LMFDB - Embedded newform 804.2.y.b.793.4

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			793.4
Character	$\chi$	$=$	804.793
Dual form			804.2.y.b.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(1.03511 - 0.303934i) q^{5} +(-4.65735 - 0.897630i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(1.03511 - 0.303934i) q^{5} +(-4.65735 - 0.897630i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(3.37592 + 3.21894i) q^{11} +(-0.254078 - 5.33375i) q^{13} +(-0.706467 - 0.815306i) q^{15} +(-1.13889 - 0.895635i) q^{17} +(-5.02744 + 0.968959i) q^{19} +(1.11822 + 4.60936i) q^{21} +(-3.70948 - 0.354212i) q^{23} +(-3.22720 + 2.07400i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-5.06141 - 8.76662i) q^{29} +(-0.338612 + 7.10834i) q^{31} +(1.52564 - 4.40804i) q^{33} +(-5.09367 + 0.486386i) q^{35} +(1.62134 - 2.80824i) q^{37} +(-4.74620 + 2.44684i) q^{39} +(-7.90358 + 3.16412i) q^{41} +(0.383067 - 2.66429i) q^{43} +(-0.448152 + 0.981315i) q^{45} +(-6.39496 + 8.98046i) q^{47} +(14.3866 + 5.75951i) q^{49} +(-0.341585 + 1.40803i) q^{51} +(-0.818964 - 5.69602i) q^{53} +(4.47278 + 2.30588i) q^{55} +(2.96987 + 4.17060i) q^{57} +(2.12121 + 1.36322i) q^{59} +(-0.675562 + 0.644148i) q^{61} +(3.72830 - 2.93197i) q^{63} +(-1.88411 - 5.44377i) q^{65} +(-2.15690 + 7.89606i) q^{67} +(1.21877 + 3.52141i) q^{69} +(7.56521 - 5.94934i) q^{71} +(-1.07574 + 1.02572i) q^{73} +(3.22720 + 2.07400i) q^{75} +(-12.8334 - 18.0220i) q^{77} +(-7.75307 - 3.99699i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(4.07464 - 16.7959i) q^{83} +(-1.45109 - 0.580928i) q^{85} +(-5.87181 + 8.24581i) q^{87} +(-1.53625 + 3.36393i) q^{89} +(-3.60441 + 25.0692i) q^{91} +(6.60664 - 2.64490i) q^{93} +(-4.90943 + 2.53099i) q^{95} +(4.41371 - 7.64477i) q^{97} +(-4.64347 + 0.443397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{13}{33}\right)$	$1$

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
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	1.03511	−	0.303934i	0.462913	−	0.135924i	−0.0419559	−	0.999119i	$-0.513359\pi$
$5$	1.03511	−	0.303934i	0.462913	−	0.135924i	0.504869	+	0.863196i	$0.331541\pi$
$6$		0			0
$7$	−4.65735	−	0.897630i	−1.76031	−	0.339272i	−0.796253	−	0.604963i	$-0.793188\pi$
$7$	−4.65735	−	0.897630i	−1.76031	−	0.339272i	−0.964058	+	0.265691i	$0.914400\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	3.37592	+	3.21894i	1.01788	+	0.970545i	0.999571	−	0.0292869i	$-0.00932364\pi$
$11$	3.37592	+	3.21894i	1.01788	+	0.970545i	0.0183078	+	0.999832i	$0.494172\pi$
$12$		0			0
$13$	−0.254078	−	5.33375i	−0.0704685	−	1.47932i	−0.706533	−	0.707680i	$-0.749742\pi$
$13$	−0.254078	−	5.33375i	−0.0704685	−	1.47932i	0.636065	−	0.771636i	$-0.280561\pi$
$14$		0			0
$15$	−0.706467	−	0.815306i	−0.182409	−	0.210511i
$16$		0			0
$17$	−1.13889	−	0.895635i	−0.276222	−	0.217223i	0.470432	−	0.882436i	$-0.344098\pi$
$17$	−1.13889	−	0.895635i	−0.276222	−	0.217223i	−0.746654	+	0.665213i	$0.768341\pi$
$18$		0			0
$19$	−5.02744	+	0.968959i	−1.15337	+	0.222294i	−0.729861	−	0.683596i	$-0.760415\pi$
$19$	−5.02744	+	0.968959i	−1.15337	+	0.222294i	−0.423512	+	0.905890i	$0.639203\pi$
$20$		0			0
$21$	1.11822	+	4.60936i	0.244015	+	1.00585i
$22$		0			0
$23$	−3.70948	−	0.354212i	−0.773480	−	0.0738584i	−0.299151	−	0.954206i	$-0.596703\pi$
$23$	−3.70948	−	0.354212i	−0.773480	−	0.0738584i	−0.474329	+	0.880348i	$0.657309\pi$
$24$		0			0
$25$	−3.22720	+	2.07400i	−0.645440	+	0.414799i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	−5.06141	−	8.76662i	−0.939880	−	1.62792i	−0.765692	−	0.643208i	$-0.777603\pi$
$29$	−5.06141	−	8.76662i	−0.939880	−	1.62792i	−0.174189	−	0.984712i	$-0.555730\pi$
$30$		0			0
$31$	−0.338612	+	7.10834i	−0.0608165	+	1.27670i	0.737868	+	0.674945i	$0.235833\pi$
$31$	−0.338612	+	7.10834i	−0.0608165	+	1.27670i	−0.798684	+	0.601750i	$0.794470\pi$
$32$		0			0
$33$	1.52564	−	4.40804i	0.265579	−	0.767341i
$34$		0			0
$35$	−5.09367	+	0.486386i	−0.860987	+	0.0822143i
$36$		0			0
$37$	1.62134	−	2.80824i	0.266547	−	0.461672i	−0.701421	−	0.712747i	$-0.747451\pi$
$37$	1.62134	−	2.80824i	0.266547	−	0.461672i	0.967968	+	0.251075i	$0.0807840\pi$
$38$		0			0
$39$	−4.74620	+	2.44684i	−0.760000	+	0.391807i
$40$		0			0
$41$	−7.90358	+	3.16412i	−1.23433	+	0.494152i	−0.894810	−	0.446446i	$-0.852689\pi$
$41$	−7.90358	+	3.16412i	−1.23433	+	0.494152i	−0.339522	+	0.940598i	$0.610265\pi$
$42$		0			0
$43$	0.383067	−	2.66429i	0.0584172	−	0.406301i	−0.939541	−	0.342436i	$-0.888748\pi$
$43$	0.383067	−	2.66429i	0.0584172	−	0.406301i	0.997959	−	0.0638652i	$-0.0203428\pi$
$44$		0			0
$45$	−0.448152	+	0.981315i	−0.0668065	+	0.146286i
$46$		0			0
$47$	−6.39496	+	8.98046i	−0.932800	+	1.30993i	0.0179051	+	0.999840i	$0.494300\pi$
$47$	−6.39496	+	8.98046i	−0.932800	+	1.30993i	−0.950706	+	0.310095i	$0.899639\pi$
$48$		0			0
$49$	14.3866	+	5.75951i	2.05522	+	0.822788i
$50$		0			0
$51$	−0.341585	+	1.40803i	−0.0478315	+	0.197164i
$52$		0			0
$53$	−0.818964	−	5.69602i	−0.112493	−	0.782408i	−0.965480	−	0.260476i	$-0.916121\pi$
$53$	−0.818964	−	5.69602i	−0.112493	−	0.782408i	0.852987	−	0.521932i	$-0.174789\pi$
$54$		0			0
$55$	4.47278	+	2.30588i	0.603110	+	0.310925i
$56$		0			0
$57$	2.96987	+	4.17060i	0.393369	+	0.552409i
$58$		0			0
$59$	2.12121	+	1.36322i	0.276158	+	0.177476i	0.671387	−	0.741107i	$-0.265699\pi$
$59$	2.12121	+	1.36322i	0.276158	+	0.177476i	−0.395230	+	0.918582i	$0.629335\pi$
$60$		0			0
$61$	−0.675562	+	0.644148i	−0.0864969	+	0.0824746i	−0.732094	−	0.681203i	$-0.761457\pi$
$61$	−0.675562	+	0.644148i	−0.0864969	+	0.0824746i	0.645597	+	0.763678i	$0.276608\pi$
$62$		0			0
$63$	3.72830	−	2.93197i	0.469721	−	0.369393i
$64$		0			0
$65$	−1.88411	−	5.44377i	−0.233695	−	0.675217i
$66$		0			0
$67$	−2.15690	+	7.89606i	−0.263507	+	0.964658i
$67$	−2.15690	+	7.89606i	−0.263507	+	0.964658i
$68$		0			0
$69$	1.21877	+	3.52141i	0.146723	+	0.423927i
$70$		0			0
$71$	7.56521	−	5.94934i	0.897825	−	0.706057i	−0.0585236	−	0.998286i	$-0.518639\pi$
$71$	7.56521	−	5.94934i	0.897825	−	0.706057i	0.956348	+	0.292229i	$0.0943969\pi$
$72$		0			0
$73$	−1.07574	+	1.02572i	−0.125906	+	0.120051i	−0.750417	−	0.660965i	$-0.770147\pi$
$73$	−1.07574	+	1.02572i	−0.125906	+	0.120051i	0.624510	+	0.781017i	$0.285299\pi$
$74$		0			0
$75$	3.22720	+	2.07400i	0.372645	+	0.239484i
$76$		0			0
$77$	−12.8334	−	18.0220i	−1.46250	−	2.05380i
$78$		0			0
$79$	−7.75307	−	3.99699i	−0.872289	−	0.449696i	−0.0368766	−	0.999320i	$-0.511741\pi$
$79$	−7.75307	−	3.99699i	−0.872289	−	0.449696i	−0.835412	+	0.549624i	$0.814771\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	4.07464	−	16.7959i	0.447250	−	1.84359i	−0.0841312	−	0.996455i	$-0.526811\pi$
$83$	4.07464	−	16.7959i	0.447250	−	1.84359i	0.531381	−	0.847133i	$-0.321673\pi$
$84$		0			0
$85$	−1.45109	−	0.580928i	−0.157393	−	0.0630105i
$86$		0			0
$87$	−5.87181	+	8.24581i	−0.629524	+	0.884043i
$88$		0			0
$89$	−1.53625	+	3.36393i	−0.162843	+	0.356576i	−0.973410	−	0.229070i	$-0.926432\pi$
$89$	−1.53625	+	3.36393i	−0.162843	+	0.356576i	0.810567	+	0.585645i	$0.199159\pi$
$90$		0			0
$91$	−3.60441	+	25.0692i	−0.377844	+	2.62797i
$92$		0			0
$93$	6.60664	−	2.64490i	0.685077	−	0.274263i
$94$		0			0
$95$	−4.90943	+	2.53099i	−0.503697	+	0.259674i
$96$		0			0
$97$	4.41371	−	7.64477i	0.448144	−	0.776209i	−0.550121	−	0.835085i	$-0.685418\pi$
$97$	4.41371	−	7.64477i	0.448144	−	0.776209i	0.998265	+	0.0588763i	$0.0187518\pi$
$98$		0			0
$99$	−4.64347	+	0.443397i	−0.466686	+	0.0445631i
$100$		0			0
$101$	3.41180	−	9.85775i	0.339487	−	0.980883i	−0.638027	−	0.770014i	$-0.720249\pi$
$101$	3.41180	−	9.85775i	0.339487	−	0.980883i	0.977514	−	0.210869i	$-0.0676294\pi$
$102$		0			0
$103$	0.633034	−	13.2890i	0.0623747	−	1.30941i	−0.723199	−	0.690639i	$-0.757329\pi$
$103$	0.633034	−	13.2890i	0.0623747	−	1.30941i	0.785574	−	0.618767i	$-0.212368\pi$
$104$		0			0
$105$	2.55842	+	4.43131i	0.249676	+	0.432452i
$106$		0			0
$107$	−3.78929	−	1.11264i	−0.366324	−	0.107563i	0.0933895	−	0.995630i	$-0.470230\pi$
$107$	−3.78929	−	1.11264i	−0.366324	−	0.107563i	−0.459714	+	0.888067i	$0.652048\pi$
$108$		0			0
$109$	−12.4528	+	8.00295i	−1.19277	+	0.766544i	−0.977690	−	0.210053i	$-0.932636\pi$
$109$	−12.4528	+	8.00295i	−1.19277	+	0.766544i	−0.215076	+	0.976597i	$0.569000\pi$
$110$		0			0
$111$	−3.22800	−	0.308236i	−0.306388	−	0.0292565i
$112$		0			0
$113$	1.81891	+	7.49766i	0.171109	+	0.705320i	0.991120	+	0.132972i	$0.0424522\pi$
$113$	1.81891	+	7.49766i	0.171109	+	0.705320i	−0.820011	+	0.572348i	$0.806033\pi$
$114$		0			0
$115$	−3.94736	+	0.760791i	−0.368093	+	0.0709441i
$116$		0			0
$117$	4.19736	+	3.30084i	0.388046	+	0.305163i
$118$		0			0
$119$	4.50027	+	5.19359i	0.412539	+	0.476095i
$120$		0			0
$121$	0.511905	+	10.7462i	0.0465368	+	0.976928i
$122$		0			0
$123$	6.16145	+	5.87493i	0.555559	+	0.529724i
$124$		0			0
$125$	−6.24247	+	7.20419i	−0.558343	+	0.644363i
$126$		0			0
$127$	1.27674	+	0.246072i	0.113292	+	0.0218353i	0.245582	−	0.969376i	$-0.421021\pi$
$127$	1.27674	+	0.246072i	0.113292	+	0.0218353i	−0.132290	+	0.991211i	$0.542233\pi$
$128$		0			0
$129$	−2.58266	+	0.758337i	−0.227390	+	0.0667678i
$130$		0			0
$131$	−5.59843	−	12.2589i	−0.489137	−	1.07106i	−0.979849	−	0.199739i	$-0.935991\pi$
$131$	−5.59843	−	12.2589i	−0.489137	−	1.07106i	0.490712	−	0.871322i	$-0.336737\pi$
$132$		0			0
$133$	24.2843			2.10571
$134$		0			0
$135$	1.07880			0.0928487
$136$		0			0
$137$	−1.57903	−	3.45759i	−0.134905	−	0.295402i	0.830108	−	0.557603i	$-0.188279\pi$
$137$	−1.57903	−	3.45759i	−0.134905	−	0.295402i	−0.965013	+	0.262201i	$0.915552\pi$
$138$		0			0
$139$	22.3503	−	6.56264i	1.89573	−	0.556636i	0.904134	−	0.427248i	$-0.140517\pi$
$139$	22.3503	−	6.56264i	1.89573	−	0.556636i	0.991594	−	0.129388i	$-0.0413012\pi$
$140$		0			0
$141$	10.8255	+	2.08644i	0.911670	+	0.175710i
$142$		0			0
$143$	16.3112	−	18.8242i	1.36401	−	1.57416i
$144$		0			0
$145$	−7.90357	−	7.53604i	−0.656356	−	0.625834i
$146$		0			0
$147$	−0.737359	−	15.4791i	−0.0608163	−	1.27669i
$148$		0			0
$149$	9.12813	+	10.5344i	0.747805	+	0.863013i	0.994354	−	0.106117i	$-0.0338419\pi$
$149$	9.12813	+	10.5344i	0.747805	+	0.863013i	−0.246548	+	0.969130i	$0.579296\pi$
$150$		0			0
$151$	−4.41848	−	3.47473i	−0.359571	−	0.282770i	0.421988	−	0.906602i	$-0.361333\pi$
$151$	−4.41848	−	3.47473i	−0.359571	−	0.282770i	−0.781559	+	0.623832i	$0.785575\pi$
$152$		0			0
$153$	1.42269	−	0.274201i	0.115018	−	0.0221679i
$154$		0			0
$155$	1.80997	+	7.46080i	0.145380	+	0.599266i
$156$		0			0
$157$	22.5770	+	2.15584i	1.80184	+	0.172055i	0.941354	−	0.337419i	$-0.109554\pi$
$157$	22.5770	+	2.15584i	1.80184	+	0.172055i	0.860486	+	0.509474i	$0.170160\pi$
$158$		0			0
$159$	−4.84107	+	3.11117i	−0.383922	+	0.246732i
$160$		0			0
$161$	16.9584	+	4.97943i	1.33651	+	0.392434i
$162$		0			0
$163$	−1.91746	−	3.32115i	−0.150187	−	0.260132i	0.781109	−	0.624395i	$-0.214654\pi$
$163$	−1.91746	−	3.32115i	−0.150187	−	0.260132i	−0.931296	+	0.364263i	$0.881321\pi$
$164$		0			0
$165$	0.239441	−	5.02648i	0.0186404	−	0.391311i
$166$		0			0
$167$	3.63748	−	10.5098i	0.281477	−	0.813274i	−0.712299	−	0.701876i	$-0.752346\pi$
$167$	3.63748	−	10.5098i	0.281477	−	0.813274i	0.993776	−	0.111398i	$-0.0355329\pi$
$168$		0			0
$169$	−15.4432	+	1.47465i	−1.18794	+	0.113434i
$170$		0			0
$171$	2.55998	−	4.43401i	0.195767	−	0.339078i
$172$		0			0
$173$	18.7991	−	9.69163i	1.42927	−	0.736841i	0.442169	−	0.896932i	$-0.354209\pi$
$173$	18.7991	−	9.69163i	1.42927	−	0.736841i	0.987102	+	0.160091i	$0.0511787\pi$
$174$		0			0
$175$	16.8919	−	6.76249i	1.27691	−	0.511196i
$176$		0			0
$177$	0.358845	−	2.49582i	0.0269724	−	0.187597i
$178$		0			0
$179$	−5.86554	+	12.8437i	−0.438411	+	0.959986i	0.553476	+	0.832865i	$0.313301\pi$
$179$	−5.86554	+	12.8437i	−0.438411	+	0.959986i	−0.991887	+	0.127121i	$0.959426\pi$
$180$		0			0
$181$	2.04839	−	2.87656i	0.152255	−	0.213813i	−0.731402	−	0.681946i	$-0.761134\pi$
$181$	2.04839	−	2.87656i	0.152255	−	0.213813i	0.883658	+	0.468133i	$0.155073\pi$
$182$		0			0
$183$	0.866576	+	0.346925i	0.0640591	+	0.0256454i
$184$		0			0
$185$	0.824736	−	3.39961i	0.0606358	−	0.249944i
$186$		0			0
$187$	−0.961821	−	6.68962i	−0.0703354	−	0.489193i
$188$		0			0
$189$	−4.21580	−	2.17340i	−0.306654	−	0.158091i
$190$		0			0
$191$	−5.31055	−	7.45763i	−0.384258	−	0.539615i	0.576466	−	0.817121i	$-0.304431\pi$
$191$	−5.31055	−	7.45763i	−0.384258	−	0.539615i	−0.960724	+	0.277506i	$0.910492\pi$
$192$		0			0
$193$	11.8487	+	7.61469i	0.852887	+	0.548117i	0.892474	−	0.451099i	$-0.148968\pi$
$193$	11.8487	+	7.61469i	0.852887	+	0.548117i	−0.0395869	+	0.999216i	$0.512604\pi$
$194$		0			0
$195$	−4.16914	+	3.97527i	−0.298558	+	0.284675i
$196$		0			0
$197$	3.50546	−	2.75673i	0.249754	−	0.196409i	−0.485432	−	0.874275i	$-0.661338\pi$
$197$	3.50546	−	2.75673i	0.249754	−	0.196409i	0.735185	+	0.677866i	$0.237095\pi$
$198$		0			0
$199$	1.94567	+	5.62164i	0.137925	+	0.398508i	0.992718	−	0.120461i	$-0.0384373\pi$
$199$	1.94567	+	5.62164i	0.137925	+	0.398508i	−0.854793	+	0.518969i	$0.826316\pi$
$200$		0			0
$201$	8.07852	−	1.31816i	0.569815	−	0.0929759i
$202$		0			0
$203$	15.7036	+	45.3725i	1.10217	+	3.18452i
$204$		0			0
$205$	−7.21936	+	5.67737i	−0.504222	+	0.396524i
$206$		0			0
$207$	2.69689	−	2.57148i	0.187447	−	0.178730i
$208$		0			0
$209$	−20.0912	−	12.9119i	−1.38974	−	0.893132i
$210$		0			0
$211$	−0.811481	−	1.13957i	−0.0558647	−	0.0784509i	0.785699	−	0.618609i	$-0.212304\pi$
$211$	−0.811481	−	1.13957i	−0.0558647	−	0.0784509i	−0.841563	+	0.540159i	$0.818364\pi$
$212$		0			0
$213$	−8.55441	−	4.41011i	−0.586139	−	0.302176i
$214$		0			0
$215$	−0.413255	−	2.87425i	−0.0281838	−	0.196022i
$216$		0			0
$217$	7.95770	−	32.8021i	0.540204	−	2.22675i
$218$		0			0
$219$	1.37991	+	0.552431i	0.0932455	+	0.0373299i
$220$		0			0
$221$	−4.48772	+	6.30213i	−0.301877	+	0.423927i
$222$		0			0
$223$	−5.87937	+	12.8740i	−0.393712	+	0.862109i	0.604157	+	0.796865i	$0.293510\pi$
$223$	−5.87937	+	12.8740i	−0.393712	+	0.862109i	−0.997869	+	0.0652438i	$0.979217\pi$
$224$		0			0
$225$	0.545945	−	3.79713i	0.0363964	−	0.253142i
$226$		0			0
$227$	−8.04584	+	3.22107i	−0.534021	+	0.213790i	−0.622969	−	0.782247i	$-0.714074\pi$
$227$	−8.04584	+	3.22107i	−0.534021	+	0.213790i	0.0889480	+	0.996036i	$0.471650\pi$
$228$		0			0
$229$	3.38078	−	1.74291i	0.223408	−	0.115175i	−0.342889	−	0.939376i	$-0.611406\pi$
$229$	3.38078	−	1.74291i	0.223408	−	0.115175i	0.566298	+	0.824201i	$0.308375\pi$
$230$		0			0
$231$	−11.0622	+	19.1603i	−0.727840	+	1.26066i
$232$		0			0
$233$	−18.8655	+	1.80144i	−1.23592	+	0.118016i	−0.692484	−	0.721433i	$-0.743484\pi$
$233$	−18.8655	+	1.80144i	−1.23592	+	0.118016i	−0.543438	+	0.839449i	$0.682878\pi$
$234$		0			0
$235$	−3.88998	+	11.2394i	−0.253755	+	0.733176i
$236$		0			0
$237$	−0.415044	+	8.71285i	−0.0269600	+	0.565961i
$238$		0			0
$239$	4.20496	+	7.28320i	0.271996	+	0.471111i	0.969373	−	0.245594i	$-0.0789829\pi$
$239$	4.20496	+	7.28320i	0.271996	+	0.471111i	−0.697377	+	0.716705i	$0.745650\pi$
$240$		0			0
$241$	13.6429	+	4.00591i	0.878815	+	0.258043i	0.689860	−	0.723943i	$-0.257672\pi$
$241$	13.6429	+	4.00591i	0.878815	+	0.258043i	0.188955	+	0.981986i	$0.439490\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	16.6421	+	1.58913i	1.06323	+	0.101526i
$246$		0			0
$247$	6.44554	+	26.5689i	0.410120	+	1.69054i
$248$		0			0
$249$	−16.9707	+	3.27084i	−1.07548	+	0.207281i
$250$		0			0
$251$	−16.7140	−	13.1440i	−1.05498	−	0.829642i	−0.0691827	−	0.997604i	$-0.522039\pi$
$251$	−16.7140	−	13.1440i	−1.05498	−	0.829642i	−0.985794	+	0.167962i	$0.946282\pi$
$252$		0			0
$253$	−11.3827	−	13.1364i	−0.715626	−	0.825876i
$254$		0			0
$255$	0.0743731	+	1.56128i	0.00465742	+	0.0977713i
$256$		0			0
$257$	−8.02310	−	7.65001i	−0.500467	−	0.477195i	0.397285	−	0.917695i	$-0.369952\pi$
$257$	−8.02310	−	7.65001i	−0.500467	−	0.477195i	−0.897752	+	0.440501i	$0.854801\pi$
$258$		0			0
$259$	−10.0719	+	11.6236i	−0.625838	+	0.722255i
$260$		0			0
$261$	9.93989	+	1.91576i	0.615264	+	0.118582i
$262$		0			0
$263$	−21.3253	+	6.26166i	−1.31497	+	0.386111i	−0.862676	−	0.505757i	$-0.831213\pi$
$263$	−21.3253	+	6.26166i	−1.31497	+	0.386111i	−0.452296	+	0.891868i	$0.649395\pi$
$264$		0			0
$265$	−2.57893	−	5.64707i	−0.158422	−	0.346897i
$266$		0			0
$267$	3.69812			0.226321
$268$		0			0
$269$	25.5099			1.55536			0.777682	−	0.628658i	$-0.216396\pi$
$269$	25.5099			1.55536			0.777682	+	0.628658i	$0.216396\pi$
$270$		0			0
$271$	−5.69901	−	12.4791i	−0.346190	−	0.758050i	−0.999999	−	0.00139065i	$-0.999557\pi$
$271$	−5.69901	−	12.4791i	−0.346190	−	0.758050i	0.653809	−	0.756660i	$-0.273170\pi$
$272$		0			0
$273$	24.3011	−	7.13544i	1.47077	−	0.431856i
$274$		0			0
$275$	−17.5708	−	3.38650i	−1.05956	−	0.204214i
$276$		0			0
$277$	−11.9592	+	13.8017i	−0.718559	+	0.829261i	−0.991133	−	0.132874i	$-0.957580\pi$
$277$	−11.9592	+	13.8017i	−0.718559	+	0.829261i	0.272574	+	0.962135i	$0.412125\pi$
$278$		0			0
$279$	−5.15038	−	4.91088i	−0.308345	−	0.294007i
$280$		0			0
$281$	−0.161282	−	3.38572i	−0.00962127	−	0.201975i	−0.998560	−	0.0536495i	$-0.982915\pi$
$281$	−0.161282	−	3.38572i	−0.00962127	−	0.201975i	0.988939	−	0.148326i	$-0.0473884\pi$
$282$		0			0
$283$	−3.36175	−	3.87967i	−0.199836	−	0.230623i	0.646983	−	0.762504i	$-0.276030\pi$
$283$	−3.36175	−	3.87967i	−0.199836	−	0.230623i	−0.846819	+	0.531882i	$0.821485\pi$
$284$		0			0
$285$	4.34171	+	3.41436i	0.257181	+	0.202249i
$286$		0			0
$287$	39.6499	−	7.64190i	2.34046	−	0.451087i
$288$		0			0
$289$	−3.51299	−	14.4807i	−0.206646	−	0.851808i
$290$		0			0
$291$	−8.78745	−	0.839099i	−0.515129	−	0.0491889i
$292$		0			0
$293$	9.88966	−	6.35570i	0.577760	−	0.371304i	−0.218886	−	0.975751i	$-0.570242\pi$
$293$	9.88966	−	6.35570i	0.577760	−	0.371304i	0.796646	+	0.604447i	$0.206606\pi$
$294$		0			0
$295$	2.61000	+	0.766366i	0.151960	+	0.0446195i
$296$		0			0
$297$	2.33229	+	4.03965i	0.135333	+	0.234404i
$298$		0			0
$299$	−0.946783	+	19.8754i	−0.0547539	+	1.14943i
$300$		0			0
$301$	−4.17563	+	12.0647i	−0.240679	+	0.695397i
$302$		0			0
$303$	−10.3842	+	0.991575i	−0.596559	+	0.0569645i
$304$		0			0
$305$	−0.503500	+	0.872087i	−0.0288303	+	0.0499356i
$306$		0			0
$307$	−30.9782	+	15.9704i	−1.76802	+	0.911477i	−0.836322	+	0.548238i	$0.815299\pi$
$307$	−30.9782	+	15.9704i	−1.76802	+	0.911477i	−0.931696	+	0.363239i	$0.881671\pi$
$308$		0			0
$309$	−12.3511	+	4.94463i	−0.702629	+	0.281290i
$310$		0			0
$311$	3.20929	−	22.3211i	0.181982	−	1.26571i	−0.670086	−	0.742284i	$-0.733743\pi$
$311$	3.20929	−	22.3211i	0.181982	−	1.26571i	0.852068	−	0.523431i	$-0.175348\pi$
$312$		0			0
$313$	6.40665	−	14.0286i	0.362125	−	0.792943i	−0.637620	−	0.770351i	$-0.720081\pi$
$313$	6.40665	−	14.0286i	0.362125	−	0.792943i	0.999745	−	0.0225919i	$-0.00719185\pi$
$314$		0			0
$315$	2.96806	−	4.16805i	0.167231	−	0.234843i
$316$		0			0
$317$	−15.3306	−	6.13744i	−0.861052	−	0.344713i	−0.101245	−	0.994862i	$-0.532282\pi$
$317$	−15.3306	−	6.13744i	−0.861052	−	0.344713i	−0.759807	+	0.650148i	$0.774707\pi$
$318$		0			0
$319$	11.1323	−	45.8878i	0.623287	−	2.56922i
$320$		0			0
$321$	0.562038	+	3.90906i	0.0313699	+	0.218183i
$322$		0			0
$323$	6.59354	+	3.39921i	0.366874	+	0.189137i
$324$		0			0
$325$	11.8821	+	16.6861i	0.659102	+	0.925579i
$326$		0			0
$327$	12.4528	+	8.00295i	0.688644	+	0.442564i
$328$		0			0
$329$	37.8447	−	36.0848i	2.08644	−	1.98942i
$330$		0			0
$331$	7.89925	−	6.21204i	0.434182	−	0.341445i	−0.377025	−	0.926203i	$-0.623053\pi$
$331$	7.89925	−	6.21204i	0.434182	−	0.341445i	0.811208	+	0.584758i	$0.198811\pi$
$332$		0			0
$333$	1.06058	+	3.06433i	0.0581192	+	0.167925i
$334$		0			0
$335$	0.167270	+	8.82881i	0.00913893	+	0.482370i
$336$		0			0
$337$	8.26156	+	23.8702i	0.450036	+	1.30029i	0.910828	+	0.412786i	$0.135444\pi$
$337$	8.26156	+	23.8702i	0.450036	+	1.30029i	−0.460792	+	0.887508i	$0.652435\pi$
$338$		0			0
$339$	6.06451	−	4.76918i	0.329379	−	0.259026i
$340$		0			0
$341$	−24.0244	+	22.9072i	−1.30100	+	1.24050i
$342$		0			0
$343$	−33.9025	−	21.7878i	−1.83056	−	1.17643i
$344$		0			0
$345$	2.33183	+	3.27460i	0.125542	+	0.176299i
$346$		0			0
$347$	−10.1450	−	5.23010i	−0.544611	−	0.280767i	0.163887	−	0.986479i	$-0.447597\pi$
$347$	−10.1450	−	5.23010i	−0.544611	−	0.280767i	−0.708498	+	0.705713i	$0.750627\pi$
$348$		0			0
$349$	5.15260	+	35.8371i	0.275813	+	1.91832i	0.382365	+	0.924011i	$0.375110\pi$
$349$	5.15260	+	35.8371i	0.275813	+	1.91832i	−0.106553	+	0.994307i	$0.533981\pi$
$350$		0			0
$351$	1.25890	−	5.18928i	0.0671954	−	0.276983i
$352$		0			0
$353$	−8.60028	−	3.44303i	−0.457747	−	0.183254i	0.131317	−	0.991340i	$-0.458079\pi$
$353$	−8.60028	−	3.44303i	−0.457747	−	0.183254i	−0.589064	+	0.808086i	$0.700504\pi$
$354$		0			0
$355$	6.02258	−	8.45753i	0.319645	−	0.448879i
$356$		0			0
$357$	2.85477	−	6.25108i	0.151091	−	0.330842i
$358$		0			0
$359$	−0.385862	+	2.68373i	−0.0203650	+	0.141642i	−0.997467	−	0.0711291i	$-0.977340\pi$
$359$	−0.385862	+	2.68373i	−0.0203650	+	0.141642i	0.977102	+	0.212771i	$0.0682489\pi$
$360$		0			0
$361$	6.69723	−	2.68117i	0.352486	−	0.141114i
$362$		0			0
$363$	9.56244	−	4.92978i	0.501898	−	0.258746i
$364$		0			0
$365$	−0.801757	+	1.38868i	−0.0419659	+	0.0726870i
$366$		0			0
$367$	−13.6193	+	1.30049i	−0.710922	+	0.0678849i	−0.444251	−	0.895903i	$-0.646530\pi$
$367$	−13.6193	+	1.30049i	−0.710922	+	0.0678849i	−0.266672	+	0.963787i	$0.585924\pi$
$368$		0			0
$369$	2.78447	−	8.04518i	0.144953	−	0.418816i
$370$		0			0
$371$	−1.29872	+	27.2635i	−0.0674261	+	1.41545i
$372$		0			0
$373$	−4.03638	−	6.99122i	−0.208996	−	0.361992i	0.742402	−	0.669954i	$-0.233686\pi$
$373$	−4.03638	−	6.99122i	−0.208996	−	0.361992i	−0.951399	+	0.307962i	$0.900353\pi$
$374$		0			0
$375$	9.14638	+	2.68562i	0.472317	+	0.138685i
$376$		0			0
$377$	−45.4730	+	29.2237i	−2.34198	+	1.50510i
$378$		0			0
$379$	−10.6631	−	1.01820i	−0.547728	−	0.0523016i	−0.182476	−	0.983210i	$-0.558411\pi$
$379$	−10.6631	−	1.01820i	−0.547728	−	0.0523016i	−0.365252	+	0.930909i	$0.619017\pi$
$380$		0			0
$381$	−0.306543	−	1.26359i	−0.0157047	−	0.0647355i
$382$		0			0
$383$	13.2794	−	2.55940i	0.678547	−	0.130779i	0.161678	−	0.986844i	$-0.448309\pi$
$383$	13.2794	−	2.55940i	0.678547	−	0.130779i	0.516869	+	0.856064i	$0.327097\pi$
$384$		0			0
$385$	−18.7615	−	14.7542i	−0.956173	−	0.751943i
$386$		0			0
$387$	1.76268	+	2.03424i	0.0896022	+	0.103406i
$388$		0			0
$389$	0.886870	+	18.6177i	0.0449661	+	0.943954i	0.902809	+	0.430042i	$0.141501\pi$
$389$	0.886870	+	18.6177i	0.0449661	+	0.943954i	−0.857843	+	0.513912i	$0.828196\pi$
$390$		0			0
$391$	3.90745	+	3.72575i	0.197608	+	0.188419i
$392$		0			0
$393$	−8.82537	+	10.1850i	−0.445181	+	0.513766i
$394$		0			0
$395$	−9.24007	−	1.78088i	−0.464918	−	0.0896057i
$396$		0			0
$397$	1.56200	−	0.458645i	0.0783945	−	0.0230187i	−0.242300	−	0.970201i	$-0.577902\pi$
$397$	1.56200	−	0.458645i	0.0783945	−	0.0230187i	0.320695	+	0.947183i	$0.396084\pi$
$398$		0			0
$399$	−10.0881	−	22.0898i	−0.505034	−	1.10587i
$400$		0			0
$401$	−22.3658			−1.11689			−0.558447	−	0.829540i	$-0.688602\pi$
$401$	−22.3658			−1.11689			−0.558447	+	0.829540i	$0.688602\pi$
$402$		0			0
$403$	38.0001			1.89292
$404$		0			0
$405$	−0.448152	−	0.981315i	−0.0222688	−	0.0487619i
$406$		0			0
$407$	14.5131	−	4.26142i	0.719386	−	0.211231i
$408$		0			0
$409$	3.57308	+	0.688655i	0.176678	+	0.0340518i	0.276823	−	0.960921i	$-0.410719\pi$
$409$	3.57308	+	0.688655i	0.176678	+	0.0340518i	−0.100145	+	0.994973i	$0.531931\pi$
$410$		0			0
$411$	−2.48918	+	2.87267i	−0.122782	+	0.141698i
$412$		0			0
$413$	−8.65554	−	8.25304i	−0.425911	−	0.406105i
$414$		0			0
$415$	−0.887167	−	18.6239i	−0.0435493	−	0.914213i
$416$		0			0
$417$	−15.2542	−	17.6043i	−0.747004	−	0.862088i
$418$		0			0
$419$	−8.37099	−	6.58302i	−0.408950	−	0.321602i	0.392403	−	0.919793i	$-0.371644\pi$
$419$	−8.37099	−	6.58302i	−0.408950	−	0.321602i	−0.801353	+	0.598192i	$0.795886\pi$
$420$		0			0
$421$	−38.1980	+	7.36207i	−1.86166	+	0.358805i	−0.991085	−	0.133233i	$-0.957464\pi$
$421$	−38.1980	+	7.36207i	−1.86166	+	0.358805i	−0.870574	+	0.492038i	$0.836252\pi$
$422$		0			0
$423$	−2.59917	−	10.7139i	−0.126376	−	0.520929i
$424$		0			0
$425$	5.53298	+	0.528335i	0.268389	+	0.0256280i
$426$		0			0
$427$	3.72454	−	2.39361i	0.180243	−	0.115835i
$428$		0			0
$429$	−23.8990	−	7.01738i	−1.15386	−	0.338802i
$430$		0			0
$431$	4.85939	+	8.41671i	0.234069	+	0.405419i	0.959002	−	0.283401i	$-0.0914626\pi$
$431$	4.85939	+	8.41671i	0.234069	+	0.405419i	−0.724933	+	0.688819i	$0.758129\pi$
$432$		0			0
$433$	0.206633	−	4.33776i	0.00993014	−	0.208459i	−0.988449	−	0.151552i	$-0.951573\pi$
$433$	0.206633	−	4.33776i	0.00993014	−	0.208459i	0.998379	−	0.0569075i	$-0.0181240\pi$
$434$		0			0
$435$	−3.57176	+	10.3199i	−0.171253	+	0.494802i
$436$		0			0
$437$	18.9924	−	1.81355i	0.908529	−	0.0867540i
$438$		0			0
$439$	1.63028	−	2.82374i	0.0778092	−	0.134770i	−0.824495	−	0.565869i	$-0.808541\pi$
$439$	1.63028	−	2.82374i	0.0778092	−	0.134770i	0.902304	+	0.431099i	$0.141874\pi$
$440$		0			0
$441$	−13.7739	+	7.10096i	−0.655902	+	0.338141i
$442$		0			0
$443$	−15.7569	+	6.30810i	−0.748631	+	0.299707i	−0.714429	−	0.699708i	$-0.753313\pi$
$443$	−15.7569	+	6.30810i	−0.748631	+	0.299707i	−0.0342025	+	0.999415i	$0.510889\pi$
$444$		0			0
$445$	−0.567772	+	3.94894i	−0.0269150	+	0.187198i
$446$		0			0
$447$	5.79048	−	12.6794i	0.273881	−	0.599715i
$448$		0			0
$449$	−8.94719	+	12.5646i	−0.422244	+	0.592959i	−0.969827	−	0.243792i	$-0.921609\pi$
$449$	−8.94719	+	12.5646i	−0.422244	+	0.592959i	0.547583	+	0.836751i	$0.315548\pi$
$450$		0			0
$451$	−36.8670	−	14.7593i	−1.73600	−	0.694989i
$452$		0			0
$453$	−1.32522	+	5.46265i	−0.0622645	+	0.256658i
$454$		0			0
$455$	3.88845	+	27.0448i	0.182293	+	1.26788i
$456$		0			0
$457$	31.8010	+	16.3946i	1.48759	+	0.766905i	0.994664	−	0.103166i	$-0.0328974\pi$
$457$	31.8010	+	16.3946i	1.48759	+	0.766905i	0.492925	+	0.870072i	$0.335928\pi$
$458$		0			0
$459$	−0.840430	−	1.18022i	−0.0392279	−	0.0550879i
$460$		0			0
$461$	−3.30912	−	2.12664i	−0.154121	−	0.0990477i	0.461307	−	0.887240i	$-0.347381\pi$
$461$	−3.30912	−	2.12664i	−0.154121	−	0.0990477i	−0.615428	+	0.788193i	$0.711017\pi$
$462$		0			0
$463$	−27.0973	+	25.8372i	−1.25932	+	1.20076i	−0.289432	+	0.957199i	$0.593466\pi$
$463$	−27.0973	+	25.8372i	−1.25932	+	1.20076i	−0.969886	+	0.243559i	$0.921685\pi$
$464$		0			0
$465$	6.03469	−	4.74574i	0.279852	−	0.220078i
$466$		0			0
$467$	7.85400	+	22.6926i	0.363440	+	1.05009i	0.967439	+	0.253105i	$0.0814519\pi$
$467$	7.85400	+	22.6926i	0.363440	+	1.05009i	−0.603999	+	0.796985i	$0.706427\pi$
$468$		0			0
$469$	17.1332	−	34.8386i	0.791136	−	1.60870i
$470$		0			0
$471$	−7.41780	−	21.4323i	−0.341794	−	0.987549i
$472$		0			0
$473$	9.86939	−	7.76138i	0.453795	−	0.356868i
$474$		0			0
$475$	14.2149	−	13.5539i	0.652225	−	0.621896i
$476$		0			0
$477$	4.84107	+	3.11117i	0.221657	+	0.142451i
$478$		0			0
$479$	−8.42928	−	11.8373i	−0.385144	−	0.540859i	0.575804	−	0.817588i	$-0.304689\pi$
$479$	−8.42928	−	11.8373i	−0.385144	−	0.540859i	−0.960948	+	0.276729i	$0.910750\pi$
$480$		0			0
$481$	−15.3904	−	7.93431i	−0.701742	−	0.361773i
$482$		0			0
$483$	−2.51532	−	17.4944i	−0.114451	−	0.796023i
$484$		0			0
$485$	2.24515	−	9.25462i	0.101947	−	0.420231i
$486$		0			0
$487$	−14.7348	−	5.89893i	−0.667698	−	0.267306i	0.0129504	−	0.999916i	$-0.495878\pi$
$487$	−14.7348	−	5.89893i	−0.667698	−	0.267306i	−0.680649	+	0.732610i	$0.738302\pi$
$488$		0			0
$489$	−2.22448	+	3.12384i	−0.100594	+	0.141265i
$490$		0			0
$491$	3.15340	−	6.90497i	0.142311	−	0.311617i	−0.825033	−	0.565084i	$-0.808844\pi$
$491$	3.15340	−	6.90497i	0.142311	−	0.311617i	0.967344	+	0.253467i	$0.0815710\pi$
$492$		0			0
$493$	−2.08729	+	14.5174i	−0.0940068	+	0.653831i
$494$		0			0
$495$	−4.67172	+	1.87027i	−0.209978	+	0.0840625i
$496$		0			0
$497$	−40.5741	+	20.9174i	−1.82000	+	0.938274i
$498$		0			0
$499$	4.30138	−	7.45021i	0.192556	−	0.333517i	−0.753540	−	0.657402i	$-0.771656\pi$
$499$	4.30138	−	7.45021i	0.192556	−	0.333517i	0.946097	+	0.323884i	$0.104989\pi$
$500$		0			0
$501$	−11.0711	+	1.05717i	−0.494622	+	0.0472307i
$502$		0			0
$503$	10.1743	−	29.3966i	0.453648	−	1.31073i	−0.454002	−	0.891001i	$-0.650004\pi$
$503$	10.1743	−	29.3966i	0.453648	−	1.31073i	0.907650	−	0.419728i	$-0.137875\pi$
$504$		0			0
$505$	0.535464	−	11.2408i	0.0238278	−	0.500208i
$506$		0			0
$507$	7.75672	+	13.4350i	0.344488	+	0.596671i
$508$		0			0
$509$	29.8293	+	8.75868i	1.32216	+	0.388221i	0.865272	−	0.501302i	$-0.167146\pi$
$509$	29.8293	+	8.75868i	1.32216	+	0.388221i	0.456889	+	0.889524i	$0.348964\pi$
$510$		0			0
$511$	5.93083	−	3.81151i	0.262364	−	0.168611i
$512$		0			0
$513$	−5.09678	−	0.486683i	−0.225028	−	0.0214876i
$514$		0			0
$515$	−3.38374	−	13.9479i	−0.149105	−	0.614620i
$516$		0			0
$517$	−50.4964	+	9.73238i	−2.22083	+	0.428030i
$518$		0			0
$519$	−16.6253	−	13.0742i	−0.729768	−	0.573896i
$520$		0			0
$521$	−9.17984	−	10.5941i	−0.402176	−	0.464136i	0.518149	−	0.855290i	$-0.326621\pi$
$521$	−9.17984	−	10.5941i	−0.402176	−	0.464136i	−0.920325	+	0.391155i	$0.872076\pi$
$522$		0			0
$523$	2.06242	+	43.2955i	0.0901832	+	1.89318i	0.364003	+	0.931398i	$0.381410\pi$
$523$	2.06242	+	43.2955i	0.0901832	+	1.89318i	−0.273820	+	0.961781i	$0.588287\pi$
$524$		0			0
$525$	−13.1685	−	12.5561i	−0.574721	−	0.547995i
$526$		0			0
$527$	6.75212	−	7.79236i	0.294127	−	0.339441i
$528$		0			0
$529$	−8.94959	−	1.72489i	−0.389113	−	0.0749953i
$530$		0			0
$531$	−2.41935	+	0.710384i	−0.104991	+	0.0308281i
$532$		0			0
$533$	18.8847	+	41.3518i	0.817988	+	1.79114i
$534$		0			0
$535$	−4.26048			−0.184197
$536$		0			0
$537$	14.1197			0.609310
$538$		0			0
$539$	30.0284	+	65.7531i	1.29342	+	2.83219i
$540$		0			0
$541$	−21.2048	+	6.22630i	−0.911667	+	0.267689i	−0.703742	−	0.710455i	$-0.748489\pi$
$541$	−21.2048	+	6.22630i	−0.911667	+	0.267689i	−0.207924	+	0.978145i	$0.566671\pi$
$542$		0			0
$543$	−3.46754	−	0.668314i	−0.148806	−	0.0286801i
$544$		0			0
$545$	−10.4576	+	12.0687i	−0.447956	+	0.516968i
$546$		0			0
$547$	−2.08034	−	1.98360i	−0.0889491	−	0.0848128i	0.644300	−	0.764773i	$-0.277149\pi$
$547$	−2.08034	−	1.98360i	−0.0889491	−	0.0848128i	−0.733249	+	0.679960i	$0.761997\pi$
$548$		0			0
$549$	−0.0444149	−	0.932383i	−0.00189558	−	0.0397931i
$550$		0			0
$551$	33.9404	+	39.1693i	1.44591	+	1.66867i
$552$		0			0
$553$	32.5209	+	25.5748i	1.38293	+	1.08755i
$554$		0			0
$555$	−3.43500	+	0.662042i	−0.145808	+	0.0281021i
$556$		0			0
$557$	−9.48174	−	39.0843i	−0.401754	−	1.65605i	−0.709590	−	0.704615i	$-0.751120\pi$
$557$	−9.48174	−	39.0843i	−0.401754	−	1.65605i	0.307836	−	0.951440i	$-0.400395\pi$
$558$		0			0
$559$	−14.3080	−	1.36625i	−0.605164	−	0.0577861i
$560$		0			0
$561$	−5.68553	+	3.65387i	−0.240043	+	0.154267i
$562$		0			0
$563$	36.1949	+	10.6278i	1.52543	+	0.447907i	0.933649	−	0.358190i	$-0.116606\pi$
$563$	36.1949	+	10.6278i	1.52543	+	0.447907i	0.591783	+	0.806097i	$0.298424\pi$
$564$		0			0
$565$	4.16156	+	7.20804i	0.175078	+	0.303244i
$566$		0			0
$567$	−0.225684	+	4.73769i	−0.00947783	+	0.198964i
$568$		0			0
$569$	2.61509	−	7.55581i	0.109630	−	0.316756i	−0.876819	−	0.480820i	$-0.840339\pi$
$569$	2.61509	−	7.55581i	0.109630	−	0.316756i	0.986450	+	0.164064i	$0.0524603\pi$
$570$		0			0
$571$	6.19650	−	0.591694i	0.259316	−	0.0247616i	0.0354115	−	0.999373i	$-0.488726\pi$
$571$	6.19650	−	0.591694i	0.259316	−	0.0247616i	0.223904	+	0.974611i	$0.428120\pi$
$572$		0			0
$573$	−4.57761	+	7.92866i	−0.191233	+	0.331224i
$574$		0			0
$575$	12.7059	−	6.55033i	0.529871	−	0.273168i
$576$		0			0
$577$	3.02361	−	1.21047i	0.125875	−	0.0503926i	−0.307870	−	0.951428i	$-0.599616\pi$
$577$	3.02361	−	1.21047i	0.125875	−	0.0503926i	0.433745	+	0.901036i	$0.357192\pi$
$578$		0			0
$579$	2.00444	−	13.9412i	0.0833018	−	0.579376i
$580$		0			0
$581$	−34.0535	+	74.5667i	−1.41278	+	3.09355i
$582$		0			0
$583$	15.5704	−	21.8655i	0.644858	−	0.905577i
$584$		0			0
$585$	5.34796	+	2.14100i	0.221111	+	0.0885194i
$586$		0			0
$587$	10.1717	−	41.9285i	0.419833	−	1.73058i	−0.232458	−	0.972606i	$-0.574677\pi$
$587$	10.1717	−	41.9285i	0.419833	−	1.73058i	0.652291	−	0.757969i	$-0.273808\pi$
$588$		0			0
$589$	−5.18534	−	36.0648i	−0.213658	−	1.48603i
$590$		0			0
$591$	−3.96383	−	2.04350i	−0.163050	−	0.0840582i
$592$		0			0
$593$	−4.39706	−	6.17481i	−0.180566	−	0.253569i	0.714366	−	0.699772i	$-0.246715\pi$
$593$	−4.39706	−	6.17481i	−0.180566	−	0.253569i	−0.894932	+	0.446203i	$0.852776\pi$
$594$		0			0
$595$	6.23676	+	4.00812i	0.255682	+	0.164317i
$596$		0			0
$597$	4.30537	−	4.10516i	0.176207	−	0.168013i
$598$		0			0
$599$	26.6001	−	20.9186i	1.08685	−	0.854709i	0.0967844	−	0.995305i	$-0.469144\pi$
$599$	26.6001	−	20.9186i	1.08685	−	0.854709i	0.990067	+	0.140596i	$0.0449018\pi$
$600$		0			0
$601$	3.20794	+	9.26873i	0.130855	+	0.378079i	0.991327	−	0.131417i	$-0.0419528\pi$
$601$	3.20794	+	9.26873i	0.130855	+	0.378079i	−0.860473	+	0.509497i	$0.829832\pi$
$602$		0			0
$603$	−4.55498	−	6.80089i	−0.185493	−	0.276954i
$604$		0			0
$605$	3.79602	+	10.9679i	0.154330	+	0.445908i
$606$		0			0
$607$	10.7321	−	8.43984i	0.435604	−	0.342563i	−0.376154	−	0.926557i	$-0.622754\pi$
$607$	10.7321	−	8.43984i	0.435604	−	0.342563i	0.811758	+	0.583995i	$0.198511\pi$
$608$		0			0
$609$	34.7487	−	33.1329i	1.40809	−	1.34261i
$610$		0			0
$611$	49.5243	+	31.8274i	2.00354	+	1.28760i
$612$		0			0
$613$	−4.42070	−	6.20801i	−0.178551	−	0.250739i	0.715595	−	0.698515i	$-0.246156\pi$
$613$	−4.42070	−	6.20801i	−0.178551	−	0.250739i	−0.894146	+	0.447776i	$0.852216\pi$
$614$		0			0
$615$	8.16334	+	4.20850i	0.329178	+	0.169703i
$616$		0			0
$617$	−0.120395	−	0.837366i	−0.00484692	−	0.0337111i	0.987254	−	0.159150i	$-0.0508753\pi$
$617$	−0.120395	−	0.837366i	−0.00484692	−	0.0337111i	−0.992101	+	0.125439i	$0.959966\pi$
$618$		0			0
$619$	1.83489	−	7.56353i	0.0737506	−	0.304004i	−0.922975	−	0.384859i	$-0.874250\pi$
$619$	1.83489	−	7.56353i	0.0737506	−	0.304004i	0.996726	+	0.0808552i	$0.0257651\pi$
$620$		0			0
$621$	−3.45943	−	1.38495i	−0.138822	−	0.0555759i
$622$		0			0
$623$	10.1744	−	14.2880i	0.407630	−	0.572436i
$624$		0			0
$625$	3.69602	−	8.09316i	0.147841	−	0.323726i
$626$		0			0
$627$	−3.39884	+	23.6394i	−0.135736	+	0.944067i
$628$		0			0
$629$	−4.36169	+	1.74616i	−0.173912	+	0.0696239i
$630$		0			0
$631$	19.3184	−	9.95931i	0.769052	−	0.396474i	−0.0286008	−	0.999591i	$-0.509105\pi$
$631$	19.3184	−	9.95931i	0.769052	−	0.396474i	0.797653	+	0.603117i	$0.206075\pi$
$632$		0			0
$633$	−0.699484	+	1.21154i	−0.0278020	+	0.0481545i
$634$		0			0
$635$	1.39635	−	0.133335i	0.0554125	−	0.00529125i
$636$		0			0
$637$	27.0645	−	78.1977i	1.07233	−	3.09831i
$638$		0			0
$639$	−0.457942	+	9.61339i	−0.0181159	+	0.380300i
$640$		0			0
$641$	11.0182	+	19.0842i	0.435195	+	0.753779i	0.997312	−	0.0732787i	$-0.0233463\pi$
$641$	11.0182	+	19.0842i	0.435195	+	0.753779i	−0.562117	+	0.827058i	$0.690013\pi$
$642$		0			0
$643$	−33.5286	−	9.84490i	−1.32224	−	0.388245i	−0.456940	−	0.889498i	$-0.651054\pi$
$643$	−33.5286	−	9.84490i	−1.32224	−	0.388245i	−0.865301	+	0.501253i	$0.832873\pi$
$644$		0			0
$645$	−2.44284	+	1.56992i	−0.0961867	+	0.0618154i
$646$		0			0
$647$	−17.9568	−	1.71466i	−0.705954	−	0.0674104i	−0.264097	−	0.964496i	$-0.585074\pi$
$647$	−17.9568	−	1.71466i	−0.705954	−	0.0674104i	−0.441857	+	0.897086i	$0.645680\pi$
$648$		0			0
$649$	2.77292	+	11.4301i	0.108847	+	0.448672i
$650$		0			0
$651$	−33.1436	+	6.38790i	−1.29900	+	0.250361i
$652$		0			0
$653$	−21.3419	−	16.7835i	−0.835175	−	0.656789i	0.106128	−	0.994352i	$-0.466155\pi$
$653$	−21.3419	−	16.7835i	−0.835175	−	0.656789i	−0.941303	+	0.337564i	$0.890397\pi$
$654$		0			0
$655$	−9.52085	−	10.9876i	−0.372010	−	0.429323i
$656$		0			0
$657$	−0.0707248	−	1.48470i	−0.00275924	−	0.0579235i
$658$		0			0
$659$	16.7400	+	15.9616i	0.652098	+	0.621774i	0.942132	−	0.335242i	$-0.108818\pi$
$659$	16.7400	+	15.9616i	0.652098	+	0.621774i	−0.290034	+	0.957016i	$0.593667\pi$
$660$		0			0
$661$	13.2498	−	15.2911i	0.515359	−	0.594756i	−0.437104	−	0.899411i	$-0.643996\pi$
$661$	13.2498	−	15.2911i	0.515359	−	0.594756i	0.952463	+	0.304655i	$0.0985413\pi$
$662$		0			0
$663$	7.59689	+	1.46418i	0.295039	+	0.0568640i
$664$		0			0
$665$	25.1368	−	7.38083i	0.974763	−	0.286216i
$666$		0			0
$667$	15.6699	+	34.3124i	0.606743	+	1.32858i
$668$		0			0
$669$	14.1530			0.547187
$670$		0			0
$671$	−4.35412			−0.168089
$672$		0			0
$673$	−0.0620713	−	0.135917i	−0.00239267	−	0.00523922i	0.908432	−	0.418033i	$-0.137280\pi$
$673$	−0.0620713	−	0.135917i	−0.00239267	−	0.00523922i	−0.910825	+	0.412794i	$0.864553\pi$
$674$		0			0
$675$	−3.68079	+	1.08078i	−0.141674	+	0.0415991i
$676$		0			0
$677$	−34.1412	−	6.58019i	−1.31215	−	0.252897i	−0.515270	−	0.857028i	$-0.672308\pi$
$677$	−34.1412	−	6.58019i	−1.31215	−	0.252897i	−0.796885	+	0.604131i	$0.793520\pi$
$678$		0			0
$679$	−27.4183	+	31.6425i	−1.05222	+	1.21433i
$680$		0			0
$681$	6.27235	+	5.98067i	0.240357	+	0.229180i
$682$		0			0
$683$	0.0107125	+	0.224883i	0.000409902	+	0.00860491i	0.999063	−	0.0432790i	$-0.0137804\pi$
$683$	0.0107125	+	0.224883i	0.000409902	+	0.00860491i	−0.998653	+	0.0518839i	$0.983477\pi$
$684$		0			0
$685$	−2.68534	−	3.09905i	−0.102602	−	0.118408i
$686$		0			0
$687$	−2.98983	−	2.35123i	−0.114069	−	0.0897051i
$688$		0			0
$689$	−30.1730	+	5.81538i	−1.14950	+	0.221548i
$690$		0			0
$691$	4.93416	+	20.3389i	0.187704	+	0.773728i	0.985342	+	0.170591i	$0.0545677\pi$
$691$	4.93416	+	20.3389i	0.187704	+	0.773728i	−0.797638	+	0.603137i	$0.793917\pi$
$692$		0			0
$693$	22.0242	+	2.10306i	0.836632	+	0.0798887i
$694$		0			0
$695$	21.1403	−	13.5861i	0.801898	−	0.515348i
$696$		0			0
$697$	11.8352	+	3.47513i	0.448291	+	0.131630i
$698$		0			0
$699$	9.47568	+	16.4124i	0.358403	+	0.620772i
$700$		0			0
$701$	1.58693	−	33.3139i	0.0599377	−	1.25825i	−0.745879	−	0.666082i	$-0.767970\pi$
$701$	1.58693	−	33.3139i	0.0599377	−	1.25825i	0.805817	−	0.592165i	$-0.201727\pi$
$702$		0			0
$703$	−5.43011	+	15.6893i	−0.204800	+	0.591732i
$704$		0			0
$705$	11.8397	−	1.13055i	0.445907	−	0.0425790i
$706$		0			0
$707$	−24.7386	+	42.8484i	−0.930389	+	1.61148i
$708$		0			0
$709$	−19.8239	+	10.2199i	−0.744502	+	0.383818i	−0.788355	−	0.615220i	$-0.789067\pi$
$709$	−19.8239	+	10.2199i	−0.744502	+	0.383818i	0.0438529	+	0.999038i	$0.486037\pi$
$710$		0			0
$711$	8.09791	−	3.24191i	0.303695	−	0.121581i
$712$		0			0
$713$	3.77394	−	26.2483i	0.141335	−	0.983007i
$714$		0			0
$715$	11.1625	−	24.4426i	0.417456	−	0.914100i
$716$		0			0
$717$	4.87823	−	6.85052i	0.182181	−	0.255837i
$718$		0			0
$719$	−10.7709	−	4.31202i	−0.401687	−	0.160811i	0.162017	−	0.986788i	$-0.448200\pi$
$719$	−10.7709	−	4.31202i	−0.401687	−	0.160811i	−0.563704	+	0.825977i	$0.690624\pi$
$720$		0			0
$721$	−14.8769	+	61.3234i	−0.554044	+	2.28380i
$722$		0			0
$723$	−2.02355	−	14.0741i	−0.0752567	−	0.523422i
$724$		0			0
$725$	34.5161	+	17.7943i	1.28190	+	0.660863i
$726$		0			0
$727$	−11.9335	−	16.7582i	−0.442589	−	0.621529i	0.531673	−	0.846950i	$-0.321564\pi$
$727$	−11.9335	−	16.7582i	−0.442589	−	0.621529i	−0.974261	+	0.225421i	$0.927624\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−2.82251	+	2.69125i	−0.104394	+	0.0995396i
$732$		0			0
$733$	−1.70083	+	1.33755i	−0.0628218	+	0.0494036i	−0.649076	−	0.760723i	$-0.724844\pi$
$733$	−1.70083	+	1.33755i	−0.0628218	+	0.0494036i	0.586254	+	0.810127i	$0.300602\pi$
$734$		0			0
$735$	−5.46787	−	15.7984i	−0.201685	−	0.582731i
$736$		0			0
$737$	−32.6984	+	19.7136i	−1.20446	+	0.726159i
$738$		0			0
$739$	−2.85250	−	8.24176i	−0.104931	−	0.303178i	0.880298	−	0.474422i	$-0.157343\pi$
$739$	−2.85250	−	8.24176i	−0.104931	−	0.303178i	−0.985229	+	0.171243i	$0.945222\pi$
$740$		0			0
$741$	21.4903	−	16.9002i	0.789467	−	0.620844i
$742$		0			0
$743$	−19.8002	+	18.8794i	−0.726397	+	0.692618i	−0.960090	−	0.279692i	$-0.909768\pi$
$743$	−19.8002	+	18.8794i	−0.726397	+	0.692618i	0.233692	+	0.972311i	$0.424919\pi$
$744$		0			0
$745$	12.6503	+	8.12988i	0.463473	+	0.297856i
$746$		0			0
$747$	10.0252	+	14.0784i	0.366802	+	0.515101i
$748$		0			0
$749$	16.6493	+	8.58331i	0.608352	+	0.313627i
$750$		0			0
$751$	−3.30274	−	22.9711i	−0.120519	−	0.838226i	−0.956971	−	0.290185i	$-0.906283\pi$
$751$	−3.30274	−	22.9711i	−0.120519	−	0.838226i	0.836452	−	0.548040i	$-0.184626\pi$
$752$		0			0
$753$	−5.01298	+	20.6638i	−0.182683	+	0.753030i
$754$		0			0
$755$	−5.62969	−	2.25379i	−0.204885	−	0.0820237i
$756$		0			0
$757$	1.14728	−	1.61112i	0.0416984	−	0.0585573i	−0.793200	−	0.608961i	$-0.791587\pi$
$757$	1.14728	−	1.61112i	0.0416984	−	0.0585573i	0.834899	+	0.550403i	$0.185526\pi$
$758$		0			0
$759$	−7.22070	+	15.8111i	−0.262095	+	0.573908i
$760$		0			0
$761$	0.580179	−	4.03523i	0.0210315	−	0.146277i	−0.976600	−	0.215064i	$-0.931004\pi$
$761$	0.580179	−	4.03523i	0.0210315	−	0.146277i	0.997631	+	0.0687873i	$0.0219130\pi$
$762$		0			0
$763$	65.1809	−	26.0945i	2.35971	−	0.944684i
$764$		0			0
$765$	1.38930	−	0.716232i	0.0502301	−	0.0258954i
$766$		0			0
$767$	6.73211	−	11.6604i	0.243082	−	0.421031i
$768$		0			0
$769$	−22.9732	+	2.19367i	−0.828434	+	0.0791059i	−0.500653	−	0.865648i	$-0.666907\pi$
$769$	−22.9732	+	2.19367i	−0.828434	+	0.0791059i	−0.327781	+	0.944754i	$0.606301\pi$
$770$		0			0
$771$	−3.62578	+	10.4760i	−0.130579	+	0.377284i
$772$		0			0
$773$	1.02503	−	21.5181i	0.0368679	−	0.773952i	−0.902427	−	0.430842i	$-0.858217\pi$
$773$	1.02503	−	21.5181i	0.0368679	−	0.773952i	0.939295	−	0.343110i	$-0.111480\pi$
$774$		0			0
$775$	−13.6499	−	23.6423i	−0.490319	−	0.849257i
$776$		0			0
$777$	14.7572	+	4.33311i	0.529412	+	0.155449i
$778$		0			0
$779$	36.6688	−	23.5656i	1.31380	−	0.844326i
$780$		0			0
$781$	44.6901	+	4.26739i	1.59914	+	0.152699i
$782$		0			0
$783$	−2.38655	−	9.83747i	−0.0852882	−	0.351563i
$784$		0			0
$785$	24.0248	−	4.63040i	0.857482	−	0.165266i
$786$		0			0
$787$	21.2076	+	16.6778i	0.755968	+	0.594500i	0.919983	−	0.391958i	$-0.128202\pi$
$787$	21.2076	+	16.6778i	0.755968	+	0.594500i	−0.164015	+	0.986458i	$0.552445\pi$
$788$		0			0
$789$	14.5546	+	16.7969i	0.518159	+	0.597987i
$790$		0			0
$791$	−1.74118	−	36.5519i	−0.0619093	−	1.29964i
$792$		0			0
$793$	3.60737	+	3.43962i	0.128101	+	0.122144i
$794$		0			0
$795$	−4.06543	+	4.69175i	−0.144186	+	0.166399i
$796$		0			0
$797$	−24.0621	−	4.63758i	−0.852322	−	0.164272i	−0.255663	−	0.966766i	$-0.582294\pi$
$797$	−24.0621	−	4.63758i	−0.852322	−	0.164272i	−0.596660	+	0.802494i	$0.703506\pi$
$798$		0			0
$799$	15.3264	−	4.50023i	0.542208	−	0.159207i
$800$		0			0
$801$	−1.53625	−	3.36393i	−0.0542809	−	0.118859i
$802$		0			0
$803$	−6.93335			−0.244673
$804$		0			0
$805$	19.0671			0.672028
$806$		0			0
$807$	−10.5972	−	23.2046i	−0.373038	−	0.816840i
$808$		0			0
$809$	7.40257	−	2.17359i	0.260261	−	0.0764194i	−0.148999	−	0.988837i	$-0.547605\pi$
$809$	7.40257	−	2.17359i	0.260261	−	0.0764194i	0.409260	+	0.912418i	$0.365787\pi$
$810$		0			0
$811$	−21.6578	−	4.17420i	−0.760509	−	0.146576i	−0.205770	−	0.978600i	$-0.565970\pi$
$811$	−21.6578	−	4.17420i	−0.760509	−	0.146576i	−0.554739	+	0.832024i	$0.687182\pi$
$812$		0			0
$813$	−8.98392	+	10.3680i	−0.315080	+	0.363621i
$814$		0			0
$815$	−2.99419	−	2.85495i	−0.104882	−	0.100005i
$816$		0			0
$817$	0.655743	+	13.7657i	0.0229415	+	0.481602i
$818$		0			0
$819$	−16.5856	−	19.1409i	−0.579549	−	0.668836i
$820$		0			0
$821$	−34.5297	−	27.1545i	−1.20509	−	0.947697i	−0.205574	−	0.978642i	$-0.565906\pi$
$821$	−34.5297	−	27.1545i	−1.20509	−	0.947697i	−0.999521	+	0.0309447i	$0.990148\pi$
$822$		0			0
$823$	54.6523	−	10.5334i	1.90506	−	0.367170i	0.906567	−	0.422063i	$-0.138694\pi$
$823$	54.6523	−	10.5334i	1.90506	−	0.367170i	0.998492	+	0.0548926i	$0.0174816\pi$
$824$		0			0
$825$	4.21872	+	17.3898i	0.146877	+	0.605435i
$826$		0			0
$827$	−48.2524	−	4.60755i	−1.67790	−	0.160220i	−0.787784	−	0.615951i	$-0.788772\pi$
$827$	−48.2524	−	4.60755i	−1.67790	−	0.160220i	−0.890117	+	0.455731i	$0.849378\pi$
$828$		0			0
$829$	8.71862	−	5.60312i	0.302810	−	0.194604i	−0.380408	−	0.924819i	$-0.624216\pi$
$829$	8.71862	−	5.60312i	0.302810	−	0.194604i	0.683218	+	0.730215i	$0.260580\pi$
$830$		0			0
$831$	17.5225	+	5.14506i	0.607847	+	0.178480i
$832$		0			0
$833$	−11.2263	−	19.4446i	−0.388969	−	0.673715i
$834$		0			0
$835$	0.570884	−	11.9843i	0.0197563	−	0.414735i
$836$		0			0
$837$	−2.32755	+	6.72501i	−0.0804518	+	0.232450i
$838$		0			0
$839$	41.5813	−	3.97053i	1.43554	−	0.137078i	0.651908	−	0.758298i	$-0.273969\pi$
$839$	41.5813	−	3.97053i	1.43554	−	0.137078i	0.783636	+	0.621220i	$0.213363\pi$
$840$		0			0
$841$	−36.7357	+	63.6282i	−1.26675	+	2.19407i
$842$		0			0
$843$	−3.01276	+	1.55319i	−0.103765	+	0.0534946i
$844$		0			0
$845$	−15.5371	+	6.22013i	−0.534494	+	0.213979i
$846$		0			0
$847$	7.26200	−	50.5083i	0.249525	−	1.73549i
$848$		0			0
$849$	−2.13255	+	4.66963i	−0.0731889	+	0.160261i
$850$		0			0
$851$	−7.00904	+	9.84282i	−0.240267	+	0.337408i
$852$		0			0
$853$	24.7331	+	9.90163i	0.846844	+	0.339025i	0.754176	−	0.656672i	$-0.228036\pi$
$853$	24.7331	+	9.90163i	0.846844	+	0.339025i	0.0926676	+	0.995697i	$0.470461\pi$
$854$		0			0
$855$	1.30220	−	5.36774i	0.0445343	−	0.183573i
$856$		0			0
$857$	6.35282	+	44.1848i	0.217008	+	1.50932i	0.748997	+	0.662574i	$0.230536\pi$
$857$	6.35282	+	44.1848i	0.217008	+	1.50932i	−0.531989	+	0.846751i	$0.678555\pi$
$858$		0			0
$859$	13.0257	+	6.71520i	0.444430	+	0.229120i	0.665890	−	0.746050i	$-0.268052\pi$
$859$	13.0257	+	6.71520i	0.444430	+	0.229120i	−0.221460	+	0.975169i	$0.571082\pi$
$860$		0			0
$861$	−23.4225	−	32.8923i	−0.798236	−	1.12097i
$862$		0			0
$863$	7.72003	+	4.96137i	0.262793	+	0.168887i	0.665402	−	0.746485i	$-0.268260\pi$
$863$	7.72003	+	4.96137i	0.262793	+	0.168887i	−0.402609	+	0.915372i	$0.631897\pi$
$864$		0			0
$865$	16.5135	−	15.7456i	0.561475	−	0.535365i
$866$		0			0
$867$	−11.7128	+	9.21104i	−0.397787	+	0.312823i
$868$		0			0
$869$	−13.3077	−	38.4502i	−0.451434	−	1.30433i
$870$		0			0
$871$	42.6636	+	9.49813i	1.44560	+	0.321832i
$872$		0			0
$873$	2.88717	+	8.34192i	0.0977157	+	0.282331i
$874$		0			0
$875$	35.5400	−	27.9490i	1.20147	−	0.944849i
$876$		0			0
$877$	7.89653	−	7.52933i	0.266647	−	0.254247i	−0.544945	−	0.838472i	$-0.683450\pi$
$877$	7.89653	−	7.52933i	0.266647	−	0.254247i	0.811592	+	0.584224i	$0.198601\pi$
$878$		0			0
$879$	−9.88966	−	6.35570i	−0.333570	−	0.214372i
$880$		0			0
$881$	20.0325	+	28.1318i	0.674913	+	0.947783i	0.999998	+	0.00209835i	$0.000667926\pi$
$881$	20.0325	+	28.1318i	0.674913	+	0.947783i	−0.325084	+	0.945685i	$0.605393\pi$
$882$		0			0
$883$	2.68898	+	1.38626i	0.0904913	+	0.0466515i	0.502878	−	0.864357i	$-0.332274\pi$
$883$	2.68898	+	1.38626i	0.0904913	+	0.0466515i	−0.412387	+	0.911009i	$0.635305\pi$
$884$		0			0
$885$	−0.387123	−	2.69250i	−0.0130130	−	0.0905075i
$886$		0			0
$887$	0.0342036	−	0.140989i	0.00114844	−	0.00473395i	−0.971234	−	0.238125i	$-0.923467\pi$
$887$	0.0342036	−	0.140989i	0.00114844	−	0.00473395i	0.972383	+	0.233391i	$0.0749823\pi$
$888$		0			0
$889$	−5.72534	−	2.29208i	−0.192022	−	0.0768739i
$890$		0			0
$891$	2.70573	−	3.79966i	0.0906453	−	0.127293i
$892$		0			0
$893$	23.4485	−	51.3451i	0.784675	−	1.71820i
$894$		0			0
$895$	−2.16780	+	15.0774i	−0.0724615	+	0.503981i
$896$		0			0
$897$	18.4726	−	7.39533i	0.616783	−	0.246923i
$898$		0			0
$899$	64.0300	−	33.0097i	2.13552	−	1.10094i
$900$		0			0
$901$	−4.16884	+	7.22064i	−0.138884	+	0.240555i
$902$		0			0
$903$	12.7090	−	1.21357i	0.422930	−	0.0403850i
$904$		0			0
$905$	1.24601	−	3.60012i	0.0414189	−	0.119672i
$906$		0			0
$907$	−0.389327	+	8.17298i	−0.0129274	+	0.271379i	0.983144	+	0.182831i	$0.0585260\pi$
$907$	−0.389327	+	8.17298i	−0.0129274	+	0.271379i	−0.996072	+	0.0885489i	$0.971777\pi$
$908$		0			0
$909$	5.21574	+	9.03392i	0.172995	+	0.299636i
$910$		0			0
$911$	12.2027	+	3.58304i	0.404294	+	0.118711i	0.477556	−	0.878601i	$-0.341523\pi$
$911$	12.2027	+	3.58304i	0.404294	+	0.118711i	−0.0732621	+	0.997313i	$0.523341\pi$
$912$		0			0
$913$	67.8205	−	43.5856i	2.24453	−	1.44247i
$914$		0			0
$915$	1.00244	+	0.0957214i	0.0331396	+	0.00316445i
$916$		0			0
$917$	15.0699	+	62.1190i	0.497652	+	2.05135i
$918$		0			0
$919$	−42.4772	+	8.18681i	−1.40119	+	0.270058i	−0.833199	−	0.552974i	$-0.813493\pi$
$919$	−42.4772	+	8.18681i	−1.40119	+	0.270058i	−0.567995	+	0.823032i	$0.692281\pi$
$920$		0			0
$921$	27.3960	+	21.5444i	0.902727	+	0.709913i
$922$		0			0
$923$	−33.6545	−	38.8393i	−1.10775	−	1.27841i
$924$		0			0
$925$	0.591895	+	12.4254i	0.0194614	+	0.408545i
$926$		0			0
$927$	9.62863	+	9.18088i	0.316246	+	0.301540i
$928$		0			0
$929$	29.4051	−	33.9352i	0.964749	−	1.11338i	−0.0287560	−	0.999586i	$-0.509155\pi$
$929$	29.4051	−	33.9352i	0.964749	−	1.11338i	0.993505	−	0.113793i	$-0.0363000\pi$
$930$		0			0
$931$	−77.9083	−	15.0156i	−2.55334	−	0.492116i
$932$		0			0
$933$	−21.6372	+	6.35325i	−0.708370	+	0.207996i
$934$		0			0
$935$	−3.02879	−	6.63213i	−0.0990521	−	0.216894i
$936$		0			0
$937$	−20.1415			−0.657994			−0.328997	−	0.944331i	$-0.606711\pi$
$937$	−20.1415			−0.657994			−0.328997	+	0.944331i	$0.606711\pi$
$938$		0			0
$939$	−15.4223			−0.503287
$940$		0			0
$941$	11.1644	+	24.4467i	0.363950	+	0.796938i	0.999687	+	0.0250328i	$0.00796901\pi$
$941$	11.1644	+	24.4467i	0.363950	+	0.796938i	−0.635737	+	0.771906i	$0.719304\pi$
$942$		0			0
$943$	30.4389	−	8.93768i	0.991228	−	0.291051i
$944$		0			0
$945$	−5.02437	−	0.968368i	−0.163443	−	0.0315010i
$946$		0			0
$947$	20.7158	−	23.9073i	0.673174	−	0.776884i	−0.311695	−	0.950182i	$-0.600897\pi$
$947$	20.7158	−	23.9073i	0.673174	−	0.776884i	0.984869	+	0.173298i	$0.0554423\pi$
$948$		0			0
$949$	5.74425	+	5.47713i	0.186466	+	0.177795i
$950$		0			0
$951$	0.785743	+	16.4948i	0.0254795	+	0.534880i
$952$		0			0
$953$	12.4812	+	14.4040i	0.404305	+	0.466592i	0.920992	−	0.389582i	$-0.127380\pi$
$953$	12.4812	+	14.4040i	0.404305	+	0.466592i	−0.516687	+	0.856174i	$0.672835\pi$
$954$		0			0
$955$	−7.76361	−	6.10537i	−0.251225	−	0.197565i
$956$		0			0
$957$	−46.3655	+	8.93622i	−1.49878	+	0.288867i
$958$		0			0
$959$	4.25044	+	17.5206i	0.137254	+	0.565769i
$960$		0			0
$961$	−19.5542	−	1.86720i	−0.630782	−	0.0602324i
$962$		0			0
$963$	3.32233	−	2.13513i	0.107061	−	0.0688036i
$964$		0			0
$965$	14.5790	+	4.28078i	0.469315	+	0.137803i
$966$		0			0
$967$	27.1130	+	46.9610i	0.871894	+	1.51016i	0.860035	+	0.510235i	$0.170442\pi$
$967$	27.1130	+	46.9610i	0.871894	+	1.51016i	0.0118588	+	0.999930i	$0.496225\pi$
$968$		0			0
$969$	0.352971	−	7.40978i	0.0113391	−	0.238036i
$970$		0			0
$971$	−2.75753	+	7.96737i	−0.0884935	+	0.255685i	−0.980560	−	0.196219i	$-0.937134\pi$
$971$	−2.75753	+	7.96737i	−0.0884935	+	0.255685i	0.892067	+	0.451904i	$0.149255\pi$
$972$		0			0
$973$	−109.984	+	10.5022i	−3.52592	+	0.336685i
$974$		0			0
$975$	10.2422	−	17.7400i	0.328013	−	0.568136i
$976$		0			0
$977$	−29.1089	+	15.0067i	−0.931277	+	0.480107i	−0.855954	−	0.517053i	$-0.827029\pi$
$977$	−29.1089	+	15.0067i	−0.931277	+	0.480107i	−0.0753231	+	0.997159i	$0.523999\pi$
$978$		0			0
$979$	−16.0145	+	6.41126i	−0.511827	+	0.204905i
$980$		0			0
$981$	2.10665	−	14.6520i	0.0672600	−	0.467804i
$982$		0			0
$983$	−24.7931	+	54.2893i	−0.790777	+	1.73156i	−0.116364	+	0.993207i	$0.537124\pi$
$983$	−24.7931	+	54.2893i	−0.790777	+	1.73156i	−0.674413	+	0.738354i	$0.735603\pi$
$984$		0			0
$985$	2.79066	−	3.91893i	0.0889178	−	0.124868i
$986$		0			0
$987$	−48.5451	−	19.4345i	−1.54521	−	0.618608i
$988$		0			0
$989$	−2.36471	+	9.74745i	−0.0751933	+	0.309951i
$990$		0			0
$991$	−0.290673	−	2.02168i	−0.00923353	−	0.0642206i	0.984684	−	0.174350i	$-0.0557825\pi$
$991$	−0.290673	−	2.02168i	−0.00923353	−	0.0642206i	−0.993917	+	0.110130i	$0.964873\pi$
$992$		0			0
$993$	−8.93214	−	4.60484i	−0.283453	−	0.146130i
$994$		0			0
$995$	3.72258	+	5.22764i	0.118014	+	0.165727i
$996$		0			0
$997$	−25.0322	−	16.0872i	−0.792777	−	0.509487i	0.0804742	−	0.996757i	$-0.474357\pi$
$997$	−25.0322	−	16.0872i	−0.792777	−	0.509487i	−0.873252	+	0.487270i	$0.837993\pi$
$998$		0			0
$999$	2.34684	−	2.23771i	0.0742507	−	0.0707979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.793.4	yes	120
67.6	even	33	inner	804.2.y.b.73.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.73.4	✓	120	67.6	even	33	inner
804.2.y.b.793.4	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(1.03511 - 0.303934i) q^{5} +(-4.65735 - 0.897630i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(1.03511 - 0.303934i) q^{5} +(-4.65735 - 0.897630i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(3.37592 + 3.21894i) q^{11} +(-0.254078 - 5.33375i) q^{13} +(-0.706467 - 0.815306i) q^{15} +(-1.13889 - 0.895635i) q^{17} +(-5.02744 + 0.968959i) q^{19} +(1.11822 + 4.60936i) q^{21} +(-3.70948 - 0.354212i) q^{23} +(-3.22720 + 2.07400i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-5.06141 - 8.76662i) q^{29} +(-0.338612 + 7.10834i) q^{31} +(1.52564 - 4.40804i) q^{33} +(-5.09367 + 0.486386i) q^{35} +(1.62134 - 2.80824i) q^{37} +(-4.74620 + 2.44684i) q^{39} +(-7.90358 + 3.16412i) q^{41} +(0.383067 - 2.66429i) q^{43} +(-0.448152 + 0.981315i) q^{45} +(-6.39496 + 8.98046i) q^{47} +(14.3866 + 5.75951i) q^{49} +(-0.341585 + 1.40803i) q^{51} +(-0.818964 - 5.69602i) q^{53} +(4.47278 + 2.30588i) q^{55} +(2.96987 + 4.17060i) q^{57} +(2.12121 + 1.36322i) q^{59} +(-0.675562 + 0.644148i) q^{61} +(3.72830 - 2.93197i) q^{63} +(-1.88411 - 5.44377i) q^{65} +(-2.15690 + 7.89606i) q^{67} +(1.21877 + 3.52141i) q^{69} +(7.56521 - 5.94934i) q^{71} +(-1.07574 + 1.02572i) q^{73} +(3.22720 + 2.07400i) q^{75} +(-12.8334 - 18.0220i) q^{77} +(-7.75307 - 3.99699i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(4.07464 - 16.7959i) q^{83} +(-1.45109 - 0.580928i) q^{85} +(-5.87181 + 8.24581i) q^{87} +(-1.53625 + 3.36393i) q^{89} +(-3.60441 + 25.0692i) q^{91} +(6.60664 - 2.64490i) q^{93} +(-4.90943 + 2.53099i) q^{95} +(4.41371 - 7.64477i) q^{97} +(-4.64347 + 0.443397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 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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