LMFDB - Embedded newform 476.3.s.a.341.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,3,Mod(341,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("476.341");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	476.s (of order $6$, degree $2$, 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:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.7
Character	$\chi$	$=$	476.341
Dual form			476.3.s.a.409.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50400 + 1.44568i) q^{3} +(4.60744 + 2.66011i) q^{5} +(5.50382 + 4.32527i) q^{7} +(-0.319995 + 0.554248i) q^{9} +O(q^{10})$	\(q+(-2.50400 + 1.44568i) q^{3} +(4.60744 + 2.66011i) q^{5} +(5.50382 + 4.32527i) q^{7} +(-0.319995 + 0.554248i) q^{9} +(3.65624 + 6.33279i) q^{11} -9.54157i q^{13} -15.3827 q^{15} +(-3.57071 + 2.06155i) q^{17} +(31.4724 + 18.1706i) q^{19} +(-20.0345 - 2.87367i) q^{21} +(11.2308 - 19.4523i) q^{23} +(1.65232 + 2.86190i) q^{25} -27.8728i q^{27} -18.4004 q^{29} +(-27.4480 + 15.8471i) q^{31} +(-18.3104 - 10.5715i) q^{33} +(13.8529 + 34.5691i) q^{35} +(-31.8347 + 55.1393i) q^{37} +(13.7941 + 23.8921i) q^{39} +44.3402i q^{41} +27.5293 q^{43} +(-2.94871 + 1.70244i) q^{45} +(-6.27261 - 3.62149i) q^{47} +(11.5842 + 47.6110i) q^{49} +(5.96071 - 10.3242i) q^{51} +(29.8295 + 51.6662i) q^{53} +38.9039i q^{55} -105.076 q^{57} +(-39.9992 + 23.0935i) q^{59} +(-54.8674 - 31.6777i) q^{61} +(-4.15846 + 1.66642i) q^{63} +(25.3816 - 43.9622i) q^{65} +(21.9831 + 38.0759i) q^{67} +64.9445i q^{69} +76.6067 q^{71} +(-39.3191 + 22.7009i) q^{73} +(-8.27482 - 4.77747i) q^{75} +(-7.26771 + 50.6688i) q^{77} +(-5.70562 + 9.88242i) q^{79} +(37.4153 + 64.8051i) q^{81} -114.732i q^{83} -21.9358 q^{85} +(46.0746 - 26.6012i) q^{87} +(-76.3692 - 44.0918i) q^{89} +(41.2698 - 52.5151i) q^{91} +(45.8199 - 79.3624i) q^{93} +(96.6713 + 167.440i) q^{95} -163.988i q^{97} -4.67991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−2.50400	+	1.44568i	−0.834666	+	0.481895i	−0.855448	−	0.517889i	$-0.826718\pi$
$3$	−2.50400	+	1.44568i	−0.834666	+	0.481895i	0.0207815	+	0.999784i	$0.493385\pi$
$4$		0			0
$5$	4.60744	+	2.66011i	0.921488	+	0.532021i	0.884109	−	0.467280i	$-0.154766\pi$
$5$	4.60744	+	2.66011i	0.921488	+	0.532021i	0.0373782	+	0.999301i	$0.488099\pi$
$6$		0			0
$7$	5.50382	+	4.32527i	0.786261	+	0.617895i
$7$	5.50382	+	4.32527i	0.786261	+	0.617895i
$8$		0			0
$9$	−0.319995	+	0.554248i	−0.0355550	+	0.0615831i
$10$		0			0
$11$	3.65624	+	6.33279i	0.332385	+	0.575708i	0.982979	−	0.183718i	$-0.0588132\pi$
$11$	3.65624	+	6.33279i	0.332385	+	0.575708i	−0.650594	+	0.759426i	$0.725480\pi$
$12$		0			0
$13$		−	9.54157i		−	0.733967i	−0.930228	−	0.366983i	$-0.880391\pi$
$13$		−	9.54157i		−	0.733967i	0.930228	−	0.366983i	$-0.119609\pi$
$14$		0			0
$15$	−15.3827			−1.02551
$16$		0			0
$17$	−3.57071	+	2.06155i	−0.210042	+	0.121268i
$17$	−3.57071	+	2.06155i	−0.210042	+	0.121268i
$18$		0			0
$19$	31.4724	+	18.1706i	1.65644	+	0.956347i	0.974338	+	0.225091i	$0.0722679\pi$
$19$	31.4724	+	18.1706i	1.65644	+	0.956347i	0.682103	+	0.731256i	$0.261065\pi$
$20$		0			0
$21$	−20.0345	−	2.87367i	−0.954025	−	0.136841i
$22$		0			0
$23$	11.2308	−	19.4523i	0.488294	−	0.845750i	−0.511615	−	0.859215i	$-0.670953\pi$
$23$	11.2308	−	19.4523i	0.488294	−	0.845750i	0.999909	+	0.0134645i	$0.00428603\pi$
$24$		0			0
$25$	1.65232	+	2.86190i	0.0660928	+	0.114476i
$26$		0			0
$27$		−	27.8728i		−	1.03232i
$28$		0			0
$29$	−18.4004			−0.634498			−0.317249	−	0.948342i	$-0.602759\pi$
$29$	−18.4004			−0.634498			−0.317249	+	0.948342i	$0.602759\pi$
$30$		0			0
$31$	−27.4480	+	15.8471i	−0.885421	+	0.511198i	−0.872442	−	0.488718i	$-0.837465\pi$
$31$	−27.4480	+	15.8471i	−0.885421	+	0.511198i	−0.0129789	+	0.999916i	$0.504131\pi$
$32$		0			0
$33$	−18.3104	−	10.5715i	−0.554862	−	0.320349i
$34$		0			0
$35$	13.8529	+	34.5691i	0.395796	+	0.987690i
$36$		0			0
$37$	−31.8347	+	55.1393i	−0.860397	+	1.49025i	0.0111499	+	0.999938i	$0.496451\pi$
$37$	−31.8347	+	55.1393i	−0.860397	+	1.49025i	−0.871547	+	0.490313i	$0.836883\pi$
$38$		0			0
$39$	13.7941	+	23.8921i	0.353695	+	0.612617i
$40$		0			0
$41$			44.3402i			1.08147i	0.841194	+	0.540734i	$0.181853\pi$
$41$			44.3402i			1.08147i	−0.841194	+	0.540734i	$0.818147\pi$
$42$		0			0
$43$	27.5293			0.640217			0.320109	−	0.947381i	$-0.396281\pi$
$43$	27.5293			0.640217			0.320109	+	0.947381i	$0.396281\pi$
$44$		0			0
$45$	−2.94871	+	1.70244i	−0.0655270	+	0.0378320i
$46$		0			0
$47$	−6.27261	−	3.62149i	−0.133460	−	0.0770530i	0.431784	−	0.901977i	$-0.357884\pi$
$47$	−6.27261	−	3.62149i	−0.133460	−	0.0770530i	−0.565243	+	0.824924i	$0.691218\pi$
$48$		0			0
$49$	11.5842	+	47.6110i	0.236411	+	0.971653i
$50$		0			0
$51$	5.96071	−	10.3242i	0.116877	−	0.202436i
$52$		0			0
$53$	29.8295	+	51.6662i	0.562821	+	0.974835i	0.997249	+	0.0741281i	$0.0236174\pi$
$53$	29.8295	+	51.6662i	0.562821	+	0.974835i	−0.434428	+	0.900707i	$0.643049\pi$
$54$		0			0
$55$			38.9039i			0.707344i
$56$		0			0
$57$	−105.076			−1.84343
$58$		0			0
$59$	−39.9992	+	23.0935i	−0.677952	+	0.391416i	−0.799083	−	0.601221i	$-0.794681\pi$
$59$	−39.9992	+	23.0935i	−0.677952	+	0.391416i	0.121131	+	0.992637i	$0.461348\pi$
$60$		0			0
$61$	−54.8674	−	31.6777i	−0.899465	−	0.519307i	−0.0224386	−	0.999748i	$-0.507143\pi$
$61$	−54.8674	−	31.6777i	−0.899465	−	0.519307i	−0.877027	+	0.480442i	$0.840476\pi$
$62$		0			0
$63$	−4.15846	+	1.66642i	−0.0660074	+	0.0264511i
$64$		0			0
$65$	25.3816	−	43.9622i	0.390486	−	0.676341i
$66$		0			0
$67$	21.9831	+	38.0759i	0.328106	+	0.568297i	0.982136	−	0.188172i	$-0.0602563\pi$
$67$	21.9831	+	38.0759i	0.328106	+	0.568297i	−0.654030	+	0.756469i	$0.726923\pi$
$68$		0			0
$69$			64.9445i			0.941225i
$70$		0			0
$71$	76.6067			1.07897			0.539484	−	0.841996i	$-0.318619\pi$
$71$	76.6067			1.07897			0.539484	+	0.841996i	$0.318619\pi$
$72$		0			0
$73$	−39.3191	+	22.7009i	−0.538617	+	0.310971i	−0.744518	−	0.667602i	$-0.767321\pi$
$73$	−39.3191	+	22.7009i	−0.538617	+	0.310971i	0.205901	+	0.978573i	$0.433987\pi$
$74$		0			0
$75$	−8.27482	−	4.77747i	−0.110331	−	0.0636996i
$76$		0			0
$77$	−7.26771	+	50.6688i	−0.0943859	+	0.658036i
$78$		0			0
$79$	−5.70562	+	9.88242i	−0.0722230	+	0.125094i	−0.899875	−	0.436147i	$-0.856343\pi$
$79$	−5.70562	+	9.88242i	−0.0722230	+	0.125094i	0.827652	+	0.561241i	$0.189676\pi$
$80$		0			0
$81$	37.4153	+	64.8051i	0.461917	+	0.800063i
$82$		0			0
$83$		−	114.732i		−	1.38231i	−0.722708	−	0.691154i	$-0.757103\pi$
$83$		−	114.732i		−	1.38231i	0.722708	−	0.691154i	$-0.242897\pi$
$84$		0			0
$85$	−21.9358			−0.258068
$86$		0			0
$87$	46.0746	−	26.6012i	0.529594	−	0.305761i
$88$		0			0
$89$	−76.3692	−	44.0918i	−0.858081	−	0.495413i	0.00528844	−	0.999986i	$-0.498317\pi$
$89$	−76.3692	−	44.0918i	−0.858081	−	0.495413i	−0.863369	+	0.504573i	$0.831650\pi$
$90$		0			0
$91$	41.2698	−	52.5151i	0.453514	−	0.577089i
$92$		0			0
$93$	45.8199	−	79.3624i	0.492687	−	0.853359i
$94$		0			0
$95$	96.6713	+	167.440i	1.01759	+	1.76252i
$96$		0			0
$97$		−	163.988i		−	1.69060i	−0.534293	−	0.845299i	$-0.679422\pi$
$97$		−	163.988i		−	1.69060i	0.534293	−	0.845299i	$-0.320578\pi$
$98$		0			0
$99$	−4.67991			−0.0472718
$100$		0			0
$101$	20.8371	−	12.0303i	0.206308	−	0.119112i	−0.393286	−	0.919416i	$-0.628662\pi$
$101$	20.8371	−	12.0303i	0.206308	−	0.119112i	0.599595	+	0.800304i	$0.295329\pi$
$102$		0			0
$103$	72.7004	+	41.9736i	0.705829	+	0.407511i	0.809515	−	0.587100i	$-0.199730\pi$
$103$	72.7004	+	41.9736i	0.705829	+	0.407511i	−0.103686	+	0.994610i	$0.533064\pi$
$104$		0			0
$105$	−84.6636	−	66.5342i	−0.806320	−	0.633659i
$106$		0			0
$107$	10.0251	−	17.3639i	0.0936923	−	0.162280i	−0.815370	−	0.578941i	$-0.803466\pi$
$107$	10.0251	−	17.3639i	0.0936923	−	0.162280i	0.909062	+	0.416661i	$0.136800\pi$
$108$		0			0
$109$	−55.0299	−	95.3146i	−0.504862	−	0.874446i	−0.999984	−	0.00562275i	$-0.998210\pi$
$109$	−55.0299	−	95.3146i	−0.504862	−	0.874446i	0.495123	−	0.868823i	$-0.335123\pi$
$110$		0			0
$111$		−	184.092i		−	1.65848i
$112$		0			0
$113$	−67.1063			−0.593861			−0.296930	−	0.954899i	$-0.595963\pi$
$113$	−67.1063			−0.593861			−0.296930	+	0.954899i	$0.595963\pi$
$114$		0			0
$115$	103.490	−	59.7500i	0.899914	−	0.519565i
$116$		0			0
$117$	5.28839	+	3.05325i	0.0451999	+	0.0260962i
$118$		0			0
$119$	−28.5693	−	4.09786i	−0.240079	−	0.0344358i
$120$		0			0
$121$	33.7638	−	58.4807i	0.279040	−	0.483311i
$122$		0			0
$123$	−64.1019	−	111.028i	−0.521153	−	0.902664i
$124$		0			0
$125$		−	115.424i		−	0.923391i
$126$		0			0
$127$	146.635			1.15461			0.577304	−	0.816529i	$-0.304105\pi$
$127$	146.635			1.15461			0.577304	+	0.816529i	$0.304105\pi$
$128$		0			0
$129$	−68.9334	+	39.7987i	−0.534368	+	0.308517i
$130$		0			0
$131$	−91.7673	−	52.9819i	−0.700514	−	0.404442i	0.107025	−	0.994256i	$-0.465868\pi$
$131$	−91.7673	−	52.9819i	−0.700514	−	0.404442i	−0.807539	+	0.589814i	$0.799201\pi$
$132$		0			0
$133$	94.6258	+	236.134i	0.711472	+	1.77544i
$134$		0			0
$135$	74.1445	−	128.422i	0.549218	−	0.951274i
$136$		0			0
$137$	111.121	+	192.467i	0.811101	+	1.40487i	0.912094	+	0.409981i	$0.134465\pi$
$137$	111.121	+	192.467i	0.811101	+	1.40487i	−0.100994	+	0.994887i	$0.532202\pi$
$138$		0			0
$139$			160.549i			1.15503i	0.816380	+	0.577515i	$0.195977\pi$
$139$			160.549i			1.15503i	−0.816380	+	0.577515i	$0.804023\pi$
$140$		0			0
$141$	20.9421			0.148526
$142$		0			0
$143$	60.4248	−	34.8863i	0.422551	−	0.243960i
$144$		0			0
$145$	−84.7788	−	48.9471i	−0.584682	−	0.337566i
$146$		0			0
$147$	−97.8372	−	102.471i	−0.665559	−	0.697081i
$148$		0			0
$149$	79.2816	−	137.320i	0.532091	−	0.921609i	−0.467207	−	0.884148i	$-0.654740\pi$
$149$	79.2816	−	137.320i	0.532091	−	0.921609i	0.999298	−	0.0374613i	$-0.0119271\pi$
$150$		0			0
$151$	89.7351	+	155.426i	0.594272	+	1.02931i	0.993649	+	0.112523i	$0.0358931\pi$
$151$	89.7351	+	155.426i	0.594272	+	1.02931i	−0.399377	+	0.916787i	$0.630774\pi$
$152$		0			0
$153$		−	2.63875i		−	0.0172467i
$154$		0			0
$155$	−168.620			−1.08787
$156$		0			0
$157$	122.382	−	70.6573i	0.779504	−	0.450047i	−0.0567505	−	0.998388i	$-0.518074\pi$
$157$	122.382	−	70.6573i	0.779504	−	0.450047i	0.836254	+	0.548342i	$0.184741\pi$
$158$		0			0
$159$	−149.386	−	86.2481i	−0.939535	−	0.542441i
$160$		0			0
$161$	145.948	−	58.4857i	0.906511	−	0.363265i
$162$		0			0
$163$	−7.08299	+	12.2681i	−0.0434539	+	0.0752644i	−0.886934	−	0.461896i	$-0.847169\pi$
$163$	−7.08299	+	12.2681i	−0.0434539	+	0.0752644i	0.843480	+	0.537160i	$0.180503\pi$
$164$		0			0
$165$	−56.2428	−	97.4154i	−0.340865	−	0.590396i
$166$		0			0
$167$			207.454i			1.24224i	0.783716	+	0.621120i	$0.213322\pi$
$167$			207.454i			1.24224i	−0.783716	+	0.621120i	$0.786678\pi$
$168$		0			0
$169$	77.9585			0.461293
$170$		0			0
$171$	−20.1420	+	11.6290i	−0.117790	+	0.0680058i
$172$		0			0
$173$	−114.481	−	66.0956i	−0.661739	−	0.382055i	0.131200	−	0.991356i	$-0.458117\pi$
$173$	−114.481	−	66.0956i	−0.661739	−	0.382055i	−0.792939	+	0.609300i	$0.791450\pi$
$174$		0			0
$175$	−3.28441	+	22.8981i	−0.0187681	+	0.130847i
$176$		0			0
$177$	66.7719	−	115.652i	0.377243	−	0.653403i
$178$		0			0
$179$	−177.381	−	307.233i	−0.990957	−	1.71639i	−0.611684	−	0.791102i	$-0.709508\pi$
$179$	−177.381	−	307.233i	−0.990957	−	1.71639i	−0.379273	−	0.925285i	$-0.623826\pi$
$180$		0			0
$181$		−	127.143i		−	0.702447i	−0.936292	−	0.351223i	$-0.885766\pi$
$181$		−	127.143i		−	0.702447i	0.936292	−	0.351223i	$-0.114234\pi$
$182$		0			0
$183$	183.184			1.00100
$184$		0			0
$185$	−293.353	+	169.367i	−1.58569	+	0.915498i
$186$		0			0
$187$	−26.1108	−	15.0751i	−0.139630	−	0.0806153i
$188$		0			0
$189$	120.557	−	153.407i	0.637868	−	0.811676i
$190$		0			0
$191$	75.5158	−	130.797i	0.395370	−	0.684802i	−0.597778	−	0.801662i	$-0.703950\pi$
$191$	75.5158	−	130.797i	0.395370	−	0.684802i	0.993148	+	0.116860i	$0.0372829\pi$
$192$		0			0
$193$	102.175	+	176.972i	0.529404	+	0.916954i	0.999412	+	0.0342918i	$0.0109176\pi$
$193$	102.175	+	176.972i	0.529404	+	0.916954i	−0.470008	+	0.882662i	$0.655749\pi$
$194$		0			0
$195$			146.775i			0.752692i
$196$		0			0
$197$	116.288			0.590294			0.295147	−	0.955452i	$-0.404631\pi$
$197$	116.288			0.590294			0.295147	+	0.955452i	$0.404631\pi$
$198$		0			0
$199$	−269.972	+	155.868i	−1.35664	+	0.783258i	−0.989170	−	0.146776i	$-0.953110\pi$
$199$	−269.972	+	155.868i	−1.35664	+	0.783258i	−0.367473	+	0.930034i	$0.619777\pi$
$200$		0			0
$201$	−110.091	−	63.5613i	−0.547718	−	0.316225i
$202$		0			0
$203$	−101.273	−	79.5867i	−0.498880	−	0.392053i
$204$		0			0
$205$	−117.950	+	204.295i	−0.575363	+	0.996559i
$206$		0			0
$207$	7.18758	+	12.4492i	0.0347226	+	0.0601413i
$208$		0			0
$209$			265.744i			1.27150i
$210$		0			0
$211$	280.107			1.32752			0.663762	−	0.747944i	$-0.268959\pi$
$211$	280.107			1.32752			0.663762	+	0.747944i	$0.268959\pi$
$212$		0			0
$213$	−191.823	+	110.749i	−0.900578	+	0.519949i
$214$		0			0
$215$	126.840	+	73.2310i	0.589952	+	0.340609i
$216$		0			0
$217$	−219.612	−	31.5002i	−1.01204	−	0.145162i
$218$		0			0
$219$	65.6366	−	113.686i	0.299710	−	0.519114i
$220$		0			0
$221$	19.6704	+	34.0702i	0.0890065	+	0.154164i
$222$		0			0
$223$			287.737i			1.29030i	0.764056	+	0.645150i	$0.223205\pi$
$223$			287.737i			1.29030i	−0.764056	+	0.645150i	$0.776795\pi$
$224$		0			0
$225$	−2.11494			−0.00939972
$226$		0			0
$227$	345.499	−	199.474i	1.52202	−	0.878740i	0.522360	−	0.852725i	$-0.325052\pi$
$227$	345.499	−	199.474i	1.52202	−	0.878740i	0.999662	−	0.0260148i	$-0.00828172\pi$
$228$		0			0
$229$	−271.476	−	156.737i	−1.18548	−	0.684440i	−0.228207	−	0.973613i	$-0.573286\pi$
$229$	−271.476	−	156.737i	−1.18548	−	0.684440i	−0.957277	+	0.289173i	$0.906620\pi$
$230$		0			0
$231$	−55.0527	−	137.381i	−0.238323	−	0.594724i
$232$		0			0
$233$	70.3820	−	121.905i	0.302068	−	0.523198i	−0.674536	−	0.738242i	$-0.735656\pi$
$233$	70.3820	−	121.905i	0.302068	−	0.523198i	0.976604	+	0.215044i	$0.0689895\pi$
$234$		0			0
$235$	−19.2671	−	33.3716i	−0.0819876	−	0.142007i
$236$		0			0
$237$		−	32.9941i		−	0.139216i
$238$		0			0
$239$	149.255			0.624497			0.312249	−	0.950000i	$-0.398918\pi$
$239$	149.255			0.624497			0.312249	+	0.950000i	$0.398918\pi$
$240$		0			0
$241$	157.661	−	91.0259i	0.654197	−	0.377701i	−0.135865	−	0.990727i	$-0.543381\pi$
$241$	157.661	−	91.0259i	0.654197	−	0.377701i	0.790062	+	0.613027i	$0.210048\pi$
$242$		0			0
$243$	29.8712	+	17.2462i	0.122927	+	0.0709718i
$244$		0			0
$245$	−73.2770	+	250.180i	−0.299090	+	1.02114i
$246$		0			0
$247$	173.376	−	300.296i	0.701927	−	1.21577i
$248$		0			0
$249$	165.866	+	287.287i	0.666127	+	1.15377i
$250$		0			0
$251$		−	339.915i		−	1.35424i	−0.735872	−	0.677121i	$-0.763227\pi$
$251$		−	339.915i		−	1.35424i	0.735872	−	0.677121i	$-0.236773\pi$
$252$		0			0
$253$	164.249			0.649207
$254$		0			0
$255$	54.9272	−	31.7122i	0.215401	−	0.124362i
$256$		0			0
$257$	−374.303	−	216.104i	−1.45643	−	0.840872i	−0.457600	−	0.889158i	$-0.651291\pi$
$257$	−374.303	−	216.104i	−1.45643	−	0.840872i	−0.998834	+	0.0482862i	$0.984624\pi$
$258$		0			0
$259$	−413.704	+	165.783i	−1.59731	+	0.640090i
$260$		0			0
$261$	5.88805	−	10.1984i	0.0225596	−	0.0390743i
$262$		0			0
$263$	−118.967	−	206.056i	−0.452345	−	0.783485i	0.546186	−	0.837664i	$-0.316079\pi$
$263$	−118.967	−	206.056i	−0.452345	−	0.783485i	−0.998531	+	0.0541792i	$0.982746\pi$
$264$		0			0
$265$			317.399i			1.19773i
$266$		0			0
$267$	254.971			0.954948
$268$		0			0
$269$	−5.07112	+	2.92781i	−0.0188517	+	0.0108841i	−0.509396	−	0.860532i	$-0.670131\pi$
$269$	−5.07112	+	2.92781i	−0.0188517	+	0.0108841i	0.490545	+	0.871416i	$0.336798\pi$
$270$		0			0
$271$	90.1256	+	52.0341i	0.332567	+	0.192008i	0.656980	−	0.753908i	$-0.271833\pi$
$271$	90.1256	+	52.0341i	0.332567	+	0.192008i	−0.324413	+	0.945915i	$0.605167\pi$
$272$		0			0
$273$	−27.4193	+	191.161i	−0.100437	+	0.700223i
$274$		0			0
$275$	−12.0826	+	20.9276i	−0.0439366	+	0.0761004i
$276$		0			0
$277$	77.8673	+	134.870i	0.281109	+	0.486896i	0.971658	−	0.236390i	$-0.0759643\pi$
$277$	77.8673	+	134.870i	0.281109	+	0.486896i	−0.690549	+	0.723286i	$0.742631\pi$
$278$		0			0
$279$		−	20.2840i		−	0.0727026i
$280$		0			0
$281$	252.051			0.896979			0.448490	−	0.893788i	$-0.351962\pi$
$281$	252.051			0.896979			0.448490	+	0.893788i	$0.351962\pi$
$282$		0			0
$283$	376.075	−	217.127i	1.32889	−	0.767234i	0.343761	−	0.939057i	$-0.388299\pi$
$283$	376.075	−	217.127i	1.32889	−	0.767234i	0.985128	+	0.171823i	$0.0549658\pi$
$284$		0			0
$285$	−484.130	−	279.512i	−1.69870	−	0.980745i
$286$		0			0
$287$	−191.783	+	244.040i	−0.668233	+	0.850315i
$288$		0			0
$289$	8.50000	−	14.7224i	0.0294118	−	0.0509427i
$290$		0			0
$291$	237.075	+	410.626i	0.814691	+	1.41109i
$292$		0			0
$293$			91.5691i			0.312522i	0.987716	+	0.156261i	$0.0499442\pi$
$293$			91.5691i			0.312522i	−0.987716	+	0.156261i	$0.950056\pi$
$294$		0			0
$295$	−245.725			−0.832966
$296$		0			0
$297$	176.512	−	101.909i	0.594318	−	0.343130i
$298$		0			0
$299$	−185.605	−	107.159i	−0.620752	−	0.358392i
$300$		0			0
$301$	151.517	+	119.072i	0.503378	+	0.395587i
$302$		0			0
$303$	−34.7841	+	60.2479i	−0.114799	+	0.198838i
$304$		0			0
$305$	−168.532	−	291.906i	−0.552564	−	0.957069i
$306$		0			0
$307$			367.215i			1.19614i	0.801444	+	0.598070i	$0.204066\pi$
$307$			367.215i			1.19614i	−0.801444	+	0.598070i	$0.795934\pi$
$308$		0			0
$309$	−242.722			−0.785509
$310$		0			0
$311$	−166.654	+	96.2177i	−0.535865	+	0.309382i	−0.743401	−	0.668845i	$-0.766789\pi$
$311$	−166.654	+	96.2177i	−0.535865	+	0.309382i	0.207536	+	0.978227i	$0.433455\pi$
$312$		0			0
$313$	376.495	+	217.370i	1.20286	+	0.694472i	0.961190	−	0.275887i	$-0.0889715\pi$
$313$	376.495	+	217.370i	1.20286	+	0.694472i	0.241670	+	0.970358i	$0.422305\pi$
$314$		0			0
$315$	−23.5927	−	3.38404i	−0.0748975	−	0.0107430i
$316$		0			0
$317$	−165.583	+	286.799i	−0.522345	+	0.904729i	0.477317	+	0.878731i	$0.341609\pi$
$317$	−165.583	+	286.799i	−0.522345	+	0.904729i	−0.999662	+	0.0259972i	$0.991724\pi$
$318$		0			0
$319$	−67.2764	−	116.526i	−0.210898	−	0.365286i
$320$		0			0
$321$			57.9724i			0.180599i
$322$		0			0
$323$	−149.838			−0.463896
$324$		0			0
$325$	27.3070	−	15.7657i	0.0840217	−	0.0485099i
$326$		0			0
$327$	275.590	+	159.112i	0.842782	+	0.486580i
$328$		0			0
$329$	−18.8594	−	47.0627i	−0.0573234	−	0.143048i
$330$		0			0
$331$	166.532	−	288.442i	0.503118	−	0.871425i	−0.496876	−	0.867822i	$-0.665520\pi$
$331$	166.532	−	288.442i	0.503118	−	0.871425i	0.999994	−	0.00360353i	$-0.00114704\pi$
$332$		0			0
$333$	−20.3739	−	35.2886i	−0.0611828	−	0.105972i
$334$		0			0
$335$			233.910i			0.698238i
$336$		0			0
$337$	−24.6794			−0.0732326			−0.0366163	−	0.999329i	$-0.511658\pi$
$337$	−24.6794			−0.0732326			−0.0366163	+	0.999329i	$0.511658\pi$
$338$		0			0
$339$	168.034	−	97.0145i	0.495676	−	0.286178i
$340$		0			0
$341$	−200.713	−	115.882i	−0.588602	−	0.339829i
$342$		0			0
$343$	−142.173	+	312.147i	−0.414499	+	0.910050i
$344$		0			0
$345$	−172.759	+	299.228i	−0.500752	+	0.867327i
$346$		0			0
$347$	107.429	+	186.072i	0.309593	+	0.536231i	0.978273	−	0.207319i	$-0.0664739\pi$
$347$	107.429	+	186.072i	0.309593	+	0.536231i	−0.668680	+	0.743550i	$0.733141\pi$
$348$		0			0
$349$		−	94.3675i		−	0.270394i	−0.990819	−	0.135197i	$-0.956833\pi$
$349$		−	94.3675i		−	0.270394i	0.990819	−	0.135197i	$-0.0431667\pi$
$350$		0			0
$351$	−265.950			−0.757692
$352$		0			0
$353$	301.397	−	174.012i	0.853817	−	0.492952i	−0.00811980	−	0.999967i	$-0.502585\pi$
$353$	301.397	−	174.012i	0.853817	−	0.492952i	0.861937	+	0.507015i	$0.169251\pi$
$354$		0			0
$355$	352.961	+	203.782i	0.994256	+	0.574034i
$356$		0			0
$357$	77.4618	−	31.0412i	0.216980	−	0.0869502i
$358$		0			0
$359$	−46.9600	+	81.3370i	−0.130808	+	0.226566i	−0.923988	−	0.382421i	$-0.875090\pi$
$359$	−46.9600	+	81.3370i	−0.130808	+	0.226566i	0.793180	+	0.608987i	$0.208424\pi$
$360$		0			0
$361$	479.840	+	831.108i	1.32920	+	2.30224i
$362$		0			0
$363$			195.247i			0.537871i
$364$		0			0
$365$	−241.547			−0.661772
$366$		0			0
$367$	−69.8966	+	40.3548i	−0.190454	+	0.109959i	−0.592195	−	0.805795i	$-0.701739\pi$
$367$	−69.8966	+	40.3548i	−0.190454	+	0.109959i	0.401741	+	0.915753i	$0.368405\pi$
$368$		0			0
$369$	−24.5754	−	14.1886i	−0.0666001	−	0.0384516i
$370$		0			0
$371$	−59.2938	+	413.383i	−0.159822	+	1.11424i
$372$		0			0
$373$	105.265	−	182.324i	0.282211	−	0.488803i	−0.689718	−	0.724078i	$-0.742266\pi$
$373$	105.265	−	182.324i	0.282211	−	0.488803i	0.971929	+	0.235275i	$0.0755990\pi$
$374$		0			0
$375$	166.866	+	289.021i	0.444977	+	0.770723i
$376$		0			0
$377$			175.569i			0.465700i
$378$		0			0
$379$	238.172			0.628423			0.314212	−	0.949353i	$-0.398260\pi$
$379$	238.172			0.628423			0.314212	+	0.949353i	$0.398260\pi$
$380$		0			0
$381$	−367.175	+	211.988i	−0.963713	+	0.556400i
$382$		0			0
$383$	−293.414	−	169.403i	−0.766095	−	0.442305i	0.0653847	−	0.997860i	$-0.479173\pi$
$383$	−293.414	−	169.403i	−0.766095	−	0.442305i	−0.831480	+	0.555555i	$0.812506\pi$
$384$		0			0
$385$	−168.270	+	214.120i	−0.437064	+	0.556157i
$386$		0			0
$387$	−8.80925	+	15.2581i	−0.0227629	+	0.0394265i
$388$		0			0
$389$	−304.730	−	527.808i	−0.783369	−	1.35683i	−0.929969	−	0.367638i	$-0.880166\pi$
$389$	−304.730	−	527.808i	−0.783369	−	1.35683i	0.146600	−	0.989196i	$-0.453167\pi$
$390$		0			0
$391$			92.6112i			0.236857i
$392$		0			0
$393$	306.380			0.779594
$394$		0			0
$395$	−52.5765	+	30.3551i	−0.133105	+	0.0768483i
$396$		0			0
$397$	275.656	+	159.150i	0.694348	+	0.400882i	0.805239	−	0.592951i	$-0.202037\pi$
$397$	275.656	+	159.150i	0.694348	+	0.400882i	−0.110891	+	0.993833i	$0.535370\pi$
$398$		0			0
$399$	−578.318	−	454.480i	−1.44942	−	1.13905i
$400$		0			0
$401$	−250.236	+	433.421i	−0.624030	+	1.08085i	0.364698	+	0.931126i	$0.381172\pi$
$401$	−250.236	+	433.421i	−0.624030	+	1.08085i	−0.988728	+	0.149725i	$0.952161\pi$
$402$		0			0
$403$	151.207	+	261.897i	0.375202	+	0.649869i
$404$		0			0
$405$			398.114i			0.982998i
$406$		0			0
$407$	−465.581			−1.14393
$408$		0			0
$409$	−164.794	+	95.1437i	−0.402919	+	0.232625i	−0.687743	−	0.725955i	$-0.741398\pi$
$409$	−164.794	+	95.1437i	−0.402919	+	0.232625i	0.284824	+	0.958580i	$0.408065\pi$
$410$		0			0
$411$	−556.493	−	321.291i	−1.35400	−	0.781730i
$412$		0			0
$413$	−320.034	−	45.9043i	−0.774901	−	0.111148i
$414$		0			0
$415$	305.198	−	528.618i	0.735417	−	1.27378i
$416$		0			0
$417$	−232.103	−	402.015i	−0.556603	−	0.964064i
$418$		0			0
$419$		−	521.760i		−	1.24525i	−0.782520	−	0.622626i	$-0.786066\pi$
$419$		−	521.760i		−	1.24525i	0.782520	−	0.622626i	$-0.213934\pi$
$420$		0			0
$421$	−36.9165			−0.0876876			−0.0438438	−	0.999038i	$-0.513960\pi$
$421$	−36.9165			−0.0876876			−0.0438438	+	0.999038i	$0.513960\pi$
$422$		0			0
$423$	4.01441	−	2.31772i	0.00949032	−	0.00547924i
$424$		0			0
$425$	−11.7999	−	6.81269i	−0.0277645	−	0.0160299i
$426$		0			0
$427$	−164.966	−	411.664i	−0.386337	−	0.964085i
$428$		0			0
$429$	−100.869	+	174.710i	−0.235126	+	0.407250i
$430$		0			0
$431$	−84.9889	−	147.205i	−0.197190	−	0.341543i	0.750426	−	0.660954i	$-0.229848\pi$
$431$	−84.9889	−	147.205i	−0.197190	−	0.341543i	−0.947616	+	0.319411i	$0.896515\pi$
$432$		0			0
$433$		−	379.314i		−	0.876014i	−0.898972	−	0.438007i	$-0.855685\pi$
$433$		−	379.314i		−	0.876014i	0.898972	−	0.438007i	$-0.144315\pi$
$434$		0			0
$435$	283.048			0.650685
$436$		0			0
$437$	706.918	−	408.139i	1.61766	−	0.933957i
$438$		0			0
$439$	667.521	+	385.393i	1.52055	+	0.877889i	0.999706	+	0.0242370i	$0.00771562\pi$
$439$	667.521	+	385.393i	1.52055	+	0.877889i	0.520843	+	0.853653i	$0.325618\pi$
$440$		0			0
$441$	−30.0952	−	8.81479i	−0.0682430	−	0.0199882i
$442$		0			0
$443$	−3.31190	+	5.73638i	−0.00747608	+	0.0129489i	−0.869739	−	0.493512i	$-0.835713\pi$
$443$	−3.31190	+	5.73638i	−0.00747608	+	0.0129489i	0.862263	+	0.506460i	$0.169046\pi$
$444$		0			0
$445$	−234.577	−	406.300i	−0.527140	−	0.913034i
$446$		0			0
$447$			458.465i			1.02565i
$448$		0			0
$449$	−451.608			−1.00581			−0.502905	−	0.864342i	$-0.667735\pi$
$449$	−451.608			−1.00581			−0.502905	+	0.864342i	$0.667735\pi$
$450$		0			0
$451$	−280.797	+	162.118i	−0.622610	+	0.359464i
$452$		0			0
$453$	−449.393	−	259.457i	−0.992038	−	0.572753i
$454$		0			0
$455$	329.844	−	132.178i	0.724931	−	0.290501i
$456$		0			0
$457$	371.788	−	643.956i	0.813541	−	1.40909i	−0.0968299	−	0.995301i	$-0.530870\pi$
$457$	371.788	−	643.956i	0.813541	−	1.40909i	0.910371	−	0.413793i	$-0.135796\pi$
$458$		0			0
$459$	57.4612	+	99.5257i	0.125188	+	0.216832i
$460$		0			0
$461$			59.5149i			0.129100i	0.997914	+	0.0645498i	$0.0205611\pi$
$461$			59.5149i			0.129100i	−0.997914	+	0.0645498i	$0.979439\pi$
$462$		0			0
$463$	644.263			1.39150			0.695748	−	0.718286i	$-0.255073\pi$
$463$	644.263			1.39150			0.695748	+	0.718286i	$0.255073\pi$
$464$		0			0
$465$	422.225	−	243.772i	0.908010	−	0.524240i
$466$		0			0
$467$	52.9592	+	30.5760i	0.113403	+	0.0654732i	0.555629	−	0.831431i	$-0.312478\pi$
$467$	52.9592	+	30.5760i	0.113403	+	0.0654732i	−0.442226	+	0.896904i	$0.645811\pi$
$468$		0			0
$469$	−43.6971	+	304.646i	−0.0931707	+	0.649564i
$470$		0			0
$471$	−204.296	+	353.852i	−0.433750	+	0.751278i
$472$		0			0
$473$	100.654	+	174.338i	0.212799	+	0.368578i
$474$		0			0
$475$			120.095i			0.252831i
$476$		0			0
$477$	−38.1812			−0.0800444
$478$		0			0
$479$	−246.996	+	142.603i	−0.515650	+	0.297710i	−0.735153	−	0.677901i	$-0.762890\pi$
$479$	−246.996	+	142.603i	−0.515650	+	0.297710i	0.219503	+	0.975612i	$0.429556\pi$
$480$		0			0
$481$	526.115	+	303.753i	1.09379	+	0.631503i
$482$		0			0
$483$	−280.902	+	357.443i	−0.581578	+	0.740048i
$484$		0			0
$485$	436.226	−	755.565i	0.899434	−	1.55787i
$486$		0			0
$487$	−80.1264	−	138.783i	−0.164531	−	0.284975i	0.771958	−	0.635674i	$-0.219278\pi$
$487$	−80.1264	−	138.783i	−0.164531	−	0.284975i	−0.936489	+	0.350698i	$0.885944\pi$
$488$		0			0
$489$		−	40.9590i		−	0.0837608i
$490$		0			0
$491$	−337.995			−0.688382			−0.344191	−	0.938900i	$-0.611847\pi$
$491$	−337.995			−0.688382			−0.344191	+	0.938900i	$0.611847\pi$
$492$		0			0
$493$	65.7027	−	37.9335i	0.133271	−	0.0769441i
$494$		0			0
$495$	−21.5624	−	12.4491i	−0.0435604	−	0.0251496i
$496$		0			0
$497$	421.630	+	331.344i	0.848350	+	0.666689i
$498$		0			0
$499$	−252.617	+	437.545i	−0.506246	+	0.876844i	0.493728	+	0.869617i	$0.335634\pi$
$499$	−252.617	+	437.545i	−0.506246	+	0.876844i	−0.999974	+	0.00722778i	$0.997699\pi$
$500$		0			0
$501$	−299.913	−	519.464i	−0.598628	−	1.03685i
$502$		0			0
$503$		−	712.287i		−	1.41608i	−0.706174	−	0.708039i	$-0.749580\pi$
$503$		−	712.287i		−	1.41608i	0.706174	−	0.708039i	$-0.250420\pi$
$504$		0			0
$505$	128.008			0.253481
$506$		0			0
$507$	−195.208	+	112.703i	−0.385025	+	0.222295i
$508$		0			0
$509$	−562.232	−	324.605i	−1.10458	−	0.637730i	−0.167160	−	0.985930i	$-0.553460\pi$
$509$	−562.232	−	324.605i	−1.10458	−	0.637730i	−0.937420	+	0.348200i	$0.886793\pi$
$510$		0			0
$511$	−314.592	−	45.1238i	−0.615641	−	0.0883049i
$512$		0			0
$513$	506.464	−	877.222i	0.987260	−	1.70998i
$514$		0			0
$515$	223.308	+	386.781i	0.433608	+	0.751032i
$516$		0			0
$517$		−	52.9642i		−	0.102445i
$518$		0			0
$519$	382.213			0.736442
$520$		0			0
$521$	737.354	−	425.712i	1.41527	−	0.817105i	0.419390	−	0.907806i	$-0.362244\pi$
$521$	737.354	−	425.712i	1.41527	−	0.817105i	0.995878	+	0.0907012i	$0.0289108\pi$
$522$		0			0
$523$	−111.442	−	64.3412i	−0.213083	−	0.123023i	0.389661	−	0.920959i	$-0.372592\pi$
$523$	−111.442	−	64.3412i	−0.213083	−	0.123023i	−0.602743	+	0.797935i	$0.705926\pi$
$524$		0			0
$525$	−24.8793	−	62.0851i	−0.0473892	−	0.118257i
$526$		0			0
$527$	65.3394	−	113.171i	0.123984	−	0.214746i
$528$		0			0
$529$	12.2399	+	21.2002i	0.0231379	+	0.0400760i
$530$		0			0
$531$		−	29.5593i		−	0.0556672i
$532$		0			0
$533$	423.075			0.793761
$534$		0			0
$535$	92.3798	−	53.3355i	0.172673	−	0.0996926i
$536$		0			0
$537$	888.325	+	512.874i	1.65424	+	0.955073i
$538$		0			0
$539$	−259.156	+	247.437i	−0.480809	+	0.459067i
$540$		0			0
$541$	22.6512	−	39.2330i	0.0418691	−	0.0725194i	−0.844331	−	0.535821i	$-0.820002\pi$
$541$	22.6512	−	39.2330i	0.0418691	−	0.0725194i	0.886201	+	0.463302i	$0.153335\pi$
$542$		0			0
$543$	183.808	+	318.366i	0.338505	+	0.586309i
$544$		0			0
$545$		−	585.541i		−	1.07439i
$546$		0			0
$547$	278.643			0.509403			0.254701	−	0.967020i	$-0.418023\pi$
$547$	278.643			0.509403			0.254701	+	0.967020i	$0.418023\pi$
$548$		0			0
$549$	35.1146	−	20.2734i	0.0639610	−	0.0369279i
$550$		0			0
$551$	−579.105	−	334.347i	−1.05101	−	0.606800i
$552$		0			0
$553$	−74.1468	+	29.7128i	−0.134081	+	0.0537302i
$554$		0			0
$555$	489.703	−	848.190i	0.882348	−	1.52827i
$556$		0			0
$557$	−8.29452	−	14.3665i	−0.0148914	−	0.0257927i	0.858484	−	0.512841i	$-0.171407\pi$
$557$	−8.29452	−	14.3665i	−0.0148914	−	0.0257927i	−0.873375	+	0.487048i	$0.838074\pi$
$558$		0			0
$559$		−	262.673i		−	0.469898i
$560$		0			0
$561$	87.1751			0.155392
$562$		0			0
$563$	−4.21829	+	2.43543i	−0.00749252	+	0.00432581i	−0.503742	−	0.863854i	$-0.668044\pi$
$563$	−4.21829	+	2.43543i	−0.00749252	+	0.00432581i	0.496249	+	0.868180i	$0.334710\pi$
$564$		0			0
$565$	−309.188	−	178.510i	−0.547235	−	0.315946i
$566$		0			0
$567$	−74.3724	+	518.507i	−0.131168	+	0.914474i
$568$		0			0
$569$	−366.502	+	634.800i	−0.644115	+	1.11564i	0.340390	+	0.940284i	$0.389441\pi$
$569$	−366.502	+	634.800i	−0.644115	+	1.11564i	−0.984505	+	0.175356i	$0.943892\pi$
$570$		0			0
$571$	−80.7119	−	139.797i	−0.141352	−	0.244828i	0.786654	−	0.617394i	$-0.211812\pi$
$571$	−80.7119	−	139.797i	−0.141352	−	0.244828i	−0.928006	+	0.372565i	$0.878478\pi$
$572$		0			0
$573$			436.688i			0.762108i
$574$		0			0
$575$	74.2273			0.129091
$576$		0			0
$577$	507.815	−	293.187i	0.880096	−	0.508123i	0.00940570	−	0.999956i	$-0.497006\pi$
$577$	507.815	−	293.187i	0.880096	−	0.508123i	0.870690	+	0.491832i	$0.163673\pi$
$578$		0			0
$579$	−511.691	−	295.425i	−0.883750	−	0.510233i
$580$		0			0
$581$	496.244	−	631.462i	0.854121	−	1.08685i
$582$		0			0
$583$	−218.128	+	377.808i	−0.374147	+	0.648042i
$584$		0			0
$585$	16.2440	+	28.1354i	0.0277674	+	0.0480946i
$586$		0			0
$587$		−	834.623i		−	1.42185i	−0.703270	−	0.710923i	$-0.748278\pi$
$587$		−	834.623i		−	1.42185i	0.703270	−	0.710923i	$-0.251722\pi$
$588$		0			0
$589$	−1151.81			−1.95553
$590$		0			0
$591$	−291.185	+	168.115i	−0.492698	+	0.284459i
$592$		0			0
$593$	608.163	+	351.123i	1.02557	+	0.592113i	0.915712	−	0.401834i	$-0.131627\pi$
$593$	608.163	+	351.123i	1.02557	+	0.592113i	0.109857	+	0.993947i	$0.464961\pi$
$594$		0			0
$595$	−120.731	−	94.8781i	−0.202909	−	0.159459i
$596$		0			0
$597$	450.673	−	780.588i	0.754896	−	1.30752i
$598$		0			0
$599$	399.660	+	692.232i	0.667213	+	1.15565i	0.978680	+	0.205389i	$0.0658460\pi$
$599$	399.660	+	692.232i	0.667213	+	1.15565i	−0.311468	+	0.950257i	$0.600821\pi$
$600$		0			0
$601$		−	39.5750i		−	0.0658486i	−0.999458	−	0.0329243i	$-0.989518\pi$
$601$		−	39.5750i		−	0.0658486i	0.999458	−	0.0329243i	$-0.0104820\pi$
$602$		0			0
$603$	−28.1379			−0.0466633
$604$		0			0
$605$	311.129	−	179.631i	0.514264	−	0.296910i
$606$		0			0
$607$	74.9030	+	43.2453i	0.123399	+	0.0712443i	0.560429	−	0.828203i	$-0.310636\pi$
$607$	74.9030	+	43.2453i	0.123399	+	0.0712443i	−0.437030	+	0.899447i	$0.643970\pi$
$608$		0			0
$609$	368.644	+	52.8767i	0.605327	+	0.0868255i
$610$		0			0
$611$	−34.5547	+	59.8505i	−0.0565543	+	0.0979550i
$612$		0			0
$613$	92.1617	+	159.629i	0.150345	+	0.260406i	0.931354	−	0.364114i	$-0.118628\pi$
$613$	92.1617	+	159.629i	0.150345	+	0.260406i	−0.781009	+	0.624520i	$0.785295\pi$
$614$		0			0
$615$		−	682.071i		−	1.10906i
$616$		0			0
$617$	737.167			1.19476			0.597380	−	0.801958i	$-0.296208\pi$
$617$	737.167			1.19476			0.597380	+	0.801958i	$0.296208\pi$
$618$		0			0
$619$	−416.619	+	240.535i	−0.673051	+	0.388586i	−0.797232	−	0.603673i	$-0.793703\pi$
$619$	−416.619	+	240.535i	−0.673051	+	0.388586i	0.124180	+	0.992260i	$0.460370\pi$
$620$		0			0
$621$	−542.188	−	313.032i	−0.873088	−	0.504078i
$622$		0			0
$623$	−229.614	−	572.990i	−0.368562	−	0.919728i
$624$		0			0
$625$	348.348	−	603.356i	0.557356	−	0.965369i
$626$		0			0
$627$	−384.182	−	665.423i	−0.612730	−	1.06128i
$628$		0			0
$629$		−	262.515i		−	0.417354i
$630$		0			0
$631$	−378.950			−0.600555			−0.300277	−	0.953852i	$-0.597079\pi$
$631$	−378.950			−0.600555			−0.300277	+	0.953852i	$0.597079\pi$
$632$		0			0
$633$	−701.388	+	404.947i	−1.10804	+	0.639726i
$634$		0			0
$635$	675.613	+	390.065i	1.06396	+	0.614276i
$636$		0			0
$637$	454.284	−	110.531i	0.713161	−	0.173518i
$638$		0			0
$639$	−24.5138	+	42.4591i	−0.0383627	+	0.0664461i
$640$		0			0
$641$	358.189	+	620.402i	0.558798	+	0.967866i	0.997597	+	0.0692808i	$0.0220704\pi$
$641$	358.189	+	620.402i	0.558798	+	0.967866i	−0.438800	+	0.898585i	$0.644596\pi$
$642$		0			0
$643$		−	737.728i		−	1.14732i	−0.819093	−	0.573661i	$-0.805523\pi$
$643$		−	737.728i		−	1.14732i	0.819093	−	0.573661i	$-0.194477\pi$
$644$		0			0
$645$	−423.475			−0.656551
$646$		0			0
$647$	673.554	−	388.877i	1.04104	−	0.601046i	0.120914	−	0.992663i	$-0.461418\pi$
$647$	673.554	−	388.877i	1.04104	−	0.601046i	0.920128	+	0.391617i	$0.128084\pi$
$648$		0			0
$649$	−292.493	−	168.871i	−0.450683	−	0.260202i
$650$		0			0
$651$	595.448	−	238.613i	0.914667	−	0.366534i
$652$		0			0
$653$	161.967	−	280.536i	0.248036	−	0.429610i	−0.714945	−	0.699181i	$-0.753548\pi$
$653$	161.967	−	280.536i	0.248036	−	0.429610i	0.962981	+	0.269570i	$0.0868816\pi$
$654$		0			0
$655$	−281.875	−	488.221i	−0.430343	−	0.745376i
$656$		0			0
$657$		−	29.0567i		−	0.0442263i
$658$		0			0
$659$	−887.078			−1.34610			−0.673048	−	0.739598i	$-0.735015\pi$
$659$	−887.078			−1.34610			−0.673048	+	0.739598i	$0.735015\pi$
$660$		0			0
$661$	−366.619	+	211.667i	−0.554642	+	0.320223i	−0.750992	−	0.660311i	$-0.770424\pi$
$661$	−366.619	+	211.667i	−0.554642	+	0.320223i	0.196350	+	0.980534i	$0.437091\pi$
$662$		0			0
$663$	−98.5095	−	56.8745i	−0.148581	−	0.0857836i
$664$		0			0
$665$	−192.159	+	1339.69i	−0.288961	+	2.01457i
$666$		0			0
$667$	−206.651	+	357.930i	−0.309821	+	0.536626i
$668$		0			0
$669$	−415.976	−	720.492i	−0.621788	−	1.07697i
$670$		0			0
$671$		−	463.285i		−	0.690440i
$672$		0			0
$673$	−508.593			−0.755711			−0.377855	−	0.925865i	$-0.623338\pi$
$673$	−508.593			−0.755711			−0.377855	+	0.925865i	$0.623338\pi$
$674$		0			0
$675$	79.7692	−	46.0547i	0.118177	−	0.0682292i
$676$		0			0
$677$	−835.924	−	482.621i	−1.23475	−	0.712882i	−0.266732	−	0.963771i	$-0.585944\pi$
$677$	−835.924	−	482.621i	−1.23475	−	0.712882i	−0.968016	+	0.250889i	$0.919277\pi$
$678$		0			0
$679$	709.292	−	902.562i	1.04461	−	1.32925i
$680$		0			0
$681$	−576.753	+	998.965i	−0.846920	+	1.46691i
$682$		0			0
$683$	−138.350	−	239.629i	−0.202562	−	0.350848i	0.746791	−	0.665059i	$-0.231593\pi$
$683$	−138.350	−	239.629i	−0.202562	−	0.350848i	−0.949353	+	0.314211i	$0.898260\pi$
$684$		0			0
$685$			1182.37i			1.72609i
$686$		0			0
$687$	906.367			1.31931
$688$		0			0
$689$	492.977	−	284.620i	0.715496	−	0.413092i
$690$		0			0
$691$	−283.715	−	163.803i	−0.410587	−	0.237052i	0.280455	−	0.959867i	$-0.409515\pi$
$691$	−283.715	−	163.803i	−0.410587	−	0.237052i	−0.691042	+	0.722815i	$0.742848\pi$
$692$		0			0
$693$	−25.7574	−	20.2419i	−0.0371680	−	0.0292090i
$694$		0			0
$695$	−427.077	+	739.720i	−0.614500	+	1.06435i
$696$		0			0
$697$	−91.4096	−	158.326i	−0.131147	−	0.227154i
$698$		0			0
$699$			407.000i			0.582261i
$700$		0			0
$701$	621.060			0.885963			0.442982	−	0.896531i	$-0.353921\pi$
$701$	621.060			0.885963			0.442982	+	0.896531i	$0.353921\pi$
$702$		0			0
$703$	−2003.83	+	1156.91i	−2.85039	+	1.64567i
$704$		0			0
$705$	96.4896	+	55.7083i	0.136865	+	0.0790188i
$706$		0			0
$707$	166.718	+	23.9134i	0.235811	+	0.0338237i
$708$		0			0
$709$	−76.0821	+	131.778i	−0.107309	+	0.185865i	−0.914679	−	0.404181i	$-0.867557\pi$
$709$	−76.0821	+	131.778i	−0.107309	+	0.185865i	0.807370	+	0.590045i	$0.200890\pi$
$710$		0			0
$711$	−3.65154	−	6.32465i	−0.00513578	−	0.00889543i
$712$		0			0
$713$			711.902i			0.998460i
$714$		0			0
$715$	371.204			0.519167
$716$		0			0
$717$	−373.734	+	215.775i	−0.521247	+	0.300942i
$718$		0			0
$719$	481.605	+	278.055i	0.669826	+	0.386724i	0.796011	−	0.605283i	$-0.206940\pi$
$719$	481.605	+	278.055i	0.669826	+	0.386724i	−0.126185	+	0.992007i	$0.540273\pi$
$720$		0			0
$721$	218.583	+	545.464i	0.303167	+	0.756538i
$722$		0			0
$723$	−263.189	+	455.857i	−0.364024	+	0.630508i
$724$		0			0
$725$	−30.4034	−	52.6603i	−0.0419357	−	0.0726348i
$726$		0			0
$727$		−	464.327i		−	0.638689i	−0.947639	−	0.319345i	$-0.896537\pi$
$727$		−	464.327i		−	0.638689i	0.947639	−	0.319345i	$-0.103463\pi$
$728$		0			0
$729$	−773.204			−1.06064
$730$		0			0
$731$	−98.2994	+	56.7532i	−0.134473	+	0.0776378i
$732$		0			0
$733$	473.403	+	273.319i	0.645843	+	0.372877i	0.786862	−	0.617129i	$-0.211705\pi$
$733$	473.403	+	273.319i	0.645843	+	0.372877i	−0.141019	+	0.990007i	$0.545038\pi$
$734$		0			0
$735$	−178.195	−	732.385i	−0.242443	−	0.996442i
$736$		0			0
$737$	−160.751	+	278.429i	−0.218115	+	0.377787i
$738$		0			0
$739$	371.095	+	642.755i	0.502158	+	0.869764i	0.999997	+	0.00249395i	$0.000793851\pi$
$739$	371.095	+	642.755i	0.502158	+	0.869764i	−0.497839	+	0.867270i	$0.665873\pi$
$740$		0			0
$741$			1002.59i			1.35302i
$742$		0			0
$743$	−1249.85			−1.68217			−0.841085	−	0.540903i	$-0.818083\pi$
$743$	−1249.85			−1.68217			−0.841085	+	0.540903i	$0.818083\pi$
$744$		0			0
$745$	730.570	−	421.795i	0.980631	−	0.566168i
$746$		0			0
$747$	63.5897	+	36.7135i	0.0851267	+	0.0491479i
$748$		0			0
$749$	130.280	−	52.2070i	0.173938	−	0.0697022i
$750$		0			0
$751$	524.780	−	908.946i	0.698775	−	1.21031i	−0.270116	−	0.962828i	$-0.587062\pi$
$751$	524.780	−	908.946i	0.698775	−	1.21031i	0.968891	−	0.247486i	$-0.0796044\pi$
$752$		0			0
$753$	491.409	+	851.146i	0.652602	+	1.13034i
$754$		0			0
$755$			954.819i			1.26466i
$756$		0			0
$757$	606.465			0.801143			0.400571	−	0.916266i	$-0.368812\pi$
$757$	606.465			0.801143			0.400571	+	0.916266i	$0.368812\pi$
$758$		0			0
$759$	−411.280	+	237.453i	−0.541871	+	0.312849i
$760$		0			0
$761$	−268.805	−	155.195i	−0.353226	−	0.203935i	0.312879	−	0.949793i	$-0.398706\pi$
$761$	−268.805	−	155.195i	−0.353226	−	0.203935i	−0.666105	+	0.745858i	$0.732040\pi$
$762$		0			0
$763$	109.386	−	762.614i	0.143363	−	0.999494i
$764$		0			0
$765$	7.01934	−	12.1579i	0.00917561	−	0.0158926i
$766$		0			0
$767$	220.349	+	381.655i	0.287286	+	0.497594i
$768$		0			0
$769$			619.668i			0.805810i	0.915242	+	0.402905i	$0.131999\pi$
$769$			619.668i			0.805810i	−0.915242	+	0.402905i	$0.868001\pi$
$770$		0			0
$771$	1249.67			1.62085
$772$		0			0
$773$	26.0713	−	15.0523i	0.0337274	−	0.0194725i	−0.483041	−	0.875597i	$-0.660468\pi$
$773$	26.0713	−	15.0523i	0.0337274	−	0.0194725i	0.516769	+	0.856125i	$0.327135\pi$
$774$		0			0
$775$	−90.7060	−	52.3691i	−0.117040	−	0.0675730i
$776$		0			0
$777$	796.245	−	1013.21i	1.02477	−	1.30400i
$778$		0			0
$779$	−805.687	+	1395.49i	−1.03426	+	1.79139i
$780$		0			0
$781$	280.093	+	485.134i	0.358633	+	0.621171i
$782$		0			0
$783$			512.871i			0.655007i
$784$		0			0
$785$	751.824			0.957738
$786$		0			0
$787$	−1096.44	+	633.031i	−1.39319	+	0.804360i	−0.993667	−	0.112362i	$-0.964158\pi$
$787$	−1096.44	+	633.031i	−1.39319	+	0.804360i	−0.399525	+	0.916722i	$0.630825\pi$
$788$		0			0
$789$	595.785	+	343.977i	0.755114	+	0.435965i
$790$		0			0
$791$	−369.341	−	290.252i	−0.466929	−	0.366944i
$792$		0			0
$793$	−302.255	+	523.521i	−0.381154	+	0.660178i
$794$		0			0
$795$	−458.858	−	794.766i	−0.577180	−	0.999705i
$796$		0			0
$797$		−	1438.14i		−	1.80445i	−0.431269	−	0.902223i	$-0.641934\pi$
$797$		−	1438.14i		−	1.80445i	0.431269	−	0.902223i	$-0.358066\pi$
$798$		0			0
$799$	29.8636			0.0373762
$800$		0			0
$801$	48.8755	−	28.2183i	0.0610181	−	0.0352288i
$802$		0			0
$803$	−287.520	−	166.000i	−0.358057	−	0.206724i
$804$		0			0
$805$	828.026	+	118.768i	1.02860	+	0.147538i
$806$		0			0
$807$	8.46538	−	14.6625i	0.0104899	−	0.0181691i
$808$		0			0
$809$	−581.479	−	1007.15i	−0.718762	−	1.24493i	−0.961490	−	0.274838i	$-0.911376\pi$
$809$	−581.479	−	1007.15i	−0.718762	−	1.24493i	0.242728	−	0.970094i	$-0.421958\pi$
$810$		0			0
$811$			1234.64i			1.52237i	0.648534	+	0.761186i	$0.275383\pi$
$811$			1234.64i			1.52237i	−0.648534	+	0.761186i	$0.724617\pi$
$812$		0			0
$813$	−300.899			−0.370110
$814$		0			0
$815$	−65.2688	+	37.6830i	−0.0800845	+	0.0462368i
$816$		0			0
$817$	866.414	+	500.224i	1.06048	+	0.612270i
$818$		0			0
$819$	15.9002	+	39.6783i	0.0194142	+	0.0484472i
$820$		0			0
$821$	129.186	−	223.756i	0.157352	−	0.272541i	−0.776561	−	0.630042i	$-0.783038\pi$
$821$	129.186	−	223.756i	0.157352	−	0.272541i	0.933913	+	0.357501i	$0.116371\pi$
$822$		0			0
$823$	503.256	+	871.664i	0.611489	+	1.05913i	0.990990	+	0.133939i	$0.0427626\pi$
$823$	503.256	+	871.664i	0.611489	+	1.05913i	−0.379500	+	0.925192i	$0.623904\pi$
$824$		0			0
$825$		−	69.8703i		−	0.0846912i
$826$		0			0
$827$	952.918			1.15226			0.576129	−	0.817358i	$-0.304562\pi$
$827$	952.918			1.15226			0.576129	+	0.817358i	$0.304562\pi$
$828$		0			0
$829$	−960.161	+	554.349i	−1.15822	+	0.668696i	−0.950876	−	0.309572i	$-0.899814\pi$
$829$	−960.161	+	554.349i	−1.15822	+	0.668696i	−0.207340	+	0.978269i	$0.566481\pi$
$830$		0			0
$831$	−389.959	−	225.143i	−0.469265	−	0.270930i
$832$		0			0
$833$	−139.516	−	146.124i	−0.167487	−	0.175419i
$834$		0			0
$835$	−551.849	+	955.831i	−0.660897	+	1.14471i
$836$		0			0
$837$	441.703	+	765.053i	0.527722	+	0.914042i
$838$		0			0
$839$			311.542i			0.371325i	0.982614	+	0.185663i	$0.0594432\pi$
$839$			311.542i			0.371325i	−0.982614	+	0.185663i	$0.940557\pi$
$840$		0			0
$841$	−502.424			−0.597413
$842$		0			0
$843$	−631.136	+	364.386i	−0.748678	+	0.432249i
$844$		0			0
$845$	359.189	+	207.378i	0.425076	+	0.245417i
$846$		0			0
$847$	438.775	−	175.830i	0.518034	−	0.207591i
$848$		0			0
$849$	−627.795	+	1087.37i	−0.739452	+	1.28077i
$850$		0			0
$851$	715.055	+	1238.51i	0.840253	+	1.45536i
$852$		0			0
$853$		−	934.407i		−	1.09544i	−0.836663	−	0.547718i	$-0.815497\pi$
$853$		−	934.407i		−	1.09544i	0.836663	−	0.547718i	$-0.184503\pi$
$854$		0			0
$855$	−123.737			−0.144722
$856$		0			0
$857$	−489.457	+	282.588i	−0.571128	+	0.329741i	−0.757600	−	0.652719i	$-0.773628\pi$
$857$	−489.457	+	282.588i	−0.571128	+	0.329741i	0.186472	+	0.982460i	$0.440295\pi$
$858$		0			0
$859$	−681.096	−	393.231i	−0.792894	−	0.457778i	0.0480863	−	0.998843i	$-0.484688\pi$
$859$	−681.096	−	393.231i	−0.792894	−	0.457778i	−0.840980	+	0.541066i	$0.818021\pi$
$860$		0			0
$861$	127.419	−	888.335i	0.147989	−	1.03175i
$862$		0			0
$863$	−223.022	+	386.285i	−0.258426	+	0.447607i	−0.965820	−	0.259212i	$-0.916537\pi$
$863$	−223.022	+	386.285i	−0.258426	+	0.447607i	0.707394	+	0.706819i	$0.249871\pi$
$864$		0			0
$865$	−351.642	−	609.063i	−0.406523	−	0.704119i
$866$		0			0
$867$			49.1533i			0.0566935i
$868$		0			0
$869$	−83.4444			−0.0960235
$870$		0			0
$871$	363.304	−	209.753i	0.417111	−	0.240819i
$872$		0			0
$873$	90.8900	+	52.4754i	0.104112	+	0.0601092i
$874$		0			0
$875$	499.239	−	635.273i	0.570559	−	0.726026i
$876$		0			0
$877$	222.150	−	384.775i	0.253306	−	0.438740i	−0.711128	−	0.703063i	$-0.751815\pi$
$877$	222.150	−	384.775i	0.253306	−	0.438740i	0.964434	+	0.264323i	$0.0851486\pi$
$878$		0			0
$879$	−132.380	−	229.289i	−0.150603	−	0.260852i
$880$		0			0
$881$		−	154.380i		−	0.175232i	−0.996154	−	0.0876162i	$-0.972075\pi$
$881$		−	154.380i		−	0.175232i	0.996154	−	0.0876162i	$-0.0279249\pi$
$882$		0			0
$883$	−1156.18			−1.30938			−0.654688	−	0.755899i	$-0.727200\pi$
$883$	−1156.18			−1.30938			−0.654688	+	0.755899i	$0.727200\pi$
$884$		0			0
$885$	615.295	−	355.241i	0.695249	−	0.401402i
$886$		0			0
$887$	−480.949	−	277.676i	−0.542220	−	0.313051i	0.203758	−	0.979021i	$-0.434684\pi$
$887$	−480.949	−	277.676i	−0.542220	−	0.313051i	−0.745978	+	0.665970i	$0.768018\pi$
$888$		0			0
$889$	807.055	+	634.237i	0.907823	+	0.713427i
$890$		0			0
$891$	−273.598	+	473.886i	−0.307069	+	0.531859i
$892$		0			0
$893$	−131.609	−	227.954i	−0.147379	−	0.255268i
$894$		0			0
$895$		−	1887.41i		−	2.10884i
$896$		0			0
$897$	619.673			0.690828
$898$		0			0
$899$	505.056	−	291.594i	0.561797	−	0.324354i
$900$		0			0
$901$	−213.025	−	122.990i	−0.236432	−	0.136504i
$902$		0			0
$903$	−551.538	−	79.1102i	−0.610784	−	0.0876082i
$904$		0			0
$905$	338.213	−	585.803i	0.373717	−	0.647296i
$906$		0			0
$907$	−451.333	−	781.731i	−0.497610	−	0.861886i	0.502386	−	0.864644i	$-0.332456\pi$
$907$	−451.333	−	781.731i	−0.497610	−	0.861886i	−0.999996	+	0.00275709i	$0.999122\pi$
$908$		0			0
$909$			15.3986i			0.0169401i
$910$		0			0
$911$	315.518			0.346343			0.173171	−	0.984892i	$-0.444599\pi$
$911$	315.518			0.346343			0.173171	+	0.984892i	$0.444599\pi$
$912$		0			0
$913$	726.571	−	419.486i	0.795806	−	0.459459i
$914$		0			0
$915$	844.008	+	487.288i	0.922413	+	0.532555i
$916$		0			0
$917$	−275.910	−	688.521i	−0.300884	−	0.750841i
$918$		0			0
$919$	791.899	−	1371.61i	0.861696	−	1.49250i	−0.00859479	−	0.999963i	$-0.502736\pi$
$919$	791.899	−	1371.61i	0.861696	−	1.49250i	0.870291	−	0.492538i	$-0.163931\pi$
$920$		0			0
$921$	−530.877	−	919.506i	−0.576414	−	0.998378i
$922$		0			0
$923$		−	730.948i		−	0.791927i
$924$		0			0
$925$	−210.404			−0.227464
$926$		0			0
$927$	−46.5275	+	26.8627i	−0.0501915	+	0.0289781i
$928$		0			0
$929$	−276.209	−	159.469i	−0.297319	−	0.171657i	0.343919	−	0.938999i	$-0.388245\pi$
$929$	−276.209	−	159.469i	−0.297319	−	0.171657i	−0.641238	+	0.767342i	$0.721579\pi$
$930$		0			0
$931$	−500.539	+	1708.92i	−0.537636	+	1.83558i
$932$		0			0
$933$	278.201	−	481.858i	0.298179	−	0.516461i
$934$		0			0
$935$	−80.2025	−	138.915i	−0.0857781	−	0.148572i
$936$		0			0
$937$		−	123.397i		−	0.131694i	−0.997830	−	0.0658468i	$-0.979025\pi$
$937$		−	123.397i		−	0.131694i	0.997830	−	0.0658468i	$-0.0209749\pi$
$938$		0			0
$939$	−1256.99			−1.33865
$940$		0			0
$941$	−1517.88	+	876.350i	−1.61305	+	0.931297i	−0.624397	+	0.781108i	$0.714655\pi$
$941$	−1517.88	+	876.350i	−1.61305	+	0.931297i	−0.988657	+	0.150189i	$0.952012\pi$
$942$		0			0
$943$	862.516	+	497.974i	0.914651	+	0.528074i
$944$		0			0
$945$	963.537	−	386.118i	1.01962	−	0.408590i
$946$		0			0
$947$	−800.627	+	1386.73i	−0.845435	+	1.46434i	0.0398083	+	0.999207i	$0.487325\pi$
$947$	−800.627	+	1386.73i	−0.845435	+	1.46434i	−0.885243	+	0.465129i	$0.846008\pi$
$948$		0			0
$949$	216.602	+	375.165i	0.228242	+	0.395327i
$950$		0			0
$951$		−	957.525i		−	1.00686i
$952$		0			0
$953$	−1258.49			−1.32055			−0.660276	−	0.751023i	$-0.729561\pi$
$953$	−1258.49			−1.32055			−0.660276	+	0.751023i	$0.729561\pi$
$954$		0			0
$955$	695.868	−	401.760i	0.728658	−	0.420691i
$956$		0			0
$957$	336.920	+	194.521i	0.352058	+	0.203261i
$958$		0			0
$959$	−220.881	+	1539.93i	−0.230324	+	1.60577i
$960$		0			0
$961$	21.7635	−	37.6955i	0.0226467	−	0.0392253i
$962$		0			0
$963$	6.41595	+	11.1127i	0.00666246	+	0.0115397i
$964$		0			0
$965$			1087.18i			1.12662i
$966$		0			0
$967$	836.556			0.865105			0.432552	−	0.901609i	$-0.357613\pi$
$967$	836.556			0.865105			0.432552	+	0.901609i	$0.357613\pi$
$968$		0			0
$969$	375.195	−	216.619i	0.387198	−	0.223549i
$970$		0			0
$971$	1268.62	+	732.439i	1.30651	+	0.754314i	0.981512	−	0.191400i	$-0.0613028\pi$
$971$	1268.62	+	732.439i	1.30651	+	0.754314i	0.324999	+	0.945714i	$0.394636\pi$
$972$		0			0
$973$	−694.417	+	883.634i	−0.713687	+	0.908154i
$974$		0			0
$975$	−45.5845	+	78.9547i	−0.0467534	+	0.0809792i
$976$		0			0
$977$	63.7189	+	110.364i	0.0652190	+	0.112963i	0.896791	−	0.442454i	$-0.145892\pi$
$977$	63.7189	+	110.364i	0.0652190	+	0.112963i	−0.831572	+	0.555417i	$0.812559\pi$
$978$		0			0
$979$		−	644.840i		−	0.658672i
$980$		0			0
$981$	70.4372			0.0718014
$982$		0			0
$983$	−972.073	+	561.227i	−0.988884	+	0.570933i	−0.904941	−	0.425538i	$-0.860085\pi$
$983$	−972.073	+	561.227i	−0.988884	+	0.570933i	−0.0839435	+	0.996471i	$0.526752\pi$
$984$		0			0
$985$	535.789	+	309.338i	0.543948	+	0.314049i
$986$		0			0
$987$	115.262	+	90.5803i	0.116780	+	0.0917733i
$988$		0			0
$989$	309.176	−	535.508i	0.312614	−	0.541464i
$990$		0			0
$991$	−828.620	−	1435.21i	−0.836146	−	1.44825i	−0.893094	−	0.449869i	$-0.851471\pi$
$991$	−828.620	−	1435.21i	−0.836146	−	1.44825i	0.0569488	−	0.998377i	$-0.481863\pi$
$992$		0			0
$993$			963.010i			0.969799i
$994$		0			0
$995$	−1658.51			−1.66684
$996$		0			0
$997$	−888.074	+	512.730i	−0.890747	+	0.514273i	−0.874187	−	0.485590i	$-0.838605\pi$
$997$	−888.074	+	512.730i	−0.890747	+	0.514273i	−0.0165600	+	0.999863i	$0.505271\pi$
$998$		0			0
$999$	1536.88	+	887.320i	1.53842	+	0.888208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.3.s.a.341.7	✓	44
7.3	odd	6	inner	476.3.s.a.409.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.3.s.a.341.7	✓	44	1.1	even	1	trivial
476.3.s.a.409.7	yes	44	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	476.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.50400 + 1.44568i) q^{3} +(4.60744 + 2.66011i) q^{5} +(5.50382 + 4.32527i) q^{7} +(-0.319995 + 0.554248i) q^{9} +O(q^{10})\)	\(q+(-2.50400 + 1.44568i) q^{3} +(4.60744 + 2.66011i) q^{5} +(5.50382 + 4.32527i) q^{7} +(-0.319995 + 0.554248i) q^{9} +(3.65624 + 6.33279i) q^{11} -9.54157i q^{13} -15.3827 q^{15} +(-3.57071 + 2.06155i) q^{17} +(31.4724 + 18.1706i) q^{19} +(-20.0345 - 2.87367i) q^{21} +(11.2308 - 19.4523i) q^{23} +(1.65232 + 2.86190i) q^{25} -27.8728i q^{27} -18.4004 q^{29} +(-27.4480 + 15.8471i) q^{31} +(-18.3104 - 10.5715i) q^{33} +(13.8529 + 34.5691i) q^{35} +(-31.8347 + 55.1393i) q^{37} +(13.7941 + 23.8921i) q^{39} +44.3402i q^{41} +27.5293 q^{43} +(-2.94871 + 1.70244i) q^{45} +(-6.27261 - 3.62149i) q^{47} +(11.5842 + 47.6110i) q^{49} +(5.96071 - 10.3242i) q^{51} +(29.8295 + 51.6662i) q^{53} +38.9039i q^{55} -105.076 q^{57} +(-39.9992 + 23.0935i) q^{59} +(-54.8674 - 31.6777i) q^{61} +(-4.15846 + 1.66642i) q^{63} +(25.3816 - 43.9622i) q^{65} +(21.9831 + 38.0759i) q^{67} +64.9445i q^{69} +76.6067 q^{71} +(-39.3191 + 22.7009i) q^{73} +(-8.27482 - 4.77747i) q^{75} +(-7.26771 + 50.6688i) q^{77} +(-5.70562 + 9.88242i) q^{79} +(37.4153 + 64.8051i) q^{81} -114.732i q^{83} -21.9358 q^{85} +(46.0746 - 26.6012i) q^{87} +(-76.3692 - 44.0918i) q^{89} +(41.2698 - 52.5151i) q^{91} +(45.8199 - 79.3624i) q^{93} +(96.6713 + 167.440i) q^{95} -163.988i q^{97} -4.67991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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