LMFDB - Embedded newform 784.2.bb.b.111.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.18
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.b.671.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44547 + 1.81256i) q^{3} +(2.77297 - 2.21137i) q^{5} +(1.94347 + 1.79525i) q^{7} +(-0.528427 + 2.31519i) q^{9} +O(q^{10})$	\(q+(1.44547 + 1.81256i) q^{3} +(2.77297 - 2.21137i) q^{5} +(1.94347 + 1.79525i) q^{7} +(-0.528427 + 2.31519i) q^{9} +(4.57508 - 1.04423i) q^{11} +(-5.78881 + 1.32126i) q^{13} +(8.01646 + 1.82970i) q^{15} +(0.938958 - 1.94977i) q^{17} -4.08024 q^{19} +(-0.444763 + 6.11762i) q^{21} +(-1.07860 - 2.23974i) q^{23} +(1.68660 - 7.38948i) q^{25} +(1.30604 - 0.628957i) q^{27} +(3.94588 + 1.90024i) q^{29} -6.72715 q^{31} +(8.50585 + 6.78319i) q^{33} +(9.35915 + 0.680429i) q^{35} +(-8.04808 - 3.87575i) q^{37} +(-10.7624 - 8.58271i) q^{39} +(0.210900 - 0.168187i) q^{41} +(3.94188 + 3.14354i) q^{43} +(3.65443 + 7.58849i) q^{45} +(-0.0216980 - 0.0950654i) q^{47} +(0.554176 + 6.97803i) q^{49} +(4.89129 - 1.11641i) q^{51} +(-10.4093 + 5.01284i) q^{53} +(10.3774 - 13.0128i) q^{55} +(-5.89784 - 7.39566i) q^{57} +(-1.91773 + 2.40476i) q^{59} +(1.79731 - 3.73215i) q^{61} +(-5.18332 + 3.55085i) q^{63} +(-13.1304 + 16.4650i) q^{65} +4.19011i q^{67} +(2.50058 - 5.19250i) q^{69} +(3.95100 + 8.20434i) q^{71} +(-1.51164 - 0.345021i) q^{73} +(15.8318 - 7.62418i) q^{75} +(10.7662 + 6.18396i) q^{77} +14.9599i q^{79} +(9.44652 + 4.54921i) q^{81} +(0.959887 - 4.20554i) q^{83} +(-1.70795 - 7.48302i) q^{85} +(2.25935 + 9.89885i) q^{87} +(-16.4153 - 3.74669i) q^{89} +(-13.6224 - 7.82452i) q^{91} +(-9.72386 - 12.1933i) q^{93} +(-11.3144 + 9.02292i) q^{95} +15.2923i q^{97} +11.1440i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 24 q^{9}+O(q^{10}) $ 120 * q - 24 * q^9	$ 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) $ 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

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
$3$	1.44547	+	1.81256i	0.834540	+	1.04648i	0.998201	+	0.0599630i	$0.0190983\pi$
$3$	1.44547	+	1.81256i	0.834540	+	1.04648i	−0.163661	+	0.986517i	$0.552330\pi$
$4$		0			0
$5$	2.77297	−	2.21137i	1.24011	−	0.988954i	0.240276	−	0.970705i	$-0.422762\pi$
$5$	2.77297	−	2.21137i	1.24011	−	0.988954i	0.999833	−	0.0182499i	$-0.00580943\pi$
$6$		0			0
$7$	1.94347	+	1.79525i	0.734564	+	0.678540i
$7$	1.94347	+	1.79525i	0.734564	+	0.678540i
$8$		0			0
$9$	−0.528427	+	2.31519i	−0.176142	+	0.771730i
$10$		0			0
$11$	4.57508	−	1.04423i	1.37944	−	0.314848i	0.532451	−	0.846461i	$-0.321271\pi$
$11$	4.57508	−	1.04423i	1.37944	−	0.314848i	0.846988	+	0.531613i	$0.178414\pi$
$12$		0			0
$13$	−5.78881	+	1.32126i	−1.60553	+	0.366451i	−0.929033	−	0.369997i	$-0.879359\pi$
$13$	−5.78881	+	1.32126i	−1.60553	+	0.366451i	−0.676494	+	0.736448i	$0.736502\pi$
$14$		0			0
$15$	8.01646	+	1.82970i	2.06984	+	0.472428i
$16$		0			0
$17$	0.938958	−	1.94977i	0.227731	−	0.472888i	−0.755525	−	0.655120i	$-0.772618\pi$
$17$	0.938958	−	1.94977i	0.227731	−	0.472888i	0.983255	+	0.182232i	$0.0583323\pi$
$18$		0			0
$19$	−4.08024			−0.936071			−0.468036	−	0.883710i	$-0.655038\pi$
$19$	−4.08024			−0.936071			−0.468036	+	0.883710i	$0.655038\pi$
$20$		0			0
$21$	−0.444763	+	6.11762i	−0.0970553	+	1.33497i
$22$		0			0
$23$	−1.07860	−	2.23974i	−0.224904	−	0.467019i	0.757731	−	0.652567i	$-0.226308\pi$
$23$	−1.07860	−	2.23974i	−0.224904	−	0.467019i	−0.982635	+	0.185548i	$0.940594\pi$
$24$		0			0
$25$	1.68660	−	7.38948i	0.337320	−	1.47790i
$26$		0			0
$27$	1.30604	−	0.628957i	0.251348	−	0.121043i
$28$		0			0
$29$	3.94588	+	1.90024i	0.732732	+	0.352865i	0.762758	−	0.646684i	$-0.223845\pi$
$29$	3.94588	+	1.90024i	0.732732	+	0.352865i	−0.0300263	+	0.999549i	$0.509559\pi$
$30$		0			0
$31$	−6.72715			−1.20823			−0.604116	−	0.796897i	$-0.706474\pi$
$31$	−6.72715			−1.20823			−0.604116	+	0.796897i	$0.706474\pi$
$32$		0			0
$33$	8.50585	+	6.78319i	1.48068	+	1.18080i
$34$		0			0
$35$	9.35915	+	0.680429i	1.58198	+	0.115013i
$36$		0			0
$37$	−8.04808	−	3.87575i	−1.32310	−	0.637169i	−0.366999	−	0.930221i	$-0.619615\pi$
$37$	−8.04808	−	3.87575i	−1.32310	−	0.637169i	−0.956097	+	0.293052i	$0.905329\pi$
$38$		0			0
$39$	−10.7624	−	8.58271i	−1.72336	−	1.37433i
$40$		0			0
$41$	0.210900	−	0.168187i	0.0329371	−	0.0262664i	−0.606883	−	0.794791i	$-0.707580\pi$
$41$	0.210900	−	0.168187i	0.0329371	−	0.0262664i	0.639820	+	0.768525i	$0.279009\pi$
$42$		0			0
$43$	3.94188	+	3.14354i	0.601130	+	0.479385i	0.876140	−	0.482056i	$-0.160110\pi$
$43$	3.94188	+	3.14354i	0.601130	+	0.479385i	−0.275010	+	0.961441i	$0.588681\pi$
$44$		0			0
$45$	3.65443	+	7.58849i	0.544770	+	1.13123i
$46$		0			0
$47$	−0.0216980	−	0.0950654i	−0.00316499	−	0.0138667i	0.973321	−	0.229449i	$-0.0736923\pi$
$47$	−0.0216980	−	0.0950654i	−0.00316499	−	0.0138667i	−0.976486	+	0.215582i	$0.930835\pi$
$48$		0			0
$49$	0.554176	+	6.97803i	0.0791679	+	0.996861i
$50$		0			0
$51$	4.89129	−	1.11641i	0.684918	−	0.156328i
$52$		0			0
$53$	−10.4093	+	5.01284i	−1.42982	+	0.688566i	−0.978965	−	0.204030i	$-0.934596\pi$
$53$	−10.4093	+	5.01284i	−1.42982	+	0.688566i	−0.450857	+	0.892596i	$0.648882\pi$
$54$		0			0
$55$	10.3774	−	13.0128i	1.39929	−	1.75465i
$56$		0			0
$57$	−5.89784	−	7.39566i	−0.781188	−	0.979579i
$58$		0			0
$59$	−1.91773	+	2.40476i	−0.249668	+	0.313074i	−0.890834	−	0.454328i	$-0.849879\pi$
$59$	−1.91773	+	2.40476i	−0.249668	+	0.313074i	0.641167	+	0.767402i	$0.278451\pi$
$60$		0			0
$61$	1.79731	−	3.73215i	0.230122	−	0.477853i	−0.753650	−	0.657276i	$-0.771709\pi$
$61$	1.79731	−	3.73215i	0.230122	−	0.477853i	0.983772	+	0.179423i	$0.0574230\pi$
$62$		0			0
$63$	−5.18332	+	3.55085i	−0.653037	+	0.447365i
$64$		0			0
$65$	−13.1304	+	16.4650i	−1.62863	+	2.04223i
$66$		0			0
$67$			4.19011i			0.511903i	0.966690	+	0.255951i	$0.0823887\pi$
$67$			4.19011i			0.511903i	−0.966690	+	0.255951i	$0.917611\pi$
$68$		0			0
$69$	2.50058	−	5.19250i	0.301034	−	0.625104i
$70$		0			0
$71$	3.95100	+	8.20434i	0.468897	+	0.973676i	0.992561	+	0.121750i	$0.0388507\pi$
$71$	3.95100	+	8.20434i	0.468897	+	0.973676i	−0.523663	+	0.851925i	$0.675435\pi$
$72$		0			0
$73$	−1.51164	−	0.345021i	−0.176924	−	0.0403817i	0.133141	−	0.991097i	$-0.457494\pi$
$73$	−1.51164	−	0.345021i	−0.176924	−	0.0403817i	−0.310065	+	0.950715i	$0.600351\pi$
$74$		0			0
$75$	15.8318	−	7.62418i	1.82809	−	0.880364i
$76$		0			0
$77$	10.7662	+	6.18396i	1.22692	+	0.704728i
$78$		0			0
$79$			14.9599i			1.68312i	0.540165	+	0.841559i	$0.318362\pi$
$79$			14.9599i			1.68312i	−0.540165	+	0.841559i	$0.681638\pi$
$80$		0			0
$81$	9.44652	+	4.54921i	1.04961	+	0.505467i
$82$		0			0
$83$	0.959887	−	4.20554i	0.105361	−	0.461618i	−0.894532	−	0.447004i	$-0.852491\pi$
$83$	0.959887	−	4.20554i	0.105361	−	0.461618i	0.999893	−	0.0146138i	$-0.00465188\pi$
$84$		0			0
$85$	−1.70795	−	7.48302i	−0.185253	−	0.811648i
$86$		0			0
$87$	2.25935	+	9.89885i	0.242228	+	1.06127i
$88$		0			0
$89$	−16.4153	−	3.74669i	−1.74002	−	0.397148i	−0.769592	−	0.638536i	$-0.779540\pi$
$89$	−16.4153	−	3.74669i	−1.74002	−	0.397148i	−0.970429	+	0.241387i	$0.922398\pi$
$90$		0			0
$91$	−13.6224	−	7.82452i	−1.42801	−	0.820232i
$92$		0			0
$93$	−9.72386	−	12.1933i	−1.00832	−	1.26439i
$94$		0			0
$95$	−11.3144	+	9.02292i	−1.16083	+	0.925732i
$96$		0			0
$97$			15.2923i			1.55269i	0.630306	+	0.776347i	$0.282930\pi$
$97$			15.2923i			1.55269i	−0.630306	+	0.776347i	$0.717070\pi$
$98$		0			0
$99$			11.1440i			1.12001i
$100$		0			0
$101$	9.05001	−	7.21714i	0.900510	−	0.718132i	−0.0594617	−	0.998231i	$-0.518938\pi$
$101$	9.05001	−	7.21714i	0.900510	−	0.718132i	0.959971	+	0.280098i	$0.0903670\pi$
$102$		0			0
$103$	−1.58264	−	1.98457i	−0.155942	−	0.195545i	0.697723	−	0.716368i	$-0.254197\pi$
$103$	−1.58264	−	1.98457i	−0.155942	−	0.195545i	−0.853665	+	0.520823i	$0.825625\pi$
$104$		0			0
$105$	12.2950	+	17.9475i	1.19987	+	1.75150i
$106$		0			0
$107$	−3.20491	−	0.731501i	−0.309831	−	0.0707169i	0.0647784	−	0.997900i	$-0.479366\pi$
$107$	−3.20491	−	0.731501i	−0.309831	−	0.0707169i	−0.374609	+	0.927183i	$0.622223\pi$
$108$		0			0
$109$	−1.59774	−	7.00016i	−0.153036	−	0.670494i	−0.991993	−	0.126296i	$-0.959691\pi$
$109$	−1.59774	−	7.00016i	−0.153036	−	0.670494i	0.838957	−	0.544198i	$-0.183166\pi$
$110$		0			0
$111$	−4.60820	−	20.1898i	−0.437391	−	1.91634i
$112$		0			0
$113$	0.836189	−	3.66358i	0.0786621	−	0.344641i	−0.920247	−	0.391338i	$-0.872012\pi$
$113$	0.836189	−	3.66358i	0.0786621	−	0.344641i	0.998909	+	0.0466969i	$0.0148695\pi$
$114$		0			0
$115$	−7.94384	−	3.82555i	−0.740767	−	0.356734i
$116$		0			0
$117$		−	14.1004i		−	1.30358i
$118$		0			0
$119$	5.32515	−	2.10366i	0.488156	−	0.192842i
$120$		0			0
$121$	9.93029	−	4.78218i	0.902754	−	0.434743i
$122$		0			0
$123$	0.609698	+	0.139159i	0.0549746	+	0.0125476i
$124$		0			0
$125$	−3.96957	−	8.24289i	−0.355049	−	0.737267i
$126$		0			0
$127$	8.81828	−	18.3114i	0.782496	−	1.62487i	0.00176879	−	0.999998i	$-0.499437\pi$
$127$	8.81828	−	18.3114i	0.782496	−	1.62487i	0.780727	−	0.624872i	$-0.214849\pi$
$128$		0			0
$129$			11.6887i			1.02914i
$130$		0			0
$131$	4.71658	−	5.91440i	0.412089	−	0.516744i	−0.531861	−	0.846832i	$-0.678507\pi$
$131$	4.71658	−	5.91440i	0.412089	−	0.516744i	0.943950	+	0.330088i	$0.107078\pi$
$132$		0			0
$133$	−7.92984	−	7.32504i	−0.687604	−	0.635161i
$134$		0			0
$135$	2.23076	−	4.63222i	0.191993	−	0.398678i
$136$		0			0
$137$	10.6554	−	13.3615i	0.910356	−	1.14155i	−0.0791213	−	0.996865i	$-0.525211\pi$
$137$	10.6554	−	13.3615i	0.910356	−	1.14155i	0.989478	−	0.144686i	$-0.0462171\pi$
$138$		0			0
$139$	10.5434	+	13.2210i	0.894276	+	1.12139i	0.992008	+	0.126174i	$0.0402697\pi$
$139$	10.5434	+	13.2210i	0.894276	+	1.12139i	−0.0977321	+	0.995213i	$0.531159\pi$
$140$		0			0
$141$	0.140948	−	0.176743i	0.0118699	−	0.0148844i
$142$		0			0
$143$	−25.1046	+	12.0897i	−2.09935	+	1.01099i
$144$		0			0
$145$	15.1439	−	3.45650i	1.25763	−	0.287047i
$146$		0			0
$147$	−11.8470	+	11.0910i	−0.977126	+	0.914768i
$148$		0			0
$149$	−4.16013	−	18.2267i	−0.340811	−	1.49319i	−0.797367	−	0.603495i	$-0.793774\pi$
$149$	−4.16013	−	18.2267i	−0.340811	−	1.49319i	0.456556	−	0.889695i	$-0.349083\pi$
$150$		0			0
$151$	5.47498	+	11.3689i	0.445548	+	0.925189i	0.995917	+	0.0902682i	$0.0287724\pi$
$151$	5.47498	+	11.3689i	0.445548	+	0.925189i	−0.550370	+	0.834921i	$0.685513\pi$
$152$		0			0
$153$	4.01791	+	3.20417i	0.324828	+	0.259042i
$154$		0			0
$155$	−18.6542	+	14.8762i	−1.49834	+	1.19489i
$156$		0			0
$157$	−15.2811	−	12.1863i	−1.21957	−	0.972571i	−0.219570	−	0.975597i	$-0.570465\pi$
$157$	−15.2811	−	12.1863i	−1.21957	−	0.972571i	−0.999995	+	0.00302581i	$0.999037\pi$
$158$		0			0
$159$	−24.1323	−	11.6215i	−1.91381	−	0.921644i
$160$		0			0
$161$	1.92466	−	6.28924i	0.151684	−	0.495662i
$162$		0			0
$163$	−11.3087	−	9.01835i	−0.885762	−	0.706372i	0.0709277	−	0.997481i	$-0.477404\pi$
$163$	−11.3087	−	9.01835i	−0.885762	−	0.706372i	−0.956690	+	0.291110i	$0.905975\pi$
$164$		0			0
$165$	38.5866			3.00396
$166$		0			0
$167$	7.49174	+	3.60783i	0.579728	+	0.279183i	0.700680	−	0.713476i	$-0.252880\pi$
$167$	7.49174	+	3.60783i	0.579728	+	0.279183i	−0.120951	+	0.992658i	$0.538594\pi$
$168$		0			0
$169$	20.0520	−	9.65654i	1.54246	−	0.742811i
$170$		0			0
$171$	2.15611	−	9.44652i	0.164882	−	0.722394i
$172$		0			0
$173$	−9.11432	−	18.9261i	−0.692949	−	1.43892i	−0.888802	−	0.458291i	$-0.848462\pi$
$173$	−9.11432	−	18.9261i	−0.692949	−	1.43892i	0.195853	−	0.980633i	$-0.437252\pi$
$174$		0			0
$175$	16.5438	−	11.3334i	1.25059	−	0.856724i
$176$		0			0
$177$	−7.13079			−0.535983
$178$		0			0
$179$	1.33194	−	2.76580i	0.0995540	−	0.206726i	−0.845243	−	0.534382i	$-0.820544\pi$
$179$	1.33194	−	2.76580i	0.0995540	−	0.206726i	0.944797	+	0.327656i	$0.106259\pi$
$180$		0			0
$181$	12.6788	+	2.89386i	0.942410	+	0.215099i	0.666009	−	0.745943i	$-0.268001\pi$
$181$	12.6788	+	2.89386i	0.942410	+	0.215099i	0.276401	+	0.961042i	$0.410858\pi$
$182$		0			0
$183$	9.36268	−	2.13697i	0.692109	−	0.157969i
$184$		0			0
$185$	−30.8878	+	7.04994i	−2.27092	+	0.518322i
$186$		0			0
$187$	2.25980	−	9.90083i	0.165253	−	0.724020i
$188$		0			0
$189$	3.66739	+	1.12231i	0.266763	+	0.0816359i
$190$		0			0
$191$	−12.0193	+	9.58505i	−0.869684	+	0.693550i	−0.952999	−	0.302973i	$-0.902021\pi$
$191$	−12.0193	+	9.58505i	−0.869684	+	0.693550i	0.0833147	+	0.996523i	$0.473449\pi$
$192$		0			0
$193$	4.00270	+	5.01923i	0.288121	+	0.361292i	0.904736	−	0.425973i	$-0.140068\pi$
$193$	4.00270	+	5.01923i	0.288121	+	0.361292i	−0.616615	+	0.787265i	$0.711497\pi$
$194$		0			0
$195$	−48.8233			−3.49631
$196$		0			0
$197$	−10.1071			−0.720102			−0.360051	−	0.932933i	$-0.617241\pi$
$197$	−10.1071			−0.720102			−0.360051	+	0.932933i	$0.617241\pi$
$198$		0			0
$199$	−6.24464	−	7.83052i	−0.442670	−	0.555091i	0.509574	−	0.860427i	$-0.329803\pi$
$199$	−6.24464	−	7.83052i	−0.442670	−	0.555091i	−0.952245	+	0.305335i	$0.901231\pi$
$200$		0			0
$201$	−7.59480	+	6.05665i	−0.535696	+	0.427203i
$202$		0			0
$203$	4.25732	+	10.7769i	0.298805	+	0.756389i
$204$		0			0
$205$	0.212896	−	0.932756i	0.0148693	−	0.0651465i
$206$		0			0
$207$	5.75539	−	1.31363i	0.400028	−	0.0913037i
$208$		0			0
$209$	−18.6674	+	4.26072i	−1.29125	+	0.294720i
$210$		0			0
$211$	8.32839	+	1.90090i	0.573350	+	0.130863i	0.499359	−	0.866395i	$-0.333569\pi$
$211$	8.32839	+	1.90090i	0.573350	+	0.130863i	0.0739916	+	0.997259i	$0.476426\pi$
$212$		0			0
$213$	−9.15979	+	19.0205i	−0.627618	+	1.30326i
$214$		0			0
$215$	17.8822			1.21956
$216$		0			0
$217$	−13.0740	−	12.0769i	−0.887523	−	0.819833i
$218$		0			0
$219$	−1.55965	−	3.23864i	−0.105391	−	0.218847i
$220$		0			0
$221$	−2.85930	+	12.5274i	−0.192338	+	0.842686i
$222$		0			0
$223$	−22.4477	+	10.8102i	−1.50321	+	0.723906i	−0.990863	−	0.134875i	$-0.956937\pi$
$223$	−22.4477	+	10.8102i	−1.50321	+	0.723906i	−0.512343	+	0.858781i	$0.671222\pi$
$224$		0			0
$225$	16.2168	+	7.80960i	1.08112	+	0.520640i
$226$		0			0
$227$	6.92816			0.459838			0.229919	−	0.973210i	$-0.426154\pi$
$227$	6.92816			0.459838			0.229919	+	0.973210i	$0.426154\pi$
$228$		0			0
$229$	−4.28471	−	3.41695i	−0.283142	−	0.225798i	0.471612	−	0.881806i	$-0.343672\pi$
$229$	−4.28471	−	3.41695i	−0.283142	−	0.225798i	−0.754754	+	0.656008i	$0.772244\pi$
$230$		0			0
$231$	4.35339	+	28.4530i	0.286432	+	1.87207i
$232$		0			0
$233$	−5.13534	−	2.47305i	−0.336427	−	0.162015i	0.258041	−	0.966134i	$-0.416923\pi$
$233$	−5.13534	−	2.47305i	−0.336427	−	0.162015i	−0.594468	+	0.804119i	$0.702637\pi$
$234$		0			0
$235$	−0.270393	−	0.215631i	−0.0176385	−	0.0140662i
$236$		0			0
$237$	−27.1156	+	21.6240i	−1.76135	+	1.40463i
$238$		0			0
$239$	6.51054	+	5.19198i	0.421132	+	0.335841i	0.811017	−	0.585022i	$-0.198914\pi$
$239$	6.51054	+	5.19198i	0.421132	+	0.335841i	−0.389886	+	0.920863i	$0.627486\pi$
$240$		0			0
$241$	9.87007	+	20.4954i	0.635787	+	1.32023i	0.931079	+	0.364819i	$0.118869\pi$
$241$	9.87007	+	20.4954i	0.635787	+	1.32023i	−0.295291	+	0.955407i	$0.595417\pi$
$242$		0			0
$243$	4.44123	+	19.4583i	0.284905	+	1.24825i
$244$		0			0
$245$	16.9677	+	18.1244i	1.08403	+	1.15792i
$246$		0			0
$247$	23.6197	−	5.39105i	1.50289	−	0.343024i
$248$		0			0
$249$	9.01026	−	4.33911i	0.571002	−	0.274980i
$250$		0			0
$251$	−2.20871	+	2.76963i	−0.139413	+	0.174818i	−0.846636	−	0.532172i	$-0.821376\pi$
$251$	−2.20871	+	2.76963i	−0.139413	+	0.174818i	0.707224	+	0.706990i	$0.249947\pi$
$252$		0			0
$253$	−7.27352	−	9.12070i	−0.457282	−	0.573414i
$254$		0			0
$255$	11.0946	−	13.9122i	0.694772	−	0.871216i
$256$		0			0
$257$	9.27941	−	19.2689i	0.578833	−	1.20196i	−0.381827	−	0.924234i	$-0.624705\pi$
$257$	9.27941	−	19.2689i	0.578833	−	1.20196i	0.960660	−	0.277726i	$-0.0895808\pi$
$258$		0			0
$259$	−8.68329	−	21.9807i	−0.539554	−	1.36581i
$260$		0			0
$261$	−6.48451	+	8.13132i	−0.401381	+	0.503316i
$262$		0			0
$263$			15.6121i			0.962683i	0.876533	+	0.481342i	$0.159850\pi$
$263$			15.6121i			0.962683i	−0.876533	+	0.481342i	$0.840150\pi$
$264$		0			0
$265$	−17.7793	+	36.9192i	−1.09218	+	2.26793i
$266$		0			0
$267$	−16.9367	−	35.1694i	−1.03651	−	2.15233i
$268$		0			0
$269$	1.57546	+	0.359588i	0.0960573	+	0.0219245i	0.270279	−	0.962782i	$-0.412884\pi$
$269$	1.57546	+	0.359588i	0.0960573	+	0.0219245i	−0.174222	+	0.984706i	$0.555741\pi$
$270$		0			0
$271$	−11.2359	+	5.41095i	−0.682535	+	0.328692i	−0.742822	−	0.669489i	$-0.766513\pi$
$271$	−11.2359	+	5.41095i	−0.682535	+	0.328692i	0.0602863	+	0.998181i	$0.480799\pi$
$272$		0			0
$273$	−5.50831	−	36.0014i	−0.333378	−	2.17890i
$274$		0			0
$275$		−	35.5687i		−	2.14487i
$276$		0			0
$277$	7.01008	+	3.37588i	0.421195	+	0.202837i	0.632462	−	0.774592i	$-0.282045\pi$
$277$	7.01008	+	3.37588i	0.421195	+	0.202837i	−0.211267	+	0.977428i	$0.567759\pi$
$278$		0			0
$279$	3.55480	−	15.5746i	0.212821	−	0.932428i
$280$		0			0
$281$	4.35932	+	19.0994i	0.260056	+	1.13938i	0.921191	+	0.389111i	$0.127218\pi$
$281$	4.35932	+	19.0994i	0.260056	+	1.13938i	−0.661135	+	0.750267i	$0.729925\pi$
$282$		0			0
$283$	−4.86056	−	21.2955i	−0.288930	−	1.26589i	−0.885996	−	0.463693i	$-0.846524\pi$
$283$	−4.86056	−	21.2955i	−0.288930	−	1.26589i	0.597066	−	0.802192i	$-0.296333\pi$
$284$		0			0
$285$	−32.7091	−	7.46563i	−1.93752	−	0.442226i
$286$		0			0
$287$	0.711816	+	0.0517505i	0.0420172	+	0.00305473i
$288$		0			0
$289$	7.67938	+	9.62964i	0.451728	+	0.566449i
$290$		0			0
$291$	−27.7181	+	22.1044i	−1.62486	+	1.29579i
$292$		0			0
$293$		−	29.5755i		−	1.72782i	−0.503648	−	0.863909i	$-0.668009\pi$
$293$		−	29.5755i		−	1.72782i	0.503648	−	0.863909i	$-0.331991\pi$
$294$		0			0
$295$			10.9092i			0.635156i
$296$		0			0
$297$	5.31847	−	4.24134i	0.308609	−	0.246107i
$298$		0			0
$299$	9.20312	+	11.5403i	0.532230	+	0.667395i
$300$		0			0
$301$	2.01750	+	13.1860i	0.116287	+	0.760030i
$302$		0			0
$303$	26.1629	+	5.97152i	1.50302	+	0.343055i
$304$		0			0
$305$	−3.26928	−	14.3236i	−0.187198	−	0.820170i
$306$		0			0
$307$	−1.17334	−	5.14075i	−0.0669662	−	0.293398i	0.930345	−	0.366686i	$-0.119508\pi$
$307$	−1.17334	−	5.14075i	−0.0669662	−	0.293398i	−0.997311	+	0.0732883i	$0.976651\pi$
$308$		0			0
$309$	1.30949	−	5.73725i	0.0744942	−	0.326381i
$310$		0			0
$311$	−22.3697	−	10.7727i	−1.26847	−	0.610862i	−0.326068	−	0.945346i	$-0.605724\pi$
$311$	−22.3697	−	10.7727i	−1.26847	−	0.610862i	−0.942401	+	0.334484i	$0.891438\pi$
$312$		0			0
$313$		−	3.86468i		−	0.218445i	−0.994017	−	0.109222i	$-0.965164\pi$
$313$		−	3.86468i		−	0.218445i	0.994017	−	0.109222i	$-0.0348361\pi$
$314$		0			0
$315$	−6.52094	+	21.3086i	−0.367414	+	1.20061i
$316$		0			0
$317$	27.1510	−	13.0752i	1.52495	−	0.734379i	0.531334	−	0.847163i	$-0.321691\pi$
$317$	27.1510	−	13.0752i	1.52495	−	0.734379i	0.993620	+	0.112784i	$0.0359767\pi$
$318$		0			0
$319$	20.0370	+	4.57332i	1.12186	+	0.256057i
$320$		0			0
$321$	−3.30671	−	6.86645i	−0.184562	−	0.383248i
$322$		0			0
$323$	−3.83117	+	7.95551i	−0.213172	+	0.442657i
$324$		0			0
$325$			45.0047i			2.49641i
$326$		0			0
$327$	10.3787	−	13.0145i	0.573944	−	0.719703i
$328$		0			0
$329$	0.128496	−	0.223710i	0.00708423	−	0.0123335i
$330$		0			0
$331$	8.98135	−	18.6500i	0.493660	−	1.02510i	−0.494142	−	0.869381i	$-0.664518\pi$
$331$	8.98135	−	18.6500i	0.493660	−	1.02510i	0.987802	−	0.155714i	$-0.0497679\pi$
$332$		0			0
$333$	13.2259	−	16.5848i	0.724775	−	0.908840i
$334$		0			0
$335$	9.26587	+	11.6190i	0.506249	+	0.634816i
$336$		0			0
$337$	9.01619	−	11.3059i	0.491143	−	0.615874i	−0.473063	−	0.881029i	$-0.656852\pi$
$337$	9.01619	−	11.3059i	0.491143	−	0.615874i	0.964206	+	0.265155i	$0.0854230\pi$
$338$		0			0
$339$	7.84913	−	3.77994i	0.426306	−	0.205298i
$340$		0			0
$341$	−30.7772	+	7.02471i	−1.66668	+	0.380409i
$342$		0			0
$343$	−11.4503	+	14.5565i	−0.618256	+	0.785977i
$344$		0			0
$345$	−4.54852	−	19.9284i	−0.244884	−	1.07291i
$346$		0			0
$347$	2.59238	+	5.38314i	0.139166	+	0.288982i	0.958890	−	0.283777i	$-0.0915874\pi$
$347$	2.59238	+	5.38314i	0.139166	+	0.288982i	−0.819724	+	0.572759i	$0.805873\pi$
$348$		0			0
$349$	14.7441	+	11.7581i	0.789236	+	0.629395i	0.932861	−	0.360237i	$-0.117304\pi$
$349$	14.7441	+	11.7581i	0.789236	+	0.629395i	−0.143624	+	0.989632i	$0.545876\pi$
$350$		0			0
$351$	−6.72941	+	5.36653i	−0.359190	+	0.286444i
$352$		0			0
$353$	14.2625	+	11.3740i	0.759119	+	0.605377i	0.924646	−	0.380828i	$-0.124361\pi$
$353$	14.2625	+	11.3740i	0.759119	+	0.605377i	−0.165527	+	0.986205i	$0.552932\pi$
$354$		0			0
$355$	29.0988	+	14.0133i	1.54441	+	0.743746i
$356$		0			0
$357$	11.5103	+	6.61137i	0.609190	+	0.349911i
$358$		0			0
$359$	19.2838	+	15.3783i	1.01776	+	0.811638i	0.982221	−	0.187730i	$-0.0601131\pi$
$359$	19.2838	+	15.3783i	1.01776	+	0.811638i	0.0355411	+	0.999368i	$0.488685\pi$
$360$		0			0
$361$	−2.35165			−0.123771
$362$		0			0
$363$	23.0219	+	11.0867i	1.20833	+	0.581903i
$364$		0			0
$365$	−4.95469	+	2.38605i	−0.259340	+	0.124892i
$366$		0			0
$367$	3.93605	−	17.2450i	0.205460	−	0.900179i	−0.762084	−	0.647478i	$-0.775824\pi$
$367$	3.93605	−	17.2450i	0.205460	−	0.900179i	0.967544	−	0.252702i	$-0.0813191\pi$
$368$		0			0
$369$	0.277940	+	0.577148i	0.0144690	+	0.0300451i
$370$		0			0
$371$	−29.2294	−	8.94488i	−1.51751	−	0.464395i
$372$		0			0
$373$	0.708793			0.0366999			0.0183500	−	0.999832i	$-0.494159\pi$
$373$	0.708793			0.0366999			0.0183500	+	0.999832i	$0.494159\pi$
$374$		0			0
$375$	9.20283	−	19.1099i	0.475232	−	0.986830i
$376$		0			0
$377$	−25.3527	−	5.78658i	−1.30573	−	0.298024i
$378$		0			0
$379$	15.9228	−	3.63427i	0.817899	−	0.186680i	0.206951	−	0.978351i	$-0.433646\pi$
$379$	15.9228	−	3.63427i	0.817899	−	0.186680i	0.610948	+	0.791671i	$0.290789\pi$
$380$		0			0
$381$	45.9369	−	10.4848i	2.35342	−	0.537152i
$382$		0			0
$383$	−4.12178	+	18.0587i	−0.210613	+	0.922757i	0.753538	+	0.657404i	$0.228346\pi$
$383$	−4.12178	+	18.0587i	−0.210613	+	0.922757i	−0.964151	+	0.265353i	$0.914512\pi$
$384$		0			0
$385$	43.5294	−	6.66011i	2.21846	−	0.339431i
$386$		0			0
$387$	−9.36088	+	7.46505i	−0.475840	+	0.379470i
$388$		0			0
$389$	10.4114	+	13.0555i	0.527878	+	0.661938i	0.972261	−	0.233899i	$-0.0751484\pi$
$389$	10.4114	+	13.0555i	0.527878	+	0.661938i	−0.444383	+	0.895837i	$0.646577\pi$
$390$		0			0
$391$	−5.37974			−0.272065
$392$		0			0
$393$	17.5378			0.884667
$394$		0			0
$395$	33.0818	+	41.4833i	1.66453	+	2.08725i
$396$		0			0
$397$	17.8317	−	14.2203i	0.894948	−	0.713697i	−0.0637976	−	0.997963i	$-0.520321\pi$
$397$	17.8317	−	14.2203i	0.894948	−	0.713697i	0.958746	+	0.284266i	$0.0917498\pi$
$398$		0			0
$399$	1.81474	−	24.9614i	0.0908506	−	1.24963i
$400$		0			0
$401$	−0.942528	+	4.12948i	−0.0470676	+	0.206217i	−0.992994	−	0.118165i	$-0.962299\pi$
$401$	−0.942528	+	4.12948i	−0.0470676	+	0.206217i	0.945926	+	0.324381i	$0.105156\pi$
$402$		0			0
$403$	38.9422	−	8.88830i	1.93985	−	0.442758i
$404$		0			0
$405$	36.2549	−	8.27494i	1.80152	−	0.411185i
$406$		0			0
$407$	−40.8678	−	9.32781i	−2.02574	−	0.462362i
$408$		0			0
$409$	1.40849	−	2.92476i	0.0696455	−	0.144620i	−0.863240	−	0.504794i	$-0.831568\pi$
$409$	1.40849	−	2.92476i	0.0696455	−	0.144620i	0.932885	+	0.360174i	$0.117283\pi$
$410$		0			0
$411$	39.6206			1.95434
$412$		0			0
$413$	−8.04421	+	1.23079i	−0.395830	+	0.0605630i
$414$		0			0
$415$	−6.63826	−	13.7845i	−0.325859	−	0.676654i
$416$		0			0
$417$	−8.72366	+	38.2209i	−0.427199	+	1.87168i
$418$		0			0
$419$	−8.42438	+	4.05697i	−0.411558	+	0.198196i	−0.628194	−	0.778056i	$-0.716206\pi$
$419$	−8.42438	+	4.05697i	−0.411558	+	0.198196i	0.216636	+	0.976252i	$0.430491\pi$
$420$		0			0
$421$	−13.2167	−	6.36482i	−0.644142	−	0.310202i	0.0831435	−	0.996538i	$-0.473504\pi$
$421$	−13.2167	−	6.36482i	−0.644142	−	0.310202i	−0.727285	+	0.686335i	$0.759218\pi$
$422$		0			0
$423$	0.231560			0.0112588
$424$		0			0
$425$	−12.8241	−	10.2269i	−0.622061	−	0.496077i
$426$		0			0
$427$	10.1932	−	4.02672i	0.493281	−	0.194867i
$428$		0			0
$429$	−58.2011	−	28.0282i	−2.80998	−	1.35321i
$430$		0			0
$431$	25.2127	+	20.1065i	1.21445	+	0.968495i	0.999966	−	0.00823097i	$-0.00262003\pi$
$431$	25.2127	+	20.1065i	1.21445	+	0.968495i	0.214489	+	0.976726i	$0.431191\pi$
$432$		0			0
$433$	−16.2970	+	12.9964i	−0.783183	+	0.624567i	−0.931238	−	0.364412i	$-0.881270\pi$
$433$	−16.2970	+	12.9964i	−0.783183	+	0.624567i	0.148055	+	0.988979i	$0.452699\pi$
$434$		0			0
$435$	28.1551	+	22.4530i	1.34993	+	1.07654i
$436$		0			0
$437$	4.40096	+	9.13869i	0.210527	+	0.437163i
$438$		0			0
$439$	−5.34531	−	23.4193i	−0.255118	−	1.11774i	−0.926400	−	0.376541i	$-0.877113\pi$
$439$	−5.34531	−	23.4193i	−0.255118	−	1.11774i	0.671282	−	0.741202i	$-0.265744\pi$
$440$		0			0
$441$	−16.4483	−	2.40436i	−0.783252	−	0.114493i
$442$		0			0
$443$	5.60975	−	1.28039i	0.266527	−	0.0608331i	−0.0871687	−	0.996194i	$-0.527782\pi$
$443$	5.60975	−	1.28039i	0.266527	−	0.0608331i	0.353696	+	0.935360i	$0.384925\pi$
$444$		0			0
$445$	−53.8045	+	25.9109i	−2.55058	+	1.22829i
$446$		0			0
$447$	27.0236	−	33.8865i	1.27817	−	1.60278i
$448$		0			0
$449$	−4.88694	−	6.12803i	−0.230629	−	0.289199i	0.653029	−	0.757333i	$-0.273498\pi$
$449$	−4.88694	−	6.12803i	−0.230629	−	0.289199i	−0.883658	+	0.468134i	$0.844927\pi$
$450$		0			0
$451$	0.789259	−	0.989699i	0.0371647	−	0.0466031i
$452$		0			0
$453$	−12.6929	+	26.3571i	−0.596364	+	1.23836i
$454$		0			0
$455$	−55.0773	+	8.42698i	−2.58207	+	0.395063i
$456$		0			0
$457$	−2.11019	+	2.64610i	−0.0987107	+	0.123779i	−0.828733	−	0.559644i	$-0.810938\pi$
$457$	−2.11019	+	2.64610i	−0.0987107	+	0.123779i	0.730023	+	0.683423i	$0.239509\pi$
$458$		0			0
$459$		−	3.13704i		−	0.146424i
$460$		0			0
$461$	−4.49068	+	9.32499i	−0.209152	+	0.434308i	−0.978984	−	0.203939i	$-0.934626\pi$
$461$	−4.49068	+	9.32499i	−0.209152	+	0.434308i	0.769832	+	0.638247i	$0.220340\pi$
$462$		0			0
$463$	0.944376	+	1.96102i	0.0438889	+	0.0911362i	0.921760	−	0.387760i	$-0.126751\pi$
$463$	0.944376	+	1.96102i	0.0438889	+	0.0911362i	−0.877871	+	0.478897i	$0.841037\pi$
$464$		0			0
$465$	−53.9279	−	12.3087i	−2.50085	−	0.570802i
$466$		0			0
$467$	−21.2648	+	10.2406i	−0.984020	+	0.473879i	−0.855486	−	0.517826i	$-0.826741\pi$
$467$	−21.2648	+	10.2406i	−0.984020	+	0.473879i	−0.128534	+	0.991705i	$0.541027\pi$
$468$		0			0
$469$	−7.52227	+	8.14336i	−0.347346	+	0.376025i
$470$		0			0
$471$		−	45.3127i		−	2.08790i
$472$		0			0
$473$	21.3170	+	10.2657i	0.980156	+	0.472018i
$474$		0			0
$475$	−6.88173	+	30.1508i	−0.315756	+	1.38342i
$476$		0			0
$477$	−6.10513	−	26.7483i	−0.279535	−	1.22472i
$478$		0			0
$479$	5.15270	+	22.5755i	0.235433	+	1.03150i	0.945054	+	0.326915i	$0.106009\pi$
$479$	5.15270	+	22.5755i	0.235433	+	1.03150i	−0.709621	+	0.704584i	$0.751134\pi$
$480$		0			0
$481$	51.7097	+	11.8024i	2.35776	+	0.538143i
$482$		0			0
$483$	14.1816	−	5.60233i	0.645287	−	0.254915i
$484$		0			0
$485$	33.8168	+	42.4050i	1.53554	+	1.92551i
$486$		0			0
$487$	−9.74360	+	7.77026i	−0.441524	+	0.352104i	−0.818880	−	0.573964i	$-0.805405\pi$
$487$	−9.74360	+	7.77026i	−0.441524	+	0.352104i	0.377356	+	0.926068i	$0.376833\pi$
$488$		0			0
$489$		−	33.5333i		−	1.51643i
$490$		0			0
$491$		−	17.7714i		−	0.802011i	−0.916076	−	0.401005i	$-0.868661\pi$
$491$		−	17.7714i		−	0.802011i	0.916076	−	0.401005i	$-0.131339\pi$
$492$		0			0
$493$	7.41003	−	5.90930i	0.333731	−	0.266142i
$494$		0			0
$495$	24.6434	+	30.9019i	1.10764	+	1.38894i
$496$		0			0
$497$	−7.05015	+	23.0379i	−0.316242	+	1.03339i
$498$		0			0
$499$	15.2651	+	3.48416i	0.683359	+	0.155972i	0.550087	−	0.835107i	$-0.314595\pi$
$499$	15.2651	+	3.48416i	0.683359	+	0.155972i	0.133272	+	0.991080i	$0.457452\pi$
$500$		0			0
$501$	4.28965	+	18.7942i	0.191648	+	0.839663i
$502$		0			0
$503$	5.07467	+	22.2336i	0.226268	+	0.991346i	0.952653	+	0.304058i	$0.0983418\pi$
$503$	5.07467	+	22.2336i	0.226268	+	0.991346i	−0.726385	+	0.687288i	$0.758801\pi$
$504$		0			0
$505$	9.13563	−	40.0258i	0.406530	−	1.78113i
$506$		0			0
$507$	46.4875	+	22.3872i	2.06458	+	0.994251i
$508$		0			0
$509$			24.9810i			1.10726i	0.832762	+	0.553631i	$0.186758\pi$
$509$			24.9810i			1.10726i	−0.832762	+	0.553631i	$0.813242\pi$
$510$		0			0
$511$	−2.31843	−	3.38430i	−0.102561	−	0.149713i
$512$		0			0
$513$	−5.32896	+	2.56629i	−0.235279	+	0.113305i
$514$		0			0
$515$	−8.77723	−	2.00334i	−0.386771	−	0.0882779i
$516$		0			0
$517$	−0.198541	−	0.412274i	−0.00873181	−	0.0181318i
$518$		0			0
$519$	21.1302	−	43.8772i	0.927511	−	1.92600i
$520$		0			0
$521$			14.9010i			0.652823i	0.945228	+	0.326412i	$0.105840\pi$
$521$			14.9010i			0.652823i	−0.945228	+	0.326412i	$0.894160\pi$
$522$		0			0
$523$	−7.43614	+	9.32463i	−0.325160	+	0.407737i	−0.917363	−	0.398051i	$-0.869687\pi$
$523$	−7.43614	+	9.32463i	−0.325160	+	0.407737i	0.592204	+	0.805788i	$0.298258\pi$
$524$		0			0
$525$	44.4559	+	13.6045i	1.94021	+	0.593751i
$526$		0			0
$527$	−6.31651	+	13.1164i	−0.275151	+	0.571358i
$528$		0			0
$529$	10.4872	−	13.1505i	0.455965	−	0.571762i
$530$		0			0
$531$	−4.55410	−	5.71066i	−0.197631	−	0.247821i
$532$		0			0
$533$	−0.998642	+	1.25226i	−0.0432560	+	0.0542413i
$534$		0			0
$535$	−10.5047	+	5.05882i	−0.454160	+	0.218712i
$536$		0			0
$537$	6.93845	−	1.58366i	0.299416	−	0.0683398i
$538$		0			0
$539$	9.82208	+	31.3464i	0.423067	+	1.35018i
$540$		0			0
$541$	7.30131	+	31.9891i	0.313908	+	1.37532i	0.848046	+	0.529923i	$0.177779\pi$
$541$	7.30131	+	31.9891i	0.313908	+	1.37532i	−0.534138	+	0.845397i	$0.679364\pi$
$542$		0			0
$543$	13.0815	+	27.1641i	0.561382	+	1.16572i
$544$		0			0
$545$	−19.9104	−	15.8780i	−0.852869	−	0.680141i
$546$		0			0
$547$	14.1530	−	11.2867i	0.605140	−	0.482583i	−0.272337	−	0.962202i	$-0.587797\pi$
$547$	14.1530	−	11.2867i	0.605140	−	0.482583i	0.877477	+	0.479619i	$0.159225\pi$
$548$		0			0
$549$	7.69088	+	6.13328i	0.328239	+	0.261762i
$550$		0			0
$551$	−16.1001	−	7.75342i	−0.685889	−	0.330307i
$552$		0			0
$553$	−26.8567	+	29.0741i	−1.14206	+	1.23636i
$554$		0			0
$555$	−57.4256	−	45.7954i	−2.43758	−	1.94391i
$556$		0			0
$557$	−2.04282			−0.0865570			−0.0432785	−	0.999063i	$-0.513780\pi$
$557$	−2.04282			−0.0865570			−0.0432785	+	0.999063i	$0.513780\pi$
$558$		0			0
$559$	−26.9722	−	12.9891i	−1.14080	−	0.549382i
$560$		0			0
$561$	21.2123	−	10.2153i	0.895583	−	0.431290i
$562$		0			0
$563$	2.75162	−	12.0556i	0.115967	−	0.508084i	−0.883264	−	0.468876i	$-0.844659\pi$
$563$	2.75162	−	12.0556i	0.115967	−	0.508084i	0.999231	−	0.0392085i	$-0.0124836\pi$
$564$		0			0
$565$	−5.78281	−	12.0081i	−0.243285	−	0.505186i
$566$		0			0
$567$	10.1921	+	25.8001i	0.428029	+	1.08350i
$568$		0			0
$569$	−28.3263			−1.18750			−0.593750	−	0.804650i	$-0.702353\pi$
$569$	−28.3263			−1.18750			−0.593750	+	0.804650i	$0.702353\pi$
$570$		0			0
$571$	11.0645	−	22.9756i	0.463034	−	0.961500i	−0.530470	−	0.847704i	$-0.677985\pi$
$571$	11.0645	−	22.9756i	0.463034	−	0.961500i	0.993504	−	0.113796i	$-0.0363012\pi$
$572$		0			0
$573$	−34.7469	−	7.93075i	−1.45157	−	0.331312i
$574$		0			0
$575$	−18.3697	+	4.19277i	−0.766070	+	0.174851i
$576$		0			0
$577$	−14.3858	+	3.28347i	−0.598890	+	0.136693i	−0.511210	−	0.859456i	$-0.670802\pi$
$577$	−14.3858	+	3.28347i	−0.598890	+	0.136693i	−0.0876801	+	0.996149i	$0.527945\pi$
$578$		0			0
$579$	−3.31187	+	14.5102i	−0.137636	+	0.603025i
$580$		0			0
$581$	9.41549	−	6.45012i	0.390621	−	0.267596i
$582$		0			0
$583$	−42.3887	+	33.8038i	−1.75556	+	1.40001i
$584$		0			0
$585$	−31.1811	−	39.0999i	−1.28918	−	1.61658i
$586$		0			0
$587$	−16.6979			−0.689196			−0.344598	−	0.938750i	$-0.611985\pi$
$587$	−16.6979			−0.689196			−0.344598	+	0.938750i	$0.611985\pi$
$588$		0			0
$589$	27.4484			1.13099
$590$		0			0
$591$	−14.6095	−	18.3197i	−0.600954	−	0.753572i
$592$		0			0
$593$	−9.64991	+	7.69554i	−0.396274	+	0.316018i	−0.801273	−	0.598299i	$-0.795843\pi$
$593$	−9.64991	+	7.69554i	−0.396274	+	0.316018i	0.404999	+	0.914317i	$0.367272\pi$
$594$		0			0
$595$	10.1145	−	17.6093i	0.414655	−	0.721909i
$596$		0			0
$597$	5.16686	−	22.6375i	0.211466	−	0.926491i
$598$		0			0
$599$	44.6409	−	10.1890i	1.82398	−	0.416311i	0.833332	−	0.552773i	$-0.186430\pi$
$599$	44.6409	−	10.1890i	1.82398	−	0.416311i	0.990645	+	0.136462i	$0.0435730\pi$
$600$		0			0
$601$	17.6526	−	4.02910i	0.720066	−	0.164350i	0.153241	−	0.988189i	$-0.451029\pi$
$601$	17.6526	−	4.02910i	0.720066	−	0.164350i	0.566825	+	0.823838i	$0.308172\pi$
$602$		0			0
$603$	−9.70088	−	2.21416i	−0.395051	−	0.0901677i
$604$		0			0
$605$	16.9612	−	35.2204i	0.689572	−	1.43191i
$606$		0			0
$607$	−20.6711			−0.839016			−0.419508	−	0.907752i	$-0.637797\pi$
$607$	−20.6711			−0.839016			−0.419508	+	0.907752i	$0.637797\pi$
$608$		0			0
$609$	−13.3799	+	23.2942i	−0.542181	+	0.943930i
$610$		0			0
$611$	0.251212	+	0.521647i	0.0101629	+	0.0211036i
$612$		0			0
$613$	1.73100	−	7.58402i	0.0699146	−	0.306316i	−0.927865	−	0.372916i	$-0.878358\pi$
$613$	1.73100	−	7.58402i	0.0699146	−	0.306316i	0.997780	+	0.0666000i	$0.0212152\pi$
$614$		0			0
$615$	1.99841	−	0.962381i	0.0805835	−	0.0388070i
$616$		0			0
$617$	1.30129	+	0.626666i	0.0523878	+	0.0252286i	0.459894	−	0.887974i	$-0.347887\pi$
$617$	1.30129	+	0.626666i	0.0523878	+	0.0252286i	−0.407506	+	0.913202i	$0.633602\pi$
$618$		0			0
$619$	−46.8049			−1.88125			−0.940624	−	0.339449i	$-0.889759\pi$
$619$	−46.8049			−1.88125			−0.940624	+	0.339449i	$0.889759\pi$
$620$		0			0
$621$	−2.81740	−	2.24680i	−0.113059	−	0.0901612i
$622$		0			0
$623$	−25.1765	−	36.7512i	−1.00868	−	1.47240i
$624$		0			0
$625$	4.90897	+	2.36403i	0.196359	+	0.0945613i
$626$		0			0
$627$	−34.7059	−	27.6770i	−1.38602	−	1.10531i
$628$		0			0
$629$	−15.1136	+	12.0527i	−0.602619	+	0.480573i
$630$		0			0
$631$	1.07685	+	0.858762i	0.0428688	+	0.0341868i	0.644690	−	0.764444i	$-0.276987\pi$
$631$	1.07685	+	0.858762i	0.0428688	+	0.0341868i	−0.601821	+	0.798631i	$0.705558\pi$
$632$		0			0
$633$	8.59291	+	17.8434i	0.341538	+	0.709210i
$634$		0			0
$635$	−16.0403	−	70.2773i	−0.636541	−	2.78887i
$636$		0			0
$637$	−12.4278	−	39.6623i	−0.492407	−	1.57148i
$638$		0			0
$639$	−21.0824	+	4.81192i	−0.834007	+	0.190357i
$640$		0			0
$641$	23.5537	−	11.3429i	0.930316	−	0.448017i	0.0935731	−	0.995612i	$-0.470171\pi$
$641$	23.5537	−	11.3429i	0.930316	−	0.448017i	0.836743	+	0.547596i	$0.184457\pi$
$642$		0			0
$643$	0.582816	−	0.730828i	0.0229840	−	0.0288210i	−0.770207	−	0.637794i	$-0.779847\pi$
$643$	0.582816	−	0.730828i	0.0229840	−	0.0288210i	0.793191	+	0.608973i	$0.208418\pi$
$644$		0			0
$645$	25.8481	+	32.4125i	1.01777	+	1.27624i
$646$		0			0
$647$	2.59651	−	3.25592i	0.102079	−	0.128003i	−0.728168	−	0.685399i	$-0.759628\pi$
$647$	2.59651	−	3.25592i	0.102079	−	0.128003i	0.830247	+	0.557396i	$0.188199\pi$
$648$		0			0
$649$	−6.26266	+	13.0046i	−0.245831	+	0.510473i
$650$		0			0
$651$	2.99199	−	41.1541i	0.117265	−	1.61296i
$652$		0			0
$653$	−22.3678	+	28.0484i	−0.875321	+	1.09762i	0.119178	+	0.992873i	$0.461974\pi$
$653$	−22.3678	+	28.0484i	−0.875321	+	1.09762i	−0.994499	+	0.104745i	$0.966597\pi$
$654$		0			0
$655$		−	26.8305i		−	1.04836i
$656$		0			0
$657$	1.59758	−	3.31740i	0.0623274	−	0.129424i
$658$		0			0
$659$	16.7166	+	34.7125i	0.651188	+	1.35221i	0.921102	+	0.389321i	$0.127290\pi$
$659$	16.7166	+	34.7125i	0.651188	+	1.35221i	−0.269914	+	0.962884i	$0.586995\pi$
$660$		0			0
$661$	−22.1532	−	5.05633i	−0.861661	−	0.196668i	−0.231216	−	0.972902i	$-0.574270\pi$
$661$	−22.1532	−	5.05633i	−0.861661	−	0.196668i	−0.630445	+	0.776234i	$0.717128\pi$
$662$		0			0
$663$	−26.8397	+	12.9253i	−1.04237	+	0.501978i
$664$		0			0
$665$	−38.1876	−	2.77631i	−1.48085	−	0.107661i
$666$		0			0
$667$		−	10.8874i		−	0.421561i
$668$		0			0
$669$	−52.0414	−	25.0618i	−2.01204	−	0.968946i
$670$		0			0
$671$	4.32560	−	18.9517i	0.166988	−	0.731622i
$672$		0			0
$673$	−4.15134	−	18.1882i	−0.160022	−	0.701103i	−0.989735	−	0.142913i	$-0.954353\pi$
$673$	−4.15134	−	18.1882i	−0.160022	−	0.701103i	0.829713	−	0.558190i	$-0.188504\pi$
$674$		0			0
$675$	−2.44489	−	10.7118i	−0.0941039	−	0.412296i
$676$		0			0
$677$	38.4347	+	8.77246i	1.47716	+	0.337153i	0.883832	−	0.467804i	$-0.154955\pi$
$677$	38.4347	+	8.77246i	1.47716	+	0.337153i	0.593333	+	0.804957i	$0.297812\pi$
$678$		0			0
$679$	−27.4534	+	29.7201i	−1.05356	+	1.14055i
$680$		0			0
$681$	10.0144	+	12.5577i	0.383753	+	0.481211i
$682$		0			0
$683$	−33.4691	+	26.6907i	−1.28066	+	1.02129i	−0.282584	+	0.959242i	$0.591192\pi$
$683$	−33.4691	+	26.6907i	−1.28066	+	1.02129i	−0.998073	+	0.0620479i	$0.980237\pi$
$684$		0			0
$685$		−	60.6142i		−	2.31595i
$686$		0			0
$687$		−	12.7054i		−	0.484740i
$688$		0			0
$689$	53.6340	−	42.7717i	2.04329	−	1.62947i
$690$		0			0
$691$	0.131609	+	0.165032i	0.00500663	+	0.00627811i	0.784328	−	0.620346i	$-0.213008\pi$
$691$	0.131609	+	0.165032i	0.00500663	+	0.00627811i	−0.779322	+	0.626624i	$0.784436\pi$
$692$		0			0
$693$	−20.0062	+	21.6580i	−0.759972	+	0.822720i
$694$		0			0
$695$	58.4728	+	13.3460i	2.21800	+	0.506244i
$696$		0			0
$697$	−0.129899	−	0.569127i	−0.00492029	−	0.0215572i
$698$		0			0
$699$	−2.94041	−	12.8828i	−0.111217	−	0.487272i
$700$		0			0
$701$	−0.842697	+	3.69210i	−0.0318282	+	0.139449i	−0.988346	−	0.152227i	$-0.951356\pi$
$701$	−0.842697	+	3.69210i	−0.0318282	+	0.139449i	0.956517	+	0.291675i	$0.0942127\pi$
$702$		0			0
$703$	32.8381	+	15.8140i	1.23851	+	0.596436i
$704$		0			0
$705$		−	0.801789i		−	0.0301971i
$706$		0			0
$707$	30.5450	+	2.22068i	1.14876	+	0.0835174i
$708$		0			0
$709$	29.1913	−	14.0578i	1.09630	−	0.527952i	0.203809	−	0.979011i	$-0.434668\pi$
$709$	29.1913	−	14.0578i	1.09630	−	0.527952i	0.892494	+	0.451059i	$0.148953\pi$
$710$		0			0
$711$	−34.6350	−	7.90520i	−1.29891	−	0.296468i
$712$		0			0
$713$	7.25593	+	15.0671i	0.271737	+	0.564267i
$714$		0			0
$715$	−42.8794	+	89.0400i	−1.60360	+	3.32991i
$716$		0			0
$717$			19.3055i			0.720978i
$718$		0			0
$719$	2.20568	−	2.76583i	0.0822579	−	0.103148i	−0.739000	−	0.673706i	$-0.764701\pi$
$719$	2.20568	−	2.76583i	0.0822579	−	0.103148i	0.821258	+	0.570558i	$0.193273\pi$
$720$		0			0
$721$	0.486971	−	6.69818i	0.0181358	−	0.249453i
$722$		0			0
$723$	−22.8822	+	47.5155i	−0.851000	+	1.76712i
$724$		0			0
$725$	20.6969	−	25.9531i	0.768663	−	0.963873i
$726$		0			0
$727$	6.61384	+	8.29350i	0.245294	+	0.307589i	0.889203	−	0.457513i	$-0.151260\pi$
$727$	6.61384	+	8.29350i	0.245294	+	0.307589i	−0.643909	+	0.765102i	$0.722688\pi$
$728$		0			0
$729$	−9.23804	+	11.5841i	−0.342150	+	0.429042i
$730$		0			0
$731$	9.83042	−	4.73408i	0.363591	−	0.175096i
$732$		0			0
$733$	37.0589	−	8.45845i	1.36880	−	0.312420i	0.525927	−	0.850530i	$-0.323719\pi$
$733$	37.0589	−	8.45845i	1.36880	−	0.312420i	0.842875	+	0.538110i	$0.180861\pi$
$734$		0			0
$735$	−8.32521	+	56.9531i	−0.307080	+	2.10075i
$736$		0			0
$737$	4.37544	+	19.1701i	0.161172	+	0.706139i
$738$		0			0
$739$	0.846493	+	1.75776i	0.0311387	+	0.0646602i	0.915958	−	0.401274i	$-0.131433\pi$
$739$	0.846493	+	1.75776i	0.0311387	+	0.0646602i	−0.884819	+	0.465934i	$0.845718\pi$
$740$		0			0
$741$	43.9131	+	35.0195i	1.61319	+	1.28647i
$742$		0			0
$743$	12.9913	−	10.3602i	0.476604	−	0.380079i	−0.355520	−	0.934669i	$-0.615696\pi$
$743$	12.9913	−	10.3602i	0.476604	−	0.380079i	0.832124	+	0.554590i	$0.187125\pi$
$744$		0			0
$745$	−51.8419	−	41.3425i	−1.89934	−	1.51467i
$746$		0			0
$747$	9.22938	+	4.44464i	0.337685	+	0.162621i
$748$		0			0
$749$	−4.91544	−	7.17527i	−0.179606	−	0.262179i
$750$		0			0
$751$	12.7896	+	10.1993i	0.466697	+	0.372179i	0.828420	−	0.560107i	$-0.189240\pi$
$751$	12.7896	+	10.1993i	0.466697	+	0.372179i	−0.361723	+	0.932286i	$0.617811\pi$
$752$		0			0
$753$	−8.21273			−0.299288
$754$		0			0
$755$	40.3228	+	19.4184i	1.46750	+	0.706710i
$756$		0			0
$757$	−5.24086	+	2.52387i	−0.190482	+	0.0917314i	−0.526694	−	0.850055i	$-0.676569\pi$
$757$	−5.24086	+	2.52387i	−0.190482	+	0.0917314i	0.336212	+	0.941786i	$0.390854\pi$
$758$		0			0
$759$	6.01817	−	26.3673i	0.218446	−	0.957073i
$760$		0			0
$761$	3.37651	+	7.01139i	0.122398	+	0.254163i	0.953161	−	0.302465i	$-0.0978094\pi$
$761$	3.37651	+	7.01139i	0.122398	+	0.254163i	−0.830762	+	0.556627i	$0.812095\pi$
$762$		0			0
$763$	9.46186	−	16.4730i	0.342542	−	0.596362i
$764$		0			0
$765$	18.2271			0.659004
$766$		0			0
$767$	7.92409	−	16.4545i	0.286122	−	0.594139i
$768$		0			0
$769$	5.27239	+	1.20339i	0.190127	+	0.0433953i	0.316524	−	0.948584i	$-0.397484\pi$
$769$	5.27239	+	1.20339i	0.190127	+	0.0433953i	−0.126397	+	0.991980i	$0.540341\pi$
$770$		0			0
$771$	48.3390	−	11.0331i	1.74089	−	0.397346i
$772$		0			0
$773$	45.0160	−	10.2746i	1.61911	−	0.369552i	0.685566	−	0.728010i	$-0.259555\pi$
$773$	45.0160	−	10.2746i	1.61911	−	0.369552i	0.933546	+	0.358459i	$0.116698\pi$
$774$		0			0
$775$	−11.3460	+	49.7101i	−0.407561	+	1.78564i
$776$		0			0
$777$	27.2899	−	47.5113i	0.979018	−	1.70446i
$778$		0			0
$779$	−0.860523	+	0.686244i	−0.0308314	+	0.0245873i
$780$		0			0
$781$	26.6434	+	33.4097i	0.953375	+	1.19549i
$782$		0			0
$783$	6.34865			0.226882
$784$		0			0
$785$	−69.3224			−2.47422
$786$		0			0
$787$	−1.41984	−	1.78042i	−0.0506118	−	0.0634652i	0.755881	−	0.654709i	$-0.227209\pi$
$787$	−1.41984	−	1.78042i	−0.0506118	−	0.0634652i	−0.806493	+	0.591243i	$0.798637\pi$
$788$		0			0
$789$	−28.2978	+	22.5667i	−1.00743	+	0.803398i
$790$		0			0
$791$	8.20215	−	5.61891i	0.291635	−	0.199785i
$792$		0			0
$793$	−5.47315	+	23.9794i	−0.194357	+	0.851534i
$794$		0			0
$795$	−92.6174	+	21.1393i	−3.28480	+	0.749735i
$796$		0			0
$797$	−13.5857	+	3.10085i	−0.481231	+	0.109838i	−0.456253	−	0.889850i	$-0.650809\pi$
$797$	−13.5857	+	3.10085i	−0.481231	+	0.109838i	−0.0249782	+	0.999688i	$0.507952\pi$
$798$		0			0
$799$	−0.205729	−	0.0469562i	−0.00727816	−	0.00166119i
$800$		0			0
$801$	17.3486	−	36.0247i	0.612982	−	1.27287i
$802$		0			0
$803$	−7.27614			−0.256769
$804$		0			0
$805$	−8.57083	−	21.6960i	−0.302082	−	0.764684i
$806$		0			0
$807$	1.62550	+	3.37538i	0.0572202	+	0.118819i
$808$		0			0
$809$	−0.400187	+	1.75333i	−0.0140698	+	0.0616439i	−0.981475	−	0.191588i	$-0.938636\pi$
$809$	−0.400187	+	1.75333i	−0.0140698	+	0.0616439i	0.967406	+	0.253232i	$0.0814935\pi$
$810$		0			0
$811$	20.6440	−	9.94163i	0.724909	−	0.349098i	−0.0347707	−	0.999395i	$-0.511070\pi$
$811$	20.6440	−	9.94163i	0.724909	−	0.349098i	0.759680	+	0.650298i	$0.225356\pi$
$812$		0			0
$813$	−26.0488	−	12.5444i	−0.913572	−	0.439953i
$814$		0			0
$815$	−51.3014			−1.79701
$816$		0			0
$817$	−16.0838	−	12.8264i	−0.562701	−	0.448739i
$818$		0			0
$819$	25.3137	−	27.4037i	0.884531	−	0.957563i
$820$		0			0
$821$	−40.6365	−	19.5695i	−1.41822	−	0.682980i	−0.441456	−	0.897283i	$-0.645538\pi$
$821$	−40.6365	−	19.5695i	−1.41822	−	0.682980i	−0.976767	+	0.214303i	$0.931252\pi$
$822$		0			0
$823$	−18.3388	−	14.6247i	−0.639250	−	0.509785i	0.249382	−	0.968405i	$-0.419772\pi$
$823$	−18.3388	−	14.6247i	−0.639250	−	0.509785i	−0.888632	+	0.458620i	$0.848344\pi$
$824$		0			0
$825$	64.4702	−	51.4133i	2.24456	−	1.78998i
$826$		0			0
$827$	−5.51140	−	4.39519i	−0.191650	−	0.152836i	0.522964	−	0.852355i	$-0.324826\pi$
$827$	−5.51140	−	4.39519i	−0.191650	−	0.152836i	−0.714614	+	0.699519i	$0.753398\pi$
$828$		0			0
$829$	0.707161	+	1.46843i	0.0245607	+	0.0510008i	0.912888	−	0.408210i	$-0.133847\pi$
$829$	0.707161	+	1.46843i	0.0245607	+	0.0510008i	−0.888328	+	0.459210i	$0.848132\pi$
$830$		0			0
$831$	4.01386	+	17.5859i	0.139239	+	0.610047i
$832$		0			0
$833$	14.1259	+	5.47156i	0.489432	+	0.189578i
$834$		0			0
$835$	28.7526	−	6.56260i	0.995026	−	0.227108i
$836$		0			0
$837$	−8.78593	+	4.23108i	−0.303686	+	0.146248i
$838$		0			0
$839$	−1.94384	+	2.43750i	−0.0671089	+	0.0841519i	−0.814253	−	0.580510i	$-0.802853\pi$
$839$	−1.94384	+	2.43750i	−0.0671089	+	0.0841519i	0.747144	+	0.664662i	$0.231425\pi$
$840$		0			0
$841$	−6.12213	−	7.67690i	−0.211108	−	0.264721i
$842$		0			0
$843$	−28.3176	+	35.5091i	−0.975309	+	1.22300i
$844$		0			0
$845$	34.2494	−	71.1197i	1.17822	−	2.44659i
$846$		0			0
$847$	27.8844	+	8.53330i	0.958121	+	0.293208i
$848$		0			0
$849$	31.5735	−	39.5919i	1.08360	−	1.35879i
$850$		0			0
$851$			22.2060i			0.761213i
$852$		0			0
$853$	−13.6430	+	28.3299i	−0.467127	+	0.969998i	0.525726	+	0.850654i	$0.323794\pi$
$853$	−13.6430	+	28.3299i	−0.467127	+	0.969998i	−0.992853	+	0.119344i	$0.961921\pi$
$854$		0			0
$855$	−14.9109	−	30.9629i	−0.509943	−	1.05891i
$856$		0			0
$857$	6.08920	+	1.38982i	0.208003	+	0.0474753i	0.325253	−	0.945627i	$-0.394551\pi$
$857$	6.08920	+	1.38982i	0.208003	+	0.0474753i	−0.117250	+	0.993102i	$0.537408\pi$
$858$		0			0
$859$	−30.6794	+	14.7744i	−1.04677	+	0.504097i	−0.876551	−	0.481309i	$-0.840161\pi$
$859$	−30.6794	+	14.7744i	−1.04677	+	0.504097i	−0.170218	+	0.985406i	$0.554447\pi$
$860$		0			0
$861$	0.935105	+	1.36501i	0.0318683	+	0.0465194i
$862$		0			0
$863$			1.81921i			0.0619266i	0.999521	+	0.0309633i	$0.00985751\pi$
$863$			1.81921i			0.0619266i	−0.999521	+	0.0309633i	$0.990142\pi$
$864$		0			0
$865$	−67.1263	−	32.3263i	−2.28236	−	1.09913i
$866$		0			0
$867$	−6.35398	+	27.8386i	−0.215793	+	0.945449i
$868$		0			0
$869$	15.6216	+	68.4427i	0.529926	+	2.32176i
$870$		0			0
$871$	−5.53621	−	24.2557i	−0.187587	−	0.821874i
$872$		0			0
$873$	−35.4045	−	8.08084i	−1.19826	−	0.273495i
$874$		0			0
$875$	7.08328	−	23.1462i	0.239459	−	0.782484i
$876$		0			0
$877$	6.36857	+	7.98593i	0.215051	+	0.269666i	0.877643	−	0.479315i	$-0.159115\pi$
$877$	6.36857	+	7.98593i	0.215051	+	0.269666i	−0.662592	+	0.748981i	$0.730543\pi$
$878$		0			0
$879$	53.6072	−	42.7503i	1.80813	−	1.44193i
$880$		0			0
$881$			12.9755i			0.437156i	0.975820	+	0.218578i	$0.0701418\pi$
$881$			12.9755i			0.437156i	−0.975820	+	0.218578i	$0.929858\pi$
$882$		0			0
$883$			40.4596i			1.36157i	0.732482	+	0.680787i	$0.238362\pi$
$883$			40.4596i			1.36157i	−0.732482	+	0.680787i	$0.761638\pi$
$884$		0			0
$885$	−19.7735	+	15.7688i	−0.664677	+	0.530063i
$886$		0			0
$887$	−27.6163	−	34.6298i	−0.927266	−	1.16275i	−0.986377	−	0.164503i	$-0.947398\pi$
$887$	−27.6163	−	34.6298i	−0.927266	−	1.16275i	0.0591111	−	0.998251i	$-0.481173\pi$
$888$		0			0
$889$	50.0115	−	19.7566i	1.67733	−	0.662616i
$890$		0			0
$891$	47.9690	+	10.9486i	1.60702	+	0.366793i
$892$		0			0
$893$	0.0885332	+	0.387889i	0.00296265	+	0.0129802i
$894$		0			0
$895$	−2.42278	−	10.6149i	−0.0809847	−	0.354817i
$896$		0			0
$897$	−7.61473	+	33.3623i	−0.254249	+	1.11394i
$898$		0			0
$899$	−26.5445	−	12.7832i	−0.885309	−	0.426342i
$900$		0			0
$901$			25.0025i			0.832953i
$902$		0			0
$903$	−20.9842	+	22.7168i	−0.698310	+	0.755967i
$904$		0			0
$905$	41.5574	−	20.0130i	1.38142	−	0.665255i
$906$		0			0
$907$	−45.3279	−	10.3458i	−1.50509	−	0.343526i	−0.611076	−	0.791572i	$-0.709263\pi$
$907$	−45.3279	−	10.3458i	−1.50509	−	0.343526i	−0.894011	+	0.448045i	$0.852120\pi$
$908$		0			0
$909$	11.9268	+	24.7662i	0.395586	+	0.821443i
$910$		0			0
$911$	6.51108	−	13.5204i	0.215722	−	0.447950i	−0.764825	−	0.644238i	$-0.777174\pi$
$911$	6.51108	−	13.5204i	0.215722	−	0.447950i	0.980546	+	0.196288i	$0.0628887\pi$
$912$		0			0
$913$		−	20.2430i		−	0.669946i
$914$		0			0
$915$	21.2368	−	26.6301i	0.702066	−	0.880363i
$916$		0			0
$917$	19.7844	−	3.02706i	0.653337	−	0.0999622i
$918$		0			0
$919$	6.53491	−	13.5699i	0.215567	−	0.447629i	−0.764943	−	0.644098i	$-0.777233\pi$
$919$	6.53491	−	13.5699i	0.215567	−	0.447629i	0.980510	+	0.196468i	$0.0629473\pi$
$920$		0			0
$921$	7.62187	−	9.55753i	0.251149	−	0.314931i
$922$		0			0
$923$	−33.7116	−	42.2731i	−1.10963	−	1.39143i
$924$		0			0
$925$	−42.2137	+	52.9343i	−1.38798	+	1.74047i
$926$		0			0
$927$	5.43096	−	2.61541i	0.178376	−	0.0859014i
$928$		0			0
$929$	15.4277	−	3.52128i	0.506168	−	0.115529i	0.0381912	−	0.999270i	$-0.487840\pi$
$929$	15.4277	−	3.52128i	0.506168	−	0.115529i	0.467976	+	0.883741i	$0.344983\pi$
$930$		0			0
$931$	−2.26117	−	28.4720i	−0.0741068	−	0.933133i
$932$		0			0
$933$	−12.8085	−	56.1178i	−0.419333	−	1.83722i
$934$		0			0
$935$	−15.6280	−	32.4519i	−0.511091	−	1.06129i
$936$		0			0
$937$	1.13958	+	0.908785i	0.0372285	+	0.0296887i	0.641927	−	0.766766i	$-0.278135\pi$
$937$	1.13958	+	0.908785i	0.0372285	+	0.0296887i	−0.604699	+	0.796454i	$0.706707\pi$
$938$		0			0
$939$	7.00495	−	5.58626i	0.228598	−	0.182301i
$940$		0			0
$941$	−15.5627	−	12.4108i	−0.507328	−	0.404581i	0.336097	−	0.941827i	$-0.390893\pi$
$941$	−15.5627	−	12.4108i	−0.507328	−	0.404581i	−0.843425	+	0.537247i	$0.819464\pi$
$942$		0			0
$943$	−0.604174	−	0.290955i	−0.0196746	−	0.00947480i
$944$		0			0
$945$	12.6514	−	4.99783i	0.411550	−	0.162579i
$946$		0			0
$947$	2.27488	+	1.81416i	0.0739237	+	0.0589522i	0.659755	−	0.751481i	$-0.270660\pi$
$947$	2.27488	+	1.81416i	0.0739237	+	0.0589522i	−0.585831	+	0.810433i	$0.699232\pi$
$948$		0			0
$949$	9.20644			0.298854
$950$		0			0
$951$	62.9455	+	30.3129i	2.04115	+	0.982964i
$952$		0			0
$953$	−43.5911	+	20.9924i	−1.41206	+	0.680010i	−0.975568	−	0.219700i	$-0.929492\pi$
$953$	−43.5911	+	20.9924i	−1.41206	+	0.680010i	−0.436488	+	0.899710i	$0.643778\pi$
$954$		0			0
$955$	−12.1330	+	53.1581i	−0.392615	+	1.72016i
$956$		0			0
$957$	20.6734	+	42.9288i	0.668276	+	1.38769i
$958$		0			0
$959$	44.6958	−	6.83857i	1.44330	−	0.220829i
$960$		0			0
$961$	14.2545			0.459823
$962$		0			0
$963$	3.38712	−	7.03344i	0.109149	−	0.226649i
$964$		0			0
$965$	22.1987	+	5.06671i	0.714602	+	0.163103i
$966$		0			0
$967$	−22.1982	+	5.06660i	−0.713847	+	0.162931i	−0.563996	−	0.825778i	$-0.690737\pi$
$967$	−22.1982	+	5.06660i	−0.713847	+	0.162931i	−0.149851	+	0.988709i	$0.547879\pi$
$968$		0			0
$969$	−19.9576	+	4.55520i	−0.641132	+	0.146334i
$970$		0			0
$971$	10.6023	−	46.4516i	0.340243	−	1.49070i	−0.458319	−	0.888788i	$-0.651548\pi$
$971$	10.6023	−	46.4516i	0.340243	−	1.49070i	0.798561	−	0.601913i	$-0.205595\pi$
$972$		0			0
$973$	−3.24414	+	44.6225i	−0.104003	+	1.43053i
$974$		0			0
$975$	−81.5736	+	65.0528i	−2.61245	+	2.08336i
$976$		0			0
$977$	12.9688	+	16.2624i	0.414909	+	0.520279i	0.944738	−	0.327825i	$-0.106316\pi$
$977$	12.9688	+	16.2624i	0.414909	+	0.520279i	−0.529830	+	0.848104i	$0.677744\pi$
$978$		0			0
$979$	−79.0139			−2.52529
$980$		0			0
$981$	17.0510			0.544396
$982$		0			0
$983$	19.7895	+	24.8152i	0.631186	+	0.791483i	0.989870	−	0.141976i	$-0.0453457\pi$
$983$	19.7895	+	24.8152i	0.631186	+	0.791483i	−0.358684	+	0.933459i	$0.616774\pi$
$984$		0			0
$985$	−28.0267	+	22.3506i	−0.893006	+	0.712148i
$986$		0			0
$987$	0.591224	−	0.0904589i	0.0188189	−	0.00287934i
$988$		0			0
$989$	2.78901	−	12.2194i	0.0886852	−	0.388555i
$990$		0			0
$991$	−10.0059	+	2.28378i	−0.317848	+	0.0725467i	−0.378468	−	0.925614i	$-0.623549\pi$
$991$	−10.0059	+	2.28378i	−0.317848	+	0.0725467i	0.0606207	+	0.998161i	$0.480692\pi$
$992$		0			0
$993$	46.7864	−	10.6787i	1.48472	−	0.338878i
$994$		0			0
$995$	−34.6324	−	7.90461i	−1.09792	−	0.250593i
$996$		0			0
$997$	−18.5945	+	38.6118i	−0.588892	+	1.22285i	0.367299	+	0.930103i	$0.380283\pi$
$997$	−18.5945	+	38.6118i	−0.588892	+	1.22285i	−0.956191	+	0.292744i	$0.905432\pi$
$998$		0			0
$999$	−12.9488			−0.409682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.b.111.18	yes	120
4.3	odd	2	inner	784.2.bb.b.111.3	✓	120
49.34	odd	14	inner	784.2.bb.b.671.3	yes	120
196.83	even	14	inner	784.2.bb.b.671.18	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.b.111.3	✓	120	4.3	odd	2	inner
784.2.bb.b.111.18	yes	120	1.1	even	1	trivial
784.2.bb.b.671.3	yes	120	49.34	odd	14	inner
784.2.bb.b.671.18	yes	120	196.83	even	14	inner

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44547 + 1.81256i) q^{3} +(2.77297 - 2.21137i) q^{5} +(1.94347 + 1.79525i) q^{7} +(-0.528427 + 2.31519i) q^{9} +O(q^{10})\)	\(q+(1.44547 + 1.81256i) q^{3} +(2.77297 - 2.21137i) q^{5} +(1.94347 + 1.79525i) q^{7} +(-0.528427 + 2.31519i) q^{9} +(4.57508 - 1.04423i) q^{11} +(-5.78881 + 1.32126i) q^{13} +(8.01646 + 1.82970i) q^{15} +(0.938958 - 1.94977i) q^{17} -4.08024 q^{19} +(-0.444763 + 6.11762i) q^{21} +(-1.07860 - 2.23974i) q^{23} +(1.68660 - 7.38948i) q^{25} +(1.30604 - 0.628957i) q^{27} +(3.94588 + 1.90024i) q^{29} -6.72715 q^{31} +(8.50585 + 6.78319i) q^{33} +(9.35915 + 0.680429i) q^{35} +(-8.04808 - 3.87575i) q^{37} +(-10.7624 - 8.58271i) q^{39} +(0.210900 - 0.168187i) q^{41} +(3.94188 + 3.14354i) q^{43} +(3.65443 + 7.58849i) q^{45} +(-0.0216980 - 0.0950654i) q^{47} +(0.554176 + 6.97803i) q^{49} +(4.89129 - 1.11641i) q^{51} +(-10.4093 + 5.01284i) q^{53} +(10.3774 - 13.0128i) q^{55} +(-5.89784 - 7.39566i) q^{57} +(-1.91773 + 2.40476i) q^{59} +(1.79731 - 3.73215i) q^{61} +(-5.18332 + 3.55085i) q^{63} +(-13.1304 + 16.4650i) q^{65} +4.19011i q^{67} +(2.50058 - 5.19250i) q^{69} +(3.95100 + 8.20434i) q^{71} +(-1.51164 - 0.345021i) q^{73} +(15.8318 - 7.62418i) q^{75} +(10.7662 + 6.18396i) q^{77} +14.9599i q^{79} +(9.44652 + 4.54921i) q^{81} +(0.959887 - 4.20554i) q^{83} +(-1.70795 - 7.48302i) q^{85} +(2.25935 + 9.89885i) q^{87} +(-16.4153 - 3.74669i) q^{89} +(-13.6224 - 7.82452i) q^{91} +(-9.72386 - 12.1933i) q^{93} +(-11.3144 + 9.02292i) q^{95} +15.2923i q^{97} +11.1440i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 24 q^{9}+O(q^{10}) \) 120 * q - 24 * q^9	\( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) \) 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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