LMFDB - Embedded newform 21.7.b.a.8.2

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			8.2
Root			$-12.1723i$ of defining polynomial
Character	$\chi$	$=$	21.8
Dual form			21.7.b.a.8.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.1723i q^{2} +(-18.4482 - 19.7146i) q^{3} -84.1649 q^{4} -4.50929i q^{5} +(-239.971 + 224.557i) q^{6} +129.642 q^{7} +245.453i q^{8} +(-48.3270 + 727.396i) q^{9} +O(q^{10})$	\(q-12.1723i q^{2} +(-18.4482 - 19.7146i) q^{3} -84.1649 q^{4} -4.50929i q^{5} +(-239.971 + 224.557i) q^{6} +129.642 q^{7} +245.453i q^{8} +(-48.3270 + 727.396i) q^{9} -54.8885 q^{10} -332.302i q^{11} +(1552.69 + 1659.27i) q^{12} -3039.75 q^{13} -1578.04i q^{14} +(-88.8987 + 83.1884i) q^{15} -2398.82 q^{16} -8747.00i q^{17} +(8854.09 + 588.251i) q^{18} +2520.10 q^{19} +379.524i q^{20} +(-2391.66 - 2555.83i) q^{21} -4044.88 q^{22} +305.657i q^{23} +(4839.00 - 4528.17i) q^{24} +15604.7 q^{25} +37000.8i q^{26} +(15231.8 - 12466.4i) q^{27} -10911.3 q^{28} -15999.0i q^{29} +(1012.59 + 1082.10i) q^{30} -45543.4 q^{31} +44908.2i q^{32} +(-6551.18 + 6130.37i) q^{33} -106471. q^{34} -584.593i q^{35} +(4067.44 - 61221.2i) q^{36} +61906.5 q^{37} -30675.4i q^{38} +(56078.0 + 59927.4i) q^{39} +1106.82 q^{40} -27561.8i q^{41} +(-31110.3 + 29112.0i) q^{42} +124173. q^{43} +27968.1i q^{44} +(3280.04 + 217.921i) q^{45} +3720.55 q^{46} +24511.9i q^{47} +(44254.0 + 47291.7i) q^{48} +16807.0 q^{49} -189945. i q^{50} +(-172443. + 161366. i) q^{51} +255841. q^{52} -257014. i q^{53} +(-151745. - 185407. i) q^{54} -1498.45 q^{55} +31821.0i q^{56} +(-46491.3 - 49682.6i) q^{57} -194745. q^{58} -158263. i q^{59} +(7482.15 - 7001.54i) q^{60} -115718. q^{61} +554367. i q^{62} +(-6265.20 + 94301.0i) q^{63} +393111. q^{64} +13707.1i q^{65} +(74620.8 + 79742.9i) q^{66} -328007. q^{67} +736190. i q^{68} +(6025.90 - 5638.83i) q^{69} -7115.84 q^{70} +384121. i q^{71} +(-178542. - 11862.0i) q^{72} +240083. q^{73} -753545. i q^{74} +(-287878. - 307639. i) q^{75} -212104. q^{76} -43080.2i q^{77} +(729454. - 682598. i) q^{78} +440967. q^{79} +10817.0i q^{80} +(-526770. - 70305.8i) q^{81} -335490. q^{82} +100434. i q^{83} +(201294. + 215111. i) q^{84} -39442.8 q^{85} -1.51147e6i q^{86} +(-315414. + 295154. i) q^{87} +81564.5 q^{88} +961635. i q^{89} +(2652.60 - 39925.7i) q^{90} -394079. q^{91} -25725.6i q^{92} +(840193. + 897867. i) q^{93} +298366. q^{94} -11363.9i q^{95} +(885345. - 828476. i) q^{96} +973015. q^{97} -204580. i q^{98} +(241715. + 16059.2i) 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 $

$2$		−	12.1723i		−	1.52154i	−0.649023	−	0.760769i	$-0.724822\pi$
$2$		−	12.1723i		−	1.52154i	0.649023	−	0.760769i	$-0.275178\pi$
$3$	−18.4482	−	19.7146i	−0.683267	−	0.730169i
$3$	−18.4482	−	19.7146i	−0.683267	−	0.730169i
$4$	−84.1649			−1.31508
$5$		−	4.50929i		−	0.0360743i	−0.999837	−	0.0180372i	$-0.994258\pi$
$5$		−	4.50929i		−	0.0360743i	0.999837	−	0.0180372i	$-0.00574172\pi$
$6$	−239.971	+	224.557i	−1.11098	+	1.03962i
$7$	129.642			0.377964
$7$	129.642			0.377964
$8$			245.453i			0.479401i
$9$	−48.3270	+	727.396i	−0.0662922	+	0.997800i
$10$	−54.8885			−0.0548885
$11$		−	332.302i		−	0.249663i	−0.992178	−	0.124832i	$-0.960161\pi$
$11$		−	332.302i		−	0.249663i	0.992178	−	0.124832i	$-0.0398391\pi$
$12$	1552.69	+	1659.27i	0.898548	+	0.960227i
$13$	−3039.75			−1.38359			−0.691796	−	0.722093i	$-0.743180\pi$
$13$	−3039.75			−1.38359			−0.691796	+	0.722093i	$0.743180\pi$
$14$		−	1578.04i		−	0.575087i
$15$	−88.8987	+	83.1884i	−0.0263403	+	0.0246484i
$16$	−2398.82			−0.585650
$17$		−	8747.00i		−	1.78038i	−0.455591	−	0.890189i	$-0.650572\pi$
$17$		−	8747.00i		−	1.78038i	0.455591	−	0.890189i	$-0.349428\pi$
$18$	8854.09	+	588.251i	1.51819	+	0.100866i
$19$	2520.10			0.367415			0.183707	−	0.982981i	$-0.441190\pi$
$19$	2520.10			0.367415			0.183707	+	0.982981i	$0.441190\pi$
$20$			379.524i			0.0474405i
$21$	−2391.66	−	2555.83i	−0.258251	−	0.275978i
$22$	−4044.88			−0.379872
$23$			305.657i			0.0251218i	0.999921	+	0.0125609i	$0.00399837\pi$
$23$			305.657i			0.0251218i	−0.999921	+	0.0125609i	$0.996002\pi$
$24$	4839.00	−	4528.17i	0.350043	−	0.327559i
$25$	15604.7			0.998699
$26$			37000.8i			2.10519i
$27$	15231.8	−	12466.4i	0.773858	−	0.633360i
$28$	−10911.3			−0.497052
$29$		−	15999.0i		−	0.655994i	−0.944679	−	0.327997i	$-0.893626\pi$
$29$		−	15999.0i		−	0.655994i	0.944679	−	0.327997i	$-0.106374\pi$
$30$	1012.59	+	1082.10i	0.0375035	+	0.0400778i
$31$	−45543.4			−1.52876			−0.764381	−	0.644765i	$-0.776955\pi$
$31$	−45543.4			−1.52876			−0.764381	+	0.644765i	$0.776955\pi$
$32$			44908.2i			1.37049i
$33$	−6551.18	+	6130.37i	−0.182296	+	0.170587i
$34$	−106471.			−2.70891
$35$		−	584.593i		−	0.0136348i
$36$	4067.44	−	61221.2i	0.0871793	−	1.31218i
$37$	61906.5			1.22217			0.611085	−	0.791565i	$-0.290734\pi$
$37$	61906.5			1.22217			0.611085	+	0.791565i	$0.290734\pi$
$38$		−	30675.4i		−	0.559035i
$39$	56078.0	+	59927.4i	0.945363	+	1.01026i
$40$	1106.82			0.0172941
$41$		−	27561.8i		−	0.399904i	−0.979806	−	0.199952i	$-0.935921\pi$
$41$		−	27561.8i		−	0.399904i	0.979806	−	0.199952i	$-0.0640786\pi$
$42$	−31110.3	+	29112.0i	−0.419911	+	0.392938i
$43$	124173.			1.56178			0.780892	−	0.624666i	$-0.214765\pi$
$43$	124173.			1.56178			0.780892	+	0.624666i	$0.214765\pi$
$44$			27968.1i			0.328326i
$45$	3280.04	+	217.921i	0.0359950	+	0.00239145i
$46$	3720.55			0.0382238
$47$			24511.9i			0.236093i	0.993008	+	0.118046i	$0.0376632\pi$
$47$			24511.9i			0.236093i	−0.993008	+	0.118046i	$0.962337\pi$
$48$	44254.0	+	47291.7i	0.400156	+	0.427623i
$49$	16807.0			0.142857
$50$		−	189945.i		−	1.51956i
$51$	−172443.	+	161366.i	−1.29998	+	1.21647i
$52$	255841.			1.81953
$53$		−	257014.i		−	1.72635i	−0.504904	−	0.863176i	$-0.668472\pi$
$53$		−	257014.i		−	1.72635i	0.504904	−	0.863176i	$-0.331528\pi$
$54$	−151745.	−	185407.i	−0.963680	−	1.17745i
$55$	−1498.45			−0.00900644
$56$			31821.0i			0.181196i
$57$	−46491.3	−	49682.6i	−0.251042	−	0.268275i
$58$	−194745.			−0.998119
$59$		−	158263.i		−	0.770591i	−0.922793	−	0.385296i	$-0.874099\pi$
$59$		−	158263.i		−	0.770591i	0.922793	−	0.385296i	$-0.125901\pi$
$60$	7482.15	−	7001.54i	0.0346396	−	0.0324145i
$61$	−115718.			−0.509813			−0.254906	−	0.966966i	$-0.582045\pi$
$61$	−115718.			−0.509813			−0.254906	+	0.966966i	$0.582045\pi$
$62$			554367.i			2.32607i
$63$	−6265.20	+	94301.0i	−0.0250561	+	0.377133i
$64$	393111.			1.49960
$65$			13707.1i			0.0499122i
$66$	74620.8	+	79742.9i	0.259554	+	0.277371i
$67$	−328007.			−1.09058			−0.545291	−	0.838247i	$-0.683581\pi$
$67$	−328007.			−1.09058			−0.545291	+	0.838247i	$0.683581\pi$
$68$			736190.i			2.34133i
$69$	6025.90	−	5638.83i	0.0183432	−	0.0171649i
$70$	−7115.84			−0.0207459
$71$			384121.i			1.07323i	0.843827	+	0.536616i	$0.180298\pi$
$71$			384121.i			1.07323i	−0.843827	+	0.536616i	$0.819702\pi$
$72$	−178542.	−	11862.0i	−0.478346	−	0.0317805i
$73$	240083.			0.617153			0.308576	−	0.951200i	$-0.400147\pi$
$73$	240083.			0.617153			0.308576	+	0.951200i	$0.400147\pi$
$74$		−	753545.i		−	1.85958i
$75$	−287878.	−	307639.i	−0.682378	−	0.729218i
$76$	−212104.			−0.483178
$77$		−	43080.2i		−	0.0943638i
$78$	729454.	−	682598.i	1.53714	−	1.43841i
$79$	440967.			0.894386			0.447193	−	0.894437i	$-0.352424\pi$
$79$	440967.			0.894386			0.447193	+	0.894437i	$0.352424\pi$
$80$			10817.0i			0.0211269i
$81$	−526770.	−	70305.8i	−0.991211	−	0.132293i
$82$	−335490.			−0.608469
$83$			100434.i			0.175650i	0.996136	+	0.0878250i	$0.0279916\pi$
$83$			100434.i			0.175650i	−0.996136	+	0.0878250i	$0.972008\pi$
$84$	201294.	+	215111.i	0.339619	+	0.362932i
$85$	−39442.8			−0.0642260
$86$		−	1.51147e6i		−	2.37631i
$87$	−315414.	+	295154.i	−0.478986	+	0.448219i
$88$	81564.5			0.119689
$89$			961635.i			1.36408i	0.731314	+	0.682041i	$0.238907\pi$
$89$			961635.i			1.36408i	−0.731314	+	0.682041i	$0.761093\pi$
$90$	2652.60	−	39925.7i	0.00363868	−	0.0547677i
$91$	−394079.			−0.522949
$92$		−	25725.6i		−	0.0330371i
$93$	840193.	+	897867.i	1.04455	+	1.11625i
$94$	298366.			0.359224
$95$		−	11363.9i		−	0.0132542i
$96$	885345.	−	828476.i	1.00069	−	0.936410i
$97$	973015.			1.06612			0.533058	−	0.846079i	$-0.321043\pi$
$97$	973015.			1.06612			0.533058	+	0.846079i	$0.321043\pi$
$98$		−	204580.i		−	0.217363i
$99$	241715.	+	16059.2i	0.249114	+	0.0165507i
$100$	−1.31337e6			−1.31337
$101$		−	1.49632e6i		−	1.45231i	−0.687530	−	0.726156i	$-0.741305\pi$
$101$		−	1.49632e6i		−	1.45231i	0.687530	−	0.726156i	$-0.258695\pi$
$102$	1.96420e6	+	2.09903e6i	1.85091	+	1.97796i
$103$	−249385.			−0.228223			−0.114111	−	0.993468i	$-0.536402\pi$
$103$	−249385.			−0.228223			−0.114111	+	0.993468i	$0.536402\pi$
$104$		−	746117.i		−	0.663295i
$105$	−11525.0	+	10784.7i	−0.00995571	+	0.00931622i
$106$	−3.12845e6			−2.62671
$107$			2.00195e6i			1.63419i	0.576506	+	0.817093i	$0.304416\pi$
$107$			2.00195e6i			1.63419i	−0.576506	+	0.817093i	$0.695584\pi$
$108$	−1.28199e6	+	1.04923e6i	−1.01768	+	0.832916i
$109$	650363.			0.502200			0.251100	−	0.967961i	$-0.419208\pi$
$109$	650363.			0.502200			0.251100	+	0.967961i	$0.419208\pi$
$110$			18239.5i			0.0137036i
$111$	−1.14206e6	−	1.22046e6i	−0.835068	−	0.892390i
$112$	−310988.			−0.221355
$113$			252965.i			0.175318i	0.996151	+	0.0876589i	$0.0279385\pi$
$113$			252965.i			0.175318i	−0.996151	+	0.0876589i	$0.972061\pi$
$114$	−604751.	+	565906.i	−0.408190	+	0.381970i
$115$	1378.30			0.000906253
$116$			1.34656e6i			0.862682i
$117$	146902.	−	2.21111e6i	0.0917214	−	1.38055i
$118$	−1.92643e6			−1.17248
$119$		−	1.13398e6i		−	0.672920i
$120$	−20418.8	−	21820.5i	−0.0118165	−	0.0126276i
$121$	1.66114e6			0.937668
$122$			1.40855e6i			0.775699i
$123$	−543368.	+	508466.i	−0.291997	+	0.273241i
$124$	3.83315e6			2.01044
$125$		−	140824.i		−	0.0721017i
$126$	1.14786e6	+	76261.9i	0.573822	+	0.0381238i
$127$	−117723.			−0.0574714			−0.0287357	−	0.999587i	$-0.509148\pi$
$127$	−117723.			−0.0574714			−0.0287357	+	0.999587i	$0.509148\pi$
$128$		−	1.91095e6i		−	0.911210i
$129$	−2.29077e6	−	2.44801e6i	−1.06712	−	1.14037i
$130$	166847.			0.0759433
$131$		−	445616.i		−	0.198220i	−0.995077	−	0.0991098i	$-0.968400\pi$
$131$		−	445616.i		−	0.198220i	0.995077	−	0.0991098i	$-0.0315995\pi$
$132$	551379.	−	515962.i	0.239734	−	0.224335i
$133$	326710.			0.138870
$134$			3.99260e6i			1.65936i
$135$	−56214.7	−	68684.8i	−0.0228480	−	0.0279164i
$136$	2.14698e6			0.853515
$137$			739804.i			0.287710i	0.989599	+	0.143855i	$0.0459499\pi$
$137$			739804.i			0.287710i	−0.989599	+	0.143855i	$0.954050\pi$
$138$	−68637.5	−	73349.0i	−0.0261171	−	0.0279098i
$139$	1.98775e6			0.740147			0.370074	−	0.929002i	$-0.379332\pi$
$139$	1.98775e6			0.740147			0.370074	+	0.929002i	$0.379332\pi$
$140$			49202.2i			0.0179308i
$141$	483240.	−	452200.i	0.172388	−	0.161314i
$142$	4.67564e6			1.63296
$143$			1.01012e6i			0.345432i
$144$	115928.	−	1.74490e6i	0.0388241	−	0.584362i
$145$	−72144.3			−0.0236645
$146$		−	2.92236e6i		−	0.939021i
$147$	−310059.	−	331342.i	−0.0976096	−	0.104310i
$148$	−5.21036e6			−1.60725
$149$		−	2.85382e6i		−	0.862715i	−0.902181	−	0.431357i	$-0.858035\pi$
$149$		−	2.85382e6i		−	0.862715i	0.902181	−	0.431357i	$-0.141965\pi$
$150$	−3.74467e6	+	3.50414e6i	−1.10953	+	1.03826i
$151$	−3.83792e6			−1.11472			−0.557359	−	0.830272i	$-0.688185\pi$
$151$	−3.83792e6			−1.11472			−0.557359	+	0.830272i	$0.688185\pi$
$152$			618566.i			0.176139i
$153$	6.36254e6	+	422716.i	1.77646	+	0.118025i
$154$	−524385.			−0.143578
$155$			205368.i			0.0551491i
$156$	−4.71980e6	−	5.04378e6i	−1.24323	−	1.32856i
$157$	707011.			0.182695			0.0913476	−	0.995819i	$-0.470883\pi$
$157$	707011.			0.182695			0.0913476	+	0.995819i	$0.470883\pi$
$158$		−	5.36759e6i		−	1.36084i
$159$	−5.06692e6	+	4.74145e6i	−1.26053	+	1.17956i
$160$	202504.			0.0494395
$161$			39626.0i			0.00949516i
$162$	−855783.	+	6.41200e6i	−0.201288	+	1.50816i
$163$	1.06306e6			0.245468			0.122734	−	0.992440i	$-0.460834\pi$
$163$	1.06306e6			0.245468			0.122734	+	0.992440i	$0.460834\pi$
$164$			2.31973e6i			0.525904i
$165$	27643.6	+	29541.2i	0.00615380	+	0.00657622i
$166$	1.22252e6			0.267258
$167$			5.04180e6i			1.08252i	0.840855	+	0.541260i	$0.182053\pi$
$167$			5.04180e6i			1.08252i	−0.840855	+	0.541260i	$0.817947\pi$
$168$	627337.	−	587040.i	0.132304	−	0.123806i
$169$	4.41329e6			0.914329
$170$			480109.i			0.0977222i
$171$	−121789.	+	1.83311e6i	−0.0243567	+	0.366606i
$172$	−1.04510e7			−2.05387
$173$		−	6.95122e6i		−	1.34253i	−0.741219	−	0.671263i	$-0.765752\pi$
$173$		−	6.95122e6i		−	1.34253i	0.741219	−	0.671263i	$-0.234248\pi$
$174$	3.59270e6	+	3.83931e6i	0.681982	+	0.728795i
$175$	2.02302e6			0.377473
$176$			797133.i			0.146215i
$177$	−3.12009e6	+	2.91967e6i	−0.562662	+	0.526520i
$178$	1.17053e7			2.07550
$179$			2.58392e6i			0.450526i	0.974298	+	0.225263i	$0.0723242\pi$
$179$			2.58392e6i			0.450526i	−0.974298	+	0.225263i	$0.927676\pi$
$180$	−276064.	−	18341.3i	−0.0473362	−	0.00314494i
$181$	−3.15404e6			−0.531902			−0.265951	−	0.963987i	$-0.585686\pi$
$181$	−3.15404e6			−0.531902			−0.265951	+	0.963987i	$0.585686\pi$
$182$			4.79685e6i			0.795686i
$183$	2.13479e6	+	2.28132e6i	0.348338	+	0.372249i
$184$	−75024.6			−0.0120434
$185$		−	279155.i		−	0.0440889i
$186$	1.09291e7	−	1.02271e7i	1.69842	−	1.58933i
$187$	−2.90664e6			−0.444495
$188$		−	2.06304e6i		−	0.310480i
$189$	1.97468e6	−	1.61617e6i	0.292491	−	0.239387i
$190$	−138324.			−0.0201668
$191$			6.36330e6i			0.913234i	0.889663	+	0.456617i	$0.150939\pi$
$191$			6.36330e6i			0.913234i	−0.889663	+	0.456617i	$0.849061\pi$
$192$	−7.25220e6	−	7.75002e6i	−1.02463	−	1.09496i
$193$	−8.95852e6			−1.24613			−0.623066	−	0.782169i	$-0.714113\pi$
$193$	−8.95852e6			−1.24613			−0.623066	+	0.782169i	$0.714113\pi$
$194$		−	1.18438e7i		−	1.62214i
$195$	270230.	−	252872.i	0.0364443	−	0.0341034i
$196$	−1.41456e6			−0.187868
$197$		−	1.10071e7i		−	1.43971i	−0.694125	−	0.719854i	$-0.744209\pi$
$197$		−	1.10071e7i		−	1.43971i	0.694125	−	0.719854i	$-0.255791\pi$
$198$	195477.	−	2.94223e6i	0.0251826	−	0.379036i
$199$	1.22773e6			0.155791			0.0778957	−	0.996962i	$-0.475180\pi$
$199$	1.22773e6			0.155791			0.0778957	+	0.996962i	$0.475180\pi$
$200$			3.83021e6i			0.478777i
$201$	6.05114e6	+	6.46651e6i	0.745159	+	0.796309i
$202$	−1.82136e7			−2.20975
$203$		−	2.07414e6i		−	0.247942i
$204$	1.45137e7	−	1.35814e7i	1.70957	−	1.59976i
$205$	−124284.			−0.0144263
$206$			3.03559e6i			0.347250i
$207$	−222334.	−	14771.5i	−0.0250666	−	0.00166538i
$208$	7.29183e6			0.810302
$209$		−	837433.i		−	0.0917299i
$210$	131274.	+	140286.i	0.0141750	+	0.0151480i
$211$	−9.08796e6			−0.967428			−0.483714	−	0.875226i	$-0.660713\pi$
$211$	−9.08796e6			−0.967428			−0.483714	+	0.875226i	$0.660713\pi$
$212$			2.16316e7i			2.27028i
$213$	7.57278e6	−	7.08635e6i	0.783640	−	0.733304i
$214$	2.43683e7			2.48648
$215$		−	559931.i		−	0.0563403i
$216$	3.05992e6	+	3.73870e6i	0.303633	+	0.370988i
$217$	−5.90432e6			−0.577818
$218$		−	7.91641e6i		−	0.764115i
$219$	−4.42910e6	−	4.73313e6i	−0.421680	−	0.450626i
$220$	126117.			0.0118442
$221$			2.65887e7i			2.46332i
$222$	−1.48558e7	+	1.39016e7i	−1.35780	+	1.27059i
$223$	2.28104e6			0.205693			0.102846	−	0.994697i	$-0.467205\pi$
$223$	2.28104e6			0.205693			0.102846	+	0.994697i	$0.467205\pi$
$224$			5.82198e6i			0.517996i
$225$	−754127.	+	1.13508e7i	−0.0662059	+	0.996502i
$226$	3.07917e6			0.266752
$227$		−	1.64809e6i		−	0.140898i	−0.997515	−	0.0704489i	$-0.977557\pi$
$227$		−	1.64809e6i		−	0.140898i	0.997515	−	0.0704489i	$-0.0224432\pi$
$228$	3.91293e6	+	4.18153e6i	0.330140	+	0.352802i
$229$	−1.39688e7			−1.16320			−0.581598	−	0.813476i	$-0.697572\pi$
$229$	−1.39688e7			−1.16320			−0.581598	+	0.813476i	$0.697572\pi$
$230$		−	16777.1i		−	0.00137890i
$231$	−849307.	+	794753.i	−0.0689015	+	0.0644757i
$232$	3.92701e6			0.314484
$233$		−	1.41901e7i		−	1.12181i	−0.827881	−	0.560904i	$-0.810454\pi$
$233$		−	1.41901e7i		−	1.12181i	0.827881	−	0.560904i	$-0.189546\pi$
$234$	−2.69142e7	−	1.78814e6i	−2.10056	−	0.139558i
$235$	110531.			0.00851689
$236$			1.33202e7i			1.01339i
$237$	−8.13506e6	−	8.69347e6i	−0.611105	−	0.653053i
$238$	−1.38031e7			−1.02387
$239$		−	2.55698e7i		−	1.87298i	−0.350696	−	0.936489i	$-0.614055\pi$
$239$		−	2.55698e7i		−	1.87298i	0.350696	−	0.936489i	$-0.385945\pi$
$240$	213252.	−	199554.i	0.0154262	−	0.0144353i
$241$	1.57154e7			1.12273			0.561364	−	0.827569i	$-0.310277\pi$
$241$	1.57154e7			1.12273			0.561364	+	0.827569i	$0.310277\pi$
$242$		−	2.02199e7i		−	1.42670i
$243$	8.33192e6	+	1.16821e7i	0.580666	+	0.814142i
$244$	9.73938e6			0.670443
$245$		−	75787.7i		−	0.00515348i
$246$	6.18920e6	+	6.61404e6i	0.415747	+	0.444285i
$247$	−7.66047e6			−0.508352
$248$		−	1.11788e7i		−	0.732890i
$249$	1.98002e6	−	1.85284e6i	0.128254	−	0.120016i
$250$	−1.71415e6			−0.109705
$251$		−	1.56968e7i		−	0.992636i	−0.868141	−	0.496318i	$-0.834685\pi$
$251$		−	1.56968e7i		−	0.992636i	0.868141	−	0.496318i	$-0.165315\pi$
$252$	527310.	−	7.93683e6i	0.0329507	−	0.495959i
$253$	101570.			0.00627200
$254$			1.43297e6i			0.0874449i
$255$	727649.	+	777597.i	0.0438835	+	0.0468958i
$256$	1.89853e6			0.113161
$257$			1.90160e7i			1.12026i	0.828403	+	0.560132i	$0.189250\pi$
$257$			1.90160e7i			1.12026i	−0.828403	+	0.560132i	$0.810750\pi$
$258$	−2.97979e7	+	2.78839e7i	−1.73511	+	1.62366i
$259$	8.02568e6			0.461937
$260$		−	1.15366e6i		−	0.0656383i
$261$	1.16376e7	+	773186.i	0.654551	+	0.0434873i
$262$	−5.42417e6			−0.301599
$263$			9.89102e6i			0.543718i	0.962337	+	0.271859i	$0.0876384\pi$
$263$			9.89102e6i			0.543718i	−0.962337	+	0.271859i	$0.912362\pi$
$264$	−1.50472e6	−	1.60801e6i	−0.0817794	−	0.0873930i
$265$	−1.15895e6			−0.0622770
$266$		−	3.97681e6i		−	0.211295i
$267$	1.89582e7	−	1.77405e7i	0.996010	−	0.932032i
$268$	2.76067e7			1.43420
$269$		−	7.54189e6i		−	0.387457i	−0.981055	−	0.193728i	$-0.937942\pi$
$269$		−	7.54189e6i		−	0.387457i	0.981055	−	0.193728i	$-0.0620581\pi$
$270$	−836052.	+	684262.i	−0.0424758	+	0.0347641i
$271$	2.58104e7			1.29684			0.648420	−	0.761283i	$-0.275430\pi$
$271$	2.58104e7			1.29684			0.648420	+	0.761283i	$0.275430\pi$
$272$			2.09825e7i			1.04268i
$273$	7.27005e6	+	7.76909e6i	0.357314	+	0.381841i
$274$	9.00512e6			0.437762
$275$		−	5.18546e6i		−	0.249338i
$276$	−507169.	+	474592.i	−0.0241227	+	0.0225732i
$277$	3.12836e6			0.147189			0.0735947	−	0.997288i	$-0.476553\pi$
$277$	3.12836e6			0.147189			0.0735947	+	0.997288i	$0.476553\pi$
$278$		−	2.41955e7i		−	1.12616i
$279$	2.20097e6	−	3.31281e7i	0.101345	−	1.52540i
$280$	143490.			0.00653654
$281$			3.57355e7i			1.61057i	0.592885	+	0.805287i	$0.297989\pi$
$281$			3.57355e7i			1.61057i	−0.592885	+	0.805287i	$0.702011\pi$
$282$	−5.50432e6	−	5.88215e6i	−0.245446	−	0.262294i
$283$	2.93612e7			1.29543			0.647716	−	0.761882i	$-0.275724\pi$
$283$	2.93612e7			1.29543			0.647716	+	0.761882i	$0.275724\pi$
$284$		−	3.23295e7i		−	1.41138i
$285$	−224033.	+	209643.i	−0.00967783	+	0.00905618i
$286$	1.22954e7			0.525588
$287$		−	3.57316e6i		−	0.151149i
$288$	−3.26661e7	−	2.17028e6i	−1.36747	−	0.0908528i
$289$	−5.23724e7			−2.16975
$290$			878162.i			0.0360065i
$291$	−1.79504e7	−	1.91826e7i	−0.728442	−	0.778444i
$292$	−2.02066e7			−0.811603
$293$			2.17938e7i			0.866424i	0.901292	+	0.433212i	$0.142620\pi$
$293$			2.17938e7i			0.866424i	−0.901292	+	0.433212i	$0.857380\pi$
$294$	−4.03320e6	+	3.77413e6i	−0.158711	+	0.148517i
$295$	−713655.			−0.0277986
$296$			1.51952e7i			0.585909i
$297$	−4.14261e6	−	5.06157e6i	−0.158127	−	0.193204i
$298$	−3.47375e7			−1.31265
$299$		−	929123.i		−	0.0347584i
$300$	2.42292e7	+	2.58924e7i	0.897379	+	0.958978i
$301$	1.60980e7			0.590299
$302$			4.67163e7i			1.69608i
$303$	−2.94993e7	+	2.76044e7i	−1.06043	+	0.992317i
$304$	−6.04527e6			−0.215176
$305$			521805.i			0.0183912i
$306$	5.14543e6	−	7.74467e7i	0.179580	−	2.70295i
$307$	1.79011e7			0.618677			0.309339	−	0.950952i	$-0.399892\pi$
$307$	1.79011e7			0.618677			0.309339	+	0.950952i	$0.399892\pi$
$308$			3.62584e6i			0.124096i
$309$	4.60071e6	+	4.91652e6i	0.155937	+	0.166641i
$310$	2.49980e6			0.0839114
$311$			4.95434e7i			1.64704i	0.567285	+	0.823522i	$0.307994\pi$
$311$			4.95434e7i			1.64704i	−0.567285	+	0.823522i	$0.692006\pi$
$312$	−1.47094e7	+	1.37645e7i	−0.484317	+	0.453208i
$313$	−3.55906e7			−1.16065			−0.580326	−	0.814384i	$-0.697075\pi$
$313$	−3.55906e7			−1.16065			−0.580326	+	0.814384i	$0.697075\pi$
$314$		−	8.60595e6i		−	0.277978i
$315$	425231.	+	28251.6i	0.0136048	+	0.000903882i
$316$	−3.71140e7			−1.17619
$317$		−	2.97002e7i		−	0.932355i	−0.884691	−	0.466177i	$-0.845631\pi$
$317$		−	2.97002e7i		−	0.932355i	0.884691	−	0.466177i	$-0.154369\pi$
$318$	5.77143e7	+	6.16760e7i	1.79474	+	1.91794i
$319$	−5.31651e6			−0.163778
$320$		−	1.77265e6i		−	0.0540971i
$321$	3.94675e7	−	3.69324e7i	1.19323	−	1.11659i
$322$	482339.			0.0144472
$323$		−	2.20433e7i		−	0.654137i
$324$	4.43355e7	+	5.91728e6i	1.30352	+	0.173975i
$325$	−4.74343e7			−1.38179
$326$		−	1.29399e7i		−	0.373489i
$327$	−1.19980e7	−	1.28216e7i	−0.343136	−	0.366690i
$328$	6.76513e6			0.191714
$329$			3.17776e6i			0.0892347i
$330$	359584.	−	336487.i	0.0100060	−	0.00936324i
$331$	3.90151e7			1.07584			0.537922	−	0.842995i	$-0.319210\pi$
$331$	3.90151e7			1.07584			0.537922	+	0.842995i	$0.319210\pi$
$332$		−	8.45305e6i		−	0.230993i
$333$	−2.99176e6	+	4.50306e7i	−0.0810203	+	1.21948i
$334$	6.13703e7			1.64710
$335$			1.47908e6i			0.0393420i
$336$	5.73717e6	+	6.13099e6i	0.151245	+	0.161626i
$337$	3.10108e6			0.0810258			0.0405129	−	0.999179i	$-0.487101\pi$
$337$	3.10108e6			0.0810258			0.0405129	+	0.999179i	$0.487101\pi$
$338$		−	5.37199e7i		−	1.39119i
$339$	4.98710e6	−	4.66676e6i	0.128011	−	0.119789i
$340$	3.31970e6			0.0844621
$341$			1.51341e7i			0.381676i
$342$	2.23132e7	+	1.48245e6i	0.557805	+	0.0370597i
$343$	2.17889e6			0.0539949
$344$			3.04786e7i			0.748721i
$345$	−25427.1	−	27172.5i	−0.000619213	−	0.000661718i
$346$	−8.46123e7			−2.04270
$347$		−	1.96943e7i		−	0.471360i	−0.971831	−	0.235680i	$-0.924268\pi$
$347$		−	1.96943e7i		−	0.471360i	0.971831	−	0.235680i	$-0.0757317\pi$
$348$	2.65468e7	−	2.48416e7i	0.629903	−	0.589442i
$349$	−4.00477e7			−0.942108			−0.471054	−	0.882104i	$-0.656126\pi$
$349$	−4.00477e7			−0.942108			−0.471054	+	0.882104i	$0.656126\pi$
$350$		−	2.46248e7i		−	0.574339i
$351$	−4.63010e7	+	3.78948e7i	−1.07070	+	0.876312i
$352$	1.49231e7			0.342161
$353$		−	5.40587e7i		−	1.22897i	−0.788928	−	0.614485i	$-0.789364\pi$
$353$		−	5.40587e7i		−	1.22897i	0.788928	−	0.614485i	$-0.210636\pi$
$354$	3.55392e7	+	3.79787e7i	0.801120	+	0.856111i
$355$	1.73212e6			0.0387161
$356$		−	8.09359e7i		−	1.79387i
$357$	−2.23558e7	+	2.09198e7i	−0.491345	+	0.459784i
$358$	3.14523e7			0.685493
$359$		−	1.84286e7i		−	0.398299i	−0.979969	−	0.199150i	$-0.936182\pi$
$359$		−	1.84286e7i		−	0.398299i	0.979969	−	0.199150i	$-0.0638180\pi$
$360$	−53489.3	+	805097.i	−0.00114646	+	0.0172560i
$361$	−4.06950e7			−0.865007
$362$			3.83919e7i			0.809308i
$363$	−3.06450e7	−	3.27486e7i	−0.640678	−	0.684656i
$364$	3.31676e7			0.687718
$365$		−	1.08260e6i		−	0.0222634i
$366$	2.77690e7	−	2.59853e7i	0.566391	−	0.530010i
$367$	1.66356e7			0.336542			0.168271	−	0.985741i	$-0.446182\pi$
$367$	1.66356e7			0.336542			0.168271	+	0.985741i	$0.446182\pi$
$368$		−	733218.i		−	0.0147126i
$369$	2.00483e7	+	1.33198e6i	0.399024	+	0.0265105i
$370$	−3.39795e6			−0.0670830
$371$		−	3.33198e7i		−	0.652500i
$372$	−7.07148e7	−	7.55689e7i	−1.37367	−	1.46796i
$373$	4.74988e7			0.915285			0.457643	−	0.889136i	$-0.348694\pi$
$373$	4.74988e7			0.915285			0.457643	+	0.889136i	$0.348694\pi$
$374$			3.53805e7i			0.676316i
$375$	−2.77628e6	+	2.59794e6i	−0.0526464	+	0.0492647i
$376$	−6.01652e6			−0.113183
$377$			4.86331e7i			0.907628i
$378$	−1.96725e7	−	2.40364e7i	−0.364237	−	0.445036i
$379$	4.51822e7			0.829946			0.414973	−	0.909834i	$-0.363791\pi$
$379$	4.51822e7			0.829946			0.414973	+	0.909834i	$0.363791\pi$
$380$			956437.i			0.0174303i
$381$	2.17179e6	+	2.32086e6i	0.0392683	+	0.0419638i
$382$	7.74560e7			1.38952
$383$			4.57264e7i			0.813900i	0.913451	+	0.406950i	$0.133408\pi$
$383$			4.57264e7i			0.813900i	−0.913451	+	0.406950i	$0.866592\pi$
$384$	−3.76734e7	+	3.52535e7i	−0.665337	+	0.622600i
$385$	−194261.			−0.00340411
$386$			1.09046e8i			1.89604i
$387$	−6.00090e6	+	9.03229e7i	−0.103534	+	1.55835i
$388$	−8.18937e7			−1.40202
$389$			5.12392e7i			0.870469i	0.900317	+	0.435235i	$0.143335\pi$
$389$			5.12392e7i			0.870469i	−0.900317	+	0.435235i	$0.856665\pi$
$390$	−3.07804e6	−	3.28932e6i	−0.0518895	−	0.0554514i
$391$	2.67358e6			0.0447264
$392$			4.12533e6i			0.0684858i
$393$	−8.78511e6	+	8.22081e6i	−0.144734	+	0.135437i
$394$	−1.33982e8			−2.19057
$395$		−	1.98845e6i		−	0.0322644i
$396$	−2.03439e7	−	1.35162e6i	−0.327604	−	0.0217655i
$397$	4.27452e7			0.683149			0.341574	−	0.939855i	$-0.389040\pi$
$397$	4.27452e7			0.683149			0.341574	+	0.939855i	$0.389040\pi$
$398$		−	1.49443e7i		−	0.237042i
$399$	−6.02721e6	−	6.44094e6i	−0.0948851	−	0.101398i
$400$	−3.74328e7			−0.584888
$401$			2.29051e7i			0.355222i	0.984101	+	0.177611i	$0.0568369\pi$
$401$			2.29051e7i			0.355222i	−0.984101	+	0.177611i	$0.943163\pi$
$402$	7.87123e7	−	7.36563e7i	1.21161	−	1.13379i
$403$	1.38441e8			2.11518
$404$			1.25938e8i			1.90990i
$405$	−317029.	+	2.37536e6i	−0.00477237	+	0.0357573i
$406$	−2.52471e7			−0.377254
$407$		−	2.05717e7i		−	0.305131i
$408$	−3.96079e7	−	4.23267e7i	−0.583179	−	0.623210i
$409$	1.72882e7			0.252686			0.126343	−	0.991987i	$-0.459676\pi$
$409$	1.72882e7			0.252686			0.126343	+	0.991987i	$0.459676\pi$
$410$			1.51282e6i			0.0219501i
$411$	1.45849e7	−	1.36481e7i	0.210077	−	0.196583i
$412$	2.09895e7			0.300130
$413$		−	2.05175e7i		−	0.291256i
$414$	−179803.	+	2.70632e6i	−0.00253394	+	0.0381397i
$415$	452888.			0.00633646
$416$		−	1.36510e8i		−	1.89620i
$417$	−3.66705e7	−	3.91877e7i	−0.505718	−	0.540432i
$418$	−1.01935e7			−0.139571
$419$			5.01970e7i			0.682395i	0.939992	+	0.341198i	$0.110833\pi$
$419$			5.01970e7i			0.682395i	−0.939992	+	0.341198i	$0.889167\pi$
$420$	969999.	−	907692.i	0.0130925	−	0.0122515i
$421$	−9.16433e7			−1.22816			−0.614079	−	0.789244i	$-0.710472\pi$
$421$	−9.16433e7			−1.22816			−0.614079	+	0.789244i	$0.710472\pi$
$422$			1.10621e8i			1.47198i
$423$	−1.78298e7	−	1.18459e6i	−0.235574	−	0.0156511i
$424$	6.30849e7			0.827614
$425$		−	1.36494e8i		−	1.77806i
$426$	−8.62572e7	−	9.21782e7i	−1.11575	−	1.19234i
$427$	−1.50019e7			−0.192691
$428$		−	1.68494e8i		−	2.14908i
$429$	1.99140e7	−	1.86348e7i	0.252224	−	0.236023i
$430$	−6.81565e6			−0.0857239
$431$		−	7.36615e6i		−	0.0920045i	−0.998941	−	0.0460022i	$-0.985352\pi$
$431$		−	7.36615e6i		−	0.0920045i	0.998941	−	0.0460022i	$-0.0146481\pi$
$432$	−3.65385e7	+	2.99047e7i	−0.453210	+	0.370927i
$433$	8.16741e7			1.00605			0.503026	−	0.864271i	$-0.332220\pi$
$433$	8.16741e7			1.00605			0.503026	+	0.864271i	$0.332220\pi$
$434$			7.18692e7i			0.879171i
$435$	1.33093e6	+	1.42229e6i	0.0161692	+	0.0172791i
$436$	−5.47377e7			−0.660431
$437$			770286.i			0.00923013i
$438$	−5.76130e7	+	5.39123e7i	−0.685644	+	0.641602i
$439$	−1.06743e8			−1.26167			−0.630833	−	0.775919i	$-0.717287\pi$
$439$	−1.06743e8			−1.26167			−0.630833	+	0.775919i	$0.717287\pi$
$440$		−	367798.i		−	0.00431769i
$441$	−812232.	+	1.22254e7i	−0.00947032	+	0.142543i
$442$	3.23646e8			3.74803
$443$		−	7.61282e7i		−	0.875658i	−0.899058	−	0.437829i	$-0.855748\pi$
$443$		−	7.61282e7i		−	0.875658i	0.899058	−	0.437829i	$-0.144252\pi$
$444$	9.61218e7	+	1.02720e8i	1.09818	+	1.17356i
$445$	4.33629e6			0.0492083
$446$		−	2.77656e7i		−	0.312969i
$447$	−5.62617e7	+	5.26478e7i	−0.629927	+	0.589465i
$448$	5.09637e7			0.566796
$449$		−	1.05286e8i		−	1.16314i	−0.813497	−	0.581569i	$-0.802439\pi$
$449$		−	1.05286e8i		−	1.16314i	0.813497	−	0.581569i	$-0.197561\pi$
$450$	1.38165e8	+	9.17946e6i	1.51621	+	0.100735i
$451$	−9.15883e6			−0.0998413
$452$		−	2.12908e7i		−	0.230556i
$453$	7.08027e7	+	7.56628e7i	0.761650	+	0.813932i
$454$	−2.00611e7			−0.214381
$455$			1.77702e6i			0.0188650i
$456$	1.21947e7	−	1.14114e7i	0.128611	−	0.120350i
$457$	1.50616e8			1.57806			0.789029	−	0.614356i	$-0.210584\pi$
$457$	1.50616e8			1.57806			0.789029	+	0.614356i	$0.210584\pi$
$458$			1.70032e8i			1.76985i
$459$	−1.09044e8	−	1.33233e8i	−1.12762	−	1.37776i
$460$	−116004.			−0.00119179
$461$			8.36975e7i			0.854299i	0.904181	+	0.427149i	$0.140482\pi$
$461$			8.36975e7i			0.854299i	−0.904181	+	0.427149i	$0.859518\pi$
$462$	9.67397e6	+	1.03380e7i	0.0981022	+	0.104836i
$463$	7.49306e7			0.754946			0.377473	−	0.926020i	$-0.376793\pi$
$463$	7.49306e7			0.754946			0.377473	+	0.926020i	$0.376793\pi$
$464$			3.83789e7i			0.384183i
$465$	4.04874e6	−	3.78868e6i	0.0402681	−	0.0376815i
$466$	−1.72727e8			−1.70687
$467$		−	1.61826e8i		−	1.58891i	−0.607325	−	0.794453i	$-0.707758\pi$
$467$		−	1.61826e8i		−	1.58891i	0.607325	−	0.794453i	$-0.292242\pi$
$468$	−1.23640e7	+	1.86097e8i	−0.120621	+	1.81553i
$469$	−4.25234e7			−0.412202
$470$		−	1.34542e6i		−	0.0129588i
$471$	−1.30431e7	−	1.39384e7i	−0.124830	−	0.133398i
$472$	3.88462e7			0.369422
$473$		−	4.12629e7i		−	0.389920i
$474$	−1.05820e8	+	9.90223e7i	−0.993644	+	0.929819i
$475$	3.93253e7			0.366936
$476$			9.54410e7i			0.884941i
$477$	1.86951e8	+	1.24207e7i	1.72255	+	0.114444i
$478$	−3.11243e8			−2.84981
$479$			1.83234e7i			0.166724i	0.996519	+	0.0833621i	$0.0265658\pi$
$479$			1.83234e7i			0.166724i	−0.996519	+	0.0833621i	$0.973434\pi$
$480$	−3.73584e6	−	3.99228e6i	−0.0337804	−	0.0360992i
$481$	−1.88181e8			−1.69098
$482$		−	1.91293e8i		−	1.70827i
$483$	781208.	−	731028.i	0.00693307	−	0.00648773i
$484$	−1.39809e8			−1.23311
$485$		−	4.38761e6i		−	0.0384594i
$486$	1.42197e8	−	1.01419e8i	1.23875	−	0.883505i
$487$	−5.15577e7			−0.446382			−0.223191	−	0.974775i	$-0.571647\pi$
$487$	−5.15577e7			−0.446382			−0.223191	+	0.974775i	$0.571647\pi$
$488$		−	2.84033e7i		−	0.244405i
$489$	−1.96116e7	−	2.09578e7i	−0.167720	−	0.179233i
$490$	−922510.			−0.00784121
$491$			3.61405e7i			0.305316i	0.988279	+	0.152658i	$0.0487833\pi$
$491$			3.61405e7i			0.305316i	−0.988279	+	0.152658i	$0.951217\pi$
$492$	4.57325e7	−	4.27950e7i	0.383999	−	0.359333i
$493$	−1.39944e8			−1.16792
$494$			9.32456e7i			0.773477i
$495$	72415.4	−	1.08996e6i	0.000597057	−	0.00898662i
$496$	1.09250e8			0.895320
$497$			4.97982e7i			0.405643i
$498$	−2.25533e7	−	2.41014e7i	−0.182609	−	0.195143i
$499$	−4.48595e7			−0.361038			−0.180519	−	0.983571i	$-0.557778\pi$
$499$	−4.48595e7			−0.361038			−0.180519	+	0.983571i	$0.557778\pi$
$500$			1.18524e7i			0.0948193i
$501$	9.93968e7	−	9.30122e7i	0.790423	−	0.739651i
$502$	−1.91066e8			−1.51033
$503$			2.08959e8i			1.64194i	0.570974	+	0.820968i	$0.306566\pi$
$503$			2.08959e8i			1.64194i	−0.570974	+	0.820968i	$0.693434\pi$
$504$	−2.31465e7	−	1.53781e6i	−0.180798	−	0.0120119i
$505$	−6.74734e6			−0.0523912
$506$		−	1.23635e6i		−	0.00954308i
$507$	−8.14173e7	−	8.70061e7i	−0.624731	−	0.667614i
$508$	9.90818e6			0.0755793
$509$			1.47475e7i			0.111832i	0.998435	+	0.0559158i	$0.0178078\pi$
$509$			1.47475e7i			0.111832i	−0.998435	+	0.0559158i	$0.982192\pi$
$510$	9.46514e6	−	8.85716e6i	0.0713537	−	0.0667704i
$511$	3.11248e7			0.233262
$512$		−	1.45410e8i		−	1.08339i
$513$	3.83857e7	−	3.14166e7i	0.284327	−	0.232706i
$514$	2.31469e8			1.70452
$515$			1.12455e6i			0.00823299i
$516$	1.92802e8	+	2.06037e8i	1.40334	+	1.49967i
$517$	8.14534e6			0.0589437
$518$		−	9.76909e7i		−	0.702854i
$519$	−1.37040e8	+	1.28238e8i	−0.980270	+	0.917304i
$520$	−3.36446e6			−0.0239279
$521$			1.41812e8i			1.00277i	0.865225	+	0.501384i	$0.167176\pi$
$521$			1.41812e8i			1.00277i	−0.865225	+	0.501384i	$0.832824\pi$
$522$	9.41145e6	−	1.41657e8i	0.0661675	−	0.995924i
$523$	1.00979e8			0.705872			0.352936	−	0.935647i	$-0.385183\pi$
$523$	1.00979e8			0.705872			0.352936	+	0.935647i	$0.385183\pi$
$524$			3.75052e7i			0.260674i
$525$	−3.73210e7	−	3.98829e7i	−0.257915	−	0.275619i
$526$	1.20396e8			0.827287
$527$			3.98368e8i			2.72178i
$528$	1.57151e7	−	1.47057e7i	0.106762	−	0.0999041i
$529$	1.47942e8			0.999369
$530$			1.41071e7i			0.0947568i
$531$	1.15120e8	+	7.64839e6i	0.768896	+	0.0510842i
$532$	−2.74975e7			−0.182624
$533$			8.37810e7i			0.553304i
$534$	−2.15942e8	−	2.30765e8i	−1.41812	−	1.51547i
$535$	9.02737e6			0.0589522
$536$		−	8.05103e7i		−	0.522826i
$537$	5.09409e7	−	4.76687e7i	0.328960	−	0.307830i
$538$	−9.18022e7			−0.589530
$539$		−	5.58500e6i		−	0.0356662i
$540$	4.73131e6	+	5.78085e6i	0.0300469	+	0.0367122i
$541$	1.00554e7			0.0635051			0.0317526	−	0.999496i	$-0.489891\pi$
$541$	1.00554e7			0.0635051			0.0317526	+	0.999496i	$0.489891\pi$
$542$		−	3.14171e8i		−	1.97319i
$543$	5.81864e7	+	6.21805e7i	0.363431	+	0.388378i
$544$	3.92812e8			2.43999
$545$		−	2.93268e6i		−	0.0181165i
$546$	9.45677e7	−	8.84933e7i	0.580985	−	0.543666i
$547$	−9.12781e7			−0.557705			−0.278853	−	0.960334i	$-0.589954\pi$
$547$	−9.12781e7			−0.557705			−0.278853	+	0.960334i	$0.589954\pi$
$548$		−	6.22655e7i		−	0.378361i
$549$	5.59230e6	−	8.41727e7i	0.0337966	−	0.508691i
$550$	−6.31190e7			−0.379378
$551$		−	4.03191e7i		−	0.241022i
$552$	1.38407e6	+	1.47908e6i	0.00822888	+	0.00879373i
$553$	5.71678e7			0.338046
$554$		−	3.80793e7i		−	0.223954i
$555$	−5.50341e6	+	5.14990e6i	−0.0321924	+	0.0301245i
$556$	−1.67299e8			−0.973350
$557$		−	6.81246e7i		−	0.394220i	−0.980381	−	0.197110i	$-0.936844\pi$
$557$		−	6.81246e7i		−	0.394220i	0.980381	−	0.197110i	$-0.0631556\pi$
$558$	−4.03245e8	−	2.67909e7i	−2.32095	−	0.154200i
$559$	−3.77455e8			−2.16087
$560$			1.40233e6i			0.00798523i
$561$	5.36224e7	+	5.73032e7i	0.303709	+	0.324556i
$562$	4.34983e8			2.45055
$563$			6.20253e7i			0.347571i	0.984784	+	0.173786i	$0.0556000\pi$
$563$			6.20253e7i			0.347571i	−0.984784	+	0.173786i	$0.944400\pi$
$564$	−4.06719e7	+	3.80594e7i	−0.226703	+	0.212141i
$565$	1.14069e6			0.00632447
$566$		−	3.57393e8i		−	1.97105i
$567$	−6.82914e7	−	9.11457e6i	−0.374642	−	0.0500020i
$568$	−9.42838e7			−0.514508
$569$		−	3.32024e8i		−	1.80232i	−0.433486	−	0.901160i	$-0.642717\pi$
$569$		−	3.32024e8i		−	1.80232i	0.433486	−	0.901160i	$-0.357283\pi$
$570$	2.55183e6	+	2.72700e6i	0.0137793	+	0.0147252i
$571$	1.91457e8			1.02840			0.514201	−	0.857670i	$-0.328088\pi$
$571$	1.91457e8			1.02840			0.514201	+	0.857670i	$0.328088\pi$
$572$		−	8.50163e7i		−	0.454270i
$573$	1.25450e8	−	1.17391e8i	0.666815	−	0.623983i
$574$	−4.34936e7			−0.229980
$575$			4.76968e6i			0.0250891i
$576$	−1.89979e7	+	2.85948e8i	−0.0994119	+	1.49630i
$577$	−1.86605e8			−0.971393			−0.485697	−	0.874127i	$-0.661434\pi$
$577$	−1.86605e8			−0.971393			−0.485697	+	0.874127i	$0.661434\pi$
$578$			6.37493e8i			3.30135i
$579$	1.65269e8	+	1.76613e8i	0.851442	+	0.909887i
$580$	6.07202e6			0.0311207
$581$			1.30205e7i			0.0663895i
$582$	−2.33496e8	+	2.18498e8i	−1.18443	+	1.10835i
$583$	−8.54062e7			−0.431007
$584$			5.89291e7i			0.295864i
$585$	−9.97052e6	−	662425.i	−0.0498024	−	0.00330879i
$586$	2.65281e8			1.31830
$587$		−	8.37252e7i		−	0.413944i	−0.978347	−	0.206972i	$-0.933639\pi$
$587$		−	8.37252e7i		−	0.413944i	0.978347	−	0.206972i	$-0.0663609\pi$
$588$	2.60961e7	+	2.78874e7i	0.128364	+	0.137175i
$589$	−1.14774e8			−0.561689
$590$			8.68683e6i			0.0422966i
$591$	−2.17000e8	+	2.03061e8i	−1.05123	+	0.983705i
$592$	−1.48503e8			−0.715764
$593$			6.93427e7i			0.332535i	0.986081	+	0.166267i	$0.0531714\pi$
$593$			6.93427e7i			0.332535i	−0.986081	+	0.166267i	$0.946829\pi$
$594$	−6.16109e7	+	5.04251e7i	−0.293967	+	0.240596i
$595$	−5.11343e6			−0.0242751
$596$			2.40191e8i			1.13454i
$597$	−2.26494e7	−	2.42041e7i	−0.106447	−	0.113754i
$598$	−1.13096e7			−0.0528862
$599$		−	3.84341e7i		−	0.178828i	−0.995995	−	0.0894141i	$-0.971501\pi$
$599$		−	3.84341e7i		−	0.178828i	0.995995	−	0.0894141i	$-0.0284995\pi$
$600$	7.55110e7	−	7.06606e7i	0.349588	−	0.327132i
$601$	−2.27925e8			−1.04995			−0.524975	−	0.851118i	$-0.675925\pi$
$601$	−2.27925e8			−1.04995			−0.524975	+	0.851118i	$0.675925\pi$
$602$		−	1.95950e8i		−	0.898162i
$603$	1.58516e7	−	2.38591e8i	0.0722971	−	1.08818i
$604$	3.23018e8			1.46594
$605$		−	7.49055e6i		−	0.0338258i
$606$	3.36009e8	+	3.59074e8i	1.50985	+	1.61349i
$607$	9.70426e6			0.0433907			0.0216953	−	0.999765i	$-0.493094\pi$
$607$	9.70426e6			0.0433907			0.0216953	+	0.999765i	$0.493094\pi$
$608$			1.13173e8i			0.503538i
$609$	−4.08908e7	+	3.82642e7i	−0.181040	+	0.169411i
$610$	6.35157e6			0.0279828
$611$		−	7.45100e7i		−	0.326656i
$612$	−5.35502e8	−	3.55779e7i	−2.33618	−	0.155212i
$613$	4.77216e7			0.207173			0.103587	−	0.994620i	$-0.466968\pi$
$613$	4.77216e7			0.207173			0.103587	+	0.994620i	$0.466968\pi$
$614$		−	2.17897e8i		−	0.941340i
$615$	2.29282e6	+	2.45021e6i	0.00985700	+	0.0105336i
$616$	1.05742e7			0.0452381
$617$		−	2.75168e7i		−	0.117150i	−0.998283	−	0.0585751i	$-0.981344\pi$
$617$		−	2.75168e7i		−	0.117150i	0.998283	−	0.0585751i	$-0.0186557\pi$
$618$	5.98453e7	−	5.60012e7i	0.253551	−	0.237264i
$619$	3.42910e8			1.44580			0.722899	−	0.690953i	$-0.242809\pi$
$619$	3.42910e8			1.44580			0.722899	+	0.690953i	$0.242809\pi$
$620$		−	1.72848e7i		−	0.0725253i
$621$	3.81045e6	+	4.65572e6i	0.0159112	+	0.0194407i
$622$	6.03058e8			2.50604
$623$			1.24668e8i			0.515574i
$624$	−1.34521e8	−	1.43755e8i	−0.553652	−	0.591657i
$625$	2.43188e8			0.996098
$626$			4.33219e8i			1.76598i
$627$	−1.65096e7	+	1.54491e7i	−0.0669783	+	0.0626760i
$628$	−5.95055e7			−0.240258
$629$		−	5.41496e8i		−	2.17592i
$630$	343887.	−	5.17604e6i	0.00137529	−	0.0207002i
$631$	−4.08631e8			−1.62646			−0.813229	−	0.581943i	$-0.802293\pi$
$631$	−4.08631e8			−1.62646			−0.813229	+	0.581943i	$0.802293\pi$
$632$			1.08237e8i			0.428769i
$633$	1.67657e8	+	1.79165e8i	0.661012	+	0.706386i
$634$	−3.61519e8			−1.41861
$635$			530849.i			0.00207324i
$636$	4.26456e8	−	3.99064e8i	1.65769	−	1.55121i
$637$	−5.10891e7			−0.197656
$638$			6.47141e7i			0.249194i
$639$	−2.79409e8	−	1.85634e7i	−1.07087	−	0.0711469i
$640$	−8.61701e6			−0.0328713
$641$			1.23507e7i			0.0468938i	0.999725	+	0.0234469i	$0.00746407\pi$
$641$			1.23507e7i			0.0468938i	−0.999725	+	0.0234469i	$0.992536\pi$
$642$	−4.49552e8	−	4.80410e8i	−1.69893	−	1.81555i
$643$	1.31848e7			0.0495954			0.0247977	−	0.999692i	$-0.492106\pi$
$643$	1.31848e7			0.0495954			0.0247977	+	0.999692i	$0.492106\pi$
$644$		−	3.33512e6i		−	0.0124869i
$645$	−1.10388e7	+	1.03297e7i	−0.0411379	+	0.0384955i
$646$	−2.68317e8			−0.995294
$647$		−	3.33543e8i		−	1.23151i	−0.787937	−	0.615756i	$-0.788851\pi$
$647$		−	3.33543e8i		−	1.23151i	0.787937	−	0.615756i	$-0.211149\pi$
$648$	1.72568e7	−	1.29297e8i	0.0634212	−	0.475187i
$649$	−5.25912e7			−0.192388
$650$			5.77385e8i			2.10245i
$651$	1.08924e8	+	1.16401e8i	0.394804	+	0.421904i
$652$	−8.94724e7			−0.322810
$653$		−	1.97148e8i		−	0.708032i	−0.935239	−	0.354016i	$-0.884816\pi$
$653$		−	1.97148e8i		−	0.708032i	0.935239	−	0.354016i	$-0.115184\pi$
$654$	−1.56069e8	+	1.46044e8i	−0.557933	+	0.522095i
$655$	−2.00941e6			−0.00715064
$656$			6.61159e7i			0.234204i
$657$	−1.16025e7	+	1.74635e8i	−0.0409124	+	0.615795i
$658$	3.86807e7			0.135774
$659$			4.96620e8i			1.73527i	0.497198	+	0.867637i	$0.334362\pi$
$659$			4.96620e8i			1.73527i	−0.497198	+	0.867637i	$0.665638\pi$
$660$	−2.32662e6	−	2.48633e6i	−0.00809272	−	0.00864823i
$661$	3.66293e8			1.26831			0.634153	−	0.773207i	$-0.281349\pi$
$661$	3.66293e8			1.26831			0.634153	+	0.773207i	$0.281349\pi$
$662$		−	4.74904e8i		−	1.63694i
$663$	5.24185e8	−	4.90514e8i	1.79864	−	1.68310i
$664$	−2.46519e7			−0.0842068
$665$		−	1.47323e6i		−	0.00500963i
$666$	5.48126e8	+	3.64166e7i	1.85549	+	0.123275i
$667$	4.89022e6			0.0164798
$668$		−	4.24343e8i		−	1.42360i
$669$	−4.20812e7	−	4.49698e7i	−0.140543	−	0.150190i
$670$	1.80038e7			0.0598604
$671$			3.84532e7i			0.127282i
$672$	1.14778e8	−	1.07405e8i	0.378225	−	0.353930i
$673$	1.08204e8			0.354976			0.177488	−	0.984123i	$-0.443203\pi$
$673$	1.08204e8			0.354976			0.177488	+	0.984123i	$0.443203\pi$
$674$		−	3.77473e7i		−	0.123284i
$675$	2.37688e8	−	1.94534e8i	0.772851	−	0.632535i
$676$	−3.71444e8			−1.20241
$677$			3.10231e8i			0.999815i	0.866079	+	0.499908i	$0.166633\pi$
$677$			3.10231e8i			0.999815i	−0.866079	+	0.499908i	$0.833367\pi$
$678$	−5.68052e7	−	6.07045e7i	−0.182263	−	0.194774i
$679$	1.26143e8			0.402954
$680$		−	9.68135e6i		−	0.0307900i
$681$	−3.24914e7	+	3.04044e7i	−0.102879	+	0.0962708i
$682$	1.84217e8			0.580734
$683$		−	5.04847e8i		−	1.58452i	−0.610184	−	0.792259i	$-0.708905\pi$
$683$		−	5.04847e8i		−	1.58452i	0.610184	−	0.792259i	$-0.291095\pi$
$684$	1.02503e7	−	1.54283e8i	0.0320310	−	0.482115i
$685$	3.33599e6			0.0103789
$686$		−	2.65221e7i		−	0.0821553i
$687$	2.57699e8	+	2.75389e8i	0.794773	+	0.849329i
$688$	−2.97869e8			−0.914660
$689$			7.81259e8i			2.38857i
$690$	−330752.	+	309507.i	−0.00100683	+	0.000942156i
$691$	1.11177e7			0.0336961			0.0168481	−	0.999858i	$-0.494637\pi$
$691$	1.11177e7			0.0336961			0.0168481	+	0.999858i	$0.494637\pi$
$692$			5.85049e8i			1.76552i
$693$	3.13364e7	+	2.08194e6i	0.0941563	+	0.00625559i
$694$	−2.39725e8			−0.717191
$695$		−	8.96336e6i		−	0.0267003i
$696$	−7.24464e7	−	7.74193e7i	−0.214877	−	0.229626i
$697$	−2.41083e8			−0.711980
$698$			4.87472e8i			1.43345i
$699$	−2.79752e8	+	2.61783e8i	−0.819109	+	0.766495i
$700$	−1.70267e8			−0.496405
$701$		−	2.42107e8i		−	0.702836i	−0.936219	−	0.351418i	$-0.885700\pi$
$701$		−	2.42107e8i		−	0.702836i	0.936219	−	0.351418i	$-0.114300\pi$
$702$	4.61267e8	+	5.63590e8i	1.33334	+	1.62912i
$703$	1.56010e8			0.449043
$704$		−	1.30632e8i		−	0.374395i
$705$	−2.03910e6	−	2.17907e6i	−0.00581931	−	0.00621877i
$706$	−6.58019e8			−1.86992
$707$		−	1.93985e8i		−	0.548922i
$708$	2.62602e8	−	2.45734e8i	0.739943	−	0.692414i
$709$	−1.14034e8			−0.319960			−0.159980	−	0.987120i	$-0.551143\pi$
$709$	−1.14034e8			−0.319960			−0.159980	+	0.987120i	$0.551143\pi$
$710$		−	2.10838e7i		−	0.0589080i
$711$	−2.13106e7	+	3.20758e8i	−0.0592908	+	0.892419i
$712$	−2.36036e8			−0.653942
$713$		−	1.39207e7i		−	0.0384053i
$714$	2.54643e8	+	2.72122e8i	0.699579	+	0.747600i
$715$	4.55491e6			0.0124612
$716$		−	2.17476e8i		−	0.592477i
$717$	−5.04096e8	+	4.71716e8i	−1.36759	+	1.27974i
$718$	−2.24319e8			−0.606028
$719$			8.44036e7i			0.227078i	0.993534	+	0.113539i	$0.0362186\pi$
$719$			8.44036e7i			0.227078i	−0.993534	+	0.113539i	$0.963781\pi$
$720$	−7.86824e6	−	522753.i	−0.0210805	−	0.00140055i
$721$	−3.23308e7			−0.0862601
$722$			4.95352e8i			1.31614i
$723$	−2.89921e8	−	3.09822e8i	−0.767122	−	0.819780i
$724$	2.65459e8			0.699491
$725$		−	2.49660e8i		−	0.655140i
$726$	−3.98625e8	+	3.73020e8i	−1.04173	+	0.974815i
$727$	4.79913e8			1.24899			0.624496	−	0.781028i	$-0.285305\pi$
$727$	4.79913e8			1.24899			0.624496	+	0.781028i	$0.285305\pi$
$728$		−	9.67280e7i		−	0.250702i
$729$	7.65974e7	−	3.79773e8i	0.197711	−	0.980260i
$730$	−1.31778e7			−0.0338746
$731$		−	1.08614e9i		−	2.78057i
$732$	−1.79674e8	−	1.92007e8i	−0.458091	−	0.489536i
$733$	−3.33741e8			−0.847419			−0.423709	−	0.905798i	$-0.639272\pi$
$733$	−3.33741e8			−0.847419			−0.423709	+	0.905798i	$0.639272\pi$
$734$		−	2.02493e8i		−	0.512061i
$735$	−1.49412e6	+	1.39815e6i	−0.00376291	+	0.00352120i
$736$	−1.37265e7			−0.0344292
$737$			1.08997e8i			0.272278i
$738$	1.62132e7	−	2.44034e8i	0.0403367	−	0.607130i
$739$	6.75619e8			1.67405			0.837025	−	0.547165i	$-0.184293\pi$
$739$	6.75619e8			1.67405			0.837025	+	0.547165i	$0.184293\pi$
$740$			2.34950e7i			0.0579803i
$741$	1.41322e8	+	1.51023e8i	0.347340	+	0.371183i
$742$	−4.05578e8			−0.992803
$743$		−	2.24758e8i		−	0.547959i	−0.961736	−	0.273980i	$-0.911660\pi$
$743$		−	2.24758e8i		−	0.547959i	0.961736	−	0.273980i	$-0.0883401\pi$
$744$	−2.20384e8	+	2.06228e8i	−0.535133	+	0.500759i
$745$	−1.28687e7			−0.0311219
$746$		−	5.78170e8i		−	1.39264i
$747$	−7.30556e7	−	4.85370e6i	−0.175264	−	0.0116442i
$748$	2.44637e8			0.584545
$749$			2.59536e8i			0.617664i
$750$	3.16230e7	+	3.37937e7i	0.0749581	+	0.0801035i
$751$	−2.90490e8			−0.685821			−0.342911	−	0.939368i	$-0.611413\pi$
$751$	−2.90490e8			−0.685821			−0.342911	+	0.939368i	$0.611413\pi$
$752$		−	5.87997e7i		−	0.138268i
$753$	−3.09455e8	+	2.89578e8i	−0.724791	+	0.678235i
$754$	5.91977e8			1.38099
$755$			1.73063e7i			0.0402127i
$756$	−1.66199e8	+	1.36025e8i	−0.384648	+	0.314813i
$757$	−1.55939e8			−0.359473			−0.179737	−	0.983715i	$-0.557525\pi$
$757$	−1.55939e8			−0.359473			−0.179737	+	0.983715i	$0.557525\pi$
$758$		−	5.49972e8i		−	1.26279i
$759$	−1.87379e6	−	2.00242e6i	−0.00428545	−	0.00457962i
$760$	2.78929e6			0.00635409
$761$			6.84141e8i			1.55236i	0.630513	+	0.776179i	$0.282845\pi$
$761$			6.84141e8i			1.55236i	−0.630513	+	0.776179i	$0.717155\pi$
$762$	2.82503e7	−	2.64356e7i	0.0638495	−	0.0597482i
$763$	8.43142e7			0.189814
$764$		−	5.35566e8i		−	1.20097i
$765$	1.90615e6	−	2.86905e7i	0.00425768	−	0.0640847i
$766$	5.56596e8			1.23838
$767$			4.81081e8i			1.06618i
$768$	−3.50245e7	−	3.74287e7i	−0.0773193	−	0.0826268i
$769$	1.33968e8			0.294592			0.147296	−	0.989092i	$-0.452943\pi$
$769$	1.33968e8			0.294592			0.147296	+	0.989092i	$0.452943\pi$
$770$			2.36461e6i			0.00517949i
$771$	3.74893e8	−	3.50812e8i	0.817982	−	0.765440i
$772$	7.53993e8			1.63876
$773$			6.50803e8i			1.40900i	0.709704	+	0.704500i	$0.248829\pi$
$773$			6.50803e8i			1.40900i	−0.709704	+	0.704500i	$0.751171\pi$
$774$	1.09944e9	+	7.30448e7i	2.37109	+	0.157531i
$775$	−7.10689e8			−1.52677
$776$			2.38830e8i			0.511097i
$777$	−1.48059e8	−	1.58223e8i	−0.315626	−	0.337292i
$778$	6.23699e8			1.32445
$779$		−	6.94584e7i		−	0.146931i
$780$	−2.27439e7	+	2.12830e7i	−0.0479271	+	0.0448485i
$781$	1.27644e8			0.267947
$782$		−	3.25437e7i		−	0.0680529i
$783$	−1.99451e8	−	2.43695e8i	−0.415480	−	0.507646i
$784$	−4.03170e7			−0.0836643
$785$		−	3.18812e6i		−	0.00659061i
$786$	1.00066e8	+	1.06935e8i	0.206072	+	0.220218i
$787$	−3.30808e8			−0.678659			−0.339330	−	0.940668i	$-0.610200\pi$
$787$	−3.30808e8			−0.678659			−0.339330	+	0.940668i	$0.610200\pi$
$788$			9.26412e8i			1.89333i
$789$	1.94997e8	−	1.82472e8i	0.397006	−	0.371505i
$790$	−2.42040e7			−0.0490915
$791$			3.27949e7i			0.0662639i
$792$	−3.94177e6	+	5.93297e7i	−0.00793443	+	0.119425i
$793$	3.51754e8			0.705373
$794$		−	5.20307e8i		−	1.03944i
$795$	2.13806e7	+	2.28482e7i	0.0425518	+	0.0454727i
$796$	−1.03332e8			−0.204878
$797$		−	3.55894e8i		−	0.702985i	−0.936191	−	0.351492i	$-0.885674\pi$
$797$		−	3.55894e8i		−	0.702985i	0.936191	−	0.351492i	$-0.114326\pi$
$798$	−7.84010e7	+	7.33650e7i	−0.154281	+	0.144371i
$799$	2.14405e8			0.420335
$800$			7.00778e8i			1.36871i
$801$	−6.99490e8	−	4.64730e7i	−1.36108	−	0.0904280i
$802$	2.78808e8			0.540484
$803$		−	7.97800e7i		−	0.154080i
$804$	−5.09294e8	−	5.44253e8i	−0.979942	−	1.04721i
$805$	178685.			0.000342532
$806$		−	1.68514e9i		−	3.21833i
$807$	−1.48685e8	+	1.39134e8i	−0.282909	+	0.264737i
$808$	3.67276e8			0.696240
$809$			5.87501e8i			1.10959i	0.831987	+	0.554796i	$0.187204\pi$
$809$			5.87501e8i			1.10959i	−0.831987	+	0.554796i	$0.812796\pi$
$810$	2.89136e7	+	3.85898e6i	0.0544060	+	0.00726135i
$811$	−8.31378e8			−1.55860			−0.779302	−	0.626648i	$-0.784426\pi$
$811$	−8.31378e8			−1.55860			−0.779302	+	0.626648i	$0.784426\pi$
$812$			1.74570e8i			0.326063i
$813$	−4.76155e8	−	5.08840e8i	−0.886088	−	0.946911i
$814$	−2.50404e8			−0.464268
$815$		−	4.79365e6i		−	0.00885510i
$816$	4.13661e8	−	3.87090e8i	0.761332	−	0.712428i
$817$	3.12927e8			0.573822
$818$		−	2.10437e8i		−	0.384471i
$819$	1.90447e7	−	2.86652e8i	0.0346674	−	0.521799i
$820$	1.04604e7			0.0189716
$821$			2.47735e8i			0.447670i	0.974627	+	0.223835i	$0.0718577\pi$
$821$			2.47735e8i			0.447670i	−0.974627	+	0.223835i	$0.928142\pi$
$822$	−1.66128e8	−	1.77532e8i	−0.299108	−	0.319640i
$823$	−4.94128e7			−0.0886420			−0.0443210	−	0.999017i	$-0.514112\pi$
$823$	−4.94128e7			−0.0886420			−0.0443210	+	0.999017i	$0.514112\pi$
$824$		−	6.12124e7i		−	0.109410i
$825$	−1.02229e8	+	9.56624e7i	−0.182059	+	0.170365i
$826$	−2.49746e8			−0.443157
$827$			6.55316e8i			1.15860i	0.815114	+	0.579301i	$0.196674\pi$
$827$			6.55316e8i			1.15860i	−0.815114	+	0.579301i	$0.803326\pi$
$828$	1.87127e7	+	1.24324e6i	0.0329645	+	0.00219010i
$829$	2.45217e7			0.0430414			0.0215207	−	0.999768i	$-0.493149\pi$
$829$	2.45217e7			0.0430414			0.0215207	+	0.999768i	$0.493149\pi$
$830$		−	5.51269e6i		−	0.00964116i
$831$	−5.77126e7	−	6.16741e7i	−0.100570	−	0.107473i
$832$	−1.19496e9			−2.07484
$833$		−	1.47011e8i		−	0.254340i
$834$	−4.77004e8	+	4.46364e8i	−0.822288	+	0.769469i
$835$	2.27350e7			0.0390512
$836$			7.04824e7i			0.120632i
$837$	−6.93709e8	+	5.67762e8i	−1.18304	+	0.968256i
$838$	6.11013e8			1.03829
$839$			3.60124e8i			0.609771i	0.952389	+	0.304885i	$0.0986181\pi$
$839$			3.60124e8i			0.609771i	−0.952389	+	0.304885i	$0.901382\pi$
$840$	−2.64714e6	−	2.82884e6i	−0.00446620	−	0.00477278i
$841$	3.38854e8			0.569672
$842$			1.11551e9i			1.86869i
$843$	7.04509e8	−	6.59256e8i	1.17599	−	1.10045i
$844$	7.64887e8			1.27224
$845$		−	1.99008e7i		−	0.0329838i
$846$	−1.44191e7	+	2.17030e8i	−0.0238138	+	0.358434i
$847$	2.15353e8			0.354405
$848$			6.16531e8i			1.01104i
$849$	−5.41662e8	−	5.78843e8i	−0.885126	−	0.945883i
$850$	−1.66145e9			−2.70539
$851$			1.89222e7i			0.0307031i
$852$	−6.37362e8	+	5.96422e8i	−1.03055	+	0.964351i
$853$	1.68590e8			0.271635			0.135818	−	0.990734i	$-0.456634\pi$
$853$	1.68590e8			0.271635			0.135818	+	0.990734i	$0.456634\pi$
$854$			1.82607e8i			0.293187i
$855$	8.26602e6	+	549181.i	0.0132251	+	0.000878653i
$856$	−4.91385e8			−0.783430
$857$		−	1.03620e9i		−	1.64628i	−0.567842	−	0.823138i	$-0.692221\pi$
$857$		−	1.03620e9i		−	1.64628i	0.567842	−	0.823138i	$-0.307779\pi$
$858$	−2.26829e8	−	2.42399e8i	−0.359117	−	0.383768i
$859$	9.54517e8			1.50593			0.752964	−	0.658061i	$-0.228623\pi$
$859$	9.54517e8			1.50593			0.752964	+	0.658061i	$0.228623\pi$
$860$			4.71266e7i			0.0740919i
$861$	−7.04432e7	+	6.59184e7i	−0.110365	+	0.103275i
$862$	−8.96630e7			−0.139988
$863$			1.07197e9i			1.66782i	0.551900	+	0.833910i	$0.313903\pi$
$863$			1.07197e9i			1.66782i	−0.551900	+	0.833910i	$0.686097\pi$
$864$	5.59844e8	+	6.84035e8i	0.868013	+	1.06056i
$865$	−3.13451e7			−0.0484307
$866$		−	9.94161e8i		−	1.53075i
$867$	9.66178e8	+	1.03250e9i	1.48252	+	1.58428i
$868$	4.96937e8			0.759875
$869$		−	1.46534e8i		−	0.223295i
$870$	1.73126e7	−	1.62005e7i	0.0262908	−	0.0246021i
$871$	9.97060e8			1.50892
$872$			1.59634e8i			0.240755i
$873$	−4.70229e7	+	7.07768e8i	−0.0706752	+	1.06377i
$874$	9.37615e6			0.0140440
$875$		−	1.82566e7i		−	0.0272519i
$876$	3.72775e8	+	3.98363e8i	0.554542	+	0.592607i
$877$	1.31532e9			1.94999			0.974995	−	0.222227i	$-0.0713327\pi$
$877$	1.31532e9			1.94999			0.974995	+	0.222227i	$0.0713327\pi$
$878$			1.29930e9i			1.91967i
$879$	4.29655e8	−	4.02057e8i	0.632635	−	0.591999i
$880$	3.59451e6			0.00527462
$881$		−	3.97302e8i		−	0.581023i	−0.956872	−	0.290511i	$-0.906175\pi$
$881$		−	3.97302e8i		−	0.581023i	0.956872	−	0.290511i	$-0.0938254\pi$
$882$	1.48811e8	+	9.88673e6i	0.216884	+	0.0144094i
$883$	−5.50815e8			−0.800062			−0.400031	−	0.916502i	$-0.631001\pi$
$883$	−5.50815e8			−0.800062			−0.400031	+	0.916502i	$0.631001\pi$
$884$		−	2.23784e9i		−	3.23945i
$885$	1.31657e7	+	1.40694e7i	0.0189939	+	0.0202976i
$886$	−9.26655e8			−1.33235
$887$		−	1.34965e9i		−	1.93397i	−0.254829	−	0.966986i	$-0.582019\pi$
$887$		−	1.34965e9i		−	1.93397i	0.254829	−	0.966986i	$-0.417981\pi$
$888$	2.99566e8	−	2.80323e8i	0.427812	−	0.400332i
$889$	−1.52619e7			−0.0217221
$890$		−	5.27827e7i		−	0.0748723i
$891$	−2.33627e7	+	1.75047e8i	−0.0330286	+	0.247469i
$892$	−1.91984e8			−0.270502
$893$			6.17723e7i			0.0867440i
$894$	6.40845e8	+	6.84835e8i	0.896893	+	0.958458i
$895$	1.16517e7			0.0162524
$896$		−	2.47738e8i		−	0.344405i
$897$	−1.83172e7	+	1.71407e7i	−0.0253795	+	0.0237493i
$898$	−1.28157e9			−1.76976
$899$			7.28650e8i			1.00286i
$900$	6.34710e7	−	9.55337e8i	0.0870659	−	1.31048i
$901$	−2.24810e9			−3.07356
$902$			1.11484e8i			0.151912i
$903$	−2.96979e8	−	3.17365e8i	−0.403332	−	0.431018i
$904$	−6.20912e7			−0.0840474
$905$			1.42225e7i			0.0191880i
$906$	9.20991e8	−	8.61832e8i	1.23843	−	1.15888i
$907$	−1.00544e9			−1.34751			−0.673757	−	0.738953i	$-0.735321\pi$
$907$	−1.00544e9			−1.34751			−0.673757	+	0.738953i	$0.735321\pi$
$908$			1.38712e8i			0.185291i
$909$	1.08842e9	+	7.23126e7i	1.44912	+	0.0962770i
$910$	2.16304e7			0.0287039
$911$		−	2.23535e8i		−	0.295658i	−0.989013	−	0.147829i	$-0.952771\pi$
$911$		−	2.23535e8i		−	0.295658i	0.989013	−	0.147829i	$-0.0472286\pi$
$912$	1.11524e8	+	1.19180e8i	0.147023	+	0.157115i
$913$	3.33745e7			0.0438534
$914$		−	1.83334e9i		−	2.40107i
$915$	1.02872e7	−	9.62637e6i	0.0134286	−	0.0125661i
$916$	1.17568e9			1.52969
$917$		−	5.77704e7i		−	0.0749200i
$918$	−1.62175e9	+	1.32731e9i	−2.09631	+	1.71572i
$919$	−5.24363e8			−0.675593			−0.337797	−	0.941219i	$-0.609682\pi$
$919$	−5.24363e8			−0.675593			−0.337797	+	0.941219i	$0.609682\pi$
$920$			338308.i			0.000434459i
$921$	−3.30243e8	−	3.52912e8i	−0.422722	−	0.451738i
$922$	1.01879e9			1.29985
$923$		−	1.16763e9i		−	1.48492i
$924$	7.14818e7	−	6.68903e7i	0.0906108	−	0.0847905i
$925$	9.66031e8			1.22058
$926$		−	9.12078e8i		−	1.14868i
$927$	1.20520e7	−	1.81402e8i	0.0151294	−	0.227721i
$928$	7.18488e8			0.899033
$929$		−	6.27106e7i		−	0.0782156i	−0.999235	−	0.0391078i	$-0.987548\pi$
$929$		−	6.27106e7i		−	0.0782156i	0.999235	−	0.0391078i	$-0.0124516\pi$
$930$	−4.61169e7	−	4.92825e7i	−0.0573339	−	0.0612695i
$931$	4.23553e7			0.0524878
$932$			1.19431e9i			1.47526i
$933$	9.76727e8	−	9.13988e8i	1.20262	−	1.12537i
$934$	−1.96980e9			−2.41758
$935$			1.31069e7i			0.0160349i
$936$	5.42723e8	+	3.60576e7i	0.661836	+	0.0439713i
$937$	1.11338e9			1.35339			0.676697	−	0.736261i	$-0.263411\pi$
$937$	1.11338e9			1.35339			0.676697	+	0.736261i	$0.263411\pi$
$938$			5.17608e8i			0.627180i
$939$	6.56583e8	+	7.01653e8i	0.793036	+	0.847472i
$940$	−9.30284e6			−0.0112004
$941$			1.99370e6i			0.00239271i	0.999999	+	0.00119636i	$0.000380812\pi$
$941$			1.99370e6i			0.00239271i	−0.999999	+	0.00119636i	$0.999619\pi$
$942$	−1.69662e8	+	1.58764e8i	−0.202971	+	0.189933i
$943$	8.42446e6			0.0100463
$944$			3.79646e8i			0.451297i
$945$	−7.28778e6	−	8.90442e6i	−0.00863574	−	0.0105514i
$946$	−5.02264e8			−0.593278
$947$			8.14047e8i			0.958517i	0.877674	+	0.479258i	$0.159094\pi$
$947$			8.14047e8i			0.958517i	−0.877674	+	0.479258i	$0.840906\pi$
$948$	6.84686e8	+	7.31685e8i	0.803649	+	0.858814i
$949$	−7.29793e8			−0.853888
$950$		−	4.78679e8i		−	0.558308i
$951$	−5.85525e8	+	5.47915e8i	−0.680776	+	0.637047i
$952$	2.78338e8			0.322598
$953$		−	3.25789e8i		−	0.376407i	−0.982130	−	0.188204i	$-0.939734\pi$
$953$		−	3.25789e8i		−	0.376407i	0.982130	−	0.188204i	$-0.0602665\pi$
$954$	1.51189e8	−	2.27562e9i	0.174130	−	2.62093i
$955$	2.86940e7			0.0329443
$956$			2.15208e9i			2.46311i
$957$	9.80801e7	+	1.04813e8i	0.111904	+	0.119585i
$958$	2.23038e8			0.253677
$959$			9.59095e7i			0.108744i
$960$	−3.49471e7	+	3.27023e7i	−0.0395000	+	0.0369628i
$961$	1.18669e9			1.33711
$962$			2.29059e9i			2.57290i
$963$	−1.45621e9	−	9.67482e7i	−1.63059	−	0.108334i
$964$	−1.32268e9			−1.47647
$965$			4.03966e7i			0.0449534i
$966$	−8.89830e6	−	9.50910e6i	−0.00987133	−	0.0105489i
$967$	−5.76758e8			−0.637844			−0.318922	−	0.947781i	$-0.603321\pi$
$967$	−5.76758e8			−0.637844			−0.318922	+	0.947781i	$0.603321\pi$
$968$			4.07731e8i			0.449519i
$969$	−4.34573e8	+	4.06659e8i	−0.477630	+	0.446950i
$970$	−5.34073e7			−0.0585175
$971$			5.81041e8i			0.634672i	0.948313	+	0.317336i	$0.102788\pi$
$971$			5.81041e8i			0.634672i	−0.948313	+	0.317336i	$0.897212\pi$
$972$	−7.01255e8	−	9.83219e8i	−0.763620	−	1.07066i
$973$	2.57696e8			0.279749
$974$			6.27576e8i			0.679187i
$975$	8.75079e8	+	9.35147e8i	0.944133	+	1.00894i
$976$	2.77587e8			0.298572
$977$		−	5.97905e8i		−	0.641133i	−0.947226	−	0.320567i	$-0.896127\pi$
$977$		−	5.97905e8i		−	0.641133i	0.947226	−	0.320567i	$-0.103873\pi$
$978$	−2.55104e8	+	2.38718e8i	−0.272710	+	0.255193i
$979$	3.19553e8			0.340561
$980$			6.37866e6i			0.00677722i
$981$	−3.14301e7	+	4.73072e8i	−0.0332919	+	0.501095i
$982$	4.39913e8			0.464550
$983$		−	1.55240e9i		−	1.63434i	−0.576398	−	0.817169i	$-0.695542\pi$
$983$		−	1.55240e9i		−	1.63434i	0.576398	−	0.817169i	$-0.304458\pi$
$984$	−1.24804e8	−	1.33371e8i	−0.130992	−	0.139984i
$985$	−4.96343e7			−0.0519365
$986$			1.70344e9i			1.77703i
$987$	6.26482e7	−	5.86240e7i	0.0651564	−	0.0609711i
$988$	6.44743e8			0.668522
$989$			3.79543e7i			0.0392349i
$990$	−1.32674e7	−	881462.i	−0.0136735	−	0.000908444i
$991$	−5.25121e8			−0.539558			−0.269779	−	0.962922i	$-0.586951\pi$
$991$	−5.25121e8			−0.539558			−0.269779	+	0.962922i	$0.586951\pi$
$992$		−	2.04527e9i		−	2.09515i
$993$	−7.19759e8	−	7.69166e8i	−0.735088	−	0.785547i
$994$	6.06159e8			0.617202
$995$		−	5.53619e6i		−	0.00562007i
$996$	−1.66648e8	+	1.55944e8i	−0.168664	+	0.157830i
$997$	−9.13652e8			−0.921924			−0.460962	−	0.887420i	$-0.652496\pi$
$997$	−9.13652e8			−0.921924			−0.460962	+	0.887420i	$0.652496\pi$
$998$			5.46044e8i			0.549333i
$999$	9.42950e8	−	7.71753e8i	0.945785	−	0.774073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.b.a.8.2	✓	12
3.2	odd	2	inner	21.7.b.a.8.11	yes	12
4.3	odd	2		336.7.d.a.113.12		12
7.6	odd	2		147.7.b.b.50.2		12
12.11	even	2		336.7.d.a.113.11		12
21.20	even	2		147.7.b.b.50.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.b.a.8.2	✓	12	1.1	even	1	trivial
21.7.b.a.8.11	yes	12	3.2	odd	2	inner
147.7.b.b.50.2		12	7.6	odd	2
147.7.b.b.50.11		12	21.20	even	2
336.7.d.a.113.11		12	12.11	even	2
336.7.d.a.113.12		12	4.3	odd	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)

\(f(q)\)	\(=\)	\(q-12.1723i q^{2} +(-18.4482 - 19.7146i) q^{3} -84.1649 q^{4} -4.50929i q^{5} +(-239.971 + 224.557i) q^{6} +129.642 q^{7} +245.453i q^{8} +(-48.3270 + 727.396i) q^{9} +O(q^{10})\)	\(q-12.1723i q^{2} +(-18.4482 - 19.7146i) q^{3} -84.1649 q^{4} -4.50929i q^{5} +(-239.971 + 224.557i) q^{6} +129.642 q^{7} +245.453i q^{8} +(-48.3270 + 727.396i) q^{9} -54.8885 q^{10} -332.302i q^{11} +(1552.69 + 1659.27i) q^{12} -3039.75 q^{13} -1578.04i q^{14} +(-88.8987 + 83.1884i) q^{15} -2398.82 q^{16} -8747.00i q^{17} +(8854.09 + 588.251i) q^{18} +2520.10 q^{19} +379.524i q^{20} +(-2391.66 - 2555.83i) q^{21} -4044.88 q^{22} +305.657i q^{23} +(4839.00 - 4528.17i) q^{24} +15604.7 q^{25} +37000.8i q^{26} +(15231.8 - 12466.4i) q^{27} -10911.3 q^{28} -15999.0i q^{29} +(1012.59 + 1082.10i) q^{30} -45543.4 q^{31} +44908.2i q^{32} +(-6551.18 + 6130.37i) q^{33} -106471. q^{34} -584.593i q^{35} +(4067.44 - 61221.2i) q^{36} +61906.5 q^{37} -30675.4i q^{38} +(56078.0 + 59927.4i) q^{39} +1106.82 q^{40} -27561.8i q^{41} +(-31110.3 + 29112.0i) q^{42} +124173. q^{43} +27968.1i q^{44} +(3280.04 + 217.921i) q^{45} +3720.55 q^{46} +24511.9i q^{47} +(44254.0 + 47291.7i) q^{48} +16807.0 q^{49} -189945. i q^{50} +(-172443. + 161366. i) q^{51} +255841. q^{52} -257014. i q^{53} +(-151745. - 185407. i) q^{54} -1498.45 q^{55} +31821.0i q^{56} +(-46491.3 - 49682.6i) q^{57} -194745. q^{58} -158263. i q^{59} +(7482.15 - 7001.54i) q^{60} -115718. q^{61} +554367. i q^{62} +(-6265.20 + 94301.0i) q^{63} +393111. q^{64} +13707.1i q^{65} +(74620.8 + 79742.9i) q^{66} -328007. q^{67} +736190. i q^{68} +(6025.90 - 5638.83i) q^{69} -7115.84 q^{70} +384121. i q^{71} +(-178542. - 11862.0i) q^{72} +240083. q^{73} -753545. i q^{74} +(-287878. - 307639. i) q^{75} -212104. q^{76} -43080.2i q^{77} +(729454. - 682598. i) q^{78} +440967. q^{79} +10817.0i q^{80} +(-526770. - 70305.8i) q^{81} -335490. q^{82} +100434. i q^{83} +(201294. + 215111. i) q^{84} -39442.8 q^{85} -1.51147e6i q^{86} +(-315414. + 295154. i) q^{87} +81564.5 q^{88} +961635. i q^{89} +(2652.60 - 39925.7i) q^{90} -394079. q^{91} -25725.6i q^{92} +(840193. + 897867. i) q^{93} +298366. q^{94} -11363.9i q^{95} +(885345. - 828476. i) q^{96} +973015. q^{97} -204580. i q^{98} +(241715. + 16059.2i) 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

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