LMFDB - Embedded newform 912.2.ci.g.319.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.2
Character	$\chi$	$=$	912.319
Dual form			912.2.ci.g.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{3} +(-1.40574 + 1.17956i) q^{5} +(-4.46660 - 2.57879i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{3} +(-1.40574 + 1.17956i) q^{5} +(-4.46660 - 2.57879i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(3.85017 - 2.22290i) q^{11} +(2.69215 + 0.474699i) q^{13} +(-1.40574 - 1.17956i) q^{15} +(-2.85688 - 1.03982i) q^{17} +(3.15385 + 3.00886i) q^{19} +(1.76400 - 4.84654i) q^{21} +(5.92256 - 7.05824i) q^{23} +(-0.283485 + 1.60772i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.331534 + 0.910882i) q^{29} +(3.33716 - 5.78013i) q^{31} +(2.85770 + 3.40567i) q^{33} +(9.32074 - 1.64350i) q^{35} -6.33772i q^{37} +2.73368i q^{39} +(6.98847 - 1.23226i) q^{41} +(-1.22260 - 1.45704i) q^{43} +(0.917534 - 1.58922i) q^{45} +(-2.27932 - 6.26239i) q^{47} +(9.80034 + 16.9747i) q^{49} +(0.527929 - 2.99404i) q^{51} +(1.82052 - 2.16961i) q^{53} +(-2.79031 + 7.66633i) q^{55} +(-2.41549 + 3.62842i) q^{57} +(-9.47029 - 3.44690i) q^{59} +(0.706102 + 0.592490i) q^{61} +(5.07923 + 0.895605i) q^{63} +(-4.34441 + 2.50825i) q^{65} +(14.4351 - 5.25396i) q^{67} +(7.97945 + 4.60694i) q^{69} +(-9.76956 + 8.19763i) q^{71} +(1.24066 + 7.03612i) q^{73} -1.63252 q^{75} -22.9295 q^{77} +(0.463885 + 2.63082i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-7.41634 - 4.28182i) q^{83} +(5.24256 - 1.90814i) q^{85} +(-0.839473 + 0.484670i) q^{87} +(-0.927132 - 0.163478i) q^{89} +(-10.8006 - 9.06279i) q^{91} +(6.27181 + 2.28275i) q^{93} +(-7.98263 - 0.509534i) q^{95} +(1.69079 - 4.64541i) q^{97} +(-2.85770 + 3.40567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{7}+O(q^{10}) $ 24 * q - 9 * q^7	$ 24 q - 9 q^{7} + 9 q^{11} - 9 q^{13} - 6 q^{17} - 3 q^{19} - 6 q^{21} + 15 q^{23} + 6 q^{25} - 12 q^{27} - 6 q^{29} + 12 q^{31} - 3 q^{33} + 30 q^{41} - 9 q^{43} + 3 q^{45} - 15 q^{47} + 27 q^{49} + 3 q^{51} + 6 q^{53} + 21 q^{55} - 9 q^{57} - 36 q^{59} - 21 q^{61} - 3 q^{63} - 9 q^{65} + 45 q^{67} - 36 q^{71} + 42 q^{75} + 108 q^{77} + 36 q^{79} - 27 q^{83} - 9 q^{85} - 9 q^{87} - 27 q^{89} - 36 q^{91} - 18 q^{93} + 30 q^{95} - 51 q^{97} + 3 q^{99}+O(q^{100}) $ 24 * q - 9 * q^7 + 9 * q^11 - 9 * q^13 - 6 * q^17 - 3 * q^19 - 6 * q^21 + 15 * q^23 + 6 * q^25 - 12 * q^27 - 6 * q^29 + 12 * q^31 - 3 * q^33 + 30 * q^41 - 9 * q^43 + 3 * q^45 - 15 * q^47 + 27 * q^49 + 3 * q^51 + 6 * q^53 + 21 * q^55 - 9 * q^57 - 36 * q^59 - 21 * q^61 - 3 * q^63 - 9 * q^65 + 45 * q^67 - 36 * q^71 + 42 * q^75 + 108 * q^77 + 36 * q^79 - 27 * q^83 - 9 * q^85 - 9 * q^87 - 27 * q^89 - 36 * q^91 - 18 * q^93 + 30 * q^95 - 51 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$		0			0
$5$	−1.40574	+	1.17956i	−0.628668	+	0.527515i	−0.900515	−	0.434826i	$-0.856810\pi$
$5$	−1.40574	+	1.17956i	−0.628668	+	0.527515i	0.271847	+	0.962341i	$0.412366\pi$
$6$		0			0
$7$	−4.46660	−	2.57879i	−1.68822	−	0.974692i	−0.955884	−	0.293744i	$-0.905099\pi$
$7$	−4.46660	−	2.57879i	−1.68822	−	0.974692i	−0.732332	−	0.680948i	$-0.761568\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	3.85017	−	2.22290i	1.16087	−	0.670228i	0.209357	−	0.977839i	$-0.432863\pi$
$11$	3.85017	−	2.22290i	1.16087	−	0.670228i	0.951512	+	0.307611i	$0.0995295\pi$
$12$		0			0
$13$	2.69215	+	0.474699i	0.746669	+	0.131658i	0.534021	−	0.845471i	$-0.320680\pi$
$13$	2.69215	+	0.474699i	0.746669	+	0.131658i	0.212647	+	0.977129i	$0.431791\pi$
$14$		0			0
$15$	−1.40574	−	1.17956i	−0.362962	−	0.304561i
$16$		0			0
$17$	−2.85688	−	1.03982i	−0.692894	−	0.252193i	−0.0285202	−	0.999593i	$-0.509079\pi$
$17$	−2.85688	−	1.03982i	−0.692894	−	0.252193i	−0.664374	+	0.747400i	$0.731302\pi$
$18$		0			0
$19$	3.15385	+	3.00886i	0.723543	+	0.690280i
$19$	3.15385	+	3.00886i	0.723543	+	0.690280i
$20$		0			0
$21$	1.76400	−	4.84654i	0.384936	−	1.05760i
$22$		0			0
$23$	5.92256	−	7.05824i	1.23494	−	1.47174i	0.404593	−	0.914497i	$-0.367413\pi$
$23$	5.92256	−	7.05824i	1.23494	−	1.47174i	0.830347	−	0.557247i	$-0.188142\pi$
$24$		0			0
$25$	−0.283485	+	1.60772i	−0.0566969	+	0.321544i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	0.331534	+	0.910882i	0.0615643	+	0.169146i	0.966661	−	0.256059i	$-0.0824241\pi$
$29$	0.331534	+	0.910882i	0.0615643	+	0.169146i	−0.905097	+	0.425205i	$0.860202\pi$
$30$		0			0
$31$	3.33716	−	5.78013i	0.599372	−	1.03814i	−0.393542	−	0.919307i	$-0.628751\pi$
$31$	3.33716	−	5.78013i	0.599372	−	1.03814i	0.992914	−	0.118836i	$-0.0379162\pi$
$32$		0			0
$33$	2.85770	+	3.40567i	0.497462	+	0.592852i
$34$		0			0
$35$	9.32074	−	1.64350i	1.57549	−	0.277802i
$36$		0			0
$37$		−	6.33772i		−	1.04192i	−0.853583	−	0.520958i	$-0.825575\pi$
$37$		−	6.33772i		−	1.04192i	0.853583	−	0.520958i	$-0.174425\pi$
$38$		0			0
$39$			2.73368i			0.437740i
$40$		0			0
$41$	6.98847	−	1.23226i	1.09142	−	0.192446i	0.401158	−	0.916009i	$-0.368608\pi$
$41$	6.98847	−	1.23226i	1.09142	−	0.192446i	0.690258	+	0.723563i	$0.257497\pi$
$42$		0			0
$43$	−1.22260	−	1.45704i	−0.186445	−	0.222197i	0.664723	−	0.747090i	$-0.268550\pi$
$43$	−1.22260	−	1.45704i	−0.186445	−	0.222197i	−0.851168	+	0.524893i	$0.824105\pi$
$44$		0			0
$45$	0.917534	−	1.58922i	0.136778	−	0.236906i
$46$		0			0
$47$	−2.27932	−	6.26239i	−0.332474	−	0.913464i	−0.987467	−	0.157829i	$-0.949551\pi$
$47$	−2.27932	−	6.26239i	−0.332474	−	0.913464i	0.654993	−	0.755635i	$-0.272672\pi$
$48$		0			0
$49$	9.80034	+	16.9747i	1.40005	+	2.42496i
$50$		0			0
$51$	0.527929	−	2.99404i	0.0739249	−	0.419249i
$52$		0			0
$53$	1.82052	−	2.16961i	0.250068	−	0.298019i	−0.626378	−	0.779519i	$-0.715463\pi$
$53$	1.82052	−	2.16961i	0.250068	−	0.298019i	0.876446	+	0.481500i	$0.159908\pi$
$54$		0			0
$55$	−2.79031	+	7.66633i	−0.376246	+	1.03373i
$56$		0			0
$57$	−2.41549	+	3.62842i	−0.319939	+	0.480596i
$58$		0			0
$59$	−9.47029	−	3.44690i	−1.23293	−	0.448749i	−0.358328	−	0.933596i	$-0.616653\pi$
$59$	−9.47029	−	3.44690i	−1.23293	−	0.448749i	−0.874599	+	0.484847i	$0.838875\pi$
$60$		0			0
$61$	0.706102	+	0.592490i	0.0904071	+	0.0758606i	0.686871	−	0.726779i	$-0.258984\pi$
$61$	0.706102	+	0.592490i	0.0904071	+	0.0758606i	−0.596464	+	0.802640i	$0.703428\pi$
$62$		0			0
$63$	5.07923	+	0.895605i	0.639923	+	0.112836i
$64$		0			0
$65$	−4.34441	+	2.50825i	−0.538858	+	0.311110i
$66$		0			0
$67$	14.4351	−	5.25396i	1.76353	−	0.641874i	0.763541	−	0.645759i	$-0.223459\pi$
$67$	14.4351	−	5.25396i	1.76353	−	0.641874i	0.999992	+	0.00388540i	$0.00123677\pi$
$68$		0			0
$69$	7.97945	+	4.60694i	0.960613	+	0.554610i
$70$		0			0
$71$	−9.76956	+	8.19763i	−1.15943	+	0.972880i	−0.999898	−	0.0143123i	$-0.995444\pi$
$71$	−9.76956	+	8.19763i	−1.15943	+	0.972880i	−0.159536	+	0.987192i	$0.551000\pi$
$72$		0			0
$73$	1.24066	+	7.03612i	0.145208	+	0.823516i	0.967200	+	0.254017i	$0.0817518\pi$
$73$	1.24066	+	7.03612i	0.145208	+	0.823516i	−0.821992	+	0.569499i	$0.807137\pi$
$74$		0			0
$75$	−1.63252			−0.188507
$76$		0			0
$77$	−22.9295			−2.61306
$78$		0			0
$79$	0.463885	+	2.63082i	0.0521912	+	0.295991i	0.999720	−	0.0236808i	$-0.00753853\pi$
$79$	0.463885	+	2.63082i	0.0521912	+	0.295991i	−0.947528	+	0.319672i	$0.896427\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−7.41634	−	4.28182i	−0.814049	−	0.469991i	0.0343111	−	0.999411i	$-0.489076\pi$
$83$	−7.41634	−	4.28182i	−0.814049	−	0.469991i	−0.848360	+	0.529420i	$0.822410\pi$
$84$		0			0
$85$	5.24256	−	1.90814i	0.568636	−	0.206966i
$86$		0			0
$87$	−0.839473	+	0.484670i	−0.0900010	+	0.0519621i
$88$		0			0
$89$	−0.927132	−	0.163478i	−0.0982758	−	0.0173287i	0.124294	−	0.992245i	$-0.460333\pi$
$89$	−0.927132	−	0.163478i	−0.0982758	−	0.0173287i	−0.222570	+	0.974917i	$0.571445\pi$
$90$		0			0
$91$	−10.8006	−	9.06279i	−1.13221	−	0.950039i
$92$		0			0
$93$	6.27181	+	2.28275i	0.650356	+	0.236710i
$94$		0			0
$95$	−7.98263	−	0.509534i	−0.819001	−	0.0522771i
$96$		0			0
$97$	1.69079	−	4.64541i	0.171674	−	0.471670i	−0.823781	−	0.566908i	$-0.808139\pi$
$97$	1.69079	−	4.64541i	0.171674	−	0.471670i	0.995454	+	0.0952390i	$0.0303615\pi$
$98$		0			0
$99$	−2.85770	+	3.40567i	−0.287210	+	0.342283i
$100$		0			0
$101$	0.848134	−	4.81001i	0.0843925	−	0.478613i	−0.913094	−	0.407750i	$-0.866313\pi$
$101$	0.848134	−	4.81001i	0.0843925	−	0.478613i	0.997486	−	0.0708634i	$-0.0225754\pi$
$102$		0			0
$103$	4.23939	+	7.34284i	0.417720	+	0.723512i	0.995710	−	0.0925320i	$-0.0294961\pi$
$103$	4.23939	+	7.34284i	0.417720	+	0.723512i	−0.577990	+	0.816044i	$0.696163\pi$
$104$		0			0
$105$	3.23706	+	8.89374i	0.315904	+	0.867940i
$106$		0			0
$107$	8.89069	−	15.3991i	0.859496	−	1.48869i	−0.0129153	−	0.999917i	$-0.504111\pi$
$107$	8.89069	−	15.3991i	0.859496	−	1.48869i	0.872411	−	0.488773i	$-0.162555\pi$
$108$		0			0
$109$	−1.29920	−	1.54833i	−0.124441	−	0.148303i	0.700227	−	0.713921i	$-0.253082\pi$
$109$	−1.29920	−	1.54833i	−0.124441	−	0.148303i	−0.824668	+	0.565618i	$0.808638\pi$
$110$		0			0
$111$	6.24144	−	1.10053i	0.592411	−	0.104458i
$112$		0			0
$113$		−	17.2212i		−	1.62004i	−0.586404	−	0.810019i	$-0.699457\pi$
$113$		−	17.2212i		−	1.62004i	0.586404	−	0.810019i	$-0.300543\pi$
$114$		0			0
$115$			16.9081i			1.57669i
$116$		0			0
$117$	−2.69215	+	0.474699i	−0.248890	+	0.0438859i
$118$		0			0
$119$	10.0790	+	12.0117i	0.923945	+	1.10111i
$120$		0			0
$121$	4.38253	−	7.59077i	0.398412	−	0.690070i
$122$		0			0
$123$	2.42707	+	6.66832i	0.218842	+	0.601263i
$124$		0			0
$125$	−6.08557	−	10.5405i	−0.544310	−	0.942772i
$126$		0			0
$127$	1.65951	−	9.41158i	0.147258	−	0.835142i	−0.818268	−	0.574837i	$-0.805066\pi$
$127$	1.65951	−	9.41158i	0.147258	−	0.835142i	0.965526	−	0.260306i	$-0.0838233\pi$
$128$		0			0
$129$	1.22260	−	1.45704i	0.107644	−	0.128285i
$130$		0			0
$131$	0.335672	−	0.922250i	0.0293278	−	0.0805774i	−0.924165	−	0.381994i	$-0.875237\pi$
$131$	0.335672	−	0.922250i	0.0293278	−	0.0805774i	0.953492	+	0.301417i	$0.0974596\pi$
$132$		0			0
$133$	−6.32776	−	21.5725i	−0.548686	−	1.87057i
$134$		0			0
$135$	1.72440	+	0.627630i	0.148413	+	0.0540178i
$136$		0			0
$137$	4.36065	+	3.65902i	0.372556	+	0.312611i	0.809772	−	0.586745i	$-0.199591\pi$
$137$	4.36065	+	3.65902i	0.372556	+	0.312611i	−0.437216	+	0.899357i	$0.644035\pi$
$138$		0			0
$139$	4.88324	+	0.861047i	0.414191	+	0.0730331i	0.376861	−	0.926270i	$-0.377003\pi$
$139$	4.88324	+	0.861047i	0.414191	+	0.0730331i	0.0373304	+	0.999303i	$0.488115\pi$
$140$		0			0
$141$	5.77145	−	3.33215i	0.486044	−	0.280618i
$142$		0			0
$143$	11.4204	−	4.15670i	0.955026	−	0.347601i
$144$		0			0
$145$	−1.54049	−	0.889403i	−0.127931	−	0.0738609i
$146$		0			0
$147$	−15.0150	+	12.5991i	−1.23842	+	1.03915i
$148$		0			0
$149$	−1.03975	−	5.89671i	−0.0851795	−	0.483077i	−0.997318	−	0.0731942i	$-0.976681\pi$
$149$	−1.03975	−	5.89671i	−0.0851795	−	0.483077i	0.912138	−	0.409883i	$-0.134430\pi$
$150$		0			0
$151$	−10.2353			−0.832933			−0.416466	−	0.909151i	$-0.636732\pi$
$151$	−10.2353			−0.832933			−0.416466	+	0.909151i	$0.636732\pi$
$152$		0			0
$153$	3.04022			0.245787
$154$		0			0
$155$	2.12681	+	12.0618i	0.170830	+	0.968824i
$156$		0			0
$157$	−8.06521	+	6.76751i	−0.643674	+	0.540106i	−0.905144	−	0.425105i	$-0.860237\pi$
$157$	−8.06521	+	6.76751i	−0.643674	+	0.540106i	0.261470	+	0.965212i	$0.415793\pi$
$158$		0			0
$159$	2.45278	+	1.41611i	0.194518	+	0.112305i
$160$		0			0
$161$	−44.6554	+	16.2533i	−3.51934	+	1.28094i
$162$		0			0
$163$	−11.4128	+	6.58919i	−0.893921	+	0.516105i	−0.875223	−	0.483720i	$-0.839285\pi$
$163$	−11.4128	+	6.58919i	−0.893921	+	0.516105i	−0.0186977	+	0.999825i	$0.505952\pi$
$164$		0			0
$165$	−8.03439	−	1.41668i	−0.625476	−	0.110288i
$166$		0			0
$167$	−8.67066	−	7.27555i	−0.670956	−	0.562999i	0.242392	−	0.970178i	$-0.422068\pi$
$167$	−8.67066	−	7.27555i	−0.670956	−	0.562999i	−0.913348	+	0.407179i	$0.866512\pi$
$168$		0			0
$169$	−5.19366	−	1.89034i	−0.399512	−	0.145411i
$170$		0			0
$171$	−3.99274	−	1.74872i	−0.305332	−	0.133728i
$172$		0			0
$173$	−7.89528	+	21.6921i	−0.600267	+	1.64922i	0.150466	+	0.988615i	$0.451922\pi$
$173$	−7.89528	+	21.6921i	−0.600267	+	1.64922i	−0.750734	+	0.660605i	$0.770300\pi$
$174$		0			0
$175$	5.41219	−	6.45000i	0.409123	−	0.487574i
$176$		0			0
$177$	1.75004	−	9.92497i	0.131541	−	0.746006i
$178$		0			0
$179$	0.516790	+	0.895107i	0.0386267	+	0.0669034i	0.884692	−	0.466175i	$-0.154368\pi$
$179$	0.516790	+	0.895107i	0.0386267	+	0.0669034i	−0.846066	+	0.533079i	$0.821035\pi$
$180$		0			0
$181$	2.57246	+	7.06776i	0.191209	+	0.525343i	0.997838	−	0.0657149i	$-0.0209328\pi$
$181$	2.57246	+	7.06776i	0.191209	+	0.525343i	−0.806629	+	0.591058i	$0.798711\pi$
$182$		0			0
$183$	−0.460875	+	0.798259i	−0.0340689	+	0.0590090i
$184$		0			0
$185$	7.47572	+	8.90922i	0.549626	+	0.655019i
$186$		0			0
$187$	−13.3109	+	2.34706i	−0.973386	+	0.171634i
$188$		0			0
$189$			5.15758i			0.375159i
$190$		0			0
$191$			11.3607i			0.822028i	0.911629	+	0.411014i	$0.134825\pi$
$191$			11.3607i			0.822028i	−0.911629	+	0.411014i	$0.865175\pi$
$192$		0			0
$193$	18.0104	−	3.17573i	1.29642	−	0.228594i	0.517481	−	0.855694i	$-0.326870\pi$
$193$	18.0104	−	3.17573i	1.29642	−	0.228594i	0.778938	+	0.627101i	$0.215759\pi$
$194$		0			0
$195$	−3.22454	−	3.84286i	−0.230914	−	0.275193i
$196$		0			0
$197$	8.65056	−	14.9832i	0.616327	−	1.06751i	−0.373824	−	0.927500i	$-0.621953\pi$
$197$	8.65056	−	14.9832i	0.616327	−	1.06751i	0.990150	−	0.140009i	$-0.0447132\pi$
$198$		0			0
$199$	2.09126	+	5.74569i	0.148246	+	0.407301i	0.991482	−	0.130241i	$-0.0415751\pi$
$199$	2.09126	+	5.74569i	0.148246	+	0.407301i	−0.843237	+	0.537542i	$0.819353\pi$
$200$		0			0
$201$	7.68078	+	13.3035i	0.541760	+	0.938357i
$202$		0			0
$203$	0.868146	−	4.92350i	0.0609319	−	0.345562i
$204$		0			0
$205$	−8.37049	+	9.97556i	−0.584620	+	0.696723i
$206$		0			0
$207$	−3.15133	+	8.65821i	−0.219033	+	0.601787i
$208$		0			0
$209$	18.8312	+	4.57394i	1.30258	+	0.316386i
$210$		0			0
$211$	−1.79449	−	0.653140i	−0.123538	−	0.0449640i	0.279512	−	0.960142i	$-0.409827\pi$
$211$	−1.79449	−	0.653140i	−0.123538	−	0.0449640i	−0.403049	+	0.915178i	$0.632050\pi$
$212$		0			0
$213$	−9.76956	−	8.19763i	−0.669399	−	0.561692i
$214$		0			0
$215$	3.43733	+	0.606095i	0.234424	+	0.0413353i
$216$		0			0
$217$	−29.8115	+	17.2117i	−2.02374	+	1.16841i
$218$		0			0
$219$	−6.71379	+	2.44362i	−0.453676	+	0.165125i
$220$		0			0
$221$	−7.19754	−	4.15550i	−0.484159	−	0.279529i
$222$		0			0
$223$	−18.2437	+	15.3083i	−1.22169	+	1.02512i	−0.222953	+	0.974829i	$0.571570\pi$
$223$	−18.2437	+	15.3083i	−1.22169	+	1.02512i	−0.998735	+	0.0502881i	$0.983986\pi$
$224$		0			0
$225$	−0.283485	−	1.60772i	−0.0188990	−	0.107181i
$226$		0			0
$227$	21.9176			1.45472			0.727362	−	0.686254i	$-0.240746\pi$
$227$	21.9176			1.45472			0.727362	+	0.686254i	$0.240746\pi$
$228$		0			0
$229$	15.7903			1.04345			0.521725	−	0.853114i	$-0.325289\pi$
$229$	15.7903			1.04345			0.521725	+	0.853114i	$0.325289\pi$
$230$		0			0
$231$	−3.98167	−	22.5812i	−0.261975	−	1.48573i
$232$		0			0
$233$	11.0589	−	9.27955i	0.724495	−	0.607923i	−0.204130	−	0.978944i	$-0.565436\pi$
$233$	11.0589	−	9.27955i	0.724495	−	0.607923i	0.928625	+	0.371020i	$0.120992\pi$
$234$		0			0
$235$	10.5910	+	6.11472i	0.690881	+	0.398880i
$236$		0			0
$237$	−2.51030	+	0.913676i	−0.163062	+	0.0593496i
$238$		0			0
$239$	−0.0921143	+	0.0531822i	−0.00595838	+	0.00344007i	−0.502976	−	0.864300i	$-0.667762\pi$
$239$	−0.0921143	+	0.0531822i	−0.00595838	+	0.00344007i	0.497018	+	0.867740i	$0.334428\pi$
$240$		0			0
$241$	4.27133	+	0.753151i	0.275141	+	0.0485147i	0.309516	−	0.950894i	$-0.399833\pi$
$241$	4.27133	+	0.753151i	0.275141	+	0.0485147i	−0.0343751	+	0.999409i	$0.510944\pi$
$242$		0			0
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$		0			0
$245$	−33.7994	−	12.3020i	−2.15937	−	0.785945i
$246$		0			0
$247$	7.06234	+	9.59744i	0.449366	+	0.610670i
$248$		0			0
$249$	2.92894	−	8.04720i	0.185614	−	0.509970i
$250$		0			0
$251$	−1.63084	+	1.94356i	−0.102938	+	0.122677i	−0.815054	−	0.579385i	$-0.803293\pi$
$251$	−1.63084	+	1.94356i	−0.102938	+	0.122677i	0.712116	+	0.702062i	$0.247737\pi$
$252$		0			0
$253$	7.11314	−	40.3406i	0.447199	−	2.53619i
$254$		0			0
$255$	2.78951	+	4.83157i	0.174686	+	0.302565i
$256$		0			0
$257$	−2.58722	−	7.10832i	−0.161386	−	0.443405i	0.832472	−	0.554067i	$-0.186925\pi$
$257$	−2.58722	−	7.10832i	−0.161386	−	0.443405i	−0.993858	+	0.110663i	$0.964703\pi$
$258$		0			0
$259$	−16.3437	+	28.3081i	−1.01555	+	1.75898i
$260$		0			0
$261$	−0.623080	−	0.742558i	−0.0385677	−	0.0459632i
$262$		0			0
$263$	−23.8451	+	4.20454i	−1.47035	+	0.259263i	−0.850716	−	0.525625i	$-0.823831\pi$
$263$	−23.8451	+	4.20454i	−1.47035	+	0.259263i	−0.619637	+	0.784888i	$0.712720\pi$
$264$		0			0
$265$			5.19733i			0.319269i
$266$		0			0
$267$		−	0.941435i		−	0.0576149i
$268$		0			0
$269$	2.08800	−	0.368171i	0.127308	−	0.0224478i	−0.109631	−	0.993972i	$-0.534967\pi$
$269$	2.08800	−	0.368171i	0.127308	−	0.0224478i	0.236939	+	0.971525i	$0.423856\pi$
$270$		0			0
$271$	1.63282	+	1.94592i	0.0991867	+	0.118206i	0.813354	−	0.581769i	$-0.197639\pi$
$271$	1.63282	+	1.94592i	0.0991867	+	0.118206i	−0.714168	+	0.699975i	$0.753195\pi$
$272$		0			0
$273$	7.04960	−	12.2103i	0.426661	−	0.738999i
$274$		0			0
$275$	2.48233	+	6.82015i	0.149690	+	0.411271i
$276$		0			0
$277$	10.0444	+	17.3973i	0.603507	+	1.04530i	0.992286	+	0.123973i	$0.0395636\pi$
$277$	10.0444	+	17.3973i	0.603507	+	1.04530i	−0.388779	+	0.921331i	$0.627103\pi$
$278$		0			0
$279$	−1.15898	+	6.57292i	−0.0693865	+	0.393511i
$280$		0			0
$281$	−1.38017	+	1.64482i	−0.0823338	+	0.0981216i	−0.805639	−	0.592407i	$-0.798178\pi$
$281$	−1.38017	+	1.64482i	−0.0823338	+	0.0981216i	0.723305	+	0.690529i	$0.242622\pi$
$282$		0			0
$283$	−7.07689	+	19.4436i	−0.420677	+	1.15580i	0.530642	+	0.847596i	$0.321951\pi$
$283$	−7.07689	+	19.4436i	−0.420677	+	1.15580i	−0.951320	+	0.308206i	$0.900271\pi$
$284$		0			0
$285$	−0.884377	−	7.94984i	−0.0523860	−	0.470908i
$286$		0			0
$287$	−34.3924	−	12.5178i	−2.03012	−	0.738904i
$288$		0			0
$289$	−5.94224	−	4.98613i	−0.349543	−	0.293302i
$290$		0			0
$291$	4.86843	+	0.858436i	0.285393	+	0.0503224i
$292$		0			0
$293$	19.6262	−	11.3312i	1.14658	−	0.661976i	0.198525	−	0.980096i	$-0.436385\pi$
$293$	19.6262	−	11.3312i	1.14658	−	0.661976i	0.948050	+	0.318120i	$0.103052\pi$
$294$		0			0
$295$	17.3786	−	6.32531i	1.01182	−	0.368274i
$296$		0			0
$297$	−3.85017	−	2.22290i	−0.223409	−	0.128985i
$298$		0			0
$299$	19.2950	−	16.1904i	1.11586	−	0.936315i
$300$		0			0
$301$	1.70347	+	9.66086i	0.0981864	+	0.556843i
$302$		0			0
$303$	4.88421			0.280590
$304$		0			0
$305$	−1.69148			−0.0968536
$306$		0			0
$307$	1.16576	+	6.61135i	0.0665334	+	0.377330i	0.999834	+	0.0182330i	$0.00580406\pi$
$307$	1.16576	+	6.61135i	0.0665334	+	0.377330i	−0.933300	+	0.359097i	$0.883085\pi$
$308$		0			0
$309$	−6.49513	+	5.45006i	−0.369495	+	0.310043i
$310$		0			0
$311$	12.5851	+	7.26603i	0.713637	+	0.412019i	0.812406	−	0.583092i	$-0.198157\pi$
$311$	12.5851	+	7.26603i	0.713637	+	0.412019i	−0.0987690	+	0.995110i	$0.531490\pi$
$312$		0			0
$313$	−3.10621	+	1.13057i	−0.175573	+	0.0639034i	−0.428311	−	0.903631i	$-0.640891\pi$
$313$	−3.10621	+	1.13057i	−0.175573	+	0.0639034i	0.252738	+	0.967535i	$0.418669\pi$
$314$		0			0
$315$	−8.19652	+	4.73226i	−0.461821	+	0.266633i
$316$		0			0
$317$	0.826494	+	0.145733i	0.0464206	+	0.00818520i	0.196810	−	0.980442i	$-0.436942\pi$
$317$	0.826494	+	0.145733i	0.0464206	+	0.00818520i	−0.150390	+	0.988627i	$0.548053\pi$
$318$		0			0
$319$	3.30126	+	2.77008i	0.184835	+	0.155095i
$320$		0			0
$321$	16.7090	+	6.08159i	0.932607	+	0.339441i
$322$		0			0
$323$	−5.88149	−	11.8754i	−0.327255	−	0.660763i
$324$		0			0
$325$	−1.52637	+	4.19366i	−0.0846676	+	0.232622i
$326$		0			0
$327$	1.29920	−	1.54833i	0.0718460	−	0.0856227i
$328$		0			0
$329$	−5.96858	+	33.8495i	−0.329058	+	1.86618i
$330$		0			0
$331$	−16.6221	−	28.7903i	−0.913631	−	1.58246i	−0.808893	−	0.587956i	$-0.799933\pi$
$331$	−16.6221	−	28.7903i	−0.913631	−	1.58246i	−0.104738	−	0.994500i	$-0.533400\pi$
$332$		0			0
$333$	2.16763	+	5.95551i	0.118785	+	0.326360i
$334$		0			0
$335$	−14.0948	+	24.4128i	−0.770079	+	1.33382i
$336$		0			0
$337$	−1.59399	−	1.89964i	−0.0868302	−	0.103480i	0.720880	−	0.693060i	$-0.243738\pi$
$337$	−1.59399	−	1.89964i	−0.0868302	−	0.103480i	−0.807710	+	0.589580i	$0.799293\pi$
$338$		0			0
$339$	16.9596	−	2.99044i	0.921120	−	0.162418i
$340$		0			0
$341$		−	29.6726i		−	1.60686i
$342$		0			0
$343$		−	64.9891i		−	3.50908i
$344$		0			0
$345$	−16.6512	+	2.93606i	−0.896471	+	0.158072i
$346$		0			0
$347$	16.4902	+	19.6523i	0.885241	+	1.05499i	0.998114	+	0.0613799i	$0.0195501\pi$
$347$	16.4902	+	19.6523i	0.885241	+	1.05499i	−0.112873	+	0.993609i	$0.536005\pi$
$348$		0			0
$349$	−4.94302	+	8.56156i	−0.264594	+	0.458290i	−0.967457	−	0.253035i	$-0.918571\pi$
$349$	−4.94302	+	8.56156i	−0.264594	+	0.458290i	0.702863	+	0.711325i	$0.251905\pi$
$350$		0			0
$351$	−0.934975	−	2.56882i	−0.0499052	−	0.137114i
$352$		0			0
$353$	6.10031	+	10.5660i	0.324687	+	0.562374i	0.981449	−	0.191724i	$-0.0614078\pi$
$353$	6.10031	+	10.5660i	0.324687	+	0.562374i	−0.656762	+	0.754098i	$0.728074\pi$
$354$		0			0
$355$	4.06390	−	23.0475i	0.215690	−	1.22324i
$356$		0			0
$357$	−10.0790	+	12.0117i	−0.533440	+	0.635729i
$358$		0			0
$359$	2.56846	−	7.05679i	0.135558	−	0.372443i	−0.853277	−	0.521458i	$-0.825388\pi$
$359$	2.56846	−	7.05679i	0.135558	−	0.372443i	0.988835	+	0.149015i	$0.0476104\pi$
$360$		0			0
$361$	0.893531	+	18.9790i	0.0470279	+	0.998894i
$362$		0			0
$363$	8.23646	+	2.99783i	0.432302	+	0.157345i
$364$		0			0
$365$	−10.0436	−	8.42756i	−0.525705	−	0.441119i
$366$		0			0
$367$	18.4405	+	3.25155i	0.962585	+	0.169730i	0.632790	−	0.774323i	$-0.281910\pi$
$367$	18.4405	+	3.25155i	0.962585	+	0.169730i	0.329794	+	0.944053i	$0.393021\pi$
$368$		0			0
$369$	−6.14556	+	3.54814i	−0.319925	+	0.184709i
$370$		0			0
$371$	−13.7265	+	4.99604i	−0.712645	+	0.259382i
$372$		0			0
$373$	16.5108	+	9.53253i	0.854898	+	0.493576i	0.862301	−	0.506397i	$-0.169023\pi$
$373$	16.5108	+	9.53253i	0.854898	+	0.493576i	−0.00740220	+	0.999973i	$0.502356\pi$
$374$		0			0
$375$	9.32363	−	7.82345i	0.481470	−	0.404001i
$376$		0			0
$377$	0.460145	+	2.60961i	0.0236987	+	0.134402i
$378$		0			0
$379$	−4.34568			−0.223222			−0.111611	−	0.993752i	$-0.535601\pi$
$379$	−4.34568			−0.223222			−0.111611	+	0.993752i	$0.535601\pi$
$380$		0			0
$381$	9.55676			0.489608
$382$		0			0
$383$	2.85003	+	16.1633i	0.145630	+	0.825906i	0.966860	+	0.255309i	$0.0821771\pi$
$383$	2.85003	+	16.1633i	0.145630	+	0.825906i	−0.821230	+	0.570597i	$0.806712\pi$
$384$		0			0
$385$	32.2331	−	27.0468i	1.64275	−	1.37843i
$386$		0			0
$387$	1.64721	+	0.951016i	0.0837323	+	0.0483429i
$388$		0			0
$389$	24.4027	−	8.88187i	1.23727	−	0.450329i	0.361188	−	0.932493i	$-0.382371\pi$
$389$	24.4027	−	8.88187i	1.23727	−	0.450329i	0.876081	+	0.482164i	$0.160149\pi$
$390$		0			0
$391$	−24.2593	+	14.0061i	−1.22685	+	0.708320i
$392$		0			0
$393$	0.966528	+	0.170425i	0.0487549	+	0.00859680i
$394$		0			0
$395$	−3.75532	−	3.15109i	−0.188951	−	0.158548i
$396$		0			0
$397$	−9.86885	−	3.59197i	−0.495303	−	0.180276i	0.0822771	−	0.996609i	$-0.473781\pi$
$397$	−9.86885	−	3.59197i	−0.495303	−	0.180276i	−0.577580	+	0.816334i	$0.696003\pi$
$398$		0			0
$399$	20.1460	−	9.97765i	1.00856	−	0.499507i
$400$		0			0
$401$	−7.25606	+	19.9359i	−0.362351	+	0.995550i	0.615846	+	0.787867i	$0.288814\pi$
$401$	−7.25606	+	19.9359i	−0.362351	+	0.995550i	−0.978196	+	0.207683i	$0.933408\pi$
$402$		0			0
$403$	11.7280	−	13.9768i	0.584211	−	0.696236i
$404$		0			0
$405$	−0.318656	+	1.80719i	−0.0158342	+	0.0898000i
$406$		0			0
$407$	−14.0881	−	24.4013i	−0.698321	−	1.20953i
$408$		0			0
$409$	1.94390	+	5.34083i	0.0961199	+	0.264087i	0.978429	−	0.206583i	$-0.0662344\pi$
$409$	1.94390	+	5.34083i	0.0961199	+	0.264087i	−0.882309	+	0.470670i	$0.844012\pi$
$410$		0			0
$411$	−2.84621	+	4.92979i	−0.140393	+	0.243168i
$412$		0			0
$413$	33.4112	+	39.8179i	1.64406	+	1.95931i
$414$		0			0
$415$	15.4761	−	2.72886i	0.759694	−	0.133955i
$416$		0			0
$417$			4.95857i			0.242822i
$418$		0			0
$419$		−	26.3350i		−	1.28655i	−0.765635	−	0.643275i	$-0.777575\pi$
$419$		−	26.3350i		−	1.28655i	0.765635	−	0.643275i	$-0.222425\pi$
$420$		0			0
$421$	−6.47601	+	1.14190i	−0.315622	+	0.0556526i	−0.329215	−	0.944255i	$-0.606784\pi$
$421$	−6.47601	+	1.14190i	−0.315622	+	0.0556526i	0.0135933	+	0.999908i	$0.495673\pi$
$422$		0			0
$423$	4.28373	+	5.10515i	0.208282	+	0.248221i
$424$		0			0
$425$	2.48162	−	4.29829i	0.120376	−	0.208498i
$426$		0			0
$427$	−1.62597	−	4.46731i	−0.0786860	−	0.216188i
$428$		0			0
$429$	6.07669	+	10.5251i	0.293385	+	0.508158i
$430$		0			0
$431$	−5.55673	+	31.5138i	−0.267658	+	1.51797i	0.493698	+	0.869633i	$0.335645\pi$
$431$	−5.55673	+	31.5138i	−0.267658	+	1.51797i	−0.761357	+	0.648333i	$0.775466\pi$
$432$		0			0
$433$	−17.6259	+	21.0058i	−0.847048	+	1.00947i	0.152727	+	0.988268i	$0.451194\pi$
$433$	−17.6259	+	21.0058i	−0.847048	+	1.00947i	−0.999775	+	0.0212040i	$0.993250\pi$
$434$		0			0
$435$	0.608387	−	1.67153i	0.0291699	−	0.0801438i
$436$		0			0
$437$	39.9161	−	4.44045i	1.90945	−	0.212416i
$438$		0			0
$439$	32.9757	+	12.0022i	1.57384	+	0.572832i	0.973854	−	0.227177i	$-0.0729496\pi$
$439$	32.9757	+	12.0022i	1.57384	+	0.572832i	0.599989	+	0.800009i	$0.295172\pi$
$440$		0			0
$441$	−15.0150	−	12.5991i	−0.715000	−	0.599956i
$442$		0			0
$443$	−27.9971	−	4.93664i	−1.33018	−	0.234547i	−0.537025	−	0.843566i	$-0.680452\pi$
$443$	−27.9971	−	4.93664i	−1.33018	−	0.234547i	−0.793155	+	0.609019i	$0.791563\pi$
$444$		0			0
$445$	1.49614	−	0.863799i	0.0709240	−	0.0409480i
$446$		0			0
$447$	5.62657	−	2.04790i	0.266128	−	0.0968625i
$448$		0			0
$449$	−23.8508	−	13.7703i	−1.12559	−	0.649859i	−0.182767	−	0.983156i	$-0.558505\pi$
$449$	−23.8508	−	13.7703i	−1.12559	−	0.649859i	−0.942822	+	0.333297i	$0.891839\pi$
$450$		0			0
$451$	24.1676	−	20.2790i	1.13801	−	0.954903i
$452$		0			0
$453$	−1.77733	−	10.0798i	−0.0835064	−	0.473588i
$454$		0			0
$455$	25.8730			1.21294
$456$		0			0
$457$	30.3056			1.41763			0.708817	−	0.705392i	$-0.249229\pi$
$457$	30.3056			1.41763			0.708817	+	0.705392i	$0.249229\pi$
$458$		0			0
$459$	0.527929	+	2.99404i	0.0246416	+	0.139750i
$460$		0			0
$461$	9.44702	−	7.92699i	0.439992	−	0.369197i	−0.395715	−	0.918374i	$-0.629503\pi$
$461$	9.44702	−	7.92699i	0.439992	−	0.369197i	0.835706	+	0.549177i	$0.185059\pi$
$462$		0			0
$463$	19.1292	+	11.0442i	0.889007	+	0.513269i	0.873618	−	0.486613i	$-0.161768\pi$
$463$	19.1292	+	11.0442i	0.889007	+	0.513269i	0.0153898	+	0.999882i	$0.495101\pi$
$464$		0			0
$465$	−11.5092	+	4.18901i	−0.533726	+	0.194261i
$466$		0			0
$467$	7.64719	−	4.41511i	0.353870	−	0.204307i	−0.312518	−	0.949912i	$-0.601173\pi$
$467$	7.64719	−	4.41511i	0.353870	−	0.204307i	0.666388	+	0.745605i	$0.267839\pi$
$468$		0			0
$469$	−78.0249	−	13.7579i	−3.60285	−	0.635280i
$470$		0			0
$471$	−8.06521	−	6.76751i	−0.371625	−	0.311831i
$472$		0			0
$473$	−7.94608	−	2.89214i	−0.365361	−	0.132981i
$474$		0			0
$475$	−5.73147	+	4.21754i	−0.262978	+	0.193514i
$476$		0			0
$477$	−0.968679	+	2.66142i	−0.0443527	+	0.121858i
$478$		0			0
$479$	9.57193	−	11.4074i	0.437353	−	0.521216i	−0.501676	−	0.865056i	$-0.667283\pi$
$479$	9.57193	−	11.4074i	0.437353	−	0.521216i	0.939029	+	0.343839i	$0.111727\pi$
$480$		0			0
$481$	3.00851	−	17.0621i	0.137176	−	0.777965i
$482$		0			0
$483$	−23.7607	−	41.1547i	−1.08115	−	1.87260i
$484$		0			0
$485$	3.10272	+	8.52464i	0.140887	+	0.387084i
$486$		0			0
$487$	13.7489	−	23.8138i	0.623023	−	1.07911i	−0.365897	−	0.930655i	$-0.619238\pi$
$487$	13.7489	−	23.8138i	0.623023	−	1.07911i	0.988920	−	0.148452i	$-0.0474289\pi$
$488$		0			0
$489$	−8.47090	−	10.0952i	−0.383067	−	0.456522i
$490$		0			0
$491$	20.6106	−	3.63420i	0.930142	−	0.164009i	0.312006	−	0.950080i	$-0.398999\pi$
$491$	20.6106	−	3.63420i	0.930142	−	0.164009i	0.618136	+	0.786071i	$0.287888\pi$
$492$		0			0
$493$		−	2.94701i		−	0.132727i
$494$		0			0
$495$		−	8.15833i		−	0.366690i
$496$		0			0
$497$	64.7767	−	11.4219i	2.90563	−	0.512341i
$498$		0			0
$499$	−4.05595	−	4.83369i	−0.181569	−	0.216386i	0.667581	−	0.744537i	$-0.267330\pi$
$499$	−4.05595	−	4.83369i	−0.181569	−	0.216386i	−0.849150	+	0.528151i	$0.822885\pi$
$500$		0			0
$501$	5.65937	−	9.80232i	0.252842	−	0.437935i
$502$		0			0
$503$	−12.7372	−	34.9952i	−0.567924	−	1.56036i	−0.807740	−	0.589539i	$-0.799309\pi$
$503$	−12.7372	−	34.9952i	−0.567924	−	1.56036i	0.239816	−	0.970818i	$-0.422913\pi$
$504$		0			0
$505$	4.48143	+	7.76206i	0.199421	+	0.345407i
$506$		0			0
$507$	0.959750	−	5.44301i	0.0426240	−	0.241733i
$508$		0			0
$509$	−8.98338	+	10.7060i	−0.398182	+	0.474534i	−0.927465	−	0.373911i	$-0.878017\pi$
$509$	−8.98338	+	10.7060i	−0.398182	+	0.474534i	0.529283	+	0.848445i	$0.322461\pi$
$510$		0			0
$511$	12.6032	−	34.6269i	0.557532	−	1.53181i
$512$		0			0
$513$	1.02882	−	4.23574i	0.0454237	−	0.187013i
$514$		0			0
$515$	−14.6208	−	5.32154i	−0.644270	−	0.234495i
$516$		0			0
$517$	−22.6964	−	19.0446i	−0.998188	−	0.837579i
$518$		0			0
$519$	−22.7336	−	4.00854i	−0.997892	−	0.175955i
$520$		0			0
$521$	−8.13410	+	4.69623i	−0.356362	+	0.205745i	−0.667484	−	0.744625i	$-0.732629\pi$
$521$	−8.13410	+	4.69623i	−0.356362	+	0.205745i	0.311122	+	0.950370i	$0.399295\pi$
$522$		0			0
$523$	−33.1646	+	12.0709i	−1.45019	+	0.527825i	−0.942644	−	0.333800i	$-0.891669\pi$
$523$	−33.1646	+	12.0709i	−1.45019	+	0.527825i	−0.507544	+	0.861626i	$0.669447\pi$
$524$		0			0
$525$	7.29183	+	4.20994i	0.318241	+	0.183737i
$526$		0			0
$527$	−15.5441	+	13.0431i	−0.677113	+	0.568165i
$528$		0			0
$529$	−10.7480	−	60.9551i	−0.467306	−	2.65022i
$530$		0			0
$531$	10.0781			0.437351
$532$		0			0
$533$	19.3990			0.840263
$534$		0			0
$535$	5.66615	+	32.1343i	0.244969	+	1.38929i
$536$		0			0
$537$	−0.791769	+	0.664373i	−0.0341673	+	0.0286698i
$538$		0			0
$539$	75.4659	+	43.5703i	3.25055	+	1.87670i
$540$		0			0
$541$	−9.78717	+	3.56224i	−0.420783	+	0.153153i	−0.543729	−	0.839261i	$-0.682988\pi$
$541$	−9.78717	+	3.56224i	−0.420783	+	0.153153i	0.122946	+	0.992413i	$0.460766\pi$
$542$		0			0
$543$	−6.51369	+	3.76068i	−0.279529	+	0.161386i
$544$		0			0
$545$	3.65269	+	0.644068i	0.156464	+	0.0275888i
$546$		0			0
$547$	0.274396	+	0.230245i	0.0117323	+	0.00984458i	0.648635	−	0.761100i	$-0.275340\pi$
$547$	0.274396	+	0.230245i	0.0117323	+	0.00984458i	−0.636903	+	0.770944i	$0.719785\pi$
$548$		0			0
$549$	−0.866162	−	0.315257i	−0.0369669	−	0.0134549i
$550$		0			0
$551$	−1.69511	+	3.87032i	−0.0722140	+	0.164881i
$552$		0			0
$553$	4.71236	−	12.9471i	0.200390	−	0.550567i
$554$		0			0
$555$	−7.47572	+	8.90922i	−0.317327	+	0.378175i
$556$		0			0
$557$	−1.44327	+	8.18518i	−0.0611532	+	0.346817i	0.938844	+	0.344344i	$0.111898\pi$
$557$	−1.44327	+	8.18518i	−0.0611532	+	0.346817i	−0.999997	+	0.00247361i	$0.999213\pi$
$558$		0			0
$559$	−2.59978	−	4.50294i	−0.109959	−	0.190454i
$560$		0			0
$561$	−4.62281	−	12.7011i	−0.195175	−	0.536240i
$562$		0			0
$563$	−2.00806	+	3.47806i	−0.0846295	+	0.146583i	−0.905233	−	0.424915i	$-0.860304\pi$
$563$	−2.00806	+	3.47806i	−0.0846295	+	0.146583i	0.820604	+	0.571498i	$0.193637\pi$
$564$		0			0
$565$	20.3135	+	24.2087i	0.854594	+	1.01847i
$566$		0			0
$567$	−5.07923	+	0.895605i	−0.213308	+	0.0376119i
$568$		0			0
$569$			15.1395i			0.634682i	0.948311	+	0.317341i	$0.102790\pi$
$569$			15.1395i			0.634682i	−0.948311	+	0.317341i	$0.897210\pi$
$570$		0			0
$571$		−	11.4839i		−	0.480587i	−0.970700	−	0.240293i	$-0.922756\pi$
$571$		−	11.4839i		−	0.480587i	0.970700	−	0.240293i	$-0.0772436\pi$
$572$		0			0
$573$	−11.1881	+	1.97276i	−0.467388	+	0.0824131i
$574$		0			0
$575$	9.66872	+	11.5227i	0.403213	+	0.480531i
$576$		0			0
$577$	−5.52794	+	9.57468i	−0.230131	+	0.398599i	−0.957847	−	0.287280i	$-0.907249\pi$
$577$	−5.52794	+	9.57468i	−0.230131	+	0.398599i	0.727715	+	0.685879i	$0.240582\pi$
$578$		0			0
$579$	6.25496	+	17.1854i	0.259947	+	0.714199i
$580$		0			0
$581$	22.0839	+	38.2504i	0.916194	+	1.58689i
$582$		0			0
$583$	2.18649	−	12.4002i	0.0905551	−	0.513564i
$584$		0			0
$585$	3.22454	−	3.84286i	0.133318	−	0.158883i
$586$		0			0
$587$	12.2220	−	33.5797i	0.504456	−	1.38598i	−0.382426	−	0.923986i	$-0.624911\pi$
$587$	12.2220	−	33.5797i	0.504456	−	1.38598i	0.886882	−	0.461996i	$-0.152867\pi$
$588$		0			0
$589$	27.9165	−	8.18862i	1.15028	−	0.337406i
$590$		0			0
$591$	16.2577	+	5.91733i	0.668754	+	0.243406i
$592$		0			0
$593$	9.57713	+	8.03616i	0.393285	+	0.330006i	0.817891	−	0.575373i	$-0.195143\pi$
$593$	9.57713	+	8.03616i	0.393285	+	0.330006i	−0.424606	+	0.905378i	$0.639587\pi$
$594$		0			0
$595$	−28.3371	−	4.99660i	−1.16171	−	0.204841i
$596$		0			0
$597$	−5.29526	+	3.05722i	−0.216721	+	0.125124i
$598$		0			0
$599$	−25.3275	+	9.21847i	−1.03486	+	0.376657i	−0.802928	−	0.596076i	$-0.796726\pi$
$599$	−25.3275	+	9.21847i	−1.03486	+	0.376657i	−0.231928	+	0.972733i	$0.574503\pi$
$600$		0			0
$601$	−12.1355	−	7.00645i	−0.495018	−	0.285799i	0.231636	−	0.972803i	$-0.425592\pi$
$601$	−12.1355	−	7.00645i	−0.495018	−	0.285799i	−0.726654	+	0.687004i	$0.758926\pi$
$602$		0			0
$603$	−11.7676	+	9.87422i	−0.479215	+	0.402109i
$604$		0			0
$605$	2.79304	+	15.8401i	0.113553	+	0.643993i
$606$		0			0
$607$	−25.6721			−1.04200			−0.521000	−	0.853557i	$-0.674441\pi$
$607$	−25.6721			−1.04200			−0.521000	+	0.853557i	$0.674441\pi$
$608$		0			0
$609$	4.99945			0.202588
$610$		0			0
$611$	−3.16354	−	17.9413i	−0.127983	−	0.725827i
$612$		0			0
$613$	5.40333	−	4.53393i	0.218238	−	0.183124i	−0.527114	−	0.849795i	$-0.676726\pi$
$613$	5.40333	−	4.53393i	0.218238	−	0.183124i	0.745352	+	0.666671i	$0.232281\pi$
$614$		0			0
$615$	−11.2775	−	6.51108i	−0.454754	−	0.262552i
$616$		0			0
$617$	5.22626	−	1.90220i	0.210401	−	0.0765799i	−0.234669	−	0.972075i	$-0.575401\pi$
$617$	5.22626	−	1.90220i	0.210401	−	0.0765799i	0.445071	+	0.895495i	$0.353179\pi$
$618$		0			0
$619$	20.4303	−	11.7954i	0.821162	−	0.474098i	−0.0296550	−	0.999560i	$-0.509441\pi$
$619$	20.4303	−	11.7954i	0.821162	−	0.474098i	0.850817	+	0.525462i	$0.176108\pi$
$620$		0			0
$621$	−9.07389	−	1.59997i	−0.364123	−	0.0642047i
$622$		0			0
$623$	3.71955	+	3.12107i	0.149021	+	0.125043i
$624$		0			0
$625$	13.3176	+	4.84720i	0.532703	+	0.193888i
$626$		0			0
$627$	−1.23444	+	19.3394i	−0.0492988	+	0.772341i
$628$		0			0
$629$	−6.59008	+	18.1061i	−0.262764	+	0.721937i
$630$		0			0
$631$	−4.53244	+	5.40155i	−0.180434	+	0.215032i	−0.848679	−	0.528909i	$-0.822601\pi$
$631$	−4.53244	+	5.40155i	−0.180434	+	0.215032i	0.668245	+	0.743941i	$0.267046\pi$
$632$		0			0
$633$	0.331608	−	1.88064i	0.0131802	−	0.0747488i
$634$		0			0
$635$	8.76866	+	15.1878i	0.347974	+	0.602708i
$636$		0			0
$637$	18.3261	+	50.3506i	0.726108	+	1.99497i
$638$		0			0
$639$	6.37663	−	11.0446i	0.252255	−	0.436919i
$640$		0			0
$641$	−4.71716	−	5.62170i	−0.186317	−	0.222044i	0.664798	−	0.747023i	$-0.268518\pi$
$641$	−4.71716	−	5.62170i	−0.186317	−	0.222044i	−0.851115	+	0.524979i	$0.824073\pi$
$642$		0			0
$643$	−16.2184	+	2.85974i	−0.639591	+	0.112777i	−0.484033	−	0.875050i	$-0.660829\pi$
$643$	−16.2184	+	2.85974i	−0.639591	+	0.112777i	−0.155558	+	0.987827i	$0.549717\pi$
$644$		0			0
$645$			3.49036i			0.137433i
$646$		0			0
$647$			35.9335i			1.41269i	0.707867	+	0.706346i	$0.249658\pi$
$647$			35.9335i			1.41269i	−0.707867	+	0.706346i	$0.750342\pi$
$648$		0			0
$649$	−44.1243	+	7.78031i	−1.73203	+	0.305404i
$650$		0			0
$651$	−22.1269	−	26.3698i	−0.867222	−	1.03352i
$652$		0			0
$653$	−4.16329	+	7.21104i	−0.162922	+	0.282190i	−0.935915	−	0.352225i	$-0.885425\pi$
$653$	−4.16329	+	7.21104i	−0.162922	+	0.282190i	0.772993	+	0.634414i	$0.218759\pi$
$654$		0			0
$655$	0.615981	+	1.69239i	0.0240684	+	0.0661273i
$656$		0			0
$657$	−3.57233	−	6.18746i	−0.139370	−	0.241396i
$658$		0			0
$659$	1.73042	−	9.81370i	0.0674076	−	0.382288i	−0.932376	−	0.361490i	$-0.882268\pi$
$659$	1.73042	−	9.81370i	0.0674076	−	0.382288i	0.999784	−	0.0207978i	$-0.00662063\pi$
$660$		0			0
$661$	13.2454	−	15.7853i	0.515187	−	0.613976i	−0.444249	−	0.895904i	$-0.646529\pi$
$661$	13.2454	−	15.7853i	0.515187	−	0.613976i	0.959436	+	0.281927i	$0.0909737\pi$
$662$		0			0
$663$	2.84253	−	7.80979i	0.110395	−	0.303307i
$664$		0			0
$665$	34.3412	+	22.8614i	1.33170	+	0.886529i
$666$		0			0
$667$	8.39275	+	3.05471i	0.324968	+	0.118279i
$668$		0			0
$669$	−18.2437	−	15.3083i	−0.705342	−	0.591852i
$670$		0			0
$671$	4.03565	+	0.711595i	0.155795	+	0.0274708i
$672$		0			0
$673$	−23.7173	+	13.6932i	−0.914234	+	0.527833i	−0.881791	−	0.471640i	$-0.843662\pi$
$673$	−23.7173	+	13.6932i	−0.914234	+	0.527833i	−0.0324432	+	0.999474i	$0.510329\pi$
$674$		0			0
$675$	1.53407	−	0.558356i	0.0590464	−	0.0214911i
$676$		0			0
$677$	19.8507	+	11.4608i	0.762924	+	0.440474i	0.830345	−	0.557250i	$-0.188144\pi$
$677$	19.8507	+	11.4608i	0.762924	+	0.440474i	−0.0674207	+	0.997725i	$0.521477\pi$
$678$		0			0
$679$	−19.5316	+	16.3890i	−0.749555	+	0.628951i
$680$		0			0
$681$	3.80596	+	21.5847i	0.145845	+	0.827126i
$682$		0			0
$683$	−0.918164			−0.0351326			−0.0175663	−	0.999846i	$-0.505592\pi$
$683$	−0.918164			−0.0351326			−0.0175663	+	0.999846i	$0.505592\pi$
$684$		0			0
$685$	−10.4460			−0.399121
$686$		0			0
$687$	2.74195	+	15.5504i	0.104612	+	0.593283i
$688$		0			0
$689$	5.93103	−	4.97672i	0.225954	−	0.189598i
$690$		0			0
$691$	28.0288	+	16.1824i	1.06626	+	0.615608i	0.927159	−	0.374669i	$-0.122244\pi$
$691$	28.0288	+	16.1824i	1.06626	+	0.615608i	0.139106	+	0.990277i	$0.455577\pi$
$692$		0			0
$693$	21.5467	−	7.84237i	0.818492	−	0.297907i
$694$		0			0
$695$	−7.88025	+	4.54966i	−0.298915	+	0.172579i
$696$		0			0
$697$	−21.2465	−	3.74633i	−0.804769	−	0.141903i
$698$		0			0
$699$	11.0589	+	9.27955i	0.418287	+	0.350985i
$700$		0			0
$701$	41.4721	+	15.0946i	1.56638	+	0.570116i	0.972187	−	0.234206i	$-0.0752491\pi$
$701$	41.4721	+	15.0946i	1.56638	+	0.570116i	0.594194	+	0.804322i	$0.297471\pi$
$702$		0			0
$703$	19.0693	−	19.9882i	0.719213	−	0.753870i
$704$		0			0
$705$	−4.18272	+	11.4919i	−0.157530	+	0.432811i
$706$		0			0
$707$	−16.1923	+	19.2972i	−0.608973	+	0.725746i
$708$		0			0
$709$	−2.16383	+	12.2717i	−0.0812643	+	0.460873i	0.916836	+	0.399264i	$0.130734\pi$
$709$	−2.16383	+	12.2717i	−0.0812643	+	0.460873i	−0.998100	+	0.0616090i	$0.980377\pi$
$710$		0			0
$711$	−1.33570	−	2.31351i	−0.0500928	−	0.0867633i
$712$		0			0
$713$	−21.0330	−	57.7877i	−0.787692	−	2.16416i
$714$		0			0
$715$	−11.1511	+	19.3144i	−0.417029	+	0.722316i
$716$		0			0
$717$	−0.0683698	−	0.0814799i	−0.00255332	−	0.00304292i
$718$		0			0
$719$	−35.7053	+	6.29580i	−1.33158	+	0.234794i	−0.793743	−	0.608254i	$-0.791870\pi$
$719$	−35.7053	+	6.29580i	−1.33158	+	0.234794i	−0.537839	+	0.843048i	$0.680759\pi$
$720$		0			0
$721$		−	43.7301i		−	1.62859i
$722$		0			0
$723$			4.33723i			0.161303i
$724$		0			0
$725$	−1.55843	+	0.274793i	−0.0578786	+	0.0102056i
$726$		0			0
$727$	−16.9554	−	20.2067i	−0.628841	−	0.749424i	0.353722	−	0.935350i	$-0.384916\pi$
$727$	−16.9554	−	20.2067i	−0.628841	−	0.749424i	−0.982564	+	0.185927i	$0.940471\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	1.97777	+	5.43387i	0.0731503	+	0.200979i
$732$		0			0
$733$	17.7872	+	30.8083i	0.656984	+	1.13793i	0.981392	+	0.192013i	$0.0615015\pi$
$733$	17.7872	+	30.8083i	0.656984	+	1.13793i	−0.324408	+	0.945917i	$0.605165\pi$
$734$		0			0
$735$	6.24588	−	35.4222i	0.230383	−	1.30657i
$736$		0			0
$737$	43.8987	−	52.3165i	1.61703	−	1.92710i
$738$		0			0
$739$	3.17412	−	8.72082i	0.116762	−	0.320800i	−0.867521	−	0.497401i	$-0.834288\pi$
$739$	3.17412	−	8.72082i	0.116762	−	0.320800i	0.984283	+	0.176600i	$0.0565101\pi$
$740$		0			0
$741$	−8.22527	+	8.62162i	−0.302163	+	0.316723i
$742$		0			0
$743$	−4.17658	−	1.52015i	−0.153224	−	0.0557690i	0.264270	−	0.964449i	$-0.414869\pi$
$743$	−4.17658	−	1.52015i	−0.153224	−	0.0557690i	−0.417494	+	0.908680i	$0.637091\pi$
$744$		0			0
$745$	8.41713	+	7.06281i	0.308380	+	0.258762i
$746$		0			0
$747$	8.43355	+	1.48706i	0.308567	+	0.0544088i
$748$		0			0
$749$	−79.4223	+	45.8545i	−2.90203	+	1.67549i
$750$		0			0
$751$	−11.4925	+	4.18294i	−0.419369	+	0.152638i	−0.543081	−	0.839680i	$-0.682742\pi$
$751$	−11.4925	+	4.18294i	−0.419369	+	0.152638i	0.123712	+	0.992318i	$0.460520\pi$
$752$		0			0
$753$	−2.19723	−	1.26857i	−0.0800714	−	0.0462293i
$754$		0			0
$755$	14.3881	−	12.0731i	0.523638	−	0.439385i
$756$		0			0
$757$	−2.76619	−	15.6878i	−0.100539	−	0.570184i	−0.992909	−	0.118879i	$-0.962070\pi$
$757$	−2.76619	−	15.6878i	−0.100539	−	0.570184i	0.892370	−	0.451305i	$-0.149041\pi$
$758$		0			0
$759$	40.9630			1.48686
$760$		0			0
$761$	−12.1119			−0.439055			−0.219527	−	0.975606i	$-0.570452\pi$
$761$	−12.1119			−0.439055			−0.219527	+	0.975606i	$0.570452\pi$
$762$		0			0
$763$	1.81020	+	10.2661i	0.0655335	+	0.371659i
$764$		0			0
$765$	−4.27378	+	3.58612i	−0.154519	+	0.129657i
$766$		0			0
$767$	−23.8592	−	13.7751i	−0.861507	−	0.497391i
$768$		0			0
$769$	−12.6707	+	4.61175i	−0.456916	+	0.166304i	−0.560216	−	0.828346i	$-0.689282\pi$
$769$	−12.6707	+	4.61175i	−0.456916	+	0.166304i	0.103300	+	0.994650i	$0.467060\pi$
$770$		0			0
$771$	6.55106	−	3.78226i	0.235931	−	0.136215i
$772$		0			0
$773$	−48.7211	−	8.59085i	−1.75238	−	0.308991i	−0.796912	−	0.604095i	$-0.793535\pi$
$773$	−48.7211	−	8.59085i	−1.75238	−	0.308991i	−0.955465	+	0.295103i	$0.904646\pi$
$774$		0			0
$775$	8.34680	+	7.00380i	0.299826	+	0.251584i
$776$		0			0
$777$	−30.7161	−	11.1797i	−1.10193	−	0.401071i
$778$		0			0
$779$	25.7483	+	17.1410i	0.922528	+	0.614139i
$780$		0			0
$781$	−19.3920	+	53.2790i	−0.693899	+	1.90647i
$782$		0			0
$783$	0.623080	−	0.742558i	0.0222671	−	0.0265368i
$784$		0			0
$785$	3.35494	−	19.0268i	0.119743	−	0.679095i
$786$		0			0
$787$	11.9409	+	20.6822i	0.425647	+	0.737242i	0.996481	−	0.0838240i	$-0.0267133\pi$
$787$	11.9409	+	20.6822i	0.425647	+	0.737242i	−0.570834	+	0.821066i	$0.693380\pi$
$788$		0			0
$789$	−8.28133	−	22.7528i	−0.294823	−	0.810020i
$790$		0			0
$791$	−44.4100	+	76.9204i	−1.57904	+	2.73497i
$792$		0			0
$793$	1.61968	+	1.93026i	0.0575165	+	0.0685455i
$794$		0			0
$795$	−5.11837	+	0.902507i	−0.181530	+	0.0320086i
$796$		0			0
$797$		−	16.4066i		−	0.581152i	−0.956852	−	0.290576i	$-0.906153\pi$
$797$		−	16.4066i		−	0.581152i	0.956852	−	0.290576i	$-0.0938470\pi$
$798$		0			0
$799$			20.2610i			0.716781i
$800$		0			0
$801$	0.927132	−	0.163478i	0.0327586	−	0.00577623i
$802$		0			0
$803$	20.4173	+	24.3324i	0.720511	+	0.858672i
$804$		0			0
$805$	43.6025	−	75.5217i	1.53678	−	2.66179i
$806$		0			0
$807$	0.725156	+	1.99235i	0.0255267	+	0.0701340i
$808$		0			0
$809$	10.5025	+	18.1908i	0.369247	+	0.639554i	0.989448	−	0.144888i	$-0.0462823\pi$
$809$	10.5025	+	18.1908i	0.369247	+	0.639554i	−0.620201	+	0.784443i	$0.712949\pi$
$810$		0			0
$811$	4.39110	−	24.9032i	0.154193	−	0.874469i	−0.805328	−	0.592830i	$-0.798011\pi$
$811$	4.39110	−	24.9032i	0.154193	−	0.874469i	0.959520	−	0.281640i	$-0.0908782\pi$
$812$		0			0
$813$	−1.63282	+	1.94592i	−0.0572655	+	0.0682464i
$814$		0			0
$815$	8.27115	−	22.7248i	0.289726	−	0.796015i
$816$		0			0
$817$	0.528127	−	8.27393i	0.0184768	−	0.289468i
$818$		0			0
$819$	13.2489	+	4.82221i	0.462955	+	0.168502i
$820$		0			0
$821$	−7.31491	−	6.13794i	−0.255292	−	0.214216i	0.506155	−	0.862443i	$-0.331066\pi$
$821$	−7.31491	−	6.13794i	−0.255292	−	0.214216i	−0.761447	+	0.648227i	$0.775511\pi$
$822$		0			0
$823$	−38.4953	−	6.78777i	−1.34186	−	0.236607i	−0.543817	−	0.839204i	$-0.683022\pi$
$823$	−38.4953	−	6.78777i	−1.34186	−	0.236607i	−0.798046	+	0.602597i	$0.794133\pi$
$824$		0			0
$825$	−6.28549	+	3.62893i	−0.218833	+	0.126343i
$826$		0			0
$827$	−1.99558	+	0.726331i	−0.0693930	+	0.0252570i	−0.376483	−	0.926423i	$-0.622867\pi$
$827$	−1.99558	+	0.726331i	−0.0693930	+	0.0252570i	0.307090	+	0.951680i	$0.400645\pi$
$828$		0			0
$829$	11.3082	+	6.52877i	0.392749	+	0.226754i	0.683350	−	0.730091i	$-0.260522\pi$
$829$	11.3082	+	6.52877i	0.392749	+	0.226754i	−0.290602	+	0.956844i	$0.593855\pi$
$830$		0			0
$831$	−15.3888	+	12.9128i	−0.533833	+	0.447939i
$832$		0			0
$833$	−10.3478	−	58.6851i	−0.358529	−	2.03332i
$834$		0			0
$835$	20.7707			0.718799
$836$		0			0
$837$	−6.67432			−0.230698
$838$		0			0
$839$	7.24456	+	41.0860i	0.250110	+	1.41845i	0.808319	+	0.588745i	$0.200378\pi$
$839$	7.24456	+	41.0860i	0.250110	+	1.41845i	−0.558209	+	0.829700i	$0.688511\pi$
$840$		0			0
$841$	21.4955	−	18.0369i	0.741224	−	0.621961i
$842$		0			0
$843$	−1.85949	−	1.07358i	−0.0640443	−	0.0369760i
$844$		0			0
$845$	9.53073	−	3.46890i	0.327867	−	0.119334i
$846$		0			0
$847$	−39.1500	+	22.6033i	−1.34521	+	0.776658i
$848$		0			0
$849$	−20.3771	−	3.59303i	−0.699340	−	0.123313i
$850$		0			0
$851$	−44.7331	−	37.5356i	−1.53343	−	1.28670i
$852$		0			0
$853$	−12.6604	−	4.60800i	−0.433483	−	0.157775i	0.116056	−	0.993243i	$-0.462975\pi$
$853$	−12.6604	−	4.60800i	−0.433483	−	0.157775i	−0.549540	+	0.835468i	$0.685197\pi$
$854$		0			0
$855$	7.67549	−	2.25142i	0.262496	−	0.0769968i
$856$		0			0
$857$	3.62903	−	9.97068i	0.123965	−	0.340592i	−0.862150	−	0.506653i	$-0.830883\pi$
$857$	3.62903	−	9.97068i	0.123965	−	0.340592i	0.986115	+	0.166061i	$0.0531049\pi$
$858$		0			0
$859$	2.66184	−	3.17226i	0.0908209	−	0.108236i	−0.718720	−	0.695300i	$-0.755272\pi$
$859$	2.66184	−	3.17226i	0.0908209	−	0.108236i	0.809541	+	0.587064i	$0.199716\pi$
$860$		0			0
$861$	6.35547	−	36.0436i	0.216594	−	1.22836i
$862$		0			0
$863$	−12.8922	−	22.3300i	−0.438856	−	0.760120i	0.558746	−	0.829339i	$-0.311283\pi$
$863$	−12.8922	−	22.3300i	−0.438856	−	0.760120i	−0.997602	+	0.0692186i	$0.977949\pi$
$864$		0			0
$865$	−14.4884	−	39.8065i	−0.492620	−	1.35346i
$866$		0			0
$867$	3.87852	−	6.71780i	0.131721	−	0.228148i
$868$		0			0
$869$	7.63408	+	9.09795i	0.258969	+	0.308627i
$870$		0			0
$871$	41.3557	−	7.29212i	1.40128	−	0.247084i
$872$		0			0
$873$			4.94354i			0.167313i
$874$		0			0
$875$			62.7737i			2.12214i
$876$		0			0
$877$	0.00549789		0.000969427i	0.000185651		3.27352e-5i	−0.173555	−	0.984824i	$-0.555526\pi$
$877$	0.00549789		0.000969427i	0.000185651		3.27352e-5i	0.173741	+	0.984791i	$0.444414\pi$
$878$		0			0
$879$	14.5671	+	17.3604i	0.491336	+	0.585552i
$880$		0			0
$881$	18.9515	−	32.8249i	0.638491	−	1.10590i	−0.347273	−	0.937764i	$-0.612892\pi$
$881$	18.9515	−	32.8249i	0.638491	−	1.10590i	0.985764	−	0.168134i	$-0.0537743\pi$
$882$		0			0
$883$	−6.43591	−	17.6825i	−0.216585	−	0.595064i	0.783053	−	0.621955i	$-0.213661\pi$
$883$	−6.43591	−	17.6825i	−0.216585	−	0.595064i	−0.999638	+	0.0268914i	$0.991439\pi$
$884$		0			0
$885$	9.24698	+	16.0162i	0.310834	+	0.538380i
$886$		0			0
$887$	−1.03580	+	5.87434i	−0.0347789	+	0.197241i	−0.997247	−	0.0741548i	$-0.976374\pi$
$887$	−1.03580	+	5.87434i	−0.0347789	+	0.197241i	0.962468	+	0.271396i	$0.0874852\pi$
$888$		0			0
$889$	−31.6829	+	37.7582i	−1.06261	+	1.26637i
$890$		0			0
$891$	1.52055	−	4.17768i	0.0509403	−	0.139957i
$892$		0			0
$893$	11.6540	−	26.6088i	0.389987	−	0.890430i
$894$		0			0
$895$	−1.78231	−	0.648707i	−0.0595759	−	0.0216839i
$896$		0			0
$897$	19.2950	+	16.1904i	0.644241	+	0.540582i
$898$		0			0
$899$	6.37140	+	1.12345i	0.212498	+	0.0374691i
$900$		0			0
$901$	−7.45700	+	4.30530i	−0.248429	+	0.143430i
$902$		0			0
$903$	−9.21828	+	3.35518i	−0.306765	+	0.111653i
$904$		0			0
$905$	−11.9531	−	6.90110i	−0.397333	−	0.229400i
$906$		0			0
$907$	−40.9181	+	34.3343i	−1.35866	+	1.14005i	−0.382270	+	0.924051i	$0.624857\pi$
$907$	−40.9181	+	34.3343i	−1.35866	+	1.14005i	−0.976393	+	0.216002i	$0.930698\pi$
$908$		0			0
$909$	0.848134	+	4.81001i	0.0281308	+	0.159538i
$910$		0			0
$911$	−50.6766			−1.67899			−0.839496	−	0.543366i	$-0.817150\pi$
$911$	−50.6766			−1.67899			−0.839496	+	0.543366i	$0.817150\pi$
$912$		0			0
$913$	−38.0722			−1.26001
$914$		0			0
$915$	−0.293722	−	1.66578i	−0.00971014	−	0.0550689i
$916$		0			0
$917$	−3.87760	+	3.25370i	−0.128050	+	0.107446i
$918$		0			0
$919$	25.8426	+	14.9203i	0.852470	+	0.492174i	0.861484	−	0.507785i	$-0.169536\pi$
$919$	25.8426	+	14.9203i	0.852470	+	0.492174i	−0.00901331	+	0.999959i	$0.502869\pi$
$920$		0			0
$921$	−6.30848	+	2.29610i	−0.207871	+	0.0756590i
$922$		0			0
$923$	−30.1925	+	17.4317i	−0.993799	+	0.573770i
$924$		0			0
$925$	10.1893	+	1.79665i	0.335022	+	0.0590734i
$926$		0			0
$927$	−6.49513	−	5.45006i	−0.213328	−	0.179003i
$928$		0			0
$929$	−10.3170	−	3.75510i	−0.338491	−	0.123201i	0.167181	−	0.985926i	$-0.446533\pi$
$929$	−10.3170	−	3.75510i	−0.338491	−	0.123201i	−0.505673	+	0.862725i	$0.668756\pi$
$930$		0			0
$931$	−20.1657	+	83.0235i	−0.660902	+	2.72098i
$932$		0			0
$933$	−4.97026	+	13.6557i	−0.162719	+	0.447067i
$934$		0			0
$935$	15.9432	−	19.0003i	0.521397	−	0.621377i
$936$		0			0
$937$	−8.35782	+	47.3996i	−0.273038	+	1.54848i	0.472087	+	0.881552i	$0.343501\pi$
$937$	−8.35782	+	47.3996i	−0.273038	+	1.54848i	−0.745125	+	0.666924i	$0.767610\pi$
$938$		0			0
$939$	−1.65278	−	2.86270i	−0.0539364	−	0.0934205i
$940$		0			0
$941$	16.0722	+	44.1581i	0.523940	+	1.43951i	0.866100	+	0.499871i	$0.166619\pi$
$941$	16.0722	+	44.1581i	0.523940	+	1.43951i	−0.342160	+	0.939642i	$0.611159\pi$
$942$		0			0
$943$	32.6921	−	56.6244i	1.06460	−	1.84394i
$944$		0			0
$945$	−6.08368	−	7.25024i	−0.197902	−	0.235850i
$946$		0			0
$947$	10.6140	−	1.87154i	0.344910	−	0.0608169i	0.00148980	−	0.999999i	$-0.499526\pi$
$947$	10.6140	−	1.87154i	0.344910	−	0.0608169i	0.343420	+	0.939182i	$0.388415\pi$
$948$		0			0
$949$			19.5313i			0.634011i
$950$		0			0
$951$			0.839244i			0.0272144i
$952$		0			0
$953$	−23.1709	+	4.08566i	−0.750580	+	0.132347i	−0.535835	−	0.844323i	$-0.680003\pi$
$953$	−23.1709	+	4.08566i	−0.750580	+	0.132347i	−0.214745	+	0.976670i	$0.568892\pi$
$954$		0			0
$955$	−13.4006	−	15.9702i	−0.433632	−	0.516783i
$956$		0			0
$957$	−2.15474	+	3.73212i	−0.0696529	+	0.120642i
$958$		0			0
$959$	−10.0414	−	27.5886i	−0.324255	−	0.890882i
$960$		0			0
$961$	−6.77327	−	11.7317i	−0.218493	−	0.378440i
$962$		0			0
$963$	−3.08770	+	17.5112i	−0.0994999	+	0.564292i
$964$		0			0
$965$	−21.5721	+	25.7086i	−0.694431	+	0.827590i
$966$		0			0
$967$	−15.0595	+	41.3757i	−0.484282	+	1.33055i	0.421507	+	0.906825i	$0.361501\pi$
$967$	−15.0595	+	41.3757i	−0.484282	+	1.33055i	−0.905789	+	0.423728i	$0.860721\pi$
$968$		0			0
$969$	10.6736	−	7.85427i	0.342887	−	0.252316i
$970$		0			0
$971$	−46.5208	−	16.9322i	−1.49292	−	0.543379i	−0.538705	−	0.842494i	$-0.681086\pi$
$971$	−46.5208	−	16.9322i	−1.49292	−	0.543379i	−0.954217	+	0.299115i	$0.903308\pi$
$972$		0			0
$973$	−19.5910	−	16.4388i	−0.628059	−	0.527004i
$974$		0			0
$975$	−4.39500	−	0.774957i	−0.140753	−	0.0248185i
$976$		0			0
$977$	0.688734	−	0.397640i	0.0220345	−	0.0127216i	−0.488942	−	0.872316i	$-0.662617\pi$
$977$	0.688734	−	0.397640i	0.0220345	−	0.0127216i	0.510977	+	0.859594i	$0.329284\pi$
$978$		0			0
$979$	−3.93301	+	1.43150i	−0.125700	+	0.0457509i
$980$		0			0
$981$	1.75041	+	1.01060i	0.0558863	+	0.0322659i
$982$		0			0
$983$	27.1905	−	22.8155i	0.867241	−	0.727702i	−0.0962742	−	0.995355i	$-0.530693\pi$
$983$	27.1905	−	22.8155i	0.867241	−	0.727702i	0.963515	+	0.267653i	$0.0862481\pi$
$984$		0			0
$985$	5.51311	+	31.2664i	0.175662	+	0.996230i
$986$		0			0
$987$	−34.3717			−1.09406
$988$		0			0
$989$	−17.5251			−0.557265
$990$		0			0
$991$	−6.38624	−	36.2182i	−0.202866	−	1.15051i	−0.900763	−	0.434310i	$-0.856992\pi$
$991$	−6.38624	−	36.2182i	−0.202866	−	1.15051i	0.697898	−	0.716197i	$-0.254119\pi$
$992$		0			0
$993$	25.4665	−	21.3689i	0.808154	−	0.678122i
$994$		0			0
$995$	−9.71716	−	5.61021i	−0.308055	−	0.177856i
$996$		0			0
$997$	7.83800	−	2.85280i	0.248232	−	0.0903491i	−0.214908	−	0.976634i	$-0.568945\pi$
$997$	7.83800	−	2.85280i	0.248232	−	0.0903491i	0.463140	+	0.886285i	$0.346723\pi$
$998$		0			0
$999$	−5.48863	+	3.16886i	−0.173653	+	0.100258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.g.319.2	yes	24
4.3	odd	2		912.2.ci.h.319.2	yes	24
19.14	odd	18		912.2.ci.h.223.2	yes	24
76.71	even	18	inner	912.2.ci.g.223.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.223.2	✓	24	76.71	even	18	inner
912.2.ci.g.319.2	yes	24	1.1	even	1	trivial
912.2.ci.h.223.2	yes	24	19.14	odd	18
912.2.ci.h.319.2	yes	24	4.3	odd	2

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{3} +(-1.40574 + 1.17956i) q^{5} +(-4.46660 - 2.57879i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{3} +(-1.40574 + 1.17956i) q^{5} +(-4.46660 - 2.57879i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(3.85017 - 2.22290i) q^{11} +(2.69215 + 0.474699i) q^{13} +(-1.40574 - 1.17956i) q^{15} +(-2.85688 - 1.03982i) q^{17} +(3.15385 + 3.00886i) q^{19} +(1.76400 - 4.84654i) q^{21} +(5.92256 - 7.05824i) q^{23} +(-0.283485 + 1.60772i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.331534 + 0.910882i) q^{29} +(3.33716 - 5.78013i) q^{31} +(2.85770 + 3.40567i) q^{33} +(9.32074 - 1.64350i) q^{35} -6.33772i q^{37} +2.73368i q^{39} +(6.98847 - 1.23226i) q^{41} +(-1.22260 - 1.45704i) q^{43} +(0.917534 - 1.58922i) q^{45} +(-2.27932 - 6.26239i) q^{47} +(9.80034 + 16.9747i) q^{49} +(0.527929 - 2.99404i) q^{51} +(1.82052 - 2.16961i) q^{53} +(-2.79031 + 7.66633i) q^{55} +(-2.41549 + 3.62842i) q^{57} +(-9.47029 - 3.44690i) q^{59} +(0.706102 + 0.592490i) q^{61} +(5.07923 + 0.895605i) q^{63} +(-4.34441 + 2.50825i) q^{65} +(14.4351 - 5.25396i) q^{67} +(7.97945 + 4.60694i) q^{69} +(-9.76956 + 8.19763i) q^{71} +(1.24066 + 7.03612i) q^{73} -1.63252 q^{75} -22.9295 q^{77} +(0.463885 + 2.63082i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-7.41634 - 4.28182i) q^{83} +(5.24256 - 1.90814i) q^{85} +(-0.839473 + 0.484670i) q^{87} +(-0.927132 - 0.163478i) q^{89} +(-10.8006 - 9.06279i) q^{91} +(6.27181 + 2.28275i) q^{93} +(-7.98263 - 0.509534i) q^{95} +(1.69079 - 4.64541i) q^{97} +(-2.85770 + 3.40567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{7}+O(q^{10}) \) 24 * q - 9 * q^7	\( 24 q - 9 q^{7} + 9 q^{11} - 9 q^{13} - 6 q^{17} - 3 q^{19} - 6 q^{21} + 15 q^{23} + 6 q^{25} - 12 q^{27} - 6 q^{29} + 12 q^{31} - 3 q^{33} + 30 q^{41} - 9 q^{43} + 3 q^{45} - 15 q^{47} + 27 q^{49} + 3 q^{51} + 6 q^{53} + 21 q^{55} - 9 q^{57} - 36 q^{59} - 21 q^{61} - 3 q^{63} - 9 q^{65} + 45 q^{67} - 36 q^{71} + 42 q^{75} + 108 q^{77} + 36 q^{79} - 27 q^{83} - 9 q^{85} - 9 q^{87} - 27 q^{89} - 36 q^{91} - 18 q^{93} + 30 q^{95} - 51 q^{97} + 3 q^{99}+O(q^{100}) \) 24 * q - 9 * q^7 + 9 * q^11 - 9 * q^13 - 6 * q^17 - 3 * q^19 - 6 * q^21 + 15 * q^23 + 6 * q^25 - 12 * q^27 - 6 * q^29 + 12 * q^31 - 3 * q^33 + 30 * q^41 - 9 * q^43 + 3 * q^45 - 15 * q^47 + 27 * q^49 + 3 * q^51 + 6 * q^53 + 21 * q^55 - 9 * q^57 - 36 * q^59 - 21 * q^61 - 3 * q^63 - 9 * q^65 + 45 * q^67 - 36 * q^71 + 42 * q^75 + 108 * q^77 + 36 * q^79 - 27 * q^83 - 9 * q^85 - 9 * q^87 - 27 * q^89 - 36 * q^91 - 18 * q^93 + 30 * q^95 - 51 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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