LMFDB - Embedded newform 4020.2.q.k.841.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, 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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 $ x^14 - x^13 + 11x^12 - 8x^11 + 88x^10 - 57x^9 + 270x^8 + 17x^7 + 458x^6 - 101x^5 + 189x^4 - 30x^3 + 54x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.7
Root			$-0.647766 + 1.12196i$ of defining polynomial
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.k.3781.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(2.01447 - 3.48916i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(2.01447 - 3.48916i) q^{7} +1.00000 q^{9} +(1.47884 - 2.56142i) q^{11} +(-0.795531 - 1.37790i) q^{13} -1.00000 q^{15} +(-2.62284 - 4.54289i) q^{17} +(0.339201 + 0.587513i) q^{19} +(-2.01447 + 3.48916i) q^{21} +(-0.358507 - 0.620953i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.40670 - 5.90058i) q^{29} +(1.61034 - 2.78918i) q^{31} +(-1.47884 + 2.56142i) q^{33} +(2.01447 - 3.48916i) q^{35} +(-1.94572 - 3.37008i) q^{37} +(0.795531 + 1.37790i) q^{39} +(-0.662081 + 1.14676i) q^{41} -10.8759 q^{43} +1.00000 q^{45} +(-3.03954 + 5.26464i) q^{47} +(-4.61614 - 7.99539i) q^{49} +(2.62284 + 4.54289i) q^{51} +1.84141 q^{53} +(1.47884 - 2.56142i) q^{55} +(-0.339201 - 0.587513i) q^{57} +3.21856 q^{59} +(0.514400 + 0.890968i) q^{61} +(2.01447 - 3.48916i) q^{63} +(-0.795531 - 1.37790i) q^{65} +(-2.98224 + 7.62274i) q^{67} +(0.358507 + 0.620953i) q^{69} +(-6.97238 + 12.0765i) q^{71} +(-3.44466 - 5.96633i) q^{73} -1.00000 q^{75} +(-5.95814 - 10.3198i) q^{77} +(5.19415 - 8.99654i) q^{79} +1.00000 q^{81} +(3.85758 + 6.68153i) q^{83} +(-2.62284 - 4.54289i) q^{85} +(-3.40670 + 5.90058i) q^{87} -0.969090 q^{89} -6.41028 q^{91} +(-1.61034 + 2.78918i) q^{93} +(0.339201 + 0.587513i) q^{95} +(4.77014 + 8.26213i) q^{97} +(1.47884 - 2.56142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.01447	−	3.48916i	0.761396	−	1.31878i	−0.180735	−	0.983532i	$-0.557848\pi$
$7$	2.01447	−	3.48916i	0.761396	−	1.31878i	0.942131	−	0.335245i	$-0.108819\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.47884	−	2.56142i	0.445887	−	0.772298i	−0.552227	−	0.833694i	$-0.686222\pi$
$11$	1.47884	−	2.56142i	0.445887	−	0.772298i	0.998114	+	0.0613955i	$0.0195551\pi$
$12$		0			0
$13$	−0.795531	−	1.37790i	−0.220641	−	0.382161i	0.734362	−	0.678758i	$-0.237481\pi$
$13$	−0.795531	−	1.37790i	−0.220641	−	0.382161i	−0.955003	+	0.296597i	$0.904148\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−2.62284	−	4.54289i	−0.636131	−	1.10181i	−0.986274	−	0.165115i	$-0.947200\pi$
$17$	−2.62284	−	4.54289i	−0.636131	−	1.10181i	0.350143	−	0.936696i	$-0.386133\pi$
$18$		0			0
$19$	0.339201	+	0.587513i	0.0778180	+	0.134785i	0.902308	−	0.431091i	$-0.141871\pi$
$19$	0.339201	+	0.587513i	0.0778180	+	0.134785i	−0.824490	+	0.565876i	$0.808538\pi$
$20$		0			0
$21$	−2.01447	+	3.48916i	−0.439592	+	0.761396i
$22$		0			0
$23$	−0.358507	−	0.620953i	−0.0747539	−	0.129478i	0.826225	−	0.563340i	$-0.190484\pi$
$23$	−0.358507	−	0.620953i	−0.0747539	−	0.129478i	−0.900979	+	0.433862i	$0.857150\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.40670	−	5.90058i	0.632608	−	1.09571i	−0.354408	−	0.935091i	$-0.615318\pi$
$29$	3.40670	−	5.90058i	0.632608	−	1.09571i	0.987016	−	0.160619i	$-0.0513490\pi$
$30$		0			0
$31$	1.61034	−	2.78918i	0.289225	−	0.500952i	−0.684400	−	0.729107i	$-0.739936\pi$
$31$	1.61034	−	2.78918i	0.289225	−	0.500952i	0.973625	+	0.228155i	$0.0732692\pi$
$32$		0			0
$33$	−1.47884	+	2.56142i	−0.257433	+	0.445887i
$34$		0			0
$35$	2.01447	−	3.48916i	0.340507	−	0.589775i
$36$		0			0
$37$	−1.94572	−	3.37008i	−0.319874	−	0.554038i	0.660588	−	0.750749i	$-0.270307\pi$
$37$	−1.94572	−	3.37008i	−0.319874	−	0.554038i	−0.980461	+	0.196711i	$0.936974\pi$
$38$		0			0
$39$	0.795531	+	1.37790i	0.127387	+	0.220641i
$40$		0			0
$41$	−0.662081	+	1.14676i	−0.103400	+	0.179094i	−0.913083	−	0.407773i	$-0.866305\pi$
$41$	−0.662081	+	1.14676i	−0.103400	+	0.179094i	0.809684	+	0.586867i	$0.199639\pi$
$42$		0			0
$43$	−10.8759			−1.65856			−0.829282	−	0.558830i	$-0.811250\pi$
$43$	−10.8759			−1.65856			−0.829282	+	0.558830i	$0.811250\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−3.03954	+	5.26464i	−0.443363	+	0.767927i	−0.997937	−	0.0642075i	$-0.979548\pi$
$47$	−3.03954	+	5.26464i	−0.443363	+	0.767927i	0.554574	+	0.832135i	$0.312881\pi$
$48$		0			0
$49$	−4.61614	−	7.99539i	−0.659449	−	1.14220i
$50$		0			0
$51$	2.62284	+	4.54289i	0.367271	+	0.636131i
$52$		0			0
$53$	1.84141			0.252937			0.126468	−	0.991971i	$-0.459636\pi$
$53$	1.84141			0.252937			0.126468	+	0.991971i	$0.459636\pi$
$54$		0			0
$55$	1.47884	−	2.56142i	0.199407	−	0.345382i
$56$		0			0
$57$	−0.339201	−	0.587513i	−0.0449282	−	0.0778180i
$58$		0			0
$59$	3.21856			0.419021			0.209511	−	0.977806i	$-0.432813\pi$
$59$	3.21856			0.419021			0.209511	+	0.977806i	$0.432813\pi$
$60$		0			0
$61$	0.514400	+	0.890968i	0.0658622	+	0.114077i	0.897076	−	0.441876i	$-0.145687\pi$
$61$	0.514400	+	0.890968i	0.0658622	+	0.114077i	−0.831214	+	0.555953i	$0.812354\pi$
$62$		0			0
$63$	2.01447	−	3.48916i	0.253799	−	0.439592i
$64$		0			0
$65$	−0.795531	−	1.37790i	−0.0986735	−	0.170908i
$66$		0			0
$67$	−2.98224	+	7.62274i	−0.364339	+	0.931266i
$67$	−2.98224	+	7.62274i	−0.364339	+	0.931266i
$68$		0			0
$69$	0.358507	+	0.620953i	0.0431592	+	0.0747539i
$70$		0			0
$71$	−6.97238	+	12.0765i	−0.827469	+	1.43322i	0.0725490	+	0.997365i	$0.476887\pi$
$71$	−6.97238	+	12.0765i	−0.827469	+	1.43322i	−0.900018	+	0.435853i	$0.856447\pi$
$72$		0			0
$73$	−3.44466	−	5.96633i	−0.403167	−	0.698306i	0.590939	−	0.806716i	$-0.298757\pi$
$73$	−3.44466	−	5.96633i	−0.403167	−	0.698306i	−0.994106	+	0.108410i	$0.965424\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−5.95814	−	10.3198i	−0.678993	−	1.17605i
$78$		0			0
$79$	5.19415	−	8.99654i	0.584388	−	1.01219i	−0.410563	−	0.911832i	$-0.634668\pi$
$79$	5.19415	−	8.99654i	0.584388	−	1.01219i	0.994951	−	0.100358i	$-0.0319987\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	3.85758	+	6.68153i	0.423425	+	0.733393i	0.996272	−	0.0862691i	$-0.0274945\pi$
$83$	3.85758	+	6.68153i	0.423425	+	0.733393i	−0.572847	+	0.819662i	$0.694161\pi$
$84$		0			0
$85$	−2.62284	−	4.54289i	−0.284487	−	0.492745i
$86$		0			0
$87$	−3.40670	+	5.90058i	−0.365237	+	0.632608i
$88$		0			0
$89$	−0.969090			−0.102723			−0.0513617	−	0.998680i	$-0.516356\pi$
$89$	−0.969090			−0.102723			−0.0513617	+	0.998680i	$0.516356\pi$
$90$		0			0
$91$	−6.41028			−0.671980
$92$		0			0
$93$	−1.61034	+	2.78918i	−0.166984	+	0.289225i
$94$		0			0
$95$	0.339201	+	0.587513i	0.0348012	+	0.0602775i
$96$		0			0
$97$	4.77014	+	8.26213i	0.484335	+	0.838893i	0.999838	−	0.0179951i	$-0.00572832\pi$
$97$	4.77014	+	8.26213i	0.484335	+	0.838893i	−0.515503	+	0.856888i	$0.672395\pi$
$98$		0			0
$99$	1.47884	−	2.56142i	0.148629	−	0.257433i
$100$		0			0
$101$	−2.10709	+	3.64959i	−0.209663	+	0.363147i	−0.951608	−	0.307313i	$-0.900570\pi$
$101$	−2.10709	+	3.64959i	−0.209663	+	0.363147i	0.741945	+	0.670460i	$0.233903\pi$
$102$		0			0
$103$	1.25035	−	2.16566i	0.123200	−	0.213389i	−0.797828	−	0.602886i	$-0.794018\pi$
$103$	1.25035	−	2.16566i	0.123200	−	0.213389i	0.921028	+	0.389496i	$0.127351\pi$
$104$		0			0
$105$	−2.01447	+	3.48916i	−0.196592	+	0.340507i
$106$		0			0
$107$	−0.117103			−0.0113208			−0.00566041	−	0.999984i	$-0.501802\pi$
$107$	−0.117103			−0.0113208			−0.00566041	+	0.999984i	$0.501802\pi$
$108$		0			0
$109$	6.47281			0.619983			0.309992	−	0.950739i	$-0.399674\pi$
$109$	6.47281			0.619983			0.309992	+	0.950739i	$0.399674\pi$
$110$		0			0
$111$	1.94572	+	3.37008i	0.184679	+	0.319874i
$112$		0			0
$113$	−9.71169	+	16.8211i	−0.913599	+	1.58240i	−0.104660	+	0.994508i	$0.533375\pi$
$113$	−9.71169	+	16.8211i	−0.913599	+	1.58240i	−0.808939	+	0.587892i	$0.799958\pi$
$114$		0			0
$115$	−0.358507	−	0.620953i	−0.0334310	−	0.0579042i
$116$		0			0
$117$	−0.795531	−	1.37790i	−0.0735469	−	0.127387i
$118$		0			0
$119$	−21.1345			−1.93739
$120$		0			0
$121$	1.12607	+	1.95041i	0.102370	+	0.177310i
$122$		0			0
$123$	0.662081	−	1.14676i	0.0596979	−	0.103400i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−1.70520	+	2.95350i	−0.151312	+	0.262081i	−0.931710	−	0.363203i	$-0.881683\pi$
$127$	−1.70520	+	2.95350i	−0.151312	+	0.262081i	0.780398	+	0.625283i	$0.215017\pi$
$128$		0			0
$129$	10.8759			0.957573
$130$		0			0
$131$	11.5182			1.00635			0.503173	−	0.864185i	$-0.332166\pi$
$131$	11.5182			1.00635			0.503173	+	0.864185i	$0.332166\pi$
$132$		0			0
$133$	2.73323			0.237001
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−2.14095			−0.182913			−0.0914567	−	0.995809i	$-0.529152\pi$
$137$	−2.14095			−0.182913			−0.0914567	+	0.995809i	$0.529152\pi$
$138$		0			0
$139$	−5.56402			−0.471934			−0.235967	−	0.971761i	$-0.575826\pi$
$139$	−5.56402			−0.471934			−0.235967	+	0.971761i	$0.575826\pi$
$140$		0			0
$141$	3.03954	−	5.26464i	0.255976	−	0.443363i
$142$		0			0
$143$	−4.70585			−0.393523
$144$		0			0
$145$	3.40670	−	5.90058i	0.282911	−	0.490016i
$146$		0			0
$147$	4.61614	+	7.99539i	0.380733	+	0.659449i
$148$		0			0
$149$	11.7958			0.966348			0.483174	−	0.875524i	$-0.339484\pi$
$149$	11.7958			0.966348			0.483174	+	0.875524i	$0.339484\pi$
$150$		0			0
$151$	1.51228	+	2.61935i	0.123068	+	0.213160i	0.920976	−	0.389619i	$-0.127393\pi$
$151$	1.51228	+	2.61935i	0.123068	+	0.213160i	−0.797908	+	0.602779i	$0.794060\pi$
$152$		0			0
$153$	−2.62284	−	4.54289i	−0.212044	−	0.367271i
$154$		0			0
$155$	1.61034	−	2.78918i	0.129345	−	0.224033i
$156$		0			0
$157$	−1.96108	−	3.39669i	−0.156511	−	0.271086i	0.777097	−	0.629381i	$-0.216691\pi$
$157$	−1.96108	−	3.39669i	−0.156511	−	0.271086i	−0.933608	+	0.358295i	$0.883358\pi$
$158$		0			0
$159$	−1.84141			−0.146033
$160$		0			0
$161$	−2.88880			−0.227670
$162$		0			0
$163$	2.37206	−	4.10853i	0.185794	−	0.321805i	−0.758050	−	0.652197i	$-0.773848\pi$
$163$	2.37206	−	4.10853i	0.185794	−	0.321805i	0.943844	+	0.330392i	$0.107181\pi$
$164$		0			0
$165$	−1.47884	+	2.56142i	−0.115127	+	0.199407i
$166$		0			0
$167$	−1.13784	+	1.97079i	−0.0880485	+	0.152504i	−0.906686	−	0.421806i	$-0.861396\pi$
$167$	−1.13784	+	1.97079i	−0.0880485	+	0.152504i	0.818638	+	0.574310i	$0.194730\pi$
$168$		0			0
$169$	5.23426	−	9.06600i	0.402635	−	0.697385i
$170$		0			0
$171$	0.339201	+	0.587513i	0.0259393	+	0.0449282i
$172$		0			0
$173$	0.382324	+	0.662205i	0.0290676	+	0.0503465i	0.880193	−	0.474615i	$-0.157413\pi$
$173$	0.382324	+	0.662205i	0.0290676	+	0.0503465i	−0.851126	+	0.524962i	$0.824080\pi$
$174$		0			0
$175$	2.01447	−	3.48916i	0.152279	−	0.263755i
$176$		0			0
$177$	−3.21856			−0.241922
$178$		0			0
$179$	−15.9147			−1.18952			−0.594759	−	0.803904i	$-0.702753\pi$
$179$	−15.9147			−1.18952			−0.594759	+	0.803904i	$0.702753\pi$
$180$		0			0
$181$	2.99097	−	5.18051i	0.222317	−	0.385064i	−0.733194	−	0.680019i	$-0.761971\pi$
$181$	2.99097	−	5.18051i	0.222317	−	0.385064i	0.955511	+	0.294955i	$0.0953047\pi$
$182$		0			0
$183$	−0.514400	−	0.890968i	−0.0380256	−	0.0658622i
$184$		0			0
$185$	−1.94572	−	3.37008i	−0.143052	−	0.247773i
$186$		0			0
$187$	−15.5150			−1.13457
$188$		0			0
$189$	−2.01447	+	3.48916i	−0.146531	+	0.253799i
$190$		0			0
$191$	1.91365	+	3.31454i	0.138467	+	0.239832i	0.926916	−	0.375268i	$-0.122449\pi$
$191$	1.91365	+	3.31454i	0.138467	+	0.239832i	−0.788450	+	0.615099i	$0.789116\pi$
$192$		0			0
$193$	−7.18305			−0.517047			−0.258523	−	0.966005i	$-0.583236\pi$
$193$	−7.18305			−0.517047			−0.258523	+	0.966005i	$0.583236\pi$
$194$		0			0
$195$	0.795531	+	1.37790i	0.0569692	+	0.0986735i
$196$		0			0
$197$	11.5593	−	20.0213i	0.823566	−	1.42646i	−0.0794451	−	0.996839i	$-0.525315\pi$
$197$	11.5593	−	20.0213i	0.823566	−	1.42646i	0.903011	−	0.429618i	$-0.141352\pi$
$198$		0			0
$199$	−13.4217	−	23.2470i	−0.951436	−	1.64794i	−0.742321	−	0.670044i	$-0.766275\pi$
$199$	−13.4217	−	23.2470i	−0.951436	−	1.64794i	−0.209114	−	0.977891i	$-0.567058\pi$
$200$		0			0
$201$	2.98224	−	7.62274i	0.210351	−	0.537667i
$202$		0			0
$203$	−13.7254	−	23.7730i	−0.963331	−	1.66854i
$204$		0			0
$205$	−0.662081	+	1.14676i	−0.0462418	+	0.0800931i
$206$		0			0
$207$	−0.358507	−	0.620953i	−0.0249180	−	0.0431592i
$208$		0			0
$209$	2.00649			0.138792
$210$		0			0
$211$	−1.30980	−	2.26864i	−0.0901704	−	0.156180i	0.817412	−	0.576053i	$-0.195408\pi$
$211$	−1.30980	−	2.26864i	−0.0901704	−	0.156180i	−0.907583	+	0.419873i	$0.862075\pi$
$212$		0			0
$213$	6.97238	−	12.0765i	0.477739	−	0.827469i
$214$		0			0
$215$	−10.8759			−0.741733
$216$		0			0
$217$	−6.48793	−	11.2374i	−0.440429	−	0.762846i
$218$		0			0
$219$	3.44466	+	5.96633i	0.232769	+	0.403167i
$220$		0			0
$221$	−4.17310	+	7.22802i	−0.280713	+	0.486209i
$222$		0			0
$223$	−17.5929			−1.17811			−0.589055	−	0.808093i	$-0.700500\pi$
$223$	−17.5929			−1.17811			−0.589055	+	0.808093i	$0.700500\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	1.78070	−	3.08427i	0.118189	−	0.204710i	−0.800861	−	0.598851i	$-0.795624\pi$
$227$	1.78070	−	3.08427i	0.118189	−	0.204710i	0.919050	+	0.394140i	$0.128958\pi$
$228$		0			0
$229$	−11.9704	−	20.7333i	−0.791025	−	1.37010i	−0.925333	−	0.379157i	$-0.876214\pi$
$229$	−11.9704	−	20.7333i	−0.791025	−	1.37010i	0.134307	−	0.990940i	$-0.457119\pi$
$230$		0			0
$231$	5.95814	+	10.3198i	0.392017	+	0.678993i
$232$		0			0
$233$	11.5277	−	19.9665i	0.755203	−	1.30805i	−0.190071	−	0.981770i	$-0.560872\pi$
$233$	11.5277	−	19.9665i	0.755203	−	1.30805i	0.945274	−	0.326279i	$-0.105795\pi$
$234$		0			0
$235$	−3.03954	+	5.26464i	−0.198278	+	0.343427i
$236$		0			0
$237$	−5.19415	+	8.99654i	−0.337397	+	0.584388i
$238$		0			0
$239$	−0.785887	+	1.36120i	−0.0508348	+	0.0880484i	−0.890323	−	0.455329i	$-0.849522\pi$
$239$	−0.785887	+	1.36120i	−0.0508348	+	0.0880484i	0.839488	+	0.543378i	$0.182855\pi$
$240$		0			0
$241$	0.751633			0.0484170			0.0242085	−	0.999707i	$-0.492293\pi$
$241$	0.751633			0.0484170			0.0242085	+	0.999707i	$0.492293\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−4.61614	−	7.99539i	−0.294914	−	0.510807i
$246$		0			0
$247$	0.539689	−	0.934769i	0.0343396	−	0.0594780i
$248$		0			0
$249$	−3.85758	−	6.68153i	−0.244464	−	0.423425i
$250$		0			0
$251$	15.1397	+	26.2227i	0.955607	+	1.65516i	0.732973	+	0.680258i	$0.238132\pi$
$251$	15.1397	+	26.2227i	0.955607	+	1.65516i	0.222634	+	0.974902i	$0.428534\pi$
$252$		0			0
$253$	−2.12070			−0.133327
$254$		0			0
$255$	2.62284	+	4.54289i	0.164248	+	0.284487i
$256$		0			0
$257$	4.51598	−	7.82191i	0.281699	−	0.487917i	−0.690104	−	0.723710i	$-0.742435\pi$
$257$	4.51598	−	7.82191i	0.281699	−	0.487917i	0.971803	+	0.235793i	$0.0757687\pi$
$258$		0			0
$259$	−15.6783			−0.974203
$260$		0			0
$261$	3.40670	−	5.90058i	0.210869	−	0.365237i
$262$		0			0
$263$	−13.4758			−0.830952			−0.415476	−	0.909604i	$-0.636385\pi$
$263$	−13.4758			−0.830952			−0.415476	+	0.909604i	$0.636385\pi$
$264$		0			0
$265$	1.84141			0.113117
$266$		0			0
$267$	0.969090			0.0593074
$268$		0			0
$269$	−3.93750			−0.240074			−0.120037	−	0.992769i	$-0.538301\pi$
$269$	−3.93750			−0.240074			−0.120037	+	0.992769i	$0.538301\pi$
$270$		0			0
$271$	6.11307			0.371342			0.185671	−	0.982612i	$-0.440554\pi$
$271$	6.11307			0.371342			0.185671	+	0.982612i	$0.440554\pi$
$272$		0			0
$273$	6.41028			0.387968
$274$		0			0
$275$	1.47884	−	2.56142i	0.0891773	−	0.154460i
$276$		0			0
$277$	10.2321			0.614786			0.307393	−	0.951583i	$-0.400543\pi$
$277$	10.2321			0.614786			0.307393	+	0.951583i	$0.400543\pi$
$278$		0			0
$279$	1.61034	−	2.78918i	0.0964082	−	0.166984i
$280$		0			0
$281$	0.432633	+	0.749342i	0.0258087	+	0.0447020i	0.878641	−	0.477482i	$-0.158451\pi$
$281$	0.432633	+	0.749342i	0.0258087	+	0.0447020i	−0.852833	+	0.522184i	$0.825117\pi$
$282$		0			0
$283$	−31.6110			−1.87908			−0.939541	−	0.342437i	$-0.888748\pi$
$283$	−31.6110			−1.87908			−0.939541	+	0.342437i	$0.888748\pi$
$284$		0			0
$285$	−0.339201	−	0.587513i	−0.0200925	−	0.0348012i
$286$		0			0
$287$	2.66748	+	4.62021i	0.157456	+	0.272722i
$288$		0			0
$289$	−5.25854	+	9.10806i	−0.309326	+	0.535768i
$290$		0			0
$291$	−4.77014	−	8.26213i	−0.279631	−	0.484335i
$292$		0			0
$293$	22.7027			1.32631			0.663154	−	0.748483i	$-0.269217\pi$
$293$	22.7027			1.32631			0.663154	+	0.748483i	$0.269217\pi$
$294$		0			0
$295$	3.21856			0.187392
$296$		0			0
$297$	−1.47884	+	2.56142i	−0.0858109	+	0.148629i
$298$		0			0
$299$	−0.570408	+	0.987975i	−0.0329875	+	0.0571361i
$300$		0			0
$301$	−21.9092	+	37.9478i	−1.26282	+	2.18728i
$302$		0			0
$303$	2.10709	−	3.64959i	0.121049	−	0.209663i
$304$		0			0
$305$	0.514400	+	0.890968i	0.0294545	+	0.0510167i
$306$		0			0
$307$	−16.1406	−	27.9564i	−0.921193	−	1.59555i	−0.797572	−	0.603224i	$-0.793883\pi$
$307$	−16.1406	−	27.9564i	−0.921193	−	1.59555i	−0.123621	−	0.992329i	$-0.539451\pi$
$308$		0			0
$309$	−1.25035	+	2.16566i	−0.0711297	+	0.123200i
$310$		0			0
$311$	−6.42942			−0.364579			−0.182289	−	0.983245i	$-0.558351\pi$
$311$	−6.42942			−0.364579			−0.182289	+	0.983245i	$0.558351\pi$
$312$		0			0
$313$	−1.54276			−0.0872018			−0.0436009	−	0.999049i	$-0.513883\pi$
$313$	−1.54276			−0.0872018			−0.0436009	+	0.999049i	$0.513883\pi$
$314$		0			0
$315$	2.01447	−	3.48916i	0.113502	−	0.196592i
$316$		0			0
$317$	−0.825808	−	1.43034i	−0.0463820	−	0.0803360i	0.841902	−	0.539630i	$-0.181436\pi$
$317$	−0.825808	−	1.43034i	−0.0463820	−	0.0803360i	−0.888284	+	0.459294i	$0.848102\pi$
$318$		0			0
$319$	−10.0759	−	17.4520i	−0.564143	−	0.977125i
$320$		0			0
$321$	0.117103			0.00653608
$322$		0			0
$323$	1.77934	−	3.08190i	0.0990049	−	0.171481i
$324$		0			0
$325$	−0.795531	−	1.37790i	−0.0441281	−	0.0764322i
$326$		0			0
$327$	−6.47281			−0.357947
$328$		0			0
$329$	12.2461	+	21.2109i	0.675150	+	1.16939i
$330$		0			0
$331$	6.91944	−	11.9848i	0.380327	−	0.658745i	−0.610782	−	0.791799i	$-0.709145\pi$
$331$	6.91944	−	11.9848i	0.380327	−	0.658745i	0.991109	+	0.133054i	$0.0424783\pi$
$332$		0			0
$333$	−1.94572	−	3.37008i	−0.106625	−	0.184679i
$334$		0			0
$335$	−2.98224	+	7.62274i	−0.162937	+	0.416475i
$336$		0			0
$337$	−6.03143	−	10.4467i	−0.328553	−	0.569070i	0.653672	−	0.756778i	$-0.273228\pi$
$337$	−6.03143	−	10.4467i	−0.328553	−	0.569070i	−0.982225	+	0.187708i	$0.939894\pi$
$338$		0			0
$339$	9.71169	−	16.8211i	0.527467	−	0.913599i
$340$		0			0
$341$	−4.76285	−	8.24950i	−0.257923	−	0.446736i
$342$		0			0
$343$	−8.99370			−0.485614
$344$		0			0
$345$	0.358507	+	0.620953i	0.0193014	+	0.0334310i
$346$		0			0
$347$	12.2895	−	21.2860i	0.659735	−	1.14269i	−0.320950	−	0.947096i	$-0.604002\pi$
$347$	12.2895	−	21.2860i	0.659735	−	1.14269i	0.980684	−	0.195598i	$-0.0626647\pi$
$348$		0			0
$349$	7.16779			0.383683			0.191841	−	0.981426i	$-0.438554\pi$
$349$	7.16779			0.383683			0.191841	+	0.981426i	$0.438554\pi$
$350$		0			0
$351$	0.795531	+	1.37790i	0.0424623	+	0.0735469i
$352$		0			0
$353$	−0.327236	−	0.566790i	−0.0174170	−	0.0301672i	0.857186	−	0.515008i	$-0.172211\pi$
$353$	−0.327236	−	0.566790i	−0.0174170	−	0.0301672i	−0.874603	+	0.484841i	$0.838878\pi$
$354$		0			0
$355$	−6.97238	+	12.0765i	−0.370055	+	0.640955i
$356$		0			0
$357$	21.1345			1.11855
$358$		0			0
$359$	−3.17595			−0.167620			−0.0838100	−	0.996482i	$-0.526709\pi$
$359$	−3.17595			−0.167620			−0.0838100	+	0.996482i	$0.526709\pi$
$360$		0			0
$361$	9.26989	−	16.0559i	0.487889	−	0.845048i
$362$		0			0
$363$	−1.12607	−	1.95041i	−0.0591034	−	0.102370i
$364$		0			0
$365$	−3.44466	−	5.96633i	−0.180302	−	0.312292i
$366$		0			0
$367$	−4.51684	+	7.82339i	−0.235777	+	0.408378i	−0.959498	−	0.281715i	$-0.909097\pi$
$367$	−4.51684	+	7.82339i	−0.235777	+	0.408378i	0.723721	+	0.690092i	$0.242430\pi$
$368$		0			0
$369$	−0.662081	+	1.14676i	−0.0344666	+	0.0596979i
$370$		0			0
$371$	3.70945	−	6.42496i	0.192585	−	0.333567i
$372$		0			0
$373$	10.5611	−	18.2923i	0.546831	−	0.947140i	−0.451658	−	0.892191i	$-0.649167\pi$
$373$	10.5611	−	18.2923i	0.546831	−	0.947140i	0.998489	−	0.0549485i	$-0.0174995\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−10.8405			−0.558316
$378$		0			0
$379$	−3.31206	−	5.73666i	−0.170129	−	0.294673i	0.768336	−	0.640047i	$-0.221085\pi$
$379$	−3.31206	−	5.73666i	−0.170129	−	0.294673i	−0.938465	+	0.345375i	$0.887752\pi$
$380$		0			0
$381$	1.70520	−	2.95350i	0.0873603	−	0.151312i
$382$		0			0
$383$	0.133978	+	0.232057i	0.00684598	+	0.0118576i	0.869428	−	0.494059i	$-0.164488\pi$
$383$	0.133978	+	0.232057i	0.00684598	+	0.0118576i	−0.862582	+	0.505917i	$0.831154\pi$
$384$		0			0
$385$	−5.95814	−	10.3198i	−0.303655	−	0.525946i
$386$		0			0
$387$	−10.8759			−0.552855
$388$		0			0
$389$	6.38734	+	11.0632i	0.323851	+	0.560926i	0.981279	−	0.192591i	$-0.0616890\pi$
$389$	6.38734	+	11.0632i	0.323851	+	0.560926i	−0.657428	+	0.753517i	$0.728356\pi$
$390$		0			0
$391$	−1.88061	+	3.25732i	−0.0951066	+	0.164730i
$392$		0			0
$393$	−11.5182			−0.581015
$394$		0			0
$395$	5.19415	−	8.99654i	0.261346	−	0.452665i
$396$		0			0
$397$	32.4347			1.62785			0.813924	−	0.580971i	$-0.197327\pi$
$397$	32.4347			1.62785			0.813924	+	0.580971i	$0.197327\pi$
$398$		0			0
$399$	−2.73323			−0.136833
$400$		0			0
$401$	20.0300			1.00025			0.500126	−	0.865953i	$-0.333287\pi$
$401$	20.0300			1.00025			0.500126	+	0.865953i	$0.333287\pi$
$402$		0			0
$403$	−5.12429			−0.255259
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−11.5096			−0.570510
$408$		0			0
$409$	−12.2965	+	21.2982i	−0.608024	+	1.05313i	0.383542	+	0.923523i	$0.374704\pi$
$409$	−12.2965	+	21.2982i	−0.608024	+	1.05313i	−0.991566	+	0.129605i	$0.958629\pi$
$410$		0			0
$411$	2.14095			0.105605
$412$		0			0
$413$	6.48368	−	11.2301i	0.319041	−	0.552595i
$414$		0			0
$415$	3.85758	+	6.68153i	0.189361	+	0.327983i
$416$		0			0
$417$	5.56402			0.272471
$418$		0			0
$419$	−1.19377	−	2.06766i	−0.0583193	−	0.101012i	0.835392	−	0.549655i	$-0.185241\pi$
$419$	−1.19377	−	2.06766i	−0.0583193	−	0.101012i	−0.893711	+	0.448643i	$0.851907\pi$
$420$		0			0
$421$	−0.238338	−	0.412813i	−0.0116159	−	0.0201193i	0.860159	−	0.510026i	$-0.170364\pi$
$421$	−0.238338	−	0.412813i	−0.0116159	−	0.0201193i	−0.871775	+	0.489907i	$0.837031\pi$
$422$		0			0
$423$	−3.03954	+	5.26464i	−0.147788	+	0.255976i
$424$		0			0
$425$	−2.62284	−	4.54289i	−0.127226	−	0.220362i
$426$		0			0
$427$	4.14497			0.200589
$428$		0			0
$429$	4.70585			0.227201
$430$		0			0
$431$	3.80478	−	6.59007i	0.183270	−	0.317433i	−0.759722	−	0.650248i	$-0.774665\pi$
$431$	3.80478	−	6.59007i	0.183270	−	0.317433i	0.942992	+	0.332815i	$0.107998\pi$
$432$		0			0
$433$	0.433672	−	0.751142i	0.0208409	−	0.0360976i	−0.855417	−	0.517940i	$-0.826699\pi$
$433$	0.433672	−	0.751142i	0.0208409	−	0.0360976i	0.876258	+	0.481843i	$0.160032\pi$
$434$		0			0
$435$	−3.40670	+	5.90058i	−0.163339	+	0.282911i
$436$		0			0
$437$	0.243212	−	0.421255i	0.0116344	−	0.0201514i
$438$		0			0
$439$	15.4885	+	26.8268i	0.739224	+	1.28037i	0.952845	+	0.303457i	$0.0981409\pi$
$439$	15.4885	+	26.8268i	0.739224	+	1.28037i	−0.213621	+	0.976917i	$0.568526\pi$
$440$		0			0
$441$	−4.61614	−	7.99539i	−0.219816	−	0.380733i
$442$		0			0
$443$	−15.0873	+	26.1320i	−0.716820	+	1.24157i	0.245433	+	0.969414i	$0.421070\pi$
$443$	−15.0873	+	26.1320i	−0.716820	+	1.24157i	−0.962253	+	0.272155i	$0.912263\pi$
$444$		0			0
$445$	−0.969090			−0.0459393
$446$		0			0
$447$	−11.7958			−0.557921
$448$		0			0
$449$	5.98151	−	10.3603i	0.282285	−	0.488932i	−0.689662	−	0.724131i	$-0.742241\pi$
$449$	5.98151	−	10.3603i	0.282285	−	0.488932i	0.971947	+	0.235199i	$0.0755743\pi$
$450$		0			0
$451$	1.95822	+	3.39174i	0.0922091	+	0.159711i
$452$		0			0
$453$	−1.51228	−	2.61935i	−0.0710533	−	0.123068i
$454$		0			0
$455$	−6.41028			−0.300519
$456$		0			0
$457$	−7.14859	+	12.3817i	−0.334397	+	0.579192i	−0.983369	−	0.181620i	$-0.941866\pi$
$457$	−7.14859	+	12.3817i	−0.334397	+	0.579192i	0.648972	+	0.760812i	$0.275199\pi$
$458$		0			0
$459$	2.62284	+	4.54289i	0.122424	+	0.212044i
$460$		0			0
$461$	17.9836			0.837582			0.418791	−	0.908083i	$-0.362454\pi$
$461$	17.9836			0.837582			0.418791	+	0.908083i	$0.362454\pi$
$462$		0			0
$463$	−10.2327	−	17.7236i	−0.475555	−	0.823686i	0.524053	−	0.851686i	$-0.324420\pi$
$463$	−10.2327	−	17.7236i	−0.475555	−	0.823686i	−0.999608	+	0.0279998i	$0.991086\pi$
$464$		0			0
$465$	−1.61034	+	2.78918i	−0.0746775	+	0.129345i
$466$		0			0
$467$	2.59920	+	4.50194i	0.120277	+	0.208325i	0.919877	−	0.392208i	$-0.128289\pi$
$467$	2.59920	+	4.50194i	0.120277	+	0.208325i	−0.799600	+	0.600533i	$0.794955\pi$
$468$		0			0
$469$	20.5893	+	25.7613i	0.950727	+	1.18954i
$470$		0			0
$471$	1.96108	+	3.39669i	0.0903619	+	0.156511i
$472$		0			0
$473$	−16.0838	+	27.8579i	−0.739532	+	1.28091i
$474$		0			0
$475$	0.339201	+	0.587513i	0.0155636	+	0.0269569i
$476$		0			0
$477$	1.84141			0.0843123
$478$		0			0
$479$	6.34803	+	10.9951i	0.290049	+	0.502379i	0.973821	−	0.227316i	$-0.0729952\pi$
$479$	6.34803	+	10.9951i	0.290049	+	0.502379i	−0.683772	+	0.729695i	$0.739662\pi$
$480$		0			0
$481$	−3.09576	+	5.36201i	−0.141154	+	0.244487i
$482$		0			0
$483$	2.88880			0.131445
$484$		0			0
$485$	4.77014	+	8.26213i	0.216601	+	0.375164i
$486$		0			0
$487$	−7.08345	−	12.2689i	−0.320982	−	0.555957i	0.659709	−	0.751521i	$-0.270680\pi$
$487$	−7.08345	−	12.2689i	−0.320982	−	0.555957i	−0.980691	+	0.195564i	$0.937346\pi$
$488$		0			0
$489$	−2.37206	+	4.10853i	−0.107268	+	0.185794i
$490$		0			0
$491$	32.0080			1.44450			0.722250	−	0.691632i	$-0.243108\pi$
$491$	32.0080			1.44450			0.722250	+	0.691632i	$0.243108\pi$
$492$		0			0
$493$	−35.7409			−1.60969
$494$		0			0
$495$	1.47884	−	2.56142i	0.0664689	−	0.115127i
$496$		0			0
$497$	28.0912	+	48.6554i	1.26006	+	2.18249i
$498$		0			0
$499$	−16.2186	−	28.0914i	−0.726043	−	1.25754i	−0.958543	−	0.284947i	$-0.908024\pi$
$499$	−16.2186	−	28.0914i	−0.726043	−	1.25754i	0.232500	−	0.972596i	$-0.425309\pi$
$500$		0			0
$501$	1.13784	−	1.97079i	0.0508348	−	0.0880485i
$502$		0			0
$503$	16.7195	−	28.9591i	0.745487	−	1.29122i	−0.204480	−	0.978871i	$-0.565550\pi$
$503$	16.7195	−	28.9591i	0.745487	−	1.29122i	0.949967	−	0.312350i	$-0.101116\pi$
$504$		0			0
$505$	−2.10709	+	3.64959i	−0.0937642	+	0.162404i
$506$		0			0
$507$	−5.23426	+	9.06600i	−0.232462	+	0.402635i
$508$		0			0
$509$	−17.2804			−0.765940			−0.382970	−	0.923761i	$-0.625099\pi$
$509$	−17.2804			−0.765940			−0.382970	+	0.923761i	$0.625099\pi$
$510$		0			0
$511$	−27.7566			−1.22788
$512$		0			0
$513$	−0.339201	−	0.587513i	−0.0149761	−	0.0259393i
$514$		0			0
$515$	1.25035	−	2.16566i	0.0550968	−	0.0954305i
$516$		0			0
$517$	8.98999	+	15.5711i	0.395379	+	0.684817i
$518$		0			0
$519$	−0.382324	−	0.662205i	−0.0167822	−	0.0290676i
$520$		0			0
$521$	−11.5957			−0.508015			−0.254008	−	0.967202i	$-0.581749\pi$
$521$	−11.5957			−0.508015			−0.254008	+	0.967202i	$0.581749\pi$
$522$		0			0
$523$	4.86867	+	8.43278i	0.212892	+	0.368740i	0.952618	−	0.304168i	$-0.0983784\pi$
$523$	4.86867	+	8.43278i	0.212892	+	0.368740i	−0.739726	+	0.672908i	$0.765045\pi$
$524$		0			0
$525$	−2.01447	+	3.48916i	−0.0879185	+	0.152279i
$526$		0			0
$527$	−16.8946			−0.735940
$528$		0			0
$529$	11.2429	−	19.4734i	0.488824	−	0.846667i
$530$		0			0
$531$	3.21856			0.139674
$532$		0			0
$533$	2.10683			0.0912568
$534$		0			0
$535$	−0.117103			−0.00506283
$536$		0			0
$537$	15.9147			0.686769
$538$		0			0
$539$	−27.3061			−1.17616
$540$		0			0
$541$	12.8255			0.551411			0.275706	−	0.961242i	$-0.411088\pi$
$541$	12.8255			0.551411			0.275706	+	0.961242i	$0.411088\pi$
$542$		0			0
$543$	−2.99097	+	5.18051i	−0.128355	+	0.222317i
$544$		0			0
$545$	6.47281			0.277265
$546$		0			0
$547$	7.47486	−	12.9468i	0.319602	−	0.553567i	−0.660803	−	0.750559i	$-0.729784\pi$
$547$	7.47486	−	12.9468i	0.319602	−	0.553567i	0.980405	+	0.196992i	$0.0631174\pi$
$548$		0			0
$549$	0.514400	+	0.890968i	0.0219541	+	0.0380256i
$550$		0			0
$551$	4.62222			0.196913
$552$		0			0
$553$	−20.9269	−	36.2464i	−0.889902	−	1.54136i
$554$		0			0
$555$	1.94572	+	3.37008i	0.0825911	+	0.143052i
$556$		0			0
$557$	19.2541	−	33.3490i	0.815821	−	1.41304i	−0.0929167	−	0.995674i	$-0.529619\pi$
$557$	19.2541	−	33.3490i	0.815821	−	1.41304i	0.908737	−	0.417369i	$-0.137048\pi$
$558$		0			0
$559$	8.65215	+	14.9860i	0.365947	+	0.633838i
$560$		0			0
$561$	15.5150			0.655044
$562$		0			0
$563$	−3.97968			−0.167724			−0.0838618	−	0.996477i	$-0.526725\pi$
$563$	−3.97968			−0.167724			−0.0838618	+	0.996477i	$0.526725\pi$
$564$		0			0
$565$	−9.71169	+	16.8211i	−0.408574	+	0.707671i
$566$		0			0
$567$	2.01447	−	3.48916i	0.0845996	−	0.146531i
$568$		0			0
$569$	−21.8974	+	37.9274i	−0.917987	+	1.59000i	−0.115520	+	0.993305i	$0.536853\pi$
$569$	−21.8974	+	37.9274i	−0.917987	+	1.59000i	−0.802468	+	0.596696i	$0.796480\pi$
$570$		0			0
$571$	−4.86063	+	8.41885i	−0.203411	+	0.352318i	−0.949625	−	0.313388i	$-0.898536\pi$
$571$	−4.86063	+	8.41885i	−0.203411	+	0.352318i	0.746214	+	0.665706i	$0.231869\pi$
$572$		0			0
$573$	−1.91365	−	3.31454i	−0.0799439	−	0.138467i
$574$		0			0
$575$	−0.358507	−	0.620953i	−0.0149508	−	0.0258955i
$576$		0			0
$577$	−13.9145	+	24.1006i	−0.579267	+	1.00332i	0.416296	+	0.909229i	$0.363328\pi$
$577$	−13.9145	+	24.1006i	−0.579267	+	1.00332i	−0.995564	+	0.0940915i	$0.970005\pi$
$578$		0			0
$579$	7.18305			0.298517
$580$		0			0
$581$	31.0839			1.28958
$582$		0			0
$583$	2.72315	−	4.71663i	0.112781	−	0.195343i
$584$		0			0
$585$	−0.795531	−	1.37790i	−0.0328912	−	0.0569692i
$586$		0			0
$587$	3.88217	+	6.72411i	0.160234	+	0.277534i	0.934953	−	0.354773i	$-0.115442\pi$
$587$	3.88217	+	6.72411i	0.160234	+	0.277534i	−0.774718	+	0.632306i	$0.782108\pi$
$588$		0			0
$589$	2.18491			0.0900275
$590$		0			0
$591$	−11.5593	+	20.0213i	−0.475486	+	0.823566i
$592$		0			0
$593$	5.59382	+	9.68879i	0.229711	+	0.397871i	0.957722	−	0.287694i	$-0.0928886\pi$
$593$	5.59382	+	9.68879i	0.229711	+	0.397871i	−0.728012	+	0.685565i	$0.759555\pi$
$594$		0			0
$595$	−21.1345			−0.866428
$596$		0			0
$597$	13.4217	+	23.2470i	0.549312	+	0.951436i
$598$		0			0
$599$	1.91450	−	3.31600i	0.0782242	−	0.135488i	−0.824260	−	0.566212i	$-0.808408\pi$
$599$	1.91450	−	3.31600i	0.0782242	−	0.135488i	0.902484	+	0.430724i	$0.141742\pi$
$600$		0			0
$601$	13.2689	+	22.9825i	0.541251	+	0.937474i	0.998833	+	0.0483065i	$0.0153824\pi$
$601$	13.2689	+	22.9825i	0.541251	+	0.937474i	−0.457582	+	0.889168i	$0.651284\pi$
$602$		0			0
$603$	−2.98224	+	7.62274i	−0.121446	+	0.310422i
$604$		0			0
$605$	1.12607	+	1.95041i	0.0457813	+	0.0792956i
$606$		0			0
$607$	−20.4414	+	35.4055i	−0.829690	+	1.43707i	0.0685917	+	0.997645i	$0.478149\pi$
$607$	−20.4414	+	35.4055i	−0.829690	+	1.43707i	−0.898282	+	0.439420i	$0.855184\pi$
$608$		0			0
$609$	13.7254	+	23.7730i	0.556180	+	0.963331i
$610$		0			0
$611$	9.67221			0.391296
$612$		0			0
$613$	−11.3259	−	19.6170i	−0.457448	−	0.792324i	0.541377	−	0.840780i	$-0.317903\pi$
$613$	−11.3259	−	19.6170i	−0.457448	−	0.792324i	−0.998825	+	0.0484563i	$0.984570\pi$
$614$		0			0
$615$	0.662081	−	1.14676i	0.0266977	−	0.0462418i
$616$		0			0
$617$	40.4341			1.62782			0.813908	−	0.580994i	$-0.197336\pi$
$617$	40.4341			1.62782			0.813908	+	0.580994i	$0.197336\pi$
$618$		0			0
$619$	5.51336	+	9.54942i	0.221601	+	0.383823i	0.955294	−	0.295657i	$-0.0955386\pi$
$619$	5.51336	+	9.54942i	0.221601	+	0.383823i	−0.733694	+	0.679480i	$0.762205\pi$
$620$		0			0
$621$	0.358507	+	0.620953i	0.0143864	+	0.0249180i
$622$		0			0
$623$	−1.95220	+	3.38131i	−0.0782132	+	0.135469i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−2.00649			−0.0801316
$628$		0			0
$629$	−10.2066	+	17.6783i	−0.406964	+	0.704882i
$630$		0			0
$631$	−9.30826	−	16.1224i	−0.370556	−	0.641821i	0.619095	−	0.785316i	$-0.287499\pi$
$631$	−9.30826	−	16.1224i	−0.370556	−	0.641821i	−0.989651	+	0.143494i	$0.954166\pi$
$632$		0			0
$633$	1.30980	+	2.26864i	0.0520599	+	0.0901704i
$634$		0			0
$635$	−1.70520	+	2.95350i	−0.0676690	+	0.117206i
$636$		0			0
$637$	−7.34457	+	12.7212i	−0.291002	+	0.504031i
$638$		0			0
$639$	−6.97238	+	12.0765i	−0.275823	+	0.477739i
$640$		0			0
$641$	−12.3550	+	21.3996i	−0.487995	+	0.845232i	−0.999905	−	0.0138072i	$-0.995605\pi$
$641$	−12.3550	+	21.3996i	−0.487995	+	0.845232i	0.511910	+	0.859039i	$0.328938\pi$
$642$		0			0
$643$	33.5875			1.32456			0.662282	−	0.749255i	$-0.269588\pi$
$643$	33.5875			1.32456			0.662282	+	0.749255i	$0.269588\pi$
$644$		0			0
$645$	10.8759			0.428239
$646$		0			0
$647$	−22.6888	−	39.2982i	−0.891990	−	1.54497i	−0.837486	−	0.546459i	$-0.815975\pi$
$647$	−22.6888	−	39.2982i	−0.891990	−	1.54497i	−0.0545048	−	0.998514i	$-0.517358\pi$
$648$		0			0
$649$	4.75973	−	8.24410i	0.186836	−	0.323609i
$650$		0			0
$651$	6.48793	+	11.2374i	0.254282	+	0.440429i
$652$		0			0
$653$	4.60834	+	7.98188i	0.180338	+	0.312355i	0.941996	−	0.335625i	$-0.108947\pi$
$653$	4.60834	+	7.98188i	0.180338	+	0.312355i	−0.761657	+	0.647980i	$0.775614\pi$
$654$		0			0
$655$	11.5182			0.450052
$656$		0			0
$657$	−3.44466	−	5.96633i	−0.134389	−	0.232769i
$658$		0			0
$659$	5.09361	−	8.82238i	0.198419	−	0.343671i	−0.749597	−	0.661894i	$-0.769753\pi$
$659$	5.09361	−	8.82238i	0.198419	−	0.343671i	0.948016	+	0.318223i	$0.103086\pi$
$660$		0			0
$661$	32.9987			1.28350			0.641751	−	0.766913i	$-0.278208\pi$
$661$	32.9987			1.28350			0.641751	+	0.766913i	$0.278208\pi$
$662$		0			0
$663$	4.17310	−	7.22802i	0.162070	−	0.280713i
$664$		0			0
$665$	2.73323			0.105990
$666$		0			0
$667$	−4.88531			−0.189160
$668$		0			0
$669$	17.5929			0.680182
$670$		0			0
$671$	3.04286			0.117468
$672$		0			0
$673$	−28.6692			−1.10512			−0.552558	−	0.833475i	$-0.686348\pi$
$673$	−28.6692			−1.10512			−0.552558	+	0.833475i	$0.686348\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	6.59788	−	11.4279i	0.253577	−	0.439208i	−0.710931	−	0.703262i	$-0.751726\pi$
$677$	6.59788	−	11.4279i	0.253577	−	0.439208i	0.964508	+	0.264053i	$0.0850595\pi$
$678$		0			0
$679$	38.4372			1.47508
$680$		0			0
$681$	−1.78070	+	3.08427i	−0.0682367	+	0.118189i
$682$		0			0
$683$	−8.35528	−	14.4718i	−0.319706	−	0.553747i	0.660721	−	0.750632i	$-0.270251\pi$
$683$	−8.35528	−	14.4718i	−0.319706	−	0.553747i	−0.980427	+	0.196885i	$0.936917\pi$
$684$		0			0
$685$	−2.14095			−0.0818013
$686$		0			0
$687$	11.9704	+	20.7333i	0.456699	+	0.791025i
$688$		0			0
$689$	−1.46490	−	2.53728i	−0.0558082	−	0.0966626i
$690$		0			0
$691$	18.3246	−	31.7392i	0.697101	−	1.20742i	−0.272366	−	0.962194i	$-0.587806\pi$
$691$	18.3246	−	31.7392i	0.697101	−	1.20742i	0.969467	−	0.245221i	$-0.0788606\pi$
$692$		0			0
$693$	−5.95814	−	10.3198i	−0.226331	−	0.392017i
$694$		0			0
$695$	−5.56402			−0.211055
$696$		0			0
$697$	6.94613			0.263103
$698$		0			0
$699$	−11.5277	+	19.9665i	−0.436016	+	0.755203i
$700$		0			0
$701$	−0.0317333	+	0.0549637i	−0.00119855	+	0.00207595i	−0.866624	−	0.498962i	$-0.833715\pi$
$701$	−0.0317333	+	0.0549637i	−0.00119855	+	0.00207595i	0.865426	+	0.501038i	$0.167048\pi$
$702$		0			0
$703$	1.31998	−	2.28627i	0.0497839	−	0.0862282i
$704$		0			0
$705$	3.03954	−	5.26464i	0.114476	−	0.198278i
$706$		0			0
$707$	8.48932	+	14.7039i	0.319274	+	0.552998i
$708$		0			0
$709$	−5.92424	−	10.2611i	−0.222490	−	0.385363i	0.733074	−	0.680149i	$-0.238085\pi$
$709$	−5.92424	−	10.2611i	−0.222490	−	0.385363i	−0.955563	+	0.294786i	$0.904752\pi$
$710$		0			0
$711$	5.19415	−	8.99654i	0.194796	−	0.337397i
$712$		0			0
$713$	−2.30927			−0.0864828
$714$		0			0
$715$	−4.70585			−0.175989
$716$		0			0
$717$	0.785887	−	1.36120i	0.0293495	−	0.0508348i
$718$		0			0
$719$	13.5290	+	23.4328i	0.504545	+	0.873897i	0.999986	+	0.00525586i	$0.00167300\pi$
$719$	13.5290	+	23.4328i	0.504545	+	0.873897i	−0.495441	+	0.868641i	$0.664994\pi$
$720$		0			0
$721$	−5.03756	−	8.72531i	−0.187609	−	0.324947i
$722$		0			0
$723$	−0.751633			−0.0279535
$724$		0			0
$725$	3.40670	−	5.90058i	0.126522	−	0.219142i
$726$		0			0
$727$	−3.11684	−	5.39852i	−0.115597	−	0.200220i	0.802421	−	0.596758i	$-0.203545\pi$
$727$	−3.11684	−	5.39852i	−0.115597	−	0.200220i	−0.918018	+	0.396538i	$0.870211\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	28.5258	+	49.4081i	1.05506	+	1.82743i
$732$		0			0
$733$	22.7516	−	39.4069i	0.840349	−	1.45553i	−0.0492511	−	0.998786i	$-0.515683\pi$
$733$	22.7516	−	39.4069i	0.840349	−	1.45553i	0.889600	−	0.456741i	$-0.150983\pi$
$734$		0			0
$735$	4.61614	+	7.99539i	0.170269	+	0.294914i
$736$		0			0
$737$	15.1148	+	18.9116i	0.556762	+	0.696618i
$738$		0			0
$739$	−5.89645	−	10.2130i	−0.216904	−	0.375690i	0.736956	−	0.675941i	$-0.236263\pi$
$739$	−5.89645	−	10.2130i	−0.216904	−	0.375690i	−0.953860	+	0.300252i	$0.902929\pi$
$740$		0			0
$741$	−0.539689	+	0.934769i	−0.0198260	+	0.0343396i
$742$		0			0
$743$	14.3166	+	24.7970i	0.525224	+	0.909715i	0.999568	+	0.0293756i	$0.00935189\pi$
$743$	14.3166	+	24.7970i	0.525224	+	0.909715i	−0.474344	+	0.880339i	$0.657315\pi$
$744$		0			0
$745$	11.7958			0.432164
$746$		0			0
$747$	3.85758	+	6.68153i	0.141142	+	0.244464i
$748$		0			0
$749$	−0.235901	+	0.408592i	−0.00861963	+	0.0149296i
$750$		0			0
$751$	18.0352			0.658112			0.329056	−	0.944310i	$-0.393269\pi$
$751$	18.0352			0.658112			0.329056	+	0.944310i	$0.393269\pi$
$752$		0			0
$753$	−15.1397	−	26.2227i	−0.551720	−	0.955607i
$754$		0			0
$755$	1.51228	+	2.61935i	0.0550377	+	0.0953280i
$756$		0			0
$757$	−5.56650	+	9.64145i	−0.202318	+	0.350425i	−0.949275	−	0.314448i	$-0.898181\pi$
$757$	−5.56650	+	9.64145i	−0.202318	+	0.350425i	0.746957	+	0.664872i	$0.231514\pi$
$758$		0			0
$759$	2.12070			0.0769765
$760$		0			0
$761$	−4.62039			−0.167489			−0.0837446	−	0.996487i	$-0.526688\pi$
$761$	−4.62039			−0.167489			−0.0837446	+	0.996487i	$0.526688\pi$
$762$		0			0
$763$	13.0393	−	22.5847i	0.472053	−	0.817620i
$764$		0			0
$765$	−2.62284	−	4.54289i	−0.0948289	−	0.164248i
$766$		0			0
$767$	−2.56047	−	4.43486i	−0.0924531	−	0.160133i
$768$		0			0
$769$	3.44864	−	5.97321i	0.124361	−	0.215400i	−0.797122	−	0.603818i	$-0.793645\pi$
$769$	3.44864	−	5.97321i	0.124361	−	0.215400i	0.921483	+	0.388419i	$0.126979\pi$
$770$		0			0
$771$	−4.51598	+	7.82191i	−0.162639	+	0.281699i
$772$		0			0
$773$	10.0363	−	17.3833i	0.360980	−	0.625235i	−0.627143	−	0.778904i	$-0.715776\pi$
$773$	10.0363	−	17.3833i	0.360980	−	0.625235i	0.988122	+	0.153669i	$0.0491090\pi$
$774$		0			0
$775$	1.61034	−	2.78918i	0.0578449	−	0.100190i
$776$		0			0
$777$	15.6783			0.562457
$778$		0			0
$779$	−0.898314			−0.0321854
$780$		0			0
$781$	20.6220	+	35.7184i	0.737915	+	1.27811i
$782$		0			0
$783$	−3.40670	+	5.90058i	−0.121746	+	0.210869i
$784$		0			0
$785$	−1.96108	−	3.39669i	−0.0699940	−	0.121233i
$786$		0			0
$787$	−4.64960	−	8.05335i	−0.165740	−	0.287071i	0.771178	−	0.636620i	$-0.219668\pi$
$787$	−4.64960	−	8.05335i	−0.165740	−	0.287071i	−0.936918	+	0.349549i	$0.886335\pi$
$788$		0			0
$789$	13.4758			0.479751
$790$		0			0
$791$	39.1277	+	67.7712i	1.39122	+	2.40967i
$792$		0			0
$793$	0.818443	−	1.41759i	0.0290638	−	0.0503399i
$794$		0			0
$795$	−1.84141			−0.0653080
$796$		0			0
$797$	−18.4373	+	31.9343i	−0.653083	+	1.13117i	0.329288	+	0.944230i	$0.393191\pi$
$797$	−18.4373	+	31.9343i	−0.653083	+	1.13117i	−0.982371	+	0.186943i	$0.940142\pi$
$798$		0			0
$799$	31.8889			1.12815
$800$		0			0
$801$	−0.969090			−0.0342411
$802$		0			0
$803$	−20.3764			−0.719068
$804$		0			0
$805$	−2.88880			−0.101817
$806$		0			0
$807$	3.93750			0.138607
$808$		0			0
$809$	31.6865			1.11404			0.557020	−	0.830499i	$-0.311945\pi$
$809$	31.6865			1.11404			0.557020	+	0.830499i	$0.311945\pi$
$810$		0			0
$811$	−20.3188	+	35.1931i	−0.713488	+	1.23580i	0.250052	+	0.968232i	$0.419552\pi$
$811$	−20.3188	+	35.1931i	−0.713488	+	1.23580i	−0.963540	+	0.267565i	$0.913781\pi$
$812$		0			0
$813$	−6.11307			−0.214395
$814$		0			0
$815$	2.37206	−	4.10853i	0.0830898	−	0.143916i
$816$		0			0
$817$	−3.68912	−	6.38975i	−0.129066	−	0.223549i
$818$		0			0
$819$	−6.41028			−0.223993
$820$		0			0
$821$	−2.30966	−	4.00046i	−0.0806078	−	0.139617i	0.822903	−	0.568181i	$-0.192353\pi$
$821$	−2.30966	−	4.00046i	−0.0806078	−	0.139617i	−0.903511	+	0.428565i	$0.859019\pi$
$822$		0			0
$823$	−25.7575	−	44.6133i	−0.897850	−	1.55512i	−0.830238	−	0.557410i	$-0.811795\pi$
$823$	−25.7575	−	44.6133i	−0.897850	−	1.55512i	−0.0676122	−	0.997712i	$-0.521538\pi$
$824$		0			0
$825$	−1.47884	+	2.56142i	−0.0514866	+	0.0891773i
$826$		0			0
$827$	5.25416	+	9.10048i	0.182705	+	0.316455i	0.942801	−	0.333357i	$-0.108181\pi$
$827$	5.25416	+	9.10048i	0.182705	+	0.316455i	−0.760096	+	0.649811i	$0.774848\pi$
$828$		0			0
$829$	10.3054			0.357920			0.178960	−	0.983856i	$-0.442727\pi$
$829$	10.3054			0.357920			0.178960	+	0.983856i	$0.442727\pi$
$830$		0			0
$831$	−10.2321			−0.354947
$832$		0			0
$833$	−24.2148	+	41.9412i	−0.838992	+	1.45318i
$834$		0			0
$835$	−1.13784	+	1.97079i	−0.0393765	+	0.0682021i
$836$		0			0
$837$	−1.61034	+	2.78918i	−0.0556613	+	0.0964082i
$838$		0			0
$839$	−22.1873	+	38.4294i	−0.765989	+	1.32673i	0.173733	+	0.984793i	$0.444417\pi$
$839$	−22.1873	+	38.4294i	−0.765989	+	1.32673i	−0.939722	+	0.341939i	$0.888916\pi$
$840$		0			0
$841$	−8.71121	−	15.0883i	−0.300387	−	0.520285i
$842$		0			0
$843$	−0.432633	−	0.749342i	−0.0149007	−	0.0258087i
$844$		0			0
$845$	5.23426	−	9.06600i	0.180064	−	0.311880i
$846$		0			0
$847$	9.07373			0.311777
$848$		0			0
$849$	31.6110			1.08489
$850$		0			0
$851$	−1.39511	+	2.41640i	−0.0478237	+	0.0828330i
$852$		0			0
$853$	−4.96832	−	8.60538i	−0.170112	−	0.294643i	0.768347	−	0.640034i	$-0.221080\pi$
$853$	−4.96832	−	8.60538i	−0.170112	−	0.294643i	−0.938459	+	0.345391i	$0.887746\pi$
$854$		0			0
$855$	0.339201	+	0.587513i	0.0116004	+	0.0200925i
$856$		0			0
$857$	28.5335			0.974686			0.487343	−	0.873211i	$-0.337966\pi$
$857$	28.5335			0.974686			0.487343	+	0.873211i	$0.337966\pi$
$858$		0			0
$859$	−3.72748	+	6.45619i	−0.127180	+	0.220282i	−0.922583	−	0.385799i	$-0.873926\pi$
$859$	−3.72748	+	6.45619i	−0.127180	+	0.220282i	0.795403	+	0.606081i	$0.207259\pi$
$860$		0			0
$861$	−2.66748	−	4.62021i	−0.0909075	−	0.157456i
$862$		0			0
$863$	2.47929			0.0843962			0.0421981	−	0.999109i	$-0.486564\pi$
$863$	2.47929			0.0843962			0.0421981	+	0.999109i	$0.486564\pi$
$864$		0			0
$865$	0.382324	+	0.662205i	0.0129994	+	0.0225156i
$866$		0			0
$867$	5.25854	−	9.10806i	0.178589	−	0.309326i
$868$		0			0
$869$	−15.3626	−	26.6089i	−0.521142	−	0.902644i
$870$		0			0
$871$	12.8759	−	1.95490i	0.436282	−	0.0662392i
$872$		0			0
$873$	4.77014	+	8.26213i	0.161445	+	0.279631i
$874$		0			0
$875$	2.01447	−	3.48916i	0.0681014	−	0.117955i
$876$		0			0
$877$	0.428389	+	0.741992i	0.0144657	+	0.0250553i	0.873168	−	0.487420i	$-0.162062\pi$
$877$	0.428389	+	0.741992i	0.0144657	+	0.0250553i	−0.858702	+	0.512475i	$0.828729\pi$
$878$		0			0
$879$	−22.7027			−0.765745
$880$		0			0
$881$	−24.2606	−	42.0205i	−0.817359	−	1.41571i	−0.907622	−	0.419789i	$-0.862104\pi$
$881$	−24.2606	−	42.0205i	−0.817359	−	1.41571i	0.0902627	−	0.995918i	$-0.471229\pi$
$882$		0			0
$883$	7.11466	−	12.3230i	0.239427	−	0.414701i	−0.721123	−	0.692807i	$-0.756374\pi$
$883$	7.11466	−	12.3230i	0.239427	−	0.414701i	0.960550	+	0.278107i	$0.0897069\pi$
$884$		0			0
$885$	−3.21856			−0.108191
$886$		0			0
$887$	27.7264	+	48.0236i	0.930963	+	1.61247i	0.781680	+	0.623680i	$0.214363\pi$
$887$	27.7264	+	48.0236i	0.930963	+	1.61247i	0.149283	+	0.988794i	$0.452303\pi$
$888$		0			0
$889$	6.87015	+	11.8995i	0.230418	+	0.399095i
$890$		0			0
$891$	1.47884	−	2.56142i	0.0495430	−	0.0858109i
$892$		0			0
$893$	−4.12406			−0.138006
$894$		0			0
$895$	−15.9147			−0.531969
$896$		0			0
$897$	0.570408	−	0.987975i	0.0190454	−	0.0329875i
$898$		0			0
$899$	−10.9719	−	19.0038i	−0.365932	−	0.633813i
$900$		0			0
$901$	−4.82971	−	8.36531i	−0.160901	−	0.278689i
$902$		0			0
$903$	21.9092	−	37.9478i	0.729092	−	1.26282i
$904$		0			0
$905$	2.99097	−	5.18051i	0.0994231	−	0.172206i
$906$		0			0
$907$	−8.20308	+	14.2082i	−0.272379	+	0.471774i	−0.969470	−	0.245208i	$-0.921144\pi$
$907$	−8.20308	+	14.2082i	−0.272379	+	0.471774i	0.697092	+	0.716982i	$0.254477\pi$
$908$		0			0
$909$	−2.10709	+	3.64959i	−0.0698877	+	0.121049i
$910$		0			0
$911$	46.8920			1.55360			0.776801	−	0.629746i	$-0.216841\pi$
$911$	46.8920			1.55360			0.776801	+	0.629746i	$0.216841\pi$
$912$		0			0
$913$	22.8190			0.755198
$914$		0			0
$915$	−0.514400	−	0.890968i	−0.0170056	−	0.0294545i
$916$		0			0
$917$	23.2029	−	40.1887i	0.766229	−	1.32715i
$918$		0			0
$919$	29.2663	+	50.6907i	0.965405	+	1.67213i	0.708523	+	0.705688i	$0.249362\pi$
$919$	29.2663	+	50.6907i	0.965405	+	1.67213i	0.256882	+	0.966443i	$0.417305\pi$
$920$		0			0
$921$	16.1406	+	27.9564i	0.531851	+	0.921193i
$922$		0			0
$923$	22.1870			0.730293
$924$		0			0
$925$	−1.94572	−	3.37008i	−0.0639748	−	0.110808i
$926$		0			0
$927$	1.25035	−	2.16566i	0.0410668	−	0.0711297i
$928$		0			0
$929$	19.7443			0.647789			0.323894	−	0.946093i	$-0.395008\pi$
$929$	19.7443			0.647789			0.323894	+	0.946093i	$0.395008\pi$
$930$		0			0
$931$	3.13160	−	5.42408i	0.102634	−	0.177767i
$932$		0			0
$933$	6.42942			0.210490
$934$		0			0
$935$	−15.5150			−0.507395
$936$		0			0
$937$	−49.9894			−1.63308			−0.816541	−	0.577287i	$-0.804111\pi$
$937$	−49.9894			−1.63308			−0.816541	+	0.577287i	$0.804111\pi$
$938$		0			0
$939$	1.54276			0.0503460
$940$		0			0
$941$	4.78909			0.156120			0.0780600	−	0.996949i	$-0.475127\pi$
$941$	4.78909			0.156120			0.0780600	+	0.996949i	$0.475127\pi$
$942$		0			0
$943$	0.949444			0.0309182
$944$		0			0
$945$	−2.01447	+	3.48916i	−0.0655306	+	0.113502i
$946$		0			0
$947$	−32.1778			−1.04564			−0.522819	−	0.852444i	$-0.675120\pi$
$947$	−32.1778			−1.04564			−0.522819	+	0.852444i	$0.675120\pi$
$948$		0			0
$949$	−5.48067	+	9.49281i	−0.177910	+	0.308150i
$950$		0			0
$951$	0.825808	+	1.43034i	0.0267787	+	0.0463820i
$952$		0			0
$953$	0.0194423			0.000629798			0.000314899	−	1.00000i	$-0.499900\pi$
$953$	0.0194423			0.000629798			0.000314899		1.00000i	$0.499900\pi$
$954$		0			0
$955$	1.91365	+	3.31454i	0.0619243	+	0.107256i
$956$		0			0
$957$	10.0759	+	17.4520i	0.325708	+	0.564143i
$958$		0			0
$959$	−4.31286	+	7.47010i	−0.139270	+	0.241222i
$960$		0			0
$961$	10.3136	+	17.8638i	0.332698	+	0.576250i
$962$		0			0
$963$	−0.117103			−0.00377361
$964$		0			0
$965$	−7.18305			−0.231230
$966$		0			0
$967$	6.72730	−	11.6520i	0.216335	−	0.374704i	−0.737349	−	0.675512i	$-0.763923\pi$
$967$	6.72730	−	11.6520i	0.216335	−	0.374704i	0.953685	+	0.300808i	$0.0972562\pi$
$968$		0			0
$969$	−1.77934	+	3.08190i	−0.0571605	+	0.0990049i
$970$		0			0
$971$	−14.0898	+	24.4043i	−0.452164	+	0.783172i	−0.998520	−	0.0543815i	$-0.982681\pi$
$971$	−14.0898	+	24.4043i	−0.452164	+	0.783172i	0.546356	+	0.837553i	$0.316015\pi$
$972$		0			0
$973$	−11.2085	+	19.4137i	−0.359329	+	0.622376i
$974$		0			0
$975$	0.795531	+	1.37790i	0.0254774	+	0.0441281i
$976$		0			0
$977$	23.6955	+	41.0418i	0.758085	+	1.31304i	0.943826	+	0.330443i	$0.107198\pi$
$977$	23.6955	+	41.0418i	0.758085	+	1.31304i	−0.185740	+	0.982599i	$0.559468\pi$
$978$		0			0
$979$	−1.43313	+	2.48225i	−0.0458030	+	0.0793331i
$980$		0			0
$981$	6.47281			0.206661
$982$		0			0
$983$	12.5349			0.399802			0.199901	−	0.979816i	$-0.435938\pi$
$983$	12.5349			0.399802			0.199901	+	0.979816i	$0.435938\pi$
$984$		0			0
$985$	11.5593	−	20.0213i	0.368310	−	0.637931i
$986$		0			0
$987$	−12.2461	−	21.2109i	−0.389798	−	0.675150i
$988$		0			0
$989$	3.89910	+	6.75344i	0.123984	+	0.214747i
$990$		0			0
$991$	24.3722			0.774208			0.387104	−	0.922036i	$-0.373475\pi$
$991$	24.3722			0.774208			0.387104	+	0.922036i	$0.373475\pi$
$992$		0			0
$993$	−6.91944	+	11.9848i	−0.219582	+	0.380327i
$994$		0			0
$995$	−13.4217	−	23.2470i	−0.425495	−	0.736979i
$996$		0			0
$997$	3.45388			0.109386			0.0546928	−	0.998503i	$-0.482582\pi$
$997$	3.45388			0.109386			0.0546928	+	0.998503i	$0.482582\pi$
$998$		0			0
$999$	1.94572	+	3.37008i	0.0615598	+	0.106625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.k.841.7	✓	14
67.29	even	3	inner	4020.2.q.k.3781.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.k.841.7	✓	14	1.1	even	1	trivial
4020.2.q.k.3781.7	yes	14	67.29	even	3	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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(2.01447 - 3.48916i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(2.01447 - 3.48916i) q^{7} +1.00000 q^{9} +(1.47884 - 2.56142i) q^{11} +(-0.795531 - 1.37790i) q^{13} -1.00000 q^{15} +(-2.62284 - 4.54289i) q^{17} +(0.339201 + 0.587513i) q^{19} +(-2.01447 + 3.48916i) q^{21} +(-0.358507 - 0.620953i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.40670 - 5.90058i) q^{29} +(1.61034 - 2.78918i) q^{31} +(-1.47884 + 2.56142i) q^{33} +(2.01447 - 3.48916i) q^{35} +(-1.94572 - 3.37008i) q^{37} +(0.795531 + 1.37790i) q^{39} +(-0.662081 + 1.14676i) q^{41} -10.8759 q^{43} +1.00000 q^{45} +(-3.03954 + 5.26464i) q^{47} +(-4.61614 - 7.99539i) q^{49} +(2.62284 + 4.54289i) q^{51} +1.84141 q^{53} +(1.47884 - 2.56142i) q^{55} +(-0.339201 - 0.587513i) q^{57} +3.21856 q^{59} +(0.514400 + 0.890968i) q^{61} +(2.01447 - 3.48916i) q^{63} +(-0.795531 - 1.37790i) q^{65} +(-2.98224 + 7.62274i) q^{67} +(0.358507 + 0.620953i) q^{69} +(-6.97238 + 12.0765i) q^{71} +(-3.44466 - 5.96633i) q^{73} -1.00000 q^{75} +(-5.95814 - 10.3198i) q^{77} +(5.19415 - 8.99654i) q^{79} +1.00000 q^{81} +(3.85758 + 6.68153i) q^{83} +(-2.62284 - 4.54289i) q^{85} +(-3.40670 + 5.90058i) q^{87} -0.969090 q^{89} -6.41028 q^{91} +(-1.61034 + 2.78918i) q^{93} +(0.339201 + 0.587513i) q^{95} +(4.77014 + 8.26213i) q^{97} +(1.47884 - 2.56142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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