LMFDB - Embedded newform 315.2.bj.b.26.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(26,315)]

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([3, 0, 5]))

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

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

chi := DirichletCharacter("315.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bj (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 312x^{2} + 36 $ x^12 + 20x^10 + 144x^8 + 452x^6 + 604x^4 + 312*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.3
Root			$-0.398211i$ of defining polynomial
Character	$\chi$	$=$	315.26
Dual form			315.2.bj.b.206.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.344861 - 0.199105i) q^{2} +(-0.920714 - 1.59472i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30243 - 1.30338i) q^{7} +1.52970i q^{8} +O(q^{10})$	\(q+(-0.344861 - 0.199105i) q^{2} +(-0.920714 - 1.59472i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30243 - 1.30338i) q^{7} +1.52970i q^{8} +(-0.344861 + 0.199105i) q^{10} +(-4.44725 + 2.56762i) q^{11} -5.09545i q^{13} +(0.534507 + 0.907912i) q^{14} +(-1.53686 + 2.66191i) q^{16} +(2.24312 + 3.88520i) q^{17} +(-3.29211 - 1.90070i) q^{19} -1.84143 q^{20} +2.04491 q^{22} +(-2.29043 - 1.32238i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.01453 + 1.75722i) q^{26} +(0.0413461 + 4.87179i) q^{28} -9.13574i q^{29} +(-4.11981 + 2.37857i) q^{31} +(3.70952 - 2.14169i) q^{32} -1.78647i q^{34} +(-2.27998 + 1.34227i) q^{35} +(4.70077 - 8.14197i) q^{37} +(0.756879 + 1.31095i) q^{38} +(1.32476 + 0.764849i) q^{40} -7.51505 q^{41} +6.73246 q^{43} +(8.18929 + 4.72809i) q^{44} +(0.526586 + 0.912074i) q^{46} +(3.91274 - 6.77706i) q^{47} +(3.60239 + 6.00190i) q^{49} +0.398211i q^{50} +(-8.12584 + 4.69146i) q^{52} +(-2.50449 + 1.44597i) q^{53} +5.13524i q^{55} +(1.99378 - 3.52202i) q^{56} +(-1.81897 + 3.15056i) q^{58} +(2.46549 + 4.27036i) q^{59} +(10.2772 + 5.93354i) q^{61} +1.89434 q^{62} +4.44174 q^{64} +(-4.41279 - 2.54773i) q^{65} +(-3.49905 - 6.06052i) q^{67} +(4.13055 - 7.15432i) q^{68} +(1.05353 - 0.00894113i) q^{70} -1.23868i q^{71} +(0.500701 - 0.289080i) q^{73} +(-3.24222 + 1.87190i) q^{74} +7.00000i q^{76} +(13.5861 - 0.115303i) q^{77} +(2.46562 - 4.27058i) q^{79} +(1.53686 + 2.66191i) q^{80} +(2.59164 + 1.49629i) q^{82} +9.75683 q^{83} +4.48624 q^{85} +(-2.32176 - 1.34047i) q^{86} +(-3.92768 - 6.80294i) q^{88} +(-3.63524 + 6.29642i) q^{89} +(-6.64133 + 11.7319i) q^{91} +4.87014i q^{92} +(-2.69870 + 1.55809i) q^{94} +(-3.29211 + 1.90070i) q^{95} -0.313935i q^{97} +(-0.0473103 - 2.78707i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} + 6 q^{5} - 2 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 + 6 * q^5 - 2 * q^7	$ 12 q + 8 q^{4} + 6 q^{5} - 2 q^{7} - 12 q^{11} + 12 q^{14} - 16 q^{16} + 6 q^{19} + 16 q^{20} + 32 q^{22} - 12 q^{23} - 6 q^{25} - 20 q^{28} + 6 q^{31} - 60 q^{32} + 2 q^{35} - 10 q^{37} + 36 q^{38} - 24 q^{41} - 4 q^{43} - 12 q^{44} - 4 q^{46} + 6 q^{49} - 12 q^{53} + 60 q^{56} + 20 q^{58} + 24 q^{59} - 24 q^{62} - 56 q^{64} - 18 q^{65} + 6 q^{67} + 60 q^{68} - 12 q^{70} - 42 q^{73} - 84 q^{74} + 36 q^{77} + 18 q^{79} + 16 q^{80} - 72 q^{82} + 24 q^{83} + 84 q^{86} + 4 q^{88} - 12 q^{89} - 18 q^{91} + 12 q^{94} + 6 q^{95} - 12 q^{98}+O(q^{100}) $ 12 * q + 8 * q^4 + 6 * q^5 - 2 * q^7 - 12 * q^11 + 12 * q^14 - 16 * q^16 + 6 * q^19 + 16 * q^20 + 32 * q^22 - 12 * q^23 - 6 * q^25 - 20 * q^28 + 6 * q^31 - 60 * q^32 + 2 * q^35 - 10 * q^37 + 36 * q^38 - 24 * q^41 - 4 * q^43 - 12 * q^44 - 4 * q^46 + 6 * q^49 - 12 * q^53 + 60 * q^56 + 20 * q^58 + 24 * q^59 - 24 * q^62 - 56 * q^64 - 18 * q^65 + 6 * q^67 + 60 * q^68 - 12 * q^70 - 42 * q^73 - 84 * q^74 + 36 * q^77 + 18 * q^79 + 16 * q^80 - 72 * q^82 + 24 * q^83 + 84 * q^86 + 4 * q^88 - 12 * q^89 - 18 * q^91 + 12 * q^94 + 6 * q^95 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.344861	−	0.199105i	−0.243853	−	0.140789i	0.373093	−	0.927794i	$-0.378297\pi$
$2$	−0.344861	−	0.199105i	−0.243853	−	0.140789i	−0.616946	+	0.787005i	$0.711630\pi$
$3$		0			0
$3$		0			0
$4$	−0.920714	−	1.59472i	−0.460357	−	0.797362i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.30243	−	1.30338i	−0.870237	−	0.492632i
$7$	−2.30243	−	1.30338i	−0.870237	−	0.492632i
$8$			1.52970i			0.540830i
$9$		0			0
$10$	−0.344861	+	0.199105i	−0.109054	+	0.0629626i
$11$	−4.44725	+	2.56762i	−1.34090	+	0.774166i	−0.986939	−	0.161096i	$-0.948497\pi$
$11$	−4.44725	+	2.56762i	−1.34090	+	0.774166i	−0.353956	+	0.935262i	$0.615164\pi$
$12$		0			0
$13$		−	5.09545i		−	1.41322i	−0.707601	−	0.706612i	$-0.750222\pi$
$13$		−	5.09545i		−	1.41322i	0.707601	−	0.706612i	$-0.249778\pi$
$14$	0.534507	+	0.907912i	0.142853	+	0.242650i
$15$		0			0
$16$	−1.53686	+	2.66191i	−0.384214	+	0.665479i
$17$	2.24312	+	3.88520i	0.544037	+	0.942299i	0.998667	+	0.0516191i	$0.0164382\pi$
$17$	2.24312	+	3.88520i	0.544037	+	0.942299i	−0.454630	+	0.890680i	$0.650228\pi$
$18$		0			0
$19$	−3.29211	−	1.90070i	−0.755261	−	0.436050i	0.0723306	−	0.997381i	$-0.476956\pi$
$19$	−3.29211	−	1.90070i	−0.755261	−	0.436050i	−0.827592	+	0.561330i	$0.810290\pi$
$20$	−1.84143			−0.411756
$21$		0			0
$22$	2.04491			0.435976
$23$	−2.29043	−	1.32238i	−0.477588	−	0.275736i	0.241823	−	0.970320i	$-0.422255\pi$
$23$	−2.29043	−	1.32238i	−0.477588	−	0.275736i	−0.719411	+	0.694585i	$0.755588\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.01453	+	1.75722i	−0.198966	+	0.344619i
$27$		0			0
$28$	0.0413461	+	4.87179i	0.00781368	+	0.920681i
$29$		−	9.13574i		−	1.69646i	−0.529624	−	0.848232i	$-0.677667\pi$
$29$		−	9.13574i		−	1.69646i	0.529624	−	0.848232i	$-0.322333\pi$
$30$		0			0
$31$	−4.11981	+	2.37857i	−0.739939	+	0.427204i	−0.822047	−	0.569419i	$-0.807168\pi$
$31$	−4.11981	+	2.37857i	−0.739939	+	0.427204i	0.0821082	+	0.996623i	$0.473835\pi$
$32$	3.70952	−	2.14169i	0.655756	−	0.378601i
$33$		0			0
$34$		−	1.78647i		−	0.306377i
$35$	−2.27998	+	1.34227i	−0.385387	+	0.226886i
$36$		0			0
$37$	4.70077	−	8.14197i	0.772801	−	1.33853i	−0.163221	−	0.986590i	$-0.552188\pi$
$37$	4.70077	−	8.14197i	0.772801	−	1.33853i	0.936022	−	0.351942i	$-0.114478\pi$
$38$	0.756879	+	1.31095i	0.122782	+	0.212665i
$39$		0			0
$40$	1.32476	+	0.764849i	0.209462	+	0.120933i
$41$	−7.51505			−1.17365			−0.586827	−	0.809712i	$-0.699623\pi$
$41$	−7.51505			−1.17365			−0.586827	+	0.809712i	$0.699623\pi$
$42$		0			0
$43$	6.73246			1.02669			0.513345	−	0.858182i	$-0.328406\pi$
$43$	6.73246			1.02669			0.513345	+	0.858182i	$0.328406\pi$
$44$	8.18929	+	4.72809i	1.23458	+	0.712786i
$45$		0			0
$46$	0.526586	+	0.912074i	0.0776409	+	0.134478i
$47$	3.91274	−	6.77706i	0.570732	−	0.988536i	−0.425759	−	0.904836i	$-0.639993\pi$
$47$	3.91274	−	6.77706i	0.570732	−	0.988536i	0.996491	−	0.0836998i	$-0.0266737\pi$
$48$		0			0
$49$	3.60239	+	6.00190i	0.514627	+	0.857414i
$50$			0.398211i			0.0563155i
$51$		0			0
$52$	−8.12584	+	4.69146i	−1.12685	+	0.650588i
$53$	−2.50449	+	1.44597i	−0.344018	+	0.198619i	−0.662047	−	0.749462i	$-0.730312\pi$
$53$	−2.50449	+	1.44597i	−0.344018	+	0.198619i	0.318029	+	0.948081i	$0.396979\pi$
$54$		0			0
$55$			5.13524i			0.692435i
$56$	1.99378	−	3.52202i	0.266430	−	0.470650i
$57$		0			0
$58$	−1.81897	+	3.15056i	−0.238843	+	0.413688i
$59$	2.46549	+	4.27036i	0.320980	+	0.555953i	0.980690	−	0.195566i	$-0.0626545\pi$
$59$	2.46549	+	4.27036i	0.320980	+	0.555953i	−0.659711	+	0.751520i	$0.729321\pi$
$60$		0			0
$61$	10.2772	+	5.93354i	1.31586	+	0.759712i	0.983060	−	0.183285i	$-0.0586733\pi$
$61$	10.2772	+	5.93354i	1.31586	+	0.759712i	0.332800	+	0.942997i	$0.392007\pi$
$62$	1.89434			0.240582
$63$		0			0
$64$	4.44174			0.555218
$65$	−4.41279	−	2.54773i	−0.547340	−	0.316007i
$66$		0			0
$67$	−3.49905	−	6.06052i	−0.427476	−	0.740411i	0.569172	−	0.822219i	$-0.307264\pi$
$67$	−3.49905	−	6.06052i	−0.427476	−	0.740411i	−0.996648	+	0.0818078i	$0.973931\pi$
$68$	4.13055	−	7.15432i	0.500902	−	0.867588i
$69$		0			0
$70$	1.05353	−	0.00894113i	0.125921	−	0.00106867i
$71$		−	1.23868i		−	0.147004i	−0.997295	−	0.0735022i	$-0.976582\pi$
$71$		−	1.23868i		−	0.147004i	0.997295	−	0.0735022i	$-0.0234176\pi$
$72$		0			0
$73$	0.500701	−	0.289080i	0.0586026	−	0.0338342i	−0.470412	−	0.882447i	$-0.655895\pi$
$73$	0.500701	−	0.289080i	0.0586026	−	0.0338342i	0.529015	+	0.848612i	$0.322562\pi$
$74$	−3.24222	+	1.87190i	−0.376900	+	0.217603i
$75$		0			0
$76$			7.00000i			0.802955i
$77$	13.5861	−	0.115303i	1.54828	−	0.0131400i
$78$		0			0
$79$	2.46562	−	4.27058i	0.277404	−	0.480478i	−0.693335	−	0.720616i	$-0.743859\pi$
$79$	2.46562	−	4.27058i	0.277404	−	0.480478i	0.970739	+	0.240138i	$0.0771926\pi$
$80$	1.53686	+	2.66191i	0.171826	+	0.297611i
$81$		0			0
$82$	2.59164	+	1.49629i	0.286199	+	0.165237i
$83$	9.75683			1.07095			0.535475	−	0.844551i	$-0.320132\pi$
$83$	9.75683			1.07095			0.535475	+	0.844551i	$0.320132\pi$
$84$		0			0
$85$	4.48624			0.486601
$86$	−2.32176	−	1.34047i	−0.250362	−	0.144547i
$87$		0			0
$88$	−3.92768	−	6.80294i	−0.418692	−	0.725196i
$89$	−3.63524	+	6.29642i	−0.385334	+	0.667419i	−0.991816	−	0.127679i	$-0.959247\pi$
$89$	−3.63524	+	6.29642i	−0.385334	+	0.667419i	0.606481	+	0.795098i	$0.292581\pi$
$90$		0			0
$91$	−6.64133	+	11.7319i	−0.696200	+	1.22984i
$92$			4.87014i			0.507747i
$93$		0			0
$94$	−2.69870	+	1.55809i	−0.278350	+	0.160705i
$95$	−3.29211	+	1.90070i	−0.337763	+	0.195008i
$96$		0			0
$97$		−	0.313935i		−	0.0318752i	−0.999873	−	0.0159376i	$-0.994927\pi$
$97$		−	0.313935i		−	0.0318752i	0.999873	−	0.0159376i	$-0.00507332\pi$
$98$	−0.0473103	−	2.78707i	−0.00477906	−	0.281537i
$99$		0			0
$100$	−0.920714	+	1.59472i	−0.0920714	+	0.159472i
$101$	−4.92727	−	8.53428i	−0.490282	−	0.849193i	0.509656	−	0.860378i	$-0.329773\pi$
$101$	−4.92727	−	8.53428i	−0.490282	−	0.849193i	−0.999937	+	0.0111855i	$0.996439\pi$
$102$		0			0
$103$	−5.69390	−	3.28738i	−0.561037	−	0.323915i	0.192525	−	0.981292i	$-0.438332\pi$
$103$	−5.69390	−	3.28738i	−0.561037	−	0.323915i	−0.753562	+	0.657377i	$0.771666\pi$
$104$	7.79451			0.764314
$105$		0			0
$106$	1.15160			0.111853
$107$	4.17019	+	2.40766i	0.403148	+	0.232757i	0.687841	−	0.725861i	$-0.258559\pi$
$107$	4.17019	+	2.40766i	0.403148	+	0.232757i	−0.284694	+	0.958619i	$0.591892\pi$
$108$		0			0
$109$	−2.69220	−	4.66303i	−0.257866	−	0.446637i	0.707804	−	0.706409i	$-0.249686\pi$
$109$	−2.69220	−	4.66303i	−0.257866	−	0.446637i	−0.965670	+	0.259772i	$0.916353\pi$
$110$	1.02245	−	1.77094i	0.0974871	−	0.168853i
$111$		0			0
$112$	7.00800	−	4.12576i	0.662194	−	0.389848i
$113$		−	9.47858i		−	0.891669i	−0.895115	−	0.445835i	$-0.852907\pi$
$113$		−	9.47858i		−	0.891669i	0.895115	−	0.445835i	$-0.147093\pi$
$114$		0			0
$115$	−2.29043	+	1.32238i	−0.213584	+	0.123313i
$116$	−14.5690	+	8.41141i	−1.35270	+	0.780980i
$117$		0			0
$118$		−	1.96357i		−	0.180761i
$119$	−0.100731	−	11.8691i	−0.00923398	−	1.08803i
$120$		0			0
$121$	7.68533	−	13.3114i	0.698667	−	1.21013i
$122$	−2.36280	−	4.09249i	−0.213918	−	0.370516i
$123$		0			0
$124$	7.58633	+	4.37997i	0.681272	+	0.393333i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.62994			0.765783			0.382892	−	0.923793i	$-0.374928\pi$
$127$	8.62994			0.765783			0.382892	+	0.923793i	$0.374928\pi$
$128$	−8.95082	−	5.16776i	−0.791148	−	0.456769i
$129$		0			0
$130$	1.01453	+	1.75722i	0.0889804	+	0.154119i
$131$	−7.75657	+	13.4348i	−0.677695	+	1.17380i	0.297979	+	0.954573i	$0.403688\pi$
$131$	−7.75657	+	13.4348i	−0.677695	+	1.17380i	−0.975673	+	0.219229i	$0.929646\pi$
$132$		0			0
$133$	5.10251	+	8.66711i	0.442444	+	0.751533i
$134$			2.78671i			0.240735i
$135$		0			0
$136$	−5.94318	+	3.43130i	−0.509624	+	0.294231i
$137$	−0.956258	+	0.552096i	−0.0816986	+	0.0471687i	−0.540293	−	0.841477i	$-0.681687\pi$
$137$	−0.956258	+	0.552096i	−0.0816986	+	0.0471687i	0.458594	+	0.888646i	$0.348353\pi$
$138$		0			0
$139$		−	6.48061i		−	0.549678i	−0.961490	−	0.274839i	$-0.911375\pi$
$139$		−	6.48061i		−	0.549678i	0.961490	−	0.274839i	$-0.0886246\pi$
$140$	4.23976	+	2.40009i	0.358325	+	0.202844i
$141$		0			0
$142$	−0.246628	+	0.427172i	−0.0206966	+	0.0358475i
$143$	13.0832	+	22.6607i	1.09407	+	1.89499i
$144$		0			0
$145$	−7.91178	−	4.56787i	−0.657038	−	0.379341i
$146$	−0.230229			−0.0190539
$147$		0			0
$148$	−17.3123			−1.42306
$149$	−14.2091	−	8.20362i	−1.16405	−	0.672066i	−0.211781	−	0.977317i	$-0.567926\pi$
$149$	−14.2091	−	8.20362i	−1.16405	−	0.672066i	−0.952272	+	0.305251i	$0.901260\pi$
$150$		0			0
$151$	−4.67919	−	8.10460i	−0.380787	−	0.659543i	0.610388	−	0.792103i	$-0.291014\pi$
$151$	−4.67919	−	8.10460i	−0.380787	−	0.659543i	−0.991175	+	0.132560i	$0.957680\pi$
$152$	2.90749	−	5.03593i	0.235829	−	0.408468i
$153$		0			0
$154$	−4.70826	−	2.66530i	−0.379402	−	0.214776i
$155$			4.75714i			0.382103i
$156$		0			0
$157$	−7.68946	+	4.43951i	−0.613686	+	0.354312i	−0.774407	−	0.632688i	$-0.781952\pi$
$157$	−7.68946	+	4.43951i	−0.613686	+	0.354312i	0.160721	+	0.987000i	$0.448618\pi$
$158$	−1.70059	+	0.981836i	−0.135292	+	0.0781107i
$159$		0			0
$160$		−	4.28338i		−	0.338631i
$161$	3.54999	+	6.03000i	0.279779	+	0.475231i
$162$		0			0
$163$	3.53445	−	6.12185i	0.276840	−	0.479501i	−0.693758	−	0.720208i	$-0.744046\pi$
$163$	3.53445	−	6.12185i	0.276840	−	0.479501i	0.970598	+	0.240708i	$0.0773795\pi$
$164$	6.91921	+	11.9844i	0.540300	+	0.935827i
$165$		0			0
$166$	−3.36474	−	1.94264i	−0.261155	−	0.150778i
$167$	−25.0272			−1.93666			−0.968331	−	0.249669i	$-0.919678\pi$
$167$	−25.0272			−1.93666			−0.968331	+	0.249669i	$0.919678\pi$
$168$		0			0
$169$	−12.9637			−0.997204
$170$	−1.54713	−	0.893235i	−0.118659	−	0.0685080i
$171$		0			0
$172$	−6.19867	−	10.7364i	−0.472644	−	0.818644i
$173$	−0.364708	+	0.631692i	−0.0277282	+	0.0480267i	−0.879557	−	0.475794i	$-0.842161\pi$
$173$	−0.364708	+	0.631692i	−0.0277282	+	0.0480267i	0.851828	+	0.523821i	$0.175494\pi$
$174$		0			0
$175$	0.0224533	+	2.64566i	0.00169731	+	0.199993i
$176$		−	15.7843i		−	1.18978i
$177$		0			0
$178$	2.50730	−	1.44759i	0.187930	−	0.108502i
$179$	−2.25510	+	1.30198i	−0.168554	+	0.0973147i	−0.581904	−	0.813258i	$-0.697692\pi$
$179$	−2.25510	+	1.30198i	−0.168554	+	0.0973147i	0.413350	+	0.910572i	$0.364359\pi$
$180$		0			0
$181$			3.89250i			0.289327i	0.989481	+	0.144663i	$0.0462100\pi$
$181$			3.89250i			0.289327i	−0.989481	+	0.144663i	$0.953790\pi$
$182$	4.62622	−	2.72356i	0.342918	−	0.201884i
$183$		0			0
$184$	2.02284	−	3.50367i	0.149126	−	0.258294i
$185$	−4.70077	−	8.14197i	−0.345607	−	0.598609i
$186$		0			0
$187$	−19.9514	−	11.5190i	−1.45899	−	0.842350i
$188$	−14.4101			−1.05096
$189$		0			0
$190$	1.51376			0.109819
$191$	6.64485	+	3.83640i	0.480804	+	0.277592i	0.720752	−	0.693193i	$-0.243797\pi$
$191$	6.64485	+	3.83640i	0.480804	+	0.277592i	−0.239947	+	0.970786i	$0.577130\pi$
$192$		0			0
$193$	0.0303002	+	0.0524815i	0.00218106	+	0.00377770i	0.867114	−	0.498110i	$-0.165972\pi$
$193$	0.0303002	+	0.0524815i	0.00218106	+	0.00377770i	−0.864933	+	0.501888i	$0.832639\pi$
$194$	−0.0625061	+	0.108264i	−0.00448768	+	0.00777288i
$195$		0			0
$196$	6.25461	−	11.2708i	0.446758	−	0.805060i
$197$			12.3018i			0.876464i	0.898862	+	0.438232i	$0.144395\pi$
$197$			12.3018i			0.876464i	−0.898862	+	0.438232i	$0.855605\pi$
$198$		0			0
$199$	−9.68559	+	5.59198i	−0.686593	+	0.396405i	−0.802335	−	0.596875i	$-0.796409\pi$
$199$	−9.68559	+	5.59198i	−0.686593	+	0.396405i	0.115741	+	0.993279i	$0.463076\pi$
$200$	1.32476	−	0.764849i	0.0936745	−	0.0540830i
$201$		0			0
$202$			3.92418i			0.276105i
$203$	−11.9074	+	21.0344i	−0.835734	+	1.47633i
$204$		0			0
$205$	−3.75753	+	6.50822i	−0.262437	+	0.454554i
$206$	1.30907	+	2.26737i	0.0912071	+	0.157975i
$207$		0			0
$208$	13.5637	+	7.83099i	0.940471	+	0.542981i
$209$	19.5211			1.35030
$210$		0			0
$211$	5.62551			0.387276			0.193638	−	0.981073i	$-0.437971\pi$
$211$	5.62551			0.387276			0.193638	+	0.981073i	$0.437971\pi$
$212$	4.61184	+	2.66265i	0.316742	+	0.182871i
$213$		0			0
$214$	−0.958756	−	1.66061i	−0.0655392	−	0.113517i
$215$	3.36623	−	5.83048i	0.229575	−	0.397636i
$216$		0			0
$217$	12.5858	−	0.106813i	0.854377	−	0.00725097i
$218$			2.14412i			0.145218i
$219$		0			0
$220$	8.18929	−	4.72809i	0.552122	−	0.318768i
$221$	19.7969	−	11.4297i	1.33168	−	0.768846i
$222$		0			0
$223$			3.16328i			0.211829i	0.994375	+	0.105914i	$0.0337770\pi$
$223$			3.16328i			0.211829i	−0.994375	+	0.105914i	$0.966223\pi$
$224$	−11.3324	+	0.0961759i	−0.757175	+	0.00642603i
$225$		0			0
$226$	−1.88724	+	3.26879i	−0.125537	+	0.217436i
$227$	−5.62242	−	9.73831i	−0.373173	−	0.646354i	0.616879	−	0.787058i	$-0.288397\pi$
$227$	−5.62242	−	9.73831i	−0.373173	−	0.646354i	−0.990052	+	0.140704i	$0.955063\pi$
$228$		0			0
$229$	19.7354	+	11.3942i	1.30415	+	0.752952i	0.981113	−	0.193434i	$-0.0619626\pi$
$229$	19.7354	+	11.3942i	1.30415	+	0.752952i	0.323038	+	0.946386i	$0.395296\pi$
$230$	1.05317			0.0694442
$231$		0			0
$232$	13.9749			0.917499
$233$	2.79461	+	1.61347i	0.183081	+	0.105702i	0.588740	−	0.808323i	$-0.299624\pi$
$233$	2.79461	+	1.61347i	0.183081	+	0.105702i	−0.405658	+	0.914025i	$0.632958\pi$
$234$		0			0
$235$	−3.91274	−	6.77706i	−0.255239	−	0.442087i
$236$	4.54003	−	7.86356i	0.295531	−	0.511874i
$237$		0			0
$238$	−2.32845	+	4.11323i	−0.150931	+	0.266621i
$239$		−	23.1272i		−	1.49598i	−0.663712	−	0.747988i	$-0.731020\pi$
$239$		−	23.1272i		−	1.49598i	0.663712	−	0.747988i	$-0.268980\pi$
$240$		0			0
$241$	12.8600	−	7.42473i	0.828386	−	0.478269i	−0.0249139	−	0.999690i	$-0.507931\pi$
$241$	12.8600	−	7.42473i	0.828386	−	0.478269i	0.853300	+	0.521421i	$0.174598\pi$
$242$	−5.30074	+	3.06038i	−0.340744	+	0.196729i
$243$		0			0
$244$		−	21.8524i		−	1.39896i
$245$	6.99899	−	0.118807i	0.447149	−	0.00759032i
$246$		0			0
$247$	−9.68492	+	16.7748i	−0.616237	+	1.06735i
$248$	−3.63849	−	6.30206i	−0.231045	−	0.400181i
$249$		0			0
$250$	0.344861	+	0.199105i	0.0218109	+	0.0125925i
$251$	12.6710			0.799789			0.399895	−	0.916561i	$-0.369047\pi$
$251$	12.6710			0.799789			0.399895	+	0.916561i	$0.369047\pi$
$252$		0			0
$253$	13.5815			0.853861
$254$	−2.97613	−	1.71827i	−0.186739	−	0.107814i
$255$		0			0
$256$	−2.38389	−	4.12901i	−0.148993	−	0.258063i
$257$	−3.98336	+	6.89937i	−0.248475	+	0.430371i	−0.963103	−	0.269134i	$-0.913263\pi$
$257$	−3.98336	+	6.89937i	−0.248475	+	0.430371i	0.714628	+	0.699505i	$0.246596\pi$
$258$		0			0
$259$	−21.4353	+	12.6194i	−1.33192	+	0.784133i
$260$			9.38291i			0.581904i
$261$		0			0
$262$	5.34987	−	3.08875i	0.330516	−	0.190824i
$263$	6.06499	−	3.50162i	0.373983	−	0.215919i	−0.301214	−	0.953557i	$-0.597392\pi$
$263$	6.06499	−	3.50162i	0.373983	−	0.215919i	0.675197	+	0.737637i	$0.264058\pi$
$264$		0			0
$265$			2.89193i			0.177650i
$266$	−0.0339888	−	4.00488i	−0.00208399	−	0.245555i
$267$		0			0
$268$	−6.44324	+	11.1600i	−0.393584	+	0.681707i
$269$	−5.08855	−	8.81364i	−0.310255	−	0.537377i	0.668163	−	0.744015i	$-0.267081\pi$
$269$	−5.08855	−	8.81364i	−0.310255	−	0.537377i	−0.978417	+	0.206638i	$0.933748\pi$
$270$		0			0
$271$	2.60706	+	1.50519i	0.158367	+	0.0914335i	0.577089	−	0.816681i	$-0.304188\pi$
$271$	2.60706	+	1.50519i	0.158367	+	0.0914335i	−0.418722	+	0.908115i	$0.637522\pi$
$272$	−13.7894			−0.836107
$273$		0			0
$274$	0.439701			0.0265633
$275$	4.44725	+	2.56762i	0.268179	+	0.154833i
$276$		0			0
$277$	16.5884	+	28.7319i	0.996700	+	1.72634i	0.568647	+	0.822581i	$0.307467\pi$
$277$	16.5884	+	28.7319i	0.996700	+	1.72634i	0.428053	+	0.903754i	$0.359200\pi$
$278$	−1.29032	+	2.23491i	−0.0773885	+	0.134041i
$279$		0			0
$280$	−2.05327	−	3.48768i	−0.122706	−	0.208429i
$281$			6.12689i			0.365500i	0.983159	+	0.182750i	$0.0584998\pi$
$281$			6.12689i			0.365500i	−0.983159	+	0.182750i	$0.941500\pi$
$282$		0			0
$283$	−7.12461	+	4.11340i	−0.423514	+	0.244516i	−0.696580	−	0.717479i	$-0.745296\pi$
$283$	−7.12461	+	4.11340i	−0.423514	+	0.244516i	0.273066	+	0.961995i	$0.411962\pi$
$284$	−1.97535	+	1.14047i	−0.117216	+	0.0676745i
$285$		0			0
$286$		−	10.4197i		−	0.616131i
$287$	17.3029	+	9.79499i	1.02136	+	0.578180i
$288$		0			0
$289$	−1.56319	+	2.70752i	−0.0919522	+	0.159266i
$290$	1.81897	+	3.15056i	0.106814	+	0.185007i
$291$		0			0
$292$	−0.922005	−	0.532320i	−0.0539562	−	0.0311516i
$293$	31.5059			1.84059			0.920297	−	0.391220i	$-0.127947\pi$
$293$	31.5059			1.84059			0.920297	+	0.391220i	$0.127947\pi$
$294$		0			0
$295$	4.93099			0.287093
$296$	12.4547	+	7.19075i	0.723918	+	0.417954i
$297$		0			0
$298$	3.26677	+	5.65821i	0.189239	+	0.327771i
$299$	−6.73813	+	11.6708i	−0.389676	+	0.674939i
$300$		0			0
$301$	−15.5010	−	8.77498i	−0.893465	−	0.505781i
$302$			3.72661i			0.214442i
$303$		0			0
$304$	10.1190	−	5.84221i	0.580364	−	0.335073i
$305$	10.2772	−	5.93354i	0.588470	−	0.339754i
$306$		0			0
$307$			23.7716i			1.35672i	0.734730	+	0.678360i	$0.237309\pi$
$307$			23.7716i			1.35672i	−0.734730	+	0.678360i	$0.762691\pi$
$308$	−12.6928	−	21.5599i	−0.723237	−	1.22849i
$309$		0			0
$310$	0.947172	−	1.64055i	0.0537958	−	0.0931770i
$311$	9.29730	+	16.1034i	0.527201	+	0.913139i	0.999497	+	0.0316995i	$0.0100920\pi$
$311$	9.29730	+	16.1034i	0.527201	+	0.913139i	−0.472296	+	0.881440i	$0.656575\pi$
$312$		0			0
$313$	−7.05481	−	4.07310i	−0.398762	−	0.230225i	0.287188	−	0.957874i	$-0.407280\pi$
$313$	−7.05481	−	4.07310i	−0.398762	−	0.230225i	−0.685950	+	0.727649i	$0.740613\pi$
$314$	3.53572			0.199532
$315$		0			0
$316$	−9.08053			−0.510820
$317$	−27.2045	−	15.7065i	−1.52795	−	0.882165i	−0.999448	−	0.0332365i	$-0.989419\pi$
$317$	−27.2045	−	15.7065i	−1.52795	−	0.882165i	−0.528507	−	0.848929i	$-0.677248\pi$
$318$		0			0
$319$	23.4571	+	40.6289i	1.31335	+	2.27478i
$320$	2.22087	−	3.84666i	0.124150	−	0.215035i
$321$		0			0
$322$	−0.0236472	−	2.78633i	−0.00131781	−	0.155276i
$323$		−	17.0540i		−	0.948910i
$324$		0			0
$325$	−4.41279	+	2.54773i	−0.244778	+	0.141322i
$326$	−2.43779	+	1.40746i	−0.135017	+	0.0779518i
$327$		0			0
$328$		−	11.4958i		−	0.634747i
$329$	−17.8419	+	10.5039i	−0.983657	+	0.579100i
$330$		0			0
$331$	−2.76563	+	4.79021i	−0.152013	+	0.263294i	−0.931967	−	0.362542i	$-0.881909\pi$
$331$	−2.76563	+	4.79021i	−0.152013	+	0.263294i	0.779955	+	0.625836i	$0.215242\pi$
$332$	−8.98325	−	15.5594i	−0.493020	−	0.853935i
$333$		0			0
$334$	8.63089	+	4.98305i	0.472261	+	0.272660i
$335$	−6.99809			−0.382347
$336$		0			0
$337$	13.3563			0.727566			0.363783	−	0.931484i	$-0.381485\pi$
$337$	13.3563			0.727566			0.363783	+	0.931484i	$0.381485\pi$
$338$	4.47065	+	2.58113i	0.243172	+	0.140395i
$339$		0			0
$340$	−4.13055	−	7.15432i	−0.224010	−	0.387997i
$341$	12.2145	−	21.1562i	0.661454	−	1.14567i
$342$		0			0
$343$	−0.471474	−	18.5143i	−0.0254572	−	0.999676i
$344$			10.2986i			0.555265i
$345$		0			0
$346$	0.251547	−	0.145230i	0.0135232	−	0.00780764i
$347$	28.0670	−	16.2045i	1.50671	−	0.869901i	0.506744	−	0.862097i	$-0.330849\pi$
$347$	28.0670	−	16.2045i	1.50671	−	0.869901i	0.999970	−	0.00780492i	$-0.00248441\pi$
$348$		0			0
$349$			6.33160i			0.338923i	0.985537	+	0.169461i	$0.0542028\pi$
$349$			6.33160i			0.338923i	−0.985537	+	0.169461i	$0.945797\pi$
$350$	0.519021	−	0.916853i	0.0277428	−	0.0490079i
$351$		0			0
$352$	−10.9981	+	19.0493i	−0.586200	+	1.01533i
$353$	−7.79492	−	13.5012i	−0.414882	−	0.718596i	0.580534	−	0.814236i	$-0.302844\pi$
$353$	−7.79492	−	13.5012i	−0.414882	−	0.718596i	−0.995416	+	0.0956395i	$0.969510\pi$
$354$		0			0
$355$	−1.07273	−	0.619340i	−0.0569345	−	0.0328712i
$356$	13.3881			0.709566
$357$		0			0
$358$	1.03693			0.0548032
$359$	9.43467	+	5.44711i	0.497943	+	0.287487i	0.727864	−	0.685722i	$-0.240513\pi$
$359$	9.43467	+	5.44711i	0.497943	+	0.287487i	−0.229921	+	0.973209i	$0.573847\pi$
$360$		0			0
$361$	−2.27469	−	3.93987i	−0.119720	−	0.207362i
$362$	0.775017	−	1.34237i	0.0407340	−	0.0705533i
$363$		0			0
$364$	24.8240	−	0.210677i	1.30113	−	0.0110425i
$365$		−	0.578159i		−	0.0302623i
$366$		0			0
$367$	−4.30786	+	2.48714i	−0.224868	+	0.129828i	−0.608202	−	0.793782i	$-0.708109\pi$
$367$	−4.30786	+	2.48714i	−0.224868	+	0.129828i	0.383334	+	0.923610i	$0.374776\pi$
$368$	7.04013	−	4.06462i	0.366992	−	0.211883i
$369$		0			0
$370$			3.74379i			0.194630i
$371$	7.65106	−	0.0649334i	0.397223	−	0.00337117i
$372$		0			0
$373$	6.43003	−	11.1371i	0.332934	−	0.576659i	−0.650151	−	0.759805i	$-0.725295\pi$
$373$	6.43003	−	11.1371i	0.332934	−	0.576659i	0.983086	+	0.183145i	$0.0586279\pi$
$374$	4.58697	+	7.94487i	0.237187	+	0.410820i
$375$		0			0
$376$	10.3669	+	5.98531i	0.534630	+	0.308669i
$377$	−46.5508			−2.39749
$378$		0			0
$379$	−37.8472			−1.94408			−0.972039	−	0.234818i	$-0.924550\pi$
$379$	−37.8472			−1.94408			−0.972039	+	0.234818i	$0.924550\pi$
$380$	6.06218	+	3.50000i	0.310983	+	0.179546i
$381$		0			0
$382$	−1.52770	−	2.64605i	−0.0781638	−	0.135384i
$383$	−14.2211	+	24.6317i	−0.726665	+	1.25862i	0.231620	+	0.972806i	$0.425597\pi$
$383$	−14.2211	+	24.6317i	−0.726665	+	1.25862i	−0.958285	+	0.285814i	$0.907736\pi$
$384$		0			0
$385$	6.69318	−	11.8235i	0.341116	−	0.602583i
$386$		−	0.0241317i		−	0.00122827i
$387$		0			0
$388$	−0.500639	+	0.289044i	−0.0254161	+	0.0146740i
$389$	−8.24116	+	4.75803i	−0.417843	+	0.241242i	−0.694154	−	0.719826i	$-0.744221\pi$
$389$	−8.24116	+	4.75803i	−0.417843	+	0.241242i	0.276311	+	0.961068i	$0.410888\pi$
$390$		0			0
$391$		−	11.8650i		−	0.600041i
$392$	−9.18109	+	5.51056i	−0.463715	+	0.278325i
$393$		0			0
$394$	2.44935	−	4.24239i	0.123396	−	0.213729i
$395$	−2.46562	−	4.27058i	−0.124059	−	0.214876i
$396$		0			0
$397$	−8.36250	−	4.82809i	−0.419702	−	0.242315i	0.275248	−	0.961373i	$-0.411240\pi$
$397$	−8.36250	−	4.82809i	−0.419702	−	0.242315i	−0.694950	+	0.719058i	$0.744573\pi$
$398$	4.45357			0.223237
$399$		0			0
$400$	3.07371			0.153686
$401$	7.76875	+	4.48529i	0.387953	+	0.223985i	0.681273	−	0.732030i	$-0.261427\pi$
$401$	7.76875	+	4.48529i	0.387953	+	0.223985i	−0.293320	+	0.956014i	$0.594760\pi$
$402$		0			0
$403$	12.1199	+	20.9923i	0.603735	+	1.04570i
$404$	−9.07322	+	15.7153i	−0.451409	+	0.781864i
$405$		0			0
$406$	8.29445	−	4.88312i	0.411647	−	0.242345i
$407$			48.2791i			2.39311i
$408$		0			0
$409$	26.3659	−	15.2223i	1.30371	−	0.752696i	0.322670	−	0.946512i	$-0.395420\pi$
$409$	26.3659	−	15.2223i	1.30371	−	0.752696i	0.981038	+	0.193815i	$0.0620863\pi$
$410$	2.59164	−	1.49629i	0.127992	−	0.0738963i
$411$		0			0
$412$			12.1069i			0.596466i
$413$	−0.110717	−	13.0457i	−0.00544802	−	0.641936i
$414$		0			0
$415$	4.87841	−	8.44966i	0.239472	−	0.414778i
$416$	−10.9129	−	18.9017i	−0.535048	−	0.926731i
$417$		0			0
$418$	−6.73205	−	3.88675i	−0.329275	−	0.190107i
$419$	−24.0920			−1.17697			−0.588485	−	0.808508i	$-0.700276\pi$
$419$	−24.0920			−1.17697			−0.588485	+	0.808508i	$0.700276\pi$
$420$		0			0
$421$	−22.3663			−1.09007			−0.545033	−	0.838415i	$-0.683483\pi$
$421$	−22.3663			−1.09007			−0.545033	+	0.838415i	$0.683483\pi$
$422$	−1.94002	−	1.12007i	−0.0944386	−	0.0545241i
$423$		0			0
$424$	−2.21189	−	3.83111i	−0.107419	−	0.186055i
$425$	2.24312	−	3.88520i	0.108807	−	0.188460i
$426$		0			0
$427$	−15.9289	−	27.0567i	−0.770852	−	1.30937i
$428$		−	8.86707i		−	0.428606i
$429$		0			0
$430$	−2.32176	+	1.34047i	−0.111965	+	0.0646432i
$431$	8.90954	−	5.14392i	0.429157	−	0.247774i	−0.269830	−	0.962908i	$-0.586968\pi$
$431$	8.90954	−	5.14392i	0.429157	−	0.247774i	0.698988	+	0.715134i	$0.253634\pi$
$432$		0			0
$433$			4.91252i			0.236080i	0.993009	+	0.118040i	$0.0376612\pi$
$433$			4.91252i			0.236080i	−0.993009	+	0.118040i	$0.962339\pi$
$434$	−4.36160	−	2.46906i	−0.209363	−	0.118519i
$435$		0			0
$436$	−4.95749	+	8.58663i	−0.237421	+	0.411225i
$437$	5.02690	+	8.70684i	0.240469	+	0.416505i
$438$		0			0
$439$	−27.0138	−	15.5964i	−1.28930	−	0.744378i	−0.310771	−	0.950485i	$-0.600587\pi$
$439$	−27.0138	−	15.5964i	−1.28930	−	0.744378i	−0.978529	+	0.206107i	$0.933920\pi$
$440$	−7.85536			−0.374490
$441$		0			0
$442$	−9.10288			−0.432980
$443$	9.14111	+	5.27762i	0.434307	+	0.250747i	0.701180	−	0.712984i	$-0.252657\pi$
$443$	9.14111	+	5.27762i	0.434307	+	0.250747i	−0.266873	+	0.963732i	$0.585990\pi$
$444$		0			0
$445$	3.63524	+	6.29642i	0.172327	+	0.298479i
$446$	0.629826	−	1.09089i	0.0298231	−	0.0516552i
$447$		0			0
$448$	−10.2268	−	5.78929i	−0.483171	−	0.273518i
$449$		−	32.9402i		−	1.55454i	−0.629166	−	0.777271i	$-0.716603\pi$
$449$		−	32.9402i		−	1.55454i	0.629166	−	0.777271i	$-0.283397\pi$
$450$		0			0
$451$	33.4213	−	19.2958i	1.57375	−	0.908603i
$452$	−15.1157	+	8.72706i	−0.710983	+	0.410486i
$453$		0			0
$454$			4.47781i			0.210154i
$455$	6.83949	+	11.6175i	0.320640	+	0.544638i
$456$		0			0
$457$	16.0797	−	27.8509i	0.752177	−	1.30281i	−0.194589	−	0.980885i	$-0.562337\pi$
$457$	16.0797	−	27.8509i	0.752177	−	1.30281i	0.946766	−	0.321923i	$-0.104329\pi$
$458$	−4.53730	−	7.85884i	−0.212014	−	0.367220i
$459$		0			0
$460$	4.21767	+	2.43507i	0.196650	+	0.113536i
$461$	39.6617			1.84723			0.923615	−	0.383322i	$-0.125220\pi$
$461$	39.6617			1.84723			0.923615	+	0.383322i	$0.125220\pi$
$462$		0			0
$463$	−34.2241			−1.59053			−0.795265	−	0.606262i	$-0.792668\pi$
$463$	−34.2241			−1.59053			−0.795265	+	0.606262i	$0.792668\pi$
$464$	24.3186	+	14.0403i	1.12896	+	0.651806i
$465$		0			0
$466$	−0.642501	−	1.11284i	−0.0297633	−	0.0515515i
$467$	14.8493	−	25.7197i	0.687144	−	1.19017i	−0.285614	−	0.958345i	$-0.592198\pi$
$467$	14.8493	−	25.7197i	0.687144	−	1.19017i	0.972758	−	0.231823i	$-0.0744690\pi$
$468$		0			0
$469$	0.157130	+	18.5145i	0.00725559	+	0.854922i
$470$			3.11619i			0.143739i
$471$		0			0
$472$	−6.53236	+	3.77146i	−0.300676	+	0.173595i
$473$	−29.9409	+	17.2864i	−1.37669	+	0.794829i
$474$		0			0
$475$			3.80140i			0.174420i
$476$	−18.8351	+	11.0886i	−0.863306	+	0.508247i
$477$		0			0
$478$	−4.60476	+	7.97567i	−0.210617	+	0.364799i
$479$	−4.69594	−	8.13361i	−0.214563	−	0.371634i	0.738574	−	0.674172i	$-0.235499\pi$
$479$	−4.69594	−	8.13361i	−0.214563	−	0.371634i	−0.953137	+	0.302538i	$0.902166\pi$
$480$		0			0
$481$	−41.4870	−	23.9525i	−1.89165	−	1.09214i
$482$	−5.91321			−0.269339
$483$		0			0
$484$	−28.3040			−1.28654
$485$	−0.271875	−	0.156967i	−0.0123452	−	0.00712752i
$486$		0			0
$487$	−3.97135	−	6.87859i	−0.179959	−	0.311699i	0.761907	−	0.647686i	$-0.224263\pi$
$487$	−3.97135	−	6.87859i	−0.179959	−	0.311699i	−0.941866	+	0.335988i	$0.890930\pi$
$488$	−9.07652	+	15.7210i	−0.410875	+	0.711656i
$489$		0			0
$490$	−2.43733	−	1.35256i	−0.110107	−	0.0611026i
$491$			10.6921i			0.482526i	0.970460	+	0.241263i	$0.0775616\pi$
$491$			10.6921i			0.482526i	−0.970460	+	0.241263i	$0.922438\pi$
$492$		0			0
$493$	35.4942	−	20.4926i	1.59858	−	0.922939i
$494$	6.67990	−	3.85664i	0.300543	−	0.173518i
$495$		0			0
$496$		−	14.6221i		−	0.656552i
$497$	−1.61447	+	2.85198i	−0.0724191	+	0.127929i
$498$		0			0
$499$	−3.61851	+	6.26745i	−0.161987	+	0.280570i	−0.935581	−	0.353112i	$-0.885124\pi$
$499$	−3.61851	+	6.26745i	−0.161987	+	0.280570i	0.773594	+	0.633681i	$0.218457\pi$
$500$	0.920714	+	1.59472i	0.0411756	+	0.0713182i
$501$		0			0
$502$	−4.36974	−	2.52287i	−0.195031	−	0.112601i
$503$	−2.22842			−0.0993603			−0.0496802	−	0.998765i	$-0.515820\pi$
$503$	−2.22842			−0.0993603			−0.0496802	+	0.998765i	$0.515820\pi$
$504$		0			0
$505$	−9.85454			−0.438521
$506$	−4.68372	−	2.70415i	−0.208217	−	0.120214i
$507$		0			0
$508$	−7.94571	−	13.7624i	−0.352534	−	0.610606i
$509$	−14.2749	+	24.7248i	−0.632724	+	1.09591i	0.354269	+	0.935144i	$0.384730\pi$
$509$	−14.2749	+	24.7248i	−0.632724	+	1.09591i	−0.986993	+	0.160766i	$0.948604\pi$
$510$		0			0
$511$	−1.52961	+	0.0129816i	−0.0676660	+	0.000574271i
$512$			22.5696i			0.997445i
$513$		0			0
$514$	2.74740	−	1.58621i	0.121183	−	0.0699649i
$515$	−5.69390	+	3.28738i	−0.250903	+	0.144859i
$516$		0			0
$517$			40.1857i			1.76736i
$518$	9.90478	−	0.0840604i	0.435191	−	0.00369340i
$519$		0			0
$520$	3.89725	−	6.75024i	0.170906	−	0.296018i
$521$	0.909280	+	1.57492i	0.0398363	+	0.0689985i	0.885256	−	0.465104i	$-0.153983\pi$
$521$	0.909280	+	1.57492i	0.0398363	+	0.0689985i	−0.845420	+	0.534102i	$0.820650\pi$
$522$		0			0
$523$	25.4727	+	14.7067i	1.11384	+	0.643077i	0.939822	−	0.341665i	$-0.110991\pi$
$523$	25.4727	+	14.7067i	1.11384	+	0.643077i	0.174021	+	0.984742i	$0.444324\pi$
$524$	28.5663			1.24793
$525$		0			0
$526$	−2.78877			−0.121596
$527$	−18.4824	−	10.6708i	−0.805108	−	0.464829i
$528$		0			0
$529$	−8.00261	−	13.8609i	−0.347940	−	0.602649i
$530$	0.575800	−	0.997314i	0.0250111	−	0.0433206i
$531$		0			0
$532$	9.12368	−	16.1170i	0.395562	−	0.698762i
$533$			38.2926i			1.65864i
$534$		0			0
$535$	4.17019	−	2.40766i	0.180293	−	0.104092i
$536$	9.27077	−	5.35248i	0.400436	−	0.231192i
$537$		0			0
$538$			4.05263i			0.174721i
$539$	−31.4313	−	17.4424i	−1.35384	−	0.751296i
$540$		0			0
$541$	0.530113	−	0.918183i	0.0227913	−	0.0394758i	−0.854405	−	0.519608i	$-0.826078\pi$
$541$	0.530113	−	0.918183i	0.0227913	−	0.0394758i	0.877196	+	0.480132i	$0.159411\pi$
$542$	−0.599381	−	1.03816i	−0.0257456	−	0.0445927i
$543$		0			0
$544$	16.6418	+	9.60814i	0.713511	+	0.411946i
$545$	−5.38440			−0.230642
$546$		0			0
$547$	12.4665			0.533030			0.266515	−	0.963831i	$-0.414128\pi$
$547$	12.4665			0.533030			0.266515	+	0.963831i	$0.414128\pi$
$548$	1.76088	+	1.01664i	0.0752211	+	0.0434289i
$549$		0			0
$550$	−1.02245	−	1.77094i	−0.0435976	−	0.0755132i
$551$	−17.3643	+	30.0758i	−0.739744	+	1.28127i
$552$		0			0
$553$	−11.2431	+	6.61907i	−0.478106	+	0.281472i
$554$		−	13.2114i		−	0.561297i
$555$		0			0
$556$	−10.3348	+	5.96679i	−0.438292	+	0.253048i
$557$	17.5701	−	10.1441i	0.744470	−	0.429820i	−0.0792222	−	0.996857i	$-0.525244\pi$
$557$	17.5701	−	10.1441i	0.744470	−	0.429820i	0.823692	+	0.567037i	$0.191910\pi$
$558$		0			0
$559$		−	34.3050i		−	1.45095i
$560$	−0.0690150	−	8.13199i	−0.00291641	−	0.343639i
$561$		0			0
$562$	1.21990	−	2.11292i	0.0514582	−	0.0891283i
$563$	−17.8781	−	30.9658i	−0.753472	−	1.30505i	−0.946130	−	0.323786i	$-0.895044\pi$
$563$	−17.8781	−	30.9658i	−0.753472	−	1.30505i	0.192658	−	0.981266i	$-0.438289\pi$
$564$		0			0
$565$	−8.20869	−	4.73929i	−0.345342	−	0.199383i
$566$	3.27600			0.137700
$567$		0			0
$568$	1.89481			0.0795043
$569$	−4.01368	−	2.31730i	−0.168262	−	0.0971463i	0.413504	−	0.910502i	$-0.364305\pi$
$569$	−4.01368	−	2.31730i	−0.168262	−	0.0971463i	−0.581766	+	0.813356i	$0.697638\pi$
$570$		0			0
$571$	9.64058	+	16.6980i	0.403446	+	0.698788i	0.994139	−	0.108108i	$-0.0344791\pi$
$571$	9.64058	+	16.6980i	0.403446	+	0.698788i	−0.590694	+	0.806896i	$0.701146\pi$
$572$	24.0917	−	41.7281i	1.00733	−	1.74474i
$573$		0			0
$574$	−4.01685	−	6.82300i	−0.167660	−	0.284787i
$575$			2.64476i			0.110294i
$576$		0			0
$577$	−6.14525	+	3.54796i	−0.255830	+	0.147703i	−0.622431	−	0.782675i	$-0.713855\pi$
$577$	−6.14525	+	3.54796i	−0.255830	+	0.147703i	0.366601	+	0.930378i	$0.380521\pi$
$578$	1.07816	−	0.622478i	0.0448457	−	0.0258917i
$579$		0			0
$580$			16.8228i			0.698529i
$581$	−22.4644	−	12.7169i	−0.931982	−	0.527585i
$582$		0			0
$583$	7.42539	−	12.8611i	0.307528	−	0.532654i
$584$	0.442205	+	0.765921i	0.0182986	+	0.0316940i
$585$		0			0
$586$	−10.8651	−	6.27299i	−0.448835	−	0.259135i
$587$	28.1728			1.16281			0.581407	−	0.813613i	$-0.302502\pi$
$587$	28.1728			1.16281			0.581407	+	0.813613i	$0.302502\pi$
$588$		0			0
$589$	18.0838			0.745130
$590$	−1.70050	−	0.981785i	−0.0700086	−	0.0404195i
$591$		0			0
$592$	14.4488	+	25.0261i	0.593843	+	1.02857i
$593$	−4.66958	+	8.08794i	−0.191757	+	0.332132i	−0.945832	−	0.324655i	$-0.894752\pi$
$593$	−4.66958	+	8.08794i	−0.191757	+	0.332132i	0.754076	+	0.656787i	$0.228085\pi$
$594$		0			0
$595$	−10.3293	−	5.84729i	−0.423459	−	0.239716i
$596$			30.2127i			1.23756i
$597$		0			0
$598$	4.64743	−	2.68320i	0.190048	−	0.109724i
$599$	18.4745	−	10.6662i	0.754846	−	0.435811i	−0.0725959	−	0.997361i	$-0.523128\pi$
$599$	18.4745	−	10.6662i	0.754846	−	0.435811i	0.827442	+	0.561551i	$0.189795\pi$
$600$		0			0
$601$			35.7597i			1.45867i	0.684157	+	0.729335i	$0.260170\pi$
$601$			35.7597i			1.45867i	−0.684157	+	0.729335i	$0.739830\pi$
$602$	3.59855	+	6.11248i	0.146666	+	0.249126i
$603$		0			0
$604$	−8.61640	+	14.9240i	−0.350596	+	0.607251i
$605$	−7.68533	−	13.3114i	−0.312453	−	0.541185i
$606$		0			0
$607$	−2.89774	−	1.67301i	−0.117616	−	0.0679055i	0.440038	−	0.897979i	$-0.354965\pi$
$607$	−2.89774	−	1.67301i	−0.117616	−	0.0679055i	−0.557654	+	0.830074i	$0.688298\pi$
$608$	−16.2828			−0.660356
$609$		0			0
$610$	−4.72560			−0.191334
$611$	−34.5322	−	19.9372i	−1.39702	−	0.806572i
$612$		0			0
$613$	19.8654	+	34.4079i	0.802357	+	1.38972i	0.918061	+	0.396440i	$0.129754\pi$
$613$	19.8654	+	34.4079i	0.802357	+	1.38972i	−0.115704	+	0.993284i	$0.536912\pi$
$614$	4.73306	−	8.19790i	0.191011	−	0.330840i
$615$		0			0
$616$	0.176379	+	20.7826i	0.00710650	+	0.837354i
$617$			33.2529i			1.33871i	0.742942	+	0.669355i	$0.233430\pi$
$617$			33.2529i			1.33871i	−0.742942	+	0.669355i	$0.766570\pi$
$618$		0			0
$619$	15.8564	−	9.15472i	0.637324	−	0.367959i	−0.146259	−	0.989246i	$-0.546723\pi$
$619$	15.8564	−	9.15472i	0.637324	−	0.367959i	0.783583	+	0.621287i	$0.213390\pi$
$620$	7.58633	−	4.37997i	0.304674	−	0.175904i
$621$		0			0
$622$		−	7.40457i		−	0.296896i
$623$	16.5765	−	9.75897i	0.664125	−	0.390985i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.62195	+	2.80930i	0.0648262	+	0.112282i
$627$		0			0
$628$	14.1596	+	8.17505i	0.565029	+	0.326220i
$629$	42.1776			1.68173
$630$		0			0
$631$	44.2729			1.76248			0.881238	−	0.472673i	$-0.156711\pi$
$631$	44.2729			1.76248			0.881238	+	0.472673i	$0.156711\pi$
$632$	6.53270	+	3.77165i	0.259857	+	0.150028i
$633$		0			0
$634$	6.25450	+	10.8331i	0.248398	+	0.430238i
$635$	4.31497	−	7.47375i	0.171234	−	0.296587i
$636$		0			0
$637$	30.5824	−	18.3558i	1.21172	−	0.727283i
$638$		−	18.6817i		−	0.739617i
$639$		0			0
$640$	−8.95082	+	5.16776i	−0.353812	+	0.204273i
$641$	−2.80892	+	1.62173i	−0.110946	+	0.0640546i	−0.554446	−	0.832220i	$-0.687070\pi$
$641$	−2.80892	+	1.62173i	−0.110946	+	0.0640546i	0.443500	+	0.896274i	$0.353737\pi$
$642$		0			0
$643$		−	38.7849i		−	1.52953i	−0.644311	−	0.764763i	$-0.722856\pi$
$643$		−	38.7849i		−	1.52953i	0.644311	−	0.764763i	$-0.277144\pi$
$644$	6.34766	−	11.2132i	0.250133	−	0.441861i
$645$		0			0
$646$	−3.39554	+	5.88125i	−0.133596	+	0.231395i
$647$	−20.2133	−	35.0104i	−0.794665	−	1.37640i	−0.923051	−	0.384677i	$-0.874313\pi$
$647$	−20.2133	−	35.0104i	−0.794665	−	1.37640i	0.128386	−	0.991724i	$-0.459020\pi$
$648$		0			0
$649$	−21.9293	−	12.6609i	−0.860801	−	0.496983i
$650$	2.02906			0.0795865
$651$		0			0
$652$	−13.0169			−0.509781
$653$	33.0989	+	19.1097i	1.29526	+	0.747819i	0.979582	−	0.201047i	$-0.0644345\pi$
$653$	33.0989	+	19.1097i	1.29526	+	0.747819i	0.315679	+	0.948866i	$0.397768\pi$
$654$		0			0
$655$	7.75657	+	13.4348i	0.303074	+	0.524940i
$656$	11.5496	−	20.0044i	0.450935	−	0.781042i
$657$		0			0
$658$	8.24436	−	0.0699686i	0.321399	−	0.00272766i
$659$		−	3.10400i		−	0.120915i	−0.998171	−	0.0604574i	$-0.980744\pi$
$659$		−	3.10400i		−	0.120915i	0.998171	−	0.0604574i	$-0.0192559\pi$
$660$		0			0
$661$	12.5985	−	7.27377i	0.490026	−	0.282917i	−0.234559	−	0.972102i	$-0.575365\pi$
$661$	12.5985	−	7.27377i	0.490026	−	0.282917i	0.724585	+	0.689185i	$0.242031\pi$
$662$	1.90751	−	1.10130i	0.0741376	−	0.0428034i
$663$		0			0
$664$			14.9250i			0.579202i
$665$	10.0572	−	0.0853538i	0.390001	−	0.00330988i
$666$		0			0
$667$	−12.0809	+	20.9248i	−0.467776	+	0.810211i
$668$	23.0429	+	39.9115i	0.891556	+	1.54422i
$669$		0			0
$670$	2.41337	+	1.39336i	0.0932365	+	0.0538301i
$671$	−60.9403			−2.35257
$672$		0			0
$673$	−32.6424			−1.25827			−0.629137	−	0.777295i	$-0.716591\pi$
$673$	−32.6424			−1.25827			−0.629137	+	0.777295i	$0.716591\pi$
$674$	−4.60607	−	2.65932i	−0.177419	−	0.102433i
$675$		0			0
$676$	11.9358	+	20.6734i	0.459070	+	0.795133i
$677$	8.30114	−	14.3780i	0.319039	−	0.552591i	−0.661249	−	0.750167i	$-0.729973\pi$
$677$	8.30114	−	14.3780i	0.319039	−	0.552591i	0.980288	+	0.197575i	$0.0633066\pi$
$678$		0			0
$679$	−0.409177	+	0.722813i	−0.0157028	+	0.0277390i
$680$			6.86260i			0.263169i
$681$		0			0
$682$	−8.42462	+	4.86396i	−0.322595	+	0.186250i
$683$	21.1988	−	12.2391i	0.811149	−	0.468317i	−0.0362057	−	0.999344i	$-0.511527\pi$
$683$	21.1988	−	12.2391i	0.811149	−	0.468317i	0.847355	+	0.531027i	$0.178194\pi$
$684$		0			0
$685$			1.10419i			0.0421890i
$686$	−3.52369	+	6.47871i	−0.134535	+	0.247358i
$687$		0			0
$688$	−10.3468	+	17.9212i	−0.394469	+	0.683241i
$689$	7.36786	+	12.7615i	0.280693	+	0.486175i
$690$		0			0
$691$	26.8707	+	15.5138i	1.02221	+	0.590174i	0.914744	−	0.404035i	$-0.132393\pi$
$691$	26.8707	+	15.5138i	1.02221	+	0.590174i	0.107467	+	0.994209i	$0.465726\pi$
$692$	1.34317			0.0510595
$693$		0			0
$694$	−12.9056			−0.489889
$695$	−5.61237	−	3.24030i	−0.212889	−	0.122912i
$696$		0			0
$697$	−16.8572	−	29.1975i	−0.638511	−	1.10593i
$698$	1.26066	−	2.18352i	0.0477165	−	0.0826474i
$699$		0			0
$700$	4.19842	−	2.47170i	0.158685	−	0.0934215i
$701$		−	30.5243i		−	1.15289i	−0.817137	−	0.576443i	$-0.804440\pi$
$701$		−	30.5243i		−	1.15289i	0.817137	−	0.576443i	$-0.195560\pi$
$702$		0			0
$703$	−30.9509	+	17.8695i	−1.16733	+	0.673960i
$704$	−19.7535	+	11.4047i	−0.744489	+	0.429831i
$705$		0			0
$706$			6.20804i			0.233643i
$707$	0.221267	+	26.0717i	0.00832159	+	0.980528i
$708$		0			0
$709$	−5.70901	+	9.88830i	−0.214406	+	0.371363i	−0.953089	−	0.302691i	$-0.902115\pi$
$709$	−5.70901	+	9.88830i	−0.214406	+	0.371363i	0.738682	+	0.674054i	$0.235448\pi$
$710$	0.246628	+	0.427172i	0.00925578	+	0.0160315i
$711$		0			0
$712$	−9.63162	−	5.56082i	−0.360960	−	0.208400i
$713$	12.5815			0.471181
$714$		0			0
$715$	26.1664			0.978567
$716$	4.15260	+	2.39751i	0.155190	+	0.0895990i
$717$		0			0
$718$	−2.16910	−	3.75699i	−0.0809500	−	0.140209i
$719$	0.0976746	−	0.169177i	0.00364265	−	0.00630925i	−0.864198	−	0.503151i	$-0.832174\pi$
$719$	0.0976746	−	0.169177i	0.00364265	−	0.00630925i	0.867841	+	0.496842i	$0.165507\pi$
$720$		0			0
$721$	8.82511	+	14.9903i	0.328664	+	0.558268i
$722$			1.81161i			0.0674211i
$723$		0			0
$724$	6.20745	−	3.58388i	0.230698	−	0.133194i
$725$	−7.91178	+	4.56787i	−0.293836	+	0.169646i
$726$		0			0
$727$		−	22.6268i		−	0.839181i	−0.907714	−	0.419590i	$-0.862174\pi$
$727$		−	22.6268i		−	0.839181i	0.907714	−	0.419590i	$-0.137826\pi$
$728$	−17.9463	−	10.1592i	−0.665135	−	0.376526i
$729$		0			0
$730$	−0.115115	+	0.199384i	−0.00426058	+	0.00737955i
$731$	15.1017	+	26.1570i	0.558558	+	0.967450i
$732$		0			0
$733$	−14.3883	−	8.30708i	−0.531443	−	0.306829i	0.210161	−	0.977667i	$-0.432601\pi$
$733$	−14.3883	−	8.30708i	−0.531443	−	0.306829i	−0.741604	+	0.670838i	$0.765935\pi$
$734$	1.98081			0.0731131
$735$		0			0
$736$	−11.3285			−0.417575
$737$	31.1222	+	17.9684i	1.14640	+	0.661876i
$738$		0			0
$739$	0.165328	+	0.286356i	0.00608168	+	0.0105338i	0.869050	−	0.494724i	$-0.164731\pi$
$739$	0.165328	+	0.286356i	0.00608168	+	0.0105338i	−0.862969	+	0.505258i	$0.831397\pi$
$740$	−8.65613	+	14.9928i	−0.318205	+	0.551148i
$741$		0			0
$742$	−2.65148	−	1.50097i	−0.0973389	−	0.0551025i
$743$		−	42.3387i		−	1.55325i	−0.629960	−	0.776627i	$-0.716929\pi$
$743$		−	42.3387i		−	1.55325i	0.629960	−	0.776627i	$-0.283071\pi$
$744$		0			0
$745$	−14.2091	+	8.20362i	−0.520580	+	0.300557i
$746$	−4.43493	+	2.56051i	−0.162374	+	0.0937468i
$747$		0			0
$748$			42.4227i			1.55113i
$749$	−6.46348	−	10.9788i	−0.236170	−	0.401158i
$750$		0			0
$751$	−4.52350	+	7.83494i	−0.165065	+	0.285901i	−0.936678	−	0.350191i	$-0.886117\pi$
$751$	−4.52350	+	7.83494i	−0.165065	+	0.285901i	0.771613	+	0.636092i	$0.219450\pi$
$752$	12.0266	+	20.8308i	0.438567	+	0.759620i
$753$		0			0
$754$	16.0535	+	9.26850i	0.584635	+	0.337539i
$755$	−9.35839			−0.340587
$756$		0			0
$757$	37.8499			1.37568			0.687839	−	0.725863i	$-0.258559\pi$
$757$	37.8499			1.37568			0.687839	+	0.725863i	$0.258559\pi$
$758$	13.0520	+	7.53557i	0.474070	+	0.273704i
$759$		0			0
$760$	−2.90749	−	5.03593i	−0.105466	−	0.182672i
$761$	5.87367	−	10.1735i	0.212920	−	0.368789i	−0.739707	−	0.672929i	$-0.765036\pi$
$761$	5.87367	−	10.1735i	0.212920	−	0.368789i	0.952627	+	0.304140i	$0.0983692\pi$
$762$		0			0
$763$	0.120897	+	14.2453i	0.00437678	+	0.515713i
$764$		−	14.1289i		−	0.511167i
$765$		0			0
$766$	9.80860	−	5.66300i	0.354399	−	0.204612i
$767$	21.7594	−	12.5628i	0.785687	−	0.453617i
$768$		0			0
$769$		−	13.1169i		−	0.473007i	−0.971631	−	0.236504i	$-0.923998\pi$
$769$		−	13.1169i		−	0.473007i	0.971631	−	0.236504i	$-0.0760015\pi$
$770$	−4.66234	+	2.74482i	−0.168019	+	0.0989166i
$771$		0			0
$772$	0.0557956	−	0.0966409i	0.00200813	−	0.00347818i
$773$	−6.28630	−	10.8882i	−0.226102	−	0.391621i	0.730547	−	0.682862i	$-0.239265\pi$
$773$	−6.28630	−	10.8882i	−0.226102	−	0.391621i	−0.956650	+	0.291241i	$0.905932\pi$
$774$		0			0
$775$	4.11981	+	2.37857i	0.147988	+	0.0854408i
$776$	0.480225			0.0172391
$777$		0			0
$778$	3.78940			0.135857
$779$	24.7404	+	14.2838i	0.886415	+	0.511772i
$780$		0			0
$781$	3.18046	+	5.50872i	0.113806	+	0.197117i
$782$	−2.36239	+	4.09179i	−0.0844790	+	0.146322i
$783$		0			0
$784$	−21.5129	+	0.365180i	−0.768318	+	0.0130421i
$785$			8.87903i			0.316906i
$786$		0			0
$787$	45.4761	−	26.2556i	1.62105	−	0.935912i	0.634406	−	0.773000i	$-0.281245\pi$
$787$	45.4761	−	26.2556i	1.62105	−	0.935912i	0.986641	−	0.162912i	$-0.0520888\pi$
$788$	19.6179	−	11.3264i	0.698859	−	0.403486i
$789$		0			0
$790$			1.96367i			0.0698643i
$791$	−12.3542	+	21.8238i	−0.439265	+	0.775964i
$792$		0			0
$793$	30.2341	−	52.3670i	1.07364	−	1.85961i
$794$	1.92260	+	3.33004i	0.0682304	+	0.118179i
$795$		0			0
$796$	17.8353	+	10.2972i	0.632156	+	0.364976i
$797$	−24.2213			−0.857964			−0.428982	−	0.903313i	$-0.641128\pi$
$797$	−24.2213			−0.857964			−0.428982	+	0.903313i	$0.641128\pi$
$798$		0			0
$799$	35.1070			1.24200
$800$	−3.70952	−	2.14169i	−0.131151	−	0.0757202i
$801$		0			0
$802$	−1.78609	−	3.09360i	−0.0630690	−	0.109239i
$803$	−1.48449	+	2.57122i	−0.0523866	+	0.0907363i
$804$		0			0
$805$	6.99713	−	0.0593836i	0.246617	−	0.00209300i
$806$		−	9.65255i		−	0.339996i
$807$		0			0
$808$	13.0549	−	7.53724i	0.459269	−	0.265159i
$809$	−9.52648	+	5.50012i	−0.334933	+	0.193374i	−0.658029	−	0.752992i	$-0.728610\pi$
$809$	−9.52648	+	5.50012i	−0.334933	+	0.193374i	0.323096	+	0.946366i	$0.395276\pi$
$810$		0			0
$811$		−	7.18512i		−	0.252304i	−0.992011	−	0.126152i	$-0.959737\pi$
$811$		−	7.18512i		−	0.252304i	0.992011	−	0.126152i	$-0.0402626\pi$
$812$	44.5074	−	0.377727i	1.56190	−	0.0132556i
$813$		0			0
$814$	9.61263	−	16.6496i	0.336922	−	0.583567i
$815$	−3.53445	−	6.12185i	−0.123807	−	0.214439i
$816$		0			0
$817$	−22.1640	−	12.7964i	−0.775420	−	0.447689i
$818$	−12.1234			−0.423885
$819$		0			0
$820$	13.8384			0.483259
$821$	−39.4307	−	22.7653i	−1.37614	−	0.794515i	−0.384448	−	0.923146i	$-0.625608\pi$
$821$	−39.4307	−	22.7653i	−1.37614	−	0.794515i	−0.991693	+	0.128631i	$0.958942\pi$
$822$		0			0
$823$	−6.30134	−	10.9142i	−0.219651	−	0.380447i	0.735050	−	0.678013i	$-0.237159\pi$
$823$	−6.30134	−	10.9142i	−0.219651	−	0.380447i	−0.954701	+	0.297566i	$0.903825\pi$
$824$	5.02869	−	8.70995i	0.175183	−	0.303425i
$825$		0			0
$826$	−2.55928	+	4.52099i	−0.0890489	+	0.157305i
$827$		−	50.5644i		−	1.75830i	−0.476549	−	0.879148i	$-0.658113\pi$
$827$		−	50.5644i		−	1.75830i	0.476549	−	0.879148i	$-0.341887\pi$
$828$		0			0
$829$	−13.3885	+	7.72987i	−0.465003	+	0.268470i	−0.714146	−	0.699997i	$-0.753185\pi$
$829$	−13.3885	+	7.72987i	−0.465003	+	0.268470i	0.249143	+	0.968467i	$0.419851\pi$
$830$	−3.36474	+	1.94264i	−0.116792	+	0.0674299i
$831$		0			0
$832$		−	22.6327i		−	0.784647i
$833$	−15.2380	+	27.4590i	−0.527965	+	0.951397i
$834$		0			0
$835$	−12.5136	+	21.6742i	−0.433051	+	0.750066i
$836$	−17.9733	−	31.1307i	−0.621621	−	1.07668i
$837$		0			0
$838$	8.30838	+	4.79684i	0.287008	+	0.165704i
$839$	48.2725			1.66655			0.833276	−	0.552858i	$-0.186463\pi$
$839$	48.2725			1.66655			0.833276	+	0.552858i	$0.186463\pi$
$840$		0			0
$841$	−54.4618			−1.87799
$842$	7.71325	+	4.45325i	0.265816	+	0.153469i
$843$		0			0
$844$	−5.17949	−	8.97114i	−0.178285	−	0.308799i
$845$	−6.48183	+	11.2269i	−0.222982	+	0.386216i
$846$		0			0
$847$	−35.0448	+	20.6316i	−1.20415	+	0.708911i
$848$		−	8.88898i		−	0.305249i
$849$		0			0
$850$	−1.54713	+	0.893235i	−0.0530661	+	0.0306377i
$851$	−21.5336	+	12.4324i	−0.738161	+	0.426178i
$852$		0			0
$853$		−	7.57394i		−	0.259327i	−0.991558	−	0.129663i	$-0.958610\pi$
$853$		−	7.57394i		−	0.259327i	0.991558	−	0.129663i	$-0.0413897\pi$
$854$	0.106105	+	12.5023i	0.00363084	+	0.427820i
$855$		0			0
$856$	−3.68299	+	6.37913i	−0.125882	+	0.218034i
$857$	0.260910	+	0.451909i	0.00891251	+	0.0154369i	0.870447	−	0.492262i	$-0.163830\pi$
$857$	0.260910	+	0.451909i	0.00891251	+	0.0154369i	−0.861535	+	0.507699i	$0.830496\pi$
$858$		0			0
$859$	39.1327	+	22.5933i	1.33519	+	0.770872i	0.986090	−	0.166213i	$-0.0531539\pi$
$859$	39.1327	+	22.5933i	1.33519	+	0.770872i	0.349100	+	0.937085i	$0.386487\pi$
$860$	−12.3973			−0.422746
$861$		0			0
$862$	−4.09673			−0.139535
$863$	−7.46024	−	4.30717i	−0.253950	−	0.146618i	0.367622	−	0.929975i	$-0.380172\pi$
$863$	−7.46024	−	4.30717i	−0.253950	−	0.146618i	−0.621571	+	0.783358i	$0.713505\pi$
$864$		0			0
$865$	0.364708	+	0.631692i	0.0124004	+	0.0214782i
$866$	0.978108	−	1.69413i	0.0332375	−	0.0575690i
$867$		0			0
$868$	−11.7582	−	19.9725i	−0.399100	−	0.677910i
$869$			25.3231i			0.859027i
$870$		0			0
$871$	−30.8811	+	17.8292i	−1.04637	+	0.604120i
$872$	7.13302	−	4.11825i	0.241555	−	0.139462i
$873$		0			0
$874$		−	4.00353i		−	0.135421i
$875$	2.30243	+	1.30338i	0.0778364	+	0.0440624i
$876$		0			0
$877$	−0.739482	+	1.28082i	−0.0249705	+	0.0432502i	−0.878241	−	0.478219i	$-0.841283\pi$
$877$	−0.739482	+	1.28082i	−0.0249705	+	0.0432502i	0.853270	+	0.521469i	$0.174616\pi$
$878$	6.21067	+	10.7572i	0.209600	+	0.363038i
$879$		0			0
$880$	−13.6696	−	7.89213i	−0.460801	−	0.266044i
$881$	−28.6082			−0.963835			−0.481918	−	0.876217i	$-0.660060\pi$
$881$	−28.6082			−0.963835			−0.481918	+	0.876217i	$0.660060\pi$
$882$		0			0
$883$	−2.70408			−0.0909996			−0.0454998	−	0.998964i	$-0.514488\pi$
$883$	−2.70408			−0.0909996			−0.0454998	+	0.998964i	$0.514488\pi$
$884$	−36.4545	−	21.0470i	−1.22610	−	0.707888i
$885$		0			0
$886$	−2.10161	−	3.64009i	−0.0706048	−	0.122291i
$887$	8.89098	−	15.3996i	0.298530	−	0.517069i	−0.677270	−	0.735735i	$-0.736837\pi$
$887$	8.89098	−	15.3996i	0.298530	−	0.517069i	0.975800	+	0.218666i	$0.0701704\pi$
$888$		0			0
$889$	−19.8698	−	11.2481i	−0.666413	−	0.377250i
$890$		−	2.89518i		−	0.0970467i
$891$		0			0
$892$	5.04456	−	2.91248i	0.168904	−	0.0975170i
$893$	−25.7623	+	14.8739i	−0.862103	+	0.497735i
$894$		0			0
$895$			2.60396i			0.0870409i
$896$	13.8731	+	23.5647i	0.463467	+	0.787243i
$897$		0			0
$898$	−6.55856	+	11.3598i	−0.218862	+	0.379080i
$899$	21.7300	+	37.6375i	0.724736	+	1.25528i
$900$		0			0
$901$	−11.2357	−	6.48696i	−0.374317	−	0.216112i
$902$	−15.3676			−0.511684
$903$		0			0
$904$	14.4994			0.482241
$905$	3.37100	+	1.94625i	0.112056	+	0.0646955i
$906$		0			0
$907$	−22.0597	−	38.2086i	−0.732481	−	1.26869i	−0.955820	−	0.293954i	$-0.905029\pi$
$907$	−22.0597	−	38.2086i	−0.732481	−	1.26869i	0.223338	−	0.974741i	$-0.428305\pi$
$908$	−10.3533	+	17.9324i	−0.343585	+	0.595108i
$909$		0			0
$910$	−0.0455591	−	5.36821i	−0.00151027	−	0.177954i
$911$		−	2.01773i		−	0.0668505i	−0.999441	−	0.0334253i	$-0.989358\pi$
$911$		−	2.01773i		−	0.0668505i	0.999441	−	0.0334253i	$-0.0106416\pi$
$912$		0			0
$913$	−43.3910	+	25.0518i	−1.43603	+	0.829094i
$914$	−11.0905	+	6.40311i	−0.366841	+	0.211796i
$915$		0			0
$916$		−	41.9633i		−	1.38651i
$917$	35.3696	−	20.8229i	1.16801	−	0.687632i
$918$		0			0
$919$	18.8068	−	32.5743i	0.620379	−	1.07453i	−0.369036	−	0.929415i	$-0.620312\pi$
$919$	18.8068	−	32.5743i	0.620379	−	1.07453i	0.989415	−	0.145113i	$-0.0463546\pi$
$920$	−2.02284	−	3.50367i	−0.0666912	−	0.115513i
$921$		0			0
$922$	−13.6778	−	7.89686i	−0.450453	−	0.260069i
$923$	−6.31164			−0.207750
$924$		0			0
$925$	−9.40153			−0.309121
$926$	11.8026	+	6.81421i	0.387856	+	0.223929i
$927$		0			0
$928$	−19.5659	−	33.8892i	−0.642283	−	1.11247i
$929$	−19.6901	+	34.1042i	−0.646010	+	1.11892i	0.338057	+	0.941126i	$0.390230\pi$
$929$	−19.6901	+	34.1042i	−0.646010	+	1.11892i	−0.984067	+	0.177797i	$0.943103\pi$
$930$		0			0
$931$	−0.451634	−	26.6060i	−0.0148017	−	0.871975i
$932$		−	5.94218i		−	0.194643i
$933$		0			0
$934$	−10.2419	+	5.91315i	−0.335124	+	0.193484i
$935$	−19.9514	+	11.5190i	−0.652481	+	0.376710i
$936$		0			0
$937$			10.4952i			0.342864i	0.985196	+	0.171432i	$0.0548394\pi$
$937$			10.4952i			0.342864i	−0.985196	+	0.171432i	$0.945161\pi$
$938$	3.63216	−	6.41622i	0.118594	−	0.209497i
$939$		0			0
$940$	−7.20503	+	12.4795i	−0.235002	+	0.407036i
$941$	11.1934	+	19.3875i	0.364895	+	0.632016i	0.988759	−	0.149516i	$-0.0477717\pi$
$941$	11.1934	+	19.3875i	0.364895	+	0.632016i	−0.623865	+	0.781532i	$0.714438\pi$
$942$		0			0
$943$	17.2127	+	9.93776i	0.560523	+	0.323618i
$944$	−15.1564			−0.493300
$945$		0			0
$946$	13.7673			0.447612
$947$	−13.3007	−	7.67919i	−0.432216	−	0.249540i	0.268074	−	0.963398i	$-0.413613\pi$
$947$	−13.3007	−	7.67919i	−0.432216	−	0.249540i	−0.700290	+	0.713858i	$0.746946\pi$
$948$		0			0
$949$	−1.47299	−	2.55130i	−0.0478154	−	0.0828186i
$950$	0.756879	−	1.31095i	0.0245564	−	0.0425329i
$951$		0			0
$952$	18.1561	−	0.154088i	0.588442	−	0.00499401i
$953$			7.83975i			0.253955i	0.991906	+	0.126977i	$0.0405275\pi$
$953$			7.83975i			0.253955i	−0.991906	+	0.126977i	$0.959472\pi$
$954$		0			0
$955$	6.64485	−	3.83640i	0.215022	−	0.124143i
$956$	−36.8815	+	21.2936i	−1.19283	+	0.688683i
$957$		0			0
$958$			3.73995i			0.120832i
$959$	2.92131	−	0.0247927i	0.0943341	−	0.000800599i
$960$		0			0
$961$	−4.18480	+	7.24829i	−0.134994	+	0.233816i
$962$	9.53816	+	16.5206i	0.307523	+	0.532645i
$963$		0			0
$964$	−23.6808	−	13.6721i	−0.762707	−	0.440349i
$965$	0.0606004			0.00195080
$966$		0			0
$967$	31.3647			1.00862			0.504310	−	0.863523i	$-0.331747\pi$
$967$	31.3647			1.00862			0.504310	+	0.863523i	$0.331747\pi$
$968$	20.3624	+	11.7562i	0.654472	+	0.377860i
$969$		0			0
$970$	0.0625061	+	0.108264i	0.00200695	+	0.00347614i
$971$	−11.3560	+	19.6691i	−0.364431	+	0.631213i	−0.988685	−	0.150009i	$-0.952070\pi$
$971$	−11.3560	+	19.6691i	−0.364431	+	0.631213i	0.624254	+	0.781222i	$0.285403\pi$
$972$		0			0
$973$	−8.44671	+	14.9212i	−0.270789	+	0.478350i
$974$			3.16287i			0.101345i
$975$		0			0
$976$	−31.5892	+	18.2380i	−1.01114	+	0.583784i
$977$	−9.38128	+	5.41629i	−0.300134	+	0.173282i	−0.642503	−	0.766283i	$-0.722104\pi$
$977$	−9.38128	+	5.41629i	−0.300134	+	0.173282i	0.342369	+	0.939566i	$0.388771\pi$
$978$		0			0
$979$		−	37.3356i		−	1.19325i
$980$	−6.63354	−	11.0521i	−0.211901	−	0.353045i
$981$		0			0
$982$	2.12885	−	3.68727i	0.0679342	−	0.117665i
$983$	−14.0614	−	24.3551i	−0.448490	−	0.776808i	0.549798	−	0.835298i	$-0.314705\pi$
$983$	−14.0614	−	24.3551i	−0.448490	−	0.776808i	−0.998288	+	0.0584896i	$0.981372\pi$
$984$		0			0
$985$	10.6536	+	6.15088i	0.339453	+	0.195983i
$986$	−16.3207			−0.519758
$987$		0			0
$988$	35.6682			1.13476
$989$	−15.4202	−	8.90288i	−0.490335	−	0.283095i
$990$		0			0
$991$	1.02979	+	1.78365i	0.0327123	+	0.0566594i	0.881918	−	0.471403i	$-0.156252\pi$
$991$	1.02979	+	1.78365i	0.0327123	+	0.0566594i	−0.849206	+	0.528062i	$0.822919\pi$
$992$	−10.1883	+	17.6467i	−0.323480	+	0.560283i
$993$		0			0
$994$	1.12461	−	0.662084i	0.0356705	−	0.0210000i
$995$			11.1840i			0.354555i
$996$		0			0
$997$	−36.8214	+	21.2589i	−1.16615	+	0.673275i	−0.952769	−	0.303695i	$-0.901780\pi$
$997$	−36.8214	+	21.2589i	−1.16615	+	0.673275i	−0.213378	+	0.976970i	$0.568446\pi$
$998$	2.49576	−	1.44093i	0.0790021	−	0.0456119i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bj.b.26.3	yes	12
3.2	odd	2		315.2.bj.a.26.4	✓	12
5.2	odd	4		1575.2.bc.c.1349.7		24
5.3	odd	4		1575.2.bc.c.1349.6		24
5.4	even	2		1575.2.bk.e.26.4		12
7.2	even	3		2205.2.b.a.881.7		12
7.3	odd	6		315.2.bj.a.206.4	yes	12
7.5	odd	6		2205.2.b.b.881.7		12
15.2	even	4		1575.2.bc.d.1349.6		24
15.8	even	4		1575.2.bc.d.1349.7		24
15.14	odd	2		1575.2.bk.f.26.3		12
21.2	odd	6		2205.2.b.b.881.6		12
21.5	even	6		2205.2.b.a.881.6		12
21.17	even	6	inner	315.2.bj.b.206.3	yes	12
35.3	even	12		1575.2.bc.d.899.6		24
35.17	even	12		1575.2.bc.d.899.7		24
35.24	odd	6		1575.2.bk.f.1151.3		12
105.17	odd	12		1575.2.bc.c.899.6		24
105.38	odd	12		1575.2.bc.c.899.7		24
105.59	even	6		1575.2.bk.e.1151.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bj.a.26.4	✓	12	3.2	odd	2
315.2.bj.a.206.4	yes	12	7.3	odd	6
315.2.bj.b.26.3	yes	12	1.1	even	1	trivial
315.2.bj.b.206.3	yes	12	21.17	even	6	inner
1575.2.bc.c.899.6		24	105.17	odd	12
1575.2.bc.c.899.7		24	105.38	odd	12
1575.2.bc.c.1349.6		24	5.3	odd	4
1575.2.bc.c.1349.7		24	5.2	odd	4
1575.2.bc.d.899.6		24	35.3	even	12
1575.2.bc.d.899.7		24	35.17	even	12
1575.2.bc.d.1349.6		24	15.2	even	4
1575.2.bc.d.1349.7		24	15.8	even	4
1575.2.bk.e.26.4		12	5.4	even	2
1575.2.bk.e.1151.4		12	105.59	even	6
1575.2.bk.f.26.3		12	15.14	odd	2
1575.2.bk.f.1151.3		12	35.24	odd	6
2205.2.b.a.881.6		12	21.5	even	6
2205.2.b.a.881.7		12	7.2	even	3
2205.2.b.b.881.6		12	21.2	odd	6
2205.2.b.b.881.7		12	7.5	odd	6

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.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.344861 - 0.199105i) q^{2} +(-0.920714 - 1.59472i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30243 - 1.30338i) q^{7} +1.52970i q^{8} +O(q^{10})\)	\(q+(-0.344861 - 0.199105i) q^{2} +(-0.920714 - 1.59472i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30243 - 1.30338i) q^{7} +1.52970i q^{8} +(-0.344861 + 0.199105i) q^{10} +(-4.44725 + 2.56762i) q^{11} -5.09545i q^{13} +(0.534507 + 0.907912i) q^{14} +(-1.53686 + 2.66191i) q^{16} +(2.24312 + 3.88520i) q^{17} +(-3.29211 - 1.90070i) q^{19} -1.84143 q^{20} +2.04491 q^{22} +(-2.29043 - 1.32238i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.01453 + 1.75722i) q^{26} +(0.0413461 + 4.87179i) q^{28} -9.13574i q^{29} +(-4.11981 + 2.37857i) q^{31} +(3.70952 - 2.14169i) q^{32} -1.78647i q^{34} +(-2.27998 + 1.34227i) q^{35} +(4.70077 - 8.14197i) q^{37} +(0.756879 + 1.31095i) q^{38} +(1.32476 + 0.764849i) q^{40} -7.51505 q^{41} +6.73246 q^{43} +(8.18929 + 4.72809i) q^{44} +(0.526586 + 0.912074i) q^{46} +(3.91274 - 6.77706i) q^{47} +(3.60239 + 6.00190i) q^{49} +0.398211i q^{50} +(-8.12584 + 4.69146i) q^{52} +(-2.50449 + 1.44597i) q^{53} +5.13524i q^{55} +(1.99378 - 3.52202i) q^{56} +(-1.81897 + 3.15056i) q^{58} +(2.46549 + 4.27036i) q^{59} +(10.2772 + 5.93354i) q^{61} +1.89434 q^{62} +4.44174 q^{64} +(-4.41279 - 2.54773i) q^{65} +(-3.49905 - 6.06052i) q^{67} +(4.13055 - 7.15432i) q^{68} +(1.05353 - 0.00894113i) q^{70} -1.23868i q^{71} +(0.500701 - 0.289080i) q^{73} +(-3.24222 + 1.87190i) q^{74} +7.00000i q^{76} +(13.5861 - 0.115303i) q^{77} +(2.46562 - 4.27058i) q^{79} +(1.53686 + 2.66191i) q^{80} +(2.59164 + 1.49629i) q^{82} +9.75683 q^{83} +4.48624 q^{85} +(-2.32176 - 1.34047i) q^{86} +(-3.92768 - 6.80294i) q^{88} +(-3.63524 + 6.29642i) q^{89} +(-6.64133 + 11.7319i) q^{91} +4.87014i q^{92} +(-2.69870 + 1.55809i) q^{94} +(-3.29211 + 1.90070i) q^{95} -0.313935i q^{97} +(-0.0473103 - 2.78707i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} + 6 q^{5} - 2 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 + 6 * q^5 - 2 * q^7	\( 12 q + 8 q^{4} + 6 q^{5} - 2 q^{7} - 12 q^{11} + 12 q^{14} - 16 q^{16} + 6 q^{19} + 16 q^{20} + 32 q^{22} - 12 q^{23} - 6 q^{25} - 20 q^{28} + 6 q^{31} - 60 q^{32} + 2 q^{35} - 10 q^{37} + 36 q^{38} - 24 q^{41} - 4 q^{43} - 12 q^{44} - 4 q^{46} + 6 q^{49} - 12 q^{53} + 60 q^{56} + 20 q^{58} + 24 q^{59} - 24 q^{62} - 56 q^{64} - 18 q^{65} + 6 q^{67} + 60 q^{68} - 12 q^{70} - 42 q^{73} - 84 q^{74} + 36 q^{77} + 18 q^{79} + 16 q^{80} - 72 q^{82} + 24 q^{83} + 84 q^{86} + 4 q^{88} - 12 q^{89} - 18 q^{91} + 12 q^{94} + 6 q^{95} - 12 q^{98}+O(q^{100}) \) 12 * q + 8 * q^4 + 6 * q^5 - 2 * q^7 - 12 * q^11 + 12 * q^14 - 16 * q^16 + 6 * q^19 + 16 * q^20 + 32 * q^22 - 12 * q^23 - 6 * q^25 - 20 * q^28 + 6 * q^31 - 60 * q^32 + 2 * q^35 - 10 * q^37 + 36 * q^38 - 24 * q^41 - 4 * q^43 - 12 * q^44 - 4 * q^46 + 6 * q^49 - 12 * q^53 + 60 * q^56 + 20 * q^58 + 24 * q^59 - 24 * q^62 - 56 * q^64 - 18 * q^65 + 6 * q^67 + 60 * q^68 - 12 * q^70 - 42 * q^73 - 84 * q^74 + 36 * q^77 + 18 * q^79 + 16 * q^80 - 72 * q^82 + 24 * q^83 + 84 * q^86 + 4 * q^88 - 12 * q^89 - 18 * q^91 + 12 * q^94 + 6 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more