LMFDB - Embedded newform 460.2.m.a.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	460.121
Dual form			460.2.m.a.441.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.68988 + 0.789819i) q^{3} +(0.841254 - 0.540641i) q^{5} +(-0.0887134 + 0.617015i) q^{7} +(4.08786 + 2.62711i) q^{9} +O(q^{10})$	\(q+(2.68988 + 0.789819i) q^{3} +(0.841254 - 0.540641i) q^{5} +(-0.0887134 + 0.617015i) q^{7} +(4.08786 + 2.62711i) q^{9} +(-0.0756169 - 0.165578i) q^{11} +(-0.108766 - 0.756483i) q^{13} +(2.68988 - 0.789819i) q^{15} +(-2.33181 + 2.69105i) q^{17} +(-0.396039 - 0.457053i) q^{19} +(-0.725959 + 1.58963i) q^{21} +(3.84048 - 2.87241i) q^{23} +(0.415415 - 0.909632i) q^{25} +(3.41333 + 3.93919i) q^{27} +(1.73736 - 2.00502i) q^{29} +(-4.00861 + 1.17703i) q^{31} +(-0.0726236 - 0.505108i) q^{33} +(0.258953 + 0.567028i) q^{35} +(-7.97131 - 5.12285i) q^{37} +(0.304918 - 2.12075i) q^{39} +(-9.42765 + 6.05878i) q^{41} +(-1.64902 - 0.484197i) q^{43} +4.85925 q^{45} +4.54332 q^{47} +(6.34361 + 1.86265i) q^{49} +(-8.39772 + 5.39689i) q^{51} +(0.279661 - 1.94508i) q^{53} +(-0.153131 - 0.0984114i) q^{55} +(-0.704307 - 1.54222i) q^{57} +(0.381709 + 2.65485i) q^{59} +(-4.25898 + 1.25055i) q^{61} +(-1.98362 + 2.28921i) q^{63} +(-0.500485 - 0.577591i) q^{65} +(0.574353 - 1.25766i) q^{67} +(12.5991 - 4.69315i) q^{69} +(2.59747 - 5.68766i) q^{71} +(3.68528 + 4.25304i) q^{73} +(1.83586 - 2.11870i) q^{75} +(0.108872 - 0.0319678i) q^{77} +(-1.73153 - 12.0430i) q^{79} +(0.0143682 + 0.0314619i) q^{81} +(-7.36058 - 4.73035i) q^{83} +(-0.506751 + 3.52453i) q^{85} +(6.25689 - 4.02106i) q^{87} +(11.8623 + 3.48309i) q^{89} +0.476410 q^{91} -11.7123 q^{93} +(-0.580271 - 0.170383i) q^{95} +(-12.2214 + 7.85422i) q^{97} +(0.125880 - 0.875514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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
$3$	2.68988	+	0.789819i	1.55300	+	0.456002i	0.941996	−	0.335624i	$-0.108947\pi$
$3$	2.68988	+	0.789819i	1.55300	+	0.456002i	0.611005	+	0.791626i	$0.290765\pi$
$4$		0			0
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$		0			0
$7$	−0.0887134	+	0.617015i	−0.0335305	+	0.233210i	−0.999694	−	0.0247190i	$-0.992131\pi$
$7$	−0.0887134	+	0.617015i	−0.0335305	+	0.233210i	0.966164	+	0.257929i	$0.0830400\pi$
$8$		0			0
$9$	4.08786	+	2.62711i	1.36262	+	0.875704i
$10$		0			0
$11$	−0.0756169	−	0.165578i	−0.0227994	−	0.0499236i	0.897890	−	0.440220i	$-0.145100\pi$
$11$	−0.0756169	−	0.165578i	−0.0227994	−	0.0499236i	−0.920689	+	0.390297i	$0.872372\pi$
$12$		0			0
$13$	−0.108766	−	0.756483i	−0.0301662	−	0.209811i	0.969163	−	0.246419i	$-0.0792538\pi$
$13$	−0.108766	−	0.756483i	−0.0301662	−	0.209811i	−0.999330	+	0.0366080i	$0.988345\pi$
$14$		0			0
$15$	2.68988	−	0.789819i	0.694523	−	0.203930i
$16$		0			0
$17$	−2.33181	+	2.69105i	−0.565547	+	0.652676i	−0.964434	−	0.264324i	$-0.914851\pi$
$17$	−2.33181	+	2.69105i	−0.565547	+	0.652676i	0.398887	+	0.917000i	$0.369397\pi$
$18$		0			0
$19$	−0.396039	−	0.457053i	−0.0908576	−	0.104855i	0.708500	−	0.705711i	$-0.249372\pi$
$19$	−0.396039	−	0.457053i	−0.0908576	−	0.104855i	−0.799358	+	0.600855i	$0.794827\pi$
$20$		0			0
$21$	−0.725959	+	1.58963i	−0.158417	+	0.346885i
$22$		0			0
$23$	3.84048	−	2.87241i	0.800795	−	0.598939i
$23$	3.84048	−	2.87241i	0.800795	−	0.598939i
$24$		0			0
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$		0			0
$27$	3.41333	+	3.93919i	0.656896	+	0.758098i
$28$		0			0
$29$	1.73736	−	2.00502i	0.322620	−	0.372323i	−0.571153	−	0.820844i	$-0.693504\pi$
$29$	1.73736	−	2.00502i	0.322620	−	0.372323i	0.893772	+	0.448521i	$0.148049\pi$
$30$		0			0
$31$	−4.00861	+	1.17703i	−0.719968	+	0.211402i	−0.621136	−	0.783703i	$-0.713329\pi$
$31$	−4.00861	+	1.17703i	−0.719968	+	0.211402i	−0.0988316	+	0.995104i	$0.531511\pi$
$32$		0			0
$33$	−0.0726236	−	0.505108i	−0.0126421	−	0.0879280i
$34$		0			0
$35$	0.258953	+	0.567028i	0.0437711	+	0.0958453i
$36$		0			0
$37$	−7.97131	−	5.12285i	−1.31047	−	0.842191i	−0.316164	−	0.948705i	$-0.602395\pi$
$37$	−7.97131	−	5.12285i	−1.31047	−	0.842191i	−0.994311	+	0.106514i	$0.966031\pi$
$38$		0			0
$39$	0.304918	−	2.12075i	0.0488260	−	0.339592i
$40$		0			0
$41$	−9.42765	+	6.05878i	−1.47235	+	0.946223i	−0.474530	+	0.880239i	$0.657382\pi$
$41$	−9.42765	+	6.05878i	−1.47235	+	0.946223i	−0.997821	+	0.0659835i	$0.978982\pi$
$42$		0			0
$43$	−1.64902	−	0.484197i	−0.251474	−	0.0738394i	0.153566	−	0.988138i	$-0.450924\pi$
$43$	−1.64902	−	0.484197i	−0.251474	−	0.0738394i	−0.405040	+	0.914299i	$0.632742\pi$
$44$		0			0
$45$	4.85925			0.724375
$46$		0			0
$47$	4.54332			0.662711			0.331356	−	0.943506i	$-0.392494\pi$
$47$	4.54332			0.662711			0.331356	+	0.943506i	$0.392494\pi$
$48$		0			0
$49$	6.34361	+	1.86265i	0.906230	+	0.266093i
$50$		0			0
$51$	−8.39772	+	5.39689i	−1.17592	+	0.755716i
$52$		0			0
$53$	0.279661	−	1.94508i	0.0384144	−	0.267178i	−0.961558	−	0.274602i	$-0.911454\pi$
$53$	0.279661	−	1.94508i	0.0384144	−	0.267178i	0.999972	+	0.00742380i	$0.00236309\pi$
$54$		0			0
$55$	−0.153131	−	0.0984114i	−0.0206482	−	0.0132698i
$56$		0			0
$57$	−0.704307	−	1.54222i	−0.0932877	−	0.204272i
$58$		0			0
$59$	0.381709	+	2.65485i	0.0496943	+	0.345632i	0.999466	+	0.0326868i	$0.0104064\pi$
$59$	0.381709	+	2.65485i	0.0496943	+	0.345632i	−0.949771	+	0.312945i	$0.898685\pi$
$60$		0			0
$61$	−4.25898	+	1.25055i	−0.545306	+	0.160116i	−0.542771	−	0.839880i	$-0.682625\pi$
$61$	−4.25898	+	1.25055i	−0.545306	+	0.160116i	−0.00253479	+	0.999997i	$0.500807\pi$
$62$		0			0
$63$	−1.98362	+	2.28921i	−0.249912	+	0.288414i
$64$		0			0
$65$	−0.500485	−	0.577591i	−0.0620775	−	0.0716413i
$66$		0			0
$67$	0.574353	−	1.25766i	0.0701684	−	0.153647i	−0.871298	−	0.490755i	$-0.836721\pi$
$67$	0.574353	−	1.25766i	0.0701684	−	0.153647i	0.941466	+	0.337107i	$0.109448\pi$
$68$		0			0
$69$	12.5991	−	4.69315i	1.51675	−	0.564989i
$70$		0			0
$71$	2.59747	−	5.68766i	0.308263	−	0.675001i	−0.690572	−	0.723264i	$-0.742641\pi$
$71$	2.59747	−	5.68766i	0.308263	−	0.675001i	0.998835	+	0.0482623i	$0.0153683\pi$
$72$		0			0
$73$	3.68528	+	4.25304i	0.431329	+	0.497780i	0.929255	−	0.369439i	$-0.120450\pi$
$73$	3.68528	+	4.25304i	0.431329	+	0.497780i	−0.497926	+	0.867220i	$0.665905\pi$
$74$		0			0
$75$	1.83586	−	2.11870i	0.211987	−	0.244646i
$76$		0			0
$77$	0.108872	−	0.0319678i	0.0124072	−	0.00364307i
$78$		0			0
$79$	−1.73153	−	12.0430i	−0.194812	−	1.35495i	−0.819054	−	0.573716i	$-0.805501\pi$
$79$	−1.73153	−	12.0430i	−0.194812	−	1.35495i	0.624242	−	0.781231i	$-0.285408\pi$
$80$		0			0
$81$	0.0143682	+	0.0314619i	0.00159646	+	0.00349576i
$82$		0			0
$83$	−7.36058	−	4.73035i	−0.807928	−	0.519224i	0.0702660	−	0.997528i	$-0.477615\pi$
$83$	−7.36058	−	4.73035i	−0.807928	−	0.519224i	−0.878194	+	0.478304i	$0.841252\pi$
$84$		0			0
$85$	−0.506751	+	3.52453i	−0.0549648	+	0.382289i
$86$		0			0
$87$	6.25689	−	4.02106i	0.670809	−	0.431103i
$88$		0			0
$89$	11.8623	+	3.48309i	1.25740	+	0.369207i	0.841527	−	0.540214i	$-0.181657\pi$
$89$	11.8623	+	3.48309i	1.25740	+	0.369207i	0.415876	+	0.909421i	$0.363475\pi$
$90$		0			0
$91$	0.476410			0.0499414
$92$		0			0
$93$	−11.7123			−1.21451
$94$		0			0
$95$	−0.580271	−	0.170383i	−0.0595345	−	0.0174809i
$96$		0			0
$97$	−12.2214	+	7.85422i	−1.24090	+	0.797475i	−0.985552	−	0.169375i	$-0.945825\pi$
$97$	−12.2214	+	7.85422i	−1.24090	+	0.797475i	−0.255344	+	0.966850i	$0.582189\pi$
$98$		0			0
$99$	0.125880	−	0.875514i	0.0126514	−	0.0879925i
$100$		0			0
$101$	11.4451	+	7.35535i	1.13883	+	0.731885i	0.967386	−	0.253308i	$-0.0815187\pi$
$101$	11.4451	+	7.35535i	1.13883	+	0.731885i	0.171449	+	0.985193i	$0.445155\pi$
$102$		0			0
$103$	−6.15719	−	13.4824i	−0.606686	−	1.32846i	−0.924818	−	0.380411i	$-0.875783\pi$
$103$	−6.15719	−	13.4824i	−0.606686	−	1.32846i	0.318132	−	0.948047i	$-0.396945\pi$
$104$		0			0
$105$	0.248702	+	1.72976i	0.0242709	+	0.168808i
$106$		0			0
$107$	−8.18745	+	2.40405i	−0.791511	+	0.232408i	−0.652406	−	0.757869i	$-0.726240\pi$
$107$	−8.18745	+	2.40405i	−0.791511	+	0.232408i	−0.139104	+	0.990278i	$0.544422\pi$
$108$		0			0
$109$	−3.91982	+	4.52372i	−0.375451	+	0.433293i	−0.911757	−	0.410730i	$-0.865274\pi$
$109$	−3.91982	+	4.52372i	−0.375451	+	0.433293i	0.536306	+	0.844024i	$0.319819\pi$
$110$		0			0
$111$	−17.3957	−	20.0757i	−1.65113	−	1.90550i
$112$		0			0
$113$	−7.94977	+	17.4076i	−0.747851	+	1.63757i	0.0223374	+	0.999750i	$0.492889\pi$
$113$	−7.94977	+	17.4076i	−0.747851	+	1.63757i	−0.770189	+	0.637816i	$0.779838\pi$
$114$		0			0
$115$	1.67787	−	4.49274i	0.156462	−	0.418951i
$116$		0			0
$117$	1.54274	−	3.37814i	0.142627	−	0.312309i
$118$		0			0
$119$	−1.45356	−	1.67749i	−0.133247	−	0.153776i
$120$		0			0
$121$	7.18177	−	8.28820i	0.652888	−	0.753473i
$122$		0			0
$123$	−30.1446	+	8.85124i	−2.71804	+	0.798089i
$124$		0			0
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$		0			0
$127$	−1.87505	−	4.10578i	−0.166384	−	0.364329i	0.808013	−	0.589164i	$-0.200543\pi$
$127$	−1.87505	−	4.10578i	−0.166384	−	0.364329i	−0.974397	+	0.224835i	$0.927816\pi$
$128$		0			0
$129$	−4.05324	−	2.60486i	−0.356868	−	0.229345i
$130$		0			0
$131$	−0.0308320	+	0.214441i	−0.00269380	+	0.0187358i	−0.991124	−	0.132941i	$-0.957558\pi$
$131$	−0.0308320	+	0.214441i	−0.00269380	+	0.0187358i	0.988430	+	0.151676i	$0.0484672\pi$
$132$		0			0
$133$	0.317143	−	0.203815i	0.0274998	−	0.0176730i
$134$		0			0
$135$	5.00117	+	1.46847i	0.430432	+	0.126386i
$136$		0			0
$137$	−2.00500			−0.171299			−0.0856494	−	0.996325i	$-0.527297\pi$
$137$	−2.00500			−0.171299			−0.0856494	+	0.996325i	$0.527297\pi$
$138$		0			0
$139$	−8.32263			−0.705916			−0.352958	−	0.935639i	$-0.614824\pi$
$139$	−8.32263			−0.705916			−0.352958	+	0.935639i	$0.614824\pi$
$140$		0			0
$141$	12.2210	+	3.58840i	1.02919	+	0.302198i
$142$		0			0
$143$	−0.117032	+	0.0752121i	−0.00978673	+	0.00628955i
$144$		0			0
$145$	0.377564	−	2.62602i	0.0313550	−	0.218079i
$146$		0			0
$147$	15.5924	+	10.0206i	1.28604	+	0.826486i
$148$		0			0
$149$	5.09039	+	11.1464i	0.417021	+	0.913148i	0.995257	+	0.0972790i	$0.0310139\pi$
$149$	5.09039	+	11.1464i	0.417021	+	0.913148i	−0.578236	+	0.815869i	$0.696259\pi$
$150$		0			0
$151$	−1.47785	−	10.2787i	−0.120266	−	0.836465i	−0.957255	−	0.289246i	$-0.906595\pi$
$151$	−1.47785	−	10.2787i	−0.120266	−	0.836465i	0.836989	−	0.547219i	$-0.184314\pi$
$152$		0			0
$153$	−16.6018	+	4.87473i	−1.34218	+	0.394099i
$154$		0			0
$155$	−2.73591	+	3.15740i	−0.219753	+	0.253609i
$156$		0			0
$157$	−12.4729	−	14.3945i	−0.995443	−	1.14880i	−0.988864	−	0.148825i	$-0.952451\pi$
$157$	−12.4729	−	14.3945i	−0.995443	−	1.14880i	−0.00657978	−	0.999978i	$-0.502094\pi$
$158$		0			0
$159$	2.28852	−	5.01116i	0.181491	−	0.397411i
$160$		0			0
$161$	1.43162	+	2.62445i	0.112827	+	0.206836i
$162$		0			0
$163$	0.777772	−	1.70308i	0.0609198	−	0.133396i	−0.876724	−	0.480995i	$-0.840276\pi$
$163$	0.777772	−	1.70308i	0.0609198	−	0.133396i	0.937643	+	0.347599i	$0.113003\pi$
$164$		0			0
$165$	−0.334177	−	0.385661i	−0.0260156	−	0.0300236i
$166$		0			0
$167$	−3.04364	+	3.51255i	−0.235524	+	0.271809i	−0.861191	−	0.508281i	$-0.830281\pi$
$167$	−3.04364	+	3.51255i	−0.235524	+	0.271809i	0.625667	+	0.780090i	$0.284827\pi$
$168$		0			0
$169$	11.9130	−	3.49796i	0.916382	−	0.269074i
$170$		0			0
$171$	−0.418224	−	2.90881i	−0.0319824	−	0.222442i
$172$		0			0
$173$	7.62231	+	16.6905i	0.579514	+	1.26896i	0.941575	+	0.336804i	$0.109346\pi$
$173$	7.62231	+	16.6905i	0.579514	+	1.26896i	−0.362061	+	0.932154i	$0.617927\pi$
$174$		0			0
$175$	0.524404	+	0.337014i	0.0396412	+	0.0254759i
$176$		0			0
$177$	−1.07010	+	7.44269i	−0.0804335	+	0.559427i
$178$		0			0
$179$	15.8504	−	10.1864i	1.18471	−	0.761370i	0.208467	−	0.978029i	$-0.433153\pi$
$179$	15.8504	−	10.1864i	1.18471	−	0.761370i	0.976247	+	0.216660i	$0.0695163\pi$
$180$		0			0
$181$	10.2090	+	2.99764i	0.758830	+	0.222813i	0.638185	−	0.769883i	$-0.279686\pi$
$181$	10.2090	+	2.99764i	0.758830	+	0.222813i	0.120645	+	0.992696i	$0.461504\pi$
$182$		0			0
$183$	−12.4438			−0.919875
$184$		0			0
$185$	−9.47551			−0.696653
$186$		0			0
$187$	0.621903	+	0.182607i	0.0454780	+	0.0133536i
$188$		0			0
$189$	−2.73335	+	1.75662i	−0.198822	+	0.127775i
$190$		0			0
$191$	0.141588	−	0.984765i	0.0102449	−	0.0712551i	−0.984058	−	0.177850i	$-0.943086\pi$
$191$	0.141588	−	0.984765i	0.0102449	−	0.0712551i	0.994303	+	0.106595i	$0.0339949\pi$
$192$		0			0
$193$	−11.9306	−	7.66730i	−0.858780	−	0.551904i	0.0355216	−	0.999369i	$-0.488691\pi$
$193$	−11.9306	−	7.66730i	−0.858780	−	0.551904i	−0.894302	+	0.447464i	$0.852327\pi$
$194$		0			0
$195$	−0.890051	−	1.94894i	−0.0637379	−	0.139567i
$196$		0			0
$197$	−0.846563	−	5.88798i	−0.0603151	−	0.419501i	−0.997500	−	0.0706677i	$-0.977487\pi$
$197$	−0.846563	−	5.88798i	−0.0603151	−	0.419501i	0.937185	−	0.348833i	$-0.113422\pi$
$198$		0			0
$199$	9.72067	−	2.85425i	0.689080	−	0.202332i	0.0815979	−	0.996665i	$-0.473998\pi$
$199$	9.72067	−	2.85425i	0.689080	−	0.202332i	0.607482	+	0.794333i	$0.292180\pi$
$200$		0			0
$201$	2.53826	−	2.92931i	0.179035	−	0.206618i
$202$		0			0
$203$	1.08300	+	1.24985i	0.0760117	+	0.0877222i
$204$		0			0
$205$	−4.65542	+	10.1939i	−0.325148	+	0.711976i
$206$		0			0
$207$	23.2455	−	1.65267i	1.61567	−	0.114869i
$208$		0			0
$209$	−0.0457307	+	0.100136i	−0.00316326	+	0.00692657i
$210$		0			0
$211$	8.97829	+	10.3615i	0.618091	+	0.713315i	0.975343	−	0.220693i	$-0.0708318\pi$
$211$	8.97829	+	10.3615i	0.618091	+	0.713315i	−0.357252	+	0.934008i	$0.616286\pi$
$212$		0			0
$213$	11.4791	−	13.2476i	0.786535	−	0.907710i
$214$		0			0
$215$	−1.64902	+	0.484197i	−0.112463	+	0.0330220i
$216$		0			0
$217$	−0.370631	−	2.57779i	−0.0251601	−	0.174992i
$218$		0			0
$219$	6.55381	+	14.3508i	0.442866	+	0.969740i
$220$		0			0
$221$	2.28936	+	1.47128i	0.153999	+	0.0989690i
$222$		0			0
$223$	−3.64718	+	25.3667i	−0.244233	+	1.69868i	0.386184	+	0.922422i	$0.373793\pi$
$223$	−3.64718	+	25.3667i	−0.244233	+	1.69868i	−0.630417	+	0.776256i	$0.717116\pi$
$224$		0			0
$225$	4.08786	−	2.62711i	0.272524	−	0.175141i
$226$		0			0
$227$	22.4504	+	6.59205i	1.49009	+	0.437530i	0.922570	−	0.385831i	$-0.126085\pi$
$227$	22.4504	+	6.59205i	1.49009	+	0.437530i	0.567519	+	0.823360i	$0.307903\pi$
$228$		0			0
$229$	8.28297			0.547354			0.273677	−	0.961822i	$-0.411760\pi$
$229$	8.28297			0.547354			0.273677	+	0.961822i	$0.411760\pi$
$230$		0			0
$231$	0.318102			0.0209296
$232$		0			0
$233$	25.9953	+	7.63291i	1.70301	+	0.500049i	0.981355	−	0.192205i	$-0.0615640\pi$
$233$	25.9953	+	7.63291i	1.70301	+	0.500049i	0.721654	+	0.692254i	$0.243382\pi$
$234$		0			0
$235$	3.82208	−	2.45630i	0.249325	−	0.160232i
$236$		0			0
$237$	4.85422	−	33.7619i	0.315316	−	2.19307i
$238$		0			0
$239$	23.5951	+	15.1637i	1.52624	+	0.980857i	0.990657	+	0.136376i	$0.0435454\pi$
$239$	23.5951	+	15.1637i	1.52624	+	0.980857i	0.535586	+	0.844481i	$0.320091\pi$
$240$		0			0
$241$	10.3889	+	22.7486i	0.669211	+	1.46537i	0.873683	+	0.486495i	$0.161725\pi$
$241$	10.3889	+	22.7486i	0.669211	+	1.46537i	−0.204473	+	0.978872i	$0.565548\pi$
$242$		0			0
$243$	−2.21156	−	15.3818i	−0.141872	−	0.986740i
$244$		0			0
$245$	6.34361	−	1.86265i	0.405279	−	0.119001i
$246$		0			0
$247$	−0.302678	+	0.349309i	−0.0192589	+	0.0222260i
$248$		0			0
$249$	−16.0629	−	18.5376i	−1.01795	−	1.17477i
$250$		0			0
$251$	2.21246	−	4.84461i	0.139649	−	0.305789i	−0.826866	−	0.562399i	$-0.809878\pi$
$251$	2.21246	−	4.84461i	0.139649	−	0.305789i	0.966515	+	0.256610i	$0.0826056\pi$
$252$		0			0
$253$	−0.766013	−	0.418695i	−0.0481588	−	0.0263231i
$254$		0			0
$255$	−4.14684	+	9.08031i	−0.259685	+	0.568631i
$256$		0			0
$257$	7.65497	+	8.83431i	0.477504	+	0.551069i	0.942484	−	0.334252i	$-0.108484\pi$
$257$	7.65497	+	8.83431i	0.477504	+	0.551069i	−0.464980	+	0.885321i	$0.653938\pi$
$258$		0			0
$259$	3.86804	−	4.46395i	0.240348	−	0.277377i
$260$		0			0
$261$	12.3695	−	3.63201i	0.765653	−	0.224816i
$262$		0			0
$263$	2.61953	+	18.2192i	0.161527	+	1.12344i	0.895757	+	0.444544i	$0.146634\pi$
$263$	2.61953	+	18.2192i	0.161527	+	1.12344i	−0.734230	+	0.678901i	$0.762457\pi$
$264$		0			0
$265$	−0.816326	−	1.78751i	−0.0501465	−	0.109806i
$266$		0			0
$267$	29.1572	+	18.7382i	1.78439	+	1.14676i
$268$		0			0
$269$	−3.21873	+	22.3868i	−0.196250	+	1.36495i	0.618797	+	0.785551i	$0.287620\pi$
$269$	−3.21873	+	22.3868i	−0.196250	+	1.36495i	−0.815047	+	0.579396i	$0.803289\pi$
$270$		0			0
$271$	4.21459	−	2.70855i	0.256018	−	0.164533i	−0.406336	−	0.913724i	$-0.633194\pi$
$271$	4.21459	−	2.70855i	0.256018	−	0.164533i	0.662354	+	0.749191i	$0.269557\pi$
$272$		0			0
$273$	1.28149	+	0.376278i	0.0775590	+	0.0227734i
$274$		0			0
$275$	−0.182027			−0.0109767
$276$		0			0
$277$	−9.30158			−0.558878			−0.279439	−	0.960163i	$-0.590148\pi$
$277$	−9.30158			−0.558878			−0.279439	+	0.960163i	$0.590148\pi$
$278$		0			0
$279$	−19.4789	−	5.71951i	−1.16617	−	0.342418i
$280$		0			0
$281$	−8.13988	+	5.23119i	−0.485585	+	0.312066i	−0.760427	−	0.649423i	$-0.775011\pi$
$281$	−8.13988	+	5.23119i	−0.485585	+	0.312066i	0.274843	+	0.961489i	$0.411374\pi$
$282$		0			0
$283$	3.58694	−	24.9477i	0.213221	−	1.48299i	−0.549082	−	0.835768i	$-0.685023\pi$
$283$	3.58694	−	24.9477i	0.213221	−	1.48299i	0.762304	−	0.647219i	$-0.224068\pi$
$284$		0			0
$285$	−1.42629	−	0.916618i	−0.0844859	−	0.0542958i
$286$		0			0
$287$	−2.90200	−	6.35450i	−0.171300	−	0.375094i
$288$		0			0
$289$	0.614929	+	4.27693i	0.0361723	+	0.251584i
$290$		0			0
$291$	−39.0775	+	11.4742i	−2.29076	+	0.672629i
$292$		0			0
$293$	14.3937	−	16.6112i	0.840890	−	0.970439i	−0.158968	−	0.987284i	$-0.550817\pi$
$293$	14.3937	−	16.6112i	0.840890	−	0.970439i	0.999858	+	0.0168449i	$0.00536214\pi$
$294$		0			0
$295$	1.75643	+	2.02703i	0.102263	+	0.118018i
$296$		0			0
$297$	0.394138	−	0.863042i	0.0228702	−	0.0500788i
$298$		0			0
$299$	−2.59064	−	2.59283i	−0.149821	−	0.149947i
$300$		0			0
$301$	0.445048	−	0.974518i	0.0256521	−	0.0561703i
$302$		0			0
$303$	24.9766	+	28.8246i	1.43487	+	1.65593i
$304$		0			0
$305$	−2.90678	+	3.35461i	−0.166442	+	0.192084i
$306$		0			0
$307$	−17.9766	+	5.27839i	−1.02598	+	0.301254i	−0.751074	−	0.660218i	$-0.770464\pi$
$307$	−17.9766	+	5.27839i	−1.02598	+	0.301254i	−0.274903	+	0.961472i	$0.588646\pi$
$308$		0			0
$309$	−5.91346	−	41.1290i	−0.336405	−	2.33975i
$310$		0			0
$311$	−8.86961	−	19.4217i	−0.502949	−	1.10131i	−0.975500	−	0.220002i	$-0.929394\pi$
$311$	−8.86961	−	19.4217i	−0.502949	−	1.10131i	0.472550	−	0.881304i	$-0.343334\pi$
$312$		0			0
$313$	6.37000	+	4.09375i	0.360054	+	0.231392i	0.708143	−	0.706069i	$-0.249533\pi$
$313$	6.37000	+	4.09375i	0.360054	+	0.231392i	−0.348090	+	0.937461i	$0.613170\pi$
$314$		0			0
$315$	−0.431081	+	2.99823i	−0.0242887	+	0.168931i
$316$		0			0
$317$	−20.4500	+	13.1424i	−1.14858	+	0.738150i	−0.969357	−	0.245658i	$-0.920996\pi$
$317$	−20.4500	+	13.1424i	−1.14858	+	0.738150i	−0.179227	+	0.983808i	$0.557360\pi$
$318$		0			0
$319$	−0.463361	−	0.136055i	−0.0259432	−	0.00761762i
$320$		0			0
$321$	−23.9220			−1.33520
$322$		0			0
$323$	2.15344			0.119821
$324$		0			0
$325$	−0.733304	−	0.215317i	−0.0406764	−	0.0119437i
$326$		0			0
$327$	−14.1168	+	9.07229i	−0.780659	+	0.501699i
$328$		0			0
$329$	−0.403053	+	2.80330i	−0.0222210	+	0.154551i
$330$		0			0
$331$	18.7397	+	12.0432i	1.03003	+	0.661957i	0.942500	−	0.334205i	$-0.108468\pi$
$331$	18.7397	+	12.0432i	1.03003	+	0.661957i	0.0875248	+	0.996162i	$0.472104\pi$
$332$		0			0
$333$	−19.1273	−	41.8830i	−1.04817	−	2.29518i
$334$		0			0
$335$	−0.196765	−	1.36853i	−0.0107504	−	0.0747707i
$336$		0			0
$337$	−14.2374	+	4.18048i	−0.775561	+	0.227725i	−0.645479	−	0.763778i	$-0.723342\pi$
$337$	−14.2374	+	4.18048i	−0.775561	+	0.227725i	−0.130082	+	0.991503i	$0.541524\pi$
$338$		0			0
$339$	−35.1327	+	40.5453i	−1.90815	+	2.20212i
$340$		0			0
$341$	0.498010	+	0.574734i	0.0269687	+	0.0311236i
$342$		0			0
$343$	−3.52472	+	7.71806i	−0.190317	+	0.416736i
$344$		0			0
$345$	8.06172	−	10.7597i	0.434029	−	0.579284i
$346$		0			0
$347$	−3.63538	+	7.96036i	−0.195157	+	0.427335i	−0.981760	−	0.190125i	$-0.939111\pi$
$347$	−3.63538	+	7.96036i	−0.195157	+	0.427335i	0.786603	+	0.617459i	$0.211838\pi$
$348$		0			0
$349$	−12.5061	−	14.4328i	−0.669434	−	0.772568i	0.314854	−	0.949140i	$-0.398044\pi$
$349$	−12.5061	−	14.4328i	−0.669434	−	0.772568i	−0.984288	+	0.176572i	$0.943499\pi$
$350$		0			0
$351$	2.60868	−	3.01058i	0.139241	−	0.160693i
$352$		0			0
$353$	−5.70624	+	1.67550i	−0.303713	+	0.0891781i	−0.430038	−	0.902811i	$-0.641500\pi$
$353$	−5.70624	+	1.67550i	−0.303713	+	0.0891781i	0.126325	+	0.991989i	$0.459682\pi$
$354$		0			0
$355$	−0.889853	−	6.18906i	−0.0472285	−	0.328481i
$356$		0			0
$357$	−2.58497	−	5.66030i	−0.136811	−	0.299575i
$358$		0			0
$359$	6.25259	+	4.01830i	0.329999	+	0.212078i	0.695140	−	0.718875i	$-0.255343\pi$
$359$	6.25259	+	4.01830i	0.329999	+	0.212078i	−0.365140	+	0.930953i	$0.618979\pi$
$360$		0			0
$361$	2.65193	−	18.4446i	0.139575	−	0.970768i
$362$		0			0
$363$	25.8643	−	16.6220i	1.35752	−	0.872426i
$364$		0			0
$365$	5.39962	+	1.58547i	0.282629	+	0.0829873i
$366$		0			0
$367$	−2.42839			−0.126761			−0.0633804	−	0.997989i	$-0.520188\pi$
$367$	−2.42839			−0.126761			−0.0633804	+	0.997989i	$0.520188\pi$
$368$		0			0
$369$	−54.4560			−2.83487
$370$		0			0
$371$	1.17534	+	0.345110i	0.0610205	+	0.0179172i
$372$		0			0
$373$	24.0048	−	15.4270i	1.24292	−	0.798777i	0.257069	−	0.966393i	$-0.417243\pi$
$373$	24.0048	−	15.4270i	1.24292	−	0.798777i	0.985852	+	0.167616i	$0.0536068\pi$
$374$		0			0
$375$	0.398971	−	2.77490i	0.0206028	−	0.143295i
$376$		0			0
$377$	−1.70573	−	1.09621i	−0.0878495	−	0.0564574i
$378$		0			0
$379$	5.34556	+	11.7051i	0.274583	+	0.601253i	0.995810	−	0.0914458i	$-0.0291488\pi$
$379$	5.34556	+	11.7051i	0.274583	+	0.601253i	−0.721227	+	0.692699i	$0.756422\pi$
$380$		0			0
$381$	−1.80082	−	12.5250i	−0.0922589	−	0.641675i
$382$		0			0
$383$	8.26364	−	2.42642i	0.422252	−	0.123984i	−0.0637015	−	0.997969i	$-0.520291\pi$
$383$	8.26364	−	2.42642i	0.422252	−	0.123984i	0.485954	+	0.873985i	$0.338472\pi$
$384$		0			0
$385$	0.0743061	−	0.0857538i	0.00378699	−	0.00437042i
$386$		0			0
$387$	−5.46895	−	6.31150i	−0.278002	−	0.320832i
$388$		0			0
$389$	3.89025	−	8.51845i	0.197243	−	0.431903i	−0.785005	−	0.619490i	$-0.787339\pi$
$389$	3.89025	−	8.51845i	0.197243	−	0.431903i	0.982248	+	0.187587i	$0.0600668\pi$
$390$		0			0
$391$	−1.22545	+	17.0328i	−0.0619737	+	0.861387i
$392$		0			0
$393$	−0.252304	+	0.552469i	−0.0127271	+	0.0278684i
$394$		0			0
$395$	−7.96761	−	9.19511i	−0.400894	−	0.462656i
$396$		0			0
$397$	8.82602	−	10.1858i	0.442965	−	0.511209i	−0.489730	−	0.871874i	$-0.662905\pi$
$397$	8.82602	−	10.1858i	0.442965	−	0.511209i	0.932695	+	0.360665i	$0.117450\pi$
$398$		0			0
$399$	1.01405	−	0.297753i	0.0507661	−	0.0149063i
$400$		0			0
$401$	1.22684	+	8.53284i	0.0612653	+	0.426110i	0.997253	+	0.0740760i	$0.0236007\pi$
$401$	1.22684	+	8.53284i	0.0612653	+	0.426110i	−0.935987	+	0.352034i	$0.885490\pi$
$402$		0			0
$403$	1.32641	+	2.90443i	0.0660730	+	0.144680i
$404$		0			0
$405$	0.0290968	+	0.0186994i	0.00144583	+	0.000929180i
$406$		0			0
$407$	−0.245465	+	1.70725i	−0.0121672	+	0.0846251i
$408$		0			0
$409$	−22.7804	+	14.6401i	−1.12642	+	0.723907i	−0.964810	−	0.262948i	$-0.915305\pi$
$409$	−22.7804	+	14.6401i	−1.12642	+	0.723907i	−0.161611	+	0.986855i	$0.551669\pi$
$410$		0			0
$411$	−5.39321	−	1.58359i	−0.266027	−	0.0781127i
$412$		0			0
$413$	−1.67194			−0.0822710
$414$		0			0
$415$	−8.74953			−0.429498
$416$		0			0
$417$	−22.3869	−	6.57337i	−1.09629	−	0.321900i
$418$		0			0
$419$	16.4119	−	10.5473i	0.801772	−	0.515267i	−0.0744218	−	0.997227i	$-0.523711\pi$
$419$	16.4119	−	10.5473i	0.801772	−	0.515267i	0.876194	+	0.481959i	$0.160075\pi$
$420$		0			0
$421$	2.33086	−	16.2115i	0.113599	−	0.790099i	−0.850770	−	0.525538i	$-0.823864\pi$
$421$	2.33086	−	16.2115i	0.113599	−	0.790099i	0.964369	−	0.264561i	$-0.0852270\pi$
$422$		0			0
$423$	18.5725	+	11.9358i	0.903024	+	0.580339i
$424$		0			0
$425$	1.47920	+	3.23899i	0.0717516	+	0.157114i
$426$		0			0
$427$	−0.393779	−	2.73879i	−0.0190563	−	0.132540i
$428$		0			0
$429$	−0.374207	+	0.109877i	−0.0180669	+	0.00530491i
$430$		0			0
$431$	−15.6278	+	18.0355i	−0.752766	+	0.868738i	−0.994833	−	0.101521i	$-0.967629\pi$
$431$	−15.6278	+	18.0355i	−0.752766	+	0.868738i	0.242067	+	0.970259i	$0.422174\pi$
$432$		0			0
$433$	5.66178	+	6.53405i	0.272088	+	0.314006i	0.875305	−	0.483571i	$-0.160660\pi$
$433$	5.66178	+	6.53405i	0.272088	+	0.314006i	−0.603217	+	0.797577i	$0.706115\pi$
$434$		0			0
$435$	3.08968	−	6.76546i	0.148139	−	0.324379i
$436$		0			0
$437$	−2.83382	−	0.617715i	−0.135560	−	0.0295493i
$438$		0			0
$439$	−15.2130	+	33.3118i	−0.726076	+	1.58988i	0.0791135	+	0.996866i	$0.474791\pi$
$439$	−15.2130	+	33.3118i	−0.726076	+	1.58988i	−0.805189	+	0.593018i	$0.797936\pi$
$440$		0			0
$441$	21.0384	+	24.2796i	1.00183	+	1.15617i
$442$		0			0
$443$	25.0502	−	28.9094i	1.19017	−	1.37353i	0.279629	−	0.960108i	$-0.409788\pi$
$443$	25.0502	−	28.9094i	1.19017	−	1.37353i	0.910540	−	0.413421i	$-0.135666\pi$
$444$		0			0
$445$	11.8623	−	3.48309i	0.562328	−	0.165114i
$446$		0			0
$447$	4.88888	+	34.0029i	0.231236	+	1.60828i
$448$		0			0
$449$	1.12652	+	2.46673i	0.0531636	+	0.116412i	0.934350	−	0.356358i	$-0.115982\pi$
$449$	1.12652	+	2.46673i	0.0531636	+	0.116412i	−0.881186	+	0.472770i	$0.843254\pi$
$450$		0			0
$451$	1.71609	+	1.10286i	0.0808075	+	0.0519318i
$452$		0			0
$453$	4.14305	−	28.8156i	0.194658	−	1.35387i
$454$		0			0
$455$	0.400782	−	0.257567i	0.0187890	−	0.0120749i
$456$		0			0
$457$	−19.3241	−	5.67406i	−0.903942	−	0.265421i	−0.203453	−	0.979085i	$-0.565216\pi$
$457$	−19.3241	−	5.67406i	−0.903942	−	0.265421i	−0.700489	+	0.713663i	$0.747035\pi$
$458$		0			0
$459$	−18.5598			−0.866298
$460$		0			0
$461$	−2.71093			−0.126261			−0.0631304	−	0.998005i	$-0.520108\pi$
$461$	−2.71093			−0.126261			−0.0631304	+	0.998005i	$0.520108\pi$
$462$		0			0
$463$	30.6482	+	8.99913i	1.42434	+	0.418225i	0.900971	−	0.433879i	$-0.142855\pi$
$463$	30.6482	+	8.99913i	1.42434	+	0.418225i	0.523373	+	0.852104i	$0.324674\pi$
$464$		0			0
$465$	−9.85303	+	6.33216i	−0.456923	+	0.293647i
$466$		0			0
$467$	−0.843037	+	5.86345i	−0.0390111	+	0.271328i	−0.999986	−	0.00530771i	$-0.998310\pi$
$467$	−0.843037	+	5.86345i	−0.0390111	+	0.271328i	0.960975	+	0.276636i	$0.0892196\pi$
$468$		0			0
$469$	0.725041	+	0.465956i	0.0334793	+	0.0215158i
$470$		0			0
$471$	−22.1815	−	48.5706i	−1.02207	−	2.23802i
$472$		0			0
$473$	0.0445217	+	0.309655i	0.00204711	+	0.0142380i
$474$		0			0
$475$	−0.580271	+	0.170383i	−0.0266247	+	0.00781770i
$476$		0			0
$477$	6.25317	−	7.21654i	0.286313	−	0.330423i
$478$		0			0
$479$	−17.2834	−	19.9462i	−0.789701	−	0.911363i	0.208069	−	0.978114i	$-0.433282\pi$
$479$	−17.2834	−	19.9462i	−0.789701	−	0.911363i	−0.997770	+	0.0667511i	$0.978737\pi$
$480$		0			0
$481$	−3.00834	+	6.58735i	−0.137169	+	0.300357i
$482$		0			0
$483$	1.77804	+	8.19018i	0.0809035	+	0.372666i
$484$		0			0
$485$	−6.03499	+	13.2148i	−0.274035	+	0.600052i
$486$		0			0
$487$	−13.5044	−	15.5849i	−0.611944	−	0.706221i	0.362212	−	0.932096i	$-0.382022\pi$
$487$	−13.5044	−	15.5849i	−0.611944	−	0.706221i	−0.974156	+	0.225875i	$0.927476\pi$
$488$		0			0
$489$	3.43724	−	3.96679i	0.155437	−	0.179384i
$490$		0			0
$491$	14.2223	−	4.17604i	0.641843	−	0.188462i	0.0554149	−	0.998463i	$-0.482352\pi$
$491$	14.2223	−	4.17604i	0.641843	−	0.188462i	0.586428	+	0.810001i	$0.300534\pi$
$492$		0			0
$493$	1.34442	+	9.35065i	0.0605496	+	0.421132i
$494$		0			0
$495$	−0.367442	−	0.804585i	−0.0165153	−	0.0361634i
$496$		0			0
$497$	3.27894	+	2.10725i	0.147081	+	0.0945231i
$498$		0			0
$499$	4.49057	−	31.2326i	0.201025	−	1.39816i	−0.600224	−	0.799832i	$-0.704922\pi$
$499$	4.49057	−	31.2326i	0.201025	−	1.39816i	0.801249	−	0.598331i	$-0.204169\pi$
$500$		0			0
$501$	−10.9613	+	7.04440i	−0.489715	+	0.314721i
$502$		0			0
$503$	−8.85740	−	2.60077i	−0.394932	−	0.115962i	0.0782358	−	0.996935i	$-0.475071\pi$
$503$	−8.85740	−	2.60077i	−0.394932	−	0.115962i	−0.473168	+	0.880972i	$0.656889\pi$
$504$		0			0
$505$	13.6049			0.605409
$506$		0			0
$507$	34.8072			1.54584
$508$		0			0
$509$	−15.0746	−	4.42631i	−0.668171	−	0.196193i	−0.0699824	−	0.997548i	$-0.522294\pi$
$509$	−15.0746	−	4.42631i	−0.668171	−	0.196193i	−0.598188	+	0.801356i	$0.704112\pi$
$510$		0			0
$511$	−2.95112	+	1.89657i	−0.130550	+	0.0838993i
$512$		0			0
$513$	0.448610	−	3.12015i	0.0198066	−	0.137758i
$514$		0			0
$515$	−12.4689	−	8.01326i	−0.549444	−	0.353106i
$516$		0			0
$517$	−0.343552	−	0.752273i	−0.0151094	−	0.0330849i
$518$		0			0
$519$	7.32058	+	50.9157i	0.321338	+	2.23495i
$520$		0			0
$521$	−10.3875	+	3.05006i	−0.455086	+	0.133625i	−0.501239	−	0.865309i	$-0.667122\pi$
$521$	−10.3875	+	3.05006i	−0.455086	+	0.133625i	0.0461525	+	0.998934i	$0.485304\pi$
$522$		0			0
$523$	6.83875	−	7.89234i	0.299038	−	0.345108i	−0.586268	−	0.810117i	$-0.699404\pi$
$523$	6.83875	−	7.89234i	0.299038	−	0.345108i	0.885306	+	0.465009i	$0.153949\pi$
$524$		0			0
$525$	1.14440	+	1.32071i	0.0499458	+	0.0576405i
$526$		0			0
$527$	6.17986	−	13.5320i	0.269199	−	0.589463i
$528$		0			0
$529$	6.49851	−	22.0629i	0.282544	−	0.959254i
$530$		0			0
$531$	−5.41420	+	11.8554i	−0.234956	+	0.514483i
$532$		0			0
$533$	5.60877	+	6.47287i	0.242943	+	0.280371i
$534$		0			0
$535$	−5.58799	+	6.44889i	−0.241590	+	0.278810i
$536$		0			0
$537$	50.6811	−	14.8813i	2.18705	−	0.642175i
$538$		0			0
$539$	−0.171270	−	1.19121i	−0.00737713	−	0.0513091i
$540$		0			0
$541$	8.81210	+	19.2958i	0.378862	+	0.829592i	0.998983	+	0.0450857i	$0.0143561\pi$
$541$	8.81210	+	19.2958i	0.378862	+	0.829592i	−0.620121	+	0.784506i	$0.712917\pi$
$542$		0			0
$543$	25.0934	+	16.1266i	1.07686	+	0.692057i
$544$		0			0
$545$	−0.851859	+	5.92481i	−0.0364896	+	0.253791i
$546$		0			0
$547$	−25.7493	+	16.5480i	−1.10096	+	0.707543i	−0.959305	−	0.282373i	$-0.908879\pi$
$547$	−25.7493	+	16.5480i	−1.10096	+	0.707543i	−0.141654	+	0.989916i	$0.545242\pi$
$548$		0			0
$549$	−20.6955	−	6.07673i	−0.883261	−	0.259349i
$550$		0			0
$551$	−1.60446			−0.0683524
$552$		0			0
$553$	7.58434			0.322519
$554$		0			0
$555$	−25.4880	−	7.48394i	−1.08190	−	0.317676i
$556$		0			0
$557$	8.56246	−	5.50276i	0.362803	−	0.233159i	−0.346521	−	0.938042i	$-0.612637\pi$
$557$	8.56246	−	5.50276i	0.362803	−	0.233159i	0.709324	+	0.704883i	$0.249001\pi$
$558$		0			0
$559$	−0.186929	+	1.30012i	−0.00790627	+	0.0549893i
$560$		0			0
$561$	1.52862	+	0.982382i	0.0645382	+	0.0414762i
$562$		0			0
$563$	−14.5113	−	31.7753i	−0.611579	−	1.33917i	−0.921489	−	0.388405i	$-0.873026\pi$
$563$	−14.5113	−	31.7753i	−0.611579	−	1.33917i	0.309910	−	0.950766i	$-0.399701\pi$
$564$		0			0
$565$	2.72347	+	18.9421i	0.114577	+	0.796902i
$566$		0			0
$567$	−0.0206871	+	0.00607428i	−0.000868776	+	0.000255096i
$568$		0			0
$569$	−20.9219	+	24.1452i	−0.877092	+	1.01222i	0.122712	+	0.992442i	$0.460841\pi$
$569$	−20.9219	+	24.1452i	−0.877092	+	1.01222i	−0.999804	+	0.0197760i	$0.993705\pi$
$570$		0			0
$571$	−2.02363	−	2.33539i	−0.0846862	−	0.0977331i	0.711825	−	0.702357i	$-0.247869\pi$
$571$	−2.02363	−	2.33539i	−0.0846862	−	0.0977331i	−0.796511	+	0.604624i	$0.793323\pi$
$572$		0			0
$573$	1.15864	−	2.53707i	0.0484029	−	0.105988i
$574$		0			0
$575$	−1.01745	−	4.68666i	−0.0424304	−	0.195447i
$576$		0			0
$577$	−4.06936	+	8.91065i	−0.169410	+	0.370955i	−0.975226	−	0.221210i	$-0.928999\pi$
$577$	−4.06936	+	8.91065i	−0.169410	+	0.370955i	0.805817	+	0.592165i	$0.201727\pi$
$578$		0			0
$579$	−26.0359	−	30.0471i	−1.08202	−	1.24871i
$580$		0			0
$581$	3.57168	−	4.12194i	0.148178	−	0.171007i
$582$		0			0
$583$	−0.343210	+	0.100776i	−0.0142143	+	0.00417370i
$584$		0			0
$585$	−0.528521	−	3.67594i	−0.0218516	−	0.151982i
$586$		0			0
$587$	−9.59592	−	21.0121i	−0.396066	−	0.867264i	−0.997654	−	0.0684572i	$-0.978192\pi$
$587$	−9.59592	−	21.0121i	−0.396066	−	0.867264i	0.601588	−	0.798807i	$-0.294535\pi$
$588$		0			0
$589$	2.12553	+	1.36600i	0.0875811	+	0.0562850i
$590$		0			0
$591$	2.37329	−	16.5066i	0.0976240	−	0.678990i
$592$		0			0
$593$	−25.2683	+	16.2390i	−1.03765	+	0.666855i	−0.944404	−	0.328788i	$-0.893360\pi$
$593$	−25.2683	+	16.2390i	−1.03765	+	0.666855i	−0.0932429	+	0.995643i	$0.529723\pi$
$594$		0			0
$595$	−2.12973	−	0.625346i	−0.0873105	−	0.0256367i
$596$		0			0
$597$	28.4018			1.16241
$598$		0			0
$599$	−40.9197			−1.67194			−0.835968	−	0.548779i	$-0.815093\pi$
$599$	−40.9197			−1.67194			−0.835968	+	0.548779i	$0.815093\pi$
$600$		0			0
$601$	19.6297	+	5.76380i	0.800712	+	0.235110i	0.656391	−	0.754421i	$-0.272082\pi$
$601$	19.6297	+	5.76380i	0.800712	+	0.235110i	0.144321	+	0.989531i	$0.453900\pi$
$602$		0			0
$603$	5.65188	−	3.63225i	0.230163	−	0.147916i
$604$		0			0
$605$	1.56075	−	10.8552i	0.0634534	−	0.441328i
$606$		0			0
$607$	−27.3223	−	17.5590i	−1.10898	−	0.712696i	−0.147907	−	0.989001i	$-0.547254\pi$
$607$	−27.3223	−	17.5590i	−1.10898	−	0.712696i	−0.961070	+	0.276305i	$0.910890\pi$
$608$		0			0
$609$	1.92598	+	4.21732i	0.0780448	+	0.170894i
$610$		0			0
$611$	−0.494158	−	3.43694i	−0.0199915	−	0.139044i
$612$		0			0
$613$	−42.5496	+	12.4937i	−1.71856	+	0.504616i	−0.984637	−	0.174614i	$-0.944132\pi$
$613$	−42.5496	+	12.4937i	−1.71856	+	0.504616i	−0.733926	+	0.679229i	$0.762314\pi$
$614$		0			0
$615$	−20.5739	+	23.7435i	−0.829619	+	0.957431i
$616$		0			0
$617$	−5.00284	−	5.77359i	−0.201407	−	0.232436i	0.646057	−	0.763289i	$-0.276417\pi$
$617$	−5.00284	−	5.77359i	−0.201407	−	0.232436i	−0.847464	+	0.530853i	$0.821871\pi$
$618$		0			0
$619$	−7.09252	+	15.5304i	−0.285072	+	0.624221i	−0.996947	−	0.0780855i	$-0.975119\pi$
$619$	−7.09252	+	15.5304i	−0.285072	+	0.624221i	0.711874	+	0.702307i	$0.247847\pi$
$620$		0			0
$621$	24.4238	+	5.32389i	0.980093	+	0.213640i
$622$		0			0
$623$	−3.20147	+	7.01024i	−0.128264	+	0.280859i
$624$		0			0
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$		0			0
$627$	−0.202100	+	0.233235i	−0.00807108	+	0.00931452i
$628$		0			0
$629$	32.3734	−	9.50569i	1.29081	−	0.379017i
$630$		0			0
$631$	5.70306	+	39.6656i	0.227035	+	1.57906i	0.710498	+	0.703699i	$0.248470\pi$
$631$	5.70306	+	39.6656i	0.227035	+	1.57906i	−0.483463	+	0.875365i	$0.660621\pi$
$632$		0			0
$633$	15.9668	+	34.9624i	0.634623	+	1.38963i
$634$		0			0
$635$	−3.79714	−	2.44028i	−0.150685	−	0.0968394i
$636$		0			0
$637$	0.719097	−	5.00143i	0.0284917	−	0.198164i
$638$		0			0
$639$	25.5602	−	16.4266i	1.01115	−	0.649825i
$640$		0			0
$641$	−22.4353	−	6.58760i	−0.886141	−	0.260194i	−0.193175	−	0.981164i	$-0.561878\pi$
$641$	−22.4353	−	6.58760i	−0.886141	−	0.260194i	−0.692966	+	0.720970i	$0.743697\pi$
$642$		0			0
$643$	−22.3529			−0.881511			−0.440755	−	0.897627i	$-0.645289\pi$
$643$	−22.3529			−0.881511			−0.440755	+	0.897627i	$0.645289\pi$
$644$		0			0
$645$	−4.81810			−0.189713
$646$		0			0
$647$	13.5992	+	3.99310i	0.534641	+	0.156985i	0.537898	−	0.843010i	$-0.319219\pi$
$647$	13.5992	+	3.99310i	0.534641	+	0.156985i	−0.00325689	+	0.999995i	$0.501037\pi$
$648$		0			0
$649$	0.410720	−	0.263954i	0.0161222	−	0.0103611i
$650$		0			0
$651$	1.03904	−	7.22668i	0.0407232	−	0.283236i
$652$		0			0
$653$	0.00163080	+	0.00104805i	6.38179e−5	+	4.10133e-5i	0.540673	−	0.841233i	$-0.318170\pi$
$653$	0.00163080	+	0.00104805i	6.38179e−5	+	4.10133e-5i	−0.540609	+	0.841274i	$0.681806\pi$
$654$		0			0
$655$	0.0899982	+	0.197069i	0.00351652	+	0.00770011i
$656$		0			0
$657$	3.89171	+	27.0675i	0.151830	+	1.05600i
$658$		0			0
$659$	32.6277	−	9.58036i	1.27100	−	0.373198i	0.424420	−	0.905466i	$-0.360478\pi$
$659$	32.6277	−	9.58036i	1.27100	−	0.373198i	0.846576	+	0.532268i	$0.178660\pi$
$660$		0			0
$661$	28.5460	−	32.9439i	1.11031	−	1.28137i	0.154305	−	0.988023i	$-0.450686\pi$
$661$	28.5460	−	32.9439i	1.11031	−	1.28137i	0.956007	−	0.293345i	$-0.0947684\pi$
$662$		0			0
$663$	4.99604	+	5.76574i	0.194030	+	0.223923i
$664$		0			0
$665$	0.156607	−	0.342921i	0.00607295	−	0.0132979i
$666$		0			0
$667$	0.913045	−	12.6906i	0.0353533	−	0.491384i
$668$		0			0
$669$	−29.8455	+	65.3526i	−1.15390	+	2.52668i
$670$		0			0
$671$	0.529114	+	0.610630i	0.0204262	+	0.0235731i
$672$		0			0
$673$	14.7541	−	17.0271i	0.568728	−	0.656347i	−0.396415	−	0.918072i	$-0.629746\pi$
$673$	14.7541	−	17.0271i	0.568728	−	0.656347i	0.965143	+	0.261724i	$0.0842911\pi$
$674$		0			0
$675$	5.00117	−	1.46847i	0.192495	−	0.0565216i
$676$		0			0
$677$	4.21158	+	29.2922i	0.161864	+	1.12579i	0.895116	+	0.445833i	$0.147092\pi$
$677$	4.21158	+	29.2922i	0.161864	+	1.12579i	−0.733252	+	0.679957i	$0.761998\pi$
$678$		0			0
$679$	−3.76197	−	8.23757i	−0.144371	−	0.316129i
$680$		0			0
$681$	55.1824	+	35.4636i	2.11460	+	1.35897i
$682$		0			0
$683$	6.32437	−	43.9869i	0.241995	−	1.68311i	−0.400087	−	0.916477i	$-0.631020\pi$
$683$	6.32437	−	43.9869i	0.241995	−	1.68311i	0.642082	−	0.766636i	$-0.278071\pi$
$684$		0			0
$685$	−1.68671	+	1.08399i	−0.0644461	+	0.0414170i
$686$		0			0
$687$	22.2802	+	6.54205i	0.850042	+	0.249595i
$688$		0			0
$689$	−1.50184			−0.0572156
$690$		0			0
$691$	31.8294			1.21085			0.605424	−	0.795903i	$-0.293004\pi$
$691$	31.8294			1.21085			0.605424	+	0.795903i	$0.293004\pi$
$692$		0			0
$693$	0.529038	+	0.155340i	0.0200965	+	0.00590087i
$694$		0			0
$695$	−7.00144	+	4.49955i	−0.265580	+	0.170678i
$696$		0			0
$697$	5.67898	−	39.4982i	0.215107	−	1.49610i
$698$		0			0
$699$	63.8956	+	41.0632i	2.41675	+	1.55315i
$700$		0			0
$701$	−18.2113	−	39.8771i	−0.687831	−	1.50614i	−0.854128	−	0.520063i	$-0.825908\pi$
$701$	−18.2113	−	39.8771i	−0.687831	−	1.50614i	0.166297	−	0.986076i	$-0.446819\pi$
$702$		0			0
$703$	0.815534	+	5.67216i	0.0307584	+	0.213930i
$704$		0			0
$705$	12.2210	−	3.58840i	0.460268	−	0.135147i
$706$		0			0
$707$	−5.55370	+	6.40931i	−0.208868	+	0.241047i
$708$		0			0
$709$	12.1776	+	14.0537i	0.457340	+	0.527798i	0.936847	−	0.349740i	$-0.113730\pi$
$709$	12.1776	+	14.0537i	0.457340	+	0.527798i	−0.479507	+	0.877538i	$0.659185\pi$
$710$		0			0
$711$	24.5601	−	53.7792i	0.921077	−	2.01688i
$712$		0			0
$713$	−12.0140	+	16.0348i	−0.449930	+	0.600506i
$714$		0			0
$715$	−0.0577911	+	0.126545i	−0.00216127	+	0.00473251i
$716$		0			0
$717$	51.4915	+	59.4243i	1.92298	+	2.21924i
$718$		0			0
$719$	4.82001	−	5.56259i	0.179756	−	0.207450i	−0.658720	−	0.752388i	$-0.728902\pi$
$719$	4.82001	−	5.56259i	0.179756	−	0.207450i	0.838476	+	0.544939i	$0.183447\pi$
$720$		0			0
$721$	8.86505	−	2.60301i	0.330152	−	0.0969413i
$722$		0			0
$723$	9.97769	+	69.3964i	0.371074	+	2.58088i
$724$		0			0
$725$	−1.10210	−	2.41327i	−0.0409311	−	0.0896267i
$726$		0			0
$727$	−0.742596	−	0.477237i	−0.0275413	−	0.0176997i	0.526798	−	0.849991i	$-0.323393\pi$
$727$	−0.742596	−	0.477237i	−0.0275413	−	0.0176997i	−0.554339	+	0.832291i	$0.687029\pi$
$728$		0			0
$729$	6.21474	−	43.2245i	0.230176	−	1.60091i
$730$		0			0
$731$	5.14821	−	3.30855i	0.190413	−	0.122371i
$732$		0			0
$733$	−20.0894	−	5.89879i	−0.742020	−	0.217877i	−0.111191	−	0.993799i	$-0.535467\pi$
$733$	−20.0894	−	5.89879i	−0.742020	−	0.217877i	−0.630829	+	0.775922i	$0.717285\pi$
$734$		0			0
$735$	18.5347			0.683663
$736$		0			0
$737$	−0.251671			−0.00927042
$738$		0			0
$739$	−13.9517	−	4.09659i	−0.513222	−	0.150695i	0.0148592	−	0.999890i	$-0.495270\pi$
$739$	−13.9517	−	4.09659i	−0.513222	−	0.150695i	−0.528081	+	0.849194i	$0.677088\pi$
$740$		0			0
$741$	−1.09006	+	0.700536i	−0.0400442	+	0.0257348i
$742$		0			0
$743$	−2.91319	+	20.2617i	−0.106875	+	0.743330i	0.863957	+	0.503566i	$0.167979\pi$
$743$	−2.91319	+	20.2617i	−0.106875	+	0.743330i	−0.970831	+	0.239764i	$0.922930\pi$
$744$		0			0
$745$	10.3085	+	6.62487i	0.377674	+	0.242717i
$746$		0			0
$747$	−17.6619	−	38.6741i	−0.646214	−	1.41501i
$748$		0			0
$749$	−0.757000	−	5.26505i	−0.0276602	−	0.192381i
$750$		0			0
$751$	42.9785	−	12.6196i	1.56831	−	0.460496i	0.621799	−	0.783177i	$-0.286402\pi$
$751$	42.9785	−	12.6196i	1.56831	−	0.460496i	0.946508	+	0.322681i	$0.104584\pi$
$752$		0			0
$753$	9.77762	−	11.2840i	0.356316	−	0.411211i
$754$		0			0
$755$	−6.80030	−	7.84797i	−0.247488	−	0.285617i
$756$		0			0
$757$	−9.56671	+	20.9482i	−0.347708	+	0.761374i	0.652286	+	0.757973i	$0.273810\pi$
$757$	−9.56671	+	20.9482i	−0.347708	+	0.761374i	−0.999994	+	0.00340155i	$0.998917\pi$
$758$		0			0
$759$	−1.72979	−	1.73125i	−0.0627873	−	0.0628404i
$760$		0			0
$761$	4.78188	−	10.4709i	0.173343	−	0.379568i	−0.802942	−	0.596057i	$-0.796733\pi$
$761$	4.78188	−	10.4709i	0.173343	−	0.379568i	0.976285	+	0.216489i	$0.0694605\pi$
$762$		0			0
$763$	−2.44346	−	2.81990i	−0.0884592	−	0.102087i
$764$		0			0
$765$	−11.3309	+	13.0765i	−0.409668	+	0.472782i
$766$		0			0
$767$	1.96683	−	0.577513i	0.0710181	−	0.0208528i
$768$		0			0
$769$	−5.86654	−	40.8027i	−0.211553	−	1.47138i	−0.767974	−	0.640482i	$-0.778735\pi$
$769$	−5.86654	−	40.8027i	−0.211553	−	1.47138i	0.556421	−	0.830901i	$-0.312174\pi$
$770$		0			0
$771$	13.6134	+	29.8092i	0.490276	+	1.07355i
$772$		0			0
$773$	8.43448	+	5.42051i	0.303367	+	0.194962i	0.683464	−	0.729985i	$-0.260473\pi$
$773$	8.43448	+	5.42051i	0.303367	+	0.194962i	−0.380096	+	0.924947i	$0.624109\pi$
$774$		0			0
$775$	−0.594569	+	4.13532i	−0.0213576	+	0.148545i
$776$		0			0
$777$	13.9303	−	8.95244i	0.499745	−	0.321167i
$778$		0			0
$779$	6.50290	+	1.90942i	0.232991	+	0.0684122i
$780$		0			0
$781$	−1.13816			−0.0407267
$782$		0			0
$783$	13.8283			0.494185
$784$		0			0
$785$	−18.2751	−	5.36605i	−0.652266	−	0.191522i
$786$		0			0
$787$	14.4844	−	9.30855i	0.516313	−	0.331814i	−0.256399	−	0.966571i	$-0.582536\pi$
$787$	14.4844	−	9.30855i	0.516313	−	0.331814i	0.772712	+	0.634757i	$0.218900\pi$
$788$		0			0
$789$	−7.34368	+	51.0764i	−0.261442	+	1.81837i
$790$		0			0
$791$	−10.0355	−	6.44941i	−0.356821	−	0.229315i
$792$		0			0
$793$	1.40925	+	3.08583i	0.0500439	+	0.109581i
$794$		0			0
$795$	−0.784012	−	5.45292i	−0.0278060	−	0.193395i
$796$		0			0
$797$	3.34644	−	0.982604i	0.118537	−	0.0348056i	−0.221926	−	0.975064i	$-0.571234\pi$
$797$	3.34644	−	0.982604i	0.118537	−	0.0348056i	0.340463	+	0.940258i	$0.389416\pi$
$798$		0			0
$799$	−10.5942	+	12.2263i	−0.374794	+	0.432535i
$800$		0			0
$801$	39.3411	+	45.4020i	1.39005	+	1.60420i
$802$		0			0
$803$	0.425540	−	0.931802i	0.0150170	−	0.0328826i
$804$		0			0
$805$	2.62324	+	1.43384i	0.0924571	+	0.0505362i
$806$		0			0
$807$	−26.3395	+	57.6755i	−0.927195	+	2.03027i
$808$		0			0
$809$	−28.5095	−	32.9018i	−1.00234	−	1.15676i	−0.987619	−	0.156873i	$-0.949859\pi$
$809$	−28.5095	−	32.9018i	−1.00234	−	1.15676i	−0.0147230	−	0.999892i	$-0.504687\pi$
$810$		0			0
$811$	25.6280	−	29.5763i	0.899920	−	1.03856i	−0.0991343	−	0.995074i	$-0.531607\pi$
$811$	25.6280	−	29.5763i	0.899920	−	1.03856i	0.999054	−	0.0434886i	$-0.0138472\pi$
$812$		0			0
$813$	13.4760	−	3.95691i	0.472624	−	0.138775i
$814$		0			0
$815$	−0.266453	−	1.85322i	−0.00933344	−	0.0649155i
$816$		0			0
$817$	0.431774	+	0.945453i	0.0151059	+	0.0330772i
$818$		0			0
$819$	1.94750	+	1.25158i	0.0680512	+	0.0437339i
$820$		0			0
$821$	4.18531	−	29.1094i	0.146068	−	1.01593i	−0.776507	−	0.630109i	$-0.783010\pi$
$821$	4.18531	−	29.1094i	0.146068	−	1.01593i	0.922575	−	0.385818i	$-0.126081\pi$
$822$		0			0
$823$	−27.2762	+	17.5294i	−0.950790	+	0.611036i	−0.921435	−	0.388534i	$-0.872982\pi$
$823$	−27.2762	+	17.5294i	−0.950790	+	0.611036i	−0.0293552	+	0.999569i	$0.509345\pi$
$824$		0			0
$825$	−0.489631	−	0.143769i	−0.0170468	−	0.00500538i
$826$		0			0
$827$	9.75291			0.339142			0.169571	−	0.985518i	$-0.445762\pi$
$827$	9.75291			0.339142			0.169571	+	0.985518i	$0.445762\pi$
$828$		0			0
$829$	−50.1918			−1.74323			−0.871617	−	0.490188i	$-0.836928\pi$
$829$	−50.1918			−1.74323			−0.871617	+	0.490188i	$0.836928\pi$
$830$		0			0
$831$	−25.0201	−	7.34657i	−0.867938	−	0.254850i
$832$		0			0
$833$	−19.8046	+	12.7276i	−0.686188	+	0.440986i
$834$		0			0
$835$	−0.661446	+	4.60046i	−0.0228903	+	0.159206i
$836$		0			0
$837$	−18.3193	−	11.7731i	−0.633207	−	0.406938i
$838$		0			0
$839$	19.4842	+	42.6645i	0.672670	+	1.47294i	0.870228	+	0.492650i	$0.163972\pi$
$839$	19.4842	+	42.6645i	0.672670	+	1.47294i	−0.197558	+	0.980291i	$0.563301\pi$
$840$		0			0
$841$	3.12544	+	21.7379i	0.107774	+	0.749584i
$842$		0			0
$843$	−26.0270	+	7.64221i	−0.896417	+	0.263212i
$844$		0			0
$845$	8.13069	−	9.38331i	0.279704	−	0.322796i
$846$		0			0
$847$	4.47683	+	5.16654i	0.153826	+	0.177524i
$848$		0			0
$849$	29.3526	−	64.2733i	1.00738	−	2.20585i
$850$		0			0
$851$	−45.3285	+	3.22270i	−1.55384	+	0.110473i
$852$		0			0
$853$	0.305470	−	0.668886i	0.0104591	−	0.0229022i	−0.904330	−	0.426833i	$-0.859629\pi$
$853$	0.305470	−	0.668886i	0.0104591	−	0.0229022i	0.914789	+	0.403931i	$0.132356\pi$
$854$		0			0
$855$	−1.92445	−	2.22094i	−0.0658149	−	0.0759545i
$856$		0			0
$857$	19.6991	−	22.7339i	0.672907	−	0.776576i	−0.311921	−	0.950108i	$-0.600972\pi$
$857$	19.6991	−	22.7339i	0.672907	−	0.776576i	0.984828	+	0.173532i	$0.0555179\pi$
$858$		0			0
$859$	14.1218	−	4.14653i	0.481829	−	0.141478i	−0.0317926	−	0.999494i	$-0.510122\pi$
$859$	14.1218	−	4.14653i	0.481829	−	0.141478i	0.513622	+	0.858017i	$0.328303\pi$
$860$		0			0
$861$	−2.78712	−	19.3849i	−0.0949849	−	0.660635i
$862$		0			0
$863$	−21.9248	−	48.0086i	−0.746329	−	1.63423i	−0.772853	−	0.634585i	$-0.781171\pi$
$863$	−21.9248	−	48.0086i	−0.746329	−	1.63423i	0.0265241	−	0.999648i	$-0.491556\pi$
$864$		0			0
$865$	15.4359	+	9.92004i	0.524836	+	0.337291i
$866$		0			0
$867$	−1.72392	+	11.9901i	−0.0585472	+	0.407205i
$868$		0			0
$869$	−1.86313	+	1.19736i	−0.0632023	+	0.0406176i
$870$		0			0
$871$	−1.01387	−	0.297698i	−0.0343536	−	0.0100871i
$872$		0			0
$873$	−70.5933			−2.38922
$874$		0			0
$875$	0.623360			0.0210734
$876$		0			0
$877$	−38.0865	−	11.1832i	−1.28609	−	0.377630i	−0.433946	−	0.900939i	$-0.642879\pi$
$877$	−38.0865	−	11.1832i	−1.28609	−	0.377630i	−0.852143	+	0.523309i	$0.824697\pi$
$878$		0			0
$879$	51.8372	−	33.3138i	1.74843	−	1.12365i
$880$		0			0
$881$	0.0887571	−	0.617319i	0.00299030	−	0.0207980i	−0.988272	−	0.152706i	$-0.951201\pi$
$881$	0.0887571	−	0.617319i	0.00299030	−	0.0207980i	0.991262	+	0.131908i	$0.0421103\pi$
$882$		0			0
$883$	4.08832	+	2.62740i	0.137583	+	0.0884192i	0.607622	−	0.794227i	$-0.292124\pi$
$883$	4.08832	+	2.62740i	0.137583	+	0.0884192i	−0.470039	+	0.882646i	$0.655760\pi$
$884$		0			0
$885$	3.12360	+	6.83973i	0.104999	+	0.229915i
$886$		0			0
$887$	−3.21411	−	22.3546i	−0.107919	−	0.750594i	−0.969874	−	0.243608i	$-0.921669\pi$
$887$	−3.21411	−	22.3546i	−0.107919	−	0.750594i	0.861955	−	0.506985i	$-0.169240\pi$
$888$		0			0
$889$	2.69967	−	0.792695i	0.0905440	−	0.0265861i
$890$		0			0
$891$	0.00412291	−	0.00475810i	0.000138123	−	0.000159402i
$892$		0			0
$893$	−1.79933	−	2.07654i	−0.0602123	−	0.0694887i
$894$		0			0
$895$	7.82700	−	17.1387i	0.261628	−	0.572885i
$896$		0			0
$897$	−4.92064	−	9.02054i	−0.164295	−	0.301187i
$898$		0			0
$899$	−4.60442	+	10.0823i	−0.153566	+	0.336263i
$900$		0			0
$901$	4.58221	+	5.28815i	0.152655	+	0.176174i
$902$		0			0
$903$	1.96682	−	2.26983i	0.0654516	−	0.0755351i
$904$		0			0
$905$	10.2090	−	2.99764i	0.339359	−	0.0996448i
$906$		0			0
$907$	8.17855	+	56.8830i	0.271564	+	1.88877i	0.432233	+	0.901762i	$0.357726\pi$
$907$	8.17855	+	56.8830i	0.271564	+	1.88877i	−0.160669	+	0.987008i	$0.551365\pi$
$908$		0			0
$909$	27.4629	+	60.1353i	0.910887	+	1.99456i
$910$		0			0
$911$	−21.4602	−	13.7916i	−0.711008	−	0.456937i	0.134491	−	0.990915i	$-0.457060\pi$
$911$	−21.4602	−	13.7916i	−0.711008	−	0.456937i	−0.845498	+	0.533978i	$0.820697\pi$
$912$		0			0
$913$	−0.226658	+	1.57644i	−0.00750130	+	0.0521727i
$914$		0			0
$915$	−10.4684	+	6.72765i	−0.346075	+	0.222409i
$916$		0			0
$917$	−0.129578	−	0.0380476i	−0.00427905	−	0.00125644i
$918$		0			0
$919$	6.34179			0.209196			0.104598	−	0.994515i	$-0.466644\pi$
$919$	6.34179			0.209196			0.104598	+	0.994515i	$0.466644\pi$
$920$		0			0
$921$	−52.5237			−1.73072
$922$		0			0
$923$	−4.58514	−	1.34632i	−0.150922	−	0.0443146i
$924$		0			0
$925$	−7.97131	+	5.12285i	−0.262095	+	0.168438i
$926$		0			0
$927$	10.2499	−	71.2897i	0.336651	−	2.34146i
$928$		0			0
$929$	−43.4343	−	27.9135i	−1.42503	−	0.915814i	−0.999943	−	0.0106631i	$-0.996606\pi$
$929$	−43.4343	−	27.9135i	−1.42503	−	0.915814i	−0.425091	−	0.905151i	$-0.639758\pi$
$930$		0			0
$931$	−1.66099	−	3.63705i	−0.0544366	−	0.119200i
$932$		0			0
$933$	−8.51850	−	59.2475i	−0.278883	−	1.93967i
$934$		0			0
$935$	0.621903	−	0.182607i	0.0203384	−	0.00597189i
$936$		0			0
$937$	4.48005	−	5.17026i	0.146357	−	0.168905i	−0.677838	−	0.735212i	$-0.737083\pi$
$937$	4.48005	−	5.17026i	0.146357	−	0.168905i	0.824195	+	0.566307i	$0.191628\pi$
$938$		0			0
$939$	13.9012	+	16.0428i	0.453648	+	0.523538i
$940$		0			0
$941$	−22.7709	+	49.8614i	−0.742311	+	1.62543i	0.0374042	+	0.999300i	$0.488091\pi$
$941$	−22.7709	+	49.8614i	−0.742311	+	1.62543i	−0.779715	+	0.626134i	$0.784636\pi$
$942$		0			0
$943$	−18.8033	+	50.3487i	−0.612321	+	1.63958i
$944$		0			0
$945$	−1.34974	+	2.95552i	−0.0439071	+	0.0961431i
$946$		0			0
$947$	−31.6587	−	36.5361i	−1.02877	−	1.18726i	−0.982101	−	0.188353i	$-0.939685\pi$
$947$	−31.6587	−	36.5361i	−1.02877	−	1.18726i	−0.0466678	−	0.998910i	$-0.514860\pi$
$948$		0			0
$949$	2.81652	−	3.25043i	0.0914280	−	0.105514i
$950$		0			0
$951$	−65.3880	+	19.1996i	−2.12035	+	0.622591i
$952$		0			0
$953$	0.945024	+	6.57278i	0.0306123	+	0.212913i	0.999386	−	0.0350327i	$-0.0111535\pi$
$953$	0.945024	+	6.57278i	0.0306123	+	0.212913i	−0.968774	+	0.247946i	$0.920244\pi$
$954$		0			0
$955$	−0.413293	−	0.904985i	−0.0133738	−	0.0292846i
$956$		0			0
$957$	−1.13892	−	0.731942i	−0.0368162	−	0.0236603i
$958$		0			0
$959$	0.177871	−	1.23712i	0.00574374	−	0.0399486i
$960$		0			0
$961$	−11.3953	+	7.32331i	−0.367590	+	0.236236i
$962$		0			0
$963$	−39.7849	−	11.6819i	−1.28205	−	0.376444i
$964$		0			0
$965$	−14.1819			−0.456531
$966$		0			0
$967$	−20.0907			−0.646072			−0.323036	−	0.946387i	$-0.604703\pi$
$967$	−20.0907			−0.646072			−0.323036	+	0.946387i	$0.604703\pi$
$968$		0			0
$969$	5.79249	+	1.70083i	0.186082	+	0.0546385i
$970$		0			0
$971$	33.6880	−	21.6499i	1.08110	−	0.694780i	0.126287	−	0.991994i	$-0.459694\pi$
$971$	33.6880	−	21.6499i	1.08110	−	0.694780i	0.954811	+	0.297214i	$0.0960575\pi$
$972$		0			0
$973$	0.738329	−	5.13519i	0.0236697	−	0.164627i
$974$		0			0
$975$	−1.80244	−	1.15836i	−0.0577241	−	0.0370971i
$976$		0			0
$977$	−0.881946	−	1.93119i	−0.0282159	−	0.0617843i	0.894999	−	0.446068i	$-0.147176\pi$
$977$	−0.881946	−	1.93119i	−0.0282159	−	0.0617843i	−0.923215	+	0.384283i	$0.874449\pi$
$978$		0			0
$979$	−0.320269	−	2.22752i	−0.0102358	−	0.0711918i
$980$		0			0
$981$	−27.9080	+	8.19453i	−0.891034	+	0.261631i
$982$		0			0
$983$	7.76964	−	8.96664i	0.247813	−	0.285992i	−0.618192	−	0.786027i	$-0.712134\pi$
$983$	7.76964	−	8.96664i	0.247813	−	0.285992i	0.866005	+	0.500036i	$0.166680\pi$
$984$		0			0
$985$	−3.89546	−	4.49560i	−0.124120	−	0.143242i
$986$		0			0
$987$	−3.29826	+	7.22218i	−0.104985	+	0.229885i
$988$		0			0
$989$	−7.72385	+	2.87713i	−0.245604	+	0.0914874i
$990$		0			0
$991$	−14.4128	+	31.5597i	−0.457839	+	1.00253i	0.530136	+	0.847913i	$0.322141\pi$
$991$	−14.4128	+	31.5597i	−0.457839	+	1.00253i	−0.987975	+	0.154615i	$0.950586\pi$
$992$		0			0
$993$	40.8954	+	47.1958i	1.29778	+	1.49771i
$994$		0			0
$995$	6.63443	−	7.65654i	0.210326	−	0.242729i
$996$		0			0
$997$	37.6147	−	11.0447i	1.19127	−	0.349789i	0.374762	−	0.927121i	$-0.377724\pi$
$997$	37.6147	−	11.0447i	1.19127	−	0.349789i	0.816509	+	0.577332i	$0.195906\pi$
$998$		0			0
$999$	−7.02882	−	48.8865i	−0.222382	−	1.54670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.121.3	✓	30
23.4	even	11	inner	460.2.m.a.441.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.121.3	✓	30	1.1	even	1	trivial
460.2.m.a.441.3	yes	30	23.4	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.68988 + 0.789819i) q^{3} +(0.841254 - 0.540641i) q^{5} +(-0.0887134 + 0.617015i) q^{7} +(4.08786 + 2.62711i) q^{9} +O(q^{10})\)	\(q+(2.68988 + 0.789819i) q^{3} +(0.841254 - 0.540641i) q^{5} +(-0.0887134 + 0.617015i) q^{7} +(4.08786 + 2.62711i) q^{9} +(-0.0756169 - 0.165578i) q^{11} +(-0.108766 - 0.756483i) q^{13} +(2.68988 - 0.789819i) q^{15} +(-2.33181 + 2.69105i) q^{17} +(-0.396039 - 0.457053i) q^{19} +(-0.725959 + 1.58963i) q^{21} +(3.84048 - 2.87241i) q^{23} +(0.415415 - 0.909632i) q^{25} +(3.41333 + 3.93919i) q^{27} +(1.73736 - 2.00502i) q^{29} +(-4.00861 + 1.17703i) q^{31} +(-0.0726236 - 0.505108i) q^{33} +(0.258953 + 0.567028i) q^{35} +(-7.97131 - 5.12285i) q^{37} +(0.304918 - 2.12075i) q^{39} +(-9.42765 + 6.05878i) q^{41} +(-1.64902 - 0.484197i) q^{43} +4.85925 q^{45} +4.54332 q^{47} +(6.34361 + 1.86265i) q^{49} +(-8.39772 + 5.39689i) q^{51} +(0.279661 - 1.94508i) q^{53} +(-0.153131 - 0.0984114i) q^{55} +(-0.704307 - 1.54222i) q^{57} +(0.381709 + 2.65485i) q^{59} +(-4.25898 + 1.25055i) q^{61} +(-1.98362 + 2.28921i) q^{63} +(-0.500485 - 0.577591i) q^{65} +(0.574353 - 1.25766i) q^{67} +(12.5991 - 4.69315i) q^{69} +(2.59747 - 5.68766i) q^{71} +(3.68528 + 4.25304i) q^{73} +(1.83586 - 2.11870i) q^{75} +(0.108872 - 0.0319678i) q^{77} +(-1.73153 - 12.0430i) q^{79} +(0.0143682 + 0.0314619i) q^{81} +(-7.36058 - 4.73035i) q^{83} +(-0.506751 + 3.52453i) q^{85} +(6.25689 - 4.02106i) q^{87} +(11.8623 + 3.48309i) q^{89} +0.476410 q^{91} -11.7123 q^{93} +(-0.580271 - 0.170383i) q^{95} +(-12.2214 + 7.85422i) q^{97} +(0.125880 - 0.875514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more