LMFDB - Embedded newform 4020.2.q.j.3781.2

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			3781.2
Root			$1.25129 + 2.16730i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.j.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -1.00000 q^{5} +(-1.97947 - 3.42854i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -1.00000 q^{5} +(-1.97947 - 3.42854i) q^{7} +1.00000 q^{9} +(-2.18153 - 3.77852i) q^{11} +(0.500000 - 0.866025i) q^{13} -1.00000 q^{15} +(3.35448 - 5.81012i) q^{17} +(-2.15791 + 3.73761i) q^{19} +(-1.97947 - 3.42854i) q^{21} +(-0.424239 + 0.734804i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(4.30910 + 7.46358i) q^{29} +(-3.00309 - 5.20151i) q^{31} +(-2.18153 - 3.77852i) q^{33} +(1.97947 + 3.42854i) q^{35} +(1.11772 - 1.93594i) q^{37} +(0.500000 - 0.866025i) q^{39} +(3.92733 + 6.80233i) q^{41} +1.31582 q^{43} -1.00000 q^{45} +(-6.67913 - 11.5686i) q^{47} +(-4.33660 + 7.51122i) q^{49} +(3.35448 - 5.81012i) q^{51} -7.00618 q^{53} +(2.18153 + 3.77852i) q^{55} +(-2.15791 + 3.73761i) q^{57} -14.1585 q^{59} +(2.05472 - 3.55888i) q^{61} +(-1.97947 - 3.42854i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(-7.15002 - 3.98462i) q^{67} +(-0.424239 + 0.734804i) q^{69} +(4.80052 + 8.31475i) q^{71} +(-6.96101 + 12.0568i) q^{73} +1.00000 q^{75} +(-8.63654 + 14.9589i) q^{77} +(5.43591 + 9.41527i) q^{79} +1.00000 q^{81} +(-7.12801 + 12.3461i) q^{83} +(-3.35448 + 5.81012i) q^{85} +(4.30910 + 7.46358i) q^{87} +6.38022 q^{89} -3.95894 q^{91} +(-3.00309 - 5.20151i) q^{93} +(2.15791 - 3.73761i) q^{95} +(4.37164 - 7.57190i) q^{97} +(-2.18153 - 3.77852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$7$	−1.97947	−	3.42854i	−0.748169	−	1.29587i	−0.948699	−	0.316180i	$-0.897600\pi$
$7$	−1.97947	−	3.42854i	−0.748169	−	1.29587i	0.200530	−	0.979688i	$-0.435734\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.18153	−	3.77852i	−0.657756	−	1.13927i	−0.981195	−	0.193017i	$-0.938173\pi$
$11$	−2.18153	−	3.77852i	−0.657756	−	1.13927i	0.323440	−	0.946249i	$-0.395161\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.35448	−	5.81012i	0.813580	−	1.40916i	−0.0967627	−	0.995307i	$-0.530849\pi$
$17$	3.35448	−	5.81012i	0.813580	−	1.40916i	0.910343	−	0.413855i	$-0.135818\pi$
$18$		0			0
$19$	−2.15791	+	3.73761i	−0.495058	+	0.857466i	−0.999984	−	0.00569714i	$-0.998187\pi$
$19$	−2.15791	+	3.73761i	−0.495058	+	0.857466i	0.504926	+	0.863163i	$0.331520\pi$
$20$		0			0
$21$	−1.97947	−	3.42854i	−0.431956	−	0.748169i
$22$		0			0
$23$	−0.424239	+	0.734804i	−0.0884600	+	0.153217i	−0.906860	−	0.421431i	$-0.861528\pi$
$23$	−0.424239	+	0.734804i	−0.0884600	+	0.153217i	0.818400	+	0.574648i	$0.194861\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	4.30910	+	7.46358i	0.800180	+	1.38595i	0.919497	+	0.393096i	$0.128596\pi$
$29$	4.30910	+	7.46358i	0.800180	+	1.38595i	−0.119317	+	0.992856i	$0.538071\pi$
$30$		0			0
$31$	−3.00309	−	5.20151i	−0.539371	−	0.934218i	−0.998938	−	0.0460748i	$-0.985329\pi$
$31$	−3.00309	−	5.20151i	−0.539371	−	0.934218i	0.459567	−	0.888143i	$-0.348005\pi$
$32$		0			0
$33$	−2.18153	−	3.77852i	−0.379755	−	0.657756i
$34$		0			0
$35$	1.97947	+	3.42854i	0.334592	+	0.579529i
$36$		0			0
$37$	1.11772	−	1.93594i	0.183752	−	0.318267i	−0.759403	−	0.650620i	$-0.774509\pi$
$37$	1.11772	−	1.93594i	0.183752	−	0.318267i	0.943155	+	0.332353i	$0.107842\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	3.92733	+	6.80233i	0.613346	+	1.06235i	0.990672	+	0.136266i	$0.0435101\pi$
$41$	3.92733	+	6.80233i	0.613346	+	1.06235i	−0.377326	+	0.926080i	$0.623157\pi$
$42$		0			0
$43$	1.31582			0.200660			0.100330	−	0.994954i	$-0.468010\pi$
$43$	1.31582			0.200660			0.100330	+	0.994954i	$0.468010\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−6.67913	−	11.5686i	−0.974251	−	1.68745i	−0.682384	−	0.730994i	$-0.739057\pi$
$47$	−6.67913	−	11.5686i	−0.974251	−	1.68745i	−0.291867	−	0.956459i	$-0.594276\pi$
$48$		0			0
$49$	−4.33660	+	7.51122i	−0.619515	+	1.07303i
$50$		0			0
$51$	3.35448	−	5.81012i	0.469721	−	0.813580i
$52$		0			0
$53$	−7.00618			−0.962373			−0.481186	−	0.876618i	$-0.659794\pi$
$53$	−7.00618			−0.962373			−0.481186	+	0.876618i	$0.659794\pi$
$54$		0			0
$55$	2.18153	+	3.77852i	0.294157	+	0.509495i
$56$		0			0
$57$	−2.15791	+	3.73761i	−0.285822	+	0.495058i
$58$		0			0
$59$	−14.1585			−1.84328			−0.921638	−	0.388050i	$-0.873149\pi$
$59$	−14.1585			−1.84328			−0.921638	+	0.388050i	$0.873149\pi$
$60$		0			0
$61$	2.05472	−	3.55888i	0.263080	−	0.455668i	−0.703979	−	0.710221i	$-0.748595\pi$
$61$	2.05472	−	3.55888i	0.263080	−	0.455668i	0.967059	+	0.254553i	$0.0819283\pi$
$62$		0			0
$63$	−1.97947	−	3.42854i	−0.249390	−	0.431956i
$64$		0			0
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	−7.15002	−	3.98462i	−0.873514	−	0.486799i
$67$	−7.15002	−	3.98462i	−0.873514	−	0.486799i
$68$		0			0
$69$	−0.424239	+	0.734804i	−0.0510724	+	0.0884600i
$70$		0			0
$71$	4.80052	+	8.31475i	0.569717	+	0.986779i	0.996594	+	0.0824691i	$0.0262806\pi$
$71$	4.80052	+	8.31475i	0.569717	+	0.986779i	−0.426876	+	0.904310i	$0.640386\pi$
$72$		0			0
$73$	−6.96101	+	12.0568i	−0.814725	+	1.41114i	0.0948008	+	0.995496i	$0.469779\pi$
$73$	−6.96101	+	12.0568i	−0.814725	+	1.41114i	−0.909525	+	0.415648i	$0.863555\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−8.63654	+	14.9589i	−0.984225	+	1.70473i
$78$		0			0
$79$	5.43591	+	9.41527i	0.611588	+	1.05930i	0.990973	+	0.134062i	$0.0428021\pi$
$79$	5.43591	+	9.41527i	0.611588	+	1.05930i	−0.379385	+	0.925239i	$0.623865\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−7.12801	+	12.3461i	−0.782400	+	1.35516i	0.148139	+	0.988967i	$0.452672\pi$
$83$	−7.12801	+	12.3461i	−0.782400	+	1.35516i	−0.930540	+	0.366191i	$0.880662\pi$
$84$		0			0
$85$	−3.35448	+	5.81012i	−0.363844	+	0.630197i
$86$		0			0
$87$	4.30910	+	7.46358i	0.461984	+	0.800180i
$88$		0			0
$89$	6.38022			0.676301			0.338151	−	0.941092i	$-0.390199\pi$
$89$	6.38022			0.676301			0.338151	+	0.941092i	$0.390199\pi$
$90$		0			0
$91$	−3.95894			−0.415010
$92$		0			0
$93$	−3.00309	−	5.20151i	−0.311406	−	0.539371i
$94$		0			0
$95$	2.15791	−	3.73761i	0.221397	−	0.383470i
$96$		0			0
$97$	4.37164	−	7.57190i	0.443872	−	0.768810i	−0.554101	−	0.832450i	$-0.686938\pi$
$97$	4.37164	−	7.57190i	0.443872	−	0.768810i	0.997973	+	0.0636402i	$0.0202710\pi$
$98$		0			0
$99$	−2.18153	−	3.77852i	−0.219252	−	0.379755i
$100$		0			0
$101$	−8.60337	−	14.9015i	−0.856067	−	1.48275i	−0.875651	−	0.482944i	$-0.839568\pi$
$101$	−8.60337	−	14.9015i	−0.856067	−	1.48275i	0.0195842	−	0.999808i	$-0.493766\pi$
$102$		0			0
$103$	−6.10526	−	10.5746i	−0.601569	−	1.04195i	−0.992584	−	0.121563i	$-0.961209\pi$
$103$	−6.10526	−	10.5746i	−0.601569	−	1.04195i	0.391015	−	0.920384i	$-0.372124\pi$
$104$		0			0
$105$	1.97947	+	3.42854i	0.193176	+	0.334592i
$106$		0			0
$107$	−2.39416			−0.231452			−0.115726	−	0.993281i	$-0.536919\pi$
$107$	−2.39416			−0.231452			−0.115726	+	0.993281i	$0.536919\pi$
$108$		0			0
$109$	6.98228			0.668781			0.334391	−	0.942435i	$-0.391470\pi$
$109$	6.98228			0.668781			0.334391	+	0.942435i	$0.391470\pi$
$110$		0			0
$111$	1.11772	−	1.93594i	0.106089	−	0.183752i
$112$		0			0
$113$	−2.00309	−	3.46945i	−0.188435	−	0.326379i	0.756294	−	0.654232i	$-0.227008\pi$
$113$	−2.00309	−	3.46945i	−0.188435	−	0.326379i	−0.944729	+	0.327853i	$0.893675\pi$
$114$		0			0
$115$	0.424239	−	0.734804i	0.0395605	−	0.0685208i
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		0			0
$119$	−26.5603			−2.43478
$120$		0			0
$121$	−4.01813	+	6.95961i	−0.365285	+	0.632692i
$122$		0			0
$123$	3.92733	+	6.80233i	0.354115	+	0.613346i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.30834	+	5.73021i	0.293567	+	0.508474i	0.974651	−	0.223732i	$-0.0718242\pi$
$127$	3.30834	+	5.73021i	0.293567	+	0.508474i	−0.681083	+	0.732206i	$0.738491\pi$
$128$		0			0
$129$	1.31582			0.115851
$130$		0			0
$131$	−4.90072			−0.428178			−0.214089	−	0.976814i	$-0.568678\pi$
$131$	−4.90072			−0.428178			−0.214089	+	0.976814i	$0.568678\pi$
$132$		0			0
$133$	17.0861			1.48155
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−4.43762			−0.379131			−0.189566	−	0.981868i	$-0.560708\pi$
$137$	−4.43762			−0.379131			−0.189566	+	0.981868i	$0.560708\pi$
$138$		0			0
$139$	−9.99157			−0.847474			−0.423737	−	0.905785i	$-0.639282\pi$
$139$	−9.99157			−0.847474			−0.423737	+	0.905785i	$0.639282\pi$
$140$		0			0
$141$	−6.67913	−	11.5686i	−0.562484	−	0.974251i
$142$		0			0
$143$	−4.36306			−0.364857
$144$		0			0
$145$	−4.30910	−	7.46358i	−0.357851	−	0.619817i
$146$		0			0
$147$	−4.33660	+	7.51122i	−0.357677	+	0.619515i
$148$		0			0
$149$	−18.3618			−1.50426			−0.752130	−	0.659015i	$-0.770973\pi$
$149$	−18.3618			−1.50426			−0.752130	+	0.659015i	$0.770973\pi$
$150$		0			0
$151$	−8.48026	+	14.6882i	−0.690114	+	1.19531i	0.281686	+	0.959507i	$0.409106\pi$
$151$	−8.48026	+	14.6882i	−0.690114	+	1.19531i	−0.971800	+	0.235806i	$0.924227\pi$
$152$		0			0
$153$	3.35448	−	5.81012i	0.271193	−	0.469721i
$154$		0			0
$155$	3.00309	+	5.20151i	0.241214	+	0.417795i
$156$		0			0
$157$	−1.40946	+	2.44125i	−0.112487	+	0.194833i	−0.916772	−	0.399410i	$-0.869215\pi$
$157$	−1.40946	+	2.44125i	−0.112487	+	0.194833i	0.804286	+	0.594243i	$0.202548\pi$
$158$		0			0
$159$	−7.00618			−0.555626
$160$		0			0
$161$	3.35907			0.264732
$162$		0			0
$163$	6.87930	+	11.9153i	0.538828	+	0.933278i	0.998967	+	0.0454311i	$0.0144661\pi$
$163$	6.87930	+	11.9153i	0.538828	+	0.933278i	−0.460139	+	0.887847i	$0.652201\pi$
$164$		0			0
$165$	2.18153	+	3.77852i	0.169832	+	0.294157i
$166$		0			0
$167$	5.99265	+	10.3796i	0.463725	+	0.803196i	0.999143	−	0.0413918i	$-0.0131792\pi$
$167$	5.99265	+	10.3796i	0.463725	+	0.803196i	−0.535418	+	0.844587i	$0.679846\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	−2.15791	+	3.73761i	−0.165019	+	0.285822i
$172$		0			0
$173$	9.98946	−	17.3022i	0.759484	−	1.31547i	−0.183630	−	0.982996i	$-0.558785\pi$
$173$	9.98946	−	17.3022i	0.759484	−	1.31547i	0.943114	−	0.332470i	$-0.107882\pi$
$174$		0			0
$175$	−1.97947	−	3.42854i	−0.149634	−	0.259173i
$176$		0			0
$177$	−14.1585			−1.06422
$178$		0			0
$179$	−23.3128			−1.74248			−0.871241	−	0.490856i	$-0.836684\pi$
$179$	−23.3128			−1.74248			−0.871241	+	0.490856i	$0.836684\pi$
$180$		0			0
$181$	3.01915	+	5.22932i	0.224412	+	0.388692i	0.956143	−	0.292901i	$-0.0946207\pi$
$181$	3.01915	+	5.22932i	0.224412	+	0.388692i	−0.731731	+	0.681593i	$0.761287\pi$
$182$		0			0
$183$	2.05472	−	3.55888i	0.151889	−	0.263080i
$184$		0			0
$185$	−1.11772	+	1.93594i	−0.0821763	+	0.142333i
$186$		0			0
$187$	−29.2715			−2.14055
$188$		0			0
$189$	−1.97947	−	3.42854i	−0.143985	−	0.249390i
$190$		0			0
$191$	10.1207	−	17.5296i	0.732311	−	1.26840i	−0.223583	−	0.974685i	$-0.571775\pi$
$191$	10.1207	−	17.5296i	0.732311	−	1.26840i	0.955893	−	0.293714i	$-0.0948914\pi$
$192$		0			0
$193$	14.5283			1.04577			0.522884	−	0.852404i	$-0.324856\pi$
$193$	14.5283			1.04577			0.522884	+	0.852404i	$0.324856\pi$
$194$		0			0
$195$	−0.500000	+	0.866025i	−0.0358057	+	0.0620174i
$196$		0			0
$197$	−9.09213	−	15.7480i	−0.647788	−	1.12200i	−0.983650	−	0.180090i	$-0.942361\pi$
$197$	−9.09213	−	15.7480i	−0.647788	−	1.12200i	0.335862	−	0.941911i	$-0.390972\pi$
$198$		0			0
$199$	8.55072	−	14.8103i	0.606144	−	1.04987i	−0.385725	−	0.922614i	$-0.626049\pi$
$199$	8.55072	−	14.8103i	0.606144	−	1.04987i	0.991870	−	0.127259i	$-0.0406180\pi$
$200$		0			0
$201$	−7.15002	−	3.98462i	−0.504324	−	0.281054i
$202$		0			0
$203$	17.0595	−	29.5479i	1.19734	−	2.07385i
$204$		0			0
$205$	−3.92733	−	6.80233i	−0.274297	−	0.475096i
$206$		0			0
$207$	−0.424239	+	0.734804i	−0.0294867	+	0.0510724i
$208$		0			0
$209$	18.8301			1.30251
$210$		0			0
$211$	−0.454624	+	0.787433i	−0.0312976	+	0.0542091i	−0.881250	−	0.472651i	$-0.843297\pi$
$211$	−0.454624	+	0.787433i	−0.0312976	+	0.0542091i	0.849952	+	0.526860i	$0.176631\pi$
$212$		0			0
$213$	4.80052	+	8.31475i	0.328926	+	0.569717i
$214$		0			0
$215$	−1.31582			−0.0897379
$216$		0			0
$217$	−11.8891	+	20.5924i	−0.807082	+	1.39791i
$218$		0			0
$219$	−6.96101	+	12.0568i	−0.470381	+	0.814725i
$220$		0			0
$221$	−3.35448	−	5.81012i	−0.225647	−	0.390831i
$222$		0			0
$223$	−11.2090			−0.750609			−0.375305	−	0.926902i	$-0.622462\pi$
$223$	−11.2090			−0.750609			−0.375305	+	0.926902i	$0.622462\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.10551	−	10.5751i	−0.405237	−	0.701891i	0.589112	−	0.808051i	$-0.299478\pi$
$227$	−6.10551	−	10.5751i	−0.405237	−	0.701891i	−0.994349	+	0.106160i	$0.966144\pi$
$228$		0			0
$229$	10.5194	−	18.2201i	0.695142	−	1.20402i	−0.274991	−	0.961447i	$-0.588675\pi$
$229$	10.5194	−	18.2201i	0.695142	−	1.20402i	0.970133	−	0.242574i	$-0.0779919\pi$
$230$		0			0
$231$	−8.63654	+	14.9589i	−0.568243	+	0.984225i
$232$		0			0
$233$	−6.47656	−	11.2177i	−0.424294	−	0.734898i	0.572061	−	0.820211i	$-0.306144\pi$
$233$	−6.47656	−	11.2177i	−0.424294	−	0.734898i	−0.996354	+	0.0853132i	$0.972811\pi$
$234$		0			0
$235$	6.67913	+	11.5686i	0.435698	+	0.754652i
$236$		0			0
$237$	5.43591	+	9.41527i	0.353100	+	0.611588i
$238$		0			0
$239$	11.4761	+	19.8772i	0.742327	+	1.28575i	0.951433	+	0.307855i	$0.0996113\pi$
$239$	11.4761	+	19.8772i	0.742327	+	1.28575i	−0.209106	+	0.977893i	$0.567055\pi$
$240$		0			0
$241$	14.0901			0.907623			0.453811	−	0.891098i	$-0.350064\pi$
$241$	14.0901			0.907623			0.453811	+	0.891098i	$0.350064\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	4.33660	−	7.51122i	0.277055	−	0.479874i
$246$		0			0
$247$	2.15791	+	3.73761i	0.137304	+	0.237818i
$248$		0			0
$249$	−7.12801	+	12.3461i	−0.451719	+	0.782400i
$250$		0			0
$251$	−13.1209	+	22.7261i	−0.828185	+	1.43446i	0.0712760	+	0.997457i	$0.477293\pi$
$251$	−13.1209	+	22.7261i	−0.828185	+	1.43446i	−0.899461	+	0.437002i	$0.856040\pi$
$252$		0			0
$253$	3.70196			0.232740
$254$		0			0
$255$	−3.35448	+	5.81012i	−0.210066	+	0.363844i
$256$		0			0
$257$	−0.398370	−	0.689997i	−0.0248496	−	0.0430408i	0.853333	−	0.521366i	$-0.174577\pi$
$257$	−0.398370	−	0.689997i	−0.0248496	−	0.0430408i	−0.878183	+	0.478325i	$0.841244\pi$
$258$		0			0
$259$	−8.84996			−0.549910
$260$		0			0
$261$	4.30910	+	7.46358i	0.266727	+	0.461984i
$262$		0			0
$263$	11.3215			0.698113			0.349057	−	0.937102i	$-0.386502\pi$
$263$	11.3215			0.698113			0.349057	+	0.937102i	$0.386502\pi$
$264$		0			0
$265$	7.00618			0.430386
$266$		0			0
$267$	6.38022			0.390463
$268$		0			0
$269$	−24.5113			−1.49448			−0.747241	−	0.664554i	$-0.768622\pi$
$269$	−24.5113			−1.49448			−0.747241	+	0.664554i	$0.768622\pi$
$270$		0			0
$271$	4.51034			0.273984			0.136992	−	0.990572i	$-0.456257\pi$
$271$	4.51034			0.273984			0.136992	+	0.990572i	$0.456257\pi$
$272$		0			0
$273$	−3.95894			−0.239606
$274$		0			0
$275$	−2.18153	−	3.77852i	−0.131551	−	0.227853i
$276$		0			0
$277$	3.58700			0.215522			0.107761	−	0.994177i	$-0.465632\pi$
$277$	3.58700			0.215522			0.107761	+	0.994177i	$0.465632\pi$
$278$		0			0
$279$	−3.00309	−	5.20151i	−0.179790	−	0.311406i
$280$		0			0
$281$	−0.0765554	+	0.132598i	−0.00456691	+	0.00791013i	−0.868300	−	0.496040i	$-0.834787\pi$
$281$	−0.0765554	+	0.132598i	−0.00456691	+	0.00791013i	0.863733	+	0.503950i	$0.168120\pi$
$282$		0			0
$283$	11.3325			0.673645			0.336823	−	0.941568i	$-0.390648\pi$
$283$	11.3325			0.673645			0.336823	+	0.941568i	$0.390648\pi$
$284$		0			0
$285$	2.15791	−	3.73761i	0.127823	−	0.221397i
$286$		0			0
$287$	15.5481	−	26.9300i	0.917773	−	1.58963i
$288$		0			0
$289$	−14.0050	−	24.2574i	−0.823826	−	1.42691i
$290$		0			0
$291$	4.37164	−	7.57190i	0.256270	−	0.443872i
$292$		0			0
$293$	−10.6224			−0.620567			−0.310283	−	0.950644i	$-0.600424\pi$
$293$	−10.6224			−0.620567			−0.310283	+	0.950644i	$0.600424\pi$
$294$		0			0
$295$	14.1585			0.824338
$296$		0			0
$297$	−2.18153	−	3.77852i	−0.126585	−	0.219252i
$298$		0			0
$299$	0.424239	+	0.734804i	0.0245344	+	0.0424948i
$300$		0			0
$301$	−2.60462	−	4.51133i	−0.150128	−	0.260029i
$302$		0			0
$303$	−8.60337	−	14.9015i	−0.494251	−	0.856067i
$304$		0			0
$305$	−2.05472	+	3.55888i	−0.117653	+	0.203781i
$306$		0			0
$307$	10.4106	−	18.0317i	0.594165	−	1.02912i	−0.399500	−	0.916733i	$-0.630816\pi$
$307$	10.4106	−	18.0317i	0.594165	−	1.02912i	0.993664	−	0.112390i	$-0.0358506\pi$
$308$		0			0
$309$	−6.10526	−	10.5746i	−0.347316	−	0.601569i
$310$		0			0
$311$	−0.0767132			−0.00435001			−0.00217500	−	0.999998i	$-0.500692\pi$
$311$	−0.0767132			−0.00435001			−0.00217500	+	0.999998i	$0.500692\pi$
$312$		0			0
$313$	−1.60053			−0.0904673			−0.0452336	−	0.998976i	$-0.514403\pi$
$313$	−1.60053			−0.0904673			−0.0452336	+	0.998976i	$0.514403\pi$
$314$		0			0
$315$	1.97947	+	3.42854i	0.111531	+	0.193176i
$316$		0			0
$317$	−8.97827	+	15.5508i	−0.504270	+	0.873421i	0.495718	+	0.868484i	$0.334905\pi$
$317$	−8.97827	+	15.5508i	−0.504270	+	0.873421i	−0.999988	+	0.00493760i	$0.998428\pi$
$318$		0			0
$319$	18.8009	−	32.5640i	1.05265	−	1.82324i
$320$		0			0
$321$	−2.39416			−0.133629
$322$		0			0
$323$	14.4773	+	25.0754i	0.805539	+	1.39523i
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$	6.98228			0.386121
$328$		0			0
$329$	−26.4423	+	45.7994i	−1.45781	+	2.52500i
$330$		0			0
$331$	−17.7325	−	30.7136i	−0.974666	−	1.68817i	−0.681032	−	0.732254i	$-0.738468\pi$
$331$	−17.7325	−	30.7136i	−0.974666	−	1.68817i	−0.293634	−	0.955918i	$-0.594865\pi$
$332$		0			0
$333$	1.11772	−	1.93594i	0.0612506	−	0.106089i
$334$		0			0
$335$	7.15002	+	3.98462i	0.390647	+	0.217703i
$336$		0			0
$337$	3.11991	−	5.40384i	0.169952	−	0.294366i	−0.768451	−	0.639909i	$-0.778972\pi$
$337$	3.11991	−	5.40384i	0.169952	−	0.294366i	0.938403	+	0.345543i	$0.112305\pi$
$338$		0			0
$339$	−2.00309	−	3.46945i	−0.108793	−	0.188435i
$340$		0			0
$341$	−13.1027	+	22.6945i	−0.709548	+	1.22897i
$342$		0			0
$343$	6.62412			0.357669
$344$		0			0
$345$	0.424239	−	0.734804i	0.0228403	−	0.0395605i
$346$		0			0
$347$	8.03797	+	13.9222i	0.431501	+	0.747382i	0.997003	−	0.0773654i	$-0.0246508\pi$
$347$	8.03797	+	13.9222i	0.431501	+	0.747382i	−0.565502	+	0.824747i	$0.691317\pi$
$348$		0			0
$349$	35.3506			1.89227			0.946137	−	0.323766i	$-0.104949\pi$
$349$	35.3506			1.89227			0.946137	+	0.323766i	$0.104949\pi$
$350$		0			0
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$		0			0
$353$	0.698101	−	1.20915i	0.0371562	−	0.0643564i	−0.846849	−	0.531833i	$-0.821503\pi$
$353$	0.698101	−	1.20915i	0.0371562	−	0.0643564i	0.884005	+	0.467477i	$0.154837\pi$
$354$		0			0
$355$	−4.80052	−	8.31475i	−0.254785	−	0.441301i
$356$		0			0
$357$	−26.5603			−1.40572
$358$		0			0
$359$	−22.7170			−1.19896			−0.599480	−	0.800390i	$-0.704626\pi$
$359$	−22.7170			−1.19896			−0.599480	+	0.800390i	$0.704626\pi$
$360$		0			0
$361$	0.186867	+	0.323664i	0.00983513	+	0.0170349i
$362$		0			0
$363$	−4.01813	+	6.95961i	−0.210897	+	0.365285i
$364$		0			0
$365$	6.96101	−	12.0568i	0.364356	−	0.631083i
$366$		0			0
$367$	9.05784	+	15.6886i	0.472815	+	0.818940i	0.999516	−	0.0311106i	$-0.00990441\pi$
$367$	9.05784	+	15.6886i	0.472815	+	0.818940i	−0.526701	+	0.850051i	$0.676571\pi$
$368$		0			0
$369$	3.92733	+	6.80233i	0.204449	+	0.354115i
$370$		0			0
$371$	13.8685	+	24.0210i	0.720018	+	1.24711i
$372$		0			0
$373$	2.91819	+	5.05445i	0.151098	+	0.261710i	0.931631	−	0.363405i	$-0.118386\pi$
$373$	2.91819	+	5.05445i	0.151098	+	0.261710i	−0.780533	+	0.625114i	$0.785052\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	8.61820			0.443860
$378$		0			0
$379$	4.94880	−	8.57157i	0.254203	−	0.440292i	−0.710476	−	0.703721i	$-0.751520\pi$
$379$	4.94880	−	8.57157i	0.254203	−	0.440292i	0.964679	+	0.263429i	$0.0848536\pi$
$380$		0			0
$381$	3.30834	+	5.73021i	0.169491	+	0.293567i
$382$		0			0
$383$	11.7464	−	20.3453i	0.600211	−	1.03960i	−0.392577	−	0.919719i	$-0.628416\pi$
$383$	11.7464	−	20.3453i	0.600211	−	1.03960i	0.992789	−	0.119878i	$-0.0382503\pi$
$384$		0			0
$385$	8.63654	−	14.9589i	0.440159	−	0.762377i
$386$		0			0
$387$	1.31582			0.0668867
$388$		0			0
$389$	12.4016	−	21.4802i	0.628787	−	1.08909i	−0.359009	−	0.933334i	$-0.616885\pi$
$389$	12.4016	−	21.4802i	0.628787	−	1.08909i	0.987795	−	0.155756i	$-0.0497815\pi$
$390$		0			0
$391$	2.84620	+	4.92976i	0.143939	+	0.249309i
$392$		0			0
$393$	−4.90072			−0.247209
$394$		0			0
$395$	−5.43591	−	9.41527i	−0.273510	−	0.473734i
$396$		0			0
$397$	15.8215			0.794056			0.397028	−	0.917806i	$-0.370042\pi$
$397$	15.8215			0.794056			0.397028	+	0.917806i	$0.370042\pi$
$398$		0			0
$399$	17.0861			0.855373
$400$		0			0
$401$	−8.65794			−0.432357			−0.216178	−	0.976354i	$-0.569359\pi$
$401$	−8.65794			−0.432357			−0.216178	+	0.976354i	$0.569359\pi$
$402$		0			0
$403$	−6.00618			−0.299189
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−9.75333			−0.483455
$408$		0			0
$409$	−11.0615	−	19.1592i	−0.546958	−	0.947359i	−0.998481	−	0.0550995i	$-0.982452\pi$
$409$	−11.0615	−	19.1592i	−0.546958	−	0.947359i	0.451523	−	0.892260i	$-0.350881\pi$
$410$		0			0
$411$	−4.43762			−0.218892
$412$		0			0
$413$	28.0263	+	48.5429i	1.37908	+	2.38864i
$414$		0			0
$415$	7.12801	−	12.3461i	0.349900	−	0.606045i
$416$		0			0
$417$	−9.99157			−0.489289
$418$		0			0
$419$	−18.2776	+	31.6577i	−0.892919	+	1.54658i	−0.0565600	+	0.998399i	$0.518013\pi$
$419$	−18.2776	+	31.6577i	−0.892919	+	1.54658i	−0.836359	+	0.548182i	$0.815320\pi$
$420$		0			0
$421$	−10.4997	+	18.1860i	−0.511725	+	0.886334i	0.488183	+	0.872742i	$0.337660\pi$
$421$	−10.4997	+	18.1860i	−0.511725	+	0.886334i	−0.999908	+	0.0135922i	$0.995673\pi$
$422$		0			0
$423$	−6.67913	−	11.5686i	−0.324750	−	0.562484i
$424$		0			0
$425$	3.35448	−	5.81012i	0.162716	−	0.281832i
$426$		0			0
$427$	−16.2690			−0.787314
$428$		0			0
$429$	−4.36306			−0.210650
$430$		0			0
$431$	−9.25096	−	16.0231i	−0.445603	−	0.771807i	0.552491	−	0.833519i	$-0.313677\pi$
$431$	−9.25096	−	16.0231i	−0.445603	−	0.771807i	−0.998094	+	0.0617116i	$0.980344\pi$
$432$		0			0
$433$	−8.12415	−	14.0714i	−0.390422	−	0.676231i	0.602083	−	0.798433i	$-0.294338\pi$
$433$	−8.12415	−	14.0714i	−0.390422	−	0.676231i	−0.992505	+	0.122203i	$0.961004\pi$
$434$		0			0
$435$	−4.30910	−	7.46358i	−0.206606	−	0.357851i
$436$		0			0
$437$	−1.83094	−	3.17128i	−0.0875856	−	0.151703i
$438$		0			0
$439$	19.0226	−	32.9482i	0.907901	−	1.57253i	0.0909253	−	0.995858i	$-0.471018\pi$
$439$	19.0226	−	32.9482i	0.907901	−	1.57253i	0.816975	−	0.576673i	$-0.195649\pi$
$440$		0			0
$441$	−4.33660	+	7.51122i	−0.206505	+	0.357677i
$442$		0			0
$443$	13.9627	+	24.1841i	0.663387	+	1.14902i	0.979720	+	0.200371i	$0.0642149\pi$
$443$	13.9627	+	24.1841i	0.663387	+	1.14902i	−0.316333	+	0.948648i	$0.602452\pi$
$444$		0			0
$445$	−6.38022			−0.302451
$446$		0			0
$447$	−18.3618			−0.868485
$448$		0			0
$449$	6.11588	+	10.5930i	0.288626	+	0.499915i	0.973482	−	0.228764i	$-0.0734683\pi$
$449$	6.11588	+	10.5930i	0.288626	+	0.499915i	−0.684856	+	0.728678i	$0.740135\pi$
$450$		0			0
$451$	17.1352	−	29.6790i	0.806863	−	1.39753i
$452$		0			0
$453$	−8.48026	+	14.6882i	−0.398438	+	0.690114i
$454$		0			0
$455$	3.95894			0.185598
$456$		0			0
$457$	4.36458	+	7.55968i	0.204167	+	0.353627i	0.949867	−	0.312655i	$-0.101218\pi$
$457$	4.36458	+	7.55968i	0.204167	+	0.353627i	−0.745700	+	0.666282i	$0.767885\pi$
$458$		0			0
$459$	3.35448	−	5.81012i	0.156574	−	0.271193i
$460$		0			0
$461$	−35.7316			−1.66419			−0.832094	−	0.554634i	$-0.812858\pi$
$461$	−35.7316			−1.66419			−0.832094	+	0.554634i	$0.812858\pi$
$462$		0			0
$463$	−1.10610	+	1.91581i	−0.0514046	+	0.0890354i	−0.890583	−	0.454821i	$-0.849703\pi$
$463$	−1.10610	+	1.91581i	−0.0514046	+	0.0890354i	0.839178	+	0.543857i	$0.183036\pi$
$464$		0			0
$465$	3.00309	+	5.20151i	0.139265	+	0.241214i
$466$		0			0
$467$	6.22760	−	10.7865i	0.288179	−	0.499140i	−0.685196	−	0.728358i	$-0.740284\pi$
$467$	6.22760	−	10.7865i	0.288179	−	0.499140i	0.973375	+	0.229218i	$0.0736169\pi$
$468$		0			0
$469$	0.491807	+	32.4016i	0.0227095	+	1.49617i
$470$		0			0
$471$	−1.40946	+	2.44125i	−0.0649443	+	0.112487i
$472$		0			0
$473$	−2.87049	−	4.97183i	−0.131985	−	0.228605i
$474$		0			0
$475$	−2.15791	+	3.73761i	−0.0990116	+	0.171493i
$476$		0			0
$477$	−7.00618			−0.320791
$478$		0			0
$479$	10.2668	−	17.7826i	0.469101	−	0.812506i	−0.530276	−	0.847825i	$-0.677912\pi$
$479$	10.2668	−	17.7826i	0.469101	−	0.812506i	0.999376	+	0.0353194i	$0.0112449\pi$
$480$		0			0
$481$	−1.11772	−	1.93594i	−0.0509636	−	0.0882715i
$482$		0			0
$483$	3.35907			0.152843
$484$		0			0
$485$	−4.37164	+	7.57190i	−0.198506	+	0.343822i
$486$		0			0
$487$	−14.3346	+	24.8283i	−0.649564	+	1.12508i	0.333663	+	0.942693i	$0.391715\pi$
$487$	−14.3346	+	24.8283i	−0.649564	+	1.12508i	−0.983227	+	0.182386i	$0.941618\pi$
$488$		0			0
$489$	6.87930	+	11.9153i	0.311093	+	0.538828i
$490$		0			0
$491$	23.8020			1.07417			0.537084	−	0.843529i	$-0.319526\pi$
$491$	23.8020			1.07417			0.537084	+	0.843529i	$0.319526\pi$
$492$		0			0
$493$	57.8191			2.60404
$494$		0			0
$495$	2.18153	+	3.77852i	0.0980524	+	0.169832i
$496$		0			0
$497$	19.0050	−	32.9176i	0.852490	−	1.47656i
$498$		0			0
$499$	−1.33497	+	2.31223i	−0.0597613	+	0.103510i	−0.894358	−	0.447352i	$-0.852367\pi$
$499$	−1.33497	+	2.31223i	−0.0597613	+	0.103510i	0.834597	+	0.550861i	$0.185701\pi$
$500$		0			0
$501$	5.99265	+	10.3796i	0.267732	+	0.463725i
$502$		0			0
$503$	−5.74366	−	9.94831i	−0.256097	−	0.443573i	0.709096	−	0.705112i	$-0.249103\pi$
$503$	−5.74366	−	9.94831i	−0.256097	−	0.443573i	−0.965193	+	0.261539i	$0.915770\pi$
$504$		0			0
$505$	8.60337	+	14.9015i	0.382845	+	0.663107i
$506$		0			0
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$		0			0
$509$	−23.6677			−1.04905			−0.524527	−	0.851394i	$-0.675758\pi$
$509$	−23.6677			−1.04905			−0.524527	+	0.851394i	$0.675758\pi$
$510$		0			0
$511$	55.1164			2.43821
$512$		0			0
$513$	−2.15791	+	3.73761i	−0.0952740	+	0.165019i
$514$		0			0
$515$	6.10526	+	10.5746i	0.269030	+	0.465973i
$516$		0			0
$517$	−29.1414	+	50.4744i	−1.28164	+	2.21986i
$518$		0			0
$519$	9.98946	−	17.3022i	0.438488	−	0.759484i
$520$		0			0
$521$	−15.1535			−0.663888			−0.331944	−	0.943299i	$-0.607704\pi$
$521$	−15.1535			−0.663888			−0.331944	+	0.943299i	$0.607704\pi$
$522$		0			0
$523$	−6.69631	+	11.5984i	−0.292809	+	0.507161i	−0.974473	−	0.224505i	$-0.927923\pi$
$523$	−6.69631	+	11.5984i	−0.292809	+	0.507161i	0.681664	+	0.731666i	$0.261257\pi$
$524$		0			0
$525$	−1.97947	−	3.42854i	−0.0863912	−	0.149634i
$526$		0			0
$527$	−40.2952			−1.75529
$528$		0			0
$529$	11.1400	+	19.2951i	0.484350	+	0.838918i
$530$		0			0
$531$	−14.1585			−0.614426
$532$		0			0
$533$	7.85466			0.340223
$534$		0			0
$535$	2.39416			0.103509
$536$		0			0
$537$	−23.3128			−1.00602
$538$		0			0
$539$	37.8417			1.62996
$540$		0			0
$541$	−38.8407			−1.66989			−0.834945	−	0.550333i	$-0.814501\pi$
$541$	−38.8407			−1.66989			−0.834945	+	0.550333i	$0.814501\pi$
$542$		0			0
$543$	3.01915	+	5.22932i	0.129564	+	0.224412i
$544$		0			0
$545$	−6.98228			−0.299088
$546$		0			0
$547$	−16.8035	−	29.1046i	−0.718467	−	1.24442i	−0.961607	−	0.274431i	$-0.911511\pi$
$547$	−16.8035	−	29.1046i	−0.718467	−	1.24442i	0.243140	−	0.969991i	$-0.421823\pi$
$548$		0			0
$549$	2.05472	−	3.55888i	0.0876933	−	0.151889i
$550$		0			0
$551$	−37.1946			−1.58454
$552$		0			0
$553$	21.5204	−	37.2745i	0.915142	−	1.58507i
$554$		0			0
$555$	−1.11772	+	1.93594i	−0.0474445	+	0.0821763i
$556$		0			0
$557$	−11.1311	−	19.2797i	−0.471641	−	0.816906i	0.527833	−	0.849348i	$-0.323005\pi$
$557$	−11.1311	−	19.2797i	−0.471641	−	0.816906i	−0.999474	+	0.0324423i	$0.989671\pi$
$558$		0			0
$559$	0.657908	−	1.13953i	0.0278265	−	0.0481970i
$560$		0			0
$561$	−29.2715			−1.23585
$562$		0			0
$563$	25.7160			1.08380			0.541900	−	0.840443i	$-0.317705\pi$
$563$	25.7160			1.08380			0.541900	+	0.840443i	$0.317705\pi$
$564$		0			0
$565$	2.00309	+	3.46945i	0.0842707	+	0.145961i
$566$		0			0
$567$	−1.97947	−	3.42854i	−0.0831299	−	0.143985i
$568$		0			0
$569$	15.8233	+	27.4067i	0.663346	+	1.14895i	0.979731	+	0.200318i	$0.0641976\pi$
$569$	15.8233	+	27.4067i	0.663346	+	1.14895i	−0.316385	+	0.948631i	$0.602469\pi$
$570$		0			0
$571$	16.7560	+	29.0222i	0.701216	+	1.21454i	0.968040	+	0.250797i	$0.0806927\pi$
$571$	16.7560	+	29.0222i	0.701216	+	1.21454i	−0.266823	+	0.963745i	$0.585974\pi$
$572$		0			0
$573$	10.1207	−	17.5296i	0.422800	−	0.732311i
$574$		0			0
$575$	−0.424239	+	0.734804i	−0.0176920	+	0.0306434i
$576$		0			0
$577$	0.415912	+	0.720381i	0.0173147	+	0.0299899i	0.874553	−	0.484930i	$-0.161155\pi$
$577$	0.415912	+	0.720381i	0.0173147	+	0.0299899i	−0.857238	+	0.514920i	$0.827822\pi$
$578$		0			0
$579$	14.5283			0.603775
$580$		0			0
$581$	56.4387			2.34147
$582$		0			0
$583$	15.2842	+	26.4730i	0.633006	+	1.09640i
$584$		0			0
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$		0			0
$587$	6.16996	−	10.6867i	0.254662	−	0.441087i	−0.710142	−	0.704058i	$-0.751369\pi$
$587$	6.16996	−	10.6867i	0.254662	−	0.441087i	0.964804	+	0.262972i	$0.0847026\pi$
$588$		0			0
$589$	25.9216			1.06808
$590$		0			0
$591$	−9.09213	−	15.7480i	−0.374000	−	0.647788i
$592$		0			0
$593$	−15.5680	+	26.9646i	−0.639301	+	1.10730i	0.346285	+	0.938129i	$0.387443\pi$
$593$	−15.5680	+	26.9646i	−0.639301	+	1.10730i	−0.985586	+	0.169173i	$0.945890\pi$
$594$		0			0
$595$	26.5603			1.08887
$596$		0			0
$597$	8.55072	−	14.8103i	0.349958	−	0.606144i
$598$		0			0
$599$	−8.52117	−	14.7591i	−0.348166	−	0.603041i	0.637758	−	0.770237i	$-0.279862\pi$
$599$	−8.52117	−	14.7591i	−0.348166	−	0.603041i	−0.985924	+	0.167196i	$0.946529\pi$
$600$		0			0
$601$	−16.7192	+	28.9585i	−0.681990	+	1.18124i	0.292382	+	0.956302i	$0.405552\pi$
$601$	−16.7192	+	28.9585i	−0.681990	+	1.18124i	−0.974373	+	0.224940i	$0.927781\pi$
$602$		0			0
$603$	−7.15002	−	3.98462i	−0.291171	−	0.162266i
$604$		0			0
$605$	4.01813	−	6.95961i	0.163360	−	0.282948i
$606$		0			0
$607$	−5.28329	−	9.15092i	−0.214442	−	0.371425i	0.738658	−	0.674081i	$-0.235460\pi$
$607$	−5.28329	−	9.15092i	−0.214442	−	0.371425i	−0.953100	+	0.302656i	$0.902127\pi$
$608$		0			0
$609$	17.0595	−	29.5479i	0.691285	−	1.19734i
$610$		0			0
$611$	−13.3583			−0.540417
$612$		0			0
$613$	11.3932	−	19.7336i	0.460168	−	0.797034i	−0.538801	−	0.842433i	$-0.681123\pi$
$613$	11.3932	−	19.7336i	0.460168	−	0.797034i	0.998969	+	0.0453992i	$0.0144560\pi$
$614$		0			0
$615$	−3.92733	−	6.80233i	−0.158365	−	0.274297i
$616$		0			0
$617$	21.0600			0.847844			0.423922	−	0.905699i	$-0.360653\pi$
$617$	21.0600			0.847844			0.423922	+	0.905699i	$0.360653\pi$
$618$		0			0
$619$	−4.21495	+	7.30051i	−0.169413	+	0.293432i	−0.938214	−	0.346056i	$-0.887521\pi$
$619$	−4.21495	+	7.30051i	−0.169413	+	0.293432i	0.768800	+	0.639489i	$0.220854\pi$
$620$		0			0
$621$	−0.424239	+	0.734804i	−0.0170241	+	0.0294867i
$622$		0			0
$623$	−12.6294	−	21.8748i	−0.505988	−	0.876397i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	18.8301			0.752004
$628$		0			0
$629$	−7.49872	−	12.9882i	−0.298994	−	0.517872i
$630$		0			0
$631$	21.3406	−	36.9629i	0.849554	−	1.47147i	−0.0320521	−	0.999486i	$-0.510204\pi$
$631$	21.3406	−	36.9629i	0.849554	−	1.47147i	0.881606	−	0.471985i	$-0.156462\pi$
$632$		0			0
$633$	−0.454624	+	0.787433i	−0.0180697	+	0.0312976i
$634$		0			0
$635$	−3.30834	−	5.73021i	−0.131287	−	0.227396i
$636$		0			0
$637$	4.33660	+	7.51122i	0.171822	+	0.297605i
$638$		0			0
$639$	4.80052	+	8.31475i	0.189906	+	0.328926i
$640$		0			0
$641$	−12.9298	−	22.3951i	−0.510698	−	0.884554i	−0.999923	−	0.0123971i	$-0.996054\pi$
$641$	−12.9298	−	22.3951i	−0.510698	−	0.884554i	0.489225	−	0.872157i	$-0.337280\pi$
$642$		0			0
$643$	−46.2568			−1.82419			−0.912095	−	0.409979i	$-0.865536\pi$
$643$	−46.2568			−1.82419			−0.912095	+	0.409979i	$0.865536\pi$
$644$		0			0
$645$	−1.31582			−0.0518102
$646$		0			0
$647$	−10.9665	+	18.9945i	−0.431136	+	0.746749i	−0.996971	−	0.0777688i	$-0.975220\pi$
$647$	−10.9665	+	18.9945i	−0.431136	+	0.746749i	0.565835	+	0.824518i	$0.308554\pi$
$648$		0			0
$649$	30.8871	+	53.4981i	1.21243	+	2.09998i
$650$		0			0
$651$	−11.8891	+	20.5924i	−0.465969	+	0.807082i
$652$		0			0
$653$	−6.57696	+	11.3916i	−0.257376	+	0.445789i	−0.965538	−	0.260261i	$-0.916191\pi$
$653$	−6.57696	+	11.3916i	−0.257376	+	0.445789i	0.708162	+	0.706050i	$0.249525\pi$
$654$		0			0
$655$	4.90072			0.191487
$656$		0			0
$657$	−6.96101	+	12.0568i	−0.271575	+	0.470381i
$658$		0			0
$659$	−12.7207	−	22.0329i	−0.495528	−	0.858280i	0.504459	−	0.863436i	$-0.331692\pi$
$659$	−12.7207	−	22.0329i	−0.495528	−	0.858280i	−0.999987	+	0.00515602i	$0.998359\pi$
$660$		0			0
$661$	−5.23129			−0.203474			−0.101737	−	0.994811i	$-0.532440\pi$
$661$	−5.23129			−0.203474			−0.101737	+	0.994811i	$0.532440\pi$
$662$		0			0
$663$	−3.35448	−	5.81012i	−0.130277	−	0.225647i
$664$		0			0
$665$	−17.0861			−0.662569
$666$		0			0
$667$	−7.31236			−0.283136
$668$		0			0
$669$	−11.2090			−0.433364
$670$		0			0
$671$	−17.9297			−0.692169
$672$		0			0
$673$	31.6884			1.22150			0.610750	−	0.791824i	$-0.290868\pi$
$673$	31.6884			1.22150			0.610750	+	0.791824i	$0.290868\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−21.7040	−	37.5924i	−0.834153	−	1.44479i	−0.894719	−	0.446630i	$-0.852624\pi$
$677$	−21.7040	−	37.5924i	−0.834153	−	1.44479i	0.0605660	−	0.998164i	$-0.480709\pi$
$678$		0			0
$679$	−34.6141			−1.32837
$680$		0			0
$681$	−6.10551	−	10.5751i	−0.233964	−	0.405237i
$682$		0			0
$683$	1.74570	−	3.02364i	0.0667973	−	0.115696i	−0.830693	−	0.556731i	$-0.812055\pi$
$683$	1.74570	−	3.02364i	0.0667973	−	0.115696i	0.897490	+	0.441035i	$0.145389\pi$
$684$		0			0
$685$	4.43762			0.169553
$686$		0			0
$687$	10.5194	−	18.2201i	0.401340	−	0.695142i
$688$		0			0
$689$	−3.50309	+	6.06753i	−0.133457	+	0.231155i
$690$		0			0
$691$	−18.0300	−	31.2289i	−0.685894	−	1.18800i	−0.973155	−	0.230151i	$-0.926078\pi$
$691$	−18.0300	−	31.2289i	−0.685894	−	1.18800i	0.287261	−	0.957852i	$-0.407255\pi$
$692$		0			0
$693$	−8.63654	+	14.9589i	−0.328075	+	0.568243i
$694$		0			0
$695$	9.99157			0.379002
$696$		0			0
$697$	52.6966			1.99602
$698$		0			0
$699$	−6.47656	−	11.2177i	−0.244966	−	0.424294i
$700$		0			0
$701$	17.1927	+	29.7787i	0.649361	+	1.12473i	0.983276	+	0.182123i	$0.0582968\pi$
$701$	17.1927	+	29.7787i	0.649361	+	1.12473i	−0.333915	+	0.942603i	$0.608370\pi$
$702$		0			0
$703$	4.82386	+	8.35518i	0.181936	+	0.315122i
$704$		0			0
$705$	6.67913	+	11.5686i	0.251551	+	0.435698i
$706$		0			0
$707$	−34.0602	+	58.9940i	−1.28097	+	2.21870i
$708$		0			0
$709$	19.7289	−	34.1715i	0.740936	−	1.28334i	−0.211134	−	0.977457i	$-0.567716\pi$
$709$	19.7289	−	34.1715i	0.740936	−	1.28334i	0.952070	−	0.305881i	$-0.0989510\pi$
$710$		0			0
$711$	5.43591	+	9.41527i	0.203863	+	0.353100i
$712$		0			0
$713$	5.09611			0.190851
$714$		0			0
$715$	4.36306			0.163169
$716$		0			0
$717$	11.4761	+	19.8772i	0.428583	+	0.742327i
$718$		0			0
$719$	−9.03380	+	15.6470i	−0.336904	+	0.583535i	−0.983849	−	0.179002i	$-0.942713\pi$
$719$	−9.03380	+	15.6470i	−0.336904	+	0.583535i	0.646945	+	0.762537i	$0.276046\pi$
$720$		0			0
$721$	−24.1703	+	41.8643i	−0.900151	+	1.55911i
$722$		0			0
$723$	14.0901			0.524016
$724$		0			0
$725$	4.30910	+	7.46358i	0.160036	+	0.277191i
$726$		0			0
$727$	−5.00748	+	8.67321i	−0.185717	+	0.321672i	−0.943818	−	0.330466i	$-0.892794\pi$
$727$	−5.00748	+	8.67321i	−0.185717	+	0.321672i	0.758101	+	0.652137i	$0.226127\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.41387	−	7.64505i	0.163253	−	0.282763i
$732$		0			0
$733$	9.00652	+	15.5998i	0.332663	+	0.576190i	0.983033	−	0.183428i	$-0.0587194\pi$
$733$	9.00652	+	15.5998i	0.332663	+	0.576190i	−0.650370	+	0.759618i	$0.725386\pi$
$734$		0			0
$735$	4.33660	−	7.51122i	0.159958	−	0.277055i
$736$		0			0
$737$	0.542009	+	35.7090i	0.0199652	+	1.31536i
$738$		0			0
$739$	12.2428	−	21.2052i	0.450360	−	0.780047i	−0.548048	−	0.836447i	$-0.684629\pi$
$739$	12.2428	−	21.2052i	0.450360	−	0.780047i	0.998408	+	0.0564001i	$0.0179622\pi$
$740$		0			0
$741$	2.15791	+	3.73761i	0.0792727	+	0.137304i
$742$		0			0
$743$	16.4040	−	28.4125i	0.601803	−	1.04235i	−0.390745	−	0.920499i	$-0.627783\pi$
$743$	16.4040	−	28.4125i	0.601803	−	1.04235i	0.992548	−	0.121855i	$-0.0388842\pi$
$744$		0			0
$745$	18.3618			0.672725
$746$		0			0
$747$	−7.12801	+	12.3461i	−0.260800	+	0.451719i
$748$		0			0
$749$	4.73917	+	8.20848i	0.173165	+	0.299931i
$750$		0			0
$751$	−11.8487			−0.432365			−0.216182	−	0.976353i	$-0.569361\pi$
$751$	−11.8487			−0.432365			−0.216182	+	0.976353i	$0.569361\pi$
$752$		0			0
$753$	−13.1209	+	22.7261i	−0.478153	+	0.828185i
$754$		0			0
$755$	8.48026	−	14.6882i	0.308628	−	0.534560i
$756$		0			0
$757$	−10.3643	−	17.9514i	−0.376695	−	0.652455i	0.613884	−	0.789396i	$-0.289606\pi$
$757$	−10.3643	−	17.9514i	−0.376695	−	0.652455i	−0.990579	+	0.136941i	$0.956273\pi$
$758$		0			0
$759$	3.70196			0.134373
$760$		0			0
$761$	−30.6742			−1.11194			−0.555969	−	0.831203i	$-0.687653\pi$
$761$	−30.6742			−1.11194			−0.555969	+	0.831203i	$0.687653\pi$
$762$		0			0
$763$	−13.8212	−	23.9390i	−0.500362	−	0.866652i
$764$		0			0
$765$	−3.35448	+	5.81012i	−0.121281	+	0.210066i
$766$		0			0
$767$	−7.07924	+	12.2616i	−0.255616	+	0.442741i
$768$		0			0
$769$	10.0510	+	17.4088i	0.362447	+	0.627777i	0.988363	−	0.152113i	$-0.0486079\pi$
$769$	10.0510	+	17.4088i	0.362447	+	0.627777i	−0.625916	+	0.779891i	$0.715275\pi$
$770$		0			0
$771$	−0.398370	−	0.689997i	−0.0143469	−	0.0248496i
$772$		0			0
$773$	−17.9354	−	31.0651i	−0.645093	−	1.11733i	−0.984280	−	0.176615i	$-0.943485\pi$
$773$	−17.9354	−	31.0651i	−0.645093	−	1.11733i	0.339187	−	0.940719i	$-0.389848\pi$
$774$		0			0
$775$	−3.00309	−	5.20151i	−0.107874	−	0.186844i
$776$		0			0
$777$	−8.84996			−0.317490
$778$		0			0
$779$	−33.8993			−1.21457
$780$		0			0
$781$	20.9450	−	36.2777i	0.749469	−	1.29812i
$782$		0			0
$783$	4.30910	+	7.46358i	0.153995	+	0.266727i
$784$		0			0
$785$	1.40946	−	2.44125i	0.0503056	−	0.0871319i
$786$		0			0
$787$	4.53956	−	7.86275i	0.161818	−	0.280277i	−0.773703	−	0.633549i	$-0.781598\pi$
$787$	4.53956	−	7.86275i	0.161818	−	0.280277i	0.935521	+	0.353272i	$0.114931\pi$
$788$		0			0
$789$	11.3215			0.403056
$790$		0			0
$791$	−7.93012	+	13.7354i	−0.281962	+	0.488373i
$792$		0			0
$793$	−2.05472	−	3.55888i	−0.0729653	−	0.126380i
$794$		0			0
$795$	7.00618			0.248484
$796$		0			0
$797$	−10.8441	−	18.7825i	−0.384116	−	0.665309i	0.607530	−	0.794297i	$-0.292160\pi$
$797$	−10.8441	−	18.7825i	−0.384116	−	0.665309i	−0.991646	+	0.128988i	$0.958827\pi$
$798$		0			0
$799$	−89.6200			−3.17053
$800$		0			0
$801$	6.38022			0.225434
$802$		0			0
$803$	60.7426			2.14356
$804$		0			0
$805$	−3.35907			−0.118392
$806$		0			0
$807$	−24.5113			−0.862839
$808$		0			0
$809$	8.41561			0.295877			0.147938	−	0.988997i	$-0.452736\pi$
$809$	8.41561			0.295877			0.147938	+	0.988997i	$0.452736\pi$
$810$		0			0
$811$	16.3989	+	28.4037i	0.575844	+	0.997390i	0.995949	+	0.0899153i	$0.0286596\pi$
$811$	16.3989	+	28.4037i	0.575844	+	0.997390i	−0.420106	+	0.907475i	$0.638007\pi$
$812$		0			0
$813$	4.51034			0.158185
$814$		0			0
$815$	−6.87930	−	11.9153i	−0.240971	−	0.417375i
$816$		0			0
$817$	−2.83941	+	4.91800i	−0.0993383	+	0.172059i
$818$		0			0
$819$	−3.95894			−0.138337
$820$		0			0
$821$	21.6575	−	37.5119i	0.755851	−	1.30917i	−0.189099	−	0.981958i	$-0.560557\pi$
$821$	21.6575	−	37.5119i	0.755851	−	1.30917i	0.944950	−	0.327215i	$-0.106110\pi$
$822$		0			0
$823$	1.26066	−	2.18353i	0.0439439	−	0.0761131i	−0.843217	−	0.537574i	$-0.819341\pi$
$823$	1.26066	−	2.18353i	0.0439439	−	0.0761131i	0.887161	+	0.461460i	$0.152674\pi$
$824$		0			0
$825$	−2.18153	−	3.77852i	−0.0759511	−	0.131551i
$826$		0			0
$827$	−6.10538	+	10.5748i	−0.212305	+	0.367723i	−0.952436	−	0.304740i	$-0.901430\pi$
$827$	−6.10538	+	10.5748i	−0.212305	+	0.367723i	0.740130	+	0.672463i	$0.234764\pi$
$828$		0			0
$829$	30.3751			1.05497			0.527486	−	0.849564i	$-0.323135\pi$
$829$	30.3751			1.05497			0.527486	+	0.849564i	$0.323135\pi$
$830$		0			0
$831$	3.58700			0.124432
$832$		0			0
$833$	29.0941	+	50.3924i	1.00805	+	1.74599i
$834$		0			0
$835$	−5.99265	−	10.3796i	−0.207384	−	0.359200i
$836$		0			0
$837$	−3.00309	−	5.20151i	−0.103802	−	0.179790i
$838$		0			0
$839$	−8.21876	−	14.2353i	−0.283743	−	0.491457i	0.688561	−	0.725179i	$-0.258243\pi$
$839$	−8.21876	−	14.2353i	−0.283743	−	0.491457i	−0.972304	+	0.233721i	$0.924910\pi$
$840$		0			0
$841$	−22.6367	+	39.2079i	−0.780576	+	1.35200i
$842$		0			0
$843$	−0.0765554	+	0.132598i	−0.00263671	+	0.00456691i
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	31.8151			1.09318
$848$		0			0
$849$	11.3325			0.388929
$850$		0			0
$851$	0.948359	+	1.64261i	0.0325093	+	0.0563078i
$852$		0			0
$853$	6.31561	−	10.9390i	0.216242	−	0.374543i	−0.737414	−	0.675441i	$-0.763953\pi$
$853$	6.31561	−	10.9390i	0.216242	−	0.374543i	0.953656	+	0.300898i	$0.0972865\pi$
$854$		0			0
$855$	2.15791	−	3.73761i	0.0737989	−	0.127823i
$856$		0			0
$857$	43.7830			1.49560			0.747799	−	0.663925i	$-0.231111\pi$
$857$	43.7830			1.49560			0.747799	+	0.663925i	$0.231111\pi$
$858$		0			0
$859$	7.68926	+	13.3182i	0.262354	+	0.454411i	0.966867	−	0.255280i	$-0.0821677\pi$
$859$	7.68926	+	13.3182i	0.262354	+	0.454411i	−0.704513	+	0.709691i	$0.748834\pi$
$860$		0			0
$861$	15.5481	−	26.9300i	0.529877	−	0.917773i
$862$		0			0
$863$	−29.7293			−1.01200			−0.505999	−	0.862534i	$-0.668876\pi$
$863$	−29.7293			−1.01200			−0.505999	+	0.862534i	$0.668876\pi$
$864$		0			0
$865$	−9.98946	+	17.3022i	−0.339652	+	0.588294i
$866$		0			0
$867$	−14.0050	−	24.2574i	−0.475636	−	0.823826i
$868$		0			0
$869$	23.7172	−	41.0794i	0.804550	−	1.39352i
$870$		0			0
$871$	−7.02579	+	4.19979i	−0.238060	+	0.142304i
$872$		0			0
$873$	4.37164	−	7.57190i	0.147957	−	0.256270i
$874$		0			0
$875$	1.97947	+	3.42854i	0.0669183	+	0.115906i
$876$		0			0
$877$	19.4259	−	33.6467i	0.655966	−	1.13617i	−0.325684	−	0.945479i	$-0.605595\pi$
$877$	19.4259	−	33.6467i	0.655966	−	1.13617i	0.981651	−	0.190688i	$-0.0610720\pi$
$878$		0			0
$879$	−10.6224			−0.358284
$880$		0			0
$881$	5.52637	−	9.57196i	0.186188	−	0.322488i	−0.757788	−	0.652501i	$-0.773720\pi$
$881$	5.52637	−	9.57196i	0.186188	−	0.322488i	0.943976	+	0.330013i	$0.107053\pi$
$882$		0			0
$883$	−17.0577	−	29.5448i	−0.574038	−	0.994263i	−0.996145	−	0.0877170i	$-0.972043\pi$
$883$	−17.0577	−	29.5448i	−0.574038	−	0.994263i	0.422108	−	0.906546i	$-0.361290\pi$
$884$		0			0
$885$	14.1585			0.475932
$886$		0			0
$887$	15.1322	−	26.2097i	0.508089	−	0.880035i	−0.491867	−	0.870670i	$-0.663686\pi$
$887$	15.1322	−	26.2097i	0.508089	−	0.880035i	0.999956	−	0.00936530i	$-0.00298111\pi$
$888$		0			0
$889$	13.0975	−	22.6855i	0.439276	−	0.760849i
$890$		0			0
$891$	−2.18153	−	3.77852i	−0.0730839	−	0.126585i
$892$		0			0
$893$	57.6518			1.92924
$894$		0			0
$895$	23.3128			0.779261
$896$		0			0
$897$	0.424239	+	0.734804i	0.0141649	+	0.0245344i
$898$		0			0
$899$	25.8812	−	44.8276i	0.863188	−	1.49509i
$900$		0			0
$901$	−23.5021	+	40.7068i	−0.782968	+	1.35614i
$902$		0			0
$903$	−2.60462	−	4.51133i	−0.0866763	−	0.150128i
$904$		0			0
$905$	−3.01915	−	5.22932i	−0.100360	−	0.173829i
$906$		0			0
$907$	18.8376	+	32.6276i	0.625491	+	1.08338i	0.988446	+	0.151575i	$0.0484345\pi$
$907$	18.8376	+	32.6276i	0.625491	+	1.08338i	−0.362955	+	0.931807i	$0.618232\pi$
$908$		0			0
$909$	−8.60337	−	14.9015i	−0.285356	−	0.494251i
$910$		0			0
$911$	1.45688			0.0482687			0.0241343	−	0.999709i	$-0.492317\pi$
$911$	1.45688			0.0482687			0.0241343	+	0.999709i	$0.492317\pi$
$912$		0			0
$913$	62.1998			2.05851
$914$		0			0
$915$	−2.05472	+	3.55888i	−0.0679270	+	0.117653i
$916$		0			0
$917$	9.70083	+	16.8023i	0.320350	+	0.554862i
$918$		0			0
$919$	24.0682	−	41.6874i	0.793937	−	1.37514i	−0.129575	−	0.991570i	$-0.541361\pi$
$919$	24.0682	−	41.6874i	0.793937	−	1.37514i	0.923512	−	0.383569i	$-0.125305\pi$
$920$		0			0
$921$	10.4106	−	18.0317i	0.343041	−	0.594165i
$922$		0			0
$923$	9.60104			0.316022
$924$		0			0
$925$	1.11772	−	1.93594i	0.0367503	−	0.0636535i
$926$		0			0
$927$	−6.10526	−	10.5746i	−0.200523	−	0.347316i
$928$		0			0
$929$	19.8678			0.651842			0.325921	−	0.945397i	$-0.394326\pi$
$929$	19.8678			0.651842			0.325921	+	0.945397i	$0.394326\pi$
$930$		0			0
$931$	−18.7160	−	32.4170i	−0.613391	−	1.06243i
$932$		0			0
$933$	−0.0767132			−0.00251148
$934$		0			0
$935$	29.2715			0.957282
$936$		0			0
$937$	32.4928			1.06150			0.530748	−	0.847530i	$-0.321911\pi$
$937$	32.4928			1.06150			0.530748	+	0.847530i	$0.321911\pi$
$938$		0			0
$939$	−1.60053			−0.0522313
$940$		0			0
$941$	−26.3640			−0.859443			−0.429722	−	0.902961i	$-0.641388\pi$
$941$	−26.3640			−0.859443			−0.429722	+	0.902961i	$0.641388\pi$
$942$		0			0
$943$	−6.66451			−0.217026
$944$		0			0
$945$	1.97947	+	3.42854i	0.0643922	+	0.111531i
$946$		0			0
$947$	28.1316			0.914155			0.457077	−	0.889427i	$-0.348896\pi$
$947$	28.1316			0.914155			0.457077	+	0.889427i	$0.348896\pi$
$948$		0			0
$949$	6.96101	+	12.0568i	0.225964	+	0.391381i
$950$		0			0
$951$	−8.97827	+	15.5508i	−0.291140	+	0.504270i
$952$		0			0
$953$	−26.5318			−0.859451			−0.429725	−	0.902960i	$-0.641390\pi$
$953$	−26.5318			−0.859451			−0.429725	+	0.902960i	$0.641390\pi$
$954$		0			0
$955$	−10.1207	+	17.5296i	−0.327499	+	0.567245i
$956$		0			0
$957$	18.8009	−	32.5640i	0.607745	−	1.05265i
$958$		0			0
$959$	8.78413	+	15.2146i	0.283655	+	0.491304i
$960$		0			0
$961$	−2.53710	+	4.39439i	−0.0818421	+	0.141755i
$962$		0			0
$963$	−2.39416			−0.0771507
$964$		0			0
$965$	−14.5283			−0.467682
$966$		0			0
$967$	−7.69009	−	13.3196i	−0.247297	−	0.428330i	0.715478	−	0.698635i	$-0.246209\pi$
$967$	−7.69009	−	13.3196i	−0.247297	−	0.428330i	−0.962775	+	0.270305i	$0.912876\pi$
$968$		0			0
$969$	14.4773	+	25.0754i	0.465078	+	0.805539i
$970$		0			0
$971$	14.9477	+	25.8902i	0.479696	+	0.830857i	0.999729	−	0.0232890i	$-0.00741378\pi$
$971$	14.9477	+	25.8902i	0.479696	+	0.830857i	−0.520033	+	0.854146i	$0.674080\pi$
$972$		0			0
$973$	19.7780	+	34.2565i	0.634054	+	1.09821i
$974$		0			0
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$		0			0
$977$	17.7764	−	30.7897i	0.568719	−	0.985050i	−0.427974	−	0.903791i	$-0.640773\pi$
$977$	17.7764	−	30.7897i	0.568719	−	0.985050i	0.996693	−	0.0812589i	$-0.0258941\pi$
$978$		0			0
$979$	−13.9186	−	24.1078i	−0.444841	−	0.770487i
$980$		0			0
$981$	6.98228			0.222927
$982$		0			0
$983$	20.0432			0.639277			0.319639	−	0.947540i	$-0.396438\pi$
$983$	20.0432			0.639277			0.319639	+	0.947540i	$0.396438\pi$
$984$		0			0
$985$	9.09213	+	15.7480i	0.289699	+	0.501774i
$986$		0			0
$987$	−26.4423	+	45.7994i	−0.841667	+	1.45781i
$988$		0			0
$989$	−0.558221	+	0.966866i	−0.0177504	+	0.0307446i
$990$		0			0
$991$	41.6063			1.32167			0.660833	−	0.750533i	$-0.270203\pi$
$991$	41.6063			1.32167			0.660833	+	0.750533i	$0.270203\pi$
$992$		0			0
$993$	−17.7325	−	30.7136i	−0.562724	−	0.974666i
$994$		0			0
$995$	−8.55072	+	14.8103i	−0.271076	+	0.469517i
$996$		0			0
$997$	−12.3386			−0.390767			−0.195383	−	0.980727i	$-0.562595\pi$
$997$	−12.3386			−0.390767			−0.195383	+	0.980727i	$0.562595\pi$
$998$		0			0
$999$	1.11772	−	1.93594i	0.0353630	−	0.0612506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.j.3781.2	yes	12
67.37	even	3	inner	4020.2.q.j.841.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.j.841.2	✓	12	67.37	even	3	inner
4020.2.q.j.3781.2	yes	12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-1.97947 - 3.42854i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-1.97947 - 3.42854i) q^{7} +1.00000 q^{9} +(-2.18153 - 3.77852i) q^{11} +(0.500000 - 0.866025i) q^{13} -1.00000 q^{15} +(3.35448 - 5.81012i) q^{17} +(-2.15791 + 3.73761i) q^{19} +(-1.97947 - 3.42854i) q^{21} +(-0.424239 + 0.734804i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(4.30910 + 7.46358i) q^{29} +(-3.00309 - 5.20151i) q^{31} +(-2.18153 - 3.77852i) q^{33} +(1.97947 + 3.42854i) q^{35} +(1.11772 - 1.93594i) q^{37} +(0.500000 - 0.866025i) q^{39} +(3.92733 + 6.80233i) q^{41} +1.31582 q^{43} -1.00000 q^{45} +(-6.67913 - 11.5686i) q^{47} +(-4.33660 + 7.51122i) q^{49} +(3.35448 - 5.81012i) q^{51} -7.00618 q^{53} +(2.18153 + 3.77852i) q^{55} +(-2.15791 + 3.73761i) q^{57} -14.1585 q^{59} +(2.05472 - 3.55888i) q^{61} +(-1.97947 - 3.42854i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(-7.15002 - 3.98462i) q^{67} +(-0.424239 + 0.734804i) q^{69} +(4.80052 + 8.31475i) q^{71} +(-6.96101 + 12.0568i) q^{73} +1.00000 q^{75} +(-8.63654 + 14.9589i) q^{77} +(5.43591 + 9.41527i) q^{79} +1.00000 q^{81} +(-7.12801 + 12.3461i) q^{83} +(-3.35448 + 5.81012i) q^{85} +(4.30910 + 7.46358i) q^{87} +6.38022 q^{89} -3.95894 q^{91} +(-3.00309 - 5.20151i) q^{93} +(2.15791 - 3.73761i) q^{95} +(4.37164 - 7.57190i) q^{97} +(-2.18153 - 3.77852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 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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