LMFDB - Embedded newform 624.2.cn.c.305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.2
Root			$0.500000 + 1.56488i$ of defining polynomial
Character	$\chi$	$=$	624.305
Dual form			624.2.cn.c.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60523 - 0.650571i) q^{3} +(-1.06488 - 1.06488i) q^{5} +(-0.366025 + 1.36603i) q^{7} +(2.15351 - 2.08863i) q^{9} +O(q^{10})$	\(q+(1.60523 - 0.650571i) q^{3} +(-1.06488 - 1.06488i) q^{5} +(-0.366025 + 1.36603i) q^{7} +(2.15351 - 2.08863i) q^{9} +(-1.06488 - 3.97420i) q^{11} +(3.59808 - 0.232051i) q^{13} +(-2.40216 - 1.01660i) q^{15} +(-2.51954 - 4.36397i) q^{17} +(3.73205 + 1.00000i) q^{19} +(0.301143 + 2.43091i) q^{21} -2.73205i q^{25} +(2.09808 - 4.75374i) q^{27} +(6.20840 + 3.58442i) q^{29} +(2.46410 - 2.46410i) q^{31} +(-4.29488 - 5.68671i) q^{33} +(1.84443 - 1.06488i) q^{35} +(-5.23205 + 1.40192i) q^{37} +(5.62477 - 2.71330i) q^{39} +(-5.42885 + 1.45466i) q^{41} +(-1.90192 + 1.09808i) q^{43} +(-4.51739 - 0.0690922i) q^{45} +(-4.25953 + 4.25953i) q^{47} +(4.33013 + 2.50000i) q^{49} +(-6.88351 - 5.36603i) q^{51} -0.779548i q^{53} +(-3.09808 + 5.36603i) q^{55} +(6.64136 - 0.822738i) q^{57} +(-2.90931 - 0.779548i) q^{59} +(3.50000 + 6.06218i) q^{61} +(2.06488 + 3.70625i) q^{63} +(-4.07863 - 3.58442i) q^{65} +(1.53590 + 5.73205i) q^{67} +(-0.779548 + 2.90931i) q^{71} +(-0.901924 - 0.901924i) q^{73} +(-1.77739 - 4.38556i) q^{75} +5.81863 q^{77} -2.00000 q^{79} +(0.275241 - 8.99579i) q^{81} +(2.90931 + 2.90931i) q^{83} +(-1.96410 + 7.33013i) q^{85} +(12.2978 + 1.71481i) q^{87} +(2.41510 + 9.01327i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(2.35237 - 5.55852i) q^{93} +(-2.90931 - 5.03908i) q^{95} +(1.63397 + 0.437822i) q^{97} +(-10.5939 - 6.33434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9	$ 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9} + 8 q^{13} + 14 q^{15} + 16 q^{19} + 4 q^{21} - 4 q^{27} - 8 q^{31} + 16 q^{33} - 28 q^{37} + 14 q^{39} - 36 q^{43} - 20 q^{45} - 4 q^{55} + 16 q^{57} + 28 q^{61} + 8 q^{63} + 40 q^{67} - 28 q^{73} - 12 q^{75} - 16 q^{79} + 4 q^{81} + 12 q^{85} + 34 q^{87} - 8 q^{91} + 4 q^{93} + 20 q^{97} - 40 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9 + 8 * q^13 + 14 * q^15 + 16 * q^19 + 4 * q^21 - 4 * q^27 - 8 * q^31 + 16 * q^33 - 28 * q^37 + 14 * q^39 - 36 * q^43 - 20 * q^45 - 4 * q^55 + 16 * q^57 + 28 * q^61 + 8 * q^63 + 40 * q^67 - 28 * q^73 - 12 * q^75 - 16 * q^79 + 4 * q^81 + 12 * q^85 + 34 * q^87 - 8 * q^91 + 4 * q^93 + 20 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.60523	−	0.650571i	0.926779	−	0.375608i
$3$	1.60523	−	0.650571i	0.926779	−	0.375608i
$4$		0			0
$5$	−1.06488	−	1.06488i	−0.476230	−	0.476230i	0.427694	−	0.903924i	$-0.359326\pi$
$5$	−1.06488	−	1.06488i	−0.476230	−	0.476230i	−0.903924	+	0.427694i	$0.859326\pi$
$6$		0			0
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	0.861617	+	0.507559i	$0.169452\pi$
$7$	−0.366025	+	1.36603i	−0.138345	+	0.516309i	−0.999962	+	0.00875026i	$0.997215\pi$
$8$		0			0
$9$	2.15351	−	2.08863i	0.717838	−	0.696210i
$10$		0			0
$11$	−1.06488	−	3.97420i	−0.321074	−	1.19826i	−0.918200	−	0.396117i	$-0.870357\pi$
$11$	−1.06488	−	3.97420i	−0.321074	−	1.19826i	0.597126	−	0.802148i	$-0.296309\pi$
$12$		0			0
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$14$		0			0
$15$	−2.40216	−	1.01660i	−0.620235	−	0.262484i
$16$		0			0
$17$	−2.51954	−	4.36397i	−0.611078	−	1.05842i	−0.991059	−	0.133424i	$-0.957403\pi$
$17$	−2.51954	−	4.36397i	−0.611078	−	1.05842i	0.379981	−	0.924994i	$-0.375930\pi$
$18$		0			0
$19$	3.73205	+	1.00000i	0.856191	+	0.229416i	0.660107	−	0.751171i	$-0.270511\pi$
$19$	3.73205	+	1.00000i	0.856191	+	0.229416i	0.196084	+	0.980587i	$0.437177\pi$
$20$		0			0
$21$	0.301143	+	2.43091i	0.0657148	+	0.530468i
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$		−	2.73205i		−	0.546410i
$26$		0			0
$27$	2.09808	−	4.75374i	0.403775	−	0.914858i
$28$		0			0
$29$	6.20840	+	3.58442i	1.15287	+	0.665610i	0.949585	−	0.313509i	$-0.101505\pi$
$29$	6.20840	+	3.58442i	1.15287	+	0.665610i	0.203286	+	0.979119i	$0.434838\pi$
$30$		0			0
$31$	2.46410	−	2.46410i	0.442566	−	0.442566i	−0.450308	−	0.892873i	$-0.648686\pi$
$31$	2.46410	−	2.46410i	0.442566	−	0.442566i	0.892873	+	0.450308i	$0.148686\pi$
$32$		0			0
$33$	−4.29488	−	5.68671i	−0.747642	−	0.989929i
$34$		0			0
$35$	1.84443	−	1.06488i	0.311766	−	0.179998i
$36$		0			0
$37$	−5.23205	+	1.40192i	−0.860144	+	0.230475i	−0.661821	−	0.749662i	$-0.730216\pi$
$37$	−5.23205	+	1.40192i	−0.860144	+	0.230475i	−0.198323	+	0.980137i	$0.563549\pi$
$38$		0			0
$39$	5.62477	−	2.71330i	0.900684	−	0.434476i
$40$		0			0
$41$	−5.42885	+	1.45466i	−0.847844	+	0.227179i	−0.656483	−	0.754341i	$-0.727957\pi$
$41$	−5.42885	+	1.45466i	−0.847844	+	0.227179i	−0.191361	+	0.981520i	$0.561290\pi$
$42$		0			0
$43$	−1.90192	+	1.09808i	−0.290041	+	0.167455i	−0.637960	−	0.770069i	$-0.720222\pi$
$43$	−1.90192	+	1.09808i	−0.290041	+	0.167455i	0.347920	+	0.937524i	$0.386888\pi$
$44$		0			0
$45$	−4.51739	−	0.0690922i	−0.673412	−	0.0102997i
$46$		0			0
$47$	−4.25953	+	4.25953i	−0.621316	+	0.621316i	−0.945868	−	0.324552i	$-0.894787\pi$
$47$	−4.25953	+	4.25953i	−0.621316	+	0.621316i	0.324552	+	0.945868i	$0.394787\pi$
$48$		0			0
$49$	4.33013	+	2.50000i	0.618590	+	0.357143i
$50$		0			0
$51$	−6.88351	−	5.36603i	−0.963884	−	0.751394i
$52$		0			0
$53$		−	0.779548i		−	0.107079i	−0.998566	−	0.0535396i	$-0.982950\pi$
$53$		−	0.779548i		−	0.107079i	0.998566	−	0.0535396i	$-0.0170503\pi$
$54$		0			0
$55$	−3.09808	+	5.36603i	−0.417745	+	0.723555i
$56$		0			0
$57$	6.64136	−	0.822738i	0.879670	−	0.108974i
$58$		0			0
$59$	−2.90931	−	0.779548i	−0.378760	−	0.101489i	0.0644157	−	0.997923i	$-0.479482\pi$
$59$	−2.90931	−	0.779548i	−0.378760	−	0.101489i	−0.443176	+	0.896435i	$0.646148\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$	2.06488	+	3.70625i	0.260151	+	0.466943i
$64$		0			0
$65$	−4.07863	−	3.58442i	−0.505892	−	0.444593i
$66$		0			0
$67$	1.53590	+	5.73205i	0.187640	+	0.700281i	0.994050	+	0.108925i	$0.0347408\pi$
$67$	1.53590	+	5.73205i	0.187640	+	0.700281i	−0.806410	+	0.591357i	$0.798593\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.779548	+	2.90931i	−0.0925153	+	0.345272i	−0.996631	−	0.0820158i	$-0.973864\pi$
$71$	−0.779548	+	2.90931i	−0.0925153	+	0.345272i	0.904116	+	0.427288i	$0.140531\pi$
$72$		0			0
$73$	−0.901924	−	0.901924i	−0.105562	−	0.105562i	0.652353	−	0.757915i	$-0.273782\pi$
$73$	−0.901924	−	0.901924i	−0.105562	−	0.105562i	−0.757915	+	0.652353i	$0.773782\pi$
$74$		0			0
$75$	−1.77739	−	4.38556i	−0.205236	−	0.506401i
$76$		0			0
$77$	5.81863			0.663094
$78$		0			0
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$		0			0
$81$	0.275241	−	8.99579i	0.0305823	−	0.999532i
$82$		0			0
$83$	2.90931	+	2.90931i	0.319339	+	0.319339i	0.848513	−	0.529174i	$-0.177498\pi$
$83$	2.90931	+	2.90931i	0.319339	+	0.319339i	−0.529174	+	0.848513i	$0.677498\pi$
$84$		0			0
$85$	−1.96410	+	7.33013i	−0.213037	+	0.795064i
$86$		0			0
$87$	12.2978	+	1.71481i	1.31846	+	0.183846i
$88$		0			0
$89$	2.41510	+	9.01327i	0.256000	+	0.955405i	0.967531	+	0.252751i	$0.0813353\pi$
$89$	2.41510	+	9.01327i	0.256000	+	0.955405i	−0.711531	+	0.702654i	$0.751998\pi$
$90$		0			0
$91$	−1.00000	+	5.00000i	−0.104828	+	0.524142i
$92$		0			0
$93$	2.35237	−	5.55852i	0.243929	−	0.576392i
$94$		0			0
$95$	−2.90931	−	5.03908i	−0.298489	−	0.516998i
$96$		0			0
$97$	1.63397	+	0.437822i	0.165905	+	0.0444541i	0.340815	−	0.940130i	$-0.389297\pi$
$97$	1.63397	+	0.437822i	0.165905	+	0.0444541i	−0.174910	+	0.984584i	$0.555964\pi$
$98$		0			0
$99$	−10.5939	−	6.33434i	−1.06472	−	0.636625i
$100$		0			0
$101$	3.01375	−	5.21997i	0.299880	−	0.519407i	−0.676229	−	0.736692i	$-0.736387\pi$
$101$	3.01375	−	5.21997i	0.299880	−	0.519407i	0.976108	+	0.217285i	$0.0697202\pi$
$102$		0			0
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$		0			0
$105$	2.26795	−	2.90931i	0.221329	−	0.283920i
$106$		0			0
$107$	16.4675	+	9.50749i	1.59197	+	0.919123i	0.992969	+	0.118374i	$0.0377682\pi$
$107$	16.4675	+	9.50749i	1.59197	+	0.919123i	0.598999	+	0.800749i	$0.295565\pi$
$108$		0			0
$109$	−13.1962	+	13.1962i	−1.26396	+	1.26396i	−0.314806	+	0.949156i	$0.601940\pi$
$109$	−13.1962	+	13.1962i	−1.26396	+	1.26396i	−0.949156	+	0.314806i	$0.898060\pi$
$110$		0			0
$111$	−7.48658	+	5.65423i	−0.710595	+	0.536676i
$112$		0			0
$113$	8.90883	−	5.14352i	0.838073	−	0.483861i	−0.0185360	−	0.999828i	$-0.505901\pi$
$113$	8.90883	−	5.14352i	0.838073	−	0.483861i	0.856609	+	0.515967i	$0.172567\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	7.26384	−	8.01478i	0.671542	−	0.740967i
$118$		0			0
$119$	6.88351	−	1.84443i	0.631010	−	0.169079i
$120$		0			0
$121$	−5.13397	+	2.96410i	−0.466725	+	0.269464i
$122$		0			0
$123$	−7.76819	+	5.86691i	−0.700434	+	0.529002i
$124$		0			0
$125$	−8.23373	+	8.23373i	−0.736447	+	0.736447i
$126$		0			0
$127$	−7.90192	−	4.56218i	−0.701182	−	0.404828i	0.106605	−	0.994301i	$-0.466002\pi$
$127$	−7.90192	−	4.56218i	−0.701182	−	0.404828i	−0.807788	+	0.589474i	$0.799335\pi$
$128$		0			0
$129$	−2.33864	+	3.00000i	−0.205906	+	0.264135i
$130$		0			0
$131$		−	7.94839i		−	0.694454i	−0.937781	−	0.347227i	$-0.887123\pi$
$131$		−	7.94839i		−	0.694454i	0.937781	−	0.347227i	$-0.112877\pi$
$132$		0			0
$133$	−2.73205	+	4.73205i	−0.236899	+	0.410321i
$134$		0			0
$135$	−7.29638	+	2.82797i	−0.627973	+	0.243393i
$136$		0			0
$137$	−6.49373	−	1.73999i	−0.554797	−	0.148657i	−0.0294822	−	0.999565i	$-0.509386\pi$
$137$	−6.49373	−	1.73999i	−0.554797	−	0.148657i	−0.525315	+	0.850908i	$0.676052\pi$
$138$		0			0
$139$	9.19615	+	15.9282i	0.780007	+	1.35101i	0.931937	+	0.362621i	$0.118118\pi$
$139$	9.19615	+	15.9282i	0.780007	+	1.35101i	−0.151929	+	0.988391i	$0.548549\pi$
$140$		0			0
$141$	−4.06639	+	9.60864i	−0.342452	+	0.809194i
$142$		0			0
$143$	−4.75374	−	14.0524i	−0.397528	−	1.17512i
$144$		0			0
$145$	−2.79423	−	10.4282i	−0.232048	−	0.866015i
$146$		0			0
$147$	8.57727	+	1.19601i	0.707441	+	0.0986455i
$148$		0			0
$149$	−2.23420	+	8.33816i	−0.183033	+	0.683089i	0.812010	+	0.583644i	$0.198374\pi$
$149$	−2.23420	+	8.33816i	−0.183033	+	0.683089i	−0.995043	+	0.0994454i	$0.968293\pi$
$150$		0			0
$151$	−0.535898	−	0.535898i	−0.0436108	−	0.0436108i	0.684965	−	0.728576i	$-0.259817\pi$
$151$	−0.535898	−	0.535898i	−0.0436108	−	0.0436108i	−0.728576	+	0.684965i	$0.759817\pi$
$152$		0			0
$153$	−14.5406	−	4.13548i	−1.17554	−	0.334334i
$154$		0			0
$155$	−5.24796			−0.421526
$156$		0			0
$157$	−4.80385			−0.383389			−0.191694	−	0.981455i	$-0.561398\pi$
$157$	−4.80385			−0.383389			−0.191694	+	0.981455i	$0.561398\pi$
$158$		0			0
$159$	−0.507152	−	1.25135i	−0.0402197	−	0.0992387i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.07180	−	4.00000i	0.0839496	−	0.313304i	−0.911164	−	0.412045i	$-0.864815\pi$
$163$	1.07180	−	4.00000i	0.0839496	−	0.313304i	0.995113	+	0.0987406i	$0.0314814\pi$
$164$		0			0
$165$	−1.48214	+	10.6292i	−0.115384	+	0.827483i
$166$		0			0
$167$	3.47998	+	12.9875i	0.269289	+	1.00500i	0.959573	+	0.281461i	$0.0908192\pi$
$167$	3.47998	+	12.9875i	0.269289	+	1.00500i	−0.690283	+	0.723539i	$0.742514\pi$
$168$		0			0
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$		0			0
$171$	10.1257	−	5.64136i	0.774328	−	0.431406i
$172$		0			0
$173$	8.72794	+	15.1172i	0.663573	+	1.14934i	0.979670	+	0.200615i	$0.0642941\pi$
$173$	8.72794	+	15.1172i	0.663573	+	1.14934i	−0.316097	+	0.948727i	$0.602373\pi$
$174$		0			0
$175$	3.73205	+	1.00000i	0.282117	+	0.0755929i
$176$		0			0
$177$	−5.17726	+	0.641364i	−0.389147	+	0.0482078i
$178$		0			0
$179$	−13.2728	+	22.9892i	−0.992056	+	1.71829i	−0.387084	+	0.922045i	$0.626518\pi$
$179$	−13.2728	+	22.9892i	−0.992056	+	1.71829i	−0.604972	+	0.796247i	$0.706816\pi$
$180$		0			0
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$		0			0
$183$	9.56218	+	7.45418i	0.706857	+	0.551029i
$184$		0			0
$185$	7.06440	+	4.07863i	0.519385	+	0.299867i
$186$		0			0
$187$	−14.6603	+	14.6603i	−1.07206	+	1.07206i
$188$		0			0
$189$	5.72579	+	4.60602i	0.416490	+	0.335038i
$190$		0			0
$191$	4.18307	−	2.41510i	0.302677	−	0.174750i	−0.340968	−	0.940075i	$-0.610755\pi$
$191$	4.18307	−	2.41510i	0.302677	−	0.174750i	0.643645	+	0.765324i	$0.277421\pi$
$192$		0			0
$193$	0.133975	−	0.0358984i	0.00964370	−	0.00258402i	−0.253994	−	0.967206i	$-0.581744\pi$
$193$	0.133975	−	0.0358984i	0.00964370	−	0.00258402i	0.263638	+	0.964622i	$0.415078\pi$
$194$		0			0
$195$	−8.87906	−	3.10037i	−0.635843	−	0.222022i
$196$		0			0
$197$	3.97420	−	1.06488i	0.283150	−	0.0758697i	−0.114449	−	0.993429i	$-0.536510\pi$
$197$	3.97420	−	1.06488i	0.283150	−	0.0758697i	0.397599	+	0.917559i	$0.369844\pi$
$198$		0			0
$199$	−11.1962	+	6.46410i	−0.793674	+	0.458228i	−0.841254	−	0.540639i	$-0.818182\pi$
$199$	−11.1962	+	6.46410i	−0.793674	+	0.458228i	0.0475802	+	0.998867i	$0.484849\pi$
$200$		0			0
$201$	6.19458	+	8.20204i	0.436932	+	0.578527i
$202$		0			0
$203$	−7.16884	+	7.16884i	−0.503154	+	0.503154i
$204$		0			0
$205$	7.33013	+	4.23205i	0.511958	+	0.295579i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	15.8968i		−	1.09960i
$210$		0			0
$211$	−0.901924	+	1.56218i	−0.0620910	+	0.107545i	−0.895400	−	0.445263i	$-0.853110\pi$
$211$	−0.901924	+	1.56218i	−0.0620910	+	0.107545i	0.833309	+	0.552808i	$0.186444\pi$
$212$		0			0
$213$	0.641364	+	5.17726i	0.0439455	+	0.354740i
$214$		0			0
$215$	3.19465	+	0.856003i	0.217873	+	0.0583789i
$216$		0			0
$217$	2.46410	+	4.26795i	0.167274	+	0.289727i
$218$		0			0
$219$	−2.03456	−	0.861027i	−0.137483	−	0.0581828i
$220$		0			0
$221$	−10.0782	−	15.1172i	−0.677930	−	1.01690i
$222$		0			0
$223$	−6.70577	−	25.0263i	−0.449052	−	1.67588i	−0.705011	−	0.709196i	$-0.749058\pi$
$223$	−6.70577	−	25.0263i	−0.449052	−	1.67588i	0.255960	−	0.966687i	$-0.417609\pi$
$224$		0			0
$225$	−5.70625	−	5.88351i	−0.380416	−	0.392234i
$226$		0			0
$227$	5.24796	−	19.5856i	0.348319	−	1.29994i	−0.540367	−	0.841429i	$-0.681715\pi$
$227$	5.24796	−	19.5856i	0.348319	−	1.29994i	0.888686	−	0.458515i	$-0.151619\pi$
$228$		0			0
$229$	−14.1244	−	14.1244i	−0.933364	−	0.933364i	0.0645507	−	0.997914i	$-0.479439\pi$
$229$	−14.1244	−	14.1244i	−0.933364	−	0.933364i	−0.997914	+	0.0645507i	$0.979439\pi$
$230$		0			0
$231$	9.34022	−	3.78543i	0.614541	−	0.249063i
$232$		0			0
$233$	−17.4559			−1.14357			−0.571786	−	0.820403i	$-0.693749\pi$
$233$	−17.4559			−1.14357			−0.571786	+	0.820403i	$0.693749\pi$
$234$		0			0
$235$	9.07180			0.591779
$236$		0			0
$237$	−3.21046	+	1.30114i	−0.208542	+	0.0845183i
$238$		0			0
$239$	6.59817	+	6.59817i	0.426800	+	0.426800i	0.887537	−	0.460737i	$-0.152415\pi$
$239$	6.59817	+	6.59817i	0.426800	+	0.426800i	−0.460737	+	0.887537i	$0.652415\pi$
$240$		0			0
$241$	3.76795	−	14.0622i	0.242715	−	0.905825i	−0.731803	−	0.681516i	$-0.761321\pi$
$241$	3.76795	−	14.0622i	0.242715	−	0.905825i	0.974518	−	0.224309i	$-0.0720123\pi$
$242$		0			0
$243$	−5.41058	−	14.6194i	−0.347089	−	0.937832i
$244$		0			0
$245$	−1.94887	−	7.27328i	−0.124509	−	0.464673i
$246$		0			0
$247$	13.6603	+	2.73205i	0.869181	+	0.173836i
$248$		0			0
$249$	6.56283	+	2.77739i	0.415902	+	0.176010i
$250$		0			0
$251$	0.494214	+	0.856003i	0.0311945	+	0.0540304i	0.881201	−	0.472741i	$-0.156736\pi$
$251$	0.494214	+	0.856003i	0.0311945	+	0.0540304i	−0.850007	+	0.526772i	$0.823402\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	1.61594	+	13.0443i	0.101194	+	0.816867i
$256$		0			0
$257$	−10.7533	+	18.6252i	−0.670770	+	1.16181i	0.306916	+	0.951737i	$0.400703\pi$
$257$	−10.7533	+	18.6252i	−0.670770	+	1.16181i	−0.977686	+	0.210071i	$0.932630\pi$
$258$		0			0
$259$		−	7.66025i		−	0.475985i
$260$		0			0
$261$	20.8564	−	5.24796i	1.29098	−	0.324840i
$262$		0			0
$263$	−19.3003	−	11.1430i	−1.19011	−	0.687109i	−0.231777	−	0.972769i	$-0.574454\pi$
$263$	−19.3003	−	11.1430i	−1.19011	−	0.687109i	−0.958331	+	0.285660i	$0.907787\pi$
$264$		0			0
$265$	−0.830127	+	0.830127i	−0.0509943	+	0.0509943i
$266$		0			0
$267$	9.74056	+	12.8972i	0.596113	+	0.789294i
$268$		0			0
$269$	12.4168	−	7.16884i	0.757066	−	0.437092i	−0.0711756	−	0.997464i	$-0.522675\pi$
$269$	12.4168	−	7.16884i	0.757066	−	0.437092i	0.828241	+	0.560372i	$0.189342\pi$
$270$		0			0
$271$	−7.46410	+	2.00000i	−0.453412	+	0.121491i	−0.478295	−	0.878199i	$-0.658745\pi$
$271$	−7.46410	+	2.00000i	−0.453412	+	0.121491i	0.0248835	+	0.999690i	$0.492079\pi$
$272$		0			0
$273$	1.64763	+	8.67671i	0.0997191	+	0.525138i
$274$		0			0
$275$	−10.8577	+	2.90931i	−0.654744	+	0.175438i
$276$		0			0
$277$	23.8923	−	13.7942i	1.43555	−	0.828815i	0.438013	−	0.898969i	$-0.355682\pi$
$277$	23.8923	−	13.7942i	1.43555	−	0.828815i	0.997536	+	0.0701536i	$0.0223490\pi$
$278$		0			0
$279$	0.159877	−	10.4531i	0.00957158	−	0.625809i
$280$		0			0
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	−0.245655	−	0.969357i	$-0.579003\pi$
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	0.969357	+	0.245655i	$0.0790030\pi$
$282$		0			0
$283$	5.70577	+	3.29423i	0.339173	+	0.195822i	0.659906	−	0.751348i	$-0.270596\pi$
$283$	5.70577	+	3.29423i	0.339173	+	0.195822i	−0.320733	+	0.947170i	$0.603929\pi$
$284$		0			0
$285$	−7.94839	−	6.19615i	−0.470822	−	0.367028i
$286$		0			0
$287$		−	7.94839i		−	0.469179i
$288$		0			0
$289$	−4.19615	+	7.26795i	−0.246832	+	0.427526i
$290$		0			0
$291$	2.90774	−	0.360213i	0.170455	−	0.0211161i
$292$		0			0
$293$	1.73999	+	0.466229i	0.101651	+	0.0272374i	0.309286	−	0.950969i	$-0.399910\pi$
$293$	1.73999	+	0.466229i	0.101651	+	0.0272374i	−0.207635	+	0.978206i	$0.566577\pi$
$294$		0			0
$295$	2.26795	+	3.92820i	0.132045	+	0.228709i
$296$		0			0
$297$	−21.1265	−	3.27599i	−1.22588	−	0.190092i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.803848	−	3.00000i	−0.0463330	−	0.172917i
$302$		0			0
$303$	1.44179	−	10.3399i	0.0828289	−	0.594012i
$304$		0			0
$305$	2.72842	−	10.1826i	0.156229	−	0.583054i
$306$		0			0
$307$	−8.39230	−	8.39230i	−0.478974	−	0.478974i	0.425829	−	0.904803i	$-0.359982\pi$
$307$	−8.39230	−	8.39230i	−0.478974	−	0.478974i	−0.904803	+	0.425829i	$0.859982\pi$
$308$		0			0
$309$	−4.50729	−	11.1213i	−0.256411	−	0.632671i
$310$		0			0
$311$	10.0782			0.571480			0.285740	−	0.958307i	$-0.407761\pi$
$311$	10.0782			0.571480			0.285740	+	0.958307i	$0.407761\pi$
$312$		0			0
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$		0			0
$315$	1.74786	−	6.14557i	0.0984807	−	0.346264i
$316$		0			0
$317$	11.3519	+	11.3519i	0.637587	+	0.637587i	0.949960	−	0.312373i	$-0.101124\pi$
$317$	11.3519	+	11.3519i	0.637587	+	0.637587i	−0.312373	+	0.949960i	$0.601124\pi$
$318$		0			0
$319$	7.63397	−	28.4904i	0.427421	−	1.59516i
$320$		0			0
$321$	32.6193	+	4.54843i	1.82063	+	0.253869i
$322$		0			0
$323$	−5.03908	−	18.8061i	−0.280382	−	1.04640i
$324$		0			0
$325$	−0.633975	−	9.83013i	−0.0351666	−	0.545277i
$326$		0			0
$327$	−12.5978	+	29.7679i	−0.696659	+	1.64617i
$328$		0			0
$329$	−4.25953	−	7.37772i	−0.234835	−	0.406747i
$330$		0			0
$331$	33.0526	+	8.85641i	1.81673	+	0.486792i	0.996376	−	0.0850595i	$-0.0271080\pi$
$331$	33.0526	+	8.85641i	1.81673	+	0.486792i	0.820357	+	0.571852i	$0.193775\pi$
$332$		0			0
$333$	−8.33919	+	13.9469i	−0.456985	+	0.764285i
$334$		0			0
$335$	4.46841	−	7.73951i	0.244135	−	0.422855i
$336$		0			0
$337$		−	18.4641i		−	1.00580i	−0.864344	−	0.502902i	$-0.832266\pi$
$337$		−	18.4641i		−	1.00580i	0.864344	−	0.502902i	$-0.167734\pi$
$338$		0			0
$339$	10.9545	−	14.0524i	0.594966	−	0.763219i
$340$		0			0
$341$	−12.4168	−	7.16884i	−0.672407	−	0.388215i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.8177	−	10.2870i	0.956502	−	0.552237i	0.0614076	−	0.998113i	$-0.480441\pi$
$347$	17.8177	−	10.2870i	0.956502	−	0.552237i	0.895095	+	0.445876i	$0.147108\pi$
$348$		0			0
$349$	27.4904	−	7.36603i	1.47153	−	0.394294i	0.568072	−	0.822979i	$-0.307689\pi$
$349$	27.4904	−	7.36603i	1.47153	−	0.394294i	0.903454	+	0.428684i	$0.141023\pi$
$350$		0			0
$351$	6.44593	−	17.5912i	0.344058	−	0.938948i
$352$		0			0
$353$	−13.6626	+	3.66088i	−0.727186	+	0.194849i	−0.603376	−	0.797457i	$-0.706178\pi$
$353$	−13.6626	+	3.66088i	−0.727186	+	0.194849i	−0.123810	+	0.992306i	$0.539511\pi$
$354$		0			0
$355$	3.92820	−	2.26795i	0.208487	−	0.120370i
$356$		0			0
$357$	9.84967	−	7.43895i	0.521300	−	0.393711i
$358$		0			0
$359$	18.2354	−	18.2354i	0.962429	−	0.962429i	−0.0368904	−	0.999319i	$-0.511745\pi$
$359$	18.2354	−	18.2354i	0.962429	−	0.962429i	0.999319	+	0.0368904i	$0.0117452\pi$
$360$		0			0
$361$	−3.52628	−	2.03590i	−0.185594	−	0.107153i
$362$		0			0
$363$	−6.31284	+	8.09808i	−0.331338	+	0.425039i
$364$		0			0
$365$			1.92089i			0.100544i
$366$		0			0
$367$	15.1962	−	26.3205i	0.793233	−	1.37392i	−0.130723	−	0.991419i	$-0.541730\pi$
$367$	15.1962	−	26.3205i	0.793233	−	1.37392i	0.923955	−	0.382500i	$-0.124937\pi$
$368$		0			0
$369$	−8.65286	+	14.4715i	−0.450450	+	0.753356i
$370$		0			0
$371$	1.06488	+	0.285334i	0.0552859	+	0.0148138i
$372$		0			0
$373$	−5.79423	−	10.0359i	−0.300014	−	0.519639i	0.676125	−	0.736787i	$-0.263658\pi$
$373$	−5.79423	−	10.0359i	−0.300014	−	0.519639i	−0.976139	+	0.217148i	$0.930325\pi$
$374$		0			0
$375$	−7.86038	+	18.5736i	−0.405908	+	0.959138i
$376$		0			0
$377$	23.1701	+	11.4564i	1.19332	+	0.590032i
$378$		0			0
$379$	−3.83013	−	14.2942i	−0.196740	−	0.734245i	−0.991809	−	0.127726i	$-0.959232\pi$
$379$	−3.83013	−	14.2942i	−0.196740	−	0.734245i	0.795069	−	0.606519i	$-0.207435\pi$
$380$		0			0
$381$	−15.6524	−	2.18257i	−0.801897	−	0.111816i
$382$		0			0
$383$	−8.51906	+	31.7936i	−0.435304	+	1.62458i	0.305035	+	0.952341i	$0.401332\pi$
$383$	−8.51906	+	31.7936i	−0.435304	+	1.62458i	−0.740339	+	0.672234i	$0.765335\pi$
$384$		0			0
$385$	−6.19615	−	6.19615i	−0.315785	−	0.315785i
$386$		0			0
$387$	−1.80234	+	6.33714i	−0.0916182	+	0.322135i
$388$		0			0
$389$	−22.4950			−1.14054			−0.570270	−	0.821457i	$-0.693161\pi$
$389$	−22.4950			−1.14054			−0.570270	+	0.821457i	$0.693161\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−5.17100	−	12.7590i	−0.260842	−	0.643605i
$394$		0			0
$395$	2.12976	+	2.12976i	0.107160	+	0.107160i
$396$		0			0
$397$	−3.56218	+	13.2942i	−0.178781	+	0.667218i	0.817096	+	0.576501i	$0.195582\pi$
$397$	−3.56218	+	13.2942i	−0.178781	+	0.667218i	−0.995877	+	0.0907168i	$0.971084\pi$
$398$		0			0
$399$	−1.30703	+	9.37341i	−0.0654332	+	0.469258i
$400$		0			0
$401$	3.22263	+	12.0270i	0.160931	+	0.600601i	0.998524	+	0.0543073i	$0.0172951\pi$
$401$	3.22263	+	12.0270i	0.160931	+	0.600601i	−0.837594	+	0.546294i	$0.816038\pi$
$402$		0			0
$403$	8.29423	−	9.43782i	0.413165	−	0.470131i
$404$		0			0
$405$	−9.87256	+	9.28636i	−0.490571	+	0.461443i
$406$		0			0
$407$	11.1430	+	19.3003i	0.552340	+	0.956681i
$408$		0			0
$409$	28.9904	+	7.76795i	1.43348	+	0.384100i	0.890246	−	0.455480i	$-0.150532\pi$
$409$	28.9904	+	7.76795i	1.43348	+	0.384100i	0.543236	+	0.839580i	$0.317199\pi$
$410$		0			0
$411$	−11.5559	+	1.43156i	−0.570011	+	0.0706135i
$412$		0			0
$413$	2.12976	−	3.68886i	0.104799	−	0.181517i
$414$		0			0
$415$		−	6.19615i		−	0.304157i
$416$		0			0
$417$	25.1244	+	19.5856i	1.23034	+	0.959113i
$418$		0			0
$419$	−8.23373	−	4.75374i	−0.402244	−	0.232236i	0.285208	−	0.958466i	$-0.407937\pi$
$419$	−8.23373	−	4.75374i	−0.402244	−	0.232236i	−0.687452	+	0.726230i	$0.741271\pi$
$420$		0			0
$421$	−7.83013	+	7.83013i	−0.381617	+	0.381617i	−0.871685	−	0.490067i	$-0.836972\pi$
$421$	−7.83013	+	7.83013i	−0.381617	+	0.381617i	0.490067	+	0.871685i	$0.336972\pi$
$422$		0			0
$423$	−0.276369	+	18.0695i	−0.0134375	+	0.878571i
$424$		0			0
$425$	−11.9226	+	6.88351i	−0.578330	+	0.333899i
$426$		0			0
$427$	−9.56218	+	2.56218i	−0.462746	+	0.123992i
$428$		0			0
$429$	−16.7729	−	19.4646i	−0.809803	−	0.939759i
$430$		0			0
$431$	−36.5473	+	9.79282i	−1.76042	+	0.471704i	−0.986800	−	0.161944i	$-0.948224\pi$
$431$	−36.5473	+	9.79282i	−1.76042	+	0.471704i	−0.773622	+	0.633648i	$0.781557\pi$
$432$		0			0
$433$	−26.8923	+	15.5263i	−1.29236	+	0.746145i	−0.979072	−	0.203512i	$-0.934764\pi$
$433$	−26.8923	+	15.5263i	−1.29236	+	0.746145i	−0.313289	+	0.949658i	$0.601431\pi$
$434$		0			0
$435$	−11.2697	−	14.9218i	−0.540339	−	0.715445i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.09808	−	0.633975i	−0.0524083	−	0.0302580i	0.473567	−	0.880758i	$-0.342966\pi$
$439$	−1.09808	−	0.633975i	−0.0524083	−	0.0302580i	−0.525975	+	0.850500i	$0.676300\pi$
$440$		0			0
$441$	14.5466	−	3.66025i	0.692694	−	0.174298i
$442$		0			0
$443$			11.2195i			0.533054i	0.963827	+	0.266527i	$0.0858762\pi$
$443$			11.2195i			0.533054i	−0.963827	+	0.266527i	$0.914124\pi$
$444$		0			0
$445$	7.02628	−	12.1699i	0.333078	−	0.576907i
$446$		0			0
$447$	1.83816	+	14.8382i	0.0869422	+	0.701821i
$448$		0			0
$449$	19.8710	+	5.32441i	0.937769	+	0.251275i	0.695165	−	0.718851i	$-0.255331\pi$
$449$	19.8710	+	5.32441i	0.937769	+	0.251275i	0.242605	+	0.970125i	$0.421998\pi$
$450$		0			0
$451$	11.5622	+	20.0263i	0.544442	+	0.943001i
$452$		0			0
$453$	−1.20888	−	0.511599i	−0.0567981	−	0.0240370i
$454$		0			0
$455$	6.38929	−	4.25953i	0.299535	−	0.199690i
$456$		0			0
$457$	−1.00962	−	3.76795i	−0.0472280	−	0.176257i	0.938283	−	0.345868i	$-0.112416\pi$
$457$	−1.00962	−	3.76795i	−0.0472280	−	0.176257i	−0.985511	+	0.169611i	$0.945749\pi$
$458$		0			0
$459$	−26.0314	+	2.82130i	−1.21504	+	0.131687i
$460$		0			0
$461$	5.50531	−	20.5461i	0.256408	−	0.956927i	−0.710894	−	0.703299i	$-0.751710\pi$
$461$	5.50531	−	20.5461i	0.256408	−	0.956927i	0.967302	−	0.253628i	$-0.0816238\pi$
$462$		0			0
$463$	−23.0526	−	23.0526i	−1.07134	−	1.07134i	−0.997251	−	0.0740918i	$-0.976394\pi$
$463$	−23.0526	−	23.0526i	−1.07134	−	1.07134i	−0.0740918	−	0.997251i	$-0.523606\pi$
$464$		0			0
$465$	−8.42417	+	3.41417i	−0.390661	+	0.158328i
$466$		0			0
$467$	−19.1679			−0.886984			−0.443492	−	0.896278i	$-0.646261\pi$
$467$	−19.1679			−0.886984			−0.443492	+	0.896278i	$0.646261\pi$
$468$		0			0
$469$	−8.39230			−0.387521
$470$		0			0
$471$	−7.71127	+	3.12525i	−0.355317	+	0.144004i
$472$		0			0
$473$	6.38929	+	6.38929i	0.293780	+	0.293780i
$474$		0			0
$475$	2.73205	−	10.1962i	0.125355	−	0.467832i
$476$		0			0
$477$	−1.62819	−	1.67877i	−0.0745496	−	0.0768655i
$478$		0			0
$479$	5.32441	+	19.8710i	0.243279	+	0.907928i	0.974241	+	0.225510i	$0.0724049\pi$
$479$	5.32441	+	19.8710i	0.243279	+	0.907928i	−0.730962	+	0.682418i	$0.760928\pi$
$480$		0			0
$481$	−18.5000	+	6.25833i	−0.843527	+	0.285355i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.27376	−	2.20622i	−0.0578385	−	0.100179i
$486$		0			0
$487$	−5.56218	−	1.49038i	−0.252046	−	0.0675356i	0.130584	−	0.991437i	$-0.458315\pi$
$487$	−5.56218	−	1.49038i	−0.252046	−	0.0675356i	−0.382630	+	0.923902i	$0.624982\pi$
$488$		0			0
$489$	−0.881808	−	7.11819i	−0.0398767	−	0.321896i
$490$		0			0
$491$	14.2612	−	24.7012i	0.643600	−	1.11475i	−0.341023	−	0.940055i	$-0.610773\pi$
$491$	14.2612	−	24.7012i	0.643600	−	1.11475i	0.984623	−	0.174693i	$-0.0558934\pi$
$492$		0			0
$493$		−	36.1244i		−	1.62696i
$494$		0			0
$495$	4.53590	+	18.0265i	0.203873	+	0.810233i
$496$		0			0
$497$	−3.68886	−	2.12976i	−0.165468	−	0.0955330i
$498$		0			0
$499$	2.46410	−	2.46410i	0.110308	−	0.110308i	−0.649798	−	0.760107i	$-0.725147\pi$
$499$	2.46410	−	2.46410i	0.110308	−	0.110308i	0.760107	+	0.649798i	$0.225147\pi$
$500$		0			0
$501$	14.0354	+	18.5839i	0.627057	+	0.830266i
$502$		0			0
$503$	−2.83286	+	1.63555i	−0.126311	+	0.0729256i	−0.561824	−	0.827257i	$-0.689900\pi$
$503$	−2.83286	+	1.63555i	−0.126311	+	0.0729256i	0.435513	+	0.900182i	$0.356567\pi$
$504$		0			0
$505$	−8.76795	+	2.34936i	−0.390169	+	0.104545i
$506$		0			0
$507$	19.6087	−	11.0679i	0.870854	−	0.491542i
$508$		0			0
$509$	−14.1568	+	3.79330i	−0.627489	+	0.168135i	−0.558530	−	0.829484i	$-0.688634\pi$
$509$	−14.1568	+	3.79330i	−0.627489	+	0.168135i	−0.0689588	+	0.997620i	$0.521968\pi$
$510$		0			0
$511$	1.56218	−	0.901924i	0.0691067	−	0.0398988i
$512$		0			0
$513$	12.5839	−	15.6431i	0.555591	−	0.690661i
$514$		0			0
$515$	−7.37772	+	7.37772i	−0.325101	+	0.325101i
$516$		0			0
$517$	21.4641	+	12.3923i	0.943990	+	0.545013i
$518$		0			0
$519$	23.8452	+	18.5885i	1.04669	+	0.815943i
$520$		0			0
$521$		−	2.49155i		−	0.109157i	−0.998509	−	0.0545785i	$-0.982618\pi$
$521$		−	2.49155i		−	0.109157i	0.998509	−	0.0545785i	$-0.0173815\pi$
$522$		0			0
$523$	−19.4904	+	33.7583i	−0.852255	+	1.47615i	0.0269137	+	0.999638i	$0.491432\pi$
$523$	−19.4904	+	33.7583i	−0.852255	+	1.47615i	−0.879169	+	0.476511i	$0.841901\pi$
$524$		0			0
$525$	6.64136	−	0.822738i	0.289853	−	0.0359072i
$526$		0			0
$527$	−16.9617	−	4.54486i	−0.738862	−	0.197977i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	−7.89343	+	4.39771i	−0.342546	+	0.190845i
$532$		0			0
$533$	−19.1959	+	6.49373i	−0.831465	+	0.281275i
$534$		0			0
$535$	−7.41154	−	27.6603i	−0.320429	−	1.19586i
$536$		0			0
$537$	−6.34978	+	45.5378i	−0.274013	+	1.96510i
$538$		0			0
$539$	5.32441	−	19.8710i	0.229339	−	0.855904i
$540$		0			0
$541$	−12.6865	−	12.6865i	−0.545437	−	0.545437i	0.379681	−	0.925118i	$-0.376034\pi$
$541$	−12.6865	−	12.6865i	−0.545437	−	0.545437i	−0.925118	+	0.379681i	$0.876034\pi$
$542$		0			0
$543$	1.95171	+	4.81568i	0.0837561	+	0.206661i
$544$		0			0
$545$	28.1047			1.20387
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$	20.1990	+	5.74477i	0.862070	+	0.245181i
$550$		0			0
$551$	19.5856	+	19.5856i	0.834376	+	0.834376i
$552$		0			0
$553$	0.732051	−	2.73205i	0.0311300	−	0.116179i
$554$		0			0
$555$	13.9934	+	1.95124i	0.593988	+	0.0828255i
$556$		0			0
$557$	−6.62616	−	24.7292i	−0.280759	−	1.04781i	−0.951883	−	0.306462i	$-0.900855\pi$
$557$	−6.62616	−	24.7292i	−0.280759	−	1.04781i	0.671123	−	0.741346i	$-0.265812\pi$
$558$		0			0
$559$	−6.58846	+	4.39230i	−0.278662	+	0.185775i
$560$		0			0
$561$	−13.9955	+	33.0706i	−0.590891	+	1.39624i
$562$		0			0
$563$	5.03908	+	8.72794i	0.212372	+	0.367839i	0.952456	−	0.304675i	$-0.0985479\pi$
$563$	5.03908	+	8.72794i	0.212372	+	0.367839i	−0.740085	+	0.672514i	$0.765215\pi$
$564$		0			0
$565$	−14.9641	−	4.00962i	−0.629544	−	0.168686i
$566$		0			0
$567$	12.1877	+	3.66867i	0.511837	+	0.154070i
$568$		0			0
$569$	−1.35022	+	2.33864i	−0.0566040	+	0.0980411i	−0.892939	−	0.450178i	$-0.851361\pi$
$569$	−1.35022	+	2.33864i	−0.0566040	+	0.0980411i	0.836335	+	0.548219i	$0.184694\pi$
$570$		0			0
$571$		−	1.94744i		−	0.0814979i	−0.999169	−	0.0407489i	$-0.987026\pi$
$571$		−	1.94744i		−	0.0814979i	0.999169	−	0.0407489i	$-0.0129744\pi$
$572$		0			0
$573$	5.14359	−	6.59817i	0.214877	−	0.275643i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−22.4904	+	22.4904i	−0.936287	+	0.936287i	−0.998088	−	0.0618016i	$-0.980315\pi$
$577$	−22.4904	+	22.4904i	−0.936287	+	0.936287i	0.0618016	+	0.998088i	$0.480315\pi$
$578$		0			0
$579$	0.191705	−	0.144785i	0.00796700	−	0.00601707i
$580$		0			0
$581$	−5.03908	+	2.90931i	−0.209056	+	0.120699i
$582$		0			0
$583$	−3.09808	+	0.830127i	−0.128309	+	0.0343803i
$584$		0			0
$585$	−16.2699	+	0.799664i	−0.672679	+	0.0330620i
$586$		0			0
$587$	18.0265	−	4.83020i	0.744035	−	0.199364i	0.133164	−	0.991094i	$-0.457486\pi$
$587$	18.0265	−	4.83020i	0.744035	−	0.199364i	0.610871	+	0.791730i	$0.290819\pi$
$588$		0			0
$589$	11.6603	−	6.73205i	0.480452	−	0.277389i
$590$		0			0
$591$	5.68671	−	4.29488i	0.233920	−	0.176668i
$592$		0			0
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	−0.887119	−	0.461541i	$-0.847297\pi$
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	0.461541	+	0.887119i	$0.347297\pi$
$594$		0			0
$595$	−9.29423	−	5.36603i	−0.381026	−	0.219986i
$596$		0			0
$597$	−13.7670	+	17.6603i	−0.563446	+	0.722786i
$598$		0			0
$599$		−	20.7270i		−	0.846881i	−0.905924	−	0.423441i	$-0.860822\pi$
$599$		−	20.7270i		−	0.846881i	0.905924	−	0.423441i	$-0.139178\pi$
$600$		0			0
$601$	−11.7942	+	20.4282i	−0.481097	+	0.833284i	−0.999765	−	0.0216919i	$-0.993095\pi$
$601$	−11.7942	+	20.4282i	−0.481097	+	0.833284i	0.518668	+	0.854976i	$0.326428\pi$
$602$		0			0
$603$	15.2797	+	9.13612i	0.622238	+	0.372052i
$604$		0			0
$605$	8.62350	+	2.31066i	0.350595	+	0.0939417i
$606$		0			0
$607$	−0.0980762	−	0.169873i	−0.00398079	−	0.00689493i	0.864028	−	0.503444i	$-0.167934\pi$
$607$	−0.0980762	−	0.169873i	−0.00398079	−	0.00689493i	−0.868009	+	0.496549i	$0.834600\pi$
$608$		0			0
$609$	−6.84378	+	16.1715i	−0.277324	+	0.655301i
$610$		0			0
$611$	−14.3377	+	16.3145i	−0.580041	+	0.660016i
$612$		0			0
$613$	−11.3564	−	42.3827i	−0.458681	−	1.71182i	−0.677035	−	0.735951i	$-0.736735\pi$
$613$	−11.3564	−	42.3827i	−0.458681	−	1.71182i	0.218354	−	0.975870i	$-0.429931\pi$
$614$		0			0
$615$	14.5198	+	2.02463i	0.585494	+	0.0816411i
$616$		0			0
$617$	4.78173	−	17.8457i	0.192505	−	0.718439i	−0.800393	−	0.599475i	$-0.795376\pi$
$617$	4.78173	−	17.8457i	0.192505	−	0.718439i	0.992899	−	0.118964i	$-0.0379573\pi$
$618$		0			0
$619$	31.6603	+	31.6603i	1.27253	+	1.27253i	0.944755	+	0.327778i	$0.106300\pi$
$619$	31.6603	+	31.6603i	1.27253	+	1.27253i	0.327778	+	0.944755i	$0.393700\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−13.1963			−0.528701
$624$		0			0
$625$	3.87564			0.155026
$626$		0			0
$627$	−10.3420	−	25.5180i	−0.413019	−	1.01909i
$628$		0			0
$629$	19.3003	+	19.3003i	0.769554	+	0.769554i
$630$		0			0
$631$	−5.73205	+	21.3923i	−0.228189	+	0.851614i	0.752912	+	0.658121i	$0.228648\pi$
$631$	−5.73205	+	21.3923i	−0.228189	+	0.851614i	−0.981102	+	0.193493i	$0.938018\pi$
$632$		0			0
$633$	−0.431485	+	3.09442i	−0.0171500	+	0.122992i
$634$		0			0
$635$	3.55644	+	13.2728i	0.141133	+	0.526715i
$636$		0			0
$637$	16.1603	+	7.99038i	0.640293	+	0.316590i
$638$		0			0
$639$	4.39771	+	7.89343i	0.173971	+	0.312259i
$640$		0			0
$641$	22.6758	+	39.2757i	0.895642	+	1.55130i	0.833008	+	0.553261i	$0.186617\pi$
$641$	22.6758	+	39.2757i	0.895642	+	1.55130i	0.0626345	+	0.998037i	$0.480050\pi$
$642$		0			0
$643$	−7.00000	−	1.87564i	−0.276053	−	0.0739682i	0.118136	−	0.992997i	$-0.462308\pi$
$643$	−7.00000	−	1.87564i	−0.276053	−	0.0739682i	−0.394190	+	0.919029i	$0.628975\pi$
$644$		0			0
$645$	5.68503	−	0.704266i	0.223848	−	0.0277305i
$646$		0			0
$647$	8.23373	−	14.2612i	0.323701	−	0.560667i	−0.657547	−	0.753413i	$-0.728406\pi$
$647$	8.23373	−	14.2612i	0.323701	−	0.560667i	0.981249	+	0.192746i	$0.0617394\pi$
$648$		0			0
$649$			12.3923i			0.486441i
$650$		0			0
$651$	6.73205	+	5.24796i	0.263850	+	0.205684i
$652$		0			0
$653$	−8.36615	−	4.83020i	−0.327393	−	0.189020i	0.327290	−	0.944924i	$-0.393865\pi$
$653$	−8.36615	−	4.83020i	−0.327393	−	0.189020i	−0.654683	+	0.755904i	$0.727198\pi$
$654$		0			0
$655$	−8.46410	+	8.46410i	−0.330720	+	0.330720i
$656$		0			0
$657$	−3.82609	−	0.0585190i	−0.149270	−	0.00228304i
$658$		0			0
$659$	−23.4834	+	13.5581i	−0.914783	+	0.528150i	−0.881967	−	0.471311i	$-0.843781\pi$
$659$	−23.4834	+	13.5581i	−0.914783	+	0.528150i	−0.0328158	+	0.999461i	$0.510447\pi$
$660$		0			0
$661$	9.42820	−	2.52628i	0.366715	−	0.0982609i	−0.0707559	−	0.997494i	$-0.522541\pi$
$661$	9.42820	−	2.52628i	0.366715	−	0.0982609i	0.437470	+	0.899233i	$0.355874\pi$
$662$		0			0
$663$	−26.0126	−	17.7100i	−1.01024	−	0.687801i
$664$		0			0
$665$	7.94839	−	2.12976i	0.308225	−	0.0825887i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−27.0457	−	35.8103i	−1.04565	−	1.38451i
$670$		0			0
$671$	20.3652	−	20.3652i	0.786189	−	0.786189i
$672$		0			0
$673$	−36.9904	−	21.3564i	−1.42587	−	0.823229i	−0.429082	−	0.903265i	$-0.641163\pi$
$673$	−36.9904	−	21.3564i	−1.42587	−	0.823229i	−0.996792	+	0.0800364i	$0.974496\pi$
$674$		0			0
$675$	−12.9875	−	5.73205i	−0.499888	−	0.220627i
$676$		0			0
$677$			9.66040i			0.371279i	0.982618	+	0.185640i	$0.0594357\pi$
$677$			9.66040i			0.371279i	−0.982618	+	0.185640i	$0.940564\pi$
$678$		0			0
$679$	−1.19615	+	2.07180i	−0.0459041	+	0.0795083i
$680$		0			0
$681$	−4.31769	−	34.8536i	−0.165454	−	1.33559i
$682$		0			0
$683$	45.2752	+	12.1315i	1.73241	+	0.464198i	0.980736	−	0.195338i	$-0.0625804\pi$
$683$	45.2752	+	12.1315i	1.73241	+	0.464198i	0.751673	+	0.659536i	$0.229247\pi$
$684$		0			0
$685$	5.06218	+	8.76795i	0.193416	+	0.335006i
$686$		0			0
$687$	−31.8617	−	13.4839i	−1.21560	−	0.514443i
$688$		0			0
$689$	−0.180895	−	2.80487i	−0.00689154	−	0.106857i
$690$		0			0
$691$	−4.88269	−	18.2224i	−0.185746	−	0.693214i	−0.994470	−	0.105025i	$-0.966508\pi$
$691$	−4.88269	−	18.2224i	−0.185746	−	0.693214i	0.808723	−	0.588189i	$-0.200159\pi$
$692$		0			0
$693$	12.5305	−	12.1530i	0.475994	−	0.461653i
$694$		0			0
$695$	7.16884	−	26.7545i	0.271930	−	1.01486i
$696$		0			0
$697$	20.0263	+	20.0263i	0.758549	+	0.758549i
$698$		0			0
$699$	−28.0207	+	11.3563i	−1.05984	+	0.429535i
$700$		0			0
$701$	−12.7786			−0.482641			−0.241320	−	0.970446i	$-0.577580\pi$
$701$	−12.7786			−0.482641			−0.241320	+	0.970446i	$0.577580\pi$
$702$		0			0
$703$	−20.9282			−0.789322
$704$		0			0
$705$	14.5623	−	5.90185i	0.548448	−	0.222277i
$706$		0			0
$707$	6.02751	+	6.02751i	0.226688	+	0.226688i
$708$		0			0
$709$	−3.03590	+	11.3301i	−0.114016	+	0.425512i	−0.999211	−	0.0397068i	$-0.987358\pi$
$709$	−3.03590	+	11.3301i	−0.114016	+	0.425512i	0.885196	+	0.465219i	$0.154024\pi$
$710$		0			0
$711$	−4.30703	+	4.17726i	−0.161526	+	0.156660i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−9.90192	+	20.0263i	−0.370311	+	0.748940i
$716$		0			0
$717$	14.8842	+	6.29899i	0.555859	+	0.235240i
$718$		0			0
$719$	3.68886	+	6.38929i	0.137571	+	0.238280i	0.926577	−	0.376106i	$-0.122737\pi$
$719$	3.68886	+	6.38929i	0.137571	+	0.238280i	−0.789005	+	0.614386i	$0.789404\pi$
$720$		0			0
$721$	9.46410	+	2.53590i	0.352462	+	0.0944418i
$722$		0			0
$723$	−3.10003	−	25.0243i	−0.115292	−	0.930665i
$724$		0			0
$725$	9.79282	−	16.9617i	0.363696	−	0.629940i
$726$		0			0
$727$			19.5167i			0.723833i	0.932211	+	0.361916i	$0.117877\pi$
$727$			19.5167i			0.723833i	−0.932211	+	0.361916i	$0.882123\pi$
$728$		0			0
$729$	−18.1962	−	19.9474i	−0.673932	−	0.738794i
$730$		0			0
$731$	9.58394	+	5.53329i	0.354475	+	0.204656i
$732$		0			0
$733$	−6.77757	+	6.77757i	−0.250335	+	0.250335i	−0.821108	−	0.570773i	$-0.806644\pi$
$733$	−6.77757	+	6.77757i	−0.250335	+	0.250335i	0.570773	+	0.821108i	$0.306644\pi$
$734$		0			0
$735$	−7.86017	−	10.4074i	−0.289927	−	0.383883i
$736$		0			0
$737$	21.1447	−	12.2079i	0.778876	−	0.449685i
$738$		0			0
$739$	11.1244	−	2.98076i	0.409216	−	0.109649i	−0.0483378	−	0.998831i	$-0.515392\pi$
$739$	11.1244	−	2.98076i	0.409216	−	0.109649i	0.457554	+	0.889182i	$0.348726\pi$
$740$		0			0
$741$	23.7052	−	4.50141i	0.870833	−	0.165363i
$742$		0			0
$743$	−8.51906	+	2.28268i	−0.312534	+	0.0837432i	−0.411677	−	0.911330i	$-0.635057\pi$
$743$	−8.51906	+	2.28268i	−0.312534	+	0.0837432i	0.0991426	+	0.995073i	$0.468390\pi$
$744$		0			0
$745$	11.2583	−	6.50000i	0.412473	−	0.238142i
$746$		0			0
$747$	12.3417	+	0.188763i	0.451560	+	0.00690649i
$748$		0			0
$749$	−19.0150	+	19.0150i	−0.694792	+	0.694792i
$750$		0			0
$751$	29.2750	+	16.9019i	1.06826	+	0.616760i	0.927705	−	0.373313i	$-0.121778\pi$
$751$	29.2750	+	16.9019i	1.06826	+	0.616760i	0.140554	+	0.990073i	$0.455112\pi$
$752$		0			0
$753$	1.35022	+	1.05256i	0.0492046	+	0.0383574i
$754$		0			0
$755$			1.14134i			0.0415375i
$756$		0			0
$757$	−8.39230	+	14.5359i	−0.305024	+	0.528316i	−0.977267	−	0.212014i	$-0.931998\pi$
$757$	−8.39230	+	14.5359i	−0.305024	+	0.528316i	0.672243	+	0.740331i	$0.265331\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−17.7412	−	4.75374i	−0.643118	−	0.172323i	−0.0775029	−	0.996992i	$-0.524695\pi$
$761$	−17.7412	−	4.75374i	−0.643118	−	0.172323i	−0.565616	+	0.824669i	$0.691361\pi$
$762$		0			0
$763$	−13.1962	−	22.8564i	−0.477733	−	0.827457i
$764$		0			0
$765$	11.0802	+	19.8878i	0.400606	+	0.719045i
$766$		0			0
$767$	−10.6488	−	2.12976i	−0.384507	−	0.0769014i
$768$		0			0
$769$	−10.8301	−	40.4186i	−0.390544	−	1.45753i	−0.829238	−	0.558895i	$-0.811225\pi$
$769$	−10.8301	−	40.4186i	−0.390544	−	1.45753i	0.438694	−	0.898636i	$-0.355441\pi$
$770$		0			0
$771$	−5.14442	+	36.8935i	−0.185272	+	1.32869i
$772$		0			0
$773$	−11.1430	+	41.5864i	−0.400787	+	1.49576i	0.410908	+	0.911677i	$0.365212\pi$
$773$	−11.1430	+	41.5864i	−0.400787	+	1.49576i	−0.811695	+	0.584081i	$0.801455\pi$
$774$		0			0
$775$	−6.73205	−	6.73205i	−0.241822	−	0.241822i
$776$		0			0
$777$	−4.98354	−	12.2965i	−0.178784	−	0.441133i
$778$		0			0
$779$	−21.7154			−0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	30.0651	−	21.9928i	1.07444	−	0.785957i
$784$		0			0
$785$	5.11553	+	5.11553i	0.182581	+	0.182581i
$786$		0			0
$787$	−4.29423	+	16.0263i	−0.153073	+	0.571275i	0.846190	+	0.532881i	$0.178891\pi$
$787$	−4.29423	+	16.0263i	−0.153073	+	0.571275i	−0.999263	+	0.0383938i	$0.987776\pi$
$788$		0			0
$789$	−38.2307	−	5.33089i	−1.36105	−	0.189785i
$790$		0			0
$791$	3.76532	+	14.0524i	0.133879	+	0.499644i
$792$		0			0
$793$	14.0000	+	21.0000i	0.497155	+	0.745732i
$794$		0			0
$795$	−0.792486	+	1.87260i	−0.0281066	+	0.0664143i
$796$		0			0
$797$	−20.1563	−	34.9118i	−0.713973	−	1.23664i	−0.963354	−	0.268232i	$-0.913561\pi$
$797$	−20.1563	−	34.9118i	−0.713973	−	1.23664i	0.249381	−	0.968405i	$-0.419773\pi$
$798$		0			0
$799$	29.3205	+	7.85641i	1.03729	+	0.277940i
$800$		0			0
$801$	24.0264	+	14.3660i	0.848929	+	0.507596i
$802$		0			0
$803$	−2.62398	+	4.54486i	−0.0925982	+	0.160385i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.2679	−	19.5856i	0.537457	−	0.689447i
$808$		0			0
$809$	−24.0261	−	13.8715i	−0.844712	−	0.487694i	0.0141514	−	0.999900i	$-0.495495\pi$
$809$	−24.0261	−	13.8715i	−0.844712	−	0.487694i	−0.858863	+	0.512205i	$0.828829\pi$
$810$		0			0
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	−0.957062	−	0.289882i	$-0.906384\pi$
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	0.289882	+	0.957062i	$0.406384\pi$
$812$		0			0
$813$	−10.6804	+	8.06639i	−0.374579	+	0.282901i
$814$		0			0
$815$	−5.40087	+	3.11819i	−0.189184	+	0.109226i
$816$		0			0
$817$	−8.19615	+	2.19615i	−0.286747	+	0.0768336i
$818$		0			0
$819$	8.28964	+	12.8562i	0.289664	+	0.449232i
$820$		0			0
$821$	41.5864	−	11.1430i	1.45137	−	0.388895i	0.554873	−	0.831935i	$-0.312767\pi$
$821$	41.5864	−	11.1430i	1.45137	−	0.388895i	0.896502	+	0.443040i	$0.146100\pi$
$822$		0			0
$823$	7.39230	−	4.26795i	0.257680	−	0.148771i	−0.365596	−	0.930774i	$-0.619135\pi$
$823$	7.39230	−	4.26795i	0.257680	−	0.148771i	0.623276	+	0.782002i	$0.285801\pi$
$824$		0			0
$825$	−15.5364	+	11.7338i	−0.540907	+	0.408519i
$826$		0			0
$827$	−31.7936	+	31.7936i	−1.10557	+	1.10557i	−0.111845	+	0.993726i	$0.535676\pi$
$827$	−31.7936	+	31.7936i	−1.10557	+	1.10557i	−0.993726	+	0.111845i	$0.964324\pi$
$828$		0			0
$829$	41.6769	+	24.0622i	1.44750	+	0.835714i	0.998332	−	0.0577338i	$-0.0183875\pi$
$829$	41.6769	+	24.0622i	1.44750	+	0.835714i	0.449167	+	0.893448i	$0.351721\pi$
$830$		0			0
$831$	29.3785	−	37.6865i	1.01913	−	1.30733i
$832$		0			0
$833$		−	25.1954i		−	0.872968i
$834$		0			0
$835$	10.1244	−	17.5359i	0.350368	−	0.606855i
$836$		0			0
$837$	−6.54383	−	16.8836i	−0.226188	−	0.583582i
$838$		0			0
$839$	−9.79282	−	2.62398i	−0.338086	−	0.0905898i	0.0857819	−	0.996314i	$-0.472661\pi$
$839$	−9.79282	−	2.62398i	−0.338086	−	0.0905898i	−0.423868	+	0.905724i	$0.639328\pi$
$840$		0			0
$841$	11.1962	+	19.3923i	0.386074	+	0.668700i
$842$		0			0
$843$	11.5814	−	27.3662i	0.398884	−	0.942540i
$844$		0			0
$845$	−15.5070	−	11.9506i	−0.533457	−	0.411112i
$846$		0			0
$847$	−2.16987	−	8.09808i	−0.0745577	−	0.278253i
$848$		0			0
$849$	11.3022	+	1.57598i	0.387890	+	0.0540873i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−22.3660	−	22.3660i	−0.765798	−	0.765798i	0.211566	−	0.977364i	$-0.432144\pi$
$853$	−22.3660	−	22.3660i	−0.765798	−	0.765798i	−0.977364	+	0.211566i	$0.932144\pi$
$854$		0			0
$855$	−16.7900	−	4.77524i	−0.574207	−	0.163310i
$856$		0			0
$857$	−3.32707			−0.113651			−0.0568253	−	0.998384i	$-0.518098\pi$
$857$	−3.32707			−0.113651			−0.0568253	+	0.998384i	$0.518098\pi$
$858$		0			0
$859$	−39.1769			−1.33670			−0.668350	−	0.743847i	$-0.732999\pi$
$859$	−39.1769			−1.33670			−0.668350	+	0.743847i	$0.732999\pi$
$860$		0			0
$861$	−5.17100	−	12.7590i	−0.176227	−	0.434825i
$862$		0			0
$863$	−18.2354	−	18.2354i	−0.620741	−	0.620741i	0.324980	−	0.945721i	$-0.394642\pi$
$863$	−18.2354	−	18.2354i	−0.620741	−	0.620741i	−0.945721	+	0.324980i	$0.894642\pi$
$864$		0			0
$865$	6.80385	−	25.3923i	0.231338	−	0.863364i
$866$		0			0
$867$	−2.00746	+	14.3966i	−0.0681769	+	0.488935i
$868$		0			0
$869$	2.12976	+	7.94839i	0.0722473	+	0.269631i
$870$		0			0
$871$	6.85641	+	20.2679i	0.232320	+	0.686753i
$872$		0			0
$873$	4.43324	−	2.46991i	0.150042	−	0.0835939i
$874$		0			0
$875$	−8.23373	−	14.2612i	−0.278351	−	0.482118i
$876$		0			0
$877$	28.9904	+	7.76795i	0.978936	+	0.262305i	0.712596	−	0.701574i	$-0.247519\pi$
$877$	28.9904	+	7.76795i	0.978936	+	0.262305i	0.266339	+	0.963879i	$0.414186\pi$
$878$		0			0
$879$	3.09640	−	0.383584i	0.104439	−	0.0129380i
$880$		0			0
$881$	−11.7417	+	20.3372i	−0.395588	+	0.685178i	−0.993176	−	0.116625i	$-0.962792\pi$
$881$	−11.7417	+	20.3372i	−0.395588	+	0.685178i	0.597588	+	0.801803i	$0.296126\pi$
$882$		0			0
$883$		−	33.3731i		−	1.12309i	−0.827445	−	0.561547i	$-0.810207\pi$
$883$		−	33.3731i		−	1.12309i	0.827445	−	0.561547i	$-0.189793\pi$
$884$		0			0
$885$	6.19615	+	4.83020i	0.208281	+	0.162365i
$886$		0			0
$887$	−21.8683	−	12.6257i	−0.734266	−	0.423929i	0.0857146	−	0.996320i	$-0.472683\pi$
$887$	−21.8683	−	12.6257i	−0.734266	−	0.423929i	−0.819981	+	0.572391i	$0.806016\pi$
$888$		0			0
$889$	9.12436	−	9.12436i	0.306021	−	0.306021i
$890$		0			0
$891$	−36.0441	+	8.48560i	−1.20752	+	0.284278i
$892$		0			0
$893$	−20.1563	+	11.6373i	−0.674505	+	0.389426i
$894$		0			0
$895$	38.6147	−	10.3468i	1.29075	−	0.345855i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	24.1305	−	6.46575i	0.804797	−	0.215645i
$900$		0			0
$901$	−3.40192	+	1.96410i	−0.113335	+	0.0654337i
$902$		0			0
$903$	−3.24207	−	4.29272i	−0.107889	−	0.142853i
$904$		0			0
$905$	3.19465	−	3.19465i	0.106194	−	0.106194i
$906$		0			0
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	0.727915	−	0.685668i	$-0.240490\pi$
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	−0.229848	+	0.973227i	$0.573823\pi$
$908$		0			0
$909$	−4.41244	−	17.5359i	−0.146351	−	0.581629i
$910$		0			0
$911$		−	1.55910i		−	0.0516552i	−0.999666	−	0.0258276i	$-0.991778\pi$
$911$		−	1.55910i		−	0.0516552i	0.999666	−	0.0258276i	$-0.00822209\pi$
$912$		0			0
$913$	8.46410	−	14.6603i	0.280121	−	0.485184i
$914$		0			0
$915$	−2.24477	−	18.1204i	−0.0742099	−	0.599043i
$916$		0			0
$917$	10.8577	+	2.90931i	0.358553	+	0.0960740i
$918$		0			0
$919$	6.70577	+	11.6147i	0.221203	+	0.383135i	0.955174	−	0.296046i	$-0.0956683\pi$
$919$	6.70577	+	11.6147i	0.221203	+	0.383135i	−0.733971	+	0.679181i	$0.762335\pi$
$920$		0			0
$921$	−18.9314	−	8.01177i	−0.623809	−	0.263997i
$922$		0			0
$923$	−2.12976	+	10.6488i	−0.0701021	+	0.350510i
$924$		0			0
$925$	3.83013	+	14.2942i	0.125934	+	0.469991i
$926$		0			0
$927$	−14.4705	−	14.9200i	−0.475272	−	0.490036i
$928$		0			0
$929$	5.27594	−	19.6901i	0.173098	−	0.646011i	−0.823770	−	0.566924i	$-0.808133\pi$
$929$	5.27594	−	19.6901i	0.173098	−	0.646011i	0.996868	−	0.0790861i	$-0.0252002\pi$
$930$		0			0
$931$	13.6603	+	13.6603i	0.447697	+	0.447697i
$932$		0			0
$933$	16.1777	−	6.55656i	0.529635	−	0.214652i
$934$		0			0
$935$	31.2229			1.02110
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$		0			0
$939$	3.21046	−	1.30114i	0.104769	−	0.0424612i
$940$		0			0
$941$	9.14570	+	9.14570i	0.298141	+	0.298141i	0.840285	−	0.542144i	$-0.182387\pi$
$941$	9.14570	+	9.14570i	0.298141	+	0.298141i	−0.542144	+	0.840285i	$0.682387\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−1.19242	−	11.0022i	−0.0387895	−	0.357900i
$946$		0			0
$947$	−2.77689	−	10.3635i	−0.0902368	−	0.336768i	0.906018	−	0.423240i	$-0.139107\pi$
$947$	−2.77689	−	10.3635i	−0.0902368	−	0.336768i	−0.996254	+	0.0864720i	$0.972441\pi$
$948$		0			0
$949$	−3.45448	−	3.03590i	−0.112137	−	0.0985494i
$950$		0			0
$951$	25.6076	+	10.8372i	0.830385	+	0.351420i
$952$		0			0
$953$	0.988427	+	1.71201i	0.0320183	+	0.0554573i	0.881591	−	0.472015i	$-0.156473\pi$
$953$	0.988427	+	1.71201i	0.0320183	+	0.0554573i	−0.849572	+	0.527472i	$0.823140\pi$
$954$		0			0
$955$	−7.02628	−	1.88269i	−0.227365	−	0.0609223i
$956$		0			0
$957$	−6.28076	−	50.7000i	−0.203028	−	1.63890i
$958$		0			0
$959$	4.75374	−	8.23373i	0.153506	−	0.265881i
$960$		0			0
$961$			18.8564i			0.608271i
$962$		0			0
$963$	55.3205	−	13.9199i	1.78268	−	0.448563i
$964$		0			0
$965$	−0.180895	−	0.104440i	−0.00582321	−	0.00336203i
$966$		0			0
$967$	27.8564	−	27.8564i	0.895802	−	0.895802i	−0.0992599	−	0.995062i	$-0.531648\pi$
$967$	27.8564	−	27.8564i	0.895802	−	0.895802i	0.995062	+	0.0992599i	$0.0316475\pi$
$968$		0			0
$969$	−20.3236	−	26.9098i	−0.652887	−	0.864467i
$970$		0			0
$971$	41.4335	−	23.9216i	1.32966	−	0.767682i	0.344416	−	0.938817i	$-0.388077\pi$
$971$	41.4335	−	23.9216i	1.32966	−	0.767682i	0.985247	+	0.171136i	$0.0547436\pi$
$972$		0			0
$973$	−25.1244	+	6.73205i	−0.805450	+	0.215820i
$974$		0			0
$975$	−7.41287	−	15.3671i	−0.237402	−	0.492143i
$976$		0			0
$977$	−22.8847	+	6.13194i	−0.732147	+	0.196178i	−0.605585	−	0.795780i	$-0.707061\pi$
$977$	−22.8847	+	6.13194i	−0.732147	+	0.196178i	−0.126562	+	0.991959i	$0.540394\pi$
$978$		0			0
$979$	33.2487	−	19.1962i	1.06263	−	0.613512i
$980$		0			0
$981$	−0.856198	+	55.9800i	−0.0273363	+	1.78730i
$982$		0			0
$983$	−30.4433	+	30.4433i	−0.970992	+	0.970992i	−0.999591	−	0.0285990i	$-0.990895\pi$
$983$	−30.4433	+	30.4433i	−0.970992	+	0.970992i	0.0285990	+	0.999591i	$0.490895\pi$
$984$		0			0
$985$	−5.36603	−	3.09808i	−0.170976	−	0.0987129i
$986$		0			0
$987$	−11.6373	−	9.07180i	−0.370418	−	0.288758i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−28.7846	+	49.8564i	−0.914373	+	1.58374i	−0.106557	+	0.994307i	$0.533983\pi$
$991$	−28.7846	+	49.8564i	−0.914373	+	1.58374i	−0.807816	+	0.589434i	$0.799351\pi$
$992$		0			0
$993$	58.8186	−	7.28650i	1.86655	−	0.231230i
$994$		0			0
$995$	18.8061	+	5.03908i	0.596193	+	0.159750i
$996$		0			0
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	0.916112	−	0.400923i	$-0.131311\pi$
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	−0.805266	+	0.592914i	$0.797977\pi$
$998$		0			0
$999$	−4.31286	+	27.8132i	−0.136453	+	0.879970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.c.305.2		8
3.2	odd	2	inner	624.2.cn.c.305.1		8
4.3	odd	2		39.2.k.b.32.2	yes	8
12.11	even	2		39.2.k.b.32.1	yes	8
13.11	odd	12	inner	624.2.cn.c.401.1		8
20.3	even	4		975.2.bp.e.149.1		8
20.7	even	4		975.2.bp.f.149.2		8
20.19	odd	2		975.2.bo.d.851.1		8
39.11	even	12	inner	624.2.cn.c.401.2		8
52.3	odd	6		507.2.k.e.80.1		8
52.7	even	12		507.2.f.f.437.3		8
52.11	even	12		39.2.k.b.11.1	✓	8
52.15	even	12		507.2.k.d.89.2		8
52.19	even	12		507.2.f.e.437.2		8
52.23	odd	6		507.2.k.f.80.2		8
52.31	even	4		507.2.k.f.488.1		8
52.35	odd	6		507.2.f.f.239.2		8
52.43	odd	6		507.2.f.e.239.3		8
52.47	even	4		507.2.k.e.488.2		8
52.51	odd	2		507.2.k.d.188.1		8
60.23	odd	4		975.2.bp.e.149.2		8
60.47	odd	4		975.2.bp.f.149.1		8
60.59	even	2		975.2.bo.d.851.2		8
156.11	odd	12		39.2.k.b.11.2	yes	8
156.23	even	6		507.2.k.f.80.1		8
156.35	even	6		507.2.f.f.239.3		8
156.47	odd	4		507.2.k.e.488.1		8
156.59	odd	12		507.2.f.f.437.2		8
156.71	odd	12		507.2.f.e.437.3		8
156.83	odd	4		507.2.k.f.488.2		8
156.95	even	6		507.2.f.e.239.2		8
156.107	even	6		507.2.k.e.80.2		8
156.119	odd	12		507.2.k.d.89.1		8
156.155	even	2		507.2.k.d.188.2		8
260.63	odd	12		975.2.bp.f.674.1		8
260.167	odd	12		975.2.bp.e.674.2		8
260.219	even	12		975.2.bo.d.401.2		8
780.167	even	12		975.2.bp.e.674.1		8
780.323	even	12		975.2.bp.f.674.2		8
780.479	odd	12		975.2.bo.d.401.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	52.11	even	12
39.2.k.b.11.2	yes	8	156.11	odd	12
39.2.k.b.32.1	yes	8	12.11	even	2
39.2.k.b.32.2	yes	8	4.3	odd	2
507.2.f.e.239.2		8	156.95	even	6
507.2.f.e.239.3		8	52.43	odd	6
507.2.f.e.437.2		8	52.19	even	12
507.2.f.e.437.3		8	156.71	odd	12
507.2.f.f.239.2		8	52.35	odd	6
507.2.f.f.239.3		8	156.35	even	6
507.2.f.f.437.2		8	156.59	odd	12
507.2.f.f.437.3		8	52.7	even	12
507.2.k.d.89.1		8	156.119	odd	12
507.2.k.d.89.2		8	52.15	even	12
507.2.k.d.188.1		8	52.51	odd	2
507.2.k.d.188.2		8	156.155	even	2
507.2.k.e.80.1		8	52.3	odd	6
507.2.k.e.80.2		8	156.107	even	6
507.2.k.e.488.1		8	156.47	odd	4
507.2.k.e.488.2		8	52.47	even	4
507.2.k.f.80.1		8	156.23	even	6
507.2.k.f.80.2		8	52.23	odd	6
507.2.k.f.488.1		8	52.31	even	4
507.2.k.f.488.2		8	156.83	odd	4
624.2.cn.c.305.1		8	3.2	odd	2	inner
624.2.cn.c.305.2		8	1.1	even	1	trivial
624.2.cn.c.401.1		8	13.11	odd	12	inner
624.2.cn.c.401.2		8	39.11	even	12	inner
975.2.bo.d.401.1		8	780.479	odd	12
975.2.bo.d.401.2		8	260.219	even	12
975.2.bo.d.851.1		8	20.19	odd	2
975.2.bo.d.851.2		8	60.59	even	2
975.2.bp.e.149.1		8	20.3	even	4
975.2.bp.e.149.2		8	60.23	odd	4
975.2.bp.e.674.1		8	780.167	even	12
975.2.bp.e.674.2		8	260.167	odd	12
975.2.bp.f.149.1		8	60.47	odd	4
975.2.bp.f.149.2		8	20.7	even	4
975.2.bp.f.674.1		8	260.63	odd	12
975.2.bp.f.674.2		8	780.323	even	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.60523 - 0.650571i) q^{3} +(-1.06488 - 1.06488i) q^{5} +(-0.366025 + 1.36603i) q^{7} +(2.15351 - 2.08863i) q^{9} +O(q^{10})\)	\(q+(1.60523 - 0.650571i) q^{3} +(-1.06488 - 1.06488i) q^{5} +(-0.366025 + 1.36603i) q^{7} +(2.15351 - 2.08863i) q^{9} +(-1.06488 - 3.97420i) q^{11} +(3.59808 - 0.232051i) q^{13} +(-2.40216 - 1.01660i) q^{15} +(-2.51954 - 4.36397i) q^{17} +(3.73205 + 1.00000i) q^{19} +(0.301143 + 2.43091i) q^{21} -2.73205i q^{25} +(2.09808 - 4.75374i) q^{27} +(6.20840 + 3.58442i) q^{29} +(2.46410 - 2.46410i) q^{31} +(-4.29488 - 5.68671i) q^{33} +(1.84443 - 1.06488i) q^{35} +(-5.23205 + 1.40192i) q^{37} +(5.62477 - 2.71330i) q^{39} +(-5.42885 + 1.45466i) q^{41} +(-1.90192 + 1.09808i) q^{43} +(-4.51739 - 0.0690922i) q^{45} +(-4.25953 + 4.25953i) q^{47} +(4.33013 + 2.50000i) q^{49} +(-6.88351 - 5.36603i) q^{51} -0.779548i q^{53} +(-3.09808 + 5.36603i) q^{55} +(6.64136 - 0.822738i) q^{57} +(-2.90931 - 0.779548i) q^{59} +(3.50000 + 6.06218i) q^{61} +(2.06488 + 3.70625i) q^{63} +(-4.07863 - 3.58442i) q^{65} +(1.53590 + 5.73205i) q^{67} +(-0.779548 + 2.90931i) q^{71} +(-0.901924 - 0.901924i) q^{73} +(-1.77739 - 4.38556i) q^{75} +5.81863 q^{77} -2.00000 q^{79} +(0.275241 - 8.99579i) q^{81} +(2.90931 + 2.90931i) q^{83} +(-1.96410 + 7.33013i) q^{85} +(12.2978 + 1.71481i) q^{87} +(2.41510 + 9.01327i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(2.35237 - 5.55852i) q^{93} +(-2.90931 - 5.03908i) q^{95} +(1.63397 + 0.437822i) q^{97} +(-10.5939 - 6.33434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9	\( 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9} + 8 q^{13} + 14 q^{15} + 16 q^{19} + 4 q^{21} - 4 q^{27} - 8 q^{31} + 16 q^{33} - 28 q^{37} + 14 q^{39} - 36 q^{43} - 20 q^{45} - 4 q^{55} + 16 q^{57} + 28 q^{61} + 8 q^{63} + 40 q^{67} - 28 q^{73} - 12 q^{75} - 16 q^{79} + 4 q^{81} + 12 q^{85} + 34 q^{87} - 8 q^{91} + 4 q^{93} + 20 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9 + 8 * q^13 + 14 * q^15 + 16 * q^19 + 4 * q^21 - 4 * q^27 - 8 * q^31 + 16 * q^33 - 28 * q^37 + 14 * q^39 - 36 * q^43 - 20 * q^45 - 4 * q^55 + 16 * q^57 + 28 * q^61 + 8 * q^63 + 40 * q^67 - 28 * q^73 - 12 * q^75 - 16 * q^79 + 4 * q^81 + 12 * q^85 + 34 * q^87 - 8 * q^91 + 4 * q^93 + 20 * q^97 - 40 * q^99

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