LMFDB - Embedded newform 150.11.d.a.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,11,Mod(101,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("150.101");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	150.d (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:	$95.3035879011$
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:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.3
Root			$-4.10977 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	150.101
Dual form			150.11.d.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274i q^{2} +(-242.269 + 18.8335i) q^{3} -512.000 q^{4} +(-426.153 - 5481.92i) q^{6} -670.530 q^{7} -11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} +O(q^{10})$	\(q+22.6274i q^{2} +(-242.269 + 18.8335i) q^{3} -512.000 q^{4} +(-426.153 - 5481.92i) q^{6} -670.530 q^{7} -11585.2i q^{8} +(58339.6 - 9125.53i) q^{9} +233268. i q^{11} +(124042. - 9642.73i) q^{12} -307781. q^{13} -15172.4i q^{14} +262144. q^{16} -672324. i q^{17} +(206487. + 1.32007e6i) q^{18} -1.55119e6 q^{19} +(162449. - 12628.4i) q^{21} -5.27826e6 q^{22} -5.57551e6i q^{23} +(218190. + 2.80674e6i) q^{24} -6.96428e6i q^{26} +(-1.39620e7 + 3.30957e6i) q^{27} +343311. q^{28} -2.97313e7i q^{29} +3.09368e7 q^{31} +5.93164e6i q^{32} +(-4.39325e6 - 5.65137e7i) q^{33} +1.52130e7 q^{34} +(-2.98699e7 + 4.67227e6i) q^{36} +8.56690e7 q^{37} -3.50994e7i q^{38} +(7.45657e7 - 5.79657e6i) q^{39} +3.59054e7i q^{41} +(285748. + 3.67579e6i) q^{42} +3.66253e7 q^{43} -1.19433e8i q^{44} +1.26159e8 q^{46} -3.28877e7i q^{47} +(-6.35094e7 + 4.93708e6i) q^{48} -2.82026e8 q^{49} +(1.26622e7 + 1.62883e8i) q^{51} +1.57584e8 q^{52} -4.59194e8i q^{53} +(-7.48870e7 - 3.15924e8i) q^{54} +7.76824e6i q^{56} +(3.75805e8 - 2.92143e7i) q^{57} +6.72743e8 q^{58} -4.88657e8i q^{59} -6.12928e7 q^{61} +7.00020e8i q^{62} +(-3.91184e7 + 6.11894e6i) q^{63} -1.34218e8 q^{64} +(1.27876e9 - 9.94079e7i) q^{66} +6.70776e8 q^{67} +3.44230e8i q^{68} +(1.05006e8 + 1.35077e9i) q^{69} +1.23330e9i q^{71} +(-1.05721e8 - 6.75878e8i) q^{72} -1.08126e9 q^{73} +1.93847e9i q^{74} +7.94209e8 q^{76} -1.56413e8i q^{77} +(1.31161e8 + 1.68723e9i) q^{78} -1.86628e9 q^{79} +(3.32023e9 - 1.06476e9i) q^{81} -8.12446e8 q^{82} +1.09562e9i q^{83} +(-8.31737e7 + 6.46574e6i) q^{84} +8.28736e8i q^{86} +(5.59944e8 + 7.20298e9i) q^{87} +2.70247e9 q^{88} +5.19876e9i q^{89} +2.06376e8 q^{91} +2.85466e9i q^{92} +(-7.49503e9 + 5.82647e8i) q^{93} +7.44163e8 q^{94} +(-1.11713e8 - 1.43705e9i) q^{96} +1.07471e10 q^{97} -6.38151e9i q^{98} +(2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 43008 q^{12} - 275240 q^{13} + 1048576 q^{16} + 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} - 7730688 q^{22} - 2752512 q^{24} - 34619508 q^{27} - 23097344 q^{28} - 21785848 q^{31} - 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} + 71014168 q^{37} + 217287240 q^{39} + 145233408 q^{42} + 470688664 q^{43} + 188814336 q^{46} - 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} + 140922880 q^{52} + 481662720 q^{54} + 1058753208 q^{57} + 1564177920 q^{58} - 1184038744 q^{61} + 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} + 297365848 q^{67} + 596268288 q^{69} - 1488715776 q^{72} - 6534269000 q^{73} + 803188736 q^{76} + 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} - 8378668032 q^{82} - 4929540096 q^{84} - 210268800 q^{87} + 3958112256 q^{88} + 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 + 43008 * q^12 - 275240 * q^13 + 1048576 * q^16 + 2907648 * q^18 - 1568728 * q^19 + 9628008 * q^21 - 7730688 * q^22 - 2752512 * q^24 - 34619508 * q^27 - 23097344 * q^28 - 21785848 * q^31 - 25974144 * q^33 + 151087104 * q^34 - 81414144 * q^36 + 71014168 * q^37 + 217287240 * q^39 + 145233408 * q^42 + 470688664 * q^43 + 188814336 * q^46 - 22020096 * q^48 - 50058420 * q^49 - 708576768 * q^51 + 140922880 * q^52 + 481662720 * q^54 + 1058753208 * q^57 + 1564177920 * q^58 - 1184038744 * q^61 + 905007096 * q^63 - 536870912 * q^64 + 3123445248 * q^66 + 297365848 * q^67 + 596268288 * q^69 - 1488715776 * q^72 - 6534269000 * q^73 + 803188736 * q^76 + 1322135040 * q^78 + 199282568 * q^79 + 1458964548 * q^81 - 8378668032 * q^82 - 4929540096 * q^84 - 210268800 * q^87 + 3958112256 * q^88 + 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			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
$5$		0			0
$5$		0			0
$6$	−426.153	−	5481.92i	−0.0548036	−	0.704980i
$7$	−670.530			−0.0398959			−0.0199479	−	0.999801i	$-0.506350\pi$
$7$	−670.530			−0.0398959			−0.0199479	+	0.999801i	$0.506350\pi$
$8$		−	11585.2i		−	0.353553i
$9$	58339.6	−	9125.53i	0.987986	−	0.154542i
$10$		0			0
$11$			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	$-0.636033\pi$
$13$	−307781.			−0.828943			−0.414471	+	0.910062i	$0.636033\pi$
$14$		−	15172.4i		−	0.0282106i
$15$		0			0
$16$	262144.			0.250000
$17$		−	672324.i		−	0.473515i	−0.971569	−	0.236758i	$-0.923915\pi$
$17$		−	672324.i		−	0.473515i	0.971569	−	0.236758i	$-0.0760847\pi$
$18$	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	$0.601412\pi$
$20$		0			0
$21$	162449.	−	12628.4i	0.0397758	−	0.00309209i
$22$	−5.27826e6			−1.02418
$23$		−	5.57551e6i		−	0.866255i	−0.901333	−	0.433127i	$-0.857410\pi$
$23$		−	5.57551e6i		−	0.866255i	0.901333	−	0.433127i	$-0.142590\pi$
$24$	218190.	+	2.80674e6i	0.0274018	+	0.352490i
$25$		0			0
$26$		−	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	$-0.258049\pi$
$30$		0			0
$31$	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
$35$		0			0
$36$	−2.98699e7	+	4.67227e6i	−0.493993	+	0.0772708i
$37$	8.56690e7			1.23542			0.617711	−	0.786406i	$-0.288060\pi$
$37$	8.56690e7			1.23542			0.617711	+	0.786406i	$0.288060\pi$
$38$		−	3.50994e7i		−	0.442978i
$39$	7.45657e7	−	5.79657e6i	0.826449	−	0.0642463i
$40$		0			0
$41$			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	$-0.460245\pi$
$43$	3.66253e7			0.249137			0.124569	+	0.992211i	$0.460245\pi$
$44$		−	1.19433e8i		−	0.724206i
$45$		0			0
$46$	1.26159e8			0.612535
$47$		−	3.28877e7i		−	0.143398i	−0.997426	−	0.0716992i	$-0.977158\pi$
$47$		−	3.28877e7i		−	0.143398i	0.997426	−	0.0716992i	$-0.0228421\pi$
$48$	−6.35094e7	+	4.93708e6i	−0.249248	+	0.0193760i
$49$	−2.82026e8			−0.998408
$50$		0			0
$51$	1.26622e7	+	1.62883e8i	0.0366993	+	0.472091i
$52$	1.57584e8			0.414471
$53$		−	4.59194e8i		−	1.09804i	−0.835810	−	0.549019i	$-0.815002\pi$
$53$		−	4.59194e8i		−	1.09804i	0.835810	−	0.549019i	$-0.184998\pi$
$54$	−7.48870e7	−	3.15924e8i	−0.163094	−	0.688041i
$55$		0			0
$56$			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	$-0.111021\pi$
$60$		0			0
$61$	−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
$65$		0			0
$66$	1.27876e9	−	9.94079e7i	1.02110	−	0.0793782i
$67$	6.70776e8			0.496825			0.248413	−	0.968654i	$-0.420091\pi$
$67$	6.70776e8			0.496825			0.248413	+	0.968654i	$0.420091\pi$
$68$			3.44230e8i			0.236758i
$69$	1.05006e8	+	1.35077e9i	0.0671382	+	0.863649i
$70$		0			0
$71$			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	$-0.583982\pi$
$73$	−1.08126e9			−0.521573			−0.260787	+	0.965396i	$0.583982\pi$
$74$			1.93847e9i			0.873575i
$75$		0			0
$76$	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	$0.598074\pi$
$80$		0			0
$81$	3.32023e9	−	1.06476e9i	0.952234	−	0.305370i
$82$	−8.12446e8			−0.219142
$83$			1.09562e9i			0.278145i	0.990282	+	0.139072i	$0.0444121\pi$
$83$			1.09562e9i			0.278145i	−0.990282	+	0.139072i	$0.955588\pi$
$84$	−8.31737e7	+	6.46574e6i	−0.0198879	+	0.00154604i
$85$		0			0
$86$			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	$0.845874\pi$
$90$		0			0
$91$	2.06376e8			0.0330714
$92$			2.85466e9i			0.433127i
$93$	−7.49503e9	+	5.82647e8i	−1.07735	+	0.0837512i
$94$	7.44163e8			0.101398
$95$		0			0
$96$	−1.11713e8	−	1.43705e9i	−0.0137009	−	0.176245i
$97$	1.07471e10			1.25150			0.625750	−	0.780024i	$-0.284793\pi$
$97$	1.07471e10			1.25150			0.625750	+	0.780024i	$0.284793\pi$
$98$		−	6.38151e9i		−	0.705981i
$99$	2.12870e9	+	1.36088e10i	0.223840	+	1.43101i
$100$		0			0
$101$		−	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	$-0.460989\pi$
$103$	2.83446e9			0.244503			0.122251	+	0.992499i	$0.460989\pi$
$104$			3.56571e9i			0.293075i
$105$		0			0
$106$	1.03904e10			0.776430
$107$			2.41202e10i			1.71974i	0.510515	+	0.859869i	$0.329455\pi$
$107$			2.41202e10i			1.71974i	−0.510515	+	0.859869i	$0.670545\pi$
$108$	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	$0.556508\pi$
$110$		0			0
$111$	−2.07549e10	+	1.61344e9i	−1.23170	+	0.0957500i
$112$	−1.75775e8			−0.00997396
$113$		−	1.39305e10i		−	0.756092i	−0.925787	−	0.378046i	$-0.876596\pi$
$113$		−	1.39305e10i		−	0.756092i	0.925787	−	0.378046i	$-0.123404\pi$
$114$	6.61043e8	+	8.50350e9i	0.0343325	+	0.441645i
$115$		0			0
$116$			1.52224e10i			0.724760i
$117$	−1.79558e10	+	2.80866e9i	−0.818984	+	0.128106i
$118$	1.10570e10			0.483313
$119$			4.50813e8i			0.0188913i
$120$		0			0
$121$	−2.84767e10			−1.09790
$122$		−	1.38690e9i		−	0.0513151i
$123$	−6.76223e8	−	8.69877e9i	−0.0240195	−	0.308981i
$124$	−1.58396e10			−0.540303
$125$		0			0
$126$	−1.38456e8	−	8.85149e8i	−0.00435972	−	0.0278717i
$127$	−4.08412e10			−1.23617			−0.618087	−	0.786110i	$-0.712092\pi$
$127$	−4.08412e10			−1.23617			−0.618087	+	0.786110i	$0.712092\pi$
$128$		−	3.03700e9i		−	0.0883883i
$129$	−8.87317e9	+	6.89781e8i	−0.248388	+	0.0193091i
$130$		0			0
$131$			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
$135$		0			0
$136$	−7.78903e9			−0.167413
$137$			9.25532e10i			1.91773i	0.283854	+	0.958867i	$0.408387\pi$
$137$			9.25532e10i			1.91773i	−0.283854	+	0.958867i	$0.591613\pi$
$138$	−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	$0.221939\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$		−	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	$0.814636\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−3.81776e10	+	2.96785e9i	−0.413225	+	0.0321232i
$157$	−9.71322e10			−1.01828			−0.509138	−	0.860685i	$-0.670036\pi$
$157$	−9.71322e10			−1.01828			−0.509138	+	0.860685i	$0.670036\pi$
$158$		−	4.22291e10i		−	0.428871i
$159$	8.64822e9	+	1.11249e11i	0.0851023	+	1.09473i
$160$		0			0
$161$			3.73855e9i			0.0345600i
$162$	2.40928e10	+	7.51283e10i	0.215929	+	0.673331i
$163$	1.39440e11			1.21185			0.605927	−	0.795520i	$-0.292802\pi$
$163$	1.39440e11			1.21185			0.605927	+	0.795520i	$0.292802\pi$
$164$		−	1.83836e10i		−	0.154957i
$165$		0			0
$166$	−2.47911e10			−0.196678
$167$			1.25840e11i			0.968804i	0.874845	+	0.484402i	$0.160963\pi$
$167$			1.25840e11i			0.968804i	−0.874845	+	0.484402i	$0.839037\pi$
$168$	−1.46303e8	−	1.88201e9i	−0.00109322	−	0.0140629i
$169$	−4.31296e10			−0.312854
$170$		0			0
$171$	−9.04958e10	+	1.41554e10i	−0.618939	+	0.0968149i
$172$	−1.87521e10			−0.124569
$173$			1.26257e11i			0.814750i	0.913261	+	0.407375i	$0.133556\pi$
$173$			1.26257e11i			0.814750i	−0.913261	+	0.407375i	$0.866444\pi$
$174$	−1.62985e11	+	1.26701e10i	−1.02188	+	0.0794389i
$175$		0			0
$176$			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	$0.701171\pi$
$180$		0			0
$181$	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
$185$		0			0
$186$	−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
$190$		0			0
$191$		−	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	$-0.250283\pi$
$193$	3.78369e11			1.41296			0.706479	+	0.707734i	$0.250283\pi$
$194$			2.43178e11i			0.884944i
$195$		0			0
$196$	1.44397e11			0.499204
$197$			1.89406e11i			0.638356i	0.947695	+	0.319178i	$0.103407\pi$
$197$			1.89406e11i			0.638356i	−0.947695	+	0.319178i	$0.896593\pi$
$198$	−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	$0.474323\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$			6.41365e10i			0.172890i
$207$	−5.08795e10	−	3.25273e11i	−0.133872	−	0.855848i
$208$	−8.06828e10			−0.207236
$209$		−	3.61843e11i		−	0.907380i
$210$		0			0
$211$	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
$215$		0			0
$216$	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
$220$		0			0
$221$			2.06928e11i			0.392517i
$222$	−3.65081e10	−	4.69631e11i	−0.0677055	−	0.870947i
$223$	2.35580e11			0.427183			0.213592	−	0.976923i	$-0.431484\pi$
$223$	2.35580e11			0.427183			0.213592	+	0.976923i	$0.431484\pi$
$224$		−	3.97734e9i		−	0.00705266i
$225$		0			0
$226$	3.15211e11			0.534638
$227$		−	4.27026e11i		−	0.708475i	−0.935155	−	0.354238i	$-0.884740\pi$
$227$		−	4.27026e11i		−	0.708475i	0.935155	−	0.354238i	$-0.115260\pi$
$228$	−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	$0.192245\pi$
$230$		0			0
$231$	2.94580e9	+	3.78941e10i	0.00447862	+	0.0576119i
$232$	−3.44444e11			−0.512483
$233$			1.03766e12i			1.51103i	0.655130	+	0.755516i	$0.272614\pi$
$233$			1.03766e12i			1.51103i	−0.655130	+	0.755516i	$0.727386\pi$
$234$	−6.35527e10	−	4.06293e11i	−0.0905847	−	0.579109i
$235$		0			0
$236$			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	$-0.291513\pi$
$240$		0			0
$241$	−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
$245$		0			0
$246$	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
$250$		0			0
$251$			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
$255$		0			0
$256$	6.87195e10			0.0625000
$257$		−	1.27943e12i		−	1.14117i	−0.821239	−	0.570584i	$-0.806717\pi$
$257$		−	1.27943e12i		−	1.14117i	0.821239	−	0.570584i	$-0.193283\pi$
$258$	−1.56080e10	−	2.00777e11i	−0.0136536	−	0.175637i
$259$	−5.74436e10			−0.0492882
$260$		0			0
$261$	−2.71314e11	−	1.73451e12i	−0.224011	−	1.43211i
$262$	−9.40164e11			−0.761548
$263$		−	1.68583e12i		−	1.33978i	−0.742459	−	0.669892i	$-0.766340\pi$
$263$		−	1.68583e12i		−	1.33978i	0.742459	−	0.669892i	$-0.233660\pi$
$264$	−6.54725e11	+	5.08968e10i	−0.510551	+	0.0396891i
$265$		0			0
$266$			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	$-0.157827\pi$
$270$		0			0
$271$	−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
$275$		0			0
$276$	−5.37632e10	−	6.91597e11i	−0.0335691	−	0.431825i
$277$	−1.69580e12			−1.03986			−0.519930	−	0.854209i	$-0.674042\pi$
$277$	−1.69580e12			−1.03986			−0.519930	+	0.854209i	$0.674042\pi$
$278$			1.80018e12i			1.08416i
$279$	1.80484e12	−	2.82315e11i	1.06762	−	0.166999i
$280$		0			0
$281$			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	$-0.411502\pi$
$283$	9.96409e11			0.548916			0.274458	+	0.961599i	$0.411502\pi$
$284$		−	6.31450e11i		−	0.341781i
$285$		0			0
$286$	1.62455e12			0.848989
$287$		−	2.40756e10i		−	0.0123643i
$288$	5.41294e10	+	3.46050e11i	0.0273194	+	0.174653i
$289$	1.56397e12			0.775783
$290$		0			0
$291$	−2.60368e12	+	2.02404e11i	−1.24774	+	0.0969962i
$292$	5.53604e11			0.260787
$293$			1.57571e12i			0.729690i	0.931068	+	0.364845i	$0.118878\pi$
$293$			1.57571e12i			0.729690i	−0.931068	+	0.364845i	$0.881122\pi$
$294$	1.20186e11	+	1.54604e12i	0.0547163	+	0.703858i
$295$		0			0
$296$		−	9.92496e11i		−	0.436787i
$297$	−7.72018e11	−	3.25690e12i	−0.334076	−	1.40936i
$298$	−1.82785e12			−0.777786
$299$			1.71603e12i			0.718076i
$300$		0			0
$301$	−2.45583e10			−0.00993955
$302$			6.98405e11i			0.278018i
$303$	2.03692e11	+	2.62024e12i	0.0797554	+	1.02595i
$304$	−4.06635e11			−0.156616
$305$		0			0
$306$	8.87518e11	−	1.38826e11i	0.330803	−	0.0517445i
$307$	3.29823e12			1.20945			0.604726	−	0.796434i	$-0.293283\pi$
$307$	3.29823e12			1.20945			0.604726	+	0.796434i	$0.293283\pi$
$308$			8.00836e10i			0.0288928i
$309$	−6.86702e11	+	5.33827e10i	−0.243768	+	0.0189499i
$310$		0			0
$311$			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	$-0.593145\pi$
$313$	−1.73318e12			−0.576930			−0.288465	+	0.957490i	$0.593145\pi$
$314$		−	2.19785e12i		−	0.720029i
$315$		0			0
$316$	9.55536e11			0.303258
$317$			1.33100e12i			0.415798i	0.978150	+	0.207899i	$0.0666625\pi$
$317$			1.33100e12i			0.415798i	−0.978150	+	0.207899i	$0.933337\pi$
$318$	−2.51727e12	+	1.95687e11i	−0.774094	+	0.0601764i
$319$	6.93538e12			2.09950
$320$		0			0
$321$	−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
$325$		0			0
$326$			3.15518e12i			0.856911i
$327$	1.31655e12	−	1.02345e11i	0.352126	−	0.0273735i
$328$	4.15973e11			0.109571
$329$			2.20522e10i			0.00572100i
$330$		0			0
$331$	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
$335$		0			0
$336$	4.25849e10	−	3.31046e9i	0.00994396	−	0.000773022i
$337$	−4.15283e12			−0.955422			−0.477711	−	0.878517i	$-0.658533\pi$
$337$	−4.15283e12			−0.955422			−0.477711	+	0.878517i	$0.658533\pi$
$338$		−	9.75911e11i		−	0.221221i
$339$	2.62360e11	+	3.37493e12i	0.0586001	+	0.753818i
$340$		0			0
$341$			7.21658e12i			1.56516i
$342$	−3.20301e11	−	2.04769e12i	−0.0684585	−	0.437656i
$343$	3.78515e11			0.0797282
$344$		−	4.24313e11i		−	0.0880833i
$345$		0			0
$346$	−2.85687e12			−0.576115
$347$			4.39939e12i			0.874470i	0.899347	+	0.437235i	$0.144042\pi$
$347$			4.39939e12i			0.874470i	−0.899347	+	0.437235i	$0.855958\pi$
$348$	−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	$0.850917\pi$
$350$		0			0
$351$	4.29724e12	−	1.01862e12i	0.806592	−	0.191195i
$352$	−1.38366e12			−0.256046
$353$		−	9.20733e11i		−	0.167981i	−0.996467	−	0.0839905i	$-0.973233\pi$
$353$		−	9.20733e11i		−	0.167981i	0.996467	−	0.0839905i	$-0.0267665\pi$
$354$	−2.67878e12	+	2.08242e11i	−0.481860	+	0.0374587i
$355$		0			0
$356$		−	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	$-0.173267\pi$
$360$		0			0
$361$	−3.72488e12			−0.607542
$362$			5.62180e12i			0.904342i
$363$	6.89902e12	−	5.36315e11i	1.09460	−	0.0850916i
$364$	−1.05665e11			−0.0165357
$365$		0			0
$366$	2.61201e10	+	3.36002e11i	0.00397712	+	0.0511607i
$367$	8.19379e12			1.23071			0.615353	−	0.788252i	$-0.289013\pi$
$367$	8.19379e12			1.23071			0.615353	+	0.788252i	$0.289013\pi$
$368$		−	1.46159e12i		−	0.216564i
$369$	3.27656e11	+	2.09471e12i	0.0478945	+	0.306190i
$370$		0			0
$371$			3.07903e11i			0.0438072i
$372$	3.83746e12	−	2.98315e11i	0.538677	−	0.0418756i
$373$	9.07322e12			1.25666			0.628329	−	0.777947i	$-0.283739\pi$
$373$	9.07322e12			1.25666			0.628329	+	0.777947i	$0.283739\pi$
$374$			3.54870e12i			0.484966i
$375$		0			0
$376$	−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	$0.228449\pi$
$380$		0			0
$381$	9.89455e12	−	7.69180e11i	1.23246	−	0.0958083i
$382$	3.57627e12			0.439657
$383$		−	6.82336e12i		−	0.827950i	−0.910288	−	0.413975i	$-0.864140\pi$
$383$		−	6.82336e12i		−	0.827950i	0.910288	−	0.413975i	$-0.135860\pi$
$384$	5.71972e10	+	7.35771e11i	0.00685045	+	0.0881225i
$385$		0			0
$386$			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	$0.987350\pi$
$390$		0			0
$391$	−3.74855e12			−0.410185
$392$			3.26733e12i			0.352991i
$393$	−7.82526e11	−	1.00662e13i	−0.0834710	−	1.07375i
$394$	−4.28577e12			−0.451386
$395$		0			0
$396$	−1.08989e12	−	6.96770e12i	−0.111920	−	0.715506i
$397$	−1.26553e12			−0.128328			−0.0641639	−	0.997939i	$-0.520438\pi$
$397$	−1.26553e12			−0.128328			−0.0641639	+	0.997939i	$0.520438\pi$
$398$			1.13803e12i			0.113956i
$399$	−2.51989e11	+	1.95890e10i	−0.0249182	+	0.00193708i
$400$		0			0
$401$			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
$405$		0			0
$406$	−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	$0.523712\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$		−	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	$0.669683\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$	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
$430$		0			0
$431$			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	$-0.576904\pi$
$433$	−7.28337e12			−0.478512			−0.239256	+	0.970956i	$0.576904\pi$
$434$		−	4.69384e11i		−	0.0304846i
$435$		0			0
$436$	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	$0.655009\pi$
$440$		0			0
$441$	−1.64533e13	+	2.57363e12i	−0.986414	+	0.154296i
$442$	−4.68225e12			−0.277551
$443$			1.83304e13i			1.07437i	0.843465	+	0.537184i	$0.180512\pi$
$443$			1.83304e13i			1.07437i	−0.843465	+	0.537184i	$0.819488\pi$
$444$	1.06265e13	−	8.26083e11i	0.615852	−	0.0478750i
$445$		0			0
$446$			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	$0.926626\pi$
$450$		0			0
$451$	−8.37559e12			−0.448883
$452$			7.13242e12i			0.378046i
$453$	−7.47774e12	+	5.81303e11i	−0.391994	+	0.0304727i
$454$	9.66249e12			0.500968
$455$		0			0
$456$	−3.38454e11	−	4.35379e12i	−0.0171663	−	0.220823i
$457$	−4.12288e11			−0.0206833			−0.0103416	−	0.999947i	$-0.503292\pi$
$457$	−4.12288e11			−0.0206833			−0.0103416	+	0.999947i	$0.503292\pi$
$458$			2.34581e13i			1.16403i
$459$	2.22510e12	+	9.38700e12i	0.109216	+	0.460748i
$460$		0			0
$461$			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	$-0.596722\pi$
$463$	−1.27323e13			−0.598416			−0.299208	+	0.954188i	$0.596722\pi$
$464$		−	7.79389e12i		−	0.362380i
$465$		0			0
$466$	−2.34795e13			−1.06846
$467$			2.26689e13i			1.02058i	0.860004	+	0.510288i	$0.170461\pi$
$467$			2.26689e13i			1.02058i	−0.860004	+	0.510288i	$0.829539\pi$
$468$	9.19337e12	−	1.43803e12i	0.409492	−	0.0640531i
$469$	−4.49775e11			−0.0198213
$470$		0			0
$471$	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
$475$		0			0
$476$		−	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	$-0.157625\pi$
$480$		0			0
$481$	−2.63673e13			−1.02409
$482$		−	2.35126e13i		−	0.903785i
$483$	−7.04098e10	−	9.05734e11i	−0.00267853	−	0.0344560i
$484$	1.45801e13			0.548950
$485$		0			0
$486$	−7.25186e12	−	1.77475e13i	−0.267466	−	0.654570i
$487$	1.13824e13			0.415516			0.207758	−	0.978180i	$-0.433383\pi$
$487$	1.13824e13			0.415516			0.207758	+	0.978180i	$0.433383\pi$
$488$			7.10091e11i			0.0256575i
$489$	−3.37821e13	+	2.62615e12i	−1.20821	+	0.0939235i
$490$		0			0
$491$			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
$495$		0			0
$496$	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	$0.569288\pi$
$500$		0			0
$501$	−2.37000e12	−	3.04871e13i	−0.0750862	−	0.965890i
$502$	−1.28248e13			−0.402283
$503$		−	3.54934e13i		−	1.10232i	−0.834399	−	0.551160i	$-0.814185\pi$
$503$		−	3.54934e13i		−	1.10232i	0.834399	−	0.551160i	$-0.185815\pi$
$504$	7.08893e10	+	4.53196e11i	0.00217986	+	0.0139359i
$505$		0			0
$506$			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	$-0.348470\pi$
$510$		0			0
$511$	7.25016e11			0.0208086
$512$			1.55494e12i			0.0441942i
$513$	2.16577e13	−	5.13377e12i	0.609574	−	0.144494i
$514$	2.89501e13			0.806928
$515$		0			0
$516$	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
$520$		0			0
$521$		−	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	$-0.733725\pi$
$523$	−5.24376e13			−1.34009			−0.670045	+	0.742320i	$0.733725\pi$
$524$		−	2.12735e13i		−	0.538495i
$525$		0			0
$526$	3.81460e13			0.947370
$527$		−	2.07996e13i		−	0.511683i
$528$	−1.15166e12	−	1.48147e13i	−0.0280644	−	0.361014i
$529$	1.03402e13			0.249603
$530$		0			0
$531$	−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
$535$		0			0
$536$		−	7.77110e12i		−	0.175654i
$537$	−5.58492e12	−	7.18431e13i	−0.125068	−	1.60884i
$538$	3.03260e13			0.672828
$539$		−	6.57877e13i		−	1.44611i
$540$		0			0
$541$	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
$545$		0			0
$546$	−8.79477e10	−	1.13134e12i	−0.00181243	−	0.0233147i
$547$	1.62332e13			0.331488			0.165744	−	0.986169i	$-0.446997\pi$
$547$	1.62332e13			0.331488			0.165744	+	0.986169i	$0.446997\pi$
$548$		−	4.73872e13i		−	0.958867i
$549$	−3.57580e12	+	5.59329e11i	−0.0716987	+	0.0112152i
$550$		0			0
$551$			4.61189e13i			0.908074i
$552$	1.56490e13	−	1.21652e12i	0.305346	−	0.0237369i
$553$	1.25140e12			0.0241974
$554$		−	3.83715e13i		−	0.735292i
$555$		0			0
$556$	−4.07335e13			−0.766615
$557$			1.12168e13i			0.209215i	0.994514	+	0.104608i	$0.0333587\pi$
$557$			1.12168e13i			0.209215i	−0.994514	+	0.104608i	$0.966641\pi$
$558$	6.38805e12	+	4.08389e13i	0.118086	+	0.754924i
$559$	−1.12726e13			−0.206521
$560$		0			0
$561$	−3.79955e13	+	2.95369e12i	−0.683783	+	0.0531557i
$562$	−5.52506e12			−0.0985497
$563$			7.98522e13i			1.41171i	0.708357	+	0.705854i	$0.249437\pi$
$563$			7.98522e13i			1.41171i	−0.708357	+	0.705854i	$0.750563\pi$
$564$	−3.17127e11	−	4.07945e12i	−0.00555697	−	0.0714835i
$565$		0			0
$566$			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	$-0.00265672\pi$
$570$		0			0
$571$	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
$575$		0			0
$576$	−7.83021e12	+	1.22481e12i	−0.123498	+	0.0193177i
$577$	−3.31000e13			−0.517546			−0.258773	−	0.965938i	$-0.583318\pi$
$577$	−3.31000e13			−0.517546			−0.258773	+	0.965938i	$0.583318\pi$
$578$			3.53887e13i			0.548562i
$579$	−9.16671e13	+	7.12600e12i	−1.40871	+	0.109510i
$580$		0			0
$581$		−	7.34648e11i		−	0.0110968i
$582$	−4.57989e12	−	5.89145e13i	−0.0685867	−	0.882282i
$583$	1.07116e14			1.59041
$584$			1.25266e13i			0.184404i
$585$		0			0
$586$	−3.56543e13			−0.515969
$587$		−	1.21022e14i		−	1.73650i	−0.496131	−	0.868248i	$-0.665246\pi$
$587$		−	1.21022e14i		−	1.73650i	0.496131	−	0.868248i	$-0.334754\pi$
$588$	−3.49830e13	+	2.71950e12i	−0.497703	+	0.0386903i
$589$	−4.79889e13			−0.676961
$590$		0			0
$591$	−3.56717e12	−	4.58873e13i	−0.0494751	−	0.636436i
$592$	2.24576e13			0.308855
$593$			8.43944e12i			0.115091i	0.998343	+	0.0575453i	$0.0183274\pi$
$593$			8.43944e12i			0.115091i	−0.998343	+	0.0575453i	$0.981673\pi$
$594$	7.36952e13	−	1.74688e13i	0.996567	−	0.236227i
$595$		0			0
$596$		−	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	$0.935184\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	−5.92893e13	+	4.60902e12i	−0.725459	+	0.0563956i
$607$	4.47536e13			0.543106			0.271553	−	0.962423i	$-0.412463\pi$
$607$	4.47536e13			0.543106			0.271553	+	0.962423i	$0.412463\pi$
$608$		−	9.20110e12i		−	0.110744i
$609$	−3.75459e11	−	4.82981e12i	−0.00448204	−	0.0576559i
$610$		0			0
$611$			1.01222e13i			0.118869i
$612$	3.14128e12	+	2.00822e13i	0.0365889	+	0.233913i
$613$	−6.78051e13			−0.783358			−0.391679	−	0.920102i	$-0.628106\pi$
$613$	−6.78051e13			−0.783358			−0.391679	+	0.920102i	$0.628106\pi$
$614$			7.46303e13i			0.855211i
$615$		0			0
$616$	−1.81209e12			−0.0204303
$617$			2.48261e12i			0.0277641i	0.999904	+	0.0138820i	$0.00441893\pi$
$617$			2.48261e12i			0.0277641i	−0.999904	+	0.0138820i	$0.995581\pi$
$618$	−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	$0.471239\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$		−	3.92175e13i		−	0.407951i
$627$	6.81476e12	+	8.76635e13i	0.0703255	+	0.904651i
$628$	4.97317e13			0.509138
$629$		−	5.75973e13i		−	0.584991i
$630$		0			0
$631$	−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
$635$		0			0
$636$	−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
$640$		0			0
$641$		−	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	$-0.418803\pi$
$643$	5.54693e13			0.504659			0.252329	+	0.967641i	$0.418803\pi$
$644$		−	1.91414e12i		−	0.0172800i
$645$		0			0
$646$	−2.35982e13			−0.209757
$647$		−	5.56652e13i		−	0.490979i	−0.969399	−	0.245489i	$-0.921051\pi$
$647$		−	5.56652e13i		−	0.490979i	0.969399	−	0.245489i	$-0.0789486\pi$
$648$	−1.23355e13	−	3.84657e13i	−0.107965	−	0.336665i
$649$	1.13988e14			0.990002
$650$		0			0
$651$	5.02564e12	−	3.90682e11i	0.0429820	−	0.00334132i
$652$	−7.13935e13			−0.605927
$653$			5.56792e13i			0.468951i	0.972122	+	0.234475i	$0.0753372\pi$
$653$			5.56792e13i			0.468951i	−0.972122	+	0.234475i	$0.924663\pi$
$654$	2.31581e12	+	2.97901e13i	0.0193560	+	0.248991i
$655$		0			0
$656$			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	$0.789439\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	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
$670$		0			0
$671$		−	1.42977e13i		−	0.105112i
$672$	7.49071e10	+	9.63587e11i	0.000546609	+	0.00703144i
$673$	9.45260e13			0.684662			0.342331	−	0.939579i	$-0.388784\pi$
$673$	9.45260e13			0.684662			0.342331	+	0.939579i	$0.388784\pi$
$674$		−	9.39679e13i		−	0.675585i
$675$		0			0
$676$	2.20824e13			0.156427
$677$			1.70106e14i			1.19612i	0.801451	+	0.598060i	$0.204062\pi$
$677$			1.70106e14i			1.19612i	−0.801451	+	0.598060i	$0.795938\pi$
$678$	−7.63660e13	+	5.93652e12i	−0.533030	+	0.0414366i
$679$	−7.20622e12			−0.0499297
$680$		0			0
$681$	8.04237e12	+	1.03455e14i	0.0549096	+	0.706344i
$682$	−1.63293e14			−1.10674
$683$		−	2.23578e14i		−	1.50427i	−0.659009	−	0.752135i	$-0.729024\pi$
$683$		−	2.23578e14i		−	1.50427i	0.659009	−	0.752135i	$-0.270976\pi$
$684$	4.63338e13	−	7.24758e12i	0.309469	−	0.0484075i
$685$		0			0
$686$			8.56481e12i			0.0563764i
$687$	−2.51163e14	+	1.95249e13i	−1.64124	+	0.127586i
$688$	9.60110e12			0.0622843
$689$			1.41331e14i			0.910210i
$690$		0			0
$691$	−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
$695$		0			0
$696$	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
$700$		0			0
$701$		−	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
$705$		0			0
$706$	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	$0.302618\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$		−	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	$0.746269\pi$
$720$		0			0
$721$	−1.90059e12			−0.00975465
$722$		−	8.42844e13i		−	0.429597i
$723$	2.51746e14	−	1.95702e13i	1.27430	−	0.0990613i
$724$	−1.27207e14			−0.639466
$725$		0			0
$726$	1.21354e13	+	1.56107e14i	0.0601688	+	0.773997i
$727$	2.99071e14			1.47266			0.736330	−	0.676622i	$-0.236557\pi$
$727$	2.99071e14			1.47266			0.736330	+	0.676622i	$0.236557\pi$
$728$		−	2.39092e12i		−	0.0116925i
$729$	1.83985e14	−	9.24165e13i	0.893602	−	0.448861i
$730$		0			0
$731$		−	2.46241e13i		−	0.117970i
$732$	−7.60286e12	+	5.91030e11i	−0.0361761	+	0.00281225i
$733$	−1.19922e14			−0.566734			−0.283367	−	0.959012i	$-0.591451\pi$
$733$	−1.19922e14			−0.566734			−0.283367	+	0.959012i	$0.591451\pi$
$734$			1.85404e14i			0.870241i
$735$		0			0
$736$	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	$0.552909\pi$
$740$		0			0
$741$	−1.15666e14	+	8.99158e12i	−0.517742	+	0.0402481i
$742$	−6.96706e12			−0.0309763
$743$			1.07061e14i			0.472809i	0.971655	+	0.236405i	$0.0759691\pi$
$743$			1.07061e14i			0.472809i	−0.971655	+	0.236405i	$0.924031\pi$
$744$	6.75011e12	+	8.68317e13i	0.0296105	+	0.380902i
$745$		0			0
$746$			2.05304e14i			0.888592i
$747$	9.99815e12	+	6.39183e13i	0.0429850	+	0.274803i
$748$	−8.02979e13			−0.342923
$749$		−	1.61733e13i		−	0.0686104i
$750$		0			0
$751$	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
$755$		0			0
$756$	−4.79332e12	+	1.13621e12i	−0.0194101	+	0.00460098i
$757$	1.73049e14			0.696130			0.348065	−	0.937470i	$-0.386839\pi$
$757$	1.73049e14			0.696130			0.348065	+	0.937470i	$0.386839\pi$
$758$			2.66589e14i			1.06536i
$759$	−3.15093e14	+	2.44946e13i	−1.25092	+	0.0972438i
$760$		0			0
$761$		−	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
$765$		0			0
$766$	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	$0.359049\pi$
$770$		0			0
$771$	2.40960e13	+	3.09965e14i	0.0884451	+	1.13774i
$772$	−1.93725e14			−0.706479
$773$			1.50965e14i			0.546991i	0.961873	+	0.273495i	$0.0881798\pi$
$773$			1.50965e14i			0.546991i	−0.961873	+	0.273495i	$0.911820\pi$
$774$	7.56265e12	+	4.83481e13i	0.0272251	+	0.174050i
$775$		0			0
$776$		−	1.24507e14i		−	0.442472i
$777$	1.39168e13	−	1.08186e12i	0.0491399	−	0.00382003i
$778$	−1.60160e13			−0.0561897
$779$		−	5.56961e13i		−	0.194150i
$780$		0			0
$781$	−2.87690e14			−0.990079
$782$		−	8.48200e13i		−	0.290044i
$783$	9.83979e13	+	4.15109e14i	0.334331	+	1.41044i
$784$	−7.39313e13			−0.249602
$785$		0			0
$786$	2.27773e14	−	1.77065e13i	0.759257	−	0.0590229i
$787$	3.42081e14			1.13306			0.566532	−	0.824039i	$-0.308285\pi$
$787$	3.42081e14			1.13306			0.566532	+	0.824039i	$0.308285\pi$
$788$		−	9.69760e13i		−	0.319178i
$789$	3.17500e13	+	4.08424e14i	0.103839	+	1.33575i
$790$		0			0
$791$			9.34082e12i			0.0301649i
$792$	1.57661e14	−	2.46615e13i	0.505939	−	0.0791394i
$793$	1.88647e13			0.0601568
$794$		−	2.86357e13i		−	0.0907415i
$795$		0			0
$796$	−2.57506e13			−0.0805791
$797$		−	5.22986e14i		−	1.62629i	−0.582059	−	0.813146i	$-0.697753\pi$
$797$		−	5.22986e14i		−	1.62629i	0.582059	−	0.813146i	$-0.302247\pi$
$798$	−4.43249e11	−	5.70185e12i	−0.00136973	−	0.0176198i
$799$	−2.21112e13			−0.0679013
$800$		0			0
$801$	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
$805$		0			0
$806$		−	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	$0.833947\pi$
$810$		0			0
$811$	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
$815$		0			0
$816$	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
$820$		0			0
$821$		−	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	$-0.518360\pi$
$823$	−4.35331e13			−0.115298			−0.0576488	+	0.998337i	$0.518360\pi$
$824$		−	3.28379e13i		−	0.0864449i
$825$		0			0
$826$	−7.41407e12			−0.0192822
$827$			2.21008e13i			0.0571321i	0.999592	+	0.0285661i	$0.00909409\pi$
$827$			2.21008e13i			0.0571321i	−0.999592	+	0.0285661i	$0.990906\pi$
$828$	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	$0.0722770\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$			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	$-0.0328014\pi$
$840$		0			0
$841$	−4.63244e14			−1.10111
$842$			4.13963e12i			0.00978141i
$843$	−4.59867e12	−	5.91561e13i	−0.0108017	−	0.138951i
$844$	−2.43184e14			−0.567837
$845$		0			0
$846$	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
$850$		0			0
$851$		−	4.77649e14i		−	1.07019i
$852$	1.18924e13	+	1.52981e14i	0.0264893	+	0.340752i
$853$	−1.82179e14			−0.403415			−0.201708	−	0.979446i	$-0.564649\pi$
$853$	−1.82179e14			−0.403415			−0.201708	+	0.979446i	$0.564649\pi$
$854$			9.29956e11i			0.00204726i
$855$		0			0
$856$	2.79438e14			0.608019
$857$		−	8.52398e14i		−	1.84390i	−0.387305	−	0.921952i	$-0.626594\pi$
$857$		−	8.52398e14i		−	1.84390i	0.387305	−	0.921952i	$-0.373406\pi$
$858$	−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	$0.410321\pi$
$860$		0			0
$861$	4.53427e11	+	5.83278e12i	0.000958279	+	0.0123271i
$862$	−1.50357e14			−0.315928
$863$			2.71494e14i			0.567161i	0.958948	+	0.283580i	$0.0915223\pi$
$863$			2.71494e14i			0.567161i	−0.958948	+	0.283580i	$0.908478\pi$
$864$	−1.96312e13	−	8.28177e13i	−0.0407735	−	0.172010i
$865$		0			0
$866$		−	1.64804e14i		−	0.338359i
$867$	−3.78903e14	+	2.94551e13i	−0.773450	+	0.0601263i
$868$	1.06210e13			0.0215558
$869$		−	4.35344e14i		−	0.878484i
$870$		0			0
$871$	−2.06452e14			−0.411840
$872$			6.29569e13i			0.124871i
$873$	6.26979e14	−	9.80726e13i	1.23646	−	0.193409i
$874$	−1.95697e14			−0.383732
$875$		0			0
$876$	−1.34121e14	+	1.04263e13i	−0.260002	+	0.0202120i
$877$	−1.90122e14			−0.366466			−0.183233	−	0.983069i	$-0.558656\pi$
$877$	−1.90122e14			−0.366466			−0.183233	+	0.983069i	$0.558656\pi$
$878$		−	3.45295e14i		−	0.661786i
$879$	−2.96761e13	−	3.81746e14i	−0.0565539	−	0.727495i
$880$		0			0
$881$			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	$-0.359915\pi$
$883$	4.57367e14			0.852042			0.426021	+	0.904713i	$0.359915\pi$
$884$		−	1.05947e14i		−	0.196258i
$885$		0			0
$886$	−4.14769e14			−0.759693
$887$		−	5.97146e14i		−	1.08758i	−0.839221	−	0.543791i	$-0.816988\pi$
$887$		−	5.97146e14i		−	1.08758i	0.839221	−	0.543791i	$-0.183012\pi$
$888$	1.86921e13	+	2.40451e14i	0.0338527	+	0.435473i
$889$	2.73852e13			0.0493182
$890$		0			0
$891$	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
$895$		0			0
$896$			2.03640e12i			0.00352633i
$897$	−3.23189e13	−	4.15742e14i	−0.0556537	−	0.715916i
$898$	−1.88685e14			−0.323113
$899$		−	9.19792e14i		−	1.56636i
$900$		0			0
$901$	−3.08727e14			−0.519938
$902$		−	1.89518e14i		−	0.317408i
$903$	5.94973e12	−	4.62519e11i	0.00990965	−	0.000770354i
$904$	−1.61388e14			−0.267319
$905$		0			0
$906$	−1.31534e13	−	1.69202e14i	−0.0215475	−	0.277181i
$907$	7.96198e14			1.29713			0.648567	−	0.761158i	$-0.275369\pi$
$907$	7.96198e14			1.29713			0.648567	+	0.761158i	$0.275369\pi$
$908$			2.18637e14i			0.354238i
$909$	−9.86964e13	−	6.30967e14i	−0.159031	−	1.01669i
$910$		0			0
$911$		−	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
$915$		0			0
$916$	−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	$0.360774\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$		−	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	$-0.0344053\pi$
$930$		0			0
$931$	4.37475e14			0.625468
$932$		−	5.31280e14i		−	0.755516i
$933$	−3.15085e13	−	4.05318e14i	−0.0445677	−	0.573308i
$934$	−5.12938e14			−0.721656
$935$		0			0
$936$	3.25390e13	+	2.08022e14i	0.0452924	+	0.289555i
$937$	3.07315e14			0.425487			0.212743	−	0.977108i	$-0.431760\pi$
$937$	3.07315e14			0.425487			0.212743	+	0.977108i	$0.431760\pi$
$938$		−	1.01773e13i		−	0.0140158i
$939$	4.19897e14	−	3.26419e13i	0.575195	−	0.0447143i
$940$		0			0
$941$			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
$945$		0			0
$946$	−1.93318e14			−0.255162
$947$		−	1.20121e15i		−	1.57713i	−0.614950	−	0.788566i	$-0.710824\pi$
$947$		−	1.20121e15i		−	1.57713i	0.614950	−	0.788566i	$-0.289176\pi$
$948$	−2.31497e14	+	1.79960e13i	−0.302345	+	0.0235037i
$949$	3.32790e14			0.432354
$950$		0			0
$951$	−2.50674e13	−	3.22461e14i	−0.0322260	−	0.414547i
$952$	5.22278e12			0.00667908
$953$		−	3.27942e13i		−	0.0417189i	−0.999782	−	0.0208594i	$-0.993360\pi$
$953$		−	3.27942e13i		−	0.0417189i	0.999782	−	0.0208594i	$-0.00664025\pi$
$954$	6.06171e14	−	9.48177e13i	0.767102	−	0.119991i
$955$		0			0
$956$			6.33279e14i			0.793060i
$957$	−1.68023e15	+	1.30617e14i	−2.09319	+	0.162720i
$958$	5.42276e14			0.672036
$959$		−	6.20597e13i		−	0.0765097i
$960$		0			0
$961$	1.37458e14			0.167708
$962$		−	5.96623e14i		−	0.724143i
$963$	2.20110e14	+	1.40716e15i	0.265771	+	1.69908i
$964$	5.32029e14			0.639072
$965$		0			0
$966$	2.04944e13	−	1.59319e12i	0.0243641	−	0.00189401i
$967$	9.87053e14			1.16737			0.583684	−	0.811981i	$-0.301611\pi$
$967$	9.87053e14			1.16737			0.583684	+	0.811981i	$0.301611\pi$
$968$			3.29909e14i			0.388166i
$969$	−1.96414e13	−	2.52663e14i	−0.0229908	−	0.295748i
$970$		0			0
$971$		−	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
$975$		0			0
$976$	−1.60675e13			−0.0181426
$977$			9.53859e14i			1.07155i	0.844361	+	0.535774i	$0.179980\pi$
$977$			9.53859e14i			1.07155i	−0.844361	+	0.535774i	$0.820020\pi$
$978$	−5.94229e13	−	7.64402e14i	−0.0664140	−	0.854333i
$979$	−1.21271e15			−1.34847
$980$		0			0
$981$	−3.17031e14	+	4.95903e13i	−0.348945	+	0.0545823i
$982$	−8.13482e14			−0.890821
$983$			6.30884e14i			0.687356i	0.939088	+	0.343678i	$0.111673\pi$
$983$			6.30884e14i			0.687356i	−0.939088	+	0.343678i	$0.888327\pi$
$984$	−1.00777e14	+	7.83420e12i	−0.109241	+	0.00849218i
$985$		0			0
$986$		−	4.52301e14i		−	0.485337i
$987$	−4.15319e11	−	5.34256e12i	−0.000443400	−	0.00570379i
$988$	−2.44442e14			−0.259652
$989$		−	2.04205e14i		−	0.215816i
$990$		0			0
$991$	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
$995$		0			0
$996$	1.05648e13	+	1.35903e14i	0.0107787	+	0.138654i
$997$	−1.62993e15			−1.65460			−0.827301	−	0.561759i	$-0.810125\pi$
$997$	−1.62993e15			−1.65460			−0.827301	+	0.561759i	$0.810125\pi$
$998$		−	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	150.11.d.a.101.3		4
3.2	odd	2	inner	150.11.d.a.101.1		4
5.2	odd	4		150.11.b.a.149.4		8
5.3	odd	4		150.11.b.a.149.5		8
5.4	even	2		6.11.b.a.5.2	✓	4
15.2	even	4		150.11.b.a.149.6		8
15.8	even	4		150.11.b.a.149.3		8
15.14	odd	2		6.11.b.a.5.4	yes	4
20.19	odd	2		48.11.e.d.17.2		4
40.19	odd	2		192.11.e.h.65.3		4
40.29	even	2		192.11.e.g.65.2		4
45.4	even	6		162.11.d.d.107.3		8
45.14	odd	6		162.11.d.d.107.2		8
45.29	odd	6		162.11.d.d.53.3		8
45.34	even	6		162.11.d.d.53.2		8
60.59	even	2		48.11.e.d.17.1		4
120.29	odd	2		192.11.e.g.65.1		4
120.59	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	5.4	even	2
6.11.b.a.5.4	yes	4	15.14	odd	2
48.11.e.d.17.1		4	60.59	even	2
48.11.e.d.17.2		4	20.19	odd	2
150.11.b.a.149.3		8	15.8	even	4
150.11.b.a.149.4		8	5.2	odd	4
150.11.b.a.149.5		8	5.3	odd	4
150.11.b.a.149.6		8	15.2	even	4
150.11.d.a.101.1		4	3.2	odd	2	inner
150.11.d.a.101.3		4	1.1	even	1	trivial
162.11.d.d.53.2		8	45.34	even	6
162.11.d.d.53.3		8	45.29	odd	6
162.11.d.d.107.2		8	45.14	odd	6
162.11.d.d.107.3		8	45.4	even	6
192.11.e.g.65.1		4	120.29	odd	2
192.11.e.g.65.2		4	40.29	even	2
192.11.e.h.65.3		4	40.19	odd	2
192.11.e.h.65.4		4	120.59	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	150.d (of order \(2\), degree \(1\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more