LMFDB - Embedded newform 21.7.b.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(8,21)]

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, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("21.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.b (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:	$4.83113575602$
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} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 $ x^12 + 642x^10 + 155265x^8 + 17813036x^6 + 1003321428x^4 + 26369892864*x^2 + 256461520896
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			8.3
Root			$-11.9090i$ of defining polynomial
Character	$\chi$	$=$	21.8
Dual form			21.7.b.a.8.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.9090i q^{2} +(-13.4494 + 23.4118i) q^{3} -77.8243 q^{4} +201.466i q^{5} +(278.811 + 160.169i) q^{6} -129.642 q^{7} +164.633i q^{8} +(-367.226 - 629.751i) q^{9} +O(q^{10})$	\(q-11.9090i q^{2} +(-13.4494 + 23.4118i) q^{3} -77.8243 q^{4} +201.466i q^{5} +(278.811 + 160.169i) q^{6} -129.642 q^{7} +164.633i q^{8} +(-367.226 - 629.751i) q^{9} +2399.25 q^{10} +2455.83i q^{11} +(1046.69 - 1822.01i) q^{12} -238.894 q^{13} +1543.90i q^{14} +(-4716.68 - 2709.60i) q^{15} -3020.14 q^{16} +2170.82i q^{17} +(-7499.70 + 4373.29i) q^{18} -1030.29 q^{19} -15678.9i q^{20} +(1743.61 - 3035.15i) q^{21} +29246.5 q^{22} -7122.54i q^{23} +(-3854.36 - 2214.22i) q^{24} -24963.4 q^{25} +2844.99i q^{26} +(19682.6 - 127.642i) q^{27} +10089.3 q^{28} -3392.63i q^{29} +(-32268.6 + 56170.9i) q^{30} +24262.4 q^{31} +46503.3i q^{32} +(-57495.5 - 33029.5i) q^{33} +25852.2 q^{34} -26118.4i q^{35} +(28579.1 + 49009.9i) q^{36} +42901.1 q^{37} +12269.8i q^{38} +(3212.98 - 5592.94i) q^{39} -33167.9 q^{40} -11901.1i q^{41} +(-36145.6 - 20764.6i) q^{42} -10544.7 q^{43} -191123. i q^{44} +(126873. - 73983.4i) q^{45} -84822.4 q^{46} +122266. i q^{47} +(40619.1 - 70706.9i) q^{48} +16807.0 q^{49} +297289. i q^{50} +(-50822.7 - 29196.2i) q^{51} +18591.7 q^{52} -128011. i q^{53} +(-1520.09 - 234400. i) q^{54} -494766. q^{55} -21343.3i q^{56} +(13856.9 - 24121.1i) q^{57} -40402.9 q^{58} +238607. i q^{59} +(367072. + 210872. i) q^{60} +28889.0 q^{61} -288941. i q^{62} +(47607.8 + 81642.0i) q^{63} +360519. q^{64} -48128.9i q^{65} +(-393349. + 684714. i) q^{66} +560622. q^{67} -168942. i q^{68} +(166752. + 95794.1i) q^{69} -311044. q^{70} +506010. i q^{71} +(103678. - 60457.5i) q^{72} -203914. q^{73} -510909. i q^{74} +(335743. - 584438. i) q^{75} +80181.9 q^{76} -318379. i q^{77} +(-66606.3 - 38263.4i) q^{78} -308446. q^{79} -608454. i q^{80} +(-261731. + 462522. i) q^{81} -141731. q^{82} +1.07225e6i q^{83} +(-135695. + 236208. i) q^{84} -437345. q^{85} +125577. i q^{86} +(79427.7 + 45629.0i) q^{87} -404311. q^{88} -465973. i q^{89} +(-881068. - 1.51093e6i) q^{90} +30970.6 q^{91} +554307. i q^{92} +(-326315. + 568026. i) q^{93} +1.45607e6 q^{94} -207569. i q^{95} +(-1.08873e6 - 625443. i) q^{96} +700720. q^{97} -200155. i q^{98} +(1.54656e6 - 901846. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) $ 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9	$ 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) $ 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9 - 1092 * q^10 - 1726 * q^12 + 384 * q^13 - 632 * q^15 + 5892 * q^16 - 40 * q^18 + 11304 * q^19 - 5488 * q^21 + 15312 * q^22 + 12138 * q^24 - 77292 * q^25 + 114796 * q^27 + 41160 * q^28 - 101908 * q^30 - 9360 * q^31 - 65744 * q^33 - 169008 * q^34 - 195652 * q^36 + 212016 * q^37 + 159544 * q^39 + 196644 * q^40 - 37730 * q^42 + 28080 * q^43 - 4760 * q^45 - 418512 * q^46 + 865742 * q^48 + 201684 * q^49 - 371880 * q^51 - 138300 * q^52 - 254170 * q^54 - 732144 * q^55 - 440624 * q^57 + 1164240 * q^58 + 677660 * q^60 + 926736 * q^61 + 2744 * q^63 - 1380108 * q^64 - 1414588 * q^66 - 223104 * q^67 + 153048 * q^69 - 382788 * q^70 - 540192 * q^72 + 600984 * q^73 + 594716 * q^75 + 604596 * q^76 + 1866140 * q^78 - 276864 * q^79 + 617596 * q^81 + 1138200 * q^82 + 1398754 * q^84 - 3002472 * q^85 - 3372824 * q^87 - 1599048 * q^88 - 788032 * q^90 - 1243032 * q^91 + 408168 * q^93 + 8059296 * q^94 - 1141658 * q^96 + 1621416 * q^97 + 5211904 * 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 $

$2$		−	11.9090i		−	1.48862i	−0.667832	−	0.744312i	$-0.732777\pi$
$2$		−	11.9090i		−	1.48862i	0.667832	−	0.744312i	$-0.267223\pi$
$3$	−13.4494	+	23.4118i	−0.498127	+	0.867104i
$3$	−13.4494	+	23.4118i	−0.498127	+	0.867104i
$4$	−77.8243			−1.21600
$5$			201.466i			1.61172i	0.592103	+	0.805862i	$0.298298\pi$
$5$			201.466i			1.61172i	−0.592103	+	0.805862i	$0.701702\pi$
$6$	278.811	+	160.169i	1.29079	+	0.741524i
$7$	−129.642			−0.377964
$7$	−129.642			−0.377964
$8$			164.633i			0.321549i
$9$	−367.226	−	629.751i	−0.503739	−	0.863856i
$10$	2399.25			2.39925
$11$			2455.83i			1.84510i	0.385873	+	0.922552i	$0.373900\pi$
$11$			2455.83i			1.84510i	−0.385873	+	0.922552i	$0.626100\pi$
$12$	1046.69	−	1822.01i	0.605724	−	1.05440i
$13$	−238.894			−0.108736			−0.0543682	−	0.998521i	$-0.517314\pi$
$13$	−238.894			−0.108736			−0.0543682	+	0.998521i	$0.517314\pi$
$14$			1543.90i			0.562647i
$15$	−4716.68	−	2709.60i	−1.39753	−	0.802843i
$16$	−3020.14			−0.737338
$17$			2170.82i			0.441851i	0.975291	+	0.220926i	$0.0709078\pi$
$17$			2170.82i			0.441851i	−0.975291	+	0.220926i	$0.929092\pi$
$18$	−7499.70	+	4373.29i	−1.28596	+	0.749879i
$19$	−1030.29			−0.150211			−0.0751053	−	0.997176i	$-0.523929\pi$
$19$	−1030.29			−0.150211			−0.0751053	+	0.997176i	$0.523929\pi$
$20$		−	15678.9i		−	1.95986i
$21$	1743.61	−	3035.15i	0.188274	−	0.327735i
$22$	29246.5			2.74667
$23$		−	7122.54i		−	0.585398i	−0.956205	−	0.292699i	$-0.905447\pi$
$23$		−	7122.54i		−	0.585398i	0.956205	−	0.292699i	$-0.0945535\pi$
$24$	−3854.36	−	2214.22i	−0.278816	−	0.160172i
$25$	−24963.4			−1.59766
$26$			2844.99i			0.161868i
$27$	19682.6	−	127.642i	0.999979	−	0.00648488i
$28$	10089.3			0.459606
$29$		−	3392.63i		−	0.139105i	−0.997578	−	0.0695525i	$-0.977843\pi$
$29$		−	3392.63i		−	0.139105i	0.997578	−	0.0695525i	$-0.0221572\pi$
$30$	−32268.6	+	56170.9i	−1.19513	+	2.08040i
$31$	24262.4			0.814420			0.407210	−	0.913335i	$-0.366502\pi$
$31$	24262.4			0.814420			0.407210	+	0.913335i	$0.366502\pi$
$32$			46503.3i			1.41917i
$33$	−57495.5	−	33029.5i	−1.59990	−	0.919096i
$34$	25852.2			0.657751
$35$		−	26118.4i		−	0.609175i
$36$	28579.1	+	49009.9i	0.612549	+	1.05045i
$37$	42901.1			0.846960			0.423480	−	0.905905i	$-0.360808\pi$
$37$	42901.1			0.846960			0.423480	+	0.905905i	$0.360808\pi$
$38$			12269.8i			0.223607i
$39$	3212.98	−	5592.94i	0.0541645	−	0.0942857i
$40$	−33167.9			−0.518248
$41$		−	11901.1i		−	0.172678i	−0.996266	−	0.0863389i	$-0.972483\pi$
$41$		−	11901.1i		−	0.172678i	0.996266	−	0.0863389i	$-0.0275168\pi$
$42$	−36145.6	−	20764.6i	−0.487874	−	0.280270i
$43$	−10544.7			−0.132626			−0.0663132	−	0.997799i	$-0.521124\pi$
$43$	−10544.7			−0.132626			−0.0663132	+	0.997799i	$0.521124\pi$
$44$		−	191123.i		−	2.24365i
$45$	126873.	−	73983.4i	1.39230	−	0.811889i
$46$	−84822.4			−0.871439
$47$			122266.i			1.17764i	0.808264	+	0.588821i	$0.200408\pi$
$47$			122266.i			1.17764i	−0.808264	+	0.588821i	$0.799592\pi$
$48$	40619.1	−	70706.9i	0.367288	−	0.639349i
$49$	16807.0			0.142857
$50$			297289.i			2.37831i
$51$	−50822.7	−	29196.2i	−0.383131	−	0.220098i
$52$	18591.7			0.132224
$53$		−	128011.i		−	0.859844i	−0.902866	−	0.429922i	$-0.858541\pi$
$53$		−	128011.i		−	0.859844i	0.902866	−	0.429922i	$-0.141459\pi$
$54$	−1520.09	−	234400.i	−0.00965356	−	1.48859i
$55$	−494766.			−2.97380
$56$		−	21343.3i		−	0.121534i
$57$	13856.9	−	24121.1i	0.0748239	−	0.130248i
$58$	−40402.9			−0.207075
$59$			238607.i			1.16179i	0.813979	+	0.580894i	$0.197297\pi$
$59$			238607.i			1.16179i	−0.813979	+	0.580894i	$0.802703\pi$
$60$	367072.	+	210872.i	1.69941	+	0.976261i
$61$	28889.0			0.127275			0.0636374	−	0.997973i	$-0.479730\pi$
$61$	28889.0			0.127275			0.0636374	+	0.997973i	$0.479730\pi$
$62$		−	288941.i		−	1.21237i
$63$	47607.8	+	81642.0i	0.190396	+	0.326507i
$64$	360519.			1.37527
$65$		−	48128.9i		−	0.175253i
$66$	−393349.	+	684714.i	−1.36819	+	2.38165i
$67$	560622.			1.86400			0.932000	−	0.362459i	$-0.118063\pi$
$67$	560622.			1.86400			0.932000	+	0.362459i	$0.118063\pi$
$68$		−	168942.i		−	0.537293i
$69$	166752.	+	95794.1i	0.507601	+	0.291603i
$70$	−311044.			−0.906833
$71$			506010.i			1.41379i	0.707319	+	0.706894i	$0.249904\pi$
$71$			506010.i			1.41379i	−0.707319	+	0.706894i	$0.750096\pi$
$72$	103678.	−	60457.5i	0.277772	−	0.161977i
$73$	−203914.			−0.524178			−0.262089	−	0.965044i	$-0.584411\pi$
$73$	−203914.			−0.524178			−0.262089	+	0.965044i	$0.584411\pi$
$74$		−	510909.i		−	1.26081i
$75$	335743.	−	584438.i	0.795836	−	1.38534i
$76$	80181.9			0.182657
$77$		−	318379.i		−	0.697384i
$78$	−66606.3	−	38263.4i	−0.140356	−	0.0806306i
$79$	−308446.			−0.625601			−0.312800	−	0.949819i	$-0.601267\pi$
$79$	−308446.			−0.625601			−0.312800	+	0.949819i	$0.601267\pi$
$80$		−	608454.i		−	1.18839i
$81$	−261731.	+	462522.i	−0.492493	+	0.870316i
$82$	−141731.			−0.257053
$83$			1.07225e6i			1.87526i	0.347631	+	0.937631i	$0.386986\pi$
$83$			1.07225e6i			1.87526i	−0.347631	+	0.937631i	$0.613014\pi$
$84$	−135695.	+	236208.i	−0.228942	+	0.398527i
$85$	−437345.			−0.712143
$86$			125577.i			0.197431i
$87$	79427.7	+	45629.0i	0.120619	+	0.0692920i
$88$	−404311.			−0.593291
$89$		−	465973.i		−	0.660983i	−0.943809	−	0.330492i	$-0.892785\pi$
$89$		−	465973.i		−	0.660983i	0.943809	−	0.330492i	$-0.107215\pi$
$90$	−881068.	−	1.51093e6i	−1.20860	−	2.07261i
$91$	30970.6			0.0410985
$92$			554307.i			0.711847i
$93$	−326315.	+	568026.i	−0.405684	+	0.706187i
$94$	1.45607e6			1.75307
$95$		−	207569.i		−	0.242098i
$96$	−1.08873e6	−	625443.i	−1.23057	−	0.706926i
$97$	700720.			0.767767			0.383883	−	0.923382i	$-0.374586\pi$
$97$	700720.			0.767767			0.383883	+	0.923382i	$0.374586\pi$
$98$		−	200155.i		−	0.212661i
$99$	1.54656e6	−	901846.i	1.59390	−	0.929452i
$100$	1.94276e6			1.94276
$101$		−	695914.i		−	0.675447i	−0.941245	−	0.337723i	$-0.890343\pi$
$101$		−	695914.i		−	0.675447i	0.941245	−	0.337723i	$-0.109657\pi$
$102$	−347698.	+	605248.i	−0.327643	+	0.570339i
$103$	854750.			0.782217			0.391109	−	0.920345i	$-0.372092\pi$
$103$	854750.			0.782217			0.391109	+	0.920345i	$0.372092\pi$
$104$		−	39329.8i		−	0.0349640i
$105$	611478.	+	351277.i	0.528218	+	0.303446i
$106$	−1.52448e6			−1.27999
$107$		−	898640.i		−	0.733558i	−0.930308	−	0.366779i	$-0.880461\pi$
$107$		−	898640.i		−	0.733558i	0.930308	−	0.366779i	$-0.119539\pi$
$108$	−1.53178e6	+	9933.64i	−1.21598	+	0.00788564i
$109$	−1.40805e6			−1.08727			−0.543636	−	0.839321i	$-0.682953\pi$
$109$	−1.40805e6			−1.08727			−0.543636	+	0.839321i	$0.682953\pi$
$110$			5.89217e6i			4.42687i
$111$	−576995.	+	1.00439e6i	−0.421893	+	0.734403i
$112$	391536.			0.278688
$113$		−	106803.i		−	0.0740198i	−0.999315	−	0.0370099i	$-0.988217\pi$
$113$		−	106803.i		−	0.0740198i	0.999315	−	0.0370099i	$-0.0117833\pi$
$114$	−287258.	−	165021.i	−0.193891	−	0.111385i
$115$	1.43495e6			0.943501
$116$			264029.i			0.169152i
$117$	87728.0	+	150444.i	0.0547748	+	0.0939325i
$118$	2.84157e6			1.72947
$119$		−	281429.i		−	0.167004i
$120$	446089.	−	776520.i	0.258153	−	0.449375i
$121$	−4.25956e6			−2.40441
$122$		−	344039.i		−	0.189464i
$123$	278627.	+	160063.i	0.149730	+	0.0860155i
$124$	−1.88820e6			−0.990338
$125$		−	1.88137e6i		−	0.963259i
$126$	972275.	−	566962.i	0.486046	−	0.283428i
$127$	−23434.4			−0.0114404			−0.00572021	−	0.999984i	$-0.501821\pi$
$127$	−23434.4			−0.0114404			−0.00572021	+	0.999984i	$0.501821\pi$
$128$		−	1.31721e6i		−	0.628095i
$129$	141821.	−	246871.i	0.0660648	−	0.115001i
$130$	−573167.			−0.260886
$131$		−	941653.i		−	0.418868i	−0.977823	−	0.209434i	$-0.932838\pi$
$131$		−	941653.i		−	0.418868i	0.977823	−	0.209434i	$-0.0671621\pi$
$132$	4.47455e6	+	2.57050e6i	1.94548	+	1.11762i
$133$	133569.			0.0567743
$134$		−	6.67645e6i		−	2.77480i
$135$	25715.5	+	3.96536e6i	0.0104518	+	1.61169i
$136$	−357388.			−0.142077
$137$		−	2.67932e6i		−	1.04199i	−0.853560	−	0.520994i	$-0.825561\pi$
$137$		−	2.67932e6i		−	1.04199i	0.853560	−	0.520994i	$-0.174439\pi$
$138$	1.14081e6	−	1.98585e6i	0.434087	−	0.755628i
$139$	−3.53125e6			−1.31487			−0.657437	−	0.753509i	$-0.728360\pi$
$139$	−3.53125e6			−1.31487			−0.657437	+	0.753509i	$0.728360\pi$
$140$			2.03264e6i			0.740759i
$141$	−2.86247e6	−	1.64441e6i	−1.02114	−	0.586615i
$142$	6.02608e6			2.10460
$143$		−	586683.i		−	0.200630i
$144$	1.10907e6	+	1.90193e6i	0.371426	+	0.636954i
$145$	683499.			0.224199
$146$			2.42841e6i			0.780304i
$147$	−226044.	+	393482.i	−0.0711610	+	0.123872i
$148$	−3.33874e6			−1.02991
$149$			1.66331e6i			0.502821i	0.967881	+	0.251410i	$0.0808944\pi$
$149$			1.66331e6i			0.502821i	−0.967881	+	0.251410i	$0.919106\pi$
$150$	−6.96008e6	−	3.99837e6i	−2.06224	−	1.18470i
$151$	−3.85333e6			−1.11919			−0.559597	−	0.828765i	$-0.689044\pi$
$151$	−3.85333e6			−1.11919			−0.559597	+	0.828765i	$0.689044\pi$
$152$		−	169620.i		−	0.0483000i
$153$	1.36707e6	−	797180.i	0.381696	−	0.222578i
$154$	−3.79157e6			−1.03814
$155$			4.88804e6i			1.31262i
$156$	−250048.	+	435266.i	−0.0658642	+	0.114652i
$157$	4.52216e6			1.16855			0.584274	−	0.811556i	$-0.301379\pi$
$157$	4.52216e6			1.16855			0.584274	+	0.811556i	$0.301379\pi$
$158$			3.67328e6i			0.931285i
$159$	2.99697e6	+	1.72167e6i	0.745575	+	0.428312i
$160$	−9.36882e6			−2.28731
$161$			923379.i			0.221260i
$162$	5.50817e6	+	3.11696e6i	1.29557	+	0.733138i
$163$	4.41429e6			1.01929			0.509646	−	0.860384i	$-0.329777\pi$
$163$	4.41429e6			1.01929			0.509646	+	0.860384i	$0.329777\pi$
$164$			926197.i			0.209977i
$165$	6.65432e6	−	1.15834e7i	1.48133	−	2.57859i
$166$	1.27694e7			2.79156
$167$			7.22776e6i			1.55187i	0.630815	+	0.775933i	$0.282721\pi$
$167$			7.22776e6i			1.55187i	−0.630815	+	0.775933i	$0.717279\pi$
$168$	499686.	+	287055.i	0.105383	+	0.0605394i
$169$	−4.76974e6			−0.988176
$170$			5.20834e6i			1.06011i
$171$	378351.	+	648829.i	0.0756670	+	0.129760i
$172$	820636.			0.161274
$173$		−	7.20836e6i		−	1.39219i	−0.717950	−	0.696094i	$-0.754919\pi$
$173$		−	7.20836e6i		−	1.39219i	0.717950	−	0.696094i	$-0.245081\pi$
$174$	543395.	−	945905.i	0.103150	−	0.179556i
$175$	3.23630e6			0.603858
$176$		−	7.41696e6i		−	1.36047i
$177$	−5.58622e6	−	3.20912e6i	−1.00739	−	0.578717i
$178$	−5.54927e6			−0.983956
$179$			1.67864e6i			0.292684i	0.989234	+	0.146342i	$0.0467500\pi$
$179$			1.67864e6i			0.292684i	−0.989234	+	0.146342i	$0.953250\pi$
$180$	−9.87381e6	+	5.75770e6i	−1.69304	+	0.987261i
$181$	5.90582e6			0.995966			0.497983	−	0.867187i	$-0.334074\pi$
$181$	5.90582e6			0.995966			0.497983	+	0.867187i	$0.334074\pi$
$182$		−	368829.i		−	0.0611802i
$183$	−388540.	+	676343.i	−0.0633990	+	0.110361i
$184$	1.17261e6			0.188234
$185$			8.64309e6i			1.36507i
$186$	6.76462e6	+	3.88609e6i	1.05125	+	0.603912i
$187$	−5.33116e6			−0.815262
$188$		−	9.51528e6i		−	1.43202i
$189$	−2.55169e6	+	16547.7i	−0.377957	+	0.00245106i
$190$	−2.47194e6			−0.360393
$191$		−	5.46493e6i		−	0.784304i	−0.919900	−	0.392152i	$-0.871731\pi$
$191$		−	5.46493e6i		−	0.784304i	0.919900	−	0.392152i	$-0.128269\pi$
$192$	−4.84878e6	+	8.44041e6i	−0.685060	+	1.19250i
$193$	7.37200e6			1.02545			0.512724	−	0.858554i	$-0.328636\pi$
$193$	7.37200e6			1.02545			0.512724	+	0.858554i	$0.328636\pi$
$194$		−	8.34488e6i		−	1.14292i
$195$	1.12678e6	+	647306.i	0.151963	+	0.0872983i
$196$	−1.30799e6			−0.173715
$197$			3.25677e6i			0.425979i	0.977054	+	0.212990i	$0.0683200\pi$
$197$			3.25677e6i			0.425979i	−0.977054	+	0.212990i	$0.931680\pi$
$198$	−1.07401e7	−	1.84180e7i	−1.38360	−	2.37272i
$199$	6.61999e6			0.840036			0.420018	−	0.907516i	$-0.362024\pi$
$199$	6.61999e6			0.840036			0.420018	+	0.907516i	$0.362024\pi$
$200$		−	4.10980e6i		−	0.513725i
$201$	−7.54004e6	+	1.31252e7i	−0.928508	+	1.61628i
$202$	−8.28763e6			−1.00549
$203$			439827.i			0.0525768i
$204$	3.95524e6	+	2.27217e6i	0.465889	+	0.267640i
$205$	2.39767e6			0.278309
$206$		−	1.01792e7i		−	1.16443i
$207$	−4.48543e6	+	2.61558e6i	−0.505700	+	0.294888i
$208$	721492.			0.0801755
$209$		−	2.53023e6i		−	0.277154i
$210$	4.18336e6	−	7.28210e6i	0.451718	−	0.786318i
$211$	8.62852e6			0.918521			0.459260	−	0.888302i	$-0.348115\pi$
$211$	8.62852e6			0.918521			0.459260	+	0.888302i	$0.348115\pi$
$212$			9.96236e6i			1.04557i
$213$	−1.18466e7	−	6.80555e6i	−1.22590	−	0.704246i
$214$	−1.07019e7			−1.09199
$215$		−	2.12440e6i		−	0.213757i
$216$	21014.1	+	3.24040e6i	0.00208521	+	0.321542i
$217$	−3.14542e6			−0.307822
$218$			1.67685e7i			1.61854i
$219$	2.74253e6	−	4.77400e6i	0.261107	−	0.454517i
$220$	3.85048e7			3.61615
$221$		−	518594.i		−	0.0480453i
$222$	1.19613e7	+	6.87143e6i	1.09325	+	0.628041i
$223$	3.28862e6			0.296551			0.148275	−	0.988946i	$-0.452628\pi$
$223$	3.28862e6			0.296551			0.148275	+	0.988946i	$0.452628\pi$
$224$		−	6.02878e6i		−	0.536395i
$225$	9.16721e6	+	1.57207e7i	0.804803	+	1.38015i
$226$	−1.27192e6			−0.110188
$227$			5.14565e6i			0.439909i	0.975510	+	0.219954i	$0.0705908\pi$
$227$			5.14565e6i			0.439909i	−0.975510	+	0.219954i	$0.929409\pi$
$228$	−1.07840e6	+	1.87720e6i	−0.0909862	+	0.158382i
$229$	−1.34923e7			−1.12352			−0.561758	−	0.827301i	$-0.689875\pi$
$229$	−1.34923e7			−1.12352			−0.561758	+	0.827301i	$0.689875\pi$
$230$		−	1.70888e7i		−	1.40452i
$231$	7.45382e6	+	4.28201e6i	0.604704	+	0.347386i
$232$	558540.			0.0447291
$233$			1.48171e7i			1.17138i	0.810537	+	0.585688i	$0.199175\pi$
$233$			1.48171e7i			1.17138i	−0.810537	+	0.585688i	$0.800825\pi$
$234$	1.79163e6	−	1.04475e6i	0.139830	−	0.0815391i
$235$	−2.46324e7			−1.89803
$236$		−	1.85694e7i		−	1.41274i
$237$	4.14841e6	−	7.22127e6i	0.311628	−	0.542461i
$238$	−3.35153e6			−0.248606
$239$		−	4.31716e6i		−	0.316231i	−0.987421	−	0.158116i	$-0.949458\pi$
$239$		−	4.31716e6i		−	0.316231i	0.987421	−	0.158116i	$-0.0505419\pi$
$240$	1.42450e7	+	8.18335e6i	1.03046	+	0.591967i
$241$	−1.91430e6			−0.136760			−0.0683799	−	0.997659i	$-0.521783\pi$
$241$	−1.91430e6			−0.136760			−0.0683799	+	0.997659i	$0.521783\pi$
$242$			5.07271e7i			3.57926i
$243$	−7.30834e6	−	1.23483e7i	−0.509331	−	0.860571i
$244$	−2.24826e6			−0.154767
$245$			3.38603e6i			0.230246i
$246$	1.90619e6	−	3.31817e6i	0.128045	−	0.222891i
$247$	246131.			0.0163334
$248$			3.99439e6i			0.261876i
$249$	−2.51033e7	−	1.44212e7i	−1.62605	−	0.934119i
$250$	−2.24052e7			−1.43393
$251$			8.28880e6i			0.524168i	0.965045	+	0.262084i	$0.0844098\pi$
$251$			8.28880e6i			0.524168i	−0.965045	+	0.262084i	$0.915590\pi$
$252$	−3.70505e6	−	6.35373e6i	−0.231522	−	0.397033i
$253$	1.74918e7			1.08012
$254$			279080.i			0.0170305i
$255$	5.88203e6	−	1.02390e7i	0.354737	−	0.617502i
$256$	7.38658e6			0.440274
$257$		−	1.90619e7i		−	1.12297i	−0.827488	−	0.561484i	$-0.810231\pi$
$257$		−	1.90619e7i		−	1.12297i	0.827488	−	0.561484i	$-0.189769\pi$
$258$	−2.93999e6	−	1.68894e6i	−0.171193	−	0.0983457i
$259$	−5.56177e6			−0.320121
$260$			3.74559e6i			0.213108i
$261$	−2.13651e6	+	1.24586e6i	−0.120167	+	0.0700727i
$262$	−1.12141e7			−0.623537
$263$		−	1.32866e7i		−	0.730376i	−0.930934	−	0.365188i	$-0.881005\pi$
$263$		−	1.32866e7i		−	0.730376i	0.930934	−	0.365188i	$-0.118995\pi$
$264$	5.43775e6	−	9.46566e6i	0.295534	−	0.514445i
$265$	2.57898e7			1.38583
$266$		−	1.59068e6i		−	0.0845156i
$267$	1.09093e7	+	6.26706e6i	0.573141	+	0.329253i
$268$	−4.36300e7			−2.26663
$269$			2.96223e7i			1.52182i	0.648859	+	0.760909i	$0.275247\pi$
$269$			2.96223e7i			1.52182i	−0.648859	+	0.760909i	$0.724753\pi$
$270$	4.72235e7	−	306245.i	2.39920	−	0.0155589i
$271$	3.11757e7			1.56642			0.783211	−	0.621756i	$-0.213580\pi$
$271$	3.11757e7			1.56642			0.783211	+	0.621756i	$0.213580\pi$
$272$		−	6.55616e6i		−	0.325794i
$273$	−416537.	+	725078.i	−0.0204723	+	0.0356367i
$274$	−3.19080e7			−1.55113
$275$		−	6.13059e7i		−	2.94784i
$276$	−1.29773e7	−	7.45510e6i	−0.617245	−	0.354590i
$277$	1.71946e7			0.809007			0.404503	−	0.914537i	$-0.367444\pi$
$277$	1.71946e7			0.809007			0.404503	+	0.914537i	$0.367444\pi$
$278$			4.20537e7i			1.95736i
$279$	−8.90978e6	−	1.52793e7i	−0.410255	−	0.703541i
$280$	4.29995e6			0.195879
$281$		−	4.05668e7i		−	1.82832i	−0.405357	−	0.914158i	$-0.632853\pi$
$281$		−	4.05668e7i		−	1.82832i	0.405357	−	0.914158i	$-0.367147\pi$
$282$	−1.95833e7	+	3.40892e7i	−0.873249	+	1.52009i
$283$	−2.40812e7			−1.06248			−0.531238	−	0.847222i	$-0.678273\pi$
$283$	−2.40812e7			−1.06248			−0.531238	+	0.847222i	$0.678273\pi$
$284$		−	3.93799e7i		−	1.71917i
$285$	4.85957e6	+	2.79168e6i	0.209924	+	0.120596i
$286$	−6.98681e6			−0.298663
$287$			1.54288e6i			0.0652661i
$288$	2.92855e7	−	1.70772e7i	1.22596	−	0.714891i
$289$	1.94251e7			0.804767
$290$		−	8.13979e6i		−	0.333748i
$291$	−9.42428e6	+	1.64051e7i	−0.382445	+	0.665734i
$292$	1.58695e7			0.637402
$293$			2.54525e7i			1.01188i	0.862570	+	0.505938i	$0.168854\pi$
$293$			2.54525e7i			1.01188i	−0.862570	+	0.505938i	$0.831146\pi$
$294$	4.68598e6	+	2.69196e6i	0.184399	+	0.105932i
$295$	−4.80711e7			−1.87248
$296$			7.06293e6i			0.272339i
$297$	313467.	+	4.83372e7i	0.0119653	+	1.84507i
$298$	1.98083e7			0.748512
$299$			1.70153e6i			0.0636541i
$300$	−2.61290e7	+	4.54835e7i	−0.967740	+	1.68457i
$301$	1.36704e6			0.0501281
$302$			4.58893e7i			1.66606i
$303$	1.62926e7	+	9.35964e6i	0.585683	+	0.336458i
$304$	3.11163e6			0.110756
$305$			5.82013e6i			0.205132i
$306$	−9.49362e6	−	1.62805e7i	−0.331335	−	0.568202i
$307$	−3.62896e7			−1.25420			−0.627100	−	0.778939i	$-0.715758\pi$
$307$	−3.62896e7			−1.25420			−0.627100	+	0.778939i	$0.715758\pi$
$308$			2.47776e7i			0.848021i
$309$	−1.14959e7	+	2.00112e7i	−0.389643	+	0.678264i
$310$	5.82116e7			1.95400
$311$		−	1.07713e7i		−	0.358086i	−0.983841	−	0.179043i	$-0.942700\pi$
$311$		−	1.07713e7i		−	0.358086i	0.983841	−	0.179043i	$-0.0573001\pi$
$312$	920782.	+	528963.i	0.0303175	+	0.0174165i
$313$	−1.99458e7			−0.650458			−0.325229	−	0.945635i	$-0.605441\pi$
$313$	−1.99458e7			−0.650458			−0.325229	+	0.945635i	$0.605441\pi$
$314$		−	5.38544e7i		−	1.73953i
$315$	−1.64481e7	+	9.59134e6i	−0.526239	+	0.306865i
$316$	2.40045e7			0.760733
$317$		−	1.33248e7i		−	0.418295i	−0.977884	−	0.209147i	$-0.932931\pi$
$317$		−	1.33248e7i		−	0.418295i	0.977884	−	0.209147i	$-0.0670689\pi$
$318$	2.05034e7	−	3.56909e7i	0.637595	−	1.10988i
$319$	8.33174e6			0.256663
$320$			7.26322e7i			2.21656i
$321$	2.10388e7	+	1.20862e7i	0.636071	+	0.365405i
$322$	1.09965e7			0.329373
$323$		−	2.23658e6i		−	0.0663708i
$324$	2.03690e7	−	3.59954e7i	0.598874	−	1.05831i
$325$	5.96360e6			0.173723
$326$		−	5.25698e7i		−	1.51734i
$327$	1.89375e7	−	3.29650e7i	0.541600	−	0.942779i
$328$	1.95932e6			0.0555244
$329$		−	1.58508e7i		−	0.445107i
$330$	−1.37946e8	−	7.92463e7i	−3.83856	−	2.20514i
$331$	3.90697e7			1.07735			0.538673	−	0.842515i	$-0.318926\pi$
$331$	3.90697e7			1.07735			0.538673	+	0.842515i	$0.318926\pi$
$332$		−	8.34471e7i		−	2.28033i
$333$	−1.57544e7	−	2.70170e7i	−0.426647	−	0.731651i
$334$	8.60754e7			2.31015
$335$			1.12946e8i			3.00425i
$336$	−5.26594e6	+	9.16657e6i	−0.138822	+	0.241651i
$337$	5.27115e7			1.37726			0.688630	−	0.725113i	$-0.258213\pi$
$337$	5.27115e7			1.37726			0.688630	+	0.725113i	$0.258213\pi$
$338$			5.68028e7i			1.47102i
$339$	2.50045e6	+	1.43644e6i	0.0641829	+	0.0368713i
$340$	3.40360e7			0.865969
$341$			5.95844e7i			1.50269i
$342$	7.72690e6	−	4.50578e6i	0.193164	−	0.112640i
$343$	−2.17889e6			−0.0539949
$344$		−	1.73601e6i		−	0.0426459i
$345$	−1.92992e7	+	3.35947e7i	−0.469983	+	0.818114i
$346$	−8.58444e7			−2.07245
$347$		−	5.42428e7i		−	1.29824i	−0.760687	−	0.649118i	$-0.775138\pi$
$347$		−	5.42428e7i		−	1.29824i	0.760687	−	0.649118i	$-0.224862\pi$
$348$	−6.18140e6	−	3.55104e6i	−0.146673	−	0.0842593i
$349$	−1.37053e7			−0.322413			−0.161206	−	0.986921i	$-0.551538\pi$
$349$	−1.37053e7			−0.322413			−0.161206	+	0.986921i	$0.551538\pi$
$350$		−	3.85411e7i		−	0.898918i
$351$	−4.70205e6	+	30492.9i	−0.108734	+	0.000705143i
$352$	−1.14204e8			−2.61851
$353$		−	1.90795e7i		−	0.433753i	−0.976199	−	0.216876i	$-0.930413\pi$
$353$		−	1.90795e7i		−	0.433753i	0.976199	−	0.216876i	$-0.0695869\pi$
$354$	−3.82174e7	+	6.65262e7i	−0.861493	+	1.49963i
$355$	−1.01944e8			−2.27864
$356$			3.62640e7i			0.803758i
$357$	6.58875e6	+	3.78505e6i	0.144810	+	0.0831892i
$358$	1.99910e7			0.435697
$359$			4.15438e6i			0.0897889i	0.998992	+	0.0448944i	$0.0142951\pi$
$359$			4.15438e6i			0.0897889i	−0.998992	+	0.0448944i	$0.985705\pi$
$360$	1.21801e7	+	2.08875e7i	0.261062	+	0.447692i
$361$	−4.59844e7			−0.977437
$362$		−	7.03324e7i		−	1.48262i
$363$	5.72886e7	−	9.97240e7i	1.19770	−	2.08487i
$364$	−2.41027e6			−0.0499759
$365$		−	4.10817e7i		−	0.844830i
$366$	8.05457e6	+	4.62712e6i	0.164285	+	0.0943773i
$367$	4.04106e7			0.817518			0.408759	−	0.912642i	$-0.365962\pi$
$367$	4.04106e7			0.817518			0.408759	+	0.912642i	$0.365962\pi$
$368$			2.15111e7i			0.431637i
$369$	−7.49475e6	+	4.37041e6i	−0.149169	+	0.0869847i
$370$	1.02931e8			2.03207
$371$			1.65956e7i			0.324991i
$372$	2.53952e7	−	4.42062e7i	0.493314	−	0.858726i
$373$	2.91186e7			0.561104			0.280552	−	0.959839i	$-0.409482\pi$
$373$	2.91186e7			0.561104			0.280552	+	0.959839i	$0.409482\pi$
$374$			6.34888e7i			1.21362i
$375$	4.40462e7	+	2.53033e7i	0.835246	+	0.479825i
$376$	−2.01291e7			−0.378669
$377$			810479.i			0.0151258i
$378$	197067.	+	3.03880e7i	0.00364870	+	0.562635i
$379$	4.44837e6			0.0817115			0.0408557	−	0.999165i	$-0.486992\pi$
$379$	4.44837e6			0.0817115			0.0408557	+	0.999165i	$0.486992\pi$
$380$			1.61539e7i			0.294392i
$381$	315179.	−	548641.i	0.00569878	−	0.00992003i
$382$	−6.50819e7			−1.16753
$383$			2.28783e7i			0.407219i	0.979052	+	0.203609i	$0.0652673\pi$
$383$			2.28783e7i			0.407219i	−0.979052	+	0.203609i	$0.934733\pi$
$384$	3.08383e7	+	1.77157e7i	0.544624	+	0.312871i
$385$	6.41424e7			1.12399
$386$		−	8.77932e7i		−	1.52651i
$387$	3.87230e6	+	6.64055e6i	0.0668091	+	0.114570i
$388$	−5.45330e7			−0.933608
$389$			9.41054e7i			1.59870i	0.600869	+	0.799348i	$0.294821\pi$
$389$			9.41054e7i			1.59870i	−0.600869	+	0.799348i	$0.705179\pi$
$390$	7.70876e6	−	1.34189e7i	0.129954	−	0.226215i
$391$	1.54617e7			0.258659
$392$			2.76699e6i			0.0459355i
$393$	2.20458e7	+	1.26647e7i	0.363202	+	0.208649i
$394$	3.87849e7			0.634123
$395$		−	6.21412e7i		−	1.00830i
$396$	−1.20360e8	+	7.01855e7i	−1.93819	+	1.13022i
$397$	7.48515e7			1.19627			0.598135	−	0.801395i	$-0.295909\pi$
$397$	7.48515e7			1.19627			0.598135	+	0.801395i	$0.295909\pi$
$398$		−	7.88374e7i		−	1.25050i
$399$	−1.79643e6	+	3.12710e6i	−0.0282808	+	0.0492292i
$400$	7.53929e7			1.17801
$401$			1.60867e7i			0.249480i	0.992189	+	0.124740i	$0.0398096\pi$
$401$			1.60867e7i			0.249480i	−0.992189	+	0.124740i	$0.960190\pi$
$402$	1.56308e8	+	8.97944e7i	2.40604	+	1.38220i
$403$	−5.79613e6			−0.0885570
$404$			5.41590e7i			0.821346i
$405$	−9.31822e7	−	5.27298e7i	−1.40271	−	0.793764i
$406$	5.23790e6			0.0782671
$407$			1.05358e8i			1.56273i
$408$	4.80666e6	−	8.36710e6i	0.0707723	−	0.123195i
$409$	−5.20692e7			−0.761046			−0.380523	−	0.924771i	$-0.624256\pi$
$409$	−5.20692e7			−0.761046			−0.380523	+	0.924771i	$0.624256\pi$
$410$		−	2.85538e7i		−	0.414298i
$411$	6.27278e7	+	3.60353e7i	0.903513	+	0.519043i
$412$	−6.65203e7			−0.951179
$413$		−	3.09334e7i		−	0.439114i
$414$	3.11490e7	+	5.34169e7i	0.438978	+	0.752797i
$415$	−2.16022e8			−3.02241
$416$		−	1.11094e7i		−	0.154315i
$417$	4.74933e7	−	8.26730e7i	0.654974	−	1.14013i
$418$	−3.01325e7			−0.412579
$419$		−	5.36870e7i		−	0.729839i	−0.931039	−	0.364920i	$-0.881096\pi$
$419$		−	5.36870e7i		−	0.729839i	0.931039	−	0.364920i	$-0.118904\pi$
$420$	−4.75878e7	−	2.73379e7i	−0.642315	−	0.368992i
$421$	−7.93150e7			−1.06294			−0.531471	−	0.847077i	$-0.678360\pi$
$421$	−7.93150e7			−1.06294			−0.531471	+	0.847077i	$0.678360\pi$
$422$		−	1.02757e8i		−	1.36733i
$423$	7.69973e7	−	4.48994e7i	1.01731	−	0.593224i
$424$	2.10748e7			0.276482
$425$		−	5.41909e7i		−	0.705927i
$426$	−8.10473e7	+	1.41081e8i	−1.04836	+	1.82491i
$427$	−3.74522e6			−0.0481054
$428$			6.99360e7i			0.892009i
$429$	1.37353e7	+	7.89055e6i	0.173967	+	0.0999391i
$430$	−2.52995e7			−0.318204
$431$			2.07791e7i			0.259534i	0.991544	+	0.129767i	$0.0414230\pi$
$431$			2.07791e7i			0.259534i	−0.991544	+	0.129767i	$0.958577\pi$
$432$	−5.94441e7	+	385496.i	−0.737323	+	0.00478155i
$433$	4.63897e7			0.571423			0.285712	−	0.958316i	$-0.407770\pi$
$433$	4.63897e7			0.571423			0.285712	+	0.958316i	$0.407770\pi$
$434$			3.74588e7i			0.458231i
$435$	−9.19267e6	+	1.60020e7i	−0.111680	+	0.194404i
$436$	1.09580e8			1.32213
$437$			7.33832e6i			0.0879331i
$438$	−5.68535e7	−	3.26607e7i	−0.676605	−	0.388690i
$439$	−7.82157e7			−0.924486			−0.462243	−	0.886753i	$-0.652955\pi$
$439$	−7.82157e7			−0.924486			−0.462243	+	0.886753i	$0.652955\pi$
$440$		−	8.14548e7i		−	0.956222i
$441$	−6.17197e6	−	1.05842e7i	−0.0719628	−	0.123408i
$442$	−6.17594e6			−0.0715214
$443$		−	5.08271e7i		−	0.584634i	−0.956322	−	0.292317i	$-0.905574\pi$
$443$		−	5.08271e7i		−	0.584634i	0.956322	−	0.292317i	$-0.0944262\pi$
$444$	4.49042e7	−	7.81660e7i	0.513024	−	0.893036i
$445$	9.38775e7			1.06532
$446$		−	3.91642e7i		−	0.441453i
$447$	−3.89410e7	−	2.23705e7i	−0.435998	−	0.250469i
$448$	−4.67384e7			−0.519804
$449$		−	3.35580e7i		−	0.370730i	−0.982670	−	0.185365i	$-0.940653\pi$
$449$		−	3.35580e7i		−	0.370730i	0.982670	−	0.185365i	$-0.0593467\pi$
$450$	1.87218e8	−	1.09172e8i	2.05452	−	1.19805i
$451$	2.92272e7			0.318609
$452$			8.31186e6i			0.0900084i
$453$	5.18251e7	−	9.02135e7i	0.557501	−	0.970459i
$454$	6.12795e7			0.654859
$455$			6.23952e6i			0.0662394i
$456$	3.97112e6	+	2.28130e6i	0.0418812	+	0.0240595i
$457$	−2.96074e7			−0.310207			−0.155103	−	0.987898i	$-0.549571\pi$
$457$	−2.96074e7			−0.310207			−0.155103	+	0.987898i	$0.549571\pi$
$458$			1.60680e8i			1.67249i
$459$	277087.	+	4.27273e7i	0.00286536	+	0.441842i
$460$	−1.11674e8			−1.14730
$461$			1.02283e8i			1.04400i	0.852946	+	0.522000i	$0.174814\pi$
$461$			1.02283e8i			1.04400i	−0.852946	+	0.522000i	$0.825186\pi$
$462$	5.09945e7	−	8.87676e7i	0.517127	−	0.900178i
$463$	−5.18398e7			−0.522300			−0.261150	−	0.965298i	$-0.584102\pi$
$463$	−5.18398e7			−0.522300			−0.261150	+	0.965298i	$0.584102\pi$
$464$			1.02462e7i			0.102568i
$465$	−1.14438e8	−	6.57413e7i	−1.13818	−	0.653852i
$466$	1.76457e8			1.74374
$467$		−	1.32804e8i		−	1.30395i	−0.758242	−	0.651973i	$-0.773942\pi$
$467$		−	1.32804e8i		−	1.30395i	0.758242	−	0.651973i	$-0.226058\pi$
$468$	−6.82737e6	−	1.17082e7i	−0.0666064	−	0.114222i
$469$	−7.26800e7			−0.704525
$470$			2.93348e8i			2.82546i
$471$	−6.08204e7	+	1.05872e8i	−0.582085	+	1.01325i
$472$	−3.92825e7			−0.373571
$473$		−	2.58961e7i		−	0.244710i
$474$	−8.59981e7	−	4.94035e7i	−0.807521	−	0.463898i
$475$	2.57197e7			0.239985
$476$			2.19020e7i			0.203078i
$477$	−8.06151e7	+	4.70090e7i	−0.742781	+	0.433138i
$478$	−5.14131e7			−0.470749
$479$			9.82255e7i			0.893754i	0.894596	+	0.446877i	$0.147464\pi$
$479$			9.82255e7i			0.893754i	−0.894596	+	0.446877i	$0.852536\pi$
$480$	1.26005e8	−	2.19341e8i	1.13937	−	1.98334i
$481$	−1.02488e7			−0.0920953
$482$			2.27974e7i			0.203584i
$483$	−2.16180e7	−	1.24189e7i	−0.191855	−	0.110215i
$484$	3.31497e8			2.92377
$485$			1.41171e8i			1.23743i
$486$	−1.47055e8	+	8.70350e7i	−1.28107	+	0.758202i
$487$	1.92195e8			1.66401			0.832003	−	0.554771i	$-0.187194\pi$
$487$	1.92195e8			1.66401			0.832003	+	0.554771i	$0.187194\pi$
$488$			4.75608e6i			0.0409251i
$489$	−5.93697e7	+	1.03347e8i	−0.507736	+	0.883832i
$490$	4.03243e7			0.342751
$491$		−	1.79519e8i		−	1.51658i	−0.651916	−	0.758291i	$-0.726034\pi$
$491$		−	1.79519e8i		−	1.51658i	0.651916	−	0.758291i	$-0.273966\pi$
$492$	−2.16839e7	−	1.24568e7i	−0.182072	−	0.104595i
$493$	7.36478e6			0.0614638
$494$		−	2.93117e6i		−	0.0243142i
$495$	1.81691e8	+	3.11579e8i	1.49802	+	2.56893i
$496$	−7.32757e7			−0.600503
$497$		−	6.56001e7i		−	0.534362i
$498$	−1.71742e8	+	2.98956e8i	−1.39055	+	2.42058i
$499$	−3.28399e7			−0.264302			−0.132151	−	0.991230i	$-0.542188\pi$
$499$	−3.28399e7			−0.264302			−0.132151	+	0.991230i	$0.542188\pi$
$500$			1.46416e8i			1.17133i
$501$	−1.69215e8	−	9.72092e7i	−1.34563	−	0.773026i
$502$	9.87114e7			0.780290
$503$		−	1.66157e8i		−	1.30561i	−0.757525	−	0.652806i	$-0.773592\pi$
$503$		−	1.66157e8i		−	1.30561i	0.757525	−	0.652806i	$-0.226408\pi$
$504$	−1.34410e7	+	7.83782e6i	−0.104988	+	0.0612215i
$505$	1.40203e8			1.08863
$506$		−	2.08310e8i		−	1.60790i
$507$	6.41502e7	−	1.11668e8i	0.492237	−	0.856852i
$508$	1.82376e6			0.0139116
$509$		−	1.16022e8i		−	0.879809i	−0.898045	−	0.439904i	$-0.855012\pi$
$509$		−	1.16022e8i		−	0.879809i	0.898045	−	0.439904i	$-0.144988\pi$
$510$	−1.21937e8	−	7.00491e7i	−0.919229	−	0.528071i
$511$	2.64358e7			0.198121
$512$		−	1.72268e8i		−	1.28350i
$513$	−2.02789e7	+	131509.i	−0.150207	+	0.000974098i
$514$	−2.27008e8			−1.67168
$515$			1.72203e8i			1.26072i
$516$	−1.10371e7	+	1.92126e7i	−0.0803350	+	0.139842i
$517$	−3.00266e8			−2.17287
$518$			6.62351e7i			0.476540i
$519$	1.68761e8	+	9.69483e7i	1.20717	+	0.693487i
$520$	7.92360e6			0.0563524
$521$			1.67422e7i			0.118386i	0.998247	+	0.0591929i	$0.0188527\pi$
$521$			1.67422e7i			0.118386i	−0.998247	+	0.0591929i	$0.981147\pi$
$522$	1.48370e7	+	2.54437e7i	0.104312	+	0.178883i
$523$	1.30088e8			0.909355			0.454678	−	0.890656i	$-0.349754\pi$
$523$	1.30088e8			0.909355			0.454678	+	0.890656i	$0.349754\pi$
$524$			7.32835e7i			0.509345i
$525$	−4.35264e7	+	7.57676e7i	−0.300798	+	0.523608i
$526$	−1.58230e8			−1.08726
$527$			5.26692e7i			0.359853i
$528$	1.73644e8	+	9.97538e7i	1.17967	+	0.677685i
$529$	9.73053e7			0.657309
$530$		−	3.07131e8i		−	2.06298i
$531$	1.50263e8	−	8.76226e7i	1.00362	−	0.585238i
$532$	−1.03949e7			−0.0690377
$533$			2.84311e6i			0.0187764i
$534$	7.46345e7	−	1.29918e8i	0.490135	−	0.853193i
$535$	1.81045e8			1.18229
$536$			9.22969e7i			0.599367i
$537$	−3.93001e7	−	2.25768e7i	−0.253788	−	0.145794i
$538$	3.52772e8			2.26542
$539$			4.12752e7i			0.263586i
$540$	−2.00129e6	−	3.08602e8i	−0.0127095	−	1.95982i
$541$	2.96453e8			1.87225			0.936125	−	0.351667i	$-0.114385\pi$
$541$	2.96453e8			1.87225			0.936125	+	0.351667i	$0.114385\pi$
$542$		−	3.71272e8i		−	2.33182i
$543$	−7.94299e7	+	1.38266e8i	−0.496117	+	0.863606i
$544$	−1.00950e8			−0.627062
$545$		−	2.83674e8i		−	1.75238i
$546$	8.63496e6	+	4.96054e6i	0.0530496	+	0.0304755i
$547$	−2.77962e8			−1.69834			−0.849169	−	0.528121i	$-0.822897\pi$
$547$	−2.77962e8			−1.69834			−0.849169	+	0.528121i	$0.822897\pi$
$548$			2.08516e8i			1.26706i
$549$	−1.06088e7	−	1.81929e7i	−0.0641133	−	0.109947i
$550$	−7.30092e8			−4.38823
$551$			3.49541e6i			0.0208951i
$552$	−1.57709e7	+	2.74528e7i	−0.0937645	+	0.163219i
$553$	3.99874e7			0.236455
$554$		−	2.04770e8i		−	1.20431i
$555$	−2.02350e8	−	1.16245e8i	−1.18365	−	0.679976i
$556$	2.74817e8			1.59889
$557$			1.33417e8i			0.772048i	0.922489	+	0.386024i	$0.126152\pi$
$557$			1.33417e8i			0.772048i	−0.922489	+	0.386024i	$0.873848\pi$
$558$	−1.81961e8	+	1.06107e8i	−1.04731	+	0.610716i
$559$	2.51907e6			0.0144213
$560$			7.88811e7i			0.449168i
$561$	7.17011e7	−	1.24812e8i	0.406104	−	0.706917i
$562$	−4.83110e8			−2.72168
$563$			2.60825e8i			1.46158i	0.682601	+	0.730791i	$0.260849\pi$
$563$			2.60825e8i			1.46158i	−0.682601	+	0.730791i	$0.739151\pi$
$564$	2.22770e8	+	1.27975e8i	1.24171	+	0.713326i
$565$	2.15171e7			0.119300
$566$			2.86783e8i			1.58163i
$567$	3.39313e7	−	5.99622e7i	0.186145	−	0.328949i
$568$	−8.33060e7			−0.454602
$569$			8.31944e6i			0.0451604i	0.999745	+	0.0225802i	$0.00718811\pi$
$569$			8.31944e6i			0.0451604i	−0.999745	+	0.0225802i	$0.992812\pi$
$570$	3.32461e7	−	5.78726e7i	0.179522	−	0.312499i
$571$	−6.03520e7			−0.324178			−0.162089	−	0.986776i	$-0.551823\pi$
$571$	−6.03520e7			−0.324178			−0.162089	+	0.986776i	$0.551823\pi$
$572$			4.56582e7i			0.243967i
$573$	1.27944e8	+	7.35002e7i	0.680074	+	0.390683i
$574$	1.83742e7			0.0971568
$575$			1.77803e8i			0.935266i
$576$	−1.32392e8	−	2.27037e8i	−0.692779	−	1.18804i
$577$	−6.79824e7			−0.353890			−0.176945	−	0.984221i	$-0.556622\pi$
$577$	−6.79824e7			−0.353890			−0.176945	+	0.984221i	$0.556622\pi$
$578$		−	2.31334e8i		−	1.19800i
$579$	−9.91492e7	+	1.72592e8i	−0.510803	+	0.889170i
$580$	−5.31928e7			−0.272627
$581$		−	1.39009e8i		−	0.708783i
$582$	1.95369e8	+	1.12234e8i	0.991028	+	0.569318i
$583$	3.14374e8			1.58650
$584$		−	3.35710e7i		−	0.168549i
$585$	−3.03092e7	+	1.76742e7i	−0.151393	+	0.0882819i
$586$	3.03114e8			1.50630
$587$			2.04657e8i			1.01184i	0.862580	+	0.505921i	$0.168847\pi$
$587$			2.04657e8i			1.01184i	−0.862580	+	0.505921i	$0.831153\pi$
$588$	1.75917e7	−	3.06225e7i	0.0865320	−	0.150629i
$589$	−2.49974e7			−0.122334
$590$			5.72478e8i			2.78742i
$591$	−7.62469e7	−	4.38017e7i	−0.369368	−	0.212192i
$592$	−1.29567e8			−0.624496
$593$			3.01942e8i			1.44797i	0.689816	+	0.723985i	$0.257691\pi$
$593$			3.01942e8i			1.44797i	−0.689816	+	0.723985i	$0.742309\pi$
$594$	5.75647e8	−	3.73308e6i	2.74661	−	0.0178118i
$595$	5.66982e7			0.269165
$596$		−	1.29446e8i		−	0.611432i
$597$	−8.90350e7	+	1.54986e8i	−0.418444	+	0.728399i
$598$	2.02635e7			0.0947571
$599$			8.61427e7i			0.400810i	0.979713	+	0.200405i	$0.0642257\pi$
$599$			8.61427e7i			0.400810i	−0.979713	+	0.200405i	$0.935774\pi$
$600$	9.62178e7	+	5.52744e7i	0.445453	+	0.255900i
$601$	9.82665e7			0.452670			0.226335	−	0.974049i	$-0.427326\pi$
$601$	9.82665e7			0.452670			0.226335	+	0.974049i	$0.427326\pi$
$602$		−	1.62800e7i		−	0.0746219i
$603$	−2.05875e8	−	3.53052e8i	−0.938970	−	1.61023i
$604$	2.99883e8			1.36095
$605$		−	8.58154e8i		−	3.87525i
$606$	1.11464e8	−	1.94029e8i	0.500860	−	0.871862i
$607$	−1.11744e8			−0.499640			−0.249820	−	0.968292i	$-0.580371\pi$
$607$	−1.11744e8			−0.499640			−0.249820	+	0.968292i	$0.580371\pi$
$608$		−	4.79121e7i		−	0.213174i
$609$	−1.02972e7	−	5.91542e6i	−0.0455895	−	0.0261899i
$610$	6.93120e7			0.305365
$611$		−	2.92086e7i		−	0.128052i
$612$	−1.06391e8	+	6.20399e7i	−0.464144	+	0.270656i
$613$	8.39830e7			0.364594			0.182297	−	0.983243i	$-0.441647\pi$
$613$	8.39830e7			0.364594			0.182297	+	0.983243i	$0.441647\pi$
$614$			4.32172e8i			1.86703i
$615$	−3.22473e7	+	5.61338e7i	−0.138633	+	0.241323i
$616$	5.24156e7			0.224243
$617$		−	5.22910e7i		−	0.222624i	−0.993786	−	0.111312i	$-0.964495\pi$
$617$		−	5.22910e7i		−	0.222624i	0.993786	−	0.111312i	$-0.0355052\pi$
$618$	2.38314e8	+	1.36905e8i	1.00968	+	0.580033i
$619$	−4.38333e8			−1.84813			−0.924064	−	0.382238i	$-0.875154\pi$
$619$	−4.38333e8			−1.84813			−0.924064	+	0.382238i	$0.875154\pi$
$620$		−	3.80408e8i		−	1.59615i
$621$	−909135.	−	1.40190e8i	−0.00379624	−	0.585386i
$622$	−1.28276e8			−0.533056
$623$			6.04096e7i			0.249828i
$624$	−9.70365e6	+	1.68914e7i	−0.0399376	+	0.0695205i
$625$	−1.10226e7			−0.0451486
$626$			2.37535e8i			0.968288i
$627$	5.92373e7	+	3.40302e7i	0.240322	+	0.138058i
$628$	−3.51934e8			−1.42096
$629$			9.31303e7i			0.374230i
$630$	1.14223e8	+	1.95880e8i	0.456807	+	0.783373i
$631$	2.56885e8			1.02247			0.511234	−	0.859441i	$-0.329188\pi$
$631$	2.56885e8			1.02247			0.511234	+	0.859441i	$0.329188\pi$
$632$		−	5.07803e7i		−	0.201161i
$633$	−1.16049e8	+	2.02009e8i	−0.457540	+	0.796453i
$634$	−1.58685e8			−0.622684
$635$		−	4.72122e6i		−	0.0184388i
$636$	−2.33237e8	−	1.33988e8i	−0.906622	−	0.520829i
$637$	−4.01509e6			−0.0155338
$638$		−	9.92227e7i		−	0.382075i
$639$	3.18660e8	−	1.85820e8i	1.22131	−	0.712181i
$640$	2.65373e8			1.01232
$641$			2.61168e8i			0.991623i	0.868430	+	0.495812i	$0.165129\pi$
$641$			2.61168e8i			0.991623i	−0.868430	+	0.495812i	$0.834871\pi$
$642$	1.43934e8	−	2.50551e8i	0.543950	−	0.946871i
$643$	−3.91833e8			−1.47390			−0.736951	−	0.675946i	$-0.763735\pi$
$643$	−3.91833e8			−1.47390			−0.736951	+	0.675946i	$0.763735\pi$
$644$		−	7.18613e7i		−	0.269053i
$645$	4.97361e7	+	2.85720e7i	0.185350	+	0.106478i
$646$	−2.66354e7			−0.0988012
$647$			4.57171e8i			1.68797i	0.536364	+	0.843987i	$0.319797\pi$
$647$			4.57171e8i			1.68797i	−0.536364	+	0.843987i	$0.680203\pi$
$648$	−7.61463e7	−	4.30896e7i	−0.279849	−	0.158361i
$649$	−5.85978e8			−2.14362
$650$		−	7.10205e7i		−	0.258609i
$651$	4.23041e7	−	7.36400e7i	0.153334	−	0.266914i
$652$	−3.43539e8			−1.23946
$653$		−	4.26334e8i		−	1.53113i	−0.643361	−	0.765563i	$-0.722461\pi$
$653$		−	4.26334e8i		−	1.53113i	0.643361	−	0.765563i	$-0.277539\pi$
$654$	−3.92580e8	−	2.25526e8i	−1.40344	−	0.806239i
$655$	1.89711e8			0.675100
$656$			3.59431e7i			0.127322i
$657$	7.48825e7	+	1.28415e8i	0.264049	+	0.452814i
$658$	−1.88767e8			−0.662597
$659$		−	1.18163e8i		−	0.412883i	−0.978459	−	0.206441i	$-0.933812\pi$
$659$		−	1.18163e8i		−	0.412883i	0.978459	−	0.206441i	$-0.0661883\pi$
$660$	−5.17867e8	+	9.01467e8i	−1.80130	+	3.13558i
$661$	4.62314e8			1.60078			0.800392	−	0.599476i	$-0.204624\pi$
$661$	4.62314e8			1.60078			0.800392	+	0.599476i	$0.204624\pi$
$662$		−	4.65280e8i		−	1.60377i
$663$	1.21412e7	+	6.97480e6i	0.0416603	+	0.0239327i
$664$	−1.76528e8			−0.602989
$665$			2.69096e7i			0.0915045i
$666$	−3.21745e8	+	1.87619e8i	−1.08915	+	0.635118i
$667$	−2.41642e7			−0.0814319
$668$		−	5.62495e8i		−	1.88708i
$669$	−4.42300e7	+	7.69925e7i	−0.147720	+	0.257140i
$670$	1.34507e9			4.47221
$671$			7.09465e7i			0.234835i
$672$	1.41145e8	+	8.10836e7i	0.465111	+	0.267193i
$673$	−2.85120e8			−0.935368			−0.467684	−	0.883896i	$-0.654912\pi$
$673$	−2.85120e8			−0.935368			−0.467684	+	0.883896i	$0.654912\pi$
$674$		−	6.27741e8i		−	2.05022i
$675$	−4.91344e8	+	3.18638e6i	−1.59762	+	0.0103606i
$676$	3.71201e8			1.20163
$677$			9.78993e7i			0.315510i	0.987478	+	0.157755i	$0.0504257\pi$
$677$			9.78993e7i			0.315510i	−0.987478	+	0.157755i	$0.949574\pi$
$678$	1.71065e7	−	2.97779e7i	0.0548875	−	0.0955443i
$679$	−9.08426e7			−0.290189
$680$		−	7.20014e7i		−	0.228989i
$681$	−1.20469e8	−	6.92060e7i	−0.381447	−	0.219130i
$682$	7.09590e8			2.23694
$683$		−	6.00287e8i		−	1.88407i	−0.335517	−	0.942034i	$-0.608911\pi$
$683$		−	6.00287e8i		−	1.88407i	0.335517	−	0.942034i	$-0.391089\pi$
$684$	−2.94449e7	−	5.04946e7i	−0.0920114	−	0.157789i
$685$	5.39791e8			1.67940
$686$			2.59484e7i			0.0803782i
$687$	1.81464e8	−	3.15879e8i	0.559654	−	0.974206i
$688$	3.18465e7			0.0977905
$689$			3.05810e7i			0.0934963i
$690$	4.00080e8	+	2.29834e8i	1.21786	+	0.699629i
$691$	2.55391e8			0.774053			0.387026	−	0.922069i	$-0.373502\pi$
$691$	2.55391e8			0.774053			0.387026	+	0.922069i	$0.373502\pi$
$692$			5.60985e8i			1.69291i
$693$	−2.00499e8	+	1.16917e8i	−0.602439	+	0.351300i
$694$	−6.45978e8			−1.93259
$695$		−	7.11426e8i		−	2.11922i
$696$	−7.51203e6	+	1.30764e7i	−0.0222808	+	0.0387848i
$697$	2.58352e7			0.0762980
$698$			1.63216e8i			0.479952i
$699$	−3.46896e8	−	1.99282e8i	−1.01570	−	0.583493i
$700$	−2.51863e8			−0.734293
$701$			4.76839e8i			1.38426i	0.721772	+	0.692130i	$0.243328\pi$
$701$			4.76839e8i			1.38426i	−0.721772	+	0.692130i	$0.756672\pi$
$702$	363140.	+	5.59967e7i	0.00104969	+	0.161864i
$703$	−4.42007e7			−0.127222
$704$			8.85375e8i			2.53752i
$705$	3.31292e8	−	5.76690e8i	0.945462	−	1.64579i
$706$	−2.27217e8			−0.645695
$707$			9.02195e7i			0.255295i
$708$	4.34743e8	+	2.49748e8i	1.22499	+	0.703723i
$709$	5.28994e8			1.48427			0.742134	−	0.670252i	$-0.233814\pi$
$709$	5.28994e8			1.48427			0.742134	+	0.670252i	$0.233814\pi$
$710$			1.21405e9i			3.39204i
$711$	1.13269e8	+	1.94244e8i	0.315140	+	0.540429i
$712$	7.67145e7			0.212538
$713$		−	1.72810e8i		−	0.476760i
$714$	4.50762e7	−	7.84654e7i	0.123838	−	0.215568i
$715$	1.18197e8			0.323360
$716$		−	1.30639e8i		−	0.355905i
$717$	1.01073e8	+	5.80633e7i	0.274205	+	0.157523i
$718$	4.94745e7			0.133662
$719$			4.14939e8i			1.11634i	0.829725	+	0.558172i	$0.188497\pi$
$719$			4.14939e8i			1.11634i	−0.829725	+	0.558172i	$0.811503\pi$
$720$	−3.83174e8	+	2.23440e8i	−1.02659	+	0.598637i
$721$	−1.10811e8			−0.295650
$722$			5.47628e8i			1.45504i
$723$	2.57462e7	−	4.48172e7i	0.0681237	−	0.118585i
$724$	−4.59616e8			−1.21110
$725$			8.46917e7i			0.222242i
$726$	−1.18761e9	−	6.82250e8i	−3.10359	−	1.78293i
$727$	1.15280e7			0.0300021			0.0150010	−	0.999887i	$-0.495225\pi$
$727$	1.15280e7			0.0300021			0.0150010	+	0.999887i	$0.495225\pi$
$728$			5.09879e6i			0.0132152i
$729$	3.87388e8	−	5.02465e6i	0.999916	−	0.0129695i
$730$	−4.89242e8			−1.25764
$731$		−	2.28907e7i		−	0.0586012i
$732$	3.02378e7	−	5.26359e7i	0.0770934	−	0.134199i
$733$	−4.09692e8			−1.04027			−0.520134	−	0.854085i	$-0.674118\pi$
$733$	−4.09692e8			−1.04027			−0.520134	+	0.854085i	$0.674118\pi$
$734$		−	4.81250e8i		−	1.21698i
$735$	−7.92732e7	−	4.55402e7i	−0.199648	−	0.114692i
$736$	3.31222e8			0.830779
$737$			1.37679e9i			3.43927i
$738$	5.20472e7	+	8.92549e7i	0.129488	+	0.222056i
$739$	5.38736e7			0.133488			0.0667440	−	0.997770i	$-0.478739\pi$
$739$	5.38736e7			0.133488			0.0667440	+	0.997770i	$0.478739\pi$
$740$		−	6.72642e8i		−	1.65993i
$741$	−3.31032e6	+	5.76237e6i	−0.00813608	+	0.0141627i
$742$	1.97637e8			0.483789
$743$		−	3.77773e8i		−	0.921011i	−0.887657	−	0.460505i	$-0.847668\pi$
$743$		−	3.77773e8i		−	0.921011i	0.887657	−	0.460505i	$-0.152332\pi$
$744$	−9.35159e7	−	5.37222e7i	−0.227074	−	0.130447i
$745$	−3.35099e8			−0.810409
$746$		−	3.46773e8i		−	0.835274i
$747$	6.75251e8	−	3.93758e8i	1.61996	−	0.944644i
$748$	4.14894e8			0.991362
$749$			1.16501e8i			0.277259i
$750$	3.01337e8	−	5.24546e8i	0.714280	−	1.24337i
$751$	1.52873e8			0.360921			0.180460	−	0.983582i	$-0.442241\pi$
$751$	1.52873e8			0.360921			0.180460	+	0.983582i	$0.442241\pi$
$752$		−	3.69261e8i		−	0.868320i
$753$	−1.94056e8	−	1.11480e8i	−0.454509	−	0.261102i
$754$	9.65199e6			0.0225166
$755$		−	7.76314e8i		−	1.80383i
$756$	1.98583e8	−	1.28782e6i	0.459597	−	0.00298049i
$757$	−4.53264e8			−1.04487			−0.522437	−	0.852678i	$-0.674977\pi$
$757$	−4.53264e8			−1.04487			−0.522437	+	0.852678i	$0.674977\pi$
$758$		−	5.29756e7i		−	0.121638i
$759$	−2.35254e8	+	4.09514e8i	−0.538037	+	0.936578i
$760$	3.41727e7			0.0778464
$761$			5.24514e8i			1.19015i	0.803669	+	0.595077i	$0.202878\pi$
$761$			5.24514e8i			1.19015i	−0.803669	+	0.595077i	$0.797122\pi$
$762$	−6.53376e6	−	3.75346e6i	−0.0147672	−	0.00848334i
$763$	1.82542e8			0.410951
$764$			4.25304e8i			0.953717i
$765$	1.60604e8	+	2.75418e8i	0.358734	+	0.615189i
$766$	2.72458e8			0.606196
$767$		−	5.70017e7i		−	0.126329i
$768$	−9.93452e7	+	1.72933e8i	−0.219312	+	0.381764i
$769$	1.67566e8			0.368475			0.184237	−	0.982882i	$-0.441018\pi$
$769$	1.67566e8			0.368475			0.184237	+	0.982882i	$0.441018\pi$
$770$		−	7.63871e8i		−	1.67320i
$771$	4.46274e8	+	2.56372e8i	0.973730	+	0.559381i
$772$	−5.73720e8			−1.24695
$773$		−	4.79724e8i		−	1.03861i	−0.854589	−	0.519306i	$-0.826191\pi$
$773$		−	4.79724e8i		−	1.03861i	0.854589	−	0.519306i	$-0.173809\pi$
$774$	7.90823e7	−	4.61152e7i	0.170552	−	0.0994538i
$775$	−6.05671e8			−1.30116
$776$			1.15362e8i			0.246875i
$777$	7.48026e7	−	1.30211e8i	0.159461	−	0.277578i
$778$	1.12070e9			2.37986
$779$			1.22617e7i			0.0259381i
$780$	−8.76912e7	−	5.03761e7i	−0.184787	−	0.106155i
$781$	−1.24268e9			−2.60859
$782$		−	1.84134e8i		−	0.385046i
$783$	−433043.	−	6.67758e7i	−0.000902080	−	0.139102i
$784$	−5.07595e7			−0.105334
$785$			9.11059e8i			1.88338i
$786$	1.50824e8	−	2.62544e8i	0.310601	−	0.540672i
$787$	8.43794e8			1.73106			0.865530	−	0.500857i	$-0.166982\pi$
$787$	8.43794e8			1.73106			0.865530	+	0.500857i	$0.166982\pi$
$788$		−	2.53456e8i		−	0.517992i
$789$	3.11063e8	+	1.78697e8i	0.633312	+	0.363820i
$790$	−7.40039e8			−1.50097
$791$			1.38461e7i			0.0279769i
$792$	1.48474e8	+	2.54615e8i	0.298864	+	0.512518i
$793$	−6.90139e6			−0.0138394
$794$		−	8.91407e8i		−	1.78080i
$795$	−3.46858e8	+	6.03787e8i	−0.690320	+	1.20166i
$796$	−5.15195e8			−1.02149
$797$			1.02981e8i			0.203415i	0.994814	+	0.101707i	$0.0324305\pi$
$797$			1.02981e8i			0.203415i	−0.994814	+	0.101707i	$0.967569\pi$
$798$	3.72406e7	+	2.13937e7i	0.0732838	+	0.0420995i
$799$	−2.65418e8			−0.520342
$800$		−	1.16088e9i		−	2.26735i
$801$	−2.93447e8	+	1.71117e8i	−0.570994	+	0.332963i
$802$	1.91577e8			0.371381
$803$		−	5.00779e8i		−	0.967162i
$804$	5.86798e8	−	1.02146e9i	1.12907	−	1.96540i
$805$	−1.86029e8			−0.356610
$806$			6.90261e7i			0.131828i
$807$	−6.93513e8	−	3.98403e8i	−1.31957	−	0.758058i
$808$	1.14570e8			0.217189
$809$		−	7.77366e8i		−	1.46818i	−0.679051	−	0.734091i	$-0.737608\pi$
$809$		−	7.77366e8i		−	1.46818i	0.679051	−	0.734091i	$-0.262392\pi$
$810$	−6.27959e8	+	1.10971e9i	−1.18162	+	2.08811i
$811$	−2.17231e8			−0.407248			−0.203624	−	0.979049i	$-0.565272\pi$
$811$	−2.17231e8			−0.407248			−0.203624	+	0.979049i	$0.565272\pi$
$812$		−	3.42292e7i		−	0.0639336i
$813$	−4.19296e8	+	7.29881e8i	−0.780277	+	1.35825i
$814$	1.25471e9			2.32632
$815$			8.89328e8i			1.64282i
$816$	1.53492e8	+	8.81766e7i	0.282497	+	0.162287i
$817$	1.08642e7			0.0199219
$818$			6.20092e8i			1.13291i
$819$	−1.13732e7	−	1.95038e7i	−0.0207029	−	0.0355032i
$820$	−1.86597e8			−0.338425
$821$			3.43837e8i			0.621332i	0.950519	+	0.310666i	$0.100552\pi$
$821$			3.43837e8i			0.621332i	−0.950519	+	0.310666i	$0.899448\pi$
$822$	4.29145e8	−	7.47025e8i	0.772660	−	1.34499i
$823$	−3.01782e8			−0.541369			−0.270684	−	0.962668i	$-0.587250\pi$
$823$	−3.01782e8			−0.541369			−0.270684	+	0.962668i	$0.587250\pi$
$824$			1.40720e8i			0.251521i
$825$	1.43528e9	+	8.24530e8i	2.55609	+	1.46840i
$826$	−3.68386e8			−0.653677
$827$		−	6.99202e8i		−	1.23619i	−0.786102	−	0.618097i	$-0.787904\pi$
$827$		−	6.99202e8i		−	1.23619i	0.786102	−	0.618097i	$-0.212096\pi$
$828$	3.49075e8	−	2.03556e8i	0.614933	−	0.358585i
$829$	9.90979e8			1.73941			0.869703	−	0.493575i	$-0.164310\pi$
$829$	9.90979e8			1.73941			0.869703	+	0.493575i	$0.164310\pi$
$830$			2.57260e9i			4.49923i
$831$	−2.31257e8	+	4.02556e8i	−0.402988	+	0.701493i
$832$	−8.61258e7			−0.149542
$833$			3.64849e7i			0.0631216i
$834$	−9.84553e8	−	5.65598e8i	−1.69723	−	0.975011i
$835$	−1.45614e9			−2.50118
$836$			1.96913e8i			0.337021i
$837$	4.77546e8	−	3.09690e6i	0.814403	−	0.00528142i
$838$	−6.39359e8			−1.08646
$839$		−	1.84225e8i		−	0.311935i	−0.987762	−	0.155967i	$-0.950151\pi$
$839$		−	1.84225e8i		−	0.311935i	0.987762	−	0.155967i	$-0.0498494\pi$
$840$	−5.78318e7	+	1.00670e8i	−0.0975728	+	0.169848i
$841$	5.83313e8			0.980650
$842$			9.44563e8i			1.58232i
$843$	9.49742e8	+	5.45600e8i	1.58534	+	0.910733i
$844$	−6.71508e8			−1.11692
$845$		−	9.60938e8i		−	1.59267i
$846$	−5.34706e8	−	9.16960e8i	−0.883089	−	1.51440i
$847$	5.52217e8			0.908781
$848$			3.86611e8i			0.633996i
$849$	3.23879e8	−	5.63785e8i	0.529248	−	0.921278i
$850$	−6.45360e8			−1.05086
$851$		−	3.05565e8i		−	0.495809i
$852$	9.21954e8	+	5.29637e8i	1.49070	+	0.856366i
$853$	−1.02654e8			−0.165397			−0.0826983	−	0.996575i	$-0.526354\pi$
$853$	−1.02654e8			−0.165397			−0.0826983	+	0.996575i	$0.526354\pi$
$854$			4.46018e7i			0.0716108i
$855$	−1.30717e8	+	7.62247e7i	−0.209138	+	0.121954i
$856$	1.47946e8			0.235875
$857$		−	7.39518e8i		−	1.17491i	−0.809255	−	0.587457i	$-0.800129\pi$
$857$		−	7.39518e8i		−	1.17491i	0.809255	−	0.587457i	$-0.199871\pi$
$858$	9.39686e7	−	1.63574e8i	0.148772	−	0.258972i
$859$	3.89632e7			0.0614717			0.0307359	−	0.999528i	$-0.490215\pi$
$859$	3.89632e7			0.0614717			0.0307359	+	0.999528i	$0.490215\pi$
$860$			1.65330e8i			0.259930i
$861$	−3.61217e7	−	2.07509e7i	−0.0565925	−	0.0325108i
$862$	2.47458e8			0.386349
$863$		−	4.04656e8i		−	0.629584i	−0.949161	−	0.314792i	$-0.898065\pi$
$863$		−	4.04656e8i		−	0.629584i	0.949161	−	0.314792i	$-0.101935\pi$
$864$	5.93578e6	+	9.15306e8i	0.00920315	+	1.41914i
$865$	1.45224e9			2.24383
$866$		−	5.52455e8i		−	0.850635i
$867$	−2.61257e8	+	4.54777e8i	−0.400876	+	0.697817i
$868$	2.44790e8			0.374312
$869$		−	7.57491e8i		−	1.15430i
$870$	1.90567e8	+	1.09475e8i	0.289395	+	0.166249i
$871$	−1.33929e8			−0.202684
$872$		−	2.31811e8i		−	0.349611i
$873$	−2.57323e8	−	4.41279e8i	−0.386754	−	0.663240i
$874$	8.73920e7			0.130899
$875$			2.43904e8i			0.364078i
$876$	−2.13435e8	+	3.71533e8i	−0.317507	+	0.552694i
$877$	1.65385e8			0.245187			0.122594	−	0.992457i	$-0.460879\pi$
$877$	1.65385e8			0.245187			0.122594	+	0.992457i	$0.460879\pi$
$878$			9.31470e8i			1.37621i
$879$	−5.95889e8	−	3.42321e8i	−0.877402	−	0.504043i
$880$	1.49426e9			2.19270
$881$		−	3.46930e7i		−	0.0507358i	−0.999678	−	0.0253679i	$-0.991924\pi$
$881$		−	3.46930e7i		−	0.0507358i	0.999678	−	0.0253679i	$-0.00807571\pi$
$882$	−1.26047e8	+	7.35020e7i	−0.183708	+	0.107126i
$883$	3.77621e8			0.548497			0.274248	−	0.961659i	$-0.411571\pi$
$883$	3.77621e8			0.548497			0.274248	+	0.961659i	$0.411571\pi$
$884$			4.03592e7i			0.0584233i
$885$	6.46528e8	−	1.12543e9i	0.932733	−	1.62364i
$886$	−6.05299e8			−0.870300
$887$			1.24149e9i			1.77899i	0.456947	+	0.889494i	$0.348943\pi$
$887$			1.24149e9i			1.77899i	−0.456947	+	0.889494i	$0.651057\pi$
$888$	−1.65356e8	−	9.49924e7i	−0.236146	−	0.135659i
$889$	3.03807e6			0.00432407
$890$		−	1.11799e9i		−	1.58587i
$891$	−1.13588e9	−	6.42768e8i	−1.60582	−	0.908701i
$892$	−2.55934e8			−0.360607
$893$		−	1.25970e8i		−	0.176894i
$894$	−2.66410e8	+	4.63748e8i	−0.372854	+	0.649038i
$895$	−3.38189e8			−0.471727
$896$			1.70766e8i			0.237398i
$897$	−3.98359e7	−	2.28846e7i	−0.0551947	−	0.0317078i
$898$	−3.99643e8			−0.551878
$899$		−	8.23134e7i		−	0.113290i
$900$	−7.13431e8	−	1.22345e9i	−0.978643	−	1.67826i
$901$	2.77888e8			0.379923
$902$		−	3.48067e8i		−	0.474289i
$903$	−1.83859e7	+	3.20048e7i	−0.0249701	+	0.0434663i
$904$	1.75833e7			0.0238010
$905$			1.18982e9i			1.60522i
$906$	−1.07435e9	−	6.17185e8i	−1.44465	−	0.829910i
$907$	8.87279e8			1.18916			0.594578	−	0.804038i	$-0.297319\pi$
$907$	8.87279e8			1.18916			0.594578	+	0.804038i	$0.297319\pi$
$908$		−	4.00456e8i		−	0.534931i
$909$	−4.38252e8	+	2.55558e8i	−0.583489	+	0.340249i
$910$	7.43064e7			0.0986057
$911$			7.79390e8i			1.03086i	0.856932	+	0.515430i	$0.172368\pi$
$911$			7.79390e8i			1.03086i	−0.856932	+	0.515430i	$0.827632\pi$
$912$	−4.18497e7	+	7.28489e7i	−0.0551706	+	0.0960370i
$913$	−2.63327e9			−3.46005
$914$			3.52594e8i			0.461782i
$915$	−1.36260e8	−	7.82774e7i	−0.177871	−	0.102182i
$916$	1.05003e9			1.36620
$917$			1.22078e8i			0.158317i
$918$	5.08839e8	−	3.29983e6i	0.657737	−	0.00426544i
$919$	9.56958e8			1.23295			0.616476	−	0.787373i	$-0.288560\pi$
$919$	9.56958e8			1.23295			0.616476	+	0.787373i	$0.288560\pi$
$920$			2.36240e8i			0.303382i
$921$	4.88074e8	−	8.49605e8i	0.624751	−	1.08752i
$922$	1.21809e9			1.55412
$923$		−	1.20883e8i		−	0.153730i
$924$	−5.80088e8	−	3.33244e8i	−0.735323	−	0.422422i
$925$	−1.07096e9			−1.35315
$926$			6.17360e8i			0.777509i
$927$	−3.13886e8	−	5.38279e8i	−0.394034	−	0.675723i
$928$	1.57769e8			0.197414
$929$		−	1.22542e9i		−	1.52840i	−0.644979	−	0.764201i	$-0.723134\pi$
$929$		−	1.22542e9i		−	1.52840i	0.644979	−	0.764201i	$-0.276866\pi$
$930$	−7.82913e8	+	1.36284e9i	−0.973340	+	1.69432i
$931$	−1.73162e7			−0.0214587
$932$		−	1.15313e9i		−	1.42440i
$933$	2.52176e8	+	1.44868e8i	0.310498	+	0.178372i
$934$	−1.58156e9			−1.94109
$935$		−	1.07405e9i		−	1.31398i
$936$	−2.47680e7	+	1.44429e7i	−0.0302039	+	0.0176128i
$937$	−1.30846e9			−1.59053			−0.795267	−	0.606259i	$-0.792669\pi$
$937$	−1.30846e9			−1.59053			−0.795267	+	0.606259i	$0.792669\pi$
$938$			8.65547e8i			1.04877i
$939$	2.68260e8	−	4.66968e8i	0.324010	−	0.564015i
$940$	1.91700e9			2.30802
$941$			1.06925e9i			1.28325i	0.767020	+	0.641623i	$0.221739\pi$
$941$			1.06925e9i			1.28325i	−0.767020	+	0.641623i	$0.778261\pi$
$942$	1.26083e9	+	7.24310e8i	1.50835	+	0.866507i
$943$	−8.47663e7			−0.101085
$944$		−	7.20625e8i		−	0.856630i
$945$	−3.33380e6	−	5.14077e8i	−0.00395043	−	0.609162i
$946$	−3.08397e8			−0.364281
$947$			5.75280e8i			0.677375i	0.940899	+	0.338688i	$0.109983\pi$
$947$			5.75280e8i			0.677375i	−0.940899	+	0.338688i	$0.890017\pi$
$948$	−3.22847e8	+	5.61990e8i	−0.378941	+	0.659635i
$949$	4.87138e7			0.0569972
$950$		−	3.06295e8i		−	0.357248i
$951$	3.11958e8	+	1.79211e8i	0.362705	+	0.208364i
$952$	4.63324e7			0.0537000
$953$		−	3.62796e7i		−	0.0419164i	−0.999780	−	0.0209582i	$-0.993328\pi$
$953$		−	3.62796e7i		−	0.0419164i	0.999780	−	0.0209582i	$-0.00667168\pi$
$954$	5.59830e8	+	9.60045e8i	0.644779	+	1.10572i
$955$	1.10100e9			1.26408
$956$			3.35980e8i			0.384538i
$957$	−1.12057e8	+	1.95061e8i	−0.127851	+	0.222554i
$958$	1.16977e9			1.33046
$959$			3.47352e8i			0.393835i
$960$	−1.70045e9	−	9.76862e8i	−1.92199	−	1.10413i
$961$	−2.98841e8			−0.336720
$962$			1.22053e8i			0.137095i
$963$	−5.65919e8	+	3.30004e8i	−0.633688	+	0.369522i
$964$	1.48979e8			0.166300
$965$			1.48520e9i			1.65274i
$966$	−1.47897e8	+	2.57449e8i	−0.164069	+	0.285601i
$967$	−4.62267e8			−0.511227			−0.255613	−	0.966779i	$-0.582277\pi$
$967$	−4.62267e8			−0.511227			−0.255613	+	0.966779i	$0.582277\pi$
$968$		−	7.01264e8i		−	0.773135i
$969$	5.23624e7	+	3.00807e7i	0.0575504	+	0.0330611i
$970$	1.68121e9			1.84207
$971$		−	4.04275e8i		−	0.441590i	−0.975320	−	0.220795i	$-0.929135\pi$
$971$		−	4.04275e8i		−	0.441590i	0.975320	−	0.220795i	$-0.0708652\pi$
$972$	5.68766e8	+	9.60993e8i	0.619348	+	1.04646i
$973$	4.57798e8			0.496976
$974$		−	2.28885e9i		−	2.47708i
$975$	−8.02070e7	+	1.39619e8i	−0.0865363	+	0.150636i
$976$	−8.72487e7			−0.0938446
$977$		−	7.23589e8i		−	0.775904i	−0.921679	−	0.387952i	$-0.873183\pi$
$977$		−	7.23589e8i		−	0.775904i	0.921679	−	0.387952i	$-0.126817\pi$
$978$	1.23075e9	+	7.07033e8i	1.31569	+	0.755829i
$979$	1.14435e9			1.21958
$980$		−	2.63515e8i		−	0.279981i
$981$	5.17073e8	+	8.86721e8i	0.547702	+	0.939247i
$982$	−2.13789e9			−2.25762
$983$		−	1.13657e9i		−	1.19656i	−0.801287	−	0.598280i	$-0.795851\pi$
$983$		−	1.13657e9i		−	1.19656i	0.801287	−	0.598280i	$-0.204149\pi$
$984$	−2.63517e7	+	4.58712e7i	−0.0276582	+	0.0481454i
$985$	−6.56127e8			−0.686561
$986$		−	8.77072e7i		−	0.0914965i
$987$	3.71096e8	+	2.13184e8i	0.385954	+	0.221720i
$988$	−1.91550e7			−0.0198614
$989$			7.51053e7i			0.0776393i
$990$	3.71060e9	−	2.16376e9i	3.82418	−	2.22999i
$991$	1.11633e9			1.14703			0.573513	−	0.819197i	$-0.305580\pi$
$991$	1.11633e9			1.14703			0.573513	+	0.819197i	$0.305580\pi$
$992$			1.12828e9i			1.15580i
$993$	−5.25464e8	+	9.14691e8i	−0.536655	+	0.934172i
$994$	−7.81232e8			−0.795464
$995$			1.33370e9i			1.35391i
$996$	1.95365e9	+	1.12232e9i	1.97728	+	1.13589i
$997$	9.21729e8			0.930075			0.465037	−	0.885291i	$-0.346041\pi$
$997$	9.21729e8			0.930075			0.465037	+	0.885291i	$0.346041\pi$
$998$			3.91090e8i			0.393446i
$999$	8.44404e8	−	5.47598e6i	0.846942	−	0.00549244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.b.a.8.3	✓	12
3.2	odd	2	inner	21.7.b.a.8.10	yes	12
4.3	odd	2		336.7.d.a.113.9		12
7.6	odd	2		147.7.b.b.50.3		12
12.11	even	2		336.7.d.a.113.10		12
21.20	even	2		147.7.b.b.50.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.b.a.8.3	✓	12	1.1	even	1	trivial
21.7.b.a.8.10	yes	12	3.2	odd	2	inner
147.7.b.b.50.3		12	7.6	odd	2
147.7.b.b.50.10		12	21.20	even	2
336.7.d.a.113.9		12	4.3	odd	2
336.7.d.a.113.10		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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.9090i q^{2} +(-13.4494 + 23.4118i) q^{3} -77.8243 q^{4} +201.466i q^{5} +(278.811 + 160.169i) q^{6} -129.642 q^{7} +164.633i q^{8} +(-367.226 - 629.751i) q^{9} +O(q^{10})\)	\(q-11.9090i q^{2} +(-13.4494 + 23.4118i) q^{3} -77.8243 q^{4} +201.466i q^{5} +(278.811 + 160.169i) q^{6} -129.642 q^{7} +164.633i q^{8} +(-367.226 - 629.751i) q^{9} +2399.25 q^{10} +2455.83i q^{11} +(1046.69 - 1822.01i) q^{12} -238.894 q^{13} +1543.90i q^{14} +(-4716.68 - 2709.60i) q^{15} -3020.14 q^{16} +2170.82i q^{17} +(-7499.70 + 4373.29i) q^{18} -1030.29 q^{19} -15678.9i q^{20} +(1743.61 - 3035.15i) q^{21} +29246.5 q^{22} -7122.54i q^{23} +(-3854.36 - 2214.22i) q^{24} -24963.4 q^{25} +2844.99i q^{26} +(19682.6 - 127.642i) q^{27} +10089.3 q^{28} -3392.63i q^{29} +(-32268.6 + 56170.9i) q^{30} +24262.4 q^{31} +46503.3i q^{32} +(-57495.5 - 33029.5i) q^{33} +25852.2 q^{34} -26118.4i q^{35} +(28579.1 + 49009.9i) q^{36} +42901.1 q^{37} +12269.8i q^{38} +(3212.98 - 5592.94i) q^{39} -33167.9 q^{40} -11901.1i q^{41} +(-36145.6 - 20764.6i) q^{42} -10544.7 q^{43} -191123. i q^{44} +(126873. - 73983.4i) q^{45} -84822.4 q^{46} +122266. i q^{47} +(40619.1 - 70706.9i) q^{48} +16807.0 q^{49} +297289. i q^{50} +(-50822.7 - 29196.2i) q^{51} +18591.7 q^{52} -128011. i q^{53} +(-1520.09 - 234400. i) q^{54} -494766. q^{55} -21343.3i q^{56} +(13856.9 - 24121.1i) q^{57} -40402.9 q^{58} +238607. i q^{59} +(367072. + 210872. i) q^{60} +28889.0 q^{61} -288941. i q^{62} +(47607.8 + 81642.0i) q^{63} +360519. q^{64} -48128.9i q^{65} +(-393349. + 684714. i) q^{66} +560622. q^{67} -168942. i q^{68} +(166752. + 95794.1i) q^{69} -311044. q^{70} +506010. i q^{71} +(103678. - 60457.5i) q^{72} -203914. q^{73} -510909. i q^{74} +(335743. - 584438. i) q^{75} +80181.9 q^{76} -318379. i q^{77} +(-66606.3 - 38263.4i) q^{78} -308446. q^{79} -608454. i q^{80} +(-261731. + 462522. i) q^{81} -141731. q^{82} +1.07225e6i q^{83} +(-135695. + 236208. i) q^{84} -437345. q^{85} +125577. i q^{86} +(79427.7 + 45629.0i) q^{87} -404311. q^{88} -465973. i q^{89} +(-881068. - 1.51093e6i) q^{90} +30970.6 q^{91} +554307. i q^{92} +(-326315. + 568026. i) q^{93} +1.45607e6 q^{94} -207569. i q^{95} +(-1.08873e6 - 625443. i) q^{96} +700720. q^{97} -200155. i q^{98} +(1.54656e6 - 901846. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) \) 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9	\( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) \) 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9 - 1092 * q^10 - 1726 * q^12 + 384 * q^13 - 632 * q^15 + 5892 * q^16 - 40 * q^18 + 11304 * q^19 - 5488 * q^21 + 15312 * q^22 + 12138 * q^24 - 77292 * q^25 + 114796 * q^27 + 41160 * q^28 - 101908 * q^30 - 9360 * q^31 - 65744 * q^33 - 169008 * q^34 - 195652 * q^36 + 212016 * q^37 + 159544 * q^39 + 196644 * q^40 - 37730 * q^42 + 28080 * q^43 - 4760 * q^45 - 418512 * q^46 + 865742 * q^48 + 201684 * q^49 - 371880 * q^51 - 138300 * q^52 - 254170 * q^54 - 732144 * q^55 - 440624 * q^57 + 1164240 * q^58 + 677660 * q^60 + 926736 * q^61 + 2744 * q^63 - 1380108 * q^64 - 1414588 * q^66 - 223104 * q^67 + 153048 * q^69 - 382788 * q^70 - 540192 * q^72 + 600984 * q^73 + 594716 * q^75 + 604596 * q^76 + 1866140 * q^78 - 276864 * q^79 + 617596 * q^81 + 1138200 * q^82 + 1398754 * q^84 - 3002472 * q^85 - 3372824 * q^87 - 1599048 * q^88 - 788032 * q^90 - 1243032 * q^91 + 408168 * q^93 + 8059296 * q^94 - 1141658 * q^96 + 1621416 * q^97 + 5211904 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more