LMFDB - Embedded newform 100.11.b.h.51.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, 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("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$63.5357252674$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.14
Character	$\chi$	$=$	100.51
Dual form			100.11.b.h.51.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.07116 + 31.7400i) q^{2} +190.073i q^{3} +(-990.851 + 258.437i) q^{4} +(-6032.92 + 773.819i) q^{6} -14056.7i q^{7} +(-12236.7 - 30397.4i) q^{8} +22921.2 q^{9} +O(q^{10})$	\(q+(4.07116 + 31.7400i) q^{2} +190.073i q^{3} +(-990.851 + 258.437i) q^{4} +(-6032.92 + 773.819i) q^{6} -14056.7i q^{7} +(-12236.7 - 30397.4i) q^{8} +22921.2 q^{9} +173205. i q^{11} +(-49122.0 - 188334. i) q^{12} +664258. q^{13} +(446160. - 57227.2i) q^{14} +(914997. - 512145. i) q^{16} -1.08730e6 q^{17} +(93315.9 + 727518. i) q^{18} +2.14038e6i q^{19} +2.67181e6 q^{21} +(-5.49751e6 + 705145. i) q^{22} +6.85374e6i q^{23} +(5.77774e6 - 2.32587e6i) q^{24} +(2.70430e6 + 2.10835e7i) q^{26} +1.55803e7i q^{27} +(3.63278e6 + 1.39281e7i) q^{28} -1.60930e7 q^{29} -3.87488e7i q^{31} +(1.99806e7 + 2.69569e7i) q^{32} -3.29216e7 q^{33} +(-4.42658e6 - 3.45109e7i) q^{34} +(-2.27115e7 + 5.92369e6i) q^{36} -1.29585e7 q^{37} +(-6.79357e7 + 8.71384e6i) q^{38} +1.26258e8i q^{39} +4.48926e7 q^{41} +(1.08774e7 + 8.48031e7i) q^{42} +8.66330e7i q^{43} +(-4.47625e7 - 1.71620e8i) q^{44} +(-2.17538e8 + 2.79027e7i) q^{46} +2.64135e8i q^{47} +(9.73451e7 + 1.73916e8i) q^{48} +8.48835e7 q^{49} -2.06667e8i q^{51} +(-6.58180e8 + 1.71669e8i) q^{52} +2.29181e8 q^{53} +(-4.94519e8 + 6.34301e7i) q^{54} +(-4.27289e8 + 1.72008e8i) q^{56} -4.06829e8 q^{57} +(-6.55170e7 - 5.10790e8i) q^{58} -5.54778e8i q^{59} +8.72720e8 q^{61} +(1.22989e9 - 1.57753e8i) q^{62} -3.22197e8i q^{63} +(-7.74268e8 + 7.43929e8i) q^{64} +(-1.34029e8 - 1.04493e9i) q^{66} -1.53061e8i q^{67} +(1.07735e9 - 2.80999e8i) q^{68} -1.30271e9 q^{69} +3.28433e9i q^{71} +(-2.80480e8 - 6.96746e8i) q^{72} -1.61594e9 q^{73} +(-5.27562e7 - 4.11303e8i) q^{74} +(-5.53154e8 - 2.12080e9i) q^{76} +2.43469e9 q^{77} +(-4.00741e9 + 5.14015e8i) q^{78} -3.08746e9i q^{79} -1.60793e9 q^{81} +(1.82765e8 + 1.42489e9i) q^{82} +1.89093e9i q^{83} +(-2.64736e9 + 6.90494e8i) q^{84} +(-2.74973e9 + 3.52697e8i) q^{86} -3.05884e9i q^{87} +(5.26498e9 - 2.11946e9i) q^{88} -8.69033e9 q^{89} -9.33729e9i q^{91} +(-1.77126e9 - 6.79104e9i) q^{92} +7.36511e9 q^{93} +(-8.38362e9 + 1.07533e9i) q^{94} +(-5.12379e9 + 3.79777e9i) q^{96} -5.78965e9 q^{97} +(3.45574e8 + 2.69420e9i) q^{98} +3.97006e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9}+O(q^{10}) $ 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9	$ 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9} + 1706016 q^{14} - 4733376 q^{16} - 13030368 q^{21} - 10190784 q^{24} - 9454368 q^{26} - 121656816 q^{29} + 335231168 q^{34} - 276632160 q^{36} + 892843248 q^{41} - 766329600 q^{44} + 433181216 q^{46} + 738102008 q^{49} - 139387968 q^{54} - 2629032384 q^{56} + 228563248 q^{61} + 1875284992 q^{64} - 1440259200 q^{66} + 943422432 q^{69} - 21045467232 q^{74} + 828422400 q^{76} - 5619065544 q^{81} + 28069573632 q^{84} + 8163556416 q^{86} - 4631088816 q^{89} - 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) $ 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9 + 1706016 * q^14 - 4733376 * q^16 - 13030368 * q^21 - 10190784 * q^24 - 9454368 * q^26 - 121656816 * q^29 + 335231168 * q^34 - 276632160 * q^36 + 892843248 * q^41 - 766329600 * q^44 + 433181216 * q^46 + 738102008 * q^49 - 139387968 * q^54 - 2629032384 * q^56 + 228563248 * q^61 + 1875284992 * q^64 - 1440259200 * q^66 + 943422432 * q^69 - 21045467232 * q^74 + 828422400 * q^76 - 5619065544 * q^81 + 28069573632 * q^84 + 8163556416 * q^86 - 4631088816 * q^89 - 63404384 * q^94 - 5617046784 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	4.07116	+	31.7400i	0.127224	+	0.991874i
$2$	4.07116	+	31.7400i	0.127224	+	0.991874i
$3$			190.073i			0.782194i	0.920349	+	0.391097i	$0.127904\pi$
$3$			190.073i			0.782194i	−0.920349	+	0.391097i	$0.872096\pi$
$4$	−990.851	+	258.437i	−0.967628	+	0.252380i
$5$		0			0
$5$		0			0
$6$	−6032.92	+	773.819i	−0.775838	+	0.0995137i
$7$		−	14056.7i		−	0.836362i	−0.908364	−	0.418181i	$-0.862668\pi$
$7$		−	14056.7i		−	0.836362i	0.908364	−	0.418181i	$-0.137332\pi$
$8$	−12236.7	−	30397.4i	−0.373434	−	0.927657i
$9$	22921.2			0.388173
$10$		0			0
$11$			173205.i			1.07547i	0.843115	+	0.537733i	$0.180719\pi$
$11$			173205.i			1.07547i	−0.843115	+	0.537733i	$0.819281\pi$
$12$	−49122.0	−	188334.i	−0.197410	−	0.756873i
$13$	664258.			1.78904			0.894519	−	0.447029i	$-0.147518\pi$
$13$	664258.			1.78904			0.894519	+	0.447029i	$0.147518\pi$
$14$	446160.	−	57227.2i	0.829566	−	0.106405i
$15$		0			0
$16$	914997.	−	512145.i	0.872609	−	0.488420i
$17$	−1.08730e6			−0.765782			−0.382891	−	0.923793i	$-0.625072\pi$
$17$	−1.08730e6			−0.765782			−0.382891	+	0.923793i	$0.625072\pi$
$18$	93315.9	+	727518.i	0.0493848	+	0.385018i
$19$			2.14038e6i			0.864417i	0.901774	+	0.432209i	$0.142266\pi$
$19$			2.14038e6i			0.864417i	−0.901774	+	0.432209i	$0.857734\pi$
$20$		0			0
$21$	2.67181e6			0.654197
$22$	−5.49751e6	+	705145.i	−1.06673	+	0.136825i
$23$			6.85374e6i			1.06485i	0.846477	+	0.532425i	$0.178719\pi$
$23$			6.85374e6i			1.06485i	−0.846477	+	0.532425i	$0.821281\pi$
$24$	5.77774e6	−	2.32587e6i	0.725607	−	0.292098i
$25$		0			0
$26$	2.70430e6	+	2.10835e7i	0.227608	+	1.77450i
$27$			1.55803e7i			1.08582i
$28$	3.63278e6	+	1.39281e7i	0.211081	+	0.809287i
$29$	−1.60930e7			−0.784595			−0.392298	−	0.919838i	$-0.628320\pi$
$29$	−1.60930e7			−0.784595			−0.392298	+	0.919838i	$0.628320\pi$
$30$		0			0
$31$		−	3.87488e7i		−	1.35347i	−0.736225	−	0.676737i	$-0.763393\pi$
$31$		−	3.87488e7i		−	1.35347i	0.736225	−	0.676737i	$-0.236607\pi$
$32$	1.99806e7	+	2.69569e7i	0.595468	+	0.803379i
$33$	−3.29216e7			−0.841223
$34$	−4.42658e6	−	3.45109e7i	−0.0974258	−	0.759560i
$35$		0			0
$36$	−2.27115e7	+	5.92369e6i	−0.375607	+	0.0979670i
$37$	−1.29585e7			−0.186873			−0.0934365	−	0.995625i	$-0.529785\pi$
$37$	−1.29585e7			−0.186873			−0.0934365	+	0.995625i	$0.529785\pi$
$38$	−6.79357e7	+	8.71384e6i	−0.857393	+	0.109974i
$39$			1.26258e8i			1.39938i
$40$		0			0
$41$	4.48926e7			0.387485			0.193743	−	0.981052i	$-0.437937\pi$
$41$	4.48926e7			0.387485			0.193743	+	0.981052i	$0.437937\pi$
$42$	1.08774e7	+	8.48031e7i	0.0832295	+	0.648881i
$43$			8.66330e7i			0.589307i	0.955604	+	0.294653i	$0.0952042\pi$
$43$			8.66330e7i			0.589307i	−0.955604	+	0.294653i	$0.904796\pi$
$44$	−4.47625e7	−	1.71620e8i	−0.271426	−	1.04065i
$45$		0			0
$46$	−2.17538e8	+	2.79027e7i	−1.05620	+	0.135474i
$47$			2.64135e8i			1.15169i	0.817559	+	0.575845i	$0.195327\pi$
$47$			2.64135e8i			1.15169i	−0.817559	+	0.575845i	$0.804673\pi$
$48$	9.73451e7	+	1.73916e8i	0.382039	+	0.682549i
$49$	8.48835e7			0.300499
$50$		0			0
$51$		−	2.06667e8i		−	0.598990i
$52$	−6.58180e8	+	1.71669e8i	−1.73112	+	0.451518i
$53$	2.29181e8			0.548025			0.274012	−	0.961726i	$-0.411649\pi$
$53$	2.29181e8			0.548025			0.274012	+	0.961726i	$0.411649\pi$
$54$	−4.94519e8	+	6.34301e7i	−1.07700	+	0.138142i
$55$		0			0
$56$	−4.27289e8	+	1.72008e8i	−0.775857	+	0.312326i
$57$	−4.06829e8			−0.676142
$58$	−6.55170e7	−	5.10790e8i	−0.0998192	−	0.778220i
$59$		−	5.54778e8i		−	0.775996i	−0.921660	−	0.387998i	$-0.873167\pi$
$59$		−	5.54778e8i		−	0.775996i	0.921660	−	0.387998i	$-0.126833\pi$
$60$		0			0
$61$	8.72720e8			1.03330			0.516649	−	0.856197i	$-0.327179\pi$
$61$	8.72720e8			1.03330			0.516649	+	0.856197i	$0.327179\pi$
$62$	1.22989e9	−	1.57753e8i	1.34248	−	0.172194i
$63$		−	3.22197e8i		−	0.324653i
$64$	−7.74268e8	+	7.43929e8i	−0.721093	+	0.692838i
$65$		0			0
$66$	−1.34029e8	−	1.04493e9i	−0.107024	−	0.834387i
$67$		−	1.53061e8i		−	0.113368i	−0.998392	−	0.0566841i	$-0.981947\pi$
$67$		−	1.53061e8i		−	0.113368i	0.998392	−	0.0566841i	$-0.0180528\pi$
$68$	1.07735e9	−	2.80999e8i	0.740993	−	0.193268i
$69$	−1.30271e9			−0.832920
$70$		0			0
$71$			3.28433e9i			1.82035i	0.414221	+	0.910176i	$0.364054\pi$
$71$			3.28433e9i			1.82035i	−0.414221	+	0.910176i	$0.635946\pi$
$72$	−2.80480e8	−	6.96746e8i	−0.144957	−	0.360091i
$73$	−1.61594e9			−0.779493			−0.389747	−	0.920922i	$-0.627437\pi$
$73$	−1.61594e9			−0.779493			−0.389747	+	0.920922i	$0.627437\pi$
$74$	−5.27562e7	−	4.11303e8i	−0.0237747	−	0.185355i
$75$		0			0
$76$	−5.53154e8	−	2.12080e9i	−0.218162	−	0.836434i
$77$	2.43469e9			0.899478
$78$	−4.00741e9	+	5.14015e8i	−1.38800	+	0.178034i
$79$		−	3.08746e9i		−	1.00338i	−0.865047	−	0.501690i	$-0.832712\pi$
$79$		−	3.08746e9i		−	1.00338i	0.865047	−	0.501690i	$-0.167288\pi$
$80$		0			0
$81$	−1.60793e9			−0.461150
$82$	1.82765e8	+	1.42489e9i	0.0492974	+	0.384337i
$83$			1.89093e9i			0.480049i	0.970767	+	0.240024i	$0.0771555\pi$
$83$			1.89093e9i			0.480049i	−0.970767	+	0.240024i	$0.922845\pi$
$84$	−2.64736e9	+	6.90494e8i	−0.633020	+	0.165106i
$85$		0			0
$86$	−2.74973e9	+	3.52697e8i	−0.584518	+	0.0749738i
$87$		−	3.05884e9i		−	0.613706i
$88$	5.26498e9	−	2.11946e9i	0.997663	−	0.401616i
$89$	−8.69033e9			−1.55627			−0.778137	−	0.628095i	$-0.783835\pi$
$89$	−8.69033e9			−1.55627			−0.778137	+	0.628095i	$0.783835\pi$
$90$		0			0
$91$		−	9.33729e9i		−	1.49628i
$92$	−1.77126e9	−	6.79104e9i	−0.268747	−	1.03038i
$93$	7.36511e9			1.05868
$94$	−8.38362e9	+	1.07533e9i	−1.14233	+	0.146523i
$95$		0			0
$96$	−5.12379e9	+	3.79777e9i	−0.628398	+	0.465771i
$97$	−5.78965e9			−0.674207			−0.337104	−	0.941468i	$-0.609447\pi$
$97$	−5.78965e9			−0.674207			−0.337104	+	0.941468i	$0.609447\pi$
$98$	3.45574e8	+	2.69420e9i	0.0382306	+	0.298057i
$99$			3.97006e9i			0.417466i
$100$		0			0
$101$	−1.07828e10			−1.02594			−0.512971	−	0.858406i	$-0.671455\pi$
$101$	−1.07828e10			−1.02594			−0.512971	+	0.858406i	$0.671455\pi$
$102$	6.55960e9	−	8.41374e8i	0.594123	−	0.0762058i
$103$			7.05867e9i			0.608887i	0.952530	+	0.304444i	$0.0984705\pi$
$103$			7.05867e9i			0.608887i	−0.952530	+	0.304444i	$0.901529\pi$
$104$	−8.12832e9	−	2.01917e10i	−0.668089	−	1.65961i
$105$		0			0
$106$	9.33035e8	+	7.27421e9i	0.0697218	+	0.543571i
$107$			1.81193e9i			0.129188i	0.997912	+	0.0645942i	$0.0205753\pi$
$107$			1.81193e9i			0.129188i	−0.997912	+	0.0645942i	$0.979425\pi$
$108$	−4.02654e9	−	1.54378e10i	−0.274039	−	1.05067i
$109$	−1.33028e10			−0.864588			−0.432294	−	0.901733i	$-0.642296\pi$
$109$	−1.33028e10			−0.864588			−0.432294	+	0.901733i	$0.642296\pi$
$110$		0			0
$111$		−	2.46307e9i		−	0.146171i
$112$	−7.19909e9	−	1.28619e10i	−0.408496	−	0.729817i
$113$	−2.35102e10			−1.27604			−0.638020	−	0.770019i	$-0.720246\pi$
$113$	−2.35102e10			−1.27604			−0.638020	+	0.770019i	$0.720246\pi$
$114$	−1.65627e9	−	1.29127e10i	−0.0860214	−	0.670648i
$115$		0			0
$116$	1.59457e10	−	4.15902e9i	0.759197	−	0.198016i
$117$	1.52256e10			0.694456
$118$	1.76086e10	−	2.25859e9i	0.769690	−	0.0987251i
$119$			1.52839e10i			0.640471i
$120$		0			0
$121$	−4.06247e9			−0.156626
$122$	3.55298e9	+	2.77001e10i	0.131460	+	1.02490i
$123$			8.53287e9i			0.303089i
$124$	1.00141e10	+	3.83943e10i	0.341590	+	1.30966i
$125$		0			0
$126$	1.02265e10	−	1.31172e9i	0.322015	−	0.0413036i
$127$			4.14600e10i			1.25490i	0.778655	+	0.627452i	$0.215902\pi$
$127$			4.14600e10i			1.25490i	−0.778655	+	0.627452i	$0.784098\pi$
$128$	−2.67645e10	−	2.15466e10i	−0.778948	−	0.627088i
$129$	−1.64666e10			−0.460952
$130$		0			0
$131$		−	1.38898e9i		−	0.0360030i	−0.999838	−	0.0180015i	$-0.994270\pi$
$131$		−	1.38898e9i		−	0.0360030i	0.999838	−	0.0180015i	$-0.00573037\pi$
$132$	3.26204e10	−	8.50816e9i	0.813991	−	0.212308i
$133$	3.00868e10			0.722966
$134$	4.85816e9	−	6.23137e8i	0.112447	−	0.0144231i
$135$		0			0
$136$	1.33050e10	+	3.30512e10i	0.285970	+	0.710383i
$137$	−4.15616e10			−0.861170			−0.430585	−	0.902550i	$-0.641693\pi$
$137$	−4.15616e10			−0.861170			−0.430585	+	0.902550i	$0.641693\pi$
$138$	−5.30355e9	−	4.13481e10i	−0.105967	−	0.826152i
$139$		−	7.90047e10i		−	1.52258i	−0.648414	−	0.761288i	$-0.724567\pi$
$139$		−	7.90047e10i		−	1.52258i	0.648414	−	0.761288i	$-0.275433\pi$
$140$		0			0
$141$	−5.02049e10			−0.900846
$142$	−1.04245e11	+	1.33711e10i	−1.80556	+	0.231592i
$143$			1.15053e11i			1.92405i
$144$	2.09728e10	−	1.17390e10i	0.338723	−	0.189591i
$145$		0			0
$146$	−6.57877e9	−	5.12900e10i	−0.0991701	−	0.773159i
$147$			1.61341e10i			0.235048i
$148$	1.28400e10	−	3.34896e9i	0.180824	−	0.0471630i
$149$	3.37967e9			0.0460197			0.0230098	−	0.999735i	$-0.492675\pi$
$149$	3.37967e9			0.0460197			0.0230098	+	0.999735i	$0.492675\pi$
$150$		0			0
$151$			6.40458e10i			0.815841i	0.913017	+	0.407921i	$0.133746\pi$
$151$			6.40458e10i			0.815841i	−0.913017	+	0.407921i	$0.866254\pi$
$152$	6.50622e10	−	2.61912e10i	0.801882	−	0.322803i
$153$	−2.49223e10			−0.297256
$154$	9.91203e9	+	7.72771e10i	0.114435	+	0.892169i
$155$		0			0
$156$	−3.26296e10	−	1.25102e11i	−0.353174	−	1.35408i
$157$	−1.27096e10			−0.133239			−0.0666197	−	0.997778i	$-0.521221\pi$
$157$	−1.27096e10			−0.133239			−0.0666197	+	0.997778i	$0.521221\pi$
$158$	9.79958e10	−	1.25695e10i	0.995227	−	0.127654i
$159$			4.35612e10i			0.428662i
$160$		0			0
$161$	9.63413e10			0.890601
$162$	−6.54614e9	−	5.10356e10i	−0.0586692	−	0.457402i
$163$			1.71627e11i			1.49158i	0.666181	+	0.745790i	$0.267928\pi$
$163$			1.71627e11i			1.49158i	−0.666181	+	0.745790i	$0.732072\pi$
$164$	−4.44819e10	+	1.16019e10i	−0.374942	+	0.0977935i
$165$		0			0
$166$	−6.00181e10	+	7.69829e9i	−0.476148	+	0.0610737i
$167$			1.27551e11i			0.981976i	0.871166	+	0.490988i	$0.163364\pi$
$167$			1.27551e11i			0.981976i	−0.871166	+	0.490988i	$0.836636\pi$
$168$	−3.26941e10	−	8.12161e10i	−0.244300	−	0.606870i
$169$	3.03380e11			2.20066
$170$		0			0
$171$			4.90601e10i			0.335543i
$172$	−2.23892e10	−	8.58405e10i	−0.148729	−	0.570230i
$173$	−1.87423e11			−1.20946			−0.604732	−	0.796429i	$-0.706720\pi$
$173$	−1.87423e11			−1.20946			−0.604732	+	0.796429i	$0.706720\pi$
$174$	9.70874e10	−	1.24530e10i	0.608719	−	0.0780780i
$175$		0			0
$176$	8.87060e10	+	1.58482e11i	0.525279	+	0.938461i
$177$	1.05448e11			0.606979
$178$	−3.53797e10	−	2.75831e11i	−0.197995	−	1.54363i
$179$			1.33805e11i			0.728126i	0.931374	+	0.364063i	$0.118611\pi$
$179$			1.33805e11i			0.728126i	−0.931374	+	0.364063i	$0.881389\pi$
$180$		0			0
$181$	3.51003e11			1.80683			0.903417	−	0.428764i	$-0.141051\pi$
$181$	3.51003e11			1.80683			0.903417	+	0.428764i	$0.141051\pi$
$182$	2.96365e11	−	3.80136e10i	1.48413	−	0.190363i
$183$			1.65881e11i			0.808239i
$184$	2.08336e11	−	8.38672e10i	0.987816	−	0.397652i
$185$		0			0
$186$	2.99845e10	+	2.33768e11i	0.134689	+	1.05008i
$187$		−	1.88326e11i		−	0.823573i
$188$	−6.82622e10	−	2.61718e11i	−0.290664	−	1.11441i
$189$	2.19009e11			0.908139
$190$		0			0
$191$		−	3.35424e11i		−	1.31956i	−0.751460	−	0.659778i	$-0.770650\pi$
$191$		−	3.35424e11i		−	1.31956i	0.751460	−	0.659778i	$-0.229350\pi$
$192$	−1.41401e11	−	1.47168e11i	−0.541934	−	0.564035i
$193$	4.42274e11			1.65160			0.825800	−	0.563964i	$-0.190724\pi$
$193$	4.42274e11			1.65160			0.825800	+	0.563964i	$0.190724\pi$
$194$	−2.35706e10	−	1.83763e11i	−0.0857752	−	0.668729i
$195$		0			0
$196$	−8.41069e10	+	2.19370e10i	−0.290771	+	0.0758399i
$197$	6.39016e10			0.215368			0.107684	−	0.994185i	$-0.465657\pi$
$197$	6.39016e10			0.215368			0.107684	+	0.994185i	$0.465657\pi$
$198$	−1.26010e11	+	1.61628e10i	−0.414074	+	0.0531116i
$199$			2.95320e11i			0.946298i	0.880982	+	0.473149i	$0.156883\pi$
$199$			2.95320e11i			0.946298i	−0.880982	+	0.473149i	$0.843117\pi$
$200$		0			0
$201$	2.90928e10			0.0886759
$202$	−4.38983e10	−	3.42244e11i	−0.130524	−	1.01761i
$203$			2.26214e11i			0.656206i
$204$	5.34104e10	+	2.04776e11i	0.151173	+	0.579600i
$205$		0			0
$206$	−2.24042e11	+	2.87370e10i	−0.603939	+	0.0774649i
$207$			1.57096e11i			0.413346i
$208$	6.07793e11	−	3.40196e11i	1.56113	−	0.873802i
$209$	−3.70725e11			−0.929651
$210$		0			0
$211$			1.50649e11i			0.360208i	0.983648	+	0.180104i	$0.0576435\pi$
$211$			1.50649e11i			0.360208i	−0.983648	+	0.180104i	$0.942356\pi$
$212$	−2.27085e11	+	5.92290e10i	−0.530284	+	0.138310i
$213$	−6.24264e11			−1.42387
$214$	−5.75107e10	+	7.37668e9i	−0.128139	+	0.0164358i
$215$		0			0
$216$	4.73602e11	−	1.90652e11i	1.00727	−	0.405483i
$217$	−5.44682e11			−1.13199
$218$	−5.41577e10	−	4.22229e11i	−0.109996	−	0.857563i
$219$		−	3.07148e11i		−	0.609715i
$220$		0			0
$221$	−7.22248e11			−1.37001
$222$	7.81776e10	−	1.00275e10i	0.144983	−	0.0185964i
$223$			8.28926e11i			1.50311i	0.659669	+	0.751556i	$0.270696\pi$
$223$			8.28926e11i			1.50311i	−0.659669	+	0.751556i	$0.729304\pi$
$224$	3.78926e11	−	2.80862e11i	0.671916	−	0.498027i
$225$		0			0
$226$	−9.57139e10	−	7.46214e11i	−0.162343	−	1.26567i
$227$			5.67893e11i			0.942187i	0.882083	+	0.471093i	$0.156140\pi$
$227$			5.67893e11i			0.942187i	−0.882083	+	0.471093i	$0.843860\pi$
$228$	4.03107e11	−	1.05140e11i	0.654254	−	0.170645i
$229$	−6.29580e10			−0.0999708			−0.0499854	−	0.998750i	$-0.515917\pi$
$229$	−6.29580e10			−0.0999708			−0.0499854	+	0.998750i	$0.515917\pi$
$230$		0			0
$231$			4.62770e11i			0.703567i
$232$	1.96925e11	+	4.89185e11i	0.292995	+	0.727835i
$233$	3.90579e11			0.568760			0.284380	−	0.958712i	$-0.408212\pi$
$233$	3.90579e11			0.568760			0.284380	+	0.958712i	$0.408212\pi$
$234$	6.19858e10	+	4.83259e11i	0.0883513	+	0.688813i
$235$		0			0
$236$	1.43375e11	+	5.49703e11i	0.195846	+	0.750875i
$237$	5.86843e11			0.784838
$238$	−4.85111e11	+	6.22233e10i	−0.635267	+	0.0814832i
$239$		−	8.56345e11i		−	1.09814i	−0.835775	−	0.549072i	$-0.814981\pi$
$239$		−	8.56345e11i		−	1.09814i	0.835775	−	0.549072i	$-0.185019\pi$
$240$		0			0
$241$	−2.19603e11			−0.270117			−0.135059	−	0.990838i	$-0.543122\pi$
$241$	−2.19603e11			−0.270117			−0.135059	+	0.990838i	$0.543122\pi$
$242$	−1.65390e10	−	1.28943e11i	−0.0199265	−	0.155353i
$243$			6.14379e11i			0.725112i
$244$	−8.64735e11	+	2.25543e11i	−0.999848	+	0.260784i
$245$		0			0
$246$	−2.70833e11	+	3.47387e10i	−0.300626	+	0.0385601i
$247$			1.42177e12i			1.54648i
$248$	−1.17786e12	+	4.74158e11i	−1.25556	+	0.505434i
$249$	−3.59415e11			−0.375491
$250$		0			0
$251$		−	3.77174e11i		−	0.378593i	−0.981920	−	0.189297i	$-0.939379\pi$
$251$		−	3.77174e11i		−	0.378593i	0.981920	−	0.189297i	$-0.0606208\pi$
$252$	8.32677e10	+	3.19250e11i	0.0819358	+	0.314143i
$253$	−1.18710e12			−1.14521
$254$	−1.31594e12	+	1.68790e11i	−1.24471	+	0.159654i
$255$		0			0
$256$	5.74926e11	−	9.37223e11i	0.522892	−	0.852399i
$257$	−8.23925e11			−0.734889			−0.367445	−	0.930045i	$-0.619767\pi$
$257$	−8.23925e11			−0.734889			−0.367445	+	0.930045i	$0.619767\pi$
$258$	−6.70383e10	−	5.22650e11i	−0.0586441	−	0.457206i
$259$			1.82154e11i			0.156293i
$260$		0			0
$261$	−3.68870e11			−0.304558
$262$	4.40861e10	−	5.65476e9i	0.0357105	−	0.00458044i
$263$			1.08787e12i			0.864568i	0.901737	+	0.432284i	$0.142292\pi$
$263$			1.08787e12i			0.864568i	−0.901737	+	0.432284i	$0.857708\pi$
$264$	4.02852e11	+	1.00073e12i	0.314142	+	0.780366i
$265$		0			0
$266$	1.22488e11	+	9.54954e11i	0.0919784	+	0.717091i
$267$		−	1.65180e12i		−	1.21731i
$268$	3.95567e10	+	1.51661e11i	0.0286119	+	0.109698i
$269$	−1.57558e12			−1.11861			−0.559305	−	0.828962i	$-0.688932\pi$
$269$	−1.57558e12			−1.11861			−0.559305	+	0.828962i	$0.688932\pi$
$270$		0			0
$271$			7.48035e11i			0.511771i	0.966707	+	0.255885i	$0.0823670\pi$
$271$			7.48035e11i			0.511771i	−0.966707	+	0.255885i	$0.917633\pi$
$272$	−9.94877e11	+	5.56857e11i	−0.668228	+	0.374023i
$273$	1.77477e12			1.17038
$274$	−1.69204e11	−	1.31916e12i	−0.109561	−	0.854172i
$275$		0			0
$276$	1.29079e12	−	3.36669e11i	0.805957	−	0.210212i
$277$	1.35578e12			0.831360			0.415680	−	0.909511i	$-0.363544\pi$
$277$	1.35578e12			0.831360			0.415680	+	0.909511i	$0.363544\pi$
$278$	2.50761e12	−	3.21641e11i	1.51020	−	0.193708i
$279$		−	8.88169e11i		−	0.525381i
$280$		0			0
$281$	−6.65579e11			−0.379899			−0.189949	−	0.981794i	$-0.560832\pi$
$281$	−6.65579e11			−0.379899			−0.189949	+	0.981794i	$0.560832\pi$
$282$	−2.04392e11	−	1.59350e12i	−0.114609	−	0.893526i
$283$		−	3.17294e12i		−	1.74795i	−0.485968	−	0.873977i	$-0.661533\pi$
$283$		−	3.17294e12i		−	1.74795i	0.485968	−	0.873977i	$-0.338467\pi$
$284$	−8.48794e11	−	3.25429e12i	−0.459421	−	1.76142i
$285$		0			0
$286$	−3.65177e12	+	4.68398e11i	−1.90841	+	0.244785i
$287$		−	6.31043e11i		−	0.324078i
$288$	4.57979e11	+	6.17885e11i	0.231144	+	0.311850i
$289$	−8.33769e11			−0.413577
$290$		0			0
$291$		−	1.10046e12i		−	0.527361i
$292$	1.60116e12	−	4.17620e11i	0.754259	−	0.196728i
$293$	−3.22248e11			−0.149229			−0.0746144	−	0.997212i	$-0.523773\pi$
$293$	−3.22248e11			−0.149229			−0.0746144	+	0.997212i	$0.523773\pi$
$294$	−5.12095e11	+	6.56844e10i	−0.233138	+	0.0299037i
$295$		0			0
$296$	1.58569e11	+	3.93906e11i	0.0697848	+	0.173354i
$297$	−2.69859e12			−1.16776
$298$	1.37592e10	+	1.07271e11i	0.00585480	+	0.0456457i
$299$			4.55265e12i			1.90506i
$300$		0			0
$301$	1.21778e12			0.492874
$302$	−2.03281e12	+	2.60741e11i	−0.809212	+	0.103794i
$303$		−	2.04951e12i		−	0.802486i
$304$	1.09619e12	+	1.95844e12i	0.422199	+	0.754298i
$305$		0			0
$306$	−1.01463e11	−	7.91032e11i	−0.0378180	−	0.294840i
$307$		−	1.97279e12i		−	0.723418i	−0.932291	−	0.361709i	$-0.882193\pi$
$307$		−	1.97279e12i		−	0.723418i	0.932291	−	0.361709i	$-0.117807\pi$
$308$	−2.41242e12	+	6.29215e11i	−0.870361	+	0.227010i
$309$	−1.34166e12			−0.476268
$310$		0			0
$311$		−	5.13332e12i		−	1.76440i	−0.470879	−	0.882198i	$-0.656063\pi$
$311$		−	5.13332e12i		−	1.76440i	0.470879	−	0.882198i	$-0.343937\pi$
$312$	3.83791e12	−	1.54498e12i	1.29814	−	0.522575i
$313$	−2.38086e10			−0.00792523			−0.00396261	−	0.999992i	$-0.501261\pi$
$313$	−2.38086e10			−0.00792523			−0.00396261	+	0.999992i	$0.501261\pi$
$314$	−5.17427e10	−	4.03401e11i	−0.0169512	−	0.132157i
$315$		0			0
$316$	7.97913e11	+	3.05921e12i	0.253233	+	0.970899i
$317$	5.06007e12			1.58074			0.790370	−	0.612630i	$-0.209889\pi$
$317$	5.06007e12			1.58074			0.790370	+	0.612630i	$0.209889\pi$
$318$	−1.38263e12	+	1.77345e11i	−0.425178	+	0.0545360i
$319$		−	2.78738e12i		−	0.843805i
$320$		0			0
$321$	−3.44400e11			−0.101050
$322$	3.92221e11	+	3.05787e12i	0.113306	+	0.883364i
$323$		−	2.32724e12i		−	0.661956i
$324$	1.59322e12	−	4.15549e11i	0.446221	−	0.116385i
$325$		0			0
$326$	−5.44742e12	+	6.98720e11i	−1.47946	+	0.189764i
$327$		−	2.52850e12i		−	0.676276i
$328$	−5.49337e11	−	1.36462e12i	−0.144700	−	0.359453i
$329$	3.71287e12			0.963230
$330$		0			0
$331$			4.65034e12i			1.17043i	0.810879	+	0.585214i	$0.198990\pi$
$331$			4.65034e12i			1.17043i	−0.810879	+	0.585214i	$0.801010\pi$
$332$	−4.88687e11	−	1.87363e12i	−0.121155	−	0.464509i
$333$	−2.97025e11			−0.0725390
$334$	−4.04846e12	+	5.19280e11i	−0.973996	+	0.124931i
$335$		0			0
$336$	2.44469e12	−	1.36835e12i	0.570858	−	0.319523i
$337$	−2.23573e11			−0.0514362			−0.0257181	−	0.999669i	$-0.508187\pi$
$337$	−2.23573e11			−0.0514362			−0.0257181	+	0.999669i	$0.508187\pi$
$338$	1.23511e12	+	9.62926e12i	0.279976	+	2.18278i
$339$		−	4.46866e12i		−	0.998111i
$340$		0			0
$341$	6.71148e12			1.45561
$342$	−1.55717e12	+	1.99732e11i	−0.332816	+	0.0426891i
$343$		−	5.16386e12i		−	1.08769i
$344$	2.63342e12	−	1.06010e12i	0.546674	−	0.220067i
$345$		0			0
$346$	−7.63031e11	−	5.94881e12i	−0.153873	−	1.19964i
$347$			3.16769e12i			0.629644i	0.949151	+	0.314822i	$0.101945\pi$
$347$			3.16769e12i			0.629644i	−0.949151	+	0.314822i	$0.898055\pi$
$348$	7.90517e11	+	3.03085e12i	0.154887	+	0.593839i
$349$	8.37634e12			1.61781			0.808904	−	0.587941i	$-0.200061\pi$
$349$	8.37634e12			1.61781			0.808904	+	0.587941i	$0.200061\pi$
$350$		0			0
$351$			1.03494e13i			1.94257i
$352$	−4.66907e12	+	3.46073e12i	−0.864007	+	0.640405i
$353$	2.56251e12			0.467512			0.233756	−	0.972295i	$-0.424898\pi$
$353$	2.56251e12			0.467512			0.233756	+	0.972295i	$0.424898\pi$
$354$	4.29298e11	+	3.34693e12i	0.0772222	+	0.602047i
$355$		0			0
$356$	8.61082e12	−	2.24590e12i	1.50589	−	0.392772i
$357$	−2.90506e12			−0.500973
$358$	−4.24696e12	+	5.44741e11i	−0.722209	+	0.0926349i
$359$			9.99628e12i			1.67636i	0.545397	+	0.838178i	$0.316379\pi$
$359$			9.99628e12i			1.67636i	−0.545397	+	0.838178i	$0.683621\pi$
$360$		0			0
$361$	1.54983e12			0.252783
$362$	1.42899e12	+	1.11408e13i	0.229872	+	1.79215i
$363$		−	7.72167e11i		−	0.122512i
$364$	2.41310e12	+	9.25187e12i	0.377632	+	1.44785i
$365$		0			0
$366$	−5.26504e12	+	6.75327e11i	−0.801672	+	0.102827i
$367$		−	2.30492e12i		−	0.346199i	−0.984904	−	0.173099i	$-0.944622\pi$
$367$		−	2.30492e12i		−	0.346199i	0.984904	−	0.173099i	$-0.0553782\pi$
$368$	3.51011e12	+	6.27115e12i	0.520094	+	0.929198i
$369$	1.02899e12			0.150411
$370$		0			0
$371$		−	3.22154e12i		−	0.458347i
$372$	−7.29773e12	+	1.90342e12i	−1.02441	+	0.267189i
$373$	−5.12634e11			−0.0710008			−0.0355004	−	0.999370i	$-0.511303\pi$
$373$	−5.12634e11			−0.0710008			−0.0355004	+	0.999370i	$0.511303\pi$
$374$	5.97746e12	−	7.66705e11i	0.816880	−	0.104778i
$375$		0			0
$376$	8.02902e12	−	3.23214e12i	1.06837	−	0.430081i
$377$	−1.06899e13			−1.40367
$378$	8.91620e11	+	6.95133e12i	0.115537	+	0.900759i
$379$		−	1.30188e13i		−	1.66485i	−0.554141	−	0.832423i	$-0.686953\pi$
$379$		−	1.30188e13i		−	1.66485i	0.554141	−	0.832423i	$-0.313047\pi$
$380$		0			0
$381$	−7.88043e12			−0.981578
$382$	1.06464e13	−	1.36557e12i	1.30883	−	0.167879i
$383$		−	7.62061e10i		−	0.00924689i	−0.999989	−	0.00462345i	$-0.998528\pi$
$383$		−	7.62061e10i		−	0.00924689i	0.999989	−	0.00462345i	$-0.00147169\pi$
$384$	4.09543e12	−	5.08720e12i	0.490505	−	0.609289i
$385$		0			0
$386$	1.80057e12	+	1.40378e13i	0.210123	+	1.63818i
$387$			1.98573e12i			0.228753i
$388$	5.73668e12	−	1.49626e12i	0.652382	−	0.170156i
$389$	5.68167e12			0.637863			0.318932	−	0.947778i	$-0.396676\pi$
$389$	5.68167e12			0.637863			0.318932	+	0.947778i	$0.396676\pi$
$390$		0			0
$391$		−	7.45209e12i		−	0.815444i
$392$	−1.03869e12	−	2.58024e12i	−0.112217	−	0.278760i
$393$	2.64008e11			0.0281614
$394$	2.60154e11	+	2.02823e12i	0.0273999	+	0.213618i
$395$		0			0
$396$	−1.02601e12	−	3.93374e12i	−0.105360	−	0.403952i
$397$	1.23091e13			1.24818			0.624088	−	0.781354i	$-0.285471\pi$
$397$	1.23091e13			1.24818			0.624088	+	0.781354i	$0.285471\pi$
$398$	−9.37346e12	+	1.20230e12i	−0.938609	+	0.120392i
$399$			5.71869e12i			0.565499i
$400$		0			0
$401$	3.21421e11			0.0309993			0.0154997	−	0.999880i	$-0.495066\pi$
$401$	3.21421e11			0.0309993			0.0154997	+	0.999880i	$0.495066\pi$
$402$	1.18442e11	+	9.23405e11i	0.0112817	+	0.0879553i
$403$		−	2.57392e13i		−	2.42142i
$404$	1.06841e13	−	2.78666e12i	0.992731	−	0.258927i
$405$		0			0
$406$	−7.18004e12	+	9.20955e11i	−0.650873	+	0.0834850i
$407$		−	2.24448e12i		−	0.200976i
$408$	−6.28214e12	+	2.52892e12i	−0.555657	+	0.223684i
$409$	−1.03801e13			−0.906952			−0.453476	−	0.891268i	$-0.649816\pi$
$409$	−1.03801e13			−0.906952			−0.453476	+	0.891268i	$0.649816\pi$
$410$		0			0
$411$		−	7.89974e12i		−	0.673602i
$412$	−1.82422e12	−	6.99409e12i	−0.153671	−	0.589176i
$413$	−7.79837e12			−0.649013
$414$	−4.98622e12	+	6.39563e11i	−0.409987	+	0.0525874i
$415$		0			0
$416$	1.32723e13	+	1.79063e13i	1.06531	+	1.43728i
$417$	1.50167e13			1.19095
$418$	−1.50928e12	−	1.17668e13i	−0.118274	−	0.922097i
$419$			1.57632e13i			1.22061i	0.792168	+	0.610303i	$0.208952\pi$
$419$			1.57632e13i			1.22061i	−0.792168	+	0.610303i	$0.791048\pi$
$420$		0			0
$421$	−1.50088e13			−1.13484			−0.567421	−	0.823428i	$-0.692059\pi$
$421$	−1.50088e13			−1.13484			−0.567421	+	0.823428i	$0.692059\pi$
$422$	−4.78159e12	+	6.13316e11i	−0.357281	+	0.0458271i
$423$			6.05428e12i			0.447055i
$424$	−2.80443e12	−	6.96653e12i	−0.204651	−	0.508379i
$425$		0			0
$426$	−2.54148e12	−	1.98141e13i	−0.181150	−	1.41230i
$427$		−	1.22676e13i		−	0.864211i
$428$	−4.68271e11	−	1.79536e12i	−0.0326046	−	0.125006i
$429$	−2.18684e13			−1.50498
$430$		0			0
$431$		−	5.91866e11i		−	0.0397958i	−0.999802	−	0.0198979i	$-0.993666\pi$
$431$		−	5.91866e11i		−	0.0397958i	0.999802	−	0.0198979i	$-0.00633411\pi$
$432$	7.97940e12	+	1.42560e13i	0.530336	+	0.947496i
$433$	2.30044e13			1.51137			0.755687	−	0.654933i	$-0.227303\pi$
$433$	2.30044e13			1.51137			0.755687	+	0.654933i	$0.227303\pi$
$434$	−2.21749e12	−	1.72882e13i	−0.144017	−	1.12280i
$435$		0			0
$436$	1.31811e13	−	3.43793e12i	0.836600	−	0.218205i
$437$	−1.46696e13			−0.920475
$438$	9.74886e12	−	1.25045e12i	0.604760	−	0.0775702i
$439$			4.54425e12i			0.278701i	0.990243	+	0.139351i	$0.0445015\pi$
$439$			4.54425e12i			0.278701i	−0.990243	+	0.139351i	$0.955498\pi$
$440$		0			0
$441$	1.94563e12			0.116645
$442$	−2.94039e12	−	2.29241e13i	−0.174298	−	1.35888i
$443$			2.40350e12i			0.140872i	0.997516	+	0.0704362i	$0.0224391\pi$
$443$			2.40350e12i			0.140872i	−0.997516	+	0.0704362i	$0.977561\pi$
$444$	6.36548e11	+	2.44053e12i	0.0368906	+	0.141439i
$445$		0			0
$446$	−2.63101e13	+	3.37469e12i	−1.49090	+	0.191232i
$447$			6.42385e11i			0.0359963i
$448$	1.04572e13	+	1.08837e13i	0.579463	+	0.603095i
$449$	2.55386e13			1.39947			0.699737	−	0.714401i	$-0.253301\pi$
$449$	2.55386e13			1.39947			0.699737	+	0.714401i	$0.253301\pi$
$450$		0			0
$451$			7.77561e12i			0.416727i
$452$	2.32951e13	−	6.07591e12i	1.23473	−	0.322047i
$453$	−1.21734e13			−0.638146
$454$	−1.80249e13	+	2.31198e12i	−0.934530	+	0.119869i
$455$		0			0
$456$	4.97825e12	+	1.23666e13i	0.252495	+	0.627228i
$457$	−1.43833e13			−0.721569			−0.360785	−	0.932649i	$-0.617491\pi$
$457$	−1.43833e13			−0.721569			−0.360785	+	0.932649i	$0.617491\pi$
$458$	−2.56312e11	−	1.99828e12i	−0.0127187	−	0.0991585i
$459$		−	1.69405e13i		−	0.831502i
$460$		0			0
$461$	3.07398e13			1.47638			0.738188	−	0.674595i	$-0.235682\pi$
$461$	3.07398e13			1.47638			0.738188	+	0.674595i	$0.235682\pi$
$462$	−1.46883e13	+	1.88401e12i	−0.697849	+	0.0895104i
$463$			1.66750e13i			0.783718i	0.920025	+	0.391859i	$0.128168\pi$
$463$			1.66750e13i			0.783718i	−0.920025	+	0.391859i	$0.871832\pi$
$464$	−1.47250e13	+	8.24193e12i	−0.684645	+	0.383212i
$465$		0			0
$466$	1.59011e12	+	1.23970e13i	0.0723598	+	0.564138i
$467$		−	6.59007e12i		−	0.296692i	−0.988936	−	0.148346i	$-0.952605\pi$
$467$		−	6.59007e12i		−	0.296692i	0.988936	−	0.148346i	$-0.0473949\pi$
$468$	−1.50863e13	+	3.93485e12i	−0.671975	+	0.175267i
$469$	−2.15154e12			−0.0948168
$470$		0			0
$471$		−	2.41575e12i		−	0.104219i
$472$	−1.68638e13	+	6.78865e12i	−0.719857	+	0.289784i
$473$	−1.50053e13			−0.633779
$474$	2.38913e12	+	1.86264e13i	0.0998500	+	0.778460i
$475$		0			0
$476$	−3.94993e12	−	1.51441e13i	−0.161642	−	0.619738i
$477$	5.25311e12			0.212728
$478$	2.71804e13	−	3.48632e12i	1.08922	−	0.139710i
$479$		−	3.32507e13i		−	1.31863i	−0.751867	−	0.659315i	$-0.770846\pi$
$479$		−	3.32507e13i		−	1.31863i	0.751867	−	0.659315i	$-0.229154\pi$
$480$		0			0
$481$	−8.60779e12			−0.334323
$482$	−8.94037e11	−	6.97018e12i	−0.0343653	−	0.267922i
$483$			1.83119e13i			0.696622i
$484$	4.02531e12	−	1.04989e12i	0.151556	−	0.0395293i
$485$		0			0
$486$	−1.95004e13	+	2.50124e12i	−0.719220	+	0.0922515i
$487$			3.49858e12i			0.127717i	0.997959	+	0.0638583i	$0.0203406\pi$
$487$			3.49858e12i			0.127717i	−0.997959	+	0.0638583i	$0.979659\pi$
$488$	−1.06792e13	−	2.65285e13i	−0.385869	−	0.958546i
$489$	−3.26216e13			−1.16670
$490$		0			0
$491$			1.49892e13i			0.525254i	0.964897	+	0.262627i	$0.0845889\pi$
$491$			1.49892e13i			0.525254i	−0.964897	+	0.262627i	$0.915411\pi$
$492$	−2.20521e12	−	8.45481e12i	−0.0764935	−	0.293277i
$493$	1.74979e13			0.600829
$494$	−4.51268e13	+	5.78824e12i	−1.53391	+	0.196749i
$495$		0			0
$496$	−1.98450e13	−	3.54550e13i	−0.661064	−	1.18105i
$497$	4.61670e13			1.52247
$498$	−1.46324e12	−	1.14078e13i	−0.0477714	−	0.372440i
$499$			2.01950e13i			0.652741i	0.945242	+	0.326370i	$0.105826\pi$
$499$			2.01950e13i			0.652741i	−0.945242	+	0.326370i	$0.894174\pi$
$500$		0			0
$501$	−2.42440e13			−0.768096
$502$	1.19715e13	−	1.53553e12i	0.375517	−	0.0481661i
$503$			3.87916e13i			1.20475i	0.798213	+	0.602376i	$0.205779\pi$
$503$			3.87916e13i			1.20475i	−0.798213	+	0.602376i	$0.794221\pi$
$504$	−9.79397e12	+	3.94263e12i	−0.301166	+	0.121237i
$505$		0			0
$506$	−4.83288e12	−	3.76786e13i	−0.145698	−	1.13590i
$507$			5.76643e13i			1.72134i
$508$	−1.07148e13	−	4.10807e13i	−0.316713	−	1.21428i
$509$	−2.53824e13			−0.742923			−0.371462	−	0.928448i	$-0.621143\pi$
$509$	−2.53824e13			−0.742923			−0.371462	+	0.928448i	$0.621143\pi$
$510$		0			0
$511$			2.27149e13i			0.651938i
$512$	3.20880e13	+	1.44325e13i	0.911997	+	0.410197i
$513$	−3.33479e13			−0.938602
$514$	−3.35433e12	−	2.61513e13i	−0.0934954	−	0.728917i
$515$		0			0
$516$	1.63160e13	−	4.25558e12i	0.446030	−	0.116335i
$517$	−4.57494e13			−1.23860
$518$	−5.78158e12	+	7.41580e11i	−0.155023	+	0.0198843i
$519$		−	3.56242e13i		−	0.946036i
$520$		0			0
$521$	9.37998e12			0.244351			0.122175	−	0.992509i	$-0.461013\pi$
$521$	9.37998e12			0.244351			0.122175	+	0.992509i	$0.461013\pi$
$522$	−1.50173e12	−	1.17079e13i	−0.0387471	−	0.302084i
$523$			1.03783e13i			0.265227i	0.991168	+	0.132614i	$0.0423370\pi$
$523$			1.03783e13i			0.265227i	−0.991168	+	0.132614i	$0.957663\pi$
$524$	3.58964e11	+	1.37627e12i	0.00908645	+	0.0348376i
$525$		0			0
$526$	−3.45290e13	+	4.42890e12i	−0.857543	+	0.109994i
$527$			4.21316e13i			1.03647i
$528$	−3.01231e13	+	1.68606e13i	−0.734058	+	0.410870i
$529$	−5.54730e12			−0.133907
$530$		0			0
$531$		−	1.27162e13i		−	0.301220i
$532$	−2.98115e13	+	7.77554e12i	−0.699562	+	0.182462i
$533$	2.98202e13			0.693226
$534$	5.24280e13	−	6.72473e12i	1.20742	−	0.154871i
$535$		0			0
$536$	−4.65267e12	+	1.87296e12i	−0.105167	+	0.0423356i
$537$	−2.54327e13			−0.569536
$538$	−6.41444e12	−	5.00089e13i	−0.142314	−	1.10952i
$539$			1.47022e13i			0.323176i
$540$		0			0
$541$	−1.08616e13			−0.234373			−0.117187	−	0.993110i	$-0.537388\pi$
$541$	−1.08616e13			−0.234373			−0.117187	+	0.993110i	$0.537388\pi$
$542$	−2.37426e13	+	3.04537e12i	−0.507612	+	0.0651094i
$543$			6.67163e13i			1.41329i
$544$	−2.17249e13	−	2.93103e13i	−0.455999	−	0.615214i
$545$		0			0
$546$	7.22537e12	+	5.63311e13i	0.148901	+	1.16087i
$547$		−	3.51242e13i		−	0.717248i	−0.933482	−	0.358624i	$-0.883246\pi$
$547$		−	3.51242e13i		−	0.717248i	0.933482	−	0.358624i	$-0.116754\pi$
$548$	4.11813e13	−	1.07410e13i	0.833293	−	0.217342i
$549$	2.00038e13			0.401098
$550$		0			0
$551$		−	3.44451e13i		−	0.678218i
$552$	1.59409e13	+	3.95991e13i	0.311041	+	0.772664i
$553$	−4.33996e13			−0.839189
$554$	5.51959e12	+	4.30323e13i	0.105769	+	0.824605i
$555$		0			0
$556$	2.04178e13	+	7.82819e13i	0.384268	+	1.47329i
$557$	−1.87712e13			−0.350120			−0.175060	−	0.984558i	$-0.556012\pi$
$557$	−1.87712e13			−0.350120			−0.175060	+	0.984558i	$0.556012\pi$
$558$	2.81905e13	−	3.61588e12i	0.521112	−	0.0668410i
$559$			5.75467e13i			1.05429i
$560$		0			0
$561$	3.57957e13			0.644194
$562$	−2.70968e12	−	2.11255e13i	−0.0483322	−	0.376812i
$563$		−	7.50975e12i		−	0.132765i	−0.997794	−	0.0663825i	$-0.978854\pi$
$563$		−	7.50975e12i		−	0.132765i	0.997794	−	0.0663825i	$-0.0211457\pi$
$564$	4.97456e13	−	1.29748e13i	0.871684	−	0.227355i
$565$		0			0
$566$	1.00709e14	−	1.29176e13i	1.73375	−	0.222381i
$567$			2.26022e13i			0.385688i
$568$	9.98354e13	−	4.01894e13i	1.68866	−	0.679783i
$569$	5.40193e13			0.905707			0.452853	−	0.891585i	$-0.350406\pi$
$569$	5.40193e13			0.905707			0.452853	+	0.891585i	$0.350406\pi$
$570$		0			0
$571$		−	7.48542e13i		−	1.23321i	−0.787274	−	0.616603i	$-0.788508\pi$
$571$		−	7.48542e13i		−	1.23321i	0.787274	−	0.616603i	$-0.211492\pi$
$572$	−2.97339e13	−	1.14000e14i	−0.485592	−	1.86176i
$573$	6.37552e13			1.03215
$574$	2.00293e13	−	2.56908e12i	0.321445	−	0.0412304i
$575$		0			0
$576$	−1.77472e13	+	1.70517e13i	−0.279909	+	0.268941i
$577$	7.48813e13			1.17083			0.585416	−	0.810733i	$-0.300931\pi$
$577$	7.48813e13			1.17083			0.585416	+	0.810733i	$0.300931\pi$
$578$	−3.39441e12	−	2.64638e13i	−0.0526169	−	0.410217i
$579$			8.40644e13i			1.29187i
$580$		0			0
$581$	2.65803e13			0.401495
$582$	3.49285e13	−	4.48014e12i	0.523076	−	0.0670929i
$583$			3.96953e13i			0.589382i
$584$	1.97738e13	+	4.91206e13i	0.291090	+	0.723102i
$585$		0			0
$586$	−1.31193e12	−	1.02282e13i	−0.0189855	−	0.148016i
$587$		−	4.76751e13i		−	0.684071i	−0.939687	−	0.342035i	$-0.888884\pi$
$587$		−	4.76751e13i		−	0.684071i	0.939687	−	0.342035i	$-0.111116\pi$
$588$	−4.16964e12	−	1.59865e13i	−0.0593215	−	0.227439i
$589$	8.29373e13			1.16997
$590$		0			0
$591$			1.21460e13i			0.168459i
$592$	−1.18570e13	+	6.63665e12i	−0.163067	+	0.0912725i
$593$	−8.03970e13			−1.09639			−0.548197	−	0.836349i	$-0.684686\pi$
$593$	−8.03970e13			−1.09639			−0.548197	+	0.836349i	$0.684686\pi$
$594$	−1.09864e13	−	8.56531e13i	−0.148567	−	1.15827i
$595$		0			0
$596$	−3.34875e12	+	8.73433e11i	−0.0445299	+	0.0116144i
$597$	−5.61325e13			−0.740189
$598$	−1.44501e14	+	1.85346e13i	−1.88958	+	0.242369i
$599$		−	5.37083e13i		−	0.696477i	−0.937406	−	0.348239i	$-0.886780\pi$
$599$		−	5.37083e13i		−	0.696477i	0.937406	−	0.348239i	$-0.113220\pi$
$600$		0			0
$601$	−3.12372e13			−0.398382			−0.199191	−	0.979961i	$-0.563831\pi$
$601$	−3.12372e13			−0.398382			−0.199191	+	0.979961i	$0.563831\pi$
$602$	4.95777e12	+	3.86522e13i	0.0627053	+	0.488869i
$603$		−	3.50835e12i		−	0.0440064i
$604$	−1.65518e13	−	6.34598e13i	−0.205902	−	0.789431i
$605$		0			0
$606$	6.50515e13	−	8.34390e12i	0.795965	−	0.102095i
$607$			7.33861e13i			0.890574i	0.895388	+	0.445287i	$0.146898\pi$
$607$			7.33861e13i			0.890574i	−0.895388	+	0.445287i	$0.853102\pi$
$608$	−5.76982e13	+	4.27661e13i	−0.694455	+	0.514733i
$609$	−4.29973e13			−0.513280
$610$		0			0
$611$			1.75453e14i			2.06042i
$612$	2.46942e13	−	6.44084e12i	0.287633	−	0.0750214i
$613$	4.41534e13			0.510108			0.255054	−	0.966927i	$-0.417907\pi$
$613$	4.41534e13			0.510108			0.255054	+	0.966927i	$0.417907\pi$
$614$	6.26164e13	−	8.03156e12i	0.717540	−	0.0920360i
$615$		0			0
$616$	−2.97926e13	−	7.40085e13i	−0.335896	−	0.834407i
$617$	5.60294e13			0.626600			0.313300	−	0.949654i	$-0.398566\pi$
$617$	5.60294e13			0.626600			0.313300	+	0.949654i	$0.398566\pi$
$618$	−5.46213e12	−	4.25844e13i	−0.0605926	−	0.472398i
$619$		−	7.65763e13i		−	0.842638i	−0.906913	−	0.421319i	$-0.861567\pi$
$619$		−	7.65763e13i		−	0.842638i	0.906913	−	0.421319i	$-0.138433\pi$
$620$		0			0
$621$	−1.06784e14			−1.15624
$622$	1.62931e14	−	2.08986e13i	1.75006	−	0.224473i
$623$			1.22158e14i			1.30161i
$624$	6.46622e13	+	1.15525e14i	0.683483	+	1.22111i
$625$		0			0
$626$	−9.69285e10	−	7.55683e11i	−0.00100828	−	0.00786083i
$627$		−	7.04648e13i		−	0.727167i
$628$	1.25933e13	−	3.28462e12i	0.128926	−	0.0336269i
$629$	1.40898e13			0.143104
$630$		0			0
$631$		−	4.84894e13i		−	0.484731i	−0.970185	−	0.242365i	$-0.922077\pi$
$631$		−	4.84894e13i		−	0.484731i	0.970185	−	0.242365i	$-0.0779232\pi$
$632$	−9.38508e13	+	3.77803e13i	−0.930792	+	0.374697i
$633$	−2.86343e13			−0.281753
$634$	2.06004e13	+	1.60606e14i	0.201108	+	1.56789i
$635$		0			0
$636$	−1.12578e13	−	4.31627e13i	−0.108186	−	0.414785i
$637$	5.63845e13			0.537604
$638$	8.84712e13	−	1.13479e13i	0.836948	−	0.107352i
$639$			7.52809e13i			0.706611i
$640$		0			0
$641$	1.29283e13			0.119468			0.0597338	−	0.998214i	$-0.480975\pi$
$641$	1.29283e13			0.119468			0.0597338	+	0.998214i	$0.480975\pi$
$642$	−1.40211e12	−	1.09312e13i	−0.0128560	−	0.100229i
$643$		−	1.48437e14i		−	1.35048i	−0.737600	−	0.675238i	$-0.764041\pi$
$643$		−	1.48437e14i		−	1.35048i	0.737600	−	0.675238i	$-0.235959\pi$
$644$	−9.54599e13	+	2.48982e13i	−0.861770	+	0.224770i
$645$		0			0
$646$	7.38666e13	−	9.47458e12i	0.656576	−	0.0842165i
$647$		−	8.95550e12i		−	0.0789894i	−0.999220	−	0.0394947i	$-0.987425\pi$
$647$		−	8.95550e12i		−	0.0789894i	0.999220	−	0.0394947i	$-0.0125748\pi$
$648$	1.96757e13	+	4.88769e13i	0.172209	+	0.427788i
$649$	9.60902e13			0.834557
$650$		0			0
$651$		−	1.03529e14i		−	0.885439i
$652$	−4.43547e13	−	1.70056e14i	−0.376445	−	1.44329i
$653$	7.28446e13			0.613524			0.306762	−	0.951786i	$-0.400754\pi$
$653$	7.28446e13			0.613524			0.306762	+	0.951786i	$0.400754\pi$
$654$	8.02545e13	−	1.02939e13i	0.670781	−	0.0860384i
$655$		0			0
$656$	4.10766e13	−	2.29915e13i	0.338123	−	0.189256i
$657$	−3.70394e13			−0.302578
$658$	1.51157e13	+	1.17846e14i	0.122546	+	0.955403i
$659$		−	2.12839e14i		−	1.71247i	−0.516584	−	0.856237i	$-0.672797\pi$
$659$		−	2.12839e14i		−	1.71247i	0.516584	−	0.856237i	$-0.327203\pi$
$660$		0			0
$661$	1.49053e14			1.18123			0.590613	−	0.806955i	$-0.298886\pi$
$661$	1.49053e14			1.18123			0.590613	+	0.806955i	$0.298886\pi$
$662$	−1.47602e14	+	1.89323e13i	−1.16092	+	0.148906i
$663$		−	1.37280e14i		−	1.07162i
$664$	5.74795e13	−	2.31388e13i	0.445321	−	0.179267i
$665$		0			0
$666$	−1.20924e12	−	9.42756e12i	−0.00922869	−	0.0719495i
$667$		−	1.10297e14i		−	0.835477i
$668$	−3.29639e13	−	1.26384e14i	−0.247831	−	0.950187i
$669$	−1.57557e14			−1.17573
$670$		0			0
$671$			1.51159e14i			1.11128i
$672$	5.33843e13	+	7.20237e13i	0.389553	+	0.525569i
$673$	−9.10177e13			−0.659251			−0.329625	−	0.944112i	$-0.606922\pi$
$673$	−9.10177e13			−0.659251			−0.329625	+	0.944112i	$0.606922\pi$
$674$	−9.10200e11	−	7.09618e12i	−0.00654391	−	0.0510182i
$675$		0			0
$676$	−3.00604e14	+	7.84045e13i	−2.12942	+	0.555402i
$677$	−1.25381e14			−0.881636			−0.440818	−	0.897596i	$-0.645312\pi$
$677$	−1.25381e14			−0.881636			−0.440818	+	0.897596i	$0.645312\pi$
$678$	1.41835e14	−	1.81926e13i	0.990001	−	0.126984i
$679$			8.13835e13i			0.563881i
$680$		0			0
$681$	−1.07941e14			−0.736973
$682$	2.73235e13	+	2.13022e14i	0.185189	+	1.44379i
$683$		−	1.14583e14i		−	0.770931i	−0.922722	−	0.385465i	$-0.874041\pi$
$683$		−	1.14583e14i		−	0.770931i	0.922722	−	0.385465i	$-0.125959\pi$
$684$	−1.26790e13	−	4.86113e13i	−0.0846843	−	0.324681i
$685$		0			0
$686$	1.63901e14	−	2.10229e13i	1.07885	−	0.138380i
$687$		−	1.19666e13i		−	0.0781966i
$688$	4.43687e13	+	7.92689e13i	0.287829	+	0.514234i
$689$	1.52236e14			0.980437
$690$		0			0
$691$			3.74076e13i			0.237449i	0.992927	+	0.118724i	$0.0378805\pi$
$691$			3.74076e13i			0.237449i	−0.992927	+	0.118724i	$0.962119\pi$
$692$	1.85709e14	−	4.84372e13i	1.17031	−	0.305245i
$693$	5.58061e13			0.349153
$694$	−1.00542e14	+	1.28962e13i	−0.624528	+	0.0801057i
$695$		0			0
$696$	−9.29809e13	+	3.74301e13i	−0.569308	+	0.229179i
$697$	−4.88118e13			−0.296729
$698$	3.41014e13	+	2.65865e14i	0.205824	+	1.60466i
$699$			7.42385e13i			0.444881i
$700$		0			0
$701$	2.22503e14			1.31446			0.657229	−	0.753691i	$-0.271729\pi$
$701$	2.22503e14			1.31446			0.657229	+	0.753691i	$0.271729\pi$
$702$	−3.28488e14	+	4.21339e13i	−1.92679	+	0.247142i
$703$		−	2.77362e13i		−	0.161536i
$704$	−1.28852e14	−	1.34107e14i	−0.745123	−	0.775511i
$705$		0			0
$706$	1.04324e13	+	8.13341e13i	0.0594786	+	0.463713i
$707$			1.51570e14i			0.858059i
$708$	−1.04484e14	+	2.72518e13i	−0.587330	+	0.153189i
$709$	−9.78657e13			−0.546260			−0.273130	−	0.961977i	$-0.588059\pi$
$709$	−9.78657e13			−0.546260			−0.273130	+	0.961977i	$0.588059\pi$
$710$		0			0
$711$		−	7.07682e13i		−	0.389485i
$712$	1.06341e14	+	2.64164e14i	0.581166	+	1.44369i
$713$	2.65574e14			1.44125
$714$	−1.18270e13	−	9.22065e13i	−0.0637357	−	0.496902i
$715$		0			0
$716$	−3.45801e13	−	1.32581e14i	−0.183764	−	0.704555i
$717$	1.62768e14			0.858961
$718$	−3.17282e14	+	4.06965e13i	−1.66273	+	0.213272i
$719$			1.39680e14i			0.726926i	0.931609	+	0.363463i	$0.118406\pi$
$719$			1.39680e14i			0.726926i	−0.931609	+	0.363463i	$0.881594\pi$
$720$		0			0
$721$	9.92219e13			0.509250
$722$	6.30960e12	+	4.91915e13i	0.0321600	+	0.250729i
$723$		−	4.17405e13i		−	0.211284i
$724$	−3.47792e14	+	9.07122e13i	−1.74834	+	0.456009i
$725$		0			0
$726$	2.45086e13	−	3.14362e12i	0.121516	−	0.0155864i
$727$			3.31152e13i			0.163063i	0.996671	+	0.0815315i	$0.0259811\pi$
$727$			3.31152e13i			0.163063i	−0.996671	+	0.0815315i	$0.974019\pi$
$728$	−2.83830e14	+	1.14258e14i	−1.38804	+	0.558764i
$729$	−2.11724e14			−1.02833
$730$		0			0
$731$		−	9.41962e13i		−	0.451281i
$732$	−4.28697e13	−	1.64363e14i	−0.203983	−	0.782075i
$733$	−3.51027e14			−1.65890			−0.829451	−	0.558580i	$-0.811347\pi$
$733$	−3.51027e14			−1.65890			−0.829451	+	0.558580i	$0.811347\pi$
$734$	7.31581e13	−	9.38370e12i	0.343386	−	0.0440447i
$735$		0			0
$736$	−1.84756e14	+	1.36942e14i	−0.855479	+	0.634084i
$737$	2.65109e13			0.121924
$738$	4.18919e12	+	3.26602e13i	0.0191359	+	0.149189i
$739$			6.54869e13i			0.297120i	0.988903	+	0.148560i	$0.0474639\pi$
$739$			6.54869e13i			0.297120i	−0.988903	+	0.148560i	$0.952536\pi$
$740$		0			0
$741$	−2.70239e14			−1.20964
$742$	1.02252e14	−	1.31154e13i	0.454622	−	0.0583126i
$743$		−	3.94592e14i		−	1.74262i	−0.490729	−	0.871312i	$-0.663269\pi$
$743$		−	3.94592e14i		−	1.74262i	0.490729	−	0.871312i	$-0.336731\pi$
$744$	−9.01246e13	−	2.23880e14i	−0.395347	−	0.982091i
$745$		0			0
$746$	−2.08702e12	−	1.62710e13i	−0.00903300	−	0.0704239i
$747$			4.33424e13i			0.186342i
$748$	4.86704e13	+	1.86603e14i	0.207853	+	0.796912i
$749$	2.54699e13			0.108048
$750$		0			0
$751$		−	2.64643e14i		−	1.10780i	−0.832584	−	0.553899i	$-0.813140\pi$
$751$		−	2.64643e14i		−	1.10780i	0.832584	−	0.553899i	$-0.186860\pi$
$752$	1.35275e14	+	2.41682e14i	0.562509	+	1.00498i
$753$	7.16906e13			0.296133
$754$	−4.35202e13	−	3.39296e14i	−0.178580	−	1.39227i
$755$		0			0
$756$	−2.17005e14	+	5.66000e13i	−0.878741	+	0.229196i
$757$	2.99343e13			0.120418			0.0602089	−	0.998186i	$-0.480823\pi$
$757$	2.99343e13			0.120418			0.0602089	+	0.998186i	$0.480823\pi$
$758$	4.13215e14	−	5.30015e13i	1.65132	−	0.211808i
$759$		−	2.25636e14i		−	0.895777i
$760$		0			0
$761$	1.89021e14			0.740605			0.370302	−	0.928911i	$-0.379254\pi$
$761$	1.89021e14			0.740605			0.370302	+	0.928911i	$0.379254\pi$
$762$	−3.20825e13	−	2.50125e14i	−0.124880	−	0.973602i
$763$			1.86993e14i			0.723109i
$764$	8.66861e13	+	3.32356e14i	0.333030	+	1.27684i
$765$		0			0
$766$	2.41878e12	−	3.10247e11i	0.00917176	−	0.00117643i
$767$		−	3.68516e14i		−	1.38829i
$768$	1.78141e14	+	1.09278e14i	0.666741	+	0.409003i
$769$	−1.99563e14			−0.742076			−0.371038	−	0.928618i	$-0.620998\pi$
$769$	−1.99563e14			−0.742076			−0.371038	+	0.928618i	$0.620998\pi$
$770$		0			0
$771$		−	1.56606e14i		−	0.574826i
$772$	−4.38228e14	+	1.14300e14i	−1.59813	+	0.416831i
$773$	−1.95460e14			−0.708208			−0.354104	−	0.935206i	$-0.615214\pi$
$773$	−1.95460e14			−0.708208			−0.354104	+	0.935206i	$0.615214\pi$
$774$	−6.30271e13	+	8.08424e12i	−0.226894	+	0.0291028i
$775$		0			0
$776$	7.08462e13	+	1.75990e14i	0.251772	+	0.625433i
$777$	−3.46227e13			−0.122252
$778$	2.31310e13	+	1.80336e14i	0.0811514	+	0.632680i
$779$			9.60873e13i			0.334949i
$780$		0			0
$781$	−5.68862e14			−1.95773
$782$	2.36529e14	−	3.03387e13i	0.808818	−	0.103744i
$783$		−	2.50734e14i		−	0.851929i
$784$	7.76681e13	−	4.34727e13i	0.262218	−	0.146770i
$785$		0			0
$786$	1.07482e12	+	8.37959e12i	0.00358280	+	0.0279325i
$787$		−	1.04188e14i		−	0.345100i	−0.985001	−	0.172550i	$-0.944799\pi$
$787$		−	1.04188e14i		−	0.345100i	0.985001	−	0.172550i	$-0.0552007\pi$
$788$	−6.33169e13	+	1.65145e13i	−0.208396	+	0.0543545i
$789$	−2.06775e14			−0.676260
$790$		0			0
$791$			3.30477e14i			1.06723i
$792$	1.20680e14	−	4.85805e13i	0.387265	−	0.155896i
$793$	5.79711e14			1.84861
$794$	5.01125e13	+	3.90692e14i	0.158798	+	1.23803i
$795$		0			0
$796$	−7.63217e13	−	2.92619e14i	−0.238827	−	0.915665i
$797$	−1.43104e14			−0.445000			−0.222500	−	0.974933i	$-0.571422\pi$
$797$	−1.43104e14			−0.445000			−0.222500	+	0.974933i	$0.571422\pi$
$798$	−1.81511e14	+	2.32817e13i	−0.560904	+	0.0719450i
$799$		−	2.87194e14i		−	0.881945i
$800$		0			0
$801$	−1.99193e14			−0.604103
$802$	1.30856e12	+	1.02019e13i	0.00394385	+	0.0307474i
$803$		−	2.79889e14i		−	0.838318i
$804$	−2.88267e13	+	7.51867e12i	−0.0858053	+	0.0223800i
$805$		0			0
$806$	8.16961e14	−	1.04788e14i	2.40174	−	0.308062i
$807$		−	2.99475e14i		−	0.874971i
$808$	1.31945e14	+	3.27768e14i	0.383122	+	0.951722i
$809$	4.37170e13			0.126156			0.0630780	−	0.998009i	$-0.479908\pi$
$809$	4.37170e13			0.126156			0.0630780	+	0.998009i	$0.479908\pi$
$810$		0			0
$811$			3.48250e14i			0.992629i	0.868143	+	0.496314i	$0.165314\pi$
$811$			3.48250e14i			0.992629i	−0.868143	+	0.496314i	$0.834686\pi$
$812$	−5.84622e13	−	2.24145e14i	−0.165613	−	0.634963i
$813$	−1.42181e14			−0.400304
$814$	7.12396e13	−	9.13763e12i	0.199342	−	0.0255689i
$815$		0			0
$816$	−1.05843e14	−	1.89099e14i	−0.292559	−	0.522684i
$817$	−1.85428e14			−0.509407
$818$	−4.22590e13	−	3.29464e14i	−0.115386	−	0.899583i
$819$		−	2.14022e14i		−	0.580816i
$820$		0			0
$821$	3.27880e14			0.879021			0.439511	−	0.898237i	$-0.355152\pi$
$821$	3.27880e14			0.879021			0.439511	+	0.898237i	$0.355152\pi$
$822$	2.50737e14	−	3.21611e13i	0.668129	−	0.0856982i
$823$			1.64425e14i			0.435481i	0.976007	+	0.217740i	$0.0698686\pi$
$823$			1.64425e14i			0.435481i	−0.976007	+	0.217740i	$0.930131\pi$
$824$	2.14566e14	−	8.63749e13i	0.564838	−	0.227379i
$825$		0			0
$826$	−3.17484e13	−	2.47520e14i	−0.0825699	−	0.643739i
$827$			8.72181e13i			0.225465i	0.993625	+	0.112732i	$0.0359603\pi$
$827$			8.72181e13i			0.225465i	−0.993625	+	0.112732i	$0.964040\pi$
$828$	−4.05994e13	−	1.55659e14i	−0.104320	−	0.399965i
$829$	−2.12343e14			−0.542333			−0.271166	−	0.962532i	$-0.587409\pi$
$829$	−2.12343e14			−0.542333			−0.271166	+	0.962532i	$0.587409\pi$
$830$		0			0
$831$			2.57697e14i			0.650285i
$832$	−5.14313e14	+	4.94160e14i	−1.29006	+	1.23951i
$833$	−9.22939e13			−0.230117
$834$	6.11353e13	+	4.76629e14i	0.151517	+	1.18127i
$835$		0			0
$836$	3.67333e14	−	9.58090e13i	0.899556	−	0.234625i
$837$	6.03719e14			1.46963
$838$	−5.00325e14	+	6.41747e13i	−1.21069	+	0.155290i
$839$			7.14552e12i			0.0171879i	0.999963	+	0.00859397i	$0.00273558\pi$
$839$			7.14552e12i			0.0171879i	−0.999963	+	0.00859397i	$0.997264\pi$
$840$		0			0
$841$	−1.61724e14			−0.384410
$842$	−6.11033e13	−	4.76379e14i	−0.144379	−	1.12562i
$843$		−	1.26509e14i		−	0.297155i
$844$	−3.89333e13	−	1.49271e14i	−0.0909094	−	0.348548i
$845$		0			0
$846$	−1.92163e14	+	2.46480e13i	−0.443422	+	0.0568760i
$847$			5.71051e13i			0.130996i
$848$	2.09700e14	−	1.17374e14i	0.478211	−	0.267666i
$849$	6.03091e14			1.36724
$850$		0			0
$851$		−	8.88144e13i		−	0.198992i
$852$	6.18552e14	−	1.61333e14i	1.37778	−	0.359356i
$853$	1.73226e14			0.383591			0.191795	−	0.981435i	$-0.438569\pi$
$853$	1.73226e14			0.383591			0.191795	+	0.981435i	$0.438569\pi$
$854$	3.89373e14	−	4.99433e13i	0.857189	−	0.109948i
$855$		0			0
$856$	5.50782e13	−	2.21721e13i	0.119842	−	0.0482434i
$857$	1.24930e14			0.270248			0.135124	−	0.990829i	$-0.456857\pi$
$857$	1.24930e14			0.270248			0.135124	+	0.990829i	$0.456857\pi$
$858$	−8.90298e13	−	6.94103e14i	−0.191469	−	1.49275i
$859$			3.15975e14i			0.675596i	0.941219	+	0.337798i	$0.109682\pi$
$859$			3.15975e14i			0.675596i	−0.941219	+	0.337798i	$0.890318\pi$
$860$		0			0
$861$	1.19944e14			0.253492
$862$	1.87858e13	−	2.40958e12i	0.0394724	−	0.00506297i
$863$		−	1.53961e14i		−	0.321631i	−0.986984	−	0.160816i	$-0.948588\pi$
$863$		−	1.53961e14i		−	0.321631i	0.986984	−	0.160816i	$-0.0514124\pi$
$864$	−4.19998e14	+	3.11304e14i	−0.872325	+	0.646571i
$865$		0			0
$866$	9.36547e13	+	7.30160e14i	0.192283	+	1.49909i
$867$		−	1.58477e14i		−	0.323498i
$868$	5.39699e14	−	1.40766e14i	1.09535	−	0.285693i
$869$	5.34762e14			1.07910
$870$		0			0
$871$		−	1.01672e14i		−	0.202820i
$872$	1.62782e14	+	4.04370e14i	0.322867	+	0.802041i
$873$	−1.32706e14			−0.261709
$874$	−5.97225e13	−	4.65614e14i	−0.117106	−	0.912996i
$875$		0			0
$876$	7.93784e13	+	3.04338e14i	0.153880	+	0.589977i
$877$	1.51963e14			0.292913			0.146457	−	0.989217i	$-0.453213\pi$
$877$	1.51963e14			0.292913			0.146457	+	0.989217i	$0.453213\pi$
$878$	−1.44234e14	+	1.85004e13i	−0.276437	+	0.0354575i
$879$		−	6.12508e13i		−	0.116726i
$880$		0			0
$881$	5.87645e14			1.10722			0.553612	−	0.832774i	$-0.313249\pi$
$881$	5.87645e14			1.10722			0.553612	+	0.832774i	$0.313249\pi$
$882$	7.92098e12	+	6.17543e13i	0.0148401	+	0.115697i
$883$			4.47094e14i			0.832904i	0.909158	+	0.416452i	$0.136727\pi$
$883$			4.47094e14i			0.832904i	−0.909158	+	0.416452i	$0.863273\pi$
$884$	7.15641e14	−	1.86656e14i	1.32566	−	0.345764i
$885$		0			0
$886$	−7.62871e13	+	9.78504e12i	−0.139728	+	0.0179223i
$887$			4.52899e14i			0.824866i	0.910988	+	0.412433i	$0.135321\pi$
$887$			4.52899e14i			0.824866i	−0.910988	+	0.412433i	$0.864679\pi$
$888$	−7.48709e13	+	3.01398e13i	−0.135596	+	0.0545853i
$889$	5.82792e14			1.04955
$890$		0			0
$891$		−	2.78501e14i		−	0.495950i
$892$	−2.14225e14	−	8.21342e14i	−0.379355	−	1.45445i
$893$	−5.65349e14			−0.995542
$894$	−2.03893e13	+	2.61525e12i	−0.0357038	+	0.00457959i
$895$		0			0
$896$	−3.02875e14	+	3.76221e14i	−0.524473	+	0.651483i
$897$	−8.65337e14			−1.49013
$898$	1.03972e14	+	8.10593e14i	0.178046	+	1.38810i
$899$			6.23583e14i			1.06193i
$900$		0			0
$901$	−2.49189e14			−0.419668
$902$	−2.46798e14	+	3.16558e13i	−0.413341	+	0.0530176i
$903$			2.31467e14i			0.385523i
$904$	2.87688e14	+	7.14651e14i	0.476518	+	1.18373i
$905$		0			0
$906$	−4.95598e13	−	3.86383e14i	−0.0811874	−	0.632961i
$907$			9.97795e14i			1.62557i	0.582566	+	0.812783i	$0.302049\pi$
$907$			9.97795e14i			1.62557i	−0.582566	+	0.812783i	$0.697951\pi$
$908$	−1.46765e14	−	5.62697e14i	−0.237789	−	0.911686i
$909$	−2.47154e14			−0.398243
$910$		0			0
$911$		−	1.01348e15i		−	1.61518i	−0.589741	−	0.807592i	$-0.700770\pi$
$911$		−	1.01348e15i		−	1.61518i	0.589741	−	0.807592i	$-0.299230\pi$
$912$	−3.72247e14	+	2.08356e14i	−0.590007	+	0.330241i
$913$	−3.27519e14			−0.516276
$914$	−5.85568e13	−	4.56526e14i	−0.0918008	−	0.715706i
$915$		0			0
$916$	6.23820e13	−	1.62707e13i	0.0967346	−	0.0252306i
$917$	−1.95245e13			−0.0301116
$918$	5.37692e14	−	6.89676e13i	0.824745	−	0.105787i
$919$			3.29429e14i			0.502556i	0.967915	+	0.251278i	$0.0808508\pi$
$919$			3.29429e14i			0.502556i	−0.967915	+	0.251278i	$0.919149\pi$
$920$		0			0
$921$	3.74975e14			0.565853
$922$	1.25147e14	+	9.75681e14i	0.187830	+	1.46438i
$923$			2.18164e15i			3.25668i
$924$	−1.19597e14	−	4.58536e14i	−0.177566	−	0.680791i
$925$		0			0
$926$	−5.29262e14	+	6.78864e13i	−0.777349	+	0.0997075i
$927$			1.61793e14i			0.236353i
$928$	−3.21547e14	−	4.33817e14i	−0.467201	−	0.630328i
$929$	6.89030e14			0.995771			0.497886	−	0.867243i	$-0.334110\pi$
$929$	6.89030e14			0.995771			0.497886	+	0.867243i	$0.334110\pi$
$930$		0			0
$931$			1.81683e14i			0.259756i
$932$	−3.87005e14	+	1.00940e14i	−0.550348	+	0.143544i
$933$	9.75705e14			1.38010
$934$	2.09169e14	−	2.68292e13i	0.294281	−	0.0377463i
$935$		0			0
$936$	−1.86311e14	−	4.62819e14i	−0.259334	−	0.644216i
$937$	−1.02170e15			−1.41458			−0.707289	−	0.706924i	$-0.750082\pi$
$937$	−1.02170e15			−1.41458			−0.707289	+	0.706924i	$0.750082\pi$
$938$	−8.75927e12	−	6.82898e13i	−0.0120630	−	0.0940463i
$939$		−	4.52537e12i		−	0.00619906i
$940$		0			0
$941$	7.35996e14			0.997532			0.498766	−	0.866737i	$-0.333787\pi$
$941$	7.35996e14			0.997532			0.498766	+	0.866737i	$0.333787\pi$
$942$	7.66758e13	−	9.83490e12i	0.103372	−	0.0132591i
$943$			3.07682e14i			0.412614i
$944$	−2.84127e14	−	5.07620e14i	−0.379012	−	0.677141i
$945$		0			0
$946$	−6.10888e13	−	4.76266e14i	−0.0806318	−	0.628629i
$947$			7.17168e14i			0.941609i	0.882237	+	0.470805i	$0.156036\pi$
$947$			7.17168e14i			0.941609i	−0.882237	+	0.470805i	$0.843964\pi$
$948$	−5.81474e14	+	1.51662e14i	−0.759431	+	0.198077i
$949$	−1.07340e15			−1.39454
$950$		0			0
$951$			9.61783e14i			1.23644i
$952$	4.64592e14	−	1.87025e14i	0.594137	−	0.239174i
$953$	4.43899e14			0.564702			0.282351	−	0.959311i	$-0.408886\pi$
$953$	4.43899e14			0.564702			0.282351	+	0.959311i	$0.408886\pi$
$954$	2.13863e13	+	1.66734e14i	0.0270641	+	0.211000i
$955$		0			0
$956$	2.21311e14	+	8.48510e14i	0.277149	+	1.06259i
$957$	5.29805e14			0.660019
$958$	1.05538e15	−	1.35369e14i	1.30791	−	0.167761i
$959$			5.84220e14i			0.720250i
$960$		0			0
$961$	−6.81841e14			−0.831891
$962$	−3.50437e13	−	2.73211e14i	−0.0425339	−	0.331606i
$963$			4.15317e13i			0.0501474i
$964$	2.17593e14	−	5.67534e13i	0.261373	−	0.0681722i
$965$		0			0
$966$	−5.81219e14	+	7.45507e13i	−0.690962	+	0.0886270i
$967$		−	1.42458e15i		−	1.68482i	−0.538837	−	0.842410i	$-0.681136\pi$
$967$		−	1.42458e15i		−	1.68482i	0.538837	−	0.842410i	$-0.318864\pi$
$968$	4.97113e13	+	1.23489e14i	0.0584895	+	0.145295i
$969$	4.42346e14			0.517778
$970$		0			0
$971$			4.62402e14i			0.535702i	0.963460	+	0.267851i	$0.0863136\pi$
$971$			4.62402e14i			0.535702i	−0.963460	+	0.267851i	$0.913686\pi$
$972$	−1.58778e14	−	6.08758e14i	−0.183004	−	0.701639i
$973$	−1.11055e15			−1.27343
$974$	−1.11045e14	+	1.42433e13i	−0.126679	+	0.0162486i
$975$		0			0
$976$	7.98535e14	−	4.46959e14i	0.901665	−	0.504683i
$977$	1.24483e15			1.39842			0.699209	−	0.714918i	$-0.253536\pi$
$977$	1.24483e15			1.39842			0.699209	+	0.714918i	$0.253536\pi$
$978$	−1.32808e14	−	1.03541e15i	−0.148433	−	1.15722i
$979$		−	1.50521e15i		−	1.67372i
$980$		0			0
$981$	−3.04915e14			−0.335609
$982$	−4.75755e14	+	6.10233e13i	−0.520986	+	0.0668249i
$983$		−	7.82351e14i		−	0.852382i	−0.904633	−	0.426191i	$-0.859855\pi$
$983$		−	7.82351e14i		−	0.852382i	0.904633	−	0.426191i	$-0.140145\pi$
$984$	2.59378e14	−	1.04414e14i	0.281162	−	0.113184i
$985$		0			0
$986$	7.12367e13	+	5.55383e14i	0.0764398	+	0.595947i
$987$			7.05717e14i			0.753433i
$988$	−3.67437e14	−	1.40876e15i	−0.390300	−	1.49641i
$989$	−5.93761e14			−0.627524
$990$		0			0
$991$		−	5.07172e14i		−	0.530624i	−0.964163	−	0.265312i	$-0.914525\pi$
$991$		−	5.07172e14i		−	0.530624i	0.964163	−	0.265312i	$-0.0854750\pi$
$992$	1.04455e15	−	7.74224e14i	1.08735	−	0.805950i
$993$	−8.83905e14			−0.915502
$994$	1.87953e14	+	1.46534e15i	0.193695	+	1.51010i
$995$		0			0
$996$	3.56127e14	−	9.28863e13i	0.363336	−	0.0947665i
$997$	5.76576e14			0.585303			0.292652	−	0.956219i	$-0.405462\pi$
$997$	5.76576e14			0.585303			0.292652	+	0.956219i	$0.405462\pi$
$998$	−6.40988e14	+	8.22170e13i	−0.647437	+	0.0830442i
$999$		−	2.01898e14i		−	0.202911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.h.51.14		24
4.3	odd	2	inner	100.11.b.h.51.13		24
5.2	odd	4		20.11.d.d.19.2	yes	24
5.3	odd	4		20.11.d.d.19.23	yes	24
5.4	even	2	inner	100.11.b.h.51.11		24
20.3	even	4		20.11.d.d.19.1	✓	24
20.7	even	4		20.11.d.d.19.24	yes	24
20.19	odd	2	inner	100.11.b.h.51.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.1	✓	24	20.3	even	4
20.11.d.d.19.2	yes	24	5.2	odd	4
20.11.d.d.19.23	yes	24	5.3	odd	4
20.11.d.d.19.24	yes	24	20.7	even	4
100.11.b.h.51.11		24	5.4	even	2	inner
100.11.b.h.51.12		24	20.19	odd	2	inner
100.11.b.h.51.13		24	4.3	odd	2	inner
100.11.b.h.51.14		24	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.07116 + 31.7400i) q^{2} +190.073i q^{3} +(-990.851 + 258.437i) q^{4} +(-6032.92 + 773.819i) q^{6} -14056.7i q^{7} +(-12236.7 - 30397.4i) q^{8} +22921.2 q^{9} +O(q^{10})\)	\(q+(4.07116 + 31.7400i) q^{2} +190.073i q^{3} +(-990.851 + 258.437i) q^{4} +(-6032.92 + 773.819i) q^{6} -14056.7i q^{7} +(-12236.7 - 30397.4i) q^{8} +22921.2 q^{9} +173205. i q^{11} +(-49122.0 - 188334. i) q^{12} +664258. q^{13} +(446160. - 57227.2i) q^{14} +(914997. - 512145. i) q^{16} -1.08730e6 q^{17} +(93315.9 + 727518. i) q^{18} +2.14038e6i q^{19} +2.67181e6 q^{21} +(-5.49751e6 + 705145. i) q^{22} +6.85374e6i q^{23} +(5.77774e6 - 2.32587e6i) q^{24} +(2.70430e6 + 2.10835e7i) q^{26} +1.55803e7i q^{27} +(3.63278e6 + 1.39281e7i) q^{28} -1.60930e7 q^{29} -3.87488e7i q^{31} +(1.99806e7 + 2.69569e7i) q^{32} -3.29216e7 q^{33} +(-4.42658e6 - 3.45109e7i) q^{34} +(-2.27115e7 + 5.92369e6i) q^{36} -1.29585e7 q^{37} +(-6.79357e7 + 8.71384e6i) q^{38} +1.26258e8i q^{39} +4.48926e7 q^{41} +(1.08774e7 + 8.48031e7i) q^{42} +8.66330e7i q^{43} +(-4.47625e7 - 1.71620e8i) q^{44} +(-2.17538e8 + 2.79027e7i) q^{46} +2.64135e8i q^{47} +(9.73451e7 + 1.73916e8i) q^{48} +8.48835e7 q^{49} -2.06667e8i q^{51} +(-6.58180e8 + 1.71669e8i) q^{52} +2.29181e8 q^{53} +(-4.94519e8 + 6.34301e7i) q^{54} +(-4.27289e8 + 1.72008e8i) q^{56} -4.06829e8 q^{57} +(-6.55170e7 - 5.10790e8i) q^{58} -5.54778e8i q^{59} +8.72720e8 q^{61} +(1.22989e9 - 1.57753e8i) q^{62} -3.22197e8i q^{63} +(-7.74268e8 + 7.43929e8i) q^{64} +(-1.34029e8 - 1.04493e9i) q^{66} -1.53061e8i q^{67} +(1.07735e9 - 2.80999e8i) q^{68} -1.30271e9 q^{69} +3.28433e9i q^{71} +(-2.80480e8 - 6.96746e8i) q^{72} -1.61594e9 q^{73} +(-5.27562e7 - 4.11303e8i) q^{74} +(-5.53154e8 - 2.12080e9i) q^{76} +2.43469e9 q^{77} +(-4.00741e9 + 5.14015e8i) q^{78} -3.08746e9i q^{79} -1.60793e9 q^{81} +(1.82765e8 + 1.42489e9i) q^{82} +1.89093e9i q^{83} +(-2.64736e9 + 6.90494e8i) q^{84} +(-2.74973e9 + 3.52697e8i) q^{86} -3.05884e9i q^{87} +(5.26498e9 - 2.11946e9i) q^{88} -8.69033e9 q^{89} -9.33729e9i q^{91} +(-1.77126e9 - 6.79104e9i) q^{92} +7.36511e9 q^{93} +(-8.38362e9 + 1.07533e9i) q^{94} +(-5.12379e9 + 3.79777e9i) q^{96} -5.78965e9 q^{97} +(3.45574e8 + 2.69420e9i) q^{98} +3.97006e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9}+O(q^{10}) \) 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9	\( 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9} + 1706016 q^{14} - 4733376 q^{16} - 13030368 q^{21} - 10190784 q^{24} - 9454368 q^{26} - 121656816 q^{29} + 335231168 q^{34} - 276632160 q^{36} + 892843248 q^{41} - 766329600 q^{44} + 433181216 q^{46} + 738102008 q^{49} - 139387968 q^{54} - 2629032384 q^{56} + 228563248 q^{61} + 1875284992 q^{64} - 1440259200 q^{66} + 943422432 q^{69} - 21045467232 q^{74} + 828422400 q^{76} - 5619065544 q^{81} + 28069573632 q^{84} + 8163556416 q^{86} - 4631088816 q^{89} - 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9 + 1706016 * q^14 - 4733376 * q^16 - 13030368 * q^21 - 10190784 * q^24 - 9454368 * q^26 - 121656816 * q^29 + 335231168 * q^34 - 276632160 * q^36 + 892843248 * q^41 - 766329600 * q^44 + 433181216 * q^46 + 738102008 * q^49 - 139387968 * q^54 - 2629032384 * q^56 + 228563248 * q^61 + 1875284992 * q^64 - 1440259200 * q^66 + 943422432 * q^69 - 21045467232 * q^74 + 828422400 * q^76 - 5619065544 * q^81 + 28069573632 * q^84 + 8163556416 * q^86 - 4631088816 * q^89 - 63404384 * q^94 - 5617046784 * q^96

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