LMFDB - Embedded newform 76.6.k.a.3.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.17
Character	$\chi$	$=$	76.3
Dual form			76.6.k.a.51.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.84094 - 4.89174i) q^{2} +(-6.78809 + 2.47066i) q^{3} +(-15.8582 + 27.7942i) q^{4} +(-7.75313 + 43.9702i) q^{5} +(31.3703 + 26.1866i) q^{6} +(149.921 - 86.5570i) q^{7} +(181.014 - 1.38754i) q^{8} +(-146.175 + 122.655i) q^{9} +O(q^{10})$	\(q+(-2.84094 - 4.89174i) q^{2} +(-6.78809 + 2.47066i) q^{3} +(-15.8582 + 27.7942i) q^{4} +(-7.75313 + 43.9702i) q^{5} +(31.3703 + 26.1866i) q^{6} +(149.921 - 86.5570i) q^{7} +(181.014 - 1.38754i) q^{8} +(-146.175 + 122.655i) q^{9} +(237.117 - 86.9902i) q^{10} +(-305.638 - 176.460i) q^{11} +(38.9766 - 227.850i) q^{12} +(196.820 - 540.759i) q^{13} +(-849.330 - 487.472i) q^{14} +(-56.0066 - 317.629i) q^{15} +(-521.037 - 881.531i) q^{16} +(146.439 + 122.877i) q^{17} +(1015.27 + 366.593i) q^{18} +(-1475.80 + 546.006i) q^{19} +(-1099.17 - 912.780i) q^{20} +(-803.824 + 957.961i) q^{21} +(5.10098 + 1996.41i) q^{22} +(-1062.30 + 187.312i) q^{23} +(-1225.31 + 456.643i) q^{24} +(1063.27 + 386.999i) q^{25} +(-3204.41 + 573.469i) q^{26} +(1566.89 - 2713.94i) q^{27} +(28.3082 + 5539.57i) q^{28} +(-5600.08 - 6673.91i) q^{29} +(-1394.65 + 1176.33i) q^{30} +(-4323.72 - 7488.90i) q^{31} +(-2831.99 + 5053.15i) q^{32} +(2510.67 + 442.700i) q^{33} +(185.058 - 1065.43i) q^{34} +(2643.57 + 7263.15i) q^{35} +(-1091.04 - 6007.90i) q^{36} -8938.85i q^{37} +(6863.56 + 5668.04i) q^{38} +4157.00i q^{39} +(-1342.42 + 7969.98i) q^{40} +(345.563 + 949.427i) q^{41} +(6969.70 + 1210.59i) q^{42} +(-7608.57 - 1341.60i) q^{43} +(9751.44 - 5696.64i) q^{44} +(-4259.86 - 7378.30i) q^{45} +(3934.21 + 4664.35i) q^{46} +(-888.873 - 1059.32i) q^{47} +(5714.81 + 4696.61i) q^{48} +(6580.72 - 11398.1i) q^{49} +(-1127.59 - 6300.68i) q^{50} +(-1297.63 - 472.299i) q^{51} +(11908.8 + 14045.9i) q^{52} +(28315.6 - 4992.80i) q^{53} +(-17727.3 + 45.2945i) q^{54} +(10128.7 - 12070.9i) q^{55} +(27017.7 - 15876.0i) q^{56} +(8668.84 - 7352.53i) q^{57} +(-16737.6 + 46354.2i) q^{58} +(702.070 + 589.106i) q^{59} +(9716.41 + 3480.36i) q^{60} +(-6708.79 - 38047.4i) q^{61} +(-24350.3 + 42426.0i) q^{62} +(-11298.0 + 31041.1i) q^{63} +(32764.1 - 502.327i) q^{64} +(22251.3 + 12846.8i) q^{65} +(-4967.09 - 13539.2i) q^{66} +(29290.8 - 24577.9i) q^{67} +(-5737.54 + 2121.56i) q^{68} +(6748.20 - 3896.08i) q^{69} +(28019.2 - 33565.8i) q^{70} +(-10264.7 + 58213.9i) q^{71} +(-26289.5 + 22405.1i) q^{72} +(-5725.28 + 2083.83i) q^{73} +(-43726.5 + 25394.7i) q^{74} -8173.72 q^{75} +(8227.63 - 49677.3i) q^{76} -61095.5 q^{77} +(20334.9 - 11809.8i) q^{78} +(-67053.1 + 24405.3i) q^{79} +(42800.8 - 16075.5i) q^{80} +(4120.86 - 23370.6i) q^{81} +(3662.62 - 4387.66i) q^{82} +(-5367.46 + 3098.90i) q^{83} +(-13878.6 - 37533.2i) q^{84} +(-6538.30 + 5486.29i) q^{85} +(15052.7 + 41030.5i) q^{86} +(54502.8 + 31467.2i) q^{87} +(-55569.7 - 31517.7i) q^{88} +(-44106.7 + 121182. i) q^{89} +(-23990.7 + 41799.4i) q^{90} +(-17299.0 - 98107.4i) q^{91} +(11639.9 - 32496.2i) q^{92} +(47852.3 + 40152.9i) q^{93} +(-2656.67 + 7357.58i) q^{94} +(-12566.0 - 69124.4i) q^{95} +(6739.16 - 41298.1i) q^{96} +(-41335.5 + 49261.7i) q^{97} +(-74452.1 + 190.230i) q^{98} +(66320.4 - 11694.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) $ 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.84094	−	4.89174i	−0.502211	−	0.864745i
$2$	−2.84094	−	4.89174i	−0.502211	−	0.864745i
$3$	−6.78809	+	2.47066i	−0.435456	+	0.158493i	−0.550441	−	0.834874i	$-0.685540\pi$
$3$	−6.78809	+	2.47066i	−0.435456	+	0.158493i	0.114985	+	0.993367i	$0.463318\pi$
$4$	−15.8582	+	27.7942i	−0.495568	+	0.868569i
$5$	−7.75313	+	43.9702i	−0.138692	+	0.786563i	0.833525	+	0.552482i	$0.186319\pi$
$5$	−7.75313	+	43.9702i	−0.138692	+	0.786563i	−0.972217	+	0.234081i	$0.924792\pi$
$6$	31.3703	+	26.1866i	0.355747	+	0.296962i
$7$	149.921	−	86.5570i	1.15643	−	0.667662i	0.205981	−	0.978556i	$-0.433962\pi$
$7$	149.921	−	86.5570i	1.15643	−	0.667662i	0.950445	+	0.310894i	$0.100628\pi$
$8$	181.014	−	1.38754i	0.999971	−	0.00766512i
$9$	−146.175	+	122.655i	−0.601542	+	0.504754i
$10$	237.117	−	86.9902i	0.749829	−	0.275087i
$11$	−305.638	−	176.460i	−0.761598	−	0.439709i	0.0682709	−	0.997667i	$-0.478252\pi$
$11$	−305.638	−	176.460i	−0.761598	−	0.439709i	−0.829869	+	0.557958i	$0.811585\pi$
$12$	38.9766	−	227.850i	0.0781359	−	0.456768i
$13$	196.820	−	540.759i	0.323007	−	0.887454i	−0.666825	−	0.745214i	$-0.732347\pi$
$13$	196.820	−	540.759i	0.323007	−	0.887454i	0.989832	−	0.142240i	$-0.0454304\pi$
$14$	−849.330	−	487.472i	−1.15813	−	0.664705i
$15$	−56.0066	−	317.629i	−0.0642704	−	0.364495i
$16$	−521.037	−	881.531i	−0.508825	−	0.860870i
$17$	146.439	+	122.877i	0.122895	+	0.103122i	0.702164	−	0.712015i	$-0.252217\pi$
$17$	146.439	+	122.877i	0.122895	+	0.103122i	−0.579269	+	0.815137i	$0.696662\pi$
$18$	1015.27	+	366.593i	0.738585	+	0.266688i
$19$	−1475.80	+	546.006i	−0.937870	+	0.346987i
$19$	−1475.80	+	546.006i	−0.937870	+	0.346987i
$20$	−1099.17	−	912.780i	−0.614453	−	0.510259i
$21$	−803.824	+	957.961i	−0.397753	+	0.474023i
$22$	5.10098	+	1996.41i	0.00224697	+	0.879415i
$23$	−1062.30	+	187.312i	−0.418724	+	0.0738323i	−0.379041	−	0.925380i	$-0.623746\pi$
$23$	−1062.30	+	187.312i	−0.418724	+	0.0738323i	−0.0396831	+	0.999212i	$0.512635\pi$
$24$	−1225.31	+	456.643i	−0.434228	+	0.161826i
$25$	1063.27	+	386.999i	0.340247	+	0.123840i
$26$	−3204.41	+	573.469i	−0.929639	+	0.166371i
$27$	1566.89	−	2713.94i	0.413647	−	0.716457i
$28$	28.3082	+	5539.57i	0.00682365	+	1.33531i
$29$	−5600.08	−	6673.91i	−1.23651	−	1.47362i	−0.827864	−	0.560928i	$-0.810444\pi$
$29$	−5600.08	−	6673.91i	−1.23651	−	1.47362i	−0.408649	−	0.912691i	$-0.634000\pi$
$30$	−1394.65	+	1176.33i	−0.282918	+	0.238631i
$31$	−4323.72	−	7488.90i	−0.808078	−	1.39963i	−0.914193	−	0.405278i	$-0.867175\pi$
$31$	−4323.72	−	7488.90i	−0.808078	−	1.39963i	0.106116	−	0.994354i	$-0.466159\pi$
$32$	−2831.99	+	5053.15i	−0.488896	+	0.872342i
$33$	2510.67	+	442.700i	0.401334	+	0.0707659i
$34$	185.058	−	1065.43i	0.0274544	−	0.158062i
$35$	2643.57	+	7263.15i	0.364771	+	1.00220i
$36$	−1091.04	−	6007.90i	−0.140309	−	0.772621i
$37$		−	8938.85i		−	1.07344i	−0.843761	−	0.536719i	$-0.819663\pi$
$37$		−	8938.85i		−	1.07344i	0.843761	−	0.536719i	$-0.180337\pi$
$38$	6863.56	+	5668.04i	0.771064	+	0.636757i
$39$			4157.00i			0.437642i
$40$	−1342.42	+	7969.98i	−0.132659	+	0.787603i
$41$	345.563	+	949.427i	0.0321046	+	0.0882068i	0.954709	−	0.297540i	$-0.0961661\pi$
$41$	345.563	+	949.427i	0.0321046	+	0.0882068i	−0.922605	+	0.385747i	$0.873944\pi$
$42$	6969.70	+	1210.59i	0.609665	+	0.105895i
$43$	−7608.57	−	1341.60i	−0.627526	−	0.110650i	−0.149164	−	0.988812i	$-0.547658\pi$
$43$	−7608.57	−	1341.60i	−0.627526	−	0.110650i	−0.478362	+	0.878163i	$0.658769\pi$
$44$	9751.44	−	5696.64i	0.759342	−	0.443595i
$45$	−4259.86	−	7378.30i	−0.313592	−	0.543157i
$46$	3934.21	+	4664.35i	0.274134	+	0.325010i
$47$	−888.873	−	1059.32i	−0.0586942	−	0.0699490i	0.735899	−	0.677092i	$-0.236760\pi$
$47$	−888.873	−	1059.32i	−0.0586942	−	0.0699490i	−0.794593	+	0.607143i	$0.792316\pi$
$48$	5714.81	+	4696.61i	0.358013	+	0.294226i
$49$	6580.72	−	11398.1i	0.391546	−	0.678178i
$50$	−1127.59	−	6300.68i	−0.0637860	−	0.356420i
$51$	−1297.63	−	472.299i	−0.0698596	−	0.0254268i
$52$	11908.8	+	14045.9i	0.610743	+	0.720347i
$53$	28315.6	−	4992.80i	1.38464	−	0.244149i	0.568821	−	0.822462i	$-0.307400\pi$
$53$	28315.6	−	4992.80i	1.38464	−	0.244149i	0.815815	+	0.578313i	$0.196289\pi$
$54$	−17727.3	+	45.2945i	−0.827291	+	0.00211379i
$55$	10128.7	−	12070.9i	0.451487	−	0.538061i
$56$	27017.7	−	15876.0i	1.15127	−	0.676507i
$57$	8668.84	−	7352.53i	0.353406	−	0.299744i
$58$	−16737.6	+	46354.2i	−0.653314	+	1.80934i
$59$	702.070	+	589.106i	0.0262573	+	0.0220325i	0.655822	−	0.754916i	$-0.272322\pi$
$59$	702.070	+	589.106i	0.0262573	+	0.0220325i	−0.629565	+	0.776948i	$0.716767\pi$
$60$	9716.41	+	3480.36i	0.348440	+	0.124809i
$61$	−6708.79	−	38047.4i	−0.230844	−	1.30918i	−0.851191	−	0.524856i	$-0.824119\pi$
$61$	−6708.79	−	38047.4i	−0.230844	−	1.30918i	0.620347	−	0.784328i	$-0.286992\pi$
$62$	−24350.3	+	42426.0i	−0.804499	+	1.40169i
$63$	−11298.0	+	31041.1i	−0.358634	+	0.985338i
$64$	32764.1	−	502.327i	0.999882	−	0.0153298i
$65$	22251.3	+	12846.8i	0.653240	+	0.377148i
$66$	−4967.09	−	13539.2i	−0.140360	−	0.382591i
$67$	29290.8	−	24577.9i	0.797158	−	0.668895i	−0.150348	−	0.988633i	$-0.548039\pi$
$67$	29290.8	−	24577.9i	0.797158	−	0.668895i	0.947506	+	0.319738i	$0.103595\pi$
$68$	−5737.54	+	2121.56i	−0.150471	+	0.0556395i
$69$	6748.20	−	3896.08i	0.170634	−	0.0985155i
$70$	28019.2	−	33565.8i	0.683456	−	0.818751i
$71$	−10264.7	+	58213.9i	−0.241657	+	1.37050i	0.586473	+	0.809969i	$0.300516\pi$
$71$	−10264.7	+	58213.9i	−0.241657	+	1.37050i	−0.828130	+	0.560536i	$0.810595\pi$
$72$	−26289.5	+	22405.1i	−0.597656	+	0.509350i
$73$	−5725.28	+	2083.83i	−0.125745	+	0.0457673i	−0.404126	−	0.914703i	$-0.632424\pi$
$73$	−5725.28	+	2083.83i	−0.125745	+	0.0457673i	0.278381	+	0.960471i	$0.410202\pi$
$74$	−43726.5	+	25394.7i	−0.928251	+	0.539093i
$75$	−8173.72			−0.167790
$76$	8227.63	−	49677.3i	0.163396	−	0.986561i
$77$	−61095.5			−1.17431
$78$	20334.9	−	11809.8i	0.378448	−	0.219788i
$79$	−67053.1	+	24405.3i	−1.20879	+	0.439964i	−0.866284	−	0.499551i	$-0.833498\pi$
$79$	−67053.1	+	24405.3i	−1.20879	+	0.439964i	−0.342507	+	0.939515i	$0.611276\pi$
$80$	42800.8	−	16075.5i	0.747699	−	0.280827i
$81$	4120.86	−	23370.6i	0.0697871	−	0.395782i
$82$	3662.62	−	4387.66i	0.0601531	−	0.0720607i
$83$	−5367.46	+	3098.90i	−0.0855211	+	0.0493756i	−0.542151	−	0.840281i	$-0.682390\pi$
$83$	−5367.46	+	3098.90i	−0.0855211	+	0.0493756i	0.456630	+	0.889657i	$0.349056\pi$
$84$	−13878.6	−	37533.2i	−0.214608	−	0.580386i
$85$	−6538.30	+	5486.29i	−0.0981562	+	0.0823628i
$86$	15052.7	+	41030.5i	0.219467	+	0.598220i
$87$	54502.8	+	31467.2i	0.772006	+	0.445718i
$88$	−55569.7	−	31517.7i	−0.764947	−	0.433858i
$89$	−44106.7	+	121182.i	−0.590241	+	1.62167i	0.179818	+	0.983700i	$0.442449\pi$
$89$	−44106.7	+	121182.i	−0.590241	+	1.62167i	−0.770058	+	0.637973i	$0.779773\pi$
$90$	−23990.7	+	41799.4i	−0.312203	+	0.543956i
$91$	−17299.0	−	98107.4i	−0.218986	−	1.24193i
$92$	11639.9	−	32496.2i	0.143378	−	0.400279i
$93$	47852.3	+	40152.9i	0.573714	+	0.481403i
$94$	−2656.67	+	7357.58i	−0.0310112	+	0.0858846i
$95$	−12566.0	−	69124.4i	−0.142852	−	0.785818i
$96$	6739.16	−	41298.1i	0.0746324	−	0.457353i
$97$	−41335.5	+	49261.7i	−0.446060	+	0.531594i	−0.941484	−	0.337057i	$-0.890568\pi$
$97$	−41335.5	+	49261.7i	−0.446060	+	0.531594i	0.495424	+	0.868651i	$0.335013\pi$
$98$	−74452.1	+	190.230i	−0.783090	+	0.00200085i
$99$	66320.4	−	11694.1i	0.680079	−	0.119916i
$100$	−27617.9	+	23415.7i	−0.276179	+	0.234157i
$101$	−101070.	−	36786.7i	−0.985873	−	0.358828i	−0.201752	−	0.979437i	$-0.564664\pi$
$101$	−101070.	−	36786.7i	−0.985873	−	0.358828i	−0.784121	+	0.620608i	$0.786886\pi$
$102$	1376.12	+	7689.45i	0.0130966	+	0.0731804i
$103$	60273.1	−	104396.i	0.559797	−	0.969596i	−0.437716	−	0.899113i	$-0.644213\pi$
$103$	60273.1	−	104396.i	0.559797	−	0.969596i	0.997513	−	0.0704831i	$-0.0224541\pi$
$104$	34876.9	−	98158.1i	0.316195	−	0.889904i
$105$	−35889.6	−	42771.5i	−0.317684	−	0.378601i
$106$	−104866.	−	124328.i	−0.906506	−	1.07474i
$107$	−35360.4	−	61246.0i	−0.298578	−	0.517152i	0.677233	−	0.735769i	$-0.263179\pi$
$107$	−35360.4	−	61246.0i	−0.298578	−	0.517152i	−0.975811	+	0.218616i	$0.929846\pi$
$108$	50583.7	+	86588.6i	0.417302	+	0.714334i
$109$	165877.	+	29248.5i	1.33727	+	0.235797i	0.796125	−	0.605132i	$-0.206880\pi$
$109$	165877.	+	29248.5i	1.33727	+	0.235797i	0.541145	+	0.840929i	$0.317991\pi$
$110$	−87822.3	−	15254.2i	−0.692027	−	0.120201i
$111$	22084.9	+	60677.7i	0.170133	+	0.467436i
$112$	−154417.	−	87060.7i	−1.16319	−	0.655809i
$113$			130433.i			0.960929i	0.877014	+	0.480465i	$0.159532\pi$
$113$			130433.i			0.960929i	−0.877014	+	0.480465i	$0.840468\pi$
$114$	−60594.3	−	21517.6i	−0.436686	−	0.155072i
$115$		−	48161.8i		−	0.339593i
$116$	274303.	−	49813.7i	1.89272	−	0.343719i
$117$	37556.8	+	103186.i	0.253644	+	0.696880i
$118$	887.219	−	5107.95i	0.00586578	−	0.0337708i
$119$	32590.2	+	5746.54i	0.210970	+	0.0371997i
$120$	−10578.7	−	57417.6i	−0.0670624	−	0.363992i
$121$	−18249.0	−	31608.2i	−0.113312	−	0.196262i
$122$	−167059.	+	140908.i	−1.01618	+	0.857108i
$123$	−4691.43	−	5591.02i	−0.0279603	−	0.0333218i
$124$	276714.	−	1414.06i	1.61613	−	0.00825873i
$125$	−95023.4	+	164585.i	−0.543946	+	0.942142i
$126$	183942.	−	32918.7i	1.03218	−	0.184721i
$127$	67748.6	+	24658.5i	0.372727	+	0.135662i	0.521590	−	0.853196i	$-0.325339\pi$
$127$	67748.6	+	24658.5i	0.372727	+	0.135662i	−0.148863	+	0.988858i	$0.547561\pi$
$128$	−95538.1	−	158847.i	−0.515408	−	0.856945i
$129$	54962.3	−	9691.33i	0.290797	−	0.0512754i
$130$	−371.366	−	145345.i	−0.00192727	−	0.754294i
$131$	−55544.1	+	66194.9i	−0.282787	+	0.337013i	−0.888675	−	0.458537i	$-0.848374\pi$
$131$	−55544.1	+	66194.9i	−0.282787	+	0.337013i	0.605888	+	0.795550i	$0.292818\pi$
$132$	−52119.2	+	62761.8i	−0.260353	+	0.313517i
$133$	−173992.	+	209598.i	−0.852906	+	1.02745i
$134$	−203442.	−	73458.7i	−0.978765	−	0.353412i
$135$	107184.	+	89938.1i	0.506169	+	0.424726i
$136$	26678.1	+	22039.3i	0.123682	+	0.102176i
$137$	−15546.3	−	88167.5i	−0.0707662	−	0.401335i	−0.999530	−	0.0306625i	$-0.990238\pi$
$137$	−15546.3	−	88167.5i	−0.0707662	−	0.401335i	0.928764	−	0.370673i	$-0.120873\pi$
$138$	−38229.8	−	21941.9i	−0.170885	−	0.0980792i
$139$	−153316.	+	421233.i	−0.673056	+	1.84921i	−0.168802	+	0.985650i	$0.553990\pi$
$139$	−153316.	+	421233.i	−0.673056	+	1.84921i	−0.504253	+	0.863556i	$0.668232\pi$
$140$	−243796.	−	41704.3i	−1.05125	−	0.179830i
$141$	8650.96	+	4994.63i	0.0366452	+	0.0211571i
$142$	313928.	−	115170.i	1.30650	−	0.479311i
$143$	−155578.	+	130546.i	−0.636223	+	0.533854i
$144$	184287.	+	64949.8i	0.740607	+	0.261019i
$145$	336871.	−	194493.i	1.33059	−	0.768216i
$146$	26458.7	+	22086.5i	0.102727	+	0.0857522i
$147$	−16509.5	+	93630.3i	−0.0630147	+	0.357374i
$148$	248448.	+	141754.i	0.932356	+	0.531962i
$149$	−71959.2	+	26191.0i	−0.265534	+	0.0966465i	−0.471356	−	0.881943i	$-0.656235\pi$
$149$	−71959.2	+	26191.0i	−0.265534	+	0.0966465i	0.205822	+	0.978589i	$0.434013\pi$
$150$	23221.0	+	39983.7i	0.0842661	+	0.145096i
$151$	238847.			0.852468			0.426234	−	0.904613i	$-0.359840\pi$
$151$	238847.			0.852468			0.426234	+	0.904613i	$0.359840\pi$
$152$	−266382.	+	100882.i	−0.935183	+	0.354166i
$153$	−36477.3			−0.125978
$154$	173568.	+	298863.i	0.589751	+	1.01548i
$155$	362811.	−	132052.i	1.21297	−	0.441486i
$156$	−115541.	−	65922.4i	−0.380122	−	0.216881i
$157$	104727.	−	593936.i	0.339086	−	1.92305i	−0.0433295	−	0.999061i	$-0.513797\pi$
$157$	104727.	−	593936.i	0.339086	−	1.92305i	0.382415	−	0.923991i	$-0.375092\pi$
$158$	309878.	+	258672.i	0.987525	+	0.824341i
$159$	−179873.	+	103850.i	−0.564252	+	0.325771i
$160$	−200231.	−	163701.i	−0.618346	−	0.505534i
$161$	−143048.	+	120031.i	−0.434928	+	0.364948i
$162$	−126030.	+	46236.1i	−0.377299	+	0.138418i
$163$	−246602.	−	142376.i	−0.726989	−	0.419727i	0.0903307	−	0.995912i	$-0.471208\pi$
$163$	−246602.	−	142376.i	−0.726989	−	0.419727i	−0.817320	+	0.576185i	$0.804541\pi$
$164$	−31868.6	−	5451.52i	−0.0925237	−	0.0158274i
$165$	−38931.2	+	106963.i	−0.111324	+	0.305859i
$166$	30407.6	+	17452.4i	0.0856470	+	0.0491570i
$167$	−57821.0	−	327919.i	−0.160433	−	0.909861i	−0.953649	−	0.300921i	$-0.902706\pi$
$167$	−57821.0	−	327919.i	−0.160433	−	0.909861i	0.793216	−	0.608940i	$-0.208405\pi$
$168$	−144174.	+	174520.i	−0.394107	+	0.477058i
$169$	30744.4	+	25797.6i	0.0828035	+	0.0694804i
$170$	45412.4	+	16397.5i	0.120518	+	0.0435166i
$171$	148754.	−	260827.i	0.389025	−	0.682121i
$172$	157947.	−	190199.i	0.407089	−	0.490215i
$173$	179537.	−	213963.i	0.456077	−	0.543531i	−0.488179	−	0.872743i	$-0.662339\pi$
$173$	179537.	−	213963.i	0.456077	−	0.543531i	0.944256	+	0.329213i	$0.106783\pi$
$174$	−909.630	−	356010.i	−0.00227767	−	0.891433i
$175$	192904.	−	34014.2i	0.476153	−	0.0839586i
$176$	3693.44	+	361372.i	0.00898773	+	0.879372i
$177$	−6221.19	−	2264.33i	−0.0149259	−	0.00543258i
$178$	718095.	−	128512.i	1.69876	−	0.304015i
$179$	−131822.	+	228323.i	−0.307508	+	0.532619i	−0.977817	−	0.209463i	$-0.932828\pi$
$179$	−131822.	+	228323.i	−0.307508	+	0.532619i	0.670309	+	0.742082i	$0.266162\pi$
$180$	272628.	−	1393.18i	0.627175	−	0.00320497i
$181$	129686.	+	154553.i	0.294236	+	0.350656i	0.892828	−	0.450397i	$-0.148718\pi$
$181$	129686.	+	154553.i	0.294236	+	0.350656i	−0.598593	+	0.801054i	$0.704273\pi$
$182$	−430770.	+	363339.i	−0.963978	+	0.813080i
$183$	139542.	+	241694.i	0.308019	+	0.533505i
$184$	−192031.	+	35380.1i	−0.418146	+	0.0770397i
$185$	393043.	+	69304.1i	0.844327	+	0.148878i
$186$	60471.9	−	348153.i	0.128166	−	0.737883i
$187$	−23074.5	−	63396.8i	−0.0482535	−	0.132575i
$188$	43538.8	−	7906.68i	0.0898425	−	0.0163155i
$189$		−	542502.i		−	1.10471i
$190$	−302439.	+	257847.i	−0.607790	+	0.518177i
$191$		−	464096.i		−	0.920501i	−0.887789	−	0.460251i	$-0.847760\pi$
$191$		−	464096.i		−	0.920501i	0.887789	−	0.460251i	$-0.152240\pi$
$192$	−221165.	+	84359.0i	−0.432975	+	0.165150i
$193$	−84004.7	−	230801.i	−0.162334	−	0.446010i	0.831681	−	0.555254i	$-0.187379\pi$
$193$	−84004.7	−	230801.i	−0.162334	−	0.446010i	−0.994015	+	0.109244i	$0.965157\pi$
$194$	358407.	+	62253.0i	0.683710	+	0.118756i
$195$	−182784.	−	32229.8i	−0.344233	−	0.0606975i
$196$	212444.	+	363659.i	0.395007	+	0.676168i
$197$	−69660.5	−	120655.i	−0.127885	−	0.221504i	0.794972	−	0.606646i	$-0.207486\pi$
$197$	−69660.5	−	120655.i	−0.127885	−	0.221504i	−0.922857	+	0.385143i	$0.874152\pi$
$198$	−245616.	−	291200.i	−0.445240	−	0.527872i
$199$	117807.	+	140397.i	0.210882	+	0.251319i	0.861109	−	0.508421i	$-0.169771\pi$
$199$	117807.	+	140397.i	0.210882	+	0.251319i	−0.650227	+	0.759740i	$0.725326\pi$
$200$	193004.	+	68576.9i	0.341186	+	0.121228i
$201$	−138105.	+	239205.i	−0.241112	+	0.417618i
$202$	107184.	+	598919.i	0.184821	+	1.03274i
$203$	−1.41724e6	−	515834.i	−2.41382	−	0.878557i
$204$	33705.3	−	28576.9i	0.0567051	−	0.0480772i
$205$	−44425.7	+	7833.45i	−0.0738328	+	0.0130187i
$206$	−681910.	+	1742.33i	−1.11959	+	0.00286063i
$207$	132307.	−	157677.i	0.214613	−	0.255766i
$208$	−579247.	+	108252.i	−0.928336	+	0.173492i
$209$	547408.	+	93539.2i	0.866854	+	0.148125i
$210$	−107267.	+	297073.i	−0.167849	+	0.464853i
$211$	67350.4	+	56513.7i	0.104144	+	0.0873871i	0.693373	−	0.720579i	$-0.256124\pi$
$211$	67350.4	+	56513.7i	0.104144	+	0.0873871i	−0.589229	+	0.807966i	$0.700568\pi$
$212$	−310262.	+	866185.i	−0.474121	+	1.32364i
$213$	−74149.3	−	420521.i	−0.111984	−	0.635096i
$214$	−199143.	+	346970.i	−0.297256	+	0.517914i
$215$	117981.	−	324149.i	0.174066	−	0.478243i
$216$	279864.	−	493435.i	0.408143	−	0.719607i
$217$	−1.29643e6	−	748496.i	−1.86896	−	1.07905i
$218$	−328169.	−	894518.i	−0.467688	−	1.27482i
$219$	33715.2	−	28290.5i	0.0475025	−	0.0398593i
$220$	174878.	+	472940.i	0.243601	+	0.658793i
$221$	95269.3	−	55003.8i	0.131212	−	0.0757551i
$222$	234078.	−	280415.i	0.318770	−	0.381873i
$223$	−122926.	+	697150.i	−0.165532	+	0.938780i	0.782982	+	0.622045i	$0.213698\pi$
$223$	−122926.	+	697150.i	−0.165532	+	0.938780i	−0.948514	+	0.316736i	$0.897413\pi$
$224$	12810.5	+	1.00270e6i	0.0170587	+	1.33522i
$225$	−202891.	+	73846.3i	−0.267182	+	0.0972461i
$226$	638044.	−	370552.i	0.830959	−	0.482589i
$227$	−7100.37			−0.00914569			−0.00457285	−	0.999990i	$-0.501456\pi$
$227$	−7100.37			−0.00914569			−0.00457285	+	0.999990i	$0.501456\pi$
$228$	66885.9	+	357541.i	0.0852113	+	0.455501i
$229$	−1.45174e6			−1.82936			−0.914679	−	0.404181i	$-0.867557\pi$
$229$	−1.45174e6			−1.82936			−0.914679	+	0.404181i	$0.867557\pi$
$230$	−235595.	+	136825.i	−0.293661	+	0.170547i
$231$	414722.	−	150946.i	0.511360	−	0.186120i
$232$	−1.02295e6	−	1.20030e6i	−1.24777	−	1.46410i
$233$	−119878.	+	679861.i	−0.144660	+	0.820409i	0.822979	+	0.568071i	$0.192310\pi$
$233$	−119878.	+	679861.i	−0.144660	+	0.820409i	−0.967639	+	0.252337i	$0.918801\pi$
$234$	398065.	−	476864.i	0.475241	−	0.569318i
$235$	53469.9	−	30870.9i	0.0631597	−	0.0364653i
$236$	−27507.3	+	10171.3i	−0.0321490	+	0.0118877i
$237$	394865.	−	331331.i	0.456644	−	0.383170i
$238$	−64476.2	−	175748.i	−0.0737831	−	0.201117i
$239$	−647852.	−	374037.i	−0.733636	−	0.423565i	0.0861148	−	0.996285i	$-0.472555\pi$
$239$	−647852.	−	374037.i	−0.733636	−	0.423565i	−0.819751	+	0.572720i	$0.805888\pi$
$240$	−250818.	+	214868.i	−0.281081	+	0.240793i
$241$	413355.	−	1.13568e6i	0.458438	−	1.25955i	−0.468210	−	0.883617i	$-0.655101\pi$
$241$	413355.	−	1.13568e6i	0.458438	−	1.25955i	0.926648	−	0.375930i	$-0.122677\pi$
$242$	−102775.	+	179066.i	−0.112810	+	0.196551i
$243$	162003.	+	918763.i	0.175998	+	0.998132i
$244$	1.16389e6	+	416897.i	1.25152	+	0.448285i
$245$	450157.	+	377727.i	0.479125	+	0.402034i
$246$	−14021.8	+	38833.0i	−0.0147729	+	0.0409131i
$247$	4791.19	+	905516.i	0.00499690	+	0.944395i
$248$	−793045.	−	1.34960e6i	−0.818782	−	1.39340i
$249$	28778.4	−	34296.8i	0.0294150	−	0.0350554i
$250$	1.07506e6	−	2746.86i	1.08789	−	0.00277963i
$251$	−190638.	+	33614.7i	−0.190997	+	0.0336779i	−0.268328	−	0.963328i	$-0.586471\pi$
$251$	−190638.	+	33614.7i	−0.190997	+	0.0336779i	0.0773314	+	0.997005i	$0.475360\pi$
$252$	−683596.	−	806274.i	−0.678107	−	0.799800i
$253$	357733.	+	130204.i	0.351364	+	0.127886i
$254$	−71846.6	−	401461.i	−0.0698750	−	0.390445i
$255$	30827.8	−	53395.4i	0.0296888	−	0.0514225i
$256$	−505618.	+	918620.i	−0.482195	+	0.876064i
$257$	550061.	+	655537.i	0.519491	+	0.619105i	0.960460	−	0.278417i	$-0.0898098\pi$
$257$	550061.	+	655537.i	0.519491	+	0.619105i	−0.440970	+	0.897522i	$0.645365\pi$
$258$	−203552.	−	241329.i	−0.190382	−	0.225714i
$259$	−773720.	−	1.34012e6i	−0.716695	−	1.24135i
$260$	−709933.	+	414731.i	−0.651304	+	0.380481i
$261$	1.63718e6	+	288679.i	1.48763	+	0.262310i
$262$	481605.	+	83651.8i	0.433449	+	0.0752873i
$263$	605631.	+	1.66396e6i	0.539906	+	1.48338i	0.846943	+	0.531683i	$0.178440\pi$
$263$	605631.	+	1.66396e6i	0.539906	+	1.48338i	−0.307037	+	0.951698i	$0.599337\pi$
$264$	455081.	+	76651.2i	0.401864	+	0.0676876i
$265$			1.28375e6i			1.12296i
$266$	1.51960e6	+	255670.i	1.31682	+	0.221552i
$267$		−	931567.i		−	0.799717i
$268$	218625.	+	1.20388e6i	0.185935	+	1.02387i
$269$	395487.	+	1.08659e6i	0.333236	+	0.915558i	0.987264	+	0.159088i	$0.0508554\pi$
$269$	395487.	+	1.08659e6i	0.333236	+	0.915558i	−0.654028	+	0.756470i	$0.726922\pi$
$270$	135451.	−	779824.i	0.113076	−	0.651009i
$271$	877429.	+	154714.i	0.725753	+	0.127970i	0.524306	−	0.851530i	$-0.324325\pi$
$271$	877429.	+	154714.i	0.725753	+	0.127970i	0.201446	+	0.979500i	$0.435436\pi$
$272$	32019.8	−	193114.i	0.0262420	−	0.158268i
$273$	359817.	+	623222.i	0.292197	+	0.506100i
$274$	−387126.	+	326527.i	−0.311513	+	0.262750i
$275$	−256686.	−	305907.i	−0.204678	−	0.243926i
$276$	1274.20	+	249346.i	0.00100685	+	0.197028i
$277$	331420.	−	574037.i	0.259525	−	0.449511i	−0.706589	−	0.707624i	$-0.749767\pi$
$277$	331420.	−	574037.i	0.259525	−	0.449511i	0.966115	+	0.258113i	$0.0831005\pi$
$278$	2.49612e6	−	446713.i	1.93711	−	0.346670i
$279$	1.55057e6	+	564362.i	1.19256	+	0.434057i
$280$	488601.	+	1.31106e6i	0.372443	+	0.999375i
$281$	−344456.	+	60736.9i	−0.260236	+	0.0458867i	−0.302244	−	0.953231i	$-0.597736\pi$
$281$	−344456.	+	60736.9i	−0.260236	+	0.0458867i	0.0420076	+	0.999117i	$0.486625\pi$
$282$	−144.381	−	56507.7i	−0.000108115	−	0.0423140i
$283$	533073.	−	635291.i	0.395658	−	0.471527i	−0.531033	−	0.847351i	$-0.678196\pi$
$283$	533073.	−	635291.i	0.395658	−	0.471527i	0.926691	+	0.375824i	$0.122640\pi$
$284$	−1.45523e6	−	1.20846e6i	−1.07062	−	0.889074i
$285$	256082.	+	438176.i	0.186753	+	0.319548i
$286$	1.08058e6	+	390177.i	0.781166	+	0.282063i
$287$	133987.	+	112428.i	0.0960190	+	0.0805695i
$288$	−205830.	−	1.08600e6i	−0.146227	−	0.771523i
$289$	−240210.	−	1.36230e6i	−0.169179	−	0.959461i
$290$	−1.90844e6	−	1.09534e6i	−1.33255	−	0.764814i
$291$	158880.	−	436519.i	0.109986	−	0.302183i
$292$	32874.0	−	192175.i	0.0225629	−	0.131899i
$293$	−2.33189e6	−	1.34632e6i	−1.58686	−	0.916176i	−0.993820	−	0.111007i	$-0.964592\pi$
$293$	−2.33189e6	−	1.34632e6i	−1.58686	−	0.916176i	−0.593044	−	0.805170i	$-0.702074\pi$
$294$	504917.	−	185237.i	0.340684	−	0.124986i
$295$	−31346.4	+	26302.7i	−0.0209716	+	0.0175973i
$296$	−12403.0	−	1.61806e6i	−0.00822804	−	1.07341i
$297$	−957804.	+	552989.i	−0.630065	+	0.363768i
$298$	332551.	+	277598.i	0.216929	+	0.181082i
$299$	−107791.	+	611316.i	−0.0697279	+	0.395446i
$300$	129620.	−	227182.i	0.0831515	−	0.145737i
$301$	−1.25681e6	+	457441.i	−0.799564	+	0.291017i
$302$	−678550.	−	1.16838e6i	−0.428119	−	0.737168i
$303$	776963.			0.486176
$304$	1.25027e6	+	1.01647e6i	0.775922	+	0.630828i
$305$	1.72497e6			1.06177
$306$	103630.	+	178437.i	0.0632675	+	0.108939i
$307$	1.11321e6	−	405176.i	0.674112	−	0.245357i	0.0177944	−	0.999842i	$-0.494336\pi$
$307$	1.11321e6	−	405176.i	0.674112	−	0.245357i	0.656317	+	0.754485i	$0.272113\pi$
$308$	968863.	−	1.69810e6i	0.581950	−	1.01997i
$309$	−151212.	+	857564.i	−0.0900926	+	0.510941i
$310$	−1.67669e6	−	1.39962e6i	−0.990941	−	0.827193i
$311$	663584.	−	383121.i	0.389041	−	0.224613i	−0.292704	−	0.956203i	$-0.594555\pi$
$311$	663584.	−	383121.i	0.389041	−	0.224613i	0.681744	+	0.731590i	$0.261222\pi$
$312$	5767.98	+	752475.i	0.00335458	+	0.437629i
$313$	540539.	−	453566.i	0.311865	−	0.261685i	−0.473398	−	0.880849i	$-0.656973\pi$
$313$	540539.	−	453566.i	0.311865	−	0.261685i	0.785262	+	0.619163i	$0.212528\pi$
$314$	−3.20290e6	+	1.17504e6i	−1.83324	+	0.672555i
$315$	−1.27729e6	−	737442.i	−0.725290	−	0.418747i
$316$	385013.	−	2.25071e6i	0.216899	−	1.26795i
$317$	−914720.	+	2.51317e6i	−0.511258	+	1.40467i	0.368669	+	0.929561i	$0.379814\pi$
$317$	−914720.	+	2.51317e6i	−0.511258	+	1.40467i	−0.879927	+	0.475109i	$0.842409\pi$
$318$	1.01901e6	+	584861.i	0.565083	+	0.324328i
$319$	533917.	+	3.02799e6i	0.293763	+	1.66601i
$320$	−231937.	+	1.44454e6i	−0.126618	+	0.788597i
$321$	391348.	+	328380.i	0.211983	+	0.177875i
$322$	993552.	+	358751.i	0.534012	+	0.192821i
$323$	−283207.	−	101385.i	−0.151042	−	0.0540714i
$324$	584217.	+	485150.i	0.309180	+	0.256752i
$325$	418547.	−	498805.i	0.219804	−	0.261952i
$326$	4115.69	+	1.61079e6i	0.00214486	+	0.839452i
$327$	−1.19825e6	+	211284.i	−0.619695	+	0.109269i
$328$	63869.1	+	171380.i	0.0327798	+	0.0879581i
$329$	−224952.	−	81875.8i	−0.114578	−	0.0417029i
$330$	633834.	−	113433.i	0.320398	−	0.0573394i
$331$	−32966.8	+	57100.2i	−0.0165389	+	0.0286462i	−0.874176	−	0.485608i	$-0.838598\pi$
$331$	−32966.8	+	57100.2i	−0.0165389	+	0.0286462i	0.857637	+	0.514255i	$0.171931\pi$
$332$	−1013.49	−	198327.i	−0.000504630	−	0.0987500i
$333$	1.09640e6	+	1.30663e6i	0.541823	+	0.645719i
$334$	−1.43983e6	+	1.21444e6i	−0.706227	+	0.595676i
$335$	853600.	+	1.47848e6i	0.415568	+	0.719785i
$336$	1.26329e6	+	209464.i	0.610459	+	0.101219i
$337$	−3.32348e6	−	586020.i	−1.59411	−	0.281085i	−0.695069	−	0.718943i	$-0.744626\pi$
$337$	−3.32348e6	−	586020.i	−1.59411	−	0.281085i	−0.899044	+	0.437858i	$0.855737\pi$
$338$	38852.3	−	223683.i	0.0184980	−	0.106498i
$339$	−322256.	−	885391.i	−0.152301	−	0.418442i
$340$	−48801.5	−	268730.i	−0.0228947	−	0.126072i
$341$			3.05186e6i			1.42128i
$342$	−1.69849e6	+	13326.9i	−0.785234	+	0.00616117i
$343$			631098.i			0.289642i
$344$	−1.37912e6	−	232291.i	−0.628356	−	0.105836i
$345$	118992.	+	326927.i	0.0538231	+	0.147878i
$346$	−1.55670e6	−	270390.i	−0.699062	−	0.121423i
$347$	−2.39293e6	−	421939.i	−1.06686	−	0.188116i	−0.387461	−	0.921886i	$-0.626648\pi$
$347$	−2.39293e6	−	421939.i	−1.06686	−	0.188116i	−0.679398	+	0.733770i	$0.737759\pi$
$348$	−1.73892e6	+	1.01585e6i	−0.769718	+	0.449657i
$349$	231669.	+	401262.i	0.101813	+	0.176345i	0.912432	−	0.409229i	$-0.134202\pi$
$349$	231669.	+	401262.i	0.101813	+	0.176345i	−0.810619	+	0.585575i	$0.800869\pi$
$350$	−714417.	−	847004.i	−0.311732	−	0.369586i
$351$	−1.15919e6	−	1.38147e6i	−0.502212	−	0.598513i
$352$	1.75724e6	−	1.04470e6i	0.755919	−	0.449403i
$353$	502238.	−	869901.i	0.214522	−	0.371564i	−0.738602	−	0.674141i	$-0.764514\pi$
$353$	502238.	−	869901.i	0.214522	−	0.371564i	0.953125	+	0.302578i	$0.0978472\pi$
$354$	6597.50	+	36865.3i	0.00279815	+	0.0156354i
$355$	−2.48009e6	−	902680.i	−1.04447	−	0.380157i
$356$	−2.66871e6	−	3.14764e6i	−1.11603	−	1.31631i
$357$	−235423.	+	41511.5i	−0.0977639	+	0.0172384i
$358$	1.49139e6	−	3810.62i	0.615014	−	0.00157140i
$359$	1.30605e6	−	1.55649e6i	0.534841	−	0.637398i	−0.429182	−	0.903218i	$-0.641198\pi$
$359$	1.30605e6	−	1.55649e6i	0.534841	−	0.637398i	0.964023	+	0.265820i	$0.0856426\pi$
$360$	−781333.	−	1.32967e6i	−0.317746	−	0.540737i
$361$	1.87985e6	−	1.61159e6i	0.759200	−	0.650858i
$362$	387606.	−	1.07346e6i	0.155460	−	0.430542i
$363$	201969.	+	169472.i	0.0804485	+	0.0675043i
$364$	3.00115e6	+	1.07499e6i	1.18723	+	0.425258i
$365$	−47237.6	−	267898.i	−0.0185591	−	0.105254i
$366$	785874.	−	1.36924e6i	0.306655	−	0.534290i
$367$	−1.32239e6	+	3.63322e6i	−0.512499	+	1.40808i	0.366126	+	0.930565i	$0.380684\pi$
$367$	−1.32239e6	+	3.63322e6i	−0.512499	+	1.40808i	−0.878625	+	0.477513i	$0.841538\pi$
$368$	718619.	+	838854.i	0.276617	+	0.322899i
$369$	−166965.	−	96397.2i	−0.0638350	−	0.0368552i
$370$	−777593.	−	2.11955e6i	−0.295289	−	0.804896i
$371$	3.81294e6	−	3.19943e6i	1.43822	−	1.20681i
$372$	−1.87487e6	+	693266.i	−0.702447	+	0.259742i
$373$	1.44440e6	−	833927.i	0.537547	−	0.310353i	−0.206537	−	0.978439i	$-0.566219\pi$
$373$	1.44440e6	−	833927.i	0.537547	−	0.310353i	0.744084	+	0.668086i	$0.232886\pi$
$374$	−244567.	+	292981.i	−0.0904105	+	0.108308i
$375$	238393.	−	1.35199e6i	0.0875416	−	0.496473i
$376$	−162368.	−	190518.i	−0.0592286	−	0.0694970i
$377$	−4.71119e6	+	1.71473e6i	−1.70717	+	0.621360i
$378$	−2.65377e6	+	1.54121e6i	−0.955288	+	0.554795i
$379$	−1.35579e6			−0.484836			−0.242418	−	0.970172i	$-0.577941\pi$
$379$	−1.35579e6			−0.484836			−0.242418	+	0.970172i	$0.577941\pi$
$380$	2.12053e6	+	746925.i	0.753330	+	0.265349i
$381$	−520806.			−0.183808
$382$	−2.27023e6	+	1.31847e6i	−0.795999	+	0.462286i
$383$	2.63175e6	−	957877.i	0.916742	−	0.333667i	0.159800	−	0.987149i	$-0.448915\pi$
$383$	2.63175e6	−	957877.i	0.916742	−	0.333667i	0.756941	+	0.653483i	$0.226693\pi$
$384$	1.04098e6	+	842222.i	0.360258	+	0.291473i
$385$	473682.	−	2.68638e6i	0.162868	−	0.923668i
$386$	−890366.	+	1.06662e6i	−0.304159	+	0.364369i
$387$	1.27673e6	−	737123.i	0.433335	−	0.250186i
$388$	−713685.	−	1.93009e6i	−0.240673	−	0.650875i
$389$	3.65779e6	−	3.06925e6i	1.22559	−	1.02839i	0.227076	−	0.973877i	$-0.427083\pi$
$389$	3.65779e6	−	3.06925e6i	1.22559	−	1.02839i	0.998513	−	0.0545147i	$-0.0173612\pi$
$390$	361618.	+	985695.i	0.120390	+	0.328156i
$391$	−178579.	−	103103.i	−0.0590729	−	0.0341058i
$392$	1.17539e6	−	2.07235e6i	0.386336	−	0.681159i
$393$	213493.	−	586568.i	0.0697273	−	0.191574i
$394$	−392314.	+	683535.i	−0.127319	+	0.221830i
$395$	−553236.	−	3.13756e6i	−0.178409	−	1.01181i
$396$	−726693.	+	2.02877e6i	−0.232870	+	0.650122i
$397$	−464066.	−	389398.i	−0.147776	−	0.123999i	0.565903	−	0.824472i	$-0.308528\pi$
$397$	−464066.	−	389398.i	−0.147776	−	0.123999i	−0.713678	+	0.700473i	$0.752972\pi$
$398$	352103.	−	975141.i	0.111420	−	0.308574i
$399$	663229.	−	1.85265e6i	0.208560	−	0.582587i
$400$	−212851.	−	1.13895e6i	−0.0665161	−	0.355921i
$401$	−730759.	+	870885.i	−0.226941	+	0.270458i	−0.867485	−	0.497464i	$-0.834265\pi$
$401$	−730759.	+	870885.i	−0.226941	+	0.270458i	0.640543	+	0.767922i	$0.278709\pi$
$402$	1.56247e6	−	3992.23i	0.482222	−	0.00123211i
$403$	−4.90069e6	+	864124.i	−1.50312	+	0.265041i
$404$	2.62525e6	−	2.22581e6i	0.800234	−	0.678475i
$405$	995659.	+	362390.i	0.301629	+	0.109784i
$406$	1.50297e6	+	8.39823e6i	0.452517	+	2.52856i
$407$	−1.57735e6	+	2.73206e6i	−0.472001	+	0.817530i
$408$	−235545.	−	83692.3i	−0.0700525	−	0.0248906i
$409$	−983156.	−	1.17168e6i	−0.290612	−	0.346338i	0.600909	−	0.799318i	$-0.294806\pi$
$409$	−983156.	−	1.17168e6i	−0.290612	−	0.346338i	−0.891521	+	0.452979i	$0.850361\pi$
$410$	164530.	+	195064.i	0.0483376	+	0.0573084i
$411$	323362.	+	560079.i	0.0944244	+	0.163548i
$412$	1.94578e6	+	3.33077e6i	0.564744	+	0.966723i
$413$	156246.	+	27550.4i	0.0450749	+	0.00794792i
$414$	−1.14719e6	−	199259.i	−0.328953	−	0.0571371i
$415$	−94644.8	−	260034.i	−0.0269759	−	0.0741158i
$416$	2.17514e6	+	2.52599e6i	0.616247	+	0.715645i
$417$		−	3.23816e6i		−	0.911923i
$418$	−1.09758e6	−	2.94352e6i	−0.307253	−	0.823997i
$419$			5.23319e6i			1.45623i	0.685453	+	0.728117i	$0.259604\pi$
$419$			5.23319e6i			1.45623i	−0.685453	+	0.728117i	$0.740396\pi$
$420$	1.75794e6	−	319244.i	0.486275	−	0.0883079i
$421$	−157492.	−	432705.i	−0.0433064	−	0.118983i	0.916154	−	0.400826i	$-0.131277\pi$
$421$	−157492.	−	432705.i	−0.0433064	−	0.118983i	−0.959461	+	0.281842i	$0.909054\pi$
$422$	85112.0	−	490012.i	0.0232653	−	0.133945i
$423$	259862.	+	45820.6i	0.0706141	+	0.0124512i
$424$	5.11859e6	−	943055.i	1.38272	−	0.254755i
$425$	108151.	+	187324.i	0.0290442	+	0.0503061i
$426$	−1.84643e6	+	1.55739e6i	−0.492956	+	0.415790i
$427$	−4.29906e6	−	5.12342e6i	−1.14105	−	1.35985i
$428$	2.26304e6	−	11564.5i	0.597148	−	0.00305153i
$429$	733546.	−	1.27054e6i	0.192435	−	0.333307i
$430$	−1.92083e6	+	343756.i	−0.500976	+	0.0896560i
$431$	191102.	+	69555.3i	0.0495531	+	0.0180359i	0.366678	−	0.930348i	$-0.380495\pi$
$431$	191102.	+	69555.3i	0.0495531	+	0.0180359i	−0.317125	+	0.948384i	$0.602717\pi$
$432$	−3.20883e6	+	32796.2i	−0.827250	+	0.00845501i
$433$	779067.	−	137371.i	0.199689	−	0.0352106i	−0.0729087	−	0.997339i	$-0.523228\pi$
$433$	779067.	−	137371.i	0.199689	−	0.0352106i	0.272598	+	0.962128i	$0.412117\pi$
$434$	21636.9	+	8.46824e6i	0.00551406	+	2.15809i
$435$	−1.80619e6	+	2.15253e6i	−0.457656	+	0.545414i
$436$	−3.44344e6	+	4.14658e6i	−0.867514	+	1.04466i
$437$	1.46547e6	−	856457.i	0.367089	−	0.214537i
$438$	−234172.	−	84554.8i	−0.0583244	−	0.0210597i
$439$	4.94430e6	+	4.14876e6i	1.22446	+	1.02744i	0.998579	+	0.0532865i	$0.0169696\pi$
$439$	4.94430e6	+	4.14876e6i	1.22446	+	1.02744i	0.225878	+	0.974156i	$0.427475\pi$
$440$	1.81668e6	−	2.19905e6i	0.447349	−	0.541506i
$441$	436106.	+	2.47328e6i	0.106781	+	0.605587i
$442$	−539718.	−	309770.i	−0.131405	−	0.0754196i
$443$	−1.71095e6	+	4.70080e6i	−0.414218	+	1.13805i	0.540708	+	0.841210i	$0.318156\pi$
$443$	−1.71095e6	+	4.70080e6i	−0.414218	+	1.13805i	−0.954926	+	0.296844i	$0.904066\pi$
$444$	−2.03672e6	−	348406.i	−0.490312	−	0.0838741i
$445$	−4.98644e6	−	2.87892e6i	−1.19369	−	0.689175i
$446$	3.75950e6	−	1.37923e6i	0.894938	−	0.328323i
$447$	423756.	−	355574.i	0.100311	−	0.0841707i
$448$	4.86856e6	−	2.91127e6i	1.14605	−	0.685312i
$449$	4.78909e6	−	2.76498e6i	1.12108	−	0.647257i	0.179405	−	0.983775i	$-0.442583\pi$
$449$	4.78909e6	−	2.76498e6i	1.12108	−	0.647257i	0.941677	+	0.336519i	$0.109249\pi$
$450$	937637.	+	782697.i	0.218275	+	0.182206i
$451$	61918.9	−	351159.i	0.0143345	−	0.0812948i
$452$	−3.62528e6	−	2.06843e6i	−0.834633	−	0.476206i
$453$	−1.62132e6	+	590111.i	−0.371212	+	0.135110i
$454$	20171.7	+	34733.2i	0.00459307	+	0.00790869i
$455$	4.44792e6			1.00723
$456$	1.55898e6	−	1.34294e6i	0.351098	−	0.302444i
$457$	4.73347e6			1.06020			0.530102	−	0.847934i	$-0.322154\pi$
$457$	4.73347e6			1.06020			0.530102	+	0.847934i	$0.322154\pi$
$458$	4.12429e6	+	7.10151e6i	0.918724	+	1.58193i
$459$	562936.	−	204892.i	0.124717	−	0.0453934i
$460$	1.33862e6	+	763758.i	0.294960	+	0.168291i
$461$	1.09890e6	−	6.23219e6i	0.240828	−	1.36580i	−0.589157	−	0.808019i	$-0.700540\pi$
$461$	1.09890e6	−	6.23219e6i	0.240828	−	1.36580i	0.829985	−	0.557786i	$-0.188349\pi$
$462$	−1.91659e6	−	1.59988e6i	−0.417757	−	0.348725i
$463$	4.46888e6	−	2.58011e6i	0.968826	−	0.559352i	0.0699481	−	0.997551i	$-0.477717\pi$
$463$	4.46888e6	−	2.58011e6i	0.968826	−	0.559352i	0.898878	+	0.438198i	$0.144383\pi$
$464$	−2.96542e6	+	8.41399e6i	−0.639426	+	1.81429i
$465$	−2.13654e6	+	1.79277e6i	−0.458224	+	0.384496i
$466$	3.66626e6	−	1.34503e6i	0.782094	−	0.286924i
$467$	1.76618e6	+	1.01971e6i	0.374752	+	0.216363i	0.675532	−	0.737330i	$-0.263914\pi$
$467$	1.76618e6	+	1.01971e6i	0.374752	+	0.216363i	−0.300781	+	0.953693i	$0.597247\pi$
$468$	−3.46357e6	−	592487.i	−0.730986	−	0.125044i
$469$	2.26392e6	−	6.22007e6i	0.475257	−	1.30576i
$470$	−302917.	−	173859.i	−0.0632527	−	0.0363038i
$471$	756520.	+	4.29044e6i	0.157133	+	0.891147i
$472$	127902.	+	105662.i	0.0264254	+	0.0218306i
$473$	2.08873e6	+	1.75265e6i	0.429269	+	0.360200i
$474$	−2.74257e6	−	990286.i	−0.560676	−	0.202449i
$475$	−1.78048e6	+	9420.70i	−0.362078	+	0.00191580i
$476$	−676542.	+	814690.i	−0.136860	+	0.164807i
$477$	−3.52663e6	+	4.20287e6i	−0.709682	+	0.845766i
$478$	10812.4	+	4.23173e6i	0.00216447	+	0.847127i
$479$	−2.57268e6	+	453633.i	−0.512327	+	0.0903371i	−0.423834	−	0.905740i	$-0.639316\pi$
$479$	−2.57268e6	+	453633.i	−0.512327	+	0.0903371i	−0.0884927	+	0.996077i	$0.528205\pi$
$480$	1.76364e6	+	616512.i	0.349386	+	0.122134i
$481$	−4.83377e6	−	1.75935e6i	−0.952628	−	0.346728i
$482$	−6.72978e6	+	1.20438e6i	−1.31942	+	0.236127i
$483$	674465.	−	1.16821e6i	0.131550	−	0.227852i
$484$	1.16792e6	−	5968.27i	0.226621	−	0.00115807i
$485$	−1.84557e6	−	2.19946e6i	−0.356267	−	0.424582i
$486$	4.03411e6	−	3.40262e6i	0.774741	−	0.653466i
$487$	−3.45831e6	−	5.98998e6i	−0.660757	−	1.14447i	−0.980417	−	0.196933i	$-0.936902\pi$
$487$	−3.45831e6	−	5.98998e6i	−0.660757	−	1.14447i	0.319660	−	0.947532i	$-0.396431\pi$
$488$	−1.26718e6	−	6.87781e6i	−0.240873	−	1.30738i
$489$	2.02572e6	+	357189.i	0.383096	+	0.0675501i
$490$	568872.	−	3.27515e6i	0.107035	−	0.616227i
$491$	−2.58023e6	−	7.08912e6i	−0.483008	−	1.32705i	−0.906902	−	0.421342i	$-0.861559\pi$
$491$	−2.58023e6	−	7.08912e6i	−0.483008	−	1.32705i	0.423893	−	0.905712i	$-0.360663\pi$
$492$	229796.	−	41731.1i	0.0427985	−	0.00777225i
$493$		−	1.66545e6i		−	0.308612i
$494$	4.41594e6	−	2.59595e6i	0.814152	−	0.478607i
$495$			3.00679e6i			0.551556i
$496$	−4.34888e6	+	7.71348e6i	−0.793731	+	1.40782i
$497$	3.49992e6	+	9.61596e6i	0.635576	+	1.74623i
$498$	−249529.	−	43341.5i	−0.0450865	−	0.00783125i
$499$	−3.77687e6	−	665964.i	−0.679017	−	0.119729i	−0.176505	−	0.984300i	$-0.556479\pi$
$499$	−3.77687e6	−	665964.i	−0.679017	−	0.119729i	−0.502511	+	0.864571i	$0.667590\pi$
$500$	−3.06762e6	−	5.25113e6i	−0.548753	−	0.939350i
$501$	1.20267e6	+	2.08309e6i	0.214068	+	0.370777i
$502$	706025.	+	837055.i	0.125043	+	0.148250i
$503$	1.22874e6	+	1.46436e6i	0.216541	+	0.258064i	0.863370	−	0.504571i	$-0.168349\pi$
$503$	1.22874e6	+	1.46436e6i	0.216541	+	0.258064i	−0.646828	+	0.762636i	$0.723905\pi$
$504$	−2.00203e6	+	5.63454e6i	−0.351070	+	0.988058i
$505$	2.40113e6	−	4.15888e6i	0.418974	−	0.725684i
$506$	−379371.	−	2.11984e6i	−0.0658701	−	0.368066i
$507$	−272433.	−	99157.4i	−0.0470695	−	0.0171319i
$508$	−1.75973e6	+	1.49198e6i	−0.302543	+	0.256510i
$509$	−170639.	+	30088.2i	−0.0291933	+	0.00514756i	−0.188226	−	0.982126i	$-0.560274\pi$
$509$	−170639.	+	30088.2i	−0.0291933	+	0.00514756i	0.159032	+	0.987273i	$0.449163\pi$
$510$	−348776.	+	891.147i	−0.0593774	+	0.000151713i
$511$	−677970.	+	807973.i	−0.114857	+	0.136881i
$512$	5.93007e6	−	136390.i	0.999736	−	0.0229936i
$513$	−830588.	+	4.86075e6i	−0.139345	+	0.815474i
$514$	1.64403e6	−	4.55309e6i	0.274474	−	0.760148i
$515$	4.12301e6	+	3.45962e6i	0.685009	+	0.574791i
$516$	−602238.	+	1.68132e6i	−0.0995736	+	0.277988i
$517$	84746.0	+	480619.i	0.0139442	+	0.0790814i
$518$	−4.35744e6	+	7.59203e6i	−0.713521	+	1.24318i
$519$	−690079.	+	1.89598e6i	−0.112455	+	0.308969i
$520$	4.04563e6	+	2.29458e6i	0.656111	+	0.372130i
$521$	6.37805e6	+	3.68237e6i	1.02942	+	0.594337i	0.916819	−	0.399303i	$-0.130748\pi$
$521$	6.37805e6	+	3.68237e6i	1.02942	+	0.594337i	0.112603	+	0.993640i	$0.464081\pi$
$522$	−3.23898e6	−	8.82877e6i	−0.520274	−	1.41816i
$523$	2.33088e6	−	1.95584e6i	0.372619	−	0.312665i	−0.437177	−	0.899375i	$-0.644022\pi$
$523$	2.33088e6	−	1.95584e6i	0.372619	−	0.312665i	0.809797	+	0.586711i	$0.199577\pi$
$524$	−959007.	−	2.59354e6i	−0.152579	−	0.412633i
$525$	−1.22541e6	+	707493.i	−0.194037	+	0.112027i
$526$	6.41908e6	−	7.68978e6i	1.01160	−	1.21185i
$527$	287053.	−	1.62796e6i	0.0450231	−	0.255339i
$528$	−917899.	−	2.44390e6i	−0.143288	−	0.381504i
$529$	−4.95479e6	+	1.80340e6i	−0.769814	+	0.280189i
$530$	6.27977e6	−	3.64705e6i	0.971078	−	0.563965i
$531$	−174882.			−0.0269159
$532$	−3.06642e6	−	8.15983e6i	−0.469734	−	1.24998i
$533$	581425.			0.0886494
$534$	−4.55698e6	+	2.64652e6i	−0.691551	+	0.401627i
$535$	2.96715e6	−	1.07996e6i	0.448183	−	0.163125i
$536$	5.26794e6	−	4.48959e6i	0.792007	−	0.674985i
$537$	330713.	−	1.87556e6i	0.0494897	−	0.280670i
$538$	4.19177e6	−	5.02156e6i	0.624370	−	0.747968i
$539$	−4.02264e6	+	2.32247e6i	−0.596402	+	0.344333i
$540$	−4.19950e6	+	1.55284e6i	−0.619745	+	0.229162i
$541$	−8.17305e6	+	6.85800e6i	−1.20058	+	1.00741i	−0.200966	+	0.979598i	$0.564408\pi$
$541$	−8.17305e6	+	6.85800e6i	−1.20058	+	1.00741i	−0.999613	+	0.0278073i	$0.991148\pi$
$542$	−1.73590e6	−	4.73168e6i	−0.253820	−	0.691859i
$543$	−1.26217e6	−	728712.i	−0.183703	−	0.106061i
$544$	−1.03563e6	+	391993.i	−0.150040	+	0.0567912i
$545$	−2.57213e6	+	7.06687e6i	−0.370938	+	1.01914i
$546$	2.02642e6	−	3.53066e6i	0.290903	−	0.506845i
$547$	−1.55429e6	−	8.81484e6i	−0.222108	−	1.25964i	−0.868136	−	0.496326i	$-0.834682\pi$
$547$	−1.55429e6	−	8.81484e6i	−0.222108	−	1.25964i	0.646028	−	0.763314i	$-0.276429\pi$
$548$	2.69708e6	+	966079.i	0.383657	+	0.137424i
$549$	5.64737e6	+	4.73871e6i	0.799679	+	0.671010i
$550$	−767187.	+	2.12470e6i	−0.108142	+	0.299497i
$551$	1.19086e7	+	6.79166e6i	1.67102	+	0.953009i
$552$	1.21611e6	−	714608.i	0.169874	−	0.0998206i
$553$	−7.94022e6	+	9.46279e6i	−1.10413	+	1.31585i
$554$	−3.74958e6	+	9580.45i	−0.519049	+	0.00132621i
$555$	−2.83924e6	+	500634.i	−0.391264	+	0.0689903i
$556$	−9.27652e6	−	1.09413e7i	−1.27262	−	1.50100i
$557$	−6.40578e6	−	2.33152e6i	−0.874852	−	0.318420i	−0.134721	−	0.990884i	$-0.543014\pi$
$557$	−6.40578e6	−	2.33152e6i	−0.874852	−	0.318420i	−0.740130	+	0.672464i	$0.765236\pi$
$558$	−1.64436e6	−	9.18830e6i	−0.223569	−	1.24925i
$559$	−2.22300e6	+	3.85035e6i	−0.300892	+	0.521160i
$560$	5.02529e6	−	6.11475e6i	0.677160	−	0.823965i
$561$	313264.	+	373333.i	0.0420246	+	0.0500829i
$562$	1.27569e6	+	1.51244e6i	0.170374	+	0.201993i
$563$	−2.62637e6	−	4.54900e6i	−0.349208	−	0.604847i	0.636901	−	0.770946i	$-0.280216\pi$
$563$	−2.62637e6	−	4.54900e6i	−0.349208	−	0.604847i	−0.986109	+	0.166099i	$0.946883\pi$
$564$	−276010.	+	161241.i	−0.0365366	+	0.0213441i
$565$	−5.73517e6	−	1.01126e6i	−0.755831	−	0.133273i
$566$	−4.62210e6	−	802830.i	−0.606455	−	0.105337i
$567$	−1.40508e6	−	3.86043e6i	−0.183545	−	0.504287i
$568$	−1.77728e6	+	1.05518e7i	−0.231145	+	1.37232i
$569$		−	1.31215e7i		−	1.69904i	−0.527556	−	0.849521i	$-0.676891\pi$
$569$		−	1.31215e7i		−	1.69904i	0.527556	−	0.849521i	$-0.323109\pi$
$570$	1.41593e6	−	2.49751e6i	0.182539	−	0.321974i
$571$			2.48009e6i			0.318330i	0.987252	+	0.159165i	$0.0508801\pi$
$571$			2.48009e6i			0.318330i	−0.987252	+	0.159165i	$0.949120\pi$
$572$	−1.16123e6	−	6.39440e6i	−0.148398	−	0.817165i
$573$	1.14662e6	+	3.15032e6i	0.145893	+	0.400838i
$574$	169322.	−	974829.i	0.0214503	−	0.123495i
$575$	−1.20200e6	−	211946.i	−0.151613	−	0.0267334i
$576$	−4.72768e6	+	4.09212e6i	−0.593734	+	0.513916i
$577$	−2.33061e6	−	4.03673e6i	−0.291427	−	0.504766i	0.682720	−	0.730680i	$-0.260797\pi$
$577$	−2.33061e6	−	4.03673e6i	−0.291427	−	0.504766i	−0.974147	+	0.225913i	$0.927463\pi$
$578$	−5.98158e6	+	5.04524e6i	−0.744726	+	0.628149i
$579$	1.14046e6	+	1.35915e6i	0.141379	+	0.168489i
$580$	63608.3	+	1.24474e7i	0.00785134	+	1.53641i
$581$	−536463.	+	929182.i	−0.0659325	+	0.114198i
$582$	−2.58670e6	+	462923.i	−0.316548	+	0.0566502i
$583$	−9.53535e6	−	3.47058e6i	−1.16189	−	0.422894i
$584$	−1.03346e6	+	385147.i	−0.125390	+	0.0467298i
$585$	−4.82831e6	+	851362.i	−0.583319	+	0.102855i
$586$	38918.4	+	1.52318e7i	0.00468178	+	1.83235i
$587$	9.09965e6	−	1.08445e7i	1.09001	−	1.29902i	0.138850	−	0.990313i	$-0.455659\pi$
$587$	9.09965e6	−	1.08445e7i	1.09001	−	1.29902i	0.951157	−	0.308707i	$-0.0998963\pi$
$588$	−2.34057e6	−	1.94368e6i	−0.279176	−	0.231836i
$589$	1.04699e7	+	8.69132e6i	1.24353	+	1.03228i
$590$	217719.	+	78613.8i	0.0257494	+	0.00929756i
$591$	770960.	+	646912.i	0.0907953	+	0.0761863i
$592$	−7.87987e6	+	4.65747e6i	−0.924092	+	0.546192i
$593$	1.80552e6	+	1.02396e7i	0.210847	+	1.19577i	0.887970	+	0.459901i	$0.152115\pi$
$593$	1.80552e6	+	1.02396e7i	0.210847	+	1.19577i	−0.677124	+	0.735869i	$0.736774\pi$
$594$	5.42613e6	+	3.11432e6i	0.630993	+	0.362157i
$595$	−505353.	+	1.38845e6i	−0.0585197	+	0.160782i
$596$	413183.	−	2.41539e6i	0.0476460	−	0.278530i
$597$	−1.14656e6	−	661966.i	−0.131662	−	0.0760151i
$598$	3.29662e6	−	1.20942e6i	0.376978	−	0.138301i
$599$	9.65810e6	−	8.10411e6i	1.09983	−	0.922865i	0.102414	−	0.994742i	$-0.467343\pi$
$599$	9.65810e6	−	8.10411e6i	1.09983	−	0.922865i	0.997414	+	0.0718767i	$0.0228988\pi$
$600$	−1.47956e6	+	11341.3i	−0.167785	+	0.00128613i
$601$	−6.39017e6	+	3.68937e6i	−0.721650	+	0.416645i	−0.815360	−	0.578955i	$-0.803461\pi$
$601$	−6.39017e6	+	3.68937e6i	−0.721650	+	0.416645i	0.0937100	+	0.995600i	$0.470127\pi$
$602$	5.80820e6	+	4.84842e6i	0.653206	+	0.545267i
$603$	−1.26697e6	+	7.18534e6i	−0.141897	+	0.804737i
$604$	−3.78768e6	+	6.63858e6i	−0.422456	+	0.740428i
$605$	1.53130e6	−	557349.i	0.170088	−	0.0619069i
$606$	−2.20730e6	−	3.80070e6i	−0.244163	−	0.420418i
$607$	8.03498e6			0.885142			0.442571	−	0.896733i	$-0.354066\pi$
$607$	8.03498e6			0.885142			0.442571	+	0.896733i	$0.354066\pi$
$608$	1.42039e6	−	9.00370e6i	0.155829	−	0.987784i
$609$	1.08948e7			1.19036
$610$	−4.90052e6	−	8.43808e6i	−0.533234	−	0.918162i
$611$	−747784.	+	272171.i	−0.0810351	+	0.0294944i
$612$	578463.	−	1.01386e6i	0.0624306	−	0.109420i
$613$	485173.	−	2.75155e6i	0.0521489	−	0.295751i	−0.947568	−	0.319555i	$-0.896467\pi$
$613$	485173.	−	2.75155e6i	0.0521489	−	0.295751i	0.999717	+	0.0238037i	$0.00757768\pi$
$614$	−5.14458e6	−	4.29446e6i	−0.550717	−	0.459714i
$615$	282212.	−	162935.i	0.0300876	−	0.0173711i
$616$	−1.10591e7	+	84772.1i	−1.17427	+	0.00900122i
$617$	1.04381e7	−	8.75861e6i	1.10385	−	0.926238i	0.106169	−	0.994348i	$-0.466141\pi$
$617$	1.04381e7	−	8.75861e6i	1.10385	−	0.926238i	0.997678	+	0.0681103i	$0.0216970\pi$
$618$	4.62456e6	−	1.69660e6i	0.487079	−	0.178693i
$619$	6.29098e6	+	3.63210e6i	0.659920	+	0.381005i	0.792247	−	0.610201i	$-0.208911\pi$
$619$	6.29098e6	+	3.63210e6i	0.659920	+	0.381005i	−0.132326	+	0.991206i	$0.542245\pi$
$620$	−2.08323e6	+	1.21782e7i	−0.217649	+	1.27234i
$621$	−1.15616e6	+	3.17651e6i	−0.120306	+	0.330538i
$622$	−3.75933e6	−	2.15766e6i	−0.389614	−	0.223618i
$623$	3.87663e6	+	2.19855e7i	0.400161	+	2.26943i
$624$	3.66452e6	−	2.16595e6i	0.376753	−	0.222683i
$625$	−3.79142e6	−	3.18138e6i	−0.388241	−	0.325773i
$626$	−3.75436e6	−	1.35562e6i	−0.382913	−	0.138262i
$627$	−3.94696e6	+	717509.i	−0.400954	+	0.0728884i
$628$	1.48472e7	+	1.23296e7i	1.50226	+	1.24752i
$629$	1.09838e6	−	1.30900e6i	0.110695	−	0.131921i
$630$	21317.4	+	8.34317e6i	0.00213985	+	0.837491i
$631$	−1.71817e7	+	3.02960e6i	−1.71788	+	0.302909i	−0.943884	−	0.330278i	$-0.892858\pi$
$631$	−1.71817e7	+	3.02960e6i	−1.71788	+	0.302909i	−0.773999	+	0.633187i	$0.781746\pi$
$632$	−1.21037e7	+	4.51075e6i	−1.20538	+	0.449217i
$633$	−596807.	−	217220.i	−0.0592004	−	0.0215472i
$634$	1.48924e7	−	2.66519e6i	1.47144	−	0.263333i
$635$	−1.60950e6	+	2.78774e6i	−0.158401	+	0.274358i
$636$	−33963.7	−	6.64630e6i	−0.00332945	−	0.651534i
$637$	−4.86843e6	−	5.80197e6i	−0.475379	−	0.566535i
$638$	1.32953e7	−	1.12141e7i	1.29315	−	1.09072i
$639$	−5.63980e6	−	9.76842e6i	−0.546401	−	0.946394i
$640$	7.72523e6	−	2.96927e6i	0.745524	−	0.286550i
$641$	−1.15278e6	−	203266.i	−0.110816	−	0.0195398i	0.117965	−	0.993018i	$-0.462363\pi$
$641$	−1.15278e6	−	203266.i	−0.110816	−	0.0195398i	−0.228781	+	0.973478i	$0.573474\pi$
$642$	494554.	−	2.84728e6i	0.0473561	−	0.272642i
$643$	1.88804e6	+	5.18735e6i	0.180088	+	0.494787i	0.996586	−	0.0825611i	$-0.0263100\pi$
$643$	1.88804e6	+	5.18735e6i	0.180088	+	0.494787i	−0.816498	+	0.577348i	$0.804088\pi$
$644$	−1.06770e6	−	5.87939e6i	−0.101446	−	0.558621i
$645$			2.49184e6i			0.235842i
$646$	308623.	+	1.67340e6i	0.0290969	+	0.157768i
$647$		−	1.44986e7i		−	1.36165i	−0.732445	−	0.680826i	$-0.761621\pi$
$647$		−	1.44986e7i		−	1.36165i	0.732445	−	0.680826i	$-0.238379\pi$
$648$	713506.	−	4.23612e6i	0.0667513	−	0.396306i
$649$	−110625.	−	303941.i	−0.0103096	−	0.0283255i
$650$	−3.62909e6	−	630349.i	−0.336910	−	0.0585191i
$651$	1.06496e7	+	1.87781e6i	0.984873	+	0.173660i
$652$	7.86788e6	−	4.59629e6i	0.724835	−	0.423437i
$653$	4.79768e6	+	8.30983e6i	0.440300	+	0.762622i	0.997712	−	0.0676146i	$-0.0215388\pi$
$653$	4.79768e6	+	8.30983e6i	0.440300	+	0.762622i	−0.557412	+	0.830236i	$0.688205\pi$
$654$	4.43769e6	+	5.26128e6i	0.405707	+	0.481002i
$655$	−2.47996e6	−	2.95550e6i	−0.225861	−	0.269171i
$656$	656898.	−	799311.i	0.0595989	−	0.0725197i
$657$	581299.	−	1.00684e6i	0.0525395	−	0.0910011i
$658$	238559.	+	1.33301e6i	0.0214798	+	0.120024i
$659$	−7.60905e6	−	2.76947e6i	−0.682522	−	0.248418i	−0.0225920	−	0.999745i	$-0.507192\pi$
$659$	−7.60905e6	−	2.76947e6i	−0.682522	−	0.248418i	−0.659930	+	0.751327i	$0.729414\pi$
$660$	−2.35556e6	−	2.77829e6i	−0.210492	−	0.248267i
$661$	1.35830e7	−	2.39504e6i	1.20918	−	0.213211i	0.467517	−	0.883984i	$-0.345149\pi$
$661$	1.35830e7	−	2.39504e6i	1.20918	−	0.213211i	0.741663	+	0.670773i	$0.234037\pi$
$662$	372976.	−	952.979i	0.0330777	−	8.45159e-5i
$663$	−510801.	+	608749.i	−0.0451303	+	0.0537841i
$664$	−967285.	+	568392.i	−0.0851401	+	0.0500297i
$665$	−7.86710e6	−	9.27553e6i	−0.689859	−	0.813363i
$666$	3.27692e6	−	9.07535e6i	0.286273	−	0.792826i
$667$	7.19907e6	+	6.04073e6i	0.626558	+	0.525745i
$668$	1.00312e7	+	3.59311e6i	0.869783	+	0.311551i
$669$	−887987.	−	5.03603e6i	−0.0767081	−	0.435033i
$670$	4.80731e6	−	8.37585e6i	0.413728	−	0.720845i
$671$	−4.66340e6	+	1.28126e7i	−0.399849	+	1.09858i
$672$	−2.56429e6	−	6.77477e6i	−0.219051	−	0.578724i
$673$	−558087.	−	322212.i	−0.0474968	−	0.0274223i	0.476064	−	0.879411i	$-0.342063\pi$
$673$	−558087.	−	322212.i	−0.0474968	−	0.0274223i	−0.523560	+	0.851989i	$0.675397\pi$
$674$	6.57515e6	+	1.79225e7i	0.557514	+	1.51966i
$675$	2.71632e6	−	2.27926e6i	0.229468	−	0.192546i
$676$	−1.20457e6	+	445413.i	−0.101383	+	0.0374883i
$677$	−7.30897e6	+	4.21983e6i	−0.612893	+	0.353854i	−0.774097	−	0.633067i	$-0.781796\pi$
$677$	−7.30897e6	+	4.21983e6i	−0.612893	+	0.353854i	0.161204	+	0.986921i	$0.448462\pi$
$678$	−3.41559e6	+	4.09173e6i	−0.285359	+	0.341848i
$679$	−1.93311e6	+	1.09632e7i	−0.160910	+	0.912566i
$680$	−1.17591e6	+	1.00217e6i	−0.0975220	+	0.0831128i
$681$	48198.0	−	17542.6i	0.00398255	−	0.00144953i
$682$	1.49289e7	−	8.67014e6i	1.22904	−	0.713781i
$683$	1.97554e7			1.62045			0.810223	−	0.586122i	$-0.199346\pi$
$683$	1.97554e7			1.62045			0.810223	+	0.586122i	$0.199346\pi$
$684$	4.89051e6	+	8.27073e6i	0.399681	+	0.675933i
$685$	3.99728e6			0.325490
$686$	3.08717e6	−	1.79291e6i	0.250467	−	0.145462i
$687$	9.85451e6	−	3.58675e6i	0.796605	−	0.289941i
$688$	2.78168e6	+	7.40621e6i	0.224046	+	0.596520i
$689$	2.87318e6	−	1.62946e7i	0.230576	−	1.30766i
$690$	1.26119e6	−	1.51085e6i	0.100846	−	0.120809i
$691$	−801594.	+	462801.i	−0.0638645	+	0.0368722i	−0.531592	−	0.847000i	$-0.678406\pi$
$691$	−801594.	+	462801.i	−0.0638645	+	0.0368722i	0.467728	+	0.883873i	$0.345073\pi$
$692$	3.09982e6	+	8.38315e6i	0.246077	+	0.665490i
$693$	8.93062e6	−	7.49368e6i	0.706397	−	0.592737i
$694$	4.73416e6	+	1.29043e7i	0.373116	+	1.01704i
$695$	−1.73330e7	−	1.00072e7i	−1.36117	−	0.785871i
$696$	9.90943e6	+	5.62038e6i	0.775400	+	0.439787i
$697$	−66058.9	+	181495.i	−0.00515050	+	0.0141509i
$698$	1.30471e6	−	2.27322e6i	0.101362	−	0.176605i
$699$	−865965.	−	4.91113e6i	−0.0670359	−	0.380180i
$700$	−2.11371e6	+	5.90102e6i	−0.163042	+	0.455179i
$701$	−9.93055e6	−	8.33272e6i	−0.763270	−	0.640460i	0.175706	−	0.984443i	$-0.443779\pi$
$701$	−9.93055e6	−	8.33272e6i	−0.763270	−	0.640460i	−0.938976	+	0.343983i	$0.888224\pi$
$702$	−3.46460e6	+	9.59512e6i	−0.265345	+	0.734865i
$703$	4.88067e6	+	1.31919e7i	0.372470	+	1.00675i
$704$	−1.01026e7	−	5.62804e6i	−0.768250	−	0.427982i
$705$	−286687.	+	341660.i	−0.0217238	+	0.0258894i
$706$	−5.68215e6	+	14518.3i	−0.429043	+	0.00109624i
$707$	−1.83367e7	+	3.23326e6i	−1.37966	+	0.243272i
$708$	161592.	−	137005.i	0.0121154	−	0.0102720i
$709$	2.26358e7	+	8.23877e6i	1.69115	+	0.615527i	0.994769	−	0.102149i	$-0.0325719\pi$
$709$	2.26358e7	+	8.23877e6i	1.69115	+	0.615527i	0.696377	+	0.717676i	$0.254794\pi$
$710$	2.63011e6	+	1.46964e7i	0.195807	+	1.09412i
$711$	6.80804e6	−	1.17919e7i	0.505066	−	0.874799i
$712$	−7.81578e6	+	2.19969e7i	−0.577793	+	1.62615i
$713$	5.99585e6	+	7.14557e6i	0.441699	+	0.526397i
$714$	871885.	+	1.03370e6i	0.0640050	+	0.0758836i
$715$	−4.53391e6	−	7.85296e6i	−0.331671	−	0.574471i
$716$	−4.25559e6	−	7.28468e6i	−0.310226	−	0.531041i
$717$	5.32179e6	+	938376.i	0.386598	+	0.0681677i
$718$	−1.13244e7	−	1.96697e6i	−0.819790	−	0.142392i
$719$	−6.74007e6	−	1.85182e7i	−0.486230	−	1.33591i	−0.904069	−	0.427386i	$-0.859435\pi$
$719$	−6.74007e6	−	1.85182e7i	−0.486230	−	1.33591i	0.417839	−	0.908521i	$-0.362788\pi$
$720$	−4.28466e6	+	7.59957e6i	−0.308024	+	0.546333i
$721$		−	2.08682e7i		−	1.49502i
$722$	−1.32240e7	−	4.61733e6i	−0.944105	−	0.329646i
$723$			8.73038e6i			0.621137i
$724$	−6.35226e6	+	1.15358e6i	−0.450383	+	0.0817899i
$725$	−3.37160e6	−	9.26340e6i	−0.238227	−	0.654524i
$726$	255232.	−	1.46944e6i	0.0179719	−	0.103469i
$727$	2.65686e7	+	4.68477e6i	1.86437	+	0.328740i	0.988190	−	0.153236i	$-0.0489693\pi$
$727$	2.65686e7	+	4.68477e6i	1.86437	+	0.328740i	0.876185	+	0.481975i	$0.160080\pi$
$728$	−3.26749e6	−	1.77348e7i	−0.228500	−	1.24022i
$729$	−486315.	−	842322.i	−0.0338921	−	0.0587029i
$730$	−1.17629e6	+	992154.i	−0.0816970	+	0.0689084i
$731$	−949343.	−	1.13138e6i	−0.0657097	−	0.0783098i
$732$	−8.93058e6	+	45636.8i	−0.616030	+	0.00314802i
$733$	−1.62036e6	+	2.80654e6i	−0.111391	+	0.192935i	−0.916331	−	0.400421i	$-0.868864\pi$
$733$	−1.62036e6	+	2.80654e6i	−0.111391	+	0.192935i	0.804940	+	0.593356i	$0.202197\pi$
$734$	2.15296e7	−	3.85299e6i	1.47501	−	0.263972i
$735$	−3.98894e6	−	1.45186e6i	−0.272358	−	0.0991300i
$736$	2.06190e6	−	5.89842e6i	0.140305	−	0.401367i
$737$	−1.32894e7	+	2.34328e6i	−0.901233	+	0.158912i
$738$	2786.58	+	1.09061e6i	0.000188335	+	0.0737101i
$739$	−1.62119e7	+	1.93206e7i	−1.09200	+	1.30139i	−0.141750	+	0.989903i	$0.545273\pi$
$739$	−1.62119e7	+	1.93206e7i	−1.09200	+	1.30139i	−0.950249	+	0.311491i	$0.899172\pi$
$740$	−8.15920e6	+	9.82529e6i	−0.547732	+	0.659578i
$741$	−2.26975e6	−	6.13489e6i	−0.151856	−	0.410451i
$742$	−2.64831e7	−	9.56250e6i	−1.76587	−	0.637620i
$743$	−2.10949e7	−	1.77007e7i	−1.40186	−	1.17630i	−0.960266	−	0.279086i	$-0.909968\pi$
$743$	−2.10949e7	−	1.77007e7i	−1.40186	−	1.17630i	−0.441595	−	0.897215i	$-0.645587\pi$
$744$	8.71766e6	+	7.20184e6i	0.577387	+	0.476992i
$745$	−593714.	−	3.36712e6i	−0.0391911	−	0.222264i
$746$	−8.18281e6	−	4.69651e6i	−0.538338	−	0.308979i
$747$	404490.	−	1.11133e6i	0.0265220	−	0.0728687i
$748$	2.12798e6	+	364018.i	0.139064	+	0.0237886i
$749$	−1.06025e7	−	6.12138e6i	−0.690566	−	0.398699i
$750$	−7.29084e6	+	2.67477e6i	−0.473287	+	0.173633i
$751$	−1.87123e7	+	1.57015e7i	−1.21067	+	1.01587i	−0.211413	+	0.977397i	$0.567806\pi$
$751$	−1.87123e7	+	1.57015e7i	−1.21067	+	1.01587i	−0.999259	+	0.0384776i	$0.987749\pi$
$752$	−470686.	+	1.33551e6i	−0.0303519	+	0.0861198i
$753$	1.21102e6	−	699182.i	0.0778330	−	0.0449369i
$754$	2.17722e7	+	1.81745e7i	1.39468	+	1.16421i
$755$	−1.85182e6	+	1.05022e7i	−0.118231	+	0.670520i
$756$	1.50784e7	+	8.60308e6i	0.959513	+	0.547457i
$757$	−1.72971e7	+	6.29564e6i	−1.09707	+	0.399301i	−0.826235	−	0.563325i	$-0.809522\pi$
$757$	−1.72971e7	+	6.29564e6i	−1.09707	+	0.399301i	−0.270834	+	0.962626i	$0.587300\pi$
$758$	3.85171e6	+	6.63217e6i	0.243490	+	0.419259i
$759$	−2.75001e6			−0.173273
$760$	−2.37053e6	−	1.24950e7i	−0.148871	−	0.784700i
$761$	−2.98980e6			−0.187146			−0.0935731	−	0.995612i	$-0.529829\pi$
$761$	−2.98980e6			−0.187146			−0.0935731	+	0.995612i	$0.529829\pi$
$762$	1.47958e6	+	2.54765e6i	0.0923103	+	0.158947i
$763$	2.74001e7	−	9.97281e6i	1.70389	−	0.620164i
$764$	1.28992e7	+	7.35971e6i	0.799519	+	0.456171i
$765$	282813.	−	1.60391e6i	0.0174722	−	0.0990895i
$766$	−1.21623e7	−	1.01525e7i	−0.748934	−	0.625177i
$767$	456746.	−	263703.i	0.0280341	−	0.0161855i
$768$	1.16258e6	−	7.48488e6i	0.0711246	−	0.457912i
$769$	1.03783e6	−	870842.i	0.0632863	−	0.0531035i	−0.610596	−	0.791942i	$-0.709070\pi$
$769$	1.03783e6	−	870842.i	0.0632863	−	0.0531035i	0.673882	+	0.738839i	$0.264626\pi$
$770$	−1.44868e7	+	5.31471e6i	−0.880531	+	0.323037i
$771$	−5.35347e6	−	3.09083e6i	−0.324339	−	0.187257i
$772$	7.74710e6	+	1.32524e6i	0.467838	+	0.0800296i
$773$	−6.03212e6	+	1.65731e7i	−0.363096	+	0.997597i	0.614833	+	0.788657i	$0.289223\pi$
$773$	−6.03212e6	+	1.65731e7i	−0.363096	+	0.997597i	−0.977929	+	0.208940i	$0.932999\pi$
$774$	−7.23293e6	−	4.15133e6i	−0.433972	−	0.249078i
$775$	−1.69909e6	−	9.63601e6i	−0.101616	−	0.576292i
$776$	−7.41395e6	+	8.97441e6i	−0.441972	+	0.534997i
$777$	8.56307e6	+	7.18527e6i	0.508835	+	0.426963i
$778$	−2.54055e7	−	9.17341e6i	−1.50480	−	0.543353i
$779$	−1.02837e6	−	1.21248e6i	−0.0607166	−	0.0715866i
$780$	3.79442e6	−	4.56924e6i	0.223311	−	0.268910i
$781$	1.34097e7	−	1.59811e7i	0.786669	−	0.937516i
$782$	2980.41	+	1.16647e6i	0.000174285	+	0.0682113i
$783$	−2.68873e7	+	4.74095e6i	−1.56727	+	0.276351i
$784$	−1.34766e7	+	137739.i	−0.783051	+	0.00800327i
$785$	2.53035e7	+	9.20974e6i	1.46557	+	0.533425i
$786$	−3.47585e6	+	622048.i	−0.200681	+	0.0359143i
$787$	1.32186e7	−	2.28953e7i	0.760761	−	1.31768i	−0.181698	−	0.983354i	$-0.558159\pi$
$787$	1.32186e7	−	2.28953e7i	0.760761	−	1.31768i	0.942459	−	0.334322i	$-0.108507\pi$
$788$	4.45821e6	−	22782.2i	0.255767	−	0.00130702i
$789$	−8.22215e6	−	9.79878e6i	−0.470211	−	0.560376i
$790$	−1.37764e7	+	1.16199e7i	−0.785359	+	0.662421i
$791$	1.12899e7	+	1.95547e7i	0.641576	+	1.11124i
$792$	1.19887e7	−	2.20881e6i	0.679140	−	0.125126i
$793$	−2.18949e7	−	3.86067e6i	−1.23640	−	0.218011i
$794$	−586449.	+	3.37634e6i	−0.0330125	+	0.190062i
$795$	−3.17171e6	−	8.71421e6i	−0.177982	−	0.489002i
$796$	−5.77043e6	+	1.04792e6i	−0.322794	+	0.0586197i
$797$			2.21267e7i			1.23387i	0.787013	+	0.616937i	$0.211627\pi$
$797$			2.21267e7i			1.23387i	−0.787013	+	0.616937i	$0.788373\pi$
$798$	−1.09469e7	+	2.01891e6i	−0.608530	+	0.112230i
$799$		−	264348.i		−	0.0146490i
$800$	−4.96673e6	+	4.27689e6i	−0.274376	+	0.236267i
$801$	−8.41633e6	−	2.31237e7i	−0.463491	−	1.27343i
$802$	6.33618e6	+	1.10055e6i	0.347850	+	0.0604193i
$803$	2.11758e6	+	373386.i	0.115891	+	0.0204347i
$804$	−4.45841e6	−	7.63187e6i	−0.243243	−	0.416381i
$805$	−4.16874e6	−	7.22047e6i	−0.226733	−	0.392713i
$806$	1.81496e7	+	2.15180e7i	0.984078	+	1.16671i
$807$	−5.36920e6	−	6.39877e6i	−0.290219	−	0.345870i
$808$	−1.83462e7	−	6.51866e6i	−0.988594	−	0.351261i
$809$	−2.77197e6	+	4.80120e6i	−0.148908	+	0.257916i	−0.930824	−	0.365468i	$-0.880909\pi$
$809$	−2.77197e6	+	4.80120e6i	−0.148908	+	0.257916i	0.781916	+	0.623384i	$0.214242\pi$
$810$	−1.05588e6	−	5.90003e6i	−0.0565463	−	0.315967i
$811$	−2.32242e7	−	8.45292e6i	−1.23991	−	0.451289i	−0.362927	−	0.931818i	$-0.618223\pi$
$811$	−2.32242e7	−	8.45292e6i	−1.23991	−	0.451289i	−0.876979	+	0.480529i	$0.840445\pi$
$812$	3.68121e7	−	3.12110e7i	1.95930	−	1.66118i
$813$	−6.33831e6	+	1.11762e6i	−0.336316	+	0.0593015i
$814$	1.78457e7	−	45596.9i	0.943999	−	0.00241198i
$815$	8.17223e6	−	9.73929e6i	0.430970	−	0.513610i
$816$	259767.	+	1.38999e6i	0.0136571	+	0.0730778i
$817$	1.19612e7	−	2.17440e6i	0.626932	−	0.113969i
$818$	−2.93847e6	+	8.13801e6i	−0.153546	+	0.425241i
$819$	1.45621e7	+	1.22190e7i	0.758601	+	0.636541i
$820$	486786.	−	1.35900e6i	0.0252815	−	0.0705806i
$821$	−517626.	−	2.93560e6i	−0.0268015	−	0.151999i	0.968470	−	0.249130i	$-0.0801445\pi$
$821$	−517626.	−	2.93560e6i	−0.0268015	−	0.151999i	−0.995272	+	0.0971310i	$0.969033\pi$
$822$	1.82111e6	−	3.17295e6i	0.0940062	−	0.163789i
$823$	1.17605e6	−	3.23118e6i	0.0605240	−	0.166288i	−0.905745	−	0.423823i	$-0.860688\pi$
$823$	1.17605e6	−	3.23118e6i	0.0605240	−	0.166288i	0.966269	+	0.257535i	$0.0829101\pi$
$824$	1.07654e7	−	1.89808e7i	0.552348	−	0.973859i
$825$	2.49820e6	+	1.44234e6i	0.127789	+	0.0737789i
$826$	−309116.	−	842585.i	−0.0157642	−	0.0429698i
$827$	1.99450e7	−	1.67359e7i	1.01408	−	0.850912i	0.0252057	−	0.999682i	$-0.491976\pi$
$827$	1.99450e7	−	1.67359e7i	1.01408	−	0.850912i	0.988872	+	0.148770i	$0.0475315\pi$
$828$	2.28436e6	+	6.17783e6i	0.115795	+	0.313156i
$829$	1.51357e7	−	8.73860e6i	0.764920	−	0.441627i	−0.0661392	−	0.997810i	$-0.521068\pi$
$829$	1.51357e7	−	8.73860e6i	0.764920	−	0.441627i	0.831060	+	0.556183i	$0.187735\pi$
$830$	−1.00314e6	+	1.20172e6i	−0.0505436	+	0.0605491i
$831$	−831460.	+	4.71544e6i	−0.0417675	+	0.236875i
$832$	6.17701e6	−	1.78164e7i	0.309364	−	0.892301i
$833$	2.36425e6	−	860516.i	0.118054	−	0.0429681i
$834$	−1.58402e7	+	9.19940e6i	−0.788581	+	0.457978i
$835$	1.48670e7			0.737914
$836$	−1.12807e7	+	1.37314e7i	−0.558242	+	0.679516i
$837$	−2.70992e7			−1.33703
$838$	2.55994e7	−	1.48671e7i	1.25927	−	0.731337i
$839$	−1.14135e7	+	4.15416e6i	−0.559774	+	0.203741i	−0.606384	−	0.795172i	$-0.707381\pi$
$839$	−1.14135e7	+	4.15416e6i	−0.559774	+	0.203741i	0.0466097	+	0.998913i	$0.485158\pi$
$840$	−6.55586e6	−	7.69245e6i	−0.320576	−	0.376155i
$841$	−9.61851e6	+	5.45493e7i	−0.468941	+	2.65949i
$842$	−1.66925e6	+	1.99969e6i	−0.0811413	+	0.0972038i
$843$	2.18814e6	−	1.26332e6i	0.106049	−	0.0612273i
$844$	−2.63881e6	+	975747.i	−0.127512	+	0.0471499i
$845$	−1.37269e6	+	1.15182e6i	−0.0661349	+	0.0554938i
$846$	−514108.	−	1.40135e6i	−0.0246961	−	0.0673163i
$847$	−5.47181e6	−	3.15915e6i	−0.262073	−	0.151308i
$848$	−1.91547e7	−	2.23596e7i	−0.914717	−	1.06776i
$849$	−2.04895e6	+	5.62946e6i	−0.0975581	+	0.268039i
$850$	609087.	−	1.06122e6i	0.0289156	−	0.0503801i
$851$	1.67436e6	+	9.49574e6i	0.0792545	+	0.449474i
$852$	1.28639e7	+	4.60778e6i	0.607120	+	0.217467i
$853$	−2.47789e6	−	2.07919e6i	−0.116603	−	0.0978413i	0.582622	−	0.812743i	$-0.302027\pi$
$853$	−2.47789e6	−	2.07919e6i	−0.116603	−	0.0978413i	−0.699225	+	0.714902i	$0.746471\pi$
$854$	−1.28491e7	+	3.55852e7i	−0.602874	+	1.66964i
$855$	1.03153e7	+	8.56296e6i	0.482577	+	0.400598i
$856$	−6.48571e6	−	1.10373e7i	−0.302533	−	0.514849i
$857$	−4.63666e6	+	5.52576e6i	−0.215652	+	0.257004i	−0.863016	−	0.505177i	$-0.831427\pi$
$857$	−4.63666e6	+	5.52576e6i	−0.215652	+	0.257004i	0.647364	+	0.762181i	$0.275872\pi$
$858$	−8.29910e6	+	21204.8i	−0.384869	+	0.000983367i
$859$	3.58535e7	−	6.32194e6i	1.65786	−	0.292326i	0.735177	−	0.677876i	$-0.237099\pi$
$859$	3.58535e7	−	6.32194e6i	1.65786	−	0.292326i	0.922687	+	0.385550i	$0.125988\pi$
$860$	7.13850e6	+	8.41958e6i	0.329125	+	0.388190i
$861$	−1.18729e6	−	432137.i	−0.0545817	−	0.0198661i
$862$	−202661.	−	1.13242e6i	−0.00928971	−	0.0519086i
$863$	1.19092e7	−	2.06274e7i	0.544322	−	0.942793i	−0.454327	−	0.890835i	$-0.650120\pi$
$863$	1.19092e7	−	2.06274e7i	0.544322	−	0.942793i	0.998649	−	0.0519585i	$-0.0165463\pi$
$864$	9.27650e6	+	1.56036e7i	0.422766	+	0.711114i
$865$	8.01604e6	+	9.55315e6i	0.364267	+	0.434116i
$866$	−2.88526e6	−	3.42073e6i	−0.130734	−	0.154997i
$867$	4.99634e6	+	8.65392e6i	0.225738	+	0.390990i
$868$	4.13629e7	−	2.41636e7i	1.86342	−	1.08858i
$869$	2.48006e7	+	4.37301e6i	1.11407	+	0.196441i
$870$	1.56609e7	+	2.72019e6i	0.701484	+	0.121843i
$871$	−7.52571e6	−	2.06767e7i	−0.336126	−	0.923498i
$872$	3.00666e7	+	5.06424e6i	1.33904	+	0.225540i
$873$		−	1.22708e7i		−	0.544927i
$874$	−8.35285e6	−	4.73553e6i	−0.369876	−	0.209696i
$875$			3.28998e7i			1.45269i
$876$	251649.	+	1.38572e6i	0.0110799	+	0.0610122i
$877$	4.28050e6	+	1.17606e7i	0.187930	+	0.516333i	0.997498	−	0.0706927i	$-0.0225210\pi$
$877$	4.28050e6	+	1.17606e7i	0.187930	+	0.516333i	−0.809568	+	0.587026i	$0.800299\pi$
$878$	6.24821e6	−	3.59726e7i	0.273539	−	1.57484i
$879$	1.91554e7	+	3.37761e6i	0.836217	+	0.147448i
$880$	−1.59182e7	−	2.63936e6i	−0.692928	−	0.114893i
$881$	1.57771e7	+	2.73268e7i	0.684839	+	1.18618i	0.973487	+	0.228741i	$0.0734609\pi$
$881$	1.57771e7	+	2.73268e7i	0.684839	+	1.18618i	−0.288648	+	0.957435i	$0.593206\pi$
$882$	1.08597e7	−	9.15974e6i	0.470052	−	0.396471i
$883$	−6.96813e6	−	8.30430e6i	−0.300756	−	0.358427i	0.594408	−	0.804164i	$-0.297386\pi$
$883$	−6.96813e6	−	8.30430e6i	−0.300756	−	0.358427i	−0.895164	+	0.445736i	$0.852942\pi$
$884$	17988.8	+	3.52019e6i	0.000774233	+	0.151508i
$885$	147797.	−	255992.i	0.00634318	−	0.0109867i
$886$	2.78558e7	−	4.98515e6i	1.19215	−	0.213351i
$887$	−3.95978e7	−	1.44124e7i	−1.68990	−	0.615075i	−0.695291	−	0.718728i	$-0.744725\pi$
$887$	−3.95978e7	−	1.44124e7i	−1.68990	−	0.615075i	−0.994614	+	0.103653i	$0.966947\pi$
$888$	4.08187e6	+	1.09529e7i	0.173711	+	0.466118i
$889$	1.22913e7	−	2.16729e6i	0.521607	−	0.0919734i
$890$	83221.6	+	3.25712e7i	0.00352177	+	1.37835i
$891$	−5.38347e6	+	6.41577e6i	−0.227179	+	0.270741i
$892$	−1.74273e7	−	1.44722e7i	−0.733363	−	0.609006i
$893$	1.89019e6	+	1.07801e6i	0.0793189	+	0.0452369i
$894$	−2.94324e6	−	1.06274e6i	−0.123163	−	0.0444717i
$895$	−9.01737e6	−	7.56647e6i	−0.376290	−	0.315744i
$896$	−2.80724e7	−	1.55450e7i	−1.16818	−	0.646874i
$897$	−778657.	−	4.41598e6i	−0.0323121	−	0.183251i
$898$	−2.71311e7	−	1.55718e7i	−1.12273	−	0.644390i
$899$	−2.57671e7	+	7.07945e7i	−1.06333	+	2.92146i
$900$	1.16498e6	−	6.81026e6i	0.0479416	−	0.280258i
$901$	4.76002e6	+	2.74820e6i	0.195342	+	0.112781i
$902$	−1.89369e6	+	694730.i	−0.0774982	+	0.0284315i
$903$	7.40115e6	−	6.21030e6i	0.302051	−	0.253451i
$904$	180980.	+	2.36102e7i	0.00736564	+	0.960901i
$905$	−7.80121e6	+	4.50403e6i	−0.316622	+	0.182802i
$906$	7.49273e6	+	6.25459e6i	0.303263	+	0.253150i
$907$	−5.62219e6	+	3.18850e7i	−0.226928	+	1.28697i	0.632038	+	0.774937i	$0.282219\pi$
$907$	−5.62219e6	+	3.18850e7i	−0.226928	+	1.28697i	−0.858966	+	0.512033i	$0.828892\pi$
$908$	112599.	−	197349.i	0.00453231	−	0.00794367i
$909$	1.92860e7	−	7.01954e6i	0.774165	−	0.281773i
$910$	−1.26363e7	−	2.17581e7i	−0.505842	−	0.870998i
$911$	1.73990e7			0.694591			0.347296	−	0.937756i	$-0.387100\pi$
$911$	1.73990e7			0.694591			0.347296	+	0.937756i	$0.387100\pi$
$912$	−1.09983e7	−	3.81091e6i	−0.437862	−	0.151720i
$913$	2.18733e6			0.0868437
$914$	−1.34475e7	−	2.31549e7i	−0.532446	−	0.916806i
$915$	−1.17092e7	+	4.26181e6i	−0.462355	+	0.168283i
$916$	2.30219e7	−	4.03498e7i	0.906571	−	1.58892i
$917$	−2.59760e6	+	1.47317e7i	−0.102012	+	0.578536i
$918$	−2.60154e6	−	2.17165e6i	−0.101888	−	0.0850517i
$919$	5.19736e6	−	3.00070e6i	0.202999	−	0.117202i	−0.395055	−	0.918658i	$-0.629274\pi$
$919$	5.19736e6	−	3.00070e6i	0.202999	−	0.117202i	0.598054	+	0.801456i	$0.295941\pi$
$920$	−66826.2	−	8.71796e6i	−0.00260302	−	0.339583i
$921$	−6.55553e6	+	5.50074e6i	−0.254659	+	0.213684i
$922$	−3.36082e7	+	1.23297e7i	−1.30202	+	0.477667i
$923$	2.94594e7	+	1.70084e7i	1.13820	+	0.657142i
$924$	−2.38129e6	+	1.39206e7i	−0.0917557	+	0.536387i
$925$	3.45933e6	−	9.50442e6i	0.132934	−	0.365234i
$926$	−2.53170e7	−	1.45307e7i	−0.970252	−	0.556875i
$927$	3.99431e6	+	2.26529e7i	0.152666	+	0.865813i
$928$	4.95836e7	−	9.39758e6i	1.89003	−	0.358217i
$929$	−3.47920e7	−	2.91940e7i	−1.32264	−	1.10982i	−0.985739	−	0.168281i	$-0.946178\pi$
$929$	−3.47920e7	−	2.91940e7i	−1.32264	−	1.10982i	−0.336896	−	0.941542i	$-0.609377\pi$
$930$	1.48395e7	+	5.35824e6i	0.562616	+	0.203149i
$931$	−3.48835e6	+	2.04144e7i	−0.131900	+	0.771904i
$932$	−1.69952e7	−	1.41133e7i	−0.640893	−	0.532216i
$933$	−3.55791e6	+	4.24015e6i	−0.133811	+	0.159469i
$934$	−29476.9	−	1.15366e7i	−0.00110564	−	0.432725i
$935$	2.96647e6	−	523068.i	0.110971	−	0.0195672i
$936$	6.94148e6	+	1.86261e7i	0.258978	+	0.694915i
$937$	2.50062e7	+	9.10150e6i	0.930461	+	0.338660i	0.762392	−	0.647115i	$-0.224025\pi$
$937$	2.50062e7	+	9.10150e6i	0.930461	+	0.338660i	0.168069	+	0.985775i	$0.446247\pi$
$938$	−3.68586e7	+	6.59631e6i	−1.36783	+	0.244790i
$939$	−2.54862e6	+	4.41433e6i	−0.0943280	+	0.163381i
$940$	10096.2	+	1.97571e6i	0.000372683	+	0.0729296i
$941$	−990139.	−	1.18000e6i	−0.0364521	−	0.0434419i	0.747510	−	0.664250i	$-0.231249\pi$
$941$	−990139.	−	1.18000e6i	−0.0364521	−	0.0434419i	−0.783962	+	0.620808i	$0.786805\pi$
$942$	1.88385e7	−	1.58896e7i	0.691701	−	0.583424i
$943$	−544931.	−	943848.i	−0.0199555	−	0.0345639i
$944$	153512.	−	925842.i	0.00560675	−	0.0338148i
$945$	2.38539e7	+	4.20609e6i	0.868920	+	0.153214i
$946$	2.63957e6	−	1.51967e7i	0.0958971	−	0.552105i
$947$	−1.06926e7	−	2.93776e7i	−0.387442	−	1.06449i	−0.968149	−	0.250376i	$-0.919446\pi$
$947$	−1.06926e7	−	2.93776e7i	−0.387442	−	1.06449i	0.580707	−	0.814113i	$-0.302776\pi$
$948$	2.94725e6	+	1.62293e7i	0.106511	+	0.586514i
$949$			3.50614e6i			0.126376i
$950$	5.10430e6	+	8.68286e6i	0.183496	+	0.312143i
$951$		−	1.93196e7i		−	0.692703i
$952$	5.90726e6	+	994984.i	0.211249	+	0.0355815i
$953$	−1.53406e7	−	4.21479e7i	−0.547154	−	1.50329i	−0.837535	−	0.546383i	$-0.816004\pi$
$953$	−1.53406e7	−	4.21479e7i	−0.547154	−	1.50329i	0.290381	−	0.956911i	$-0.406218\pi$
$954$	3.05783e7	+	5.31125e6i	1.08778	+	0.188941i
$955$	2.04064e7	+	3.59820e6i	0.724032	+	0.127666i
$956$	2.06698e7	−	1.20750e7i	0.731462	−	0.427308i
$957$	−1.11054e7	−	1.92352e7i	−0.391972	−	0.678916i
$958$	9.52788e6	+	1.12961e7i	0.335415	+	0.397664i
$959$	−9.96223e6	−	1.18725e7i	−0.349792	−	0.416866i
$960$	−1.99456e6	−	1.03787e7i	−0.0698505	−	0.363467i
$961$	−2.30745e7	+	3.99662e7i	−0.805979	+	1.39600i
$962$	5.12616e6	+	2.86437e7i	0.178589	+	0.997911i
$963$	1.26809e7	+	4.61549e6i	0.440642	+	0.160381i
$964$	2.50104e7	+	2.94987e7i	0.866817	+	1.02238i
$965$	1.07997e7	−	1.90427e6i	0.373329	−	0.0658281i
$966$	−7.63068e6	+	19496.9i	−0.263100	+	0.000672238i
$967$	1.46724e7	−	1.74859e7i	0.504586	−	0.601342i	−0.452279	−	0.891877i	$-0.649389\pi$
$967$	1.46724e7	−	1.74859e7i	0.504586	−	0.601342i	0.956864	+	0.290535i	$0.0938332\pi$
$968$	−3.34718e6	−	5.69620e6i	−0.114813	−	0.195388i
$969$	2.17292e6	−	11497.2i	0.0743420	−	0.000393352i
$970$	−5.51605e6	+	1.52766e7i	−0.188234	+	0.521310i
$971$	9.18576e6	+	7.70777e6i	0.312656	+	0.262350i	0.785589	−	0.618749i	$-0.212360\pi$
$971$	9.18576e6	+	7.70777e6i	0.312656	+	0.262350i	−0.472933	+	0.881099i	$0.656805\pi$
$972$	−2.81054e7	−	1.00672e7i	−0.954165	−	0.341776i
$973$	1.34753e7	+	7.64223e7i	0.456306	+	2.58784i
$974$	−1.94765e7	+	3.39343e7i	−0.657831	+	1.14615i
$975$	−1.60876e6	+	4.42002e6i	−0.0541974	+	0.148906i
$976$	−3.00445e7	+	2.57381e7i	−1.00958	+	0.864872i
$977$	−3.46432e7	−	2.00012e7i	−1.16113	−	0.670379i	−0.209556	−	0.977797i	$-0.567202\pi$
$977$	−3.46432e7	−	2.00012e7i	−1.16113	−	0.670379i	−0.951575	+	0.307418i	$0.900535\pi$
$978$	−4.00766e6	−	1.09240e7i	−0.133981	−	0.365204i
$979$	3.48645e7	−	2.92548e7i	1.16259	−	0.975530i
$980$	−1.76373e7	+	6.52171e6i	−0.586633	+	0.216918i
$981$	−2.78345e7	+	1.60702e7i	−0.923444	+	0.533151i
$982$	−2.73479e7	+	3.27615e7i	−0.904992	+	1.08414i
$983$	2.81547e6	−	1.59673e7i	0.0929324	−	0.527046i	−0.902429	−	0.430839i	$-0.858218\pi$
$983$	2.81547e6	−	1.59673e7i	0.0929324	−	0.527046i	0.995361	−	0.0962071i	$-0.0306711\pi$
$984$	−856972.	−	1.00554e6i	−0.0282149	−	0.0331065i
$985$	5.84533e6	−	2.12753e6i	0.191963	−	0.0698690i
$986$	−8.14692e6	+	4.73142e6i	−0.266871	+	0.154989i
$987$	1.72928e6			0.0565032
$988$	−2.52441e7	−	1.42267e7i	−0.822749	−	0.463672i
$989$	8.33388e6			0.270930
$990$	1.47084e7	−	8.54209e6i	0.476956	−	0.276998i
$991$	−1.25191e7	+	4.55659e6i	−0.404939	+	0.147386i	−0.536456	−	0.843928i	$-0.680237\pi$
$991$	−1.25191e7	+	4.55659e6i	−0.404939	+	0.147386i	0.131517	+	0.991314i	$0.458015\pi$
$992$	5.00872e7	−	639915.i	1.61602	−	0.0206464i
$993$	82706.4	−	469051.i	0.00266174	−	0.0150955i
$994$	3.70957e7	−	4.44390e7i	1.19085	−	1.42659i
$995$	−7.08666e6	+	4.09149e6i	−0.226926	+	0.131016i
$996$	496879.	+	1.34376e6i	0.0158709	+	0.0429213i
$997$	−1.57187e7	+	1.31895e7i	−0.500816	+	0.420235i	−0.857884	−	0.513844i	$-0.828221\pi$
$997$	−1.57187e7	+	1.31895e7i	−0.500816	+	0.420235i	0.357067	+	0.934079i	$0.383777\pi$
$998$	7.47212e6	+	2.03674e7i	0.237475	+	0.647305i
$999$	−2.42595e7	−	1.40062e7i	−0.769073	−	0.444024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.k.a.3.17	✓	288
4.3	odd	2	inner	76.6.k.a.3.44	yes	288
19.13	odd	18	inner	76.6.k.a.51.44	yes	288
76.51	even	18	inner	76.6.k.a.51.17	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.k.a.3.17	✓	288	1.1	even	1	trivial
76.6.k.a.3.44	yes	288	4.3	odd	2	inner
76.6.k.a.51.17	yes	288	76.51	even	18	inner
76.6.k.a.51.44	yes	288	19.13	odd	18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.84094 - 4.89174i) q^{2} +(-6.78809 + 2.47066i) q^{3} +(-15.8582 + 27.7942i) q^{4} +(-7.75313 + 43.9702i) q^{5} +(31.3703 + 26.1866i) q^{6} +(149.921 - 86.5570i) q^{7} +(181.014 - 1.38754i) q^{8} +(-146.175 + 122.655i) q^{9} +O(q^{10})\)	\(q+(-2.84094 - 4.89174i) q^{2} +(-6.78809 + 2.47066i) q^{3} +(-15.8582 + 27.7942i) q^{4} +(-7.75313 + 43.9702i) q^{5} +(31.3703 + 26.1866i) q^{6} +(149.921 - 86.5570i) q^{7} +(181.014 - 1.38754i) q^{8} +(-146.175 + 122.655i) q^{9} +(237.117 - 86.9902i) q^{10} +(-305.638 - 176.460i) q^{11} +(38.9766 - 227.850i) q^{12} +(196.820 - 540.759i) q^{13} +(-849.330 - 487.472i) q^{14} +(-56.0066 - 317.629i) q^{15} +(-521.037 - 881.531i) q^{16} +(146.439 + 122.877i) q^{17} +(1015.27 + 366.593i) q^{18} +(-1475.80 + 546.006i) q^{19} +(-1099.17 - 912.780i) q^{20} +(-803.824 + 957.961i) q^{21} +(5.10098 + 1996.41i) q^{22} +(-1062.30 + 187.312i) q^{23} +(-1225.31 + 456.643i) q^{24} +(1063.27 + 386.999i) q^{25} +(-3204.41 + 573.469i) q^{26} +(1566.89 - 2713.94i) q^{27} +(28.3082 + 5539.57i) q^{28} +(-5600.08 - 6673.91i) q^{29} +(-1394.65 + 1176.33i) q^{30} +(-4323.72 - 7488.90i) q^{31} +(-2831.99 + 5053.15i) q^{32} +(2510.67 + 442.700i) q^{33} +(185.058 - 1065.43i) q^{34} +(2643.57 + 7263.15i) q^{35} +(-1091.04 - 6007.90i) q^{36} -8938.85i q^{37} +(6863.56 + 5668.04i) q^{38} +4157.00i q^{39} +(-1342.42 + 7969.98i) q^{40} +(345.563 + 949.427i) q^{41} +(6969.70 + 1210.59i) q^{42} +(-7608.57 - 1341.60i) q^{43} +(9751.44 - 5696.64i) q^{44} +(-4259.86 - 7378.30i) q^{45} +(3934.21 + 4664.35i) q^{46} +(-888.873 - 1059.32i) q^{47} +(5714.81 + 4696.61i) q^{48} +(6580.72 - 11398.1i) q^{49} +(-1127.59 - 6300.68i) q^{50} +(-1297.63 - 472.299i) q^{51} +(11908.8 + 14045.9i) q^{52} +(28315.6 - 4992.80i) q^{53} +(-17727.3 + 45.2945i) q^{54} +(10128.7 - 12070.9i) q^{55} +(27017.7 - 15876.0i) q^{56} +(8668.84 - 7352.53i) q^{57} +(-16737.6 + 46354.2i) q^{58} +(702.070 + 589.106i) q^{59} +(9716.41 + 3480.36i) q^{60} +(-6708.79 - 38047.4i) q^{61} +(-24350.3 + 42426.0i) q^{62} +(-11298.0 + 31041.1i) q^{63} +(32764.1 - 502.327i) q^{64} +(22251.3 + 12846.8i) q^{65} +(-4967.09 - 13539.2i) q^{66} +(29290.8 - 24577.9i) q^{67} +(-5737.54 + 2121.56i) q^{68} +(6748.20 - 3896.08i) q^{69} +(28019.2 - 33565.8i) q^{70} +(-10264.7 + 58213.9i) q^{71} +(-26289.5 + 22405.1i) q^{72} +(-5725.28 + 2083.83i) q^{73} +(-43726.5 + 25394.7i) q^{74} -8173.72 q^{75} +(8227.63 - 49677.3i) q^{76} -61095.5 q^{77} +(20334.9 - 11809.8i) q^{78} +(-67053.1 + 24405.3i) q^{79} +(42800.8 - 16075.5i) q^{80} +(4120.86 - 23370.6i) q^{81} +(3662.62 - 4387.66i) q^{82} +(-5367.46 + 3098.90i) q^{83} +(-13878.6 - 37533.2i) q^{84} +(-6538.30 + 5486.29i) q^{85} +(15052.7 + 41030.5i) q^{86} +(54502.8 + 31467.2i) q^{87} +(-55569.7 - 31517.7i) q^{88} +(-44106.7 + 121182. i) q^{89} +(-23990.7 + 41799.4i) q^{90} +(-17299.0 - 98107.4i) q^{91} +(11639.9 - 32496.2i) q^{92} +(47852.3 + 40152.9i) q^{93} +(-2656.67 + 7357.58i) q^{94} +(-12566.0 - 69124.4i) q^{95} +(6739.16 - 41298.1i) q^{96} +(-41335.5 + 49261.7i) q^{97} +(-74452.1 + 190.230i) q^{98} +(66320.4 - 11694.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Introduction

L-functions

Modular forms

Varieties

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