LMFDB - Embedded newform 315.2.m.a.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(8,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("315.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.m (of order $4$, 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 $\Q(i)$
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} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$-0.556948i$ of defining polynomial
Character	$\chi$	$=$	315.197
Dual form			315.2.m.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96418 + 1.96418i) q^{2} -5.71600i q^{4} +(-1.65089 - 1.50816i) q^{5} +(0.707107 + 0.707107i) q^{7} +(7.29890 + 7.29890i) q^{8} +O(q^{10})$	\(q+(-1.96418 + 1.96418i) q^{2} -5.71600i q^{4} +(-1.65089 - 1.50816i) q^{5} +(0.707107 + 0.707107i) q^{7} +(7.29890 + 7.29890i) q^{8} +(6.20495 - 0.280357i) q^{10} -0.248425i q^{11} +(-3.37141 + 3.37141i) q^{13} -2.77777 q^{14} -17.2407 q^{16} +(-1.75881 + 1.75881i) q^{17} +3.91639i q^{19} +(-8.62065 + 9.43652i) q^{20} +(0.487951 + 0.487951i) q^{22} +(2.22082 + 2.22082i) q^{23} +(0.450907 + 4.97963i) q^{25} -13.2441i q^{26} +(4.04182 - 4.04182i) q^{28} -2.65164 q^{29} -2.96443 q^{31} +(19.2660 - 19.2660i) q^{32} -6.90922i q^{34} +(-0.100929 - 2.23379i) q^{35} +(1.76257 + 1.76257i) q^{37} +(-7.69249 - 7.69249i) q^{38} +(-1.04181 - 23.0576i) q^{40} +7.42003i q^{41} +(-0.716003 + 0.716003i) q^{43} -1.42000 q^{44} -8.72418 q^{46} +(-3.34257 + 3.34257i) q^{47} +1.00000i q^{49} +(-10.6665 - 8.89522i) q^{50} +(19.2710 + 19.2710i) q^{52} +(-4.25628 - 4.25628i) q^{53} +(-0.374665 + 0.410123i) q^{55} +10.3222i q^{56} +(5.20830 - 5.20830i) q^{58} -4.88610 q^{59} +9.55025 q^{61} +(5.82267 - 5.82267i) q^{62} +41.2024i q^{64} +(10.6505 - 0.481217i) q^{65} +(-5.98889 - 5.98889i) q^{67} +(10.0533 + 10.0533i) q^{68} +(4.58580 + 4.18932i) q^{70} +6.31723i q^{71} +(-10.3263 + 10.3263i) q^{73} -6.92401 q^{74} +22.3861 q^{76} +(0.175663 - 0.175663i) q^{77} -11.2561i q^{79} +(28.4626 + 26.0017i) q^{80} +(-14.5743 - 14.5743i) q^{82} +(10.1710 + 10.1710i) q^{83} +(5.55616 - 0.251043i) q^{85} -2.81272i q^{86} +(1.81323 - 1.81323i) q^{88} +1.91884 q^{89} -4.76790 q^{91} +(12.6942 - 12.6942i) q^{92} -13.1308i q^{94} +(5.90654 - 6.46554i) q^{95} +(1.07023 + 1.07023i) q^{97} +(-1.96418 - 1.96418i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{5} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^5 + 24 * q^8	$ 12 q - 4 q^{5} + 24 q^{8} + 16 q^{10} - 4 q^{13} - 4 q^{14} - 20 q^{16} + 8 q^{17} - 12 q^{20} - 8 q^{22} + 8 q^{23} - 8 q^{25} - 32 q^{29} + 48 q^{32} + 8 q^{35} + 4 q^{37} + 24 q^{38} - 28 q^{40} + 40 q^{43} - 64 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{50} + 36 q^{52} - 40 q^{53} - 16 q^{55} - 28 q^{58} - 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{65} - 48 q^{67} + 32 q^{68} + 8 q^{70} - 20 q^{73} - 64 q^{74} + 16 q^{76} + 36 q^{80} + 20 q^{82} + 24 q^{83} - 56 q^{89} + 8 q^{92} + 56 q^{95} + 12 q^{97}+O(q^{100}) $ 12 * q - 4 * q^5 + 24 * q^8 + 16 * q^10 - 4 * q^13 - 4 * q^14 - 20 * q^16 + 8 * q^17 - 12 * q^20 - 8 * q^22 + 8 * q^23 - 8 * q^25 - 32 * q^29 + 48 * q^32 + 8 * q^35 + 4 * q^37 + 24 * q^38 - 28 * q^40 + 40 * q^43 - 64 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^50 + 36 * q^52 - 40 * q^53 - 16 * q^55 - 28 * q^58 - 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^65 - 48 * q^67 + 32 * q^68 + 8 * q^70 - 20 * q^73 - 64 * q^74 + 16 * q^76 + 36 * q^80 + 20 * q^82 + 24 * q^83 - 56 * q^89 + 8 * q^92 + 56 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.96418	+	1.96418i	−1.38888	+	1.38888i	−0.561214	+	0.827671i	$0.689666\pi$
$2$	−1.96418	+	1.96418i	−1.38888	+	1.38888i	−0.827671	+	0.561214i	$0.810334\pi$
$3$		0			0
$3$		0			0
$4$		−	5.71600i		−	2.85800i
$5$	−1.65089	−	1.50816i	−0.738303	−	0.674470i
$5$	−1.65089	−	1.50816i	−0.738303	−	0.674470i
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	7.29890	+	7.29890i	2.58055	+	2.58055i
$9$		0			0
$10$	6.20495	−	0.280357i	1.96218	−	0.0886565i
$11$		−	0.248425i		−	0.0749029i	−0.999298	−	0.0374515i	$-0.988076\pi$
$11$		−	0.248425i		−	0.0749029i	0.999298	−	0.0374515i	$-0.0119240\pi$
$12$		0			0
$13$	−3.37141	+	3.37141i	−0.935061	+	0.935061i	−0.998016	−	0.0629552i	$-0.979947\pi$
$13$	−3.37141	+	3.37141i	−0.935061	+	0.935061i	0.0629552	+	0.998016i	$0.479947\pi$
$14$	−2.77777			−0.742390
$15$		0			0
$16$	−17.2407			−4.31017
$17$	−1.75881	+	1.75881i	−0.426573	+	0.426573i	−0.887459	−	0.460886i	$-0.847532\pi$
$17$	−1.75881	+	1.75881i	−0.426573	+	0.426573i	0.460886	+	0.887459i	$0.347532\pi$
$18$		0			0
$19$			3.91639i			0.898481i	0.893411	+	0.449241i	$0.148305\pi$
$19$			3.91639i			0.898481i	−0.893411	+	0.449241i	$0.851695\pi$
$20$	−8.62065	+	9.43652i	−1.92764	+	2.11007i
$21$		0			0
$22$	0.487951	+	0.487951i	0.104032	+	0.104032i
$23$	2.22082	+	2.22082i	0.463073	+	0.463073i	0.899661	−	0.436588i	$-0.143813\pi$
$23$	2.22082	+	2.22082i	0.463073	+	0.463073i	−0.436588	+	0.899661i	$0.643813\pi$
$24$		0			0
$25$	0.450907	+	4.97963i	0.0901814	+	0.995925i
$26$		−	13.2441i		−	2.59738i
$27$		0			0
$28$	4.04182	−	4.04182i	0.763833	−	0.763833i
$29$	−2.65164			−0.492398			−0.246199	−	0.969219i	$-0.579182\pi$
$29$	−2.65164			−0.492398			−0.246199	+	0.969219i	$0.579182\pi$
$30$		0			0
$31$	−2.96443			−0.532427			−0.266213	−	0.963914i	$-0.585773\pi$
$31$	−2.96443			−0.532427			−0.266213	+	0.963914i	$0.585773\pi$
$32$	19.2660	−	19.2660i	3.40578	−	3.40578i
$33$		0			0
$34$		−	6.90922i		−	1.18492i
$35$	−0.100929	−	2.23379i	−0.0170601	−	0.377579i
$36$		0			0
$37$	1.76257	+	1.76257i	0.289765	+	0.289765i	0.836987	−	0.547222i	$-0.184315\pi$
$37$	1.76257	+	1.76257i	0.289765	+	0.289765i	−0.547222	+	0.836987i	$0.684315\pi$
$38$	−7.69249	−	7.69249i	−1.24789	−	1.24789i
$39$		0			0
$40$	−1.04181	−	23.0576i	−0.164724	−	3.64573i
$41$			7.42003i			1.15881i	0.815038	+	0.579407i	$0.196716\pi$
$41$			7.42003i			1.15881i	−0.815038	+	0.579407i	$0.803284\pi$
$42$		0			0
$43$	−0.716003	+	0.716003i	−0.109189	+	0.109189i	−0.759591	−	0.650401i	$-0.774601\pi$
$43$	−0.716003	+	0.716003i	−0.109189	+	0.109189i	0.650401	+	0.759591i	$0.274601\pi$
$44$	−1.42000			−0.214073
$45$		0			0
$46$	−8.72418			−1.28631
$47$	−3.34257	+	3.34257i	−0.487564	+	0.487564i	−0.907537	−	0.419972i	$-0.862040\pi$
$47$	−3.34257	+	3.34257i	−0.487564	+	0.487564i	0.419972	+	0.907537i	$0.362040\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	−10.6665	−	8.89522i	−1.50848	−	1.25797i
$51$		0			0
$52$	19.2710	+	19.2710i	2.67241	+	2.67241i
$53$	−4.25628	−	4.25628i	−0.584645	−	0.584645i	0.351531	−	0.936176i	$-0.385661\pi$
$53$	−4.25628	−	4.25628i	−0.584645	−	0.584645i	−0.936176	+	0.351531i	$0.885661\pi$
$54$		0			0
$55$	−0.374665	+	0.410123i	−0.0505198	+	0.0553010i
$56$			10.3222i			1.37936i
$57$		0			0
$58$	5.20830	−	5.20830i	0.683884	−	0.683884i
$59$	−4.88610			−0.636116			−0.318058	−	0.948071i	$-0.603031\pi$
$59$	−4.88610			−0.636116			−0.318058	+	0.948071i	$0.603031\pi$
$60$		0			0
$61$	9.55025			1.22278			0.611392	−	0.791328i	$-0.290610\pi$
$61$	9.55025			1.22278			0.611392	+	0.791328i	$0.290610\pi$
$62$	5.82267	−	5.82267i	0.739480	−	0.739480i
$63$		0			0
$64$			41.2024i			5.15030i
$65$	10.6505	−	0.481217i	1.32103	−	0.0596877i
$66$		0			0
$67$	−5.98889	−	5.98889i	−0.731660	−	0.731660i	0.239289	−	0.970948i	$-0.423086\pi$
$67$	−5.98889	−	5.98889i	−0.731660	−	0.731660i	−0.970948	+	0.239289i	$0.923086\pi$
$68$	10.0533	+	10.0533i	1.21915	+	1.21915i
$69$		0			0
$70$	4.58580	+	4.18932i	0.548109	+	0.500720i
$71$			6.31723i			0.749717i	0.927082	+	0.374858i	$0.122309\pi$
$71$			6.31723i			0.749717i	−0.927082	+	0.374858i	$0.877691\pi$
$72$		0			0
$73$	−10.3263	+	10.3263i	−1.20860	+	1.20860i	−0.237125	+	0.971479i	$0.576205\pi$
$73$	−10.3263	+	10.3263i	−1.20860	+	1.20860i	−0.971479	+	0.237125i	$0.923795\pi$
$74$	−6.92401			−0.804900
$75$		0			0
$76$	22.3861			2.56786
$77$	0.175663	−	0.175663i	0.0200187	−	0.0200187i
$78$		0			0
$79$		−	11.2561i		−	1.26641i	−0.773985	−	0.633204i	$-0.781739\pi$
$79$		−	11.2561i		−	1.26641i	0.773985	−	0.633204i	$-0.218261\pi$
$80$	28.4626	+	26.0017i	3.18221	+	2.90708i
$81$		0			0
$82$	−14.5743	−	14.5743i	−1.60946	−	1.60946i
$83$	10.1710	+	10.1710i	1.11641	+	1.11641i	0.992264	+	0.124149i	$0.0396200\pi$
$83$	10.1710	+	10.1710i	1.11641	+	1.11641i	0.124149	+	0.992264i	$0.460380\pi$
$84$		0			0
$85$	5.55616	−	0.251043i	0.602651	−	0.0272294i
$86$		−	2.81272i		−	0.303303i
$87$		0			0
$88$	1.81323	−	1.81323i	0.193291	−	0.193291i
$89$	1.91884			0.203396			0.101698	−	0.994815i	$-0.467572\pi$
$89$	1.91884			0.203396			0.101698	+	0.994815i	$0.467572\pi$
$90$		0			0
$91$	−4.76790			−0.499811
$92$	12.6942	−	12.6942i	1.32346	−	1.32346i
$93$		0			0
$94$		−	13.1308i		−	1.35434i
$95$	5.90654	−	6.46554i	0.605998	−	0.663351i
$96$		0			0
$97$	1.07023	+	1.07023i	0.108666	+	0.108666i	0.759349	−	0.650684i	$-0.225518\pi$
$97$	1.07023	+	1.07023i	0.108666	+	0.108666i	−0.650684	+	0.759349i	$0.725518\pi$
$98$	−1.96418	−	1.96418i	−0.198412	−	0.198412i
$99$		0			0
$100$	28.4636	−	2.57738i	2.84636	−	0.257738i
$101$		−	8.86551i		−	0.882151i	−0.897470	−	0.441076i	$-0.854597\pi$
$101$		−	8.86551i		−	0.882151i	0.897470	−	0.441076i	$-0.145403\pi$
$102$		0			0
$103$	−12.8870	+	12.8870i	−1.26979	+	1.26979i	−0.323600	+	0.946194i	$0.604893\pi$
$103$	−12.8870	+	12.8870i	−1.26979	+	1.26979i	−0.946194	+	0.323600i	$0.895107\pi$
$104$	−49.2152			−4.82594
$105$		0			0
$106$	16.7202			1.62401
$107$	−0.890257	+	0.890257i	−0.0860644	+	0.0860644i	−0.748828	−	0.662764i	$-0.769383\pi$
$107$	−0.890257	+	0.890257i	−0.0860644	+	0.0860644i	0.662764	+	0.748828i	$0.269383\pi$
$108$		0			0
$109$		−	0.924031i		−	0.0885061i	−0.999020	−	0.0442531i	$-0.985909\pi$
$109$		−	0.924031i		−	0.0885061i	0.999020	−	0.0442531i	$-0.0140908\pi$
$110$	−0.0696476	−	1.54146i	−0.00664064	−	0.146973i
$111$		0			0
$112$	−12.1910	−	12.1910i	−1.15194	−	1.15194i
$113$	4.32422	+	4.32422i	0.406788	+	0.406788i	0.880617	−	0.473829i	$-0.157128\pi$
$113$	4.32422	+	4.32422i	0.406788	+	0.406788i	−0.473829	+	0.880617i	$0.657128\pi$
$114$		0			0
$115$	−0.316988	−	7.01570i	−0.0295593	−	0.654217i
$116$			15.1568i			1.40727i
$117$		0			0
$118$	9.59718	−	9.59718i	0.883492	−	0.883492i
$119$	−2.48733			−0.228013
$120$		0			0
$121$	10.9383			0.994390
$122$	−18.7584	+	18.7584i	−1.69831	+	1.69831i
$123$		0			0
$124$			16.9447i			1.52168i
$125$	6.76567	−	8.90088i	0.605140	−	0.796119i
$126$		0			0
$127$	−9.90911	−	9.90911i	−0.879291	−	0.879291i	0.114170	−	0.993461i	$-0.463579\pi$
$127$	−9.90911	−	9.90911i	−0.879291	−	0.879291i	−0.993461	+	0.114170i	$0.963579\pi$
$128$	−42.3969	−	42.3969i	−3.74740	−	3.74740i
$129$		0			0
$130$	−19.9742	+	21.8646i	−1.75186	+	1.91766i
$131$		−	5.19668i		−	0.454036i	−0.973891	−	0.227018i	$-0.927102\pi$
$131$		−	5.19668i		−	0.454036i	0.973891	−	0.227018i	$-0.0728977\pi$
$132$		0			0
$133$	−2.76930	+	2.76930i	−0.240129	+	0.240129i
$134$	23.5265			2.03238
$135$		0			0
$136$	−25.6747			−2.20159
$137$	4.28754	−	4.28754i	0.366309	−	0.366309i	−0.499820	−	0.866129i	$-0.666601\pi$
$137$	4.28754	−	4.28754i	0.366309	−	0.366309i	0.866129	+	0.499820i	$0.166601\pi$
$138$		0			0
$139$		−	10.5755i		−	0.897004i	−0.893782	−	0.448502i	$-0.851958\pi$
$139$		−	10.5755i		−	0.897004i	0.893782	−	0.448502i	$-0.148042\pi$
$140$	−12.7683	+	0.576909i	−1.07912	+	0.0487577i
$141$		0			0
$142$	−12.4082	−	12.4082i	−1.04127	−	1.04127i
$143$	0.837543	+	0.837543i	0.0700388	+	0.0700388i
$144$		0			0
$145$	4.37758	+	3.99910i	0.363539	+	0.332107i
$146$		−	40.5655i		−	3.35722i
$147$		0			0
$148$	10.0749	−	10.0749i	0.828148	−	0.828148i
$149$	23.2814			1.90728			0.953641	−	0.300945i	$-0.0973021\pi$
$149$	23.2814			1.90728			0.953641	+	0.300945i	$0.0973021\pi$
$150$		0			0
$151$	13.2865			1.08124			0.540619	−	0.841267i	$-0.318190\pi$
$151$	13.2865			1.08124			0.540619	+	0.841267i	$0.318190\pi$
$152$	−28.5853	+	28.5853i	−2.31858	+	2.31858i
$153$		0			0
$154$			0.690067i			0.0556072i
$155$	4.89396	+	4.47083i	0.393092	+	0.359106i
$156$		0			0
$157$	−4.82641	−	4.82641i	−0.385189	−	0.385189i	0.487778	−	0.872968i	$-0.337807\pi$
$157$	−4.82641	−	4.82641i	−0.385189	−	0.385189i	−0.872968	+	0.487778i	$0.837807\pi$
$158$	22.1090	+	22.1090i	1.75890	+	1.75890i
$159$		0			0
$160$	−60.8624	+	2.74993i	−4.81159	+	0.217401i
$161$			3.14072i			0.247523i
$162$		0			0
$163$	3.30623	−	3.30623i	0.258964	−	0.258964i	−0.565669	−	0.824633i	$-0.691382\pi$
$163$	3.30623	−	3.30623i	0.258964	−	0.258964i	0.824633	+	0.565669i	$0.191382\pi$
$164$	42.4129			3.31189
$165$		0			0
$166$	−39.9553			−3.10114
$167$	3.97778	−	3.97778i	0.307810	−	0.307810i	−0.536249	−	0.844060i	$-0.680159\pi$
$167$	3.97778	−	3.97778i	0.307810	−	0.307810i	0.844060	+	0.536249i	$0.180159\pi$
$168$		0			0
$169$		−	9.73282i		−	0.748679i
$170$	−10.4202	+	11.4064i	−0.799194	+	0.874831i
$171$		0			0
$172$	4.09268	+	4.09268i	0.312064	+	0.312064i
$173$	−15.3803	−	15.3803i	−1.16934	−	1.16934i	−0.982364	−	0.186978i	$-0.940131\pi$
$173$	−15.3803	−	15.3803i	−1.16934	−	1.16934i	−0.186978	−	0.982364i	$-0.559869\pi$
$174$		0			0
$175$	−3.20229	+	3.83997i	−0.242070	+	0.290274i
$176$			4.28302i			0.322845i
$177$		0			0
$178$	−3.76894	+	3.76894i	−0.282494	+	0.282494i
$179$	−22.4863			−1.68070			−0.840352	−	0.542041i	$-0.817652\pi$
$179$	−22.4863			−1.68070			−0.840352	+	0.542041i	$0.817652\pi$
$180$		0			0
$181$	5.56307			0.413500			0.206750	−	0.978394i	$-0.433711\pi$
$181$	5.56307			0.413500			0.206750	+	0.978394i	$0.433711\pi$
$182$	9.36500	−	9.36500i	0.694180	−	0.694180i
$183$		0			0
$184$			32.4191i			2.38997i
$185$	−0.251580	−	5.56806i	−0.0184965	−	0.409372i
$186$		0			0
$187$	0.436931	+	0.436931i	0.0319516	+	0.0319516i
$188$	19.1062	+	19.1062i	1.39346	+	1.39346i
$189$		0			0
$190$	1.09799	+	24.3010i	0.0796562	+	1.76298i
$191$			10.0091i			0.724230i	0.932133	+	0.362115i	$0.117945\pi$
$191$			10.0091i			0.724230i	−0.932133	+	0.362115i	$0.882055\pi$
$192$		0			0
$193$	5.10673	−	5.10673i	0.367590	−	0.367590i	−0.499007	−	0.866598i	$-0.666302\pi$
$193$	5.10673	−	5.10673i	0.367590	−	0.367590i	0.866598	+	0.499007i	$0.166302\pi$
$194$	−4.20425			−0.301848
$195$		0			0
$196$	5.71600			0.408286
$197$	4.32422	−	4.32422i	0.308088	−	0.308088i	−0.536080	−	0.844167i	$-0.680095\pi$
$197$	4.32422	−	4.32422i	0.308088	−	0.308088i	0.844167	+	0.536080i	$0.180095\pi$
$198$		0			0
$199$			13.5542i			0.960831i	0.877041	+	0.480416i	$0.159514\pi$
$199$			13.5542i			0.960831i	−0.877041	+	0.480416i	$0.840486\pi$
$200$	−33.0547	+	39.6369i	−2.33732	+	2.80275i
$201$		0			0
$202$	17.4135	+	17.4135i	1.22521	+	1.22521i
$203$	−1.87499	−	1.87499i	−0.131599	−	0.131599i
$204$		0			0
$205$	11.1906	−	12.2497i	0.781585	−	0.855556i
$206$		−	50.6248i		−	3.52720i
$207$		0			0
$208$	58.1254	−	58.1254i	4.03027	−	4.03027i
$209$	0.972929			0.0672989
$210$		0			0
$211$	−16.9166			−1.16459			−0.582294	−	0.812978i	$-0.697845\pi$
$211$	−16.9166			−1.16459			−0.582294	+	0.812978i	$0.697845\pi$
$212$	−24.3289	+	24.3289i	−1.67092	+	1.67092i
$213$		0			0
$214$		−	3.49725i		−	0.239067i
$215$	2.26189	−	0.102198i	0.154260	−	0.00696988i
$216$		0			0
$217$	−2.09617	−	2.09617i	−0.142297	−	0.142297i
$218$	1.81496	+	1.81496i	0.122925	+	0.122925i
$219$		0			0
$220$	2.34427	+	2.14158i	0.158050	+	0.144386i
$221$		−	11.8593i		−	0.797744i
$222$		0			0
$223$	7.46128	−	7.46128i	0.499644	−	0.499644i	−0.411683	−	0.911327i	$-0.635059\pi$
$223$	7.46128	−	7.46128i	0.499644	−	0.499644i	0.911327	+	0.411683i	$0.135059\pi$
$224$	27.2462			1.82047
$225$		0			0
$226$	−16.9871			−1.12996
$227$	−7.75452	+	7.75452i	−0.514686	+	0.514686i	−0.915959	−	0.401273i	$-0.868568\pi$
$227$	−7.75452	+	7.75452i	−0.514686	+	0.514686i	0.401273	+	0.915959i	$0.368568\pi$
$228$		0			0
$229$		−	12.1905i		−	0.805573i	−0.915294	−	0.402787i	$-0.868042\pi$
$229$		−	12.1905i		−	0.805573i	0.915294	−	0.402787i	$-0.131958\pi$
$230$	14.4027	+	13.1575i	0.949686	+	0.867577i
$231$		0			0
$232$	−19.3541	−	19.3541i	−1.27066	−	1.27066i
$233$	17.0691	+	17.0691i	1.11824	+	1.11824i	0.992000	+	0.126235i	$0.0402894\pi$
$233$	17.0691	+	17.0691i	1.11824	+	1.11824i	0.126235	+	0.992000i	$0.459711\pi$
$234$		0			0
$235$	10.5594	−	0.477101i	0.688817	−	0.0311226i
$236$			27.9290i			1.81802i
$237$		0			0
$238$	4.88556	−	4.88556i	0.316684	−	0.316684i
$239$	−15.6083			−1.00962			−0.504808	−	0.863231i	$-0.668437\pi$
$239$	−15.6083			−1.00962			−0.504808	+	0.863231i	$0.668437\pi$
$240$		0			0
$241$	19.4210			1.25101			0.625507	−	0.780219i	$-0.284892\pi$
$241$	19.4210			1.25101			0.625507	+	0.780219i	$0.284892\pi$
$242$	−21.4848	+	21.4848i	−1.38109	+	1.38109i
$243$		0			0
$244$		−	54.5893i		−	3.49472i
$245$	1.50816	−	1.65089i	0.0963528	−	0.105472i
$246$		0			0
$247$	−13.2038	−	13.2038i	−0.840135	−	0.840135i
$248$	−21.6371	−	21.6371i	−1.37395	−	1.37395i
$249$		0			0
$250$	4.19393	+	30.7719i	0.265247	+	1.94619i
$251$			21.7281i			1.37147i	0.727853	+	0.685734i	$0.240518\pi$
$251$			21.7281i			1.37147i	−0.727853	+	0.685734i	$0.759482\pi$
$252$		0			0
$253$	0.551707	−	0.551707i	0.0346855	−	0.0346855i
$254$	38.9265			2.44247
$255$		0			0
$256$	84.1456			5.25910
$257$	1.95493	−	1.95493i	0.121945	−	0.121945i	−0.643500	−	0.765446i	$-0.722519\pi$
$257$	1.95493	−	1.95493i	0.121945	−	0.121945i	0.765446	+	0.643500i	$0.222519\pi$
$258$		0			0
$259$			2.49265i			0.154886i
$260$	−2.75064	−	60.8781i	−0.170587	−	3.77550i
$261$		0			0
$262$	10.2072	+	10.2072i	0.630604	+	0.630604i
$263$	−5.40146	−	5.40146i	−0.333068	−	0.333068i	0.520682	−	0.853750i	$-0.325678\pi$
$263$	−5.40146	−	5.40146i	−0.333068	−	0.333068i	−0.853750	+	0.520682i	$0.825678\pi$
$264$		0			0
$265$	0.607519	+	13.4458i	0.0373196	+	0.825970i
$266$		−	10.8788i		−	0.667023i
$267$		0			0
$268$	−34.2325	+	34.2325i	−2.09108	+	2.09108i
$269$	−21.6690			−1.32118			−0.660590	−	0.750747i	$-0.729694\pi$
$269$	−21.6690			−1.32118			−0.660590	+	0.750747i	$0.729694\pi$
$270$		0			0
$271$	4.91623			0.298640			0.149320	−	0.988789i	$-0.452292\pi$
$271$	4.91623			0.298640			0.149320	+	0.988789i	$0.452292\pi$
$272$	30.3230	−	30.3230i	1.83860	−	1.83860i
$273$		0			0
$274$			16.8430i			1.01752i
$275$	1.23706	−	0.112016i	0.0745977	−	0.00675485i
$276$		0			0
$277$	17.4586	+	17.4586i	1.04898	+	1.04898i	0.998737	+	0.0502482i	$0.0160012\pi$
$277$	17.4586	+	17.4586i	1.04898	+	1.04898i	0.0502482	+	0.998737i	$0.483999\pi$
$278$	20.7722	+	20.7722i	1.24584	+	1.24584i
$279$		0			0
$280$	15.5675	−	17.0409i	0.930338	−	1.01839i
$281$			14.4804i			0.863830i	0.901914	+	0.431915i	$0.142162\pi$
$281$			14.4804i			0.863830i	−0.901914	+	0.431915i	$0.857838\pi$
$282$		0			0
$283$	−18.5661	+	18.5661i	−1.10364	+	1.10364i	−0.109671	+	0.993968i	$0.534980\pi$
$283$	−18.5661	+	18.5661i	−1.10364	+	1.10364i	−0.993968	+	0.109671i	$0.965020\pi$
$284$	36.1093			2.14269
$285$		0			0
$286$	−3.29017			−0.194552
$287$	−5.24676	+	5.24676i	−0.309706	+	0.309706i
$288$		0			0
$289$			10.8132i			0.636071i
$290$	−16.4533	+	0.743406i	−0.966172	+	0.0436543i
$291$		0			0
$292$	59.0253	+	59.0253i	3.45419	+	3.45419i
$293$	−11.7184	−	11.7184i	−0.684596	−	0.684596i	0.276437	−	0.961032i	$-0.410846\pi$
$293$	−11.7184	−	11.7184i	−0.684596	−	0.684596i	−0.961032	+	0.276437i	$0.910846\pi$
$294$		0			0
$295$	8.06644	+	7.36903i	0.469646	+	0.429041i
$296$			25.7296i			1.49551i
$297$		0			0
$298$	−45.7288	+	45.7288i	−2.64900	+	2.64900i
$299$	−14.9746			−0.866004
$300$		0			0
$301$	−1.01258			−0.0583642
$302$	−26.0970	+	26.0970i	−1.50172	+	1.50172i
$303$		0			0
$304$		−	67.5212i		−	3.87261i
$305$	−15.7665	−	14.4033i	−0.902785	−	0.824731i
$306$		0			0
$307$	−20.9578	−	20.9578i	−1.19612	−	1.19612i	−0.975317	−	0.220807i	$-0.929131\pi$
$307$	−20.9578	−	20.9578i	−1.19612	−	1.19612i	−0.220807	−	0.975317i	$-0.570869\pi$
$308$	−1.00409	−	1.00409i	−0.0572133	−	0.0572133i
$309$		0			0
$310$	−18.3941	+	0.831097i	−1.04472	+	0.0472031i
$311$		−	15.2031i		−	0.862090i	−0.902330	−	0.431045i	$-0.858145\pi$
$311$		−	15.2031i		−	0.862090i	0.902330	−	0.431045i	$-0.141855\pi$
$312$		0			0
$313$	0.179190	−	0.179190i	0.0101284	−	0.0101284i	−0.702024	−	0.712153i	$-0.747720\pi$
$313$	0.179190	−	0.179190i	0.0101284	−	0.0101284i	0.712153	+	0.702024i	$0.247720\pi$
$314$	18.9599			1.06997
$315$		0			0
$316$	−64.3398			−3.61940
$317$	−10.2500	+	10.2500i	−0.575697	+	0.575697i	−0.933715	−	0.358018i	$-0.883453\pi$
$317$	−10.2500	+	10.2500i	−0.575697	+	0.575697i	0.358018	+	0.933715i	$0.383453\pi$
$318$		0			0
$319$			0.658734i			0.0368820i
$320$	62.1398	−	68.0209i	3.47372	−	3.80248i
$321$		0			0
$322$	−6.16893	−	6.16893i	−0.343781	−	0.343781i
$323$	−6.88817	−	6.88817i	−0.383268	−	0.383268i
$324$		0			0
$325$	−18.3086	−	15.2682i	−1.01558	−	0.846926i
$326$			12.9881i			0.719342i
$327$		0			0
$328$	−54.1581	+	54.1581i	−2.99038	+	2.99038i
$329$	−4.72711			−0.260614
$330$		0			0
$331$	18.5908			1.02184			0.510920	−	0.859628i	$-0.329305\pi$
$331$	18.5908			1.02184			0.510920	+	0.859628i	$0.329305\pi$
$332$	58.1375	−	58.1375i	3.19071	−	3.19071i
$333$		0			0
$334$			15.6262i			0.855025i
$335$	0.854823	+	18.9192i	0.0467040	+	1.03367i
$336$		0			0
$337$	12.2286	+	12.2286i	0.666132	+	0.666132i	0.956818	−	0.290686i	$-0.0938836\pi$
$337$	12.2286	+	12.2286i	0.666132	+	0.666132i	−0.290686	+	0.956818i	$0.593884\pi$
$338$	19.1170	+	19.1170i	1.03983	+	1.03983i
$339$		0			0
$340$	−1.43496	−	31.7590i	−0.0778217	−	1.72238i
$341$			0.736438i			0.0398803i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−10.4521			−0.563538
$345$		0			0
$346$	60.4193			3.24816
$347$	10.3260	−	10.3260i	0.554327	−	0.554327i	−0.373360	−	0.927687i	$-0.621794\pi$
$347$	10.3260	−	10.3260i	0.554327	−	0.554327i	0.927687	+	0.373360i	$0.121794\pi$
$348$		0			0
$349$			2.62685i			0.140612i	0.997525	+	0.0703060i	$0.0223976\pi$
$349$			2.62685i			0.140612i	−0.997525	+	0.0703060i	$0.977602\pi$
$350$	−1.25252	−	13.8323i	−0.0669497	−	0.739365i
$351$		0			0
$352$	−4.78616	−	4.78616i	−0.255103	−	0.255103i
$353$	1.84420	+	1.84420i	0.0981569	+	0.0981569i	0.754480	−	0.656323i	$-0.227889\pi$
$353$	1.84420	+	1.84420i	0.0981569	+	0.0981569i	−0.656323	+	0.754480i	$0.727889\pi$
$354$		0			0
$355$	9.52739	−	10.4291i	0.505661	−	0.553518i
$356$		−	10.9681i		−	0.581307i
$357$		0			0
$358$	44.1671	−	44.1671i	2.33430	−	2.33430i
$359$	−25.9440			−1.36927			−0.684637	−	0.728884i	$-0.740039\pi$
$359$	−25.9440			−1.36927			−0.684637	+	0.728884i	$0.740039\pi$
$360$		0			0
$361$	3.66191			0.192732
$362$	−10.9269	+	10.9269i	−0.574303	+	0.574303i
$363$		0			0
$364$			27.2533i			1.42846i
$365$	32.6214	−	1.47392i	1.70748	−	0.0771487i
$366$		0			0
$367$	−13.5250	−	13.5250i	−0.706000	−	0.706000i	0.259691	−	0.965692i	$-0.416379\pi$
$367$	−13.5250	−	13.5250i	−0.706000	−	0.706000i	−0.965692	+	0.259691i	$0.916379\pi$
$368$	−38.2885	−	38.2885i	−1.99592	−	1.99592i
$369$		0			0
$370$	11.4308	+	10.4425i	0.594260	+	0.542881i
$371$		−	6.01929i		−	0.312506i
$372$		0			0
$373$	2.02011	−	2.02011i	0.104597	−	0.104597i	−0.652871	−	0.757469i	$-0.726436\pi$
$373$	2.02011	−	2.02011i	0.104597	−	0.104597i	0.757469	+	0.652871i	$0.226436\pi$
$374$	−1.71642			−0.0887541
$375$		0			0
$376$	−48.7942			−2.51637
$377$	8.93978	−	8.93978i	0.460422	−	0.460422i
$378$		0			0
$379$			4.11882i			0.211570i	0.994389	+	0.105785i	$0.0337355\pi$
$379$			4.11882i			0.211570i	−0.994389	+	0.105785i	$0.966265\pi$
$380$	−36.9571	−	33.7618i	−1.89586	−	1.73194i
$381$		0			0
$382$	−19.6596	−	19.6596i	−1.00587	−	1.00587i
$383$	−18.0158	−	18.0158i	−0.920566	−	0.920566i	0.0765031	−	0.997069i	$-0.475624\pi$
$383$	−18.0158	−	18.0158i	−0.920566	−	0.920566i	−0.997069	+	0.0765031i	$0.975624\pi$
$384$		0			0
$385$	−0.554929	+	0.0250732i	−0.0282818	+	0.00127785i
$386$			20.0611i			1.02108i
$387$		0			0
$388$	6.11745	−	6.11745i	0.310566	−	0.310566i
$389$	−19.1306			−0.969960			−0.484980	−	0.874525i	$-0.661173\pi$
$389$	−19.1306			−0.969960			−0.484980	+	0.874525i	$0.661173\pi$
$390$		0			0
$391$	−7.81199			−0.395069
$392$	−7.29890	+	7.29890i	−0.368650	+	0.368650i
$393$		0			0
$394$			16.9871i			0.855797i
$395$	−16.9760	+	18.5826i	−0.854154	+	0.934993i
$396$		0			0
$397$	0.442442	+	0.442442i	0.0222055	+	0.0222055i	0.718122	−	0.695917i	$-0.245002\pi$
$397$	0.442442	+	0.442442i	0.0222055	+	0.0222055i	−0.695917	+	0.718122i	$0.745002\pi$
$398$	−26.6229	−	26.6229i	−1.33448	−	1.33448i
$399$		0			0
$400$	−7.77394	−	85.8522i	−0.388697	−	4.29261i
$401$		−	14.9814i		−	0.748137i	−0.927401	−	0.374068i	$-0.877963\pi$
$401$		−	14.9814i		−	0.748137i	0.927401	−	0.374068i	$-0.122037\pi$
$402$		0			0
$403$	9.99430	−	9.99430i	0.497852	−	0.497852i
$404$	−50.6753			−2.52119
$405$		0			0
$406$	7.36565			0.365551
$407$	0.437867	−	0.437867i	0.0217042	−	0.0217042i
$408$		0			0
$409$			33.1093i			1.63715i	0.574401	+	0.818574i	$0.305235\pi$
$409$			33.1093i			1.63715i	−0.574401	+	0.818574i	$0.694765\pi$
$410$	2.08026	+	46.0410i	0.102737	+	2.27380i
$411$		0			0
$412$	73.6621	+	73.6621i	3.62907	+	3.62907i
$413$	−3.45500	−	3.45500i	−0.170009	−	0.170009i
$414$		0			0
$415$	−1.45175	−	32.1307i	−0.0712638	−	1.57724i
$416$			129.907i			6.36923i
$417$		0			0
$418$	−1.91101	+	1.91101i	−0.0934704	+	0.0934704i
$419$	−5.14936			−0.251562			−0.125781	−	0.992058i	$-0.540144\pi$
$419$	−5.14936			−0.251562			−0.125781	+	0.992058i	$0.540144\pi$
$420$		0			0
$421$	−2.85311			−0.139052			−0.0695261	−	0.997580i	$-0.522149\pi$
$421$	−2.85311			−0.139052			−0.0695261	+	0.997580i	$0.522149\pi$
$422$	33.2273	−	33.2273i	1.61748	−	1.61748i
$423$		0			0
$424$		−	62.1323i		−	3.01741i
$425$	−9.55125	−	7.96514i	−0.463304	−	0.386366i
$426$		0			0
$427$	6.75305	+	6.75305i	0.326803	+	0.326803i
$428$	5.08871	+	5.08871i	0.245972	+	0.245972i
$429$		0			0
$430$	−4.24203	+	4.64350i	−0.204569	+	0.223929i
$431$			22.0594i			1.06256i	0.847196	+	0.531281i	$0.178289\pi$
$431$			22.0594i			1.06256i	−0.847196	+	0.531281i	$0.821711\pi$
$432$		0			0
$433$	−10.9563	+	10.9563i	−0.526528	+	0.526528i	−0.919535	−	0.393007i	$-0.871435\pi$
$433$	−10.9563	+	10.9563i	−0.526528	+	0.526528i	0.393007	+	0.919535i	$0.371435\pi$
$434$	8.23450			0.395269
$435$		0			0
$436$	−5.28176			−0.252951
$437$	−8.69760	+	8.69760i	−0.416062	+	0.416062i
$438$		0			0
$439$			7.45413i			0.355766i	0.984052	+	0.177883i	$0.0569249\pi$
$439$			7.45413i			0.355766i	−0.984052	+	0.177883i	$0.943075\pi$
$440$	−5.72809	+	0.258811i	−0.273076	+	0.0123383i
$441$		0			0
$442$	23.2938	+	23.2938i	1.10797	+	1.10797i
$443$	−4.02408	−	4.02408i	−0.191190	−	0.191190i	0.605020	−	0.796210i	$-0.293165\pi$
$443$	−4.02408	−	4.02408i	−0.191190	−	0.191190i	−0.796210	+	0.605020i	$0.793165\pi$
$444$		0			0
$445$	−3.16780	−	2.89391i	−0.150168	−	0.137185i
$446$			29.3106i			1.38790i
$447$		0			0
$448$	−29.1345	+	29.1345i	−1.37648	+	1.37648i
$449$	22.8230			1.07708			0.538542	−	0.842599i	$-0.318975\pi$
$449$	22.8230			1.07708			0.538542	+	0.842599i	$0.318975\pi$
$450$		0			0
$451$	1.84332			0.0867986
$452$	24.7172	−	24.7172i	1.16260	−	1.16260i
$453$		0			0
$454$		−	30.4625i		−	1.42968i
$455$	7.87129	+	7.19075i	0.369012	+	0.337107i
$456$		0			0
$457$	21.3136	+	21.3136i	0.997009	+	0.997009i	0.999996	−	0.00298687i	$-0.000950751\pi$
$457$	21.3136	+	21.3136i	0.997009	+	0.997009i	−0.00298687	+	0.999996i	$0.500951\pi$
$458$	23.9444	+	23.9444i	1.11885	+	1.11885i
$459$		0			0
$460$	−40.1017	+	1.81191i	−1.86975	+	0.0844805i
$461$			19.3297i			0.900275i	0.892959	+	0.450137i	$0.148625\pi$
$461$			19.3297i			0.900275i	−0.892959	+	0.450137i	$0.851375\pi$
$462$		0			0
$463$	7.95996	−	7.95996i	0.369931	−	0.369931i	−0.497521	−	0.867452i	$-0.665756\pi$
$463$	7.95996	−	7.95996i	0.369931	−	0.369931i	0.867452	+	0.497521i	$0.165756\pi$
$464$	45.7161			2.12232
$465$		0			0
$466$	−67.0536			−3.10620
$467$	24.9349	−	24.9349i	1.15385	−	1.15385i	0.168076	−	0.985774i	$-0.446244\pi$
$467$	24.9349	−	24.9349i	1.15385	−	1.15385i	0.985774	−	0.168076i	$-0.0537555\pi$
$468$		0			0
$469$		−	8.46957i		−	0.391088i
$470$	−19.8034	+	21.6776i	−0.913462	+	0.999914i
$471$		0			0
$472$	−35.6632	−	35.6632i	−1.64153	−	1.64153i
$473$	0.177873	+	0.177873i	0.00817861	+	0.00817861i
$474$		0			0
$475$	−19.5022	+	1.76593i	−0.894820	+	0.0810262i
$476$			14.2176i			0.651661i
$477$		0			0
$478$	30.6575	−	30.6575i	1.40224	−	1.40224i
$479$	40.2495			1.83905			0.919524	−	0.393034i	$-0.128574\pi$
$479$	40.2495			1.83905			0.919524	+	0.393034i	$0.128574\pi$
$480$		0			0
$481$	−11.8847			−0.541896
$482$	−38.1462	+	38.1462i	−1.73751	+	1.73751i
$483$		0			0
$484$		−	62.5233i		−	2.84197i
$485$	−0.152759	−	3.38092i	−0.00693644	−	0.153520i
$486$		0			0
$487$	24.9159	+	24.9159i	1.12905	+	1.12905i	0.990332	+	0.138717i	$0.0442978\pi$
$487$	24.9159	+	24.9159i	1.12905	+	1.12905i	0.138717	+	0.990332i	$0.455702\pi$
$488$	69.7063	+	69.7063i	3.15546	+	3.15546i
$489$		0			0
$490$	0.280357	+	6.20495i	0.0126652	+	0.280311i
$491$		−	7.29487i		−	0.329213i	−0.986359	−	0.164607i	$-0.947365\pi$
$491$		−	7.29487i		−	0.329213i	0.986359	−	0.164607i	$-0.0526354\pi$
$492$		0			0
$493$	4.66372	−	4.66372i	0.210044	−	0.210044i
$494$	51.8691			2.33370
$495$		0			0
$496$	51.1088			2.29485
$497$	−4.46695	+	4.46695i	−0.200370	+	0.200370i
$498$		0			0
$499$			8.99153i			0.402516i	0.979538	+	0.201258i	$0.0645030\pi$
$499$			8.99153i			0.402516i	−0.979538	+	0.201258i	$0.935497\pi$
$500$	−50.8775	−	38.6726i	−2.27531	−	1.72949i
$501$		0			0
$502$	−42.6779	−	42.6779i	−1.90481	−	1.90481i
$503$	14.4521	+	14.4521i	0.644386	+	0.644386i	0.951631	−	0.307245i	$-0.0994070\pi$
$503$	14.4521	+	14.4521i	0.644386	+	0.644386i	−0.307245	+	0.951631i	$0.599407\pi$
$504$		0			0
$505$	−13.3706	+	14.6360i	−0.594984	+	0.651294i
$506$			2.16730i			0.0963485i
$507$		0			0
$508$	−56.6405	+	56.6405i	−2.51302	+	2.51302i
$509$	20.2009			0.895391			0.447695	−	0.894186i	$-0.352245\pi$
$509$	20.2009			0.895391			0.447695	+	0.894186i	$0.352245\pi$
$510$		0			0
$511$	−14.6036			−0.646026
$512$	−80.4832	+	80.4832i	−3.55689	+	3.55689i
$513$		0			0
$514$			7.67967i			0.338736i
$515$	40.7107	−	1.83942i	1.79393	−	0.0810546i
$516$		0			0
$517$	0.830379	+	0.830379i	0.0365200	+	0.0365200i
$518$	−4.89601	−	4.89601i	−0.215119	−	0.215119i
$519$		0			0
$520$	81.2491	+	74.2243i	3.56301	+	3.25495i
$521$			21.7026i			0.950810i	0.879767	+	0.475405i	$0.157698\pi$
$521$			21.7026i			0.950810i	−0.879767	+	0.475405i	$0.842302\pi$
$522$		0			0
$523$	3.17763	−	3.17763i	0.138948	−	0.138948i	−0.634211	−	0.773160i	$-0.718675\pi$
$523$	3.17763	−	3.17763i	0.138948	−	0.138948i	0.773160	+	0.634211i	$0.218675\pi$
$524$	−29.7043			−1.29764
$525$		0			0
$526$	21.2189			0.925186
$527$	5.21385	−	5.21385i	0.227119	−	0.227119i
$528$		0			0
$529$		−	13.1359i		−	0.571126i
$530$	−27.6033	−	25.2167i	−1.19901	−	1.09534i
$531$		0			0
$532$	15.8294	+	15.8294i	0.686289	+	0.686289i
$533$	−25.0160	−	25.0160i	−1.08356	−	1.08356i
$534$		0			0
$535$	2.81237	−	0.127071i	0.121589	−	0.00549374i
$536$		−	87.4246i		−	3.77617i
$537$		0			0
$538$	42.5617	−	42.5617i	1.83497	−	1.83497i
$539$	0.248425			0.0107004
$540$		0			0
$541$	17.9333			0.771012			0.385506	−	0.922705i	$-0.374027\pi$
$541$	17.9333			0.771012			0.385506	+	0.922705i	$0.374027\pi$
$542$	−9.65636	+	9.65636i	−0.414776	+	0.414776i
$543$		0			0
$544$			67.7703i			2.90563i
$545$	−1.39359	+	1.52548i	−0.0596947	+	0.0653443i
$546$		0			0
$547$	3.40977	+	3.40977i	0.145791	+	0.145791i	0.776235	−	0.630444i	$-0.217127\pi$
$547$	3.40977	+	3.40977i	0.145791	+	0.145791i	−0.630444	+	0.776235i	$0.717127\pi$
$548$	−24.5076	−	24.5076i	−1.04691	−	1.04691i
$549$		0			0
$550$	−2.20979	+	2.64984i	−0.0942260	+	0.112989i
$551$		−	10.3849i		−	0.442410i
$552$		0			0
$553$	7.95925	−	7.95925i	0.338462	−	0.338462i
$554$	−68.5836			−2.91384
$555$		0			0
$556$	−60.4497			−2.56364
$557$	−0.275161	+	0.275161i	−0.0116590	+	0.0116590i	−0.712912	−	0.701253i	$-0.752624\pi$
$557$	−0.275161	+	0.275161i	−0.0116590	+	0.0116590i	0.701253	+	0.712912i	$0.252624\pi$
$558$		0			0
$559$		−	4.82788i		−	0.204198i
$560$	1.74008	+	38.5121i	0.0735318	+	1.62743i
$561$		0			0
$562$	−28.4422	−	28.4422i	−1.19976	−	1.19976i
$563$	25.1442	+	25.1442i	1.05970	+	1.05970i	0.998101	+	0.0616005i	$0.0196205\pi$
$563$	25.1442	+	25.1442i	1.05970	+	1.05970i	0.0616005	+	0.998101i	$0.480380\pi$
$564$		0			0
$565$	−0.617216	−	13.6604i	−0.0259665	−	0.574699i
$566$		−	72.9342i		−	3.06565i
$567$		0			0
$568$	−46.1088	+	46.1088i	−1.93468	+	1.93468i
$569$	26.6023			1.11523			0.557614	−	0.830101i	$-0.311717\pi$
$569$	26.6023			1.11523			0.557614	+	0.830101i	$0.311717\pi$
$570$		0			0
$571$	−33.9064			−1.41894			−0.709469	−	0.704736i	$-0.751065\pi$
$571$	−33.9064			−1.41894			−0.709469	+	0.704736i	$0.751065\pi$
$572$	4.78740	−	4.78740i	0.200171	−	0.200171i
$573$		0			0
$574$		−	20.6111i		−	0.860293i
$575$	−10.0575	+	12.0602i	−0.419426	+	0.502947i
$576$		0			0
$577$	−16.6238	−	16.6238i	−0.692057	−	0.692057i	0.270627	−	0.962684i	$-0.412769\pi$
$577$	−16.6238	−	16.6238i	−0.692057	−	0.692057i	−0.962684	+	0.270627i	$0.912769\pi$
$578$	−21.2391	−	21.2391i	−0.883429	−	0.883429i
$579$		0			0
$580$	22.8589	−	25.0223i	0.949163	−	1.03899i
$581$			14.3840i			0.596747i
$582$		0			0
$583$	−1.05737	+	1.05737i	−0.0437916	+	0.0437916i
$584$	−150.741			−6.23773
$585$		0			0
$586$	46.0340			1.90165
$587$	4.60012	−	4.60012i	0.189867	−	0.189867i	−0.605772	−	0.795639i	$-0.707135\pi$
$587$	4.60012	−	4.60012i	0.189867	−	0.189867i	0.795639	+	0.605772i	$0.207135\pi$
$588$		0			0
$589$		−	11.6098i		−	0.478376i
$590$	−30.3180	+	1.36985i	−1.24817	+	0.0563959i
$591$		0			0
$592$	−30.3879	−	30.3879i	−1.24894	−	1.24894i
$593$	17.6196	+	17.6196i	0.723551	+	0.723551i	0.969327	−	0.245775i	$-0.0790426\pi$
$593$	17.6196	+	17.6196i	0.723551	+	0.723551i	−0.245775	+	0.969327i	$0.579043\pi$
$594$		0			0
$595$	4.10631	+	3.75129i	0.168342	+	0.153788i
$596$		−	133.076i		−	5.45102i
$597$		0			0
$598$	29.4128	−	29.4128i	1.20278	−	1.20278i
$599$	1.79409			0.0733046			0.0366523	−	0.999328i	$-0.488331\pi$
$599$	1.79409			0.0733046			0.0366523	+	0.999328i	$0.488331\pi$
$600$		0			0
$601$	−27.6926			−1.12960			−0.564802	−	0.825227i	$-0.691047\pi$
$601$	−27.6926			−1.12960			−0.564802	+	0.825227i	$0.691047\pi$
$602$	1.98889	−	1.98889i	0.0810612	−	0.0810612i
$603$		0			0
$604$		−	75.9456i		−	3.09018i
$605$	−18.0580	−	16.4967i	−0.734160	−	0.670686i
$606$		0			0
$607$	−9.55102	−	9.55102i	−0.387664	−	0.387664i	0.486189	−	0.873853i	$-0.338387\pi$
$607$	−9.55102	−	9.55102i	−0.387664	−	0.387664i	−0.873853	+	0.486189i	$0.838387\pi$
$608$	75.4532	+	75.4532i	3.06003	+	3.06003i
$609$		0			0
$610$	59.2588	−	2.67748i	2.39932	−	0.108408i
$611$		−	22.5384i		−	0.911805i
$612$		0			0
$613$	32.8779	−	32.8779i	1.32793	−	1.32793i	0.420750	−	0.907177i	$-0.361767\pi$
$613$	32.8779	−	32.8779i	1.32793	−	1.32793i	0.907177	−	0.420750i	$-0.138233\pi$
$614$	82.3298			3.32256
$615$		0			0
$616$	2.56429			0.103318
$617$	1.11112	−	1.11112i	0.0447319	−	0.0447319i	−0.684387	−	0.729119i	$-0.739930\pi$
$617$	1.11112	−	1.11112i	0.0447319	−	0.0447319i	0.729119	+	0.684387i	$0.239930\pi$
$618$		0			0
$619$			28.3646i			1.14007i	0.821621	+	0.570035i	$0.193070\pi$
$619$			28.3646i			1.14007i	−0.821621	+	0.570035i	$0.806930\pi$
$620$	25.5553	−	27.9739i	1.02633	−	1.12346i
$621$		0			0
$622$	29.8617	+	29.8617i	1.19734	+	1.19734i
$623$	1.35682	+	1.35682i	0.0543599	+	0.0543599i
$624$		0			0
$625$	−24.5934	+	4.49069i	−0.983735	+	0.179628i
$626$			0.703922i			0.0281344i
$627$		0			0
$628$	−27.5878	+	27.5878i	−1.10087	+	1.10087i
$629$	−6.20004			−0.247212
$630$		0			0
$631$	−21.8241			−0.868803			−0.434401	−	0.900719i	$-0.643040\pi$
$631$	−21.8241			−0.868803			−0.434401	+	0.900719i	$0.643040\pi$
$632$	82.1570	−	82.1570i	3.26803	−	3.26803i
$633$		0			0
$634$		−	40.2657i		−	1.59915i
$635$	1.41437	+	31.3034i	0.0561277	+	1.24224i
$636$		0			0
$637$	−3.37141	−	3.37141i	−0.133580	−	0.133580i
$638$	−1.29387	−	1.29387i	−0.0512249	−	0.0512249i
$639$		0			0
$640$	6.05152	+	133.934i	0.239207	+	5.29422i
$641$		−	1.91757i		−	0.0757395i	−0.999283	−	0.0378697i	$-0.987943\pi$
$641$		−	1.91757i		−	0.0757395i	0.999283	−	0.0378697i	$-0.0120572\pi$
$642$		0			0
$643$	20.2152	−	20.2152i	0.797209	−	0.797209i	−0.185446	−	0.982654i	$-0.559373\pi$
$643$	20.2152	−	20.2152i	0.797209	−	0.797209i	0.982654	+	0.185446i	$0.0593730\pi$
$644$	17.9523			0.707421
$645$		0			0
$646$	27.0592			1.06463
$647$	24.4807	−	24.4807i	0.962435	−	0.962435i	−0.0368841	−	0.999320i	$-0.511743\pi$
$647$	24.4807	−	24.4807i	0.962435	−	0.962435i	0.999320	+	0.0368841i	$0.0117432\pi$
$648$		0			0
$649$			1.21383i			0.0476470i
$650$	65.9507	−	5.97186i	2.58680	−	0.234236i
$651$		0			0
$652$	−18.8984	−	18.8984i	−0.740119	−	0.740119i
$653$	−17.3242	−	17.3242i	−0.677950	−	0.677950i	0.281586	−	0.959536i	$-0.409140\pi$
$653$	−17.3242	−	17.3242i	−0.677950	−	0.677950i	−0.959536	+	0.281586i	$0.909140\pi$
$654$		0			0
$655$	−7.83743	+	8.57918i	−0.306234	+	0.335216i
$656$		−	127.926i		−	4.99469i
$657$		0			0
$658$	9.28490	−	9.28490i	0.361963	−	0.361963i
$659$	29.9820			1.16793			0.583967	−	0.811777i	$-0.301500\pi$
$659$	29.9820			1.16793			0.583967	+	0.811777i	$0.301500\pi$
$660$		0			0
$661$	36.5460			1.42147			0.710737	−	0.703458i	$-0.248362\pi$
$661$	36.5460			1.42147			0.710737	+	0.703458i	$0.248362\pi$
$662$	−36.5156	+	36.5156i	−1.41922	+	1.41922i
$663$		0			0
$664$			148.474i			5.76192i
$665$	8.74838	−	0.395276i	0.339248	−	0.0153281i
$666$		0			0
$667$	−5.88882	−	5.88882i	−0.228016	−	0.228016i
$668$	−22.7370	−	22.7370i	−0.879722	−	0.879722i
$669$		0			0
$670$	−38.8398	−	35.4818i	−1.50051	−	1.37078i
$671$		−	2.37252i		−	0.0915902i
$672$		0			0
$673$	−27.4562	+	27.4562i	−1.05836	+	1.05836i	−0.0601718	+	0.998188i	$0.519165\pi$
$673$	−27.4562	+	27.4562i	−1.05836	+	1.05836i	−0.998188	+	0.0601718i	$0.980835\pi$
$674$	−48.0382			−1.85036
$675$		0			0
$676$	−55.6328			−2.13972
$677$	−18.4107	+	18.4107i	−0.707582	+	0.707582i	−0.966026	−	0.258444i	$-0.916790\pi$
$677$	−18.4107	+	18.4107i	−0.707582	+	0.707582i	0.258444	+	0.966026i	$0.416790\pi$
$678$		0			0
$679$			1.51354i			0.0580842i
$680$	42.3862	+	38.7215i	1.62544	+	1.48490i
$681$		0			0
$682$	−1.44650	−	1.44650i	−0.0553892	−	0.0553892i
$683$	−6.18268	−	6.18268i	−0.236574	−	0.236574i	0.578856	−	0.815430i	$-0.303499\pi$
$683$	−6.18268	−	6.18268i	−0.236574	−	0.236574i	−0.815430	+	0.578856i	$0.803499\pi$
$684$		0			0
$685$	−13.5446	+	0.611981i	−0.517512	+	0.0233826i
$686$		−	2.77777i		−	0.106056i
$687$		0			0
$688$	12.3444	−	12.3444i	0.470625	−	0.470625i
$689$	28.6993			1.09336
$690$		0			0
$691$	39.0569			1.48579			0.742897	−	0.669406i	$-0.233451\pi$
$691$	39.0569			1.48579			0.742897	+	0.669406i	$0.233451\pi$
$692$	−87.9138	+	87.9138i	−3.34198	+	3.34198i
$693$		0			0
$694$			40.5641i			1.53979i
$695$	−15.9496	+	17.4591i	−0.605002	+	0.662261i
$696$		0			0
$697$	−13.0504	−	13.0504i	−0.494319	−	0.494319i
$698$	−5.15960	−	5.15960i	−0.195294	−	0.195294i
$699$		0			0
$700$	21.9493	+	18.3043i	0.829604	+	0.691837i
$701$			41.7309i			1.57615i	0.615577	+	0.788077i	$0.288923\pi$
$701$			41.7309i			1.57615i	−0.615577	+	0.788077i	$0.711077\pi$
$702$		0			0
$703$	−6.90291	+	6.90291i	−0.260348	+	0.260348i
$704$	10.2357			0.385773
$705$		0			0
$706$	−7.24468			−0.272657
$707$	6.26886	−	6.26886i	0.235765	−	0.235765i
$708$		0			0
$709$			20.9505i			0.786812i	0.919365	+	0.393406i	$0.128703\pi$
$709$			20.9505i			0.786812i	−0.919365	+	0.393406i	$0.871297\pi$
$710$	1.77108	+	39.1981i	0.0664673	+	1.47108i
$711$		0			0
$712$	14.0054	+	14.0054i	0.524874	+	0.524874i
$713$	−6.58346	−	6.58346i	−0.246553	−	0.246553i
$714$		0			0
$715$	−0.119546	−	2.64584i	−0.00447078	−	0.0989489i
$716$			128.532i			4.80346i
$717$		0			0
$718$	50.9587	−	50.9587i	1.90176	−	1.90176i
$719$	26.9899			1.00655			0.503277	−	0.864125i	$-0.332128\pi$
$719$	26.9899			1.00655			0.503277	+	0.864125i	$0.332128\pi$
$720$		0			0
$721$	−18.2250			−0.678734
$722$	−7.19264	+	7.19264i	−0.267682	+	0.267682i
$723$		0			0
$724$		−	31.7985i		−	1.18178i
$725$	−1.19564	−	13.2042i	−0.0444051	−	0.490391i
$726$		0			0
$727$	9.84200	+	9.84200i	0.365020	+	0.365020i	0.865657	−	0.500637i	$-0.166901\pi$
$727$	9.84200	+	9.84200i	0.365020	+	0.365020i	−0.500637	+	0.865657i	$0.666901\pi$
$728$	−34.8004	−	34.8004i	−1.28979	−	1.28979i
$729$		0			0
$730$	−61.1792	+	66.9693i	−2.26434	+	2.47865i
$731$		−	2.51862i		−	0.0931545i
$732$		0			0
$733$	12.9130	−	12.9130i	0.476951	−	0.476951i	−0.427204	−	0.904155i	$-0.640501\pi$
$733$	12.9130	−	12.9130i	0.476951	−	0.476951i	0.904155	+	0.427204i	$0.140501\pi$
$734$	53.1311			1.96111
$735$		0			0
$736$	85.5727			3.15425
$737$	−1.48779	+	1.48779i	−0.0548035	+	0.0548035i
$738$		0			0
$739$			27.4269i			1.00891i	0.863437	+	0.504457i	$0.168307\pi$
$739$			27.4269i			1.00891i	−0.863437	+	0.504457i	$0.831693\pi$
$740$	−31.8270	+	1.43803i	−1.16998	+	0.0528631i
$741$		0			0
$742$	11.8230	+	11.8230i	0.434035	+	0.434035i
$743$	−9.43704	−	9.43704i	−0.346212	−	0.346212i	0.512485	−	0.858696i	$-0.328725\pi$
$743$	−9.43704	−	9.43704i	−0.346212	−	0.346212i	−0.858696	+	0.512485i	$0.828725\pi$
$744$		0			0
$745$	−38.4351	−	35.1120i	−1.40815	−	1.28640i
$746$			7.93572i			0.290547i
$747$		0			0
$748$	2.49750	−	2.49750i	0.0913177	−	0.0913177i
$749$	−1.25901			−0.0460033
$750$		0			0
$751$	−43.6512			−1.59286			−0.796428	−	0.604734i	$-0.793279\pi$
$751$	−43.6512			−1.59286			−0.796428	+	0.604734i	$0.793279\pi$
$752$	57.6282	−	57.6282i	2.10149	−	2.10149i
$753$		0			0
$754$			35.1187i			1.27895i
$755$	−21.9346	−	20.0381i	−0.798281	−	0.729263i
$756$		0			0
$757$	15.2034	+	15.2034i	0.552579	+	0.552579i	0.927184	−	0.374606i	$-0.122222\pi$
$757$	15.2034	+	15.2034i	0.552579	+	0.552579i	−0.374606	+	0.927184i	$0.622222\pi$
$758$	−8.09011	−	8.09011i	−0.293846	−	0.293846i
$759$		0			0
$760$	90.3026	−	4.08012i	3.27562	−	0.148001i
$761$			6.27530i			0.227479i	0.993511	+	0.113740i	$0.0362830\pi$
$761$			6.27530i			0.227479i	−0.993511	+	0.113740i	$0.963717\pi$
$762$		0			0
$763$	0.653389	−	0.653389i	0.0236543	−	0.0236543i
$764$	57.2118			2.06985
$765$		0			0
$766$	70.7727			2.55712
$767$	16.4731	−	16.4731i	0.594808	−	0.594808i
$768$		0			0
$769$			36.5294i			1.31728i	0.752456	+	0.658642i	$0.228869\pi$
$769$			36.5294i			1.31728i	−0.752456	+	0.658642i	$0.771131\pi$
$770$	1.04073	−	1.13923i	0.0375054	−	0.0410549i
$771$		0			0
$772$	−29.1901	−	29.1901i	−1.05057	−	1.05057i
$773$	17.5844	+	17.5844i	0.632468	+	0.632468i	0.948686	−	0.316219i	$-0.102413\pi$
$773$	17.5844	+	17.5844i	0.632468	+	0.632468i	−0.316219	+	0.948686i	$0.602413\pi$
$774$		0			0
$775$	−1.33668	−	14.7617i	−0.0480150	−	0.530258i
$776$			15.6230i			0.560834i
$777$		0			0
$778$	37.5759	−	37.5759i	1.34716	−	1.34716i
$779$	−29.0597			−1.04117
$780$		0			0
$781$	1.56936			0.0561560
$782$	15.3441	−	15.3441i	0.548705	−	0.548705i
$783$		0			0
$784$		−	17.2407i		−	0.615739i
$785$	0.688896	+	15.2469i	0.0245878	+	0.544185i
$786$		0			0
$787$	16.9793	+	16.9793i	0.605246	+	0.605246i	0.941700	−	0.336454i	$-0.109228\pi$
$787$	16.9793	+	16.9793i	0.605246	+	0.605246i	−0.336454	+	0.941700i	$0.609228\pi$
$788$	−24.7172	−	24.7172i	−0.880516	−	0.880516i
$789$		0			0
$790$	−3.15572	−	69.8435i	−0.112275	−	2.48492i
$791$			6.11537i			0.217437i
$792$		0			0
$793$	−32.1978	+	32.1978i	−1.14338	+	1.14338i
$794$	−1.73807			−0.0616818
$795$		0			0
$796$	77.4758			2.74606
$797$	19.7309	−	19.7309i	0.698903	−	0.698903i	−0.265271	−	0.964174i	$-0.585461\pi$
$797$	19.7309	−	19.7309i	0.698903	−	0.698903i	0.964174	+	0.265271i	$0.0854614\pi$
$798$		0			0
$799$		−	11.7579i		−	0.415964i
$800$	104.625	+	87.2503i	3.69904	+	3.08477i
$801$		0			0
$802$	29.4262	+	29.4262i	1.03908	+	1.03908i
$803$	2.56531	+	2.56531i	0.0905280	+	0.0905280i
$804$		0			0
$805$	4.73670	−	5.18499i	0.166947	−	0.182747i
$806$			39.2612i			1.38292i
$807$		0			0
$808$	64.7084	−	64.7084i	2.27643	−	2.27643i
$809$	31.7336			1.11569			0.557846	−	0.829944i	$-0.311628\pi$
$809$	31.7336			1.11569			0.557846	+	0.829944i	$0.311628\pi$
$810$		0			0
$811$	−14.7328			−0.517338			−0.258669	−	0.965966i	$-0.583284\pi$
$811$	−14.7328			−0.517338			−0.258669	+	0.965966i	$0.583284\pi$
$812$	−10.7175	+	10.7175i	−0.376110	+	0.376110i
$813$		0			0
$814$			1.72010i			0.0602894i
$815$	−10.4446	+	0.471914i	−0.365857	+	0.0165304i
$816$		0			0
$817$	−2.80415	−	2.80415i	−0.0981046	−	0.0981046i
$818$	−65.0326	−	65.0326i	−2.27381	−	2.27381i
$819$		0			0
$820$	−70.0193	−	63.9655i	−2.44518	−	2.23377i
$821$		−	24.0674i		−	0.839959i	−0.907534	−	0.419980i	$-0.862037\pi$
$821$		−	24.0674i		−	0.839959i	0.907534	−	0.419980i	$-0.137963\pi$
$822$		0			0
$823$	27.6196	−	27.6196i	0.962759	−	0.962759i	−0.0365723	−	0.999331i	$-0.511644\pi$
$823$	27.6196	−	27.6196i	0.962759	−	0.962759i	0.999331	+	0.0365723i	$0.0116439\pi$
$824$	−188.122			−6.55353
$825$		0			0
$826$	13.5725			0.472247
$827$	−16.3828	+	16.3828i	−0.569687	+	0.569687i	−0.932041	−	0.362354i	$-0.881973\pi$
$827$	−16.3828	+	16.3828i	−0.569687	+	0.569687i	0.362354	+	0.932041i	$0.381973\pi$
$828$		0			0
$829$		−	30.5709i		−	1.06177i	−0.847443	−	0.530886i	$-0.821859\pi$
$829$		−	30.5709i		−	1.06177i	0.847443	−	0.530886i	$-0.178141\pi$
$830$	65.9621	+	60.2590i	2.28958	+	2.09162i
$831$		0			0
$832$	−138.910	−	138.910i	−4.81585	−	4.81585i
$833$	−1.75881	−	1.75881i	−0.0609390	−	0.0609390i
$834$		0			0
$835$	−12.5660	+	0.567768i	−0.434865	+	0.0196484i
$836$		−	5.56126i		−	0.192340i
$837$		0			0
$838$	10.1143	−	10.1143i	0.349391	−	0.349391i
$839$	−51.9468			−1.79340			−0.896701	−	0.442638i	$-0.854043\pi$
$839$	−51.9468			−1.79340			−0.896701	+	0.442638i	$0.854043\pi$
$840$		0			0
$841$	−21.9688			−0.757544
$842$	5.60403	−	5.60403i	0.193128	−	0.193128i
$843$		0			0
$844$			96.6955i			3.32840i
$845$	−14.6787	+	16.0679i	−0.504961	+	0.552751i
$846$		0			0
$847$	7.73454	+	7.73454i	0.265762	+	0.265762i
$848$	73.3812	+	73.3812i	2.51992	+	2.51992i
$849$		0			0
$850$	34.4053	−	3.11541i	1.18009	−	0.106858i
$851$			7.82871i			0.268365i
$852$		0			0
$853$	−4.07950	+	4.07950i	−0.139679	+	0.139679i	−0.773489	−	0.633810i	$-0.781490\pi$
$853$	−4.07950	+	4.07950i	−0.139679	+	0.139679i	0.633810	+	0.773489i	$0.281490\pi$
$854$	−26.5284			−0.907783
$855$		0			0
$856$	−12.9958			−0.444187
$857$	−10.5745	+	10.5745i	−0.361217	+	0.361217i	−0.864261	−	0.503044i	$-0.832214\pi$
$857$	−10.5745	+	10.5745i	−0.361217	+	0.361217i	0.503044	+	0.864261i	$0.332214\pi$
$858$		0			0
$859$			33.2826i			1.13559i	0.823171	+	0.567794i	$0.192203\pi$
$859$			33.2826i			1.13559i	−0.823171	+	0.567794i	$0.807797\pi$
$860$	−0.584167	−	12.9290i	−0.0199199	−	0.440875i
$861$		0			0
$862$	−43.3286	−	43.3286i	−1.47578	−	1.47578i
$863$	−11.6428	−	11.6428i	−0.396326	−	0.396326i	0.480609	−	0.876935i	$-0.340416\pi$
$863$	−11.6428	−	11.6428i	−0.396326	−	0.396326i	−0.876935	+	0.480609i	$0.840416\pi$
$864$		0			0
$865$	2.19530	+	48.5872i	0.0746425	+	1.65201i
$866$		−	43.0405i		−	1.46257i
$867$		0			0
$868$	−11.9817	+	11.9817i	−0.406685	+	0.406685i
$869$	−2.79629			−0.0948577
$870$		0			0
$871$	40.3820			1.36829
$872$	6.74441	−	6.74441i	0.228394	−	0.228394i
$873$		0			0
$874$		−	34.1673i		−	1.15573i
$875$	11.0779	−	1.50982i	0.374502	−	0.0510412i
$876$		0			0
$877$	16.0669	+	16.0669i	0.542541	+	0.542541i	0.924273	−	0.381732i	$-0.124672\pi$
$877$	16.0669	+	16.0669i	0.542541	+	0.542541i	−0.381732	+	0.924273i	$0.624672\pi$
$878$	−14.6412	−	14.6412i	−0.494118	−	0.494118i
$879$		0			0
$880$	6.45947	−	7.07081i	0.217749	−	0.238357i
$881$			33.9802i			1.14482i	0.819967	+	0.572411i	$0.193992\pi$
$881$			33.9802i			1.14482i	−0.819967	+	0.572411i	$0.806008\pi$
$882$		0			0
$883$	12.8883	−	12.8883i	0.433726	−	0.433726i	−0.456168	−	0.889894i	$-0.650778\pi$
$883$	12.8883	−	12.8883i	0.433726	−	0.433726i	0.889894	+	0.456168i	$0.150778\pi$
$884$	−67.7879			−2.27995
$885$		0			0
$886$	15.8080			0.531082
$887$	−8.51813	+	8.51813i	−0.286011	+	0.286011i	−0.835501	−	0.549490i	$-0.814822\pi$
$887$	−8.51813	+	8.51813i	−0.286011	+	0.286011i	0.549490	+	0.835501i	$0.314822\pi$
$888$		0			0
$889$		−	14.0136i		−	0.470001i
$890$	11.9063	−	0.537958i	0.399100	−	0.0180324i
$891$		0			0
$892$	−42.6487	−	42.6487i	−1.42798	−	1.42798i
$893$	−13.0908	−	13.0908i	−0.438067	−	0.438067i
$894$		0			0
$895$	37.1225	+	33.9129i	1.24087	+	1.13358i
$896$		−	59.9583i		−	2.00307i
$897$		0			0
$898$	−44.8285	+	44.8285i	−1.49595	+	1.49595i
$899$	7.86060			0.262166
$900$		0			0
$901$	14.9719			0.498788
$902$	−3.62062	+	3.62062i	−0.120553	+	0.120553i
$903$		0			0
$904$			63.1241i			2.09947i
$905$	−9.18404	−	8.39000i	−0.305288	−	0.278893i
$906$		0			0
$907$	1.99425	+	1.99425i	0.0662179	+	0.0662179i	0.739440	−	0.673222i	$-0.235090\pi$
$907$	1.99425	+	1.99425i	0.0662179	+	0.0662179i	−0.673222	+	0.739440i	$0.735090\pi$
$908$	44.3249	+	44.3249i	1.47097	+	1.47097i
$909$		0			0
$910$	−29.5846	+	1.33671i	−0.980718	+	0.0443115i
$911$		−	5.34768i		−	0.177176i	−0.996068	−	0.0885882i	$-0.971764\pi$
$911$		−	5.34768i		−	0.177176i	0.996068	−	0.0885882i	$-0.0282355\pi$
$912$		0			0
$913$	2.52673	−	2.52673i	0.0836226	−	0.0836226i
$914$	−83.7275			−2.76946
$915$		0			0
$916$	−69.6812			−2.30233
$917$	3.67461	−	3.67461i	0.121346	−	0.121346i
$918$		0			0
$919$			35.0647i			1.15668i	0.815796	+	0.578339i	$0.196299\pi$
$919$			35.0647i			1.15668i	−0.815796	+	0.578339i	$0.803701\pi$
$920$	48.8932	−	53.5205i	1.61196	−	1.76452i
$921$		0			0
$922$	−37.9670	−	37.9670i	−1.25038	−	1.25038i
$923$	−21.2980	−	21.2980i	−0.701031	−	0.701031i
$924$		0			0
$925$	−7.98219	+	9.57170i	−0.262453	+	0.314716i
$926$			31.2696i			1.02758i
$927$		0			0
$928$	−51.0866	+	51.0866i	−1.67700	+	1.67700i
$929$	11.2129			0.367883			0.183941	−	0.982937i	$-0.441114\pi$
$929$	11.2129			0.367883			0.183941	+	0.982937i	$0.441114\pi$
$930$		0			0
$931$	−3.91639			−0.128354
$932$	97.5672	−	97.5672i	3.19592	−	3.19592i
$933$		0			0
$934$			97.9533i			3.20513i
$935$	−0.0623653	−	1.38029i	−0.00203956	−	0.0451403i
$936$		0			0
$937$	1.24982	+	1.24982i	0.0408298	+	0.0408298i	0.727227	−	0.686397i	$-0.240809\pi$
$937$	1.24982	+	1.24982i	0.0408298	+	0.0408298i	−0.686397	+	0.727227i	$0.740809\pi$
$938$	16.6358	+	16.6358i	0.543177	+	0.543177i
$939$		0			0
$940$	−2.72711	−	60.3574i	−0.0889486	−	1.96864i
$941$			2.58136i			0.0841499i	0.999114	+	0.0420750i	$0.0133968\pi$
$941$			2.58136i			0.0841499i	−0.999114	+	0.0420750i	$0.986603\pi$
$942$		0			0
$943$	−16.4786	+	16.4786i	−0.536616	+	0.536616i
$944$	84.2398			2.74177
$945$		0			0
$946$	−0.698749			−0.0227183
$947$	−40.6372	+	40.6372i	−1.32053	+	1.32053i	−0.407184	+	0.913346i	$0.633489\pi$
$947$	−40.6372	+	40.6372i	−1.32053	+	1.32053i	−0.913346	+	0.407184i	$0.866511\pi$
$948$		0			0
$949$		−	69.6285i		−	2.26024i
$950$	34.8371	−	41.7743i	1.13027	−	1.35534i
$951$		0			0
$952$	−18.1547	−	18.1547i	−0.588399	−	0.588399i
$953$	−31.8867	−	31.8867i	−1.03291	−	1.03291i	−0.999440	−	0.0334725i	$-0.989343\pi$
$953$	−31.8867	−	31.8867i	−1.03291	−	1.03291i	−0.0334725	−	0.999440i	$-0.510657\pi$
$954$		0			0
$955$	15.0953	−	16.5239i	0.488471	−	0.534701i
$956$			89.2171i			2.88549i
$957$		0			0
$958$	−79.0573	+	79.0573i	−2.55423	+	2.55423i
$959$	6.06350			0.195801
$960$		0			0
$961$	−22.2122			−0.716522
$962$	23.3437	−	23.3437i	0.752631	−	0.752631i
$963$		0			0
$964$		−	111.010i		−	3.57540i
$965$	−16.1324	+	0.728908i	−0.519321	+	0.0234644i
$966$		0			0
$967$	41.0973	+	41.0973i	1.32160	+	1.32160i	0.912482	+	0.409118i	$0.134163\pi$
$967$	41.0973	+	41.0973i	1.32160	+	1.32160i	0.409118	+	0.912482i	$0.365837\pi$
$968$	79.8374	+	79.8374i	2.56607	+	2.56607i
$969$		0			0
$970$	6.94078	+	6.34069i	0.222855	+	0.203587i
$971$		−	8.55398i		−	0.274510i	−0.990536	−	0.137255i	$-0.956172\pi$
$971$		−	8.55398i		−	0.274510i	0.990536	−	0.137255i	$-0.0438280\pi$
$972$		0			0
$973$	7.47803	−	7.47803i	0.239735	−	0.239735i
$974$	−97.8788			−3.13624
$975$		0			0
$976$	−164.653			−5.27041
$977$	−19.2987	+	19.2987i	−0.617420	+	0.617420i	−0.944869	−	0.327449i	$-0.893811\pi$
$977$	−19.2987	+	19.2987i	−0.617420	+	0.617420i	0.327449	+	0.944869i	$0.393811\pi$
$978$		0			0
$979$		−	0.476687i		−	0.0152350i
$980$	−9.43652	−	8.62065i	−0.301439	−	0.275376i
$981$		0			0
$982$	14.3284	+	14.3284i	0.457239	+	0.457239i
$983$	11.4633	+	11.4633i	0.365624	+	0.365624i	0.865878	−	0.500255i	$-0.166760\pi$
$983$	11.4633	+	11.4633i	0.365624	+	0.365624i	−0.500255	+	0.865878i	$0.666760\pi$
$984$		0			0
$985$	−13.6604	+	0.617216i	−0.435258	+	0.0196661i
$986$			18.3208i			0.583453i
$987$		0			0
$988$	−75.4727	+	75.4727i	−2.40111	+	2.40111i
$989$	−3.18023			−0.101125
$990$		0			0
$991$	42.4919			1.34980			0.674899	−	0.737910i	$-0.264187\pi$
$991$	42.4919			1.34980			0.674899	+	0.737910i	$0.264187\pi$
$992$	−57.1127	+	57.1127i	−1.81333	+	1.81333i
$993$		0			0
$994$		−	17.5478i		−	0.556582i
$995$	20.4419	−	22.3766i	0.648052	−	0.709384i
$996$		0			0
$997$	−16.2954	−	16.2954i	−0.516082	−	0.516082i	0.400302	−	0.916383i	$-0.368905\pi$
$997$	−16.2954	−	16.2954i	−0.516082	−	0.516082i	−0.916383	+	0.400302i	$0.868905\pi$
$998$	−17.6610	−	17.6610i	−0.559049	−	0.559049i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.m.a.197.1	yes	12
3.2	odd	2		315.2.m.b.197.6	yes	12
5.2	odd	4		1575.2.m.d.1268.1		12
5.3	odd	4		315.2.m.b.8.6	yes	12
5.4	even	2		1575.2.m.c.1457.6		12
15.2	even	4		1575.2.m.c.1268.6		12
15.8	even	4	inner	315.2.m.a.8.1	✓	12
15.14	odd	2		1575.2.m.d.1457.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.1	✓	12	15.8	even	4	inner
315.2.m.a.197.1	yes	12	1.1	even	1	trivial
315.2.m.b.8.6	yes	12	5.3	odd	4
315.2.m.b.197.6	yes	12	3.2	odd	2
1575.2.m.c.1268.6		12	15.2	even	4
1575.2.m.c.1457.6		12	5.4	even	2
1575.2.m.d.1268.1		12	5.2	odd	4
1575.2.m.d.1457.1		12	15.14	odd	2

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.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96418 + 1.96418i) q^{2} -5.71600i q^{4} +(-1.65089 - 1.50816i) q^{5} +(0.707107 + 0.707107i) q^{7} +(7.29890 + 7.29890i) q^{8} +O(q^{10})\)	\(q+(-1.96418 + 1.96418i) q^{2} -5.71600i q^{4} +(-1.65089 - 1.50816i) q^{5} +(0.707107 + 0.707107i) q^{7} +(7.29890 + 7.29890i) q^{8} +(6.20495 - 0.280357i) q^{10} -0.248425i q^{11} +(-3.37141 + 3.37141i) q^{13} -2.77777 q^{14} -17.2407 q^{16} +(-1.75881 + 1.75881i) q^{17} +3.91639i q^{19} +(-8.62065 + 9.43652i) q^{20} +(0.487951 + 0.487951i) q^{22} +(2.22082 + 2.22082i) q^{23} +(0.450907 + 4.97963i) q^{25} -13.2441i q^{26} +(4.04182 - 4.04182i) q^{28} -2.65164 q^{29} -2.96443 q^{31} +(19.2660 - 19.2660i) q^{32} -6.90922i q^{34} +(-0.100929 - 2.23379i) q^{35} +(1.76257 + 1.76257i) q^{37} +(-7.69249 - 7.69249i) q^{38} +(-1.04181 - 23.0576i) q^{40} +7.42003i q^{41} +(-0.716003 + 0.716003i) q^{43} -1.42000 q^{44} -8.72418 q^{46} +(-3.34257 + 3.34257i) q^{47} +1.00000i q^{49} +(-10.6665 - 8.89522i) q^{50} +(19.2710 + 19.2710i) q^{52} +(-4.25628 - 4.25628i) q^{53} +(-0.374665 + 0.410123i) q^{55} +10.3222i q^{56} +(5.20830 - 5.20830i) q^{58} -4.88610 q^{59} +9.55025 q^{61} +(5.82267 - 5.82267i) q^{62} +41.2024i q^{64} +(10.6505 - 0.481217i) q^{65} +(-5.98889 - 5.98889i) q^{67} +(10.0533 + 10.0533i) q^{68} +(4.58580 + 4.18932i) q^{70} +6.31723i q^{71} +(-10.3263 + 10.3263i) q^{73} -6.92401 q^{74} +22.3861 q^{76} +(0.175663 - 0.175663i) q^{77} -11.2561i q^{79} +(28.4626 + 26.0017i) q^{80} +(-14.5743 - 14.5743i) q^{82} +(10.1710 + 10.1710i) q^{83} +(5.55616 - 0.251043i) q^{85} -2.81272i q^{86} +(1.81323 - 1.81323i) q^{88} +1.91884 q^{89} -4.76790 q^{91} +(12.6942 - 12.6942i) q^{92} -13.1308i q^{94} +(5.90654 - 6.46554i) q^{95} +(1.07023 + 1.07023i) q^{97} +(-1.96418 - 1.96418i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^5 + 24 * q^8	\( 12 q - 4 q^{5} + 24 q^{8} + 16 q^{10} - 4 q^{13} - 4 q^{14} - 20 q^{16} + 8 q^{17} - 12 q^{20} - 8 q^{22} + 8 q^{23} - 8 q^{25} - 32 q^{29} + 48 q^{32} + 8 q^{35} + 4 q^{37} + 24 q^{38} - 28 q^{40} + 40 q^{43} - 64 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{50} + 36 q^{52} - 40 q^{53} - 16 q^{55} - 28 q^{58} - 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{65} - 48 q^{67} + 32 q^{68} + 8 q^{70} - 20 q^{73} - 64 q^{74} + 16 q^{76} + 36 q^{80} + 20 q^{82} + 24 q^{83} - 56 q^{89} + 8 q^{92} + 56 q^{95} + 12 q^{97}+O(q^{100}) \) 12 * q - 4 * q^5 + 24 * q^8 + 16 * q^10 - 4 * q^13 - 4 * q^14 - 20 * q^16 + 8 * q^17 - 12 * q^20 - 8 * q^22 + 8 * q^23 - 8 * q^25 - 32 * q^29 + 48 * q^32 + 8 * q^35 + 4 * q^37 + 24 * q^38 - 28 * q^40 + 40 * q^43 - 64 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^50 + 36 * q^52 - 40 * q^53 - 16 * q^55 - 28 * q^58 - 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^65 - 48 * q^67 + 32 * q^68 + 8 * q^70 - 20 * q^73 - 64 * q^74 + 16 * q^76 + 36 * q^80 + 20 * q^82 + 24 * q^83 - 56 * q^89 + 8 * q^92 + 56 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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