LMFDB - Embedded newform 624.2.cn.c.401.1

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			401.1
Root			$0.500000 + 0.564882i$ of defining polynomial
Character	$\chi$	$=$	624.401
Dual form			624.2.cn.c.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.239203 + 1.71545i) q^{3} +(1.06488 - 1.06488i) q^{5} +(-0.366025 - 1.36603i) q^{7} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})$	\(q+(-0.239203 + 1.71545i) q^{3} +(1.06488 - 1.06488i) q^{5} +(-0.366025 - 1.36603i) q^{7} +(-2.88556 - 0.820682i) q^{9} +(1.06488 - 3.97420i) q^{11} +(3.59808 + 0.232051i) q^{13} +(1.57203 + 2.08148i) q^{15} +(2.51954 - 4.36397i) q^{17} +(3.73205 - 1.00000i) q^{19} +(2.43091 - 0.301143i) q^{21} +2.73205i q^{25} +(2.09808 - 4.75374i) q^{27} +(-6.20840 + 3.58442i) q^{29} +(2.46410 + 2.46410i) q^{31} +(6.56283 + 2.77739i) q^{33} +(-1.84443 - 1.06488i) q^{35} +(-5.23205 - 1.40192i) q^{37} +(-1.25874 + 6.11683i) q^{39} +(5.42885 + 1.45466i) q^{41} +(-1.90192 - 1.09808i) q^{43} +(-3.94672 + 2.19886i) q^{45} +(4.25953 + 4.25953i) q^{47} +(4.33013 - 2.50000i) q^{49} +(6.88351 + 5.36603i) q^{51} -0.779548i q^{53} +(-3.09808 - 5.36603i) q^{55} +(0.822738 + 6.64136i) q^{57} +(2.90931 - 0.779548i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-0.0648824 + 4.24214i) q^{63} +(4.07863 - 3.58442i) q^{65} +(1.53590 - 5.73205i) q^{67} +(0.779548 + 2.90931i) q^{71} +(-0.901924 + 0.901924i) q^{73} +(-4.68671 - 0.653513i) q^{75} -5.81863 q^{77} -2.00000 q^{79} +(7.65296 + 4.73626i) q^{81} +(-2.90931 + 2.90931i) q^{83} +(-1.96410 - 7.33013i) q^{85} +(-4.66384 - 11.5076i) q^{87} +(-2.41510 + 9.01327i) q^{89} +(-1.00000 - 5.00000i) q^{91} +(-4.81647 + 3.63763i) q^{93} +(2.90931 - 5.03908i) q^{95} +(1.63397 - 0.437822i) q^{97} +(-6.33434 + 10.5939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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
$3$	−0.239203	+	1.71545i	−0.138104	+	0.990418i
$3$	−0.239203	+	1.71545i	−0.138104	+	0.990418i
$4$		0			0
$5$	1.06488	−	1.06488i	0.476230	−	0.476230i	−0.427694	−	0.903924i	$-0.640674\pi$
$5$	1.06488	−	1.06488i	0.476230	−	0.476230i	0.903924	+	0.427694i	$0.140674\pi$
$6$		0			0
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	−0.999962	−	0.00875026i	$-0.997215\pi$
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	0.861617	−	0.507559i	$-0.169452\pi$
$8$		0			0
$9$	−2.88556	−	0.820682i	−0.961855	−	0.273561i
$10$		0			0
$11$	1.06488	−	3.97420i	0.321074	−	1.19826i	−0.597126	−	0.802148i	$-0.703691\pi$
$11$	1.06488	−	3.97420i	0.321074	−	1.19826i	0.918200	−	0.396117i	$-0.129643\pi$
$12$		0			0
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$14$		0			0
$15$	1.57203	+	2.08148i	0.405897	+	0.537436i
$16$		0			0
$17$	2.51954	−	4.36397i	0.611078	−	1.05842i	−0.379981	−	0.924994i	$-0.624070\pi$
$17$	2.51954	−	4.36397i	0.611078	−	1.05842i	0.991059	−	0.133424i	$-0.0425971\pi$
$18$		0			0
$19$	3.73205	−	1.00000i	0.856191	−	0.229416i	0.196084	−	0.980587i	$-0.437177\pi$
$19$	3.73205	−	1.00000i	0.856191	−	0.229416i	0.660107	+	0.751171i	$0.270511\pi$
$20$		0			0
$21$	2.43091	−	0.301143i	0.530468	−	0.0657148i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		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	$-0.898495\pi$
$29$	−6.20840	+	3.58442i	−1.15287	+	0.665610i	−0.203286	+	0.979119i	$0.565162\pi$
$30$		0			0
$31$	2.46410	+	2.46410i	0.442566	+	0.442566i	0.892873	−	0.450308i	$-0.148686\pi$
$31$	2.46410	+	2.46410i	0.442566	+	0.442566i	−0.450308	+	0.892873i	$0.648686\pi$
$32$		0			0
$33$	6.56283	+	2.77739i	1.14244	+	0.483482i
$34$		0			0
$35$	−1.84443	−	1.06488i	−0.311766	−	0.179998i
$36$		0			0
$37$	−5.23205	−	1.40192i	−0.860144	−	0.230475i	−0.198323	−	0.980137i	$-0.563549\pi$
$37$	−5.23205	−	1.40192i	−0.860144	−	0.230475i	−0.661821	+	0.749662i	$0.730216\pi$
$38$		0			0
$39$	−1.25874	+	6.11683i	−0.201560	+	0.979476i
$40$		0			0
$41$	5.42885	+	1.45466i	0.847844	+	0.227179i	0.656483	−	0.754341i	$-0.272043\pi$
$41$	5.42885	+	1.45466i	0.847844	+	0.227179i	0.191361	+	0.981520i	$0.438710\pi$
$42$		0			0
$43$	−1.90192	−	1.09808i	−0.290041	−	0.167455i	0.347920	−	0.937524i	$-0.386888\pi$
$43$	−1.90192	−	1.09808i	−0.290041	−	0.167455i	−0.637960	+	0.770069i	$0.720222\pi$
$44$		0			0
$45$	−3.94672	+	2.19886i	−0.588342	+	0.327786i
$46$		0			0
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	0.945868	−	0.324552i	$-0.105213\pi$
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	−0.324552	+	0.945868i	$0.605213\pi$
$48$		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
$57$	0.822738	+	6.64136i	0.108974	+	0.879670i
$58$		0			0
$59$	2.90931	−	0.779548i	0.378760	−	0.101489i	−0.0644157	−	0.997923i	$-0.520518\pi$
$59$	2.90931	−	0.779548i	0.378760	−	0.101489i	0.443176	+	0.896435i	$0.353852\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$		0			0
$63$	−0.0648824	+	4.24214i	−0.00817442	+	0.534460i
$64$		0			0
$65$	4.07863	−	3.58442i	0.505892	−	0.444593i
$66$		0			0
$67$	1.53590	−	5.73205i	0.187640	−	0.700281i	−0.806410	−	0.591357i	$-0.798593\pi$
$67$	1.53590	−	5.73205i	0.187640	−	0.700281i	0.994050	−	0.108925i	$-0.0347408\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.779548	+	2.90931i	0.0925153	+	0.345272i	0.996631	−	0.0820158i	$-0.0261358\pi$
$71$	0.779548	+	2.90931i	0.0925153	+	0.345272i	−0.904116	+	0.427288i	$0.859469\pi$
$72$		0			0
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	−0.757915	−	0.652353i	$-0.773782\pi$
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	0.652353	+	0.757915i	$0.273782\pi$
$74$		0			0
$75$	−4.68671	−	0.653513i	−0.541174	−	0.0754612i
$76$		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
$81$	7.65296	+	4.73626i	0.850329	+	0.526251i
$82$		0			0
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	−0.848513	−	0.529174i	$-0.822502\pi$
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	0.529174	+	0.848513i	$0.322502\pi$
$84$		0			0
$85$	−1.96410	−	7.33013i	−0.213037	−	0.795064i
$86$		0			0
$87$	−4.66384	−	11.5076i	−0.500017	−	1.23375i
$88$		0			0
$89$	−2.41510	+	9.01327i	−0.256000	+	0.955405i	0.711531	+	0.702654i	$0.248002\pi$
$89$	−2.41510	+	9.01327i	−0.256000	+	0.955405i	−0.967531	+	0.252751i	$0.918665\pi$
$90$		0			0
$91$	−1.00000	−	5.00000i	−0.104828	−	0.524142i
$92$		0			0
$93$	−4.81647	+	3.63763i	−0.499445	+	0.377205i
$94$		0			0
$95$	2.90931	−	5.03908i	0.298489	−	0.516998i
$96$		0			0
$97$	1.63397	−	0.437822i	0.165905	−	0.0444541i	−0.174910	−	0.984584i	$-0.555964\pi$
$97$	1.63397	−	0.437822i	0.165905	−	0.0444541i	0.340815	+	0.940130i	$0.389297\pi$
$98$		0			0
$99$	−6.33434	+	10.5939i	−0.636625	+	1.06472i
$100$		0			0
$101$	−3.01375	−	5.21997i	−0.299880	−	0.519407i	0.676229	−	0.736692i	$-0.263613\pi$
$101$	−3.01375	−	5.21997i	−0.299880	−	0.519407i	−0.976108	+	0.217285i	$0.930280\pi$
$102$		0			0
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$		0			0
$105$	2.26795	−	2.90931i	0.221329	−	0.283920i
$106$		0			0
$107$	−16.4675	+	9.50749i	−1.59197	+	0.919123i	−0.598999	+	0.800749i	$0.704435\pi$
$107$	−16.4675	+	9.50749i	−1.59197	+	0.919123i	−0.992969	+	0.118374i	$0.962232\pi$
$108$		0			0
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.949156	−	0.314806i	$-0.898060\pi$
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.314806	−	0.949156i	$-0.601940\pi$
$110$		0			0
$111$	3.65646	−	8.64000i	0.347055	−	0.820072i
$112$		0			0
$113$	−8.90883	−	5.14352i	−0.838073	−	0.483861i	0.0185360	−	0.999828i	$-0.494099\pi$
$113$	−8.90883	−	5.14352i	−0.838073	−	0.483861i	−0.856609	+	0.515967i	$0.827433\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−10.1920	−	3.62247i	−0.942254	−	0.334898i
$118$		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
$123$	−3.79399	+	8.96499i	−0.342093	+	0.808346i
$124$		0			0
$125$	8.23373	+	8.23373i	0.736447	+	0.736447i
$126$		0			0
$127$	−7.90192	+	4.56218i	−0.701182	+	0.404828i	−0.807788	−	0.589474i	$-0.799335\pi$
$127$	−7.90192	+	4.56218i	−0.701182	+	0.404828i	0.106605	+	0.994301i	$0.466002\pi$
$128$		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
$135$	−2.82797	−	7.29638i	−0.243393	−	0.627973i
$136$		0			0
$137$	6.49373	−	1.73999i	0.554797	−	0.148657i	0.0294822	−	0.999565i	$-0.490614\pi$
$137$	6.49373	−	1.73999i	0.554797	−	0.148657i	0.525315	+	0.850908i	$0.323948\pi$
$138$		0			0
$139$	9.19615	−	15.9282i	0.780007	−	1.35101i	−0.151929	−	0.988391i	$-0.548549\pi$
$139$	9.19615	−	15.9282i	0.780007	−	1.35101i	0.931937	−	0.362621i	$-0.118118\pi$
$140$		0			0
$141$	−8.32592	+	6.28814i	−0.701169	+	0.529557i
$142$		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
$147$	3.25286	+	8.02614i	0.268291	+	0.661985i
$148$		0			0
$149$	2.23420	+	8.33816i	0.183033	+	0.683089i	0.995043	+	0.0994454i	$0.0317068\pi$
$149$	2.23420	+	8.33816i	0.183033	+	0.683089i	−0.812010	+	0.583644i	$0.801626\pi$
$150$		0			0
$151$	−0.535898	+	0.535898i	−0.0436108	+	0.0436108i	−0.728576	−	0.684965i	$-0.759817\pi$
$151$	−0.535898	+	0.535898i	−0.0436108	+	0.0436108i	0.684965	+	0.728576i	$0.259817\pi$
$152$		0			0
$153$	−10.8517	+	10.5248i	−0.877310	+	0.850878i
$154$		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
$159$	1.33728	+	0.186470i	0.106053	+	0.0147880i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.07180	+	4.00000i	0.0839496	+	0.313304i	0.995113	−	0.0987406i	$-0.0314814\pi$
$163$	1.07180	+	4.00000i	0.0839496	+	0.313304i	−0.911164	+	0.412045i	$0.864815\pi$
$164$		0			0
$165$	9.94624	−	4.03104i	0.774313	−	0.313816i
$166$		0			0
$167$	−3.47998	+	12.9875i	−0.269289	+	1.00500i	0.690283	+	0.723539i	$0.257486\pi$
$167$	−3.47998	+	12.9875i	−0.269289	+	1.00500i	−0.959573	+	0.281461i	$0.909181\pi$
$168$		0			0
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$		0			0
$171$	−11.5898	−	0.177262i	−0.886291	−	0.0135556i
$172$		0			0
$173$	−8.72794	+	15.1172i	−0.663573	+	1.14934i	0.316097	+	0.948727i	$0.397627\pi$
$173$	−8.72794	+	15.1172i	−0.663573	+	1.14934i	−0.979670	+	0.200615i	$0.935706\pi$
$174$		0			0
$175$	3.73205	−	1.00000i	0.282117	−	0.0755929i
$176$		0			0
$177$	0.641364	+	5.17726i	0.0482078	+	0.389147i
$178$		0			0
$179$	13.2728	+	22.9892i	0.992056	+	1.71829i	0.604972	+	0.796247i	$0.293184\pi$
$179$	13.2728	+	22.9892i	0.992056	+	1.71829i	0.387084	+	0.922045i	$0.373482\pi$
$180$		0			0
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$		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
$189$	−7.26168	−	1.12603i	−0.528210	−	0.0819070i
$190$		0			0
$191$	−4.18307	−	2.41510i	−0.302677	−	0.174750i	0.340968	−	0.940075i	$-0.389245\pi$
$191$	−4.18307	−	2.41510i	−0.302677	−	0.174750i	−0.643645	+	0.765324i	$0.722579\pi$
$192$		0			0
$193$	0.133975	+	0.0358984i	0.00964370	+	0.00258402i	0.263638	−	0.964622i	$-0.415078\pi$
$193$	0.133975	+	0.0358984i	0.00964370	+	0.00258402i	−0.253994	+	0.967206i	$0.581744\pi$
$194$		0			0
$195$	5.17329	+	7.85411i	0.370467	+	0.562445i
$196$		0			0
$197$	−3.97420	−	1.06488i	−0.283150	−	0.0758697i	0.114449	−	0.993429i	$-0.463490\pi$
$197$	−3.97420	−	1.06488i	−0.283150	−	0.0758697i	−0.397599	+	0.917559i	$0.630156\pi$
$198$		0			0
$199$	−11.1962	−	6.46410i	−0.793674	−	0.458228i	0.0475802	−	0.998867i	$-0.484849\pi$
$199$	−11.1962	−	6.46410i	−0.793674	−	0.458228i	−0.841254	+	0.540639i	$0.818182\pi$
$200$		0			0
$201$	9.46568	+	4.00588i	0.667657	+	0.282553i
$202$		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	0.833309	−	0.552808i	$-0.186444\pi$
$211$	−0.901924	−	1.56218i	−0.0620910	−	0.107545i	−0.895400	+	0.445263i	$0.853110\pi$
$212$		0			0
$213$	−5.17726	+	0.641364i	−0.354740	+	0.0439455i
$214$		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
$219$	−1.33147	−	1.76295i	−0.0899722	−	0.119129i
$220$		0			0
$221$	10.0782	−	15.1172i	0.677930	−	1.01690i
$222$		0			0
$223$	−6.70577	+	25.0263i	−0.449052	+	1.67588i	0.255960	+	0.966687i	$0.417609\pi$
$223$	−6.70577	+	25.0263i	−0.449052	+	1.67588i	−0.705011	+	0.709196i	$0.749058\pi$
$224$		0			0
$225$	2.24214	−	7.88351i	0.149476	−	0.525567i
$226$		0			0
$227$	−5.24796	−	19.5856i	−0.348319	−	1.29994i	−0.888686	−	0.458515i	$-0.848381\pi$
$227$	−5.24796	−	19.5856i	−0.348319	−	1.29994i	0.540367	−	0.841429i	$-0.318285\pi$
$228$		0			0
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	−0.997914	−	0.0645507i	$-0.979439\pi$
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	0.0645507	+	0.997914i	$0.479439\pi$
$230$		0			0
$231$	1.39183	−	9.98158i	0.0915757	−	0.656740i
$232$		0			0
$233$	17.4559			1.14357			0.571786	−	0.820403i	$-0.306251\pi$
$233$	17.4559			1.14357			0.571786	+	0.820403i	$0.306251\pi$
$234$		0			0
$235$	9.07180			0.591779
$236$		0			0
$237$	0.478405	−	3.43091i	0.0310757	−	0.222861i
$238$		0			0
$239$	−6.59817	+	6.59817i	−0.426800	+	0.426800i	−0.887537	−	0.460737i	$-0.847585\pi$
$239$	−6.59817	+	6.59817i	−0.426800	+	0.426800i	0.460737	+	0.887537i	$0.347585\pi$
$240$		0			0
$241$	3.76795	+	14.0622i	0.242715	+	0.905825i	0.974518	+	0.224309i	$0.0720123\pi$
$241$	3.76795	+	14.0622i	0.242715	+	0.905825i	−0.731803	+	0.681516i	$0.761321\pi$
$242$		0			0
$243$	−9.95544	+	11.9954i	−0.638642	+	0.769504i
$244$		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
$249$	−4.29488	−	5.68671i	−0.272177	−	0.360380i
$250$		0			0
$251$	−0.494214	+	0.856003i	−0.0311945	+	0.0540304i	−0.881201	−	0.472741i	$-0.843264\pi$
$251$	−0.494214	+	0.856003i	−0.0311945	+	0.0540304i	0.850007	+	0.526772i	$0.176598\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	13.0443	−	1.61594i	0.816867	−	0.101194i
$256$		0			0
$257$	10.7533	+	18.6252i	0.670770	+	1.16181i	0.977686	+	0.210071i	$0.0673696\pi$
$257$	10.7533	+	18.6252i	0.670770	+	1.16181i	−0.306916	+	0.951737i	$0.599297\pi$
$258$		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	$-0.425546\pi$
$263$	19.3003	−	11.1430i	1.19011	−	0.687109i	0.958331	+	0.285660i	$0.0922127\pi$
$264$		0			0
$265$	−0.830127	−	0.830127i	−0.0509943	−	0.0509943i
$266$		0			0
$267$	−14.8842	−	6.29899i	−0.910896	−	0.385492i
$268$		0			0
$269$	−12.4168	−	7.16884i	−0.757066	−	0.437092i	0.0711756	−	0.997464i	$-0.477325\pi$
$269$	−12.4168	−	7.16884i	−0.757066	−	0.437092i	−0.828241	+	0.560372i	$0.810658\pi$
$270$		0			0
$271$	−7.46410	−	2.00000i	−0.453412	−	0.121491i	0.0248835	−	0.999690i	$-0.492079\pi$
$271$	−7.46410	−	2.00000i	−0.453412	−	0.121491i	−0.478295	+	0.878199i	$0.658745\pi$
$272$		0			0
$273$	8.81647	−	0.519441i	0.533597	−	0.0314380i
$274$		0			0
$275$	10.8577	+	2.90931i	0.654744	+	0.175438i
$276$		0			0
$277$	23.8923	+	13.7942i	1.43555	+	0.828815i	0.997536	−	0.0701536i	$-0.0223490\pi$
$277$	23.8923	+	13.7942i	1.43555	+	0.828815i	0.438013	+	0.898969i	$0.355682\pi$
$278$		0			0
$279$	−5.08808	−	9.13257i	−0.304615	−	0.546752i
$280$		0			0
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	0.245655	−	0.969357i	$-0.420997\pi$
$281$	−12.1315	−	12.1315i	−0.723703	−	0.723703i	−0.969357	+	0.245655i	$0.920997\pi$
$282$		0			0
$283$	5.70577	−	3.29423i	0.339173	−	0.195822i	−0.320733	−	0.947170i	$-0.603929\pi$
$283$	5.70577	−	3.29423i	0.339173	−	0.195822i	0.659906	+	0.751348i	$0.270596\pi$
$284$		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
$291$	0.360213	+	2.90774i	0.0211161	+	0.170455i
$292$		0			0
$293$	−1.73999	+	0.466229i	−0.101651	+	0.0272374i	−0.309286	−	0.950969i	$-0.600090\pi$
$293$	−1.73999	+	0.466229i	−0.101651	+	0.0272374i	0.207635	+	0.978206i	$0.433423\pi$
$294$		0			0
$295$	2.26795	−	3.92820i	0.132045	−	0.228709i
$296$		0			0
$297$	−16.6581	−	13.4003i	−0.966601	−	0.777567i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.803848	+	3.00000i	−0.0463330	+	0.172917i
$302$		0			0
$303$	9.67552	−	3.92132i	0.555844	−	0.225274i
$304$		0			0
$305$	−2.72842	−	10.1826i	−0.156229	−	0.583054i
$306$		0			0
$307$	−8.39230	+	8.39230i	−0.478974	+	0.478974i	−0.904803	−	0.425829i	$-0.859982\pi$
$307$	−8.39230	+	8.39230i	−0.478974	+	0.478974i	0.425829	+	0.904803i	$0.359982\pi$
$308$		0			0
$309$	−11.8850	−	1.65724i	−0.676115	−	0.0942773i
$310$		0			0
$311$	−10.0782			−0.571480			−0.285740	−	0.958307i	$-0.592239\pi$
$311$	−10.0782			−0.571480			−0.285740	+	0.958307i	$0.592239\pi$
$312$		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
$315$	4.44829	+	4.58648i	0.250633	+	0.258419i
$316$		0			0
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	−0.949960	−	0.312373i	$-0.898876\pi$
$317$	−11.3519	+	11.3519i	−0.637587	+	0.637587i	0.312373	+	0.949960i	$0.398876\pi$
$318$		0			0
$319$	7.63397	+	28.4904i	0.427421	+	1.59516i
$320$		0			0
$321$	−12.3706	−	30.5234i	−0.690460	−	1.70365i
$322$		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
$327$	25.7939	−	19.4808i	1.42641	−	1.07729i
$328$		0			0
$329$	4.25953	−	7.37772i	0.234835	−	0.406747i
$330$		0			0
$331$	33.0526	−	8.85641i	1.81673	−	0.486792i	0.820357	−	0.571852i	$-0.193775\pi$
$331$	33.0526	−	8.85641i	1.81673	−	0.486792i	0.996376	+	0.0850595i	$0.0271080\pi$
$332$		0			0
$333$	13.9469	+	8.33919i	0.764285	+	0.456985i
$334$		0			0
$335$	−4.46841	−	7.73951i	−0.244135	−	0.422855i
$336$		0			0
$337$			18.4641i			1.00580i	0.864344	+	0.502902i	$0.167734\pi$
$337$			18.4641i			1.00580i	−0.864344	+	0.502902i	$0.832266\pi$
$338$		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	$-0.519559\pi$
$347$	−17.8177	−	10.2870i	−0.956502	−	0.552237i	−0.895095	+	0.445876i	$0.852892\pi$
$348$		0			0
$349$	27.4904	+	7.36603i	1.47153	+	0.394294i	0.903454	−	0.428684i	$-0.141023\pi$
$349$	27.4904	+	7.36603i	1.47153	+	0.394294i	0.568072	+	0.822979i	$0.307689\pi$
$350$		0			0
$351$	8.65215	−	16.6175i	0.461818	−	0.886975i
$352$		0			0
$353$	13.6626	+	3.66088i	0.727186	+	0.194849i	0.603376	−	0.797457i	$-0.293822\pi$
$353$	13.6626	+	3.66088i	0.727186	+	0.194849i	0.123810	+	0.992306i	$0.460489\pi$
$354$		0			0
$355$	3.92820	+	2.26795i	0.208487	+	0.120370i
$356$		0			0
$357$	4.81059	−	11.3671i	0.254603	−	0.601613i
$358$		0			0
$359$	−18.2354	−	18.2354i	−0.962429	−	0.962429i	0.0368904	−	0.999319i	$-0.488255\pi$
$359$	−18.2354	−	18.2354i	−0.962429	−	0.962429i	−0.999319	+	0.0368904i	$0.988255\pi$
$360$		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	0.923955	+	0.382500i	$0.124937\pi$
$367$	15.1962	+	26.3205i	0.793233	+	1.37392i	−0.130723	+	0.991419i	$0.541730\pi$
$368$		0			0
$369$	−14.4715	−	8.65286i	−0.753356	−	0.450450i
$370$		0			0
$371$	−1.06488	+	0.285334i	−0.0552859	+	0.0148138i
$372$		0			0
$373$	−5.79423	+	10.0359i	−0.300014	+	0.519639i	−0.976139	−	0.217148i	$-0.930325\pi$
$373$	−5.79423	+	10.0359i	−0.300014	+	0.519639i	0.676125	+	0.736787i	$0.263658\pi$
$374$		0			0
$375$	−16.0941	+	12.1550i	−0.831096	+	0.627684i
$376$		0			0
$377$	−23.1701	+	11.4564i	−1.19332	+	0.590032i
$378$		0			0
$379$	−3.83013	+	14.2942i	−0.196740	+	0.734245i	0.795069	+	0.606519i	$0.207435\pi$
$379$	−3.83013	+	14.2942i	−0.196740	+	0.734245i	−0.991809	+	0.127726i	$0.959232\pi$
$380$		0			0
$381$	−5.93605	−	14.6467i	−0.304113	−	0.750372i
$382$		0			0
$383$	8.51906	+	31.7936i	0.435304	+	1.62458i	0.740339	+	0.672234i	$0.234665\pi$
$383$	8.51906	+	31.7936i	0.435304	+	1.62458i	−0.305035	+	0.952341i	$0.598668\pi$
$384$		0			0
$385$	−6.19615	+	6.19615i	−0.315785	+	0.315785i
$386$		0			0
$387$	4.58695	+	4.72944i	0.233168	+	0.240411i
$388$		0			0
$389$	22.4950			1.14054			0.570270	−	0.821457i	$-0.306839\pi$
$389$	22.4950			1.14054			0.570270	+	0.821457i	$0.306839\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	13.6351	+	1.90128i	0.687800	+	0.0959066i
$394$		0			0
$395$	−2.12976	+	2.12976i	−0.107160	+	0.107160i
$396$		0			0
$397$	−3.56218	−	13.2942i	−0.178781	−	0.667218i	−0.995877	−	0.0907168i	$-0.971084\pi$
$397$	−3.56218	−	13.2942i	−0.178781	−	0.667218i	0.817096	−	0.576501i	$-0.195582\pi$
$398$		0			0
$399$	8.77113	−	3.55479i	0.439106	−	0.177962i
$400$		0			0
$401$	−3.22263	+	12.0270i	−0.160931	+	0.600601i	0.837594	+	0.546294i	$0.183962\pi$
$401$	−3.22263	+	12.0270i	−0.160931	+	0.600601i	−0.998524	+	0.0543073i	$0.982705\pi$
$402$		0			0
$403$	8.29423	+	9.43782i	0.413165	+	0.470131i
$404$		0			0
$405$	13.1931	−	3.10594i	0.655569	−	0.154336i
$406$		0			0
$407$	−11.1430	+	19.3003i	−0.552340	+	0.956681i
$408$		0			0
$409$	28.9904	−	7.76795i	1.43348	−	0.384100i	0.543236	−	0.839580i	$-0.317199\pi$
$409$	28.9904	−	7.76795i	1.43348	−	0.384100i	0.890246	+	0.455480i	$0.150532\pi$
$410$		0			0
$411$	1.43156	+	11.5559i	0.0706135	+	0.570011i
$412$		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	$-0.592063\pi$
$419$	8.23373	−	4.75374i	0.402244	−	0.232236i	0.687452	+	0.726230i	$0.258729\pi$
$420$		0			0
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	0.490067	−	0.871685i	$-0.336972\pi$
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	−0.871685	+	0.490067i	$0.836972\pi$
$422$		0			0
$423$	−8.79543	−	15.7869i	−0.427648	−	0.767584i
$424$		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
$429$	22.9691	+	11.5162i	1.10896	+	0.556007i
$430$		0			0
$431$	36.5473	+	9.79282i	1.76042	+	0.471704i	0.986800	−	0.161944i	$-0.0517764\pi$
$431$	36.5473	+	9.79282i	1.76042	+	0.471704i	0.773622	+	0.633648i	$0.218443\pi$
$432$		0			0
$433$	−26.8923	−	15.5263i	−1.29236	−	0.746145i	−0.313289	−	0.949658i	$-0.601431\pi$
$433$	−26.8923	−	15.5263i	−1.29236	−	0.746145i	−0.979072	+	0.203512i	$0.934764\pi$
$434$		0			0
$435$	−17.2207	−	7.28782i	−0.825670	−	0.349424i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.09808	+	0.633975i	−0.0524083	+	0.0302580i	−0.525975	−	0.850500i	$-0.676300\pi$
$439$	−1.09808	+	0.633975i	−0.0524083	+	0.0302580i	0.473567	+	0.880758i	$0.342966\pi$
$440$		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
$447$	−14.8382	+	1.83816i	−0.701821	+	0.0869422i
$448$		0			0
$449$	−19.8710	+	5.32441i	−0.937769	+	0.251275i	−0.695165	−	0.718851i	$-0.744669\pi$
$449$	−19.8710	+	5.32441i	−0.937769	+	0.251275i	−0.242605	+	0.970125i	$0.578002\pi$
$450$		0			0
$451$	11.5622	−	20.0263i	0.544442	−	0.943001i
$452$		0			0
$453$	−0.791121	−	1.04750i	−0.0371701	−	0.0492157i
$454$		0			0
$455$	−6.38929	−	4.25953i	−0.299535	−	0.199690i
$456$		0			0
$457$	−1.00962	+	3.76795i	−0.0472280	+	0.176257i	−0.985511	−	0.169611i	$-0.945749\pi$
$457$	−1.00962	+	3.76795i	−0.0472280	+	0.176257i	0.938283	+	0.345868i	$0.112416\pi$
$458$		0			0
$459$	−15.4590	−	21.1332i	−0.721565	−	0.986412i
$460$		0			0
$461$	−5.50531	−	20.5461i	−0.256408	−	0.956927i	−0.967302	−	0.253628i	$-0.918376\pi$
$461$	−5.50531	−	20.5461i	−0.256408	−	0.956927i	0.710894	−	0.703299i	$-0.248290\pi$
$462$		0			0
$463$	−23.0526	+	23.0526i	−1.07134	+	1.07134i	−0.0740918	+	0.997251i	$0.523606\pi$
$463$	−23.0526	+	23.0526i	−1.07134	+	1.07134i	−0.997251	+	0.0740918i	$0.976394\pi$
$464$		0			0
$465$	−1.25532	+	9.00263i	−0.0582143	+	0.417487i
$466$		0			0
$467$	19.1679			0.886984			0.443492	−	0.896278i	$-0.353739\pi$
$467$	19.1679			0.886984			0.443492	+	0.896278i	$0.353739\pi$
$468$		0			0
$469$	−8.39230			−0.387521
$470$		0			0
$471$	1.14909	−	8.24078i	0.0529474	−	0.379715i
$472$		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
$477$	−0.639761	+	2.24944i	−0.0292926	+	0.102995i
$478$		0			0
$479$	−5.32441	+	19.8710i	−0.243279	+	0.907928i	0.730962	+	0.682418i	$0.239072\pi$
$479$	−5.32441	+	19.8710i	−0.243279	+	0.907928i	−0.974241	+	0.225510i	$0.927595\pi$
$480$		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	−0.382630	−	0.923902i	$-0.624982\pi$
$487$	−5.56218	+	1.49038i	−0.252046	+	0.0675356i	0.130584	+	0.991437i	$0.458315\pi$
$488$		0			0
$489$	−7.11819	+	0.881808i	−0.321896	+	0.0398767i
$490$		0			0
$491$	−14.2612	−	24.7012i	−0.643600	−	1.11475i	−0.984623	−	0.174693i	$-0.944107\pi$
$491$	−14.2612	−	24.7012i	−0.643600	−	1.11475i	0.341023	−	0.940055i	$-0.389227\pi$
$492$		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	0.760107	−	0.649798i	$-0.225147\pi$
$499$	2.46410	+	2.46410i	0.110308	+	0.110308i	−0.649798	+	0.760107i	$0.725147\pi$
$500$		0			0
$501$	−21.4470	−	9.07638i	−0.958181	−	0.405503i
$502$		0			0
$503$	2.83286	+	1.63555i	0.126311	+	0.0729256i	0.561824	−	0.827257i	$-0.310100\pi$
$503$	2.83286	+	1.63555i	0.126311	+	0.0729256i	−0.435513	+	0.900182i	$0.643433\pi$
$504$		0			0
$505$	−8.76795	−	2.34936i	−0.390169	−	0.104545i
$506$		0			0
$507$	−5.94846	+	21.7167i	−0.264180	+	0.964473i
$508$		0			0
$509$	14.1568	+	3.79330i	0.627489	+	0.168135i	0.558530	−	0.829484i	$-0.311366\pi$
$509$	14.1568	+	3.79330i	0.627489	+	0.168135i	0.0689588	+	0.997620i	$0.478032\pi$
$510$		0			0
$511$	1.56218	+	0.901924i	0.0691067	+	0.0398988i
$512$		0			0
$513$	3.07638	−	19.8393i	0.135826	−	0.875926i
$514$		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	−0.879169	−	0.476511i	$-0.841901\pi$
$523$	−19.4904	−	33.7583i	−0.852255	−	1.47615i	0.0269137	−	0.999638i	$-0.491432\pi$
$524$		0			0
$525$	0.822738	+	6.64136i	0.0359072	+	0.289853i
$526$		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
$531$	−9.03477	−	0.138184i	−0.392076	−	0.00599669i
$532$		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
$537$	−42.6117	+	17.2698i	−1.83883	+	0.745247i
$538$		0			0
$539$	−5.32441	−	19.8710i	−0.229339	−	0.855904i
$540$		0			0
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	−0.925118	−	0.379681i	$-0.876034\pi$
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	0.379681	+	0.925118i	$0.376034\pi$
$542$		0			0
$543$	5.14636	+	0.717608i	0.220852	+	0.0307955i
$544$		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
$549$	−15.0746	+	14.6204i	−0.643368	+	0.623984i
$550$		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
$555$	−5.30689	−	13.0943i	−0.225265	−	0.555821i
$556$		0			0
$557$	6.62616	−	24.7292i	0.280759	−	1.04781i	−0.671123	−	0.741346i	$-0.734188\pi$
$557$	6.62616	−	24.7292i	0.280759	−	1.04781i	0.951883	−	0.306462i	$-0.0991454\pi$
$558$		0			0
$559$	−6.58846	−	4.39230i	−0.278662	−	0.185775i
$560$		0			0
$561$	28.6558	−	21.6422i	1.20985	−	0.913735i
$562$		0			0
$563$	−5.03908	+	8.72794i	−0.212372	+	0.367839i	−0.952456	−	0.304675i	$-0.901452\pi$
$563$	−5.03908	+	8.72794i	−0.212372	+	0.367839i	0.740085	+	0.672514i	$0.234785\pi$
$564$		0			0
$565$	−14.9641	+	4.00962i	−0.629544	+	0.168686i
$566$		0			0
$567$	3.66867	−	12.1877i	0.154070	−	0.511837i
$568$		0			0
$569$	1.35022	+	2.33864i	0.0566040	+	0.0980411i	0.892939	−	0.450178i	$-0.148639\pi$
$569$	1.35022	+	2.33864i	0.0566040	+	0.0980411i	−0.836335	+	0.548219i	$0.815306\pi$
$570$		0			0
$571$			1.94744i			0.0814979i	0.999169	+	0.0407489i	$0.0129744\pi$
$571$			1.94744i			0.0814979i	−0.999169	+	0.0407489i	$0.987026\pi$
$572$		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	0.0618016	−	0.998088i	$-0.480315\pi$
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	−0.998088	+	0.0618016i	$0.980315\pi$
$578$		0			0
$579$	−0.0936291	+	0.221240i	−0.00389109	+	0.00919443i
$580$		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
$585$	−14.7108	+	6.99582i	−0.608218	+	0.289241i
$586$		0			0
$587$	−18.0265	−	4.83020i	−0.744035	−	0.199364i	−0.133164	−	0.991094i	$-0.542514\pi$
$587$	−18.0265	−	4.83020i	−0.744035	−	0.199364i	−0.610871	+	0.791730i	$0.709181\pi$
$588$		0			0
$589$	11.6603	+	6.73205i	0.480452	+	0.277389i
$590$		0			0
$591$	2.77739	−	6.56283i	0.114247	−	0.269959i
$592$		0			0
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	0.887119	−	0.461541i	$-0.152703\pi$
$593$	10.3635	+	10.3635i	0.425578	+	0.425578i	−0.461541	+	0.887119i	$0.652703\pi$
$594$		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	0.518668	−	0.854976i	$-0.326428\pi$
$601$	−11.7942	−	20.4282i	−0.481097	−	0.833284i	−0.999765	+	0.0216919i	$0.993095\pi$
$602$		0			0
$603$	−9.13612	+	15.2797i	−0.372052	+	0.622238i
$604$		0			0
$605$	−8.62350	+	2.31066i	−0.350595	+	0.0939417i
$606$		0			0
$607$	−0.0980762	+	0.169873i	−0.00398079	+	0.00689493i	−0.868009	−	0.496549i	$-0.834600\pi$
$607$	−0.0980762	+	0.169873i	−0.00398079	+	0.00689493i	0.864028	+	0.503444i	$0.167934\pi$
$608$		0			0
$609$	−14.0126	+	10.5830i	−0.567820	+	0.428845i
$610$		0			0
$611$	14.3377	+	16.3145i	0.580041	+	0.660016i
$612$		0			0
$613$	−11.3564	+	42.3827i	−0.458681	+	1.71182i	0.218354	+	0.975870i	$0.429931\pi$
$613$	−11.3564	+	42.3827i	−0.458681	+	1.71182i	−0.677035	+	0.735951i	$0.736735\pi$
$614$		0			0
$615$	5.50650	+	13.5868i	0.222044	+	0.547873i
$616$		0			0
$617$	−4.78173	−	17.8457i	−0.192505	−	0.718439i	−0.992899	−	0.118964i	$-0.962043\pi$
$617$	−4.78173	−	17.8457i	−0.192505	−	0.718439i	0.800393	−	0.599475i	$-0.204624\pi$
$618$		0			0
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.327778	−	0.944755i	$-0.393700\pi$
$619$	31.6603	−	31.6603i	1.27253	−	1.27253i	0.944755	−	0.327778i	$-0.106300\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	13.1963			0.528701
$624$		0			0
$625$	3.87564			0.155026
$626$		0			0
$627$	27.2702	+	3.80255i	1.08907	+	0.151859i
$628$		0			0
$629$	−19.3003	+	19.3003i	−0.769554	+	0.769554i
$630$		0			0
$631$	−5.73205	−	21.3923i	−0.228189	−	0.851614i	−0.981102	−	0.193493i	$-0.938018\pi$
$631$	−5.73205	−	21.3923i	−0.228189	−	0.851614i	0.752912	−	0.658121i	$-0.228648\pi$
$632$		0			0
$633$	2.89559	−	1.17353i	0.115089	−	0.0466437i
$634$		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
$639$	0.138184	−	9.03477i	0.00546649	−	0.357410i
$640$		0			0
$641$	−22.6758	+	39.2757i	−0.895642	+	1.55130i	−0.0626345	+	0.998037i	$0.519950\pi$
$641$	−22.6758	+	39.2757i	−0.895642	+	1.55130i	−0.833008	+	0.553261i	$0.813383\pi$
$642$		0			0
$643$	−7.00000	+	1.87564i	−0.276053	+	0.0739682i	−0.394190	−	0.919029i	$-0.628975\pi$
$643$	−7.00000	+	1.87564i	−0.276053	+	0.0739682i	0.118136	+	0.992997i	$0.462308\pi$
$644$		0			0
$645$	−0.704266	−	5.68503i	−0.0277305	−	0.223848i
$646$		0			0
$647$	−8.23373	−	14.2612i	−0.323701	−	0.560667i	0.657547	−	0.753413i	$-0.271594\pi$
$647$	−8.23373	−	14.2612i	−0.323701	−	0.560667i	−0.981249	+	0.192746i	$0.938261\pi$
$648$		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	$-0.606135\pi$
$653$	8.36615	−	4.83020i	0.327393	−	0.189020i	0.654683	+	0.755904i	$0.272802\pi$
$654$		0			0
$655$	−8.46410	−	8.46410i	−0.330720	−	0.330720i
$656$		0			0
$657$	3.34275	−	1.86237i	0.130413	−	0.0726578i
$658$		0			0
$659$	23.4834	+	13.5581i	0.914783	+	0.528150i	0.881967	−	0.471311i	$-0.156219\pi$
$659$	23.4834	+	13.5581i	0.914783	+	0.528150i	0.0328158	+	0.999461i	$0.489553\pi$
$660$		0			0
$661$	9.42820	+	2.52628i	0.366715	+	0.0982609i	0.437470	−	0.899233i	$-0.355874\pi$
$661$	9.42820	+	2.52628i	0.366715	+	0.0982609i	−0.0707559	+	0.997494i	$0.522541\pi$
$662$		0			0
$663$	23.5222	+	20.9047i	0.913526	+	0.811871i
$664$		0			0
$665$	−7.94839	−	2.12976i	−0.308225	−	0.0825887i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−41.3274	−	17.4898i	−1.59781	−	0.676194i
$670$		0			0
$671$	−20.3652	−	20.3652i	−0.786189	−	0.786189i
$672$		0			0
$673$	−36.9904	+	21.3564i	−1.42587	+	0.823229i	−0.996792	−	0.0800364i	$-0.974496\pi$
$673$	−36.9904	+	21.3564i	−1.42587	+	0.823229i	−0.429082	+	0.903265i	$0.641163\pi$
$674$		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
$681$	34.8536	−	4.31769i	1.33559	−	0.165454i
$682$		0			0
$683$	−45.2752	+	12.1315i	−1.73241	+	0.464198i	−0.980736	−	0.195338i	$-0.937420\pi$
$683$	−45.2752	+	12.1315i	−1.73241	+	0.464198i	−0.751673	+	0.659536i	$0.770753\pi$
$684$		0			0
$685$	5.06218	−	8.76795i	0.193416	−	0.335006i
$686$		0			0
$687$	−20.8511	−	27.6083i	−0.795519	−	1.05332i
$688$		0			0
$689$	0.180895	−	2.80487i	0.00689154	−	0.106857i
$690$		0			0
$691$	−4.88269	+	18.2224i	−0.185746	+	0.693214i	0.808723	+	0.588189i	$0.200159\pi$
$691$	−4.88269	+	18.2224i	−0.185746	+	0.693214i	−0.994470	+	0.105025i	$0.966508\pi$
$692$		0			0
$693$	16.7900	+	4.77524i	0.637800	+	0.181396i
$694$		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
$699$	−4.17549	+	29.9448i	−0.157932	+	1.13261i
$700$		0			0
$701$	12.7786			0.482641			0.241320	−	0.970446i	$-0.422420\pi$
$701$	12.7786			0.482641			0.241320	+	0.970446i	$0.422420\pi$
$702$		0			0
$703$	−20.9282			−0.789322
$704$		0			0
$705$	−2.17000	+	15.5622i	−0.0817268	+	0.586108i
$706$		0			0
$707$	−6.02751	+	6.02751i	−0.226688	+	0.226688i
$708$		0			0
$709$	−3.03590	−	11.3301i	−0.114016	−	0.425512i	0.885196	−	0.465219i	$-0.154024\pi$
$709$	−3.03590	−	11.3301i	−0.114016	−	0.425512i	−0.999211	+	0.0397068i	$0.987358\pi$
$710$		0			0
$711$	5.77113	+	1.64136i	0.216434	+	0.0615559i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−9.90192	−	20.0263i	−0.370311	−	0.748940i
$716$		0			0
$717$	−9.74056	−	12.8972i	−0.363768	−	0.481653i
$718$		0			0
$719$	−3.68886	+	6.38929i	−0.137571	+	0.238280i	−0.926577	−	0.376106i	$-0.877263\pi$
$719$	−3.68886	+	6.38929i	−0.137571	+	0.238280i	0.789005	+	0.614386i	$0.210596\pi$
$720$		0			0
$721$	9.46410	−	2.53590i	0.352462	−	0.0944418i
$722$		0			0
$723$	−25.0243	+	3.10003i	−0.930665	+	0.115292i
$724$		0			0
$725$	−9.79282	−	16.9617i	−0.363696	−	0.629940i
$726$		0			0
$727$		−	19.5167i		−	0.723833i	−0.932211	−	0.361916i	$-0.882123\pi$
$727$		−	19.5167i		−	0.723833i	0.932211	−	0.361916i	$-0.117877\pi$
$728$		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	0.570773	−	0.821108i	$-0.306644\pi$
$733$	−6.77757	−	6.77757i	−0.250335	−	0.250335i	−0.821108	+	0.570773i	$0.806644\pi$
$734$		0			0
$735$	12.0108	+	5.08298i	0.443025	+	0.187489i
$736$		0			0
$737$	−21.1447	−	12.2079i	−0.778876	−	0.449685i
$738$		0			0
$739$	11.1244	+	2.98076i	0.409216	+	0.109649i	0.457554	−	0.889182i	$-0.348726\pi$
$739$	11.1244	+	2.98076i	0.409216	+	0.109649i	−0.0483378	+	0.998831i	$0.515392\pi$
$740$		0			0
$741$	1.41914	+	24.0870i	0.0521334	+	0.884860i
$742$		0			0
$743$	8.51906	+	2.28268i	0.312534	+	0.0837432i	0.411677	−	0.911330i	$-0.364943\pi$
$743$	8.51906	+	2.28268i	0.312534	+	0.0837432i	−0.0991426	+	0.995073i	$0.531610\pi$
$744$		0			0
$745$	11.2583	+	6.50000i	0.412473	+	0.238142i
$746$		0			0
$747$	10.7826	−	6.00739i	0.394516	−	0.219799i
$748$		0			0
$749$	19.0150	+	19.0150i	0.694792	+	0.694792i
$750$		0			0
$751$	29.2750	−	16.9019i	1.06826	−	0.616760i	0.140554	−	0.990073i	$-0.455112\pi$
$751$	29.2750	−	16.9019i	1.06826	−	0.616760i	0.927705	+	0.373313i	$0.121778\pi$
$752$		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	0.672243	−	0.740331i	$-0.265331\pi$
$757$	−8.39230	−	14.5359i	−0.305024	−	0.528316i	−0.977267	+	0.212014i	$0.931998\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.7412	−	4.75374i	0.643118	−	0.172323i	0.0775029	−	0.996992i	$-0.475305\pi$
$761$	17.7412	−	4.75374i	0.643118	−	0.172323i	0.565616	+	0.824669i	$0.308639\pi$
$762$		0			0
$763$	−13.1962	+	22.8564i	−0.477733	+	0.827457i
$764$		0			0
$765$	−0.348161	+	22.7635i	−0.0125878	+	0.823014i
$766$		0			0
$767$	10.6488	−	2.12976i	0.384507	−	0.0769014i
$768$		0			0
$769$	−10.8301	+	40.4186i	−0.390544	+	1.45753i	0.438694	+	0.898636i	$0.355441\pi$
$769$	−10.8301	+	40.4186i	−0.390544	+	1.45753i	−0.829238	+	0.558895i	$0.811225\pi$
$770$		0			0
$771$	−34.5229	+	13.9915i	−1.24331	+	0.503893i
$772$		0			0
$773$	11.1430	+	41.5864i	0.400787	+	1.49576i	0.811695	+	0.584081i	$0.198545\pi$
$773$	11.1430	+	41.5864i	0.400787	+	1.49576i	−0.410908	+	0.911677i	$0.634788\pi$
$774$		0			0
$775$	−6.73205	+	6.73205i	−0.241822	+	0.241822i
$776$		0			0
$777$	−13.1408	−	1.83235i	−0.471424	−	0.0657353i
$778$		0			0
$779$	21.7154			0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	4.01372	+	37.0335i	0.143439	+	1.32347i
$784$		0			0
$785$	−5.11553	+	5.11553i	−0.182581	+	0.182581i
$786$		0			0
$787$	−4.29423	−	16.0263i	−0.153073	−	0.571275i	−0.999263	−	0.0383938i	$-0.987776\pi$
$787$	−4.29423	−	16.0263i	−0.153073	−	0.571275i	0.846190	−	0.532881i	$-0.178891\pi$
$788$		0			0
$789$	14.4987	+	35.7742i	0.516167	+	1.27360i
$790$		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
$795$	1.62261	−	1.22548i	0.0575482	−	0.0434632i
$796$		0			0
$797$	20.1563	−	34.9118i	0.713973	−	1.23664i	−0.249381	−	0.968405i	$-0.580227\pi$
$797$	20.1563	−	34.9118i	0.713973	−	1.23664i	0.963354	−	0.268232i	$-0.0864395\pi$
$798$		0			0
$799$	29.3205	−	7.85641i	1.03729	−	0.277940i
$800$		0			0
$801$	14.3660	−	24.0264i	0.507596	−	0.848929i
$802$		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	$-0.504505\pi$
$809$	24.0261	−	13.8715i	0.844712	−	0.487694i	0.858863	+	0.512205i	$0.171171\pi$
$810$		0			0
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	0.289882	−	0.957062i	$-0.406384\pi$
$811$	−19.0000	−	19.0000i	−0.667180	−	0.667180i	−0.957062	+	0.289882i	$0.906384\pi$
$812$		0			0
$813$	5.21634	−	12.3259i	0.182945	−	0.432289i
$814$		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
$819$	−1.21785	+	15.2485i	−0.0425549	+	0.532826i
$820$		0			0
$821$	−41.5864	−	11.1430i	−1.45137	−	0.388895i	−0.554873	−	0.831935i	$-0.687233\pi$
$821$	−41.5864	−	11.1430i	−1.45137	−	0.388895i	−0.896502	+	0.443040i	$0.853900\pi$
$822$		0			0
$823$	7.39230	+	4.26795i	0.257680	+	0.148771i	0.623276	−	0.782002i	$-0.285801\pi$
$823$	7.39230	+	4.26795i	0.257680	+	0.148771i	−0.365596	+	0.930774i	$0.619135\pi$
$824$		0			0
$825$	−7.58798	+	17.9300i	−0.264180	+	0.624242i
$826$		0			0
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.993726	+	0.111845i	$0.0356760\pi$
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.111845	+	0.993726i	$0.464324\pi$
$828$		0			0
$829$	41.6769	−	24.0622i	1.44750	−	0.835714i	0.449167	−	0.893448i	$-0.351721\pi$
$829$	41.6769	−	24.0622i	1.44750	−	0.835714i	0.998332	+	0.0577338i	$0.0183875\pi$
$830$		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
$837$	16.8836	−	6.54383i	0.583582	−	0.226188i
$838$		0			0
$839$	9.79282	−	2.62398i	0.338086	−	0.0905898i	−0.0857819	−	0.996314i	$-0.527339\pi$
$839$	9.79282	−	2.62398i	0.338086	−	0.0905898i	0.423868	+	0.905724i	$0.360672\pi$
$840$		0			0
$841$	11.1962	−	19.3923i	0.386074	−	0.668700i
$842$		0			0
$843$	23.7128	−	17.9091i	0.816714	−	0.616822i
$844$		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
$849$	4.28626	+	10.5760i	0.147104	+	0.362967i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	−0.977364	−	0.211566i	$-0.932144\pi$
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	0.211566	+	0.977364i	$0.432144\pi$
$854$		0			0
$855$	−12.5305	+	12.1530i	−0.428534	+	0.415623i
$856$		0			0
$857$	3.32707			0.113651			0.0568253	−	0.998384i	$-0.481902\pi$
$857$	3.32707			0.113651			0.0568253	+	0.998384i	$0.481902\pi$
$858$		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
$861$	13.6351	+	1.90128i	0.464683	+	0.0647953i
$862$		0			0
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	−0.324980	−	0.945721i	$-0.605358\pi$
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	0.945721	+	0.324980i	$0.105358\pi$
$864$		0			0
$865$	6.80385	+	25.3923i	0.231338	+	0.863364i
$866$		0			0
$867$	13.4716	−	5.45979i	0.457518	−	0.185424i
$868$		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
$873$	−5.07425	−	0.0776093i	−0.171737	−	0.00262668i
$874$		0			0
$875$	8.23373	−	14.2612i	0.278351	−	0.482118i
$876$		0			0
$877$	28.9904	−	7.76795i	0.978936	−	0.262305i	0.266339	−	0.963879i	$-0.414186\pi$
$877$	28.9904	−	7.76795i	0.978936	−	0.262305i	0.712596	+	0.701574i	$0.247519\pi$
$878$		0			0
$879$	−0.383584	−	3.09640i	−0.0129380	−	0.104439i
$880$		0			0
$881$	11.7417	+	20.3372i	0.395588	+	0.685178i	0.993176	−	0.116625i	$-0.0372076\pi$
$881$	11.7417	+	20.3372i	0.395588	+	0.685178i	−0.597588	+	0.801803i	$0.703874\pi$
$882$		0			0
$883$			33.3731i			1.12309i	0.827445	+	0.561547i	$0.189793\pi$
$883$			33.3731i			1.12309i	−0.827445	+	0.561547i	$0.810207\pi$
$884$		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	$-0.527317\pi$
$887$	21.8683	−	12.6257i	0.734266	−	0.423929i	0.819981	+	0.572391i	$0.193984\pi$
$888$		0			0
$889$	9.12436	+	9.12436i	0.306021	+	0.306021i
$890$		0			0
$891$	26.9723	−	25.3708i	0.903607	−	0.849954i
$892$		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
$903$	−4.95408	−	2.09657i	−0.164861	−	0.0697695i
$904$		0			0
$905$	−3.19465	−	3.19465i	−0.106194	−	0.106194i
$906$		0			0
$907$	15.0000	−	8.66025i	0.498067	−	0.287559i	−0.229848	−	0.973227i	$-0.573823\pi$
$907$	15.0000	−	8.66025i	0.498067	−	0.287559i	0.727915	+	0.685668i	$0.240490\pi$
$908$		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
$915$	18.1204	−	2.24477i	0.599043	−	0.0742099i
$916$		0			0
$917$	−10.8577	+	2.90931i	−0.358553	+	0.0960740i
$918$		0			0
$919$	6.70577	−	11.6147i	0.221203	−	0.383135i	−0.733971	−	0.679181i	$-0.762335\pi$
$919$	6.70577	−	11.6147i	0.221203	−	0.383135i	0.955174	+	0.296046i	$0.0956683\pi$
$920$		0			0
$921$	−12.3892	−	16.4041i	−0.408236	−	0.540533i
$922$		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
$927$	5.68585	−	19.9918i	0.186748	−	0.656616i
$928$		0			0
$929$	−5.27594	−	19.6901i	−0.173098	−	0.646011i	−0.996868	−	0.0790861i	$-0.974800\pi$
$929$	−5.27594	−	19.6901i	−0.173098	−	0.646011i	0.823770	−	0.566924i	$-0.191867\pi$
$930$		0			0
$931$	13.6603	−	13.6603i	0.447697	−	0.447697i
$932$		0			0
$933$	2.41072	−	17.2886i	0.0789234	−	0.566004i
$934$		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
$939$	−0.478405	+	3.43091i	−0.0156122	+	0.111963i
$940$		0			0
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	−0.840285	−	0.542144i	$-0.817613\pi$
$941$	−9.14570	+	9.14570i	−0.298141	+	0.298141i	0.542144	+	0.840285i	$0.317613\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−8.93193	+	6.53374i	−0.290556	+	0.212543i
$946$		0			0
$947$	2.77689	−	10.3635i	0.0902368	−	0.336768i	−0.906018	−	0.423240i	$-0.860893\pi$
$947$	2.77689	−	10.3635i	0.0902368	−	0.336768i	0.996254	+	0.0864720i	$0.0275593\pi$
$948$		0			0
$949$	−3.45448	+	3.03590i	−0.112137	+	0.0985494i
$950$		0			0
$951$	−16.7583	−	22.1891i	−0.543425	−	0.719531i
$952$		0			0
$953$	−0.988427	+	1.71201i	−0.0320183	+	0.0554573i	−0.881591	−	0.472015i	$-0.843527\pi$
$953$	−0.988427	+	1.71201i	−0.0320183	+	0.0554573i	0.849572	+	0.527472i	$0.176860\pi$
$954$		0			0
$955$	−7.02628	+	1.88269i	−0.227365	+	0.0609223i
$956$		0			0
$957$	−50.7000	+	6.28076i	−1.63890	+	0.203028i
$958$		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	0.995062	−	0.0992599i	$-0.0316475\pi$
$967$	27.8564	+	27.8564i	0.895802	+	0.895802i	−0.0992599	+	0.995062i	$0.531648\pi$
$968$		0			0
$969$	31.0556	+	13.1428i	0.997651	+	0.422207i
$970$		0			0
$971$	−41.4335	−	23.9216i	−1.32966	−	0.767682i	−0.344416	−	0.938817i	$-0.611923\pi$
$971$	−41.4335	−	23.9216i	−1.32966	−	0.767682i	−0.985247	+	0.171136i	$0.945256\pi$
$972$		0			0
$973$	−25.1244	−	6.73205i	−0.805450	−	0.215820i
$974$		0			0
$975$	−16.7115	−	3.43895i	−0.535196	−	0.110134i
$976$		0			0
$977$	22.8847	+	6.13194i	0.732147	+	0.196178i	0.605585	−	0.795780i	$-0.292939\pi$
$977$	22.8847	+	6.13194i	0.732147	+	0.196178i	0.126562	+	0.991959i	$0.459606\pi$
$978$		0			0
$979$	33.2487	+	19.1962i	1.06263	+	0.613512i
$980$		0			0
$981$	27.2485	+	48.9082i	0.869978	+	1.56152i
$982$		0			0
$983$	30.4433	+	30.4433i	0.970992	+	0.970992i	0.999591	−	0.0285990i	$-0.00910459\pi$
$983$	30.4433	+	30.4433i	0.970992	+	0.970992i	−0.0285990	+	0.999591i	$0.509105\pi$
$984$		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	−0.807816	−	0.589434i	$-0.799351\pi$
$991$	−28.7846	−	49.8564i	−0.914373	−	1.58374i	−0.106557	−	0.994307i	$-0.533983\pi$
$992$		0			0
$993$	7.28650	+	58.8186i	0.231230	+	1.86655i
$994$		0			0
$995$	−18.8061	+	5.03908i	−0.596193	+	0.159750i
$996$		0			0
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	−0.805266	−	0.592914i	$-0.797977\pi$
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	0.916112	+	0.400923i	$0.131311\pi$
$998$		0			0
$999$	−17.6416	+	21.9305i	−0.558156	+	0.693850i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	4.3	odd	2
39.2.k.b.11.2	yes	8	12.11	even	2
39.2.k.b.32.1	yes	8	156.71	odd	12
39.2.k.b.32.2	yes	8	52.19	even	12
507.2.f.e.239.2		8	156.11	odd	12
507.2.f.e.239.3		8	52.11	even	12
507.2.f.e.437.2		8	52.23	odd	6
507.2.f.e.437.3		8	156.23	even	6
507.2.f.f.239.2		8	52.15	even	12
507.2.f.f.239.3		8	156.119	odd	12
507.2.f.f.437.2		8	156.107	even	6
507.2.f.f.437.3		8	52.3	odd	6
507.2.k.d.89.1		8	156.155	even	2
507.2.k.d.89.2		8	52.51	odd	2
507.2.k.d.188.1		8	52.7	even	12
507.2.k.d.188.2		8	156.59	odd	12
507.2.k.e.80.1		8	52.31	even	4
507.2.k.e.80.2		8	156.83	odd	4
507.2.k.e.488.1		8	156.35	even	6
507.2.k.e.488.2		8	52.35	odd	6
507.2.k.f.80.1		8	156.47	odd	4
507.2.k.f.80.2		8	52.47	even	4
507.2.k.f.488.1		8	52.43	odd	6
507.2.k.f.488.2		8	156.95	even	6
624.2.cn.c.305.1		8	39.32	even	12	inner
624.2.cn.c.305.2		8	13.6	odd	12	inner
624.2.cn.c.401.1		8	1.1	even	1	trivial
624.2.cn.c.401.2		8	3.2	odd	2	inner
975.2.bo.d.401.1		8	60.59	even	2
975.2.bo.d.401.2		8	20.19	odd	2
975.2.bo.d.851.1		8	260.19	even	12
975.2.bo.d.851.2		8	780.539	odd	12
975.2.bp.e.149.1		8	260.123	odd	12
975.2.bp.e.149.2		8	780.383	even	12
975.2.bp.e.674.1		8	60.47	odd	4
975.2.bp.e.674.2		8	20.7	even	4
975.2.bp.f.149.1		8	780.227	even	12
975.2.bp.f.149.2		8	260.227	odd	12
975.2.bp.f.674.1		8	20.3	even	4
975.2.bp.f.674.2		8	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.239203 + 1.71545i) q^{3} +(1.06488 - 1.06488i) q^{5} +(-0.366025 - 1.36603i) q^{7} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})\)	\(q+(-0.239203 + 1.71545i) q^{3} +(1.06488 - 1.06488i) q^{5} +(-0.366025 - 1.36603i) q^{7} +(-2.88556 - 0.820682i) q^{9} +(1.06488 - 3.97420i) q^{11} +(3.59808 + 0.232051i) q^{13} +(1.57203 + 2.08148i) q^{15} +(2.51954 - 4.36397i) q^{17} +(3.73205 - 1.00000i) q^{19} +(2.43091 - 0.301143i) q^{21} +2.73205i q^{25} +(2.09808 - 4.75374i) q^{27} +(-6.20840 + 3.58442i) q^{29} +(2.46410 + 2.46410i) q^{31} +(6.56283 + 2.77739i) q^{33} +(-1.84443 - 1.06488i) q^{35} +(-5.23205 - 1.40192i) q^{37} +(-1.25874 + 6.11683i) q^{39} +(5.42885 + 1.45466i) q^{41} +(-1.90192 - 1.09808i) q^{43} +(-3.94672 + 2.19886i) q^{45} +(4.25953 + 4.25953i) q^{47} +(4.33013 - 2.50000i) q^{49} +(6.88351 + 5.36603i) q^{51} -0.779548i q^{53} +(-3.09808 - 5.36603i) q^{55} +(0.822738 + 6.64136i) q^{57} +(2.90931 - 0.779548i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-0.0648824 + 4.24214i) q^{63} +(4.07863 - 3.58442i) q^{65} +(1.53590 - 5.73205i) q^{67} +(0.779548 + 2.90931i) q^{71} +(-0.901924 + 0.901924i) q^{73} +(-4.68671 - 0.653513i) q^{75} -5.81863 q^{77} -2.00000 q^{79} +(7.65296 + 4.73626i) q^{81} +(-2.90931 + 2.90931i) q^{83} +(-1.96410 - 7.33013i) q^{85} +(-4.66384 - 11.5076i) q^{87} +(-2.41510 + 9.01327i) q^{89} +(-1.00000 - 5.00000i) q^{91} +(-4.81647 + 3.63763i) q^{93} +(2.90931 - 5.03908i) q^{95} +(1.63397 - 0.437822i) q^{97} +(-6.33434 + 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more