LMFDB - Embedded newform 336.2.bc.f.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 $ x^16 - 6x^15 + 19x^14 - 42x^13 + 65x^12 - 48x^11 - 94x^10 + 444x^9 - 962x^8 + 1332x^7 - 846x^6 - 1296x^5 + 5265x^4 - 10206x^3 + 13851x^2 - 13122*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.7
Root			$0.934861 + 1.45809i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.2.bc.f.257.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45809 - 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.23495 + 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +O(q^{10})$	\(q+(1.45809 - 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.23495 + 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +(0.309539 + 0.178712i) q^{11} -4.04570i q^{13} +(-5.84742 - 3.02246i) q^{15} +(-0.0519689 + 0.0900129i) q^{17} +(2.12615 - 1.22753i) q^{19} +(-1.93502 + 4.15400i) q^{21} +(-1.15188 + 0.665037i) q^{23} +(-4.72127 + 8.17749i) q^{25} +(-0.723015 - 5.14560i) q^{27} -4.97265i q^{29} +(6.83007 + 3.94335i) q^{31} +(0.618407 - 0.0287968i) q^{33} +(8.90704 + 4.66504i) q^{35} +(5.45622 + 9.45046i) q^{37} +(-3.78216 - 5.89900i) q^{39} +6.15464 q^{41} -0.502751 q^{43} +(-11.3517 + 1.05950i) q^{45} +(-5.72578 - 9.91734i) q^{47} +(2.99000 - 6.32929i) q^{49} +(0.00837401 + 0.179831i) q^{51} +(5.08143 + 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(-3.77364 + 6.53614i) q^{59} +(8.20485 - 4.73707i) q^{61} +(1.06198 + 7.86589i) q^{63} +(-13.3151 + 7.68750i) q^{65} +(1.34375 - 2.32744i) q^{67} +(-1.05783 + 2.04653i) q^{69} +5.78975i q^{71} +(-0.203925 - 0.117736i) q^{73} +(0.760762 + 16.3373i) q^{75} +(-0.944856 + 0.0388878i) q^{77} +(1.61247 + 2.79289i) q^{79} +(-5.86465 - 6.82685i) q^{81} +9.07747 q^{83} +0.394999 q^{85} +(-4.64874 - 7.25058i) q^{87} +(3.41213 + 5.90999i) q^{89} +(5.72862 + 9.04192i) q^{91} +(13.6454 - 0.635411i) q^{93} +(-8.08008 - 4.66504i) q^{95} +5.14243i q^{97} +(0.874774 - 0.620114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^7 + 2 * q^9	$ 16 q - 4 q^{7} + 2 q^{9} - 8 q^{15} + 6 q^{19} + 14 q^{21} - 18 q^{25} + 48 q^{31} - 12 q^{33} - 2 q^{37} + 22 q^{39} - 20 q^{43} - 42 q^{45} - 28 q^{49} - 6 q^{51} - 8 q^{57} + 36 q^{61} + 32 q^{63} - 14 q^{67} + 30 q^{73} - 54 q^{75} - 28 q^{79} + 30 q^{81} + 16 q^{85} - 78 q^{87} - 66 q^{91} + 16 q^{93} - 20 q^{99}+O(q^{100}) $ 16 * q - 4 * q^7 + 2 * q^9 - 8 * q^15 + 6 * q^19 + 14 * q^21 - 18 * q^25 + 48 * q^31 - 12 * q^33 - 2 * q^37 + 22 * q^39 - 20 * q^43 - 42 * q^45 - 28 * q^49 - 6 * q^51 - 8 * q^57 + 36 * q^61 + 32 * q^63 - 14 * q^67 + 30 * q^73 - 54 * q^75 - 28 * q^79 + 30 * q^81 + 16 * q^85 - 78 * q^87 - 66 * q^91 + 16 * q^93 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.45809	−	0.934861i	0.841830	−	0.539743i
$3$	1.45809	−	0.934861i	0.841830	−	0.539743i
$4$		0			0
$5$	−1.90017	−	3.29119i	−0.849781	−	1.47186i	−0.881404	−	0.472364i	$-0.843401\pi$
$5$	−1.90017	−	3.29119i	−0.849781	−	1.47186i	0.0316229	−	0.999500i	$-0.489932\pi$
$6$		0			0
$7$	−2.23495	+	1.41598i	−0.844732	+	0.535190i
$7$	−2.23495	+	1.41598i	−0.844732	+	0.535190i
$8$		0			0
$9$	1.25207	−	2.72623i	0.417356	−	0.908743i
$10$		0			0
$11$	0.309539	+	0.178712i	0.0933294	+	0.0538838i	0.545938	−	0.837825i	$-0.316173\pi$
$11$	0.309539	+	0.178712i	0.0933294	+	0.0538838i	−0.452609	+	0.891709i	$0.649507\pi$
$12$		0			0
$13$		−	4.04570i		−	1.12207i	−0.827791	−	0.561037i	$-0.810403\pi$
$13$		−	4.04570i		−	1.12207i	0.827791	−	0.561037i	$-0.189597\pi$
$14$		0			0
$15$	−5.84742	−	3.02246i	−1.50980	−	0.780396i
$16$		0			0
$17$	−0.0519689	+	0.0900129i	−0.0126043	+	0.0218313i	−0.872259	−	0.489045i	$-0.837346\pi$
$17$	−0.0519689	+	0.0900129i	−0.0126043	+	0.0218313i	0.859654	+	0.510876i	$0.170679\pi$
$18$		0			0
$19$	2.12615	−	1.22753i	0.487772	−	0.281615i	−0.235878	−	0.971783i	$-0.575796\pi$
$19$	2.12615	−	1.22753i	0.487772	−	0.281615i	0.723650	+	0.690167i	$0.242463\pi$
$20$		0			0
$21$	−1.93502	+	4.15400i	−0.422256	+	0.906477i
$22$		0			0
$23$	−1.15188	+	0.665037i	−0.240183	+	0.138670i	−0.615261	−	0.788323i	$-0.710949\pi$
$23$	−1.15188	+	0.665037i	−0.240183	+	0.138670i	0.375078	+	0.926993i	$0.377616\pi$
$24$		0			0
$25$	−4.72127	+	8.17749i	−0.944255	+	1.63550i
$26$		0			0
$27$	−0.723015	−	5.14560i	−0.139144	−	0.990272i
$28$		0			0
$29$		−	4.97265i		−	0.923398i	−0.887037	−	0.461699i	$-0.847240\pi$
$29$		−	4.97265i		−	0.923398i	0.887037	−	0.461699i	$-0.152760\pi$
$30$		0			0
$31$	6.83007	+	3.94335i	1.22672	+	0.708246i	0.966342	−	0.257262i	$-0.0828202\pi$
$31$	6.83007	+	3.94335i	1.22672	+	0.708246i	0.260376	+	0.965507i	$0.416154\pi$
$32$		0			0
$33$	0.618407	−	0.0287968i	0.107651	−	0.00501288i
$34$		0			0
$35$	8.90704	+	4.66504i	1.50556	+	0.788535i
$36$		0			0
$37$	5.45622	+	9.45046i	0.896998	+	1.55365i	0.831312	+	0.555805i	$0.187590\pi$
$37$	5.45622	+	9.45046i	0.896998	+	1.55365i	0.0656853	+	0.997840i	$0.479077\pi$
$38$		0			0
$39$	−3.78216	−	5.89900i	−0.605631	−	0.944596i
$40$		0			0
$41$	6.15464			0.961193			0.480597	−	0.876942i	$-0.340420\pi$
$41$	6.15464			0.961193			0.480597	+	0.876942i	$0.340420\pi$
$42$		0			0
$43$	−0.502751			−0.0766688			−0.0383344	−	0.999265i	$-0.512205\pi$
$43$	−0.502751			−0.0766688			−0.0383344	+	0.999265i	$0.512205\pi$
$44$		0			0
$45$	−11.3517	+	1.05950i	−1.69221	+	0.157941i
$46$		0			0
$47$	−5.72578	−	9.91734i	−0.835190	−	1.44659i	−0.893875	−	0.448316i	$-0.852024\pi$
$47$	−5.72578	−	9.91734i	−0.835190	−	1.44659i	0.0586849	−	0.998277i	$-0.481309\pi$
$48$		0			0
$49$	2.99000	−	6.32929i	0.427143	−	0.904184i
$50$		0			0
$51$	0.00837401	+	0.179831i	0.00117260	+	0.0251814i
$52$		0			0
$53$	5.08143	+	2.93376i	0.697988	+	0.402983i	0.806597	−	0.591101i	$-0.201307\pi$
$53$	5.08143	+	2.93376i	0.697988	+	0.402983i	−0.108610	+	0.994084i	$0.534640\pi$
$54$		0			0
$55$		−	1.35833i		−	0.183158i
$56$		0			0
$57$	1.95255	−	3.77751i	0.258622	−	0.500344i
$58$		0			0
$59$	−3.77364	+	6.53614i	−0.491286	+	0.850933i	−0.999950	−	0.0100329i	$-0.996806\pi$
$59$	−3.77364	+	6.53614i	−0.491286	+	0.850933i	0.508664	+	0.860965i	$0.330140\pi$
$60$		0			0
$61$	8.20485	−	4.73707i	1.05052	−	0.606520i	0.127727	−	0.991809i	$-0.459232\pi$
$61$	8.20485	−	4.73707i	1.05052	−	0.606520i	0.922796	+	0.385289i	$0.125898\pi$
$62$		0			0
$63$	1.06198	+	7.86589i	0.133797	+	0.991009i
$64$		0			0
$65$	−13.3151	+	7.68750i	−1.65154	+	0.953517i
$66$		0			0
$67$	1.34375	−	2.32744i	0.164165	−	0.284342i	−0.772193	−	0.635388i	$-0.780840\pi$
$67$	1.34375	−	2.32744i	0.164165	−	0.284342i	0.936358	+	0.351045i	$0.114174\pi$
$68$		0			0
$69$	−1.05783	+	2.04653i	−0.127348	+	0.246374i
$70$		0			0
$71$			5.78975i			0.687117i	0.939131	+	0.343558i	$0.111632\pi$
$71$			5.78975i			0.687117i	−0.939131	+	0.343558i	$0.888368\pi$
$72$		0			0
$73$	−0.203925	−	0.117736i	−0.0238676	−	0.0137800i	0.488019	−	0.872833i	$-0.337720\pi$
$73$	−0.203925	−	0.117736i	−0.0238676	−	0.0137800i	−0.511886	+	0.859053i	$0.671053\pi$
$74$		0			0
$75$	0.760762	+	16.3373i	0.0878453	+	1.88647i
$76$		0			0
$77$	−0.944856	+	0.0388878i	−0.107676	+	0.00443168i
$78$		0			0
$79$	1.61247	+	2.79289i	0.181418	+	0.314224i	0.942364	−	0.334591i	$-0.108598\pi$
$79$	1.61247	+	2.79289i	0.181418	+	0.314224i	−0.760946	+	0.648815i	$0.775265\pi$
$80$		0			0
$81$	−5.86465	−	6.82685i	−0.651628	−	0.758539i
$82$		0			0
$83$	9.07747			0.996382			0.498191	−	0.867067i	$-0.333998\pi$
$83$	9.07747			0.996382			0.498191	+	0.867067i	$0.333998\pi$
$84$		0			0
$85$	0.394999			0.0428436
$86$		0			0
$87$	−4.64874	−	7.25058i	−0.498397	−	0.777344i
$88$		0			0
$89$	3.41213	+	5.90999i	0.361685	+	0.626457i	0.988238	−	0.152921i	$-0.0488681\pi$
$89$	3.41213	+	5.90999i	0.361685	+	0.626457i	−0.626553	+	0.779379i	$0.715535\pi$
$90$		0			0
$91$	5.72862	+	9.04192i	0.600523	+	0.947851i
$92$		0			0
$93$	13.6454	−	0.635411i	1.41496	−	0.0658890i
$94$		0			0
$95$	−8.08008	−	4.66504i	−0.828999	−	0.478623i
$96$		0			0
$97$			5.14243i			0.522134i	0.965321	+	0.261067i	$0.0840744\pi$
$97$			5.14243i			0.522134i	−0.965321	+	0.261067i	$0.915926\pi$
$98$		0			0
$99$	0.874774	−	0.620114i	0.0879181	−	0.0623238i
$100$		0			0
$101$	−6.43891	+	11.1525i	−0.640695	+	1.10972i	0.344583	+	0.938756i	$0.388020\pi$
$101$	−6.43891	+	11.1525i	−0.640695	+	1.10972i	−0.985278	+	0.170960i	$0.945313\pi$
$102$		0			0
$103$	−4.88120	+	2.81816i	−0.480959	+	0.277682i	−0.720816	−	0.693126i	$-0.756233\pi$
$103$	−4.88120	+	2.81816i	−0.480959	+	0.277682i	0.239857	+	0.970808i	$0.422899\pi$
$104$		0			0
$105$	17.3484	−	1.52479i	1.69303	−	0.148804i
$106$		0			0
$107$	−7.62737	+	4.40366i	−0.737365	+	0.425718i	−0.821111	−	0.570769i	$-0.806645\pi$
$107$	−7.62737	+	4.40366i	−0.737365	+	0.425718i	0.0837453	+	0.996487i	$0.473312\pi$
$108$		0			0
$109$	2.23862	−	3.87741i	0.214421	−	0.371389i	−0.738672	−	0.674065i	$-0.764547\pi$
$109$	2.23862	−	3.87741i	0.214421	−	0.371389i	0.953093	+	0.302676i	$0.0978801\pi$
$110$		0			0
$111$	16.7905	+	8.67883i	1.59369	+	0.823758i
$112$		0			0
$113$		−	4.00000i		−	0.376288i	−0.982141	−	0.188144i	$-0.939753\pi$
$113$		−	4.00000i		−	0.376288i	0.982141	−	0.188144i	$-0.0602472\pi$
$114$		0			0
$115$	4.37753	+	2.52737i	0.408206	+	0.235678i
$116$		0			0
$117$	−11.0295	−	5.06549i	−1.01968	−	0.468304i
$118$		0			0
$119$	−0.0113084	−	0.274761i	−0.00103664	−	0.0251873i
$120$		0			0
$121$	−5.43612	−	9.41564i	−0.494193	−	0.855968i
$122$		0			0
$123$	8.97404	−	5.75374i	0.809162	−	0.518797i
$124$		0			0
$125$	16.8832			1.51008
$126$		0			0
$127$	−12.9198			−1.14645			−0.573223	−	0.819399i	$-0.694307\pi$
$127$	−12.9198			−1.14645			−0.573223	+	0.819399i	$0.694307\pi$
$128$		0			0
$129$	−0.733058	+	0.470003i	−0.0645421	+	0.0413814i
$130$		0			0
$131$	−2.66384	−	4.61391i	−0.232741	−	0.403119i	0.725873	−	0.687829i	$-0.241436\pi$
$131$	−2.66384	−	4.61391i	−0.232741	−	0.403119i	−0.958614	+	0.284710i	$0.908103\pi$
$132$		0			0
$133$	−3.01367	+	5.75406i	−0.261319	+	0.498940i
$134$		0			0
$135$	−15.5613	+	12.1571i	−1.33930	+	1.04632i
$136$		0			0
$137$	−4.37380	−	2.52521i	−0.373679	−	0.215744i	0.301386	−	0.953502i	$-0.402551\pi$
$137$	−4.37380	−	2.52521i	−0.373679	−	0.215744i	−0.675064	+	0.737759i	$0.735884\pi$
$138$		0			0
$139$		−	21.2651i		−	1.80368i	−0.432067	−	0.901841i	$-0.642216\pi$
$139$		−	21.2651i		−	1.80368i	0.432067	−	0.901841i	$-0.357784\pi$
$140$		0			0
$141$	−17.6200	−	9.10759i	−1.48388	−	0.766997i
$142$		0			0
$143$	0.723015	−	1.25230i	0.0604616	−	0.104723i
$144$		0			0
$145$	−16.3659	+	9.44887i	−1.35912	+	0.784686i
$146$		0			0
$147$	−1.55731	−	12.0239i	−0.128445	−	0.991717i
$148$		0			0
$149$	−10.5482	+	6.09001i	−0.864143	+	0.498913i	−0.865398	−	0.501086i	$-0.832934\pi$
$149$	−10.5482	+	6.09001i	−0.864143	+	0.498913i	0.00125437	+	0.999999i	$0.499601\pi$
$150$		0			0
$151$	−4.10880	+	7.11665i	−0.334369	+	0.579145i	−0.983363	−	0.181649i	$-0.941857\pi$
$151$	−4.10880	+	7.11665i	−0.334369	+	0.579145i	0.648994	+	0.760793i	$0.275190\pi$
$152$		0			0
$153$	0.180327	+	0.254381i	0.0145786	+	0.0205655i
$154$		0			0
$155$		−	29.9721i		−	2.40741i
$156$		0			0
$157$	11.2104	+	6.47230i	0.894683	+	0.516546i	0.875472	−	0.483270i	$-0.160551\pi$
$157$	11.2104	+	6.47230i	0.894683	+	0.516546i	0.0192119	+	0.999815i	$0.493884\pi$
$158$		0			0
$159$	10.1519	−	0.472732i	0.805094	−	0.0374901i
$160$		0			0
$161$	1.63271	−	3.11736i	0.128676	−	0.245683i
$162$		0			0
$163$	−1.09237	−	1.89205i	−0.0855613	−	0.148197i	0.820069	−	0.572265i	$-0.193935\pi$
$163$	−1.09237	−	1.89205i	−0.0855613	−	0.148197i	−0.905630	+	0.424068i	$0.860602\pi$
$164$		0			0
$165$	−1.26985	−	1.98058i	−0.0988579	−	0.154188i
$166$		0			0
$167$	−0.464592			−0.0359512			−0.0179756	−	0.999838i	$-0.505722\pi$
$167$	−0.464592			−0.0359512			−0.0179756	+	0.999838i	$0.505722\pi$
$168$		0			0
$169$	−3.36765			−0.259050
$170$		0			0
$171$	−0.684452	−	7.33333i	−0.0523414	−	0.560793i
$172$		0			0
$173$	4.62587	+	8.01224i	0.351698	+	0.609159i	0.986547	−	0.163477i	$-0.0522710\pi$
$173$	4.62587	+	8.01224i	0.351698	+	0.609159i	−0.634849	+	0.772636i	$0.718938\pi$
$174$		0			0
$175$	−1.02735	−	24.9615i	−0.0776603	−	1.88691i
$176$		0			0
$177$	0.608065	+	13.0581i	0.0457050	+	0.981509i
$178$		0			0
$179$	−1.77096	−	1.02246i	−0.132367	−	0.0764224i	0.432354	−	0.901704i	$-0.357683\pi$
$179$	−1.77096	−	1.02246i	−0.132367	−	0.0764224i	−0.564722	+	0.825282i	$0.691016\pi$
$180$		0			0
$181$		−	17.6193i		−	1.30963i	−0.755790	−	0.654815i	$-0.772747\pi$
$181$		−	17.6193i		−	1.30963i	0.755790	−	0.654815i	$-0.227253\pi$
$182$		0			0
$183$	7.53492	−	14.5775i	0.556998	−	1.07760i
$184$		0			0
$185$	20.7355	−	35.9149i	1.52450	−	2.64052i
$186$		0			0
$187$	−0.0321728	+	0.0185750i	−0.00235271	+	0.00135834i
$188$		0			0
$189$	8.90198	+	10.4764i	0.647524	+	0.762045i
$190$		0			0
$191$	19.4811	−	11.2474i	1.40960	−	0.813834i	0.414252	−	0.910162i	$-0.364043\pi$
$191$	19.4811	−	11.2474i	1.40960	−	0.813834i	0.995350	+	0.0963279i	$0.0307097\pi$
$192$		0			0
$193$	−4.81985	+	8.34823i	−0.346940	+	0.600918i	−0.985704	−	0.168484i	$-0.946113\pi$
$193$	−4.81985	+	8.34823i	−0.346940	+	0.600918i	0.638764	+	0.769403i	$0.279446\pi$
$194$		0			0
$195$	−12.2280	+	23.6569i	−0.875662	+	1.69411i
$196$		0			0
$197$		−	15.3750i		−	1.09542i	−0.836667	−	0.547712i	$-0.815499\pi$
$197$		−	15.3750i		−	1.09542i	0.836667	−	0.547712i	$-0.184501\pi$
$198$		0			0
$199$	3.96967	+	2.29189i	0.281403	+	0.162468i	0.634058	−	0.773285i	$-0.281388\pi$
$199$	3.96967	+	2.29189i	0.281403	+	0.162468i	−0.352656	+	0.935753i	$0.614721\pi$
$200$		0			0
$201$	−0.216525	−	4.64985i	−0.0152725	−	0.327975i
$202$		0			0
$203$	7.04117	+	11.1136i	0.494194	+	0.780023i
$204$		0			0
$205$	−11.6948	−	20.2561i	−0.816804	−	1.41475i
$206$		0			0
$207$	0.370814	+	3.97296i	0.0257734	+	0.276140i
$208$		0			0
$209$	0.877501			0.0606980
$210$		0			0
$211$	0.870400			0.0599208			0.0299604	−	0.999551i	$-0.490462\pi$
$211$	0.870400			0.0599208			0.0299604	+	0.999551i	$0.490462\pi$
$212$		0			0
$213$	5.41261	+	8.44199i	0.370866	+	0.578436i
$214$		0			0
$215$	0.955311	+	1.65465i	0.0651517	+	0.112846i
$216$		0			0
$217$	−20.8486	+	0.858072i	−1.41529	+	0.0582497i
$218$		0			0
$219$	−0.407409	+	0.0189714i	−0.0275301	+	0.00128197i
$220$		0			0
$221$	0.364165	+	0.210251i	0.0244964	+	0.0141430i
$222$		0			0
$223$			1.21373i			0.0812777i	0.999174	+	0.0406388i	$0.0129393\pi$
$223$			1.21373i			0.0812777i	−0.999174	+	0.0406388i	$0.987061\pi$
$224$		0			0
$225$	16.3823	+	23.1100i	1.09216	+	1.54067i
$226$		0			0
$227$	−6.67205	+	11.5563i	−0.442840	+	0.767021i	−0.997899	−	0.0647898i	$-0.979362\pi$
$227$	−6.67205	+	11.5563i	−0.442840	+	0.767021i	0.555059	+	0.831811i	$0.312696\pi$
$228$		0			0
$229$	9.60627	−	5.54618i	0.634800	−	0.366502i	−0.147808	−	0.989016i	$-0.547222\pi$
$229$	9.60627	−	5.54618i	0.634800	−	0.366502i	0.782609	+	0.622514i	$0.213889\pi$
$230$		0			0
$231$	−1.34133	+	0.940012i	−0.0882533	+	0.0618482i
$232$		0			0
$233$	−7.08411	+	4.09001i	−0.464095	+	0.267946i	−0.713765	−	0.700386i	$-0.753011\pi$
$233$	−7.08411	+	4.09001i	−0.464095	+	0.267946i	0.249669	+	0.968331i	$0.419678\pi$
$234$		0			0
$235$	−21.7599	+	37.6892i	−1.41946	+	2.45857i
$236$		0			0
$237$	4.96210	+	2.56485i	0.322323	+	0.166605i
$238$		0			0
$239$			22.5944i			1.46151i	0.682638	+	0.730757i	$0.260833\pi$
$239$			22.5944i			1.46151i	−0.682638	+	0.730757i	$0.739167\pi$
$240$		0			0
$241$	4.24127	+	2.44870i	0.273205	+	0.157735i	0.630343	−	0.776317i	$-0.282914\pi$
$241$	4.24127	+	2.44870i	0.273205	+	0.157735i	−0.357138	+	0.934051i	$0.616248\pi$
$242$		0			0
$243$	−14.9334	−	4.47154i	−0.957976	−	0.286850i
$244$		0			0
$245$	−26.5124	+	2.18606i	−1.69381	+	0.139662i
$246$		0			0
$247$	−4.96622	−	8.60175i	−0.315993	−	0.547316i
$248$		0			0
$249$	13.2358	−	8.48618i	0.838785	−	0.537790i
$250$		0			0
$251$	−9.17857			−0.579346			−0.289673	−	0.957126i	$-0.593547\pi$
$251$	−9.17857			−0.579346			−0.289673	+	0.957126i	$0.593547\pi$
$252$		0			0
$253$	−0.475401			−0.0298882
$254$		0			0
$255$	0.575945	−	0.369269i	0.0360671	−	0.0231245i
$256$		0			0
$257$	6.31055	+	10.9302i	0.393641	+	0.681806i	0.992927	−	0.118729i	$-0.0378819\pi$
$257$	6.31055	+	10.9302i	0.393641	+	0.681806i	−0.599286	+	0.800535i	$0.704549\pi$
$258$		0			0
$259$	−25.5760	−	13.3954i	−1.58922	−	0.832349i
$260$		0			0
$261$	−13.5566	−	6.22610i	−0.839132	−	0.385386i
$262$		0			0
$263$	25.2489	+	14.5775i	1.55692	+	0.898886i	0.997549	+	0.0699665i	$0.0222892\pi$
$263$	25.2489	+	14.5775i	1.55692	+	0.898886i	0.559367	+	0.828920i	$0.311044\pi$
$264$		0			0
$265$		−	22.2986i		−	1.36979i
$266$		0			0
$267$	10.5002	+	5.42744i	0.642603	+	0.332154i
$268$		0			0
$269$	2.23640	−	3.87356i	0.136356	−	0.236175i	−0.789759	−	0.613418i	$-0.789794\pi$
$269$	2.23640	−	3.87356i	0.136356	−	0.236175i	0.926115	+	0.377242i	$0.123128\pi$
$270$		0			0
$271$	14.4985	−	8.37071i	0.880721	−	0.508485i	0.00982495	−	0.999952i	$-0.496873\pi$
$271$	14.4985	−	8.37071i	0.880721	−	0.508485i	0.870896	+	0.491467i	$0.163539\pi$
$272$		0			0
$273$	16.8058	+	7.82849i	1.01713	+	0.473802i
$274$		0			0
$275$	−2.92283	+	1.68750i	−0.176254	+	0.101760i
$276$		0			0
$277$	−0.510924	+	0.884946i	−0.0306984	+	0.0531713i	−0.880966	−	0.473179i	$-0.843106\pi$
$277$	−0.510924	+	0.884946i	−0.0306984	+	0.0531713i	0.850268	+	0.526350i	$0.176440\pi$
$278$		0			0
$279$	19.3022	−	13.6830i	1.15559	−	0.819181i
$280$		0			0
$281$			13.9453i			0.831907i	0.909386	+	0.415953i	$0.136552\pi$
$281$			13.9453i			0.831907i	−0.909386	+	0.415953i	$0.863448\pi$
$282$		0			0
$283$	−14.0386	−	8.10519i	−0.834508	−	0.481803i	0.0208856	−	0.999782i	$-0.493351\pi$
$283$	−14.0386	−	8.10519i	−0.834508	−	0.481803i	−0.855394	+	0.517978i	$0.826685\pi$
$284$		0			0
$285$	−16.1427	+	0.751701i	−0.956209	+	0.0445269i
$286$		0			0
$287$	−13.7553	+	8.71485i	−0.811950	+	0.514421i
$288$		0			0
$289$	8.49460	+	14.7131i	0.499682	+	0.865475i
$290$		0			0
$291$	4.80746	+	7.49814i	0.281818	+	0.439549i
$292$		0			0
$293$	−19.2067			−1.12207			−0.561034	−	0.827793i	$-0.689596\pi$
$293$	−19.2067			−1.12207			−0.561034	+	0.827793i	$0.689596\pi$
$294$		0			0
$295$	28.6822			1.66994
$296$		0			0
$297$	0.695781	−	1.72198i	0.0403733	−	0.0999192i
$298$		0			0
$299$	2.69054	+	4.66015i	0.155598	+	0.269503i
$300$		0			0
$301$	1.12362	−	0.711886i	0.0647646	−	0.0410324i
$302$		0			0
$303$	1.03753	+	22.2809i	0.0596047	+	1.28000i
$304$		0			0
$305$	−31.1812	−	18.0025i	−1.78543	−	1.03082i
$306$		0			0
$307$			0.480498i			0.0274235i	0.999906	+	0.0137117i	$0.00436472\pi$
$307$			0.480498i			0.0274235i	−0.999906	+	0.0137117i	$0.995635\pi$
$308$		0			0
$309$	−4.48265	+	8.67239i	−0.255009	+	0.493355i
$310$		0			0
$311$	−4.66653	+	8.08266i	−0.264615	+	0.458326i	−0.967463	−	0.253014i	$-0.918578\pi$
$311$	−4.66653	+	8.08266i	−0.264615	+	0.458326i	0.702848	+	0.711340i	$0.251911\pi$
$312$		0			0
$313$	15.5147	−	8.95742i	0.876943	−	0.506303i	0.00729351	−	0.999973i	$-0.497678\pi$
$313$	15.5147	−	8.95742i	0.876943	−	0.506303i	0.869649	+	0.493670i	$0.164345\pi$
$314$		0			0
$315$	23.8702	−	18.4417i	1.34493	−	1.03907i
$316$		0			0
$317$	19.3275	−	11.1587i	1.08554	−	0.626736i	0.153153	−	0.988202i	$-0.451057\pi$
$317$	19.3275	−	11.1587i	1.08554	−	0.626736i	0.932385	+	0.361467i	$0.117724\pi$
$318$		0			0
$319$	0.888674	−	1.53923i	0.0497562	−	0.0861802i
$320$		0			0
$321$	−7.00459	+	13.5515i	−0.390958	+	0.756370i
$322$		0			0
$323$			0.255174i			0.0141983i
$324$		0			0
$325$	33.0836	+	19.1008i	1.83515	+	1.05952i
$326$		0			0
$327$	−0.360721	−	7.74643i	−0.0199479	−	0.428378i
$328$		0			0
$329$	26.8396	+	14.0572i	1.47971	+	0.774996i
$330$		0			0
$331$	7.05860	+	12.2259i	0.387976	+	0.671994i	0.992177	−	0.124838i	$-0.0398411\pi$
$331$	7.05860	+	12.2259i	0.387976	+	0.671994i	−0.604201	+	0.796832i	$0.706508\pi$
$332$		0			0
$333$	32.5957	−	3.04230i	1.78623	−	0.166717i
$334$		0			0
$335$	−10.2134			−0.558018
$336$		0			0
$337$	−18.4042			−1.00254			−0.501270	−	0.865291i	$-0.667134\pi$
$337$	−18.4042			−1.00254			−0.501270	+	0.865291i	$0.667134\pi$
$338$		0			0
$339$	−3.73945	−	5.83237i	−0.203099	−	0.316771i
$340$		0			0
$341$	1.40945	+	2.44124i	0.0763259	+	0.132200i
$342$		0			0
$343$	2.27965	+	18.3794i	0.123089	+	0.992396i
$344$		0			0
$345$	8.74557	−	0.407247i	0.470846	−	0.0219254i
$346$		0			0
$347$	−27.6474	−	15.9623i	−1.48419	−	0.856899i	−0.484354	−	0.874872i	$-0.660945\pi$
$347$	−27.6474	−	15.9623i	−1.48419	−	0.856899i	−0.999838	+	0.0179729i	$0.994279\pi$
$348$		0			0
$349$			14.7367i			0.788840i	0.918930	+	0.394420i	$0.129055\pi$
$349$			14.7367i			0.788840i	−0.918930	+	0.394420i	$0.870945\pi$
$350$		0			0
$351$	−20.8175	+	2.92510i	−1.11116	+	0.156130i
$352$		0			0
$353$	−13.5686	+	23.5016i	−0.722185	+	1.25086i	0.237937	+	0.971281i	$0.423529\pi$
$353$	−13.5686	+	23.5016i	−0.722185	+	1.25086i	−0.960122	+	0.279581i	$0.909804\pi$
$354$		0			0
$355$	19.0551	−	11.0015i	1.01134	−	0.583899i
$356$		0			0
$357$	−0.273352	−	0.390055i	−0.0144673	−	0.0206439i
$358$		0			0
$359$	16.9479	−	9.78486i	0.894475	−	0.516425i	0.0190713	−	0.999818i	$-0.493929\pi$
$359$	16.9479	−	9.78486i	0.894475	−	0.516425i	0.875404	+	0.483393i	$0.160596\pi$
$360$		0			0
$361$	−6.48633	+	11.2346i	−0.341386	+	0.591297i
$362$		0			0
$363$	−16.7287	−	8.64686i	−0.878029	−	0.453842i
$364$		0			0
$365$			0.894875i			0.0468399i
$366$		0			0
$367$	1.16258	+	0.671213i	0.0606860	+	0.0350371i	0.530036	−	0.847975i	$-0.322178\pi$
$367$	1.16258	+	0.671213i	0.0606860	+	0.0350371i	−0.469350	+	0.883012i	$0.655512\pi$
$368$		0			0
$369$	7.70603	−	16.7790i	0.401160	−	0.873478i
$370$		0			0
$371$	−15.5109	+	0.638387i	−0.805285	+	0.0331434i
$372$		0			0
$373$	−6.52378	−	11.2995i	−0.337788	−	0.585066i	0.646228	−	0.763144i	$-0.276345\pi$
$373$	−6.52378	−	11.2995i	−0.337788	−	0.585066i	−0.984016	+	0.178078i	$0.943012\pi$
$374$		0			0
$375$	24.6172	−	15.7834i	1.27123	−	0.815053i
$376$		0			0
$377$	−20.1178			−1.03612
$378$		0			0
$379$	20.0822			1.03156			0.515778	−	0.856722i	$-0.327503\pi$
$379$	20.0822			1.03156			0.515778	+	0.856722i	$0.327503\pi$
$380$		0			0
$381$	−18.8383	+	12.0782i	−0.965113	+	0.618786i
$382$		0			0
$383$	11.2613	+	19.5052i	0.575428	+	0.996670i	0.995995	+	0.0894085i	$0.0284977\pi$
$383$	11.2613	+	19.5052i	0.575428	+	0.996670i	−0.420567	+	0.907261i	$0.638169\pi$
$384$		0			0
$385$	1.92337	+	3.03581i	0.0980242	+	0.154719i
$386$		0			0
$387$	−0.629479	+	1.37061i	−0.0319982	+	0.0696723i
$388$		0			0
$389$	32.1899	+	18.5848i	1.63209	+	0.942289i	0.983447	+	0.181197i	$0.0579973\pi$
$389$	32.1899	+	18.5848i	1.63209	+	0.942289i	0.648645	+	0.761091i	$0.275336\pi$
$390$		0			0
$391$		−	0.138245i		−	0.00699136i
$392$		0			0
$393$	−8.19750	−	4.23719i	−0.413509	−	0.213738i
$394$		0			0
$395$	6.12795	−	10.6139i	0.308330	−	0.534044i
$396$		0			0
$397$	−24.0288	+	13.8730i	−1.20597	+	0.696268i	−0.961877	−	0.273483i	$-0.911824\pi$
$397$	−24.0288	+	13.8730i	−1.20597	+	0.696268i	−0.244095	+	0.969751i	$0.578491\pi$
$398$		0			0
$399$	0.985032	+	11.2073i	0.0493133	+	0.561068i
$400$		0			0
$401$	19.7233	−	11.3872i	0.984933	−	0.568651i	0.0811773	−	0.996700i	$-0.474132\pi$
$401$	19.7233	−	11.3872i	0.984933	−	0.568651i	0.903756	+	0.428048i	$0.140799\pi$
$402$		0			0
$403$	15.9536	−	27.6324i	0.794704	−	1.37647i
$404$		0			0
$405$	−11.3246	+	32.2738i	−0.562725	+	1.60370i
$406$		0			0
$407$			3.90038i			0.193334i
$408$		0			0
$409$	−22.6849	−	13.0972i	−1.12170	−	0.647613i	−0.179865	−	0.983691i	$-0.557566\pi$
$409$	−22.6849	−	13.0972i	−1.12170	−	0.647613i	−0.941834	+	0.336078i	$0.890899\pi$
$410$		0			0
$411$	−8.73813	+	0.406900i	−0.431020	+	0.0200709i
$412$		0			0
$413$	−0.821144	−	19.9513i	−0.0404059	−	0.981741i
$414$		0			0
$415$	−17.2487	−	29.8757i	−0.846707	−	1.46654i
$416$		0			0
$417$	−19.8799	−	31.0065i	−0.973524	−	1.51839i
$418$		0			0
$419$	8.93992			0.436744			0.218372	−	0.975866i	$-0.429925\pi$
$419$	8.93992			0.436744			0.218372	+	0.975866i	$0.429925\pi$
$420$		0			0
$421$	−5.00735			−0.244043			−0.122022	−	0.992527i	$-0.538938\pi$
$421$	−5.00735			−0.244043			−0.122022	+	0.992527i	$0.538938\pi$
$422$		0			0
$423$	−34.2060	+	3.19260i	−1.66315	+	0.155229i
$424$		0			0
$425$	−0.490719	−	0.849951i	−0.0238034	−	0.0412287i
$426$		0			0
$427$	−11.6298	+	22.2050i	−0.562807	+	1.07458i
$428$		0			0
$429$	−0.116503	−	2.50189i	−0.00562482	−	0.120792i
$430$		0			0
$431$	−5.62468	−	3.24741i	−0.270931	−	0.156422i	0.358379	−	0.933576i	$-0.383329\pi$
$431$	−5.62468	−	3.24741i	−0.270931	−	0.156422i	−0.629311	+	0.777154i	$0.716663\pi$
$432$		0			0
$433$			1.05254i			0.0505818i	0.999680	+	0.0252909i	$0.00805120\pi$
$433$			1.05254i			0.0505818i	−0.999680	+	0.0252909i	$0.991949\pi$
$434$		0			0
$435$	−15.0296	+	29.0772i	−0.720616	+	1.39414i
$436$		0			0
$437$	−1.63271	+	2.82794i	−0.0781032	+	0.135279i
$438$		0			0
$439$	−25.8990	+	14.9528i	−1.23609	+	0.713658i	−0.968293	−	0.249817i	$-0.919630\pi$
$439$	−25.8990	+	14.9528i	−1.23609	+	0.713658i	−0.267799	+	0.963475i	$0.586296\pi$
$440$		0			0
$441$	−13.5114	−	16.0761i	−0.643400	−	0.765530i
$442$		0			0
$443$	26.7104	−	15.4212i	1.26905	−	0.732685i	0.294240	−	0.955732i	$-0.404934\pi$
$443$	26.7104	−	15.4212i	1.26905	−	0.732685i	0.974808	+	0.223047i	$0.0716002\pi$
$444$		0			0
$445$	12.9672	−	22.4599i	0.614707	−	1.06470i
$446$		0			0
$447$	−9.68695	+	18.7409i	−0.458177	+	0.886415i
$448$		0			0
$449$			36.6953i			1.73176i	0.500253	+	0.865879i	$0.333240\pi$
$449$			36.6953i			1.73176i	−0.500253	+	0.865879i	$0.666760\pi$
$450$		0			0
$451$	1.90510	+	1.09991i	0.0897076	+	0.0517927i
$452$		0			0
$453$	0.662071	+	14.2179i	0.0311068	+	0.668015i
$454$		0			0
$455$	18.8733	−	36.0351i	0.884795	−	1.68935i
$456$		0			0
$457$	11.8750	+	20.5681i	0.555489	+	0.962135i	0.997865	+	0.0653057i	$0.0208022\pi$
$457$	11.8750	+	20.5681i	0.555489	+	0.962135i	−0.442376	+	0.896830i	$0.645864\pi$
$458$		0			0
$459$	0.500745	+	0.202331i	0.0233728	+	0.00944400i
$460$		0			0
$461$	10.5938			0.493404			0.246702	−	0.969091i	$-0.420653\pi$
$461$	10.5938			0.493404			0.246702	+	0.969091i	$0.420653\pi$
$462$		0			0
$463$	0.367649			0.0170861			0.00854305	−	0.999964i	$-0.497281\pi$
$463$	0.367649			0.0170861			0.00854305	+	0.999964i	$0.497281\pi$
$464$		0			0
$465$	−28.0197	−	43.7021i	−1.29938	−	2.02663i
$466$		0			0
$467$	−15.7847	−	27.3399i	−0.730428	−	1.26514i	−0.956700	−	0.291075i	$-0.905987\pi$
$467$	−15.7847	−	27.3399i	−0.730428	−	1.26514i	0.226272	−	0.974064i	$-0.427346\pi$
$468$		0			0
$469$	0.292400	+	7.10444i	0.0135018	+	0.328053i
$470$		0			0
$471$	22.3964	−	1.04291i	1.03197	−	0.0480549i
$472$		0			0
$473$	−0.155621	−	0.0898478i	−0.00715546	−	0.00413120i
$474$		0			0
$475$			23.1821i			1.06367i
$476$		0			0
$477$	14.3604	−	10.1799i	0.657518	−	0.466104i
$478$		0			0
$479$	6.01497	−	10.4182i	0.274831	−	0.476022i	−0.695261	−	0.718757i	$-0.744711\pi$
$479$	6.01497	−	10.4182i	0.274831	−	0.476022i	0.970093	+	0.242735i	$0.0780447\pi$
$480$		0			0
$481$	38.2337	−	22.0742i	1.74331	−	1.00650i
$482$		0			0
$483$	−0.533658	−	6.07176i	−0.0242823	−	0.276275i
$484$		0			0
$485$	16.9247	−	9.77148i	0.768511	−	0.443700i
$486$		0			0
$487$	−9.47737	+	16.4153i	−0.429461	+	0.743848i	−0.996825	−	0.0796188i	$-0.974630\pi$
$487$	−9.47737	+	16.4153i	−0.429461	+	0.743848i	0.567365	+	0.823467i	$0.307963\pi$
$488$		0			0
$489$	−3.36159	−	1.73756i	−0.152016	−	0.0785753i
$490$		0			0
$491$			15.8373i			0.714727i	0.933965	+	0.357364i	$0.116324\pi$
$491$			15.8373i			0.714727i	−0.933965	+	0.357364i	$0.883676\pi$
$492$		0			0
$493$	0.447602	+	0.258423i	0.0201590	+	0.0116388i
$494$		0			0
$495$	−3.70313	−	1.70073i	−0.166443	−	0.0764419i
$496$		0			0
$497$	−8.19817	−	12.9398i	−0.367738	−	0.580429i
$498$		0			0
$499$	10.0988	+	17.4916i	0.452084	+	0.783033i	0.998515	−	0.0544710i	$-0.0173473\pi$
$499$	10.0988	+	17.4916i	0.452084	+	0.783033i	−0.546431	+	0.837504i	$0.684014\pi$
$500$		0			0
$501$	−0.677418	+	0.434329i	−0.0302648	+	0.0194044i
$502$		0			0
$503$	−36.8663			−1.64379			−0.821893	−	0.569641i	$-0.807082\pi$
$503$	−36.8663			−1.64379			−0.821893	+	0.569641i	$0.807082\pi$
$504$		0			0
$505$	48.9400			2.17780
$506$		0			0
$507$	−4.91034	+	3.14829i	−0.218076	+	0.139820i
$508$		0			0
$509$	−5.13197	−	8.88884i	−0.227471	−	0.393991i	0.729587	−	0.683888i	$-0.239712\pi$
$509$	−5.13197	−	8.88884i	−0.227471	−	0.393991i	−0.957058	+	0.289897i	$0.906379\pi$
$510$		0			0
$511$	0.622475	−	0.0256194i	0.0275367	−	0.00113334i
$512$		0			0
$513$	−7.85364	−	10.0528i	−0.346747	−	0.443842i
$514$		0			0
$515$	18.5502	+	10.7100i	0.817419	+	0.471937i
$516$		0			0
$517$		−	4.09307i		−	0.180013i
$518$		0			0
$519$	14.2353	+	7.35804i	0.624859	+	0.322982i
$520$		0			0
$521$	7.98887	−	13.8371i	0.349999	−	0.606216i	−0.636250	−	0.771483i	$-0.719515\pi$
$521$	7.98887	−	13.8371i	0.349999	−	0.606216i	0.986249	+	0.165267i	$0.0528486\pi$
$522$		0			0
$523$	−0.676700	+	0.390693i	−0.0295900	+	0.0170838i	−0.514722	−	0.857357i	$-0.672105\pi$
$523$	−0.676700	+	0.390693i	−0.0295900	+	0.0170838i	0.485132	+	0.874441i	$0.338772\pi$
$524$		0			0
$525$	−24.8335	−	35.4358i	−1.08382	−	1.54654i
$526$		0			0
$527$	−0.709904	+	0.409863i	−0.0309239	+	0.0178539i
$528$		0			0
$529$	−10.6155	+	18.3865i	−0.461541	+	0.799413i
$530$		0			0
$531$	13.0942	+	18.4715i	0.568238	+	0.801595i
$532$		0			0
$533$		−	24.8998i		−	1.07853i
$534$		0			0
$535$	28.9865	+	16.7354i	1.25320	+	0.723534i
$536$		0			0
$537$	−3.53808	+	0.164754i	−0.152679	+	0.00710967i
$538$		0			0
$539$	2.05664	−	1.42481i	0.0885859	−	0.0613709i
$540$		0			0
$541$	3.63362	+	6.29362i	0.156222	+	0.270584i	0.933503	−	0.358569i	$-0.116735\pi$
$541$	3.63362	+	6.29362i	0.156222	+	0.270584i	−0.777282	+	0.629153i	$0.783402\pi$
$542$		0			0
$543$	−16.4716	−	25.6905i	−0.706863	−	1.10249i
$544$		0			0
$545$	−17.0150			−0.728845
$546$		0			0
$547$	−41.2546			−1.76392			−0.881960	−	0.471325i	$-0.843776\pi$
$547$	−41.2546			−1.76392			−0.881960	+	0.471325i	$0.843776\pi$
$548$		0			0
$549$	−2.64131	−	28.2994i	−0.112729	−	1.20779i
$550$		0			0
$551$	−6.10409	−	10.5726i	−0.260043	−	0.450408i
$552$		0			0
$553$	−7.55847	−	3.95873i	−0.321419	−	0.168342i
$554$		0			0
$555$	−3.34121	−	71.7521i	−0.141826	−	3.04571i
$556$		0			0
$557$	−5.48798	−	3.16849i	−0.232533	−	0.134253i	0.379207	−	0.925312i	$-0.376197\pi$
$557$	−5.48798	−	3.16849i	−0.232533	−	0.134253i	−0.611740	+	0.791059i	$0.709530\pi$
$558$		0			0
$559$			2.03398i			0.0860281i
$560$		0			0
$561$	−0.0295459	+	0.0571611i	−0.00124743	+	0.00241335i
$562$		0			0
$563$	7.73130	−	13.3910i	0.325836	−	0.564364i	−0.655846	−	0.754895i	$-0.727688\pi$
$563$	7.73130	−	13.3910i	0.325836	−	0.564364i	0.981681	+	0.190531i	$0.0610211\pi$
$564$		0			0
$565$	−13.1647	+	7.60067i	−0.553845	+	0.319763i
$566$		0			0
$567$	22.7739	+	6.95343i	0.956413	+	0.292017i
$568$		0			0
$569$	10.2364	−	5.90999i	0.429132	−	0.247760i	−0.269845	−	0.962904i	$-0.586972\pi$
$569$	10.2364	−	5.90999i	0.429132	−	0.247760i	0.698977	+	0.715144i	$0.253639\pi$
$570$		0			0
$571$	18.0386	−	31.2438i	0.754892	−	1.30751i	−0.190536	−	0.981680i	$-0.561023\pi$
$571$	18.0386	−	31.2438i	0.754892	−	1.30751i	0.945428	−	0.325831i	$-0.105644\pi$
$572$		0			0
$573$	17.8905	−	34.6119i	0.747385	−	1.44593i
$574$		0			0
$575$		−	12.5593i		−	0.523759i
$576$		0			0
$577$	−20.4253	−	11.7926i	−0.850316	−	0.490930i	0.0104412	−	0.999945i	$-0.496676\pi$
$577$	−20.4253	−	11.7926i	−0.850316	−	0.490930i	−0.860758	+	0.509015i	$0.830010\pi$
$578$		0			0
$579$	0.776646	+	16.6784i	0.0322763	+	0.693130i
$580$		0			0
$581$	−20.2877	+	12.8535i	−0.841676	+	0.533254i
$582$		0			0
$583$	1.04860	+	1.81623i	0.0434285	+	0.0752204i
$584$		0			0
$585$	4.28642	+	45.9254i	0.177222	+	1.89878i
$586$		0			0
$587$	−0.287490			−0.0118660			−0.00593298	−	0.999982i	$-0.501889\pi$
$587$	−0.287490			−0.0118660			−0.00593298	+	0.999982i	$0.501889\pi$
$588$		0			0
$589$	19.3623			0.797812
$590$		0			0
$591$	−14.3735	−	22.4182i	−0.591247	−	0.922160i
$592$		0			0
$593$	−5.71589	−	9.90021i	−0.234723	−	0.406553i	0.724469	−	0.689308i	$-0.242085\pi$
$593$	−5.71589	−	9.90021i	−0.234723	−	0.406553i	−0.959192	+	0.282755i	$0.908752\pi$
$594$		0			0
$595$	−0.882803	+	0.559311i	−0.0361914	+	0.0229295i
$596$		0			0
$597$	7.93076	−	0.369304i	0.324584	−	0.0151146i
$598$		0			0
$599$	−18.7842	−	10.8451i	−0.767502	−	0.443117i	0.0644810	−	0.997919i	$-0.479461\pi$
$599$	−18.7842	−	10.8451i	−0.767502	−	0.443117i	−0.831983	+	0.554802i	$0.812794\pi$
$600$		0			0
$601$			23.7036i			0.966889i	0.875375	+	0.483445i	$0.160615\pi$
$601$			23.7036i			0.966889i	−0.875375	+	0.483445i	$0.839385\pi$
$602$		0			0
$603$	−4.66268	−	6.57749i	−0.189879	−	0.267856i
$604$		0			0
$605$	−20.6591	+	35.7826i	−0.839912	+	1.45477i
$606$		0			0
$607$	18.5031	−	10.6828i	0.751017	−	0.433600i	−0.0750445	−	0.997180i	$-0.523910\pi$
$607$	18.5031	−	10.6828i	0.751017	−	0.433600i	0.826061	+	0.563580i	$0.190577\pi$
$608$		0			0
$609$	20.6564	+	9.62217i	0.837039	+	0.389910i
$610$		0			0
$611$	−40.1225	+	23.1647i	−1.62318	+	0.937145i
$612$		0			0
$613$	−19.8248	+	34.3376i	−0.800716	+	1.38688i	0.118429	+	0.992962i	$0.462214\pi$
$613$	−19.8248	+	34.3376i	−0.800716	+	1.38688i	−0.919145	+	0.393918i	$0.871119\pi$
$614$		0			0
$615$	−35.9888	−	18.6022i	−1.45121	−	0.750112i
$616$		0			0
$617$			28.6296i			1.15258i	0.817244	+	0.576292i	$0.195501\pi$
$617$			28.6296i			1.15258i	−0.817244	+	0.576292i	$0.804499\pi$
$618$		0			0
$619$	32.9529	+	19.0254i	1.32449	+	0.764694i	0.984441	−	0.175714i	$-0.0562235\pi$
$619$	32.9529	+	19.0254i	1.32449	+	0.764694i	0.340047	+	0.940408i	$0.389557\pi$
$620$		0			0
$621$	4.25485	+	5.44628i	0.170741	+	0.218552i
$622$		0			0
$623$	−15.9944	−	8.37701i	−0.640801	−	0.335618i
$624$		0			0
$625$	−8.47450	−	14.6783i	−0.338980	−	0.587130i
$626$		0			0
$627$	1.27948	−	0.820342i	0.0510974	−	0.0327613i
$628$		0			0
$629$	−1.13422			−0.0452242
$630$		0			0
$631$	3.65235			0.145398			0.0726989	−	0.997354i	$-0.476839\pi$
$631$	3.65235			0.145398			0.0726989	+	0.997354i	$0.476839\pi$
$632$		0			0
$633$	1.26912	−	0.813704i	0.0504432	−	0.0323418i
$634$		0			0
$635$	24.5498	+	42.5215i	0.974228	+	1.68741i
$636$		0			0
$637$	−25.6064	−	12.0966i	−1.01456	−	0.479286i
$638$		0			0
$639$	15.7842	+	7.24916i	0.624413	+	0.286772i
$640$		0			0
$641$	21.2563	+	12.2723i	0.839574	+	0.484728i	0.857119	−	0.515118i	$-0.172252\pi$
$641$	21.2563	+	12.2723i	0.839574	+	0.484728i	−0.0175456	+	0.999846i	$0.505585\pi$
$642$		0			0
$643$		−	27.3936i		−	1.08030i	−0.841569	−	0.540149i	$-0.818368\pi$
$643$		−	27.3936i		−	1.08030i	0.841569	−	0.540149i	$-0.181632\pi$
$644$		0			0
$645$	2.93980	+	1.51955i	0.115754	+	0.0598321i
$646$		0			0
$647$	16.1181	−	27.9173i	0.633667	−	1.09754i	−0.353129	−	0.935575i	$-0.614882\pi$
$647$	16.1181	−	27.9173i	0.633667	−	1.09754i	0.986796	−	0.161969i	$-0.0517845\pi$
$648$		0			0
$649$	−2.33618	+	1.34879i	−0.0917029	+	0.0529447i
$650$		0			0
$651$	−29.5970	+	20.7417i	−1.16000	+	0.812930i
$652$		0			0
$653$	−13.5027	+	7.79579i	−0.528401	+	0.305073i	−0.740365	−	0.672205i	$-0.765347\pi$
$653$	−13.5027	+	7.79579i	−0.528401	+	0.305073i	0.211964	+	0.977278i	$0.432014\pi$
$654$		0			0
$655$	−10.1235	+	17.5344i	−0.395558	+	0.685126i
$656$		0			0
$657$	−0.576304	+	0.408533i	−0.0224838	+	0.0159384i
$658$		0			0
$659$			35.1100i			1.36769i	0.729626	+	0.683847i	$0.239694\pi$
$659$			35.1100i			1.36769i	−0.729626	+	0.683847i	$0.760306\pi$
$660$		0			0
$661$	6.96082	+	4.01883i	0.270745	+	0.156314i	0.629226	−	0.777222i	$-0.283372\pi$
$661$	6.96082	+	4.01883i	0.270745	+	0.156314i	−0.358481	+	0.933537i	$0.616705\pi$
$662$		0			0
$663$	0.727541	−	0.0338787i	0.0282553	−	0.00131574i
$664$		0			0
$665$	24.6642	−	1.01511i	0.956436	−	0.0393644i
$666$		0			0
$667$	3.30700	+	5.72789i	0.128047	+	0.221785i
$668$		0			0
$669$	1.13467	+	1.76974i	0.0438690	+	0.0684220i
$670$		0			0
$671$	3.38629			0.130726
$672$		0			0
$673$	28.1744			1.08604			0.543022	−	0.839719i	$-0.317280\pi$
$673$	28.1744			1.08604			0.543022	+	0.839719i	$0.317280\pi$
$674$		0			0
$675$	45.4917	+	18.3814i	1.75098	+	0.707499i
$676$		0			0
$677$	−17.3844	−	30.1106i	−0.668135	−	1.15724i	−0.978425	−	0.206602i	$-0.933760\pi$
$677$	−17.3844	−	30.1106i	−0.668135	−	1.15724i	0.310290	−	0.950642i	$-0.399574\pi$
$678$		0			0
$679$	−7.28158	−	11.4931i	−0.279441	−	0.441063i
$680$		0			0
$681$	1.07510	+	23.0877i	0.0411980	+	0.884721i
$682$		0			0
$683$	40.7393	+	23.5209i	1.55885	+	0.900001i	0.997368	+	0.0725098i	$0.0231009\pi$
$683$	40.7393	+	23.5209i	1.55885	+	0.900001i	0.561479	+	0.827491i	$0.310232\pi$
$684$		0			0
$685$			19.1933i			0.733339i
$686$		0			0
$687$	8.82192	−	17.0674i	0.336577	−	0.651161i
$688$		0			0
$689$	11.8691	−	20.5579i	0.452177	−	0.783194i
$690$		0			0
$691$	27.1758	−	15.6900i	1.03382	−	0.596874i	0.115740	−	0.993279i	$-0.463076\pi$
$691$	27.1758	−	15.6900i	1.03382	−	0.596874i	0.918076	+	0.396406i	$0.129743\pi$
$692$		0			0
$693$	−1.07701	+	2.62459i	−0.0409121	+	0.0996998i
$694$		0			0
$695$	−69.9874	+	40.4073i	−2.65478	+	1.53274i
$696$		0			0
$697$	−0.319850	+	0.553997i	−0.0121152	+	0.0209841i
$698$		0			0
$699$	−6.50569	+	12.5863i	−0.246068	+	0.476057i
$700$		0			0
$701$			29.9818i			1.13240i	0.824268	+	0.566199i	$0.191587\pi$
$701$			29.9818i			1.13240i	−0.824268	+	0.566199i	$0.808413\pi$
$702$		0			0
$703$	23.2015	+	13.3954i	0.875061	+	0.505217i
$704$		0			0
$705$	3.50628	+	75.2968i	0.132054	+	2.83584i
$706$		0			0
$707$	−1.40111	−	34.0427i	−0.0526940	−	1.28031i
$708$		0			0
$709$	−11.5451	−	19.9968i	−0.433587	−	0.750995i	0.563592	−	0.826053i	$-0.309419\pi$
$709$	−11.5451	−	19.9968i	−0.433587	−	0.750995i	−0.997179	+	0.0750583i	$0.976086\pi$
$710$		0			0
$711$	9.63298	−	0.899089i	0.361265	−	0.0337185i
$712$		0			0
$713$	−10.4899			−0.392849
$714$		0			0
$715$	−5.49540			−0.205516
$716$		0			0
$717$	21.1227	+	32.9448i	0.788841	+	1.23035i
$718$		0			0
$719$	22.5340	+	39.0300i	0.840376	+	1.45557i	0.889577	+	0.456785i	$0.150999\pi$
$719$	22.5340	+	39.0300i	0.840376	+	1.45557i	−0.0492012	+	0.998789i	$0.515668\pi$
$720$		0			0
$721$	6.91877	−	13.2101i	0.257669	−	0.491971i
$722$		0			0
$723$	8.47337	−	0.394571i	0.315128	−	0.0146743i
$724$		0			0
$725$	40.6638	+	23.4772i	1.51022	+	0.871923i
$726$		0			0
$727$		−	3.14662i		−	0.116702i	−0.998296	−	0.0583508i	$-0.981416\pi$
$727$		−	3.14662i		−	0.116702i	0.998296	−	0.0583508i	$-0.0185842\pi$
$728$		0			0
$729$	−25.9545	+	7.44070i	−0.961278	+	0.275582i
$730$		0			0
$731$	0.0261274	−	0.0452541i	0.000966358	−	0.00167378i
$732$		0			0
$733$	14.9590	−	8.63657i	0.552522	−	0.318999i	−0.197616	−	0.980279i	$-0.563320\pi$
$733$	14.9590	−	8.63657i	0.552522	−	0.318999i	0.750139	+	0.661281i	$0.229987\pi$
$734$		0			0
$735$	−36.6138	+	27.9729i	−1.35052	+	1.03180i
$736$		0			0
$737$	0.831885	−	0.480289i	0.0306429	−	0.0176917i
$738$		0			0
$739$	0.996550	−	1.72607i	0.0366587	−	0.0634947i	−0.847114	−	0.531411i	$-0.821662\pi$
$739$	0.996550	−	1.72607i	0.0366587	−	0.0634947i	0.883773	+	0.467917i	$0.154995\pi$
$740$		0			0
$741$	−15.2827	−	7.89942i	−0.561423	−	0.290192i
$742$		0			0
$743$		−	5.54435i		−	0.203402i	−0.994815	−	0.101701i	$-0.967571\pi$
$743$		−	5.54435i		−	0.203402i	0.994815	−	0.101701i	$-0.0324286\pi$
$744$		0			0
$745$	40.0867	+	23.1441i	1.46866	+	0.847934i
$746$		0			0
$747$	11.3656	−	24.7473i	0.415846	−	0.905456i
$748$		0			0
$749$	10.8113	−	20.6422i	0.395036	−	0.754248i
$750$		0			0
$751$	−22.0897	−	38.2605i	−0.806065	−	1.39615i	−0.915569	−	0.402160i	$-0.868260\pi$
$751$	−22.0897	−	38.2605i	−0.806065	−	1.39615i	0.109504	−	0.993986i	$-0.465074\pi$
$752$		0			0
$753$	−13.3832	+	8.58069i	−0.487711	+	0.312698i
$754$		0			0
$755$	31.2296			1.13656
$756$		0			0
$757$	10.6250			0.386172			0.193086	−	0.981182i	$-0.438150\pi$
$757$	10.6250			0.386172			0.193086	+	0.981182i	$0.438150\pi$
$758$		0			0
$759$	−0.693179	+	0.444434i	−0.0251608	+	0.0161319i
$760$		0			0
$761$	−13.9084	−	24.0900i	−0.504178	−	0.873262i	−0.999988	−	0.00483132i	$-0.998462\pi$
$761$	−13.9084	−	24.0900i	−0.504178	−	0.873262i	0.495810	−	0.868431i	$-0.334871\pi$
$762$		0			0
$763$	0.487125	+	11.8357i	0.0176351	+	0.428480i
$764$		0			0
$765$	0.494565	−	1.07686i	0.0178811	−	0.0389339i
$766$		0			0
$767$	26.4432	+	15.2670i	0.954809	+	0.551259i
$768$		0			0
$769$			10.2707i			0.370369i	0.982704	+	0.185185i	$0.0592883\pi$
$769$			10.2707i			0.370369i	−0.982704	+	0.185185i	$0.940712\pi$
$770$		0			0
$771$	19.4196	+	10.0377i	0.699379	+	0.361500i
$772$		0			0
$773$	−20.2953	+	35.1525i	−0.729972	+	1.26435i	0.226923	+	0.973913i	$0.427133\pi$
$773$	−20.2953	+	35.1525i	−0.729972	+	1.26435i	−0.956895	+	0.290435i	$0.906200\pi$
$774$		0			0
$775$	−64.4933	+	37.2352i	−2.31667	+	1.33753i
$776$		0			0
$777$	−49.8151	+	4.37834i	−1.78711	+	0.157072i
$778$		0			0
$779$	13.0857	−	7.55502i	0.468843	−	0.270687i
$780$		0			0
$781$	−1.03470	+	1.79215i	−0.0370244	+	0.0641282i
$782$		0			0
$783$	−25.5873	+	3.59530i	−0.914415	+	0.128486i
$784$		0			0
$785$		−	49.1938i		−	1.75580i
$786$		0			0
$787$	−22.6225	−	13.0611i	−0.806404	−	0.465578i	0.0393014	−	0.999227i	$-0.487487\pi$
$787$	−22.6225	−	13.0611i	−0.806404	−	0.465578i	−0.845706	+	0.533650i	$0.820820\pi$
$788$		0			0
$789$	50.4432	−	2.34894i	1.79583	−	0.0836246i
$790$		0			0
$791$	5.66392	+	8.93980i	0.201386	+	0.317863i
$792$		0			0
$793$	−19.1647	−	33.1943i	−0.680560	−	1.17876i
$794$		0			0
$795$	−20.8461	−	32.5134i	−0.739334	−	1.15313i
$796$		0			0
$797$	−38.0284			−1.34704			−0.673518	−	0.739171i	$-0.735218\pi$
$797$	−38.0284			−1.34704			−0.673518	+	0.739171i	$0.735218\pi$
$798$		0			0
$799$	1.19025			0.0421080
$800$		0			0
$801$	20.3842	−	1.90255i	0.720240	−	0.0672233i
$802$		0			0
$803$	−0.0420818	−	0.0728879i	−0.00148504	−	0.00257216i
$804$		0			0
$805$	−13.3622	+	0.549955i	−0.470957	+	0.0193834i
$806$		0			0
$807$	−0.360362	−	7.73874i	−0.0126854	−	0.272416i
$808$		0			0
$809$	−25.8553	−	14.9276i	−0.909024	−	0.524825i	−0.0289068	−	0.999582i	$-0.509203\pi$
$809$	−25.8553	−	14.9276i	−0.909024	−	0.524825i	−0.880117	+	0.474757i	$0.842536\pi$
$810$		0			0
$811$		−	15.4099i		−	0.541114i	−0.962704	−	0.270557i	$-0.912792\pi$
$811$		−	15.4099i		−	0.541114i	0.962704	−	0.270557i	$-0.0872079\pi$
$812$		0			0
$813$	13.3147	−	25.7594i	0.466967	−	0.903420i
$814$		0			0
$815$	−4.15139	+	7.19042i	−0.145417	+	0.251869i
$816$		0			0
$817$	−1.06892	+	0.617144i	−0.0373969	+	0.0215911i
$818$		0			0
$819$	31.8230	−	4.29644i	1.11199	−	0.150130i
$820$		0			0
$821$	25.0908	−	14.4862i	0.875674	−	0.505570i	0.00644422	−	0.999979i	$-0.497949\pi$
$821$	25.0908	−	14.4862i	0.875674	−	0.505570i	0.869230	+	0.494409i	$0.164615\pi$
$822$		0			0
$823$	−3.58962	+	6.21741i	−0.125126	+	0.216725i	−0.921782	−	0.387708i	$-0.873267\pi$
$823$	−3.58962	+	6.21741i	−0.125126	+	0.216725i	0.796656	+	0.604433i	$0.206600\pi$
$824$		0			0
$825$	−2.68419	+	5.19298i	−0.0934513	+	0.180796i
$826$		0			0
$827$			37.6512i			1.30926i	0.755949	+	0.654630i	$0.227176\pi$
$827$			37.6512i			1.30926i	−0.755949	+	0.654630i	$0.772824\pi$
$828$		0			0
$829$	−43.4385	−	25.0792i	−1.50868	−	0.871038i	−0.999949	−	0.0101139i	$-0.996781\pi$
$829$	−43.4385	−	25.0792i	−1.50868	−	0.871038i	−0.508733	−	0.860924i	$-0.669886\pi$
$830$		0			0
$831$	0.0823277	+	1.76798i	0.00285592	+	0.0613304i
$832$		0			0
$833$	0.414330	+	0.598065i	0.0143557	+	0.0207217i
$834$		0			0
$835$	0.882803	+	1.52906i	0.0305506	+	0.0529153i
$836$		0			0
$837$	15.3526	−	37.9960i	0.530665	−	1.31333i
$838$		0			0
$839$	10.2849			0.355073			0.177536	−	0.984114i	$-0.443187\pi$
$839$	10.2849			0.355073			0.177536	+	0.984114i	$0.443187\pi$
$840$		0			0
$841$	4.27275			0.147336
$842$		0			0
$843$	13.0369	+	20.3335i	0.449016	+	0.700324i
$844$		0			0
$845$	6.39910	+	11.0836i	0.220136	+	0.381286i
$846$		0			0
$847$	25.4818	+	13.3460i	0.875566	+	0.458575i
$848$		0			0
$849$	−28.0468	+	1.30603i	−0.962564	+	0.0448228i
$850$		0			0
$851$	−12.5698	−	7.25719i	−0.430888	−	0.248773i
$852$		0			0
$853$		−	29.0278i		−	0.993891i	−0.867782	−	0.496946i	$-0.834455\pi$
$853$		−	29.0278i		−	0.993891i	0.867782	−	0.496946i	$-0.165545\pi$
$854$		0			0
$855$	−22.8348	+	16.1872i	−0.780933	+	0.553591i
$856$		0			0
$857$	7.98887	−	13.8371i	0.272895	−	0.472668i	−0.696707	−	0.717356i	$-0.745352\pi$
$857$	7.98887	−	13.8371i	0.272895	−	0.472668i	0.969602	+	0.244688i	$0.0786856\pi$
$858$		0			0
$859$	4.98253	−	2.87666i	0.170002	−	0.0981505i	−0.412585	−	0.910919i	$-0.635374\pi$
$859$	4.98253	−	2.87666i	0.170002	−	0.0981505i	0.582587	+	0.812769i	$0.302041\pi$
$860$		0			0
$861$	−11.9093	+	25.5664i	−0.405869	+	0.871299i
$862$		0			0
$863$	10.7735	−	6.22006i	0.366733	−	0.211733i	−0.305297	−	0.952257i	$-0.598756\pi$
$863$	10.7735	−	6.22006i	0.366733	−	0.211733i	0.672030	+	0.740524i	$0.265422\pi$
$864$		0			0
$865$	17.5798	−	30.4492i	0.597733	−	1.03530i
$866$		0			0
$867$	26.1406	+	13.5118i	0.887781	+	0.458883i
$868$		0			0
$869$			1.15268i			0.0391019i
$870$		0			0
$871$	−9.41612	−	5.43640i	−0.319053	−	0.184205i
$872$		0			0
$873$	14.0194	+	6.43867i	0.474486	+	0.217916i
$874$		0			0
$875$	−37.7331	+	23.9062i	−1.27561	+	0.808179i
$876$		0			0
$877$	21.9672	+	38.0484i	0.741781	+	1.28480i	0.951684	+	0.307080i	$0.0993521\pi$
$877$	21.9672	+	38.0484i	0.741781	+	1.28480i	−0.209902	+	0.977722i	$0.567315\pi$
$878$		0			0
$879$	−28.0052	+	17.9556i	−0.944591	+	0.605628i
$880$		0			0
$881$	51.0805			1.72095			0.860473	−	0.509496i	$-0.170168\pi$
$881$	51.0805			1.72095			0.860473	+	0.509496i	$0.170168\pi$
$882$		0			0
$883$	34.3823			1.15706			0.578529	−	0.815662i	$-0.303627\pi$
$883$	34.3823			1.15706			0.578529	+	0.815662i	$0.303627\pi$
$884$		0			0
$885$	41.8213	−	26.8139i	1.40581	−	0.901339i
$886$		0			0
$887$	−20.8829	−	36.1703i	−0.701180	−	1.21448i	−0.968053	−	0.250748i	$-0.919324\pi$
$887$	−20.8829	−	36.1703i	−0.701180	−	1.21448i	0.266873	−	0.963732i	$-0.414010\pi$
$888$		0			0
$889$	28.8751	−	18.2942i	0.968440	−	0.613567i
$890$		0			0
$891$	−0.595295	−	3.16126i	−0.0199431	−	0.105906i
$892$		0			0
$893$	−24.3477	−	14.0572i	−0.814765	−	0.470405i
$894$		0			0
$895$			7.77140i			0.259769i
$896$		0			0
$897$	8.27965	+	4.27965i	0.276449	+	0.142893i
$898$		0			0
$899$	19.6089	−	33.9636i	0.653993	−	1.13275i
$900$		0			0
$901$	−0.528153	+	0.304929i	−0.0175953	+	0.0101587i
$902$		0			0
$903$	0.972832	−	2.08843i	0.0323738	−	0.0694985i
$904$		0			0
$905$	−57.9883	+	33.4795i	−1.92760	+	1.11290i
$906$		0			0
$907$	−18.9839	+	32.8811i	−0.630350	+	1.09180i	0.357130	+	0.934055i	$0.383755\pi$
$907$	−18.9839	+	32.8811i	−0.630350	+	1.09180i	−0.987480	+	0.157744i	$0.949578\pi$
$908$		0			0
$909$	22.3424	+	31.5176i	0.741049	+	1.04537i
$910$		0			0
$911$		−	55.0007i		−	1.82225i	−0.412127	−	0.911126i	$-0.635214\pi$
$911$		−	55.0007i		−	1.82225i	0.412127	−	0.911126i	$-0.364786\pi$
$912$		0			0
$913$	2.80983	+	1.62226i	0.0929918	+	0.0536888i
$914$		0			0
$915$	−62.2949	+	2.90083i	−2.05940	+	0.0958983i
$916$		0			0
$917$	12.4868	+	6.53991i	0.412349	+	0.215967i
$918$		0			0
$919$	13.5889	+	23.5367i	0.448256	+	0.776403i	0.998273	−	0.0587510i	$-0.0187118\pi$
$919$	13.5889	+	23.5367i	0.448256	+	0.776403i	−0.550016	+	0.835154i	$0.685378\pi$
$920$		0			0
$921$	0.449199	+	0.700611i	0.0148016	+	0.0230859i
$922$		0			0
$923$	23.4236			0.770996
$924$		0			0
$925$	−103.041			−3.38798
$926$		0			0
$927$	1.57136	+	16.8358i	0.0516103	+	0.552960i
$928$		0			0
$929$	−0.982860	−	1.70236i	−0.0322466	−	0.0558527i	0.849452	−	0.527666i	$-0.176933\pi$
$929$	−0.982860	−	1.70236i	−0.0322466	−	0.0558527i	−0.881698	+	0.471814i	$0.843600\pi$
$930$		0			0
$931$	−1.41222	−	17.1273i	−0.0462838	−	0.561326i
$932$		0			0
$933$	0.751941	+	16.1478i	0.0246174	+	0.528656i
$934$		0			0
$935$	0.122267	+	0.0705911i	0.00399857	+	0.00230858i
$936$		0			0
$937$		−	31.0157i		−	1.01324i	−0.862170	−	0.506620i	$-0.830895\pi$
$937$		−	31.0157i		−	1.01324i	0.862170	−	0.506620i	$-0.169105\pi$
$938$		0			0
$939$	14.2479	−	27.5648i	0.464963	−	0.899544i
$940$		0			0
$941$	16.7914	−	29.0836i	0.547384	−	0.948097i	−0.451069	−	0.892489i	$-0.648957\pi$
$941$	16.7914	−	29.0836i	0.547384	−	0.948097i	0.998453	−	0.0556078i	$-0.0177096\pi$
$942$		0			0
$943$	−7.08940	+	4.09307i	−0.230863	+	0.133289i
$944$		0			0
$945$	17.5645	−	49.2050i	0.571374	−	1.60064i
$946$		0			0
$947$	−8.89077	+	5.13309i	−0.288911	+	0.166803i	−0.637451	−	0.770491i	$-0.720011\pi$
$947$	−8.89077	+	5.13309i	−0.288911	+	0.166803i	0.348539	+	0.937294i	$0.386678\pi$
$948$		0			0
$949$	−0.476325	+	0.825019i	−0.0154622	+	0.0267813i
$950$		0			0
$951$	17.7494	−	34.3389i	0.575563	−	1.11352i
$952$		0			0
$953$			1.00920i			0.0326911i	0.999866	+	0.0163455i	$0.00520318\pi$
$953$			1.00920i			0.0326911i	−0.999866	+	0.0163455i	$0.994797\pi$
$954$		0			0
$955$	−74.0347	−	42.7439i	−2.39571	−	1.38316i
$956$		0			0
$957$	−0.143196	−	3.07512i	−0.00462888	−	0.0994046i
$958$		0			0
$959$	13.3509	−	0.549486i	0.431122	−	0.0177438i
$960$		0			0
$961$	15.5999	+	27.0199i	0.503224	+	0.871610i
$962$		0			0
$963$	2.45541	+	26.3076i	0.0791245	+	0.847752i
$964$		0			0
$965$	36.6341			1.17929
$966$		0			0
$967$	−1.83020			−0.0588552			−0.0294276	−	0.999567i	$-0.509368\pi$
$967$	−1.83020			−0.0588552			−0.0294276	+	0.999567i	$0.509368\pi$
$968$		0			0
$969$	0.238553	+	0.372068i	0.00766342	+	0.0119525i
$970$		0			0
$971$	−7.28478	−	12.6176i	−0.233780	−	0.404918i	0.725138	−	0.688604i	$-0.241776\pi$
$971$	−7.28478	−	12.6176i	−0.233780	−	0.404918i	−0.958917	+	0.283686i	$0.908443\pi$
$972$		0			0
$973$	30.1110	+	47.5264i	0.965313	+	1.52363i
$974$		0			0
$975$	66.0956	−	3.07781i	2.11675	−	0.0985689i
$976$		0			0
$977$	5.93615	+	3.42724i	0.189914	+	0.109647i	0.591942	−	0.805980i	$-0.298361\pi$
$977$	5.93615	+	3.42724i	0.189914	+	0.109647i	−0.402028	+	0.915627i	$0.631695\pi$
$978$		0			0
$979$			2.43916i			0.0779559i
$980$		0			0
$981$	−7.76780	−	10.9578i	−0.248007	−	0.349855i
$982$		0			0
$983$	−29.5934	+	51.2573i	−0.943883	+	1.63485i	−0.185910	+	0.982567i	$0.559523\pi$
$983$	−29.5934	+	51.2573i	−0.943883	+	1.63485i	−0.757973	+	0.652286i	$0.773810\pi$
$984$		0			0
$985$	−50.6020	+	29.2151i	−1.61231	+	0.930870i
$986$		0			0
$987$	52.2761	−	4.59464i	1.66397	−	0.146249i
$988$		0			0
$989$	0.579108	−	0.334348i	0.0184146	−	0.0106317i
$990$		0			0
$991$	28.2143	−	48.8686i	0.896256	−	1.55236i	0.0640132	−	0.997949i	$-0.479610\pi$
$991$	28.2143	−	48.8686i	0.896256	−	1.55236i	0.832243	−	0.554412i	$-0.187057\pi$
$992$		0			0
$993$	21.7216	+	11.2276i	0.689313	+	0.356297i
$994$		0			0
$995$		−	17.4199i		−	0.552249i
$996$		0			0
$997$	−45.5831	−	26.3174i	−1.44363	−	0.833480i	−0.445541	−	0.895262i	$-0.646988\pi$
$997$	−45.5831	−	26.3174i	−1.44363	−	0.833480i	−0.998090	+	0.0617814i	$0.980322\pi$
$998$		0			0
$999$	44.6834	−	34.9084i	1.41372	−	1.10445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bc.f.17.7		16
3.2	odd	2	inner	336.2.bc.f.17.5		16
4.3	odd	2		168.2.u.a.17.2	✓	16
7.3	odd	6		2352.2.k.i.881.16		16
7.4	even	3		2352.2.k.i.881.1		16
7.5	odd	6	inner	336.2.bc.f.257.5		16
12.11	even	2		168.2.u.a.17.4	yes	16
21.5	even	6	inner	336.2.bc.f.257.7		16
21.11	odd	6		2352.2.k.i.881.15		16
21.17	even	6		2352.2.k.i.881.2		16
28.3	even	6		1176.2.k.a.881.1		16
28.11	odd	6		1176.2.k.a.881.16		16
28.19	even	6		168.2.u.a.89.4	yes	16
28.23	odd	6		1176.2.u.b.1097.5		16
28.27	even	2		1176.2.u.b.521.7		16
84.11	even	6		1176.2.k.a.881.2		16
84.23	even	6		1176.2.u.b.1097.7		16
84.47	odd	6		168.2.u.a.89.2	yes	16
84.59	odd	6		1176.2.k.a.881.15		16
84.83	odd	2		1176.2.u.b.521.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.2	✓	16	4.3	odd	2
168.2.u.a.17.4	yes	16	12.11	even	2
168.2.u.a.89.2	yes	16	84.47	odd	6
168.2.u.a.89.4	yes	16	28.19	even	6
336.2.bc.f.17.5		16	3.2	odd	2	inner
336.2.bc.f.17.7		16	1.1	even	1	trivial
336.2.bc.f.257.5		16	7.5	odd	6	inner
336.2.bc.f.257.7		16	21.5	even	6	inner
1176.2.k.a.881.1		16	28.3	even	6
1176.2.k.a.881.2		16	84.11	even	6
1176.2.k.a.881.15		16	84.59	odd	6
1176.2.k.a.881.16		16	28.11	odd	6
1176.2.u.b.521.5		16	84.83	odd	2
1176.2.u.b.521.7		16	28.27	even	2
1176.2.u.b.1097.5		16	28.23	odd	6
1176.2.u.b.1097.7		16	84.23	even	6
2352.2.k.i.881.1		16	7.4	even	3
2352.2.k.i.881.2		16	21.17	even	6
2352.2.k.i.881.15		16	21.11	odd	6
2352.2.k.i.881.16		16	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45809 - 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.23495 + 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +O(q^{10})\)	\(q+(1.45809 - 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.23495 + 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +(0.309539 + 0.178712i) q^{11} -4.04570i q^{13} +(-5.84742 - 3.02246i) q^{15} +(-0.0519689 + 0.0900129i) q^{17} +(2.12615 - 1.22753i) q^{19} +(-1.93502 + 4.15400i) q^{21} +(-1.15188 + 0.665037i) q^{23} +(-4.72127 + 8.17749i) q^{25} +(-0.723015 - 5.14560i) q^{27} -4.97265i q^{29} +(6.83007 + 3.94335i) q^{31} +(0.618407 - 0.0287968i) q^{33} +(8.90704 + 4.66504i) q^{35} +(5.45622 + 9.45046i) q^{37} +(-3.78216 - 5.89900i) q^{39} +6.15464 q^{41} -0.502751 q^{43} +(-11.3517 + 1.05950i) q^{45} +(-5.72578 - 9.91734i) q^{47} +(2.99000 - 6.32929i) q^{49} +(0.00837401 + 0.179831i) q^{51} +(5.08143 + 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(-3.77364 + 6.53614i) q^{59} +(8.20485 - 4.73707i) q^{61} +(1.06198 + 7.86589i) q^{63} +(-13.3151 + 7.68750i) q^{65} +(1.34375 - 2.32744i) q^{67} +(-1.05783 + 2.04653i) q^{69} +5.78975i q^{71} +(-0.203925 - 0.117736i) q^{73} +(0.760762 + 16.3373i) q^{75} +(-0.944856 + 0.0388878i) q^{77} +(1.61247 + 2.79289i) q^{79} +(-5.86465 - 6.82685i) q^{81} +9.07747 q^{83} +0.394999 q^{85} +(-4.64874 - 7.25058i) q^{87} +(3.41213 + 5.90999i) q^{89} +(5.72862 + 9.04192i) q^{91} +(13.6454 - 0.635411i) q^{93} +(-8.08008 - 4.66504i) q^{95} +5.14243i q^{97} +(0.874774 - 0.620114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^7 + 2 * q^9	\( 16 q - 4 q^{7} + 2 q^{9} - 8 q^{15} + 6 q^{19} + 14 q^{21} - 18 q^{25} + 48 q^{31} - 12 q^{33} - 2 q^{37} + 22 q^{39} - 20 q^{43} - 42 q^{45} - 28 q^{49} - 6 q^{51} - 8 q^{57} + 36 q^{61} + 32 q^{63} - 14 q^{67} + 30 q^{73} - 54 q^{75} - 28 q^{79} + 30 q^{81} + 16 q^{85} - 78 q^{87} - 66 q^{91} + 16 q^{93} - 20 q^{99}+O(q^{100}) \) 16 * q - 4 * q^7 + 2 * q^9 - 8 * q^15 + 6 * q^19 + 14 * q^21 - 18 * q^25 + 48 * q^31 - 12 * q^33 - 2 * q^37 + 22 * q^39 - 20 * q^43 - 42 * q^45 - 28 * q^49 - 6 * q^51 - 8 * q^57 + 36 * q^61 + 32 * q^63 - 14 * q^67 + 30 * q^73 - 54 * q^75 - 28 * q^79 + 30 * q^81 + 16 * q^85 - 78 * q^87 - 66 * q^91 + 16 * q^93 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more