LMFDB - Embedded newform 150.11.b.a.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,11,Mod(149,150)]

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, 1]))

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

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

chi := DirichletCharacter("150.149");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	150.b (of order $2$, degree $1$, not 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:	$8$
Coefficient field:	8.0.3421020160000.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 967x^{4} + 194481 $ x^8 + 967*x^4 + 194481
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.3
Root			$2.90605 - 2.90605i$ of defining polynomial
Character	$\chi$	$=$	150.149
Dual form			150.11.b.a.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.6274 q^{2} +(18.8335 - 242.269i) q^{3} +512.000 q^{4} +(-426.153 + 5481.92i) q^{6} +670.530i q^{7} -11585.2 q^{8} +(-58339.6 - 9125.53i) q^{9} +O(q^{10})$	\(q-22.6274 q^{2} +(18.8335 - 242.269i) q^{3} +512.000 q^{4} +(-426.153 + 5481.92i) q^{6} +670.530i q^{7} -11585.2 q^{8} +(-58339.6 - 9125.53i) q^{9} -233268. i q^{11} +(9642.73 - 124042. i) q^{12} -307781. i q^{13} -15172.4i q^{14} +262144. q^{16} +672324. q^{17} +(1.32007e6 + 206487. i) q^{18} +1.55119e6 q^{19} +(162449. + 12628.4i) q^{21} +5.27826e6i q^{22} -5.57551e6 q^{23} +(-218190. + 2.80674e6i) q^{24} +6.96428e6i q^{26} +(-3.30957e6 + 1.39620e7i) q^{27} +343311. i q^{28} -2.97313e7i q^{29} +3.09368e7 q^{31} -5.93164e6 q^{32} +(-5.65137e7 - 4.39325e6i) q^{33} -1.52130e7 q^{34} +(-2.98699e7 - 4.67227e6i) q^{36} -8.56690e7i q^{37} -3.50994e7 q^{38} +(-7.45657e7 - 5.79657e6i) q^{39} -3.59054e7i q^{41} +(-3.67579e6 - 285748. i) q^{42} +3.66253e7i q^{43} -1.19433e8i q^{44} +1.26159e8 q^{46} +3.28877e7 q^{47} +(4.93708e6 - 6.35094e7i) q^{48} +2.82026e8 q^{49} +(1.26622e7 - 1.62883e8i) q^{51} -1.57584e8i q^{52} -4.59194e8 q^{53} +(7.48870e7 - 3.15924e8i) q^{54} -7.76824e6i q^{56} +(2.92143e7 - 3.75805e8i) q^{57} +6.72743e8i q^{58} -4.88657e8i q^{59} -6.12928e7 q^{61} -7.00020e8 q^{62} +(6.11894e6 - 3.91184e7i) q^{63} +1.34218e8 q^{64} +(1.27876e9 + 9.94079e7i) q^{66} -6.70776e8i q^{67} +3.44230e8 q^{68} +(-1.05006e8 + 1.35077e9i) q^{69} -1.23330e9i q^{71} +(6.75878e8 + 1.05721e8i) q^{72} -1.08126e9i q^{73} +1.93847e9i q^{74} +7.94209e8 q^{76} +1.56413e8 q^{77} +(1.68723e9 + 1.31161e8i) q^{78} +1.86628e9 q^{79} +(3.32023e9 + 1.06476e9i) q^{81} +8.12446e8i q^{82} +1.09562e9 q^{83} +(8.31737e7 + 6.46574e6i) q^{84} -8.28736e8i q^{86} +(-7.20298e9 - 5.59944e8i) q^{87} +2.70247e9i q^{88} +5.19876e9i q^{89} +2.06376e8 q^{91} -2.85466e9 q^{92} +(5.82647e8 - 7.49503e9i) q^{93} -7.44163e8 q^{94} +(-1.11713e8 + 1.43705e9i) q^{96} -1.07471e10i q^{97} -6.38151e9 q^{98} +(-2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9}+O(q^{10}) $ 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9	$ 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99}+O(q^{100}) $ 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9 + 2097152 * q^16 + 3137456 * q^19 + 19256016 * q^21 + 5505024 * q^24 - 43571696 * q^31 - 302174208 * q^34 - 162828288 * q^36 - 434574480 * q^39 + 377628672 * q^46 + 100116840 * q^49 - 1417153536 * q^51 - 963325440 * q^54 - 2368077488 * q^61 + 1073741824 * q^64 + 6246890496 * q^66 - 1192536576 * q^69 + 1606377472 * q^76 - 398565136 * q^79 + 2917929096 * q^81 + 9859080192 * q^84 + 16634464160 * q^91 - 17010954240 * q^94 + 2818572288 * q^96 + 5253825024 * 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 $

$2$	−22.6274			−0.707107
$2$	−22.6274			−0.707107
$3$	18.8335	−	242.269i	0.0775039	−	0.996992i
$3$	18.8335	−	242.269i	0.0775039	−	0.996992i
$4$	512.000			0.500000
$5$		0			0
$5$		0			0
$6$	−426.153	+	5481.92i	−0.0548036	+	0.704980i
$7$			670.530i			0.0398959i	0.999801	+	0.0199479i	$0.00635004\pi$
$7$			670.530i			0.0398959i	−0.999801	+	0.0199479i	$0.993650\pi$
$8$	−11585.2			−0.353553
$9$	−58339.6	−	9125.53i	−0.987986	−	0.154542i
$10$		0			0
$11$		−	233268.i		−	1.44841i	−0.689583	−	0.724206i	$-0.742206\pi$
$11$		−	233268.i		−	1.44841i	0.689583	−	0.724206i	$-0.257794\pi$
$12$	9642.73	−	124042.i	0.0387520	−	0.498496i
$13$		−	307781.i		−	0.828943i	−0.910062	−	0.414471i	$-0.863967\pi$
$13$		−	307781.i		−	0.828943i	0.910062	−	0.414471i	$-0.136033\pi$
$14$		−	15172.4i		−	0.0282106i
$15$		0			0
$16$	262144.			0.250000
$17$	672324.			0.473515			0.236758	−	0.971569i	$-0.423915\pi$
$17$	672324.			0.473515			0.236758	+	0.971569i	$0.423915\pi$
$18$	1.32007e6	+	206487.i	0.698612	+	0.109277i
$19$	1.55119e6			0.626465			0.313233	−	0.949676i	$-0.398588\pi$
$19$	1.55119e6			0.626465			0.313233	+	0.949676i	$0.398588\pi$
$20$		0			0
$21$	162449.	+	12628.4i	0.0397758	+	0.00309209i
$22$			5.27826e6i			1.02418i
$23$	−5.57551e6			−0.866255			−0.433127	−	0.901333i	$-0.642590\pi$
$23$	−5.57551e6			−0.866255			−0.433127	+	0.901333i	$0.642590\pi$
$24$	−218190.	+	2.80674e6i	−0.0274018	+	0.352490i
$25$		0			0
$26$			6.96428e6i			0.586151i
$27$	−3.30957e6	+	1.39620e7i	−0.230650	+	0.973037i
$28$			343311.i			0.0199479i
$29$		−	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	$0.318310\pi$
$32$	−5.93164e6			−0.176777
$33$	−5.65137e7	−	4.39325e6i	−1.44406	−	0.112258i
$34$	−1.52130e7			−0.334826
$35$		0			0
$36$	−2.98699e7	−	4.67227e6i	−0.493993	−	0.0772708i
$37$		−	8.56690e7i		−	1.23542i	−0.786406	−	0.617711i	$-0.788060\pi$
$37$		−	8.56690e7i		−	1.23542i	0.786406	−	0.617711i	$-0.211940\pi$
$38$	−3.50994e7			−0.442978
$39$	−7.45657e7	−	5.79657e6i	−0.826449	−	0.0642463i
$40$		0			0
$41$		−	3.59054e7i		−	0.309913i	−0.987921	−	0.154957i	$-0.950476\pi$
$41$		−	3.59054e7i		−	0.309913i	0.987921	−	0.154957i	$-0.0495238\pi$
$42$	−3.67579e6	−	285748.i	−0.0281258	−	0.00218644i
$43$			3.66253e7i			0.249137i	0.992211	+	0.124569i	$0.0397547\pi$
$43$			3.66253e7i			0.249137i	−0.992211	+	0.124569i	$0.960245\pi$
$44$		−	1.19433e8i		−	0.724206i
$45$		0			0
$46$	1.26159e8			0.612535
$47$	3.28877e7			0.143398			0.0716992	−	0.997426i	$-0.477158\pi$
$47$	3.28877e7			0.143398			0.0716992	+	0.997426i	$0.477158\pi$
$48$	4.93708e6	−	6.35094e7i	0.0193760	−	0.249248i
$49$	2.82026e8			0.998408
$50$		0			0
$51$	1.26622e7	−	1.62883e8i	0.0366993	−	0.472091i
$52$		−	1.57584e8i		−	0.414471i
$53$	−4.59194e8			−1.09804			−0.549019	−	0.835810i	$-0.684998\pi$
$53$	−4.59194e8			−1.09804			−0.549019	+	0.835810i	$0.684998\pi$
$54$	7.48870e7	−	3.15924e8i	0.163094	−	0.688041i
$55$		0			0
$56$		−	7.76824e6i		−	0.0141053i
$57$	2.92143e7	−	3.75805e8i	0.0485535	−	0.624581i
$58$			6.72743e8i			1.02497i
$59$		−	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	$0.511552\pi$
$62$	−7.00020e8			−0.764103
$63$	6.11894e6	−	3.91184e7i	0.00616557	−	0.0394166i
$64$	1.34218e8			0.125000
$65$		0			0
$66$	1.27876e9	+	9.94079e7i	1.02110	+	0.0793782i
$67$		−	6.70776e8i		−	0.496825i	−0.968654	−	0.248413i	$-0.920091\pi$
$67$		−	6.70776e8i		−	0.496825i	0.968654	−	0.248413i	$-0.0799089\pi$
$68$	3.44230e8			0.236758
$69$	−1.05006e8	+	1.35077e9i	−0.0671382	+	0.863649i
$70$		0			0
$71$		−	1.23330e9i		−	0.683561i	−0.939780	−	0.341781i	$-0.888970\pi$
$71$		−	1.23330e9i		−	0.683561i	0.939780	−	0.341781i	$-0.111030\pi$
$72$	6.75878e8	+	1.05721e8i	0.349306	+	0.0546387i
$73$		−	1.08126e9i		−	0.521573i	−0.965396	−	0.260787i	$-0.916018\pi$
$73$		−	1.08126e9i		−	0.521573i	0.965396	−	0.260787i	$-0.0839819\pi$
$74$			1.93847e9i			0.873575i
$75$		0			0
$76$	7.94209e8			0.313233
$77$	1.56413e8			0.0577857
$78$	1.68723e9	+	1.31161e8i	0.584388	+	0.0454290i
$79$	1.86628e9			0.606515			0.303258	−	0.952909i	$-0.401926\pi$
$79$	1.86628e9			0.606515			0.303258	+	0.952909i	$0.401926\pi$
$80$		0			0
$81$	3.32023e9	+	1.06476e9i	0.952234	+	0.305370i
$82$			8.12446e8i			0.219142i
$83$	1.09562e9			0.278145			0.139072	−	0.990282i	$-0.455588\pi$
$83$	1.09562e9			0.278145			0.139072	+	0.990282i	$0.455588\pi$
$84$	8.31737e7	+	6.46574e6i	0.0198879	+	0.00154604i
$85$		0			0
$86$		−	8.28736e8i		−	0.176167i
$87$	−7.20298e9	−	5.59944e8i	−1.44516	−	0.112344i
$88$			2.70247e9i			0.512091i
$89$			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
$92$	−2.85466e9			−0.433127
$93$	5.82647e8	−	7.49503e9i	0.0837512	−	1.07735i
$94$	−7.44163e8			−0.101398
$95$		0			0
$96$	−1.11713e8	+	1.43705e9i	−0.0137009	+	0.176245i
$97$		−	1.07471e10i		−	1.25150i	−0.780024	−	0.625750i	$-0.784793\pi$
$97$		−	1.07471e10i		−	1.25150i	0.780024	−	0.625750i	$-0.215207\pi$
$98$	−6.38151e9			−0.705981
$99$	−2.12870e9	+	1.36088e10i	−0.223840	+	1.43101i
$100$		0			0
$101$			1.08154e10i			1.02905i	0.857475	+	0.514525i	$0.172032\pi$
$101$			1.08154e10i			1.02905i	−0.857475	+	0.514525i	$0.827968\pi$
$102$	−2.86513e8	+	3.68563e9i	−0.0259503	+	0.333819i
$103$			2.83446e9i			0.244503i	0.992499	+	0.122251i	$0.0390114\pi$
$103$			2.83446e9i			0.244503i	−0.992499	+	0.122251i	$0.960989\pi$
$104$			3.56571e9i			0.293075i
$105$		0			0
$106$	1.03904e10			0.776430
$107$	−2.41202e10			−1.71974			−0.859869	−	0.510515i	$-0.829455\pi$
$107$	−2.41202e10			−1.71974			−0.859869	+	0.510515i	$0.829455\pi$
$108$	−1.69450e9	+	7.14855e9i	−0.115325	+	0.486518i
$109$	5.43424e9			0.353188			0.176594	−	0.984284i	$-0.443492\pi$
$109$	5.43424e9			0.353188			0.176594	+	0.984284i	$0.443492\pi$
$110$		0			0
$111$	−2.07549e10	−	1.61344e9i	−1.23170	−	0.0957500i
$112$			1.75775e8i			0.00997396i
$113$	−1.39305e10			−0.756092			−0.378046	−	0.925787i	$-0.623404\pi$
$113$	−1.39305e10			−0.756092			−0.378046	+	0.925787i	$0.623404\pi$
$114$	−6.61043e8	+	8.50350e9i	−0.0343325	+	0.441645i
$115$		0			0
$116$		−	1.52224e10i		−	0.724760i
$117$	−2.80866e9	+	1.79558e10i	−0.128106	+	0.818984i
$118$			1.10570e10i			0.483313i
$119$			4.50813e8i			0.0188913i
$120$		0			0
$121$	−2.84767e10			−1.09790
$122$	1.38690e9			0.0513151
$123$	−8.69877e9	−	6.76223e8i	−0.308981	−	0.0240195i
$124$	1.58396e10			0.540303
$125$		0			0
$126$	−1.38456e8	+	8.85149e8i	−0.00435972	+	0.0278717i
$127$			4.08412e10i			1.23617i	0.786110	+	0.618087i	$0.212092\pi$
$127$			4.08412e10i			1.23617i	−0.786110	+	0.618087i	$0.787908\pi$
$128$	−3.03700e9			−0.0883883
$129$	8.87317e9	+	6.89781e8i	0.248388	+	0.0193091i
$130$		0			0
$131$		−	4.15498e10i		−	1.07699i	−0.842628	−	0.538495i	$-0.818993\pi$
$131$		−	4.15498e10i		−	1.07699i	0.842628	−	0.538495i	$-0.181007\pi$
$132$	−2.89350e10	−	2.24934e9i	−0.722028	−	0.0561289i
$133$			1.04012e9i			0.0249934i
$134$			1.51779e10i			0.351308i
$135$		0			0
$136$	−7.78903e9			−0.167413
$137$	−9.25532e10			−1.91773			−0.958867	−	0.283854i	$-0.908387\pi$
$137$	−9.25532e10			−1.91773			−0.958867	+	0.283854i	$0.908387\pi$
$138$	2.37602e9	−	3.05645e10i	0.0474739	−	0.610692i
$139$	−7.95575e10			−1.53323			−0.766615	−	0.642107i	$-0.778061\pi$
$139$	−7.95575e10			−1.53323			−0.766615	+	0.642107i	$0.778061\pi$
$140$		0			0
$141$	6.19389e8	−	7.96767e9i	0.0111139	−	0.142967i
$142$			2.79064e10i			0.483351i
$143$	−7.17955e10			−1.20065
$144$	−1.52934e10	−	2.39220e9i	−0.246997	−	0.0386354i
$145$		0			0
$146$			2.44661e10i			0.368808i
$147$	5.31152e9	−	6.83261e10i	0.0773806	−	0.995405i
$148$		−	4.38625e10i		−	0.617711i
$149$			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	$0.437014\pi$
$152$	−1.79709e10			−0.221489
$153$	−3.92231e10	−	6.13531e9i	−0.467827	−	0.0731778i
$154$	−3.53923e9			−0.0408606
$155$		0			0
$156$	−3.81776e10	−	2.96785e9i	−0.413225	−	0.0321232i
$157$			9.71322e10i			1.01828i	0.860685	+	0.509138i	$0.170036\pi$
$157$			9.71322e10i			1.01828i	−0.860685	+	0.509138i	$0.829964\pi$
$158$	−4.22291e10			−0.428871
$159$	−8.64822e9	+	1.11249e11i	−0.0851023	+	1.09473i
$160$		0			0
$161$		−	3.73855e9i		−	0.0345600i
$162$	−7.51283e10	−	2.40928e10i	−0.673331	−	0.215929i
$163$			1.39440e11i			1.21185i	0.795520	+	0.605927i	$0.207198\pi$
$163$			1.39440e11i			1.21185i	−0.795520	+	0.605927i	$0.792802\pi$
$164$		−	1.83836e10i		−	0.154957i
$165$		0			0
$166$	−2.47911e10			−0.196678
$167$	−1.25840e11			−0.968804			−0.484402	−	0.874845i	$-0.660963\pi$
$167$	−1.25840e11			−0.968804			−0.484402	+	0.874845i	$0.660963\pi$
$168$	−1.88201e9	−	1.46303e8i	−0.0140629	−	0.00109322i
$169$	4.31296e10			0.312854
$170$		0			0
$171$	−9.04958e10	−	1.41554e10i	−0.618939	−	0.0968149i
$172$			1.87521e10i			0.124569i
$173$	1.26257e11			0.814750			0.407375	−	0.913261i	$-0.366444\pi$
$173$	1.26257e11			0.814750			0.407375	+	0.913261i	$0.366444\pi$
$174$	1.62985e11	+	1.26701e10i	1.02188	+	0.0794389i
$175$		0			0
$176$		−	6.11499e10i		−	0.362103i
$177$	−1.18386e11	−	9.20310e9i	−0.681452	−	0.0529746i
$178$		−	1.17635e11i		−	0.658317i
$179$			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	$0.279155\pi$
$182$	−4.66976e9			−0.0233850
$183$	−1.15435e9	+	1.48493e10i	−0.00562450	+	0.0723522i
$184$	6.45936e10			0.306267
$185$		0			0
$186$	−1.31838e10	+	1.69593e11i	−0.0592210	+	0.761805i
$187$		−	1.56832e11i		−	0.685846i
$188$	1.68385e10			0.0716992
$189$	−9.36194e9	−	2.21916e9i	−0.0388201	−	0.00920196i
$190$		0			0
$191$			1.58050e11i			0.621769i	0.950448	+	0.310884i	$0.100625\pi$
$191$			1.58050e11i			0.621769i	−0.950448	+	0.310884i	$0.899375\pi$
$192$	2.52778e9	−	3.25168e10i	0.00968799	−	0.124624i
$193$			3.78369e11i			1.41296i	0.707734	+	0.706479i	$0.249717\pi$
$193$			3.78369e11i			1.41296i	−0.707734	+	0.706479i	$0.750283\pi$
$194$			2.43178e11i			0.884944i
$195$		0			0
$196$	1.44397e11			0.499204
$197$	−1.89406e11			−0.638356			−0.319178	−	0.947695i	$-0.603407\pi$
$197$	−1.89406e11			−0.638356			−0.319178	+	0.947695i	$0.603407\pi$
$198$	4.81669e10	−	3.07932e11i	0.158279	−	1.01188i
$199$	−5.02942e10			−0.161158			−0.0805791	−	0.996748i	$-0.525677\pi$
$199$	−5.02942e10			−0.161158			−0.0805791	+	0.996748i	$0.525677\pi$
$200$		0			0
$201$	−1.62508e11	−	1.26330e10i	−0.495331	−	0.0385059i
$202$		−	2.44725e11i		−	0.727648i
$203$	1.99357e10			0.0578298
$204$	6.48304e9	−	8.33962e10i	0.0183496	−	0.236045i
$205$		0			0
$206$		−	6.41365e10i		−	0.172890i
$207$	3.25273e11	+	5.08795e10i	0.855848	+	0.133872i
$208$		−	8.06828e10i		−	0.207236i
$209$		−	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	$0.307780\pi$
$212$	−2.35108e11			−0.549019
$213$	−2.98791e11	−	2.32273e10i	−0.681505	−	0.0529787i
$214$	5.45778e11			1.21604
$215$		0			0
$216$	3.83422e10	−	1.61753e11i	0.0815470	−	0.344020i
$217$			2.07440e10i			0.0431117i
$218$	−1.22963e11			−0.249742
$219$	−2.61955e11	−	2.03638e10i	−0.520004	−	0.0404240i
$220$		0			0
$221$		−	2.06928e11i		−	0.392517i
$222$	4.69631e11	+	3.65081e10i	0.870947	+	0.0677055i
$223$			2.35580e11i			0.427183i	0.976923	+	0.213592i	$0.0685162\pi$
$223$			2.35580e11i			0.427183i	−0.976923	+	0.213592i	$0.931484\pi$
$224$		−	3.97734e9i		−	0.00705266i
$225$		0			0
$226$	3.15211e11			0.534638
$227$	4.27026e11			0.708475			0.354238	−	0.935155i	$-0.384740\pi$
$227$	4.27026e11			0.708475			0.354238	+	0.935155i	$0.384740\pi$
$228$	1.49577e10	−	1.92412e11i	0.0242768	−	0.312290i
$229$	−1.03671e12			−1.64619			−0.823096	−	0.567902i	$-0.807755\pi$
$229$	−1.03671e12			−1.64619			−0.823096	+	0.567902i	$0.807755\pi$
$230$		0			0
$231$	2.94580e9	−	3.78941e10i	0.00447862	−	0.0576119i
$232$			3.44444e11i			0.512483i
$233$	1.03766e12			1.51103			0.755516	−	0.655130i	$-0.227386\pi$
$233$	1.03766e12			1.51103			0.755516	+	0.655130i	$0.227386\pi$
$234$	6.35527e10	−	4.06293e11i	0.0905847	−	0.579109i
$235$		0			0
$236$		−	2.50192e11i		−	0.341754i
$237$	3.51485e10	−	4.52142e11i	0.0470073	−	0.604691i
$238$		−	1.02007e10i		−	0.0133582i
$239$		−	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	$0.720682\pi$
$242$	6.44354e11			0.776333
$243$	3.20490e11	−	7.84337e11i	0.378253	−	0.925702i
$244$	−3.13819e10			−0.0362852
$245$		0			0
$246$	1.96831e11	+	1.53012e10i	0.218483	+	0.0169844i
$247$		−	4.77426e11i		−	0.519304i
$248$	−3.58410e11			−0.382052
$249$	2.06344e10	−	2.65436e11i	0.0215573	−	0.277308i
$250$		0			0
$251$		−	5.66781e11i		−	0.568914i	−0.958689	−	0.284457i	$-0.908187\pi$
$251$		−	5.66781e11i		−	0.568914i	0.958689	−	0.284457i	$-0.0918133\pi$
$252$	3.13290e9	−	2.00286e10i	0.00308279	−	0.0197083i
$253$			1.30059e12i			1.25469i
$254$		−	9.24130e11i		−	0.874107i
$255$		0			0
$256$	6.87195e10			0.0625000
$257$	1.27943e12			1.14117			0.570584	−	0.821239i	$-0.306717\pi$
$257$	1.27943e12			1.14117			0.570584	+	0.821239i	$0.306717\pi$
$258$	−2.00777e11	−	1.56080e10i	−0.175637	−	0.0136536i
$259$	5.74436e10			0.0492882
$260$		0			0
$261$	−2.71314e11	+	1.73451e12i	−0.224011	+	1.43211i
$262$			9.40164e11i			0.761548i
$263$	−1.68583e12			−1.33978			−0.669892	−	0.742459i	$-0.733660\pi$
$263$	−1.68583e12			−1.33978			−0.669892	+	0.742459i	$0.733660\pi$
$264$	6.54725e11	+	5.08968e10i	0.510551	+	0.0396891i
$265$		0			0
$266$		−	2.35352e10i		−	0.0176730i
$267$	1.25950e12	+	9.79107e10i	0.928200	+	0.0721562i
$268$		−	3.43437e11i		−	0.248413i
$269$		−	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	$0.704765\pi$
$272$	1.76246e11			0.118379
$273$	3.88677e9	−	4.99985e10i	0.00256316	−	0.0329719i
$274$	2.09424e12			1.35604
$275$		0			0
$276$	−5.37632e10	+	6.91597e11i	−0.0335691	+	0.431825i
$277$			1.69580e12i			1.03986i	0.854209	+	0.519930i	$0.174042\pi$
$277$			1.69580e12i			1.03986i	−0.854209	+	0.519930i	$0.825958\pi$
$278$	1.80018e12			1.08416
$279$	−1.80484e12	−	2.82315e11i	−1.06762	−	0.166999i
$280$		0			0
$281$		−	2.44175e11i		−	0.139370i	−0.997569	−	0.0696851i	$-0.977801\pi$
$281$		−	2.44175e11i		−	0.139370i	0.997569	−	0.0696851i	$-0.0221995\pi$
$282$	−1.40152e10	+	1.80288e11i	−0.00785874	+	0.101093i
$283$			9.96409e11i			0.548916i	0.961599	+	0.274458i	$0.0884984\pi$
$283$			9.96409e11i			0.548916i	−0.961599	+	0.274458i	$0.911502\pi$
$284$		−	6.31450e11i		−	0.341781i
$285$		0			0
$286$	1.62455e12			0.848989
$287$	2.40756e10			0.0123643
$288$	3.46050e11	+	5.41294e10i	0.174653	+	0.0273194i
$289$	−1.56397e12			−0.775783
$290$		0			0
$291$	−2.60368e12	−	2.02404e11i	−1.24774	−	0.0969962i
$292$		−	5.53604e11i		−	0.260787i
$293$	1.57571e12			0.729690			0.364845	−	0.931068i	$-0.381122\pi$
$293$	1.57571e12			0.729690			0.364845	+	0.931068i	$0.381122\pi$
$294$	−1.20186e11	+	1.54604e12i	−0.0547163	+	0.703858i
$295$		0			0
$296$			9.92496e11i			0.436787i
$297$	3.25690e12	+	7.72018e11i	1.40936	+	0.334076i
$298$		−	1.82785e12i		−	0.777786i
$299$			1.71603e12i			0.718076i
$300$		0			0
$301$	−2.45583e10			−0.00993955
$302$	−6.98405e11			−0.278018
$303$	2.62024e12	+	2.03692e11i	1.02595	+	0.0797554i
$304$	4.06635e11			0.156616
$305$		0			0
$306$	8.87518e11	+	1.38826e11i	0.330803	+	0.0517445i
$307$		−	3.29823e12i		−	1.20945i	−0.796434	−	0.604726i	$-0.793283\pi$
$307$		−	3.29823e12i		−	1.20945i	0.796434	−	0.604726i	$-0.206717\pi$
$308$	8.00836e10			0.0288928
$309$	6.86702e11	+	5.33827e10i	0.243768	+	0.0189499i
$310$		0			0
$311$		−	1.67301e12i		−	0.575038i	−0.957775	−	0.287519i	$-0.907170\pi$
$311$		−	1.67301e12i		−	0.575038i	0.957775	−	0.287519i	$-0.0928304\pi$
$312$	8.63862e11	+	6.71547e10i	0.292194	+	0.0227145i
$313$		−	1.73318e12i		−	0.576930i	−0.957490	−	0.288465i	$-0.906855\pi$
$313$		−	1.73318e12i		−	0.576930i	0.957490	−	0.288465i	$-0.0931449\pi$
$314$		−	2.19785e12i		−	0.720029i
$315$		0			0
$316$	9.55536e11			0.303258
$317$	−1.33100e12			−0.415798			−0.207899	−	0.978150i	$-0.566663\pi$
$317$	−1.33100e12			−0.415798			−0.207899	+	0.978150i	$0.566663\pi$
$318$	1.95687e11	−	2.51727e12i	0.0601764	−	0.774094i
$319$	−6.93538e12			−2.09950
$320$		0			0
$321$	−4.54267e11	+	5.84358e12i	−0.133286	+	1.71456i
$322$			8.45937e10i			0.0244376i
$323$	1.04290e12			0.296641
$324$	1.69996e12	+	5.45157e11i	0.476117	+	0.152685i
$325$		0			0
$326$		−	3.15518e12i		−	0.856911i
$327$	1.02345e11	−	1.31655e12i	0.0273735	−	0.352126i
$328$			4.15973e11i			0.109571i
$329$			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	$0.297575\pi$
$332$	5.60959e11			0.139072
$333$	−7.81775e11	+	4.99789e12i	−0.190924	+	1.22058i
$334$	2.84743e12			0.685048
$335$		0			0
$336$	4.25849e10	+	3.31046e9i	0.00994396	+	0.000773022i
$337$			4.15283e12i			0.955422i	0.878517	+	0.477711i	$0.158533\pi$
$337$			4.15283e12i			0.955422i	−0.878517	+	0.477711i	$0.841467\pi$
$338$	−9.75911e11			−0.221221
$339$	−2.62360e11	+	3.37493e12i	−0.0586001	+	0.753818i
$340$		0			0
$341$		−	7.21658e12i		−	1.56516i
$342$	2.04769e12	+	3.20301e11i	0.437656	+	0.0684585i
$343$			3.78515e11i			0.0797282i
$344$		−	4.24313e11i		−	0.0880833i
$345$		0			0
$346$	−2.85687e12			−0.576115
$347$	−4.39939e12			−0.874470			−0.437235	−	0.899347i	$-0.644042\pi$
$347$	−4.39939e12			−0.874470			−0.437235	+	0.899347i	$0.644042\pi$
$348$	−3.68793e12	−	2.86691e11i	−0.722580	−	0.0561718i
$349$	9.24002e12			1.78462			0.892310	−	0.451423i	$-0.149083\pi$
$349$	9.24002e12			1.78462			0.892310	+	0.451423i	$0.149083\pi$
$350$		0			0
$351$	4.29724e12	+	1.01862e12i	0.806592	+	0.191195i
$352$			1.38366e12i			0.256046i
$353$	−9.20733e11			−0.167981			−0.0839905	−	0.996467i	$-0.526767\pi$
$353$	−9.20733e11			−0.167981			−0.0839905	+	0.996467i	$0.526767\pi$
$354$	2.67878e12	+	2.08242e11i	0.481860	+	0.0374587i
$355$		0			0
$356$			2.66177e12i			0.465500i
$357$	1.09218e11	+	8.49037e9i	0.0188345	+	0.00146415i
$358$		−	6.70999e12i		−	1.14106i
$359$		−	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
$362$	−5.62180e12			−0.904342
$363$	−5.36315e11	+	6.89902e12i	−0.0850916	+	1.09460i
$364$	1.05665e11			0.0165357
$365$		0			0
$366$	2.61201e10	−	3.36002e11i	0.00397712	−	0.0511607i
$367$		−	8.19379e12i		−	1.23071i	−0.788252	−	0.615353i	$-0.789013\pi$
$367$		−	8.19379e12i		−	1.23071i	0.788252	−	0.615353i	$-0.210987\pi$
$368$	−1.46159e12			−0.216564
$369$	−3.27656e11	+	2.09471e12i	−0.0478945	+	0.306190i
$370$		0			0
$371$		−	3.07903e11i		−	0.0438072i
$372$	2.98315e11	−	3.83746e12i	0.0418756	−	0.538677i
$373$			9.07322e12i			1.25666i	0.777947	+	0.628329i	$0.216261\pi$
$373$			9.07322e12i			1.25666i	−0.777947	+	0.628329i	$0.783739\pi$
$374$			3.54870e12i			0.484966i
$375$		0			0
$376$	−3.81012e11			−0.0506990
$377$	−9.15072e12			−1.20157
$378$	2.11837e11	+	5.02140e10i	0.0274500	+	0.00650677i
$379$	−1.17817e13			−1.50665			−0.753324	−	0.657650i	$-0.771551\pi$
$379$	−1.17817e13			−1.50665			−0.753324	+	0.657650i	$0.771551\pi$
$380$		0			0
$381$	9.89455e12	+	7.69180e11i	1.23246	+	0.0958083i
$382$		−	3.57627e12i		−	0.439657i
$383$	−6.82336e12			−0.827950			−0.413975	−	0.910288i	$-0.635860\pi$
$383$	−6.82336e12			−0.827950			−0.413975	+	0.910288i	$0.635860\pi$
$384$	−5.71972e10	+	7.35771e11i	−0.00685045	+	0.0881225i
$385$		0			0
$386$		−	8.56152e12i		−	0.999112i
$387$	3.34225e11	−	2.13670e12i	0.0385021	−	0.246144i
$388$		−	5.50249e12i		−	0.625750i
$389$			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
$392$	−3.26733e12			−0.352991
$393$	−1.00662e13	−	7.82526e11i	−1.07375	−	0.0834710i
$394$	4.28577e12			0.451386
$395$		0			0
$396$	−1.08989e12	+	6.96770e12i	−0.111920	+	0.715506i
$397$			1.26553e12i			0.128328i	0.997939	+	0.0641639i	$0.0204380\pi$
$397$			1.26553e12i			0.128328i	−0.997939	+	0.0641639i	$0.979562\pi$
$398$	1.13803e12			0.113956
$399$	2.51989e11	+	1.95890e10i	0.0249182	+	0.00193708i
$400$		0			0
$401$		−	1.50259e13i		−	1.44917i	−0.689187	−	0.724583i	$-0.742032\pi$
$401$		−	1.50259e13i		−	1.44917i	0.689187	−	0.724583i	$-0.257968\pi$
$402$	3.67714e12	+	2.85853e11i	0.350252	+	0.0272278i
$403$		−	9.52175e12i		−	0.895760i
$404$			5.53749e12i			0.514525i
$405$		0			0
$406$	−4.51094e11			−0.0408919
$407$	−1.99839e13			−1.78940
$408$	−1.46694e11	+	1.88704e12i	−0.0129752	+	0.166909i
$409$	1.70362e12			0.148852			0.0744261	−	0.997227i	$-0.476288\pi$
$409$	1.70362e12			0.148852			0.0744261	+	0.997227i	$0.476288\pi$
$410$		0			0
$411$	−1.74310e12	+	2.24228e13i	−0.148632	+	1.91197i
$412$			1.45124e12i			0.122251i
$413$	3.27659e11			0.0272692
$414$	−7.36009e12	−	1.15127e12i	−0.605176	−	0.0946621i
$415$		0			0
$416$			1.82564e12i			0.146538i
$417$	−1.49834e12	+	1.92743e13i	−0.118831	+	1.52862i
$418$			8.18758e12i			0.641615i
$419$			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	$0.497798\pi$
$422$	−1.07473e13			−0.803043
$423$	−1.91865e12	−	3.00118e11i	−0.141676	−	0.0221610i
$424$	5.31988e12			0.388215
$425$		0			0
$426$	6.76086e12	+	5.25574e11i	0.481897	+	0.0374616i
$427$		−	4.10986e10i		−	0.00289526i
$428$	−1.23495e13			−0.859869
$429$	−1.35216e12	+	1.73938e13i	−0.0930552	+	1.19704i
$430$		0			0
$431$		−	6.64491e12i		−	0.446789i	−0.974728	−	0.223395i	$-0.928286\pi$
$431$		−	6.64491e12i		−	0.446789i	0.974728	−	0.223395i	$-0.0717139\pi$
$432$	−8.67584e11	+	3.66006e12i	−0.0576624	+	0.243259i
$433$		−	7.28337e12i		−	0.478512i	−0.970956	−	0.239256i	$-0.923096\pi$
$433$		−	7.28337e12i		−	0.478512i	0.970956	−	0.239256i	$-0.0769036\pi$
$434$		−	4.69384e11i		−	0.0304846i
$435$		0			0
$436$	2.78233e12			0.176594
$437$	−8.64868e12			−0.542678
$438$	5.92738e12	+	4.60781e11i	0.367699	+	0.0285841i
$439$	1.52600e13			0.935907			0.467954	−	0.883753i	$-0.344991\pi$
$439$	1.52600e13			0.935907			0.467954	+	0.883753i	$0.344991\pi$
$440$		0			0
$441$	−1.64533e13	−	2.57363e12i	−0.986414	−	0.154296i
$442$			4.68225e12i			0.277551i
$443$	1.83304e13			1.07437			0.537184	−	0.843465i	$-0.319488\pi$
$443$	1.83304e13			1.07437			0.537184	+	0.843465i	$0.319488\pi$
$444$	−1.06265e13	−	8.26083e11i	−0.615852	−	0.0478750i
$445$		0			0
$446$		−	5.33057e12i		−	0.302064i
$447$	1.95706e13	+	1.52138e12i	1.09665	+	0.0852508i
$448$			8.99970e10i			0.00498698i
$449$			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
$452$	−7.13242e12			−0.378046
$453$	5.81303e11	−	7.47774e12i	0.0304727	−	0.391994i
$454$	−9.66249e12			−0.500968
$455$		0			0
$456$	−3.38454e11	+	4.35379e12i	−0.0171663	+	0.220823i
$457$			4.12288e11i			0.0206833i	0.999947	+	0.0103416i	$0.00329191\pi$
$457$			4.12288e11i			0.0206833i	−0.999947	+	0.0103416i	$0.996708\pi$
$458$	2.34581e13			1.16403
$459$	−2.22510e12	+	9.38700e12i	−0.109216	+	0.460748i
$460$		0			0
$461$		−	1.66247e11i		−	0.00798453i	−0.999992	−	0.00399226i	$-0.998729\pi$
$461$		−	1.66247e11i		−	0.00798453i	0.999992	−	0.00399226i	$-0.00127078\pi$
$462$	−6.66559e10	+	8.57446e11i	−0.00316686	+	0.0407377i
$463$		−	1.27323e13i		−	0.598416i	−0.954188	−	0.299208i	$-0.903278\pi$
$463$		−	1.27323e13i		−	0.598416i	0.954188	−	0.299208i	$-0.0967224\pi$
$464$		−	7.79389e12i		−	0.362380i
$465$		0			0
$466$	−2.34795e13			−1.06846
$467$	−2.26689e13			−1.02058			−0.510288	−	0.860004i	$-0.670461\pi$
$467$	−2.26689e13			−1.02058			−0.510288	+	0.860004i	$0.670461\pi$
$468$	−1.43803e12	+	9.19337e12i	−0.0640531	+	0.409492i
$469$	4.49775e11			0.0198213
$470$		0			0
$471$	2.35321e13	+	1.82934e12i	1.01521	+	0.0789203i
$472$			5.66120e12i			0.241657i
$473$	8.54352e12			0.360854
$474$	−7.95321e11	+	1.02308e13i	−0.0332392	+	0.427581i
$475$		0			0
$476$			2.30816e11i			0.00944565i
$477$	2.67892e13	+	4.19039e12i	1.08485	+	0.169693i
$478$			2.79873e13i			1.12156i
$479$		−	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
$482$	2.35126e13			0.903785
$483$	−9.05734e11	−	7.04098e10i	−0.0344560	−	0.00267853i
$484$	−1.45801e13			−0.548950
$485$		0			0
$486$	−7.25186e12	+	1.77475e13i	−0.267466	+	0.654570i
$487$		−	1.13824e13i		−	0.415516i	−0.978180	−	0.207758i	$-0.933383\pi$
$487$		−	1.13824e13i		−	0.415516i	0.978180	−	0.207758i	$-0.0666167\pi$
$488$	7.10091e11			0.0256575
$489$	3.37821e13	+	2.62615e12i	1.20821	+	0.0939235i
$490$		0			0
$491$		−	3.59512e13i		−	1.25981i	−0.776672	−	0.629906i	$-0.783094\pi$
$491$		−	3.59512e13i		−	1.25981i	0.776672	−	0.629906i	$-0.216906\pi$
$492$	−4.45377e12	−	3.46226e11i	−0.154491	−	0.0120098i
$493$		−	1.99891e13i		−	0.686370i
$494$			1.08029e13i			0.367203i
$495$		0			0
$496$	8.10990e12			0.270151
$497$	8.26965e11			0.0272713
$498$	−4.66903e11	+	6.00612e12i	−0.0152433	+	0.196086i
$499$	1.33630e13			0.431917			0.215958	−	0.976403i	$-0.430712\pi$
$499$	1.33630e13			0.431917			0.215958	+	0.976403i	$0.430712\pi$
$500$		0			0
$501$	−2.37000e12	+	3.04871e13i	−0.0750862	+	0.965890i
$502$			1.28248e13i			0.402283i
$503$	−3.54934e13			−1.10232			−0.551160	−	0.834399i	$-0.685815\pi$
$503$	−3.54934e13			−1.10232			−0.551160	+	0.834399i	$0.685815\pi$
$504$	−7.08893e10	+	4.53196e11i	−0.00217986	+	0.0139359i
$505$		0			0
$506$		−	2.94290e13i		−	0.887203i
$507$	8.12280e11	−	1.04490e13i	0.0242474	−	0.311913i
$508$			2.09107e13i			0.618087i
$509$		−	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
$512$	−1.55494e12			−0.0441942
$513$	−5.13377e12	+	2.16577e13i	−0.144494	+	0.609574i
$514$	−2.89501e13			−0.806928
$515$		0			0
$516$	4.54307e12	+	3.53168e11i	0.124194	+	0.00965456i
$517$		−	7.67166e12i		−	0.207700i
$518$	−1.29980e12			−0.0348520
$519$	2.37785e12	−	3.05881e13i	0.0631464	−	0.812299i
$520$		0			0
$521$			2.06244e13i			0.537270i	0.963242	+	0.268635i	$0.0865726\pi$
$521$			2.06244e13i			0.537270i	−0.963242	+	0.268635i	$0.913427\pi$
$522$	6.13914e12	−	3.92476e13i	0.158400	−	1.01265i
$523$		−	5.24376e13i		−	1.34009i	−0.742320	−	0.670045i	$-0.766275\pi$
$523$		−	5.24376e13i		−	1.34009i	0.742320	−	0.670045i	$-0.233725\pi$
$524$		−	2.12735e13i		−	0.538495i
$525$		0			0
$526$	3.81460e13			0.947370
$527$	2.07996e13			0.511683
$528$	−1.48147e13	−	1.15166e12i	−0.361014	−	0.0280644i
$529$	−1.03402e13			−0.249603
$530$		0			0
$531$	−4.45925e12	+	2.85080e13i	−0.105631	+	0.675297i
$532$			5.32541e11i			0.0124967i
$533$	−1.10510e13			−0.256900
$534$	−2.84992e13	−	2.21547e12i	−0.656337	−	0.0510221i
$535$		0			0
$536$			7.77110e12i			0.175654i
$537$	7.18431e13	+	5.58492e12i	1.60884	+	0.125068i
$538$			3.03260e13i			0.672828i
$539$		−	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	$0.154178\pi$
$542$	3.96770e13			0.848286
$543$	4.67919e12	−	6.01919e13i	0.0991223	−	1.27509i
$544$	−3.98798e12			−0.0837064
$545$		0			0
$546$	−8.79477e10	+	1.13134e12i	−0.00181243	+	0.0233147i
$547$		−	1.62332e13i		−	0.331488i	−0.986169	−	0.165744i	$-0.946997\pi$
$547$		−	1.62332e13i		−	0.331488i	0.986169	−	0.165744i	$-0.0530025\pi$
$548$	−4.73872e13			−0.958867
$549$	3.57580e12	+	5.59329e11i	0.0716987	+	0.0112152i
$550$		0			0
$551$		−	4.61189e13i		−	0.908074i
$552$	1.21652e12	−	1.56490e13i	0.0237369	−	0.305346i
$553$			1.25140e12i			0.0241974i
$554$		−	3.83715e13i		−	0.735292i
$555$		0			0
$556$	−4.07335e13			−0.766615
$557$	−1.12168e13			−0.209215			−0.104608	−	0.994514i	$-0.533359\pi$
$557$	−1.12168e13			−0.209215			−0.104608	+	0.994514i	$0.533359\pi$
$558$	4.08389e13	+	6.38805e12i	0.754924	+	0.118086i
$559$	1.12726e13			0.206521
$560$		0			0
$561$	−3.79955e13	−	2.95369e12i	−0.683783	−	0.0531557i
$562$			5.52506e12i			0.0985497i
$563$	7.98522e13			1.41171			0.705854	−	0.708357i	$-0.250563\pi$
$563$	7.98522e13			1.41171			0.705854	+	0.708357i	$0.250563\pi$
$564$	3.17127e11	−	4.07945e12i	0.00555697	−	0.0714835i
$565$		0			0
$566$		−	2.25462e13i		−	0.388142i
$567$	−7.13953e11	+	2.22632e12i	−0.0121830	+	0.0379902i
$568$			1.42881e13i			0.241675i
$569$		−	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	$0.151899\pi$
$572$	−3.67593e13			−0.600326
$573$	3.82907e13	+	2.97664e12i	0.619899	+	0.0481895i
$574$	−5.44769e11			−0.00874285
$575$		0			0
$576$	−7.83021e12	−	1.22481e12i	−0.123498	−	0.0193177i
$577$			3.31000e13i			0.517546i	0.965938	+	0.258773i	$0.0833182\pi$
$577$			3.31000e13i			0.517546i	−0.965938	+	0.258773i	$0.916682\pi$
$578$	3.53887e13			0.548562
$579$	9.16671e13	+	7.12600e12i	1.40871	+	0.109510i
$580$		0			0
$581$			7.34648e11i			0.0110968i
$582$	5.89145e13	+	4.57989e12i	0.882282	+	0.0685867i
$583$			1.07116e14i			1.59041i
$584$			1.25266e13i			0.184404i
$585$		0			0
$586$	−3.56543e13			−0.515969
$587$	1.21022e14			1.73650			0.868248	−	0.496131i	$-0.165246\pi$
$587$	1.21022e14			1.73650			0.868248	+	0.496131i	$0.165246\pi$
$588$	2.71950e12	−	3.49830e13i	0.0386903	−	0.497703i
$589$	4.79889e13			0.676961
$590$		0			0
$591$	−3.56717e12	+	4.58873e13i	−0.0494751	+	0.636436i
$592$		−	2.24576e13i		−	0.308855i
$593$	8.43944e12			0.115091			0.0575453	−	0.998343i	$-0.481673\pi$
$593$	8.43944e12			0.115091			0.0575453	+	0.998343i	$0.481673\pi$
$594$	−7.36952e13	−	1.74688e13i	−0.996567	−	0.236227i
$595$		0			0
$596$			4.13596e13i			0.549977i
$597$	−9.47213e11	+	1.21847e13i	−0.0124904	+	0.160673i
$598$		−	3.88294e13i		−	0.507756i
$599$			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	$0.441333\pi$
$602$	5.55692e11			0.00702832
$603$	−6.12119e12	+	3.91328e13i	−0.0767802	+	0.490857i
$604$	1.58031e13			0.196588
$605$		0			0
$606$	−5.92893e13	−	4.60902e12i	−0.725459	−	0.0563956i
$607$		−	4.47536e13i		−	0.543106i	−0.962423	−	0.271553i	$-0.912463\pi$
$607$		−	4.47536e13i		−	0.543106i	0.962423	−	0.271553i	$-0.0875372\pi$
$608$	−9.20110e12			−0.110744
$609$	3.75459e11	−	4.82981e12i	0.00448204	−	0.0576559i
$610$		0			0
$611$		−	1.01222e13i		−	0.118869i
$612$	−2.00822e13	−	3.14128e12i	−0.233913	−	0.0365889i
$613$		−	6.78051e13i		−	0.783358i	−0.920102	−	0.391679i	$-0.871894\pi$
$613$		−	6.78051e13i		−	0.783358i	0.920102	−	0.391679i	$-0.128106\pi$
$614$			7.46303e13i			0.855211i
$615$		0			0
$616$	−1.81209e12			−0.0204303
$617$	−2.48261e12			−0.0277641			−0.0138820	−	0.999904i	$-0.504419\pi$
$617$	−2.48261e12			−0.0277641			−0.0138820	+	0.999904i	$0.504419\pi$
$618$	−1.55383e13	−	1.20791e12i	−0.172370	−	0.0133996i
$619$	−1.64000e13			−0.180464			−0.0902320	−	0.995921i	$-0.528761\pi$
$619$	−1.64000e13			−0.180464			−0.0902320	+	0.995921i	$0.528761\pi$
$620$		0			0
$621$	1.84526e13	−	7.78454e13i	0.199801	−	0.842898i
$622$			3.78559e13i			0.406613i
$623$	−3.48592e12			−0.0371431
$624$	−1.95470e13	−	1.51954e12i	−0.206612	−	0.0160616i
$625$		0			0
$626$			3.92175e13i			0.407951i
$627$	−8.76635e13	−	6.81476e12i	−0.904651	−	0.0703255i
$628$			4.97317e13i			0.509138i
$629$		−	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	$0.521855\pi$
$632$	−2.16213e13			−0.214435
$633$	8.94532e12	−	1.15070e14i	0.0880192	−	1.13226i
$634$	3.01171e13			0.294014
$635$		0			0
$636$	−4.42789e12	+	5.69593e13i	−0.0425511	+	0.547367i
$637$		−	8.68020e13i		−	0.827623i
$638$	1.56930e14			1.48457
$639$	−1.12545e13	+	7.19503e13i	−0.105639	+	0.675349i
$640$		0			0
$641$			5.42348e13i			0.501173i	0.968094	+	0.250587i	$0.0806235\pi$
$641$			5.42348e13i			0.501173i	−0.968094	+	0.250587i	$0.919377\pi$
$642$	1.02789e13	−	1.32225e14i	0.0942477	−	1.21238i
$643$			5.54693e13i			0.504659i	0.967641	+	0.252329i	$0.0811966\pi$
$643$			5.54693e13i			0.504659i	−0.967641	+	0.252329i	$0.918803\pi$
$644$		−	1.91414e12i		−	0.0172800i
$645$		0			0
$646$	−2.35982e13			−0.209757
$647$	5.56652e13			0.490979			0.245489	−	0.969399i	$-0.421051\pi$
$647$	5.56652e13			0.490979			0.245489	+	0.969399i	$0.421051\pi$
$648$	−3.84657e13	−	1.23355e13i	−0.336665	−	0.107965i
$649$	−1.13988e14			−0.990002
$650$		0			0
$651$	5.02564e12	+	3.90682e11i	0.0429820	+	0.00334132i
$652$			7.13935e13i			0.605927i
$653$	5.56792e13			0.468951			0.234475	−	0.972122i	$-0.424663\pi$
$653$	5.56792e13			0.468951			0.234475	+	0.972122i	$0.424663\pi$
$654$	−2.31581e12	+	2.97901e13i	−0.0193560	+	0.248991i
$655$		0			0
$656$		−	9.41238e12i		−	0.0774784i
$657$	−9.86706e12	+	6.30802e13i	−0.0806048	+	0.515307i
$658$		−	4.98984e11i		−	0.00404536i
$659$			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	$0.808447\pi$
$662$	−1.06793e14			−0.839945
$663$	−5.01323e13	−	3.89717e12i	−0.391336	−	0.0304216i
$664$	−1.26931e13			−0.0983390
$665$		0			0
$666$	1.76895e13	−	1.13089e14i	0.135004	−	0.863080i
$667$			1.65767e14i			1.25565i
$668$	−6.44300e13			−0.484402
$669$	5.70737e13	+	4.43679e12i	0.425898	+	0.0331084i
$670$		0			0
$671$			1.42977e13i			0.105112i
$672$	−9.63587e11	−	7.49071e10i	−0.00703144	−	0.000546609i
$673$			9.45260e13i			0.684662i	0.939579	+	0.342331i	$0.111216\pi$
$673$			9.45260e13i			0.684662i	−0.939579	+	0.342331i	$0.888784\pi$
$674$		−	9.39679e13i		−	0.675585i
$675$		0			0
$676$	2.20824e13			0.156427
$677$	−1.70106e14			−1.19612			−0.598060	−	0.801451i	$-0.704062\pi$
$677$	−1.70106e14			−1.19612			−0.598060	+	0.801451i	$0.704062\pi$
$678$	5.93652e12	−	7.63660e13i	0.0414366	−	0.533030i
$679$	7.20622e12			0.0499297
$680$		0			0
$681$	8.04237e12	−	1.03455e14i	0.0549096	−	0.706344i
$682$			1.63293e14i			1.10674i
$683$	−2.23578e14			−1.50427			−0.752135	−	0.659009i	$-0.770976\pi$
$683$	−2.23578e14			−1.50427			−0.752135	+	0.659009i	$0.770976\pi$
$684$	−4.63338e13	−	7.24758e12i	−0.309469	−	0.0484075i
$685$		0			0
$686$		−	8.56481e12i		−	0.0563764i
$687$	−1.95249e13	+	2.51163e14i	−0.127586	+	1.64124i
$688$			9.60110e12i			0.0622843i
$689$			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	$0.511129\pi$
$692$	6.46435e13			0.407375
$693$	−9.12509e12	−	1.42735e12i	−0.0570915	−	0.00893029i
$694$	9.95468e13			0.618344
$695$		0			0
$696$	8.34482e13	+	6.48708e12i	0.510941	+	0.0397194i
$697$		−	2.41401e13i		−	0.146749i
$698$	−2.09078e14			−1.26192
$699$	1.95426e13	−	2.51392e14i	0.117111	−	1.50649i
$700$		0			0
$701$			1.10962e14i			0.655516i	0.944762	+	0.327758i	$0.106293\pi$
$701$			1.10962e14i			0.655516i	−0.944762	+	0.327758i	$0.893707\pi$
$702$	−9.72354e13	−	2.30488e13i	−0.570346	−	0.135195i
$703$		−	1.32889e14i		−	0.773948i
$704$		−	3.13087e13i		−	0.181052i
$705$		0			0
$706$	2.08338e13			0.118781
$707$	−7.25206e12			−0.0410548
$708$	−6.06138e13	−	4.71199e12i	−0.340726	−	0.0264873i
$709$	−2.08219e14			−1.16222			−0.581112	−	0.813824i	$-0.697382\pi$
$709$	−2.08219e14			−1.16222			−0.581112	+	0.813824i	$0.697382\pi$
$710$		0			0
$711$	−1.08878e14	−	1.70308e13i	−0.599229	−	0.0937318i
$712$		−	6.02289e13i		−	0.329158i
$713$	−1.72489e14			−0.936080
$714$	−2.47132e12	−	1.92115e11i	−0.0133180	−	0.00103531i
$715$		0			0
$716$			1.51830e14i			0.806848i
$717$	−2.99656e14	−	2.32946e13i	−1.58135	−	0.122931i
$718$			1.39746e14i			0.732347i
$719$			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
$722$	8.42844e13			0.429597
$723$	−1.95702e13	+	2.51746e14i	−0.0990613	+	1.27430i
$724$	1.27207e14			0.639466
$725$		0			0
$726$	1.21354e13	−	1.56107e14i	0.0601688	−	0.773997i
$727$		−	2.99071e14i		−	1.47266i	−0.676622	−	0.736330i	$-0.736557\pi$
$727$		−	2.99071e14i		−	1.47266i	0.676622	−	0.736330i	$-0.263443\pi$
$728$	−2.39092e12			−0.0116925
$729$	−1.83985e14	−	9.24165e13i	−0.893602	−	0.448861i
$730$		0			0
$731$			2.46241e13i			0.117970i
$732$	−5.91030e11	+	7.60286e12i	−0.00281225	+	0.0361761i
$733$		−	1.19922e14i		−	0.566734i	−0.959012	−	0.283367i	$-0.908549\pi$
$733$		−	1.19922e14i		−	0.566734i	0.959012	−	0.283367i	$-0.0914514\pi$
$734$			1.85404e14i			0.870241i
$735$		0			0
$736$	3.30719e13			0.153134
$737$	−1.56471e14			−0.719608
$738$	7.41400e12	−	4.73978e13i	0.0338666	−	0.216509i
$739$	7.29345e13			0.330911			0.165455	−	0.986217i	$-0.447091\pi$
$739$	7.29345e13			0.330911			0.165455	+	0.986217i	$0.447091\pi$
$740$		0			0
$741$	−1.15666e14	−	8.99158e12i	−0.517742	−	0.0402481i
$742$			6.96706e12i			0.0309763i
$743$	1.07061e14			0.472809			0.236405	−	0.971655i	$-0.424031\pi$
$743$	1.07061e14			0.472809			0.236405	+	0.971655i	$0.424031\pi$
$744$	−6.75011e12	+	8.68317e13i	−0.0296105	+	0.380902i
$745$		0			0
$746$		−	2.05304e14i		−	0.888592i
$747$	−6.39183e13	−	9.99815e12i	−0.274803	−	0.0429850i
$748$		−	8.02979e13i		−	0.342923i
$749$		−	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	$0.374323\pi$
$752$	8.62131e12			0.0358496
$753$	−1.37313e14	−	1.06744e13i	−0.567203	−	0.0440931i
$754$	2.07057e14			0.849638
$755$		0			0
$756$	−4.79332e12	−	1.13621e12i	−0.0194101	−	0.00460098i
$757$		−	1.73049e14i		−	0.696130i	−0.937470	−	0.348065i	$-0.886839\pi$
$757$		−	1.73049e14i		−	0.696130i	0.937470	−	0.348065i	$-0.113161\pi$
$758$	2.66589e14			1.06536
$759$	3.15093e14	+	2.44946e13i	1.25092	+	0.0972438i
$760$		0			0
$761$			1.10156e14i			0.431604i	0.976437	+	0.215802i	$0.0692365\pi$
$761$			1.10156e14i			0.431604i	−0.976437	+	0.215802i	$0.930764\pi$
$762$	−2.23888e14	−	1.74046e13i	−0.871477	−	0.0677467i
$763$			3.64382e12i			0.0140907i
$764$			8.09218e13i			0.310884i
$765$		0			0
$766$	1.54395e14			0.585449
$767$	−1.50399e14			−0.566589
$768$	1.29423e12	−	1.66486e13i	0.00484400	−	0.0623120i
$769$	−2.30458e14			−0.856959			−0.428480	−	0.903551i	$-0.640951\pi$
$769$	−2.30458e14			−0.856959			−0.428480	+	0.903551i	$0.640951\pi$
$770$		0			0
$771$	2.40960e13	−	3.09965e14i	0.0884451	−	1.13774i
$772$			1.93725e14i			0.706479i
$773$	1.50965e14			0.546991			0.273495	−	0.961873i	$-0.411820\pi$
$773$	1.50965e14			0.546991			0.273495	+	0.961873i	$0.411820\pi$
$774$	−7.56265e12	+	4.83481e13i	−0.0272251	+	0.174050i
$775$		0			0
$776$			1.24507e14i			0.442472i
$777$	1.08186e12	−	1.39168e13i	0.00382003	−	0.0491399i
$778$		−	1.60160e13i		−	0.0561897i
$779$		−	5.56961e13i		−	0.194150i
$780$		0			0
$781$	−2.87690e14			−0.990079
$782$	8.48200e13			0.290044
$783$	4.15109e14	+	9.83979e13i	1.41044	+	0.334331i
$784$	7.39313e13			0.249602
$785$		0			0
$786$	2.27773e14	+	1.77065e13i	0.759257	+	0.0590229i
$787$		−	3.42081e14i		−	1.13306i	−0.824039	−	0.566532i	$-0.808285\pi$
$787$		−	3.42081e14i		−	1.13306i	0.824039	−	0.566532i	$-0.191715\pi$
$788$	−9.69760e13			−0.319178
$789$	−3.17500e13	+	4.08424e14i	−0.103839	+	1.33575i
$790$		0			0
$791$		−	9.34082e12i		−	0.0301649i
$792$	2.46615e13	−	1.57661e14i	0.0791394	−	0.505939i
$793$			1.88647e13i			0.0601568i
$794$		−	2.86357e13i		−	0.0907415i
$795$		0			0
$796$	−2.57506e13			−0.0805791
$797$	5.22986e14			1.62629			0.813146	−	0.582059i	$-0.197753\pi$
$797$	5.22986e14			1.62629			0.813146	+	0.582059i	$0.197753\pi$
$798$	−5.70185e12	−	4.43249e11i	−0.0176198	−	0.00136973i
$799$	2.21112e13			0.0679013
$800$		0			0
$801$	4.74415e13	−	3.03294e14i	0.143878	−	0.919816i
$802$			3.39997e14i			1.02472i
$803$	−2.52223e14			−0.755453
$804$	−8.32043e13	−	6.46811e12i	−0.247665	−	0.0192530i
$805$		0			0
$806$			2.15453e14i			0.633398i
$807$	−3.24697e14	−	2.52412e13i	−0.948660	−	0.0737468i
$808$		−	1.25299e14i		−	0.363824i
$809$			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	$0.328052\pi$
$812$	1.02071e13			0.0289149
$813$	−3.30243e13	+	4.24817e14i	−0.0929782	+	1.19605i
$814$	4.52183e14			1.26530
$815$		0			0
$816$	3.31932e12	−	4.26989e13i	0.00917482	−	0.118023i
$817$			5.68128e13i			0.156076i
$818$	−3.85484e13			−0.105254
$819$	−1.20399e13	−	1.88329e12i	−0.0326741	−	0.00511090i
$820$		0			0
$821$			6.68322e14i			1.79172i	0.444336	+	0.895860i	$0.353440\pi$
$821$			6.68322e14i			1.79172i	−0.444336	+	0.895860i	$0.646560\pi$
$822$	3.94418e13	−	5.07370e14i	0.105099	−	1.35196i
$823$		−	4.35331e13i		−	0.115298i	−0.998337	−	0.0576488i	$-0.981640\pi$
$823$		−	4.35331e13i		−	0.115298i	0.998337	−	0.0576488i	$-0.0183604\pi$
$824$		−	3.28379e13i		−	0.0864449i
$825$		0			0
$826$	−7.41407e12			−0.0192822
$827$	−2.21008e13			−0.0571321			−0.0285661	−	0.999592i	$-0.509094\pi$
$827$	−2.21008e13			−0.0571321			−0.0285661	+	0.999592i	$0.509094\pi$
$828$	1.66540e14	+	2.60503e13i	0.427924	+	0.0669362i
$829$	−7.62973e14			−1.94866			−0.974331	−	0.225119i	$-0.927723\pi$
$829$	−7.62973e14			−1.94866			−0.974331	+	0.225119i	$0.927723\pi$
$830$		0			0
$831$	4.10839e14	+	3.19377e13i	1.03673	+	0.0805933i
$832$		−	4.13096e13i		−	0.103618i
$833$	1.89613e14			0.472761
$834$	3.39037e13	−	4.36128e14i	0.0840265	−	1.08090i
$835$		0			0
$836$		−	1.85264e14i		−	0.453690i
$837$	−1.02388e14	+	4.31940e14i	−0.249241	+	1.05147i
$838$		−	5.03342e14i		−	1.21799i
$839$		−	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
$842$	−4.13963e12			−0.00978141
$843$	−5.91561e13	−	4.59867e12i	−0.138951	−	0.0108017i
$844$	2.43184e14			0.567837
$845$		0			0
$846$	4.34142e13	+	6.79088e12i	0.100180	+	0.0156702i
$847$		−	1.90945e13i		−	0.0438017i
$848$	−1.20375e14			−0.274509
$849$	2.41399e14	+	1.87658e13i	0.547265	+	0.0425431i
$850$		0			0
$851$			4.77649e14i			1.07019i
$852$	−1.52981e14	−	1.18924e13i	−0.340752	−	0.0264893i
$853$		−	1.82179e14i		−	0.403415i	−0.979446	−	0.201708i	$-0.935351\pi$
$853$		−	1.82179e14i		−	0.403415i	0.979446	−	0.201708i	$-0.0646491\pi$
$854$			9.29956e11i			0.00204726i
$855$		0			0
$856$	2.79438e14			0.608019
$857$	8.52398e14			1.84390			0.921952	−	0.387305i	$-0.126594\pi$
$857$	8.52398e14			1.84390			0.921952	+	0.387305i	$0.126594\pi$
$858$	3.05958e13	−	3.93577e14i	0.0658000	−	0.846435i
$859$	−2.60062e14			−0.556046			−0.278023	−	0.960574i	$-0.589679\pi$
$859$	−2.60062e14			−0.556046			−0.278023	+	0.960574i	$0.589679\pi$
$860$		0			0
$861$	4.53427e11	−	5.83278e12i	0.000958279	−	0.0123271i
$862$			1.50357e14i			0.315928i
$863$	2.71494e14			0.567161			0.283580	−	0.958948i	$-0.408478\pi$
$863$	2.71494e14			0.567161			0.283580	+	0.958948i	$0.408478\pi$
$864$	1.96312e13	−	8.28177e13i	0.0407735	−	0.172010i
$865$		0			0
$866$			1.64804e14i			0.338359i
$867$	−2.94551e13	+	3.78903e14i	−0.0601263	+	0.773450i
$868$			1.06210e13i			0.0215558i
$869$		−	4.35344e14i		−	0.878484i
$870$		0			0
$871$	−2.06452e14			−0.411840
$872$	−6.29569e13			−0.124871
$873$	−9.80726e13	+	6.26979e14i	−0.193409	+	1.23646i
$874$	1.95697e14			0.383732
$875$		0			0
$876$	−1.34121e14	−	1.04263e13i	−0.260002	−	0.0202120i
$877$			1.90122e14i			0.366466i	0.983069	+	0.183233i	$0.0586563\pi$
$877$			1.90122e14i			0.366466i	−0.983069	+	0.183233i	$0.941344\pi$
$878$	−3.45295e14			−0.661786
$879$	2.96761e13	−	3.81746e14i	0.0565539	−	0.727495i
$880$		0			0
$881$		−	6.12829e14i		−	1.15468i	−0.816506	−	0.577338i	$-0.804092\pi$
$881$		−	6.12829e14i		−	1.15468i	0.816506	−	0.577338i	$-0.195908\pi$
$882$	3.72295e14	+	5.82347e13i	0.697500	+	0.109104i
$883$			4.57367e14i			0.852042i	0.904713	+	0.426021i	$0.140085\pi$
$883$			4.57367e14i			0.852042i	−0.904713	+	0.426021i	$0.859915\pi$
$884$		−	1.05947e14i		−	0.196258i
$885$		0			0
$886$	−4.14769e14			−0.759693
$887$	5.97146e14			1.08758			0.543791	−	0.839221i	$-0.316988\pi$
$887$	5.97146e14			1.08758			0.543791	+	0.839221i	$0.316988\pi$
$888$	2.40451e14	+	1.86921e13i	0.435473	+	0.0338527i
$889$	−2.73852e13			−0.0493182
$890$		0			0
$891$	2.48375e14	−	7.74505e14i	0.442302	−	1.37923i
$892$			1.20617e14i			0.213592i
$893$	5.10150e13			0.0898340
$894$	−4.42832e14	−	3.44248e13i	−0.775446	−	0.0602815i
$895$		0			0
$896$		−	2.03640e12i		−	0.00352633i
$897$	4.15742e14	+	3.23189e13i	0.715916	+	0.0556537i
$898$		−	1.88685e14i		−	0.323113i
$899$		−	9.19792e14i		−	1.56636i
$900$		0			0
$901$	−3.08727e14			−0.519938
$902$	1.89518e14			0.317408
$903$	−4.62519e11	+	5.94973e12i	−0.000770354	+	0.00990965i
$904$	1.61388e14			0.267319
$905$		0			0
$906$	−1.31534e13	+	1.69202e14i	−0.0215475	+	0.277181i
$907$		−	7.96198e14i		−	1.29713i	−0.761158	−	0.648567i	$-0.775369\pi$
$907$		−	7.96198e14i		−	1.29713i	0.761158	−	0.648567i	$-0.224631\pi$
$908$	2.18637e14			0.354238
$909$	9.86964e13	−	6.30967e14i	0.159031	−	1.01669i
$910$		0			0
$911$			5.95524e14i			0.949089i	0.880231	+	0.474545i	$0.157387\pi$
$911$			5.95524e14i			0.949089i	−0.880231	+	0.474545i	$0.842613\pi$
$912$	7.65834e12	−	9.85151e13i	0.0121384	−	0.156145i
$913$		−	2.55574e14i		−	0.402869i
$914$		−	9.32901e12i		−	0.0146253i
$915$		0			0
$916$	−5.30796e14			−0.823096
$917$	2.78603e13			0.0429675
$918$	5.03483e13	−	2.12403e14i	0.0772274	−	0.325798i
$919$	−5.55318e14			−0.847157			−0.423579	−	0.905859i	$-0.639226\pi$
$919$	−5.55318e14			−0.847157			−0.423579	+	0.905859i	$0.639226\pi$
$920$		0			0
$921$	−7.99058e14	−	6.21170e13i	−1.20581	−	0.0937373i
$922$			3.76174e12i			0.00564591i
$923$	−3.79586e14			−0.566633
$924$	1.50825e12	−	1.94018e13i	0.00223931	−	0.0288059i
$925$		0			0
$926$			2.88100e14i			0.423144i
$927$	2.58659e13	−	1.65361e14i	0.0377859	−	0.241566i
$928$			1.76356e14i			0.256241i
$929$		−	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
$932$	5.31280e14			0.755516
$933$	−4.05318e14	−	3.15085e13i	−0.573308	−	0.0445677i
$934$	5.12938e14			0.721656
$935$		0			0
$936$	3.25390e13	−	2.08022e14i	0.0452924	−	0.289555i
$937$		−	3.07315e14i		−	0.425487i	−0.977108	−	0.212743i	$-0.931760\pi$
$937$		−	3.07315e14i		−	0.425487i	0.977108	−	0.212743i	$-0.0682398\pi$
$938$	−1.01773e13			−0.0140158
$939$	−4.19897e14	−	3.26419e13i	−0.575195	−	0.0447143i
$940$		0			0
$941$		−	2.63150e14i		−	0.356661i	−0.983971	−	0.178330i	$-0.942930\pi$
$941$		−	2.63150e14i		−	0.356661i	0.983971	−	0.178330i	$-0.0570696\pi$
$942$	−5.32471e14	−	4.13931e13i	−0.717863	−	0.0558051i
$943$			2.00191e14i			0.268464i
$944$		−	1.28098e14i		−	0.170877i
$945$		0			0
$946$	−1.93318e14			−0.255162
$947$	1.20121e15			1.57713			0.788566	−	0.614950i	$-0.210824\pi$
$947$	1.20121e15			1.57713			0.788566	+	0.614950i	$0.210824\pi$
$948$	1.79960e13	−	2.31497e14i	0.0235037	−	0.302345i
$949$	−3.32790e14			−0.432354
$950$		0			0
$951$	−2.50674e13	+	3.22461e14i	−0.0322260	+	0.414547i
$952$		−	5.22278e12i		−	0.00667908i
$953$	−3.27942e13			−0.0417189			−0.0208594	−	0.999782i	$-0.506640\pi$
$953$	−3.27942e13			−0.0417189			−0.0208594	+	0.999782i	$0.506640\pi$
$954$	−6.06171e14	−	9.48177e13i	−0.767102	−	0.119991i
$955$		0			0
$956$		−	6.33279e14i		−	0.793060i
$957$	−1.30617e14	+	1.68023e15i	−0.162720	+	2.09319i
$958$			5.42276e14i			0.672036i
$959$		−	6.20597e13i		−	0.0765097i
$960$		0			0
$961$	1.37458e14			0.167708
$962$	5.96623e14			0.724143
$963$	1.40716e15	+	2.20110e14i	1.69908	+	0.265771i
$964$	−5.32029e14			−0.639072
$965$		0			0
$966$	2.04944e13	+	1.59319e12i	0.0243641	+	0.00189401i
$967$		−	9.87053e14i		−	1.16737i	−0.811981	−	0.583684i	$-0.801611\pi$
$967$		−	9.87053e14i		−	1.16737i	0.811981	−	0.583684i	$-0.198389\pi$
$968$	3.29909e14			0.388166
$969$	1.96414e13	−	2.52663e14i	0.0229908	−	0.295748i
$970$		0			0
$971$			5.42431e14i			0.628418i	0.949354	+	0.314209i	$0.101739\pi$
$971$			5.42431e14i			0.628418i	−0.949354	+	0.314209i	$0.898261\pi$
$972$	1.64091e14	−	4.01580e14i	0.189127	−	0.462851i
$973$		−	5.33457e13i		−	0.0611695i
$974$			2.57554e14i			0.293814i
$975$		0			0
$976$	−1.60675e13			−0.0181426
$977$	−9.53859e14			−1.07155			−0.535774	−	0.844361i	$-0.679980\pi$
$977$	−9.53859e14			−1.07155			−0.535774	+	0.844361i	$0.679980\pi$
$978$	−7.64402e14	−	5.94229e13i	−0.854333	−	0.0664140i
$979$	1.21271e15			1.34847
$980$		0			0
$981$	−3.17031e14	−	4.95903e13i	−0.348945	−	0.0545823i
$982$			8.13482e14i			0.890821i
$983$	6.30884e14			0.687356			0.343678	−	0.939088i	$-0.388327\pi$
$983$	6.30884e14			0.687356			0.343678	+	0.939088i	$0.388327\pi$
$984$	1.00777e14	+	7.83420e12i	0.109241	+	0.00849218i
$985$		0			0
$986$			4.52301e14i			0.485337i
$987$	5.34256e12	+	4.15319e11i	0.00570379	+	0.000443400i
$988$		−	2.44442e14i		−	0.259652i
$989$		−	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	$0.416712\pi$
$992$	−1.83506e14			−0.191026
$993$	8.88866e13	−	1.14342e15i	0.0920640	−	1.18429i
$994$	−1.87121e13			−0.0192837
$995$		0			0
$996$	1.05648e13	−	1.35903e14i	0.0107787	−	0.138654i
$997$			1.62993e15i			1.65460i	0.561759	+	0.827301i	$0.310125\pi$
$997$			1.62993e15i			1.65460i	−0.561759	+	0.827301i	$0.689875\pi$
$998$	−3.02369e14			−0.305411
$999$	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.b.a.149.3		8
3.2	odd	2	inner	150.11.b.a.149.5		8
5.2	odd	4		150.11.d.a.101.1		4
5.3	odd	4		6.11.b.a.5.4	yes	4
5.4	even	2	inner	150.11.b.a.149.6		8
15.2	even	4		150.11.d.a.101.3		4
15.8	even	4		6.11.b.a.5.2	✓	4
15.14	odd	2	inner	150.11.b.a.149.4		8
20.3	even	4		48.11.e.d.17.1		4
40.3	even	4		192.11.e.h.65.4		4
40.13	odd	4		192.11.e.g.65.1		4
45.13	odd	12		162.11.d.d.107.2		8
45.23	even	12		162.11.d.d.107.3		8
45.38	even	12		162.11.d.d.53.2		8
45.43	odd	12		162.11.d.d.53.3		8
60.23	odd	4		48.11.e.d.17.2		4
120.53	even	4		192.11.e.g.65.2		4
120.83	odd	4		192.11.e.h.65.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.2	✓	4	15.8	even	4
6.11.b.a.5.4	yes	4	5.3	odd	4
48.11.e.d.17.1		4	20.3	even	4
48.11.e.d.17.2		4	60.23	odd	4
150.11.b.a.149.3		8	1.1	even	1	trivial
150.11.b.a.149.4		8	15.14	odd	2	inner
150.11.b.a.149.5		8	3.2	odd	2	inner
150.11.b.a.149.6		8	5.4	even	2	inner
150.11.d.a.101.1		4	5.2	odd	4
150.11.d.a.101.3		4	15.2	even	4
162.11.d.d.53.2		8	45.38	even	12
162.11.d.d.53.3		8	45.43	odd	12
162.11.d.d.107.2		8	45.13	odd	12
162.11.d.d.107.3		8	45.23	even	12
192.11.e.g.65.1		4	40.13	odd	4
192.11.e.g.65.2		4	120.53	even	4
192.11.e.h.65.3		4	120.83	odd	4
192.11.e.h.65.4		4	40.3	even	4

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.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-22.6274 q^{2} +(18.8335 - 242.269i) q^{3} +512.000 q^{4} +(-426.153 + 5481.92i) q^{6} +670.530i q^{7} -11585.2 q^{8} +(-58339.6 - 9125.53i) q^{9} +O(q^{10})\)	\(q-22.6274 q^{2} +(18.8335 - 242.269i) q^{3} +512.000 q^{4} +(-426.153 + 5481.92i) q^{6} +670.530i q^{7} -11585.2 q^{8} +(-58339.6 - 9125.53i) q^{9} -233268. i q^{11} +(9642.73 - 124042. i) q^{12} -307781. i q^{13} -15172.4i q^{14} +262144. q^{16} +672324. q^{17} +(1.32007e6 + 206487. i) q^{18} +1.55119e6 q^{19} +(162449. + 12628.4i) q^{21} +5.27826e6i q^{22} -5.57551e6 q^{23} +(-218190. + 2.80674e6i) q^{24} +6.96428e6i q^{26} +(-3.30957e6 + 1.39620e7i) q^{27} +343311. i q^{28} -2.97313e7i q^{29} +3.09368e7 q^{31} -5.93164e6 q^{32} +(-5.65137e7 - 4.39325e6i) q^{33} -1.52130e7 q^{34} +(-2.98699e7 - 4.67227e6i) q^{36} -8.56690e7i q^{37} -3.50994e7 q^{38} +(-7.45657e7 - 5.79657e6i) q^{39} -3.59054e7i q^{41} +(-3.67579e6 - 285748. i) q^{42} +3.66253e7i q^{43} -1.19433e8i q^{44} +1.26159e8 q^{46} +3.28877e7 q^{47} +(4.93708e6 - 6.35094e7i) q^{48} +2.82026e8 q^{49} +(1.26622e7 - 1.62883e8i) q^{51} -1.57584e8i q^{52} -4.59194e8 q^{53} +(7.48870e7 - 3.15924e8i) q^{54} -7.76824e6i q^{56} +(2.92143e7 - 3.75805e8i) q^{57} +6.72743e8i q^{58} -4.88657e8i q^{59} -6.12928e7 q^{61} -7.00020e8 q^{62} +(6.11894e6 - 3.91184e7i) q^{63} +1.34218e8 q^{64} +(1.27876e9 + 9.94079e7i) q^{66} -6.70776e8i q^{67} +3.44230e8 q^{68} +(-1.05006e8 + 1.35077e9i) q^{69} -1.23330e9i q^{71} +(6.75878e8 + 1.05721e8i) q^{72} -1.08126e9i q^{73} +1.93847e9i q^{74} +7.94209e8 q^{76} +1.56413e8 q^{77} +(1.68723e9 + 1.31161e8i) q^{78} +1.86628e9 q^{79} +(3.32023e9 + 1.06476e9i) q^{81} +8.12446e8i q^{82} +1.09562e9 q^{83} +(8.31737e7 + 6.46574e6i) q^{84} -8.28736e8i q^{86} +(-7.20298e9 - 5.59944e8i) q^{87} +2.70247e9i q^{88} +5.19876e9i q^{89} +2.06376e8 q^{91} -2.85466e9 q^{92} +(5.82647e8 - 7.49503e9i) q^{93} -7.44163e8 q^{94} +(-1.11713e8 + 1.43705e9i) q^{96} -1.07471e10i q^{97} -6.38151e9 q^{98} +(-2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9}+O(q^{10}) \) 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9	\( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99}+O(q^{100}) \) 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9 + 2097152 * q^16 + 3137456 * q^19 + 19256016 * q^21 + 5505024 * q^24 - 43571696 * q^31 - 302174208 * q^34 - 162828288 * q^36 - 434574480 * q^39 + 377628672 * q^46 + 100116840 * q^49 - 1417153536 * q^51 - 963325440 * q^54 - 2368077488 * q^61 + 1073741824 * q^64 + 6246890496 * q^66 - 1192536576 * q^69 + 1606377472 * q^76 - 398565136 * q^79 + 2917929096 * q^81 + 9859080192 * q^84 + 16634464160 * q^91 - 17010954240 * q^94 + 2818572288 * q^96 + 5253825024 * q^99

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