LMFDB - Embedded newform 21.6.g.c.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, 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:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 $ x^16 - 171x^14 + 21495x^12 - 1128902x^10 + 42970860x^8 - 655075344x^6 + 7244325760x^4 - 29387167488*x^2 + 90230547456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.7
Root			$5.89199 - 3.40174i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.6.g.c.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.89199 - 3.40174i) q^{2} +(14.3605 - 6.06423i) q^{3} +(7.14372 - 12.3733i) q^{4} +(7.45706 + 12.9160i) q^{5} +(63.9832 - 84.5813i) q^{6} +(-125.096 - 34.0278i) q^{7} +120.507i q^{8} +(169.450 - 174.171i) q^{9} +O(q^{10})$	\(q+(5.89199 - 3.40174i) q^{2} +(14.3605 - 6.06423i) q^{3} +(7.14372 - 12.3733i) q^{4} +(7.45706 + 12.9160i) q^{5} +(63.9832 - 84.5813i) q^{6} +(-125.096 - 34.0278i) q^{7} +120.507i q^{8} +(169.450 - 174.171i) q^{9} +(87.8738 + 50.7340i) q^{10} +(-83.2023 - 48.0368i) q^{11} +(27.5532 - 221.008i) q^{12} +416.854i q^{13} +(-852.821 + 225.054i) q^{14} +(185.413 + 140.259i) q^{15} +(638.534 + 1105.97i) q^{16} +(104.249 - 180.565i) q^{17} +(405.913 - 1602.64i) q^{18} +(-2296.16 + 1325.69i) q^{19} +213.085 q^{20} +(-2002.80 + 269.956i) q^{21} -653.636 q^{22} +(2267.02 - 1308.86i) q^{23} +(730.783 + 1730.55i) q^{24} +(1451.28 - 2513.70i) q^{25} +(1418.03 + 2456.10i) q^{26} +(1377.18 - 3528.78i) q^{27} +(-1314.69 + 1304.77i) q^{28} -7220.50i q^{29} +(1569.58 + 195.680i) q^{30} +(3721.66 + 2148.70i) q^{31} +(4184.88 + 2416.14i) q^{32} +(-1486.14 - 185.277i) q^{33} -1418.52i q^{34} +(-493.347 - 1869.49i) q^{35} +(-944.567 - 3340.89i) q^{36} +(-1839.50 - 3186.10i) q^{37} +(-9019.31 + 15621.9i) q^{38} +(2527.90 + 5986.24i) q^{39} +(-1556.47 + 898.629i) q^{40} -15452.3 q^{41} +(-10882.2 + 8403.60i) q^{42} -6011.11 q^{43} +(-1188.75 + 686.324i) q^{44} +(3513.20 + 889.813i) q^{45} +(8904.83 - 15423.6i) q^{46} +(-1953.72 - 3383.94i) q^{47} +(15876.6 + 12010.1i) q^{48} +(14491.2 + 8513.51i) q^{49} -19747.6i q^{50} +(402.087 - 3225.20i) q^{51} +(5157.85 + 2977.89i) q^{52} +(31434.3 + 18148.6i) q^{53} +(-3889.66 - 25476.4i) q^{54} -1432.85i q^{55} +(4100.60 - 15075.0i) q^{56} +(-24934.8 + 32962.1i) q^{57} +(-24562.3 - 42543.1i) q^{58} +(-3913.73 + 6778.77i) q^{59} +(3060.01 - 1292.19i) q^{60} +(17488.2 - 10096.8i) q^{61} +29237.3 q^{62} +(-27124.3 + 16022.2i) q^{63} -7989.78 q^{64} +(-5384.08 + 3108.50i) q^{65} +(-9386.57 + 3963.80i) q^{66} +(-21969.0 + 38051.4i) q^{67} +(-1489.45 - 2579.81i) q^{68} +(24618.3 - 32543.7i) q^{69} +(-9266.33 - 9336.79i) q^{70} -26028.0i q^{71} +(20988.9 + 20420.0i) q^{72} +(44090.5 + 25455.6i) q^{73} +(-21676.6 - 12515.0i) q^{74} +(5597.58 - 44899.0i) q^{75} +37881.4i q^{76} +(8773.71 + 8840.43i) q^{77} +(35258.0 + 26671.6i) q^{78} +(25057.2 + 43400.3i) q^{79} +(-9523.16 + 16494.6i) q^{80} +(-1622.28 - 59026.7i) q^{81} +(-91044.6 + 52564.6i) q^{82} -107835. q^{83} +(-10967.2 + 26709.8i) q^{84} +3109.57 q^{85} +(-35417.4 + 20448.3i) q^{86} +(-43786.8 - 103690. i) q^{87} +(5788.78 - 10026.5i) q^{88} +(68389.3 + 118454. i) q^{89} +(23726.6 - 6708.22i) q^{90} +(14184.6 - 52146.9i) q^{91} -37400.6i q^{92} +(66475.3 + 8287.50i) q^{93} +(-23022.6 - 13292.1i) q^{94} +(-34245.2 - 19771.5i) q^{95} +(74749.2 + 9319.01i) q^{96} -25183.4i q^{97} +(114343. + 866.170i) q^{98} +(-22465.3 + 6351.59i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	5.89199	−	3.40174i	1.04157	−	0.601349i	0.121290	−	0.992617i	$-0.461297\pi$
$2$	5.89199	−	3.40174i	1.04157	−	0.601349i	0.920277	+	0.391268i	$0.127963\pi$
$3$	14.3605	−	6.06423i	0.921229	−	0.389021i
$3$	14.3605	−	6.06423i	0.921229	−	0.389021i
$4$	7.14372	−	12.3733i	0.223241	−	0.386665i
$5$	7.45706	+	12.9160i	0.133396	+	0.231048i	0.924984	−	0.380007i	$-0.124078\pi$
$5$	7.45706	+	12.9160i	0.133396	+	0.231048i	−0.791588	+	0.611056i	$0.790745\pi$
$6$	63.9832	−	84.5813i	0.725585	−	0.959171i
$7$	−125.096	−	34.0278i	−0.964939	−	0.262476i
$7$	−125.096	−	34.0278i	−0.964939	−	0.262476i
$8$			120.507i			0.665714i
$9$	169.450	−	174.171i	0.697326	−	0.716754i
$10$	87.8738	+	50.7340i	0.277881	+	0.160435i
$11$	−83.2023	−	48.0368i	−0.207326	−	0.119700i	0.392742	−	0.919649i	$-0.371526\pi$
$11$	−83.2023	−	48.0368i	−0.207326	−	0.119700i	−0.600068	+	0.799949i	$0.704860\pi$
$12$	27.5532	−	221.008i	0.0552356	−	0.443053i
$13$			416.854i			0.684109i	0.939680	+	0.342055i	$0.111123\pi$
$13$			416.854i			0.684109i	−0.939680	+	0.342055i	$0.888877\pi$
$14$	−852.821	+	225.054i	−1.16289	+	0.306879i
$15$	185.413	+	140.259i	0.212771	+	0.160955i
$16$	638.534	+	1105.97i	0.623568	+	1.08005i
$17$	104.249	−	180.565i	0.0874884	−	0.151534i	−0.818960	−	0.573850i	$-0.805449\pi$
$17$	104.249	−	180.565i	0.0874884	−	0.151534i	0.906449	+	0.422316i	$0.138783\pi$
$18$	405.913	−	1602.64i	0.295292	−	1.16588i
$19$	−2296.16	+	1325.69i	−1.45921	+	0.842476i	−0.998973	−	0.0453185i	$-0.985570\pi$
$19$	−2296.16	+	1325.69i	−1.45921	+	0.842476i	−0.460239	+	0.887795i	$0.652236\pi$
$20$	213.085			0.119118
$21$	−2002.80	+	269.956i	−0.991038	+	0.133581i
$22$	−653.636			−0.287925
$23$	2267.02	−	1308.86i	0.893584	−	0.515911i	0.0184706	−	0.999829i	$-0.494120\pi$
$23$	2267.02	−	1308.86i	0.893584	−	0.515911i	0.875113	+	0.483919i	$0.160787\pi$
$24$	730.783	+	1730.55i	0.258977	+	0.613275i
$25$	1451.28	−	2513.70i	0.464411	−	0.804384i
$26$	1418.03	+	2456.10i	0.411388	+	0.712545i
$27$	1377.18	−	3528.78i	0.363564	−	0.931569i
$28$	−1314.69	+	1304.77i	−0.316904	+	0.314513i
$29$		−	7220.50i		−	1.59431i	−0.603776	−	0.797154i	$-0.706338\pi$
$29$		−	7220.50i		−	1.59431i	0.603776	−	0.797154i	$-0.293662\pi$
$30$	1569.58	+	195.680i	0.318405	+	0.0396957i
$31$	3721.66	+	2148.70i	0.695557	+	0.401580i	0.805690	−	0.592337i	$-0.201794\pi$
$31$	3721.66	+	2148.70i	0.695557	+	0.401580i	−0.110133	+	0.993917i	$0.535128\pi$
$32$	4184.88	+	2416.14i	0.722450	+	0.417107i
$33$	−1486.14	−	185.277i	−0.237560	−	0.0296167i
$34$		−	1418.52i		−	0.210444i
$35$	−493.347	−	1869.49i	−0.0680742	−	0.257961i
$36$	−944.567	−	3340.89i	−0.121472	−	0.429641i
$37$	−1839.50	−	3186.10i	−0.220900	−	0.382609i	0.734182	−	0.678953i	$-0.237566\pi$
$37$	−1839.50	−	3186.10i	−0.220900	−	0.382609i	−0.955081	+	0.296344i	$0.904233\pi$
$38$	−9019.31	+	15621.9i	−1.01324	+	1.75499i
$39$	2527.90	+	5986.24i	0.266133	+	0.630221i
$40$	−1556.47	+	898.629i	−0.153812	+	0.0888035i
$41$	−15452.3			−1.43560			−0.717798	−	0.696251i	$-0.754850\pi$
$41$	−15452.3			−1.43560			−0.717798	+	0.696251i	$0.754850\pi$
$42$	−10882.2	+	8403.60i	−0.951904	+	0.735093i
$43$	−6011.11			−0.495774			−0.247887	−	0.968789i	$-0.579736\pi$
$43$	−6011.11			−0.495774			−0.247887	+	0.968789i	$0.579736\pi$
$44$	−1188.75	+	686.324i	−0.0925674	+	0.0534438i
$45$	3513.20	+	889.813i	0.258625	+	0.0655040i
$46$	8904.83	−	15423.6i	0.620485	−	1.07471i
$47$	−1953.72	−	3383.94i	−0.129008	−	0.223449i	0.794284	−	0.607546i	$-0.207846\pi$
$47$	−1953.72	−	3383.94i	−0.129008	−	0.223449i	−0.923293	+	0.384097i	$0.874513\pi$
$48$	15876.6	+	12010.1i	0.994611	+	0.752394i
$49$	14491.2	+	8513.51i	0.862213	+	0.506546i
$50$		−	19747.6i		−	1.11709i
$51$	402.087	−	3225.20i	0.0216469	−	0.173633i
$52$	5157.85	+	2977.89i	0.264521	+	0.152721i
$53$	31434.3	+	18148.6i	1.53714	+	0.887469i	0.999004	+	0.0446107i	$0.0142047\pi$
$53$	31434.3	+	18148.6i	1.53714	+	0.887469i	0.538136	+	0.842858i	$0.319129\pi$
$54$	−3889.66	−	25476.4i	−0.181521	−	1.18892i
$55$		−	1432.85i		−	0.0638697i
$56$	4100.60	−	15075.0i	0.174734	−	0.642373i
$57$	−24934.8	+	32962.1i	−1.01653	+	1.34378i
$58$	−24562.3	−	42543.1i	−0.958736	−	1.66058i
$59$	−3913.73	+	6778.77i	−0.146373	+	0.253525i	−0.929884	−	0.367852i	$-0.880093\pi$
$59$	−3913.73	+	6778.77i	−0.146373	+	0.253525i	0.783511	+	0.621377i	$0.213427\pi$
$60$	3060.01	−	1292.19i	0.109735	−	0.0463393i
$61$	17488.2	−	10096.8i	0.601758	−	0.347425i	−0.167975	−	0.985791i	$-0.553723\pi$
$61$	17488.2	−	10096.8i	0.601758	−	0.347425i	0.769733	+	0.638366i	$0.220389\pi$
$62$	29237.3			0.965959
$63$	−27124.3	+	16022.2i	−0.861007	+	0.508593i
$64$	−7989.78			−0.243829
$65$	−5384.08	+	3108.50i	−0.158062	+	0.0912573i
$66$	−9386.57	+	3963.80i	−0.265245	+	0.112009i
$67$	−21969.0	+	38051.4i	−0.597892	+	1.03558i	0.395240	+	0.918578i	$0.370662\pi$
$67$	−21969.0	+	38051.4i	−0.597892	+	1.03558i	−0.993132	+	0.117001i	$0.962672\pi$
$68$	−1489.45	−	2579.81i	−0.0390621	−	0.0676575i
$69$	24618.3	−	32543.7i	0.622495	−	0.822894i
$70$	−9266.33	−	9336.79i	−0.226028	−	0.227747i
$71$		−	26028.0i		−	0.612765i	−0.951908	−	0.306383i	$-0.900881\pi$
$71$		−	26028.0i		−	0.612765i	0.951908	−	0.306383i	$-0.0991187\pi$
$72$	20988.9	+	20420.0i	0.477154	+	0.464220i
$73$	44090.5	+	25455.6i	0.968361	+	0.559084i	0.898736	−	0.438490i	$-0.144486\pi$
$73$	44090.5	+	25455.6i	0.968361	+	0.559084i	0.0696251	+	0.997573i	$0.477820\pi$
$74$	−21676.6	−	12515.0i	−0.460164	−	0.265676i
$75$	5597.58	−	44899.0i	0.114907	−	0.921687i
$76$			37881.4i			0.752302i
$77$	8773.71	+	8840.43i	0.168638	+	0.169921i
$78$	35258.0	+	26671.6i	0.656178	+	0.496379i
$79$	25057.2	+	43400.3i	0.451715	+	0.782393i	0.998493	−	0.0548850i	$-0.0174792\pi$
$79$	25057.2	+	43400.3i	0.451715	+	0.782393i	−0.546778	+	0.837278i	$0.684146\pi$
$80$	−9523.16	+	16494.6i	−0.166363	+	0.288149i
$81$	−1622.28	−	59026.7i	−0.0274735	−	0.999623i
$82$	−91044.6	+	52564.6i	−1.49527	+	0.863294i
$83$	−107835.			−1.71817			−0.859086	−	0.511832i	$-0.828967\pi$
$83$	−107835.			−1.71817			−0.859086	+	0.511832i	$0.828967\pi$
$84$	−10967.2	+	26709.8i	−0.169589	+	0.413021i
$85$	3109.57			0.0466824
$86$	−35417.4	+	20448.3i	−0.516382	+	0.298133i
$87$	−43786.8	−	103690.i	−0.620219	−	1.46872i
$88$	5788.78	−	10026.5i	0.0796857	−	0.138020i
$89$	68389.3	+	118454.i	0.915194	+	1.58516i	0.806617	+	0.591075i	$0.201296\pi$
$89$	68389.3	+	118454.i	0.915194	+	1.58516i	0.108577	+	0.994088i	$0.465370\pi$
$90$	23726.6	−	6708.22i	0.308766	−	0.0872973i
$91$	14184.6	−	52146.9i	0.179562	−	0.660123i
$92$		−	37400.6i		−	0.460690i
$93$	66475.3	+	8287.50i	0.796990	+	0.0993611i
$94$	−23022.6	−	13292.1i	−0.268741	−	0.155158i
$95$	−34245.2	−	19771.5i	−0.389306	−	0.224766i
$96$	74749.2	+	9319.01i	0.827805	+	0.103203i
$97$		−	25183.4i		−	0.271759i	−0.990725	−	0.135880i	$-0.956614\pi$
$97$		−	25183.4i		−	0.271759i	0.990725	−	0.135880i	$-0.0433861\pi$
$98$	114343.	+	866.170i	1.20266	+	0.00911041i
$99$	−22465.3	+	6351.59i	−0.230369	+	0.0651320i
$100$	−20735.1	−	35914.3i	−0.207351	−	0.359143i
$101$	39031.4	−	67604.3i	0.380724	−	0.659434i	−0.610442	−	0.792061i	$-0.709008\pi$
$101$	39031.4	−	67604.3i	0.380724	−	0.659434i	0.991166	+	0.132628i	$0.0423414\pi$
$102$	−8602.21	−	20370.7i	−0.0818672	−	0.193867i
$103$	−84863.5	+	48996.0i	−0.788184	+	0.455059i	−0.839323	−	0.543633i	$-0.817048\pi$
$103$	−84863.5	+	48996.0i	−0.788184	+	0.455059i	0.0511385	+	0.998692i	$0.483715\pi$
$104$	−50233.9			−0.455421
$105$	−18421.8	−	23855.1i	−0.163064	−	0.211159i
$106$	246947.			2.13471
$107$	116995.	−	67547.4i	0.987892	−	0.570360i	0.0832486	−	0.996529i	$-0.473470\pi$
$107$	116995.	−	67547.4i	0.987892	−	0.570360i	0.904644	+	0.426169i	$0.140137\pi$
$108$	−33824.4	−	42248.9i	−0.279043	−	0.348542i
$109$	−37566.0	+	65066.2i	−0.302851	+	0.524553i	−0.976781	−	0.214242i	$-0.931272\pi$
$109$	−37566.0	+	65066.2i	−0.302851	+	0.524553i	0.673930	+	0.738796i	$0.264605\pi$
$110$	−4874.20	−	8442.36i	−0.0384080	−	0.0665246i
$111$	−45737.5	−	34599.0i	−0.352342	−	0.266536i
$112$	−42244.4	−	160081.i	−0.318218	−	1.20585i
$113$			88078.7i			0.648895i	0.945904	+	0.324448i	$0.105178\pi$
$113$			88078.7i			0.648895i	−0.945904	+	0.324448i	$0.894822\pi$
$114$	−34787.3	+	279034.i	−0.250702	+	2.01092i
$115$	33810.5	+	19520.5i	0.238401	+	0.137641i
$116$	−89341.3	−	51581.3i	−0.616464	−	0.355915i
$117$	72604.0	+	70635.9i	0.490338	+	0.477047i
$118$			53254.0i			0.352085i
$119$	−19185.4	+	19040.7i	−0.124195	+	0.123258i
$120$	−16902.3	+	22343.6i	−0.107150	+	0.141645i
$121$	−75910.4	−	131481.i	−0.471344	−	0.816392i
$122$	68693.8	−	118981.i	0.417847	−	0.723733i
$123$	−221903.	+	93706.1i	−1.32251	+	0.558477i
$124$	53173.0	−	30699.5i	0.310554	−	0.179298i
$125$	89895.8			0.514594
$126$	−105313.	+	186672.i	−0.590955	+	1.04750i
$127$	−141581.			−0.778923			−0.389462	−	0.921043i	$-0.627339\pi$
$127$	−141581.			−0.778923			−0.389462	+	0.921043i	$0.627339\pi$
$128$	−180992.	+	104496.i	−0.976414	+	0.563733i
$129$	−86322.8	+	36452.8i	−0.456721	+	0.192866i
$130$	−21148.7	+	36630.5i	−0.109755	+	0.190101i
$131$	−76598.4	−	132672.i	−0.389979	−	0.675464i	0.602467	−	0.798144i	$-0.294185\pi$
$131$	−76598.4	−	132672.i	−0.389979	−	0.675464i	−0.992446	+	0.122680i	$0.960851\pi$
$132$	−12909.0	+	17064.8i	−0.0644850	+	0.0852446i
$133$	332352.	−	87705.6i	1.62918	−	0.429930i
$134$			298931.i			1.43817i
$135$	55847.4	−	8526.64i	0.263736	−	0.0402665i
$136$	21759.4	+	12562.8i	0.100879	+	0.0582423i
$137$	−78150.0	−	45119.9i	−0.355736	−	0.205384i	0.311473	−	0.950255i	$-0.399178\pi$
$137$	−78150.0	−	45119.9i	−0.355736	−	0.205384i	−0.667209	+	0.744871i	$0.732511\pi$
$138$	34345.8	−	275492.i	0.153524	−	1.23144i
$139$			133215.i			0.584814i	0.956294	+	0.292407i	$0.0944562\pi$
$139$			133215.i			0.584814i	−0.956294	+	0.292407i	$0.905544\pi$
$140$	−26656.1	−	7250.80i	−0.114941	−	0.0312655i
$141$	−48577.5	−	36747.4i	−0.205772	−	0.155661i
$142$	−88540.4	−	153357.i	−0.368486	−	0.638236i
$143$	20024.3	−	34683.2i	0.0818876	−	0.141833i
$144$	300828.	+	76193.0i	1.20896	+	0.306203i
$145$	93260.0	−	53843.7i	0.368362	−	0.212674i
$146$	346374.			1.34482
$147$	259730.	+	34380.6i	0.991352	+	0.131226i
$148$	−52563.5			−0.197256
$149$	−24381.5	+	14076.7i	−0.0899694	+	0.0519439i	−0.544310	−	0.838884i	$-0.683208\pi$
$149$	−24381.5	+	14076.7i	−0.0899694	+	0.0519439i	0.454340	+	0.890828i	$0.349875\pi$
$150$	−119754.	−	283586.i	−0.434572	−	1.02910i
$151$	3273.37	−	5669.65i	0.0116830	−	0.0202355i	−0.860125	−	0.510084i	$-0.829614\pi$
$151$	3273.37	−	5669.65i	0.0116830	−	0.0202355i	0.871808	+	0.489848i	$0.162948\pi$
$152$	−159755.	−	276704.i	−0.560849	−	0.971418i
$153$	−13784.2	−	48754.0i	−0.0476050	−	0.168377i
$154$	81767.5	+	22241.8i	0.277830	+	0.0755733i
$155$			64092.0i			0.214276i
$156$	92128.1	+	11485.7i	0.303096	+	0.0377872i
$157$	−59033.7	−	34083.1i	−0.191140	−	0.110355i	0.401376	−	0.915913i	$-0.368532\pi$
$157$	−59033.7	−	34083.1i	−0.191140	−	0.110355i	−0.592516	+	0.805559i	$0.701865\pi$
$158$	295273.	+	170476.i	0.940982	+	0.543276i
$159$	561470.	+	69998.7i	1.76130	+	0.219582i
$160$			72069.2i			0.222561i
$161$	−328133.	+	86592.4i	−0.997667	+	0.263278i
$162$	−210352.	−	342266.i	−0.629738	−	1.02465i
$163$	−211908.	−	367035.i	−0.624709	−	1.08203i	−0.988597	−	0.150585i	$-0.951884\pi$
$163$	−211908.	−	367035.i	−0.624709	−	1.08203i	0.363888	−	0.931443i	$-0.381449\pi$
$164$	−110387.	+	191195.i	−0.320484	+	0.555095i
$165$	−8689.16	−	20576.5i	−0.0248466	−	0.0588386i
$166$	−635366.	+	366829.i	−1.78959	+	1.03322i
$167$	30916.2			0.0857818			0.0428909	−	0.999080i	$-0.486343\pi$
$167$	30916.2			0.0857818			0.0428909	+	0.999080i	$0.486343\pi$
$168$	−32531.6	−	241352.i	−0.0889267	−	0.659748i
$169$	197526.			0.531995
$170$	18321.6	−	10578.0i	0.0486228	−	0.0280724i
$171$	−158188.	+	624564.i	−0.413698	+	1.63338i
$172$	−42941.7	+	74377.2i	−0.110677	+	0.191699i
$173$	89609.9	+	155209.i	0.227636	+	0.394277i	0.957107	−	0.289735i	$-0.0935671\pi$
$173$	89609.9	+	155209.i	0.227636	+	0.394277i	−0.729471	+	0.684012i	$0.760234\pi$
$174$	−610719.	−	461991.i	−1.52921	−	1.15681i
$175$	−267086.	+	265071.i	−0.659259	+	0.654284i
$176$		−	122693.i		−	0.298563i
$177$	−15095.2	+	121081.i	−0.0362163	+	0.290497i
$178$	805899.	+	465286.i	1.90647	+	1.10070i
$179$	−123131.	−	71089.4i	−0.287232	−	0.165834i	0.349461	−	0.936951i	$-0.386365\pi$
$179$	−123131.	−	71089.4i	−0.287232	−	0.165834i	−0.636693	+	0.771117i	$0.719698\pi$
$180$	36107.2	−	37113.2i	0.0830640	−	0.0853782i
$181$			321437.i			0.729288i	0.931147	+	0.364644i	$0.118809\pi$
$181$			321437.i			0.729288i	−0.931147	+	0.364644i	$0.881191\pi$
$182$	−93814.7	−	355502.i	−0.209939	−	0.795542i
$183$	189911.	−	251049.i	0.419201	−	0.554154i
$184$	157727.	+	273192.i	0.343449	+	0.594871i
$185$	27434.5	−	47517.9i	0.0589342	−	0.102077i
$186$	419864.	−	177302.i	0.889869	−	0.375778i
$187$	−17347.5	+	10015.6i	−0.0362772	+	0.0209447i
$188$	−55827.3			−0.115200
$189$	−292357.	+	394575.i	−0.595332	+	0.803480i
$190$	−269030.			−0.540651
$191$	457970.	−	264409.i	0.908352	−	0.524437i	0.0284511	−	0.999595i	$-0.490943\pi$
$191$	457970.	−	264409.i	0.908352	−	0.524437i	0.879900	+	0.475158i	$0.157609\pi$
$192$	−114738.	+	48451.9i	−0.224622	+	0.0948544i
$193$	47616.0	−	82473.4i	0.0920153	−	0.159375i	−0.816344	−	0.577566i	$-0.804002\pi$
$193$	47616.0	−	82473.4i	0.0920153	−	0.159375i	0.908359	+	0.418191i	$0.137336\pi$
$194$	−85667.4	−	148380.i	−0.163422	−	0.283056i
$195$	−58467.6	+	77290.1i	−0.110111	+	0.145558i
$196$	208861.	−	118486.i	0.388345	−	0.220306i
$197$		−	705756.i		−	1.29565i	−0.761787	−	0.647827i	$-0.775678\pi$
$197$		−	705756.i		−	1.29565i	0.761787	−	0.647827i	$-0.224322\pi$
$198$	−110759.	+	113845.i	−0.200778	+	0.206371i
$199$	−75610.4	−	43653.7i	−0.135347	−	0.0781426i	0.430798	−	0.902449i	$-0.358232\pi$
$199$	−75610.4	−	43653.7i	−0.135347	−	0.0781426i	−0.566145	+	0.824306i	$0.691566\pi$
$200$	302919.	+	174890.i	0.535490	+	0.309165i
$201$	−84733.9	+	679663.i	−0.147934	+	1.18660i
$202$		−	531099.i		−	0.915792i
$203$	−245698.	+	903259.i	−0.418467	+	1.53841i
$204$	−37034.0	−	28015.1i	−0.0623053	−	0.0471321i
$205$	−115228.	−	199581.i	−0.191503	−	0.331692i
$206$	−333343.	+	577368.i	−0.547298	+	0.947948i
$207$	156180.	−	616636.i	0.253338	−	1.00024i
$208$	−461029.	+	266175.i	−0.738873	+	0.426588i
$209$	254728.			0.403376
$210$	−189690.	−	77888.2i	−0.296822	−	0.121877i
$211$	−330657.			−0.511294			−0.255647	−	0.966770i	$-0.582289\pi$
$211$	−330657.			−0.511294			−0.255647	+	0.966770i	$0.582289\pi$
$212$	449115.	−	259297.i	0.686307	−	0.396239i
$213$	−157840.	−	373775.i	−0.238378	−	0.564497i
$214$	459558.	−	795977.i	0.685971	−	1.18814i
$215$	−44825.2	−	77639.5i	−0.0661342	−	0.114548i
$216$	425243.	+	165960.i	0.620159	+	0.242030i
$217$	−392451.	−	395435.i	−0.565765	−	0.570067i
$218$			511160.i			0.728476i
$219$	787532.	+	98181.9i	1.10958	+	0.138332i
$220$	−17729.1	−	10235.9i	−0.0246962	−	0.0142584i
$221$	75269.2	+	43456.7i	0.103666	+	0.0598516i
$222$	−387182.	−	48270.1i	−0.527269	−	0.0657349i
$223$		−	232532.i		−	0.313128i	−0.987668	−	0.156564i	$-0.949958\pi$
$223$		−	232532.i		−	0.313128i	0.987668	−	0.156564i	$-0.0500417\pi$
$224$	−441297.	−	444653.i	−0.587640	−	0.592108i
$225$	−191894.	−	678719.i	−0.252700	−	0.893786i
$226$	299621.	+	518959.i	0.390212	+	0.675868i
$227$	224126.	−	388198.i	0.288687	−	0.500021i	−0.684809	−	0.728722i	$-0.740115\pi$
$227$	224126.	−	388198.i	0.288687	−	0.500021i	0.973497	+	0.228701i	$0.0734479\pi$
$228$	229722.	+	543998.i	0.292661	+	0.693043i
$229$	498966.	−	288078.i	0.628756	−	0.363012i	−0.151514	−	0.988455i	$-0.548415\pi$
$229$	498966.	−	288078.i	0.628756	−	0.363012i	0.780270	+	0.625443i	$0.215082\pi$
$230$	265615.			0.331080
$231$	179606.	+	73747.5i	0.221457	+	0.0909321i
$232$	870122.			1.06135
$233$	−352442.	+	203483.i	−0.425303	+	0.245549i	−0.697344	−	0.716737i	$-0.745635\pi$
$233$	−352442.	+	203483.i	−0.425303	+	0.245549i	0.272041	+	0.962286i	$0.412301\pi$
$234$	668067.	+	169206.i	0.797592	+	0.202012i
$235$	29138.0	−	50468.5i	0.0344183	−	0.0596143i
$236$	55917.1	+	96851.3i	0.0653529	+	0.113195i
$237$	623024.	+	471299.i	0.720499	+	0.545036i
$238$	−48269.0	+	177451.i	−0.0552365	+	0.203066i
$239$			266151.i			0.301393i	0.988580	+	0.150696i	$0.0481516\pi$
$239$			266151.i			0.301393i	−0.988580	+	0.150696i	$0.951848\pi$
$240$	−36730.6	+	294622.i	−0.0411624	+	0.330170i
$241$	336439.	+	194243.i	0.373133	+	0.215428i	0.674826	−	0.737977i	$-0.264219\pi$
$241$	336439.	+	194243.i	0.373133	+	0.215428i	−0.301693	+	0.953405i	$0.597552\pi$
$242$	−894527.	−	516456.i	−0.981873	−	0.566885i
$243$	−381249.	−	837817.i	−0.414183	−	0.910194i
$244$		−	288516.i		−	0.310238i
$245$	−1898.76	+	250654.i	−0.00202094	+	0.266784i
$246$	−988685.	+	1.30697e6i	−1.04165	+	1.37698i
$247$	−552619.	−	957163.i	−0.576346	−	0.998260i
$248$	−258934.	+	448487.i	−0.267338	+	0.463042i
$249$	−1.54858e6	+	653939.i	−1.58283	+	0.668404i
$250$	529666.	−	305803.i	0.535984	−	0.309450i
$251$	−1.09673e6			−1.09879			−0.549397	−	0.835561i	$-0.685143\pi$
$251$	−1.09673e6			−1.09879			−0.549397	+	0.835561i	$0.685143\pi$
$252$	4478.81	+	450074.i	0.00444285	+	0.446461i
$253$	−251495.			−0.247017
$254$	−834192.	+	481621.i	−0.811301	+	0.468405i
$255$	44655.1	−	18857.1i	0.0430052	−	0.0181604i
$256$	−583099.	+	1.00996e6i	−0.556086	+	0.963170i
$257$	50161.9	+	86882.9i	0.0473741	+	0.0820544i	0.888740	−	0.458411i	$-0.151581\pi$
$257$	50161.9	+	86882.9i	0.0473741	+	0.0820544i	−0.841366	+	0.540466i	$0.818248\pi$
$258$	−384610.	+	508427.i	−0.359726	+	0.475532i
$259$	121698.	+	461164.i	0.112729	+	0.427175i
$260$			88825.1i			0.0814896i
$261$	−1.25760e6	−	1.22352e6i	−1.14273	−	1.11175i
$262$	−902635.	−	521136.i	−0.812379	−	0.469027i
$263$	1.13012e6	+	652475.i	1.00748	+	0.581667i	0.910452	−	0.413615i	$-0.135734\pi$
$263$	1.13012e6	+	652475.i	1.00748	+	0.581667i	0.0970250	+	0.995282i	$0.469067\pi$
$264$	22327.2	−	179090.i	0.0197163	−	0.158147i
$265$			541340.i			0.473539i
$266$	1.65986e6	−	1.64734e6i	1.43836	−	1.42751i
$267$	1.70044e6	+	1.28633e6i	1.45976	+	1.10427i
$268$	313880.	+	543657.i	0.266948	+	0.462368i
$269$	630360.	−	1.09182e6i	0.531139	−	0.919960i	−0.468201	−	0.883622i	$-0.655098\pi$
$269$	630360.	−	1.09182e6i	0.531139	−	0.919960i	0.999340	−	0.0363375i	$-0.0115691\pi$
$270$	300047.	−	240217.i	0.250484	−	0.200537i
$271$	1.08027e6	−	623692.i	0.893527	−	0.515878i	0.0184323	−	0.999830i	$-0.494132\pi$
$271$	1.08027e6	−	623692.i	0.893527	−	0.515878i	0.875094	+	0.483952i	$0.160799\pi$
$272$	266267.			0.218220
$273$	−112532.	−	834876.i	−0.0913839	−	0.677978i
$274$	−613945.			−0.494030
$275$	−241500.	+	139430.i	−0.192569	+	0.111180i
$276$	−226806.	−	537093.i	−0.179218	−	0.424401i
$277$	−329450.	+	570623.i	−0.257982	+	0.446838i	−0.965701	−	0.259656i	$-0.916391\pi$
$277$	−329450.	+	570623.i	−0.257982	+	0.446838i	0.707719	+	0.706494i	$0.249724\pi$
$278$	453165.	+	784905.i	0.351677	+	0.609123i
$279$	1.00488e6	−	284109.i	0.772864	−	0.218511i
$280$	225287.	−	59451.9i	0.171728	−	0.0453180i
$281$		−	1.28896e6i		−	0.973809i	−0.873455	−	0.486904i	$-0.838126\pi$
$281$		−	1.28896e6i		−	0.973809i	0.873455	−	0.486904i	$-0.161874\pi$
$282$	−411223.	−	51267.4i	−0.307932	−	0.0383900i
$283$	−873894.	−	504543.i	−0.648624	−	0.374483i	0.139305	−	0.990250i	$-0.455513\pi$
$283$	−873894.	−	504543.i	−0.648624	−	0.374483i	−0.787929	+	0.615766i	$0.788847\pi$
$284$	−322051.	−	185936.i	−0.236935	−	0.136795i
$285$	−611678.	−	76258.2i	−0.446078	−	0.0556127i
$286$		−	272471.i		−	0.196972i
$287$	1.93302e6	+	525807.i	1.38526	+	0.376809i
$288$	1.12995e6	−	319470.i	0.802746	−	0.226960i
$289$	688193.	+	1.19198e6i	0.484692	+	0.839510i
$290$	366325.	−	634493.i	0.255783	−	0.443029i
$291$	−152718.	−	361647.i	−0.105720	−	0.250353i
$292$	629940.	−	363696.i	0.432357	−	0.249621i
$293$	−1.94711e6			−1.32502			−0.662508	−	0.749055i	$-0.730508\pi$
$293$	−1.94711e6			−1.32502			−0.662508	+	0.749055i	$0.730508\pi$
$294$	1.64728e6	−	680963.i	1.11147	−	0.459468i
$295$	−116739.			−0.0781021
$296$	383948.	−	221673.i	0.254709	−	0.147056i
$297$	−284096.	+	227447.i	−0.186885	+	0.149620i
$298$	−95770.5	+	165879.i	−0.0624728	+	0.108206i
$299$	545604.	+	945014.i	0.352939	+	0.611309i
$300$	−515561.	−	390006.i	−0.330732	−	0.250189i
$301$	751968.	+	204545.i	0.478391	+	0.130129i
$302$		−	44540.7i		−	0.0281022i
$303$	150543.	−	1.20753e6i	0.0942008	−	0.755599i
$304$	−2.93235e6	−	1.69299e6i	−1.81984	−	1.05068i
$305$	260822.	+	150585.i	0.160544	+	0.0926901i
$306$	−247065.	−	240368.i	−0.150837	−	0.146748i
$307$			1.97804e6i			1.19782i	0.800818	+	0.598908i	$0.204398\pi$
$307$			1.97804e6i			1.19782i	−0.800818	+	0.598908i	$0.795602\pi$
$308$	172062.	−	45406.1i	0.103350	−	0.0272733i
$309$	−921563.	+	1.21824e6i	−0.549071	+	0.725833i
$310$	218024.	+	377629.i	0.128855	+	0.223183i
$311$	−535732.	+	927914.i	−0.314084	+	0.544010i	−0.979242	−	0.202693i	$-0.935031\pi$
$311$	−535732.	+	927914.i	−0.314084	+	0.544010i	0.665158	+	0.746703i	$0.268364\pi$
$312$	−721385.	+	304630.i	−0.419547	+	0.177168i
$313$	−360508.	+	208140.i	−0.207996	+	0.120086i	−0.600380	−	0.799715i	$-0.704984\pi$
$313$	−360508.	+	208140.i	−0.207996	+	0.120086i	0.392384	+	0.919802i	$0.371650\pi$
$314$	−463768.			−0.265446
$315$	−409210.	−	230859.i	−0.232364	−	0.131090i
$316$	716005.			0.403365
$317$	−2.50467e6	+	1.44607e6i	−1.39992	+	0.808242i	−0.994383	−	0.105839i	$-0.966247\pi$
$317$	−2.50467e6	+	1.44607e6i	−1.39992	+	0.808242i	−0.405532	+	0.914081i	$0.632914\pi$
$318$	3.54630e6	−	1.49755e6i	1.96656	−	0.830448i
$319$	−346850.	+	600762.i	−0.190838	+	0.330541i
$320$	−59580.2	−	103196.i	−0.0325258	−	0.0563363i
$321$	1.27049e6	−	1.67950e6i	0.688193	−	0.909743i
$322$	−1.63879e6	+	1.62643e6i	−0.880815	+	0.874168i
$323$			552808.i			0.294828i
$324$	−741944.	−	401597.i	−0.392653	−	0.212534i
$325$	1.04784e6	+	604973.i	0.550286	+	0.317708i
$326$	−2.49712e6	−	1.44171e6i	−1.30135	−	0.751337i
$327$	−144891.	+	1.16220e6i	−0.0749330	+	0.601049i
$328$		−	1.86211e6i		−	0.955697i
$329$	129255.	+	489800.i	0.0658352	+	0.249476i
$330$	−121193.	−	91678.6i	−0.0612620	−	0.0463429i
$331$	1.73878e6	+	3.01165e6i	0.872315	+	1.51089i	0.859595	+	0.510975i	$0.170716\pi$
$331$	1.73878e6	+	3.01165e6i	0.872315	+	1.51089i	0.0127200	+	0.999919i	$0.495951\pi$
$332$	−770347.	+	1.33428e6i	−0.383567	+	0.664357i
$333$	−866631.	−	219498.i	−0.428276	−	0.108473i
$334$	182158.	−	105169.i	0.0893475	−	0.0515848i
$335$	−655295.			−0.319025
$336$	−1.57742e6	−	2.04267e6i	−0.762254	−	0.987075i
$337$	916887.			0.439786			0.219893	−	0.975524i	$-0.429429\pi$
$337$	916887.			0.439786			0.219893	+	0.975524i	$0.429429\pi$
$338$	1.16382e6	−	671933.i	0.554108	−	0.319915i
$339$	534129.	+	1.26486e6i	0.252434	+	0.597781i
$340$	22213.9	−	38475.6i	0.0104214	−	0.0180505i
$341$	−206434.	−	357554.i	−0.0961379	−	0.166516i
$342$	1.19256e6	+	4.21804e6i	0.551336	+	1.95005i
$343$	−1.52310e6	−	1.55811e6i	−0.699027	−	0.715096i
$344$		−	724382.i		−	0.330044i
$345$	603915.	+	75290.3i	0.273167	+	0.0340558i
$346$	1.05596e6	+	609660.i	0.474196	+	0.273777i
$347$	−1.07207e6	−	618962.i	−0.477970	−	0.275956i	0.241600	−	0.970376i	$-0.422328\pi$
$347$	−1.07207e6	−	618962.i	−0.477970	−	0.275956i	−0.719570	+	0.694420i	$0.755661\pi$
$348$	−1.59579e6	−	198948.i	−0.706363	−	0.0880625i
$349$		−	2.19902e6i		−	0.966419i	−0.875505	−	0.483210i	$-0.839471\pi$
$349$		−	2.19902e6i		−	0.966419i	0.875505	−	0.483210i	$-0.160529\pi$
$350$	−671968.	+	2.47035e6i	−0.293210	+	1.07793i
$351$	1.47098e6	+	574083.i	0.637295	+	0.248718i
$352$	−232128.	−	402057.i	−0.0998550	−	0.172954i
$353$	1.33455e6	−	2.31152e6i	0.570032	−	0.987325i	−0.426530	−	0.904474i	$-0.640264\pi$
$353$	1.33455e6	−	2.31152e6i	0.570032	−	0.987325i	0.996562	−	0.0828512i	$-0.0264026\pi$
$354$	322944.	+	764756.i	0.136968	+	0.324350i
$355$	336177.	−	194092.i	0.141578	−	0.0817404i
$356$	1.95422e6			0.817237
$357$	−160046.	+	389779.i	−0.0664622	+	0.161863i
$358$	−967312.			−0.398896
$359$	3.93862e6	−	2.27396e6i	1.61290	−	0.931210i	0.624209	−	0.781257i	$-0.285421\pi$
$359$	3.93862e6	−	2.27396e6i	1.61290	−	0.931210i	0.988693	−	0.149952i	$-0.0479119\pi$
$360$	−107229.	+	423365.i	−0.0436069	+	0.172171i
$361$	2.27685e6	−	3.94363e6i	0.919533	−	1.59268i
$362$	1.09345e6	+	1.89390e6i	0.438557	+	0.759602i
$363$	−1.88744e6	−	1.42780e6i	−0.751809	−	0.568721i
$364$	−543898.	−	548033.i	−0.215161	−	0.216797i
$365$			759296.i			0.298318i
$366$	264950.	−	2.12521e6i	0.103386	−	0.829275i
$367$	−1.84905e6	−	1.06755e6i	−0.716609	−	0.413735i	0.0968940	−	0.995295i	$-0.469109\pi$
$367$	−1.84905e6	−	1.06755e6i	−0.716609	−	0.413735i	−0.813503	+	0.581560i	$0.802443\pi$
$368$	2.89513e6	+	1.67151e6i	1.11442	+	0.643411i
$369$	−2.61839e6	+	2.69134e6i	−1.00108	+	1.02897i
$370$		−	373300.i		−	0.141760i
$371$	−3.31476e6	−	3.33996e6i	−1.25031	−	1.25981i
$372$	577425.	−	763315.i	0.216341	−	0.285987i
$373$	1.62927e6	+	2.82198e6i	0.606346	+	1.05022i	0.991837	+	0.127511i	$0.0406987\pi$
$373$	1.62927e6	+	2.82198e6i	0.606346	+	1.05022i	−0.385491	+	0.922711i	$0.625968\pi$
$374$	−68141.1	+	118024.i	−0.0251901	+	0.0436305i
$375$	1.29095e6	−	545149.i	0.474059	−	0.200188i
$376$	407789.	−	235437.i	0.148753	−	0.0858826i
$377$	3.00989e6			1.09068
$378$	−380322.	+	3.31936e6i	−0.136906	+	1.19488i
$379$	−3.32017e6			−1.18730			−0.593652	−	0.804722i	$-0.702314\pi$
$379$	−3.32017e6			−1.18730			−0.593652	+	0.804722i	$0.702314\pi$
$380$	−489276.	+	282484.i	−0.173818	+	0.100354i
$381$	−2.03318e6	+	858578.i	−0.717567	+	0.303017i
$382$	1.79891e6	−	3.11580e6i	0.630739	−	1.09247i
$383$	−1.73101e6	−	2.99819e6i	−0.602978	−	1.04439i	−0.992368	−	0.123316i	$-0.960647\pi$
$383$	−1.73101e6	−	2.99819e6i	−0.602978	−	1.04439i	0.389389	−	0.921073i	$-0.372686\pi$
$384$	−1.96545e6	+	2.59819e6i	−0.680197	+	0.899173i
$385$	−48756.9	+	179245.i	−0.0167642	+	0.0616304i
$386$		−	647910.i		−	0.221333i
$387$	−1.01858e6	+	1.04696e6i	−0.345716	+	0.355348i
$388$	−311601.	−	179903.i	−0.105080	−	0.0606679i
$389$	2.15824e6	+	1.24606e6i	0.723147	+	0.417509i	0.815910	−	0.578179i	$-0.196237\pi$
$389$	2.15824e6	+	1.24606e6i	0.723147	+	0.417509i	−0.0927629	+	0.995688i	$0.529570\pi$
$390$	−81569.9	+	654285.i	−0.0271562	+	0.217824i
$391$		−	545792.i		−	0.180545i
$392$	−1.02594e6	+	1.74630e6i	−0.337215	+	0.573988i
$393$	−1.90455e6	−	1.44074e6i	−0.622030	−	0.470547i
$394$	−2.40080e6	−	4.15831e6i	−0.779141	−	1.34951i
$395$	−373705.	+	647276.i	−0.120514	+	0.208736i
$396$	−81895.6	+	323343.i	−0.0262435	+	0.103616i
$397$	2.63999e6	−	1.52420e6i	0.840670	−	0.485361i	−0.0168218	−	0.999859i	$-0.505355\pi$
$397$	2.63999e6	−	1.52420e6i	0.840670	−	0.485361i	0.857492	+	0.514497i	$0.172021\pi$
$398$	−593994.			−0.187964
$399$	4.24088e6	−	3.27496e6i	1.33360	−	1.02985i
$400$	3.70678e6			1.15837
$401$	−44663.4	+	25786.4i	−0.0138705	+	0.00800812i	−0.506919	−	0.861994i	$-0.669216\pi$
$401$	−44663.4	+	25786.4i	−0.0138705	+	0.00800812i	0.493049	+	0.870002i	$0.335882\pi$
$402$	1.81279e6	+	4.29281e6i	0.559477	+	1.32488i
$403$	−895695.	+	1.55139e6i	−0.274725	+	0.475837i
$404$	−557659.	−	965893.i	−0.169987	−	0.294426i
$405$	750291.	−	461119.i	0.227296	−	0.139693i
$406$	1.62500e6	+	6.15780e6i	0.489260	+	1.85400i
$407$			353455.i			0.105766i
$408$	388660.	+	48454.4i	0.115590	+	0.0144106i
$409$	3.93107e6	+	2.26960e6i	1.16199	+	0.670875i	0.951780	−	0.306782i	$-0.0992522\pi$
$409$	3.93107e6	+	2.26960e6i	1.16199	+	0.670875i	0.210209	+	0.977656i	$0.432585\pi$
$410$	−1.35785e6	−	783954.i	−0.398925	−	0.230320i
$411$	−1.39589e6	−	174027.i	−0.407613	−	0.0508172i
$412$			1.40005e6i			0.406351i
$413$	720260.	−	714824.i	0.207785	−	0.206217i
$414$	−1.17743e6	−	4.16450e6i	−0.337624	−	1.19416i
$415$	−804135.	−	1.39280e6i	−0.229197	−	0.396981i
$416$	−1.00718e6	+	1.74448e6i	−0.285347	+	0.494235i
$417$	807850.	+	1.91305e6i	0.227505	+	0.538747i
$418$	1.50085e6	−	866518.i	0.420144	−	0.242570i
$419$	−1.89078e6			−0.526145			−0.263072	−	0.964776i	$-0.584736\pi$
$419$	−1.89078e6			−0.526145			−0.263072	+	0.964776i	$0.584736\pi$
$420$	−426767.	+	57523.4i	−0.118050	+	0.0159119i
$421$	−5.04901e6			−1.38836			−0.694178	−	0.719803i	$-0.744232\pi$
$421$	−5.04901e6			−1.38836			−0.694178	+	0.719803i	$0.744232\pi$
$422$	−1.94823e6	+	1.12481e6i	−0.532547	+	0.307466i
$423$	−920443.	−	233128.i	−0.250119	−	0.0633494i
$424$	−2.18703e6	+	3.78805e6i	−0.590801	+	1.02330i
$425$	−302591.	−	524102.i	−0.0812612	−	0.140748i
$426$	−2.20148e6	−	1.66535e6i	−0.587747	−	0.444613i
$427$	−2.53129e6	+	667992.i	−0.671850	+	0.177297i
$428$		−	1.93016e6i		−	0.509312i
$429$	77233.5	−	619501.i	0.0202611	−	0.162517i
$430$	−528219.	−	304968.i	−0.137766	−	0.0795394i
$431$	2.83060e6	+	1.63425e6i	0.733982	+	0.423765i	0.819877	−	0.572539i	$-0.194042\pi$
$431$	2.83060e6	+	1.63425e6i	0.733982	+	0.423765i	−0.0858949	+	0.996304i	$0.527375\pi$
$432$	4.78211e6	−	730120.i	1.23285	−	0.188228i
$433$		−	1.69788e6i		−	0.435198i	−0.976038	−	0.217599i	$-0.930177\pi$
$433$		−	1.69788e6i		−	0.435198i	0.976038	−	0.217599i	$-0.0698226\pi$
$434$	−3.65749e6	−	994883.i	−0.932091	−	0.253541i
$435$	1.01274e6	−	1.33877e6i	0.256612	−	0.339222i
$436$	536722.	+	929630.i	0.135218	+	0.234204i
$437$	−3.47029e6	+	6.01072e6i	−0.869285	+	1.50565i
$438$	4.97412e6	−	2.10049e6i	1.23889	−	0.523162i
$439$	−3.83060e6	+	2.21160e6i	−0.948650	+	0.547703i	−0.892661	−	0.450728i	$-0.851164\pi$
$439$	−3.83060e6	+	2.21160e6i	−0.948650	+	0.547703i	−0.0559885	+	0.998431i	$0.517831\pi$
$440$	172669.			0.0425190
$441$	3.93835e6	−	1.08134e6i	0.964312	−	0.264767i
$442$	591314.			0.143967
$443$	−4.52080e6	+	2.61008e6i	−1.09447	+	0.631895i	−0.934764	−	0.355269i	$-0.884389\pi$
$443$	−4.52080e6	+	2.61008e6i	−1.09447	+	0.631895i	−0.159710	+	0.987164i	$0.551056\pi$
$444$	−754840.	+	318757.i	−0.181718	+	0.0767366i
$445$	−1.01997e6	+	1.76663e6i	−0.244166	+	0.422908i
$446$	−791015.	−	1.37008e6i	−0.188299	−	0.326143i
$447$	−264767.	+	350004.i	−0.0626752	+	0.0828522i
$448$	999493.	+	271875.i	0.235280	+	0.0639991i
$449$			3.80274e6i			0.890186i	0.895484	+	0.445093i	$0.146829\pi$
$449$			3.80274e6i			0.890186i	−0.895484	+	0.445093i	$0.853171\pi$
$450$	−3.43946e6	−	3.34623e6i	−0.800681	−	0.778978i
$451$	1.28566e6	+	742278.i	0.297636	+	0.171840i
$452$	1.08982e6	+	629209.i	0.250905	+	0.144860i
$453$	12625.3	−	101270.i	0.00289066	−	0.0231864i
$454$		−	3.04968e6i		−	0.694407i
$455$	779305.	−	205654.i	0.176473	−	0.0465702i
$456$	−3.97217e6	−	3.00482e6i	−0.894572	−	0.676717i
$457$	−918745.	−	1.59131e6i	−0.205781	−	0.356423i	0.744600	−	0.667510i	$-0.232640\pi$
$457$	−918745.	−	1.59131e6i	−0.205781	−	0.356423i	−0.950381	+	0.311088i	$0.899307\pi$
$458$	1.95993e6	−	3.39471e6i	0.436594	−	0.756203i
$459$	−493604.	−	616543.i	−0.109357	−	0.136594i
$460$	483066.	−	278898.i	0.106442	−	0.0614542i
$461$	7.79775e6			1.70890			0.854450	−	0.519533i	$-0.173894\pi$
$461$	7.79775e6			1.70890			0.854450	+	0.519533i	$0.173894\pi$
$462$	1.30911e6	−	176453.i	0.285345	−	0.0384613i
$463$	254809.			0.0552410			0.0276205	−	0.999618i	$-0.491207\pi$
$463$	254809.			0.0552410			0.0276205	+	0.999618i	$0.491207\pi$
$464$	7.98568e6	−	4.61053e6i	1.72193	−	0.994160i
$465$	388669.	+	920395.i	0.0833580	+	0.197398i
$466$	−1.38439e6	+	2.39784e6i	−0.295321	+	0.511511i
$467$	−2.49262e6	−	4.31735e6i	−0.528889	−	0.916063i	−0.999432	−	0.0336859i	$-0.989275\pi$
$467$	−2.49262e6	−	4.31735e6i	−0.528889	−	0.916063i	0.470543	−	0.882377i	$-0.344058\pi$
$468$	1.39266e6	−	393746.i	0.293921	−	0.0831002i
$469$	4.04304e6	−	4.01253e6i	0.848743	−	0.842338i
$470$		−	396480.i		−	0.0827897i
$471$	−1.05444e6	−	131458.i	−0.219014	−	0.0273045i
$472$	−816890.	−	471632.i	−0.168775	−	0.0974425i
$473$	500138.	+	288755.i	0.102787	+	0.0593439i
$474$	5.27409e6	+	657523.i	1.07821	+	0.134420i
$475$			7.69581e6i			1.56502i
$476$	98540.1	+	373408.i	0.0199340	+	0.0755381i
$477$	8.48750e6	−	2.39967e6i	1.70798	−	0.482897i
$478$	905377.	+	1.56816e6i	0.181242	+	0.313921i
$479$	3.85608e6	−	6.67893e6i	0.767904	−	1.33005i	−0.170793	−	0.985307i	$-0.554633\pi$
$479$	3.85608e6	−	6.67893e6i	0.767904	−	1.33005i	0.938697	−	0.344742i	$-0.112034\pi$
$480$	437044.	+	1.03495e6i	0.0865809	+	0.205030i
$481$	1.32814e6	−	766802.i	0.261747	−	0.151119i
$482$	2.64306e6			0.518191
$483$	−4.18706e6	+	3.23339e6i	−0.816659	+	0.630653i
$484$	−2.16913e6			−0.420894
$485$	325268.	−	187794.i	0.0627896	−	0.0362516i
$486$	−5.09635e6	−	3.63951e6i	−0.978744	−	0.698959i
$487$	4.06026e6	−	7.03257e6i	0.775767	−	1.34367i	−0.158596	−	0.987344i	$-0.550697\pi$
$487$	4.06026e6	−	7.03257e6i	0.775767	−	1.34367i	0.934363	−	0.356323i	$-0.115970\pi$
$488$	1.21674e6	+	2.10746e6i	0.231286	+	0.400599i
$489$	−5.26890e6	−	3.98576e6i	−0.996432	−	0.753771i
$490$	841474.	+	1.48331e6i	0.158325	+	0.279089i
$491$			7.72726e6i			1.44651i	0.690581	+	0.723255i	$0.257355\pi$
$491$			7.72726e6i			1.44651i	−0.690581	+	0.723255i	$0.742645\pi$
$492$	−425759.	+	3.41508e6i	−0.0792960	+	0.636045i
$493$	−1.30377e6	−	752732.i	−0.241593	−	0.139484i
$494$	−6.51205e6	−	3.75973e6i	−1.20061	−	0.693170i
$495$	−249562.	−	242797.i	−0.0457789	−	0.0445380i
$496$			5.48808e6i			1.00165i
$497$	−885675.	+	3.25600e6i	−0.160836	+	0.591281i
$498$	−6.89966e6	+	9.12086e6i	−1.24668	+	1.64802i
$499$	−1.16537e6	−	2.01848e6i	−0.209514	−	0.362889i	0.742048	−	0.670347i	$-0.233855\pi$
$499$	−1.16537e6	−	2.01848e6i	−0.209514	−	0.362889i	−0.951561	+	0.307459i	$0.900521\pi$
$500$	642191.	−	1.11231e6i	0.114879	−	0.198976i
$501$	443974.	−	187483.i	0.0790247	−	0.0333709i
$502$	−6.46194e6	+	3.73080e6i	−1.14447	+	0.660759i
$503$	−3.86914e6			−0.681859			−0.340930	−	0.940089i	$-0.610742\pi$
$503$	−3.86914e6			−0.681859			−0.340930	+	0.940089i	$0.610742\pi$
$504$	−1.93079e6	−	3.26867e6i	−0.338578	−	0.573185i
$505$	1.16424e6			0.203148
$506$	−1.48180e6	+	855520.i	−0.257285	+	0.148544i
$507$	2.83658e6	−	1.19784e6i	0.490089	−	0.206957i
$508$	−1.01141e6	+	1.75182e6i	−0.173888	+	0.301183i
$509$	−2.14951e6	−	3.72307e6i	−0.367744	−	0.636952i	0.621468	−	0.783439i	$-0.286536\pi$
$509$	−2.14951e6	−	3.72307e6i	−0.367744	−	0.636952i	−0.989213	+	0.146488i	$0.953203\pi$
$510$	198960.	−	263011.i	0.0338720	−	0.0447764i
$511$	−4.64936e6	−	4.68471e6i	−0.787663	−	0.793653i
$512$			1.24648e6i			0.210142i
$513$	1.51584e6	+	9.92836e6i	0.254307	+	1.66565i
$514$	591107.	+	341276.i	0.0986866	+	0.0569767i
$515$	−1.26566e6	−	730731.i	−0.210281	−	0.121406i
$516$	−165625.	+	1.32851e6i	−0.0273843	+	0.219654i
$517$			375402.i			0.0617689i
$518$	2.28581e6	+	2.30319e6i	0.374296	+	0.377142i
$519$	2.22807e6	+	1.68547e6i	0.363087	+	0.274664i
$520$	−374597.	−	648820.i	−0.0607513	−	0.105224i
$521$	−2.28516e6	+	3.95801e6i	−0.368827	+	0.638827i	−0.989382	−	0.145336i	$-0.953574\pi$
$521$	−2.28516e6	+	3.95801e6i	−0.368827	+	0.638827i	0.620556	+	0.784162i	$0.286907\pi$
$522$	−1.15719e7	−	2.93090e6i	−1.85878	−	0.470787i
$523$	−1.86520e6	+	1.07688e6i	−0.298176	+	0.172152i	−0.641623	−	0.767020i	$-0.721739\pi$
$523$	−1.86520e6	+	1.07688e6i	−0.298176	+	0.172152i	0.343447	+	0.939172i	$0.388405\pi$
$524$	−2.18879e6			−0.348238
$525$	−2.22805e6	+	5.42623e6i	−0.352799	+	0.859211i
$526$	8.87821e6			1.39914
$527$	775961.	−	448001.i	0.121706	−	0.0702672i
$528$	−744036.	−	1.76193e6i	−0.116147	−	0.275045i
$529$	208072.	−	360392.i	0.0323277	−	0.0559933i
$530$	1.84150e6	+	3.18957e6i	0.284762	+	0.493222i
$531$	517486.	+	1.83032e6i	0.0796457	+	0.281703i
$532$	1.28902e6	−	4.73883e6i	0.197461	−	0.725925i
$533$		−	6.44133e6i		−	0.982104i
$534$	1.43947e7	+	1.79460e6i	2.18449	+	0.272342i
$535$	1.74488e6	+	1.00741e6i	0.263561	+	0.152167i
$536$	−4.58546e6	−	2.64742e6i	−0.689400	−	0.398025i
$537$	−2.19932e6	−	274191.i	−0.329119	−	0.0410314i
$538$		−	8.57730e6i		−	1.27760i
$539$	−796739.	−	1.40446e6i	−0.118126	−	0.208227i
$540$	293456.	−	751928.i	0.0433070	−	0.110967i
$541$	2.73312e6	+	4.73390e6i	0.401481	+	0.695386i	0.993905	−	0.110240i	$-0.0351621\pi$
$541$	2.73312e6	+	4.73390e6i	0.401481	+	0.695386i	−0.592423	+	0.805627i	$0.701829\pi$
$542$	4.24328e6	−	7.34958e6i	0.620445	−	1.07464i
$543$	1.94927e6	+	4.61601e6i	0.283708	+	0.671841i
$544$	872541.	−	503762.i	0.126412	−	0.0729840i
$545$	−1.12053e6			−0.161596
$546$	−3.50307e6	−	4.53628e6i	−0.502884	−	0.651206i
$547$	7.32611e6			1.04690			0.523450	−	0.852056i	$-0.324645\pi$
$547$	7.32611e6			1.04690			0.523450	+	0.852056i	$0.324645\pi$
$548$	−1.11656e6	+	644648.i	−0.158830	+	0.0917004i
$549$	1.20481e6	−	4.75686e6i	0.170603	−	0.673581i
$550$	−948612.	+	1.64304e6i	−0.133716	+	0.231602i
$551$	9.57214e6	+	1.65794e7i	1.34317	+	2.32643i
$552$	3.92175e6	+	2.96669e6i	0.547813	+	0.414404i
$553$	−1.65774e6	−	6.28186e6i	−0.230518	−	0.873525i
$554$			4.48281e6i			0.620549i
$555$	105814.	−	848752.i	0.0145818	−	0.116963i
$556$	1.64831e6	+	951654.i	0.226127	+	0.130555i
$557$	−6.61232e6	−	3.81763e6i	−0.903059	−	0.521381i	−0.0248673	−	0.999691i	$-0.507916\pi$
$557$	−6.61232e6	−	3.81763e6i	−0.903059	−	0.521381i	−0.878191	+	0.478310i	$0.841250\pi$
$558$	4.95427e6	−	5.09231e6i	0.673588	−	0.692355i
$559$		−	2.50575e6i		−	0.339163i
$560$	1.75259e6	−	1.73936e6i	0.236162	−	0.234380i
$561$	−188383.	+	249029.i	−0.0252717	+	0.0334074i
$562$	−4.38471e6	−	7.59454e6i	−0.585599	−	1.01429i
$563$	1.08788e6	−	1.88427e6i	0.144648	−	0.250537i	−0.784594	−	0.620010i	$-0.787129\pi$
$563$	1.08788e6	−	1.88427e6i	0.144648	−	0.250537i	0.929241	+	0.369473i	$0.120462\pi$
$564$	−801710.	+	338550.i	−0.106125	+	0.0448151i
$565$	−1.13762e6	+	656807.i	−0.149926	+	0.0865599i
$566$	−6.86531e6			−0.900780
$567$	−1.80561e6	+	7.43923e6i	−0.235866	+	0.971786i
$568$	3.13656e6			0.407927
$569$	−7.26339e6	+	4.19352e6i	−0.940500	+	0.542998i	−0.890117	−	0.455732i	$-0.849378\pi$
$569$	−7.26339e6	+	4.19352e6i	−0.940500	+	0.542998i	−0.0503832	+	0.998730i	$0.516044\pi$
$570$	−3.86342e6	+	1.63146e6i	−0.498063	+	0.210324i
$571$	−1.27236e6	+	2.20380e6i	−0.163313	+	0.282867i	−0.936055	−	0.351854i	$-0.885551\pi$
$571$	−1.27236e6	+	2.20380e6i	−0.163313	+	0.282867i	0.772742	+	0.634720i	$0.218885\pi$
$572$	−286097.	−	495534.i	−0.0365614	−	0.0633262i
$573$	4.97326e6	−	6.57430e6i	0.632783	−	0.836494i
$574$	1.31780e7	−	3.47759e6i	1.66944	−	0.440554i
$575$		−	7.59813e6i		−	0.958379i
$576$	−1.35387e6	+	1.39159e6i	−0.170028	+	0.174765i
$577$	−8.83680e6	−	5.10193e6i	−1.10498	−	0.637962i	−0.167458	−	0.985879i	$-0.553556\pi$
$577$	−8.83680e6	−	5.10193e6i	−1.10498	−	0.637962i	−0.937525	+	0.347917i	$0.886889\pi$
$578$	8.10965e6	+	4.68211e6i	1.00968	+	0.582938i
$579$	183654.	−	1.47312e6i	0.0227669	−	0.182617i
$580$		−	1.53858e6i		−	0.189911i
$581$	1.34898e7	+	3.66941e6i	1.65793	+	0.450978i
$582$	−2.13004e6	−	1.61131e6i	−0.260664	−	0.197184i
$583$	−1.74360e6	−	3.02001e6i	−0.212459	−	0.367990i
$584$	−3.06759e6	+	5.31322e6i	−0.372190	+	0.644652i
$585$	−370922.	+	1.46449e6i	−0.0448118	+	0.176928i
$586$	−1.14723e7	+	6.62356e6i	−1.38009	+	0.796797i
$587$	1.90974e6			0.228760			0.114380	−	0.993437i	$-0.463512\pi$
$587$	1.90974e6			0.228760			0.114380	+	0.993437i	$0.463512\pi$
$588$	2.28084e6	−	2.96810e6i	0.272051	−	0.354027i
$589$	−1.13940e7			−1.35329
$590$	−687828.	+	397118.i	−0.0813486	+	0.0469666i
$591$	−4.27987e6	−	1.01350e7i	−0.504037	−	1.19359i
$592$	2.34916e6	−	4.06887e6i	0.275492	−	0.477166i
$593$	−4.84251e6	−	8.38747e6i	−0.565502	−	0.979477i	−0.997003	−	0.0773651i	$-0.975349\pi$
$593$	−4.84251e6	−	8.38747e6i	−0.565502	−	0.979477i	0.431501	−	0.902112i	$-0.357984\pi$
$594$	−900175.	+	2.30654e6i	−0.104679	+	0.268222i
$595$	−388996.	−	105812.i	−0.0450456	−	0.0122530i
$596$			402239.i			0.0463841i
$597$	−1.35053e6	−	168371.i	−0.155085	−	0.0193345i
$598$	6.42939e6	+	3.71201e6i	0.735220	+	0.424479i
$599$	3.49308e6	+	2.01673e6i	0.397779	+	0.229658i	0.685525	−	0.728049i	$-0.259573\pi$
$599$	3.49308e6	+	2.01673e6i	0.397779	+	0.229658i	−0.287746	+	0.957707i	$0.592906\pi$
$600$	5.41065e6	+	674548.i	0.613580	+	0.0764953i
$601$			1.16260e7i			1.31293i	0.754356	+	0.656466i	$0.227949\pi$
$601$			1.16260e7i			1.31293i	−0.754356	+	0.656466i	$0.772051\pi$
$602$	5.12640e6	−	1.35283e6i	0.576529	−	0.152143i
$603$	2.90481e6	+	1.02742e7i	0.325330	+	1.15068i
$604$	−46768.1	−	81004.7i	−0.00521624	−	0.00903479i
$605$	1.13214e6	−	1.96092e6i	0.125751	−	0.217807i
$606$	−3.22071e6	−	7.62687e6i	−0.356262	−	0.843654i
$607$	6.50750e6	−	3.75711e6i	0.716873	−	0.413887i	−0.0967276	−	0.995311i	$-0.530838\pi$
$607$	6.50750e6	−	3.75711e6i	0.716873	−	0.413887i	0.813601	+	0.581424i	$0.197504\pi$
$608$	−1.28122e7			−1.40561
$609$	1.94922e6	+	1.44613e7i	0.212969	+	1.58002i
$610$	2.04901e6			0.222956
$611$	1.41061e6	−	814415.i	0.152863	−	0.0882557i
$612$	−701718.	−	177729.i	−0.0757328	−	0.0191814i
$613$	−1.87051e6	+	3.23983e6i	−0.201053	+	0.348233i	−0.948868	−	0.315674i	$-0.897770\pi$
$613$	−1.87051e6	+	3.23983e6i	−0.201053	+	0.348233i	0.747815	+	0.663907i	$0.231103\pi$
$614$	6.72880e6	+	1.16546e7i	0.720305	+	1.24761i
$615$	−2.86505e6	−	2.16732e6i	−0.305453	−	0.231066i
$616$	−1.06533e6	+	1.05730e6i	−0.113119	+	0.112265i
$617$		−	1.48513e7i		−	1.57055i	−0.619146	−	0.785276i	$-0.712521\pi$
$617$		−	1.48513e7i		−	1.57055i	0.619146	−	0.785276i	$-0.287479\pi$
$618$	−1.28570e6	+	1.03128e7i	−0.135415	+	1.08619i
$619$	7.24514e6	+	4.18298e6i	0.760011	+	0.438793i	0.829300	−	0.558804i	$-0.188740\pi$
$619$	7.24514e6	+	4.18298e6i	0.760011	+	0.438793i	−0.0692886	+	0.997597i	$0.522073\pi$
$620$	793029.	+	457855.i	0.0828533	+	0.0478354i
$621$	−1.49660e6	−	9.80234e6i	−0.155731	−	1.02000i
$622$			7.28969e6i			0.755497i
$623$	−4.52453e6	−	1.71453e7i	−0.467040	−	1.76980i
$624$	−5.00647e6	+	6.61820e6i	−0.514719	+	0.680423i
$625$	−3.86491e6	−	6.69421e6i	−0.395766	−	0.685488i
$626$	−1.41607e6	+	2.45271e6i	−0.144428	+	0.250156i
$627$	3.65803e6	−	1.54473e6i	0.371602	−	0.156922i
$628$	−843441.	+	486961.i	−0.0853406	+	0.0492714i
$629$	−767065.			−0.0773047
$630$	−3.19638e6	+	31808.1i	−0.320854	+	0.00319290i
$631$	8.21939e6			0.821800			0.410900	−	0.911680i	$-0.365215\pi$
$631$	8.21939e6			0.821800			0.410900	+	0.911680i	$0.365215\pi$
$632$	−5.23004e6	+	3.01957e6i	−0.520850	+	0.300713i
$633$	−4.74841e6	+	2.00518e6i	−0.471019	+	0.198904i
$634$	−9.83832e6	+	1.70405e7i	−0.972071	+	1.68368i
$635$	−1.05577e6	−	1.82866e6i	−0.103905	−	0.179969i
$636$	4.87710e6	−	6.44718e6i	0.478100	−	0.632015i
$637$	−3.54889e6	+	6.04072e6i	−0.346533	+	0.589848i
$638$			4.71958e6i			0.459041i
$639$	−4.53332e6	−	4.41044e6i	−0.439202	−	0.427297i
$640$	−2.69933e6	−	1.55846e6i	−0.260499	−	0.150399i
$641$	−4.27272e6	−	2.46686e6i	−0.410733	−	0.237137i	0.280372	−	0.959891i	$-0.409542\pi$
$641$	−4.27272e6	−	2.46686e6i	−0.410733	−	0.237137i	−0.691104	+	0.722755i	$0.742876\pi$
$642$	1.77250e6	−	1.42175e7i	0.169727	−	1.36140i
$643$			1.06965e7i			1.02027i	0.860094	+	0.510135i	$0.170405\pi$
$643$			1.06965e7i			1.02027i	−0.860094	+	0.510135i	$0.829595\pi$
$644$	−1.27266e6	+	4.67868e6i	−0.120920	+	0.444538i
$645$	−1.11454e6	−	843115.i	−0.105486	−	0.0797971i
$646$	1.88051e6	+	3.25714e6i	0.177294	+	0.307083i
$647$	−4.35883e6	+	7.54972e6i	−0.409364	+	0.709039i	−0.994819	−	0.101666i	$-0.967583\pi$
$647$	−4.35883e6	+	7.54972e6i	−0.409364	+	0.709039i	0.585455	+	0.810705i	$0.300916\pi$
$648$	7.11314e6	−	195497.i	0.665463	−	0.0182895i
$649$	651262.	−	376006.i	0.0606937	−	0.0350415i
$650$	8.23186e6			0.764213
$651$	−8.03382e6	−	3.29875e6i	−0.742967	−	0.305068i
$652$	−6.05524e6			−0.557844
$653$	8.54082e6	−	4.93104e6i	0.783820	−	0.452539i	−0.0539621	−	0.998543i	$-0.517185\pi$
$653$	8.54082e6	−	4.93104e6i	0.783820	−	0.452539i	0.837783	+	0.546004i	$0.183852\pi$
$654$	3.09979e6	+	7.34053e6i	0.283392	+	0.671093i
$655$	1.14240e6	−	1.97869e6i	0.104043	−	0.180208i
$656$	−9.86678e6	−	1.70898e7i	−0.895192	−	1.55052i
$657$	1.19048e7	−	3.36583e6i	1.07599	−	0.304214i
$658$	2.42774e6	+	2.44620e6i	0.218594	+	0.220256i
$659$			7.63431e6i			0.684788i	0.939556	+	0.342394i	$0.111238\pi$
$659$			7.63431e6i			0.684788i	−0.939556	+	0.342394i	$0.888762\pi$
$660$	−316673.	−	39479.7i	−0.0282977	−	0.00352788i
$661$	1.21457e7	+	7.01235e6i	1.08124	+	0.624252i	0.931229	−	0.364434i	$-0.118737\pi$
$661$	1.21457e7	+	7.01235e6i	1.08124	+	0.624252i	0.150006	+	0.988685i	$0.452071\pi$
$662$	2.04897e7	+	1.18297e7i	1.81715	+	1.04913i
$663$	1.34444e6	+	167612.i	0.118784	+	0.0148088i
$664$		−	1.29949e7i		−	1.14381i
$665$	3.61117e6	+	3.63863e6i	0.316661	+	0.319068i
$666$	−5.85286e6	+	1.65478e6i	−0.511308	+	0.144562i
$667$	−9.45065e6	−	1.63690e7i	−0.822521	−	1.42465i
$668$	220857.	−	382535.i	0.0191500	−	0.0331688i
$669$	−1.41013e6	−	3.33929e6i	−0.121813	−	0.288462i
$670$	−3.86100e6	+	2.22915e6i	−0.332286	+	0.191846i
$671$	−1.94008e6			−0.166347
$672$	−9.03374e6	−	3.70932e6i	−0.771693	−	0.316863i
$673$	−1.03156e7			−0.877920			−0.438960	−	0.898507i	$-0.644653\pi$
$673$	−1.03156e7			−0.877920			−0.438960	+	0.898507i	$0.644653\pi$
$674$	5.40229e6	−	3.11902e6i	0.458067	−	0.264465i
$675$	−6.87161e6	−	8.58308e6i	−0.580495	−	0.725076i
$676$	1.41107e6	−	2.44405e6i	0.118763	−	0.205704i
$677$	2.26863e6	+	3.92938e6i	0.190236	+	0.329498i	0.945328	−	0.326120i	$-0.105741\pi$
$677$	2.26863e6	+	3.92938e6i	0.190236	+	0.329498i	−0.755093	+	0.655618i	$0.772408\pi$
$678$	7.44981e6	+	5.63556e6i	0.622402	+	0.470828i
$679$	−856935.	+	3.15035e6i	−0.0713302	+	0.262231i
$680$			374725.i			0.0310771i
$681$	864450.	−	6.93388e6i	0.0714286	−	0.572939i
$682$	−2.43261e6	−	1.40447e6i	−0.200268	−	0.115625i
$683$	780773.	+	450779.i	0.0640432	+	0.0369754i	0.531680	−	0.846946i	$-0.321561\pi$
$683$	780773.	+	450779.i	0.0640432	+	0.0369754i	−0.467636	+	0.883921i	$0.654894\pi$
$684$	6.59786e6	+	6.41901e6i	0.539216	+	0.524600i
$685$		−	1.34585e6i		−	0.109590i
$686$	−1.42744e7	−	3.99920e6i	−1.15811	−	0.324461i
$687$	5.41844e6	−	7.16280e6i	0.438009	−	0.579016i
$688$	−3.83830e6	−	6.64812e6i	−0.309149	−	0.535461i
$689$	−7.56530e6	+	1.31035e7i	−0.607125	+	1.05157i
$690$	3.81438e6	−	1.61075e6i	0.305001	−	0.128797i
$691$	1.48175e7	−	8.55486e6i	1.18053	−	0.681582i	0.224396	−	0.974498i	$-0.427959\pi$
$691$	1.48175e7	−	8.55486e6i	1.18053	−	0.681582i	0.956138	+	0.292916i	$0.0946257\pi$
$692$	2.56059e6			0.203271
$693$	3.02646e6	−	30117.1i	0.239387	−	0.00238221i
$694$	−8.42220e6			−0.663784
$695$	−1.72061e6	+	993395.i	−0.135120	+	0.0780117i
$696$	1.24954e7	−	5.27662e6i	0.977750	−	0.412889i
$697$	−1.61089e6	+	2.79014e6i	−0.125598	+	0.217542i
$698$	−7.48050e6	−	1.29566e7i	−0.581155	−	1.00659i
$699$	−3.82730e6	+	5.05942e6i	−0.296278	+	0.391658i
$700$	1.37181e6	+	5.19832e6i	0.105815	+	0.400976i
$701$			2.02857e6i			0.155917i	0.996957	+	0.0779587i	$0.0248402\pi$
$701$			2.02857e6i			0.155917i	−0.996957	+	0.0779587i	$0.975160\pi$
$702$	1.06199e7	−	1.62142e6i	0.813351	−	0.124180i
$703$	8.44757e6	+	4.87721e6i	0.644679	+	0.372206i
$704$	664768.	+	383804.i	0.0505520	+	0.0291862i
$705$	112385.	−	901454.i	0.00851597	−	0.0683079i
$706$		−	1.81592e7i		−	1.37115i
$707$	−7.18311e6	+	7.12890e6i	−0.540461	+	0.536382i
$708$	1.39033e6	+	1.05174e6i	0.104240	+	0.0788545i
$709$	8.39469e6	+	1.45400e7i	0.627176	+	1.08630i	0.988116	+	0.153711i	$0.0491225\pi$
$709$	8.39469e6	+	1.45400e7i	0.627176	+	1.08630i	−0.360940	+	0.932589i	$0.617544\pi$
$710$	1.32050e6	−	2.28718e6i	0.0983090	−	0.170276i
$711$	1.18050e7	+	2.98995e6i	0.875775	+	0.221814i
$712$	−1.42745e7	+	8.24140e6i	−1.05527	+	0.609258i
$713$	1.12494e7			0.828718
$714$	382937.	+	2.84101e6i	0.0281113	+	0.208558i
$715$	597290.			0.0436939
$716$	−1.75922e6	+	1.01569e6i	−0.128244	+	0.0740418i
$717$	1.61400e6	+	3.82207e6i	0.117248	+	0.277652i
$718$	1.54709e7	−	2.67964e7i	1.11996	−	1.93983i
$719$	1.31852e7	+	2.28374e7i	0.951183	+	1.64750i	0.742871	+	0.669435i	$0.233464\pi$
$719$	1.31852e7	+	2.28374e7i	0.951183	+	1.64750i	0.208312	+	0.978062i	$0.433203\pi$
$720$	1.25918e6	+	4.45367e6i	0.0905228	+	0.320175i
$721$	1.22833e7	−	3.24150e6i	0.879991	−	0.232224i
$722$		−	3.09811e7i		−	2.21184i
$723$	6.00938e6	+	749192.i	0.427547	+	0.0533024i
$724$	3.97723e6	+	2.29625e6i	0.281990	+	0.162807i
$725$	−1.81502e7	−	1.04790e7i	−1.28244	−	0.740415i
$726$	−1.59778e7	−	1.99196e6i	−1.12506	−	0.140262i
$727$			1.63660e7i			1.14844i	0.818702	+	0.574218i	$0.194694\pi$
$727$			1.63660e7i			1.14844i	−0.818702	+	0.574218i	$0.805306\pi$
$728$	6.28407e6	+	1.70935e6i	0.439453	+	0.119537i
$729$	−1.05557e7	−	9.71953e6i	−0.735642	−	0.677371i
$730$	2.58293e6	+	4.47377e6i	0.179393	+	0.310718i
$731$	−626654.	+	1.08540e6i	−0.0433745	+	0.0751268i
$732$	−1.74963e6	−	4.14325e6i	−0.120689	−	0.285801i
$733$	−2.29516e7	+	1.32511e7i	−1.57781	+	0.910946i	−0.582640	+	0.812730i	$0.697980\pi$
$733$	−2.29516e7	+	1.32511e7i	−1.57781	+	0.910946i	−0.995165	+	0.0982164i	$0.968686\pi$
$734$	−1.45261e7			−0.995196
$735$	1.49276e6	+	3.61104e6i	0.101923	+	0.246555i
$736$	1.26496e7			0.860759
$737$	3.65574e6	−	2.11064e6i	0.247917	−	0.143135i
$738$	−6.27227e6	+	2.47644e7i	−0.423920	+	1.67374i
$739$	6.83956e6	−	1.18465e7i	0.460698	−	0.797953i	−0.538297	−	0.842755i	$-0.680932\pi$
$739$	6.83956e6	−	1.18465e7i	0.460698	−	0.797953i	0.998996	+	0.0448018i	$0.0142656\pi$
$740$	−391969.	−	678910.i	−0.0263131	−	0.0455756i
$741$	−1.37404e7	−	1.03942e7i	−0.919290	−	0.695416i
$742$	−3.08922e7	−	8.40308e6i	−2.05987	−	0.560310i
$743$			9.39766e6i			0.624522i	0.949996	+	0.312261i	$0.101086\pi$
$743$			9.39766e6i			0.624522i	−0.949996	+	0.312261i	$0.898914\pi$
$744$	−998704.	+	8.01075e6i	−0.0661461	+	0.530568i
$745$	−363629.	−	209941.i	−0.0240031	−	0.0138582i
$746$	1.91993e7	+	1.10847e7i	1.26310	+	0.729251i
$747$	−1.82727e7	+	1.87818e7i	−1.19813	+	1.23151i
$748$			286195.i			0.0187029i
$749$	−1.69342e7	+	4.46883e6i	−1.10296	+	0.291065i
$750$	5.75183e6	−	7.60351e6i	0.373381	−	0.493584i
$751$	6.75217e6	+	1.16951e7i	0.436862	+	0.756666i	0.997446	−	0.0714312i	$-0.0227566\pi$
$751$	6.75217e6	+	1.16951e7i	0.436862	+	0.756666i	−0.560584	+	0.828098i	$0.689423\pi$
$752$	2.49503e6	−	4.32152e6i	0.160891	−	0.278671i
$753$	−1.57497e7	+	6.65084e6i	−1.01224	+	0.427454i
$754$	1.77343e7	−	1.02389e7i	1.13602	−	0.655880i
$755$	97638.9			0.00623383
$756$	2.79367e6	+	6.43615e6i	0.177775	+	0.409564i
$757$	−7.36283e6			−0.466987			−0.233494	−	0.972358i	$-0.575016\pi$
$757$	−7.36283e6			−0.466987			−0.233494	+	0.972358i	$0.575016\pi$
$758$	−1.95624e7	+	1.12944e7i	−1.23666	+	0.713984i
$759$	−3.61160e6	+	1.52512e6i	−0.227559	+	0.0960948i
$760$	2.38260e6	−	4.12679e6i	0.149630	−	0.259166i
$761$	1.24156e6	+	2.15044e6i	0.0777150	+	0.134606i	0.902264	−	0.431185i	$-0.141904\pi$
$761$	1.24156e6	+	2.15044e6i	0.0777150	+	0.134606i	−0.824549	+	0.565791i	$0.808571\pi$
$762$	−9.05879e6	+	1.19751e7i	−0.565175	+	0.747121i
$763$	6.91343e6	−	6.86126e6i	0.429915	−	0.426671i
$764$		−	7.55547e6i		−	0.468304i
$765$	526917.	−	541598.i	0.0325528	−	0.0334598i
$766$	−2.03981e7	−	1.17769e7i	−1.25608	−	0.725201i
$767$	−2.82576e6	−	1.63145e6i	−0.173439	−	0.100135i
$768$	−2.24900e6	+	1.80396e7i	−0.137590	+	1.10363i
$769$		−	2.15050e7i		−	1.31136i	−0.755038	−	0.655681i	$-0.772382\pi$
$769$		−	2.15050e7i		−	1.31136i	0.755038	−	0.655681i	$-0.227618\pi$
$770$	322470.	+	1.22197e6i	0.0196003	+	0.0742733i
$771$	1.24723e6	+	943492.i	0.0755632	+	0.0571614i
$772$	−680311.	−	1.17833e6i	−0.0410832	−	0.0711582i
$773$	−4.96275e6	+	8.59573e6i	−0.298726	+	0.517409i	−0.975845	−	0.218465i	$-0.929895\pi$
$773$	−4.96275e6	+	8.59573e6i	−0.298726	+	0.517409i	0.677119	+	0.735874i	$0.263228\pi$
$774$	−2.43999e6	+	9.63366e6i	−0.146398	+	0.578015i
$775$	1.08024e7	−	6.23676e6i	0.646049	−	0.372996i
$776$	3.03478e6			0.180914
$777$	4.54426e6	+	5.88456e6i	0.270029	+	0.349673i
$778$	1.69551e7			1.00427
$779$	3.54809e7	−	2.04849e7i	2.09484	−	1.20946i
$780$	538656.	+	1.27558e6i	0.0317011	+	0.0750706i
$781$	−1.25030e6	+	2.16558e6i	−0.0733478	+	0.127042i
$782$	−1.85664e6	−	3.21580e6i	−0.108570	−	0.188050i
$783$	−2.54796e7	−	9.94393e6i	−1.48521	−	0.579634i
$784$	−162587.	+	2.14631e7i	−0.00944703	+	1.24710i
$785$		−	1.01664e6i		−	0.0588834i
$786$	−1.61226e7	−	2.01001e6i	−0.930849	−	0.116049i
$787$	−897903.	−	518404.i	−0.0516764	−	0.0298354i	0.473939	−	0.880558i	$-0.342832\pi$
$787$	−897903.	−	518404.i	−0.0516764	−	0.0298354i	−0.525616	+	0.850722i	$0.676165\pi$
$788$	−8.73253e6	−	5.04173e6i	−0.500985	−	0.289244i
$789$	2.01859e7	+	2.51658e6i	1.15440	+	0.143919i
$790$			5.08500e6i			0.289883i
$791$	2.99712e6	−	1.10183e7i	0.170319	−	0.626144i
$792$	−765412.	−	2.70723e6i	−0.0433593	−	0.153360i
$793$	4.20891e6	+	7.29004e6i	0.237677	+	0.411668i
$794$	1.03699e7	−	1.79611e7i	0.583743	−	1.01107i
$795$	3.28281e6	+	7.77393e6i	0.184216	+	0.436237i
$796$	−1.08028e6	+	623699.i	−0.0604301	+	0.0348893i
$797$	1.52399e7			0.849838			0.424919	−	0.905231i	$-0.360303\pi$
$797$	1.52399e7			0.849838			0.424919	+	0.905231i	$0.360303\pi$
$798$	1.38467e7	−	3.37224e7i	0.769731	−	1.87461i
$799$	−814695.			−0.0451469
$800$	1.21469e7	−	7.01302e6i	0.671028	−	0.387418i
$801$	3.22198e7	+	8.16056e6i	1.77436	+	0.449406i
$802$	−175438.	+	303867.i	−0.00963135	+	0.0166820i
$803$	−2.44562e6	−	4.23593e6i	−0.133844	−	0.231825i
$804$	7.80435e6	+	5.90376e6i	0.425791	+	0.322099i
$805$	−3.56534e6	−	3.59245e6i	−0.193915	−	0.195389i
$806$			1.21877e7i			0.660821i
$807$	2.43129e6	−	1.95017e7i	0.131417	−	1.05412i
$808$	8.14680e6	+	4.70356e6i	0.438994	+	0.253453i
$809$	−4.72275e6	−	2.72668e6i	−0.253702	−	0.146475i	0.367756	−	0.929922i	$-0.380126\pi$
$809$	−4.72275e6	−	2.72668e6i	−0.253702	−	0.146475i	−0.621458	+	0.783447i	$0.713459\pi$
$810$	2.85210e6	−	5.26921e6i	0.152740	−	0.282184i
$811$		−	9.69507e6i		−	0.517605i	−0.965930	−	0.258803i	$-0.916672\pi$
$811$		−	9.69507e6i		−	0.517605i	0.965930	−	0.258803i	$-0.0833279\pi$
$812$	9.42108e6	+	9.49272e6i	0.501430	+	0.505243i
$813$	1.17310e7	−	1.55075e7i	0.622456	−	0.822842i
$814$	1.20236e6	+	2.08255e6i	0.0636025	+	0.110163i
$815$	3.16042e6	−	5.47400e6i	0.166667	−	0.288676i
$816$	3.82373e6	−	1.61470e6i	0.201030	−	0.0848921i
$817$	1.38025e7	−	7.96886e6i	0.723439	−	0.417678i
$818$	3.08824e7			1.61372
$819$	−6.67891e6	−	1.13069e7i	−0.347933	−	0.589023i
$820$	−3.29264e6			−0.171005
$821$	−1.41785e7	+	8.18596e6i	−0.734129	+	0.423849i	−0.819931	−	0.572463i	$-0.805988\pi$
$821$	−1.41785e7	+	8.18596e6i	−0.734129	+	0.423849i	0.0858020	+	0.996312i	$0.472655\pi$
$822$	−8.81659e6	+	3.72311e6i	−0.455115	+	0.192188i
$823$	−1.18770e7	+	2.05715e7i	−0.611233	+	1.05869i	0.379800	+	0.925069i	$0.375993\pi$
$823$	−1.18770e7	+	2.05715e7i	−0.611233	+	1.05869i	−0.991033	+	0.133618i	$0.957341\pi$
$824$	−5.90436e6	−	1.02267e7i	−0.302939	−	0.524706i
$825$	−2.62254e6	+	3.46681e6i	−0.134149	+	0.177335i
$826$	1.81212e6	−	6.66188e6i	0.0924136	−	0.339740i
$827$			2.87632e7i			1.46242i	0.682151	+	0.731211i	$0.261045\pi$
$827$			2.87632e7i			1.46242i	−0.682151	+	0.731211i	$0.738955\pi$
$828$	−6.51411e6	−	6.33754e6i	−0.330202	−	0.321251i
$829$	−3.19576e7	−	1.84508e7i	−1.61506	−	0.932455i	−0.988173	−	0.153344i	$-0.950996\pi$
$829$	−3.19576e7	−	1.84508e7i	−1.61506	−	0.932455i	−0.626886	−	0.779111i	$-0.715671\pi$
$830$	−9.47592e6	−	5.47092e6i	−0.477448	−	0.275655i
$831$	−1.27068e6	+	1.01923e7i	−0.0638313	+	0.512000i
$832$		−	3.33057e6i		−	0.166805i
$833$	3.04794e6	−	1.72908e6i	0.152193	−	0.0863380i
$834$	1.12675e7	+	8.52356e6i	0.560937	+	0.424332i
$835$	230544.	+	399314.i	0.0114429	+	0.0198197i
$836$	1.81970e6	−	3.15182e6i	0.0900503	−	0.155972i
$837$	1.27077e7	−	1.01738e7i	0.626979	−	0.501959i
$838$	−1.11404e7	+	6.43194e6i	−0.548015	+	0.316397i
$839$	−2.41096e7			−1.18246			−0.591229	−	0.806504i	$-0.701357\pi$
$839$	−2.41096e7			−1.18246			−0.591229	+	0.806504i	$0.701357\pi$
$840$	2.87472e6	−	2.21996e6i	0.140571	−	0.108554i
$841$	−3.16245e7			−1.54182
$842$	−2.97487e7	+	1.71754e7i	−1.44607	+	0.834887i
$843$	−7.81655e6	−	1.85102e7i	−0.378832	−	0.897101i
$844$	−2.36212e6	+	4.09131e6i	−0.114142	+	0.197700i
$845$	1.47296e6	+	2.55124e6i	0.0709659	+	0.122917i
$846$	−6.21629e6	+	1.75753e6i	−0.298611	+	0.0844260i
$847$	5.02212e6	+	1.90308e7i	0.240535	+	0.911484i
$848$			4.63539e7i			2.21359i
$849$	−1.56093e7	−	1.94601e6i	−0.743213	−	0.0926566i
$850$	−3.56572e6	−	2.05867e6i	−0.169278	−	0.0977327i
$851$	−8.34035e6	−	4.81530e6i	−0.394785	−	0.227929i
$852$	−5.75239e6	−	717153.i	−0.271487	−	0.0338464i
$853$			1.08498e7i			0.510561i	0.966867	+	0.255281i	$0.0821678\pi$
$853$			1.08498e7i			0.510561i	−0.966867	+	0.255281i	$0.917832\pi$
$854$	−1.26420e7	+	1.25466e7i	−0.593159	+	0.588683i
$855$	−9.24648e6	+	2.61425e6i	−0.432575	+	0.122302i
$856$	8.13994e6	+	1.40988e7i	0.379697	+	0.657654i
$857$	1.45403e7	−	2.51845e7i	0.676270	−	1.17133i	−0.299825	−	0.953994i	$-0.596928\pi$
$857$	1.45403e7	−	2.51845e7i	0.676270	−	1.17133i	0.976096	−	0.217341i	$-0.0697382\pi$
$858$	−1.65233e6	−	3.91283e6i	−0.0766262	−	0.181456i
$859$	3.18658e7	−	1.83977e7i	1.47347	−	0.850709i	0.473918	−	0.880569i	$-0.342839\pi$
$859$	3.18658e7	−	1.83977e7i	1.47347	−	0.850709i	0.999554	+	0.0298598i	$0.00950607\pi$
$860$	−1.28087e6			−0.0590555
$861$	3.09478e7	−	4.17143e6i	1.42273	−	0.191768i
$862$	2.22372e7			1.01932
$863$	−2.47342e6	+	1.42803e6i	−0.113050	+	0.0652695i	−0.555459	−	0.831544i	$-0.687457\pi$
$863$	−2.47342e6	+	1.42803e6i	−0.113050	+	0.0652695i	0.442409	+	0.896814i	$0.354124\pi$
$864$	1.42894e7	−	1.14400e7i	0.651221	−	0.521367i
$865$	−1.33645e6	+	2.31480e6i	−0.0607314	+	0.105190i
$866$	−5.77575e6	−	1.00039e7i	−0.261706	−	0.453288i
$867$	1.71113e7	+	1.29442e7i	0.773099	+	0.584826i
$868$	−7.69639e6	+	2.03103e6i	−0.346727	+	0.0914992i
$869$		−	4.81467e6i		−	0.216280i
$870$	1.41291e6	−	1.13331e7i	0.0632872	−	0.507636i
$871$	−1.58619e7	−	9.15785e6i	−0.708449	−	0.409023i
$872$	−7.84095e6	−	4.52697e6i	−0.349202	−	0.201612i
$873$	−4.38622e6	−	4.26733e6i	−0.194785	−	0.189505i
$874$			4.72202e7i			2.09098i
$875$	−1.12456e7	−	3.05896e6i	−0.496551	−	0.135068i
$876$	6.84074e6	−	9.04297e6i	0.301192	−	0.398154i
$877$	2.67593e6	+	4.63485e6i	0.117483	+	0.203487i	0.918770	−	0.394794i	$-0.129184\pi$
$877$	2.67593e6	+	4.63485e6i	0.117483	+	0.203487i	−0.801286	+	0.598281i	$0.795851\pi$
$878$	−1.50466e7	+	2.60615e7i	−0.658722	+	1.14094i
$879$	−2.79615e7	+	1.18077e7i	−1.22064	+	0.515458i
$880$	1.58470e6	−	914925.i	0.0689826	−	0.0398271i
$881$	2.78347e6			0.120822			0.0604111	−	0.998174i	$-0.480759\pi$
$881$	2.78347e6			0.120822			0.0604111	+	0.998174i	$0.480759\pi$
$882$	1.95263e7	−	1.97685e7i	0.845178	−	0.855661i
$883$	−626626.			−0.0270462			−0.0135231	−	0.999909i	$-0.504305\pi$
$883$	−626626.			−0.0270462			−0.0135231	+	0.999909i	$0.504305\pi$
$884$	1.07540e6	−	620885.i	0.0462851	−	0.0267227i
$885$	−1.67644e6	+	707935.i	−0.0719499	+	0.0303833i
$886$	−1.77577e7	+	3.07572e7i	−0.759979	+	1.31632i
$887$	−2.13727e7	−	3.70186e7i	−0.912117	−	1.57983i	−0.811068	−	0.584951i	$-0.801114\pi$
$887$	−2.13727e7	−	3.70186e7i	−0.912117	−	1.57983i	−0.101049	−	0.994881i	$-0.532220\pi$
$888$	4.16943e6	−	5.51169e6i	0.177437	−	0.234559i
$889$	1.77112e7	+	4.81768e6i	0.751613	+	0.204448i
$890$			1.38786e7i			0.587316i
$891$	−2.70048e6	+	4.98908e6i	−0.113958	+	0.210536i
$892$	−2.87719e6	−	1.66115e6i	−0.121076	−	0.0699030i
$893$	8.97211e6	+	5.18005e6i	0.376501	+	0.217373i
$894$	−369385.	+	2.96289e6i	−0.0154574	+	0.123986i
$895$		−	2.12047e6i		−	0.0884861i
$896$	2.61972e7	−	6.91328e6i	1.09015	−	0.287683i
$897$	1.35660e7	+	1.02622e7i	0.562950	+	0.425855i
$898$	1.29359e7	+	2.24057e7i	0.535312	+	0.927188i
$899$	1.55147e7	−	2.68723e7i	0.640242	−	1.10893i
$900$	−9.76882e6	−	2.47422e6i	−0.402009	−	0.101820i
$901$	6.55400e6	−	3.78395e6i	0.268964	−	0.155286i
$902$	1.01002e7			0.413344
$903$	1.20391e7	−	1.62273e6i	0.491331	−	0.0662259i
$904$	−1.06141e7			−0.431979
$905$	−4.15168e6	+	2.39697e6i	−0.168501	+	0.0972840i
$906$	−270105.	−	639628.i	−0.0109323	−	0.0258885i
$907$	−3.52054e6	+	6.09776e6i	−0.142099	+	0.246123i	−0.928287	−	0.371865i	$-0.878719\pi$
$907$	−3.52054e6	+	6.09776e6i	−0.142099	+	0.246123i	0.786188	+	0.617988i	$0.212052\pi$
$908$	−3.20219e6	−	5.54635e6i	−0.128894	−	0.223251i
$909$	−5.16086e6	−	1.82537e7i	−0.207163	−	0.732726i
$910$	3.89208e6	−	3.86271e6i	0.155804	−	0.154628i
$911$		−	1.05335e6i		−	0.0420509i	−0.999779	−	0.0210255i	$-0.993307\pi$
$911$		−	1.05335e6i		−	0.0420509i	0.999779	−	0.0210255i	$-0.00669310\pi$
$912$	−5.23769e7	−	6.52985e6i	−2.08522	−	0.259966i
$913$	8.97215e6	+	5.18008e6i	0.356221	+	0.205664i
$914$	−1.08265e7	−	6.25067e6i	−0.428669	−	0.247492i
$915$	4.65873e6	+	580805.i	0.183956	+	0.0229339i
$916$		−	8.23180e6i		−	0.324157i
$917$	5.06764e6	+	1.92033e7i	0.199013	+	0.754141i
$918$	−5.00563e6	−	1.95355e6i	−0.196043	−	0.0765101i
$919$	−9.09983e6	−	1.57614e7i	−0.355422	−	0.615609i	0.631768	−	0.775158i	$-0.282330\pi$
$919$	−9.09983e6	−	1.57614e7i	−0.355422	−	0.615609i	−0.987190	+	0.159548i	$0.948996\pi$
$920$	−2.35236e6	+	4.07441e6i	−0.0916294	+	0.158707i
$921$	1.19953e7	+	2.84058e7i	0.465975	+	1.10346i
$922$	4.59443e7	−	2.65259e7i	1.77993	−	1.02765i
$923$	1.08499e7			0.419198
$924$	2.19555e6	−	1.69548e6i	0.0845987	−	0.0653301i
$925$	−1.06785e7			−0.410353
$926$	1.50133e6	−	866794.i	0.0575372	−	0.0332191i
$927$	−5.84644e6	+	2.30832e7i	−0.223456	+	0.882259i
$928$	1.74457e7	−	3.02169e7i	0.664997	−	1.15181i
$929$	1.68357e7	+	2.91603e7i	0.640018	+	1.10854i	0.985428	+	0.170091i	$0.0544063\pi$
$929$	1.68357e7	+	2.91603e7i	0.640018	+	1.10854i	−0.345411	+	0.938452i	$0.612260\pi$
$930$	5.42098e6	+	4.10081e6i	0.205528	+	0.155476i
$931$	−4.45604e7	−	337554.i	−1.68490	−	0.0127635i
$932$			5.81450e6i			0.219267i
$933$	−2.06631e6	+	1.65742e7i	−0.0777124	+	0.623343i
$934$	−2.93730e7	−	1.69585e7i	−1.10175	−	0.636094i
$935$	−258723.	−	149374.i	−0.00967846	−	0.00558786i
$936$	−8.51214e6	+	8.74930e6i	−0.317577	+	0.326425i
$937$		−	3.25239e7i		−	1.21019i	−0.796153	−	0.605095i	$-0.793135\pi$
$937$		−	3.25239e7i		−	1.21019i	0.796153	−	0.605095i	$-0.206865\pi$
$938$	1.01720e7	−	3.73952e7i	0.377484	−	1.38774i
$939$	−3.91489e6	+	5.17520e6i	−0.144896	+	0.191542i
$940$	−416307.	−	721065.i	−0.0153672	−	0.0266167i
$941$	8.14740e6	−	1.41117e7i	0.299947	−	0.519524i	−0.676176	−	0.736740i	$-0.736364\pi$
$941$	8.14740e6	−	1.41117e7i	0.299947	−	0.519524i	0.976124	+	0.217216i	$0.0696976\pi$
$942$	−6.65996e6	+	2.81240e6i	−0.244537	+	0.103264i
$943$	−3.50305e7	+	2.02249e7i	−1.28282	+	0.740639i
$944$	−9.99618e6			−0.365093
$945$	−7.27645e6	−	833714.i	−0.265058	−	0.0303695i
$946$	3.92908e6			0.142746
$947$	1.05238e7	−	6.07589e6i	0.381325	−	0.220158i	−0.297069	−	0.954856i	$-0.596009\pi$
$947$	1.05238e7	−	6.07589e6i	0.381325	−	0.220158i	0.678395	+	0.734698i	$0.262676\pi$
$948$	1.02822e7	−	4.34202e6i	0.371592	−	0.156917i
$949$	−1.06113e7	+	1.83793e7i	−0.382474	+	0.662465i
$950$	2.61792e7	+	4.53437e7i	0.941124	+	1.63007i
$951$	−2.71991e7	+	3.59552e7i	−0.975220	+	1.28917i
$952$	−2.29453e6	−	2.31198e6i	−0.0820545	−	0.0826784i
$953$		−	2.91378e7i		−	1.03926i	−0.854391	−	0.519630i	$-0.826070\pi$
$953$		−	2.91378e7i		−	1.03926i	0.854391	−	0.519630i	$-0.173930\pi$
$954$	4.18453e7	−	4.30111e7i	1.48859	−	1.53007i
$955$	6.83022e6	+	3.94343e6i	0.242341	+	0.139915i
$956$	3.29316e6	+	1.90131e6i	0.116538	+	0.0672833i
$957$	−1.33779e6	+	1.07306e7i	−0.0472182	+	0.378744i
$958$		−	5.24696e7i		−	1.84711i
$959$	8.24095e6	+	8.30361e6i	0.289355	+	0.291555i
$960$	−1.48141e6	−	1.12064e6i	−0.0518796	−	0.0392454i
$961$	−5.08073e6	−	8.80008e6i	−0.177467	−	0.307382i
$962$	5.21693e6	−	9.03598e6i	0.181751	−	0.314802i
$963$	8.06009e6	−	3.18232e7i	0.280075	−	1.10580i
$964$	4.80685e6	−	2.77524e6i	0.166597	−	0.0961850i
$965$	1.42030e6			0.0490978
$966$	−1.36709e7	+	3.32944e7i	−0.471363	+	1.14796i
$967$	4.05970e7			1.39614			0.698068	−	0.716032i	$-0.254043\pi$
$967$	4.05970e7			1.39614			0.698068	+	0.716032i	$0.254043\pi$
$968$	1.58444e7	−	9.14775e6i	0.543484	−	0.313780i
$969$	3.35236e6	+	7.93863e6i	0.114694	+	0.271604i
$970$	1.27765e6	−	2.21296e6i	0.0435997	−	0.0755169i
$971$	−5.60678e6	−	9.71123e6i	−0.190838	−	0.330542i	0.754690	−	0.656082i	$-0.227787\pi$
$971$	−5.60678e6	−	9.71123e6i	−0.190838	−	0.330542i	−0.945528	+	0.325540i	$0.894454\pi$
$972$	−1.30901e7	−	1.26784e6i	−0.444403	−	0.0430425i
$973$	4.53303e6	−	1.66648e7i	0.153499	−	0.564309i
$974$		−	5.52478e7i		−	1.86603i
$975$	1.87163e7	+	2.33337e6i	0.630534	+	0.0786090i
$976$	2.23337e7	+	1.28943e7i	0.750474	+	0.433286i
$977$	2.45020e7	+	1.41462e7i	0.821231	+	0.474138i	0.850841	−	0.525424i	$-0.176093\pi$
$977$	2.45020e7	+	1.41462e7i	0.821231	+	0.474138i	−0.0296098	+	0.999562i	$0.509426\pi$
$978$	−4.46029e7	−	5.56066e6i	−1.49113	−	0.185900i
$979$		−	1.31408e7i		−	0.438194i
$980$	3.08785e6	+	1.81410e6i	0.102705	+	0.0603386i
$981$	4.96710e6	+	1.75684e7i	0.164790	+	0.582854i
$982$	2.62861e7	+	4.55289e7i	0.869858	+	1.50664i
$983$	−1.72039e7	+	2.97981e7i	−0.567863	+	0.983568i	0.428914	+	0.903345i	$0.358896\pi$
$983$	−1.72039e7	+	2.97981e7i	−0.567863	+	0.983568i	−0.996777	+	0.0802222i	$0.974437\pi$
$984$	−1.12923e7	−	2.67409e7i	−0.371786	−	0.880416i
$985$	9.11555e6	−	5.26286e6i	0.299359	−	0.172835i
$986$	−1.02424e7			−0.335513
$987$	4.82643e6	+	6.24995e6i	0.157701	+	0.204213i
$988$	−1.57910e7			−0.514657
$989$	−1.36273e7	+	7.86772e6i	−0.443015	+	0.255775i
$990$	−2.29635e6	−	581614.i	−0.0744647	−	0.0188602i
$991$	2.48971e7	−	4.31231e7i	0.805313	−	1.39484i	−0.110766	−	0.993846i	$-0.535330\pi$
$991$	2.48971e7	−	4.31231e7i	0.805313	−	1.39484i	0.916079	−	0.400997i	$-0.131336\pi$
$992$	1.03831e7	+	1.79841e7i	0.335004	+	0.580243i
$993$	4.32331e7	+	3.27045e7i	1.39137	+	1.05253i
$994$	5.85770e6	+	2.21972e7i	0.188045	+	0.712577i
$995$		−	1.30211e6i		−	0.0416956i
$996$	−2.97121e6	+	2.38325e7i	−0.0949042	+	0.761240i
$997$	8.76673e6	+	5.06147e6i	0.279318	+	0.161265i	0.633115	−	0.774058i	$-0.281776\pi$
$997$	8.76673e6	+	5.06147e6i	0.279318	+	0.161265i	−0.353796	+	0.935322i	$0.615109\pi$
$998$	−1.37327e7	−	7.92859e6i	−0.436445	−	0.251982i
$999$	−1.37764e7	+	2.10334e6i	−0.436738	+	0.0666801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.g.c.17.7	yes	16
3.2	odd	2	inner	21.6.g.c.17.2	yes	16
7.3	odd	6		147.6.c.c.146.14		16
7.4	even	3		147.6.c.c.146.13		16
7.5	odd	6	inner	21.6.g.c.5.2	✓	16
21.5	even	6	inner	21.6.g.c.5.7	yes	16
21.11	odd	6		147.6.c.c.146.4		16
21.17	even	6		147.6.c.c.146.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.2	✓	16	7.5	odd	6	inner
21.6.g.c.5.7	yes	16	21.5	even	6	inner
21.6.g.c.17.2	yes	16	3.2	odd	2	inner
21.6.g.c.17.7	yes	16	1.1	even	1	trivial
147.6.c.c.146.3		16	21.17	even	6
147.6.c.c.146.4		16	21.11	odd	6
147.6.c.c.146.13		16	7.4	even	3
147.6.c.c.146.14		16	7.3	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.89199 - 3.40174i) q^{2} +(14.3605 - 6.06423i) q^{3} +(7.14372 - 12.3733i) q^{4} +(7.45706 + 12.9160i) q^{5} +(63.9832 - 84.5813i) q^{6} +(-125.096 - 34.0278i) q^{7} +120.507i q^{8} +(169.450 - 174.171i) q^{9} +O(q^{10})\)	\(q+(5.89199 - 3.40174i) q^{2} +(14.3605 - 6.06423i) q^{3} +(7.14372 - 12.3733i) q^{4} +(7.45706 + 12.9160i) q^{5} +(63.9832 - 84.5813i) q^{6} +(-125.096 - 34.0278i) q^{7} +120.507i q^{8} +(169.450 - 174.171i) q^{9} +(87.8738 + 50.7340i) q^{10} +(-83.2023 - 48.0368i) q^{11} +(27.5532 - 221.008i) q^{12} +416.854i q^{13} +(-852.821 + 225.054i) q^{14} +(185.413 + 140.259i) q^{15} +(638.534 + 1105.97i) q^{16} +(104.249 - 180.565i) q^{17} +(405.913 - 1602.64i) q^{18} +(-2296.16 + 1325.69i) q^{19} +213.085 q^{20} +(-2002.80 + 269.956i) q^{21} -653.636 q^{22} +(2267.02 - 1308.86i) q^{23} +(730.783 + 1730.55i) q^{24} +(1451.28 - 2513.70i) q^{25} +(1418.03 + 2456.10i) q^{26} +(1377.18 - 3528.78i) q^{27} +(-1314.69 + 1304.77i) q^{28} -7220.50i q^{29} +(1569.58 + 195.680i) q^{30} +(3721.66 + 2148.70i) q^{31} +(4184.88 + 2416.14i) q^{32} +(-1486.14 - 185.277i) q^{33} -1418.52i q^{34} +(-493.347 - 1869.49i) q^{35} +(-944.567 - 3340.89i) q^{36} +(-1839.50 - 3186.10i) q^{37} +(-9019.31 + 15621.9i) q^{38} +(2527.90 + 5986.24i) q^{39} +(-1556.47 + 898.629i) q^{40} -15452.3 q^{41} +(-10882.2 + 8403.60i) q^{42} -6011.11 q^{43} +(-1188.75 + 686.324i) q^{44} +(3513.20 + 889.813i) q^{45} +(8904.83 - 15423.6i) q^{46} +(-1953.72 - 3383.94i) q^{47} +(15876.6 + 12010.1i) q^{48} +(14491.2 + 8513.51i) q^{49} -19747.6i q^{50} +(402.087 - 3225.20i) q^{51} +(5157.85 + 2977.89i) q^{52} +(31434.3 + 18148.6i) q^{53} +(-3889.66 - 25476.4i) q^{54} -1432.85i q^{55} +(4100.60 - 15075.0i) q^{56} +(-24934.8 + 32962.1i) q^{57} +(-24562.3 - 42543.1i) q^{58} +(-3913.73 + 6778.77i) q^{59} +(3060.01 - 1292.19i) q^{60} +(17488.2 - 10096.8i) q^{61} +29237.3 q^{62} +(-27124.3 + 16022.2i) q^{63} -7989.78 q^{64} +(-5384.08 + 3108.50i) q^{65} +(-9386.57 + 3963.80i) q^{66} +(-21969.0 + 38051.4i) q^{67} +(-1489.45 - 2579.81i) q^{68} +(24618.3 - 32543.7i) q^{69} +(-9266.33 - 9336.79i) q^{70} -26028.0i q^{71} +(20988.9 + 20420.0i) q^{72} +(44090.5 + 25455.6i) q^{73} +(-21676.6 - 12515.0i) q^{74} +(5597.58 - 44899.0i) q^{75} +37881.4i q^{76} +(8773.71 + 8840.43i) q^{77} +(35258.0 + 26671.6i) q^{78} +(25057.2 + 43400.3i) q^{79} +(-9523.16 + 16494.6i) q^{80} +(-1622.28 - 59026.7i) q^{81} +(-91044.6 + 52564.6i) q^{82} -107835. q^{83} +(-10967.2 + 26709.8i) q^{84} +3109.57 q^{85} +(-35417.4 + 20448.3i) q^{86} +(-43786.8 - 103690. i) q^{87} +(5788.78 - 10026.5i) q^{88} +(68389.3 + 118454. i) q^{89} +(23726.6 - 6708.22i) q^{90} +(14184.6 - 52146.9i) q^{91} -37400.6i q^{92} +(66475.3 + 8287.50i) q^{93} +(-23022.6 - 13292.1i) q^{94} +(-34245.2 - 19771.5i) q^{95} +(74749.2 + 9319.01i) q^{96} -25183.4i q^{97} +(114343. + 866.170i) q^{98} +(-22465.3 + 6351.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more