LMFDB - Embedded newform 804.2.y.b.121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.5
Character	$\chi$	$=$	804.121
Dual form			804.2.y.b.505.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{3} +(2.24994 - 1.44595i) q^{5} +(2.21379 + 0.886268i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{3} +(2.24994 - 1.44595i) q^{5} +(2.21379 + 0.886268i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.240925 + 5.05764i) q^{11} +(3.25247 - 0.310573i) q^{13} +(0.380622 - 2.64728i) q^{15} +(0.620152 + 2.55630i) q^{17} +(-0.689895 + 0.276192i) q^{19} +(2.11952 - 1.09269i) q^{21} +(0.936879 + 0.180569i) q^{23} +(0.894377 - 1.95841i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(0.974121 - 1.68723i) q^{29} +(-7.90618 - 0.754949i) q^{31} +(3.98008 + 3.12997i) q^{33} +(6.26239 - 1.20698i) q^{35} +(-3.51395 - 6.08634i) q^{37} +(1.89520 - 2.66143i) q^{39} +(-1.77758 + 1.69491i) q^{41} +(2.03516 + 0.597576i) q^{43} +(-1.75143 - 2.02126i) q^{45} +(-4.00788 - 11.5800i) q^{47} +(-0.950738 - 0.906526i) q^{49} +(2.33804 + 1.20534i) q^{51} +(-4.25911 + 1.25059i) q^{53} +(7.85514 + 11.0310i) q^{55} +(-0.243053 + 0.702255i) q^{57} +(5.12694 + 11.2264i) q^{59} +(0.457763 - 9.60964i) q^{61} +(0.562192 - 2.31739i) q^{63} +(6.86877 - 5.40166i) q^{65} +(2.69049 - 7.73054i) q^{67} +(0.749990 - 0.589798i) q^{69} +(-2.64422 + 10.8996i) q^{71} +(0.635094 - 13.3323i) q^{73} +(-0.894377 - 1.95841i) q^{75} +(-3.94907 + 11.4101i) q^{77} +(3.59430 + 5.04749i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-1.66036 - 0.855976i) q^{83} +(5.09158 + 4.85481i) q^{85} +(-0.637207 - 1.84109i) q^{87} +(2.92096 + 3.37097i) q^{89} +(7.47553 + 2.19501i) q^{91} +(-5.74800 + 5.48071i) q^{93} +(-1.15286 + 1.61897i) q^{95} +(0.507256 + 0.878592i) q^{97} +(4.97187 - 0.958250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{26}{33}\right)$	$1$

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
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$		0			0
$5$	2.24994	−	1.44595i	1.00620	−	0.646647i	0.0697946	−	0.997561i	$-0.477766\pi$
$5$	2.24994	−	1.44595i	1.00620	−	0.646647i	0.936407	+	0.350915i	$0.114129\pi$
$6$		0			0
$7$	2.21379	+	0.886268i	0.836734	+	0.334978i	0.750151	−	0.661267i	$-0.229981\pi$
$7$	2.21379	+	0.886268i	0.836734	+	0.334978i	0.0865836	+	0.996245i	$0.472405\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	0.240925	+	5.05764i	0.0726417	+	1.52494i	0.681595	+	0.731730i	$0.261287\pi$
$11$	0.240925	+	5.05764i	0.0726417	+	1.52494i	−0.608953	+	0.793206i	$0.708410\pi$
$12$		0			0
$13$	3.25247	−	0.310573i	0.902072	−	0.0861374i	0.366297	−	0.930498i	$-0.380626\pi$
$13$	3.25247	−	0.310573i	0.902072	−	0.0861374i	0.535775	+	0.844361i	$0.320019\pi$
$14$		0			0
$15$	0.380622	−	2.64728i	0.0982761	−	0.683525i
$16$		0			0
$17$	0.620152	+	2.55630i	0.150409	+	0.619995i	0.996247	+	0.0865547i	$0.0275857\pi$
$17$	0.620152	+	2.55630i	0.150409	+	0.619995i	−0.845838	+	0.533440i	$0.820899\pi$
$18$		0			0
$19$	−0.689895	+	0.276192i	−0.158273	+	0.0633628i	−0.449446	−	0.893307i	$-0.648379\pi$
$19$	−0.689895	+	0.276192i	−0.158273	+	0.0633628i	0.291173	+	0.956670i	$0.405954\pi$
$20$		0			0
$21$	2.11952	−	1.09269i	0.462518	−	0.238444i
$22$		0			0
$23$	0.936879	+	0.180569i	0.195353	+	0.0376511i	0.285989	−	0.958233i	$-0.407678\pi$
$23$	0.936879	+	0.180569i	0.195353	+	0.0376511i	−0.0906362	+	0.995884i	$0.528890\pi$
$24$		0			0
$25$	0.894377	−	1.95841i	0.178875	−	0.391683i
$26$		0			0
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$		0			0
$29$	0.974121	−	1.68723i	0.180890	−	0.313310i	−0.761294	−	0.648407i	$-0.775436\pi$
$29$	0.974121	−	1.68723i	0.180890	−	0.313310i	0.942184	+	0.335097i	$0.108769\pi$
$30$		0			0
$31$	−7.90618	−	0.754949i	−1.41999	−	0.135593i	−0.643368	−	0.765557i	$-0.722464\pi$
$31$	−7.90618	−	0.754949i	−1.41999	−	0.135593i	−0.776624	+	0.629964i	$0.783070\pi$
$32$		0			0
$33$	3.98008	+	3.12997i	0.692843	+	0.544858i
$34$		0			0
$35$	6.26239	−	1.20698i	1.05854	−	0.204016i
$36$		0			0
$37$	−3.51395	−	6.08634i	−0.577689	−	1.00059i	−0.995744	−	0.0921655i	$-0.970621\pi$
$37$	−3.51395	−	6.08634i	−0.577689	−	1.00059i	0.418054	−	0.908422i	$-0.362712\pi$
$38$		0			0
$39$	1.89520	−	2.66143i	0.303474	−	0.426170i
$40$		0			0
$41$	−1.77758	+	1.69491i	−0.277611	+	0.264701i	−0.816074	−	0.577948i	$-0.803854\pi$
$41$	−1.77758	+	1.69491i	−0.277611	+	0.264701i	0.538463	+	0.842649i	$0.319005\pi$
$42$		0			0
$43$	2.03516	+	0.597576i	0.310358	+	0.0911295i	0.433203	−	0.901296i	$-0.357383\pi$
$43$	2.03516	+	0.597576i	0.310358	+	0.0911295i	−0.122844	+	0.992426i	$0.539202\pi$
$44$		0			0
$45$	−1.75143	−	2.02126i	−0.261087	−	0.301311i
$46$		0			0
$47$	−4.00788	−	11.5800i	−0.584610	−	1.68912i	−0.716269	−	0.697824i	$-0.754152\pi$
$47$	−4.00788	−	11.5800i	−0.584610	−	1.68912i	0.131659	−	0.991295i	$-0.457969\pi$
$48$		0			0
$49$	−0.950738	−	0.906526i	−0.135820	−	0.129504i
$50$		0			0
$51$	2.33804	+	1.20534i	0.327391	+	0.168782i
$52$		0			0
$53$	−4.25911	+	1.25059i	−0.585034	+	0.171781i	−0.560838	−	0.827926i	$-0.689521\pi$
$53$	−4.25911	+	1.25059i	−0.585034	+	0.171781i	−0.0241963	+	0.999707i	$0.507703\pi$
$54$		0			0
$55$	7.85514	+	11.0310i	1.05919	+	1.48742i
$56$		0			0
$57$	−0.243053	+	0.702255i	−0.0321931	+	0.0930160i
$58$		0			0
$59$	5.12694	+	11.2264i	0.667471	+	1.46156i	0.875393	+	0.483412i	$0.160603\pi$
$59$	5.12694	+	11.2264i	0.667471	+	1.46156i	−0.207922	+	0.978145i	$0.566670\pi$
$60$		0			0
$61$	0.457763	−	9.60964i	0.0586106	−	1.23039i	−0.757633	−	0.652680i	$-0.773644\pi$
$61$	0.457763	−	9.60964i	0.0586106	−	1.23039i	0.816244	−	0.577707i	$-0.196053\pi$
$62$		0			0
$63$	0.562192	−	2.31739i	0.0708295	−	0.291963i
$64$		0			0
$65$	6.86877	−	5.40166i	0.851966	−	0.669993i
$66$		0			0
$67$	2.69049	−	7.73054i	0.328696	−	0.944436i
$67$	2.69049	−	7.73054i	0.328696	−	0.944436i
$68$		0			0
$69$	0.749990	−	0.589798i	0.0902881	−	0.0710034i
$70$		0			0
$71$	−2.64422	+	10.8996i	−0.313811	+	1.29355i	0.568423	+	0.822736i	$0.307554\pi$
$71$	−2.64422	+	10.8996i	−0.313811	+	1.29355i	−0.882234	+	0.470810i	$0.843962\pi$
$72$		0			0
$73$	0.635094	−	13.3323i	0.0743321	−	1.56042i	−0.586538	−	0.809922i	$-0.699509\pi$
$73$	0.635094	−	13.3323i	0.0743321	−	1.56042i	0.660870	−	0.750501i	$-0.270188\pi$
$74$		0			0
$75$	−0.894377	−	1.95841i	−0.103274	−	0.226138i
$76$		0			0
$77$	−3.94907	+	11.4101i	−0.450038	+	1.30030i
$78$		0			0
$79$	3.59430	+	5.04749i	0.404391	+	0.567887i	0.965681	−	0.259732i	$-0.0836342\pi$
$79$	3.59430	+	5.04749i	0.404391	+	0.567887i	−0.561290	+	0.827619i	$0.689695\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	−1.66036	−	0.855976i	−0.182248	−	0.0939556i	0.364688	−	0.931130i	$-0.381176\pi$
$83$	−1.66036	−	0.855976i	−0.182248	−	0.0939556i	−0.546936	+	0.837174i	$0.684206\pi$
$84$		0			0
$85$	5.09158	+	4.85481i	0.552259	+	0.526578i
$86$		0			0
$87$	−0.637207	−	1.84109i	−0.0683158	−	0.197386i
$88$		0			0
$89$	2.92096	+	3.37097i	0.309621	+	0.357322i	0.889139	−	0.457638i	$-0.151304\pi$
$89$	2.92096	+	3.37097i	0.309621	+	0.357322i	−0.579517	+	0.814960i	$0.696759\pi$
$90$		0			0
$91$	7.47553	+	2.19501i	0.783649	+	0.230100i
$92$		0			0
$93$	−5.74800	+	5.48071i	−0.596040	+	0.568323i
$94$		0			0
$95$	−1.15286	+	1.61897i	−0.118281	+	0.166102i
$96$		0			0
$97$	0.507256	+	0.878592i	0.0515040	+	0.0892075i	0.890628	−	0.454733i	$-0.150265\pi$
$97$	0.507256	+	0.878592i	0.0515040	+	0.0892075i	−0.839124	+	0.543940i	$0.816932\pi$
$98$		0			0
$99$	4.97187	−	0.958250i	0.499692	−	0.0963078i
$100$		0			0
$101$	−14.2592	−	11.2136i	−1.41884	−	1.11579i	−0.975642	−	0.219370i	$-0.929600\pi$
$101$	−14.2592	−	11.2136i	−1.41884	−	1.11579i	−0.443203	−	0.896421i	$-0.646158\pi$
$102$		0			0
$103$	13.5261	+	1.29159i	1.33277	+	0.127264i	0.737001	−	0.675892i	$-0.236241\pi$
$103$	13.5261	+	1.29159i	1.33277	+	0.127264i	0.595769	+	0.803156i	$0.296847\pi$
$104$		0			0
$105$	3.18882	−	5.52320i	0.311197	−	0.539009i
$106$		0			0
$107$	−3.63634	−	2.33693i	−0.351538	−	0.225920i	0.352939	−	0.935646i	$-0.385182\pi$
$107$	−3.63634	−	2.33693i	−0.351538	−	0.225920i	−0.704477	+	0.709726i	$0.748819\pi$
$108$		0			0
$109$	2.53865	−	5.55888i	0.243159	−	0.532444i	−0.748223	−	0.663447i	$-0.769093\pi$
$109$	2.53865	−	5.55888i	0.243159	−	0.532444i	0.991382	+	0.131004i	$0.0418199\pi$
$110$		0			0
$111$	−6.90089	−	1.33004i	−0.655004	−	0.126242i
$112$		0			0
$113$	−12.6800	+	6.53699i	−1.19283	+	0.614948i	−0.936168	−	0.351553i	$-0.885654\pi$
$113$	−12.6800	+	6.53699i	−1.19283	+	0.614948i	−0.256664	+	0.966501i	$0.582623\pi$
$114$		0			0
$115$	2.36901	−	0.948408i	0.220911	−	0.0884395i
$116$		0			0
$117$	−0.770286	−	3.17516i	−0.0712129	−	0.293544i
$118$		0			0
$119$	−0.892682	+	6.20874i	−0.0818321	+	0.569155i
$120$		0			0
$121$	−14.5715	+	1.39141i	−1.32468	+	0.126492i
$122$		0			0
$123$	0.116867	+	2.45333i	0.0105375	+	0.221210i
$124$		0			0
$125$	1.08364	+	7.53688i	0.0969237	+	0.674119i
$126$		0			0
$127$	−4.40765	−	1.76456i	−0.391116	−	0.156579i	0.167765	−	0.985827i	$-0.446345\pi$
$127$	−4.40765	−	1.76456i	−0.391116	−	0.156579i	−0.558881	+	0.829248i	$0.688769\pi$
$128$		0			0
$129$	1.78436	−	1.14674i	0.157104	−	0.100965i
$130$		0			0
$131$	−7.83709	+	9.04448i	−0.684729	+	0.790220i	−0.986605	−	0.163127i	$-0.947842\pi$
$131$	−7.83709	+	9.04448i	−0.684729	+	0.790220i	0.301876	+	0.953347i	$0.402387\pi$
$132$		0			0
$133$	−1.77206			−0.153657
$134$		0			0
$135$	−2.67450			−0.230185
$136$		0			0
$137$	1.69887	−	1.96060i	0.145144	−	0.167505i	−0.678522	−	0.734580i	$-0.737379\pi$
$137$	1.69887	−	1.96060i	0.145144	−	0.167505i	0.823667	+	0.567074i	$0.191925\pi$
$138$		0			0
$139$	−10.4574	+	6.72053i	−0.886981	+	0.570028i	−0.902903	−	0.429845i	$-0.858568\pi$
$139$	−10.4574	+	6.72053i	−0.886981	+	0.570028i	0.0159214	+	0.999873i	$0.494932\pi$
$140$		0			0
$141$	−11.3762	−	4.55434i	−0.958049	−	0.383545i
$142$		0			0
$143$	2.35437	+	16.3750i	0.196882	+	1.36934i
$144$		0			0
$145$	−0.247929	−	5.20468i	−0.0205894	−	0.432225i
$146$		0			0
$147$	−1.30771	+	0.124871i	−0.107858	+	0.0102992i
$148$		0			0
$149$	−0.128389	+	0.892962i	−0.0105180	+	0.0731543i	−0.994404	−	0.105640i	$-0.966311\pi$
$149$	−0.128389	+	0.892962i	−0.0105180	+	0.0731543i	0.983886	+	0.178795i	$0.0572198\pi$
$150$		0			0
$151$	−5.73097	−	23.6234i	−0.466380	−	1.92244i	−0.376268	−	0.926511i	$-0.622793\pi$
$151$	−5.73097	−	23.6234i	−0.466380	−	1.92244i	−0.0901118	−	0.995932i	$-0.528722\pi$
$152$		0			0
$153$	2.44203	−	0.977640i	0.197426	−	0.0790375i
$154$		0			0
$155$	−18.8800	+	9.73333i	−1.51648	+	0.781800i
$156$		0			0
$157$	15.4862	+	2.98471i	1.23593	+	0.238206i	0.765038	−	0.643985i	$-0.222720\pi$
$157$	15.4862	+	2.98471i	1.23593	+	0.238206i	0.470892	+	0.882191i	$0.343932\pi$
$158$		0			0
$159$	−1.84399	+	4.03778i	−0.146238	+	0.320217i
$160$		0			0
$161$	1.91402	+	1.23007i	0.150846	+	0.0969429i
$162$		0			0
$163$	−6.78331	+	11.7490i	−0.531310	+	0.920256i	0.468022	+	0.883717i	$0.344967\pi$
$163$	−6.78331	+	11.7490i	−0.531310	+	0.920256i	−0.999332	+	0.0365391i	$0.988367\pi$
$164$		0			0
$165$	13.4807	+	1.28725i	1.04947	+	0.100212i
$166$		0			0
$167$	8.50664	+	6.68969i	0.658263	+	0.517664i	0.890493	−	0.454997i	$-0.150360\pi$
$167$	8.50664	+	6.68969i	0.658263	+	0.517664i	−0.232230	+	0.972661i	$0.574602\pi$
$168$		0			0
$169$	−2.28299	+	0.440011i	−0.175615	+	0.0338470i
$170$		0			0
$171$	0.371563	+	0.643566i	0.0284141	+	0.0492147i
$172$		0			0
$173$	−3.88923	+	5.46166i	−0.295693	+	0.415242i	−0.935519	−	0.353278i	$-0.885067\pi$
$173$	−3.88923	+	5.46166i	−0.295693	+	0.415242i	0.639826	+	0.768520i	$0.279006\pi$
$174$		0			0
$175$	3.71564	−	3.54286i	0.280876	−	0.267815i
$176$		0			0
$177$	11.8418	+	3.47707i	0.890085	+	0.261352i
$178$		0			0
$179$	5.96575	+	6.88484i	0.445901	+	0.514597i	0.933552	−	0.358441i	$-0.116692\pi$
$179$	5.96575	+	6.88484i	0.445901	+	0.514597i	−0.487651	+	0.873039i	$0.662146\pi$
$180$		0			0
$181$	2.20978	+	6.38473i	0.164251	+	0.474573i	0.996851	−	0.0793027i	$-0.0252694\pi$
$181$	2.20978	+	6.38473i	0.164251	+	0.474573i	−0.832599	+	0.553876i	$0.813148\pi$
$182$		0			0
$183$	−6.96271	−	6.63893i	−0.514698	−	0.490764i
$184$		0			0
$185$	−16.7067	−	8.61289i	−1.22830	−	0.633232i
$186$		0			0
$187$	−12.7795	+	3.75239i	−0.934526	+	0.274402i
$188$		0			0
$189$	−1.38321	−	1.94244i	−0.100614	−	0.141292i
$190$		0			0
$191$	4.50342	−	13.0118i	0.325856	−	0.941498i	−0.656475	−	0.754347i	$-0.727953\pi$
$191$	4.50342	−	13.0118i	0.325856	−	0.941498i	0.982331	−	0.187151i	$-0.0599253\pi$
$192$		0			0
$193$	−6.42870	−	14.0769i	−0.462748	−	1.01328i	−0.986853	−	0.161623i	$-0.948327\pi$
$193$	−6.42870	−	14.0769i	−0.462748	−	1.01328i	0.524105	−	0.851654i	$-0.324400\pi$
$194$		0			0
$195$	0.415785	−	8.72840i	0.0297750	−	0.625054i
$196$		0			0
$197$	2.23568	−	9.21560i	0.159286	−	0.656584i	−0.835039	−	0.550191i	$-0.814555\pi$
$197$	2.23568	−	9.21560i	0.159286	−	0.656584i	0.994324	−	0.106393i	$-0.0339301\pi$
$198$		0			0
$199$	−16.7167	+	13.1461i	−1.18501	+	0.931904i	−0.998719	−	0.0505904i	$-0.983890\pi$
$199$	−16.7167	+	13.1461i	−1.18501	+	0.931904i	−0.186293	+	0.982494i	$0.559647\pi$
$200$		0			0
$201$	−4.08045	−	7.09577i	−0.287813	−	0.500497i
$202$		0			0
$203$	3.65184	−	2.87184i	0.256309	−	0.201563i
$204$		0			0
$205$	−1.54868	+	6.38373i	−0.108164	+	0.445859i
$206$		0			0
$207$	0.0453989	−	0.953040i	0.00315544	−	0.0662409i
$208$		0			0
$209$	−1.56309	−	3.42270i	−0.108121	−	0.236753i
$210$		0			0
$211$	1.98318	−	5.73002i	0.136528	−	0.394471i	−0.855925	−	0.517100i	$-0.827011\pi$
$211$	1.98318	−	5.73002i	0.136528	−	0.394471i	0.992453	+	0.122629i	$0.0391327\pi$
$212$		0			0
$213$	6.50579	+	9.13610i	0.445769	+	0.625995i
$214$		0			0
$215$	5.44303	−	1.59822i	0.371212	−	0.108998i
$216$		0			0
$217$	−16.8336	−	8.67830i	−1.14274	−	0.589121i
$218$		0			0
$219$	−9.65995	−	9.21074i	−0.652759	−	0.622404i
$220$		0			0
$221$	2.81094	+	8.12169i	0.189084	+	0.546324i
$222$		0			0
$223$	9.53681	+	11.0061i	0.638632	+	0.737020i	0.979132	−	0.203224i	$-0.0651419\pi$
$223$	9.53681	+	11.0061i	0.638632	+	0.737020i	−0.340500	+	0.940244i	$0.610596\pi$
$224$		0			0
$225$	−2.06576	−	0.606563i	−0.137718	−	0.0404375i
$226$		0			0
$227$	−14.7519	+	14.0659i	−0.979120	+	0.933589i	−0.997804	−	0.0662360i	$-0.978901\pi$
$227$	−14.7519	+	14.0659i	−0.979120	+	0.933589i	0.0186835	+	0.999825i	$0.494052\pi$
$228$		0			0
$229$	−5.04518	+	7.08497i	−0.333395	+	0.468188i	−0.946912	−	0.321494i	$-0.895815\pi$
$229$	−5.04518	+	7.08497i	−0.333395	+	0.468188i	0.613516	+	0.789682i	$0.289754\pi$
$230$		0			0
$231$	6.03708	+	10.4565i	0.397210	+	0.687989i
$232$		0			0
$233$	11.3034	−	2.17855i	0.740508	−	0.142721i	0.194972	−	0.980809i	$-0.437538\pi$
$233$	11.3034	−	2.17855i	0.740508	−	0.142721i	0.545536	+	0.838087i	$0.316326\pi$
$234$		0			0
$235$	−25.7616	−	20.2591i	−1.68050	−	1.32156i
$236$		0			0
$237$	6.16841	+	0.589011i	0.400681	+	0.0382604i
$238$		0			0
$239$	3.30688	−	5.72769i	0.213904	−	0.370493i	−0.739029	−	0.673674i	$-0.764715\pi$
$239$	3.30688	−	5.72769i	0.213904	−	0.370493i	0.952933	+	0.303181i	$0.0980486\pi$
$240$		0			0
$241$	10.9208	+	7.01838i	0.703472	+	0.452094i	0.842852	−	0.538145i	$-0.180875\pi$
$241$	10.9208	+	7.01838i	0.703472	+	0.452094i	−0.139381	+	0.990239i	$0.544511\pi$
$242$		0			0
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$		0			0
$245$	−3.44989	−	0.664911i	−0.220405	−	0.0424796i
$246$		0			0
$247$	−2.15808	+	1.11257i	−0.137315	+	0.0707910i
$248$		0			0
$249$	−1.73421	+	0.694273i	−0.109901	+	0.0439978i
$250$		0			0
$251$	4.40650	+	18.1638i	0.278136	+	1.14649i	0.923802	+	0.382871i	$0.125065\pi$
$251$	4.40650	+	18.1638i	0.278136	+	1.14649i	−0.645666	+	0.763620i	$0.723420\pi$
$252$		0			0
$253$	−0.687533	+	4.78190i	−0.0432248	+	0.300635i
$254$		0			0
$255$	7.00330	−	0.668734i	0.438563	−	0.0418777i
$256$		0			0
$257$	−0.690702	−	14.4996i	−0.0430848	−	0.904461i	−0.912173	−	0.409805i	$-0.865597\pi$
$257$	−0.690702	−	14.4996i	−0.0430848	−	0.904461i	0.869088	−	0.494657i	$-0.164706\pi$
$258$		0			0
$259$	−2.38502	−	16.5882i	−0.148198	−	1.03074i
$260$		0			0
$261$	−1.80869	−	0.724088i	−0.111955	−	0.0448199i
$262$		0			0
$263$	4.32231	−	2.77778i	0.266525	−	0.171285i	−0.400552	−	0.916274i	$-0.631182\pi$
$263$	4.32231	−	2.77778i	0.266525	−	0.171285i	0.667077	+	0.744989i	$0.267545\pi$
$264$		0			0
$265$	−7.77445	+	8.97219i	−0.477581	+	0.551157i
$266$		0			0
$267$	4.46043			0.272974
$268$		0			0
$269$	−15.4431			−0.941580			−0.470790	−	0.882245i	$-0.656031\pi$
$269$	−15.4431			−0.941580			−0.470790	+	0.882245i	$0.656031\pi$
$270$		0			0
$271$	−5.06837	+	5.84921i	−0.307881	+	0.355314i	−0.888512	−	0.458853i	$-0.848260\pi$
$271$	−5.06837	+	5.84921i	−0.307881	+	0.355314i	0.580631	+	0.814167i	$0.302806\pi$
$272$		0			0
$273$	6.55431	−	4.21220i	0.396685	−	0.254934i
$274$		0			0
$275$	10.1204	+	4.05161i	0.610285	+	0.244321i
$276$		0			0
$277$	2.27102	+	15.7953i	0.136452	+	0.949046i	0.936888	+	0.349628i	$0.113692\pi$
$277$	2.27102	+	15.7953i	0.136452	+	0.949046i	−0.800436	+	0.599418i	$0.795399\pi$
$278$		0			0
$279$	0.377903	+	7.93315i	0.0226244	+	0.474945i
$280$		0			0
$281$	1.05447	−	0.100689i	0.0629043	−	0.00600663i	−0.0635564	−	0.997978i	$-0.520244\pi$
$281$	1.05447	−	0.100689i	0.0629043	−	0.00600663i	0.126461	+	0.991972i	$0.459638\pi$
$282$		0			0
$283$	−1.82141	+	12.6682i	−0.108272	+	0.753047i	0.861275	+	0.508140i	$0.169667\pi$
$283$	−1.82141	+	12.6682i	−0.108272	+	0.753047i	−0.969546	+	0.244907i	$0.921242\pi$
$284$		0			0
$285$	0.468570	+	1.93147i	0.0277557	+	0.114410i
$286$		0			0
$287$	−5.43733	+	2.17678i	−0.320955	+	0.128491i
$288$		0			0
$289$	8.96011	−	4.61926i	0.527065	−	0.271721i
$290$		0			0
$291$	0.996178	+	0.191997i	0.0583970	+	0.0112551i
$292$		0			0
$293$	−5.53173	+	12.1128i	−0.323167	+	0.707638i	−0.999583	−	0.0288826i	$-0.990805\pi$
$293$	−5.53173	+	12.1128i	−0.323167	+	0.707638i	0.676416	+	0.736520i	$0.263532\pi$
$294$		0			0
$295$	27.7681	+	17.8455i	1.61672	+	1.03900i
$296$		0			0
$297$	2.53169	−	4.38501i	0.146903	−	0.254444i
$298$		0			0
$299$	3.10325	+	0.296324i	0.179465	+	0.0171369i
$300$		0			0
$301$	3.97580	+	3.12660i	0.229161	+	0.180214i
$302$		0			0
$303$	−17.8124	+	3.43307i	−1.02330	+	0.197225i
$304$		0			0
$305$	−12.8651	−	22.2830i	−0.736652	−	1.27592i
$306$		0			0
$307$	1.11409	−	1.56452i	0.0635846	−	0.0892920i	−0.781559	−	0.623831i	$-0.785575\pi$
$307$	1.11409	−	1.56452i	0.0635846	−	0.0892920i	0.845144	+	0.534539i	$0.179515\pi$
$308$		0			0
$309$	9.83385	−	9.37656i	0.559428	−	0.533414i
$310$		0			0
$311$	27.3417	+	8.02825i	1.55041	+	0.455240i	0.941222	−	0.337788i	$-0.109679\pi$
$311$	27.3417	+	8.02825i	1.55041	+	0.455240i	0.609184	+	0.793029i	$0.291497\pi$
$312$		0			0
$313$	−0.304085	−	0.350933i	−0.0171879	−	0.0198359i	0.747091	−	0.664722i	$-0.231450\pi$
$313$	−0.304085	−	0.350933i	−0.0171879	−	0.0198359i	−0.764278	+	0.644886i	$0.776905\pi$
$314$		0			0
$315$	−2.08592	−	6.02687i	−0.117528	−	0.339576i
$316$		0			0
$317$	1.79202	+	1.70868i	0.100650	+	0.0959693i	0.738734	−	0.673998i	$-0.235424\pi$
$317$	1.79202	+	1.70868i	0.100650	+	0.0959693i	−0.638084	+	0.769967i	$0.720273\pi$
$318$		0			0
$319$	8.76808	+	4.52026i	0.490918	+	0.253086i
$320$		0			0
$321$	−4.14743	+	1.21780i	−0.231487	+	0.0679707i
$322$		0			0
$323$	−1.13387	−	1.59230i	−0.0630903	−	0.0885979i
$324$		0			0
$325$	2.30070	−	6.64744i	0.127620	−	0.368734i
$326$		0			0
$327$	−2.53865	−	5.55888i	−0.140388	−	0.307407i
$328$		0			0
$329$	1.39039	−	29.1878i	0.0766545	−	1.60918i
$330$		0			0
$331$	7.35654	−	30.3241i	0.404352	−	1.66676i	−0.297718	−	0.954654i	$-0.596225\pi$
$331$	7.35654	−	30.3241i	0.404352	−	1.66676i	0.702070	−	0.712108i	$-0.252259\pi$
$332$		0			0
$333$	−5.52430	+	4.34436i	−0.302730	+	0.238069i
$334$		0			0
$335$	−5.12450	−	21.2835i	−0.279982	−	1.16284i
$336$		0			0
$337$	2.89269	−	2.27484i	0.157575	−	0.123918i	−0.536259	−	0.844054i	$-0.680163\pi$
$337$	2.89269	−	2.27484i	0.157575	−	0.123918i	0.693833	+	0.720135i	$0.255920\pi$
$338$		0			0
$339$	−3.36330	+	13.8637i	−0.182669	+	0.752973i
$340$		0			0
$341$	1.91346	−	40.1685i	0.103620	−	2.17525i
$342$		0			0
$343$	−8.23552	−	18.0333i	−0.444676	−	0.973705i
$344$		0			0
$345$	0.834612	−	2.41145i	0.0449340	−	0.129828i
$346$		0			0
$347$	2.56959	+	3.60849i	0.137943	+	0.193714i	0.877769	−	0.479085i	$-0.159031\pi$
$347$	2.56959	+	3.60849i	0.137943	+	0.193714i	−0.739826	+	0.672799i	$0.765092\pi$
$348$		0			0
$349$	5.16556	−	1.51674i	0.276506	−	0.0811894i	−0.140540	−	0.990075i	$-0.544884\pi$
$349$	5.16556	−	1.51674i	0.276506	−	0.0811894i	0.417045	+	0.908886i	$0.363066\pi$
$350$		0			0
$351$	−2.90406	−	1.49715i	−0.155007	−	0.0799117i
$352$		0			0
$353$	−1.12975	−	1.07722i	−0.0601306	−	0.0573344i	0.659418	−	0.751776i	$-0.270803\pi$
$353$	−1.12975	−	1.07722i	−0.0601306	−	0.0573344i	−0.719549	+	0.694442i	$0.755651\pi$
$354$		0			0
$355$	9.81094	+	28.3468i	0.520710	+	1.50449i
$356$		0			0
$357$	4.10767	+	4.74051i	0.217401	+	0.250894i
$358$		0			0
$359$	17.9989	+	5.28495i	0.949945	+	0.278929i	0.719764	−	0.694219i	$-0.244250\pi$
$359$	17.9989	+	5.28495i	0.949945	+	0.278929i	0.230181	+	0.973148i	$0.426068\pi$
$360$		0			0
$361$	−13.3513	+	12.7304i	−0.702699	+	0.670022i
$362$		0			0
$363$	−8.49074	+	11.9236i	−0.445648	+	0.625825i
$364$		0			0
$365$	−17.8488	−	30.9150i	−0.934249	−	1.61817i
$366$		0			0
$367$	2.63124	−	0.507130i	0.137350	−	0.0264720i	−0.120113	−	0.992760i	$-0.538326\pi$
$367$	2.63124	−	0.507130i	0.137350	−	0.0264720i	0.257463	+	0.966288i	$0.417114\pi$
$368$		0			0
$369$	1.93064	+	1.51827i	0.100505	+	0.0790380i
$370$		0			0
$371$	−10.5371	−	1.00618i	−0.547061	−	0.0522380i
$372$		0			0
$373$	10.1800	−	17.6323i	0.527101	−	0.912965i	−0.472401	−	0.881384i	$-0.656612\pi$
$373$	10.1800	−	17.6323i	0.527101	−	0.912965i	0.999501	−	0.0315811i	$-0.0100543\pi$
$374$		0			0
$375$	6.40563	+	4.11665i	0.330785	+	0.212583i
$376$		0			0
$377$	2.64429	−	5.79018i	0.136188	−	0.298210i
$378$		0			0
$379$	−22.7439	−	4.38353i	−1.16828	−	0.225167i	−0.432016	−	0.901866i	$-0.642198\pi$
$379$	−22.7439	−	4.38353i	−1.16828	−	0.225167i	−0.736260	+	0.676699i	$0.763410\pi$
$380$		0			0
$381$	−4.21996	+	2.17554i	−0.216195	+	0.111456i
$382$		0			0
$383$	17.8400	−	7.14206i	0.911582	−	0.364942i	0.132005	−	0.991249i	$-0.457858\pi$
$383$	17.8400	−	7.14206i	0.911582	−	0.364942i	0.779577	+	0.626307i	$0.215434\pi$
$384$		0			0
$385$	7.61322	+	31.3821i	0.388005	+	1.59938i
$386$		0			0
$387$	0.301860	−	2.09949i	0.0153444	−	0.106723i
$388$		0			0
$389$	9.16497	−	0.875149i	0.464683	−	0.0443718i	0.139911	−	0.990164i	$-0.455318\pi$
$389$	9.16497	−	0.875149i	0.464683	−	0.0443718i	0.324772	+	0.945792i	$0.394712\pi$
$390$		0			0
$391$	0.119420	+	2.50693i	0.00603931	+	0.126781i
$392$		0			0
$393$	1.70316	+	11.8458i	0.0859131	+	0.597539i
$394$		0			0
$395$	15.3854	+	6.15937i	0.774121	+	0.309911i
$396$		0			0
$397$	13.9858	−	8.98815i	0.701929	−	0.451102i	−0.140380	−	0.990098i	$-0.544832\pi$
$397$	13.9858	−	8.98815i	0.701929	−	0.451102i	0.842309	+	0.538995i	$0.181196\pi$
$398$		0			0
$399$	−1.16045	+	1.33924i	−0.0580954	+	0.0670457i
$400$		0			0
$401$	19.6771			0.982626			0.491313	−	0.870983i	$-0.336517\pi$
$401$	19.6771			0.982626			0.491313	+	0.870983i	$0.336517\pi$
$402$		0			0
$403$	−25.9491			−1.29261
$404$		0			0
$405$	−1.75143	+	2.02126i	−0.0870291	+	0.100437i
$406$		0			0
$407$	29.9359	−	19.2386i	1.48387	−	0.953624i
$408$		0			0
$409$	30.7765	+	12.3210i	1.52180	+	0.609237i	0.973833	−	0.227264i	$-0.0729780\pi$
$409$	30.7765	+	12.3210i	1.52180	+	0.609237i	0.547966	+	0.836500i	$0.315402\pi$
$410$		0			0
$411$	−0.369200	−	2.56784i	−0.0182113	−	0.126662i
$412$		0			0
$413$	1.40034	+	29.3968i	0.0689064	+	1.44652i
$414$		0			0
$415$	−4.97340	+	0.474903i	−0.244135	+	0.0233120i
$416$		0			0
$417$	−1.76907	+	12.3042i	−0.0866318	+	0.602537i
$418$		0			0
$419$	−1.72282	−	7.10156i	−0.0841652	−	0.346934i	0.914122	−	0.405440i	$-0.132882\pi$
$419$	−1.72282	−	7.10156i	−0.0841652	−	0.346934i	−0.998287	+	0.0585058i	$0.981366\pi$
$420$		0			0
$421$	27.0054	−	10.8113i	1.31616	−	0.526912i	0.395929	−	0.918281i	$-0.370422\pi$
$421$	27.0054	−	10.8113i	1.31616	−	0.526912i	0.920234	+	0.391369i	$0.127998\pi$
$422$		0			0
$423$	−10.8918	+	5.61510i	−0.529576	+	0.273015i
$424$		0			0
$425$	5.56095	+	1.07178i	0.269746	+	0.0519892i
$426$		0			0
$427$	9.53011	−	20.8680i	0.461194	−	1.00987i
$428$		0			0
$429$	13.9172	+	8.94402i	0.671927	+	0.431821i
$430$		0			0
$431$	−12.3344	+	21.3637i	−0.594125	+	1.02905i	0.399545	+	0.916714i	$0.369168\pi$
$431$	−12.3344	+	21.3637i	−0.594125	+	1.02905i	−0.993670	+	0.112341i	$0.964165\pi$
$432$		0			0
$433$	16.8617	+	1.61010i	0.810324	+	0.0773766i	0.491989	−	0.870602i	$-0.336270\pi$
$433$	16.8617	+	1.61010i	0.810324	+	0.0773766i	0.318335	+	0.947978i	$0.396876\pi$
$434$		0			0
$435$	−4.09579	−	3.22097i	−0.196378	−	0.154434i
$436$		0			0
$437$	−0.696219	+	0.134185i	−0.0333047	+	0.00641895i
$438$		0			0
$439$	5.78112	+	10.0132i	0.275918	+	0.477904i	0.970366	−	0.241639i	$-0.0776849\pi$
$439$	5.78112	+	10.0132i	0.275918	+	0.477904i	−0.694448	+	0.719542i	$0.744352\pi$
$440$		0			0
$441$	−0.761995	+	1.07007i	−0.0362855	+	0.0509558i
$442$		0			0
$443$	−9.60770	+	9.16092i	−0.456475	+	0.435248i	−0.883103	−	0.469179i	$-0.844550\pi$
$443$	−9.60770	+	9.16092i	−0.456475	+	0.435248i	0.426628	+	0.904427i	$0.359701\pi$
$444$		0			0
$445$	11.4462	+	3.36091i	0.542603	+	0.159322i
$446$		0			0
$447$	0.590779	+	0.681795i	0.0279429	+	0.0322478i
$448$		0			0
$449$	−7.55479	−	21.8281i	−0.356533	−	1.03013i	−0.970562	−	0.240851i	$-0.922574\pi$
$449$	−7.55479	−	21.8281i	−0.356533	−	1.03013i	0.614029	−	0.789283i	$-0.289548\pi$
$450$		0			0
$451$	−9.00053	−	8.58199i	−0.423818	−	0.404110i
$452$		0			0
$453$	−21.6063	−	11.1388i	−1.01515	−	0.523348i
$454$		0			0
$455$	19.9933	−	5.87058i	0.937302	−	0.275217i
$456$		0			0
$457$	20.1748	+	28.3316i	0.943738	+	1.32529i	0.945612	+	0.325297i	$0.105464\pi$
$457$	20.1748	+	28.3316i	0.943738	+	1.32529i	−0.00187373	+	0.999998i	$0.500596\pi$
$458$		0			0
$459$	0.860336	−	2.48578i	0.0401571	−	0.116026i
$460$		0			0
$461$	8.78276	+	19.2316i	0.409054	+	0.895703i	0.996271	+	0.0862742i	$0.0274961\pi$
$461$	8.78276	+	19.2316i	0.409054	+	0.895703i	−0.587217	+	0.809429i	$0.699777\pi$
$462$		0			0
$463$	−0.844970	+	17.7381i	−0.0392691	+	0.824359i	0.890225	+	0.455522i	$0.150547\pi$
$463$	−0.844970	+	17.7381i	−0.0392691	+	0.824359i	−0.929494	+	0.368838i	$0.879756\pi$
$464$		0			0
$465$	−5.00783	+	20.6425i	−0.232232	+	0.957275i
$466$		0			0
$467$	14.9888	−	11.7873i	0.693597	−	0.545451i	−0.207946	−	0.978140i	$-0.566678\pi$
$467$	14.9888	−	11.7873i	0.693597	−	0.545451i	0.901543	+	0.432689i	$0.142435\pi$
$468$		0			0
$469$	12.8075	−	14.7293i	0.591397	−	0.680136i
$470$		0			0
$471$	12.3970	−	9.74909i	0.571223	−	0.449214i
$472$		0			0
$473$	−2.53200	+	10.4371i	−0.116422	+	0.479897i
$474$		0			0
$475$	−0.0761278	+	1.59812i	−0.00349298	+	0.0733267i
$476$		0			0
$477$	1.84399	+	4.03778i	0.0844307	+	0.184877i
$478$		0			0
$479$	0.804151	−	2.32344i	0.0367426	−	0.106161i	−0.925138	−	0.379632i	$-0.876051\pi$
$479$	0.804151	−	2.32344i	0.0367426	−	0.106161i	0.961880	+	0.273471i	$0.0881718\pi$
$480$		0			0
$481$	−13.3192	−	18.7043i	−0.607305	−	0.852841i
$482$		0			0
$483$	2.18304	−	0.640998i	0.0993318	−	0.0291664i
$484$		0			0
$485$	2.41169	+	1.24331i	0.109509	+	0.0564559i
$486$		0			0
$487$	2.86359	+	2.73042i	0.129761	+	0.123727i	0.752181	−	0.658956i	$-0.229002\pi$
$487$	2.86359	+	2.73042i	0.129761	+	0.123727i	−0.622420	+	0.782684i	$0.713850\pi$
$488$		0			0
$489$	4.43721	+	12.8205i	0.200657	+	0.579762i
$490$		0			0
$491$	−1.69045	−	1.95088i	−0.0762889	−	0.0880421i	0.716322	−	0.697770i	$-0.245824\pi$
$491$	−1.69045	−	1.95088i	−0.0762889	−	0.0880421i	−0.792611	+	0.609728i	$0.791279\pi$
$492$		0			0
$493$	4.91717	+	1.44381i	0.221458	+	0.0650259i
$494$		0			0
$495$	9.80082	−	9.34506i	0.440514	−	0.420029i
$496$		0			0
$497$	−15.5137	+	21.7860i	−0.695886	+	0.977235i
$498$		0			0
$499$	−2.68230	−	4.64588i	−0.120076	−	0.207978i	0.799721	−	0.600371i	$-0.204981\pi$
$499$	−2.68230	−	4.64588i	−0.120076	−	0.207978i	−0.919798	+	0.392393i	$0.871647\pi$
$500$		0			0
$501$	10.6264	−	2.04807i	0.474752	−	0.0915010i
$502$		0			0
$503$	32.0300	+	25.1886i	1.42815	+	1.12311i	0.972489	+	0.232950i	$0.0748379\pi$
$503$	32.0300	+	25.1886i	1.42815	+	1.12311i	0.455657	+	0.890156i	$0.349405\pi$
$504$		0			0
$505$	−48.2965	−	4.61176i	−2.14917	−	0.205221i
$506$		0			0
$507$	−1.16250	+	2.01352i	−0.0516287	+	0.0894235i
$508$		0			0
$509$	−24.1414	−	15.5147i	−1.07005	−	0.687678i	−0.117810	−	0.993036i	$-0.537587\pi$
$509$	−24.1414	−	15.5147i	−1.07005	−	0.687678i	−0.952237	+	0.305358i	$0.901224\pi$
$510$		0			0
$511$	13.2219	−	28.9520i	0.584903	−	1.28076i
$512$		0			0
$513$	0.729697	+	0.140638i	0.0322169	+	0.00620930i
$514$		0			0
$515$	32.3005	−	16.6521i	1.42333	−	0.733778i
$516$		0			0
$517$	57.6020	−	23.0603i	2.53333	−	1.01419i
$518$		0			0
$519$	1.58074	+	6.51591i	0.0693869	+	0.286017i
$520$		0			0
$521$	5.39421	−	37.5176i	0.236325	−	1.64367i	−0.433499	−	0.901154i	$-0.642721\pi$
$521$	5.39421	−	37.5176i	0.236325	−	1.64367i	0.669824	−	0.742520i	$-0.266370\pi$
$522$		0			0
$523$	−30.0475	+	2.86919i	−1.31389	+	0.125461i	−0.728361	−	0.685193i	$-0.759718\pi$
$523$	−30.0475	+	2.86919i	−1.31389	+	0.125461i	−0.585525	+	0.810654i	$0.699112\pi$
$524$		0			0
$525$	−0.244285	−	5.12818i	−0.0106615	−	0.223812i
$526$		0			0
$527$	−2.97316	−	20.6788i	−0.129513	−	0.900782i
$528$		0			0
$529$	−20.5073	−	8.20989i	−0.891623	−	0.356952i
$530$		0			0
$531$	10.3825	−	6.67244i	0.450563	−	0.289559i
$532$		0			0
$533$	−5.25511	+	6.06472i	−0.227624	+	0.262692i
$534$		0			0
$535$	−11.5606			−0.499809
$536$		0			0
$537$	9.10995			0.393123
$538$		0			0
$539$	4.35583	−	5.02689i	0.187619	−	0.216524i
$540$		0			0
$541$	−18.1215	+	11.6460i	−0.779104	+	0.500700i	−0.868736	−	0.495275i	$-0.835067\pi$
$541$	−18.1215	+	11.6460i	−0.779104	+	0.500700i	0.0896323	+	0.995975i	$0.471431\pi$
$542$		0			0
$543$	6.27235	+	2.51107i	0.269172	+	0.107760i
$544$		0			0
$545$	−2.32603	−	16.1779i	−0.0996361	−	0.692984i
$546$		0			0
$547$	−1.11299	−	23.3646i	−0.0475881	−	0.998998i	−0.888801	−	0.458294i	$-0.848461\pi$
$547$	−1.11299	−	23.3646i	−0.0475881	−	0.998998i	0.841213	−	0.540704i	$-0.181842\pi$
$548$		0			0
$549$	−9.57697	+	0.914490i	−0.408735	+	0.0390295i
$550$		0			0
$551$	−0.206042	+	1.43305i	−0.00877768	+	0.0610501i
$552$		0			0
$553$	3.48360	+	14.3596i	0.148138	+	0.610633i
$554$		0			0
$555$	−17.4497	+	6.98582i	−0.740700	+	0.296531i
$556$		0			0
$557$	−4.71880	+	2.43271i	−0.199942	+	0.103077i	−0.555290	−	0.831657i	$-0.687393\pi$
$557$	−4.71880	+	2.43271i	−0.199942	+	0.103077i	0.355348	+	0.934734i	$0.384362\pi$
$558$		0			0
$559$	6.80487	+	1.31153i	0.287815	+	0.0554718i
$560$		0			0
$561$	−5.53290	+	12.1154i	−0.233599	+	0.511511i
$562$		0			0
$563$	−21.7994	−	14.0097i	−0.918737	−	0.590436i	−0.00644607	−	0.999979i	$-0.502052\pi$
$563$	−21.7994	−	14.0097i	−0.918737	−	0.590436i	−0.912291	+	0.409543i	$0.865688\pi$
$564$		0			0
$565$	−19.0770	+	33.0424i	−0.802576	+	1.39010i
$566$		0			0
$567$	−2.37381	−	0.226671i	−0.0996906	−	0.00951929i
$568$		0			0
$569$	26.4546	+	20.8041i	1.10904	+	0.872155i	0.992647	−	0.121049i	$-0.0386258\pi$
$569$	26.4546	+	20.8041i	1.10904	+	0.872155i	0.116389	+	0.993204i	$0.462868\pi$
$570$		0			0
$571$	26.9558	−	5.19530i	1.12806	−	0.217417i	0.409118	−	0.912482i	$-0.365837\pi$
$571$	26.9558	−	5.19530i	1.12806	−	0.217417i	0.718947	+	0.695065i	$0.244624\pi$
$572$		0			0
$573$	−6.88453	−	11.9243i	−0.287605	−	0.498147i
$574$		0			0
$575$	1.19155	−	1.67330i	0.0496911	−	0.0697814i
$576$		0			0
$577$	−26.7774	+	25.5322i	−1.11476	+	1.06292i	−0.117200	+	0.993108i	$0.537392\pi$
$577$	−26.7774	+	25.5322i	−1.11476	+	1.06292i	−0.997560	+	0.0698129i	$0.977760\pi$
$578$		0			0
$579$	−14.8485	−	4.35991i	−0.617083	−	0.181192i
$580$		0			0
$581$	−2.91707	−	3.36648i	−0.121020	−	0.139665i
$582$		0			0
$583$	−7.35115	−	21.2398i	−0.304454	−	0.879661i
$584$		0			0
$585$	−6.32421	−	6.03012i	−0.261474	−	0.249315i
$586$		0			0
$587$	−24.4175	−	12.5881i	−1.00782	−	0.519566i	−0.126437	−	0.991975i	$-0.540354\pi$
$587$	−24.4175	−	12.5881i	−1.00782	−	0.519566i	−0.881379	+	0.472409i	$0.843385\pi$
$588$		0			0
$589$	5.66295	−	1.66279i	0.233338	−	0.0685141i
$590$		0			0
$591$	−5.50063	−	7.72455i	−0.226266	−	0.317746i
$592$		0			0
$593$	−13.5097	+	39.0337i	−0.554777	+	1.60292i	0.223298	+	0.974750i	$0.428318\pi$
$593$	−13.5097	+	39.0337i	−0.554777	+	1.60292i	−0.778074	+	0.628172i	$0.783803\pi$
$594$		0			0
$595$	6.96903	+	15.2600i	0.285702	+	0.625601i
$596$		0			0
$597$	−1.01190	+	21.2425i	−0.0414145	+	0.869397i
$598$		0			0
$599$	4.91003	−	20.2394i	0.200618	−	0.826960i	−0.779152	−	0.626835i	$-0.784350\pi$
$599$	4.91003	−	20.2394i	0.200618	−	0.826960i	0.979770	−	0.200125i	$-0.0641349\pi$
$600$		0			0
$601$	−8.13788	+	6.39970i	−0.331951	+	0.261049i	−0.770197	−	0.637806i	$-0.779842\pi$
$601$	−8.13788	+	6.39970i	−0.331951	+	0.261049i	0.438246	+	0.898855i	$0.355600\pi$
$602$		0			0
$603$	−8.03475	−	1.56294i	−0.327200	−	0.0636478i
$604$		0			0
$605$	−30.7730	+	24.2002i	−1.25110	+	0.983877i
$606$		0			0
$607$	11.0691	−	45.6273i	0.449279	−	1.85195i	−0.0702907	−	0.997527i	$-0.522393\pi$
$607$	11.0691	−	45.6273i	0.449279	−	1.85195i	0.519570	−	0.854428i	$-0.326092\pi$
$608$		0			0
$609$	0.221056	−	4.64053i	0.00895762	−	0.188044i
$610$		0			0
$611$	−16.6319	−	36.4189i	−0.672856	−	1.47335i
$612$		0			0
$613$	−8.69536	+	25.1236i	−0.351202	+	1.01473i	0.621648	+	0.783297i	$0.286464\pi$
$613$	−8.69536	+	25.1236i	−0.351202	+	1.01473i	−0.972850	+	0.231436i	$0.925658\pi$
$614$		0			0
$615$	3.81033	+	5.35086i	0.153647	+	0.215768i
$616$		0			0
$617$	16.9187	−	4.96779i	0.681123	−	0.199996i	0.0771725	−	0.997018i	$-0.475411\pi$
$617$	16.9187	−	4.96779i	0.681123	−	0.199996i	0.603950	+	0.797022i	$0.293593\pi$
$618$		0			0
$619$	−26.5830	−	13.7045i	−1.06846	−	0.550831i	−0.168010	−	0.985785i	$-0.553734\pi$
$619$	−26.5830	−	13.7045i	−1.06846	−	0.550831i	−0.900452	+	0.434955i	$0.856764\pi$
$620$		0			0
$621$	−0.690530	−	0.658419i	−0.0277100	−	0.0264214i
$622$		0			0
$623$	3.47881	+	10.0514i	0.139376	+	0.402700i
$624$		0			0
$625$	20.3855	+	23.5262i	0.815421	+	0.941046i
$626$		0			0
$627$	−3.61031	−	1.06008i	−0.144182	−	0.0423356i
$628$		0			0
$629$	13.3793	−	12.7572i	0.533469	−	0.508662i
$630$		0			0
$631$	15.1548	−	21.2819i	0.603302	−	0.847220i	−0.394114	−	0.919062i	$-0.628948\pi$
$631$	15.1548	−	21.2819i	0.603302	−	0.847220i	0.997416	+	0.0718420i	$0.0228877\pi$
$632$		0			0
$633$	−3.03175	−	5.25115i	−0.120501	−	0.208715i
$634$		0			0
$635$	−12.4684	+	2.40309i	−0.494793	+	0.0953636i
$636$		0			0
$637$	−3.37378	−	2.65317i	−0.133674	−	0.105123i
$638$		0			0
$639$	11.1650	+	1.06613i	0.441680	+	0.0421753i
$640$		0			0
$641$	14.9380	−	25.8734i	0.590017	−	1.02194i	−0.404212	−	0.914665i	$-0.632454\pi$
$641$	14.9380	−	25.8734i	0.590017	−	1.02194i	0.994229	−	0.107274i	$-0.0342123\pi$
$642$		0			0
$643$	20.6119	+	13.2465i	0.812855	+	0.522390i	0.879787	−	0.475367i	$-0.157685\pi$
$643$	20.6119	+	13.2465i	0.812855	+	0.522390i	−0.0669326	+	0.997758i	$0.521321\pi$
$644$		0			0
$645$	2.35658	−	5.16018i	0.0927901	−	0.203182i
$646$		0			0
$647$	−13.8587	−	2.67104i	−0.544841	−	0.105009i	−0.0905983	−	0.995888i	$-0.528878\pi$
$647$	−13.8587	−	2.67104i	−0.544841	−	0.105009i	−0.454243	+	0.890878i	$0.650090\pi$
$648$		0			0
$649$	−55.5441	+	28.6350i	−2.18030	+	1.12402i
$650$		0			0
$651$	−17.5823	+	7.03887i	−0.689103	+	0.275875i
$652$		0			0
$653$	7.58525	+	31.2668i	0.296834	+	1.22356i	0.903493	+	0.428603i	$0.140994\pi$
$653$	7.58525	+	31.2668i	0.296834	+	1.22356i	−0.606659	+	0.794962i	$0.707491\pi$
$654$		0			0
$655$	−4.55511	+	31.6815i	−0.177983	+	1.23790i
$656$		0			0
$657$	−13.2869	+	1.26875i	−0.518373	+	0.0494986i
$658$		0			0
$659$	−2.24079	−	47.0400i	−0.0872888	−	1.83242i	−0.441510	−	0.897256i	$-0.645557\pi$
$659$	−2.24079	−	47.0400i	−0.0872888	−	1.83242i	0.354222	−	0.935161i	$-0.384746\pi$
$660$		0			0
$661$	−1.34019	−	9.32121i	−0.0521273	−	0.362553i	−0.999144	−	0.0413687i	$-0.986828\pi$
$661$	−1.34019	−	9.32121i	−0.0521273	−	0.362553i	0.947017	−	0.321184i	$-0.104081\pi$
$662$		0			0
$663$	7.97874	+	3.19420i	0.309868	+	0.124053i
$664$		0			0
$665$	−3.98703	+	2.56231i	−0.154610	+	0.0993621i
$666$		0			0
$667$	1.21729	−	1.40483i	0.0471338	−	0.0543953i
$668$		0			0
$669$	14.5631			0.563042
$670$		0			0
$671$	48.7124			1.88052
$672$		0			0
$673$	−28.3361	+	32.7016i	−1.09227	+	1.26055i	−0.129113	+	0.991630i	$0.541213\pi$
$673$	−28.3361	+	32.7016i	−1.09227	+	1.26055i	−0.963162	+	0.268922i	$0.913332\pi$
$674$		0			0
$675$	−1.81120	+	1.16399i	−0.0697130	+	0.0448018i
$676$		0			0
$677$	−34.8171	−	13.9387i	−1.33813	−	0.535706i	−0.411406	−	0.911452i	$-0.634962\pi$
$677$	−34.8171	−	13.9387i	−1.33813	−	0.535706i	−0.926723	+	0.375746i	$0.877387\pi$
$678$		0			0
$679$	0.344289	+	2.39458i	0.0132126	+	0.0918957i
$680$		0			0
$681$	0.969867	+	20.3600i	0.0371654	+	0.780197i
$682$		0			0
$683$	−2.41541	+	0.230644i	−0.0924232	+	0.00882534i	−0.141165	−	0.989986i	$-0.545085\pi$
$683$	−2.41541	+	0.230644i	−0.0924232	+	0.00882534i	0.0487420	+	0.998811i	$0.484479\pi$
$684$		0			0
$685$	0.987426	−	6.86770i	0.0377276	−	0.262401i
$686$		0			0
$687$	2.05057	+	8.45257i	0.0782341	+	0.322485i
$688$		0			0
$689$	−13.4642	+	5.39026i	−0.512946	+	0.205353i
$690$		0			0
$691$	−45.5027	+	23.4583i	−1.73100	+	0.892394i	−0.761195	+	0.648523i	$0.775387\pi$
$691$	−45.5027	+	23.4583i	−1.73100	+	0.892394i	−0.969808	+	0.243871i	$0.921583\pi$
$692$		0			0
$693$	11.8560	+	2.28505i	0.450371	+	0.0868018i
$694$		0			0
$695$	−13.8109	+	30.2415i	−0.523875	+	1.14713i
$696$		0			0
$697$	−5.43508	−	3.49292i	−0.205868	−	0.132304i
$698$		0			0
$699$	5.75570	−	9.96916i	0.217700	−	0.377068i
$700$		0			0
$701$	−34.9099	−	3.33349i	−1.31853	−	0.125904i	−0.588041	−	0.808831i	$-0.700101\pi$
$701$	−34.9099	−	3.33349i	−1.31853	−	0.125904i	−0.730486	+	0.682927i	$0.760707\pi$
$702$		0			0
$703$	4.10525	+	3.22841i	0.154833	+	0.121762i
$704$		0			0
$705$	−32.1811	+	6.20239i	−1.21201	+	0.233596i
$706$		0			0
$707$	−21.6287	−	37.4620i	−0.813430	−	1.40890i
$708$		0			0
$709$	−5.76058	+	8.08960i	−0.216343	+	0.303811i	−0.908458	−	0.417976i	$-0.862740\pi$
$709$	−5.76058	+	8.08960i	−0.216343	+	0.303811i	0.692115	+	0.721787i	$0.256679\pi$
$710$		0			0
$711$	4.48459	−	4.27605i	0.168185	−	0.160364i
$712$		0			0
$713$	−7.27081	−	2.13490i	−0.272294	−	0.0799528i
$714$		0			0
$715$	28.9745	+	33.4384i	1.08359	+	1.25052i
$716$		0			0
$717$	−2.16315	−	6.25001i	−0.0807843	−	0.233411i
$718$		0			0
$719$	−9.66483	−	9.21539i	−0.360437	−	0.343676i	0.488123	−	0.872775i	$-0.337682\pi$
$719$	−9.66483	−	9.21539i	−0.360437	−	0.343676i	−0.848560	+	0.529099i	$0.822530\pi$
$720$		0			0
$721$	28.7994	+	14.8471i	1.07254	+	0.552935i
$722$		0			0
$723$	12.4558	−	3.65734i	0.463235	−	0.136018i
$724$		0			0
$725$	−2.43306	−	3.41675i	−0.0903614	−	0.126895i
$726$		0			0
$727$	3.23077	−	9.33469i	0.119823	−	0.346205i	−0.869100	−	0.494636i	$-0.835301\pi$
$727$	3.23077	−	9.33469i	0.119823	−	0.346205i	0.988923	+	0.148432i	$0.0474225\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	−0.265478	+	5.57306i	−0.00981905	+	0.206127i
$732$		0			0
$733$	−12.7067	+	52.3776i	−0.469332	+	1.93461i	−0.141194	+	0.989982i	$0.545094\pi$
$733$	−12.7067	+	52.3776i	−0.469332	+	1.93461i	−0.328138	+	0.944630i	$0.606421\pi$
$734$		0			0
$735$	−2.76170	+	2.17183i	−0.101867	+	0.0801090i
$736$		0			0
$737$	39.7465	+	11.7451i	1.46408	+	0.432635i
$738$		0			0
$739$	−11.5553	+	9.08715i	−0.425067	+	0.334276i	−0.807668	−	0.589637i	$-0.799271\pi$
$739$	−11.5553	+	9.08715i	−0.425067	+	0.334276i	0.382601	+	0.923914i	$0.375028\pi$
$740$		0			0
$741$	−0.572420	+	2.35955i	−0.0210284	+	0.0866801i
$742$		0			0
$743$	0.123349	−	2.58942i	0.00452525	−	0.0949967i	−0.995475	−	0.0950265i	$-0.969706\pi$
$743$	0.123349	−	2.58942i	0.00452525	−	0.0949967i	1.00000		2.97169e-5i	$9.45918e-6\pi$
$744$		0			0
$745$	1.00231	+	2.19475i	0.0367217	+	0.0804094i
$746$		0			0
$747$	−0.610969	+	1.76528i	−0.0223542	+	0.0645882i
$748$		0			0
$749$	−5.97895	−	8.39626i	−0.218466	−	0.306793i
$750$		0			0
$751$	−40.3993	+	11.8623i	−1.47419	+	0.432862i	−0.917459	−	0.397830i	$-0.869763\pi$
$751$	−40.3993	+	11.8623i	−1.47419	+	0.432862i	−0.556732	+	0.830692i	$0.687945\pi$
$752$		0			0
$753$	16.6130	+	8.56457i	0.605410	+	0.312110i
$754$		0			0
$755$	−47.0524	−	44.8644i	−1.71241	−	1.63278i
$756$		0			0
$757$	−9.30545	−	26.8863i	−0.338212	−	0.977201i	−0.977992	−	0.208642i	$-0.933096\pi$
$757$	−9.30545	−	26.8863i	−0.338212	−	0.977201i	0.639780	−	0.768558i	$-0.279026\pi$
$758$		0			0
$759$	3.16368	+	3.65108i	0.114834	+	0.132526i
$760$		0			0
$761$	16.5705	+	4.86553i	0.600679	+	0.176375i	0.567914	−	0.823088i	$-0.307751\pi$
$761$	16.5705	+	4.86553i	0.600679	+	0.176375i	0.0327651	+	0.999463i	$0.489569\pi$
$762$		0			0
$763$	10.5467	−	10.0563i	0.381816	−	0.364061i
$764$		0			0
$765$	4.08079	−	5.73067i	0.147541	−	0.207193i
$766$		0			0
$767$	20.1618	+	34.9213i	0.728001	+	1.26094i
$768$		0			0
$769$	24.9858	−	4.81562i	0.901010	−	0.173656i	0.282348	−	0.959312i	$-0.408887\pi$
$769$	24.9858	−	4.81562i	0.901010	−	0.173656i	0.618663	+	0.785657i	$0.287675\pi$
$770$		0			0
$771$	−11.4104	−	8.97323i	−0.410935	−	0.323163i
$772$		0			0
$773$	42.5346	+	4.06156i	1.52986	+	0.146084i	0.825763	−	0.564017i	$-0.190745\pi$
$773$	42.5346	+	4.06156i	1.52986	+	0.146084i	0.704099	+	0.710102i	$0.251351\pi$
$774$		0			0
$775$	−8.54961	+	14.8084i	−0.307111	+	0.531932i
$776$		0			0
$777$	−14.0984	−	9.06047i	−0.505776	−	0.325043i
$778$		0			0
$779$	0.758218	−	1.66027i	0.0271660	−	0.0594852i
$780$		0			0
$781$	−55.7634	−	10.7475i	−1.99537	−	0.384576i
$782$		0			0
$783$	−1.73167	+	0.892736i	−0.0618847	+	0.0319038i
$784$		0			0
$785$	39.1586	−	15.6767i	1.39763	−	0.559527i
$786$		0			0
$787$	1.84578	+	7.60840i	0.0657949	+	0.271210i	0.995201	−	0.0978473i	$-0.0311957\pi$
$787$	1.84578	+	7.60840i	0.0657949	+	0.271210i	−0.929407	+	0.369058i	$0.879681\pi$
$788$		0			0
$789$	0.731206	−	5.08565i	0.0260316	−	0.181054i
$790$		0			0
$791$	−33.8644	+	3.23365i	−1.20408	+	0.114976i
$792$		0			0
$793$	−1.49563	−	31.3972i	−0.0531115	−	1.11495i
$794$		0			0
$795$	1.68955	+	11.7511i	0.0599221	+	0.416768i
$796$		0			0
$797$	4.99154	+	1.99831i	0.176809	+	0.0707838i	0.458378	−	0.888757i	$-0.348431\pi$
$797$	4.99154	+	1.99831i	0.176809	+	0.0707838i	−0.281569	+	0.959541i	$0.590855\pi$
$798$		0			0
$799$	27.1165	−	17.4267i	0.959314	−	0.616514i
$800$		0			0
$801$	2.92096	−	3.37097i	0.103207	−	0.119107i
$802$		0			0
$803$	67.5828			2.38494
$804$		0			0
$805$	6.08504			0.214469
$806$		0			0
$807$	−10.1131	+	11.6711i	−0.355996	+	0.410842i
$808$		0			0
$809$	−13.3525	+	8.58116i	−0.469450	+	0.301697i	−0.753895	−	0.656995i	$-0.771827\pi$
$809$	−13.3525	+	8.58116i	−0.469450	+	0.301697i	0.284444	+	0.958693i	$0.408191\pi$
$810$		0			0
$811$	−33.0286	−	13.2227i	−1.15979	−	0.464311i	−0.289660	−	0.957130i	$-0.593542\pi$
$811$	−33.0286	−	13.2227i	−1.15979	−	0.464311i	−0.870132	+	0.492819i	$0.835966\pi$
$812$		0			0
$813$	1.10146	+	7.66083i	0.0386299	+	0.268677i
$814$		0			0
$815$	1.72646	+	36.2429i	0.0604753	+	1.26953i
$816$		0			0
$817$	−1.56909	+	0.149830i	−0.0548955	+	0.00524188i
$818$		0			0
$819$	1.10879	−	7.71182i	0.0387444	−	0.269473i
$820$		0			0
$821$	−1.71535	−	7.07075i	−0.0598660	−	0.246771i	0.934014	−	0.357236i	$-0.116281\pi$
$821$	−1.71535	−	7.07075i	−0.0598660	−	0.246771i	−0.993880	+	0.110466i	$0.964766\pi$
$822$		0			0
$823$	−20.5787	+	8.23846i	−0.717328	+	0.287175i	−0.701470	−	0.712699i	$-0.747472\pi$
$823$	−20.5787	+	8.23846i	−0.717328	+	0.287175i	−0.0158585	+	0.999874i	$0.505048\pi$
$824$		0			0
$825$	9.68947	−	4.99527i	0.337344	−	0.173913i
$826$		0			0
$827$	−17.6712	−	3.40585i	−0.614489	−	0.118433i	−0.127496	−	0.991839i	$-0.540694\pi$
$827$	−17.6712	−	3.40585i	−0.614489	−	0.118433i	−0.486993	+	0.873406i	$0.661906\pi$
$828$		0			0
$829$	14.0150	−	30.6886i	0.486762	−	1.06586i	−0.493786	−	0.869583i	$-0.664387\pi$
$829$	14.0150	−	30.6886i	0.486762	−	1.06586i	0.980548	−	0.196277i	$-0.0628852\pi$
$830$		0			0
$831$	13.4245	+	8.62739i	0.465690	+	0.299281i
$832$		0			0
$833$	1.72775	−	2.99256i	0.0598631	−	0.103686i
$834$		0			0
$835$	28.8123	+	2.75124i	0.997092	+	0.0952107i
$836$		0			0
$837$	6.24295	+	4.90951i	0.215788	+	0.169697i
$838$		0			0
$839$	−13.8981	+	2.67863i	−0.479815	+	0.0924767i	−0.423423	−	0.905932i	$-0.639172\pi$
$839$	−13.8981	+	2.67863i	−0.479815	+	0.0924767i	−0.0563915	+	0.998409i	$0.517960\pi$
$840$		0			0
$841$	12.6022	+	21.8276i	0.434558	+	0.752676i
$842$		0			0
$843$	0.614434	−	0.862851i	0.0211622	−	0.0297182i
$844$		0			0
$845$	−4.50036	+	4.29108i	−0.154817	+	0.147618i
$846$		0			0
$847$	−33.4914	−	9.83396i	−1.15078	−	0.337899i
$848$		0			0
$849$	8.38123	+	9.67245i	0.287643	+	0.331958i
$850$		0			0
$851$	−2.19314	−	6.33667i	−0.0751799	−	0.217218i
$852$		0			0
$853$	15.4337	+	14.7160i	0.528439	+	0.503866i	0.906667	−	0.421847i	$-0.138618\pi$
$853$	15.4337	+	14.7160i	0.528439	+	0.503866i	−0.378228	+	0.925713i	$0.623466\pi$
$854$		0			0
$855$	1.76656	+	0.910723i	0.0604149	+	0.0311461i
$856$		0			0
$857$	46.9923	−	13.7982i	1.60523	−	0.471337i	0.648232	−	0.761443i	$-0.275509\pi$
$857$	46.9923	−	13.7982i	1.60523	−	0.471337i	0.956995	+	0.290106i	$0.0936905\pi$
$858$		0			0
$859$	−0.768017	−	1.07853i	−0.0262044	−	0.0367989i	0.801266	−	0.598308i	$-0.204160\pi$
$859$	−0.768017	−	1.07853i	−0.0262044	−	0.0367989i	−0.827470	+	0.561509i	$0.810221\pi$
$860$		0			0
$861$	−1.91559	+	5.53475i	−0.0652833	+	0.188624i
$862$		0			0
$863$	−2.45527	−	5.37628i	−0.0835782	−	0.183011i	0.863229	−	0.504813i	$-0.168439\pi$
$863$	−2.45527	−	5.37628i	−0.0835782	−	0.183011i	−0.946807	+	0.321802i	$0.895711\pi$
$864$		0			0
$865$	−0.853254	+	17.9120i	−0.0290115	+	0.609026i
$866$		0			0
$867$	2.37662	−	9.79657i	0.0807143	−	0.332709i
$868$		0			0
$869$	−24.6624	+	19.3948i	−0.836616	+	0.657922i
$870$		0			0
$871$	6.34985	−	25.9789i	0.215156	−	0.880262i
$872$		0			0
$873$	0.797460	−	0.627129i	0.0269899	−	0.0212251i
$874$		0			0
$875$	−4.28075	+	17.6455i	−0.144716	+	0.596526i
$876$		0			0
$877$	−1.45282	+	30.4985i	−0.0490583	+	1.02986i	0.831381	+	0.555703i	$0.187551\pi$
$877$	−1.45282	+	30.4985i	−0.0490583	+	1.02986i	−0.880440	+	0.474158i	$0.842752\pi$
$878$		0			0
$879$	5.53173	+	12.1128i	0.186581	+	0.408555i
$880$		0			0
$881$	5.31839	−	15.3665i	0.179181	−	0.517710i	−0.819266	−	0.573413i	$-0.805619\pi$
$881$	5.31839	−	15.3665i	0.179181	−	0.517710i	0.998447	+	0.0557035i	$0.0177402\pi$
$882$		0			0
$883$	−4.34922	−	6.10763i	−0.146363	−	0.205538i	0.734886	−	0.678191i	$-0.237236\pi$
$883$	−4.34922	−	6.10763i	−0.146363	−	0.205538i	−0.881249	+	0.472653i	$0.843296\pi$
$884$		0			0
$885$	31.6710	−	9.29943i	1.06461	−	0.312597i
$886$		0			0
$887$	−32.4115	−	16.7093i	−1.08827	−	0.561044i	−0.181812	−	0.983333i	$-0.558196\pi$
$887$	−32.4115	−	16.7093i	−1.08827	−	0.561044i	−0.906461	+	0.422290i	$0.861227\pi$
$888$		0			0
$889$	−8.19375	−	7.81273i	−0.274810	−	0.262031i
$890$		0			0
$891$	−1.65607	−	4.78489i	−0.0554804	−	0.160300i
$892$		0			0
$893$	5.96333	+	6.88205i	0.199555	+	0.230299i
$894$		0			0
$895$	23.3777	+	6.86430i	0.781429	+	0.229448i
$896$		0			0
$897$	2.25614	−	2.15123i	0.0753303	−	0.0718273i
$898$		0			0
$899$	−8.97535	+	12.6041i	−0.299345	+	0.420371i
$900$		0			0
$901$	−5.83818	−	10.1120i	−0.194498	−	0.336880i
$902$		0			0
$903$	4.96652	−	0.957219i	0.165276	−	0.0318543i
$904$		0			0
$905$	14.2038	+	11.1700i	0.472151	+	0.371304i
$906$		0			0
$907$	−29.8575	−	2.85104i	−0.991401	−	0.0946673i	−0.413267	−	0.910610i	$-0.635613\pi$
$907$	−29.8575	−	2.85104i	−0.991401	−	0.0946673i	−0.578133	+	0.815942i	$0.696219\pi$
$908$		0			0
$909$	−9.07013	+	15.7099i	−0.300837	+	0.521065i
$910$		0			0
$911$	46.4417	+	29.8463i	1.53868	+	0.988851i	0.988055	+	0.154100i	$0.0492477\pi$
$911$	46.4417	+	29.8463i	1.53868	+	0.988851i	0.550627	+	0.834751i	$0.314389\pi$
$912$		0			0
$913$	3.92920	−	8.60374i	0.130037	−	0.284742i
$914$		0			0
$915$	−25.2652	−	4.86946i	−0.835241	−	0.160980i
$916$		0			0
$917$	−25.3655	+	13.0768i	−0.837643	+	0.431835i
$918$		0			0
$919$	37.5614	−	15.0373i	1.23904	−	0.496035i	0.342715	−	0.939440i	$-0.388654\pi$
$919$	37.5614	−	15.0373i	1.23904	−	0.496035i	0.896322	+	0.443404i	$0.146229\pi$
$920$		0			0
$921$	−0.452813	−	1.86652i	−0.0149207	−	0.0615039i
$922$		0			0
$923$	−5.21511	+	36.2719i	−0.171657	+	1.19390i
$924$		0			0
$925$	−15.0624	+	1.43828i	−0.495247	+	0.0472904i
$926$		0			0
$927$	−0.646527	−	13.5723i	−0.0212347	−	0.445772i
$928$		0			0
$929$	−0.883186	−	6.14269i	−0.0289764	−	0.201535i	0.970191	−	0.242343i	$-0.0779159\pi$
$929$	−0.883186	−	6.14269i	−0.0289764	−	0.201535i	−0.999167	+	0.0408078i	$0.987007\pi$
$930$		0			0
$931$	0.906284	+	0.362822i	0.0297023	+	0.0118910i
$932$		0			0
$933$	23.9724	−	15.4061i	0.784820	−	0.504373i
$934$		0			0
$935$	−23.3272	+	26.9210i	−0.762881	+	0.880412i
$936$		0			0
$937$	−0.452292			−0.0147757			−0.00738787	−	0.999973i	$-0.502352\pi$
$937$	−0.452292			−0.0147757			−0.00738787	+	0.999973i	$0.502352\pi$
$938$		0			0
$939$	−0.464351			−0.0151535
$940$		0			0
$941$	−33.8106	+	39.0196i	−1.10220	+	1.27200i	−0.142857	+	0.989743i	$0.545629\pi$
$941$	−33.8106	+	39.0196i	−1.10220	+	1.27200i	−0.959338	+	0.282258i	$0.908917\pi$
$942$		0			0
$943$	−1.97142	+	1.26695i	−0.0641983	+	0.0412577i
$944$		0			0
$945$	−5.92079	−	2.37033i	−0.192603	−	0.0771068i
$946$		0			0
$947$	4.59856	+	31.9837i	0.149433	+	1.03933i	0.917150	+	0.398542i	$0.130484\pi$
$947$	4.59856	+	31.9837i	0.149433	+	1.03933i	−0.767717	+	0.640789i	$0.778607\pi$
$948$		0			0
$949$	−2.07502	−	43.5600i	−0.0673579	−	1.41402i
$950$		0			0
$951$	2.46486	−	0.235366i	0.0799285	−	0.00763225i
$952$		0			0
$953$	3.32200	−	23.1050i	0.107610	−	0.748444i	−0.862549	−	0.505974i	$-0.831133\pi$
$953$	3.32200	−	23.1050i	0.107610	−	0.748444i	0.970159	−	0.242470i	$-0.0779577\pi$
$954$		0			0
$955$	−8.68191	−	35.7873i	−0.280940	−	1.15805i
$956$		0			0
$957$	9.15805	−	3.66633i	0.296038	−	0.118516i
$958$		0			0
$959$	5.49856	−	2.83471i	0.177558	−	0.0915374i
$960$		0			0
$961$	31.4980	+	6.07074i	1.01606	+	0.195830i
$962$		0			0
$963$	−1.79564	+	3.93191i	−0.0578637	+	0.126704i
$964$		0			0
$965$	−34.8186	−	22.3765i	−1.12085	−	0.720326i
$966$		0			0
$967$	2.66736	−	4.62001i	0.0857766	−	0.148569i	−0.819945	−	0.572442i	$-0.805996\pi$
$967$	2.66736	−	4.62001i	0.0857766	−	0.148569i	0.905722	+	0.423872i	$0.139330\pi$
$968$		0			0
$969$	−1.94591	−	0.185812i	−0.0625115	−	0.00596913i
$970$		0			0
$971$	−22.4278	−	17.6374i	−0.719743	−	0.566012i	0.189699	−	0.981842i	$-0.439249\pi$
$971$	−22.4278	−	17.6374i	−0.719743	−	0.566012i	−0.909442	+	0.415830i	$0.863491\pi$
$972$		0			0
$973$	−29.1066	+	5.60984i	−0.933115	+	0.179843i
$974$		0			0
$975$	−3.51716	−	6.09190i	−0.112639	−	0.195097i
$976$		0			0
$977$	−9.60138	+	13.4832i	−0.307175	+	0.431367i	−0.939090	−	0.343670i	$-0.888330\pi$
$977$	−9.60138	+	13.4832i	−0.307175	+	0.431367i	0.631915	+	0.775038i	$0.282269\pi$
$978$		0			0
$979$	−16.3454	+	15.5853i	−0.522402	+	0.498109i
$980$		0			0
$981$	−5.86358	−	1.72170i	−0.187210	−	0.0549698i
$982$		0			0
$983$	−26.4603	−	30.5368i	−0.843952	−	0.973972i	0.155953	−	0.987764i	$-0.450155\pi$
$983$	−26.4603	−	30.5368i	−0.843952	−	0.973972i	−0.999905	+	0.0137924i	$0.995610\pi$
$984$		0			0
$985$	−8.29512	−	23.9672i	−0.264305	−	0.763658i
$986$		0			0
$987$	−21.1482	−	20.1647i	−0.673153	−	0.641850i
$988$		0			0
$989$	1.79879	+	0.927341i	0.0571982	+	0.0294877i
$990$		0			0
$991$	−8.45871	+	2.48370i	−0.268700	+	0.0788973i	−0.413307	−	0.910592i	$-0.635626\pi$
$991$	−8.45871	+	2.48370i	−0.268700	+	0.0788973i	0.144607	+	0.989489i	$0.453808\pi$
$992$		0			0
$993$	−18.0999	−	25.4177i	−0.574383	−	0.806608i
$994$		0			0
$995$	−18.6028	+	53.7493i	−0.589749	+	1.70397i
$996$		0			0
$997$	−19.2022	−	42.0469i	−0.608139	−	1.33164i	−0.923839	−	0.382780i	$-0.874967\pi$
$997$	−19.2022	−	42.0469i	−0.608139	−	1.33164i	0.315700	−	0.948859i	$-0.397761\pi$
$998$		0			0
$999$	−0.334401	+	7.01994i	−0.0105800	+	0.222101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.121.5	✓	120
67.36	even	33	inner	804.2.y.b.505.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.121.5	✓	120	1.1	even	1	trivial
804.2.y.b.505.5	yes	120	67.36	even	33	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{3} +(2.24994 - 1.44595i) q^{5} +(2.21379 + 0.886268i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{3} +(2.24994 - 1.44595i) q^{5} +(2.21379 + 0.886268i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.240925 + 5.05764i) q^{11} +(3.25247 - 0.310573i) q^{13} +(0.380622 - 2.64728i) q^{15} +(0.620152 + 2.55630i) q^{17} +(-0.689895 + 0.276192i) q^{19} +(2.11952 - 1.09269i) q^{21} +(0.936879 + 0.180569i) q^{23} +(0.894377 - 1.95841i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(0.974121 - 1.68723i) q^{29} +(-7.90618 - 0.754949i) q^{31} +(3.98008 + 3.12997i) q^{33} +(6.26239 - 1.20698i) q^{35} +(-3.51395 - 6.08634i) q^{37} +(1.89520 - 2.66143i) q^{39} +(-1.77758 + 1.69491i) q^{41} +(2.03516 + 0.597576i) q^{43} +(-1.75143 - 2.02126i) q^{45} +(-4.00788 - 11.5800i) q^{47} +(-0.950738 - 0.906526i) q^{49} +(2.33804 + 1.20534i) q^{51} +(-4.25911 + 1.25059i) q^{53} +(7.85514 + 11.0310i) q^{55} +(-0.243053 + 0.702255i) q^{57} +(5.12694 + 11.2264i) q^{59} +(0.457763 - 9.60964i) q^{61} +(0.562192 - 2.31739i) q^{63} +(6.86877 - 5.40166i) q^{65} +(2.69049 - 7.73054i) q^{67} +(0.749990 - 0.589798i) q^{69} +(-2.64422 + 10.8996i) q^{71} +(0.635094 - 13.3323i) q^{73} +(-0.894377 - 1.95841i) q^{75} +(-3.94907 + 11.4101i) q^{77} +(3.59430 + 5.04749i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-1.66036 - 0.855976i) q^{83} +(5.09158 + 4.85481i) q^{85} +(-0.637207 - 1.84109i) q^{87} +(2.92096 + 3.37097i) q^{89} +(7.47553 + 2.19501i) q^{91} +(-5.74800 + 5.48071i) q^{93} +(-1.15286 + 1.61897i) q^{95} +(0.507256 + 0.878592i) q^{97} +(4.97187 - 0.958250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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