LMFDB - Embedded newform 33.6.e.b.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.e (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:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} + \cdots + 25599187870096 $ x^20 - x^19 + 78x^18 + 79x^17 + 10573x^16 - 33409x^15 + 1262953x^14 - 1581925x^13 + 89291182x^12 - 100741271x^11 + 2277268901x^10 - 1144062486x^9 + 70677624924x^8 + 93641098134x^7 + 1732079176577x^6 + 1113900934906x^5 + 27749747552381x^4 + 4154923377746x^3 + 57625758470132x^2 + 60036938210920x + 25599187870096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.5
Root			$7.96653 - 5.78803i$ of defining polynomial
Character	$\chi$	$=$	33.4
Dual form			33.6.e.b.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.77555 + 6.37581i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(26.4708 + 81.4687i) q^{4} +(31.3852 - 22.8027i) q^{5} +(-78.9800 + 57.3823i) q^{6} +(-67.6896 - 208.327i) q^{7} +(-179.871 + 553.584i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})$	\(q+(8.77555 + 6.37581i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(26.4708 + 81.4687i) q^{4} +(31.3852 - 22.8027i) q^{5} +(-78.9800 + 57.3823i) q^{6} +(-67.6896 - 208.327i) q^{7} +(-179.871 + 553.584i) q^{8} +(-65.5304 - 47.6106i) q^{9} +420.808 q^{10} +(313.554 + 250.469i) q^{11} -770.951 q^{12} +(32.8450 + 23.8633i) q^{13} +(734.241 - 2259.76i) q^{14} +(107.893 + 332.060i) q^{15} +(-2890.37 + 2099.97i) q^{16} +(516.753 - 375.443i) q^{17} +(-271.509 - 835.619i) q^{18} +(427.464 - 1315.60i) q^{19} +(2688.50 + 1953.31i) q^{20} +1971.43 q^{21} +(1154.67 + 4197.17i) q^{22} -799.310 q^{23} +(-4238.16 - 3079.21i) q^{24} +(-500.610 + 1540.72i) q^{25} +(136.085 + 418.826i) q^{26} +(589.773 - 428.495i) q^{27} +(15180.3 - 11029.2i) q^{28} +(-1319.88 - 4062.16i) q^{29} +(-1170.33 + 3601.91i) q^{30} +(-4931.04 - 3582.61i) q^{31} -20127.3 q^{32} +(-3015.93 + 1987.28i) q^{33} +6928.55 q^{34} +(-6874.87 - 4994.88i) q^{35} +(2144.13 - 6598.96i) q^{36} +(3018.37 + 9289.60i) q^{37} +(12139.2 - 8819.67i) q^{38} +(-295.605 + 214.769i) q^{39} +(6977.94 + 21475.9i) q^{40} +(-1351.42 + 4159.25i) q^{41} +(17300.4 + 12569.5i) q^{42} +2017.22 q^{43} +(-12105.3 + 32175.0i) q^{44} -3142.33 q^{45} +(-7014.39 - 5096.25i) q^{46} +(110.244 - 339.295i) q^{47} +(-9936.20 - 30580.5i) q^{48} +(-25221.1 + 18324.2i) q^{49} +(-14216.5 + 10328.9i) q^{50} +(1776.44 + 5467.32i) q^{51} +(-1074.68 + 3307.52i) q^{52} +(-28795.3 - 20921.0i) q^{53} +7907.59 q^{54} +(15552.3 + 711.130i) q^{55} +127502. q^{56} +(10072.0 + 7317.76i) q^{57} +(14316.9 - 44063.0i) q^{58} +(-3667.59 - 11287.7i) q^{59} +(-24196.5 + 17579.8i) q^{60} +(-22766.8 + 16541.0i) q^{61} +(-20430.6 - 62878.8i) q^{62} +(-5482.85 + 16874.5i) q^{63} +(-84136.1 - 61128.5i) q^{64} +1574.99 q^{65} +(-39137.0 - 1789.54i) q^{66} +21369.8 q^{67} +(44265.7 + 32160.9i) q^{68} +(2223.00 - 6841.70i) q^{69} +(-28484.3 - 87665.7i) q^{70} +(-1968.99 + 1430.56i) q^{71} +(38143.5 - 27712.9i) q^{72} +(20773.7 + 63934.8i) q^{73} +(-32740.8 + 100766. i) q^{74} +(-11795.5 - 8569.94i) q^{75} +118495. q^{76} +(30955.1 - 82276.0i) q^{77} -3963.42 q^{78} +(-26787.6 - 19462.3i) q^{79} +(-42829.7 + 131816. i) q^{80} +(2027.46 + 6239.88i) q^{81} +(-38378.0 + 27883.3i) q^{82} +(54821.4 - 39830.1i) q^{83} +(52185.4 + 160610. i) q^{84} +(7657.29 - 23566.7i) q^{85} +(17702.2 + 12861.4i) q^{86} +38440.9 q^{87} +(-195055. + 128527. i) q^{88} +69719.1 q^{89} +(-27575.7 - 20034.9i) q^{90} +(2748.10 - 8457.79i) q^{91} +(-21158.4 - 65118.8i) q^{92} +(44379.4 - 32243.5i) q^{93} +(3130.73 - 2274.61i) q^{94} +(-16583.1 - 51037.6i) q^{95} +(55977.0 - 172280. i) q^{96} +(136758. + 99360.2i) q^{97} -338161. q^{98} +(-8622.37 - 31341.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	8.77555	+	6.37581i	1.55131	+	1.12709i	0.942707	+	0.333622i	$0.108271\pi$
$2$	8.77555	+	6.37581i	1.55131	+	1.12709i	0.608606	+	0.793473i	$0.291729\pi$
$3$	−2.78115	+	8.55951i	−0.178411	+	0.549093i
$3$	−2.78115	+	8.55951i	−0.178411	+	0.549093i
$4$	26.4708	+	81.4687i	0.827212	+	2.54590i
$5$	31.3852	−	22.8027i	0.561436	−	0.407907i	−0.270548	−	0.962706i	$-0.587205\pi$
$5$	31.3852	−	22.8027i	0.561436	−	0.407907i	0.831984	+	0.554800i	$0.187205\pi$
$6$	−78.9800	+	57.3823i	−0.895651	+	0.650728i
$7$	−67.6896	−	208.327i	−0.522128	−	1.60694i	−0.769927	−	0.638132i	$-0.779707\pi$
$7$	−67.6896	−	208.327i	−0.522128	−	1.60694i	0.247799	−	0.968811i	$-0.420293\pi$
$8$	−179.871	+	553.584i	−0.993654	+	3.05815i
$9$	−65.5304	−	47.6106i	−0.269672	−	0.195928i
$10$	420.808			1.33071
$11$	313.554	+	250.469i	0.781324	+	0.624125i
$11$	313.554	+	250.469i	0.781324	+	0.624125i
$12$	−770.951			−1.54552
$13$	32.8450	+	23.8633i	0.0539027	+	0.0391626i	0.614410	−	0.788987i	$-0.289394\pi$
$13$	32.8450	+	23.8633i	0.0539027	+	0.0391626i	−0.560508	+	0.828149i	$0.689394\pi$
$14$	734.241	−	2259.76i	1.00119	−	3.08136i
$15$	107.893	+	332.060i	0.123812	+	0.381055i
$16$	−2890.37	+	2099.97i	−2.82262	+	2.05076i
$17$	516.753	−	375.443i	0.433672	−	0.315081i	−0.349444	−	0.936957i	$-0.613629\pi$
$17$	516.753	−	375.443i	0.433672	−	0.315081i	0.783115	+	0.621876i	$0.213629\pi$
$18$	−271.509	−	835.619i	−0.197516	−	0.607893i
$19$	427.464	−	1315.60i	0.271653	−	0.836063i	−0.718432	−	0.695597i	$-0.755140\pi$
$19$	427.464	−	1315.60i	0.271653	−	0.836063i	0.990086	−	0.140466i	$-0.0448601\pi$
$20$	2688.50	+	1953.31i	1.50291	+	1.09193i
$21$	1971.43			0.975514
$22$	1154.67	+	4197.17i	0.508630	+	1.84884i
$23$	−799.310			−0.315062			−0.157531	−	0.987514i	$-0.550353\pi$
$23$	−799.310			−0.315062			−0.157531	+	0.987514i	$0.550353\pi$
$24$	−4238.16	−	3079.21i	−1.50193	−	1.09122i
$25$	−500.610	+	1540.72i	−0.160195	+	0.493030i
$26$	136.085	+	418.826i	0.0394800	+	0.121507i
$27$	589.773	−	428.495i	0.155695	−	0.113119i
$28$	15180.3	−	11029.2i	3.65920	−	2.65857i
$29$	−1319.88	−	4062.16i	−0.291433	−	0.896937i	−0.984396	−	0.175965i	$-0.943695\pi$
$29$	−1319.88	−	4062.16i	−0.291433	−	0.896937i	0.692964	−	0.720972i	$-0.256305\pi$
$30$	−1170.33	+	3601.91i	−0.237414	+	0.730684i
$31$	−4931.04	−	3582.61i	−0.921583	−	0.669569i	0.0223345	−	0.999751i	$-0.492890\pi$
$31$	−4931.04	−	3582.61i	−0.921583	−	0.669569i	−0.943918	+	0.330181i	$0.892890\pi$
$32$	−20127.3			−3.47464
$33$	−3015.93	+	1987.28i	−0.482100	+	0.317669i
$34$	6928.55			1.02789
$35$	−6874.87	−	4994.88i	−0.948624	−	0.689216i
$36$	2144.13	−	6598.96i	0.275737	−	0.848632i
$37$	3018.37	+	9289.60i	0.362467	+	1.11556i	0.951552	+	0.307488i	$0.0994884\pi$
$37$	3018.37	+	9289.60i	0.362467	+	1.11556i	−0.589085	+	0.808071i	$0.700512\pi$
$38$	12139.2	−	8819.67i	1.36374	−	0.990816i
$39$	−295.605	+	214.769i	−0.0311207	+	0.0226105i
$40$	6977.94	+	21475.9i	0.689568	+	2.12227i
$41$	−1351.42	+	4159.25i	−0.125554	+	0.386416i	−0.994002	−	0.109365i	$-0.965118\pi$
$41$	−1351.42	+	4159.25i	−0.125554	+	0.386416i	0.868448	+	0.495781i	$0.165118\pi$
$42$	17300.4	+	12569.5i	1.51333	+	1.09950i
$43$	2017.22			0.166373			0.0831864	−	0.996534i	$-0.473490\pi$
$43$	2017.22			0.166373			0.0831864	+	0.996534i	$0.473490\pi$
$44$	−12105.3	+	32175.0i	−0.942638	+	2.50545i
$45$	−3142.33			−0.231324
$46$	−7014.39	−	5096.25i	−0.488759	−	0.355105i
$47$	110.244	−	339.295i	0.00727961	−	0.0224043i	−0.947351	−	0.320198i	$-0.896251\pi$
$47$	110.244	−	339.295i	0.00727961	−	0.0224043i	0.954630	+	0.297793i	$0.0962506\pi$
$48$	−9936.20	−	30580.5i	−0.622468	−	1.91576i
$49$	−25221.1	+	18324.2i	−1.50063	+	1.09027i
$50$	−14216.5	+	10328.9i	−0.804204	+	0.584288i
$51$	1776.44	+	5467.32i	0.0956368	+	0.294340i
$52$	−1074.68	+	3307.52i	−0.0551150	+	0.169626i
$53$	−28795.3	−	20921.0i	−1.40810	−	1.02304i	−0.993596	−	0.112992i	$-0.963956\pi$
$53$	−28795.3	−	20921.0i	−1.40810	−	1.02304i	−0.414500	−	0.910049i	$-0.636044\pi$
$54$	7907.59			0.369028
$55$	15552.3	+	711.130i	0.693248	+	0.0316988i
$56$	127502.			5.43309
$57$	10072.0	+	7317.76i	0.410610	+	0.298326i
$58$	14316.9	−	44063.0i	0.558830	−	1.71990i
$59$	−3667.59	−	11287.7i	−0.137167	−	0.422158i	0.858753	−	0.512389i	$-0.171239\pi$
$59$	−3667.59	−	11287.7i	−0.137167	−	0.422158i	−0.995921	+	0.0902311i	$0.971239\pi$
$60$	−24196.5	+	17579.8i	−0.867708	+	0.630427i
$61$	−22766.8	+	16541.0i	−0.783388	+	0.569164i	−0.905994	−	0.423291i	$-0.860875\pi$
$61$	−22766.8	+	16541.0i	−0.783388	+	0.569164i	0.122606	+	0.992455i	$0.460875\pi$
$62$	−20430.6	−	62878.8i	−0.674996	−	2.07742i
$63$	−5482.85	+	16874.5i	−0.174043	+	0.535648i
$64$	−84136.1	−	61128.5i	−2.56763	−	1.86549i
$65$	1574.99			0.0462376
$66$	−39137.0	−	1789.54i	−1.10593	−	0.0505686i
$67$	21369.8			0.581586			0.290793	−	0.956786i	$-0.406081\pi$
$67$	21369.8			0.581586			0.290793	+	0.956786i	$0.406081\pi$
$68$	44265.7	+	32160.9i	1.16090	+	0.843444i
$69$	2223.00	−	6841.70i	0.0562105	−	0.172998i
$70$	−28484.3	−	87665.7i	−0.694801	−	2.13838i
$71$	−1968.99	+	1430.56i	−0.0463551	+	0.0336790i	−0.610722	−	0.791845i	$-0.709121\pi$
$71$	−1968.99	+	1430.56i	−0.0463551	+	0.0336790i	0.564366	+	0.825524i	$0.309121\pi$
$72$	38143.5	−	27712.9i	0.867140	−	0.630014i
$73$	20773.7	+	63934.8i	0.456253	+	1.40420i	0.869657	+	0.493656i	$0.164340\pi$
$73$	20773.7	+	63934.8i	0.456253	+	1.40420i	−0.413404	+	0.910548i	$0.635660\pi$
$74$	−32740.8	+	100766.i	−0.695041	+	2.13912i
$75$	−11795.5	−	8569.94i	−0.242138	−	0.175924i
$76$	118495.			2.35324
$77$	30955.1	−	82276.0i	0.594983	−	1.58142i
$78$	−3963.42			−0.0737622
$79$	−26787.6	−	19462.3i	−0.482910	−	0.350854i	0.319542	−	0.947572i	$-0.396471\pi$
$79$	−26787.6	−	19462.3i	−0.482910	−	0.350854i	−0.802451	+	0.596718i	$0.796471\pi$
$80$	−42829.7	+	131816.i	−0.748204	+	2.30274i
$81$	2027.46	+	6239.88i	0.0343352	+	0.105673i
$82$	−38378.0	+	27883.3i	−0.630301	+	0.457941i
$83$	54821.4	−	39830.1i	0.873484	−	0.634623i	−0.0580356	−	0.998315i	$-0.518484\pi$
$83$	54821.4	−	39830.1i	0.873484	−	0.634623i	0.931520	+	0.363691i	$0.118484\pi$
$84$	52185.4	+	160610.i	0.806957	+	2.48356i
$85$	7657.29	−	23566.7i	0.114955	−	0.353795i
$86$	17702.2	+	12861.4i	0.258096	+	0.187518i
$87$	38440.9			0.544497
$88$	−195055.	+	128527.i	−2.68504	+	1.76924i
$89$	69719.1			0.932989			0.466495	−	0.884524i	$-0.345517\pi$
$89$	69719.1			0.932989			0.466495	+	0.884524i	$0.345517\pi$
$90$	−27575.7	−	20034.9i	−0.358856	−	0.260724i
$91$	2748.10	−	8457.79i	0.0347880	−	0.107066i
$92$	−21158.4	−	65118.8i	−0.260623	−	0.802115i
$93$	44379.4	−	32243.5i	0.532076	−	0.386576i
$94$	3130.73	−	2274.61i	0.0365448	−	0.0265513i
$95$	−16583.1	−	51037.6i	−0.188520	−	0.580205i
$96$	55977.0	−	172280.i	0.619914	−	1.90790i
$97$	136758.	+	99360.2i	1.47578	+	1.07222i	0.978886	+	0.204407i	$0.0655267\pi$
$97$	136758.	+	99360.2i	1.47578	+	1.07222i	0.496895	+	0.867811i	$0.334473\pi$
$98$	−338161.			−3.55679
$99$	−8622.37	−	31341.8i	−0.0884176	−	0.321393i
$100$	−138772.			−1.38772
$101$	−51456.8	−	37385.6i	−0.501926	−	0.364671i	0.307826	−	0.951443i	$-0.400398\pi$
$101$	−51456.8	−	37385.6i	−0.501926	−	0.364671i	−0.809752	+	0.586772i	$0.800398\pi$
$102$	−19269.4	+	59305.0i	−0.183386	+	0.564405i
$103$	−22346.7	−	68775.9i	−0.207548	−	0.638768i	−0.999599	−	0.0283130i	$-0.990986\pi$
$103$	−22346.7	−	68775.9i	−0.207548	−	0.638768i	0.792051	−	0.610455i	$-0.209014\pi$
$104$	−19118.2	+	13890.2i	−0.173326	+	0.125928i
$105$	61873.8	−	44953.9i	0.547688	−	0.397919i
$106$	−119306.	−	367187.i	−1.03133	−	3.17411i
$107$	−22166.4	+	68221.1i	−0.187170	+	0.576049i	−0.999979	−	0.00648071i	$-0.997937\pi$
$107$	−22166.4	+	68221.1i	−0.187170	+	0.576049i	0.812809	+	0.582530i	$0.197937\pi$
$108$	50520.7	+	36705.5i	0.416783	+	0.302811i
$109$	87556.4			0.705865			0.352932	−	0.935649i	$-0.385185\pi$
$109$	87556.4			0.705865			0.352932	+	0.935649i	$0.385185\pi$
$110$	131946.	+	105399.i	1.03972	+	0.830531i
$111$	−87909.0			−0.677214
$112$	633129.	+	459995.i	4.76922	+	3.46504i
$113$	−60708.7	+	186842.i	−0.447255	+	1.37651i	0.432737	+	0.901520i	$0.357548\pi$
$113$	−60708.7	+	186842.i	−0.447255	+	1.37651i	−0.879992	+	0.474988i	$0.842452\pi$
$114$	41731.0	+	128435.i	0.300743	+	0.925593i
$115$	−25086.5	+	18226.4i	−0.176887	+	0.128516i
$116$	296001.	−	215057.i	2.04243	−	1.48391i
$117$	−1016.20	−	3127.54i	−0.00686300	−	0.0211221i
$118$	39783.0	−	122440.i	0.263022	−	0.809500i
$119$	−113194.	−	82240.1i	−0.732749	−	0.532373i
$120$	−203230.			−1.28835
$121$	35581.8	+	157071.i	0.220935	+	0.975289i
$122$	−305253.			−1.85678
$123$	−31842.6	−	23135.0i	−0.189778	−	0.137882i
$124$	161342.	−	496560.i	0.942310	−	2.90013i
$125$	56883.5	+	175069.i	0.325620	+	1.00216i
$126$	−155704.	+	113125.i	−0.873720	+	0.634795i
$127$	−152225.	+	110598.i	−0.837484	+	0.608468i	−0.921667	−	0.387982i	$-0.873172\pi$
$127$	−152225.	+	110598.i	−0.837484	+	0.608468i	0.0841825	+	0.996450i	$0.473172\pi$
$128$	−149568.	−	460322.i	−0.806888	−	2.48335i
$129$	−5610.20	+	17266.4i	−0.0296828	+	0.0913541i
$130$	13821.4	+	10041.9i	0.0717289	+	0.0521141i
$131$	345605.			1.75955			0.879776	−	0.475388i	$-0.157692\pi$
$131$	345605.			1.75955			0.879776	+	0.475388i	$0.157692\pi$
$132$	−241735.	−	193099.i	−1.20755	−	0.964597i
$133$	−303009.			−1.48534
$134$	187532.	+	136250.i	0.902221	+	0.655502i
$135$	8739.31	−	26896.8i	0.0412708	−	0.127018i
$136$	114891.	+	353598.i	0.532646	+	1.63931i
$137$	36871.0	−	26788.3i	0.167835	−	0.121939i	−0.500697	−	0.865623i	$-0.666923\pi$
$137$	36871.0	−	26788.3i	0.167835	−	0.121939i	0.668532	+	0.743683i	$0.266923\pi$
$138$	63129.5	−	45866.3i	0.282185	−	0.205020i
$139$	−19547.2	−	60160.1i	−0.0858119	−	0.264102i	0.898939	−	0.438075i	$-0.144339\pi$
$139$	−19547.2	−	60160.1i	−0.0858119	−	0.264102i	−0.984750	+	0.173973i	$0.944339\pi$
$140$	224943.	−	692305.i	0.969959	−	2.98523i
$141$	2597.59	+	1887.26i	0.0110033	+	0.00799437i
$142$	−26399.9			−0.109871
$143$	4321.68	+	15709.1i	0.0176731	+	0.0642407i
$144$	289388.			1.16299
$145$	−134053.	−	97395.0i	−0.529487	−	0.384695i
$146$	−225336.	+	693512.i	−0.874879	+	2.69260i
$147$	−86702.5	−	266843.i	−0.330932	−	1.01850i
$148$	−676913.	+	491806.i	−2.54026	+	1.84561i
$149$	60321.5	−	43826.1i	0.222590	−	0.161721i	−0.470902	−	0.882186i	$-0.656071\pi$
$149$	60321.5	−	43826.1i	0.222590	−	0.161721i	0.693492	+	0.720464i	$0.256071\pi$
$150$	−48871.8	−	150412.i	−0.177350	−	0.545826i
$151$	−11587.9	+	35663.9i	−0.0413583	+	0.127288i	−0.969604	−	0.244680i	$-0.921317\pi$
$151$	−11587.9	+	35663.9i	−0.0413583	+	0.127288i	0.928245	+	0.371968i	$0.121317\pi$
$152$	651406.	+	473274.i	2.28688	+	1.66151i
$153$	−51738.1			−0.178683
$154$	796224.	−	524654.i	2.70541	−	1.78267i
$155$	−236455.			−0.790531
$156$	−25321.9	−	18397.4i	−0.0833075	−	0.0605264i
$157$	−120640.	+	371290.i	−0.390608	+	1.20217i	0.541722	+	0.840557i	$0.317772\pi$
$157$	−120640.	+	371290.i	−0.390608	+	1.20217i	−0.932330	+	0.361609i	$0.882228\pi$
$158$	−110988.	−	341585.i	−0.353698	−	1.08857i
$159$	259158.	−	188289.i	0.812965	−	0.590653i
$160$	−631698.	+	458956.i	−1.95079	+	1.41733i
$161$	54105.0	+	166518.i	0.164502	+	0.506286i
$162$	−21992.2	+	67685.1i	−0.0658388	+	0.202631i
$163$	−274567.	−	199485.i	−0.809431	−	0.588086i	0.104234	−	0.994553i	$-0.466761\pi$
$163$	−274567.	−	199485.i	−0.809431	−	0.588086i	−0.913666	+	0.406467i	$0.866761\pi$
$164$	−374622.			−1.08763
$165$	−49340.3	+	131143.i	−0.141089	+	0.375002i
$166$	735037.			2.07033
$167$	−50921.1	−	36996.3i	−0.141288	−	0.102652i	0.514896	−	0.857253i	$-0.327831\pi$
$167$	−50921.1	−	36996.3i	−0.141288	−	0.102652i	−0.656184	+	0.754601i	$0.727831\pi$
$168$	−354602.	+	1.09135e6i	−0.969323	+	2.98327i
$169$	−114227.	−	351553.i	−0.307645	−	0.946835i
$170$	217454.	−	157990.i	0.577092	−	0.419282i
$171$	−90648.2	+	65859.8i	−0.237066	+	0.172238i
$172$	53397.4	+	164340.i	0.137626	+	0.423568i
$173$	−146159.	+	449831.i	−0.371287	+	1.14270i	0.574662	+	0.818391i	$0.305133\pi$
$173$	−146159.	+	449831.i	−0.371287	+	1.14270i	−0.945950	+	0.324314i	$0.894867\pi$
$174$	337340.	+	245092.i	0.844685	+	0.613699i
$175$	354859.			0.875913
$176$	−1.43227e6	−	65490.3i	−3.48531	−	0.159366i
$177$	106817.			0.256276
$178$	611823.	+	444516.i	1.44736	+	1.05157i
$179$	89865.8	−	276578.i	0.209634	−	0.645187i	−0.789857	−	0.613291i	$-0.789845\pi$
$179$	89865.8	−	276578.i	0.209634	−	0.645187i	0.999491	−	0.0318964i	$-0.0101547\pi$
$180$	−83180.0	−	256002.i	−0.191354	−	0.588927i
$181$	313275.	−	227608.i	0.710771	−	0.516406i	−0.172651	−	0.984983i	$-0.555233\pi$
$181$	313275.	−	227608.i	0.710771	−	0.516406i	0.883422	+	0.468578i	$0.155233\pi$
$182$	78041.4	−	56700.4i	0.174641	−	0.126884i
$183$	−78265.2	−	240875.i	−0.172759	−	0.531698i
$184$	143772.	−	442486.i	0.313062	−	0.963507i
$185$	306560.	+	222729.i	0.658546	+	0.478462i
$186$	595032.			1.26112
$187$	256067.	+	11708.7i	0.535488	+	0.0244852i
$188$	30560.1			0.0630609
$189$	−129189.	−	93861.1i	−0.263069	−	0.191131i
$190$	179880.	−	553614.i	0.361492	−	1.11256i
$191$	−254984.	−	784759.i	−0.505742	−	1.55651i	−0.799520	−	0.600640i	$-0.794913\pi$
$191$	−254984.	−	784759.i	−0.505742	−	1.55651i	0.293778	−	0.955874i	$-0.405087\pi$
$192$	757225.	−	550156.i	1.48242	−	1.07704i
$193$	390657.	−	283829.i	0.754923	−	0.548484i	−0.142426	−	0.989805i	$-0.545490\pi$
$193$	390657.	−	283829.i	0.754923	−	0.548484i	0.897349	+	0.441322i	$0.145490\pi$
$194$	566621.	+	1.74388e6i	1.08091	+	3.32669i
$195$	−4380.29	+	13481.2i	−0.00824929	+	0.0253887i
$196$	−2.16047e6	−	1.56968e6i	−4.01706	−	2.91857i
$197$	300533.			0.551730			0.275865	−	0.961196i	$-0.411036\pi$
$197$	300533.			0.551730			0.275865	+	0.961196i	$0.411036\pi$
$198$	124164.	−	330016.i	0.225077	−	0.598236i
$199$	−946020.			−1.69343			−0.846716	−	0.532045i	$-0.821424\pi$
$199$	−946020.			−1.69343			−0.846716	+	0.532045i	$0.821424\pi$
$200$	−762873.	−	554259.i	−1.34858	−	0.979801i
$201$	−59432.7	+	182915.i	−0.103761	+	0.319344i
$202$	−213199.	−	656158.i	−0.367626	−	1.13144i
$203$	−756916.	+	549932.i	−1.28916	+	0.936631i
$204$	−398392.	+	289448.i	−0.670247	+	0.486963i
$205$	52427.4	+	161355.i	0.0871311	+	0.268162i
$206$	242398.	−	746025.i	0.397980	−	1.22486i
$207$	52379.1	+	38055.6i	0.0849635	+	0.0617296i
$208$	−145046.			−0.232460
$209$	463549.	−	305445.i	0.734057	−	0.483690i
$210$	829595.			1.29813
$211$	850656.	+	618038.i	1.31537	+	0.955672i	0.999977	+	0.00671130i	$0.00213629\pi$
$211$	850656.	+	618038.i	1.31537	+	0.955672i	0.315393	+	0.948961i	$0.397864\pi$
$212$	942174.	−	2.89971e6i	1.43976	−	4.43114i
$213$	−6768.79	−	20832.2i	−0.0102226	−	0.0314620i
$214$	−629487.	+	457349.i	−0.939621	+	0.682674i
$215$	63310.9	−	45998.1i	0.0934077	−	0.0678646i
$216$	131126.	+	403563.i	0.191229	+	0.588541i
$217$	−412575.	+	1.26977e6i	−0.594776	+	1.83053i
$218$	768355.	+	558243.i	1.09502	+	0.795576i
$219$	−605025.			−0.852439
$220$	353748.	+	1.28585e6i	0.492761	+	1.79116i
$221$	25932.0			0.0357154
$222$	−771450.	−	560491.i	−1.05057	−	0.763284i
$223$	169535.	−	521775.i	0.228296	−	0.702621i	−0.769645	−	0.638472i	$-0.779567\pi$
$223$	169535.	−	521775.i	0.228296	−	0.702621i	0.997940	−	0.0641491i	$-0.0204333\pi$
$224$	1.36241e6	+	4.19305e6i	1.81421	+	5.58355i
$225$	106160.	−	77129.5i	0.139799	−	0.101570i
$226$	−1.72402e6	+	1.25258e6i	−2.24529	+	1.63130i
$227$	−124962.	−	384593.i	−0.160958	−	0.495378i	0.837758	−	0.546042i	$-0.183866\pi$
$227$	−124962.	−	384593.i	−0.160958	−	0.495378i	−0.998716	+	0.0506643i	$0.983866\pi$
$228$	−329554.	+	1.01426e6i	−0.419845	+	1.29215i
$229$	−76471.5	−	55559.8i	−0.0963632	−	0.0700119i	0.538560	−	0.842587i	$-0.318968\pi$
$229$	−76471.5	−	55559.8i	−0.0963632	−	0.0700119i	−0.634924	+	0.772575i	$0.718968\pi$
$230$	−336356.			−0.419257
$231$	618151.	+	493782.i	0.762193	+	0.608843i
$232$	2.48616e6			3.03255
$233$	−581255.	−	422306.i	−0.701418	−	0.509610i	0.178976	−	0.983853i	$-0.442722\pi$
$233$	−581255.	−	422306.i	−0.701418	−	0.509610i	−0.880394	+	0.474244i	$0.842722\pi$
$234$	11022.9	−	33924.9i	0.0131600	−	0.0405023i
$235$	−4276.81	−	13162.7i	−0.00505185	−	0.0155480i
$236$	822509.	−	597588.i	0.961304	−	0.698428i
$237$	241088.	−	175161.i	0.278808	−	0.202566i
$238$	−468991.	−	1.44340e6i	−0.536688	−	1.65176i
$239$	−22144.1	+	68152.6i	−0.0250763	+	0.0771770i	−0.962811	−	0.270174i	$-0.912919\pi$
$239$	−22144.1	+	68152.6i	−0.0250763	+	0.0771770i	0.937735	+	0.347351i	$0.112919\pi$
$240$	−1.00917e6	−	733202.i	−1.13093	−	0.821667i
$241$	237149.			0.263014			0.131507	−	0.991315i	$-0.458018\pi$
$241$	237149.			0.263014			0.131507	+	0.991315i	$0.458018\pi$
$242$	−689206.	+	1.60525e6i	−0.756503	+	1.76199i
$243$	−59049.0			−0.0641500
$244$	−1.95023e6	−	1.41692e6i	−2.09706	−	1.52360i
$245$	−373729.	+	1.15022e6i	−0.397779	+	1.22424i
$246$	−131932.	−	406045.i	−0.138999	−	0.427795i
$247$	45434.5	−	33010.1i	0.0473852	−	0.0344274i
$248$	2.87023e6	−	2.08534e6i	2.96338	−	2.15302i
$249$	188459.	+	580018.i	0.192628	+	0.592847i
$250$	−617026.	+	1.89901e6i	−0.624386	+	1.92166i
$251$	−826366.	−	600390.i	−0.827919	−	0.601518i	0.0910507	−	0.995846i	$-0.470977\pi$
$251$	−826366.	−	600390.i	−0.827919	−	0.601518i	−0.918970	+	0.394328i	$0.870977\pi$
$252$	−1.51988e6			−1.50767
$253$	−250627.	−	200202.i	−0.246165	−	0.196638i
$254$	−2.04101e6			−1.98500
$255$	180424.	+	131085.i	0.173757	+	0.126242i
$256$	594000.	−	1.82814e6i	0.566483	−	1.74345i
$257$	−109152.	−	335936.i	−0.103086	−	0.317266i	0.886190	−	0.463321i	$-0.153342\pi$
$257$	−109152.	−	335936.i	−0.103086	−	0.317266i	−0.989276	+	0.146055i	$0.953342\pi$
$258$	−159320.	+	115753.i	−0.149012	+	0.108264i
$259$	1.73096e6	−	1.25762e6i	1.60339	−	1.16493i
$260$	41691.3	+	128313.i	0.0382483	+	0.117716i
$261$	−106910.	+	329035.i	−0.0971442	+	0.298979i
$262$	3.03288e6	+	2.20351e6i	2.72962	+	1.98318i
$263$	1.20912e6			1.07790			0.538950	−	0.842338i	$-0.318821\pi$
$263$	1.20912e6			1.07790			0.538950	+	0.842338i	$0.318821\pi$
$264$	−557650.	−	2.02703e6i	−0.492438	−	1.78999i
$265$	−1.38080e6			−1.20786
$266$	−2.65907e6	−	1.93193e6i	−2.30423	−	1.67412i
$267$	−193899.	+	596761.i	−0.166456	+	0.512298i
$268$	565676.	+	1.74097e6i	0.481095	+	1.48066i
$269$	−81918.1	+	59517.0i	−0.0690238	+	0.0501488i	−0.621762	−	0.783206i	$-0.713583\pi$
$269$	−81918.1	+	59517.0i	−0.0690238	+	0.0501488i	0.552738	+	0.833355i	$0.313583\pi$
$270$	248181.	−	180314.i	0.207186	−	0.150529i
$271$	−11458.8	−	35266.5i	−0.00947796	−	0.0291702i	0.946206	−	0.323566i	$-0.104882\pi$
$271$	−11458.8	−	35266.5i	−0.00947796	−	0.0291702i	−0.955684	+	0.294396i	$0.904882\pi$
$272$	−705186.	+	2.17034e6i	−0.577938	+	1.77871i
$273$	64751.6	+	47044.8i	0.0525828	+	0.0382037i
$274$	494360.			0.397802
$275$	−542870.	+	357712.i	−0.432877	+	0.285234i
$276$	616229.			0.486933
$277$	−520856.	−	378424.i	−0.407867	−	0.296333i	0.364871	−	0.931058i	$-0.381113\pi$
$277$	−520856.	−	378424.i	−0.407867	−	0.296333i	−0.772738	+	0.634725i	$0.781113\pi$
$278$	212032.	−	652567.i	0.164547	−	0.506423i
$279$	152563.	+	469540.i	0.117338	+	0.361129i
$280$	4.00168e6	−	2.90739e6i	3.05033	−	2.21619i
$281$	1.84764e6	−	1.34239e6i	1.39589	−	1.01417i	0.400698	−	0.916210i	$-0.368768\pi$
$281$	1.84764e6	−	1.34239e6i	1.39589	−	1.01417i	0.995190	−	0.0979624i	$-0.0312325\pi$
$282$	10762.5	+	33123.5i	0.00805915	+	0.0248035i
$283$	43539.5	−	134001.i	0.0323160	−	0.0994584i	−0.933598	−	0.358323i	$-0.883349\pi$
$283$	43539.5	−	134001.i	0.0323160	−	0.0994584i	0.965913	+	0.258865i	$0.0833485\pi$
$284$	−168666.	−	122543.i	−0.124089	−	0.0901558i
$285$	482977.			0.352220
$286$	−62232.9	+	165410.i	−0.0449889	+	0.119577i
$287$	957960.			0.686504
$288$	1.31895e6	+	958271.i	0.937014	+	0.680781i
$289$	−312684.	+	962341.i	−0.220222	+	0.677773i
$290$	−555414.	−	1.70939e6i	−0.387813	−	1.19357i
$291$	−1.23082e6	+	894242.i	−0.852043	+	0.619045i
$292$	−4.65879e6	+	3.38481e6i	−3.19754	+	2.32315i
$293$	−88335.2	−	271868.i	−0.0601125	−	0.185007i	0.916491	−	0.400055i	$-0.131009\pi$
$293$	−88335.2	−	271868.i	−0.0601125	−	0.185007i	−0.976603	+	0.215048i	$0.931009\pi$
$294$	940478.	−	2.89449e6i	0.634571	−	1.95301i
$295$	−372498.	−	270635.i	−0.249212	−	0.181063i
$296$	−5.68550e6			−3.77172
$297$	292251.	+	13363.2i	0.192249	+	0.00879059i
$298$	808781.			0.527582
$299$	−26253.3	−	19074.1i	−0.0169827	−	0.0123386i
$300$	385946.	−	1.18782e6i	0.247584	−	0.761986i
$301$	−136545.	−	420242.i	−0.0868679	−	0.267352i
$302$	−329077.	+	239088.i	−0.207625	+	0.150848i
$303$	463112.	−	336470.i	0.289787	−	0.210543i
$304$	1.52719e6	+	4.70022e6i	0.947786	+	2.91699i
$305$	−337360.	+	1.03829e6i	−0.207656	+	0.639098i
$306$	−454031.	−	329872.i	−0.277193	−	0.201392i
$307$	2.62633e6			1.59039			0.795194	−	0.606355i	$-0.207369\pi$
$307$	2.62633e6			1.59039			0.795194	+	0.606355i	$0.207369\pi$
$308$	7.52232e6	+	343958.i	4.51830	+	0.206599i
$309$	650838.			0.387772
$310$	−2.07502e6	−	1.50759e6i	−1.22636	−	0.891004i
$311$	−92222.2	+	283831.i	−0.0540673	+	0.166402i	−0.974444	−	0.224631i	$-0.927882\pi$
$311$	−92222.2	+	283831.i	−0.0540673	+	0.166402i	0.920377	+	0.391033i	$0.127882\pi$
$312$	−65722.4	−	202273.i	−0.0382232	−	0.117639i
$313$	913041.	−	663363.i	0.526780	−	0.382728i	−0.292372	−	0.956305i	$-0.594444\pi$
$313$	913041.	−	663363.i	0.526780	−	0.382728i	0.819152	+	0.573577i	$0.194444\pi$
$314$	−3.42596e6	+	2.48910e6i	−1.96091	+	1.42468i
$315$	212703.	+	654633.i	0.120781	+	0.371725i
$316$	876481.	−	2.69753e6i	0.493770	−	1.51967i
$317$	−91772.5	−	66676.7i	−0.0512938	−	0.0372671i	0.561843	−	0.827244i	$-0.310093\pi$
$317$	−91772.5	−	66676.7i	−0.0512938	−	0.0372671i	−0.613137	+	0.789977i	$0.710093\pi$
$318$	3.47475e6			1.92688
$319$	603591.	−	1.60430e6i	0.332098	−	0.882689i
$320$	−4.03452e6			−2.20251
$321$	−522291.	−	379467.i	−0.282911	−	0.205547i
$322$	−586886.	+	1.80625e6i	−0.315438	+	0.970819i
$323$	−273039.	−	840328.i	−0.145619	−	0.448170i
$324$	−454687.	+	330349.i	−0.240630	+	0.174828i
$325$	−53209.0	+	38658.6i	−0.0279433	+	0.0203020i
$326$	−1.13760e6	−	3.50118e6i	−0.592852	−	1.82461i
$327$	−243508.	+	749439.i	−0.125934	+	0.387585i
$328$	−2.05941e6	−	1.49625e6i	−1.05696	−	0.767927i
$329$	−78146.6			−0.0398034
$330$	−1.26913e6	+	836263.i	−0.641536	+	0.422725i
$331$	−993938.			−0.498643			−0.249321	−	0.968421i	$-0.580208\pi$
$331$	−993938.			−0.498643			−0.249321	+	0.968421i	$0.580208\pi$
$332$	4.69607e6	+	3.41189e6i	2.33824	+	1.69883i
$333$	244488.	−	752458.i	0.120822	−	0.371853i
$334$	−210979.	−	649327.i	−0.103484	−	0.318491i
$335$	670696.	−	487289.i	0.326523	−	0.237233i
$336$	−5.69816e6	+	4.13996e6i	−2.75351	+	2.00054i
$337$	−168894.	−	519802.i	−0.0810101	−	0.249324i	0.902346	−	0.431013i	$-0.141844\pi$
$337$	−168894.	−	519802.i	−0.0810101	−	0.249324i	−0.983356	+	0.181689i	$0.941844\pi$
$338$	1.23904e6	−	3.81336e6i	0.589918	−	1.81558i
$339$	−1.43044e6	−	1.03927e6i	−0.676036	−	0.491169i
$340$	2.12265e6			0.995818
$341$	−648818.	−	2.35842e6i	−0.302160	−	1.09833i
$342$	−1.21540e6			−0.561892
$343$	2.54621e6	+	1.84993e6i	1.16858	+	0.849024i
$344$	−362839.	+	1.11670e6i	−0.165317	+	0.508793i
$345$	−86239.8	−	265419.i	−0.0390085	−	0.120056i
$346$	−4.15066e6	+	3.01563e6i	−1.86392	+	1.35422i
$347$	−2.94835e6	+	2.14210e6i	−1.31448	+	0.955029i	−0.314501	+	0.949257i	$0.601837\pi$
$347$	−2.94835e6	+	2.14210e6i	−1.31448	+	0.955029i	−0.999983	+	0.00577194i	$0.998163\pi$
$348$	1.01756e6	+	3.13173e6i	0.450414	+	1.38623i
$349$	599671.	−	1.84560e6i	0.263542	−	0.811098i	−0.728484	−	0.685063i	$-0.759775\pi$
$349$	599671.	−	1.84560e6i	0.263542	−	0.811098i	0.992026	−	0.126035i	$-0.0402253\pi$
$350$	3.11409e6	+	2.26252e6i	1.35882	+	0.987237i
$351$	29596.4			0.0128224
$352$	−6.31099e6	−	5.04125e6i	−2.71482	−	2.16861i
$353$	−106849.			−0.0456386			−0.0228193	−	0.999740i	$-0.507264\pi$
$353$	−106849.			−0.0456386			−0.0228193	+	0.999740i	$0.507264\pi$
$354$	937380.	+	681046.i	0.397564	+	0.288847i
$355$	−29176.7	+	89796.6i	−0.0122875	+	0.0378172i
$356$	1.84552e6	+	5.67992e6i	0.771780	+	2.37529i
$357$	1.01874e6	−	740161.i	0.423053	−	0.307366i
$358$	2.55203e6	−	1.85416e6i	1.05240	−	0.764610i
$359$	67012.4	+	206243.i	0.0274422	+	0.0844585i	0.963840	−	0.266483i	$-0.0858616\pi$
$359$	67012.4	+	206243.i	0.0274422	+	0.0844585i	−0.936397	+	0.350941i	$0.885862\pi$
$360$	565213.	−	1.73955e6i	0.229856	−	0.707424i
$361$	455135.	+	330675.i	0.183811	+	0.133547i
$362$	4.20035e6			1.68467
$363$	−1.44341e6	−	132276.i	−0.574941	−	0.0526885i
$364$	761789.			0.301357
$365$	2.10987e6	+	1.53291e6i	0.828941	+	0.602261i
$366$	848956.	−	2.61282e6i	0.331270	−	1.01955i
$367$	−56705.9	−	174523.i	−0.0219767	−	0.0676374i	0.939467	−	0.342640i	$-0.111321\pi$
$367$	−56705.9	−	174523.i	−0.0219767	−	0.0676374i	−0.961443	+	0.275003i	$0.911321\pi$
$368$	2.31030e6	−	1.67853e6i	0.889301	−	0.646115i
$369$	286583.	−	208215.i	0.109568	−	0.0796060i
$370$	1.27016e6	+	3.90914e6i	0.482339	+	1.48449i
$371$	−2.40927e6	+	7.41498e6i	−0.908764	+	2.79689i
$372$	3.80159e6	+	2.76202e6i	1.42432	+	1.03483i
$373$	−4.72995e6			−1.76029			−0.880145	−	0.474705i	$-0.842555\pi$
$373$	−4.72995e6			−1.76029			−0.880145	+	0.474705i	$0.842555\pi$
$374$	2.17248e6	+	1.73539e6i	0.803112	+	0.641530i
$375$	−1.65671e6			−0.608371
$376$	167999.	+	122058.i	0.0612825	+	0.0445243i
$377$	53585.1	−	164918.i	0.0194174	−	0.0597606i
$378$	−535261.	−	1.64737e6i	−0.192680	−	0.593008i
$379$	−3.49564e6	+	2.53973e6i	−1.25005	+	0.908217i	−0.998225	−	0.0595551i	$-0.981032\pi$
$379$	−3.49564e6	+	2.53973e6i	−1.25005	+	0.908217i	−0.251828	+	0.967772i	$0.581032\pi$
$380$	3.71900e6	−	2.70201e6i	1.32120	−	0.959905i
$381$	−523303.	−	1.61056e6i	−0.184689	−	0.568414i
$382$	2.76585e6	−	8.51242e6i	0.969774	−	2.98466i
$383$	280423.	+	203739.i	0.0976824	+	0.0709704i	0.635554	−	0.772056i	$-0.280772\pi$
$383$	280423.	+	203739.i	0.0976824	+	0.0709704i	−0.537872	+	0.843027i	$0.680772\pi$
$384$	4.35610e6			1.50754
$385$	−904583.	−	3.28811e6i	−0.311026	−	1.13056i
$386$	5.23787e6			1.78931
$387$	−132189.	−	96041.2i	−0.0448662	−	0.0325972i
$388$	−4.47466e6	+	1.37716e7i	−1.50897	+	4.64414i
$389$	−245745.	−	756324.i	−0.0823398	−	0.253416i	0.901408	−	0.432970i	$-0.142534\pi$
$389$	−245745.	−	756324.i	−0.0823398	−	0.253416i	−0.983748	+	0.179554i	$0.942534\pi$
$390$	−124393.	+	90376.7i	−0.0414127	+	0.0300881i
$391$	−413046.	+	300096.i	−0.136633	+	0.0992700i
$392$	−5.60747e6	−	1.72580e7i	−1.84311	−	5.67252i
$393$	−961181.	+	2.95821e6i	−0.313924	+	0.966158i
$394$	2.63734e6	+	1.91614e6i	0.855905	+	0.621852i
$395$	−1.28453e6			−0.414238
$396$	2.32514e6	−	1.53210e6i	0.745093	−	0.490962i
$397$	−3.25240e6			−1.03568			−0.517842	−	0.855476i	$-0.673265\pi$
$397$	−3.25240e6			−1.03568			−0.517842	+	0.855476i	$0.673265\pi$
$398$	−8.30185e6	−	6.03165e6i	−2.62704	−	1.90866i
$399$	842715.	−	2.59361e6i	0.265002	−	0.815591i
$400$	−1.78852e6	−	5.50451e6i	−0.558913	−	1.72016i
$401$	3.24218e6	−	2.35558e6i	1.00688	−	0.731538i	0.0433238	−	0.999061i	$-0.486205\pi$
$401$	3.24218e6	−	2.35558e6i	1.00688	−	0.731538i	0.963551	+	0.267523i	$0.0862053\pi$
$402$	−1.68779e6	+	1.22625e6i	−0.520898	+	0.378454i
$403$	−76467.1	−	235341.i	−0.0234537	−	0.0721832i
$404$	1.68365e6	−	5.18175e6i	0.513214	−	1.57951i
$405$	205918.	+	149608.i	0.0623817	+	0.0453230i
$406$	−1.01486e7			−3.05557
$407$	−1.38033e6	+	3.66880e6i	−0.413045	+	1.09784i
$408$	−3.34615e6			−0.995166
$409$	−2.39161e6	−	1.73761e6i	−0.706940	−	0.513622i	0.175245	−	0.984525i	$-0.443928\pi$
$409$	−2.39161e6	−	1.73761e6i	−0.706940	−	0.513622i	−0.882185	+	0.470903i	$0.843928\pi$
$410$	−568689.	+	1.75024e6i	−0.167076	+	0.514208i
$411$	126751.	+	390100.i	0.0370124	+	0.113912i
$412$	5.01155e6	−	3.64111e6i	1.45455	−	1.05679i
$413$	−2.10327e6	+	1.52812e6i	−0.606765	+	0.440841i
$414$	217020.	+	667918.i	0.0622298	+	0.191524i
$415$	812348.	−	2.50015e6i	0.231538	−	0.712600i
$416$	−661079.	−	480302.i	−0.187292	−	0.136076i
$417$	569304.			0.160326
$418$	6.01536e6	+	275052.i	1.68392	+	0.0769971i
$419$	−693679.			−0.193029			−0.0965147	−	0.995332i	$-0.530769\pi$
$419$	−693679.			−0.193029			−0.0965147	+	0.995332i	$0.530769\pi$
$420$	5.30019e6	+	3.85081e6i	1.46611	+	1.06519i
$421$	914792.	−	2.81544e6i	0.251546	−	0.774179i	−0.742945	−	0.669353i	$-0.766571\pi$
$421$	914792.	−	2.81544e6i	0.251546	−	0.774179i	0.994491	−	0.104826i	$-0.0334285\pi$
$422$	3.52448e6	+	1.08472e7i	0.963417	+	2.96509i
$423$	−23378.3	+	16985.3i	−0.00635276	+	0.00461555i
$424$	1.67610e7	−	1.21776e7i	4.52777	−	3.28962i
$425$	319760.	+	984122.i	0.0858722	+	0.264287i
$426$	73422.3	−	225971.i	0.0196022	−	0.0603292i
$427$	4.98702e6	+	3.62328e6i	1.32364	+	0.961683i
$428$	−6.14465e6			−1.62139
$429$	−146481.	−	6697.85i	−0.0384272	−	0.00175708i
$430$	848863.			0.221394
$431$	4.87092e6	+	3.53893e6i	1.26304	+	0.917653i	0.998903	−	0.0468317i	$-0.0149124\pi$
$431$	4.87092e6	+	3.53893e6i	1.26304	+	0.917653i	0.264138	+	0.964485i	$0.414912\pi$
$432$	−804832.	+	2.47702e6i	−0.207489	+	0.638587i
$433$	1.25654e6	+	3.86724e6i	0.322075	+	0.991245i	0.972744	+	0.231883i	$0.0744887\pi$
$433$	1.25654e6	+	3.86724e6i	0.322075	+	0.991245i	−0.650669	+	0.759362i	$0.725511\pi$
$434$	−1.17164e7	+	8.51247e6i	−2.98587	+	2.16936i
$435$	1.20647e6	−	876555.i	0.305700	−	0.222104i
$436$	2.31769e6	+	7.13310e6i	0.583900	+	1.79706i
$437$	−341676.	+	1.05157e6i	−0.0855876	+	0.263412i
$438$	−5.30943e6	−	3.85753e6i	−1.32240	−	0.960779i
$439$	4.07619e6			1.00947			0.504735	−	0.863274i	$-0.331590\pi$
$439$	4.07619e6			1.00947			0.504735	+	0.863274i	$0.331590\pi$
$440$	−3.19108e6	+	8.48162e6i	−0.785788	+	2.08856i
$441$	2.52518e6			0.618295
$442$	227568.	+	165338.i	0.0554058	+	0.0402547i
$443$	1.16621e6	−	3.58924e6i	0.282338	−	0.868946i	−0.704846	−	0.709360i	$-0.748984\pi$
$443$	1.16621e6	−	3.58924e6i	0.282338	−	0.868946i	0.987184	−	0.159586i	$-0.0510159\pi$
$444$	−2.32702e6	−	7.16183e6i	−0.560199	−	1.72412i
$445$	2.18815e6	−	1.58978e6i	0.523813	−	0.380573i
$446$	4.81450e6	−	3.49794e6i	1.14608	−	0.832675i
$447$	207367.	+	638209.i	0.0490874	+	0.151076i
$448$	−7.03958e6	+	2.16656e7i	−1.65711	+	5.10006i
$449$	−6.03269e6	−	4.38301e6i	−1.41220	−	1.02602i	−0.992998	−	0.118127i	$-0.962311\pi$
$449$	−6.03269e6	−	4.38301e6i	−1.41220	−	1.02602i	−0.419199	−	0.907894i	$-0.637689\pi$
$450$	1.42337e6			0.331350
$451$	−1.46551e6	+	965661.i	−0.339270	+	0.223555i
$452$	−1.68288e7			−3.87442
$453$	−273038.	−	198374.i	−0.0625140	−	0.0454191i
$454$	1.35548e6	−	4.17175e6i	0.308642	−	0.949901i
$455$	−106611.	−	328113.i	−0.0241419	−	0.0743011i
$456$	−5.86266e6	+	4.25947e6i	−1.32033	+	0.959275i
$457$	−3.94251e6	+	2.86440e6i	−0.883044	+	0.641569i	−0.934055	−	0.357129i	$-0.883756\pi$
$457$	−3.94251e6	+	2.86440e6i	−0.883044	+	0.641569i	0.0510108	+	0.998698i	$0.483756\pi$
$458$	−316841.	−	975136.i	−0.0705793	−	0.217221i
$459$	143892.	−	442853.i	0.0318789	−	0.0981133i
$460$	−2.14894e6	−	1.56130e6i	−0.473511	−	0.344026i
$461$	−142994.			−0.0313376			−0.0156688	−	0.999877i	$-0.504988\pi$
$461$	−142994.			−0.0313376			−0.0156688	+	0.999877i	$0.504988\pi$
$462$	2.27636e6	+	8.27443e6i	0.496176	+	1.80357i
$463$	1.04836e6			0.227279			0.113639	−	0.993522i	$-0.463749\pi$
$463$	1.04836e6			0.227279			0.113639	+	0.993522i	$0.463749\pi$
$464$	1.23454e7	+	8.96943e6i	2.66200	+	1.93406i
$465$	657617.	−	2.02394e6i	0.141040	−	0.434075i
$466$	−2.40829e6	−	7.41194e6i	−0.513740	−	1.58113i
$467$	4.70506e6	−	3.41843e6i	0.998328	−	0.725328i	0.0365993	−	0.999330i	$-0.488347\pi$
$467$	4.70506e6	−	3.41843e6i	0.998328	−	0.725328i	0.961729	+	0.274002i	$0.0883475\pi$
$468$	227897.	−	165577.i	0.0480976	−	0.0349450i
$469$	−1.44651e6	−	4.45191e6i	−0.303662	−	0.934575i
$470$	46391.4	−	142778.i	0.00968707	−	0.0298137i
$471$	−2.84255e6	−	2.06523e6i	−0.590412	−	0.428960i
$472$	6.90838e6			1.42732
$473$	632509.	+	505251.i	0.129991	+	0.103838i
$474$	3.23247e6			0.660829
$475$	1.81297e6	+	1.31720e6i	0.368686	+	0.267866i
$476$	3.70367e6	−	1.13987e7i	0.749229	−	2.30589i
$477$	890905.	+	2.74193e6i	0.179282	+	0.551772i
$478$	−628855.	+	456890.i	−0.125887	+	0.0914622i
$479$	6.20512e6	−	4.50829e6i	1.23570	−	0.897786i	0.238392	−	0.971169i	$-0.423380\pi$
$479$	6.20512e6	−	4.50829e6i	1.23570	−	0.897786i	0.997304	+	0.0733832i	$0.0233796\pi$
$480$	−2.17159e6	−	6.68345e6i	−0.430203	−	1.32403i
$481$	−122542.	+	377145.i	−0.0241502	+	0.0743268i
$482$	2.08111e6	+	1.51202e6i	0.408016	+	0.296441i
$483$	−1.57579e6			−0.307347
$484$	−1.18545e7	+	7.05660e6i	−2.30022	+	1.36925i
$485$	6.55784e6			1.26592
$486$	−518188.	−	376485.i	−0.0995168	−	0.0723032i
$487$	−2.30524e6	+	7.09479e6i	−0.440446	+	1.35555i	0.446955	+	0.894556i	$0.352508\pi$
$487$	−2.30524e6	+	7.09479e6i	−0.440446	+	1.35555i	−0.887401	+	0.460998i	$0.847492\pi$
$488$	−5.06178e6	−	1.55786e7i	−0.962175	−	2.96127i
$489$	2.47111e6	−	1.79536e6i	0.467325	−	0.339532i
$490$	−1.06133e7	+	7.71098e6i	−1.99691	+	1.45084i
$491$	1.12782e6	+	3.47108e6i	0.211124	+	0.649772i	0.999406	+	0.0344582i	$0.0109706\pi$
$491$	1.12782e6	+	3.47108e6i	0.211124	+	0.649772i	−0.788283	+	0.615313i	$0.789029\pi$
$492$	1.04188e6	−	3.20658e6i	0.194046	−	0.597212i
$493$	−2.20716e6	−	1.60360e6i	−0.408994	−	0.297151i
$494$	609178.			0.112312
$495$	−985293.	−	787056.i	−0.180739	−	0.144375i
$496$	2.17759e7			3.97441
$497$	431304.	+	313360.i	0.0783235	+	0.0569054i
$498$	−2.04425e6	+	6.29156e6i	−0.369369	+	1.13680i
$499$	2.61645e6	+	8.05260e6i	0.470393	+	1.44772i	0.852072	+	0.523425i	$0.175346\pi$
$499$	2.61645e6	+	8.05260e6i	0.470393	+	1.44772i	−0.381679	+	0.924295i	$0.624654\pi$
$500$	−1.27569e7	+	9.26845e6i	−2.28203	+	1.65799i
$501$	458290.	−	332967.i	0.0815729	−	0.0592662i
$502$	−3.42384e6	−	1.05375e7i	−0.606393	−	1.86629i
$503$	3.02546e6	−	9.31141e6i	0.533177	−	1.64095i	−0.214378	−	0.976751i	$-0.568772\pi$
$503$	3.02546e6	−	9.31141e6i	0.533177	−	1.64095i	0.747555	−	0.664200i	$-0.231228\pi$
$504$	−8.35525e6	−	6.07045e6i	−1.46515	−	1.06450i
$505$	−2.46747e6			−0.430551
$506$	−922941.	−	3.35484e6i	−0.160250	−	0.582499i
$507$	3.32680e6			0.574787
$508$	−1.30398e7	−	9.47396e6i	−2.24187	−	1.62882i
$509$	1.56152e6	−	4.80588e6i	0.267149	−	0.822201i	−0.724041	−	0.689757i	$-0.757717\pi$
$509$	1.56152e6	−	4.80588e6i	0.267149	−	0.822201i	0.991190	−	0.132444i	$-0.0422826\pi$
$510$	747540.	+	2.30069e6i	0.127265	+	0.391682i
$511$	1.19132e7	−	8.65544e6i	2.01825	−	1.46635i
$512$	4.33823e6	−	3.15191e6i	0.731371	−	0.531372i
$513$	−311621.	−	959071.i	−0.0522797	−	0.160900i
$514$	1.18399e6	−	3.64396e6i	0.197671	−	0.608367i
$515$	−2.26963e6	−	1.64898e6i	−0.377083	−	0.273967i
$516$	−1.55518e6			−0.257132
$517$	119550.	−	78774.8i	0.0196709	−	0.0129617i
$518$	2.32085e7			3.80034
$519$	−3.44384e6	−	2.50210e6i	−0.561209	−	0.407742i
$520$	−283295.	+	871891.i	−0.0459441	+	0.141401i
$521$	815918.	+	2.51114e6i	0.131690	+	0.405300i	0.995060	−	0.0992706i	$-0.0316509\pi$
$521$	815918.	+	2.51114e6i	0.131690	+	0.405300i	−0.863371	+	0.504570i	$0.831651\pi$
$522$	−3.03606e6	+	2.20583e6i	−0.487679	+	0.354319i
$523$	−587362.	+	426743.i	−0.0938969	+	0.0682201i	−0.633743	−	0.773544i	$-0.718482\pi$
$523$	−587362.	+	426743.i	−0.0938969	+	0.0682201i	0.539846	+	0.841764i	$0.318482\pi$
$524$	9.14845e6	+	2.81560e7i	1.45552	+	4.47964i
$525$	−986918.	+	3.03742e6i	−0.156273	+	0.480957i
$526$	1.06107e7	+	7.70910e6i	1.67216	+	1.21490i
$527$	−3.89320e6			−0.610633
$528$	4.54391e6	−	1.20774e7i	0.709325	−	1.88533i
$529$	−5.79745e6			−0.900736
$530$	−1.21173e7	−	8.80374e6i	−1.87377	−	1.36137i
$531$	−297075.	+	914303.i	−0.0457225	+	0.140719i
$532$	−8.02089e6	−	2.46858e7i	−1.22869	−	3.78153i
$533$	−143641.	+	104361.i	−0.0219007	+	0.0159118i
$534$	−5.50641e6	+	4.00064e6i	−0.835633	+	0.607123i
$535$	859929.	+	2.64659e6i	0.129891	+	0.399762i
$536$	−3.84380e6	+	1.18300e7i	−0.577895	+	1.77858i
$537$	2.11745e6	+	1.53841e6i	0.316867	+	0.230217i
$538$	−1.09835e6			−0.163600
$539$	−1.24978e7	−	571464.i	−1.85295	−	0.0847260i
$540$	2.42259e6			0.357515
$541$	8.62074e6	+	6.26334e6i	1.26634	+	0.920052i	0.999051	−	0.0435631i	$-0.0138709\pi$
$541$	8.62074e6	+	6.26334e6i	1.26634	+	0.920052i	0.267293	+	0.963615i	$0.413871\pi$
$542$	124295.	−	382542.i	0.0181743	−	0.0559346i
$543$	1.07694e6	+	3.31450e6i	0.156745	+	0.482412i
$544$	−1.04008e7	+	7.55665e6i	−1.50685	+	1.09479i
$545$	2.74797e6	−	1.99652e6i	0.396298	−	0.287927i
$546$	268282.	+	825688.i	0.0385133	+	0.118532i
$547$	−506090.	+	1.55758e6i	−0.0723201	+	0.222578i	−0.980683	−	0.195605i	$-0.937333\pi$
$547$	−506090.	+	1.55758e6i	−0.0723201	+	0.222578i	0.908363	+	0.418183i	$0.137333\pi$
$548$	3.15841e6	+	2.29472e6i	0.449280	+	0.326421i
$549$	2.27944e6			0.322773
$550$	−7.04469e6	−	322118.i	−0.993013	−	0.0454055i
$551$	−5.90837e6			−0.829065
$552$	3.38761e6	+	2.46124e6i	0.473201	+	0.343800i
$553$	−2.24129e6	+	6.89797e6i	−0.311663	+	0.959199i
$554$	−2.15804e6	−	6.64176e6i	−0.298734	−	0.919410i
$555$	−2.75904e6	+	2.00456e6i	−0.380212	+	0.276240i
$556$	4.38373e6	−	3.18497e6i	0.601391	−	0.436936i
$557$	3.83067e6	+	1.17896e7i	0.523163	+	1.61013i	0.767920	+	0.640546i	$0.221292\pi$
$557$	3.83067e6	+	1.17896e7i	0.523163	+	1.61013i	−0.244757	+	0.969585i	$0.578708\pi$
$558$	−1.65487e6	+	5.09318e6i	−0.224999	+	0.692474i
$559$	66255.6	+	48137.5i	0.00896794	+	0.00651559i
$560$	3.03600e7			4.09102
$561$	−812382.	+	2.15925e6i	−0.108982	+	0.289664i
$562$	2.47728e7			3.30853
$563$	−7.26569e6	−	5.27883e6i	−0.966064	−	0.701887i	−0.0115130	−	0.999934i	$-0.503665\pi$
$563$	−7.26569e6	−	5.27883e6i	−0.966064	−	0.701887i	−0.954551	+	0.298047i	$0.903665\pi$
$564$	−84992.4	+	261580.i	−0.0112508	+	0.0346263i
$565$	2.35515e6	+	7.24840e6i	0.310383	+	0.955259i
$566$	1.23645e6	−	898331.i	0.162231	−	0.117868i
$567$	1.16270e6	−	844750.i	0.151883	−	0.110350i
$568$	−437770.	−	1.34732e6i	−0.0569345	−	0.175226i
$569$	2.87829e6	−	8.85847e6i	0.372695	−	1.14704i	−0.572325	−	0.820027i	$-0.693958\pi$
$569$	2.87829e6	−	8.85847e6i	0.372695	−	1.14704i	0.945020	−	0.327012i	$-0.106042\pi$
$570$	4.23839e6	+	3.07937e6i	0.546404	+	0.396986i
$571$	−5.89599e6			−0.756774			−0.378387	−	0.925647i	$-0.623521\pi$
$571$	−5.89599e6			−0.756774			−0.378387	+	0.925647i	$0.623521\pi$
$572$	−1.16540e6	+	767913.i	−0.148931	+	0.0981346i
$573$	7.42630e6			0.944900
$574$	8.40663e6	+	6.10777e6i	1.06498	+	0.773755i
$575$	400142.	−	1.23151e6i	0.0504713	−	0.155335i
$576$	2.60311e6	+	8.01154e6i	0.326916	+	1.00614i
$577$	−4.51904e6	+	3.28327e6i	−0.565075	+	0.410551i	−0.833313	−	0.552801i	$-0.813559\pi$
$577$	−4.51904e6	+	3.28327e6i	−0.565075	+	0.410551i	0.268238	+	0.963353i	$0.413559\pi$
$578$	−8.87968e6	+	6.45146e6i	−1.10555	+	0.803227i
$579$	1.34296e6	+	4.13321e6i	0.166482	+	0.512378i
$580$	4.38616e6	−	1.34992e7i	0.541396	−	1.66624i
$581$	−1.20085e7	−	8.72470e6i	−1.47587	−	1.07228i
$582$	−1.65026e7			−2.01951
$583$	−3.78884e6	−	1.37722e7i	−0.461673	−	1.67816i
$584$	−3.91299e7			−4.74763
$585$	−103210.	−	74986.3i	−0.0124690	−	0.00905925i
$586$	958187.	−	2.94900e6i	0.115267	−	0.354756i
$587$	1.50232e6	+	4.62366e6i	0.179956	+	0.553848i	0.999825	−	0.0187034i	$-0.00595384\pi$
$587$	1.50232e6	+	4.62366e6i	0.179956	+	0.553848i	−0.819869	+	0.572551i	$0.805954\pi$
$588$	1.94443e7	−	1.41271e7i	2.31925	−	1.68504i
$589$	−6.82112e6	+	4.95583e6i	−0.810153	+	0.588611i
$590$	−1.54335e6	−	4.74995e6i	−0.182530	−	0.561771i
$591$	−835828.	+	2.57241e6i	−0.0984347	+	0.302951i
$592$	−2.82321e7	−	2.05118e7i	−3.31085	−	2.40547i
$593$	−7.37203e6			−0.860896			−0.430448	−	0.902615i	$-0.641644\pi$
$593$	−7.37203e6			−0.860896			−0.430448	+	0.902615i	$0.641644\pi$
$594$	2.47946e6	+	1.98060e6i	0.288331	+	0.230320i
$595$	−5.42791e6			−0.628550
$596$	5.16721e6	+	3.75420e6i	0.595855	+	0.432914i
$597$	2.63103e6	−	8.09747e6i	0.302127	−	0.929851i
$598$	−108774.	−	334772.i	−0.0124386	−	0.0382822i
$599$	−3.41614e6	+	2.48197e6i	−0.389017	+	0.282638i	−0.765053	−	0.643968i	$-0.777287\pi$
$599$	−3.41614e6	+	2.48197e6i	−0.389017	+	0.282638i	0.376035	+	0.926605i	$0.377287\pi$
$600$	6.86585e6	−	4.98833e6i	0.778604	−	0.565689i
$601$	−4.36395e6	−	1.34309e7i	−0.492826	−	1.51676i	−0.820317	−	0.571909i	$-0.806203\pi$
$601$	−4.36395e6	−	1.34309e7i	−0.492826	−	1.51676i	0.327491	−	0.944854i	$-0.393797\pi$
$602$	1.48113e6	−	4.55844e6i	0.166572	−	0.512655i
$603$	−1.40037e6	−	1.01743e6i	−0.156838	−	0.113949i
$604$	−3.21224e6			−0.358274
$605$	4.69839e6	+	4.11835e6i	0.521868	+	0.457441i
$606$	6.20933e6			0.686852
$607$	8.29504e6	+	6.02670e6i	0.913791	+	0.663908i	0.941971	−	0.335695i	$-0.108971\pi$
$607$	8.29504e6	+	6.02670e6i	0.913791	+	0.663908i	−0.0281797	+	0.999603i	$0.508971\pi$
$608$	−8.60367e6	+	2.64794e7i	−0.943898	+	2.90502i
$609$	−2.60205e6	−	8.00827e6i	−0.284297	−	0.874975i
$610$	−9.58044e6	+	6.96060e6i	−1.04246	+	0.757394i
$611$	11717.6	−	8513.35i	0.00126980	−	0.000922566i
$612$	−1.36955e6	−	4.21504e6i	−0.147808	−	0.454907i
$613$	−4.44460e6	+	1.36791e7i	−0.477728	+	1.47030i	0.364514	+	0.931198i	$0.381235\pi$
$613$	−4.44460e6	+	1.36791e7i	−0.477728	+	1.47030i	−0.842242	+	0.539099i	$0.818765\pi$
$614$	2.30475e7	+	1.67450e7i	2.46719	+	1.79252i
$615$	−1.52693e6			−0.162791
$616$	3.99788e7	+	3.19353e7i	4.24500	+	3.39093i
$617$	8.26153e6			0.873670			0.436835	−	0.899542i	$-0.356099\pi$
$617$	8.26153e6			0.873670			0.436835	+	0.899542i	$0.356099\pi$
$618$	5.71146e6	+	4.14962e6i	0.601556	+	0.437056i
$619$	1.51440e6	−	4.66085e6i	0.158860	−	0.488921i	−0.839672	−	0.543094i	$-0.817253\pi$
$619$	1.51440e6	−	4.66085e6i	0.158860	−	0.488921i	0.998532	+	0.0541739i	$0.0172525\pi$
$620$	−6.25915e6	−	1.92637e7i	−0.653937	−	2.01261i
$621$	−471412.	+	342501.i	−0.0490537	+	0.0356396i
$622$	−2.61895e6	+	1.90278e6i	−0.271426	+	0.197203i
$623$	−4.71925e6	−	1.45244e7i	−0.487139	−	1.49926i
$624$	403396.	−	1.24152e6i	0.0414734	−	0.127642i
$625$	1.68169e6	+	1.22182e6i	0.172205	+	0.125114i
$626$	1.22419e7			1.24857
$627$	1.32526e6	+	4.81724e6i	0.134627	+	0.489361i
$628$	−3.34420e7			−3.38371
$629$	5.04747e6	+	3.66720e6i	0.508683	+	0.369580i
$630$	−2.30723e6	+	7.10092e6i	−0.231600	+	0.712793i
$631$	4.93563e6	+	1.51903e7i	0.493479	+	1.51877i	0.819313	+	0.573346i	$0.194355\pi$
$631$	4.93563e6	+	1.51903e7i	0.493479	+	1.51877i	−0.325834	+	0.945427i	$0.605645\pi$
$632$	1.55923e7	−	1.13285e7i	1.55281	−	1.12818i
$633$	−7.65591e6	+	5.56234e6i	−0.759429	+	0.551758i
$634$	−380237.	−	1.17025e6i	−0.0375691	−	0.115626i
$635$	−2.25568e6	+	6.94228e6i	−0.221995	+	0.683231i
$636$	2.21998e7	+	1.61291e7i	2.17624	+	1.58113i
$637$	−1.26566e6			−0.123586
$638$	1.55255e7	−	1.02302e7i	1.51006	−	0.995021i
$639$	197138.			0.0190994
$640$	−1.51908e7	−	1.10368e7i	−1.46599	−	1.06510i
$641$	3.33477e6	−	1.02634e7i	0.320569	−	0.986609i	−0.652833	−	0.757502i	$-0.726420\pi$
$641$	3.33477e6	−	1.02634e7i	0.320569	−	0.986609i	0.973401	−	0.229107i	$-0.0735805\pi$
$642$	−2.16399e6	−	6.66006e6i	−0.207213	−	0.637736i
$643$	−414230.	+	300956.i	−0.0395107	+	0.0287062i	−0.607365	−	0.794423i	$-0.707774\pi$
$643$	−414230.	+	300956.i	−0.0395107	+	0.0287062i	0.567855	+	0.823129i	$0.307774\pi$
$644$	−1.21338e7	+	8.81572e6i	−1.15287	+	0.837612i
$645$	217644.	+	669838.i	0.0205990	+	0.0633973i
$646$	2.96170e6	−	9.11518e6i	0.279229	−	0.859378i
$647$	9.25546e6	+	6.72449e6i	0.869236	+	0.631537i	0.930382	−	0.366592i	$-0.119476\pi$
$647$	9.25546e6	+	6.72449e6i	0.869236	+	0.631537i	−0.0611461	+	0.998129i	$0.519476\pi$
$648$	−3.81898e6			−0.357281
$649$	1.67722e6	−	4.45792e6i	0.156307	−	0.415452i
$650$	−713419.			−0.0662310
$651$	−9.72121e6	−	7.06288e6i	−0.899017	−	0.653174i
$652$	8.98376e6	−	2.76492e7i	0.827636	−	2.54720i
$653$	3.06087e6	+	9.42040e6i	0.280907	+	0.864543i	0.987596	+	0.157018i	$0.0501881\pi$
$653$	3.06087e6	+	9.42040e6i	0.280907	+	0.864543i	−0.706689	+	0.707525i	$0.749812\pi$
$654$	−6.91520e6	+	5.02418e6i	−0.632208	+	0.459326i
$655$	1.08469e7	−	7.88073e6i	0.987875	−	0.717734i
$656$	−4.82821e6	−	1.48597e7i	−0.438053	−	1.34819i
$657$	1.68267e6	−	5.17872e6i	0.152084	−	0.468068i
$658$	−685779.	−	498248.i	−0.0617475	−	0.0448622i
$659$	−3.43885e6			−0.308461			−0.154231	−	0.988035i	$-0.549290\pi$
$659$	−3.43885e6			−0.308461			−0.154231	+	0.988035i	$0.549290\pi$
$660$	−1.19901e7	−	548247.i	−1.07143	−	0.0489910i
$661$	−1.76956e7			−1.57529			−0.787646	−	0.616128i	$-0.788701\pi$
$661$	−1.76956e7			−1.57529			−0.787646	+	0.616128i	$0.788701\pi$
$662$	−8.72236e6	−	6.33716e6i	−0.773551	−	0.562018i
$663$	−72121.0	+	221966.i	−0.00637203	+	0.0196111i
$664$	1.21886e7	+	3.75125e7i	1.07283	+	3.30184i
$665$	−9.51001e6	+	6.90943e6i	−0.833925	+	0.605882i
$666$	6.94305e6	−	5.04442e6i	0.606547	−	0.440682i
$667$	1.05499e6	+	3.24693e6i	0.0918193	+	0.282591i
$668$	1.66612e6	−	5.12780e6i	0.144466	−	0.444621i
$669$	3.99464e6	+	2.90227e6i	0.345074	+	0.250711i
$670$	8.99259e6			0.773923
$671$	−1.12816e7	−	515852.i	−0.967310	−	0.0442302i
$672$	−3.96795e7			−3.38956
$673$	1.20083e7	+	8.72452e6i	1.02198	+	0.742512i	0.966688	−	0.255958i	$-0.0823908\pi$
$673$	1.20083e7	+	8.72452e6i	1.02198	+	0.742512i	0.0552927	+	0.998470i	$0.482391\pi$
$674$	1.83202e6	−	5.63839e6i	0.155339	−	0.478085i
$675$	364944.	+	1.12318e6i	0.0308296	+	0.0948836i
$676$	2.56169e7	−	1.86118e7i	2.15606	−	1.56647i
$677$	1.53492e7	−	1.11518e7i	1.28710	−	0.935135i	0.287361	−	0.957822i	$-0.407222\pi$
$677$	1.53492e7	−	1.11518e7i	1.28710	−	0.935135i	0.999743	+	0.0226869i	$0.00722208\pi$
$678$	−5.92666e6	−	1.82404e7i	−0.495149	−	1.52391i
$679$	1.14424e7	−	3.52159e7i	0.952447	−	2.93133i
$680$	1.16689e7	+	8.47792e6i	0.967734	+	0.703100i
$681$	3.63946e6			0.300725
$682$	9.34308e6	−	2.48331e7i	0.769182	−	2.04442i
$683$	1.23287e7			1.01127			0.505633	−	0.862749i	$-0.331259\pi$
$683$	1.23287e7			1.01127			0.505633	+	0.862749i	$0.331259\pi$
$684$	−7.76504e6	−	5.64163e6i	−0.634605	−	0.461068i
$685$	546357.	−	1.68151e6i	0.0444887	−	0.136922i
$686$	1.05496e7	+	3.24683e7i	0.855905	+	2.63420i
$687$	688244.	−	500038.i	0.0556353	−	0.0404214i
$688$	−5.83051e6	+	4.23612e6i	−0.469608	+	0.341190i
$689$	−446537.	−	1.37430e6i	−0.0358352	−	0.110289i
$690$	935458.	−	2.87904e6i	0.0748000	−	0.230211i
$691$	−1.71200e7	−	1.24384e7i	−1.36398	−	0.990990i	−0.998181	−	0.0602961i	$-0.980796\pi$
$691$	−1.71200e7	−	1.24384e7i	−1.36398	−	0.990990i	−0.365800	−	0.930694i	$-0.619204\pi$
$692$	−4.05161e7			−3.21634
$693$	−5.94571e6	+	3.91779e6i	−0.470295	+	0.309890i
$694$	−3.95310e7			−3.11559
$695$	−1.98530e6	−	1.44241e6i	−0.155907	−	0.113273i
$696$	−6.91438e6	+	2.12803e7i	−0.541041	+	1.66515i
$697$	863210.	+	2.65669e6i	0.0673030	+	0.207137i
$698$	1.70296e7	−	1.23727e7i	1.32302	−	0.961231i
$699$	5.23129e6	−	3.80076e6i	0.404964	−	0.294223i
$700$	9.39340e6	+	2.89099e7i	0.724566	+	2.22998i
$701$	−4.81363e6	+	1.48148e7i	−0.369980	+	1.13868i	0.576824	+	0.816868i	$0.304292\pi$
$701$	−4.81363e6	+	1.48148e7i	−0.369980	+	1.13868i	−0.946804	+	0.321812i	$0.895708\pi$
$702$	259725.	+	188701.i	0.0198916	+	0.0144521i
$703$	1.35116e7			1.03114
$704$	−1.10705e7	−	4.02406e7i	−0.841850	−	3.06008i
$705$	124561.			0.00943860
$706$	−937655.	−	681246.i	−0.0707997	−	0.0514390i
$707$	−4.30534e6	+	1.32505e7i	−0.323936	+	0.996971i
$708$	2.82753e6	+	8.70226e6i	0.211995	+	0.652452i
$709$	8.62245e6	−	6.26458e6i	0.644192	−	0.468033i	−0.217096	−	0.976150i	$-0.569658\pi$
$709$	8.62245e6	−	6.26458e6i	0.644192	−	0.468033i	0.861288	+	0.508117i	$0.169658\pi$
$710$	−828567.	+	601989.i	−0.0616853	+	0.0448170i
$711$	828788.	+	2.55075e6i	0.0614850	+	0.189231i
$712$	−1.25404e7	+	3.85954e7i	−0.927068	+	2.85322i
$713$	3.94143e6	+	2.86362e6i	0.290356	+	0.210956i
$714$	1.36592e7			1.00272
$715$	493846.	+	394486.i	0.0361265	+	0.0288580i
$716$	2.49113e7			1.81599
$717$	−521767.	−	379086.i	−0.0379034	−	0.0275384i
$718$	−726896.	+	2.23715e6i	−0.0526212	+	0.161951i
$719$	−6.47603e6	−	1.99312e7i	−0.467183	−	1.43784i	−0.856217	−	0.516617i	$-0.827191\pi$
$719$	−6.47603e6	−	1.99312e7i	−0.467183	−	1.43784i	0.389034	−	0.921223i	$-0.372809\pi$
$720$	9.08250e6	−	6.59882e6i	0.652941	−	0.474390i
$721$	−1.28152e7	+	9.31082e6i	−0.918098	+	0.667037i
$722$	1.88574e6	+	5.80371e6i	0.134629	+	0.414345i
$723$	−659547.	+	2.02988e6i	−0.0469245	+	0.144419i
$724$	2.68356e7	+	1.94972e7i	1.90267	+	1.38237i
$725$	6.91939e6			0.488903
$726$	−1.18234e7	−	1.03637e7i	−0.832529	−	0.729749i
$727$	−296119.			−0.0207793			−0.0103896	−	0.999946i	$-0.503307\pi$
$727$	−296119.			−0.0207793			−0.0103896	+	0.999946i	$0.503307\pi$
$728$	4.18780e6	+	3.04261e6i	0.292858	+	0.212774i
$729$	164224.	−	505430.i	0.0114451	−	0.0352243i
$730$	8.74173e6	+	2.69043e7i	0.607142	+	1.86859i
$731$	1.04241e6	−	757352.i	0.0721512	−	0.0524209i
$732$	1.75521e7	−	1.27523e7i	1.21074	−	0.879654i
$733$	−8.05044e6	−	2.47767e7i	−0.553426	−	1.70327i	−0.700064	−	0.714080i	$-0.746845\pi$
$733$	−8.05044e6	−	2.47767e7i	−0.553426	−	1.70327i	0.146638	−	0.989190i	$-0.453155\pi$
$734$	615099.	−	1.89308e6i	0.0421410	−	0.129697i
$735$	−8.80591e6	−	6.39787e6i	−0.601251	−	0.436835i
$736$	1.60879e7			1.09473
$737$	6.70060e6	+	5.35247e6i	0.454407	+	0.362982i
$738$	3.84247e6			0.259698
$739$	−1.08943e7	−	7.91517e6i	−0.733818	−	0.533150i	0.156951	−	0.987606i	$-0.449834\pi$
$739$	−1.08943e7	−	7.91517e6i	−0.733818	−	0.533150i	−0.890769	+	0.454456i	$0.849834\pi$
$740$	−1.00306e7	+	3.08709e7i	−0.673357	+	2.07238i
$741$	156190.	+	480703.i	0.0104498	+	0.0321611i
$742$	−6.84192e7	+	4.97095e7i	−4.56214	+	3.31459i
$743$	−1.34801e7	+	9.79390e6i	−0.895824	+	0.650854i	−0.937390	−	0.348282i	$-0.886765\pi$
$743$	−1.34801e7	+	9.79390e6i	−0.895824	+	0.650854i	0.0415661	+	0.999136i	$0.486765\pi$
$744$	9.86696e6	+	3.03674e7i	0.653508	+	2.01129i
$745$	893848.	−	2.75098e6i	0.0590029	−	0.181592i
$746$	−4.15079e7	−	3.01572e7i	−2.73076	−	1.98401i
$747$	−5.48880e6			−0.359895
$748$	5.82441e6	+	2.11714e7i	0.380625	+	1.38355i
$749$	1.57127e7			1.02340
$750$	−1.45385e7	−	1.05629e7i	−0.943774	−	0.685692i
$751$	−3.78148e6	+	1.16382e7i	−0.244660	+	0.752985i	0.751032	+	0.660265i	$0.229556\pi$
$751$	−3.78148e6	+	1.16382e7i	−0.244660	+	0.752985i	−0.995692	+	0.0927200i	$0.970444\pi$
$752$	393866.	+	1.21219e6i	0.0253983	+	0.0781678i
$753$	7.43729e6	−	5.40351e6i	0.477999	−	0.347287i
$754$	1.52173e6	−	1.10560e6i	0.0974783	−	0.0708221i
$755$	449544.	+	1.38356e6i	0.0287015	+	0.0883343i
$756$	4.22701e6	−	1.30094e7i	0.268986	−	0.827853i
$757$	1.44776e7	+	1.05186e7i	0.918244	+	0.667143i	0.943086	−	0.332548i	$-0.107908\pi$
$757$	1.44776e7	+	1.05186e7i	0.918244	+	0.667143i	−0.0248427	+	0.999691i	$0.507908\pi$
$758$	−4.68690e7			−2.96287
$759$	2.41067e6	−	1.58845e6i	0.151891	−	0.100085i
$760$	3.12364e7			1.96168
$761$	1.23126e7	+	8.94561e6i	0.770703	+	0.559949i	0.902174	−	0.431371i	$-0.141970\pi$
$761$	1.23126e7	+	8.94561e6i	0.770703	+	0.559949i	−0.131471	+	0.991320i	$0.541970\pi$
$762$	5.67636e6	−	1.74700e7i	0.354146	−	1.08995i
$763$	−5.92665e6	−	1.82404e7i	−0.368551	−	1.13428i
$764$	5.71837e7	−	4.15464e7i	3.54437	−	2.57513i
$765$	−1.62381e6	+	1.17977e6i	−0.100319	+	0.0728858i
$766$	1.16186e6	+	3.57584e6i	0.0715455	+	0.220195i
$767$	148899.	−	458264.i	0.00913910	−	0.0281273i
$768$	1.39960e7	+	1.01687e7i	0.856252	+	0.622103i
$769$	9.90796e6			0.604183			0.302091	−	0.953279i	$-0.402315\pi$
$769$	9.90796e6			0.604183			0.302091	+	0.953279i	$0.402315\pi$
$770$	1.30261e7	−	3.46224e7i	0.791751	−	2.10441i
$771$	3.17902e6			0.192600
$772$	3.34642e7	+	2.43132e7i	2.02086	+	1.46824i
$773$	−8.90154e6	+	2.73961e7i	−0.535817	+	1.64907i	0.206061	+	0.978539i	$0.433935\pi$
$773$	−8.90154e6	+	2.73961e7i	−0.535817	+	1.64907i	−0.741878	+	0.670535i	$0.766065\pi$
$774$	−547694.	−	1.68563e6i	−0.0328613	−	0.101137i
$775$	7.98832e6	−	5.80385e6i	0.477751	−	0.347106i
$776$	−7.96029e7	+	5.78349e7i	−4.74542	+	3.44775i
$777$	5.95052e6	+	1.83138e7i	0.353592	+	1.08824i
$778$	2.66564e6	−	8.20398e6i	0.157889	−	0.485932i
$779$	4.89421e6	+	3.55585e6i	0.288961	+	0.209942i
$780$	−1.21424e6			−0.0714610
$781$	−975696.	−	44613.7i	−0.0572383	−	0.00261722i
$782$	−5.53806e6			−0.323848
$783$	−2.51904e6	−	1.83019e6i	−0.146836	−	0.106682i
$784$	3.44179e7	−	1.05927e8i	1.99984	−	6.15487i
$785$	4.68012e6	+	1.44039e7i	0.271071	+	0.834270i
$786$	−2.72959e7	+	1.98316e7i	−1.57594	+	1.14499i
$787$	−2.38068e7	+	1.72967e7i	−1.37014	+	0.995463i	−0.372411	+	0.928068i	$0.621469\pi$
$787$	−2.38068e7	+	1.72967e7i	−1.37014	+	0.995463i	−0.997726	+	0.0673957i	$0.978531\pi$
$788$	7.95534e6	+	2.44840e7i	0.456397	+	1.40465i
$789$	−3.36274e6	+	1.03494e7i	−0.192309	+	0.591867i
$790$	−1.12724e7	−	8.18990e6i	−0.642613	−	0.466886i
$791$	4.30336e7			2.44550
$792$	1.89013e7	+	864260.i	1.07072	+	0.0489589i
$793$	−1.14250e6			−0.0645166
$794$	−2.85416e7	−	2.07367e7i	−1.60667	−	1.16732i
$795$	3.84022e6	−	1.18190e7i	0.215496	−	0.663228i
$796$	−2.50419e7	−	7.70710e7i	−1.40083	−	4.31130i
$797$	−2.08999e7	+	1.51847e7i	−1.16546	+	0.846758i	−0.990459	−	0.137810i	$-0.955994\pi$
$797$	−2.08999e7	+	1.51847e7i	−1.16546	+	0.846758i	−0.175004	+	0.984568i	$0.555994\pi$
$798$	2.39317e7	−	1.73874e7i	1.33035	−	0.966555i
$799$	−70417.2	−	216722.i	−0.00390222	−	0.0120098i
$800$	1.00759e7	−	3.10104e7i	0.556620	−	1.71310i
$801$	−4.56872e6	−	3.31937e6i	−0.251601	−	0.182799i
$802$	4.34706e7			2.38649
$803$	−9.49999e6	+	2.52502e7i	−0.519917	+	1.38190i
$804$	−1.64751e7			−0.898850
$805$	5.49515e6	+	3.99246e6i	0.298875	+	0.217146i
$806$	829452.	−	2.55279e6i	0.0449732	−	0.138413i
$807$	−281609.	−	866704.i	−0.0152217	−	0.0468476i
$808$	2.99516e7	−	2.17611e7i	1.61396	−	1.17261i
$809$	27132.3	−	19712.8i	0.00145753	−	0.00105895i	−0.587056	−	0.809546i	$-0.699713\pi$
$809$	27132.3	−	19712.8i	0.00145753	−	0.00105895i	0.588514	+	0.808487i	$0.299713\pi$
$810$	853172.	+	2.62579e6i	0.0456903	+	0.140620i
$811$	−446267.	+	1.37347e6i	−0.0238255	+	0.0733274i	−0.962262	−	0.272124i	$-0.912274\pi$
$811$	−446267.	+	1.37347e6i	−0.0238255	+	0.0733274i	0.938437	+	0.345451i	$0.112274\pi$
$812$	−6.48384e7	−	4.71078e7i	−3.45098	−	2.50728i
$813$	333732.			0.0177081
$814$	−3.55048e7	+	2.33951e7i	−1.87813	+	1.23755i
$815$	−1.31661e7			−0.694328
$816$	−1.66158e7	−	1.20721e7i	−0.873566	−	0.634683i
$817$	862289.	−	2.65385e6i	0.0451957	−	0.139098i
$818$	−9.90905e6	−	3.04969e7i	−0.517784	−	1.59358i
$819$	−582764.	+	423403.i	−0.0303587	+	0.0220569i
$820$	−1.17576e7	+	8.54238e6i	−0.610637	+	0.443654i
$821$	−6.13945e6	−	1.88953e7i	−0.317886	−	0.978353i	−0.974550	−	0.224170i	$-0.928033\pi$
$821$	−6.13945e6	−	1.88953e7i	−0.317886	−	0.978353i	0.656664	−	0.754183i	$-0.271967\pi$
$822$	−1.37489e6	+	4.23148e6i	−0.0709723	+	0.218430i
$823$	1.57265e7	+	1.14260e7i	0.809342	+	0.588021i	0.913640	−	0.406525i	$-0.133260\pi$
$823$	1.57265e7	+	1.14260e7i	0.809342	+	0.588021i	−0.104298	+	0.994546i	$0.533260\pi$
$824$	4.20928e7			2.15968
$825$	−1.55203e6	−	5.64155e6i	−0.0793901	−	0.288578i
$826$	−2.82004e7			−1.43815
$827$	−1.50937e7	−	1.09662e7i	−0.767420	−	0.557563i	0.133757	−	0.991014i	$-0.457296\pi$
$827$	−1.50937e7	−	1.09662e7i	−0.767420	−	0.557563i	−0.901177	+	0.433451i	$0.857296\pi$
$828$	−1.71383e6	+	5.27462e6i	−0.0868743	+	0.267372i
$829$	−9.19628e6	−	2.83032e7i	−0.464757	−	1.43037i	−0.859288	−	0.511492i	$-0.829093\pi$
$829$	−9.19628e6	−	2.83032e7i	−0.464757	−	1.43037i	0.394531	−	0.918883i	$-0.370907\pi$
$830$	2.30693e7	−	1.67608e7i	1.16236	−	0.844501i
$831$	4.68771e6	−	3.40582e6i	0.235482	−	0.171088i
$832$	−1.30472e6	−	4.01552e6i	−0.0653446	−	0.201110i
$833$	−6.15340e6	+	1.89382e7i	−0.307257	+	0.945641i
$834$	4.99596e6	+	3.62978e6i	0.248716	+	0.180703i
$835$	−2.44178e6			−0.121197
$836$	3.71547e7	+	2.96794e7i	1.83865	+	1.46872i
$837$	−4.44333e6			−0.219227
$838$	−6.08741e6	−	4.42276e6i	−0.299449	−	0.217562i
$839$	7.32237e6	−	2.25359e7i	0.359126	−	1.10528i	−0.594452	−	0.804131i	$-0.702631\pi$
$839$	7.32237e6	−	2.25359e7i	0.359126	−	1.10528i	0.953578	−	0.301145i	$-0.0973689\pi$
$840$	1.37565e7	+	4.23383e7i	0.672684	+	2.07031i
$841$	1.83479e6	−	1.33306e6i	0.0894534	−	0.0649917i
$842$	2.59785e7	−	1.88745e7i	1.26280	−	0.917477i
$843$	6.35161e6	+	1.95482e7i	0.307833	+	0.947412i
$844$	−2.78332e7	+	8.56618e7i	−1.34495	+	4.13934i
$845$	−1.16014e7	−	8.42889e6i	−0.558943	−	0.406096i
$846$	−313453.			−0.0150573
$847$	3.03137e7	−	1.80447e7i	1.45188	−	0.864255i
$848$	1.27163e8			6.07254
$849$	1.02589e6	+	745353.i	0.0488463	+	0.0354889i
$850$	−3.46850e6	+	1.06749e7i	−0.164662	+	0.506779i
$851$	−2.41262e6	−	7.42527e6i	−0.114200	−	0.351470i
$852$	1.51800e6	−	1.10289e6i	0.0716427	−	0.0520515i
$853$	9.84443e6	−	7.15240e6i	0.463253	−	0.336573i	−0.331553	−	0.943437i	$-0.607573\pi$
$853$	9.84443e6	−	7.15240e6i	0.463253	−	0.336573i	0.794806	+	0.606864i	$0.207573\pi$
$854$	2.06625e7	+	6.35925e7i	0.969477	+	2.98374i
$855$	−1.34323e6	+	4.13405e6i	−0.0628400	+	0.193402i
$856$	−3.37791e7	−	2.45419e7i	−1.57566	−	1.14479i
$857$	−3.92879e7			−1.82729			−0.913645	−	0.406514i	$-0.866744\pi$
$857$	−3.92879e7			−1.82729			−0.913645	+	0.406514i	$0.866744\pi$
$858$	−1.24275e6	−	992713.i	−0.0576322	−	0.0460369i
$859$	−6.06087e6			−0.280254			−0.140127	−	0.990134i	$-0.544751\pi$
$859$	−6.06087e6			−0.280254			−0.140127	+	0.990134i	$0.544751\pi$
$860$	5.42329e6	+	3.94025e6i	0.250044	+	0.181668i
$861$	−2.66423e6	+	8.19967e6i	−0.122480	+	0.376954i
$862$	2.01814e7	+	6.21121e7i	0.925090	+	2.84713i
$863$	1.28679e7	−	9.34907e6i	0.588139	−	0.427308i	−0.253510	−	0.967333i	$-0.581585\pi$
$863$	1.28679e7	−	9.34907e6i	0.588139	−	0.427308i	0.841649	+	0.540025i	$0.181585\pi$
$864$	−1.18705e7	+	8.62444e6i	−0.540986	+	0.393049i
$865$	5.67012e6	+	1.74508e7i	0.257663	+	0.793006i
$866$	−1.36299e7	+	4.19486e7i	−0.617588	+	1.90074i
$867$	−7.36755e6	−	5.35284e6i	−0.332870	−	0.241844i
$868$	−1.14368e8			−5.15235
$869$	−3.52466e6	−	1.28119e7i	−0.158332	−	0.575527i
$870$	1.61762e7			0.724568
$871$	701890.	+	509953.i	0.0313490	+	0.0227764i
$872$	−1.57488e7	+	4.84698e7i	−0.701385	+	2.15864i
$873$	−4.23118e6	−	1.30222e7i	−0.187899	−	0.578295i
$874$	−9.70301e6	+	7.04965e6i	−0.429663	+	0.312168i
$875$	3.26213e7	−	2.37008e7i	1.44039	−	1.04651i
$876$	−1.60155e7	−	4.92906e7i	−0.705148	−	2.17022i
$877$	1.10432e7	−	3.39876e7i	0.484838	−	1.49218i	−0.347377	−	0.937726i	$-0.612927\pi$
$877$	1.10432e7	−	3.39876e7i	0.484838	−	1.49218i	0.832215	−	0.554453i	$-0.187073\pi$
$878$	3.57708e7	+	2.59890e7i	1.56600	+	1.13777i
$879$	2.57273e6			0.112311
$880$	−4.64453e7	+	3.06041e7i	−2.02179	+	1.33221i
$881$	1.72470e7			0.748642			0.374321	−	0.927299i	$-0.377876\pi$
$881$	1.72470e7			0.748642			0.374321	+	0.927299i	$0.377876\pi$
$882$	2.21598e7	+	1.61001e7i	0.959168	+	0.696877i
$883$	−7.29629e6	+	2.24557e7i	−0.314920	+	0.969225i	0.660867	+	0.750503i	$0.270189\pi$
$883$	−7.29629e6	+	2.24557e7i	−0.314920	+	0.969225i	−0.975787	+	0.218722i	$0.929811\pi$
$884$	686441.	+	2.11265e6i	0.0295442	+	0.0909278i
$885$	3.35248e6	−	2.43572e6i	0.143882	−	0.104537i
$886$	3.31185e7	−	2.40620e7i	1.41738	−	1.02979i
$887$	−3.32904e6	−	1.02457e7i	−0.142073	−	0.437255i	0.854550	−	0.519369i	$-0.173833\pi$
$887$	−3.32904e6	−	1.02457e7i	−0.142073	−	0.437255i	−0.996623	+	0.0821140i	$0.973833\pi$
$888$	1.58122e7	−	4.86650e7i	0.672916	−	2.07102i
$889$	3.33446e7	+	2.42263e7i	1.41505	+	1.02809i
$890$	2.93384e7			1.24154
$891$	−927176.	+	2.46436e6i	−0.0391262	+	0.103994i
$892$	4.69961e7			1.97765
$893$	−399250.	−	290072.i	−0.0167539	−	0.0121724i
$894$	−2.24934e6	+	6.92277e6i	−0.0941265	+	0.289692i
$895$	−3.48628e6	−	1.07297e7i	−0.145480	−	0.447742i
$896$	−8.57734e7	+	6.23180e7i	−3.56930	+	2.59325i
$897$	236280.	−	171667.i	0.00980495	−	0.00712371i
$898$	−2.49950e7	−	7.69266e7i	−1.03434	−	3.18336i
$899$	−8.04478e6	+	2.47593e7i	−0.331982	+	1.02174i
$900$	9.09377e6	+	6.60701e6i	0.374229	+	0.271893i
$901$	−2.27347e7			−0.932992
$902$	−1.90175e7	−	869574.i	−0.778282	−	0.0355869i
$903$	3.97682e6			0.162299
$904$	−9.25132e7	−	6.72148e7i	−3.76515	−	2.73555i
$905$	4.64214e6	−	1.42870e7i	0.188407	−	0.579857i
$906$	−1.13127e6	−	3.48168e6i	−0.0457872	−	0.140918i
$907$	−1.00345e7	+	7.29046e6i	−0.405019	+	0.294264i	−0.771582	−	0.636130i	$-0.780534\pi$
$907$	−1.00345e7	+	7.29046e6i	−0.405019	+	0.294264i	0.366563	+	0.930393i	$0.380534\pi$
$908$	2.80244e7	−	2.03610e7i	1.12803	−	0.819565i
$909$	1.59204e6	+	4.89978e6i	0.0639062	+	0.196683i
$910$	1.15642e6	−	3.55910e6i	0.0462928	−	0.142475i
$911$	2.90502e7	+	2.11062e7i	1.15972	+	0.842586i	0.989743	−	0.142861i	$-0.0456303\pi$
$911$	2.90502e7	+	2.11062e7i	1.15972	+	0.842586i	0.169978	+	0.985448i	$0.445630\pi$
$912$	−4.44790e7			−1.77079
$913$	2.71657e7	+	1.24215e6i	1.07856	+	0.0493171i
$914$	−5.28606e7			−2.09299
$915$	−7.94898e6	−	5.77527e6i	−0.313876	−	0.228044i
$916$	2.50212e6	−	7.70075e6i	0.0985304	−	0.303245i
$917$	−2.33939e7	−	7.19989e7i	−0.918711	−	2.82750i
$918$	4.08627e6	−	2.96885e6i	0.160037	−	0.116274i
$919$	−1.11992e6	+	813669.i	−0.0437419	+	0.0317804i	−0.609441	−	0.792831i	$-0.708606\pi$
$919$	−1.11992e6	+	813669.i	−0.0437419	+	0.0317804i	0.565699	+	0.824611i	$0.308606\pi$
$920$	−5.57754e6	−	1.71659e7i	−0.217257	−	0.668647i
$921$	−7.30422e6	+	2.24801e7i	−0.283743	+	0.873271i
$922$	−1.25485e6	−	911704.i	−0.0486144	−	0.0353205i
$923$	−98809.2			−0.00381762
$924$	−2.38648e7	+	6.34308e7i	−0.919557	+	2.44411i
$925$	−1.58237e7			−0.608069
$926$	9.19995e6	+	6.68416e6i	0.352580	+	0.256165i
$927$	−1.81008e6	+	5.57085e6i	−0.0691828	+	0.212923i
$928$	2.65655e7	+	8.17602e7i	1.01262	+	3.11653i
$929$	−2.16777e7	+	1.57498e7i	−0.824090	+	0.598736i	−0.917881	−	0.396855i	$-0.870101\pi$
$929$	−2.16777e7	+	1.57498e7i	−0.824090	+	0.598736i	0.0937911	+	0.995592i	$0.470101\pi$
$930$	1.86752e7	−	1.35683e7i	0.708040	−	0.514421i
$931$	1.33262e7	+	4.10138e7i	0.503885	+	1.55080i
$932$	1.90185e7	−	5.85328e7i	0.717193	−	2.20729i
$933$	−2.17297e6	−	1.57875e6i	−0.0817239	−	0.0593759i
$934$	6.30848e7			2.36623
$935$	8.30371e6	−	5.47154e6i	0.310630	−	0.204682i
$936$	1.91414e6			0.0714141
$937$	−2.48929e7	−	1.80857e7i	−0.926246	−	0.672957i	0.0188250	−	0.999823i	$-0.494007\pi$
$937$	−2.48929e7	−	1.80857e7i	−0.926246	−	0.672957i	−0.945071	+	0.326866i	$0.894007\pi$
$938$	1.56906e7	−	4.82906e7i	0.582280	−	1.79207i
$939$	3.13876e6	+	9.66010e6i	0.116170	+	0.357534i
$940$	959136.	−	696853.i	0.0354047	−	0.0257230i
$941$	2.25683e7	−	1.63968e7i	0.830853	−	0.603650i	−0.0889474	−	0.996036i	$-0.528350\pi$
$941$	2.25683e7	−	1.63968e7i	0.830853	−	0.603650i	0.919801	+	0.392386i	$0.128350\pi$
$942$	−1.17774e7	−	3.62471e7i	−0.432436	−	1.33090i
$943$	1.08020e6	−	3.32453e6i	0.0395573	−	0.121745i
$944$	3.43045e7	+	2.49237e7i	1.25292	+	0.910296i
$945$	−6.19490e6			−0.225660
$946$	2.32923e6	+	8.46661e6i	0.0846222	+	0.307597i
$947$	−1.01024e7			−0.366059			−0.183030	−	0.983107i	$-0.558590\pi$
$947$	−1.01024e7			−0.366059			−0.183030	+	0.983107i	$0.558590\pi$
$948$	2.06519e7	+	1.50045e7i	0.746345	+	0.542251i
$949$	−843382.	+	2.59566e6i	−0.0303990	+	0.0935584i
$950$	7.51160e6	+	2.31183e7i	0.270037	+	0.831089i
$951$	825953.	−	600090.i	0.0296145	−	0.0215162i
$952$	6.58871e7	−	4.78698e7i	2.35618	−	1.71186i
$953$	5.72799e6	+	1.76289e7i	0.204301	+	0.628773i	0.999741	+	0.0227417i	$0.00723953\pi$
$953$	5.72799e6	+	1.76289e7i	0.204301	+	0.628773i	−0.795441	+	0.606032i	$0.792760\pi$
$954$	−9.66381e6	+	2.97421e7i	−0.343777	+	1.05804i
$955$	−2.58973e7	−	1.88155e7i	−0.918854	−	0.667586i
$956$	−6.13848e6			−0.217228
$957$	1.20533e7	+	9.62824e6i	0.425428	+	0.339834i
$958$	8.31974e7			2.92884
$959$	−8.07651e6	−	5.86793e6i	−0.283581	−	0.206034i
$960$	1.12206e7	−	3.45335e7i	0.392951	−	1.20938i
$961$	2.63317e6	+	8.10408e6i	0.0919753	+	0.283071i
$962$	−3.47998e6	+	2.52835e6i	−0.121238	+	0.0880845i
$963$	4.70062e6	−	3.41520e6i	0.163339	−	0.118673i
$964$	6.27751e6	+	1.93202e7i	0.217568	+	0.669605i
$965$	5.78879e6	−	1.78161e7i	0.200110	−	0.615876i
$966$	−1.38284e7	−	1.00469e7i	−0.476792	−	0.346410i
$967$	1.43629e6			0.0493941			0.0246970	−	0.999695i	$-0.492138\pi$
$967$	1.43629e6			0.0493941			0.0246970	+	0.999695i	$0.492138\pi$
$968$	−9.33523e7	−	8.55495e6i	−3.20211	−	0.293447i
$969$	7.95216e6			0.272067
$970$	5.75487e7	+	4.18116e7i	1.96384	+	1.42681i
$971$	3.70003e6	−	1.13875e7i	0.125938	−	0.387597i	−0.868133	−	0.496332i	$-0.834680\pi$
$971$	3.70003e6	−	1.13875e7i	0.125938	−	0.387597i	0.994071	+	0.108735i	$0.0346799\pi$
$972$	−1.56307e6	−	4.81065e6i	−0.0530657	−	0.163319i
$973$	−1.12098e7	+	8.14442e6i	−0.379592	+	0.275790i
$974$	−6.54647e7	+	4.75629e7i	−2.21111	+	1.60646i
$975$	−182916.	−	562959.i	−0.00616228	−	0.0189655i
$976$	3.10686e7	−	9.56193e7i	1.04399	−	3.21308i
$977$	−1.80022e7	−	1.30794e7i	−0.603379	−	0.438381i	0.243698	−	0.969851i	$-0.421640\pi$
$977$	−1.80022e7	−	1.30794e7i	−0.603379	−	0.438381i	−0.847077	+	0.531471i	$0.821640\pi$
$978$	3.31322e7			1.10765
$979$	2.18607e7	+	1.74625e7i	0.728967	+	0.582302i
$980$	−1.03600e8			−3.44583
$981$	−5.73760e6	−	4.16861e6i	−0.190352	−	0.138299i
$982$	−1.22337e7	+	3.76514e7i	−0.404835	+	1.24596i
$983$	9.20976e6	+	2.83447e7i	0.303994	+	0.935596i	0.980051	+	0.198747i	$0.0636872\pi$
$983$	9.20976e6	+	2.83447e7i	0.303994	+	0.935596i	−0.676057	+	0.736849i	$0.736313\pi$
$984$	1.85347e7	−	1.34663e7i	0.610237	−	0.443363i
$985$	9.43228e6	−	6.85296e6i	0.309761	−	0.225054i
$986$	−9.14483e6	−	2.81449e7i	−0.299560	−	0.921950i
$987$	217338.	−	668896.i	0.00710137	−	0.0218558i
$988$	3.89197e6	+	2.82768e6i	0.126846	+	0.0921592i
$989$	−1.61239e6			−0.0524177
$990$	−3.62836e6	−	1.31889e7i	−0.117658	−	0.427681i
$991$	−5.77652e7			−1.86845			−0.934227	−	0.356680i	$-0.883909\pi$
$991$	−5.77652e7			−1.86845			−0.934227	+	0.356680i	$0.883909\pi$
$992$	9.92484e7	+	7.21082e7i	3.20217	+	2.32651i
$993$	2.76429e6	−	8.50762e6i	0.0889634	−	0.273801i
$994$	1.78700e6	+	5.49982e6i	0.0573665	+	0.176556i
$995$	−2.96910e7	+	2.15718e7i	−0.950753	+	0.690763i
$996$	−4.22646e7	+	3.07071e7i	−1.34998	+	0.980821i
$997$	3.04621e6	+	9.37526e6i	0.0970558	+	0.298707i	0.987784	−	0.155829i	$-0.0498050\pi$
$997$	3.04621e6	+	9.37526e6i	0.0970558	+	0.298707i	−0.890728	+	0.454536i	$0.849805\pi$
$998$	−2.83811e7	+	8.73480e7i	−0.901991	+	2.77604i
$999$	5.76071e6	+	4.18540e6i	0.182626	+	0.132685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.e.b.4.5	✓	20
3.2	odd	2		99.6.f.b.37.1		20
11.3	even	5	inner	33.6.e.b.25.5	yes	20
11.5	even	5		363.6.a.r.1.1		10
11.6	odd	10		363.6.a.t.1.10		10
33.5	odd	10		1089.6.a.bk.1.10		10
33.14	odd	10		99.6.f.b.91.1		20
33.17	even	10		1089.6.a.bi.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.b.4.5	✓	20	1.1	even	1	trivial
33.6.e.b.25.5	yes	20	11.3	even	5	inner
99.6.f.b.37.1		20	3.2	odd	2
99.6.f.b.91.1		20	33.14	odd	10
363.6.a.r.1.1		10	11.5	even	5
363.6.a.t.1.10		10	11.6	odd	10
1089.6.a.bi.1.1		10	33.17	even	10
1089.6.a.bk.1.10		10	33.5	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(8.77555 + 6.37581i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(26.4708 + 81.4687i) q^{4} +(31.3852 - 22.8027i) q^{5} +(-78.9800 + 57.3823i) q^{6} +(-67.6896 - 208.327i) q^{7} +(-179.871 + 553.584i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})\)	\(q+(8.77555 + 6.37581i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(26.4708 + 81.4687i) q^{4} +(31.3852 - 22.8027i) q^{5} +(-78.9800 + 57.3823i) q^{6} +(-67.6896 - 208.327i) q^{7} +(-179.871 + 553.584i) q^{8} +(-65.5304 - 47.6106i) q^{9} +420.808 q^{10} +(313.554 + 250.469i) q^{11} -770.951 q^{12} +(32.8450 + 23.8633i) q^{13} +(734.241 - 2259.76i) q^{14} +(107.893 + 332.060i) q^{15} +(-2890.37 + 2099.97i) q^{16} +(516.753 - 375.443i) q^{17} +(-271.509 - 835.619i) q^{18} +(427.464 - 1315.60i) q^{19} +(2688.50 + 1953.31i) q^{20} +1971.43 q^{21} +(1154.67 + 4197.17i) q^{22} -799.310 q^{23} +(-4238.16 - 3079.21i) q^{24} +(-500.610 + 1540.72i) q^{25} +(136.085 + 418.826i) q^{26} +(589.773 - 428.495i) q^{27} +(15180.3 - 11029.2i) q^{28} +(-1319.88 - 4062.16i) q^{29} +(-1170.33 + 3601.91i) q^{30} +(-4931.04 - 3582.61i) q^{31} -20127.3 q^{32} +(-3015.93 + 1987.28i) q^{33} +6928.55 q^{34} +(-6874.87 - 4994.88i) q^{35} +(2144.13 - 6598.96i) q^{36} +(3018.37 + 9289.60i) q^{37} +(12139.2 - 8819.67i) q^{38} +(-295.605 + 214.769i) q^{39} +(6977.94 + 21475.9i) q^{40} +(-1351.42 + 4159.25i) q^{41} +(17300.4 + 12569.5i) q^{42} +2017.22 q^{43} +(-12105.3 + 32175.0i) q^{44} -3142.33 q^{45} +(-7014.39 - 5096.25i) q^{46} +(110.244 - 339.295i) q^{47} +(-9936.20 - 30580.5i) q^{48} +(-25221.1 + 18324.2i) q^{49} +(-14216.5 + 10328.9i) q^{50} +(1776.44 + 5467.32i) q^{51} +(-1074.68 + 3307.52i) q^{52} +(-28795.3 - 20921.0i) q^{53} +7907.59 q^{54} +(15552.3 + 711.130i) q^{55} +127502. q^{56} +(10072.0 + 7317.76i) q^{57} +(14316.9 - 44063.0i) q^{58} +(-3667.59 - 11287.7i) q^{59} +(-24196.5 + 17579.8i) q^{60} +(-22766.8 + 16541.0i) q^{61} +(-20430.6 - 62878.8i) q^{62} +(-5482.85 + 16874.5i) q^{63} +(-84136.1 - 61128.5i) q^{64} +1574.99 q^{65} +(-39137.0 - 1789.54i) q^{66} +21369.8 q^{67} +(44265.7 + 32160.9i) q^{68} +(2223.00 - 6841.70i) q^{69} +(-28484.3 - 87665.7i) q^{70} +(-1968.99 + 1430.56i) q^{71} +(38143.5 - 27712.9i) q^{72} +(20773.7 + 63934.8i) q^{73} +(-32740.8 + 100766. i) q^{74} +(-11795.5 - 8569.94i) q^{75} +118495. q^{76} +(30955.1 - 82276.0i) q^{77} -3963.42 q^{78} +(-26787.6 - 19462.3i) q^{79} +(-42829.7 + 131816. i) q^{80} +(2027.46 + 6239.88i) q^{81} +(-38378.0 + 27883.3i) q^{82} +(54821.4 - 39830.1i) q^{83} +(52185.4 + 160610. i) q^{84} +(7657.29 - 23566.7i) q^{85} +(17702.2 + 12861.4i) q^{86} +38440.9 q^{87} +(-195055. + 128527. i) q^{88} +69719.1 q^{89} +(-27575.7 - 20034.9i) q^{90} +(2748.10 - 8457.79i) q^{91} +(-21158.4 - 65118.8i) q^{92} +(44379.4 - 32243.5i) q^{93} +(3130.73 - 2274.61i) q^{94} +(-16583.1 - 51037.6i) q^{95} +(55977.0 - 172280. i) q^{96} +(136758. + 99360.2i) q^{97} -338161. q^{98} +(-8622.37 - 31341.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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