LMFDB - Embedded newform 315.2.m.a.197.5

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			197.5
Root			$-2.01185i$ of defining polynomial
Character	$\chi$	$=$	315.197
Dual form			315.2.m.a.8.5

$q$-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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.28118	−	1.28118i	0.905930	−	0.905930i	−0.0900110	−	0.995941i	$-0.528690\pi$
$2$	1.28118	−	1.28118i	0.905930	−	0.905930i	0.995941	+	0.0900110i	$0.0286902\pi$
$3$		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	0.321876	−	0.946782i	$-0.395687\pi$
$13$	4.57421	−	4.57421i	1.26866	−	1.26866i	0.946782	−	0.321876i	$-0.104313\pi$
$14$	1.81186			0.484240
$15$		0			0
$16$	4.92000			1.23000
$17$	−5.27126	+	5.27126i	−1.27847	+	1.27847i	−0.336943	+	0.941525i	$0.609393\pi$
$17$	−5.27126	+	5.27126i	−1.27847	+	1.27847i	−0.941525	+	0.336943i	$0.890607\pi$
$18$		0			0
$19$			3.06412i			0.702958i	0.936196	+	0.351479i	$0.114321\pi$
$19$			3.06412i			0.702958i	−0.936196	+	0.351479i	$0.885679\pi$
$20$	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	$-0.440652\pi$
$23$	−3.82371	−	3.82371i	−0.797299	−	0.797299i	−0.982669	+	0.185370i	$0.940652\pi$
$24$		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	$-0.662023\pi$
$29$	−5.24853			−0.974628			−0.487314	+	0.873227i	$0.662023\pi$
$30$		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	0.635193	−	0.772354i	$-0.280921\pi$
$37$	−0.834319	−	0.834319i	−0.137161	−	0.137161i	−0.772354	+	0.635193i	$0.780921\pi$
$38$	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	−0.364386	−	0.931248i	$-0.618721\pi$
$43$	3.71717	−	3.71717i	0.566862	−	0.566862i	0.931248	+	0.364386i	$0.118721\pi$
$44$	−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	$-0.644735\pi$
$47$	3.14814	−	3.14814i	0.459204	−	0.459204i	0.898394	+	0.439190i	$0.144735\pi$
$48$		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	$-0.404178\pi$
$53$	−4.79411	−	4.79411i	−0.658522	−	0.658522i	−0.955030	+	0.296508i	$0.904178\pi$
$54$		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	$-0.541063\pi$
$59$	−1.97629			−0.257291			−0.128646	+	0.991691i	$0.541063\pi$
$60$		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	−0.920320	−	0.391167i	$-0.872072\pi$
$67$	−10.7350	−	10.7350i	−1.31149	−	1.31149i	−0.391167	−	0.920320i	$-0.627928\pi$
$68$	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	−0.647494	−	0.762070i	$-0.724183\pi$
$73$	0.978941	−	0.978941i	0.114576	−	0.114576i	0.762070	+	0.647494i	$0.224183\pi$
$74$	−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	$-0.926022\pi$
$79$		−	4.09428i		−	0.460642i	0.973115	−	0.230321i	$-0.0739776\pi$
$80$	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	$-0.157792\pi$
$83$	3.68028	+	3.68028i	0.403964	+	0.403964i	−0.475664	+	0.879627i	$0.657792\pi$
$84$		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	$-0.628142\pi$
$89$	−7.39217			−0.783569			−0.391784	+	0.920057i	$0.628142\pi$
$90$		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	0.533661	−	0.845699i	$-0.320816\pi$
$97$	−3.07322	−	3.07322i	−0.312038	−	0.312038i	−0.845699	+	0.533661i	$0.820816\pi$
$98$	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	−0.797177	−	0.603745i	$-0.793674\pi$
$103$	−1.96312	+	1.96312i	−0.193432	+	0.193432i	0.603745	+	0.797177i	$0.293674\pi$
$104$	8.40572			0.824248
$105$		0			0
$106$	−12.2842			−1.19315
$107$	11.4237	−	11.4237i	1.10437	−	1.10437i	0.110497	−	0.993876i	$-0.464756\pi$
$107$	11.4237	−	11.4237i	1.10437	−	1.10437i	0.993876	−	0.110497i	$-0.0352441\pi$
$108$		0			0
$109$			18.1899i			1.74228i	0.491034	+	0.871140i	$0.336619\pi$
$109$			18.1899i			1.74228i	−0.491034	+	0.871140i	$0.663381\pi$
$110$	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	$-0.135211\pi$
$113$	5.30459	+	5.30459i	0.499014	+	0.499014i	−0.412117	+	0.911131i	$0.635211\pi$
$114$		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	0.876858	−	0.480749i	$-0.159635\pi$
$127$	4.46393	+	4.46393i	0.396110	+	0.396110i	−0.480749	+	0.876858i	$0.659635\pi$
$128$	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	$-0.751009\pi$
$137$	−0.0524664	+	0.0524664i	−0.00448250	+	0.00448250i	0.704862	+	0.709344i	$0.251009\pi$
$138$		0			0
$139$			15.6674i			1.32890i	0.747335	+	0.664448i	$0.231333\pi$
$139$			15.6674i			1.32890i	−0.747335	+	0.664448i	$0.768667\pi$
$140$	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	$-0.432928\pi$
$149$	5.10614			0.418312			0.209156	+	0.977882i	$0.432928\pi$
$150$		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	0.882835	−	0.469684i	$-0.155632\pi$
$157$	5.17676	+	5.17676i	0.413150	+	0.413150i	−0.469684	+	0.882835i	$0.655632\pi$
$158$	−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	−0.460516	−	0.887651i	$-0.652336\pi$
$163$	5.45330	−	5.45330i	0.427135	−	0.427135i	0.887651	+	0.460516i	$0.152336\pi$
$164$	5.37784			0.419938
$165$		0			0
$166$	9.43020			0.731925
$167$	13.4700	−	13.4700i	1.04234	−	1.04234i	0.0432737	−	0.999063i	$-0.486221\pi$
$167$	13.4700	−	13.4700i	1.04234	−	1.04234i	0.999063	−	0.0432737i	$-0.0137787\pi$
$168$		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	$-0.165450\pi$
$173$	4.88296	+	4.88296i	0.371244	+	0.371244i	−0.496686	+	0.867930i	$0.665450\pi$
$174$		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	$-0.280114\pi$
$179$	17.0489			1.27429			0.637147	+	0.770742i	$0.280114\pi$
$180$		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	−0.987680	−	0.156490i	$-0.949982\pi$
$193$	−11.5473	+	11.5473i	−0.831190	+	0.831190i	0.156490	+	0.987680i	$0.449982\pi$
$194$	−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	$-0.663888\pi$
$197$	5.30459	−	5.30459i	0.377936	−	0.377936i	0.870357	+	0.492421i	$0.163888\pi$
$198$		0			0
$199$			7.06135i			0.500566i	0.968173	+	0.250283i	$0.0805236\pi$
$199$			7.06135i			0.500566i	−0.968173	+	0.250283i	$0.919476\pi$
$200$	−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	−0.0148628	−	0.999890i	$-0.504731\pi$
$223$	14.7096	−	14.7096i	0.985027	−	0.985027i	0.999890	+	0.0148628i	$0.00473113\pi$
$224$	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	$-0.762163\pi$
$227$	−0.813981	+	0.813981i	−0.0540258	+	0.0540258i	0.679578	+	0.733604i	$0.262163\pi$
$228$		0			0
$229$			19.2790i			1.27399i	0.770866	+	0.636997i	$0.219824\pi$
$229$			19.2790i			1.27399i	−0.770866	+	0.636997i	$0.780176\pi$
$230$	−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	$-0.249942\pi$
$233$	0.00390031	+	0.00390031i	0.000255518	+	0.000255518i	−0.706979	+	0.707235i	$0.749942\pi$
$234$		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	$-0.486953\pi$
$239$	1.26696			0.0819530			0.0409765	+	0.999160i	$0.486953\pi$
$240$		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	$-0.841688\pi$
$257$	−6.44051	+	6.44051i	−0.401748	+	0.401748i	0.477101	+	0.878849i	$0.341688\pi$
$258$		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	$-0.100866\pi$
$263$	10.3565	+	10.3565i	0.638611	+	0.638611i	−0.311602	+	0.950213i	$0.600866\pi$
$264$		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	$-0.418728\pi$
$269$	8.28454			0.505117			0.252559	+	0.967582i	$0.418728\pi$
$270$		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	0.831704	−	0.555219i	$-0.187366\pi$
$277$	4.60162	+	4.60162i	0.276485	+	0.276485i	−0.555219	+	0.831704i	$0.687366\pi$
$278$	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	−0.649980	−	0.759951i	$-0.725223\pi$
$283$	1.84999	−	1.84999i	0.109970	−	0.109970i	0.759951	+	0.649980i	$0.225223\pi$
$284$	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	$-0.399912\pi$
$293$	−10.9840	−	10.9840i	−0.641692	−	0.641692i	−0.950971	+	0.309279i	$0.899912\pi$
$294$		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	−0.781865	−	0.623448i	$-0.785731\pi$
$307$	−24.6231	−	24.6231i	−1.40531	−	1.40531i	−0.623448	−	0.781865i	$-0.714269\pi$
$308$	−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	−0.972083	−	0.234639i	$-0.924609\pi$
$313$	−13.0467	+	13.0467i	−0.737444	+	0.737444i	0.234639	+	0.972083i	$0.424609\pi$
$314$	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	$-0.768746\pi$
$317$	−1.48198	+	1.48198i	−0.0832361	+	0.0832361i	0.664263	+	0.747499i	$0.268746\pi$
$318$		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	0.906164	−	0.422926i	$-0.138997\pi$
$337$	8.87106	+	8.87106i	0.483238	+	0.483238i	−0.422926	+	0.906164i	$0.638997\pi$
$338$	−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	$-0.808400\pi$
$347$	−4.80618	+	4.80618i	−0.258009	+	0.258009i	0.566235	+	0.824244i	$0.308400\pi$
$348$		0			0
$349$			35.9770i			1.92580i	0.269854	+	0.962901i	$0.413025\pi$
$349$			35.9770i			1.92580i	−0.269854	+	0.962901i	$0.586975\pi$
$350$	−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	$-0.471379\pi$
$353$	−17.0253	−	17.0253i	−0.906166	−	0.906166i	−0.995960	+	0.0897948i	$0.971379\pi$
$354$		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	$-0.474542\pi$
$359$	3.02758			0.159789			0.0798947	+	0.996803i	$0.474542\pi$
$360$		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	0.405052	−	0.914293i	$-0.367253\pi$
$367$	−9.75566	−	9.75566i	−0.509241	−	0.509241i	−0.914293	+	0.405052i	$0.867253\pi$
$368$	−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	−0.990463	−	0.137781i	$-0.956003\pi$
$373$	−16.4680	+	16.4680i	−0.852682	+	0.852682i	0.137781	+	0.990463i	$0.456003\pi$
$374$	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	$0.407202\pi$
$379$			37.2929i			1.91561i	−0.287422	+	0.957804i	$0.592798\pi$
$380$	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	$-0.0942130\pi$
$383$	13.0112	+	13.0112i	0.664841	+	0.664841i	−0.291676	+	0.956517i	$0.594213\pi$
$384$		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	$-0.419424\pi$
$389$	9.87898			0.500884			0.250442	+	0.968132i	$0.419424\pi$
$390$		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	0.697469	−	0.716615i	$-0.254309\pi$
$397$	−0.381469	−	0.381469i	−0.0191454	−	0.0191454i	−0.716615	+	0.697469i	$0.754309\pi$
$398$	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	$-0.870922\pi$
$409$		−	15.9561i		−	0.788976i	0.918901	−	0.394488i	$-0.129078\pi$
$410$	−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	$-0.616419\pi$
$419$	−14.6415			−0.715286			−0.357643	+	0.933858i	$0.616419\pi$
$420$		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	−0.271821	−	0.962348i	$-0.587626\pi$
$433$	14.3689	−	14.3689i	0.690527	−	0.690527i	0.962348	+	0.271821i	$0.0876259\pi$
$434$	−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	$-0.748800\pi$
$439$		−	29.7425i		−	1.41953i	0.704437	−	0.709767i	$-0.251200\pi$
$440$	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	$-0.0823845\pi$
$443$	14.9597	+	14.9597i	0.710754	+	0.710754i	−0.255939	+	0.966693i	$0.582384\pi$
$444$		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	$-0.403714\pi$
$449$	12.6248			0.595801			0.297900	+	0.954597i	$0.403714\pi$
$450$		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	−0.996862	−	0.0791546i	$-0.974778\pi$
$457$	−23.0026	−	23.0026i	−1.07602	−	1.07602i	−0.0791546	−	0.996862i	$-0.525222\pi$
$458$	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	−0.418115	−	0.908394i	$-0.637309\pi$
$463$	10.5496	−	10.5496i	0.490280	−	0.490280i	0.908394	+	0.418115i	$0.137309\pi$
$464$	−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	$-0.853134\pi$
$467$	−9.72972	+	9.72972i	−0.450238	+	0.450238i	0.445196	+	0.895433i	$0.353134\pi$
$468$		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	$-0.739339\pi$
$479$	−29.8978			−1.36607			−0.683033	+	0.730388i	$0.739339\pi$
$480$		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	0.537653	−	0.843166i	$-0.319311\pi$
$487$	−6.74208	−	6.74208i	−0.305513	−	0.305513i	−0.843166	+	0.537653i	$0.819311\pi$
$488$	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	$0.155955\pi$
$499$			21.0239i			0.941159i	−0.882358	+	0.470579i	$0.844045\pi$
$500$	−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	$-0.278447\pi$
$503$	−2.83078	−	2.83078i	−0.126218	−	0.126218i	−0.767394	+	0.641176i	$0.778447\pi$
$504$		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	$-0.340225\pi$
$509$	21.7097			0.962267			0.481133	+	0.876647i	$0.340225\pi$
$510$		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	−0.195375	−	0.980729i	$-0.562592\pi$
$523$	17.9604	−	17.9604i	0.785353	−	0.785353i	0.980729	+	0.195375i	$0.0625925\pi$
$524$	−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	0.636071	−	0.771630i	$-0.280558\pi$
$547$	−3.17046	−	3.17046i	−0.135559	−	0.135559i	−0.771630	+	0.636071i	$0.780558\pi$
$548$	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	$-0.533000\pi$
$557$	21.0318	−	21.0318i	0.891144	−	0.891144i	0.994631	+	0.103487i	$0.0329999\pi$
$558$		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	$-0.135219\pi$
$563$	11.8395	+	11.8395i	0.498977	+	0.498977i	−0.412142	+	0.911119i	$0.635219\pi$
$564$		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	$-0.478439\pi$
$569$	3.22907			0.135370			0.0676848	+	0.997707i	$0.478439\pi$
$570$		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	0.907882	−	0.419226i	$-0.137699\pi$
$577$	11.7379	+	11.7379i	0.488655	+	0.488655i	−0.419226	+	0.907882i	$0.637699\pi$
$578$	−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	$-0.677886\pi$
$587$	7.69625	−	7.69625i	0.317658	−	0.317658i	0.847867	+	0.530209i	$0.177886\pi$
$588$		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	$-0.242857\pi$
$593$	0.772725	+	0.772725i	0.0317320	+	0.0317320i	−0.691063	+	0.722795i	$0.742857\pi$
$594$		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	$-0.453016\pi$
$599$	7.19884			0.294136			0.147068	+	0.989126i	$0.453016\pi$
$600$		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	0.233911	−	0.972258i	$-0.424848\pi$
$607$	−18.1909	−	18.1909i	−0.738347	−	0.738347i	−0.972258	+	0.233911i	$0.924848\pi$
$608$	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	−0.0902447	+	0.995920i	$0.528765\pi$
$613$	−26.8922	+	26.8922i	−1.08616	+	1.08616i	−0.995920	+	0.0902447i	$0.971235\pi$
$614$	−63.0931			−2.54623
$615$		0			0
$616$	5.38245			0.216865
$617$	−32.4145	+	32.4145i	−1.30496	+	1.30496i	−0.379952	+	0.925006i	$0.624059\pi$
$617$	−32.4145	+	32.4145i	−1.30496	+	1.30496i	−0.925006	+	0.379952i	$0.875941\pi$
$618$		0			0
$619$		−	44.1635i		−	1.77508i	−0.460729	−	0.887541i	$-0.652412\pi$
$619$		−	44.1635i		−	1.77508i	0.460729	−	0.887541i	$-0.347588\pi$
$620$	−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	−0.405495	+	0.914097i	$0.632901\pi$
$643$	−33.4615	+	33.4615i	−1.31959	+	1.31959i	−0.914097	+	0.405495i	$0.867099\pi$
$644$	−6.93699			−0.273356
$645$		0			0
$646$	−41.3866			−1.62834
$647$	33.6527	−	33.6527i	1.32302	−	1.32302i	0.411706	−	0.911317i	$-0.364933\pi$
$647$	33.6527	−	33.6527i	1.32302	−	1.32302i	0.911317	−	0.411706i	$-0.135067\pi$
$648$		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	−0.986017	−	0.166643i	$-0.946707\pi$
$653$	−29.4549	−	29.4549i	−1.15266	−	1.15266i	−0.166643	−	0.986017i	$-0.553293\pi$
$654$		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	$-0.694358\pi$
$659$	−29.4372			−1.14671			−0.573354	+	0.819307i	$0.694358\pi$
$660$		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	−0.811047	−	0.584981i	$-0.801102\pi$
$673$	−5.86468	+	5.86468i	−0.226067	+	0.226067i	0.584981	+	0.811047i	$0.301102\pi$
$674$	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	$-0.677213\pi$
$677$	8.34109	−	8.34109i	0.320574	−	0.320574i	0.848987	+	0.528413i	$0.177213\pi$
$678$		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	$-0.0477943\pi$
$683$	21.9309	+	21.9309i	0.839162	+	0.839162i	−0.149587	+	0.988749i	$0.547794\pi$
$684$		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	$-0.891424\pi$
$709$		−	17.8148i		−	0.669048i	0.942387	−	0.334524i	$-0.108576\pi$
$710$	−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	$-0.661598\pi$
$719$	−26.0712			−0.972292			−0.486146	+	0.873878i	$0.661598\pi$
$720$		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	0.921743	−	0.387802i	$-0.126766\pi$
$727$	14.3966	+	14.3966i	0.533941	+	0.533941i	−0.387802	+	0.921743i	$0.626766\pi$
$728$	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	−0.693772	−	0.720194i	$-0.744053\pi$
$733$	0.715347	−	0.715347i	0.0264219	−	0.0264219i	0.720194	+	0.693772i	$0.244053\pi$
$734$	−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	$-0.851209\pi$
$739$		−	24.4989i		−	0.901205i	0.892725	−	0.450602i	$-0.148791\pi$
$740$	−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	$-0.0355145\pi$
$743$	24.0536	+	24.0536i	0.882441	+	0.882441i	−0.111341	+	0.993782i	$0.535515\pi$
$744$		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	0.860986	−	0.508629i	$-0.169848\pi$
$757$	9.69461	+	9.69461i	0.352357	+	0.352357i	−0.508629	+	0.860986i	$0.669848\pi$
$758$	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	$-0.801695\pi$
$769$		−	32.3602i		−	1.16694i	0.812135	−	0.583469i	$-0.198305\pi$
$770$	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	$-0.0274317\pi$
$773$	25.3066	+	25.3066i	0.910216	+	0.910216i	−0.0860725	+	0.996289i	$0.527432\pi$
$774$		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	0.0901209	−	0.995931i	$-0.471275\pi$
$787$	−25.4112	−	25.4112i	−0.905810	−	0.905810i	−0.995931	+	0.0901209i	$0.971275\pi$
$788$	−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	$-0.690722\pi$
$797$	7.39217	−	7.39217i	0.261844	−	0.261844i	0.825803	+	0.563959i	$0.190722\pi$
$798$		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	$-0.508770\pi$
$809$	−1.56712			−0.0550969			−0.0275485	+	0.999620i	$0.508770\pi$
$810$		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	−0.855260	−	0.518199i	$-0.826603\pi$
$823$	−9.66959	+	9.66959i	−0.337061	+	0.337061i	0.518199	+	0.855260i	$0.326603\pi$
$824$	−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	$-0.744659\pi$
$827$	0.682391	−	0.682391i	0.0237291	−	0.0237291i	0.718872	+	0.695143i	$0.244659\pi$
$828$		0			0
$829$			10.3444i			0.359276i	0.983733	+	0.179638i	$0.0574926\pi$
$829$			10.3444i			0.359276i	−0.983733	+	0.179638i	$0.942507\pi$
$830$	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	$-0.770603\pi$
$839$	−43.5272			−1.50273			−0.751363	+	0.659889i	$0.770603\pi$
$840$		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	−0.707669	−	0.706544i	$-0.750253\pi$
$853$	−0.0328516	+	0.0328516i	−0.00112482	+	0.00112482i	0.706544	+	0.707669i	$0.250253\pi$
$854$	3.42296			0.117131
$855$		0			0
$856$	20.9926			0.717513
$857$	32.6070	−	32.6070i	1.11384	−	1.11384i	0.121208	−	0.992627i	$-0.461323\pi$
$857$	32.6070	−	32.6070i	1.11384	−	1.11384i	0.992627	−	0.121208i	$-0.0386769\pi$
$858$		0			0
$859$		−	3.46726i		−	0.118301i	−0.998249	−	0.0591506i	$-0.981161\pi$
$859$		−	3.46726i		−	0.118301i	0.998249	−	0.0591506i	$-0.0188392\pi$
$860$	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	−0.996477	−	0.0838692i	$-0.973272\pi$
$863$	−31.7372	−	31.7372i	−1.08035	−	1.08035i	−0.0838692	−	0.996477i	$-0.526728\pi$
$864$		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	0.608793	−	0.793329i	$-0.291654\pi$
$877$	−5.46491	−	5.46491i	−0.184537	−	0.184537i	−0.793329	+	0.608793i	$0.791654\pi$
$878$	−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	−0.532064	−	0.846704i	$-0.678584\pi$
$883$	9.34962	−	9.34962i	0.314640	−	0.314640i	0.846704	+	0.532064i	$0.178584\pi$
$884$	61.8630			2.08068
$885$		0			0
$886$	38.3320			1.28779
$887$	−32.1054	+	32.1054i	−1.07799	+	1.07799i	−0.0813035	+	0.996689i	$0.525908\pi$
$887$	−32.1054	+	32.1054i	−1.07799	+	1.07799i	−0.996689	+	0.0813035i	$0.974092\pi$
$888$		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	0.745148	−	0.666899i	$-0.232379\pi$
$907$	2.35659	+	2.35659i	0.0782493	+	0.0782493i	−0.666899	+	0.745148i	$0.732379\pi$
$908$	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	$0.160540\pi$
$919$			29.2988i			0.966478i	−0.875489	+	0.483239i	$0.839460\pi$
$920$	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	$-0.334196\pi$
$929$	30.3363			0.995301			0.497651	+	0.867378i	$0.334196\pi$
$930$		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	0.943417	−	0.331609i	$-0.107591\pi$
$937$	18.7277	+	18.7277i	0.611808	+	0.611808i	−0.331609	+	0.943417i	$0.607591\pi$
$938$	−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	$-0.618482\pi$
$947$	17.4742	−	17.4742i	0.567834	−	0.567834i	0.931521	+	0.363687i	$0.118482\pi$
$948$		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	$-0.495758\pi$
$953$	−30.4565	−	30.4565i	−0.986584	−	0.986584i	−0.999911	+	0.0133276i	$0.995758\pi$
$954$		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	0.353446	−	0.935455i	$-0.385010\pi$
$967$	−18.0985	−	18.0985i	−0.582009	−	0.582009i	−0.935455	+	0.353446i	$0.885010\pi$
$968$	−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	$-0.580957\pi$
$977$	22.3872	−	22.3872i	0.716231	−	0.716231i	0.967831	+	0.251601i	$0.0809569\pi$
$978$		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	$-0.455520\pi$
$983$	−26.6802	−	26.6802i	−0.850968	−	0.850968i	−0.990252	+	0.139285i	$0.955520\pi$
$984$		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	0.997673	+	0.0681847i	$0.0217207\pi$
$997$	33.6548	+	33.6548i	1.06586	+	1.06586i	0.0681847	+	0.997673i	$0.478279\pi$
$998$	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.a.197.5	yes	12
3.2	odd	2		315.2.m.b.197.2	yes	12
5.2	odd	4		1575.2.m.d.1268.5		12
5.3	odd	4		315.2.m.b.8.2	yes	12
5.4	even	2		1575.2.m.c.1457.2		12
15.2	even	4		1575.2.m.c.1268.2		12
15.8	even	4	inner	315.2.m.a.8.5	✓	12
15.14	odd	2		1575.2.m.d.1457.5		12

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

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

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