LMFDB - Embedded newform 1148.2.i.e.165.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.7
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.e.821.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.224795 + 0.389356i) q^{3} +(0.393901 + 0.682257i) q^{5} +(1.75718 + 1.97796i) q^{7} +(1.39893 + 2.42303i) q^{9} +O(q^{10})$	\(q+(-0.224795 + 0.389356i) q^{3} +(0.393901 + 0.682257i) q^{5} +(1.75718 + 1.97796i) q^{7} +(1.39893 + 2.42303i) q^{9} +(-1.55200 + 2.68814i) q^{11} +5.59137 q^{13} -0.354188 q^{15} +(-2.69122 + 4.66133i) q^{17} +(-2.41193 - 4.17758i) q^{19} +(-1.16514 + 0.239532i) q^{21} +(-3.51228 - 6.08344i) q^{23} +(2.18968 - 3.79264i) q^{25} -2.60666 q^{27} -7.52560 q^{29} +(-2.45362 + 4.24979i) q^{31} +(-0.697763 - 1.20856i) q^{33} +(-0.657324 + 1.97797i) q^{35} +(4.60604 + 7.97789i) q^{37} +(-1.25691 + 2.17703i) q^{39} -1.00000 q^{41} +11.7730 q^{43} +(-1.10208 + 1.90887i) q^{45} +(2.78143 + 4.81759i) q^{47} +(-0.824657 + 6.95125i) q^{49} +(-1.20995 - 2.09569i) q^{51} +(-2.97376 + 5.15070i) q^{53} -2.44534 q^{55} +2.16875 q^{57} +(5.10083 - 8.83489i) q^{59} +(-2.44701 - 4.23835i) q^{61} +(-2.33447 + 7.02472i) q^{63} +(2.20245 + 3.81475i) q^{65} +(-5.87182 + 10.1703i) q^{67} +3.15817 q^{69} -1.39569 q^{71} +(2.14014 - 3.70683i) q^{73} +(0.984459 + 1.70513i) q^{75} +(-8.04418 + 1.65375i) q^{77} +(-4.05037 - 7.01545i) q^{79} +(-3.61084 + 6.25416i) q^{81} +2.10452 q^{83} -4.24031 q^{85} +(1.69172 - 2.93014i) q^{87} +(8.08070 + 13.9962i) q^{89} +(9.82503 + 11.0595i) q^{91} +(-1.10312 - 1.91066i) q^{93} +(1.90012 - 3.29111i) q^{95} +2.23832 q^{97} -8.68459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	$ 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) $ 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.224795	+	0.389356i	−0.129785	+	0.224795i	−0.923593	−	0.383374i	$-0.874762\pi$
$3$	−0.224795	+	0.389356i	−0.129785	+	0.224795i	0.793808	+	0.608168i	$0.208096\pi$
$4$		0			0
$5$	0.393901	+	0.682257i	0.176158	+	0.305115i	0.940561	−	0.339624i	$-0.110300\pi$
$5$	0.393901	+	0.682257i	0.176158	+	0.305115i	−0.764403	+	0.644738i	$0.776966\pi$
$6$		0			0
$7$	1.75718	+	1.97796i	0.664151	+	0.747599i
$7$	1.75718	+	1.97796i	0.664151	+	0.747599i
$8$		0			0
$9$	1.39893	+	2.42303i	0.466312	+	0.807675i
$10$		0			0
$11$	−1.55200	+	2.68814i	−0.467946	+	0.810506i	−0.999329	−	0.0366257i	$-0.988339\pi$
$11$	−1.55200	+	2.68814i	−0.467946	+	0.810506i	0.531383	+	0.847131i	$0.321672\pi$
$12$		0			0
$13$	5.59137			1.55077			0.775383	−	0.631491i	$-0.217557\pi$
$13$	5.59137			1.55077			0.775383	+	0.631491i	$0.217557\pi$
$14$		0			0
$15$	−0.354188			−0.0914510
$16$		0			0
$17$	−2.69122	+	4.66133i	−0.652717	+	1.13054i	0.329744	+	0.944071i	$0.393038\pi$
$17$	−2.69122	+	4.66133i	−0.652717	+	1.13054i	−0.982461	+	0.186469i	$0.940296\pi$
$18$		0			0
$19$	−2.41193	−	4.17758i	−0.553334	−	0.958402i	−0.998031	−	0.0627212i	$-0.980022\pi$
$19$	−2.41193	−	4.17758i	−0.553334	−	0.958402i	0.444697	−	0.895681i	$-0.353311\pi$
$20$		0			0
$21$	−1.16514	+	0.239532i	−0.254253	+	0.0522702i
$22$		0			0
$23$	−3.51228	−	6.08344i	−0.732361	−	1.26849i	−0.955872	−	0.293784i	$-0.905085\pi$
$23$	−3.51228	−	6.08344i	−0.732361	−	1.26849i	0.223511	−	0.974701i	$-0.428248\pi$
$24$		0			0
$25$	2.18968	−	3.79264i	0.437937	−	0.758529i
$26$		0			0
$27$	−2.60666			−0.501652
$28$		0			0
$29$	−7.52560			−1.39747			−0.698734	−	0.715382i	$-0.746253\pi$
$29$	−7.52560			−1.39747			−0.698734	+	0.715382i	$0.746253\pi$
$30$		0			0
$31$	−2.45362	+	4.24979i	−0.440683	+	0.763286i	−0.997740	−	0.0671885i	$-0.978597\pi$
$31$	−2.45362	+	4.24979i	−0.440683	+	0.763286i	0.557057	+	0.830474i	$0.311930\pi$
$32$		0			0
$33$	−0.697763	−	1.20856i	−0.121465	−	0.210384i
$34$		0			0
$35$	−0.657324	+	1.97797i	−0.111108	+	0.334338i
$36$		0			0
$37$	4.60604	+	7.97789i	0.757228	+	1.31156i	0.944259	+	0.329203i	$0.106780\pi$
$37$	4.60604	+	7.97789i	0.757228	+	1.31156i	−0.187032	+	0.982354i	$0.559887\pi$
$38$		0			0
$39$	−1.25691	+	2.17703i	−0.201267	+	0.348604i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	11.7730			1.79536			0.897680	−	0.440648i	$-0.145251\pi$
$43$	11.7730			1.79536			0.897680	+	0.440648i	$0.145251\pi$
$44$		0			0
$45$	−1.10208	+	1.90887i	−0.164289	+	0.284557i
$46$		0			0
$47$	2.78143	+	4.81759i	0.405714	+	0.702717i	0.994404	−	0.105641i	$-0.0336896\pi$
$47$	2.78143	+	4.81759i	0.405714	+	0.702717i	−0.588690	+	0.808359i	$0.700356\pi$
$48$		0			0
$49$	−0.824657	+	6.95125i	−0.117808	+	0.993036i
$50$		0			0
$51$	−1.20995	−	2.09569i	−0.169426	−	0.293455i
$52$		0			0
$53$	−2.97376	+	5.15070i	−0.408477	+	0.707504i	−0.994719	−	0.102632i	$-0.967273\pi$
$53$	−2.97376	+	5.15070i	−0.408477	+	0.707504i	0.586242	+	0.810136i	$0.300607\pi$
$54$		0			0
$55$	−2.44534			−0.329730
$56$		0			0
$57$	2.16875			0.287259
$58$		0			0
$59$	5.10083	−	8.83489i	0.664071	−	1.15020i	−0.315465	−	0.948937i	$-0.602161\pi$
$59$	5.10083	−	8.83489i	0.664071	−	1.15020i	0.979536	−	0.201268i	$-0.0645060\pi$
$60$		0			0
$61$	−2.44701	−	4.23835i	−0.313308	−	0.542666i	0.665768	−	0.746159i	$-0.268104\pi$
$61$	−2.44701	−	4.23835i	−0.313308	−	0.542666i	−0.979076	+	0.203493i	$0.934771\pi$
$62$		0			0
$63$	−2.33447	+	7.02472i	−0.294116	+	0.885032i
$64$		0			0
$65$	2.20245	+	3.81475i	0.273180	+	0.473162i
$66$		0			0
$67$	−5.87182	+	10.1703i	−0.717358	+	1.24250i	0.244686	+	0.969602i	$0.421315\pi$
$67$	−5.87182	+	10.1703i	−0.717358	+	1.24250i	−0.962043	+	0.272897i	$0.912018\pi$
$68$		0			0
$69$	3.15817			0.380199
$70$		0			0
$71$	−1.39569			−0.165638			−0.0828188	−	0.996565i	$-0.526392\pi$
$71$	−1.39569			−0.165638			−0.0828188	+	0.996565i	$0.526392\pi$
$72$		0			0
$73$	2.14014	−	3.70683i	0.250484	−	0.433851i	−0.713175	−	0.700986i	$-0.752744\pi$
$73$	2.14014	−	3.70683i	0.250484	−	0.433851i	0.963659	+	0.267135i	$0.0860769\pi$
$74$		0			0
$75$	0.984459	+	1.70513i	0.113676	+	0.196892i
$76$		0			0
$77$	−8.04418	+	1.65375i	−0.916720	+	0.188462i
$78$		0			0
$79$	−4.05037	−	7.01545i	−0.455702	−	0.789299i	0.543026	−	0.839716i	$-0.317278\pi$
$79$	−4.05037	−	7.01545i	−0.455702	−	0.789299i	−0.998728	+	0.0504165i	$0.983945\pi$
$80$		0			0
$81$	−3.61084	+	6.25416i	−0.401204	+	0.694906i
$82$		0			0
$83$	2.10452			0.231001			0.115500	−	0.993307i	$-0.463153\pi$
$83$	2.10452			0.231001			0.115500	+	0.993307i	$0.463153\pi$
$84$		0			0
$85$	−4.24031			−0.459926
$86$		0			0
$87$	1.69172	−	2.93014i	0.181371	−	0.314144i
$88$		0			0
$89$	8.08070	+	13.9962i	0.856553	+	1.48359i	0.875197	+	0.483767i	$0.160732\pi$
$89$	8.08070	+	13.9962i	0.856553	+	1.48359i	−0.0186441	+	0.999826i	$0.505935\pi$
$90$		0			0
$91$	9.82503	+	11.0595i	1.02994	+	1.15935i
$92$		0			0
$93$	−1.10312	−	1.91066i	−0.114388	−	0.198127i
$94$		0			0
$95$	1.90012	−	3.29111i	0.194948	−	0.337661i
$96$		0			0
$97$	2.23832			0.227267			0.113634	−	0.993523i	$-0.463751\pi$
$97$	2.23832			0.227267			0.113634	+	0.993523i	$0.463751\pi$
$98$		0			0
$99$	−8.68459			−0.872834
$100$		0			0
$101$	3.07233	−	5.32143i	0.305708	−	0.529502i	−0.671711	−	0.740814i	$-0.734440\pi$
$101$	3.07233	−	5.32143i	0.305708	−	0.529502i	0.977419	+	0.211312i	$0.0677735\pi$
$102$		0			0
$103$	−0.736747	−	1.27608i	−0.0725938	−	0.125736i	0.827444	−	0.561549i	$-0.189794\pi$
$103$	−0.736747	−	1.27608i	−0.0725938	−	0.125736i	−0.900037	+	0.435813i	$0.856461\pi$
$104$		0			0
$105$	−0.622371	−	0.700570i	−0.0607372	−	0.0683687i
$106$		0			0
$107$	−4.21778	−	7.30541i	−0.407748	−	0.706241i	0.586889	−	0.809668i	$-0.300353\pi$
$107$	−4.21778	−	7.30541i	−0.407748	−	0.706241i	−0.994637	+	0.103427i	$0.967019\pi$
$108$		0			0
$109$	5.08060	−	8.79985i	0.486633	−	0.842873i	−0.513249	−	0.858240i	$-0.671558\pi$
$109$	5.08060	−	8.79985i	0.486633	−	0.842873i	0.999882	+	0.0153668i	$0.00489159\pi$
$110$		0			0
$111$	−4.14165			−0.393108
$112$		0			0
$113$	8.34801			0.785315			0.392657	−	0.919685i	$-0.371556\pi$
$113$	8.34801			0.785315			0.392657	+	0.919685i	$0.371556\pi$
$114$		0			0
$115$	2.76698	−	4.79255i	0.258022	−	0.446908i
$116$		0			0
$117$	7.82196	+	13.5480i	0.723140	+	1.25252i
$118$		0			0
$119$	−13.9489	+	2.86766i	−1.27869	+	0.262878i
$120$		0			0
$121$	0.682590	+	1.18228i	0.0620536	+	0.107480i
$122$		0			0
$123$	0.224795	−	0.389356i	0.0202691	−	0.0351071i
$124$		0			0
$125$	7.38909			0.660901
$126$		0			0
$127$	−15.6031			−1.38455			−0.692274	−	0.721635i	$-0.743391\pi$
$127$	−15.6031			−1.38455			−0.692274	+	0.721635i	$0.743391\pi$
$128$		0			0
$129$	−2.64650	+	4.58388i	−0.233012	+	0.403588i
$130$		0			0
$131$	5.88131	+	10.1867i	0.513853	+	0.890019i	0.999871	+	0.0160705i	$0.00511561\pi$
$131$	5.88131	+	10.1867i	0.513853	+	0.890019i	−0.486018	+	0.873949i	$0.661551\pi$
$132$		0			0
$133$	4.02490	−	12.1114i	0.349003	−	1.05019i
$134$		0			0
$135$	−1.02677	−	1.77841i	−0.0883701	−	0.153062i
$136$		0			0
$137$	−2.24802	+	3.89369i	−0.192061	+	0.332660i	−0.945933	−	0.324361i	$-0.894851\pi$
$137$	−2.24802	+	3.89369i	−0.192061	+	0.332660i	0.753872	+	0.657022i	$0.228184\pi$
$138$		0			0
$139$	1.41035			0.119624			0.0598121	−	0.998210i	$-0.480950\pi$
$139$	1.41035			0.119624			0.0598121	+	0.998210i	$0.480950\pi$
$140$		0			0
$141$	−2.50101			−0.210623
$142$		0			0
$143$	−8.67781	+	15.0304i	−0.725675	+	1.25691i
$144$		0			0
$145$	−2.96434	−	5.13439i	−0.246175	−	0.426388i
$146$		0			0
$147$	−2.52114	−	1.88369i	−0.207940	−	0.155364i
$148$		0			0
$149$	−4.25142	−	7.36368i	−0.348290	−	0.603256i	0.637656	−	0.770321i	$-0.279904\pi$
$149$	−4.25142	−	7.36368i	−0.348290	−	0.603256i	−0.985946	+	0.167066i	$0.946571\pi$
$150$		0			0
$151$	1.34269	−	2.32561i	0.109267	−	0.189256i	−0.806207	−	0.591634i	$-0.798483\pi$
$151$	1.34269	−	2.32561i	0.109267	−	0.189256i	0.915473	+	0.402378i	$0.131816\pi$
$152$		0			0
$153$	−15.0594			−1.21748
$154$		0			0
$155$	−3.86594			−0.310520
$156$		0			0
$157$	2.13375	−	3.69577i	0.170292	−	0.294954i	−0.768230	−	0.640174i	$-0.778862\pi$
$157$	2.13375	−	3.69577i	0.170292	−	0.294954i	0.938522	+	0.345220i	$0.112196\pi$
$158$		0			0
$159$	−1.33697	−	2.31570i	−0.106029	−	0.183647i
$160$		0			0
$161$	5.86112	−	17.6368i	0.461921	−	1.38998i
$162$		0			0
$163$	−9.36660	−	16.2234i	−0.733649	−	1.27072i	−0.955314	−	0.295594i	$-0.904482\pi$
$163$	−9.36660	−	16.2234i	−0.733649	−	1.27072i	0.221665	−	0.975123i	$-0.428851\pi$
$164$		0			0
$165$	0.549700	−	0.952109i	0.0427941	−	0.0741216i
$166$		0			0
$167$	11.3399			0.877510			0.438755	−	0.898607i	$-0.355420\pi$
$167$	11.3399			0.877510			0.438755	+	0.898607i	$0.355420\pi$
$168$		0			0
$169$	18.2634			1.40488
$170$		0			0
$171$	6.74825	−	11.6883i	0.516052	−	0.893828i
$172$		0			0
$173$	6.25114	+	10.8273i	0.475266	+	0.823184i	0.999599	−	0.0283291i	$-0.00901864\pi$
$173$	6.25114	+	10.8273i	0.475266	+	0.823184i	−0.524333	+	0.851513i	$0.675685\pi$
$174$		0			0
$175$	11.3494	−	2.33324i	0.857931	−	0.176376i
$176$		0			0
$177$	2.29328	+	3.97208i	0.172373	+	0.298559i
$178$		0			0
$179$	3.48094	−	6.02916i	0.260178	−	0.450641i	−0.706111	−	0.708101i	$-0.749552\pi$
$179$	3.48094	−	6.02916i	0.260178	−	0.450641i	0.966289	+	0.257460i	$0.0828856\pi$
$180$		0			0
$181$	18.3297			1.36244			0.681219	−	0.732080i	$-0.261450\pi$
$181$	18.3297			1.36244			0.681219	+	0.732080i	$0.261450\pi$
$182$		0			0
$183$	2.20031			0.162651
$184$		0			0
$185$	−3.62865	+	6.28500i	−0.266784	+	0.462083i
$186$		0			0
$187$	−8.35356	−	14.4688i	−0.610872	−	1.05806i
$188$		0			0
$189$	−4.58037	−	5.15588i	−0.333173	−	0.375035i
$190$		0			0
$191$	−9.64207	−	16.7005i	−0.697675	−	1.20841i	−0.969270	−	0.245998i	$-0.920884\pi$
$191$	−9.64207	−	16.7005i	−0.697675	−	1.20841i	0.271595	−	0.962412i	$-0.412449\pi$
$192$		0			0
$193$	−0.698517	+	1.20987i	−0.0502803	+	0.0870881i	−0.890070	−	0.455824i	$-0.849345\pi$
$193$	−0.698517	+	1.20987i	−0.0502803	+	0.0870881i	0.839790	+	0.542912i	$0.182678\pi$
$194$		0			0
$195$	−1.98040			−0.141819
$196$		0			0
$197$	12.8161			0.913108			0.456554	−	0.889696i	$-0.349084\pi$
$197$	12.8161			0.913108			0.456554	+	0.889696i	$0.349084\pi$
$198$		0			0
$199$	0.836697	−	1.44920i	0.0593119	−	0.102731i	−0.834845	−	0.550485i	$-0.814443\pi$
$199$	0.836697	−	1.44920i	0.0593119	−	0.102731i	0.894157	+	0.447754i	$0.147776\pi$
$200$		0			0
$201$	−2.63991	−	4.57246i	−0.186205	−	0.322517i
$202$		0			0
$203$	−13.2238	−	14.8853i	−0.928129	−	1.04475i
$204$		0			0
$205$	−0.393901	−	0.682257i	−0.0275113	−	0.0476509i
$206$		0			0
$207$	9.82689	−	17.0207i	0.683016	−	1.18302i
$208$		0			0
$209$	14.9732			1.03572
$210$		0			0
$211$	−13.1602			−0.905984			−0.452992	−	0.891515i	$-0.649643\pi$
$211$	−13.1602			−0.905984			−0.452992	+	0.891515i	$0.649643\pi$
$212$		0			0
$213$	0.313743	−	0.543420i	0.0214973	−	0.0372345i
$214$		0			0
$215$	4.63739	+	8.03219i	0.316267	+	0.547791i
$216$		0			0
$217$	−12.7174	+	2.61448i	−0.863312	+	0.177482i
$218$		0			0
$219$	0.962184	+	1.66655i	0.0650184	+	0.112615i
$220$		0			0
$221$	−15.0476	+	26.0632i	−1.01221	+	1.75320i
$222$		0			0
$223$	11.1114			0.744072			0.372036	−	0.928218i	$-0.378660\pi$
$223$	11.1114			0.744072			0.372036	+	0.928218i	$0.378660\pi$
$224$		0			0
$225$	12.2529			0.816860
$226$		0			0
$227$	8.03259	−	13.9129i	0.533142	−	0.923428i	−0.466109	−	0.884727i	$-0.654345\pi$
$227$	8.03259	−	13.9129i	0.533142	−	0.923428i	0.999251	−	0.0387012i	$-0.0123220\pi$
$228$		0			0
$229$	12.7063	+	22.0079i	0.839655	+	1.45433i	0.890183	+	0.455603i	$0.150576\pi$
$229$	12.7063	+	22.0079i	0.839655	+	1.45433i	−0.0505278	+	0.998723i	$0.516090\pi$
$230$		0			0
$231$	1.16439	−	3.50381i	0.0766115	−	0.230534i
$232$		0			0
$233$	−10.0279	−	17.3688i	−0.656948	−	1.13787i	−0.981402	−	0.191966i	$-0.938514\pi$
$233$	−10.0279	−	17.3688i	−0.656948	−	1.13787i	0.324454	−	0.945902i	$-0.394820\pi$
$234$		0			0
$235$	−2.19122	+	3.79531i	−0.142940	+	0.247579i
$236$		0			0
$237$	3.64201			0.236574
$238$		0			0
$239$	6.32352			0.409034			0.204517	−	0.978863i	$-0.434438\pi$
$239$	6.32352			0.409034			0.204517	+	0.978863i	$0.434438\pi$
$240$		0			0
$241$	−12.6061	+	21.8344i	−0.812030	+	1.40648i	0.0994116	+	0.995046i	$0.468304\pi$
$241$	−12.6061	+	21.8344i	−0.812030	+	1.40648i	−0.911441	+	0.411430i	$0.865029\pi$
$242$		0			0
$243$	−5.53339	−	9.58411i	−0.354967	−	0.614821i
$244$		0			0
$245$	−5.06738	+	2.17548i	−0.323743	+	0.138986i
$246$		0			0
$247$	−13.4860	−	23.3584i	−0.858092	−	1.48626i
$248$		0			0
$249$	−0.473085	+	0.819407i	−0.0299805	+	0.0519278i
$250$		0			0
$251$	15.3360			0.967998			0.483999	−	0.875069i	$-0.339184\pi$
$251$	15.3360			0.967998			0.483999	+	0.875069i	$0.339184\pi$
$252$		0			0
$253$	21.8042			1.37082
$254$		0			0
$255$	0.953199	−	1.65099i	0.0596916	−	0.103389i
$256$		0			0
$257$	−7.63556	−	13.2252i	−0.476293	−	0.824964i	0.523338	−	0.852125i	$-0.324687\pi$
$257$	−7.63556	−	13.2252i	−0.476293	−	0.824964i	−0.999631	+	0.0271610i	$0.991353\pi$
$258$		0			0
$259$	−7.68633	+	23.1291i	−0.477605	+	1.43717i
$260$		0			0
$261$	−10.5278	−	18.2347i	−0.651655	−	1.12870i
$262$		0			0
$263$	−12.6360	+	21.8862i	−0.779169	+	1.34956i	0.153253	+	0.988187i	$0.451025\pi$
$263$	−12.6360	+	21.8862i	−0.779169	+	1.34956i	−0.932422	+	0.361373i	$0.882308\pi$
$264$		0			0
$265$	−4.68547			−0.287826
$266$		0			0
$267$	−7.26600			−0.444672
$268$		0			0
$269$	3.55377	−	6.15531i	0.216677	−	0.375296i	−0.737113	−	0.675770i	$-0.763811\pi$
$269$	3.55377	−	6.15531i	0.216677	−	0.375296i	0.953790	+	0.300474i	$0.0971447\pi$
$270$		0			0
$271$	−0.507630	−	0.879241i	−0.0308363	−	0.0534101i	0.850195	−	0.526467i	$-0.176484\pi$
$271$	−0.507630	−	0.879241i	−0.0308363	−	0.0534101i	−0.881032	+	0.473057i	$0.843150\pi$
$272$		0			0
$273$	−6.51470	+	1.33931i	−0.394288	+	0.0810589i
$274$		0			0
$275$	6.79678	+	11.7724i	0.409861	+	0.709900i
$276$		0			0
$277$	11.5387	−	19.9857i	0.693296	−	1.20082i	−0.277456	−	0.960738i	$-0.589491\pi$
$277$	11.5387	−	19.9857i	0.693296	−	1.20082i	0.970752	−	0.240086i	$-0.0771755\pi$
$278$		0			0
$279$	−13.7298			−0.821983
$280$		0			0
$281$	−19.3572			−1.15475			−0.577377	−	0.816478i	$-0.695924\pi$
$281$	−19.3572			−1.15475			−0.577377	+	0.816478i	$0.695924\pi$
$282$		0			0
$283$	−0.0887335	+	0.153691i	−0.00527466	+	0.00913597i	−0.868651	−	0.495425i	$-0.835012\pi$
$283$	−0.0887335	+	0.153691i	−0.00527466	+	0.00913597i	0.863376	+	0.504561i	$0.168346\pi$
$284$		0			0
$285$	0.854276	+	1.47965i	0.0506029	+	0.0876468i
$286$		0			0
$287$	−1.75718	−	1.97796i	−0.103723	−	0.116755i
$288$		0			0
$289$	−5.98535	−	10.3669i	−0.352080	−	0.609820i
$290$		0			0
$291$	−0.503163	+	0.871505i	−0.0294960	+	0.0510885i
$292$		0			0
$293$	27.8143			1.62493			0.812465	−	0.583010i	$-0.198125\pi$
$293$	27.8143			1.62493			0.812465	+	0.583010i	$0.198125\pi$
$294$		0			0
$295$	8.03689			0.467926
$296$		0			0
$297$	4.04554	−	7.00708i	0.234746	−	0.406592i
$298$		0			0
$299$	−19.6384	−	34.0148i	−1.13572	−	1.96713i
$300$		0			0
$301$	20.6872	+	23.2865i	1.19239	+	1.34221i
$302$		0			0
$303$	1.38129	+	2.39246i	0.0793529	+	0.137443i
$304$		0			0
$305$	1.92777	−	3.33899i	0.110384	−	0.191190i
$306$		0			0
$307$	25.7021			1.46690			0.733448	−	0.679745i	$-0.237910\pi$
$307$	25.7021			1.46690			0.733448	+	0.679745i	$0.237910\pi$
$308$		0			0
$309$	0.662468			0.0376865
$310$		0			0
$311$	7.78782	−	13.4889i	0.441606	−	0.764885i	−0.556202	−	0.831047i	$-0.687742\pi$
$311$	7.78782	−	13.4889i	0.441606	−	0.764885i	0.997809	+	0.0661620i	$0.0210754\pi$
$312$		0			0
$313$	−10.8186	−	18.7384i	−0.611505	−	1.05916i	−0.990987	−	0.133959i	$-0.957231\pi$
$313$	−10.8186	−	18.7384i	−0.611505	−	1.05916i	0.379482	−	0.925199i	$-0.376102\pi$
$314$		0			0
$315$	−5.71222	+	1.17434i	−0.321847	+	0.0661664i
$316$		0			0
$317$	−11.9868	−	20.7618i	−0.673248	−	1.16610i	−0.976978	−	0.213341i	$-0.931565\pi$
$317$	−11.9868	−	20.7618i	−0.673248	−	1.16610i	0.303730	−	0.952758i	$-0.401768\pi$
$318$		0			0
$319$	11.6797	−	20.2299i	0.653939	−	1.13266i
$320$		0			0
$321$	3.79254			0.211679
$322$		0			0
$323$	25.9641			1.44468
$324$		0			0
$325$	12.2433	−	21.2061i	0.679138	−	1.17630i
$326$		0			0
$327$	2.28418	+	3.95632i	0.126316	+	0.218785i
$328$		0			0
$329$	−4.64152	+	13.9669i	−0.255895	+	0.770021i
$330$		0			0
$331$	4.82459	+	8.35643i	0.265183	+	0.459311i	0.967612	−	0.252444i	$-0.0812342\pi$
$331$	4.82459	+	8.35643i	0.265183	+	0.459311i	−0.702428	+	0.711754i	$0.747901\pi$
$332$		0			0
$333$	−12.8871	+	22.3211i	−0.706208	+	1.22319i
$334$		0			0
$335$	−9.25168			−0.505473
$336$		0			0
$337$	−0.606481			−0.0330371			−0.0165186	−	0.999864i	$-0.505258\pi$
$337$	−0.606481			−0.0330371			−0.0165186	+	0.999864i	$0.505258\pi$
$338$		0			0
$339$	−1.87659	+	3.25035i	−0.101922	+	0.176535i
$340$		0			0
$341$	−7.61604	−	13.1914i	−0.412432	−	0.714353i
$342$		0			0
$343$	−15.1984	+	10.5834i	−0.820635	+	0.571452i
$344$		0			0
$345$	1.24401	+	2.15468i	0.0669751	+	0.116004i
$346$		0			0
$347$	−9.35674	+	16.2063i	−0.502296	+	0.870002i	0.497700	+	0.867349i	$0.334178\pi$
$347$	−9.35674	+	16.2063i	−0.502296	+	0.870002i	−0.999996	+	0.00265321i	$0.999155\pi$
$348$		0			0
$349$	20.5477			1.09989			0.549945	−	0.835201i	$-0.314649\pi$
$349$	20.5477			1.09989			0.549945	+	0.835201i	$0.314649\pi$
$350$		0			0
$351$	−14.5748			−0.777946
$352$		0			0
$353$	1.97498	−	3.42077i	0.105118	−	0.182069i	−0.808669	−	0.588265i	$-0.799811\pi$
$353$	1.97498	−	3.42077i	0.105118	−	0.182069i	0.913786	+	0.406195i	$0.133145\pi$
$354$		0			0
$355$	−0.549764	−	0.952218i	−0.0291784	−	0.0505385i
$356$		0			0
$357$	2.01910	−	6.07572i	0.106862	−	0.321561i
$358$		0			0
$359$	−1.02067	−	1.76785i	−0.0538690	−	0.0933038i	0.837833	−	0.545926i	$-0.183822\pi$
$359$	−1.02067	−	1.76785i	−0.0538690	−	0.0933038i	−0.891702	+	0.452622i	$0.850489\pi$
$360$		0			0
$361$	−2.13477	+	3.69753i	−0.112356	+	0.194607i
$362$		0			0
$363$	−0.613771			−0.0322146
$364$		0			0
$365$	3.37201			0.176499
$366$		0			0
$367$	8.30437	−	14.3836i	0.433485	−	0.750817i	−0.563686	−	0.825989i	$-0.690617\pi$
$367$	8.30437	−	14.3836i	0.433485	−	0.750817i	0.997171	+	0.0751717i	$0.0239505\pi$
$368$		0			0
$369$	−1.39893	−	2.42303i	−0.0728256	−	0.126138i
$370$		0			0
$371$	−15.4133	+	3.16872i	−0.800219	+	0.164512i
$372$		0			0
$373$	6.91875	+	11.9836i	0.358239	+	0.620489i	0.987667	−	0.156571i	$-0.0500439\pi$
$373$	6.91875	+	11.9836i	0.358239	+	0.620489i	−0.629427	+	0.777059i	$0.716711\pi$
$374$		0			0
$375$	−1.66103	+	2.87699i	−0.0857752	+	0.148567i
$376$		0			0
$377$	−42.0784			−2.16715
$378$		0			0
$379$	−5.23579			−0.268944			−0.134472	−	0.990917i	$-0.542934\pi$
$379$	−5.23579			−0.268944			−0.134472	+	0.990917i	$0.542934\pi$
$380$		0			0
$381$	3.50749	−	6.07515i	0.179694	−	0.311239i
$382$		0			0
$383$	−4.22812	−	7.32331i	−0.216047	−	0.374204i	0.737549	−	0.675293i	$-0.235983\pi$
$383$	−4.22812	−	7.32331i	−0.216047	−	0.374204i	−0.953596	+	0.301090i	$0.902650\pi$
$384$		0			0
$385$	−4.29690	−	4.83679i	−0.218990	−	0.246506i
$386$		0			0
$387$	16.4696	+	28.5262i	0.837197	+	1.45007i
$388$		0			0
$389$	13.0207	−	22.5525i	0.660175	−	1.14346i	−0.320395	−	0.947284i	$-0.603815\pi$
$389$	13.0207	−	22.5525i	0.660175	−	1.14346i	0.980569	−	0.196172i	$-0.0628512\pi$
$390$		0			0
$391$	37.8093			1.91210
$392$		0			0
$393$	−5.28836			−0.266762
$394$		0			0
$395$	3.19089	−	5.52679i	0.160551	−	0.278083i
$396$		0			0
$397$	1.71398	+	2.96869i	0.0860220	+	0.148994i	0.905826	−	0.423649i	$-0.139251\pi$
$397$	1.71398	+	2.96869i	0.0860220	+	0.148994i	−0.819804	+	0.572644i	$0.805918\pi$
$398$		0			0
$399$	3.81089	+	4.28971i	0.190783	+	0.214754i
$400$		0			0
$401$	−1.13399	−	1.96413i	−0.0566289	−	0.0980841i	0.836321	−	0.548240i	$-0.184702\pi$
$401$	−1.13399	−	1.96413i	−0.0566289	−	0.0980841i	−0.892950	+	0.450156i	$0.851369\pi$
$402$		0			0
$403$	−13.7191	+	23.7622i	−0.683397	+	1.18368i
$404$		0			0
$405$	−5.68926			−0.282702
$406$		0			0
$407$	−28.5943			−1.41737
$408$		0			0
$409$	5.52309	−	9.56627i	0.273099	−	0.473022i	−0.696555	−	0.717504i	$-0.745285\pi$
$409$	5.52309	−	9.56627i	0.273099	−	0.473022i	0.969654	+	0.244482i	$0.0786179\pi$
$410$		0			0
$411$	−1.01069	−	1.75056i	−0.0498535	−	0.0863489i
$412$		0			0
$413$	26.4381	−	5.43523i	1.30093	−	0.267450i
$414$		0			0
$415$	0.828972	+	1.43582i	0.0406927	+	0.0704817i
$416$		0			0
$417$	−0.317039	+	0.549128i	−0.0155255	+	0.0268909i
$418$		0			0
$419$	−29.0178			−1.41761			−0.708805	−	0.705404i	$-0.750765\pi$
$419$	−29.0178			−1.41761			−0.708805	+	0.705404i	$0.750765\pi$
$420$		0			0
$421$	11.2610			0.548827			0.274414	−	0.961612i	$-0.411516\pi$
$421$	11.2610			0.548827			0.274414	+	0.961612i	$0.411516\pi$
$422$		0			0
$423$	−7.78209	+	13.4790i	−0.378378	+	0.655370i
$424$		0			0
$425$	11.7858	+	20.4137i	0.571698	+	0.990209i
$426$		0			0
$427$	4.08346	−	12.2876i	0.197612	−	0.594640i
$428$		0			0
$429$	−3.90145	−	6.75752i	−0.188364	−	0.326256i
$430$		0			0
$431$	−8.27381	+	14.3307i	−0.398535	+	0.690283i	−0.993545	−	0.113435i	$-0.963815\pi$
$431$	−8.27381	+	14.3307i	−0.398535	+	0.690283i	0.595010	+	0.803718i	$0.297148\pi$
$432$		0			0
$433$	−4.65533			−0.223721			−0.111860	−	0.993724i	$-0.535681\pi$
$433$	−4.65533			−0.223721			−0.111860	+	0.993724i	$0.535681\pi$
$434$		0			0
$435$	2.66548			0.127800
$436$		0			0
$437$	−16.9427	+	29.3456i	−0.810480	+	1.40379i
$438$		0			0
$439$	11.3923	+	19.7320i	0.543725	+	0.941759i	0.998686	+	0.0512479i	$0.0163199\pi$
$439$	11.3923	+	19.7320i	0.543725	+	0.941759i	−0.454961	+	0.890511i	$0.650347\pi$
$440$		0			0
$441$	−17.9967	+	7.72618i	−0.856986	+	0.367914i
$442$		0			0
$443$	14.8029	+	25.6393i	0.703305	+	1.21816i	0.967300	+	0.253637i	$0.0816267\pi$
$443$	14.8029	+	25.6393i	0.703305	+	1.21816i	−0.263994	+	0.964524i	$0.585040\pi$
$444$		0			0
$445$	−6.36600	+	11.0262i	−0.301777	+	0.522694i
$446$		0			0
$447$	3.82279			0.180812
$448$		0			0
$449$	−2.83513			−0.133798			−0.0668990	−	0.997760i	$-0.521311\pi$
$449$	−2.83513			−0.133798			−0.0668990	+	0.997760i	$0.521311\pi$
$450$		0			0
$451$	1.55200	−	2.68814i	0.0730808	−	0.126580i
$452$		0			0
$453$	0.603661	+	1.04557i	0.0283625	+	0.0491253i
$454$		0			0
$455$	−3.67534	+	11.0596i	−0.172303	+	0.518480i
$456$		0			0
$457$	−13.8301	−	23.9544i	−0.646943	−	1.12054i	−0.983849	−	0.179000i	$-0.942714\pi$
$457$	−13.8301	−	23.9544i	−0.646943	−	1.12054i	0.336906	−	0.941538i	$-0.390620\pi$
$458$		0			0
$459$	7.01511	−	12.1505i	0.327437	−	0.567138i
$460$		0			0
$461$	4.80680			0.223875			0.111937	−	0.993715i	$-0.464294\pi$
$461$	4.80680			0.223875			0.111937	+	0.993715i	$0.464294\pi$
$462$		0			0
$463$	31.2899			1.45416			0.727082	−	0.686551i	$-0.240876\pi$
$463$	31.2899			1.45416			0.727082	+	0.686551i	$0.240876\pi$
$464$		0			0
$465$	0.869043	−	1.50523i	0.0403009	−	0.0698032i
$466$		0			0
$467$	−5.44685	−	9.43422i	−0.252050	−	0.436564i	0.712040	−	0.702139i	$-0.247771\pi$
$467$	−5.44685	−	9.43422i	−0.252050	−	0.436564i	−0.964090	+	0.265575i	$0.914438\pi$
$468$		0			0
$469$	−30.4343	+	6.25678i	−1.40532	+	0.288911i
$470$		0			0
$471$	0.959313	+	1.66158i	0.0442028	+	0.0765616i
$472$		0			0
$473$	−18.2716	+	31.6474i	−0.840131	+	1.45515i
$474$		0			0
$475$	−21.1254			−0.969300
$476$		0			0
$477$	−16.6404			−0.761911
$478$		0			0
$479$	−7.06921	+	12.2442i	−0.323000	+	0.559453i	−0.981106	−	0.193473i	$-0.938025\pi$
$479$	−7.06921	+	12.2442i	−0.323000	+	0.559453i	0.658105	+	0.752926i	$0.271358\pi$
$480$		0			0
$481$	25.7540	+	44.6073i	1.17428	+	2.03392i
$482$		0			0
$483$	5.54946	+	6.24673i	0.252509	+	0.284236i
$484$		0			0
$485$	0.881679	+	1.52711i	0.0400350	+	0.0693426i
$486$		0			0
$487$	17.3884	−	30.1176i	0.787945	−	1.36476i	−0.139279	−	0.990253i	$-0.544479\pi$
$487$	17.3884	−	30.1176i	0.787945	−	1.36476i	0.927224	−	0.374507i	$-0.122188\pi$
$488$		0			0
$489$	8.42226			0.380868
$490$		0			0
$491$	31.6187			1.42693			0.713466	−	0.700690i	$-0.247124\pi$
$491$	31.6187			1.42693			0.713466	+	0.700690i	$0.247124\pi$
$492$		0			0
$493$	20.2530	−	35.0793i	0.912151	−	1.57989i
$494$		0			0
$495$	−3.42087	−	5.92512i	−0.153757	−	0.266315i
$496$		0			0
$497$	−2.45247	−	2.76062i	−0.110008	−	0.123831i
$498$		0			0
$499$	−15.4326	−	26.7301i	−0.690860	−	1.19660i	−0.971556	−	0.236808i	$-0.923899\pi$
$499$	−15.4326	−	26.7301i	−0.690860	−	1.19660i	0.280696	−	0.959797i	$-0.409435\pi$
$500$		0			0
$501$	−2.54916	+	4.41527i	−0.113888	+	0.197260i
$502$		0			0
$503$	−18.3660			−0.818900			−0.409450	−	0.912333i	$-0.634279\pi$
$503$	−18.3660			−0.818900			−0.409450	+	0.912333i	$0.634279\pi$
$504$		0			0
$505$	4.84078			0.215412
$506$		0			0
$507$	−4.10552	+	7.11097i	−0.182333	+	0.315809i
$508$		0			0
$509$	18.5145	+	32.0681i	0.820641	+	1.42139i	0.905205	+	0.424974i	$0.139717\pi$
$509$	18.5145	+	32.0681i	0.820641	+	1.42139i	−0.0845640	+	0.996418i	$0.526950\pi$
$510$		0			0
$511$	11.0926	−	2.28044i	0.490706	−	0.100881i
$512$		0			0
$513$	6.28708	+	10.8895i	0.277581	+	0.480785i
$514$		0			0
$515$	0.580411	−	1.00530i	0.0255760	−	0.0442989i
$516$		0			0
$517$	−17.2672			−0.759408
$518$		0			0
$519$	−5.62090			−0.246730
$520$		0			0
$521$	13.1176	−	22.7203i	0.574690	−	0.995393i	−0.421385	−	0.906882i	$-0.638456\pi$
$521$	13.1176	−	22.7203i	0.574690	−	0.995393i	0.996075	−	0.0885111i	$-0.0282109\pi$
$522$		0			0
$523$	−0.873014	−	1.51210i	−0.0381742	−	0.0661197i	0.846307	−	0.532695i	$-0.178821\pi$
$523$	−0.873014	−	1.51210i	−0.0381742	−	0.0661197i	−0.884481	+	0.466576i	$0.845488\pi$
$524$		0			0
$525$	−1.64282	+	4.94344i	−0.0716984	+	0.215750i
$526$		0			0
$527$	−13.2065	−	22.8743i	−0.575283	−	0.996419i
$528$		0			0
$529$	−13.1722	+	22.8149i	−0.572704	+	0.991952i
$530$		0			0
$531$	28.5429			1.23866
$532$		0			0
$533$	−5.59137			−0.242189
$534$		0			0
$535$	3.32278	−	5.75523i	0.143656	−	0.248820i
$536$		0			0
$537$	1.56499	+	2.71065i	0.0675345	+	0.116973i
$538$		0			0
$539$	−17.4061	−	13.0051i	−0.749734	−	0.560171i
$540$		0			0
$541$	−7.15481	−	12.3925i	−0.307609	−	0.532795i	0.670230	−	0.742154i	$-0.266196\pi$
$541$	−7.15481	−	12.3925i	−0.307609	−	0.532795i	−0.977839	+	0.209359i	$0.932862\pi$
$542$		0			0
$543$	−4.12043	+	7.13679i	−0.176825	+	0.306269i
$544$		0			0
$545$	8.00502			0.342897
$546$		0			0
$547$	1.40140			0.0599194			0.0299597	−	0.999551i	$-0.490462\pi$
$547$	1.40140			0.0599194			0.0299597	+	0.999551i	$0.490462\pi$
$548$		0			0
$549$	6.84643	−	11.8584i	0.292198	−	0.506102i
$550$		0			0
$551$	18.1512	+	31.4388i	0.773266	+	1.33934i
$552$		0			0
$553$	6.75906	−	20.3389i	0.287424	−	0.864896i
$554$		0			0
$555$	−1.63140	−	2.82567i	−0.0692492	−	0.119943i
$556$		0			0
$557$	6.70640	−	11.6158i	0.284159	−	0.492178i	−0.688246	−	0.725478i	$-0.741619\pi$
$557$	6.70640	−	11.6158i	0.284159	−	0.492178i	0.972405	+	0.233300i	$0.0749523\pi$
$558$		0			0
$559$	65.8270			2.78419
$560$		0			0
$561$	7.51135			0.317129
$562$		0			0
$563$	10.1839	−	17.6391i	0.429202	−	0.743400i	−0.567600	−	0.823304i	$-0.692128\pi$
$563$	10.1839	−	17.6391i	0.429202	−	0.743400i	0.996803	+	0.0799042i	$0.0254614\pi$
$564$		0			0
$565$	3.28829	+	5.69549i	0.138340	+	0.239611i
$566$		0			0
$567$	−18.7154	+	3.84756i	−0.785971	+	0.161582i
$568$		0			0
$569$	6.96226	+	12.0590i	0.291873	+	0.505539i	0.974253	−	0.225459i	$-0.0723882\pi$
$569$	6.96226	+	12.0590i	0.291873	+	0.505539i	−0.682380	+	0.730998i	$0.739055\pi$
$570$		0			0
$571$	−20.0273	+	34.6884i	−0.838118	+	1.45166i	0.0533480	+	0.998576i	$0.483011\pi$
$571$	−20.0273	+	34.6884i	−0.838118	+	1.45166i	−0.891466	+	0.453087i	$0.850323\pi$
$572$		0			0
$573$	8.66995			0.362192
$574$		0			0
$575$	−30.7631			−1.28291
$576$		0			0
$577$	−20.9356	+	36.2616i	−0.871562	+	1.50959i	−0.0111821	+	0.999937i	$0.503559\pi$
$577$	−20.9356	+	36.2616i	−0.871562	+	1.50959i	−0.860380	+	0.509653i	$0.829774\pi$
$578$		0			0
$579$	−0.314046	−	0.543944i	−0.0130513	−	0.0226055i
$580$		0			0
$581$	3.69801	+	4.16265i	0.153419	+	0.172696i
$582$		0			0
$583$	−9.23055	−	15.9878i	−0.382290	−	0.662146i
$584$		0			0
$585$	−6.16216	+	10.6732i	−0.254774	+	0.441282i
$586$		0			0
$587$	12.4478			0.513775			0.256888	−	0.966441i	$-0.417303\pi$
$587$	12.4478			0.513775			0.256888	+	0.966441i	$0.417303\pi$
$588$		0			0
$589$	23.6718			0.975379
$590$		0			0
$591$	−2.88099	+	4.99002i	−0.118508	+	0.205262i
$592$		0			0
$593$	6.34775	+	10.9946i	0.260671	+	0.451495i	0.966420	−	0.256966i	$-0.0827229\pi$
$593$	6.34775	+	10.9946i	0.260671	+	0.451495i	−0.705749	+	0.708462i	$0.749390\pi$
$594$		0			0
$595$	−7.45097	−	8.38716i	−0.305460	−	0.343840i
$596$		0			0
$597$	0.376171	+	0.651547i	0.0153956	+	0.0266660i
$598$		0			0
$599$	−18.9542	+	32.8297i	−0.774448	+	1.34138i	0.160656	+	0.987010i	$0.448639\pi$
$599$	−18.9542	+	32.8297i	−0.774448	+	1.34138i	−0.935104	+	0.354373i	$0.884694\pi$
$600$		0			0
$601$	22.3859			0.913139			0.456569	−	0.889688i	$-0.349078\pi$
$601$	22.3859			0.913139			0.456569	+	0.889688i	$0.349078\pi$
$602$		0			0
$603$	−32.8572			−1.33805
$604$		0			0
$605$	−0.537746	+	0.931404i	−0.0218625	+	0.0378669i
$606$		0			0
$607$	−23.3720	−	40.4815i	−0.948640	−	1.64309i	−0.748293	−	0.663368i	$-0.769126\pi$
$607$	−23.3720	−	40.4815i	−0.948640	−	1.64309i	−0.200347	−	0.979725i	$-0.564207\pi$
$608$		0			0
$609$	8.76834	−	1.80262i	0.355311	−	0.0730460i
$610$		0			0
$611$	15.5520	+	26.9369i	0.629168	+	1.08975i
$612$		0			0
$613$	0.147710	−	0.255842i	0.00596596	−	0.0103333i	−0.863027	−	0.505158i	$-0.831434\pi$
$613$	0.147710	−	0.255842i	0.00596596	−	0.0103333i	0.868993	+	0.494824i	$0.164768\pi$
$614$		0			0
$615$	0.354188			0.0142822
$616$		0			0
$617$	−42.2704			−1.70174			−0.850871	−	0.525375i	$-0.823925\pi$
$617$	−42.2704			−1.70174			−0.850871	+	0.525375i	$0.823925\pi$
$618$		0			0
$619$	−15.9567	+	27.6378i	−0.641354	+	1.11086i	0.343777	+	0.939051i	$0.388294\pi$
$619$	−15.9567	+	27.6378i	−0.641354	+	1.11086i	−0.985131	+	0.171806i	$0.945040\pi$
$620$		0			0
$621$	9.15532	+	15.8575i	0.367390	+	0.636339i
$622$		0			0
$623$	−13.4847	+	40.5771i	−0.540252	+	1.62569i
$624$		0			0
$625$	−8.03784	−	13.9219i	−0.321514	−	0.556878i
$626$		0			0
$627$	−3.36591	+	5.82992i	−0.134421	+	0.232825i
$628$		0			0
$629$	−49.5835			−1.97702
$630$		0			0
$631$	−5.19942			−0.206986			−0.103493	−	0.994630i	$-0.533002\pi$
$631$	−5.19942			−0.206986			−0.103493	+	0.994630i	$0.533002\pi$
$632$		0			0
$633$	2.95834	−	5.12400i	0.117583	−	0.203661i
$634$		0			0
$635$	−6.14607	−	10.6453i	−0.243899	−	0.422446i
$636$		0			0
$637$	−4.61096	+	38.8670i	−0.182693	+	1.53997i
$638$		0			0
$639$	−1.95248	−	3.38179i	−0.0772388	−	0.133781i
$640$		0			0
$641$	4.45267	−	7.71225i	0.175870	−	0.304615i	−0.764592	−	0.644514i	$-0.777060\pi$
$641$	4.45267	−	7.71225i	0.175870	−	0.304615i	0.940462	+	0.339899i	$0.110393\pi$
$642$		0			0
$643$	−24.4281			−0.963350			−0.481675	−	0.876350i	$-0.659971\pi$
$643$	−24.4281			−0.963350			−0.481675	+	0.876350i	$0.659971\pi$
$644$		0			0
$645$	−4.16984			−0.164187
$646$		0			0
$647$	12.4142	−	21.5020i	0.488052	−	0.845331i	−0.511853	−	0.859073i	$-0.671041\pi$
$647$	12.4142	−	21.5020i	0.488052	−	0.845331i	0.999906	+	0.0137417i	$0.00437425\pi$
$648$		0			0
$649$	15.8330	+	27.4235i	0.621498	+	1.07647i
$650$		0			0
$651$	1.84084	−	5.53931i	0.0721481	−	0.217103i
$652$		0			0
$653$	12.0357	+	20.8465i	0.470995	+	0.815787i	0.999450	−	0.0331744i	$-0.0105617\pi$
$653$	12.0357	+	20.8465i	0.470995	+	0.815787i	−0.528455	+	0.848962i	$0.677228\pi$
$654$		0			0
$655$	−4.63332	+	8.02514i	−0.181039	+	0.313568i
$656$		0			0
$657$	11.9756			0.467215
$658$		0			0
$659$	−3.61093			−0.140662			−0.0703310	−	0.997524i	$-0.522406\pi$
$659$	−3.61093			−0.140662			−0.0703310	+	0.997524i	$0.522406\pi$
$660$		0			0
$661$	14.0442	−	24.3253i	0.546258	−	0.946146i	−0.452269	−	0.891882i	$-0.649385\pi$
$661$	14.0442	−	24.3253i	0.546258	−	0.946146i	0.998527	−	0.0542644i	$-0.0172814\pi$
$662$		0			0
$663$	−6.76525	−	11.7178i	−0.262741	−	0.455080i
$664$		0			0
$665$	9.84853	−	2.02469i	0.381910	−	0.0785142i
$666$		0			0
$667$	26.4320	+	45.7815i	1.02345	+	1.77267i
$668$		0			0
$669$	−2.49778	+	4.32628i	−0.0965697	+	0.167264i
$670$		0			0
$671$	15.1911			0.586445
$672$		0			0
$673$	34.0798			1.31368			0.656840	−	0.754030i	$-0.271893\pi$
$673$	34.0798			1.31368			0.656840	+	0.754030i	$0.271893\pi$
$674$		0			0
$675$	−5.70777	+	9.88614i	−0.219692	+	0.380518i
$676$		0			0
$677$	−4.66455	−	8.07924i	−0.179273	−	0.310510i	0.762359	−	0.647155i	$-0.224041\pi$
$677$	−4.66455	−	8.07924i	−0.179273	−	0.310510i	−0.941632	+	0.336645i	$0.890708\pi$
$678$		0			0
$679$	3.93313	+	4.42731i	0.150940	+	0.169905i
$680$		0			0
$681$	3.61137	+	6.25508i	0.138388	+	0.239695i
$682$		0			0
$683$	7.39513	−	12.8087i	0.282967	−	0.490113i	−0.689147	−	0.724621i	$-0.742015\pi$
$683$	7.39513	−	12.8087i	0.282967	−	0.490113i	0.972114	+	0.234509i	$0.0753481\pi$
$684$		0			0
$685$	−3.54200			−0.135333
$686$		0			0
$687$	−11.4252			−0.435900
$688$		0			0
$689$	−16.6274	+	28.7995i	−0.633453	+	1.09717i
$690$		0			0
$691$	13.8551	+	23.9977i	0.527072	+	0.912915i	0.999502	+	0.0315473i	$0.0100435\pi$
$691$	13.8551	+	23.9977i	0.527072	+	0.912915i	−0.472430	+	0.881368i	$0.656623\pi$
$692$		0			0
$693$	−15.2604	−	17.1778i	−0.579693	−	0.652530i
$694$		0			0
$695$	0.555538	+	0.962220i	0.0210728	+	0.0364991i
$696$		0			0
$697$	2.69122	−	4.66133i	0.101937	−	0.176561i
$698$		0			0
$699$	9.01686			0.341049
$700$		0			0
$701$	−3.12039			−0.117856			−0.0589278	−	0.998262i	$-0.518768\pi$
$701$	−3.12039			−0.117856			−0.0589278	+	0.998262i	$0.518768\pi$
$702$		0			0
$703$	22.2188	−	38.4842i	0.837999	−	1.45146i
$704$		0			0
$705$	−0.985151	−	1.70633i	−0.0371029	−	0.0642642i
$706$		0			0
$707$	15.9242	−	3.27375i	0.598891	−	0.123122i
$708$		0			0
$709$	−17.4532	−	30.2298i	−0.655467	−	1.13530i	−0.981776	−	0.190039i	$-0.939138\pi$
$709$	−17.4532	−	30.2298i	−0.655467	−	1.13530i	0.326309	−	0.945263i	$-0.394195\pi$
$710$		0			0
$711$	11.3324	−	19.6283i	0.424998	−	0.736119i
$712$		0			0
$713$	34.4712			1.29096
$714$		0			0
$715$	−13.6728			−0.511334
$716$		0			0
$717$	−1.42149	+	2.46210i	−0.0530867	+	0.0919488i
$718$		0			0
$719$	17.9327	+	31.0603i	0.668777	+	1.15836i	0.978246	+	0.207446i	$0.0665151\pi$
$719$	17.9327	+	31.0603i	0.668777	+	1.15836i	−0.309470	+	0.950909i	$0.600152\pi$
$720$		0			0
$721$	1.22945	−	3.69956i	0.0457870	−	0.137779i
$722$		0			0
$723$	−5.66757	−	9.81652i	−0.210779	−	0.365080i
$724$		0			0
$725$	−16.4787	+	28.5419i	−0.612002	+	1.06002i
$726$		0			0
$727$	−8.15799			−0.302563			−0.151282	−	0.988491i	$-0.548340\pi$
$727$	−8.15799			−0.302563			−0.151282	+	0.988491i	$0.548340\pi$
$728$		0			0
$729$	−16.6895			−0.618131
$730$		0			0
$731$	−31.6837	+	54.8777i	−1.17186	+	2.02973i
$732$		0			0
$733$	−18.6500	−	32.3028i	−0.688854	−	1.19313i	−0.972209	−	0.234115i	$-0.924781\pi$
$733$	−18.6500	−	32.3028i	−0.688854	−	1.19313i	0.283355	−	0.959015i	$-0.408553\pi$
$734$		0			0
$735$	0.292084	−	2.46205i	0.0107737	−	0.0908142i
$736$		0			0
$737$	−18.2261	−	31.5686i	−0.671369	−	1.16284i
$738$		0			0
$739$	−0.400623	+	0.693899i	−0.0147371	+	0.0255255i	−0.873300	−	0.487183i	$-0.838024\pi$
$739$	−0.400623	+	0.693899i	−0.0147371	+	0.0255255i	0.858563	+	0.512708i	$0.171358\pi$
$740$		0			0
$741$	12.1263			0.445471
$742$		0			0
$743$	16.3460			0.599678			0.299839	−	0.953990i	$-0.403067\pi$
$743$	16.3460			0.599678			0.299839	+	0.953990i	$0.403067\pi$
$744$		0			0
$745$	3.34928	−	5.80113i	0.122708	−	0.212537i
$746$		0			0
$747$	2.94408	+	5.09930i	0.107718	+	0.186574i
$748$		0			0
$749$	7.03843	−	21.1795i	0.257179	−	0.773882i
$750$		0			0
$751$	19.9388	+	34.5349i	0.727575	+	1.26020i	0.957905	+	0.287085i	$0.0926862\pi$
$751$	19.9388	+	34.5349i	0.727575	+	1.26020i	−0.230330	+	0.973113i	$0.573980\pi$
$752$		0			0
$753$	−3.44745	+	5.97115i	−0.125632	+	0.217601i
$754$		0			0
$755$	2.11556			0.0769930
$756$		0			0
$757$	24.7946			0.901177			0.450588	−	0.892732i	$-0.351214\pi$
$757$	24.7946			0.901177			0.450588	+	0.892732i	$0.351214\pi$
$758$		0			0
$759$	−4.90148	+	8.48961i	−0.177912	+	0.308153i
$760$		0			0
$761$	−6.42136	−	11.1221i	−0.232774	−	0.403177i	0.725849	−	0.687854i	$-0.241447\pi$
$761$	−6.42136	−	11.1221i	−0.232774	−	0.403177i	−0.958624	+	0.284677i	$0.908114\pi$
$762$		0			0
$763$	26.3333	−	5.41368i	0.953328	−	0.195988i
$764$		0			0
$765$	−5.93191	−	10.2744i	−0.214469	−	0.371471i
$766$		0			0
$767$	28.5206	−	49.3991i	1.02982	−	1.78370i
$768$		0			0
$769$	−43.3315			−1.56258			−0.781288	−	0.624171i	$-0.785437\pi$
$769$	−43.3315			−1.56258			−0.781288	+	0.624171i	$0.785437\pi$
$770$		0			0
$771$	6.86574			0.247264
$772$		0			0
$773$	−22.1775	+	38.4125i	−0.797669	+	1.38160i	0.123462	+	0.992349i	$0.460600\pi$
$773$	−22.1775	+	38.4125i	−0.797669	+	1.38160i	−0.921131	+	0.389254i	$0.872733\pi$
$774$		0			0
$775$	10.7453	+	18.6114i	0.385983	+	0.668542i
$776$		0			0
$777$	−7.27762	−	8.19203i	−0.261083	−	0.293887i
$778$		0			0
$779$	2.41193	+	4.17758i	0.0864162	+	0.149677i
$780$		0			0
$781$	2.16611	−	3.75181i	0.0775094	−	0.134250i
$782$		0			0
$783$	19.6167			0.701043
$784$		0			0
$785$	3.36195			0.119993
$786$		0			0
$787$	19.4469	−	33.6831i	0.693208	−	1.20067i	−0.277573	−	0.960705i	$-0.589530\pi$
$787$	19.4469	−	33.6831i	0.693208	−	1.20067i	0.970781	−	0.239967i	$-0.0771367\pi$
$788$		0			0
$789$	−5.68101	−	9.83980i	−0.202249	−	0.350306i
$790$		0			0
$791$	14.6689	+	16.5120i	0.521567	+	0.587100i
$792$		0			0
$793$	−13.6822	−	23.6982i	−0.485868	−	0.841548i
$794$		0			0
$795$	1.05327	−	1.82432i	0.0373557	−	0.0647019i
$796$		0			0
$797$	−18.0342			−0.638803			−0.319401	−	0.947619i	$-0.603482\pi$
$797$	−18.0342			−0.638803			−0.319401	+	0.947619i	$0.603482\pi$
$798$		0			0
$799$	−29.9418			−1.05927
$800$		0			0
$801$	−22.6087	+	39.1595i	−0.798841	+	1.38363i
$802$		0			0
$803$	6.64299	+	11.5060i	0.234426	+	0.406038i
$804$		0			0
$805$	14.3416	−	2.94838i	0.505474	−	0.103917i
$806$		0			0
$807$	1.59774	+	2.76737i	0.0562431	+	0.0974159i
$808$		0			0
$809$	24.9713	−	43.2515i	0.877943	−	1.52064i	0.0243486	−	0.999704i	$-0.492249\pi$
$809$	24.9713	−	43.2515i	0.877943	−	1.52064i	0.853594	−	0.520938i	$-0.174418\pi$
$810$		0			0
$811$	2.43604			0.0855409			0.0427705	−	0.999085i	$-0.486382\pi$
$811$	2.43604			0.0855409			0.0427705	+	0.999085i	$0.486382\pi$
$812$		0			0
$813$	0.456451			0.0160084
$814$		0			0
$815$	7.37904	−	12.7809i	0.258476	−	0.447694i
$816$		0			0
$817$	−28.3955	−	49.1825i	−0.993433	−	1.72068i
$818$		0			0
$819$	−13.0529	+	39.2778i	−0.456105	+	1.37248i
$820$		0			0
$821$	5.30902	+	9.19549i	0.185286	+	0.320925i	0.943673	−	0.330880i	$-0.107346\pi$
$821$	5.30902	+	9.19549i	0.185286	+	0.320925i	−0.758387	+	0.651805i	$0.774012\pi$
$822$		0			0
$823$	−25.2201	+	43.6824i	−0.879116	+	1.52267i	−0.0268034	+	0.999641i	$0.508533\pi$
$823$	−25.2201	+	43.6824i	−0.879116	+	1.52267i	−0.852313	+	0.523033i	$0.824801\pi$
$824$		0			0
$825$	−6.11152			−0.212776
$826$		0			0
$827$	16.6086			0.577538			0.288769	−	0.957399i	$-0.406754\pi$
$827$	16.6086			0.577538			0.288769	+	0.957399i	$0.406754\pi$
$828$		0			0
$829$	7.92526	−	13.7270i	0.275256	−	0.476757i	−0.694944	−	0.719064i	$-0.744571\pi$
$829$	7.92526	−	13.7270i	0.275256	−	0.476757i	0.970200	+	0.242307i	$0.0779041\pi$
$830$		0			0
$831$	5.18770	+	8.98536i	0.179959	+	0.311699i
$832$		0			0
$833$	−30.1828	−	22.5514i	−1.04577	−	0.781359i
$834$		0			0
$835$	4.46682	+	7.73675i	0.154581	+	0.267741i
$836$		0			0
$837$	6.39576	−	11.0778i	0.221070	−	0.382904i
$838$		0			0
$839$	−20.4364			−0.705544			−0.352772	−	0.935709i	$-0.614761\pi$
$839$	−20.4364			−0.705544			−0.352772	+	0.935709i	$0.614761\pi$
$840$		0			0
$841$	27.6346			0.952917
$842$		0			0
$843$	4.35140	−	7.53684i	0.149870	−	0.259583i
$844$		0			0
$845$	7.19398	+	12.4603i	0.247481	+	0.428649i
$846$		0			0
$847$	−1.13907	+	3.42761i	−0.0391390	+	0.117774i
$848$		0			0
$849$	−0.0398937	−	0.0690978i	−0.00136915	−	0.00237143i
$850$		0			0
$851$	32.3554	−	56.0411i	1.10913	−	1.92106i
$852$		0			0
$853$	−38.5432			−1.31969			−0.659847	−	0.751400i	$-0.729379\pi$
$853$	−38.5432			−1.31969			−0.659847	+	0.751400i	$0.729379\pi$
$854$		0			0
$855$	10.6326			0.363627
$856$		0			0
$857$	−21.0696	+	36.4936i	−0.719723	+	1.24660i	0.241387	+	0.970429i	$0.422398\pi$
$857$	−21.0696	+	36.4936i	−0.719723	+	1.24660i	−0.961109	+	0.276168i	$0.910935\pi$
$858$		0			0
$859$	7.12255	+	12.3366i	0.243018	+	0.420920i	0.961573	−	0.274551i	$-0.0885291\pi$
$859$	7.12255	+	12.3366i	0.243018	+	0.420920i	−0.718554	+	0.695471i	$0.755196\pi$
$860$		0			0
$861$	1.16514	−	0.239532i	0.0397077	−	0.00816324i
$862$		0			0
$863$	−5.20184	−	9.00986i	−0.177073	−	0.306699i	0.763804	−	0.645448i	$-0.223329\pi$
$863$	−5.20184	−	9.00986i	−0.177073	−	0.306699i	−0.940877	+	0.338749i	$0.889996\pi$
$864$		0			0
$865$	−4.92467	+	8.52978i	−0.167444	+	0.290021i
$866$		0			0
$867$	5.38191			0.182779
$868$		0			0
$869$	25.1447			0.852975
$870$		0			0
$871$	−32.8315	+	56.8659i	−1.11245	+	1.92683i
$872$		0			0
$873$	3.13127	+	5.42351i	0.105977	+	0.183558i
$874$		0			0
$875$	12.9839	+	14.6153i	0.438937	+	0.494089i
$876$		0			0
$877$	1.19100	+	2.06287i	0.0402172	+	0.0696582i	0.885433	−	0.464766i	$-0.153862\pi$
$877$	1.19100	+	2.06287i	0.0402172	+	0.0696582i	−0.845216	+	0.534425i	$0.820528\pi$
$878$		0			0
$879$	−6.25251	+	10.8297i	−0.210892	+	0.365276i
$880$		0			0
$881$	−38.7986			−1.30716			−0.653579	−	0.756858i	$-0.726733\pi$
$881$	−38.7986			−1.30716			−0.653579	+	0.756858i	$0.726733\pi$
$882$		0			0
$883$	−35.8165			−1.20532			−0.602660	−	0.797998i	$-0.705892\pi$
$883$	−35.8165			−1.20532			−0.602660	+	0.797998i	$0.705892\pi$
$884$		0			0
$885$	−1.80665	+	3.12921i	−0.0607299	+	0.105187i
$886$		0			0
$887$	−17.2499	−	29.8777i	−0.579196	−	1.00320i	−0.995572	−	0.0940038i	$-0.970033\pi$
$887$	−17.2499	−	29.8777i	−0.579196	−	1.00320i	0.416376	−	0.909192i	$-0.363300\pi$
$888$		0			0
$889$	−27.4173	−	30.8622i	−0.919548	−	1.03509i
$890$		0			0
$891$	−11.2080	−	19.4129i	−0.375484	−	0.650357i
$892$		0			0
$893$	13.4172	−	23.2393i	0.448990	−	0.777674i
$894$		0			0
$895$	5.48459			0.183330
$896$		0			0
$897$	17.6585			0.589600
$898$		0			0
$899$	18.4650	−	31.9822i	0.615841	−	1.06667i
$900$		0			0
$901$	−16.0061	−	27.7234i	−0.533240	−	0.923599i
$902$		0			0
$903$	−13.7171	+	2.82001i	−0.456477	+	0.0938439i
$904$		0			0
$905$	7.22011	+	12.5056i	0.240005	+	0.415700i
$906$		0			0
$907$	−1.37861	+	2.38783i	−0.0457761	+	0.0792866i	−0.888006	−	0.459833i	$-0.847909\pi$
$907$	−1.37861	+	2.38783i	−0.0457761	+	0.0792866i	0.842230	+	0.539119i	$0.181243\pi$
$908$		0			0
$909$	17.1919			0.570221
$910$		0			0
$911$	4.19693			0.139051			0.0695253	−	0.997580i	$-0.477852\pi$
$911$	4.19693			0.139051			0.0695253	+	0.997580i	$0.477852\pi$
$912$		0			0
$913$	−3.26621	+	5.65724i	−0.108096	+	0.187227i
$914$		0			0
$915$	0.866704	+	1.50117i	0.0286523	+	0.0496273i
$916$		0			0
$917$	−9.81445	+	29.5329i	−0.324102	+	0.975263i
$918$		0			0
$919$	−5.40651	−	9.36435i	−0.178344	−	0.308901i	0.762969	−	0.646435i	$-0.223741\pi$
$919$	−5.40651	−	9.36435i	−0.178344	−	0.308901i	−0.941314	+	0.337533i	$0.890407\pi$
$920$		0			0
$921$	−5.77770	+	10.0073i	−0.190382	+	0.329751i
$922$		0			0
$923$	−7.80381			−0.256865
$924$		0			0
$925$	40.3430			1.32647
$926$		0			0
$927$	2.06132	−	3.57031i	0.0677027	−	0.117264i
$928$		0			0
$929$	14.1786	+	24.5581i	0.465185	+	0.805724i	0.999210	−	0.0397449i	$-0.0126545\pi$
$929$	14.1786	+	24.5581i	0.465185	+	0.805724i	−0.534025	+	0.845469i	$0.679321\pi$
$930$		0			0
$931$	31.0284	−	13.3208i	1.01692	−	0.436573i
$932$		0			0
$933$	3.50132	+	6.06447i	0.114628	+	0.198542i
$934$		0			0
$935$	6.58096	−	11.3986i	0.215220	−	0.372772i
$936$		0			0
$937$	−11.1289			−0.363565			−0.181783	−	0.983339i	$-0.558187\pi$
$937$	−11.1289			−0.363565			−0.181783	+	0.983339i	$0.558187\pi$
$938$		0			0
$939$	9.72789			0.317458
$940$		0			0
$941$	21.5438	−	37.3150i	0.702308	−	1.21643i	−0.265347	−	0.964153i	$-0.585486\pi$
$941$	21.5438	−	37.3150i	0.702308	−	1.21643i	0.967654	−	0.252280i	$-0.0811803\pi$
$942$		0			0
$943$	3.51228	+	6.08344i	0.114375	+	0.198104i
$944$		0			0
$945$	1.71342	−	5.15590i	0.0557376	−	0.167721i
$946$		0			0
$947$	−9.37042	−	16.2300i	−0.304498	−	0.527406i	0.672652	−	0.739959i	$-0.265155\pi$
$947$	−9.37042	−	16.2300i	−0.304498	−	0.527406i	−0.977149	+	0.212554i	$0.931822\pi$
$948$		0			0
$949$	11.9663	−	20.7262i	0.388443	−	0.672802i
$950$		0			0
$951$	10.7783			0.349511
$952$		0			0
$953$	−13.7933			−0.446807			−0.223404	−	0.974726i	$-0.571717\pi$
$953$	−13.7933			−0.446807			−0.223404	+	0.974726i	$0.571717\pi$
$954$		0			0
$955$	7.59605	−	13.1567i	0.245802	−	0.425742i
$956$		0			0
$957$	5.25109	+	9.09515i	0.169743	+	0.294004i
$958$		0			0
$959$	−11.6517	+	2.39540i	−0.376254	+	0.0773515i
$960$		0			0
$961$	3.45950	+	5.99202i	0.111597	+	0.193291i
$962$		0			0
$963$	11.8008	−	20.4396i	0.380275	−	0.658656i
$964$		0			0
$965$	−1.10059			−0.0354291
$966$		0			0
$967$	−9.71189			−0.312313			−0.156157	−	0.987732i	$-0.549910\pi$
$967$	−9.71189			−0.312313			−0.156157	+	0.987732i	$0.549910\pi$
$968$		0			0
$969$	−5.83660	+	10.1093i	−0.187499	+	0.324757i
$970$		0			0
$971$	29.2045	+	50.5838i	0.937218	+	1.62331i	0.770629	+	0.637284i	$0.219942\pi$
$971$	29.2045	+	50.5838i	0.937218	+	1.62331i	0.166589	+	0.986026i	$0.446725\pi$
$972$		0			0
$973$	2.47823	+	2.78961i	0.0794484	+	0.0894309i
$974$		0			0
$975$	5.50447	+	9.53403i	0.176284	+	0.305333i
$976$		0			0
$977$	−25.5319	+	44.2225i	−0.816837	+	1.41480i	0.0911651	+	0.995836i	$0.470941\pi$
$977$	−25.5319	+	44.2225i	−0.816837	+	1.41480i	−0.908002	+	0.418967i	$0.862392\pi$
$978$		0			0
$979$	−50.1650			−1.60328
$980$		0			0
$981$	28.4297			0.907690
$982$		0			0
$983$	30.8688	−	53.4662i	0.984560	−	1.70531i	0.340686	−	0.940177i	$-0.389341\pi$
$983$	30.8688	−	53.4662i	0.984560	−	1.70531i	0.643874	−	0.765131i	$-0.277326\pi$
$984$		0			0
$985$	5.04827	+	8.74386i	0.160851	+	0.278603i
$986$		0			0
$987$	−4.39472	−	4.94690i	−0.139885	−	0.157461i
$988$		0			0
$989$	−41.3499	−	71.6202i	−1.31485	−	2.27739i
$990$		0			0
$991$	18.0049	−	31.1855i	0.571946	−	0.990639i	−0.424421	−	0.905465i	$-0.639522\pi$
$991$	18.0049	−	31.1855i	0.571946	−	0.990639i	0.996366	−	0.0851736i	$-0.0271445\pi$
$992$		0			0
$993$	−4.33817			−0.137668
$994$		0			0
$995$	1.31831			0.0417931
$996$		0			0
$997$	7.88071	−	13.6498i	0.249585	−	0.432293i	−0.713826	−	0.700323i	$-0.753039\pi$
$997$	7.88071	−	13.6498i	0.249585	−	0.432293i	0.963411	+	0.268030i	$0.0863726\pi$
$998$		0			0
$999$	−12.0064	−	20.7957i	−0.379865	−	0.657946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.e.165.7	✓	30
7.2	even	3	inner	1148.2.i.e.821.7	yes	30
7.3	odd	6		8036.2.a.r.1.7		15
7.4	even	3		8036.2.a.q.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.e.165.7	✓	30	1.1	even	1	trivial
1148.2.i.e.821.7	yes	30	7.2	even	3	inner
8036.2.a.q.1.9		15	7.4	even	3
8036.2.a.r.1.7		15	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.224795 + 0.389356i) q^{3} +(0.393901 + 0.682257i) q^{5} +(1.75718 + 1.97796i) q^{7} +(1.39893 + 2.42303i) q^{9} +O(q^{10})\)	\(q+(-0.224795 + 0.389356i) q^{3} +(0.393901 + 0.682257i) q^{5} +(1.75718 + 1.97796i) q^{7} +(1.39893 + 2.42303i) q^{9} +(-1.55200 + 2.68814i) q^{11} +5.59137 q^{13} -0.354188 q^{15} +(-2.69122 + 4.66133i) q^{17} +(-2.41193 - 4.17758i) q^{19} +(-1.16514 + 0.239532i) q^{21} +(-3.51228 - 6.08344i) q^{23} +(2.18968 - 3.79264i) q^{25} -2.60666 q^{27} -7.52560 q^{29} +(-2.45362 + 4.24979i) q^{31} +(-0.697763 - 1.20856i) q^{33} +(-0.657324 + 1.97797i) q^{35} +(4.60604 + 7.97789i) q^{37} +(-1.25691 + 2.17703i) q^{39} -1.00000 q^{41} +11.7730 q^{43} +(-1.10208 + 1.90887i) q^{45} +(2.78143 + 4.81759i) q^{47} +(-0.824657 + 6.95125i) q^{49} +(-1.20995 - 2.09569i) q^{51} +(-2.97376 + 5.15070i) q^{53} -2.44534 q^{55} +2.16875 q^{57} +(5.10083 - 8.83489i) q^{59} +(-2.44701 - 4.23835i) q^{61} +(-2.33447 + 7.02472i) q^{63} +(2.20245 + 3.81475i) q^{65} +(-5.87182 + 10.1703i) q^{67} +3.15817 q^{69} -1.39569 q^{71} +(2.14014 - 3.70683i) q^{73} +(0.984459 + 1.70513i) q^{75} +(-8.04418 + 1.65375i) q^{77} +(-4.05037 - 7.01545i) q^{79} +(-3.61084 + 6.25416i) q^{81} +2.10452 q^{83} -4.24031 q^{85} +(1.69172 - 2.93014i) q^{87} +(8.08070 + 13.9962i) q^{89} +(9.82503 + 11.0595i) q^{91} +(-1.10312 - 1.91066i) q^{93} +(1.90012 - 3.29111i) q^{95} +2.23832 q^{97} -8.68459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9}+O(q^{10}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9	\( 30 q + q^{3} - 3 q^{5} + 3 q^{7} - 30 q^{9} - 9 q^{11} + 14 q^{13} + 4 q^{15} - 3 q^{17} - 7 q^{19} - 3 q^{21} + q^{23} - 32 q^{25} + 22 q^{27} + 36 q^{29} - 30 q^{31} + 16 q^{33} - 47 q^{35} - 23 q^{37} - 5 q^{39} - 30 q^{41} + 24 q^{43} + 13 q^{45} + 16 q^{47} - 31 q^{49} - 29 q^{51} - 33 q^{53} + 74 q^{55} + 32 q^{57} + 10 q^{59} - q^{61} - 75 q^{63} - 16 q^{65} - 20 q^{67} + 42 q^{69} + 10 q^{71} + 3 q^{73} + 51 q^{75} - 15 q^{77} - 25 q^{79} - 43 q^{81} + 36 q^{83} + 72 q^{85} + 53 q^{87} + 11 q^{89} - 41 q^{91} - 65 q^{93} + 30 q^{95} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 30 * q + q^3 - 3 * q^5 + 3 * q^7 - 30 * q^9 - 9 * q^11 + 14 * q^13 + 4 * q^15 - 3 * q^17 - 7 * q^19 - 3 * q^21 + q^23 - 32 * q^25 + 22 * q^27 + 36 * q^29 - 30 * q^31 + 16 * q^33 - 47 * q^35 - 23 * q^37 - 5 * q^39 - 30 * q^41 + 24 * q^43 + 13 * q^45 + 16 * q^47 - 31 * q^49 - 29 * q^51 - 33 * q^53 + 74 * q^55 + 32 * q^57 + 10 * q^59 - q^61 - 75 * q^63 - 16 * q^65 - 20 * q^67 + 42 * q^69 + 10 * q^71 + 3 * q^73 + 51 * q^75 - 15 * q^77 - 25 * q^79 - 43 * q^81 + 36 * q^83 + 72 * q^85 + 53 * q^87 + 11 * q^89 - 41 * q^91 - 65 * q^93 + 30 * q^95 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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