LMFDB - Embedded newform 6.11.b.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,11,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	6.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:	$3.81214351604$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{85})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 37x^{2} + 38x + 531 $ x^4 - 2x^3 - 37x^2 + 38*x + 531
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.2
Root			$5.10977 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.11.b.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.6274i q^{2} +(242.269 - 18.8335i) q^{3} -512.000 q^{4} -4818.41i q^{5} +(-426.153 - 5481.92i) q^{6} +670.530 q^{7} +11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} +O(q^{10})$	\(q-22.6274i q^{2} +(242.269 - 18.8335i) q^{3} -512.000 q^{4} -4818.41i q^{5} +(-426.153 - 5481.92i) q^{6} +670.530 q^{7} +11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} -109028. q^{10} +233268. i q^{11} +(-124042. + 9642.73i) q^{12} +307781. q^{13} -15172.4i q^{14} +(-90747.4 - 1.16735e6i) q^{15} +262144. q^{16} +672324. i q^{17} +(-206487. - 1.32007e6i) q^{18} -1.55119e6 q^{19} +2.46703e6i q^{20} +(162449. - 12628.4i) q^{21} +5.27826e6 q^{22} +5.57551e6i q^{23} +(218190. + 2.80674e6i) q^{24} -1.34515e7 q^{25} -6.96428e6i q^{26} +(1.39620e7 - 3.30957e6i) q^{27} -343311. q^{28} -2.97313e7i q^{29} +(-2.64142e7 + 2.05338e6i) q^{30} +3.09368e7 q^{31} -5.93164e6i q^{32} +(4.39325e6 + 5.65137e7i) q^{33} +1.52130e7 q^{34} -3.23089e6i q^{35} +(-2.98699e7 + 4.67227e6i) q^{36} -8.56690e7 q^{37} +3.50994e7i q^{38} +(7.45657e7 - 5.79657e6i) q^{39} +5.58225e7 q^{40} +3.59054e7i q^{41} +(-285748. - 3.67579e6i) q^{42} -3.66253e7 q^{43} -1.19433e8i q^{44} +(-4.39706e7 - 2.81104e8i) q^{45} +1.26159e8 q^{46} +3.28877e7i q^{47} +(6.35094e7 - 4.93708e6i) q^{48} -2.82026e8 q^{49} +3.04372e8i q^{50} +(1.26622e7 + 1.62883e8i) q^{51} -1.57584e8 q^{52} +4.59194e8i q^{53} +(-7.48870e7 - 3.15924e8i) q^{54} +1.12398e9 q^{55} +7.76824e6i q^{56} +(-3.75805e8 + 2.92143e7i) q^{57} -6.72743e8 q^{58} -4.88657e8i q^{59} +(4.64627e7 + 5.97684e8i) q^{60} -6.12928e7 q^{61} -7.00020e8i q^{62} +(3.91184e7 - 6.11894e6i) q^{63} -1.34218e8 q^{64} -1.48301e9i q^{65} +(1.27876e9 - 9.94079e7i) q^{66} -6.70776e8 q^{67} -3.44230e8i q^{68} +(1.05006e8 + 1.35077e9i) q^{69} -7.31067e7 q^{70} +1.23330e9i q^{71} +(1.05721e8 + 6.75878e8i) q^{72} +1.08126e9 q^{73} +1.93847e9i q^{74} +(-3.25888e9 + 2.53338e8i) q^{75} +7.94209e8 q^{76} +1.56413e8i q^{77} +(-1.31161e8 - 1.68723e9i) q^{78} -1.86628e9 q^{79} -1.26312e9i q^{80} +(3.32023e9 - 1.06476e9i) q^{81} +8.12446e8 q^{82} -1.09562e9i q^{83} +(-8.31737e7 + 6.46574e6i) q^{84} +3.23953e9 q^{85} +8.28736e8i q^{86} +(-5.59944e8 - 7.20298e9i) q^{87} -2.70247e9 q^{88} +5.19876e9i q^{89} +(-6.36066e9 + 9.94940e8i) q^{90} +2.06376e8 q^{91} -2.85466e9i q^{92} +(7.49503e9 - 5.82647e8i) q^{93} +7.44163e8 q^{94} +7.47427e9i q^{95} +(-1.11713e8 - 1.43705e9i) q^{96} -1.07471e10 q^{97} +6.38151e9i q^{98} +(2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9}+O(q^{10}) $ 4 * q + 84 * q^3 - 2048 * q^4 + 5376 * q^6 - 45112 * q^7 + 159012 * q^9	\( 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} - 53760 q^{10} - 43008 q^{12} + 275240 q^{13} - 1180800 q^{15} + 1048576 q^{16} - 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} + 7730688 q^{22} - 2752512 q^{24} - 33732380 q^{25} + 34619508 q^{27} + 23097344 q^{28} - 85731840 q^{30} - 21785848 q^{31} + 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} - 71014168 q^{37} + 217287240 q^{39} + 27525120 q^{40} - 145233408 q^{42} - 470688664 q^{43} + 312318720 q^{45} + 188814336 q^{46} + 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} - 140922880 q^{52} + 481662720 q^{54} + 2701359360 q^{55} - 1058753208 q^{57} - 1564177920 q^{58} + 604569600 q^{60} - 1184038744 q^{61} - 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} - 297365848 q^{67} + 596268288 q^{69} - 3962250240 q^{70} + 1488715776 q^{72} + 6534269000 q^{73} - 5150031180 q^{75} + 803188736 q^{76} - 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} + 8378668032 q^{82} - 4929540096 q^{84} - 12880512000 q^{85} + 210268800 q^{87} - 3958112256 q^{88} - 9243763200 q^{90} + 8317232080 q^{91} + 31744468392 q^{93} + 8505477120 q^{94} + 1409286144 q^{96} - 39176355064 q^{97} - 2626912512 q^{99}+O(q^{100}) \) 4 * q + 84 * q^3 - 2048 * q^4 + 5376 * q^6 - 45112 * q^7 + 159012 * q^9 - 53760 * q^10 - 43008 * q^12 + 275240 * q^13 - 1180800 * q^15 + 1048576 * q^16 - 2907648 * q^18 - 1568728 * q^19 + 9628008 * q^21 + 7730688 * q^22 - 2752512 * q^24 - 33732380 * q^25 + 34619508 * q^27 + 23097344 * q^28 - 85731840 * q^30 - 21785848 * q^31 + 25974144 * q^33 + 151087104 * q^34 - 81414144 * q^36 - 71014168 * q^37 + 217287240 * q^39 + 27525120 * q^40 - 145233408 * q^42 - 470688664 * q^43 + 312318720 * q^45 + 188814336 * q^46 + 22020096 * q^48 - 50058420 * q^49 - 708576768 * q^51 - 140922880 * q^52 + 481662720 * q^54 + 2701359360 * q^55 - 1058753208 * q^57 - 1564177920 * q^58 + 604569600 * q^60 - 1184038744 * q^61 - 905007096 * q^63 - 536870912 * q^64 + 3123445248 * q^66 - 297365848 * q^67 + 596268288 * q^69 - 3962250240 * q^70 + 1488715776 * q^72 + 6534269000 * q^73 - 5150031180 * q^75 + 803188736 * q^76 - 1322135040 * q^78 + 199282568 * q^79 + 1458964548 * q^81 + 8378668032 * q^82 - 4929540096 * q^84 - 12880512000 * q^85 + 210268800 * q^87 - 3958112256 * q^88 - 9243763200 * q^90 + 8317232080 * q^91 + 31744468392 * q^93 + 8505477120 * q^94 + 1409286144 * q^96 - 39176355064 * q^97 - 2626912512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$		−	22.6274i		−	0.707107i
$2$		−	22.6274i		−	0.707107i
$3$	242.269	−	18.8335i	0.996992	−	0.0775039i
$3$	242.269	−	18.8335i	0.996992	−	0.0775039i
$4$	−512.000			−0.500000
$5$		−	4818.41i		−	1.54189i	−0.636900	−	0.770946i	$-0.719784\pi$
$5$		−	4818.41i		−	1.54189i	0.636900	−	0.770946i	$-0.280216\pi$
$6$	−426.153	−	5481.92i	−0.0548036	−	0.704980i
$7$	670.530			0.0398959			0.0199479	−	0.999801i	$-0.493650\pi$
$7$	670.530			0.0398959			0.0199479	+	0.999801i	$0.493650\pi$
$8$			11585.2i			0.353553i
$9$	58339.6	−	9125.53i	0.987986	−	0.154542i
$10$	−109028.			−1.09028
$11$			233268.i			1.44841i	0.689583	+	0.724206i	$0.257794\pi$
$11$			233268.i			1.44841i	−0.689583	+	0.724206i	$0.742206\pi$
$12$	−124042.	+	9642.73i	−0.498496	+	0.0387520i
$13$	307781.			0.828943			0.414471	−	0.910062i	$-0.363967\pi$
$13$	307781.			0.828943			0.414471	+	0.910062i	$0.363967\pi$
$14$		−	15172.4i		−	0.0282106i
$15$	−90747.4	−	1.16735e6i	−0.119503	−	1.53725i
$16$	262144.			0.250000
$17$			672324.i			0.473515i	0.971569	+	0.236758i	$0.0760847\pi$
$17$			672324.i			0.473515i	−0.971569	+	0.236758i	$0.923915\pi$
$18$	−206487.	−	1.32007e6i	−0.109277	−	0.698612i
$19$	−1.55119e6			−0.626465			−0.313233	−	0.949676i	$-0.601412\pi$
$19$	−1.55119e6			−0.626465			−0.313233	+	0.949676i	$0.601412\pi$
$20$			2.46703e6i			0.770946i
$21$	162449.	−	12628.4i	0.0397758	−	0.00309209i
$22$	5.27826e6			1.02418
$23$			5.57551e6i			0.866255i	0.901333	+	0.433127i	$0.142590\pi$
$23$			5.57551e6i			0.866255i	−0.901333	+	0.433127i	$0.857410\pi$
$24$	218190.	+	2.80674e6i	0.0274018	+	0.352490i
$25$	−1.34515e7			−1.37743
$26$		−	6.96428e6i		−	0.586151i
$27$	1.39620e7	−	3.30957e6i	0.973037	−	0.230650i
$28$	−343311.			−0.0199479
$29$		−	2.97313e7i		−	1.44952i	−0.689001	−	0.724760i	$-0.741951\pi$
$29$		−	2.97313e7i		−	1.44952i	0.689001	−	0.724760i	$-0.258049\pi$
$30$	−2.64142e7	+	2.05338e6i	−1.08700	+	0.0845012i
$31$	3.09368e7			1.08061			0.540303	−	0.841471i	$-0.318310\pi$
$31$	3.09368e7			1.08061			0.540303	+	0.841471i	$0.318310\pi$
$32$		−	5.93164e6i		−	0.176777i
$33$	4.39325e6	+	5.65137e7i	0.112258	+	1.44406i
$34$	1.52130e7			0.334826
$35$		−	3.23089e6i		−	0.0615151i
$36$	−2.98699e7	+	4.67227e6i	−0.493993	+	0.0772708i
$37$	−8.56690e7			−1.23542			−0.617711	−	0.786406i	$-0.711940\pi$
$37$	−8.56690e7			−1.23542			−0.617711	+	0.786406i	$0.711940\pi$
$38$			3.50994e7i			0.442978i
$39$	7.45657e7	−	5.79657e6i	0.826449	−	0.0642463i
$40$	5.58225e7			0.545141
$41$			3.59054e7i			0.309913i	0.987921	+	0.154957i	$0.0495238\pi$
$41$			3.59054e7i			0.309913i	−0.987921	+	0.154957i	$0.950476\pi$
$42$	−285748.	−	3.67579e6i	−0.00218644	−	0.0281258i
$43$	−3.66253e7			−0.249137			−0.124569	−	0.992211i	$-0.539755\pi$
$43$	−3.66253e7			−0.249137			−0.124569	+	0.992211i	$0.539755\pi$
$44$		−	1.19433e8i		−	0.724206i
$45$	−4.39706e7	−	2.81104e8i	−0.238287	−	1.52337i
$46$	1.26159e8			0.612535
$47$			3.28877e7i			0.143398i	0.997426	+	0.0716992i	$0.0228421\pi$
$47$			3.28877e7i			0.143398i	−0.997426	+	0.0716992i	$0.977158\pi$
$48$	6.35094e7	−	4.93708e6i	0.249248	−	0.0193760i
$49$	−2.82026e8			−0.998408
$50$			3.04372e8i			0.973991i
$51$	1.26622e7	+	1.62883e8i	0.0366993	+	0.472091i
$52$	−1.57584e8			−0.414471
$53$			4.59194e8i			1.09804i	0.835810	+	0.549019i	$0.184998\pi$
$53$			4.59194e8i			1.09804i	−0.835810	+	0.549019i	$0.815002\pi$
$54$	−7.48870e7	−	3.15924e8i	−0.163094	−	0.688041i
$55$	1.12398e9			2.23330
$56$			7.76824e6i			0.0141053i
$57$	−3.75805e8	+	2.92143e7i	−0.624581	+	0.0485535i
$58$	−6.72743e8			−1.02497
$59$		−	4.88657e8i		−	0.683508i	−0.939789	−	0.341754i	$-0.888979\pi$
$59$		−	4.88657e8i		−	0.683508i	0.939789	−	0.341754i	$-0.111021\pi$
$60$	4.64627e7	+	5.97684e8i	0.0597514	+	0.768627i
$61$	−6.12928e7			−0.0725705			−0.0362852	−	0.999341i	$-0.511552\pi$
$61$	−6.12928e7			−0.0725705			−0.0362852	+	0.999341i	$0.511552\pi$
$62$		−	7.00020e8i		−	0.764103i
$63$	3.91184e7	−	6.11894e6i	0.0394166	−	0.00616557i
$64$	−1.34218e8			−0.125000
$65$		−	1.48301e9i		−	1.27814i
$66$	1.27876e9	−	9.94079e7i	1.02110	−	0.0793782i
$67$	−6.70776e8			−0.496825			−0.248413	−	0.968654i	$-0.579909\pi$
$67$	−6.70776e8			−0.496825			−0.248413	+	0.968654i	$0.579909\pi$
$68$		−	3.44230e8i		−	0.236758i
$69$	1.05006e8	+	1.35077e9i	0.0671382	+	0.863649i
$70$	−7.31067e7			−0.0434977
$71$			1.23330e9i			0.683561i	0.939780	+	0.341781i	$0.111030\pi$
$71$			1.23330e9i			0.683561i	−0.939780	+	0.341781i	$0.888970\pi$
$72$	1.05721e8	+	6.75878e8i	0.0546387	+	0.349306i
$73$	1.08126e9			0.521573			0.260787	−	0.965396i	$-0.416018\pi$
$73$	1.08126e9			0.521573			0.260787	+	0.965396i	$0.416018\pi$
$74$			1.93847e9i			0.873575i
$75$	−3.25888e9	+	2.53338e8i	−1.37329	+	0.106756i
$76$	7.94209e8			0.313233
$77$			1.56413e8i			0.0577857i
$78$	−1.31161e8	−	1.68723e9i	−0.0454290	−	0.584388i
$79$	−1.86628e9			−0.606515			−0.303258	−	0.952909i	$-0.598074\pi$
$79$	−1.86628e9			−0.606515			−0.303258	+	0.952909i	$0.598074\pi$
$80$		−	1.26312e9i		−	0.385473i
$81$	3.32023e9	−	1.06476e9i	0.952234	−	0.305370i
$82$	8.12446e8			0.219142
$83$		−	1.09562e9i		−	0.278145i	−0.990282	−	0.139072i	$-0.955588\pi$
$83$		−	1.09562e9i		−	0.278145i	0.990282	−	0.139072i	$-0.0444121\pi$
$84$	−8.31737e7	+	6.46574e6i	−0.0198879	+	0.00154604i
$85$	3.23953e9			0.730109
$86$			8.28736e8i			0.176167i
$87$	−5.59944e8	−	7.20298e9i	−0.112344	−	1.44516i
$88$	−2.70247e9			−0.512091
$89$			5.19876e9i			0.931000i	0.885048	+	0.465500i	$0.154126\pi$
$89$			5.19876e9i			0.931000i	−0.885048	+	0.465500i	$0.845874\pi$
$90$	−6.36066e9	+	9.94940e8i	−1.07718	+	0.168494i
$91$	2.06376e8			0.0330714
$92$		−	2.85466e9i		−	0.433127i
$93$	7.49503e9	−	5.82647e8i	1.07735	−	0.0837512i
$94$	7.44163e8			0.101398
$95$			7.47427e9i			0.965941i
$96$	−1.11713e8	−	1.43705e9i	−0.0137009	−	0.176245i
$97$	−1.07471e10			−1.25150			−0.625750	−	0.780024i	$-0.715207\pi$
$97$	−1.07471e10			−1.25150			−0.625750	+	0.780024i	$0.715207\pi$
$98$			6.38151e9i			0.705981i
$99$	2.12870e9	+	1.36088e10i	0.223840	+	1.43101i
$100$	6.88716e9			0.688716
$101$		−	1.08154e10i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$101$		−	1.08154e10i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$102$	3.68563e9	−	2.86513e8i	0.333819	−	0.0259503i
$103$	−2.83446e9			−0.244503			−0.122251	−	0.992499i	$-0.539011\pi$
$103$	−2.83446e9			−0.244503			−0.122251	+	0.992499i	$0.539011\pi$
$104$			3.56571e9i			0.293075i
$105$	−6.08488e7	−	7.82744e8i	−0.00476766	−	0.0613301i
$106$	1.03904e10			0.776430
$107$		−	2.41202e10i		−	1.71974i	−0.510515	−	0.859869i	$-0.670545\pi$
$107$		−	2.41202e10i		−	1.71974i	0.510515	−	0.859869i	$-0.329455\pi$
$108$	−7.14855e9	+	1.69450e9i	−0.486518	+	0.115325i
$109$	−5.43424e9			−0.353188			−0.176594	−	0.984284i	$-0.556508\pi$
$109$	−5.43424e9			−0.353188			−0.176594	+	0.984284i	$0.556508\pi$
$110$		−	2.54328e10i		−	1.57918i
$111$	−2.07549e10	+	1.61344e9i	−1.23170	+	0.0957500i
$112$	1.75775e8			0.00997396
$113$			1.39305e10i			0.756092i	0.925787	+	0.378046i	$0.123404\pi$
$113$			1.39305e10i			0.756092i	−0.925787	+	0.378046i	$0.876596\pi$
$114$	6.61043e8	+	8.50350e9i	0.0343325	+	0.441645i
$115$	2.68651e10			1.33567
$116$			1.52224e10i			0.724760i
$117$	1.79558e10	−	2.80866e9i	0.818984	−	0.128106i
$118$	−1.10570e10			−0.483313
$119$			4.50813e8i			0.0188913i
$120$	1.35241e10	−	1.05133e9i	0.543501	−	0.0422506i
$121$	−2.84767e10			−1.09790
$122$			1.38690e9i			0.0513151i
$123$	6.76223e8	+	8.69877e9i	0.0240195	+	0.308981i
$124$	−1.58396e10			−0.540303
$125$			1.77600e10i			0.581958i
$126$	−1.38456e8	−	8.85149e8i	−0.00435972	−	0.0278717i
$127$	4.08412e10			1.23617			0.618087	−	0.786110i	$-0.287908\pi$
$127$	4.08412e10			1.23617			0.618087	+	0.786110i	$0.287908\pi$
$128$			3.03700e9i			0.0883883i
$129$	−8.87317e9	+	6.89781e8i	−0.248388	+	0.0193091i
$130$	−3.35568e10			−0.903782
$131$			4.15498e10i			1.07699i	0.842628	+	0.538495i	$0.181007\pi$
$131$			4.15498e10i			1.07699i	−0.842628	+	0.538495i	$0.818993\pi$
$132$	−2.24934e9	−	2.89350e10i	−0.0561289	−	0.722028i
$133$	−1.04012e9			−0.0249934
$134$			1.51779e10i			0.351308i
$135$	−1.59469e10	−	6.72748e10i	−0.355637	−	1.50032i
$136$	−7.78903e9			−0.167413
$137$		−	9.25532e10i		−	1.91773i	−0.283854	−	0.958867i	$-0.591613\pi$
$137$		−	9.25532e10i		−	1.91773i	0.283854	−	0.958867i	$-0.408387\pi$
$138$	3.05645e10	−	2.37602e9i	0.610692	−	0.0474739i
$139$	7.95575e10			1.53323			0.766615	−	0.642107i	$-0.221939\pi$
$139$	7.95575e10			1.53323			0.766615	+	0.642107i	$0.221939\pi$
$140$			1.65421e9i			0.0307576i
$141$	6.19389e8	+	7.96767e9i	0.0111139	+	0.142967i
$142$	2.79064e10			0.483351
$143$			7.17955e10i			1.20065i
$144$	1.52934e10	−	2.39220e9i	0.246997	−	0.0386354i
$145$	−1.43258e11			−2.23500
$146$		−	2.44661e10i		−	0.368808i
$147$	−6.83261e10	+	5.31152e9i	−0.995405	+	0.0773806i
$148$	4.38625e10			0.617711
$149$			8.07804e10i			1.09995i	0.835180	+	0.549977i	$0.185364\pi$
$149$			8.07804e10i			1.09995i	−0.835180	+	0.549977i	$0.814636\pi$
$150$	5.73238e9	+	7.37400e10i	0.0754881	+	0.971061i
$151$	3.08654e10			0.393176			0.196588	−	0.980486i	$-0.437014\pi$
$151$	3.08654e10			0.393176			0.196588	+	0.980486i	$0.437014\pi$
$152$		−	1.79709e10i		−	0.221489i
$153$	6.13531e9	+	3.92231e10i	0.0731778	+	0.467827i
$154$	3.53923e9			0.0408606
$155$		−	1.49066e11i		−	1.66618i
$156$	−3.81776e10	+	2.96785e9i	−0.413225	+	0.0321232i
$157$	9.71322e10			1.01828			0.509138	−	0.860685i	$-0.329964\pi$
$157$	9.71322e10			1.01828			0.509138	+	0.860685i	$0.329964\pi$
$158$			4.22291e10i			0.428871i
$159$	8.64822e9	+	1.11249e11i	0.0851023	+	1.09473i
$160$	−2.85811e10			−0.272571
$161$			3.73855e9i			0.0345600i
$162$	−2.40928e10	−	7.51283e10i	−0.215929	−	0.673331i
$163$	−1.39440e11			−1.21185			−0.605927	−	0.795520i	$-0.707198\pi$
$163$	−1.39440e11			−1.21185			−0.605927	+	0.795520i	$0.707198\pi$
$164$		−	1.83836e10i		−	0.154957i
$165$	2.72306e11	−	2.11685e10i	2.22658	−	0.173089i
$166$	−2.47911e10			−0.196678
$167$		−	1.25840e11i		−	0.968804i	−0.874845	−	0.484402i	$-0.839037\pi$
$167$		−	1.25840e11i		−	0.968804i	0.874845	−	0.484402i	$-0.160963\pi$
$168$	1.46303e8	+	1.88201e9i	0.00109322	+	0.0140629i
$169$	−4.31296e10			−0.312854
$170$		−	7.33023e10i		−	0.516265i
$171$	−9.04958e10	+	1.41554e10i	−0.618939	+	0.0968149i
$172$	1.87521e10			0.124569
$173$		−	1.26257e11i		−	0.814750i	−0.913261	−	0.407375i	$-0.866444\pi$
$173$		−	1.26257e11i		−	0.814750i	0.913261	−	0.407375i	$-0.133556\pi$
$174$	−1.62985e11	+	1.26701e10i	−1.02188	+	0.0794389i
$175$	−9.01961e9			−0.0549538
$176$			6.11499e10i			0.362103i
$177$	−9.20310e9	−	1.18386e11i	−0.0529746	−	0.681452i
$178$	1.17635e11			0.658317
$179$			2.96543e11i			1.61370i	0.590758	+	0.806848i	$0.298829\pi$
$179$			2.96543e11i			1.61370i	−0.590758	+	0.806848i	$0.701171\pi$
$180$	2.25129e10	+	1.43925e11i	0.119143	+	0.761684i
$181$	2.48451e11			1.27893			0.639466	−	0.768819i	$-0.279155\pi$
$181$	2.48451e11			1.27893			0.639466	+	0.768819i	$0.279155\pi$
$182$		−	4.66976e9i		−	0.0233850i
$183$	−1.48493e10	+	1.15435e9i	−0.0723522	+	0.00562450i
$184$	−6.45936e10			−0.306267
$185$			4.12789e11i			1.90489i
$186$	−1.31838e10	−	1.69593e11i	−0.0592210	−	0.761805i
$187$	−1.56832e11			−0.685846
$188$		−	1.68385e10i		−	0.0716992i
$189$	9.36194e9	−	2.21916e9i	0.0388201	−	0.00920196i
$190$	1.69123e11			0.683024
$191$		−	1.58050e11i		−	0.621769i	−0.950448	−	0.310884i	$-0.899375\pi$
$191$		−	1.58050e11i		−	0.621769i	0.950448	−	0.310884i	$-0.100625\pi$
$192$	−3.25168e10	+	2.52778e9i	−0.124624	+	0.00968799i
$193$	−3.78369e11			−1.41296			−0.706479	−	0.707734i	$-0.749717\pi$
$193$	−3.78369e11			−1.41296			−0.706479	+	0.707734i	$0.749717\pi$
$194$			2.43178e11i			0.884944i
$195$	−2.79303e10	−	3.59288e11i	−0.0990609	−	1.27430i
$196$	1.44397e11			0.499204
$197$		−	1.89406e11i		−	0.638356i	−0.947695	−	0.319178i	$-0.896593\pi$
$197$		−	1.89406e11i		−	0.638356i	0.947695	−	0.319178i	$-0.103407\pi$
$198$	3.07932e11	−	4.81669e10i	1.01188	−	0.158279i
$199$	5.02942e10			0.161158			0.0805791	−	0.996748i	$-0.474323\pi$
$199$	5.02942e10			0.161158			0.0805791	+	0.996748i	$0.474323\pi$
$200$		−	1.55839e11i		−	0.486996i
$201$	−1.62508e11	+	1.26330e10i	−0.495331	+	0.0385059i
$202$	−2.44725e11			−0.727648
$203$		−	1.99357e10i		−	0.0578298i
$204$	−6.48304e9	−	8.33962e10i	−0.0183496	−	0.236045i
$205$	1.73007e11			0.477853
$206$			6.41365e10i			0.172890i
$207$	5.08795e10	+	3.25273e11i	0.133872	+	0.855848i
$208$	8.06828e10			0.207236
$209$		−	3.61843e11i		−	0.907380i
$210$	−1.77115e10	+	1.37685e9i	−0.0433669	+	0.00337125i
$211$	4.74970e11			1.13567			0.567837	−	0.823141i	$-0.307780\pi$
$211$	4.74970e11			1.13567			0.567837	+	0.823141i	$0.307780\pi$
$212$		−	2.35108e11i		−	0.549019i
$213$	2.32273e10	+	2.98791e11i	0.0529787	+	0.681505i
$214$	−5.45778e11			−1.21604
$215$			1.76476e11i			0.384143i
$216$	3.83422e10	+	1.61753e11i	0.0815470	+	0.344020i
$217$	2.07440e10			0.0431117
$218$			1.22963e11i			0.249742i
$219$	2.61955e11	−	2.03638e10i	0.520004	−	0.0404240i
$220$	−5.75479e11			−1.11665
$221$			2.06928e11i			0.392517i
$222$	3.65081e10	+	4.69631e11i	0.0677055	+	0.870947i
$223$	−2.35580e11			−0.427183			−0.213592	−	0.976923i	$-0.568516\pi$
$223$	−2.35580e11			−0.427183			−0.213592	+	0.976923i	$0.568516\pi$
$224$		−	3.97734e9i		−	0.00705266i
$225$	−7.84754e11	+	1.22752e11i	−1.36088	+	0.212870i
$226$	3.15211e11			0.534638
$227$			4.27026e11i			0.708475i	0.935155	+	0.354238i	$0.115260\pi$
$227$			4.27026e11i			0.708475i	−0.935155	+	0.354238i	$0.884740\pi$
$228$	1.92412e11	−	1.49577e10i	0.312290	−	0.0242768i
$229$	1.03671e12			1.64619			0.823096	−	0.567902i	$-0.192245\pi$
$229$	1.03671e12			1.64619			0.823096	+	0.567902i	$0.192245\pi$
$230$		−	6.07888e11i		−	0.944462i
$231$	2.94580e9	+	3.78941e10i	0.00447862	+	0.0576119i
$232$	3.44444e11			0.512483
$233$		−	1.03766e12i		−	1.51103i	−0.655130	−	0.755516i	$-0.727386\pi$
$233$		−	1.03766e12i		−	1.51103i	0.655130	−	0.755516i	$-0.272614\pi$
$234$	−6.35527e10	−	4.06293e11i	−0.0905847	−	0.579109i
$235$	1.58466e11			0.221105
$236$			2.50192e11i			0.341754i
$237$	−4.52142e11	+	3.51485e10i	−0.604691	+	0.0470073i
$238$	1.02007e10			0.0133582
$239$		−	1.23687e12i		−	1.58612i	−0.609144	−	0.793060i	$-0.708487\pi$
$239$		−	1.23687e12i		−	1.58612i	0.609144	−	0.793060i	$-0.291513\pi$
$240$	−2.37889e10	−	3.06014e11i	−0.0298757	−	0.384314i
$241$	−1.03912e12			−1.27814			−0.639072	−	0.769147i	$-0.720682\pi$
$241$	−1.03912e12			−1.27814			−0.639072	+	0.769147i	$0.720682\pi$
$242$			6.44354e11i			0.776333i
$243$	7.84337e11	−	3.20490e11i	0.925702	−	0.378253i
$244$	3.13819e10			0.0362852
$245$			1.35892e12i			1.53944i
$246$	1.96831e11	−	1.53012e10i	0.218483	−	0.0169844i
$247$	−4.77426e11			−0.519304
$248$			3.58410e11i			0.382052i
$249$	−2.06344e10	−	2.65436e11i	−0.0215573	−	0.277308i
$250$	4.01862e11			0.411507
$251$			5.66781e11i			0.568914i	0.958689	+	0.284457i	$0.0918133\pi$
$251$			5.66781e11i			0.568914i	−0.958689	+	0.284457i	$0.908187\pi$
$252$	−2.00286e10	+	3.13290e9i	−0.0197083	+	0.00308279i
$253$	−1.30059e12			−1.25469
$254$		−	9.24130e11i		−	0.874107i
$255$	7.84839e11	−	6.10116e10i	0.727913	−	0.0565864i
$256$	6.87195e10			0.0625000
$257$			1.27943e12i			1.14117i	0.821239	+	0.570584i	$0.193283\pi$
$257$			1.27943e12i			1.14117i	−0.821239	+	0.570584i	$0.806717\pi$
$258$	1.56080e10	+	2.00777e11i	0.0136536	+	0.175637i
$259$	−5.74436e10			−0.0492882
$260$			7.59303e11i			0.639070i
$261$	−2.71314e11	−	1.73451e12i	−0.224011	−	1.43211i
$262$	9.40164e11			0.761548
$263$			1.68583e12i			1.33978i	0.742459	+	0.669892i	$0.233660\pi$
$263$			1.68583e12i			1.33978i	−0.742459	+	0.669892i	$0.766340\pi$
$264$	−6.54725e11	+	5.08968e10i	−0.510551	+	0.0396891i
$265$	2.21259e12			1.69306
$266$			2.35352e10i			0.0176730i
$267$	9.79107e10	+	1.25950e12i	0.0721562	+	0.928200i
$268$	3.43437e11			0.248413
$269$		−	1.34023e12i		−	0.951523i	−0.879574	−	0.475761i	$-0.842173\pi$
$269$		−	1.34023e12i		−	0.951523i	0.879574	−	0.475761i	$-0.157827\pi$
$270$	−1.52225e12	+	3.60837e11i	−1.06088	+	0.251473i
$271$	−1.75349e12			−1.19966			−0.599829	−	0.800129i	$-0.704765\pi$
$271$	−1.75349e12			−1.19966			−0.599829	+	0.800129i	$0.704765\pi$
$272$			1.76246e11i			0.118379i
$273$	4.99985e10	−	3.88677e9i	0.0329719	−	0.00256316i
$274$	−2.09424e12			−1.35604
$275$		−	3.13780e12i		−	1.99509i
$276$	−5.37632e10	−	6.91597e11i	−0.0335691	−	0.431825i
$277$	1.69580e12			1.03986			0.519930	−	0.854209i	$-0.325958\pi$
$277$	1.69580e12			1.03986			0.519930	+	0.854209i	$0.325958\pi$
$278$		−	1.80018e12i		−	1.08416i
$279$	1.80484e12	−	2.82315e11i	1.06762	−	0.166999i
$280$	3.74306e10			0.0217489
$281$			2.44175e11i			0.139370i	0.997569	+	0.0696851i	$0.0221995\pi$
$281$			2.44175e11i			0.139370i	−0.997569	+	0.0696851i	$0.977801\pi$
$282$	1.80288e11	−	1.40152e10i	0.101093	−	0.00785874i
$283$	−9.96409e11			−0.548916			−0.274458	−	0.961599i	$-0.588498\pi$
$283$	−9.96409e11			−0.548916			−0.274458	+	0.961599i	$0.588498\pi$
$284$		−	6.31450e11i		−	0.341781i
$285$	1.40766e11	+	1.81078e12i	0.0748643	+	0.963036i
$286$	1.62455e12			0.848989
$287$			2.40756e10i			0.0123643i
$288$	−5.41294e10	−	3.46050e11i	−0.0273194	−	0.174653i
$289$	1.56397e12			0.775783
$290$			3.24155e12i			1.58039i
$291$	−2.60368e12	+	2.02404e11i	−1.24774	+	0.0969962i
$292$	−5.53604e11			−0.260787
$293$		−	1.57571e12i		−	0.729690i	−0.931068	−	0.364845i	$-0.881122\pi$
$293$		−	1.57571e12i		−	0.729690i	0.931068	−	0.364845i	$-0.118878\pi$
$294$	1.20186e11	+	1.54604e12i	0.0547163	+	0.703858i
$295$	−2.35455e12			−1.05390
$296$		−	9.92496e11i		−	0.436787i
$297$	7.72018e11	+	3.25690e12i	0.334076	+	1.40936i
$298$	1.82785e12			0.777786
$299$			1.71603e12i			0.718076i
$300$	1.66854e12	−	1.29709e11i	0.686644	−	0.0533782i
$301$	−2.45583e10			−0.00993955
$302$		−	6.98405e11i		−	0.278018i
$303$	−2.03692e11	−	2.62024e12i	−0.0797554	−	1.02595i
$304$	−4.06635e11			−0.156616
$305$			2.95334e11i			0.111896i
$306$	8.87518e11	−	1.38826e11i	0.330803	−	0.0517445i
$307$	−3.29823e12			−1.20945			−0.604726	−	0.796434i	$-0.706717\pi$
$307$	−3.29823e12			−1.20945			−0.604726	+	0.796434i	$0.706717\pi$
$308$		−	8.00836e10i		−	0.0288928i
$309$	−6.86702e11	+	5.33827e10i	−0.243768	+	0.0189499i
$310$	−3.37299e12			−1.17816
$311$			1.67301e12i			0.575038i	0.957775	+	0.287519i	$0.0928304\pi$
$311$			1.67301e12i			0.575038i	−0.957775	+	0.287519i	$0.907170\pi$
$312$	6.71547e10	+	8.63862e11i	0.0227145	+	0.292194i
$313$	1.73318e12			0.576930			0.288465	−	0.957490i	$-0.406855\pi$
$313$	1.73318e12			0.576930			0.288465	+	0.957490i	$0.406855\pi$
$314$		−	2.19785e12i		−	0.720029i
$315$	−2.94836e10	−	1.88489e11i	−0.00950664	−	0.0607761i
$316$	9.55536e11			0.303258
$317$		−	1.33100e12i		−	0.415798i	−0.978150	−	0.207899i	$-0.933337\pi$
$317$		−	1.33100e12i		−	0.415798i	0.978150	−	0.207899i	$-0.0666625\pi$
$318$	2.51727e12	−	1.95687e11i	0.774094	−	0.0601764i
$319$	6.93538e12			2.09950
$320$			6.46716e11i			0.192737i
$321$	−4.54267e11	−	5.84358e12i	−0.133286	−	1.71456i
$322$	8.45937e10			0.0244376
$323$		−	1.04290e12i		−	0.296641i
$324$	−1.69996e12	+	5.45157e11i	−0.476117	+	0.152685i
$325$	−4.14010e12			−1.14181
$326$			3.15518e12i			0.856911i
$327$	−1.31655e12	+	1.02345e11i	−0.352126	+	0.0273735i
$328$	−4.15973e11			−0.109571
$329$			2.20522e10i			0.00572100i
$330$	−4.78988e11	−	6.16159e12i	−0.122393	−	1.57443i
$331$	4.71961e12			1.18786			0.593931	−	0.804516i	$-0.297575\pi$
$331$	4.71961e12			1.18786			0.593931	+	0.804516i	$0.297575\pi$
$332$			5.60959e11i			0.139072i
$333$	−4.99789e12	+	7.81775e11i	−1.22058	+	0.190924i
$334$	−2.84743e12			−0.685048
$335$			3.23208e12i			0.766051i
$336$	4.25849e10	−	3.31046e9i	0.00994396	−	0.000773022i
$337$	4.15283e12			0.955422			0.477711	−	0.878517i	$-0.341467\pi$
$337$	4.15283e12			0.955422			0.477711	+	0.878517i	$0.341467\pi$
$338$			9.75911e11i			0.221221i
$339$	2.62360e11	+	3.37493e12i	0.0586001	+	0.753818i
$340$	−1.65864e12			−0.365055
$341$			7.21658e12i			1.56516i
$342$	3.20301e11	+	2.04769e12i	0.0684585	+	0.437656i
$343$	−3.78515e11			−0.0797282
$344$		−	4.24313e11i		−	0.0880833i
$345$	6.50859e12	−	5.05963e11i	1.33165	−	0.103520i
$346$	−2.85687e12			−0.576115
$347$		−	4.39939e12i		−	0.874470i	−0.899347	−	0.437235i	$-0.855958\pi$
$347$		−	4.39939e12i		−	0.874470i	0.899347	−	0.437235i	$-0.144042\pi$
$348$	2.86691e11	+	3.68793e12i	0.0561718	+	0.722580i
$349$	−9.24002e12			−1.78462			−0.892310	−	0.451423i	$-0.850917\pi$
$349$	−9.24002e12			−1.78462			−0.892310	+	0.451423i	$0.850917\pi$
$350$			2.04091e11i			0.0388582i
$351$	4.29724e12	−	1.01862e12i	0.806592	−	0.191195i
$352$	1.38366e12			0.256046
$353$			9.20733e11i			0.167981i	0.996467	+	0.0839905i	$0.0267665\pi$
$353$			9.20733e11i			0.167981i	−0.996467	+	0.0839905i	$0.973233\pi$
$354$	−2.67878e12	+	2.08242e11i	−0.481860	+	0.0374587i
$355$	5.94255e12			1.05398
$356$		−	2.66177e12i		−	0.465500i
$357$	8.49037e9	+	1.09218e11i	0.00146415	+	0.0188345i
$358$	6.70999e12			1.14106
$359$		−	6.17595e12i		−	1.03569i	−0.855473	−	0.517847i	$-0.826733\pi$
$359$		−	6.17595e12i		−	1.03569i	0.855473	−	0.517847i	$-0.173267\pi$
$360$	3.25666e12	−	5.09409e11i	0.538592	−	0.0842470i
$361$	−3.72488e12			−0.607542
$362$		−	5.62180e12i		−	0.904342i
$363$	−6.89902e12	+	5.36315e11i	−1.09460	+	0.0850916i
$364$	−1.05665e11			−0.0165357
$365$		−	5.20995e12i		−	0.804209i
$366$	2.61201e10	+	3.36002e11i	0.00397712	+	0.0511607i
$367$	−8.19379e12			−1.23071			−0.615353	−	0.788252i	$-0.710987\pi$
$367$	−8.19379e12			−1.23071			−0.615353	+	0.788252i	$0.710987\pi$
$368$			1.46159e12i			0.216564i
$369$	3.27656e11	+	2.09471e12i	0.0478945	+	0.306190i
$370$	9.34034e12			1.34696
$371$			3.07903e11i			0.0438072i
$372$	−3.83746e12	+	2.98315e11i	−0.538677	+	0.0418756i
$373$	−9.07322e12			−1.25666			−0.628329	−	0.777947i	$-0.716261\pi$
$373$	−9.07322e12			−1.25666			−0.628329	+	0.777947i	$0.716261\pi$
$374$			3.54870e12i			0.484966i
$375$	3.34481e11	+	4.30269e12i	0.0451041	+	0.580208i
$376$	−3.81012e11			−0.0506990
$377$		−	9.15072e12i		−	1.20157i
$378$	−5.02140e10	−	2.11837e11i	−0.00650677	−	0.0274500i
$379$	1.17817e13			1.50665			0.753324	−	0.657650i	$-0.228449\pi$
$379$	1.17817e13			1.50665			0.753324	+	0.657650i	$0.228449\pi$
$380$		−	3.82683e12i		−	0.482971i
$381$	9.89455e12	−	7.69180e11i	1.23246	−	0.0958083i
$382$	−3.57627e12			−0.439657
$383$			6.82336e12i			0.827950i	0.910288	+	0.413975i	$0.135860\pi$
$383$			6.82336e12i			0.827950i	−0.910288	+	0.413975i	$0.864140\pi$
$384$	5.71972e10	+	7.35771e11i	0.00685045	+	0.0881225i
$385$	7.53664e11			0.0890993
$386$			8.56152e12i			0.999112i
$387$	−2.13670e12	+	3.34225e11i	−0.246144	+	0.0385021i
$388$	5.50249e12			0.625750
$389$			7.07814e11i			0.0794642i	0.999210	+	0.0397321i	$0.0126504\pi$
$389$			7.07814e11i			0.0794642i	−0.999210	+	0.0397321i	$0.987350\pi$
$390$	−8.12977e12	+	6.31990e11i	−0.901063	+	0.0700466i
$391$	−3.74855e12			−0.410185
$392$		−	3.26733e12i		−	0.352991i
$393$	7.82526e11	+	1.00662e13i	0.0834710	+	1.07375i
$394$	−4.28577e12			−0.451386
$395$			8.99251e12i			0.935181i
$396$	−1.08989e12	−	6.96770e12i	−0.111920	−	0.715506i
$397$	1.26553e12			0.128328			0.0641639	−	0.997939i	$-0.479562\pi$
$397$	1.26553e12			0.128328			0.0641639	+	0.997939i	$0.479562\pi$
$398$		−	1.13803e12i		−	0.113956i
$399$	−2.51989e11	+	1.95890e10i	−0.0249182	+	0.00193708i
$400$	−3.52622e12			−0.344358
$401$			1.50259e13i			1.44917i	0.689187	+	0.724583i	$0.257968\pi$
$401$			1.50259e13i			1.44917i	−0.689187	+	0.724583i	$0.742032\pi$
$402$	2.85853e11	+	3.67714e12i	0.0272278	+	0.350252i
$403$	9.52175e12			0.895760
$404$			5.53749e12i			0.514525i
$405$	−5.13045e12	−	1.59983e13i	−0.470848	−	1.46824i
$406$	−4.51094e11			−0.0408919
$407$		−	1.99839e13i		−	1.78940i
$408$	−1.88704e12	+	1.46694e11i	−0.166909	+	0.0129752i
$409$	−1.70362e12			−0.148852			−0.0744261	−	0.997227i	$-0.523712\pi$
$409$	−1.70362e12			−0.148852			−0.0744261	+	0.997227i	$0.523712\pi$
$410$		−	3.91470e12i		−	0.337893i
$411$	−1.74310e12	−	2.24228e13i	−0.148632	−	1.91197i
$412$	1.45124e12			0.122251
$413$		−	3.27659e11i		−	0.0272692i
$414$	7.36009e12	−	1.15127e12i	0.605176	−	0.0946621i
$415$	−5.27917e12			−0.428869
$416$		−	1.82564e12i		−	0.146538i
$417$	1.92743e13	−	1.49834e12i	1.52862	−	0.118831i
$418$	−8.18758e12			−0.641615
$419$			2.22448e13i			1.72250i	0.508185	+	0.861248i	$0.330317\pi$
$419$			2.22448e13i			1.72250i	−0.508185	+	0.861248i	$0.669683\pi$
$420$	3.11546e10	+	4.00765e11i	0.00238383	+	0.0306650i
$421$	1.82948e11			0.0138330			0.00691650	−	0.999976i	$-0.497798\pi$
$421$	1.82948e11			0.0138330			0.00691650	+	0.999976i	$0.497798\pi$
$422$		−	1.07473e13i		−	0.803043i
$423$	3.00118e11	+	1.91865e12i	0.0221610	+	0.141676i
$424$	−5.31988e12			−0.388215
$425$		−	9.04375e12i		−	0.652235i
$426$	6.76086e12	−	5.25574e11i	0.481897	−	0.0374616i
$427$	−4.10986e10			−0.00289526
$428$			1.23495e13i			0.859869i
$429$	1.35216e12	+	1.73938e13i	0.0930552	+	1.19704i
$430$	3.99319e12			0.271630
$431$			6.64491e12i			0.446789i	0.974728	+	0.223395i	$0.0717139\pi$
$431$			6.64491e12i			0.446789i	−0.974728	+	0.223395i	$0.928286\pi$
$432$	3.66006e12	−	8.67584e11i	0.243259	−	0.0576624i
$433$	7.28337e12			0.478512			0.239256	−	0.970956i	$-0.423096\pi$
$433$	7.28337e12			0.478512			0.239256	+	0.970956i	$0.423096\pi$
$434$		−	4.69384e11i		−	0.0304846i
$435$	−3.47069e13	+	2.69804e12i	−2.22828	+	0.173222i
$436$	2.78233e12			0.176594
$437$		−	8.64868e12i		−	0.542678i
$438$	−4.60781e11	−	5.92738e12i	−0.0285841	−	0.367699i
$439$	−1.52600e13			−0.935907			−0.467954	−	0.883753i	$-0.655009\pi$
$439$	−1.52600e13			−0.935907			−0.467954	+	0.883753i	$0.655009\pi$
$440$			1.30216e13i			0.789590i
$441$	−1.64533e13	+	2.57363e12i	−0.986414	+	0.154296i
$442$	4.68225e12			0.277551
$443$		−	1.83304e13i		−	1.07437i	−0.843465	−	0.537184i	$-0.819488\pi$
$443$		−	1.83304e13i		−	1.07437i	0.843465	−	0.537184i	$-0.180512\pi$
$444$	1.06265e13	−	8.26083e11i	0.615852	−	0.0478750i
$445$	2.50498e13			1.43550
$446$			5.33057e12i			0.302064i
$447$	1.52138e12	+	1.95706e13i	0.0852508	+	1.09665i
$448$	−8.99970e10			−0.00498698
$449$			8.33876e12i			0.456951i	0.973550	+	0.228475i	$0.0733741\pi$
$449$			8.33876e12i			0.456951i	−0.973550	+	0.228475i	$0.926626\pi$
$450$	2.77756e12	+	1.77570e13i	0.150522	+	0.962290i
$451$	−8.37559e12			−0.448883
$452$		−	7.13242e12i		−	0.378046i
$453$	7.47774e12	−	5.81303e11i	0.391994	−	0.0304727i
$454$	9.66249e12			0.500968
$455$		−	9.94405e11i		−	0.0509925i
$456$	−3.38454e11	−	4.35379e12i	−0.0171663	−	0.220823i
$457$	4.12288e11			0.0206833			0.0103416	−	0.999947i	$-0.496708\pi$
$457$	4.12288e11			0.0206833			0.0103416	+	0.999947i	$0.496708\pi$
$458$		−	2.34581e13i		−	1.16403i
$459$	2.22510e12	+	9.38700e12i	0.109216	+	0.460748i
$460$	−1.37549e13			−0.667836
$461$			1.66247e11i			0.00798453i	0.999992	+	0.00399226i	$0.00127078\pi$
$461$			1.66247e11i			0.00798453i	−0.999992	+	0.00399226i	$0.998729\pi$
$462$	8.57446e11	−	6.66559e10i	0.0407377	−	0.00316686i
$463$	1.27323e13			0.598416			0.299208	−	0.954188i	$-0.403278\pi$
$463$	1.27323e13			0.598416			0.299208	+	0.954188i	$0.403278\pi$
$464$		−	7.79389e12i		−	0.362380i
$465$	−2.80743e12	−	3.61142e13i	−0.129135	−	1.66116i
$466$	−2.34795e13			−1.06846
$467$		−	2.26689e13i		−	1.02058i	−0.860004	−	0.510288i	$-0.829539\pi$
$467$		−	2.26689e13i		−	1.02058i	0.860004	−	0.510288i	$-0.170461\pi$
$468$	−9.19337e12	+	1.43803e12i	−0.409492	+	0.0640531i
$469$	−4.49775e11			−0.0198213
$470$		−	3.58569e12i		−	0.156345i
$471$	2.35321e13	−	1.82934e12i	1.01521	−	0.0789203i
$472$	5.66120e12			0.241657
$473$		−	8.54352e12i		−	0.360854i
$474$	7.95321e11	+	1.02308e13i	0.0332392	+	0.427581i
$475$	2.08658e13			0.862913
$476$		−	2.30816e11i		−	0.00944565i
$477$	4.19039e12	+	2.67892e13i	0.169693	+	1.08485i
$478$	−2.79873e13			−1.12156
$479$		−	2.39654e13i		−	0.950402i	−0.879877	−	0.475201i	$-0.842375\pi$
$479$		−	2.39654e13i		−	0.950402i	0.879877	−	0.475201i	$-0.157625\pi$
$480$	−6.92432e12	+	5.38281e11i	−0.271751	+	0.0211253i
$481$	−2.63673e13			−1.02409
$482$			2.35126e13i			0.903785i
$483$	7.04098e10	+	9.05734e11i	0.00267853	+	0.0344560i
$484$	1.45801e13			0.548950
$485$			5.17838e13i			1.92968i
$486$	−7.25186e12	−	1.77475e13i	−0.267466	−	0.654570i
$487$	−1.13824e13			−0.415516			−0.207758	−	0.978180i	$-0.566617\pi$
$487$	−1.13824e13			−0.415516			−0.207758	+	0.978180i	$0.566617\pi$
$488$		−	7.10091e11i		−	0.0256575i
$489$	−3.37821e13	+	2.62615e12i	−1.20821	+	0.0939235i
$490$	3.07488e13			1.08855
$491$			3.59512e13i			1.25981i	0.776672	+	0.629906i	$0.216906\pi$
$491$			3.59512e13i			1.25981i	−0.776672	+	0.629906i	$0.783094\pi$
$492$	−3.46226e11	−	4.45377e12i	−0.0120098	−	0.154491i
$493$	1.99891e13			0.686370
$494$			1.08029e13i			0.367203i
$495$	6.55727e13	−	1.02569e13i	2.20647	−	0.345137i
$496$	8.10990e12			0.270151
$497$			8.26965e11i			0.0272713i
$498$	−6.00612e12	+	4.66903e11i	−0.196086	+	0.0152433i
$499$	−1.33630e13			−0.431917			−0.215958	−	0.976403i	$-0.569288\pi$
$499$	−1.33630e13			−0.431917			−0.215958	+	0.976403i	$0.569288\pi$
$500$		−	9.09310e12i		−	0.290979i
$501$	−2.37000e12	−	3.04871e13i	−0.0750862	−	0.965890i
$502$	1.28248e13			0.402283
$503$			3.54934e13i			1.10232i	0.834399	+	0.551160i	$0.185815\pi$
$503$			3.54934e13i			1.10232i	−0.834399	+	0.551160i	$0.814185\pi$
$504$	7.08893e10	+	4.53196e11i	0.00217986	+	0.0139359i
$505$	−5.21132e13			−1.58668
$506$			2.94290e13i			0.887203i
$507$	−1.04490e13	+	8.12280e11i	−0.311913	+	0.0242474i
$508$	−2.09107e13			−0.618087
$509$		−	6.07337e13i		−	1.77763i	−0.458269	−	0.888813i	$-0.651530\pi$
$509$		−	6.07337e13i		−	1.77763i	0.458269	−	0.888813i	$-0.348470\pi$
$510$	−1.38054e12	−	1.77589e13i	−0.0400126	−	0.514712i
$511$	7.25016e11			0.0208086
$512$		−	1.55494e12i		−	0.0441942i
$513$	−2.16577e13	+	5.13377e12i	−0.609574	+	0.144494i
$514$	2.89501e13			0.806928
$515$			1.36576e13i			0.376997i
$516$	4.54307e12	−	3.53168e11i	0.124194	−	0.00965456i
$517$	−7.67166e12			−0.207700
$518$			1.29980e12i			0.0348520i
$519$	−2.37785e12	−	3.05881e13i	−0.0631464	−	0.812299i
$520$	1.71811e13			0.451891
$521$		−	2.06244e13i		−	0.537270i	−0.963242	−	0.268635i	$-0.913427\pi$
$521$		−	2.06244e13i		−	0.537270i	0.963242	−	0.268635i	$-0.0865726\pi$
$522$	−3.92476e13	+	6.13914e12i	−1.01265	+	0.158400i
$523$	5.24376e13			1.34009			0.670045	−	0.742320i	$-0.266275\pi$
$523$	5.24376e13			1.34009			0.670045	+	0.742320i	$0.266275\pi$
$524$		−	2.12735e13i		−	0.538495i
$525$	−2.18517e12	+	1.69871e11i	−0.0547885	+	0.00425914i
$526$	3.81460e13			0.947370
$527$			2.07996e13i			0.511683i
$528$	1.15166e12	+	1.48147e13i	0.0280644	+	0.361014i
$529$	1.03402e13			0.249603
$530$		−	5.00652e13i		−	1.19717i
$531$	−4.45925e12	−	2.85080e13i	−0.105631	−	0.675297i
$532$	5.32541e11			0.0124967
$533$			1.10510e13i			0.256900i
$534$	2.84992e13	−	2.21547e12i	0.656337	−	0.0510221i
$535$	−1.16221e14			−2.65165
$536$		−	7.77110e12i		−	0.175654i
$537$	5.58492e12	+	7.18431e13i	0.125068	+	1.60884i
$538$	−3.03260e13			−0.672828
$539$		−	6.57877e13i		−	1.44611i
$540$	8.16480e12	+	3.44447e13i	0.177818	+	0.750159i
$541$	8.20249e13			1.76994			0.884972	−	0.465645i	$-0.154178\pi$
$541$	8.20249e13			1.76994			0.884972	+	0.465645i	$0.154178\pi$
$542$			3.96770e13i			0.848286i
$543$	6.01919e13	−	4.67919e12i	1.27509	−	0.0991223i
$544$	3.98798e12			0.0837064
$545$			2.61844e13i			0.544578i
$546$	−8.79477e10	−	1.13134e12i	−0.00181243	−	0.0233147i
$547$	−1.62332e13			−0.331488			−0.165744	−	0.986169i	$-0.553003\pi$
$547$	−1.62332e13			−0.331488			−0.165744	+	0.986169i	$0.553003\pi$
$548$			4.73872e13i			0.958867i
$549$	−3.57580e12	+	5.59329e11i	−0.0716987	+	0.0112152i
$550$	−7.10004e13			−1.41074
$551$			4.61189e13i			0.908074i
$552$	−1.56490e13	+	1.21652e12i	−0.305346	+	0.0237369i
$553$	−1.25140e12			−0.0241974
$554$		−	3.83715e13i		−	0.735292i
$555$	7.77424e12	+	1.00006e14i	0.147636	+	1.89916i
$556$	−4.07335e13			−0.766615
$557$		−	1.12168e13i		−	0.209215i	−0.994514	−	0.104608i	$-0.966641\pi$
$557$		−	1.12168e13i		−	0.209215i	0.994514	−	0.104608i	$-0.0333587\pi$
$558$	−6.38805e12	−	4.08389e13i	−0.118086	−	0.754924i
$559$	−1.12726e13			−0.206521
$560$		−	8.46958e11i		−	0.0153788i
$561$	−3.79955e13	+	2.95369e12i	−0.683783	+	0.0531557i
$562$	5.52506e12			0.0985497
$563$		−	7.98522e13i		−	1.41171i	−0.708357	−	0.705854i	$-0.750563\pi$
$563$		−	7.98522e13i		−	1.41171i	0.708357	−	0.705854i	$-0.249437\pi$
$564$	−3.17127e11	−	4.07945e12i	−0.00555697	−	0.0714835i
$565$	6.71230e13			1.16581
$566$			2.25462e13i			0.388142i
$567$	2.22632e12	−	7.13953e11i	0.0379902	−	0.0121830i
$568$	−1.42881e13			−0.241675
$569$		−	9.95594e11i		−	0.0166925i	−0.999965	−	0.00834624i	$-0.997343\pi$
$569$		−	9.95594e11i		−	0.0166925i	0.999965	−	0.00834624i	$-0.00265672\pi$
$570$	4.09734e13	−	3.18518e12i	0.680969	−	0.0529370i
$571$	1.07836e14			1.77657			0.888283	−	0.459297i	$-0.151899\pi$
$571$	1.07836e14			1.77657			0.888283	+	0.459297i	$0.151899\pi$
$572$		−	3.67593e13i		−	0.600326i
$573$	−2.97664e12	−	3.82907e13i	−0.0481895	−	0.619899i
$574$	5.44769e11			0.00874285
$575$		−	7.49989e13i		−	1.19321i
$576$	−7.83021e12	+	1.22481e12i	−0.123498	+	0.0193177i
$577$	3.31000e13			0.517546			0.258773	−	0.965938i	$-0.416682\pi$
$577$	3.31000e13			0.517546			0.258773	+	0.965938i	$0.416682\pi$
$578$		−	3.53887e13i		−	0.548562i
$579$	−9.16671e13	+	7.12600e12i	−1.40871	+	0.109510i
$580$	7.33480e13			1.11750
$581$		−	7.34648e11i		−	0.0110968i
$582$	4.57989e12	+	5.89145e13i	0.0685867	+	0.882282i
$583$	−1.07116e14			−1.59041
$584$			1.25266e13i			0.184404i
$585$	−1.35333e13	−	8.65184e13i	−0.197526	−	1.26278i
$586$	−3.56543e13			−0.515969
$587$			1.21022e14i			1.73650i	0.496131	+	0.868248i	$0.334754\pi$
$587$			1.21022e14i			1.73650i	−0.496131	+	0.868248i	$0.665246\pi$
$588$	3.49830e13	−	2.71950e12i	0.497703	−	0.0386903i
$589$	−4.79889e13			−0.676961
$590$			5.32774e13i			0.745217i
$591$	−3.56717e12	−	4.58873e13i	−0.0494751	−	0.636436i
$592$	−2.24576e13			−0.308855
$593$		−	8.43944e12i		−	0.115091i	−0.998343	−	0.0575453i	$-0.981673\pi$
$593$		−	8.43944e12i		−	0.115091i	0.998343	−	0.0575453i	$-0.0183274\pi$
$594$	7.36952e13	−	1.74688e13i	0.996567	−	0.236227i
$595$	2.17220e12			0.0291283
$596$		−	4.13596e13i		−	0.549977i
$597$	1.21847e13	−	9.47213e11i	0.160673	−	0.0124904i
$598$	3.88294e13			0.507756
$599$			3.11882e13i			0.404443i	0.979340	+	0.202221i	$0.0648160\pi$
$599$			3.11882e13i			0.404443i	−0.979340	+	0.202221i	$0.935184\pi$
$600$	−2.93498e12	−	3.77549e13i	−0.0377441	−	0.485531i
$601$	2.87401e13			0.366535			0.183267	−	0.983063i	$-0.441333\pi$
$601$	2.87401e13			0.366535			0.183267	+	0.983063i	$0.441333\pi$
$602$			5.55692e11i			0.00702832i
$603$	−3.91328e13	+	6.12119e12i	−0.490857	+	0.0767802i
$604$	−1.58031e13			−0.196588
$605$			1.37212e14i			1.69284i
$606$	−5.92893e13	+	4.60902e12i	−0.725459	+	0.0563956i
$607$	−4.47536e13			−0.543106			−0.271553	−	0.962423i	$-0.587537\pi$
$607$	−4.47536e13			−0.543106			−0.271553	+	0.962423i	$0.587537\pi$
$608$			9.20110e12i			0.110744i
$609$	−3.75459e11	−	4.82981e12i	−0.00448204	−	0.0576559i
$610$	6.68264e12			0.0791223
$611$			1.01222e13i			0.118869i
$612$	−3.14128e12	−	2.00822e13i	−0.0365889	−	0.233913i
$613$	6.78051e13			0.783358			0.391679	−	0.920102i	$-0.371894\pi$
$613$	6.78051e13			0.783358			0.391679	+	0.920102i	$0.371894\pi$
$614$			7.46303e13i			0.855211i
$615$	4.19143e13	−	3.25832e12i	0.476416	−	0.0370355i
$616$	−1.81209e12			−0.0204303
$617$		−	2.48261e12i		−	0.0277641i	−0.999904	−	0.0138820i	$-0.995581\pi$
$617$		−	2.48261e12i		−	0.0277641i	0.999904	−	0.0138820i	$-0.00441893\pi$
$618$	1.20791e12	+	1.55383e13i	0.0133996	+	0.172370i
$619$	1.64000e13			0.180464			0.0902320	−	0.995921i	$-0.471239\pi$
$619$	1.64000e13			0.180464			0.0902320	+	0.995921i	$0.471239\pi$
$620$			7.63220e13i			0.833088i
$621$	1.84526e13	+	7.78454e13i	0.199801	+	0.842898i
$622$	3.78559e13			0.406613
$623$			3.48592e12i			0.0371431i
$624$	1.95470e13	−	1.51954e12i	0.206612	−	0.0160616i
$625$	−4.57873e13			−0.480114
$626$		−	3.92175e13i		−	0.407951i
$627$	−6.81476e12	−	8.76635e13i	−0.0703255	−	0.904651i
$628$	−4.97317e13			−0.509138
$629$		−	5.75973e13i		−	0.584991i
$630$	−4.26501e12	+	6.67137e11i	−0.0429752	+	0.00672221i
$631$	−1.37258e13			−0.137211			−0.0686056	−	0.997644i	$-0.521855\pi$
$631$	−1.37258e13			−0.137211			−0.0686056	+	0.997644i	$0.521855\pi$
$632$		−	2.16213e13i		−	0.214435i
$633$	1.15070e14	−	8.94532e12i	1.13226	−	0.0880192i
$634$	−3.01171e13			−0.294014
$635$		−	1.96790e14i		−	1.90605i
$636$	−4.42789e12	−	5.69593e13i	−0.0425511	−	0.547367i
$637$	−8.68020e13			−0.827623
$638$		−	1.56930e14i		−	1.48457i
$639$	1.12545e13	+	7.19503e13i	0.105639	+	0.675349i
$640$	1.46335e13			0.136285
$641$		−	5.42348e13i		−	0.501173i	−0.968094	−	0.250587i	$-0.919377\pi$
$641$		−	5.42348e13i		−	0.501173i	0.968094	−	0.250587i	$-0.0806235\pi$
$642$	−1.32225e14	+	1.02789e13i	−1.21238	+	0.0942477i
$643$	−5.54693e13			−0.504659			−0.252329	−	0.967641i	$-0.581197\pi$
$643$	−5.54693e13			−0.504659			−0.252329	+	0.967641i	$0.581197\pi$
$644$		−	1.91414e12i		−	0.0172800i
$645$	3.32365e12	+	4.27546e13i	0.0297726	+	0.382987i
$646$	−2.35982e13			−0.209757
$647$			5.56652e13i			0.490979i	0.969399	+	0.245489i	$0.0789486\pi$
$647$			5.56652e13i			0.490979i	−0.969399	+	0.245489i	$0.921051\pi$
$648$	1.23355e13	+	3.84657e13i	0.107965	+	0.336665i
$649$	1.13988e14			0.990002
$650$			9.36799e13i			0.807383i
$651$	5.02564e12	−	3.90682e11i	0.0429820	−	0.00334132i
$652$	7.13935e13			0.605927
$653$		−	5.56792e13i		−	0.468951i	−0.972122	−	0.234475i	$-0.924663\pi$
$653$		−	5.56792e13i		−	0.468951i	0.972122	−	0.234475i	$-0.0753372\pi$
$654$	2.31581e12	+	2.97901e13i	0.0193560	+	0.248991i
$655$	2.00204e14			1.66060
$656$			9.41238e12i			0.0774784i
$657$	6.30802e13	−	9.86706e12i	0.515307	−	0.0806048i
$658$	4.98984e11			0.00404536
$659$			1.52699e14i			1.22860i	0.789074	+	0.614298i	$0.210561\pi$
$659$			1.52699e14i			1.22860i	−0.789074	+	0.614298i	$0.789439\pi$
$660$	−1.39421e14	+	1.08383e13i	−1.11329	+	0.0865446i
$661$	−2.08036e14			−1.64866			−0.824329	−	0.566111i	$-0.808447\pi$
$661$	−2.08036e14			−1.64866			−0.824329	+	0.566111i	$0.808447\pi$
$662$		−	1.06793e14i		−	0.839945i
$663$	3.89717e12	+	5.01323e13i	0.0304216	+	0.391336i
$664$	1.26931e13			0.0983390
$665$			5.01172e12i			0.0385371i
$666$	1.76895e13	+	1.13089e14i	0.135004	+	0.863080i
$667$	1.65767e14			1.25565
$668$			6.44300e13i			0.484402i
$669$	−5.70737e13	+	4.43679e12i	−0.425898	+	0.0331084i
$670$	7.31335e13			0.541680
$671$		−	1.42977e13i		−	0.105112i
$672$	−7.49071e10	−	9.63587e11i	−0.000546609	−	0.00703144i
$673$	−9.45260e13			−0.684662			−0.342331	−	0.939579i	$-0.611216\pi$
$673$	−9.45260e13			−0.684662			−0.342331	+	0.939579i	$0.611216\pi$
$674$		−	9.39679e13i		−	0.675585i
$675$	−1.87810e14	+	4.45186e13i	−1.34029	+	0.317704i
$676$	2.20824e13			0.156427
$677$		−	1.70106e14i		−	1.19612i	−0.801451	−	0.598060i	$-0.795938\pi$
$677$		−	1.70106e14i		−	1.19612i	0.801451	−	0.598060i	$-0.204062\pi$
$678$	7.63660e13	−	5.93652e12i	0.533030	−	0.0414366i
$679$	−7.20622e12			−0.0499297
$680$			3.75308e13i			0.258133i
$681$	8.04237e12	+	1.03455e14i	0.0549096	+	0.706344i
$682$	1.63293e14			1.10674
$683$			2.23578e14i			1.50427i	0.659009	+	0.752135i	$0.270976\pi$
$683$			2.23578e14i			1.50427i	−0.659009	+	0.752135i	$0.729024\pi$
$684$	4.63338e13	−	7.24758e12i	0.309469	−	0.0484075i
$685$	−4.45960e14			−2.95694
$686$			8.56481e12i			0.0563764i
$687$	2.51163e14	−	1.95249e13i	1.64124	−	0.127586i
$688$	−9.60110e12			−0.0622843
$689$			1.41331e14i			0.910210i
$690$	−1.14486e13	−	1.47273e14i	−0.0731996	−	0.941622i
$691$	−1.10134e13			−0.0699090			−0.0349545	−	0.999389i	$-0.511129\pi$
$691$	−1.10134e13			−0.0699090			−0.0349545	+	0.999389i	$0.511129\pi$
$692$			6.46435e13i			0.407375i
$693$	1.42735e12	+	9.12509e12i	0.00893029	+	0.0570915i
$694$	−9.95468e13			−0.618344
$695$		−	3.83341e14i		−	2.36408i
$696$	8.34482e13	−	6.48708e12i	0.510941	−	0.0397194i
$697$	−2.41401e13			−0.146749
$698$			2.09078e14i			1.26192i
$699$	−1.95426e13	−	2.51392e14i	−0.117111	−	1.50649i
$700$	4.61804e12			0.0274769
$701$		−	1.10962e14i		−	0.655516i	−0.944762	−	0.327758i	$-0.893707\pi$
$701$		−	1.10962e14i		−	0.655516i	0.944762	−	0.327758i	$-0.106293\pi$
$702$	−2.30488e13	−	9.72354e13i	−0.135195	−	0.570346i
$703$	1.32889e14			0.773948
$704$		−	3.13087e13i		−	0.181052i
$705$	3.83915e13	−	2.98447e12i	0.220440	−	0.0171365i
$706$	2.08338e13			0.118781
$707$		−	7.25206e12i		−	0.0410548i
$708$	4.71199e12	+	6.06138e13i	0.0264873	+	0.340726i
$709$	2.08219e14			1.16222			0.581112	−	0.813824i	$-0.302618\pi$
$709$	2.08219e14			1.16222			0.581112	+	0.813824i	$0.302618\pi$
$710$		−	1.34465e14i		−	0.745275i
$711$	−1.08878e14	+	1.70308e13i	−0.599229	+	0.0937318i
$712$	−6.02289e13			−0.329158
$713$			1.72489e14i			0.936080i
$714$	2.47132e12	−	1.92115e11i	0.0133180	−	0.00103531i
$715$	3.45940e14			1.85127
$716$		−	1.51830e14i		−	0.806848i
$717$	−2.32946e13	−	2.99656e14i	−0.122931	−	1.58135i
$718$	−1.39746e14			−0.732347
$719$			2.74910e14i			1.43069i	0.698771	+	0.715346i	$0.253731\pi$
$719$			2.74910e14i			1.43069i	−0.698771	+	0.715346i	$0.746269\pi$
$720$	−1.15266e13	−	7.36898e13i	−0.0595716	−	0.380842i
$721$	−1.90059e12			−0.00975465
$722$			8.42844e13i			0.429597i
$723$	−2.51746e14	+	1.95702e13i	−1.27430	+	0.0990613i
$724$	−1.27207e14			−0.639466
$725$			3.99930e14i			1.99661i
$726$	1.21354e13	+	1.56107e14i	0.0601688	+	0.773997i
$727$	−2.99071e14			−1.47266			−0.736330	−	0.676622i	$-0.763443\pi$
$727$	−2.99071e14			−1.47266			−0.736330	+	0.676622i	$0.763443\pi$
$728$			2.39092e12i			0.0116925i
$729$	1.83985e14	−	9.24165e13i	0.893602	−	0.448861i
$730$	−1.17888e14			−0.568662
$731$		−	2.46241e13i		−	0.117970i
$732$	7.60286e12	−	5.91030e11i	0.0361761	−	0.00281225i
$733$	1.19922e14			0.566734			0.283367	−	0.959012i	$-0.408549\pi$
$733$	1.19922e14			0.566734			0.283367	+	0.959012i	$0.408549\pi$
$734$			1.85404e14i			0.870241i
$735$	2.55931e13	+	3.29223e14i	0.119313	+	1.53481i
$736$	3.30719e13			0.153134
$737$		−	1.56471e14i		−	0.719608i
$738$	4.73978e13	−	7.41400e12i	0.216509	−	0.0338666i
$739$	−7.29345e13			−0.330911			−0.165455	−	0.986217i	$-0.552909\pi$
$739$	−7.29345e13			−0.330911			−0.165455	+	0.986217i	$0.552909\pi$
$740$		−	2.11348e14i		−	0.952443i
$741$	−1.15666e14	+	8.99158e12i	−0.517742	+	0.0402481i
$742$	6.96706e12			0.0309763
$743$		−	1.07061e14i		−	0.472809i	−0.971655	−	0.236405i	$-0.924031\pi$
$743$		−	1.07061e14i		−	0.472809i	0.971655	−	0.236405i	$-0.0759691\pi$
$744$	6.75011e12	+	8.68317e13i	0.0296105	+	0.380902i
$745$	3.89234e14			1.69601
$746$			2.05304e14i			0.888592i
$747$	−9.99815e12	−	6.39183e13i	−0.0429850	−	0.274803i
$748$	8.02979e13			0.342923
$749$		−	1.61733e13i		−	0.0686104i
$750$	9.73587e13	−	7.56845e12i	0.410269	−	0.0318934i
$751$	1.83777e14			0.769292			0.384646	−	0.923064i	$-0.374323\pi$
$751$	1.83777e14			0.769292			0.384646	+	0.923064i	$0.374323\pi$
$752$			8.62131e12i			0.0358496i
$753$	1.06744e13	+	1.37313e14i	0.0440931	+	0.567203i
$754$	−2.07057e14			−0.849638
$755$		−	1.48722e14i		−	0.606236i
$756$	−4.79332e12	+	1.13621e12i	−0.0194101	+	0.00460098i
$757$	−1.73049e14			−0.696130			−0.348065	−	0.937470i	$-0.613161\pi$
$757$	−1.73049e14			−0.696130			−0.348065	+	0.937470i	$0.613161\pi$
$758$		−	2.66589e14i		−	1.06536i
$759$	−3.15093e14	+	2.44946e13i	−1.25092	+	0.0972438i
$760$	−8.65912e13			−0.341512
$761$		−	1.10156e14i		−	0.431604i	−0.976437	−	0.215802i	$-0.930764\pi$
$761$		−	1.10156e14i		−	0.431604i	0.976437	−	0.215802i	$-0.0692365\pi$
$762$	−1.74046e13	−	2.23888e14i	−0.0677467	−	0.871477i
$763$	−3.64382e12			−0.0140907
$764$			8.09218e13i			0.310884i
$765$	1.88993e14	−	2.95625e13i	0.721338	−	0.112832i
$766$	1.54395e14			0.585449
$767$		−	1.50399e14i		−	0.566589i
$768$	1.66486e13	−	1.29423e12i	0.0623120	−	0.00484400i
$769$	2.30458e14			0.856959			0.428480	−	0.903551i	$-0.359049\pi$
$769$	2.30458e14			0.856959			0.428480	+	0.903551i	$0.359049\pi$
$770$		−	1.70535e13i		−	0.0630027i
$771$	2.40960e13	+	3.09965e14i	0.0884451	+	1.13774i
$772$	1.93725e14			0.706479
$773$		−	1.50965e14i		−	0.546991i	−0.961873	−	0.273495i	$-0.911820\pi$
$773$		−	1.50965e14i		−	0.546991i	0.961873	−	0.273495i	$-0.0881798\pi$
$774$	7.56265e12	+	4.83481e13i	0.0272251	+	0.174050i
$775$	−4.16146e14			−1.48846
$776$		−	1.24507e14i		−	0.442472i
$777$	−1.39168e13	+	1.08186e12i	−0.0491399	+	0.00382003i
$778$	1.60160e13			0.0561897
$779$		−	5.56961e13i		−	0.194150i
$780$	1.43003e13	+	1.83956e14i	0.0495305	+	0.637148i
$781$	−2.87690e14			−0.990079
$782$			8.48200e13i			0.290044i
$783$	−9.83979e13	−	4.15109e14i	−0.334331	−	1.41044i
$784$	−7.39313e13			−0.249602
$785$		−	4.68023e14i		−	1.57007i
$786$	2.27773e14	−	1.77065e13i	0.759257	−	0.0590229i
$787$	−3.42081e14			−1.13306			−0.566532	−	0.824039i	$-0.691715\pi$
$787$	−3.42081e14			−1.13306			−0.566532	+	0.824039i	$0.691715\pi$
$788$			9.69760e13i			0.319178i
$789$	3.17500e13	+	4.08424e14i	0.103839	+	1.33575i
$790$	2.03477e14			0.661273
$791$			9.34082e12i			0.0301649i
$792$	−1.57661e14	+	2.46615e13i	−0.505939	+	0.0791394i
$793$	−1.88647e13			−0.0601568
$794$		−	2.86357e13i		−	0.0907415i
$795$	5.36042e14	−	4.16707e13i	1.68796	−	0.131218i
$796$	−2.57506e13			−0.0805791
$797$			5.22986e14i			1.62629i	0.582059	+	0.813146i	$0.302247\pi$
$797$			5.22986e14i			1.62629i	−0.582059	+	0.813146i	$0.697753\pi$
$798$	4.43249e11	+	5.70185e12i	0.00136973	+	0.0176198i
$799$	−2.21112e13			−0.0679013
$800$			7.97893e13i			0.243498i
$801$	4.74415e13	+	3.03294e14i	0.143878	+	0.919816i
$802$	3.39997e14			1.02472
$803$			2.52223e14i			0.755453i
$804$	8.32043e13	−	6.46811e12i	0.247665	−	0.0192530i
$805$	1.80139e13			0.0532878
$806$		−	2.15453e14i		−	0.633398i
$807$	−2.52412e13	−	3.24697e14i	−0.0737468	−	0.948660i
$808$	1.25299e14			0.363824
$809$			3.45374e14i			0.996661i	0.866987	+	0.498331i	$0.166053\pi$
$809$			3.45374e14i			0.996661i	−0.866987	+	0.498331i	$0.833947\pi$
$810$	−3.61999e14	+	1.16089e14i	−1.03820	+	0.332940i
$811$	3.60870e14			1.02860			0.514301	−	0.857610i	$-0.328052\pi$
$811$	3.60870e14			1.02860			0.514301	+	0.857610i	$0.328052\pi$
$812$			1.02071e13i			0.0289149i
$813$	−4.24817e14	+	3.30243e13i	−1.19605	+	0.0929782i
$814$	−4.52183e14			−1.26530
$815$			6.71881e14i			1.86855i
$816$	3.31932e12	+	4.26989e13i	0.00917482	+	0.118023i
$817$	5.68128e13			0.156076
$818$			3.85484e13i			0.105254i
$819$	1.20399e13	−	1.88329e12i	0.0326741	−	0.00511090i
$820$	−8.85796e13			−0.238927
$821$		−	6.68322e14i		−	1.79172i	−0.444336	−	0.895860i	$-0.646560\pi$
$821$		−	6.68322e14i		−	1.79172i	0.444336	−	0.895860i	$-0.353440\pi$
$822$	−5.07370e14	+	3.94418e13i	−1.35196	+	0.105099i
$823$	4.35331e13			0.115298			0.0576488	−	0.998337i	$-0.481640\pi$
$823$	4.35331e13			0.115298			0.0576488	+	0.998337i	$0.481640\pi$
$824$		−	3.28379e13i		−	0.0864449i
$825$	−5.90957e13	−	7.60193e14i	−0.154627	−	1.98909i
$826$	−7.41407e12			−0.0192822
$827$		−	2.21008e13i		−	0.0571321i	−0.999592	−	0.0285661i	$-0.990906\pi$
$827$		−	2.21008e13i		−	0.0571321i	0.999592	−	0.0285661i	$-0.00909409\pi$
$828$	−2.60503e13	−	1.66540e14i	−0.0669362	−	0.427924i
$829$	7.62973e14			1.94866			0.974331	−	0.225119i	$-0.0722770\pi$
$829$	7.62973e14			1.94866			0.974331	+	0.225119i	$0.0722770\pi$
$830$			1.19454e14i			0.303256i
$831$	4.10839e14	−	3.19377e13i	1.03673	−	0.0805933i
$832$	−4.13096e13			−0.103618
$833$		−	1.89613e14i		−	0.472761i
$834$	−3.39037e13	−	4.36128e14i	−0.0840265	−	1.08090i
$835$	−6.06349e14			−1.49379
$836$			1.85264e14i			0.453690i
$837$	4.31940e14	−	1.02388e14i	1.05147	−	0.249241i
$838$	5.03342e14			1.21799
$839$		−	8.55289e13i		−	0.205732i	−0.994695	−	0.102866i	$-0.967199\pi$
$839$		−	8.55289e13i		−	0.205732i	0.994695	−	0.102866i	$-0.0328014\pi$
$840$	9.06828e12	−	7.04948e11i	0.0216835	−	0.00168562i
$841$	−4.63244e14			−1.10111
$842$		−	4.13963e12i		−	0.00978141i
$843$	4.59867e12	+	5.91561e13i	0.0108017	+	0.138951i
$844$	−2.43184e14			−0.567837
$845$			2.07816e14i			0.482387i
$846$	4.34142e13	−	6.79088e12i	0.100180	−	0.0156702i
$847$	−1.90945e13			−0.0438017
$848$			1.20375e14i			0.274509i
$849$	−2.41399e14	+	1.87658e13i	−0.547265	+	0.0425431i
$850$	−2.04637e14			−0.461200
$851$		−	4.77649e14i		−	1.07019i
$852$	−1.18924e13	−	1.52981e14i	−0.0264893	−	0.340752i
$853$	1.82179e14			0.403415			0.201708	−	0.979446i	$-0.435351\pi$
$853$	1.82179e14			0.403415			0.201708	+	0.979446i	$0.435351\pi$
$854$			9.29956e11i			0.00204726i
$855$	6.82067e13	+	4.36046e14i	0.149278	+	0.954337i
$856$	2.79438e14			0.608019
$857$			8.52398e14i			1.84390i	0.387305	+	0.921952i	$0.373406\pi$
$857$			8.52398e14i			1.84390i	−0.387305	+	0.921952i	$0.626594\pi$
$858$	3.93577e14	−	3.05958e13i	0.846435	−	0.0658000i
$859$	2.60062e14			0.556046			0.278023	−	0.960574i	$-0.410321\pi$
$859$	2.60062e14			0.556046			0.278023	+	0.960574i	$0.410321\pi$
$860$		−	9.03556e13i		−	0.192071i
$861$	4.53427e11	+	5.83278e12i	0.000958279	+	0.0123271i
$862$	1.50357e14			0.315928
$863$		−	2.71494e14i		−	0.567161i	−0.958948	−	0.283580i	$-0.908478\pi$
$863$		−	2.71494e14i		−	0.567161i	0.958948	−	0.283580i	$-0.0915223\pi$
$864$	−1.96312e13	−	8.28177e13i	−0.0407735	−	0.172010i
$865$	−6.08358e14			−1.25626
$866$		−	1.64804e14i		−	0.338359i
$867$	3.78903e14	−	2.94551e13i	0.773450	−	0.0601263i
$868$	−1.06210e13			−0.0215558
$869$		−	4.35344e14i		−	0.878484i
$870$	6.10497e13	+	7.85328e14i	0.122486	+	1.57563i
$871$	−2.06452e14			−0.411840
$872$		−	6.29569e13i		−	0.124871i
$873$	−6.26979e14	+	9.80726e13i	−1.23646	+	0.193409i
$874$	−1.95697e14			−0.383732
$875$			1.19086e13i			0.0232177i
$876$	−1.34121e14	+	1.04263e13i	−0.260002	+	0.0202120i
$877$	1.90122e14			0.366466			0.183233	−	0.983069i	$-0.441344\pi$
$877$	1.90122e14			0.366466			0.183233	+	0.983069i	$0.441344\pi$
$878$			3.45295e14i			0.661786i
$879$	−2.96761e13	−	3.81746e14i	−0.0565539	−	0.727495i
$880$	2.94645e14			0.558324
$881$			6.12829e14i			1.15468i	0.816506	+	0.577338i	$0.195908\pi$
$881$			6.12829e14i			1.15468i	−0.816506	+	0.577338i	$0.804092\pi$
$882$	5.82347e13	+	3.72295e14i	0.109104	+	0.697500i
$883$	−4.57367e14			−0.852042			−0.426021	−	0.904713i	$-0.640085\pi$
$883$	−4.57367e14			−0.852042			−0.426021	+	0.904713i	$0.640085\pi$
$884$		−	1.05947e14i		−	0.196258i
$885$	−5.70435e14	+	4.43443e13i	−1.05073	+	0.0816811i
$886$	−4.14769e14			−0.759693
$887$			5.97146e14i			1.08758i	0.839221	+	0.543791i	$0.183012\pi$
$887$			5.97146e14i			1.08758i	−0.839221	+	0.543791i	$0.816988\pi$
$888$	−1.86921e13	−	2.40451e14i	−0.0338527	−	0.435473i
$889$	2.73852e13			0.0493182
$890$		−	5.66812e14i		−	1.01505i
$891$	2.48375e14	+	7.74505e14i	0.442302	+	1.37923i
$892$	1.20617e14			0.213592
$893$		−	5.10150e13i		−	0.0898340i
$894$	4.42832e14	−	3.44248e13i	0.775446	−	0.0602815i
$895$	1.42886e15			2.48815
$896$			2.03640e12i			0.00352633i
$897$	3.23189e13	+	4.15742e14i	0.0556537	+	0.715916i
$898$	1.88685e14			0.323113
$899$		−	9.19792e14i		−	1.56636i
$900$	4.01794e14	−	6.28489e13i	0.680442	−	0.106435i
$901$	−3.08727e14			−0.519938
$902$			1.89518e14i			0.317408i
$903$	−5.94973e12	+	4.62519e11i	−0.00990965	+	0.000770354i
$904$	−1.61388e14			−0.267319
$905$		−	1.19714e15i		−	1.97198i
$906$	−1.31534e13	−	1.69202e14i	−0.0215475	−	0.277181i
$907$	−7.96198e14			−1.29713			−0.648567	−	0.761158i	$-0.724631\pi$
$907$	−7.96198e14			−1.29713			−0.648567	+	0.761158i	$0.724631\pi$
$908$		−	2.18637e14i		−	0.354238i
$909$	−9.86964e13	−	6.30967e14i	−0.159031	−	1.01669i
$910$	−2.25008e13			−0.0360571
$911$		−	5.95524e14i		−	0.949089i	−0.880231	−	0.474545i	$-0.842613\pi$
$911$		−	5.95524e14i		−	0.949089i	0.880231	−	0.474545i	$-0.157387\pi$
$912$	−9.85151e13	+	7.65834e12i	−0.156145	+	0.0121384i
$913$	2.55574e14			0.402869
$914$		−	9.32901e12i		−	0.0146253i
$915$	5.56216e12	+	7.15503e13i	0.00867237	+	0.111559i
$916$	−5.30796e14			−0.823096
$917$			2.78603e13i			0.0429675i
$918$	2.12403e14	−	5.03483e13i	0.325798	−	0.0772274i
$919$	5.55318e14			0.847157			0.423579	−	0.905859i	$-0.360774\pi$
$919$	5.55318e14			0.847157			0.423579	+	0.905859i	$0.360774\pi$
$920$			3.11239e14i			0.472231i
$921$	−7.99058e14	+	6.21170e13i	−1.20581	+	0.0937373i
$922$	3.76174e12			0.00564591
$923$			3.79586e14i			0.566633i
$924$	−1.50825e12	−	1.94018e13i	−0.00223931	−	0.0288059i
$925$	1.15237e15			1.70171
$926$		−	2.88100e14i		−	0.423144i
$927$	−1.65361e14	+	2.58659e13i	−0.241566	+	0.0377859i
$928$	−1.76356e14			−0.256241
$929$		−	1.49292e14i		−	0.215754i	−0.994164	−	0.107877i	$-0.965595\pi$
$929$		−	1.49292e14i		−	0.215754i	0.994164	−	0.107877i	$-0.0344053\pi$
$930$	−8.17170e14	+	6.35250e13i	−1.17462	+	0.0913124i
$931$	4.37475e14			0.625468
$932$			5.31280e14i			0.755516i
$933$	3.15085e13	+	4.05318e14i	0.0445677	+	0.573308i
$934$	−5.12938e14			−0.721656
$935$			7.55681e14i			1.05750i
$936$	3.25390e13	+	2.08022e14i	0.0452924	+	0.289555i
$937$	−3.07315e14			−0.425487			−0.212743	−	0.977108i	$-0.568240\pi$
$937$	−3.07315e14			−0.425487			−0.212743	+	0.977108i	$0.568240\pi$
$938$			1.01773e13i			0.0140158i
$939$	4.19897e14	−	3.26419e13i	0.575195	−	0.0447143i
$940$	−8.11348e13			−0.110552
$941$			2.63150e14i			0.356661i	0.983971	+	0.178330i	$0.0570696\pi$
$941$			2.63150e14i			0.356661i	−0.983971	+	0.178330i	$0.942930\pi$
$942$	−4.13931e13	−	5.32471e14i	−0.0558051	−	0.717863i
$943$	−2.00191e14			−0.268464
$944$		−	1.28098e14i		−	0.170877i
$945$	−1.06929e13	−	4.51097e13i	−0.0141884	−	0.0598565i
$946$	−1.93318e14			−0.255162
$947$			1.20121e15i			1.57713i	0.614950	+	0.788566i	$0.289176\pi$
$947$			1.20121e15i			1.57713i	−0.614950	+	0.788566i	$0.710824\pi$
$948$	2.31497e14	−	1.79960e13i	0.302345	−	0.0235037i
$949$	3.32790e14			0.432354
$950$		−	4.72139e14i		−	0.610171i
$951$	−2.50674e13	−	3.22461e14i	−0.0322260	−	0.414547i
$952$	−5.22278e12			−0.00667908
$953$			3.27942e13i			0.0417189i	0.999782	+	0.0208594i	$0.00664025\pi$
$953$			3.27942e13i			0.0417189i	−0.999782	+	0.0208594i	$0.993360\pi$
$954$	6.06171e14	−	9.48177e13i	0.767102	−	0.119991i
$955$	−7.61552e14			−0.958700
$956$			6.33279e14i			0.793060i
$957$	1.68023e15	−	1.30617e14i	2.09319	−	0.162720i
$958$	−5.42276e14			−0.672036
$959$		−	6.20597e13i		−	0.0765097i
$960$	1.21799e13	+	1.56679e14i	0.0149378	+	0.192157i
$961$	1.37458e14			0.167708
$962$			5.96623e14i			0.724143i
$963$	−2.20110e14	−	1.40716e15i	−0.265771	−	1.69908i
$964$	5.32029e14			0.639072
$965$			1.82314e15i			2.17863i
$966$	2.04944e13	−	1.59319e12i	0.0243641	−	0.00189401i
$967$	−9.87053e14			−1.16737			−0.583684	−	0.811981i	$-0.698389\pi$
$967$	−9.87053e14			−1.16737			−0.583684	+	0.811981i	$0.698389\pi$
$968$		−	3.29909e14i		−	0.388166i
$969$	−1.96414e13	−	2.52663e14i	−0.0229908	−	0.295748i
$970$	1.17173e15			1.36449
$971$		−	5.42431e14i		−	0.628418i	−0.949354	−	0.314209i	$-0.898261\pi$
$971$		−	5.42431e14i		−	0.628418i	0.949354	−	0.314209i	$-0.101739\pi$
$972$	−4.01580e14	+	1.64091e14i	−0.462851	+	0.189127i
$973$	5.33457e13			0.0611695
$974$			2.57554e14i			0.293814i
$975$	−1.00302e15	+	7.79725e13i	−1.13838	+	0.0884949i
$976$	−1.60675e13			−0.0181426
$977$		−	9.53859e14i		−	1.07155i	−0.844361	−	0.535774i	$-0.820020\pi$
$977$		−	9.53859e14i		−	1.07155i	0.844361	−	0.535774i	$-0.179980\pi$
$978$	5.94229e13	+	7.64402e14i	0.0664140	+	0.854333i
$979$	−1.21271e15			−1.34847
$980$		−	6.95765e14i		−	0.769719i
$981$	−3.17031e14	+	4.95903e13i	−0.348945	+	0.0545823i
$982$	8.13482e14			0.890821
$983$		−	6.30884e14i		−	0.687356i	−0.939088	−	0.343678i	$-0.888327\pi$
$983$		−	6.30884e14i		−	0.687356i	0.939088	−	0.343678i	$-0.111673\pi$
$984$	−1.00777e14	+	7.83420e12i	−0.109241	+	0.00849218i
$985$	−9.12638e14			−0.984277
$986$		−	4.52301e14i		−	0.485337i
$987$	4.15319e11	+	5.34256e12i	0.000443400	+	0.00570379i
$988$	2.44442e14			0.259652
$989$		−	2.04205e14i		−	0.215816i
$990$	−2.32088e14	−	1.48374e15i	−0.244049	−	1.56021i
$991$	4.94498e14			0.517364			0.258682	−	0.965963i	$-0.416712\pi$
$991$	4.94498e14			0.517364			0.258682	+	0.965963i	$0.416712\pi$
$992$		−	1.83506e14i		−	0.191026i
$993$	1.14342e15	−	8.88866e13i	1.18429	−	0.0920640i
$994$	1.87121e13			0.0192837
$995$		−	2.42338e14i		−	0.248488i
$996$	1.05648e13	+	1.35903e14i	0.0107787	+	0.138654i
$997$	1.62993e15			1.65460			0.827301	−	0.561759i	$-0.189875\pi$
$997$	1.62993e15			1.65460			0.827301	+	0.561759i	$0.189875\pi$
$998$			3.02369e14i			0.305411i
$999$	−1.19611e15	+	2.83527e14i	−1.20211	+	0.284949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.11.b.a.5.2	✓	4
3.2	odd	2	inner	6.11.b.a.5.4	yes	4
4.3	odd	2		48.11.e.d.17.2		4
5.2	odd	4		150.11.b.a.149.5		8
5.3	odd	4		150.11.b.a.149.4		8
5.4	even	2		150.11.d.a.101.3		4
8.3	odd	2		192.11.e.h.65.3		4
8.5	even	2		192.11.e.g.65.2		4
9.2	odd	6		162.11.d.d.53.3		8
9.4	even	3		162.11.d.d.107.3		8
9.5	odd	6		162.11.d.d.107.2		8
9.7	even	3		162.11.d.d.53.2		8
12.11	even	2		48.11.e.d.17.1		4
15.2	even	4		150.11.b.a.149.3		8
15.8	even	4		150.11.b.a.149.6		8
15.14	odd	2		150.11.d.a.101.1		4
24.5	odd	2		192.11.e.g.65.1		4
24.11	even	2		192.11.e.h.65.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.2	✓	4	1.1	even	1	trivial
6.11.b.a.5.4	yes	4	3.2	odd	2	inner
48.11.e.d.17.1		4	12.11	even	2
48.11.e.d.17.2		4	4.3	odd	2
150.11.b.a.149.3		8	15.2	even	4
150.11.b.a.149.4		8	5.3	odd	4
150.11.b.a.149.5		8	5.2	odd	4
150.11.b.a.149.6		8	15.8	even	4
150.11.d.a.101.1		4	15.14	odd	2
150.11.d.a.101.3		4	5.4	even	2
162.11.d.d.53.2		8	9.7	even	3
162.11.d.d.53.3		8	9.2	odd	6
162.11.d.d.107.2		8	9.5	odd	6
162.11.d.d.107.3		8	9.4	even	3
192.11.e.g.65.1		4	24.5	odd	2
192.11.e.g.65.2		4	8.5	even	2
192.11.e.h.65.3		4	8.3	odd	2
192.11.e.h.65.4		4	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-22.6274i q^{2} +(242.269 - 18.8335i) q^{3} -512.000 q^{4} -4818.41i q^{5} +(-426.153 - 5481.92i) q^{6} +670.530 q^{7} +11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} +O(q^{10})\)	\(q-22.6274i q^{2} +(242.269 - 18.8335i) q^{3} -512.000 q^{4} -4818.41i q^{5} +(-426.153 - 5481.92i) q^{6} +670.530 q^{7} +11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} -109028. q^{10} +233268. i q^{11} +(-124042. + 9642.73i) q^{12} +307781. q^{13} -15172.4i q^{14} +(-90747.4 - 1.16735e6i) q^{15} +262144. q^{16} +672324. i q^{17} +(-206487. - 1.32007e6i) q^{18} -1.55119e6 q^{19} +2.46703e6i q^{20} +(162449. - 12628.4i) q^{21} +5.27826e6 q^{22} +5.57551e6i q^{23} +(218190. + 2.80674e6i) q^{24} -1.34515e7 q^{25} -6.96428e6i q^{26} +(1.39620e7 - 3.30957e6i) q^{27} -343311. q^{28} -2.97313e7i q^{29} +(-2.64142e7 + 2.05338e6i) q^{30} +3.09368e7 q^{31} -5.93164e6i q^{32} +(4.39325e6 + 5.65137e7i) q^{33} +1.52130e7 q^{34} -3.23089e6i q^{35} +(-2.98699e7 + 4.67227e6i) q^{36} -8.56690e7 q^{37} +3.50994e7i q^{38} +(7.45657e7 - 5.79657e6i) q^{39} +5.58225e7 q^{40} +3.59054e7i q^{41} +(-285748. - 3.67579e6i) q^{42} -3.66253e7 q^{43} -1.19433e8i q^{44} +(-4.39706e7 - 2.81104e8i) q^{45} +1.26159e8 q^{46} +3.28877e7i q^{47} +(6.35094e7 - 4.93708e6i) q^{48} -2.82026e8 q^{49} +3.04372e8i q^{50} +(1.26622e7 + 1.62883e8i) q^{51} -1.57584e8 q^{52} +4.59194e8i q^{53} +(-7.48870e7 - 3.15924e8i) q^{54} +1.12398e9 q^{55} +7.76824e6i q^{56} +(-3.75805e8 + 2.92143e7i) q^{57} -6.72743e8 q^{58} -4.88657e8i q^{59} +(4.64627e7 + 5.97684e8i) q^{60} -6.12928e7 q^{61} -7.00020e8i q^{62} +(3.91184e7 - 6.11894e6i) q^{63} -1.34218e8 q^{64} -1.48301e9i q^{65} +(1.27876e9 - 9.94079e7i) q^{66} -6.70776e8 q^{67} -3.44230e8i q^{68} +(1.05006e8 + 1.35077e9i) q^{69} -7.31067e7 q^{70} +1.23330e9i q^{71} +(1.05721e8 + 6.75878e8i) q^{72} +1.08126e9 q^{73} +1.93847e9i q^{74} +(-3.25888e9 + 2.53338e8i) q^{75} +7.94209e8 q^{76} +1.56413e8i q^{77} +(-1.31161e8 - 1.68723e9i) q^{78} -1.86628e9 q^{79} -1.26312e9i q^{80} +(3.32023e9 - 1.06476e9i) q^{81} +8.12446e8 q^{82} -1.09562e9i q^{83} +(-8.31737e7 + 6.46574e6i) q^{84} +3.23953e9 q^{85} +8.28736e8i q^{86} +(-5.59944e8 - 7.20298e9i) q^{87} -2.70247e9 q^{88} +5.19876e9i q^{89} +(-6.36066e9 + 9.94940e8i) q^{90} +2.06376e8 q^{91} -2.85466e9i q^{92} +(7.49503e9 - 5.82647e8i) q^{93} +7.44163e8 q^{94} +7.47427e9i q^{95} +(-1.11713e8 - 1.43705e9i) q^{96} -1.07471e10 q^{97} +6.38151e9i q^{98} +(2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9}+O(q^{10}) \) 4 * q + 84 * q^3 - 2048 * q^4 + 5376 * q^6 - 45112 * q^7 + 159012 * q^9	\( 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} - 53760 q^{10} - 43008 q^{12} + 275240 q^{13} - 1180800 q^{15} + 1048576 q^{16} - 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} + 7730688 q^{22} - 2752512 q^{24} - 33732380 q^{25} + 34619508 q^{27} + 23097344 q^{28} - 85731840 q^{30} - 21785848 q^{31} + 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} - 71014168 q^{37} + 217287240 q^{39} + 27525120 q^{40} - 145233408 q^{42} - 470688664 q^{43} + 312318720 q^{45} + 188814336 q^{46} + 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} - 140922880 q^{52} + 481662720 q^{54} + 2701359360 q^{55} - 1058753208 q^{57} - 1564177920 q^{58} + 604569600 q^{60} - 1184038744 q^{61} - 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} - 297365848 q^{67} + 596268288 q^{69} - 3962250240 q^{70} + 1488715776 q^{72} + 6534269000 q^{73} - 5150031180 q^{75} + 803188736 q^{76} - 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} + 8378668032 q^{82} - 4929540096 q^{84} - 12880512000 q^{85} + 210268800 q^{87} - 3958112256 q^{88} - 9243763200 q^{90} + 8317232080 q^{91} + 31744468392 q^{93} + 8505477120 q^{94} + 1409286144 q^{96} - 39176355064 q^{97} - 2626912512 q^{99}+O(q^{100}) \) 4 * q + 84 * q^3 - 2048 * q^4 + 5376 * q^6 - 45112 * q^7 + 159012 * q^9 - 53760 * q^10 - 43008 * q^12 + 275240 * q^13 - 1180800 * q^15 + 1048576 * q^16 - 2907648 * q^18 - 1568728 * q^19 + 9628008 * q^21 + 7730688 * q^22 - 2752512 * q^24 - 33732380 * q^25 + 34619508 * q^27 + 23097344 * q^28 - 85731840 * q^30 - 21785848 * q^31 + 25974144 * q^33 + 151087104 * q^34 - 81414144 * q^36 - 71014168 * q^37 + 217287240 * q^39 + 27525120 * q^40 - 145233408 * q^42 - 470688664 * q^43 + 312318720 * q^45 + 188814336 * q^46 + 22020096 * q^48 - 50058420 * q^49 - 708576768 * q^51 - 140922880 * q^52 + 481662720 * q^54 + 2701359360 * q^55 - 1058753208 * q^57 - 1564177920 * q^58 + 604569600 * q^60 - 1184038744 * q^61 - 905007096 * q^63 - 536870912 * q^64 + 3123445248 * q^66 - 297365848 * q^67 + 596268288 * q^69 - 3962250240 * q^70 + 1488715776 * q^72 + 6534269000 * q^73 - 5150031180 * q^75 + 803188736 * q^76 - 1322135040 * q^78 + 199282568 * q^79 + 1458964548 * q^81 + 8378668032 * q^82 - 4929540096 * q^84 - 12880512000 * q^85 + 210268800 * q^87 - 3958112256 * q^88 - 9243763200 * q^90 + 8317232080 * q^91 + 31744468392 * q^93 + 8505477120 * q^94 + 1409286144 * q^96 - 39176355064 * q^97 - 2626912512 * q^99

Introduction

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