LMFDB - Embedded newform 315.2.j.f.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.827721 - 1.43366i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.2.j.f.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32772 + 2.29968i) q^{2} +(-2.52569 - 4.37462i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.35341 - 1.20891i) q^{7} +8.10275 q^{8} +O(q^{10})$	\(q+(-1.32772 + 2.29968i) q^{2} +(-2.52569 - 4.37462i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.35341 - 1.20891i) q^{7} +8.10275 q^{8} +(-1.32772 - 2.29968i) q^{10} +(-2.19797 - 3.80699i) q^{11} +3.39593 q^{13} +(5.90478 - 3.80699i) q^{14} +(-5.70682 + 9.88450i) q^{16} +(1.32772 + 2.29968i) q^{17} +(3.68113 - 6.37590i) q^{19} +5.05137 q^{20} +11.6731 q^{22} +(2.37910 - 4.12071i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.50885 + 7.80956i) q^{26} +(0.655442 + 13.3486i) q^{28} -3.70682 q^{29} +(-0.759511 - 1.31551i) q^{31} +(-7.05137 - 12.2133i) q^{32} -7.05137 q^{34} +(2.22365 - 1.43366i) q^{35} +(0.223653 - 0.387378i) q^{37} +(9.77503 + 16.9308i) q^{38} +(-4.05137 + 7.01719i) q^{40} -6.49868 q^{41} -1.13642 q^{43} +(-11.1027 + 19.2305i) q^{44} +(6.31755 + 10.9423i) q^{46} +(1.25951 - 2.18154i) q^{47} +(4.07706 + 5.69013i) q^{49} +2.65544 q^{50} +(-8.57706 - 14.8559i) q^{52} +(-2.65544 - 4.59936i) q^{53} +4.39593 q^{55} +(-19.0691 - 9.79551i) q^{56} +(4.92162 - 8.52449i) q^{58} +(-7.30071 - 12.6452i) q^{59} +(4.12976 - 7.15295i) q^{61} +4.03367 q^{62} +14.6218 q^{64} +(-1.69797 + 2.94096i) q^{65} +(3.95748 + 6.85455i) q^{67} +(6.70682 - 11.6165i) q^{68} +(0.344558 + 7.01719i) q^{70} +12.2258 q^{71} +(-7.53454 - 13.0502i) q^{73} +(0.593898 + 1.02866i) q^{74} -37.1895 q^{76} +(0.570395 + 11.6165i) q^{77} +(-1.28520 + 2.22603i) q^{79} +(-5.70682 - 9.88450i) q^{80} +(8.62844 - 14.9449i) q^{82} +0.552694 q^{83} -2.65544 q^{85} +(1.50885 - 2.61341i) q^{86} +(-17.8096 - 30.8471i) q^{88} +(6.45748 - 11.1847i) q^{89} +(-7.99201 - 4.10538i) q^{91} -24.0354 q^{92} +(3.34456 + 5.79294i) q^{94} +(3.68113 + 6.37590i) q^{95} -2.53235 q^{97} +(-18.4987 + 1.82103i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + q^7 + 12 * q^8	$ 6 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + q^{7} + 12 q^{8} - 2 q^{10} - 10 q^{11} + 14 q^{13} + 2 q^{14} - 4 q^{16} + 2 q^{17} + q^{19} + 12 q^{20} + 4 q^{22} - 10 q^{23} - 3 q^{25} - 8 q^{28} + 8 q^{29} + q^{31} - 24 q^{32} - 24 q^{34} + q^{35} - 11 q^{37} + 28 q^{38} - 6 q^{40} + 4 q^{41} - 6 q^{43} - 30 q^{44} + 16 q^{46} + 2 q^{47} - 3 q^{49} + 4 q^{50} - 24 q^{52} - 4 q^{53} + 20 q^{55} - 42 q^{56} + 14 q^{58} - 4 q^{59} + 22 q^{61} + 60 q^{62} + 40 q^{64} - 7 q^{65} + 15 q^{67} + 10 q^{68} + 14 q^{70} + 32 q^{71} - 9 q^{73} - 6 q^{74} - 60 q^{76} - 26 q^{77} + 7 q^{79} - 4 q^{80} + 6 q^{82} + 28 q^{83} - 4 q^{85} - 18 q^{86} - 40 q^{88} + 30 q^{89} - 3 q^{91} - 36 q^{92} + 32 q^{94} + q^{95} - 8 q^{97} - 68 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + q^7 + 12 * q^8 - 2 * q^10 - 10 * q^11 + 14 * q^13 + 2 * q^14 - 4 * q^16 + 2 * q^17 + q^19 + 12 * q^20 + 4 * q^22 - 10 * q^23 - 3 * q^25 - 8 * q^28 + 8 * q^29 + q^31 - 24 * q^32 - 24 * q^34 + q^35 - 11 * q^37 + 28 * q^38 - 6 * q^40 + 4 * q^41 - 6 * q^43 - 30 * q^44 + 16 * q^46 + 2 * q^47 - 3 * q^49 + 4 * q^50 - 24 * q^52 - 4 * q^53 + 20 * q^55 - 42 * q^56 + 14 * q^58 - 4 * q^59 + 22 * q^61 + 60 * q^62 + 40 * q^64 - 7 * q^65 + 15 * q^67 + 10 * q^68 + 14 * q^70 + 32 * q^71 - 9 * q^73 - 6 * q^74 - 60 * q^76 - 26 * q^77 + 7 * q^79 - 4 * q^80 + 6 * q^82 + 28 * q^83 - 4 * q^85 - 18 * q^86 - 40 * q^88 + 30 * q^89 - 3 * q^91 - 36 * q^92 + 32 * q^94 + q^95 - 8 * q^97 - 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.32772	+	2.29968i	−0.938841	+	1.62612i	−0.171203	+	0.985236i	$0.554765\pi$
$2$	−1.32772	+	2.29968i	−0.938841	+	1.62612i	−0.767638	+	0.640884i	$0.778568\pi$
$3$		0			0
$3$		0			0
$4$	−2.52569	−	4.37462i	−1.26284	−	2.18731i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.35341	−	1.20891i	−0.889505	−	0.456926i
$7$	−2.35341	−	1.20891i	−0.889505	−	0.456926i
$8$	8.10275			2.86475
$9$		0			0
$10$	−1.32772	−	2.29968i	−0.419862	−	0.727223i
$11$	−2.19797	−	3.80699i	−0.662712	−	1.14785i	−0.979900	−	0.199488i	$-0.936072\pi$
$11$	−2.19797	−	3.80699i	−0.662712	−	1.14785i	0.317189	−	0.948362i	$-0.397261\pi$
$12$		0			0
$13$	3.39593			0.941862			0.470931	−	0.882170i	$-0.343918\pi$
$13$	3.39593			0.941862			0.470931	+	0.882170i	$0.343918\pi$
$14$	5.90478	−	3.80699i	1.57812	−	1.01746i
$15$		0			0
$16$	−5.70682	+	9.88450i	−1.42670	+	2.47112i
$17$	1.32772	+	2.29968i	0.322020	+	0.557754i	0.980905	−	0.194489i	$-0.0623049\pi$
$17$	1.32772	+	2.29968i	0.322020	+	0.557754i	−0.658885	+	0.752244i	$0.728972\pi$
$18$		0			0
$19$	3.68113	−	6.37590i	0.844509	−	1.46273i	−0.0415379	−	0.999137i	$-0.513226\pi$
$19$	3.68113	−	6.37590i	0.844509	−	1.46273i	0.886047	−	0.463596i	$-0.153441\pi$
$20$	5.05137			1.12952
$21$		0			0
$22$	11.6731			2.48872
$23$	2.37910	−	4.12071i	0.496076	−	0.859228i	−0.503914	−	0.863754i	$-0.668107\pi$
$23$	2.37910	−	4.12071i	0.496076	−	0.859228i	0.999990	+	0.00452549i	$0.00144051\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−4.50885	+	7.80956i	−0.884258	+	1.53158i
$27$		0			0
$28$	0.655442	+	13.3486i	0.123867	+	2.52265i
$29$	−3.70682			−0.688339			−0.344169	−	0.938908i	$-0.611839\pi$
$29$	−3.70682			−0.688339			−0.344169	+	0.938908i	$0.611839\pi$
$30$		0			0
$31$	−0.759511	−	1.31551i	−0.136412	−	0.236273i	0.789724	−	0.613462i	$-0.210224\pi$
$31$	−0.759511	−	1.31551i	−0.136412	−	0.236273i	−0.926136	+	0.377190i	$0.876890\pi$
$32$	−7.05137	−	12.2133i	−1.24652	−	2.15903i
$33$		0			0
$34$	−7.05137			−1.20930
$35$	2.22365	−	1.43366i	0.375866	−	0.242332i
$36$		0			0
$37$	0.223653	−	0.387378i	0.0367683	−	0.0636846i	−0.847056	−	0.531504i	$-0.821627\pi$
$37$	0.223653	−	0.387378i	0.0367683	−	0.0636846i	0.883824	+	0.467820i	$0.154960\pi$
$38$	9.77503	+	16.9308i	1.58572	+	2.74655i
$39$		0			0
$40$	−4.05137	+	7.01719i	−0.640579	+	1.10951i
$41$	−6.49868			−1.01492			−0.507462	−	0.861674i	$-0.669416\pi$
$41$	−6.49868			−1.01492			−0.507462	+	0.861674i	$0.669416\pi$
$42$		0			0
$43$	−1.13642			−0.173303			−0.0866513	−	0.996239i	$-0.527617\pi$
$43$	−1.13642			−0.173303			−0.0866513	+	0.996239i	$0.527617\pi$
$44$	−11.1027	+	19.2305i	−1.67380	+	2.89911i
$45$		0			0
$46$	6.31755	+	10.9423i	0.931472	+	1.61336i
$47$	1.25951	−	2.18154i	0.183718	−	0.318210i	−0.759425	−	0.650594i	$-0.774520\pi$
$47$	1.25951	−	2.18154i	0.183718	−	0.318210i	0.943144	+	0.332385i	$0.107853\pi$
$48$		0			0
$49$	4.07706	+	5.69013i	0.582437	+	0.812876i
$50$	2.65544			0.375536
$51$		0			0
$52$	−8.57706	−	14.8559i	−1.18942	−	2.06014i
$53$	−2.65544	−	4.59936i	−0.364753	−	0.631771i	0.623983	−	0.781438i	$-0.285513\pi$
$53$	−2.65544	−	4.59936i	−0.364753	−	0.631771i	−0.988737	+	0.149667i	$0.952180\pi$
$54$		0			0
$55$	4.39593			0.592747
$56$	−19.0691	−	9.79551i	−2.54821	−	1.30898i
$57$		0			0
$58$	4.92162	−	8.52449i	0.646240	−	1.11932i
$59$	−7.30071	−	12.6452i	−0.950472	−	1.64627i	−0.744405	−	0.667728i	$-0.767267\pi$
$59$	−7.30071	−	12.6452i	−0.950472	−	1.64627i	−0.206067	−	0.978538i	$-0.566066\pi$
$60$		0			0
$61$	4.12976	−	7.15295i	0.528761	−	0.915841i	−0.470677	−	0.882306i	$-0.655990\pi$
$61$	4.12976	−	7.15295i	0.528761	−	0.915841i	0.999438	−	0.0335351i	$-0.0106765\pi$
$62$	4.03367			0.512277
$63$		0			0
$64$	14.6218			1.82772
$65$	−1.69797	+	2.94096i	−0.210607	+	0.364782i
$66$		0			0
$67$	3.95748	+	6.85455i	0.483483	+	0.837417i	0.999820	−	0.0189687i	$-0.00603827\pi$
$67$	3.95748	+	6.85455i	0.483483	+	0.837417i	−0.516337	+	0.856385i	$0.672705\pi$
$68$	6.70682	−	11.6165i	0.813321	−	1.40871i
$69$		0			0
$70$	0.344558	+	7.01719i	0.0411825	+	0.838714i
$71$	12.2258			1.45094			0.725470	−	0.688254i	$-0.241622\pi$
$71$	12.2258			1.45094			0.725470	+	0.688254i	$0.241622\pi$
$72$		0			0
$73$	−7.53454	−	13.0502i	−0.881851	−	1.52741i	−0.849281	−	0.527941i	$-0.822964\pi$
$73$	−7.53454	−	13.0502i	−0.881851	−	1.52741i	−0.0325700	−	0.999469i	$-0.510369\pi$
$74$	0.593898	+	1.02866i	0.0690392	+	0.119579i
$75$		0			0
$76$	−37.1895			−4.26593
$77$	0.570395	+	11.6165i	0.0650026	+	1.32383i
$78$		0			0
$79$	−1.28520	+	2.22603i	−0.144596	+	0.250448i	−0.929222	−	0.369522i	$-0.879522\pi$
$79$	−1.28520	+	2.22603i	−0.144596	+	0.250448i	0.784626	+	0.619969i	$0.212855\pi$
$80$	−5.70682	−	9.88450i	−0.638041	−	1.10512i
$81$		0			0
$82$	8.62844	−	14.9449i	0.952851	−	1.65039i
$83$	0.552694			0.0606660			0.0303330	−	0.999540i	$-0.490343\pi$
$83$	0.552694			0.0606660			0.0303330	+	0.999540i	$0.490343\pi$
$84$		0			0
$85$	−2.65544			−0.288023
$86$	1.50885	−	2.61341i	0.162704	−	0.281811i
$87$		0			0
$88$	−17.8096	−	30.8471i	−1.89851	−	3.28831i
$89$	6.45748	−	11.1847i	0.684491	−	1.18557i	−0.289105	−	0.957297i	$-0.593358\pi$
$89$	6.45748	−	11.1847i	0.684491	−	1.18557i	0.973596	−	0.228276i	$-0.0733089\pi$
$90$		0			0
$91$	−7.99201	−	4.10538i	−0.837791	−	0.430361i
$92$	−24.0354			−2.50586
$93$		0			0
$94$	3.34456	+	5.79294i	0.344965	+	0.597497i
$95$	3.68113	+	6.37590i	0.377676	+	0.654154i
$96$		0			0
$97$	−2.53235			−0.257122			−0.128561	−	0.991702i	$-0.541036\pi$
$97$	−2.53235			−0.257122			−0.128561	+	0.991702i	$0.541036\pi$
$98$	−18.4987	+	1.82103i	−1.86865	+	0.183952i
$99$		0			0
$100$	−2.52569	+	4.37462i	−0.252569	+	0.437462i
$101$	−1.71699	−	2.97391i	−0.170847	−	0.295915i	0.767869	−	0.640606i	$-0.221317\pi$
$101$	−1.71699	−	2.97391i	−0.170847	−	0.295915i	−0.938716	+	0.344691i	$0.887984\pi$
$102$		0			0
$103$	−6.61958	+	11.4655i	−0.652247	+	1.12973i	0.330329	+	0.943866i	$0.392840\pi$
$103$	−6.61958	+	11.4655i	−0.652247	+	1.12973i	−0.982576	+	0.185859i	$0.940493\pi$
$104$	27.5164			2.69820
$105$		0			0
$106$	14.1027			1.36978
$107$	−3.27635	+	5.67480i	−0.316736	+	0.548604i	−0.979805	−	0.199955i	$-0.935920\pi$
$107$	−3.27635	+	5.67480i	−0.316736	+	0.548604i	0.663069	+	0.748559i	$0.269254\pi$
$108$		0			0
$109$	6.33657	+	10.9753i	0.606934	+	1.05124i	0.991743	+	0.128244i	$0.0409339\pi$
$109$	6.33657	+	10.9753i	0.606934	+	1.05124i	−0.384809	+	0.922996i	$0.625733\pi$
$110$	−5.83657	+	10.1092i	−0.556495	+	0.963878i
$111$		0			0
$112$	25.3800	−	16.3632i	2.39818	−	1.54618i
$113$	−7.41363			−0.697416			−0.348708	−	0.937231i	$-0.613379\pi$
$113$	−7.41363			−0.697416			−0.348708	+	0.937231i	$0.613379\pi$
$114$		0			0
$115$	2.37910	+	4.12071i	0.221852	+	0.384259i
$116$	9.36226	+	16.2159i	0.869264	+	1.50561i
$117$		0			0
$118$	38.7733			3.56937
$119$	−0.344558	−	7.01719i	−0.0315855	−	0.643264i
$120$		0			0
$121$	−4.16211	+	7.20898i	−0.378373	+	0.655362i
$122$	10.9663	+	18.9942i	0.992845	+	1.71966i
$123$		0			0
$124$	−3.83657	+	6.64514i	−0.344534	+	0.596751i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−16.0177			−1.42134			−0.710671	−	0.703525i	$-0.751608\pi$
$127$	−16.0177			−1.42134			−0.710671	+	0.703525i	$0.751608\pi$
$128$	−5.31088	+	9.19872i	−0.469420	+	0.813060i
$129$		0			0
$130$	−4.50885	−	7.80956i	−0.395452	−	0.684944i
$131$	−1.12309	+	1.94525i	−0.0981248	+	0.169957i	−0.910908	−	0.412609i	$-0.864618\pi$
$131$	−1.12309	+	1.94525i	−0.0981248	+	0.169957i	0.812784	+	0.582566i	$0.197951\pi$
$132$		0			0
$133$	−16.3711	+	10.5549i	−1.41956	+	0.915229i
$134$	−21.0177			−1.81565
$135$		0			0
$136$	10.7582	+	18.6337i	0.922507	+	1.59783i
$137$	5.51552	+	9.55316i	0.471222	+	0.816181i	0.999458	−	0.0329166i	$-0.0104796\pi$
$137$	5.51552	+	9.55316i	0.471222	+	0.816181i	−0.528236	+	0.849098i	$0.677146\pi$
$138$		0			0
$139$	7.46501			0.633174			0.316587	−	0.948564i	$-0.397463\pi$
$139$	7.46501			0.633174			0.316587	+	0.948564i	$0.397463\pi$
$140$	−11.8879	−	6.10667i	−1.00471	−	0.516108i
$141$		0			0
$142$	−16.2325	+	28.1155i	−1.36220	+	2.35940i
$143$	−7.46414	−	12.9283i	−0.624183	−	1.08112i
$144$		0			0
$145$	1.85341	−	3.21020i	0.153917	−	0.266592i
$146$	40.0151			3.31167
$147$		0			0
$148$	−2.25951			−0.185731
$149$	−0.208136	+	0.360503i	−0.0170512	+	0.0295335i	−0.874425	−	0.485161i	$-0.838761\pi$
$149$	−0.208136	+	0.360503i	−0.0170512	+	0.0295335i	0.857374	+	0.514694i	$0.172094\pi$
$150$		0			0
$151$	9.23250	+	15.9912i	0.751330	+	1.30134i	0.947178	+	0.320708i	$0.103921\pi$
$151$	9.23250	+	15.9912i	0.751330	+	1.30134i	−0.195848	+	0.980634i	$0.562746\pi$
$152$	29.8273	−	51.6623i	2.41931	−	4.19037i
$153$		0			0
$154$	−27.4717	−	14.1118i	−2.21373	−	1.13716i
$155$	1.51902			0.122011
$156$		0			0
$157$	3.75819	+	6.50938i	0.299936	+	0.519505i	0.976121	−	0.217227i	$-0.0697012\pi$
$157$	3.75819	+	6.50938i	0.299936	+	0.519505i	−0.676185	+	0.736732i	$0.736368\pi$
$158$	−3.41277	−	5.91109i	−0.271505	−	0.470261i
$159$		0			0
$160$	14.1027			1.11492
$161$	−10.5806	+	6.82160i	−0.833865	+	0.537618i
$162$		0			0
$163$	3.60407	−	6.24243i	0.282292	−	0.488945i	−0.689657	−	0.724137i	$-0.742238\pi$
$163$	3.60407	−	6.24243i	0.282292	−	0.488945i	0.971949	+	0.235192i	$0.0755718\pi$
$164$	16.4136	+	28.4292i	1.28169	+	2.21995i
$165$		0			0
$166$	−0.733823	+	1.27102i	−0.0569557	+	0.0986502i
$167$	4.06908			0.314875			0.157437	−	0.987529i	$-0.449677\pi$
$167$	4.06908			0.314875			0.157437	+	0.987529i	$0.449677\pi$
$168$		0			0
$169$	−1.46765			−0.112896
$170$	3.52569	−	6.10667i	0.270408	−	0.468360i
$171$		0			0
$172$	2.87024	+	4.97141i	0.218854	+	0.379066i
$173$	−3.36226	+	5.82360i	−0.255628	+	0.442760i	−0.965066	−	0.262007i	$-0.915615\pi$
$173$	−3.36226	+	5.82360i	−0.255628	+	0.442760i	0.709438	+	0.704768i	$0.248949\pi$
$174$		0			0
$175$	0.129755	+	2.64257i	0.00980858	+	0.199759i
$176$	50.1736			3.78197
$177$		0			0
$178$	17.1475	+	29.7003i	1.28526	+	2.22613i
$179$	−1.74049	−	3.01462i	−0.130090	−	0.225323i	0.793621	−	0.608413i	$-0.208193\pi$
$179$	−1.74049	−	3.01462i	−0.130090	−	0.225323i	−0.923711	+	0.383090i	$0.874860\pi$
$180$		0			0
$181$	−5.53235			−0.411217			−0.205608	−	0.978634i	$-0.565917\pi$
$181$	−5.53235			−0.411217			−0.205608	+	0.978634i	$0.565917\pi$
$182$	20.0522	−	12.9283i	1.48637	−	0.958307i
$183$		0			0
$184$	19.2772	−	33.3891i	1.42113	−	2.46148i
$185$	0.223653	+	0.387378i	0.0164433	+	0.0284806i
$186$		0			0
$187$	5.83657	−	10.1092i	0.426812	−	0.739261i
$188$	−12.7245			−0.928031
$189$		0			0
$190$	−19.5501			−1.41831
$191$	6.36226	−	11.0198i	0.460357	−	0.797362i	−0.538622	−	0.842548i	$-0.681055\pi$
$191$	6.36226	−	11.0198i	0.460357	−	0.797362i	0.998979	+	0.0451862i	$0.0143881\pi$
$192$		0			0
$193$	2.74267	+	4.75045i	0.197422	+	0.341945i	0.947692	−	0.319187i	$-0.103410\pi$
$193$	2.74267	+	4.75045i	0.197422	+	0.341945i	−0.750270	+	0.661132i	$0.770076\pi$
$194$	3.36226	−	5.82360i	0.241396	−	0.418110i
$195$		0			0
$196$	14.5948	−	32.2071i	1.04248	−	2.30051i
$197$	14.5120			1.03394			0.516969	−	0.856004i	$-0.327060\pi$
$197$	14.5120			1.03394			0.516969	+	0.856004i	$0.327060\pi$
$198$		0			0
$199$	−2.71348	−	4.69989i	−0.192354	−	0.333166i	0.753676	−	0.657246i	$-0.228279\pi$
$199$	−2.71348	−	4.69989i	−0.192354	−	0.333166i	−0.946030	+	0.324080i	$0.894945\pi$
$200$	−4.05137	−	7.01719i	−0.286475	−	0.496190i
$201$		0			0
$202$	9.11872			0.641591
$203$	8.72365	+	4.48122i	0.612280	+	0.314520i
$204$		0			0
$205$	3.24934	−	5.62802i	0.226944	−	0.393078i
$206$	−17.5779	−	30.4459i	−1.22471	−	2.12126i
$207$		0			0
$208$	−19.3800	+	33.5671i	−1.34376	+	2.32746i
$209$	−32.3640			−2.23866
$210$		0			0
$211$	−18.1922			−1.25240			−0.626200	−	0.779662i	$-0.715391\pi$
$211$	−18.1922			−1.25240			−0.626200	+	0.779662i	$0.715391\pi$
$212$	−13.4136	+	23.2331i	−0.921252	+	1.59566i
$213$		0			0
$214$	−8.70015	−	15.0691i	−0.594730	−	1.03010i
$215$	0.568211	−	0.984170i	0.0387516	−	0.0671198i
$216$		0			0
$217$	0.197101	+	4.01412i	0.0133801	+	0.272496i
$218$	−33.6528			−2.27926
$219$		0			0
$220$	−11.1027	−	19.2305i	−0.748547	−	1.29652i
$221$	4.50885	+	7.80956i	0.303298	+	0.525328i
$222$		0			0
$223$	2.41627			0.161806			0.0809028	−	0.996722i	$-0.474220\pi$
$223$	2.41627			0.161806			0.0809028	+	0.996722i	$0.474220\pi$
$224$	1.82991	+	37.2675i	0.122266	+	2.49004i
$225$		0			0
$226$	9.84324	−	17.0490i	0.654762	−	1.13408i
$227$	10.6900	+	18.5156i	0.709519	+	1.22892i	0.965036	+	0.262118i	$0.0844210\pi$
$227$	10.6900	+	18.5156i	0.709519	+	1.22892i	−0.255517	+	0.966805i	$0.582246\pi$
$228$		0			0
$229$	6.29186	−	10.8978i	0.415778	−	0.720149i	−0.579732	−	0.814807i	$-0.696843\pi$
$229$	6.29186	−	10.8978i	0.415778	−	0.720149i	0.995510	+	0.0946587i	$0.0301760\pi$
$230$	−12.6351			−0.833134
$231$		0			0
$232$	−30.0354			−1.97192
$233$	−9.49868	+	16.4522i	−0.622279	+	1.07782i	0.366781	+	0.930307i	$0.380460\pi$
$233$	−9.49868	+	16.4522i	−0.622279	+	1.07782i	−0.989060	+	0.147512i	$0.952874\pi$
$234$		0			0
$235$	1.25951	+	2.18154i	0.0821614	+	0.142308i
$236$	−36.8786	+	63.8757i	−2.40060	+	4.15795i
$237$		0			0
$238$	16.5948	+	8.52449i	1.07568	+	0.552561i
$239$	23.5837			1.52550			0.762752	−	0.646691i	$-0.223848\pi$
$239$	23.5837			1.52550			0.762752	+	0.646691i	$0.223848\pi$
$240$		0			0
$241$	−2.36893	−	4.10310i	−0.152596	−	0.264304i	0.779585	−	0.626296i	$-0.215430\pi$
$241$	−2.36893	−	4.10310i	−0.152596	−	0.264304i	−0.932181	+	0.361992i	$0.882097\pi$
$242$	−11.0522	−	19.1430i	−0.710465	−	1.23056i
$243$		0			0
$244$	−41.7219			−2.67097
$245$	−6.96633	+	0.685774i	−0.445062	+	0.0438125i
$246$		0			0
$247$	12.5009	−	21.6521i	0.795411	−	1.37769i
$248$	−6.15412	−	10.6593i	−0.390787	−	0.676863i
$249$		0			0
$250$	−1.32772	+	2.29968i	−0.0839725	+	0.145445i
$251$	8.32859			0.525696			0.262848	−	0.964837i	$-0.415338\pi$
$251$	8.32859			0.525696			0.262848	+	0.964837i	$0.415338\pi$
$252$		0			0
$253$	−20.9167			−1.31502
$254$	21.2670	−	36.8356i	1.33441	−	2.31127i
$255$		0			0
$256$	0.519021	+	0.898971i	0.0324388	+	0.0561857i
$257$	−8.30738	+	14.3888i	−0.518200	+	0.897549i	0.481576	+	0.876404i	$0.340064\pi$
$257$	−8.30738	+	14.3888i	−0.518200	+	0.897549i	−0.999776	+	0.0211448i	$0.993269\pi$
$258$		0			0
$259$	−0.994654	+	0.641283i	−0.0618048	+	0.0398474i
$260$	17.1541			1.06385
$261$		0			0
$262$	−2.98230	−	5.16549i	−0.184247	−	0.319125i
$263$	−8.31088	−	14.3949i	−0.512471	−	0.887626i	−0.999895	−	0.0144608i	$-0.995397\pi$
$263$	−8.31088	−	14.3949i	−0.512471	−	0.887626i	0.487424	−	0.873165i	$-0.337936\pi$
$264$		0			0
$265$	5.31088			0.326245
$266$	−2.53672	−	51.6623i	−0.155536	−	3.16762i
$267$		0			0
$268$	19.9907	−	34.6249i	1.22113	−	2.11505i
$269$	9.86094	+	17.0796i	0.601232	+	1.04136i	0.992635	+	0.121145i	$0.0386566\pi$
$269$	9.86094	+	17.0796i	0.601232	+	1.04136i	−0.391403	+	0.920219i	$0.628010\pi$
$270$		0			0
$271$	6.57706	−	11.3918i	0.399528	−	0.692003i	−0.594140	−	0.804362i	$-0.702507\pi$
$271$	6.57706	−	11.3918i	0.399528	−	0.692003i	0.993668	+	0.112359i	$0.0358407\pi$
$272$	−30.3082			−1.83771
$273$		0			0
$274$	−29.2923			−1.76961
$275$	−2.19797	+	3.80699i	−0.132542	+	0.229570i
$276$		0			0
$277$	7.61958	+	13.1975i	0.457816	+	0.792961i	0.998845	−	0.0480427i	$-0.0152983\pi$
$277$	7.61958	+	13.1975i	0.457816	+	0.792961i	−0.541029	+	0.841004i	$0.681965\pi$
$278$	−9.91145	+	17.1671i	−0.594449	+	1.02962i
$279$		0			0
$280$	18.0177	−	11.6165i	1.07676	−	0.694221i
$281$	−1.68648			−0.100607			−0.0503034	−	0.998734i	$-0.516019\pi$
$281$	−1.68648			−0.100607			−0.0503034	+	0.998734i	$0.516019\pi$
$282$		0			0
$283$	−0.483164	−	0.836864i	−0.0287211	−	0.0497464i	0.851308	−	0.524667i	$-0.175810\pi$
$283$	−0.483164	−	0.836864i	−0.0287211	−	0.0497464i	−0.880029	+	0.474921i	$0.842477\pi$
$284$	−30.8786	−	53.4834i	−1.83231	−	3.17365i
$285$		0			0
$286$	39.6412			2.34403
$287$	15.2940	+	7.85634i	0.902779	+	0.463745i
$288$		0			0
$289$	4.97431	−	8.61576i	0.292607	−	0.506810i
$290$	4.92162	+	8.52449i	0.289007	+	0.500576i
$291$		0			0
$292$	−38.0598	+	65.9215i	−2.22728	+	3.85776i
$293$	31.7219			1.85321			0.926606	−	0.376034i	$-0.122712\pi$
$293$	31.7219			1.85321			0.926606	+	0.376034i	$0.122712\pi$
$294$		0			0
$295$	14.6014			0.850128
$296$	1.81220	−	3.13883i	0.105332	−	0.182441i
$297$		0			0
$298$	−0.552694	−	0.957294i	−0.0320167	−	0.0554545i
$299$	8.07925	−	13.9937i	0.467235	−	0.809275i
$300$		0			0
$301$	2.67446	+	1.37383i	0.154154	+	0.0791865i
$302$	−49.0328			−2.82152
$303$		0			0
$304$	42.0151	+	72.7722i	2.40973	+	4.17377i
$305$	4.12976	+	7.15295i	0.236469	+	0.409576i
$306$		0			0
$307$	−3.60143			−0.205544			−0.102772	−	0.994705i	$-0.532771\pi$
$307$	−3.60143			−0.205544			−0.102772	+	0.994705i	$0.532771\pi$
$308$	49.3773	−	31.8350i	2.81353	−	1.81397i
$309$		0			0
$310$	−2.01684	+	3.49326i	−0.114549	+	0.198404i
$311$	−5.06154	−	8.76685i	−0.287014	−	0.497123i	0.686082	−	0.727525i	$-0.259329\pi$
$311$	−5.06154	−	8.76685i	−0.287014	−	0.497123i	−0.973096	+	0.230402i	$0.925996\pi$
$312$		0			0
$313$	9.10493	−	15.7702i	0.514641	−	0.891385i	−0.485214	−	0.874395i	$-0.661258\pi$
$313$	9.10493	−	15.7702i	0.514641	−	0.891385i	0.999856	−	0.0169896i	$-0.00540821\pi$
$314$	−19.9593			−1.12637
$315$		0			0
$316$	12.9840			0.730409
$317$	−5.03454	+	8.72008i	−0.282768	+	0.489768i	−0.972065	−	0.234710i	$-0.924586\pi$
$317$	−5.03454	+	8.72008i	−0.282768	+	0.489768i	0.689298	+	0.724478i	$0.257919\pi$
$318$		0			0
$319$	8.14746	+	14.1118i	0.456170	+	0.790110i
$320$	−7.31088	+	12.6628i	−0.408691	+	0.707873i
$321$		0			0
$322$	−1.63947	−	33.3891i	−0.0913641	−	1.86070i
$323$	19.5501			1.08779
$324$		0			0
$325$	−1.69797	−	2.94096i	−0.0941862	−	0.163135i
$326$	9.57040	+	16.5764i	0.530055	+	0.918082i
$327$		0			0
$328$	−52.6572			−2.90751
$329$	−5.60143	+	3.61141i	−0.308817	+	0.199103i
$330$		0			0
$331$	−3.75951	+	6.51166i	−0.206641	+	0.357913i	−0.950654	−	0.310252i	$-0.899587\pi$
$331$	−3.75951	+	6.51166i	−0.206641	+	0.357913i	0.744013	+	0.668165i	$0.232920\pi$
$332$	−1.39593	−	2.41782i	−0.0766117	−	0.132695i
$333$		0			0
$334$	−5.40260	+	9.35757i	−0.295617	+	0.512024i
$335$	−7.91495			−0.432440
$336$		0			0
$337$	13.1852			0.718241			0.359121	−	0.933291i	$-0.383077\pi$
$337$	13.1852			0.718241			0.359121	+	0.933291i	$0.383077\pi$
$338$	1.94863	−	3.37512i	0.105991	−	0.183582i
$339$		0			0
$340$	6.70682	+	11.6165i	0.363728	+	0.629996i
$341$	−3.33876	+	5.78290i	−0.180804	+	0.313161i
$342$		0			0
$343$	−2.71612	−	18.3200i	−0.146657	−	0.989187i
$344$	−9.20814			−0.496469
$345$		0			0
$346$	−8.92829	−	15.4642i	−0.479988	−	0.831363i
$347$	−13.0514	−	22.6056i	−0.700634	−	1.21353i	−0.968244	−	0.250007i	$-0.919567\pi$
$347$	−13.0514	−	22.6056i	−0.700634	−	1.21353i	0.267610	−	0.963527i	$-0.413766\pi$
$348$		0			0
$349$	33.3056			1.78281			0.891404	−	0.453209i	$-0.149721\pi$
$349$	33.3056			1.78281			0.891404	+	0.453209i	$0.149721\pi$
$350$	−6.24934	−	3.21020i	−0.334041	−	0.171592i
$351$		0			0
$352$	−30.9974	+	53.6890i	−1.65216	+	2.86163i
$353$	−16.0009	−	27.7143i	−0.851640	−	1.47508i	−0.879727	−	0.475478i	$-0.842275\pi$
$353$	−16.0009	−	27.7143i	−0.851640	−	1.47508i	0.0280873	−	0.999605i	$-0.491058\pi$
$354$		0			0
$355$	−6.11292	+	10.5879i	−0.324440	+	0.561947i
$356$	−65.2383			−3.45762
$357$		0			0
$358$	9.24354			0.488536
$359$	−8.07925	+	13.9937i	−0.426406	+	0.738557i	−0.996551	−	0.0829872i	$-0.973554\pi$
$359$	−8.07925	+	13.9937i	−0.426406	+	0.738557i	0.570144	+	0.821545i	$0.306887\pi$
$360$		0			0
$361$	−17.6014	−	30.4866i	−0.926391	−	1.60456i
$362$	7.34542	−	12.7226i	0.386067	−	0.668687i
$363$		0			0
$364$	2.22584	+	45.3309i	0.116666	+	2.37599i
$365$	15.0691			0.788751
$366$		0			0
$367$	−9.87243	−	17.0995i	−0.515337	−	0.892589i	−0.999842	−	0.0178007i	$-0.994334\pi$
$367$	−9.87243	−	17.0995i	−0.515337	−	0.892589i	0.484505	−	0.874789i	$-0.339000\pi$
$368$	27.1541	+	47.0323i	1.41551	+	2.45173i
$369$		0			0
$370$	−1.18780			−0.0617506
$371$	0.689115	+	14.0344i	0.0357771	+	0.728628i
$372$		0			0
$373$	−4.28169	+	7.41611i	−0.221698	+	0.383992i	−0.955324	−	0.295562i	$-0.904493\pi$
$373$	−4.28169	+	7.41611i	−0.221698	+	0.383992i	0.733626	+	0.679554i	$0.237826\pi$
$374$	15.4987	+	26.8445i	0.801418	+	1.38810i
$375$		0			0
$376$	10.2055	−	17.6764i	0.526308	−	0.911593i
$377$	−12.5881			−0.648320
$378$		0			0
$379$	19.7919			1.01664			0.508320	−	0.861168i	$-0.330267\pi$
$379$	19.7919			1.01664			0.508320	+	0.861168i	$0.330267\pi$
$380$	18.5948	−	32.2071i	0.953891	−	1.65219i
$381$		0			0
$382$	16.8946	+	29.2623i	0.864404	+	1.49719i
$383$	−1.24181	+	2.15088i	−0.0634535	+	0.109905i	−0.896007	−	0.444040i	$-0.853545\pi$
$383$	−1.24181	+	2.15088i	−0.0634535	+	0.109905i	0.832553	+	0.553945i	$0.186878\pi$
$384$		0			0
$385$	−10.3454	−	5.31430i	−0.527252	−	0.270842i
$386$	−14.5660			−0.741391
$387$		0			0
$388$	6.39593	+	11.0781i	0.324704	+	0.562404i
$389$	10.5089	+	18.2019i	0.532820	+	0.922871i	0.999265	+	0.0383212i	$0.0122010\pi$
$389$	10.5089	+	18.2019i	0.532820	+	0.922871i	−0.466446	+	0.884550i	$0.654466\pi$
$390$		0			0
$391$	12.6351			0.638985
$392$	33.0354	+	46.1057i	1.66854	+	2.32869i
$393$		0			0
$394$	−19.2679	+	33.3730i	−0.970703	+	1.68131i
$395$	−1.28520	−	2.22603i	−0.0646653	−	0.112004i
$396$		0			0
$397$	4.12090	−	7.13762i	0.206822	−	0.358227i	−0.743890	−	0.668303i	$-0.767021\pi$
$397$	4.12090	−	7.13762i	0.206822	−	0.358227i	0.950712	+	0.310076i	$0.100354\pi$
$398$	14.4110			0.722358
$399$		0			0
$400$	11.4136			0.570682
$401$	−7.55005	+	13.0771i	−0.377032	+	0.653038i	−0.990629	−	0.136581i	$-0.956389\pi$
$401$	−7.55005	+	13.0771i	−0.377032	+	0.653038i	0.613597	+	0.789619i	$0.289722\pi$
$402$		0			0
$403$	−2.57925	−	4.46739i	−0.128481	−	0.222536i
$404$	−8.67314	+	15.0223i	−0.431505	+	0.747389i
$405$		0			0
$406$	−21.8879	+	14.1118i	−1.08628	+	0.700357i
$407$	−1.96633			−0.0974672
$408$		0			0
$409$	9.63642	+	16.6908i	0.476490	+	0.825306i	0.999637	−	0.0269371i	$-0.00857538\pi$
$409$	9.63642	+	16.6908i	0.476490	+	0.825306i	−0.523147	+	0.852243i	$0.675242\pi$
$410$	8.62844	+	14.9449i	0.426128	+	0.738075i
$411$		0			0
$412$	66.8760			3.29474
$413$	1.89461	+	38.5853i	0.0932278	+	1.89866i
$414$		0			0
$415$	−0.276347	+	0.478647i	−0.0135653	+	0.0234959i
$416$	−23.9460	−	41.4757i	−1.17405	−	2.03351i
$417$		0			0
$418$	42.9704	−	74.4268i	2.10175	−	3.64034i
$419$	−23.7272			−1.15915			−0.579574	−	0.814920i	$-0.696781\pi$
$419$	−23.7272			−1.15915			−0.579574	+	0.814920i	$0.696781\pi$
$420$		0			0
$421$	−14.5971			−0.711417			−0.355709	−	0.934597i	$-0.615760\pi$
$421$	−14.5971			−0.711417			−0.355709	+	0.934597i	$0.615760\pi$
$422$	24.1541	−	41.8362i	1.17580	−	2.03655i
$423$		0			0
$424$	−21.5164	−	37.2675i	−1.04493	−	1.80987i
$425$	1.32772	−	2.29968i	0.0644039	−	0.111551i
$426$		0			0
$427$	−18.3663	+	11.8413i	−0.888807	+	0.573040i
$428$	33.1001			1.59995
$429$		0			0
$430$	1.50885	+	2.61341i	0.0727632	+	0.126030i
$431$	−10.5501	−	18.2732i	−0.508178	−	0.880191i	−0.999955	−	0.00946931i	$-0.996986\pi$
$431$	−10.5501	−	18.2732i	−0.508178	−	0.880191i	0.491777	−	0.870721i	$-0.336348\pi$
$432$		0			0
$433$	−11.3959			−0.547654			−0.273827	−	0.961779i	$-0.588289\pi$
$433$	−11.3959			−0.547654			−0.273827	+	0.961779i	$0.588289\pi$
$434$	−9.49288	−	4.87636i	−0.455673	−	0.234073i
$435$		0			0
$436$	32.0084	−	55.4402i	1.53292	−	2.65510i
$437$	−17.5155	−	30.3378i	−0.837881	−	1.45125i
$438$		0			0
$439$	−0.836572	+	1.44899i	−0.0399274	+	0.0691563i	−0.885299	−	0.465023i	$-0.846046\pi$
$439$	−0.836572	+	1.44899i	−0.0399274	+	0.0691563i	0.845371	+	0.534179i	$0.179379\pi$
$440$	35.6191			1.69808
$441$		0			0
$442$	−23.9460			−1.13899
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	−0.928450	−	0.371457i	$-0.878858\pi$
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	0.785916	+	0.618333i	$0.212192\pi$
$444$		0			0
$445$	6.45748	+	11.1847i	0.306114	+	0.530205i
$446$	−3.20814	+	5.55666i	−0.151910	+	0.263115i
$447$		0			0
$448$	−34.4110	−	17.6764i	−1.62577	−	0.835133i
$449$	0.724518			0.0341921			0.0170961	−	0.999854i	$-0.494558\pi$
$449$	0.724518			0.0341921			0.0170961	+	0.999854i	$0.494558\pi$
$450$		0			0
$451$	14.2839	+	24.7404i	0.672602	+	1.16498i
$452$	18.7245	+	32.4318i	0.880727	+	1.52546i
$453$		0			0
$454$	−56.7733			−2.66450
$455$	7.55137	−	4.86860i	0.354014	−	0.228243i
$456$		0			0
$457$	−13.7874	+	23.8804i	−0.644947	+	1.11708i	0.339367	+	0.940654i	$0.389787\pi$
$457$	−13.7874	+	23.8804i	−0.644947	+	1.11708i	−0.984314	+	0.176426i	$0.943546\pi$
$458$	16.7077	+	28.9386i	0.780699	+	1.35221i
$459$		0			0
$460$	12.0177	−	20.8153i	0.560328	−	0.970517i
$461$	37.2586			1.73531			0.867653	−	0.497170i	$-0.165628\pi$
$461$	37.2586			1.73531			0.867653	+	0.497170i	$0.165628\pi$
$462$		0			0
$463$	−0.393293			−0.0182779			−0.00913893	−	0.999958i	$-0.502909\pi$
$463$	−0.393293			−0.0182779			−0.00913893	+	0.999958i	$0.502909\pi$
$464$	21.1541	−	36.6400i	0.982055	−	1.70097i
$465$		0			0
$466$	−25.2232	−	43.6879i	−1.16844	−	2.02380i
$467$	19.5501	−	33.8617i	0.904669	−	1.56693i	0.0833072	−	0.996524i	$-0.473452\pi$
$467$	19.5501	−	33.8617i	0.904669	−	1.56693i	0.821361	−	0.570408i	$-0.193215\pi$
$468$		0			0
$469$	−1.02701	−	20.9158i	−0.0474228	−	0.965802i
$470$	−6.68912			−0.308546
$471$		0			0
$472$	−59.1559	−	102.461i	−2.72287	−	4.71615i
$473$	2.49782	+	4.32634i	0.114850	+	0.198925i
$474$		0			0
$475$	−7.36226			−0.337804
$476$	−29.8273	+	19.2305i	−1.36713	+	0.881430i
$477$		0			0
$478$	−31.3126	+	54.2350i	−1.43221	+	2.48065i
$479$	4.82991	+	8.36564i	0.220684	+	0.382236i	0.955016	−	0.296555i	$-0.0958377\pi$
$479$	4.82991	+	8.36564i	0.220684	+	0.382236i	−0.734332	+	0.678791i	$0.762504\pi$
$480$		0			0
$481$	0.759511	−	1.31551i	0.0346307	−	0.0599821i
$482$	12.5811			0.573053
$483$		0			0
$484$	42.0487			1.91131
$485$	1.26618	−	2.19308i	0.0574941	−	0.0995827i
$486$		0			0
$487$	−20.9035	−	36.2059i	−0.947226	−	1.64064i	−0.751231	−	0.660039i	$-0.770540\pi$
$487$	−20.9035	−	36.2059i	−0.947226	−	1.64064i	−0.195995	−	0.980605i	$-0.562794\pi$
$488$	33.4624	−	57.9585i	1.51477	−	2.62366i
$489$		0			0
$490$	7.67228	−	16.9308i	0.346598	−	0.764858i
$491$	−3.51638			−0.158692			−0.0793460	−	0.996847i	$-0.525283\pi$
$491$	−3.51638			−0.158692			−0.0793460	+	0.996847i	$0.525283\pi$
$492$		0			0
$493$	−4.92162	−	8.52449i	−0.221659	−	0.383924i
$494$	33.1953	+	57.4960i	1.49353	+	2.58687i
$495$		0			0
$496$	17.3375			0.778479
$497$	−28.7724	−	14.7800i	−1.29062	−	0.662972i
$498$		0			0
$499$	4.41495	−	7.64692i	0.197640	−	0.342323i	−0.750122	−	0.661299i	$-0.770005\pi$
$499$	4.41495	−	7.64692i	0.197640	−	0.342323i	0.947763	+	0.318976i	$0.103339\pi$
$500$	−2.52569	−	4.37462i	−0.112952	−	0.195639i
$501$		0			0
$502$	−11.0580	+	19.1531i	−0.493544	+	0.854844i
$503$	9.24354			0.412149			0.206075	−	0.978536i	$-0.433931\pi$
$503$	9.24354			0.412149			0.206075	+	0.978536i	$0.433931\pi$
$504$		0			0
$505$	3.43397			0.152810
$506$	27.7715	−	48.1017i	1.23459	−	2.13838i
$507$		0			0
$508$	40.4557	+	70.0713i	1.79493	+	3.10891i
$509$	16.7582	−	29.0260i	0.742794	−	1.28656i	−0.208425	−	0.978038i	$-0.566834\pi$
$509$	16.7582	−	29.0260i	0.742794	−	1.28656i	0.951218	−	0.308518i	$-0.0998330\pi$
$510$		0			0
$511$	1.95529	+	39.8211i	0.0864970	+	1.76158i
$512$	−24.0000			−1.06066
$513$		0			0
$514$	−22.0598	−	38.2086i	−0.973015	−	1.68531i
$515$	−6.61958	−	11.4655i	−0.291694	−	0.505228i
$516$		0			0
$517$	−11.0734			−0.487010
$518$	−0.154123	−	3.13883i	−0.00677176	−	0.137912i
$519$		0			0
$520$	−13.7582	+	23.8299i	−0.603337	+	1.04501i
$521$	−2.29318	−	3.97191i	−0.100466	−	0.174013i	0.811411	−	0.584477i	$-0.198700\pi$
$521$	−2.29318	−	3.97191i	−0.100466	−	0.174013i	−0.911877	+	0.410464i	$0.865367\pi$
$522$		0			0
$523$	−8.40478	+	14.5575i	−0.367515	+	0.636555i	−0.989176	−	0.146731i	$-0.953125\pi$
$523$	−8.40478	+	14.5575i	−0.367515	+	0.636555i	0.621661	+	0.783286i	$0.286458\pi$
$524$	11.3463			0.495665
$525$		0			0
$526$	44.1382			1.92451
$527$	2.01684	−	3.49326i	0.0878548	−	0.152169i
$528$		0			0
$529$	0.179810	+	0.311440i	0.00781782	+	0.0135409i
$530$	−7.05137	+	12.2133i	−0.306292	+	0.530514i
$531$		0			0
$532$	87.5221	+	44.9589i	3.79457	+	1.94921i
$533$	−22.0691			−0.955918
$534$		0			0
$535$	−3.27635	−	5.67480i	−0.141649	−	0.245343i
$536$	32.0664	+	55.5407i	1.38506	+	2.39899i
$537$		0			0
$538$	−52.3703			−2.25784
$539$	12.7010	−	28.0280i	0.547071	−	1.20725i
$540$		0			0
$541$	9.99868	−	17.3182i	0.429877	−	0.744569i	−0.566985	−	0.823728i	$-0.691890\pi$
$541$	9.99868	−	17.3182i	0.429877	−	0.744569i	0.996862	+	0.0791595i	$0.0252236\pi$
$542$	17.4650	+	30.2503i	0.750186	+	1.29936i
$543$		0			0
$544$	18.7245	−	32.4318i	0.802807	−	1.39050i
$545$	−12.6731			−0.542858
$546$		0			0
$547$	8.17883			0.349702			0.174851	−	0.984595i	$-0.444056\pi$
$547$	8.17883			0.349702			0.174851	+	0.984595i	$0.444056\pi$
$548$	27.8609	−	48.2566i	1.19016	−	2.06142i
$549$		0			0
$550$	−5.83657	−	10.1092i	−0.248872	−	0.431059i
$551$	−13.6453	+	23.6343i	−0.581308	+	1.00686i
$552$		0			0
$553$	5.71567	−	3.68506i	0.243055	−	0.156705i
$554$	−40.4667			−1.71927
$555$		0			0
$556$	−18.8543	−	32.6566i	−0.799599	−	1.38495i
$557$	6.89725	+	11.9464i	0.292246	+	0.506185i	0.974340	−	0.225079i	$-0.0722641\pi$
$557$	6.89725	+	11.9464i	0.292246	+	0.506185i	−0.682095	+	0.731264i	$0.738931\pi$
$558$		0			0
$559$	−3.85921			−0.163227
$560$	1.48098	+	30.1613i	0.0625828	+	1.27455i
$561$		0			0
$562$	2.23917	−	3.87836i	0.0944537	−	0.163599i
$563$	14.6014	+	25.2904i	0.615377	+	1.06586i	0.990318	+	0.138815i	$0.0443295\pi$
$563$	14.6014	+	25.2904i	0.615377	+	1.06586i	−0.374941	+	0.927049i	$0.622337\pi$
$564$		0			0
$565$	3.70682	−	6.42039i	0.155947	−	0.270108i
$566$	2.56603			0.107858
$567$		0			0
$568$	99.0629			4.15659
$569$	−16.5736	+	28.7062i	−0.694800	+	1.20343i	0.275449	+	0.961316i	$0.411174\pi$
$569$	−16.5736	+	28.7062i	−0.694800	+	1.20343i	−0.970248	+	0.242112i	$0.922160\pi$
$570$		0			0
$571$	7.88663	+	13.6600i	0.330045	+	0.571655i	0.982520	−	0.186155i	$-0.0596027\pi$
$571$	7.88663	+	13.6600i	0.330045	+	0.571655i	−0.652475	+	0.757810i	$0.726269\pi$
$572$	−37.7042	+	65.3056i	−1.57649	+	2.73056i
$573$		0			0
$574$	−38.3733	+	24.7404i	−1.60167	+	1.03264i
$575$	−4.75819			−0.198430
$576$		0			0
$577$	22.4021	+	38.8017i	0.932613	+	1.61533i	0.778835	+	0.627228i	$0.215811\pi$
$577$	22.4021	+	38.8017i	0.932613	+	1.61533i	0.153778	+	0.988105i	$0.450856\pi$
$578$	13.2090	+	22.8787i	0.549422	+	0.951627i
$579$		0			0
$580$	−18.7245			−0.777493
$581$	−1.30071	−	0.668159i	−0.0539627	−	0.0277199i
$582$		0			0
$583$	−11.6731	+	20.2185i	−0.483452	+	0.837364i
$584$	−61.0505	−	105.743i	−2.52629	−	4.37566i
$585$		0			0
$586$	−42.1178	+	72.9502i	−1.73987	+	3.01354i
$587$	−2.23917			−0.0924204			−0.0462102	−	0.998932i	$-0.514714\pi$
$587$	−2.23917			−0.0924204			−0.0462102	+	0.998932i	$0.514714\pi$
$588$		0			0
$589$	−11.1834			−0.460805
$590$	−19.3866	+	33.5786i	−0.798135	+	1.38241i
$591$		0			0
$592$	2.55269	+	4.42140i	0.104915	+	0.181718i
$593$	3.96546	−	6.86838i	0.162842	−	0.282051i	−0.773045	−	0.634351i	$-0.781267\pi$
$593$	3.96546	−	6.86838i	0.162842	−	0.282051i	0.935887	+	0.352301i	$0.114601\pi$
$594$		0			0
$595$	6.24934	+	3.21020i	0.256198	+	0.131605i
$596$	2.10275			0.0861319
$597$		0			0
$598$	21.4540	+	37.1594i	0.877318	+	1.51956i
$599$	21.1718	+	36.6707i	0.865057	+	1.49832i	0.866990	+	0.498325i	$0.166051\pi$
$599$	21.1718	+	36.6707i	0.865057	+	1.49832i	−0.00193301	+	0.999998i	$0.500615\pi$
$600$		0			0
$601$	−26.3596			−1.07523			−0.537616	−	0.843190i	$-0.680675\pi$
$601$	−26.3596			−1.07523			−0.537616	+	0.843190i	$0.680675\pi$
$602$	−6.71032	+	4.32634i	−0.273492	+	0.176329i
$603$		0			0
$604$	46.6368	−	80.7774i	1.89763	−	3.28678i
$605$	−4.16211	−	7.20898i	−0.169214	−	0.293087i
$606$		0			0
$607$	2.02655	−	3.51009i	0.0822552	−	0.142470i	−0.821963	−	0.569541i	$-0.807121\pi$
$607$	2.02655	−	3.51009i	0.0822552	−	0.142470i	0.904218	+	0.427071i	$0.140454\pi$
$608$	−103.828			−4.21078
$609$		0			0
$610$	−21.9327			−0.888027
$611$	4.27721	−	7.40835i	0.173037	−	0.299710i
$612$		0			0
$613$	19.2122	+	33.2764i	0.775972	+	1.34402i	0.934247	+	0.356628i	$0.116074\pi$
$613$	19.2122	+	33.2764i	0.775972	+	1.34402i	−0.158275	+	0.987395i	$0.550593\pi$
$614$	4.78169	−	8.28214i	0.192973	−	0.334240i
$615$		0			0
$616$	4.62177	+	94.1260i	0.186216	+	3.79244i
$617$	−20.4110			−0.821716			−0.410858	−	0.911699i	$-0.634771\pi$
$617$	−20.4110			−0.821716			−0.410858	+	0.911699i	$0.634771\pi$
$618$		0			0
$619$	−18.3609	−	31.8021i	−0.737988	−	1.27823i	−0.953400	−	0.301710i	$-0.902443\pi$
$619$	−18.3609	−	31.8021i	−0.737988	−	1.27823i	0.215411	−	0.976523i	$-0.430891\pi$
$620$	−3.83657	−	6.64514i	−0.154080	−	0.266875i
$621$		0			0
$622$	26.8813			1.07784
$623$	−28.7184	+	18.5156i	−1.15058	+	0.741811i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	24.1776	+	41.8769i	0.966332	+	1.67374i
$627$		0			0
$628$	18.9840	−	32.8813i	0.757545	−	1.31211i
$629$	1.18780			0.0473605
$630$		0			0
$631$	−7.20814			−0.286951			−0.143476	−	0.989654i	$-0.545828\pi$
$631$	−7.20814			−0.286951			−0.143476	+	0.989654i	$0.545828\pi$
$632$	−10.4136	+	18.0369i	−0.414232	+	0.717471i
$633$		0			0
$634$	−13.3689	−	23.1557i	−0.530948	−	0.919629i
$635$	8.00885	−	13.8717i	0.317822	−	0.550483i
$636$		0			0
$637$	13.8454	+	19.3233i	0.548576	+	0.765617i
$638$	−43.2702			−1.71308
$639$		0			0
$640$	−5.31088	−	9.19872i	−0.209931	−	0.363611i
$641$	−14.2334	−	24.6529i	−0.562184	−	0.973732i	−0.997306	−	0.0733599i	$-0.976628\pi$
$641$	−14.2334	−	24.6529i	−0.562184	−	0.973732i	0.435121	−	0.900372i	$-0.356705\pi$
$642$		0			0
$643$	−34.4340			−1.35794			−0.678972	−	0.734164i	$-0.737574\pi$
$643$	−34.4340			−1.35794			−0.678972	+	0.734164i	$0.737574\pi$
$644$	56.5651	+	29.0567i	2.22898	+	1.14499i
$645$		0			0
$646$	−25.9570	+	44.9589i	−1.02127	+	1.76888i
$647$	−11.7414	−	20.3366i	−0.461600	−	0.799515i	0.537441	−	0.843302i	$-0.319391\pi$
$647$	−11.7414	−	20.3366i	−0.461600	−	0.799515i	−0.999041	+	0.0437865i	$0.986058\pi$
$648$		0			0
$649$	−32.0934	+	55.5875i	−1.25978	+	2.18200i
$650$	9.01770			0.353703
$651$		0			0
$652$	−36.4110			−1.42596
$653$	24.4482	−	42.3455i	0.956731	−	1.65711i	0.226374	−	0.974040i	$-0.427313\pi$
$653$	24.4482	−	42.3455i	0.956731	−	1.65711i	0.730357	−	0.683066i	$-0.239354\pi$
$654$		0			0
$655$	−1.12309	−	1.94525i	−0.0438827	−	0.0760071i
$656$	37.0868	−	64.2362i	1.44800	−	2.50800i
$657$		0			0
$658$	−0.867948	−	17.6764i	−0.0338361	−	0.689099i
$659$	39.6598			1.54493			0.772463	−	0.635059i	$-0.219024\pi$
$659$	39.6598			1.54493			0.772463	+	0.635059i	$0.219024\pi$
$660$		0			0
$661$	−12.9583	−	22.4445i	−0.504021	−	0.872990i	−0.999989	−	0.00464937i	$-0.998520\pi$
$661$	−12.9583	−	22.4445i	−0.504021	−	0.872990i	0.495968	−	0.868341i	$-0.334813\pi$
$662$	−9.98316	−	17.2913i	−0.388007	−	0.672047i
$663$		0			0
$664$	4.47834			0.173793
$665$	−0.955292	−	19.4553i	−0.0370446	−	0.754443i
$666$		0			0
$667$	−8.81887	+	15.2747i	−0.341468	+	0.591440i
$668$	−10.2772	−	17.8007i	−0.397637	−	0.688728i
$669$		0			0
$670$	10.5089	−	18.2019i	0.405992	−	0.703199i
$671$	−36.3082			−1.40166
$672$		0			0
$673$	42.3666			1.63311			0.816557	−	0.577265i	$-0.195880\pi$
$673$	42.3666			1.63311			0.816557	+	0.577265i	$0.195880\pi$
$674$	−17.5062	+	30.3216i	−0.674314	+	1.16795i
$675$		0			0
$676$	3.70682	+	6.42039i	0.142570	+	0.246938i
$677$	15.9292	−	27.5901i	0.612207	−	1.06037i	−0.378661	−	0.925536i	$-0.623615\pi$
$677$	15.9292	−	27.5901i	0.612207	−	1.06037i	0.990868	−	0.134838i	$-0.0430514\pi$
$678$		0			0
$679$	5.95966	+	3.06139i	0.228711	+	0.117485i
$680$	−21.5164			−0.825116
$681$		0			0
$682$	−8.86588	−	15.3561i	−0.339492	−	0.588017i
$683$	−22.1373	−	38.3429i	−0.847060	−	1.46715i	−0.883820	−	0.467826i	$-0.845037\pi$
$683$	−22.1373	−	38.3429i	−0.847060	−	1.46715i	0.0367607	−	0.999324i	$-0.488296\pi$
$684$		0			0
$685$	−11.0310			−0.421474
$686$	45.7364	+	18.0776i	1.74622	+	0.690208i
$687$		0			0
$688$	6.48535	−	11.2330i	0.247252	−	0.428252i
$689$	−9.01770	−	15.6191i	−0.343547	−	0.595041i
$690$		0			0
$691$	−6.49736	+	11.2538i	−0.247171	+	0.428113i	−0.962740	−	0.270429i	$-0.912834\pi$
$691$	−6.49736	+	11.2538i	−0.247171	+	0.428113i	0.715569	+	0.698542i	$0.246168\pi$
$692$	33.9681			1.29127
$693$		0			0
$694$	69.3143			2.63114
$695$	−3.73250	+	6.46489i	−0.141582	+	0.245227i
$696$		0			0
$697$	−8.62844	−	14.9449i	−0.326825	−	0.566078i
$698$	−44.2206	+	76.5923i	−1.67377	+	2.89906i
$699$		0			0
$700$	11.2325	−	7.24193i	0.424549	−	0.273719i
$701$	20.2206			0.763720			0.381860	−	0.924220i	$-0.375284\pi$
$701$	20.2206			0.763720			0.381860	+	0.924220i	$0.375284\pi$
$702$		0			0
$703$	−1.64659	−	2.85198i	−0.0621024	−	0.107564i
$704$	−32.1382	−	55.6649i	−1.21125	−	2.09795i
$705$		0			0
$706$	84.9787			3.19822
$707$	0.445576	+	9.07451i	0.0167576	+	0.341282i
$708$		0			0
$709$	−5.66648	+	9.81463i	−0.212809	+	0.368596i	−0.952593	−	0.304249i	$-0.901595\pi$
$709$	−5.66648	+	9.81463i	−0.212809	+	0.368596i	0.739784	+	0.672845i	$0.234928\pi$
$710$	−16.2325	−	28.1155i	−0.609195	−	1.05516i
$711$		0			0
$712$	52.3233	−	90.6266i	1.96090	−	3.39638i
$713$	−7.22779			−0.270683
$714$		0			0
$715$	14.9283			0.558286
$716$	−8.79186	+	15.2280i	−0.328567	+	0.569095i
$717$		0			0
$718$	−21.4540	−	37.1594i	−0.800655	−	1.38678i
$719$	−18.9797	+	32.8737i	−0.707822	+	1.22598i	0.257842	+	0.966187i	$0.416989\pi$
$719$	−18.9797	+	32.8737i	−0.707822	+	1.22598i	−0.965663	+	0.259796i	$0.916345\pi$
$720$		0			0
$721$	29.4393	−	18.9804i	1.09638	−	0.706867i
$722$	93.4792			3.47893
$723$		0			0
$724$	13.9730	+	24.2019i	0.519302	+	0.899458i
$725$	1.85341	+	3.21020i	0.0688339	+	0.119224i
$726$		0			0
$727$	11.2799			0.418347			0.209173	−	0.977879i	$-0.432923\pi$
$727$	11.2799			0.418347			0.209173	+	0.977879i	$0.432923\pi$
$728$	−64.7573	−	33.2649i	−2.40006	−	1.23288i
$729$		0			0
$730$	−20.0075	+	34.6541i	−0.740512	+	1.28260i
$731$	−1.50885	−	2.61341i	−0.0558069	−	0.0966603i
$732$		0			0
$733$	−14.8388	+	25.7015i	−0.548082	+	0.949306i	0.450324	+	0.892865i	$0.351308\pi$
$733$	−14.8388	+	25.7015i	−0.548082	+	0.949306i	−0.998406	+	0.0564406i	$0.982025\pi$
$734$	52.4313			1.93528
$735$		0			0
$736$	−67.1036			−2.47347
$737$	17.3968	−	30.1321i	0.640819	−	1.10993i
$738$		0			0
$739$	−5.69883	−	9.87066i	−0.209635	−	0.363098i	0.741965	−	0.670439i	$-0.233894\pi$
$739$	−5.69883	−	9.87066i	−0.209635	−	0.363098i	−0.951600	+	0.307341i	$0.900561\pi$
$740$	1.12976	−	1.95679i	0.0415306	−	0.0719332i
$741$		0			0
$742$	−33.1895	−	17.0490i	−1.21843	−	0.625888i
$743$	24.1364			0.885479			0.442740	−	0.896650i	$-0.354007\pi$
$743$	24.1364			0.885479			0.442740	+	0.896650i	$0.354007\pi$
$744$		0			0
$745$	−0.208136	−	0.360503i	−0.00762552	−	0.0132078i
$746$	−11.3698	−	19.6931i	−0.416278	−	0.721014i
$747$		0			0
$748$	−58.9654			−2.15599
$749$	14.5709	−	9.39430i	0.532410	−	0.343260i
$750$		0			0
$751$	−6.93133	+	12.0054i	−0.252928	+	0.438084i	−0.964331	−	0.264700i	$-0.914727\pi$
$751$	−6.93133	+	12.0054i	−0.252928	+	0.438084i	0.711403	+	0.702785i	$0.248060\pi$
$752$	14.3756	+	24.8993i	0.524224	+	0.907982i
$753$		0			0
$754$	16.7135	−	28.9486i	0.608669	−	1.05425i
$755$	−18.4650			−0.672010
$756$		0			0
$757$	−11.1054			−0.403632			−0.201816	−	0.979423i	$-0.564684\pi$
$757$	−11.1054			−0.403632			−0.201816	+	0.979423i	$0.564684\pi$
$758$	−26.2781	+	45.5150i	−0.954463	+	1.65318i
$759$		0			0
$760$	29.8273	+	51.6623i	1.08195	+	1.87399i
$761$	17.0969	−	29.6128i	0.619764	−	1.07346i	−0.369765	−	0.929125i	$-0.620562\pi$
$761$	17.0969	−	29.6128i	0.619764	−	1.07346i	0.989529	−	0.144337i	$-0.0461050\pi$
$762$		0			0
$763$	−1.64441	−	33.4896i	−0.0595315	−	1.21241i
$764$	−64.2763			−2.32544
$765$		0			0
$766$	−3.29755	−	5.71153i	−0.119145	−	0.206366i
$767$	−24.7927	−	42.9423i	−0.895214	−	1.55056i
$768$		0			0
$769$	−10.3330			−0.372616			−0.186308	−	0.982491i	$-0.559652\pi$
$769$	−10.3330			−0.372616			−0.186308	+	0.982491i	$0.559652\pi$
$770$	25.9570	−	16.7353i	0.935426	−	0.603097i
$771$		0			0
$772$	13.8543	−	23.9963i	0.498626	−	0.863646i
$773$	13.0009	+	22.5182i	0.467609	+	0.809922i	0.999315	−	0.0370069i	$-0.0117823\pi$
$773$	13.0009	+	22.5182i	0.467609	+	0.809922i	−0.531706	+	0.846929i	$0.678449\pi$
$774$		0			0
$775$	−0.759511	+	1.31551i	−0.0272824	+	0.0472545i
$776$	−20.5190			−0.736590
$777$		0			0
$778$	−55.8113			−2.00093
$779$	−23.9225	+	41.4350i	−0.857112	+	1.48456i
$780$		0			0
$781$	−26.8720	−	46.5436i	−0.961555	−	1.66546i
$782$	−16.7759	+	29.0567i	−0.599905	+	1.03907i
$783$		0			0
$784$	−79.5111	+	7.82717i	−2.83968	+	0.279542i
$785$	−7.51638			−0.268271
$786$		0			0
$787$	−3.35789	−	5.81604i	−0.119696	−	0.207319i	0.799951	−	0.600065i	$-0.204859\pi$
$787$	−3.35789	−	5.81604i	−0.119696	−	0.207319i	−0.919647	+	0.392746i	$0.871525\pi$
$788$	−36.6528	−	63.4845i	−1.30570	−	2.26154i
$789$		0			0
$790$	6.82554			0.242842
$791$	17.4473	+	8.96243i	0.620355	+	0.318667i
$792$		0			0
$793$	14.0244	−	24.2909i	0.498020	−	0.862596i
$794$	10.9428	+	18.9535i	0.388346	+	0.672636i
$795$		0			0
$796$	−13.7068	+	23.7409i	−0.485825	+	0.841474i
$797$	24.8609			0.880620			0.440310	−	0.897846i	$-0.354869\pi$
$797$	24.8609			0.880620			0.440310	+	0.897846i	$0.354869\pi$
$798$		0			0
$799$	6.68912			0.236644
$800$	−7.05137	+	12.2133i	−0.249304	+	0.431807i
$801$		0			0
$802$	−20.0487	−	34.7254i	−0.707945	−	1.22620i
$803$	−33.1213	+	57.3678i	−1.16883	+	2.02447i
$804$		0			0
$805$	−0.617400	−	12.5738i	−0.0217605	−	0.443170i
$806$	13.6981			0.482494
$807$		0			0
$808$	−13.9123	−	24.0968i	−0.489433	−	0.847724i
$809$	20.4003	+	35.3344i	0.717236	+	1.24229i	0.962091	+	0.272730i	$0.0879266\pi$
$809$	20.4003	+	35.3344i	0.717236	+	1.24229i	−0.244854	+	0.969560i	$0.578740\pi$
$810$		0			0
$811$	23.7352			0.833456			0.416728	−	0.909031i	$-0.363177\pi$
$811$	23.7352			0.833456			0.416728	+	0.909031i	$0.363177\pi$
$812$	−2.42960	−	49.4808i	−0.0852624	−	1.73644i
$813$		0			0
$814$	2.61073	−	4.52192i	0.0915062	−	0.158493i
$815$	3.60407	+	6.24243i	0.126245	+	0.218663i
$816$		0			0
$817$	−4.18331	+	7.24571i	−0.146356	+	0.253495i
$818$	−51.1779			−1.78939
$819$		0			0
$820$	−32.8273			−1.14638
$821$	−5.95880	+	10.3209i	−0.207963	+	0.360203i	−0.951073	−	0.308967i	$-0.900017\pi$
$821$	−5.95880	+	10.3209i	−0.207963	+	0.360203i	0.743109	+	0.669170i	$0.233350\pi$
$822$		0			0
$823$	−11.3866	−	19.7222i	−0.396913	−	0.687473i	0.596430	−	0.802665i	$-0.296585\pi$
$823$	−11.3866	−	19.7222i	−0.396913	−	0.687473i	−0.993343	+	0.115192i	$0.963252\pi$
$824$	−53.6368	+	92.9017i	−1.86853	+	3.23638i
$825$		0			0
$826$	−91.2493	−	46.8735i	−3.17497	−	1.63094i
$827$	0.143430			0.00498755			0.00249377	−	0.999997i	$-0.499206\pi$
$827$	0.143430			0.00498755			0.00249377	+	0.999997i	$0.499206\pi$
$828$		0			0
$829$	16.4597	+	28.5090i	0.571668	+	0.990157i	0.996395	+	0.0848361i	$0.0270367\pi$
$829$	16.4597	+	28.5090i	0.571668	+	0.990157i	−0.424727	+	0.905321i	$0.639630\pi$
$830$	−0.733823	−	1.27102i	−0.0254714	−	0.0441177i
$831$		0			0
$832$	49.6545			1.72146
$833$	−7.67228	+	16.9308i	−0.265829	+	0.586619i
$834$		0			0
$835$	−2.03454	+	3.52392i	−0.0704081	+	0.121950i
$836$	81.7413	+	141.580i	2.82708	+	4.89665i
$837$		0			0
$838$	31.5030	−	54.5649i	1.08825	−	1.88491i
$839$	−38.5074			−1.32942			−0.664712	−	0.747100i	$-0.731446\pi$
$839$	−38.5074			−1.32942			−0.664712	+	0.747100i	$0.731446\pi$
$840$		0			0
$841$	−15.2595			−0.526190
$842$	19.3808	−	33.5686i	0.667907	−	1.15685i
$843$		0			0
$844$	45.9477	+	79.5838i	1.58159	+	2.73939i
$845$	0.733823	−	1.27102i	0.0252443	−	0.0437244i
$846$		0			0
$847$	18.5102	−	11.9341i	0.636017	−	0.410059i
$848$	60.6165			2.08158
$849$		0			0
$850$	3.52569	+	6.10667i	0.120930	+	0.209457i
$851$	−1.06418	−	1.84322i	−0.0364798	−	0.0631848i
$852$		0			0
$853$	24.0044			0.821894			0.410947	−	0.911659i	$-0.365198\pi$
$853$	24.0044			0.821894			0.410947	+	0.911659i	$0.365198\pi$
$854$	−2.84588	−	57.9585i	−0.0973839	−	1.98330i
$855$		0			0
$856$	−26.5474	+	45.9815i	−0.907372	+	1.57161i
$857$	−23.0522	−	39.9276i	−0.787449	−	1.36390i	−0.927525	−	0.373762i	$-0.878068\pi$
$857$	−23.0522	−	39.9276i	−0.787449	−	1.36390i	0.140075	−	0.990141i	$-0.455266\pi$
$858$		0			0
$859$	24.5230	−	42.4752i	0.836716	−	1.44923i	−0.0559103	−	0.998436i	$-0.517806\pi$
$859$	24.5230	−	42.4752i	0.836716	−	1.44923i	0.892626	−	0.450798i	$-0.148861\pi$
$860$	−5.74049			−0.195749
$861$		0			0
$862$	56.0301			1.90839
$863$	16.2772	−	28.1930i	0.554083	−	0.959699i	−0.443892	−	0.896081i	$-0.646402\pi$
$863$	16.2772	−	28.1930i	0.554083	−	0.959699i	0.997974	−	0.0636189i	$-0.0202642\pi$
$864$		0			0
$865$	−3.36226	−	5.82360i	−0.114320	−	0.198008i
$866$	15.1306	−	26.2070i	0.514159	−	0.890550i
$867$		0			0
$868$	17.0624	−	11.0006i	0.579136	−	0.373386i
$869$	11.2993			0.383302
$870$		0			0
$871$	13.4393	+	23.2776i	0.455374	+	0.788731i
$872$	51.3436	+	88.9298i	1.73872	+	3.01154i
$873$		0			0
$874$	93.0229			3.14655
$875$	−2.35341	−	1.20891i	−0.0795597	−	0.0408687i
$876$		0			0
$877$	7.32859	−	12.6935i	0.247469	−	0.428628i	−0.715354	−	0.698762i	$-0.753735\pi$
$877$	7.32859	−	12.6935i	0.247469	−	0.428628i	0.962823	+	0.270134i	$0.0870679\pi$
$878$	−2.22147	−	3.84770i	−0.0749709	−	0.129853i
$879$		0			0
$880$	−25.0868	+	43.4516i	−0.845675	+	1.46475i
$881$	31.3782			1.05716			0.528580	−	0.848884i	$-0.322725\pi$
$881$	31.3782			1.05716			0.528580	+	0.848884i	$0.322725\pi$
$882$		0			0
$883$	37.5474			1.26357			0.631786	−	0.775143i	$-0.282322\pi$
$883$	37.5474			1.26357			0.631786	+	0.775143i	$0.282322\pi$
$884$	22.7759	−	39.4490i	0.766036	−	1.32681i
$885$		0			0
$886$	−7.96633	−	13.7981i	−0.267634	−	0.463556i
$887$	−21.0389	+	36.4405i	−0.706417	+	1.22355i	0.259760	+	0.965673i	$0.416356\pi$
$887$	−21.0389	+	36.4405i	−0.706417	+	1.22355i	−0.966178	+	0.257878i	$0.916977\pi$
$888$		0			0
$889$	37.6962	+	19.3640i	1.26429	+	0.649448i
$890$	−34.2949			−1.14957
$891$		0			0
$892$	−6.10275	−	10.5703i	−0.204335	−	0.353919i
$893$	−9.27284	−	16.0610i	−0.310304	−	0.537462i
$894$		0			0
$895$	3.48098			0.116356
$896$	23.6191	−	15.2280i	0.789060	−	0.508730i
$897$		0			0
$898$	−0.961958	+	1.66616i	−0.0321010	+	0.0556005i
$899$	2.81537	+	4.87636i	0.0938977	+	0.162636i
$900$		0			0
$901$	7.05137	−	12.2133i	0.234915	−	0.406885i
$902$	−75.8600			−2.52586
$903$		0			0
$904$	−60.0708			−1.99793
$905$	2.76618	−	4.79116i	0.0919508	−	0.159263i
$906$		0			0
$907$	−14.3778	−	24.9030i	−0.477406	−	0.826892i	0.522258	−	0.852787i	$-0.325090\pi$
$907$	−14.3778	−	24.9030i	−0.477406	−	0.826892i	−0.999665	+	0.0258955i	$0.991756\pi$
$908$	53.9991	−	93.5292i	1.79202	−	3.10387i
$909$		0			0
$910$	1.17009	+	23.8299i	0.0387882	+	0.789953i
$911$	15.8362			0.524678			0.262339	−	0.964976i	$-0.415506\pi$
$911$	15.8362			0.524678			0.262339	+	0.964976i	$0.415506\pi$
$912$		0			0
$913$	−1.21480	−	2.10410i	−0.0402041	−	0.0696355i
$914$	−36.6116	−	63.4131i	−1.21100	−	2.09752i
$915$		0			0
$916$	−63.5651			−2.10025
$917$	4.99472	−	3.22025i	0.164940	−	0.106342i
$918$		0			0
$919$	−18.2715	+	31.6472i	−0.602722	+	1.04395i	0.389685	+	0.920948i	$0.372584\pi$
$919$	−18.2715	+	31.6472i	−0.602722	+	1.04395i	−0.992407	+	0.122997i	$0.960749\pi$
$920$	19.2772	+	33.3891i	0.635551	+	1.10081i
$921$		0			0
$922$	−49.4690	+	85.6829i	−1.62918	+	2.82182i
$923$	41.5181			1.36659
$924$		0			0
$925$	−0.447306			−0.0147073
$926$	0.522183	−	0.904447i	0.0171600	−	0.0297220i
$927$		0			0
$928$	26.1382	+	45.2726i	0.858027	+	1.48615i
$929$	20.5602	−	35.6114i	0.674559	−	1.16837i	−0.302038	−	0.953296i	$-0.597667\pi$
$929$	20.5602	−	35.6114i	0.674559	−	1.16837i	0.976598	−	0.215075i	$-0.0689996\pi$
$930$		0			0
$931$	51.2879	−	5.04885i	1.68089	−	0.165469i
$932$	95.9628			3.14337
$933$		0			0
$934$	51.9140	+	89.9178i	1.69868	+	2.94220i
$935$	5.83657	+	10.1092i	0.190876	+	0.330607i
$936$		0			0
$937$	10.3393			0.337770			0.168885	−	0.985636i	$-0.445983\pi$
$937$	10.3393			0.337770			0.168885	+	0.985636i	$0.445983\pi$
$938$	49.4632	+	25.4086i	1.61503	+	0.829619i
$939$		0			0
$940$	6.36226	−	11.0198i	0.207514	−	0.359425i
$941$	−11.0545	−	19.1470i	−0.360368	−	0.624175i	0.627654	−	0.778493i	$-0.284015\pi$
$941$	−11.0545	−	19.1470i	−0.360368	−	0.624175i	−0.988021	+	0.154318i	$0.950682\pi$
$942$		0			0
$943$	−15.4610	+	26.7792i	−0.503479	+	0.872051i
$944$	166.655			5.42417
$945$		0			0
$946$	−13.2656			−0.431302
$947$	−16.4641	+	28.5167i	−0.535013	+	0.926669i	0.464150	+	0.885757i	$0.346360\pi$
$947$	−16.4641	+	28.5167i	−0.535013	+	0.926669i	−0.999163	+	0.0409126i	$0.986973\pi$
$948$		0			0
$949$	−25.5868	−	44.3176i	−0.830582	−	1.43861i
$950$	9.77503	−	16.9308i	0.317144	−	0.549309i
$951$		0			0
$952$	−2.79186	−	56.8585i	−0.0904848	−	1.84279i
$953$	−15.2081			−0.492640			−0.246320	−	0.969189i	$-0.579221\pi$
$953$	−15.2081			−0.492640			−0.246320	+	0.969189i	$0.579221\pi$
$954$		0			0
$955$	6.36226	+	11.0198i	0.205878	+	0.356591i
$956$	−59.5651	−	103.170i	−1.92647	−	3.33675i
$957$		0			0
$958$	−25.6511			−0.828749
$959$	−1.43133	−	29.1503i	−0.0462202	−	0.941311i
$960$		0			0
$961$	14.3463	−	24.8485i	0.462783	−	0.801564i
$962$	2.01684	+	3.49326i	0.0650254	+	0.112627i
$963$		0			0
$964$	−11.9663	+	20.7263i	−0.385409	+	0.667549i
$965$	−5.48535			−0.176580
$966$		0			0
$967$	11.1718			0.359262			0.179631	−	0.983734i	$-0.442510\pi$
$967$	11.1718			0.359262			0.179631	+	0.983734i	$0.442510\pi$
$968$	−33.7245	+	58.4126i	−1.08395	+	1.87745i
$969$		0			0
$970$	3.36226	+	5.82360i	0.107956	+	0.186985i
$971$	−11.3756	+	19.7031i	−0.365060	+	0.632303i	−0.988786	−	0.149341i	$-0.952285\pi$
$971$	−11.3756	+	19.7031i	−0.365060	+	0.632303i	0.623726	+	0.781643i	$0.285618\pi$
$972$		0			0
$973$	−17.5682	−	9.02454i	−0.563211	−	0.289313i
$974$	111.016			3.55718
$975$		0			0
$976$	47.1355	+	81.6411i	1.50877	+	2.61327i
$977$	−3.70331	−	6.41433i	−0.118479	−	0.205212i	0.800686	−	0.599084i	$-0.204469\pi$
$977$	−3.70331	−	6.41433i	−0.118479	−	0.205212i	−0.919165	+	0.393872i	$0.871135\pi$
$978$		0			0
$979$	−56.7733			−1.81448
$980$	20.5948	+	28.7430i	0.657876	+	0.918161i
$981$		0			0
$982$	4.66877	−	8.08655i	0.148987	−	0.258052i
$983$	−0.0212057	−	0.0367293i	−0.000676355	−	0.00117148i	0.865687	−	0.500586i	$-0.166882\pi$
$983$	−0.0212057	−	0.0367293i	−0.000676355	−	0.00117148i	−0.866363	+	0.499414i	$0.833549\pi$
$984$		0			0
$985$	−7.25601	+	12.5678i	−0.231196	+	0.400442i
$986$	26.1382			0.832408
$987$		0			0
$988$	−126.293			−4.01792
$989$	−2.70365	+	4.68287i	−0.0859712	+	0.148907i
$990$		0			0
$991$	11.3676	+	19.6893i	0.361104	+	0.625450i	0.988143	−	0.153538i	$-0.0490666\pi$
$991$	11.3676	+	19.6893i	0.361104	+	0.625450i	−0.627039	+	0.778988i	$0.715733\pi$
$992$	−10.7112	+	18.5523i	−0.340080	+	0.589037i
$993$		0			0
$994$	72.1909	−	46.5436i	2.28976	−	1.47627i
$995$	5.42697			0.172046
$996$		0			0
$997$	2.51684	+	4.35929i	0.0797090	+	0.138060i	0.903124	−	0.429379i	$-0.141268\pi$
$997$	2.51684	+	4.35929i	0.0797090	+	0.138060i	−0.823415	+	0.567439i	$0.807934\pi$
$998$	11.7237	+	20.3060i	0.371106	+	0.642774i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.f.226.1	yes	6
3.2	odd	2		315.2.j.g.226.3	yes	6
7.2	even	3		2205.2.a.be.1.3		3
7.4	even	3	inner	315.2.j.f.46.1	✓	6
7.5	odd	6		2205.2.a.bd.1.3		3
21.2	odd	6		2205.2.a.bb.1.1		3
21.5	even	6		2205.2.a.bc.1.1		3
21.11	odd	6		315.2.j.g.46.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.j.f.46.1	✓	6	7.4	even	3	inner
315.2.j.f.226.1	yes	6	1.1	even	1	trivial
315.2.j.g.46.3	yes	6	21.11	odd	6
315.2.j.g.226.3	yes	6	3.2	odd	2
2205.2.a.bb.1.1		3	21.2	odd	6
2205.2.a.bc.1.1		3	21.5	even	6
2205.2.a.bd.1.3		3	7.5	odd	6
2205.2.a.be.1.3		3	7.2	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32772 + 2.29968i) q^{2} +(-2.52569 - 4.37462i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.35341 - 1.20891i) q^{7} +8.10275 q^{8} +O(q^{10})\)	\(q+(-1.32772 + 2.29968i) q^{2} +(-2.52569 - 4.37462i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.35341 - 1.20891i) q^{7} +8.10275 q^{8} +(-1.32772 - 2.29968i) q^{10} +(-2.19797 - 3.80699i) q^{11} +3.39593 q^{13} +(5.90478 - 3.80699i) q^{14} +(-5.70682 + 9.88450i) q^{16} +(1.32772 + 2.29968i) q^{17} +(3.68113 - 6.37590i) q^{19} +5.05137 q^{20} +11.6731 q^{22} +(2.37910 - 4.12071i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.50885 + 7.80956i) q^{26} +(0.655442 + 13.3486i) q^{28} -3.70682 q^{29} +(-0.759511 - 1.31551i) q^{31} +(-7.05137 - 12.2133i) q^{32} -7.05137 q^{34} +(2.22365 - 1.43366i) q^{35} +(0.223653 - 0.387378i) q^{37} +(9.77503 + 16.9308i) q^{38} +(-4.05137 + 7.01719i) q^{40} -6.49868 q^{41} -1.13642 q^{43} +(-11.1027 + 19.2305i) q^{44} +(6.31755 + 10.9423i) q^{46} +(1.25951 - 2.18154i) q^{47} +(4.07706 + 5.69013i) q^{49} +2.65544 q^{50} +(-8.57706 - 14.8559i) q^{52} +(-2.65544 - 4.59936i) q^{53} +4.39593 q^{55} +(-19.0691 - 9.79551i) q^{56} +(4.92162 - 8.52449i) q^{58} +(-7.30071 - 12.6452i) q^{59} +(4.12976 - 7.15295i) q^{61} +4.03367 q^{62} +14.6218 q^{64} +(-1.69797 + 2.94096i) q^{65} +(3.95748 + 6.85455i) q^{67} +(6.70682 - 11.6165i) q^{68} +(0.344558 + 7.01719i) q^{70} +12.2258 q^{71} +(-7.53454 - 13.0502i) q^{73} +(0.593898 + 1.02866i) q^{74} -37.1895 q^{76} +(0.570395 + 11.6165i) q^{77} +(-1.28520 + 2.22603i) q^{79} +(-5.70682 - 9.88450i) q^{80} +(8.62844 - 14.9449i) q^{82} +0.552694 q^{83} -2.65544 q^{85} +(1.50885 - 2.61341i) q^{86} +(-17.8096 - 30.8471i) q^{88} +(6.45748 - 11.1847i) q^{89} +(-7.99201 - 4.10538i) q^{91} -24.0354 q^{92} +(3.34456 + 5.79294i) q^{94} +(3.68113 + 6.37590i) q^{95} -2.53235 q^{97} +(-18.4987 + 1.82103i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + q^7 + 12 * q^8	\( 6 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + q^{7} + 12 q^{8} - 2 q^{10} - 10 q^{11} + 14 q^{13} + 2 q^{14} - 4 q^{16} + 2 q^{17} + q^{19} + 12 q^{20} + 4 q^{22} - 10 q^{23} - 3 q^{25} - 8 q^{28} + 8 q^{29} + q^{31} - 24 q^{32} - 24 q^{34} + q^{35} - 11 q^{37} + 28 q^{38} - 6 q^{40} + 4 q^{41} - 6 q^{43} - 30 q^{44} + 16 q^{46} + 2 q^{47} - 3 q^{49} + 4 q^{50} - 24 q^{52} - 4 q^{53} + 20 q^{55} - 42 q^{56} + 14 q^{58} - 4 q^{59} + 22 q^{61} + 60 q^{62} + 40 q^{64} - 7 q^{65} + 15 q^{67} + 10 q^{68} + 14 q^{70} + 32 q^{71} - 9 q^{73} - 6 q^{74} - 60 q^{76} - 26 q^{77} + 7 q^{79} - 4 q^{80} + 6 q^{82} + 28 q^{83} - 4 q^{85} - 18 q^{86} - 40 q^{88} + 30 q^{89} - 3 q^{91} - 36 q^{92} + 32 q^{94} + q^{95} - 8 q^{97} - 68 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + q^7 + 12 * q^8 - 2 * q^10 - 10 * q^11 + 14 * q^13 + 2 * q^14 - 4 * q^16 + 2 * q^17 + q^19 + 12 * q^20 + 4 * q^22 - 10 * q^23 - 3 * q^25 - 8 * q^28 + 8 * q^29 + q^31 - 24 * q^32 - 24 * q^34 + q^35 - 11 * q^37 + 28 * q^38 - 6 * q^40 + 4 * q^41 - 6 * q^43 - 30 * q^44 + 16 * q^46 + 2 * q^47 - 3 * q^49 + 4 * q^50 - 24 * q^52 - 4 * q^53 + 20 * q^55 - 42 * q^56 + 14 * q^58 - 4 * q^59 + 22 * q^61 + 60 * q^62 + 40 * q^64 - 7 * q^65 + 15 * q^67 + 10 * q^68 + 14 * q^70 + 32 * q^71 - 9 * q^73 - 6 * q^74 - 60 * q^76 - 26 * q^77 + 7 * q^79 - 4 * q^80 + 6 * q^82 + 28 * q^83 - 4 * q^85 - 18 * q^86 - 40 * q^88 + 30 * q^89 - 3 * q^91 - 36 * q^92 + 32 * q^94 + q^95 - 8 * q^97 - 68 * q^98

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