LMFDB - Embedded newform 368.2.m.e.289.2

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			289.2
Character	$\chi$	$=$	368.289
Dual form			368.2.m.e.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21882 - 0.783290i) q^{3} +(-1.24491 + 2.72597i) q^{5} +(-1.62369 - 0.476758i) q^{7} +(-0.374258 - 0.819511i) q^{9} +O(q^{10})$	\(q+(-1.21882 - 0.783290i) q^{3} +(-1.24491 + 2.72597i) q^{5} +(-1.62369 - 0.476758i) q^{7} +(-0.374258 - 0.819511i) q^{9} +(3.72943 - 4.30399i) q^{11} +(6.20950 - 1.82327i) q^{13} +(3.65254 - 2.34735i) q^{15} +(-0.846356 - 5.88654i) q^{17} +(0.0398636 - 0.277257i) q^{19} +(1.60555 + 1.85290i) q^{21} +(-4.79340 + 0.152709i) q^{23} +(-2.60679 - 3.00840i) q^{25} +(-0.804325 + 5.59421i) q^{27} +(-0.171530 - 1.19302i) q^{29} +(2.51819 - 1.61834i) q^{31} +(-7.91679 + 2.32458i) q^{33} +(3.32097 - 3.83260i) q^{35} +(0.110238 + 0.241387i) q^{37} +(-8.99644 - 2.64159i) q^{39} +(2.41581 - 5.28989i) q^{41} +(4.76425 + 3.06179i) q^{43} +2.69988 q^{45} +1.51532 q^{47} +(-3.47971 - 2.23627i) q^{49} +(-3.57931 + 7.83759i) q^{51} +(-6.33809 - 1.86103i) q^{53} +(7.08974 + 15.5244i) q^{55} +(-0.265760 + 0.306703i) q^{57} +(3.08055 - 0.904532i) q^{59} +(7.37216 - 4.73780i) q^{61} +(0.216970 + 1.50906i) q^{63} +(-2.76007 + 19.1967i) q^{65} +(-2.04000 - 2.35428i) q^{67} +(5.96192 + 3.56850i) q^{69} +(-1.43689 - 1.65826i) q^{71} +(-1.80221 + 12.5346i) q^{73} +(0.820770 + 5.70858i) q^{75} +(-8.10739 + 5.21030i) q^{77} +(0.627270 - 0.184183i) q^{79} +(3.59227 - 4.14571i) q^{81} +(-5.74370 - 12.5769i) q^{83} +(17.1001 + 5.02105i) q^{85} +(-0.725415 + 1.58844i) q^{87} +(-8.24726 - 5.30019i) q^{89} -10.9516 q^{91} -4.33686 q^{93} +(0.706168 + 0.453826i) q^{95} +(1.58933 - 3.48015i) q^{97} +(-4.92294 - 1.44550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

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
$3$	−1.21882	−	0.783290i	−0.703688	−	0.452233i	0.139240	−	0.990259i	$-0.455534\pi$
$3$	−1.21882	−	0.783290i	−0.703688	−	0.452233i	−0.842928	+	0.538026i	$0.819170\pi$
$4$		0			0
$5$	−1.24491	+	2.72597i	−0.556739	+	1.21909i	0.396824	+	0.917895i	$0.370112\pi$
$5$	−1.24491	+	2.72597i	−0.556739	+	1.21909i	−0.953563	+	0.301194i	$0.902615\pi$
$6$		0			0
$7$	−1.62369	−	0.476758i	−0.613697	−	0.180198i	−0.0399111	−	0.999203i	$-0.512707\pi$
$7$	−1.62369	−	0.476758i	−0.613697	−	0.180198i	−0.573785	+	0.819006i	$0.694526\pi$
$8$		0			0
$9$	−0.374258	−	0.819511i	−0.124753	−	0.273170i
$10$		0			0
$11$	3.72943	−	4.30399i	1.12447	−	1.29770i	0.174741	−	0.984614i	$-0.444091\pi$
$11$	3.72943	−	4.30399i	1.12447	−	1.29770i	0.949724	−	0.313087i	$-0.101363\pi$
$12$		0			0
$13$	6.20950	−	1.82327i	1.72221	−	0.505685i	0.736830	−	0.676078i	$-0.236322\pi$
$13$	6.20950	−	1.82327i	1.72221	−	0.505685i	0.985376	+	0.170393i	$0.0545038\pi$
$14$		0			0
$15$	3.65254	−	2.34735i	0.943083	−	0.606083i
$16$		0			0
$17$	−0.846356	−	5.88654i	−0.205272	−	1.42769i	−0.788324	−	0.615260i	$-0.789051\pi$
$17$	−0.846356	−	5.88654i	−0.205272	−	1.42769i	0.583052	−	0.812435i	$-0.301858\pi$
$18$		0			0
$19$	0.0398636	−	0.277257i	0.00914533	−	0.0636072i	−0.984738	−	0.174045i	$-0.944316\pi$
$19$	0.0398636	−	0.277257i	0.00914533	−	0.0636072i	0.993883	+	0.110438i	$0.0352253\pi$
$20$		0			0
$21$	1.60555	+	1.85290i	0.350360	+	0.404337i
$22$		0			0
$23$	−4.79340	+	0.152709i	−0.999493	+	0.0318421i
$23$	−4.79340	+	0.152709i	−0.999493	+	0.0318421i
$24$		0			0
$25$	−2.60679	−	3.00840i	−0.521359	−	0.601680i
$26$		0			0
$27$	−0.804325	+	5.59421i	−0.154792	+	1.07661i
$28$		0			0
$29$	−0.171530	−	1.19302i	−0.0318524	−	0.221538i	0.967678	−	0.252190i	$-0.0811508\pi$
$29$	−0.171530	−	1.19302i	−0.0318524	−	0.221538i	−0.999530	+	0.0306519i	$0.990242\pi$
$30$		0			0
$31$	2.51819	−	1.61834i	0.452280	−	0.290663i	−0.294601	−	0.955620i	$-0.595187\pi$
$31$	2.51819	−	1.61834i	0.452280	−	0.290663i	0.746881	+	0.664958i	$0.231550\pi$
$32$		0			0
$33$	−7.91679	+	2.32458i	−1.37814	+	0.404657i
$34$		0			0
$35$	3.32097	−	3.83260i	0.561346	−	0.647828i
$36$		0			0
$37$	0.110238	+	0.241387i	0.0181230	+	0.0396838i	0.918477	−	0.395474i	$-0.129420\pi$
$37$	0.110238	+	0.241387i	0.0181230	+	0.0396838i	−0.900354	+	0.435158i	$0.856692\pi$
$38$		0			0
$39$	−8.99644	−	2.64159i	−1.44058	−	0.422993i
$40$		0			0
$41$	2.41581	−	5.28989i	0.377286	−	0.826142i	−0.621790	−	0.783184i	$-0.713594\pi$
$41$	2.41581	−	5.28989i	0.377286	−	0.826142i	0.999077	−	0.0429584i	$-0.0136783\pi$
$42$		0			0
$43$	4.76425	+	3.06179i	0.726541	+	0.466919i	0.850907	−	0.525317i	$-0.176053\pi$
$43$	4.76425	+	3.06179i	0.726541	+	0.466919i	−0.124366	+	0.992236i	$0.539690\pi$
$44$		0			0
$45$	2.69988			0.402474
$46$		0			0
$47$	1.51532			0.221032			0.110516	−	0.993874i	$-0.464750\pi$
$47$	1.51532			0.221032			0.110516	+	0.993874i	$0.464750\pi$
$48$		0			0
$49$	−3.47971	−	2.23627i	−0.497101	−	0.319468i
$50$		0			0
$51$	−3.57931	+	7.83759i	−0.501203	+	1.09748i
$52$		0			0
$53$	−6.33809	−	1.86103i	−0.870604	−	0.255632i	−0.184232	−	0.982883i	$-0.558980\pi$
$53$	−6.33809	−	1.86103i	−0.870604	−	0.255632i	−0.686372	+	0.727251i	$0.740798\pi$
$54$		0			0
$55$	7.08974	+	15.5244i	0.955980	+	2.09330i
$56$		0			0
$57$	−0.265760	+	0.306703i	−0.0352007	+	0.0406238i
$58$		0			0
$59$	3.08055	−	0.904532i	0.401054	−	0.117760i	−0.0749841	−	0.997185i	$-0.523891\pi$
$59$	3.08055	−	0.904532i	0.401054	−	0.117760i	0.476038	+	0.879425i	$0.342072\pi$
$60$		0			0
$61$	7.37216	−	4.73780i	0.943908	−	0.606613i	0.0244076	−	0.999702i	$-0.492230\pi$
$61$	7.37216	−	4.73780i	0.943908	−	0.606613i	0.919500	+	0.393089i	$0.128594\pi$
$62$		0			0
$63$	0.216970	+	1.50906i	0.0273357	+	0.190124i
$64$		0			0
$65$	−2.76007	+	19.1967i	−0.342344	+	2.38106i
$66$		0			0
$67$	−2.04000	−	2.35428i	−0.249225	−	0.287621i	0.617328	−	0.786706i	$-0.288215\pi$
$67$	−2.04000	−	2.35428i	−0.249225	−	0.287621i	−0.866553	+	0.499085i	$0.833670\pi$
$68$		0			0
$69$	5.96192	+	3.56850i	0.717731	+	0.429597i
$70$		0			0
$71$	−1.43689	−	1.65826i	−0.170528	−	0.196800i	0.664052	−	0.747686i	$-0.268835\pi$
$71$	−1.43689	−	1.65826i	−0.170528	−	0.196800i	−0.834580	+	0.550886i	$0.814290\pi$
$72$		0			0
$73$	−1.80221	+	12.5346i	−0.210933	+	1.46707i	0.559118	+	0.829088i	$0.311140\pi$
$73$	−1.80221	+	12.5346i	−0.210933	+	1.46707i	−0.770051	+	0.637982i	$0.779769\pi$
$74$		0			0
$75$	0.820770	+	5.70858i	0.0947744	+	0.659170i
$76$		0			0
$77$	−8.10739	+	5.21030i	−0.923923	+	0.593769i
$78$		0			0
$79$	0.627270	−	0.184183i	0.0705734	−	0.0207222i	−0.246255	−	0.969205i	$-0.579200\pi$
$79$	0.627270	−	0.184183i	0.0705734	−	0.0207222i	0.316829	+	0.948483i	$0.397382\pi$
$80$		0			0
$81$	3.59227	−	4.14571i	0.399142	−	0.460634i
$82$		0			0
$83$	−5.74370	−	12.5769i	−0.630453	−	1.38050i	−0.907667	−	0.419691i	$-0.862139\pi$
$83$	−5.74370	−	12.5769i	−0.630453	−	1.38050i	0.277215	−	0.960808i	$-0.410589\pi$
$84$		0			0
$85$	17.1001	+	5.02105i	1.85477	+	0.544610i
$86$		0			0
$87$	−0.725415	+	1.58844i	−0.0777727	+	0.170298i
$88$		0			0
$89$	−8.24726	−	5.30019i	−0.874208	−	0.561819i	0.0248295	−	0.999692i	$-0.492096\pi$
$89$	−8.24726	−	5.30019i	−0.874208	−	0.561819i	−0.899037	+	0.437873i	$0.855732\pi$
$90$		0			0
$91$	−10.9516			−1.14804
$92$		0			0
$93$	−4.33686			−0.449711
$94$		0			0
$95$	0.706168	+	0.453826i	0.0724513	+	0.0465616i
$96$		0			0
$97$	1.58933	−	3.48015i	0.161372	−	0.353355i	−0.811623	−	0.584182i	$-0.801416\pi$
$97$	1.58933	−	3.48015i	0.161372	−	0.353355i	0.972995	+	0.230826i	$0.0741429\pi$
$98$		0			0
$99$	−4.92294	−	1.44550i	−0.494774	−	0.145279i
$100$		0			0
$101$	8.10040	+	17.7374i	0.806020	+	1.76494i	0.623645	+	0.781708i	$0.285651\pi$
$101$	8.10040	+	17.7374i	0.806020	+	1.76494i	0.182375	+	0.983229i	$0.441622\pi$
$102$		0			0
$103$	10.4226	−	12.0283i	1.02697	−	1.18519i	0.0444521	−	0.999012i	$-0.485846\pi$
$103$	10.4226	−	12.0283i	1.02697	−	1.18519i	0.982517	−	0.186174i	$-0.0596087\pi$
$104$		0			0
$105$	−7.04971	+	2.06998i	−0.687981	+	0.202010i
$106$		0			0
$107$	−16.9209	+	10.8744i	−1.63580	+	1.05127i	−0.691400	+	0.722472i	$0.743006\pi$
$107$	−16.9209	+	10.8744i	−1.63580	+	1.05127i	−0.944402	+	0.328794i	$0.893358\pi$
$108$		0			0
$109$	0.111997	+	0.778955i	0.0107273	+	0.0746103i	0.994482	−	0.104909i	$-0.0334550\pi$
$109$	0.111997	+	0.778955i	0.0107273	+	0.0746103i	−0.983755	+	0.179519i	$0.942546\pi$
$110$		0			0
$111$	0.0547157	−	0.380556i	0.00519339	−	0.0361208i
$112$		0			0
$113$	3.29370	+	3.80113i	0.309845	+	0.357581i	0.889219	−	0.457481i	$-0.151248\pi$
$113$	3.29370	+	3.80113i	0.309845	+	0.357581i	−0.579374	+	0.815062i	$0.696703\pi$
$114$		0			0
$115$	5.55106	−	13.2568i	0.517639	−	1.23620i
$116$		0			0
$117$	−3.81815	−	4.40638i	−0.352988	−	0.407370i
$118$		0			0
$119$	−1.43223	+	9.96141i	−0.131293	+	0.913161i
$120$		0			0
$121$	−3.05023	−	21.2148i	−0.277294	−	1.92862i
$122$		0			0
$123$	−7.08797	+	4.55516i	−0.639100	+	0.410725i
$124$		0			0
$125$	−2.93093	+	0.860600i	−0.262151	+	0.0769744i
$126$		0			0
$127$	−5.25667	+	6.06652i	−0.466454	+	0.538317i	−0.939422	−	0.342763i	$-0.888637\pi$
$127$	−5.25667	+	6.06652i	−0.466454	+	0.538317i	0.472968	+	0.881080i	$0.343183\pi$
$128$		0			0
$129$	−3.40850	−	7.46357i	−0.300102	−	0.657131i
$130$		0			0
$131$	9.85560	+	2.89387i	0.861088	+	0.252838i	0.682321	−	0.731053i	$-0.260971\pi$
$131$	9.85560	+	2.89387i	0.861088	+	0.252838i	0.178767	+	0.983891i	$0.442789\pi$
$132$		0			0
$133$	−0.196911	+	0.431174i	−0.0170743	+	0.0373876i
$134$		0			0
$135$	−14.2483	−	9.15683i	−1.22630	−	0.788094i
$136$		0			0
$137$	−3.77645			−0.322644			−0.161322	−	0.986902i	$-0.551576\pi$
$137$	−3.77645			−0.322644			−0.161322	+	0.986902i	$0.551576\pi$
$138$		0			0
$139$	15.4948			1.31425			0.657127	−	0.753780i	$-0.271772\pi$
$139$	15.4948			1.31425			0.657127	+	0.753780i	$0.271772\pi$
$140$		0			0
$141$	−1.84691	−	1.18693i	−0.155538	−	0.0999579i
$142$		0			0
$143$	15.3105	−	33.5254i	1.28033	−	2.80354i
$144$		0			0
$145$	3.46567	+	1.01761i	0.287808	+	0.0845081i
$146$		0			0
$147$	2.48950	+	5.45124i	0.205330	+	0.449611i
$148$		0			0
$149$	−2.27098	+	2.62085i	−0.186046	+	0.214708i	−0.841109	−	0.540866i	$-0.818097\pi$
$149$	−2.27098	+	2.62085i	−0.186046	+	0.214708i	0.655063	+	0.755574i	$0.272642\pi$
$150$		0			0
$151$	6.92849	−	2.03439i	0.563832	−	0.165556i	0.0126188	−	0.999920i	$-0.495983\pi$
$151$	6.92849	−	2.03439i	0.563832	−	0.165556i	0.551213	+	0.834364i	$0.314165\pi$
$152$		0			0
$153$	−4.50733	+	2.89668i	−0.364396	+	0.234183i
$154$		0			0
$155$	1.27663	+	8.87918i	0.102542	+	0.713193i
$156$		0			0
$157$	−1.50395	+	10.4602i	−0.120029	+	0.834817i	0.837491	+	0.546450i	$0.184021\pi$
$157$	−1.50395	+	10.4602i	−0.120029	+	0.834817i	−0.957520	+	0.288367i	$0.906888\pi$
$158$		0			0
$159$	6.26728	+	7.23283i	0.497028	+	0.573601i
$160$		0			0
$161$	7.85579	+	2.03734i	0.619123	+	0.160565i
$162$		0			0
$163$	9.33884	+	10.7776i	0.731475	+	0.844167i	0.992637	−	0.121128i	$-0.0386512\pi$
$163$	9.33884	+	10.7776i	0.731475	+	0.844167i	−0.261162	+	0.965295i	$0.584106\pi$
$164$		0			0
$165$	3.51894	−	24.4748i	0.273949	−	1.90536i
$166$		0			0
$167$	3.16328	+	22.0011i	0.244782	+	1.70249i	0.627490	+	0.778624i	$0.284082\pi$
$167$	3.16328	+	22.0011i	0.244782	+	1.70249i	−0.382709	+	0.923869i	$0.625009\pi$
$168$		0			0
$169$	24.2973	−	15.6149i	1.86902	−	1.20115i
$170$		0			0
$171$	−0.242135	+	0.0710972i	−0.0185165	+	0.00543694i
$172$		0			0
$173$	6.62414	−	7.64466i	0.503624	−	0.581213i	−0.445831	−	0.895117i	$-0.647092\pi$
$173$	6.62414	−	7.64466i	0.503624	−	0.581213i	0.949455	+	0.313904i	$0.101637\pi$
$174$		0			0
$175$	2.79834	+	6.12751i	0.211535	+	0.463196i
$176$		0			0
$177$	−4.46316	−	1.31050i	−0.335472	−	0.0985034i
$178$		0			0
$179$	1.67035	−	3.65755i	0.124848	−	0.273378i	−0.836880	−	0.547387i	$-0.815623\pi$
$179$	1.67035	−	3.65755i	0.124848	−	0.273378i	0.961727	+	0.274009i	$0.0883498\pi$
$180$		0			0
$181$	−4.98075	−	3.20093i	−0.370216	−	0.237923i	0.342282	−	0.939597i	$-0.388800\pi$
$181$	−4.98075	−	3.20093i	−0.370216	−	0.237923i	−0.712498	+	0.701674i	$0.752436\pi$
$182$		0			0
$183$	−12.6964			−0.938547
$184$		0			0
$185$	−0.795249			−0.0584678
$186$		0			0
$187$	−28.4920	−	18.3107i	−2.08354	−	1.33901i
$188$		0			0
$189$	3.97306	−	8.69978i	0.288997	−	0.632816i
$190$		0			0
$191$	5.85265	+	1.71849i	0.423483	+	0.124346i	0.486528	−	0.873665i	$-0.338263\pi$
$191$	5.85265	+	1.71849i	0.423483	+	0.124346i	−0.0630454	+	0.998011i	$0.520081\pi$
$192$		0			0
$193$	−0.784737	−	1.71833i	−0.0564866	−	0.123688i	0.879284	−	0.476298i	$-0.158022\pi$
$193$	−0.784737	−	1.71833i	−0.0564866	−	0.123688i	−0.935771	+	0.352610i	$0.885294\pi$
$194$		0			0
$195$	18.4006	−	21.2354i	1.31770	−	1.52070i
$196$		0			0
$197$	−19.6275	+	5.76316i	−1.39840	+	0.410608i	−0.892135	−	0.451769i	$-0.850793\pi$
$197$	−19.6275	+	5.76316i	−1.39840	+	0.410608i	−0.506267	+	0.862377i	$0.668975\pi$
$198$		0			0
$199$	−1.91388	+	1.22998i	−0.135671	+	0.0871907i	−0.606716	−	0.794919i	$-0.707513\pi$
$199$	−1.91388	+	1.22998i	−0.135671	+	0.0871907i	0.471045	+	0.882109i	$0.343877\pi$
$200$		0			0
$201$	0.642310	+	4.46736i	0.0453050	+	0.315103i
$202$		0			0
$203$	−0.290270	+	2.01887i	−0.0203729	+	0.141697i
$204$		0			0
$205$	11.4126	+	13.1708i	0.797090	+	0.919891i
$206$		0			0
$207$	1.91912	+	3.87109i	0.133388	+	0.269059i
$208$		0			0
$209$	−1.04464	−	1.20558i	−0.0722596	−	0.0833920i
$210$		0			0
$211$	−0.248547	+	1.72869i	−0.0171107	+	0.119008i	−0.996587	−	0.0825536i	$-0.973692\pi$
$211$	−0.248547	+	1.72869i	−0.0171107	+	0.119008i	0.979476	+	0.201561i	$0.0646015\pi$
$212$		0			0
$213$	0.452418	+	3.14664i	0.0309992	+	0.215604i
$214$		0			0
$215$	−14.2774	+	9.17552i	−0.973710	+	0.625765i
$216$		0			0
$217$	−4.86031	+	1.42712i	−0.329939	+	0.0968790i
$218$		0			0
$219$	12.0148	−	13.8659i	0.811888	−	0.936969i
$220$		0			0
$221$	−15.9882	−	35.0093i	−1.07548	−	2.35498i
$222$		0			0
$223$	−9.61910	−	2.82442i	−0.644142	−	0.189137i	−0.0566846	−	0.998392i	$-0.518053\pi$
$223$	−9.61910	−	2.82442i	−0.644142	−	0.189137i	−0.587458	+	0.809255i	$0.699871\pi$
$224$		0			0
$225$	−1.48980	+	3.26221i	−0.0993202	+	0.217481i
$226$		0			0
$227$	9.25723	+	5.94926i	0.614424	+	0.394866i	0.810514	−	0.585720i	$-0.199188\pi$
$227$	9.25723	+	5.94926i	0.614424	+	0.394866i	−0.196090	+	0.980586i	$0.562824\pi$
$228$		0			0
$229$	−10.8863			−0.719384			−0.359692	−	0.933071i	$-0.617118\pi$
$229$	−10.8863			−0.719384			−0.359692	+	0.933071i	$0.617118\pi$
$230$		0			0
$231$	13.9627			0.918676
$232$		0			0
$233$	8.61756	+	5.53817i	0.564555	+	0.362818i	0.791574	−	0.611073i	$-0.209262\pi$
$233$	8.61756	+	5.53817i	0.564555	+	0.362818i	−0.227019	+	0.973890i	$0.572898\pi$
$234$		0			0
$235$	−1.88643	+	4.13071i	−0.123057	+	0.269458i
$236$		0			0
$237$	−0.908800	−	0.266848i	−0.0590329	−	0.0173336i
$238$		0			0
$239$	−6.43456	−	14.0897i	−0.416217	−	0.911389i	−0.995365	−	0.0961663i	$-0.969342\pi$
$239$	−6.43456	−	14.0897i	−0.416217	−	0.911389i	0.579148	−	0.815222i	$-0.303385\pi$
$240$		0			0
$241$	4.46587	−	5.15389i	0.287672	−	0.331991i	−0.593458	−	0.804865i	$-0.702238\pi$
$241$	4.46587	−	5.15389i	0.287672	−	0.331991i	0.881130	+	0.472874i	$0.156783\pi$
$242$		0			0
$243$	8.64275	−	2.53774i	0.554433	−	0.162796i
$244$		0			0
$245$	10.4279	−	6.70161i	0.666215	−	0.428150i
$246$		0			0
$247$	−0.257983	−	1.79431i	−0.0164151	−	0.114169i
$248$		0			0
$249$	−2.85084	+	19.8281i	−0.180665	+	1.25655i
$250$		0			0
$251$	−5.36728	−	6.19417i	−0.338780	−	0.390973i	0.560639	−	0.828060i	$-0.310555\pi$
$251$	−5.36728	−	6.19417i	−0.338780	−	0.390973i	−0.899419	+	0.437088i	$0.856010\pi$
$252$		0			0
$253$	−17.2194	+	21.2003i	−1.08257	+	1.33285i
$254$		0			0
$255$	−16.9091	−	19.5141i	−1.05889	−	1.22202i
$256$		0			0
$257$	0.362794	−	2.52329i	0.0226305	−	0.157398i	−0.975373	−	0.220563i	$-0.929210\pi$
$257$	0.362794	−	2.52329i	0.0226305	−	0.157398i	0.998003	+	0.0631652i	$0.0201195\pi$
$258$		0			0
$259$	−0.0639086	−	0.444494i	−0.00397109	−	0.0276195i
$260$		0			0
$261$	−0.913496	+	0.587068i	−0.0565440	+	0.0363386i
$262$		0			0
$263$	−2.98224	+	0.875664i	−0.183893	+	0.0539957i	−0.372382	−	0.928079i	$-0.621459\pi$
$263$	−2.98224	+	0.875664i	−0.183893	+	0.0539957i	0.188490	+	0.982075i	$0.439641\pi$
$264$		0			0
$265$	12.9634	−	14.9606i	0.796338	−	0.919023i
$266$		0			0
$267$	5.90036	+	12.9200i	0.361096	+	0.790691i
$268$		0			0
$269$	25.1319	+	7.37939i	1.53232	+	0.449929i	0.935759	−	0.352640i	$-0.114716\pi$
$269$	25.1319	+	7.37939i	1.53232	+	0.449929i	0.596559	+	0.802569i	$0.296534\pi$
$270$		0			0
$271$	6.14039	−	13.4456i	0.373002	−	0.816761i	−0.626306	−	0.779577i	$-0.715434\pi$
$271$	6.14039	−	13.4456i	0.373002	−	0.816761i	0.999308	−	0.0371837i	$-0.0118387\pi$
$272$		0			0
$273$	13.3480	+	8.57825i	0.807859	+	0.519179i
$274$		0			0
$275$	−22.6700			−1.36705
$276$		0			0
$277$	4.59471			0.276069			0.138035	−	0.990427i	$-0.455921\pi$
$277$	4.59471			0.276069			0.138035	+	0.990427i	$0.455921\pi$
$278$		0			0
$279$	−2.26870	−	1.45801i	−0.135824	−	0.0872885i
$280$		0			0
$281$	3.62633	−	7.94056i	0.216329	−	0.473694i	−0.770092	−	0.637933i	$-0.779790\pi$
$281$	3.62633	−	7.94056i	0.216329	−	0.473694i	0.986421	+	0.164239i	$0.0525169\pi$
$282$		0			0
$283$	24.1350	+	7.08667i	1.43468	+	0.421259i	0.904444	−	0.426593i	$-0.140286\pi$
$283$	24.1350	+	7.08667i	1.43468	+	0.421259i	0.530233	+	0.847852i	$0.322105\pi$
$284$		0			0
$285$	−0.505216	−	1.10627i	−0.0299264	−	0.0655297i
$286$		0			0
$287$	−6.44452	+	7.43738i	−0.380408	+	0.439014i
$288$		0			0
$289$	−17.6236	+	5.17476i	−1.03668	+	0.304398i
$290$		0			0
$291$	−4.66308	+	2.99678i	−0.273354	+	0.175674i
$292$		0			0
$293$	−2.86438	−	19.9222i	−0.167339	−	1.16387i	−0.884357	−	0.466812i	$-0.845403\pi$
$293$	−2.86438	−	19.9222i	−0.167339	−	1.16387i	0.717018	−	0.697055i	$-0.245506\pi$
$294$		0			0
$295$	−1.36928	+	9.52354i	−0.0797225	+	0.554482i
$296$		0			0
$297$	21.0777	+	24.3250i	1.22305	+	1.41148i
$298$		0			0
$299$	−29.4862	+	9.68793i	−1.70523	+	0.560267i
$300$		0			0
$301$	−6.27592	−	7.24279i	−0.361738	−	0.417468i
$302$		0			0
$303$	4.02058	−	27.9637i	0.230976	−	1.60647i
$304$		0			0
$305$	3.73743	+	25.9944i	0.214004	+	1.48843i
$306$		0			0
$307$	21.0792	−	13.5468i	1.20306	−	0.773157i	0.223573	−	0.974687i	$-0.428228\pi$
$307$	21.0792	−	13.5468i	1.20306	−	0.773157i	0.979482	+	0.201531i	$0.0645915\pi$
$308$		0			0
$309$	−22.1250	+	6.49648i	−1.25865	+	0.369572i
$310$		0			0
$311$	−8.65354	+	9.98672i	−0.490697	+	0.566295i	−0.946052	−	0.324015i	$-0.894967\pi$
$311$	−8.65354	+	9.98672i	−0.490697	+	0.566295i	0.455355	+	0.890310i	$0.349512\pi$
$312$		0			0
$313$	11.9242	+	26.1103i	0.673995	+	1.47584i	0.868883	+	0.495018i	$0.164838\pi$
$313$	11.9242	+	26.1103i	0.673995	+	1.47584i	−0.194888	+	0.980826i	$0.562434\pi$
$314$		0			0
$315$	−4.38376	−	1.28719i	−0.246997	−	0.0725248i
$316$		0			0
$317$	−1.90446	+	4.17020i	−0.106965	+	0.234222i	−0.955544	−	0.294847i	$-0.904731\pi$
$317$	−1.90446	+	4.17020i	−0.106965	+	0.234222i	0.848579	+	0.529069i	$0.177459\pi$
$318$		0			0
$319$	−5.77445	−	3.71101i	−0.323307	−	0.207777i
$320$		0			0
$321$	29.1413			1.62651
$322$		0			0
$323$	−1.66582			−0.0926889
$324$		0			0
$325$	−21.6720	−	13.9278i	−1.20215	−	0.772573i
$326$		0			0
$327$	0.473643	−	1.03713i	0.0261925	−	0.0573536i
$328$		0			0
$329$	−2.46041	−	0.722441i	−0.135647	−	0.0398294i
$330$		0			0
$331$	9.05452	+	19.8266i	0.497682	+	1.08977i	0.977216	+	0.212247i	$0.0680783\pi$
$331$	9.05452	+	19.8266i	0.497682	+	1.08977i	−0.479534	+	0.877523i	$0.659194\pi$
$332$		0			0
$333$	0.156562	−	0.180682i	0.00857954	−	0.00990132i
$334$		0			0
$335$	8.95730	−	2.63010i	0.489389	−	0.143698i
$336$		0			0
$337$	−13.6111	+	8.74729i	−0.741441	+	0.476495i	−0.856036	−	0.516917i	$-0.827080\pi$
$337$	−13.6111	+	8.74729i	−0.741441	+	0.476495i	0.114594	+	0.993412i	$0.463443\pi$
$338$		0			0
$339$	−1.03705	−	7.21283i	−0.0563248	−	0.391747i
$340$		0			0
$341$	2.42608	−	16.8737i	0.131380	−	0.913765i
$342$		0			0
$343$	12.3411	+	14.2423i	0.666354	+	0.769014i
$344$		0			0
$345$	−17.1496	+	11.8096i	−0.923306	+	0.635805i
$346$		0			0
$347$	−14.8262	−	17.1103i	−0.795910	−	0.918529i	0.202240	−	0.979336i	$-0.435178\pi$
$347$	−14.8262	−	17.1103i	−0.795910	−	0.918529i	−0.998150	+	0.0608074i	$0.980632\pi$
$348$		0			0
$349$	−2.85877	+	19.8832i	−0.153026	+	1.06432i	0.758083	+	0.652158i	$0.226136\pi$
$349$	−2.85877	+	19.8832i	−0.153026	+	1.06432i	−0.911110	+	0.412164i	$0.864773\pi$
$350$		0			0
$351$	5.20531	+	36.2037i	0.277839	+	1.93241i
$352$		0			0
$353$	−10.0158	+	6.43675i	−0.533086	+	0.342594i	−0.779330	−	0.626614i	$-0.784440\pi$
$353$	−10.0158	+	6.43675i	−0.533086	+	0.342594i	0.246243	+	0.969208i	$0.420804\pi$
$354$		0			0
$355$	6.30917	−	1.85254i	0.334856	−	0.0983226i
$356$		0			0
$357$	9.54832	−	11.0193i	0.505350	−	0.583206i
$358$		0			0
$359$	8.75463	+	19.1700i	0.462052	+	1.01175i	0.987015	+	0.160628i	$0.0513518\pi$
$359$	8.75463	+	19.1700i	0.462052	+	1.01175i	−0.524963	+	0.851125i	$0.675921\pi$
$360$		0			0
$361$	18.1551	+	5.33081i	0.955531	+	0.280569i
$362$		0			0
$363$	−12.8997	+	28.2463i	−0.677057	+	1.48255i
$364$		0			0
$365$	−31.9254	−	20.5172i	−1.67105	−	1.07392i
$366$		0			0
$367$	−20.0368			−1.04591			−0.522957	−	0.852359i	$-0.675171\pi$
$367$	−20.0368			−1.04591			−0.522957	+	0.852359i	$0.675171\pi$
$368$		0			0
$369$	−5.23926			−0.272745
$370$		0			0
$371$	9.40382	+	6.04347i	0.488222	+	0.313761i
$372$		0			0
$373$	−15.2895	+	33.4793i	−0.791660	+	1.73349i	−0.119820	+	0.992796i	$0.538232\pi$
$373$	−15.2895	+	33.4793i	−0.791660	+	1.73349i	−0.671839	+	0.740697i	$0.734495\pi$
$374$		0			0
$375$	4.24639	+	1.24685i	0.219283	+	0.0643872i
$376$		0			0
$377$	−3.24032	−	7.09531i	−0.166885	−	0.365427i
$378$		0			0
$379$	−18.8525	+	21.7570i	−0.968389	+	1.11758i	0.0246383	+	0.999696i	$0.492157\pi$
$379$	−18.8525	+	21.7570i	−0.968389	+	1.11758i	−0.993027	+	0.117884i	$0.962389\pi$
$380$		0			0
$381$	11.1588	−	3.27652i	0.571683	−	0.167861i
$382$		0			0
$383$	−4.93249	+	3.16992i	−0.252038	+	0.161975i	−0.660560	−	0.750774i	$-0.729681\pi$
$383$	−4.93249	+	3.16992i	−0.252038	+	0.161975i	0.408521	+	0.912749i	$0.366045\pi$
$384$		0			0
$385$	−4.11016	−	28.5868i	−0.209473	−	1.45692i
$386$		0			0
$387$	0.726117	−	5.05025i	0.0369106	−	0.256719i
$388$		0			0
$389$	−1.74414	−	2.01285i	−0.0884316	−	0.102056i	0.709809	−	0.704394i	$-0.248781\pi$
$389$	−1.74414	−	2.01285i	−0.0884316	−	0.102056i	−0.798241	+	0.602339i	$0.794236\pi$
$390$		0			0
$391$	4.95585	+	28.0873i	0.250628	+	1.42043i
$392$		0			0
$393$	−9.74550	−	11.2469i	−0.491596	−	0.567332i
$394$		0			0
$395$	−0.278816	+	1.93921i	−0.0140287	+	0.0975721i
$396$		0			0
$397$	−0.269534	−	1.87465i	−0.0135275	−	0.0940861i	0.981939	−	0.189197i	$-0.0605885\pi$
$397$	−0.269534	−	1.87465i	−0.0135275	−	0.0940861i	−0.995467	+	0.0951110i	$0.969679\pi$
$398$		0			0
$399$	0.577734	−	0.371287i	0.0289229	−	0.0185876i
$400$		0			0
$401$	20.4068	−	5.99199i	1.01907	−	0.299226i	0.270811	−	0.962633i	$-0.412708\pi$
$401$	20.4068	−	5.99199i	1.01907	−	0.299226i	0.748259	+	0.663407i	$0.230890\pi$
$402$		0			0
$403$	12.6860	−	14.6404i	0.631935	−	0.729292i
$404$		0			0
$405$	6.82900	+	14.9534i	0.339336	+	0.743042i
$406$		0			0
$407$	1.45005	+	0.425774i	0.0718764	+	0.0211048i
$408$		0			0
$409$	2.03619	−	4.45864i	0.100683	−	0.220466i	−0.852586	−	0.522586i	$-0.824967\pi$
$409$	2.03619	−	4.45864i	0.100683	−	0.220466i	0.953270	+	0.302121i	$0.0976945\pi$
$410$		0			0
$411$	4.60282	+	2.95805i	0.227040	+	0.145910i
$412$		0			0
$413$	−5.43310			−0.267346
$414$		0			0
$415$	41.4347			2.03395
$416$		0			0
$417$	−18.8854	−	12.1369i	−0.924824	−	0.594349i
$418$		0			0
$419$	−2.81732	+	6.16906i	−0.137635	+	0.301378i	−0.965881	−	0.258986i	$-0.916612\pi$
$419$	−2.81732	+	6.16906i	−0.137635	+	0.301378i	0.828246	+	0.560364i	$0.189339\pi$
$420$		0			0
$421$	22.0263	+	6.46751i	1.07350	+	0.315207i	0.770274	−	0.637713i	$-0.220119\pi$
$421$	22.0263	+	6.46751i	1.07350	+	0.315207i	0.303222	+	0.952920i	$0.401938\pi$
$422$		0			0
$423$	−0.567121	−	1.24182i	−0.0275743	−	0.0603794i
$424$		0			0
$425$	−15.5028	+	17.8912i	−0.751995	+	0.867849i
$426$		0			0
$427$	−14.2289	+	4.17797i	−0.688583	+	0.202186i
$428$		0			0
$429$	−44.9210	+	28.8690i	−2.16880	+	1.39381i
$430$		0			0
$431$	3.37161	+	23.4501i	0.162405	+	1.12955i	0.894083	+	0.447901i	$0.147828\pi$
$431$	3.37161	+	23.4501i	0.162405	+	1.12955i	−0.731678	+	0.681650i	$0.761263\pi$
$432$		0			0
$433$	3.30166	−	22.9635i	0.158668	−	1.10356i	−0.742424	−	0.669930i	$-0.766324\pi$
$433$	3.30166	−	22.9635i	0.158668	−	1.10356i	0.901092	−	0.433628i	$-0.142767\pi$
$434$		0			0
$435$	−3.42695	−	3.95491i	−0.164310	−	0.189624i
$436$		0			0
$437$	−0.148742	+	1.33509i	−0.00711531	+	0.0638661i
$438$		0			0
$439$	−17.2845	−	19.9474i	−0.824946	−	0.952038i	0.174522	−	0.984653i	$-0.444162\pi$
$439$	−17.2845	−	19.9474i	−0.824946	−	0.952038i	−0.999468	+	0.0326153i	$0.989616\pi$
$440$		0			0
$441$	−0.530341	+	3.68860i	−0.0252543	+	0.175648i
$442$		0			0
$443$	−0.0170465	−	0.118561i	−0.000809904	−	0.00563300i	0.989412	−	0.145131i	$-0.0463603\pi$
$443$	−0.0170465	−	0.118561i	−0.000809904	−	0.00563300i	−0.990222	+	0.139498i	$0.955451\pi$
$444$		0			0
$445$	24.7152	−	15.8835i	1.17161	−	0.752950i
$446$		0			0
$447$	4.82081	−	1.41552i	0.228016	−	0.0669517i
$448$		0			0
$449$	25.0253	−	28.8807i	1.18102	−	1.36296i	0.263797	−	0.964578i	$-0.415025\pi$
$449$	25.0253	−	28.8807i	1.18102	−	1.36296i	0.917218	−	0.398386i	$-0.130429\pi$
$450$		0			0
$451$	−13.7580	−	30.1259i	−0.647841	−	1.41857i
$452$		0			0
$453$	−10.0381	−	2.94746i	−0.471632	−	0.138484i
$454$		0			0
$455$	13.6337	−	29.8536i	0.639156	−	1.39956i
$456$		0			0
$457$	16.1547	+	10.3820i	0.755685	+	0.485649i	0.860883	−	0.508802i	$-0.169912\pi$
$457$	16.1547	+	10.3820i	0.755685	+	0.485649i	−0.105199	+	0.994451i	$0.533548\pi$
$458$		0			0
$459$	33.6112			1.56884
$460$		0			0
$461$	14.9421			0.695925			0.347962	−	0.937508i	$-0.386874\pi$
$461$	14.9421			0.695925			0.347962	+	0.937508i	$0.386874\pi$
$462$		0			0
$463$	−25.3179	−	16.2708i	−1.17662	−	0.756169i	−0.201860	−	0.979414i	$-0.564699\pi$
$463$	−25.3179	−	16.2708i	−1.17662	−	0.756169i	−0.974762	+	0.223245i	$0.928335\pi$
$464$		0			0
$465$	5.39898	−	11.8221i	0.250372	−	0.548238i
$466$		0			0
$467$	9.88962	+	2.90385i	0.457637	+	0.134374i	0.502422	−	0.864622i	$-0.332442\pi$
$467$	9.88962	+	2.90385i	0.457637	+	0.134374i	−0.0447855	+	0.998997i	$0.514260\pi$
$468$		0			0
$469$	2.18990	+	4.79520i	0.101120	+	0.221422i
$470$		0			0
$471$	10.0265	−	11.5711i	0.461994	−	0.533170i
$472$		0			0
$473$	30.9458	−	9.08652i	1.42289	−	0.417799i
$474$		0			0
$475$	−0.938017	+	0.602827i	−0.0430392	+	0.0276596i
$476$		0			0
$477$	0.846946	+	5.89064i	0.0387790	+	0.269714i
$478$		0			0
$479$	−0.200519	+	1.39464i	−0.00916193	+	0.0637226i	−0.993889	−	0.110380i	$-0.964793\pi$
$479$	−0.200519	+	1.39464i	−0.00916193	+	0.0637226i	0.984728	+	0.174102i	$0.0557024\pi$
$480$		0			0
$481$	1.12464	+	1.29790i	0.0512790	+	0.0591791i
$482$		0			0
$483$	−7.97900	−	8.63652i	−0.363057	−	0.392975i
$484$		0			0
$485$	7.50820	+	8.66492i	0.340930	+	0.393454i
$486$		0			0
$487$	−1.22265	+	8.50373i	−0.0554036	+	0.385341i	0.943187	+	0.332263i	$0.107812\pi$
$487$	−1.22265	+	8.50373i	−0.0554036	+	0.385341i	−0.998590	+	0.0530777i	$0.983097\pi$
$488$		0			0
$489$	−2.94041	−	20.4510i	−0.132970	−	0.924827i
$490$		0			0
$491$	25.4027	−	16.3253i	1.14641	−	0.736753i	0.177488	−	0.984123i	$-0.443203\pi$
$491$	25.4027	−	16.3253i	1.14641	−	0.736753i	0.968921	+	0.247370i	$0.0795664\pi$
$492$		0			0
$493$	−6.87757	+	2.01944i	−0.309750	+	0.0909509i
$494$		0			0
$495$	10.0690	−	11.6202i	0.452568	−	0.522291i
$496$		0			0
$497$	1.54248	+	3.37756i	0.0691896	+	0.151504i
$498$		0			0
$499$	−18.5530	−	5.44765i	−0.830547	−	0.243870i	−0.161295	−	0.986906i	$-0.551567\pi$
$499$	−18.5530	−	5.44765i	−0.830547	−	0.243870i	−0.669252	+	0.743036i	$0.733385\pi$
$500$		0			0
$501$	13.3777	−	29.2932i	0.597673	−	1.30872i
$502$		0			0
$503$	−11.7429	−	7.54670i	−0.523590	−	0.336491i	0.252001	−	0.967727i	$-0.418911\pi$
$503$	−11.7429	−	7.54670i	−0.523590	−	0.336491i	−0.775591	+	0.631236i	$0.782548\pi$
$504$		0			0
$505$	−58.4358			−2.60036
$506$		0			0
$507$	−41.8451			−1.85841
$508$		0			0
$509$	14.3340	+	9.21187i	0.635341	+	0.408309i	0.818284	−	0.574815i	$-0.194926\pi$
$509$	14.3340	+	9.21187i	0.635341	+	0.408309i	−0.182942	+	0.983124i	$0.558562\pi$
$510$		0			0
$511$	8.90222	−	19.4931i	0.393811	−	0.862326i
$512$		0			0
$513$	1.51897	+	0.446010i	0.0670642	+	0.0196918i
$514$		0			0
$515$	19.8136	+	43.3858i	0.873092	+	1.91181i
$516$		0			0
$517$	5.65128	−	6.52192i	0.248543	−	0.286834i
$518$		0			0
$519$	−14.0616	+	4.12887i	−0.617238	+	0.181237i
$520$		0			0
$521$	−18.9814	+	12.1986i	−0.831588	+	0.534429i	−0.885782	−	0.464101i	$-0.846377\pi$
$521$	−18.9814	+	12.1986i	−0.831588	+	0.534429i	0.0541939	+	0.998530i	$0.482741\pi$
$522$		0			0
$523$	−0.675624	−	4.69907i	−0.0295430	−	0.205476i	0.969704	−	0.244284i	$-0.0785530\pi$
$523$	−0.675624	−	4.69907i	−0.0295430	−	0.205476i	−0.999247	+	0.0388081i	$0.987644\pi$
$524$		0			0
$525$	1.38894	−	9.66027i	0.0606182	−	0.421609i
$526$		0			0
$527$	−11.6577	−	13.4537i	−0.507818	−	0.586053i
$528$		0			0
$529$	22.9534	−	1.46399i	0.997972	−	0.0636518i
$530$		0			0
$531$	−1.89420	−	2.18602i	−0.0822011	−	0.0948652i
$532$		0			0
$533$	5.35607	−	37.2523i	0.231997	−	1.61357i
$534$		0			0
$535$	−8.57829	−	59.6633i	−0.370872	−	2.57947i
$536$		0			0
$537$	−4.90078	+	3.14954i	−0.211484	+	0.135913i
$538$		0			0
$539$	−22.6022	+	6.63661i	−0.973547	+	0.285859i
$540$		0			0
$541$	−27.1114	+	31.2883i	−1.16561	+	1.34519i	−0.238168	+	0.971224i	$0.576547\pi$
$541$	−27.1114	+	31.2883i	−1.16561	+	1.34519i	−0.927444	+	0.373963i	$0.877999\pi$
$542$		0			0
$543$	3.56339	+	7.80274i	0.152920	+	0.334848i
$544$		0			0
$545$	−2.26283	−	0.664427i	−0.0969290	−	0.0284609i
$546$		0			0
$547$	−13.2859	+	29.0920i	−0.568063	+	1.24388i	0.379760	+	0.925085i	$0.376007\pi$
$547$	−13.2859	+	29.0920i	−0.568063	+	1.24388i	−0.947823	+	0.318798i	$0.896721\pi$
$548$		0			0
$549$	−6.64177	−	4.26840i	−0.283464	−	0.182171i
$550$		0			0
$551$	−0.337611			−0.0143827
$552$		0			0
$553$	−1.10630			−0.0470447
$554$		0			0
$555$	0.969268	+	0.622911i	0.0411431	+	0.0264411i
$556$		0			0
$557$	6.01149	−	13.1633i	0.254715	−	0.557748i	−0.738471	−	0.674285i	$-0.764452\pi$
$557$	6.01149	−	13.1633i	0.254715	−	0.557748i	0.993186	+	0.116537i	$0.0371792\pi$
$558$		0			0
$559$	35.1661	+	10.3257i	1.48737	+	0.436730i
$560$		0			0
$561$	20.3841	+	44.6350i	0.860619	+	1.88449i
$562$		0			0
$563$	18.0618	−	20.8444i	0.761213	−	0.878487i	−0.234391	−	0.972142i	$-0.575310\pi$
$563$	18.0618	−	20.8444i	0.761213	−	0.878487i	0.995605	+	0.0936552i	$0.0298551\pi$
$564$		0			0
$565$	−14.4621	+	4.24646i	−0.608426	+	0.178650i
$566$		0			0
$567$	−7.80923	+	5.01869i	−0.327957	+	0.210765i
$568$		0			0
$569$	2.60620	+	18.1265i	0.109257	+	0.759902i	0.968622	+	0.248539i	$0.0799504\pi$
$569$	2.60620	+	18.1265i	0.109257	+	0.759902i	−0.859364	+	0.511364i	$0.829141\pi$
$570$		0			0
$571$	5.29062	−	36.7971i	0.221406	−	1.53991i	−0.511323	−	0.859389i	$-0.670844\pi$
$571$	5.29062	−	36.7971i	0.221406	−	1.53991i	0.732728	−	0.680521i	$-0.238247\pi$
$572$		0			0
$573$	−5.78727	−	6.67886i	−0.241767	−	0.279013i
$574$		0			0
$575$	12.9548	+	14.0224i	0.540253	+	0.584774i
$576$		0			0
$577$	−11.4691	−	13.2360i	−0.477464	−	0.551022i	0.465009	−	0.885306i	$-0.346051\pi$
$577$	−11.4691	−	13.2360i	−0.477464	−	0.551022i	−0.942473	+	0.334284i	$0.891506\pi$
$578$		0			0
$579$	−0.389499	+	2.70902i	−0.0161870	+	0.112583i
$580$		0			0
$581$	3.32982	+	23.1594i	0.138144	+	0.960813i
$582$		0			0
$583$	−31.6473	+	20.3385i	−1.31070	+	0.842334i
$584$		0			0
$585$	16.7649	−	4.92261i	0.693143	−	0.203525i
$586$		0			0
$587$	31.5950	−	36.4625i	1.30406	−	1.50497i	0.581862	−	0.813287i	$-0.302324\pi$
$587$	31.5950	−	36.4625i	1.30406	−	1.50497i	0.722202	−	0.691683i	$-0.243130\pi$
$588$		0			0
$589$	−0.348313	−	0.762699i	−0.0143520	−	0.0314265i
$590$		0			0
$591$	28.4367	+	8.34977i	1.16973	+	0.343464i
$592$		0			0
$593$	−13.3820	+	29.3024i	−0.549532	+	1.20331i	0.407468	+	0.913219i	$0.366412\pi$
$593$	−13.3820	+	29.3024i	−0.549532	+	1.20331i	−0.957000	+	0.290088i	$0.906316\pi$
$594$		0			0
$595$	−25.3715	−	16.3052i	−1.04013	−	0.668450i
$596$		0			0
$597$	3.29611			0.134901
$598$		0			0
$599$	−17.5873			−0.718599			−0.359299	−	0.933222i	$-0.616984\pi$
$599$	−17.5873			−0.718599			−0.359299	+	0.933222i	$0.616984\pi$
$600$		0			0
$601$	1.41537	+	0.909602i	0.0577341	+	0.0371034i	0.569189	−	0.822206i	$-0.307257\pi$
$601$	1.41537	+	0.909602i	0.0577341	+	0.0371034i	−0.511455	+	0.859310i	$0.670893\pi$
$602$		0			0
$603$	−1.16587	+	2.55291i	−0.0474781	+	0.103962i
$604$		0			0
$605$	61.6281	+	18.0956i	2.50554	+	0.735693i
$606$		0			0
$607$	−6.42753	−	14.0743i	−0.260885	−	0.571259i	0.733181	−	0.680033i	$-0.238035\pi$
$607$	−6.42753	−	14.0743i	−0.260885	−	0.571259i	−0.994066	+	0.108774i	$0.965307\pi$
$608$		0			0
$609$	1.93515	−	2.23328i	0.0784162	−	0.0904971i
$610$		0			0
$611$	9.40938	−	2.76284i	0.380663	−	0.111773i
$612$		0			0
$613$	18.3144	−	11.7699i	0.739712	−	0.475384i	−0.115732	−	0.993281i	$-0.536921\pi$
$613$	18.3144	−	11.7699i	0.739712	−	0.475384i	0.855443	+	0.517897i	$0.173285\pi$
$614$		0			0
$615$	−3.59335	−	24.9923i	−0.144898	−	1.00779i
$616$		0			0
$617$	−1.43390	+	9.97297i	−0.0577265	+	0.401497i	0.940387	+	0.340106i	$0.110463\pi$
$617$	−1.43390	+	9.97297i	−0.0577265	+	0.401497i	−0.998114	+	0.0613912i	$0.980446\pi$
$618$		0			0
$619$	16.7694	+	19.3529i	0.674018	+	0.777858i	0.984999	−	0.172558i	$-0.0552032\pi$
$619$	16.7694	+	19.3529i	0.674018	+	0.777858i	−0.310982	+	0.950416i	$0.600658\pi$
$620$		0			0
$621$	3.00117	−	26.9381i	0.120433	−	1.08099i
$622$		0			0
$623$	10.8641	+	12.5378i	0.435260	+	0.502317i
$624$		0			0
$625$	4.13532	−	28.7618i	0.165413	−	1.15047i
$626$		0			0
$627$	0.328915	+	2.28765i	0.0131356	+	0.0913601i
$628$		0			0
$629$	1.32763	−	0.853218i	0.0529362	−	0.0340200i
$630$		0			0
$631$	18.1411	−	5.32670i	0.722184	−	0.212052i	0.100072	−	0.994980i	$-0.468093\pi$
$631$	18.1411	−	5.32670i	0.722184	−	0.212052i	0.622113	+	0.782928i	$0.286275\pi$
$632$		0			0
$633$	1.65700	−	1.91228i	0.0658597	−	0.0760062i
$634$		0			0
$635$	−9.99307	−	21.8818i	−0.396563	−	0.868351i
$636$		0			0
$637$	−25.6846	−	7.54168i	−1.01766	−	0.298812i
$638$		0			0
$639$	−0.821196	+	1.79817i	−0.0324860	+	0.0711345i
$640$		0			0
$641$	−21.4152	−	13.7627i	−0.845849	−	0.543594i	0.0444285	−	0.999013i	$-0.485853\pi$
$641$	−21.4152	−	13.7627i	−0.845849	−	0.543594i	−0.890278	+	0.455418i	$0.849490\pi$
$642$		0			0
$643$	−28.9449			−1.14147			−0.570737	−	0.821133i	$-0.693343\pi$
$643$	−28.9449			−1.14147			−0.570737	+	0.821133i	$0.693343\pi$
$644$		0			0
$645$	24.5887			0.968180
$646$		0			0
$647$	30.7038	+	19.7321i	1.20709	+	0.775750i	0.980169	−	0.198163i	$-0.0634977\pi$
$647$	30.7038	+	19.7321i	1.20709	+	0.775750i	0.226921	+	0.973913i	$0.427134\pi$
$648$		0			0
$649$	7.59561	−	16.6321i	0.298154	−	0.652866i
$650$		0			0
$651$	7.04171	+	2.06763i	0.275986	+	0.0810369i
$652$		0			0
$653$	−1.29021	−	2.82516i	−0.0504897	−	0.110557i	0.882706	−	0.469926i	$-0.155719\pi$
$653$	−1.29021	−	2.82516i	−0.0504897	−	0.110557i	−0.933196	+	0.359369i	$0.882992\pi$
$654$		0			0
$655$	−20.1579	+	23.2634i	−0.787634	+	0.908978i
$656$		0			0
$657$	10.9468	−	3.21426i	0.427074	−	0.125400i
$658$		0			0
$659$	−24.0401	+	15.4497i	−0.936471	+	0.601834i	−0.917392	−	0.397984i	$-0.869710\pi$
$659$	−24.0401	+	15.4497i	−0.936471	+	0.601834i	−0.0190791	+	0.999818i	$0.506073\pi$
$660$		0			0
$661$	0.118046	+	0.821026i	0.00459145	+	0.0319342i	0.991988	−	0.126329i	$-0.0403196\pi$
$661$	0.118046	+	0.821026i	0.00459145	+	0.0319342i	−0.987397	+	0.158263i	$0.949410\pi$
$662$		0			0
$663$	−7.93564	+	55.1936i	−0.308195	+	2.14354i
$664$		0			0
$665$	−0.930231	−	1.07354i	−0.0360728	−	0.0416302i
$666$		0			0
$667$	1.00440	+	5.69242i	0.0388904	+	0.220411i
$668$		0			0
$669$	9.51164	+	10.9770i	0.367741	+	0.424396i
$670$		0			0
$671$	7.10250	−	49.3990i	0.274189	−	1.90703i
$672$		0			0
$673$	0.0946665	+	0.658420i	0.00364912	+	0.0253802i	0.991565	−	0.129613i	$-0.0413735\pi$
$673$	0.0946665	+	0.658420i	0.00364912	+	0.0253802i	−0.987916	+	0.154993i	$0.950464\pi$
$674$		0			0
$675$	18.9263	−	12.1632i	0.728474	−	0.468162i
$676$		0			0
$677$	1.48477	−	0.435967i	0.0570643	−	0.0167556i	−0.253076	−	0.967446i	$-0.581442\pi$
$677$	1.48477	−	0.435967i	0.0570643	−	0.0167556i	0.310140	+	0.950691i	$0.399624\pi$
$678$		0			0
$679$	−4.23977	+	4.89295i	−0.162707	+	0.187774i
$680$		0			0
$681$	−6.62293	−	14.5022i	−0.253791	−	0.555725i
$682$		0			0
$683$	38.1512	+	11.2022i	1.45982	+	0.428641i	0.912774	−	0.408465i	$-0.133936\pi$
$683$	38.1512	+	11.2022i	1.45982	+	0.428641i	0.547042	+	0.837105i	$0.315754\pi$
$684$		0			0
$685$	4.70132	−	10.2945i	0.179628	−	0.393331i
$686$		0			0
$687$	13.2684	+	8.52710i	0.506222	+	0.325329i
$688$		0			0
$689$	−42.7495			−1.62863
$690$		0			0
$691$	−37.9101			−1.44217			−0.721083	−	0.692848i	$-0.756356\pi$
$691$	−37.9101			−1.44217			−0.721083	+	0.692848i	$0.756356\pi$
$692$		0			0
$693$	7.30416	+	4.69410i	0.277462	+	0.178314i
$694$		0			0
$695$	−19.2896	+	42.2383i	−0.731697	+	1.60219i
$696$		0			0
$697$	−33.1838	−	9.74363i	−1.25692	−	0.369066i
$698$		0			0
$699$	−6.16529	−	13.5001i	−0.233193	−	0.510621i
$700$		0			0
$701$	15.7581	−	18.1858i	0.595175	−	0.686868i	−0.375622	−	0.926773i	$-0.622571\pi$
$701$	15.7581	−	18.1858i	0.595175	−	0.686868i	0.970796	+	0.239905i	$0.0771162\pi$
$702$		0			0
$703$	0.0713208	−	0.0209417i	0.00268992	−	0.000789830i
$704$		0			0
$705$	5.53477	−	3.55698i	0.208452	−	0.133964i
$706$		0			0
$707$	−4.69608	−	32.6619i	−0.176614	−	1.22838i
$708$		0			0
$709$	−6.71882	+	46.7304i	−0.252331	+	1.75500i	0.331811	+	0.943346i	$0.392340\pi$
$709$	−6.71882	+	46.7304i	−0.252331	+	1.75500i	−0.584142	+	0.811651i	$0.698569\pi$
$710$		0			0
$711$	−0.385701	−	0.445122i	−0.0144649	−	0.0166934i
$712$		0			0
$713$	−11.8235	+	8.14191i	−0.442795	+	0.304917i
$714$		0			0
$715$	72.3289	+	83.4720i	2.70495	+	3.12168i
$716$		0			0
$717$	−3.19375	+	22.2130i	−0.119273	+	0.829560i
$718$		0			0
$719$	−1.05591	−	7.34398i	−0.0393786	−	0.273884i	0.960613	−	0.277888i	$-0.0896345\pi$
$719$	−1.05591	−	7.34398i	−0.0393786	−	0.273884i	−0.999992	+	0.00400411i	$0.998725\pi$
$720$		0			0
$721$	−22.6576	+	14.5612i	−0.843815	+	0.542287i
$722$		0			0
$723$	−9.48010	+	2.78361i	−0.352569	+	0.103523i
$724$		0			0
$725$	−3.14193	+	3.62598i	−0.116688	+	0.134666i
$726$		0			0
$727$	0.0592470	+	0.129733i	0.00219735	+	0.00481153i	0.910727	−	0.413008i	$-0.135522\pi$
$727$	0.0592470	+	0.129733i	0.00219735	+	0.00481153i	−0.908530	+	0.417819i	$0.862795\pi$
$728$		0			0
$729$	−28.3118	−	8.31310i	−1.04859	−	0.307893i
$730$		0			0
$731$	13.9911	−	30.6363i	0.517480	−	1.13312i
$732$		0			0
$733$	9.86010	+	6.33670i	0.364191	+	0.234051i	0.709919	−	0.704283i	$-0.248732\pi$
$733$	9.86010	+	6.33670i	0.364191	+	0.234051i	−0.345728	+	0.938335i	$0.612368\pi$
$734$		0			0
$735$	−17.9591			−0.662431
$736$		0			0
$737$	−17.7408			−0.653492
$738$		0			0
$739$	32.2777	+	20.7436i	1.18735	+	0.763066i	0.976724	−	0.214500i	$-0.0688121\pi$
$739$	32.2777	+	20.7436i	1.18735	+	0.763066i	0.210630	+	0.977566i	$0.432448\pi$
$740$		0			0
$741$	−1.09103	+	2.38903i	−0.0400800	+	0.0877630i
$742$		0			0
$743$	−36.4038	−	10.6891i	−1.33553	−	0.392146i	−0.465456	−	0.885071i	$-0.654110\pi$
$743$	−36.4038	−	10.6891i	−1.33553	−	0.392146i	−0.870072	+	0.492925i	$0.835928\pi$
$744$		0			0
$745$	−4.31719	−	9.45333i	−0.158170	−	0.346343i
$746$		0			0
$747$	−8.15732	+	9.41405i	−0.298461	+	0.344442i
$748$		0			0
$749$	32.6587	−	9.58945i	1.19332	−	0.350391i
$750$		0			0
$751$	−33.2057	+	21.3400i	−1.21169	+	0.778707i	−0.980941	−	0.194306i	$-0.937754\pi$
$751$	−33.2057	+	21.3400i	−1.21169	+	0.778707i	−0.230751	+	0.973013i	$0.574118\pi$
$752$		0			0
$753$	1.68993	+	11.7537i	0.0615846	+	0.428330i
$754$		0			0
$755$	−3.07965	+	21.4194i	−0.112080	+	0.779533i
$756$		0			0
$757$	−26.2688	−	30.3158i	−0.954756	−	1.10185i	−0.994718	−	0.102646i	$-0.967269\pi$
$757$	−26.2688	−	30.3158i	−0.954756	−	1.10185i	0.0399619	−	0.999201i	$-0.487276\pi$
$758$		0			0
$759$	37.5933	−	12.3516i	1.36455	−	0.448335i
$760$		0			0
$761$	0.519729	+	0.599799i	0.0188402	+	0.0217427i	0.765091	−	0.643922i	$-0.222694\pi$
$761$	0.519729	+	0.599799i	0.0188402	+	0.0217427i	−0.746251	+	0.665664i	$0.768148\pi$
$762$		0			0
$763$	0.189525	−	1.31818i	0.00686126	−	0.0477211i
$764$		0			0
$765$	−2.28506	−	15.8929i	−0.0826164	−	0.574610i
$766$		0			0
$767$	17.4795	−	11.2334i	0.631148	−	0.405614i
$768$		0			0
$769$	−15.5796	+	4.57460i	−0.561816	+	0.164964i	−0.550296	−	0.834969i	$-0.685485\pi$
$769$	−15.5796	+	4.57460i	−0.561816	+	0.164964i	−0.0115201	+	0.999934i	$0.503667\pi$
$770$		0			0
$771$	−2.41865	+	2.79127i	−0.0871054	+	0.100525i
$772$		0			0
$773$	−1.65862	−	3.63186i	−0.0596563	−	0.130629i	0.877456	−	0.479657i	$-0.159239\pi$
$773$	−1.65862	−	3.63186i	−0.0596563	−	0.130629i	−0.937112	+	0.349028i	$0.886512\pi$
$774$		0			0
$775$	−11.4330	−	3.35704i	−0.410686	−	0.120588i
$776$		0			0
$777$	−0.270275	+	0.591819i	−0.00969605	+	0.0212314i
$778$		0			0
$779$	−1.37036	−	0.880676i	−0.0490982	−	0.0315535i
$780$		0			0
$781$	−12.4959			−0.447140
$782$		0			0
$783$	6.81196			0.243440
$784$		0			0
$785$	−26.6419	−	17.1217i	−0.950892	−	0.611101i
$786$		0			0
$787$	−1.06373	+	2.32925i	−0.0379181	+	0.0830290i	−0.927643	−	0.373468i	$-0.878169\pi$
$787$	−1.06373	+	2.32925i	−0.0379181	+	0.0830290i	0.889725	+	0.456497i	$0.150896\pi$
$788$		0			0
$789$	4.32072	+	1.26868i	0.153822	+	0.0451661i
$790$		0			0
$791$	−3.53572	−	7.74216i	−0.125716	−	0.275279i
$792$		0			0
$793$	37.1391	−	42.8608i	1.31885	−	1.52203i
$794$		0			0
$795$	−27.5186	+	8.08020i	−0.975985	+	0.286575i
$796$		0			0
$797$	−5.13078	+	3.29736i	−0.181742	+	0.116798i	−0.628348	−	0.777932i	$-0.716269\pi$
$797$	−5.13078	+	3.29736i	−0.181742	+	0.116798i	0.446607	+	0.894730i	$0.352632\pi$
$798$		0			0
$799$	−1.28250	−	8.91998i	−0.0453716	−	0.315566i
$800$		0			0
$801$	−1.25696	+	8.74236i	−0.0444125	+	0.308896i
$802$		0			0
$803$	47.2278	+	54.5038i	1.66663	+	1.92340i
$804$		0			0
$805$	−15.3334	+	18.8783i	−0.540433	+	0.665374i
$806$		0			0
$807$	−24.8511	−	28.6797i	−0.874801	−	1.00957i
$808$		0			0
$809$	−0.0599891	+	0.417234i	−0.00210911	+	0.0146692i	−0.990849	−	0.134976i	$-0.956904\pi$
$809$	−0.0599891	+	0.417234i	−0.00210911	+	0.0146692i	0.988740	+	0.149646i	$0.0478132\pi$
$810$		0			0
$811$	−2.76787	−	19.2510i	−0.0971932	−	0.675993i	−0.978922	−	0.204236i	$-0.934529\pi$
$811$	−2.76787	−	19.2510i	−0.0971932	−	0.675993i	0.881728	−	0.471757i	$-0.156380\pi$
$812$		0			0
$813$	−18.0158	+	11.5781i	−0.631843	+	0.406061i
$814$		0			0
$815$	−41.0054	+	12.0403i	−1.43636	+	0.421752i
$816$		0			0
$817$	1.03882	−	1.19887i	0.0363439	−	0.0419431i
$818$		0			0
$819$	4.09871	+	8.97492i	0.143220	+	0.313609i
$820$		0			0
$821$	6.54813	+	1.92271i	0.228531	+	0.0671029i	0.393993	−	0.919113i	$-0.371093\pi$
$821$	6.54813	+	1.92271i	0.228531	+	0.0671029i	−0.165462	+	0.986216i	$0.552911\pi$
$822$		0			0
$823$	−0.946059	+	2.07158i	−0.0329775	+	0.0722107i	−0.925404	−	0.378982i	$-0.876274\pi$
$823$	−0.946059	+	2.07158i	−0.0329775	+	0.0722107i	0.892426	+	0.451193i	$0.149001\pi$
$824$		0			0
$825$	27.6307	+	17.7572i	0.961977	+	0.618225i
$826$		0			0
$827$	2.32388			0.0808093			0.0404047	−	0.999183i	$-0.487135\pi$
$827$	2.32388			0.0808093			0.0404047	+	0.999183i	$0.487135\pi$
$828$		0			0
$829$	−6.89147			−0.239351			−0.119675	−	0.992813i	$-0.538185\pi$
$829$	−6.89147			−0.239351			−0.119675	+	0.992813i	$0.538185\pi$
$830$		0			0
$831$	−5.60014	−	3.59899i	−0.194267	−	0.124848i
$832$		0			0
$833$	−10.2188	+	22.3761i	−0.354061	+	0.775286i
$834$		0			0
$835$	−63.9121	−	18.7663i	−2.21177	−	0.649434i
$836$		0			0
$837$	7.02789	+	15.3889i	0.242919	+	0.531920i
$838$		0			0
$839$	3.23620	−	3.73478i	0.111726	−	0.128939i	−0.697132	−	0.716943i	$-0.745541\pi$
$839$	3.23620	−	3.73478i	0.111726	−	0.128939i	0.808858	+	0.588004i	$0.200086\pi$
$840$		0			0
$841$	26.4314	−	7.76097i	0.911428	−	0.267620i
$842$		0			0
$843$	−10.6396	+	6.83767i	−0.366448	+	0.235502i
$844$		0			0
$845$	12.3179	+	85.6727i	0.423748	+	2.94723i
$846$		0			0
$847$	−5.16171	+	35.9005i	−0.177358	+	1.23355i
$848$		0			0
$849$	−23.8654	−	27.5421i	−0.819057	−	0.945243i
$850$		0			0
$851$	−0.565276	−	1.14023i	−0.0193774	−	0.0390866i
$852$		0			0
$853$	8.34340	+	9.62880i	0.285673	+	0.329684i	0.880389	−	0.474251i	$-0.157281\pi$
$853$	8.34340	+	9.62880i	0.285673	+	0.329684i	−0.594717	+	0.803935i	$0.702736\pi$
$854$		0			0
$855$	0.107627	−	0.748560i	0.00368076	−	0.0256002i
$856$		0			0
$857$	2.61045	+	18.1561i	0.0891713	+	0.620200i	0.984577	+	0.174949i	$0.0559762\pi$
$857$	2.61045	+	18.1561i	0.0891713	+	0.620200i	−0.895406	+	0.445250i	$0.853115\pi$
$858$		0			0
$859$	3.42596	−	2.20173i	0.116892	−	0.0751220i	−0.480888	−	0.876782i	$-0.659686\pi$
$859$	3.42596	−	2.20173i	0.116892	−	0.0751220i	0.597781	+	0.801660i	$0.296049\pi$
$860$		0			0
$861$	13.6804	−	4.01692i	0.466225	−	0.136896i
$862$		0			0
$863$	−10.1236	+	11.6833i	−0.344612	+	0.397704i	−0.901426	−	0.432934i	$-0.857478\pi$
$863$	−10.1236	+	11.6833i	−0.344612	+	0.397704i	0.556813	+	0.830638i	$0.312024\pi$
$864$		0			0
$865$	12.5927	+	27.5741i	0.428163	+	0.937546i
$866$		0			0
$867$	25.5334	+	7.49729i	0.867160	+	0.254621i
$868$		0			0
$869$	1.54664	−	3.38666i	0.0524660	−	0.114885i
$870$		0			0
$871$	−16.9599	−	10.8994i	−0.574663	−	0.369313i
$872$		0			0
$873$	−3.44684			−0.116658
$874$		0			0
$875$	5.16922			0.174752
$876$		0			0
$877$	44.3677	+	28.5134i	1.49819	+	0.962830i	0.995129	+	0.0985797i	$0.0314299\pi$
$877$	44.3677	+	28.5134i	1.49819	+	0.962830i	0.503063	+	0.864250i	$0.332206\pi$
$878$		0			0
$879$	−12.1137	+	26.5253i	−0.408584	+	0.894675i
$880$		0			0
$881$	10.7912	+	3.16859i	0.363566	+	0.106752i	0.458413	−	0.888739i	$-0.348418\pi$
$881$	10.7912	+	3.16859i	0.363566	+	0.106752i	−0.0948473	+	0.995492i	$0.530236\pi$
$882$		0			0
$883$	−3.72392	−	8.15424i	−0.125320	−	0.274412i	0.836565	−	0.547868i	$-0.184560\pi$
$883$	−3.72392	−	8.15424i	−0.125320	−	0.274412i	−0.961884	+	0.273456i	$0.911833\pi$
$884$		0			0
$885$	9.12861	−	10.5350i	0.306855	−	0.354129i
$886$		0			0
$887$	53.1163	−	15.5963i	1.78347	−	0.523674i	0.787741	−	0.616007i	$-0.211251\pi$
$887$	53.1163	−	15.5963i	1.78347	−	0.523674i	0.995728	+	0.0923329i	$0.0294324\pi$
$888$		0			0
$889$	11.4275	−	7.34398i	0.383265	−	0.246309i
$890$		0			0
$891$	−4.44595	−	30.9222i	−0.148945	−	1.03593i
$892$		0			0
$893$	0.0604061	−	0.420133i	0.00202141	−	0.0140592i
$894$		0			0
$895$	7.89093	+	9.10662i	0.263765	+	0.304401i
$896$		0			0
$897$	43.5269	+	11.2884i	1.45332	+	0.376908i
$898$		0			0
$899$	−2.36266	−	2.72665i	−0.0787990	−	0.0909389i
$900$		0			0
$901$	−5.59075	+	38.8845i	−0.186255	+	1.29543i
$902$		0			0
$903$	1.97602	+	13.7435i	0.0657580	+	0.457357i
$904$		0			0
$905$	14.9262	−	9.59248i	0.496164	−	0.318865i
$906$		0			0
$907$	8.62760	−	2.53329i	0.286475	−	0.0841166i	−0.135338	−	0.990799i	$-0.543212\pi$
$907$	8.62760	−	2.53329i	0.286475	−	0.0841166i	0.421813	+	0.906683i	$0.361394\pi$
$908$		0			0
$909$	11.5044	−	13.2767i	0.381575	−	0.440361i
$910$		0			0
$911$	−11.7469	−	25.7221i	−0.389192	−	0.852211i	−0.998253	−	0.0590876i	$-0.981181\pi$
$911$	−11.7469	−	25.7221i	−0.389192	−	0.852211i	0.609061	−	0.793123i	$-0.291546\pi$
$912$		0			0
$913$	−75.5517	−	22.1840i	−2.50040	−	0.734183i
$914$		0			0
$915$	15.8059	−	34.6100i	0.522526	−	1.14417i
$916$		0			0
$917$	−14.6228	−	9.39747i	−0.482886	−	0.310332i
$918$		0			0
$919$	25.9114			0.854740			0.427370	−	0.904077i	$-0.359440\pi$
$919$	25.9114			0.854740			0.427370	+	0.904077i	$0.359440\pi$
$920$		0			0
$921$	−36.3029			−1.19622
$922$		0			0
$923$	−11.9459	−	7.67714i	−0.393203	−	0.252696i
$924$		0			0
$925$	0.438822	−	0.960885i	0.0144284	−	0.0315937i
$926$		0			0
$927$	−13.7581	−	4.03974i	−0.451875	−	0.132682i
$928$		0			0
$929$	7.79579	+	17.0704i	0.255771	+	0.560061i	0.993341	−	0.115210i	$-0.0367540\pi$
$929$	7.79579	+	17.0704i	0.255771	+	0.560061i	−0.737570	+	0.675271i	$0.764027\pi$
$930$		0			0
$931$	−0.758737	+	0.875629i	−0.0248666	+	0.0286976i
$932$		0			0
$933$	18.3696	−	5.39381i	0.601395	−	0.176585i
$934$		0			0
$935$	85.3843	−	54.8732i	2.79236	−	1.79454i
$936$		0			0
$937$	−4.51811	−	31.4242i	−0.147600	−	1.02658i	−0.920133	−	0.391607i	$-0.871919\pi$
$937$	−4.51811	−	31.4242i	−0.147600	−	1.02658i	0.772532	−	0.634975i	$-0.218990\pi$
$938$		0			0
$939$	5.91849	−	41.1640i	0.193143	−	1.34334i
$940$		0			0
$941$	0.148908	+	0.171849i	0.00485426	+	0.00560211i	0.758172	−	0.652055i	$-0.226093\pi$
$941$	0.148908	+	0.171849i	0.00485426	+	0.00560211i	−0.753317	+	0.657657i	$0.771548\pi$
$942$		0			0
$943$	−10.7721	+	25.7255i	−0.350789	+	0.837737i
$944$		0			0
$945$	18.7692	+	21.6608i	0.610563	+	0.704627i
$946$		0			0
$947$	−3.06237	+	21.2992i	−0.0995135	+	0.692132i	0.877597	+	0.479399i	$0.159145\pi$
$947$	−3.06237	+	21.2992i	−0.0995135	+	0.692132i	−0.977110	+	0.212733i	$0.931764\pi$
$948$		0			0
$949$	11.6633	+	81.1198i	0.378606	+	2.63326i
$950$		0			0
$951$	5.58768	−	3.59098i	0.181193	−	0.116446i
$952$		0			0
$953$	20.6688	−	6.06889i	0.669527	−	0.196591i	0.0707344	−	0.997495i	$-0.477466\pi$
$953$	20.6688	−	6.06889i	0.669527	−	0.196591i	0.598792	+	0.800904i	$0.295648\pi$
$954$		0			0
$955$	−11.9706	+	13.8148i	−0.387358	+	0.447035i
$956$		0			0
$957$	4.13123	+	9.04614i	0.133544	+	0.292420i
$958$		0			0
$959$	6.13177	+	1.80045i	0.198005	+	0.0581396i
$960$		0			0
$961$	−9.15562	+	20.0480i	−0.295343	+	0.646710i
$962$		0			0
$963$	15.2444	+	9.79701i	0.491245	+	0.315704i
$964$		0			0
$965$	5.66105			0.182235
$966$		0			0
$967$	−18.1310			−0.583054			−0.291527	−	0.956563i	$-0.594163\pi$
$967$	−18.1310			−0.583054			−0.291527	+	0.956563i	$0.594163\pi$
$968$		0			0
$969$	2.03035	+	1.30482i	0.0652241	+	0.0419170i
$970$		0			0
$971$	−13.2810	+	29.0813i	−0.426207	+	0.933264i	0.567720	+	0.823222i	$0.307826\pi$
$971$	−13.2810	+	29.0813i	−0.426207	+	0.933264i	−0.993927	+	0.110042i	$0.964902\pi$
$972$		0			0
$973$	−25.1588	−	7.38728i	−0.806553	−	0.236825i
$974$		0			0
$975$	15.5049	+	33.9510i	0.496554	+	1.08730i
$976$		0			0
$977$	12.7468	−	14.7105i	0.407805	−	0.470632i	−0.514278	−	0.857623i	$-0.671940\pi$
$977$	12.7468	−	14.7105i	0.407805	−	0.470632i	0.922083	+	0.386991i	$0.126486\pi$
$978$		0			0
$979$	−53.5695	+	15.7294i	−1.71209	+	0.502715i
$980$		0			0
$981$	0.596446	−	0.383313i	0.0190431	−	0.0122382i
$982$		0			0
$983$	2.54180	+	17.6786i	0.0810709	+	0.563861i	0.989357	+	0.145510i	$0.0464824\pi$
$983$	2.54180	+	17.6786i	0.0810709	+	0.563861i	−0.908286	+	0.418350i	$0.862608\pi$
$984$		0			0
$985$	8.72425	−	60.6785i	0.277978	−	1.93338i
$986$		0			0
$987$	2.43292	+	2.80774i	0.0774407	+	0.0893713i
$988$		0			0
$989$	−23.3045	−	13.9489i	−0.741040	−	0.443548i
$990$		0			0
$991$	−26.5935	−	30.6906i	−0.844771	−	0.974918i	0.155145	−	0.987892i	$-0.450416\pi$
$991$	−26.5935	−	30.6906i	−0.844771	−	0.974918i	−0.999916	+	0.0129741i	$0.995870\pi$
$992$		0			0
$993$	4.49415	−	31.2575i	0.142617	−	0.991926i
$994$		0			0
$995$	−0.970270	−	6.74838i	−0.0307596	−	0.213938i
$996$		0			0
$997$	35.9090	−	23.0773i	1.13725	−	0.730865i	0.170188	−	0.985412i	$-0.445563\pi$
$997$	35.9090	−	23.0773i	1.13725	−	0.730865i	0.967061	+	0.254547i	$0.0819262\pi$
$998$		0			0
$999$	−1.43904	+	0.422539i	−0.0455291	+	0.0133685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.289.2		30
4.3	odd	2		184.2.i.b.105.2	✓	30
23.4	even	11		8464.2.a.cg.1.5		15
23.16	even	11	inner	368.2.m.e.177.2		30
23.19	odd	22		8464.2.a.ch.1.5		15
92.19	even	22		4232.2.a.ba.1.11		15
92.27	odd	22		4232.2.a.bb.1.11		15
92.39	odd	22		184.2.i.b.177.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.105.2	✓	30	4.3	odd	2
184.2.i.b.177.2	yes	30	92.39	odd	22
368.2.m.e.177.2		30	23.16	even	11	inner
368.2.m.e.289.2		30	1.1	even	1	trivial
4232.2.a.ba.1.11		15	92.19	even	22
4232.2.a.bb.1.11		15	92.27	odd	22
8464.2.a.cg.1.5		15	23.4	even	11
8464.2.a.ch.1.5		15	23.19	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)

\(f(q)\)	\(=\)	\(q+(-1.21882 - 0.783290i) q^{3} +(-1.24491 + 2.72597i) q^{5} +(-1.62369 - 0.476758i) q^{7} +(-0.374258 - 0.819511i) q^{9} +O(q^{10})\)	\(q+(-1.21882 - 0.783290i) q^{3} +(-1.24491 + 2.72597i) q^{5} +(-1.62369 - 0.476758i) q^{7} +(-0.374258 - 0.819511i) q^{9} +(3.72943 - 4.30399i) q^{11} +(6.20950 - 1.82327i) q^{13} +(3.65254 - 2.34735i) q^{15} +(-0.846356 - 5.88654i) q^{17} +(0.0398636 - 0.277257i) q^{19} +(1.60555 + 1.85290i) q^{21} +(-4.79340 + 0.152709i) q^{23} +(-2.60679 - 3.00840i) q^{25} +(-0.804325 + 5.59421i) q^{27} +(-0.171530 - 1.19302i) q^{29} +(2.51819 - 1.61834i) q^{31} +(-7.91679 + 2.32458i) q^{33} +(3.32097 - 3.83260i) q^{35} +(0.110238 + 0.241387i) q^{37} +(-8.99644 - 2.64159i) q^{39} +(2.41581 - 5.28989i) q^{41} +(4.76425 + 3.06179i) q^{43} +2.69988 q^{45} +1.51532 q^{47} +(-3.47971 - 2.23627i) q^{49} +(-3.57931 + 7.83759i) q^{51} +(-6.33809 - 1.86103i) q^{53} +(7.08974 + 15.5244i) q^{55} +(-0.265760 + 0.306703i) q^{57} +(3.08055 - 0.904532i) q^{59} +(7.37216 - 4.73780i) q^{61} +(0.216970 + 1.50906i) q^{63} +(-2.76007 + 19.1967i) q^{65} +(-2.04000 - 2.35428i) q^{67} +(5.96192 + 3.56850i) q^{69} +(-1.43689 - 1.65826i) q^{71} +(-1.80221 + 12.5346i) q^{73} +(0.820770 + 5.70858i) q^{75} +(-8.10739 + 5.21030i) q^{77} +(0.627270 - 0.184183i) q^{79} +(3.59227 - 4.14571i) q^{81} +(-5.74370 - 12.5769i) q^{83} +(17.1001 + 5.02105i) q^{85} +(-0.725415 + 1.58844i) q^{87} +(-8.24726 - 5.30019i) q^{89} -10.9516 q^{91} -4.33686 q^{93} +(0.706168 + 0.453826i) q^{95} +(1.58933 - 3.48015i) q^{97} +(-4.92294 - 1.44550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) \) 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

Varieties

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Representations

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Database

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