LMFDB - Embedded newform 368.2.m.e.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(49,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("368.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	368.193
Dual form			368.2.m.e.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.946512 + 1.09233i) q^{3} +(0.287791 + 2.00163i) q^{5} +(-2.03440 + 4.45471i) q^{7} +(0.129638 - 0.901650i) q^{9} +(-2.31075 - 0.678496i) q^{11} +(-0.495265 - 1.08448i) q^{13} +(-1.91405 + 2.20893i) q^{15} +(-1.02802 - 0.660668i) q^{17} +(-2.91826 + 1.87545i) q^{19} +(-6.79161 + 1.99420i) q^{21} +(4.78032 - 0.385375i) q^{23} +(0.873770 - 0.256562i) q^{25} +(4.75536 - 3.05608i) q^{27} +(7.49200 + 4.81481i) q^{29} +(4.26756 - 4.92503i) q^{31} +(-1.44601 - 3.16631i) q^{33} +(-9.50215 - 2.79008i) q^{35} +(-1.34510 + 9.35539i) q^{37} +(0.715838 - 1.56747i) q^{39} +(1.02432 + 7.12429i) q^{41} +(2.55380 + 2.94724i) q^{43} +1.84208 q^{45} +3.20546 q^{47} +(-11.1216 - 12.8350i) q^{49} +(-0.251363 - 1.74827i) q^{51} +(2.14296 - 4.69244i) q^{53} +(0.693086 - 4.82052i) q^{55} +(-4.81079 - 1.41257i) q^{57} +(2.44490 + 5.35359i) q^{59} +(-2.70508 + 3.12183i) q^{61} +(3.75285 + 2.41181i) q^{63} +(2.02819 - 1.30344i) q^{65} +(2.30775 - 0.677616i) q^{67} +(4.94559 + 4.85694i) q^{69} +(-7.52876 + 2.21064i) q^{71} +(9.24698 - 5.94267i) q^{73} +(1.10729 + 0.711609i) q^{75} +(7.72348 - 8.91337i) q^{77} +(-6.57553 - 14.3984i) q^{79} +(5.21720 + 1.53191i) q^{81} +(1.02340 - 7.11789i) q^{83} +(1.02656 - 2.24785i) q^{85} +(1.83189 + 12.7410i) q^{87} +(-2.07491 - 2.39457i) q^{89} +5.83860 q^{91} +9.41908 q^{93} +(-4.59381 - 5.30154i) q^{95} +(-1.79018 - 12.4510i) q^{97} +(-0.911326 + 1.99553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$	$1$

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
$3$	0.946512	+	1.09233i	0.546469	+	0.630659i	0.960057	−	0.279805i	$-0.0902699\pi$
$3$	0.946512	+	1.09233i	0.546469	+	0.630659i	−0.413588	+	0.910464i	$0.635724\pi$
$4$		0			0
$5$	0.287791	+	2.00163i	0.128704	+	0.895156i	0.947200	+	0.320643i	$0.103899\pi$
$5$	0.287791	+	2.00163i	0.128704	+	0.895156i	−0.818496	+	0.574512i	$0.805192\pi$
$6$		0			0
$7$	−2.03440	+	4.45471i	−0.768930	+	1.68372i	−0.0399353	+	0.999202i	$0.512715\pi$
$7$	−2.03440	+	4.45471i	−0.768930	+	1.68372i	−0.728995	+	0.684519i	$0.760012\pi$
$8$		0			0
$9$	0.129638	−	0.901650i	0.0432125	−	0.300550i
$10$		0			0
$11$	−2.31075	−	0.678496i	−0.696716	−	0.204574i	−0.0858500	−	0.996308i	$-0.527361\pi$
$11$	−2.31075	−	0.678496i	−0.696716	−	0.204574i	−0.610866	+	0.791734i	$0.709179\pi$
$12$		0			0
$13$	−0.495265	−	1.08448i	−0.137362	−	0.300780i	0.828433	−	0.560088i	$-0.189233\pi$
$13$	−0.495265	−	1.08448i	−0.137362	−	0.300780i	−0.965795	+	0.259308i	$0.916506\pi$
$14$		0			0
$15$	−1.91405	+	2.20893i	−0.494205	+	0.570343i
$16$		0			0
$17$	−1.02802	−	0.660668i	−0.249331	−	0.160235i	0.410006	−	0.912083i	$-0.365527\pi$
$17$	−1.02802	−	0.660668i	−0.249331	−	0.160235i	−0.659337	+	0.751847i	$0.729163\pi$
$18$		0			0
$19$	−2.91826	+	1.87545i	−0.669495	+	0.430258i	−0.830743	−	0.556656i	$-0.812084\pi$
$19$	−2.91826	+	1.87545i	−0.669495	+	0.430258i	0.161249	+	0.986914i	$0.448448\pi$
$20$		0			0
$21$	−6.79161	+	1.99420i	−1.48205	+	0.435169i
$22$		0			0
$23$	4.78032	−	0.385375i	0.996766	−	0.0803563i
$23$	4.78032	−	0.385375i	0.996766	−	0.0803563i
$24$		0			0
$25$	0.873770	−	0.256562i	0.174754	−	0.0513124i
$26$		0			0
$27$	4.75536	−	3.05608i	0.915169	−	0.588144i
$28$		0			0
$29$	7.49200	+	4.81481i	1.39123	+	0.894089i	0.999660	−	0.0260602i	$-0.00829616\pi$
$29$	7.49200	+	4.81481i	1.39123	+	0.894089i	0.391569	+	0.920149i	$0.371933\pi$
$30$		0			0
$31$	4.26756	−	4.92503i	0.766477	−	0.884562i	−0.229579	−	0.973290i	$-0.573735\pi$
$31$	4.26756	−	4.92503i	0.766477	−	0.884562i	0.996056	+	0.0887285i	$0.0282803\pi$
$32$		0			0
$33$	−1.44601	−	3.16631i	−0.251717	−	0.551184i
$34$		0			0
$35$	−9.50215	−	2.79008i	−1.60616	−	0.471610i
$36$		0			0
$37$	−1.34510	+	9.35539i	−0.221133	+	1.53802i	0.512629	+	0.858610i	$0.328672\pi$
$37$	−1.34510	+	9.35539i	−0.221133	+	1.53802i	−0.733762	+	0.679406i	$0.762237\pi$
$38$		0			0
$39$	0.715838	−	1.56747i	0.114626	−	0.250996i
$40$		0			0
$41$	1.02432	+	7.12429i	0.159972	+	1.11263i	0.898681	+	0.438603i	$0.144527\pi$
$41$	1.02432	+	7.12429i	0.159972	+	1.11263i	−0.738709	+	0.674024i	$0.764564\pi$
$42$		0			0
$43$	2.55380	+	2.94724i	0.389450	+	0.449450i	0.916290	−	0.400515i	$-0.131169\pi$
$43$	2.55380	+	2.94724i	0.389450	+	0.449450i	−0.526840	+	0.849965i	$0.676623\pi$
$44$		0			0
$45$	1.84208			0.274601
$46$		0			0
$47$	3.20546			0.467564			0.233782	−	0.972289i	$-0.424890\pi$
$47$	3.20546			0.467564			0.233782	+	0.972289i	$0.424890\pi$
$48$		0			0
$49$	−11.1216	−	12.8350i	−1.58880	−	1.83358i
$50$		0			0
$51$	−0.251363	−	1.74827i	−0.0351979	−	0.244807i
$52$		0			0
$53$	2.14296	−	4.69244i	0.294359	−	0.644556i	−0.703448	−	0.710747i	$-0.748357\pi$
$53$	2.14296	−	4.69244i	0.294359	−	0.644556i	0.997807	+	0.0661907i	$0.0210846\pi$
$54$		0			0
$55$	0.693086	−	4.82052i	0.0934558	−	0.649999i
$56$		0			0
$57$	−4.81079	−	1.41257i	−0.637204	−	0.187100i
$58$		0			0
$59$	2.44490	+	5.35359i	0.318299	+	0.696978i	0.999379	−	0.0352308i	$-0.0112166\pi$
$59$	2.44490	+	5.35359i	0.318299	+	0.696978i	−0.681080	+	0.732209i	$0.738489\pi$
$60$		0			0
$61$	−2.70508	+	3.12183i	−0.346350	+	0.399709i	−0.902020	−	0.431693i	$-0.857916\pi$
$61$	−2.70508	+	3.12183i	−0.346350	+	0.399709i	0.555670	+	0.831403i	$0.312462\pi$
$62$		0			0
$63$	3.75285	+	2.41181i	0.472815	+	0.303860i
$64$		0			0
$65$	2.02819	−	1.30344i	0.251566	−	0.161672i
$66$		0			0
$67$	2.30775	−	0.677616i	0.281936	−	0.0827840i	−0.137707	−	0.990473i	$-0.543973\pi$
$67$	2.30775	−	0.677616i	0.281936	−	0.0827840i	0.419643	+	0.907689i	$0.362155\pi$
$68$		0			0
$69$	4.94559	+	4.85694i	0.595379	+	0.584707i
$70$		0			0
$71$	−7.52876	+	2.21064i	−0.893499	+	0.262355i	−0.696080	−	0.717964i	$-0.745074\pi$
$71$	−7.52876	+	2.21064i	−0.893499	+	0.262355i	−0.197419	+	0.980319i	$0.563256\pi$
$72$		0			0
$73$	9.24698	−	5.94267i	1.08228	−	0.695537i	0.127195	−	0.991878i	$-0.459403\pi$
$73$	9.24698	−	5.94267i	1.08228	−	0.695537i	0.955082	+	0.296341i	$0.0957664\pi$
$74$		0			0
$75$	1.10729	+	0.711609i	0.127858	+	0.0821696i
$76$		0			0
$77$	7.72348	−	8.91337i	0.880172	−	1.01577i
$78$		0			0
$79$	−6.57553	−	14.3984i	−0.739805	−	1.61995i	−0.783875	−	0.620919i	$-0.786760\pi$
$79$	−6.57553	−	14.3984i	−0.739805	−	1.61995i	0.0440701	−	0.999028i	$-0.485968\pi$
$80$		0			0
$81$	5.21720	+	1.53191i	0.579689	+	0.170212i
$82$		0			0
$83$	1.02340	−	7.11789i	0.112332	−	0.781290i	−0.853308	−	0.521407i	$-0.825407\pi$
$83$	1.02340	−	7.11789i	0.112332	−	0.781290i	0.965640	−	0.259882i	$-0.0836837\pi$
$84$		0			0
$85$	1.02656	−	2.24785i	0.111346	−	0.243813i
$86$		0			0
$87$	1.83189	+	12.7410i	0.196399	+	1.36598i
$88$		0			0
$89$	−2.07491	−	2.39457i	−0.219940	−	0.253824i	0.635047	−	0.772473i	$-0.280981\pi$
$89$	−2.07491	−	2.39457i	−0.219940	−	0.253824i	−0.854987	+	0.518649i	$0.826435\pi$
$90$		0			0
$91$	5.83860			0.612052
$92$		0			0
$93$	9.41908			0.976713
$94$		0			0
$95$	−4.59381	−	5.30154i	−0.471315	−	0.543926i
$96$		0			0
$97$	−1.79018	−	12.4510i	−0.181765	−	1.26420i	−0.852587	−	0.522585i	$-0.824968\pi$
$97$	−1.79018	−	12.4510i	−0.181765	−	1.26420i	0.670822	−	0.741618i	$-0.265941\pi$
$98$		0			0
$99$	−0.911326	+	1.99553i	−0.0915917	+	0.200558i
$100$		0			0
$101$	−2.05780	+	14.3123i	−0.204759	+	1.42413i	0.585159	+	0.810918i	$0.301032\pi$
$101$	−2.05780	+	14.3123i	−0.204759	+	1.42413i	−0.789918	+	0.613212i	$0.789877\pi$
$102$		0			0
$103$	−1.37011	−	0.402302i	−0.135001	−	0.0396400i	0.213534	−	0.976936i	$-0.431503\pi$
$103$	−1.37011	−	0.402302i	−0.135001	−	0.0396400i	−0.348535	+	0.937296i	$0.613321\pi$
$104$		0			0
$105$	−5.94620	−	13.0204i	−0.580290	−	1.27066i
$106$		0			0
$107$	7.97915	−	9.20843i	0.771374	−	0.890213i	−0.225081	−	0.974340i	$-0.572265\pi$
$107$	7.97915	−	9.20843i	0.771374	−	0.890213i	0.996455	+	0.0841270i	$0.0268102\pi$
$108$		0			0
$109$	−13.5546	−	8.71102i	−1.29830	−	0.834364i	−0.305270	−	0.952266i	$-0.598747\pi$
$109$	−13.5546	−	8.71102i	−1.29830	−	0.834364i	−0.993025	+	0.117902i	$0.962383\pi$
$110$		0			0
$111$	−11.4924	+	7.38569i	−1.09081	+	0.701019i
$112$		0			0
$113$	5.91013	−	1.73537i	0.555978	−	0.163250i	0.00834020	−	0.999965i	$-0.497345\pi$
$113$	5.91013	−	1.73537i	0.555978	−	0.163250i	0.547638	+	0.836715i	$0.315527\pi$
$114$		0			0
$115$	2.14711	+	9.45752i	0.200219	+	0.881919i
$116$		0			0
$117$	−1.04202	+	0.305966i	−0.0963352	+	0.0282866i
$118$		0			0
$119$	5.03448	−	3.23546i	0.461510	−	0.296595i
$120$		0			0
$121$	−4.37460	−	2.81138i	−0.397691	−	0.255580i
$122$		0			0
$123$	−6.81257	+	7.86213i	−0.614269	+	0.708904i
$124$		0			0
$125$	4.96529	+	10.8725i	0.444109	+	0.972463i
$126$		0			0
$127$	−16.0231	−	4.70481i	−1.42182	−	0.417485i	−0.521702	−	0.853128i	$-0.674703\pi$
$127$	−16.0231	−	4.70481i	−1.42182	−	0.417485i	−0.900120	+	0.435643i	$0.856521\pi$
$128$		0			0
$129$	−0.802167	+	5.57920i	−0.0706269	+	0.491221i
$130$		0			0
$131$	0.951568	−	2.08364i	0.0831389	−	0.182049i	−0.863497	−	0.504354i	$-0.831731\pi$
$131$	0.951568	−	2.08364i	0.0831389	−	0.182049i	0.946636	+	0.322306i	$0.104458\pi$
$132$		0			0
$133$	−2.41769	−	16.8154i	−0.209640	−	1.45808i
$134$		0			0
$135$	7.48569	+	8.63895i	0.644266	+	0.743523i
$136$		0			0
$137$	20.7171			1.76998			0.884992	−	0.465607i	$-0.154164\pi$
$137$	20.7171			1.76998			0.884992	+	0.465607i	$0.154164\pi$
$138$		0			0
$139$	−0.114710			−0.00972957			−0.00486479	−	0.999988i	$-0.501549\pi$
$139$	−0.114710			−0.00972957			−0.00486479	+	0.999988i	$0.501549\pi$
$140$		0			0
$141$	3.03401	+	3.50143i	0.255510	+	0.294874i
$142$		0			0
$143$	0.408617	+	2.84199i	0.0341702	+	0.237659i
$144$		0			0
$145$	−7.48134	+	16.3819i	−0.621292	+	1.36044i
$146$		0			0
$147$	3.49339	−	24.2971i	0.288130	−	2.00399i
$148$		0			0
$149$	−12.4002	−	3.64102i	−1.01586	−	0.298284i	−0.268912	−	0.963165i	$-0.586664\pi$
$149$	−12.4002	−	3.64102i	−1.01586	−	0.298284i	−0.746949	+	0.664881i	$0.768482\pi$
$150$		0			0
$151$	−1.11361	−	2.43847i	−0.0906244	−	0.198440i	0.858892	−	0.512156i	$-0.171153\pi$
$151$	−1.11361	−	2.43847i	−0.0906244	−	0.198440i	−0.949517	+	0.313716i	$0.898426\pi$
$152$		0			0
$153$	−0.728961	+	0.841266i	−0.0589330	+	0.0680123i
$154$		0			0
$155$	11.0862	+	7.12470i	0.890469	+	0.572270i
$156$		0			0
$157$	−15.4336	+	9.91859i	−1.23174	+	0.791590i	−0.984161	−	0.177278i	$-0.943271\pi$
$157$	−15.4336	+	9.91859i	−1.23174	+	0.791590i	−0.247577	+	0.968868i	$0.579634\pi$
$158$		0			0
$159$	7.15405	−	2.10062i	0.567353	−	0.166590i
$160$		0			0
$161$	−8.00834	+	22.0790i	−0.631146	+	1.74007i
$162$		0			0
$163$	−9.38422	+	2.75545i	−0.735029	+	0.215824i	−0.627761	−	0.778406i	$-0.716028\pi$
$163$	−9.38422	+	2.75545i	−0.735029	+	0.215824i	−0.107268	+	0.994230i	$0.534210\pi$
$164$		0			0
$165$	5.92163	−	3.80560i	0.460999	−	0.296266i
$166$		0			0
$167$	13.1023	+	8.42036i	1.01389	+	0.651587i	0.938397	−	0.345559i	$-0.112311\pi$
$167$	13.1023	+	8.42036i	1.01389	+	0.651587i	0.0754924	+	0.997146i	$0.475947\pi$
$168$		0			0
$169$	7.58238	−	8.75054i	0.583260	−	0.673118i
$170$		0			0
$171$	1.31268	+	2.87438i	0.100383	+	0.219809i
$172$		0			0
$173$	2.85447	+	0.838147i	0.217021	+	0.0637231i	0.388436	−	0.921476i	$-0.373016\pi$
$173$	2.85447	+	0.838147i	0.217021	+	0.0637231i	−0.171415	+	0.985199i	$0.554834\pi$
$174$		0			0
$175$	−0.634687	+	4.41434i	−0.0479778	+	0.333693i
$176$		0			0
$177$	−3.53378	+	7.73789i	−0.265615	+	0.581616i
$178$		0			0
$179$	0.152622	+	1.06151i	0.0114075	+	0.0793409i	0.994730	−	0.102530i	$-0.0326938\pi$
$179$	0.152622	+	1.06151i	0.0114075	+	0.0793409i	−0.983322	+	0.181871i	$0.941785\pi$
$180$		0			0
$181$	8.45277	+	9.75501i	0.628289	+	0.725084i	0.977259	−	0.212050i	$-0.0680139\pi$
$181$	8.45277	+	9.75501i	0.628289	+	0.725084i	−0.348970	+	0.937134i	$0.613468\pi$
$182$		0			0
$183$	−5.97047			−0.441350
$184$		0			0
$185$	−19.1131			−1.40523
$186$		0			0
$187$	1.92723	+	2.22414i	0.140933	+	0.162645i
$188$		0			0
$189$	3.93967	+	27.4010i	0.286569	+	1.99313i
$190$		0			0
$191$	9.19376	−	20.1315i	0.665237	−	1.45667i	−0.212323	−	0.977200i	$-0.568103\pi$
$191$	9.19376	−	20.1315i	0.665237	−	1.45667i	0.877560	−	0.479467i	$-0.159170\pi$
$192$		0			0
$193$	−0.476280	+	3.31260i	−0.0342834	+	0.238446i	−0.999757	−	0.0220557i	$-0.992979\pi$
$193$	−0.476280	+	3.31260i	−0.0342834	+	0.238446i	0.965473	+	0.260502i	$0.0838880\pi$
$194$		0			0
$195$	3.34350	+	0.981740i	0.239433	+	0.0703039i
$196$		0			0
$197$	−1.97491	−	4.32446i	−0.140707	−	0.308105i	0.826139	−	0.563467i	$-0.190533\pi$
$197$	−1.97491	−	4.32446i	−0.140707	−	0.308105i	−0.966846	+	0.255362i	$0.917805\pi$
$198$		0			0
$199$	6.08520	−	7.02270i	0.431369	−	0.497826i	−0.497898	−	0.867236i	$-0.665895\pi$
$199$	6.08520	−	7.02270i	0.431369	−	0.497826i	0.929267	+	0.369410i	$0.120440\pi$
$200$		0			0
$201$	2.92450	+	1.87946i	0.206278	+	0.132567i
$202$		0			0
$203$	−36.6903	+	23.5794i	−2.57515	+	1.65495i
$204$		0			0
$205$	−13.9654	+	4.10061i	−0.975386	+	0.286399i
$206$		0			0
$207$	0.272236	−	4.36014i	0.0189217	−	0.303050i
$208$		0			0
$209$	8.01585	−	2.35366i	0.554468	−	0.162806i
$210$		0			0
$211$	−17.5848	+	11.3011i	−1.21059	+	0.777997i	−0.980757	−	0.195234i	$-0.937453\pi$
$211$	−17.5848	+	11.3011i	−1.21059	+	0.777997i	−0.229830	+	0.973231i	$0.573817\pi$
$212$		0			0
$213$	−9.54082	−	6.13151i	−0.653726	−	0.420124i
$214$		0			0
$215$	−5.16432	+	5.95994i	−0.352204	+	0.406465i
$216$		0			0
$217$	13.2577	+	29.0302i	0.899988	+	1.97070i
$218$		0			0
$219$	15.2438	+	4.47597i	1.03008	+	0.302458i
$220$		0			0
$221$	−0.207338	+	1.44207i	−0.0139471	+	0.0970042i
$222$		0			0
$223$	−2.31661	+	5.07266i	−0.155131	+	0.339690i	−0.971200	−	0.238264i	$-0.923422\pi$
$223$	−2.31661	+	5.07266i	−0.155131	+	0.339690i	0.816069	+	0.577955i	$0.196149\pi$
$224$		0			0
$225$	−0.118056	−	0.821095i	−0.00787037	−	0.0547397i
$226$		0			0
$227$	4.28566	+	4.94591i	0.284449	+	0.328272i	0.879935	−	0.475094i	$-0.157586\pi$
$227$	4.28566	+	4.94591i	0.284449	+	0.328272i	−0.595486	+	0.803366i	$0.703040\pi$
$228$		0			0
$229$	−11.3038			−0.746975			−0.373487	−	0.927635i	$-0.621838\pi$
$229$	−11.3038			−0.746975			−0.373487	+	0.927635i	$0.621838\pi$
$230$		0			0
$231$	17.0467			1.12159
$232$		0			0
$233$	−12.0920	−	13.9549i	−0.792174	−	0.914217i	0.205751	−	0.978604i	$-0.434036\pi$
$233$	−12.0920	−	13.9549i	−0.792174	−	0.914217i	−0.997925	+	0.0643871i	$0.979491\pi$
$234$		0			0
$235$	0.922502	+	6.41614i	0.0601774	+	0.418543i
$236$		0			0
$237$	9.50404	−	20.8109i	0.617354	−	1.35182i
$238$		0			0
$239$	−0.307319	+	2.13745i	−0.0198788	+	0.138260i	−0.997344	−	0.0728373i	$-0.976795\pi$
$239$	−0.307319	+	2.13745i	−0.0198788	+	0.138260i	0.977465	+	0.211097i	$0.0677037\pi$
$240$		0			0
$241$	3.59835	+	1.05657i	0.231790	+	0.0680596i	0.395565	−	0.918438i	$-0.370549\pi$
$241$	3.59835	+	1.05657i	0.231790	+	0.0680596i	−0.163775	+	0.986498i	$0.552367\pi$
$242$		0			0
$243$	−3.77987	−	8.27675i	−0.242479	−	0.530954i
$244$		0			0
$245$	22.4903	−	25.9552i	1.43685	−	1.65822i
$246$		0			0
$247$	3.47920	+	2.23595i	0.221376	+	0.142270i
$248$		0			0
$249$	8.74376	−	5.61928i	0.554114	−	0.356107i
$250$		0			0
$251$	18.9816	−	5.57349i	1.19810	−	0.351795i	0.378977	−	0.925406i	$-0.376276\pi$
$251$	18.9816	−	5.57349i	1.19810	−	0.351795i	0.819128	+	0.573611i	$0.194458\pi$
$252$		0			0
$253$	−11.3076	−	2.35293i	−0.710902	−	0.147927i
$254$		0			0
$255$	3.42705	−	1.00627i	0.214610	−	0.0630152i
$256$		0			0
$257$	−9.72659	+	6.25090i	−0.606728	+	0.389921i	−0.807629	−	0.589691i	$-0.799250\pi$
$257$	−9.72659	+	6.25090i	−0.606728	+	0.389921i	0.200901	+	0.979612i	$0.435613\pi$
$258$		0			0
$259$	−38.9391	−	25.0246i	−2.41956	−	1.55495i
$260$		0			0
$261$	5.31252	−	6.13098i	0.328837	−	0.379498i
$262$		0			0
$263$	8.71422	+	19.0815i	0.537342	+	1.17662i	0.962447	+	0.271471i	$0.0875100\pi$
$263$	8.71422	+	19.0815i	0.537342	+	1.17662i	−0.425105	+	0.905144i	$0.639763\pi$
$264$		0			0
$265$	10.0092	+	2.93898i	0.614863	+	0.180540i
$266$		0			0
$267$	0.651745	−	4.53299i	0.0398861	−	0.277414i
$268$		0			0
$269$	10.9123	−	23.8946i	0.665336	−	1.45688i	−0.212129	−	0.977242i	$-0.568040\pi$
$269$	10.9123	−	23.8946i	0.665336	−	1.45688i	0.877465	−	0.479641i	$-0.159233\pi$
$270$		0			0
$271$	3.95984	+	27.5413i	0.240543	+	1.67301i	0.649425	+	0.760426i	$0.275010\pi$
$271$	3.95984	+	27.5413i	0.240543	+	1.67301i	−0.408882	+	0.912587i	$0.634081\pi$
$272$		0			0
$273$	5.52631	+	6.37770i	0.334468	+	0.385996i
$274$		0			0
$275$	−2.19314			−0.132251
$276$		0			0
$277$	15.0981			0.907160			0.453580	−	0.891216i	$-0.350147\pi$
$277$	15.0981			0.907160			0.453580	+	0.891216i	$0.350147\pi$
$278$		0			0
$279$	−3.88742	−	4.48632i	−0.232733	−	0.268589i
$280$		0			0
$281$	1.07223	+	7.45754i	0.0639640	+	0.444879i	0.996486	+	0.0837650i	$0.0266945\pi$
$281$	1.07223	+	7.45754i	0.0639640	+	0.444879i	−0.932522	+	0.361114i	$0.882396\pi$
$282$		0			0
$283$	1.50297	−	3.29105i	0.0893425	−	0.195633i	−0.859686	−	0.510823i	$-0.829341\pi$
$283$	1.50297	−	3.29105i	0.0893425	−	0.195633i	0.949029	+	0.315190i	$0.102068\pi$
$284$		0			0
$285$	1.44295	−	10.0359i	0.0854730	−	0.594478i
$286$		0			0
$287$	−33.8205	−	9.93060i	−1.99636	−	0.586185i
$288$		0			0
$289$	−6.44171	−	14.1054i	−0.378924	−	0.829729i
$290$		0			0
$291$	11.9062	−	13.7405i	0.697952	−	0.805480i
$292$		0			0
$293$	−7.38108	−	4.74353i	−0.431207	−	0.277120i	0.306980	−	0.951716i	$-0.400682\pi$
$293$	−7.38108	−	4.74353i	−0.431207	−	0.277120i	−0.738187	+	0.674596i	$0.764318\pi$
$294$		0			0
$295$	−10.0123	+	6.43450i	−0.582938	+	0.374631i
$296$		0			0
$297$	−13.0620	+	3.83534i	−0.757933	+	0.222549i
$298$		0			0
$299$	−2.78546	−	4.99330i	−0.161087	−	0.288770i
$300$		0			0
$301$	−18.3245	+	5.38057i	−1.05621	+	0.310131i
$302$		0			0
$303$	−17.5816	+	11.2990i	−1.01004	+	0.649110i
$304$		0			0
$305$	−7.02724	−	4.51614i	−0.402379	−	0.258593i
$306$		0			0
$307$	18.9935	−	21.9197i	1.08402	−	1.25102i	0.117870	−	0.993029i	$-0.462394\pi$
$307$	18.9935	−	21.9197i	1.08402	−	1.25102i	0.966147	−	0.257993i	$-0.0830610\pi$
$308$		0			0
$309$	−0.857382	−	1.87740i	−0.0487748	−	0.106802i
$310$		0			0
$311$	9.51432	+	2.79366i	0.539508	+	0.158414i	0.540123	−	0.841586i	$-0.318378\pi$
$311$	9.51432	+	2.79366i	0.539508	+	0.158414i	−0.000615350		1.00000i	$0.500196\pi$
$312$		0			0
$313$	−0.248434	+	1.72789i	−0.0140423	+	0.0976664i	−0.995637	−	0.0933083i	$-0.970256\pi$
$313$	−0.248434	+	1.72789i	−0.0140423	+	0.0976664i	0.981595	+	0.190975i	$0.0611649\pi$
$314$		0			0
$315$	−3.74752	+	8.20591i	−0.211149	+	0.462351i
$316$		0			0
$317$	−1.51382	−	10.5289i	−0.0850248	−	0.591360i	−0.987139	−	0.159863i	$-0.948895\pi$
$317$	−1.51382	−	10.5289i	−0.0850248	−	0.591360i	0.902114	−	0.431497i	$-0.142014\pi$
$318$		0			0
$319$	−14.0453	−	16.2091i	−0.786384	−	0.907536i
$320$		0			0
$321$	17.6111			0.982953
$322$		0			0
$323$	4.23908			0.235869
$324$		0			0
$325$	−0.710984	−	0.820519i	−0.0394383	−	0.0455142i
$326$		0			0
$327$	−3.31427	−	23.0512i	−0.183279	−	1.27474i
$328$		0			0
$329$	−6.52118	+	14.2794i	−0.359524	+	0.787248i
$330$		0			0
$331$	−1.51243	+	10.5192i	−0.0831307	+	0.578187i	0.905098	+	0.425203i	$0.139797\pi$
$331$	−1.51243	+	10.5192i	−0.0831307	+	0.578187i	−0.988229	+	0.152984i	$0.951112\pi$
$332$		0			0
$333$	8.26091	+	2.42562i	0.452695	+	0.132923i
$334$		0			0
$335$	2.02048	+	4.42424i	0.110391	+	0.241722i
$336$		0			0
$337$	17.6329	−	20.3494i	0.960524	−	1.10850i	−0.0335102	−	0.999438i	$-0.510669\pi$
$337$	17.6329	−	20.3494i	0.960524	−	1.10850i	0.994035	−	0.109066i	$-0.0347859\pi$
$338$		0			0
$339$	7.48962	+	4.81329i	0.406780	+	0.261422i
$340$		0			0
$341$	−13.2029	+	8.48497i	−0.714976	+	0.459487i
$342$		0			0
$343$	46.9100	−	13.7740i	2.53290	−	0.743727i
$344$		0			0
$345$	−8.29850	+	11.2970i	−0.446776	+	0.608211i
$346$		0			0
$347$	−2.03573	+	0.597743i	−0.109283	+	0.0320885i	−0.335917	−	0.941892i	$-0.609046\pi$
$347$	−2.03573	+	0.597743i	−0.109283	+	0.0320885i	0.226634	+	0.973980i	$0.427228\pi$
$348$		0			0
$349$	27.9677	−	17.9738i	1.49708	−	0.962114i	0.501807	−	0.864980i	$-0.332669\pi$
$349$	27.9677	−	17.9738i	1.49708	−	0.962114i	0.995271	−	0.0971338i	$-0.0309675\pi$
$350$		0			0
$351$	−5.66942	−	3.64352i	−0.302611	−	0.194476i
$352$		0			0
$353$	−10.5917	+	12.2234i	−0.563737	+	0.650587i	−0.964028	−	0.265801i	$-0.914364\pi$
$353$	−10.5917	+	12.2234i	−0.563737	+	0.650587i	0.400291	+	0.916388i	$0.368909\pi$
$354$		0			0
$355$	−6.59159	−	14.4336i	−0.349845	−	0.766055i
$356$		0			0
$357$	8.29941	+	2.43693i	0.439251	+	0.128976i
$358$		0			0
$359$	−2.20907	+	15.3644i	−0.116590	+	0.810902i	0.844675	+	0.535279i	$0.179793\pi$
$359$	−2.20907	+	15.3644i	−0.116590	+	0.810902i	−0.961266	+	0.275624i	$0.911116\pi$
$360$		0			0
$361$	−2.89396	+	6.33690i	−0.152314	+	0.333521i
$362$		0			0
$363$	−1.06964	−	7.43953i	−0.0561417	−	0.390474i
$364$		0			0
$365$	14.5562	+	16.7988i	0.761907	+	0.879288i
$366$		0			0
$367$	6.66147			0.347726			0.173863	−	0.984770i	$-0.444375\pi$
$367$	6.66147			0.347726			0.173863	+	0.984770i	$0.444375\pi$
$368$		0			0
$369$	6.55640			0.341313
$370$		0			0
$371$	16.5438	+	19.0926i	0.858911	+	0.991237i
$372$		0			0
$373$	−1.77775	−	12.3645i	−0.0920485	−	0.640211i	−0.982656	−	0.185438i	$-0.940629\pi$
$373$	−1.77775	−	12.3645i	−0.0920485	−	0.640211i	0.890607	−	0.454773i	$-0.150280\pi$
$374$		0			0
$375$	−7.17666	+	15.7147i	−0.370601	+	0.811503i
$376$		0			0
$377$	1.51104	−	10.5095i	0.0778226	−	0.541268i
$378$		0			0
$379$	6.57981	+	1.93201i	0.337982	+	0.0992405i	0.446320	−	0.894874i	$-0.352734\pi$
$379$	6.57981	+	1.93201i	0.337982	+	0.0992405i	−0.108337	+	0.994114i	$0.534553\pi$
$380$		0			0
$381$	−10.0269	−	21.9558i	−0.513691	−	1.12483i
$382$		0			0
$383$	9.37648	−	10.8210i	0.479116	−	0.552929i	−0.463809	−	0.885935i	$-0.653518\pi$
$383$	9.37648	−	10.8210i	0.479116	−	0.552929i	0.942925	+	0.333006i	$0.108063\pi$
$384$		0			0
$385$	20.0640	+	12.8944i	1.02256	+	0.657157i
$386$		0			0
$387$	2.98844	−	1.92056i	0.151911	−	0.0976274i
$388$		0			0
$389$	−2.72729	+	0.800806i	−0.138279	+	0.0406025i	−0.350140	−	0.936697i	$-0.613866\pi$
$389$	−2.72729	+	0.800806i	−0.138279	+	0.0406025i	0.211861	+	0.977300i	$0.432048\pi$
$390$		0			0
$391$	−5.16887	−	2.76203i	−0.261401	−	0.139682i
$392$		0			0
$393$	3.17670	−	0.932765i	0.160244	−	0.0470517i
$394$		0			0
$395$	26.9279	−	17.3055i	1.35489	−	0.870734i
$396$		0			0
$397$	−21.9208	−	14.0877i	−1.10018	−	0.707040i	−0.141045	−	0.990003i	$-0.545046\pi$
$397$	−21.9208	−	14.0877i	−1.10018	−	0.707040i	−0.959131	+	0.282963i	$0.908683\pi$
$398$		0			0
$399$	16.0797	−	18.5569i	0.804990	−	0.929008i
$400$		0			0
$401$	−2.25873	−	4.94592i	−0.112795	−	0.246988i	0.844812	−	0.535063i	$-0.179712\pi$
$401$	−2.25873	−	4.94592i	−0.112795	−	0.246988i	−0.957608	+	0.288075i	$0.906985\pi$
$402$		0			0
$403$	−7.45467	−	2.18889i	−0.371343	−	0.109036i
$404$		0			0
$405$	−1.56485	+	10.8838i	−0.0777580	+	0.540819i
$406$		0			0
$407$	9.45579	−	20.7053i	0.468706	−	1.02632i
$408$		0			0
$409$	5.16662	+	35.9346i	0.255473	+	1.77685i	0.564136	+	0.825682i	$0.309209\pi$
$409$	5.16662	+	35.9346i	0.255473	+	1.77685i	−0.308663	+	0.951171i	$0.599882\pi$
$410$		0			0
$411$	19.6090	+	22.6300i	0.967241	+	1.11626i
$412$		0			0
$413$	−28.8226			−1.41827
$414$		0			0
$415$	14.5419			0.713833
$416$		0			0
$417$	−0.108574	−	0.125302i	−0.00531691	−	0.00613604i
$418$		0			0
$419$	2.64411	+	18.3902i	0.129173	+	0.898420i	0.946605	+	0.322395i	$0.104488\pi$
$419$	2.64411	+	18.3902i	0.129173	+	0.898420i	−0.817432	+	0.576025i	$0.804603\pi$
$420$		0			0
$421$	−1.21625	+	2.66322i	−0.0592765	+	0.129797i	−0.936952	−	0.349458i	$-0.886366\pi$
$421$	−1.21625	+	2.66322i	−0.0592765	+	0.129797i	0.877676	+	0.479255i	$0.159093\pi$
$422$		0			0
$423$	0.415548	−	2.89020i	0.0202047	−	0.140526i
$424$		0			0
$425$	−1.06775	−	0.313521i	−0.0517937	−	0.0152080i
$426$		0			0
$427$	−8.40364	−	18.4014i	−0.406680	−	0.890506i
$428$		0			0
$429$	−2.71764	+	3.13633i	−0.131209	+	0.151423i
$430$		0			0
$431$	−19.4160	−	12.4779i	−0.935233	−	0.601038i	−0.0181940	−	0.999834i	$-0.505792\pi$
$431$	−19.4160	−	12.4779i	−0.935233	−	0.601038i	−0.917039	+	0.398796i	$0.869428\pi$
$432$		0			0
$433$	11.2530	−	7.23187i	0.540785	−	0.347541i	−0.241561	−	0.970386i	$-0.577659\pi$
$433$	11.2530	−	7.23187i	0.540785	−	0.347541i	0.782346	+	0.622844i	$0.214023\pi$
$434$		0			0
$435$	−24.9756	+	7.33351i	−1.19749	+	0.351615i
$436$		0			0
$437$	−13.2275	+	10.0899i	−0.632756	+	0.482665i
$438$		0			0
$439$	−17.7285	+	5.20555i	−0.846135	+	0.248448i	−0.675934	−	0.736962i	$-0.736260\pi$
$439$	−17.7285	+	5.20555i	−0.846135	+	0.248448i	−0.170200	+	0.985409i	$0.554441\pi$
$440$		0			0
$441$	−13.0145	+	8.36391i	−0.619738	+	0.398281i
$442$		0			0
$443$	−4.83425	−	3.10679i	−0.229682	−	0.147608i	0.420738	−	0.907182i	$-0.361771\pi$
$443$	−4.83425	−	3.10679i	−0.229682	−	0.147608i	−0.650421	+	0.759574i	$0.725407\pi$
$444$		0			0
$445$	4.19591	−	4.84233i	0.198905	−	0.229549i
$446$		0			0
$447$	−7.75970	−	16.9914i	−0.367021	−	0.803665i
$448$		0			0
$449$	6.09943	+	1.79095i	0.287850	+	0.0845204i	0.422470	−	0.906377i	$-0.361163\pi$
$449$	6.09943	+	1.79095i	0.287850	+	0.0845204i	−0.134620	+	0.990897i	$0.542981\pi$
$450$		0			0
$451$	2.46687	−	17.1574i	0.116160	−	0.807912i
$452$		0			0
$453$	1.60957	−	3.52448i	0.0756244	−	0.165594i
$454$		0			0
$455$	1.68030	+	11.6867i	0.0787735	+	0.547882i
$456$		0			0
$457$	−3.67026	−	4.23571i	−0.171688	−	0.198138i	0.663384	−	0.748279i	$-0.269119\pi$
$457$	−3.67026	−	4.23571i	−0.171688	−	0.198138i	−0.835072	+	0.550141i	$0.814574\pi$
$458$		0			0
$459$	−6.90766			−0.322422
$460$		0			0
$461$	−13.7185			−0.638935			−0.319467	−	0.947597i	$-0.603504\pi$
$461$	−13.7185			−0.638935			−0.319467	+	0.947597i	$0.603504\pi$
$462$		0			0
$463$	−20.7081	−	23.8984i	−0.962388	−	1.11065i	−0.993804	−	0.111148i	$-0.964547\pi$
$463$	−20.7081	−	23.8984i	−0.962388	−	1.11065i	0.0314159	−	0.999506i	$-0.489998\pi$
$464$		0			0
$465$	2.71072	+	18.8535i	0.125707	+	0.874310i
$466$		0			0
$467$	−3.36011	+	7.35762i	−0.155487	+	0.340470i	−0.971304	−	0.237840i	$-0.923560\pi$
$467$	−3.36011	+	7.35762i	−0.155487	+	0.340470i	0.815817	+	0.578310i	$0.196288\pi$
$468$		0			0
$469$	−1.67629	+	11.6589i	−0.0774041	+	0.538357i
$470$		0			0
$471$	−25.4425	−	7.47060i	−1.17233	−	0.344227i
$472$		0			0
$473$	−3.90149	−	8.54306i	−0.179391	−	0.392810i
$474$		0			0
$475$	−2.06872	+	2.38743i	−0.0949193	+	0.109543i
$476$		0			0
$477$	−3.95313	−	2.54052i	−0.181001	−	0.116322i
$478$		0			0
$479$	17.4426	−	11.2097i	0.796973	−	0.512183i	−0.0776540	−	0.996980i	$-0.524743\pi$
$479$	17.4426	−	11.2097i	0.796973	−	0.512183i	0.874627	+	0.484797i	$0.161107\pi$
$480$		0			0
$481$	10.8119	−	3.17466i	0.492980	−	0.144752i
$482$		0			0
$483$	−31.6976	+	12.1502i	−1.44229	+	0.552854i
$484$		0			0
$485$	24.4070	−	7.16654i	1.10826	−	0.325416i
$486$		0			0
$487$	3.91084	−	2.51334i	0.177217	−	0.113891i	−0.449025	−	0.893519i	$-0.648229\pi$
$487$	3.91084	−	2.51334i	0.177217	−	0.113891i	0.626242	+	0.779629i	$0.284592\pi$
$488$		0			0
$489$	−11.8922	−	7.64262i	−0.537782	−	0.345611i
$490$		0			0
$491$	−20.3645	+	23.5019i	−0.919036	+	1.06062i	0.0789299	+	0.996880i	$0.474850\pi$
$491$	−20.3645	+	23.5019i	−0.919036	+	1.06062i	−0.997966	+	0.0637443i	$0.979696\pi$
$492$		0			0
$493$	−4.52092	−	9.89944i	−0.203612	−	0.445848i
$494$		0			0
$495$	−4.25657	−	1.24984i	−0.191319	−	0.0561762i
$496$		0			0
$497$	5.46871	−	38.0357i	0.245305	−	1.70614i
$498$		0			0
$499$	2.73629	−	5.99164i	0.122493	−	0.268223i	−0.838445	−	0.544987i	$-0.816535\pi$
$499$	2.73629	−	5.99164i	0.122493	−	0.268223i	0.960938	+	0.276764i	$0.0892620\pi$
$500$		0			0
$501$	3.20368	+	22.2821i	0.143130	+	0.995491i
$502$		0			0
$503$	19.8350	+	22.8909i	0.884401	+	1.02065i	0.999627	+	0.0273137i	$0.00869530\pi$
$503$	19.8350	+	22.8909i	0.884401	+	1.02065i	−0.115226	+	0.993339i	$0.536759\pi$
$504$		0			0
$505$	−29.2402			−1.30117
$506$		0			0
$507$	16.7353			0.743242
$508$		0			0
$509$	1.73047	+	1.99707i	0.0767018	+	0.0885186i	0.792803	−	0.609478i	$-0.208621\pi$
$509$	1.73047	+	1.99707i	0.0767018	+	0.0885186i	−0.716102	+	0.697996i	$0.754075\pi$
$510$		0			0
$511$	7.66085	+	53.2824i	0.338896	+	2.35707i
$512$		0			0
$513$	−8.14584	+	17.8369i	−0.359647	+	0.787518i
$514$		0			0
$515$	0.410953	−	2.85824i	0.0181087	−	0.125949i
$516$		0			0
$517$	−7.40701	−	2.17489i	−0.325760	−	0.0956517i
$518$		0			0
$519$	1.78625	+	3.91135i	0.0784078	+	0.171689i
$520$		0			0
$521$	−9.96216	+	11.4970i	−0.436450	+	0.503691i	−0.930778	−	0.365585i	$-0.880869\pi$
$521$	−9.96216	+	11.4970i	−0.436450	+	0.503691i	0.494328	+	0.869276i	$0.335414\pi$
$522$		0			0
$523$	19.5237	+	12.5471i	0.853710	+	0.548646i	0.892730	−	0.450592i	$-0.148787\pi$
$523$	19.5237	+	12.5471i	0.853710	+	0.548646i	−0.0390195	+	0.999238i	$0.512423\pi$
$524$		0			0
$525$	−5.42267	+	3.48494i	−0.236665	+	0.152095i
$526$		0			0
$527$	−7.64094	+	2.24358i	−0.332845	+	0.0977320i
$528$		0			0
$529$	22.7030	−	3.68444i	0.987086	−	0.160193i
$530$		0			0
$531$	5.14402	−	1.51042i	0.223231	−	0.0655466i
$532$		0			0
$533$	7.21883	−	4.63926i	0.312682	−	0.200949i
$534$		0			0
$535$	20.7282	+	13.3212i	0.896158	+	0.575926i
$536$		0			0
$537$	−1.01506	+	1.17145i	−0.0438032	+	0.0505516i
$538$		0			0
$539$	16.9907	+	37.2045i	0.731843	+	1.60251i
$540$		0			0
$541$	−12.2291	−	3.59080i	−0.525772	−	0.154380i	0.00806601	−	0.999967i	$-0.497432\pi$
$541$	−12.2291	−	3.59080i	−0.525772	−	0.154380i	−0.533838	+	0.845587i	$0.679251\pi$
$542$		0			0
$543$	−2.65508	+	18.4665i	−0.113940	+	0.792472i
$544$		0			0
$545$	13.5353	−	29.6382i	0.579790	−	1.26956i
$546$		0			0
$547$	2.97795	+	20.7121i	0.127328	+	0.885586i	0.948921	+	0.315512i	$0.102176\pi$
$547$	2.97795	+	20.7121i	0.127328	+	0.885586i	−0.821593	+	0.570074i	$0.806915\pi$
$548$		0			0
$549$	2.46412	+	2.84374i	0.105166	+	0.121368i
$550$		0			0
$551$	−30.8935			−1.31611
$552$		0			0
$553$	77.5179			3.29640
$554$		0			0
$555$	−18.0908	−	20.8779i	−0.767912	−	0.886218i
$556$		0			0
$557$	1.83205	+	12.7422i	0.0776266	+	0.539905i	0.991112	+	0.133032i	$0.0424715\pi$
$557$	1.83205	+	12.7422i	0.0776266	+	0.539905i	−0.913485	+	0.406872i	$0.866619\pi$
$558$		0			0
$559$	1.93141	−	4.22920i	0.0816900	−	0.178876i
$560$		0			0
$561$	−0.605358	+	4.21036i	−0.0255582	+	0.177761i
$562$		0			0
$563$	4.65110	+	1.36569i	0.196021	+	0.0575568i	0.378269	−	0.925696i	$-0.376519\pi$
$563$	4.65110	+	1.36569i	0.196021	+	0.0575568i	−0.182249	+	0.983252i	$0.558338\pi$
$564$		0			0
$565$	5.17445	+	11.3305i	0.217691	+	0.476676i
$566$		0			0
$567$	−17.4381	+	20.1246i	−0.732330	+	0.845154i
$568$		0			0
$569$	−36.5382	−	23.4817i	−1.53176	−	0.984403i	−0.989555	−	0.144157i	$-0.953953\pi$
$569$	−36.5382	−	23.4817i	−1.53176	−	0.984403i	−0.542206	−	0.840246i	$-0.682411\pi$
$570$		0			0
$571$	21.8343	−	14.0320i	0.913735	−	0.587222i	0.00290148	−	0.999996i	$-0.499076\pi$
$571$	21.8343	−	14.0320i	0.913735	−	0.587222i	0.910833	+	0.412774i	$0.135440\pi$
$572$		0			0
$573$	30.6924	−	9.01209i	1.28219	−	0.376485i
$574$		0			0
$575$	4.07803	−	1.56318i	0.170066	−	0.0651891i
$576$		0			0
$577$	−2.94535	+	0.864832i	−0.122616	+	0.0360034i	−0.342465	−	0.939531i	$-0.611262\pi$
$577$	−2.94535	+	0.864832i	−0.122616	+	0.0360034i	0.219849	+	0.975534i	$0.429444\pi$
$578$		0			0
$579$	−4.06927	+	2.61516i	−0.169113	+	0.108682i
$580$		0			0
$581$	29.6261	+	19.0395i	1.22910	+	0.789894i
$582$		0			0
$583$	−8.13565	+	9.38904i	−0.336944	+	0.388854i
$584$		0			0
$585$	−0.912316	−	1.99769i	−0.0377196	−	0.0825944i
$586$		0			0
$587$	−22.8756	−	6.71688i	−0.944177	−	0.277235i	−0.226816	−	0.973938i	$-0.572832\pi$
$587$	−22.8756	−	6.71688i	−0.944177	−	0.277235i	−0.717360	+	0.696702i	$0.754650\pi$
$588$		0			0
$589$	−3.21720	+	22.3761i	−0.132562	+	0.921992i
$590$		0			0
$591$	2.85447	−	6.25042i	0.117417	−	0.257108i
$592$		0			0
$593$	4.69535	+	32.6569i	0.192815	+	1.34106i	0.824513	+	0.565843i	$0.191449\pi$
$593$	4.69535	+	32.6569i	0.192815	+	1.34106i	−0.631698	+	0.775214i	$0.717642\pi$
$594$		0			0
$595$	7.92508	+	9.14603i	0.324896	+	0.374951i
$596$		0			0
$597$	13.4309			0.549688
$598$		0			0
$599$	−10.2143			−0.417343			−0.208672	−	0.977986i	$-0.566914\pi$
$599$	−10.2143			−0.417343			−0.208672	+	0.977986i	$0.566914\pi$
$600$		0			0
$601$	10.5471	+	12.1720i	0.430225	+	0.496507i	0.928925	−	0.370268i	$-0.120734\pi$
$601$	10.5471	+	12.1720i	0.430225	+	0.496507i	−0.498699	+	0.866775i	$0.666189\pi$
$602$		0			0
$603$	−0.311801	−	2.16863i	−0.0126975	−	0.0883132i
$604$		0			0
$605$	4.36837	−	9.56541i	0.177600	−	0.388889i
$606$		0			0
$607$	−4.25593	+	29.6006i	−0.172743	+	1.20145i	0.700314	+	0.713835i	$0.253043\pi$
$607$	−4.25593	+	29.6006i	−0.172743	+	1.20145i	−0.873057	+	0.487618i	$0.837866\pi$
$608$		0			0
$609$	−60.4844	−	17.7598i	−2.45095	−	0.719665i
$610$		0			0
$611$	−1.58755	−	3.47625i	−0.0642255	−	0.140634i
$612$		0			0
$613$	−15.5308	+	17.9235i	−0.627285	+	0.723925i	−0.977073	−	0.212904i	$-0.931708\pi$
$613$	−15.5308	+	17.9235i	−0.627285	+	0.723925i	0.349789	+	0.936829i	$0.386253\pi$
$614$		0			0
$615$	−17.6977	−	11.3736i	−0.713638	−	0.458628i
$616$		0			0
$617$	−27.8288	+	17.8845i	−1.12035	+	0.720003i	−0.963523	−	0.267624i	$-0.913762\pi$
$617$	−27.8288	+	17.8845i	−1.12035	+	0.720003i	−0.156823	+	0.987627i	$0.550125\pi$
$618$		0			0
$619$	−32.1699	+	9.44593i	−1.29302	+	0.379664i	−0.854684	−	0.519149i	$-0.826249\pi$
$619$	−32.1699	+	9.44593i	−1.29302	+	0.379664i	−0.438333	+	0.898813i	$0.644431\pi$
$620$		0			0
$621$	21.5544	−	16.4417i	0.864949	−	0.659781i
$622$		0			0
$623$	14.8883	−	4.37160i	0.596488	−	0.175145i
$624$		0			0
$625$	−16.5032	+	10.6060i	−0.660129	+	0.424239i
$626$		0			0
$627$	10.1581	+	6.52821i	0.405675	+	0.260711i
$628$		0			0
$629$	7.56359	−	8.72885i	0.301580	−	0.348042i
$630$		0			0
$631$	−5.60059	−	12.2636i	−0.222956	−	0.488205i	0.764789	−	0.644281i	$-0.222843\pi$
$631$	−5.60059	−	12.2636i	−0.222956	−	0.488205i	−0.987745	+	0.156075i	$0.950116\pi$
$632$		0			0
$633$	−28.9887	−	8.51186i	−1.15220	−	0.338316i
$634$		0			0
$635$	4.80598	−	33.4263i	0.190720	−	1.32648i
$636$		0			0
$637$	−8.41118	+	18.4179i	−0.333263	+	0.729745i
$638$		0			0
$639$	1.01721	+	7.07488i	0.0402404	+	0.279878i
$640$		0			0
$641$	−0.794968	−	0.917442i	−0.0313993	−	0.0362368i	0.739833	−	0.672791i	$-0.234905\pi$
$641$	−0.794968	−	0.917442i	−0.0313993	−	0.0362368i	−0.771232	+	0.636554i	$0.780359\pi$
$642$		0			0
$643$	1.08705			0.0428692			0.0214346	−	0.999770i	$-0.493177\pi$
$643$	1.08705			0.0428692			0.0214346	+	0.999770i	$0.493177\pi$
$644$		0			0
$645$	−11.3983			−0.448809
$646$		0			0
$647$	−17.0486	−	19.6752i	−0.670250	−	0.773510i	0.314165	−	0.949368i	$-0.398275\pi$
$647$	−17.0486	−	19.6752i	−0.670250	−	0.773510i	−0.984416	+	0.175858i	$0.943730\pi$
$648$		0			0
$649$	−2.01716	−	14.0297i	−0.0791804	−	0.550712i
$650$		0			0
$651$	−19.1621	+	41.9592i	−0.751024	+	1.64451i
$652$		0			0
$653$	−4.99425	+	34.7358i	−0.195440	+	1.35932i	0.621871	+	0.783119i	$0.286373\pi$
$653$	−4.99425	+	34.7358i	−0.195440	+	1.35932i	−0.817311	+	0.576196i	$0.804536\pi$
$654$		0			0
$655$	4.44453	+	1.30503i	0.173662	+	0.0509918i
$656$		0			0
$657$	−4.15945	−	9.10793i	−0.162276	−	0.355334i
$658$		0			0
$659$	23.9237	−	27.6094i	0.931934	−	1.07551i	−0.0650489	−	0.997882i	$-0.520720\pi$
$659$	23.9237	−	27.6094i	0.931934	−	1.07551i	0.996983	−	0.0776266i	$-0.0247342\pi$
$660$		0			0
$661$	−5.63736	−	3.62291i	−0.219268	−	0.140915i	0.426396	−	0.904537i	$-0.359783\pi$
$661$	−5.63736	−	3.62291i	−0.219268	−	0.140915i	−0.645664	+	0.763622i	$0.723419\pi$
$662$		0			0
$663$	−1.77147	+	1.13845i	−0.0687982	+	0.0442139i
$664$		0			0
$665$	32.9624	−	9.67864i	1.27823	−	0.375322i
$666$		0			0
$667$	37.6697	+	20.1291i	1.45858	+	0.779403i
$668$		0			0
$669$	−7.73373	+	2.27083i	−0.299003	+	0.0877953i
$670$		0			0
$671$	8.36891	−	5.37837i	0.323078	−	0.207630i
$672$		0			0
$673$	0.885256	+	0.568920i	0.0341241	+	0.0219302i	0.557592	−	0.830115i	$-0.311726\pi$
$673$	0.885256	+	0.568920i	0.0341241	+	0.0219302i	−0.523468	+	0.852046i	$0.675362\pi$
$674$		0			0
$675$	3.37102	−	3.89036i	0.129751	−	0.149740i
$676$		0			0
$677$	−10.3281	−	22.6154i	−0.396941	−	0.869180i	−0.997571	−	0.0696528i	$-0.977811\pi$
$677$	−10.3281	−	22.6154i	−0.396941	−	0.869180i	0.600630	−	0.799527i	$-0.294916\pi$
$678$		0			0
$679$	59.1073	+	17.3555i	2.26833	+	0.666042i
$680$		0			0
$681$	−1.34616	+	9.36274i	−0.0515849	+	0.358781i
$682$		0			0
$683$	16.6253	−	36.4044i	0.636150	−	1.39297i	−0.267020	−	0.963691i	$-0.586039\pi$
$683$	16.6253	−	36.4044i	0.636150	−	1.39297i	0.903170	−	0.429283i	$-0.141234\pi$
$684$		0			0
$685$	5.96220	+	41.4680i	0.227804	+	1.58441i
$686$		0			0
$687$	−10.6992	−	12.3475i	−0.408199	−	0.471086i
$688$		0			0
$689$	−6.15018			−0.234303
$690$		0			0
$691$	−4.88876			−0.185977			−0.0929886	−	0.995667i	$-0.529642\pi$
$691$	−4.88876			−0.185977			−0.0929886	+	0.995667i	$0.529642\pi$
$692$		0			0
$693$	−7.03549	−	8.11938i	−0.267256	−	0.308430i
$694$		0			0
$695$	−0.0330125	−	0.229607i	−0.00125223	−	0.00870948i
$696$		0			0
$697$	3.65377	−	8.00064i	0.138396	−	0.303046i
$698$		0			0
$699$	3.79819	−	26.4170i	0.143661	−	0.999183i
$700$		0			0
$701$	−6.34687	−	1.86361i	−0.239718	−	0.0703875i	0.159667	−	0.987171i	$-0.448958\pi$
$701$	−6.34687	−	1.86361i	−0.239718	−	0.0703875i	−0.399385	+	0.916783i	$0.630776\pi$
$702$		0			0
$703$	−13.6202	−	29.8241i	−0.513697	−	1.12484i
$704$		0			0
$705$	−6.13541	+	7.08064i	−0.231073	+	0.266672i
$706$		0			0
$707$	−59.5709	−	38.2839i	−2.24039	−	1.43981i
$708$		0			0
$709$	5.57750	−	3.58444i	0.209467	−	0.134616i	−0.431701	−	0.902017i	$-0.642086\pi$
$709$	5.57750	−	3.58444i	0.209467	−	0.134616i	0.641168	+	0.767400i	$0.278450\pi$
$710$		0			0
$711$	−13.8348	+	4.06225i	−0.518844	+	0.152346i
$712$		0			0
$713$	18.5023	−	25.1878i	0.692918	−	0.943292i
$714$		0			0
$715$	−5.57102	+	1.63580i	−0.208344	+	0.0611754i
$716$		0			0
$717$	−2.62569	+	1.68743i	−0.0980582	+	0.0630182i
$718$		0			0
$719$	0.804416	+	0.516967i	0.0299997	+	0.0192796i	0.555555	−	0.831480i	$-0.312506\pi$
$719$	0.804416	+	0.516967i	0.0299997	+	0.0192796i	−0.525555	+	0.850760i	$0.676142\pi$
$720$		0			0
$721$	4.57949	−	5.28502i	0.170549	−	0.196824i
$722$		0			0
$723$	2.25175	+	4.93065i	0.0837436	+	0.183373i
$724$		0			0
$725$	7.78159	+	2.28488i	0.289001	+	0.0848583i
$726$		0			0
$727$	−2.60882	+	18.1447i	−0.0967557	+	0.672951i	0.882499	+	0.470315i	$0.155860\pi$
$727$	−2.60882	+	18.1447i	−0.0967557	+	0.672951i	−0.979254	+	0.202635i	$0.935049\pi$
$728$		0			0
$729$	12.2397	−	26.8012i	0.453322	−	0.992636i
$730$		0			0
$731$	−0.678206	−	4.71703i	−0.0250844	−	0.174466i
$732$		0			0
$733$	1.80200	+	2.07961i	0.0665582	+	0.0768123i	0.788052	−	0.615608i	$-0.211090\pi$
$733$	1.80200	+	2.07961i	0.0665582	+	0.0768123i	−0.721494	+	0.692421i	$0.756544\pi$
$734$		0			0
$735$	49.6391			1.83096
$736$		0			0
$737$	−5.79238			−0.213365
$738$		0			0
$739$	15.2461	+	17.5949i	0.560837	+	0.647240i	0.963373	−	0.268164i	$-0.0864169\pi$
$739$	15.2461	+	17.5949i	0.560837	+	0.647240i	−0.402537	+	0.915404i	$0.631871\pi$
$740$		0			0
$741$	0.850707	+	5.91680i	0.0312515	+	0.217359i
$742$		0			0
$743$	13.9109	−	30.4607i	0.510343	−	1.11750i	−0.462625	−	0.886554i	$-0.653092\pi$
$743$	13.9109	−	30.4607i	0.510343	−	1.11750i	0.972968	−	0.230941i	$-0.0741804\pi$
$744$		0			0
$745$	3.71931	−	25.8684i	0.136265	−	0.947744i
$746$		0			0
$747$	−6.28517	−	1.84549i	−0.229962	−	0.0675230i
$748$		0			0
$749$	24.7881	+	54.2784i	0.905738	+	1.98329i
$750$		0			0
$751$	−8.27355	+	9.54818i	−0.301906	+	0.348418i	−0.886350	−	0.463016i	$-0.846767\pi$
$751$	−8.27355	+	9.54818i	−0.301906	+	0.348418i	0.584444	+	0.811434i	$0.301313\pi$
$752$		0			0
$753$	24.0544	+	15.4588i	0.876590	+	0.563350i
$754$		0			0
$755$	4.56042	−	2.93081i	0.165971	−	0.106663i
$756$		0			0
$757$	11.9747	−	3.51609i	0.435228	−	0.127794i	−0.0567771	−	0.998387i	$-0.518082\pi$
$757$	11.9747	−	3.51609i	0.435228	−	0.127794i	0.492005	+	0.870592i	$0.336264\pi$
$758$		0			0
$759$	−8.13259	−	14.5787i	−0.295194	−	0.529175i
$760$		0			0
$761$	−38.6184	+	11.3394i	−1.39991	+	0.411052i	−0.892655	−	0.450741i	$-0.851160\pi$
$761$	−38.6184	+	11.3394i	−1.39991	+	0.411052i	−0.507260	+	0.861793i	$0.669341\pi$
$762$		0			0
$763$	66.3805	−	42.6602i	2.40314	−	1.54440i
$764$		0			0
$765$	−1.89369	−	1.21700i	−0.0684665	−	0.0440007i
$766$		0			0
$767$	4.59498	−	5.30289i	0.165915	−	0.191476i
$768$		0			0
$769$	−4.13363	−	9.05139i	−0.149063	−	0.326401i	0.820341	−	0.571875i	$-0.193784\pi$
$769$	−4.13363	−	9.05139i	−0.149063	−	0.326401i	−0.969403	+	0.245474i	$0.921057\pi$
$770$		0			0
$771$	−16.0344	−	4.70813i	−0.577465	−	0.169559i
$772$		0			0
$773$	7.13150	−	49.6006i	0.256502	−	1.78401i	−0.300786	−	0.953692i	$-0.597249\pi$
$773$	7.13150	−	49.6006i	0.256502	−	1.78401i	0.557288	−	0.830319i	$-0.311842\pi$
$774$		0			0
$775$	2.46529	−	5.39824i	0.0885560	−	0.193911i
$776$		0			0
$777$	−9.52108	−	66.2206i	−0.341567	−	2.37565i
$778$		0			0
$779$	−16.3505	−	18.8695i	−0.585817	−	0.676069i
$780$		0			0
$781$	18.8970			0.676187
$782$		0			0
$783$	50.3416			1.79906
$784$		0			0
$785$	−24.2950	−	28.0379i	−0.867126	−	1.00072i
$786$		0			0
$787$	1.69032	+	11.7564i	0.0602533	+	0.419071i	0.997516	+	0.0704459i	$0.0224422\pi$
$787$	1.69032	+	11.7564i	0.0602533	+	0.419071i	−0.937262	+	0.348625i	$0.886649\pi$
$788$		0			0
$789$	−12.5952	+	27.5797i	−0.448402	+	0.981864i
$790$		0			0
$791$	−4.29298	+	29.8584i	−0.152641	+	1.06164i
$792$		0			0
$793$	4.72529	+	1.38747i	0.167800	+	0.0492705i
$794$		0			0
$795$	6.26353	+	13.7152i	0.222144	+	0.486428i
$796$		0			0
$797$	10.1813	−	11.7499i	0.360642	−	0.416203i	−0.546213	−	0.837646i	$-0.683931\pi$
$797$	10.1813	−	11.7499i	0.360642	−	0.416203i	0.906855	+	0.421444i	$0.138476\pi$
$798$		0			0
$799$	−3.29527	−	2.11774i	−0.116578	−	0.0749204i
$800$		0			0
$801$	−2.42805	+	1.56041i	−0.0857910	+	0.0551345i
$802$		0			0
$803$	−25.3995	+	7.45797i	−0.896329	+	0.263186i
$804$		0			0
$805$	−46.4986	−	9.67561i	−1.63886	−	0.341020i
$806$		0			0
$807$	36.4296	−	10.6967i	1.28238	−	0.376541i
$808$		0			0
$809$	28.2390	−	18.1481i	0.992829	−	0.638052i	0.0599345	−	0.998202i	$-0.480911\pi$
$809$	28.2390	−	18.1481i	0.992829	−	0.638052i	0.932894	+	0.360150i	$0.117274\pi$
$810$		0			0
$811$	−39.2773	−	25.2420i	−1.37921	−	0.886367i	−0.379961	−	0.925003i	$-0.624063\pi$
$811$	−39.2773	−	25.2420i	−1.37921	−	0.886367i	−0.999253	+	0.0386353i	$0.987699\pi$
$812$		0			0
$813$	−26.3362	+	30.3936i	−0.923652	+	1.06595i
$814$		0			0
$815$	−8.21609	−	17.9907i	−0.287797	−	0.630188i
$816$		0			0
$817$	−12.9800	−	3.81129i	−0.454114	−	0.133340i
$818$		0			0
$819$	0.756903	−	5.26437i	0.0264483	−	0.183952i
$820$		0			0
$821$	−10.2323	+	22.4056i	−0.357110	+	0.781962i	0.642764	+	0.766065i	$0.277788\pi$
$821$	−10.2323	+	22.4056i	−0.357110	+	0.781962i	−0.999874	+	0.0158973i	$0.994940\pi$
$822$		0			0
$823$	−3.88031	−	26.9882i	−0.135259	−	0.940748i	−0.938546	−	0.345155i	$-0.887826\pi$
$823$	−3.88031	−	26.9882i	−0.135259	−	0.940748i	0.803287	−	0.595593i	$-0.203083\pi$
$824$		0			0
$825$	−2.07583	−	2.39564i	−0.0722712	−	0.0834054i
$826$		0			0
$827$	−35.1129			−1.22100			−0.610498	−	0.792018i	$-0.709031\pi$
$827$	−35.1129			−1.22100			−0.610498	+	0.792018i	$0.709031\pi$
$828$		0			0
$829$	4.43108			0.153898			0.0769488	−	0.997035i	$-0.475482\pi$
$829$	4.43108			0.153898			0.0769488	+	0.997035i	$0.475482\pi$
$830$		0			0
$831$	14.2906	+	16.4922i	0.495735	+	0.572109i
$832$		0			0
$833$	2.95355	+	20.5424i	0.102334	+	0.711751i
$834$		0			0
$835$	−13.0837	+	28.6493i	−0.452780	+	0.991451i
$836$		0			0
$837$	5.24249	−	36.4623i	0.181207	−	1.26032i
$838$		0			0
$839$	−5.58428	−	1.63969i	−0.192791	−	0.0566085i	0.183912	−	0.982943i	$-0.441124\pi$
$839$	−5.58428	−	1.63969i	−0.192791	−	0.0566085i	−0.376703	+	0.926334i	$0.622942\pi$
$840$		0			0
$841$	20.9006	+	45.7658i	0.720709	+	1.57813i
$842$		0			0
$843$	−7.13124	+	8.22989i	−0.245613	+	0.283452i
$844$		0			0
$845$	19.6975	+	12.6588i	0.677613	+	0.435476i
$846$		0			0
$847$	21.4236	−	13.7681i	0.736122	−	0.473077i
$848$		0			0
$849$	5.01751	−	1.47327i	0.172201	−	0.0505626i
$850$		0			0
$851$	−2.82468	+	45.2402i	−0.0968290	+	1.55081i
$852$		0			0
$853$	37.8674	−	11.1189i	1.29655	−	0.380703i	0.440576	−	0.897715i	$-0.354774\pi$
$853$	37.8674	−	11.1189i	1.29655	−	0.380703i	0.855978	+	0.517012i	$0.172956\pi$
$854$		0			0
$855$	−5.37566	+	3.45473i	−0.183844	+	0.118149i
$856$		0			0
$857$	9.20302	+	5.91442i	0.314369	+	0.202033i	0.688304	−	0.725422i	$-0.258355\pi$
$857$	9.20302	+	5.91442i	0.314369	+	0.202033i	−0.373935	+	0.927455i	$0.621992\pi$
$858$		0			0
$859$	−12.3814	+	14.2889i	−0.422447	+	0.487530i	−0.926581	−	0.376096i	$-0.877266\pi$
$859$	−12.3814	+	14.2889i	−0.422447	+	0.487530i	0.504134	+	0.863625i	$0.331812\pi$
$860$		0			0
$861$	−21.1640	−	46.3427i	−0.721267	−	1.57936i
$862$		0			0
$863$	−13.7174	−	4.02779i	−0.466946	−	0.137108i	0.0397918	−	0.999208i	$-0.487331\pi$
$863$	−13.7174	−	4.02779i	−0.466946	−	0.137108i	−0.506738	+	0.862100i	$0.669149\pi$
$864$		0			0
$865$	−0.856170	+	5.95479i	−0.0291107	+	0.202469i
$866$		0			0
$867$	9.31062	−	20.3874i	0.316205	−	0.692393i
$868$		0			0
$869$	5.42512	+	37.7325i	0.184035	+	1.27999i
$870$		0			0
$871$	−1.87781	−	2.16710i	−0.0636271	−	0.0734295i
$872$		0			0
$873$	−11.4585			−0.387811
$874$		0			0
$875$	−58.5351			−1.97885
$876$		0			0
$877$	−8.63189	−	9.96173i	−0.291478	−	0.336384i	0.591057	−	0.806630i	$-0.298711\pi$
$877$	−8.63189	−	9.96173i	−0.291478	−	0.336384i	−0.882535	+	0.470246i	$0.844165\pi$
$878$		0			0
$879$	−1.80476	−	12.5524i	−0.0608732	−	0.423382i
$880$		0			0
$881$	15.7928	−	34.5813i	0.532071	−	1.16507i	−0.432592	−	0.901590i	$-0.642401\pi$
$881$	15.7928	−	34.5813i	0.532071	−	1.16507i	0.964664	−	0.263484i	$-0.0848717\pi$
$882$		0			0
$883$	−4.42012	+	30.7426i	−0.148749	+	1.03457i	0.769523	+	0.638619i	$0.220494\pi$
$883$	−4.42012	+	30.7426i	−0.148749	+	1.03457i	−0.918272	+	0.395951i	$0.870415\pi$
$884$		0			0
$885$	−16.5054	−	4.84642i	−0.554822	−	0.162910i
$886$		0			0
$887$	−4.19498	−	9.18572i	−0.140854	−	0.308426i	0.826038	−	0.563615i	$-0.190590\pi$
$887$	−4.19498	−	9.18572i	−0.140854	−	0.308426i	−0.966891	+	0.255189i	$0.917862\pi$
$888$		0			0
$889$	53.5560	−	61.8069i	1.79621	−	2.07294i
$890$		0			0
$891$	−11.0162	−	7.07971i	−0.369058	−	0.237179i
$892$		0			0
$893$	−9.35437	+	6.01169i	−0.313032	+	0.201173i
$894$		0			0
$895$	−2.08082	+	0.610985i	−0.0695543	+	0.0204230i
$896$		0			0
$897$	2.81787	−	7.76887i	0.0940861	−	0.259395i
$898$		0			0
$899$	55.6857	−	16.3508i	1.85722	−	0.545329i
$900$		0			0
$901$	−5.30315	+	3.40813i	−0.176674	+	0.113541i
$902$		0			0
$903$	−23.2218	−	14.9237i	−0.772772	−	0.496630i
$904$		0			0
$905$	−17.0933	+	19.7267i	−0.568200	+	0.655738i
$906$		0			0
$907$	4.42315	+	9.68536i	0.146868	+	0.321597i	0.968741	−	0.248074i	$-0.0797977\pi$
$907$	4.42315	+	9.68536i	0.146868	+	0.321597i	−0.821873	+	0.569671i	$0.807070\pi$
$908$		0			0
$909$	12.6379	+	3.71083i	0.419174	+	0.123081i
$910$		0			0
$911$	−0.616648	+	4.28888i	−0.0204305	+	0.142097i	−0.997483	−	0.0708992i	$-0.977413\pi$
$911$	−0.616648	+	4.28888i	−0.0204305	+	0.142097i	0.977053	+	0.212996i	$0.0683222\pi$
$912$		0			0
$913$	−7.19427	+	15.7533i	−0.238096	+	0.521357i
$914$		0			0
$915$	−1.71825	−	11.9507i	−0.0568035	−	0.395077i
$916$		0			0
$917$	7.34616	+	8.47792i	0.242591	+	0.279965i
$918$		0			0
$919$	−21.0208			−0.693411			−0.346705	−	0.937974i	$-0.612700\pi$
$919$	−21.0208			−0.693411			−0.346705	+	0.937974i	$0.612700\pi$
$920$		0			0
$921$	41.9212			1.38135
$922$		0			0
$923$	6.12612	+	7.06992i	0.201644	+	0.232709i
$924$		0			0
$925$	1.22493	+	8.51957i	0.0402754	+	0.280122i
$926$		0			0
$927$	−0.540353	+	1.18321i	−0.0177475	+	0.0388617i
$928$		0			0
$929$	6.62972	−	46.1107i	0.217514	−	1.51284i	−0.529657	−	0.848212i	$-0.677680\pi$
$929$	6.62972	−	46.1107i	0.217514	−	1.51284i	0.747171	−	0.664631i	$-0.231411\pi$
$930$		0			0
$931$	56.5273	+	16.5979i	1.85261	+	0.543975i
$932$		0			0
$933$	5.95382	+	13.0370i	0.194919	+	0.426814i
$934$		0			0
$935$	−3.89727	+	4.49769i	−0.127454	+	0.147090i
$936$		0			0
$937$	−2.68085	−	1.72288i	−0.0875796	−	0.0562840i	0.496118	−	0.868255i	$-0.334758\pi$
$937$	−2.68085	−	1.72288i	−0.0875796	−	0.0562840i	−0.583698	+	0.811971i	$0.698395\pi$
$938$		0			0
$939$	−2.12258	+	1.36410i	−0.0692679	+	0.0445158i
$940$		0			0
$941$	28.1409	−	8.26293i	0.917369	−	0.269364i	0.211229	−	0.977437i	$-0.432253\pi$
$941$	28.1409	−	8.26293i	0.917369	−	0.269364i	0.706139	+	0.708073i	$0.250435\pi$
$942$		0			0
$943$	7.64210	+	33.6617i	0.248861	+	1.09617i
$944$		0			0
$945$	−53.7129	+	15.7715i	−1.74728	+	0.513048i
$946$		0			0
$947$	7.93653	−	5.10050i	0.257903	−	0.165744i	−0.405300	−	0.914184i	$-0.632833\pi$
$947$	7.93653	−	5.10050i	0.257903	−	0.165744i	0.663203	+	0.748440i	$0.269197\pi$
$948$		0			0
$949$	−11.0244	−	7.08496i	−0.357867	−	0.229987i
$950$		0			0
$951$	10.0682	−	11.6193i	0.326483	−	0.376782i
$952$		0			0
$953$	8.17663	+	17.9043i	0.264867	+	0.579978i	0.994603	−	0.103751i	$-0.0330845\pi$
$953$	8.17663	+	17.9043i	0.264867	+	0.579978i	−0.729736	+	0.683729i	$0.760357\pi$
$954$		0			0
$955$	42.9417	+	12.6088i	1.38956	+	0.408012i
$956$		0			0
$957$	4.41173	−	30.6843i	0.142611	−	0.991881i
$958$		0			0
$959$	−42.1469	+	92.2887i	−1.36099	+	2.98016i
$960$		0			0
$961$	−1.63207	−	11.3513i	−0.0526474	−	0.366171i
$962$		0			0
$963$	−7.26838	−	8.38816i	−0.234220	−	0.270305i
$964$		0			0
$965$	−6.76766			−0.217859
$966$		0			0
$967$	15.0388			0.483616			0.241808	−	0.970324i	$-0.422260\pi$
$967$	15.0388			0.483616			0.241808	+	0.970324i	$0.422260\pi$
$968$		0			0
$969$	4.01234	+	4.63049i	0.128895	+	0.148753i
$970$		0			0
$971$	−0.818893	−	5.69552i	−0.0262795	−	0.182778i	0.972454	−	0.233096i	$-0.0748856\pi$
$971$	−0.818893	−	5.69552i	−0.0262795	−	0.182778i	−0.998733	+	0.0503179i	$0.983977\pi$
$972$		0			0
$973$	0.233366	−	0.511000i	0.00748136	−	0.0163819i
$974$		0			0
$975$	0.223326	−	1.55326i	0.00715214	−	0.0497442i
$976$		0			0
$977$	48.3172	+	14.1872i	1.54580	+	0.453889i	0.939843	−	0.341607i	$-0.110971\pi$
$977$	48.3172	+	14.1872i	1.54580	+	0.453889i	0.605960	+	0.795495i	$0.292789\pi$
$978$		0			0
$979$	3.16988	+	6.94107i	0.101310	+	0.221838i
$980$		0			0
$981$	−9.61147	+	11.0922i	−0.306871	+	0.354148i
$982$		0			0
$983$	7.91299	+	5.08537i	0.252385	+	0.162198i	0.660716	−	0.750636i	$-0.270253\pi$
$983$	7.91299	+	5.08537i	0.252385	+	0.162198i	−0.408331	+	0.912834i	$0.633889\pi$
$984$		0			0
$985$	8.08760	−	5.19758i	0.257692	−	0.165609i
$986$		0			0
$987$	−21.7702	+	6.39232i	−0.692954	+	0.203470i
$988$		0			0
$989$	13.3438	+	13.1046i	0.424307	+	0.416701i
$990$		0			0
$991$	−20.7895	+	6.10435i	−0.660401	+	0.193911i	−0.594724	−	0.803930i	$-0.702739\pi$
$991$	−20.7895	+	6.10435i	−0.660401	+	0.193911i	−0.0656765	+	0.997841i	$0.520921\pi$
$992$		0			0
$993$	−12.9220	+	8.30446i	−0.410067	+	0.263534i
$994$		0			0
$995$	15.8081	+	10.1593i	0.501151	+	0.322070i
$996$		0			0
$997$	−5.08200	+	5.86494i	−0.160949	+	0.185745i	−0.830496	−	0.557025i	$-0.811943\pi$
$997$	−5.08200	+	5.86494i	−0.160949	+	0.185745i	0.669547	+	0.742770i	$0.266488\pi$
$998$		0			0
$999$	22.1944	+	48.5990i	0.702200	+	1.53760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.193.2		30
4.3	odd	2		184.2.i.b.9.2	✓	30
23.8	even	11		8464.2.a.cg.1.6		15
23.15	odd	22		8464.2.a.ch.1.6		15
23.18	even	11	inner	368.2.m.e.225.2		30
92.15	even	22		4232.2.a.ba.1.10		15
92.31	odd	22		4232.2.a.bb.1.10		15
92.87	odd	22		184.2.i.b.41.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.9.2	✓	30	4.3	odd	2
184.2.i.b.41.2	yes	30	92.87	odd	22
368.2.m.e.193.2		30	1.1	even	1	trivial
368.2.m.e.225.2		30	23.18	even	11	inner
4232.2.a.ba.1.10		15	92.15	even	22
4232.2.a.bb.1.10		15	92.31	odd	22
8464.2.a.cg.1.6		15	23.8	even	11
8464.2.a.ch.1.6		15	23.15	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.946512 + 1.09233i) q^{3} +(0.287791 + 2.00163i) q^{5} +(-2.03440 + 4.45471i) q^{7} +(0.129638 - 0.901650i) q^{9} +(-2.31075 - 0.678496i) q^{11} +(-0.495265 - 1.08448i) q^{13} +(-1.91405 + 2.20893i) q^{15} +(-1.02802 - 0.660668i) q^{17} +(-2.91826 + 1.87545i) q^{19} +(-6.79161 + 1.99420i) q^{21} +(4.78032 - 0.385375i) q^{23} +(0.873770 - 0.256562i) q^{25} +(4.75536 - 3.05608i) q^{27} +(7.49200 + 4.81481i) q^{29} +(4.26756 - 4.92503i) q^{31} +(-1.44601 - 3.16631i) q^{33} +(-9.50215 - 2.79008i) q^{35} +(-1.34510 + 9.35539i) q^{37} +(0.715838 - 1.56747i) q^{39} +(1.02432 + 7.12429i) q^{41} +(2.55380 + 2.94724i) q^{43} +1.84208 q^{45} +3.20546 q^{47} +(-11.1216 - 12.8350i) q^{49} +(-0.251363 - 1.74827i) q^{51} +(2.14296 - 4.69244i) q^{53} +(0.693086 - 4.82052i) q^{55} +(-4.81079 - 1.41257i) q^{57} +(2.44490 + 5.35359i) q^{59} +(-2.70508 + 3.12183i) q^{61} +(3.75285 + 2.41181i) q^{63} +(2.02819 - 1.30344i) q^{65} +(2.30775 - 0.677616i) q^{67} +(4.94559 + 4.85694i) q^{69} +(-7.52876 + 2.21064i) q^{71} +(9.24698 - 5.94267i) q^{73} +(1.10729 + 0.711609i) q^{75} +(7.72348 - 8.91337i) q^{77} +(-6.57553 - 14.3984i) q^{79} +(5.21720 + 1.53191i) q^{81} +(1.02340 - 7.11789i) q^{83} +(1.02656 - 2.24785i) q^{85} +(1.83189 + 12.7410i) q^{87} +(-2.07491 - 2.39457i) q^{89} +5.83860 q^{91} +9.41908 q^{93} +(-4.59381 - 5.30154i) q^{95} +(-1.79018 - 12.4510i) q^{97} +(-0.911326 + 1.99553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

L-functions

Modular forms

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Database

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