LMFDB - Embedded newform 4020.2.q.j.841.3

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} + \cdots + 81 $ x^12 - x^11 + 30x^10 - 53x^9 + 798x^8 - 1096x^7 + 4060x^6 - 915x^5 + 10392x^4 - 7038x^3 + 4869x^2 - 675x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.3
Root			$0.307496 - 0.532598i$ of defining polynomial
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.j.3781.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -1.00000 q^{5} +(-0.550200 + 0.952975i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -1.00000 q^{5} +(-0.550200 + 0.952975i) q^{7} +1.00000 q^{9} +(-0.589441 + 1.02094i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(-1.83022 - 3.17003i) q^{17} +(-3.26255 - 5.65090i) q^{19} +(-0.550200 + 0.952975i) q^{21} +(4.11217 + 7.12248i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(4.58485 - 7.94120i) q^{29} +(1.12291 - 1.94493i) q^{31} +(-0.589441 + 1.02094i) q^{33} +(0.550200 - 0.952975i) q^{35} +(-5.58203 - 9.66835i) q^{37} +(0.500000 + 0.866025i) q^{39} +(-4.73507 + 8.20139i) q^{41} +3.52510 q^{43} -1.00000 q^{45} +(5.16548 - 8.94687i) q^{47} +(2.89456 + 5.01352i) q^{49} +(-1.83022 - 3.17003i) q^{51} +1.24582 q^{53} +(0.589441 - 1.02094i) q^{55} +(-3.26255 - 5.65090i) q^{57} +8.73327 q^{59} +(7.40027 + 12.8176i) q^{61} +(-0.550200 + 0.952975i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(8.12438 + 0.997229i) q^{67} +(4.11217 + 7.12248i) q^{69} +(3.07575 - 5.32736i) q^{71} +(-4.45329 - 7.71333i) q^{73} +1.00000 q^{75} +(-0.648621 - 1.12345i) q^{77} +(-1.22597 + 2.12344i) q^{79} +1.00000 q^{81} +(-5.48704 - 9.50384i) q^{83} +(1.83022 + 3.17003i) q^{85} +(4.58485 - 7.94120i) q^{87} +7.19709 q^{89} -1.10040 q^{91} +(1.12291 - 1.94493i) q^{93} +(3.26255 + 5.65090i) q^{95} +(3.18799 + 5.52175i) q^{97} +(-0.589441 + 1.02094i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * 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
$7$	−0.550200	+	0.952975i	−0.207956	+	0.360191i	−0.951071	−	0.308974i	$-0.900014\pi$
$7$	−0.550200	+	0.952975i	−0.207956	+	0.360191i	0.743114	+	0.669164i	$0.233348\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.589441	+	1.02094i	−0.177723	+	0.307826i	−0.941100	−	0.338127i	$-0.890207\pi$
$11$	−0.589441	+	1.02094i	−0.177723	+	0.307826i	0.763377	+	0.645953i	$0.223540\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−1.83022	−	3.17003i	−0.443894	−	0.768846i	0.554081	−	0.832463i	$-0.313070\pi$
$17$	−1.83022	−	3.17003i	−0.443894	−	0.768846i	−0.997974	+	0.0636166i	$0.979737\pi$
$18$		0			0
$19$	−3.26255	−	5.65090i	−0.748480	−	1.29641i	−0.948551	−	0.316624i	$-0.897451\pi$
$19$	−3.26255	−	5.65090i	−0.748480	−	1.29641i	0.200071	−	0.979781i	$-0.435883\pi$
$20$		0			0
$21$	−0.550200	+	0.952975i	−0.120064	+	0.207956i
$22$		0			0
$23$	4.11217	+	7.12248i	0.857446	+	1.48514i	0.874357	+	0.485283i	$0.161283\pi$
$23$	4.11217	+	7.12248i	0.857446	+	1.48514i	−0.0169115	+	0.999857i	$0.505383\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	4.58485	−	7.94120i	0.851386	−	1.47464i	−0.0285719	−	0.999592i	$-0.509096\pi$
$29$	4.58485	−	7.94120i	0.851386	−	1.47464i	0.879958	−	0.475052i	$-0.157571\pi$
$30$		0			0
$31$	1.12291	−	1.94493i	0.201680	−	0.349320i	−0.747390	−	0.664386i	$-0.768693\pi$
$31$	1.12291	−	1.94493i	0.201680	−	0.349320i	0.949070	+	0.315066i	$0.102027\pi$
$32$		0			0
$33$	−0.589441	+	1.02094i	−0.102609	+	0.177723i
$34$		0			0
$35$	0.550200	−	0.952975i	0.0930008	−	0.161082i
$36$		0			0
$37$	−5.58203	−	9.66835i	−0.917680	−	1.58947i	−0.802930	−	0.596073i	$-0.796727\pi$
$37$	−5.58203	−	9.66835i	−0.917680	−	1.58947i	−0.114750	−	0.993394i	$-0.536607\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	−4.73507	+	8.20139i	−0.739494	+	1.28084i	0.213229	+	0.977002i	$0.431602\pi$
$41$	−4.73507	+	8.20139i	−0.739494	+	1.28084i	−0.952723	+	0.303839i	$0.901731\pi$
$42$		0			0
$43$	3.52510			0.537572			0.268786	−	0.963200i	$-0.413377\pi$
$43$	3.52510			0.537572			0.268786	+	0.963200i	$0.413377\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	5.16548	−	8.94687i	0.753462	−	1.30503i	−0.192673	−	0.981263i	$-0.561716\pi$
$47$	5.16548	−	8.94687i	0.753462	−	1.30503i	0.946135	−	0.323772i	$-0.104951\pi$
$48$		0			0
$49$	2.89456	+	5.01352i	0.413508	+	0.716218i
$50$		0			0
$51$	−1.83022	−	3.17003i	−0.256282	−	0.443894i
$52$		0			0
$53$	1.24582			0.171126			0.0855629	−	0.996333i	$-0.472731\pi$
$53$	1.24582			0.171126			0.0855629	+	0.996333i	$0.472731\pi$
$54$		0			0
$55$	0.589441	−	1.02094i	0.0794802	−	0.137664i
$56$		0			0
$57$	−3.26255	−	5.65090i	−0.432135	−	0.748480i
$58$		0			0
$59$	8.73327			1.13697			0.568487	−	0.822692i	$-0.307529\pi$
$59$	8.73327			1.13697			0.568487	+	0.822692i	$0.307529\pi$
$60$		0			0
$61$	7.40027	+	12.8176i	0.947507	+	1.64113i	0.750652	+	0.660697i	$0.229739\pi$
$61$	7.40027	+	12.8176i	0.947507	+	1.64113i	0.196854	+	0.980433i	$0.436927\pi$
$62$		0			0
$63$	−0.550200	+	0.952975i	−0.0693187	+	0.120064i
$64$		0			0
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$	8.12438	+	0.997229i	0.992551	+	0.121831i
$67$	8.12438	+	0.997229i	0.992551	+	0.121831i
$68$		0			0
$69$	4.11217	+	7.12248i	0.495047	+	0.857446i
$70$		0			0
$71$	3.07575	−	5.32736i	0.365024	−	0.632241i	−0.623756	−	0.781619i	$-0.714394\pi$
$71$	3.07575	−	5.32736i	0.365024	−	0.632241i	0.988780	+	0.149379i	$0.0477273\pi$
$72$		0			0
$73$	−4.45329	−	7.71333i	−0.521218	−	0.902777i	−0.999695	−	0.0246766i	$-0.992144\pi$
$73$	−4.45329	−	7.71333i	−0.521218	−	0.902777i	0.478477	−	0.878100i	$-0.341189\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−0.648621	−	1.12345i	−0.0739173	−	0.128028i
$78$		0			0
$79$	−1.22597	+	2.12344i	−0.137932	+	0.238906i	−0.926714	−	0.375768i	$-0.877379\pi$
$79$	−1.22597	+	2.12344i	−0.137932	+	0.238906i	0.788781	+	0.614674i	$0.210712\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−5.48704	−	9.50384i	−0.602281	−	1.04318i	−0.992475	−	0.122449i	$-0.960925\pi$
$83$	−5.48704	−	9.50384i	−0.602281	−	1.04318i	0.390194	−	0.920733i	$-0.372408\pi$
$84$		0			0
$85$	1.83022	+	3.17003i	0.198515	+	0.343839i
$86$		0			0
$87$	4.58485	−	7.94120i	0.491548	−	0.851386i
$88$		0			0
$89$	7.19709			0.762890			0.381445	−	0.924392i	$-0.375427\pi$
$89$	7.19709			0.762890			0.381445	+	0.924392i	$0.375427\pi$
$90$		0			0
$91$	−1.10040			−0.115353
$92$		0			0
$93$	1.12291	−	1.94493i	0.116440	−	0.201680i
$94$		0			0
$95$	3.26255	+	5.65090i	0.334730	+	0.579770i
$96$		0			0
$97$	3.18799	+	5.52175i	0.323691	+	0.560649i	0.981247	−	0.192757i	$-0.0617429\pi$
$97$	3.18799	+	5.52175i	0.323691	+	0.560649i	−0.657556	+	0.753406i	$0.728410\pi$
$98$		0			0
$99$	−0.589441	+	1.02094i	−0.0592411	+	0.102609i
$100$		0			0
$101$	7.77764	−	13.4713i	0.773904	−	1.34044i	−0.161504	−	0.986872i	$-0.551634\pi$
$101$	7.77764	−	13.4713i	0.773904	−	1.34044i	0.935408	−	0.353570i	$-0.115032\pi$
$102$		0			0
$103$	−2.21517	+	3.83680i	−0.218268	+	0.378051i	−0.954278	−	0.298919i	$-0.903374\pi$
$103$	−2.21517	+	3.83680i	−0.218268	+	0.378051i	0.736011	+	0.676970i	$0.236707\pi$
$104$		0			0
$105$	0.550200	−	0.952975i	0.0536940	−	0.0930008i
$106$		0			0
$107$	14.6613			1.41736			0.708682	−	0.705528i	$-0.249290\pi$
$107$	14.6613			1.41736			0.708682	+	0.705528i	$0.249290\pi$
$108$		0			0
$109$	−0.127209			−0.0121844			−0.00609222	−	0.999981i	$-0.501939\pi$
$109$	−0.127209			−0.0121844			−0.00609222	+	0.999981i	$0.501939\pi$
$110$		0			0
$111$	−5.58203	−	9.66835i	−0.529823	−	0.917680i
$112$		0			0
$113$	2.12291	−	3.67698i	0.199706	−	0.345902i	−0.748727	−	0.662879i	$-0.769335\pi$
$113$	2.12291	−	3.67698i	0.199706	−	0.345902i	0.948433	+	0.316977i	$0.102668\pi$
$114$		0			0
$115$	−4.11217	−	7.12248i	−0.383461	−	0.664175i
$116$		0			0
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$		0			0
$119$	4.02795			0.369242
$120$		0			0
$121$	4.80512	+	8.32271i	0.436829	+	0.756610i
$122$		0			0
$123$	−4.73507	+	8.20139i	−0.426947	+	0.739494i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−5.22138	+	9.04370i	−0.463323	+	0.802499i	−0.999124	−	0.0418455i	$-0.986676\pi$
$127$	−5.22138	+	9.04370i	−0.463323	+	0.802499i	0.535801	+	0.844344i	$0.320010\pi$
$128$		0			0
$129$	3.52510			0.310368
$130$		0			0
$131$	4.81740			0.420899			0.210449	−	0.977605i	$-0.432507\pi$
$131$	4.81740			0.420899			0.210449	+	0.977605i	$0.432507\pi$
$132$		0			0
$133$	7.18022			0.622604
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−0.833998			−0.0712533			−0.0356266	−	0.999365i	$-0.511343\pi$
$137$	−0.833998			−0.0712533			−0.0356266	+	0.999365i	$0.511343\pi$
$138$		0			0
$139$	−10.8727			−0.922206			−0.461103	−	0.887347i	$-0.652546\pi$
$139$	−10.8727			−0.922206			−0.461103	+	0.887347i	$0.652546\pi$
$140$		0			0
$141$	5.16548	−	8.94687i	0.435012	−	0.753462i
$142$		0			0
$143$	−1.17888			−0.0985831
$144$		0			0
$145$	−4.58485	+	7.94120i	−0.380751	+	0.659481i
$146$		0			0
$147$	2.89456	+	5.01352i	0.238739	+	0.413508i
$148$		0			0
$149$	−3.32992			−0.272798			−0.136399	−	0.990654i	$-0.543553\pi$
$149$	−3.32992			−0.272798			−0.136399	+	0.990654i	$0.543553\pi$
$150$		0			0
$151$	−0.834754	−	1.44584i	−0.0679313	−	0.117661i	0.830059	−	0.557675i	$-0.188307\pi$
$151$	−0.834754	−	1.44584i	−0.0679313	−	0.117661i	−0.897991	+	0.440015i	$0.854973\pi$
$152$		0			0
$153$	−1.83022	−	3.17003i	−0.147965	−	0.256282i
$154$		0			0
$155$	−1.12291	+	1.94493i	−0.0901941	+	0.156221i
$156$		0			0
$157$	9.29941	+	16.1071i	0.742174	+	1.28548i	0.951504	+	0.307638i	$0.0995385\pi$
$157$	9.29941	+	16.1071i	0.742174	+	1.28548i	−0.209330	+	0.977845i	$0.567128\pi$
$158$		0			0
$159$	1.24582			0.0987996
$160$		0			0
$161$	−9.05006			−0.713245
$162$		0			0
$163$	4.29454	−	7.43836i	0.336374	−	0.582617i	−0.647374	−	0.762173i	$-0.724133\pi$
$163$	4.29454	−	7.43836i	0.336374	−	0.582617i	0.983748	+	0.179555i	$0.0574659\pi$
$164$		0			0
$165$	0.589441	−	1.02094i	0.0458879	−	0.0794802i
$166$		0			0
$167$	−5.73292	+	9.92970i	−0.443626	+	0.768384i	−0.997955	−	0.0639141i	$-0.979642\pi$
$167$	−5.73292	+	9.92970i	−0.443626	+	0.768384i	0.554329	+	0.832298i	$0.312975\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−3.26255	−	5.65090i	−0.249493	−	0.432135i
$172$		0			0
$173$	−5.77239	−	9.99807i	−0.438867	−	0.760139i	0.558736	−	0.829346i	$-0.311287\pi$
$173$	−5.77239	−	9.99807i	−0.438867	−	0.760139i	−0.997602	+	0.0692065i	$0.977953\pi$
$174$		0			0
$175$	−0.550200	+	0.952975i	−0.0415912	+	0.0720381i
$176$		0			0
$177$	8.73327			0.656433
$178$		0			0
$179$	23.1723			1.73198			0.865990	−	0.500061i	$-0.166689\pi$
$179$	23.1723			1.73198			0.865990	+	0.500061i	$0.166689\pi$
$180$		0			0
$181$	11.6327	−	20.1484i	0.864650	−	1.49762i	−0.00274431	−	0.999996i	$-0.500874\pi$
$181$	11.6327	−	20.1484i	0.864650	−	1.49762i	0.867394	−	0.497621i	$-0.165793\pi$
$182$		0			0
$183$	7.40027	+	12.8176i	0.547043	+	0.947507i
$184$		0			0
$185$	5.58203	+	9.66835i	0.410399	+	0.710832i
$186$		0			0
$187$	4.31523			0.315561
$188$		0			0
$189$	−0.550200	+	0.952975i	−0.0400212	+	0.0693187i
$190$		0			0
$191$	−1.97540	−	3.42150i	−0.142935	−	0.247571i	0.785665	−	0.618652i	$-0.212321\pi$
$191$	−1.97540	−	3.42150i	−0.142935	−	0.247571i	−0.928601	+	0.371080i	$0.878987\pi$
$192$		0			0
$193$	−16.6912			−1.20146			−0.600729	−	0.799452i	$-0.705123\pi$
$193$	−16.6912			−1.20146			−0.600729	+	0.799452i	$0.705123\pi$
$194$		0			0
$195$	−0.500000	−	0.866025i	−0.0358057	−	0.0620174i
$196$		0			0
$197$	8.67221	−	15.0207i	0.617869	−	1.07018i	−0.372005	−	0.928231i	$-0.621330\pi$
$197$	8.67221	−	15.0207i	0.617869	−	1.07018i	0.989874	−	0.141950i	$-0.0453372\pi$
$198$		0			0
$199$	−12.8250	−	22.2136i	−0.909141	−	1.57468i	−0.815260	−	0.579096i	$-0.803406\pi$
$199$	−12.8250	−	22.2136i	−0.909141	−	1.57468i	−0.0938817	−	0.995583i	$-0.529928\pi$
$200$		0			0
$201$	8.12438	+	0.997229i	0.573050	+	0.0703391i
$202$		0			0
$203$	5.04518	+	8.73850i	0.354102	+	0.613322i
$204$		0			0
$205$	4.73507	−	8.20139i	0.330712	−	0.572810i
$206$		0			0
$207$	4.11217	+	7.12248i	0.285815	+	0.495047i
$208$		0			0
$209$	7.69232			0.532089
$210$		0			0
$211$	−5.91507	−	10.2452i	−0.407210	−	0.705309i	0.587366	−	0.809322i	$-0.300165\pi$
$211$	−5.91507	−	10.2452i	−0.407210	−	0.705309i	−0.994576	+	0.104013i	$0.966832\pi$
$212$		0			0
$213$	3.07575	−	5.32736i	0.210747	−	0.365024i
$214$		0			0
$215$	−3.52510			−0.240410
$216$		0			0
$217$	1.23565	+	2.14021i	0.0838813	+	0.145287i
$218$		0			0
$219$	−4.45329	−	7.71333i	−0.300926	−	0.521218i
$220$		0			0
$221$	1.83022	−	3.17003i	0.123114	−	0.213240i
$222$		0			0
$223$	14.1821			0.949705			0.474853	−	0.880065i	$-0.342501\pi$
$223$	14.1821			0.949705			0.474853	+	0.880065i	$0.342501\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	11.0669	−	19.1684i	0.734533	−	1.27225i	−0.220395	−	0.975411i	$-0.570734\pi$
$227$	11.0669	−	19.1684i	0.734533	−	1.27225i	0.954928	−	0.296838i	$-0.0959322\pi$
$228$		0			0
$229$	8.26322	+	14.3123i	0.546049	+	0.945784i	0.998540	+	0.0540155i	$0.0172020\pi$
$229$	8.26322	+	14.3123i	0.546049	+	0.945784i	−0.452491	+	0.891769i	$0.649465\pi$
$230$		0			0
$231$	−0.648621	−	1.12345i	−0.0426762	−	0.0739173i
$232$		0			0
$233$	2.96682	−	5.13868i	0.194363	−	0.336646i	−0.752329	−	0.658788i	$-0.771069\pi$
$233$	2.96682	−	5.13868i	0.194363	−	0.336646i	0.946691	+	0.322142i	$0.104403\pi$
$234$		0			0
$235$	−5.16548	+	8.94687i	−0.336959	+	0.583629i
$236$		0			0
$237$	−1.22597	+	2.12344i	−0.0796353	+	0.137932i
$238$		0			0
$239$	12.6186	−	21.8561i	0.816230	−	1.41375i	−0.0922117	−	0.995739i	$-0.529394\pi$
$239$	12.6186	−	21.8561i	0.816230	−	1.41375i	0.908442	−	0.418012i	$-0.137273\pi$
$240$		0			0
$241$	−16.6342			−1.07150			−0.535752	−	0.844376i	$-0.679972\pi$
$241$	−16.6342			−1.07150			−0.535752	+	0.844376i	$0.679972\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−2.89456	−	5.01352i	−0.184927	−	0.320302i
$246$		0			0
$247$	3.26255	−	5.65090i	0.207591	−	0.359558i
$248$		0			0
$249$	−5.48704	−	9.50384i	−0.347727	−	0.602281i
$250$		0			0
$251$	11.1153	+	19.2523i	0.701593	+	1.21520i	0.967907	+	0.251309i	$0.0808610\pi$
$251$	11.1153	+	19.2523i	0.701593	+	1.21520i	−0.266313	+	0.963886i	$0.585806\pi$
$252$		0			0
$253$	−9.69552			−0.609552
$254$		0			0
$255$	1.83022	+	3.17003i	0.114613	+	0.198515i
$256$		0			0
$257$	−4.81593	+	8.34143i	−0.300409	+	0.520324i	−0.976229	−	0.216743i	$-0.930457\pi$
$257$	−4.81593	+	8.34143i	−0.300409	+	0.520324i	0.675819	+	0.737067i	$0.263790\pi$
$258$		0			0
$259$	12.2849			0.763349
$260$		0			0
$261$	4.58485	−	7.94120i	0.283795	−	0.491548i
$262$		0			0
$263$	−11.9838			−0.738955			−0.369477	−	0.929240i	$-0.620463\pi$
$263$	−11.9838			−0.738955			−0.369477	+	0.929240i	$0.620463\pi$
$264$		0			0
$265$	−1.24582			−0.0765298
$266$		0			0
$267$	7.19709			0.440455
$268$		0			0
$269$	−27.5058			−1.67706			−0.838531	−	0.544854i	$-0.816585\pi$
$269$	−27.5058			−1.67706			−0.838531	+	0.544854i	$0.816585\pi$
$270$		0			0
$271$	−6.99762			−0.425075			−0.212538	−	0.977153i	$-0.568173\pi$
$271$	−6.99762			−0.425075			−0.212538	+	0.977153i	$0.568173\pi$
$272$		0			0
$273$	−1.10040			−0.0665993
$274$		0			0
$275$	−0.589441	+	1.02094i	−0.0355446	+	0.0615651i
$276$		0			0
$277$	−3.51028			−0.210912			−0.105456	−	0.994424i	$-0.533630\pi$
$277$	−3.51028			−0.210912			−0.105456	+	0.994424i	$0.533630\pi$
$278$		0			0
$279$	1.12291	−	1.94493i	0.0672267	−	0.116440i
$280$		0			0
$281$	1.60328	+	2.77696i	0.0956437	+	0.165660i	0.909877	−	0.414878i	$-0.136176\pi$
$281$	1.60328	+	2.77696i	0.0956437	+	0.165660i	−0.814233	+	0.580538i	$0.802842\pi$
$282$		0			0
$283$	0.280187			0.0166554			0.00832771	−	0.999965i	$-0.497349\pi$
$283$	0.280187			0.0166554			0.00832771	+	0.999965i	$0.497349\pi$
$284$		0			0
$285$	3.26255	+	5.65090i	0.193257	+	0.334730i
$286$		0			0
$287$	−5.21048	−	9.02481i	−0.307565	−	0.532718i
$288$		0			0
$289$	1.80059	−	3.11871i	0.105917	−	0.183454i
$290$		0			0
$291$	3.18799	+	5.52175i	0.186883	+	0.323691i
$292$		0			0
$293$	7.10378			0.415007			0.207504	−	0.978234i	$-0.433466\pi$
$293$	7.10378			0.415007			0.207504	+	0.978234i	$0.433466\pi$
$294$		0			0
$295$	−8.73327			−0.508471
$296$		0			0
$297$	−0.589441	+	1.02094i	−0.0342028	+	0.0592411i
$298$		0			0
$299$	−4.11217	+	7.12248i	−0.237813	+	0.411904i
$300$		0			0
$301$	−1.93951	+	3.35933i	−0.111791	+	0.193629i
$302$		0			0
$303$	7.77764	−	13.4713i	0.446814	−	0.773904i
$304$		0			0
$305$	−7.40027	−	12.8176i	−0.423738	−	0.733936i
$306$		0			0
$307$	−5.76165	−	9.97946i	−0.328835	−	0.569558i	0.653446	−	0.756973i	$-0.273323\pi$
$307$	−5.76165	−	9.97946i	−0.328835	−	0.569558i	−0.982281	+	0.187415i	$0.939989\pi$
$308$		0			0
$309$	−2.21517	+	3.83680i	−0.126017	+	0.218268i
$310$		0			0
$311$	9.66677			0.548152			0.274076	−	0.961708i	$-0.411628\pi$
$311$	9.66677			0.548152			0.274076	+	0.961708i	$0.411628\pi$
$312$		0			0
$313$	−19.8904			−1.12427			−0.562136	−	0.827045i	$-0.690020\pi$
$313$	−19.8904			−1.12427			−0.562136	+	0.827045i	$0.690020\pi$
$314$		0			0
$315$	0.550200	−	0.952975i	0.0310003	−	0.0536940i
$316$		0			0
$317$	−2.59315	−	4.49147i	−0.145646	−	0.252266i	0.783968	−	0.620801i	$-0.213193\pi$
$317$	−2.59315	−	4.49147i	−0.145646	−	0.252266i	−0.929614	+	0.368535i	$0.879859\pi$
$318$		0			0
$319$	5.40500	+	9.36174i	0.302622	+	0.524157i
$320$		0			0
$321$	14.6613			0.818316
$322$		0			0
$323$	−11.9424	+	20.6848i	−0.664491	+	1.15093i
$324$		0			0
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$		0			0
$327$	−0.127209			−0.00703469
$328$		0			0
$329$	5.68409	+	9.84514i	0.313374	+	0.542780i
$330$		0			0
$331$	−3.39598	+	5.88201i	−0.186660	+	0.323305i	−0.944135	−	0.329560i	$-0.893100\pi$
$331$	−3.39598	+	5.88201i	−0.186660	+	0.323305i	0.757475	+	0.652865i	$0.226433\pi$
$332$		0			0
$333$	−5.58203	−	9.66835i	−0.305893	−	0.529823i
$334$		0			0
$335$	−8.12438	−	0.997229i	−0.443882	−	0.0544845i
$336$		0			0
$337$	6.38886	+	11.0658i	0.348023	+	0.602794i	0.985898	−	0.167346i	$-0.0535197\pi$
$337$	6.38886	+	11.0658i	0.348023	+	0.602794i	−0.637875	+	0.770140i	$0.720186\pi$
$338$		0			0
$339$	2.12291	−	3.67698i	0.115301	−	0.199706i
$340$		0			0
$341$	1.32378	+	2.29285i	0.0716865	+	0.124165i
$342$		0			0
$343$	−14.0732			−0.759879
$344$		0			0
$345$	−4.11217	−	7.12248i	−0.221392	−	0.383461i
$346$		0			0
$347$	−6.55027	+	11.3454i	−0.351637	+	0.609053i	−0.986536	−	0.163542i	$-0.947708\pi$
$347$	−6.55027	+	11.3454i	−0.351637	+	0.609053i	0.634900	+	0.772595i	$0.281041\pi$
$348$		0			0
$349$	−11.1701			−0.597921			−0.298961	−	0.954265i	$-0.596640\pi$
$349$	−11.1701			−0.597921			−0.298961	+	0.954265i	$0.596640\pi$
$350$		0			0
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$		0			0
$353$	12.0197	+	20.8187i	0.639744	+	1.10807i	0.985489	+	0.169741i	$0.0542930\pi$
$353$	12.0197	+	20.8187i	0.639744	+	1.10807i	−0.345745	+	0.938329i	$0.612374\pi$
$354$		0			0
$355$	−3.07575	+	5.32736i	−0.163244	+	0.282747i
$356$		0			0
$357$	4.02795			0.213182
$358$		0			0
$359$	2.57364			0.135831			0.0679157	−	0.997691i	$-0.478365\pi$
$359$	2.57364			0.135831			0.0679157	+	0.997691i	$0.478365\pi$
$360$		0			0
$361$	−11.7885	+	20.4182i	−0.620445	+	1.07464i
$362$		0			0
$363$	4.80512	+	8.32271i	0.252203	+	0.436829i
$364$		0			0
$365$	4.45329	+	7.71333i	0.233096	+	0.403734i
$366$		0			0
$367$	−4.74432	+	8.21741i	−0.247652	+	0.428945i	−0.962874	−	0.269952i	$-0.912992\pi$
$367$	−4.74432	+	8.21741i	−0.247652	+	0.428945i	0.715222	+	0.698897i	$0.246326\pi$
$368$		0			0
$369$	−4.73507	+	8.20139i	−0.246498	+	0.426947i
$370$		0			0
$371$	−0.685448	+	1.18723i	−0.0355867	+	0.0616379i
$372$		0			0
$373$	−16.2664	+	28.1742i	−0.842241	+	1.45880i	0.0457545	+	0.998953i	$0.485431\pi$
$373$	−16.2664	+	28.1742i	−0.842241	+	1.45880i	−0.887996	+	0.459852i	$0.847903\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	9.16971			0.472264
$378$		0			0
$379$	19.4141	+	33.6262i	0.997235	+	1.72726i	0.562970	+	0.826477i	$0.309659\pi$
$379$	19.4141	+	33.6262i	0.997235	+	1.72726i	0.434265	+	0.900785i	$0.357008\pi$
$380$		0			0
$381$	−5.22138	+	9.04370i	−0.267500	+	0.463323i
$382$		0			0
$383$	−19.3203	−	33.4638i	−0.987223	−	1.70992i	−0.631608	−	0.775288i	$-0.717605\pi$
$383$	−19.3203	−	33.4638i	−0.987223	−	1.70992i	−0.355615	−	0.934633i	$-0.615728\pi$
$384$		0			0
$385$	0.648621	+	1.12345i	0.0330568	+	0.0572561i
$386$		0			0
$387$	3.52510			0.179191
$388$		0			0
$389$	15.5748	+	26.9763i	0.789673	+	1.36775i	0.926168	+	0.377112i	$0.123083\pi$
$389$	15.5748	+	26.9763i	0.789673	+	1.36775i	−0.136495	+	0.990641i	$0.543584\pi$
$390$		0			0
$391$	15.0523	−	26.0714i	0.761229	−	1.31849i
$392$		0			0
$393$	4.81740			0.243006
$394$		0			0
$395$	1.22597	−	2.12344i	0.0616853	−	0.106842i
$396$		0			0
$397$	7.53785			0.378314			0.189157	−	0.981947i	$-0.439425\pi$
$397$	7.53785			0.378314			0.189157	+	0.981947i	$0.439425\pi$
$398$		0			0
$399$	7.18022			0.359461
$400$		0			0
$401$	21.2999			1.06366			0.531832	−	0.846850i	$-0.321504\pi$
$401$	21.2999			1.06366			0.531832	+	0.846850i	$0.321504\pi$
$402$		0			0
$403$	2.24582			0.111872
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	13.1611			0.652372
$408$		0			0
$409$	−4.93011	+	8.53921i	−0.243778	+	0.422237i	−0.961787	−	0.273797i	$-0.911720\pi$
$409$	−4.93011	+	8.53921i	−0.243778	+	0.422237i	0.718009	+	0.696034i	$0.245054\pi$
$410$		0			0
$411$	−0.833998			−0.0411381
$412$		0			0
$413$	−4.80505	+	8.32259i	−0.236441	+	0.409528i
$414$		0			0
$415$	5.48704	+	9.50384i	0.269348	+	0.466525i
$416$		0			0
$417$	−10.8727			−0.532436
$418$		0			0
$419$	0.661016	+	1.14491i	0.0322927	+	0.0559327i	0.881720	−	0.471773i	$-0.156386\pi$
$419$	0.661016	+	1.14491i	0.0322927	+	0.0559327i	−0.849427	+	0.527706i	$0.823052\pi$
$420$		0			0
$421$	−8.94550	−	15.4941i	−0.435977	−	0.755134i	0.561398	−	0.827546i	$-0.310264\pi$
$421$	−8.94550	−	15.4941i	−0.435977	−	0.755134i	−0.997375	+	0.0724119i	$0.976930\pi$
$422$		0			0
$423$	5.16548	−	8.94687i	0.251154	−	0.435012i
$424$		0			0
$425$	−1.83022	−	3.17003i	−0.0887787	−	0.153769i
$426$		0			0
$427$	−16.2865			−0.788160
$428$		0			0
$429$	−1.17888			−0.0569170
$430$		0			0
$431$	1.59453	−	2.76181i	0.0768059	−	0.133032i	−0.825064	−	0.565039i	$-0.808861\pi$
$431$	1.59453	−	2.76181i	0.0768059	−	0.133032i	0.901870	+	0.432007i	$0.142194\pi$
$432$		0			0
$433$	−4.21629	+	7.30283i	−0.202622	+	0.350952i	−0.949372	−	0.314153i	$-0.898280\pi$
$433$	−4.21629	+	7.30283i	−0.202622	+	0.350952i	0.746750	+	0.665104i	$0.231613\pi$
$434$		0			0
$435$	−4.58485	+	7.94120i	−0.219827	+	0.380751i
$436$		0			0
$437$	26.8323	−	46.4749i	1.28356	−	2.22320i
$438$		0			0
$439$	−15.7918	−	27.3521i	−0.753700	−	1.30545i	−0.946018	−	0.324114i	$-0.894934\pi$
$439$	−15.7918	−	27.3521i	−0.753700	−	1.30545i	0.192318	−	0.981333i	$-0.438399\pi$
$440$		0			0
$441$	2.89456	+	5.01352i	0.137836	+	0.238739i
$442$		0			0
$443$	−15.7479	+	27.2761i	−0.748203	+	1.29593i	0.200480	+	0.979698i	$0.435750\pi$
$443$	−15.7479	+	27.2761i	−0.748203	+	1.29593i	−0.948683	+	0.316228i	$0.897583\pi$
$444$		0			0
$445$	−7.19709			−0.341175
$446$		0			0
$447$	−3.32992			−0.157500
$448$		0			0
$449$	17.1863	−	29.7675i	0.811070	−	1.40482i	−0.101045	−	0.994882i	$-0.532219\pi$
$449$	17.1863	−	29.7675i	0.811070	−	1.40482i	0.912116	−	0.409933i	$-0.134448\pi$
$450$		0			0
$451$	−5.58209	−	9.66847i	−0.262851	−	0.455271i
$452$		0			0
$453$	−0.834754	−	1.44584i	−0.0392202	−	0.0679313i
$454$		0			0
$455$	1.10040			0.0515876
$456$		0			0
$457$	16.3788	−	28.3689i	0.766167	−	1.32704i	−0.173461	−	0.984841i	$-0.555495\pi$
$457$	16.3788	−	28.3689i	0.766167	−	1.32704i	0.939627	−	0.342199i	$-0.111172\pi$
$458$		0			0
$459$	−1.83022	−	3.17003i	−0.0854274	−	0.147965i
$460$		0			0
$461$	−1.30790			−0.0609148			−0.0304574	−	0.999536i	$-0.509696\pi$
$461$	−1.30790			−0.0609148			−0.0304574	+	0.999536i	$0.509696\pi$
$462$		0			0
$463$	−4.87930	−	8.45120i	−0.226760	−	0.392761i	0.730086	−	0.683356i	$-0.239480\pi$
$463$	−4.87930	−	8.45120i	−0.226760	−	0.392761i	−0.956846	+	0.290595i	$0.906147\pi$
$464$		0			0
$465$	−1.12291	+	1.94493i	−0.0520736	+	0.0901941i
$466$		0			0
$467$	−15.2035	−	26.3332i	−0.703532	−	1.21855i	−0.967219	−	0.253945i	$-0.918272\pi$
$467$	−15.2035	−	26.3332i	−0.703532	−	1.21855i	0.263687	−	0.964608i	$-0.415062\pi$
$468$		0			0
$469$	−5.42037	+	7.19365i	−0.250289	+	0.332172i
$470$		0			0
$471$	9.29941	+	16.1071i	0.428494	+	0.742174i
$472$		0			0
$473$	−2.07784	+	3.59892i	−0.0955391	+	0.165479i
$474$		0			0
$475$	−3.26255	−	5.65090i	−0.149696	−	0.259281i
$476$		0			0
$477$	1.24582			0.0570420
$478$		0			0
$479$	1.11692	+	1.93456i	0.0510332	+	0.0883922i	0.890414	−	0.455152i	$-0.150415\pi$
$479$	1.11692	+	1.93456i	0.0510332	+	0.0883922i	−0.839380	+	0.543545i	$0.817082\pi$
$480$		0			0
$481$	5.58203	−	9.66835i	0.254519	−	0.440839i
$482$		0			0
$483$	−9.05006			−0.411792
$484$		0			0
$485$	−3.18799	−	5.52175i	−0.144759	−	0.250730i
$486$		0			0
$487$	−15.2557	−	26.4237i	−0.691304	−	1.19737i	−0.971411	−	0.237405i	$-0.923703\pi$
$487$	−15.2557	−	26.4237i	−0.691304	−	1.19737i	0.280107	−	0.959969i	$-0.409630\pi$
$488$		0			0
$489$	4.29454	−	7.43836i	0.194206	−	0.336374i
$490$		0			0
$491$	10.5642			0.476756			0.238378	−	0.971172i	$-0.423384\pi$
$491$	10.5642			0.476756			0.238378	+	0.971172i	$0.423384\pi$
$492$		0			0
$493$	−33.5652			−1.51170
$494$		0			0
$495$	0.589441	−	1.02094i	0.0264934	−	0.0458879i
$496$		0			0
$497$	3.38456	+	5.86223i	0.151818	+	0.262957i
$498$		0			0
$499$	−12.1578	−	21.0579i	−0.544257	−	0.942680i	−0.998653	−	0.0518808i	$-0.983478\pi$
$499$	−12.1578	−	21.0579i	−0.544257	−	0.942680i	0.454397	−	0.890800i	$-0.349855\pi$
$500$		0			0
$501$	−5.73292	+	9.92970i	−0.256128	+	0.443626i
$502$		0			0
$503$	0.535297	−	0.927162i	0.0238677	−	0.0413401i	−0.853845	−	0.520528i	$-0.825735\pi$
$503$	0.535297	−	0.927162i	0.0238677	−	0.0413401i	0.877713	+	0.479188i	$0.159069\pi$
$504$		0			0
$505$	−7.77764	+	13.4713i	−0.346101	+	0.599464i
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$		0			0
$509$	−7.89902			−0.350118			−0.175059	−	0.984558i	$-0.556012\pi$
$509$	−7.89902			−0.350118			−0.175059	+	0.984558i	$0.556012\pi$
$510$		0			0
$511$	9.80081			0.433562
$512$		0			0
$513$	−3.26255	−	5.65090i	−0.144045	−	0.249493i
$514$		0			0
$515$	2.21517	−	3.83680i	0.0976123	−	0.169069i
$516$		0			0
$517$	6.08949	+	10.5473i	0.267815	+	0.463870i
$518$		0			0
$519$	−5.77239	−	9.99807i	−0.253380	−	0.438867i
$520$		0			0
$521$	31.4657			1.37854			0.689268	−	0.724506i	$-0.257932\pi$
$521$	31.4657			1.37854			0.689268	+	0.724506i	$0.257932\pi$
$522$		0			0
$523$	10.6369	+	18.4237i	0.465119	+	0.805610i	0.999207	−	0.0398188i	$-0.0126781\pi$
$523$	10.6369	+	18.4237i	0.465119	+	0.805610i	−0.534088	+	0.845429i	$0.679345\pi$
$524$		0			0
$525$	−0.550200	+	0.952975i	−0.0240127	+	0.0415912i
$526$		0			0
$527$	−8.22067			−0.358098
$528$		0			0
$529$	−22.3198	+	38.6590i	−0.970427	+	1.68083i
$530$		0			0
$531$	8.73327			0.378992
$532$		0			0
$533$	−9.47015			−0.410198
$534$		0			0
$535$	−14.6613			−0.633865
$536$		0			0
$537$	23.1723			0.999960
$538$		0			0
$539$	−6.82469			−0.293960
$540$		0			0
$541$	0.429557			0.0184681			0.00923405	−	0.999957i	$-0.497061\pi$
$541$	0.429557			0.0184681			0.00923405	+	0.999957i	$0.497061\pi$
$542$		0			0
$543$	11.6327	−	20.1484i	0.499206	−	0.864650i
$544$		0			0
$545$	0.127209			0.00544905
$546$		0			0
$547$	−9.68237	+	16.7704i	−0.413988	+	0.717049i	−0.995322	−	0.0966166i	$-0.969198\pi$
$547$	−9.68237	+	16.7704i	−0.413988	+	0.717049i	0.581333	+	0.813666i	$0.302531\pi$
$548$		0			0
$549$	7.40027	+	12.8176i	0.315836	+	0.547043i
$550$		0			0
$551$	−59.8332			−2.54898
$552$		0			0
$553$	−1.34906	−	2.33664i	−0.0573678	−	0.0993640i
$554$		0			0
$555$	5.58203	+	9.66835i	0.236944	+	0.410399i
$556$		0			0
$557$	1.71292	−	2.96686i	0.0725787	−	0.125710i	−0.827452	−	0.561536i	$-0.810210\pi$
$557$	1.71292	−	2.96686i	0.0725787	−	0.125710i	0.900031	+	0.435826i	$0.143544\pi$
$558$		0			0
$559$	1.76255	+	3.05282i	0.0745479	+	0.129121i
$560$		0			0
$561$	4.31523			0.182189
$562$		0			0
$563$	−38.9250			−1.64049			−0.820247	−	0.572009i	$-0.806164\pi$
$563$	−38.9250			−1.64049			−0.820247	+	0.572009i	$0.806164\pi$
$564$		0			0
$565$	−2.12291	+	3.67698i	−0.0893114	+	0.154692i
$566$		0			0
$567$	−0.550200	+	0.952975i	−0.0231062	+	0.0400212i
$568$		0			0
$569$	16.3476	−	28.3149i	0.685328	−	1.18702i	−0.288006	−	0.957629i	$-0.592992\pi$
$569$	16.3476	−	28.3149i	0.685328	−	1.18702i	0.973334	−	0.229394i	$-0.0736744\pi$
$570$		0			0
$571$	−4.36307	+	7.55706i	−0.182589	+	0.316253i	−0.942761	−	0.333468i	$-0.891781\pi$
$571$	−4.36307	+	7.55706i	−0.182589	+	0.316253i	0.760173	+	0.649721i	$0.225114\pi$
$572$		0			0
$573$	−1.97540	−	3.42150i	−0.0825237	−	0.142935i
$574$		0			0
$575$	4.11217	+	7.12248i	0.171489	+	0.297028i
$576$		0			0
$577$	2.51029	−	4.34795i	0.104505	−	0.181008i	−0.809031	−	0.587766i	$-0.800008\pi$
$577$	2.51029	−	4.34795i	0.104505	−	0.181008i	0.913536	+	0.406758i	$0.133341\pi$
$578$		0			0
$579$	−16.6912			−0.693663
$580$		0			0
$581$	12.0759			0.500992
$582$		0			0
$583$	−0.734335	+	1.27191i	−0.0304130	+	0.0526769i
$584$		0			0
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$		0			0
$587$	−1.17510	−	2.03533i	−0.0485016	−	0.0840072i	0.840755	−	0.541415i	$-0.182111\pi$
$587$	−1.17510	−	2.03533i	−0.0485016	−	0.0840072i	−0.889257	+	0.457408i	$0.848778\pi$
$588$		0			0
$589$	−14.6542			−0.603814
$590$		0			0
$591$	8.67221	−	15.0207i	0.356727	−	0.617869i
$592$		0			0
$593$	19.1748	+	33.2117i	0.787414	+	1.36384i	0.927546	+	0.373709i	$0.121914\pi$
$593$	19.1748	+	33.2117i	0.787414	+	1.36384i	−0.140132	+	0.990133i	$0.544753\pi$
$594$		0			0
$595$	−4.02795			−0.165130
$596$		0			0
$597$	−12.8250	−	22.2136i	−0.524893	−	0.909141i
$598$		0			0
$599$	15.1881	−	26.3066i	0.620570	−	1.07486i	−0.368810	−	0.929505i	$-0.620235\pi$
$599$	15.1881	−	26.3066i	0.620570	−	1.07486i	0.989380	−	0.145354i	$-0.0464321\pi$
$600$		0			0
$601$	18.8525	+	32.6535i	0.769009	+	1.33196i	0.938101	+	0.346362i	$0.112583\pi$
$601$	18.8525	+	32.6535i	0.769009	+	1.33196i	−0.169092	+	0.985600i	$0.554083\pi$
$602$		0			0
$603$	8.12438	+	0.997229i	0.330850	+	0.0406103i
$604$		0			0
$605$	−4.80512	−	8.32271i	−0.195356	−	0.338366i
$606$		0			0
$607$	1.71292	−	2.96687i	0.0695254	−	0.120422i	−0.829167	−	0.559001i	$-0.811185\pi$
$607$	1.71292	−	2.96687i	0.0695254	−	0.120422i	0.898692	+	0.438579i	$0.144518\pi$
$608$		0			0
$609$	5.04518	+	8.73850i	0.204441	+	0.354102i
$610$		0			0
$611$	10.3310			0.417946
$612$		0			0
$613$	22.3393	+	38.6929i	0.902277	+	1.56279i	0.824531	+	0.565817i	$0.191439\pi$
$613$	22.3393	+	38.6929i	0.902277	+	1.56279i	0.0777468	+	0.996973i	$0.475227\pi$
$614$		0			0
$615$	4.73507	−	8.20139i	0.190937	−	0.330712i
$616$		0			0
$617$	−0.269780			−0.0108609			−0.00543047	−	0.999985i	$-0.501729\pi$
$617$	−0.269780			−0.0108609			−0.00543047	+	0.999985i	$0.501729\pi$
$618$		0			0
$619$	2.26633	+	3.92540i	0.0910915	+	0.157775i	0.907971	−	0.419034i	$-0.137631\pi$
$619$	2.26633	+	3.92540i	0.0910915	+	0.157775i	−0.816879	+	0.576809i	$0.804298\pi$
$620$		0			0
$621$	4.11217	+	7.12248i	0.165016	+	0.285815i
$622$		0			0
$623$	−3.95984	+	6.85864i	−0.158648	+	0.274786i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	7.69232			0.307202
$628$		0			0
$629$	−20.4327	+	35.3904i	−0.814704	+	1.41111i
$630$		0			0
$631$	2.96580	+	5.13691i	0.118067	+	0.204497i	0.919001	−	0.394254i	$-0.128997\pi$
$631$	2.96580	+	5.13691i	0.118067	+	0.204497i	−0.800935	+	0.598751i	$0.795664\pi$
$632$		0			0
$633$	−5.91507	−	10.2452i	−0.235103	−	0.407210i
$634$		0			0
$635$	5.22138	−	9.04370i	0.207204	−	0.358888i
$636$		0			0
$637$	−2.89456	+	5.01352i	−0.114687	+	0.198643i
$638$		0			0
$639$	3.07575	−	5.32736i	0.121675	−	0.210747i
$640$		0			0
$641$	−1.10945	+	1.92162i	−0.0438206	+	0.0758995i	−0.887104	−	0.461570i	$-0.847286\pi$
$641$	−1.10945	+	1.92162i	−0.0438206	+	0.0758995i	0.843283	+	0.537469i	$0.180620\pi$
$642$		0			0
$643$	35.6290			1.40507			0.702535	−	0.711649i	$-0.252051\pi$
$643$	35.6290			1.40507			0.702535	+	0.711649i	$0.252051\pi$
$644$		0			0
$645$	−3.52510			−0.138801
$646$		0			0
$647$	21.2079	+	36.7331i	0.833767	+	1.44413i	0.895030	+	0.446005i	$0.147154\pi$
$647$	21.2079	+	36.7331i	0.833767	+	1.44413i	−0.0612630	+	0.998122i	$0.519513\pi$
$648$		0			0
$649$	−5.14775	+	8.91616i	−0.202067	+	0.349990i
$650$		0			0
$651$	1.23565	+	2.14021i	0.0484289	+	0.0838813i
$652$		0			0
$653$	5.50356	+	9.53244i	0.215371	+	0.373033i	0.953387	−	0.301749i	$-0.0975706\pi$
$653$	5.50356	+	9.53244i	0.215371	+	0.373033i	−0.738016	+	0.674783i	$0.764237\pi$
$654$		0			0
$655$	−4.81740			−0.188232
$656$		0			0
$657$	−4.45329	−	7.71333i	−0.173739	−	0.300926i
$658$		0			0
$659$	−1.49622	+	2.59154i	−0.0582846	+	0.100952i	−0.893695	−	0.448674i	$-0.851896\pi$
$659$	−1.49622	+	2.59154i	−0.0582846	+	0.100952i	0.835411	+	0.549626i	$0.185230\pi$
$660$		0			0
$661$	−34.9573			−1.35968			−0.679842	−	0.733359i	$-0.737951\pi$
$661$	−34.9573			−1.35968			−0.679842	+	0.733359i	$0.737951\pi$
$662$		0			0
$663$	1.83022	−	3.17003i	0.0710799	−	0.123114i
$664$		0			0
$665$	−7.18022			−0.278437
$666$		0			0
$667$	75.4147			2.92007
$668$		0			0
$669$	14.1821			0.548313
$670$		0			0
$671$	−17.4481			−0.673576
$672$		0			0
$673$	−18.1603			−0.700029			−0.350014	−	0.936744i	$-0.613823\pi$
$673$	−18.1603			−0.700029			−0.350014	+	0.936744i	$0.613823\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−23.2194	+	40.2172i	−0.892393	+	1.54567i	−0.0553957	+	0.998464i	$0.517642\pi$
$677$	−23.2194	+	40.2172i	−0.892393	+	1.54567i	−0.836998	+	0.547206i	$0.815691\pi$
$678$		0			0
$679$	−7.01612			−0.269254
$680$		0			0
$681$	11.0669	−	19.1684i	0.424083	−	0.734533i
$682$		0			0
$683$	−13.4869	−	23.3600i	−0.516062	−	0.893845i	−0.999826	−	0.0186468i	$-0.994064\pi$
$683$	−13.4869	−	23.3600i	−0.516062	−	0.893845i	0.483764	−	0.875198i	$-0.339269\pi$
$684$		0			0
$685$	0.833998			0.0318654
$686$		0			0
$687$	8.26322	+	14.3123i	0.315261	+	0.546049i
$688$		0			0
$689$	0.622908	+	1.07891i	0.0237309	+	0.0411031i
$690$		0			0
$691$	−13.2380	+	22.9288i	−0.503596	+	0.872254i	0.496395	+	0.868097i	$0.334657\pi$
$691$	−13.2380	+	22.9288i	−0.503596	+	0.872254i	−0.999991	+	0.00415771i	$0.998677\pi$
$692$		0			0
$693$	−0.648621	−	1.12345i	−0.0246391	−	0.0426762i
$694$		0			0
$695$	10.8727			0.412423
$696$		0			0
$697$	34.6649			1.31303
$698$		0			0
$699$	2.96682	−	5.13868i	0.112215	−	0.194363i
$700$		0			0
$701$	18.9887	−	32.8894i	0.717193	−	1.24221i	−0.244915	−	0.969544i	$-0.578760\pi$
$701$	18.9887	−	32.8894i	0.717193	−	1.24221i	0.962108	−	0.272669i	$-0.0879065\pi$
$702$		0			0
$703$	−36.4233	+	63.0870i	−1.37373	+	2.37937i
$704$		0			0
$705$	−5.16548	+	8.94687i	−0.194543	+	0.336959i
$706$		0			0
$707$	8.55852	+	14.8238i	0.321876	+	0.557506i
$708$		0			0
$709$	−16.8930	−	29.2596i	−0.634431	−	1.09887i	−0.986635	−	0.162944i	$-0.947901\pi$
$709$	−16.8930	−	29.2596i	−0.634431	−	1.09887i	0.352204	−	0.935923i	$-0.385432\pi$
$710$		0			0
$711$	−1.22597	+	2.12344i	−0.0459775	+	0.0796353i
$712$		0			0
$713$	18.4703			0.691719
$714$		0			0
$715$	1.17888			0.0440877
$716$		0			0
$717$	12.6186	−	21.8561i	0.471250	−	0.816230i
$718$		0			0
$719$	−24.8064	−	42.9659i	−0.925121	−	1.60236i	−0.791366	−	0.611342i	$-0.790630\pi$
$719$	−24.8064	−	42.9659i	−0.925121	−	1.60236i	−0.133755	−	0.991014i	$-0.542703\pi$
$720$		0			0
$721$	−2.43758	−	4.22201i	−0.0907802	−	0.157236i
$722$		0			0
$723$	−16.6342			−0.618633
$724$		0			0
$725$	4.58485	−	7.94120i	0.170277	−	0.294929i
$726$		0			0
$727$	−15.7465	−	27.2737i	−0.584005	−	1.01153i	−0.994999	−	0.0998877i	$-0.968152\pi$
$727$	−15.7465	−	27.2737i	−0.584005	−	1.01153i	0.410994	−	0.911638i	$-0.365182\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.45171	−	11.1747i	−0.238625	−	0.413311i
$732$		0			0
$733$	−19.4492	+	33.6871i	−0.718374	+	1.24426i	0.243270	+	0.969959i	$0.421780\pi$
$733$	−19.4492	+	33.6871i	−0.718374	+	1.24426i	−0.961644	+	0.274301i	$0.911553\pi$
$734$		0			0
$735$	−2.89456	−	5.01352i	−0.106767	−	0.184927i
$736$		0			0
$737$	−5.80696	+	7.70671i	−0.213902	+	0.283880i
$738$		0			0
$739$	−13.6016	−	23.5587i	−0.500344	−	0.866622i	−1.00000		0.000397539i	$-0.999873\pi$
$739$	−13.6016	−	23.5587i	−0.500344	−	0.866622i	0.499656	−	0.866224i	$-0.333460\pi$
$740$		0			0
$741$	3.26255	−	5.65090i	0.119853	−	0.207591i
$742$		0			0
$743$	−0.431423	−	0.747246i	−0.0158274	−	0.0274138i	0.858003	−	0.513644i	$-0.171705\pi$
$743$	−0.431423	−	0.747246i	−0.0158274	−	0.0274138i	−0.873831	+	0.486230i	$0.838372\pi$
$744$		0			0
$745$	3.32992			0.121999
$746$		0			0
$747$	−5.48704	−	9.50384i	−0.200760	−	0.347727i
$748$		0			0
$749$	−8.06667	+	13.9719i	−0.294750	+	0.510522i
$750$		0			0
$751$	51.9831			1.89689			0.948444	−	0.316944i	$-0.102657\pi$
$751$	51.9831			1.89689			0.948444	+	0.316944i	$0.102657\pi$
$752$		0			0
$753$	11.1153	+	19.2523i	0.405065	+	0.701593i
$754$		0			0
$755$	0.834754	+	1.44584i	0.0303798	+	0.0526194i
$756$		0			0
$757$	−12.4768	+	21.6104i	−0.453475	+	0.785442i	−0.998599	−	0.0529134i	$-0.983149\pi$
$757$	−12.4768	+	21.6104i	−0.453475	+	0.785442i	0.545124	+	0.838355i	$0.316483\pi$
$758$		0			0
$759$	−9.69552			−0.351925
$760$		0			0
$761$	−30.7143			−1.11339			−0.556697	−	0.830716i	$-0.687932\pi$
$761$	−30.7143			−1.11339			−0.556697	+	0.830716i	$0.687932\pi$
$762$		0			0
$763$	0.0699906	−	0.121227i	0.00253383	−	0.00438872i
$764$		0			0
$765$	1.83022	+	3.17003i	0.0661718	+	0.114613i
$766$		0			0
$767$	4.36664	+	7.56323i	0.157670	+	0.273093i
$768$		0			0
$769$	−22.1945	+	38.4420i	−0.800353	+	1.38625i	0.119031	+	0.992891i	$0.462021\pi$
$769$	−22.1945	+	38.4420i	−0.800353	+	1.38625i	−0.919384	+	0.393362i	$0.871312\pi$
$770$		0			0
$771$	−4.81593	+	8.34143i	−0.173441	+	0.300409i
$772$		0			0
$773$	−24.2720	+	42.0404i	−0.873004	+	1.51209i	−0.0141307	+	0.999900i	$0.504498\pi$
$773$	−24.2720	+	42.0404i	−0.873004	+	1.51209i	−0.858874	+	0.512188i	$0.828835\pi$
$774$		0			0
$775$	1.12291	−	1.94493i	0.0403360	−	0.0698641i
$776$		0			0
$777$	12.2849			0.440719
$778$		0			0
$779$	61.7936			2.21399
$780$		0			0
$781$	3.62595	+	6.28033i	0.129747	+	0.224728i
$782$		0			0
$783$	4.58485	−	7.94120i	0.163849	−	0.283795i
$784$		0			0
$785$	−9.29941	−	16.1071i	−0.331910	−	0.574885i
$786$		0			0
$787$	−16.9491	−	29.3567i	−0.604171	−	1.04645i	−0.992182	−	0.124800i	$-0.960171\pi$
$787$	−16.9491	−	29.3567i	−0.604171	−	1.04645i	0.388011	−	0.921655i	$-0.373162\pi$
$788$		0			0
$789$	−11.9838			−0.426636
$790$		0			0
$791$	2.33605	+	4.04615i	0.0830603	+	0.143865i
$792$		0			0
$793$	−7.40027	+	12.8176i	−0.262791	+	0.455168i
$794$		0			0
$795$	−1.24582			−0.0441845
$796$		0			0
$797$	−21.4290	+	37.1161i	−0.759053	+	1.31472i	0.184281	+	0.982874i	$0.441005\pi$
$797$	−21.4290	+	37.1161i	−0.759053	+	1.31472i	−0.943334	+	0.331845i	$0.892329\pi$
$798$		0			0
$799$	−37.8158			−1.33783
$800$		0			0
$801$	7.19709			0.254297
$802$		0			0
$803$	10.4998			0.370530
$804$		0			0
$805$	9.05006			0.318973
$806$		0			0
$807$	−27.5058			−0.968252
$808$		0			0
$809$	42.4308			1.49179			0.745893	−	0.666065i	$-0.232023\pi$
$809$	42.4308			1.49179			0.745893	+	0.666065i	$0.232023\pi$
$810$		0			0
$811$	11.8418	−	20.5106i	0.415822	−	0.720224i	−0.579693	−	0.814835i	$-0.696827\pi$
$811$	11.8418	−	20.5106i	0.415822	−	0.720224i	0.995514	+	0.0946111i	$0.0301608\pi$
$812$		0			0
$813$	−6.99762			−0.245417
$814$		0			0
$815$	−4.29454	+	7.43836i	−0.150431	+	0.260554i
$816$		0			0
$817$	−11.5008	−	19.9200i	−0.402362	−	0.696912i
$818$		0			0
$819$	−1.10040			−0.0384511
$820$		0			0
$821$	4.69814	+	8.13742i	0.163966	+	0.283998i	0.936288	−	0.351234i	$-0.114238\pi$
$821$	4.69814	+	8.13742i	0.163966	+	0.283998i	−0.772321	+	0.635232i	$0.780904\pi$
$822$		0			0
$823$	−20.2804	−	35.1267i	−0.706930	−	1.22444i	−0.965990	−	0.258578i	$-0.916746\pi$
$823$	−20.2804	−	35.1267i	−0.706930	−	1.22444i	0.259061	−	0.965861i	$-0.416587\pi$
$824$		0			0
$825$	−0.589441	+	1.02094i	−0.0205217	+	0.0355446i
$826$		0			0
$827$	15.1528	+	26.2454i	0.526915	+	0.912643i	0.999508	+	0.0313624i	$0.00998459\pi$
$827$	15.1528	+	26.2454i	0.526915	+	0.912643i	−0.472593	+	0.881281i	$0.656682\pi$
$828$		0			0
$829$	−22.3326			−0.775642			−0.387821	−	0.921735i	$-0.626772\pi$
$829$	−22.3326			−0.775642			−0.387821	+	0.921735i	$0.626772\pi$
$830$		0			0
$831$	−3.51028			−0.121770
$832$		0			0
$833$	10.5954	−	18.3517i	0.367108	−	0.635849i
$834$		0			0
$835$	5.73292	−	9.92970i	0.198396	−	0.343632i
$836$		0			0
$837$	1.12291	−	1.94493i	0.0388134	−	0.0672267i
$838$		0			0
$839$	4.34310	−	7.52248i	0.149941	−	0.259705i	−0.781265	−	0.624200i	$-0.785425\pi$
$839$	4.34310	−	7.52248i	0.149941	−	0.259705i	0.931205	+	0.364495i	$0.118758\pi$
$840$		0			0
$841$	−27.5418	−	47.7037i	−0.949716	−	1.64496i
$842$		0			0
$843$	1.60328	+	2.77696i	0.0552199	+	0.0956437i
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	−10.5751			−0.363365
$848$		0			0
$849$	0.280187			0.00961601
$850$		0			0
$851$	45.9084	−	79.5158i	1.57372	−	2.72576i
$852$		0			0
$853$	8.24107	+	14.2739i	0.282169	+	0.488731i	0.971919	−	0.235317i	$-0.0756129\pi$
$853$	8.24107	+	14.2739i	0.282169	+	0.488731i	−0.689750	+	0.724048i	$0.742280\pi$
$854$		0			0
$855$	3.26255	+	5.65090i	0.111577	+	0.193257i
$856$		0			0
$857$	−24.0863			−0.822772			−0.411386	−	0.911461i	$-0.634955\pi$
$857$	−24.0863			−0.822772			−0.411386	+	0.911461i	$0.634955\pi$
$858$		0			0
$859$	19.9354	−	34.5292i	0.680188	−	1.17812i	−0.294735	−	0.955579i	$-0.595231\pi$
$859$	19.9354	−	34.5292i	0.680188	−	1.17812i	0.974923	−	0.222541i	$-0.0714353\pi$
$860$		0			0
$861$	−5.21048	−	9.02481i	−0.177573	−	0.307565i
$862$		0			0
$863$	−45.2344			−1.53980			−0.769898	−	0.638167i	$-0.779693\pi$
$863$	−45.2344			−1.53980			−0.769898	+	0.638167i	$0.779693\pi$
$864$		0			0
$865$	5.77239	+	9.99807i	0.196267	+	0.339945i
$866$		0			0
$867$	1.80059	−	3.11871i	0.0611512	−	0.105917i
$868$		0			0
$869$	−1.44528	−	2.50329i	−0.0490276	−	0.0849183i
$870$		0			0
$871$	3.19856	+	7.53453i	0.108379	+	0.255298i
$872$		0			0
$873$	3.18799	+	5.52175i	0.107897	+	0.186883i
$874$		0			0
$875$	0.550200	−	0.952975i	0.0186002	−	0.0322164i
$876$		0			0
$877$	4.06823	+	7.04638i	0.137374	+	0.237939i	0.926502	−	0.376290i	$-0.122800\pi$
$877$	4.06823	+	7.04638i	0.137374	+	0.237939i	−0.789128	+	0.614229i	$0.789467\pi$
$878$		0			0
$879$	7.10378			0.239604
$880$		0			0
$881$	13.8350	+	23.9630i	0.466114	+	0.807333i	0.999251	−	0.0386961i	$-0.0123204\pi$
$881$	13.8350	+	23.9630i	0.466114	+	0.807333i	−0.533137	+	0.846029i	$0.678987\pi$
$882$		0			0
$883$	22.4030	−	38.8032i	0.753922	−	1.30583i	−0.191986	−	0.981398i	$-0.561493\pi$
$883$	22.4030	−	38.8032i	0.753922	−	1.30583i	0.945908	−	0.324434i	$-0.105174\pi$
$884$		0			0
$885$	−8.73327			−0.293566
$886$		0			0
$887$	4.70319	+	8.14617i	0.157918	+	0.273522i	0.934118	−	0.356965i	$-0.116189\pi$
$887$	4.70319	+	8.14617i	0.157918	+	0.273522i	−0.776200	+	0.630487i	$0.782855\pi$
$888$		0			0
$889$	−5.74561	−	9.95169i	−0.192702	−	0.333769i
$890$		0			0
$891$	−0.589441	+	1.02094i	−0.0197470	+	0.0342028i
$892$		0			0
$893$	−67.4105			−2.25581
$894$		0			0
$895$	−23.1723			−0.774565
$896$		0			0
$897$	−4.11217	+	7.12248i	−0.137301	+	0.237813i
$898$		0			0
$899$	−10.2967	−	17.8345i	−0.343415	−	0.594813i
$900$		0			0
$901$	−2.28012	−	3.94928i	−0.0759617	−	0.131569i
$902$		0			0
$903$	−1.93951	+	3.35933i	−0.0645429	+	0.111791i
$904$		0			0
$905$	−11.6327	+	20.1484i	−0.386683	+	0.669755i
$906$		0			0
$907$	6.19999	−	10.7387i	0.205867	−	0.356573i	−0.744541	−	0.667576i	$-0.767332\pi$
$907$	6.19999	−	10.7387i	0.205867	−	0.356573i	0.950409	+	0.311004i	$0.100665\pi$
$908$		0			0
$909$	7.77764	−	13.4713i	0.257968	−	0.446814i
$910$		0			0
$911$	−32.3176			−1.07073			−0.535365	−	0.844621i	$-0.679826\pi$
$911$	−32.3176			−1.07073			−0.535365	+	0.844621i	$0.679826\pi$
$912$		0			0
$913$	12.9372			0.428157
$914$		0			0
$915$	−7.40027	−	12.8176i	−0.244645	−	0.423738i
$916$		0			0
$917$	−2.65054	+	4.59086i	−0.0875284	+	0.151604i
$918$		0			0
$919$	24.8807	+	43.0946i	0.820737	+	1.42156i	0.905134	+	0.425126i	$0.139770\pi$
$919$	24.8807	+	43.0946i	0.820737	+	1.42156i	−0.0843968	+	0.996432i	$0.526896\pi$
$920$		0			0
$921$	−5.76165	−	9.97946i	−0.189853	−	0.328835i
$922$		0			0
$923$	6.15150			0.202479
$924$		0			0
$925$	−5.58203	−	9.66835i	−0.183536	−	0.317894i
$926$		0			0
$927$	−2.21517	+	3.83680i	−0.0727559	+	0.126017i
$928$		0			0
$929$	8.38322			0.275044			0.137522	−	0.990499i	$-0.456086\pi$
$929$	8.38322			0.275044			0.137522	+	0.990499i	$0.456086\pi$
$930$		0			0
$931$	18.8873	−	32.7137i	0.619006	−	1.07215i
$932$		0			0
$933$	9.66677			0.316476
$934$		0			0
$935$	−4.31523			−0.141123
$936$		0			0
$937$	−51.9476			−1.69706			−0.848528	−	0.529151i	$-0.822511\pi$
$937$	−51.9476			−1.69706			−0.848528	+	0.529151i	$0.822511\pi$
$938$		0			0
$939$	−19.8904			−0.649099
$940$		0			0
$941$	16.2896			0.531026			0.265513	−	0.964107i	$-0.414459\pi$
$941$	16.2896			0.531026			0.265513	+	0.964107i	$0.414459\pi$
$942$		0			0
$943$	−77.8856			−2.53630
$944$		0			0
$945$	0.550200	−	0.952975i	0.0178980	−	0.0310003i
$946$		0			0
$947$	−2.49425			−0.0810522			−0.0405261	−	0.999178i	$-0.512903\pi$
$947$	−2.49425			−0.0810522			−0.0405261	+	0.999178i	$0.512903\pi$
$948$		0			0
$949$	4.45329	−	7.71333i	0.144560	−	0.250385i
$950$		0			0
$951$	−2.59315	−	4.49147i	−0.0840887	−	0.145646i
$952$		0			0
$953$	11.9196			0.386113			0.193056	−	0.981188i	$-0.438160\pi$
$953$	11.9196			0.386113			0.193056	+	0.981188i	$0.438160\pi$
$954$		0			0
$955$	1.97540	+	3.42150i	0.0639226	+	0.110717i
$956$		0			0
$957$	5.40500	+	9.36174i	0.174719	+	0.302622i
$958$		0			0
$959$	0.458866	−	0.794779i	0.0148176	−	0.0256648i
$960$		0			0
$961$	12.9782	+	22.4788i	0.418650	+	0.725123i
$962$		0			0
$963$	14.6613			0.472455
$964$		0			0
$965$	16.6912			0.537309
$966$		0			0
$967$	−6.64293	+	11.5059i	−0.213622	+	0.370005i	−0.952845	−	0.303456i	$-0.901859\pi$
$967$	−6.64293	+	11.5059i	−0.213622	+	0.370005i	0.739223	+	0.673460i	$0.235193\pi$
$968$		0			0
$969$	−11.9424	+	20.6848i	−0.383644	+	0.664491i
$970$		0			0
$971$	9.04198	−	15.6612i	0.290171	−	0.502591i	−0.683679	−	0.729783i	$-0.739621\pi$
$971$	9.04198	−	15.6612i	0.290171	−	0.502591i	0.973850	+	0.227192i	$0.0729545\pi$
$972$		0			0
$973$	5.98214	−	10.3614i	0.191778	−	0.332170i
$974$		0			0
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$		0			0
$977$	7.76151	+	13.4433i	0.248313	+	0.430090i	0.963058	−	0.269295i	$-0.0867906\pi$
$977$	7.76151	+	13.4433i	0.248313	+	0.430090i	−0.714745	+	0.699385i	$0.753457\pi$
$978$		0			0
$979$	−4.24226	+	7.34781i	−0.135583	+	0.234837i
$980$		0			0
$981$	−0.127209			−0.00406148
$982$		0			0
$983$	−4.34963			−0.138732			−0.0693658	−	0.997591i	$-0.522098\pi$
$983$	−4.34963			−0.138732			−0.0693658	+	0.997591i	$0.522098\pi$
$984$		0			0
$985$	−8.67221	+	15.0207i	−0.276319	+	0.478599i
$986$		0			0
$987$	5.68409	+	9.84514i	0.180927	+	0.313374i
$988$		0			0
$989$	14.4958	+	25.1074i	0.460939	+	0.798370i
$990$		0			0
$991$	−27.7433			−0.881296			−0.440648	−	0.897680i	$-0.645251\pi$
$991$	−27.7433			−0.881296			−0.440648	+	0.897680i	$0.645251\pi$
$992$		0			0
$993$	−3.39598	+	5.88201i	−0.107768	+	0.186660i
$994$		0			0
$995$	12.8250	+	22.2136i	0.406580	+	0.704218i
$996$		0			0
$997$	−18.2526			−0.578065			−0.289033	−	0.957319i	$-0.593334\pi$
$997$	−18.2526			−0.578065			−0.289033	+	0.957319i	$0.593334\pi$
$998$		0			0
$999$	−5.58203	−	9.66835i	−0.176608	−	0.305893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.j.841.3	✓	12
67.29	even	3	inner	4020.2.q.j.3781.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.j.841.3	✓	12	1.1	even	1	trivial
4020.2.q.j.3781.3	yes	12	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-0.550200 + 0.952975i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-0.550200 + 0.952975i) q^{7} +1.00000 q^{9} +(-0.589441 + 1.02094i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(-1.83022 - 3.17003i) q^{17} +(-3.26255 - 5.65090i) q^{19} +(-0.550200 + 0.952975i) q^{21} +(4.11217 + 7.12248i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(4.58485 - 7.94120i) q^{29} +(1.12291 - 1.94493i) q^{31} +(-0.589441 + 1.02094i) q^{33} +(0.550200 - 0.952975i) q^{35} +(-5.58203 - 9.66835i) q^{37} +(0.500000 + 0.866025i) q^{39} +(-4.73507 + 8.20139i) q^{41} +3.52510 q^{43} -1.00000 q^{45} +(5.16548 - 8.94687i) q^{47} +(2.89456 + 5.01352i) q^{49} +(-1.83022 - 3.17003i) q^{51} +1.24582 q^{53} +(0.589441 - 1.02094i) q^{55} +(-3.26255 - 5.65090i) q^{57} +8.73327 q^{59} +(7.40027 + 12.8176i) q^{61} +(-0.550200 + 0.952975i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(8.12438 + 0.997229i) q^{67} +(4.11217 + 7.12248i) q^{69} +(3.07575 - 5.32736i) q^{71} +(-4.45329 - 7.71333i) q^{73} +1.00000 q^{75} +(-0.648621 - 1.12345i) q^{77} +(-1.22597 + 2.12344i) q^{79} +1.00000 q^{81} +(-5.48704 - 9.50384i) q^{83} +(1.83022 + 3.17003i) q^{85} +(4.58485 - 7.94120i) q^{87} +7.19709 q^{89} -1.10040 q^{91} +(1.12291 - 1.94493i) q^{93} +(3.26255 + 5.65090i) q^{95} +(3.18799 + 5.52175i) q^{97} +(-0.589441 + 1.02094i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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