LMFDB - Embedded newform 3.21.b.a.2.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,21,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	3.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:	$7.60541295308$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 116898x^{4} + 3059043456x^{2} + 18153107947520 $ x^6 + 116898x^4 + 3059043456x^2 + 18153107947520
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{14}\cdot 3^{19}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.5
Root			$161.041i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.21.b.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+966.247i q^{2} +(56662.8 - 16616.6i) q^{3} +114943. q^{4} -1.69009e7i q^{5} +(1.60557e7 + 5.47503e7i) q^{6} +2.16509e8 q^{7} +1.12425e9i q^{8} +(2.93456e9 - 1.88308e9i) q^{9} +O(q^{10})$	\(q+966.247i q^{2} +(56662.8 - 16616.6i) q^{3} +114943. q^{4} -1.69009e7i q^{5} +(1.60557e7 + 5.47503e7i) q^{6} +2.16509e8 q^{7} +1.12425e9i q^{8} +(2.93456e9 - 1.88308e9i) q^{9} +1.63305e10 q^{10} +1.25226e10i q^{11} +(6.51298e9 - 1.90995e9i) q^{12} -9.02553e10 q^{13} +2.09201e11i q^{14} +(-2.80835e11 - 9.57653e11i) q^{15} -9.65774e11 q^{16} +5.69903e11i q^{17} +(1.81952e12 + 2.83551e12i) q^{18} +4.66402e12 q^{19} -1.94264e12i q^{20} +(1.22680e13 - 3.59764e12i) q^{21} -1.20999e13 q^{22} -1.67575e13i q^{23} +(1.86811e13 + 6.37030e13i) q^{24} -1.90273e14 q^{25} -8.72090e13i q^{26} +(1.34990e14 - 1.55463e14i) q^{27} +2.48862e13 q^{28} +5.50759e14i q^{29} +(9.25329e14 - 2.71356e14i) q^{30} -5.98050e14 q^{31} +2.45682e14i q^{32} +(2.08083e14 + 7.09566e14i) q^{33} -5.50667e14 q^{34} -3.65920e15i q^{35} +(3.37307e14 - 2.16447e14i) q^{36} -6.64814e15 q^{37} +4.50660e15i q^{38} +(-5.11412e15 + 1.49973e15i) q^{39} +1.90008e16 q^{40} -6.99239e15i q^{41} +(3.47621e15 + 1.18539e16i) q^{42} +1.44085e16 q^{43} +1.43938e15i q^{44} +(-3.18258e16 - 4.95968e16i) q^{45} +1.61919e16 q^{46} +9.26870e16i q^{47} +(-5.47234e16 + 1.60478e16i) q^{48} -3.29160e16 q^{49} -1.83851e17i q^{50} +(9.46983e15 + 3.22923e16i) q^{51} -1.03742e16 q^{52} -1.20900e16i q^{53} +(1.50216e17 + 1.30434e17i) q^{54} +2.11643e17 q^{55} +2.43410e17i q^{56} +(2.64277e17 - 7.75001e16i) q^{57} -5.32170e17 q^{58} -1.03162e17i q^{59} +(-3.22800e16 - 1.10075e17i) q^{60} -3.83144e17 q^{61} -5.77864e17i q^{62} +(6.35360e17 - 4.07705e17i) q^{63} -1.25008e18 q^{64} +1.52540e18i q^{65} +(-6.85616e17 + 2.01059e17i) q^{66} +1.36192e18 q^{67} +6.55062e16i q^{68} +(-2.78453e17 - 9.49528e17i) q^{69} +3.53569e18 q^{70} -7.04530e17i q^{71} +(2.11705e18 + 3.29917e18i) q^{72} +1.09222e18 q^{73} -6.42374e18i q^{74} +(-1.07814e19 + 3.16169e18i) q^{75} +5.36096e17 q^{76} +2.71126e18i q^{77} +(-1.44911e18 - 4.94150e18i) q^{78} -6.22330e18 q^{79} +1.63225e19i q^{80} +(5.06566e18 - 1.10521e19i) q^{81} +6.75637e18 q^{82} -1.97733e19i q^{83} +(1.41012e18 - 4.13523e17i) q^{84} +9.63188e18 q^{85} +1.39222e19i q^{86} +(9.15174e18 + 3.12076e19i) q^{87} -1.40785e19 q^{88} +8.06929e18i q^{89} +(4.79227e19 - 3.07516e19i) q^{90} -1.95411e19 q^{91} -1.92616e18i q^{92} +(-3.38872e19 + 9.93755e18i) q^{93} -8.95585e19 q^{94} -7.88262e19i q^{95} +(4.08239e18 + 1.39210e19i) q^{96} +5.28539e19 q^{97} -3.18050e19i q^{98} +(2.35811e19 + 3.67484e19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9}+O(q^{10}) $ 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9	$ 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9} - 10880304480 q^{10} + 63957886128 q^{12} + 17847879276 q^{13} - 487764624960 q^{15} - 317472843648 q^{16} + 9564155313120 q^{18} - 14958020195124 q^{19} + 25978999888044 q^{21} - 71051286019680 q^{22} + 294048705803904 q^{24} - 397204775017050 q^{25} + 10\!\cdots\!98 q^{27}+ \cdots - 17\!\cdots\!80 q^{99}+O(q^{100}) $ 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9 - 10880304480 * q^10 + 63957886128 * q^12 + 17847879276 * q^13 - 487764624960 * q^15 - 317472843648 * q^16 + 9564155313120 * q^18 - 14958020195124 * q^19 + 25978999888044 * q^21 - 71051286019680 * q^22 + 294048705803904 * q^24 - 397204775017050 * q^25 + 1077025592505798 * q^27 - 2034284889273504 * q^28 + 3061064118304800 * q^30 - 2182905165483348 * q^31 + 3811197222014400 * q^33 - 7566372644651136 * q^34 + 6910111676037744 * q^36 - 1934341462168404 * q^37 - 15813602040849876 * q^39 + 44482420967535360 * q^40 - 86552595699685920 * q^42 + 58194987502184076 * q^43 - 81854223046416000 * q^45 + 151411391218915776 * q^46 - 154489681080035712 * q^48 + 188165158287453522 * q^49 - 117657755976045312 * q^51 - 230547517796956704 * q^52 + 489800358305152272 * q^54 - 393208608470140800 * q^55 + 1211071992434087436 * q^57 - 1639827118548168480 * q^58 + 2591328282252814080 * q^60 - 2999109545381544468 * q^61 + 444547436097192876 * q^63 - 83569554960393216 * q^64 + 120735307117251360 * q^66 + 4488155969890198476 * q^67 - 3511312424189451648 * q^69 - 1812568842584740800 * q^70 - 10414532525611288320 * q^72 + 15738405804262597836 * q^73 - 20871070048457840250 * q^75 + 27275280223392575328 * q^76 - 13410777930056987040 * q^78 + 17679940751103803436 * q^79 - 13011625055229011514 * q^81 - 35403353112903693120 * q^82 + 60397598618988279264 * q^84 - 22576574831711316480 * q^85 + 17858271599894295360 * q^87 - 95000209108729447680 * q^88 + 179562325304911301280 * q^90 - 6461010485165713512 * q^91 - 24838278011742494484 * q^93 - 311754310853935072896 * q^94 + 184738040137761352704 * q^96 + 223240336245548394636 * q^97 - 178130031568853028480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			966.247i			0.943601i	0.881705	+	0.471800i	$0.156396\pi$
$2$			966.247i			0.943601i	−0.881705	+	0.471800i	$0.843604\pi$
$3$	56662.8	−	16616.6i	0.959590	−	0.281403i
$3$	56662.8	−	16616.6i	0.959590	−	0.281403i
$4$	114943.			0.109618
$5$		−	1.69009e7i		−	1.73065i	−0.501208	−	0.865327i	$-0.667111\pi$
$5$		−	1.69009e7i		−	1.73065i	0.501208	−	0.865327i	$-0.332889\pi$
$6$	1.60557e7	+	5.47503e7i	0.265532	+	0.905469i
$7$	2.16509e8			0.766471			0.383236	−	0.923651i	$-0.374810\pi$
$7$	2.16509e8			0.766471			0.383236	+	0.923651i	$0.374810\pi$
$8$			1.12425e9i			1.04704i
$9$	2.93456e9	−	1.88308e9i	0.841625	−	0.540063i
$10$	1.63305e10			1.63305
$11$			1.25226e10i			0.482800i	0.970426	+	0.241400i	$0.0776066\pi$
$11$			1.25226e10i			0.482800i	−0.970426	+	0.241400i	$0.922393\pi$
$12$	6.51298e9	−	1.90995e9i	0.105188	−	0.0308468i
$13$	−9.02553e10			−0.654696			−0.327348	−	0.944904i	$-0.606155\pi$
$13$	−9.02553e10			−0.654696			−0.327348	+	0.944904i	$0.606155\pi$
$14$			2.09201e11i			0.723243i
$15$	−2.80835e11	−	9.57653e11i	−0.487011	−	1.66072i
$16$	−9.65774e11			−0.878366
$17$			5.69903e11i			0.282691i	0.989960	+	0.141345i	$0.0451428\pi$
$17$			5.69903e11i			0.282691i	−0.989960	+	0.141345i	$0.954857\pi$
$18$	1.81952e12	+	2.83551e12i	0.509604	+	0.794157i
$19$	4.66402e12			0.760720			0.380360	−	0.924839i	$-0.375800\pi$
$19$	4.66402e12			0.760720			0.380360	+	0.924839i	$0.375800\pi$
$20$		−	1.94264e12i		−	0.189711i
$21$	1.22680e13	−	3.59764e12i	0.735498	−	0.215687i
$22$	−1.20999e13			−0.455571
$23$		−	1.67575e13i		−	0.404512i	−0.979333	−	0.202256i	$-0.935173\pi$
$23$		−	1.67575e13i		−	0.404512i	0.979333	−	0.202256i	$-0.0648273\pi$
$24$	1.86811e13	+	6.37030e13i	0.294639	+	1.00473i
$25$	−1.90273e14			−1.99516
$26$		−	8.72090e13i		−	0.617771i
$27$	1.34990e14	−	1.55463e14i	0.655639	−	0.755075i
$28$	2.48862e13			0.0840190
$29$			5.50759e14i			1.30913i	0.756007	+	0.654564i	$0.227148\pi$
$29$			5.50759e14i			1.30913i	−0.756007	+	0.654564i	$0.772852\pi$
$30$	9.25329e14	−	2.71356e14i	1.56705	−	0.459544i
$31$	−5.98050e14			−0.729661			−0.364830	−	0.931074i	$-0.618873\pi$
$31$	−5.98050e14			−0.729661			−0.364830	+	0.931074i	$0.618873\pi$
$32$			2.45682e14i			0.218210i
$33$	2.08083e14	+	7.09566e14i	0.135862	+	0.463290i
$34$	−5.50667e14			−0.266747
$35$		−	3.65920e15i		−	1.32650i
$36$	3.37307e14	−	2.16447e14i	0.0922572	−	0.0592006i
$37$	−6.64814e15			−1.38256			−0.691278	−	0.722589i	$-0.742952\pi$
$37$	−6.64814e15			−1.38256			−0.691278	+	0.722589i	$0.742952\pi$
$38$			4.50660e15i			0.717815i
$39$	−5.11412e15	+	1.49973e15i	−0.628239	+	0.184233i
$40$	1.90008e16			1.81206
$41$		−	6.99239e15i		−	0.520939i	−0.965482	−	0.260470i	$-0.916123\pi$
$41$		−	6.99239e15i		−	0.520939i	0.965482	−	0.260470i	$-0.0838774\pi$
$42$	3.47621e15	+	1.18539e16i	0.203523	+	0.694016i
$43$	1.44085e16			0.666705			0.333353	−	0.942802i	$-0.391820\pi$
$43$	1.44085e16			0.666705			0.333353	+	0.942802i	$0.391820\pi$
$44$			1.43938e15i			0.0529236i
$45$	−3.18258e16	−	4.95968e16i	−0.934662	−	1.45656i
$46$	1.61919e16			0.381698
$47$			9.26870e16i			1.76214i	0.472986	+	0.881070i	$0.343176\pi$
$47$			9.26870e16i			1.76214i	−0.472986	+	0.881070i	$0.656824\pi$
$48$	−5.47234e16	+	1.60478e16i	−0.842871	+	0.247175i
$49$	−3.29160e16			−0.412521
$50$		−	1.83851e17i		−	1.88263i
$51$	9.46983e15	+	3.22923e16i	0.0795501	+	0.271267i
$52$	−1.03742e16			−0.0717664
$53$		−	1.20900e16i		−	0.0691302i	−0.999402	−	0.0345651i	$-0.988995\pi$
$53$		−	1.20900e16i		−	0.0691302i	0.999402	−	0.0345651i	$-0.0110046\pi$
$54$	1.50216e17	+	1.30434e17i	0.712489	+	0.618661i
$55$	2.11643e17			0.835560
$56$			2.43410e17i			0.802523i
$57$	2.64277e17	−	7.75001e16i	0.729979	−	0.214069i
$58$	−5.32170e17			−1.23529
$59$		−	1.03162e17i		−	0.201836i	−0.994895	−	0.100918i	$-0.967822\pi$
$59$		−	1.03162e17i		−	0.201836i	0.994895	−	0.100918i	$-0.0321780\pi$
$60$	−3.22800e16	−	1.10075e17i	−0.0533852	−	0.182044i
$61$	−3.83144e17			−0.537110			−0.268555	−	0.963264i	$-0.586546\pi$
$61$	−3.83144e17			−0.537110			−0.268555	+	0.963264i	$0.586546\pi$
$62$		−	5.77864e17i		−	0.688508i
$63$	6.35360e17	−	4.07705e17i	0.645081	−	0.413943i
$64$	−1.25008e18			−1.08427
$65$			1.52540e18i			1.13305i
$66$	−6.85616e17	+	2.01059e17i	−0.437161	+	0.128199i
$67$	1.36192e18			0.747141			0.373571	−	0.927602i	$-0.378133\pi$
$67$	1.36192e18			0.747141			0.373571	+	0.927602i	$0.378133\pi$
$68$			6.55062e16i			0.0309880i
$69$	−2.78453e17	−	9.49528e17i	−0.113831	−	0.388165i
$70$	3.53569e18			1.25168
$71$		−	7.04530e17i		−	0.216429i	−0.994128	−	0.108215i	$-0.965487\pi$
$71$		−	7.04530e17i		−	0.216429i	0.994128	−	0.108215i	$-0.0345134\pi$
$72$	2.11705e18	+	3.29917e18i	0.565466	+	0.881211i
$73$	1.09222e18			0.254144			0.127072	−	0.991893i	$-0.459442\pi$
$73$	1.09222e18			0.254144			0.127072	+	0.991893i	$0.459442\pi$
$74$		−	6.42374e18i		−	1.30458i
$75$	−1.07814e19	+	3.16169e18i	−1.91454	+	0.561444i
$76$	5.36096e17			0.0833885
$77$			2.71126e18i			0.370053i
$78$	−1.44911e18	−	4.94150e18i	−0.173843	−	0.592807i
$79$	−6.22330e18			−0.657279			−0.328640	−	0.944455i	$-0.606590\pi$
$79$	−6.22330e18			−0.657279			−0.328640	+	0.944455i	$0.606590\pi$
$80$			1.63225e19i			1.52015i
$81$	5.06566e18	−	1.10521e19i	0.416664	−	0.909061i
$82$	6.75637e18			0.491558
$83$		−	1.97733e19i		−	1.27438i	−0.770708	−	0.637189i	$-0.780097\pi$
$83$		−	1.97733e19i		−	1.27438i	0.770708	−	0.637189i	$-0.219903\pi$
$84$	1.41012e18	−	4.13523e17i	0.0806238	−	0.0236432i
$85$	9.63188e18			0.489240
$86$			1.39222e19i			0.629104i
$87$	9.15174e18	+	3.12076e19i	0.368393	+	1.25623i
$88$	−1.40785e19			−0.505509
$89$			8.06929e18i			0.258783i	0.991594	+	0.129391i	$0.0413023\pi$
$89$			8.06929e18i			0.258783i	−0.991594	+	0.129391i	$0.958698\pi$
$90$	4.79227e19	−	3.07516e19i	1.37441	−	0.881948i
$91$	−1.95411e19			−0.501805
$92$		−	1.92616e18i		−	0.0443418i
$93$	−3.38872e19	+	9.93755e18i	−0.700175	+	0.205329i
$94$	−8.95585e19			−1.66276
$95$		−	7.88262e19i		−	1.31654i
$96$	4.08239e18	+	1.39210e19i	0.0614048	+	0.209392i
$97$	5.28539e19			0.716737			0.358368	−	0.933580i	$-0.383333\pi$
$97$	5.28539e19			0.716737			0.358368	+	0.933580i	$0.383333\pi$
$98$		−	3.18050e19i		−	0.389256i
$99$	2.35811e19	+	3.67484e19i	0.260743	+	0.406337i
$100$	−2.18705e19			−0.218705
$101$			2.16210e20i			1.95732i	0.205477	+	0.978662i	$0.434125\pi$
$101$			2.16210e20i			1.95732i	−0.205477	+	0.978662i	$0.565875\pi$
$102$	−3.12023e19	+	9.15020e18i	−0.255968	+	0.0750635i
$103$	2.09163e20			1.55637			0.778184	−	0.628036i	$-0.216141\pi$
$103$	2.09163e20			1.55637			0.778184	+	0.628036i	$0.216141\pi$
$104$		−	1.01469e20i		−	0.685490i
$105$	−6.08034e19	−	2.07341e20i	−0.373280	−	1.27289i
$106$	1.16819e19			0.0652313
$107$			6.28235e19i			0.319363i	0.987169	+	0.159681i	$0.0510467\pi$
$107$			6.28235e19i			0.319363i	−0.987169	+	0.159681i	$0.948953\pi$
$108$	1.55161e19	−	1.78694e19i	0.0718698	−	0.0827698i
$109$	1.95100e20			0.824122			0.412061	−	0.911156i	$-0.364809\pi$
$109$	1.95100e20			0.824122			0.412061	+	0.911156i	$0.364809\pi$
$110$			2.04500e20i			0.788435i
$111$	−3.76702e20	+	1.10469e20i	−1.32669	+	0.389056i
$112$	−2.09099e20			−0.673242
$113$		−	6.02137e20i		−	1.77382i	−0.461938	−	0.886912i	$-0.652846\pi$
$113$		−	6.02137e20i		−	1.77382i	0.461938	−	0.886912i	$-0.347154\pi$
$114$	7.48842e19	+	2.55356e20i	0.201996	+	0.688808i
$115$	−2.83217e20			−0.700070
$116$			6.33058e19i			0.143504i
$117$	−2.64860e20	+	1.69958e20i	−0.551008	+	0.353577i
$118$	9.96799e19			0.190453
$119$			1.23389e20i			0.216674i
$120$	1.07664e21	−	3.15728e20i	1.73883	−	0.509918i
$121$	5.15935e20			0.766904
$122$		−	3.70212e20i		−	0.506818i
$123$	−1.16190e20	−	3.96208e20i	−0.146594	−	0.499888i
$124$	−6.87416e19			−0.0799839
$125$			1.60400e21i			1.72228i
$126$	3.93944e20	+	6.13915e20i	0.390597	+	0.608699i
$127$	−1.19909e21			−1.09854			−0.549270	−	0.835645i	$-0.685094\pi$
$127$	−1.19909e21			−1.09854			−0.549270	+	0.835645i	$0.685094\pi$
$128$		−	9.50266e20i		−	0.804907i
$129$	8.16426e20	−	2.39420e20i	0.639764	−	0.187613i
$130$	−1.47391e21			−1.06915
$131$		−	5.89281e20i		−	0.395922i	−0.980210	−	0.197961i	$-0.936568\pi$
$131$		−	5.89281e20i		−	0.395922i	0.980210	−	0.197961i	$-0.0634320\pi$
$132$	2.39176e19	+	8.15594e19i	0.0148929	+	0.0507849i
$133$	1.00980e21			0.583070
$134$			1.31595e21i			0.705003i
$135$	−2.62747e21	−	2.28146e21i	−1.30677	−	1.13468i
$136$	−6.40711e20			−0.295987
$137$		−	6.46900e20i		−	0.277736i	−0.990311	−	0.138868i	$-0.955654\pi$
$137$		−	6.46900e20i		−	0.277736i	0.990311	−	0.138868i	$-0.0443463\pi$
$138$	9.17478e20	−	2.69054e20i	0.366273	−	0.107411i
$139$	1.05424e21			0.391554			0.195777	−	0.980648i	$-0.437277\pi$
$139$	1.05424e21			0.391554			0.195777	+	0.980648i	$0.437277\pi$
$140$		−	4.20599e20i		−	0.145408i
$141$	1.54014e21	+	5.25191e21i	0.495872	+	1.69093i
$142$	6.80750e20			0.204223
$143$		−	1.13023e21i		−	0.316087i
$144$	−2.83412e21	+	1.81863e21i	−0.739254	+	0.474373i
$145$	9.30834e21			2.26565
$146$			1.05535e21i			0.239811i
$147$	−1.86511e21	+	5.46952e20i	−0.395851	+	0.116085i
$148$	−7.64155e20			−0.151553
$149$		−	5.22509e21i		−	0.968794i	−0.874848	−	0.484397i	$-0.839039\pi$
$149$		−	5.22509e21i		−	0.968794i	0.874848	−	0.484397i	$-0.160961\pi$
$150$	−3.05497e21	−	1.04175e22i	−0.529779	−	1.80656i
$151$	−5.95678e21			−0.966590			−0.483295	−	0.875458i	$-0.660560\pi$
$151$	−5.95678e21			−0.966590			−0.483295	+	0.875458i	$0.660560\pi$
$152$			5.24351e21i			0.796501i
$153$	1.07317e21	+	1.67242e21i	0.152671	+	0.237919i
$154$	−2.61974e21			−0.349182
$155$			1.01076e22i			1.26279i
$156$	−5.87831e20	+	1.72384e20i	−0.0688663	+	0.0201953i
$157$	−3.23931e21			−0.356005			−0.178003	−	0.984030i	$-0.556964\pi$
$157$	−3.23931e21			−0.356005			−0.178003	+	0.984030i	$0.556964\pi$
$158$		−	6.01324e21i		−	0.620209i
$159$	−2.00894e20	−	6.85053e20i	−0.0194534	−	0.0663366i
$160$	4.15225e21			0.377645
$161$		−	3.62816e21i		−	0.310047i
$162$	1.06790e22	+	4.89468e21i	0.857790	+	0.393164i
$163$	−1.39117e22			−1.05076			−0.525381	−	0.850867i	$-0.676077\pi$
$163$	−1.39117e22			−1.05076			−0.525381	+	0.850867i	$0.676077\pi$
$164$		−	8.03724e20i		−	0.0571043i
$165$	1.19923e22	−	3.51679e21i	0.801795	−	0.235129i
$166$	1.91059e22			1.20250
$167$		−	9.88451e21i		−	0.585855i	−0.956135	−	0.292928i	$-0.905371\pi$
$167$		−	9.88451e21i		−	0.585855i	0.956135	−	0.292928i	$-0.0946295\pi$
$168$	4.04464e21	+	1.37923e22i	0.225833	+	0.770093i
$169$	−1.08589e22			−0.571374
$170$			9.30677e21i			0.461647i
$171$	1.36869e22	−	8.78274e21i	0.640240	−	0.410837i
$172$	1.65615e21			0.0730829
$173$			1.39027e22i			0.578946i	0.957186	+	0.289473i	$0.0934801\pi$
$173$			1.39027e22i			0.578946i	−0.957186	+	0.289473i	$0.906520\pi$
$174$	−3.01542e22	+	8.84284e21i	−1.18537	+	0.347615i
$175$	−4.11959e22			−1.52923
$176$		−	1.20940e22i		−	0.424075i
$177$	−1.71420e21	−	5.84544e21i	−0.0567974	−	0.193680i
$178$	−7.79692e21			−0.244187
$179$		−	3.67360e22i		−	1.08783i	−0.839140	−	0.543916i	$-0.816941\pi$
$179$		−	3.67360e22i		−	1.08783i	0.839140	−	0.543916i	$-0.183059\pi$
$180$	−3.65815e21	−	5.70079e21i	−0.102456	−	0.159665i
$181$	6.04126e22			1.60082			0.800409	−	0.599454i	$-0.204616\pi$
$181$	6.04126e22			1.60082			0.800409	+	0.599454i	$0.204616\pi$
$182$		−	1.88815e22i		−	0.473504i
$183$	−2.17100e22	+	6.36654e21i	−0.515405	+	0.151145i
$184$	1.88396e22			0.423539
$185$			1.12360e23i			2.39272i
$186$	−9.60213e21	−	3.27434e22i	−0.193748	−	0.660685i
$187$	−7.13666e21			−0.136483
$188$			1.06537e22i			0.193162i
$189$	2.92266e22	−	3.36592e22i	0.502528	−	0.578743i
$190$	7.61656e22			1.24229
$191$		−	3.28308e22i		−	0.508098i	−0.967191	−	0.254049i	$-0.918238\pi$
$191$		−	3.28308e22i		−	0.508098i	0.967191	−	0.254049i	$-0.0817625\pi$
$192$	−7.08328e22	+	2.07720e22i	−1.04045	+	0.305117i
$193$	1.73648e22			0.242156			0.121078	−	0.992643i	$-0.461365\pi$
$193$	1.73648e22			0.242156			0.121078	+	0.992643i	$0.461365\pi$
$194$			5.10699e22i			0.676313i
$195$	2.53469e22	+	8.64333e22i	0.318844	+	1.08726i
$196$	−3.78346e21			−0.0452198
$197$		−	1.20494e23i		−	1.36868i	−0.729163	−	0.684340i	$-0.760091\pi$
$197$		−	1.20494e23i		−	1.36868i	0.729163	−	0.684340i	$-0.239909\pi$
$198$	−3.55080e22	+	2.27852e22i	−0.383419	+	0.246037i
$199$	−1.99116e22			−0.204444			−0.102222	−	0.994762i	$-0.532595\pi$
$199$	−1.99116e22			−0.204444			−0.102222	+	0.994762i	$0.532595\pi$
$200$		−	2.13914e23i		−	2.08901i
$201$	7.71701e22	−	2.26304e22i	0.716949	−	0.210248i
$202$	−2.08913e23			−1.84693
$203$			1.19244e23i			1.00341i
$204$	1.08849e21	+	3.71177e21i	0.00872012	+	0.0297357i
$205$	−1.18178e23			−0.901565
$206$			2.02103e23i			1.46859i
$207$	−3.15558e22	−	4.91760e22i	−0.218462	−	0.340447i
$208$	8.71662e22			0.575062
$209$			5.84057e22i			0.367276i
$210$	2.00342e23	−	5.87511e22i	1.20110	−	0.352227i
$211$	1.95010e23			1.11489			0.557444	−	0.830214i	$-0.311782\pi$
$211$	1.95010e23			1.11489			0.557444	+	0.830214i	$0.311782\pi$
$212$		−	1.38966e21i		−	0.00757791i
$213$	−1.17069e22	−	3.99206e22i	−0.0609038	−	0.207683i
$214$	−6.07030e22			−0.301351
$215$		−	2.43517e23i		−	1.15384i
$216$	1.74779e23	+	1.51762e23i	0.790591	+	0.686477i
$217$	−1.29483e23			−0.559264
$218$			1.88515e23i			0.777642i
$219$	6.18881e22	−	1.81489e22i	0.243874	−	0.0715170i
$220$	2.43269e22			0.0915924
$221$		−	5.14368e22i		−	0.185076i
$222$	−1.06741e23	−	3.63987e23i	−0.367113	−	1.25186i
$223$	−1.67964e23			−0.552290			−0.276145	−	0.961116i	$-0.589057\pi$
$223$	−1.67964e23			−0.552290			−0.276145	+	0.961116i	$0.589057\pi$
$224$			5.31924e22i			0.167251i
$225$	−5.58369e23	+	3.58301e23i	−1.67918	+	1.07751i
$226$	5.81813e23			1.67378
$227$			2.93558e23i			0.808044i	0.914749	+	0.404022i	$0.132388\pi$
$227$			2.93558e23i			0.808044i	−0.914749	+	0.404022i	$0.867612\pi$
$228$	3.03767e22	−	8.90807e21i	0.0800188	−	0.0234658i
$229$	−4.53837e23			−1.14431			−0.572157	−	0.820144i	$-0.693893\pi$
$229$	−4.53837e23			−1.14431			−0.572157	+	0.820144i	$0.693893\pi$
$230$		−	2.73658e23i		−	0.660586i
$231$	4.50518e22	+	1.53627e23i	0.104134	+	0.355099i
$232$	−6.19189e23			−1.37070
$233$		−	8.08608e23i		−	1.71466i	−0.514764	−	0.857332i	$-0.672120\pi$
$233$		−	8.08608e23i		−	1.71466i	0.514764	−	0.857332i	$-0.327880\pi$
$234$	−1.64222e23	−	2.55920e23i	−0.333635	−	0.519931i
$235$	1.56649e24			3.04965
$236$		−	1.18577e22i		−	0.0221249i
$237$	−3.52630e23	+	1.03410e23i	−0.630718	+	0.184960i
$238$	−1.19224e23			−0.204454
$239$			4.25932e23i			0.700424i	0.936670	+	0.350212i	$0.113890\pi$
$239$			4.25932e23i			0.700424i	−0.936670	+	0.350212i	$0.886110\pi$
$240$	2.71223e23	+	9.24876e23i	0.427774	+	1.45872i
$241$	6.34788e23			0.960414			0.480207	−	0.877155i	$-0.340562\pi$
$241$	6.34788e23			0.960414			0.480207	+	0.877155i	$0.340562\pi$
$242$			4.98520e23i			0.723651i
$243$	1.03387e23	−	7.10414e23i	0.144014	−	0.989576i
$244$	−4.40396e22			−0.0588769
$245$			5.56311e23i			0.713932i
$246$	3.82835e23	−	1.12268e23i	0.471694	−	0.138326i
$247$	−4.20953e23			−0.498040
$248$		−	6.72356e23i		−	0.763981i
$249$	−3.28565e23	−	1.12041e24i	−0.358614	−	1.22288i
$250$	−1.54986e24			−1.62514
$251$			1.39254e24i			1.40305i	0.712647	+	0.701523i	$0.247496\pi$
$251$			1.39254e24i			1.40305i	−0.712647	+	0.701523i	$0.752504\pi$
$252$	7.30300e22	−	4.68627e22i	0.0707125	−	0.0453756i
$253$	2.09848e23			0.195298
$254$		−	1.15862e24i		−	1.03658i
$255$	5.45769e23	−	1.60049e23i	0.469469	−	0.137674i
$256$	−3.92608e23			−0.324758
$257$		−	9.51043e23i		−	0.756605i	−0.925682	−	0.378302i	$-0.876508\pi$
$257$		−	9.51043e23i		−	0.756605i	0.925682	−	0.378302i	$-0.123492\pi$
$258$	2.31339e23	+	7.88869e23i	0.177032	+	0.603681i
$259$	−1.43938e24			−1.05969
$260$			1.75333e23i			0.124203i
$261$	1.03713e24	+	1.61624e24i	0.707011	+	1.10179i
$262$	5.69391e23			0.373592
$263$		−	1.12227e24i		−	0.708828i	−0.935089	−	0.354414i	$-0.884680\pi$
$263$		−	1.12227e24i		−	0.708828i	0.935089	−	0.354414i	$-0.115320\pi$
$264$	−7.97727e23	+	2.33936e23i	−0.485082	+	0.142252i
$265$	−2.04332e23			−0.119640
$266$			9.75720e23i			0.550185i
$267$	1.34084e23	+	4.57228e23i	0.0728222	+	0.248325i
$268$	1.56543e23			0.0819001
$269$			1.94761e24i			0.981702i	0.871244	+	0.490851i	$0.163314\pi$
$269$			1.94761e24i			0.981702i	−0.871244	+	0.490851i	$0.836686\pi$
$270$	2.20445e24	−	2.53878e24i	1.07069	−	1.23307i
$271$	3.46648e24			1.62254			0.811270	−	0.584671i	$-0.198776\pi$
$271$	3.46648e24			1.62254			0.811270	+	0.584671i	$0.198776\pi$
$272$		−	5.50397e23i		−	0.248306i
$273$	−1.10725e24	+	3.24706e23i	−0.481527	+	0.141210i
$274$	6.25066e23			0.262072
$275$		−	2.38272e24i		−	0.963264i
$276$	−3.20061e22	−	1.09141e23i	−0.0124779	−	0.0425499i
$277$	−3.69477e24			−1.38928			−0.694641	−	0.719357i	$-0.744437\pi$
$277$	−3.69477e24			−1.38928			−0.694641	+	0.719357i	$0.744437\pi$
$278$			1.01866e24i			0.369470i
$279$	−1.75502e24	+	1.12618e24i	−0.614100	+	0.394063i
$280$	4.11385e24			1.38889
$281$			3.90206e23i			0.127125i	0.997978	+	0.0635624i	$0.0202462\pi$
$281$			3.90206e23i			0.127125i	−0.997978	+	0.0635624i	$0.979754\pi$
$282$	−5.07464e24	+	1.48816e24i	−1.59556	+	0.467905i
$283$	−4.13515e24			−1.25495			−0.627476	−	0.778636i	$-0.715912\pi$
$283$	−4.13515e24			−1.25495			−0.627476	+	0.778636i	$0.715912\pi$
$284$		−	8.09806e22i		−	0.0237245i
$285$	−1.30982e24	−	4.46652e24i	−0.370479	−	1.26334i
$286$	1.09208e24			0.298260
$287$		−	1.51392e24i		−	0.399285i
$288$	4.62640e23	+	7.20970e23i	0.117847	+	0.183650i
$289$	3.73944e24			0.920086
$290$			8.99415e24i			2.13786i
$291$	2.99485e24	−	8.78250e23i	0.687773	−	0.201692i
$292$	1.25542e23			0.0278588
$293$		−	2.17376e24i		−	0.466160i	−0.972458	−	0.233080i	$-0.925120\pi$
$293$		−	2.17376e24i		−	0.466160i	0.972458	−	0.233080i	$-0.0748804\pi$
$294$	−5.28490e23	−	1.80216e24i	−0.109538	−	0.373526i
$295$	−1.74353e24			−0.349309
$296$		−	7.47414e24i		−	1.44759i
$297$	1.94680e24	+	1.69043e24i	0.364550	+	0.316543i
$298$	5.04873e24			0.914154
$299$			1.51246e24i			0.264832i
$300$	−1.23925e24	+	3.63414e23i	−0.209867	+	0.0615444i
$301$	3.11957e24			0.511011
$302$		−	5.75572e24i		−	0.912075i
$303$	3.59268e24	+	1.22511e25i	0.550797	+	1.87823i
$304$	−4.50439e24			−0.668190
$305$			6.47548e24i			0.929552i
$306$	−1.61597e24	+	1.03695e24i	−0.224501	+	0.144060i
$307$	−6.54963e24			−0.880710			−0.440355	−	0.897824i	$-0.645147\pi$
$307$	−6.54963e24			−0.880710			−0.440355	+	0.897824i	$0.645147\pi$
$308$			3.11639e23i			0.0405644i
$309$	1.18518e25	−	3.47557e24i	1.49347	−	0.437967i
$310$	−9.76644e24			−1.19157
$311$		−	2.06588e24i		−	0.244062i	−0.992526	−	0.122031i	$-0.961059\pi$
$311$		−	2.06588e24i		−	0.244062i	0.992526	−	0.122031i	$-0.0389408\pi$
$312$	−1.68607e24	−	5.74953e24i	−0.192899	−	0.657789i
$313$	−2.71448e24			−0.300776			−0.150388	−	0.988627i	$-0.548052\pi$
$313$	−2.71448e24			−0.300776			−0.150388	+	0.988627i	$0.548052\pi$
$314$		−	3.12998e24i		−	0.335927i
$315$	−6.89058e24	−	1.07382e25i	−0.716392	−	1.11641i
$316$	−7.15323e23			−0.0720496
$317$		−	6.59005e24i		−	0.643126i	−0.946888	−	0.321563i	$-0.895792\pi$
$317$		−	6.59005e24i		−	0.643126i	0.946888	−	0.321563i	$-0.104208\pi$
$318$	6.61931e23	−	1.94114e23i	0.0625952	−	0.0183563i
$319$	−6.89694e24			−0.632047
$320$			2.11274e25i			1.87649i
$321$	1.04391e24	+	3.55976e24i	0.0898697	+	0.306457i
$322$	3.50570e24			0.292560
$323$			2.65804e24i			0.215048i
$324$	5.82261e23	−	1.27035e24i	0.0456738	−	0.0996494i
$325$	1.71732e25			1.30622
$326$		−	1.34421e25i		−	0.991499i
$327$	1.10549e25	−	3.24189e24i	0.790819	−	0.231911i
$328$	7.86117e24			0.545442
$329$			2.00676e25i			1.35063i
$330$	3.39808e24	+	1.15875e25i	0.221868	+	0.756574i
$331$	−1.16645e25			−0.738903			−0.369452	−	0.929250i	$-0.620454\pi$
$331$	−1.16645e25			−0.738903			−0.369452	+	0.929250i	$0.620454\pi$
$332$		−	2.27280e24i		−	0.139695i
$333$	−1.95094e25	+	1.25190e25i	−1.16359	+	0.746667i
$334$	9.55087e24			0.552813
$335$		−	2.30176e25i		−	1.29304i
$336$	−1.18481e25	+	3.47451e24i	−0.646036	+	0.189453i
$337$	3.10853e25			1.64534			0.822671	−	0.568517i	$-0.192483\pi$
$337$	3.10853e25			1.64534			0.822671	+	0.568517i	$0.192483\pi$
$338$		−	1.04924e25i		−	0.539149i
$339$	−1.00055e25	−	3.41188e25i	−0.499160	−	1.70214i
$340$	1.10711e24			0.0536294
$341$		−	7.48915e24i		−	0.352280i
$342$	8.48630e24	+	1.32249e25i	0.387666	+	0.604131i
$343$	−2.44024e25			−1.08266
$344$			1.61987e25i			0.698065i
$345$	−1.60479e25	+	4.70610e24i	−0.671780	+	0.197002i
$346$	−1.34334e25			−0.546294
$347$			4.08646e25i			1.61455i	0.590173	+	0.807277i	$0.299060\pi$
$347$			4.08646e25i			1.61455i	−0.590173	+	0.807277i	$0.700940\pi$
$348$	1.05193e24	+	3.58708e24i	0.0403824	+	0.137705i
$349$	4.66764e24			0.174118			0.0870590	−	0.996203i	$-0.472253\pi$
$349$	4.66764e24			0.174118			0.0870590	+	0.996203i	$0.472253\pi$
$350$		−	3.98054e25i		−	1.44299i
$351$	−1.21836e25	+	1.40314e25i	−0.429244	+	0.494344i
$352$	−3.07658e24			−0.105352
$353$		−	3.01314e25i		−	1.00293i	−0.865177	−	0.501466i	$-0.832794\pi$
$353$		−	3.01314e25i		−	1.00293i	0.865177	−	0.501466i	$-0.167206\pi$
$354$	5.64814e24	−	1.65634e24i	0.182757	−	0.0535940i
$355$	−1.19072e25			−0.374564
$356$			9.27506e23i			0.0283672i
$357$	2.05031e24	+	6.99158e24i	0.0609729	+	0.207918i
$358$	3.54961e25			1.02648
$359$			2.86341e25i			0.805265i	0.915362	+	0.402632i	$0.131905\pi$
$359$			2.86341e25i			0.805265i	−0.915362	+	0.402632i	$0.868095\pi$
$360$	5.57590e25	−	3.57801e25i	1.52507	−	0.978625i
$361$	−1.58369e25			−0.421306
$362$			5.83735e25i			1.51053i
$363$	2.92343e25	−	8.57306e24i	0.735913	−	0.215809i
$364$	−2.24611e24			−0.0550069
$365$		−	1.84595e25i		−	0.439836i
$366$	−6.15165e24	−	2.09772e25i	−0.142620	−	0.486337i
$367$	7.22452e25			1.62985			0.814926	−	0.579564i	$-0.196777\pi$
$367$	7.22452e25			1.62985			0.814926	+	0.579564i	$0.196777\pi$
$368$			1.61840e25i			0.355309i
$369$	−1.31672e25	−	2.05196e25i	−0.281340	−	0.438435i
$370$	−1.08567e26			−2.25778
$371$		−	2.61760e24i		−	0.0529863i
$372$	−3.89509e24	+	1.14225e24i	−0.0767517	+	0.0225077i
$373$	−1.46006e25			−0.280081			−0.140040	−	0.990146i	$-0.544723\pi$
$373$	−1.46006e25			−0.280081			−0.140040	+	0.990146i	$0.544723\pi$
$374$		−	6.89578e24i		−	0.128786i
$375$	2.66529e25	+	9.08869e25i	0.484654	+	1.65268i
$376$	−1.04203e26			−1.84502
$377$		−	4.97090e25i		−	0.857080i
$378$	3.25231e25	+	2.82401e25i	0.546102	+	0.474186i
$379$	3.01611e25			0.493236			0.246618	−	0.969113i	$-0.420681\pi$
$379$	3.01611e25			0.493236			0.246618	+	0.969113i	$0.420681\pi$
$380$		−	9.06050e24i		−	0.144317i
$381$	−6.79440e25	+	1.99248e25i	−1.05415	+	0.309132i
$382$	3.17226e25			0.479442
$383$		−	1.21509e26i		−	1.78904i	−0.447028	−	0.894520i	$-0.647518\pi$
$383$		−	1.21509e26i		−	1.78904i	0.447028	−	0.894520i	$-0.352482\pi$
$384$	−1.57902e25	−	5.38448e25i	−0.226503	−	0.772380i
$385$	4.58227e25			0.640433
$386$			1.67787e25i			0.228499i
$387$	4.22826e25	−	2.71324e25i	0.561116	−	0.360063i
$388$	6.07517e24			0.0785672
$389$			1.22813e26i			1.54791i	0.633238	+	0.773957i	$0.281725\pi$
$389$			1.22813e26i			1.54791i	−0.633238	+	0.773957i	$0.718275\pi$
$390$	−8.35159e25	+	2.44913e25i	−1.02594	+	0.300861i
$391$	9.55015e24			0.114352
$392$		−	3.70057e25i		−	0.431925i
$393$	−9.79184e24	−	3.33903e25i	−0.111414	−	0.379923i
$394$	1.16427e26			1.29149
$395$			1.05179e26i			1.13752i
$396$	2.71048e24	+	4.22396e24i	0.0285821	+	0.0445418i
$397$	−6.88928e25			−0.708384			−0.354192	−	0.935173i	$-0.615244\pi$
$397$	−6.88928e25			−0.708384			−0.354192	+	0.935173i	$0.615244\pi$
$398$		−	1.92395e25i		−	0.192914i
$399$	5.72183e25	−	1.67795e25i	0.559508	−	0.164078i
$400$	1.83761e26			1.75248
$401$			6.26223e25i			0.582486i	0.956649	+	0.291243i	$0.0940687\pi$
$401$			6.26223e25i			0.582486i	−0.956649	+	0.291243i	$0.905931\pi$
$402$	2.18666e25	+	7.45654e25i	0.198390	+	0.676514i
$403$	5.39772e25			0.477706
$404$			2.48518e25i			0.214558i
$405$	−1.86790e26	−	8.56142e25i	−1.57327	−	0.721100i
$406$	−1.15220e26			−0.946817
$407$		−	8.32519e25i		−	0.667499i
$408$	−3.63045e25	+	1.06464e25i	−0.284026	+	0.0832918i
$409$	2.40850e25			0.183871			0.0919355	−	0.995765i	$-0.470695\pi$
$409$	2.40850e25			0.183871			0.0919355	+	0.995765i	$0.470695\pi$
$410$		−	1.14189e26i		−	0.850717i
$411$	−1.07493e25	−	3.66552e25i	−0.0781557	−	0.266512i
$412$	2.40418e25			0.170606
$413$		−	2.23355e25i		−	0.154702i
$414$	4.75162e25	−	3.04907e25i	0.321246	−	0.206141i
$415$	−3.34187e26			−2.20551
$416$		−	2.21741e25i		−	0.142861i
$417$	5.97362e25	−	1.75178e25i	0.375731	−	0.110184i
$418$	−5.64343e25			−0.346562
$419$			1.02283e26i			0.613288i	0.951824	+	0.306644i	$0.0992061\pi$
$419$			1.02283e26i			0.613288i	−0.951824	+	0.306644i	$0.900794\pi$
$420$	−6.98891e24	−	2.38323e25i	−0.0409182	−	0.139532i
$421$	1.06952e26			0.611459			0.305729	−	0.952118i	$-0.401100\pi$
$421$	1.06952e26			0.611459			0.305729	+	0.952118i	$0.401100\pi$
$422$			1.88427e26i			1.05201i
$423$	1.74537e26	+	2.71996e26i	0.951667	+	1.48306i
$424$	1.35921e25			0.0723818
$425$		−	1.08437e26i		−	0.564013i
$426$	3.85732e25	−	1.13117e25i	0.195970	−	0.0574689i
$427$	−8.29542e25			−0.411680
$428$			7.22111e24i			0.0350079i
$429$	−1.87806e25	−	6.40421e25i	−0.0889479	−	0.303314i
$430$	2.35297e26			1.08876
$431$		−	2.56939e26i		−	1.16160i	−0.814045	−	0.580802i	$-0.802739\pi$
$431$		−	2.56939e26i		−	1.16160i	0.814045	−	0.580802i	$-0.197261\pi$
$432$	−1.30370e26	+	1.50142e26i	−0.575891	+	0.663232i
$433$	−7.83727e25			−0.338287			−0.169144	−	0.985591i	$-0.554100\pi$
$433$	−7.83727e25			−0.338287			−0.169144	+	0.985591i	$0.554100\pi$
$434$		−	1.25113e26i		−	0.527722i
$435$	5.27436e26	−	1.54673e26i	2.17409	−	0.637560i
$436$	2.24253e25			0.0903386
$437$		−	7.81574e25i		−	0.307720i
$438$	1.75363e25	+	5.97992e25i	0.0674835	+	0.230120i
$439$	−3.02722e26			−1.13867			−0.569335	−	0.822105i	$-0.692799\pi$
$439$	−3.02722e26			−1.13867			−0.569335	+	0.822105i	$0.692799\pi$
$440$			2.37939e26i			0.874861i
$441$	−9.65942e25	+	6.19836e25i	−0.347188	+	0.222788i
$442$	4.97006e25			0.174638
$443$			3.67155e26i			1.26128i	0.776075	+	0.630640i	$0.217208\pi$
$443$			3.67155e26i			1.26128i	−0.776075	+	0.630640i	$0.782792\pi$
$444$	−4.32992e25	+	1.26976e25i	−0.145429	+	0.0426475i
$445$	1.36378e26			0.447863
$446$		−	1.62295e26i		−	0.521141i
$447$	−8.68231e25	−	2.96068e26i	−0.272622	−	0.929644i
$448$	−2.70653e26			−0.831061
$449$			3.24768e26i			0.975237i	0.873057	+	0.487619i	$0.162134\pi$
$449$			3.24768e26i			0.975237i	−0.873057	+	0.487619i	$0.837866\pi$
$450$	−3.46207e26	−	5.39523e26i	−1.01674	−	1.58447i
$451$	8.75628e25			0.251510
$452$		−	6.92113e25i		−	0.194443i
$453$	−3.37528e26	+	9.89813e25i	−0.927529	+	0.272001i
$454$	−2.83649e26			−0.762470
$455$			3.30263e26i			0.868451i
$456$	8.71292e25	+	2.97112e26i	0.224138	+	0.764314i
$457$	4.63144e26			1.16561			0.582806	−	0.812611i	$-0.301955\pi$
$457$	4.63144e26			1.16561			0.582806	+	0.812611i	$0.301955\pi$
$458$		−	4.38519e26i		−	1.07978i
$459$	8.85989e25	+	7.69313e25i	0.213453	+	0.185343i
$460$	−3.25538e25			−0.0767402
$461$		−	4.10375e26i		−	0.946610i	−0.880899	−	0.473305i	$-0.843061\pi$
$461$		−	4.10375e26i		−	0.946610i	0.880899	−	0.473305i	$-0.156939\pi$
$462$	−1.48442e26	+	4.35312e25i	−0.335071	+	0.0982609i
$463$	3.33389e26			0.736447			0.368223	−	0.929737i	$-0.379966\pi$
$463$	3.33389e26			0.736447			0.368223	+	0.929737i	$0.379966\pi$
$464$		−	5.31909e26i		−	1.14989i
$465$	1.67954e26	+	5.72725e26i	0.355353	+	1.21176i
$466$	7.81315e26			1.61796
$467$		−	4.82357e26i		−	0.977687i	−0.872372	−	0.488843i	$-0.837419\pi$
$467$		−	4.82357e26i		−	0.977687i	0.872372	−	0.488843i	$-0.162581\pi$
$468$	−3.04437e25	+	1.95355e25i	−0.0604004	+	0.0387584i
$469$	2.94868e26			0.572663
$470$			1.51362e27i			2.87765i
$471$	−1.83549e26	+	5.38263e25i	−0.341619	+	0.100181i
$472$	1.15979e26			0.211330
$473$			1.80432e26i			0.321886i
$474$	−9.99195e25	−	3.40727e26i	−0.174529	−	0.595146i
$475$	−8.87439e26			−1.51776
$476$			1.41827e25i			0.0237514i
$477$	−2.27665e25	−	3.54789e25i	−0.0373346	−	0.0581816i
$478$	−4.11555e26			−0.660920
$479$		−	6.98757e26i		−	1.09893i	−0.835516	−	0.549466i	$-0.814831\pi$
$479$		−	6.98757e26i		−	1.09893i	0.835516	−	0.549466i	$-0.185169\pi$
$480$	2.35278e26	−	6.89962e25i	0.362384	−	0.106271i
$481$	6.00030e26			0.905153
$482$			6.13362e26i			0.906247i
$483$	−6.02875e25	−	2.05582e26i	−0.0872481	−	0.297518i
$484$	5.93029e25			0.0840664
$485$		−	8.93279e26i		−	1.24042i
$486$	6.86436e26	+	9.98975e25i	0.933764	+	0.135891i
$487$	−1.03466e27			−1.37882			−0.689412	−	0.724369i	$-0.742131\pi$
$487$	−1.03466e27			−1.37882			−0.689412	+	0.724369i	$0.742131\pi$
$488$		−	4.30748e26i		−	0.562374i
$489$	−7.88276e26	+	2.31165e26i	−1.00830	+	0.295688i
$490$	−5.37534e26			−0.673666
$491$			1.00139e27i			1.22967i	0.788655	+	0.614836i	$0.210778\pi$
$491$			1.00139e27i			1.22967i	−0.788655	+	0.614836i	$0.789222\pi$
$492$	−1.33551e25	−	4.55413e25i	−0.0160693	−	0.0547967i
$493$	−3.13879e26			−0.370078
$494$		−	4.06745e26i		−	0.469951i
$495$	6.21081e26	−	3.98542e26i	0.703228	−	0.451255i
$496$	5.77581e26			0.640909
$497$		−	1.52537e26i		−	0.165887i
$498$	1.08259e27	−	3.17475e26i	1.15391	−	0.338388i
$499$	−1.43215e27			−1.49618			−0.748091	−	0.663596i	$-0.769029\pi$
$499$	−1.43215e27			−1.49618			−0.748091	+	0.663596i	$0.769029\pi$
$500$			1.84368e26i			0.188793i
$501$	−1.64247e26	−	5.60084e26i	−0.164861	−	0.562181i
$502$	−1.34554e27			−1.32392
$503$			1.58001e27i			1.52398i	0.647589	+	0.761990i	$0.275777\pi$
$503$			1.58001e27i			1.52398i	−0.647589	+	0.761990i	$0.724223\pi$
$504$	4.58361e26	+	7.14301e26i	0.433413	+	0.675423i
$505$	3.65415e27			3.38745
$506$			2.02765e26i			0.184284i
$507$	−6.15298e26	+	1.80438e26i	−0.548284	+	0.160786i
$508$	−1.37827e26			−0.120420
$509$			1.56711e27i			1.34252i	0.741220	+	0.671262i	$0.234248\pi$
$509$			1.56711e27i			1.34252i	−0.741220	+	0.671262i	$0.765752\pi$
$510$	1.54647e26	+	5.27348e26i	0.129909	+	0.442991i
$511$	2.36475e26			0.194794
$512$		−	1.37578e27i		−	1.11135i
$513$	6.29597e26	−	7.25084e26i	0.498757	−	0.574400i
$514$	9.18943e26			0.713933
$515$		−	3.53504e27i		−	2.69353i
$516$	9.38422e25	−	2.75196e25i	0.0701296	−	0.0205658i
$517$	−1.16068e27			−0.850762
$518$		−	1.39080e27i		−	0.999924i
$519$	2.31015e26	+	7.87766e26i	0.162917	+	0.555551i
$520$	−1.71492e27			−1.18635
$521$			2.40254e27i			1.63040i	0.579180	+	0.815200i	$0.303373\pi$
$521$			2.40254e27i			1.63040i	−0.579180	+	0.815200i	$0.696627\pi$
$522$	−1.56169e27	+	1.00212e27i	−1.03965	+	0.667136i
$523$	−9.27732e25			−0.0605907			−0.0302953	−	0.999541i	$-0.509645\pi$
$523$	−9.27732e25			−0.0605907			−0.0302953	+	0.999541i	$0.509645\pi$
$524$		−	6.77336e25i		−	0.0434002i
$525$	−2.33428e27	+	6.84535e26i	−1.46744	+	0.430331i
$526$	1.08439e27			0.668851
$527$		−	3.40831e26i		−	0.206268i
$528$	−2.00961e26	−	6.85280e26i	−0.119336	−	0.406938i
$529$	1.43534e27			0.836370
$530$		−	1.97435e26i		−	0.112893i
$531$	−1.94262e26	−	3.02735e26i	−0.109004	−	0.169870i
$532$	1.16070e26			0.0639149
$533$			6.31100e26i			0.341056i
$534$	−4.41796e26	+	1.29558e26i	−0.234320	+	0.0687151i
$535$	1.06177e27			0.552706
$536$			1.53113e27i			0.782284i
$537$	−6.10427e26	−	2.08157e27i	−0.306119	−	1.04387i
$538$	−1.88187e27			−0.926335
$539$		−	4.12194e26i		−	0.199166i
$540$	−3.02009e26	−	2.62237e26i	−0.143246	−	0.124382i
$541$	1.21454e27			0.565508			0.282754	−	0.959192i	$-0.408752\pi$
$541$	1.21454e27			0.565508			0.282754	+	0.959192i	$0.408752\pi$
$542$			3.34947e27i			1.53103i
$543$	3.42315e27	−	1.00385e27i	1.53613	−	0.450475i
$544$	−1.40015e26			−0.0616858
$545$		−	3.29736e27i		−	1.42627i
$546$	−3.13747e26	−	1.06988e27i	−0.133245	−	0.454369i
$547$	1.64525e27			0.686056			0.343028	−	0.939325i	$-0.388547\pi$
$547$	1.64525e27			0.686056			0.343028	+	0.939325i	$0.388547\pi$
$548$		−	7.43565e25i		−	0.0304448i
$549$	−1.12436e27	+	7.21492e26i	−0.452045	+	0.290073i
$550$	2.30229e27			0.908937
$551$			2.56875e27i			0.995879i
$552$	1.06750e27	−	3.13049e26i	0.406423	−	0.119185i
$553$	−1.34740e27			−0.503786
$554$		−	3.57006e27i		−	1.31093i
$555$	1.86703e27	+	6.36661e27i	0.673320	+	2.29603i
$556$	1.21177e26			0.0429213
$557$			4.13140e26i			0.143729i	0.997414	+	0.0718646i	$0.0228950\pi$
$557$			4.13140e26i			0.143729i	−0.997414	+	0.0718646i	$0.977105\pi$
$558$	−1.08817e27	−	1.69578e27i	−0.371838	−	0.579465i
$559$	−1.30044e27			−0.436489
$560$			3.53396e27i			1.16515i
$561$	−4.04383e26	+	1.18587e26i	−0.130968	+	0.0384068i
$562$	−3.77035e26			−0.119955
$563$		−	5.17992e26i		−	0.161897i	−0.996718	−	0.0809486i	$-0.974205\pi$
$563$		−	5.17992e26i		−	0.161897i	0.996718	−	0.0809486i	$-0.0257950\pi$
$564$	1.77028e26	+	6.03669e26i	0.0543564	+	0.185356i
$565$	−1.01767e28			−3.06988
$566$		−	3.99558e27i		−	1.18417i
$567$	1.09676e27	−	2.39287e27i	0.319361	−	0.696769i
$568$	7.92065e26			0.226609
$569$		−	3.74368e27i		−	1.05239i	−0.850365	−	0.526194i	$-0.823619\pi$
$569$		−	3.74368e27i		−	1.05239i	0.850365	−	0.526194i	$-0.176381\pi$
$570$	4.31576e27	−	1.26561e27i	1.19209	−	0.349584i
$571$	−2.71153e27			−0.735957			−0.367979	−	0.929834i	$-0.619950\pi$
$571$	−2.71153e27			−0.735957			−0.367979	+	0.929834i	$0.619950\pi$
$572$		−	1.29912e26i		−	0.0346488i
$573$	−5.45535e26	−	1.86028e27i	−0.142980	−	0.487566i
$574$	1.46282e27			0.376765
$575$			3.18851e27i			0.807066i
$576$	−3.66843e27	+	2.35400e27i	−0.912547	+	0.585573i
$577$	3.76717e27			0.920994			0.460497	−	0.887661i	$-0.347671\pi$
$577$	3.76717e27			0.920994			0.460497	+	0.887661i	$0.347671\pi$
$578$			3.61322e27i			0.868194i
$579$	9.83937e26	−	2.88543e26i	0.232371	−	0.0681436i
$580$	1.06993e27			0.248355
$581$		−	4.28110e27i		−	0.976774i
$582$	8.48607e26	+	2.89376e27i	0.190317	+	0.648983i
$583$	1.51398e26			0.0333761
$584$			1.22792e27i			0.266098i
$585$	2.87245e27	+	4.47638e27i	0.611919	+	0.953604i
$586$	2.10039e27			0.439869
$587$		−	1.33917e27i		−	0.275711i	−0.990452	−	0.137855i	$-0.955979\pi$
$587$		−	1.33917e27i		−	0.275711i	0.990452	−	0.137855i	$-0.0440209\pi$
$588$	−2.14381e26	+	6.28681e25i	−0.0433924	+	0.0127250i
$589$	−2.78932e27			−0.555067
$590$		−	1.68468e27i		−	0.329608i
$591$	−2.00219e27	−	6.82751e27i	−0.385151	−	1.31337i
$592$	6.42060e27			1.21439
$593$			9.08606e27i			1.68977i	0.534945	+	0.844887i	$0.320332\pi$
$593$			9.08606e27i			1.68977i	−0.534945	+	0.844887i	$0.679668\pi$
$594$	−1.63337e27	+	1.88109e27i	−0.298690	+	0.343990i
$595$	2.08539e27			0.374988
$596$		−	6.00586e26i		−	0.106197i
$597$	−1.12825e27	+	3.30862e26i	−0.196182	+	0.0575312i
$598$	−1.46141e27			−0.249896
$599$			4.82175e27i			0.810843i	0.914130	+	0.405422i	$0.132875\pi$
$599$			4.82175e27i			0.810843i	−0.914130	+	0.405422i	$0.867125\pi$
$600$	−3.55452e27	−	1.21210e28i	−0.587853	−	2.00459i
$601$	4.89202e27			0.795690			0.397845	−	0.917453i	$-0.369758\pi$
$601$	4.89202e27			0.795690			0.397845	+	0.917453i	$0.369758\pi$
$602$			3.01428e27i			0.482190i
$603$	3.99663e27	−	2.56460e27i	0.628813	−	0.403504i
$604$	−6.84689e26			−0.105956
$605$		−	8.71976e27i		−	1.32724i
$606$	−1.18376e28	+	3.47141e27i	−1.77230	+	0.519732i
$607$	6.52583e27			0.961056			0.480528	−	0.876979i	$-0.340445\pi$
$607$	6.52583e27			0.961056			0.480528	+	0.876979i	$0.340445\pi$
$608$			1.14587e27i			0.165996i
$609$	1.98144e27	+	6.75673e27i	0.282362	+	0.962861i
$610$	−6.25691e27			−0.877125
$611$		−	8.36550e27i		−	1.15366i
$612$	1.23354e26	+	1.92232e26i	0.0167355	+	0.0260802i
$613$	−1.12770e28			−1.50518			−0.752591	−	0.658488i	$-0.771196\pi$
$613$	−1.12770e28			−1.50518			−0.752591	+	0.658488i	$0.771196\pi$
$614$		−	6.32856e27i		−	0.831038i
$615$	−6.69628e27	+	1.96371e27i	−0.865132	+	0.253703i
$616$	−3.04812e27			−0.387459
$617$			6.12604e27i			0.766175i	0.923712	+	0.383088i	$0.125139\pi$
$617$			6.12604e27i			0.766175i	−0.923712	+	0.383088i	$0.874861\pi$
$618$	3.35826e27	+	1.14517e28i	0.413266	+	1.40924i
$619$	5.94136e27			0.719415			0.359707	−	0.933065i	$-0.382876\pi$
$619$	5.94136e27			0.719415			0.359707	+	0.933065i	$0.382876\pi$
$620$			1.16180e27i			0.138424i
$621$	−2.60518e27	−	2.26210e27i	−0.305437	−	0.265214i
$622$	1.99615e27			0.230297
$623$			1.74707e27i			0.198349i
$624$	4.93908e27	−	1.44840e27i	0.551824	−	0.161824i
$625$	8.96312e27			0.985505
$626$		−	2.62286e27i		−	0.283812i
$627$	9.70502e26	+	3.30943e27i	0.103353	+	0.352434i
$628$	−3.72336e26			−0.0390246
$629$		−	3.78879e27i		−	0.390836i
$630$	1.03757e28	−	6.65801e27i	1.05345	−	0.675988i
$631$	−5.00895e27			−0.500556			−0.250278	−	0.968174i	$-0.580522\pi$
$631$	−5.00895e27			−0.500556			−0.250278	+	0.968174i	$0.580522\pi$
$632$		−	6.99652e27i		−	0.688195i
$633$	1.10498e28	−	3.24039e27i	1.06984	−	0.313733i
$634$	6.36761e27			0.606854
$635$			2.02658e28i			1.90119i
$636$	−2.30914e25	−	7.87419e25i	−0.00213245	−	0.00727168i
$637$	2.97085e27			0.270076
$638$		−	6.66415e27i		−	0.596400i
$639$	−1.32669e27	−	2.06749e27i	−0.116885	−	0.182152i
$640$	−1.60604e28			−1.39301
$641$			1.11219e28i			0.949726i	0.880060	+	0.474863i	$0.157502\pi$
$641$			1.11219e28i			0.949726i	−0.880060	+	0.474863i	$0.842498\pi$
$642$	−3.43960e27	+	1.00868e27i	−0.289173	+	0.0848011i
$643$	−7.44041e27			−0.615867			−0.307934	−	0.951408i	$-0.599637\pi$
$643$	−7.44041e27			−0.615867			−0.307934	+	0.951408i	$0.599637\pi$
$644$		−	4.17030e26i		−	0.0339867i
$645$	−4.04641e27	−	1.37983e28i	−0.324693	−	1.10721i
$646$	−2.56832e27			−0.202920
$647$		−	1.41922e28i		−	1.10410i	−0.833812	−	0.552048i	$-0.813846\pi$
$647$		−	1.41922e28i		−	1.10410i	0.833812	−	0.552048i	$-0.186154\pi$
$648$	1.24252e28	+	5.69505e27i	0.951819	+	0.436262i
$649$	1.29185e27			0.0974466
$650$			1.65935e28i			1.23255i
$651$	−7.33690e27	+	2.15157e27i	−0.536664	+	0.157379i
$652$	−1.59905e27			−0.115182
$653$		−	3.43236e27i		−	0.243479i	−0.992562	−	0.121739i	$-0.961153\pi$
$653$		−	3.43236e27i		−	0.243479i	0.992562	−	0.121739i	$-0.0388472\pi$
$654$	3.13247e27	+	1.06818e28i	0.218831	+	0.746218i
$655$	−9.95939e27			−0.685204
$656$			6.75306e27i			0.457575i
$657$	3.20518e27	−	2.05674e27i	0.213894	−	0.137254i
$658$	−1.93902e28			−1.27445
$659$		−	6.09589e27i		−	0.394623i	−0.980341	−	0.197312i	$-0.936779\pi$
$659$		−	6.09589e27i		−	0.394623i	0.980341	−	0.197312i	$-0.0632211\pi$
$660$	1.37843e27	−	4.04229e26i	0.0878911	−	0.0257744i
$661$	−6.58053e27			−0.413282			−0.206641	−	0.978417i	$-0.566253\pi$
$661$	−6.58053e27			−0.413282			−0.206641	+	0.978417i	$0.566253\pi$
$662$		−	1.12708e28i		−	0.697230i
$663$	−8.54703e26	−	2.91455e27i	−0.0520811	−	0.177597i
$664$	2.22301e28			1.33432
$665$		−	1.70666e28i		−	1.00909i
$666$	−1.20964e28	−	1.88509e28i	−0.704556	−	1.09797i
$667$	9.22936e27			0.529558
$668$		−	1.13615e27i		−	0.0642202i
$669$	−9.51731e27	+	2.79099e27i	−0.529972	+	0.155416i
$670$	2.22407e28			1.22012
$671$		−	4.79796e27i		−	0.259317i
$672$	8.83876e26	+	3.01403e27i	0.0470651	+	0.160493i
$673$	1.83305e28			0.961665			0.480832	−	0.876813i	$-0.340335\pi$
$673$	1.83305e28			0.961665			0.480832	+	0.876813i	$0.340335\pi$
$674$			3.00361e28i			1.55255i
$675$	−2.56850e28	+	2.95805e28i	−1.30810	+	1.50650i
$676$	−1.24816e27			−0.0626328
$677$			2.23933e28i			1.10721i	0.832778	+	0.553606i	$0.186749\pi$
$677$			2.23933e28i			1.10721i	−0.832778	+	0.553606i	$0.813251\pi$
$678$	3.29672e28	−	9.66774e27i	1.60614	−	0.471008i
$679$	1.14434e28			0.549358
$680$			1.08286e28i			0.512252i
$681$	4.87792e27	+	1.66338e28i	0.227386	+	0.775390i
$682$	7.23636e27			0.332412
$683$		−	3.72332e28i		−	1.68548i	−0.538320	−	0.842740i	$-0.680941\pi$
$683$		−	3.72332e28i		−	1.68548i	0.538320	−	0.842740i	$-0.319059\pi$
$684$	1.57321e27	−	1.00951e27i	0.0701818	−	0.0450351i
$685$	−1.09332e28			−0.480664
$686$		−	2.35787e28i		−	1.02160i
$687$	−2.57157e28	+	7.54122e27i	−1.09807	+	0.322014i
$688$	−1.39153e28			−0.585611
$689$			1.09119e27i			0.0452592i
$690$	−4.54726e27	−	1.55062e28i	−0.185891	−	0.633892i
$691$	4.07748e28			1.64290			0.821450	−	0.570281i	$-0.193166\pi$
$691$	4.07748e28			1.64290			0.821450	+	0.570281i	$0.193166\pi$
$692$			1.59801e27i			0.0634629i
$693$	5.10553e27	+	7.95636e27i	0.199852	+	0.311445i
$694$	−3.94853e28			−1.52349
$695$		−	1.78176e28i		−	0.677644i
$696$	−3.50850e28	+	1.02888e28i	−1.31531	+	0.385720i
$697$	3.98498e27			0.147265
$698$			4.51010e27i			0.164298i
$699$	−1.34363e28	−	4.58180e28i	−0.482512	−	1.64537i
$700$	−4.73517e27			−0.167631
$701$			4.74803e28i			1.65704i	0.559959	+	0.828521i	$0.310817\pi$
$701$			4.74803e28i			1.65704i	−0.559959	+	0.828521i	$0.689183\pi$
$702$	−1.35578e28	−	1.17724e28i	−0.466463	−	0.405035i
$703$	−3.10071e28			−1.05174
$704$		−	1.56542e28i		−	0.523485i
$705$	8.87620e28	−	2.60298e28i	2.92641	−	0.858182i
$706$	2.91143e28			0.946367
$707$			4.68115e28i			1.50023i
$708$	−1.97035e26	−	6.71891e26i	−0.00622601	−	0.0212308i
$709$	−2.11316e28			−0.658371			−0.329186	−	0.944265i	$-0.606774\pi$
$709$	−2.11316e28			−0.658371			−0.329186	+	0.944265i	$0.606774\pi$
$710$		−	1.15053e28i		−	0.353439i
$711$	−1.82627e28	+	1.17190e28i	−0.553182	+	0.354972i
$712$	−9.07187e27			−0.270955
$713$			1.00218e28i			0.295156i
$714$	−6.75559e27	+	1.98110e27i	−0.196192	+	0.0575340i
$715$	−1.91019e28			−0.547037
$716$		−	4.22254e27i		−	0.119246i
$717$	7.07753e27	+	2.41345e28i	0.197102	+	0.672120i
$718$	−2.76676e28			−0.759848
$719$			1.61710e28i			0.437974i	0.975728	+	0.218987i	$0.0702752\pi$
$719$			1.61710e28i			0.437974i	−0.975728	+	0.218987i	$0.929725\pi$
$720$	3.07365e28	+	4.78993e28i	0.820975	+	1.27939i
$721$	4.52857e28			1.19291
$722$		−	1.53023e28i		−	0.397544i
$723$	3.59689e28	−	1.05480e28i	0.921603	−	0.270263i
$724$	6.94399e27			0.175478
$725$		−	1.04795e29i		−	2.61192i
$726$	8.28370e27	+	2.82476e28i	0.203638	+	0.694408i
$727$	3.27552e28			0.794211			0.397105	−	0.917773i	$-0.370015\pi$
$727$	3.27552e28			0.794211			0.397105	+	0.917773i	$0.370015\pi$
$728$		−	2.19690e28i		−	0.525408i
$729$	−5.94645e27	−	4.19720e28i	−0.140276	−	0.990112i
$730$	1.78364e28			0.415029
$731$			8.21144e27i			0.188471i
$732$	−2.49541e27	+	7.31787e26i	−0.0564977	+	0.0165682i
$733$	−6.32502e28			−1.41261			−0.706305	−	0.707908i	$-0.749639\pi$
$733$	−6.32502e28			−1.41261			−0.706305	+	0.707908i	$0.749639\pi$
$734$			6.98067e28i			1.53793i
$735$	9.24398e27	+	3.15221e28i	0.200903	+	0.685081i
$736$	4.11702e27			0.0882683
$737$			1.70547e28i			0.360720i
$738$	1.98270e28	−	1.27228e28i	0.413708	−	0.265473i
$739$	−2.74643e28			−0.565358			−0.282679	−	0.959215i	$-0.591223\pi$
$739$	−2.74643e28			−0.565358			−0.282679	+	0.959215i	$0.591223\pi$
$740$			1.29149e28i			0.262286i
$741$	−2.38524e28	+	6.99480e27i	−0.477914	+	0.140150i
$742$	2.52924e27			0.0499979
$743$		−	1.56845e28i		−	0.305902i	−0.988234	−	0.152951i	$-0.951122\pi$
$743$		−	1.56845e28i		−	0.305902i	0.988234	−	0.152951i	$-0.0488777\pi$
$744$	−1.11723e28	−	3.80976e28i	−0.214987	−	0.733108i
$745$	−8.83088e28			−1.67665
$746$		−	1.41078e28i		−	0.264284i
$747$	−3.72348e28	−	5.80260e28i	−0.688245	−	1.07255i
$748$	−8.20308e26			−0.0149610
$749$			1.36019e28i			0.244782i
$750$	−8.78192e28	+	2.57533e28i	−1.55947	+	0.457320i
$751$	8.46072e28			1.48254			0.741272	−	0.671204i	$-0.234223\pi$
$751$	8.46072e28			1.48254			0.741272	+	0.671204i	$0.234223\pi$
$752$		−	8.95147e28i		−	1.54780i
$753$	2.31393e28	+	7.89055e28i	0.394822	+	1.34635i
$754$	4.80312e28			0.808741
$755$			1.00675e29i			1.67283i
$756$	3.35939e27	−	3.86888e27i	0.0550861	−	0.0634407i
$757$	−7.71463e28			−1.24841			−0.624204	−	0.781262i	$-0.714577\pi$
$757$	−7.71463e28			−1.24841			−0.624204	+	0.781262i	$0.714577\pi$
$758$			2.91430e28i			0.465418i
$759$	1.18906e28	−	3.48695e27i	0.187406	−	0.0549576i
$760$	8.86201e28			1.37847
$761$		−	6.31745e28i		−	0.969829i	−0.874562	−	0.484914i	$-0.838851\pi$
$761$		−	6.31745e28i		−	0.969829i	0.874562	−	0.484914i	$-0.161149\pi$
$762$	−1.92523e28	−	6.56506e28i	−0.291697	−	0.994693i
$763$	4.22409e28			0.631666
$764$		−	3.77366e27i		−	0.0556967i
$765$	2.82653e28	−	1.81376e28i	0.411756	−	0.264220i
$766$	1.17408e29			1.68814
$767$			9.31091e27i			0.132141i
$768$	−2.22463e28	+	6.52380e27i	−0.311634	+	0.0913879i
$769$	−6.05612e28			−0.837396			−0.418698	−	0.908126i	$-0.637513\pi$
$769$	−6.05612e28			−0.837396			−0.418698	+	0.908126i	$0.637513\pi$
$770$			4.42761e28i			0.604313i
$771$	−1.58031e28	−	5.38888e28i	−0.212911	−	0.726030i
$772$	1.99595e27			0.0265447
$773$			7.26434e25i			0.000953677i	1.00000		0.000476838i	$0.000151782\pi$
$773$			7.26434e25i			0.000953677i	−1.00000		0.000476838i	$0.999848\pi$
$774$	2.62166e28	+	4.08555e28i	0.339756	+	0.529469i
$775$	1.13793e29			1.45579
$776$			5.94208e28i			0.750449i
$777$	−8.15595e28	+	2.39176e28i	−1.01687	+	0.298200i
$778$	−1.18667e29			−1.46061
$779$		−	3.26127e28i		−	0.396289i
$780$	2.91344e27	+	9.93488e27i	0.0349510	+	0.119184i
$781$	8.82254e27			0.104492
$782$			9.22781e27i			0.107902i
$783$	8.56228e28	+	7.43471e28i	0.988489	+	0.858315i
$784$	3.17894e28			0.362345
$785$			5.47474e28i			0.616122i
$786$	3.22633e28	−	9.46133e27i	0.358495	−	0.105130i
$787$	−7.78305e28			−0.853891			−0.426945	−	0.904277i	$-0.640410\pi$
$787$	−7.78305e28			−0.853891			−0.426945	+	0.904277i	$0.640410\pi$
$788$		−	1.38499e28i		−	0.150032i
$789$	−1.86483e28	−	6.35911e28i	−0.199466	−	0.680184i
$790$	−1.01629e29			−1.07337
$791$		−	1.30368e29i		−	1.35959i
$792$	−4.13142e28	+	2.65110e28i	−0.425449	+	0.273007i
$793$	3.45808e28			0.351644
$794$		−	6.65675e28i		−	0.668432i
$795$	−1.15780e28	+	3.39530e27i	−0.114806	+	0.0336672i
$796$	−2.28869e27			−0.0224107
$797$		−	1.10510e29i		−	1.06861i	−0.845292	−	0.534304i	$-0.820574\pi$
$797$		−	1.10510e29i		−	1.06861i	0.845292	−	0.534304i	$-0.179426\pi$
$798$	1.62131e28	+	5.52870e28i	0.154824	+	0.527952i
$799$	−5.28226e28			−0.498140
$800$		−	4.67468e28i		−	0.435363i
$801$	1.51951e28	+	2.36798e28i	0.139759	+	0.217798i
$802$	−6.05086e28			−0.549634
$803$			1.36774e28i			0.122701i
$804$	8.87014e27	−	2.60120e27i	0.0785905	−	0.0230470i
$805$	−6.13191e28			−0.536583
$806$			5.21554e28i			0.450763i
$807$	3.23626e28	+	1.10357e29i	0.276254	+	0.942031i
$808$	−2.43074e29			−2.04939
$809$			8.70530e28i			0.724934i	0.931997	+	0.362467i	$0.118065\pi$
$809$			8.70530e28i			0.724934i	−0.931997	+	0.362467i	$0.881935\pi$
$810$	8.27245e28	−	1.80485e29i	0.680431	−	1.48454i
$811$	2.28060e29			1.85285			0.926427	−	0.376475i	$-0.122864\pi$
$811$	2.28060e29			1.85285			0.926427	+	0.376475i	$0.122864\pi$
$812$			1.37063e28i			0.109992i
$813$	1.96420e29	−	5.76010e28i	1.55697	−	0.456588i
$814$	8.04419e28			0.629852
$815$			2.35120e29i			1.81850i
$816$	−9.14571e27	−	3.11870e28i	−0.0698741	−	0.238272i
$817$	6.72015e28			0.507176
$818$			2.32720e28i			0.173501i
$819$	−5.73446e28	+	3.67976e28i	−0.422332	+	0.271007i
$820$	−1.35837e28			−0.0988277
$821$			5.93047e28i			0.426243i	0.977026	+	0.213122i	$0.0683631\pi$
$821$			5.93047e28i			0.426243i	−0.977026	+	0.213122i	$0.931637\pi$
$822$	3.54180e28	−	1.03864e28i	0.251481	−	0.0737478i
$823$	−3.02866e28			−0.212448			−0.106224	−	0.994342i	$-0.533876\pi$
$823$	−3.02866e28			−0.212448			−0.106224	+	0.994342i	$0.533876\pi$
$824$			2.35151e29i			1.62957i
$825$	−3.95926e28	−	1.35011e29i	−0.271066	−	0.924338i
$826$	2.15816e28			0.145977
$827$		−	1.75378e29i		−	1.17198i	−0.810319	−	0.585989i	$-0.800706\pi$
$827$		−	1.75378e29i		−	1.17198i	0.810319	−	0.585989i	$-0.199294\pi$
$828$	−3.62711e27	−	5.65242e27i	−0.0239474	−	0.0373191i
$829$	1.46303e29			0.954352			0.477176	−	0.878808i	$-0.341660\pi$
$829$	1.46303e29			0.954352			0.477176	+	0.878808i	$0.341660\pi$
$830$		−	3.22907e29i		−	2.08112i
$831$	−2.09356e29	+	6.13945e28i	−1.33314	+	0.390948i
$832$	1.12826e29			0.709866
$833$		−	1.87589e28i		−	0.116616i
$834$	1.69266e28	+	5.77199e28i	0.103970	+	0.354540i
$835$	−1.67057e29			−1.01391
$836$			6.71331e27i			0.0402600i
$837$	−8.07309e28	+	9.29748e28i	−0.478394	+	0.550948i
$838$	−9.88309e28			−0.578699
$839$		−	2.87462e29i		−	1.66326i	−0.555328	−	0.831631i	$-0.687407\pi$
$839$		−	2.87462e29i		−	1.66326i	0.555328	−	0.831631i	$-0.312593\pi$
$840$	2.33102e29	−	6.83580e28i	1.33276	−	0.390838i
$841$	−1.26341e29			−0.713815
$842$			1.03342e29i			0.576973i
$843$	6.48388e27	+	2.21102e28i	0.0357733	+	0.121988i
$844$	2.24149e28			0.122212
$845$			1.83526e29i			0.988850i
$846$	−2.62815e29	+	1.68646e29i	−1.39942	+	0.897993i
$847$	1.11705e29			0.587810
$848$			1.16762e28i			0.0607216i
$849$	−2.34309e29	+	6.87121e28i	−1.20424	+	0.353147i
$850$	1.04777e29			0.532203
$851$			1.11406e29i			0.559260i
$852$	−1.34562e27	−	4.58859e27i	−0.00667615	−	0.0227658i
$853$	1.45397e29			0.712962			0.356481	−	0.934303i	$-0.383976\pi$
$853$	1.45397e29			0.712962			0.356481	+	0.934303i	$0.383976\pi$
$854$		−	8.01542e28i		−	0.388461i
$855$	−1.48436e29	−	2.31321e29i	−0.711016	−	1.10803i
$856$	−7.06291e28			−0.334384
$857$			9.04227e28i			0.423125i	0.977364	+	0.211563i	$0.0678553\pi$
$857$			9.04227e28i			0.423125i	−0.977364	+	0.211563i	$0.932145\pi$
$858$	6.18805e28	−	1.81467e28i	0.286207	−	0.0839313i
$859$	−1.64395e29			−0.751549			−0.375775	−	0.926711i	$-0.622623\pi$
$859$	−1.64395e29			−0.751549			−0.375775	+	0.926711i	$0.622623\pi$
$860$		−	2.79905e28i		−	0.126481i
$861$	−2.51561e28	−	8.57827e28i	−0.112360	−	0.383150i
$862$	2.48267e29			1.09609
$863$		−	2.46130e29i		−	1.07413i	−0.843541	−	0.537065i	$-0.819533\pi$
$863$		−	2.46130e29i		−	1.07413i	0.843541	−	0.537065i	$-0.180467\pi$
$864$	3.81945e28	+	3.31647e28i	0.164765	+	0.143067i
$865$	2.34968e29			1.00195
$866$		−	7.57274e28i		−	0.319208i
$867$	2.11887e29	−	6.21367e28i	0.882905	−	0.258915i
$868$	−1.48832e28			−0.0613054
$869$		−	7.79319e28i		−	0.317335i
$870$	1.49452e29	+	5.09634e29i	0.601602	+	2.05147i
$871$	−1.22920e29			−0.489150
$872$			2.19340e29i			0.862886i
$873$	1.55103e29	−	9.95283e28i	0.603223	−	0.387083i
$874$	7.55194e28			0.290365
$875$			3.47280e29i			1.32008i
$876$	7.11359e27	−	2.08609e27i	0.0267330	−	0.00783955i
$877$	2.08903e29			0.776157			0.388079	−	0.921626i	$-0.373139\pi$
$877$	2.08903e29			0.776157			0.388079	+	0.921626i	$0.373139\pi$
$878$		−	2.92504e29i		−	1.07445i
$879$	−3.61204e28	−	1.23171e29i	−0.131179	−	0.447322i
$880$	−2.04400e29			−0.733927
$881$		−	1.34640e29i		−	0.477985i	−0.971021	−	0.238992i	$-0.923183\pi$
$881$		−	1.34640e29i		−	0.477985i	0.971021	−	0.238992i	$-0.0768171\pi$
$882$	−5.98915e28	−	9.33338e28i	−0.210223	−	0.327607i
$883$	9.71686e28			0.337224			0.168612	−	0.985682i	$-0.446071\pi$
$883$	9.71686e28			0.337224			0.168612	+	0.985682i	$0.446071\pi$
$884$		−	5.91228e27i		−	0.0202877i
$885$	−9.87933e28	+	2.89715e28i	−0.335193	+	0.0982965i
$886$	−3.54762e29			−1.19014
$887$			4.51174e29i			1.49661i	0.663357	+	0.748303i	$0.269131\pi$
$887$			4.51174e29i			1.49661i	−0.663357	+	0.748303i	$0.730869\pi$
$888$	−1.24195e29	−	4.23506e29i	−0.407355	−	1.38909i
$889$	−2.59615e29			−0.841999
$890$			1.31775e29i			0.422604i
$891$	1.38400e29	+	6.34352e28i	0.438895	+	0.201165i
$892$	−1.93062e28			−0.0605409
$893$			4.32294e29i			1.34049i
$894$	2.86075e29	−	8.38926e28i	0.877213	−	0.257246i
$895$	−6.20872e29			−1.88266
$896$		−	2.05741e29i		−	0.616938i
$897$	2.51318e28	+	8.57000e28i	0.0745246	+	0.254130i
$898$	−3.13806e29			−0.920234
$899$		−	3.29382e29i		−	0.955219i
$900$	−6.41805e28	+	4.11841e28i	−0.184068	+	0.118115i
$901$	6.89012e27			0.0195425
$902$			8.46073e28i			0.237325i
$903$	1.76764e29	−	5.18366e28i	0.490360	−	0.143800i
$904$	6.76950e29			1.85726
$905$		−	1.02103e30i		−	2.77046i
$906$	−9.56404e28	−	3.26135e29i	−0.256661	−	0.875217i
$907$	1.12030e29			0.297344			0.148672	−	0.988887i	$-0.452500\pi$
$907$	1.12030e29			0.297344			0.148672	+	0.988887i	$0.452500\pi$
$908$			3.37423e28i			0.0885761i
$909$	4.07142e29	+	6.34483e29i	1.05708	+	1.64733i
$910$	−3.19115e29			−0.819471
$911$			1.66926e29i			0.423976i	0.977272	+	0.211988i	$0.0679937\pi$
$911$			1.66926e29i			0.423976i	−0.977272	+	0.211988i	$0.932006\pi$
$912$	−2.55231e29	+	7.48475e28i	−0.641188	+	0.188031i
$913$	2.47613e29			0.615270
$914$			4.47511e29i			1.09987i
$915$	1.07600e29	+	3.66919e29i	0.261579	+	0.891988i
$916$	−5.21653e28			−0.125437
$917$		−	1.27585e29i		−	0.303463i
$918$	−7.43346e28	+	8.56084e28i	−0.174890	+	0.201414i
$919$	−5.21162e29			−1.21288			−0.606439	−	0.795130i	$-0.707403\pi$
$919$	−5.21162e29			−1.21288			−0.606439	+	0.795130i	$0.707403\pi$
$920$		−	3.18406e29i		−	0.732998i
$921$	−3.71120e29	+	1.08832e29i	−0.845120	+	0.247834i
$922$	3.96523e29			0.893222
$923$			6.35876e28i			0.141695i
$924$	5.17838e27	+	1.76584e28i	0.0114150	+	0.0389252i
$925$	1.26496e30			2.75842
$926$			3.22136e29i			0.694912i
$927$	6.13802e29	−	3.93871e29i	1.30988	−	0.840537i
$928$	−1.35312e29			−0.285664
$929$			5.04438e28i			0.105354i	0.998612	+	0.0526770i	$0.0167754\pi$
$929$			5.04438e28i			0.105354i	−0.998612	+	0.0526770i	$0.983225\pi$
$930$	−5.53394e29	+	1.62285e29i	−1.14342	+	0.335311i
$931$	−1.53521e29			−0.313813
$932$		−	9.29437e28i		−	0.187958i
$933$	−3.43278e28	−	1.17058e29i	−0.0686799	−	0.234200i
$934$	4.66076e29			0.922546
$935$			1.20616e29i			0.236205i
$936$	−1.91075e29	−	2.97768e29i	−0.370208	−	0.576925i
$937$	−3.90829e29			−0.749189			−0.374594	−	0.927189i	$-0.622218\pi$
$937$	−3.90829e29			−0.749189			−0.374594	+	0.927189i	$0.622218\pi$
$938$			2.84915e29i			0.540365i
$939$	−1.53810e29	+	4.51053e28i	−0.288621	+	0.0846392i
$940$	1.80057e29			0.334297
$941$			3.20779e29i			0.589263i	0.955611	+	0.294632i	$0.0951969\pi$
$941$			3.20779e29i			0.589263i	−0.955611	+	0.294632i	$0.904803\pi$
$942$	−5.20095e28	−	1.77353e29i	−0.0945309	−	0.322352i
$943$	−1.17175e29			−0.210726
$944$			9.96310e28i			0.177286i
$945$	−5.68871e29	−	4.93957e29i	−1.00160	−	0.869702i
$946$	−1.74342e29			−0.303731
$947$		−	8.67373e29i		−	1.49522i	−0.664136	−	0.747612i	$-0.731200\pi$
$947$		−	8.67373e29i		−	1.49522i	0.664136	−	0.747612i	$-0.268800\pi$
$948$	−4.05322e28	+	1.18862e28i	−0.0691380	+	0.0202750i
$949$	−9.85785e28			−0.166387
$950$		−	8.57485e29i		−	1.43216i
$951$	−1.09504e29	−	3.73411e29i	−0.180978	−	0.617137i
$952$	−1.38720e29			−0.226866
$953$			1.08888e30i			1.76218i	0.472944	+	0.881092i	$0.343191\pi$
$953$			1.08888e30i			1.76218i	−0.472944	+	0.881092i	$0.656809\pi$
$954$	3.42813e28	−	2.19980e28i	0.0549002	−	0.0352290i
$955$	−5.54870e29			−0.879342
$956$			4.89578e28i			0.0767790i
$957$	−3.90800e29	+	1.14603e29i	−0.606506	+	0.177860i
$958$	6.75172e29			1.03695
$959$		−	1.40060e29i		−	0.212876i
$960$	3.51066e29	+	1.19714e30i	0.528051	+	1.80066i
$961$	−3.14126e29			−0.467595
$962$			5.79777e29i			0.854103i
$963$	1.18302e29	+	1.84360e29i	0.172476	+	0.268784i
$964$	7.29643e28			0.105279
$965$		−	2.93480e29i		−	0.419089i
$966$	1.98643e29	−	5.82526e28i	0.280738	−	0.0823274i
$967$	5.40407e28			0.0755886			0.0377943	−	0.999286i	$-0.487967\pi$
$967$	5.40407e28			0.0755886			0.0377943	+	0.999286i	$0.487967\pi$
$968$			5.80038e29i			0.802976i
$969$	4.41675e28	+	1.50612e29i	0.0605153	+	0.206358i
$970$	8.63128e29			1.17046
$971$		−	2.43913e29i		−	0.327373i	−0.986512	−	0.163686i	$-0.947661\pi$
$971$		−	2.43913e29i		−	0.327373i	0.986512	−	0.163686i	$-0.0523385\pi$
$972$	1.18836e28	−	8.16570e28i	0.0157865	−	0.108475i
$973$	2.28253e29			0.300115
$974$		−	9.99739e29i		−	1.30106i
$975$	9.73081e29	−	2.85360e29i	1.25344	−	0.367575i
$976$	3.70030e29			0.471779
$977$		−	1.98479e29i		−	0.250477i	−0.992127	−	0.125239i	$-0.960030\pi$
$977$		−	1.98479e29i		−	0.250477i	0.992127	−	0.125239i	$-0.0399697\pi$
$978$	−2.23362e29	−	7.61669e29i	−0.279011	−	0.951432i
$979$	−1.01048e29			−0.124940
$980$			6.39439e28i			0.0782597i
$981$	5.72533e29	−	3.67389e29i	0.693602	−	0.445078i
$982$	−9.67592e29			−1.16032
$983$			9.50707e29i			1.12853i	0.825595	+	0.564263i	$0.190839\pi$
$983$			9.50707e29i			1.12853i	−0.825595	+	0.564263i	$0.809161\pi$
$984$	4.45436e29	−	1.30626e29i	0.523400	−	0.153489i
$985$	−2.03645e30			−2.36871
$986$		−	3.03285e29i		−	0.349206i
$987$	3.33455e29	+	1.13709e30i	0.380071	+	1.29605i
$988$	−4.83855e28			−0.0545941
$989$		−	2.41451e29i		−	0.269690i
$990$	3.85090e29	+	6.00117e29i	0.425805	+	0.663566i
$991$	1.21756e30			1.33277			0.666386	−	0.745607i	$-0.267840\pi$
$991$	1.21756e30			1.33277			0.666386	+	0.745607i	$0.267840\pi$
$992$		−	1.46930e29i		−	0.159219i
$993$	−6.60946e29	+	1.93825e29i	−0.709044	+	0.207930i
$994$	1.47389e29			0.156531
$995$			3.36524e29i			0.353822i
$996$	−3.77661e28	−	1.28783e29i	−0.0393105	−	0.134050i
$997$	7.70433e29			0.793932			0.396966	−	0.917833i	$-0.370063\pi$
$997$	7.70433e29			0.793932			0.396966	+	0.917833i	$0.370063\pi$
$998$		−	1.38382e30i		−	1.41180i
$999$	−8.97433e29	+	1.03354e30i	−0.906457	+	1.04393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.21.b.a.2.5	yes	6
3.2	odd	2	inner	3.21.b.a.2.2	✓	6
4.3	odd	2		48.21.e.c.17.2		6
12.11	even	2		48.21.e.c.17.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.21.b.a.2.2	✓	6	3.2	odd	2	inner
3.21.b.a.2.5	yes	6	1.1	even	1	trivial
48.21.e.c.17.1		6	12.11	even	2
48.21.e.c.17.2		6	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+966.247i q^{2} +(56662.8 - 16616.6i) q^{3} +114943. q^{4} -1.69009e7i q^{5} +(1.60557e7 + 5.47503e7i) q^{6} +2.16509e8 q^{7} +1.12425e9i q^{8} +(2.93456e9 - 1.88308e9i) q^{9} +O(q^{10})\)	\(q+966.247i q^{2} +(56662.8 - 16616.6i) q^{3} +114943. q^{4} -1.69009e7i q^{5} +(1.60557e7 + 5.47503e7i) q^{6} +2.16509e8 q^{7} +1.12425e9i q^{8} +(2.93456e9 - 1.88308e9i) q^{9} +1.63305e10 q^{10} +1.25226e10i q^{11} +(6.51298e9 - 1.90995e9i) q^{12} -9.02553e10 q^{13} +2.09201e11i q^{14} +(-2.80835e11 - 9.57653e11i) q^{15} -9.65774e11 q^{16} +5.69903e11i q^{17} +(1.81952e12 + 2.83551e12i) q^{18} +4.66402e12 q^{19} -1.94264e12i q^{20} +(1.22680e13 - 3.59764e12i) q^{21} -1.20999e13 q^{22} -1.67575e13i q^{23} +(1.86811e13 + 6.37030e13i) q^{24} -1.90273e14 q^{25} -8.72090e13i q^{26} +(1.34990e14 - 1.55463e14i) q^{27} +2.48862e13 q^{28} +5.50759e14i q^{29} +(9.25329e14 - 2.71356e14i) q^{30} -5.98050e14 q^{31} +2.45682e14i q^{32} +(2.08083e14 + 7.09566e14i) q^{33} -5.50667e14 q^{34} -3.65920e15i q^{35} +(3.37307e14 - 2.16447e14i) q^{36} -6.64814e15 q^{37} +4.50660e15i q^{38} +(-5.11412e15 + 1.49973e15i) q^{39} +1.90008e16 q^{40} -6.99239e15i q^{41} +(3.47621e15 + 1.18539e16i) q^{42} +1.44085e16 q^{43} +1.43938e15i q^{44} +(-3.18258e16 - 4.95968e16i) q^{45} +1.61919e16 q^{46} +9.26870e16i q^{47} +(-5.47234e16 + 1.60478e16i) q^{48} -3.29160e16 q^{49} -1.83851e17i q^{50} +(9.46983e15 + 3.22923e16i) q^{51} -1.03742e16 q^{52} -1.20900e16i q^{53} +(1.50216e17 + 1.30434e17i) q^{54} +2.11643e17 q^{55} +2.43410e17i q^{56} +(2.64277e17 - 7.75001e16i) q^{57} -5.32170e17 q^{58} -1.03162e17i q^{59} +(-3.22800e16 - 1.10075e17i) q^{60} -3.83144e17 q^{61} -5.77864e17i q^{62} +(6.35360e17 - 4.07705e17i) q^{63} -1.25008e18 q^{64} +1.52540e18i q^{65} +(-6.85616e17 + 2.01059e17i) q^{66} +1.36192e18 q^{67} +6.55062e16i q^{68} +(-2.78453e17 - 9.49528e17i) q^{69} +3.53569e18 q^{70} -7.04530e17i q^{71} +(2.11705e18 + 3.29917e18i) q^{72} +1.09222e18 q^{73} -6.42374e18i q^{74} +(-1.07814e19 + 3.16169e18i) q^{75} +5.36096e17 q^{76} +2.71126e18i q^{77} +(-1.44911e18 - 4.94150e18i) q^{78} -6.22330e18 q^{79} +1.63225e19i q^{80} +(5.06566e18 - 1.10521e19i) q^{81} +6.75637e18 q^{82} -1.97733e19i q^{83} +(1.41012e18 - 4.13523e17i) q^{84} +9.63188e18 q^{85} +1.39222e19i q^{86} +(9.15174e18 + 3.12076e19i) q^{87} -1.40785e19 q^{88} +8.06929e18i q^{89} +(4.79227e19 - 3.07516e19i) q^{90} -1.95411e19 q^{91} -1.92616e18i q^{92} +(-3.38872e19 + 9.93755e18i) q^{93} -8.95585e19 q^{94} -7.88262e19i q^{95} +(4.08239e18 + 1.39210e19i) q^{96} +5.28539e19 q^{97} -3.18050e19i q^{98} +(2.35811e19 + 3.67484e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9}+O(q^{10}) \) 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9	\( 6 q - 4122 q^{3} - 2125200 q^{4} - 96401232 q^{6} + 559607916 q^{7} - 1087483482 q^{9} - 10880304480 q^{10} + 63957886128 q^{12} + 17847879276 q^{13} - 487764624960 q^{15} - 317472843648 q^{16} + 9564155313120 q^{18} - 14958020195124 q^{19} + 25978999888044 q^{21} - 71051286019680 q^{22} + 294048705803904 q^{24} - 397204775017050 q^{25} + 10\!\cdots\!98 q^{27}+ \cdots - 17\!\cdots\!80 q^{99}+O(q^{100}) \) 6 * q - 4122 * q^3 - 2125200 * q^4 - 96401232 * q^6 + 559607916 * q^7 - 1087483482 * q^9 - 10880304480 * q^10 + 63957886128 * q^12 + 17847879276 * q^13 - 487764624960 * q^15 - 317472843648 * q^16 + 9564155313120 * q^18 - 14958020195124 * q^19 + 25978999888044 * q^21 - 71051286019680 * q^22 + 294048705803904 * q^24 - 397204775017050 * q^25 + 1077025592505798 * q^27 - 2034284889273504 * q^28 + 3061064118304800 * q^30 - 2182905165483348 * q^31 + 3811197222014400 * q^33 - 7566372644651136 * q^34 + 6910111676037744 * q^36 - 1934341462168404 * q^37 - 15813602040849876 * q^39 + 44482420967535360 * q^40 - 86552595699685920 * q^42 + 58194987502184076 * q^43 - 81854223046416000 * q^45 + 151411391218915776 * q^46 - 154489681080035712 * q^48 + 188165158287453522 * q^49 - 117657755976045312 * q^51 - 230547517796956704 * q^52 + 489800358305152272 * q^54 - 393208608470140800 * q^55 + 1211071992434087436 * q^57 - 1639827118548168480 * q^58 + 2591328282252814080 * q^60 - 2999109545381544468 * q^61 + 444547436097192876 * q^63 - 83569554960393216 * q^64 + 120735307117251360 * q^66 + 4488155969890198476 * q^67 - 3511312424189451648 * q^69 - 1812568842584740800 * q^70 - 10414532525611288320 * q^72 + 15738405804262597836 * q^73 - 20871070048457840250 * q^75 + 27275280223392575328 * q^76 - 13410777930056987040 * q^78 + 17679940751103803436 * q^79 - 13011625055229011514 * q^81 - 35403353112903693120 * q^82 + 60397598618988279264 * q^84 - 22576574831711316480 * q^85 + 17858271599894295360 * q^87 - 95000209108729447680 * q^88 + 179562325304911301280 * q^90 - 6461010485165713512 * q^91 - 24838278011742494484 * q^93 - 311754310853935072896 * q^94 + 184738040137761352704 * q^96 + 223240336245548394636 * q^97 - 178130031568853028480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

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