	+	503993.i	0.00193486	+	0.0505910i
$631$	186121.	+	135225.i	0.0186090	+	0.0135202i	0.597051	−	0.802203i	$-0.296339\pi$
$631$	186121.	+	135225.i	0.0186090	+	0.0135202i	−0.578442	+	0.815724i	$0.696339\pi$
$632$	4.64622e6			0.462708
$633$	1.98827e7	+	1.44456e7i	1.97226	+	1.43293i
$634$	1.43955e6	−	4.43048e6i	0.142234	−	0.437752i
$635$	−2.25348e6	+	828682.i	−0.221778	+	0.0815556i
$636$	1.40084e6	+	4.31136e6i	0.137324	+	0.422641i
$637$	222214.	−	683903.i	0.0216981	−	0.0667799i
$638$	−4.30308e6	+	1.32435e7i	−0.418531	+	1.28811i
$639$	1.85963e6	+	5.72336e6i	0.180167	+	0.554497i
$640$	−566273.	−	719858.i	−0.0546482	−	0.0694699i
$641$	−4.28518e6	+	1.31884e7i	−0.411930	+	1.26779i	0.503038	+	0.864264i	$0.332216\pi$
$641$	−4.28518e6	+	1.31884e7i	−0.411930	+	1.26779i	−0.914968	+	0.403526i	$0.867784\pi$
$642$	−1.22549e7	−	8.90368e6i	−1.17347	−	0.852573i
$643$	3.24094e6			0.309131			0.154566	−	0.987983i	$-0.450602\pi$
$643$	3.24094e6			0.309131			0.154566	+	0.987983i	$0.450602\pi$
$644$	−597439.	−	434065.i	−0.0567648	−	0.0412421i
$645$	−1.27050e7	−	1.61509e7i	−1.20248	−	1.52861i
$646$	117407.	−	85301.5i	0.0110692	−	0.00804221i
$647$	5.56497e6	−	4.04319e6i	0.522639	−	0.379720i	−0.294958	−	0.955510i	$-0.595306\pi$
$647$	5.56497e6	−	4.04319e6i	0.522639	−	0.379720i	0.817597	+	0.575791i	$0.195306\pi$
$648$	−1.39583e6	−	4.29591e6i	−0.130585	−	0.401899i
$649$	−2.64568e7			−2.46562
$650$	538381.	−	41241.3i	0.0499812	−	0.00382868i
$651$	1.71787e6			0.158869
$652$	−2.21439e6	−	6.81520e6i	−0.204003	−	0.627856i
$653$	−1.32884e7	+	9.65462e6i	−1.21953	+	0.886038i	−0.996061	−	0.0886740i	$-0.971737\pi$
$653$	−1.32884e7	+	9.65462e6i	−1.21953	+	0.886038i	−0.223466	+	0.974712i	$0.571737\pi$
$654$	5.76665e6	−	4.18971e6i	0.527204	−	0.383036i
$655$	3.40662e6	−	5.08688e6i	0.310256	−	0.463285i
$656$	1.79200e6	+	1.30197e6i	0.162584	+	0.118125i
$657$	−697901.			−0.0630783
$658$	−314493.	−	228492.i	−0.0283169	−	0.0205734i
$659$	−5.73118e6	+	1.76388e7i	−0.514080	+	1.58217i	0.270871	+	0.962616i	$0.412688\pi$
$659$	−5.73118e6	+	1.76388e7i	−0.514080	+	1.58217i	−0.784950	+	0.619559i	$0.787312\pi$
$660$	−384987.	−	1.00663e7i	−0.0344022	−	0.899516i
$661$	6.14173e6	+	1.89023e7i	0.546748	+	1.68272i	0.716797	+	0.697282i	$0.245607\pi$
$661$	6.14173e6	+	1.89023e7i	0.546748	+	1.68272i	−0.170049	+	0.985436i	$0.554393\pi$
$662$	−1.07743e6	+	3.31598e6i	−0.0955526	+	0.294081i
$663$	−59313.6	+	182549.i	−0.00524048	+	0.0161285i
$664$	−1.80491e6	−	5.55493e6i	−0.158867	−	0.488943i
$665$	−65929.2	+	98447.6i	−0.00578128	+	0.00863279i
$666$	−1.05666e6	+	3.25207e6i	−0.0923102	+	0.284102i
$667$	−1.87346e7	−	1.36115e7i	−1.63054	−	1.18465i
$668$	−1.28470e6			−0.111394
$669$	−5.49445e6	−	3.99195e6i	−0.474634	−	0.344842i
$670$	1.13875e7	+	3.22444e6i	0.980036	+	0.277503i
$671$	−918095.	+	667035.i	−0.0787193	+	0.0571929i
$672$	−215049.	+	156243.i	−0.0183703	+	0.0133468i
$673$	−1.79777e6	−	5.53296e6i	−0.153001	−	0.470890i	0.844951	−	0.534843i	$-0.179629\pi$
$673$	−1.79777e6	−	5.53296e6i	−0.153001	−	0.470890i	−0.997953	+	0.0639529i	$0.979629\pi$
$674$	4.51791e6			0.383078
$675$	1.57873e6	+	3.83399e6i	0.133367	+	0.323886i
$676$	−5.91083e6			−0.497487
$677$	−7.02043e6	−	2.16067e7i	−0.588698	−	1.81182i	−0.583885	−	0.811836i	$-0.698468\pi$
$677$	−7.02043e6	−	2.16067e7i	−0.588698	−	1.81182i	−0.00481250	−	0.999988i	$-0.501532\pi$
$678$	1.26373e7	−	9.18152e6i	1.05579	−	0.767079i
$679$	1.04617e6	−	760088.i	0.0870820	−	0.0632688i
$680$	−726871.	+	267296.i	−0.0602816	+	0.0221676i
$681$	−1.06150e7	−	7.71227e6i	−0.877109	−	0.637257i
$682$	−1.45239e7			−1.19570
$683$	−7.20323e6	−	5.23345e6i	−0.590848	−	0.429276i	0.251771	−	0.967787i	$-0.418987\pi$
$683$	−7.20323e6	−	5.23345e6i	−0.590848	−	0.429276i	−0.842618	+	0.538511i	$0.818987\pi$
$684$	−147805.	+	454898.i	−0.0120795	+	0.0371770i
$685$	−1.54038e7	−	4.36167e6i	−1.25430	−	0.355162i
$686$	−522931.	−	1.60941e6i	−0.0424262	−	0.130574i
$687$	3.75801e6	−	1.15660e7i	0.303785	−	0.934953i
$688$	1.41666e6	−	4.36002e6i	0.114102	−	0.351170i
$689$	−184243.	−	567043.i	−0.0147858	−	0.0455059i
$690$	1.61187e7	+	4.56409e6i	1.28886	+	0.364949i
$691$	1.11728e6	−	3.43863e6i	0.0890156	−	0.273962i	−0.896632	−	0.442776i	$-0.853994\pi$
$691$	1.11728e6	−	3.43863e6i	0.0890156	−	0.273962i	0.985648	+	0.168814i	$0.0539937\pi$
$692$	4.60113e6	+	3.34291e6i	0.365257	+	0.265375i
$693$	−1.23757e6			−0.0978897
$694$	−5.32586e6	−	3.86946e6i	−0.419750	−	0.304966i
$695$	7.15018e6	−	2.62937e6i	0.561506	−	0.206485i
$696$	−6.74356e6	+	4.89949e6i	−0.527675	+	0.383378i
$697$	1.51528e6	−	1.10092e6i	0.118144	−	0.0858365i
$698$	−1.18675e6	−	3.65243e6i	−0.0921974	−	0.283755i
$699$	−7.80471e6			−0.604176
$700$	481660.	−	409641.i	0.0371531	−	0.0315979i
$701$	1.26501e6			0.0972295			0.0486148	−	0.998818i	$-0.484519\pi$
$701$	1.26501e6			0.0972295			0.0486148	+	0.998818i	$0.484519\pi$
$702$	70844.1	+	218036.i	0.00542577	+	0.0166988i
$703$	−649876.	+	472163.i	−0.0495955	+	0.0360333i
$704$	1.81815e6	−	1.32097e6i	0.138261	−	0.100452i
$705$	8.48489e6	+	2.40254e6i	0.642944	+	0.182053i
$706$	8.91769e6	+	6.47908e6i	0.673349	+	0.489217i
$707$	785413.			0.0590948
$708$	−1.28124e7	−	9.30874e6i	−0.960610	−	0.697924i
$709$	3.11809e6	−	9.59649e6i	0.232955	−	0.716963i	−0.764431	−	0.644706i	$-0.776980\pi$
$709$	3.11809e6	−	9.59649e6i	0.232955	−	0.716963i	0.997386	−	0.0722571i	$-0.0230202\pi$
$710$	4.19800e6	−	6.26858e6i	0.312533	−	0.466684i
$711$	4.00135e6	+	1.23149e7i	0.296847	+	0.913600i
$712$	2.18176e6	−	6.71476e6i	0.161290	−	0.496399i
$713$	7.46374e6	−	2.29710e7i	0.549835	−	1.69222i
$714$	69457.2	+	213767.i	0.00509884	+	0.0156926i
$715$	50634.7	+	1.32395e6i	0.00370410	+	0.0968514i
$716$	−791924.	+	2.43729e6i	−0.0577299	+	0.177674i
$717$	−684834.	−	497561.i	−0.0497494	−	0.0361450i
$718$	−1.05681e7			−0.765044
$719$	−1.51066e7	−	1.09756e7i	−1.08979	−	0.791780i	−0.110428	−	0.993884i	$-0.535222\pi$
$719$	−1.51066e7	−	1.09756e7i	−1.08979	−	0.791780i	−0.979364	+	0.202104i	$0.935222\pi$
$720$	1.42032e6	−	2.12086e6i	0.102107	−	0.152469i
$721$	−1.70010e6	+	1.23519e6i	−0.121797	+	0.0884906i
$722$	7.92192e6	−	5.75561e6i	0.565571	−	0.410912i
$723$	1.01683e7	+	3.12948e7i	0.723441	+	2.22652i
$724$	2.81927e6			0.199890
$725$	1.51040e7	−	1.28456e7i	1.06720	−	0.907632i
$726$	1.14944e7			0.809366
$727$	5.00431e6	+	1.54017e7i	0.351162	+	1.08077i	0.958201	+	0.286094i	$0.0923571\pi$
$727$	5.00431e6	+	1.54017e7i	0.351162	+	1.08077i	−0.607039	+	0.794672i	$0.707643\pi$
$728$	28284.0	−	20549.5i	0.00197793	−	0.00143705i
$729$	4.82997e6	−	3.50918e6i	0.336609	−	0.244561i
$730$	540948.	+	687664.i	0.0375706	+	0.0477605i
$731$	−3.13613e6	−	2.27853e6i	−0.217070	−	0.157711i
$732$	−679305.			−0.0468584
$733$	4.54593e6	+	3.30281e6i	0.312509	+	0.227051i	0.732972	−	0.680258i	$-0.238132\pi$
$733$	4.54593e6	+	3.30281e6i	0.312509	+	0.227051i	−0.420463	+	0.907310i	$0.638132\pi$
$734$	2.56948e6	−	7.90805e6i	0.176038	−	0.541788i
$735$	1.18106e7	+	1.50139e7i	0.806406	+	1.02512i
$736$	1.15490e6	+	3.55443e6i	0.0785871	+	0.241866i
$737$	−8.97402e6	+	2.76192e7i	−0.608581	+	1.87302i
$738$	−1.90760e6	+	5.87099e6i	−0.128928	+	0.396799i
$739$	−3.45915e6	−	1.06462e7i	−0.233001	−	0.717104i	−0.997380	−	0.0723367i	$-0.976954\pi$
$739$	−3.45915e6	−	1.06462e7i	−0.233001	−	0.717104i	0.764379	−	0.644767i	$-0.223046\pi$
$740$	4.02339e6	−	1.47954e6i	0.270093	−	0.0993225i
$741$	45924.5	−	141341.i	0.00307255	−	0.00945634i
$742$	−564846.	−	410384.i	−0.0376635	−	0.0273641i
$743$	−2.66404e7			−1.77039			−0.885196	−	0.465218i	$-0.845976\pi$
$743$	−2.66404e7			−1.77039			−0.885196	+	0.465218i	$0.845976\pi$
$744$	−7.03357e6	−	5.11019e6i	−0.465847	−	0.338458i
$745$	1.11181e6	+	2.90705e7i	0.0733903	+	1.91894i
$746$	−1.30795e7	+	9.50282e6i	−0.860487	+	0.625180i
$747$	1.31690e7	−	9.56787e6i	0.863481	−	0.627355i
$748$	−587232.	−	1.80731e6i	−0.0383756	−	0.118108i
$749$	2.33300e6			0.151954
$750$	−7.04780e6	+	1.24929e7i	−0.457510	+	0.810978i
$751$	6.14470e6			0.397558			0.198779	−	0.980044i	$-0.436302\pi$
$751$	6.14470e6			0.397558			0.198779	+	0.980044i	$0.436302\pi$
$752$	607943.	+	1.87106e6i	0.0392029	+	0.120654i
$753$	1.41736e7	−	1.02977e7i	0.910944	−	0.661839i
$754$	886935.	−	644396.i	0.0568150	−	0.0412785i
$755$	259801.	+	6.79303e6i	0.0165872	+	0.433707i
$756$	217191.	+	157798.i	0.0138209	+	0.0100415i
$757$	−8.92380e6			−0.565992			−0.282996	−	0.959121i	$-0.591328\pi$
$757$	−8.92380e6			−0.565992			−0.282996	+	0.959121i	$0.591328\pi$
$758$	−2.70022e6	−	1.96182e6i	−0.170697	−	0.124019i
$759$	−1.27024e7	+	3.90941e7i	−0.800355	+	2.46324i
$760$	562791.	−	206958.i	0.0353438	−	0.0129971i
$761$	−4.04499e6	−	1.24492e7i	−0.253195	−	0.779255i	−0.994180	−	0.107733i	$-0.965641\pi$
$761$	−4.04499e6	−	1.24492e7i	−0.253195	−	0.779255i	0.740985	−	0.671522i	$-0.234359\pi$
$762$	1.08978e6	−	3.35401e6i	0.0679913	−	0.209256i
$763$	−339244.	+	1.04409e6i	−0.0210961	+	0.0649270i
$764$	3.62048e6	+	1.11427e7i	0.224405	+	0.690648i
$765$	−1.33446e6	−	1.69639e6i	−0.0824424	−	0.104802i
$766$	1.12204e6	−	3.45328e6i	0.0690933	−	0.212647i
$767$	1.68513e6	+	1.22432e6i	0.103429	+	0.0751458i
$768$	1.34527e6			0.0823010
$769$	−1.97568e6	−	1.43542e6i	−0.120476	−	0.0875310i	0.525916	−	0.850537i	$-0.323723\pi$
$769$	−1.97568e6	−	1.43542e6i	−0.120476	−	0.0875310i	−0.646392	+	0.763006i	$0.723723\pi$
$770$	959251.	+	1.21942e6i	0.0583049	+	0.0741184i
$771$	−1.62421e6	+	1.18006e6i	−0.0984024	+	0.0714936i
$772$	−316004.	+	229590.i	−0.0190831	+	0.0138647i
$773$	1.71199e6	+	5.26897e6i	0.103051	+	0.317159i	0.989268	−	0.146112i	$-0.0466759\pi$
$773$	1.71199e6	+	5.26897e6i	0.103051	+	0.317159i	−0.886217	+	0.463270i	$0.846676\pi$
$774$	1.27763e7			0.766573
$775$	1.76104e7	+	1.08423e7i	1.05321	+	0.648435i
$776$	−6.54444e6			−0.390138
$777$	−384461.	−	1.18325e6i	−0.0228454	−	0.0703110i
$778$	3.82130e6	−	2.77633e6i	0.226340	−	0.164446i
$779$	−1.17323e6	+	852401.i	−0.0692690	+	0.0503269i
$780$	−441306.	+	658971.i	−0.0259719	+	0.0387820i
$781$	1.49765e7	+	1.08811e7i	0.878585	+	0.638330i
$782$	3.16022e6			0.184800
$783$	6.81072e6	+	4.94828e6i	0.396998	+	0.288436i
$784$	−1.31692e6	+	4.05307e6i	−0.0765192	+	0.235502i
$785$	−757722.	−	1.98122e7i	−0.0438870	−	1.14751i
$786$	2.77877e6	+	8.55219e6i	0.160434	+	0.493766i
$787$	−4.33200e6	+	1.33325e7i	−0.249317	+	0.767319i	0.745579	+	0.666417i	$0.232173\pi$
$787$	−4.33200e6	+	1.33325e7i	−0.249317	+	0.767319i	−0.994896	+	0.100902i	$0.967827\pi$
$788$	1.09311e6	−	3.36425e6i	0.0627118	−	0.193007i
$789$	−7.13453e6	−	2.19578e7i	−0.408012	−	1.25573i
$790$	9.03277e6	−	1.34880e7i	0.514936	−	0.768918i
$791$	−743435.	+	2.28806e6i	−0.0422476	+	0.130025i
$792$	5.06705e6	+	3.68142e6i	0.287040	+	0.208547i
$793$	89344.3			0.00504527
$794$	−2.42027e6	−	1.75843e6i	−0.136242	−	0.0989858i
$795$	1.52393e7	+	4.31510e6i	0.855160	+	0.242143i
$796$	2.21639e6	−	1.61030e6i	0.123983	−	0.0900792i
$797$	2.47048e7	−	1.79491e7i	1.37764	−	1.00091i	0.380541	−	0.924764i	$-0.375738\pi$
$797$	2.47048e7	−	1.79491e7i	1.37764	−	1.00091i	0.997097	−	0.0761480i	$-0.0242622\pi$
$798$	−53778.3	−	165513.i	−0.00298951	−	0.00920076i
$799$	1.66355e6			0.0921866
$800$	−3.19065e6	+	244412.i	−0.176260	+	0.0135020i
$801$	1.96765e7			1.08359
$802$	−3.92002e6	−	1.20646e7i	−0.215205	−	0.662333i
$803$	−1.73684e6	+	1.26189e6i	−0.0950543	+	0.0690610i
$804$	−1.40636e7	+	1.02178e7i	−0.767286	+	0.557466i
$805$	−2.42158e6	+	890500.i	−0.131707	+	0.0484333i
$806$	925077.	+	672108.i	0.0501580	+	0.0364419i
$807$	−4.03208e7			−2.17944
$808$	−3.21575e6	−	2.33638e6i	−0.173282	−	0.125897i
$809$	−9.72046e6	+	2.99165e7i	−0.522174	+	1.60709i	0.247662	+	0.968846i	$0.420338\pi$
$809$	−9.72046e6	+	2.99165e7i	−0.522174	+	1.60709i	−0.769837	+	0.638241i	$0.779662\pi$
$810$	−1.51847e7	−	4.29964e6i	−0.813193	−	0.230260i
$811$	907637.	+	2.79342e6i	0.0484574	+	0.149137i	0.972357	−	0.233497i	$-0.0750170\pi$
$811$	907637.	+	2.79342e6i	0.0484574	+	0.149137i	−0.923900	+	0.382634i	$0.875017\pi$
$812$	396715.	−	1.22096e6i	0.0211149	−	0.0649849i
$813$	6.22361e6	−	1.91543e7i	0.330229	−	1.01634i
$814$	3.25046e6	+	1.00039e7i	0.171943	+	0.529185i
$815$	−2.40896e7	−	6.82111e6i	−1.27039	−	0.359717i
$816$	351515.	−	1.08185e6i	0.0184807	−	0.0568778i
$817$	2.42820e6	+	1.76419e6i	0.127271	+	0.0924676i
$818$	1.16077e7			0.606542
$819$	78825.1	+	57269.8i	0.00410634	+	0.00298343i
$820$	7.26347e6	−	2.67103e6i	0.377233	−	0.138722i
$821$	2.26542e6	−	1.64592e6i	0.117298	−	0.0852220i	−0.527590	−	0.849499i	$-0.676904\pi$
$821$	2.26542e6	−	1.64592e6i	0.117298	−	0.0852220i	0.644888	+	0.764277i	$0.276904\pi$
$822$	1.90237e7	−	1.38215e7i	0.982009	−	0.713472i
$823$	9.31366e6	+	2.86645e7i	0.479315	+	1.47518i	0.840049	+	0.542510i	$0.182526\pi$
$823$	9.31366e6	+	2.86645e7i	0.479315	+	1.47518i	−0.360734	+	0.932669i	$0.617474\pi$
$824$	1.06352e7			0.545665
$825$	−2.99709e7	−	1.84524e7i	−1.53308	−	0.943880i
$826$	2.43914e6			0.124390
$827$	−6.38718e6	−	1.96577e7i	−0.324747	−	0.999469i	−0.971555	−	0.236816i	$-0.923896\pi$
$827$	−6.38718e6	−	1.96577e7i	−0.324747	−	0.999469i	0.646807	−	0.762654i	$-0.276104\pi$
$828$	−8.42646e6	+	6.12218e6i	−0.427139	+	0.310335i
$829$	2.80740e7	−	2.03970e7i	1.41879	−	1.03081i	0.426820	−	0.904336i	$-0.359634\pi$
$829$	2.80740e7	−	2.03970e7i	1.41879	−	1.03081i	0.991970	−	0.126475i	$-0.0403663\pi$
$830$	−1.96350e7	−	5.55975e6i	−0.989315	−	0.280130i
$831$	−1.76148e7	−	1.27979e7i	−0.884861	−	0.642889i
$832$	−176934.			−0.00886139
$833$	2.91534e6	+	2.11812e6i	0.145572	+	0.105764i
$834$	−3.45783e6	+	1.06421e7i	−0.172143	+	0.529801i
$835$	−2.49760e6	+	3.72949e6i	−0.123967	+	0.185112i
$836$	454674.	+	1.39934e6i	0.0225001	+	0.0692481i
$837$	−2.71334e6	+	8.35080e6i	−0.133872	+	0.412016i
$838$	−6.57993e6	+	2.02509e7i	−0.323676	+	0.996173i
$839$	−5.73499e6	−	1.76505e7i	−0.281273	−	0.865669i	−0.987491	−	0.157675i	$-0.949600\pi$
$839$	−5.73499e6	−	1.76505e7i	−0.281273	−	0.865669i	0.706218	−	0.707994i	$-0.250400\pi$
$840$	35493.2	+	928043.i	0.00173559	+	0.0453806i
$841$	6.10199e6	−	1.87800e7i	0.297496	−	0.915599i
$842$	4.68436e6	+	3.40339e6i	0.227704	+	0.165437i
$843$	−2.10466e7			−1.02003
$844$	1.54977e7	+	1.12597e7i	0.748877	+	0.544091i
$845$	−1.14913e7	+	1.71592e7i	−0.553641	+	0.826714i
$846$	−4.43570e6	+	3.22272e6i	−0.213077	+	0.154809i
$847$	−1.43222e6	+	1.04057e6i	−0.0685963	+	0.0498381i
$848$	1.09190e6	+	3.36052e6i	0.0521426	+	0.160478i
$849$	−3.07960e7			−1.46631
$850$	−637157.	+	2.62977e6i	−0.0302482	+	0.124845i
$851$	−1.74925e7			−0.827997
$852$	3.42429e6	+	1.05389e7i	0.161611	+	0.497389i
$853$	3.19583e7	−	2.32191e7i	1.50387	−	1.09263i	0.535067	−	0.844810i	$-0.320286\pi$
$853$	3.19583e7	−	2.32191e7i	1.50387	−	1.09263i	0.968807	−	0.247818i	$-0.0797136\pi$
$854$	84642.2	−	61496.2i	0.00397139	−	0.00288538i
$855$	1.03322e6	+	1.31345e6i	0.0483369	+	0.0614468i
$856$	−9.55213e6	−	6.94003e6i	−0.445570	−	0.323726i
$857$	8.85492e6			0.411844			0.205922	−	0.978568i	$-0.433981\pi$
$857$	8.85492e6			0.411844			0.205922	+	0.978568i	$0.433981\pi$
$858$	−1.57438e6	−	1.14385e6i	−0.0730114	−	0.0530459i
$859$	−4.50615e6	+	1.38685e7i	−0.208364	+	0.641278i	0.791194	+	0.611565i	$0.209460\pi$
$859$	−4.50615e6	+	1.38685e7i	−0.208364	+	0.641278i	−0.999558	+	0.0297138i	$0.990540\pi$
$860$	−9.90303e6	−	1.25889e7i	−0.456585	−	0.580420i
$861$	−694071.	−	2.13613e6i	−0.0319078	−	0.0982020i
$862$	−5.76549e6	+	1.77444e7i	−0.264282	+	0.813377i
$863$	−4.90376e6	+	1.50922e7i	−0.224131	+	0.689805i	0.774247	+	0.632883i	$0.218129\pi$
$863$	−4.90376e6	+	1.50922e7i	−0.224131	+	0.689805i	−0.998379	+	0.0569218i	$0.981871\pi$
$864$	−419850.	−	1.29216e6i	−0.0191342	−	0.0588889i
$865$	1.86496e7	−	6.85811e6i	0.847480	−	0.311648i
$866$	1.69112e6	−	5.20472e6i	0.0766264	−	0.235832i
$867$	2.28011e7	+	1.65660e7i	1.03017	+	0.748461i
$868$	1.33901e6			0.0603231
$869$	3.22248e7	+	2.34127e7i	1.44758	+	1.05172i
$870$	1.11300e6	+	2.91018e7i	0.0498538	+	1.30353i
$871$	1.84969e6	−	1.34388e6i	0.0826141	−	0.0600226i
$872$	4.49485e6	−	3.26570e6i	0.200182	−	0.145440i
$873$	−5.63610e6	−	1.73461e7i	−0.250290	−	0.770313i
$874$	−2.44685e6			−0.108350
$875$	−252791.	−	2.19465e6i	−0.0111620	−	0.0969048i
$876$	−1.28510e6			−0.0565819
$877$	−1.95718e6	−	6.02358e6i	−0.0859273	−	0.264457i	0.898856	−	0.438244i	$-0.144400\pi$
$877$	−1.95718e6	−	6.02358e6i	−0.0859273	−	0.264457i	−0.984783	+	0.173787i	$0.944400\pi$
$878$	−3.80147e6	+	2.76193e6i	−0.166424	+	0.120914i
$879$	4.23964e7	−	3.08028e7i	1.85079	−	1.34468i
$880$	−300081.	−	7.84623e6i	−0.0130627	−	0.341550i
$881$	1.29204e6	+	938721.i	0.0560836	+	0.0407471i	0.615474	−	0.788157i	$-0.288965\pi$
$881$	1.29204e6	+	938721.i	0.0560836	+	0.0407471i	−0.559390	+	0.828904i	$0.688965\pi$
$882$	−1.18769e7			−0.514080
$883$	3.63205e6	+	2.63884e6i	0.156765	+	0.113897i	0.663403	−	0.748263i	$-0.269112\pi$
$883$	3.63205e6	+	2.63884e6i	0.156765	+	0.113897i	−0.506637	+	0.862159i	$0.669112\pi$
$884$	−46232.4	+	142289.i	−0.00198983	+	0.00612407i
$885$	−5.19321e7	+	1.90972e7i	−2.22883	+	0.819619i
$886$	−5.97631e6	−	1.83932e7i	−0.255770	−	0.787178i
$887$	2.92746e6	−	9.00979e6i	0.124934	−	0.384508i	−0.868955	−	0.494891i	$-0.835208\pi$
$887$	2.92746e6	−	9.00979e6i	0.124934	−	0.384508i	0.993889	+	0.110383i	$0.0352078\pi$
$888$	−1.94572e6	+	5.98830e6i	−0.0828032	+	0.254842i
$889$	167844.	+	516570.i	0.00712280	+	0.0219217i
$890$	−1.52514e7	−	1.93879e7i	−0.645409	−	0.820457i
$891$	1.19664e7	−	3.68289e7i	0.504975	−	1.55415i
$892$	−4.28268e6	−	3.11155e6i	−0.180220	−	0.130938i
$893$	−1.28803e6			−0.0540500
$894$	−3.45693e7	−	2.51161e7i	−1.44659	−	1.05101i
$895$	5.53589e6	+	7.03733e6i	0.231009	+	0.293664i
$896$	−167622.	+	121784.i	−0.00697526	+	0.00506782i
$897$	2.61818e6	−	1.90222e6i	0.108647	−	0.0789368i
$898$	1.41338e6	+	4.34993e6i	0.0584881	+	0.180008i
$899$	4.19889e7			1.73275
$900$	−3.39562e6	−	8.24639e6i	−0.139738	−	0.339357i
$901$	2.98781e6			0.122614
$902$	5.86809e6	+	1.80601e7i	0.240149	+	0.739102i
$903$	−3.76080e6	+	2.73238e6i	−0.153483	+	0.111512i
$904$	9.85021e6	−	7.15659e6i	0.400889	−	0.291263i
$905$	5.48098e6	−	8.18438e6i	0.222452	−	0.332173i
$906$	−8.07796e6	−	5.86898e6i	−0.326950	−	0.237543i
$907$	2.91761e7			1.17763			0.588815	−	0.808268i	$-0.299595\pi$
$907$	2.91761e7			1.17763			0.588815	+	0.808268i	$0.299595\pi$
$908$	−8.27396e6	−	6.01138e6i	−0.333042	−	0.241969i
$909$	3.42319e6	−	1.05355e7i	0.137411	−	0.422908i
$910$	−4668.18	−	122059.i	−0.000186872	−	0.00488615i
$911$	−1.38157e7	−	4.25205e7i	−0.551542	−	1.69747i	−0.704906	−	0.709301i	$-0.749011\pi$
$911$	−1.38157e7	−	4.25205e7i	−0.551542	−	1.69747i	0.153364	−	0.988170i	$-0.450989\pi$
$912$	−272166.	+	837642.i	−0.0108355	+	0.0333481i
$913$	1.54735e7	−	4.76225e7i	0.614343	−	1.89075i
$914$	4.11400e6	+	1.26616e7i	0.162892	+	0.501329i
$915$	−1.32065e6	+	1.97203e6i	−0.0521475	+	0.0778683i
$916$	2.92920e6	−	9.01516e6i	0.115348	−	0.355005i
$917$	−1.12045e6	−	814056.i	−0.0440017	−	0.0319691i
$918$	−1.14886e6			−0.0449944
$919$	−1.35348e7	−	9.83364e6i	−0.528646	−	0.384084i	0.291205	−	0.956661i	$-0.405944\pi$
$919$	−1.35348e7	−	9.83364e6i	−0.528646	−	0.384084i	−0.819851	+	0.572577i	$0.805944\pi$
$920$	1.25638e7	+	3.55751e6i	0.489386	+	0.138572i
$921$	−1.27404e7	+	9.25646e6i	−0.494920	+	0.359580i
$922$	−1.83930e7	+	1.33633e7i	−0.712568	+	0.517711i
$923$	−450374.	−	1.38611e6i	−0.0174008	−	0.0535541i
$924$	−2.27884e6			−0.0878080
$925$	3.52681e6	−	1.45563e7i	0.135527	−	0.559368i
$926$	1.42834e7			0.547400
$927$	9.15905e6	+	2.81887e7i	0.350067	+	1.07739i
$928$	−5.25632e6	+	3.81894e6i	−0.200360	+	0.145570i
$929$	2.19209e7	−	1.59265e7i	0.833333	−	0.605452i	−0.0871671	−	0.996194i	$-0.527781\pi$
$929$	2.19209e7	−	1.59265e7i	0.833333	−	0.605452i	0.920500	+	0.390742i	$0.127781\pi$
$930$	−2.85090e7	+	1.04837e7i	−1.08087	+	0.397474i
$931$	−2.25725e6	−	1.63999e6i	−0.0853504	−	0.0620107i
$932$	−6.08343e6			−0.229408
$933$	−2.68649e7	−	1.95185e7i	−1.01037	−	0.734078i
$934$	4.66978e6	−	1.43721e7i	0.175158	−	0.539080i
$935$	−6.38829e6	−	1.80888e6i	−0.238977	−	0.0676677i
$936$	−152376.	−	468965.i	−0.00568495	−	0.0174965i
$937$	−1.39410e7	+	4.29061e7i	−0.518735	+	1.59650i	0.257646	+	0.966239i	$0.417053\pi$
$937$	−1.39410e7	+	4.29061e7i	−0.518735	+	1.59650i	−0.776381	+	0.630264i	$0.782947\pi$
$938$	827345.	−	2.54631e6i	0.0307029	−	0.0944938i
$939$	8.88554e6	+	2.73469e7i	0.328867	+	1.01215i
$940$	6.61360e6	+	1.87268e6i	0.244128	+	0.0691264i
$941$	−9.54543e6	+	2.93778e7i	−0.351416	+	1.08155i	0.606643	+	0.794975i	$0.292516\pi$
$941$	−9.54543e6	+	2.93778e7i	−0.351416	+	1.08155i	−0.958059	+	0.286572i	$0.907484\pi$
$942$	2.35597e7	+	1.71172e7i	0.865054	+	0.628498i
$943$	−3.15795e7			−1.15645
$944$	−9.98670e6	−	7.25576e6i	−0.364747	−	0.265004i
$945$	880334.	−	323729.i	0.0320677	−	0.0117924i
$946$	3.17960e7	−	2.31012e7i	1.15517	−	0.839278i
$947$	−1.02809e7	+	7.46951e6i	−0.372526	+	0.270656i	−0.758258	−	0.651955i	$-0.773949\pi$
$947$	−1.02809e7	+	7.46951e6i	−0.372526	+	0.270656i	0.385732	+	0.922611i	$0.373949\pi$
$948$	7.36801e6	+	2.26764e7i	0.266274	+	0.819508i
$949$	169021.			0.00609220
$950$	493329.	−	2.03614e6i	0.0177349	−	0.0731978i
$951$	2.39063e7			0.857159
$952$	54138.9	+	166622.i	0.00193605	+	0.00595855i
$953$	−3.13175e7	+	2.27535e7i	−1.11701	+	0.811552i	−0.983753	−	0.179530i	$-0.942542\pi$
$953$	−3.13175e7	+	2.27535e7i	−1.11701	+	0.811552i	−0.133253	+	0.991082i	$0.542542\pi$
$954$	−7.96675e6	+	5.78818e6i	−0.283407	+	0.205907i
$955$	3.93859e7	+	1.11524e7i	1.39744	+	0.395693i
$956$	−533798.	−	387827.i	−0.0188900	−	0.0137244i
$957$	−7.14603e7			−2.52223
$958$	−5.06090e6	−	3.67696e6i	−0.178162	−	0.129442i
$959$	−1.11914e6	+	3.44436e6i	−0.0392951	+	0.120938i
$960$	2.61535e6	−	3.90532e6i	0.0915907	−	0.136766i
$961$	4.68638e6	+	1.44232e7i	0.163693	+	0.503794i
$962$	255907.	−	787600.i	0.00891546	−	0.0274390i
$963$	1.01683e7	−	3.12949e7i	0.353332	−	1.08744i
$964$	7.92576e6	+	2.43930e7i	0.274693	+	0.845419i
$965$	52155.5	+	1.36371e6i	0.00180294	+	0.0471416i
$966$	1.17108e6	−	3.60421e6i	0.0403779	−	0.124270i
$967$	−1.27200e7	−	9.24165e6i	−0.437444	−	0.317822i	0.347174	−	0.937801i	$-0.387141\pi$
$967$	−1.27200e7	−	9.24165e6i	−0.437444	−	0.317822i	−0.784619	+	0.619979i	$0.787141\pi$
$968$	8.95940e6			0.307320
$969$	602509.	+	437749.i	0.0206136	+	0.0149767i
$970$	−1.27231e7	+	1.89986e7i	−0.434175	+	0.648323i
$971$	−3.18387e7	+	2.31322e7i	−1.08370	+	0.787352i	−0.978324	−	0.207081i	$-0.933604\pi$
$971$	−3.18387e7	+	2.31322e7i	−1.08370	+	0.787352i	−0.105373	+	0.994433i	$0.533604\pi$
$972$	1.45797e7	−	1.05928e7i	0.494975	−	0.359620i
$973$	−532560.	−	1.63905e6i	−0.0180338	−	0.0555022i
$974$	−7.96905e6			−0.269159
$975$	1.05505e6	+	2.56223e6i	0.0355437	+	0.0863190i
$976$	−529489.			−0.0177923
$977$	9.17392e6	+	2.82344e7i	0.307481	+	0.946330i	0.978740	+	0.205107i	$0.0657541\pi$
$977$	9.17392e6	+	2.82344e7i	0.307481	+	0.946330i	−0.671258	+	0.741223i	$0.734246\pi$
$978$	2.97508e7	−	2.16152e7i	0.994606	−	0.722623i
$979$	4.89683e7	−	3.55776e7i	1.63290	−	1.18637i
$980$	9.20586e6	+	1.17027e7i	0.306196	+	0.389242i
$981$	1.25268e7	+	9.10123e6i	0.415592	+	0.301945i
$982$	2.45572e7			0.812644
$983$	−1.18654e7	−	8.62072e6i	−0.391651	−	0.284551i	0.374481	−	0.927235i	$-0.377821\pi$
$983$	−1.18654e7	−	8.62072e6i	−0.391651	−	0.284551i	−0.766132	+	0.642684i	$0.777821\pi$
$984$	−3.51262e6	+	1.08107e7i	−0.115649	+	0.355933i
$985$	−7.64132e6	−	9.71380e6i	−0.250945	−	0.319006i
$986$	1.69770e6	+	5.22498e6i	0.0556119	+	0.171156i
$987$	616458.	−	1.89726e6i	0.0201424	−	0.0619919i
$988$	35796.2	−	110169.i	0.00116666	−	0.00359061i
$989$	2.01970e7	+	6.21601e7i	0.656594	+	2.02079i
$990$	2.05381e7	−	7.55258e6i	0.665997	−	0.244910i
$991$	−1.66113e7	+	5.11242e7i	−0.537302	+	1.65365i	0.201319	+	0.979526i	$0.435477\pi$
$991$	−1.66113e7	+	5.11242e7i	−0.537302	+	1.65365i	−0.738621	+	0.674121i	$0.764523\pi$
$992$	−5.48236e6	−	3.98317e6i	−0.176884	−	0.128514i
$993$	−1.78926e7			−0.575837
$994$	−1.38074e6	−	1.00316e6i	−0.0443246	−	0.0322037i
$995$	−365808.	−	9.56480e6i	−0.0117137	−	0.306280i
$996$	2.42492e7	−	1.76181e7i	0.774551	−	0.562744i
$997$	−1.20008e7	+	8.71912e6i	−0.382361	+	0.277802i	−0.762318	−	0.647203i	$-0.775939\pi$
$997$	−1.20008e7	+	8.71912e6i	−0.382361	+	0.277802i	0.379957	+	0.925004i	$0.375939\pi$
$998$	−663940.	−	2.04340e6i	−0.0211010	−	0.0649421i
$999$	6.35917e6			0.201598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.d.a.31.2	yes	24
25.21	even	5	inner	50.6.d.a.21.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.d.a.21.2	✓	24	25.21	even	5	inner
50.6.d.a.31.2	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 + 3.80423i) q^{2} +(-16.6068 + 12.0655i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(2.13641 + 55.8609i) q^{5} +(-66.4272 - 48.2622i) q^{6} +12.6460 q^{7} +(-51.7771 - 37.6183i) q^{8} +(55.1171 - 169.633i) q^{9} +O(q^{10})\)	\(q+(1.23607 + 3.80423i) q^{2} +(-16.6068 + 12.0655i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(2.13641 + 55.8609i) q^{5} +(-66.4272 - 48.2622i) q^{6} +12.6460 q^{7} +(-51.7771 - 37.6183i) q^{8} +(55.1171 - 169.633i) q^{9} +(-209.867 + 77.1752i) q^{10} +(-169.549 - 521.819i) q^{11} +(101.492 - 312.359i) q^{12} +(-13.3485 + 41.0825i) q^{13} +(15.6313 + 48.1082i) q^{14} +(-709.470 - 901.893i) q^{15} +(79.1084 - 243.470i) q^{16} +(-175.126 - 127.237i) q^{17} +713.451 q^{18} +(135.594 + 98.5151i) q^{19} +(-553.001 - 702.986i) q^{20} +(-210.009 + 152.581i) q^{21} +(1775.54 - 1290.01i) q^{22} +(1127.84 + 3471.12i) q^{23} +1313.74 q^{24} +(-3115.87 + 238.684i) q^{25} -172.787 q^{26} +(-410.009 - 1261.88i) q^{27} +(-163.693 + 118.930i) q^{28} +(-5133.12 + 3729.43i) q^{29} +(2554.05 - 3813.79i) q^{30} +(-5353.87 - 3889.81i) q^{31} +1024.00 q^{32} +(9111.69 + 6620.03i) q^{33} +(267.569 - 823.494i) q^{34} +(27.0170 + 706.416i) q^{35} +(881.874 + 2714.13i) q^{36} +(-1481.06 + 4558.22i) q^{37} +(-207.170 + 637.603i) q^{38} +(-274.006 - 843.305i) q^{39} +(1990.77 - 2972.68i) q^{40} +(-2673.77 + 8229.01i) q^{41} +(-840.037 - 610.322i) q^{42} +17907.8 q^{43} +(7102.17 + 5160.03i) q^{44} +(9593.60 + 2716.48i) q^{45} +(-11810.9 + 8581.09i) q^{46} +(-6217.25 + 4517.09i) q^{47} +(1623.87 + 4997.75i) q^{48} -16647.1 q^{49} +(-4759.44 - 11558.5i) q^{50} +4443.47 q^{51} +(-213.576 - 657.319i) q^{52} +(-11166.5 + 8112.94i) q^{53} +(4293.67 - 3119.54i) q^{54} +(28787.0 - 10586.0i) q^{55} +(-654.772 - 475.720i) q^{56} -3440.43 q^{57} +(-20532.5 - 14917.7i) q^{58} +(14900.7 - 45859.6i) q^{59} +(17665.5 + 5002.08i) q^{60} +(-639.145 - 1967.09i) q^{61} +(8179.99 - 25175.4i) q^{62} +(697.010 - 2145.18i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-2323.42 - 657.890i) q^{65} +(-13921.4 + 42845.7i) q^{66} +(-42820.3 - 31110.7i) q^{67} +3463.49 q^{68} +(-60610.7 - 44036.3i) q^{69} +(-2653.97 + 975.957i) q^{70} +(-27296.0 + 19831.7i) q^{71} +(-9235.10 + 6709.69i) q^{72} +(-1209.13 - 3721.31i) q^{73} -19171.2 q^{74} +(48864.8 - 41558.4i) q^{75} -2681.66 q^{76} +(-2144.12 - 6598.91i) q^{77} +(2869.43 - 2084.76i) q^{78} +(-58732.3 + 42671.5i) q^{79} +(13769.5 + 3898.91i) q^{80} +(57098.7 + 41484.6i) q^{81} -34610.0 q^{82} +(73832.9 + 53642.8i) q^{83} +(1283.46 - 3950.09i) q^{84} +(6733.42 - 10054.5i) q^{85} +(22135.2 + 68125.3i) q^{86} +(40247.1 - 123868. i) q^{87} +(-10851.1 + 33396.4i) q^{88} +(34090.0 + 104918. i) q^{89} +(1524.22 + 39854.0i) q^{90} +(-168.805 + 519.528i) q^{91} +(-47243.4 - 34324.4i) q^{92} +135843. q^{93} +(-24869.0 - 18068.4i) q^{94} +(-5213.45 + 7784.89i) q^{95} +(-17005.4 + 12355.1i) q^{96} +(82727.6 - 60105.1i) q^{97} +(-20576.9 - 63329.3i) q^{98} -97862.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9	\( 24 q - 24 q^{2} - 11 q^{3} - 96 q^{4} - 120 q^{5} - 44 q^{6} + 548 q^{7} - 384 q^{8} - 893 q^{9} + 320 q^{10} - 327 q^{11} - 96 q^{12} - 1161 q^{13} - 948 q^{14} + 760 q^{15} - 1536 q^{16} + 83 q^{17} + 7368 q^{18} - 6250 q^{19} + 2320 q^{20} + 6193 q^{21} + 852 q^{22} + 2069 q^{23} + 2176 q^{24} - 14380 q^{25} + 15976 q^{26} - 18935 q^{27} - 592 q^{28} - 11775 q^{29} - 9840 q^{30} + 2103 q^{31} + 24576 q^{32} - 11747 q^{33} + 972 q^{34} + 33235 q^{35} - 14288 q^{36} + 4148 q^{37} + 14260 q^{38} - 12576 q^{39} + 1600 q^{40} - 26427 q^{41} + 24772 q^{42} + 13024 q^{43} + 3408 q^{44} - 65535 q^{45} - 16964 q^{46} + 29803 q^{47} - 1536 q^{48} + 38368 q^{49} - 14020 q^{50} + 194058 q^{51} - 18576 q^{52} - 29011 q^{53} + 11820 q^{54} - 4185 q^{55} - 2368 q^{56} - 78040 q^{57} - 47100 q^{58} + 31430 q^{59} + 28160 q^{60} - 18362 q^{61} - 15828 q^{62} - 95886 q^{63} - 24576 q^{64} - 193280 q^{65} + 28992 q^{66} - 71657 q^{67} - 10432 q^{68} + 245919 q^{69} - 107460 q^{70} - 153827 q^{71} - 1792 q^{72} + 108264 q^{73} - 27648 q^{74} + 126020 q^{75} + 85920 q^{76} + 96141 q^{77} - 55724 q^{78} + 66670 q^{79} - 33280 q^{80} + 17709 q^{81} - 42408 q^{82} - 30621 q^{83} - 140352 q^{84} - 64895 q^{85} - 94444 q^{86} - 265360 q^{87} - 20928 q^{88} + 351835 q^{89} - 101720 q^{90} + 19323 q^{91} - 67856 q^{92} + 707998 q^{93} + 119212 q^{94} + 158570 q^{95} - 11264 q^{96} + 11058 q^{97} + 18532 q^{98} - 455966 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 11 * q^3 - 96 * q^4 - 120 * q^5 - 44 * q^6 + 548 * q^7 - 384 * q^8 - 893 * q^9 + 320 * q^10 - 327 * q^11 - 96 * q^12 - 1161 * q^13 - 948 * q^14 + 760 * q^15 - 1536 * q^16 + 83 * q^17 + 7368 * q^18 - 6250 * q^19 + 2320 * q^20 + 6193 * q^21 + 852 * q^22 + 2069 * q^23 + 2176 * q^24 - 14380 * q^25 + 15976 * q^26 - 18935 * q^27 - 592 * q^28 - 11775 * q^29 - 9840 * q^30 + 2103 * q^31 + 24576 * q^32 - 11747 * q^33 + 972 * q^34 + 33235 * q^35 - 14288 * q^36 + 4148 * q^37 + 14260 * q^38 - 12576 * q^39 + 1600 * q^40 - 26427 * q^41 + 24772 * q^42 + 13024 * q^43 + 3408 * q^44 - 65535 * q^45 - 16964 * q^46 + 29803 * q^47 - 1536 * q^48 + 38368 * q^49 - 14020 * q^50 + 194058 * q^51 - 18576 * q^52 - 29011 * q^53 + 11820 * q^54 - 4185 * q^55 - 2368 * q^56 - 78040 * q^57 - 47100 * q^58 + 31430 * q^59 + 28160 * q^60 - 18362 * q^61 - 15828 * q^62 - 95886 * q^63 - 24576 * q^64 - 193280 * q^65 + 28992 * q^66 - 71657 * q^67 - 10432 * q^68 + 245919 * q^69 - 107460 * q^70 - 153827 * q^71 - 1792 * q^72 + 108264 * q^73 - 27648 * q^74 + 126020 * q^75 + 85920 * q^76 + 96141 * q^77 - 55724 * q^78 + 66670 * q^79 - 33280 * q^80 + 17709 * q^81 - 42408 * q^82 - 30621 * q^83 - 140352 * q^84 - 64895 * q^85 - 94444 * q^86 - 265360 * q^87 - 20928 * q^88 + 351835 * q^89 - 101720 * q^90 + 19323 * q^91 - 67856 * q^92 + 707998 * q^93 + 119212 * q^94 + 158570 * q^95 - 11264 * q^96 + 11058 * q^97 + 18532 * q^98 - 455966 * q^99

Introduction

L-functions

Modular forms

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