LMFDB - Embedded newform 150.11.d.d.101.10

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 451853 x^{12} + 31595028 x^{11} + 79693501240 x^{10} - 10455174924036 x^{9} + \cdots + 36\!\cdots\!87 $ x^14 - 6x^13 - 451853x^12 + 31595028x^11 + 79693501240x^10 - 10455174924036x^9 - 6531861074725822x^8 + 1272696059454411732x^7 + 215696966483401582742x^6 - 63664078934012968776084x^5 - 288992727952897261055608x^4 + 1040905657503589682991249636x^3 - 48275719234338322467113084079x^2 - 5315723027583579014105238793830*x + 365506222838083753530266599230387
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{35}\cdot 3^{29}\cdot 5^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.10
Root			$114.339 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	150.101
Dual form			150.11.d.d.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274i q^{2} +(-121.467 + 210.463i) q^{3} -512.000 q^{4} +(-4762.24 - 2748.49i) q^{6} -2558.79 q^{7} -11585.2i q^{8} +(-29540.5 - 51128.7i) q^{9} +O(q^{10})$	\(q+22.6274i q^{2} +(-121.467 + 210.463i) q^{3} -512.000 q^{4} +(-4762.24 - 2748.49i) q^{6} -2558.79 q^{7} -11585.2i q^{8} +(-29540.5 - 51128.7i) q^{9} +307918. i q^{11} +(62191.1 - 107757. i) q^{12} -584993. q^{13} -57898.9i q^{14} +262144. q^{16} +1.73434e6i q^{17} +(1.15691e6 - 668426. i) q^{18} -913369. q^{19} +(310809. - 538532. i) q^{21} -6.96740e6 q^{22} +1.13580e7i q^{23} +(2.43827e6 + 1.40722e6i) q^{24} -1.32369e7i q^{26} +(1.43489e7 - 6743.80i) q^{27} +1.31010e6 q^{28} +7.97174e6i q^{29} -5.14403e7 q^{31} +5.93164e6i q^{32} +(-6.48055e7 - 3.74019e7i) q^{33} -3.92436e7 q^{34} +(1.51247e7 + 2.61779e7i) q^{36} -2.58947e7 q^{37} -2.06672e7i q^{38} +(7.10573e7 - 1.23119e8i) q^{39} -6.12373e7i q^{41} +(1.21856e7 + 7.03280e6i) q^{42} +8.89704e7 q^{43} -1.57654e8i q^{44} -2.57001e8 q^{46} +1.43331e8i q^{47} +(-3.18419e7 + 5.51717e7i) q^{48} -2.75928e8 q^{49} +(-3.65014e8 - 2.10665e8i) q^{51} +2.99516e8 q^{52} +9.31529e7i q^{53} +(152595. + 3.24679e8i) q^{54} +2.96442e7i q^{56} +(1.10944e8 - 1.92230e8i) q^{57} -1.80380e8 q^{58} -6.93075e8i q^{59} -3.34878e8 q^{61} -1.16396e9i q^{62} +(7.55881e7 + 1.30828e8i) q^{63} -1.34218e8 q^{64} +(8.46309e8 - 1.46638e9i) q^{66} -2.14235e8 q^{67} -8.87981e8i q^{68} +(-2.39043e9 - 1.37962e9i) q^{69} -8.45402e7i q^{71} +(-5.92338e8 + 3.42234e8i) q^{72} +1.52196e9 q^{73} -5.85931e8i q^{74} +4.67645e8 q^{76} -7.87899e8i q^{77} +(2.78587e9 + 1.60784e9i) q^{78} +4.64851e9 q^{79} +(-1.74150e9 + 3.02074e9i) q^{81} +1.38564e9 q^{82} +6.88013e9i q^{83} +(-1.59134e8 + 2.75728e8i) q^{84} +2.01317e9i q^{86} +(-1.67776e9 - 9.68304e8i) q^{87} +3.56731e9 q^{88} -3.95183e9i q^{89} +1.49687e9 q^{91} -5.81527e9i q^{92} +(6.24830e9 - 1.08263e10i) q^{93} -3.24322e9 q^{94} +(-1.24839e9 - 7.20499e8i) q^{96} -9.48309e9 q^{97} -6.24353e9i q^{98} +(1.57435e10 - 9.09607e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 22 q^{3} - 7168 q^{4} - 6784 q^{6} - 28466 q^{7} - 118958 q^{9}+O(q^{10}) $ 14 * q + 22 * q^3 - 7168 * q^4 - 6784 * q^6 - 28466 * q^7 - 118958 * q^9	$ 14 q + 22 q^{3} - 7168 q^{4} - 6784 q^{6} - 28466 q^{7} - 118958 q^{9} - 11264 q^{12} - 1473590 q^{13} + 3670016 q^{16} - 926464 q^{18} + 2045302 q^{19} - 4714822 q^{21} + 6946944 q^{22} + 3473408 q^{24} - 29984966 q^{27} + 14574592 q^{28} + 2933182 q^{31} - 94398708 q^{33} + 81089664 q^{34} + 60906496 q^{36} - 65206484 q^{37} - 317162410 q^{39} - 145249664 q^{42} + 523420558 q^{43} - 389380224 q^{46} + 5767168 q^{48} + 1327037880 q^{49} + 605541012 q^{51} + 754478080 q^{52} - 173975680 q^{54} - 303021034 q^{57} + 763332480 q^{58} - 745863254 q^{61} - 3429820738 q^{63} - 1879048192 q^{64} + 3492778368 q^{66} - 1059130154 q^{67} - 985447992 q^{69} + 474349568 q^{72} + 4118860900 q^{73} - 1047194624 q^{76} + 1793952640 q^{78} + 3863766388 q^{79} - 8765793182 q^{81} + 3625547136 q^{82} + 2413988864 q^{84} + 11014377480 q^{87} - 3556835328 q^{88} - 11461151470 q^{91} + 30776293826 q^{93} - 3855022080 q^{94} - 1778384896 q^{96} - 35728415702 q^{97} + 4077474108 q^{99}+O(q^{100}) $ 14 * q + 22 * q^3 - 7168 * q^4 - 6784 * q^6 - 28466 * q^7 - 118958 * q^9 - 11264 * q^12 - 1473590 * q^13 + 3670016 * q^16 - 926464 * q^18 + 2045302 * q^19 - 4714822 * q^21 + 6946944 * q^22 + 3473408 * q^24 - 29984966 * q^27 + 14574592 * q^28 + 2933182 * q^31 - 94398708 * q^33 + 81089664 * q^34 + 60906496 * q^36 - 65206484 * q^37 - 317162410 * q^39 - 145249664 * q^42 + 523420558 * q^43 - 389380224 * q^46 + 5767168 * q^48 + 1327037880 * q^49 + 605541012 * q^51 + 754478080 * q^52 - 173975680 * q^54 - 303021034 * q^57 + 763332480 * q^58 - 745863254 * q^61 - 3429820738 * q^63 - 1879048192 * q^64 + 3492778368 * q^66 - 1059130154 * q^67 - 985447992 * q^69 + 474349568 * q^72 + 4118860900 * q^73 - 1047194624 * q^76 + 1793952640 * q^78 + 3863766388 * q^79 - 8765793182 * q^81 + 3625547136 * q^82 + 2413988864 * q^84 + 11014377480 * q^87 - 3556835328 * q^88 - 11461151470 * q^91 + 30776293826 * q^93 - 3855022080 * q^94 - 1778384896 * q^96 - 35728415702 * q^97 + 4077474108 * 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
$3$	−121.467	+	210.463i	−0.499864	+	0.866104i
$3$	−121.467	+	210.463i	−0.499864	+	0.866104i
$4$	−512.000			−0.500000
$5$		0			0
$5$		0			0
$6$	−4762.24	−	2748.49i	−0.612428	−	0.353457i
$7$	−2558.79			−0.152246			−0.0761228	−	0.997098i	$-0.524254\pi$
$7$	−2558.79			−0.152246			−0.0761228	+	0.997098i	$0.524254\pi$
$8$		−	11585.2i		−	0.353553i
$9$	−29540.5	−	51128.7i	−0.500271	−	0.865869i
$10$		0			0
$11$			307918.i			1.91193i	0.293478	+	0.955966i	$0.405187\pi$
$11$			307918.i			1.91193i	−0.293478	+	0.955966i	$0.594813\pi$
$12$	62191.1	−	107757.i	0.249932	−	0.433052i
$13$	−584993.			−1.57556			−0.787778	−	0.615960i	$-0.788768\pi$
$13$	−584993.			−1.57556			−0.787778	+	0.615960i	$0.788768\pi$
$14$		−	57898.9i		−	0.107654i
$15$		0			0
$16$	262144.			0.250000
$17$			1.73434e6i			1.22149i	0.791828	+	0.610744i	$0.209129\pi$
$17$			1.73434e6i			1.22149i	−0.791828	+	0.610744i	$0.790871\pi$
$18$	1.15691e6	−	668426.i	0.612262	−	0.353745i
$19$	−913369.			−0.368874			−0.184437	−	0.982844i	$-0.559046\pi$
$19$	−913369.			−0.368874			−0.184437	+	0.982844i	$0.559046\pi$
$20$		0			0
$21$	310809.	−	538532.i	0.0761022	−	0.131861i
$22$	−6.96740e6			−1.35194
$23$			1.13580e7i			1.76466i	0.470631	+	0.882330i	$0.344026\pi$
$23$			1.13580e7i			1.76466i	−0.470631	+	0.882330i	$0.655974\pi$
$24$	2.43827e6	+	1.40722e6i	0.306214	+	0.176729i
$25$		0			0
$26$		−	1.32369e7i		−	1.11409i
$27$	1.43489e7	−	6743.80i	1.00000	−	0.000469987i
$28$	1.31010e6			0.0761228
$29$			7.97174e6i			0.388654i	0.980937	+	0.194327i	$0.0622523\pi$
$29$			7.97174e6i			0.388654i	−0.980937	+	0.194327i	$0.937748\pi$
$30$		0			0
$31$	−5.14403e7			−1.79678			−0.898390	−	0.439199i	$-0.855262\pi$
$31$	−5.14403e7			−1.79678			−0.898390	+	0.439199i	$0.855262\pi$
$32$			5.93164e6i			0.176777i
$33$	−6.48055e7	−	3.74019e7i	−1.65593	−	0.955706i
$34$	−3.92436e7			−0.863722
$35$		0			0
$36$	1.51247e7	+	2.61779e7i	0.250136	+	0.432934i
$37$	−2.58947e7			−0.373425			−0.186712	−	0.982415i	$-0.559783\pi$
$37$	−2.58947e7			−0.373425			−0.186712	+	0.982415i	$0.559783\pi$
$38$		−	2.06672e7i		−	0.260833i
$39$	7.10573e7	−	1.23119e8i	0.787564	−	1.36459i
$40$		0			0
$41$		−	6.12373e7i		−	0.528563i	−0.964446	−	0.264281i	$-0.914865\pi$
$41$		−	6.12373e7i		−	0.528563i	0.964446	−	0.264281i	$-0.0851348\pi$
$42$	1.21856e7	+	7.03280e6i	0.0932395	+	0.0538124i
$43$	8.89704e7			0.605206			0.302603	−	0.953117i	$-0.402144\pi$
$43$	8.89704e7			0.605206			0.302603	+	0.953117i	$0.402144\pi$
$44$		−	1.57654e8i		−	0.955966i
$45$		0			0
$46$	−2.57001e8			−1.24780
$47$			1.43331e8i			0.624959i	0.949924	+	0.312480i	$0.101160\pi$
$47$			1.43331e8i			0.624959i	−0.949924	+	0.312480i	$0.898840\pi$
$48$	−3.18419e7	+	5.51717e7i	−0.124966	+	0.216526i
$49$	−2.75928e8			−0.976821
$50$		0			0
$51$	−3.65014e8	−	2.10665e8i	−1.05793	−	0.610578i
$52$	2.99516e8			0.787778
$53$			9.31529e7i			0.222750i	0.993778	+	0.111375i	$0.0355254\pi$
$53$			9.31529e7i			0.222750i	−0.993778	+	0.111375i	$0.964475\pi$
$54$	152595.	+	3.24679e8i	0.000332331	+	0.707107i
$55$		0			0
$56$			2.96442e7i			0.0538270i
$57$	1.10944e8	−	1.92230e8i	0.184387	−	0.319483i
$58$	−1.80380e8			−0.274820
$59$		−	6.93075e8i		−	0.969438i	−0.874670	−	0.484719i	$-0.838922\pi$
$59$		−	6.93075e8i		−	0.969438i	0.874670	−	0.484719i	$-0.161078\pi$
$60$		0			0
$61$	−3.34878e8			−0.396495			−0.198247	−	0.980152i	$-0.563525\pi$
$61$	−3.34878e8			−0.396495			−0.198247	+	0.980152i	$0.563525\pi$
$62$		−	1.16396e9i		−	1.27051i
$63$	7.55881e7	+	1.30828e8i	0.0761641	+	0.131825i
$64$	−1.34218e8			−0.125000
$65$		0			0
$66$	8.46309e8	−	1.46638e9i	0.675786	−	1.17092i
$67$	−2.14235e8			−0.158678			−0.0793389	−	0.996848i	$-0.525281\pi$
$67$	−2.14235e8			−0.158678			−0.0793389	+	0.996848i	$0.525281\pi$
$68$		−	8.87981e8i		−	0.610744i
$69$	−2.39043e9	−	1.37962e9i	−1.52838	−	0.882091i
$70$		0			0
$71$		−	8.45402e7i		−	0.0468567i	−0.999726	−	0.0234283i	$-0.992542\pi$
$71$		−	8.45402e7i		−	0.0468567i	0.999726	−	0.0234283i	$-0.00745815\pi$
$72$	−5.92338e8	+	3.42234e8i	−0.306131	+	0.176873i
$73$	1.52196e9			0.734158			0.367079	−	0.930190i	$-0.380358\pi$
$73$	1.52196e9			0.734158			0.367079	+	0.930190i	$0.380358\pi$
$74$		−	5.85931e8i		−	0.264051i
$75$		0			0
$76$	4.67645e8			0.184437
$77$		−	7.87899e8i		−	0.291083i
$78$	2.78587e9	+	1.60784e9i	0.964914	+	0.556892i
$79$	4.64851e9			1.51070			0.755350	−	0.655322i	$-0.227467\pi$
$79$	4.64851e9			1.51070			0.755350	+	0.655322i	$0.227467\pi$
$80$		0			0
$81$	−1.74150e9	+	3.02074e9i	−0.499457	+	0.866339i
$82$	1.38564e9			0.373750
$83$			6.88013e9i			1.74665i	0.487137	+	0.873326i	$0.338041\pi$
$83$			6.88013e9i			1.74665i	−0.487137	+	0.873326i	$0.661959\pi$
$84$	−1.59134e8	+	2.75728e8i	−0.0380511	+	0.0659303i
$85$		0			0
$86$			2.01317e9i			0.427945i
$87$	−1.67776e9	−	9.68304e8i	−0.336615	−	0.194274i
$88$	3.56731e9			0.675970
$89$		−	3.95183e9i		−	0.707698i	−0.935303	−	0.353849i	$-0.884873\pi$
$89$		−	3.95183e9i		−	0.707698i	0.935303	−	0.353849i	$-0.115127\pi$
$90$		0			0
$91$	1.49687e9			0.239871
$92$		−	5.81527e9i		−	0.882330i
$93$	6.24830e9	−	1.08263e10i	0.898146	−	1.55620i
$94$	−3.24322e9			−0.441913
$95$		0			0
$96$	−1.24839e9	−	7.20499e8i	−0.153107	−	0.0883644i
$97$	−9.48309e9			−1.10431			−0.552155	−	0.833741i	$-0.686194\pi$
$97$	−9.48309e9			−1.10431			−0.552155	+	0.833741i	$0.686194\pi$
$98$		−	6.24353e9i		−	0.690717i
$99$	1.57435e10	−	9.09607e9i	1.65548	−	0.956484i
$100$		0			0
$101$			1.39593e10i			1.32818i	0.747655	+	0.664088i	$0.231180\pi$
$101$			1.39593e10i			1.32818i	−0.747655	+	0.664088i	$0.768820\pi$
$102$	4.76680e9	−	8.25933e9i	0.431744	−	0.748073i
$103$	1.41609e10			1.22153			0.610767	−	0.791810i	$-0.290861\pi$
$103$	1.41609e10			1.22153			0.610767	+	0.791810i	$0.290861\pi$
$104$			6.77728e9i			0.557043i
$105$		0			0
$106$	−2.10781e9			−0.157508
$107$			3.74972e9i			0.267350i	0.991025	+	0.133675i	$0.0426778\pi$
$107$			3.74972e9i			0.267350i	−0.991025	+	0.133675i	$0.957322\pi$
$108$	−7.34664e9	+	3.45283e6i	−0.500000	+	0.000234994i
$109$	2.77857e9			0.180588			0.0902941	−	0.995915i	$-0.471219\pi$
$109$	2.77857e9			0.180588			0.0902941	+	0.995915i	$0.471219\pi$
$110$		0			0
$111$	3.14536e9	−	5.44989e9i	0.186662	−	0.323425i
$112$	−6.70772e8			−0.0380614
$113$		−	1.24553e10i		−	0.676022i	−0.941142	−	0.338011i	$-0.890246\pi$
$113$		−	1.24553e10i		−	0.676022i	0.941142	−	0.338011i	$-0.109754\pi$
$114$	4.34968e9	+	2.51038e9i	0.225909	+	0.130381i
$115$		0			0
$116$		−	4.08153e9i		−	0.194327i
$117$	1.72810e10	+	2.99099e10i	0.788205	+	1.36422i
$118$	1.56825e10			0.685496
$119$		−	4.43781e9i		−	0.185966i
$120$		0			0
$121$	−6.88764e10			−2.65548
$122$		−	7.57742e9i		−	0.280364i
$123$	1.28882e10	+	7.43831e9i	0.457790	+	0.264210i
$124$	2.63374e10			0.898390
$125$		0			0
$126$	−2.96029e9	+	1.71036e9i	−0.0932142	+	0.0538562i
$127$	4.61253e10			1.39611			0.698056	−	0.716043i	$-0.254049\pi$
$127$	4.61253e10			1.39611			0.698056	+	0.716043i	$0.254049\pi$
$128$		−	3.03700e9i		−	0.0883883i
$129$	−1.08070e10	+	1.87250e10i	−0.302521	+	0.524171i
$130$		0			0
$131$			2.86208e10i			0.741866i	0.928660	+	0.370933i	$0.120962\pi$
$131$			2.86208e10i			0.741866i	−0.928660	+	0.370933i	$0.879038\pi$
$132$	3.31804e10	+	1.91498e10i	0.827965	+	0.477853i
$133$	2.33712e9			0.0561595
$134$		−	4.84758e9i		−	0.112202i
$135$		0			0
$136$	2.00927e10			0.431861
$137$		−	1.47382e10i		−	0.305380i	−0.988274	−	0.152690i	$-0.951206\pi$
$137$		−	1.47382e10i		−	0.305380i	0.988274	−	0.152690i	$-0.0487936\pi$
$138$	3.12172e10	−	5.40893e10i	0.623732	−	1.08073i
$139$	8.45766e10			1.62996			0.814979	−	0.579491i	$-0.196749\pi$
$139$	8.45766e10			1.62996			0.814979	+	0.579491i	$0.196749\pi$
$140$		0			0
$141$	−3.01660e10	−	1.74100e10i	−0.541279	−	0.312395i
$142$	1.91293e9			0.0331327
$143$		−	1.80130e11i		−	3.01235i
$144$	−7.74387e9	−	1.34031e10i	−0.125068	−	0.216467i
$145$		0			0
$146$			3.44381e10i			0.519128i
$147$	3.35161e10	−	5.80727e10i	0.488278	−	0.846029i
$148$	1.32581e10			0.186712
$149$		−	2.60962e10i		−	0.355342i	−0.984090	−	0.177671i	$-0.943144\pi$
$149$		−	2.60962e10i		−	0.355342i	0.984090	−	0.177671i	$-0.0568563\pi$
$150$		0			0
$151$	−5.73633e10			−0.730718			−0.365359	−	0.930867i	$-0.619054\pi$
$151$	−5.73633e10			−0.730718			−0.365359	+	0.930867i	$0.619054\pi$
$152$			1.05816e10i			0.130417i
$153$	8.86744e10	−	5.12332e10i	1.05765	−	0.611075i
$154$	1.78281e10			0.205827
$155$		0			0
$156$	−3.63813e10	+	6.30371e10i	−0.393782	+	0.682297i
$157$	1.00828e11			1.05702			0.528509	−	0.848928i	$-0.322751\pi$
$157$	1.00828e11			1.05702			0.528509	+	0.848928i	$0.322751\pi$
$158$			1.05184e11i			1.06823i
$159$	−1.96053e10	−	1.13150e10i	−0.192924	−	0.111345i
$160$		0			0
$161$		−	2.90627e10i		−	0.268662i
$162$	−6.83514e10	−	3.94056e10i	−0.612594	−	0.353170i
$163$	1.68795e11			1.46697			0.733487	−	0.679704i	$-0.237892\pi$
$163$	1.68795e11			1.46697			0.733487	+	0.679704i	$0.237892\pi$
$164$			3.13535e10i			0.264281i
$165$		0			0
$166$	−1.55680e11			−1.23507
$167$			1.89852e10i			0.146162i	0.997326	+	0.0730808i	$0.0232831\pi$
$167$			1.89852e10i			0.146162i	−0.997326	+	0.0730808i	$0.976717\pi$
$168$	−6.23902e9	−	3.60079e9i	−0.0466197	−	0.0269062i
$169$	2.04358e11			1.48237
$170$		0			0
$171$	2.69814e10	+	4.66993e10i	0.184537	+	0.319396i
$172$	−4.55529e10			−0.302603
$173$			9.84409e10i			0.635250i	0.948216	+	0.317625i	$0.102885\pi$
$173$			9.84409e10i			0.635250i	−0.948216	+	0.317625i	$0.897115\pi$
$174$	2.19102e10	−	3.79633e10i	0.137373	−	0.238023i
$175$		0			0
$176$			8.07190e10i			0.477983i
$177$	1.45867e11	+	8.41858e10i	0.839634	+	0.484588i
$178$	8.94197e10			0.500418
$179$		−	1.27260e11i		−	0.692510i	−0.938140	−	0.346255i	$-0.887453\pi$
$179$		−	1.27260e11i		−	0.692510i	0.938140	−	0.346255i	$-0.112547\pi$
$180$		0			0
$181$	6.05416e10			0.311646			0.155823	−	0.987785i	$-0.450197\pi$
$181$	6.05416e10			0.311646			0.155823	+	0.987785i	$0.450197\pi$
$182$			3.38704e10i			0.169615i
$183$	4.06766e10	−	7.04795e10i	0.198194	−	0.343405i
$184$	1.31585e11			0.623901
$185$		0			0
$186$	2.44971e11	+	1.41383e11i	1.10040	+	0.635085i
$187$	−5.34035e11			−2.33540
$188$		−	7.33856e10i		−	0.312480i
$189$	−3.67159e10	+	1.72560e7i	−0.152246	+	7.15535e-5i
$190$		0			0
$191$		−	1.63713e11i		−	0.644044i	−0.946732	−	0.322022i	$-0.895637\pi$
$191$		−	1.63713e11i		−	0.644044i	0.946732	−	0.322022i	$-0.104363\pi$
$192$	1.63030e10	−	2.82479e10i	0.0624830	−	0.108263i
$193$	6.17778e10			0.230699			0.115349	−	0.993325i	$-0.463201\pi$
$193$	6.17778e10			0.230699			0.115349	+	0.993325i	$0.463201\pi$
$194$		−	2.14578e11i		−	0.780865i
$195$		0			0
$196$	1.41275e11			0.488411
$197$		−	4.74457e11i		−	1.59906i	−0.600624	−	0.799532i	$-0.705081\pi$
$197$		−	4.74457e11i		−	1.59906i	0.600624	−	0.799532i	$-0.294919\pi$
$198$	2.05821e11	+	3.56234e11i	0.676337	+	1.17060i
$199$	−4.54774e11			−1.45724			−0.728618	−	0.684920i	$-0.759837\pi$
$199$	−4.54774e11			−1.45724			−0.728618	+	0.684920i	$0.759837\pi$
$200$		0			0
$201$	2.60225e10	−	4.50886e10i	0.0793174	−	0.137431i
$202$	−3.15862e11			−0.939162
$203$		−	2.03980e10i		−	0.0591709i
$204$	1.86887e11	+	1.07860e11i	0.528967	+	0.305289i
$205$		0			0
$206$			3.20425e11i			0.863755i
$207$	5.80717e11	−	3.35520e11i	1.52796	−	0.882809i
$208$	−1.53352e11			−0.393889
$209$		−	2.81243e11i		−	0.705262i
$210$		0			0
$211$	−7.31546e11			−1.74916			−0.874580	−	0.484882i	$-0.838863\pi$
$211$	−7.31546e11			−1.74916			−0.874580	+	0.484882i	$0.838863\pi$
$212$		−	4.76943e10i		−	0.111375i
$213$	1.77926e10	+	1.02688e10i	0.0405827	+	0.0234220i
$214$	−8.48465e10			−0.189045
$215$		0			0
$216$	−7.81285e7	−	1.66235e11i	−0.000166166	−	0.353553i
$217$	1.31625e11			0.273552
$218$			6.28719e10i			0.127695i
$219$	−1.84868e11	+	3.20317e11i	−0.366979	+	0.635857i
$220$		0			0
$221$		−	1.01457e12i		−	1.92452i
$222$	1.23317e11	+	7.11713e10i	0.228696	+	0.131990i
$223$	−3.28261e11			−0.595244			−0.297622	−	0.954684i	$-0.596194\pi$
$223$	−3.28261e11			−0.595244			−0.297622	+	0.954684i	$0.596194\pi$
$224$		−	1.51778e10i		−	0.0269135i
$225$		0			0
$226$	2.81830e11			0.478020
$227$			1.03387e12i			1.71529i	0.514242	+	0.857645i	$0.328073\pi$
$227$			1.03387e12i			1.71529i	−0.514242	+	0.857645i	$0.671927\pi$
$228$	−5.68034e10	+	9.84220e10i	−0.0921935	+	0.159742i
$229$	1.18769e11			0.188593			0.0942966	−	0.995544i	$-0.469940\pi$
$229$	1.18769e11			0.188593			0.0942966	+	0.995544i	$0.469940\pi$
$230$		0			0
$231$	1.65824e11	+	9.57038e10i	0.252108	+	0.145502i
$232$	9.23545e10			0.137410
$233$			2.79945e10i			0.0407655i	0.999792	+	0.0203827i	$0.00648848\pi$
$233$			2.79945e10i			0.0407655i	−0.999792	+	0.0203827i	$0.993512\pi$
$234$	−6.76784e11	+	3.91024e11i	−0.964652	+	0.557345i
$235$		0			0
$236$			3.54854e11i			0.484719i
$237$	−5.64640e11	+	9.78340e11i	−0.755145	+	1.30842i
$238$	1.00416e11			0.131498
$239$		−	6.56177e11i		−	0.841456i	−0.907187	−	0.420728i	$-0.861775\pi$
$239$		−	6.56177e11i		−	0.841456i	0.907187	−	0.420728i	$-0.138225\pi$
$240$		0			0
$241$	4.99981e11			0.614990			0.307495	−	0.951550i	$-0.400509\pi$
$241$	4.99981e11			0.614990			0.307495	+	0.951550i	$0.400509\pi$
$242$		−	1.55849e12i		−	1.87771i
$243$	−4.24219e11	−	7.33441e11i	−0.500678	−	0.865633i
$244$	1.71457e11			0.198247
$245$		0			0
$246$	−1.68310e11	+	2.91627e11i	−0.186824	+	0.323707i
$247$	5.34314e11			0.581181
$248$			5.95948e11i			0.635257i
$249$	−1.44801e12	−	8.35709e11i	−1.51278	−	0.873089i
$250$		0			0
$251$		−	1.34567e12i		−	1.35073i	−0.737483	−	0.675366i	$-0.763986\pi$
$251$		−	1.34567e12i		−	1.35073i	0.737483	−	0.675366i	$-0.236014\pi$
$252$	−3.87011e10	−	6.69838e10i	−0.0380821	−	0.0659124i
$253$	−3.49732e12			−3.37391
$254$			1.04370e12i			0.987200i
$255$		0			0
$256$	6.87195e10			0.0625000
$257$			1.23554e12i			1.10203i	0.834496	+	0.551014i	$0.185759\pi$
$257$			1.23554e12i			1.10203i	−0.834496	+	0.551014i	$0.814241\pi$
$258$	−4.23698e11	−	2.44534e11i	−0.370645	−	0.213915i
$259$	6.62593e10			0.0568523
$260$		0			0
$261$	4.07585e11	−	2.35489e11i	0.336524	−	0.194433i
$262$	−6.47615e11			−0.524579
$263$			1.03958e12i			0.826190i	0.910688	+	0.413095i	$0.135552\pi$
$263$			1.03958e12i			0.826190i	−0.910688	+	0.413095i	$0.864448\pi$
$264$	−4.33310e11	+	7.50787e11i	−0.337893	+	0.585460i
$265$		0			0
$266$			5.28830e10i			0.0397107i
$267$	8.31715e11	+	4.80017e11i	0.612940	+	0.353753i
$268$	1.09688e11			0.0793389
$269$			2.34665e12i			1.66605i	0.553237	+	0.833024i	$0.313392\pi$
$269$			2.34665e12i			1.66605i	−0.553237	+	0.833024i	$0.686608\pi$
$270$		0			0
$271$	−1.33094e12			−0.910568			−0.455284	−	0.890346i	$-0.650462\pi$
$271$	−1.33094e12			−0.910568			−0.455284	+	0.890346i	$0.650462\pi$
$272$			4.54646e11i			0.305372i
$273$	−1.81821e11	+	3.15037e11i	−0.119903	+	0.207753i
$274$	3.33487e11			0.215936
$275$		0			0
$276$	1.22390e12	+	7.06364e11i	0.764189	+	0.441045i
$277$	−2.64862e12			−1.62413			−0.812067	−	0.583565i	$-0.801657\pi$
$277$	−2.64862e12			−1.62413			−0.812067	+	0.583565i	$0.801657\pi$
$278$			1.91375e12i			1.15255i
$279$	1.51957e12	+	2.63007e12i	0.898877	+	1.55577i
$280$		0			0
$281$			1.21736e11i			0.0694845i	0.999396	+	0.0347422i	$0.0110610\pi$
$281$			1.21736e11i			0.0694845i	−0.999396	+	0.0347422i	$0.988939\pi$
$282$	3.93944e11	−	6.82578e11i	0.220896	−	0.382742i
$283$	−1.12121e12			−0.617669			−0.308835	−	0.951116i	$-0.599939\pi$
$283$	−1.12121e12			−0.617669			−0.308835	+	0.951116i	$0.599939\pi$
$284$			4.32846e10i			0.0234283i
$285$		0			0
$286$	4.07588e12			2.13006
$287$			1.56693e11i			0.0804714i
$288$	3.03277e11	−	1.75224e11i	0.153065	−	0.0884363i
$289$	−9.91933e11			−0.492032
$290$		0			0
$291$	1.15188e12	−	1.99584e12i	0.552005	−	0.956447i
$292$	−7.79245e11			−0.367079
$293$			1.34998e11i			0.0625158i	0.999511	+	0.0312579i	$0.00995132\pi$
$293$			1.34998e11i			0.0625158i	−0.999511	+	0.0312579i	$0.990049\pi$
$294$	1.31403e12	+	7.58384e11i	0.598233	+	0.345265i
$295$		0			0
$296$			2.99997e11i			0.132026i
$297$	2.07654e9	+	4.41829e12i	0.000898583	+	1.91193i
$298$	5.90491e11			0.251265
$299$		−	6.64432e12i		−	2.78032i
$300$		0			0
$301$	−2.27657e11			−0.0921400
$302$		−	1.29798e12i		−	0.516695i
$303$	−2.93791e12	−	1.69559e12i	−1.15034	−	0.663907i
$304$	−2.39434e11			−0.0922185
$305$		0			0
$306$	1.15928e12	+	2.00647e12i	0.432095	+	0.747870i
$307$	−7.47897e11			−0.274252			−0.137126	−	0.990554i	$-0.543787\pi$
$307$	−7.47897e11			−0.274252			−0.137126	+	0.990554i	$0.543787\pi$
$308$			4.03404e11i			0.145542i
$309$	−1.72009e12	+	2.98035e12i	−0.610601	+	1.05798i
$310$		0			0
$311$			3.20249e12i			1.10074i	0.834920	+	0.550371i	$0.185514\pi$
$311$			3.20249e12i			1.10074i	−0.834920	+	0.550371i	$0.814486\pi$
$312$	−1.42637e12	−	8.23216e11i	−0.482457	−	0.278446i
$313$	2.33939e12			0.778719			0.389360	−	0.921086i	$-0.372696\pi$
$313$	2.33939e12			0.778719			0.389360	+	0.921086i	$0.372696\pi$
$314$			2.28147e12i			0.747424i
$315$		0			0
$316$	−2.38004e12			−0.755350
$317$		−	3.02338e12i		−	0.944487i	−0.881468	−	0.472244i	$-0.843444\pi$
$317$		−	3.02338e12i		−	0.944487i	0.881468	−	0.472244i	$-0.156556\pi$
$318$	2.56029e11	−	4.43617e11i	0.0787326	−	0.136418i
$319$	−2.45465e12			−0.743080
$320$		0			0
$321$	−7.89179e11	−	4.55468e11i	−0.231553	−	0.133639i
$322$	6.57613e11			0.189973
$323$		−	1.58409e12i		−	0.450575i
$324$	8.91648e11	−	1.54662e12i	0.249729	−	0.433169i
$325$		0			0
$326$			3.81940e12i			1.03731i
$327$	−3.37505e11	+	5.84787e11i	−0.0902696	+	0.156408i
$328$	−7.09449e11			−0.186875
$329$		−	3.66755e11i		−	0.0951473i
$330$		0			0
$331$	6.87491e12			1.73032			0.865162	−	0.501493i	$-0.167216\pi$
$331$	6.87491e12			1.73032			0.865162	+	0.501493i	$0.167216\pi$
$332$		−	3.52263e12i		−	0.873326i
$333$	7.64944e11	+	1.32396e12i	0.186814	+	0.323337i
$334$	−4.29586e11			−0.103352
$335$		0			0
$336$	8.14767e10	−	1.41173e11i	0.0190255	−	0.0329651i
$337$	5.86698e12			1.34979			0.674894	−	0.737915i	$-0.264189\pi$
$337$	5.86698e12			1.34979			0.674894	+	0.737915i	$0.264189\pi$
$338$			4.62409e12i			1.04820i
$339$	2.62137e12	+	1.51290e12i	0.585505	+	0.337919i
$340$		0			0
$341$		−	1.58394e13i		−	3.43532i
$342$	−1.05669e12	+	6.10519e11i	−0.225847	+	0.130487i
$343$	1.42884e12			0.300962
$344$		−	1.03074e12i		−	0.213973i
$345$		0			0
$346$	−2.22746e12			−0.449190
$347$		−	2.23641e12i		−	0.444534i	−0.974986	−	0.222267i	$-0.928654\pi$
$347$		−	2.23641e12i		−	0.444534i	0.974986	−	0.222267i	$-0.0713457\pi$
$348$	8.59013e11	+	4.95772e11i	0.168307	+	0.0971372i
$349$	3.36529e11			0.0649972			0.0324986	−	0.999472i	$-0.489654\pi$
$349$	3.36529e11			0.0649972			0.0324986	+	0.999472i	$0.489654\pi$
$350$		0			0
$351$	−8.39400e12	+	3.94507e9i	−1.57555	+	0.000740491i
$352$	−1.82646e12			−0.337985
$353$			6.28025e12i			1.14579i	0.819630	+	0.572893i	$0.194179\pi$
$353$			6.28025e12i			1.14579i	−0.819630	+	0.572893i	$0.805821\pi$
$354$	−1.90491e12	+	3.30059e12i	−0.342655	+	0.593711i
$355$		0			0
$356$			2.02334e12i			0.353849i
$357$	9.33996e11	+	5.39048e11i	0.161066	+	0.0929578i
$358$	2.87956e12			0.489679
$359$		−	9.17335e12i		−	1.53835i	−0.639037	−	0.769176i	$-0.720667\pi$
$359$		−	9.17335e12i		−	1.53835i	0.639037	−	0.769176i	$-0.279333\pi$
$360$		0			0
$361$	−5.29682e12			−0.863932
$362$			1.36990e12i			0.220367i
$363$	8.36621e12	−	1.44959e13i	1.32738	−	2.29992i
$364$	−7.66400e11			−0.119936
$365$		0			0
$366$	1.59477e12	+	9.20407e11i	0.242824	+	0.140144i
$367$	4.19255e12			0.629720			0.314860	−	0.949138i	$-0.398042\pi$
$367$	4.19255e12			0.629720			0.314860	+	0.949138i	$0.398042\pi$
$368$			2.97742e12i			0.441165i
$369$	−3.13098e12	+	1.80898e12i	−0.457666	+	0.264425i
$370$		0			0
$371$		−	2.38359e11i		−	0.0339127i
$372$	−3.19913e12	+	5.54306e12i	−0.449073	+	0.778099i
$373$	−9.12343e12			−1.26361			−0.631806	−	0.775126i	$-0.717686\pi$
$373$	−9.12343e12			−1.26361			−0.631806	+	0.775126i	$0.717686\pi$
$374$		−	1.20838e13i		−	1.65138i
$375$		0			0
$376$	1.66053e12			0.220956
$377$		−	4.66341e12i		−	0.612346i
$378$	−3.90458e8	−	8.30785e11i	−5.05960e−5	−	0.107654i
$379$	1.82186e12			0.232980			0.116490	−	0.993192i	$-0.462836\pi$
$379$	1.82186e12			0.232980			0.116490	+	0.993192i	$0.462836\pi$
$380$		0			0
$381$	−5.60270e12	+	9.70767e12i	−0.697866	+	1.20918i
$382$	3.70440e12			0.455408
$383$		−	4.55603e12i		−	0.552831i	−0.961038	−	0.276416i	$-0.910853\pi$
$383$		−	4.55603e12i		−	0.552831i	0.961038	−	0.276416i	$-0.0891466\pi$
$384$	6.39177e11	+	3.68895e11i	0.0765535	+	0.0441822i
$385$		0			0
$386$			1.39787e12i			0.163129i
$387$	−2.62823e12	−	4.54894e12i	−0.302767	−	0.524029i
$388$	4.85534e12			0.552155
$389$		−	1.04071e13i		−	1.16837i	−0.811621	−	0.584184i	$-0.801415\pi$
$389$		−	1.04071e13i		−	1.16837i	0.811621	−	0.584184i	$-0.198585\pi$
$390$		0			0
$391$	−1.96985e13			−2.15551
$392$			3.19669e12i			0.345358i
$393$	−6.02363e12	−	3.47649e12i	−0.642533	−	0.370832i
$394$	1.07357e13			1.13071
$395$		0			0
$396$	−8.06065e12	+	4.65719e12i	−0.827741	+	0.478242i
$397$	1.37443e13			1.39370			0.696851	−	0.717216i	$-0.254584\pi$
$397$	1.37443e13			1.39370			0.696851	+	0.717216i	$0.254584\pi$
$398$		−	1.02904e13i		−	1.03042i
$399$	−2.83883e11	+	4.91878e11i	−0.0280721	+	0.0486399i
$400$		0			0
$401$		−	6.39840e12i		−	0.617091i	−0.951210	−	0.308546i	$-0.900158\pi$
$401$		−	6.39840e12i		−	0.617091i	0.951210	−	0.308546i	$-0.0998423\pi$
$402$	1.02024e12	+	5.88822e11i	0.0971787	+	0.0560859i
$403$	3.00922e13			2.83092
$404$		−	7.14714e12i		−	0.664088i
$405$		0			0
$406$	4.61555e11			0.0418401
$407$		−	7.97347e12i		−	0.713962i
$408$	−2.44060e12	+	4.22878e12i	−0.215872	+	0.374036i
$409$	−3.80936e12			−0.332840			−0.166420	−	0.986055i	$-0.553221\pi$
$409$	−3.80936e12			−0.332840			−0.166420	+	0.986055i	$0.553221\pi$
$410$		0			0
$411$	3.10184e12	+	1.79020e12i	0.264491	+	0.152649i
$412$	−7.25040e12			−0.610767
$413$			1.77343e12i			0.147593i
$414$	7.59195e12	+	1.31401e13i	0.624240	+	1.08043i
$415$		0			0
$416$		−	3.46997e12i		−	0.278521i
$417$	−1.02733e13	+	1.78003e13i	−0.814758	+	1.41171i
$418$	6.36380e12			0.498695
$419$		−	3.09596e12i		−	0.239731i	−0.992790	−	0.119866i	$-0.961754\pi$
$419$		−	3.09596e12i		−	0.239731i	0.992790	−	0.119866i	$-0.0382464\pi$
$420$		0			0
$421$	1.32456e13			1.00152			0.500762	−	0.865585i	$-0.333053\pi$
$421$	1.32456e13			1.00152			0.500762	+	0.865585i	$0.333053\pi$
$422$		−	1.65530e13i		−	1.23684i
$423$	7.32834e12	−	4.23408e12i	0.541132	−	0.312649i
$424$	1.07920e12			0.0787539
$425$		0			0
$426$	−2.32357e11	+	4.02601e11i	−0.0165618	+	0.0286963i
$427$	8.56883e11			0.0603646
$428$		−	1.91986e12i		−	0.133675i
$429$	3.79107e13	+	2.18799e13i	2.60901	+	1.50577i
$430$		0			0
$431$			1.62542e13i			1.09289i	0.837493	+	0.546447i	$0.184020\pi$
$431$			1.62542e13i			1.09289i	−0.837493	+	0.546447i	$0.815980\pi$
$432$	3.76148e12	−	1.76785e9i	0.250000	−	0.000117497i
$433$	1.54806e13			1.01707			0.508533	−	0.861043i	$-0.330188\pi$
$433$	1.54806e13			1.01707			0.508533	+	0.861043i	$0.330188\pi$
$434$			2.97833e12i			0.193430i
$435$		0			0
$436$	−1.42263e12			−0.0902941
$437$		−	1.03740e13i		−	0.650937i
$438$	−7.24795e12	−	4.18309e12i	−0.449619	−	0.259494i
$439$	3.90092e12			0.239246			0.119623	−	0.992819i	$-0.461831\pi$
$439$	3.90092e12			0.239246			0.119623	+	0.992819i	$0.461831\pi$
$440$		0			0
$441$	8.15105e12	+	1.41078e13i	0.488676	+	0.845799i
$442$	2.29572e13			1.36084
$443$			2.45614e11i			0.0143958i	0.999974	+	0.00719788i	$0.00229118\pi$
$443$			2.45614e11i			0.0143958i	−0.999974	+	0.00719788i	$0.997709\pi$
$444$	−1.61042e12	+	2.79034e12i	−0.0933308	+	0.161712i
$445$		0			0
$446$		−	7.42770e12i		−	0.420901i
$447$	5.49230e12	+	3.16983e12i	0.307763	+	0.177623i
$448$	3.43435e11			0.0190307
$449$		−	1.98559e13i		−	1.08807i	−0.839062	−	0.544035i	$-0.816896\pi$
$449$		−	1.98559e13i		−	1.08807i	0.839062	−	0.544035i	$-0.183104\pi$
$450$		0			0
$451$	1.88561e13			1.01058
$452$			6.37710e12i			0.338011i
$453$	6.96775e12	−	1.20729e13i	0.365260	−	0.632877i
$454$	−2.33939e13			−1.21289
$455$		0			0
$456$	−2.22704e12	−	1.28531e12i	−0.112954	−	0.0651906i
$457$	−1.99765e13			−1.00216			−0.501082	−	0.865400i	$-0.667065\pi$
$457$	−1.99765e13			−1.00216			−0.501082	+	0.865400i	$0.667065\pi$
$458$			2.68744e12i			0.133355i
$459$	1.16960e10	+	2.48858e13i	0.000574083	+	1.22149i
$460$		0			0
$461$			8.27940e12i			0.397644i	0.980036	+	0.198822i	$0.0637115\pi$
$461$			8.27940e12i			0.397644i	−0.980036	+	0.198822i	$0.936288\pi$
$462$	−2.16553e12	+	3.75217e12i	−0.102886	+	0.178267i
$463$	−2.67896e13			−1.25910			−0.629552	−	0.776958i	$-0.716762\pi$
$463$	−2.67896e13			−1.25910			−0.629552	+	0.776958i	$0.716762\pi$
$464$			2.08974e12i			0.0971635i
$465$		0			0
$466$	−6.33443e11			−0.0288256
$467$			2.88012e12i			0.129666i	0.997896	+	0.0648330i	$0.0206515\pi$
$467$			2.88012e12i			0.129666i	−0.997896	+	0.0648330i	$0.979349\pi$
$468$	−8.84787e12	−	1.53139e13i	−0.394103	−	0.682112i
$469$	5.48183e11			0.0241580
$470$		0			0
$471$	−1.22473e13	+	2.12205e13i	−0.528365	+	0.915487i
$472$	−8.02944e12			−0.342748
$473$			2.73956e13i			1.15711i
$474$	−2.21373e13	−	1.27764e13i	−0.925194	−	0.533968i
$475$		0			0
$476$			2.27216e12i			0.0929831i
$477$	4.76279e12	−	2.75179e12i	0.192872	−	0.111435i
$478$	1.48476e13			0.594999
$479$		−	1.23922e13i		−	0.491441i	−0.969341	−	0.245720i	$-0.920976\pi$
$479$		−	1.23922e13i		−	0.491441i	0.969341	−	0.245720i	$-0.0790245\pi$
$480$		0			0
$481$	1.51482e13			0.588351
$482$			1.13133e13i			0.434864i
$483$	6.11662e12	+	3.53015e12i	0.232689	+	0.134294i
$484$	3.52647e13			1.32774
$485$		0			0
$486$	1.65959e13	−	9.59898e12i	0.612095	−	0.354033i
$487$	2.18095e13			0.796161			0.398080	−	0.917351i	$-0.369677\pi$
$487$	2.18095e13			0.796161			0.398080	+	0.917351i	$0.369677\pi$
$488$			3.87964e12i			0.140182i
$489$	−2.05031e13	+	3.55252e13i	−0.733288	+	1.27055i
$490$		0			0
$491$		−	1.97546e13i		−	0.692248i	−0.938189	−	0.346124i	$-0.887498\pi$
$491$		−	1.97546e13i		−	0.692248i	0.938189	−	0.346124i	$-0.112502\pi$
$492$	−6.59876e12	−	3.80842e12i	−0.228895	−	0.132105i
$493$	−1.38257e13			−0.474736
$494$			1.20901e13i			0.410957i
$495$		0			0
$496$	−1.34848e13			−0.449195
$497$			2.16321e11i			0.00713372i
$498$	1.89099e13	−	3.27648e13i	0.617367	−	1.06970i
$499$	4.31220e13			1.39379			0.696894	−	0.717175i	$-0.254565\pi$
$499$	4.31220e13			1.39379			0.696894	+	0.717175i	$0.254565\pi$
$500$		0			0
$501$	−3.99569e12	−	2.30608e12i	−0.126591	−	0.0730609i
$502$	3.04490e13			0.955112
$503$			2.59678e13i			0.806482i	0.915094	+	0.403241i	$0.132116\pi$
$503$			2.59678e13i			0.806482i	−0.915094	+	0.403241i	$0.867884\pi$
$504$	1.51567e12	−	8.75706e11i	0.0466071	−	0.0269281i
$505$		0			0
$506$		−	7.91354e13i		−	2.38571i
$507$	−2.48227e13	+	4.30098e13i	−0.740986	+	1.28389i
$508$	−2.36161e13			−0.698056
$509$			7.56645e12i			0.221464i	0.993850	+	0.110732i	$0.0353195\pi$
$509$			7.56645e12i			0.221464i	−0.993850	+	0.110732i	$0.964680\pi$
$510$		0			0
$511$	−3.89439e12			−0.111772
$512$			1.55494e12i			0.0441942i
$513$	−1.31058e13	+	6.15958e9i	−0.368874	+	0.000173366i
$514$	−2.79572e13			−0.779252
$515$		0			0
$516$	5.53317e12	−	9.58720e12i	0.151261	−	0.262086i
$517$	−4.41343e13			−1.19488
$518$			1.49928e12i			0.0402006i
$519$	−2.07182e13	−	1.19573e13i	−0.550193	−	0.317539i
$520$		0			0
$521$			5.28897e13i			1.37779i	0.724862	+	0.688894i	$0.241903\pi$
$521$			5.28897e13i			1.37779i	−0.724862	+	0.688894i	$0.758097\pi$
$522$	5.32852e12	+	9.22259e12i	0.137485	+	0.237958i
$523$	−4.85684e13			−1.24121			−0.620604	−	0.784124i	$-0.713113\pi$
$523$	−4.85684e13			−1.24121			−0.620604	+	0.784124i	$0.713113\pi$
$524$		−	1.46539e13i		−	0.370933i
$525$		0			0
$526$	−2.35231e13			−0.584205
$527$		−	8.92148e13i		−	2.19474i
$528$	−1.69884e13	−	9.80469e12i	−0.413983	−	0.238927i
$529$	−8.75767e13			−2.11402
$530$		0			0
$531$	−3.54360e13	+	2.04738e13i	−0.839406	+	0.484982i
$532$	−1.19661e12			−0.0280797
$533$			3.58234e13i			0.832780i
$534$	−1.08615e13	+	1.88196e13i	−0.250141	+	0.433414i
$535$		0			0
$536$			2.48196e12i			0.0561011i
$537$	2.67835e13	+	1.54579e13i	0.599786	+	0.346161i
$538$	−5.30987e13			−1.17807
$539$		−	8.49633e13i		−	1.86762i
$540$		0			0
$541$	2.80349e13			0.604940			0.302470	−	0.953159i	$-0.402189\pi$
$541$	2.80349e13			0.604940			0.302470	+	0.953159i	$0.402189\pi$
$542$		−	3.01157e13i		−	0.643869i
$543$	−7.35381e12	+	1.27418e13i	−0.155781	+	0.269917i
$544$	−1.02875e13			−0.215931
$545$		0			0
$546$	−7.12847e12	−	4.11414e12i	−0.146904	−	0.0847843i
$547$	−4.87658e13			−0.995814			−0.497907	−	0.867230i	$-0.665898\pi$
$547$	−4.87658e13			−0.995814			−0.497907	+	0.867230i	$0.665898\pi$
$548$			7.54594e12i			0.152690i
$549$	9.89247e12	+	1.71219e13i	0.198355	+	0.343312i
$550$		0			0
$551$		−	7.28114e12i		−	0.143364i
$552$	−1.59832e13	+	2.76937e13i	−0.311866	+	0.540363i
$553$	−1.18946e13			−0.229997
$554$		−	5.99315e13i		−	1.14844i
$555$		0			0
$556$	−4.33032e13			−0.814979
$557$			6.67097e13i			1.24427i	0.782912	+	0.622133i	$0.213734\pi$
$557$			6.67097e13i			1.24427i	−0.782912	+	0.622133i	$0.786266\pi$
$558$	−5.95118e13	+	3.43840e13i	−1.10010	+	0.635602i
$559$	−5.20470e13			−0.953536
$560$		0			0
$561$	6.48676e13	−	1.12395e14i	1.16738	−	2.02270i
$562$	−2.75457e12			−0.0491329
$563$			5.63387e13i			0.996013i	0.867173	+	0.498006i	$0.165934\pi$
$563$			5.63387e13i			0.996013i	−0.867173	+	0.498006i	$0.834066\pi$
$564$	1.54450e13	+	8.91393e12i	0.270640	+	0.156197i
$565$		0			0
$566$		−	2.53702e13i		−	0.436758i
$567$	4.45614e12	−	7.72944e12i	0.0760402	−	0.131896i
$568$	−9.79418e11			−0.0165663
$569$			8.02547e13i			1.34558i	0.739834	+	0.672789i	$0.234904\pi$
$569$			8.02547e13i			1.34558i	−0.739834	+	0.672789i	$0.765096\pi$
$570$		0			0
$571$	9.58491e13			1.57909			0.789546	−	0.613691i	$-0.210316\pi$
$571$	9.58491e13			1.57909			0.789546	+	0.613691i	$0.210316\pi$
$572$			9.22266e13i			1.50618i
$573$	3.44555e13	+	1.98857e13i	0.557809	+	0.321935i
$574$	−3.54557e12			−0.0569019
$575$		0			0
$576$	3.96486e12	+	6.86238e12i	0.0625339	+	0.108234i
$577$	−8.63768e13			−1.35057			−0.675287	−	0.737555i	$-0.735980\pi$
$577$	−8.63768e13			−1.35057			−0.675287	+	0.737555i	$0.735980\pi$
$578$		−	2.24449e13i		−	0.347919i
$579$	−7.50396e12	+	1.30019e13i	−0.115318	+	0.199809i
$580$		0			0
$581$		−	1.76048e13i		−	0.265920i
$582$	4.51607e13	+	2.60641e13i	0.676310	+	0.390327i
$583$	−2.86835e13			−0.425882
$584$		−	1.76323e13i		−	0.259564i
$585$		0			0
$586$	−3.05466e12			−0.0442054
$587$		−	9.88132e13i		−	1.41783i	−0.705293	−	0.708916i	$-0.749185\pi$
$587$		−	9.88132e13i		−	1.41783i	0.705293	−	0.708916i	$-0.250815\pi$
$588$	−1.71603e13	+	2.97332e13i	−0.244139	+	0.423014i
$589$	4.69839e13			0.662785
$590$		0			0
$591$	9.98557e13	+	5.76309e13i	1.38495	+	0.799315i
$592$	−6.78815e12			−0.0933562
$593$			8.93073e13i			1.21790i	0.793207	+	0.608952i	$0.208410\pi$
$593$			8.93073e13i			1.21790i	−0.793207	+	0.608952i	$0.791590\pi$
$594$	−9.99746e13	+	4.69868e10i	−1.35194	+	0.000635394i
$595$		0			0
$596$			1.33613e13i			0.177671i
$597$	5.52400e13	−	9.57131e13i	0.728420	−	1.26212i
$598$	1.50344e14			1.96598
$599$			1.15548e14i			1.49840i	0.662345	+	0.749199i	$0.269561\pi$
$599$			1.15548e14i			1.49840i	−0.662345	+	0.749199i	$0.730439\pi$
$600$		0			0
$601$	−7.51737e13			−0.958724			−0.479362	−	0.877617i	$-0.659132\pi$
$601$	−7.51737e13			−0.958724			−0.479362	+	0.877617i	$0.659132\pi$
$602$		−	5.15129e12i		−	0.0651528i
$603$	6.32861e12	+	1.09536e13i	0.0793820	+	0.137394i
$604$	2.93700e13			0.365359
$605$		0			0
$606$	3.83668e13	−	6.64773e13i	0.469453	−	0.813411i
$607$	−5.43749e13			−0.659864			−0.329932	−	0.944005i	$-0.607026\pi$
$607$	−5.43749e13			−0.659864			−0.329932	+	0.944005i	$0.607026\pi$
$608$		−	5.41778e12i		−	0.0652083i
$609$	4.29304e12	+	2.47769e12i	0.0512481	+	0.0295774i
$610$		0			0
$611$		−	8.38477e13i		−	0.984657i
$612$	−4.54013e13	+	2.62314e13i	−0.528824	+	0.305538i
$613$	−7.88380e13			−0.910821			−0.455411	−	0.890282i	$-0.650508\pi$
$613$	−7.88380e13			−0.910821			−0.455411	+	0.890282i	$0.650508\pi$
$614$		−	1.69230e13i		−	0.193925i
$615$		0			0
$616$	−9.12800e12			−0.102913
$617$		−	1.10771e14i		−	1.23880i	−0.785075	−	0.619400i	$-0.787376\pi$
$617$		−	1.10771e14i		−	1.23880i	0.785075	−	0.619400i	$-0.212624\pi$
$618$	−6.74377e13	−	3.89211e13i	−0.748102	−	0.431760i
$619$	−9.45555e13			−1.04048			−0.520240	−	0.854020i	$-0.674157\pi$
$619$	−9.45555e13			−1.04048			−0.520240	+	0.854020i	$0.674157\pi$
$620$		0			0
$621$	7.65958e10	+	1.62974e14i	0.000829367	+	1.76466i
$622$	−7.24640e13			−0.778342
$623$			1.01119e13i			0.107744i
$624$	1.86272e13	−	3.22750e13i	0.196891	−	0.341149i
$625$		0			0
$626$			5.29344e13i			0.550638i
$627$	5.91913e13	+	3.41618e13i	0.610830	+	0.352535i
$628$	−5.16238e13			−0.528509
$629$		−	4.49102e13i		−	0.456134i
$630$		0			0
$631$	7.78757e13			0.778494			0.389247	−	0.921134i	$-0.372735\pi$
$631$	7.78757e13			0.778494			0.389247	+	0.921134i	$0.372735\pi$
$632$		−	5.38541e13i		−	0.534113i
$633$	8.88587e13	−	1.53964e14i	0.874342	−	1.51495i
$634$	6.84112e13			0.667853
$635$		0			0
$636$	1.00379e13	+	5.79329e12i	0.0964622	+	0.0556723i
$637$	1.61416e14			1.53904
$638$		−	5.55423e13i		−	0.525437i
$639$	−4.32243e12	+	2.49736e12i	−0.0405717	+	0.0234410i
$640$		0			0
$641$			1.51490e14i			1.39989i	0.714199	+	0.699943i	$0.246791\pi$
$641$			1.51490e14i			1.39989i	−0.714199	+	0.699943i	$0.753209\pi$
$642$	1.03061e13	−	1.78571e13i	0.0944969	−	0.163733i
$643$	4.69260e13			0.426932			0.213466	−	0.976950i	$-0.431525\pi$
$643$	4.69260e13			0.426932			0.213466	+	0.976950i	$0.431525\pi$
$644$			1.48801e13i			0.134331i
$645$		0			0
$646$	3.58439e13			0.318605
$647$			1.54469e14i			1.36245i	0.732075	+	0.681224i	$0.238552\pi$
$647$			1.54469e14i			1.36245i	−0.732075	+	0.681224i	$0.761448\pi$
$648$	3.49959e13	+	2.01757e13i	0.306297	+	0.176585i
$649$	2.13411e14			1.85350
$650$		0			0
$651$	−1.59881e13	+	2.77022e13i	−0.136739	+	0.236924i
$652$	−8.64232e13			−0.733487
$653$		−	1.69764e14i		−	1.42981i	−0.699221	−	0.714905i	$-0.746470\pi$
$653$		−	1.69764e14i		−	1.42981i	0.699221	−	0.714905i	$-0.253530\pi$
$654$	−1.32322e13	−	7.63687e12i	−0.110597	−	0.0638302i
$655$		0			0
$656$		−	1.60530e13i		−	0.132141i
$657$	−4.49596e13	−	7.78159e13i	−0.367278	−	0.635685i
$658$	8.29872e12			0.0672793
$659$			8.79359e13i			0.707520i	0.935336	+	0.353760i	$0.115097\pi$
$659$			8.79359e13i			0.707520i	−0.935336	+	0.353760i	$0.884903\pi$
$660$		0			0
$661$	8.38672e13			0.664638			0.332319	−	0.943167i	$-0.392169\pi$
$661$	8.38672e13			0.664638			0.332319	+	0.943167i	$0.392169\pi$
$662$			1.55562e14i			1.22352i
$663$	2.13531e14	+	1.23237e14i	1.66683	+	0.961999i
$664$	7.97079e13			0.617534
$665$		0			0
$666$	−2.99579e13	+	1.73087e13i	−0.228634	+	0.132097i
$667$	−9.05427e13			−0.685842
$668$		−	9.72043e12i		−	0.0730808i
$669$	3.98729e13	−	6.90869e13i	0.297541	−	0.515543i
$670$		0			0
$671$		−	1.03115e14i		−	0.758071i
$672$	3.19438e12	+	1.84361e12i	0.0233099	+	0.0134531i
$673$	−1.31172e14			−0.950095			−0.475047	−	0.879960i	$-0.657569\pi$
$673$	−1.31172e14			−0.950095			−0.475047	+	0.879960i	$0.657569\pi$
$674$			1.32755e14i			0.954444i
$675$		0			0
$676$	−1.04631e14			−0.741187
$677$			2.41877e14i			1.70079i	0.526143	+	0.850396i	$0.323638\pi$
$677$			2.41877e14i			1.70079i	−0.526143	+	0.850396i	$0.676362\pi$
$678$	−3.42331e13	+	5.93149e13i	−0.238945	+	0.414015i
$679$	2.42653e13			0.168126
$680$		0			0
$681$	−2.17592e14	−	1.25581e14i	−1.48562	−	0.857412i
$682$	3.58405e14			2.42914
$683$			1.54102e13i			0.103682i	0.998655	+	0.0518411i	$0.0165089\pi$
$683$			1.54102e13i			0.103682i	−0.998655	+	0.0518411i	$0.983491\pi$
$684$	−1.38145e13	−	2.39101e13i	−0.0922686	−	0.159698i
$685$		0			0
$686$			3.23309e13i			0.212813i
$687$	−1.44265e13	+	2.49965e13i	−0.0942710	+	0.163341i
$688$	2.33231e13			0.151302
$689$		−	5.44938e13i		−	0.350955i
$690$		0			0
$691$	−2.63409e14			−1.67202			−0.836008	−	0.548717i	$-0.815116\pi$
$691$	−2.63409e14			−1.67202			−0.836008	+	0.548717i	$0.815116\pi$
$692$		−	5.04017e13i		−	0.317625i
$693$	−4.02843e13	+	2.32750e13i	−0.252040	+	0.145621i
$694$	5.06043e13			0.314333
$695$		0			0
$696$	−1.12180e13	+	1.94372e13i	−0.0686864	+	0.119011i
$697$	1.06206e14			0.645633
$698$			7.61477e12i			0.0459600i
$699$	−5.89181e12	−	3.40041e12i	−0.0353071	−	0.0203772i
$700$		0			0
$701$			9.18313e13i			0.542501i	0.962509	+	0.271251i	$0.0874372\pi$
$701$			9.18313e13i			0.542501i	−0.962509	+	0.271251i	$0.912563\pi$
$702$	−8.92668e10	−	1.89935e14i	−0.000523606	−	1.11409i
$703$	2.36515e13			0.137747
$704$		−	4.13281e13i		−	0.238991i
$705$		0			0
$706$	−1.42106e14			−0.810193
$707$		−	3.57188e13i		−	0.202209i
$708$	−7.46838e13	−	4.31031e13i	−0.419817	−	0.242294i
$709$	−4.38552e12			−0.0244788			−0.0122394	−	0.999925i	$-0.503896\pi$
$709$	−4.38552e12			−0.0244788			−0.0122394	+	0.999925i	$0.503896\pi$
$710$		0			0
$711$	−1.37319e14	−	2.37672e14i	−0.755759	−	1.30807i
$712$	−4.57829e13			−0.250209
$713$		−	5.84256e14i		−	3.17070i
$714$	−1.21973e13	+	2.11339e13i	−0.0657311	+	0.113891i
$715$		0			0
$716$			6.51570e13i			0.346255i
$717$	1.38101e14	+	7.97038e13i	0.728788	+	0.420614i
$718$	2.07569e14			1.08778
$719$		−	5.69268e13i		−	0.296260i	−0.988968	−	0.148130i	$-0.952675\pi$
$719$		−	5.69268e13i		−	0.296260i	0.988968	−	0.148130i	$-0.0473253\pi$
$720$		0			0
$721$	−3.62349e13			−0.185973
$722$		−	1.19853e14i		−	0.610892i
$723$	−6.07312e13	+	1.05228e14i	−0.307412	+	0.532645i
$724$	−3.09973e13			−0.155823
$725$		0			0
$726$	3.28006e14	+	1.89306e14i	1.62629	+	0.938600i
$727$	−2.18001e14			−1.07346			−0.536730	−	0.843754i	$-0.680341\pi$
$727$	−2.18001e14			−1.07346			−0.536730	+	0.843754i	$0.680341\pi$
$728$		−	1.73416e13i		−	0.0848073i
$729$	2.05891e14	−	1.93532e11i	1.00000	−	0.000939974i
$730$		0			0
$731$			1.54305e14i			0.739252i
$732$	−2.08264e13	+	3.60855e13i	−0.0990968	+	0.171703i
$733$	1.49315e14			0.705639			0.352819	−	0.935691i	$-0.385223\pi$
$733$	1.49315e14			0.705639			0.352819	+	0.935691i	$0.385223\pi$
$734$			9.48665e13i			0.445279i
$735$		0			0
$736$	−6.73713e13			−0.311951
$737$		−	6.59669e13i		−	0.303381i
$738$	−4.09326e13	−	7.08460e13i	−0.186977	−	0.323619i
$739$	−2.30224e14			−1.04455			−0.522275	−	0.852777i	$-0.674916\pi$
$739$	−2.30224e14			−1.04455			−0.522275	+	0.852777i	$0.674916\pi$
$740$		0			0
$741$	−6.49015e13	+	1.12453e14i	−0.290512	+	0.503363i
$742$	5.39345e12			0.0239799
$743$		−	1.93674e14i		−	0.855319i	−0.903940	−	0.427660i	$-0.859338\pi$
$743$		−	1.93674e14i		−	0.855319i	0.903940	−	0.427660i	$-0.140662\pi$
$744$	−1.25425e14	−	7.23880e13i	−0.550199	−	0.317542i
$745$		0			0
$746$		−	2.06440e14i		−	0.893509i
$747$	3.51772e14	−	2.03243e14i	1.51237	−	0.873800i
$748$	2.73426e14			1.16770
$749$		−	9.59476e12i		−	0.0407029i
$750$		0			0
$751$	−9.04063e13			−0.378442			−0.189221	−	0.981935i	$-0.560596\pi$
$751$	−9.04063e13			−0.378442			−0.189221	+	0.981935i	$0.560596\pi$
$752$			3.75734e13i			0.156240i
$753$	2.83214e14	+	1.63454e14i	1.16987	+	0.675183i
$754$	1.05521e14			0.432994
$755$		0			0
$756$	1.87985e13	−	8.83507e9i	0.0761228	−	3.57767e-5i
$757$	1.36124e14			0.547589			0.273794	−	0.961788i	$-0.411721\pi$
$757$	1.36124e14			0.547589			0.273794	+	0.961788i	$0.411721\pi$
$758$			4.12239e13i			0.164741i
$759$	4.24810e14	−	7.36058e14i	1.68650	−	2.92216i
$760$		0			0
$761$			2.70630e13i			0.106036i	0.998594	+	0.0530179i	$0.0168840\pi$
$761$			2.70630e13i			0.106036i	−0.998594	+	0.0530179i	$0.983116\pi$
$762$	−2.19659e14	−	1.26775e14i	−0.855018	−	0.493466i
$763$	−7.10979e12			−0.0274938
$764$			8.38209e13i			0.322022i
$765$		0			0
$766$	1.03091e14			0.390911
$767$			4.05444e14i			1.52740i
$768$	−8.34715e12	+	1.44629e13i	−0.0312415	+	0.0541315i
$769$	1.77894e13			0.0661499			0.0330749	−	0.999453i	$-0.489470\pi$
$769$	1.77894e13			0.0661499			0.0330749	+	0.999453i	$0.489470\pi$
$770$		0			0
$771$	−2.60037e14	−	1.50078e14i	−0.954471	−	0.550865i
$772$	−3.16302e13			−0.115349
$773$			3.27154e12i			0.0118537i	0.999982	+	0.00592685i	$0.00188659\pi$
$773$			3.27154e12i			0.0118537i	−0.999982	+	0.00592685i	$0.998113\pi$
$774$	1.02931e14	−	5.94701e13i	0.370545	−	0.214089i
$775$		0			0
$776$			1.09864e14i			0.390433i
$777$	−8.04832e12	+	1.39451e13i	−0.0284184	+	0.0492400i
$778$	2.35485e14			0.826161
$779$			5.59322e13i			0.194973i
$780$		0			0
$781$	2.60315e13			0.0895867
$782$		−	4.45727e14i		−	1.52418i
$783$	5.37599e10	+	1.14386e14i	0.000182662	+	0.388654i
$784$	−7.23328e13			−0.244205
$785$		0			0
$786$	7.86639e13	−	1.36299e14i	0.262218	−	0.454340i
$787$	2.33479e14			0.773348			0.386674	−	0.922217i	$-0.373624\pi$
$787$	2.33479e14			0.773348			0.386674	+	0.922217i	$0.373624\pi$
$788$			2.42922e14i			0.799532i
$789$	−2.18794e14	−	1.26275e14i	−0.715567	−	0.412983i
$790$		0			0
$791$			3.18704e13i			0.102921i
$792$	−1.05380e14	−	1.82392e14i	−0.338168	−	0.585301i
$793$	1.95901e14			0.624699
$794$			3.10998e14i			0.985497i
$795$		0			0
$796$	2.32844e14			0.728618
$797$			2.11549e14i			0.657837i	0.944358	+	0.328919i	$0.106684\pi$
$797$			2.11549e14i			0.657837i	−0.944358	+	0.328919i	$0.893316\pi$
$798$	−1.11299e13	−	6.42354e12i	−0.0343936	−	0.0198500i
$799$	−2.48585e14			−0.763380
$800$		0			0
$801$	−2.02052e14	+	1.16739e14i	−0.612774	+	0.354041i
$802$	1.44779e14			0.436350
$803$			4.68640e14i			1.40366i
$804$	−1.33235e13	+	2.30854e13i	−0.0396587	+	0.0687157i
$805$		0			0
$806$			6.80908e14i			2.00177i
$807$	−4.93884e14	−	2.85041e14i	−1.44297	−	0.832798i
$808$	1.61721e14			0.469581
$809$			3.14777e14i			0.908365i	0.890909	+	0.454182i	$0.150069\pi$
$809$			3.14777e14i			0.908365i	−0.890909	+	0.454182i	$0.849931\pi$
$810$		0			0
$811$	3.47802e14			0.991351			0.495675	−	0.868508i	$-0.334921\pi$
$811$	3.47802e14			0.991351			0.495675	+	0.868508i	$0.334921\pi$
$812$			1.04438e13i			0.0295855i
$813$	1.61665e14	−	2.80114e14i	0.455160	−	0.788646i
$814$	1.80419e14			0.504848
$815$		0			0
$816$	−9.56863e13	−	5.52245e13i	−0.264484	−	0.152645i
$817$	−8.12628e13			−0.223245
$818$		−	8.61959e13i		−	0.235353i
$819$	−4.42185e13	−	7.65332e13i	−0.120001	−	0.207697i
$820$		0			0
$821$		−	4.64511e14i		−	1.24532i	−0.782493	−	0.622659i	$-0.786052\pi$
$821$		−	4.64511e14i		−	1.24532i	0.782493	−	0.622659i	$-0.213948\pi$
$822$	−4.05076e13	+	7.01867e13i	−0.107939	+	0.187023i
$823$	−5.13449e14			−1.35987			−0.679936	−	0.733271i	$-0.737993\pi$
$823$	−5.13449e14			−1.35987			−0.679936	+	0.733271i	$0.737993\pi$
$824$		−	1.64058e14i		−	0.431878i
$825$		0			0
$826$	−4.01282e13			−0.104364
$827$		−	4.22697e14i		−	1.09270i	−0.837557	−	0.546351i	$-0.816017\pi$
$827$		−	4.22697e14i		−	1.09270i	0.837557	−	0.546351i	$-0.183983\pi$
$828$	−2.97327e14	+	1.71786e14i	−0.763982	+	0.441404i
$829$	4.62254e13			0.118061			0.0590307	−	0.998256i	$-0.481199\pi$
$829$	4.62254e13			0.118061			0.0590307	+	0.998256i	$0.481199\pi$
$830$		0			0
$831$	3.21721e14	−	5.57438e14i	0.811846	−	1.40667i
$832$	7.85164e13			0.196944
$833$		−	4.78552e14i		−	1.19317i
$834$	−4.02774e14	−	2.32458e14i	−0.998231	−	0.576121i
$835$		0			0
$836$			1.43996e14i			0.352631i
$837$	−7.38111e14	+	3.46903e11i	−1.79678	+	0.000844463i
$838$	7.00535e13			0.169516
$839$		−	2.08381e14i		−	0.501242i	−0.968085	−	0.250621i	$-0.919365\pi$
$839$		−	2.08381e14i		−	0.501242i	0.968085	−	0.250621i	$-0.0806348\pi$
$840$		0			0
$841$	3.57159e14			0.848948
$842$			2.99714e14i			0.708184i
$843$	−2.56210e13	−	1.47869e13i	−0.0601808	−	0.0347328i
$844$	3.74552e14			0.874580
$845$		0			0
$846$	9.58063e13	+	1.65821e14i	0.221076	+	0.382638i
$847$	1.76240e14			0.404286
$848$			2.44195e13i			0.0556874i
$849$	1.36190e14	−	2.35974e14i	0.308751	−	0.534966i
$850$		0			0
$851$		−	2.94111e14i		−	0.658968i
$852$	−9.10981e12	−	5.25765e12i	−0.0202914	−	0.0117110i
$853$	−3.63013e14			−0.803853			−0.401926	−	0.915672i	$-0.631659\pi$
$853$	−3.63013e14			−0.803853			−0.401926	+	0.915672i	$0.631659\pi$
$854$			1.93890e13i			0.0426842i
$855$		0			0
$856$	4.34414e13			0.0945225
$857$			5.58355e14i			1.20783i	0.797049	+	0.603915i	$0.206393\pi$
$857$			5.58355e14i			1.20783i	−0.797049	+	0.603915i	$0.793607\pi$
$858$	−4.95085e14	+	8.57822e14i	−1.06474	+	1.84485i
$859$	−7.64265e14			−1.63410			−0.817049	−	0.576569i	$-0.804391\pi$
$859$	−7.64265e14			−1.63410			−0.817049	+	0.576569i	$0.804391\pi$
$860$		0			0
$861$	−3.29782e13	−	1.90331e13i	−0.0696966	−	0.0402248i
$862$	−3.67790e14			−0.772793
$863$			4.35789e13i			0.0910380i	0.998963	+	0.0455190i	$0.0144941\pi$
$863$			4.35789e13i			0.0910380i	−0.998963	+	0.0455190i	$0.985506\pi$
$864$	4.00018e10	+	8.51126e13i	8.30828e−5	+	0.176777i
$865$		0			0
$866$			3.50286e14i			0.719174i
$867$	1.20487e14	−	2.08765e14i	0.245949	−	0.426150i
$868$	−6.73920e13			−0.136776
$869$			1.43136e15i			2.88835i
$870$		0			0
$871$	1.25326e14			0.250006
$872$		−	3.21904e13i		−	0.0638476i
$873$	2.80135e14	+	4.84858e14i	0.552455	+	0.956188i
$874$	2.34737e14			0.460282
$875$		0			0
$876$	9.46526e13	−	1.64002e14i	0.183490	−	0.317929i
$877$	−1.26826e14			−0.244461			−0.122231	−	0.992502i	$-0.539005\pi$
$877$	−1.26826e14			−0.244461			−0.122231	+	0.992502i	$0.539005\pi$
$878$			8.82677e13i			0.169172i
$879$	−2.84122e13	−	1.63978e13i	−0.0541452	−	0.0312494i
$880$		0			0
$881$			3.00486e14i			0.566167i	0.959095	+	0.283083i	$0.0913573\pi$
$881$			3.00486e14i			0.566167i	−0.959095	+	0.283083i	$0.908643\pi$
$882$	−3.19224e14	+	1.84437e14i	−0.598070	+	0.345546i
$883$	−6.16859e14			−1.14917			−0.574583	−	0.818446i	$-0.694836\pi$
$883$	−6.16859e14			−1.14917			−0.574583	+	0.818446i	$0.694836\pi$
$884$			5.19462e14i			0.962260i
$885$		0			0
$886$	−5.55761e12			−0.0101793
$887$			4.41126e14i			0.803423i	0.915766	+	0.401712i	$0.131585\pi$
$887$			4.41126e14i			0.803423i	−0.915766	+	0.401712i	$0.868415\pi$
$888$	−6.31383e13	−	3.64397e13i	−0.114348	−	0.0659949i
$889$	−1.18025e14			−0.212552
$890$		0			0
$891$	−9.30140e14	−	5.36240e14i	−1.65638	−	0.954928i
$892$	1.68070e14			0.297622
$893$		−	1.30914e14i		−	0.230531i
$894$	−7.17251e13	+	1.24277e14i	−0.125598	+	0.217621i
$895$		0			0
$896$			7.77105e12i			0.0134567i
$897$	1.39838e15	+	8.07066e14i	2.40804	+	1.38978i
$898$	4.49287e14			0.769382
$899$		−	4.10069e14i		−	0.698326i
$900$		0			0
$901$	−1.61559e14			−0.272086
$902$			4.26665e14i			0.714585i
$903$	2.76528e13	−	4.79134e13i	0.0460575	−	0.0798028i
$904$	−1.44297e14			−0.239010
$905$		0			0
$906$	2.73178e14	+	1.57662e14i	0.447512	+	0.258278i
$907$	1.27334e14			0.207447			0.103724	−	0.994606i	$-0.466924\pi$
$907$	1.27334e14			0.207447			0.103724	+	0.994606i	$0.466924\pi$
$908$		−	5.29343e14i		−	0.857645i
$909$	7.13718e14	−	4.12364e14i	1.15003	−	0.664448i
$910$		0			0
$911$			6.60635e13i			0.105286i	0.998613	+	0.0526429i	$0.0167645\pi$
$911$			6.60635e13i			0.105286i	−0.998613	+	0.0526429i	$0.983235\pi$
$912$	2.90834e13	−	5.03921e13i	0.0460967	−	0.0798708i
$913$	−2.11852e15			−3.33948
$914$		−	4.52017e14i		−	0.708637i
$915$		0			0
$916$	−6.08098e13			−0.0942966
$917$		−	7.32347e13i		−	0.112946i
$918$	−5.63102e14	+	2.64651e11i	−0.863722	+	0.000405938i
$919$	−9.72143e14			−1.48304			−0.741520	−	0.670931i	$-0.765895\pi$
$919$	−9.72143e14			−1.48304			−0.741520	+	0.670931i	$0.765895\pi$
$920$		0			0
$921$	9.08448e13	−	1.57405e14i	0.137089	−	0.237531i
$922$	−1.87341e14			−0.281177
$923$			4.94554e13i			0.0738253i
$924$	−8.49018e13	−	4.90003e13i	−0.126054	−	0.0727511i
$925$		0			0
$926$		−	6.06180e14i		−	0.890321i
$927$	−4.18321e14	−	7.24030e14i	−0.611099	−	1.05769i
$928$	−4.72855e13			−0.0687050
$929$			9.23847e14i			1.33512i	0.744554	+	0.667562i	$0.232662\pi$
$929$			9.23847e14i			1.33512i	−0.744554	+	0.667562i	$0.767338\pi$
$930$		0			0
$931$	2.52024e14			0.360324
$932$		−	1.43332e13i		−	0.0203827i
$933$	−6.74006e14	−	3.88997e14i	−0.953356	−	0.550221i
$934$	−6.51696e13			−0.0916877
$935$		0			0
$936$	3.46513e14	−	2.00204e14i	0.482326	−	0.278673i
$937$	5.03322e14			0.696864			0.348432	−	0.937334i	$-0.386714\pi$
$937$	5.03322e14			0.696864			0.348432	+	0.937334i	$0.386714\pi$
$938$			1.24040e13i			0.0170823i
$939$	−2.84159e14	+	4.92356e14i	−0.389254	+	0.674452i
$940$		0			0
$941$		−	2.70557e14i		−	0.366699i	−0.983048	−	0.183350i	$-0.941306\pi$
$941$		−	2.70557e14i		−	0.366699i	0.983048	−	0.183350i	$-0.0586941\pi$
$942$	−4.80166e14	−	2.77124e14i	−0.647347	−	0.373611i
$943$	6.95530e14			0.932734
$944$		−	1.81685e14i		−	0.242360i
$945$		0			0
$946$	−6.19893e14			−0.818202
$947$			3.14693e14i			0.413179i	0.978428	+	0.206589i	$0.0662364\pi$
$947$			3.14693e14i			0.413179i	−0.978428	+	0.206589i	$0.933764\pi$
$948$	2.89096e14	−	5.00910e14i	0.377572	−	0.654211i
$949$	−8.90337e14			−1.15671
$950$		0			0
$951$	6.36310e14	+	3.67241e14i	0.818024	+	0.472115i
$952$	−5.14131e13			−0.0657490
$953$		−	4.68717e14i		−	0.596275i	−0.954523	−	0.298138i	$-0.903635\pi$
$953$		−	4.68717e14i		−	0.596275i	0.954523	−	0.298138i	$-0.0963654\pi$
$954$	6.22658e13	+	1.07770e14i	0.0787967	+	0.136381i
$955$		0			0
$956$			3.35962e14i			0.420728i
$957$	2.98159e14	−	5.16613e14i	0.371439	−	0.643585i
$958$	2.80404e14			0.347501
$959$			3.77119e13i			0.0464928i
$960$		0			0
$961$	1.82647e15			2.22842
$962$			3.42765e14i			0.416027i
$963$	1.91718e14	−	1.10769e14i	0.231490	−	0.133748i
$964$	−2.55990e14			−0.307495
$965$		0			0
$966$	−7.98783e13	+	1.38403e14i	−0.0949605	+	0.164536i
$967$	−7.00055e14			−0.827942			−0.413971	−	0.910290i	$-0.635859\pi$
$967$	−7.00055e14			−0.827942			−0.413971	+	0.910290i	$0.635859\pi$
$968$			7.97949e14i			0.938855i
$969$	3.33393e14	+	1.92415e14i	0.390245	+	0.225226i
$970$		0			0
$971$		−	9.90759e14i		−	1.14781i	−0.818920	−	0.573907i	$-0.805427\pi$
$971$		−	9.90759e14i		−	1.14781i	0.818920	−	0.573907i	$-0.194573\pi$
$972$	2.17200e14	+	3.75522e14i	0.250339	+	0.432817i
$973$	−2.16414e14			−0.248154
$974$			4.93492e14i			0.562971i
$975$		0			0
$976$	−8.77862e13			−0.0991237
$977$			2.42922e14i			0.272894i	0.990647	+	0.136447i	$0.0435683\pi$
$977$			2.42922e14i			0.272894i	−0.990647	+	0.136447i	$0.956432\pi$
$978$	−8.03843e14	−	4.63931e14i	−0.898415	−	0.518513i
$979$	1.21684e15			1.35307
$980$		0			0
$981$	−8.20805e13	−	1.42065e14i	−0.0903431	−	0.156366i
$982$	4.46997e14			0.489493
$983$			4.32198e14i			0.470885i	0.971888	+	0.235443i	$0.0756540\pi$
$983$			4.32198e14i			0.470885i	−0.971888	+	0.235443i	$0.924346\pi$
$984$	8.61746e13	−	1.49313e14i	0.0934122	−	0.161853i
$985$		0			0
$986$		−	3.12840e14i		−	0.335689i
$987$	7.71884e13	+	4.45486e13i	0.0824074	+	0.0475607i
$988$	−2.73569e14			−0.290591
$989$			1.01052e15i			1.06798i
$990$		0			0
$991$	−5.53231e14			−0.578813			−0.289406	−	0.957206i	$-0.593458\pi$
$991$	−5.53231e14			−0.578813			−0.289406	+	0.957206i	$0.593458\pi$
$992$		−	3.05125e14i		−	0.317629i
$993$	−8.35075e14	+	1.44692e15i	−0.864927	+	1.49864i
$994$	−4.89478e12			−0.00504430
$995$		0			0
$996$	7.41383e14	+	4.27883e14i	0.756391	+	0.436544i
$997$	−7.38968e14			−0.750153			−0.375076	−	0.926994i	$-0.622384\pi$
$997$	−7.38968e14			−0.750153			−0.375076	+	0.926994i	$0.622384\pi$
$998$			9.75740e14i			0.985556i
$999$	−3.71561e14	+	1.74629e11i	−0.373425	+	0.000175505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.11.d.d.101.10	yes	14
3.2	odd	2	inner	150.11.d.d.101.3	yes	14
5.2	odd	4		150.11.b.c.149.12		28
5.3	odd	4		150.11.b.c.149.17		28
5.4	even	2		150.11.d.c.101.5	✓	14
15.2	even	4		150.11.b.c.149.18		28
15.8	even	4		150.11.b.c.149.11		28
15.14	odd	2		150.11.d.c.101.12	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.11.b.c.149.11		28	15.8	even	4
150.11.b.c.149.12		28	5.2	odd	4
150.11.b.c.149.17		28	5.3	odd	4
150.11.b.c.149.18		28	15.2	even	4
150.11.d.c.101.5	✓	14	5.4	even	2
150.11.d.c.101.12	yes	14	15.14	odd	2
150.11.d.d.101.3	yes	14	3.2	odd	2	inner
150.11.d.d.101.10	yes	14	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+22.6274i q^{2} +(-121.467 + 210.463i) q^{3} -512.000 q^{4} +(-4762.24 - 2748.49i) q^{6} -2558.79 q^{7} -11585.2i q^{8} +(-29540.5 - 51128.7i) q^{9} +O(q^{10})\)	\(q+22.6274i q^{2} +(-121.467 + 210.463i) q^{3} -512.000 q^{4} +(-4762.24 - 2748.49i) q^{6} -2558.79 q^{7} -11585.2i q^{8} +(-29540.5 - 51128.7i) q^{9} +307918. i q^{11} +(62191.1 - 107757. i) q^{12} -584993. q^{13} -57898.9i q^{14} +262144. q^{16} +1.73434e6i q^{17} +(1.15691e6 - 668426. i) q^{18} -913369. q^{19} +(310809. - 538532. i) q^{21} -6.96740e6 q^{22} +1.13580e7i q^{23} +(2.43827e6 + 1.40722e6i) q^{24} -1.32369e7i q^{26} +(1.43489e7 - 6743.80i) q^{27} +1.31010e6 q^{28} +7.97174e6i q^{29} -5.14403e7 q^{31} +5.93164e6i q^{32} +(-6.48055e7 - 3.74019e7i) q^{33} -3.92436e7 q^{34} +(1.51247e7 + 2.61779e7i) q^{36} -2.58947e7 q^{37} -2.06672e7i q^{38} +(7.10573e7 - 1.23119e8i) q^{39} -6.12373e7i q^{41} +(1.21856e7 + 7.03280e6i) q^{42} +8.89704e7 q^{43} -1.57654e8i q^{44} -2.57001e8 q^{46} +1.43331e8i q^{47} +(-3.18419e7 + 5.51717e7i) q^{48} -2.75928e8 q^{49} +(-3.65014e8 - 2.10665e8i) q^{51} +2.99516e8 q^{52} +9.31529e7i q^{53} +(152595. + 3.24679e8i) q^{54} +2.96442e7i q^{56} +(1.10944e8 - 1.92230e8i) q^{57} -1.80380e8 q^{58} -6.93075e8i q^{59} -3.34878e8 q^{61} -1.16396e9i q^{62} +(7.55881e7 + 1.30828e8i) q^{63} -1.34218e8 q^{64} +(8.46309e8 - 1.46638e9i) q^{66} -2.14235e8 q^{67} -8.87981e8i q^{68} +(-2.39043e9 - 1.37962e9i) q^{69} -8.45402e7i q^{71} +(-5.92338e8 + 3.42234e8i) q^{72} +1.52196e9 q^{73} -5.85931e8i q^{74} +4.67645e8 q^{76} -7.87899e8i q^{77} +(2.78587e9 + 1.60784e9i) q^{78} +4.64851e9 q^{79} +(-1.74150e9 + 3.02074e9i) q^{81} +1.38564e9 q^{82} +6.88013e9i q^{83} +(-1.59134e8 + 2.75728e8i) q^{84} +2.01317e9i q^{86} +(-1.67776e9 - 9.68304e8i) q^{87} +3.56731e9 q^{88} -3.95183e9i q^{89} +1.49687e9 q^{91} -5.81527e9i q^{92} +(6.24830e9 - 1.08263e10i) q^{93} -3.24322e9 q^{94} +(-1.24839e9 - 7.20499e8i) q^{96} -9.48309e9 q^{97} -6.24353e9i q^{98} +(1.57435e10 - 9.09607e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 22 q^{3} - 7168 q^{4} - 6784 q^{6} - 28466 q^{7} - 118958 q^{9}+O(q^{10}) \) 14 * q + 22 * q^3 - 7168 * q^4 - 6784 * q^6 - 28466 * q^7 - 118958 * q^9	\( 14 q + 22 q^{3} - 7168 q^{4} - 6784 q^{6} - 28466 q^{7} - 118958 q^{9} - 11264 q^{12} - 1473590 q^{13} + 3670016 q^{16} - 926464 q^{18} + 2045302 q^{19} - 4714822 q^{21} + 6946944 q^{22} + 3473408 q^{24} - 29984966 q^{27} + 14574592 q^{28} + 2933182 q^{31} - 94398708 q^{33} + 81089664 q^{34} + 60906496 q^{36} - 65206484 q^{37} - 317162410 q^{39} - 145249664 q^{42} + 523420558 q^{43} - 389380224 q^{46} + 5767168 q^{48} + 1327037880 q^{49} + 605541012 q^{51} + 754478080 q^{52} - 173975680 q^{54} - 303021034 q^{57} + 763332480 q^{58} - 745863254 q^{61} - 3429820738 q^{63} - 1879048192 q^{64} + 3492778368 q^{66} - 1059130154 q^{67} - 985447992 q^{69} + 474349568 q^{72} + 4118860900 q^{73} - 1047194624 q^{76} + 1793952640 q^{78} + 3863766388 q^{79} - 8765793182 q^{81} + 3625547136 q^{82} + 2413988864 q^{84} + 11014377480 q^{87} - 3556835328 q^{88} - 11461151470 q^{91} + 30776293826 q^{93} - 3855022080 q^{94} - 1778384896 q^{96} - 35728415702 q^{97} + 4077474108 q^{99}+O(q^{100}) \) 14 * q + 22 * q^3 - 7168 * q^4 - 6784 * q^6 - 28466 * q^7 - 118958 * q^9 - 11264 * q^12 - 1473590 * q^13 + 3670016 * q^16 - 926464 * q^18 + 2045302 * q^19 - 4714822 * q^21 + 6946944 * q^22 + 3473408 * q^24 - 29984966 * q^27 + 14574592 * q^28 + 2933182 * q^31 - 94398708 * q^33 + 81089664 * q^34 + 60906496 * q^36 - 65206484 * q^37 - 317162410 * q^39 - 145249664 * q^42 + 523420558 * q^43 - 389380224 * q^46 + 5767168 * q^48 + 1327037880 * q^49 + 605541012 * q^51 + 754478080 * q^52 - 173975680 * q^54 - 303021034 * q^57 + 763332480 * q^58 - 745863254 * q^61 - 3429820738 * q^63 - 1879048192 * q^64 + 3492778368 * q^66 - 1059130154 * q^67 - 985447992 * q^69 + 474349568 * q^72 + 4118860900 * q^73 - 1047194624 * q^76 + 1793952640 * q^78 + 3863766388 * q^79 - 8765793182 * q^81 + 3625547136 * q^82 + 2413988864 * q^84 + 11014377480 * q^87 - 3556835328 * q^88 - 11461151470 * q^91 + 30776293826 * q^93 - 3855022080 * q^94 - 1778384896 * q^96 - 35728415702 * q^97 + 4077474108 * q^99

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