LMFDB - Embedded newform 441.2.w.a.62.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			62.3
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38347 + 0.544011i) q^{2} +(3.58304 - 1.72550i) q^{4} +(-1.76892 - 2.21816i) q^{5} +(1.05543 - 2.42612i) q^{7} +(-3.77859 + 3.01333i) q^{8} +O(q^{10})$	\(q+(-2.38347 + 0.544011i) q^{2} +(3.58304 - 1.72550i) q^{4} +(-1.76892 - 2.21816i) q^{5} +(1.05543 - 2.42612i) q^{7} +(-3.77859 + 3.01333i) q^{8} +(5.42288 + 4.32461i) q^{10} +(6.16474 - 1.40706i) q^{11} +(-4.61324 + 1.05294i) q^{13} +(-1.19575 + 6.35675i) q^{14} +(2.40779 - 3.01928i) q^{16} +(-5.30898 - 2.55667i) q^{17} -2.33339i q^{19} +(-10.1656 - 4.89548i) q^{20} +(-13.9280 + 6.70738i) q^{22} +(2.79247 + 5.79862i) q^{23} +(-0.678541 + 2.97288i) q^{25} +(10.4227 - 5.01931i) q^{26} +(-0.404621 - 10.5140i) q^{28} +(-1.73570 + 3.60421i) q^{29} -0.397539i q^{31} +(0.0975386 - 0.202541i) q^{32} +(14.0447 + 3.20560i) q^{34} +(-7.24851 + 1.95051i) q^{35} +(-4.60121 - 2.21582i) q^{37} +(1.26939 + 5.56158i) q^{38} +(13.3681 + 3.05118i) q^{40} +(-6.80496 - 8.53316i) q^{41} +(1.14089 - 1.43063i) q^{43} +(19.6607 - 15.6788i) q^{44} +(-9.81027 - 12.3017i) q^{46} +(-0.0473720 - 0.207550i) q^{47} +(-4.77213 - 5.12121i) q^{49} -7.45491i q^{50} +(-14.7126 + 11.7329i) q^{52} +(-3.08737 - 6.41100i) q^{53} +(-14.0261 - 11.1854i) q^{55} +(3.32265 + 12.3477i) q^{56} +(2.17625 - 9.53478i) q^{58} +(0.482247 - 0.604718i) q^{59} +(-0.228309 + 0.474089i) q^{61} +(0.216266 + 0.947522i) q^{62} +(-1.84096 + 8.06577i) q^{64} +(10.4961 + 8.37034i) q^{65} -0.381019 q^{67} -23.4339 q^{68} +(16.2155 - 8.59225i) q^{70} +(-1.49888 - 3.11247i) q^{71} +(1.75344 + 0.400211i) q^{73} +(12.1723 + 2.77824i) q^{74} +(-4.02628 - 8.36065i) q^{76} +(3.09276 - 16.4415i) q^{77} -1.77113 q^{79} -10.9565 q^{80} +(20.8616 + 16.6365i) q^{82} +(1.40933 - 6.17467i) q^{83} +(3.72008 + 16.2987i) q^{85} +(-1.94099 + 4.03051i) q^{86} +(-19.0541 + 23.8931i) q^{88} +(-2.90632 + 12.7334i) q^{89} +(-2.31440 + 12.3036i) q^{91} +(20.0111 + 15.9583i) q^{92} +(0.225819 + 0.468919i) q^{94} +(-5.17585 + 4.12760i) q^{95} +6.82677i q^{97} +(14.1602 + 9.61016i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$-1$

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 $

$2$	−2.38347	+	0.544011i	−1.68537	+	0.384674i	−0.954586	−	0.297937i	$-0.903702\pi$
$2$	−2.38347	+	0.544011i	−1.68537	+	0.384674i	−0.730782	+	0.682611i	$0.760844\pi$
$3$		0			0
$3$		0			0
$4$	3.58304	−	1.72550i	1.79152	−	0.862751i
$5$	−1.76892	−	2.21816i	−0.791087	−	0.991992i	−0.999901	−	0.0140366i	$-0.995532\pi$
$5$	−1.76892	−	2.21816i	−0.791087	−	0.991992i	0.208814	−	0.977955i	$-0.433040\pi$
$6$		0			0
$7$	1.05543	−	2.42612i	0.398916	−	0.916988i
$7$	1.05543	−	2.42612i	0.398916	−	0.916988i
$8$	−3.77859	+	3.01333i	−1.33593	+	1.06537i
$9$		0			0
$10$	5.42288	+	4.32461i	1.71487	+	1.36756i
$11$	6.16474	−	1.40706i	1.85874	−	0.424245i	0.862142	−	0.506666i	$-0.169122\pi$
$11$	6.16474	−	1.40706i	1.85874	−	0.424245i	0.996598	+	0.0824210i	$0.0262652\pi$
$12$		0			0
$13$	−4.61324	+	1.05294i	−1.27948	+	0.292034i	−0.807654	−	0.589657i	$-0.799263\pi$
$13$	−4.61324	+	1.05294i	−1.27948	+	0.292034i	−0.471829	+	0.881690i	$0.656406\pi$
$14$	−1.19575	+	6.35675i	−0.319578	+	1.69891i
$15$		0			0
$16$	2.40779	−	3.01928i	0.601949	−	0.754820i
$17$	−5.30898	−	2.55667i	−1.28762	−	0.620084i	−0.340281	−	0.940324i	$-0.610522\pi$
$17$	−5.30898	−	2.55667i	−1.28762	−	0.620084i	−0.947336	+	0.320240i	$0.896236\pi$
$18$		0			0
$19$		−	2.33339i		−	0.535317i	−0.963514	−	0.267659i	$-0.913750\pi$
$19$		−	2.33339i		−	0.535317i	0.963514	−	0.267659i	$-0.0862500\pi$
$20$	−10.1656	−	4.89548i	−2.27309	−	1.09466i
$21$		0			0
$22$	−13.9280	+	6.70738i	−2.96946	+	1.43002i
$23$	2.79247	+	5.79862i	0.582270	+	1.20910i	0.959167	+	0.282840i	$0.0912766\pi$
$23$	2.79247	+	5.79862i	0.582270	+	1.20910i	−0.376898	+	0.926255i	$0.623009\pi$
$24$		0			0
$25$	−0.678541	+	2.97288i	−0.135708	+	0.594576i
$26$	10.4227	−	5.01931i	2.04406	−	0.984368i
$27$		0			0
$28$	−0.404621	−	10.5140i	−0.0764662	−	1.98697i
$29$	−1.73570	+	3.60421i	−0.322311	+	0.669286i	−0.997672	−	0.0682019i	$-0.978274\pi$
$29$	−1.73570	+	3.60421i	−0.322311	+	0.669286i	0.675360	+	0.737488i	$0.263988\pi$
$30$		0			0
$31$		−	0.397539i		−	0.0714001i	−0.999363	−	0.0357000i	$-0.988634\pi$
$31$		−	0.397539i		−	0.0714001i	0.999363	−	0.0357000i	$-0.0113661\pi$
$32$	0.0975386	−	0.202541i	0.0172425	−	0.0358045i
$33$		0			0
$34$	14.0447	+	3.20560i	2.40864	+	0.549756i
$35$	−7.24851	+	1.95051i	−1.22522	+	0.329696i
$36$		0			0
$37$	−4.60121	−	2.21582i	−0.756434	−	0.364279i	0.0155854	−	0.999879i	$-0.495039\pi$
$37$	−4.60121	−	2.21582i	−0.756434	−	0.364279i	−0.772019	+	0.635599i	$0.780753\pi$
$38$	1.26939	+	5.56158i	0.205923	+	0.902207i
$39$		0			0
$40$	13.3681	+	3.05118i	2.11368	+	0.482434i
$41$	−6.80496	−	8.53316i	−1.06276	−	1.33266i	−0.940363	−	0.340174i	$-0.889514\pi$
$41$	−6.80496	−	8.53316i	−1.06276	−	1.33266i	−0.122394	−	0.992482i	$-0.539057\pi$
$42$		0			0
$43$	1.14089	−	1.43063i	0.173983	−	0.218168i	−0.687192	−	0.726475i	$-0.741157\pi$
$43$	1.14089	−	1.43063i	0.173983	−	0.218168i	0.861176	+	0.508307i	$0.169729\pi$
$44$	19.6607	−	15.6788i	2.96395	−	2.36367i
$45$		0			0
$46$	−9.81027	−	12.3017i	−1.44645	−	1.81379i
$47$	−0.0473720	−	0.207550i	−0.00690992	−	0.0302743i	0.971355	−	0.237631i	$-0.0763710\pi$
$47$	−0.0473720	−	0.207550i	−0.00690992	−	0.0302743i	−0.978265	+	0.207357i	$0.933514\pi$
$48$		0			0
$49$	−4.77213	−	5.12121i	−0.681733	−	0.731601i
$50$		−	7.45491i		−	1.05428i
$51$		0			0
$52$	−14.7126	+	11.7329i	−2.04027	+	1.62706i
$53$	−3.08737	−	6.41100i	−0.424083	−	0.880618i	−0.998091	−	0.0617679i	$-0.980326\pi$
$53$	−3.08737	−	6.41100i	−0.424083	−	0.880618i	0.574007	−	0.818850i	$-0.305388\pi$
$54$		0			0
$55$	−14.0261	−	11.1854i	−1.89127	−	1.50824i
$56$	3.32265	+	12.3477i	0.444008	+	1.65003i
$57$		0			0
$58$	2.17625	−	9.53478i	0.285756	−	1.25198i
$59$	0.482247	−	0.604718i	0.0627832	−	0.0787276i	−0.749448	−	0.662063i	$-0.769681\pi$
$59$	0.482247	−	0.604718i	0.0627832	−	0.0787276i	0.812231	+	0.583335i	$0.198253\pi$
$60$		0			0
$61$	−0.228309	+	0.474089i	−0.0292320	+	0.0607009i	−0.915074	−	0.403287i	$-0.867868\pi$
$61$	−0.228309	+	0.474089i	−0.0292320	+	0.0607009i	0.885842	+	0.463988i	$0.153582\pi$
$62$	0.216266	+	0.947522i	0.0274658	+	0.120335i
$63$		0			0
$64$	−1.84096	+	8.06577i	−0.230120	+	1.00822i
$65$	10.4961	+	8.37034i	1.30188	+	1.03821i
$66$		0			0
$67$	−0.381019			−0.0465489			−0.0232744	−	0.999729i	$-0.507409\pi$
$67$	−0.381019			−0.0465489			−0.0232744	+	0.999729i	$0.507409\pi$
$68$	−23.4339			−2.84177
$69$		0			0
$70$	16.2155	−	8.59225i	1.93812	−	1.02697i
$71$	−1.49888	−	3.11247i	−0.177885	−	0.369382i	0.792893	−	0.609361i	$-0.208574\pi$
$71$	−1.49888	−	3.11247i	−0.177885	−	0.369382i	−0.970778	+	0.239979i	$0.922860\pi$
$72$		0			0
$73$	1.75344	+	0.400211i	0.205224	+	0.0468411i	0.323897	−	0.946092i	$-0.395007\pi$
$73$	1.75344	+	0.400211i	0.205224	+	0.0468411i	−0.118673	+	0.992933i	$0.537864\pi$
$74$	12.1723	+	2.77824i	1.41500	+	0.322964i
$75$		0			0
$76$	−4.02628	−	8.36065i	−0.461846	−	0.959033i
$77$	3.09276	−	16.4415i	0.352453	−	1.87368i
$78$		0			0
$79$	−1.77113			−0.199267			−0.0996337	−	0.995024i	$-0.531767\pi$
$79$	−1.77113			−0.199267			−0.0996337	+	0.995024i	$0.531767\pi$
$80$	−10.9565			−1.22497
$81$		0			0
$82$	20.8616	+	16.6365i	2.30377	+	1.83720i
$83$	1.40933	−	6.17467i	0.154694	−	0.677758i	−0.836789	−	0.547525i	$-0.815570\pi$
$83$	1.40933	−	6.17467i	0.154694	−	0.677758i	0.991483	−	0.130233i	$-0.0415727\pi$
$84$		0			0
$85$	3.72008	+	16.2987i	0.403499	+	1.76785i
$86$	−1.94099	+	4.03051i	−0.209302	+	0.434621i
$87$		0			0
$88$	−19.0541	+	23.8931i	−2.03118	+	2.54701i
$89$	−2.90632	+	12.7334i	−0.308069	+	1.34974i	0.549553	+	0.835459i	$0.314798\pi$
$89$	−2.90632	+	12.7334i	−0.308069	+	1.34974i	−0.857622	+	0.514281i	$0.828059\pi$
$90$		0			0
$91$	−2.31440	+	12.3036i	−0.242615	+	1.28977i
$92$	20.0111	+	15.9583i	2.08630	+	1.66377i
$93$		0			0
$94$	0.225819	+	0.468919i	0.0232915	+	0.0483653i
$95$	−5.17585	+	4.12760i	−0.531031	+	0.423483i
$96$		0			0
$97$			6.82677i			0.693153i	0.938022	+	0.346577i	$0.112656\pi$
$97$			6.82677i			0.693153i	−0.938022	+	0.346577i	$0.887344\pi$
$98$	14.1602	+	9.61016i	1.43040	+	0.970773i
$99$		0			0
$100$	2.69847	+	11.8228i	0.269847	+	1.18228i
$101$	3.73165	+	4.67934i	0.371313	+	0.465612i	0.932022	−	0.362401i	$-0.118043\pi$
$101$	3.73165	+	4.67934i	0.371313	+	0.465612i	−0.560709	+	0.828013i	$0.689471\pi$
$102$		0			0
$103$	−3.70849	+	2.95742i	−0.365408	+	0.291404i	−0.788931	−	0.614482i	$-0.789365\pi$
$103$	−3.70849	+	2.95742i	−0.365408	+	0.291404i	0.423522	+	0.905886i	$0.360794\pi$
$104$	14.2587	−	17.8798i	1.39818	−	1.75326i
$105$		0			0
$106$	10.8463	+	13.6009i	1.05349	+	1.32103i
$107$	−12.4174	−	2.83420i	−1.20044	−	0.273992i	−0.424869	−	0.905255i	$-0.639680\pi$
$107$	−12.4174	−	2.83420i	−1.20044	−	0.273992i	−0.775569	+	0.631263i	$0.782537\pi$
$108$		0			0
$109$	−0.540987	−	2.37022i	−0.0518171	−	0.227026i	0.942389	−	0.334520i	$-0.108574\pi$
$109$	−0.540987	−	2.37022i	−0.0518171	−	0.227026i	−0.994206	+	0.107495i	$0.965717\pi$
$110$	39.5157	+	19.0297i	3.76767	+	1.81442i
$111$		0			0
$112$	−4.78387	−	9.02825i	−0.452034	−	0.853089i
$113$	−4.28730	−	0.978548i	−0.403315	−	0.0920540i	0.0160512	−	0.999871i	$-0.494891\pi$
$113$	−4.28730	−	0.978548i	−0.403315	−	0.0920540i	−0.419366	+	0.907817i	$0.637748\pi$
$114$		0			0
$115$	7.92260	−	16.4515i	0.738787	−	1.53411i
$116$			15.9090i			1.47711i
$117$		0			0
$118$	−0.820447	+	1.70368i	−0.0755282	+	0.156836i
$119$	−11.8061	+	10.1818i	−1.08226	+	0.933368i
$120$		0			0
$121$	26.1136	−	12.5756i	2.37396	−	1.14324i
$122$	0.286258	−	1.25418i	0.0259166	−	0.113548i
$123$		0			0
$124$	−0.685954	−	1.42440i	−0.0616005	−	0.127915i
$125$	−4.98624	+	2.40124i	−0.445982	+	0.214774i
$126$		0			0
$127$	−7.83752	−	3.77435i	−0.695467	−	0.334919i	0.0525316	−	0.998619i	$-0.483271\pi$
$127$	−7.83752	−	3.77435i	−0.695467	−	0.334919i	−0.747999	+	0.663700i	$0.768985\pi$
$128$		−	19.7764i		−	1.74801i
$129$		0			0
$130$	−29.5706	−	14.2405i	−2.59352	−	1.24897i
$131$	7.04393	−	8.83281i	0.615431	−	0.771726i	−0.372262	−	0.928128i	$-0.621418\pi$
$131$	7.04393	−	8.83281i	0.615431	−	0.771726i	0.987694	+	0.156401i	$0.0499893\pi$
$132$		0			0
$133$	−5.66110	−	2.46274i	−0.490879	−	0.213547i
$134$	0.908148	−	0.207279i	0.0784520	−	0.0179062i
$135$		0			0
$136$	27.7646	−	6.33708i	2.38079	−	0.543400i
$137$	3.06225	+	2.44206i	0.261625	+	0.208639i	0.745513	−	0.666491i	$-0.232204\pi$
$137$	3.06225	+	2.44206i	0.261625	+	0.208639i	−0.483888	+	0.875130i	$0.660776\pi$
$138$		0			0
$139$	−4.44613	+	3.54567i	−0.377116	+	0.300740i	−0.793643	−	0.608383i	$-0.791818\pi$
$139$	−4.44613	+	3.54567i	−0.377116	+	0.300740i	0.416528	+	0.909123i	$0.363247\pi$
$140$	−22.6061	+	19.4961i	−1.91056	+	1.64772i
$141$		0			0
$142$	5.26576	+	6.60306i	0.441893	+	0.554116i
$143$	−26.9579	+	12.9822i	−2.25433	+	1.08563i
$144$		0			0
$145$	11.0650	−	2.52553i	0.918902	−	0.209733i
$146$	−4.39699			−0.363897
$147$		0			0
$148$	−20.3097			−1.66945
$149$	4.61947	−	1.05436i	0.378441	−	0.0863768i	−0.0290689	−	0.999577i	$-0.509254\pi$
$149$	4.61947	−	1.05436i	0.378441	−	0.0863768i	0.407510	+	0.913201i	$0.366397\pi$
$150$		0			0
$151$	13.9398	−	6.71306i	1.13441	−	0.546301i	0.230092	−	0.973169i	$-0.426097\pi$
$151$	13.9398	−	6.71306i	1.13441	−	0.546301i	0.904314	+	0.426868i	$0.140383\pi$
$152$	7.03128	+	8.81695i	0.570312	+	0.715149i
$153$		0			0
$154$	1.57285	+	40.8703i	0.126744	+	3.29342i
$155$	−0.881805	+	0.703216i	−0.0708283	+	0.0564837i
$156$		0			0
$157$	16.3412	+	13.0317i	1.30417	+	1.04004i	0.996059	+	0.0886893i	$0.0282678\pi$
$157$	16.3412	+	13.0317i	1.30417	+	1.04004i	0.308110	+	0.951351i	$0.400304\pi$
$158$	4.22143	−	0.963513i	0.335839	−	0.0766530i
$159$		0			0
$160$	−0.621807	+	0.141923i	−0.0491581	+	0.0112200i
$161$	17.0154	−	0.654819i	1.34100	−	0.0516069i
$162$		0			0
$163$	8.89881	−	11.1588i	0.697009	−	0.874021i	−0.299788	−	0.954006i	$-0.596916\pi$
$163$	8.89881	−	11.1588i	0.697009	−	0.874021i	0.996796	+	0.0799850i	$0.0254872\pi$
$164$	−39.1065	−	18.8327i	−3.05370	−	1.47059i
$165$		0			0
$166$			15.4838i			1.20178i
$167$	14.9380	+	7.19374i	1.15593	+	0.556669i	0.910811	−	0.412823i	$-0.135457\pi$
$167$	14.9380	+	7.19374i	1.15593	+	0.556669i	0.245123	+	0.969492i	$0.421172\pi$
$168$		0			0
$169$	8.46071	−	4.07446i	0.650824	−	0.313420i
$170$	−17.7334	−	36.8238i	−1.36009	−	2.82426i
$171$		0			0
$172$	1.61930	−	7.09460i	0.123470	−	0.540958i
$173$	3.54199	−	1.70573i	0.269293	−	0.129685i	−0.294365	−	0.955693i	$-0.595108\pi$
$173$	3.54199	−	1.70573i	0.269293	−	0.129685i	0.563658	+	0.826009i	$0.309394\pi$
$174$		0			0
$175$	6.49641	+	4.78389i	0.491083	+	0.361628i
$176$	10.5951	−	22.0010i	0.798637	−	1.65839i
$177$		0			0
$178$		−	31.9308i		−	2.39331i
$179$	−1.63755	+	3.40041i	−0.122396	+	0.254159i	−0.953160	−	0.302467i	$-0.902190\pi$
$179$	−1.63755	+	3.40041i	−0.122396	+	0.254159i	0.830764	+	0.556625i	$0.187904\pi$
$180$		0			0
$181$	6.89033	+	1.57267i	0.512154	+	0.116896i	0.470785	−	0.882248i	$-0.343971\pi$
$181$	6.89033	+	1.57267i	0.512154	+	0.116896i	0.0413695	+	0.999144i	$0.486828\pi$
$182$	−1.17700	−	30.5843i	−0.0872452	−	2.26706i
$183$		0			0
$184$	−28.0247	−	13.4960i	−2.06601	−	0.994938i
$185$	3.22413	+	14.1258i	0.237043	+	1.03855i
$186$		0			0
$187$	−36.3259	−	8.29115i	−2.65641	−	0.606309i
$188$	−0.527864	−	0.661921i	−0.0384985	−	0.0482756i
$189$		0			0
$190$	10.0910	−	12.6537i	0.732079	−	0.917998i
$191$	−15.4975	+	12.3588i	−1.12136	+	0.894252i	−0.995210	−	0.0977598i	$-0.968832\pi$
$191$	−15.4975	+	12.3588i	−1.12136	+	0.894252i	−0.126146	+	0.992012i	$0.540261\pi$
$192$		0			0
$193$	−12.3044	−	15.4292i	−0.885691	−	1.11062i	−0.993200	−	0.116417i	$-0.962859\pi$
$193$	−12.3044	−	15.4292i	−0.885691	−	1.11062i	0.107510	−	0.994204i	$-0.465712\pi$
$194$	−3.71384	−	16.2714i	−0.266638	−	1.16822i
$195$		0			0
$196$	−25.9354	−	10.1152i	−1.85253	−	0.722514i
$197$		−	5.51994i		−	0.393280i	−0.980476	−	0.196640i	$-0.936997\pi$
$197$		−	5.51994i		−	0.393280i	0.980476	−	0.196640i	$-0.0630030\pi$
$198$		0			0
$199$	7.91594	−	6.31275i	0.561146	−	0.447499i	−0.301385	−	0.953502i	$-0.597449\pi$
$199$	7.91594	−	6.31275i	0.561146	−	0.447499i	0.862532	+	0.506003i	$0.168878\pi$
$200$	−6.39434	−	13.2780i	−0.452148	−	0.938895i
$201$		0			0
$202$	−11.4399	−	9.12302i	−0.804909	−	0.641893i
$203$	6.91235	+	8.01502i	0.485152	+	0.562544i
$204$		0			0
$205$	−6.89045	+	30.1890i	−0.481250	+	2.10849i
$206$	7.23021	−	9.06639i	0.503752	−	0.631685i
$207$		0			0
$208$	−7.92861	+	16.4639i	−0.549750	+	1.14157i
$209$	−3.28323	−	14.3848i	−0.227106	−	0.995016i
$210$		0			0
$211$	5.40999	−	23.7027i	0.372439	−	1.63176i	−0.347468	−	0.937692i	$-0.612959\pi$
$211$	5.40999	−	23.7027i	0.372439	−	1.63176i	0.719907	−	0.694070i	$-0.244184\pi$
$212$	−22.1244	−	17.6436i	−1.51951	−	1.21177i
$213$		0			0
$214$	31.1384			2.12858
$215$	−5.19150			−0.354057
$216$		0			0
$217$	−0.964478	−	0.419575i	−0.0654730	−	0.0284826i
$218$	2.57885	+	5.35504i	0.174662	+	0.362689i
$219$		0			0
$220$	−69.5564	−	15.8758i	−4.68949	−	1.07035i
$221$	27.1836	+	6.20449i	1.82857	+	0.417359i
$222$		0			0
$223$	8.13248	+	16.8873i	0.544591	+	1.13086i	0.973749	+	0.227626i	$0.0730963\pi$
$223$	8.13248	+	16.8873i	0.544591	+	1.13086i	−0.429157	+	0.903230i	$0.641189\pi$
$224$	−0.388443	−	0.450408i	−0.0259540	−	0.0300942i
$225$		0			0
$226$	10.7510			0.715145
$227$	24.9124			1.65349			0.826747	−	0.562574i	$-0.190189\pi$
$227$	24.9124			1.65349			0.826747	+	0.562574i	$0.190189\pi$
$228$		0			0
$229$	−19.0643	−	15.2032i	−1.25980	−	1.00466i	−0.999231	−	0.0392036i	$-0.987518\pi$
$229$	−19.0643	−	15.2032i	−1.25980	−	1.00466i	−0.260571	−	0.965455i	$-0.583911\pi$
$230$	−9.93351	+	43.5215i	−0.654996	+	2.86973i
$231$		0			0
$232$	−4.30218	−	18.8491i	−0.282452	−	1.23750i
$233$	4.24370	−	8.81214i	0.278014	−	0.577302i	−0.714471	−	0.699665i	$-0.753333\pi$
$233$	4.24370	−	8.81214i	0.278014	−	0.577302i	0.992485	+	0.122362i	$0.0390470\pi$
$234$		0			0
$235$	−0.376582	+	0.472219i	−0.0245655	+	0.0308042i
$236$	0.684468	−	2.99885i	0.0445551	−	0.195208i
$237$		0			0
$238$	22.6004	−	30.6907i	1.46496	−	1.98939i
$239$	−14.6187	−	11.6580i	−0.945606	−	0.754096i	0.0237595	−	0.999718i	$-0.492436\pi$
$239$	−14.6187	−	11.6580i	−0.945606	−	0.754096i	−0.969366	+	0.245622i	$0.921008\pi$
$240$		0			0
$241$	−2.72309	−	5.65455i	−0.175409	−	0.364241i	0.794665	−	0.607048i	$-0.207646\pi$
$241$	−2.72309	−	5.65455i	−0.175409	−	0.364241i	−0.970075	+	0.242806i	$0.921932\pi$
$242$	−55.3996	+	44.1797i	−3.56122	+	2.83998i
$243$		0			0
$244$			2.09263i			0.133967i
$245$	−2.91814	+	19.6444i	−0.186433	+	1.25503i
$246$		0			0
$247$	2.45693	+	10.7645i	0.156331	+	0.684929i
$248$	1.19792	+	1.50214i	0.0760677	+	0.0953859i
$249$		0			0
$250$	10.5782	−	8.43586i	0.669027	−	0.533531i
$251$	15.9448	−	19.9941i	1.00642	−	1.26202i	0.0415960	−	0.999135i	$-0.486756\pi$
$251$	15.9448	−	19.9941i	1.00642	−	1.26202i	0.964828	−	0.262881i	$-0.0846728\pi$
$252$		0			0
$253$	25.3739	+	31.8178i	1.59524	+	2.00037i
$254$	20.7338	+	4.73235i	1.30095	+	0.296934i
$255$		0			0
$256$	7.07668	+	31.0050i	0.442293	+	1.93781i
$257$	−11.7375	−	5.65246i	−0.732162	−	0.352591i	0.0303718	−	0.999539i	$-0.490331\pi$
$257$	−11.7375	−	5.65246i	−0.732162	−	0.352591i	−0.762534	+	0.646948i	$0.776045\pi$
$258$		0			0
$259$	−10.2321	+	8.82443i	−0.635793	+	0.548324i
$260$	52.0509	+	11.8803i	3.22806	+	0.736784i
$261$		0			0
$262$	−11.9838	+	24.8847i	−0.740365	+	1.53738i
$263$			4.74637i			0.292674i	0.989235	+	0.146337i	$0.0467484\pi$
$263$			4.74637i			0.292674i	−0.989235	+	0.146337i	$0.953252\pi$
$264$		0			0
$265$	−8.75929	+	18.1889i	−0.538079	+	1.11733i
$266$	14.8328	+	2.79016i	0.909458	+	0.171076i
$267$		0			0
$268$	−1.36521	+	0.657449i	−0.0833933	+	0.0401601i
$269$	2.88003	−	12.6182i	0.175599	−	0.769348i	−0.808030	−	0.589141i	$-0.799466\pi$
$269$	2.88003	−	12.6182i	0.175599	−	0.769348i	0.983629	−	0.180207i	$-0.0576767\pi$
$270$		0			0
$271$	5.80428	+	12.0527i	0.352585	+	0.732149i	0.999538	−	0.0303797i	$-0.00967164\pi$
$271$	5.80428	+	12.0527i	0.352585	+	0.732149i	−0.646954	+	0.762529i	$0.723957\pi$
$272$	−20.5022	+	9.87336i	−1.24313	+	0.598660i
$273$		0			0
$274$	−8.62729	−	4.15468i	−0.521193	−	0.250994i
$275$			19.2818i			1.16274i
$276$		0			0
$277$	−13.7425	−	6.61805i	−0.825708	−	0.397640i	−0.0272042	−	0.999630i	$-0.508660\pi$
$277$	−13.7425	−	6.61805i	−0.825708	−	0.397640i	−0.798504	+	0.601990i	$0.794375\pi$
$278$	8.66833	−	10.8697i	0.519892	−	0.651924i
$279$		0			0
$280$	21.5116	−	29.2123i	1.28557	−	1.74577i
$281$	20.2390	−	4.61942i	1.20736	−	0.275572i	0.428949	−	0.903329i	$-0.358884\pi$
$281$	20.2390	−	4.61942i	1.20736	−	0.275572i	0.778409	+	0.627757i	$0.216027\pi$
$282$		0			0
$283$	23.1604	−	5.28622i	1.37674	−	0.314233i	0.530797	−	0.847499i	$-0.321893\pi$
$283$	23.1604	−	5.28622i	1.37674	−	0.314233i	0.845947	+	0.533266i	$0.179036\pi$
$284$	−10.7411	−	8.56577i	−0.637369	−	0.508285i
$285$		0			0
$286$	57.1908	−	45.6082i	3.38176	−	2.69687i
$287$	−27.8846	+	7.50351i	−1.64598	+	0.442918i
$288$		0			0
$289$	11.0494	+	13.8555i	0.649964	+	0.815029i
$290$	−24.9993	+	12.0390i	−1.46801	+	0.706956i
$291$		0			0
$292$	6.97321	−	1.59159i	0.408076	−	0.0931407i
$293$	6.67026			0.389681			0.194840	−	0.980835i	$-0.437581\pi$
$293$	6.67026			0.389681			0.194840	+	0.980835i	$0.437581\pi$
$294$		0			0
$295$	−2.19442			−0.127764
$296$	24.0631	−	5.49225i	1.39864	−	0.319230i
$297$		0			0
$298$	−10.4368	+	5.02609i	−0.604586	+	0.291153i
$299$	−18.9879	−	23.8101i	−1.09810	−	1.37697i
$300$		0			0
$301$	−2.26674	−	4.27785i	−0.130653	−	0.246571i
$302$	−29.5731	+	23.5838i	−1.70174	+	1.35710i
$303$		0			0
$304$	−7.04517	−	5.61834i	−0.404068	−	0.322234i
$305$	1.45547	−	0.332201i	0.0833398	−	0.0190218i
$306$		0			0
$307$	18.4105	−	4.20209i	1.05075	−	0.239826i	0.337925	−	0.941173i	$-0.390275\pi$
$307$	18.4105	−	4.20209i	1.05075	−	0.239826i	0.712820	+	0.701347i	$0.247418\pi$
$308$	−17.2883	−	64.2471i	−0.985093	−	3.66082i
$309$		0			0
$310$	1.71920	−	2.15581i	0.0976439	−	0.122442i
$311$	6.03911	+	2.90828i	0.342447	+	0.164914i	0.597200	−	0.802092i	$-0.296280\pi$
$311$	6.03911	+	2.90828i	0.342447	+	0.164914i	−0.254753	+	0.967006i	$0.581994\pi$
$312$		0			0
$313$		−	29.7200i		−	1.67988i	−0.542683	−	0.839938i	$-0.682591\pi$
$313$		−	29.7200i		−	1.67988i	0.542683	−	0.839938i	$-0.317409\pi$
$314$	−46.0381	−	22.1708i	−2.59808	−	1.25117i
$315$		0			0
$316$	−6.34602	+	3.05608i	−0.356992	+	0.171918i
$317$	8.90526	+	18.4920i	0.500169	+	1.03861i	0.986336	+	0.164746i	$0.0526806\pi$
$317$	8.90526	+	18.4920i	0.500169	+	1.03861i	−0.486167	+	0.873866i	$0.661605\pi$
$318$		0			0
$319$	−5.62878	+	24.6613i	−0.315151	+	1.38077i
$320$	21.1477	−	10.1842i	1.18219	−	0.569314i
$321$		0			0
$322$	−40.1995	+	10.8173i	−2.24023	+	0.602825i
$323$	−5.96572	+	12.3879i	−0.331942	+	0.689284i
$324$		0			0
$325$		−	14.4291i		−	0.800381i
$326$	−15.1396	+	31.4376i	−0.838502	+	1.74117i
$327$		0			0
$328$	51.4264	+	11.7377i	2.83955	+	0.648108i
$329$	−0.553540	−	0.104125i	−0.0305176	−	0.00574059i
$330$		0			0
$331$	10.6008	+	5.10509i	0.582675	+	0.280601i	0.701911	−	0.712265i	$-0.252330\pi$
$331$	10.6008	+	5.10509i	0.582675	+	0.280601i	−0.119236	+	0.992866i	$0.538045\pi$
$332$	−5.60473	−	24.5559i	−0.307599	−	1.34768i
$333$		0			0
$334$	−39.5177	−	9.01965i	−2.16231	−	0.493533i
$335$	0.673994	+	0.845162i	0.0368242	+	0.0461761i
$336$		0			0
$337$	9.14102	−	11.4625i	0.497943	−	0.624401i	−0.467821	−	0.883823i	$-0.654961\pi$
$337$	9.14102	−	11.4625i	0.497943	−	0.624401i	0.965764	+	0.259423i	$0.0835322\pi$
$338$	−17.9493	+	14.3141i	−0.976312	+	0.778583i
$339$		0			0
$340$	41.4527	+	51.9801i	2.24809	+	2.81901i
$341$	−0.559362	−	2.45073i	−0.0302912	−	0.132714i
$342$		0			0
$343$	−17.4613	+	6.17267i	−0.942823	+	0.333293i
$344$			8.84362i			0.476816i
$345$		0			0
$346$	−7.51430	+	5.99245i	−0.403971	+	0.322156i
$347$	1.07168	+	2.22537i	0.0575309	+	0.119464i	0.927752	−	0.373197i	$-0.121738\pi$
$347$	1.07168	+	2.22537i	0.0575309	+	0.119464i	−0.870221	+	0.492661i	$0.836024\pi$
$348$		0			0
$349$	9.62208	+	7.67336i	0.515058	+	0.410745i	0.846224	−	0.532827i	$-0.178870\pi$
$349$	9.62208	+	7.67336i	0.515058	+	0.410745i	−0.331166	+	0.943573i	$0.607442\pi$
$350$	−18.0865	−	7.86814i	−0.966764	−	0.420570i
$351$		0			0
$352$	0.316312	−	1.38586i	0.0168595	−	0.0738663i
$353$	15.0009	−	18.8106i	0.798420	−	1.00119i	−0.201345	−	0.979520i	$-0.564531\pi$
$353$	15.0009	−	18.8106i	0.798420	−	1.00119i	0.999765	−	0.0216665i	$-0.00689720\pi$
$354$		0			0
$355$	−4.25254	+	8.83049i	−0.225701	+	0.468674i
$356$	11.5581	+	50.6393i	0.612577	+	2.68388i
$357$		0			0
$358$	2.05319	−	8.99562i	0.108515	−	0.475433i
$359$	0.672132	+	0.536007i	0.0354737	+	0.0282894i	0.641066	−	0.767486i	$-0.278492\pi$
$359$	0.672132	+	0.536007i	0.0354737	+	0.0282894i	−0.605592	+	0.795775i	$0.707064\pi$
$360$		0			0
$361$	13.5553			0.713435
$362$	−17.2785			−0.908135
$363$		0			0
$364$	12.9373	+	48.0778i	0.678099	+	2.51996i
$365$	−2.21397	−	4.59735i	−0.115884	−	0.240636i
$366$		0			0
$367$	−10.9358	−	2.49603i	−0.570846	−	0.130292i	−0.0726520	−	0.997357i	$-0.523146\pi$
$367$	−10.9358	−	2.49603i	−0.570846	−	0.130292i	−0.498194	+	0.867065i	$0.666003\pi$
$368$	24.2313	+	5.53064i	1.26315	+	0.288305i
$369$		0			0
$370$	−15.3692	−	31.9146i	−0.799009	−	1.65916i
$371$	−18.8124	+	0.723973i	−0.976689	+	0.0375868i
$372$		0			0
$373$	−11.5655			−0.598839			−0.299420	−	0.954122i	$-0.596793\pi$
$373$	−11.5655			−0.598839			−0.299420	+	0.954122i	$0.596793\pi$
$374$	91.0922			4.71026
$375$		0			0
$376$	0.804417	+	0.641501i	0.0414846	+	0.0330829i
$377$	4.21216	−	18.4547i	0.216938	−	0.950465i
$378$		0			0
$379$	6.32306	+	27.7031i	0.324794	+	1.42301i	0.828912	+	0.559379i	$0.188960\pi$
$379$	6.32306	+	27.7031i	0.324794	+	1.42301i	−0.504118	+	0.863635i	$0.668182\pi$
$380$	−11.4231	+	23.7203i	−0.585992	+	1.21683i
$381$		0			0
$382$	30.2144	−	37.8876i	1.54590	−	1.93850i
$383$	−4.10370	+	17.9795i	−0.209689	+	0.918708i	0.755085	+	0.655627i	$0.227596\pi$
$383$	−4.10370	+	17.9795i	−0.209689	+	0.918708i	−0.964774	+	0.263081i	$0.915261\pi$
$384$		0			0
$385$	−41.9407	+	22.2235i	−2.13750	+	1.13261i
$386$	37.7209	+	30.0814i	1.91994	+	1.53110i
$387$		0			0
$388$	11.7796	+	24.4606i	0.598019	+	1.24180i
$389$	28.5354	−	22.7563i	1.44680	−	1.15379i	0.486901	−	0.873457i	$-0.338127\pi$
$389$	28.5354	−	22.7563i	1.44680	−	1.15379i	0.959903	−	0.280331i	$-0.0904443\pi$
$390$		0			0
$391$		−	37.9242i		−	1.91791i
$392$	33.4638	+	4.97099i	1.69018	+	0.251073i
$393$		0			0
$394$	3.00291	+	13.1566i	0.151285	+	0.662821i
$395$	3.13299	+	3.92864i	0.157638	+	0.197672i
$396$		0			0
$397$	11.9636	−	9.54069i	0.600438	−	0.478833i	−0.275471	−	0.961309i	$-0.588834\pi$
$397$	11.9636	−	9.54069i	0.600438	−	0.478833i	0.875909	+	0.482476i	$0.160262\pi$
$398$	−15.4332	+	19.3526i	−0.773596	+	0.970059i
$399$		0			0
$400$	7.34217	+	9.20679i	0.367108	+	0.460339i
$401$	−13.6850	−	3.12352i	−0.683397	−	0.155981i	−0.133293	−	0.991077i	$-0.542555\pi$
$401$	−13.6850	−	3.12352i	−0.683397	−	0.155981i	−0.550105	+	0.835096i	$0.685412\pi$
$402$		0			0
$403$	0.418585	+	1.83394i	0.0208512	+	0.0913552i
$404$	21.4449	+	10.3273i	1.06692	+	0.513803i
$405$		0			0
$406$	−20.8356	−	15.3432i	−1.03406	−	0.761468i
$407$	−31.4831	−	7.18580i	−1.56056	−	0.356187i
$408$		0			0
$409$	−8.15243	+	16.9287i	−0.403112	+	0.837070i	0.596300	+	0.802762i	$0.296637\pi$
$409$	−8.15243	+	16.9287i	−0.403112	+	0.837070i	−0.999411	+	0.0343081i	$0.989077\pi$
$410$		−	75.7031i		−	3.73871i
$411$		0			0
$412$	−8.18464	+	16.9956i	−0.403228	+	0.837312i
$413$	−0.958141	−	1.80823i	−0.0471470	−	0.0889770i
$414$		0			0
$415$	−16.1894	+	7.79641i	−0.794707	+	0.382711i
$416$	−0.236705	+	1.03707i	−0.0116054	+	0.0508467i
$417$		0			0
$418$	15.6510	+	32.4996i	0.765514	+	1.58961i
$419$	−11.6595	+	5.61490i	−0.569602	+	0.274306i	−0.696437	−	0.717618i	$-0.745232\pi$
$419$	−11.6595	+	5.61490i	−0.569602	+	0.274306i	0.126835	+	0.991924i	$0.459518\pi$
$420$		0			0
$421$	−12.1770	−	5.86413i	−0.593470	−	0.285800i	0.112941	−	0.993602i	$-0.463973\pi$
$421$	−12.1770	−	5.86413i	−0.593470	−	0.285800i	−0.706411	+	0.707802i	$0.749687\pi$
$422$			59.4378i			2.89339i
$423$		0			0
$424$	30.9844	+	14.9213i	1.50473	+	0.724642i
$425$	11.2030	−	14.0482i	0.543427	−	0.681436i
$426$		0			0
$427$	0.909232	+	1.05427i	0.0440008	+	0.0510199i
$428$	−49.3826	+	11.2712i	−2.38700	+	0.544816i
$429$		0			0
$430$	12.3738	−	2.82424i	0.596717	−	0.136197i
$431$	26.9910	+	21.5246i	1.30011	+	1.03680i	0.996464	+	0.0840204i	$0.0267761\pi$
$431$	26.9910	+	21.5246i	1.30011	+	1.03680i	0.303648	+	0.952784i	$0.401795\pi$
$432$		0			0
$433$	−25.5534	+	20.3782i	−1.22802	+	0.979312i	−0.228035	+	0.973653i	$0.573230\pi$
$433$	−25.5534	+	20.3782i	−1.22802	+	0.979312i	−0.999984	+	0.00565934i	$0.998199\pi$
$434$	2.52706	+	0.475358i	0.121303	+	0.0228179i
$435$		0			0
$436$	−6.02820	−	7.55912i	−0.288698	−	0.362016i
$437$	13.5305	−	6.51593i	0.647250	−	0.311699i
$438$		0			0
$439$	−5.78102	+	1.31948i	−0.275913	+	0.0629754i	−0.358238	−	0.933630i	$-0.616623\pi$
$439$	−5.78102	+	1.31948i	−0.275913	+	0.0629754i	0.0823252	+	0.996606i	$0.473765\pi$
$440$	86.7041			4.13345
$441$		0			0
$442$	−68.1667			−3.24236
$443$	27.1023	−	6.18592i	1.28767	−	0.293902i	0.476739	−	0.879045i	$-0.341819\pi$
$443$	27.1023	−	6.18592i	1.28767	−	0.293902i	0.810930	+	0.585143i	$0.198962\pi$
$444$		0			0
$445$	33.3858	−	16.0778i	1.58264	−	0.762160i
$446$	−28.5704	−	35.8262i	−1.35285	−	1.69642i
$447$		0			0
$448$	17.6255	+	12.9793i	0.832728	+	0.613213i
$449$	−13.9580	+	11.1312i	−0.658721	+	0.525312i	−0.894826	−	0.446415i	$-0.852700\pi$
$449$	−13.9580	+	11.1312i	−0.658721	+	0.525312i	0.236105	+	0.971727i	$0.424129\pi$
$450$		0			0
$451$	−53.9575	−	43.0297i	−2.54076	−	2.02619i
$452$	−17.0501	+	3.89156i	−0.801967	+	0.183044i
$453$		0			0
$454$	−59.3780	+	13.5526i	−2.78675	+	0.636056i
$455$	31.3853	−	16.6304i	1.47137	−	0.779646i
$456$		0			0
$457$	−21.1925	+	26.5745i	−0.991343	+	1.24310i	−0.0214003	+	0.999771i	$0.506812\pi$
$457$	−21.1925	+	26.5745i	−0.991343	+	1.24310i	−0.969943	+	0.243334i	$0.921759\pi$
$458$	53.7098	+	25.8653i	2.50970	+	1.20861i
$459$		0			0
$460$		−	72.6168i		−	3.38577i
$461$	−14.9439	−	7.19660i	−0.696006	−	0.335179i	0.0522080	−	0.998636i	$-0.483374\pi$
$461$	−14.9439	−	7.19660i	−0.696006	−	0.335179i	−0.748214	+	0.663457i	$0.769088\pi$
$462$		0			0
$463$	−19.4404	+	9.36200i	−0.903471	+	0.435089i	−0.827141	−	0.561994i	$-0.810034\pi$
$463$	−19.4404	+	9.36200i	−0.903471	+	0.435089i	−0.0763298	+	0.997083i	$0.524320\pi$
$464$	6.70293	+	13.9188i	0.311176	+	0.646163i
$465$		0			0
$466$	−5.32083	+	23.3121i	−0.246483	+	1.07991i
$467$	17.4373	−	8.39738i	0.806904	−	0.388585i	0.0155015	−	0.999880i	$-0.495066\pi$
$467$	17.4373	−	8.39738i	0.806904	−	0.388585i	0.791403	+	0.611295i	$0.209351\pi$
$468$		0			0
$469$	−0.402140	+	0.924399i	−0.0185691	+	0.0426848i
$470$	0.640680	−	1.33039i	0.0295524	−	0.0613661i
$471$		0			0
$472$			3.73815i			0.172062i
$473$	5.02029	−	10.4247i	0.230833	−	0.479330i
$474$		0			0
$475$	6.93690	+	1.58330i	0.318287	+	0.0726469i
$476$	−24.7328	+	56.8534i	−1.13363	+	2.60587i
$477$		0			0
$478$	41.1854	+	19.8338i	1.88378	+	0.907178i
$479$	−3.10199	−	13.5907i	−0.141734	−	0.620976i	−0.995032	−	0.0995534i	$-0.968259\pi$
$479$	−3.10199	−	13.5907i	−0.141734	−	0.620976i	0.853298	−	0.521423i	$-0.174599\pi$
$480$		0			0
$481$	23.5596	+	5.37733i	1.07423	+	0.245185i
$482$	9.56653	+	11.9961i	0.435744	+	0.546405i
$483$		0			0
$484$	71.8668	−	90.1181i	3.26667	−	4.09628i
$485$	15.1429	−	12.0760i	0.687602	−	0.548344i
$486$		0			0
$487$	4.08334	+	5.12035i	0.185034	+	0.232025i	0.865693	−	0.500575i	$-0.166878\pi$
$487$	4.08334	+	5.12035i	0.185034	+	0.232025i	−0.680659	+	0.732600i	$0.738307\pi$
$488$	−0.565898	−	2.47936i	−0.0256170	−	0.112235i
$489$		0			0
$490$	−3.73148	−	48.4093i	−0.168571	−	2.18691i
$491$		−	11.2378i		−	0.507153i	−0.967315	−	0.253577i	$-0.918393\pi$
$491$		−	11.2378i		−	0.507153i	0.967315	−	0.253577i	$-0.0816070\pi$
$492$		0			0
$493$	18.4296	−	14.6971i	0.830027	−	0.661924i
$494$	−11.7120	−	24.3203i	−0.526949	−	1.09422i
$495$		0			0
$496$	−1.20028	−	0.957192i	−0.0538942	−	0.0429792i
$497$	−9.13319	+	0.351481i	−0.409680	+	0.0157661i
$498$		0			0
$499$	2.31499	−	10.1426i	0.103633	−	0.454046i	−0.896311	−	0.443427i	$-0.853763\pi$
$499$	2.31499	−	10.1426i	0.103633	−	0.454046i	0.999944	−	0.0106193i	$-0.00338030\pi$
$500$	−13.7225	+	17.2075i	−0.613691	+	0.769544i
$501$		0			0
$502$	−27.1268	+	56.3295i	−1.21073	+	2.51411i
$503$	0.0155092	+	0.0679501i	0.000691519	+	0.00302974i	0.975272	−	0.221006i	$-0.0709340\pi$
$503$	0.0155092	+	0.0679501i	0.000691519	+	0.00302974i	−0.974581	+	0.224036i	$0.928077\pi$
$504$		0			0
$505$	3.77853	−	16.5548i	0.168142	−	0.736680i
$506$	−77.7871	−	62.0331i	−3.45806	−	2.75771i
$507$		0			0
$508$	−34.5948			−1.53490
$509$	22.1454			0.981577			0.490789	−	0.871279i	$-0.336709\pi$
$509$	22.1454			0.981577			0.490789	+	0.871279i	$0.336709\pi$
$510$		0			0
$511$	2.82159	−	3.83166i	0.124820	−	0.169503i
$512$	−16.5728	−	34.4137i	−0.732420	−	1.52089i
$513$		0			0
$514$	31.0509	+	7.08716i	1.36960	+	0.312601i
$515$	13.1201	+	2.99457i	0.578140	+	0.131957i
$516$		0			0
$517$	−0.584072	−	1.21284i	−0.0256875	−	0.0533406i
$518$	19.5874	−	26.5992i	0.860619	−	1.16870i
$519$		0			0
$520$	−64.8830			−2.84531
$521$	−11.1863			−0.490083			−0.245041	−	0.969513i	$-0.578802\pi$
$521$	−11.1863			−0.490083			−0.245041	+	0.969513i	$0.578802\pi$
$522$		0			0
$523$	−25.2189	−	20.1114i	−1.10274	−	0.879409i	−0.109332	−	0.994005i	$-0.534871\pi$
$523$	−25.2189	−	20.1114i	−1.10274	−	0.879409i	−0.993412	+	0.114596i	$0.963443\pi$
$524$	9.99767	−	43.8027i	0.436750	−	1.91353i
$525$		0			0
$526$	−2.58208	−	11.3128i	−0.112584	−	0.493263i
$527$	−1.01638	+	2.11053i	−0.0442740	+	0.0919360i
$528$		0			0
$529$	−11.4858	+	14.4028i	−0.499383	+	0.626207i
$530$	10.9826	−	48.1178i	0.477052	−	2.09010i
$531$		0			0
$532$	−24.5334	+	0.944141i	−1.06366	+	0.0409337i
$533$	40.3779	+	32.2003i	1.74896	+	1.39475i
$534$		0			0
$535$	15.6788	+	32.5573i	0.677853	+	1.40758i
$536$	1.43972	−	1.14814i	0.0621863	−	0.0495919i
$537$		0			0
$538$			31.6420i			1.36418i
$539$	−36.6248	−	24.8563i	−1.57754	−	1.07064i
$540$		0			0
$541$	1.74072	+	7.62659i	0.0748394	+	0.327893i	0.998464	−	0.0554058i	$-0.0176452\pi$
$541$	1.74072	+	7.62659i	0.0748394	+	0.327893i	−0.923625	+	0.383298i	$0.874788\pi$
$542$	−20.3911	−	25.5697i	−0.875874	−	1.09831i
$543$		0			0
$544$	−1.03566	+	0.825912i	−0.0444036	+	0.0354107i
$545$	−4.30056	+	5.39273i	−0.184216	+	0.230999i
$546$		0			0
$547$	3.54971	+	4.45120i	0.151775	+	0.190320i	0.851906	−	0.523695i	$-0.175447\pi$
$547$	3.54971	+	4.45120i	0.151775	+	0.190320i	−0.700131	+	0.714014i	$0.746875\pi$
$548$	15.1860	+	3.46609i	0.648712	+	0.148064i
$549$		0			0
$550$	−10.4895	−	45.9576i	−0.447274	−	1.95964i
$551$	8.41005	+	4.05007i	0.358280	+	0.172539i
$552$		0			0
$553$	−1.86930	+	4.29697i	−0.0794909	+	0.182726i
$554$	36.3552	+	8.29783i	1.54458	+	0.352541i
$555$		0			0
$556$	−9.81261	+	20.3761i	−0.416147	+	0.864139i
$557$		−	15.8171i		−	0.670192i	−0.942184	−	0.335096i	$-0.891231\pi$
$557$		−	15.8171i		−	0.670192i	0.942184	−	0.335096i	$-0.108769\pi$
$558$		0			0
$559$	−3.75681	+	7.80111i	−0.158896	+	0.329952i
$560$	−11.5638	+	26.5817i	−0.488659	+	1.12328i
$561$		0			0
$562$	−45.7261	+	22.0205i	−1.92884	+	0.928879i
$563$	−1.63212	+	7.15077i	−0.0687855	+	0.301369i	−0.997605	−	0.0691625i	$-0.977967\pi$
$563$	−1.63212	+	7.15077i	−0.0687855	+	0.301369i	0.928820	+	0.370531i	$0.120824\pi$
$564$		0			0
$565$	5.41333	+	11.2409i	0.227740	+	0.472908i
$566$	−52.3264	+	25.1991i	−2.19944	+	1.05920i
$567$		0			0
$568$	15.0426	+	7.24411i	0.631172	+	0.303956i
$569$			10.2964i			0.431647i	0.976432	+	0.215823i	$0.0692436\pi$
$569$			10.2964i			0.431647i	−0.976432	+	0.215823i	$0.930756\pi$
$570$		0			0
$571$	−9.52979	−	4.58930i	−0.398809	−	0.192056i	0.223719	−	0.974654i	$-0.428180\pi$
$571$	−9.52979	−	4.58930i	−0.398809	−	0.192056i	−0.622528	+	0.782597i	$0.713894\pi$
$572$	−74.1904	+	93.0318i	−3.10206	+	3.88986i
$573$		0			0
$574$	62.3802	−	33.0540i	2.60370	−	1.37965i
$575$	−19.1334	+	4.36707i	−0.797918	+	0.182120i
$576$		0			0
$577$	34.4962	−	7.87354i	1.43610	−	0.327780i	0.567530	−	0.823353i	$-0.307899\pi$
$577$	34.4962	−	7.87354i	1.43610	−	0.327780i	0.868566	+	0.495573i	$0.165042\pi$
$578$	−33.8734	−	27.0132i	−1.40895	−	1.12360i
$579$		0			0
$580$	35.2887	−	28.1418i	1.46529	−	1.16853i
$581$	−13.4930	−	9.93614i	−0.559786	−	0.412221i
$582$		0			0
$583$	−28.0535	−	35.1780i	−1.16186	−	1.45692i
$584$	−7.83150	+	3.77145i	−0.324070	+	0.156064i
$585$		0			0
$586$	−15.8984	+	3.62870i	−0.656755	+	0.149900i
$587$	27.9850			1.15507			0.577533	−	0.816367i	$-0.304015\pi$
$587$	27.9850			1.15507			0.577533	+	0.816367i	$0.304015\pi$
$588$		0			0
$589$	−0.927615			−0.0382217
$590$	5.23033	−	1.19379i	0.215329	−	0.0491475i
$591$		0			0
$592$	−17.7690	+	8.55708i	−0.730300	+	0.351694i
$593$	−2.75010	−	3.44852i	−0.112933	−	0.141614i	0.722152	−	0.691734i	$-0.243153\pi$
$593$	−2.75010	−	3.44852i	−0.112933	−	0.141614i	−0.835085	+	0.550121i	$0.814582\pi$
$594$		0			0
$595$	43.4690	+	8.17684i	1.78206	+	0.335218i
$596$	14.7324	−	11.7487i	0.603464	−	0.481247i
$597$		0			0
$598$	58.2101	+	46.4210i	2.38039	+	1.89830i
$599$	−28.2260	+	6.44239i	−1.15328	+	0.263229i	−0.756066	−	0.654496i	$-0.772881\pi$
$599$	−28.2260	+	6.44239i	−1.15328	+	0.263229i	−0.397216	+	0.917725i	$0.630024\pi$
$600$		0			0
$601$	−14.6523	+	3.34429i	−0.597680	+	0.136417i	−0.510649	−	0.859789i	$-0.670595\pi$
$601$	−14.6523	+	3.34429i	−0.597680	+	0.136417i	−0.0870306	+	0.996206i	$0.527738\pi$
$602$	7.72992	+	8.96300i	0.315048	+	0.365305i
$603$		0			0
$604$	38.3636	−	48.1064i	1.56099	−	1.95742i
$605$	−74.0877	−	35.6788i	−3.01209	−	1.45055i
$606$		0			0
$607$		−	34.1281i		−	1.38522i	−0.721314	−	0.692608i	$-0.756462\pi$
$607$		−	34.1281i		−	1.38522i	0.721314	−	0.692608i	$-0.243538\pi$
$608$	−0.472608	−	0.227596i	−0.0191668	−	0.00923023i
$609$		0			0
$610$	−3.28834	+	1.58358i	−0.133141	+	0.0641173i
$611$	0.437077	+	0.907599i	0.0176822	+	0.0367175i
$612$		0			0
$613$	8.71895	−	38.2002i	0.352155	−	1.54289i	−0.420039	−	0.907506i	$-0.637984\pi$
$613$	8.71895	−	38.2002i	0.352155	−	1.54289i	0.772194	−	0.635387i	$-0.219159\pi$
$614$	−41.5950	+	20.0311i	−1.67864	+	0.808389i
$615$		0			0
$616$	37.8573	+	71.4452i	1.52531	+	2.87861i
$617$	12.6412	−	26.2498i	0.508917	−	1.05678i	−0.475302	−	0.879823i	$-0.657661\pi$
$617$	12.6412	−	26.2498i	0.508917	−	1.05678i	0.984219	−	0.176954i	$-0.0566244\pi$
$618$		0			0
$619$		−	11.0613i		−	0.444590i	−0.974980	−	0.222295i	$-0.928645\pi$
$619$		−	11.0613i		−	0.444590i	0.974980	−	0.222295i	$-0.0713547\pi$
$620$	−1.94615	+	4.04121i	−0.0781591	+	0.162299i
$621$		0			0
$622$	−15.9762	−	3.64646i	−0.640587	−	0.146210i
$623$	27.8254	+	20.4903i	1.11480	+	0.820928i
$624$		0			0
$625$	27.8834	+	13.4279i	1.11534	+	0.537117i
$626$	16.1680	+	70.8368i	0.646205	+	2.83121i
$627$		0			0
$628$	81.0374	+	18.4963i	3.23374	+	0.738081i
$629$	18.7626	+	23.5275i	0.748113	+	0.938105i
$630$		0			0
$631$	−16.6176	+	20.8379i	−0.661538	+	0.829542i	−0.993510	−	0.113747i	$-0.963715\pi$
$631$	−16.6176	+	20.8379i	−0.661538	+	0.829542i	0.331972	+	0.943289i	$0.392286\pi$
$632$	6.69237	−	5.33699i	0.266208	−	0.212294i
$633$		0			0
$634$	−31.2853	−	39.2305i	−1.24250	−	1.55804i
$635$	5.49186	+	24.0614i	0.217938	+	0.954849i
$636$		0			0
$637$	27.4073	+	18.6006i	1.08592	+	0.736983i
$638$		−	61.8416i		−	2.44833i
$639$		0			0
$640$	−43.8673	+	34.9830i	−1.73401	+	1.38282i
$641$	5.26842	+	10.9400i	0.208090	+	0.432104i	0.978726	−	0.205172i	$-0.0657755\pi$
$641$	5.26842	+	10.9400i	0.208090	+	0.432104i	−0.770636	+	0.637276i	$0.780061\pi$
$642$		0			0
$643$	−5.07245	−	4.04514i	−0.200038	−	0.159525i	0.518348	−	0.855170i	$-0.326547\pi$
$643$	−5.07245	−	4.04514i	−0.200038	−	0.159525i	−0.718386	+	0.695645i	$0.755119\pi$
$644$	59.8370	−	31.7064i	2.35791	−	1.24941i
$645$		0			0
$646$	7.47993	−	32.7717i	0.294294	−	1.28939i
$647$	−25.0076	+	31.3585i	−0.983150	+	1.23283i	−0.0106469	+	0.999943i	$0.503389\pi$
$647$	−25.0076	+	31.3585i	−0.983150	+	1.23283i	−0.972504	+	0.232888i	$0.925182\pi$
$648$		0			0
$649$	2.12205	−	4.40648i	0.0832978	−	0.172970i
$650$	7.84958	+	34.3913i	0.307886	+	1.34894i
$651$		0			0
$652$	12.6304	−	55.3372i	0.494643	−	2.16717i
$653$	8.23157	+	6.56446i	0.322126	+	0.256887i	0.771179	−	0.636618i	$-0.219667\pi$
$653$	8.23157	+	6.56446i	0.322126	+	0.256887i	−0.449053	+	0.893505i	$0.648239\pi$
$654$		0			0
$655$	−32.0528			−1.25241
$656$	−42.1489			−1.64564
$657$		0			0
$658$	1.37599	−	0.0529535i	0.0536417	−	0.00206434i
$659$	−9.88101	−	20.5181i	−0.384909	−	0.799273i	−0.999942	−	0.0107709i	$-0.996571\pi$
$659$	−9.88101	−	20.5181i	−0.384909	−	0.799273i	0.615033	−	0.788502i	$-0.289143\pi$
$660$		0			0
$661$	−32.0383	−	7.31254i	−1.24615	−	0.284425i	−0.451927	−	0.892055i	$-0.649263\pi$
$661$	−32.0383	−	7.31254i	−1.24615	−	0.284425i	−0.794220	+	0.607630i	$0.792120\pi$
$662$	−28.0440	−	6.40086i	−1.08996	−	0.248777i
$663$		0			0
$664$	13.2810	+	27.5783i	0.515404	+	1.07025i
$665$	4.55130	+	16.9136i	0.176492	+	0.655882i
$666$		0			0
$667$	−25.7463			−0.996902
$668$	65.9362			2.55115
$669$		0			0
$670$	−2.06622	−	1.64776i	−0.0798251	−	0.0636584i
$671$	−0.740395	+	3.24388i	−0.0285826	+	0.125229i
$672$		0			0
$673$	−0.340168	−	1.49037i	−0.0131125	−	0.0574497i	0.967948	−	0.251149i	$-0.0808085\pi$
$673$	−0.340168	−	1.49037i	−0.0131125	−	0.0574497i	−0.981061	+	0.193699i	$0.937951\pi$
$674$	−15.5516	+	32.2933i	−0.599026	+	1.24389i
$675$		0			0
$676$	23.2846	−	29.1979i	0.895561	−	1.12300i
$677$	−11.5056	+	50.4092i	−0.442195	+	1.93738i	−0.111005	+	0.993820i	$0.535407\pi$
$677$	−11.5056	+	50.4092i	−0.442195	+	1.93738i	−0.331190	+	0.943564i	$0.607450\pi$
$678$		0			0
$679$	16.5626	+	7.20518i	0.635613	+	0.276510i
$680$	−63.1701	−	50.3765i	−2.42246	−	1.93185i
$681$		0			0
$682$	2.66645	+	5.53693i	0.102103	+	0.212020i
$683$	25.8254	−	20.5951i	0.988183	−	0.788050i	0.0108898	−	0.999941i	$-0.496534\pi$
$683$	25.8254	−	20.5951i	0.988183	−	0.788050i	0.977293	+	0.211891i	$0.0679622\pi$
$684$		0			0
$685$		−	11.1124i		−	0.424582i
$686$	38.2606	−	24.2115i	1.46079	−	0.924401i
$687$		0			0
$688$	−1.57244	−	6.88931i	−0.0599487	−	0.262652i
$689$	20.9932	+	26.3246i	0.799777	+	1.00289i
$690$		0			0
$691$	−0.479517	+	0.382402i	−0.0182417	+	0.0145473i	−0.632568	−	0.774505i	$-0.717999\pi$
$691$	−0.479517	+	0.382402i	−0.0182417	+	0.0145473i	0.614327	+	0.789052i	$0.289428\pi$
$692$	9.74787	−	12.2234i	0.370558	−	0.464665i
$693$		0			0
$694$	−3.76495	−	4.72110i	−0.142915	−	0.179210i
$695$	15.7297	+	3.59021i	0.596663	+	0.136184i
$696$		0			0
$697$	14.3110	+	62.7004i	0.542066	+	2.37495i
$698$	−27.1083	−	13.0547i	−1.02607	−	0.494127i
$699$		0			0
$700$	31.5316	+	5.93132i	1.19178	+	0.224183i
$701$	−7.02160	−	1.60263i	−0.265202	−	0.0605307i	0.0878520	−	0.996134i	$-0.472000\pi$
$701$	−7.02160	−	1.60263i	−0.265202	−	0.0605307i	−0.353054	+	0.935603i	$0.614857\pi$
$702$		0			0
$703$	−5.17039	+	10.7364i	−0.195005	+	0.404932i
$704$			52.3138i			1.97165i
$705$		0			0
$706$	−25.5211	+	52.9952i	−0.960500	+	1.99450i
$707$	15.2912	−	4.11471i	0.575083	−	0.154750i
$708$		0			0
$709$	7.23008	−	3.48182i	0.271531	−	0.130763i	−0.293164	−	0.956062i	$-0.594708\pi$
$709$	7.23008	−	3.48182i	0.271531	−	0.130763i	0.564695	+	0.825300i	$0.308994\pi$
$710$	5.33191	−	23.3606i	0.200103	−	0.876709i
$711$		0			0
$712$	−27.3882	−	56.8721i	−1.02642	−	2.13137i
$713$	2.30518	−	1.11011i	0.0863295	−	0.0415741i
$714$		0			0
$715$	76.4832	+	36.8323i	2.86031	+	1.37745i
$716$			15.0094i			0.560928i
$717$		0			0
$718$	−1.89360	−	0.911909i	−0.0706685	−	0.0340322i
$719$	−6.54854	+	8.21161i	−0.244219	+	0.306241i	−0.888800	−	0.458295i	$-0.848460\pi$
$719$	−6.54854	+	8.21161i	−0.244219	+	0.306241i	0.644581	+	0.764536i	$0.277032\pi$
$720$		0			0
$721$	3.26101	+	12.1186i	0.121446	+	0.451320i
$722$	−32.3086	+	7.37422i	−1.20240	+	0.274440i
$723$		0			0
$724$	27.4020	−	6.25433i	1.01839	−	0.232440i
$725$	−9.53716	−	7.60563i	−0.354201	−	0.282466i
$726$		0			0
$727$	30.4298	−	24.2669i	1.12858	−	0.900011i	0.132740	−	0.991151i	$-0.457623\pi$
$727$	30.4298	−	24.2669i	1.12858	−	0.900011i	0.995838	+	0.0911403i	$0.0290512\pi$
$728$	−28.3296	−	53.4643i	−1.04996	−	1.98152i
$729$		0			0
$730$	7.77794	+	9.75323i	0.287874	+	0.360983i
$731$	−9.71458	+	4.67830i	−0.359307	+	0.173033i
$732$		0			0
$733$	−6.02192	+	1.37446i	−0.222425	+	0.0507670i	−0.332281	−	0.943181i	$-0.607818\pi$
$733$	−6.02192	+	1.37446i	−0.222425	+	0.0507670i	0.109856	+	0.993948i	$0.464961\pi$
$734$	27.4231			1.01221
$735$		0			0
$736$	1.44683			0.0533309
$737$	−2.34888	+	0.536118i	−0.0865223	+	0.0197481i
$738$		0			0
$739$	−3.21693	+	1.54919i	−0.118337	+	0.0569880i	−0.492115	−	0.870530i	$-0.663776\pi$
$739$	−3.21693	+	1.54919i	−0.118337	+	0.0569880i	0.373779	+	0.927518i	$0.378062\pi$
$740$	35.9264	+	45.0503i	1.32068	+	1.65608i
$741$		0			0
$742$	44.4449	−	11.9597i	1.63162	−	0.439055i
$743$	9.75148	−	7.77655i	0.357747	−	0.285294i	−0.428079	−	0.903741i	$-0.640809\pi$
$743$	9.75148	−	7.77655i	0.357747	−	0.285294i	0.785826	+	0.618447i	$0.212238\pi$
$744$		0			0
$745$	−10.5102	−	8.38163i	−0.385065	−	0.307079i
$746$	27.5660	−	6.29177i	1.00926	−	0.230358i
$747$		0			0
$748$	−144.464	+	32.9729i	−5.28212	+	1.20561i
$749$	−19.9818	+	27.1349i	−0.730121	+	0.991487i
$750$		0			0
$751$	12.5112	−	15.6886i	0.456541	−	0.572485i	−0.499277	−	0.866442i	$-0.666401\pi$
$751$	12.5112	−	15.6886i	0.456541	−	0.572485i	0.955818	+	0.293958i	$0.0949724\pi$
$752$	−0.740714	−	0.356709i	−0.0270111	−	0.0130078i
$753$		0			0
$754$			46.2777i			1.68533i
$755$	−39.5491	−	19.0459i	−1.43934	−	0.693150i
$756$		0			0
$757$	3.27051	−	1.57500i	0.118869	−	0.0572442i	−0.373504	−	0.927628i	$-0.621844\pi$
$757$	3.27051	−	1.57500i	0.118869	−	0.0572442i	0.492373	+	0.870384i	$0.336130\pi$
$758$	−30.1416	−	62.5898i	−1.09479	−	2.27336i
$759$		0			0
$760$	7.11961	−	31.1930i	0.258255	−	1.13149i
$761$	−48.2631	+	23.2423i	−1.74954	+	0.842533i	−0.770895	+	0.636962i	$0.780191\pi$
$761$	−48.2631	+	23.2423i	−1.74954	+	0.842533i	−0.978642	+	0.205571i	$0.934095\pi$
$762$		0			0
$763$	−6.32141	−	1.18910i	−0.228850	−	0.0430485i
$764$	−34.2029	+	71.0230i	−1.23742	+	2.56952i
$765$		0			0
$766$		−	45.0860i		−	1.62902i
$767$	−1.58799	+	3.29749i	−0.0573389	+	0.119065i
$768$		0			0
$769$	−20.6418	−	4.71136i	−0.744364	−	0.169896i	−0.166514	−	0.986039i	$-0.553251\pi$
$769$	−20.6418	−	4.71136i	−0.744364	−	0.169896i	−0.577850	+	0.816143i	$0.696108\pi$
$770$	87.8746	−	75.7852i	3.16678	−	2.73111i
$771$		0			0
$772$	−70.7104	−	34.0523i	−2.54492	−	1.22557i
$773$	−9.58430	−	41.9916i	−0.344723	−	1.51033i	−0.788972	−	0.614429i	$-0.789387\pi$
$773$	−9.58430	−	41.9916i	−0.344723	−	1.51033i	0.444249	−	0.895903i	$-0.353471\pi$
$774$		0			0
$775$	1.18184	+	0.269746i	0.0424528	+	0.00968957i
$776$	−20.5713	−	25.7956i	−0.738466	−	0.926007i
$777$		0			0
$778$	−55.6337	+	69.7625i	−1.99457	+	2.50111i
$779$	−19.9112	+	15.8787i	−0.713393	+	0.568912i
$780$		0			0
$781$	−13.6197	−	17.0785i	−0.487350	−	0.611118i
$782$	20.6312	+	90.3911i	0.737770	+	3.23238i
$783$		0			0
$784$	−26.9527	+	2.07756i	−0.962595	+	0.0741987i
$785$		−	59.2994i		−	2.11649i
$786$		0			0
$787$	13.4064	−	10.6913i	0.477888	−	0.381103i	−0.354714	−	0.934975i	$-0.615422\pi$
$787$	13.4064	−	10.6913i	0.477888	−	0.381103i	0.832602	+	0.553872i	$0.186850\pi$
$788$	−9.52468	−	19.7782i	−0.339303	−	0.704569i
$789$		0			0
$790$	−9.60462	−	7.65943i	−0.341717	−	0.272510i
$791$	−6.89902	+	9.36871i	−0.245301	+	0.333113i
$792$		0			0
$793$	0.554057	−	2.42748i	0.0196751	−	0.0862024i
$794$	−23.3247	+	29.2483i	−0.827764	+	1.03798i
$795$		0			0
$796$	17.4705	−	36.2778i	0.619225	−	1.28583i
$797$	0.301988	+	1.32310i	0.0106970	+	0.0468665i	0.979995	−	0.199023i	$-0.0637770\pi$
$797$	0.301988	+	1.32310i	0.0106970	+	0.0468665i	−0.969298	+	0.245890i	$0.920920\pi$
$798$		0			0
$799$	−0.279141	+	1.22300i	−0.00987529	+	0.0432665i
$800$	0.535946	+	0.427403i	0.0189486	+	0.0151110i
$801$		0			0
$802$	34.3171			1.21178
$803$	11.3726			0.401331
$804$		0			0
$805$	−31.5515	−	36.5846i	−1.11204	−	1.28944i
$806$	−1.99537	−	4.14343i	−0.0702840	−	0.145946i
$807$		0			0
$808$	−28.2008	−	6.43665i	−0.992101	−	0.226441i
$809$	−43.1825	−	9.85612i	−1.51822	−	0.346523i	−0.619479	−	0.785013i	$-0.712656\pi$
$809$	−43.1825	−	9.85612i	−1.51822	−	0.346523i	−0.898736	+	0.438490i	$0.855513\pi$
$810$		0			0
$811$	16.9139	+	35.1220i	0.593926	+	1.23330i	0.953840	+	0.300315i	$0.0970917\pi$
$811$	16.9139	+	35.1220i	0.593926	+	1.23330i	−0.359914	+	0.932985i	$0.617194\pi$
$812$	38.5972	+	16.7909i	1.35450	+	0.589244i
$813$		0			0
$814$	78.9481			2.76713
$815$	−40.4932			−1.41842
$816$		0			0
$817$	−3.33821	−	2.66214i	−0.116789	−	0.0931364i
$818$	10.2217	−	44.7841i	0.357392	−	1.56584i
$819$		0			0
$820$	27.4025	+	120.058i	0.956936	+	4.19261i
$821$	−17.9154	+	37.2016i	−0.625250	+	1.29835i	0.312130	+	0.950039i	$0.398957\pi$
$821$	−17.9154	+	37.2016i	−0.625250	+	1.29835i	−0.937381	+	0.348306i	$0.886757\pi$
$822$		0			0
$823$	−0.126122	+	0.158152i	−0.00439633	+	0.00551282i	−0.784025	−	0.620730i	$-0.786837\pi$
$823$	−0.126122	+	0.158152i	−0.00439633	+	0.00551282i	0.779628	+	0.626242i	$0.215408\pi$
$824$	5.10120	−	22.3498i	0.177709	−	0.778592i
$825$		0			0
$826$	3.26740	+	3.78862i	0.113687	+	0.131823i
$827$	−7.58127	−	6.04586i	−0.263627	−	0.210235i	0.482751	−	0.875757i	$-0.339637\pi$
$827$	−7.58127	−	6.04586i	−0.263627	−	0.210235i	−0.746378	+	0.665522i	$0.768209\pi$
$828$		0			0
$829$	14.3579	+	29.8145i	0.498671	+	1.03550i	0.986682	+	0.162664i	$0.0520085\pi$
$829$	14.3579	+	29.8145i	0.498671	+	1.03550i	−0.488010	+	0.872838i	$0.662277\pi$
$830$	34.3456	−	27.3897i	1.19215	−	0.950711i
$831$		0			0
$832$		−	39.1478i		−	1.35720i
$833$	12.2419	+	39.3892i	0.424156	+	1.36475i
$834$		0			0
$835$	−10.4672	−	45.8600i	−0.362234	−	1.58705i
$836$	−36.5849	−	45.8761i	−1.26532	−	1.58666i
$837$		0			0
$838$	24.7354	−	19.7258i	0.854470	−	0.681417i
$839$	35.0227	−	43.9170i	1.20912	−	1.51618i	0.413359	−	0.910568i	$-0.364355\pi$
$839$	35.0227	−	43.9170i	1.20912	−	1.51618i	0.795757	−	0.605616i	$-0.207073\pi$
$840$		0			0
$841$	8.10349	+	10.1615i	0.279431	+	0.350395i
$842$	32.2136	+	7.35255i	1.11016	+	0.253386i
$843$		0			0
$844$	−21.5149	−	94.2628i	−0.740572	−	3.24466i
$845$	−24.0042	−	11.5598i	−0.825768	−	0.397669i
$846$		0			0
$847$	−2.94892	−	76.6274i	−0.101326	−	2.63295i
$848$	−26.7904	−	6.11472i	−0.919984	−	0.209980i
$849$		0			0
$850$	−19.0597	+	39.5780i	−0.653744	+	1.35751i
$851$		−	32.8683i		−	1.12671i
$852$		0			0
$853$	13.9047	−	28.8734i	0.476088	−	0.988606i	−0.515222	−	0.857057i	$-0.672291\pi$
$853$	13.9047	−	28.8734i	0.476088	−	0.988606i	0.991310	−	0.131549i	$-0.0419952\pi$
$854$	−2.74067	−	2.01820i	−0.0937836	−	0.0690613i
$855$		0			0
$856$	55.4608	−	26.7085i	1.89561	−	0.912877i
$857$	6.40176	−	28.0479i	0.218680	−	0.958099i	−0.739775	−	0.672854i	$-0.765068\pi$
$857$	6.40176	−	28.0479i	0.218680	−	0.958099i	0.958455	−	0.285245i	$-0.0920749\pi$
$858$		0			0
$859$	18.2021	+	37.7970i	0.621046	+	1.28962i	0.939783	+	0.341772i	$0.111027\pi$
$859$	18.2021	+	37.7970i	0.621046	+	1.28962i	−0.318737	+	0.947843i	$0.603259\pi$
$860$	−18.6014	+	8.95795i	−0.634301	+	0.305463i
$861$		0			0
$862$	−76.0419	−	36.6199i	−2.59000	−	1.24728i
$863$		−	13.9903i		−	0.476234i	−0.971236	−	0.238117i	$-0.923470\pi$
$863$		−	13.9903i		−	0.476234i	0.971236	−	0.238117i	$-0.0765302\pi$
$864$		0			0
$865$	−10.0491	−	4.83940i	−0.341680	−	0.164544i
$866$	49.8198	−	62.4721i	1.69295	−	2.12289i
$867$		0			0
$868$	−4.17974	+	0.160853i	−0.141870	+	0.00545970i
$869$	−10.9185	+	2.49209i	−0.370386	+	0.0845382i
$870$		0			0
$871$	1.75773	−	0.401191i	0.0595585	−	0.0135938i
$872$	9.18642	+	7.32592i	0.311091	+	0.248087i
$873$		0			0
$874$	−28.7047	+	22.8912i	−0.970951	+	0.774308i
$875$	0.563079	+	14.6316i	0.0190355	+	0.494637i
$876$		0			0
$877$	−6.33330	−	7.94171i	−0.213860	−	0.268173i	0.663317	−	0.748338i	$-0.269148\pi$
$877$	−6.33330	−	7.94171i	−0.213860	−	0.268173i	−0.877178	+	0.480166i	$0.840577\pi$
$878$	13.0611	−	6.28989i	0.440790	−	0.212273i
$879$		0			0
$880$	−67.5437	+	15.4164i	−2.27690	+	0.519687i
$881$	19.7131			0.664150			0.332075	−	0.943253i	$-0.392251\pi$
$881$	19.7131			0.664150			0.332075	+	0.943253i	$0.392251\pi$
$882$		0			0
$883$	12.4577			0.419235			0.209617	−	0.977783i	$-0.432778\pi$
$883$	12.4577			0.419235			0.209617	+	0.977783i	$0.432778\pi$
$884$	108.106	−	24.6745i	3.63600	−	0.829893i
$885$		0			0
$886$	−61.2323	+	29.4879i	−2.05714	+	0.990666i
$887$	13.2335	+	16.5942i	0.444336	+	0.557180i	0.952680	−	0.303974i	$-0.0983136\pi$
$887$	13.2335	+	16.5942i	0.444336	+	0.557180i	−0.508344	+	0.861154i	$0.669742\pi$
$888$		0			0
$889$	−17.4290	+	15.0312i	−0.584550	+	0.504130i
$890$	−70.8277	+	56.4832i	−2.37415	+	1.89332i
$891$		0			0
$892$	58.2781	+	46.4752i	1.95129	+	1.55611i
$893$	−0.484297	+	0.110538i	−0.0162064	+	0.00369900i
$894$		0			0
$895$	10.4394	−	2.38272i	0.348949	−	0.0796454i
$896$	−47.9800	−	20.8727i	−1.60290	−	0.697307i
$897$		0			0
$898$	27.2131	−	34.1241i	0.908113	−	1.13874i
$899$	1.43282	+	0.690008i	0.0477871	+	0.0230130i
$900$		0			0
$901$			41.9293i			1.39687i
$902$	152.015	+	73.2065i	5.06154	+	2.43751i
$903$		0			0
$904$	19.1486	−	9.22150i	0.636874	−	0.306702i
$905$	−8.70003	−	18.0658i	−0.289199	−	0.600528i
$906$		0			0
$907$	−5.33293	+	23.3651i	−0.177077	+	0.775825i	0.805893	+	0.592061i	$0.201685\pi$
$907$	−5.33293	+	23.3651i	−0.177077	+	0.775825i	−0.982970	+	0.183764i	$0.941172\pi$
$908$	89.2622	−	42.9864i	2.96227	−	1.42655i
$909$		0			0
$910$	−65.7589	+	56.7121i	−2.17989	+	1.87999i
$911$	14.8937	−	30.9270i	0.493449	−	1.02466i	−0.494399	−	0.869235i	$-0.664612\pi$
$911$	14.8937	−	30.9270i	0.493449	−	1.02466i	0.987848	−	0.155423i	$-0.0496741\pi$
$912$		0			0
$913$		−	40.0483i		−	1.32540i
$914$	36.0548	−	74.8686i	1.19259	−	2.47643i
$915$		0			0
$916$	−94.5413	−	21.5784i	−3.12373	−	0.712972i
$917$	−13.9951	−	26.4119i	−0.462158	−	0.872196i
$918$		0			0
$919$	−35.5457	−	17.1179i	−1.17255	−	0.564668i	−0.256815	−	0.966461i	$-0.582673\pi$
$919$	−35.5457	−	17.1179i	−1.17255	−	0.564668i	−0.915731	+	0.401792i	$0.868387\pi$
$920$	19.6373	+	86.0368i	0.647424	+	2.83655i
$921$		0			0
$922$	39.5333	+	9.02323i	1.30196	+	0.297164i
$923$	10.1920	+	12.7803i	0.335473	+	0.420669i
$924$		0			0
$925$	9.70949	−	12.1753i	0.319246	−	0.400322i
$926$	41.2425	−	32.8898i	1.35531	−	1.08083i
$927$		0			0
$928$	0.560703	+	0.703100i	0.0184060	+	0.0230804i
$929$	3.22075	+	14.1110i	0.105670	+	0.462969i	0.999883	+	0.0153268i	$0.00487886\pi$
$929$	3.22075	+	14.1110i	0.105670	+	0.462969i	−0.894213	+	0.447642i	$0.852264\pi$
$930$		0			0
$931$	−11.9498	+	11.1353i	−0.391639	+	0.364943i
$932$		−	38.8968i		−	1.27411i
$933$		0			0
$934$	−36.9931	+	29.5010i	−1.21045	+	0.965303i
$935$	45.8667	+	95.2431i	1.50000	+	3.11478i
$936$		0			0
$937$	39.3025	+	31.3427i	1.28396	+	1.02392i	0.997838	+	0.0657265i	$0.0209365\pi$
$937$	39.3025	+	31.3427i	1.28396	+	1.02392i	0.286118	+	0.958194i	$0.407635\pi$
$938$	0.455604	−	2.42204i	0.0148760	−	0.0790826i
$939$		0			0
$940$	−0.534495	+	2.34178i	−0.0174333	+	0.0763803i
$941$	9.01826	−	11.3085i	0.293987	−	0.368648i	−0.612799	−	0.790238i	$-0.709957\pi$
$941$	9.01826	−	11.3085i	0.293987	−	0.368648i	0.906786	+	0.421591i	$0.138528\pi$
$942$		0			0
$943$	30.4779	−	63.2879i	0.992496	−	2.06094i
$944$	−0.664662	−	2.91207i	−0.0216329	−	0.0947799i
$945$		0			0
$946$	−6.29453	+	27.5781i	−0.204653	+	0.896643i
$947$	27.9903	+	22.3216i	0.909564	+	0.725353i	0.961936	−	0.273274i	$-0.0881067\pi$
$947$	27.9903	+	22.3216i	0.909564	+	0.725353i	−0.0523720	+	0.998628i	$0.516678\pi$
$948$		0			0
$949$	−8.51043			−0.276260
$950$	−17.3952			−0.564376
$951$		0			0
$952$	13.9291	−	74.0486i	0.451444	−	2.39993i
$953$	24.9888	+	51.8897i	0.809466	+	1.68087i	0.729403	+	0.684084i	$0.239798\pi$
$953$	24.9888	+	51.8897i	0.809466	+	1.68087i	0.0800627	+	0.996790i	$0.474488\pi$
$954$		0			0
$955$	54.8277	+	12.5141i	1.77418	+	0.404945i
$956$	−72.4955	−	16.5466i	−2.34467	−	0.535156i
$957$		0			0
$958$	14.7870	+	30.7056i	0.477747	+	0.992052i
$959$	9.15673	−	4.85196i	0.295686	−	0.156678i
$960$		0			0
$961$	30.8420			0.994902
$962$	−59.0790			−1.90478
$963$		0			0
$964$	−19.5139	−	15.5618i	−0.628499	−	0.501212i
$965$	−12.4590	+	54.5863i	−0.401068	+	1.75720i
$966$		0			0
$967$	−11.1430	−	48.8206i	−0.358334	−	1.56996i	−0.757343	−	0.653017i	$-0.773503\pi$
$967$	−11.1430	−	48.8206i	−0.358334	−	1.56996i	0.399009	−	0.916947i	$-0.369354\pi$
$968$	−60.7781	+	126.207i	−1.95348	+	4.05645i
$969$		0			0
$970$	−29.5231	+	37.0208i	−0.947929	+	1.18866i
$971$	11.9803	−	52.4893i	0.384467	−	1.68446i	−0.298818	−	0.954310i	$-0.596593\pi$
$971$	11.9803	−	52.4893i	0.384467	−	1.68446i	0.683286	−	0.730151i	$-0.260550\pi$
$972$		0			0
$973$	3.90964	+	14.5291i	0.125337	+	0.465780i
$974$	−12.5181	−	9.98282i	−0.401105	−	0.319870i
$975$		0			0
$976$	0.881685	+	1.83084i	0.0282220	+	0.0586037i
$977$	7.27366	−	5.80055i	0.232705	−	0.185576i	−0.500194	−	0.865913i	$-0.666738\pi$
$977$	7.27366	−	5.80055i	0.232705	−	0.185576i	0.732899	+	0.680337i	$0.238167\pi$
$978$		0			0
$979$			82.5876i			2.63951i
$980$	23.4406	+	75.4219i	0.748783	+	2.40927i
$981$		0			0
$982$	6.11348	+	26.7849i	0.195089	+	0.854740i
$983$	15.3425	+	19.2389i	0.489349	+	0.613625i	0.963790	−	0.266663i	$-0.0859210\pi$
$983$	15.3425	+	19.2389i	0.489349	+	0.613625i	−0.474441	+	0.880288i	$0.657350\pi$
$984$		0			0
$985$	−12.2441	+	9.76437i	−0.390130	+	0.311119i
$986$	−35.9310	+	45.0560i	−1.14427	+	1.43488i
$987$		0			0
$988$	27.3775	+	34.3303i	0.870994	+	1.09219i
$989$	11.4815	+	2.62059i	0.365092	+	0.0833298i
$990$		0			0
$991$	2.45014	+	10.7348i	0.0778314	+	0.341002i	0.998819	−	0.0485908i	$-0.0154730\pi$
$991$	2.45014	+	10.7348i	0.0778314	+	0.341002i	−0.920987	+	0.389592i	$0.872616\pi$
$992$	−0.0805179	−	0.0387754i	−0.00255645	−	0.00123112i
$993$		0			0
$994$	21.5775	−	5.80630i	0.684396	−	0.184165i
$995$	−28.0054	−	6.39205i	−0.887831	−	0.202642i
$996$		0			0
$997$	−21.7600	+	45.1851i	−0.689145	+	1.43103i	0.202955	+	0.979188i	$0.434945\pi$
$997$	−21.7600	+	45.1851i	−0.689145	+	1.43103i	−0.892100	+	0.451837i	$0.850769\pi$
$998$			25.4340i			0.805100i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.3	✓	120
3.2	odd	2	inner	441.2.w.a.62.18	yes	120
49.34	odd	14	inner	441.2.w.a.377.18	yes	120
147.83	even	14	inner	441.2.w.a.377.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.3	✓	120	1.1	even	1	trivial
441.2.w.a.62.18	yes	120	3.2	odd	2	inner
441.2.w.a.377.3	yes	120	147.83	even	14	inner
441.2.w.a.377.18	yes	120	49.34	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38347 + 0.544011i) q^{2} +(3.58304 - 1.72550i) q^{4} +(-1.76892 - 2.21816i) q^{5} +(1.05543 - 2.42612i) q^{7} +(-3.77859 + 3.01333i) q^{8} +O(q^{10})\)	\(q+(-2.38347 + 0.544011i) q^{2} +(3.58304 - 1.72550i) q^{4} +(-1.76892 - 2.21816i) q^{5} +(1.05543 - 2.42612i) q^{7} +(-3.77859 + 3.01333i) q^{8} +(5.42288 + 4.32461i) q^{10} +(6.16474 - 1.40706i) q^{11} +(-4.61324 + 1.05294i) q^{13} +(-1.19575 + 6.35675i) q^{14} +(2.40779 - 3.01928i) q^{16} +(-5.30898 - 2.55667i) q^{17} -2.33339i q^{19} +(-10.1656 - 4.89548i) q^{20} +(-13.9280 + 6.70738i) q^{22} +(2.79247 + 5.79862i) q^{23} +(-0.678541 + 2.97288i) q^{25} +(10.4227 - 5.01931i) q^{26} +(-0.404621 - 10.5140i) q^{28} +(-1.73570 + 3.60421i) q^{29} -0.397539i q^{31} +(0.0975386 - 0.202541i) q^{32} +(14.0447 + 3.20560i) q^{34} +(-7.24851 + 1.95051i) q^{35} +(-4.60121 - 2.21582i) q^{37} +(1.26939 + 5.56158i) q^{38} +(13.3681 + 3.05118i) q^{40} +(-6.80496 - 8.53316i) q^{41} +(1.14089 - 1.43063i) q^{43} +(19.6607 - 15.6788i) q^{44} +(-9.81027 - 12.3017i) q^{46} +(-0.0473720 - 0.207550i) q^{47} +(-4.77213 - 5.12121i) q^{49} -7.45491i q^{50} +(-14.7126 + 11.7329i) q^{52} +(-3.08737 - 6.41100i) q^{53} +(-14.0261 - 11.1854i) q^{55} +(3.32265 + 12.3477i) q^{56} +(2.17625 - 9.53478i) q^{58} +(0.482247 - 0.604718i) q^{59} +(-0.228309 + 0.474089i) q^{61} +(0.216266 + 0.947522i) q^{62} +(-1.84096 + 8.06577i) q^{64} +(10.4961 + 8.37034i) q^{65} -0.381019 q^{67} -23.4339 q^{68} +(16.2155 - 8.59225i) q^{70} +(-1.49888 - 3.11247i) q^{71} +(1.75344 + 0.400211i) q^{73} +(12.1723 + 2.77824i) q^{74} +(-4.02628 - 8.36065i) q^{76} +(3.09276 - 16.4415i) q^{77} -1.77113 q^{79} -10.9565 q^{80} +(20.8616 + 16.6365i) q^{82} +(1.40933 - 6.17467i) q^{83} +(3.72008 + 16.2987i) q^{85} +(-1.94099 + 4.03051i) q^{86} +(-19.0541 + 23.8931i) q^{88} +(-2.90632 + 12.7334i) q^{89} +(-2.31440 + 12.3036i) q^{91} +(20.0111 + 15.9583i) q^{92} +(0.225819 + 0.468919i) q^{94} +(-5.17585 + 4.12760i) q^{95} +6.82677i q^{97} +(14.1602 + 9.61016i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

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