LMFDB - Embedded newform 693.2.by.d.163.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(37,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 6]))

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

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

chi := DirichletCharacter("693.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.by (of order $15$, degree $8$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			163.8
Character	$\chi$	$=$	693.163
Dual form			693.2.by.d.676.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82701 + 2.02911i) q^{2} +(-0.570229 + 5.42537i) q^{4} +(-2.89339 - 0.615009i) q^{5} +(-2.43409 - 1.03693i) q^{7} +(-7.63253 + 5.54536i) q^{8} +O(q^{10})$	\(q+(1.82701 + 2.02911i) q^{2} +(-0.570229 + 5.42537i) q^{4} +(-2.89339 - 0.615009i) q^{5} +(-2.43409 - 1.03693i) q^{7} +(-7.63253 + 5.54536i) q^{8} +(-4.03835 - 6.99462i) q^{10} +(0.272985 + 3.30537i) q^{11} +(1.13875 - 3.50471i) q^{13} +(-2.34307 - 6.83351i) q^{14} +(-14.5248 - 3.08734i) q^{16} +(-0.929192 + 1.03197i) q^{17} +(0.159341 + 1.51602i) q^{19} +(4.98655 - 15.3470i) q^{20} +(-6.20820 + 6.59288i) q^{22} +(-2.58882 + 4.48397i) q^{23} +(3.42574 + 1.52524i) q^{25} +(9.19193 - 4.09251i) q^{26} +(7.01372 - 12.6145i) q^{28} +(3.24703 + 2.35910i) q^{29} +(-3.19840 + 0.679841i) q^{31} +(-10.8381 - 18.7722i) q^{32} -3.79163 q^{34} +(6.40504 + 4.49723i) q^{35} +(4.05967 - 1.80748i) q^{37} +(-2.78506 + 3.09312i) q^{38} +(25.4943 - 11.3508i) q^{40} +(-6.29070 + 4.57046i) q^{41} -5.34560 q^{43} +(-18.0885 - 0.403773i) q^{44} +(-13.8283 + 2.93929i) q^{46} +(0.799720 + 7.60882i) q^{47} +(4.84954 + 5.04796i) q^{49} +(3.16401 + 9.73783i) q^{50} +(18.3650 + 8.17662i) q^{52} +(2.84045 - 0.603756i) q^{53} +(1.24298 - 9.73162i) q^{55} +(24.3284 - 5.58346i) q^{56} +(1.14550 + 10.8987i) q^{58} +(-0.800740 + 7.61853i) q^{59} +(0.892795 + 0.189769i) q^{61} +(-7.22300 - 5.24781i) q^{62} +(9.11197 - 28.0438i) q^{64} +(-5.45027 + 9.44014i) q^{65} +(5.18003 + 8.97207i) q^{67} +(-5.06898 - 5.62967i) q^{68} +(2.57673 + 21.2130i) q^{70} +(-3.30052 - 10.1580i) q^{71} +(-0.531901 + 5.06070i) q^{73} +(11.0846 + 4.93520i) q^{74} -8.31585 q^{76} +(2.76298 - 8.32862i) q^{77} +(3.79892 + 4.21913i) q^{79} +(40.1271 + 17.8657i) q^{80} +(-20.7671 - 4.41419i) q^{82} +(0.465946 + 1.43403i) q^{83} +(3.32319 - 2.41444i) q^{85} +(-9.76649 - 10.8468i) q^{86} +(-20.4130 - 23.7145i) q^{88} +(5.95694 - 10.3177i) q^{89} +(-6.40595 + 7.34995i) q^{91} +(-22.8510 - 16.6022i) q^{92} +(-13.9780 + 15.5242i) q^{94} +(0.471334 - 4.48445i) q^{95} +(2.60091 - 8.00477i) q^{97} +(-1.38266 + 19.0629i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 10 q^{4} - q^{7} - 8 q^{8}+O(q^{10}) $ 64 * q + 10 * q^4 - q^7 - 8 * q^8	$ 64 q + 10 q^{4} - q^{7} - 8 q^{8} - 22 q^{10} + 13 q^{11} - 8 q^{13} + 26 q^{14} - 4 q^{17} + 10 q^{19} - 24 q^{20} - 38 q^{22} + 8 q^{23} - 2 q^{25} - 4 q^{26} - 67 q^{28} - 2 q^{29} + 25 q^{31} - 72 q^{32} - 56 q^{34} - 19 q^{35} - 12 q^{37} + 37 q^{38} - 9 q^{40} - 20 q^{41} - 100 q^{43} + 5 q^{44} - 33 q^{46} + 18 q^{47} + 29 q^{49} + 46 q^{50} + 26 q^{52} + 49 q^{53} - 24 q^{55} + 48 q^{56} - 40 q^{58} - q^{59} + 3 q^{61} - 4 q^{62} - 24 q^{64} - 82 q^{65} + 76 q^{67} + 39 q^{68} + 59 q^{70} - 70 q^{71} - 3 q^{73} - 32 q^{74} + 104 q^{76} - 38 q^{77} - 15 q^{79} + 83 q^{80} + 42 q^{82} - 68 q^{83} + 62 q^{85} + 47 q^{86} - 64 q^{88} - 82 q^{89} - 10 q^{91} - 190 q^{92} - 6 q^{94} + 53 q^{95} - 32 q^{97} + 152 q^{98}+O(q^{100}) $ 64 * q + 10 * q^4 - q^7 - 8 * q^8 - 22 * q^10 + 13 * q^11 - 8 * q^13 + 26 * q^14 - 4 * q^17 + 10 * q^19 - 24 * q^20 - 38 * q^22 + 8 * q^23 - 2 * q^25 - 4 * q^26 - 67 * q^28 - 2 * q^29 + 25 * q^31 - 72 * q^32 - 56 * q^34 - 19 * q^35 - 12 * q^37 + 37 * q^38 - 9 * q^40 - 20 * q^41 - 100 * q^43 + 5 * q^44 - 33 * q^46 + 18 * q^47 + 29 * q^49 + 46 * q^50 + 26 * q^52 + 49 * q^53 - 24 * q^55 + 48 * q^56 - 40 * q^58 - q^59 + 3 * q^61 - 4 * q^62 - 24 * q^64 - 82 * q^65 + 76 * q^67 + 39 * q^68 + 59 * q^70 - 70 * q^71 - 3 * q^73 - 32 * q^74 + 104 * q^76 - 38 * q^77 - 15 * q^79 + 83 * q^80 + 42 * q^82 - 68 * q^83 + 62 * q^85 + 47 * q^86 - 64 * q^88 - 82 * q^89 - 10 * q^91 - 190 * q^92 - 6 * q^94 + 53 * q^95 - 32 * q^97 + 152 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.82701	+	2.02911i	1.29189	+	1.43479i	0.839869	+	0.542789i	$0.182632\pi$
$2$	1.82701	+	2.02911i	1.29189	+	1.43479i	0.452026	+	0.892005i	$0.350702\pi$
$3$		0			0
$3$		0			0
$4$	−0.570229	+	5.42537i	−0.285115	+	2.71268i
$5$	−2.89339	−	0.615009i	−1.29396	−	0.275040i	−0.491047	−	0.871133i	$-0.663386\pi$
$5$	−2.89339	−	0.615009i	−1.29396	−	0.275040i	−0.802916	+	0.596092i	$0.796719\pi$
$6$		0			0
$7$	−2.43409	−	1.03693i	−0.919998	−	0.391923i
$7$	−2.43409	−	1.03693i	−0.919998	−	0.391923i
$8$	−7.63253	+	5.54536i	−2.69851	+	1.96058i
$9$		0			0
$10$	−4.03835	−	6.99462i	−1.27704	−	2.21189i
$11$	0.272985	+	3.30537i	0.0823082	+	0.996607i
$11$	0.272985	+	3.30537i	0.0823082	+	0.996607i
$12$		0			0
$13$	1.13875	−	3.50471i	0.315832	−	0.972031i	−0.659579	−	0.751636i	$-0.729265\pi$
$13$	1.13875	−	3.50471i	0.315832	−	0.972031i	0.975411	−	0.220395i	$-0.0707348\pi$
$14$	−2.34307	−	6.83351i	−0.626211	−	1.82633i
$15$		0			0
$16$	−14.5248	−	3.08734i	−3.63119	−	0.771834i
$17$	−0.929192	+	1.03197i	−0.225362	+	0.250290i	−0.845213	−	0.534430i	$-0.820526\pi$
$17$	−0.929192	+	1.03197i	−0.225362	+	0.250290i	0.619851	+	0.784720i	$0.287193\pi$
$18$		0			0
$19$	0.159341	+	1.51602i	0.0365552	+	0.347800i	0.997478	+	0.0709819i	$0.0226132\pi$
$19$	0.159341	+	1.51602i	0.0365552	+	0.347800i	−0.960922	+	0.276818i	$0.910720\pi$
$20$	4.98655	−	15.3470i	1.11503	−	3.43170i
$21$		0			0
$22$	−6.20820	+	6.59288i	−1.32359	+	1.40561i
$23$	−2.58882	+	4.48397i	−0.539806	+	0.934972i	0.459108	+	0.888381i	$0.348169\pi$
$23$	−2.58882	+	4.48397i	−0.539806	+	0.934972i	−0.998914	+	0.0465914i	$0.985164\pi$
$24$		0			0
$25$	3.42574	+	1.52524i	0.685148	+	0.305048i
$26$	9.19193	−	4.09251i	1.80269	−	0.802608i
$27$		0			0
$28$	7.01372	−	12.6145i	1.32547	−	2.38392i
$29$	3.24703	+	2.35910i	0.602958	+	0.438074i	0.846927	−	0.531708i	$-0.178450\pi$
$29$	3.24703	+	2.35910i	0.602958	+	0.438074i	−0.243970	+	0.969783i	$0.578450\pi$
$30$		0			0
$31$	−3.19840	+	0.679841i	−0.574450	+	0.122103i	−0.485971	−	0.873975i	$-0.661534\pi$
$31$	−3.19840	+	0.679841i	−0.574450	+	0.122103i	−0.0884789	+	0.996078i	$0.528201\pi$
$32$	−10.8381	−	18.7722i	−1.91593	−	3.31849i
$33$		0			0
$34$	−3.79163			−0.650259
$35$	6.40504	+	4.49723i	1.08265	+	0.760171i
$36$		0			0
$37$	4.05967	−	1.80748i	0.667405	−	0.297148i	−0.0449271	−	0.998990i	$-0.514306\pi$
$37$	4.05967	−	1.80748i	0.667405	−	0.297148i	0.712332	+	0.701842i	$0.247639\pi$
$38$	−2.78506	+	3.09312i	−0.451796	+	0.501770i
$39$		0			0
$40$	25.4943	−	11.3508i	4.03101	−	1.79472i
$41$	−6.29070	+	4.57046i	−0.982442	+	0.713786i	−0.958253	−	0.285921i	$-0.907700\pi$
$41$	−6.29070	+	4.57046i	−0.982442	+	0.713786i	−0.0241891	+	0.999707i	$0.507700\pi$
$42$		0			0
$43$	−5.34560			−0.815196			−0.407598	−	0.913161i	$-0.633634\pi$
$43$	−5.34560			−0.815196			−0.407598	+	0.913161i	$0.633634\pi$
$44$	−18.0885	−	0.403773i	−2.72695	−	0.0608710i
$45$		0			0
$46$	−13.8283	+	2.93929i	−2.03887	+	0.433374i
$47$	0.799720	+	7.60882i	0.116651	+	1.10986i	0.883629	+	0.468188i	$0.155093\pi$
$47$	0.799720	+	7.60882i	0.116651	+	1.10986i	−0.766978	+	0.641673i	$0.778240\pi$
$48$		0			0
$49$	4.84954	+	5.04796i	0.692792	+	0.721137i
$50$	3.16401	+	9.73783i	0.447459	+	1.37714i
$51$		0			0
$52$	18.3650	+	8.17662i	2.54676	+	1.13389i
$53$	2.84045	−	0.603756i	0.390165	−	0.0829322i	−0.00865206	−	0.999963i	$-0.502754\pi$
$53$	2.84045	−	0.603756i	0.390165	−	0.0829322i	0.398817	+	0.917030i	$0.369421\pi$
$54$		0			0
$55$	1.24298	−	9.73162i	0.167603	−	1.31221i
$56$	24.3284	−	5.58346i	3.25102	−	0.746121i
$57$		0			0
$58$	1.14550	+	10.8987i	0.150411	+	1.43107i
$59$	−0.800740	+	7.61853i	−0.104247	+	0.991848i	0.809928	+	0.586530i	$0.199506\pi$
$59$	−0.800740	+	7.61853i	−0.104247	+	0.991848i	−0.914175	+	0.405319i	$0.867160\pi$
$60$		0			0
$61$	0.892795	+	0.189769i	0.114311	+	0.0242975i	0.264712	−	0.964328i	$-0.414723\pi$
$61$	0.892795	+	0.189769i	0.114311	+	0.0242975i	−0.150401	+	0.988625i	$0.548057\pi$
$62$	−7.22300	−	5.24781i	−0.917321	−	0.666473i
$63$		0			0
$64$	9.11197	−	28.0438i	1.13900	−	3.50547i
$65$	−5.45027	+	9.44014i	−0.676023	+	1.17091i
$66$		0			0
$67$	5.18003	+	8.97207i	0.632841	+	1.09611i	0.986968	+	0.160915i	$0.0514446\pi$
$67$	5.18003	+	8.97207i	0.632841	+	1.09611i	−0.354127	+	0.935197i	$0.615222\pi$
$68$	−5.06898	−	5.62967i	−0.614704	−	0.682698i
$69$		0			0
$70$	2.57673	+	21.2130i	0.307979	+	2.53544i
$71$	−3.30052	−	10.1580i	−0.391700	−	1.20553i	−0.931502	−	0.363737i	$-0.881501\pi$
$71$	−3.30052	−	10.1580i	−0.391700	−	1.20553i	0.539801	−	0.841792i	$-0.318499\pi$
$72$		0			0
$73$	−0.531901	+	5.06070i	−0.0622543	+	0.592310i	0.918276	+	0.395941i	$0.129582\pi$
$73$	−0.531901	+	5.06070i	−0.0622543	+	0.592310i	−0.980530	+	0.196369i	$0.937085\pi$
$74$	11.0846	+	4.93520i	1.28856	+	0.573705i
$75$		0			0
$76$	−8.31585			−0.953894
$77$	2.76298	−	8.32862i	0.314870	−	0.949135i
$78$		0			0
$79$	3.79892	+	4.21913i	0.427412	+	0.474689i	0.917930	−	0.396742i	$-0.129859\pi$
$79$	3.79892	+	4.21913i	0.427412	+	0.474689i	−0.490518	+	0.871431i	$0.663193\pi$
$80$	40.1271	+	17.8657i	4.48635	+	1.99745i
$81$		0			0
$82$	−20.7671	−	4.41419i	−2.29335	−	0.487466i
$83$	0.465946	+	1.43403i	0.0511442	+	0.157406i	0.973367	−	0.229254i	$-0.0736287\pi$
$83$	0.465946	+	1.43403i	0.0511442	+	0.157406i	−0.922222	+	0.386660i	$0.873629\pi$
$84$		0			0
$85$	3.32319	−	2.41444i	0.360450	−	0.261883i
$86$	−9.76649	−	10.8468i	−1.05315	−	1.16964i
$87$		0			0
$88$	−20.4130	−	23.7145i	−2.17604	−	2.52798i
$89$	5.95694	−	10.3177i	0.631434	−	1.09368i	−0.355825	−	0.934553i	$-0.615800\pi$
$89$	5.95694	−	10.3177i	0.631434	−	1.09368i	0.987259	−	0.159123i	$-0.0508667\pi$
$90$		0			0
$91$	−6.40595	+	7.34995i	−0.671526	+	0.770484i
$92$	−22.8510	−	16.6022i	−2.38238	−	1.73090i
$93$		0			0
$94$	−13.9780	+	15.5242i	−1.44172	+	1.60119i
$95$	0.471334	−	4.48445i	0.0483579	−	0.460094i
$96$		0			0
$97$	2.60091	−	8.00477i	0.264082	−	0.812761i	−0.727821	−	0.685767i	$-0.759467\pi$
$97$	2.60091	−	8.00477i	0.264082	−	0.812761i	0.991903	−	0.126994i	$-0.0405330\pi$
$98$	−1.38266	+	19.0629i	−0.139670	+	1.92565i
$99$		0			0
$100$	−10.2284	+	17.7162i	−1.02284	+	1.77162i
$101$	2.79642	−	0.594398i	0.278254	−	0.0591448i	−0.0666706	−	0.997775i	$-0.521238\pi$
$101$	2.79642	−	0.594398i	0.278254	−	0.0591448i	0.344925	+	0.938630i	$0.387904\pi$
$102$		0			0
$103$	11.1818	−	4.97846i	1.10178	−	0.490542i	0.226424	−	0.974029i	$-0.427297\pi$
$103$	11.1818	−	4.97846i	1.10178	−	0.490542i	0.875352	+	0.483487i	$0.160630\pi$
$104$	10.7433	+	33.0646i	1.05347	+	3.24225i
$105$		0			0
$106$	6.41462	+	4.66049i	0.623043	+	0.452667i
$107$	−1.75175	−	16.6668i	−0.169348	−	1.61124i	−0.667813	−	0.744329i	$-0.732770\pi$
$107$	−1.75175	−	16.6668i	−0.169348	−	1.61124i	0.498465	−	0.866910i	$-0.333897\pi$
$108$		0			0
$109$	7.66711	+	13.2798i	0.734376	+	1.27198i	0.954996	+	0.296617i	$0.0958586\pi$
$109$	7.66711	+	13.2798i	0.734376	+	1.27198i	−0.220620	+	0.975360i	$0.570808\pi$
$110$	22.0174	−	15.2577i	2.09928	−	1.45476i
$111$		0			0
$112$	32.1532	+	22.5761i	3.03819	+	2.13324i
$113$	−8.98635	+	6.52897i	−0.845365	+	0.614193i	−0.923864	−	0.382721i	$-0.874987\pi$
$113$	−8.98635	+	6.52897i	−0.845365	+	0.614193i	0.0784993	+	0.996914i	$0.474987\pi$
$114$		0			0
$115$	10.2481	−	11.3817i	0.955645	−	1.06135i
$116$	−14.6506	+	16.2711i	−1.36027	+	1.51073i
$117$		0			0
$118$	−16.9218	+	12.2944i	−1.55778	+	1.13179i
$119$	3.33182	−	1.54840i	0.305427	−	0.141942i
$120$		0			0
$121$	−10.8510	+	1.80464i	−0.986451	+	0.164058i
$122$	1.24609	+	2.15829i	0.112815	+	0.195402i
$123$		0			0
$124$	−1.86457	−	17.7402i	−0.167443	−	1.59311i
$125$	2.99151	+	2.17346i	0.267569	+	0.194400i
$126$		0			0
$127$	−2.48103	−	7.63581i	−0.220155	−	0.677569i	−0.998747	−	0.0500382i	$-0.984066\pi$
$127$	−2.48103	−	7.63581i	−0.220155	−	0.677569i	0.778592	−	0.627531i	$-0.215934\pi$
$128$	33.9470	−	15.1142i	3.00052	−	1.33592i
$129$		0			0
$130$	−29.1128	+	6.18811i	−2.55336	+	0.542733i
$131$	−6.05426	+	10.4863i	−0.528963	+	0.916191i	0.470466	+	0.882418i	$0.344086\pi$
$131$	−6.05426	+	10.4863i	−0.528963	+	0.916191i	−0.999430	+	0.0337733i	$0.989248\pi$
$132$		0			0
$133$	1.18417	−	3.85536i	0.102680	−	0.334302i
$134$	−8.74129	+	26.9029i	−0.755132	+	2.32406i
$135$		0			0
$136$	1.36943	−	13.0293i	0.117428	−	1.11725i
$137$	7.54286	−	8.37719i	0.644430	−	0.715712i	−0.329094	−	0.944297i	$-0.606743\pi$
$137$	7.54286	−	8.37719i	0.644430	−	0.715712i	0.973524	+	0.228585i	$0.0734100\pi$
$138$		0			0
$139$	−6.91415	−	5.02342i	−0.586450	−	0.426081i	0.254594	−	0.967048i	$-0.418058\pi$
$139$	−6.91415	−	5.02342i	−0.586450	−	0.426081i	−0.841044	+	0.540967i	$0.818058\pi$
$140$	−28.0515	+	32.1852i	−2.37078	+	2.72015i
$141$		0			0
$142$	14.5815	−	25.2559i	1.22365	−	2.11943i
$143$	11.8952	+	2.80725i	0.994728	+	0.234754i
$144$		0			0
$145$	−7.94405	−	8.82276i	−0.659717	−	0.732690i
$146$	−11.2405	+	8.16669i	−0.930269	+	0.675880i
$147$		0			0
$148$	7.49131	+	23.0559i	0.615782	+	1.89518i
$149$	−6.32149	−	1.34368i	−0.517877	−	0.110078i	−0.0584442	−	0.998291i	$-0.518614\pi$
$149$	−6.32149	−	1.34368i	−0.517877	−	0.110078i	−0.459433	+	0.888213i	$0.651947\pi$
$150$		0			0
$151$	11.5986	+	5.16405i	0.943884	+	0.420244i	0.820200	−	0.572078i	$-0.193862\pi$
$151$	11.5986	+	5.16405i	0.943884	+	0.420244i	0.123684	+	0.992322i	$0.460529\pi$
$152$	−9.62307	−	10.6875i	−0.780534	−	0.866871i
$153$		0			0
$154$	21.9477	−	9.61015i	1.76859	−	0.774408i
$155$	9.67233			0.776900
$156$		0			0
$157$	−11.0609	−	4.92461i	−0.882752	−	0.393027i	−0.0852621	−	0.996359i	$-0.527173\pi$
$157$	−11.0609	−	4.92461i	−0.882752	−	0.393027i	−0.797490	+	0.603332i	$0.793839\pi$
$158$	−1.62037	+	15.4168i	−0.128910	+	1.22650i
$159$		0			0
$160$	19.8139	+	60.9808i	1.56642	+	4.82096i
$161$	10.9510	−	8.22993i	0.863058	−	0.648609i
$162$		0			0
$163$	5.12927	+	5.69663i	0.401756	+	0.446195i	0.909744	−	0.415169i	$-0.136278\pi$
$163$	5.12927	+	5.69663i	0.401756	+	0.446195i	−0.507989	+	0.861364i	$0.669611\pi$
$164$	−21.2093	−	36.7356i	−1.65617	−	2.86857i
$165$		0			0
$166$	−2.05852	+	3.56545i	−0.159772	+	0.276733i
$167$	4.93044	−	15.1743i	0.381529	−	1.17422i	−0.557439	−	0.830218i	$-0.688216\pi$
$167$	4.93044	−	15.1743i	0.381529	−	1.17422i	0.938967	−	0.344006i	$-0.111784\pi$
$168$		0			0
$169$	−0.469004	−	0.340752i	−0.0360773	−	0.0262117i
$170$	10.9707	+	2.33189i	0.841411	+	0.178848i
$171$		0			0
$172$	3.04822	−	29.0018i	0.232424	−	2.21137i
$173$	−1.37414	−	13.0740i	−0.104474	−	0.994001i	−0.913668	−	0.406460i	$-0.866763\pi$
$173$	−1.37414	−	13.0740i	−0.104474	−	0.994001i	0.809195	−	0.587540i	$-0.199904\pi$
$174$		0			0
$175$	−6.75698	−	7.26482i	−0.510780	−	0.549169i
$176$	6.23974	−	48.8526i	0.470338	−	3.68240i
$177$		0			0
$178$	31.8192	−	6.76337i	2.38495	−	0.506936i
$179$	−9.14459	−	4.07143i	−0.683499	−	0.304313i	0.0354549	−	0.999371i	$-0.488712\pi$
$179$	−9.14459	−	4.07143i	−0.683499	−	0.304313i	−0.718954	+	0.695058i	$0.755379\pi$
$180$		0			0
$181$	−1.84046	−	5.66435i	−0.136800	−	0.421028i	0.859065	−	0.511866i	$-0.171046\pi$
$181$	−1.84046	−	5.66435i	−0.136800	−	0.421028i	−0.995866	+	0.0908378i	$0.971046\pi$
$182$	−26.6176	+	0.430114i	−1.97303	+	0.0318822i
$183$		0			0
$184$	−5.10596	−	48.5800i	−0.376416	−	3.58136i
$185$	−12.8578	+	2.73301i	−0.945326	+	0.200935i
$186$		0			0
$187$	−3.66471	−	2.78961i	−0.267990	−	0.203997i
$188$	−41.7367			−3.04396
$189$		0			0
$190$	9.96055	−	7.23676i	0.722614	−	0.525010i
$191$	−3.71311	+	1.65318i	−0.268671	+	0.119620i	−0.536651	−	0.843804i	$-0.680311\pi$
$191$	−3.71311	+	1.65318i	−0.268671	+	0.119620i	0.267979	+	0.963425i	$0.413644\pi$
$192$		0			0
$193$	−6.35499	+	7.05793i	−0.457442	+	0.508041i	−0.927103	−	0.374806i	$-0.877709\pi$
$193$	−6.35499	+	7.05793i	−0.457442	+	0.508041i	0.469661	+	0.882847i	$0.344376\pi$
$194$	20.9944	−	9.34732i	1.50731	−	0.671098i
$195$		0			0
$196$	−30.1524	+	23.4321i	−2.15374	+	1.67372i
$197$	6.93685			0.494230			0.247115	−	0.968986i	$-0.420517\pi$
$197$	6.93685			0.494230			0.247115	+	0.968986i	$0.420517\pi$
$198$		0			0
$199$	9.93057	+	17.2003i	0.703960	+	1.21929i	0.967066	+	0.254527i	$0.0819198\pi$
$199$	9.93057	+	17.2003i	0.703960	+	1.21929i	−0.263106	+	0.964767i	$0.584747\pi$
$200$	−34.6051	+	7.35554i	−2.44695	+	0.520115i
$201$		0			0
$202$	6.31520	+	4.58826i	0.444336	+	0.322829i
$203$	−5.45731	−	9.10920i	−0.383028	−	0.639341i
$204$		0			0
$205$	21.0123	−	9.35529i	1.46756	−	0.653402i
$206$	30.5311	+	13.5933i	2.12720	+	0.947093i
$207$		0			0
$208$	−27.3603	+	47.3894i	−1.89709	+	3.28586i
$209$	−4.96753	+	0.940532i	−0.343611	+	0.0650580i
$210$		0			0
$211$	−5.02451	+	15.4638i	−0.345901	+	1.06458i	0.615198	+	0.788373i	$0.289076\pi$
$211$	−5.02451	+	15.4638i	−0.345901	+	1.06458i	−0.961099	+	0.276202i	$0.910924\pi$
$212$	1.65589	+	15.7547i	0.113727	+	1.08204i
$213$		0			0
$214$	30.6182	−	34.0049i	2.09302	−	2.32453i
$215$	15.4669	+	3.28759i	1.05483	+	0.224212i
$216$		0			0
$217$	8.49013	+	1.66173i	0.576348	+	0.112806i
$218$	−12.9382	+	39.8198i	−0.876289	+	2.69694i
$219$		0			0
$220$	52.0888	+	12.2929i	3.51183	+	0.828785i
$221$	2.55865	+	4.43170i	0.172113	+	0.298109i
$222$		0			0
$223$	−21.7121	+	15.7748i	−1.45395	+	1.05636i	−0.469061	+	0.883166i	$0.655408\pi$
$223$	−21.7121	+	15.7748i	−1.45395	+	1.05636i	−0.984888	+	0.173191i	$0.944592\pi$
$224$	6.91544	+	56.9315i	0.462058	+	3.80390i
$225$		0			0
$226$	−29.6662	−	6.30574i	−1.97336	−	0.419451i
$227$	−0.753217	+	7.16638i	−0.0499928	+	0.475649i	0.940671	+	0.339320i	$0.110197\pi$
$227$	−0.753217	+	7.16638i	−0.0499928	+	0.475649i	−0.990664	+	0.136329i	$0.956470\pi$
$228$		0			0
$229$	0.985557	+	1.09457i	0.0651275	+	0.0723314i	0.774828	−	0.632172i	$-0.217836\pi$
$229$	0.985557	+	1.09457i	0.0651275	+	0.0723314i	−0.709701	+	0.704503i	$0.751170\pi$
$230$	41.8182			2.75741
$231$		0			0
$232$	−37.8651			−2.48597
$233$	9.28518	+	10.3122i	0.608292	+	0.675577i	0.966085	−	0.258224i	$-0.0831373\pi$
$233$	9.28518	+	10.3122i	0.608292	+	0.675577i	−0.357793	+	0.933801i	$0.616471\pi$
$234$		0			0
$235$	2.36559	−	22.5071i	0.154314	−	1.46820i
$236$	−40.8767	−	8.68862i	−2.66085	−	0.565581i
$237$		0			0
$238$	9.22915	+	3.93166i	0.598237	+	0.254852i
$239$	16.3818	−	11.9021i	1.05965	−	0.769881i	0.0856267	−	0.996327i	$-0.472711\pi$
$239$	16.3818	−	11.9021i	1.05965	−	0.769881i	0.974024	+	0.226446i	$0.0727108\pi$
$240$		0			0
$241$	−3.02983	−	5.24783i	−0.195169	−	0.338042i	0.751787	−	0.659406i	$-0.229192\pi$
$241$	−3.02983	−	5.24783i	−0.195169	−	0.338042i	−0.946956	+	0.321364i	$0.895859\pi$
$242$	−23.4867	−	18.7206i	−1.50978	−	1.20341i
$243$		0			0
$244$	−1.53867	+	4.73553i	−0.0985030	+	0.303161i
$245$	−10.9271	−	17.5882i	−0.698105	−	1.12367i
$246$		0			0
$247$	5.49467	+	1.16793i	0.349618	+	0.0743135i
$248$	20.6419	−	22.9252i	1.31076	−	1.45575i
$249$		0			0
$250$	1.05535	+	10.0410i	0.0667465	+	0.635051i
$251$	−7.22339	+	22.2313i	−0.455936	+	1.40323i	0.414097	+	0.910233i	$0.364098\pi$
$251$	−7.22339	+	22.2313i	−0.455936	+	1.40323i	−0.870033	+	0.492994i	$0.835902\pi$
$252$		0			0
$253$	−15.5279	−	7.33295i	−0.976230	−	0.461019i
$254$	10.9610	−	18.9850i	0.687754	−	1.19123i
$255$		0			0
$256$	38.8146	+	17.2814i	2.42591	+	1.08008i
$257$	5.24093	−	2.33341i	0.326920	−	0.145554i	−0.236713	−	0.971580i	$-0.576070\pi$
$257$	5.24093	−	2.33341i	0.326920	−	0.145554i	0.563633	+	0.826025i	$0.309403\pi$
$258$		0			0
$259$	−11.7558	+	0.189962i	−0.730471	+	0.0118037i
$260$	−48.1084	−	34.9528i	−2.98355	−	2.16768i
$261$		0			0
$262$	−32.3390	+	6.87387i	−1.99791	+	0.424669i
$263$	10.9714	+	19.0030i	0.676526	+	1.17178i	0.976020	+	0.217679i	$0.0698486\pi$
$263$	10.9714	+	19.0030i	0.676526	+	1.17178i	−0.299495	+	0.954098i	$0.596818\pi$
$264$		0			0
$265$	−8.58983			−0.527669
$266$	9.98642	−	4.64100i	0.612307	−	0.284558i
$267$		0			0
$268$	−51.6306	+	22.9874i	−3.15384	+	1.40418i
$269$	−19.4466	+	21.5977i	−1.18568	+	1.31683i	−0.248237	+	0.968699i	$0.579851\pi$
$269$	−19.4466	+	21.5977i	−1.18568	+	1.31683i	−0.937445	+	0.348134i	$0.886815\pi$
$270$		0			0
$271$	16.7861	−	7.47366i	1.01968	−	0.453993i	0.172340	−	0.985037i	$-0.444867\pi$
$271$	16.7861	−	7.47366i	1.01968	−	0.453993i	0.847344	+	0.531045i	$0.178200\pi$
$272$	16.6824	−	12.1204i	1.01152	−	0.734910i
$273$		0			0
$274$	30.7791			1.85943
$275$	−4.10630	+	11.7397i	−0.247619	+	0.707932i
$276$		0			0
$277$	−13.6917	+	2.91027i	−0.822657	+	0.174861i	−0.599963	−	0.800027i	$-0.704818\pi$
$277$	−13.6917	+	2.91027i	−0.822657	+	0.174861i	−0.222693	+	0.974889i	$0.571485\pi$
$278$	−2.43920	−	23.2074i	−0.146293	−	1.39189i
$279$		0			0
$280$	−73.8254	+	1.19295i	−4.41191	+	0.0712922i
$281$	−0.0381451	−	0.117398i	−0.00227554	−	0.00700340i	0.949912	−	0.312517i	$-0.101172\pi$
$281$	−0.0381451	−	0.117398i	−0.00227554	−	0.00700340i	−0.952188	+	0.305513i	$0.901172\pi$
$282$		0			0
$283$	−18.9137	−	8.42094i	−1.12431	−	0.500573i	−0.241542	−	0.970390i	$-0.577653\pi$
$283$	−18.9137	−	8.42094i	−1.12431	−	0.500573i	−0.882764	+	0.469817i	$0.844320\pi$
$284$	56.9928	−	12.1142i	3.38190	−	0.718845i
$285$		0			0
$286$	16.0365	+	29.2655i	0.948260	+	1.73051i
$287$	20.0514	−	4.60186i	1.18359	−	0.271639i
$288$		0			0
$289$	1.57541	+	14.9891i	0.0926715	+	0.881710i
$290$	3.38841	−	32.2386i	0.198975	−	1.89312i
$291$		0			0
$292$	−27.1529	−	5.77152i	−1.58900	−	0.337753i
$293$	−7.19595	−	5.22817i	−0.420392	−	0.305433i	0.357403	−	0.933950i	$-0.383662\pi$
$293$	−7.19595	−	5.22817i	−0.420392	−	0.305433i	−0.777796	+	0.628517i	$0.783662\pi$
$294$		0			0
$295$	7.00232	−	21.5509i	0.407691	−	1.25474i
$296$	−20.9624	+	36.3080i	−1.21842	+	2.11036i
$297$		0			0
$298$	−8.82301	−	15.2819i	−0.511103	−	0.885256i
$299$	12.7670	+	14.1792i	0.738334	+	0.820003i
$300$		0			0
$301$	13.0116	+	5.54302i	0.749979	+	0.319495i
$302$	10.7125	+	32.9696i	0.616434	+	1.89719i
$303$		0			0
$304$	2.36609	−	22.5119i	0.135705	−	1.29114i
$305$	−2.46649	−	1.09815i	−0.141231	−	0.0628801i
$306$		0			0
$307$	25.6429			1.46352			0.731759	−	0.681564i	$-0.238700\pi$
$307$	25.6429			1.46352			0.731759	+	0.681564i	$0.238700\pi$
$308$	43.6103	+	19.7394i	2.48493	+	1.12476i
$309$		0			0
$310$	17.6715	+	19.6262i	1.00367	+	1.11469i
$311$	−16.0831	−	7.16065i	−0.911988	−	0.406043i	−0.103550	−	0.994624i	$-0.533020\pi$
$311$	−16.0831	−	7.16065i	−0.911988	−	0.406043i	−0.808438	+	0.588581i	$0.799687\pi$
$312$		0			0
$313$	−8.24078	−	1.75163i	−0.465796	−	0.0990081i	−0.0309660	−	0.999520i	$-0.509858\pi$
$313$	−8.24078	−	1.75163i	−0.465796	−	0.0990081i	−0.434830	+	0.900512i	$0.643192\pi$
$314$	−10.2158	−	31.4410i	−0.576510	−	1.77432i
$315$		0			0
$316$	−25.0566	+	18.2047i	−1.40954	+	1.02409i
$317$	−13.6371	−	15.1455i	−0.765934	−	0.850656i	0.226426	−	0.974028i	$-0.427296\pi$
$317$	−13.6371	−	15.1455i	−0.765934	−	0.850656i	−0.992360	+	0.123372i	$0.960629\pi$
$318$		0			0
$319$	−6.91132	+	11.3766i	−0.386960	+	0.636969i
$320$	−43.6117	+	75.5376i	−2.43797	+	4.22268i
$321$		0			0
$322$	36.7070	+	7.18449i	2.04560	+	0.400376i
$323$	−1.71255	−	1.24424i	−0.0952890	−	0.0692315i
$324$		0			0
$325$	9.24657	−	10.2694i	0.512908	−	0.569642i
$326$	−2.18781	+	20.8157i	−0.121172	+	1.15287i
$327$		0			0
$328$	22.6691	−	69.7684i	1.25169	−	3.85231i
$329$	5.94325	−	19.3498i	0.327662	−	1.06679i
$330$		0			0
$331$	−0.849512	+	1.47140i	−0.0466934	+	0.0808754i	−0.888428	−	0.459017i	$-0.848202\pi$
$331$	−0.849512	+	1.47140i	−0.0466934	+	0.0808754i	0.841734	+	0.539892i	$0.181535\pi$
$332$	−8.04586	+	1.71020i	−0.441574	+	0.0938594i
$333$		0			0
$334$	39.7983	−	17.7193i	2.17766	−	0.969559i
$335$	−9.46993	−	29.1455i	−0.517398	−	1.59239i
$336$		0			0
$337$	0.755056	+	0.548580i	0.0411305	+	0.0298831i	0.608161	−	0.793814i	$-0.291908\pi$
$337$	0.755056	+	0.548580i	0.0411305	+	0.0298831i	−0.567030	+	0.823697i	$0.691908\pi$
$338$	−0.165457	−	1.57422i	−0.00899967	−	0.0856262i
$339$		0			0
$340$	11.2042	+	19.4063i	0.607635	+	1.05245i
$341$	−3.12024	−	10.3863i	−0.168971	−	0.562451i
$342$		0			0
$343$	−6.56981	−	17.3158i	−0.354736	−	0.934966i
$344$	40.8005	−	29.6433i	2.19981	−	1.59826i
$345$		0			0
$346$	24.0180	−	26.6747i	1.29122	−	1.43404i
$347$	−7.29507	+	8.10200i	−0.391620	+	0.434938i	−0.906423	−	0.422370i	$-0.861198\pi$
$347$	−7.29507	+	8.10200i	−0.391620	+	0.434938i	0.514803	+	0.857308i	$0.327865\pi$
$348$		0			0
$349$	21.6434	−	15.7248i	1.15854	−	0.841730i	0.168949	−	0.985625i	$-0.445963\pi$
$349$	21.6434	−	15.7248i	1.15854	−	0.841730i	0.989593	+	0.143894i	$0.0459625\pi$
$350$	2.39599	−	26.9836i	0.128071	−	1.44233i
$351$		0			0
$352$	59.0904	−	40.9486i	3.14953	−	2.18257i
$353$	−1.33159	−	2.30637i	−0.0708732	−	0.122756i	0.828411	−	0.560121i	$-0.189245\pi$
$353$	−1.33159	−	2.30637i	−0.0708732	−	0.122756i	−0.899284	+	0.437365i	$0.855912\pi$
$354$		0			0
$355$	3.30246	+	31.4208i	0.175276	+	1.66764i
$356$	52.5806	+	38.2020i	2.78677	+	2.02470i
$357$		0			0
$358$	−8.44593	−	25.9939i	−0.446381	−	1.37382i
$359$	5.17745	−	2.30515i	0.273255	−	0.121661i	−0.265534	−	0.964101i	$-0.585548\pi$
$359$	5.17745	−	2.30515i	0.273255	−	0.121661i	0.538790	+	0.842440i	$0.318882\pi$
$360$		0			0
$361$	16.3119	−	3.46719i	0.858519	−	0.182484i
$362$	8.13102	−	14.0833i	0.427357	−	0.740204i
$363$		0			0
$364$	−36.2233	−	38.9458i	−1.89862	−	2.04132i
$365$	4.65137	−	14.3155i	0.243464	−	0.749305i
$366$		0			0
$367$	0.363132	−	3.45497i	0.0189554	−	0.180348i	−0.980948	−	0.194272i	$-0.937766\pi$
$367$	0.363132	−	3.45497i	0.0189554	−	0.180348i	0.999903	+	0.0139238i	$0.00443223\pi$
$368$	51.4456	−	57.1361i	2.68179	−	2.97842i
$369$		0			0
$370$	−29.0370	−	21.0966i	−1.50956	−	1.09676i
$371$	−7.53994	−	1.47576i	−0.391454	−	0.0766175i
$372$		0			0
$373$	16.3259	−	28.2772i	0.845322	−	1.46414i	−0.0400200	−	0.999199i	$-0.512742\pi$
$373$	16.3259	−	28.2772i	0.845322	−	1.46414i	0.885342	−	0.464941i	$-0.153925\pi$
$374$	−1.03506	−	12.5327i	−0.0535217	−	0.648053i
$375$		0			0
$376$	−48.2975	−	53.6399i	−2.49076	−	2.76626i
$377$	11.9655	−	8.69345i	0.616255	−	0.447736i
$378$		0			0
$379$	6.07900	+	18.7092i	0.312257	+	0.961029i	0.976869	+	0.213840i	$0.0685971\pi$
$379$	6.07900	+	18.7092i	0.312257	+	0.961029i	−0.664611	+	0.747189i	$0.731403\pi$
$380$	24.0610	+	5.11432i	1.23430	+	0.262359i
$381$		0			0
$382$	−10.1384	−	4.51390i	−0.518725	−	0.230951i
$383$	19.0729	+	21.1826i	0.974579	+	1.08238i	0.996581	+	0.0826213i	$0.0263292\pi$
$383$	19.0729	+	21.1826i	0.974579	+	1.08238i	−0.0220023	+	0.999758i	$0.507004\pi$
$384$		0			0
$385$	−13.1165	+	22.3987i	−0.668481	+	1.14154i
$386$	−25.9319			−1.31990
$387$		0			0
$388$	41.9457	+	18.6754i	2.12947	+	0.948101i
$389$	1.03320	−	9.83028i	0.0523855	−	0.498415i	−0.936600	−	0.350401i	$-0.886045\pi$
$389$	1.03320	−	9.83028i	0.0523855	−	0.498415i	0.988985	−	0.148014i	$-0.0472881\pi$
$390$		0			0
$391$	−2.22182	−	6.83806i	−0.112362	−	0.345816i
$392$	−65.0071	−	11.6363i	−3.28335	−	0.587720i
$393$		0			0
$394$	12.6737	+	14.0756i	0.638493	+	0.709118i
$395$	−8.39696	−	14.5440i	−0.422497	−	0.731786i
$396$		0			0
$397$	−0.375365	+	0.650151i	−0.0188390	+	0.0326301i	−0.875291	−	0.483596i	$-0.839330\pi$
$397$	−0.375365	+	0.650151i	−0.0188390	+	0.0326301i	0.856452	+	0.516226i	$0.172664\pi$
$398$	−16.7578	+	51.5753i	−0.839994	+	2.58524i
$399$		0			0
$400$	−45.0492	−	32.7302i	−2.25246	−	1.63651i
$401$	22.3631	+	4.75342i	1.11676	+	0.237374i	0.729086	−	0.684422i	$-0.239946\pi$
$401$	22.3631	+	4.75342i	1.11676	+	0.237374i	0.387673	+	0.921797i	$0.373279\pi$
$402$		0			0
$403$	−1.25953	+	11.9836i	−0.0627417	+	0.596947i
$404$	1.63023	+	15.5106i	0.0811067	+	0.771679i
$405$		0			0
$406$	8.51295	−	27.7161i	0.422491	−	1.37553i
$407$	7.08262	+	12.9253i	0.351073	+	0.640683i
$408$		0			0
$409$	−22.4690	+	4.77594i	−1.11102	+	0.236155i	−0.726640	−	0.687018i	$-0.758919\pi$
$409$	−22.4690	+	4.77594i	−1.11102	+	0.236155i	−0.384383	+	0.923174i	$0.625586\pi$
$410$	57.3727	+	25.5440i	2.83344	+	1.26153i
$411$		0			0
$412$	20.6338	+	63.5042i	1.01655	+	3.12863i
$413$	9.84897	−	17.7138i	0.484636	−	0.871641i
$414$		0			0
$415$	−0.466219	−	4.43578i	−0.0228858	−	0.217744i
$416$	−78.1329	+	16.6077i	−3.83078	+	0.814258i
$417$		0			0
$418$	−10.9842	−	8.36127i	−0.537254	−	0.408963i
$419$	−25.5585			−1.24862			−0.624308	−	0.781178i	$-0.714619\pi$
$419$	−25.5585			−1.24862			−0.624308	+	0.781178i	$0.714619\pi$
$420$		0			0
$421$	26.6833	−	19.3866i	1.30046	−	0.944843i	0.300505	−	0.953780i	$-0.402845\pi$
$421$	26.6833	−	19.3866i	1.30046	−	0.944843i	0.999960	+	0.00893735i	$0.00284489\pi$
$422$	−40.5576	+	18.0574i	−1.97431	+	0.879021i
$423$		0			0
$424$	−18.3318	+	20.3595i	−0.890269	+	0.988743i
$425$	−4.75718	+	2.11803i	−0.230757	+	0.102740i
$426$		0			0
$427$	−1.97636	−	1.38768i	−0.0956428	−	0.0671547i
$428$	91.4223			4.41906
$429$		0			0
$430$	21.5874	+	37.3905i	1.04104	+	1.80313i
$431$	−7.84354	+	1.66720i	−0.377810	+	0.0803061i	−0.392903	−	0.919580i	$-0.628529\pi$
$431$	−7.84354	+	1.66720i	−0.377810	+	0.0803061i	0.0150924	+	0.999886i	$0.495196\pi$
$432$		0			0
$433$	10.7729	+	7.82695i	0.517711	+	0.376139i	0.815741	−	0.578417i	$-0.196330\pi$
$433$	10.7729	+	7.82695i	0.517711	+	0.376139i	−0.298030	+	0.954557i	$0.596330\pi$
$434$	12.1398	+	20.2634i	0.582727	+	0.972674i
$435$		0			0
$436$	−76.4200	+	34.0244i	−3.65985	+	1.62947i
$437$	−7.21031	−	3.21024i	−0.344916	−	0.153566i
$438$		0			0
$439$	−12.8240	+	22.2118i	−0.612057	+	1.06011i	0.378837	+	0.925464i	$0.376324\pi$
$439$	−12.8240	+	22.2118i	−0.612057	+	1.06011i	−0.990893	+	0.134650i	$0.957009\pi$
$440$	44.4782	+	81.1696i	2.12042	+	3.86961i
$441$		0			0
$442$	−4.31771	+	13.2886i	−0.205373	+	0.632072i
$443$	−0.0826612	−	0.786469i	−0.00392735	−	0.0373663i	0.992383	−	0.123193i	$-0.0393135\pi$
$443$	−0.0826612	−	0.786469i	−0.00392735	−	0.0373663i	−0.996310	+	0.0858269i	$0.972647\pi$
$444$		0			0
$445$	−23.5812	+	26.1896i	−1.11786	+	1.24151i
$446$	−71.6770	−	15.2354i	−3.39400	−	0.721418i
$447$		0			0
$448$	−51.2588	+	58.8124i	−2.42175	+	2.77863i
$449$	5.04083	−	15.5141i	0.237891	−	0.732154i	−0.758833	−	0.651285i	$-0.774230\pi$
$449$	5.04083	−	15.5141i	0.237891	−	0.732154i	0.996725	−	0.0808695i	$-0.0257697\pi$
$450$		0			0
$451$	−16.8243	−	19.5454i	−0.792227	−	0.920358i
$452$	−30.2978	−	52.4773i	−1.42509	−	2.46832i
$453$		0			0
$454$	−15.9175	+	11.5647i	−0.747044	+	0.542760i
$455$	23.0552	−	17.3266i	1.08084	−	0.812282i
$456$		0			0
$457$	0.868238	+	0.184550i	0.0406144	+	0.00863287i	0.228174	−	0.973620i	$-0.426724\pi$
$457$	0.868238	+	0.184550i	0.0406144	+	0.00863287i	−0.187560	+	0.982253i	$0.560058\pi$
$458$	−0.420375	+	3.99960i	−0.0196428	+	0.186889i
$459$		0			0
$460$	55.9062	+	62.0902i	2.60664	+	2.89497i
$461$	−41.2046			−1.91909			−0.959545	−	0.281555i	$-0.909150\pi$
$461$	−41.2046			−1.91909			−0.959545	+	0.281555i	$0.909150\pi$
$462$		0			0
$463$	30.2155			1.40423			0.702116	−	0.712063i	$-0.252239\pi$
$463$	30.2155			1.40423			0.702116	+	0.712063i	$0.252239\pi$
$464$	−39.8790	−	44.2901i	−1.85134	−	2.05612i
$465$		0			0
$466$	−3.96045	+	37.6812i	−0.183464	+	1.74555i
$467$	−15.4339	−	3.28059i	−0.714198	−	0.151807i	−0.163538	−	0.986537i	$-0.552291\pi$
$467$	−15.4339	−	3.28059i	−0.714198	−	0.151807i	−0.550660	+	0.834730i	$0.685624\pi$
$468$		0			0
$469$	−3.30520	−	27.2101i	−0.152620	−	1.25645i
$470$	49.9913	−	36.3208i	2.30593	−	1.67535i
$471$		0			0
$472$	−36.1358	−	62.5891i	−1.66329	−	2.88090i
$473$	−1.45927	−	17.6692i	−0.0670973	−	0.812430i
$474$		0			0
$475$	−1.76644	+	5.43654i	−0.0810498	+	0.249446i
$476$	6.50074	+	18.9593i	0.297961	+	0.868997i
$477$		0			0
$478$	54.0803	+	11.4951i	2.47358	+	0.525775i
$479$	20.2727	−	22.5151i	0.926283	−	1.02874i	−0.0732233	−	0.997316i	$-0.523329\pi$
$479$	20.2727	−	22.5151i	0.926283	−	1.02874i	0.999506	−	0.0314257i	$-0.0100048\pi$
$480$		0			0
$481$	−1.71175	−	16.2862i	−0.0780491	−	0.742587i
$482$	5.11284	−	15.7357i	0.232884	−	0.716742i
$483$		0			0
$484$	−3.60328	−	59.8995i	−0.163786	−	2.72270i
$485$	−12.4484	+	21.5613i	−0.565255	+	0.979050i
$486$		0			0
$487$	1.81556	+	0.808339i	0.0822708	+	0.0366293i	0.447460	−	0.894304i	$-0.352329\pi$
$487$	1.81556	+	0.808339i	0.0822708	+	0.0366293i	−0.365189	+	0.930934i	$0.618996\pi$
$488$	−7.86662	+	3.50245i	−0.356105	+	0.158548i
$489$		0			0
$490$	15.7245	−	54.3062i	0.710358	−	2.45330i
$491$	23.9546	+	17.4041i	1.08106	+	0.785434i	0.977867	−	0.209228i	$-0.0670950\pi$
$491$	23.9546	+	17.4041i	1.08106	+	0.785434i	0.103190	+	0.994662i	$0.467095\pi$
$492$		0			0
$493$	−5.45164	+	1.15878i	−0.245530	+	0.0521889i
$494$	7.66900	+	13.2831i	0.345044	+	0.597634i
$495$		0			0
$496$	48.5550			2.18018
$497$	−2.49937	+	28.1478i	−0.112112	+	1.26260i
$498$		0			0
$499$	−36.8685	+	16.4149i	−1.65046	+	0.734833i	−0.999701	−	0.0244493i	$-0.992217\pi$
$499$	−36.8685	+	16.4149i	−1.65046	+	0.734833i	−0.650761	+	0.759282i	$0.725550\pi$
$500$	−13.4977	+	14.9907i	−0.603634	+	0.670403i
$501$		0			0
$502$	−58.3069	+	25.9599i	−2.60236	+	1.15865i
$503$	−5.51881	+	4.00965i	−0.246072	+	0.178781i	−0.703984	−	0.710216i	$-0.748597\pi$
$503$	−5.51881	+	4.00965i	−0.246072	+	0.178781i	0.457912	+	0.888997i	$0.348597\pi$
$504$		0			0
$505$	−8.45670			−0.376318
$506$	−13.4903	−	44.9051i	−0.599719	−	1.99628i
$507$		0			0
$508$	42.8418	−	9.10632i	1.90080	−	0.404027i
$509$	2.41312	+	22.9593i	0.106960	+	1.01766i	0.907979	+	0.419016i	$0.137625\pi$
$509$	2.41312	+	22.9593i	0.106960	+	1.01766i	−0.801019	+	0.598639i	$0.795708\pi$
$510$		0			0
$511$	6.54229	−	11.7666i	0.289414	−	0.520525i
$512$	12.8832	+	39.6503i	0.569361	+	1.75231i
$513$		0			0
$514$	14.3100	+	6.37122i	0.631187	+	0.281022i
$515$	−35.4151	+	7.52771i	−1.56058	+	0.331711i
$516$		0			0
$517$	−24.9317	+	4.72047i	−1.09649	+	0.207606i
$518$	−21.8635	−	23.5067i	−0.960627	−	1.03283i
$519$		0			0
$520$	−10.7496	−	102.276i	−0.471402	−	4.48509i
$521$	−3.21708	+	30.6085i	−0.140943	+	1.34098i	0.664046	+	0.747691i	$0.268838\pi$
$521$	−3.21708	+	30.6085i	−0.140943	+	1.34098i	−0.804989	+	0.593289i	$0.797829\pi$
$522$		0			0
$523$	11.0116	+	2.34059i	0.481504	+	0.102347i	0.442268	−	0.896883i	$-0.354174\pi$
$523$	11.0116	+	2.34059i	0.481504	+	0.102347i	0.0392363	+	0.999230i	$0.487507\pi$
$524$	−53.4397	−	38.8262i	−2.33452	−	1.69613i
$525$		0			0
$526$	−18.5142	+	56.9810i	−0.807259	+	2.48449i
$527$	2.27035	−	3.93237i	0.0988981	−	0.171297i
$528$		0			0
$529$	−1.90398	−	3.29780i	−0.0827819	−	0.143382i
$530$	−15.6938	−	17.4297i	−0.681693	−	0.757097i
$531$		0			0
$532$	20.2415	+	8.62297i	0.877580	+	0.373853i
$533$	8.85460	+	27.2517i	0.383535	+	1.18040i
$534$		0			0
$535$	−5.18173	+	49.3008i	−0.224026	+	2.13146i
$536$	−89.2900	−	39.7545i	−3.85674	−	1.71713i
$537$		0			0
$538$	−79.3532			−3.42116
$539$	−15.3615	+	17.4076i	−0.661668	+	0.749797i
$540$		0			0
$541$	−10.2171	−	11.3473i	−0.439269	−	0.487858i	0.482336	−	0.875986i	$-0.339788\pi$
$541$	−10.2171	−	11.3473i	−0.439269	−	0.487858i	−0.921605	+	0.388128i	$0.873122\pi$
$542$	45.8333	+	20.4063i	1.96871	+	0.876526i
$543$		0			0
$544$	29.4431	+	6.25832i	1.26236	+	0.268323i
$545$	−14.0167	−	43.1391i	−0.600411	−	1.84787i
$546$		0			0
$547$	16.3080	−	11.8485i	0.697281	−	0.506605i	−0.181764	−	0.983342i	$-0.558181\pi$
$547$	16.3080	−	11.8485i	0.697281	−	0.506605i	0.879046	+	0.476738i	$0.158181\pi$
$548$	41.1482	+	45.6997i	1.75776	+	1.95219i
$549$		0			0
$550$	−31.3234	+	13.1165i	−1.33563	+	0.559290i
$551$	−3.05907	+	5.29847i	−0.130321	+	0.225723i
$552$		0			0
$553$	−4.87195	−	14.2089i	−0.207176	−	0.604226i
$554$	−30.9202	−	22.4649i	−1.31368	−	0.954441i
$555$		0			0
$556$	31.1966	−	34.6473i	1.32303	−	1.46937i
$557$	−3.19436	+	30.3923i	−0.135349	+	1.28776i	0.690277	+	0.723545i	$0.257489\pi$
$557$	−3.19436	+	30.3923i	−0.135349	+	1.28776i	−0.825626	+	0.564217i	$0.809178\pi$
$558$		0			0
$559$	−6.08729	+	18.7348i	−0.257465	+	0.792396i
$560$	−79.1473	−	85.0958i	−3.34458	−	3.59595i
$561$		0			0
$562$	0.168522	−	0.291889i	0.00710868	−	0.0123126i
$563$	10.5665	−	2.24597i	0.445324	−	0.0946564i	0.0202085	−	0.999796i	$-0.493567\pi$
$563$	10.5665	−	2.24597i	0.445324	−	0.0946564i	0.425115	+	0.905139i	$0.360234\pi$
$564$		0			0
$565$	30.0164	−	13.3642i	1.26280	−	0.562234i
$566$	−17.4687	−	53.7632i	−0.734265	−	2.25983i
$567$		0			0
$568$	81.5209	+	59.2284i	3.42054	+	2.48517i
$569$	−4.62625	−	44.0158i	−0.193942	−	1.84524i	−0.468248	−	0.883597i	$-0.655115\pi$
$569$	−4.62625	−	44.0158i	−0.193942	−	1.84524i	0.274306	−	0.961642i	$-0.411552\pi$
$570$		0			0
$571$	4.64510	+	8.04554i	0.194391	+	0.336696i	0.946701	−	0.322114i	$-0.104394\pi$
$571$	4.64510	+	8.04554i	0.194391	+	0.336696i	−0.752310	+	0.658810i	$0.771060\pi$
$572$	−22.0134	+	62.9352i	−0.920426	+	2.63145i
$573$		0			0
$574$	45.9718	+	32.2786i	1.91883	+	1.34728i
$575$	−15.7078	+	11.4124i	−0.655059	+	0.475928i
$576$		0			0
$577$	−6.21130	+	6.89835i	−0.258580	+	0.287182i	−0.858430	−	0.512930i	$-0.828560\pi$
$577$	−6.21130	+	6.89835i	−0.258580	+	0.287182i	0.599851	+	0.800112i	$0.295227\pi$
$578$	−27.5361	+	30.5819i	−1.14535	+	1.27204i
$579$		0			0
$580$	52.3966	−	38.0684i	2.17565	−	1.58070i
$581$	0.352844	−	3.97371i	0.0146384	−	0.164857i
$582$		0			0
$583$	2.77104	+	9.22391i	0.114765	+	0.382015i
$584$	−24.0036	−	41.5755i	−0.993278	−	1.72041i
$585$		0			0
$586$	−2.53861	−	24.1533i	−0.104869	−	0.997763i
$587$	17.8718	+	12.9846i	0.737647	+	0.535932i	0.891973	−	0.452088i	$-0.149321\pi$
$587$	17.8718	+	12.9846i	0.737647	+	0.535932i	−0.154326	+	0.988020i	$0.549321\pi$
$588$		0			0
$589$	−1.54029	−	4.74053i	−0.0634666	−	0.195330i
$590$	56.5224	−	25.1654i	2.32699	−	1.03604i
$591$		0			0
$592$	−64.5461	+	13.7197i	−2.65283	+	0.563876i
$593$	9.03720	−	15.6529i	0.371113	−	0.642787i	−0.618624	−	0.785687i	$-0.712309\pi$
$593$	9.03720	−	15.6529i	0.371113	−	0.642787i	0.989737	+	0.142900i	$0.0456427\pi$
$594$		0			0
$595$	−10.5925	+	2.43103i	−0.434251	+	0.0996624i
$596$	10.8946	−	33.5302i	0.446262	−	1.37345i
$597$		0			0
$598$	−5.44557	+	51.8111i	−0.222686	+	2.11871i
$599$	−26.9506	+	29.9317i	−1.10117	+	1.22297i	−0.128273	+	0.991739i	$0.540943\pi$
$599$	−26.9506	+	29.9317i	−1.10117	+	1.22297i	−0.972898	+	0.231235i	$0.925723\pi$
$600$		0			0
$601$	−23.6913	−	17.2128i	−0.966390	−	0.702123i	−0.0117638	−	0.999931i	$-0.503745\pi$
$601$	−23.6913	−	17.2128i	−0.966390	−	0.702123i	−0.954626	+	0.297808i	$0.903745\pi$
$602$	12.5251	+	36.5292i	0.510485	+	1.48882i
$603$		0			0
$604$	−34.6307	+	59.9822i	−1.40910	+	2.44064i
$605$	32.5059	+	1.45192i	1.32155	+	0.0590290i
$606$		0			0
$607$	29.6344	+	32.9123i	1.20282	+	1.33587i	0.927184	+	0.374607i	$0.122222\pi$
$607$	29.6344	+	32.9123i	1.20282	+	1.33587i	0.275637	+	0.961262i	$0.411111\pi$
$608$	26.7321	−	19.4220i	1.08413	−	0.787668i
$609$		0			0
$610$	−2.27805	−	7.01112i	−0.0922356	−	0.283872i
$611$	27.5774	+	5.86175i	1.11566	+	0.237141i
$612$		0			0
$613$	7.52525	+	3.35046i	0.303942	+	0.135324i	0.553040	−	0.833155i	$-0.313468\pi$
$613$	7.52525	+	3.35046i	0.303942	+	0.135324i	−0.249098	+	0.968478i	$0.580134\pi$
$614$	46.8500	+	52.0322i	1.89071	+	2.09985i
$615$		0			0
$616$	25.0967	+	78.8902i	1.01117	+	3.17858i
$617$	17.3878			0.700008			0.350004	−	0.936748i	$-0.386180\pi$
$617$	17.3878			0.700008			0.350004	+	0.936748i	$0.386180\pi$
$618$		0			0
$619$	−10.1456	−	4.51712i	−0.407787	−	0.181558i	0.192583	−	0.981281i	$-0.438313\pi$
$619$	−10.1456	−	4.51712i	−0.407787	−	0.181558i	−0.600370	+	0.799722i	$0.704980\pi$
$620$	−5.51545	+	52.4760i	−0.221506	+	2.10749i
$621$		0			0
$622$	−14.8543	−	45.7169i	−0.595604	−	1.83308i
$623$	−25.1985	+	18.9373i	−1.00956	+	0.758706i
$624$		0			0
$625$	−19.8649	−	22.0622i	−0.794596	−	0.882489i
$626$	−11.5018	−	19.9217i	−0.459704	−	0.796230i
$627$		0			0
$628$	33.0250	−	57.2010i	1.31784	−	2.28257i
$629$	−1.90694	+	5.86896i	−0.0760347	+	0.234011i
$630$		0			0
$631$	30.9172	+	22.4626i	1.23079	+	0.894224i	0.996949	−	0.0780503i	$-0.0248695\pi$
$631$	30.9172	+	22.4626i	1.23079	+	0.894224i	0.233844	+	0.972274i	$0.424869\pi$
$632$	−52.3920	−	11.1363i	−2.08404	−	0.442976i
$633$		0			0
$634$	5.81669	−	55.3421i	0.231010	−	2.19792i
$635$	2.48248	+	23.6192i	0.0985143	+	0.937301i
$636$		0			0
$637$	23.2140	−	11.2479i	0.919774	−	0.445657i
$638$	−35.7115	+	6.76147i	−1.41383	+	0.267689i
$639$		0			0
$640$	−107.517	+	22.8535i	−4.24999	+	0.903364i
$641$	9.76556	+	4.34791i	0.385716	+	0.171732i	0.590428	−	0.807090i	$-0.298959\pi$
$641$	9.76556	+	4.34791i	0.385716	+	0.171732i	−0.204712	+	0.978822i	$0.565626\pi$
$642$		0			0
$643$	1.67813	+	5.16474i	0.0661788	+	0.203677i	0.978678	−	0.205402i	$-0.0658501\pi$
$643$	1.67813	+	5.16474i	0.0661788	+	0.203677i	−0.912499	+	0.409079i	$0.865850\pi$
$644$	38.4058	+	64.1060i	1.51340	+	2.52613i
$645$		0			0
$646$	−0.604160	−	5.74820i	−0.0237704	−	0.226160i
$647$	4.01124	−	0.852615i	0.157698	−	0.0335198i	−0.128386	−	0.991724i	$-0.540980\pi$
$647$	4.01124	−	0.852615i	0.157698	−	0.0335198i	0.286084	+	0.958205i	$0.407646\pi$
$648$		0			0
$649$	−25.4007	−	0.566995i	−0.997063	−	0.0222565i
$650$	37.7312			1.47994
$651$		0			0
$652$	−33.8312	+	24.5798i	−1.32493	+	0.962619i
$653$	−24.0241	+	10.6962i	−0.940134	+	0.418575i	−0.818827	−	0.574040i	$-0.805375\pi$
$653$	−24.0241	+	10.6962i	−0.940134	+	0.418575i	−0.121307	+	0.992615i	$0.538709\pi$
$654$		0			0
$655$	23.9665	−	26.6175i	0.936449	−	1.04003i
$656$	105.482	−	46.9634i	4.11836	−	1.83361i
$657$		0			0
$658$	50.1212	−	23.2929i	1.95393	−	0.908050i
$659$	−21.6905			−0.844941			−0.422470	−	0.906377i	$-0.638837\pi$
$659$	−21.6905			−0.844941			−0.422470	+	0.906377i	$0.638837\pi$
$660$		0			0
$661$	−16.5967	−	28.7464i	−0.645538	−	1.11810i	−0.984177	−	0.177188i	$-0.943300\pi$
$661$	−16.5967	−	28.7464i	−0.645538	−	1.11810i	0.338639	−	0.940916i	$-0.390033\pi$
$662$	−4.53769	+	0.964517i	−0.176362	+	0.0374870i
$663$		0			0
$664$	−11.5086	−	8.36147i	−0.446619	−	0.324488i
$665$	−5.79733	+	10.4268i	−0.224811	+	0.404333i
$666$		0			0
$667$	−18.9841	+	8.45227i	−0.735068	+	0.327273i
$668$	79.5148	+	35.4023i	3.07652	+	1.36975i
$669$		0			0
$670$	41.8375	−	72.4647i	1.61632	−	2.79955i
$671$	−0.383538	+	3.00282i	−0.0148063	+	0.115923i
$672$		0			0
$673$	−14.0671	+	43.2940i	−0.542246	+	1.66886i	0.185204	+	0.982700i	$0.440705\pi$
$673$	−14.0671	+	43.2940i	−0.542246	+	1.66886i	−0.727450	+	0.686161i	$0.759295\pi$
$674$	0.266371	+	2.53435i	0.0102602	+	0.0976196i
$675$		0			0
$676$	2.11614	−	2.35022i	0.0813901	−	0.0903929i
$677$	4.63239	+	0.984645i	0.178037	+	0.0378430i	0.296068	−	0.955167i	$-0.404325\pi$
$677$	4.63239	+	0.984645i	0.178037	+	0.0378430i	−0.118030	+	0.993010i	$0.537658\pi$
$678$		0			0
$679$	−14.6312	+	16.7873i	−0.561495	+	0.644239i
$680$	−11.9754	+	36.8565i	−0.459236	+	1.41338i
$681$		0			0
$682$	15.3742	−	25.3073i	0.588709	−	0.969065i
$683$	13.2832	+	23.0072i	0.508269	+	0.880347i	0.999954	+	0.00957420i	$0.00304761\pi$
$683$	13.2832	+	23.0072i	0.508269	+	0.880347i	−0.491686	+	0.870773i	$0.663619\pi$
$684$		0			0
$685$	−26.9765	+	19.5996i	−1.03072	+	0.748860i
$686$	23.1325	−	44.9671i	0.883202	−	1.71685i
$687$		0			0
$688$	77.6437	+	16.5037i	2.96014	+	0.629196i
$689$	1.11857	−	10.6425i	0.0426140	−	0.405445i
$690$		0			0
$691$	27.6928	+	30.7560i	1.05348	+	1.17001i	0.985034	+	0.172358i	$0.0551386\pi$
$691$	27.6928	+	30.7560i	1.05348	+	1.17001i	0.0684496	+	0.997655i	$0.478195\pi$
$692$	71.7150			2.72620
$693$		0			0
$694$	−29.7680			−1.12998
$695$	16.9159	+	18.7870i	0.641656	+	0.712631i
$696$		0			0
$697$	1.12868	−	10.7387i	0.0427518	−	0.406756i
$698$	71.4501	+	15.1872i	2.70442	+	0.574843i
$699$		0			0
$700$	43.2674	−	32.5165i	1.63535	−	1.22901i
$701$	−11.2545	+	8.17689i	−0.425078	+	0.308837i	−0.779678	−	0.626181i	$-0.784617\pi$
$701$	−11.2545	+	8.17689i	−0.425078	+	0.308837i	0.354600	+	0.935018i	$0.384617\pi$
$702$		0			0
$703$	3.38705	+	5.86655i	0.127745	+	0.221261i
$704$	95.1825	+	22.4629i	3.58733	+	0.846603i
$705$		0			0
$706$	2.24705	−	6.91571i	0.0845688	−	0.260276i
$707$	−7.42308	−	1.45288i	−0.279174	−	0.0546413i
$708$		0			0
$709$	−46.0277	−	9.78349i	−1.72861	−	0.367427i	−0.766956	−	0.641700i	$-0.778229\pi$
$709$	−46.0277	−	9.78349i	−1.72861	−	0.367427i	−0.961652	+	0.274273i	$0.911563\pi$
$710$	−57.7225	+	64.1074i	−2.16629	+	2.40591i
$711$		0			0
$712$	11.7489	+	111.784i	0.440310	+	4.18927i
$713$	5.23170	−	16.1015i	0.195929	−	0.603007i
$714$		0			0
$715$	−32.6910	−	15.4381i	−1.22258	−	0.577354i
$716$	27.3035	−	47.2911i	1.02038	−	1.76735i
$717$		0			0
$718$	14.1367	+	6.29405i	0.527576	+	0.234892i
$719$	−1.58591	+	0.706091i	−0.0591443	+	0.0263327i	−0.436096	−	0.899900i	$-0.643639\pi$
$719$	−1.58591	+	0.706091i	−0.0591443	+	0.0263327i	0.376951	+	0.926233i	$0.376972\pi$
$720$		0			0
$721$	−32.3798	+	0.523226i	−1.20589	+	0.0194859i
$722$	36.8373	+	26.7639i	1.37094	+	0.996048i
$723$		0			0
$724$	31.7807	−	6.75519i	1.18112	−	0.251055i
$725$	7.52528	+	13.0342i	0.279482	+	0.484077i
$726$		0			0
$727$	41.0278			1.52164			0.760818	−	0.648965i	$-0.224798\pi$
$727$	41.0278			1.52164			0.760818	+	0.648965i	$0.224798\pi$
$728$	8.13552	−	91.6220i	0.301523	−	3.39574i
$729$		0			0
$730$	37.5457	−	16.7164i	1.38963	−	0.618703i
$731$	4.96709	−	5.51651i	0.183714	−	0.204036i
$732$		0			0
$733$	25.7060	−	11.4450i	0.949471	−	0.422732i	0.127231	−	0.991873i	$-0.459391\pi$
$733$	25.7060	−	11.4450i	0.949471	−	0.422732i	0.822240	+	0.569141i	$0.192724\pi$
$734$	7.67395	−	5.57545i	0.283251	−	0.205794i
$735$		0			0
$736$	112.232			4.13692
$737$	−28.2419	+	19.5712i	−1.04031	+	0.720913i
$738$		0			0
$739$	−8.00442	+	1.70139i	−0.294447	+	0.0625867i	−0.352767	−	0.935711i	$-0.614759\pi$
$739$	−8.00442	+	1.70139i	−0.294447	+	0.0625867i	0.0583195	+	0.998298i	$0.481426\pi$
$740$	−7.49570	−	71.3168i	−0.275547	−	2.62166i
$741$		0			0
$742$	−10.7811	−	17.9956i	−0.395787	−	0.660638i
$743$	−4.59609	−	14.1453i	−0.168614	−	0.518941i	0.830670	−	0.556765i	$-0.187957\pi$
$743$	−4.59609	−	14.1453i	−0.168614	−	0.518941i	−0.999284	+	0.0378236i	$0.987957\pi$
$744$		0			0
$745$	17.4642	+	7.77555i	0.639838	+	0.284874i
$746$	87.2051	−	18.5360i	3.19281	−	0.678652i
$747$		0			0
$748$	17.2244	−	18.2917i	0.629786	−	0.668810i
$749$	−13.0184	+	42.3848i	−0.475682	+	1.54871i
$750$		0			0
$751$	−0.598761	−	5.69683i	−0.0218491	−	0.207880i	0.978151	−	0.207896i	$-0.0666616\pi$
$751$	−0.598761	−	5.69683i	−0.0218491	−	0.207880i	−1.00000		1.58462e-5i	$0.999995\pi$
$752$	11.8753	−	112.986i	0.433046	−	4.12016i
$753$		0			0
$754$	39.5011	+	8.39622i	1.43855	+	0.305772i
$755$	−30.3834	−	22.0749i	−1.10577	−	0.803387i
$756$		0			0
$757$	2.50546	−	7.71103i	0.0910627	−	0.280262i	−0.895145	−	0.445775i	$-0.852928\pi$
$757$	2.50546	−	7.71103i	0.0910627	−	0.280262i	0.986208	+	0.165513i	$0.0529281\pi$
$758$	−26.8566	+	46.5170i	−0.975476	+	1.68957i
$759$		0			0
$760$	21.2704	+	36.8414i	0.771558	+	1.33638i
$761$	−35.9896	−	39.9704i	−1.30462	−	1.44893i	−0.817889	−	0.575376i	$-0.804856\pi$
$761$	−35.9896	−	39.9704i	−1.30462	−	1.44893i	−0.486731	−	0.873552i	$-0.661811\pi$
$762$		0			0
$763$	−4.89213	−	40.2745i	−0.177107	−	1.45804i
$764$	−6.85181	−	21.0877i	−0.247890	−	0.762926i
$765$		0			0
$766$	−8.13525	+	77.4018i	−0.293939	+	2.79664i
$767$	25.7889	+	11.4820i	0.931183	+	0.414589i
$768$		0			0
$769$	−19.4203			−0.700314			−0.350157	−	0.936691i	$-0.613872\pi$
$769$	−19.4203			−0.700314			−0.350157	+	0.936691i	$0.613872\pi$
$770$	−69.4134	+	14.3079i	−2.50149	+	0.515621i
$771$		0			0
$772$	−34.6680	−	38.5028i	−1.24773	−	1.38574i
$773$	33.6263	+	14.9714i	1.20945	+	0.538484i	0.909594	−	0.415499i	$-0.136393\pi$
$773$	33.6263	+	14.9714i	1.20945	+	0.538484i	0.299861	+	0.953983i	$0.403060\pi$
$774$		0			0
$775$	−11.9938	−	2.54937i	−0.430831	−	0.0915759i
$776$	24.5378	+	75.5196i	0.880856	+	2.71100i
$777$		0			0
$778$	21.8344	−	15.8636i	0.782800	−	0.568737i
$779$	−7.93129	−	8.80859i	−0.284168	−	0.315601i
$780$		0			0
$781$	32.6749	−	13.6824i	1.16920	−	0.489596i
$782$	9.81585	−	17.0015i	0.351014	−	0.607974i
$783$		0			0
$784$	−54.8538	−	88.2927i	−1.95906	−	3.15331i
$785$	28.9747	+	21.0513i	1.03415	+	0.751355i
$786$		0			0
$787$	−11.7738	+	13.0762i	−0.419692	+	0.466115i	−0.915500	−	0.402317i	$-0.868205\pi$
$787$	−11.7738	+	13.0762i	−0.419692	+	0.466115i	0.495809	+	0.868432i	$0.334872\pi$
$788$	−3.95559	+	37.6350i	−0.140912	+	1.34069i
$789$		0			0
$790$	14.1699	−	43.6103i	0.504141	−	1.55159i
$791$	28.6436	−	6.57383i	1.01845	−	0.233738i
$792$		0			0
$793$	1.68176	−	2.91289i	0.0597209	−	0.103440i
$794$	−2.00502	+	0.426180i	−0.0711555	+	0.0151246i
$795$		0			0
$796$	−98.9804	+	44.0689i	−3.50827	+	1.56198i
$797$	1.37517	+	4.23234i	0.0487110	+	0.149917i	0.972453	−	0.233097i	$-0.0748860\pi$
$797$	1.37517	+	4.23234i	0.0487110	+	0.149917i	−0.923742	+	0.383014i	$0.874886\pi$
$798$		0			0
$799$	−8.59519	−	6.24477i	−0.304076	−	0.220924i
$800$	−8.49656	−	80.8394i	−0.300399	−	2.85810i
$801$		0			0
$802$	31.2125	+	54.0616i	1.10215	+	1.90898i
$803$	−16.8727	−	0.376633i	−0.595424	−	0.0132911i
$804$		0			0
$805$	−36.7469	+	17.0775i	−1.29516	+	0.601901i
$806$	−26.6172	+	19.3385i	−0.937552	+	0.681171i
$807$		0			0
$808$	−18.0476	+	20.0439i	−0.634913	+	0.705143i
$809$	4.71837	−	5.24028i	0.165889	−	0.184238i	−0.654469	−	0.756089i	$-0.727108\pi$
$809$	4.71837	−	5.24028i	0.165889	−	0.184238i	0.820358	+	0.571851i	$0.193774\pi$
$810$		0			0
$811$	21.3389	−	15.5036i	0.749311	−	0.544407i	−0.146302	−	0.989240i	$-0.546737\pi$
$811$	21.3389	−	15.5036i	0.749311	−	0.544407i	0.895613	+	0.444833i	$0.146737\pi$
$812$	52.5327	−	24.4136i	1.84354	−	0.856749i
$813$		0			0
$814$	−13.2867	+	37.9861i	−0.465699	+	1.33141i
$815$	−11.3375	−	19.6371i	−0.397135	−	0.687859i
$816$		0			0
$817$	−0.851771	−	8.10406i	−0.0297997	−	0.283525i
$818$	−50.7422	−	36.8664i	−1.77416	−	1.28900i
$819$		0			0
$820$	38.7740	+	119.334i	1.35405	+	4.16733i
$821$	−31.5854	+	14.0627i	−1.10234	+	0.490793i	−0.875538	−	0.483149i	$-0.839493\pi$
$821$	−31.5854	+	14.0627i	−1.10234	+	0.490793i	−0.226800	+	0.973941i	$0.572826\pi$
$822$		0			0
$823$	−5.44063	+	1.15644i	−0.189649	+	0.0403111i	−0.301757	−	0.953385i	$-0.597573\pi$
$823$	−5.44063	+	1.15644i	−0.189649	+	0.0403111i	0.112108	+	0.993696i	$0.464240\pi$
$824$	−57.7381	+	100.005i	−2.01140	+	3.48385i
$825$		0			0
$826$	53.9375	−	12.3789i	1.87672	−	0.430716i
$827$	11.7289	−	36.0978i	0.407854	−	1.25524i	−0.510635	−	0.859797i	$-0.670590\pi$
$827$	11.7289	−	36.0978i	0.407854	−	1.25524i	0.918489	−	0.395447i	$-0.129410\pi$
$828$		0			0
$829$	−1.09022	+	10.3727i	−0.0378648	+	0.360260i	0.959141	+	0.282930i	$0.0913063\pi$
$829$	−1.09022	+	10.3727i	−0.0378648	+	0.360260i	−0.997006	+	0.0773303i	$0.975360\pi$
$830$	8.14888	−	9.05024i	0.282852	−	0.314139i
$831$		0			0
$832$	−87.9090	−	63.8696i	−3.04770	−	2.21428i
$833$	−9.71552	+	0.314069i	−0.336623	+	0.0108818i
$834$		0			0
$835$	−23.5980	+	40.8730i	−0.816643	+	1.41447i
$836$	−2.27011	−	27.4870i	−0.0785133	−	0.950657i
$837$		0			0
$838$	−46.6958	−	51.8609i	−1.61308	−	1.79151i
$839$	−4.67083	+	3.39356i	−0.161255	+	0.117159i	−0.665486	−	0.746410i	$-0.731776\pi$
$839$	−4.67083	+	3.39356i	−0.161255	+	0.117159i	0.504231	+	0.863569i	$0.331776\pi$
$840$		0			0
$841$	−3.98368	−	12.2605i	−0.137368	−	0.422776i
$842$	88.0882	+	18.7237i	3.03572	+	0.645262i
$843$		0			0
$844$	−81.0319	−	36.0777i	−2.78923	−	1.24185i
$845$	1.14745	+	1.27437i	0.0394734	+	0.0438396i
$846$		0			0
$847$	28.2834	+	6.85907i	0.971831	+	0.235680i
$848$	−43.1209			−1.48078
$849$		0			0
$850$	−12.9891	−	5.78314i	−0.445524	−	0.198360i
$851$	−2.40507	+	22.8827i	−0.0824446	+	0.784408i
$852$		0			0
$853$	−10.9548	−	33.7155i	−0.375086	−	1.15440i	−0.943420	−	0.331599i	$-0.892412\pi$
$853$	−10.9548	−	33.7155i	−0.375086	−	1.15440i	0.568334	−	0.822798i	$-0.307588\pi$
$854$	−0.795087	−	6.54556i	−0.0272073	−	0.223985i
$855$		0			0
$856$	105.794	+	117.496i	3.61595	+	4.01592i
$857$	−10.9928	−	19.0401i	−0.375507	−	0.650398i	0.614895	−	0.788609i	$-0.289198\pi$
$857$	−10.9928	−	19.0401i	−0.375507	−	0.650398i	−0.990403	+	0.138211i	$0.955865\pi$
$858$		0			0
$859$	−25.8432	+	44.7618i	−0.881759	+	1.52725i	−0.0323756	+	0.999476i	$0.510307\pi$
$859$	−25.8432	+	44.7618i	−0.881759	+	1.52725i	−0.849384	+	0.527776i	$0.823026\pi$
$860$	−26.6561	+	82.0390i	−0.908965	+	2.79751i
$861$		0			0
$862$	−17.7132	−	12.8694i	−0.603314	−	0.438333i
$863$	−2.41339	−	0.512982i	−0.0821528	−	0.0174621i	0.166652	−	0.986016i	$-0.446704\pi$
$863$	−2.41339	−	0.512982i	−0.0821528	−	0.0174621i	−0.248805	+	0.968554i	$0.580038\pi$
$864$		0			0
$865$	−4.06474	+	38.6734i	−0.138205	+	1.31493i
$866$	3.80049	+	36.1592i	0.129146	+	1.22874i
$867$		0			0
$868$	−13.8568	+	45.1145i	−0.470332	+	1.53129i
$869$	−12.9087	+	13.7086i	−0.437899	+	0.465033i
$870$		0			0
$871$	37.3432	−	7.93755i	1.26533	−	0.268954i
$872$	−132.161	−	58.8418i	−4.47553	−	1.99264i
$873$		0			0
$874$	−6.65943	−	20.4956i	−0.225259	−	0.693275i
$875$	−5.02786	−	8.39238i	−0.169973	−	0.283714i
$876$		0			0
$877$	−2.84496	−	27.0680i	−0.0960674	−	0.914020i	−0.931332	−	0.364172i	$-0.881352\pi$
$877$	−2.84496	−	27.0680i	−0.0960674	−	0.914020i	0.835264	−	0.549849i	$-0.185315\pi$
$878$	−68.4998	+	14.5601i	−2.31176	+	0.491379i
$879$		0			0
$880$	−48.0988	+	137.512i	−1.62141	+	4.63553i
$881$	28.6307			0.964592			0.482296	−	0.876008i	$-0.339803\pi$
$881$	28.6307			0.964592			0.482296	+	0.876008i	$0.339803\pi$
$882$		0			0
$883$	−28.3156	+	20.5725i	−0.952896	+	0.692320i	−0.951490	−	0.307679i	$-0.900448\pi$
$883$	−28.3156	+	20.5725i	−0.952896	+	0.692320i	−0.00140631	+	0.999999i	$0.500448\pi$
$884$	−25.5026	+	11.3545i	−0.857747	+	0.381893i
$885$		0			0
$886$	1.44481	−	1.60462i	0.0485392	−	0.0539082i
$887$	25.3595	−	11.2908i	0.851488	−	0.379107i	0.0658769	−	0.997828i	$-0.479016\pi$
$887$	25.3595	−	11.2908i	0.851488	−	0.379107i	0.785611	+	0.618721i	$0.212349\pi$
$888$		0			0
$889$	−1.87879	+	21.1589i	−0.0630126	+	0.709646i
$890$	−96.2248			−3.22546
$891$		0			0
$892$	−73.2030	−	126.791i	−2.45102	−	4.24529i
$893$	−11.4077	+	2.42479i	−0.381745	+	0.0811425i
$894$		0			0
$895$	23.9549	+	17.4043i	0.800724	+	0.581760i
$896$	−98.3023	+	1.58847i	−3.28405	+	0.0530670i
$897$		0			0
$898$	40.6894	−	18.1161i	1.35782	−	0.604541i
$899$	−11.9891	−	5.33790i	−0.399859	−	0.178029i
$900$		0			0
$901$	−2.01626	+	3.49227i	−0.0671714	+	0.116344i
$902$	8.92142	−	69.8481i	0.297051	−	2.32569i
$903$		0			0
$904$	32.3831	−	99.6651i	1.07705	−	3.31481i
$905$	1.84154	+	17.5211i	0.0612148	+	0.582420i
$906$		0			0
$907$	4.67044	−	5.18705i	0.155079	−	0.172233i	−0.660599	−	0.750739i	$-0.729697\pi$
$907$	4.67044	−	5.18705i	0.155079	−	0.172233i	0.815678	+	0.578506i	$0.196364\pi$
$908$	−38.4507	−	8.17296i	−1.27603	−	0.271229i
$909$		0			0
$910$	77.2796	+	15.1256i	2.56179	+	0.501408i
$911$	−0.290598	+	0.894368i	−0.00962794	+	0.0296317i	−0.955755	−	0.294164i	$-0.904959\pi$
$911$	−0.290598	+	0.894368i	−0.00962794	+	0.0296317i	0.946127	+	0.323795i	$0.104959\pi$
$912$		0			0
$913$	−4.61282	+	1.93159i	−0.152662	+	0.0639264i
$914$	1.21181	+	2.09892i	0.0400832	+	0.0694261i
$915$		0			0
$916$	−6.50045	+	4.72285i	−0.214781	+	0.156048i
$917$	25.6102	−	19.2467i	0.845722	−	0.635581i
$918$		0			0
$919$	−0.450828	−	0.0958264i	−0.0148714	−	0.00316102i	0.200470	−	0.979700i	$-0.435753\pi$
$919$	−0.450828	−	0.0958264i	−0.0148714	−	0.00316102i	−0.215341	+	0.976539i	$0.569086\pi$
$920$	−15.1036	+	143.701i	−0.497950	+	4.73768i
$921$		0			0
$922$	−75.2814	−	83.6085i	−2.47926	−	2.75350i
$923$	−39.3592			−1.29552
$924$		0			0
$925$	16.6642			0.547916
$926$	55.2041	+	61.3103i	1.81412	+	2.01478i
$927$		0			0
$928$	9.09383	−	86.5220i	0.298520	−	2.84023i
$929$	32.7669	+	6.96483i	1.07505	+	0.228509i	0.711229	−	0.702961i	$-0.248139\pi$
$929$	32.7669	+	6.96483i	1.07505	+	0.228509i	0.363820	+	0.931469i	$0.381472\pi$
$930$		0			0
$931$	−6.88011	+	8.15637i	−0.225486	+	0.267314i
$932$	−61.2423	+	44.4952i	−2.00606	+	1.45749i
$933$		0			0
$934$	−21.5414	−	37.3108i	−0.704856	−	1.22085i
$935$	8.88779	+	10.3253i	0.290662	+	0.337672i
$936$		0			0
$937$	−1.27573	+	3.92629i	−0.0416762	+	0.128266i	−0.969730	−	0.244180i	$-0.921481\pi$
$937$	−1.27573	+	3.92629i	−0.0416762	+	0.128266i	0.928054	+	0.372447i	$0.121481\pi$
$938$	49.1735	−	56.4199i	1.60557	−	1.84217i
$939$		0			0
$940$	120.761	+	25.6684i	3.93877	+	0.837212i
$941$	−21.7643	+	24.1718i	−0.709497	+	0.787977i	−0.984858	−	0.173364i	$-0.944536\pi$
$941$	−21.7643	+	24.1718i	−0.709497	+	0.787977i	0.275360	+	0.961341i	$0.411203\pi$
$942$		0			0
$943$	−4.20831	−	40.0394i	−0.137041	−	1.30386i
$944$	35.1516	−	108.185i	1.14409	−	3.52113i
$945$		0			0
$946$	33.1865	−	35.2429i	1.07899	−	1.14585i
$947$	−3.10178	+	5.37244i	−0.100794	+	0.174581i	−0.912012	−	0.410163i	$-0.865472\pi$
$947$	−3.10178	+	5.37244i	−0.100794	+	0.174581i	0.811218	+	0.584744i	$0.198805\pi$
$948$		0			0
$949$	17.1306	+	7.62702i	0.556082	+	0.247584i
$950$	−14.2586	+	6.34835i	−0.462611	+	0.205968i
$951$		0			0
$952$	−16.8438	+	30.2943i	−0.545910	+	0.981845i
$953$	31.1650	+	22.6427i	1.00953	+	0.733469i	0.964111	−	0.265498i	$-0.0855365\pi$
$953$	31.1650	+	22.6427i	1.00953	+	0.733469i	0.0454228	+	0.998968i	$0.485536\pi$
$954$		0			0
$955$	11.7602	−	2.49971i	0.380551	−	0.0808887i
$956$	55.2317	+	95.6642i	1.78632	+	3.09400i
$957$		0			0
$958$	82.7240			2.67269
$959$	−27.0465	+	12.5694i	−0.873378	+	0.405886i
$960$		0			0
$961$	−18.5523	+	8.26003i	−0.598462	+	0.266452i
$962$	29.9191	−	33.2285i	0.964629	−	1.07133i
$963$		0			0
$964$	30.1991	−	13.4455i	0.972647	−	0.433050i
$965$	22.7281	−	16.5130i	0.731645	−	0.531571i
$966$		0			0
$967$	10.9914			0.353461			0.176730	−	0.984259i	$-0.443448\pi$
$967$	10.9914			0.353461			0.176730	+	0.984259i	$0.443448\pi$
$968$	72.8129	−	73.9464i	2.34030	−	2.37673i
$969$		0			0
$970$	−66.4937	+	14.1337i	−2.13498	+	0.453805i
$971$	3.25084	+	30.9296i	0.104324	+	0.992580i	0.914003	+	0.405707i	$0.132975\pi$
$971$	3.25084	+	30.9296i	0.104324	+	0.992580i	−0.809679	+	0.586873i	$0.800359\pi$
$972$		0			0
$973$	11.6207	+	19.3969i	0.372542	+	0.621837i
$974$	1.67685	+	5.16081i	0.0537297	+	0.165363i
$975$		0			0
$976$	−12.3818	−	5.51272i	−0.396331	−	0.176458i
$977$	34.2609	−	7.28238i	1.09610	−	0.232984i	0.375840	−	0.926685i	$-0.377354\pi$
$977$	34.2609	−	7.28238i	1.09610	−	0.232984i	0.720263	+	0.693701i	$0.244021\pi$
$978$		0			0
$979$	35.7300	+	16.8733i	1.14194	+	0.539273i
$980$	101.654	−	49.2541i	3.24720	−	1.57336i
$981$		0			0
$982$	8.45079	+	80.4039i	0.269676	+	2.56579i
$983$	2.72094	−	25.8880i	0.0867845	−	0.825700i	−0.861389	−	0.507946i	$-0.830405\pi$
$983$	2.72094	−	25.8880i	0.0867845	−	0.825700i	0.948173	−	0.317754i	$-0.102928\pi$
$984$		0			0
$985$	−20.0710	−	4.26623i	−0.639516	−	0.135933i
$986$	−12.3115	−	8.94484i	−0.392079	−	0.284862i
$987$		0			0
$988$	−9.46966	+	29.1446i	−0.301270	+	0.927214i
$989$	13.8388	−	23.9695i	0.440048	−	0.762186i
$990$		0			0
$991$	−18.5643	−	32.1543i	−0.589713	−	1.02141i	−0.994270	−	0.106900i	$-0.965907\pi$
$991$	−18.5643	−	32.1543i	−0.589713	−	1.02141i	0.404556	−	0.914513i	$-0.367426\pi$
$992$	47.4268	+	52.6728i	1.50580	+	1.67236i
$993$		0			0
$994$	−61.6812	+	46.3550i	−1.95641	+	1.47029i
$995$	−18.1547	−	55.8744i	−0.575543	−	1.77134i
$996$		0			0
$997$	1.49883	−	14.2604i	0.0474684	−	0.451632i	−0.944812	−	0.327614i	$-0.893755\pi$
$997$	1.49883	−	14.2604i	0.0474684	−	0.451632i	0.992280	−	0.124018i	$-0.0395779\pi$
$998$	−100.667	−	44.8198i	−3.18656	−	1.41875i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.by.d.163.8		64
3.2	odd	2		231.2.y.a.163.1	yes	64
7.4	even	3	inner	693.2.by.d.361.1		64
11.5	even	5	inner	693.2.by.d.478.1		64
21.11	odd	6		231.2.y.a.130.8	yes	64
33.5	odd	10		231.2.y.a.16.8	✓	64
77.60	even	15	inner	693.2.by.d.676.8		64
231.137	odd	30		231.2.y.a.214.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.16.8	✓	64	33.5	odd	10
231.2.y.a.130.8	yes	64	21.11	odd	6
231.2.y.a.163.1	yes	64	3.2	odd	2
231.2.y.a.214.1	yes	64	231.137	odd	30
693.2.by.d.163.8		64	1.1	even	1	trivial
693.2.by.d.361.1		64	7.4	even	3	inner
693.2.by.d.478.1		64	11.5	even	5	inner
693.2.by.d.676.8		64	77.60	even	15	inner

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.by (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82701 + 2.02911i) q^{2} +(-0.570229 + 5.42537i) q^{4} +(-2.89339 - 0.615009i) q^{5} +(-2.43409 - 1.03693i) q^{7} +(-7.63253 + 5.54536i) q^{8} +O(q^{10})\)	\(q+(1.82701 + 2.02911i) q^{2} +(-0.570229 + 5.42537i) q^{4} +(-2.89339 - 0.615009i) q^{5} +(-2.43409 - 1.03693i) q^{7} +(-7.63253 + 5.54536i) q^{8} +(-4.03835 - 6.99462i) q^{10} +(0.272985 + 3.30537i) q^{11} +(1.13875 - 3.50471i) q^{13} +(-2.34307 - 6.83351i) q^{14} +(-14.5248 - 3.08734i) q^{16} +(-0.929192 + 1.03197i) q^{17} +(0.159341 + 1.51602i) q^{19} +(4.98655 - 15.3470i) q^{20} +(-6.20820 + 6.59288i) q^{22} +(-2.58882 + 4.48397i) q^{23} +(3.42574 + 1.52524i) q^{25} +(9.19193 - 4.09251i) q^{26} +(7.01372 - 12.6145i) q^{28} +(3.24703 + 2.35910i) q^{29} +(-3.19840 + 0.679841i) q^{31} +(-10.8381 - 18.7722i) q^{32} -3.79163 q^{34} +(6.40504 + 4.49723i) q^{35} +(4.05967 - 1.80748i) q^{37} +(-2.78506 + 3.09312i) q^{38} +(25.4943 - 11.3508i) q^{40} +(-6.29070 + 4.57046i) q^{41} -5.34560 q^{43} +(-18.0885 - 0.403773i) q^{44} +(-13.8283 + 2.93929i) q^{46} +(0.799720 + 7.60882i) q^{47} +(4.84954 + 5.04796i) q^{49} +(3.16401 + 9.73783i) q^{50} +(18.3650 + 8.17662i) q^{52} +(2.84045 - 0.603756i) q^{53} +(1.24298 - 9.73162i) q^{55} +(24.3284 - 5.58346i) q^{56} +(1.14550 + 10.8987i) q^{58} +(-0.800740 + 7.61853i) q^{59} +(0.892795 + 0.189769i) q^{61} +(-7.22300 - 5.24781i) q^{62} +(9.11197 - 28.0438i) q^{64} +(-5.45027 + 9.44014i) q^{65} +(5.18003 + 8.97207i) q^{67} +(-5.06898 - 5.62967i) q^{68} +(2.57673 + 21.2130i) q^{70} +(-3.30052 - 10.1580i) q^{71} +(-0.531901 + 5.06070i) q^{73} +(11.0846 + 4.93520i) q^{74} -8.31585 q^{76} +(2.76298 - 8.32862i) q^{77} +(3.79892 + 4.21913i) q^{79} +(40.1271 + 17.8657i) q^{80} +(-20.7671 - 4.41419i) q^{82} +(0.465946 + 1.43403i) q^{83} +(3.32319 - 2.41444i) q^{85} +(-9.76649 - 10.8468i) q^{86} +(-20.4130 - 23.7145i) q^{88} +(5.95694 - 10.3177i) q^{89} +(-6.40595 + 7.34995i) q^{91} +(-22.8510 - 16.6022i) q^{92} +(-13.9780 + 15.5242i) q^{94} +(0.471334 - 4.48445i) q^{95} +(2.60091 - 8.00477i) q^{97} +(-1.38266 + 19.0629i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 10 q^{4} - q^{7} - 8 q^{8}+O(q^{10}) \) 64 * q + 10 * q^4 - q^7 - 8 * q^8	\( 64 q + 10 q^{4} - q^{7} - 8 q^{8} - 22 q^{10} + 13 q^{11} - 8 q^{13} + 26 q^{14} - 4 q^{17} + 10 q^{19} - 24 q^{20} - 38 q^{22} + 8 q^{23} - 2 q^{25} - 4 q^{26} - 67 q^{28} - 2 q^{29} + 25 q^{31} - 72 q^{32} - 56 q^{34} - 19 q^{35} - 12 q^{37} + 37 q^{38} - 9 q^{40} - 20 q^{41} - 100 q^{43} + 5 q^{44} - 33 q^{46} + 18 q^{47} + 29 q^{49} + 46 q^{50} + 26 q^{52} + 49 q^{53} - 24 q^{55} + 48 q^{56} - 40 q^{58} - q^{59} + 3 q^{61} - 4 q^{62} - 24 q^{64} - 82 q^{65} + 76 q^{67} + 39 q^{68} + 59 q^{70} - 70 q^{71} - 3 q^{73} - 32 q^{74} + 104 q^{76} - 38 q^{77} - 15 q^{79} + 83 q^{80} + 42 q^{82} - 68 q^{83} + 62 q^{85} + 47 q^{86} - 64 q^{88} - 82 q^{89} - 10 q^{91} - 190 q^{92} - 6 q^{94} + 53 q^{95} - 32 q^{97} + 152 q^{98}+O(q^{100}) \) 64 * q + 10 * q^4 - q^7 - 8 * q^8 - 22 * q^10 + 13 * q^11 - 8 * q^13 + 26 * q^14 - 4 * q^17 + 10 * q^19 - 24 * q^20 - 38 * q^22 + 8 * q^23 - 2 * q^25 - 4 * q^26 - 67 * q^28 - 2 * q^29 + 25 * q^31 - 72 * q^32 - 56 * q^34 - 19 * q^35 - 12 * q^37 + 37 * q^38 - 9 * q^40 - 20 * q^41 - 100 * q^43 + 5 * q^44 - 33 * q^46 + 18 * q^47 + 29 * q^49 + 46 * q^50 + 26 * q^52 + 49 * q^53 - 24 * q^55 + 48 * q^56 - 40 * q^58 - q^59 + 3 * q^61 - 4 * q^62 - 24 * q^64 - 82 * q^65 + 76 * q^67 + 39 * q^68 + 59 * q^70 - 70 * q^71 - 3 * q^73 - 32 * q^74 + 104 * q^76 - 38 * q^77 - 15 * q^79 + 83 * q^80 + 42 * q^82 - 68 * q^83 + 62 * q^85 + 47 * q^86 - 64 * q^88 - 82 * q^89 - 10 * q^91 - 190 * q^92 - 6 * q^94 + 53 * q^95 - 32 * q^97 + 152 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more