LMFDB - Embedded newform 21.6.c.a.20.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.c (of order $2$, degree $1$, 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 484x^{10} + 194194x^{8} - 39867800x^{6} + 5398720873x^{4} - 310089434788x^{2} + 9371104623076 $ x^12 - 484x^10 + 194194x^8 - 39867800x^6 + 5398720873x^4 - 310089434788*x^2 + 9371104623076
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.2
Root			$13.7499 + 10.2458i$ of defining polynomial
Character	$\chi$	$=$	21.20
Dual form			21.6.c.a.20.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.2458i q^{2} +(4.60012 - 14.8943i) q^{3} -72.9763 q^{4} +73.2992 q^{5} +(-152.604 - 47.1319i) q^{6} +(55.7250 + 117.054i) q^{7} +419.835i q^{8} +(-200.678 - 137.031i) q^{9} +O(q^{10})$	\(q-10.2458i q^{2} +(4.60012 - 14.8943i) q^{3} -72.9763 q^{4} +73.2992 q^{5} +(-152.604 - 47.1319i) q^{6} +(55.7250 + 117.054i) q^{7} +419.835i q^{8} +(-200.678 - 137.031i) q^{9} -751.009i q^{10} -237.986i q^{11} +(-335.700 + 1086.93i) q^{12} +63.3779i q^{13} +(1199.31 - 570.947i) q^{14} +(337.186 - 1091.74i) q^{15} +1966.30 q^{16} +814.556 q^{17} +(-1403.99 + 2056.10i) q^{18} -64.1691i q^{19} -5349.11 q^{20} +(1999.78 - 291.518i) q^{21} -2438.35 q^{22} +988.504i q^{23} +(6253.13 + 1931.29i) q^{24} +2247.78 q^{25} +649.357 q^{26} +(-2964.11 + 2358.59i) q^{27} +(-4066.61 - 8542.20i) q^{28} -1569.70i q^{29} +(-11185.7 - 3454.73i) q^{30} +5256.16i q^{31} -6711.62i q^{32} +(-3544.62 - 1094.76i) q^{33} -8345.77i q^{34} +(4084.60 + 8579.99i) q^{35} +(14644.7 + 10000.0i) q^{36} +11308.5 q^{37} -657.464 q^{38} +(943.966 + 291.546i) q^{39} +30773.6i q^{40} +3795.80 q^{41} +(-2986.84 - 20489.3i) q^{42} -15837.6 q^{43} +17367.3i q^{44} +(-14709.5 - 10044.3i) q^{45} +10128.0 q^{46} +23236.9 q^{47} +(9045.24 - 29286.6i) q^{48} +(-10596.4 + 13045.7i) q^{49} -23030.3i q^{50} +(3747.06 - 12132.2i) q^{51} -4625.09i q^{52} -19952.5i q^{53} +(24165.6 + 30369.7i) q^{54} -17444.2i q^{55} +(-49143.5 + 23395.3i) q^{56} +(-955.751 - 295.186i) q^{57} -16082.8 q^{58} -34515.5 q^{59} +(-24606.6 + 79671.0i) q^{60} -12095.9i q^{61} +53853.6 q^{62} +(4857.28 - 31126.2i) q^{63} -5844.15 q^{64} +4645.55i q^{65} +(-11216.7 + 36317.5i) q^{66} -29255.2 q^{67} -59443.3 q^{68} +(14723.0 + 4547.24i) q^{69} +(87908.9 - 41850.0i) q^{70} +54089.1i q^{71} +(57530.4 - 84251.6i) q^{72} +73706.7i q^{73} -115864. i q^{74} +(10340.1 - 33479.0i) q^{75} +4682.83i q^{76} +(27857.3 - 13261.8i) q^{77} +(2987.12 - 9671.69i) q^{78} -49241.9 q^{79} +144129. q^{80} +(21494.1 + 54998.1i) q^{81} -38891.0i q^{82} -112435. q^{83} +(-145937. + 21274.0i) q^{84} +59706.3 q^{85} +162268. i q^{86} +(-23379.5 - 7220.80i) q^{87} +99914.8 q^{88} +71787.2 q^{89} +(-102911. + 150711. i) q^{90} +(-7418.66 + 3531.74i) q^{91} -72137.4i q^{92} +(78286.6 + 24179.0i) q^{93} -238081. i q^{94} -4703.55i q^{95} +(-99964.5 - 30874.3i) q^{96} +18031.4i q^{97} +(133664. + 108569. i) q^{98} +(-32611.4 + 47758.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9}+O(q^{10}) $ 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9	$ 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9} + 1392 q^{15} + 4868 q^{16} - 3804 q^{18} + 4116 q^{21} - 8752 q^{22} + 7812 q^{25} - 8204 q^{28} - 27876 q^{30} + 54864 q^{36} + 27464 q^{37} - 16080 q^{39} - 3444 q^{42} - 73840 q^{43} + 59144 q^{46} + 6972 q^{49} + 23760 q^{51} + 103968 q^{57} - 71512 q^{58} - 152676 q^{60} - 120624 q^{63} - 198788 q^{64} + 79344 q^{67} + 368760 q^{70} + 226644 q^{72} + 394644 q^{78} - 247104 q^{79} - 248868 q^{81} - 608076 q^{84} - 320112 q^{85} + 595456 q^{88} + 310128 q^{91} + 397272 q^{93} + 696576 q^{99}+O(q^{100}) $ 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9 + 1392 * q^15 + 4868 * q^16 - 3804 * q^18 + 4116 * q^21 - 8752 * q^22 + 7812 * q^25 - 8204 * q^28 - 27876 * q^30 + 54864 * q^36 + 27464 * q^37 - 16080 * q^39 - 3444 * q^42 - 73840 * q^43 + 59144 * q^46 + 6972 * q^49 + 23760 * q^51 + 103968 * q^57 - 71512 * q^58 - 152676 * q^60 - 120624 * q^63 - 198788 * q^64 + 79344 * q^67 + 368760 * q^70 + 226644 * q^72 + 394644 * q^78 - 247104 * q^79 - 248868 * q^81 - 608076 * q^84 - 320112 * q^85 + 595456 * q^88 + 310128 * q^91 + 397272 * q^93 + 696576 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	10.2458i		−	1.81122i	−0.424114	−	0.905609i	$-0.639414\pi$
$2$		−	10.2458i		−	1.81122i	0.424114	−	0.905609i	$-0.360586\pi$
$3$	4.60012	−	14.8943i	0.295098	−	0.955467i
$3$	4.60012	−	14.8943i	0.295098	−	0.955467i
$4$	−72.9763			−2.28051
$5$	73.2992			1.31122			0.655608	−	0.755101i	$-0.272412\pi$
$5$	73.2992			1.31122			0.655608	+	0.755101i	$0.272412\pi$
$6$	−152.604	−	47.1319i	−1.73056	−	0.534487i
$7$	55.7250	+	117.054i	0.429838	+	0.902906i
$7$	55.7250	+	117.054i	0.429838	+	0.902906i
$8$			419.835i			2.31928i
$9$	−200.678	−	137.031i	−0.825834	−	0.563913i
$10$		−	751.009i		−	2.37490i
$11$		−	237.986i		−	0.593020i	−0.955030	−	0.296510i	$-0.904177\pi$
$11$		−	237.986i		−	0.593020i	0.955030	−	0.296510i	$-0.0958228\pi$
$12$	−335.700	+	1086.93i	−0.672974	+	2.17895i
$13$			63.3779i			0.104011i	0.998647	+	0.0520055i	$0.0165613\pi$
$13$			63.3779i			0.104011i	−0.998647	+	0.0520055i	$0.983439\pi$
$14$	1199.31	−	570.947i	1.63536	−	0.778531i
$15$	337.186	−	1091.74i	0.386937	−	1.25282i
$16$	1966.30			1.92022
$17$	814.556			0.683595			0.341797	−	0.939774i	$-0.388964\pi$
$17$	814.556			0.683595			0.341797	+	0.939774i	$0.388964\pi$
$18$	−1403.99	+	2056.10i	−1.02137	+	1.49577i
$19$		−	64.1691i		−	0.0407795i	−0.999792	−	0.0203898i	$-0.993509\pi$
$19$		−	64.1691i		−	0.0407795i	0.999792	−	0.0203898i	$-0.00649071\pi$
$20$	−5349.11			−2.99024
$21$	1999.78	−	291.518i	0.989541	−	0.144251i
$22$	−2438.35			−1.07409
$23$			988.504i			0.389636i	0.980839	+	0.194818i	$0.0624116\pi$
$23$			988.504i			0.389636i	−0.980839	+	0.194818i	$0.937588\pi$
$24$	6253.13	+	1931.29i	2.21600	+	0.684416i
$25$	2247.78			0.719289
$26$	649.357			0.188387
$27$	−2964.11	+	2358.59i	−0.782502	+	0.622648i
$28$	−4066.61	−	8542.20i	−0.980251	−	2.05909i
$29$		−	1569.70i		−	0.346594i	−0.984870	−	0.173297i	$-0.944558\pi$
$29$		−	1569.70i		−	0.346594i	0.984870	−	0.173297i	$-0.0554420\pi$
$30$	−11185.7	−	3454.73i	−2.26914	−	0.700828i
$31$			5256.16i			0.982346i	0.871062	+	0.491173i	$0.163432\pi$
$31$			5256.16i			0.982346i	−0.871062	+	0.491173i	$0.836568\pi$
$32$		−	6711.62i		−	1.15865i
$33$	−3544.62	−	1094.76i	−0.566611	−	0.174999i
$34$		−	8345.77i		−	1.23814i
$35$	4084.60	+	8579.99i	0.563611	+	1.18390i
$36$	14644.7	+	10000.0i	1.88332	+	1.28601i
$37$	11308.5			1.35800			0.678999	−	0.734139i	$-0.262414\pi$
$37$	11308.5			1.35800			0.678999	+	0.734139i	$0.262414\pi$
$38$	−657.464			−0.0738606
$39$	943.966	+	291.546i	0.0993791	+	0.0306935i
$40$			30773.6i			3.04108i
$41$	3795.80			0.352650			0.176325	−	0.984332i	$-0.443579\pi$
$41$	3795.80			0.352650			0.176325	+	0.984332i	$0.443579\pi$
$42$	−2986.84	−	20489.3i	−0.261269	−	1.79227i
$43$	−15837.6			−1.30622			−0.653111	−	0.757262i	$-0.726536\pi$
$43$	−15837.6			−1.30622			−0.653111	+	0.757262i	$0.726536\pi$
$44$			17367.3i			1.35239i
$45$	−14709.5	−	10044.3i	−1.08285	−	0.739412i
$46$	10128.0			0.705715
$47$	23236.9			1.53438			0.767192	−	0.641418i	$-0.221654\pi$
$47$	23236.9			1.53438			0.767192	+	0.641418i	$0.221654\pi$
$48$	9045.24	−	29286.6i	0.566653	−	1.83471i
$49$	−10596.4	+	13045.7i	−0.630478	+	0.776207i
$50$		−	23030.3i		−	1.30279i
$51$	3747.06	−	12132.2i	0.201727	−	0.653152i
$52$		−	4625.09i		−	0.237198i
$53$		−	19952.5i		−	0.975681i	−0.872933	−	0.487840i	$-0.837785\pi$
$53$		−	19952.5i		−	0.975681i	0.872933	−	0.487840i	$-0.162215\pi$
$54$	24165.6	+	30369.7i	1.12775	+	1.41728i
$55$		−	17444.2i		−	0.777577i
$56$	−49143.5	+	23395.3i	−2.09409	+	0.996917i
$57$	−955.751	−	295.186i	−0.0389635	−	0.0120340i
$58$	−16082.8			−0.627757
$59$	−34515.5			−1.29087			−0.645437	−	0.763814i	$-0.723325\pi$
$59$	−34515.5			−1.29087			−0.645437	+	0.763814i	$0.723325\pi$
$60$	−24606.6	+	79671.0i	−0.882415	+	2.85708i
$61$		−	12095.9i		−	0.416212i	−0.978106	−	0.208106i	$-0.933270\pi$
$61$		−	12095.9i		−	0.416212i	0.978106	−	0.208106i	$-0.0667299\pi$
$62$	53853.6			1.77924
$63$	4857.28	−	31126.2i	0.154185	−	0.988042i
$64$	−5844.15			−0.178349
$65$			4645.55i			0.136381i
$66$	−11216.7	+	36317.5i	−0.316961	+	1.02626i
$67$	−29255.2			−0.796189			−0.398094	−	0.917345i	$-0.630328\pi$
$67$	−29255.2			−0.796189			−0.398094	+	0.917345i	$0.630328\pi$
$68$	−59443.3			−1.55894
$69$	14723.0	+	4547.24i	0.372284	+	0.114981i
$70$	87908.9	−	41850.0i	2.14431	−	1.02082i
$71$			54089.1i			1.27340i	0.771113	+	0.636699i	$0.219701\pi$
$71$			54089.1i			1.27340i	−0.771113	+	0.636699i	$0.780299\pi$
$72$	57530.4	−	84251.6i	1.30787	−	1.91534i
$73$			73706.7i			1.61883i	0.587240	+	0.809413i	$0.300214\pi$
$73$			73706.7i			1.61883i	−0.587240	+	0.809413i	$0.699786\pi$
$74$		−	115864.i		−	2.45963i
$75$	10340.1	−	33479.0i	0.212261	−	0.687257i
$76$			4682.83i			0.0929981i
$77$	27857.3	−	13261.8i	0.535441	−	0.254903i
$78$	2987.12	−	9671.69i	0.0555925	−	0.179997i
$79$	−49241.9			−0.887701			−0.443851	−	0.896101i	$-0.646388\pi$
$79$	−49241.9			−0.887701			−0.443851	+	0.896101i	$0.646388\pi$
$80$	144129.			2.51782
$81$	21494.1	+	54998.1i	0.364004	+	0.931397i
$82$		−	38891.0i		−	0.638725i
$83$	−112435.			−1.79146			−0.895732	−	0.444595i	$-0.853348\pi$
$83$	−112435.			−1.79146			−0.895732	+	0.444595i	$0.853348\pi$
$84$	−145937.	+	21274.0i	−2.25666	+	0.328965i
$85$	59706.3			0.896340
$86$			162268.i			2.36585i
$87$	−23379.5	−	7220.80i	−0.331159	−	0.102279i
$88$	99914.8			1.37538
$89$	71787.2			0.960665			0.480332	−	0.877087i	$-0.340516\pi$
$89$	71787.2			0.960665			0.480332	+	0.877087i	$0.340516\pi$
$90$	−102911.	+	150711.i	−1.33924	+	1.96127i
$91$	−7418.66	+	3531.74i	−0.0939122	+	0.0447079i
$92$		−	72137.4i		−	0.888568i
$93$	78286.6	+	24179.0i	0.938599	+	0.289888i
$94$		−	238081.i		−	2.77910i
$95$		−	4703.55i		−	0.0534708i
$96$	−99964.5	−	30874.3i	−1.10705	−	0.341915i
$97$			18031.4i			0.194581i	0.995256	+	0.0972905i	$0.0310176\pi$
$97$			18031.4i			0.194581i	−0.995256	+	0.0972905i	$0.968982\pi$
$98$	133664.	+	108569.i	1.40588	+	1.14193i
$99$	−32611.4	+	47758.4i	−0.334412	+	0.489736i
$100$	−164035.			−1.64035
$101$	−113298.			−1.10515			−0.552574	−	0.833464i	$-0.686354\pi$
$101$	−113298.			−1.10515			−0.552574	+	0.833464i	$0.686354\pi$
$102$	−124304.	−	38391.6i	−1.18300	−	0.365372i
$103$			28838.5i			0.267842i	0.990992	+	0.133921i	$0.0427569\pi$
$103$			28838.5i			0.267842i	−0.990992	+	0.133921i	$0.957243\pi$
$104$	−26608.3			−0.241231
$105$	146582.	−	21368.1i	1.29750	−	0.189144i
$106$	−204429.			−1.76717
$107$		−	163105.i		−	1.37724i	−0.725125	−	0.688618i	$-0.758218\pi$
$107$		−	163105.i		−	1.37724i	0.725125	−	0.688618i	$-0.241782\pi$
$108$	216310.	−	172121.i	1.78450	−	1.41995i
$109$	80804.9			0.651436			0.325718	−	0.945467i	$-0.394394\pi$
$109$	80804.9			0.651436			0.325718	+	0.945467i	$0.394394\pi$
$110$	−178729.			−1.40836
$111$	52020.3	−	168431.i	0.400742	−	1.29752i
$112$	109572.	+	230164.i	0.825384	+	1.73378i
$113$		−	166803.i		−	1.22887i	−0.788966	−	0.614437i	$-0.789383\pi$
$113$		−	166803.i		−	1.22887i	0.788966	−	0.614437i	$-0.210617\pi$
$114$	−3024.42	+	9792.43i	−0.0217961	+	0.0705714i
$115$			72456.6i			0.510897i
$116$			114551.i			0.790411i
$117$	8684.73	−	12718.5i	0.0586532	−	0.0858959i
$118$			353638.i			2.33805i
$119$	45391.2	+	95347.3i	0.293835	+	0.617222i
$120$	458350.	+	141562.i	2.90565	+	0.897418i
$121$	104414.			0.648328
$122$	−123932.			−0.753851
$123$	17461.1	−	56535.6i	0.104066	−	0.336945i
$124$		−	383575.i		−	2.24025i
$125$	−64299.8			−0.368073
$126$	−318913.	−	49766.7i	−1.78956	−	0.279263i
$127$	−134331.			−0.739040			−0.369520	−	0.929223i	$-0.620478\pi$
$127$	−134331.			−0.739040			−0.369520	+	0.929223i	$0.620478\pi$
$128$		−	154894.i		−	0.835620i
$129$	−72854.7	+	235889.i	−0.385464	+	1.24805i
$130$	47597.4			0.247016
$131$	206373.			1.05069			0.525346	−	0.850889i	$-0.323936\pi$
$131$	206373.			1.05069			0.525346	+	0.850889i	$0.323936\pi$
$132$	258673.	+	79891.9i	1.29216	+	0.399087i
$133$	7511.28	−	3575.83i	0.0368201	−	0.0175286i
$134$			299743.i			1.44207i
$135$	−217267.	+	172883.i	−1.02603	+	0.816426i
$136$			341979.i			1.58545i
$137$			104556.i			0.475936i	0.971273	+	0.237968i	$0.0764813\pi$
$137$			104556.i			0.475936i	−0.971273	+	0.237968i	$0.923519\pi$
$138$	46590.1	−	150849.i	0.208255	−	0.674287i
$139$		−	106570.i		−	0.467842i	−0.972256	−	0.233921i	$-0.924844\pi$
$139$		−	106570.i		−	0.467842i	0.972256	−	0.233921i	$-0.0751558\pi$
$140$	−298079.	−	626137.i	−1.28532	−	2.69991i
$141$	106893.	−	346097.i	0.452794	−	1.46605i
$142$	554186.			2.30640
$143$	15083.0			0.0616806
$144$	−394593.	−	269444.i	−1.58578	−	1.08284i
$145$		−	115058.i		−	0.454460i
$146$	755184.			2.93205
$147$	145561.	+	217838.i	0.555588	+	0.831458i
$148$	−825250.			−3.09693
$149$			234489.i			0.865279i	0.901567	+	0.432640i	$0.142418\pi$
$149$			234489.i			0.865279i	−0.901567	+	0.432640i	$0.857582\pi$
$150$	−343019.	−	105942.i	−1.24477	−	0.384450i
$151$	−82844.4			−0.295679			−0.147840	−	0.989011i	$-0.547232\pi$
$151$	−82844.4			−0.295679			−0.147840	+	0.989011i	$0.547232\pi$
$152$	26940.5			0.0945793
$153$	−163463.	−	111619.i	−0.564536	−	0.385488i
$154$	−135877.	−	285420.i	−0.461684	−	0.969800i
$155$			385273.i			1.28807i
$156$	−68887.2	−	21276.0i	−0.226635	−	0.0699968i
$157$		−	65986.0i		−	0.213650i	−0.994278	−	0.106825i	$-0.965932\pi$
$157$		−	65986.0i		−	0.213650i	0.994278	−	0.106825i	$-0.0340684\pi$
$158$			504522.i			1.60782i
$159$	−297178.	−	91784.0i	−0.932231	−	0.287922i
$160$		−	491956.i		−	1.51924i
$161$	−115709.	+	55084.4i	−0.351804	+	0.167480i
$162$	563499.	−	220224.i	1.68696	−	0.659291i
$163$	−327678.			−0.966001			−0.483001	−	0.875620i	$-0.660453\pi$
$163$	−327678.			−0.966001			−0.483001	+	0.875620i	$0.660453\pi$
$164$	−277003.			−0.804221
$165$	−259818.	−	80245.3i	−0.742949	−	0.229462i
$166$			1.15199e6i			3.24473i
$167$	96558.3			0.267916			0.133958	−	0.990987i	$-0.457231\pi$
$167$	96558.3			0.267916			0.133958	+	0.990987i	$0.457231\pi$
$168$	122390.	+	839578.i	0.334558	+	2.29503i
$169$	367276.			0.989182
$170$		−	611739.i		−	1.62347i
$171$	−8793.15	+	12877.3i	−0.0229961	+	0.0336771i
$172$	1.15577e6			2.97885
$173$	−137087.			−0.348243			−0.174121	−	0.984724i	$-0.555709\pi$
$173$	−137087.			−0.348243			−0.174121	+	0.984724i	$0.555709\pi$
$174$	−73982.8	+	239541.i	−0.185250	+	0.599801i
$175$	125257.	+	263112.i	0.309178	+	0.649450i
$176$		−	467952.i		−	1.13873i
$177$	−158775.	+	514082.i	−0.380934	+	1.23339i
$178$		−	735517.i		−	1.73997i
$179$		−	203680.i		−	0.475135i	−0.971371	−	0.237567i	$-0.923650\pi$
$179$		−	203680.i		−	0.475135i	0.971371	−	0.237567i	$-0.0763500\pi$
$180$	1.07345e6	+	732993.i	2.46945	+	1.68624i
$181$		−	733278.i		−	1.66369i	−0.555009	−	0.831845i	$-0.687285\pi$
$181$		−	733278.i		−	1.66369i	0.555009	−	0.831845i	$-0.312715\pi$
$182$	36185.4	+	76010.1i	0.0809758	+	0.170095i
$183$	−180160.	−	55642.8i	−0.397677	−	0.122823i
$184$	−415009.			−0.903676
$185$	828901.			1.78063
$186$	247733.	−	802109.i	0.525051	−	1.70001i
$187$		−	193853.i		−	0.405385i
$188$	−1.69574e6			−3.49918
$189$	−441258.	−	215530.i	−0.898542	−	0.438888i
$190$	−48191.6			−0.0968473
$191$		−	768632.i		−	1.52453i	−0.647267	−	0.762263i	$-0.724088\pi$
$191$		−	768632.i		−	1.52453i	0.647267	−	0.762263i	$-0.275912\pi$
$192$	−26883.8	+	87044.2i	−0.0526305	+	0.170407i
$193$	−278059.			−0.537334			−0.268667	−	0.963233i	$-0.586583\pi$
$193$	−278059.			−0.537334			−0.268667	+	0.963233i	$0.586583\pi$
$194$	184746.			0.352428
$195$	69192.0	+	21370.1i	0.130308	+	0.0402458i
$196$	773289.	−	952029.i	1.43781	−	1.77015i
$197$			224299.i			0.411776i	0.978576	+	0.205888i	$0.0660082\pi$
$197$			224299.i			0.411776i	−0.978576	+	0.205888i	$0.933992\pi$
$198$	489323.	+	334130.i	0.887019	+	0.605692i
$199$			283632.i			0.507718i	0.967241	+	0.253859i	$0.0817000\pi$
$199$			283632.i			0.507718i	−0.967241	+	0.253859i	$0.918300\pi$
$200$			943696.i			1.66823i
$201$	−134578.	+	435734.i	−0.234954	+	0.760732i
$202$			1.16083e6i			2.00166i
$203$	183740.	−	87471.4i	0.312942	−	0.148979i
$204$	−273447.	+	885364.i	−0.460042	+	1.48952i
$205$	278229.			0.462400
$206$	295473.			0.485121
$207$	135455.	−	198371.i	0.219721	−	0.321774i
$208$			124620.i			0.199724i
$209$	−15271.3			−0.0241831
$210$	−218933.	−	1.50185e6i	−0.342581	−	2.35006i
$211$	96651.9			0.149453			0.0747264	−	0.997204i	$-0.476192\pi$
$211$	96651.9			0.149453			0.0747264	+	0.997204i	$0.476192\pi$
$212$			1.45606e6i			2.22505i
$213$	805617.	+	248817.i	1.21669	+	0.375777i
$214$	−1.67114e6			−2.49447
$215$	−1.16088e6			−1.71274
$216$	−990218.	−	1.24444e6i	−1.44410	−	1.81485i
$217$	−615257.	+	292900.i	−0.886966	+	0.422250i
$218$		−	827911.i		−	1.17989i
$219$	1.09781e6	+	339060.i	1.54673	+	0.477712i
$220$			1.27301e6i			1.77327i
$221$			51624.8i			0.0711014i
$222$	−1.72571e6	−	532989.i	−2.35009	−	0.725832i
$223$		−	438734.i		−	0.590798i	−0.955374	−	0.295399i	$-0.904547\pi$
$223$		−	438734.i		−	0.590798i	0.955374	−	0.295399i	$-0.0954526\pi$
$224$	785624.	−	374005.i	1.04615	−	0.498032i
$225$	−451079.	−	308015.i	−0.594013	−	0.405616i
$226$	−1.70903e6			−2.22576
$227$	702045.			0.904275			0.452137	−	0.891948i	$-0.350662\pi$
$227$	702045.			0.904275			0.452137	+	0.891948i	$0.350662\pi$
$228$	69747.2	+	21541.6i	0.0888567	+	0.0274436i
$229$		−	418280.i		−	0.527082i	−0.964648	−	0.263541i	$-0.915110\pi$
$229$		−	418280.i		−	0.527082i	0.964648	−	0.263541i	$-0.0848904\pi$
$230$	742375.			0.925345
$231$	−69377.2	−	475919.i	−0.0855435	−	0.586818i
$232$	659014.			0.803849
$233$		−	1.19771e6i		−	1.44531i	−0.691208	−	0.722656i	$-0.742921\pi$
$233$		−	1.19771e6i		−	1.44531i	0.691208	−	0.722656i	$-0.257079\pi$
$234$	−130311.	−	88981.9i	−0.155576	−	0.106234i
$235$	1.70325e6			2.01191
$236$	2.51881e6			2.94385
$237$	−226519.	+	733421.i	−0.261959	+	0.848169i
$238$	976909.	−	465069.i	1.11792	−	0.532200i
$239$			1.24466e6i			1.40947i	0.709470	+	0.704736i	$0.248935\pi$
$239$			1.24466e6i			1.40947i	−0.709470	+	0.704736i	$0.751065\pi$
$240$	663009.	−	2.14669e6i	0.743004	−	2.40570i
$241$			23511.7i			0.0260760i	0.999915	+	0.0130380i	$0.00415024\pi$
$241$			23511.7i			0.0260760i	−0.999915	+	0.0130380i	$0.995850\pi$
$242$		−	1.06980e6i		−	1.17426i
$243$	918031.	−	67140.6i	0.997336	−	0.0729406i
$244$			882716.i			0.949176i
$245$	−776711.	+	956241.i	−0.826693	+	1.01778i
$246$	−579252.	−	178903.i	−0.610281	−	0.188487i
$247$	4066.90			0.00424152
$248$	−2.20672e6			−2.27834
$249$	−517217.	+	1.67464e6i	−0.528658	+	1.71168i
$250$			658802.i			0.666661i
$251$	−483287.			−0.484195			−0.242098	−	0.970252i	$-0.577835\pi$
$251$	−483287.			−0.484195			−0.242098	+	0.970252i	$0.577835\pi$
$252$	−354467.	+	2.27148e6i	−0.351620	+	2.25324i
$253$	235250.			0.231062
$254$			1.37633e6i			1.33856i
$255$	274656.	−	889281.i	0.264508	−	0.856424i
$256$	−1.77402e6			−1.69184
$257$	−697129.			−0.658386			−0.329193	−	0.944263i	$-0.606777\pi$
$257$	−697129.			−0.658386			−0.329193	+	0.944263i	$0.606777\pi$
$258$	2.41687e6	+	746454.i	2.26049	+	0.698159i
$259$	630164.	+	1.32370e6i	0.583720	+	1.22614i
$260$		−	339015.i		−	0.311018i
$261$	−215097.	+	315003.i	−0.195449	+	0.286229i
$262$		−	2.11446e6i		−	1.90303i
$263$		−	454708.i		−	0.405363i	−0.979245	−	0.202681i	$-0.935034\pi$
$263$		−	454708.i		−	0.405363i	0.979245	−	0.202681i	$-0.0649655\pi$
$264$	459620.	−	1.48816e6i	0.405872	−	1.31413i
$265$		−	1.46250e6i		−	1.27933i
$266$	−36637.2	−	76959.0i	−0.0317481	−	0.0666892i
$267$	330230.	−	1.06922e6i	0.283490	−	0.917883i
$268$	2.13494e6			1.81572
$269$	−1.26132e6			−1.06278			−0.531392	−	0.847126i	$-0.678331\pi$
$269$	−1.26132e6			−1.06278			−0.531392	+	0.847126i	$0.678331\pi$
$270$	1.77132e6	+	2.22608e6i	1.47873	+	1.85836i
$271$			1.75801e6i			1.45411i	0.686577	+	0.727057i	$0.259112\pi$
$271$			1.75801e6i			1.45411i	−0.686577	+	0.727057i	$0.740888\pi$
$272$	1.60166e6			1.31265
$273$	18475.8	+	126742.i	0.0150037	+	0.102923i
$274$	1.07126e6			0.862024
$275$		−	534939.i		−	0.426552i
$276$	−1.07443e6	−	331841.i	−0.848998	−	0.262215i
$277$	−579921.			−0.454119			−0.227059	−	0.973881i	$-0.572911\pi$
$277$	−579921.			−0.454119			−0.227059	+	0.973881i	$0.572911\pi$
$278$	−1.09190e6			−0.847365
$279$	720256.	−	1.05479e6i	0.553958	−	0.811255i
$280$	−3.60218e6	+	1.71486e6i	−2.74581	+	1.30717i
$281$		−	887445.i		−	0.670464i	−0.942136	−	0.335232i	$-0.891185\pi$
$281$		−	887445.i		−	0.670464i	0.942136	−	0.335232i	$-0.108815\pi$
$282$	−3.54603e6	−	1.09520e6i	−2.65534	−	0.820108i
$283$			695661.i			0.516335i	0.966100	+	0.258167i	$0.0831186\pi$
$283$			695661.i			0.516335i	−0.966100	+	0.258167i	$0.916881\pi$
$284$		−	3.94723e6i		−	2.90400i
$285$	−70055.8	−	21636.9i	−0.0510896	−	0.0157791i
$286$		−	154538.i		−	0.111717i
$287$	211521.	+	444314.i	0.151582	+	0.318409i
$288$	−919699.	+	1.34687e6i	−0.653378	+	0.956853i
$289$	−756356.			−0.532698
$290$	−1.17886e6			−0.823125
$291$	268564.	+	82946.7i	0.185916	+	0.0574205i
$292$		−	5.37885e6i		−	3.69175i
$293$	2.41780e6			1.64533			0.822663	−	0.568530i	$-0.192487\pi$
$293$	2.41780e6			1.64533			0.822663	+	0.568530i	$0.192487\pi$
$294$	2.23192e6	−	1.49139e6i	1.50595	−	1.00629i
$295$	−2.52996e6			−1.69261
$296$			4.74769e6i			3.14958i
$297$	561310.	+	705417.i	0.369242	+	0.464039i
$298$	2.40252e6			1.56721
$299$	−62649.3			−0.0405264
$300$	−754579.	+	2.44317e6i	−0.484063	+	1.56730i
$301$	−882548.	−	1.85385e6i	−0.561464	−	1.17940i
$302$			848807.i			0.535539i
$303$	−521187.	+	1.68750e6i	−0.326127	+	1.05593i
$304$		−	126176.i		−	0.0783056i
$305$		−	886622.i		−	0.545744i
$306$	−1.14363e6	+	1.67481e6i	−0.698202	+	1.02250i
$307$			2.10484e6i			1.27460i	0.770617	+	0.637298i	$0.219948\pi$
$307$			2.10484e6i			1.27460i	−0.770617	+	0.637298i	$0.780052\pi$
$308$	−2.03292e6	+	967795.i	−1.22108	+	0.581308i
$309$	429528.	+	132661.i	0.255914	+	0.0790397i
$310$	3.94742e6			2.33297
$311$	1.33156e6			0.780657			0.390328	−	0.920676i	$-0.372361\pi$
$311$	1.33156e6			0.780657			0.390328	+	0.920676i	$0.372361\pi$
$312$	−122401.	+	396310.i	−0.0711868	+	0.230488i
$313$		−	2.68703e6i		−	1.55028i	−0.631788	−	0.775142i	$-0.717678\pi$
$313$		−	2.68703e6i		−	1.55028i	0.631788	−	0.775142i	$-0.282322\pi$
$314$	−676079.			−0.386967
$315$	356035.	−	2.28153e6i	0.202170	−	1.29554i
$316$	3.59349e6			2.02441
$317$		−	1.36978e6i		−	0.765602i	−0.923831	−	0.382801i	$-0.874959\pi$
$317$		−	1.36978e6i		−	0.765602i	0.923831	−	0.382801i	$-0.125041\pi$
$318$	−940400.	+	3.04482e6i	−0.521489	+	1.68847i
$319$	−373565.			−0.205537
$320$	−428372.			−0.233854
$321$	−2.42933e6	−	750304.i	−1.31590	−	0.406419i
$322$	564384.	+	1.18553e6i	0.303343	+	0.637194i
$323$		−	52269.3i		−	0.0278767i
$324$	−1.56856e6	−	4.01356e6i	−0.830116	−	2.12406i
$325$			142459.i			0.0748140i
$326$			3.35732e6i			1.74964i
$327$	371713.	−	1.20353e6i	0.192237	−	0.622425i
$328$			1.59361e6i			0.817894i
$329$	1.29488e6	+	2.71998e6i	0.659537	+	1.38540i
$330$	−822177.	+	2.66204e6i	−0.415605	+	1.34564i
$331$	675406.			0.338840			0.169420	−	0.985544i	$-0.445811\pi$
$331$	675406.			0.338840			0.169420	+	0.985544i	$0.445811\pi$
$332$	8.20513e6			4.08545
$333$	−2.26936e6	−	1.54961e6i	−1.12148	−	0.765792i
$334$		−	989317.i		−	0.485254i
$335$	−2.14438e6			−1.04398
$336$	3.93217e6	−	573214.i	1.90014	−	0.276993i
$337$	1.11714e6			0.535838			0.267919	−	0.963442i	$-0.413664\pi$
$337$	1.11714e6			0.535838			0.267919	+	0.963442i	$0.413664\pi$
$338$		−	3.76304e6i		−	1.79162i
$339$	−2.48440e6	−	767314.i	−1.17415	−	0.362638i
$340$	−4.35715e6			−2.04411
$341$	1.25089e6			0.582551
$342$	131938.	+	90092.8i	0.0609966	+	0.0416510i
$343$	−2.11754e6	−	513386.i	−0.971846	−	0.235618i
$344$		−	6.64916e6i		−	3.02950i
$345$	1.07919e6	+	333309.i	0.488145	+	0.150765i
$346$			1.40457e6i			0.630744i
$347$		−	805408.i		−	0.359081i	−0.983751	−	0.179540i	$-0.942539\pi$
$347$		−	805408.i		−	0.359081i	0.983751	−	0.179540i	$-0.0574611\pi$
$348$	1.70615e6	+	526948.i	0.755211	+	0.233249i
$349$			3.67675e6i			1.61585i	0.589287	+	0.807924i	$0.299409\pi$
$349$			3.67675e6i			1.61585i	−0.589287	+	0.807924i	$0.700591\pi$
$350$	2.69579e6	−	1.28336e6i	1.17630	−	0.559989i
$351$	−149482.	−	187859.i	−0.0647622	−	0.0813889i
$352$	−1.59727e6			−0.687102
$353$	−2.54872e6			−1.08864			−0.544321	−	0.838877i	$-0.683213\pi$
$353$	−2.54872e6			−1.08864			−0.544321	+	0.838877i	$0.683213\pi$
$354$	5.26718e6	+	1.62678e6i	2.23393	+	0.689955i
$355$			3.96469e6i			1.66970i
$356$	−5.23877e6			−2.19081
$357$	1.62893e6	−	237458.i	0.676445	−	0.0986090i
$358$	−2.08687e6			−0.860572
$359$			2.74337e6i			1.12344i	0.827329	+	0.561718i	$0.189859\pi$
$359$			2.74337e6i			1.12344i	−0.827329	+	0.561718i	$0.810141\pi$
$360$	4.21693e6	−	6.17558e6i	1.71491	−	2.51143i
$361$	2.47198e6			0.998337
$362$	−7.51302e6			−3.01330
$363$	480316.	−	1.55517e6i	0.191320	−	0.619456i
$364$	541386.	−	257733.i	0.214168	−	0.101957i
$365$			5.40265e6i			2.12263i
$366$	−570104.	+	1.84588e6i	−0.222460	+	0.720279i
$367$		−	3.04407e6i		−	1.17975i	−0.807495	−	0.589874i	$-0.799177\pi$
$367$		−	3.04407e6i		−	1.17975i	0.807495	−	0.589874i	$-0.200823\pi$
$368$			1.94370e6i			0.748185i
$369$	−761732.	−	520141.i	−0.291230	−	0.198864i
$370$		−	8.49275e6i		−	3.22511i
$371$	2.33553e6	−	1.11185e6i	0.880948	−	0.419385i
$372$	−5.71307e6	−	1.76449e6i	−2.14049	−	0.661094i
$373$	−1.13635e6			−0.422902			−0.211451	−	0.977389i	$-0.567819\pi$
$373$	−1.13635e6			−0.422902			−0.211451	+	0.977389i	$0.567819\pi$
$374$	−1.98618e6			−0.734241
$375$	−295787.	+	957697.i	−0.108618	+	0.351682i
$376$			9.75568e6i			3.55867i
$377$	99484.1			0.0360496
$378$	−2.20828e6	+	4.52104e6i	−0.794922	+	1.62746i
$379$	2.11965e6			0.757995			0.378998	−	0.925398i	$-0.376269\pi$
$379$	2.11965e6			0.757995			0.378998	+	0.925398i	$0.376269\pi$
$380$			343248.i			0.121941i
$381$	−617941.	+	2.00077e6i	−0.218089	+	0.706129i
$382$	−7.87525e6			−2.76125
$383$	4.43402e6			1.54455			0.772273	−	0.635291i	$-0.219120\pi$
$383$	4.43402e6			1.54455			0.772273	+	0.635291i	$0.219120\pi$
$384$	−2.30703e6	−	712531.i	−0.798408	−	0.246590i
$385$	2.04192e6	−	972077.i	0.702079	−	0.334233i
$386$			2.84894e6i			0.973229i
$387$	3.17824e6	+	2.17023e6i	1.07872	+	0.736595i
$388$		−	1.31587e6i		−	0.443744i
$389$			495729.i			0.166100i	0.996545	+	0.0830502i	$0.0264662\pi$
$389$			495729.i			0.166100i	−0.996545	+	0.0830502i	$0.973534\pi$
$390$	218954.	−	708927.i	0.0728939	−	0.236015i
$391$			805192.i			0.266353i
$392$	−5.47705e6	−	4.44876e6i	−1.80025	−	1.46226i
$393$	949343.	−	3.07378e6i	0.310057	−	1.00390i
$394$	2.29812e6			0.745816
$395$	−3.60939e6			−1.16397
$396$	2.37986e6	−	3.48524e6i	0.762629	−	1.11685i
$397$			19953.4i			0.00635392i	0.999995	+	0.00317696i	$0.00101126\pi$
$397$			19953.4i			0.00635392i	−0.999995	+	0.00317696i	$0.998989\pi$
$398$	2.90604e6			0.919588
$399$	−18706.5	−	128324.i	−0.00588247	−	0.0403530i
$400$	4.41981e6			1.38119
$401$		−	3.27975e6i		−	1.01854i	−0.860606	−	0.509272i	$-0.829915\pi$
$401$		−	3.27975e6i		−	1.01854i	0.860606	−	0.509272i	$-0.170085\pi$
$402$	4.46445e6	+	1.37885e6i	1.37785	+	0.425552i
$403$	−333124.			−0.102175
$404$	8.26810e6			2.52030
$405$	1.57550e6	+	4.03132e6i	0.477289	+	1.22126i
$406$	−896214.	−	1.88256e6i	−0.269834	−	0.566805i
$407$		−	2.69125e6i		−	0.805319i
$408$	5.09353e6	+	1.57315e6i	1.51485	+	0.467863i
$409$			1.89585e6i			0.560396i	0.959942	+	0.280198i	$0.0904001\pi$
$409$			1.89585e6i			0.560396i	−0.959942	+	0.280198i	$0.909600\pi$
$410$		−	2.85068e6i		−	0.837507i
$411$	1.55729e6	+	480972.i	0.454741	+	0.140448i
$412$		−	2.10453e6i		−	0.610817i
$413$	−1.92338e6	−	4.04019e6i	−0.554867	−	1.16554i
$414$	−2.03247e6	−	1.38785e6i	−0.582804	−	0.397962i
$415$	−8.24143e6			−2.34900
$416$	425368.			0.120512
$417$	−1.58729e6	−	490237.i	−0.447008	−	0.138059i
$418$			156467.i			0.0438008i
$419$	151699.			0.0422130			0.0211065	−	0.999777i	$-0.493281\pi$
$419$	151699.			0.0422130			0.0211065	+	0.999777i	$0.493281\pi$
$420$	−1.06970e7	+	1.55936e6i	−2.95897	+	0.431345i
$421$	4.56414e6			1.25503			0.627514	−	0.778605i	$-0.284072\pi$
$421$	4.56414e6			1.25503			0.627514	+	0.778605i	$0.284072\pi$
$422$		−	990276.i		−	0.270692i
$423$	−4.66313e6	−	3.18417e6i	−1.26715	−	0.865258i
$424$	8.37677e6			2.26288
$425$	1.83094e6			0.491702
$426$	2.54932e6	−	8.25419e6i	0.680614	−	2.20369i
$427$	1.41588e6	−	674046.i	0.375800	−	0.178904i
$428$			1.19028e7i			3.14080i
$429$	69383.8	−	224651.i	0.0182018	−	0.0589338i
$430$			1.18941e7i			3.10214i
$431$			2.09819e6i			0.544065i	0.962288	+	0.272033i	$0.0876959\pi$
$431$			2.09819e6i			0.544065i	−0.962288	+	0.272033i	$0.912304\pi$
$432$	−5.82835e6	+	4.63770e6i	−1.50258	+	1.19562i
$433$			1.90211e6i			0.487545i	0.969832	+	0.243773i	$0.0783850\pi$
$433$			1.90211e6i			0.487545i	−0.969832	+	0.243773i	$0.921615\pi$
$434$	3.00099e6	+	6.30379e6i	0.764787	+	1.60649i
$435$	−1.71370e6	−	529279.i	−0.434221	−	0.134110i
$436$	−5.89685e6			−1.48561
$437$	63431.4			0.0158892
$438$	3.47394e6	−	1.12479e7i	0.865241	−	2.80147i
$439$		−	5.44478e6i		−	1.34840i	−0.738548	−	0.674200i	$-0.764488\pi$
$439$		−	5.44478e6i		−	1.34840i	0.738548	−	0.674200i	$-0.235512\pi$
$440$	7.32368e6			1.80342
$441$	3.91413e6	−	1.16595e6i	0.958383	−	0.285484i
$442$	528938.			0.128780
$443$		−	3.14646e6i		−	0.761750i	−0.924626	−	0.380875i	$-0.875623\pi$
$443$		−	3.14646e6i		−	0.761750i	0.924626	−	0.380875i	$-0.124377\pi$
$444$	−3.79625e6	+	1.22915e7i	−0.913898	+	2.95901i
$445$	5.26194e6			1.25964
$446$	−4.49518e6			−1.07006
$447$	3.49253e6	+	1.07868e6i	0.826746	+	0.255342i
$448$	−325665.	−	684083.i	−0.0766614	−	0.161033i
$449$		−	3.39222e6i		−	0.794086i	−0.917800	−	0.397043i	$-0.870036\pi$
$449$		−	3.39222e6i		−	0.794086i	0.917800	−	0.397043i	$-0.129964\pi$
$450$	−3.15586e6	+	4.62166e6i	−0.734659	+	1.07589i
$451$		−	903345.i		−	0.209128i
$452$			1.21727e7i			2.80246i
$453$	−381094.	+	1.23391e6i	−0.0872543	+	0.282512i
$454$		−	7.19301e6i		−	1.63784i
$455$	−543782.	+	258873.i	−0.123139	+	0.0586218i
$456$	123929.	−	401258.i	0.0279102	−	0.0903674i
$457$	1.15372e6			0.258411			0.129206	−	0.991618i	$-0.458757\pi$
$457$	1.15372e6			0.258411			0.129206	+	0.991618i	$0.458757\pi$
$458$	−4.28561e6			−0.954660
$459$	−2.41444e6	+	1.92120e6i	−0.534914	+	0.425639i
$460$		−	5.28761e6i		−	1.16511i
$461$	1.23356e6			0.270339			0.135170	−	0.990822i	$-0.456842\pi$
$461$	1.23356e6			0.270339			0.135170	+	0.990822i	$0.456842\pi$
$462$	−4.87617e6	+	710825.i	−1.06285	+	0.154938i
$463$	−3.22552e6			−0.699274			−0.349637	−	0.936885i	$-0.613695\pi$
$463$	−3.22552e6			−0.699274			−0.349637	+	0.936885i	$0.613695\pi$
$464$		−	3.08650e6i		−	0.665536i
$465$	5.73835e6	+	1.77230e6i	1.23071	+	0.380106i
$466$	−1.22715e7			−2.61777
$467$	−2.58165e6			−0.547780			−0.273890	−	0.961761i	$-0.588310\pi$
$467$	−2.58165e6			−0.547780			−0.273890	+	0.961761i	$0.588310\pi$
$468$	−633779.	+	928152.i	−0.133759	+	0.195886i
$469$	−1.63025e6	−	3.42445e6i	−0.342232	−	0.718883i
$470$		−	1.74511e7i		−	3.64400i
$471$	−982813.	−	303544.i	−0.204135	−	0.0630477i
$472$		−	1.44908e7i		−	2.99390i
$473$			3.76911e6i			0.774615i
$474$	7.51448e6	+	2.32087e6i	1.53622	+	0.474465i
$475$		−	144238.i		−	0.0293323i
$476$	−3.31248e6	−	6.95810e6i	−0.670094	−	1.40758i
$477$	−2.73411e6	+	4.00402e6i	−0.550199	+	0.805751i
$478$	1.27525e7			2.55286
$479$	−2.84704e6			−0.566962			−0.283481	−	0.958978i	$-0.591489\pi$
$479$	−2.84704e6			−0.566962			−0.283481	+	0.958978i	$0.591489\pi$
$480$	−7.32732e6	−	2.26306e6i	−1.45158	−	0.448325i
$481$			716706.i			0.141247i
$482$	240896.			0.0472293
$483$	288167.	+	1.97679e6i	0.0562052	+	0.385561i
$484$	−7.61974e6			−1.47852
$485$			1.32169e6i			0.255138i
$486$	−687909.	−	9.40596e6i	−0.132111	−	1.80639i
$487$	5382.73			0.00102844			0.000514221	−	1.00000i	$-0.499836\pi$
$487$	5382.73			0.00102844			0.000514221		1.00000i	$0.499836\pi$
$488$	5.07830e6			0.965314
$489$	−1.50736e6	+	4.88051e6i	−0.285065	+	0.922982i
$490$	9.79745e6	+	7.95802e6i	1.84341	+	1.49732i
$491$			623789.i			0.116771i	0.998294	+	0.0583853i	$0.0185952\pi$
$491$			623789.i			0.116771i	−0.998294	+	0.0583853i	$0.981405\pi$
$492$	−1.27425e6	+	4.12576e6i	−0.237324	+	0.768407i
$493$		−	1.27861e6i		−	0.236930i
$494$		−	41668.7i		−	0.00768232i
$495$	−2.39039e6	+	3.50066e6i	−0.438486	+	0.642150i
$496$			1.03352e7i			1.88632i
$497$	−6.33137e6	+	3.01412e6i	−1.14976	+	0.547355i
$498$	1.71580e7	+	5.29930e6i	3.10023	+	0.957514i
$499$	5.48238e6			0.985640			0.492820	−	0.870131i	$-0.335966\pi$
$499$	5.48238e6			0.985640			0.492820	+	0.870131i	$0.335966\pi$
$500$	4.69236e6			0.839395
$501$	444180.	−	1.43816e6i	0.0790615	−	0.255985i
$502$			4.95166e6i			0.876983i
$503$	−7.04138e6			−1.24090			−0.620452	−	0.784245i	$-0.713051\pi$
$503$	−7.04138e6			−1.24090			−0.620452	+	0.784245i	$0.713051\pi$
$504$	1.30679e7	+	2.03926e6i	2.29155	+	0.357599i
$505$	−8.30469e6			−1.44909
$506$		−	2.41032e6i		−	0.418503i
$507$	1.68952e6	−	5.47031e6i	0.291906	−	0.945130i
$508$	9.80301e6			1.68539
$509$	−1.23522e6			−0.211325			−0.105663	−	0.994402i	$-0.533696\pi$
$509$	−1.23522e6			−0.211325			−0.105663	+	0.994402i	$0.533696\pi$
$510$	−9.11139e6	−	2.81407e6i	−1.55117	−	0.479082i
$511$	−8.62769e6	+	4.10731e6i	−1.46165	+	0.695833i
$512$			1.32197e7i			2.22867i
$513$	151348.	+	190205.i	0.0253913	+	0.0319101i
$514$			7.14265e6i			1.19248i
$515$			2.11384e6i			0.351199i
$516$	5.31667e6	−	1.72143e7i	0.879054	−	2.84620i
$517$		−	5.53005e6i		−	0.909920i
$518$	1.35624e7	−	6.45653e6i	2.22081	−	1.05724i
$519$	−630619.	+	2.04181e6i	−0.102766	+	0.332735i
$520$	−1.95037e6			−0.316306
$521$	2.65806e6			0.429013			0.214506	−	0.976723i	$-0.431186\pi$
$521$	2.65806e6			0.429013			0.214506	+	0.976723i	$0.431186\pi$
$522$	3.22746e6	+	2.20384e6i	0.518423	+	0.354000i
$523$			8.11005e6i			1.29649i	0.761432	+	0.648245i	$0.224497\pi$
$523$			8.11005e6i			1.29649i	−0.761432	+	0.648245i	$0.775503\pi$
$524$	−1.50604e7			−2.39611
$525$	4.49506e6	−	655269.i	0.711766	−	0.103758i
$526$	−4.65885e6			−0.734200
$527$			4.28144e6i			0.671526i
$528$	−6.96980e6	−	2.15264e6i	−1.08802	−	0.336036i
$529$	5.45920e6			0.848184
$530$	−1.49845e7			−2.31714
$531$	6.92649e6	+	4.72968e6i	1.06605	+	0.727940i
$532$	−548145.	+	260951.i	−0.0839686	+	0.0399742i
$533$			240570.i			0.0366794i
$534$	−1.09550e7	−	3.38347e6i	−1.66249	−	0.513463i
$535$		−	1.19555e7i		−	1.80585i
$536$		−	1.22824e7i		−	1.84659i
$537$	−3.03367e6	−	936955.i	−0.453975	−	0.140211i
$538$			1.29232e7i			1.92493i
$539$	3.10469e6	+	2.52180e6i	0.460306	+	0.373886i
$540$	1.58554e7	−	1.26163e7i	2.33987	−	1.86187i
$541$	4.11443e6			0.604389			0.302194	−	0.953246i	$-0.402281\pi$
$541$	4.11443e6			0.604389			0.302194	+	0.953246i	$0.402281\pi$
$542$	1.80122e7			2.63372
$543$	−1.09216e7	−	3.37317e6i	−1.58960	−	0.490951i
$544$		−	5.46699e6i		−	0.792047i
$545$	5.92294e6			0.854173
$546$	1.29857e6	−	189300.i	0.186416	−	0.0271749i
$547$	8.29884e6			1.18590			0.592952	−	0.805238i	$-0.297963\pi$
$547$	8.29884e6			1.18590			0.592952	+	0.805238i	$0.297963\pi$
$548$		−	7.63013e6i		−	1.08538i
$549$	−1.65752e6	+	2.42738e6i	−0.234707	+	0.343722i
$550$	−5.48087e6			−0.772579
$551$	−100726.			−0.0141339
$552$	−1.90909e6	+	6.18125e6i	−0.266673	+	0.863432i
$553$	−2.74401e6	−	5.76398e6i	−0.381568	−	0.801511i
$554$			5.94175e6i			0.822508i
$555$	3.81305e6	−	1.23459e7i	0.525460	−	1.70133i
$556$			7.77712e6i			1.06692i
$557$		−	1.30905e7i		−	1.78780i	−0.448269	−	0.893899i	$-0.647959\pi$
$557$		−	1.30905e7i		−	1.78780i	0.448269	−	0.893899i	$-0.352041\pi$
$558$	−1.08072e7	−	7.37960e6i	−1.46936	−	1.00334i
$559$		−	1.00375e6i		−	0.135861i
$560$	8.03157e6	+	1.68709e7i	1.08226	+	2.27336i
$561$	−2.88729e6	−	891746.i	−0.387332	−	0.119628i
$562$	−9.09258e6			−1.21436
$563$	1.39979e7			1.86119			0.930595	−	0.366051i	$-0.119290\pi$
$563$	1.39979e7			1.86119			0.930595	+	0.366051i	$0.119290\pi$
$564$	−7.80064e6	+	2.52569e7i	−1.03260	+	3.34335i
$565$		−	1.22265e7i		−	1.61132i
$566$	7.12760e6			0.935195
$567$	−5.24000e6	+	5.58075e6i	−0.684501	+	0.729012i
$568$	−2.27085e7			−2.95337
$569$			7.90475e6i			1.02355i	0.859121	+	0.511773i	$0.171011\pi$
$569$			7.90475e6i			1.02355i	−0.859121	+	0.511773i	$0.828989\pi$
$570$	−221687.	+	717778.i	−0.0285794	+	0.0925343i
$571$	2.34007e6			0.300358			0.150179	−	0.988659i	$-0.452015\pi$
$571$	2.34007e6			0.300358			0.150179	+	0.988659i	$0.452015\pi$
$572$	−1.10070e6			−0.140663
$573$	−1.14482e7	−	3.53580e6i	−1.45664	−	0.449885i
$574$	4.55236e6	−	2.16720e6i	0.576709	−	0.274549i
$575$			2.22194e6i			0.280261i
$576$	1.17279e6	+	800829.i	0.147287	+	0.100573i
$577$			1.34986e7i			1.68791i	0.536417	+	0.843953i	$0.319777\pi$
$577$			1.34986e7i			1.68791i	−0.536417	+	0.843953i	$0.680223\pi$
$578$			7.74947e6i			0.964833i
$579$	−1.27911e6	+	4.14149e6i	−0.158566	+	0.513405i
$580$			8.39648e6i			1.03640i
$581$	−6.26547e6	−	1.31611e7i	−0.770040	−	1.61752i
$582$	849855.	−	2.75166e6i	0.104001	−	0.336734i
$583$	−4.74841e6			−0.578598
$584$	−3.09447e7			−3.75452
$585$	636584.	−	932258.i	0.0769070	−	0.112628i
$586$		−	2.47723e7i		−	2.98004i
$587$	3.29677e6			0.394906			0.197453	−	0.980312i	$-0.436733\pi$
$587$	3.29677e6			0.394906			0.197453	+	0.980312i	$0.436733\pi$
$588$	−1.06225e7	−	1.58970e7i	−1.26702	−	1.89615i
$589$	337283.			0.0400596
$590$			2.59214e7i			3.06569i
$591$	3.34076e6	+	1.03180e6i	0.393438	+	0.121514i
$592$	2.22359e7			2.60765
$593$	142588.			0.0166512			0.00832562	−	0.999965i	$-0.497350\pi$
$593$	142588.			0.0166512			0.00832562	+	0.999965i	$0.497350\pi$
$594$	7.22756e6	−	5.75107e6i	0.840476	−	0.668778i
$595$	3.32714e6	+	6.98888e6i	0.385282	+	0.809311i
$596$		−	1.71121e7i		−	1.97328i
$597$	4.22449e6	+	1.30474e6i	0.485108	+	0.149827i
$598$			641892.i			0.0734022i
$599$		−	7.94570e6i		−	0.904826i	−0.891808	−	0.452413i	$-0.850563\pi$
$599$		−	7.94570e6i		−	0.904826i	0.891808	−	0.452413i	$-0.149437\pi$
$600$	1.40557e7	+	4.34112e6i	1.59394	+	0.492293i
$601$			9.95474e6i			1.12420i	0.827069	+	0.562100i	$0.190006\pi$
$601$			9.95474e6i			1.12420i	−0.827069	+	0.562100i	$0.809994\pi$
$602$	−1.89942e7	+	9.04241e6i	−2.13614	+	1.01693i
$603$	5.87087e6	+	4.00886e6i	0.657520	+	0.448981i
$604$	6.04568e6			0.674299
$605$	7.65345e6			0.850098
$606$	1.72897e7	+	5.33997e6i	1.91252	+	0.590687i
$607$			1.09452e7i			1.20574i	0.797841	+	0.602868i	$0.205975\pi$
$607$			1.09452e7i			1.20574i	−0.797841	+	0.602868i	$0.794025\pi$
$608$	−430679.			−0.0472492
$609$	−457596.	−	3.13905e6i	−0.0499964	−	0.342969i
$610$	−9.08415e6			−0.988461
$611$			1.47271e6i			0.159593i
$612$	1.19289e7	+	8.14557e6i	1.28743	+	0.879109i
$613$	−4.24023e6			−0.455762			−0.227881	−	0.973689i	$-0.573180\pi$
$613$	−4.24023e6			−0.455762			−0.227881	+	0.973689i	$0.573180\pi$
$614$	2.15657e7			2.30857
$615$	1.27989e6	−	4.14401e6i	0.136453	−	0.441808i
$616$	5.56776e6	+	1.16955e7i	0.591192	+	1.24184i
$617$		−	7.07280e6i		−	0.747961i	−0.927437	−	0.373980i	$-0.877993\pi$
$617$		−	7.07280e6i		−	0.747961i	0.927437	−	0.373980i	$-0.122007\pi$
$618$	1.35921e6	−	4.40085e6i	0.143158	−	0.463517i
$619$		−	1.48040e7i		−	1.55293i	−0.630158	−	0.776467i	$-0.717010\pi$
$619$		−	1.48040e7i		−	1.55293i	0.630158	−	0.776467i	$-0.282990\pi$
$620$		−	2.81158e7i		−	2.93745i
$621$	−2.33147e6	−	2.93004e6i	−0.242606	−	0.304891i
$622$		−	1.36429e7i		−	1.41394i
$623$	4.00034e6	+	8.40300e6i	0.412931	+	0.867390i
$624$	1.85612e6	+	573268.i	0.190830	+	0.0589381i
$625$	−1.17374e7			−1.20191
$626$	−2.75307e7			−2.80790
$627$	−70250.0	+	227455.i	−0.00713638	+	0.0231061i
$628$			4.81542e6i			0.487231i
$629$	9.21137e6			0.928320
$630$	−2.33761e7	−	3.64786e6i	−2.34650	−	0.366174i
$631$	1.72214e7			1.72184			0.860922	−	0.508737i	$-0.169887\pi$
$631$	1.72214e7			1.72184			0.860922	+	0.508737i	$0.169887\pi$
$632$		−	2.06735e7i		−	2.05883i
$633$	444611.	−	1.43956e6i	0.0441033	−	0.142797i
$634$	−1.40345e7			−1.38667
$635$	−9.84639e6			−0.969042
$636$	2.16869e7	+	6.69806e6i	2.12596	+	0.656608i
$637$	−826810.	−	671580.i	−0.0807341	−	0.0655766i
$638$			3.82748e6i			0.372272i
$639$	7.41188e6	−	1.08545e7i	0.718085	−	1.05162i
$640$		−	1.13536e7i		−	1.09568i
$641$			1.86269e7i			1.79059i	0.445476	+	0.895294i	$0.353035\pi$
$641$			1.86269e7i			1.79059i	−0.445476	+	0.895294i	$0.646965\pi$
$642$	−7.68746e6	+	2.48904e7i	−0.736114	+	2.38339i
$643$		−	5.13948e6i		−	0.490221i	−0.969495	−	0.245111i	$-0.921176\pi$
$643$		−	5.13948e6i		−	0.490221i	0.969495	−	0.245111i	$-0.0788243\pi$
$644$	8.44399e6	−	4.01986e6i	0.802293	−	0.381941i
$645$	−5.34019e6	+	1.72905e7i	−0.505426	+	1.63647i
$646$	−535541.			−0.0504907
$647$	−3.15049e6			−0.295881			−0.147940	−	0.988996i	$-0.547264\pi$
$647$	−3.15049e6			−0.295881			−0.147940	+	0.988996i	$0.547264\pi$
$648$	−2.30901e7	+	9.02398e6i	−2.16017	+	0.844230i
$649$			8.21419e6i			0.765514i
$650$	1.45961e6			0.135504
$651$	1.53227e6	+	1.05112e7i	0.141704	+	0.972072i
$652$	2.39127e7			2.20298
$653$			1.93756e7i			1.77817i	0.457745	+	0.889083i	$0.348657\pi$
$653$			1.93756e7i			1.77817i	−0.457745	+	0.889083i	$0.651343\pi$
$654$	−1.23311e7	−	3.80849e6i	−1.12735	−	0.348184i
$655$	1.51270e7			1.37768
$656$	7.46369e6			0.677164
$657$	1.01001e7	−	1.47913e7i	0.912877	−	1.33688i
$658$	2.78684e7	−	1.32671e7i	2.50927	−	1.19457i
$659$		−	1.33721e7i		−	1.19946i	−0.800201	−	0.599732i	$-0.795274\pi$
$659$		−	1.33721e7i		−	1.19946i	0.800201	−	0.599732i	$-0.204726\pi$
$660$	1.89606e7	+	5.85601e6i	1.69430	+	0.523290i
$661$			1.20025e7i			1.06848i	0.845333	+	0.534241i	$0.179402\pi$
$661$			1.20025e7i			1.06848i	−0.845333	+	0.534241i	$0.820598\pi$
$662$		−	6.92007e6i		−	0.613714i
$663$	768913.	+	237481.i	0.0679350	+	0.0209819i
$664$		−	4.72044e7i		−	4.15491i
$665$	550571.	−	262105.i	0.0482791	−	0.0229838i
$666$	−1.58770e7	+	2.32514e7i	−1.38702	+	2.03125i
$667$	1.55165e6			0.135045
$668$	−7.04647e6			−0.610985
$669$	−6.53462e6	−	2.01823e6i	−0.564488	−	0.174343i
$670$			2.19709e7i			1.89087i
$671$	−2.87866e6			−0.246822
$672$	−1.95656e6	−	1.34218e7i	−0.167136	−	1.14653i
$673$	−1.60189e7			−1.36331			−0.681654	−	0.731675i	$-0.738739\pi$
$673$	−1.60189e7			−1.36331			−0.681654	+	0.731675i	$0.738739\pi$
$674$		−	1.14460e7i		−	0.970519i
$675$	−6.66267e6	+	5.30158e6i	−0.562845	+	0.447863i
$676$	−2.68025e7			−2.25584
$677$	−1.36964e7			−1.14851			−0.574257	−	0.818675i	$-0.694709\pi$
$677$	−1.36964e7			−1.14851			−0.574257	+	0.818675i	$0.694709\pi$
$678$	−7.86174e6	+	2.54547e7i	−0.656817	+	2.12664i
$679$	−2.11065e6	+	1.00480e6i	−0.175688	+	0.0836384i
$680$			2.50668e7i			2.07887i
$681$	3.22949e6	−	1.04564e7i	0.266850	−	0.864005i
$682$		−	1.28164e7i		−	1.05513i
$683$			1.15151e7i			0.944532i	0.881456	+	0.472266i	$0.156564\pi$
$683$			1.15151e7i			0.944532i	−0.881456	+	0.472266i	$0.843436\pi$
$684$	641692.	−	939739.i	0.0524429	−	0.0768010i
$685$			7.66389e6i			0.624055i
$686$	−5.26005e6	+	2.16959e7i	−0.426756	+	1.76022i
$687$	−6.22996e6	−	1.92414e6i	−0.503609	−	0.155541i
$688$	−3.11414e7			−2.50823
$689$	1.26455e6			0.101482
$690$	3.41502e6	−	1.10571e7i	0.273068	−	0.884137i
$691$		−	3.17540e6i		−	0.252990i	−0.991967	−	0.126495i	$-0.959627\pi$
$691$		−	3.17540e6i		−	0.252990i	0.991967	−	0.126495i	$-0.0403728\pi$
$692$	1.00041e7			0.794171
$693$	−7.40760e6	−	1.15596e6i	−0.585928	−	0.0914347i
$694$	−8.25205e6			−0.650374
$695$		−	7.81153e6i		−	0.613443i
$696$	3.03155e6	−	9.81552e6i	0.237214	−	0.768052i
$697$	3.09189e6			0.241069
$698$	3.76712e7			2.92665
$699$	−1.78390e7	−	5.50961e6i	−1.38095	−	0.426509i
$700$	−9.14083e6	−	1.92010e7i	−0.705084	−	1.48108i
$701$		−	508437.i		−	0.0390789i	−0.999809	−	0.0195394i	$-0.993780\pi$
$701$		−	508437.i		−	0.0390789i	0.999809	−	0.0195394i	$-0.00621999\pi$
$702$	−1.92477e6	+	1.53156e6i	−0.147413	+	0.117299i
$703$		−	725654.i		−	0.0553785i
$704$			1.39082e6i			0.105765i
$705$	7.83515e6	−	2.53686e7i	0.593710	−	1.92231i
$706$			2.61137e7i			1.97177i
$707$	−6.31356e6	−	1.32621e7i	−0.475035	−	0.997845i
$708$	1.15868e7	−	3.75158e7i	0.868725	−	2.81275i
$709$	−1.24662e7			−0.931366			−0.465683	−	0.884952i	$-0.654191\pi$
$709$	−1.24662e7			−0.931366			−0.465683	+	0.884952i	$0.654191\pi$
$710$	4.06214e7			3.02419
$711$	9.88175e6	+	6.74766e6i	0.733094	+	0.500586i
$712$			3.01388e7i			2.22805i
$713$	−5.19574e6			−0.382757
$714$	−2.43295e6	−	1.66897e7i	−0.178602	−	1.22519i
$715$	1.10557e6			0.0808766
$716$			1.48638e7i			1.08355i
$717$	1.85383e7	+	5.72560e6i	1.34670	+	0.415932i
$718$	2.81080e7			2.03479
$719$	1.61840e7			1.16752			0.583760	−	0.811926i	$-0.301581\pi$
$719$	1.61840e7			1.16752			0.583760	+	0.811926i	$0.301581\pi$
$720$	−2.89234e7	−	1.97501e7i	−2.07930	−	1.41983i
$721$	−3.37567e6	+	1.60702e6i	−0.241836	+	0.115129i
$722$		−	2.53274e7i		−	1.80821i
$723$	350189.	+	108157.i	0.0249147	+	0.00769498i
$724$			5.35119e7i			3.79406i
$725$		−	3.52833e6i		−	0.249301i
$726$	−1.59339e7	−	4.92122e6i	−1.12197	−	0.346523i
$727$		−	1.37063e7i		−	0.961796i	−0.876776	−	0.480898i	$-0.840311\pi$
$727$		−	1.37063e7i		−	0.961796i	0.876776	−	0.480898i	$-0.159689\pi$
$728$	−1.48275e6	−	3.11461e6i	−0.103690	−	0.217809i
$729$	3.22305e6	−	1.39822e7i	0.224620	−	0.974447i
$730$	5.53544e7			3.84455
$731$	−1.29006e7			−0.892926
$732$	1.31474e7	+	4.06061e6i	0.906906	+	0.280100i
$733$		−	2.11177e7i		−	1.45173i	−0.687837	−	0.725865i	$-0.741440\pi$
$733$		−	2.11177e7i		−	1.45173i	0.687837	−	0.725865i	$-0.258560\pi$
$734$	−3.11889e7			−2.13678
$735$	1.06695e7	+	1.59674e7i	0.728496	+	1.09022i
$736$	6.63446e6			0.451451
$737$			6.96232e6i			0.472156i
$738$	−5.32926e6	+	7.80455e6i	−0.360185	+	0.527481i
$739$	−2.27372e7			−1.53153			−0.765765	−	0.643121i	$-0.777639\pi$
$739$	−2.27372e7			−1.53153			−0.765765	+	0.643121i	$0.777639\pi$
$740$	−6.04902e7			−4.06074
$741$	18708.3	−	60573.5i	0.00125166	−	0.00405263i
$742$	−1.13918e7	−	2.39293e7i	−0.759598	−	1.59559i
$743$		−	8.15459e6i		−	0.541914i	−0.962592	−	0.270957i	$-0.912660\pi$
$743$		−	8.15459e6i		−	0.541914i	0.962592	−	0.270957i	$-0.0873400\pi$
$744$	−1.01512e7	+	3.28675e7i	−0.672334	+	2.17688i
$745$			1.71878e7i			1.13457i
$746$			1.16428e7i			0.765967i
$747$	2.25633e7	+	1.54071e7i	1.47945	+	1.01023i
$748$			1.41467e7i			0.924485i
$749$	1.90922e7	−	9.08904e6i	1.24351	−	0.591989i
$750$	9.81237e6	+	3.03057e6i	0.636973	+	0.196730i
$751$	−9.59688e6			−0.620912			−0.310456	−	0.950588i	$-0.600482\pi$
$751$	−9.59688e6			−0.620912			−0.310456	+	0.950588i	$0.600482\pi$
$752$	4.56908e7			2.94635
$753$	−2.22318e6	+	7.19820e6i	−0.142885	+	0.462633i
$754$		−	1.01929e6i		−	0.0652936i
$755$	−6.07243e6			−0.387699
$756$	3.22014e7	+	1.57286e7i	2.04913	+	1.00089i
$757$	−1.27794e7			−0.810535			−0.405267	−	0.914198i	$-0.632822\pi$
$757$	−1.27794e7			−0.810535			−0.405267	+	0.914198i	$0.632822\pi$
$758$		−	2.17175e7i		−	1.37289i
$759$	1.08218e6	−	3.50387e6i	0.0681859	−	0.220772i
$760$	1.97472e6			0.124014
$761$	−1.82472e7			−1.14218			−0.571091	−	0.820886i	$-0.693480\pi$
$761$	−1.82472e7			−1.14218			−0.571091	+	0.820886i	$0.693480\pi$
$762$	2.04994e7	+	6.33130e6i	1.27895	+	0.395007i
$763$	4.50286e6	+	9.45857e6i	0.280012	+	0.588185i
$764$			5.60920e7i			3.47670i
$765$	−1.19817e7	−	8.18161e6i	−0.740229	−	0.505458i
$766$		−	4.54301e7i		−	2.79751i
$767$		−	2.18752e6i		−	0.134265i
$768$	−8.16073e6	+	2.64228e7i	−0.499259	+	1.61650i
$769$		−	1.88190e6i		−	0.114757i	−0.998352	−	0.0573787i	$-0.981726\pi$
$769$		−	1.88190e6i		−	0.114757i	0.998352	−	0.0573787i	$-0.0182743\pi$
$770$	−9.95970e6	−	2.09211e7i	−0.605368	−	1.27162i
$771$	−3.20688e6	+	1.03832e7i	−0.194288	+	0.629066i
$772$	2.02918e7			1.22540
$773$	−1.03151e7			−0.620903			−0.310452	−	0.950589i	$-0.600480\pi$
$773$	−1.03151e7			−0.620903			−0.310452	+	0.950589i	$0.600480\pi$
$774$	2.22358e7	−	3.25636e7i	1.33413	−	1.95380i
$775$			1.18147e7i			0.706590i
$776$	−7.57022e6			−0.451288
$777$	2.26144e7	−	3.29662e6i	1.34379	−	0.195892i
$778$	5.07914e6			0.300844
$779$		−	243573.i		−	0.0143809i
$780$	−5.04938e6	−	1.55951e6i	−0.297168	−	0.0917809i
$781$	1.28724e7			0.755150
$782$	8.24983e6			0.482423
$783$	3.70227e6	+	4.65276e6i	0.215806	+	0.271210i
$784$	−2.08358e7	+	2.56518e7i	−1.21065	+	1.49049i
$785$		−	4.83672e6i		−	0.280141i
$786$	−3.14933e7	−	9.72677e6i	−1.81828	−	0.561581i
$787$		−	3.28643e6i		−	0.189142i	−0.995518	−	0.0945709i	$-0.969852\pi$
$787$		−	3.28643e6i		−	0.189142i	0.995518	−	0.0945709i	$-0.0301479\pi$
$788$		−	1.63685e7i		−	0.939059i
$789$	−6.77254e6	−	2.09171e6i	−0.387311	−	0.119622i
$790$			3.69811e7i			2.10820i
$791$	1.95250e7	−	9.29509e6i	1.10956	−	0.528217i
$792$	−2.00507e7	−	1.36914e7i	−1.13584	−	0.775595i
$793$	766614.			0.0432906
$794$	204439.			0.0115083
$795$	−2.17829e7	−	6.72770e6i	−1.22236	−	0.377527i
$796$		−	2.06984e7i		−	1.15786i
$797$	−2.39117e7			−1.33341			−0.666706	−	0.745321i	$-0.732296\pi$
$797$	−2.39117e7			−1.33341			−0.666706	+	0.745321i	$0.732296\pi$
$798$	−1.31478e6	+	191663.i	−0.0730881	+	0.0106544i
$799$	1.89278e7			1.04890
$800$		−	1.50862e7i		−	0.833404i
$801$	−1.44061e7	−	9.83706e6i	−0.793350	−	0.541731i
$802$	−3.36036e7			−1.84480
$803$	1.75411e7			0.959995
$804$	9.82097e6	−	3.17983e7i	0.535814	−	1.73486i
$805$	−8.48136e6	+	4.03764e6i	−0.461292	+	0.219603i
$806$			3.41313e6i			0.185061i
$807$	−5.80223e6	+	1.87864e7i	−0.313625	+	1.01545i
$808$		−	4.75667e7i		−	2.56315i
$809$		−	8.55140e6i		−	0.459374i	−0.973265	−	0.229687i	$-0.926230\pi$
$809$		−	8.55140e6i		−	0.459374i	0.973265	−	0.229687i	$-0.0737702\pi$
$810$	4.13040e7	−	1.61423e7i	2.21197	−	0.864474i
$811$		−	1.95536e7i		−	1.04394i	−0.852965	−	0.521968i	$-0.825198\pi$
$811$		−	1.95536e7i		−	1.04394i	0.852965	−	0.521968i	$-0.174802\pi$
$812$	−1.34087e7	+	6.38334e6i	−0.713667	+	0.339749i
$813$	2.61843e7	+	8.08707e6i	1.38936	+	0.429106i
$814$	−2.75740e7			−1.45861
$815$	−2.40185e7			−1.26664
$816$	7.36785e6	−	2.38556e7i	0.387361	−	1.25419i
$817$			1.01628e6i			0.0532671i
$818$	1.94245e7			1.01500
$819$	1.97272e6	+	307844.i	0.102767	+	0.0160369i
$820$	−2.03041e7			−1.05451
$821$			3.61123e6i			0.186981i	0.995620	+	0.0934905i	$0.0298025\pi$
$821$			3.61123e6i			0.186981i	−0.995620	+	0.0934905i	$0.970198\pi$
$822$	4.92794e6	−	1.59556e7i	0.254382	−	0.823635i
$823$	2.73413e7			1.40708			0.703541	−	0.710654i	$-0.251601\pi$
$823$	2.73413e7			1.40708			0.703541	+	0.710654i	$0.251601\pi$
$824$	−1.21074e7			−0.621202
$825$	−7.96752e6	−	2.46079e6i	−0.407557	−	0.125875i
$826$	−4.13949e7	+	1.97065e7i	−2.11104	+	1.00499i
$827$			1.08272e7i			0.550491i	0.961374	+	0.275246i	$0.0887592\pi$
$827$			1.08272e7i			0.550491i	−0.961374	+	0.275246i	$0.911241\pi$
$828$	−9.88505e6	+	1.44764e7i	−0.501075	+	0.733810i
$829$			3.47853e7i			1.75796i	0.476856	+	0.878982i	$0.341776\pi$
$829$			3.47853e7i			1.75796i	−0.476856	+	0.878982i	$0.658224\pi$
$830$			8.44400e7i			4.25455i
$831$	−2.66771e6	+	8.63749e6i	−0.134010	+	0.433896i
$832$		−	370390.i		−	0.0185503i
$833$	−8.63139e6	+	1.06265e7i	−0.430991	+	0.530611i
$834$	−5.02287e6	+	1.62630e7i	−0.250056	+	0.809629i
$835$	7.07765e6			0.351296
$836$	1.11445e6			0.0551497
$837$	−1.23971e7	−	1.55799e7i	−0.611655	−	0.768688i
$838$		−	1.55427e6i		−	0.0764570i
$839$	1.55238e7			0.761363			0.380681	−	0.924706i	$-0.375689\pi$
$839$	1.55238e7			0.761363			0.380681	+	0.924706i	$0.375689\pi$
$840$	8.97107e6	+	6.15404e7i	0.438678	+	3.00928i
$841$	1.80472e7			0.879873
$842$		−	4.67632e7i		−	2.27313i
$843$	−1.32178e7	−	4.08236e6i	−0.640606	−	0.197853i
$844$	−7.05330e6			−0.340829
$845$	2.69211e7			1.29703
$846$	−3.26244e7	+	4.77775e7i	−1.56717	+	2.29508i
$847$	5.81846e6	+	1.22221e7i	0.278676	+	0.585379i
$848$		−	3.92327e7i		−	1.87352i
$849$	1.03614e7	+	3.20013e6i	0.493341	+	0.152369i
$850$		−	1.87594e7i		−	0.890579i
$851$			1.11785e7i			0.529124i
$852$	−5.87910e7	−	1.81577e7i	−2.77467	−	0.856964i
$853$		−	2.03197e7i		−	0.956189i	−0.878308	−	0.478095i	$-0.841328\pi$
$853$		−	2.03197e7i		−	0.956189i	0.878308	−	0.478095i	$-0.158672\pi$
$854$	−6.90614e6	−	1.45068e7i	−0.324034	−	0.680656i
$855$	−644531.	+	943897.i	−0.0301529	+	0.0441580i
$856$	6.84773e7			3.19420
$857$	−1.04717e6			−0.0487043			−0.0243521	−	0.999703i	$-0.507752\pi$
$857$	−1.04717e6			−0.0487043			−0.0243521	+	0.999703i	$0.507752\pi$
$858$	−2.30172e6	−	710892.i	−0.106742	−	0.0329675i
$859$		−	1.42509e7i		−	0.658958i	−0.944163	−	0.329479i	$-0.893127\pi$
$859$		−	1.42509e7i		−	0.658958i	0.944163	−	0.329479i	$-0.106873\pi$
$860$	8.47168e7			3.90592
$861$	7.59076e6	−	1.10654e6i	0.348961	−	0.0508699i
$862$	2.14976e7			0.985421
$863$			3.45867e7i			1.58082i	0.612578	+	0.790410i	$0.290132\pi$
$863$			3.45867e7i			1.58082i	−0.612578	+	0.790410i	$0.709868\pi$
$864$	1.58299e7	+	1.98940e7i	0.721431	+	0.906646i
$865$	−1.00484e7			−0.456622
$866$	1.94886e7			0.883051
$867$	−3.47933e6	+	1.12654e7i	−0.157198	+	0.508976i
$868$	4.48992e7	−	2.13748e7i	2.02274	−	0.962946i
$869$			1.17189e7i			0.526425i
$870$	−5.42289e6	+	1.75582e7i	−0.242903	+	0.786469i
$871$		−	1.85413e6i		−	0.0828124i
$872$			3.39248e7i			1.51086i
$873$	2.47086e6	−	3.61850e6i	0.109727	−	0.160692i
$874$		−	649905.i		−	0.0287787i
$875$	−3.58311e6	−	7.52657e6i	−0.158212	−	0.332336i
$876$	−8.01139e7	−	2.47434e7i	−3.52734	−	1.08943i
$877$	3.46186e7			1.51988			0.759942	−	0.649990i	$-0.225227\pi$
$877$	3.46186e7			1.51988			0.759942	+	0.649990i	$0.225227\pi$
$878$	−5.57861e7			−2.44225
$879$	1.11222e7	−	3.60114e7i	0.485532	−	1.57205i
$880$		−	3.43005e7i		−	1.49312i
$881$	1.09303e7			0.474451			0.237226	−	0.971455i	$-0.423762\pi$
$881$	1.09303e7			0.474451			0.237226	+	0.971455i	$0.423762\pi$
$882$	−1.19460e7	−	4.01034e7i	−0.517074	−	1.73584i
$883$	−4.16221e7			−1.79648			−0.898240	−	0.439505i	$-0.855154\pi$
$883$	−4.16221e7			−1.79648			−0.898240	+	0.439505i	$0.855154\pi$
$884$		−	3.76739e6i		−	0.162147i
$885$	−1.16381e7	+	3.76818e7i	−0.499487	+	1.61724i
$886$	−3.22380e7			−1.37970
$887$	−1.21043e7			−0.516572			−0.258286	−	0.966068i	$-0.583158\pi$
$887$	−1.21043e7			−0.516572			−0.258286	+	0.966068i	$0.583158\pi$
$888$	7.07133e7	+	2.18400e7i	3.00932	+	0.929436i
$889$	−7.48562e6	−	1.57241e7i	−0.317668	−	0.667284i
$890$		−	5.39128e7i		−	2.28148i
$891$	1.30888e7	−	5.11529e6i	0.552337	−	0.215862i
$892$			3.20172e7i			1.34732i
$893$		−	1.49109e6i		−	0.0625714i
$894$	1.10519e7	−	3.57838e7i	0.462480	−	1.49742i
$895$		−	1.49296e7i		−	0.623004i
$896$	1.81310e7	−	8.63146e6i	0.754487	−	0.359182i
$897$	−288194.	+	933114.i	−0.0119593	+	0.0387216i
$898$	−3.47560e7			−1.43826
$899$	8.25058e6			0.340475
$900$	3.29181e7	+	2.24778e7i	1.35465	+	0.925012i
$901$		−	1.62524e7i		−	0.666970i
$902$	−9.25549e6			−0.378777
$903$	−3.16716e7	+	4.61694e6i	−1.29256	+	0.188423i
$904$	7.00297e7			2.85011
$905$		−	5.37487e7i		−	2.18146i
$906$	1.26423e7	+	3.90462e6i	0.511690	+	0.158037i
$907$	−1.45100e7			−0.585664			−0.292832	−	0.956164i	$-0.594598\pi$
$907$	−1.45100e7			−0.585664			−0.292832	+	0.956164i	$0.594598\pi$
$908$	−5.12327e7			−2.06221
$909$	2.27365e7	+	1.55254e7i	0.912669	+	0.623207i
$910$	2.65236e6	+	5.57148e6i	0.106177	+	0.223032i
$911$		−	4.04836e6i		−	0.161616i	−0.996730	−	0.0808078i	$-0.974250\pi$
$911$		−	4.04836e6i		−	0.161616i	0.996730	−	0.0808078i	$-0.0257500\pi$
$912$	−1.87930e6	−	580425.i	−0.0748184	−	0.0231078i
$913$			2.67580e7i			1.06237i
$914$		−	1.18208e7i		−	0.468040i
$915$	−1.32056e7	−	4.07857e6i	−0.521440	−	0.161048i
$916$			3.05245e7i			1.20202i
$917$	1.15002e7	+	2.41569e7i	0.451628	+	0.948676i
$918$	1.96842e7	+	2.47378e7i	0.770924	+	0.968846i
$919$	−4.05052e6			−0.158206			−0.0791028	−	0.996866i	$-0.525206\pi$
$919$	−4.05052e6			−0.158206			−0.0791028	+	0.996866i	$0.525206\pi$
$920$	−3.04198e7			−1.18491
$921$	3.13500e7	+	9.68252e6i	1.21784	+	0.376131i
$922$		−	1.26388e7i		−	0.489644i
$923$	−3.42805e6			−0.132447
$924$	5.06290e6	+	3.47308e7i	0.195083	+	1.33824i
$925$	2.54189e7			0.976792
$926$			3.30480e7i			1.26654i
$927$	3.95176e6	−	5.78724e6i	0.151040	−	0.221193i
$928$	−1.05352e7			−0.401581
$929$	3.41602e7			1.29862			0.649308	−	0.760525i	$-0.275059\pi$
$929$	3.41602e7			1.29862			0.649308	+	0.760525i	$0.275059\pi$
$930$	1.81586e7	−	5.87940e7i	0.688456	−	2.22908i
$931$	837132.	+	679964.i	0.0316534	+	0.0257106i
$932$			8.74044e7i			3.29605i
$933$	6.12535e6	−	1.98326e7i	0.230370	−	0.745892i
$934$			2.64511e7i			0.992148i
$935$		−	1.42093e7i		−	0.531548i
$936$	5.33969e6	+	3.64615e6i	0.199217	+	0.136033i
$937$			2.79009e7i			1.03817i	0.854722	+	0.519086i	$0.173727\pi$
$937$			2.79009e7i			1.03817i	−0.854722	+	0.519086i	$0.826273\pi$
$938$	−3.50862e7	+	1.67032e7i	−1.30205	+	0.619858i
$939$	−4.00213e7	−	1.23607e7i	−1.48124	−	0.457486i
$940$	−1.24297e8			−4.58818
$941$	3.53618e7			1.30185			0.650925	−	0.759142i	$-0.274381\pi$
$941$	3.53618e7			1.30185			0.650925	+	0.759142i	$0.274381\pi$
$942$	−3.11005e6	+	1.00697e7i	−0.114193	+	0.369734i
$943$			3.75216e6i			0.137405i
$944$	−6.78679e7			−2.47876
$945$	−3.23439e7	−	1.57982e7i	−1.17818	−	0.575477i
$946$	3.86175e7			1.40300
$947$		−	1.35602e6i		−	0.0491349i	−0.999698	−	0.0245675i	$-0.992179\pi$
$947$		−	1.35602e6i		−	0.0491349i	0.999698	−	0.0245675i	$-0.00782085\pi$
$948$	1.65305e7	−	5.35224e7i	0.597400	−	1.93426i
$949$	−4.67138e6			−0.168376
$950$	−1.47783e6			−0.0531271
$951$	−2.04019e7	−	6.30117e6i	−0.731508	−	0.225928i
$952$	−4.00302e7	+	1.90568e7i	−1.43151	+	0.681487i
$953$			3.25424e6i			0.116069i	0.998315	+	0.0580346i	$0.0184834\pi$
$953$			3.25424e6i			0.116069i	−0.998315	+	0.0580346i	$0.981517\pi$
$954$	4.10244e7	+	2.80131e7i	1.45939	+	0.996530i
$955$		−	5.63401e7i		−	1.99898i
$956$		−	9.08308e7i		−	3.21432i
$957$	−1.71845e6	+	5.56398e6i	−0.0606536	+	0.196384i
$958$			2.91702e7i			1.02689i
$959$	−1.22388e7	+	5.82640e6i	−0.429725	+	0.204576i
$960$	−1.97056e6	+	6.38028e6i	−0.0690100	+	0.223440i
$961$	1.00192e6			0.0349963
$962$	7.34322e6			0.255829
$963$	−2.23504e7	+	3.27316e7i	−0.776641	+	1.13737i
$964$		−	1.71580e6i		−	0.0594666i
$965$	−2.03815e7			−0.704561
$966$	2.02538e7	−	2.95250e6i	0.698334	−	0.101800i
$967$	−1.93276e7			−0.664680			−0.332340	−	0.943160i	$-0.607838\pi$
$967$	−1.93276e7			−0.664680			−0.332340	+	0.943160i	$0.607838\pi$
$968$			4.38366e7i			1.50366i
$969$	−778513.	−	240445.i	−0.0266352	−	0.00822635i
$970$	1.35417e7			0.462110
$971$	−603594.			−0.0205446			−0.0102723	−	0.999947i	$-0.503270\pi$
$971$	−603594.			−0.0205446			−0.0102723	+	0.999947i	$0.503270\pi$
$972$	−6.69945e7	+	4.89967e6i	−2.27444	+	0.166342i
$973$	1.24745e7	−	5.93864e6i	0.422418	−	0.201097i
$974$		−	55150.3i		−	0.00186273i
$975$	2.12183e6	+	655331.i	0.0714823	+	0.0220775i
$976$		−	2.37843e7i		−	0.799218i
$977$		−	8.97624e6i		−	0.300856i	−0.988621	−	0.150428i	$-0.951935\pi$
$977$		−	8.97624e6i		−	0.300856i	0.988621	−	0.150428i	$-0.0480651\pi$
$978$	5.00047e7	+	1.54441e7i	1.67172	+	0.516315i
$979$		−	1.70843e7i		−	0.569693i
$980$	5.66815e7	−	6.97830e7i	1.88528	−	2.32105i
$981$	−1.62157e7	−	1.10728e7i	−0.537978	−	0.367353i
$982$	6.39121e6			0.211497
$983$	−6.64620e6			−0.219376			−0.109688	−	0.993966i	$-0.534985\pi$
$983$	−6.64620e6			−0.219376			−0.109688	+	0.993966i	$0.534985\pi$
$984$	2.37356e7	+	7.33080e6i	0.781471	+	0.241359i
$985$			1.64409e7i			0.539927i
$986$	−1.31003e7			−0.429131
$987$	4.64687e7	−	6.77399e6i	1.51834	−	0.221336i
$988$	−296788.			−0.00967283
$989$		−	1.56555e7i		−	0.508951i
$990$	3.58670e7	+	2.44914e7i	1.16307	+	0.794194i
$991$	2.63927e7			0.853689			0.426844	−	0.904325i	$-0.359625\pi$
$991$	2.63927e7			0.853689			0.426844	+	0.904325i	$0.359625\pi$
$992$	3.52773e7			1.13820
$993$	3.10695e6	−	1.00597e7i	0.0999911	−	0.323751i
$994$	3.08820e7	+	6.48699e7i	0.991380	+	2.08246i
$995$			2.07900e7i			0.665728i
$996$	3.77446e7	−	1.22209e8i	1.20561	−	3.90351i
$997$		−	2.42476e7i		−	0.772558i	−0.922382	−	0.386279i	$-0.873760\pi$
$997$		−	2.42476e7i		−	0.772558i	0.922382	−	0.386279i	$-0.126240\pi$
$998$		−	5.61714e7i		−	1.78521i
$999$	−3.35196e7	+	2.66720e7i	−1.06264	+	0.845554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.c.a.20.2	yes	12
3.2	odd	2	inner	21.6.c.a.20.11	yes	12
4.3	odd	2		336.6.k.d.209.6		12
7.6	odd	2	inner	21.6.c.a.20.1	✓	12
12.11	even	2		336.6.k.d.209.8		12
21.20	even	2	inner	21.6.c.a.20.12	yes	12
28.27	even	2		336.6.k.d.209.7		12
84.83	odd	2		336.6.k.d.209.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.c.a.20.1	✓	12	7.6	odd	2	inner
21.6.c.a.20.2	yes	12	1.1	even	1	trivial
21.6.c.a.20.11	yes	12	3.2	odd	2	inner
21.6.c.a.20.12	yes	12	21.20	even	2	inner
336.6.k.d.209.5		12	84.83	odd	2
336.6.k.d.209.6		12	4.3	odd	2
336.6.k.d.209.7		12	28.27	even	2
336.6.k.d.209.8		12	12.11	even	2

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.2458i q^{2} +(4.60012 - 14.8943i) q^{3} -72.9763 q^{4} +73.2992 q^{5} +(-152.604 - 47.1319i) q^{6} +(55.7250 + 117.054i) q^{7} +419.835i q^{8} +(-200.678 - 137.031i) q^{9} +O(q^{10})\)	\(q-10.2458i q^{2} +(4.60012 - 14.8943i) q^{3} -72.9763 q^{4} +73.2992 q^{5} +(-152.604 - 47.1319i) q^{6} +(55.7250 + 117.054i) q^{7} +419.835i q^{8} +(-200.678 - 137.031i) q^{9} -751.009i q^{10} -237.986i q^{11} +(-335.700 + 1086.93i) q^{12} +63.3779i q^{13} +(1199.31 - 570.947i) q^{14} +(337.186 - 1091.74i) q^{15} +1966.30 q^{16} +814.556 q^{17} +(-1403.99 + 2056.10i) q^{18} -64.1691i q^{19} -5349.11 q^{20} +(1999.78 - 291.518i) q^{21} -2438.35 q^{22} +988.504i q^{23} +(6253.13 + 1931.29i) q^{24} +2247.78 q^{25} +649.357 q^{26} +(-2964.11 + 2358.59i) q^{27} +(-4066.61 - 8542.20i) q^{28} -1569.70i q^{29} +(-11185.7 - 3454.73i) q^{30} +5256.16i q^{31} -6711.62i q^{32} +(-3544.62 - 1094.76i) q^{33} -8345.77i q^{34} +(4084.60 + 8579.99i) q^{35} +(14644.7 + 10000.0i) q^{36} +11308.5 q^{37} -657.464 q^{38} +(943.966 + 291.546i) q^{39} +30773.6i q^{40} +3795.80 q^{41} +(-2986.84 - 20489.3i) q^{42} -15837.6 q^{43} +17367.3i q^{44} +(-14709.5 - 10044.3i) q^{45} +10128.0 q^{46} +23236.9 q^{47} +(9045.24 - 29286.6i) q^{48} +(-10596.4 + 13045.7i) q^{49} -23030.3i q^{50} +(3747.06 - 12132.2i) q^{51} -4625.09i q^{52} -19952.5i q^{53} +(24165.6 + 30369.7i) q^{54} -17444.2i q^{55} +(-49143.5 + 23395.3i) q^{56} +(-955.751 - 295.186i) q^{57} -16082.8 q^{58} -34515.5 q^{59} +(-24606.6 + 79671.0i) q^{60} -12095.9i q^{61} +53853.6 q^{62} +(4857.28 - 31126.2i) q^{63} -5844.15 q^{64} +4645.55i q^{65} +(-11216.7 + 36317.5i) q^{66} -29255.2 q^{67} -59443.3 q^{68} +(14723.0 + 4547.24i) q^{69} +(87908.9 - 41850.0i) q^{70} +54089.1i q^{71} +(57530.4 - 84251.6i) q^{72} +73706.7i q^{73} -115864. i q^{74} +(10340.1 - 33479.0i) q^{75} +4682.83i q^{76} +(27857.3 - 13261.8i) q^{77} +(2987.12 - 9671.69i) q^{78} -49241.9 q^{79} +144129. q^{80} +(21494.1 + 54998.1i) q^{81} -38891.0i q^{82} -112435. q^{83} +(-145937. + 21274.0i) q^{84} +59706.3 q^{85} +162268. i q^{86} +(-23379.5 - 7220.80i) q^{87} +99914.8 q^{88} +71787.2 q^{89} +(-102911. + 150711. i) q^{90} +(-7418.66 + 3531.74i) q^{91} -72137.4i q^{92} +(78286.6 + 24179.0i) q^{93} -238081. i q^{94} -4703.55i q^{95} +(-99964.5 - 30874.3i) q^{96} +18031.4i q^{97} +(133664. + 108569. i) q^{98} +(-32611.4 + 47758.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9}+O(q^{10}) \) 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9	\( 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9} + 1392 q^{15} + 4868 q^{16} - 3804 q^{18} + 4116 q^{21} - 8752 q^{22} + 7812 q^{25} - 8204 q^{28} - 27876 q^{30} + 54864 q^{36} + 27464 q^{37} - 16080 q^{39} - 3444 q^{42} - 73840 q^{43} + 59144 q^{46} + 6972 q^{49} + 23760 q^{51} + 103968 q^{57} - 71512 q^{58} - 152676 q^{60} - 120624 q^{63} - 198788 q^{64} + 79344 q^{67} + 368760 q^{70} + 226644 q^{72} + 394644 q^{78} - 247104 q^{79} - 248868 q^{81} - 608076 q^{84} - 320112 q^{85} + 595456 q^{88} + 310128 q^{91} + 397272 q^{93} + 696576 q^{99}+O(q^{100}) \) 12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9 + 1392 * q^15 + 4868 * q^16 - 3804 * q^18 + 4116 * q^21 - 8752 * q^22 + 7812 * q^25 - 8204 * q^28 - 27876 * q^30 + 54864 * q^36 + 27464 * q^37 - 16080 * q^39 - 3444 * q^42 - 73840 * q^43 + 59144 * q^46 + 6972 * q^49 + 23760 * q^51 + 103968 * q^57 - 71512 * q^58 - 152676 * q^60 - 120624 * q^63 - 198788 * q^64 + 79344 * q^67 + 368760 * q^70 + 226644 * q^72 + 394644 * q^78 - 247104 * q^79 - 248868 * q^81 - 608076 * q^84 - 320112 * q^85 + 595456 * q^88 + 310128 * q^91 + 397272 * q^93 + 696576 * q^99

Introduction

L-functions

Modular forms

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