LMFDB - Embedded newform 315.2.m.b.8.2

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			8.2
Root			$-2.01185i$ of defining polynomial
Character	$\chi$	$=$	315.8
Dual form			315.2.m.b.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28118 - 1.28118i) q^{2} +1.28283i q^{4} +(-0.565689 + 2.16333i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.918816 + 0.918816i) q^{8} +O(q^{10})$	\(q+(-1.28118 - 1.28118i) q^{2} +1.28283i q^{4} +(-0.565689 + 2.16333i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.918816 + 0.918816i) q^{8} +(3.49636 - 2.04686i) q^{10} -4.14225i q^{11} +(4.57421 + 4.57421i) q^{13} -1.81186 q^{14} +4.92000 q^{16} +(5.27126 + 5.27126i) q^{17} -3.06412i q^{19} +(-2.77519 - 0.725686i) q^{20} +(-5.30696 + 5.30696i) q^{22} +(3.82371 - 3.82371i) q^{23} +(-4.35999 - 2.44755i) q^{25} -11.7208i q^{26} +(0.907101 + 0.907101i) q^{28} +5.24853 q^{29} -2.42509 q^{31} +(-4.46577 - 4.46577i) q^{32} -13.5068i q^{34} +(1.12970 + 1.92971i) q^{35} +(-0.834319 + 0.834319i) q^{37} +(-3.92569 + 3.92569i) q^{38} +(-1.46794 - 2.50747i) q^{40} +4.19215i q^{41} +(3.71717 + 3.71717i) q^{43} +5.31382 q^{44} -9.79772 q^{46} +(-3.14814 - 3.14814i) q^{47} -1.00000i q^{49} +(2.45018 + 8.72167i) q^{50} +(-5.86796 + 5.86796i) q^{52} +(4.79411 - 4.79411i) q^{53} +(8.96105 + 2.34323i) q^{55} +1.29940i q^{56} +(-6.72431 - 6.72431i) q^{58} +1.97629 q^{59} +1.88920 q^{61} +(3.10697 + 3.10697i) q^{62} +1.60288i q^{64} +(-12.4831 + 7.30794i) q^{65} +(-10.7350 + 10.7350i) q^{67} +(-6.76215 + 6.76215i) q^{68} +(1.02495 - 3.91965i) q^{70} +9.76123i q^{71} +(0.978941 + 0.978941i) q^{73} +2.13782 q^{74} +3.93076 q^{76} +(-2.92901 - 2.92901i) q^{77} +4.09428i q^{79} +(-2.78319 + 10.6436i) q^{80} +(5.37089 - 5.37089i) q^{82} +(-3.68028 + 3.68028i) q^{83} +(-14.3854 + 8.42158i) q^{85} -9.52470i q^{86} +(3.80597 + 3.80597i) q^{88} +7.39217 q^{89} +6.46891 q^{91} +(4.90519 + 4.90519i) q^{92} +8.06666i q^{94} +(6.62871 + 1.73334i) q^{95} +(-3.07322 + 3.07322i) q^{97} +(-1.28118 + 1.28118i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−1.28118	−	1.28118i	−0.905930	−	0.905930i	0.0900110	−	0.995941i	$-0.471310\pi$
$2$	−1.28118	−	1.28118i	−0.905930	−	0.905930i	−0.995941	+	0.0900110i	$0.971310\pi$
$3$		0			0
$3$		0			0
$4$			1.28283i			0.641417i
$5$	−0.565689	+	2.16333i	−0.252984	+	0.967470i
$5$	−0.565689	+	2.16333i	−0.252984	+	0.967470i
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−0.918816	+	0.918816i	−0.324851	+	0.324851i
$9$		0			0
$10$	3.49636	−	2.04686i	1.10565	−	0.647275i
$11$		−	4.14225i		−	1.24894i	−0.781051	−	0.624468i	$-0.785316\pi$
$11$		−	4.14225i		−	1.24894i	0.781051	−	0.624468i	$-0.214684\pi$
$12$		0			0
$13$	4.57421	+	4.57421i	1.26866	+	1.26866i	0.946782	+	0.321876i	$0.104313\pi$
$13$	4.57421	+	4.57421i	1.26866	+	1.26866i	0.321876	+	0.946782i	$0.395687\pi$
$14$	−1.81186			−0.484240
$15$		0			0
$16$	4.92000			1.23000
$17$	5.27126	+	5.27126i	1.27847	+	1.27847i	0.941525	+	0.336943i	$0.109393\pi$
$17$	5.27126	+	5.27126i	1.27847	+	1.27847i	0.336943	+	0.941525i	$0.390607\pi$
$18$		0			0
$19$		−	3.06412i		−	0.702958i	−0.936196	−	0.351479i	$-0.885679\pi$
$19$		−	3.06412i		−	0.702958i	0.936196	−	0.351479i	$-0.114321\pi$
$20$	−2.77519	−	0.725686i	−0.620552	−	0.162268i
$21$		0			0
$22$	−5.30696	+	5.30696i	−1.13145	+	1.13145i
$23$	3.82371	−	3.82371i	0.797299	−	0.797299i	−0.185370	−	0.982669i	$-0.559348\pi$
$23$	3.82371	−	3.82371i	0.797299	−	0.797299i	0.982669	+	0.185370i	$0.0593482\pi$
$24$		0			0
$25$	−4.35999	−	2.44755i	−0.871998	−	0.489509i
$26$		−	11.7208i		−	2.29863i
$27$		0			0
$28$	0.907101	+	0.907101i	0.171426	+	0.171426i
$29$	5.24853			0.974628			0.487314	−	0.873227i	$-0.337977\pi$
$29$	5.24853			0.974628			0.487314	+	0.873227i	$0.337977\pi$
$30$		0			0
$31$	−2.42509			−0.435558			−0.217779	−	0.975998i	$-0.569881\pi$
$31$	−2.42509			−0.435558			−0.217779	+	0.975998i	$0.569881\pi$
$32$	−4.46577	−	4.46577i	−0.789444	−	0.789444i
$33$		0			0
$34$		−	13.5068i		−	2.31640i
$35$	1.12970	+	1.92971i	0.190955	+	0.326180i
$36$		0			0
$37$	−0.834319	+	0.834319i	−0.137161	+	0.137161i	−0.772354	−	0.635193i	$-0.780921\pi$
$37$	−0.834319	+	0.834319i	−0.137161	+	0.137161i	0.635193	+	0.772354i	$0.280921\pi$
$38$	−3.92569	+	3.92569i	−0.636831	+	0.636831i
$39$		0			0
$40$	−1.46794	−	2.50747i	−0.232101	−	0.396465i
$41$			4.19215i			0.654704i	0.944902	+	0.327352i	$0.106156\pi$
$41$			4.19215i			0.654704i	−0.944902	+	0.327352i	$0.893844\pi$
$42$		0			0
$43$	3.71717	+	3.71717i	0.566862	+	0.566862i	0.931248	−	0.364386i	$-0.118721\pi$
$43$	3.71717	+	3.71717i	0.566862	+	0.566862i	−0.364386	+	0.931248i	$0.618721\pi$
$44$	5.31382			0.801089
$45$		0			0
$46$	−9.79772			−1.44459
$47$	−3.14814	−	3.14814i	−0.459204	−	0.459204i	0.439190	−	0.898394i	$-0.355265\pi$
$47$	−3.14814	−	3.14814i	−0.459204	−	0.459204i	−0.898394	+	0.439190i	$0.855265\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	2.45018	+	8.72167i	0.346508	+	1.23343i
$51$		0			0
$52$	−5.86796	+	5.86796i	−0.813739	+	0.813739i
$53$	4.79411	−	4.79411i	0.658522	−	0.658522i	−0.296508	−	0.955030i	$-0.595822\pi$
$53$	4.79411	−	4.79411i	0.658522	−	0.658522i	0.955030	+	0.296508i	$0.0958222\pi$
$54$		0			0
$55$	8.96105	+	2.34323i	1.20831	+	0.315961i
$56$			1.29940i			0.173640i
$57$		0			0
$58$	−6.72431	−	6.72431i	−0.882945	−	0.882945i
$59$	1.97629			0.257291			0.128646	−	0.991691i	$-0.458937\pi$
$59$	1.97629			0.257291			0.128646	+	0.991691i	$0.458937\pi$
$60$		0			0
$61$	1.88920			0.241887			0.120944	−	0.992659i	$-0.461408\pi$
$61$	1.88920			0.241887			0.120944	+	0.992659i	$0.461408\pi$
$62$	3.10697	+	3.10697i	0.394585	+	0.394585i
$63$		0			0
$64$			1.60288i			0.200360i
$65$	−12.4831	+	7.30794i	−1.54834	+	0.906439i
$66$		0			0
$67$	−10.7350	+	10.7350i	−1.31149	+	1.31149i	−0.391167	+	0.920320i	$0.627928\pi$
$67$	−10.7350	+	10.7350i	−1.31149	+	1.31149i	−0.920320	+	0.391167i	$0.872072\pi$
$68$	−6.76215	+	6.76215i	−0.820032	+	0.820032i
$69$		0			0
$70$	1.02495	−	3.91965i	0.122505	−	0.468488i
$71$			9.76123i			1.15844i	0.815170	+	0.579222i	$0.196644\pi$
$71$			9.76123i			1.15844i	−0.815170	+	0.579222i	$0.803356\pi$
$72$		0			0
$73$	0.978941	+	0.978941i	0.114576	+	0.114576i	0.762070	−	0.647494i	$-0.224183\pi$
$73$	0.978941	+	0.978941i	0.114576	+	0.114576i	−0.647494	+	0.762070i	$0.724183\pi$
$74$	2.13782			0.248517
$75$		0			0
$76$	3.93076			0.450890
$77$	−2.92901	−	2.92901i	−0.333792	−	0.333792i
$78$		0			0
$79$			4.09428i			0.460642i	0.973115	+	0.230321i	$0.0739776\pi$
$79$			4.09428i			0.460642i	−0.973115	+	0.230321i	$0.926022\pi$
$80$	−2.78319	+	10.6436i	−0.311171	+	1.18999i
$81$		0			0
$82$	5.37089	−	5.37089i	0.593116	−	0.593116i
$83$	−3.68028	+	3.68028i	−0.403964	+	0.403964i	−0.879627	−	0.475664i	$-0.842208\pi$
$83$	−3.68028	+	3.68028i	−0.403964	+	0.403964i	0.475664	+	0.879627i	$0.342208\pi$
$84$		0			0
$85$	−14.3854	+	8.42158i	−1.56031	+	0.913448i
$86$		−	9.52470i		−	1.02707i
$87$		0			0
$88$	3.80597	+	3.80597i	0.405717	+	0.405717i
$89$	7.39217			0.783569			0.391784	−	0.920057i	$-0.371858\pi$
$89$	7.39217			0.783569			0.391784	+	0.920057i	$0.371858\pi$
$90$		0			0
$91$	6.46891			0.678126
$92$	4.90519	+	4.90519i	0.511402	+	0.511402i
$93$		0			0
$94$			8.06666i			0.832013i
$95$	6.62871	+	1.73334i	0.680091	+	0.177837i
$96$		0			0
$97$	−3.07322	+	3.07322i	−0.312038	+	0.312038i	−0.845699	−	0.533661i	$-0.820816\pi$
$97$	−3.07322	+	3.07322i	−0.312038	+	0.312038i	0.533661	+	0.845699i	$0.320816\pi$
$98$	−1.28118	+	1.28118i	−0.129419	+	0.129419i
$99$		0			0
$100$	3.13980	−	5.59315i	0.313980	−	0.559315i
$101$		−	0.759784i		−	0.0756013i	−0.999285	−	0.0378006i	$-0.987965\pi$
$101$		−	0.759784i		−	0.0756013i	0.999285	−	0.0378006i	$-0.0120352\pi$
$102$		0			0
$103$	−1.96312	−	1.96312i	−0.193432	−	0.193432i	0.603745	−	0.797177i	$-0.293674\pi$
$103$	−1.96312	−	1.96312i	−0.193432	−	0.193432i	−0.797177	+	0.603745i	$0.793674\pi$
$104$	−8.40572			−0.824248
$105$		0			0
$106$	−12.2842			−1.19315
$107$	−11.4237	−	11.4237i	−1.10437	−	1.10437i	−0.993876	−	0.110497i	$-0.964756\pi$
$107$	−11.4237	−	11.4237i	−1.10437	−	1.10437i	−0.110497	−	0.993876i	$-0.535244\pi$
$108$		0			0
$109$		−	18.1899i		−	1.74228i	−0.491034	−	0.871140i	$-0.663381\pi$
$109$		−	18.1899i		−	1.74228i	0.491034	−	0.871140i	$-0.336619\pi$
$110$	−8.47862	−	14.4828i	−0.808404	−	1.38088i
$111$		0			0
$112$	3.47897	−	3.47897i	0.328732	−	0.328732i
$113$	−5.30459	+	5.30459i	−0.499014	+	0.499014i	−0.911131	−	0.412117i	$-0.864789\pi$
$113$	−5.30459	+	5.30459i	−0.499014	+	0.499014i	0.412117	+	0.911131i	$0.364789\pi$
$114$		0			0
$115$	6.10892	+	10.4350i	0.569660	+	0.973068i
$116$			6.73300i			0.625143i
$117$		0			0
$118$	−2.53198	−	2.53198i	−0.233088	−	0.233088i
$119$	7.45469			0.683370
$120$		0			0
$121$	−6.15824			−0.559840
$122$	−2.42040	−	2.42040i	−0.219133	−	0.219133i
$123$		0			0
$124$		−	3.11098i		−	0.279375i
$125$	7.76125	−	8.04755i	0.694187	−	0.719795i
$126$		0			0
$127$	4.46393	−	4.46393i	0.396110	−	0.396110i	−0.480749	−	0.876858i	$-0.659635\pi$
$127$	4.46393	−	4.46393i	0.396110	−	0.396110i	0.876858	+	0.480749i	$0.159635\pi$
$128$	−6.87796	+	6.87796i	−0.607931	+	0.607931i
$129$		0			0
$130$	25.3559	+	6.63031i	2.22386	+	0.581516i
$131$		−	2.72941i		−	0.238470i	−0.992866	−	0.119235i	$-0.961956\pi$
$131$		−	2.72941i		−	0.238470i	0.992866	−	0.119235i	$-0.0380441\pi$
$132$		0			0
$133$	−2.16666	−	2.16666i	−0.187873	−	0.187873i
$134$	27.5068			2.37623
$135$		0			0
$136$	−9.68664			−0.830622
$137$	0.0524664	+	0.0524664i	0.00448250	+	0.00448250i	0.709344	−	0.704862i	$-0.248991\pi$
$137$	0.0524664	+	0.0524664i	0.00448250	+	0.00448250i	−0.704862	+	0.709344i	$0.748991\pi$
$138$		0			0
$139$		−	15.6674i		−	1.32890i	−0.747335	−	0.664448i	$-0.768667\pi$
$139$		−	15.6674i		−	1.32890i	0.747335	−	0.664448i	$-0.231333\pi$
$140$	−2.47550	+	1.44922i	−0.209218	+	0.122482i
$141$		0			0
$142$	12.5059	−	12.5059i	1.04947	−	1.04947i
$143$	18.9475	−	18.9475i	1.58447	−	1.58447i
$144$		0			0
$145$	−2.96904	+	11.3543i	−0.246565	+	0.942924i
$146$		−	2.50839i		−	0.207596i
$147$		0			0
$148$	−1.07029	−	1.07029i	−0.0879776	−	0.0879776i
$149$	−5.10614			−0.418312			−0.209156	−	0.977882i	$-0.567072\pi$
$149$	−5.10614			−0.418312			−0.209156	+	0.977882i	$0.567072\pi$
$150$		0			0
$151$	2.13920			0.174085			0.0870426	−	0.996205i	$-0.472258\pi$
$151$	2.13920			0.174085			0.0870426	+	0.996205i	$0.472258\pi$
$152$	2.81537	+	2.81537i	0.228356	+	0.228356i
$153$		0			0
$154$			7.50518i			0.604784i
$155$	1.37185	−	5.24626i	0.110189	−	0.421390i
$156$		0			0
$157$	5.17676	−	5.17676i	0.413150	−	0.413150i	−0.469684	−	0.882835i	$-0.655632\pi$
$157$	5.17676	−	5.17676i	0.413150	−	0.413150i	0.882835	+	0.469684i	$0.155632\pi$
$158$	5.24550	−	5.24550i	0.417309	−	0.417309i
$159$		0			0
$160$	12.1872	−	7.13469i	0.963480	−	0.564047i
$161$		−	5.40755i		−	0.426174i
$162$		0			0
$163$	5.45330	+	5.45330i	0.427135	+	0.427135i	0.887651	−	0.460516i	$-0.152336\pi$
$163$	5.45330	+	5.45330i	0.427135	+	0.427135i	−0.460516	+	0.887651i	$0.652336\pi$
$164$	−5.37784			−0.419938
$165$		0			0
$166$	9.43020			0.731925
$167$	−13.4700	−	13.4700i	−1.04234	−	1.04234i	−0.999063	−	0.0432737i	$-0.986221\pi$
$167$	−13.4700	−	13.4700i	−1.04234	−	1.04234i	−0.0432737	−	0.999063i	$-0.513779\pi$
$168$		0			0
$169$			28.8468i			2.21898i
$170$	29.2198	+	7.64068i	2.24105	+	0.586013i
$171$		0			0
$172$	−4.76851	+	4.76851i	−0.363595	+	0.363595i
$173$	−4.88296	+	4.88296i	−0.371244	+	0.371244i	−0.867930	−	0.496686i	$-0.834550\pi$
$173$	−4.88296	+	4.88296i	−0.371244	+	0.371244i	0.496686	+	0.867930i	$0.334550\pi$
$174$		0			0
$175$	−4.81366	+	1.35230i	−0.363878	+	0.102225i
$176$		−	20.3799i		−	1.53619i
$177$		0			0
$178$	−9.47069	−	9.47069i	−0.709858	−	0.709858i
$179$	−17.0489			−1.27429			−0.637147	−	0.770742i	$-0.719886\pi$
$179$	−17.0489			−1.27429			−0.637147	+	0.770742i	$0.719886\pi$
$180$		0			0
$181$	−15.8349			−1.17700			−0.588498	−	0.808498i	$-0.700281\pi$
$181$	−15.8349			−1.17700			−0.588498	+	0.808498i	$0.700281\pi$
$182$	−8.28783	−	8.28783i	−0.614335	−	0.614335i
$183$		0			0
$184$			7.02658i			0.518006i
$185$	−1.33294	−	2.27687i	−0.0979998	−	0.167399i
$186$		0			0
$187$	21.8349	−	21.8349i	1.59672	−	1.59672i
$188$	4.03855	−	4.03855i	0.294541	−	0.294541i
$189$		0			0
$190$	−6.27184	−	10.7133i	−0.455007	−	0.777223i
$191$			0.295615i			0.0213899i	0.999943	+	0.0106950i	$0.00340438\pi$
$191$			0.295615i			0.0213899i	−0.999943	+	0.0106950i	$0.996596\pi$
$192$		0			0
$193$	−11.5473	−	11.5473i	−0.831190	−	0.831190i	0.156490	−	0.987680i	$-0.449982\pi$
$193$	−11.5473	−	11.5473i	−0.831190	−	0.831190i	−0.987680	+	0.156490i	$0.949982\pi$
$194$	7.87468			0.565369
$195$		0			0
$196$	1.28283			0.0916311
$197$	−5.30459	−	5.30459i	−0.377936	−	0.377936i	0.492421	−	0.870357i	$-0.336112\pi$
$197$	−5.30459	−	5.30459i	−0.377936	−	0.377936i	−0.870357	+	0.492421i	$0.836112\pi$
$198$		0			0
$199$		−	7.06135i		−	0.500566i	−0.968173	−	0.250283i	$-0.919476\pi$
$199$		−	7.06135i		−	0.500566i	0.968173	−	0.250283i	$-0.0805236\pi$
$200$	6.25488	−	1.75719i	0.442286	−	0.124252i
$201$		0			0
$202$	−0.973418	+	0.973418i	−0.0684895	+	0.0684895i
$203$	3.71127	−	3.71127i	0.260480	−	0.260480i
$204$		0			0
$205$	−9.06900	−	2.37145i	−0.633407	−	0.165630i
$206$			5.03021i			0.350471i
$207$		0			0
$208$	22.5051	+	22.5051i	1.56045	+	1.56045i
$209$	−12.6924			−0.877950
$210$		0			0
$211$	14.2937			0.984019			0.492010	−	0.870590i	$-0.336263\pi$
$211$	14.2937			0.984019			0.492010	+	0.870590i	$0.336263\pi$
$212$	6.15006	+	6.15006i	0.422388	+	0.422388i
$213$		0			0
$214$			29.2717i			2.00097i
$215$	−10.1442	+	5.93869i	−0.691830	+	0.405016i
$216$		0			0
$217$	−1.71479	+	1.71479i	−0.116408	+	0.116408i
$218$	−23.3046	+	23.3046i	−1.57838	+	1.57838i
$219$		0			0
$220$	−3.00597	+	11.4956i	−0.202663	+	0.775030i
$221$			48.2237i			3.24388i
$222$		0			0
$223$	14.7096	+	14.7096i	0.985027	+	0.985027i	0.999890	−	0.0148628i	$-0.00473113\pi$
$223$	14.7096	+	14.7096i	0.985027	+	0.985027i	−0.0148628	+	0.999890i	$0.504731\pi$
$224$	−6.31555			−0.421976
$225$		0			0
$226$	13.5923			0.904143
$227$	0.813981	+	0.813981i	0.0540258	+	0.0540258i	0.733604	−	0.679578i	$-0.237837\pi$
$227$	0.813981	+	0.813981i	0.0540258	+	0.0540258i	−0.679578	+	0.733604i	$0.737837\pi$
$228$		0			0
$229$		−	19.2790i		−	1.27399i	−0.770866	−	0.636997i	$-0.780176\pi$
$229$		−	19.2790i		−	1.27399i	0.770866	−	0.636997i	$-0.219824\pi$
$230$	5.54246	−	21.1957i	0.365459	−	1.39760i
$231$		0			0
$232$	−4.82244	+	4.82244i	−0.316609	+	0.316609i
$233$	−0.00390031	+	0.00390031i	−0.000255518	+	0.000255518i	−0.707235	−	0.706979i	$-0.750058\pi$
$233$	−0.00390031	+	0.00390031i	−0.000255518	+	0.000255518i	0.706979	+	0.707235i	$0.250058\pi$
$234$		0			0
$235$	8.59134	−	5.02960i	0.560437	−	0.328095i
$236$			2.53526i			0.165031i
$237$		0			0
$238$	−9.55078	−	9.55078i	−0.619085	−	0.619085i
$239$	−1.26696			−0.0819530			−0.0409765	−	0.999160i	$-0.513047\pi$
$239$	−1.26696			−0.0819530			−0.0409765	+	0.999160i	$0.513047\pi$
$240$		0			0
$241$	−6.14879			−0.396078			−0.198039	−	0.980194i	$-0.563457\pi$
$241$	−6.14879			−0.396078			−0.198039	+	0.980194i	$0.563457\pi$
$242$	7.88980	+	7.88980i	0.507176	+	0.507176i
$243$		0			0
$244$			2.42353i			0.155151i
$245$	2.16333	+	0.565689i	0.138210	+	0.0361406i
$246$		0			0
$247$	14.0159	−	14.0159i	0.891813	−	0.891813i
$248$	2.22821	−	2.22821i	0.141491	−	0.141491i
$249$		0			0
$250$	−20.2539	+	0.366802i	−1.28097	+	0.0231986i
$251$		−	1.50823i		−	0.0951987i	−0.998867	−	0.0475994i	$-0.984843\pi$
$251$		−	1.50823i		−	0.0951987i	0.998867	−	0.0475994i	$-0.0151571\pi$
$252$		0			0
$253$	−15.8388	−	15.8388i	−0.995776	−	0.995776i
$254$	−11.4382			−0.717695
$255$		0			0
$256$	20.8296			1.30185
$257$	6.44051	+	6.44051i	0.401748	+	0.401748i	0.878849	−	0.477101i	$-0.158312\pi$
$257$	6.44051	+	6.44051i	0.401748	+	0.401748i	−0.477101	+	0.878849i	$0.658312\pi$
$258$		0			0
$259$			1.17991i			0.0733158i
$260$	−9.37488	−	16.0138i	−0.581406	−	0.993132i
$261$		0			0
$262$	−3.49686	+	3.49686i	−0.216037	+	0.216037i
$263$	−10.3565	+	10.3565i	−0.638611	+	0.638611i	−0.950213	−	0.311602i	$-0.899134\pi$
$263$	−10.3565	+	10.3565i	−0.638611	+	0.638611i	0.311602	+	0.950213i	$0.399134\pi$
$264$		0			0
$265$	7.65927	+	13.0832i	0.470505	+	0.803696i
$266$			5.55176i			0.340400i
$267$		0			0
$268$	−13.7712	−	13.7712i	−0.841210	−	0.841210i
$269$	−8.28454			−0.505117			−0.252559	−	0.967582i	$-0.581272\pi$
$269$	−8.28454			−0.505117			−0.252559	+	0.967582i	$0.581272\pi$
$270$		0			0
$271$	−18.8028			−1.14219			−0.571093	−	0.820885i	$-0.693480\pi$
$271$	−18.8028			−1.14219			−0.571093	+	0.820885i	$0.693480\pi$
$272$	25.9346	+	25.9346i	1.57252	+	1.57252i
$273$		0			0
$274$		−	0.134438i		−	0.00812167i
$275$	−10.1383	+	18.0602i	−0.611365	+	1.08907i
$276$		0			0
$277$	4.60162	−	4.60162i	0.276485	−	0.276485i	−0.555219	−	0.831704i	$-0.687366\pi$
$277$	4.60162	−	4.60162i	0.276485	−	0.276485i	0.831704	+	0.555219i	$0.187366\pi$
$278$	−20.0728	+	20.0728i	−1.20389	+	1.20389i
$279$		0			0
$280$	−2.81104	−	0.735058i	−0.167992	−	0.0439281i
$281$		−	14.7052i		−	0.877236i	−0.898673	−	0.438618i	$-0.855468\pi$
$281$		−	14.7052i		−	0.877236i	0.898673	−	0.438618i	$-0.144532\pi$
$282$		0			0
$283$	1.84999	+	1.84999i	0.109970	+	0.109970i	0.759951	−	0.649980i	$-0.225223\pi$
$283$	1.84999	+	1.84999i	0.109970	+	0.109970i	−0.649980	+	0.759951i	$0.725223\pi$
$284$	−12.5220			−0.743047
$285$		0			0
$286$	−48.5503			−2.87084
$287$	2.96430	+	2.96430i	0.174977	+	0.174977i
$288$		0			0
$289$			38.5723i			2.26896i
$290$	18.3508	−	10.7430i	1.07759	−	0.630852i
$291$		0			0
$292$	−1.25582	+	1.25582i	−0.0734913	+	0.0734913i
$293$	10.9840	−	10.9840i	0.641692	−	0.641692i	−0.309279	−	0.950971i	$-0.600088\pi$
$293$	10.9840	−	10.9840i	0.641692	−	0.641692i	0.950971	+	0.309279i	$0.100088\pi$
$294$		0			0
$295$	−1.11797	+	4.27537i	−0.0650906	+	0.248922i
$296$		−	1.53317i		−	0.0891138i
$297$		0			0
$298$	6.54188	+	6.54188i	0.378961	+	0.378961i
$299$	34.9809			2.02300
$300$		0			0
$301$	5.25687			0.303001
$302$	−2.74069	−	2.74069i	−0.157709	−	0.157709i
$303$		0			0
$304$		−	15.0755i		−	0.864639i
$305$	−1.06870	+	4.08696i	−0.0611935	+	0.234019i
$306$		0			0
$307$	−24.6231	+	24.6231i	−1.40531	+	1.40531i	−0.623448	+	0.781865i	$0.714269\pi$
$307$	−24.6231	+	24.6231i	−1.40531	+	1.40531i	−0.781865	+	0.623448i	$0.785731\pi$
$308$	3.75744	−	3.75744i	0.214100	−	0.214100i
$309$		0			0
$310$	−8.47897	+	4.96382i	−0.481573	+	0.281926i
$311$			22.5359i			1.27789i	0.769251	+	0.638947i	$0.220630\pi$
$311$			22.5359i			1.27789i	−0.769251	+	0.638947i	$0.779370\pi$
$312$		0			0
$313$	−13.0467	−	13.0467i	−0.737444	−	0.737444i	0.234639	−	0.972083i	$-0.424609\pi$
$313$	−13.0467	−	13.0467i	−0.737444	−	0.737444i	−0.972083	+	0.234639i	$0.924609\pi$
$314$	−13.2647			−0.748571
$315$		0			0
$316$	−5.25228			−0.295464
$317$	1.48198	+	1.48198i	0.0832361	+	0.0832361i	0.747499	−	0.664263i	$-0.231254\pi$
$317$	1.48198	+	1.48198i	0.0832361	+	0.0832361i	−0.664263	+	0.747499i	$0.731254\pi$
$318$		0			0
$319$		−	21.7407i		−	1.21725i
$320$	−3.46757	−	0.906734i	−0.193843	−	0.0506880i
$321$		0			0
$322$	−6.92803	+	6.92803i	−0.386084	+	0.386084i
$323$	16.1518	−	16.1518i	0.898710	−	0.898710i
$324$		0			0
$325$	−8.74793	−	31.1391i	−0.485248	−	1.72729i
$326$		−	13.9733i		−	0.773909i
$327$		0			0
$328$	−3.85182	−	3.85182i	−0.212681	−	0.212681i
$329$	−4.45215			−0.245455
$330$		0			0
$331$	23.4613			1.28955			0.644775	−	0.764372i	$-0.276951\pi$
$331$	23.4613			1.28955			0.644775	+	0.764372i	$0.276951\pi$
$332$	−4.72120	−	4.72120i	−0.259109	−	0.259109i
$333$		0			0
$334$			34.5148i			1.88857i
$335$	−17.1506	−	29.2960i	−0.937040	−	1.60061i
$336$		0			0
$337$	8.87106	−	8.87106i	0.483238	−	0.483238i	−0.422926	−	0.906164i	$-0.638997\pi$
$337$	8.87106	−	8.87106i	0.483238	−	0.483238i	0.906164	+	0.422926i	$0.138997\pi$
$338$	36.9579	−	36.9579i	2.01024	−	2.01024i
$339$		0			0
$340$	−10.8035	−	18.4540i	−0.585902	−	1.00081i
$341$			10.0453i			0.543984i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−6.83078			−0.368291
$345$		0			0
$346$	12.5119			0.672642
$347$	4.80618	+	4.80618i	0.258009	+	0.258009i	0.824244	−	0.566235i	$-0.191600\pi$
$347$	4.80618	+	4.80618i	0.258009	+	0.258009i	−0.566235	+	0.824244i	$0.691600\pi$
$348$		0			0
$349$		−	35.9770i		−	1.92580i	−0.269854	−	0.962901i	$-0.586975\pi$
$349$		−	35.9770i		−	1.92580i	0.269854	−	0.962901i	$-0.413025\pi$
$350$	7.89969	+	4.43461i	0.422256	+	0.237040i
$351$		0			0
$352$	−18.4983	+	18.4983i	−0.985965	+	0.985965i
$353$	17.0253	−	17.0253i	0.906166	−	0.906166i	−0.0897948	−	0.995960i	$-0.528621\pi$
$353$	17.0253	−	17.0253i	0.906166	−	0.906166i	0.995960	+	0.0897948i	$0.0286211\pi$
$354$		0			0
$355$	−21.1168	−	5.52182i	−1.12076	−	0.293068i
$356$			9.48294i			0.502595i
$357$		0			0
$358$	21.8427	+	21.8427i	1.15442	+	1.15442i
$359$	−3.02758			−0.159789			−0.0798947	−	0.996803i	$-0.525458\pi$
$359$	−3.02758			−0.159789			−0.0798947	+	0.996803i	$0.525458\pi$
$360$		0			0
$361$	9.61114			0.505850
$362$	20.2873	+	20.2873i	1.06628	+	1.06628i
$363$		0			0
$364$			8.29854i			0.434962i
$365$	−2.67155	+	1.56399i	−0.139835	+	0.0818632i
$366$		0			0
$367$	−9.75566	+	9.75566i	−0.509241	+	0.509241i	−0.914293	−	0.405052i	$-0.867253\pi$
$367$	−9.75566	+	9.75566i	−0.509241	+	0.509241i	0.405052	+	0.914293i	$0.367253\pi$
$368$	18.8127	−	18.8127i	0.980679	−	0.980679i
$369$		0			0
$370$	−1.20934	+	4.62482i	−0.0628708	+	0.240433i
$371$		−	6.77990i		−	0.351995i
$372$		0			0
$373$	−16.4680	−	16.4680i	−0.852682	−	0.852682i	0.137781	−	0.990463i	$-0.456003\pi$
$373$	−16.4680	−	16.4680i	−0.852682	−	0.852682i	−0.990463	+	0.137781i	$0.956003\pi$
$374$	−55.9487			−2.89304
$375$		0			0
$376$	5.78513			0.298345
$377$	24.0079	+	24.0079i	1.23647	+	1.23647i
$378$		0			0
$379$		−	37.2929i		−	1.91561i	−0.287422	−	0.957804i	$-0.592798\pi$
$379$		−	37.2929i		−	1.91561i	0.287422	−	0.957804i	$-0.407202\pi$
$380$	−2.22359	+	8.50354i	−0.114068	+	0.436222i
$381$		0			0
$382$	0.378735	−	0.378735i	0.0193778	−	0.0193778i
$383$	−13.0112	+	13.0112i	−0.664841	+	0.664841i	−0.956517	−	0.291676i	$-0.905787\pi$
$383$	−13.0112	+	13.0112i	−0.664841	+	0.664841i	0.291676	+	0.956517i	$0.405787\pi$
$384$		0			0
$385$	7.99333	−	4.67951i	0.407378	−	0.238490i
$386$			29.5882i			1.50600i
$387$		0			0
$388$	−3.94243	−	3.94243i	−0.200147	−	0.200147i
$389$	−9.87898			−0.500884			−0.250442	−	0.968132i	$-0.580576\pi$
$389$	−9.87898			−0.500884			−0.250442	+	0.968132i	$0.580576\pi$
$390$		0			0
$391$	40.3116			2.03864
$392$	0.918816	+	0.918816i	0.0464072	+	0.0464072i
$393$		0			0
$394$			13.5923i			0.684768i
$395$	−8.85727	−	2.31609i	−0.445658	−	0.116535i
$396$		0			0
$397$	−0.381469	+	0.381469i	−0.0191454	+	0.0191454i	−0.716615	−	0.697469i	$-0.754309\pi$
$397$	−0.381469	+	0.381469i	−0.0191454	+	0.0191454i	0.697469	+	0.716615i	$0.254309\pi$
$398$	−9.04684	+	9.04684i	−0.453477	+	0.453477i
$399$		0			0
$400$	−21.4512	−	12.0419i	−1.07256	−	0.602097i
$401$			20.9162i			1.04450i	0.852792	+	0.522251i	$0.174908\pi$
$401$			20.9162i			1.04450i	−0.852792	+	0.522251i	$0.825092\pi$
$402$		0			0
$403$	−11.0929	−	11.0929i	−0.552574	−	0.552574i
$404$	0.974677			0.0484920
$405$		0			0
$406$	−9.50960			−0.471954
$407$	3.45596	+	3.45596i	0.171306	+	0.171306i
$408$		0			0
$409$			15.9561i			0.788976i	0.918901	+	0.394488i	$0.129078\pi$
$409$			15.9561i			0.788976i	−0.918901	+	0.394488i	$0.870922\pi$
$410$	8.58075	+	14.6573i	0.423773	+	0.723871i
$411$		0			0
$412$	2.51836	−	2.51836i	0.124071	−	0.124071i
$413$	1.39745	−	1.39745i	0.0687640	−	0.0687640i
$414$		0			0
$415$	−5.87977	−	10.0436i	−0.288627	−	0.493019i
$416$		−	40.8547i		−	2.00307i
$417$		0			0
$418$	16.2612	+	16.2612i	0.795361	+	0.795361i
$419$	14.6415			0.715286			0.357643	−	0.933858i	$-0.383581\pi$
$419$	14.6415			0.715286			0.357643	+	0.933858i	$0.383581\pi$
$420$		0			0
$421$	29.4256			1.43412			0.717058	−	0.697014i	$-0.245488\pi$
$421$	29.4256			1.43412			0.717058	+	0.697014i	$0.245488\pi$
$422$	−18.3128	−	18.3128i	−0.891452	−	0.891452i
$423$		0			0
$424$			8.80982i			0.427843i
$425$	−10.0810	−	35.8843i	−0.489000	−	1.74064i
$426$		0			0
$427$	1.33586	−	1.33586i	0.0646470	−	0.0646470i
$428$	14.6548	−	14.6548i	0.708364	−	0.708364i
$429$		0			0
$430$	20.6051	+	5.38802i	0.993665	+	0.259834i
$431$		−	22.9228i		−	1.10415i	−0.833794	−	0.552076i	$-0.813836\pi$
$431$		−	22.9228i		−	1.10415i	0.833794	−	0.552076i	$-0.186164\pi$
$432$		0			0
$433$	14.3689	+	14.3689i	0.690527	+	0.690527i	0.962348	−	0.271821i	$-0.0876259\pi$
$433$	14.3689	+	14.3689i	0.690527	+	0.690527i	−0.271821	+	0.962348i	$0.587626\pi$
$434$	4.39391			0.210915
$435$		0			0
$436$	23.3347			1.11753
$437$	−11.7163	−	11.7163i	−0.560468	−	0.560468i
$438$		0			0
$439$			29.7425i			1.41953i	0.704437	+	0.709767i	$0.251200\pi$
$439$			29.7425i			1.41953i	−0.704437	+	0.709767i	$0.748800\pi$
$440$	−10.3866	+	6.08057i	−0.495160	+	0.289880i
$441$		0			0
$442$	61.7831	−	61.7831i	2.93872	−	2.93872i
$443$	−14.9597	+	14.9597i	−0.710754	+	0.710754i	−0.966693	−	0.255939i	$-0.917616\pi$
$443$	−14.9597	+	14.9597i	−0.710754	+	0.710754i	0.255939	+	0.966693i	$0.417616\pi$
$444$		0			0
$445$	−4.18167	+	15.9917i	−0.198230	+	0.758080i
$446$		−	37.6912i		−	1.78473i
$447$		0			0
$448$	1.13341	+	1.13341i	0.0535486	+	0.0535486i
$449$	−12.6248			−0.595801			−0.297900	−	0.954597i	$-0.596286\pi$
$449$	−12.6248			−0.595801			−0.297900	+	0.954597i	$0.596286\pi$
$450$		0			0
$451$	17.3649			0.817683
$452$	−6.80491	−	6.80491i	−0.320076	−	0.320076i
$453$		0			0
$454$		−	2.08571i		−	0.0978871i
$455$	−3.65939	+	13.9944i	−0.171555	+	0.656067i
$456$		0			0
$457$	−23.0026	+	23.0026i	−1.07602	+	1.07602i	−0.0791546	+	0.996862i	$0.525222\pi$
$457$	−23.0026	+	23.0026i	−1.07602	+	1.07602i	−0.996862	+	0.0791546i	$0.974778\pi$
$458$	−24.6999	+	24.6999i	−1.15415	+	1.15415i
$459$		0			0
$460$	−13.3864	+	7.83673i	−0.624142	+	0.365390i
$461$			33.6976i			1.56945i	0.619842	+	0.784727i	$0.287197\pi$
$461$			33.6976i			1.56945i	−0.619842	+	0.784727i	$0.712803\pi$
$462$		0			0
$463$	10.5496	+	10.5496i	0.490280	+	0.490280i	0.908394	−	0.418115i	$-0.137309\pi$
$463$	10.5496	+	10.5496i	0.490280	+	0.490280i	−0.418115	+	0.908394i	$0.637309\pi$
$464$	25.8228			1.19879
$465$		0			0
$466$	0.00999398			0.000462962
$467$	9.72972	+	9.72972i	0.450238	+	0.450238i	0.895433	−	0.445196i	$-0.146866\pi$
$467$	9.72972	+	9.72972i	0.450238	+	0.450238i	−0.445196	+	0.895433i	$0.646866\pi$
$468$		0			0
$469$			15.1816i			0.701019i
$470$	−17.4509	−	4.56323i	−0.804948	−	0.210486i
$471$		0			0
$472$	−1.81585	+	1.81585i	−0.0835812	+	0.0835812i
$473$	15.3974	−	15.3974i	0.707975	−	0.707975i
$474$		0			0
$475$	−7.49958	+	13.3596i	−0.344104	+	0.612978i
$476$			9.56313i			0.438325i
$477$		0			0
$478$	1.62321	+	1.62321i	0.0742437	+	0.0742437i
$479$	29.8978			1.36607			0.683033	−	0.730388i	$-0.260661\pi$
$479$	29.8978			1.36607			0.683033	+	0.730388i	$0.260661\pi$
$480$		0			0
$481$	−7.63270			−0.348021
$482$	7.87770	+	7.87770i	0.358819	+	0.358819i
$483$		0			0
$484$		−	7.90001i		−	0.359091i
$485$	−4.90990	−	8.38687i	−0.222947	−	0.380828i
$486$		0			0
$487$	−6.74208	+	6.74208i	−0.305513	+	0.305513i	−0.843166	−	0.537653i	$-0.819311\pi$
$487$	−6.74208	+	6.74208i	−0.305513	+	0.305513i	0.537653	+	0.843166i	$0.319311\pi$
$488$	−1.73583	+	1.73583i	−0.0785772	+	0.0785772i
$489$		0			0
$490$	−2.04686	−	3.49636i	−0.0924678	−	0.157949i
$491$		−	39.9275i		−	1.80190i	−0.433921	−	0.900951i	$-0.642870\pi$
$491$		−	39.9275i		−	1.80190i	0.433921	−	0.900951i	$-0.357130\pi$
$492$		0			0
$493$	27.6664	+	27.6664i	1.24603	+	1.24603i
$494$	−35.9138			−1.61584
$495$		0			0
$496$	−11.9314			−0.535737
$497$	6.90223	+	6.90223i	0.309607	+	0.309607i
$498$		0			0
$499$		−	21.0239i		−	0.941159i	−0.882358	−	0.470579i	$-0.844045\pi$
$499$		−	21.0239i		−	0.941159i	0.882358	−	0.470579i	$-0.155955\pi$
$500$	10.3237	+	9.95640i	0.461689	+	0.445264i
$501$		0			0
$502$	−1.93231	+	1.93231i	−0.0862434	+	0.0862434i
$503$	2.83078	−	2.83078i	0.126218	−	0.126218i	−0.641176	−	0.767394i	$-0.721553\pi$
$503$	2.83078	−	2.83078i	0.126218	−	0.126218i	0.767394	+	0.641176i	$0.221553\pi$
$504$		0			0
$505$	1.64366	+	0.429801i	0.0731420	+	0.0191259i
$506$			40.5846i			1.80421i
$507$		0			0
$508$	5.72649	+	5.72649i	0.254072	+	0.254072i
$509$	−21.7097			−0.962267			−0.481133	−	0.876647i	$-0.659775\pi$
$509$	−21.7097			−0.962267			−0.481133	+	0.876647i	$0.659775\pi$
$510$		0			0
$511$	1.38443			0.0612436
$512$	−12.9304	−	12.9304i	−0.571450	−	0.571450i
$513$		0			0
$514$		−	16.5029i		−	0.727911i
$515$	5.35739	−	3.13636i	0.236075	−	0.138204i
$516$		0			0
$517$	−13.0404	+	13.0404i	−0.573516	+	0.573516i
$518$	1.51167	−	1.51167i	0.0664189	−	0.0664189i
$519$		0			0
$520$	4.75503	−	18.1843i	0.208522	−	0.797436i
$521$			10.1879i			0.446338i	0.974780	+	0.223169i	$0.0716402\pi$
$521$			10.1879i			0.446338i	−0.974780	+	0.223169i	$0.928360\pi$
$522$		0			0
$523$	17.9604	+	17.9604i	0.785353	+	0.785353i	0.980729	−	0.195375i	$-0.0625925\pi$
$523$	17.9604	+	17.9604i	0.785353	+	0.785353i	−0.195375	+	0.980729i	$0.562592\pi$
$524$	3.50138			0.152959
$525$		0			0
$526$	26.5371			1.15707
$527$	−12.7833	−	12.7833i	−0.556847	−	0.556847i
$528$		0			0
$529$		−	6.24157i		−	0.271373i
$530$	6.94906	−	26.5748i	0.301848	−	1.15434i
$531$		0			0
$532$	2.77947	−	2.77947i	0.120505	−	0.120505i
$533$	−19.1758	+	19.1758i	−0.830595	+	0.830595i
$534$		0			0
$535$	31.1756	−	18.2510i	1.34784	−	0.789060i
$536$		−	19.7270i		−	0.852075i
$537$		0			0
$538$	10.6140	+	10.6140i	0.457601	+	0.457601i
$539$	−4.14225			−0.178419
$540$		0			0
$541$	−19.8027			−0.851385			−0.425693	−	0.904868i	$-0.639970\pi$
$541$	−19.8027			−0.851385			−0.425693	+	0.904868i	$0.639970\pi$
$542$	24.0897	+	24.0897i	1.03474	+	1.03474i
$543$		0			0
$544$		−	47.0805i		−	2.01856i
$545$	39.3508	+	10.2899i	1.68561	+	0.440769i
$546$		0			0
$547$	−3.17046	+	3.17046i	−0.135559	+	0.135559i	−0.771630	−	0.636071i	$-0.780558\pi$
$547$	−3.17046	+	3.17046i	−0.135559	+	0.135559i	0.636071	+	0.771630i	$0.280558\pi$
$548$	−0.0673057	+	0.0673057i	−0.00287516	+	0.00287516i
$549$		0			0
$550$	36.1273	−	10.1493i	1.54047	−	0.432767i
$551$		−	16.0822i		−	0.685123i
$552$		0			0
$553$	2.89509	+	2.89509i	0.123112	+	0.123112i
$554$	−11.7910			−0.500951
$555$		0			0
$556$	20.0987			0.852377
$557$	−21.0318	−	21.0318i	−0.891144	−	0.891144i	0.103487	−	0.994631i	$-0.467000\pi$
$557$	−21.0318	−	21.0318i	−0.891144	−	0.891144i	−0.994631	+	0.103487i	$0.967000\pi$
$558$		0			0
$559$			34.0062i			1.43831i
$560$	5.55814	+	9.49417i	0.234874	+	0.401202i
$561$		0			0
$562$	−18.8399	+	18.8399i	−0.794715	+	0.794715i
$563$	−11.8395	+	11.8395i	−0.498977	+	0.498977i	−0.911119	−	0.412142i	$-0.864781\pi$
$563$	−11.8395	+	11.8395i	−0.498977	+	0.498977i	0.412142	+	0.911119i	$0.364781\pi$
$564$		0			0
$565$	−8.47483	−	14.4763i	−0.356539	−	0.609024i
$566$		−	4.74033i		−	0.199251i
$567$		0			0
$568$	−8.96878	−	8.96878i	−0.376321	−	0.376321i
$569$	−3.22907			−0.135370			−0.0676848	−	0.997707i	$-0.521561\pi$
$569$	−3.22907			−0.135370			−0.0676848	+	0.997707i	$0.521561\pi$
$570$		0			0
$571$	−45.1687			−1.89025			−0.945126	−	0.326706i	$-0.894061\pi$
$571$	−45.1687			−1.89025			−0.945126	+	0.326706i	$0.894061\pi$
$572$	24.3065	+	24.3065i	1.01631	+	1.01631i
$573$		0			0
$574$		−	7.59559i		−	0.317034i
$575$	−26.0301	+	7.31265i	−1.08553	+	0.304958i
$576$		0			0
$577$	11.7379	−	11.7379i	0.488655	−	0.488655i	−0.419226	−	0.907882i	$-0.637699\pi$
$577$	11.7379	−	11.7379i	0.488655	−	0.488655i	0.907882	+	0.419226i	$0.137699\pi$
$578$	49.4180	−	49.4180i	2.05552	−	2.05552i
$579$		0			0
$580$	−14.5657	−	3.80879i	−0.604808	−	0.158151i
$581$			5.20471i			0.215928i
$582$		0			0
$583$	−19.8584	−	19.8584i	−0.822452	−	0.822452i
$584$	−1.79893			−0.0744404
$585$		0			0
$586$	−28.1449			−1.16266
$587$	−7.69625	−	7.69625i	−0.317658	−	0.317658i	0.530209	−	0.847867i	$-0.322114\pi$
$587$	−7.69625	−	7.69625i	−0.317658	−	0.317658i	−0.847867	+	0.530209i	$0.822114\pi$
$588$		0			0
$589$			7.43076i			0.306179i
$590$	6.90983	−	4.04520i	0.284473	−	0.166538i
$591$		0			0
$592$	−4.10485	+	4.10485i	−0.168708	+	0.168708i
$593$	−0.772725	+	0.772725i	−0.0317320	+	0.0317320i	−0.722795	−	0.691063i	$-0.757143\pi$
$593$	−0.772725	+	0.772725i	−0.0317320	+	0.0317320i	0.691063	+	0.722795i	$0.257143\pi$
$594$		0			0
$595$	−4.21704	+	16.1269i	−0.172882	+	0.661140i
$596$		−	6.55034i		−	0.268312i
$597$		0			0
$598$	−44.8168	−	44.8168i	−1.83270	−	1.83270i
$599$	−7.19884			−0.294136			−0.147068	−	0.989126i	$-0.546984\pi$
$599$	−7.19884			−0.294136			−0.147068	+	0.989126i	$0.546984\pi$
$600$		0			0
$601$	14.3551			0.585559			0.292779	−	0.956180i	$-0.405420\pi$
$601$	14.3551			0.585559			0.292779	+	0.956180i	$0.405420\pi$
$602$	−6.73498	−	6.73498i	−0.274497	−	0.274497i
$603$		0			0
$604$			2.74423i			0.111661i
$605$	3.48365	−	13.3223i	0.141631	−	0.541629i
$606$		0			0
$607$	−18.1909	+	18.1909i	−0.738347	+	0.738347i	−0.972258	−	0.233911i	$-0.924848\pi$
$607$	−18.1909	+	18.1909i	−0.738347	+	0.738347i	0.233911	+	0.972258i	$0.424848\pi$
$608$	−13.6837	+	13.6837i	−0.554946	+	0.554946i
$609$		0			0
$610$	6.60532	−	3.86693i	0.267441	−	0.156567i
$611$		−	28.8005i		−	1.16514i
$612$		0			0
$613$	−26.8922	−	26.8922i	−1.08616	−	1.08616i	−0.995920	−	0.0902447i	$-0.971235\pi$
$613$	−26.8922	−	26.8922i	−1.08616	−	1.08616i	−0.0902447	−	0.995920i	$-0.528765\pi$
$614$	63.0931			2.54623
$615$		0			0
$616$	5.38245			0.216865
$617$	32.4145	+	32.4145i	1.30496	+	1.30496i	0.925006	+	0.379952i	$0.124059\pi$
$617$	32.4145	+	32.4145i	1.30496	+	1.30496i	0.379952	+	0.925006i	$0.375941\pi$
$618$		0			0
$619$			44.1635i			1.77508i	0.460729	+	0.887541i	$0.347588\pi$
$619$			44.1635i			1.77508i	−0.460729	+	0.887541i	$0.652412\pi$
$620$	6.73008	+	1.75985i	0.270287	+	0.0706773i
$621$		0			0
$622$	28.8725	−	28.8725i	1.15768	−	1.15768i
$623$	5.22706	−	5.22706i	0.209418	−	0.209418i
$624$		0			0
$625$	13.0190	+	21.3426i	0.520762	+	0.853702i
$626$			33.4303i			1.33614i
$627$		0			0
$628$	6.64093	+	6.64093i	0.265002	+	0.265002i
$629$	−8.79582			−0.350712
$630$		0			0
$631$	−23.5286			−0.936659			−0.468330	−	0.883554i	$-0.655144\pi$
$631$	−23.5286			−0.936659			−0.468330	+	0.883554i	$0.655144\pi$
$632$	−3.76189	−	3.76189i	−0.149640	−	0.149640i
$633$		0			0
$634$		−	3.79735i		−	0.150812i
$635$	7.13176	+	12.1822i	0.283015	+	0.483434i
$636$		0			0
$637$	4.57421	−	4.57421i	0.181237	−	0.181237i
$638$	−27.8538	+	27.8538i	−1.10274	+	1.10274i
$639$		0			0
$640$	−10.9885	−	18.7701i	−0.434359	−	0.741953i
$641$		−	6.92503i		−	0.273522i	−0.990604	−	0.136761i	$-0.956331\pi$
$641$		−	6.92503i		−	0.273522i	0.990604	−	0.136761i	$-0.0436693\pi$
$642$		0			0
$643$	−33.4615	−	33.4615i	−1.31959	−	1.31959i	−0.914097	−	0.405495i	$-0.867099\pi$
$643$	−33.4615	−	33.4615i	−1.31959	−	1.31959i	−0.405495	−	0.914097i	$-0.632901\pi$
$644$	6.93699			0.273356
$645$		0			0
$646$	−41.3866			−1.62834
$647$	−33.6527	−	33.6527i	−1.32302	−	1.32302i	−0.911317	−	0.411706i	$-0.864933\pi$
$647$	−33.6527	−	33.6527i	−1.32302	−	1.32302i	−0.411706	−	0.911317i	$-0.635067\pi$
$648$		0			0
$649$		−	8.18630i		−	0.321340i
$650$	−28.6871	+	51.1024i	−1.12520	+	2.00440i
$651$		0			0
$652$	−6.99568	+	6.99568i	−0.273972	+	0.273972i
$653$	29.4549	−	29.4549i	1.15266	−	1.15266i	0.166643	−	0.986017i	$-0.446707\pi$
$653$	29.4549	−	29.4549i	1.15266	−	1.15266i	0.986017	−	0.166643i	$-0.0532926\pi$
$654$		0			0
$655$	5.90461	+	1.54400i	0.230712	+	0.0603290i
$656$			20.6254i			0.805286i
$657$		0			0
$658$	5.70399	+	5.70399i	0.222365	+	0.222365i
$659$	29.4372			1.14671			0.573354	−	0.819307i	$-0.305642\pi$
$659$	29.4372			1.14671			0.573354	+	0.819307i	$0.305642\pi$
$660$		0			0
$661$	16.3460			0.635787			0.317893	−	0.948126i	$-0.397025\pi$
$661$	16.3460			0.635787			0.317893	+	0.948126i	$0.397025\pi$
$662$	−30.0581	−	30.0581i	−1.16824	−	1.16824i
$663$		0			0
$664$		−	6.76301i		−	0.262456i
$665$	5.91286	−	3.46155i	0.229291	−	0.134233i
$666$		0			0
$667$	20.0689	−	20.0689i	0.777070	−	0.777070i
$668$	17.2797	−	17.2797i	0.668573	−	0.668573i
$669$		0			0
$670$	−15.5603	+	59.5064i	−0.601148	+	2.29893i
$671$		−	7.82553i		−	0.302101i
$672$		0			0
$673$	−5.86468	−	5.86468i	−0.226067	−	0.226067i	0.584981	−	0.811047i	$-0.301102\pi$
$673$	−5.86468	−	5.86468i	−0.226067	−	0.226067i	−0.811047	+	0.584981i	$0.801102\pi$
$674$	−22.7308			−0.875559
$675$		0			0
$676$	−37.0057			−1.42330
$677$	−8.34109	−	8.34109i	−0.320574	−	0.320574i	0.528413	−	0.848987i	$-0.322787\pi$
$677$	−8.34109	−	8.34109i	−0.320574	−	0.320574i	−0.848987	+	0.528413i	$0.822787\pi$
$678$		0			0
$679$			4.34618i			0.166791i
$680$	5.47963	−	20.9554i	0.210134	−	0.803603i
$681$		0			0
$682$	12.8698	−	12.8698i	0.492811	−	0.492811i
$683$	−21.9309	+	21.9309i	−0.839162	+	0.839162i	−0.988749	−	0.149587i	$-0.952206\pi$
$683$	−21.9309	+	21.9309i	−0.839162	+	0.839162i	0.149587	+	0.988749i	$0.452206\pi$
$684$		0			0
$685$	−0.143182	+	0.0838224i	−0.00547069	+	0.00320269i
$686$			1.81186i			0.0691771i
$687$		0			0
$688$	18.2885	+	18.2885i	0.697241	+	0.697241i
$689$	43.8586			1.67088
$690$		0			0
$691$	−31.5075			−1.19860			−0.599300	−	0.800525i	$-0.704554\pi$
$691$	−31.5075			−1.19860			−0.599300	+	0.800525i	$0.704554\pi$
$692$	−6.26402	−	6.26402i	−0.238123	−	0.238123i
$693$		0			0
$694$		−	12.3151i		−	0.467476i
$695$	33.8938	+	8.86291i	1.28567	+	0.336189i
$696$		0			0
$697$	−22.0979	+	22.0979i	−0.837018	+	0.837018i
$698$	−46.0929	+	46.0929i	−1.74464	+	1.74464i
$699$		0			0
$700$	−1.73478	−	6.17512i	−0.0655686	−	0.233398i
$701$		−	37.1532i		−	1.40326i	−0.712543	−	0.701628i	$-0.752457\pi$
$701$		−	37.1532i		−	1.40326i	0.712543	−	0.701628i	$-0.247543\pi$
$702$		0			0
$703$	2.55646	+	2.55646i	0.0964186	+	0.0964186i
$704$	6.63955			0.250237
$705$		0			0
$706$	−43.6249			−1.64184
$707$	−0.537248	−	0.537248i	−0.0202053	−	0.0202053i
$708$		0			0
$709$			17.8148i			0.669048i	0.942387	+	0.334524i	$0.108576\pi$
$709$			17.8148i			0.669048i	−0.942387	+	0.334524i	$0.891424\pi$
$710$	19.9799	+	34.1288i	0.749832	+	1.28083i
$711$		0			0
$712$	−6.79205	+	6.79205i	−0.254543	+	0.254543i
$713$	−9.27283	+	9.27283i	−0.347270	+	0.347270i
$714$		0			0
$715$	30.2713	+	51.7082i	1.13208	+	1.93378i
$716$		−	21.8709i		−	0.817355i
$717$		0			0
$718$	3.87886	+	3.87886i	0.144758	+	0.144758i
$719$	26.0712			0.972292			0.486146	−	0.873878i	$-0.338402\pi$
$719$	26.0712			0.972292			0.486146	+	0.873878i	$0.338402\pi$
$720$		0			0
$721$	−2.77627			−0.103394
$722$	−12.3136	−	12.3136i	−0.458264	−	0.458264i
$723$		0			0
$724$		−	20.3135i		−	0.754946i
$725$	−22.8836	−	12.8460i	−0.849874	−	0.477089i
$726$		0			0
$727$	14.3966	−	14.3966i	0.533941	−	0.533941i	−0.387802	−	0.921743i	$-0.626766\pi$
$727$	14.3966	−	14.3966i	0.533941	−	0.533941i	0.921743	+	0.387802i	$0.126766\pi$
$728$	−5.94374	+	5.94374i	−0.220290	+	0.220290i
$729$		0			0
$730$	5.42648	+	1.41897i	0.200843	+	0.0525185i
$731$			39.1883i			1.44943i
$732$		0			0
$733$	0.715347	+	0.715347i	0.0264219	+	0.0264219i	0.720194	−	0.693772i	$-0.244053\pi$
$733$	0.715347	+	0.715347i	0.0264219	+	0.0264219i	−0.693772	+	0.720194i	$0.744053\pi$
$734$	24.9975			0.922673
$735$		0			0
$736$	−34.1516			−1.25885
$737$	44.4670	+	44.4670i	1.63796	+	1.63796i
$738$		0			0
$739$			24.4989i			0.901205i	0.892725	+	0.450602i	$0.148791\pi$
$739$			24.4989i			0.901205i	−0.892725	+	0.450602i	$0.851209\pi$
$740$	2.92085	−	1.70994i	0.107373	−	0.0628588i
$741$		0			0
$742$	−8.68626	+	8.68626i	−0.318883	+	0.318883i
$743$	−24.0536	+	24.0536i	−0.882441	+	0.882441i	−0.993782	−	0.111341i	$-0.964485\pi$
$743$	−24.0536	+	24.0536i	−0.882441	+	0.882441i	0.111341	+	0.993782i	$0.464485\pi$
$744$		0			0
$745$	2.88849	−	11.0463i	0.105826	−	0.404704i
$746$			42.1969i			1.54494i
$747$		0			0
$748$	28.0105	+	28.0105i	1.02417	+	1.02417i
$749$	−16.1556			−0.590312
$750$		0			0
$751$	−9.50757			−0.346936			−0.173468	−	0.984839i	$-0.555497\pi$
$751$	−9.50757			−0.346936			−0.173468	+	0.984839i	$0.555497\pi$
$752$	−15.4889	−	15.4889i	−0.564821	−	0.564821i
$753$		0			0
$754$		−	61.5168i		−	2.24031i
$755$	−1.21012	+	4.62779i	−0.0440408	+	0.168422i
$756$		0			0
$757$	9.69461	−	9.69461i	0.352357	−	0.352357i	−0.508629	−	0.860986i	$-0.669848\pi$
$757$	9.69461	−	9.69461i	0.352357	−	0.352357i	0.860986	+	0.508629i	$0.169848\pi$
$758$	−47.7789	+	47.7789i	−1.73541	+	1.73541i
$759$		0			0
$760$	−7.68319	+	4.49794i	−0.278699	+	0.163158i
$761$		−	1.20458i		−	0.0436662i	−0.999762	−	0.0218331i	$-0.993050\pi$
$761$		−	1.20458i		−	0.0436662i	0.999762	−	0.0218331i	$-0.00695024\pi$
$762$		0			0
$763$	−12.8622	−	12.8622i	−0.465644	−	0.465644i
$764$	−0.379225			−0.0137199
$765$		0			0
$766$	33.3393			1.20460
$767$	9.03998	+	9.03998i	0.326415	+	0.326415i
$768$		0			0
$769$			32.3602i			1.16694i	0.812135	+	0.583469i	$0.198305\pi$
$769$			32.3602i			1.16694i	−0.812135	+	0.583469i	$0.801695\pi$
$770$	−16.2362	−	4.24560i	−0.585111	−	0.153001i
$771$		0			0
$772$	14.8132	−	14.8132i	0.533140	−	0.533140i
$773$	−25.3066	+	25.3066i	−0.910216	+	0.910216i	−0.996289	−	0.0860725i	$-0.972568\pi$
$773$	−25.3066	+	25.3066i	−0.910216	+	0.910216i	0.0860725	+	0.996289i	$0.472568\pi$
$774$		0			0
$775$	10.5734	+	5.93551i	0.379806	+	0.213210i
$776$		−	5.64744i		−	0.202731i
$777$		0			0
$778$	12.6567	+	12.6567i	0.453766	+	0.453766i
$779$	12.8453			0.460229
$780$		0			0
$781$	40.4335			1.44682
$782$	−51.6463	−	51.6463i	−1.84687	−	1.84687i
$783$		0			0
$784$		−	4.92000i		−	0.175714i
$785$	8.27060	+	14.1275i	0.295190	+	0.504231i
$786$		0			0
$787$	−25.4112	+	25.4112i	−0.905810	+	0.905810i	−0.995931	−	0.0901209i	$-0.971275\pi$
$787$	−25.4112	+	25.4112i	−0.905810	+	0.905810i	0.0901209	+	0.995931i	$0.471275\pi$
$788$	6.80491	−	6.80491i	0.242415	−	0.242415i
$789$		0			0
$790$	8.38042	+	14.3151i	0.298162	+	0.509307i
$791$			7.50182i			0.266734i
$792$		0			0
$793$	8.64159	+	8.64159i	0.306872	+	0.306872i
$794$	0.977459			0.0346887
$795$		0			0
$796$	9.05854			0.321071
$797$	−7.39217	−	7.39217i	−0.261844	−	0.261844i	0.563959	−	0.825803i	$-0.309278\pi$
$797$	−7.39217	−	7.39217i	−0.261844	−	0.261844i	−0.825803	+	0.563959i	$0.809278\pi$
$798$		0			0
$799$		−	33.1893i		−	1.17415i
$800$	8.54054	+	30.4009i	0.301954	+	1.07483i
$801$		0			0
$802$	26.7973	−	26.7973i	0.946246	−	0.946246i
$803$	4.05502	−	4.05502i	0.143098	−	0.143098i
$804$		0			0
$805$	11.6983	+	3.05899i	0.412311	+	0.107815i
$806$			28.4238i			1.00119i
$807$		0			0
$808$	0.698102	+	0.698102i	0.0245591	+	0.0245591i
$809$	1.56712			0.0550969			0.0275485	−	0.999620i	$-0.491230\pi$
$809$	1.56712			0.0550969			0.0275485	+	0.999620i	$0.491230\pi$
$810$		0			0
$811$	13.6470			0.479210			0.239605	−	0.970870i	$-0.422982\pi$
$811$	13.6470			0.479210			0.239605	+	0.970870i	$0.422982\pi$
$812$	4.76095	+	4.76095i	0.167077	+	0.167077i
$813$		0			0
$814$		−	8.85540i		−	0.310382i
$815$	−14.8822	+	8.71241i	−0.521299	+	0.305182i
$816$		0			0
$817$	11.3899	−	11.3899i	0.398481	−	0.398481i
$818$	20.4425	−	20.4425i	0.714757	−	0.714757i
$819$		0			0
$820$	3.04218	−	11.6340i	0.106238	−	0.406278i
$821$			21.7023i			0.757414i	0.925517	+	0.378707i	$0.123631\pi$
$821$			21.7023i			0.757414i	−0.925517	+	0.378707i	$0.876369\pi$
$822$		0			0
$823$	−9.66959	−	9.66959i	−0.337061	−	0.337061i	0.518199	−	0.855260i	$-0.326603\pi$
$823$	−9.66959	−	9.66959i	−0.337061	−	0.337061i	−0.855260	+	0.518199i	$0.826603\pi$
$824$	3.60749			0.125673
$825$		0			0
$826$	−3.58076			−0.124591
$827$	−0.682391	−	0.682391i	−0.0237291	−	0.0237291i	0.695143	−	0.718872i	$-0.255341\pi$
$827$	−0.682391	−	0.682391i	−0.0237291	−	0.0237291i	−0.718872	+	0.695143i	$0.755341\pi$
$828$		0			0
$829$		−	10.3444i		−	0.359276i	−0.983733	−	0.179638i	$-0.942507\pi$
$829$		−	10.3444i		−	0.359276i	0.983733	−	0.179638i	$-0.0574926\pi$
$830$	−5.33456	+	20.4006i	−0.185165	+	0.708116i
$831$		0			0
$832$	−7.33193	+	7.33193i	−0.254189	+	0.254189i
$833$	5.27126	−	5.27126i	0.182638	−	0.182638i
$834$		0			0
$835$	36.7598	−	21.5202i	1.27212	−	0.744736i
$836$		−	16.2822i		−	0.563132i
$837$		0			0
$838$	−18.7584	−	18.7584i	−0.647999	−	0.647999i
$839$	43.5272			1.50273			0.751363	−	0.659889i	$-0.229397\pi$
$839$	43.5272			1.50273			0.751363	+	0.659889i	$0.229397\pi$
$840$		0			0
$841$	−1.45290			−0.0501001
$842$	−37.6994	−	37.6994i	−1.29921	−	1.29921i
$843$		0			0
$844$			18.3365i			0.631167i
$845$	−62.4051	−	16.3183i	−2.14680	−	0.561368i
$846$		0			0
$847$	−4.35453	+	4.35453i	−0.149624	+	0.149624i
$848$	23.5871	−	23.5871i	0.809983	−	0.809983i
$849$		0			0
$850$	−33.0586	+	58.8897i	−1.13390	+	2.01990i
$851$			6.38039i			0.218717i
$852$		0			0
$853$	−0.0328516	−	0.0328516i	−0.00112482	−	0.00112482i	0.706544	−	0.707669i	$-0.250253\pi$
$853$	−0.0328516	−	0.0328516i	−0.00112482	−	0.00112482i	−0.707669	+	0.706544i	$0.750253\pi$
$854$	−3.42296			−0.117131
$855$		0			0
$856$	20.9926			0.717513
$857$	−32.6070	−	32.6070i	−1.11384	−	1.11384i	−0.992627	−	0.121208i	$-0.961323\pi$
$857$	−32.6070	−	32.6070i	−1.11384	−	1.11384i	−0.121208	−	0.992627i	$-0.538677\pi$
$858$		0			0
$859$			3.46726i			0.118301i	0.998249	+	0.0591506i	$0.0188392\pi$
$859$			3.46726i			0.118301i	−0.998249	+	0.0591506i	$0.981161\pi$
$860$	−7.61836	−	13.0134i	−0.259784	−	0.443752i
$861$		0			0
$862$	−29.3682	+	29.3682i	−1.00028	+	1.00028i
$863$	31.7372	−	31.7372i	1.08035	−	1.08035i	0.0838692	−	0.996477i	$-0.473272\pi$
$863$	31.7372	−	31.7372i	1.08035	−	1.08035i	0.996477	−	0.0838692i	$-0.0267278\pi$
$864$		0			0
$865$	−7.80121	−	13.3257i	−0.265249	−	0.453087i
$866$		−	36.8183i		−	1.25114i
$867$		0			0
$868$	−2.19980	−	2.19980i	−0.0746660	−	0.0746660i
$869$	16.9595			0.575312
$870$		0			0
$871$	−98.2081			−3.32766
$872$	16.7132	+	16.7132i	0.565981	+	0.565981i
$873$		0			0
$874$			30.0214i			1.01549i
$875$	−0.202445	−	11.1785i	−0.00684389	−	0.377903i
$876$		0			0
$877$	−5.46491	+	5.46491i	−0.184537	+	0.184537i	−0.793329	−	0.608793i	$-0.791654\pi$
$877$	−5.46491	+	5.46491i	−0.184537	+	0.184537i	0.608793	+	0.793329i	$0.291654\pi$
$878$	38.1055	−	38.1055i	1.28600	−	1.28600i
$879$		0			0
$880$	44.0884	+	11.5287i	1.48622	+	0.388632i
$881$		−	49.0241i		−	1.65166i	−0.563916	−	0.825832i	$-0.690706\pi$
$881$		−	49.0241i		−	1.65166i	0.563916	−	0.825832i	$-0.309294\pi$
$882$		0			0
$883$	9.34962	+	9.34962i	0.314640	+	0.314640i	0.846704	−	0.532064i	$-0.178584\pi$
$883$	9.34962	+	9.34962i	0.314640	+	0.314640i	−0.532064	+	0.846704i	$0.678584\pi$
$884$	−61.8630			−2.08068
$885$		0			0
$886$	38.3320			1.28779
$887$	32.1054	+	32.1054i	1.07799	+	1.07799i	0.996689	+	0.0813035i	$0.0259083\pi$
$887$	32.1054	+	32.1054i	1.07799	+	1.07799i	0.0813035	+	0.996689i	$0.474092\pi$
$888$		0			0
$889$		−	6.31295i		−	0.211730i
$890$	25.8457	−	15.1308i	0.866350	−	0.507184i
$891$		0			0
$892$	−18.8700	+	18.8700i	−0.631813	+	0.631813i
$893$	−9.64630	+	9.64630i	−0.322801	+	0.322801i
$894$		0			0
$895$	9.64438	−	36.8824i	0.322376	−	1.23284i
$896$			9.72690i			0.324953i
$897$		0			0
$898$	16.1746	+	16.1746i	0.539754	+	0.539754i
$899$	−12.7281			−0.424507
$900$		0			0
$901$	50.5420			1.68380
$902$	−22.2476	−	22.2476i	−0.740763	−	0.740763i
$903$		0			0
$904$		−	9.74789i		−	0.324210i
$905$	8.95762	−	34.2561i	0.297761	−	1.13871i
$906$		0			0
$907$	2.35659	−	2.35659i	0.0782493	−	0.0782493i	−0.666899	−	0.745148i	$-0.732379\pi$
$907$	2.35659	−	2.35659i	0.0782493	−	0.0782493i	0.745148	+	0.666899i	$0.232379\pi$
$908$	−1.04420	+	1.04420i	−0.0346531	+	0.0346531i
$909$		0			0
$910$	22.6176	−	13.2410i	0.749767	−	0.438934i
$911$			19.2308i			0.637144i	0.947899	+	0.318572i	$0.103203\pi$
$911$			19.2308i			0.637144i	−0.947899	+	0.318572i	$0.896797\pi$
$912$		0			0
$913$	15.2447	+	15.2447i	0.504525	+	0.504525i
$914$	58.9409			1.94959
$915$		0			0
$916$	24.7318			0.817162
$917$	−1.92998	−	1.92998i	−0.0637337	−	0.0637337i
$918$		0			0
$919$		−	29.2988i		−	0.966478i	−0.875489	−	0.483239i	$-0.839460\pi$
$919$		−	29.2988i		−	0.966478i	0.875489	−	0.483239i	$-0.160540\pi$
$920$	−15.2008	−	3.97486i	−0.501156	−	0.131047i
$921$		0			0
$922$	43.1726	−	43.1726i	1.42181	−	1.42181i
$923$	−44.6499	+	44.6499i	−1.46967	+	1.46967i
$924$		0			0
$925$	5.67966	−	1.59559i	0.186746	−	0.0524627i
$926$		−	27.0317i		−	0.888318i
$927$		0			0
$928$	−23.4387	−	23.4387i	−0.769414	−	0.769414i
$929$	−30.3363			−0.995301			−0.497651	−	0.867378i	$-0.665804\pi$
$929$	−30.3363			−0.995301			−0.497651	+	0.867378i	$0.665804\pi$
$930$		0			0
$931$	−3.06412			−0.100423
$932$	−0.00500345	−	0.00500345i	−0.000163893	−	0.000163893i
$933$		0			0
$934$		−	24.9310i		−	0.815768i
$935$	34.8843	+	59.5878i	1.14084	+	1.94873i
$936$		0			0
$937$	18.7277	−	18.7277i	0.611808	−	0.611808i	−0.331609	−	0.943417i	$-0.607591\pi$
$937$	18.7277	−	18.7277i	0.611808	−	0.611808i	0.943417	+	0.331609i	$0.107591\pi$
$938$	19.4503	−	19.4503i	0.635074	−	0.635074i
$939$		0			0
$940$	6.45215	+	11.0213i	0.210446	+	0.359474i
$941$			2.53282i			0.0825676i	0.999147	+	0.0412838i	$0.0131448\pi$
$941$			2.53282i			0.0825676i	−0.999147	+	0.0412838i	$0.986855\pi$
$942$		0			0
$943$	16.0296	+	16.0296i	0.521995	+	0.521995i
$944$	9.72337			0.316469
$945$		0			0
$946$	−39.4537			−1.28275
$947$	−17.4742	−	17.4742i	−0.567834	−	0.567834i	0.363687	−	0.931521i	$-0.381518\pi$
$947$	−17.4742	−	17.4742i	−0.567834	−	0.567834i	−0.931521	+	0.363687i	$0.881518\pi$
$948$		0			0
$949$			8.95576i			0.290716i
$950$	26.7243	−	7.50767i	0.867050	−	0.243581i
$951$		0			0
$952$	−6.84949	+	6.84949i	−0.221993	+	0.221993i
$953$	30.4565	−	30.4565i	0.986584	−	0.986584i	−0.0133276	−	0.999911i	$-0.504242\pi$
$953$	30.4565	−	30.4565i	0.986584	−	0.986584i	0.999911	+	0.0133276i	$0.00424244\pi$
$954$		0			0
$955$	−0.639513	−	0.167226i	−0.0206941	−	0.00541131i
$956$		−	1.62530i		−	0.0525661i
$957$		0			0
$958$	−38.3044	−	38.3044i	−1.23756	−	1.23756i
$959$	0.0741987			0.00239600
$960$		0			0
$961$	−25.1190			−0.810289
$962$	9.77885	+	9.77885i	0.315283	+	0.315283i
$963$		0			0
$964$		−	7.88788i		−	0.254052i
$965$	31.5127	−	18.4484i	1.01443	−	0.593874i
$966$		0			0
$967$	−18.0985	+	18.0985i	−0.582009	+	0.582009i	−0.935455	−	0.353446i	$-0.885010\pi$
$967$	−18.0985	+	18.0985i	−0.582009	+	0.582009i	0.353446	+	0.935455i	$0.385010\pi$
$968$	5.65829	−	5.65829i	0.181864	−	0.181864i
$969$		0			0
$970$	−4.45462	+	17.0355i	−0.143029	+	0.546978i
$971$			38.7995i			1.24514i	0.782566	+	0.622568i	$0.213911\pi$
$971$			38.7995i			1.24514i	−0.782566	+	0.622568i	$0.786089\pi$
$972$		0			0
$973$	−11.0786	−	11.0786i	−0.355162	−	0.355162i
$974$	17.2756			0.553546
$975$		0			0
$976$	9.29486			0.297521
$977$	−22.3872	−	22.3872i	−0.716231	−	0.716231i	0.251601	−	0.967831i	$-0.419043\pi$
$977$	−22.3872	−	22.3872i	−0.716231	−	0.716231i	−0.967831	+	0.251601i	$0.919043\pi$
$978$		0			0
$979$		−	30.6202i		−	0.978627i
$980$	−0.725686	+	2.77519i	−0.0231812	+	0.0886503i
$981$		0			0
$982$	−51.1542	+	51.1542i	−1.63240	+	1.63240i
$983$	26.6802	−	26.6802i	0.850968	−	0.850968i	−0.139285	−	0.990252i	$-0.544480\pi$
$983$	26.6802	−	26.6802i	0.850968	−	0.850968i	0.990252	+	0.139285i	$0.0444803\pi$
$984$		0			0
$985$	14.4763	−	8.47483i	0.461254	−	0.270030i
$986$		−	70.8911i		−	2.25763i
$987$		0			0
$988$	17.9801	+	17.9801i	0.572025	+	0.572025i
$989$	28.4267			0.903918
$990$		0			0
$991$	44.0522			1.39936			0.699682	−	0.714454i	$-0.253325\pi$
$991$	44.0522			1.39936			0.699682	+	0.714454i	$0.253325\pi$
$992$	10.8299	+	10.8299i	0.343849	+	0.343849i
$993$		0			0
$994$		−	17.6860i		−	0.560965i
$995$	15.2760	+	3.99453i	0.484282	+	0.126635i
$996$		0			0
$997$	33.6548	−	33.6548i	1.06586	−	1.06586i	0.0681847	−	0.997673i	$-0.478279\pi$
$997$	33.6548	−	33.6548i	1.06586	−	1.06586i	0.997673	−	0.0681847i	$-0.0217207\pi$
$998$	−26.9354	+	26.9354i	−0.852624	+	0.852624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.m.b.8.2	yes	12
3.2	odd	2		315.2.m.a.8.5	✓	12
5.2	odd	4		315.2.m.a.197.5	yes	12
5.3	odd	4		1575.2.m.c.1457.2		12
5.4	even	2		1575.2.m.d.1268.5		12
15.2	even	4	inner	315.2.m.b.197.2	yes	12
15.8	even	4		1575.2.m.d.1457.5		12
15.14	odd	2		1575.2.m.c.1268.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.5	✓	12	3.2	odd	2
315.2.m.a.197.5	yes	12	5.2	odd	4
315.2.m.b.8.2	yes	12	1.1	even	1	trivial
315.2.m.b.197.2	yes	12	15.2	even	4	inner
1575.2.m.c.1268.2		12	15.14	odd	2
1575.2.m.c.1457.2		12	5.3	odd	4
1575.2.m.d.1268.5		12	5.4	even	2
1575.2.m.d.1457.5		12	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(-1.28118 - 1.28118i) q^{2} +1.28283i q^{4} +(-0.565689 + 2.16333i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.918816 + 0.918816i) q^{8} +O(q^{10})\)	\(q+(-1.28118 - 1.28118i) q^{2} +1.28283i q^{4} +(-0.565689 + 2.16333i) q^{5} +(0.707107 - 0.707107i) q^{7} +(-0.918816 + 0.918816i) q^{8} +(3.49636 - 2.04686i) q^{10} -4.14225i q^{11} +(4.57421 + 4.57421i) q^{13} -1.81186 q^{14} +4.92000 q^{16} +(5.27126 + 5.27126i) q^{17} -3.06412i q^{19} +(-2.77519 - 0.725686i) q^{20} +(-5.30696 + 5.30696i) q^{22} +(3.82371 - 3.82371i) q^{23} +(-4.35999 - 2.44755i) q^{25} -11.7208i q^{26} +(0.907101 + 0.907101i) q^{28} +5.24853 q^{29} -2.42509 q^{31} +(-4.46577 - 4.46577i) q^{32} -13.5068i q^{34} +(1.12970 + 1.92971i) q^{35} +(-0.834319 + 0.834319i) q^{37} +(-3.92569 + 3.92569i) q^{38} +(-1.46794 - 2.50747i) q^{40} +4.19215i q^{41} +(3.71717 + 3.71717i) q^{43} +5.31382 q^{44} -9.79772 q^{46} +(-3.14814 - 3.14814i) q^{47} -1.00000i q^{49} +(2.45018 + 8.72167i) q^{50} +(-5.86796 + 5.86796i) q^{52} +(4.79411 - 4.79411i) q^{53} +(8.96105 + 2.34323i) q^{55} +1.29940i q^{56} +(-6.72431 - 6.72431i) q^{58} +1.97629 q^{59} +1.88920 q^{61} +(3.10697 + 3.10697i) q^{62} +1.60288i q^{64} +(-12.4831 + 7.30794i) q^{65} +(-10.7350 + 10.7350i) q^{67} +(-6.76215 + 6.76215i) q^{68} +(1.02495 - 3.91965i) q^{70} +9.76123i q^{71} +(0.978941 + 0.978941i) q^{73} +2.13782 q^{74} +3.93076 q^{76} +(-2.92901 - 2.92901i) q^{77} +4.09428i q^{79} +(-2.78319 + 10.6436i) q^{80} +(5.37089 - 5.37089i) q^{82} +(-3.68028 + 3.68028i) q^{83} +(-14.3854 + 8.42158i) q^{85} -9.52470i q^{86} +(3.80597 + 3.80597i) q^{88} +7.39217 q^{89} +6.46891 q^{91} +(4.90519 + 4.90519i) q^{92} +8.06666i q^{94} +(6.62871 + 1.73334i) q^{95} +(-3.07322 + 3.07322i) q^{97} +(-1.28118 + 1.28118i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 24 q^{8}+O(q^{10}) \) 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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