LMFDB - Embedded newform 441.2.s.d.362.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.14
Character	$\chi$	$=$	441.362
Dual form			441.2.s.d.374.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.367369 - 0.212101i) q^{2} +(1.71145 + 0.266368i) q^{3} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(2.85810 + 0.911750i) q^{9} +O(q^{10})$	\(q+(0.367369 - 0.212101i) q^{2} +(1.71145 + 0.266368i) q^{3} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(2.85810 + 0.911750i) q^{9} +(1.32533 - 0.765180i) q^{10} -3.70603i q^{11} +(-1.97731 + 2.45520i) q^{12} +(-5.23479 + 3.02231i) q^{13} +(6.17426 + 0.960957i) q^{15} +(-1.47635 - 2.55711i) q^{16} +(-0.532108 - 0.921637i) q^{17} +(1.24336 - 0.271255i) q^{18} +(-3.16265 - 1.82596i) q^{19} +(-3.28304 + 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} +0.363239i q^{23} +(-0.431642 + 2.77335i) q^{24} +8.01497 q^{25} +(-1.28207 + 2.22060i) q^{26} +(4.64862 + 2.32172i) q^{27} +(-0.857560 - 0.495112i) q^{29} +(2.47205 - 0.956538i) q^{30} +(0.939786 + 0.542586i) q^{31} +(-3.89147 - 2.24674i) q^{32} +(0.987169 - 6.34268i) q^{33} +(-0.390960 - 0.225721i) q^{34} +(-4.03805 + 3.67525i) q^{36} +(4.00186 - 6.93143i) q^{37} -1.54915 q^{38} +(-9.76411 + 3.77814i) q^{39} +5.84605i q^{40} +(2.09005 + 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} +(5.84149 + 3.37259i) q^{44} +(10.3109 + 3.28925i) q^{45} +(0.0770432 + 0.133443i) q^{46} +(-2.83849 - 4.91640i) q^{47} +(-1.84556 - 4.76962i) q^{48} +(2.94445 - 1.69998i) q^{50} +(-0.665179 - 1.71907i) q^{51} -11.0015i q^{52} +(3.92463 - 2.26589i) q^{53} +(2.20019 - 0.133048i) q^{54} -13.3700i q^{55} +(-4.92633 - 3.96745i) q^{57} -0.420055 q^{58} +(-5.62746 + 9.74705i) q^{59} +(-7.13341 + 8.85745i) q^{60} +(0.0238258 - 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(-18.8852 + 10.9034i) q^{65} +(-0.982630 - 2.53948i) q^{66} +(4.86489 - 8.42624i) q^{67} +1.93693 q^{68} +(-0.0967553 + 0.621664i) q^{69} -5.55775i q^{71} +(-1.47746 + 4.63146i) q^{72} +(-1.95561 + 1.12907i) q^{73} -3.39519i q^{74} +(13.7172 + 2.13493i) q^{75} +(5.75619 - 3.32334i) q^{76} +(-2.78569 + 3.45894i) q^{78} +(-3.26604 - 5.65694i) q^{79} +(-5.32612 - 9.22511i) q^{80} +(7.33743 + 5.21174i) q^{81} +(1.53564 + 0.886601i) q^{82} +(-1.52977 + 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} +1.60991i q^{86} +(-1.33579 - 1.07578i) q^{87} +6.00552 q^{88} +(-7.47952 + 12.9549i) q^{89} +(4.48557 - 0.978588i) q^{90} +(-0.572542 - 0.330557i) q^{92} +(1.46387 + 1.17894i) q^{93} +(-2.08554 - 1.20409i) q^{94} +(-11.4097 - 6.58737i) q^{95} +(-6.06158 - 4.88174i) q^{96} +(-1.67018 - 0.964277i) q^{97} +(3.37897 - 10.5922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 - 8 * q^9	$ 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.367369	−	0.212101i	0.259769	−	0.149978i	−0.364460	−	0.931219i	$-0.618746\pi$
$2$	0.367369	−	0.212101i	0.259769	−	0.149978i	0.624229	+	0.781241i	$0.285413\pi$
$3$	1.71145	+	0.266368i	0.988104	+	0.153788i
$3$	1.71145	+	0.266368i	0.988104	+	0.153788i
$4$	−0.910027	+	1.57621i	−0.455013	+	0.788106i
$5$	3.60763			1.61338			0.806690	−	0.590975i	$-0.201257\pi$
$5$	3.60763			1.61338			0.806690	+	0.590975i	$0.201257\pi$
$6$	0.685229	−	0.265143i	0.279744	−	0.108244i
$7$		0			0
$7$		0			0
$8$			1.62047i			0.572923i
$9$	2.85810	+	0.911750i	0.952699	+	0.303917i
$10$	1.32533	−	0.765180i	0.419106	−	0.241971i
$11$		−	3.70603i		−	1.11741i	−0.829366	−	0.558705i	$-0.811298\pi$
$11$		−	3.70603i		−	1.11741i	0.829366	−	0.558705i	$-0.188702\pi$
$12$	−1.97731	+	2.45520i	−0.570802	+	0.708755i
$13$	−5.23479	+	3.02231i	−1.45187	+	0.838238i	−0.998588	−	0.0531292i	$-0.983080\pi$
$13$	−5.23479	+	3.02231i	−1.45187	+	0.838238i	−0.453283	+	0.891367i	$0.649747\pi$
$14$		0			0
$15$	6.17426	+	0.960957i	1.59419	+	0.248118i
$16$	−1.47635	−	2.55711i	−0.369088	−	0.639279i
$17$	−0.532108	−	0.921637i	−0.129055	−	0.223530i	0.794256	−	0.607584i	$-0.207861\pi$
$17$	−0.532108	−	0.921637i	−0.129055	−	0.223530i	−0.923311	+	0.384054i	$0.874528\pi$
$18$	1.24336	−	0.271255i	0.293062	−	0.0639355i
$19$	−3.16265	−	1.82596i	−0.725561	−	0.418903i	0.0912348	−	0.995829i	$-0.470919\pi$
$19$	−3.16265	−	1.82596i	−0.725561	−	0.418903i	−0.816796	+	0.576926i	$0.804252\pi$
$20$	−3.28304	+	5.68639i	−0.734109	+	1.27151i
$21$		0			0
$22$	−0.786052	−	1.36148i	−0.167587	−	0.290269i
$23$			0.363239i			0.0757406i	0.999283	+	0.0378703i	$0.0120574\pi$
$23$			0.363239i			0.0757406i	−0.999283	+	0.0378703i	$0.987943\pi$
$24$	−0.431642	+	2.77335i	−0.0881085	+	0.566107i
$25$	8.01497			1.60299
$26$	−1.28207	+	2.22060i	−0.251434	+	0.435496i
$27$	4.64862	+	2.32172i	0.894627	+	0.446814i
$28$		0			0
$29$	−0.857560	−	0.495112i	−0.159245	−	0.0919401i	0.418260	−	0.908327i	$-0.362640\pi$
$29$	−0.857560	−	0.495112i	−0.159245	−	0.0919401i	−0.577505	+	0.816387i	$0.695973\pi$
$30$	2.47205	−	0.956538i	0.451333	−	0.174639i
$31$	0.939786	+	0.542586i	0.168791	+	0.0974513i	0.582015	−	0.813178i	$-0.302264\pi$
$31$	0.939786	+	0.542586i	0.168791	+	0.0974513i	−0.413225	+	0.910629i	$0.635598\pi$
$32$	−3.89147	−	2.24674i	−0.687921	−	0.397171i
$33$	0.987169	−	6.34268i	0.171844	−	1.10412i
$34$	−0.390960	−	0.225721i	−0.0670490	−	0.0387108i
$35$		0			0
$36$	−4.03805	+	3.67525i	−0.673009	+	0.612542i
$37$	4.00186	−	6.93143i	0.657902	−	1.13952i	−0.323256	−	0.946312i	$-0.604777\pi$
$37$	4.00186	−	6.93143i	0.657902	−	1.13952i	0.981158	−	0.193208i	$-0.0618893\pi$
$38$	−1.54915			−0.251305
$39$	−9.76411	+	3.77814i	−1.56351	+	0.604986i
$40$			5.84605i			0.924342i
$41$	2.09005	+	3.62007i	0.326411	+	0.565360i	0.981797	−	0.189934i	$-0.0608275\pi$
$41$	2.09005	+	3.62007i	0.326411	+	0.565360i	−0.655386	+	0.755294i	$0.727494\pi$
$42$		0			0
$43$	−1.89758	+	3.28670i	−0.289378	+	0.501217i	−0.973661	−	0.227999i	$-0.926782\pi$
$43$	−1.89758	+	3.28670i	−0.289378	+	0.501217i	0.684284	+	0.729216i	$0.260115\pi$
$44$	5.84149	+	3.37259i	0.880638	+	0.508437i
$45$	10.3109	+	3.28925i	1.53706	+	0.490333i
$46$	0.0770432	+	0.133443i	0.0113594	+	0.0196751i
$47$	−2.83849	−	4.91640i	−0.414036	−	0.717131i	0.581291	−	0.813696i	$-0.302548\pi$
$47$	−2.83849	−	4.91640i	−0.414036	−	0.717131i	−0.995327	+	0.0965648i	$0.969215\pi$
$48$	−1.84556	−	4.76962i	−0.266384	−	0.688435i
$49$		0			0
$50$	2.94445	−	1.69998i	0.416408	−	0.240413i
$51$	−0.665179	−	1.71907i	−0.0931436	−	0.240718i
$52$		−	11.0015i		−	1.52564i
$53$	3.92463	−	2.26589i	0.539089	−	0.311243i	−0.205621	−	0.978632i	$-0.565921\pi$
$53$	3.92463	−	2.26589i	0.539089	−	0.311243i	0.744710	+	0.667389i	$0.232588\pi$
$54$	2.20019	−	0.133048i	0.299409	−	0.0181055i
$55$		−	13.3700i		−	1.80281i
$56$		0			0
$57$	−4.92633	−	3.96745i	−0.652508	−	0.525502i
$58$	−0.420055			−0.0551559
$59$	−5.62746	+	9.74705i	−0.732633	+	1.26896i	0.223121	+	0.974791i	$0.428376\pi$
$59$	−5.62746	+	9.74705i	−0.732633	+	1.26896i	−0.955754	+	0.294167i	$0.904958\pi$
$60$	−7.13341	+	8.85745i	−0.920920	+	1.14349i
$61$	0.0238258	−	0.0137558i	0.00305058	−	0.00176126i	−0.498474	−	0.866905i	$-0.666106\pi$
$61$	0.0238258	−	0.0137558i	0.00305058	−	0.00176126i	0.501525	+	0.865143i	$0.332773\pi$
$62$	0.460331			0.0584621
$63$		0			0
$64$	3.99926			0.499908
$65$	−18.8852	+	10.9034i	−2.34242	+	1.35240i
$66$	−0.982630	−	2.53948i	−0.120953	−	0.312589i
$67$	4.86489	−	8.42624i	0.594341	−	1.02943i	−0.399298	−	0.916821i	$-0.630746\pi$
$67$	4.86489	−	8.42624i	0.594341	−	1.02943i	0.993640	−	0.112608i	$-0.0359204\pi$
$68$	1.93693			0.234887
$69$	−0.0967553	+	0.621664i	−0.0116480	+	0.0748396i
$70$		0			0
$71$		−	5.55775i		−	0.659584i	−0.944054	−	0.329792i	$-0.893021\pi$
$71$		−	5.55775i		−	0.659584i	0.944054	−	0.329792i	$-0.106979\pi$
$72$	−1.47746	+	4.63146i	−0.174121	+	0.545823i
$73$	−1.95561	+	1.12907i	−0.228887	+	0.132148i	−0.610058	−	0.792356i	$-0.708854\pi$
$73$	−1.95561	+	1.12907i	−0.228887	+	0.132148i	0.381172	+	0.924504i	$0.375521\pi$
$74$		−	3.39519i		−	0.394683i
$75$	13.7172	+	2.13493i	1.58392	+	0.246521i
$76$	5.75619	−	3.32334i	0.660280	−	0.381213i
$77$		0			0
$78$	−2.78569	+	3.45894i	−0.315417	+	0.391648i
$79$	−3.26604	−	5.65694i	−0.367458	−	0.636456i	0.621710	−	0.783248i	$-0.286438\pi$
$79$	−3.26604	−	5.65694i	−0.367458	−	0.636456i	−0.989167	+	0.146792i	$0.953105\pi$
$80$	−5.32612	−	9.22511i	−0.595479	−	1.03140i
$81$	7.33743	+	5.21174i	0.815270	+	0.579082i
$82$	1.53564	+	0.886601i	0.169583	+	0.0979087i
$83$	−1.52977	+	2.64964i	−0.167914	+	0.290836i	−0.937686	−	0.347483i	$-0.887036\pi$
$83$	−1.52977	+	2.64964i	−0.167914	+	0.290836i	0.769772	+	0.638319i	$0.220370\pi$
$84$		0			0
$85$	−1.91965	−	3.32492i	−0.208215	−	0.360639i
$86$			1.60991i			0.173601i
$87$	−1.33579	−	1.07578i	−0.143211	−	0.115336i
$88$	6.00552			0.640190
$89$	−7.47952	+	12.9549i	−0.792827	+	1.37322i	0.131382	+	0.991332i	$0.458058\pi$
$89$	−7.47952	+	12.9549i	−0.792827	+	1.37322i	−0.924210	+	0.381886i	$0.875275\pi$
$90$	4.48557	−	0.978588i	0.472821	−	0.103152i
$91$		0			0
$92$	−0.572542	−	0.330557i	−0.0596916	−	0.0344630i
$93$	1.46387	+	1.17894i	0.151796	+	0.122250i
$94$	−2.08554	−	1.20409i	−0.215107	−	0.124192i
$95$	−11.4097	−	6.58737i	−1.17061	−	0.675850i
$96$	−6.06158	−	4.88174i	−0.618657	−	0.498240i
$97$	−1.67018	−	0.964277i	−0.169581	−	0.0979075i	0.412807	−	0.910818i	$-0.364548\pi$
$97$	−1.67018	−	0.964277i	−0.169581	−	0.0979075i	−0.582388	+	0.812911i	$0.697882\pi$
$98$		0			0
$99$	3.37897	−	10.5922i	0.339600	−	1.06456i
$100$	−7.29384	+	12.6333i	−0.729384	+	1.26333i
$101$	−6.43623			−0.640429			−0.320214	−	0.947345i	$-0.603755\pi$
$101$	−6.43623			−0.640429			−0.320214	+	0.947345i	$0.603755\pi$
$102$	−0.608982	−	0.490448i	−0.0602982	−	0.0485616i
$103$		−	9.72162i		−	0.957899i	−0.877842	−	0.478950i	$-0.841018\pi$
$103$		−	9.72162i		−	0.957899i	0.877842	−	0.478950i	$-0.158982\pi$
$104$	−4.89756	−	8.48283i	−0.480246	−	0.831810i
$105$		0			0
$106$	0.961191	−	1.66483i	0.0933591	−	0.161703i
$107$	−3.43139	−	1.98112i	−0.331725	−	0.191522i	0.324881	−	0.945755i	$-0.394676\pi$
$107$	−3.43139	−	1.98112i	−0.331725	−	0.191522i	−0.656607	+	0.754233i	$0.728009\pi$
$108$	−7.88988	+	5.21438i	−0.759204	+	0.501754i
$109$	8.66263	+	15.0041i	0.829729	+	1.43713i	0.898250	+	0.439484i	$0.144839\pi$
$109$	8.66263	+	15.0041i	0.829729	+	1.43713i	−0.0685210	+	0.997650i	$0.521828\pi$
$110$	−2.83578	−	4.91172i	−0.270381	−	0.468314i
$111$	8.69529	−	10.7968i	0.825320	−	1.02479i
$112$		0			0
$113$	−8.50273	+	4.90905i	−0.799869	+	0.461805i	−0.843425	−	0.537246i	$-0.819465\pi$
$113$	−8.50273	+	4.90905i	−0.799869	+	0.461805i	0.0435562	+	0.999051i	$0.486131\pi$
$114$	−2.65128	−	0.412643i	−0.248315	−	0.0386476i
$115$			1.31043i			0.122198i
$116$	1.56080	−	0.901131i	0.144917	−	0.0836679i
$117$	−17.7171	+	3.86523i	−1.63795	+	0.357341i
$118$			4.77435i			0.439515i
$119$		0			0
$120$	−1.55720	+	10.0052i	−0.142153	+	0.913346i
$121$	−2.73468			−0.248607
$122$	0.00583524	−	0.0101069i	0.000528298	−	0.000915039i
$123$	2.61273	+	6.75228i	0.235582	+	0.608832i
$124$	−1.71046	+	0.987535i	−0.153604	+	0.0886833i
$125$	10.8769			0.972858
$126$		0			0
$127$	−11.7328			−1.04112			−0.520560	−	0.853825i	$-0.674277\pi$
$127$	−11.7328			−1.04112			−0.520560	+	0.853825i	$0.674277\pi$
$128$	9.25214	−	5.34173i	0.817782	−	0.472146i
$129$	−4.12307	+	5.11955i	−0.363016	+	0.450752i
$130$	−4.62522	+	8.01111i	−0.405659	+	0.702621i
$131$	21.0026			1.83500			0.917502	−	0.397732i	$-0.130203\pi$
$131$	21.0026			1.83500			0.917502	+	0.397732i	$0.130203\pi$
$132$	9.09905	+	7.32799i	0.791971	+	0.637820i
$133$		0			0
$134$		−	4.12738i		−	0.356552i
$135$	16.7705	+	8.37588i	1.44337	+	0.720881i
$136$	1.49349	−	0.862265i	0.128065	−	0.0739386i
$137$			11.2720i			0.963033i	0.876437	+	0.481516i	$0.159914\pi$
$137$			11.2720i			0.963033i	−0.876437	+	0.481516i	$0.840086\pi$
$138$	0.0963104	+	0.248902i	0.00819849	+	0.0211879i
$139$	−2.80312	+	1.61838i	−0.237758	+	0.137269i	−0.614146	−	0.789193i	$-0.710499\pi$
$139$	−2.80312	+	1.61838i	−0.237758	+	0.137269i	0.376388	+	0.926462i	$0.377166\pi$
$140$		0			0
$141$	−3.54834	−	9.17024i	−0.298824	−	0.772274i
$142$	−1.17880	−	2.04175i	−0.0989229	−	0.171340i
$143$	11.2008	+	19.4003i	0.936656	+	1.62234i
$144$	−1.88810	−	8.65454i	−0.157342	−	0.721212i
$145$	−3.09376	−	1.78618i	−0.256922	−	0.148334i
$146$	−0.478954	+	0.829572i	−0.0396385	+	0.0686559i
$147$		0			0
$148$	7.28360	+	12.6156i	0.598709	+	1.03699i
$149$		−	17.9055i		−	1.46688i	−0.679755	−	0.733439i	$-0.737914\pi$
$149$		−	17.9055i		−	1.46688i	0.679755	−	0.733439i	$-0.262086\pi$
$150$	5.49209	−	2.12512i	0.448427	−	0.173515i
$151$	−18.5989			−1.51356			−0.756778	−	0.653672i	$-0.773228\pi$
$151$	−18.5989			−1.51356			−0.756778	+	0.653672i	$0.773228\pi$
$152$	2.95891	−	5.12498i	0.239999	−	0.415691i
$153$	−0.680512	−	3.11928i	−0.0550161	−	0.252179i
$154$		0			0
$155$	3.39040	+	1.95745i	0.272323	+	0.157226i
$156$	2.93046	−	18.8285i	0.234624	−	1.50749i
$157$	−6.64220	−	3.83488i	−0.530106	−	0.306057i	0.210954	−	0.977496i	$-0.432343\pi$
$157$	−6.64220	−	3.83488i	−0.530106	−	0.306057i	−0.741059	+	0.671439i	$0.765676\pi$
$158$	−2.39968	−	1.38546i	−0.190908	−	0.110221i
$159$	7.32035	−	2.83254i	0.580542	−	0.224635i
$160$	−14.0390	−	8.10540i	−1.10988	−	0.640788i
$161$		0			0
$162$	3.80095	+	0.358358i	0.298631	+	0.0281552i
$163$	1.99657	−	3.45815i	0.156383	−	0.270864i	−0.777179	−	0.629280i	$-0.783350\pi$
$163$	1.99657	−	3.45815i	0.156383	−	0.270864i	0.933562	+	0.358416i	$0.116683\pi$
$164$	−7.60800			−0.594085
$165$	3.56134	−	22.8820i	0.277250	−	1.78136i
$166$			1.29786i			0.100733i
$167$	−4.26254	−	7.38293i	−0.329845	−	0.571308i	0.652636	−	0.757672i	$-0.273663\pi$
$167$	−4.26254	−	7.38293i	−0.329845	−	0.571308i	−0.982481	+	0.186363i	$0.940330\pi$
$168$		0			0
$169$	11.7687	−	20.3840i	0.905285	−	1.56800i
$170$	−1.41044	−	0.814316i	−0.108176	−	0.0624552i
$171$	−7.37434	−	8.10230i	−0.563930	−	0.619598i
$172$	−3.45369	−	5.98197i	−0.263341	−	0.456121i
$173$	0.217445	+	0.376626i	0.0165320	+	0.0286343i	0.874173	−	0.485615i	$-0.161404\pi$
$173$	0.217445	+	0.376626i	0.0165320	+	0.0286343i	−0.857641	+	0.514249i	$0.828071\pi$
$174$	−0.718901	−	0.111889i	−0.0544997	−	0.00848229i
$175$		0			0
$176$	−9.47675	+	5.47140i	−0.714337	+	0.412423i
$177$	−12.2274	+	15.1826i	−0.919068	+	1.14119i
$178$			6.34564i			0.475626i
$179$	15.0838	−	8.70862i	1.12741	−	0.650913i	0.184130	−	0.982902i	$-0.441053\pi$
$179$	15.0838	−	8.70862i	1.12741	−	0.650913i	0.943283	+	0.331989i	$0.107720\pi$
$180$	−14.5678	+	13.2589i	−1.08582	+	0.988262i
$181$			17.7421i			1.31876i	0.751809	+	0.659381i	$0.229182\pi$
$181$			17.7421i			1.31876i	−0.751809	+	0.659381i	$0.770818\pi$
$182$		0			0
$183$	0.0444407	−	0.0171959i	0.00328515	−	0.00127116i
$184$	−0.588618			−0.0433935
$185$	14.4372	−	25.0060i	1.06145	−	1.83848i
$186$	0.787832	+	0.122618i	0.0577666	+	0.00899076i
$187$	−3.41562	+	1.97201i	−0.249775	+	0.144208i
$188$	10.3324			0.753567
$189$		0			0
$190$	−5.58874			−0.405450
$191$	−0.215525	+	0.124433i	−0.0155948	+	0.00900367i	−0.507777	−	0.861488i	$-0.669533\pi$
$191$	−0.215525	+	0.124433i	−0.0155948	+	0.00900367i	0.492182	+	0.870492i	$0.336199\pi$
$192$	6.84452	+	1.06528i	0.493961	+	0.0768797i
$193$	4.14876	−	7.18586i	0.298634	−	0.517250i	−0.677190	−	0.735809i	$-0.736802\pi$
$193$	4.14876	−	7.18586i	0.298634	−	0.517250i	0.975824	+	0.218559i	$0.0701356\pi$
$194$	−0.818095			−0.0587358
$195$	−35.2253	+	13.6301i	−2.52253	+	0.976072i
$196$		0			0
$197$			22.5819i			1.60889i	0.594026	+	0.804446i	$0.297538\pi$
$197$			22.5819i			1.60889i	−0.594026	+	0.804446i	$0.702462\pi$
$198$	−1.00528	−	4.60793i	−0.0714422	−	0.327471i
$199$	5.30010	−	3.06002i	0.375714	−	0.216919i	−0.300238	−	0.953864i	$-0.597066\pi$
$199$	5.30010	−	3.06002i	0.375714	−	0.216919i	0.675952	+	0.736946i	$0.263733\pi$
$200$			12.9880i			0.918392i
$201$	10.5705	−	13.1252i	0.745584	−	0.925780i
$202$	−2.36447	+	1.36513i	−0.166364	+	0.0960500i
$203$		0			0
$204$	3.31495	+	0.515936i	0.232093	+	0.0361227i
$205$	7.54011	+	13.0599i	0.526624	+	0.912140i
$206$	−2.06196	−	3.57142i	−0.143664	−	0.248833i
$207$	−0.331183	+	1.03817i	−0.0230188	+	0.0721580i
$208$	15.4568	+	8.92397i	1.07173	+	0.618766i
$209$	−6.76705	+	11.7209i	−0.468087	+	0.810750i
$210$		0			0
$211$	1.95472	+	3.38567i	0.134568	+	0.233079i	0.925432	−	0.378913i	$-0.123702\pi$
$211$	1.95472	+	3.38567i	0.134568	+	0.233079i	−0.790864	+	0.611992i	$0.790369\pi$
$212$			8.24806i			0.566479i
$213$	1.48041	−	9.51180i	0.101436	−	0.651738i
$214$	−1.68078			−0.114896
$215$	−6.84575	+	11.8572i	−0.466876	+	0.808653i
$216$	−3.76227	+	7.53295i	−0.255990	+	0.512552i
$217$		0			0
$218$	6.36476	+	3.67470i	0.431076	+	0.248882i
$219$	−3.64767	+	1.41143i	−0.246487	+	0.0953758i
$220$	21.0739	+	12.1670i	1.42080	+	0.820302i
$221$	5.57095	+	3.21639i	0.374742	+	0.216358i
$222$	0.904370	−	5.81068i	0.0606974	−	0.389988i
$223$	22.3165	+	12.8845i	1.49443	+	0.862807i	0.999980	−	0.00640186i	$-0.00203779\pi$
$223$	22.3165	+	12.8845i	1.49443	+	0.862807i	0.494446	+	0.869209i	$0.335371\pi$
$224$		0			0
$225$	22.9076	+	7.30765i	1.52717	+	0.487176i
$226$	−2.08243	+	3.60687i	−0.138521	+	0.239925i
$227$	24.6102			1.63344			0.816718	−	0.577037i	$-0.195791\pi$
$227$	24.6102			1.63344			0.816718	+	0.577037i	$0.195791\pi$
$228$	10.7366	−	4.15445i	0.711051	−	0.275135i
$229$			4.55260i			0.300844i	0.988622	+	0.150422i	$0.0480633\pi$
$229$			4.55260i			0.300844i	−0.988622	+	0.150422i	$0.951937\pi$
$230$	0.277943	+	0.481412i	0.0183270	+	0.0317433i
$231$		0			0
$232$	0.802315	−	1.38965i	0.0526746	−	0.0912351i
$233$	22.6338	+	13.0676i	1.48279	+	0.856090i	0.999809	−	0.0195398i	$-0.00622009\pi$
$233$	22.6338	+	13.0676i	1.48279	+	0.856090i	0.482983	+	0.875630i	$0.339553\pi$
$234$	−5.68891	+	5.17778i	−0.371895	+	0.338482i
$235$	−10.2402	−	17.7365i	−0.667997	−	1.15700i
$236$	−10.2423	−	17.7402i	−0.666716	−	1.15479i
$237$	−4.08282	−	10.5515i	−0.265207	−	0.685395i
$238$		0			0
$239$	14.8933	−	8.59865i	0.963367	−	0.556200i	0.0661594	−	0.997809i	$-0.478925\pi$
$239$	14.8933	−	8.59865i	0.963367	−	0.556200i	0.897208	+	0.441609i	$0.145592\pi$
$240$	−6.65809	−	17.2070i	−0.429778	−	1.11071i
$241$			16.7348i			1.07798i	0.842312	+	0.538991i	$0.181194\pi$
$241$			16.7348i			1.07798i	−0.842312	+	0.538991i	$0.818806\pi$
$242$	−1.00464	+	0.580026i	−0.0645804	+	0.0372855i
$243$	11.1694	+	10.8741i	0.716515	+	0.697571i
$244$			0.0500727i			0.00320558i
$245$		0			0
$246$	2.39200	+	1.92641i	0.152508	+	0.122824i
$247$	22.0744			1.40456
$248$	−0.879245	+	1.52290i	−0.0558321	+	0.0967040i
$249$	−3.32390	+	4.12723i	−0.210643	+	0.261553i
$250$	3.99583	−	2.30699i	0.252719	−	0.145907i
$251$	−5.33468			−0.336722			−0.168361	−	0.985725i	$-0.553847\pi$
$251$	−5.33468			−0.336722			−0.168361	+	0.985725i	$0.553847\pi$
$252$		0			0
$253$	1.34618			0.0846334
$254$	−4.31028	+	2.48854i	−0.270451	+	0.156145i
$255$	−2.39972	−	6.20176i	−0.150276	−	0.388369i
$256$	−1.73330	+	3.00216i	−0.108331	+	0.187635i
$257$	−24.6200			−1.53576			−0.767878	−	0.640596i	$-0.778687\pi$
$257$	−24.6200			−1.53576			−0.767878	+	0.640596i	$0.778687\pi$
$258$	−0.428828	+	2.75527i	−0.0266977	+	0.171536i
$259$		0			0
$260$		−	39.6894i		−	2.46143i
$261$	−1.99957	−	2.19696i	−0.123770	−	0.135988i
$262$	7.71569	−	4.45466i	0.476677	−	0.275210i
$263$			30.7806i			1.89801i	0.315258	+	0.949006i	$0.397909\pi$
$263$			30.7806i			1.89801i	−0.315258	+	0.949006i	$0.602091\pi$
$264$	10.2781	+	1.59968i	0.632575	+	0.0984534i
$265$	14.1586	−	8.17447i	0.869756	−	0.502154i
$266$		0			0
$267$	−16.2516	+	20.1793i	−0.994580	+	1.23495i
$268$	8.85436	+	15.3362i	0.540866	+	0.936808i
$269$	6.99046	+	12.1078i	0.426216	+	0.738227i	0.996533	−	0.0831971i	$-0.0265131\pi$
$269$	6.99046	+	12.1078i	0.426216	+	0.738227i	−0.570317	+	0.821424i	$0.693180\pi$
$270$	7.93748	−	0.479987i	0.483060	−	0.0292111i
$271$	5.59679	+	3.23131i	0.339981	+	0.196288i	0.660264	−	0.751034i	$-0.270445\pi$
$271$	5.59679	+	3.23131i	0.339981	+	0.196288i	−0.320283	+	0.947322i	$0.603778\pi$
$272$	−1.57115	+	2.72132i	−0.0952652	+	0.165004i
$273$		0			0
$274$	2.39080	+	4.14099i	0.144433	+	0.250166i
$275$		−	29.7037i		−	1.79120i
$276$	−0.891825	−	0.718238i	−0.0536816	−	0.0432328i
$277$	−19.1197			−1.14879			−0.574395	−	0.818578i	$-0.694763\pi$
$277$	−19.1197			−1.14879			−0.574395	+	0.818578i	$0.694763\pi$
$278$	−0.686519	+	1.18909i	−0.0411747	+	0.0713167i
$279$	2.19130	+	2.40761i	0.131190	+	0.144140i
$280$		0			0
$281$	20.0611	+	11.5823i	1.19674	+	0.690940i	0.959828	−	0.280591i	$-0.0905304\pi$
$281$	20.0611	+	11.5823i	1.19674	+	0.690940i	0.236915	+	0.971530i	$0.423864\pi$
$282$	−3.24856	−	2.61626i	−0.193449	−	0.155796i
$283$	−13.8239	−	7.98126i	−0.821748	−	0.474436i	0.0292708	−	0.999572i	$-0.490681\pi$
$283$	−13.8239	−	7.98126i	−0.821748	−	0.474436i	−0.851019	+	0.525135i	$0.824015\pi$
$284$	8.76020	+	5.05770i	0.519822	+	0.300120i
$285$	−17.7723	−	14.3131i	−1.05274	−	0.847834i
$286$	8.22963	+	4.75138i	0.486628	+	0.280955i
$287$		0			0
$288$	−9.07373	−	9.96945i	−0.534674	−	0.587455i
$289$	7.93372	−	13.7416i	0.466690	−	0.808330i
$290$	−1.51540			−0.0889873
$291$	−2.60156	−	2.09519i	−0.152506	−	0.122822i
$292$		−	4.10994i		−	0.240516i
$293$	−3.34849	−	5.79975i	−0.195621	−	0.338825i	0.751483	−	0.659752i	$-0.229339\pi$
$293$	−3.34849	−	5.79975i	−0.195621	−	0.338825i	−0.947104	+	0.320927i	$0.896005\pi$
$294$		0			0
$295$	−20.3018	+	35.1637i	−1.18202	+	2.04731i
$296$	11.2322	+	6.48490i	0.652857	+	0.376927i
$297$	8.60436	−	17.2279i	0.499275	−	0.999666i
$298$	−3.79777	−	6.57794i	−0.219999	−	0.381050i
$299$	−1.09782	−	1.90148i	−0.0634886	−	0.109966i
$300$	−15.8481	+	19.6784i	−0.914992	+	1.13613i
$301$		0			0
$302$	−6.83266	+	3.94484i	−0.393175	+	0.227000i
$303$	−11.0153	−	1.71441i	−0.632810	−	0.0984901i
$304$			10.7830i			0.618448i
$305$	0.0859547	−	0.0496259i	0.00492175	−	0.00284157i
$306$	−0.911599	−	1.00159i	−0.0521127	−	0.0572570i
$307$			8.59068i			0.490296i	0.969486	+	0.245148i	$0.0788365\pi$
$307$			8.59068i			0.490296i	−0.969486	+	0.245148i	$0.921163\pi$
$308$		0			0
$309$	2.58953	−	16.6380i	0.147313	−	0.946504i
$310$	1.66070			0.0943216
$311$	2.11723	−	3.66714i	0.120057	−	0.207945i	−0.799733	−	0.600356i	$-0.795026\pi$
$311$	2.11723	−	3.66714i	0.120057	−	0.207945i	0.919790	+	0.392411i	$0.128359\pi$
$312$	−6.12236	−	15.8225i	−0.346610	−	0.895770i
$313$	−3.10288	+	1.79145i	−0.175385	+	0.101259i	−0.585123	−	0.810945i	$-0.698954\pi$
$313$	−3.10288	+	1.79145i	−0.175385	+	0.101259i	0.409737	+	0.912204i	$0.365620\pi$
$314$	−3.25352			−0.183607
$315$		0			0
$316$	11.8887			0.668793
$317$	7.69566	−	4.44309i	0.432231	−	0.249549i	−0.268065	−	0.963401i	$-0.586384\pi$
$317$	7.69566	−	4.44309i	0.432231	−	0.249549i	0.700297	+	0.713852i	$0.253051\pi$
$318$	2.08849	−	2.59324i	0.117116	−	0.145422i
$319$	−1.83490	+	3.17814i	−0.102735	+	0.177942i
$320$	14.4278			0.806541
$321$	−5.34494	−	4.30459i	−0.298325	−	0.240259i
$322$		0			0
$323$			3.88642i			0.216246i
$324$	−14.8921	+	6.82252i	−0.827336	+	0.379029i
$325$	−41.9567	+	24.2237i	−2.32734	+	1.34369i
$326$		−	1.69389i		−	0.0938160i
$327$	10.8290	+	27.9862i	0.598845	+	1.54764i
$328$	−5.86622	+	3.38686i	−0.323908	+	0.187008i
$329$		0			0
$330$	−3.54496	−	9.16150i	−0.195144	−	0.504324i
$331$	−7.89126	−	13.6681i	−0.433743	−	0.751265i	0.563449	−	0.826151i	$-0.309474\pi$
$331$	−7.89126	−	13.6681i	−0.433743	−	0.751265i	−0.997192	+	0.0748861i	$0.976141\pi$
$332$	−2.78426	−	4.82248i	−0.152806	−	0.264668i
$333$	17.7574	−	16.1620i	0.973102	−	0.885672i
$334$	−3.13185	−	1.80817i	−0.171367	−	0.0989388i
$335$	17.5507	−	30.3987i	0.958898	−	1.66086i
$336$		0			0
$337$	−6.79951	−	11.7771i	−0.370393	−	0.641539i	0.619233	−	0.785207i	$-0.287444\pi$
$337$	−6.79951	−	11.7771i	−0.370393	−	0.641539i	−0.989626	+	0.143668i	$0.954110\pi$
$338$		−	9.98459i		−	0.543090i
$339$	−15.8596	+	6.13672i	−0.861374	+	0.333301i
$340$	6.98771			0.378962
$341$	2.01084	−	3.48288i	0.108893	−	0.188608i
$342$	−4.42761	−	1.41243i	−0.239417	−	0.0763756i
$343$		0			0
$344$	−5.32600	−	3.07497i	−0.287159	−	0.165791i
$345$	−0.349057	+	2.24273i	−0.0187926	+	0.120745i
$346$	0.159765	+	0.0922404i	0.00858902	+	0.00495887i
$347$	−12.0065	−	6.93198i	−0.644545	−	0.372128i	0.141818	−	0.989893i	$-0.454705\pi$
$347$	−12.0065	−	6.93198i	−0.644545	−	0.372128i	−0.786363	+	0.617765i	$0.788038\pi$
$348$	2.91127	−	1.12649i	0.156060	−	0.0603861i
$349$	1.55204	+	0.896072i	0.0830789	+	0.0479656i	0.540964	−	0.841046i	$-0.318060\pi$
$349$	1.55204	+	0.896072i	0.0830789	+	0.0479656i	−0.457885	+	0.889011i	$0.651393\pi$
$350$		0			0
$351$	−31.3515	+	1.89585i	−1.67342	+	0.101193i
$352$	−8.32649	+	14.4219i	−0.443804	+	0.768690i
$353$	−7.76098			−0.413075			−0.206538	−	0.978439i	$-0.566220\pi$
$353$	−7.76098			−0.413075			−0.206538	+	0.978439i	$0.566220\pi$
$354$	−1.27174	+	8.17105i	−0.0675920	+	0.434286i
$355$		−	20.0503i		−	1.06416i
$356$	−13.6131	−	23.5786i	−0.721494	−	1.24966i
$357$		0			0
$358$	3.69421	−	6.39855i	0.195245	−	0.338174i
$359$	−19.5557	−	11.2905i	−1.03211	−	0.595890i	−0.114523	−	0.993421i	$-0.536534\pi$
$359$	−19.5557	−	11.2905i	−1.03211	−	0.595890i	−0.917589	+	0.397531i	$0.869867\pi$
$360$	−5.33014	+	16.7086i	−0.280923	+	0.880620i
$361$	−2.83177	−	4.90477i	−0.149041	−	0.258146i
$362$	3.76312	+	6.51791i	0.197785	+	0.342574i
$363$	−4.68025	−	0.728431i	−0.245650	−	0.0382327i
$364$		0			0
$365$	−7.05511	+	4.07327i	−0.369281	+	0.213205i
$366$	0.0126789	−	0.0157432i	0.000662735	−	0.000822908i
$367$		−	15.6188i		−	0.815297i	−0.913139	−	0.407648i	$-0.866349\pi$
$367$		−	15.6188i		−	0.815297i	0.913139	−	0.407648i	$-0.133651\pi$
$368$	0.928844	−	0.536268i	0.0484193	−	0.0279549i
$369$	2.67296	+	12.2521i	0.139149	+	0.637819i
$370$		−	12.2486i		−	0.636773i
$371$		0			0
$372$	−3.19041	+	1.23450i	−0.165415	+	0.0640059i
$373$	−25.2458			−1.30718			−0.653589	−	0.756850i	$-0.726738\pi$
$373$	−25.2458			−1.30718			−0.653589	+	0.756850i	$0.726738\pi$
$374$	−0.836528	+	1.44891i	−0.0432558	+	0.0749213i
$375$	18.6152	+	2.89726i	0.961285	+	0.149614i
$376$	7.96689	−	4.59969i	0.410861	−	0.237211i
$377$	5.98553			0.308271
$378$		0			0
$379$	14.7721			0.758792			0.379396	−	0.925234i	$-0.376132\pi$
$379$	14.7721			0.758792			0.379396	+	0.925234i	$0.376132\pi$
$380$	20.7662	−	11.9894i	1.06528	−	0.615041i
$381$	−20.0801	−	3.12525i	−1.02874	−	0.160112i
$382$	−0.0527847	+	0.0914258i	−0.00270070	+	0.00467775i
$383$	10.5901			0.541127			0.270564	−	0.962702i	$-0.412790\pi$
$383$	10.5901			0.541127			0.270564	+	0.962702i	$0.412790\pi$
$384$	17.2574	−	6.67760i	0.880664	−	0.340765i
$385$		0			0
$386$		−	3.51982i		−	0.179154i
$387$	−8.42010	+	7.66358i	−0.428018	+	0.389562i
$388$	3.03981	−	1.75504i	0.154323	−	0.0890984i
$389$			13.5841i			0.688743i	0.938834	+	0.344371i	$0.111908\pi$
$389$			13.5841i			0.688743i	−0.938834	+	0.344371i	$0.888092\pi$
$390$	−10.0497	+	12.4786i	−0.508887	+	0.631877i
$391$	0.334775	−	0.193282i	0.0169303	−	0.00977471i
$392$		0			0
$393$	35.9448	+	5.59442i	1.81317	+	0.282201i
$394$	4.78963	+	8.29588i	0.241298	+	0.417940i
$395$	−11.7826	−	20.4081i	−0.592849	−	1.02684i
$396$	13.6206	+	14.9652i	0.684461	+	0.752028i
$397$	−33.6977	−	19.4554i	−1.69124	−	0.976437i	−0.953520	−	0.301330i	$-0.902569\pi$
$397$	−33.6977	−	19.4554i	−1.69124	−	0.976437i	−0.737719	−	0.675108i	$-0.764097\pi$
$398$	1.29806	−	2.24831i	0.0650660	−	0.112698i
$399$		0			0
$400$	−11.8329	−	20.4952i	−0.591645	−	1.02476i
$401$			28.7470i			1.43556i	0.696272	+	0.717778i	$0.254841\pi$
$401$			28.7470i			1.43556i	−0.696272	+	0.717778i	$0.745159\pi$
$402$	1.09940	−	7.06380i	0.0548333	−	0.352310i
$403$	−6.55945			−0.326749
$404$	5.85714	−	10.1449i	0.291404	−	0.504726i
$405$	26.4707	+	18.8020i	1.31534	+	0.934279i
$406$		0			0
$407$	−25.6881	−	14.8310i	−1.27331	−	0.735147i
$408$	2.78570	−	1.07790i	0.137913	−	0.0533641i
$409$	16.3485	+	9.43879i	0.808379	+	0.466718i	0.846393	−	0.532559i	$-0.178770\pi$
$409$	16.3485	+	9.43879i	0.808379	+	0.466718i	−0.0380133	+	0.999277i	$0.512103\pi$
$410$	5.54001	+	3.19852i	0.273601	+	0.157964i
$411$	−3.00250	+	19.2914i	−0.148103	+	0.951576i
$412$	15.3233	+	8.84693i	0.754927	+	0.435857i
$413$		0			0
$414$	0.0985305	+	0.451636i	0.00484251	+	0.0221967i
$415$	−5.51884	+	9.55891i	−0.270909	+	0.469228i
$416$	27.1614			1.33170
$417$	−5.22847	+	2.02311i	−0.256039	+	0.0990722i
$418$			5.74118i			0.280810i
$419$	−3.31895	−	5.74860i	−0.162142	−	0.280837i	0.773495	−	0.633802i	$-0.218507\pi$
$419$	−3.31895	−	5.74860i	−0.162142	−	0.280837i	−0.935636	+	0.352965i	$0.885173\pi$
$420$		0			0
$421$	−9.70574	+	16.8108i	−0.473029	+	0.819310i	−0.999523	−	0.0308686i	$-0.990173\pi$
$421$	−9.70574	+	16.8108i	−0.473029	+	0.819310i	0.526495	+	0.850178i	$0.323506\pi$
$422$	1.43621	+	0.829194i	0.0699134	+	0.0403645i
$423$	−3.63014	−	16.6395i	−0.176503	−	0.809042i
$424$	3.67180	+	6.35975i	0.178318	+	0.308857i
$425$	−4.26483	−	7.38690i	−0.206874	−	0.358317i
$426$	−1.47360	−	3.80833i	−0.0713962	−	0.184514i
$427$		0			0
$428$	6.24532	−	3.60574i	0.301879	−	0.174290i
$429$	14.0019	+	36.1861i	0.676018	+	1.74708i
$430$			5.80795i			0.280084i
$431$	−21.0604	+	12.1592i	−1.01444	+	0.585690i	−0.912490	−	0.409099i	$-0.865843\pi$
$431$	−21.0604	+	12.1592i	−1.01444	+	0.585690i	−0.101955	+	0.994789i	$0.532510\pi$
$432$	−0.926094	−	15.3147i	−0.0445567	−	0.736829i
$433$			3.32148i			0.159620i	0.996810	+	0.0798101i	$0.0254314\pi$
$433$			3.32148i			0.159620i	−0.996810	+	0.0798101i	$0.974569\pi$
$434$		0			0
$435$	−4.81902	−	3.88103i	−0.231054	−	0.186081i
$436$	−31.5329			−1.51015
$437$	0.663259	−	1.14880i	0.0317280	−	0.0549544i
$438$	−1.04067	+	1.29219i	−0.0497254	+	0.0617432i
$439$	23.3126	−	13.4595i	1.11265	−	0.642389i	0.173136	−	0.984898i	$-0.444610\pi$
$439$	23.3126	−	13.4595i	1.11265	−	0.642389i	0.939515	+	0.342509i	$0.111277\pi$
$440$	21.6657			1.03287
$441$		0			0
$442$	2.72879			0.129795
$443$	−22.8837	+	13.2119i	−1.08724	+	0.627717i	−0.932839	−	0.360292i	$-0.882677\pi$
$443$	−22.8837	+	13.2119i	−1.08724	+	0.627717i	−0.154397	+	0.988009i	$0.549344\pi$
$444$	9.10511	+	23.5310i	0.432109	+	1.11673i
$445$	−26.9833	+	46.7365i	−1.27913	+	2.21552i
$446$	10.9312			0.517607
$447$	4.76946	−	30.6444i	0.225588	−	1.44943i
$448$		0			0
$449$			19.6314i			0.926464i	0.886237	+	0.463232i	$0.153310\pi$
$449$			19.6314i			0.926464i	−0.886237	+	0.463232i	$0.846690\pi$
$450$	9.96548	−	2.17410i	0.469777	−	0.102488i
$451$	13.4161	−	7.74578i	0.631739	−	0.364735i
$452$		−	17.8695i		−	0.840509i
$453$	−31.8310	−	4.95415i	−1.49555	−	0.232766i
$454$	9.04102	−	5.21983i	0.424316	−	0.244979i
$455$		0			0
$456$	6.42914	−	7.98297i	0.301072	−	0.373837i
$457$	12.6244	+	21.8660i	0.590543	+	1.02285i	0.994159	+	0.107922i	$0.0344196\pi$
$457$	12.6244	+	21.8660i	0.590543	+	1.02285i	−0.403617	+	0.914928i	$0.632247\pi$
$458$	0.965609	+	1.67248i	0.0451199	+	0.0781500i
$459$	−0.333784	−	5.51974i	−0.0155797	−	0.257639i
$460$	−2.06552	−	1.19253i	−0.0963053	−	0.0556019i
$461$	7.23618	−	12.5334i	0.337023	−	0.583740i	−0.646849	−	0.762618i	$-0.723913\pi$
$461$	7.23618	−	12.5334i	0.337023	−	0.583740i	0.983871	+	0.178878i	$0.0572468\pi$
$462$		0			0
$463$	−10.0168	−	17.3495i	−0.465519	−	0.806302i	0.533706	−	0.845670i	$-0.320799\pi$
$463$	−10.0168	−	17.3495i	−0.465519	−	0.806302i	−0.999225	+	0.0393681i	$0.987466\pi$
$464$			2.92384i			0.135736i
$465$	5.28108	+	4.25316i	0.244904	+	0.197236i
$466$	11.0866			0.513578
$467$	−11.7815	+	20.4062i	−0.545183	+	0.944285i	0.453412	+	0.891301i	$0.350207\pi$
$467$	−11.7815	+	20.4062i	−0.545183	+	0.944285i	−0.998595	+	0.0529842i	$0.983127\pi$
$468$	10.0306	−	31.4434i	0.463666	−	1.45347i
$469$		0			0
$470$	−7.52386	−	4.34390i	−0.347050	−	0.200369i
$471$	−10.3463	−	8.33246i	−0.476732	−	0.383939i
$472$	−15.7948	−	9.11914i	−0.727015	−	0.419742i
$473$	12.1806	+	7.03248i	0.560065	+	0.323354i
$474$	−3.73788	−	3.01033i	−0.171687	−	0.138269i
$475$	−25.3485	−	14.6350i	−1.16307	−	0.671499i
$476$		0			0
$477$	13.2829	−	2.89784i	0.608182	−	0.132683i
$478$	3.64756	−	6.31775i	0.166835	−	0.288967i
$479$	−24.9347			−1.13930			−0.569648	−	0.821889i	$-0.692921\pi$
$479$	−24.9347			−1.13930			−0.569648	+	0.821889i	$0.692921\pi$
$480$	−21.8679	−	17.6115i	−0.998129	−	0.803851i
$481$			48.3795i			2.20591i
$482$	3.54945	+	6.14783i	0.161673	+	0.280026i
$483$		0			0
$484$	2.48863	−	4.31043i	0.113119	−	0.195929i
$485$	−6.02537	−	3.47875i	−0.273598	−	0.157962i
$486$	6.40967	+	1.62576i	0.290749	+	0.0737461i
$487$	2.50331	+	4.33586i	0.113436	+	0.196476i	0.917153	−	0.398534i	$-0.130481\pi$
$487$	2.50331	+	4.33586i	0.113436	+	0.196476i	−0.803718	+	0.595011i	$0.797148\pi$
$488$	0.0222909	+	0.0386090i	0.00100906	+	0.00174775i
$489$	4.33816	−	5.38662i	0.196178	−	0.243592i
$490$		0			0
$491$	18.6960	−	10.7942i	0.843740	−	0.487134i	−0.0147936	−	0.999891i	$-0.504709\pi$
$491$	18.6960	−	10.7942i	0.843740	−	0.487134i	0.858534	+	0.512757i	$0.171376\pi$
$492$	−13.0207	−	2.02653i	−0.587017	−	0.0913629i
$493$			1.05381i			0.0474613i
$494$	8.10945	−	4.68200i	0.364862	−	0.210653i
$495$	12.1901	−	38.2127i	0.547903	−	1.71753i
$496$		−	3.20419i		−	0.143872i
$497$		0			0
$498$	−0.345709	+	2.22122i	−0.0154916	+	0.0995351i
$499$	35.8130			1.60321			0.801604	−	0.597855i	$-0.203980\pi$
$499$	35.8130			1.60321			0.801604	+	0.597855i	$0.203980\pi$
$500$	−9.89826	+	17.1443i	−0.442664	+	0.766716i
$501$	−5.32852	−	13.7709i	−0.238061	−	0.615238i
$502$	−1.95979	+	1.13149i	−0.0874699	+	0.0505008i
$503$	−23.9969			−1.06997			−0.534984	−	0.844862i	$-0.679682\pi$
$503$	−23.9969			−1.06997			−0.534984	+	0.844862i	$0.679682\pi$
$504$		0			0
$505$	−23.2195			−1.03325
$506$	0.494543	−	0.285525i	0.0219851	−	0.0126931i
$507$	25.5711	−	31.7513i	1.13565	−	1.41012i
$508$	10.6772	−	18.4934i	0.473724	−	0.820514i
$509$	18.1419			0.804124			0.402062	−	0.915612i	$-0.368294\pi$
$509$	18.1419			0.804124			0.402062	+	0.915612i	$0.368294\pi$
$510$	−2.19698	−	1.76935i	−0.0972838	−	0.0783483i
$511$		0			0
$512$			22.8374i			1.00928i
$513$	−10.4626	−	15.8309i	−0.461935	−	0.698953i
$514$	−9.04464	+	5.22192i	−0.398942	+	0.230329i
$515$		−	35.0720i		−	1.54546i
$516$	−4.31740	−	11.1578i	−0.190063	−	0.491193i
$517$	−18.2203	+	10.5195i	−0.801330	+	0.462648i
$518$		0			0
$519$	0.271824	+	0.702495i	0.0119318	+	0.0308361i
$520$	−17.6686	−	30.6029i	−0.774819	−	1.34203i
$521$	0.419693	+	0.726930i	0.0183871	+	0.0318474i	0.875073	−	0.483992i	$-0.160814\pi$
$521$	0.419693	+	0.726930i	0.0183871	+	0.0318474i	−0.856685	+	0.515839i	$0.827480\pi$
$522$	−1.20056	−	0.382985i	−0.0525469	−	0.0167628i
$523$	14.1017	+	8.14160i	0.616623	+	0.356008i	0.775553	−	0.631282i	$-0.217471\pi$
$523$	14.1017	+	8.14160i	0.616623	+	0.356008i	−0.158930	+	0.987290i	$0.550804\pi$
$524$	−19.1129	+	33.1045i	−0.834951	+	1.44618i
$525$		0			0
$526$	6.52858	+	11.3078i	0.284660	+	0.493045i
$527$		−	1.15486i		−	0.0503063i
$528$	−17.6764	+	6.83971i	−0.769264	+	0.297660i
$529$	22.8681			0.994263
$530$	3.46762	−	6.00609i	0.150624	−	0.260888i
$531$	−24.9707	+	22.7272i	−1.08364	+	0.986275i
$532$		0			0
$533$	−21.8819	−	12.6335i	−0.947812	−	0.547219i
$534$	−1.69028	+	10.8602i	−0.0731454	+	0.469968i
$535$	−12.3792	−	7.14713i	−0.535199	−	0.308997i
$536$	13.6545	+	7.88342i	0.589784	+	0.340512i
$537$	28.1348	−	10.8865i	1.21410	−	0.469787i
$538$	5.13615	+	2.96536i	0.221435	+	0.127846i
$539$		0			0
$540$	−28.4638	+	18.8115i	−1.22488	+	0.809520i
$541$	0.933466	−	1.61681i	0.0401328	−	0.0695121i	−0.845261	−	0.534353i	$-0.820555\pi$
$541$	0.933466	−	1.61681i	0.0401328	−	0.0695121i	0.885394	+	0.464841i	$0.153889\pi$
$542$	2.74145			0.117755
$543$	−4.72594	+	30.3647i	−0.202810	+	1.30307i
$544$			4.78203i			0.205028i
$545$	31.2515	+	54.1292i	1.33867	+	2.31864i
$546$		0			0
$547$	7.55792	−	13.0907i	0.323153	−	0.559718i	−0.657984	−	0.753032i	$-0.728590\pi$
$547$	7.55792	−	13.0907i	0.323153	−	0.559718i	0.981137	+	0.193315i	$0.0619238\pi$
$548$	−17.7671	−	10.2578i	−0.758972	−	0.438193i
$549$	0.0806384	−	0.0175923i	0.00344156	−	0.000750823i
$550$	−6.30018	−	10.9122i	−0.268641	−	0.465299i
$551$	1.80811	+	3.13173i	0.0770279	+	0.133416i
$552$	−1.00739	−	0.156789i	−0.0428773	−	0.00667339i
$553$		0			0
$554$	−7.02398	+	4.05529i	−0.298420	+	0.172293i
$555$	31.3693	−	38.9508i	1.33155	−	1.65337i
$556$		−	5.89108i		−	0.249838i
$557$	5.47481	−	3.16088i	0.231975	−	0.133931i	−0.379508	−	0.925189i	$-0.623907\pi$
$557$	5.47481	−	3.16088i	0.231975	−	0.133931i	0.611483	+	0.791258i	$0.290573\pi$
$558$	1.31567	+	0.419707i	0.0556968	+	0.0177676i
$559$		−	22.9402i		−	0.970269i
$560$		0			0
$561$	−6.37093	+	2.46517i	−0.268981	+	0.104080i
$562$	9.82641			0.414502
$563$	−4.82545	+	8.35793i	−0.203369	+	0.352245i	−0.949612	−	0.313429i	$-0.898522\pi$
$563$	−4.82545	+	8.35793i	−0.203369	+	0.352245i	0.746243	+	0.665673i	$0.231856\pi$
$564$	17.6833	+	2.75222i	0.744603	+	0.115889i
$565$	−30.6747	+	17.7100i	−1.29049	+	0.745066i
$566$	−6.77132			−0.284620
$567$		0			0
$568$	9.00618			0.377891
$569$	−13.4785	+	7.78184i	−0.565050	+	0.326232i	−0.755170	−	0.655529i	$-0.772446\pi$
$569$	−13.4785	+	7.78184i	−0.565050	+	0.326232i	0.190120	+	0.981761i	$0.439112\pi$
$570$	−9.56482	−	1.48866i	−0.400626	−	0.0623532i
$571$	20.9434	−	36.2750i	0.876454	−	1.51806i	0.0212481	−	0.999774i	$-0.493236\pi$
$571$	20.9434	−	36.2750i	0.876454	−	1.51806i	0.855206	−	0.518288i	$-0.173431\pi$
$572$	−40.7720			−1.70476
$573$	−0.402004	+	0.155552i	−0.0167939	+	0.00649827i
$574$		0			0
$575$			2.91135i			0.121412i
$576$	11.4303	+	3.64633i	0.476262	+	0.151930i
$577$	34.9417	−	20.1736i	1.45464	−	0.839838i	0.455903	−	0.890030i	$-0.349317\pi$
$577$	34.9417	−	20.1736i	1.45464	−	0.839838i	0.998740	+	0.0501916i	$0.0159832\pi$
$578$		−	6.73099i		−	0.279972i
$579$	9.01446	−	11.1931i	0.374628	−	0.465170i
$580$	5.63080	−	3.25094i	0.233806	−	0.134988i
$581$		0			0
$582$	−1.40013	−	0.217914i	−0.0580371	−	0.00903284i
$583$	−8.39744	−	14.5448i	−0.347787	−	0.602384i
$584$	−1.82963	−	3.16901i	−0.0757106	−	0.131135i
$585$	−63.9168	+	13.9443i	−2.64263	+	0.576526i
$586$	−2.46026	−	1.42043i	−0.101632	−	0.0586775i
$587$	1.91520	−	3.31723i	0.0790490	−	0.136917i	−0.823791	−	0.566894i	$-0.808145\pi$
$587$	1.91520	−	3.31723i	0.0790490	−	0.136917i	0.902840	+	0.429977i	$0.141478\pi$
$588$		0			0
$589$	−1.98148	−	3.43202i	−0.0816453	−	0.141414i
$590$			17.2241i			0.709104i
$591$	−6.01509	+	38.6476i	−0.247428	+	1.58975i
$592$	−23.6326			−0.971294
$593$	6.25717	−	10.8377i	0.256951	−	0.445053i	−0.708472	−	0.705738i	$-0.750615\pi$
$593$	6.25717	−	10.8377i	0.256951	−	0.445053i	0.965424	+	0.260686i	$0.0839487\pi$
$594$	−0.493079	−	8.15399i	−0.0202313	−	0.334562i
$595$		0			0
$596$	28.2229	+	16.2945i	1.15606	+	0.667449i
$597$	9.88593	−	3.82527i	0.404604	−	0.156558i
$598$	−0.806611	−	0.465697i	−0.0329848	−	0.0190438i
$599$	−6.62258	−	3.82355i	−0.270591	−	0.156226i	0.358565	−	0.933505i	$-0.383266\pi$
$599$	−6.62258	−	3.82355i	−0.270591	−	0.156226i	−0.629156	+	0.777279i	$0.716599\pi$
$600$	−3.45960	+	22.2283i	−0.141237	+	0.907467i
$601$	−29.8513	−	17.2346i	−1.21766	−	0.703015i	−0.253242	−	0.967403i	$-0.581497\pi$
$601$	−29.8513	−	17.2346i	−1.21766	−	0.703015i	−0.964416	+	0.264388i	$0.914830\pi$
$602$		0			0
$603$	21.5869	−	19.6474i	0.879088	−	0.800105i
$604$	16.9255	−	29.3158i	0.688688	−	1.19284i
$605$	−9.86569			−0.401097
$606$	−4.41029	+	1.70652i	−0.179156	+	0.0693227i
$607$		−	12.4098i		−	0.503696i	−0.967767	−	0.251848i	$-0.918962\pi$
$607$		−	12.4098i		−	0.503696i	0.967767	−	0.251848i	$-0.0810384\pi$
$608$	8.20490	+	14.2113i	0.332753	+	0.576344i
$609$		0			0
$610$	0.0210514	−	0.0364621i	0.000852346	−	0.00147631i
$611$	29.7178	+	17.1576i	1.20225	+	0.694121i
$612$	5.53593	+	1.76599i	0.223777	+	0.0713861i
$613$	0.834482	+	1.44537i	0.0337044	+	0.0583778i	0.882386	−	0.470527i	$-0.155936\pi$
$613$	0.834482	+	1.44537i	0.0337044	+	0.0583778i	−0.848681	+	0.528905i	$0.822603\pi$
$614$	1.82209	+	3.15595i	0.0735335	+	0.127364i
$615$	9.42577	+	24.3597i	0.380084	+	0.982277i
$616$		0			0
$617$	−13.5698	+	7.83453i	−0.546300	+	0.315406i	−0.747628	−	0.664118i	$-0.768807\pi$
$617$	−13.5698	+	7.83453i	−0.546300	+	0.315406i	0.201329	+	0.979524i	$0.435474\pi$
$618$	−2.57762	−	6.66154i	−0.103687	−	0.267966i
$619$		−	3.58460i		−	0.144077i	−0.997402	−	0.0720387i	$-0.977049\pi$
$619$		−	3.58460i		−	0.144077i	0.997402	−	0.0720387i	$-0.0229505\pi$
$620$	−6.17071	+	3.56266i	−0.247822	+	0.143080i
$621$	−0.843338	+	1.68856i	−0.0338420	+	0.0677596i
$622$		−	1.79626i		−	0.0720234i
$623$		0			0
$624$	24.0764	+	19.3901i	0.963827	+	0.776225i
$625$	−0.835100			−0.0334040
$626$	−0.759935	+	1.31625i	−0.0303731	+	0.0526078i
$627$	−14.7035	+	18.2571i	−0.587202	+	0.729119i
$628$	12.0892	−	6.97968i	0.482410	−	0.278520i
$629$	−8.51769			−0.339622
$630$		0			0
$631$	23.1493			0.921557			0.460779	−	0.887515i	$-0.347570\pi$
$631$	23.1493			0.921557			0.460779	+	0.887515i	$0.347570\pi$
$632$	9.16691	−	5.29252i	0.364640	−	0.210525i
$633$	2.44356	+	6.31507i	0.0971228	+	0.251001i
$634$	1.88476	−	3.26451i	0.0748536	−	0.129650i
$635$	−42.3277			−1.67972
$636$	−2.19702	+	14.1161i	−0.0871176	+	0.559741i
$637$		0			0
$638$			1.55674i			0.0616318i
$639$	5.06728	−	15.8846i	0.200458	−	0.628385i
$640$	33.3783	−	19.2710i	1.31939	−	0.761751i
$641$		−	23.5059i		−	0.928426i	−0.885724	−	0.464213i	$-0.846337\pi$
$641$		−	23.5059i		−	0.928426i	0.885724	−	0.464213i	$-0.153663\pi$
$642$	−2.87657	−	0.447707i	−0.113529	−	0.0176696i
$643$	4.83255	−	2.79007i	0.190577	−	0.110030i	−0.401676	−	0.915782i	$-0.631572\pi$
$643$	4.83255	−	2.79007i	0.190577	−	0.110030i	0.592253	+	0.805752i	$0.298239\pi$
$644$		0			0
$645$	−14.8745	+	18.4694i	−0.585683	+	0.727233i
$646$	0.824312	+	1.42775i	0.0324321	+	0.0561741i
$647$	1.95089	+	3.37904i	0.0766974	+	0.132844i	0.901823	−	0.432105i	$-0.142229\pi$
$647$	1.95089	+	3.37904i	0.0766974	+	0.132844i	−0.825126	+	0.564949i	$0.808896\pi$
$648$	−8.44547	+	11.8901i	−0.331769	+	0.467087i
$649$	36.1229	+	20.8556i	1.41795	+	0.818652i
$650$	−10.2757	+	17.7981i	−0.403047	+	0.698098i
$651$		0			0
$652$	3.63386	+	6.29402i	0.142313	+	0.246493i
$653$		−	6.11395i		−	0.239257i	−0.992819	−	0.119629i	$-0.961830\pi$
$653$		−	6.11395i		−	0.239257i	0.992819	−	0.119629i	$-0.0381704\pi$
$654$	9.91413	+	7.98442i	0.387673	+	0.312215i
$655$	75.7694			2.96056
$656$	6.17129	−	10.6890i	0.240948	−	0.417335i
$657$	−6.61875	+	1.44397i	−0.258222	+	0.0563346i
$658$		0			0
$659$	24.7031	+	14.2623i	0.962296	+	0.555582i	0.896879	−	0.442276i	$-0.145829\pi$
$659$	24.7031	+	14.2623i	0.962296	+	0.555582i	0.0654174	+	0.997858i	$0.479162\pi$
$660$	32.8260	+	26.4367i	1.27775	+	1.02905i
$661$	21.7672	+	12.5673i	0.846648	+	0.488812i	0.859518	−	0.511105i	$-0.170764\pi$
$661$	21.7672	+	12.5673i	0.846648	+	0.488812i	−0.0128707	+	0.999917i	$0.504097\pi$
$662$	−5.79801	−	3.34748i	−0.225346	−	0.130104i
$663$	8.67763	+	6.98860i	0.337011	+	0.271415i
$664$	−4.29366	−	2.47895i	−0.166626	−	0.0962018i
$665$		0			0
$666$	3.09556	−	9.70378i	0.119951	−	0.376014i
$667$	0.179844	−	0.311499i	0.00696360	−	0.0120613i
$668$	15.5161			0.600335
$669$	34.7615	+	27.9955i	1.34396	+	1.08237i
$670$		−	14.8901i		−	0.575253i
$671$	−0.0509796	−	0.0882993i	−0.00196805	−	0.00340875i
$672$		0			0
$673$	12.5278	−	21.6988i	0.482912	−	0.836428i	−0.516895	−	0.856049i	$-0.672912\pi$
$673$	12.5278	−	21.6988i	0.482912	−	0.836428i	0.999808	+	0.0196203i	$0.00624575\pi$
$674$	−4.99586	−	2.88436i	−0.192433	−	0.111101i
$675$	37.2585	+	18.6085i	1.43408	+	0.716241i
$676$	21.4197	+	37.0999i	0.823833	+	1.42692i
$677$	16.8081	+	29.1126i	0.645989	+	1.11889i	0.984072	+	0.177770i	$0.0568883\pi$
$677$	16.8081	+	29.1126i	0.645989	+	1.11889i	−0.338083	+	0.941116i	$0.609778\pi$
$678$	−4.52471	+	5.61827i	−0.173771	+	0.215768i
$679$		0			0
$680$	5.38794	−	3.11073i	0.206618	−	0.119291i
$681$	42.1190	+	6.55537i	1.61400	+	0.251202i
$682$		−	1.70600i		−	0.0653262i
$683$	−33.3824	+	19.2734i	−1.27734	+	0.737475i	−0.976359	−	0.216155i	$-0.930648\pi$
$683$	−33.3824	+	19.2734i	−1.27734	+	0.737475i	−0.300984	+	0.953629i	$0.597315\pi$
$684$	19.4818	−	4.25021i	0.744905	−	0.162511i
$685$			40.6652i			1.55374i
$686$		0			0
$687$	−1.21267	+	7.79153i	−0.0462661	+	0.297265i
$688$	11.2059			0.427223
$689$	−13.6964	+	23.7229i	−0.521792	+	0.903770i
$690$	0.347452	+	0.897945i	0.0132273	+	0.0341842i
$691$	−26.1768	+	15.1132i	−0.995812	+	0.574932i	−0.907006	−	0.421117i	$-0.861638\pi$
$691$	−26.1768	+	15.1132i	−0.995812	+	0.574932i	−0.0888052	+	0.996049i	$0.528305\pi$
$692$	−0.791523			−0.0300892
$693$		0			0
$694$	−5.88111			−0.223244
$695$	−10.1126	+	5.83852i	−0.383593	+	0.221468i
$696$	1.74328	−	2.16460i	0.0660788	−	0.0820490i
$697$	2.22426	−	3.85253i	0.0842499	−	0.145925i
$698$	0.760229			0.0287751
$699$	35.2558	+	28.3935i	1.33350	+	1.07394i
$700$		0			0
$701$		−	29.6057i		−	1.11819i	−0.829103	−	0.559096i	$-0.811148\pi$
$701$		−	29.6057i		−	1.11819i	0.829103	−	0.559096i	$-0.188852\pi$
$702$	−11.1155	+	7.34615i	−0.419526	+	0.277262i
$703$	−25.3130	+	14.6145i	−0.954697	+	0.551194i
$704$		−	14.8214i		−	0.558602i
$705$	−12.8011	−	33.0828i	−0.482117	−	1.24597i
$706$	−2.85114	+	1.64611i	−0.107304	+	0.0619521i
$707$		0			0
$708$	−12.8037	−	33.0895i	−0.481193	−	1.24358i
$709$	−1.78201	−	3.08652i	−0.0669246	−	0.115917i	0.830622	−	0.556837i	$-0.187985\pi$
$709$	−1.78201	−	3.08652i	−0.0669246	−	0.115917i	−0.897546	+	0.440921i	$0.854652\pi$
$710$	−4.25268	−	7.36586i	−0.159600	−	0.276436i
$711$	−4.17693	−	19.1459i	−0.156647	−	0.718027i
$712$	−20.9931	−	12.1203i	−0.786748	−	0.454229i
$713$	−0.197088	+	0.341367i	−0.00738102	+	0.0127843i
$714$		0			0
$715$	40.4082	+	69.9891i	1.51118	+	2.61744i
$716$			31.7003i			1.18470i
$717$	27.7795	−	10.7490i	1.03744	−	0.401430i
$718$	−9.57889			−0.357481
$719$	−0.806410	+	1.39674i	−0.0300740	+	0.0520897i	−0.880671	−	0.473729i	$-0.842908\pi$
$719$	−0.806410	+	1.39674i	−0.0300740	+	0.0520897i	0.850597	+	0.525819i	$0.176241\pi$
$720$	−6.81157	−	31.2223i	−0.253852	−	1.16359i
$721$		0			0
$722$	−2.08061	−	1.20124i	−0.0774322	−	0.0447055i
$723$	−4.45761	+	28.6407i	−0.165780	+	1.06516i
$724$	−27.9654	−	16.1458i	−1.03933	−	0.600055i
$725$	−6.87332	−	3.96831i	−0.255269	−	0.147379i
$726$	−1.87388	+	0.725081i	−0.0695462	+	0.0269103i
$727$	−10.4930	−	6.05816i	−0.389166	−	0.224685i	0.292633	−	0.956225i	$-0.405469\pi$
$727$	−10.4930	−	6.05816i	−0.389166	−	0.224685i	−0.681799	+	0.731540i	$0.738802\pi$
$728$		0			0
$729$	16.2193	+	21.5855i	0.600714	+	0.799464i
$730$	−1.72789	+	2.99279i	−0.0639519	+	0.110768i
$731$	4.03886			0.149383
$732$	−0.0133378	+	0.0856968i	−0.000492979	+	0.00316744i
$733$		−	40.4065i		−	1.49245i	−0.665694	−	0.746225i	$-0.731864\pi$
$733$		−	40.4065i		−	1.49245i	0.665694	−	0.746225i	$-0.268136\pi$
$734$	−3.31277	−	5.73788i	−0.122276	−	0.211789i
$735$		0			0
$736$	0.816104	−	1.41353i	0.0300820	−	0.0521035i
$737$	−31.2279	−	18.0294i	−1.15030	−	0.664123i
$738$	3.58064	+	3.93411i	0.131805	+	0.144816i
$739$	10.2317	+	17.7219i	0.376380	+	0.651909i	0.990533	−	0.137278i	$-0.0438354\pi$
$739$	10.2317	+	17.7219i	0.376380	+	0.651909i	−0.614153	+	0.789187i	$0.710502\pi$
$740$	26.2765	+	45.5123i	0.965944	+	1.67306i
$741$	37.7792	+	5.87992i	1.38785	+	0.216004i
$742$		0			0
$743$	37.1209	−	21.4318i	1.36184	−	0.786256i	0.371967	−	0.928246i	$-0.378683\pi$
$743$	37.1209	−	21.4318i	1.36184	−	0.786256i	0.989868	+	0.141990i	$0.0453501\pi$
$744$	−1.91043	+	2.37215i	−0.0700398	+	0.0869673i
$745$		−	64.5965i		−	2.36663i
$746$	−9.27453	+	5.35465i	−0.339565	+	0.196048i
$747$	−6.78803	+	6.17815i	−0.248361	+	0.226047i
$748$		−	7.17832i		−	0.262465i
$749$		0			0
$750$	7.45316	−	2.88393i	0.272151	−	0.105306i
$751$	−43.0056			−1.56930			−0.784649	−	0.619940i	$-0.787157\pi$
$751$	−43.0056			−1.56930			−0.784649	+	0.619940i	$0.787157\pi$
$752$	−8.38120	+	14.5167i	−0.305631	+	0.529368i
$753$	−9.13001	−	1.42099i	−0.332716	−	0.0517837i
$754$	2.19890	−	1.26953i	0.0800792	−	0.0462337i
$755$	−67.0979			−2.44194
$756$		0			0
$757$	−13.0766			−0.475276			−0.237638	−	0.971354i	$-0.576373\pi$
$757$	−13.0766			−0.475276			−0.237638	+	0.971354i	$0.576373\pi$
$758$	5.42682	−	3.13317i	0.197111	−	0.113802i
$759$	2.30391	+	0.358578i	0.0836266	+	0.0130156i
$760$	10.6746	−	18.4890i	0.387210	−	0.670667i
$761$	23.1833			0.840393			0.420196	−	0.907433i	$-0.361961\pi$
$761$	23.1833			0.840393			0.420196	+	0.907433i	$0.361961\pi$
$762$	−8.03968	+	3.11088i	−0.291247	+	0.112695i
$763$		0			0
$764$		−	0.452950i		−	0.0163872i
$765$	−2.45503	−	11.2532i	−0.0887619	−	0.406860i
$766$	3.89046	−	2.24616i	0.140568	−	0.0811571i
$767$		−	68.0317i		−	2.45648i
$768$	−3.76612	+	4.67633i	−0.135898	+	0.168743i
$769$	−11.4527	+	6.61219i	−0.412993	+	0.238442i	−0.692075	−	0.721826i	$-0.743303\pi$
$769$	−11.4527	+	6.61219i	−0.412993	+	0.238442i	0.279082	+	0.960267i	$0.409970\pi$
$770$		0			0
$771$	−42.1359	−	6.55799i	−1.51749	−	0.236180i
$772$	7.55096	+	13.0787i	0.271765	+	0.470711i
$773$	9.81595	+	17.0017i	0.353055	+	0.611509i	0.986783	−	0.162047i	$-0.0518095\pi$
$773$	9.81595	+	17.0017i	0.353055	+	0.611509i	−0.633728	+	0.773556i	$0.718476\pi$
$774$	−1.46783	+	4.60127i	−0.0527602	+	0.165389i
$775$	7.53236	+	4.34881i	0.270570	+	0.156214i
$776$	1.56258	−	2.70647i	0.0560935	−	0.0971567i
$777$		0			0
$778$	2.88120	+	4.99039i	0.103296	+	0.178914i
$779$		−	15.2653i		−	0.546938i
$780$	10.5720	−	67.9263i	0.378538	−	2.43215i
$781$	−20.5972			−0.737026
$782$	0.0819906	−	0.142012i	0.00293198	−	0.00507833i
$783$	−2.83696	−	4.29260i	−0.101385	−	0.153405i
$784$		0			0
$785$	−23.9626	−	13.8348i	−0.855262	−	0.493786i
$786$	14.3916	−	5.56869i	0.513330	−	0.198629i
$787$	14.8621	+	8.58063i	0.529776	+	0.305866i	0.740925	−	0.671588i	$-0.234387\pi$
$787$	14.8621	+	8.58063i	0.529776	+	0.305866i	−0.211149	+	0.977454i	$0.567721\pi$
$788$	−35.5938	−	20.5501i	−1.26798	−	0.732067i
$789$	−8.19897	+	52.6793i	−0.291891	+	1.87543i
$790$	−8.65715	−	4.99821i	−0.308008	−	0.177828i
$791$		0			0
$792$	17.1643	+	5.47553i	0.609909	+	0.194564i
$793$	−0.0831488	+	0.144018i	−0.00295270	+	0.00511423i
$794$	−16.5060			−0.585776
$795$	26.4091	−	10.2188i	0.936634	−	0.362422i
$796$			11.1388i			0.394804i
$797$	11.2772	+	19.5326i	0.399458	+	0.691882i	0.993659	−	0.112435i	$-0.0358650\pi$
$797$	11.2772	+	19.5326i	0.399458	+	0.691882i	−0.594201	+	0.804317i	$0.702532\pi$
$798$		0			0
$799$	−3.02076	+	5.23211i	−0.106867	+	0.185099i
$800$	−31.1900	−	18.0076i	−1.10273	−	0.636663i
$801$	−33.1888	+	30.2069i	−1.17267	+	1.06731i
$802$	6.09725	+	10.5607i	0.215301	+	0.372913i
$803$	4.18438	+	7.24755i	0.147663	+	0.255761i
$804$	11.0687	+	28.6056i	0.390362	+	1.00884i
$805$		0			0
$806$	−2.40974	+	1.39126i	−0.0848794	+	0.0490051i
$807$	8.73865	+	22.5839i	0.307615	+	0.794992i
$808$		−	10.4297i		−	0.366916i
$809$	41.7578	−	24.1089i	1.46813	−	0.847624i	0.468765	−	0.883323i	$-0.344699\pi$
$809$	41.7578	−	24.1089i	1.46813	−	0.847624i	0.999363	+	0.0356994i	$0.0113659\pi$
$810$	13.7124	+	1.29282i	0.481805	+	0.0454251i
$811$		−	11.2304i		−	0.394354i	−0.980368	−	0.197177i	$-0.936823\pi$
$811$		−	11.2304i		−	0.394354i	0.980368	−	0.197177i	$-0.0631774\pi$
$812$		0			0
$813$	8.71789	+	7.02102i	0.305750	+	0.246238i
$814$	−12.5827			−0.441023
$815$	7.20287	−	12.4757i	0.252305	−	0.437006i
$816$	−3.41382	+	4.23889i	−0.119508	+	0.148391i
$817$	12.0027	−	6.92978i	0.419922	−	0.242442i
$818$	8.00789			0.279989
$819$		0			0
$820$	−27.4468			−0.958484
$821$	34.6778	−	20.0212i	1.21026	−	0.698746i	0.247447	−	0.968902i	$-0.420409\pi$
$821$	34.6778	−	20.0212i	1.21026	−	0.698746i	0.962817	+	0.270156i	$0.0870752\pi$
$822$	2.98870	+	7.72391i	0.104243	+	0.269402i
$823$	−4.98922	+	8.64158i	−0.173913	+	0.301227i	−0.939785	−	0.341767i	$-0.888975\pi$
$823$	−4.98922	+	8.64158i	−0.173913	+	0.301227i	0.765871	+	0.642994i	$0.222308\pi$
$824$	15.7536			0.548803
$825$	7.91213	−	50.8364i	0.275465	−	1.76989i
$826$		0			0
$827$			20.8802i			0.726077i	0.931774	+	0.363038i	$0.118261\pi$
$827$			20.8802i			0.726077i	−0.931774	+	0.363038i	$0.881739\pi$
$828$	−1.33499	−	1.46678i	−0.0463943	−	0.0509741i
$829$	13.9123	−	8.03228i	0.483195	−	0.278973i	−0.238552	−	0.971130i	$-0.576673\pi$
$829$	13.9123	−	8.03228i	0.483195	−	0.278973i	0.721747	+	0.692157i	$0.243339\pi$
$830$			4.68219i			0.162521i
$831$	−32.7223	−	5.09287i	−1.13512	−	0.176670i
$832$	−20.9353	+	12.0870i	−0.725801	+	0.419042i
$833$		0			0
$834$	−1.49168	+	1.85219i	−0.0516525	+	0.0641361i
$835$	−15.3776	−	26.6349i	−0.532165	−	0.921737i
$836$	−12.3164	−	21.3326i	−0.425971	−	0.737804i
$837$	3.10898	+	4.70419i	0.107462	+	0.162601i
$838$	−2.43856	−	1.40790i	−0.0842387	−	0.0486352i
$839$	10.1943	−	17.6570i	0.351946	−	0.609589i	−0.634644	−	0.772805i	$-0.718853\pi$
$839$	10.1943	−	17.6570i	0.351946	−	0.609589i	0.986590	+	0.163216i	$0.0521866\pi$
$840$		0			0
$841$	−14.0097	−	24.2656i	−0.483094	−	0.836743i
$842$			8.23437i			0.283775i
$843$	31.2483	+	25.1660i	1.07625	+	0.866764i
$844$	−7.11538			−0.244922
$845$	42.4571	−	73.5378i	1.46057	−	2.52978i
$846$	−4.86286	−	5.34290i	−0.167188	−	0.183693i
$847$		0			0
$848$	−11.5883	−	6.69048i	−0.397942	−	0.229752i
$849$	−21.5330	−	17.3417i	−0.739010	−	0.595167i
$850$	−3.13353	−	1.80914i	−0.107479	−	0.0620531i
$851$	2.51777	+	1.45363i	0.0863079	+	0.0498299i
$852$	13.6454	+	10.9894i	0.467484	+	0.376492i
$853$	−7.80792	−	4.50790i	−0.267338	−	0.154348i	0.360339	−	0.932821i	$-0.382661\pi$
$853$	−7.80792	−	4.50790i	−0.267338	−	0.154348i	−0.627677	+	0.778474i	$0.715994\pi$
$854$		0			0
$855$	−26.6039	−	29.2301i	−0.909833	−	0.999648i
$856$	3.21034	−	5.56047i	0.109727	−	0.190053i
$857$	−32.3316			−1.10443			−0.552213	−	0.833703i	$-0.686216\pi$
$857$	−32.3316			−1.10443			−0.552213	+	0.833703i	$0.686216\pi$
$858$	12.8190	+	10.3238i	0.437632	+	0.352450i
$859$		−	44.0422i		−	1.50270i	−0.659905	−	0.751349i	$-0.729403\pi$
$859$		−	44.0422i		−	1.50270i	0.659905	−	0.751349i	$-0.270597\pi$
$860$	−12.4596	−	21.5807i	−0.424870	−	0.735896i
$861$		0			0
$862$	−5.15796	+	8.93385i	−0.175681	+	0.304288i
$863$	5.30668	+	3.06381i	0.180641	+	0.104293i	0.587594	−	0.809156i	$-0.300075\pi$
$863$	5.30668	+	3.06381i	0.180641	+	0.104293i	−0.406953	+	0.913449i	$0.633409\pi$
$864$	−12.8737	−	19.4791i	−0.437971	−	0.662693i
$865$	0.784460	+	1.35873i	0.0266725	+	0.0461980i
$866$	0.704488	+	1.22021i	0.0239395	+	0.0414644i
$867$	17.2385	−	21.4047i	0.585449	−	0.726943i
$868$		0			0
$869$	−20.9648	+	12.1040i	−0.711182	+	0.410601i
$870$	−2.59353	−	0.403654i	−0.0879287	−	0.0136852i
$871$			58.8128i			1.99280i
$872$	−24.3137	+	14.0375i	−0.823367	+	0.475371i
$873$	−3.89435	−	4.27878i	−0.131804	−	0.144815i
$874$		−	0.562710i		−	0.0190340i
$875$		0			0
$876$	1.09476	−	7.03394i	0.0369884	−	0.237655i
$877$	−2.26408			−0.0764526			−0.0382263	−	0.999269i	$-0.512171\pi$
$877$	−2.26408			−0.0764526			−0.0382263	+	0.999269i	$0.512171\pi$
$878$	5.70956	−	9.88924i	0.192688	−	0.333746i
$879$	−4.18589	−	10.8179i	−0.141186	−	0.364878i
$880$	−34.1886	+	19.7388i	−1.15250	+	0.665394i
$881$	19.2955			0.650083			0.325041	−	0.945700i	$-0.394622\pi$
$881$	19.2955			0.650083			0.325041	+	0.945700i	$0.394622\pi$
$882$		0			0
$883$	−0.833572			−0.0280519			−0.0140260	−	0.999902i	$-0.504465\pi$
$883$	−0.833572			−0.0280519			−0.0140260	+	0.999902i	$0.504465\pi$
$884$	−10.1394	+	5.85400i	−0.341026	+	0.196891i
$885$	−44.1119	+	54.7731i	−1.48281	+	1.84118i
$886$	−5.60451	+	9.70729i	−0.188287	+	0.326123i
$887$	−57.5480			−1.93227			−0.966136	−	0.258034i	$-0.916925\pi$
$887$	−57.5480			−1.93227			−0.966136	+	0.258034i	$0.916925\pi$
$888$	17.4959	+	14.0905i	0.587124	+	0.472845i
$889$		0			0
$890$			22.8927i			0.767365i
$891$	19.3149	−	27.1927i	0.647072	−	0.910991i
$892$	−40.6173	+	23.4504i	−1.35997	+	0.785177i
$893$			20.7318i			0.693763i
$894$	−4.74753	−	12.2694i	−0.158781	−	0.410350i
$895$	54.4166	−	31.4174i	1.81895	−	1.05017i
$896$		0			0
$897$	−1.37237	−	3.54671i	−0.0458220	−	0.118421i
$898$	4.16384	+	7.21198i	0.138949	+	0.240667i
$899$	−0.537282	−	0.930600i	−0.0179194	−	0.0310372i
$900$	−32.3649	+	29.4570i	−1.07883	+	0.981901i
$901$	−4.17665	−	2.41139i	−0.139144	−	0.0803350i
$902$	3.28577	−	5.69112i	0.109404	−	0.189494i
$903$		0			0
$904$	−7.95498	−	13.7784i	−0.264579	−	0.458263i
$905$			64.0070i			2.12766i
$906$	−12.7445	+	4.93137i	−0.423408	+	0.163834i
$907$	−10.1124			−0.335777			−0.167889	−	0.985806i	$-0.553695\pi$
$907$	−10.1124			−0.335777			−0.167889	+	0.985806i	$0.553695\pi$
$908$	−22.3959	+	38.7909i	−0.743235	+	1.28732i
$909$	−18.3954	−	5.86823i	−0.610135	−	0.194637i
$910$		0			0
$911$	−16.9986	−	9.81416i	−0.563190	−	0.325158i	0.191235	−	0.981544i	$-0.438751\pi$
$911$	−16.9986	−	9.81416i	−0.563190	−	0.325158i	−0.754425	+	0.656387i	$0.772084\pi$
$912$	−2.87225	+	18.4545i	−0.0951097	+	0.611091i
$913$	9.81965	+	5.66937i	0.324983	+	0.187629i
$914$	9.27560	+	5.35527i	0.306810	+	0.177137i
$915$	0.160326	−	0.0620365i	0.00530020	−	0.00205087i
$916$	−7.17586	−	4.14299i	−0.237097	−	0.136888i
$917$		0			0
$918$	−1.29336	−	1.95699i	−0.0426873	−	0.0645902i
$919$	−8.52434	+	14.7646i	−0.281192	+	0.487039i	−0.971679	−	0.236306i	$-0.924063\pi$
$919$	−8.52434	+	14.7646i	−0.281192	+	0.487039i	0.690487	+	0.723345i	$0.257396\pi$
$920$	−2.12352			−0.0700102
$921$	−2.28828	+	14.7025i	−0.0754015	+	0.484463i
$922$		−	6.13919i		−	0.202184i
$923$	16.7972	+	29.0937i	0.552888	+	0.957630i
$924$		0			0
$925$	32.0748	−	55.5552i	1.05461	−	1.82664i
$926$	−7.35970	−	4.24912i	−0.241855	−	0.139635i
$927$	8.86368	−	27.7853i	0.291121	−	0.912590i
$928$	2.22478	+	3.85343i	0.0730319	+	0.126495i
$929$	−4.32511	−	7.49131i	−0.141902	−	0.245782i	0.786311	−	0.617831i	$-0.211989\pi$
$929$	−4.32511	−	7.49131i	−0.141902	−	0.245782i	−0.928213	+	0.372049i	$0.878655\pi$
$930$	2.84220	+	0.442358i	0.0931995	+	0.0145055i
$931$		0			0
$932$	−41.1948	+	23.7838i	−1.34938	+	0.779065i
$933$	4.60033	−	5.71215i	0.150608	−	0.187008i
$934$			9.99546i			0.327061i
$935$	−12.3223	+	7.11427i	−0.402981	+	0.232661i
$936$	−6.26349	−	28.7101i	−0.204729	−	0.938419i
$937$		−	34.9586i		−	1.14205i	−0.820933	−	0.571025i	$-0.806546\pi$
$937$		−	34.9586i		−	1.14205i	0.820933	−	0.571025i	$-0.193454\pi$
$938$		0			0
$939$	−5.78760	+	2.23946i	−0.188871	+	0.0730821i
$940$	37.2754			1.21579
$941$	20.5472	−	35.5887i	0.669818	−	1.16016i	−0.308136	−	0.951342i	$-0.599705\pi$
$941$	20.5472	−	35.5887i	0.669818	−	1.16016i	0.977955	−	0.208817i	$-0.0669614\pi$
$942$	−5.56822	−	0.866634i	−0.181423	−	0.0282365i
$943$	−1.31495	+	0.759187i	−0.0428207	+	0.0247225i
$944$	33.2324			1.08162
$945$		0			0
$946$	5.96637			0.193983
$947$	29.2164	−	16.8681i	0.949405	−	0.548139i	0.0565088	−	0.998402i	$-0.482003\pi$
$947$	29.2164	−	16.8681i	0.949405	−	0.548139i	0.892896	+	0.450263i	$0.148670\pi$
$948$	20.3469	+	3.16678i	0.660837	+	0.102852i
$949$	6.82481	−	11.8209i	0.221543	−	0.383723i
$950$	−12.4164			−0.402840
$951$	14.3542	−	5.55423i	0.465467	−	0.180108i
$952$		0			0
$953$		−	18.7823i		−	0.608420i	−0.952605	−	0.304210i	$-0.901608\pi$
$953$		−	18.7823i		−	0.608420i	0.952605	−	0.304210i	$-0.0983925\pi$
$954$	4.26509	−	3.88188i	0.138087	−	0.125681i
$955$	−0.777532	+	0.448908i	−0.0251603	+	0.0145263i
$956$			31.3000i			1.01231i
$957$	−3.98689	+	4.95046i	−0.128878	+	0.160026i
$958$	−9.16024	+	5.28867i	−0.295954	+	0.170869i
$959$		0			0
$960$	24.6925	+	3.84312i	0.796946	+	0.124036i
$961$	−14.9112	−	25.8270i	−0.481006	−	0.833128i
$962$	10.2613	+	17.7731i	0.330838	+	0.573028i
$963$	−8.00097	−	8.79079i	−0.257828	−	0.283279i
$964$	−26.3776	−	15.2291i	−0.849564	−	0.490496i
$965$	14.9672	−	25.9239i	0.481810	−	0.834520i
$966$		0			0
$967$	−17.5860	−	30.4599i	−0.565529	−	0.979525i	−0.997000	−	0.0773981i	$-0.975339\pi$
$967$	−17.5860	−	30.4599i	−0.565529	−	0.979525i	0.431471	−	0.902127i	$-0.357995\pi$
$968$		−	4.43146i		−	0.142433i
$969$	−1.03522	+	6.65140i	−0.0332560	+	0.213674i
$970$	−2.95138			−0.0947631
$971$	19.7981	−	34.2913i	0.635351	−	1.10046i	−0.351090	−	0.936342i	$-0.614189\pi$
$971$	19.7981	−	34.2913i	0.635351	−	1.10046i	0.986441	−	0.164118i	$-0.0524779\pi$
$972$	−27.3043	+	7.70961i	−0.875784	+	0.247286i
$973$		0			0
$974$	1.83928	+	1.06191i	0.0589342	+	0.0340257i
$975$	−78.2591	+	30.2817i	−2.50630	+	0.969789i
$976$	−0.0703505	−	0.0406169i	−0.00225187	−	0.00130012i
$977$	30.3364	+	17.5147i	0.970546	+	0.560345i	0.899403	−	0.437121i	$-0.144002\pi$
$977$	30.3364	+	17.5147i	0.970546	+	0.560345i	0.0711433	+	0.997466i	$0.477335\pi$
$978$	0.451199	−	2.89900i	0.0144277	−	0.0926999i
$979$	48.0113	+	27.7193i	1.53445	+	0.885914i
$980$		0			0
$981$	11.0786	+	50.7813i	0.353714	+	1.62132i
$982$	4.57890	−	7.93088i	0.146118	−	0.253085i
$983$	−44.1731			−1.40890			−0.704451	−	0.709752i	$-0.748807\pi$
$983$	−44.1731			−1.40890			−0.704451	+	0.709752i	$0.748807\pi$
$984$	−10.9419	+	4.23386i	−0.348814	+	0.134970i
$985$			81.4669i			2.59575i
$986$	0.223514	+	0.387138i	0.00711814	+	0.0123290i
$987$		0			0
$988$	−20.0883	+	34.7940i	−0.639094	+	1.10694i
$989$	−1.19386	−	0.689274i	−0.0379625	−	0.0219176i
$990$	−3.62668	−	16.6237i	−0.115263	−	0.528335i
$991$	−13.4443	−	23.2862i	−0.427073	−	0.739712i	0.569539	−	0.821964i	$-0.307122\pi$
$991$	−13.4443	−	23.2862i	−0.427073	−	0.739712i	−0.996611	+	0.0822528i	$0.973789\pi$
$992$	−2.43810	−	4.22291i	−0.0774097	−	0.134078i
$993$	−9.86473	−	25.4941i	−0.313048	−	0.809032i
$994$		0			0
$995$	19.1208	−	11.0394i	0.606170	−	0.349972i
$996$	−3.48056	−	8.99506i	−0.110286	−	0.285019i
$997$		−	31.1515i		−	0.986578i	−0.869866	−	0.493289i	$-0.835795\pi$
$997$		−	31.1515i		−	0.986578i	0.869866	−	0.493289i	$-0.164205\pi$
$998$	13.1566	−	7.59595i	0.416464	−	0.240446i
$999$	34.6959	−	22.9304i	1.09773	−	0.725485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.d.362.14		48
3.2	odd	2		1323.2.s.d.656.12		48
7.2	even	3		441.2.o.e.146.11	✓	48
7.3	odd	6		441.2.i.d.227.14		48
7.4	even	3		441.2.i.d.227.13		48
7.5	odd	6		441.2.o.e.146.12	yes	48
7.6	odd	2	inner	441.2.s.d.362.13		48
9.4	even	3		1323.2.i.d.1097.19		48
9.5	odd	6		441.2.i.d.68.12		48
21.2	odd	6		1323.2.o.e.440.13		48
21.5	even	6		1323.2.o.e.440.14		48
21.11	odd	6		1323.2.i.d.521.3		48
21.17	even	6		1323.2.i.d.521.19		48
21.20	even	2		1323.2.s.d.656.11		48
63.4	even	3		1323.2.s.d.962.11		48
63.5	even	6		441.2.o.e.293.11	yes	48
63.13	odd	6		1323.2.i.d.1097.3		48
63.23	odd	6		441.2.o.e.293.12	yes	48
63.31	odd	6		1323.2.s.d.962.12		48
63.32	odd	6	inner	441.2.s.d.374.13		48
63.40	odd	6		1323.2.o.e.881.13		48
63.41	even	6		441.2.i.d.68.11		48
63.58	even	3		1323.2.o.e.881.14		48
63.59	even	6	inner	441.2.s.d.374.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.11		48	63.41	even	6
441.2.i.d.68.12		48	9.5	odd	6
441.2.i.d.227.13		48	7.4	even	3
441.2.i.d.227.14		48	7.3	odd	6
441.2.o.e.146.11	✓	48	7.2	even	3
441.2.o.e.146.12	yes	48	7.5	odd	6
441.2.o.e.293.11	yes	48	63.5	even	6
441.2.o.e.293.12	yes	48	63.23	odd	6
441.2.s.d.362.13		48	7.6	odd	2	inner
441.2.s.d.362.14		48	1.1	even	1	trivial
441.2.s.d.374.13		48	63.32	odd	6	inner
441.2.s.d.374.14		48	63.59	even	6	inner
1323.2.i.d.521.3		48	21.11	odd	6
1323.2.i.d.521.19		48	21.17	even	6
1323.2.i.d.1097.3		48	63.13	odd	6
1323.2.i.d.1097.19		48	9.4	even	3
1323.2.o.e.440.13		48	21.2	odd	6
1323.2.o.e.440.14		48	21.5	even	6
1323.2.o.e.881.13		48	63.40	odd	6
1323.2.o.e.881.14		48	63.58	even	3
1323.2.s.d.656.11		48	21.20	even	2
1323.2.s.d.656.12		48	3.2	odd	2
1323.2.s.d.962.11		48	63.4	even	3
1323.2.s.d.962.12		48	63.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.367369 - 0.212101i) q^{2} +(1.71145 + 0.266368i) q^{3} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(2.85810 + 0.911750i) q^{9} +O(q^{10})\)	\(q+(0.367369 - 0.212101i) q^{2} +(1.71145 + 0.266368i) q^{3} +(-0.910027 + 1.57621i) q^{4} +3.60763 q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(2.85810 + 0.911750i) q^{9} +(1.32533 - 0.765180i) q^{10} -3.70603i q^{11} +(-1.97731 + 2.45520i) q^{12} +(-5.23479 + 3.02231i) q^{13} +(6.17426 + 0.960957i) q^{15} +(-1.47635 - 2.55711i) q^{16} +(-0.532108 - 0.921637i) q^{17} +(1.24336 - 0.271255i) q^{18} +(-3.16265 - 1.82596i) q^{19} +(-3.28304 + 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} +0.363239i q^{23} +(-0.431642 + 2.77335i) q^{24} +8.01497 q^{25} +(-1.28207 + 2.22060i) q^{26} +(4.64862 + 2.32172i) q^{27} +(-0.857560 - 0.495112i) q^{29} +(2.47205 - 0.956538i) q^{30} +(0.939786 + 0.542586i) q^{31} +(-3.89147 - 2.24674i) q^{32} +(0.987169 - 6.34268i) q^{33} +(-0.390960 - 0.225721i) q^{34} +(-4.03805 + 3.67525i) q^{36} +(4.00186 - 6.93143i) q^{37} -1.54915 q^{38} +(-9.76411 + 3.77814i) q^{39} +5.84605i q^{40} +(2.09005 + 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} +(5.84149 + 3.37259i) q^{44} +(10.3109 + 3.28925i) q^{45} +(0.0770432 + 0.133443i) q^{46} +(-2.83849 - 4.91640i) q^{47} +(-1.84556 - 4.76962i) q^{48} +(2.94445 - 1.69998i) q^{50} +(-0.665179 - 1.71907i) q^{51} -11.0015i q^{52} +(3.92463 - 2.26589i) q^{53} +(2.20019 - 0.133048i) q^{54} -13.3700i q^{55} +(-4.92633 - 3.96745i) q^{57} -0.420055 q^{58} +(-5.62746 + 9.74705i) q^{59} +(-7.13341 + 8.85745i) q^{60} +(0.0238258 - 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(-18.8852 + 10.9034i) q^{65} +(-0.982630 - 2.53948i) q^{66} +(4.86489 - 8.42624i) q^{67} +1.93693 q^{68} +(-0.0967553 + 0.621664i) q^{69} -5.55775i q^{71} +(-1.47746 + 4.63146i) q^{72} +(-1.95561 + 1.12907i) q^{73} -3.39519i q^{74} +(13.7172 + 2.13493i) q^{75} +(5.75619 - 3.32334i) q^{76} +(-2.78569 + 3.45894i) q^{78} +(-3.26604 - 5.65694i) q^{79} +(-5.32612 - 9.22511i) q^{80} +(7.33743 + 5.21174i) q^{81} +(1.53564 + 0.886601i) q^{82} +(-1.52977 + 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} +1.60991i q^{86} +(-1.33579 - 1.07578i) q^{87} +6.00552 q^{88} +(-7.47952 + 12.9549i) q^{89} +(4.48557 - 0.978588i) q^{90} +(-0.572542 - 0.330557i) q^{92} +(1.46387 + 1.17894i) q^{93} +(-2.08554 - 1.20409i) q^{94} +(-11.4097 - 6.58737i) q^{95} +(-6.06158 - 4.88174i) q^{96} +(-1.67018 - 0.964277i) q^{97} +(3.37897 - 10.5922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 - 8 * q^9	\( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 - 8 * q^9 - 40 * q^15 - 24 * q^16 + 32 * q^18 + 48 * q^25 + 48 * q^30 - 120 * q^32 - 8 * q^36 - 32 * q^39 + 96 * q^44 + 48 * q^50 + 48 * q^53 + 80 * q^57 - 72 * q^60 - 48 * q^64 - 120 * q^65 + 32 * q^72 - 88 * q^78 - 24 * q^79 + 120 * q^81 - 24 * q^85 - 144 * q^92 + 16 * q^93 - 96 * q^95 - 72 * q^99

Introduction

L-functions

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