LMFDB - Embedded newform 572.2.bv.a.41.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(41,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 18, 5]))

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

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

chi := DirichletCharacter("572.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bv (of order $60$, degree $16$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			41.14
Character	$\chi$	$=$	572.41
Dual form			572.2.bv.a.293.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17604 - 2.41674i) q^{3} +(-2.60150 + 0.412038i) q^{5} +(-4.67346 - 0.244925i) q^{7} +(-0.791886 - 7.53429i) q^{9} +O(q^{10})$	\(q+(2.17604 - 2.41674i) q^{3} +(-2.60150 + 0.412038i) q^{5} +(-4.67346 - 0.244925i) q^{7} +(-0.791886 - 7.53429i) q^{9} +(1.02183 + 3.15529i) q^{11} +(-3.20300 - 1.65554i) q^{13} +(-4.66519 + 7.18377i) q^{15} +(1.65482 - 0.736772i) q^{17} +(-1.61119 - 2.48102i) q^{19} +(-10.7616 + 10.7616i) q^{21} +(1.36235 - 0.786555i) q^{23} +(1.84276 - 0.598749i) q^{25} +(-12.0387 - 8.74664i) q^{27} +(-1.20259 - 5.65775i) q^{29} +(1.11856 - 7.06231i) q^{31} +(9.84907 + 4.39654i) q^{33} +(12.2589 - 1.28847i) q^{35} +(6.19179 + 4.02099i) q^{37} +(-10.9709 + 4.13830i) q^{39} +(-1.52565 + 0.0799559i) q^{41} +(-2.46467 + 4.26893i) q^{43} +(5.16450 + 19.2742i) q^{45} +(0.373867 - 0.733754i) q^{47} +(14.8196 + 1.55760i) q^{49} +(1.82037 - 5.60251i) q^{51} +(-0.294980 + 0.214316i) q^{53} +(-3.95840 - 7.78746i) q^{55} +(-9.50201 - 1.50497i) q^{57} +(0.798508 - 15.2364i) q^{59} +(3.32318 + 7.46398i) q^{61} +(1.85550 + 35.4051i) q^{63} +(9.01475 + 2.98713i) q^{65} +(2.65162 + 0.710499i) q^{67} +(1.06364 - 5.00403i) q^{69} +(0.683107 - 1.77955i) q^{71} +(2.94967 + 5.78905i) q^{73} +(2.56290 - 5.75637i) q^{75} +(-4.00268 - 14.9964i) q^{77} +(-3.48647 - 4.79872i) q^{79} +(-25.1044 + 5.33610i) q^{81} +(-1.60599 - 10.1398i) q^{83} +(-4.00143 + 2.59856i) q^{85} +(-16.2902 - 9.40516i) q^{87} +(0.136159 - 0.508151i) q^{89} +(14.5636 + 8.52157i) q^{91} +(-14.6337 - 18.0711i) q^{93} +(5.21380 + 5.79051i) q^{95} +(-10.0919 - 8.17229i) q^{97} +(22.9637 - 10.1974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 28 q^{9}+O(q^{10}) $ 224 * q + 28 * q^9	$ 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) $ 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$

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
$3$	2.17604	−	2.41674i	1.25634	−	1.39531i	0.372152	−	0.928172i	$-0.378620\pi$
$3$	2.17604	−	2.41674i	1.25634	−	1.39531i	0.884187	−	0.467133i	$-0.154713\pi$
$4$		0			0
$5$	−2.60150	+	0.412038i	−1.16343	+	0.184269i	−0.708138	−	0.706074i	$-0.750464\pi$
$5$	−2.60150	+	0.412038i	−1.16343	+	0.184269i	−0.455290	+	0.890343i	$0.650464\pi$
$6$		0			0
$7$	−4.67346	−	0.244925i	−1.76640	−	0.0925731i	−0.858775	−	0.512353i	$-0.828774\pi$
$7$	−4.67346	−	0.244925i	−1.76640	−	0.0925731i	−0.907626	+	0.419780i	$0.862107\pi$
$8$		0			0
$9$	−0.791886	−	7.53429i	−0.263962	−	2.51143i
$10$		0			0
$11$	1.02183	+	3.15529i	0.308094	+	0.951356i
$11$	1.02183	+	3.15529i	0.308094	+	0.951356i
$12$		0			0
$13$	−3.20300	−	1.65554i	−0.888352	−	0.459163i
$13$	−3.20300	−	1.65554i	−0.888352	−	0.459163i
$14$		0			0
$15$	−4.66519	+	7.18377i	−1.20455	+	1.85484i
$16$		0			0
$17$	1.65482	−	0.736772i	0.401352	−	0.178694i	−0.196126	−	0.980579i	$-0.562836\pi$
$17$	1.65482	−	0.736772i	0.401352	−	0.178694i	0.597478	+	0.801885i	$0.296169\pi$
$18$		0			0
$19$	−1.61119	−	2.48102i	−0.369633	−	0.569185i	0.604091	−	0.796915i	$-0.293536\pi$
$19$	−1.61119	−	2.48102i	−0.369633	−	0.569185i	−0.973724	+	0.227730i	$0.926870\pi$
$20$		0			0
$21$	−10.7616	+	10.7616i	−2.34836	+	2.34836i
$22$		0			0
$23$	1.36235	−	0.786555i	0.284070	−	0.164008i	−0.351194	−	0.936303i	$-0.614224\pi$
$23$	1.36235	−	0.786555i	0.284070	−	0.164008i	0.635265	+	0.772295i	$0.280891\pi$
$24$		0			0
$25$	1.84276	−	0.598749i	0.368552	−	0.119750i
$26$		0			0
$27$	−12.0387	−	8.74664i	−2.31685	−	1.68329i
$28$		0			0
$29$	−1.20259	−	5.65775i	−0.223316	−	1.05062i	−0.936778	−	0.349925i	$-0.886207\pi$
$29$	−1.20259	−	5.65775i	−0.223316	−	1.05062i	0.713462	−	0.700694i	$-0.247126\pi$
$30$		0			0
$31$	1.11856	−	7.06231i	0.200899	−	1.26843i	−0.656717	−	0.754137i	$-0.728055\pi$
$31$	1.11856	−	7.06231i	0.200899	−	1.26843i	0.857616	−	0.514290i	$-0.171945\pi$
$32$		0			0
$33$	9.84907	+	4.39654i	1.71450	+	0.765340i
$34$		0			0
$35$	12.2589	−	1.28847i	2.07214	−	0.217790i
$36$		0			0
$37$	6.19179	+	4.02099i	1.01792	+	0.661047i	0.941843	−	0.336055i	$-0.109093\pi$
$37$	6.19179	+	4.02099i	1.01792	+	0.661047i	0.0760808	+	0.997102i	$0.475759\pi$
$38$		0			0
$39$	−10.9709	+	4.13830i	−1.75674	+	0.662658i
$40$		0			0
$41$	−1.52565	+	0.0799559i	−0.238266	+	0.0124870i	−0.171095	−	0.985254i	$-0.554731\pi$
$41$	−1.52565	+	0.0799559i	−0.238266	+	0.0124870i	−0.0671710	+	0.997741i	$0.521397\pi$
$42$		0			0
$43$	−2.46467	+	4.26893i	−0.375859	+	0.651006i	−0.990455	−	0.137835i	$-0.955985\pi$
$43$	−2.46467	+	4.26893i	−0.375859	+	0.651006i	0.614597	+	0.788842i	$0.289319\pi$
$44$		0			0
$45$	5.16450	+	19.2742i	0.769879	+	2.87323i
$46$		0			0
$47$	0.373867	−	0.733754i	0.0545340	−	0.107029i	−0.862131	−	0.506685i	$-0.830871\pi$
$47$	0.373867	−	0.733754i	0.0545340	−	0.107029i	0.916665	+	0.399656i	$0.130871\pi$
$48$		0			0
$49$	14.8196	+	1.55760i	2.11708	+	0.222514i
$50$		0			0
$51$	1.82037	−	5.60251i	0.254902	−	0.784508i
$52$		0			0
$53$	−0.294980	+	0.214316i	−0.0405186	+	0.0294385i	−0.607860	−	0.794044i	$-0.707972\pi$
$53$	−0.294980	+	0.214316i	−0.0405186	+	0.0294385i	0.567342	+	0.823483i	$0.307972\pi$
$54$		0			0
$55$	−3.95840	−	7.78746i	−0.533750	−	1.05006i
$56$		0			0
$57$	−9.50201	−	1.50497i	−1.25857	−	0.199338i
$58$		0			0
$59$	0.798508	−	15.2364i	0.103957	−	1.98362i	−0.0645489	−	0.997915i	$-0.520561\pi$
$59$	0.798508	−	15.2364i	0.103957	−	1.98362i	0.168506	−	0.985701i	$-0.446106\pi$
$60$		0			0
$61$	3.32318	+	7.46398i	0.425490	+	0.955665i	0.991360	+	0.131171i	$0.0418736\pi$
$61$	3.32318	+	7.46398i	0.425490	+	0.955665i	−0.565870	+	0.824494i	$0.691460\pi$
$62$		0			0
$63$	1.85550	+	35.4051i	0.233771	+	4.46063i
$64$		0			0
$65$	9.01475	+	2.98713i	1.11814	+	0.370507i
$66$		0			0
$67$	2.65162	+	0.710499i	0.323947	+	0.0868013i	0.417128	−	0.908848i	$-0.363037\pi$
$67$	2.65162	+	0.710499i	0.323947	+	0.0868013i	−0.0931809	+	0.995649i	$0.529703\pi$
$68$		0			0
$69$	1.06364	−	5.00403i	0.128047	−	0.602414i
$70$		0			0
$71$	0.683107	−	1.77955i	0.0810699	−	0.211194i	−0.887054	−	0.461665i	$-0.847252\pi$
$71$	0.683107	−	1.77955i	0.0810699	−	0.211194i	0.968124	+	0.250471i	$0.0805855\pi$
$72$		0			0
$73$	2.94967	+	5.78905i	0.345233	+	0.677557i	0.996705	−	0.0811152i	$-0.0258482\pi$
$73$	2.94967	+	5.78905i	0.345233	+	0.677557i	−0.651472	+	0.758673i	$0.725848\pi$
$74$		0			0
$75$	2.56290	−	5.75637i	0.295938	−	0.664689i
$76$		0			0
$77$	−4.00268	−	14.9964i	−0.456148	−	1.70900i
$78$		0			0
$79$	−3.48647	−	4.79872i	−0.392259	−	0.539898i	0.566521	−	0.824047i	$-0.308289\pi$
$79$	−3.48647	−	4.79872i	−0.392259	−	0.539898i	−0.958780	+	0.284149i	$0.908289\pi$
$80$		0			0
$81$	−25.1044	+	5.33610i	−2.78937	+	0.592900i
$82$		0			0
$83$	−1.60599	−	10.1398i	−0.176280	−	1.11299i	−0.904132	−	0.427253i	$-0.859481\pi$
$83$	−1.60599	−	10.1398i	−0.176280	−	1.11299i	0.727852	−	0.685734i	$-0.240519\pi$
$84$		0			0
$85$	−4.00143	+	2.59856i	−0.434017	+	0.281854i
$86$		0			0
$87$	−16.2902	−	9.40516i	−1.74649	−	1.00834i
$88$		0			0
$89$	0.136159	−	0.508151i	0.0144328	−	0.0538639i	−0.958334	−	0.285650i	$-0.907790\pi$
$89$	0.136159	−	0.508151i	0.0144328	−	0.0538639i	0.972767	+	0.231786i	$0.0744571\pi$
$90$		0			0
$91$	14.5636	+	8.52157i	1.52668	+	0.893304i
$92$		0			0
$93$	−14.6337	−	18.0711i	−1.51745	−	1.87389i
$94$		0			0
$95$	5.21380	+	5.79051i	0.534925	+	0.594094i
$96$		0			0
$97$	−10.0919	−	8.17229i	−1.02468	−	0.829770i	−0.0391445	−	0.999234i	$-0.512463\pi$
$97$	−10.0919	−	8.17229i	−1.02468	−	0.829770i	−0.985537	+	0.169463i	$0.945797\pi$
$98$		0			0
$99$	22.9637	−	10.1974i	2.30794	−	1.02488i
$100$		0			0
$101$	−8.41766	−	3.74778i	−0.837588	−	0.372918i	−0.0573142	−	0.998356i	$-0.518254\pi$
$101$	−8.41766	−	3.74778i	−0.837588	−	0.372918i	−0.780274	+	0.625438i	$0.784920\pi$
$102$		0			0
$103$	14.6287	+	4.75316i	1.44141	+	0.468343i	0.922337	−	0.386387i	$-0.126277\pi$
$103$	14.6287	+	4.75316i	1.44141	+	0.468343i	0.519074	+	0.854729i	$0.326277\pi$
$104$		0			0
$105$	23.5621	−	32.4304i	2.29942	−	3.16488i
$106$		0			0
$107$	−2.32224	−	2.09095i	−0.224499	−	0.202140i	0.549204	−	0.835688i	$-0.314931\pi$
$107$	−2.32224	−	2.09095i	−0.224499	−	0.202140i	−0.773703	+	0.633549i	$0.781598\pi$
$108$		0			0
$109$	−4.29312	−	4.29312i	−0.411207	−	0.411207i	0.470952	−	0.882159i	$-0.343910\pi$
$109$	−4.29312	−	4.29312i	−0.411207	−	0.411207i	−0.882159	+	0.470952i	$0.843910\pi$
$110$		0			0
$111$	23.1913	−	6.21408i	2.20122	−	0.589815i
$112$		0			0
$113$	−10.2871	−	2.18659i	−0.967730	−	0.205697i	−0.303174	−	0.952935i	$-0.598046\pi$
$113$	−10.2871	−	2.18659i	−0.967730	−	0.205697i	−0.664557	+	0.747238i	$0.731380\pi$
$114$		0			0
$115$	−3.22007	+	2.60756i	−0.300273	+	0.243157i
$116$		0			0
$117$	−9.93688	+	25.4433i	−0.918665	+	2.35223i
$118$		0			0
$119$	−7.91417	+	3.03797i	−0.725491	+	0.278490i
$120$		0			0
$121$	−8.91172	+	6.44836i	−0.810156	+	0.586214i
$122$		0			0
$123$	−3.12665	+	3.86109i	−0.281920	+	0.348142i
$124$		0			0
$125$	7.18701	−	3.66197i	0.642826	−	0.327536i
$126$		0			0
$127$	−1.18191	+	11.2452i	−0.104878	+	0.997847i	0.807880	+	0.589347i	$0.200615\pi$
$127$	−1.18191	+	11.2452i	−0.104878	+	0.997847i	−0.912758	+	0.408500i	$0.866052\pi$
$128$		0			0
$129$	4.95367	+	15.2458i	0.436147	+	1.34232i
$130$		0			0
$131$		−	3.18477i		−	0.278255i	−0.990274	−	0.139127i	$-0.955570\pi$
$131$		−	3.18477i		−	0.278255i	0.990274	−	0.139127i	$-0.0444297\pi$
$132$		0			0
$133$	6.92218	+	11.9896i	0.600229	+	1.03963i
$134$		0			0
$135$	34.9227	+	17.7940i	3.00567	+	1.53146i
$136$		0			0
$137$	−3.51354	−	1.34872i	−0.300182	−	0.115229i	0.203615	−	0.979051i	$-0.434731\pi$
$137$	−3.51354	−	1.34872i	−0.300182	−	0.115229i	−0.503797	+	0.863822i	$0.668064\pi$
$138$		0			0
$139$	−0.495975	+	0.446578i	−0.0420681	+	0.0378783i	−0.689897	−	0.723908i	$-0.742344\pi$
$139$	−0.495975	+	0.446578i	−0.0420681	+	0.0378783i	0.647828	+	0.761786i	$0.275677\pi$
$140$		0			0
$141$	−0.959744	−	2.50022i	−0.0808250	−	0.210556i
$142$		0			0
$143$	1.95077	−	11.7981i	0.163132	−	0.986604i
$144$		0			0
$145$	5.45976	+	14.2232i	0.453408	+	1.18117i
$146$		0			0
$147$	36.0123	−	32.4256i	2.97024	−	2.67442i
$148$		0			0
$149$	19.0864	+	7.32660i	1.56362	+	0.600218i	0.977674	−	0.210130i	$-0.0673886\pi$
$149$	19.0864	+	7.32660i	1.56362	+	0.600218i	0.585949	+	0.810348i	$0.300722\pi$
$150$		0			0
$151$	−13.3919	−	6.82352i	−1.08982	−	0.555290i	−0.185714	−	0.982604i	$-0.559460\pi$
$151$	−13.3919	−	6.82352i	−1.08982	−	0.555290i	−0.904103	+	0.427314i	$0.859460\pi$
$152$		0			0
$153$	−6.86148	−	11.8844i	−0.554718	−	0.960799i
$154$		0			0
$155$			18.8335i			1.51274i
$156$		0			0
$157$	6.25585	+	19.2535i	0.499271	+	1.53660i	0.810194	+	0.586162i	$0.199362\pi$
$157$	6.25585	+	19.2535i	0.499271	+	1.53660i	−0.310923	+	0.950435i	$0.600638\pi$
$158$		0			0
$159$	−0.123944	+	1.17925i	−0.00982941	+	0.0935206i
$160$		0			0
$161$	−6.55954	+	3.34225i	−0.516964	+	0.263407i
$162$		0			0
$163$	−3.11711	+	3.84931i	−0.244151	+	0.301501i	−0.884460	−	0.466616i	$-0.845473\pi$
$163$	−3.11711	+	3.84931i	−0.244151	+	0.301501i	0.640309	+	0.768117i	$0.278806\pi$
$164$		0			0
$165$	−27.4339	−	7.37943i	−2.13573	−	0.574488i
$166$		0			0
$167$	7.68929	−	2.95164i	0.595015	−	0.228405i	−0.0421767	−	0.999110i	$-0.513429\pi$
$167$	7.68929	−	2.95164i	0.595015	−	0.228405i	0.637192	+	0.770705i	$0.280096\pi$
$168$		0			0
$169$	7.51840	+	10.6054i	0.578338	+	0.815797i
$170$		0			0
$171$	−17.4168	+	14.1039i	−1.33190	+	1.07855i
$172$		0			0
$173$	−0.181642	−	0.0386091i	−0.0138100	−	0.00293540i	0.201002	−	0.979591i	$-0.435580\pi$
$173$	−0.181642	−	0.0386091i	−0.0138100	−	0.00293540i	−0.214811	+	0.976656i	$0.568914\pi$
$174$		0			0
$175$	−8.75870	+	2.34689i	−0.662096	+	0.177408i
$176$		0			0
$177$	−35.0849	−	35.0849i	−2.63714	−	2.63714i
$178$		0			0
$179$	14.5101	+	13.0649i	1.08453	+	0.976518i	0.999802	−	0.0198861i	$-0.00633036\pi$
$179$	14.5101	+	13.0649i	1.08453	+	0.976518i	0.0847306	+	0.996404i	$0.472997\pi$
$180$		0			0
$181$	3.47335	−	4.78065i	0.258172	−	0.355343i	−0.660180	−	0.751107i	$-0.729520\pi$
$181$	3.47335	−	4.78065i	0.258172	−	0.355343i	0.918352	+	0.395764i	$0.129520\pi$
$182$		0			0
$183$	25.2699	+	8.21068i	1.86800	+	0.606951i
$184$		0			0
$185$	−17.7647	−	7.90938i	−1.30609	−	0.581509i
$186$		0			0
$187$	4.01568	+	4.46857i	0.293655	+	0.326774i
$188$		0			0
$189$	54.1201	+	43.8256i	3.93666	+	3.18784i
$190$		0			0
$191$	−15.2254	−	16.9095i	−1.10167	−	1.22353i	−0.972745	−	0.231877i	$-0.925513\pi$
$191$	−15.2254	−	16.9095i	−1.10167	−	1.22353i	−0.128927	−	0.991654i	$-0.541153\pi$
$192$		0			0
$193$	7.69057	+	9.49706i	0.553579	+	0.683614i	0.974732	−	0.223376i	$-0.0717078\pi$
$193$	7.69057	+	9.49706i	0.553579	+	0.683614i	−0.421153	+	0.906990i	$0.638374\pi$
$194$		0			0
$195$	26.8356	−	15.2862i	1.92174	−	1.09467i
$196$		0			0
$197$	−2.77949	+	10.3732i	−0.198030	+	0.739059i	0.793431	+	0.608660i	$0.208292\pi$
$197$	−2.77949	+	10.3732i	−0.198030	+	0.739059i	−0.991462	+	0.130399i	$0.958374\pi$
$198$		0			0
$199$	−16.3836	−	9.45908i	−1.16140	−	0.670536i	−0.209763	−	0.977752i	$-0.567269\pi$
$199$	−16.3836	−	9.45908i	−1.16140	−	0.670536i	−0.951640	+	0.307216i	$0.900603\pi$
$200$		0			0
$201$	7.48712	−	4.86220i	0.528101	−	0.342953i
$202$		0			0
$203$	4.23454	+	26.7358i	0.297206	+	1.87649i
$204$		0			0
$205$	3.93604	−	0.836631i	0.274905	−	0.0584328i
$206$		0			0
$207$	−7.00496	−	9.64150i	−0.486878	−	0.670130i
$208$		0			0
$209$	6.18197	−	7.61897i	0.427616	−	0.527015i
$210$		0			0
$211$	10.6602	−	23.9433i	0.733882	−	1.64832i	−0.0271678	−	0.999631i	$-0.508649\pi$
$211$	10.6602	−	23.9433i	0.733882	−	1.64832i	0.761049	−	0.648694i	$-0.224684\pi$
$212$		0			0
$213$	−2.81425	−	5.52328i	−0.192829	−	0.378449i
$214$		0			0
$215$	4.65288	−	12.1212i	0.317324	−	0.826657i
$216$		0			0
$217$	−6.95728	+	32.7314i	−0.472291	+	2.22195i
$218$		0			0
$219$	20.4092	+	5.46864i	1.37913	+	0.369536i
$220$		0			0
$221$	−6.52013	−	0.379730i	−0.438591	−	0.0255434i
$222$		0			0
$223$	−0.885890	−	16.9038i	−0.0593236	−	1.13196i	−0.852418	−	0.522862i	$-0.824864\pi$
$223$	−0.885890	−	16.9038i	−0.0593236	−	1.13196i	0.793094	−	0.609099i	$-0.208469\pi$
$224$		0			0
$225$	−5.97040	−	13.4097i	−0.398027	−	0.893983i
$226$		0			0
$227$	−1.28554	+	24.5296i	−0.0853244	+	1.62809i	0.535779	+	0.844358i	$0.320018\pi$
$227$	−1.28554	+	24.5296i	−0.0853244	+	1.62809i	−0.621104	+	0.783728i	$0.713315\pi$
$228$		0			0
$229$	−8.11481	−	1.28526i	−0.536242	−	0.0849324i	−0.117561	−	0.993066i	$-0.537508\pi$
$229$	−8.11481	−	1.28526i	−0.536242	−	0.0849324i	−0.418681	+	0.908133i	$0.637508\pi$
$230$		0			0
$231$	−44.9524	−	22.9593i	−2.95765	−	1.51061i
$232$		0			0
$233$	21.9726	−	15.9640i	1.43947	−	1.04584i	0.451321	−	0.892362i	$-0.350953\pi$
$233$	21.9726	−	15.9640i	1.43947	−	1.04584i	0.988152	−	0.153476i	$-0.0490469\pi$
$234$		0			0
$235$	−0.670280	+	2.06291i	−0.0437243	+	0.134569i
$236$		0			0
$237$	−19.1840	−	2.01632i	−1.24613	−	0.130974i
$238$		0			0
$239$	3.46797	−	6.80628i	0.224324	−	0.440261i	−0.751224	−	0.660048i	$-0.770536\pi$
$239$	3.46797	−	6.80628i	0.224324	−	0.440261i	0.975548	+	0.219786i	$0.0705360\pi$
$240$		0			0
$241$	−1.78778	−	6.67208i	−0.115161	−	0.429787i	0.884138	−	0.467226i	$-0.154747\pi$
$241$	−1.78778	−	6.67208i	−0.115161	−	0.429787i	−0.999299	+	0.0374394i	$0.988080\pi$
$242$		0			0
$243$	−19.4112	+	33.6212i	−1.24523	+	2.15680i
$244$		0			0
$245$	−39.1949	+	2.05412i	−2.50407	+	0.131233i
$246$		0			0
$247$	1.05323	+	10.6141i	0.0670155	+	0.675359i
$248$		0			0
$249$	−28.0000	−	18.1834i	−1.77442	−	1.15233i
$250$		0			0
$251$	13.6293	−	1.43250i	0.860275	−	0.0904185i	0.335891	−	0.941901i	$-0.390962\pi$
$251$	13.6293	−	1.43250i	0.860275	−	0.0904185i	0.524384	+	0.851482i	$0.324296\pi$
$252$		0			0
$253$	3.87391	+	3.49489i	0.243550	+	0.219722i
$254$		0			0
$255$	−2.42724	+	15.3250i	−0.152000	+	0.959689i
$256$		0			0
$257$	2.22749	+	10.4795i	0.138947	+	0.653694i	0.991397	+	0.130886i	$0.0417821\pi$
$257$	2.22749	+	10.4795i	0.138947	+	0.653694i	−0.852451	+	0.522808i	$0.824885\pi$
$258$		0			0
$259$	−27.9522	−	20.3085i	−1.73686	−	1.26191i
$260$		0			0
$261$	−41.6748	+	13.5410i	−2.57961	+	0.838165i
$262$		0			0
$263$	7.35100	−	4.24410i	0.453282	−	0.261703i	−0.255933	−	0.966694i	$-0.582383\pi$
$263$	7.35100	−	4.24410i	0.453282	−	0.261703i	0.709215	+	0.704992i	$0.249049\pi$
$264$		0			0
$265$	0.679086	−	0.679086i	0.0417159	−	0.0417159i
$266$		0			0
$267$	−0.931782	−	1.43482i	−0.0570241	−	0.0878094i
$268$		0			0
$269$	9.46422	−	4.21374i	0.577044	−	0.256917i	−0.0973966	−	0.995246i	$-0.531052\pi$
$269$	9.46422	−	4.21374i	0.577044	−	0.256917i	0.674441	+	0.738329i	$0.264385\pi$
$270$		0			0
$271$	6.56386	−	10.1075i	0.398726	−	0.613984i	−0.581101	−	0.813832i	$-0.697378\pi$
$271$	6.56386	−	10.1075i	0.398726	−	0.613984i	0.979827	+	0.199847i	$0.0640445\pi$
$272$		0			0
$273$	52.2854	−	16.6531i	3.16446	−	1.00789i
$274$		0			0
$275$	3.77222	+	5.20262i	0.227473	+	0.313730i
$276$		0			0
$277$	1.71925	+	16.3576i	0.103300	+	0.982831i	0.916280	+	0.400539i	$0.131177\pi$
$277$	1.71925	+	16.3576i	0.103300	+	0.982831i	−0.812980	+	0.582292i	$0.802156\pi$
$278$		0			0
$279$	−54.0952	−	2.83501i	−3.23860	−	0.169728i
$280$		0			0
$281$	−2.61472	+	0.414131i	−0.155981	+	0.0247050i	−0.233937	−	0.972252i	$-0.575161\pi$
$281$	−2.61472	+	0.414131i	−0.155981	+	0.0247050i	0.0779555	+	0.996957i	$0.475161\pi$
$282$		0			0
$283$	−2.24146	+	2.48940i	−0.133241	+	0.147979i	−0.806073	−	0.591816i	$-0.798411\pi$
$283$	−2.24146	+	2.48940i	−0.133241	+	0.147979i	0.672832	+	0.739795i	$0.265078\pi$
$284$		0			0
$285$	25.3396			1.50099
$286$		0			0
$287$	7.14964			0.422030
$288$		0			0
$289$	−9.17963	+	10.1950i	−0.539978	+	0.599707i
$290$		0			0
$291$	−41.7108	+	6.60634i	−2.44513	+	0.387270i
$292$		0			0
$293$	−16.4870	−	0.864047i	−0.963181	−	0.0504782i	−0.435743	−	0.900071i	$-0.643514\pi$
$293$	−16.4870	−	0.864047i	−0.963181	−	0.0504782i	−0.527439	+	0.849593i	$0.676848\pi$
$294$		0			0
$295$	4.20066	+	39.9667i	0.244572	+	2.32695i
$296$		0			0
$297$	15.2966	−	46.9232i	0.887600	−	2.72276i
$298$		0			0
$299$	−5.66578	+	0.263909i	−0.327661	+	0.0152623i
$300$		0			0
$301$	12.5641	−	19.3470i	0.724182	−	1.11514i
$302$		0			0
$303$	−27.3746	+	12.1880i	−1.57263	+	0.700180i
$304$		0			0
$305$	−11.7207	−	18.0483i	−0.671125	−	1.03344i
$306$		0			0
$307$	−9.08621	+	9.08621i	−0.518578	+	0.518578i	−0.917141	−	0.398563i	$-0.869509\pi$
$307$	−9.08621	+	9.08621i	−0.518578	+	0.518578i	0.398563	+	0.917141i	$0.369509\pi$
$308$		0			0
$309$	43.3199	−	25.0107i	2.46438	−	1.42281i
$310$		0			0
$311$	−15.1449	+	4.92089i	−0.858790	+	0.279038i	−0.705123	−	0.709085i	$-0.749108\pi$
$311$	−15.1449	+	4.92089i	−0.858790	+	0.279038i	−0.153667	+	0.988123i	$0.549108\pi$
$312$		0			0
$313$	1.73720	+	1.26215i	0.0981921	+	0.0713407i	0.635798	−	0.771856i	$-0.280671\pi$
$313$	1.73720	+	1.26215i	0.0981921	+	0.0713407i	−0.537606	+	0.843196i	$0.680671\pi$
$314$		0			0
$315$	−19.4153	−	91.3420i	−1.09393	−	5.14654i
$316$		0			0
$317$	0.995700	−	6.28660i	0.0559241	−	0.353091i	−0.943820	−	0.330460i	$-0.892796\pi$
$317$	0.995700	−	6.28660i	0.0559241	−	0.353091i	0.999744	−	0.0226302i	$-0.00720404\pi$
$318$		0			0
$319$	16.6230	−	9.57581i	0.930710	−	0.536142i
$320$		0			0
$321$	−10.1066	+	1.06224i	−0.564093	+	0.0592886i
$322$		0			0
$323$	−4.49418	−	2.91855i	−0.250063	−	0.162393i
$324$		0			0
$325$	−6.89361	−	1.13296i	−0.382388	−	0.0628455i
$326$		0			0
$327$	−19.7174	+	1.03334i	−1.09037	+	0.0571440i
$328$		0			0
$329$	−1.92696	+	3.33760i	−0.106237	+	0.184008i
$330$		0			0
$331$	−6.20304	−	23.1501i	−0.340950	−	1.27244i	−0.897273	−	0.441476i	$-0.854455\pi$
$331$	−6.20304	−	23.1501i	−0.340950	−	1.27244i	0.556323	−	0.830966i	$-0.312212\pi$
$332$		0			0
$333$	25.3921	−	49.8349i	1.39148	−	2.73093i
$334$		0			0
$335$	−7.19094	−	0.755799i	−0.392883	−	0.0412937i
$336$		0			0
$337$	−1.16426	+	3.58321i	−0.0634211	+	0.195190i	−0.977746	−	0.209791i	$-0.932722\pi$
$337$	−1.16426	+	3.58321i	−0.0634211	+	0.195190i	0.914325	+	0.404981i	$0.132722\pi$
$338$		0			0
$339$	−27.6696	+	20.1032i	−1.50281	+	1.09185i
$340$		0			0
$341$	23.4266	−	3.68712i	1.26862	−	0.199669i
$342$		0			0
$343$	−36.5213	−	5.78440i	−1.97196	−	0.312328i
$344$		0			0
$345$	−0.705212	+	13.4563i	−0.0379674	+	0.724460i
$346$		0			0
$347$	0.857119	+	1.92512i	0.0460126	+	0.103346i	0.935089	−	0.354413i	$-0.115319\pi$
$347$	0.857119	+	1.92512i	0.0460126	+	0.103346i	−0.889077	+	0.457758i	$0.848652\pi$
$348$		0			0
$349$	0.878549	+	16.7637i	0.0470276	+	0.897341i	0.915677	+	0.401914i	$0.131655\pi$
$349$	0.878549	+	16.7637i	0.0470276	+	0.897341i	−0.868650	+	0.495427i	$0.835012\pi$
$350$		0			0
$351$	24.0796	+	47.9460i	1.28527	+	2.55917i
$352$		0			0
$353$	7.40555	+	1.98431i	0.394158	+	0.105614i	0.450454	−	0.892800i	$-0.351262\pi$
$353$	7.40555	+	1.98431i	0.394158	+	0.105614i	−0.0562957	+	0.998414i	$0.517929\pi$
$354$		0			0
$355$	−1.04386	+	4.91098i	−0.0554024	+	0.260648i
$356$		0			0
$357$	−9.87960	+	25.7372i	−0.522884	+	1.36216i
$358$		0			0
$359$	−0.585152	−	1.14843i	−0.0308831	−	0.0606116i	0.875049	−	0.484034i	$-0.160829\pi$
$359$	−0.585152	−	1.14843i	−0.0308831	−	0.0606116i	−0.905933	+	0.423422i	$0.860829\pi$
$360$		0			0
$361$	4.16848	−	9.36255i	0.219393	−	0.492766i
$362$		0			0
$363$	−3.80826	+	35.5692i	−0.199882	+	1.86690i
$364$		0			0
$365$	−10.0589	−	13.8449i	−0.526506	−	0.724673i
$366$		0			0
$367$	15.8278	−	3.36431i	0.826206	−	0.175615i	0.224643	−	0.974441i	$-0.427878\pi$
$367$	15.8278	−	3.36431i	0.826206	−	0.175615i	0.601563	+	0.798826i	$0.294545\pi$
$368$		0			0
$369$	1.81055	+	11.4314i	0.0942535	+	0.595093i
$370$		0			0
$371$	1.43107	−	0.929346i	0.0742973	−	0.0482493i
$372$		0			0
$373$	17.5343	+	10.1234i	0.907890	+	0.524171i	0.879752	−	0.475433i	$-0.157709\pi$
$373$	17.5343	+	10.1234i	0.907890	+	0.524171i	0.0281386	+	0.999604i	$0.491042\pi$
$374$		0			0
$375$	6.78922	−	25.3377i	0.350594	−	1.30843i
$376$		0			0
$377$	−5.51472	+	20.1127i	−0.284022	+	1.03586i
$378$		0			0
$379$	9.06755	+	11.1975i	0.465769	+	0.575177i	0.954860	−	0.297056i	$-0.0960048\pi$
$379$	9.06755	+	11.1975i	0.465769	+	0.575177i	−0.489091	+	0.872233i	$0.662672\pi$
$380$		0			0
$381$	24.6047	+	27.3263i	1.26054	+	1.39997i
$382$		0			0
$383$	13.8108	+	11.1837i	0.705697	+	0.571462i	0.913564	−	0.406695i	$-0.133319\pi$
$383$	13.8108	+	11.1837i	0.705697	+	0.571462i	−0.207867	+	0.978157i	$0.566652\pi$
$384$		0			0
$385$	16.5921	+	37.3639i	0.845610	+	1.90424i
$386$		0			0
$387$	34.1151	+	15.1890i	1.73417	+	0.772101i
$388$		0			0
$389$	−20.4678	−	6.65040i	−1.03776	−	0.337189i	−0.259906	−	0.965634i	$-0.583692\pi$
$389$	−20.4678	−	6.65040i	−1.03776	−	0.337189i	−0.777854	+	0.628445i	$0.783692\pi$
$390$		0			0
$391$	1.67493	−	2.30535i	0.0847050	−	0.116586i
$392$		0			0
$393$	−7.69676	−	6.93020i	−0.388250	−	0.349582i
$394$		0			0
$395$	11.0473	+	11.0473i	0.555851	+	0.555851i
$396$		0			0
$397$	−21.7569	+	5.82974i	−1.09195	+	0.292586i	−0.759481	−	0.650529i	$-0.774547\pi$
$397$	−21.7569	+	5.82974i	−1.09195	+	0.292586i	−0.332465	+	0.943115i	$0.607880\pi$
$398$		0			0
$399$	44.0386	+	9.36070i	2.20469	+	0.468621i
$400$		0			0
$401$	−24.3453	+	19.7144i	−1.21575	+	0.984491i	−0.215778	+	0.976442i	$0.569229\pi$
$401$	−24.3453	+	19.7144i	−1.21575	+	0.984491i	−0.999968	+	0.00804903i	$0.997438\pi$
$402$		0			0
$403$	−15.2746	+	20.7687i	−0.760885	+	1.03456i
$404$		0			0
$405$	63.1104	−	24.2258i	3.13598	−	1.20379i
$406$		0			0
$407$	−6.36043	+	23.6457i	−0.315275	+	1.17207i
$408$		0			0
$409$	8.38971	−	10.3604i	0.414844	−	0.512290i	−0.526298	−	0.850300i	$-0.676420\pi$
$409$	8.38971	−	10.3604i	0.414844	−	0.512290i	0.941143	+	0.338010i	$0.109754\pi$
$410$		0			0
$411$	−10.9051	+	5.55644i	−0.537910	+	0.274079i
$412$		0			0
$413$	−7.46358	+	71.0112i	−0.367259	+	3.49424i
$414$		0			0
$415$	8.35596	+	25.7170i	0.410178	+	1.26240i
$416$		0			0
$417$			2.17042i			0.106286i
$418$		0			0
$419$	8.05356	+	13.9492i	0.393442	+	0.681462i	0.992901	−	0.118944i	$-0.0379508\pi$
$419$	8.05356	+	13.9492i	0.393442	+	0.681462i	−0.599459	+	0.800406i	$0.704617\pi$
$420$		0			0
$421$	−1.58190	−	0.806020i	−0.0770972	−	0.0392830i	0.415017	−	0.909814i	$-0.363776\pi$
$421$	−1.58190	−	0.806020i	−0.0770972	−	0.0392830i	−0.492114	+	0.870531i	$0.663776\pi$
$422$		0			0
$423$	−5.82438	−	2.23577i	−0.283191	−	0.108707i
$424$		0			0
$425$	2.60829	−	2.34851i	0.126521	−	0.113920i
$426$		0			0
$427$	−13.7026	−	35.6965i	−0.663116	−	1.72748i
$428$		0			0
$429$	−24.2679	−	30.3876i	−1.17167	−	1.46713i
$430$		0			0
$431$	−9.43653	−	24.5830i	−0.454542	−	1.18412i	−0.949099	−	0.314977i	$-0.898003\pi$
$431$	−9.43653	−	24.5830i	−0.454542	−	1.18412i	0.494557	−	0.869145i	$-0.335330\pi$
$432$		0			0
$433$	−14.4264	+	12.9896i	−0.693289	+	0.624240i	−0.938520	−	0.345224i	$-0.887803\pi$
$433$	−14.4264	+	12.9896i	−0.693289	+	0.624240i	0.245231	+	0.969465i	$0.421136\pi$
$434$		0			0
$435$	46.2543	+	17.7554i	2.21772	+	0.851305i
$436$		0			0
$437$	−4.14647	−	2.11273i	−0.198353	−	0.101066i
$438$		0			0
$439$	−14.3772	−	24.9020i	−0.686186	−	1.18851i	−0.973063	−	0.230541i	$-0.925950\pi$
$439$	−14.3772	−	24.9020i	−0.686186	−	1.18851i	0.286877	−	0.957967i	$-0.407383\pi$
$440$		0			0
$441$		−	112.888i		−	5.37563i
$442$		0			0
$443$	−8.25228	−	25.3979i	−0.392078	−	1.20669i	−0.931214	−	0.364472i	$-0.881249\pi$
$443$	−8.25228	−	25.3979i	−0.392078	−	1.20669i	0.539137	−	0.842218i	$-0.318751\pi$
$444$		0			0
$445$	−0.144840	+	1.37806i	−0.00686607	+	0.0653263i
$446$		0			0
$447$	59.2394	−	30.1840i	2.80193	−	1.42765i
$448$		0			0
$449$	−9.61680	+	11.8758i	−0.453845	+	0.560452i	−0.951788	−	0.306758i	$-0.900756\pi$
$449$	−9.61680	+	11.8758i	−0.453845	+	0.560452i	0.497942	+	0.867210i	$0.334089\pi$
$450$		0			0
$451$	−1.81124	−	4.73217i	−0.0852881	−	0.222829i
$452$		0			0
$453$	−45.6320	+	17.5165i	−2.14398	+	0.822996i
$454$		0			0
$455$	−41.3984	−	16.1681i	−1.94079	−	0.757975i
$456$		0			0
$457$	3.85847	−	3.12453i	0.180492	−	0.146159i	−0.534817	−	0.844968i	$-0.679619\pi$
$457$	3.85847	−	3.12453i	0.180492	−	0.146159i	0.715309	+	0.698809i	$0.246286\pi$
$458$		0			0
$459$	−26.3662	−	5.60430i	−1.23067	−	0.261586i
$460$		0			0
$461$	38.0836	−	10.2045i	1.77373	−	0.475270i	0.784314	−	0.620364i	$-0.213015\pi$
$461$	38.0836	−	10.2045i	1.77373	−	0.475270i	0.989418	+	0.145094i	$0.0463483\pi$
$462$		0			0
$463$	16.6972	+	16.6972i	0.775984	+	0.775984i	0.979145	−	0.203162i	$-0.0651217\pi$
$463$	16.6972	+	16.6972i	0.775984	+	0.775984i	−0.203162	+	0.979145i	$0.565122\pi$
$464$		0			0
$465$	45.5157	+	40.9825i	2.11074	+	1.90052i
$466$		0			0
$467$	19.9135	−	27.4086i	0.921487	−	1.26832i	−0.0416019	−	0.999134i	$-0.513246\pi$
$467$	19.9135	−	27.4086i	0.921487	−	1.26832i	0.963089	−	0.269184i	$-0.0867539\pi$
$468$		0			0
$469$	−12.2182	−	3.96993i	−0.564184	−	0.183315i
$470$		0			0
$471$	60.1437	+	26.7777i	2.77128	+	1.23385i
$472$		0			0
$473$	−15.9882	−	3.41461i	−0.735138	−	0.157004i
$474$		0			0
$475$	−4.45455	−	3.60722i	−0.204389	−	0.165511i
$476$		0			0
$477$	1.84831	+	2.05275i	0.0846281	+	0.0939890i
$478$		0			0
$479$	−11.3191	−	13.9779i	−0.517182	−	0.638666i	0.449916	−	0.893071i	$-0.351454\pi$
$479$	−11.3191	−	13.9779i	−0.517182	−	0.638666i	−0.967098	+	0.254404i	$0.918121\pi$
$480$		0			0
$481$	−13.1754	−	23.1300i	−0.600746	−	1.05464i
$482$		0			0
$483$	−6.19648	+	23.1256i	−0.281950	+	1.05225i
$484$		0			0
$485$	29.6215	+	17.1020i	1.34504	+	0.776561i
$486$		0			0
$487$	10.2619	−	6.66413i	0.465009	−	0.301980i	−0.290787	−	0.956788i	$-0.593917\pi$
$487$	10.2619	−	6.66413i	0.465009	−	0.301980i	0.755796	+	0.654807i	$0.227250\pi$
$488$		0			0
$489$	2.51982	+	15.9095i	0.113950	+	0.719453i
$490$		0			0
$491$	0.844984	−	0.179607i	0.0381336	−	0.00810555i	−0.188805	−	0.982015i	$-0.560462\pi$
$491$	0.844984	−	0.179607i	0.0381336	−	0.00810555i	0.226939	+	0.973909i	$0.427128\pi$
$492$		0			0
$493$	−6.15855	−	8.47651i	−0.277367	−	0.381763i
$494$		0			0
$495$	−55.5384	+	35.9905i	−2.49627	+	1.61765i
$496$		0			0
$497$	−3.62833	+	8.14936i	−0.162753	+	0.365549i
$498$		0			0
$499$	7.68414	+	15.0810i	0.343989	+	0.675117i	0.996584	−	0.0825904i	$-0.0263193\pi$
$499$	7.68414	+	15.0810i	0.343989	+	0.675117i	−0.652594	+	0.757708i	$0.726319\pi$
$500$		0			0
$501$	9.59887	−	25.0059i	0.428846	−	1.11718i
$502$		0			0
$503$	8.99568	−	42.3213i	0.401097	−	1.88701i	−0.0574566	−	0.998348i	$-0.518299\pi$
$503$	8.99568	−	42.3213i	0.401097	−	1.88701i	0.458554	−	0.888667i	$-0.348368\pi$
$504$		0			0
$505$	23.4428	+	6.28147i	1.04319	+	0.279522i
$506$		0			0
$507$	41.9907	+	4.90770i	1.86487	+	0.217959i
$508$		0			0
$509$	−1.41997	−	27.0946i	−0.0629389	−	1.20095i	−0.829400	−	0.558655i	$-0.811317\pi$
$509$	−1.41997	−	27.0946i	−0.0629389	−	1.20095i	0.766461	−	0.642291i	$-0.222016\pi$
$510$		0			0
$511$	−12.3673	−	27.7773i	−0.547096	−	1.22880i
$512$		0			0
$513$	−2.30389	+	43.9608i	−0.101719	+	1.94092i
$514$		0			0
$515$	−40.0151	−	6.33778i	−1.76328	−	0.279276i
$516$		0			0
$517$	2.69724	+	0.429883i	0.118624	+	0.0189062i
$518$		0			0
$519$	−0.488568	+	0.354966i	−0.0214458	+	0.0155813i
$520$		0			0
$521$	12.7542	−	39.2535i	0.558773	−	1.71973i	−0.126994	−	0.991903i	$-0.540533\pi$
$521$	12.7542	−	39.2535i	0.558773	−	1.71973i	0.685767	−	0.727822i	$-0.259467\pi$
$522$		0			0
$523$	−19.7369	−	2.07443i	−0.863035	−	0.0907086i	−0.337341	−	0.941382i	$-0.609528\pi$
$523$	−19.7369	−	2.07443i	−0.863035	−	0.0907086i	−0.525694	+	0.850674i	$0.676194\pi$
$524$		0			0
$525$	−13.3875	+	26.2744i	−0.584278	+	1.14671i
$526$		0			0
$527$	−3.35230	−	12.5110i	−0.146028	−	0.544986i
$528$		0			0
$529$	−10.2627	+	17.7755i	−0.446203	+	0.772846i
$530$		0			0
$531$	−115.428	+	6.04933i	−5.00915	+	0.262518i
$532$		0			0
$533$	5.01902	+	2.26967i	0.217398	+	0.0983103i
$534$		0			0
$535$	6.90285	+	4.48276i	0.298436	+	0.193807i
$536$		0			0
$537$	63.1490	−	6.63723i	2.72508	−	0.286418i
$538$		0			0
$539$	10.2284	+	48.3516i	0.440570	+	2.08265i
$540$		0			0
$541$	−4.01312	+	25.3378i	−0.172537	+	1.08936i	0.737656	+	0.675176i	$0.235932\pi$
$541$	−4.01312	+	25.3378i	−0.172537	+	1.08936i	−0.910194	+	0.414182i	$0.864068\pi$
$542$		0			0
$543$	−3.99544	−	18.7971i	−0.171461	−	0.806659i
$544$		0			0
$545$	12.9375	+	9.39964i	0.554182	+	0.402636i
$546$		0			0
$547$	−34.1003	+	11.0798i	−1.45802	+	0.473740i	−0.927465	−	0.373909i	$-0.878017\pi$
$547$	−34.1003	+	11.0798i	−1.45802	+	0.473740i	−0.530557	+	0.847649i	$0.678017\pi$
$548$		0			0
$549$	53.6042	−	30.9484i	2.28777	−	1.32085i
$550$		0			0
$551$	−12.0994	+	12.0994i	−0.515452	+	0.515452i
$552$		0			0
$553$	15.1185	+	23.2805i	0.642906	+	0.989988i
$554$		0			0
$555$	−57.7717	+	25.7216i	−2.45227	+	1.09182i
$556$		0			0
$557$	13.3482	−	20.5544i	0.565582	−	0.870919i	−0.433968	−	0.900928i	$-0.642887\pi$
$557$	13.3482	−	20.5544i	0.565582	−	0.870919i	0.999550	+	0.0300089i	$0.00955357\pi$
$558$		0			0
$559$	14.9617	−	9.59303i	0.632813	−	0.405742i
$560$		0			0
$561$	19.5377	+	0.0189545i	0.824880	+	0.000800261i
$562$		0			0
$563$	−4.09744	−	38.9846i	−0.172687	−	1.64300i	−0.646886	−	0.762587i	$-0.723929\pi$
$563$	−4.09744	−	38.9846i	−0.172687	−	1.64300i	0.474199	−	0.880417i	$-0.342738\pi$
$564$		0			0
$565$	27.6629	+	1.44975i	1.16379	+	0.0609915i
$566$		0			0
$567$	118.631	−	18.7893i	4.98204	−	0.789077i
$568$		0			0
$569$	5.50382	−	6.11262i	0.230732	−	0.256254i	−0.616650	−	0.787237i	$-0.711511\pi$
$569$	5.50382	−	6.11262i	0.230732	−	0.256254i	0.847382	+	0.530983i	$0.178177\pi$
$570$		0			0
$571$	−12.5687			−0.525986			−0.262993	−	0.964798i	$-0.584710\pi$
$571$	−12.5687			−0.525986			−0.262993	+	0.964798i	$0.584710\pi$
$572$		0			0
$573$	−73.9971			−3.09127
$574$		0			0
$575$	2.03954	−	2.26514i	0.0850547	−	0.0944628i
$576$		0			0
$577$	−10.5904	+	1.67735i	−0.440884	+	0.0698292i	−0.372930	−	0.927859i	$-0.621647\pi$
$577$	−10.5904	+	1.67735i	−0.440884	+	0.0698292i	−0.0679537	+	0.997688i	$0.521647\pi$
$578$		0			0
$579$	39.6869	+	2.07990i	1.64933	+	0.0864379i
$580$		0			0
$581$	5.02201	+	47.7813i	0.208348	+	1.98230i
$582$		0			0
$583$	−0.977648	−	0.711753i	−0.0404901	−	0.0294778i
$584$		0			0
$585$	15.3672	−	70.2852i	0.635356	−	2.90594i
$586$		0			0
$587$	−11.2124	+	17.2656i	−0.462786	+	0.712627i	−0.990609	−	0.136727i	$-0.956342\pi$
$587$	−11.2124	+	17.2656i	−0.462786	+	0.712627i	0.527823	+	0.849354i	$0.323008\pi$
$588$		0			0
$589$	−19.3239	+	8.60358i	−0.796229	+	0.354504i
$590$		0			0
$591$	19.0210	+	29.2898i	0.782419	+	1.20482i
$592$		0			0
$593$	17.0737	−	17.0737i	0.701133	−	0.701133i	−0.263521	−	0.964654i	$-0.584884\pi$
$593$	17.0737	−	17.0737i	0.701133	−	0.701133i	0.964654	+	0.263521i	$0.0848838\pi$
$594$		0			0
$595$	19.3370	−	11.1642i	0.792739	−	0.457688i
$596$		0			0
$597$	−58.5115	+	19.0116i	−2.39472	+	0.778091i
$598$		0			0
$599$	−16.1898	−	11.7626i	−0.661498	−	0.480606i	0.205670	−	0.978621i	$-0.434063\pi$
$599$	−16.1898	−	11.7626i	−0.661498	−	0.480606i	−0.867169	+	0.498015i	$0.834063\pi$
$600$		0			0
$601$	0.305001	+	1.43492i	0.0124412	+	0.0585315i	0.983930	−	0.178553i	$-0.0571416\pi$
$601$	0.305001	+	1.43492i	0.0124412	+	0.0585315i	−0.971489	+	0.237084i	$0.923808\pi$
$602$		0			0
$603$	3.25333	−	20.5407i	0.132486	−	0.836482i
$604$		0			0
$605$	20.5269	−	20.4474i	0.834537	−	0.831304i
$606$		0			0
$607$	36.3772	−	3.82340i	1.47650	−	0.155187i	0.668213	−	0.743970i	$-0.267059\pi$
$607$	36.3772	−	3.82340i	1.47650	−	0.155187i	0.808291	+	0.588783i	$0.200393\pi$
$608$		0			0
$609$	73.8280	+	47.9445i	2.99166	+	1.94281i
$610$		0			0
$611$	−2.41225	+	1.73126i	−0.0975892	+	0.0700395i
$612$		0			0
$613$	40.6252	−	2.12908i	1.64084	−	0.0859927i	0.790580	−	0.612359i	$-0.209779\pi$
$613$	40.6252	−	2.12908i	1.64084	−	0.0859927i	0.850258	+	0.526366i	$0.176446\pi$
$614$		0			0
$615$	6.54306	−	11.3329i	0.263842	−	0.456987i
$616$		0			0
$617$	1.37552	+	5.13350i	0.0553763	+	0.206667i	0.988071	−	0.154000i	$-0.0492156\pi$
$617$	1.37552	+	5.13350i	0.0553763	+	0.206667i	−0.932695	+	0.360667i	$0.882549\pi$
$618$		0			0
$619$	−2.34273	+	4.59787i	−0.0941623	+	0.184804i	−0.933283	−	0.359141i	$-0.883070\pi$
$619$	−2.34273	+	4.59787i	−0.0941623	+	0.184804i	0.839121	+	0.543945i	$0.183070\pi$
$620$		0			0
$621$	−23.2807	−	2.44690i	−0.934222	−	0.0981906i
$622$		0			0
$623$	−0.760791	+	2.34147i	−0.0304804	+	0.0938091i
$624$		0			0
$625$	−25.0259	+	18.1824i	−1.00104	+	0.727295i
$626$		0			0
$627$	−4.96085	−	31.5194i	−0.198117	−	1.25876i
$628$		0			0
$629$	13.2088	+	2.09207i	0.526671	+	0.0834164i
$630$		0			0
$631$	1.13800	−	21.7142i	0.0453029	−	0.864430i	−0.877599	−	0.479395i	$-0.840856\pi$
$631$	1.13800	−	21.7142i	0.0453029	−	0.864430i	0.922902	−	0.385035i	$-0.125811\pi$
$632$		0			0
$633$	−34.6676	−	77.8647i	−1.37791	−	3.09484i
$634$		0			0
$635$	−1.55868	−	29.7413i	−0.0618542	−	1.18025i
$636$		0			0
$637$	−44.8883	−	29.5233i	−1.77854	−	1.16976i
$638$		0			0
$639$	−13.9486	−	3.73752i	−0.551799	−	0.147854i
$640$		0			0
$641$	−3.15815	+	14.8579i	−0.124739	+	0.586853i	0.870729	+	0.491763i	$0.163647\pi$
$641$	−3.15815	+	14.8579i	−0.124739	+	0.586853i	−0.995469	+	0.0950903i	$0.969686\pi$
$642$		0			0
$643$	−6.46879	+	16.8518i	−0.255104	+	0.664569i	−0.999997	−	0.00261559i	$-0.999167\pi$
$643$	−6.46879	+	16.8518i	−0.255104	+	0.664569i	0.744892	+	0.667185i	$0.232501\pi$
$644$		0			0
$645$	−19.1689	−	37.6210i	−0.754773	−	1.48133i
$646$		0			0
$647$	3.10080	−	6.96451i	0.121905	−	0.273803i	−0.842277	−	0.539045i	$-0.818785\pi$
$647$	3.10080	−	6.96451i	0.121905	−	0.273803i	0.964182	+	0.265242i	$0.0854518\pi$
$648$		0			0
$649$	48.8913	−	13.0496i	1.91915	−	0.512240i
$650$		0			0
$651$	63.9640	+	88.0389i	2.50695	+	3.45052i
$652$		0			0
$653$	−13.1357	+	2.79208i	−0.514040	+	0.109263i	−0.457626	−	0.889145i	$-0.651300\pi$
$653$	−13.1357	+	2.79208i	−0.514040	+	0.109263i	−0.0564142	+	0.998407i	$0.517967\pi$
$654$		0			0
$655$	1.31225	+	8.28519i	0.0512737	+	0.323729i
$656$		0			0
$657$	41.2806	−	26.8079i	1.61051	−	1.04588i
$658$		0			0
$659$	20.5911	+	11.8883i	0.802115	+	0.463101i	0.844210	−	0.536012i	$-0.180070\pi$
$659$	20.5911	+	11.8883i	0.802115	+	0.463101i	−0.0420953	+	0.999114i	$0.513403\pi$
$660$		0			0
$661$	0.103978	−	0.388053i	0.00404429	−	0.0150935i	−0.963874	−	0.266358i	$-0.914180\pi$
$661$	0.103978	−	0.388053i	0.00404429	−	0.0150935i	0.967918	+	0.251264i	$0.0808464\pi$
$662$		0			0
$663$	−15.1058	+	14.9311i	−0.586660	+	0.579878i
$664$		0			0
$665$	−22.9482	−	28.3387i	−0.889894	−	1.09893i
$666$		0			0
$667$	−6.08849	−	6.76195i	−0.235747	−	0.261824i
$668$		0			0
$669$	−42.7798	−	34.6424i	−1.65396	−	1.33935i
$670$		0			0
$671$	−20.1553	+	18.1125i	−0.778087	+	0.699227i
$672$		0			0
$673$	−31.2246	−	13.9021i	−1.20362	−	0.535886i	−0.295801	−	0.955250i	$-0.595587\pi$
$673$	−31.2246	−	13.9021i	−1.20362	−	0.535886i	−0.907818	+	0.419364i	$0.862253\pi$
$674$		0			0
$675$	−27.4215	−	8.90978i	−1.05545	−	0.342938i
$676$		0			0
$677$	−6.17935	+	8.50514i	−0.237492	+	0.326879i	−0.911082	−	0.412226i	$-0.864751\pi$
$677$	−6.17935	+	8.50514i	−0.237492	+	0.326879i	0.673590	+	0.739105i	$0.264751\pi$
$678$		0			0
$679$	45.1626	+	40.6646i	1.73318	+	1.56056i
$680$		0			0
$681$	56.4843	+	56.4843i	2.16448	+	2.16448i
$682$		0			0
$683$	16.0980	−	4.31345i	0.615973	−	0.165050i	0.0626768	−	0.998034i	$-0.480036\pi$
$683$	16.0980	−	4.31345i	0.615973	−	0.165050i	0.553297	+	0.832984i	$0.313370\pi$
$684$		0			0
$685$	9.69621	+	2.06099i	0.370473	+	0.0787465i
$686$		0			0
$687$	−20.7643	+	16.8146i	−0.792208	+	0.641518i
$688$		0			0
$689$	1.29963	−	0.198102i	0.0495119	−	0.00754709i
$690$		0			0
$691$	−11.5843	+	4.44679i	−0.440687	+	0.169164i	−0.568587	−	0.822623i	$-0.692510\pi$
$691$	−11.5843	+	4.44679i	−0.440687	+	0.169164i	0.127900	+	0.991787i	$0.459176\pi$
$692$		0			0
$693$	−109.817	+	42.0328i	−4.17162	+	1.59669i
$694$		0			0
$695$	1.10627	−	1.36613i	0.0419634	−	0.0518204i
$696$		0			0
$697$	−2.46576	+	1.25637i	−0.0933974	+	0.0475884i
$698$		0			0
$699$	9.23240	−	87.8404i	0.349202	−	3.32243i
$700$		0			0
$701$	3.66568	+	11.2818i	0.138451	+	0.426107i	0.996111	−	0.0881096i	$-0.0280826\pi$
$701$	3.66568	+	11.2818i	0.138451	+	0.426107i	−0.857660	+	0.514217i	$0.828083\pi$
$702$		0			0
$703$		−	21.8406i		−	0.823732i
$704$		0			0
$705$	3.52696	+	6.10887i	0.132833	+	0.230074i
$706$		0			0
$707$	38.4216	+	19.5768i	1.44499	+	0.736261i
$708$		0			0
$709$	44.2326	+	16.9793i	1.66119	+	0.637672i	0.994215	−	0.107407i	$-0.0342547\pi$
$709$	44.2326	+	16.9793i	1.66119	+	0.637672i	0.666977	+	0.745079i	$0.267588\pi$
$710$		0			0
$711$	−33.3940	+	30.0681i	−1.25237	+	1.12764i
$712$		0			0
$713$	−4.03102	−	10.5012i	−0.150963	−	0.393272i
$714$		0			0
$715$	−0.213683	+	31.4965i	−0.00799129	+	1.17790i
$716$		0			0
$717$	−8.90254	−	23.1919i	−0.332472	−	0.866118i
$718$		0			0
$719$	14.5965	−	13.1427i	0.544357	−	0.490142i	−0.350458	−	0.936579i	$-0.613974\pi$
$719$	14.5965	−	13.1427i	0.544357	−	0.490142i	0.894815	+	0.446437i	$0.147307\pi$
$720$		0			0
$721$	−67.2025	−	25.7966i	−2.50275	−	0.960717i
$722$		0			0
$723$	−20.0150	−	10.1981i	−0.744365	−	0.379273i
$724$		0			0
$725$	−5.60366	−	9.70583i	−0.208115	−	0.360465i
$726$		0			0
$727$		−	4.22288i		−	0.156618i	−0.996929	−	0.0783089i	$-0.975048\pi$
$727$		−	4.22288i		−	0.156618i	0.996929	−	0.0783089i	$-0.0249520\pi$
$728$		0			0
$729$	15.2211	+	46.8457i	0.563744	+	1.73503i
$730$		0			0
$731$	−0.933347	+	8.88020i	−0.0345211	+	0.328446i
$732$		0			0
$733$	9.20955	−	4.69250i	0.340163	−	0.173322i	−0.275561	−	0.961284i	$-0.588864\pi$
$733$	9.20955	−	4.69250i	0.340163	−	0.173322i	0.615724	+	0.787962i	$0.288864\pi$
$734$		0			0
$735$	−80.3255	+	99.1937i	−2.96285	+	3.65881i
$736$		0			0
$737$	0.467680	+	9.09264i	0.0172272	+	0.334932i
$738$		0			0
$739$	−3.86955	+	1.48538i	−0.142344	+	0.0546406i	−0.428497	−	0.903543i	$-0.640957\pi$
$739$	−3.86955	+	1.48538i	−0.142344	+	0.0546406i	0.286153	+	0.958184i	$0.407623\pi$
$740$		0			0
$741$	27.9434	+	20.5513i	1.02653	+	0.754972i
$742$		0			0
$743$	14.1940	−	11.4941i	0.520728	−	0.421677i	−0.332587	−	0.943073i	$-0.607922\pi$
$743$	14.1940	−	11.4941i	0.520728	−	0.421677i	0.853315	+	0.521395i	$0.174588\pi$
$744$		0			0
$745$	−52.6723	−	11.1958i	−1.92976	−	0.410184i
$746$		0			0
$747$	−75.1244	+	20.1295i	−2.74866	+	0.736501i
$748$		0			0
$749$	10.3407	+	10.3407i	0.377842	+	0.377842i
$750$		0			0
$751$	17.7112	+	15.9472i	0.646290	+	0.581922i	0.925704	−	0.378249i	$-0.123474\pi$
$751$	17.7112	+	15.9472i	0.646290	+	0.581922i	−0.279414	+	0.960171i	$0.590140\pi$
$752$		0			0
$753$	26.1960	−	36.0557i	0.954635	−	1.31394i
$754$		0			0
$755$	37.6506	+	12.2334i	1.37025	+	0.445220i
$756$		0			0
$757$	−3.31470	−	1.47580i	−0.120475	−	0.0536389i	0.345614	−	0.938377i	$-0.387671\pi$
$757$	−3.31470	−	1.47580i	−0.120475	−	0.0536389i	−0.466089	+	0.884738i	$0.654337\pi$
$758$		0			0
$759$	16.8760	−	1.75719i	0.612561	−	0.0637820i
$760$		0			0
$761$	17.0439	+	13.8019i	0.617840	+	0.500317i	0.886384	−	0.462950i	$-0.153209\pi$
$761$	17.0439	+	13.8019i	0.617840	+	0.500317i	−0.268544	+	0.963267i	$0.586543\pi$
$762$		0			0
$763$	19.0122	+	21.1152i	0.688289	+	0.764422i
$764$		0			0
$765$	22.7470	+	28.0902i	0.822419	+	1.01560i
$766$		0			0
$767$	−27.7821	+	47.4803i	−1.00315	+	1.71442i
$768$		0			0
$769$	7.09767	−	26.4889i	0.255949	−	0.955213i	−0.711612	−	0.702573i	$-0.752034\pi$
$769$	7.09767	−	26.4889i	0.255949	−	0.955213i	0.967560	−	0.252640i	$-0.0812989\pi$
$770$		0			0
$771$	30.1733	+	17.4206i	1.08667	+	0.627387i
$772$		0			0
$773$	6.28170	−	4.07938i	0.225937	−	0.146725i	−0.426707	−	0.904390i	$-0.640326\pi$
$773$	6.28170	−	4.07938i	0.225937	−	0.146725i	0.652644	+	0.757665i	$0.273660\pi$
$774$		0			0
$775$	−2.16731	−	13.6839i	−0.0778521	−	0.491539i
$776$		0			0
$777$	−109.905	+	23.3611i	−3.94283	+	0.838075i
$778$		0			0
$779$	2.65649	+	3.65634i	0.0951786	+	0.131002i
$780$		0			0
$781$	6.31303	+	0.336994i	0.225898	+	0.0120586i
$782$		0			0
$783$	−35.0087	+	78.6307i	−1.25111	+	2.81003i
$784$		0			0
$785$	−24.2078	−	47.5104i	−0.864012	−	1.69572i
$786$		0			0
$787$	−12.0358	+	31.3544i	−0.429031	+	1.11766i	0.533334	+	0.845904i	$0.320939\pi$
$787$	−12.0358	+	31.3544i	−0.429031	+	1.11766i	−0.962365	+	0.271759i	$0.912395\pi$
$788$		0			0
$789$	5.73920	−	27.0008i	0.204321	−	0.961254i
$790$		0			0
$791$	47.5408	+	12.7385i	1.69036	+	0.452930i
$792$		0			0
$793$	1.71276	−	29.4088i	0.0608218	−	1.04434i
$794$		0			0
$795$	−0.163454	−	3.11889i	−0.00579712	−	0.110616i
$796$		0			0
$797$	0.372215	+	0.836008i	0.0131845	+	0.0296129i	0.920018	−	0.391877i	$-0.128174\pi$
$797$	0.372215	+	0.836008i	0.0131845	+	0.0296129i	−0.906833	+	0.421490i	$0.861507\pi$
$798$		0			0
$799$	0.0780710	−	1.48968i	0.00276195	−	0.0527012i
$800$		0			0
$801$	−3.93638	−	0.623461i	−0.139085	−	0.0220289i
$802$		0			0
$803$	−15.2521	+	15.2225i	−0.538234	+	0.537191i
$804$		0			0
$805$	15.6875	−	11.3977i	0.552913	−	0.401715i
$806$		0			0
$807$	10.4110	−	32.0419i	0.366486	−	1.12793i
$808$		0			0
$809$	7.02728	+	0.738597i	0.247066	+	0.0259677i	0.227252	−	0.973836i	$-0.427026\pi$
$809$	7.02728	+	0.738597i	0.247066	+	0.0259677i	0.0198141	+	0.999804i	$0.493693\pi$
$810$		0			0
$811$	21.3264	−	41.8555i	0.748873	−	1.46975i	−0.129404	−	0.991592i	$-0.541306\pi$
$811$	21.3264	−	41.8555i	0.748873	−	1.46975i	0.878276	−	0.478153i	$-0.158694\pi$
$812$		0			0
$813$	−10.1439	−	37.8574i	−0.355761	−	1.32772i
$814$		0			0
$815$	6.52311	−	11.2984i	0.228495	−	0.395764i
$816$		0			0
$817$	14.5624	−	0.763182i	0.509473	−	0.0267003i
$818$		0			0
$819$	52.6713	−	116.474i	1.84048	−	4.06994i
$820$		0			0
$821$	22.8130	+	14.8149i	0.796177	+	0.517044i	0.877461	−	0.479647i	$-0.159235\pi$
$821$	22.8130	+	14.8149i	0.796177	+	0.517044i	−0.0812839	+	0.996691i	$0.525902\pi$
$822$		0			0
$823$	−22.4361	+	2.35813i	−0.782075	+	0.0821994i	−0.487147	−	0.873320i	$-0.661962\pi$
$823$	−22.4361	+	2.35813i	−0.782075	+	0.0821994i	−0.294928	+	0.955519i	$0.595296\pi$
$824$		0			0
$825$	20.7819	+	2.20465i	0.723532	+	0.0767561i
$826$		0			0
$827$	4.96469	−	31.3458i	0.172639	−	1.09000i	−0.737394	−	0.675463i	$-0.763944\pi$
$827$	4.96469	−	31.3458i	0.172639	−	1.09000i	0.910033	−	0.414537i	$-0.136056\pi$
$828$		0			0
$829$	−0.368912	−	1.73560i	−0.0128129	−	0.0602797i	0.971277	−	0.237953i	$-0.0764764\pi$
$829$	−0.368912	−	1.73560i	−0.0128129	−	0.0602797i	−0.984090	+	0.177673i	$0.943143\pi$
$830$		0			0
$831$	43.2732	+	31.4398i	1.50113	+	1.09063i
$832$		0			0
$833$	25.6712	−	8.34109i	0.889456	−	0.289002i
$834$		0			0
$835$	−18.7875	+	10.8470i	−0.650169	+	0.375375i
$836$		0			0
$837$	−75.2374	+	75.2374i	−2.60059	+	2.60059i
$838$		0			0
$839$	2.08795	+	3.21516i	0.0720840	+	0.111000i	0.872874	−	0.487945i	$-0.162253\pi$
$839$	2.08795	+	3.21516i	0.0720840	+	0.111000i	−0.800790	+	0.598945i	$0.795587\pi$
$840$		0			0
$841$	−4.07114	+	1.81259i	−0.140384	+	0.0625030i
$842$		0			0
$843$	−4.68889	+	7.22026i	−0.161494	+	0.248679i
$844$		0			0
$845$	−23.9289	−	24.4920i	−0.823181	−	0.842551i
$846$		0			0
$847$	43.2279	−	27.9534i	1.48533	−	0.960491i
$848$		0			0
$849$	1.13871	+	10.8341i	0.0390803	+	0.371824i
$850$		0			0
$851$	11.5981	+	0.607832i	0.397579	+	0.0208362i
$852$		0			0
$853$	46.2167	−	7.32001i	1.58243	−	0.250632i	0.697580	−	0.716507i	$-0.254260\pi$
$853$	46.2167	−	7.32001i	1.58243	−	0.250632i	0.884851	+	0.465875i	$0.154260\pi$
$854$		0			0
$855$	39.4986	−	43.8677i	1.35083	−	1.50024i
$856$		0			0
$857$	−54.3944			−1.85808			−0.929038	−	0.369985i	$-0.879363\pi$
$857$	−54.3944			−1.85808			−0.929038	+	0.369985i	$0.879363\pi$
$858$		0			0
$859$	−0.493353			−0.0168330			−0.00841650	−	0.999965i	$-0.502679\pi$
$859$	−0.493353			−0.0168330			−0.00841650	+	0.999965i	$0.502679\pi$
$860$		0			0
$861$	15.5579	−	17.2788i	0.530212	−	0.588861i
$862$		0			0
$863$	12.6781	−	2.00802i	0.431568	−	0.0683537i	0.0631287	−	0.998005i	$-0.479892\pi$
$863$	12.6781	−	2.00802i	0.431568	−	0.0683537i	0.368440	+	0.929652i	$0.379892\pi$
$864$		0			0
$865$	0.488450	+	0.0255986i	0.0166078	+	0.000870377i
$866$		0			0
$867$	4.66343	+	44.3696i	0.158378	+	1.50687i
$868$		0			0
$869$	11.5788	−	15.9043i	0.392782	−	0.539517i
$870$		0			0
$871$	−7.31687	−	6.66558i	−0.247923	−	0.225854i
$872$		0			0
$873$	−53.5807	+	82.5071i	−1.81343	+	2.79244i
$874$		0			0
$875$	−34.4851	+	15.3538i	−1.16581	+	0.519052i
$876$		0			0
$877$	−7.97910	−	12.2867i	−0.269435	−	0.414894i	0.677892	−	0.735162i	$-0.262894\pi$
$877$	−7.97910	−	12.2867i	−0.269435	−	0.414894i	−0.947327	+	0.320268i	$0.896227\pi$
$878$		0			0
$879$	−37.9646	+	37.9646i	−1.28051	+	1.28051i
$880$		0			0
$881$	−5.44643	+	3.14450i	−0.183495	+	0.105941i	−0.588934	−	0.808181i	$-0.700452\pi$
$881$	−5.44643	+	3.14450i	−0.183495	+	0.105941i	0.405439	+	0.914122i	$0.367119\pi$
$882$		0			0
$883$	12.2630	−	3.98450i	0.412684	−	0.134089i	−0.0953141	−	0.995447i	$-0.530386\pi$
$883$	12.2630	−	3.98450i	0.412684	−	0.134089i	0.507998	+	0.861358i	$0.330386\pi$
$884$		0			0
$885$	105.730	+	76.8172i	3.55407	+	2.58218i
$886$		0			0
$887$	−6.11492	−	28.7685i	−0.205319	−	0.965950i	−0.953252	−	0.302176i	$-0.902287\pi$
$887$	−6.11492	−	28.7685i	−0.205319	−	0.965950i	0.747933	−	0.663774i	$-0.231046\pi$
$888$		0			0
$889$	8.27785	−	52.2643i	0.277630	−	1.75289i
$890$		0			0
$891$	−42.4894	−	73.7590i	−1.42345	−	2.47102i
$892$		0			0
$893$	−2.42283	+	0.254650i	−0.0810770	+	0.00852153i
$894$		0			0
$895$	−43.1312	−	28.0097i	−1.44172	−	0.936262i
$896$		0			0
$897$	−11.6912	+	14.2670i	−0.390357	+	0.476361i
$898$		0			0
$899$	−41.3020	+	2.16454i	−1.37750	+	0.0721916i
$900$		0			0
$901$	−0.330236	+	0.571986i	−0.0110018	+	0.0190556i
$902$		0			0
$903$	−19.4167	−	72.4641i	−0.646147	−	2.41145i
$904$		0			0
$905$	−7.06611	+	13.8680i	−0.234886	+	0.460989i
$906$		0			0
$907$	33.8588	+	3.55870i	1.12426	+	0.118165i	0.648360	−	0.761333i	$-0.275455\pi$
$907$	33.8588	+	3.55870i	1.12426	+	0.118165i	0.475902	+	0.879498i	$0.342122\pi$
$908$		0			0
$909$	−21.5710	+	66.3889i	−0.715467	+	2.20198i
$910$		0			0
$911$	−7.57628	+	5.50449i	−0.251013	+	0.182372i	−0.706176	−	0.708037i	$-0.749581\pi$
$911$	−7.57628	+	5.50449i	−0.251013	+	0.182372i	0.455162	+	0.890408i	$0.349581\pi$
$912$		0			0
$913$	30.3530	−	15.4285i	1.00454	−	0.510610i
$914$		0			0
$915$	−69.1228	−	10.9480i	−2.28513	−	0.361929i
$916$		0			0
$917$	−0.780032	+	14.8839i	−0.0257589	+	0.491509i
$918$		0			0
$919$	−6.79566	−	15.2633i	−0.224168	−	0.503490i	0.766090	−	0.642733i	$-0.222200\pi$
$919$	−6.79566	−	15.2633i	−0.224168	−	0.503490i	−0.990258	+	0.139243i	$0.955533\pi$
$920$		0			0
$921$	2.18703	+	41.7310i	0.0720651	+	1.37508i
$922$		0			0
$923$	−5.13411	+	4.56900i	−0.168991	+	0.150390i
$924$		0			0
$925$	13.8175	+	3.70240i	0.454318	+	0.121734i
$926$		0			0
$927$	24.2274	−	113.981i	0.795732	−	3.74363i
$928$		0			0
$929$	16.7138	−	43.5410i	0.548363	−	1.42853i	−0.326979	−	0.945032i	$-0.606031\pi$
$929$	16.7138	−	43.5410i	0.548363	−	1.42853i	0.875342	−	0.483503i	$-0.160636\pi$
$930$		0			0
$931$	−20.0127	−	39.2772i	−0.655891	−	1.28726i
$932$		0			0
$933$	−21.0635	+	47.3094i	−0.689588	+	1.54884i
$934$		0			0
$935$	−12.2880	−	9.97039i	−0.401861	−	0.326067i
$936$		0			0
$937$	−30.1325	−	41.4738i	−0.984384	−	1.35489i	−0.934434	−	0.356137i	$-0.884094\pi$
$937$	−30.1325	−	41.4738i	−0.984384	−	1.35489i	−0.0499505	−	0.998752i	$-0.515906\pi$
$938$		0			0
$939$	6.83049	−	1.45187i	0.222905	−	0.0473798i
$940$		0			0
$941$	9.23590	+	58.3132i	0.301082	+	1.90096i	0.419093	+	0.907943i	$0.362348\pi$
$941$	9.23590	+	58.3132i	0.301082	+	1.90096i	−0.118011	+	0.993012i	$0.537652\pi$
$942$		0			0
$943$	−2.01558	+	1.30894i	−0.0656364	+	0.0426248i
$944$		0			0
$945$	−158.851	−	91.7129i	−5.16744	−	2.98342i
$946$		0			0
$947$	−7.69828	+	28.7304i	−0.250161	+	0.933612i	0.720559	+	0.693394i	$0.243885\pi$
$947$	−7.69828	+	28.7304i	−0.250161	+	0.933612i	−0.970719	+	0.240218i	$0.922781\pi$
$948$		0			0
$949$	0.136200	−	23.4256i	0.00442124	−	0.760428i
$950$		0			0
$951$	−13.0264	−	16.0863i	−0.422410	−	0.521633i
$952$		0			0
$953$	−15.9511	−	17.7155i	−0.516706	−	0.573860i	0.427165	−	0.904174i	$-0.359512\pi$
$953$	−15.9511	−	17.7155i	−0.516706	−	0.573860i	−0.943871	+	0.330313i	$0.892846\pi$
$954$		0			0
$955$	46.5763	+	37.7168i	1.50717	+	1.22049i
$956$		0			0
$957$	13.0301	−	61.0108i	0.421204	−	1.97220i
$958$		0			0
$959$	16.0900	+	7.16375i	0.519575	+	0.231330i
$960$		0			0
$961$	−19.1422	−	6.21969i	−0.617492	−	0.200635i
$962$		0			0
$963$	−13.9149	+	19.1522i	−0.448401	+	0.617170i
$964$		0			0
$965$	−23.9202	−	21.5378i	−0.770018	−	0.693327i
$966$		0			0
$967$	1.93195	+	1.93195i	0.0621274	+	0.0621274i	0.737488	−	0.675360i	$-0.236012\pi$
$967$	1.93195	+	1.93195i	0.0621274	+	0.0621274i	−0.675360	+	0.737488i	$0.736012\pi$
$968$		0			0
$969$	−16.8329	+	4.51036i	−0.540751	+	0.144894i
$970$		0			0
$971$	35.3101	+	7.50540i	1.13316	+	0.240860i	0.736059	−	0.676917i	$-0.236684\pi$
$971$	35.3101	+	7.50540i	1.13316	+	0.240860i	0.397097	+	0.917777i	$0.370018\pi$
$972$		0			0
$973$	2.42730	−	1.96559i	0.0778156	−	0.0630138i
$974$		0			0
$975$	−17.7389	+	14.1947i	−0.568098	+	0.454593i
$976$		0			0
$977$	−5.84516	+	2.24375i	−0.187003	+	0.0717839i	−0.450068	−	0.892994i	$-0.648600\pi$
$977$	−5.84516	+	2.24375i	−0.187003	+	0.0717839i	0.263064	+	0.964778i	$0.415267\pi$
$978$		0			0
$979$	1.74250	−	0.0896253i	0.0556904	−	0.00286444i
$980$		0			0
$981$	−28.9460	+	35.7453i	−0.924173	+	1.14126i
$982$		0			0
$983$	−10.1297	+	5.16132i	−0.323086	+	0.164621i	−0.608010	−	0.793930i	$-0.708032\pi$
$983$	−10.1297	+	5.16132i	−0.323086	+	0.164621i	0.284924	+	0.958550i	$0.408032\pi$
$984$		0			0
$985$	2.95670	−	28.1311i	0.0942083	−	0.896332i
$986$		0			0
$987$	3.87295	+	11.9197i	0.123277	+	0.379409i
$988$		0			0
$989$			7.75439i			0.246575i
$990$		0			0
$991$	15.5533	+	26.9391i	0.494067	+	0.855750i	0.999977	−	0.00683691i	$-0.00217627\pi$
$991$	15.5533	+	26.9391i	0.494067	+	0.855750i	−0.505909	+	0.862587i	$0.668843\pi$
$992$		0			0
$993$	−69.4458	−	35.3844i	−2.20379	−	1.12289i
$994$		0			0
$995$	46.5195	+	17.8572i	1.47477	+	0.566110i
$996$		0			0
$997$	10.5063	−	9.45991i	0.332738	−	0.299598i	−0.485778	−	0.874082i	$-0.661464\pi$
$997$	10.5063	−	9.45991i	0.332738	−	0.299598i	0.818516	+	0.574484i	$0.194797\pi$
$998$		0			0
$999$	−39.3710	−	102.565i	−1.24564	−	3.24501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bv.a.41.14	✓	224
11.7	odd	10	inner	572.2.bv.a.249.1	yes	224
13.7	odd	12	inner	572.2.bv.a.85.1	yes	224
143.7	even	60	inner	572.2.bv.a.293.14	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bv.a.41.14	✓	224	1.1	even	1	trivial
572.2.bv.a.85.1	yes	224	13.7	odd	12	inner
572.2.bv.a.249.1	yes	224	11.7	odd	10	inner
572.2.bv.a.293.14	yes	224	143.7	even	60	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17604 - 2.41674i) q^{3} +(-2.60150 + 0.412038i) q^{5} +(-4.67346 - 0.244925i) q^{7} +(-0.791886 - 7.53429i) q^{9} +O(q^{10})\)	\(q+(2.17604 - 2.41674i) q^{3} +(-2.60150 + 0.412038i) q^{5} +(-4.67346 - 0.244925i) q^{7} +(-0.791886 - 7.53429i) q^{9} +(1.02183 + 3.15529i) q^{11} +(-3.20300 - 1.65554i) q^{13} +(-4.66519 + 7.18377i) q^{15} +(1.65482 - 0.736772i) q^{17} +(-1.61119 - 2.48102i) q^{19} +(-10.7616 + 10.7616i) q^{21} +(1.36235 - 0.786555i) q^{23} +(1.84276 - 0.598749i) q^{25} +(-12.0387 - 8.74664i) q^{27} +(-1.20259 - 5.65775i) q^{29} +(1.11856 - 7.06231i) q^{31} +(9.84907 + 4.39654i) q^{33} +(12.2589 - 1.28847i) q^{35} +(6.19179 + 4.02099i) q^{37} +(-10.9709 + 4.13830i) q^{39} +(-1.52565 + 0.0799559i) q^{41} +(-2.46467 + 4.26893i) q^{43} +(5.16450 + 19.2742i) q^{45} +(0.373867 - 0.733754i) q^{47} +(14.8196 + 1.55760i) q^{49} +(1.82037 - 5.60251i) q^{51} +(-0.294980 + 0.214316i) q^{53} +(-3.95840 - 7.78746i) q^{55} +(-9.50201 - 1.50497i) q^{57} +(0.798508 - 15.2364i) q^{59} +(3.32318 + 7.46398i) q^{61} +(1.85550 + 35.4051i) q^{63} +(9.01475 + 2.98713i) q^{65} +(2.65162 + 0.710499i) q^{67} +(1.06364 - 5.00403i) q^{69} +(0.683107 - 1.77955i) q^{71} +(2.94967 + 5.78905i) q^{73} +(2.56290 - 5.75637i) q^{75} +(-4.00268 - 14.9964i) q^{77} +(-3.48647 - 4.79872i) q^{79} +(-25.1044 + 5.33610i) q^{81} +(-1.60599 - 10.1398i) q^{83} +(-4.00143 + 2.59856i) q^{85} +(-16.2902 - 9.40516i) q^{87} +(0.136159 - 0.508151i) q^{89} +(14.5636 + 8.52157i) q^{91} +(-14.6337 - 18.0711i) q^{93} +(5.21380 + 5.79051i) q^{95} +(-10.0919 - 8.17229i) q^{97} +(22.9637 - 10.1974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 28 q^{9}+O(q^{10}) \) 224 * q + 28 * q^9	\( 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) \) 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more