LMFDB - Embedded newform 405.3.i.b.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(26,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	405.26
Dual form			405.3.i.b.296.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93649 - 1.11803i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.00000 - 5.19615i) q^{7} +6.70820i q^{8} +O(q^{10})$	\(q+(-1.93649 - 1.11803i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.00000 - 5.19615i) q^{7} +6.70820i q^{8} +5.00000 q^{10} +(3.87298 + 2.23607i) q^{11} +(-8.00000 - 13.8564i) q^{13} +(-11.6190 + 6.70820i) q^{14} +(9.50000 - 16.4545i) q^{16} -4.47214i q^{17} -2.00000 q^{19} +(-1.93649 - 1.11803i) q^{20} +(-5.00000 - 8.66025i) q^{22} +(-11.6190 + 6.70820i) q^{23} +(2.50000 - 4.33013i) q^{25} +35.7771i q^{26} +6.00000 q^{28} +(-27.1109 - 15.6525i) q^{29} +(9.00000 + 15.5885i) q^{31} +(-13.5554 + 7.82624i) q^{32} +(-5.00000 + 8.66025i) q^{34} +13.4164i q^{35} -16.0000 q^{37} +(3.87298 + 2.23607i) q^{38} +(-7.50000 - 12.9904i) q^{40} +(-54.2218 + 31.3050i) q^{41} +(-8.00000 + 13.8564i) q^{43} +4.47214i q^{44} +30.0000 q^{46} +(-42.6028 - 24.5967i) q^{47} +(6.50000 + 11.2583i) q^{49} +(-9.68246 + 5.59017i) q^{50} +(8.00000 - 13.8564i) q^{52} -4.47214i q^{53} -10.0000 q^{55} +(34.8569 + 20.1246i) q^{56} +(35.0000 + 60.6218i) q^{58} +(-3.87298 + 2.23607i) q^{59} +(-41.0000 + 71.0141i) q^{61} -40.2492i q^{62} -41.0000 q^{64} +(30.9839 + 17.8885i) q^{65} +(-12.0000 - 20.7846i) q^{67} +(3.87298 - 2.23607i) q^{68} +(15.0000 - 25.9808i) q^{70} +125.220i q^{71} -74.0000 q^{73} +(30.9839 + 17.8885i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(23.2379 - 13.4164i) q^{77} +(-69.0000 + 119.512i) q^{79} +42.4853i q^{80} +140.000 q^{82} +(-81.3327 - 46.9574i) q^{83} +(5.00000 + 8.66025i) q^{85} +(30.9839 - 17.8885i) q^{86} +(-15.0000 + 25.9808i) q^{88} -107.331i q^{89} -96.0000 q^{91} +(-11.6190 - 6.70820i) q^{92} +(55.0000 + 95.2628i) q^{94} +(3.87298 - 2.23607i) q^{95} +(83.0000 - 143.760i) q^{97} -29.0689i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 12 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 12 * q^7	$ 4 q + 2 q^{4} + 12 q^{7} + 20 q^{10} - 32 q^{13} + 38 q^{16} - 8 q^{19} - 20 q^{22} + 10 q^{25} + 24 q^{28} + 36 q^{31} - 20 q^{34} - 64 q^{37} - 30 q^{40} - 32 q^{43} + 120 q^{46} + 26 q^{49} + 32 q^{52} - 40 q^{55} + 140 q^{58} - 164 q^{61} - 164 q^{64} - 48 q^{67} + 60 q^{70} - 296 q^{73} - 4 q^{76} - 276 q^{79} + 560 q^{82} + 20 q^{85} - 60 q^{88} - 384 q^{91} + 220 q^{94} + 332 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 + 12 * q^7 + 20 * q^10 - 32 * q^13 + 38 * q^16 - 8 * q^19 - 20 * q^22 + 10 * q^25 + 24 * q^28 + 36 * q^31 - 20 * q^34 - 64 * q^37 - 30 * q^40 - 32 * q^43 + 120 * q^46 + 26 * q^49 + 32 * q^52 - 40 * q^55 + 140 * q^58 - 164 * q^61 - 164 * q^64 - 48 * q^67 + 60 * q^70 - 296 * q^73 - 4 * q^76 - 276 * q^79 + 560 * q^82 + 20 * q^85 - 60 * q^88 - 384 * q^91 + 220 * q^94 + 332 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.93649	−	1.11803i	−0.968246	−	0.559017i	−0.0695448	−	0.997579i	$-0.522155\pi$
$2$	−1.93649	−	1.11803i	−0.968246	−	0.559017i	−0.898701	+	0.438562i	$0.855488\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.125000	+	0.216506i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	3.00000	−	5.19615i	0.428571	−	0.742307i	−0.568175	−	0.822908i	$-0.692350\pi$
$7$	3.00000	−	5.19615i	0.428571	−	0.742307i	0.996747	+	0.0806002i	$0.0256837\pi$
$8$			6.70820i			0.838525i
$9$		0			0
$10$	5.00000			0.500000
$11$	3.87298	+	2.23607i	0.352089	+	0.203279i	0.665605	−	0.746304i	$-0.268174\pi$
$11$	3.87298	+	2.23607i	0.352089	+	0.203279i	−0.313516	+	0.949583i	$0.601507\pi$
$12$		0			0
$13$	−8.00000	−	13.8564i	−0.615385	−	1.06588i	−0.990317	−	0.138825i	$-0.955667\pi$
$13$	−8.00000	−	13.8564i	−0.615385	−	1.06588i	0.374932	−	0.927052i	$-0.377666\pi$
$14$	−11.6190	+	6.70820i	−0.829925	+	0.479157i
$15$		0			0
$16$	9.50000	−	16.4545i	0.593750	−	1.02841i
$17$		−	4.47214i		−	0.263067i	−0.991312	−	0.131533i	$-0.958010\pi$
$17$		−	4.47214i		−	0.263067i	0.991312	−	0.131533i	$-0.0419901\pi$
$18$		0			0
$19$	−2.00000			−0.105263			−0.0526316	−	0.998614i	$-0.516761\pi$
$19$	−2.00000			−0.105263			−0.0526316	+	0.998614i	$0.516761\pi$
$20$	−1.93649	−	1.11803i	−0.0968246	−	0.0559017i
$21$		0			0
$22$	−5.00000	−	8.66025i	−0.227273	−	0.393648i
$23$	−11.6190	+	6.70820i	−0.505172	+	0.291661i	−0.730847	−	0.682542i	$-0.760875\pi$
$23$	−11.6190	+	6.70820i	−0.505172	+	0.291661i	0.225675	+	0.974203i	$0.427541\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$			35.7771i			1.37604i
$27$		0			0
$28$	6.00000			0.214286
$29$	−27.1109	−	15.6525i	−0.934858	−	0.539741i	−0.0465133	−	0.998918i	$-0.514811\pi$
$29$	−27.1109	−	15.6525i	−0.934858	−	0.539741i	−0.888345	+	0.459177i	$0.848144\pi$
$30$		0			0
$31$	9.00000	+	15.5885i	0.290323	+	0.502853i	0.973886	−	0.227038i	$-0.0729041\pi$
$31$	9.00000	+	15.5885i	0.290323	+	0.502853i	−0.683563	+	0.729891i	$0.739571\pi$
$32$	−13.5554	+	7.82624i	−0.423608	+	0.244570i
$33$		0			0
$34$	−5.00000	+	8.66025i	−0.147059	+	0.254713i
$35$			13.4164i			0.383326i
$36$		0			0
$37$	−16.0000			−0.432432			−0.216216	−	0.976346i	$-0.569372\pi$
$37$	−16.0000			−0.432432			−0.216216	+	0.976346i	$0.569372\pi$
$38$	3.87298	+	2.23607i	0.101921	+	0.0588439i
$39$		0			0
$40$	−7.50000	−	12.9904i	−0.187500	−	0.324760i
$41$	−54.2218	+	31.3050i	−1.32248	+	0.763535i	−0.984124	−	0.177482i	$-0.943205\pi$
$41$	−54.2218	+	31.3050i	−1.32248	+	0.763535i	−0.338358	+	0.941017i	$0.609872\pi$
$42$		0			0
$43$	−8.00000	+	13.8564i	−0.186047	+	0.322242i	−0.943929	−	0.330149i	$-0.892901\pi$
$43$	−8.00000	+	13.8564i	−0.186047	+	0.322242i	0.757882	+	0.652391i	$0.226234\pi$
$44$			4.47214i			0.101639i
$45$		0			0
$46$	30.0000			0.652174
$47$	−42.6028	−	24.5967i	−0.906443	−	0.523335i	−0.0271580	−	0.999631i	$-0.508646\pi$
$47$	−42.6028	−	24.5967i	−0.906443	−	0.523335i	−0.879285	+	0.476296i	$0.841979\pi$
$48$		0			0
$49$	6.50000	+	11.2583i	0.132653	+	0.229762i
$50$	−9.68246	+	5.59017i	−0.193649	+	0.111803i
$51$		0			0
$52$	8.00000	−	13.8564i	0.153846	−	0.266469i
$53$		−	4.47214i		−	0.0843799i	−0.999110	−	0.0421900i	$-0.986567\pi$
$53$		−	4.47214i		−	0.0843799i	0.999110	−	0.0421900i	$-0.0134335\pi$
$54$		0			0
$55$	−10.0000			−0.181818
$56$	34.8569	+	20.1246i	0.622444	+	0.359368i
$57$		0			0
$58$	35.0000	+	60.6218i	0.603448	+	1.04520i
$59$	−3.87298	+	2.23607i	−0.0656438	+	0.0378995i	−0.532463	−	0.846453i	$-0.678733\pi$
$59$	−3.87298	+	2.23607i	−0.0656438	+	0.0378995i	0.466819	+	0.884353i	$0.345400\pi$
$60$		0			0
$61$	−41.0000	+	71.0141i	−0.672131	+	1.16417i	0.305167	+	0.952299i	$0.401288\pi$
$61$	−41.0000	+	71.0141i	−0.672131	+	1.16417i	−0.977299	+	0.211867i	$0.932046\pi$
$62$		−	40.2492i		−	0.649181i
$63$		0			0
$64$	−41.0000			−0.640625
$65$	30.9839	+	17.8885i	0.476675	+	0.275208i
$66$		0			0
$67$	−12.0000	−	20.7846i	−0.179104	−	0.310218i	0.762470	−	0.647024i	$-0.223987\pi$
$67$	−12.0000	−	20.7846i	−0.179104	−	0.310218i	−0.941574	+	0.336806i	$0.890653\pi$
$68$	3.87298	−	2.23607i	0.0569556	−	0.0328834i
$69$		0			0
$70$	15.0000	−	25.9808i	0.214286	−	0.371154i
$71$			125.220i			1.76366i	0.471568	+	0.881830i	$0.343688\pi$
$71$			125.220i			1.76366i	−0.471568	+	0.881830i	$0.656312\pi$
$72$		0			0
$73$	−74.0000			−1.01370			−0.506849	−	0.862035i	$-0.669190\pi$
$73$	−74.0000			−1.01370			−0.506849	+	0.862035i	$0.669190\pi$
$74$	30.9839	+	17.8885i	0.418701	+	0.241737i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.0131579	−	0.0227901i
$77$	23.2379	−	13.4164i	0.301791	−	0.174239i
$78$		0			0
$79$	−69.0000	+	119.512i	−0.873418	+	1.51280i	−0.0149790	+	0.999888i	$0.504768\pi$
$79$	−69.0000	+	119.512i	−0.873418	+	1.51280i	−0.858439	+	0.512916i	$0.828565\pi$
$80$			42.4853i			0.531066i
$81$		0			0
$82$	140.000			1.70732
$83$	−81.3327	−	46.9574i	−0.979911	−	0.565752i	−0.0776680	−	0.996979i	$-0.524747\pi$
$83$	−81.3327	−	46.9574i	−0.979911	−	0.565752i	−0.902243	+	0.431227i	$0.858081\pi$
$84$		0			0
$85$	5.00000	+	8.66025i	0.0588235	+	0.101885i
$86$	30.9839	−	17.8885i	0.360278	−	0.208006i
$87$		0			0
$88$	−15.0000	+	25.9808i	−0.170455	+	0.295236i
$89$		−	107.331i		−	1.20597i	−0.797753	−	0.602985i	$-0.793978\pi$
$89$		−	107.331i		−	1.20597i	0.797753	−	0.602985i	$-0.206022\pi$
$90$		0			0
$91$	−96.0000			−1.05495
$92$	−11.6190	−	6.70820i	−0.126293	−	0.0729153i
$93$		0			0
$94$	55.0000	+	95.2628i	0.585106	+	1.01343i
$95$	3.87298	−	2.23607i	0.0407682	−	0.0235376i
$96$		0			0
$97$	83.0000	−	143.760i	0.855670	−	1.48206i	−0.0203519	−	0.999793i	$-0.506479\pi$
$97$	83.0000	−	143.760i	0.855670	−	1.48206i	0.876022	−	0.482271i	$-0.160188\pi$
$98$		−	29.0689i		−	0.296621i
$99$		0			0
$100$	5.00000			0.0500000
$101$	58.0948	+	33.5410i	0.575196	+	0.332089i	0.759222	−	0.650832i	$-0.225580\pi$
$101$	58.0948	+	33.5410i	0.575196	+	0.332089i	−0.184026	+	0.982921i	$0.558913\pi$
$102$		0			0
$103$	−13.0000	−	22.5167i	−0.126214	−	0.218608i	0.795993	−	0.605306i	$-0.206949\pi$
$103$	−13.0000	−	22.5167i	−0.126214	−	0.218608i	−0.922207	+	0.386697i	$0.873616\pi$
$104$	92.9516	−	53.6656i	0.893765	−	0.516016i
$105$		0			0
$106$	−5.00000	+	8.66025i	−0.0471698	+	0.0817005i
$107$		−	201.246i		−	1.88080i	−0.340064	−	0.940402i	$-0.610449\pi$
$107$		−	201.246i		−	1.88080i	0.340064	−	0.940402i	$-0.389551\pi$
$108$		0			0
$109$	38.0000			0.348624			0.174312	−	0.984690i	$-0.444230\pi$
$109$	38.0000			0.348624			0.174312	+	0.984690i	$0.444230\pi$
$110$	19.3649	+	11.1803i	0.176045	+	0.101639i
$111$		0			0
$112$	−57.0000	−	98.7269i	−0.508929	−	0.881490i
$113$	−27.1109	+	15.6525i	−0.239919	+	0.138517i	−0.615140	−	0.788418i	$-0.710900\pi$
$113$	−27.1109	+	15.6525i	−0.239919	+	0.138517i	0.375220	+	0.926936i	$0.377567\pi$
$114$		0			0
$115$	15.0000	−	25.9808i	0.130435	−	0.225920i
$116$		−	31.3050i		−	0.269870i
$117$		0			0
$118$	10.0000			0.0847458
$119$	−23.2379	−	13.4164i	−0.195276	−	0.112743i
$120$		0			0
$121$	−50.5000	−	87.4686i	−0.417355	−	0.722881i
$122$	158.792	−	91.6788i	1.30158	−	0.751465i
$123$		0			0
$124$	−9.00000	+	15.5885i	−0.0725806	+	0.125713i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−26.0000			−0.204724			−0.102362	−	0.994747i	$-0.532640\pi$
$127$	−26.0000			−0.204724			−0.102362	+	0.994747i	$0.532640\pi$
$128$	133.618	+	77.1443i	1.04389	+	0.602690i
$129$		0			0
$130$	−40.0000	−	69.2820i	−0.307692	−	0.532939i
$131$	−11.6190	+	6.70820i	−0.0886943	+	0.0512077i	−0.543691	−	0.839285i	$-0.682974\pi$
$131$	−11.6190	+	6.70820i	−0.0886943	+	0.0512077i	0.454997	+	0.890493i	$0.349640\pi$
$132$		0			0
$133$	−6.00000	+	10.3923i	−0.0451128	+	0.0781376i
$134$			53.6656i			0.400490i
$135$		0			0
$136$	30.0000			0.220588
$137$	−104.571	−	60.3738i	−0.763289	−	0.440685i	0.0671866	−	0.997740i	$-0.478598\pi$
$137$	−104.571	−	60.3738i	−0.763289	−	0.440685i	−0.830475	+	0.557055i	$0.811931\pi$
$138$		0			0
$139$	41.0000	+	71.0141i	0.294964	+	0.510893i	0.974977	−	0.222308i	$-0.0713590\pi$
$139$	41.0000	+	71.0141i	0.294964	+	0.510893i	−0.680012	+	0.733201i	$0.738026\pi$
$140$	−11.6190	+	6.70820i	−0.0829925	+	0.0479157i
$141$		0			0
$142$	140.000	−	242.487i	0.985915	−	1.70766i
$143$		−	71.5542i		−	0.500379i
$144$		0			0
$145$	70.0000			0.482759
$146$	143.300	+	82.7345i	0.981509	+	0.566675i
$147$		0			0
$148$	−8.00000	−	13.8564i	−0.0540541	−	0.0936244i
$149$	96.8246	−	55.9017i	0.649829	−	0.375179i	−0.138561	−	0.990354i	$-0.544248\pi$
$149$	96.8246	−	55.9017i	0.649829	−	0.375179i	0.788391	+	0.615175i	$0.210915\pi$
$150$		0			0
$151$	79.0000	−	136.832i	0.523179	−	0.906172i	−0.476457	−	0.879198i	$-0.658079\pi$
$151$	79.0000	−	136.832i	0.523179	−	0.906172i	0.999636	−	0.0269747i	$-0.00858735\pi$
$152$		−	13.4164i		−	0.0882658i
$153$		0			0
$154$	−60.0000			−0.389610
$155$	−34.8569	−	20.1246i	−0.224883	−	0.129836i
$156$		0			0
$157$	−82.0000	−	142.028i	−0.522293	−	0.904638i	−0.999664	−	0.0259359i	$-0.991743\pi$
$157$	−82.0000	−	142.028i	−0.522293	−	0.904638i	0.477371	−	0.878702i	$-0.341590\pi$
$158$	267.236	−	154.289i	1.69137	−	0.976511i
$159$		0			0
$160$	17.5000	−	30.3109i	0.109375	−	0.189443i
$161$			80.4984i			0.499990i
$162$		0			0
$163$	236.000			1.44785			0.723926	−	0.689877i	$-0.242336\pi$
$163$	236.000			1.44785			0.723926	+	0.689877i	$0.242336\pi$
$164$	−54.2218	−	31.3050i	−0.330621	−	0.190884i
$165$		0			0
$166$	105.000	+	181.865i	0.632530	+	1.09557i
$167$	−81.3327	+	46.9574i	−0.487022	+	0.281182i	−0.723338	−	0.690494i	$-0.757393\pi$
$167$	−81.3327	+	46.9574i	−0.487022	+	0.281182i	0.236316	+	0.971676i	$0.424060\pi$
$168$		0			0
$169$	−43.5000	+	75.3442i	−0.257396	+	0.445824i
$170$		−	22.3607i		−	0.131533i
$171$		0			0
$172$	−16.0000			−0.0930233
$173$	11.6190	+	6.70820i	0.0671616	+	0.0387757i	0.533205	−	0.845986i	$-0.320988\pi$
$173$	11.6190	+	6.70820i	0.0671616	+	0.0387757i	−0.466043	+	0.884762i	$0.654321\pi$
$174$		0			0
$175$	−15.0000	−	25.9808i	−0.0857143	−	0.148461i
$176$	73.5867	−	42.4853i	0.418106	−	0.241394i
$177$		0			0
$178$	−120.000	+	207.846i	−0.674157	+	1.16767i
$179$		−	192.302i		−	1.07431i	−0.843483	−	0.537156i	$-0.819499\pi$
$179$		−	192.302i		−	1.07431i	0.843483	−	0.537156i	$-0.180501\pi$
$180$		0			0
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$	185.903	+	107.331i	1.02145	+	0.589732i
$183$		0			0
$184$	−45.0000	−	77.9423i	−0.244565	−	0.423599i
$185$	30.9839	−	17.8885i	0.167480	−	0.0966948i
$186$		0			0
$187$	10.0000	−	17.3205i	0.0534759	−	0.0926230i
$188$		−	49.1935i		−	0.261668i
$189$		0			0
$190$	−10.0000			−0.0526316
$191$	−178.157	−	102.859i	−0.932760	−	0.538529i	−0.0450769	−	0.998984i	$-0.514353\pi$
$191$	−178.157	−	102.859i	−0.932760	−	0.538529i	−0.887684	+	0.460454i	$0.847687\pi$
$192$		0			0
$193$	107.000	+	185.329i	0.554404	+	0.960256i	0.997950	+	0.0640043i	$0.0203871\pi$
$193$	107.000	+	185.329i	0.554404	+	0.960256i	−0.443545	+	0.896252i	$0.646280\pi$
$194$	−321.458	+	185.594i	−1.65700	+	0.956668i
$195$		0			0
$196$	−6.50000	+	11.2583i	−0.0331633	+	0.0574405i
$197$			93.9149i			0.476725i	0.971176	+	0.238363i	$0.0766107\pi$
$197$			93.9149i			0.476725i	−0.971176	+	0.238363i	$0.923389\pi$
$198$		0			0
$199$	−242.000			−1.21608			−0.608040	−	0.793906i	$-0.708044\pi$
$199$	−242.000			−1.21608			−0.608040	+	0.793906i	$0.708044\pi$
$200$	29.0474	+	16.7705i	0.145237	+	0.0838525i
$201$		0			0
$202$	−75.0000	−	129.904i	−0.371287	−	0.643088i
$203$	−162.665	+	93.9149i	−0.801307	+	0.462635i
$204$		0			0
$205$	70.0000	−	121.244i	0.341463	−	0.591432i
$206$			58.1378i			0.282222i
$207$		0			0
$208$	−304.000			−1.46154
$209$	−7.74597	−	4.47214i	−0.0370620	−	0.0213978i
$210$		0			0
$211$	−1.00000	−	1.73205i	−0.00473934	−	0.00820877i	0.863646	−	0.504099i	$-0.168175\pi$
$211$	−1.00000	−	1.73205i	−0.00473934	−	0.00820877i	−0.868385	+	0.495890i	$0.834842\pi$
$212$	3.87298	−	2.23607i	0.0182688	−	0.0105475i
$213$		0			0
$214$	−225.000	+	389.711i	−1.05140	+	1.82108i
$215$		−	35.7771i		−	0.166405i
$216$		0			0
$217$	108.000			0.497696
$218$	−73.5867	−	42.4853i	−0.337554	−	0.194887i
$219$		0			0
$220$	−5.00000	−	8.66025i	−0.0227273	−	0.0393648i
$221$	−61.9677	+	35.7771i	−0.280397	+	0.161887i
$222$		0			0
$223$	−43.0000	+	74.4782i	−0.192825	+	0.333983i	−0.946185	−	0.323625i	$-0.895098\pi$
$223$	−43.0000	+	74.4782i	−0.192825	+	0.333983i	0.753360	+	0.657608i	$0.228432\pi$
$224$			93.9149i			0.419263i
$225$		0			0
$226$	70.0000			0.309735
$227$	−50.3488	−	29.0689i	−0.221801	−	0.128057i	0.384983	−	0.922924i	$-0.374207\pi$
$227$	−50.3488	−	29.0689i	−0.221801	−	0.128057i	−0.606784	+	0.794867i	$0.707541\pi$
$228$		0			0
$229$	141.000	+	244.219i	0.615721	+	1.06646i	0.990258	+	0.139247i	$0.0444683\pi$
$229$	141.000	+	244.219i	0.615721	+	1.06646i	−0.374537	+	0.927212i	$0.622198\pi$
$230$	−58.0948	+	33.5410i	−0.252586	+	0.145831i
$231$		0			0
$232$	105.000	−	181.865i	0.452586	−	0.783902i
$233$			362.243i			1.55469i	0.629074	+	0.777346i	$0.283434\pi$
$233$			362.243i			1.55469i	−0.629074	+	0.777346i	$0.716566\pi$
$234$		0			0
$235$	110.000			0.468085
$236$	−3.87298	−	2.23607i	−0.0164109	−	0.00947486i
$237$		0			0
$238$	30.0000	+	51.9615i	0.126050	+	0.218326i
$239$	216.887	−	125.220i	0.907477	−	0.523932i	0.0278587	−	0.999612i	$-0.491131\pi$
$239$	216.887	−	125.220i	0.907477	−	0.523932i	0.879619	+	0.475680i	$0.157798\pi$
$240$		0			0
$241$	−131.000	+	226.899i	−0.543568	+	0.941488i	0.455127	+	0.890427i	$0.349594\pi$
$241$	−131.000	+	226.899i	−0.543568	+	0.941488i	−0.998696	+	0.0510617i	$0.983739\pi$
$242$			225.843i			0.933235i
$243$		0			0
$244$	−82.0000			−0.336066
$245$	−25.1744	−	14.5344i	−0.102753	−	0.0593243i
$246$		0			0
$247$	16.0000	+	27.7128i	0.0647773	+	0.112198i
$248$	−104.571	+	60.3738i	−0.421655	+	0.243443i
$249$		0			0
$250$	12.5000	−	21.6506i	0.0500000	−	0.0866025i
$251$		−	469.574i		−	1.87081i	−0.353573	−	0.935407i	$-0.615033\pi$
$251$		−	469.574i		−	1.87081i	0.353573	−	0.935407i	$-0.384967\pi$
$252$		0			0
$253$	−60.0000			−0.237154
$254$	50.3488	+	29.0689i	0.198224	+	0.114444i
$255$		0			0
$256$	−90.5000	−	156.751i	−0.353516	−	0.612307i
$257$	−174.284	+	100.623i	−0.678149	+	0.391529i	−0.799157	−	0.601122i	$-0.794721\pi$
$257$	−174.284	+	100.623i	−0.678149	+	0.391529i	0.121008	+	0.992651i	$0.461387\pi$
$258$		0			0
$259$	−48.0000	+	83.1384i	−0.185328	+	0.320998i
$260$			35.7771i			0.137604i
$261$		0			0
$262$	30.0000			0.114504
$263$	−50.3488	−	29.0689i	−0.191440	−	0.110528i	0.401216	−	0.915983i	$-0.368588\pi$
$263$	−50.3488	−	29.0689i	−0.191440	−	0.110528i	−0.592657	+	0.805455i	$0.701921\pi$
$264$		0			0
$265$	5.00000	+	8.66025i	0.0188679	+	0.0326802i
$266$	23.2379	−	13.4164i	0.0873605	−	0.0504376i
$267$		0			0
$268$	12.0000	−	20.7846i	0.0447761	−	0.0775545i
$269$			371.187i			1.37988i	0.723867	+	0.689939i	$0.242363\pi$
$269$			371.187i			1.37988i	−0.723867	+	0.689939i	$0.757637\pi$
$270$		0			0
$271$	82.0000			0.302583			0.151292	−	0.988489i	$-0.451657\pi$
$271$	82.0000			0.302583			0.151292	+	0.988489i	$0.451657\pi$
$272$	−73.5867	−	42.4853i	−0.270539	−	0.156196i
$273$		0			0
$274$	135.000	+	233.827i	0.492701	+	0.853383i
$275$	19.3649	−	11.1803i	0.0704179	−	0.0406558i
$276$		0			0
$277$	−12.0000	+	20.7846i	−0.0433213	+	0.0750347i	−0.886873	−	0.462013i	$-0.847127\pi$
$277$	−12.0000	+	20.7846i	−0.0433213	+	0.0750347i	0.843552	+	0.537048i	$0.180461\pi$
$278$		−	183.358i		−	0.659560i
$279$		0			0
$280$	−90.0000			−0.321429
$281$	−162.665	−	93.9149i	−0.578880	−	0.334217i	0.181808	−	0.983334i	$-0.441805\pi$
$281$	−162.665	−	93.9149i	−0.578880	−	0.334217i	−0.760688	+	0.649117i	$0.775138\pi$
$282$		0			0
$283$	72.0000	+	124.708i	0.254417	+	0.440663i	0.964737	−	0.263216i	$-0.0847831\pi$
$283$	72.0000	+	124.708i	0.254417	+	0.440663i	−0.710320	+	0.703879i	$0.751450\pi$
$284$	−108.444	+	62.6099i	−0.381843	+	0.220457i
$285$		0			0
$286$	−80.0000	+	138.564i	−0.279720	+	0.484490i
$287$			375.659i			1.30892i
$288$		0			0
$289$	269.000			0.930796
$290$	−135.554	−	78.2624i	−0.467429	−	0.269870i
$291$		0			0
$292$	−37.0000	−	64.0859i	−0.126712	−	0.219472i
$293$	−406.663	+	234.787i	−1.38793	+	0.801321i	−0.993082	−	0.117425i	$-0.962536\pi$
$293$	−406.663	+	234.787i	−1.38793	+	0.801321i	−0.394847	+	0.918747i	$0.629203\pi$
$294$		0			0
$295$	5.00000	−	8.66025i	0.0169492	−	0.0293568i
$296$		−	107.331i		−	0.362606i
$297$		0			0
$298$	−250.000			−0.838926
$299$	185.903	+	107.331i	0.621750	+	0.358967i
$300$		0			0
$301$	48.0000	+	83.1384i	0.159468	+	0.276207i
$302$	−305.966	+	176.649i	−1.01313	+	0.584932i
$303$		0			0
$304$	−19.0000	+	32.9090i	−0.0625000	+	0.108253i
$305$		−	183.358i		−	0.601172i
$306$		0			0
$307$	184.000			0.599349			0.299674	−	0.954042i	$-0.403122\pi$
$307$	184.000			0.599349			0.299674	+	0.954042i	$0.403122\pi$
$308$	23.2379	+	13.4164i	0.0754477	+	0.0435598i
$309$		0			0
$310$	45.0000	+	77.9423i	0.145161	+	0.251427i
$311$	−139.427	+	80.4984i	−0.448320	+	0.258837i	−0.707120	−	0.707093i	$-0.750006\pi$
$311$	−139.427	+	80.4984i	−0.448320	+	0.258837i	0.258801	+	0.965931i	$0.416673\pi$
$312$		0			0
$313$	197.000	−	341.214i	0.629393	−	1.09014i	−0.358281	−	0.933614i	$-0.616637\pi$
$313$	197.000	−	341.214i	0.629393	−	1.09014i	0.987674	−	0.156527i	$-0.0500297\pi$
$314$			366.715i			1.16788i
$315$		0			0
$316$	−138.000			−0.436709
$317$	391.171	+	225.843i	1.23398	+	0.712438i	0.967857	−	0.251501i	$-0.0809243\pi$
$317$	391.171	+	225.843i	1.23398	+	0.712438i	0.266122	+	0.963939i	$0.414258\pi$
$318$		0			0
$319$	−70.0000	−	121.244i	−0.219436	−	0.380074i
$320$	79.3962	−	45.8394i	0.248113	−	0.143248i
$321$		0			0
$322$	90.0000	−	155.885i	0.279503	−	0.484114i
$323$			8.94427i			0.0276912i
$324$		0			0
$325$	−80.0000			−0.246154
$326$	−457.012	−	263.856i	−1.40188	−	0.809374i
$327$		0			0
$328$	−210.000	−	363.731i	−0.640244	−	1.10893i
$329$	−255.617	+	147.580i	−0.776951	+	0.448573i
$330$		0			0
$331$	99.0000	−	171.473i	0.299094	−	0.518045i	−0.676835	−	0.736135i	$-0.736649\pi$
$331$	99.0000	−	171.473i	0.299094	−	0.518045i	0.975929	+	0.218089i	$0.0699824\pi$
$332$		−	93.9149i		−	0.282876i
$333$		0			0
$334$	210.000			0.628743
$335$	46.4758	+	26.8328i	0.138734	+	0.0800980i
$336$		0			0
$337$	−197.000	−	341.214i	−0.584570	−	1.01250i	−0.994929	−	0.100581i	$-0.967930\pi$
$337$	−197.000	−	341.214i	−0.584570	−	1.01250i	0.410359	−	0.911924i	$-0.365403\pi$
$338$	168.475	−	97.2690i	0.498446	−	0.287778i
$339$		0			0
$340$	−5.00000	+	8.66025i	−0.0147059	+	0.0254713i
$341$			80.4984i			0.236066i
$342$		0			0
$343$	372.000			1.08455
$344$	−92.9516	−	53.6656i	−0.270208	−	0.156005i
$345$		0			0
$346$	−15.0000	−	25.9808i	−0.0433526	−	0.0750889i
$347$	158.792	−	91.6788i	0.457615	−	0.264204i	−0.253426	−	0.967355i	$-0.581557\pi$
$347$	158.792	−	91.6788i	0.457615	−	0.264204i	0.711041	+	0.703151i	$0.248224\pi$
$348$		0			0
$349$	181.000	−	313.501i	0.518625	−	0.898284i	−0.481141	−	0.876643i	$-0.659778\pi$
$349$	181.000	−	313.501i	0.518625	−	0.898284i	0.999766	−	0.0216411i	$-0.00688911\pi$
$350$			67.0820i			0.191663i
$351$		0			0
$352$	−70.0000			−0.198864
$353$	−267.236	−	154.289i	−0.757042	−	0.437078i	0.0711907	−	0.997463i	$-0.477320\pi$
$353$	−267.236	−	154.289i	−0.757042	−	0.437078i	−0.828233	+	0.560384i	$0.810653\pi$
$354$		0			0
$355$	−140.000	−	242.487i	−0.394366	−	0.683062i
$356$	92.9516	−	53.6656i	0.261100	−	0.150746i
$357$		0			0
$358$	−215.000	+	372.391i	−0.600559	+	1.04020i
$359$		−	295.161i		−	0.822175i	−0.911596	−	0.411088i	$-0.865149\pi$
$359$		−	295.161i		−	0.822175i	0.911596	−	0.411088i	$-0.134851\pi$
$360$		0			0
$361$	−357.000			−0.988920
$362$	−3.87298	−	2.23607i	−0.0106988	−	0.00617698i
$363$		0			0
$364$	−48.0000	−	83.1384i	−0.131868	−	0.228402i
$365$	143.300	−	82.7345i	0.392604	−	0.226670i
$366$		0			0
$367$	93.0000	−	161.081i	0.253406	−	0.438912i	−0.711055	−	0.703136i	$-0.751782\pi$
$367$	93.0000	−	161.081i	0.253406	−	0.438912i	0.964461	+	0.264224i	$0.0851158\pi$
$368$			254.912i			0.692695i
$369$		0			0
$370$	−80.0000			−0.216216
$371$	−23.2379	−	13.4164i	−0.0626358	−	0.0361628i
$372$		0			0
$373$	22.0000	+	38.1051i	0.0589812	+	0.102158i	0.894008	−	0.448050i	$-0.147881\pi$
$373$	22.0000	+	38.1051i	0.0589812	+	0.102158i	−0.835027	+	0.550209i	$0.814548\pi$
$374$	−38.7298	+	22.3607i	−0.103556	+	0.0597879i
$375$		0			0
$376$	165.000	−	285.788i	0.438830	−	0.760075i
$377$			500.879i			1.32859i
$378$		0			0
$379$	−362.000			−0.955145			−0.477573	−	0.878592i	$-0.658483\pi$
$379$	−362.000			−0.955145			−0.477573	+	0.878592i	$0.658483\pi$
$380$	3.87298	+	2.23607i	0.0101921	+	0.00588439i
$381$		0			0
$382$	230.000	+	398.372i	0.602094	+	1.04286i
$383$	313.712	−	181.122i	0.819090	−	0.472902i	−0.0310123	−	0.999519i	$-0.509873\pi$
$383$	313.712	−	181.122i	0.819090	−	0.472902i	0.850103	+	0.526617i	$0.176540\pi$
$384$		0			0
$385$	−30.0000	+	51.9615i	−0.0779221	+	0.134965i
$386$		−	478.519i		−	1.23969i
$387$		0			0
$388$	166.000			0.427835
$389$	383.425	+	221.371i	0.985669	+	0.569076i	0.903977	−	0.427581i	$-0.140634\pi$
$389$	383.425	+	221.371i	0.985669	+	0.569076i	0.0816923	+	0.996658i	$0.473968\pi$
$390$		0			0
$391$	30.0000	+	51.9615i	0.0767263	+	0.132894i
$392$	−75.5232	+	43.6033i	−0.192661	+	0.111233i
$393$		0			0
$394$	105.000	−	181.865i	0.266497	−	0.461587i
$395$		−	308.577i		−	0.781209i
$396$		0			0
$397$	124.000			0.312343			0.156171	−	0.987730i	$-0.450085\pi$
$397$	124.000			0.312343			0.156171	+	0.987730i	$0.450085\pi$
$398$	468.631	+	270.564i	1.17746	+	0.679810i
$399$		0			0
$400$	−47.5000	−	82.2724i	−0.118750	−	0.205681i
$401$	232.379	−	134.164i	0.579499	−	0.334574i	−0.181435	−	0.983403i	$-0.558074\pi$
$401$	232.379	−	134.164i	0.579499	−	0.334574i	0.760934	+	0.648829i	$0.224741\pi$
$402$		0			0
$403$	144.000	−	249.415i	0.357320	−	0.618897i
$404$			67.0820i			0.166045i
$405$		0			0
$406$	420.000			1.03448
$407$	−61.9677	−	35.7771i	−0.152255	−	0.0879044i
$408$		0			0
$409$	−229.000	−	396.640i	−0.559902	−	0.969779i	−0.997504	−	0.0706102i	$-0.977505\pi$
$409$	−229.000	−	396.640i	−0.559902	−	0.969779i	0.437602	−	0.899169i	$-0.355828\pi$
$410$	−271.109	+	156.525i	−0.661241	+	0.381768i
$411$		0			0
$412$	13.0000	−	22.5167i	0.0315534	−	0.0546521i
$413$			26.8328i			0.0649705i
$414$		0			0
$415$	210.000			0.506024
$416$	216.887	+	125.220i	0.521363	+	0.301009i
$417$		0			0
$418$	10.0000	+	17.3205i	0.0239234	+	0.0414366i
$419$	515.107	−	297.397i	1.22937	−	0.709778i	0.262473	−	0.964939i	$-0.415462\pi$
$419$	515.107	−	297.397i	1.22937	−	0.709778i	0.966899	+	0.255161i	$0.0821285\pi$
$420$		0			0
$421$	−281.000	+	486.706i	−0.667458	+	1.15607i	0.311154	+	0.950359i	$0.399284\pi$
$421$	−281.000	+	486.706i	−0.667458	+	1.15607i	−0.978612	+	0.205712i	$0.934049\pi$
$422$			4.47214i			0.0105975i
$423$		0			0
$424$	30.0000			0.0707547
$425$	−19.3649	−	11.1803i	−0.0455645	−	0.0263067i
$426$		0			0
$427$	246.000	+	426.084i	0.576112	+	0.997856i
$428$	174.284	−	100.623i	0.407206	−	0.235101i
$429$		0			0
$430$	−40.0000	+	69.2820i	−0.0930233	+	0.161121i
$431$		−	348.827i		−	0.809342i	−0.914462	−	0.404671i	$-0.867386\pi$
$431$		−	348.827i		−	0.809342i	0.914462	−	0.404671i	$-0.132614\pi$
$432$		0			0
$433$	226.000			0.521940			0.260970	−	0.965347i	$-0.415958\pi$
$433$	226.000			0.521940			0.260970	+	0.965347i	$0.415958\pi$
$434$	−209.141	−	120.748i	−0.481892	−	0.278220i
$435$		0			0
$436$	19.0000	+	32.9090i	0.0435780	+	0.0754793i
$437$	23.2379	−	13.4164i	0.0531760	−	0.0307012i
$438$		0			0
$439$	1.00000	−	1.73205i	0.00227790	−	0.00394545i	−0.864884	−	0.501971i	$-0.832608\pi$
$439$	1.00000	−	1.73205i	0.00227790	−	0.00394545i	0.867162	+	0.498026i	$0.165942\pi$
$440$		−	67.0820i		−	0.152459i
$441$		0			0
$442$	160.000			0.361991
$443$	174.284	+	100.623i	0.393418	+	0.227140i	0.683640	−	0.729819i	$-0.260396\pi$
$443$	174.284	+	100.623i	0.393418	+	0.227140i	−0.290222	+	0.956959i	$0.593729\pi$
$444$		0			0
$445$	120.000	+	207.846i	0.269663	+	0.467070i
$446$	166.538	−	96.1509i	0.373404	−	0.215585i
$447$		0			0
$448$	−123.000	+	213.042i	−0.274554	+	0.475541i
$449$		−	313.050i		−	0.697215i	−0.937269	−	0.348607i	$-0.886655\pi$
$449$		−	313.050i		−	0.697215i	0.937269	−	0.348607i	$-0.113345\pi$
$450$		0			0
$451$	−280.000			−0.620843
$452$	−27.1109	−	15.6525i	−0.0599798	−	0.0346294i
$453$		0			0
$454$	65.0000	+	112.583i	0.143172	+	0.247981i
$455$	185.903	−	107.331i	0.408578	−	0.235893i
$456$		0			0
$457$	−167.000	+	289.252i	−0.365427	+	0.632938i	−0.988845	−	0.148951i	$-0.952410\pi$
$457$	−167.000	+	289.252i	−0.365427	+	0.632938i	0.623418	+	0.781889i	$0.285744\pi$
$458$		−	630.571i		−	1.37679i
$459$		0			0
$460$	30.0000			0.0652174
$461$	81.3327	+	46.9574i	0.176427	+	0.101860i	0.585613	−	0.810591i	$-0.300854\pi$
$461$	81.3327	+	46.9574i	0.176427	+	0.101860i	−0.409186	+	0.912451i	$0.634187\pi$
$462$		0			0
$463$	−183.000	−	316.965i	−0.395248	−	0.684590i	0.597884	−	0.801582i	$-0.296008\pi$
$463$	−183.000	−	316.965i	−0.395248	−	0.684590i	−0.993133	+	0.116992i	$0.962675\pi$
$464$	−515.107	+	297.397i	−1.11014	+	0.640942i
$465$		0			0
$466$	405.000	−	701.481i	0.869099	−	1.50532i
$467$		−	451.686i		−	0.967207i	−0.875287	−	0.483604i	$-0.839328\pi$
$467$		−	451.686i		−	0.967207i	0.875287	−	0.483604i	$-0.160672\pi$
$468$		0			0
$469$	−144.000			−0.307036
$470$	−213.014	−	122.984i	−0.453221	−	0.261668i
$471$		0			0
$472$	−15.0000	−	25.9808i	−0.0317797	−	0.0550440i
$473$	−61.9677	+	35.7771i	−0.131010	+	0.0756387i
$474$		0			0
$475$	−5.00000	+	8.66025i	−0.0105263	+	0.0182321i
$476$		−	26.8328i		−	0.0563715i
$477$		0			0
$478$	−560.000			−1.17155
$479$	−511.234	−	295.161i	−1.06729	−	0.616202i	−0.139853	−	0.990172i	$-0.544663\pi$
$479$	−511.234	−	295.161i	−1.06729	−	0.616202i	−0.927441	+	0.373970i	$0.877996\pi$
$480$		0			0
$481$	128.000	+	221.703i	0.266112	+	0.460920i
$482$	507.361	−	292.925i	1.05262	−	0.607728i
$483$		0			0
$484$	50.5000	−	87.4686i	0.104339	−	0.180720i
$485$			371.187i			0.765335i
$486$		0			0
$487$	−886.000			−1.81930			−0.909651	−	0.415374i	$-0.863651\pi$
$487$	−886.000			−1.81930			−0.909651	+	0.415374i	$0.863651\pi$
$488$	−476.377	−	275.036i	−0.976182	−	0.563599i
$489$		0			0
$490$	32.5000	+	56.2917i	0.0663265	+	0.114881i
$491$	352.441	−	203.482i	0.717803	−	0.414424i	−0.0961402	−	0.995368i	$-0.530650\pi$
$491$	352.441	−	203.482i	0.717803	−	0.414424i	0.813944	+	0.580944i	$0.197316\pi$
$492$		0			0
$493$	−70.0000	+	121.244i	−0.141988	+	0.245930i
$494$		−	71.5542i		−	0.144847i
$495$		0			0
$496$	342.000			0.689516
$497$	650.661	+	375.659i	1.30918	+	0.755854i
$498$		0			0
$499$	1.00000	+	1.73205i	0.00200401	+	0.00347104i	0.867026	−	0.498263i	$-0.166029\pi$
$499$	1.00000	+	1.73205i	0.00200401	+	0.00347104i	−0.865022	+	0.501735i	$0.832695\pi$
$500$	−9.68246	+	5.59017i	−0.0193649	+	0.0111803i
$501$		0			0
$502$	−525.000	+	909.327i	−1.04582	+	1.81141i
$503$			219.135i			0.435655i	0.975987	+	0.217828i	$0.0698971\pi$
$503$			219.135i			0.435655i	−0.975987	+	0.217828i	$0.930103\pi$
$504$		0			0
$505$	−150.000			−0.297030
$506$	116.190	+	67.0820i	0.229624	+	0.132573i
$507$		0			0
$508$	−13.0000	−	22.5167i	−0.0255906	−	0.0443241i
$509$	693.264	−	400.256i	1.36201	−	0.786358i	0.372120	−	0.928185i	$-0.378631\pi$
$509$	693.264	−	400.256i	1.36201	−	0.786358i	0.989892	+	0.141827i	$0.0452975\pi$
$510$		0			0
$511$	−222.000	+	384.515i	−0.434442	+	0.752476i
$512$		−	212.426i		−	0.414895i
$513$		0			0
$514$	450.000			0.875486
$515$	50.3488	+	29.0689i	0.0977646	+	0.0564444i
$516$		0			0
$517$	−110.000	−	190.526i	−0.212766	−	0.368521i
$518$	185.903	−	107.331i	0.358886	−	0.207203i
$519$		0			0
$520$	−120.000	+	207.846i	−0.230769	+	0.399704i
$521$			527.712i			1.01288i	0.862274	+	0.506441i	$0.169039\pi$
$521$			527.712i			1.01288i	−0.862274	+	0.506441i	$0.830961\pi$
$522$		0			0
$523$	376.000			0.718929			0.359465	−	0.933159i	$-0.382959\pi$
$523$	376.000			0.718929			0.359465	+	0.933159i	$0.382959\pi$
$524$	−11.6190	−	6.70820i	−0.0221736	−	0.0128019i
$525$		0			0
$526$	65.0000	+	112.583i	0.123574	+	0.214037i
$527$	69.7137	−	40.2492i	0.132284	−	0.0763742i
$528$		0			0
$529$	−174.500	+	302.243i	−0.329868	+	0.571348i
$530$		−	22.3607i		−	0.0421900i
$531$		0			0
$532$	−12.0000			−0.0225564
$533$	867.548	+	500.879i	1.62767	+	0.939736i
$534$		0			0
$535$	225.000	+	389.711i	0.420561	+	0.728433i
$536$	139.427	−	80.4984i	0.260126	−	0.150184i
$537$		0			0
$538$	415.000	−	718.801i	0.771375	−	1.33606i
$539$			58.1378i			0.107862i
$540$		0			0
$541$	−198.000			−0.365989			−0.182994	−	0.983114i	$-0.558579\pi$
$541$	−198.000			−0.365989			−0.182994	+	0.983114i	$0.558579\pi$
$542$	−158.792	−	91.6788i	−0.292975	−	0.169149i
$543$		0			0
$544$	35.0000	+	60.6218i	0.0643382	+	0.111437i
$545$	−73.5867	+	42.4853i	−0.135021	+	0.0779547i
$546$		0			0
$547$	−512.000	+	886.810i	−0.936015	+	1.62122i	−0.163200	+	0.986593i	$0.552182\pi$
$547$	−512.000	+	886.810i	−0.936015	+	1.62122i	−0.772815	+	0.634632i	$0.781152\pi$
$548$		−	120.748i		−	0.220342i
$549$		0			0
$550$	−50.0000			−0.0909091
$551$	54.2218	+	31.3050i	0.0984061	+	0.0568148i
$552$		0			0
$553$	414.000	+	717.069i	0.748644	+	1.29669i
$554$	46.4758	−	26.8328i	0.0838913	−	0.0484347i
$555$		0			0
$556$	−41.0000	+	71.0141i	−0.0737410	+	0.127723i
$557$		−	67.0820i		−	0.120435i	−0.998185	−	0.0602173i	$-0.980821\pi$
$557$		−	67.0820i		−	0.120435i	0.998185	−	0.0602173i	$-0.0191794\pi$
$558$		0			0
$559$	256.000			0.457961
$560$	220.760	+	127.456i	0.394214	+	0.227600i
$561$		0			0
$562$	210.000	+	363.731i	0.373665	+	0.647208i
$563$	−220.760	+	127.456i	−0.392114	+	0.226387i	−0.683076	−	0.730348i	$-0.739358\pi$
$563$	−220.760	+	127.456i	−0.392114	+	0.226387i	0.290962	+	0.956735i	$0.406025\pi$
$564$		0			0
$565$	35.0000	−	60.6218i	0.0619469	−	0.107295i
$566$		−	321.994i		−	0.568894i
$567$		0			0
$568$	−840.000			−1.47887
$569$	743.613	+	429.325i	1.30688	+	0.754526i	0.981574	−	0.191084i	$-0.0612004\pi$
$569$	743.613	+	429.325i	1.30688	+	0.754526i	0.325303	+	0.945610i	$0.394534\pi$
$570$		0			0
$571$	−481.000	−	833.116i	−0.842382	−	1.45905i	−0.887876	−	0.460083i	$-0.847819\pi$
$571$	−481.000	−	833.116i	−0.842382	−	1.45905i	0.0454939	−	0.998965i	$-0.485514\pi$
$572$	61.9677	−	35.7771i	0.108335	−	0.0625474i
$573$		0			0
$574$	420.000	−	727.461i	0.731707	−	1.26735i
$575$			67.0820i			0.116664i
$576$		0			0
$577$	−886.000			−1.53553			−0.767764	−	0.640732i	$-0.778631\pi$
$577$	−886.000			−1.53553			−0.767764	+	0.640732i	$0.778631\pi$
$578$	−520.916	−	300.751i	−0.901239	−	0.520331i
$579$		0			0
$580$	35.0000	+	60.6218i	0.0603448	+	0.104520i
$581$	−487.996	+	281.745i	−0.839924	+	0.484930i
$582$		0			0
$583$	10.0000	−	17.3205i	0.0171527	−	0.0297093i
$584$		−	496.407i		−	0.850012i
$585$		0			0
$586$	1050.00			1.79181
$587$	−569.329	−	328.702i	−0.969895	−	0.559969i	−0.0706910	−	0.997498i	$-0.522520\pi$
$587$	−569.329	−	328.702i	−0.969895	−	0.559969i	−0.899204	+	0.437529i	$0.855854\pi$
$588$		0			0
$589$	−18.0000	−	31.1769i	−0.0305603	−	0.0529319i
$590$	−19.3649	+	11.1803i	−0.0328219	+	0.0189497i
$591$		0			0
$592$	−152.000	+	263.272i	−0.256757	+	0.444716i
$593$			111.803i			0.188539i	0.995547	+	0.0942693i	$0.0300515\pi$
$593$			111.803i			0.188539i	−0.995547	+	0.0942693i	$0.969949\pi$
$594$		0			0
$595$	60.0000			0.100840
$596$	96.8246	+	55.9017i	0.162457	+	0.0937948i
$597$		0			0
$598$	−240.000	−	415.692i	−0.401338	−	0.695137i
$599$	−193.649	+	111.803i	−0.323287	+	0.186650i	−0.652857	−	0.757481i	$-0.726430\pi$
$599$	−193.649	+	111.803i	−0.323287	+	0.186650i	0.329570	+	0.944131i	$0.393096\pi$
$600$		0			0
$601$	−1.00000	+	1.73205i	−0.00166389	+	0.00288195i	−0.866856	−	0.498558i	$-0.833863\pi$
$601$	−1.00000	+	1.73205i	−0.00166389	+	0.00288195i	0.865192	+	0.501440i	$0.167196\pi$
$602$		−	214.663i		−	0.356582i
$603$		0			0
$604$	158.000			0.261589
$605$	195.586	+	112.921i	0.323282	+	0.186647i
$606$		0			0
$607$	253.000	+	438.209i	0.416804	+	0.721926i	0.995616	−	0.0935354i	$-0.0298168\pi$
$607$	253.000	+	438.209i	0.416804	+	0.721926i	−0.578812	+	0.815461i	$0.696483\pi$
$608$	27.1109	−	15.6525i	0.0445903	−	0.0257442i
$609$		0			0
$610$	−205.000	+	355.070i	−0.336066	+	0.582083i
$611$			787.096i			1.28821i
$612$		0			0
$613$	556.000			0.907015			0.453507	−	0.891253i	$-0.350173\pi$
$613$	556.000			0.907015			0.453507	+	0.891253i	$0.350173\pi$
$614$	−356.314	−	205.718i	−0.580317	−	0.335046i
$615$		0			0
$616$	90.0000	+	155.885i	0.146104	+	0.253059i
$617$	−81.3327	+	46.9574i	−0.131820	+	0.0761060i	−0.564460	−	0.825461i	$-0.690915\pi$
$617$	−81.3327	+	46.9574i	−0.131820	+	0.0761060i	0.432640	+	0.901567i	$0.357582\pi$
$618$		0			0
$619$	401.000	−	694.552i	0.647819	−	1.12206i	−0.335824	−	0.941925i	$-0.609015\pi$
$619$	401.000	−	694.552i	0.647819	−	1.12206i	0.983643	−	0.180131i	$-0.0576521\pi$
$620$		−	40.2492i		−	0.0649181i
$621$		0			0
$622$	360.000			0.578778
$623$	−557.710	−	321.994i	−0.895200	−	0.516844i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−762.978	+	440.505i	−1.21881	+	0.703683i
$627$		0			0
$628$	82.0000	−	142.028i	0.130573	−	0.226160i
$629$			71.5542i			0.113759i
$630$		0			0
$631$	−698.000			−1.10618			−0.553090	−	0.833121i	$-0.686552\pi$
$631$	−698.000			−1.10618			−0.553090	+	0.833121i	$0.686552\pi$
$632$	−801.708	−	462.866i	−1.26852	−	0.732383i
$633$		0			0
$634$	−505.000	−	874.686i	−0.796530	−	1.37963i
$635$	50.3488	−	29.0689i	0.0792894	−	0.0457778i
$636$		0			0
$637$	104.000	−	180.133i	0.163265	−	0.282784i
$638$			313.050i			0.490673i
$639$		0			0
$640$	−345.000			−0.539062
$641$	790.089	+	456.158i	1.23259	+	0.711635i	0.967569	−	0.252608i	$-0.0812885\pi$
$641$	790.089	+	456.158i	1.23259	+	0.711635i	0.265019	+	0.964243i	$0.414622\pi$
$642$		0			0
$643$	−78.0000	−	135.100i	−0.121306	−	0.210109i	0.798977	−	0.601362i	$-0.205375\pi$
$643$	−78.0000	−	135.100i	−0.121306	−	0.210109i	−0.920283	+	0.391253i	$0.872042\pi$
$644$	−69.7137	+	40.2492i	−0.108251	+	0.0624988i
$645$		0			0
$646$	10.0000	−	17.3205i	0.0154799	−	0.0268119i
$647$		−	755.791i		−	1.16815i	−0.811701	−	0.584073i	$-0.801458\pi$
$647$		−	755.791i		−	1.16815i	0.811701	−	0.584073i	$-0.198542\pi$
$648$		0			0
$649$	−20.0000			−0.0308166
$650$	154.919	+	89.4427i	0.238337	+	0.137604i
$651$		0			0
$652$	118.000	+	204.382i	0.180982	+	0.313469i
$653$	422.155	−	243.731i	0.646486	−	0.373249i	−0.140623	−	0.990063i	$-0.544910\pi$
$653$	422.155	−	243.731i	0.646486	−	0.373249i	0.787109	+	0.616815i	$0.211577\pi$
$654$		0			0
$655$	15.0000	−	25.9808i	0.0229008	−	0.0396653i
$656$			1189.59i			1.81340i
$657$		0			0
$658$	660.000			1.00304
$659$	352.441	+	203.482i	0.534813	+	0.308774i	0.742974	−	0.669320i	$-0.233415\pi$
$659$	352.441	+	203.482i	0.534813	+	0.308774i	−0.208161	+	0.978094i	$0.566748\pi$
$660$		0			0
$661$	−341.000	−	590.629i	−0.515885	−	0.893539i	−0.999830	−	0.0184406i	$-0.994130\pi$
$661$	−341.000	−	590.629i	−0.515885	−	0.893539i	0.483945	−	0.875098i	$-0.339203\pi$
$662$	−383.425	+	221.371i	−0.579192	+	0.334397i
$663$		0			0
$664$	315.000	−	545.596i	0.474398	−	0.821681i
$665$		−	26.8328i		−	0.0403501i
$666$		0			0
$667$	420.000			0.629685
$668$	−81.3327	−	46.9574i	−0.121755	−	0.0702956i
$669$		0			0
$670$	−60.0000	−	103.923i	−0.0895522	−	0.155109i
$671$	−317.585	+	183.358i	−0.473300	+	0.273260i
$672$		0			0
$673$	447.000	−	774.227i	0.664190	−	1.15041i	−0.315314	−	0.948987i	$-0.602110\pi$
$673$	447.000	−	774.227i	0.664190	−	1.15041i	0.979504	−	0.201424i	$-0.0645568\pi$
$674$			881.011i			1.30714i
$675$		0			0
$676$	−87.0000			−0.128698
$677$	−476.377	−	275.036i	−0.703659	−	0.406258i	0.105050	−	0.994467i	$-0.466500\pi$
$677$	−476.377	−	275.036i	−0.703659	−	0.406258i	−0.808709	+	0.588209i	$0.799833\pi$
$678$		0			0
$679$	−498.000	−	862.561i	−0.733432	−	1.27034i
$680$	−58.0948	+	33.5410i	−0.0854335	+	0.0493250i
$681$		0			0
$682$	90.0000	−	155.885i	0.131965	−	0.228570i
$683$		−	442.741i		−	0.648231i	−0.946018	−	0.324115i	$-0.894933\pi$
$683$		−	442.741i		−	0.648231i	0.946018	−	0.324115i	$-0.105067\pi$
$684$		0			0
$685$	270.000			0.394161
$686$	−720.375	−	415.909i	−1.05011	−	0.606281i
$687$		0			0
$688$	152.000	+	263.272i	0.220930	+	0.382662i
$689$	−61.9677	+	35.7771i	−0.0899387	+	0.0519261i
$690$		0			0
$691$	379.000	−	656.447i	0.548480	−	0.949996i	−0.449898	−	0.893080i	$-0.648540\pi$
$691$	379.000	−	656.447i	0.548480	−	0.949996i	0.998379	−	0.0569163i	$-0.0181268\pi$
$692$			13.4164i			0.0193879i
$693$		0			0
$694$	−410.000			−0.590778
$695$	−158.792	−	91.6788i	−0.228478	−	0.131912i
$696$		0			0
$697$	140.000	+	242.487i	0.200861	+	0.347901i
$698$	−701.010	+	404.728i	−1.00431	+	0.579840i
$699$		0			0
$700$	15.0000	−	25.9808i	0.0214286	−	0.0371154i
$701$			782.624i			1.11644i	0.829693	+	0.558220i	$0.188515\pi$
$701$			782.624i			1.11644i	−0.829693	+	0.558220i	$0.811485\pi$
$702$		0			0
$703$	32.0000			0.0455192
$704$	−158.792	−	91.6788i	−0.225557	−	0.130226i
$705$		0			0
$706$	345.000	+	597.558i	0.488669	+	0.846399i
$707$	348.569	−	201.246i	0.493025	−	0.284648i
$708$		0			0
$709$	1.00000	−	1.73205i	0.00141044	−	0.00244295i	−0.865319	−	0.501221i	$-0.832884\pi$
$709$	1.00000	−	1.73205i	0.00141044	−	0.00244295i	0.866730	+	0.498778i	$0.166218\pi$
$710$			626.099i			0.881830i
$711$		0			0
$712$	720.000			1.01124
$713$	−209.141	−	120.748i	−0.293326	−	0.169352i
$714$		0			0
$715$	80.0000	+	138.564i	0.111888	+	0.193796i
$716$	166.538	−	96.1509i	0.232595	−	0.134289i
$717$		0			0
$718$	−330.000	+	571.577i	−0.459610	+	0.796068i
$719$		−	858.650i		−	1.19423i	−0.802156	−	0.597114i	$-0.796314\pi$
$719$		−	858.650i		−	1.19423i	0.802156	−	0.597114i	$-0.203686\pi$
$720$		0			0
$721$	−156.000			−0.216366
$722$	691.328	+	399.138i	0.957517	+	0.552823i
$723$		0			0
$724$	1.00000	+	1.73205i	0.00138122	+	0.00239234i
$725$	−135.554	+	78.2624i	−0.186972	+	0.107948i
$726$		0			0
$727$	−337.000	+	583.701i	−0.463549	+	0.802890i	−0.999135	−	0.0415906i	$-0.986757\pi$
$727$	−337.000	+	583.701i	−0.463549	+	0.802890i	0.535586	+	0.844481i	$0.320091\pi$
$728$		−	643.988i		−	0.884598i
$729$		0			0
$730$	−370.000			−0.506849
$731$	61.9677	+	35.7771i	0.0847712	+	0.0489427i
$732$		0			0
$733$	−328.000	−	568.113i	−0.447476	−	0.775051i	0.550745	−	0.834674i	$-0.314344\pi$
$733$	−328.000	−	568.113i	−0.447476	−	0.775051i	−0.998221	+	0.0596222i	$0.981010\pi$
$734$	−360.187	+	207.954i	−0.490719	+	0.283317i
$735$		0			0
$736$	105.000	−	181.865i	0.142663	−	0.247100i
$737$		−	107.331i		−	0.145633i
$738$		0			0
$739$	598.000			0.809202			0.404601	−	0.914493i	$-0.367410\pi$
$739$	598.000			0.809202			0.404601	+	0.914493i	$0.367410\pi$
$740$	30.9839	+	17.8885i	0.0418701	+	0.0241737i
$741$		0			0
$742$	30.0000	+	51.9615i	0.0404313	+	0.0700290i
$743$	−677.772	+	391.312i	−0.912210	+	0.526665i	−0.881142	−	0.472853i	$-0.843224\pi$
$743$	−677.772	+	391.312i	−0.912210	+	0.526665i	−0.0310685	+	0.999517i	$0.509891\pi$
$744$		0			0
$745$	−125.000	+	216.506i	−0.167785	+	0.290613i
$746$		−	98.3870i		−	0.131886i
$747$		0			0
$748$	20.0000			0.0267380
$749$	−1045.71	−	603.738i	−1.39614	−	0.806059i
$750$		0			0
$751$	169.000	+	292.717i	0.225033	+	0.389769i	0.956329	−	0.292291i	$-0.0944176\pi$
$751$	169.000	+	292.717i	0.225033	+	0.389769i	−0.731296	+	0.682060i	$0.761084\pi$
$752$	−809.454	+	467.338i	−1.07640	+	0.621460i
$753$		0			0
$754$	560.000	−	969.948i	0.742706	−	1.28640i
$755$			353.299i			0.467945i
$756$		0			0
$757$	−656.000			−0.866579			−0.433289	−	0.901255i	$-0.642647\pi$
$757$	−656.000			−0.866579			−0.433289	+	0.901255i	$0.642647\pi$
$758$	701.010	+	404.728i	0.924815	+	0.533942i
$759$		0			0
$760$	15.0000	+	25.9808i	0.0197368	+	0.0341852i
$761$	−255.617	+	147.580i	−0.335896	+	0.193930i	−0.658456	−	0.752619i	$-0.728790\pi$
$761$	−255.617	+	147.580i	−0.335896	+	0.193930i	0.322560	+	0.946549i	$0.395457\pi$
$762$		0			0
$763$	114.000	−	197.454i	0.149410	−	0.258786i
$764$		−	205.718i		−	0.269265i
$765$		0			0
$766$	−810.000			−1.05744
$767$	61.9677	+	35.7771i	0.0807924	+	0.0466455i
$768$		0			0
$769$	41.0000	+	71.0141i	0.0533160	+	0.0923460i	0.891452	−	0.453116i	$-0.149688\pi$
$769$	41.0000	+	71.0141i	0.0533160	+	0.0923460i	−0.838136	+	0.545462i	$0.816354\pi$
$770$	116.190	−	67.0820i	0.150895	−	0.0871195i
$771$		0			0
$772$	−107.000	+	185.329i	−0.138601	+	0.240064i
$773$			1059.90i			1.37115i	0.728004	+	0.685573i	$0.240448\pi$
$773$			1059.90i			1.37115i	−0.728004	+	0.685573i	$0.759552\pi$
$774$		0			0
$775$	90.0000			0.116129
$776$	964.373	+	556.781i	1.24275	+	0.717501i
$777$		0			0
$778$	−495.000	−	857.365i	−0.636247	−	1.10201i
$779$	108.444	−	62.6099i	0.139209	−	0.0803721i
$780$		0			0
$781$	−280.000	+	484.974i	−0.358515	+	0.620966i
$782$		−	134.164i		−	0.171565i
$783$		0			0
$784$	247.000			0.315051
$785$	317.585	+	183.358i	0.404566	+	0.233577i
$786$		0			0
$787$	268.000	+	464.190i	0.340534	+	0.589822i	0.984532	−	0.175205i	$-0.0560589\pi$
$787$	268.000	+	464.190i	0.340534	+	0.589822i	−0.643998	+	0.765027i	$0.722726\pi$
$788$	−81.3327	+	46.9574i	−0.103214	+	0.0595906i
$789$		0			0
$790$	−345.000	+	597.558i	−0.436709	+	0.756402i
$791$			187.830i			0.237459i
$792$		0			0
$793$	1312.00			1.65448
$794$	−240.125	−	138.636i	−0.302424	−	0.174605i
$795$		0			0
$796$	−121.000	−	209.578i	−0.152010	−	0.263289i
$797$	352.441	−	203.482i	0.442210	−	0.255310i	−0.262325	−	0.964980i	$-0.584489\pi$
$797$	352.441	−	203.482i	0.442210	−	0.255310i	0.704535	+	0.709670i	$0.251156\pi$
$798$		0			0
$799$	−110.000	+	190.526i	−0.137672	+	0.238455i
$800$			78.2624i			0.0978280i
$801$		0			0
$802$	−600.000			−0.748130
$803$	−286.601	−	165.469i	−0.356913	−	0.206064i
$804$		0			0
$805$	−90.0000	−	155.885i	−0.111801	−	0.193645i
$806$	−557.710	+	321.994i	−0.691947	+	0.399496i
$807$		0			0
$808$	−225.000	+	389.711i	−0.278465	+	0.482316i
$809$			1091.20i			1.34883i	0.738354	+	0.674414i	$0.235603\pi$
$809$			1091.20i			1.34883i	−0.738354	+	0.674414i	$0.764397\pi$
$810$		0			0
$811$	−558.000			−0.688039			−0.344020	−	0.938962i	$-0.611789\pi$
$811$	−558.000			−0.688039			−0.344020	+	0.938962i	$0.611789\pi$
$812$	−162.665	−	93.9149i	−0.200327	−	0.115659i
$813$		0			0
$814$	80.0000	+	138.564i	0.0982801	+	0.170226i
$815$	−457.012	+	263.856i	−0.560751	+	0.323750i
$816$		0			0
$817$	16.0000	−	27.7128i	0.0195838	−	0.0339202i
$818$			1024.12i			1.25198i
$819$		0			0
$820$	140.000			0.170732
$821$	336.950	+	194.538i	0.410414	+	0.236952i	0.690967	−	0.722886i	$-0.257185\pi$
$821$	336.950	+	194.538i	0.410414	+	0.236952i	−0.280554	+	0.959838i	$0.590518\pi$
$822$		0			0
$823$	107.000	+	185.329i	0.130012	+	0.225188i	0.923681	−	0.383162i	$-0.125165\pi$
$823$	107.000	+	185.329i	0.130012	+	0.225188i	−0.793669	+	0.608350i	$0.791832\pi$
$824$	151.046	−	87.2067i	0.183309	−	0.105833i
$825$		0			0
$826$	30.0000	−	51.9615i	0.0363196	−	0.0629074i
$827$		−	31.3050i		−	0.0378536i	−0.999821	−	0.0189268i	$-0.993975\pi$
$827$		−	31.3050i		−	0.0378536i	0.999821	−	0.0189268i	$-0.00602495\pi$
$828$		0			0
$829$	318.000			0.383595			0.191797	−	0.981435i	$-0.438568\pi$
$829$	318.000			0.383595			0.191797	+	0.981435i	$0.438568\pi$
$830$	−406.663	−	234.787i	−0.489956	−	0.282876i
$831$		0			0
$832$	328.000	+	568.113i	0.394231	+	0.682828i
$833$	50.3488	−	29.0689i	0.0604427	−	0.0348966i
$834$		0			0
$835$	105.000	−	181.865i	0.125749	−	0.217803i
$836$		−	8.94427i		−	0.0106989i
$837$		0			0
$838$	−1330.00			−1.58711
$839$	54.2218	+	31.3050i	0.0646267	+	0.0373122i	0.531965	−	0.846766i	$-0.321454\pi$
$839$	54.2218	+	31.3050i	0.0646267	+	0.0373122i	−0.467338	+	0.884078i	$0.654787\pi$
$840$		0			0
$841$	69.5000	+	120.378i	0.0826397	+	0.143136i
$842$	1088.31	−	628.335i	1.29253	−	0.746241i
$843$		0			0
$844$	1.00000	−	1.73205i	0.00118483	−	0.00205219i
$845$		−	194.538i		−	0.230222i
$846$		0			0
$847$	−606.000			−0.715466
$848$	−73.5867	−	42.4853i	−0.0867767	−	0.0501006i
$849$		0			0
$850$	25.0000	+	43.3013i	0.0294118	+	0.0509427i
$851$	185.903	−	107.331i	0.218453	−	0.126124i
$852$		0			0
$853$	342.000	−	592.361i	0.400938	−	0.694445i	−0.592901	−	0.805275i	$-0.702018\pi$
$853$	342.000	−	592.361i	0.400938	−	0.694445i	0.993839	+	0.110830i	$0.0353510\pi$
$854$		−	1100.15i		−	1.28823i
$855$		0			0
$856$	1350.00			1.57710
$857$	−1297.45	−	749.083i	−1.51394	−	0.874076i	−0.999867	−	0.0163313i	$-0.994801\pi$
$857$	−1297.45	−	749.083i	−1.51394	−	0.874076i	−0.514077	−	0.857744i	$-0.671865\pi$
$858$		0			0
$859$	421.000	+	729.193i	0.490105	+	0.848886i	0.999935	−	0.0113886i	$-0.00362518\pi$
$859$	421.000	+	729.193i	0.490105	+	0.848886i	−0.509830	+	0.860275i	$0.670292\pi$
$860$	30.9839	−	17.8885i	0.0360278	−	0.0208006i
$861$		0			0
$862$	−390.000	+	675.500i	−0.452436	+	0.783642i
$863$		−	1015.17i		−	1.17633i	−0.808740	−	0.588166i	$-0.799850\pi$
$863$		−	1015.17i		−	1.17633i	0.808740	−	0.588166i	$-0.200150\pi$
$864$		0			0
$865$	−30.0000			−0.0346821
$866$	−437.647	−	252.676i	−0.505366	−	0.291773i
$867$		0			0
$868$	54.0000	+	93.5307i	0.0622120	+	0.107754i
$869$	−534.472	+	308.577i	−0.615042	+	0.355095i
$870$		0			0
$871$	−192.000	+	332.554i	−0.220436	+	0.381807i
$872$			254.912i			0.292330i
$873$		0			0
$874$	−60.0000			−0.0686499
$875$	58.0948	+	33.5410i	0.0663940	+	0.0383326i
$876$		0			0
$877$	78.0000	+	135.100i	0.0889396	+	0.154048i	0.907063	−	0.420995i	$-0.138319\pi$
$877$	78.0000	+	135.100i	0.0889396	+	0.154048i	−0.818124	+	0.575042i	$0.804986\pi$
$878$	−3.87298	+	2.23607i	−0.00441114	+	0.00254677i
$879$		0			0
$880$	−95.0000	+	164.545i	−0.107955	+	0.186983i
$881$		−	125.220i		−	0.142134i	−0.997472	−	0.0710669i	$-0.977360\pi$
$881$		−	125.220i		−	0.142134i	0.997472	−	0.0710669i	$-0.0226404\pi$
$882$		0			0
$883$	−964.000			−1.09173			−0.545866	−	0.837872i	$-0.683799\pi$
$883$	−964.000			−1.09173			−0.545866	+	0.837872i	$0.683799\pi$
$884$	−61.9677	−	35.7771i	−0.0700992	−	0.0404718i
$885$		0			0
$886$	−225.000	−	389.711i	−0.253950	−	0.439855i
$887$	−824.945	+	476.282i	−0.930040	+	0.536959i	−0.886824	−	0.462107i	$-0.847094\pi$
$887$	−824.945	+	476.282i	−0.930040	+	0.536959i	−0.0432158	+	0.999066i	$0.513760\pi$
$888$		0			0
$889$	−78.0000	+	135.100i	−0.0877390	+	0.151968i
$890$		−	536.656i		−	0.602985i
$891$		0			0
$892$	−86.0000			−0.0964126
$893$	85.2056	+	49.1935i	0.0954150	+	0.0550879i
$894$		0			0
$895$	215.000	+	372.391i	0.240223	+	0.416079i
$896$	801.708	−	462.866i	0.894763	−	0.516592i
$897$		0			0
$898$	−350.000	+	606.218i	−0.389755	+	0.675075i
$899$		−	563.489i		−	0.626795i
$900$		0			0
$901$	−20.0000			−0.0221976
$902$	542.218	+	313.050i	0.601128	+	0.347062i
$903$		0			0
$904$	−105.000	−	181.865i	−0.116150	−	0.201178i
$905$	−3.87298	+	2.23607i	−0.00427954	+	0.00247079i
$906$		0			0
$907$	−642.000	+	1111.98i	−0.707828	+	1.22599i	0.257833	+	0.966189i	$0.416991\pi$
$907$	−642.000	+	1111.98i	−0.707828	+	1.22599i	−0.965661	+	0.259805i	$0.916342\pi$
$908$		−	58.1378i		−	0.0640284i
$909$		0			0
$910$	−480.000			−0.527473
$911$	−54.2218	−	31.3050i	−0.0595190	−	0.0343633i	0.469945	−	0.882696i	$-0.344274\pi$
$911$	−54.2218	−	31.3050i	−0.0595190	−	0.0343633i	−0.529464	+	0.848332i	$0.677607\pi$
$912$		0			0
$913$	−210.000	−	363.731i	−0.230011	−	0.398391i
$914$	646.788	−	373.423i	0.707646	−	0.408559i
$915$		0			0
$916$	−141.000	+	244.219i	−0.153930	+	0.266615i
$917$			80.4984i			0.0877846i
$918$		0			0
$919$	418.000			0.454842			0.227421	−	0.973797i	$-0.426971\pi$
$919$	418.000			0.454842			0.227421	+	0.973797i	$0.426971\pi$
$920$	174.284	+	100.623i	0.189439	+	0.109373i
$921$		0			0
$922$	−105.000	−	181.865i	−0.113883	−	0.197251i
$923$	1735.10	−	1001.76i	1.87984	−	1.08533i
$924$		0			0
$925$	−40.0000	+	69.2820i	−0.0432432	+	0.0748995i
$926$			818.401i			0.883802i
$927$		0			0
$928$	490.000			0.528017
$929$	147.173	+	84.9706i	0.158421	+	0.0914646i	0.577115	−	0.816663i	$-0.304179\pi$
$929$	147.173	+	84.9706i	0.158421	+	0.0914646i	−0.418694	+	0.908128i	$0.637512\pi$
$930$		0			0
$931$	−13.0000	−	22.5167i	−0.0139635	−	0.0241855i
$932$	−313.712	+	181.122i	−0.336600	+	0.194336i
$933$		0			0
$934$	−505.000	+	874.686i	−0.540685	+	0.936494i
$935$			44.7214i			0.0478303i
$936$		0			0
$937$	534.000			0.569904			0.284952	−	0.958542i	$-0.408022\pi$
$937$	534.000			0.569904			0.284952	+	0.958542i	$0.408022\pi$
$938$	278.855	+	160.997i	0.297287	+	0.171638i
$939$		0			0
$940$	55.0000	+	95.2628i	0.0585106	+	0.101343i
$941$	−112.317	+	64.8460i	−0.119359	+	0.0689118i	−0.558491	−	0.829511i	$-0.688619\pi$
$941$	−112.317	+	64.8460i	−0.119359	+	0.0689118i	0.439132	+	0.898423i	$0.355286\pi$
$942$		0			0
$943$	420.000	−	727.461i	0.445387	−	0.771433i
$944$			84.9706i			0.0900112i
$945$		0			0
$946$	160.000			0.169133
$947$	1312.94	+	758.027i	1.38642	+	0.800451i	0.992910	−	0.118869i	$-0.0379267\pi$
$947$	1312.94	+	758.027i	1.38642	+	0.800451i	0.393512	+	0.919320i	$0.371260\pi$
$948$		0			0
$949$	592.000	+	1025.37i	0.623815	+	1.08048i
$950$	19.3649	−	11.1803i	0.0203841	−	0.0117688i
$951$		0			0
$952$	90.0000	−	155.885i	0.0945378	−	0.163744i
$953$		−	406.964i		−	0.427035i	−0.976939	−	0.213518i	$-0.931508\pi$
$953$		−	406.964i		−	0.427035i	0.976939	−	0.213518i	$-0.0684920\pi$
$954$		0			0
$955$	460.000			0.481675
$956$	216.887	+	125.220i	0.226869	+	0.130983i
$957$		0			0
$958$	660.000	+	1143.15i	0.688935	+	1.19327i
$959$	−627.423	+	362.243i	−0.654247	+	0.377730i
$960$		0			0
$961$	318.500	−	551.658i	0.331426	−	0.574046i
$962$		−	572.433i		−	0.595045i
$963$		0			0
$964$	−262.000			−0.271784
$965$	−414.409	−	239.259i	−0.429440	−	0.247937i
$966$		0			0
$967$	−337.000	−	583.701i	−0.348501	−	0.603621i	0.637483	−	0.770465i	$-0.279976\pi$
$967$	−337.000	−	583.701i	−0.348501	−	0.603621i	−0.985983	+	0.166844i	$0.946642\pi$
$968$	586.757	−	338.764i	0.606154	−	0.349963i
$969$		0			0
$970$	415.000	−	718.801i	0.427835	−	0.741032i
$971$		−	1328.22i		−	1.36789i	−0.729532	−	0.683947i	$-0.760262\pi$
$971$		−	1328.22i		−	1.36789i	0.729532	−	0.683947i	$-0.239738\pi$
$972$		0			0
$973$	492.000			0.505653
$974$	1715.73	+	990.578i	1.76153	+	1.01702i
$975$		0			0
$976$	779.000	+	1349.27i	0.798156	+	1.38245i
$977$	321.458	−	185.594i	0.329025	−	0.189963i	−0.326383	−	0.945238i	$-0.605830\pi$
$977$	321.458	−	185.594i	0.329025	−	0.189963i	0.655408	+	0.755275i	$0.272497\pi$
$978$		0			0
$979$	240.000	−	415.692i	0.245148	−	0.424609i
$980$		−	29.0689i		−	0.0296621i
$981$		0			0
$982$	−910.000			−0.926680
$983$	383.425	+	221.371i	0.390056	+	0.225199i	0.682185	−	0.731180i	$-0.261030\pi$
$983$	383.425	+	221.371i	0.390056	+	0.225199i	−0.292128	+	0.956379i	$0.594363\pi$
$984$		0			0
$985$	−105.000	−	181.865i	−0.106599	−	0.184635i
$986$	271.109	−	156.525i	0.274958	−	0.158747i
$987$		0			0
$988$	−16.0000	+	27.7128i	−0.0161943	+	0.0280494i
$989$		−	214.663i		−	0.217050i
$990$		0			0
$991$	962.000			0.970737			0.485368	−	0.874310i	$-0.338686\pi$
$991$	962.000			0.970737			0.485368	+	0.874310i	$0.338686\pi$
$992$	−243.998	−	140.872i	−0.245966	−	0.142008i
$993$		0			0
$994$	−840.000	−	1454.92i	−0.845070	−	1.46370i
$995$	468.631	−	270.564i	0.470986	−	0.271924i
$996$		0			0
$997$	−12.0000	+	20.7846i	−0.0120361	+	0.0208472i	−0.871981	−	0.489540i	$-0.837165\pi$
$997$	−12.0000	+	20.7846i	−0.0120361	+	0.0208472i	0.859945	+	0.510387i	$0.170498\pi$
$998$		−	4.47214i		−	0.00448110i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.i.b.26.1		4
3.2	odd	2	inner	405.3.i.b.26.2		4
9.2	odd	6		15.3.c.a.11.1	✓	2
9.4	even	3	inner	405.3.i.b.296.2		4
9.5	odd	6	inner	405.3.i.b.296.1		4
9.7	even	3		15.3.c.a.11.2	yes	2
36.7	odd	6		240.3.l.b.161.2		2
36.11	even	6		240.3.l.b.161.1		2
45.2	even	12		75.3.d.b.74.4		4
45.7	odd	12		75.3.d.b.74.2		4
45.29	odd	6		75.3.c.e.26.2		2
45.34	even	6		75.3.c.e.26.1		2
45.38	even	12		75.3.d.b.74.1		4
45.43	odd	12		75.3.d.b.74.3		4
72.11	even	6		960.3.l.b.641.2		2
72.29	odd	6		960.3.l.c.641.1		2
72.43	odd	6		960.3.l.b.641.1		2
72.61	even	6		960.3.l.c.641.2		2
180.7	even	12		1200.3.c.f.449.3		4
180.43	even	12		1200.3.c.f.449.2		4
180.47	odd	12		1200.3.c.f.449.1		4
180.79	odd	6		1200.3.l.g.401.1		2
180.83	odd	12		1200.3.c.f.449.4		4
180.119	even	6		1200.3.l.g.401.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.c.a.11.1	✓	2	9.2	odd	6
15.3.c.a.11.2	yes	2	9.7	even	3
75.3.c.e.26.1		2	45.34	even	6
75.3.c.e.26.2		2	45.29	odd	6
75.3.d.b.74.1		4	45.38	even	12
75.3.d.b.74.2		4	45.7	odd	12
75.3.d.b.74.3		4	45.43	odd	12
75.3.d.b.74.4		4	45.2	even	12
240.3.l.b.161.1		2	36.11	even	6
240.3.l.b.161.2		2	36.7	odd	6
405.3.i.b.26.1		4	1.1	even	1	trivial
405.3.i.b.26.2		4	3.2	odd	2	inner
405.3.i.b.296.1		4	9.5	odd	6	inner
405.3.i.b.296.2		4	9.4	even	3	inner
960.3.l.b.641.1		2	72.43	odd	6
960.3.l.b.641.2		2	72.11	even	6
960.3.l.c.641.1		2	72.29	odd	6
960.3.l.c.641.2		2	72.61	even	6
1200.3.c.f.449.1		4	180.47	odd	12
1200.3.c.f.449.2		4	180.43	even	12
1200.3.c.f.449.3		4	180.7	even	12
1200.3.c.f.449.4		4	180.83	odd	12
1200.3.l.g.401.1		2	180.79	odd	6
1200.3.l.g.401.2		2	180.119	even	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93649 - 1.11803i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.00000 - 5.19615i) q^{7} +6.70820i q^{8} +O(q^{10})\)	\(q+(-1.93649 - 1.11803i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.00000 - 5.19615i) q^{7} +6.70820i q^{8} +5.00000 q^{10} +(3.87298 + 2.23607i) q^{11} +(-8.00000 - 13.8564i) q^{13} +(-11.6190 + 6.70820i) q^{14} +(9.50000 - 16.4545i) q^{16} -4.47214i q^{17} -2.00000 q^{19} +(-1.93649 - 1.11803i) q^{20} +(-5.00000 - 8.66025i) q^{22} +(-11.6190 + 6.70820i) q^{23} +(2.50000 - 4.33013i) q^{25} +35.7771i q^{26} +6.00000 q^{28} +(-27.1109 - 15.6525i) q^{29} +(9.00000 + 15.5885i) q^{31} +(-13.5554 + 7.82624i) q^{32} +(-5.00000 + 8.66025i) q^{34} +13.4164i q^{35} -16.0000 q^{37} +(3.87298 + 2.23607i) q^{38} +(-7.50000 - 12.9904i) q^{40} +(-54.2218 + 31.3050i) q^{41} +(-8.00000 + 13.8564i) q^{43} +4.47214i q^{44} +30.0000 q^{46} +(-42.6028 - 24.5967i) q^{47} +(6.50000 + 11.2583i) q^{49} +(-9.68246 + 5.59017i) q^{50} +(8.00000 - 13.8564i) q^{52} -4.47214i q^{53} -10.0000 q^{55} +(34.8569 + 20.1246i) q^{56} +(35.0000 + 60.6218i) q^{58} +(-3.87298 + 2.23607i) q^{59} +(-41.0000 + 71.0141i) q^{61} -40.2492i q^{62} -41.0000 q^{64} +(30.9839 + 17.8885i) q^{65} +(-12.0000 - 20.7846i) q^{67} +(3.87298 - 2.23607i) q^{68} +(15.0000 - 25.9808i) q^{70} +125.220i q^{71} -74.0000 q^{73} +(30.9839 + 17.8885i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(23.2379 - 13.4164i) q^{77} +(-69.0000 + 119.512i) q^{79} +42.4853i q^{80} +140.000 q^{82} +(-81.3327 - 46.9574i) q^{83} +(5.00000 + 8.66025i) q^{85} +(30.9839 - 17.8885i) q^{86} +(-15.0000 + 25.9808i) q^{88} -107.331i q^{89} -96.0000 q^{91} +(-11.6190 - 6.70820i) q^{92} +(55.0000 + 95.2628i) q^{94} +(3.87298 - 2.23607i) q^{95} +(83.0000 - 143.760i) q^{97} -29.0689i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 12 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 12 * q^7	\( 4 q + 2 q^{4} + 12 q^{7} + 20 q^{10} - 32 q^{13} + 38 q^{16} - 8 q^{19} - 20 q^{22} + 10 q^{25} + 24 q^{28} + 36 q^{31} - 20 q^{34} - 64 q^{37} - 30 q^{40} - 32 q^{43} + 120 q^{46} + 26 q^{49} + 32 q^{52} - 40 q^{55} + 140 q^{58} - 164 q^{61} - 164 q^{64} - 48 q^{67} + 60 q^{70} - 296 q^{73} - 4 q^{76} - 276 q^{79} + 560 q^{82} + 20 q^{85} - 60 q^{88} - 384 q^{91} + 220 q^{94} + 332 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 + 12 * q^7 + 20 * q^10 - 32 * q^13 + 38 * q^16 - 8 * q^19 - 20 * q^22 + 10 * q^25 + 24 * q^28 + 36 * q^31 - 20 * q^34 - 64 * q^37 - 30 * q^40 - 32 * q^43 + 120 * q^46 + 26 * q^49 + 32 * q^52 - 40 * q^55 + 140 * q^58 - 164 * q^61 - 164 * q^64 - 48 * q^67 + 60 * q^70 - 296 * q^73 - 4 * q^76 - 276 * q^79 + 560 * q^82 + 20 * q^85 - 60 * q^88 - 384 * q^91 + 220 * q^94 + 332 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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