LMFDB - Embedded newform 50.6.d.a.21.6

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			21.6
Character	$\chi$	$=$	50.21
Dual form			50.6.d.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 - 3.80423i) q^{2} +(19.6428 + 14.2713i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-42.2315 + 36.6265i) q^{5} +(78.5712 - 57.0853i) q^{6} +208.145 q^{7} +(-51.7771 + 37.6183i) q^{8} +(107.078 + 329.551i) q^{9} +O(q^{10})$	\(q+(1.23607 - 3.80423i) q^{2} +(19.6428 + 14.2713i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-42.2315 + 36.6265i) q^{5} +(78.5712 - 57.0853i) q^{6} +208.145 q^{7} +(-51.7771 + 37.6183i) q^{8} +(107.078 + 329.551i) q^{9} +(87.1346 + 205.931i) q^{10} +(-78.0392 + 240.180i) q^{11} +(-120.046 - 369.464i) q^{12} +(146.158 + 449.827i) q^{13} +(257.281 - 791.829i) q^{14} +(-1352.25 + 116.748i) q^{15} +(79.1084 + 243.470i) q^{16} +(1742.17 - 1265.76i) q^{17} +1386.04 q^{18} +(-1523.40 + 1106.82i) q^{19} +(891.112 - 76.9350i) q^{20} +(4088.54 + 2970.50i) q^{21} +(817.237 + 593.757i) q^{22} +(935.235 - 2878.36i) q^{23} -1553.91 q^{24} +(441.996 - 3093.58i) q^{25} +1891.91 q^{26} +(-776.627 + 2390.21i) q^{27} +(-2694.28 - 1957.51i) q^{28} +(-6038.94 - 4387.55i) q^{29} +(-1227.34 + 5288.59i) q^{30} +(-2495.39 + 1813.01i) q^{31} +1024.00 q^{32} +(-4960.59 + 3604.08i) q^{33} +(-2661.81 - 8192.20i) q^{34} +(-8790.25 + 7623.61i) q^{35} +(1713.24 - 5272.82i) q^{36} +(1100.98 + 3388.45i) q^{37} +(2327.55 + 7163.47i) q^{38} +(-3548.69 + 10921.7i) q^{39} +(808.797 - 3485.09i) q^{40} +(-2421.84 - 7453.67i) q^{41} +(16354.2 - 11882.0i) q^{42} -1729.68 q^{43} +(3268.95 - 2375.03i) q^{44} +(-16592.4 - 9995.55i) q^{45} +(-9793.91 - 7115.69i) q^{46} +(-14675.1 - 10662.1i) q^{47} +(-1920.74 + 5911.42i) q^{48} +26517.1 q^{49} +(-11222.4 - 5505.33i) q^{50} +52285.3 q^{51} +(2338.52 - 7197.24i) q^{52} +(21104.2 + 15333.1i) q^{53} +(8132.94 + 5908.93i) q^{54} +(-5501.24 - 13001.5i) q^{55} +(-10777.1 + 7830.03i) q^{56} -45719.6 q^{57} +(-24155.8 + 17550.2i) q^{58} +(-4796.32 - 14761.5i) q^{59} +(18601.9 + 11206.1i) q^{60} +(596.158 - 1834.79i) q^{61} +(3812.62 + 11734.0i) q^{62} +(22287.6 + 68594.2i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-22648.1 - 13643.6i) q^{65} +(7579.11 + 23326.1i) q^{66} +(7008.56 - 5092.02i) q^{67} -34455.1 q^{68} +(59448.6 - 43191.9i) q^{69} +(18136.6 + 42863.4i) q^{70} +(-14144.0 - 10276.2i) q^{71} +(-17941.3 - 13035.1i) q^{72} +(4560.00 - 14034.2i) q^{73} +14251.3 q^{74} +(52831.6 - 54458.8i) q^{75} +30128.5 q^{76} +(-16243.4 + 49992.1i) q^{77} +(37162.3 + 27000.0i) q^{78} +(57236.3 + 41584.6i) q^{79} +(-12258.3 - 7384.65i) q^{80} +(18754.3 - 13625.8i) q^{81} -31349.0 q^{82} +(11873.1 - 8626.33i) q^{83} +(-24986.9 - 76901.9i) q^{84} +(-27214.1 + 117265. i) q^{85} +(-2138.01 + 6580.10i) q^{86} +(-56005.6 - 172368. i) q^{87} +(-4994.51 - 15371.5i) q^{88} +(14304.0 - 44023.1i) q^{89} +(-58534.6 + 50765.9i) q^{90} +(30421.9 + 93629.1i) q^{91} +(-39175.6 + 28462.8i) q^{92} -74890.6 q^{93} +(-58700.5 + 42648.4i) q^{94} +(23796.7 - 102539. i) q^{95} +(20114.2 + 14613.8i) q^{96} +(-386.278 - 280.648i) q^{97} +(32777.0 - 100877. i) q^{98} -87507.8 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 $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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
$3$	19.6428	+	14.2713i	1.26009	+	0.915506i	0.998762	−	0.0497448i	$-0.0158408\pi$
$3$	19.6428	+	14.2713i	1.26009	+	0.915506i	0.261324	+	0.965251i	$0.415841\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−42.2315	+	36.6265i	−0.755460	+	0.655195i
$5$	−42.2315	+	36.6265i	−0.755460	+	0.655195i
$6$	78.5712	−	57.0853i	0.891016	−	0.647361i
$7$	208.145			1.60554			0.802768	−	0.596292i	$-0.203360\pi$
$7$	208.145			1.60554			0.802768	+	0.596292i	$0.203360\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$	107.078	+	329.551i	0.440649	+	1.35618i
$10$	87.1346	+	205.931i	0.275544	+	0.651211i
$11$	−78.0392	+	240.180i	−0.194460	+	0.598487i	0.805522	+	0.592566i	$0.201885\pi$
$11$	−78.0392	+	240.180i	−0.194460	+	0.598487i	−0.999982	+	0.00592157i	$0.998115\pi$
$12$	−120.046	−	369.464i	−0.240655	−	0.740660i
$13$	146.158	+	449.827i	0.239863	+	0.738223i	0.996439	+	0.0843168i	$0.0268708\pi$
$13$	146.158	+	449.827i	0.239863	+	0.738223i	−0.756576	+	0.653906i	$0.773129\pi$
$14$	257.281	−	791.829i	0.350822	−	1.07972i
$15$	−1352.25	+	116.748i	−1.55178	+	0.133974i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	1742.17	−	1265.76i	1.46207	−	1.06226i	0.479257	−	0.877675i	$-0.340906\pi$
$17$	1742.17	−	1265.76i	1.46207	−	1.06226i	0.982817	−	0.184584i	$-0.0590939\pi$
$18$	1386.04			1.00831
$19$	−1523.40	+	1106.82i	−0.968123	+	0.703382i	−0.955023	−	0.296532i	$-0.904170\pi$
$19$	−1523.40	+	1106.82i	−0.968123	+	0.703382i	−0.0130999	+	0.999914i	$0.504170\pi$
$20$	891.112	−	76.9350i	0.498147	−	0.0430080i
$21$	4088.54	+	2970.50i	2.02311	+	1.46988i
$22$	817.237	+	593.757i	0.359991	+	0.261548i
$23$	935.235	−	2878.36i	0.368639	−	1.13455i	−0.579032	−	0.815305i	$-0.696569\pi$
$23$	935.235	−	2878.36i	0.368639	−	1.13455i	0.947671	−	0.319249i	$-0.103431\pi$
$24$	−1553.91			−0.550678
$25$	441.996	−	3093.58i	0.141439	−	0.989947i
$26$	1891.91			0.548866
$27$	−776.627	+	2390.21i	−0.205023	+	0.630997i
$28$	−2694.28	−	1957.51i	−0.649453	−	0.471855i
$29$	−6038.94	−	4387.55i	−1.33342	−	0.968784i	−0.999659	−	0.0261255i	$-0.991683\pi$
$29$	−6038.94	−	4387.55i	−1.33342	−	0.968784i	−0.333758	−	0.942659i	$-0.608317\pi$
$30$	−1227.34	+	5288.59i	−0.248979	+	1.07284i
$31$	−2495.39	+	1813.01i	−0.466374	+	0.338841i	−0.796027	−	0.605262i	$-0.793069\pi$
$31$	−2495.39	+	1813.01i	−0.466374	+	0.338841i	0.329652	+	0.944102i	$0.393069\pi$
$32$	1024.00			0.176777
$33$	−4960.59	+	3604.08i	−0.792955	+	0.576116i
$34$	−2661.81	−	8192.20i	−0.394893	−	1.21535i
$35$	−8790.25	+	7623.61i	−1.21292	+	1.05194i
$36$	1713.24	−	5272.82i	0.220324	−	0.678089i
$37$	1100.98	+	3388.45i	0.132213	+	0.406909i	0.995146	−	0.0984088i	$-0.0313753\pi$
$37$	1100.98	+	3388.45i	0.132213	+	0.406909i	−0.862933	+	0.505318i	$0.831375\pi$
$38$	2327.55	+	7163.47i	0.261481	+	0.804756i
$39$	−3548.69	+	10921.7i	−0.373599	+	1.14982i
$40$	808.797	−	3485.09i	0.0799263	−	0.344401i
$41$	−2421.84	−	7453.67i	−0.225002	−	0.692485i	−0.998291	−	0.0584320i	$-0.981390\pi$
$41$	−2421.84	−	7453.67i	−0.225002	−	0.692485i	0.773289	−	0.634053i	$-0.218610\pi$
$42$	16354.2	−	11882.0i	1.43056	−	1.03936i
$43$	−1729.68			−0.142658			−0.0713289	−	0.997453i	$-0.522724\pi$
$43$	−1729.68			−0.142658			−0.0713289	+	0.997453i	$0.522724\pi$
$44$	3268.95	−	2375.03i	0.254552	−	0.184943i
$45$	−16592.4	−	9995.55i	−1.22145	−	0.735826i
$46$	−9793.91	−	7115.69i	−0.682435	−	0.495818i
$47$	−14675.1	−	10662.1i	−0.969030	−	0.704041i	−0.0137995	−	0.999905i	$-0.504393\pi$
$47$	−14675.1	−	10662.1i	−0.969030	−	0.704041i	−0.955230	+	0.295863i	$0.904393\pi$
$48$	−1920.74	+	5911.42i	−0.120328	+	0.370330i
$49$	26517.1			1.57774
$50$	−11222.4	−	5505.33i	−0.634832	−	0.311429i
$51$	52285.3			2.81484
$52$	2338.52	−	7197.24i	0.119932	−	0.369111i
$53$	21104.2	+	15333.1i	1.03200	+	0.749790i	0.968707	−	0.248206i	$-0.0798409\pi$
$53$	21104.2	+	15333.1i	1.03200	+	0.749790i	0.0632894	+	0.997995i	$0.479841\pi$
$54$	8132.94	+	5908.93i	0.379545	+	0.275756i
$55$	−5501.24	−	13001.5i	−0.245219	−	0.579542i
$56$	−10777.1	+	7830.03i	−0.459232	+	0.333652i
$57$	−45719.6			−1.86387
$58$	−24155.8	+	17550.2i	−0.942868	+	0.685034i
$59$	−4796.32	−	14761.5i	−0.179382	−	0.552080i	0.820425	−	0.571754i	$-0.193737\pi$
$59$	−4796.32	−	14761.5i	−0.179382	−	0.552080i	−0.999806	+	0.0196747i	$0.993737\pi$
$60$	18601.9	+	11206.1i	0.667082	+	0.401863i
$61$	596.158	−	1834.79i	0.0205134	−	0.0631336i	−0.940276	−	0.340414i	$-0.889433\pi$
$61$	596.158	−	1834.79i	0.0205134	−	0.0631336i	0.960789	+	0.277280i	$0.0894329\pi$
$62$	3812.62	+	11734.0i	0.125963	+	0.387676i
$63$	22287.6	+	68594.2i	0.707477	+	2.17739i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−22648.1	−	13643.6i	−0.664887	−	0.400540i
$66$	7579.11	+	23326.1i	0.214170	+	0.659147i
$67$	7008.56	−	5092.02i	0.190740	−	0.138581i	−0.488317	−	0.872666i	$-0.662389\pi$
$67$	7008.56	−	5092.02i	0.190740	−	0.138581i	0.679057	+	0.734086i	$0.262389\pi$
$68$	−34455.1			−0.903611
$69$	59448.6	−	43191.9i	1.50321	−	1.09214i
$70$	18136.6	+	42863.4i	0.442395	+	1.04554i
$71$	−14144.0	−	10276.2i	−0.332986	−	0.241929i	0.408711	−	0.912664i	$-0.365979\pi$
$71$	−14144.0	−	10276.2i	−0.332986	−	0.241929i	−0.741697	+	0.670736i	$0.765979\pi$
$72$	−17941.3	−	13035.1i	−0.407871	−	0.296336i
$73$	4560.00	−	14034.2i	0.100151	−	0.308235i	−0.888410	−	0.459050i	$-0.848190\pi$
$73$	4560.00	−	14034.2i	0.100151	−	0.308235i	0.988562	+	0.150815i	$0.0481899\pi$
$74$	14251.3			0.302535
$75$	52831.6	−	54458.8i	1.08453	−	1.11793i
$76$	30128.5			0.598333
$77$	−16243.4	+	49992.1i	−0.312213	+	0.960892i
$78$	37162.3	+	27000.0i	0.691618	+	0.502490i
$79$	57236.3	+	41584.6i	1.03182	+	0.749661i	0.968672	−	0.248343i	$-0.0798859\pi$
$79$	57236.3	+	41584.6i	1.03182	+	0.749661i	0.0631483	+	0.998004i	$0.479886\pi$
$80$	−12258.3	−	7384.65i	−0.214144	−	0.129005i
$81$	18754.3	−	13625.8i	0.317605	−	0.230754i
$82$	−31349.0			−0.514860
$83$	11873.1	−	8626.33i	0.189178	−	0.137446i	−0.489165	−	0.872191i	$-0.662698\pi$
$83$	11873.1	−	8626.33i	0.189178	−	0.137446i	0.678343	+	0.734746i	$0.262698\pi$
$84$	−24986.9	−	76901.9i	−0.386380	−	1.18916i
$85$	−27214.1	+	117265.i	−0.408551	+	1.76044i
$86$	−2138.01	+	6580.10i	−0.0311719	+	0.0959371i
$87$	−56005.6	−	172368.i	−0.793292	−	2.44150i
$88$	−4994.51	−	15371.5i	−0.0687521	−	0.211597i
$89$	14304.0	−	44023.1i	0.191418	−	0.589123i	−0.808582	−	0.588383i	$-0.799765\pi$
$89$	14304.0	−	44023.1i	0.191418	−	0.589123i	1.00000		0.000739538i	$-0.000235402\pi$
$90$	−58534.6	+	50765.9i	−0.761739	+	0.660641i
$91$	30421.9	+	93629.1i	0.385109	+	1.18524i
$92$	−39175.6	+	28462.8i	−0.482554	+	0.350596i
$93$	−74890.6			−0.897883
$94$	−58700.5	+	42648.4i	−0.685208	+	0.497832i
$95$	23796.7	−	102539.i	0.270525	−	1.16569i
$96$	20114.2	+	14613.8i	0.222754	+	0.161840i
$97$	−386.278	−	280.648i	−0.00416842	−	0.00302853i	0.585699	−	0.810529i	$-0.300820\pi$
$97$	−386.278	−	280.648i	−0.00416842	−	0.00302853i	−0.589868	+	0.807500i	$0.700820\pi$
$98$	32777.0	−	100877.i	0.344750	−	1.06103i
$99$	−87507.8			−0.897343
$100$	−34815.1	+	35887.4i	−0.348151	+	0.358874i
$101$	−108246.			−1.05587			−0.527935	−	0.849285i	$-0.677033\pi$
$101$	−108246.			−1.05587			−0.527935	+	0.849285i	$0.677033\pi$
$102$	64628.2	−	198905.i	0.615066	−	1.89298i
$103$	28354.6	+	20600.8i	0.263348	+	0.191334i	0.711622	−	0.702563i	$-0.247961\pi$
$103$	28354.6	+	20600.8i	0.263348	+	0.191334i	−0.448274	+	0.893896i	$0.647961\pi$
$104$	−24489.3	−	17792.5i	−0.222021	−	0.161308i
$105$	−281464.	+	24300.5i	−2.49144	+	0.215100i
$106$	84416.6	−	61332.3i	0.729732	−	0.530181i
$107$	97114.4			0.820019			0.410010	−	0.912081i	$-0.365525\pi$
$107$	97114.4			0.820019			0.410010	+	0.912081i	$0.365525\pi$
$108$	32531.8	−	23635.7i	0.268379	−	0.194989i
$109$	−30196.5	−	92935.1i	−0.243439	−	0.749227i	−0.995889	−	0.0905786i	$-0.971128\pi$
$109$	−30196.5	−	92935.1i	−0.243439	−	0.749227i	0.752451	−	0.658649i	$-0.228872\pi$
$110$	−56260.4	+	4857.29i	−0.443324	+	0.0382747i
$111$	−26731.5	+	82271.1i	−0.205928	+	0.633782i
$112$	16466.0	+	50677.0i	0.124034	+	0.381739i
$113$	33868.8	+	104238.i	0.249519	+	0.767942i	0.994860	+	0.101258i	$0.0322868\pi$
$113$	33868.8	+	104238.i	0.249519	+	0.767942i	−0.745341	+	0.666684i	$0.767713\pi$
$114$	−56512.6	+	173928.i	−0.407270	+	1.25345i
$115$	65927.8	+	155812.i	0.464862	+	1.09864i
$116$	36906.7	+	113587.i	0.254660	+	0.783763i
$117$	−132591.	+	96332.9i	−0.895465	+	0.650594i
$118$	−62084.8			−0.410469
$119$	362624.	−	263462.i	2.34741	−	1.70549i
$120$	65623.9	−	56914.3i	0.416015	−	0.360801i
$121$	78696.8	+	57176.5i	0.488645	+	0.355021i
$122$	−6243.05	−	4535.84i	−0.0379749	−	0.0275904i
$123$	58802.0	−	180974.i	0.350453	−	1.07858i
$124$	49351.6			0.288235
$125$	94641.1	+	146835.i	0.541757	+	0.840535i
$126$	288497.			1.61888
$127$	36089.8	−	111073.i	0.198552	−	0.611081i	−0.801364	−	0.598177i	$-0.795892\pi$
$127$	36089.8	−	111073.i	0.198552	−	0.611081i	0.999917	−	0.0129048i	$-0.00410784\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$	−33975.8	−	24684.9i	−0.179761	−	0.130604i
$130$	−79898.0	+	69293.9i	−0.414646	+	0.359614i
$131$	−103894.	+	75483.1i	−0.528945	+	0.384301i	−0.819963	−	0.572417i	$-0.806006\pi$
$131$	−103894.	+	75483.1i	−0.528945	+	0.384301i	0.291018	+	0.956718i	$0.406006\pi$
$132$	98106.1			0.490073
$133$	−317088.	+	230378.i	−1.55436	+	1.12931i
$134$	−10708.1	−	32956.2i	−0.0515171	−	0.158553i
$135$	−54747.0	−	129387.i	−0.258539	−	0.611023i
$136$	−42588.9	+	131075.i	−0.197446	+	0.607677i
$137$	69447.0	+	213736.i	0.316120	+	0.972918i	0.975291	+	0.220924i	$0.0709074\pi$
$137$	69447.0	+	213736.i	0.316120	+	0.972918i	−0.659171	+	0.751993i	$0.729093\pi$
$138$	−90829.4	−	279544.i	−0.406002	−	1.24955i
$139$	−20858.5	+	64195.9i	−0.0915685	+	0.281819i	−0.986344	−	0.164697i	$-0.947335\pi$
$139$	−20858.5	+	64195.9i	−0.0915685	+	0.281819i	0.894776	+	0.446516i	$0.147335\pi$
$140$	185480.	−	16013.6i	0.799792	−	0.0690508i
$141$	−136098.	−	418867.i	−0.576507	−	1.77431i
$142$	−56576.0	+	41104.8i	−0.235457	+	0.171069i
$143$	−119445.			−0.488461
$144$	−71765.2	+	52140.5i	−0.288408	+	0.209541i
$145$	415734.	−	35892.8i	1.64209	−	0.141771i
$146$	−47752.9	−	34694.5i	−0.185403	−	0.134703i
$147$	520871.	+	378435.i	1.98809	+	1.44443i
$148$	17615.6	−	54215.3i	0.0661064	−	0.203455i
$149$	−473120.			−1.74584			−0.872922	−	0.487860i	$-0.837778\pi$
$149$	−473120.			−1.74584			−0.872922	+	0.487860i	$0.837778\pi$
$150$	−141870.	−	268298.i	−0.514829	−	0.973620i
$151$	−282379.			−1.00783			−0.503917	−	0.863752i	$-0.668108\pi$
$151$	−282379.			−1.00783			−0.503917	+	0.863752i	$0.668108\pi$
$152$	37240.8	−	114615.i	0.130741	−	0.402378i
$153$	603682.	+	438600.i	2.08487	+	1.51475i
$154$	170103.	+	123587.i	0.577978	+	0.419925i
$155$	38979.9	−	167964.i	0.130320	−	0.561547i
$156$	148649.	−	108000.i	0.489048	−	0.355314i
$157$	−455640.			−1.47527			−0.737637	−	0.675197i	$-0.764059\pi$
$157$	−455640.			−1.47527			−0.737637	+	0.675197i	$0.764059\pi$
$158$	228945.	−	166339.i	0.729607	−	0.530091i
$159$	195721.	+	602369.i	0.613968	+	1.88960i
$160$	−43245.0	+	37505.6i	−0.133548	+	0.115823i
$161$	194664.	−	599114.i	0.591863	−	1.82157i
$162$	−28654.0	−	88187.8i	−0.0857822	−	0.264010i
$163$	185765.	+	571726.i	0.547640	+	1.68546i	0.714629	+	0.699503i	$0.246595\pi$
$163$	185765.	+	571726.i	0.547640	+	1.68546i	−0.166990	+	0.985959i	$0.553405\pi$
$164$	−38749.5	+	119259.i	−0.112501	+	0.346243i
$165$	77488.2	−	333895.i	0.221578	−	0.954773i
$166$	−18140.5	−	55830.8i	−0.0510952	−	0.157255i
$167$	−491934.	+	357411.i	−1.36495	+	0.991692i	−0.366834	+	0.930287i	$0.619558\pi$
$167$	−491934.	+	357411.i	−1.36495	+	0.991692i	−0.998113	+	0.0614053i	$0.980442\pi$
$168$	−323438.			−0.884133
$169$	119400.	−	86749.1i	0.321579	−	0.233641i
$170$	412464.	+	248476.i	1.09462	+	0.659420i
$171$	−527875.	−	383523.i	−1.38051	−	1.00300i
$172$	22389.5	+	16266.9i	0.0577063	+	0.0419261i
$173$	203091.	−	625049.i	0.515911	−	1.58781i	−0.265708	−	0.964054i	$-0.585606\pi$
$173$	203091.	−	625049.i	0.515911	−	1.58781i	0.781619	−	0.623756i	$-0.214394\pi$
$174$	−724952.			−1.81525
$175$	91999.0	−	643913.i	0.227085	−	1.58939i
$176$	−64650.2			−0.157322
$177$	116454.	−	358408.i	0.279396	−	0.859893i
$178$	−149793.	−	108831.i	−0.354358	−	0.257456i
$179$	160614.	+	116693.i	0.374672	+	0.272215i	0.759145	−	0.650921i	$-0.225617\pi$
$179$	160614.	+	116693.i	0.374672	+	0.272215i	−0.384474	+	0.923136i	$0.625617\pi$
$180$	120772.	+	285429.i	0.277834	+	0.656624i
$181$	−610250.	+	443372.i	−1.38456	+	1.00594i	−0.388120	+	0.921609i	$0.626875\pi$
$181$	−610250.	+	443372.i	−1.38456	+	1.00594i	−0.996438	+	0.0843313i	$0.973125\pi$
$182$	393790.			0.881223
$183$	37895.0	−	27532.4i	0.0836478	−	0.0607737i
$184$	59855.0	+	184215.i	0.130333	+	0.401125i
$185$	−170603.	−	102775.i	−0.366486	−	0.220778i
$186$	−92569.8	+	284901.i	−0.196195	+	0.603825i
$187$	168053.	+	517214.i	0.351433	+	1.08160i
$188$	89686.4	+	276026.i	0.185068	+	0.569581i
$189$	−161651.	+	497509.i	−0.329172	+	1.01309i
$190$	−360669.	−	217274.i	−0.724811	−	0.436640i
$191$	48184.0	+	148295.i	0.0955696	+	0.294133i	0.987402	−	0.158234i	$-0.0505799\pi$
$191$	48184.0	+	148295.i	0.0955696	+	0.294133i	−0.891832	+	0.452367i	$0.850580\pi$
$192$	80456.9	−	58455.4i	0.157511	−	0.114438i
$193$	45585.1			0.0880906			0.0440453	−	0.999030i	$-0.485975\pi$
$193$	45585.1			0.0880906			0.0440453	+	0.999030i	$0.485975\pi$
$194$	−1545.11	+	1122.59i	−0.00294751	+	0.00214149i
$195$	−250159.	−	591217.i	−0.471117	−	1.11342i
$196$	−343245.	−	249382.i	−0.638211	−	0.463687i
$197$	−249296.	−	181124.i	−0.457667	−	0.332515i	0.334948	−	0.942236i	$-0.391281\pi$
$197$	−249296.	−	181124.i	−0.457667	−	0.332515i	−0.792615	+	0.609722i	$0.791281\pi$
$198$	−108166.	+	332899.i	−0.196077	+	0.603462i
$199$	350578.			0.627555			0.313778	−	0.949497i	$-0.398405\pi$
$199$	350578.			0.627555			0.313778	+	0.949497i	$0.398405\pi$
$200$	93490.0	+	176804.i	0.165269	+	0.312548i
$201$	210338.			0.367220
$202$	−133800.	+	411794.i	−0.230716	+	0.710071i
$203$	−1.25697e6	−	913244.i	−2.14085	−	1.55542i
$204$	−676795.	−	491721.i	−1.13863	−	0.827262i
$205$	375280.	+	226076.i	0.623693	+	0.375724i
$206$	113418.	−	82403.3i	0.186215	−	0.135293i
$207$	1.04871e6			1.70110
$208$	−97957.4	+	71170.2i	−0.156992	+	0.114062i
$209$	−146950.	−	452265.i	−0.232704	−	0.716189i
$210$	−255464.	+	1.10079e6i	−0.399744	+	1.72249i
$211$	121441.	−	373756.i	0.187784	−	0.577939i	−0.812201	−	0.583377i	$-0.801731\pi$
$211$	121441.	−	373756.i	0.187784	−	0.577939i	0.999985	+	0.00543805i	$0.00173099\pi$
$212$	−128977.	−	396951.i	−0.197094	−	0.606592i
$213$	−131172.	−	403707.i	−0.198104	−	0.609702i
$214$	120040.	−	369445.i	0.179181	−	0.551462i
$215$	73047.1	−	63352.3i	0.107772	−	0.0934687i
$216$	−49704.1	−	152974.i	−0.0724866	−	0.223091i
$217$	−519402.	+	377368.i	−0.748781	+	0.544021i
$218$	−390871.			−0.557048
$219$	289858.	−	210594.i	0.408390	−	0.296713i
$220$	−51063.4	+	220031.i	−0.0711301	+	0.306498i
$221$	824007.	+	598676.i	1.13488	+	0.824539i
$222$	279936.	+	203385.i	0.381221	+	0.276973i
$223$	211055.	−	649559.i	0.284206	−	0.874695i	−0.702430	−	0.711753i	$-0.747902\pi$
$223$	211055.	−	649559.i	0.284206	−	0.874695i	0.986636	−	0.162942i	$-0.0520984\pi$
$224$	213140.			0.283821
$225$	1.06682e6	−	185593.i	1.40487	−	0.244403i
$226$	438408.			0.570962
$227$	105055.	−	323325.i	0.135316	−	0.416461i	−0.860323	−	0.509750i	$-0.829738\pi$
$227$	105055.	−	323325.i	0.135316	−	0.416461i	0.995639	+	0.0932889i	$0.0297380\pi$
$228$	591807.	+	429973.i	0.753951	+	0.547777i
$229$	−514370.	−	373712.i	−0.648167	−	0.470921i	0.214479	−	0.976729i	$-0.431195\pi$
$229$	−514370.	−	373712.i	−0.648167	−	0.470921i	−0.862646	+	0.505808i	$0.831195\pi$
$230$	674234.	−	58210.6i	0.840410	−	0.0725575i
$231$	−1.03252e6	+	750170.i	−1.27312	+	0.924974i
$232$	477731.			0.582725
$233$	1.14826e6	−	834262.i	1.38564	−	1.00673i	0.389317	−	0.921104i	$-0.372711\pi$
$233$	1.14826e6	−	834262.i	1.38564	−	1.00673i	0.996327	−	0.0856254i	$-0.0272888\pi$
$234$	202581.	+	623479.i	0.241857	+	0.744359i
$235$	1.01027e6	−	87222.4i	1.19335	−	0.103029i
$236$	−76741.1	+	236185.i	−0.0896908	+	0.276040i
$237$	530814.	+	1.63368e6i	0.613863	+	1.88928i
$238$	−554040.	−	1.70516e6i	−0.634014	−	1.95129i
$239$	−444413.	+	1.36776e6i	−0.503260	+	1.54887i	0.300417	+	0.953808i	$0.402874\pi$
$239$	−444413.	+	1.36776e6i	−0.503260	+	1.54887i	−0.803677	+	0.595066i	$0.797126\pi$
$240$	−135399.	−	319998.i	−0.151736	−	0.358607i
$241$	396040.	+	1.21889e6i	0.439235	+	1.35182i	0.888684	+	0.458519i	$0.151620\pi$
$241$	396040.	+	1.21889e6i	0.439235	+	1.35182i	−0.449450	+	0.893306i	$0.648380\pi$
$242$	314787.	−	228706.i	0.345524	−	0.251038i
$243$	1.17356e6			1.27494
$244$	−24972.2	+	18143.4i	−0.0268523	+	0.0195094i
$245$	−1.11986e6	+	971230.i	−1.19192	+	1.03373i
$246$	−615782.	−	447392.i	−0.648768	−	0.471358i
$247$	−720533.	−	523498.i	−0.751470	−	0.545975i
$248$	61001.9	−	187745.i	0.0629817	−	0.193838i
$249$	356331.			0.364213
$250$	675578.	−	178538.i	0.683637	−	0.180667i
$251$	−6830.54			−0.00684338			−0.00342169	−	0.999994i	$-0.501089\pi$
$251$	−6830.54			−0.00684338			−0.00342169	+	0.999994i	$0.501089\pi$
$252$	356602.	−	1.09751e6i	0.353738	−	1.08870i
$253$	618338.	+	449249.i	0.607330	+	0.441251i
$254$	−377937.	−	274587.i	−0.367566	−	0.267052i
$255$	−2.20809e6	+	1.91503e6i	−2.12650	+	1.84427i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−1.32809e6			−1.25428			−0.627139	−	0.778907i	$-0.715774\pi$
$257$	−1.32809e6			−1.25428			−0.627139	+	0.778907i	$0.715774\pi$
$258$	−135903.	+	98739.5i	−0.127110	+	0.0923510i
$259$	229162.	+	705288.i	0.212272	+	0.653307i
$260$	164850.	+	389602.i	0.151236	+	0.357427i
$261$	799286.	−	2.45995e6i	0.726274	−	2.23524i
$262$	158735.	+	488537.i	0.142863	+	0.439687i
$263$	−202933.	−	624562.i	−0.180910	−	0.556783i	0.818944	−	0.573873i	$-0.194560\pi$
$263$	−202933.	−	624562.i	−0.180910	−	0.556783i	−0.999854	+	0.0170900i	$0.994560\pi$
$264$	121266.	−	373218.i	0.107085	−	0.329574i
$265$	−1.45286e6	+	125434.i	−1.27089	+	0.109723i
$266$	484467.	+	1.49104e6i	0.419817	+	1.29206i
$267$	909239.	−	660601.i	0.780548	−	0.567102i
$268$	−138609.			−0.117884
$269$	−439709.	+	319467.i	−0.370497	+	0.269182i	−0.757417	−	0.652931i	$-0.773539\pi$
$269$	−439709.	+	319467.i	−0.370497	+	0.269182i	0.386920	+	0.922113i	$0.373539\pi$
$270$	−559890.	+	48338.6i	−0.467405	+	0.0403538i
$271$	−209880.	−	152487.i	−0.173599	−	0.126127i	0.497593	−	0.867411i	$-0.334217\pi$
$271$	−209880.	−	152487.i	−0.173599	−	0.126127i	−0.671192	+	0.741284i	$0.734217\pi$
$272$	445997.	+	324036.i	0.365518	+	0.265565i
$273$	−738639.	+	2.27330e6i	−0.599827	+	1.84608i
$274$	898941.			0.723360
$275$	708524.	+	347579.i	0.564966	+	0.277155i
$276$	−1.17572e6			−0.929033
$277$	191249.	−	588605.i	0.149762	−	0.460919i	−0.847831	−	0.530267i	$-0.822092\pi$
$277$	191249.	−	588605.i	0.149762	−	0.460919i	0.997593	+	0.0693477i	$0.0220918\pi$
$278$	218433.	+	158701.i	0.169514	+	0.123159i
$279$	−864680.	−	628227.i	−0.665035	−	0.483177i
$280$	168347.	−	725402.i	0.128324	−	0.552947i
$281$	−260617.	+	189350.i	−0.196896	+	0.143054i	−0.681865	−	0.731478i	$-0.738831\pi$
$281$	−260617.	+	189350.i	−0.196896	+	0.143054i	0.484969	+	0.874531i	$0.338831\pi$
$282$	−1.76169e6			−1.31919
$283$	−1.20193e6	+	873257.i	−0.892103	+	0.648151i	−0.936425	−	0.350867i	$-0.885887\pi$
$283$	−1.20193e6	+	873257.i	−0.892103	+	0.648151i	0.0443228	+	0.999017i	$0.485887\pi$
$284$	86440.4	+	266036.i	0.0635947	+	0.195724i
$285$	1.93081e6	−	1.67455e6i	1.40808	−	1.22120i
$286$	−147643.	+	454398.i	−0.106733	+	0.328489i
$287$	−504094.	−	1.55144e6i	−0.361249	−	1.11181i
$288$	109647.	+	337460.i	0.0778964	+	0.239741i
$289$	994254.	−	3.06000e6i	0.700249	−	2.15515i
$290$	377331.	−	1.62591e6i	0.263468	−	1.13528i
$291$	−3582.37	−	11025.4i	−0.00247992	−	0.00763242i
$292$	−191012.	+	138778.i	−0.131100	+	0.0952497i
$293$	53384.5			0.0363284			0.0181642	−	0.999835i	$-0.494218\pi$
$293$	53384.5			0.0363284			0.0181642	+	0.999835i	$0.494218\pi$
$294$	2.08348e6	−	1.51374e6i	1.40579	−	1.02137i
$295$	743219.	+	447729.i	0.497235	+	0.299544i
$296$	−184473.	−	134028.i	−0.122378	−	0.0889129i
$297$	−513473.	−	373060.i	−0.337774	−	0.245407i
$298$	−584808.	+	1.79985e6i	−0.381481	+	1.17408i
$299$	1.43145e6			0.925976
$300$	−1.19603e6	+	208071.i	−0.767252	+	0.133478i
$301$	−360024.			−0.229042
$302$	−349039.	+	1.07423e6i	−0.220220	+	0.677767i
$303$	−2.12626e6	−	1.54482e6i	−1.33049	−	0.966655i
$304$	−389991.	−	283345.i	−0.242031	−	0.175846i
$305$	42025.2	+	99320.9i	0.0258678	+	0.0611352i
$306$	2.41473e6	−	1.75440e6i	1.47423	−	1.07109i
$307$	−893383.			−0.540993			−0.270497	−	0.962721i	$-0.587188\pi$
$307$	−893383.			−0.540993			−0.270497	+	0.962721i	$0.587188\pi$
$308$	680413.	−	494349.i	0.408692	−	0.296932i
$309$	262963.	+	809316.i	0.156674	+	0.482194i
$310$	−590790.	−	355903.i	−0.349163	−	0.210343i
$311$	−607069.	+	1.86836e6i	−0.355907	+	1.09537i	0.599574	+	0.800319i	$0.295337\pi$
$311$	−607069.	+	1.86836e6i	−0.355907	+	1.09537i	−0.955482	+	0.295051i	$0.904663\pi$
$312$	−227116.	−	698991.i	−0.132087	−	0.406523i
$313$	615522.	+	1.89438e6i	0.355126	+	1.09297i	0.955936	+	0.293574i	$0.0948447\pi$
$313$	615522.	+	1.89438e6i	0.355126	+	1.09297i	−0.600810	+	0.799392i	$0.705155\pi$
$314$	−563202.	+	1.73336e6i	−0.322359	+	0.992120i
$315$	−3.45361e6	−	2.08052e6i	−1.96109	−	1.18140i
$316$	−349797.	−	1.07657e6i	−0.197060	−	0.606489i
$317$	−2.35008e6	+	1.70744e6i	−1.31352	+	0.954325i	−0.313527	+	0.949579i	$0.601511\pi$
$317$	−2.35008e6	+	1.70744e6i	−1.31352	+	0.954325i	−0.999989	+	0.00474619i	$0.998489\pi$
$318$	2.53347e6			1.40491
$319$	1.52508e6	−	1.10803e6i	0.839102	−	0.609643i
$320$	89225.8	+	210873.i	0.0487097	+	0.115119i
$321$	1.90760e6	+	1.38595e6i	1.03330	+	0.750733i
$322$	−2.03855e6	−	1.48109e6i	−1.09567	−	0.796053i
$323$	−1.25306e6	+	3.85653e6i	−0.668293	+	2.05679i
$324$	−370905.			−0.196291
$325$	1.45618e6	−	253329.i	0.764727	−	0.133038i
$326$	2.40459e6			1.25313
$327$	733165.	−	2.25645e6i	0.379169	−	1.16696i
$328$	405790.	+	294824.i	0.208265	+	0.151314i
$329$	−3.05455e6	−	2.21926e6i	−1.55581	−	1.13036i
$330$	−1.17443e6	−	707500.i	−0.593667	−	0.357636i
$331$	1.76310e6	−	1.28097e6i	0.884521	−	0.642642i	−0.0499227	−	0.998753i	$-0.515898\pi$
$331$	1.76310e6	−	1.28097e6i	0.884521	−	0.642642i	0.934444	+	0.356111i	$0.115898\pi$
$332$	−234816.			−0.116918
$333$	−998779.	+	725655.i	−0.493581	+	0.358608i
$334$	751608.	+	2.31321e6i	0.368659	+	1.13462i
$335$	−109479.	+	471743.i	−0.0532990	+	0.229664i
$336$	−399791.	+	1.23043e6i	−0.193190	+	0.594578i
$337$	−367148.	−	1.12996e6i	−0.176103	−	0.541988i	0.823579	−	0.567201i	$-0.191974\pi$
$337$	−367148.	−	1.12996e6i	−0.176103	−	0.541988i	−0.999682	+	0.0252127i	$0.991974\pi$
$338$	−182427.	−	561452.i	−0.0868554	−	0.267313i
$339$	−822330.	+	2.53087e6i	−0.388640	+	1.19611i
$340$	1.45509e6	−	1.26197e6i	0.682642	−	0.592042i
$341$	−240710.	−	740829.i	−0.112101	−	0.345010i
$342$	−2.11150e6	+	1.53409e6i	−0.976170	+	0.709229i
$343$	2.02111e6			0.927588
$344$	89557.9	−	65067.7i	0.0408045	−	0.0296462i
$345$	−928632.	+	4.00146e6i	−0.420045	+	1.80997i
$346$	−2.12679e6	−	1.54521e6i	−0.955069	−	0.693898i
$347$	−152085.	−	110496.i	−0.0678053	−	0.0492634i	0.553366	−	0.832938i	$-0.313343\pi$
$347$	−152085.	−	110496.i	−0.0678053	−	0.0492634i	−0.621172	+	0.783675i	$0.713343\pi$
$348$	−896090.	+	2.75788e6i	−0.396646	+	1.22075i
$349$	2.01788e6			0.886812			0.443406	−	0.896321i	$-0.353770\pi$
$349$	2.01788e6			0.886812			0.443406	+	0.896321i	$0.353770\pi$
$350$	−2.33587e6	−	1.14590e6i	−1.01925	−	0.500010i
$351$	−1.18869e6			−0.514993
$352$	−79912.1	+	245944.i	−0.0343760	+	0.105799i
$353$	−1.43948e6	−	1.04584e6i	−0.614850	−	0.446715i	0.236269	−	0.971688i	$-0.424075\pi$
$353$	−1.43948e6	−	1.04584e6i	−0.614850	−	0.446715i	−0.851119	+	0.524973i	$0.824075\pi$
$354$	−1.21952e6	−	886033.i	−0.517226	−	0.375787i
$355$	973703.	−	84065.5i	0.410068	−	0.0354036i
$356$	−599173.	+	435325.i	−0.250569	+	0.182049i
$357$	1.08829e7			4.51933
$358$	642456.	−	466772.i	0.264933	−	0.192485i
$359$	245617.	+	755933.i	0.100583	+	0.309562i	0.988668	−	0.150116i	$-0.0479648\pi$
$359$	245617.	+	755933.i	0.100583	+	0.309562i	−0.888086	+	0.459678i	$0.847965\pi$
$360$	1.23512e6	−	106635.i	0.502288	−	0.0433655i
$361$	330555.	−	1.01734e6i	0.133498	−	0.410865i
$362$	932378.	+	2.86957e6i	0.373956	+	1.15092i
$363$	729839.	+	2.24621e6i	0.290710	+	0.894715i
$364$	486751.	−	1.49807e6i	0.192554	−	0.592621i
$365$	321449.	+	759703.i	0.126293	+	0.298477i
$366$	−57898.5	−	178193.i	−0.0225925	−	0.0695326i
$367$	−22755.4	+	16532.8i	−0.00881901	+	0.00640739i	−0.592186	−	0.805801i	$-0.701735\pi$
$367$	−22755.4	+	16532.8i	−0.00881901	+	0.00640739i	0.583367	+	0.812209i	$0.301735\pi$
$368$	774780.			0.298235
$369$	2.19704e6	−	1.59624e6i	0.839986	−	0.610286i
$370$	−601855.	+	521977.i	−0.228553	+	0.198220i
$371$	4.39271e6	+	3.19149e6i	1.65691	+	1.20381i
$372$	969404.	+	704313.i	0.363201	+	0.263881i
$373$	1.08881e6	−	3.35103e6i	0.405211	−	1.24711i	−0.515507	−	0.856885i	$-0.672396\pi$
$373$	1.08881e6	−	3.35103e6i	0.405211	−	1.24711i	0.920719	−	0.390227i	$-0.127604\pi$
$374$	2.17533e6			0.804165
$375$	−236521.	+	4.23491e6i	−0.0868543	+	1.55513i
$376$	1.16092e6			0.423482
$377$	1.09100e6	−	3.35776e6i	0.395341	−	1.21673i
$378$	1.69283e6	+	1.22991e6i	0.609373	+	0.442735i
$379$	−2.68477e6	−	1.95060e6i	−0.960082	−	0.697541i	−0.00691232	−	0.999976i	$-0.502200\pi$
$379$	−2.68477e6	−	1.95060e6i	−0.960082	−	0.697541i	−0.953170	+	0.302436i	$0.902200\pi$
$380$	−1.27237e6	+	1.10350e6i	−0.452016	+	0.392025i
$381$	2.29406e6	−	1.66673e6i	0.809642	−	0.588239i
$382$	623707.			0.218687
$383$	2.13851e6	−	1.55372e6i	0.744928	−	0.541222i	−0.149323	−	0.988788i	$-0.547709\pi$
$383$	2.13851e6	−	1.55372e6i	0.744928	−	0.541222i	0.894250	+	0.447567i	$0.147709\pi$
$384$	−122927.	−	378331.i	−0.0425422	−	0.130931i
$385$	−1.14505e6	−	2.70618e6i	−0.393708	−	0.930476i
$386$	56346.3	−	173416.i	0.0192485	−	0.0592408i
$387$	−185210.	−	570019.i	−0.0628619	−	0.193469i
$388$	2360.72	+	7265.56i	0.000796097	+	0.00245013i
$389$	44964.4	−	138386.i	0.0150659	−	0.0463680i	−0.943241	−	0.332109i	$-0.892240\pi$
$389$	44964.4	−	138386.i	0.0150659	−	0.0463680i	0.958307	+	0.285741i	$0.0922398\pi$
$390$	−2.55834e6	+	220876.i	−0.851719	+	0.0735339i
$391$	−2.01398e6	−	6.19839e6i	−0.666212	−	2.05039i
$392$	−1.37298e6	+	997528.i	−0.451283	+	0.327876i
$393$	−3.11800e6			−1.01835
$394$	−997184.	+	724497.i	−0.323620	+	0.235123i
$395$	−3.94028e6	+	340187.i	−1.27067	+	0.109705i
$396$	1.13272e6	+	822972.i	0.362983	+	0.263723i
$397$	−520141.	−	377905.i	−0.165632	−	0.120339i	0.501881	−	0.864937i	$-0.332641\pi$
$397$	−520141.	−	377905.i	−0.165632	−	0.120339i	−0.667514	+	0.744598i	$0.732641\pi$
$398$	433338.	−	1.33368e6i	0.137126	−	0.422030i
$399$	−9.51629e6			−2.99251
$400$	788162.	−	137115.i	0.246301	−	0.0428486i
$401$	3.94492e6			1.22512			0.612559	−	0.790425i	$-0.290140\pi$
$401$	3.94492e6			1.22512			0.612559	+	0.790425i	$0.290140\pi$
$402$	259992.	−	800172.i	0.0802406	−	0.246955i
$403$	−1.18026e6	−	857510.i	−0.362006	−	0.263013i
$404$	1.40117e6	+	1.01801e6i	0.427108	+	0.310312i
$405$	−292956.	+	1.26234e6i	−0.0887492	+	0.382418i
$406$	−5.02789e6	+	3.65298e6i	−1.51381	+	1.09985i
$407$	−899758.			−0.269240
$408$	−2.70718e6	+	1.96688e6i	−0.805132	+	0.584962i
$409$	1.35026e6	+	4.15568e6i	0.399126	+	1.22838i	0.925702	+	0.378254i	$0.123475\pi$
$409$	1.35026e6	+	4.15568e6i	0.399126	+	1.22838i	−0.526576	+	0.850128i	$0.676525\pi$
$410$	1.32392e6	−	1.14821e6i	0.388956	−	0.337334i
$411$	−1.68616e6	+	5.18947e6i	−0.492374	+	1.51537i
$412$	−173288.	−	533325.i	−0.0502950	−	0.154792i
$413$	−998327.	−	3.07253e6i	−0.288003	−	0.886383i
$414$	1.29627e6	−	3.98952e6i	0.371703	−	1.14398i
$415$	−185467.	+	799174.i	−0.0528624	+	0.227783i
$416$	149666.	+	460623.i	0.0424022	+	0.130501i
$417$	−1.32588e6	+	963309.i	−0.373391	+	0.271285i
$418$	−1.90216e6			−0.532484
$419$	3.88771e6	−	2.82459e6i	1.08183	−	0.785995i	0.103828	−	0.994595i	$-0.466891\pi$
$419$	3.88771e6	−	2.82459e6i	1.08183	−	0.785995i	0.978001	+	0.208600i	$0.0668907\pi$
$420$	3.87188e6	+	2.33250e6i	1.07102	+	0.645205i
$421$	1.24222e6	+	902528.i	0.341582	+	0.248174i	0.745329	−	0.666697i	$-0.232292\pi$
$421$	1.24222e6	+	902528.i	0.341582	+	0.248174i	−0.403747	+	0.914871i	$0.632292\pi$
$422$	−1.27174e6	−	923976.i	−0.347631	−	0.252569i
$423$	1.94233e6	−	5.97787e6i	0.527803	−	1.62441i
$424$	−1.66952e6			−0.450999
$425$	−3.14571e6	−	5.94903e6i	−0.844786	−	1.59762i
$426$	−1.69793e6			−0.453311
$427$	124087.	−	381901.i	0.0329349	−	0.101363i
$428$	−1.25708e6	−	913319.i	−0.331705	−	0.240998i
$429$	−2.34624e6	−	1.70465e6i	−0.615503	−	0.447189i
$430$	−150715.	−	356195.i	−0.0393084	−	0.0929003i
$431$	−2.03336e6	+	1.47733e6i	−0.527257	+	0.383074i	−0.819331	−	0.573321i	$-0.805655\pi$
$431$	−2.03336e6	+	1.47733e6i	−0.527257	+	0.383074i	0.292074	+	0.956396i	$0.405655\pi$
$432$	−643384.			−0.165867
$433$	−4.36983e6	+	3.17486e6i	−1.12007	+	0.813777i	−0.984219	−	0.176953i	$-0.943376\pi$
$433$	−4.36983e6	+	3.17486e6i	−1.12007	+	0.813777i	−0.135849	+	0.990730i	$0.543376\pi$
$434$	793576.	+	2.44238e6i	0.202239	+	0.622427i
$435$	8.67842e6	+	5.22805e6i	2.19896	+	1.32470i
$436$	−483143.	+	1.48696e6i	−0.121719	+	0.374614i
$437$	1.76107e6	+	5.42003e6i	0.441137	+	1.35768i
$438$	−442864.	−	1.36299e6i	−0.110302	−	0.339476i
$439$	−382654.	+	1.17769e6i	−0.0947644	+	0.291655i	−0.987192	−	0.159535i	$-0.949000\pi$
$439$	−382654.	+	1.17769e6i	−0.0947644	+	0.291655i	0.892428	+	0.451190i	$0.149000\pi$
$440$	773930.	+	466230.i	0.190577	+	0.114807i
$441$	2.83939e6	+	8.73875e6i	0.695231	+	2.13970i
$442$	3.29603e6	−	2.39471e6i	0.802482	−	0.583037i
$443$	8.11585e6			1.96483			0.982414	−	0.186716i	$-0.0597843\pi$
$443$	8.11585e6			1.96483			0.982414	+	0.186716i	$0.0597843\pi$
$444$	1.11974e6	−	813542.i	0.269564	−	0.195849i
$445$	1.00834e6	+	2.38307e6i	0.241382	+	0.570475i
$446$	−2.21019e6	−	1.60580e6i	−0.526130	−	0.382256i
$447$	−9.29340e6	−	6.75205e6i	−2.19991	−	1.59833i
$448$	263455.	−	810833.i	0.0620172	−	0.190869i
$449$	−5.40498e6			−1.26525			−0.632627	−	0.774456i	$-0.718024\pi$
$449$	−5.40498e6			−1.26525			−0.632627	+	0.774456i	$0.718024\pi$
$450$	612625.	−	4.28784e6i	0.142614	−	0.998176i
$451$	1.97922e6			0.458198
$452$	541902.	−	1.66780e6i	0.124760	−	0.383971i
$453$	−5.54670e6	−	4.02992e6i	−1.26996	−	0.922679i
$454$	−1.10015e6	−	799302.i	−0.250501	−	0.182000i
$455$	−4.71407e6	−	2.83984e6i	−1.06750	−	0.643082i
$456$	2.36723e6	−	1.71989e6i	0.533124	−	0.387337i
$457$	−3.17688e6			−0.711557			−0.355778	−	0.934570i	$-0.615784\pi$
$457$	−3.17688e6			−0.711557			−0.355778	+	0.934570i	$0.615784\pi$
$458$	−2.05748e6	+	1.49485e6i	−0.458323	+	0.332991i
$459$	1.67242e6	+	5.14719e6i	0.370523	+	1.14035i
$460$	611953.	−	2.63689e6i	0.134841	−	0.581029i
$461$	388651.	−	1.19614e6i	0.0851741	−	0.262139i	−0.899395	−	0.437138i	$-0.855992\pi$
$461$	388651.	−	1.19614e6i	0.0851741	−	0.262139i	0.984569	+	0.174999i	$0.0559922\pi$
$462$	1.57755e6	+	4.85520e6i	0.343857	+	1.05828i
$463$	1.27845e6	+	3.93467e6i	0.277161	+	0.853013i	0.988640	+	0.150306i	$0.0480258\pi$
$463$	1.27845e6	+	3.93467e6i	0.277161	+	0.853013i	−0.711479	+	0.702708i	$0.751974\pi$
$464$	590508.	−	1.81740e6i	0.127330	−	0.391881i
$465$	3.16274e6	−	2.74298e6i	0.678314	−	0.588288i
$466$	−1.75439e6	−	5.39946e6i	−0.374250	−	1.15182i
$467$	2.00995e6	−	1.46031e6i	0.426474	−	0.309852i	−0.353763	−	0.935335i	$-0.615098\pi$
$467$	2.00995e6	−	1.46031e6i	0.426474	−	0.309852i	0.780238	+	0.625483i	$0.215098\pi$
$468$	2.62226e6			0.553428
$469$	1.45879e6	−	1.05988e6i	0.306240	−	0.222496i
$470$	916946.	−	3.95110e6i	0.191469	−	0.825037i
$471$	−8.95005e6	−	6.50259e6i	−1.85897	−	1.35062i
$472$	803643.	+	583881.i	0.166038	+	0.120634i
$473$	134983.	−	415435.i	0.0277413	−	0.0853788i
$474$	6.87100e6			1.40467
$475$	2.75069e6	+	5.20198e6i	0.559381	+	1.05788i
$476$	−7.17165e6			−1.45078
$477$	−2.79325e6	+	8.59673e6i	−0.562099	+	1.72996i
$478$	4.65395e6	+	3.38130e6i	0.931649	+	0.676883i
$479$	5.40532e6	+	3.92720e6i	1.07642	+	0.782067i	0.977056	−	0.212984i	$-0.0683182\pi$
$479$	5.40532e6	+	3.92720e6i	1.07642	+	0.782067i	0.0993671	+	0.995051i	$0.468318\pi$
$480$	−1.38471e6	+	119550.i	−0.274318	+	0.0236835i
$481$	−1.36330e6	+	990498.i	−0.268677	+	0.195205i
$482$	5.12645e6			1.00508
$483$	1.23739e7	−	8.99016e6i	2.41345	−	1.75348i
$484$	−480952.	−	1.48022e6i	−0.0933229	−	0.287218i
$485$	26592.3	−	2295.87i	0.00513335	−	0.000443192i
$486$	1.45059e6	−	4.46447e6i	0.278584	−	0.857392i
$487$	2.31121e6	+	7.11317e6i	0.441587	+	1.35907i	0.886183	+	0.463335i	$0.153347\pi$
$487$	2.31121e6	+	7.11317e6i	0.441587	+	1.35907i	−0.444596	+	0.895731i	$0.646653\pi$
$488$	38154.1	+	117426.i	0.00725257	+	0.0223211i
$489$	−4.51034e6	+	1.38814e7i	−0.852978	+	2.62519i
$490$	2.31056e6	+	5.46070e6i	0.434737	+	1.02744i
$491$	−1.15172e6	−	3.54462e6i	−0.215597	−	0.663539i	−0.999111	−	0.0421646i	$-0.986575\pi$
$491$	−1.15172e6	−	3.54462e6i	−0.215597	−	0.663539i	0.783514	−	0.621374i	$-0.213425\pi$
$492$	−2.46313e6	+	1.78957e6i	−0.458748	+	0.333300i
$493$	−1.60745e7			−2.97865
$494$	−2.88213e6	+	2.09399e6i	−0.531369	+	0.386062i
$495$	3.69558e6	−	3.20510e6i	0.677907	−	0.587935i
$496$	−638821.	−	464130.i	−0.116594	−	0.0847102i
$497$	−2.94399e6	−	2.13894e6i	−0.534621	−	0.388425i
$498$	440449.	−	1.35556e6i	0.0795834	−	0.244932i
$499$	−358697.			−0.0644877			−0.0322438	−	0.999480i	$-0.510265\pi$
$499$	−358697.			−0.0644877			−0.0322438	+	0.999480i	$0.510265\pi$
$500$	155863.	−	2.79074e6i	0.0278817	−	0.499222i
$501$	−1.47637e7			−2.62785
$502$	−8443.02	+	25984.9i	−0.00149533	+	0.00460217i
$503$	8.41763e6	+	6.11576e6i	1.48344	+	1.07778i	0.976428	+	0.215842i	$0.0692496\pi$
$503$	8.41763e6	+	6.11576e6i	1.48344	+	1.07778i	0.507011	+	0.861940i	$0.330750\pi$
$504$	−3.73438e6	−	2.71319e6i	−0.654851	−	0.475777i
$505$	4.57141e6	−	3.96469e6i	0.797667	−	0.691801i
$506$	2.47335e6	−	1.79700e6i	0.429447	−	0.312012i
$507$	3.58337e6			0.619116
$508$	−1.51175e6	+	1.09835e6i	−0.259908	+	0.188835i
$509$	815759.	+	2.51065e6i	0.139562	+	0.429528i	0.996272	−	0.0862711i	$-0.0274951\pi$
$509$	815759.	+	2.51065e6i	0.139562	+	0.429528i	−0.856710	+	0.515799i	$0.827495\pi$
$510$	4.55586e6	+	1.07672e7i	0.775613	+	1.83306i
$511$	949138.	−	2.92115e6i	0.160797	−	0.494881i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$	−1.46241e6	−	4.50084e6i	−0.245344	−	0.755092i
$514$	−1.64161e6	+	5.05235e6i	−0.274070	+	0.843501i
$515$	−1.95199e6	+	168527.i	−0.324310	+	0.0279996i
$516$	207642.	+	639055.i	0.0343313	+	0.105661i
$517$	3.70606e6	−	2.69261e6i	0.609797	−	0.443044i
$518$	2.96634e6			0.485731
$519$	1.29095e7	−	9.37933e6i	2.10374	−	1.52846i
$520$	1.68590e6	−	145554.i	0.273416	−	0.0236056i
$521$	−445755.	−	323860.i	−0.0719452	−	0.0522712i	0.551231	−	0.834352i	$-0.314158\pi$
$521$	−445755.	−	323860.i	−0.0719452	−	0.0522712i	−0.623176	+	0.782081i	$0.714158\pi$
$522$	−8.37023e6	−	6.08133e6i	−1.34450	−	0.976837i
$523$	1.86835e6	−	5.75020e6i	0.298679	−	0.919240i	−0.683281	−	0.730155i	$-0.739448\pi$
$523$	1.86835e6	−	5.75020e6i	0.298679	−	0.919240i	0.981961	−	0.189085i	$-0.0605522\pi$
$524$	2.05471e6			0.326906
$525$	1.09966e7	−	1.13353e7i	1.74125	−	1.79488i
$526$	−2.62681e6			−0.413966
$527$	−2.05257e6	+	6.31716e6i	−0.321937	+	0.990821i
$528$	−1.26991e6	−	922645.i	−0.198239	−	0.144029i
$529$	−2.20316e6	−	1.60069e6i	−0.342300	−	0.248696i
$530$	−1.31865e6	+	5.68204e6i	−0.203911	+	0.878647i
$531$	4.35110e6	−	3.16126e6i	0.669673	−	0.486546i
$532$	6.27107e6			0.960645
$533$	2.99889e6	−	2.17882e6i	0.457239	−	0.332203i
$534$	−1.38919e6	−	4.27550e6i	−0.210819	−	0.648834i
$535$	−4.10128e6	+	3.55696e6i	−0.619492	+	0.537273i
$536$	−171330.	+	527300.i	−0.0257586	+	0.0792767i
$537$	1.48955e6	+	4.58435e6i	0.222904	+	0.686029i
$538$	671816.	+	2.06764e6i	0.100068	+	0.307977i
$539$	−2.06938e6	+	6.36888e6i	−0.306808	+	0.944259i
$540$	−508171.	+	2.18970e6i	−0.0749938	+	0.323147i
$541$	718887.	+	2.21251e6i	0.105601	+	0.325006i	0.989871	−	0.141970i	$-0.0453435\pi$
$541$	718887.	+	2.21251e6i	0.105601	+	0.325006i	−0.884270	+	0.466976i	$0.845344\pi$
$542$	−839519.	+	609946.i	−0.122753	+	0.0891853i
$543$	−1.83145e7			−2.66561
$544$	1.78399e6	−	1.29614e6i	0.258461	−	0.187783i
$545$	4.67913e6	+	2.81880e6i	0.674798	+	0.406511i
$546$	7.73513e6	+	5.61990e6i	1.11042	+	0.806765i
$547$	7.12517e6	+	5.17674e6i	1.01819	+	0.739755i	0.965910	−	0.258878i	$-0.0833526\pi$
$547$	7.12517e6	+	5.17674e6i	1.01819	+	0.739755i	0.0522755	+	0.998633i	$0.483353\pi$
$548$	1.11115e6	−	3.41977e6i	0.158060	−	0.486459i
$549$	668491.			0.0946596
$550$	2.19805e6	−	2.26575e6i	0.309836	−	0.319379i
$551$	1.40560e7			1.97234
$552$	−1.45327e6	+	4.47271e6i	−0.203001	+	0.624774i
$553$	1.19134e7	+	8.65561e6i	1.65662	+	1.20361i
$554$	−2.00279e6	−	1.45511e6i	−0.277243	−	0.201429i
$555$	−1.88439e6	−	4.45351e6i	−0.259680	−	0.613720i
$556$	873733.	−	634804.i	0.119865	−	0.0870869i
$557$	−4.43842e6			−0.606164			−0.303082	−	0.952964i	$-0.598016\pi$
$557$	−4.43842e6			−0.606164			−0.303082	+	0.952964i	$0.598016\pi$
$558$	−3.45872e6	+	2.51291e6i	−0.470251	+	0.341657i
$559$	−252807.	−	778059.i	−0.0342183	−	0.105313i
$560$	−2.55151e6	−	1.53708e6i	−0.343816	−	0.207121i
$561$	−4.08030e6	+	1.25579e7i	−0.547375	+	1.68465i
$562$	398188.	+	1.22550e6i	0.0531799	+	0.163671i
$563$	393117.	+	1.20989e6i	0.0522698	+	0.160870i	0.973784	−	0.227475i	$-0.0730469\pi$
$563$	393117.	+	1.20989e6i	0.0522698	+	0.160870i	−0.921514	+	0.388345i	$0.873047\pi$
$564$	−2.17757e6	+	6.70187e6i	−0.288253	+	0.887153i
$565$	−5.24819e6	−	3.16161e6i	−0.691654	−	0.416665i
$566$	1.83639e6	+	5.65184e6i	0.240949	+	0.741564i
$567$	3.90360e6	−	2.83613e6i	0.509926	−	0.370483i
$568$	1.11891e6			0.145520
$569$	−5.43750e6	+	3.95057e6i	−0.704074	+	0.511540i	−0.881257	−	0.472638i	$-0.843302\pi$
$569$	−5.43750e6	+	3.95057e6i	−0.704074	+	0.511540i	0.177182	+	0.984178i	$0.443302\pi$
$570$	−3.98376e6	−	9.41509e6i	−0.513578	−	1.21377i
$571$	−1.06021e7	−	7.70290e6i	−1.36083	−	0.988698i	−0.998392	−	0.0566889i	$-0.981946\pi$
$571$	−1.06021e7	−	7.70290e6i	−1.36083	−	0.988698i	−0.362434	−	0.932009i	$-0.618054\pi$
$572$	1.54613e6	+	1.12333e6i	0.197586	+	0.143555i
$573$	−1.16990e6	+	3.60058e6i	−0.148855	+	0.458127i
$574$	−6.52513e6			−0.826626
$575$	−8.49107e6	−	4.16545e6i	−1.07101	−	0.525403i
$576$	1.41931e6			0.178246
$577$	1.52917e6	−	4.70631e6i	0.191213	−	0.588492i	−0.808787	−	0.588101i	$-0.799876\pi$
$577$	1.52917e6	−	4.70631e6i	0.191213	−	0.588492i	1.00000		0.000390704i	$-0.000124365\pi$
$578$	−1.04120e7	−	7.56473e6i	−1.29632	−	0.941833i
$579$	895419.	+	650560.i	0.111002	+	0.0806475i
$580$	−5.71893e6	−	3.44519e6i	−0.705903	−	0.425249i
$581$	2.47133e6	−	1.79552e6i	0.303732	−	0.220674i
$582$	−46371.2			−0.00567467
$583$	−5.32964e6	+	3.87221e6i	−0.649422	+	0.471833i
$584$	291840.	+	898190.i	0.0354089	+	0.108977i
$585$	2.07117e6	−	8.92462e6i	0.250222	−	1.07820i
$586$	65986.9	−	203087.i	0.00793804	−	0.0244308i
$587$	−4.01718e6	−	1.23636e7i	−0.481201	−	1.48098i	−0.837409	−	0.546577i	$-0.815931\pi$
$587$	−4.01718e6	−	1.23636e7i	−0.481201	−	1.48098i	0.356208	−	0.934407i	$-0.384069\pi$
$588$	−3.18328e6	−	9.79713e6i	−0.379692	−	1.16857i
$589$	1.79482e6	−	5.52388e6i	0.213173	−	0.656079i
$590$	2.62193e6	−	2.27395e6i	0.310093	−	0.268937i
$591$	−2.31199e6	−	7.11557e6i	−0.272281	−	0.837994i
$592$	−737892.	+	536110.i	−0.0865344	+	0.0628709i
$593$	−3.04053e6			−0.355069			−0.177535	−	0.984115i	$-0.556812\pi$
$593$	−3.04053e6			−0.355069			−0.177535	+	0.984115i	$0.556812\pi$
$594$	−2.05389e6	+	1.49224e6i	−0.238843	+	0.173529i
$595$	−5.66446e6	+	2.44080e7i	−0.655943	+	2.82644i
$596$	6.12419e6	+	4.44949e6i	0.706209	+	0.513091i
$597$	6.88633e6	+	5.00321e6i	0.790774	+	0.574531i
$598$	1.76938e6	−	5.44558e6i	0.202333	−	0.622717i
$599$	−1.33985e7			−1.52577			−0.762886	−	0.646533i	$-0.776218\pi$
$599$	−1.33985e7			−1.52577			−0.762886	+	0.646533i	$0.776218\pi$
$600$	−686822.	+	4.80715e6i	−0.0778872	+	0.545142i
$601$	−965382.			−0.109022			−0.0545109	−	0.998513i	$-0.517360\pi$
$601$	−965382.			−0.109022			−0.0545109	+	0.998513i	$0.517360\pi$
$602$	−445014.	+	1.36961e6i	−0.0500475	+	0.154030i
$603$	2.42854e6	+	1.76444e6i	0.271989	+	0.197612i
$604$	3.65518e6	+	2.65565e6i	0.407678	+	0.296195i
$605$	−5.41766e6	+	467738.i	−0.601760	+	0.0519535i
$606$	−8.50505e6	+	6.17928e6i	−0.940796	+	0.683528i
$607$	2.63380e6			0.290142			0.145071	−	0.989421i	$-0.453659\pi$
$607$	2.63380e6			0.290142			0.145071	+	0.989421i	$0.453659\pi$
$608$	−1.55996e6	+	1.13338e6i	−0.171142	+	0.124342i
$609$	−1.16573e7	−	3.58774e7i	−1.27366	−	3.91992i
$610$	429785.	−	37105.9i	0.0467656	−	0.00403755i
$611$	2.65122e6	−	8.15962e6i	0.287305	−	0.884233i
$612$	−3.68937e6	−	1.13547e7i	−0.398175	−	1.22546i
$613$	4.06080e6	+	1.24979e7i	0.436476	+	1.34333i	0.891567	+	0.452890i	$0.149607\pi$
$613$	4.06080e6	+	1.24979e7i	0.436476	+	1.34333i	−0.455091	+	0.890445i	$0.650393\pi$
$614$	−1.10428e6	+	3.39863e6i	−0.118211	+	0.363817i
$615$	4.14515e6	+	9.79651e6i	0.441929	+	1.04444i
$616$	−1.03958e6	−	3.19950e6i	−0.110384	−	0.339727i
$617$	3.65978e6	−	2.65898e6i	0.387027	−	0.281192i	−0.377209	−	0.926128i	$-0.623116\pi$
$617$	3.65978e6	−	2.65898e6i	0.387027	−	0.281192i	0.764236	+	0.644936i	$0.223116\pi$
$618$	3.40386e6			0.358509
$619$	2.34047e6	−	1.70045e6i	0.245514	−	0.178377i	−0.458222	−	0.888838i	$-0.651514\pi$
$619$	2.34047e6	−	1.70045e6i	0.245514	−	0.178377i	0.703736	+	0.710461i	$0.251514\pi$
$620$	−2.08419e6	+	1.80758e6i	−0.217750	+	0.188850i
$621$	6.15355e6	+	4.47082e6i	0.640320	+	0.465220i
$622$	6.35730e6	+	4.61885e6i	0.658866	+	0.478694i
$623$	2.97730e6	−	9.16317e6i	0.307328	−	0.945858i
$624$	−2.93985e6			−0.302248
$625$	−9.37490e6	−	2.73470e6i	−0.959990	−	0.280034i
$626$	7.96748e6			0.812616
$627$	3.56792e6	−	1.09809e7i	0.362449	−	1.11550i
$628$	5.89793e6	+	4.28510e6i	0.596761	+	0.433572i
$629$	6.20707e6	+	4.50970e6i	0.625548	+	0.454487i
$630$	−1.21837e7	+	1.05666e7i	−1.22300	+	1.06068i
$631$	−2.40950e6	+	1.75061e6i	−0.240910	+	0.175031i	−0.701688	−	0.712484i	$-0.747570\pi$
$631$	−2.40950e6	+	1.75061e6i	−0.240910	+	0.175031i	0.460779	+	0.887515i	$0.347570\pi$
$632$	−4.52787e6			−0.450922
$633$	7.71943e6	−	5.60849e6i	0.765731	−	0.556336i
$634$	3.59061e6	+	1.10508e7i	0.354769	+	1.09187i
$635$	2.54409e6	+	6.01262e6i	0.250379	+	0.591738i
$636$	3.13154e6	−	9.63790e6i	0.306984	−	0.944799i
$637$	3.87568e6	+	1.19281e7i	0.378442	+	1.16473i
$638$	−2.33011e6	−	7.17133e6i	−0.226634	−	0.697506i
$639$	1.87203e6	−	5.76152e6i	0.181368	−	0.558193i
$640$	912499.	−	78781.4i	0.0880608	−	0.00760280i
$641$	−29975.2	−	92254.2i	−0.00288149	−	0.00886832i	0.949605	−	0.313448i	$-0.101484\pi$
$641$	−29975.2	−	92254.2i	−0.00288149	−	0.00886832i	−0.952487	+	0.304579i	$0.901484\pi$
$642$	7.63039e6	−	5.54381e6i	0.730650	−	0.530848i
$643$	1.25450e7			1.19658			0.598290	−	0.801279i	$-0.295847\pi$
$643$	1.25450e7			1.19658			0.598290	+	0.801279i	$0.295847\pi$
$644$	−8.15419e6	+	5.92437e6i	−0.774758	+	0.562895i
$645$	2.33897e6	−	201937.i	0.221373	−	0.0191125i
$646$	1.31223e7	+	9.53388e6i	1.23716	+	0.898852i
$647$	397547.	+	288835.i	0.0373360	+	0.0271262i	0.606297	−	0.795238i	$-0.292654\pi$
$647$	397547.	+	288835.i	0.0373360	+	0.0271262i	−0.568961	+	0.822365i	$0.692654\pi$
$648$	−458463.	+	1.41101e6i	−0.0428911	+	0.132005i
$649$	3.91973e6			0.365295
$650$	836215.	−	5.85277e6i	0.0776309	−	0.543348i
$651$	−1.55881e7			−1.44158
$652$	2.97224e6	−	9.14762e6i	0.273820	−	0.842731i
$653$	−5.84327e6	−	4.24539e6i	−0.536257	−	0.389614i	0.286436	−	0.958099i	$-0.407529\pi$
$653$	−5.84327e6	−	4.24539e6i	−0.536257	−	0.389614i	−0.822693	+	0.568486i	$0.807529\pi$
$654$	−7.67780e6	−	5.57825e6i	−0.701928	−	0.509981i
$655$	1.62290e6	−	6.99302e6i	0.147804	−	0.636886i
$656$	1.62316e6	−	1.17930e6i	0.147266	−	0.106995i
$657$	5.11327e6			0.462152
$658$	−1.22182e7	+	8.87703e6i	−1.10012	+	0.799287i
$659$	4.78623e6	+	1.47305e7i	0.429319	+	1.32131i	0.898798	+	0.438363i	$0.144442\pi$
$659$	4.78623e6	+	1.47305e7i	0.429319	+	1.32131i	−0.469479	+	0.882944i	$0.655558\pi$
$660$	−4.14317e6	+	3.59328e6i	−0.370231	+	0.321094i
$661$	652942.	−	2.00955e6i	0.0581261	−	0.178894i	−0.917778	−	0.397094i	$-0.870019\pi$
$661$	652942.	−	2.00955e6i	0.0581261	−	0.178894i	0.975904	+	0.218200i	$0.0700186\pi$
$662$	−2.69378e6	−	8.29062e6i	−0.238901	−	0.735261i
$663$	7.64190e6	+	2.35194e7i	0.675177	+	2.07798i
$664$	−290248.	+	893293.i	−0.0255476	+	0.0786274i
$665$	4.95315e6	−	2.13430e7i	0.434338	−	1.87155i
$666$	1.52600e6	+	4.69654e6i	0.133312	+	0.410291i
$667$	−1.82768e7	+	1.32788e7i	−1.59069	+	1.15570i
$668$	9.72902e6			0.843583
$669$	1.34158e7	−	9.74714e6i	1.15891	−	0.841999i
$670$	1.65929e6	+	999589.i	0.142803	+	0.0860269i
$671$	394155.	+	286370.i	0.0337956	+	0.0245540i
$672$	4.18667e6	+	3.04179e6i	0.357639	+	0.259840i
$673$	−4.92092e6	+	1.51450e7i	−0.418802	+	1.28894i	0.490003	+	0.871721i	$0.336996\pi$
$673$	−4.92092e6	+	1.51450e7i	−0.418802	+	1.28894i	−0.908805	+	0.417220i	$0.863004\pi$
$674$	−4.75246e6			−0.402966
$675$	7.05106e6	+	3.45902e6i	0.595655	+	0.292209i
$676$	−2.36138e6			−0.198746
$677$	−1.47179e6	+	4.52969e6i	−0.123416	+	0.379837i	−0.993609	−	0.112875i	$-0.963994\pi$
$677$	−1.47179e6	+	4.52969e6i	−0.123416	+	0.379837i	0.870193	+	0.492711i	$0.163994\pi$
$678$	8.61155e6	+	6.25666e6i	0.719461	+	0.522719i
$679$	−80401.7	−	58415.3i	−0.00669254	−	0.00486241i
$680$	−3.00223e6	−	7.09538e6i	−0.248984	−	0.588442i
$681$	6.67784e6	−	4.85173e6i	0.551783	−	0.400893i
$682$	−3.11581e6			−0.256514
$683$	5.96312e6	−	4.33246e6i	0.489127	−	0.355372i	−0.315721	−	0.948852i	$-0.602247\pi$
$683$	5.96312e6	−	4.33246e6i	0.489127	−	0.355372i	0.804849	+	0.593480i	$0.202247\pi$
$684$	3.22608e6	+	9.92886e6i	0.263655	+	0.811445i
$685$	−1.07613e7	−	6.48278e6i	−0.876267	−	0.527880i
$686$	2.49823e6	−	7.68876e6i	0.202685	−	0.623801i
$687$	−4.77030e6	−	1.46815e7i	−0.385615	−	1.18680i
$688$	−136832.	−	421127.i	−0.0110209	−	0.0339189i
$689$	−3.81270e6	+	1.17343e7i	−0.305974	+	0.941690i
$690$	1.40746e7	+	8.47880e6i	1.12542	+	0.677972i
$691$	3.54736e6	+	1.09176e7i	0.282625	+	0.869829i	0.987101	+	0.160101i	$0.0511820\pi$
$691$	3.54736e6	+	1.09176e7i	0.282625	+	0.869829i	−0.704476	+	0.709728i	$0.748818\pi$
$692$	−8.50717e6	+	6.18082e6i	−0.675336	+	0.490660i
$693$	−1.82143e7			−1.44072
$694$	−608341.	+	441986.i	−0.0479456	+	0.0348345i
$695$	−1.47039e6	−	3.47506e6i	−0.115470	−	0.272898i
$696$	9.38397e6	+	6.81785e6i	0.734283	+	0.533488i
$697$	−1.36539e7	−	9.92011e6i	−1.06457	−	0.773454i
$698$	2.49424e6	−	7.67647e6i	0.193775	−	0.596380i
$699$	3.44611e7			2.66770
$700$	−7.24658e6	+	7.46977e6i	−0.558969	+	0.576185i
$701$	1.87075e7			1.43788			0.718938	−	0.695074i	$-0.244628\pi$
$701$	1.87075e7			1.43788			0.718938	+	0.695074i	$0.244628\pi$
$702$	−1.46930e6	+	4.52205e6i	−0.112530	+	0.346332i
$703$	−5.42763e6	−	3.94340e6i	−0.414211	−	0.300942i
$704$	836850.	+	608007.i	0.0636379	+	0.0462357i
$705$	2.10893e7	+	1.27046e7i	1.59804	+	0.962692i
$706$	−5.75792e6	+	4.18338e6i	−0.434764	+	0.315875i
$707$	−2.25309e7			−1.69524
$708$	−4.87808e6	+	3.54413e6i	−0.365734	+	0.265721i
$709$	−6.91240e6	−	2.12742e7i	−0.516432	−	1.58941i	−0.780661	−	0.624954i	$-0.785118\pi$
$709$	−6.91240e6	−	2.12742e7i	−0.516432	−	1.58941i	0.264229	−	0.964460i	$-0.414882\pi$
$710$	883759.	−	3.80810e6i	0.0657943	−	0.283506i
$711$	−7.57553e6	+	2.33151e7i	−0.562003	+	1.72967i
$712$	915455.	+	2.81748e6i	0.0676764	+	0.208286i
$713$	2.88471e6	+	8.87822e6i	0.212509	+	0.654037i
$714$	1.34520e7	−	4.14010e7i	0.987510	−	3.03924i
$715$	5.04436e6	−	4.37487e6i	0.369012	−	0.320037i
$716$	−981586.	−	3.02101e6i	−0.0715559	−	0.220226i
$717$	−2.82493e7	+	2.05243e7i	−2.05215	+	1.49098i
$718$	3.17934e6			0.230158
$719$	−588964.	+	427907.i	−0.0424880	+	0.0308694i	−0.608827	−	0.793303i	$-0.708359\pi$
$719$	−588964.	+	427907.i	−0.0424880	+	0.0308694i	0.566339	+	0.824173i	$0.308359\pi$
$720$	1.12103e6	−	4.83048e6i	0.0805907	−	0.347263i
$721$	5.90185e6	+	4.28795e6i	0.422815	+	0.307193i
$722$	−3.46161e6	−	2.51501e6i	−0.247136	−	0.179555i
$723$	−9.61579e6	+	2.95943e7i	−0.684131	+	2.10554i
$724$	1.20690e7			0.855704
$725$	−1.62424e7	+	1.67427e7i	−1.14764	+	1.18299i
$726$	9.44724e6			0.665217
$727$	6.63900e6	−	2.04327e7i	0.465872	−	1.43381i	−0.392011	−	0.919961i	$-0.628221\pi$
$727$	6.63900e6	−	2.04327e7i	0.465872	−	1.43381i	0.857883	−	0.513845i	$-0.171779\pi$
$728$	−5.09732e6	−	3.70342e6i	−0.356462	−	0.258985i
$729$	1.84946e7	+	1.34371e7i	1.28892	+	0.936457i
$730$	3.28741e6	−	283822.i	0.228322	−	0.0197124i
$731$	−3.01341e6	+	2.18937e6i	−0.208576	+	0.151539i
$732$	−749454.			−0.0516972
$733$	−6.12571e6	+	4.45059e6i	−0.421111	+	0.305955i	−0.778085	−	0.628159i	$-0.783809\pi$
$733$	−6.12571e6	+	4.45059e6i	−0.421111	+	0.305955i	0.356974	+	0.934114i	$0.383809\pi$
$734$	34767.2	+	107002.i	0.00238193	+	0.00733084i
$735$	−3.58579e7	+	3.09582e6i	−2.44831	+	0.211377i
$736$	957680.	−	2.94744e6i	0.0651667	−	0.200563i
$737$	676058.	+	2.08069e6i	0.0458474	+	0.141104i
$738$	−3.35678e6	−	1.03311e7i	−0.226872	−	0.698242i
$739$	5.91421e6	−	1.82021e7i	0.398369	−	1.22605i	−0.527937	−	0.849284i	$-0.677034\pi$
$739$	5.91421e6	−	1.82021e7i	0.398369	−	1.22605i	0.926306	−	0.376771i	$-0.122966\pi$
$740$	1.24178e6	+	2.93479e6i	0.0833617	+	0.197014i
$741$	−6.68228e6	−	2.05659e7i	−0.447073	−	1.37595i
$742$	1.75709e7	−	1.27660e7i	1.17161	−	0.851225i
$743$	1.15705e7			0.768921			0.384460	−	0.923141i	$-0.374387\pi$
$743$	1.15705e7			0.768921			0.384460	+	0.923141i	$0.374387\pi$
$744$	3.87761e6	−	2.81725e6i	0.256822	−	0.186592i
$745$	1.99805e7	−	1.73287e7i	1.31891	−	1.14387i
$746$	−1.14022e7	−	8.28419e6i	−0.750139	−	0.545008i
$747$	4.11416e6	+	2.98912e6i	0.269762	+	0.195993i
$748$	2.68885e6	−	8.27543e6i	0.175717	−	0.540800i
$749$	2.02138e7			1.31657
$750$	1.58182e7	+	6.13442e6i	1.02684	+	0.398217i
$751$	−1.37580e7			−0.890134			−0.445067	−	0.895497i	$-0.646820\pi$
$751$	−1.37580e7			−0.890134			−0.445067	+	0.895497i	$0.646820\pi$
$752$	1.43498e6	−	4.41642e6i	0.0925341	−	0.284791i
$753$	−134171.	−	97480.9i	−0.00862326	−	0.00626516i
$754$	−1.14251e7	−	8.30083e6i	−0.731867	−	0.531732i
$755$	1.19253e7	−	1.03425e7i	0.761378	−	0.660328i
$756$	6.77131e6	−	4.91964e6i	0.430892	−	0.313061i
$757$	1.88999e7			1.19873			0.599364	−	0.800477i	$-0.295420\pi$
$757$	1.88999e7			1.19873			0.599364	+	0.800477i	$0.295420\pi$
$758$	−1.07391e7	+	7.80239e6i	−0.678881	+	0.493236i
$759$	5.73451e6	+	1.76490e7i	0.361320	+	1.11203i
$760$	2.62523e6	+	6.20438e6i	0.164867	+	0.389641i
$761$	1.54928e6	−	4.76821e6i	0.0969772	−	0.298465i	−0.890787	−	0.454422i	$-0.849846\pi$
$761$	1.54928e6	−	4.76821e6i	0.0969772	−	0.298465i	0.987764	+	0.155957i	$0.0498460\pi$
$762$	−3.50502e6	−	1.07873e7i	−0.218677	−	0.673018i
$763$	−6.28523e6	−	1.93439e7i	−0.390849	−	1.20291i
$764$	770945.	−	2.37272e6i	0.0477848	−	0.147066i
$765$	−4.15588e7	+	3.58801e6i	−2.56749	+	0.221667i
$766$	−3.26735e6	−	1.00559e7i	−0.201198	−	0.619224i
$767$	5.93913e6	−	4.31503e6i	0.364531	−	0.264847i
$768$	−1.59120e6			−0.0973470
$769$	−1.38227e7	+	1.00427e7i	−0.842899	+	0.612402i	−0.923179	−	0.384370i	$-0.874419\pi$
$769$	−1.38227e7	+	1.00427e7i	−0.842899	+	0.612402i	0.0802801	+	0.996772i	$0.474419\pi$
$770$	−1.17103e7	+	1.01102e6i	−0.711772	+	0.0614515i
$771$	−2.60874e7	−	1.89536e7i	−1.58050	−	1.14830i
$772$	−590066.	−	428708.i	−0.0356334	−	0.0258892i
$773$	−3.81751e6	+	1.17491e7i	−0.229790	+	0.707221i	0.767980	+	0.640474i	$0.221262\pi$
$773$	−3.81751e6	+	1.17491e7i	−0.229790	+	0.707221i	−0.997770	+	0.0667469i	$0.978738\pi$
$774$	−2.39741e6			−0.143844
$775$	4.50574e6	+	8.52105e6i	0.269471	+	0.509611i
$776$	30557.8			0.00182166
$777$	−5.56402e6	+	1.71243e7i	−0.330625	+	1.01756i
$778$	−470873.	−	342109.i	−0.0278904	−	0.0202636i
$779$	1.19393e7	+	8.67440e6i	0.704912	+	0.512148i
$780$	−2.32201e6	+	1.00055e7i	−0.136656	+	0.588847i
$781$	3.57192e6	−	2.59515e6i	0.209544	−	0.152242i
$782$	−2.60695e7			−1.52446
$783$	1.51772e7	−	1.10269e7i	0.884681	−	0.642758i
$784$	2.09773e6	+	6.45614e6i	0.121887	+	0.375131i
$785$	1.92424e7	−	1.66885e7i	1.11451	−	0.966593i
$786$	−3.85406e6	+	1.18616e7i	−0.222517	+	0.684836i
$787$	−6.07677e6	−	1.87024e7i	−0.349733	−	1.07637i	−0.959001	−	0.283402i	$-0.908537\pi$
$787$	−6.07677e6	−	1.87024e7i	−0.349733	−	1.07637i	0.609268	−	0.792964i	$-0.291463\pi$
$788$	1.52356e6	+	4.68904e6i	0.0874066	+	0.269010i
$789$	4.92717e6	−	1.51643e7i	0.281777	−	0.867219i
$790$	−3.57630e6	+	1.54102e7i	−0.203876	+	0.878497i
$791$	7.04961e6	+	2.16965e7i	0.400612	+	1.23296i
$792$	4.53090e6	−	3.29189e6i	0.256668	−	0.186480i
$793$	912470.			0.0515271
$794$	−2.08057e6	+	1.51162e6i	−0.117120	+	0.0850925i
$795$	−3.03283e7	−	1.82703e7i	−1.70188	−	1.02525i
$796$	−4.53798e6	−	3.29703e6i	−0.253851	−	0.184434i
$797$	−5.60001e6	−	4.06865e6i	−0.312279	−	0.226884i	0.420595	−	0.907249i	$-0.361821\pi$
$797$	−5.60001e6	−	4.06865e6i	−0.312279	−	0.226884i	−0.732874	+	0.680364i	$0.761821\pi$
$798$	−1.17628e7	+	3.62021e7i	−0.653887	+	2.01246i
$799$	−3.90623e7			−2.16467
$800$	452604.	−	3.16783e6i	0.0250031	−	0.175000i
$801$	1.60395e7			0.883303
$802$	4.87619e6	−	1.50074e7i	0.267698	−	0.823890i
$803$	3.01488e6	+	2.19044e6i	0.164999	+	0.119879i
$804$	−2.72267e6	−	1.97813e6i	−0.148544	−	0.107923i
$805$	1.37225e7	+	3.24313e7i	0.746353	+	1.76390i
$806$	−4.72105e6	+	3.43004e6i	−0.255977	+	0.185978i
$807$	−1.31963e7			−0.713296
$808$	5.60469e6	−	4.07204e6i	0.302011	−	0.219424i
$809$	−2.78735e6	−	8.57858e6i	−0.149734	−	0.460834i	0.847855	−	0.530227i	$-0.177893\pi$
$809$	−2.78735e6	−	8.57858e6i	−0.149734	−	0.460834i	−0.997589	+	0.0693939i	$0.977893\pi$
$810$	4.44011e6	+	2.67481e6i	0.237783	+	0.143245i
$811$	−2.15524e6	+	6.63315e6i	−0.115065	+	0.354134i	−0.991961	−	0.126547i	$-0.959610\pi$
$811$	−2.15524e6	+	6.63315e6i	−0.115065	+	0.354134i	0.876896	+	0.480681i	$0.159610\pi$
$812$	7.68194e6	+	2.36426e7i	0.408866	+	1.25836i
$813$	−1.94644e6	−	5.99052e6i	−0.103280	−	0.317862i
$814$	−1.11216e6	+	3.42288e6i	−0.0588311	+	0.181063i
$815$	−2.87855e7	−	1.73409e7i	−1.51803	−	0.914488i
$816$	4.13621e6	+	1.27299e7i	0.217459	+	0.669269i
$817$	2.63500e6	−	1.91444e6i	0.138110	−	0.100343i
$818$	1.74781e7			0.913297
$819$	−2.75981e7	+	2.00512e7i	−1.43770	+	1.04455i
$820$	−2.73158e6	−	6.45573e6i	−0.141866	−	0.335283i
$821$	6.15457e6	+	4.47156e6i	0.318669	+	0.231527i	0.735607	−	0.677408i	$-0.236897\pi$
$821$	6.15457e6	+	4.47156e6i	0.318669	+	0.231527i	−0.416938	+	0.908935i	$0.636897\pi$
$822$	1.76577e7	+	1.28291e7i	0.911496	+	0.662241i
$823$	1.03574e7	−	3.18768e7i	0.533030	−	1.64050i	−0.214839	−	0.976649i	$-0.568923\pi$
$823$	1.03574e7	−	3.18768e7i	0.533030	−	1.64050i	0.747869	−	0.663847i	$-0.231077\pi$
$824$	−2.24309e6			−0.115087
$825$	8.95697e6	+	1.69390e7i	0.458170	+	0.866469i
$826$	−1.29226e7			−0.659022
$827$	−9.14590e6	+	2.81482e7i	−0.465010	+	1.43116i	0.393959	+	0.919128i	$0.371105\pi$
$827$	−9.14590e6	+	2.81482e7i	−0.465010	+	1.43116i	−0.858969	+	0.512027i	$0.828895\pi$
$828$	−1.35748e7	−	9.86264e6i	−0.688108	−	0.499939i
$829$	244955.	+	177970.i	0.0123794	+	0.00899417i	0.593958	−	0.804496i	$-0.297565\pi$
$829$	244955.	+	177970.i	0.0123794	+	0.00899417i	−0.581578	+	0.813490i	$0.697565\pi$
$830$	2.81099e6	+	1.69339e6i	0.141633	+	0.0853223i
$831$	1.21569e7	−	8.83247e6i	0.610687	−	0.443690i
$832$	1.93731e6			0.0970267
$833$	4.61975e7	−	3.35644e7i	2.30678	−	1.67597i
$834$	2.02577e6	+	6.23466e6i	0.100850	+	0.310383i
$835$	7.68438e6	−	3.31118e7i	0.381411	−	1.64349i
$836$	−2.35120e6	+	7.23625e6i	−0.116352	+	0.358095i
$837$	−2.39549e6	−	7.37255e6i	−0.118190	−	0.363751i
$838$	−5.93989e6	−	1.82811e7i	−0.292192	−	0.899275i
$839$	−2.57710e6	+	7.93148e6i	−0.126394	+	0.389000i	−0.994152	−	0.107986i	$-0.965560\pi$
$839$	−2.57710e6	+	7.93148e6i	−0.126394	+	0.389000i	0.867759	+	0.496986i	$0.165560\pi$
$840$	1.36593e7	−	1.18464e7i	0.667927	−	0.579279i
$841$	1.08800e7	+	3.34851e7i	0.530441	+	1.63253i
$842$	4.96890e6	−	3.61011e6i	0.241535	−	0.175485i
$843$	−7.82153e6			−0.379073
$844$	−5.08697e6	+	3.69590e6i	−0.245812	+	0.178593i
$845$	−1.86512e6	+	8.03674e6i	−0.0898595	+	0.387203i
$846$	−2.03403e7	−	1.47781e7i	−0.977085	−	0.709894i
$847$	1.63803e7	+	1.19010e7i	0.784537	+	0.569999i
$848$	−2.06363e6	+	6.35121e6i	−0.0985469	+	0.303296i
$849$	−3.60719e7			−1.71751
$850$	−2.65198e7	+	4.61360e6i	−1.25899	+	0.219025i
$851$	1.07829e7			0.510399
$852$	−2.09876e6	+	6.45931e6i	−0.0990520	+	0.304851i
$853$	−2.41588e7	−	1.75524e7i	−1.13685	−	0.825971i	−0.150174	−	0.988660i	$-0.547983\pi$
$853$	−2.41588e7	−	1.75524e7i	−1.13685	−	0.825971i	−0.986677	+	0.162689i	$0.947983\pi$
$854$	−1.29946e6	−	944110.i	−0.0609701	−	0.0442974i
$855$	3.63401e7	−	3.13745e6i	1.70008	−	0.146778i
$856$	−5.02830e6	+	3.65327e6i	−0.234551	+	0.170411i
$857$	−1.83636e7			−0.854093			−0.427047	−	0.904230i	$-0.640446\pi$
$857$	−1.83636e7			−0.854093			−0.427047	+	0.904230i	$0.640446\pi$
$858$	−9.38497e6	+	6.81858e6i	−0.435226	+	0.316210i
$859$	215575.	+	663471.i	0.00996816	+	0.0306788i	0.955917	−	0.293637i	$-0.0948658\pi$
$859$	215575.	+	663471.i	0.00996816	+	0.0306788i	−0.945949	+	0.324316i	$0.894866\pi$
$860$	−1.54134e6	+	133073.i	−0.0710645	+	0.00613542i
$861$	1.22393e7	−	3.76687e7i	0.562664	−	1.73170i
$862$	3.10670e6	+	9.56145e6i	0.142407	+	0.438284i
$863$	−2.21185e6	−	6.80738e6i	−0.101095	−	0.311138i	0.887699	−	0.460424i	$-0.152303\pi$
$863$	−2.21185e6	−	6.80738e6i	−0.101095	−	0.311138i	−0.988794	+	0.149286i	$0.952303\pi$
$864$	−795266.	+	2.44758e6i	−0.0362433	+	0.111545i
$865$	1.43165e7	+	3.38352e7i	0.650576	+	1.53755i
$866$	6.67650e6	+	2.05482e7i	0.302520	+	0.931061i
$867$	6.32002e7	−	4.59176e7i	2.85542	−	2.07459i
$868$	1.02723e7			0.462772
$869$	−1.44545e7	+	1.05018e7i	−0.649311	+	0.471752i
$870$	3.06158e7	−	2.65525e7i	1.37135	−	1.18934i
$871$	3.31488e6	+	2.40840e6i	0.148055	+	0.107568i
$872$	5.05954e6	+	3.67597e6i	0.225330	+	0.163712i
$873$	51126.0	−	157350.i	0.00227042	−	0.00698763i
$874$	2.27958e7			1.00943
$875$	1.96990e7	+	3.05630e7i	0.869810	+	1.34951i
$876$	−5.73255e6			−0.252399
$877$	4.81684e6	−	1.48247e7i	0.211477	−	0.650859i	−0.787908	−	0.615793i	$-0.788836\pi$
$877$	4.81684e6	−	1.48247e7i	0.211477	−	0.650859i	0.999385	−	0.0350661i	$-0.0111642\pi$
$878$	4.00721e6	+	2.91141e6i	0.175431	+	0.127458i
$879$	1.04862e6	+	761868.i	0.0457769	+	0.0332589i
$880$	2.73028e6	−	2.36791e6i	0.118850	−	0.103076i
$881$	−1.58584e7	+	1.15218e7i	−0.688364	+	0.500126i	−0.876122	−	0.482089i	$-0.839878\pi$
$881$	−1.58584e7	+	1.15218e7i	−0.688364	+	0.500126i	0.187758	+	0.982215i	$0.439878\pi$
$882$	3.67539e7			1.59086
$883$	−1.34431e7	+	9.76700e6i	−0.580228	+	0.421560i	−0.838806	−	0.544430i	$-0.816746\pi$
$883$	−1.34431e7	+	9.76700e6i	−0.580228	+	0.421560i	0.258579	+	0.965990i	$0.416746\pi$
$884$	−5.03588e6	−	1.54989e7i	−0.216743	−	0.667066i
$885$	8.20922e6	+	1.94014e7i	0.352325	+	0.832673i
$886$	1.00317e7	−	3.08745e7i	0.429331	−	1.32134i
$887$	1.04234e7	+	3.20798e7i	0.444834	+	1.36906i	0.882665	+	0.470002i	$0.155747\pi$
$887$	1.04234e7	+	3.20798e7i	0.444834	+	1.36906i	−0.437831	+	0.899057i	$0.644253\pi$
$888$	−1.71082e6	−	5.26535e6i	−0.0728066	−	0.224076i
$889$	7.51189e6	−	2.31192e7i	0.318783	−	0.981113i
$890$	1.03121e7	−	890304.i	0.436387	−	0.0376759i
$891$	1.80907e6	+	5.56774e6i	0.0763415	+	0.234955i
$892$	−8.84077e6	+	6.42320e6i	−0.372030	+	0.270296i
$893$	3.41571e7			1.43335
$894$	−3.71736e7	+	2.70082e7i	−1.55557	+	1.13019i
$895$	−1.10570e7	+	954618.i	−0.461403	+	0.0398357i
$896$	−2.75894e6	−	2.00449e6i	−0.114808	−	0.0834130i
$897$	2.81178e7	+	2.04288e7i	1.16681	+	0.847737i
$898$	−6.68092e6	+	2.05618e7i	−0.276468	+	0.850882i
$899$	2.30242e7			0.950135
$900$	−1.55547e7	−	7.63062e6i	−0.640109	−	0.314017i
$901$	5.61752e7			2.30533
$902$	2.44645e6	−	7.52940e6i	0.100120	−	0.308137i
$903$	−7.07188e6	−	5.13802e6i	−0.288613	−	0.209689i
$904$	−5.67487e6	−	4.12303e6i	−0.230959	−	0.167801i
$905$	9.53256e6	−	4.10756e7i	0.386891	−	1.66710i
$906$	−2.21868e7	+	1.61197e7i	−0.897996	+	0.652433i
$907$	−1.50238e7			−0.606402			−0.303201	−	0.952927i	$-0.598055\pi$
$907$	−1.50238e7			−0.606402			−0.303201	+	0.952927i	$0.598055\pi$
$908$	−4.40058e6	+	3.19721e6i	−0.177131	+	0.128693i
$909$	−1.15908e7	−	3.56727e7i	−0.465267	−	1.43195i
$910$	−1.66303e7	+	1.44231e7i	−0.665729	+	0.577373i
$911$	2.58590e6	−	7.95858e6i	0.103232	−	0.317717i	−0.886079	−	0.463534i	$-0.846581\pi$
$911$	2.58590e6	−	7.95858e6i	0.103232	−	0.317717i	0.989312	+	0.145817i	$0.0465812\pi$
$912$	−3.61680e6	−	1.11314e7i	−0.143992	−	0.443161i
$913$	1.14530e6	+	3.52488e6i	0.0454719	+	0.139948i
$914$	−3.92683e6	+	1.20856e7i	−0.155481	+	0.478521i
$915$	−591949.	+	2.55070e6i	−0.0233739	+	0.100718i
$916$	3.14355e6	+	9.67485e6i	0.123789	+	0.380983i
$917$	−2.16249e7	+	1.57114e7i	−0.849239	+	0.617009i
$918$	2.16483e7			0.847847
$919$	9.12691e6	−	6.63109e6i	0.356480	−	0.258998i	−0.395102	−	0.918637i	$-0.629291\pi$
$919$	9.12691e6	−	6.63109e6i	0.356480	−	0.258998i	0.751582	+	0.659639i	$0.229291\pi$
$920$	−9.27491e6	−	5.58738e6i	−0.361277	−	0.217640i
$921$	−1.75485e7	−	1.27498e7i	−0.681698	−	0.495283i
$922$	−4.07001e6	−	2.95703e6i	−0.157677	−	0.114559i
$923$	2.55527e6	−	7.86430e6i	0.0987261	−	0.303848i
$924$	2.04202e7			0.786830
$925$	1.09691e7	−	1.90828e6i	0.421518	−	0.0733309i
$926$	1.65486e7			0.634212
$927$	−3.75288e6	+	1.15502e7i	−0.143438	+	0.441458i
$928$	−6.18388e6	−	4.49285e6i	−0.235717	−	0.171258i
$929$	150276.	+	109182.i	0.00571280	+	0.00415059i	0.590638	−	0.806937i	$-0.298876\pi$
$929$	150276.	+	109182.i	0.00571280	+	0.00415059i	−0.584925	+	0.811087i	$0.698876\pi$
$930$	−6.52556e6	−	1.54223e7i	−0.247406	−	0.584711i
$931$	−4.03963e7	+	2.93496e7i	−1.52745	+	1.10976i
$932$	−2.27093e7			−0.856375
$933$	−3.85886e7	+	2.80362e7i	−1.45129	+	1.05442i
$934$	−3.07093e6	−	9.45134e6i	−0.115187	−	0.354508i
$935$	−2.60409e7	−	1.56875e7i	−0.974152	−	0.586848i
$936$	3.24129e6	−	9.97567e6i	0.120928	−	0.372180i
$937$	2.47080e6	+	7.60435e6i	0.0919368	+	0.282952i	0.986443	−	0.164103i	$-0.0524728\pi$
$937$	2.47080e6	+	7.60435e6i	0.0919368	+	0.282952i	−0.894507	+	0.447055i	$0.852473\pi$
$938$	−2.22884e6	−	6.85966e6i	−0.0827126	−	0.254563i
$939$	−1.49448e7	+	4.59953e7i	−0.553127	+	1.70235i
$940$	−1.38975e7	−	8.37210e6i	−0.512999	−	0.309040i
$941$	−1.29317e7	−	3.97998e7i	−0.476084	−	1.46523i	−0.844491	−	0.535570i	$-0.820097\pi$
$941$	−1.29317e7	−	3.97998e7i	−0.476084	−	1.46523i	0.368407	−	0.929665i	$-0.379903\pi$
$942$	−3.58002e7	+	2.60104e7i	−1.31449	+	0.955035i
$943$	−2.37193e7			−0.868606
$944$	3.21457e6	−	2.33552e6i	0.117407	−	0.0853010i
$945$	−1.13953e7	−	2.69313e7i	−0.415094	−	0.981018i
$946$	−1.41356e6	−	1.02701e6i	−0.0513554	−	0.0373119i
$947$	3.62500e7	+	2.63372e7i	1.31351	+	0.954320i	0.999989	+	0.00473903i	$0.00150849\pi$
$947$	3.62500e7	+	2.63372e7i	1.31351	+	0.954320i	0.313521	+	0.949581i	$0.398492\pi$
$948$	8.49302e6	−	2.61388e7i	0.306932	−	0.944638i
$949$	6.97946e6			0.251568
$950$	2.31896e7	−	4.03425e6i	0.833649	−	0.145029i
$951$	−7.05296e7			−2.52883
$952$	−8.86464e6	+	2.72826e7i	−0.317007	+	0.975647i
$953$	−3.89426e7	−	2.82934e7i	−1.38897	−	1.00915i	−0.995978	−	0.0896030i	$-0.971440\pi$
$953$	−3.89426e7	−	2.82934e7i	−1.38897	−	1.00915i	−0.392992	−	0.919542i	$-0.628560\pi$
$954$	2.92512e7	+	2.12523e7i	1.04058	+	0.756022i
$955$	−7.46642e6	−	4.49791e6i	−0.264913	−	0.159589i
$956$	1.86158e7	−	1.35252e7i	0.658775	−	0.478628i
$957$	4.57698e7			1.61547
$958$	2.16213e7	−	1.57088e7i	0.761146	−	0.553005i
$959$	1.44550e7	+	4.44879e7i	0.507542	+	1.56205i
$960$	−1.25680e6	+	5.41551e6i	−0.0440136	+	0.189654i
$961$	−5.90691e6	+	1.81796e7i	−0.206325	+	0.635003i
$962$	2.08294e6	+	6.41064e6i	0.0725670	+	0.223338i
$963$	1.03988e7	+	3.20041e7i	0.361340	+	1.11209i
$964$	6.33664e6	−	1.95022e7i	0.219617	−	0.675912i
$965$	−1.92513e6	+	1.66962e6i	−0.0665489	+	0.0577165i
$966$	−1.89056e7	−	5.81856e7i	−0.651851	−	2.00619i
$967$	4.26861e7	−	3.10133e7i	1.46798	−	1.06655i	0.486789	−	0.873519i	$-0.338168\pi$
$967$	4.26861e7	−	3.10133e7i	1.46798	−	1.06655i	0.981193	−	0.193032i	$-0.0618320\pi$
$968$	−6.22557e6			−0.213546
$969$	−7.96516e7	+	5.78702e7i	−2.72511	+	1.97991i
$970$	24135.8	−	104001.i	0.000823632	−	0.00354901i
$971$	7.57592e6	+	5.50422e6i	0.257862	+	0.187348i	0.709204	−	0.705003i	$-0.249055\pi$
$971$	7.57592e6	+	5.50422e6i	0.257862	+	0.187348i	−0.451342	+	0.892351i	$0.649055\pi$
$972$	−1.51908e7	−	1.10368e7i	−0.515722	−	0.374694i
$973$	−4.34158e6	+	1.33620e7i	−0.147017	+	0.452470i
$974$	2.99169e7			1.01046
$975$	3.22188e7	+	1.58055e7i	1.08542	+	0.532473i
$976$	493877.			0.0165957
$977$	6.19532e6	−	1.90672e7i	0.207648	−	0.639074i	−0.791946	−	0.610591i	$-0.790932\pi$
$977$	6.19532e6	−	1.90672e7i	0.207648	−	0.639074i	0.999594	−	0.0284838i	$-0.00906789\pi$
$978$	4.72329e7	+	3.43167e7i	1.57906	+	1.14725i
$979$	9.45720e6	+	6.87106e6i	0.315359	+	0.229122i
$980$	2.36297e7	−	2.04009e6i	0.785948	−	0.0678555i
$981$	2.73935e7	−	1.99025e7i	0.908814	−	0.660292i
$982$	−1.49082e7			−0.493339
$983$	−1.87605e6	+	1.36303e6i	−0.0619241	+	0.0449905i	−0.618317	−	0.785929i	$-0.712185\pi$
$983$	−1.87605e6	+	1.36303e6i	−0.0619241	+	0.0449905i	0.556393	+	0.830920i	$0.312185\pi$
$984$	3.76333e6	+	1.15823e7i	0.123904	+	0.381336i
$985$	1.71621e7	−	1.48170e6i	0.563611	−	0.0486599i
$986$	−1.98692e7	+	6.11510e7i	−0.650860	+	2.00314i
$987$	−2.83281e7	−	8.71849e7i	−0.925602	−	2.84871i
$988$	4.40351e6	+	1.35526e7i	0.143518	+	0.441703i
$989$	−1.61766e6	+	4.97864e6i	−0.0525892	+	0.161853i
$990$	−7.62495e6	−	1.80206e7i	−0.247257	−	0.584360i
$991$	−1.74062e7	−	5.35708e7i	−0.563015	−	1.73278i	−0.673777	−	0.738934i	$-0.735329\pi$
$991$	−1.74062e7	−	5.35708e7i	−0.563015	−	1.73278i	0.110763	−	0.993847i	$-0.464671\pi$
$992$	−2.55528e6	+	1.85652e6i	−0.0824441	+	0.0598992i
$993$	5.29135e7			1.70292
$994$	−1.17760e7	+	8.55575e6i	−0.378034	+	0.274658i
$995$	−1.48054e7	+	1.28404e7i	−0.474093	+	0.411171i
$996$	−4.61244e6	−	3.35114e6i	−0.147327	−	0.107039i
$997$	2.14997e7	+	1.56205e7i	0.685007	+	0.497687i	0.875015	−	0.484096i	$-0.160851\pi$
$997$	2.14997e7	+	1.56205e7i	0.685007	+	0.497687i	−0.190008	+	0.981783i	$0.560851\pi$
$998$	−443374.	+	1.36457e6i	−0.0140911	+	0.0433679i
$999$	−8.95417e6			−0.283865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.d.a.21.6	✓	24
25.6	even	5	inner	50.6.d.a.31.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.d.a.21.6	✓	24	1.1	even	1	trivial
50.6.d.a.31.6	yes	24	25.6	even	5	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} +(19.6428 + 14.2713i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-42.2315 + 36.6265i) q^{5} +(78.5712 - 57.0853i) q^{6} +208.145 q^{7} +(-51.7771 + 37.6183i) q^{8} +(107.078 + 329.551i) q^{9} +O(q^{10})\)	\(q+(1.23607 - 3.80423i) q^{2} +(19.6428 + 14.2713i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-42.2315 + 36.6265i) q^{5} +(78.5712 - 57.0853i) q^{6} +208.145 q^{7} +(-51.7771 + 37.6183i) q^{8} +(107.078 + 329.551i) q^{9} +(87.1346 + 205.931i) q^{10} +(-78.0392 + 240.180i) q^{11} +(-120.046 - 369.464i) q^{12} +(146.158 + 449.827i) q^{13} +(257.281 - 791.829i) q^{14} +(-1352.25 + 116.748i) q^{15} +(79.1084 + 243.470i) q^{16} +(1742.17 - 1265.76i) q^{17} +1386.04 q^{18} +(-1523.40 + 1106.82i) q^{19} +(891.112 - 76.9350i) q^{20} +(4088.54 + 2970.50i) q^{21} +(817.237 + 593.757i) q^{22} +(935.235 - 2878.36i) q^{23} -1553.91 q^{24} +(441.996 - 3093.58i) q^{25} +1891.91 q^{26} +(-776.627 + 2390.21i) q^{27} +(-2694.28 - 1957.51i) q^{28} +(-6038.94 - 4387.55i) q^{29} +(-1227.34 + 5288.59i) q^{30} +(-2495.39 + 1813.01i) q^{31} +1024.00 q^{32} +(-4960.59 + 3604.08i) q^{33} +(-2661.81 - 8192.20i) q^{34} +(-8790.25 + 7623.61i) q^{35} +(1713.24 - 5272.82i) q^{36} +(1100.98 + 3388.45i) q^{37} +(2327.55 + 7163.47i) q^{38} +(-3548.69 + 10921.7i) q^{39} +(808.797 - 3485.09i) q^{40} +(-2421.84 - 7453.67i) q^{41} +(16354.2 - 11882.0i) q^{42} -1729.68 q^{43} +(3268.95 - 2375.03i) q^{44} +(-16592.4 - 9995.55i) q^{45} +(-9793.91 - 7115.69i) q^{46} +(-14675.1 - 10662.1i) q^{47} +(-1920.74 + 5911.42i) q^{48} +26517.1 q^{49} +(-11222.4 - 5505.33i) q^{50} +52285.3 q^{51} +(2338.52 - 7197.24i) q^{52} +(21104.2 + 15333.1i) q^{53} +(8132.94 + 5908.93i) q^{54} +(-5501.24 - 13001.5i) q^{55} +(-10777.1 + 7830.03i) q^{56} -45719.6 q^{57} +(-24155.8 + 17550.2i) q^{58} +(-4796.32 - 14761.5i) q^{59} +(18601.9 + 11206.1i) q^{60} +(596.158 - 1834.79i) q^{61} +(3812.62 + 11734.0i) q^{62} +(22287.6 + 68594.2i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-22648.1 - 13643.6i) q^{65} +(7579.11 + 23326.1i) q^{66} +(7008.56 - 5092.02i) q^{67} -34455.1 q^{68} +(59448.6 - 43191.9i) q^{69} +(18136.6 + 42863.4i) q^{70} +(-14144.0 - 10276.2i) q^{71} +(-17941.3 - 13035.1i) q^{72} +(4560.00 - 14034.2i) q^{73} +14251.3 q^{74} +(52831.6 - 54458.8i) q^{75} +30128.5 q^{76} +(-16243.4 + 49992.1i) q^{77} +(37162.3 + 27000.0i) q^{78} +(57236.3 + 41584.6i) q^{79} +(-12258.3 - 7384.65i) q^{80} +(18754.3 - 13625.8i) q^{81} -31349.0 q^{82} +(11873.1 - 8626.33i) q^{83} +(-24986.9 - 76901.9i) q^{84} +(-27214.1 + 117265. i) q^{85} +(-2138.01 + 6580.10i) q^{86} +(-56005.6 - 172368. i) q^{87} +(-4994.51 - 15371.5i) q^{88} +(14304.0 - 44023.1i) q^{89} +(-58534.6 + 50765.9i) q^{90} +(30421.9 + 93629.1i) q^{91} +(-39175.6 + 28462.8i) q^{92} -74890.6 q^{93} +(-58700.5 + 42648.4i) q^{94} +(23796.7 - 102539. i) q^{95} +(20114.2 + 14613.8i) q^{96} +(-386.278 - 280.648i) q^{97} +(32777.0 - 100877. i) q^{98} -87507.8 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

Varieties

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Database

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