LMFDB - Embedded newform 722.2.e.r.389.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			389.3
Character	$\chi$	$=$	722.389
Dual form			722.2.e.r.245.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.983662 - 0.825390i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.47284 - 1.26401i) q^{5} +(0.983662 + 0.825390i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.234623 + 1.33061i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.983662 - 0.825390i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.47284 - 1.26401i) q^{5} +(0.983662 + 0.825390i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.234623 + 1.33061i) q^{9} +(0.641755 - 3.63957i) q^{10} +(2.01484 + 3.48980i) q^{11} +(-0.642040 + 1.11205i) q^{12} +(3.74710 + 3.14419i) q^{13} +(0.415780 + 0.151331i) q^{14} +(-4.45940 + 1.62309i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.0463455 + 0.262838i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(-0.0986596 - 0.559526i) q^{21} +(-3.08691 + 2.59022i) q^{22} +(8.65391 - 3.14977i) q^{23} +(-1.20664 - 0.439181i) q^{24} +(6.63266 + 5.56547i) q^{25} +(-2.44575 + 4.23616i) q^{26} +(2.79360 + 4.83866i) q^{27} +(-0.0768330 + 0.435741i) q^{28} +(-0.0388245 + 0.220185i) q^{29} +(-2.37280 - 4.10980i) q^{30} +(-1.73993 + 3.01364i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.86236 + 1.76976i) q^{33} +(-0.250797 + 0.0912828i) q^{34} +(-1.25265 + 1.05110i) q^{35} +(-0.234623 - 1.33061i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(0.641755 + 3.63957i) q^{40} +(-6.02473 + 5.05535i) q^{41} +(0.533894 - 0.194322i) q^{42} +(5.29537 + 1.92736i) q^{43} +(-3.08691 - 2.59022i) q^{44} +(2.49672 - 4.32444i) q^{45} +(4.60465 + 7.97549i) q^{46} +(0.381797 - 2.16528i) q^{47} +(0.222978 - 1.26457i) q^{48} +(3.40211 + 5.89263i) q^{49} +(-4.32916 + 7.49833i) q^{50} +(0.262532 + 0.220291i) q^{51} +(-4.59650 - 1.67299i) q^{52} +(-9.34281 + 3.40050i) q^{53} +(-4.28005 + 3.59139i) q^{54} +(-2.58606 - 14.6663i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(-0.609423 - 3.45621i) q^{59} +(3.63534 - 3.05041i) q^{60} +(-3.83352 + 1.39529i) q^{61} +(-3.26999 - 1.19018i) q^{62} +(0.457965 + 0.384278i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.03879 - 15.6556i) q^{65} +(-0.898528 + 5.09581i) q^{66} +(0.0256588 - 0.145518i) q^{67} +(-0.133446 - 0.231136i) q^{68} +(5.91273 - 10.2412i) q^{69} +(-1.25265 - 1.05110i) q^{70} +(-10.7774 - 3.92267i) q^{71} +(1.26966 - 0.462117i) q^{72} +(1.08951 - 0.914211i) q^{73} +(0.251621 + 1.42701i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(1.09069 + 6.18564i) q^{78} +(7.81624 - 6.55861i) q^{79} +(-3.47284 + 1.26401i) q^{80} +(2.93278 + 1.06744i) q^{81} +(-6.02473 - 5.05535i) q^{82} +(1.64439 - 2.84817i) q^{83} +(0.284079 + 0.492039i) q^{84} +(0.171280 - 0.971376i) q^{85} +(-0.978546 + 5.54961i) q^{86} +(0.143548 + 0.248633i) q^{87} +(2.01484 - 3.48980i) q^{88} +(-4.56620 - 3.83149i) q^{89} +(4.69229 + 1.70786i) q^{90} +(2.03378 - 0.740236i) q^{91} +(-7.05473 + 5.91962i) q^{92} +(0.775931 + 4.40052i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(0.709311 + 4.02270i) q^{97} +(-5.21234 + 4.37367i) q^{98} +(-5.11630 + 1.86218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 6 * q^7 - 12 * q^8	$ 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.983662	−	0.825390i	0.567917	−	0.476539i	−0.313037	−	0.949741i	$-0.601346\pi$
$3$	0.983662	−	0.825390i	0.567917	−	0.476539i	0.880954	+	0.473202i	$0.156902\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−3.47284	−	1.26401i	−1.55310	−	0.565282i	−0.583958	−	0.811784i	$-0.698497\pi$
$5$	−3.47284	−	1.26401i	−1.55310	−	0.565282i	−0.969142	+	0.246501i	$0.920719\pi$
$6$	0.983662	+	0.825390i	0.401578	+	0.336964i
$7$	0.221232	−	0.383185i	0.0836177	−	0.144830i	−0.821184	−	0.570664i	$-0.806686\pi$
$7$	0.221232	−	0.383185i	0.0836177	−	0.144830i	0.904801	+	0.425834i	$0.140019\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.234623	+	1.33061i	−0.0782077	+	0.443538i
$10$	0.641755	−	3.63957i	0.202941	−	1.15093i
$11$	2.01484	+	3.48980i	0.607496	+	1.05221i	0.991652	+	0.128946i	$0.0411593\pi$
$11$	2.01484	+	3.48980i	0.607496	+	1.05221i	−0.384156	+	0.923268i	$0.625507\pi$
$12$	−0.642040	+	1.11205i	−0.185341	+	0.321020i
$13$	3.74710	+	3.14419i	1.03926	+	0.872041i	0.991923	−	0.126838i	$-0.0404827\pi$
$13$	3.74710	+	3.14419i	1.03926	+	0.872041i	0.0473350	+	0.998879i	$0.484927\pi$
$14$	0.415780	+	0.151331i	0.111122	+	0.0404450i
$15$	−4.45940	+	1.62309i	−1.15141	+	0.419080i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.0463455	+	0.262838i	0.0112404	+	0.0637476i	0.989912	−	0.141683i	$-0.0452515\pi$
$17$	0.0463455	+	0.262838i	0.0112404	+	0.0637476i	−0.978672	+	0.205431i	$0.934140\pi$
$18$	−1.35114			−0.318467
$19$		0			0
$19$		0			0
$20$	3.69572			0.826388
$21$	−0.0986596	−	0.559526i	−0.0215293	−	0.122099i
$22$	−3.08691	+	2.59022i	−0.658131	+	0.552238i
$23$	8.65391	−	3.14977i	1.80447	−	0.656772i	0.806626	−	0.591062i	$-0.201291\pi$
$23$	8.65391	−	3.14977i	1.80447	−	0.656772i	0.997839	−	0.0657101i	$-0.0209313\pi$
$24$	−1.20664	−	0.439181i	−0.246304	−	0.0896474i
$25$	6.63266	+	5.56547i	1.32653	+	1.11309i
$26$	−2.44575	+	4.23616i	−0.479650	+	0.830779i
$27$	2.79360	+	4.83866i	0.537629	+	0.931201i
$28$	−0.0768330	+	0.435741i	−0.0145201	+	0.0823474i
$29$	−0.0388245	+	0.220185i	−0.00720953	+	0.0408873i	−0.988200	−	0.153167i	$-0.951053\pi$
$29$	−0.0388245	+	0.220185i	−0.00720953	+	0.0408873i	0.980991	+	0.194054i	$0.0621638\pi$
$30$	−2.37280	−	4.10980i	−0.433211	−	0.750344i
$31$	−1.73993	+	3.01364i	−0.312500	+	0.541266i	−0.978903	−	0.204326i	$-0.934500\pi$
$31$	−1.73993	+	3.01364i	−0.312500	+	0.541266i	0.666403	+	0.745592i	$0.267833\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	4.86236	+	1.76976i	0.846429	+	0.308075i
$34$	−0.250797	+	0.0912828i	−0.0430114	+	0.0156549i
$35$	−1.25265	+	1.05110i	−0.211737	+	0.177668i
$36$	−0.234623	−	1.33061i	−0.0391039	−	0.221769i
$37$	1.44903			0.238219			0.119109	−	0.992881i	$-0.461996\pi$
$37$	1.44903			0.238219			0.119109	+	0.992881i	$0.461996\pi$
$38$		0			0
$39$	6.28106			1.00577
$40$	0.641755	+	3.63957i	0.101470	+	0.575467i
$41$	−6.02473	+	5.05535i	−0.940904	+	0.789513i	−0.977742	−	0.209809i	$-0.932716\pi$
$41$	−6.02473	+	5.05535i	−0.940904	+	0.789513i	0.0368381	+	0.999321i	$0.488271\pi$
$42$	0.533894	−	0.194322i	0.0823816	−	0.0299845i
$43$	5.29537	+	1.92736i	0.807537	+	0.293919i	0.712606	−	0.701564i	$-0.247515\pi$
$43$	5.29537	+	1.92736i	0.807537	+	0.293919i	0.0949310	+	0.995484i	$0.469737\pi$
$44$	−3.08691	−	2.59022i	−0.465369	−	0.390491i
$45$	2.49672	−	4.32444i	0.372189	−	0.644650i
$46$	4.60465	+	7.97549i	0.678919	+	1.17592i
$47$	0.381797	−	2.16528i	0.0556907	−	0.315838i	−0.944218	−	0.329320i	$-0.893181\pi$
$47$	0.381797	−	2.16528i	0.0556907	−	0.315838i	0.999909	+	0.0134821i	$0.00429162\pi$
$48$	0.222978	−	1.26457i	0.0321841	−	0.182525i
$49$	3.40211	+	5.89263i	0.486016	+	0.841805i
$50$	−4.32916	+	7.49833i	−0.612236	+	1.06042i
$51$	0.262532	+	0.220291i	0.0367619	+	0.0308469i
$52$	−4.59650	−	1.67299i	−0.637420	−	0.232002i
$53$	−9.34281	+	3.40050i	−1.28333	+	0.467095i	−0.891533	−	0.452955i	$-0.850370\pi$
$53$	−9.34281	+	3.40050i	−1.28333	+	0.467095i	−0.391800	+	0.920050i	$0.628147\pi$
$54$	−4.28005	+	3.59139i	−0.582441	+	0.488726i
$55$	−2.58606	−	14.6663i	−0.348704	−	1.97760i
$56$	−0.442463			−0.0591267
$57$		0			0
$58$	−0.223582			−0.0293577
$59$	−0.609423	−	3.45621i	−0.0793401	−	0.449960i	−0.998435	−	0.0559238i	$-0.982190\pi$
$59$	−0.609423	−	3.45621i	−0.0793401	−	0.449960i	0.919095	−	0.394036i	$-0.128922\pi$
$60$	3.63534	−	3.05041i	0.469320	−	0.393806i
$61$	−3.83352	+	1.39529i	−0.490832	+	0.178648i	−0.575566	−	0.817755i	$-0.695218\pi$
$61$	−3.83352	+	1.39529i	−0.490832	+	0.178648i	0.0847339	+	0.996404i	$0.472996\pi$
$62$	−3.26999	−	1.19018i	−0.415289	−	0.151153i
$63$	0.457965	+	0.384278i	0.0576981	+	0.0484145i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−9.03879	−	15.6556i	−1.12112	−	1.94184i
$66$	−0.898528	+	5.09581i	−0.110601	+	0.627250i
$67$	0.0256588	−	0.145518i	0.00313472	−	0.0177779i	−0.983200	−	0.182530i	$-0.941571\pi$
$67$	0.0256588	−	0.145518i	0.00313472	−	0.0177779i	0.986335	+	0.164752i	$0.0526824\pi$
$68$	−0.133446	−	0.231136i	−0.0161828	−	0.0280294i
$69$	5.91273	−	10.2412i	0.711810	−	1.23289i
$70$	−1.25265	−	1.05110i	−0.149720	−	0.125630i
$71$	−10.7774	−	3.92267i	−1.27905	−	0.465535i	−0.388930	−	0.921267i	$-0.627155\pi$
$71$	−10.7774	−	3.92267i	−1.27905	−	0.465535i	−0.890117	+	0.455732i	$0.849378\pi$
$72$	1.26966	−	0.462117i	0.149631	−	0.0544611i
$73$	1.08951	−	0.914211i	0.127518	−	0.107000i	−0.576798	−	0.816887i	$-0.695698\pi$
$73$	1.08951	−	0.914211i	0.127518	−	0.107000i	0.704316	+	0.709886i	$0.251254\pi$
$74$	0.251621	+	1.42701i	0.0292504	+	0.165887i
$75$	11.1180			1.28379
$76$		0			0
$77$	1.78298			0.203190
$78$	1.09069	+	6.18564i	0.123497	+	0.700386i
$79$	7.81624	−	6.55861i	0.879396	−	0.737901i	−0.0866589	−	0.996238i	$-0.527619\pi$
$79$	7.81624	−	6.55861i	0.879396	−	0.737901i	0.966055	+	0.258337i	$0.0831746\pi$
$80$	−3.47284	+	1.26401i	−0.388275	+	0.141321i
$81$	2.93278	+	1.06744i	0.325864	+	0.118605i
$82$	−6.02473	−	5.05535i	−0.665320	−	0.558270i
$83$	1.64439	−	2.84817i	0.180495	−	0.312627i	−0.761554	−	0.648101i	$-0.775563\pi$
$83$	1.64439	−	2.84817i	0.180495	−	0.312627i	0.942049	+	0.335475i	$0.108897\pi$
$84$	0.284079	+	0.492039i	0.0309956	+	0.0536859i
$85$	0.171280	−	0.971376i	0.0185779	−	0.105361i
$86$	−0.978546	+	5.54961i	−0.105519	+	0.598430i
$87$	0.143548	+	0.248633i	0.0153900	+	0.0266562i
$88$	2.01484	−	3.48980i	0.214782	−	0.372014i
$89$	−4.56620	−	3.83149i	−0.484016	−	0.406137i	0.367860	−	0.929881i	$-0.380091\pi$
$89$	−4.56620	−	3.83149i	−0.484016	−	0.406137i	−0.851876	+	0.523744i	$0.824535\pi$
$90$	4.69229	+	1.70786i	0.494611	+	0.180024i
$91$	2.03378	−	0.740236i	0.213198	−	0.0775979i
$92$	−7.05473	+	5.91962i	−0.735507	+	0.617163i
$93$	0.775931	+	4.40052i	0.0804603	+	0.456313i
$94$	2.19868			0.226776
$95$		0			0
$96$	1.28408			0.131056
$97$	0.709311	+	4.02270i	0.0720196	+	0.408443i	0.999410	+	0.0343483i	$0.0109355\pi$
$97$	0.709311	+	4.02270i	0.0720196	+	0.408443i	−0.927390	+	0.374095i	$0.877953\pi$
$98$	−5.21234	+	4.37367i	−0.526526	+	0.441808i
$99$	−5.11630	+	1.86218i	−0.514208	+	0.187156i
$100$	−8.13617	−	2.96132i	−0.813617	−	0.296132i
$101$	0.325781	+	0.273363i	0.0324165	+	0.0272006i	0.658852	−	0.752273i	$-0.271042\pi$
$101$	0.325781	+	0.273363i	0.0324165	+	0.0272006i	−0.626435	+	0.779473i	$0.715487\pi$
$102$	−0.171356	+	0.296797i	−0.0169668	+	0.0293873i
$103$	2.26809	+	3.92845i	0.223482	+	0.387081i	0.955863	−	0.293813i	$-0.0949244\pi$
$103$	2.26809	+	3.92845i	0.223482	+	0.387081i	−0.732381	+	0.680895i	$0.761591\pi$
$104$	0.849399	−	4.81718i	0.0832904	−	0.472363i
$105$	−0.364618	+	2.06785i	−0.0355831	+	0.201802i
$106$	−4.97120	−	8.61038i	−0.482846	−	0.836314i
$107$	1.58576	−	2.74661i	0.153301	−	0.265525i	−0.779138	−	0.626852i	$-0.784343\pi$
$107$	1.58576	−	2.74661i	0.153301	−	0.265525i	0.932439	+	0.361327i	$0.117676\pi$
$108$	−4.28005	−	3.59139i	−0.411848	−	0.345582i
$109$	6.37217	+	2.31928i	0.610343	+	0.222147i	0.628653	−	0.777686i	$-0.283606\pi$
$109$	6.37217	+	2.31928i	0.610343	+	0.222147i	−0.0183104	+	0.999832i	$0.505829\pi$
$110$	13.9944	−	5.09355i	1.33431	−	0.485651i
$111$	1.42535	−	1.19601i	0.135289	−	0.113521i
$112$	−0.0768330	−	0.435741i	−0.00726003	−	0.0411737i
$113$	−10.0444			−0.944893			−0.472447	−	0.881359i	$-0.656629\pi$
$113$	−10.0444			−0.944893			−0.472447	+	0.881359i	$0.656629\pi$
$114$		0			0
$115$	−34.0350			−3.17378
$116$	−0.0388245	−	0.220185i	−0.00360477	−	0.0204437i
$117$	−5.06286	+	4.24824i	−0.468062	+	0.392750i
$118$	3.29788	−	1.20033i	0.303594	−	0.110499i
$119$	0.110969	+	0.0403893i	0.0101725	+	0.00370248i
$120$	3.63534	+	3.05041i	0.331859	+	0.278463i
$121$	−2.61913	+	4.53647i	−0.238103	+	0.412406i
$122$	−2.03977	−	3.53299i	−0.184672	−	0.319862i
$123$	−1.75366	+	9.94550i	−0.158122	+	0.896756i
$124$	0.604270	−	3.42699i	0.0542651	−	0.307752i
$125$	−6.76007	−	11.7088i	−0.604639	−	1.04727i
$126$	−0.298915	+	0.517736i	−0.0266295	+	0.0461236i
$127$	10.7864	+	9.05083i	0.957134	+	0.803131i	0.980485	−	0.196596i	$-0.0629888\pi$
$127$	10.7864	+	9.05083i	0.957134	+	0.803131i	−0.0233502	+	0.999727i	$0.507433\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	6.79968	−	2.47488i	0.598678	−	0.217901i
$130$	13.8482	−	11.6200i	1.21457	−	1.01914i
$131$	2.75085	+	15.6008i	0.240343	+	1.36305i	0.831065	+	0.556176i	$0.187732\pi$
$131$	2.75085	+	15.6008i	0.240343	+	1.36305i	−0.590722	+	0.806875i	$0.701157\pi$
$132$	−5.17442			−0.450375
$133$		0			0
$134$	0.147763			0.0127648
$135$	−3.58562	−	20.3350i	−0.308601	−	1.75016i
$136$	0.204452	−	0.171556i	0.0175316	−	0.0147108i
$137$	−2.07431	+	0.754987i	−0.177220	+	0.0645029i	−0.429106	−	0.903254i	$-0.641171\pi$
$137$	−2.07431	+	0.754987i	−0.177220	+	0.0645029i	0.251886	+	0.967757i	$0.418949\pi$
$138$	11.1123	+	4.04455i	0.945942	+	0.344295i
$139$	−13.0721	−	10.9688i	−1.10876	−	0.930362i	−0.110780	−	0.993845i	$-0.535335\pi$
$139$	−13.0721	−	10.9688i	−1.10876	−	0.930362i	−0.997983	+	0.0634825i	$0.979779\pi$
$140$	0.817610	−	1.41614i	0.0691007	−	0.119686i
$141$	−1.41164	−	2.44503i	−0.118881	−	0.205909i
$142$	1.99159	−	11.2949i	0.167131	−	0.947845i
$143$	−3.42280	+	19.4117i	−0.286229	+	1.62328i
$144$	0.675571	+	1.17012i	0.0562975	+	0.0975102i
$145$	0.413147	−	0.715592i	0.0343100	−	0.0594267i
$146$	1.08951	+	0.914211i	0.0901689	+	0.0756607i
$147$	8.21025	+	2.98829i	0.677170	+	0.246470i
$148$	−1.36164	+	0.495597i	−0.111926	+	0.0407378i
$149$	10.3767	−	8.70705i	0.850089	−	0.713309i	−0.109720	−	0.993962i	$-0.534996\pi$
$149$	10.3767	−	8.70705i	0.850089	−	0.713309i	0.959809	+	0.280653i	$0.0905511\pi$
$150$	1.93062	+	10.9491i	0.157634	+	0.893988i
$151$	−9.15317			−0.744875			−0.372437	−	0.928057i	$-0.621478\pi$
$151$	−9.15317			−0.744875			−0.372437	+	0.928057i	$0.621478\pi$
$152$		0			0
$153$	−0.360610			−0.0291536
$154$	0.309612	+	1.75590i	0.0249492	+	0.141494i
$155$	9.85176	−	8.26660i	0.791312	−	0.663990i
$156$	−5.90227	+	2.14825i	−0.472560	+	0.171998i
$157$	15.4018	+	5.60581i	1.22920	+	0.447392i	0.873323	−	0.487141i	$-0.161960\pi$
$157$	15.4018	+	5.60581i	1.22920	+	0.447392i	0.355876	+	0.934533i	$0.384182\pi$
$158$	7.81624	+	6.55861i	0.621827	+	0.521775i
$159$	−6.38342	+	11.0564i	−0.506238	+	0.876830i
$160$	−1.84786	−	3.20059i	−0.146086	−	0.253028i
$161$	0.707578	−	4.01287i	0.0557650	−	0.316259i
$162$	−0.541955	+	3.07358i	−0.0425800	+	0.241483i
$163$	6.88612	+	11.9271i	0.539363	+	0.934204i	0.998938	+	0.0460652i	$0.0146682\pi$
$163$	6.88612	+	11.9271i	0.539363	+	0.934204i	−0.459576	+	0.888139i	$0.651998\pi$
$164$	3.93236	−	6.81105i	0.307066	−	0.531854i
$165$	−14.6492	−	12.2921i	−1.14044	−	0.956942i
$166$	3.09044	+	1.12483i	0.239865	+	0.0873036i
$167$	9.70966	−	3.53403i	0.751356	−	0.273471i	0.0621797	−	0.998065i	$-0.480195\pi$
$167$	9.70966	−	3.53403i	0.751356	−	0.273471i	0.689176	+	0.724594i	$0.257973\pi$
$168$	−0.435234	+	0.365205i	−0.0335791	+	0.0281762i
$169$	1.89740	+	10.7607i	0.145954	+	0.827745i
$170$	0.986361			0.0756504
$171$		0			0
$172$	−5.63522			−0.429682
$173$	−1.70384	−	9.66295i	−0.129540	−	0.734660i	−0.978507	−	0.206214i	$-0.933886\pi$
$173$	−1.70384	−	9.66295i	−0.129540	−	0.734660i	0.848967	−	0.528447i	$-0.177225\pi$
$174$	−0.219929	+	0.184542i	−0.0166727	+	0.0139901i
$175$	3.59996	−	1.31028i	0.272131	−	0.0990476i
$176$	3.78665	+	1.37823i	0.285430	+	0.103888i
$177$	−3.45219	−	2.89673i	−0.259482	−	0.217731i
$178$	2.98037	−	5.16216i	0.223388	−	0.386920i
$179$	4.39915	+	7.61955i	0.328808	+	0.569512i	0.982276	−	0.187442i	$-0.0600197\pi$
$179$	4.39915	+	7.61955i	0.328808	+	0.569512i	−0.653468	+	0.756955i	$0.726686\pi$
$180$	−0.867101	+	4.91757i	−0.0646299	+	0.366534i
$181$	2.52272	−	14.3070i	0.187512	−	1.06343i	−0.735173	−	0.677880i	$-0.762899\pi$
$181$	2.52272	−	14.3070i	0.187512	−	1.06343i	0.922685	−	0.385554i	$-0.125990\pi$
$182$	1.08215	+	1.87434i	0.0802145	+	0.138936i
$183$	−2.61923	+	4.53664i	−0.193619	+	0.335358i
$184$	−7.05473	−	5.91962i	−0.520082	−	0.436400i
$185$	−5.03224	−	1.83159i	−0.369978	−	0.134661i
$186$	−4.19893	+	1.52828i	−0.307880	+	0.112059i
$187$	−0.823874	+	0.691312i	−0.0602476	+	0.0505538i
$188$	0.381797	+	2.16528i	0.0278454	+	0.157919i
$189$	2.47214			0.179821
$190$		0			0
$191$	12.7302			0.921122			0.460561	−	0.887628i	$-0.347648\pi$
$191$	12.7302			0.921122			0.460561	+	0.887628i	$0.347648\pi$
$192$	0.222978	+	1.26457i	0.0160921	+	0.0912626i
$193$	13.3890	−	11.2347i	0.963759	−	0.808690i	−0.0178014	−	0.999842i	$-0.505667\pi$
$193$	13.3890	−	11.2347i	0.963759	−	0.808690i	0.981561	+	0.191152i	$0.0612222\pi$
$194$	−3.83842	+	1.39707i	−0.275582	+	0.100304i
$195$	−21.8131	−	7.93932i	−1.56207	−	0.568547i
$196$	−5.21234	−	4.37367i	−0.372310	−	0.312405i
$197$	12.2556	−	21.2274i	0.873178	−	1.51239i	0.0144872	−	0.999895i	$-0.495388\pi$
$197$	12.2556	−	21.2274i	0.873178	−	1.51239i	0.858691	−	0.512494i	$-0.171278\pi$
$198$	−2.72233	−	4.71521i	−0.193467	−	0.335095i
$199$	2.85931	−	16.2159i	0.202691	−	1.14952i	−0.698341	−	0.715765i	$-0.746078\pi$
$199$	2.85931	−	16.2159i	0.202691	−	1.14952i	0.901032	−	0.433753i	$-0.142811\pi$
$200$	1.50350	−	8.52679i	0.106314	−	0.602935i
$201$	−0.0948696	−	0.164319i	−0.00669159	−	0.0115902i
$202$	−0.212639	+	0.368301i	−0.0149612	+	0.0259136i
$203$	0.0757822	+	0.0635888i	0.00531887	+	0.00446306i
$204$	−0.322044	−	0.117214i	−0.0225476	−	0.00820664i
$205$	27.3129	−	9.94109i	1.90762	−	0.694316i
$206$	−3.47492	+	2.91580i	−0.242109	+	0.203153i
$207$	2.16072	+	12.2540i	0.150180	+	0.851714i
$208$	4.89149			0.339164
$209$		0			0
$210$	−2.09975			−0.144897
$211$	4.77193	+	27.0630i	0.328513	+	1.86309i	0.483739	+	0.875212i	$0.339278\pi$
$211$	4.77193	+	27.0630i	0.328513	+	1.86309i	−0.155226	+	0.987879i	$0.549611\pi$
$212$	7.61633	−	6.39086i	0.523091	−	0.438926i
$213$	−13.8391	+	5.03702i	−0.948239	+	0.345131i
$214$	2.98025	+	1.08472i	0.203726	+	0.0741500i
$215$	−15.9538	−	13.3868i	−1.08804	−	0.912973i
$216$	2.79360	−	4.83866i	0.190081	−	0.329229i
$217$	0.769854	+	1.33343i	0.0522611	+	0.0905189i
$218$	−1.17753	+	6.67810i	−0.0797523	+	0.452298i
$219$	0.317133	−	1.79855i	0.0214298	−	0.121535i
$220$	7.44627	+	12.8973i	0.502027	+	0.869536i
$221$	−0.652752	+	1.13060i	−0.0439089	+	0.0760524i
$222$	1.42535	+	1.19601i	0.0956634	+	0.0802712i
$223$	−19.1421	−	6.96715i	−1.28185	−	0.466555i	−0.390806	−	0.920473i	$-0.627804\pi$
$223$	−19.1421	−	6.96715i	−1.28185	−	0.466555i	−0.891043	+	0.453918i	$0.850026\pi$
$224$	0.415780	−	0.151331i	0.0277804	−	0.0101113i
$225$	−8.96166	+	7.51973i	−0.597444	+	0.501315i
$226$	−1.74418	−	9.89175i	−0.116021	−	0.657990i
$227$	−22.1493			−1.47010			−0.735051	−	0.678011i	$-0.762842\pi$
$227$	−22.1493			−1.47010			−0.735051	+	0.678011i	$0.762842\pi$
$228$		0			0
$229$	12.7148			0.840216			0.420108	−	0.907474i	$-0.361992\pi$
$229$	12.7148			0.840216			0.420108	+	0.907474i	$0.361992\pi$
$230$	−5.91011	−	33.5179i	−0.389701	−	2.21011i
$231$	1.75385	−	1.47166i	0.115395	−	0.0968279i
$232$	0.210098	−	0.0764694i	0.0137936	−	0.00502046i
$233$	8.15819	+	2.96934i	0.534461	+	0.194528i	0.595129	−	0.803630i	$-0.297101\pi$
$233$	8.15819	+	2.96934i	0.534461	+	0.194528i	−0.0606683	+	0.998158i	$0.519323\pi$
$234$	−5.06286	−	4.24824i	−0.330970	−	0.277716i
$235$	−4.06285	+	7.03706i	−0.265031	+	0.459047i
$236$	1.75476	+	3.03934i	0.114225	+	0.197844i
$237$	2.27513	−	12.9029i	0.147785	−	0.838133i
$238$	−0.0205062	+	0.116296i	−0.00132922	+	0.00753837i
$239$	−10.9375	−	18.9442i	−0.707485	−	1.22540i	−0.965787	−	0.259336i	$-0.916496\pi$
$239$	−10.9375	−	18.9442i	−0.707485	−	1.22540i	0.258302	−	0.966064i	$-0.416837\pi$
$240$	−2.37280	+	4.10980i	−0.153163	+	0.265287i
$241$	−14.5267	−	12.1893i	−0.935745	−	0.785183i	0.0410952	−	0.999155i	$-0.486915\pi$
$241$	−14.5267	−	12.1893i	−0.935745	−	0.785183i	−0.976840	+	0.213972i	$0.931360\pi$
$242$	−4.92235	−	1.79159i	−0.316421	−	0.115168i
$243$	−11.9849	+	4.36213i	−0.768829	+	0.279831i
$244$	3.12512	−	2.62228i	0.200065	−	0.167874i
$245$	−4.36664	−	24.7645i	−0.278975	−	1.58214i
$246$	−10.0989			−0.643884
$247$		0			0
$248$	3.47985			0.220971
$249$	−0.733325	−	4.15889i	−0.0464726	−	0.263559i
$250$	10.3570	−	8.69058i	0.655036	−	0.549641i
$251$	−2.72770	+	0.992801i	−0.172171	+	0.0626650i	−0.426667	−	0.904409i	$-0.640312\pi$
$251$	−2.72770	+	0.992801i	−0.172171	+	0.0626650i	0.254497	+	0.967074i	$0.418090\pi$
$252$	−0.561777	−	0.204470i	−0.0353886	−	0.0128804i
$253$	28.4283	+	23.8541i	1.78727	+	1.49970i
$254$	−7.04029	+	12.1941i	−0.441747	+	0.765129i
$255$	−0.633283	−	1.09688i	−0.0396577	−	0.0686892i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	3.97741	−	22.5570i	0.248104	−	1.40707i	−0.565067	−	0.825045i	$-0.691150\pi$
$257$	3.97741	−	22.5570i	0.248104	−	1.40707i	0.813171	−	0.582024i	$-0.197739\pi$
$258$	3.61803	+	6.26662i	0.225249	+	0.390143i
$259$	0.320571	−	0.555245i	0.0199193	−	0.0345013i
$260$	13.8482	+	11.6200i	0.858830	+	0.720644i
$261$	−0.283872	−	0.103321i	−0.0175712	−	0.00639541i
$262$	−14.8861	+	5.41811i	−0.919669	+	0.334732i
$263$	−3.87799	+	3.25402i	−0.239127	+	0.200652i	−0.754474	−	0.656330i	$-0.772108\pi$
$263$	−3.87799	+	3.25402i	−0.239127	+	0.200652i	0.515346	+	0.856982i	$0.327663\pi$
$264$	−0.898528	−	5.09581i	−0.0553006	−	0.313625i
$265$	36.7443			2.25719
$266$		0			0
$267$	−7.65407			−0.468421
$268$	0.0256588	+	0.145518i	0.00156736	+	0.00888893i
$269$	−15.8892	+	13.3327i	−0.968784	+	0.812906i	−0.982360	−	0.187001i	$-0.940123\pi$
$269$	−15.8892	+	13.3327i	−0.968784	+	0.812906i	0.0135754	+	0.999908i	$0.495679\pi$
$270$	19.4035	−	7.06229i	1.18086	−	0.429797i
$271$	−5.91508	−	2.15291i	−0.359316	−	0.130780i	0.156053	−	0.987749i	$-0.450123\pi$
$271$	−5.91508	−	2.15291i	−0.359316	−	0.130780i	−0.515369	+	0.856968i	$0.672345\pi$
$272$	0.204452	+	0.171556i	0.0123967	+	0.0104021i
$273$	1.38957	−	2.40681i	0.0841006	−	0.145667i
$274$	−1.10372	−	1.91169i	−0.0666780	−	0.115490i
$275$	−6.05862	+	34.3602i	−0.365349	+	2.07200i
$276$	−2.05347	+	11.6458i	−0.123604	+	0.700996i
$277$	−3.58804	−	6.21467i	−0.215584	−	0.373403i	0.737869	−	0.674944i	$-0.235832\pi$
$277$	−3.58804	−	6.21467i	−0.215584	−	0.373403i	−0.953453	+	0.301541i	$0.902499\pi$
$278$	8.53222	−	14.7782i	0.511729	−	0.886340i
$279$	−3.60177	−	3.02224i	−0.215632	−	0.180937i
$280$	1.53660	+	0.559278i	0.0918297	+	0.0334233i
$281$	−2.60662	+	0.948733i	−0.155498	+	0.0565967i	−0.418597	−	0.908172i	$-0.637478\pi$
$281$	−2.60662	+	0.948733i	−0.155498	+	0.0565967i	0.263098	+	0.964769i	$0.415256\pi$
$282$	2.16276	−	1.81477i	0.128790	−	0.108068i
$283$	1.34553	+	7.63089i	0.0799836	+	0.453609i	0.998327	+	0.0578244i	$0.0184164\pi$
$283$	1.34553	+	7.63089i	0.0799836	+	0.453609i	−0.918343	+	0.395785i	$0.870473\pi$
$284$	11.4691			0.680567
$285$		0			0
$286$	−19.7111			−1.16554
$287$	0.604270	+	3.42699i	0.0356689	+	0.202289i
$288$	−1.03503	+	0.868497i	−0.0609900	+	0.0511767i
$289$	15.9078	−	5.78998i	0.935755	−	0.340587i
$290$	0.776463	+	0.282609i	0.0455955	+	0.0165954i
$291$	4.01802	+	3.37152i	0.235540	+	0.197642i
$292$	−0.711130	+	1.23171i	−0.0416157	+	0.0720806i
$293$	0.391435	+	0.677985i	0.0228679	+	0.0396083i	0.877233	−	0.480065i	$-0.159387\pi$
$293$	0.391435	+	0.677985i	0.0228679	+	0.0396083i	−0.854365	+	0.519673i	$0.826054\pi$
$294$	−1.51719	+	8.60443i	−0.0884845	+	0.501820i
$295$	−2.25225	+	12.7732i	−0.131131	+	0.743683i
$296$	−0.724514	−	1.25490i	−0.0421115	−	0.0729393i
$297$	−11.2573	+	19.4982i	−0.653215	+	1.13140i
$298$	10.3767	+	8.70705i	0.601104	+	0.504386i
$299$	42.3305	+	15.4071i	2.44804	+	0.891013i
$300$	−10.4475	+	3.80257i	−0.603186	+	0.219542i
$301$	1.91004	−	1.60271i	0.110093	−	0.0923789i
$302$	−1.58943	−	9.01412i	−0.0914615	−	0.518704i
$303$	0.546090			0.0313720
$304$		0			0
$305$	15.0769			0.863298
$306$	−0.0626193	−	0.355132i	−0.00357971	−	0.0203015i
$307$	−21.5785	+	18.1065i	−1.23155	+	1.03339i	−0.233416	+	0.972377i	$0.574990\pi$
$307$	−21.5785	+	18.1065i	−1.23155	+	1.03339i	−0.998137	+	0.0610179i	$0.980565\pi$
$308$	−1.67546	+	0.609816i	−0.0954680	+	0.0347475i
$309$	5.47354	+	1.99220i	0.311379	+	0.113333i
$310$	9.85176	+	8.26660i	0.559542	+	0.469512i
$311$	−1.93414	+	3.35002i	−0.109675	+	0.189962i	−0.915639	−	0.402003i	$-0.868314\pi$
$311$	−1.93414	+	3.35002i	−0.109675	+	0.189962i	0.805964	+	0.591965i	$0.201648\pi$
$312$	−3.14053	−	5.43956i	−0.177798	−	0.307954i
$313$	5.27678	−	29.9261i	0.298261	−	1.69152i	−0.355382	−	0.934721i	$-0.615649\pi$
$313$	5.27678	−	29.9261i	0.298261	−	1.69152i	0.653643	−	0.756803i	$-0.273240\pi$
$314$	−2.84614	+	16.1413i	−0.160617	+	0.910905i
$315$	−1.10471	−	1.91341i	−0.0622432	−	0.107808i
$316$	−5.10169	+	8.83638i	−0.286992	+	0.497085i
$317$	4.08151	+	3.42479i	0.229240	+	0.192356i	0.750172	−	0.661243i	$-0.229971\pi$
$317$	4.08151	+	3.42479i	0.229240	+	0.192356i	−0.520931	+	0.853599i	$0.674415\pi$
$318$	−11.9969	−	4.36652i	−0.672753	−	0.244862i
$319$	−0.846626	+	0.308147i	−0.0474020	+	0.0172529i
$320$	2.83108	−	2.37556i	0.158262	−	0.132798i
$321$	−0.707178	−	4.01060i	−0.0394708	−	0.223850i
$322$	4.07478			0.227079
$323$		0			0
$324$	−3.12099			−0.173389
$325$	7.35437	+	41.7087i	0.407947	+	2.31358i
$326$	−10.5502	+	8.85263i	−0.584319	+	0.490302i
$327$	8.18237	−	2.97814i	0.452486	−	0.164691i
$328$	7.39042	+	2.68989i	0.408068	+	0.148525i
$329$	−0.745235	−	0.625326i	−0.0410861	−	0.0344754i
$330$	9.56159	−	16.5612i	0.526348	−	0.911662i
$331$	10.2740	+	17.7951i	0.564711	+	0.978108i	0.997077	+	0.0764094i	$0.0243456\pi$
$331$	10.2740	+	17.7951i	0.564711	+	0.978108i	−0.432366	+	0.901698i	$0.642321\pi$
$332$	−0.571090	+	3.23881i	−0.0313427	+	0.177753i
$333$	−0.339976	+	1.92810i	−0.0186305	+	0.105659i
$334$	5.16640	+	8.94847i	0.282693	+	0.489638i
$335$	−0.273045	+	0.472928i	−0.0149180	+	0.0258388i
$336$	−0.435234	−	0.365205i	−0.0237440	−	0.0199236i
$337$	−12.4814	−	4.54285i	−0.679905	−	0.247465i	−0.0210980	−	0.999777i	$-0.506716\pi$
$337$	−12.4814	−	4.54285i	−0.679905	−	0.247465i	−0.658807	+	0.752312i	$0.728938\pi$
$338$	−10.2677	+	3.73715i	−0.558491	+	0.203274i
$339$	−9.88024	+	8.29051i	−0.536621	+	0.450279i
$340$	0.171280	+	0.971376i	0.00928895	+	0.0526803i
$341$	−14.0227			−0.759370
$342$		0			0
$343$	6.10787			0.329794
$344$	−0.978546	−	5.54961i	−0.0527596	−	0.299215i
$345$	−33.4789	+	28.0921i	−1.80244	+	1.51243i
$346$	9.22028	−	3.35591i	0.495685	−	0.180415i
$347$	−28.3245	−	10.3093i	−1.52054	−	0.553431i	−0.559257	−	0.828994i	$-0.688914\pi$
$347$	−28.3245	−	10.3093i	−1.52054	−	0.553431i	−0.961283	+	0.275563i	$0.911136\pi$
$348$	−0.219929	−	0.184542i	−0.0117894	−	0.00989249i
$349$	−17.5326	+	30.3674i	−0.938501	+	1.62553i	−0.170232	+	0.985404i	$0.554452\pi$
$349$	−17.5326	+	30.3674i	−0.938501	+	1.62553i	−0.768269	+	0.640127i	$0.778882\pi$
$350$	1.91550	+	3.31774i	0.102388	+	0.177341i
$351$	−4.74577	+	26.9146i	−0.253310	+	1.43659i
$352$	−0.699745	+	3.96845i	−0.0372965	+	0.211519i
$353$	−6.77053	−	11.7269i	−0.360359	−	0.624160i	0.627661	−	0.778487i	$-0.284012\pi$
$353$	−6.77053	−	11.7269i	−0.360359	−	0.624160i	−0.988020	+	0.154327i	$0.950679\pi$
$354$	2.25325	−	3.90275i	0.119759	−	0.207429i
$355$	32.4700	+	27.2456i	1.72333	+	1.44605i
$356$	5.60127	+	2.03870i	0.296867	+	0.108051i
$357$	0.142493	−	0.0518630i	0.00754151	−	0.00274488i
$358$	−6.73989	+	5.65544i	−0.356214	+	0.298899i
$359$	−4.08199	−	23.1501i	−0.215439	−	1.22182i	−0.880143	−	0.474708i	$-0.842554\pi$
$359$	−4.08199	−	23.1501i	−0.215439	−	1.22182i	0.664704	−	0.747107i	$-0.268558\pi$
$360$	−4.99344			−0.263177
$361$		0			0
$362$	14.5278			0.763562
$363$	1.16802	+	6.62415i	0.0613050	+	0.347678i
$364$	−1.65795	+	1.39119i	−0.0869004	+	0.0729181i
$365$	−4.93928	+	1.79775i	−0.258534	+	0.0940986i
$366$	−4.92254	−	1.79166i	−0.257306	−	0.0936516i
$367$	−9.72331	−	8.15883i	−0.507553	−	0.425887i	0.352714	−	0.935731i	$-0.385259\pi$
$367$	−9.72331	−	8.15883i	−0.507553	−	0.425887i	−0.860267	+	0.509844i	$0.829703\pi$
$368$	4.60465	−	7.97549i	0.240034	−	0.415751i
$369$	−5.31318	−	9.20269i	−0.276593	−	0.479073i
$370$	0.929920	−	5.27384i	0.0483443	−	0.274174i
$371$	−0.763905	+	4.33232i	−0.0396600	+	0.224923i
$372$	−2.23420	−	3.86975i	−0.115838	−	0.200637i
$373$	−1.32475	+	2.29454i	−0.0685930	+	0.118807i	−0.898282	−	0.439419i	$-0.855184\pi$
$373$	−1.32475	+	2.29454i	−0.0685930	+	0.118807i	0.829689	+	0.558226i	$0.188518\pi$
$374$	−0.823874	−	0.691312i	−0.0426015	−	0.0357469i
$375$	−16.3139	−	5.93779i	−0.842448	−	0.306626i
$376$	−2.06608	+	0.751992i	−0.106550	+	0.0387810i
$377$	−0.837782	+	0.702983i	−0.0431480	+	0.0362055i
$378$	0.429282	+	2.43458i	0.0220799	+	0.125221i
$379$	18.1672			0.933187			0.466593	−	0.884472i	$-0.345481\pi$
$379$	18.1672			0.933187			0.466593	+	0.884472i	$0.345481\pi$
$380$		0			0
$381$	18.0806			0.926297
$382$	2.21057	+	12.5368i	0.113103	+	0.641436i
$383$	17.6254	−	14.7895i	0.900616	−	0.755706i	−0.0696951	−	0.997568i	$-0.522203\pi$
$383$	17.6254	−	14.7895i	0.900616	−	0.755706i	0.970311	+	0.241862i	$0.0777582\pi$
$384$	−1.20664	+	0.439181i	−0.0615761	+	0.0224119i
$385$	−6.19201	−	2.25371i	−0.315574	−	0.114860i
$386$	13.3890	+	11.2347i	0.681481	+	0.571830i
$387$	−3.80699	+	6.59390i	−0.193520	+	0.335187i
$388$	−2.04238	−	3.53750i	−0.103686	−	0.179590i
$389$	−2.87746	+	16.3189i	−0.145893	+	0.827400i	0.820753	+	0.571283i	$0.193554\pi$
$389$	−2.87746	+	16.3189i	−0.145893	+	0.827400i	−0.966646	+	0.256117i	$0.917557\pi$
$390$	4.03090	−	22.8604i	0.204113	−	1.15758i
$391$	1.22895	+	2.12860i	0.0621506	+	0.107648i
$392$	3.40211	−	5.89263i	0.171833	−	0.297623i
$393$	15.5827	+	13.0754i	0.786042	+	0.659568i
$394$	23.0331	+	8.38335i	1.16039	+	0.422347i
$395$	−35.4347	+	12.8972i	−1.78291	+	0.648927i
$396$	4.17085	−	3.49976i	0.209593	−	0.175869i
$397$	−3.09004	−	17.5245i	−0.155085	−	0.879529i	−0.958708	−	0.284391i	$-0.908209\pi$
$397$	−3.09004	−	17.5245i	−0.155085	−	0.879529i	0.803624	−	0.595138i	$-0.202902\pi$
$398$	16.4661			0.825371
$399$		0			0
$400$	8.65833			0.432916
$401$	5.31736	+	30.1563i	0.265536	+	1.50593i	0.767503	+	0.641045i	$0.221499\pi$
$401$	5.31736	+	30.1563i	0.265536	+	1.50593i	−0.501967	+	0.864887i	$0.667390\pi$
$402$	0.145349	−	0.121962i	0.00724933	−	0.00608291i
$403$	−15.9951	+	5.82175i	−0.796775	+	0.290002i
$404$	−0.399630	−	0.145453i	−0.0198823	−	0.00723658i
$405$	−8.83580	−	7.41412i	−0.439054	−	0.368410i
$406$	−0.0494633	+	0.0856730i	−0.00245482	+	0.00425188i
$407$	2.91955	+	5.05682i	0.144717	+	0.250657i
$408$	0.0595113	−	0.337505i	0.00294625	−	0.0167090i
$409$	1.58771	−	9.00437i	0.0785074	−	0.445237i	−0.920062	−	0.391772i	$-0.871862\pi$
$409$	1.58771	−	9.00437i	0.0785074	−	0.445237i	0.998570	−	0.0534654i	$-0.0170267\pi$
$410$	14.5329	+	25.1717i	0.717729	+	1.24314i
$411$	−1.41726	+	2.45477i	−0.0699083	+	0.121085i
$412$	−3.47492	−	2.91580i	−0.171197	−	0.143651i
$413$	−1.45919	−	0.531101i	−0.0718020	−	0.0261338i
$414$	−11.6927	+	4.25578i	−0.574663	+	0.209160i
$415$	−9.31081	+	7.81270i	−0.457050	+	0.383510i
$416$	0.849399	+	4.81718i	0.0416452	+	0.236182i
$417$	−21.9121			−1.07304
$418$		0			0
$419$	12.6157			0.616315			0.308158	−	0.951335i	$-0.400288\pi$
$419$	12.6157			0.616315			0.308158	+	0.951335i	$0.400288\pi$
$420$	−0.364618	−	2.06785i	−0.0177915	−	0.100901i
$421$	25.4751	−	21.3761i	1.24158	−	1.04181i	0.244180	−	0.969730i	$-0.421481\pi$
$421$	25.4751	−	21.3761i	1.24158	−	1.04181i	0.997399	−	0.0720781i	$-0.0229631\pi$
$422$	−25.8232	+	9.39887i	−1.25705	+	0.457530i
$423$	2.79157	+	1.01605i	0.135731	+	0.0494019i
$424$	7.61633	+	6.39086i	0.369881	+	0.310367i
$425$	−1.15542	+	2.00125i	−0.0560463	+	0.0970750i
$426$	−7.36363	−	12.7542i	−0.356769	−	0.617942i
$427$	−0.313444	+	1.77763i	−0.0151686	+	0.0860255i
$428$	−0.550728	+	3.12333i	−0.0266204	+	0.150972i
$429$	12.6553	+	21.9196i	0.611004	+	1.05829i
$430$	10.4131	−	18.0360i	0.502164	−	0.869773i
$431$	−17.6125	−	14.7786i	−0.848363	−	0.711861i	0.111065	−	0.993813i	$-0.464574\pi$
$431$	−17.6125	−	14.7786i	−0.848363	−	0.711861i	−0.959429	+	0.281952i	$0.909018\pi$
$432$	5.25026	+	1.91094i	0.252603	+	0.0919400i
$433$	−32.6160	+	11.8713i	−1.56743	+	0.570496i	−0.972422	−	0.233227i	$-0.925072\pi$
$433$	−32.6160	+	11.8713i	−1.56743	+	0.570496i	−0.595004	+	0.803723i	$0.702849\pi$
$434$	−1.17948	+	0.989705i	−0.0566171	+	0.0475074i
$435$	−0.184245	−	1.04491i	−0.00883389	−	0.0500995i
$436$	−6.78112			−0.324757
$437$		0			0
$438$	1.82629			0.0872637
$439$	−6.33500	−	35.9276i	−0.302353	−	1.71473i	−0.635709	−	0.771929i	$-0.719292\pi$
$439$	−6.33500	−	35.9276i	−0.302353	−	1.71473i	0.333356	−	0.942801i	$-0.391819\pi$
$440$	−11.4083	+	9.57273i	−0.543871	+	0.456362i
$441$	−8.63903	+	3.14435i	−0.411383	+	0.149731i
$442$	−1.22677	−	0.446509i	−0.0583516	−	0.0212383i
$443$	9.00738	+	7.55809i	0.427953	+	0.359096i	0.831179	−	0.556005i	$-0.187667\pi$
$443$	9.00738	+	7.55809i	0.427953	+	0.359096i	−0.403225	+	0.915101i	$0.632111\pi$
$444$	−0.930333	+	1.61138i	−0.0441517	+	0.0764729i
$445$	11.0146	+	19.0779i	0.522143	+	0.904378i
$446$	3.53732	−	20.0611i	0.167497	−	0.949921i
$447$	3.02041	−	17.1296i	0.142860	−	0.810201i
$448$	0.221232	+	0.383185i	0.0104522	+	0.0181038i
$449$	4.34551	−	7.52664i	0.205077	−	0.355204i	−0.745080	−	0.666975i	$-0.767589\pi$
$449$	4.34551	−	7.52664i	0.205077	−	0.355204i	0.950157	+	0.311771i	$0.100922\pi$
$450$	−8.96166	−	7.51973i	−0.422457	−	0.354483i
$451$	−29.7810	−	10.8394i	−1.40233	−	0.510407i
$452$	9.43860	−	3.43537i	0.443955	−	0.161586i
$453$	−9.00363	+	7.55494i	−0.423027	+	0.354962i
$454$	−3.84619	−	21.8128i	−0.180511	−	1.02373i
$455$	−7.99866			−0.374983
$456$		0			0
$457$	−13.0286			−0.609454			−0.304727	−	0.952440i	$-0.598565\pi$
$457$	−13.0286			−0.609454			−0.304727	+	0.952440i	$0.598565\pi$
$458$	2.20790	+	12.5216i	0.103168	+	0.585096i
$459$	−1.14232	+	0.958516i	−0.0533187	+	0.0447397i
$460$	31.9824	−	11.6406i	1.49119	−	0.542748i
$461$	−8.49726	−	3.09275i	−0.395757	−	0.144044i	0.136473	−	0.990644i	$-0.456423\pi$
$461$	−8.49726	−	3.09275i	−0.395757	−	0.144044i	−0.532230	+	0.846600i	$0.678646\pi$
$462$	1.75385	+	1.47166i	0.0815966	+	0.0684677i
$463$	8.86025	−	15.3464i	0.411771	−	0.713208i	−0.583313	−	0.812248i	$-0.698244\pi$
$463$	8.86025	−	15.3464i	0.411771	−	0.713208i	0.995083	+	0.0990396i	$0.0315771\pi$
$464$	0.111791	+	0.193627i	0.00518976	+	0.00898892i
$465$	2.86762	−	16.2631i	0.132983	−	0.754182i
$466$	−1.50757	+	8.54987i	−0.0698369	+	0.396065i
$467$	3.93886	+	6.82231i	0.182269	+	0.315699i	0.942653	−	0.333775i	$-0.108323\pi$
$467$	3.93886	+	6.82231i	0.182269	+	0.315699i	−0.760384	+	0.649474i	$0.774989\pi$
$468$	3.30455	−	5.72364i	0.152753	−	0.264576i
$469$	−0.0500837	−	0.0420252i	−0.00231265	−	0.00194055i
$470$	−7.63566	−	2.77915i	−0.352207	−	0.128193i
$471$	19.7772	−	7.19830i	0.911284	−	0.331680i
$472$	−2.68845	+	2.25588i	−0.123746	+	0.103835i
$473$	3.94322	+	22.3631i	0.181309	+	1.02826i
$474$	13.1019			0.601792
$475$		0			0
$476$	−0.118090			−0.00541266
$477$	−2.33272	−	13.2295i	−0.106808	−	0.605738i
$478$	16.7571	−	14.0609i	0.766454	−	0.643131i
$479$	28.3598	−	10.3221i	1.29579	−	0.471629i	0.400167	−	0.916442i	$-0.368952\pi$
$479$	28.3598	−	10.3221i	1.29579	−	0.471629i	0.895624	+	0.444813i	$0.146730\pi$
$480$	−4.45940	−	1.62309i	−0.203543	−	0.0740835i
$481$	5.42965	+	4.55602i	0.247571	+	0.207737i
$482$	9.48160	−	16.4226i	0.431875	−	0.748030i
$483$	−2.61617	−	4.53134i	−0.119040	−	0.206183i
$484$	0.909614	−	5.15868i	0.0413461	−	0.234485i
$485$	2.62141	−	14.8668i	0.119032	−	0.675065i
$486$	−6.37701	−	11.0453i	−0.289267	−	0.501025i
$487$	−17.8850	+	30.9777i	−0.810445	+	1.40373i	0.102107	+	0.994773i	$0.467442\pi$
$487$	−17.8850	+	30.9777i	−0.810445	+	1.40373i	−0.912553	+	0.408959i	$0.865892\pi$
$488$	3.12512	+	2.62228i	0.141467	+	0.118705i
$489$	16.6181	+	6.04851i	0.751498	+	0.273523i
$490$	23.6300	−	8.60061i	1.06749	−	0.388536i
$491$	−13.9976	+	11.7454i	−0.631705	+	0.530063i	−0.901458	−	0.432866i	$-0.857502\pi$
$491$	−13.9976	+	11.7454i	−0.631705	+	0.530063i	0.269753	+	0.962929i	$0.413058\pi$
$492$	−1.75366	−	9.94550i	−0.0790611	−	0.448378i
$493$	−0.0596724			−0.00268751
$494$		0			0
$495$	20.1219			0.904413
$496$	0.604270	+	3.42699i	0.0271325	+	0.153876i
$497$	−3.88742	+	3.26193i	−0.174375	+	0.146318i
$498$	3.96837	−	1.44437i	0.177827	−	0.0647237i
$499$	−16.6307	−	6.05307i	−0.744491	−	0.270972i	−0.0582051	−	0.998305i	$-0.518538\pi$
$499$	−16.6307	−	6.05307i	−0.744491	−	0.270972i	−0.686286	+	0.727332i	$0.740760\pi$
$500$	10.3570	+	8.69058i	0.463181	+	0.388655i
$501$	6.63407	−	11.4905i	0.296388	−	0.513360i
$502$	−1.45138	−	2.51386i	−0.0647782	−	0.112199i
$503$	−1.76952	+	10.0354i	−0.0788989	+	0.447458i	0.919608	+	0.392837i	$0.128506\pi$
$503$	−1.76952	+	10.0354i	−0.0788989	+	0.447458i	−0.998507	+	0.0546212i	$0.982605\pi$
$504$	0.103812	−	0.588748i	0.00462416	−	0.0262249i
$505$	−0.785853	−	1.36114i	−0.0349700	−	0.0605698i
$506$	−18.5552	+	32.1386i	−0.824881	+	1.42874i
$507$	10.7482	+	9.01878i	0.477343	+	0.400538i
$508$	−13.2314	−	4.81584i	−0.587050	−	0.213669i
$509$	7.92745	−	2.88536i	0.351378	−	0.127891i	−0.160300	−	0.987068i	$-0.551246\pi$
$509$	7.92745	−	2.88536i	0.351378	−	0.127891i	0.511678	+	0.859177i	$0.329024\pi$
$510$	0.970246	−	0.814133i	0.0429632	−	0.0360504i
$511$	−0.109276	−	0.619738i	−0.00483411	−	0.0274156i
$512$	1.00000			0.0441942
$513$		0			0
$514$	22.9050			1.01030
$515$	−2.91111	−	16.5098i	−0.128279	−	0.727507i
$516$	−5.54315	+	4.65125i	−0.244024	+	0.204760i
$517$	8.32563	−	3.03028i	0.366161	−	0.133272i
$518$	0.602476	+	0.219283i	0.0264713	+	0.00963476i
$519$	−9.65170	−	8.09874i	−0.423663	−	0.355495i
$520$	−9.03879	+	15.6556i	−0.396377	+	0.686545i
$521$	−4.48183	−	7.76275i	−0.196352	−	0.340092i	0.750991	−	0.660313i	$-0.229576\pi$
$521$	−4.48183	−	7.76275i	−0.196352	−	0.340092i	−0.947343	+	0.320221i	$0.896243\pi$
$522$	0.0524574	−	0.297501i	0.00229600	−	0.0130213i
$523$	−0.371595	+	2.10742i	−0.0162487	+	0.0921512i	−0.991854	−	0.127382i	$-0.959342\pi$
$523$	−0.371595	+	2.10742i	−0.0162487	+	0.0921512i	0.975605	+	0.219534i	$0.0704536\pi$
$524$	−7.92075	−	13.7191i	−0.346020	−	0.599324i
$525$	2.45965	−	4.26024i	0.107348	−	0.185932i
$526$	−3.87799	−	3.25402i	−0.169089	−	0.141882i
$527$	−0.872738	−	0.317651i	−0.0380171	−	0.0138371i
$528$	4.86236	−	1.76976i	0.211607	−	0.0770187i
$529$	47.3501	−	39.7315i	2.05870	−	1.72746i
$530$	6.38059	+	36.1861i	0.277155	+	1.57182i
$531$	4.74186			0.205779
$532$		0			0
$533$	−38.4702			−1.66633
$534$	−1.32912	−	7.53779i	−0.0575164	−	0.326192i
$535$	−8.97882	+	7.53412i	−0.388188	+	0.325729i
$536$	−0.138852	+	0.0505379i	−0.00599748	+	0.00218290i
$537$	10.6164	+	3.86405i	0.458131	+	0.166746i
$538$	−15.8892	−	13.3327i	−0.685034	−	0.574812i
$539$	−13.7094	+	23.7454i	−0.590506	+	1.02279i
$540$	10.3244	+	17.8823i	0.444290	+	0.769533i
$541$	−2.03369	+	11.5336i	−0.0874351	+	0.495869i	0.909369	+	0.415990i	$0.136565\pi$
$541$	−2.03369	+	11.5336i	−0.0874351	+	0.495869i	−0.996805	+	0.0798797i	$0.974546\pi$
$542$	1.09306	−	6.19907i	0.0469511	−	0.266273i
$543$	−9.32739	−	16.1555i	−0.400277	−	0.693299i
$544$	−0.133446	+	0.231136i	−0.00572147	+	0.00990988i
$545$	−19.1979	−	16.1090i	−0.822348	−	0.690032i
$546$	2.61154	+	0.950522i	0.111763	+	0.0406786i
$547$	23.4826	−	8.54697i	1.00404	−	0.365442i	0.212901	−	0.977074i	$-0.431709\pi$
$547$	23.4826	−	8.54697i	1.00404	−	0.365442i	0.791143	+	0.611632i	$0.209487\pi$
$548$	1.69099	−	1.41891i	0.0722357	−	0.0606129i
$549$	−0.957157	−	5.42830i	−0.0408504	−	0.231674i
$550$	−34.8902			−1.48772
$551$		0			0
$552$	−11.8255			−0.503325
$553$	−0.783956	−	4.44603i	−0.0333372	−	0.189065i
$554$	5.49720	−	4.61270i	0.233554	−	0.195975i
$555$	−6.46179	+	2.35190i	−0.274288	+	0.0998326i
$556$	16.0353	+	5.83638i	0.680049	+	0.247518i
$557$	7.04429	+	5.91086i	0.298476	+	0.250451i	0.779710	−	0.626141i	$-0.215367\pi$
$557$	7.04429	+	5.91086i	0.298476	+	0.250451i	−0.481234	+	0.876592i	$0.659811\pi$
$558$	2.35089	−	4.07185i	0.0995209	−	0.172375i
$559$	13.7823	+	23.8717i	0.582930	+	1.00966i
$560$	−0.283953	+	1.61038i	−0.0119992	+	0.0680509i
$561$	−0.239811	+	1.36004i	−0.0101248	+	0.0574207i
$562$	−1.38696	−	2.40228i	−0.0585052	−	0.101334i
$563$	−9.86122	+	17.0801i	−0.415601	+	0.719842i	−0.995491	−	0.0948526i	$-0.969762\pi$
$563$	−9.86122	+	17.0801i	−0.415601	+	0.719842i	0.579890	+	0.814694i	$0.303095\pi$
$564$	2.16276	+	1.81477i	0.0910684	+	0.0764155i
$565$	34.8824	+	12.6962i	1.46751	+	0.534131i
$566$	−7.28131	+	2.65018i	−0.306056	+	0.111395i
$567$	1.05785	−	0.887642i	0.0444256	−	0.0372775i
$568$	1.99159	+	11.2949i	0.0835653	+	0.473923i
$569$	22.1469			0.928446			0.464223	−	0.885718i	$-0.346334\pi$
$569$	22.1469			0.928446			0.464223	+	0.885718i	$0.346334\pi$
$570$		0			0
$571$	−3.02145			−0.126444			−0.0632218	−	0.998000i	$-0.520138\pi$
$571$	−3.02145			−0.126444			−0.0632218	+	0.998000i	$0.520138\pi$
$572$	−3.42280	−	19.4117i	−0.143114	−	0.811642i
$573$	12.5222	−	10.5073i	0.523121	−	0.438951i
$574$	−3.26999	+	1.19018i	−0.136487	+	0.0496771i
$575$	74.9284	+	27.2717i	3.12473	+	1.13731i
$576$	−1.03503	−	0.868497i	−0.0431264	−	0.0361874i
$577$	−1.15469	+	1.99998i	−0.0480704	+	0.0832603i	−0.889059	−	0.457792i	$-0.848641\pi$
$577$	−1.15469	+	1.99998i	−0.0480704	+	0.0832603i	0.840989	+	0.541052i	$0.181974\pi$
$578$	8.46438	+	14.6607i	0.352072	+	0.609807i
$579$	3.89722	−	22.1022i	0.161963	−	0.918538i
$580$	−0.143485	+	0.813741i	−0.00595787	+	0.0337888i
$581$	−0.727582	−	1.26021i	−0.0301852	−	0.0522823i
$582$	−2.62258	+	4.54243i	−0.108709	+	0.188290i
$583$	−30.6913	−	25.7531i	−1.27110	−	1.06658i
$584$	−1.33649	−	0.486442i	−0.0553042	−	0.0201291i
$585$	22.9523	−	8.35396i	0.948962	−	0.345394i
$586$	−0.599713	+	0.503219i	−0.0247739	+	0.0207878i
$587$	4.87761	+	27.6623i	0.201320	+	1.14174i	0.903126	+	0.429376i	$0.141266\pi$
$587$	4.87761	+	27.6623i	0.201320	+	1.14174i	−0.701805	+	0.712369i	$0.747622\pi$
$588$	−8.73716			−0.360315
$589$		0			0
$590$	−12.9702			−0.533975
$591$	−5.46548	−	30.9963i	−0.224820	−	1.27502i
$592$	1.11002	−	0.931417i	0.0456215	−	0.0382810i
$593$	11.3645	−	4.13636i	0.466686	−	0.169860i	−0.0979645	−	0.995190i	$-0.531233\pi$
$593$	11.3645	−	4.13636i	0.466686	−	0.169860i	0.564651	+	0.825330i	$0.309011\pi$
$594$	−21.1568	−	7.70045i	−0.868075	−	0.315953i
$595$	−0.334324	−	0.280531i	−0.0137059	−	0.0115006i
$596$	−6.77288	+	11.7310i	−0.277428	+	0.480519i
$597$	−10.5719	−	18.3110i	−0.432679	−	0.749421i
$598$	−7.82237	+	44.3628i	−0.319880	+	1.81413i
$599$	3.38658	−	19.2062i	0.138372	−	0.784745i	−0.834080	−	0.551643i	$-0.814001\pi$
$599$	3.38658	−	19.2062i	0.138372	−	0.784745i	0.972452	−	0.233103i	$-0.0748878\pi$
$600$	−5.55899	−	9.62845i	−0.226945	−	0.393080i
$601$	19.4816	−	33.7431i	0.794671	−	1.37641i	−0.128376	−	0.991726i	$-0.540977\pi$
$601$	19.4816	−	33.7431i	0.794671	−	1.37641i	0.923048	−	0.384685i	$-0.125690\pi$
$602$	1.91004	+	1.60271i	0.0778474	+	0.0653217i
$603$	0.187608	+	0.0682838i	0.00764000	+	0.00278073i
$604$	8.60117	−	3.13057i	0.349977	−	0.127381i
$605$	14.8300	−	12.4438i	0.602923	−	0.505913i
$606$	0.0948275	+	0.537793i	0.00385210	+	0.0218464i
$607$	8.46029			0.343393			0.171696	−	0.985150i	$-0.445075\pi$
$607$	8.46029			0.343393			0.171696	+	0.985150i	$0.445075\pi$
$608$		0			0
$609$	0.127030			0.00514750
$610$	2.61807	+	14.8478i	0.106003	+	0.601170i
$611$	8.23867	−	6.91306i	0.333301	−	0.279673i
$612$	0.338863	−	0.123336i	0.0136977	−	0.00498556i
$613$	2.73914	+	0.996964i	0.110633	+	0.0402670i	0.396743	−	0.917930i	$-0.370140\pi$
$613$	2.73914	+	0.996964i	0.110633	+	0.0402670i	−0.286111	+	0.958197i	$0.592363\pi$
$614$	−21.5785	−	18.1065i	−0.870839	−	0.730721i
$615$	18.6614	−	32.3225i	0.752500	−	1.30337i
$616$	−0.891491	−	1.54411i	−0.0359192	−	0.0622139i
$617$	−0.524253	+	2.97318i	−0.0211056	+	0.119696i	−0.993540	−	0.113479i	$-0.963800\pi$
$617$	−0.524253	+	2.97318i	−0.0211056	+	0.119696i	0.972435	+	0.233175i	$0.0749116\pi$
$618$	−1.01147	+	5.73632i	−0.0406872	+	0.230749i
$619$	1.96406	+	3.40186i	0.0789423	+	0.136732i	0.902794	−	0.430074i	$-0.141512\pi$
$619$	1.96406	+	3.40186i	0.0789423	+	0.136732i	−0.823852	+	0.566806i	$0.808179\pi$
$620$	−6.43028	+	11.1376i	−0.258246	+	0.447295i
$621$	39.4163	+	33.0742i	1.58172	+	1.32722i
$622$	−3.63499	−	1.32303i	−0.145750	−	0.0530485i
$623$	−2.47836	+	0.902048i	−0.0992933	+	0.0361398i
$624$	4.81157	−	4.03739i	0.192617	−	0.161625i
$625$	1.15910	+	6.57360i	0.0463641	+	0.262944i
$626$	30.3878			1.21454
$627$		0			0
$628$	−16.3903			−0.654043
$629$	0.0671559	+	0.380860i	0.00267768	+	0.0151859i
$630$	1.69251	−	1.42018i	0.0674312	−	0.0565815i
$631$	−9.52539	+	3.46696i	−0.379200	+	0.138018i	−0.524586	−	0.851358i	$-0.675780\pi$
$631$	−9.52539	+	3.46696i	−0.379200	+	0.138018i	0.145386	+	0.989375i	$0.453558\pi$
$632$	−9.58804	−	3.48976i	−0.381392	−	0.138815i
$633$	27.0315	+	22.6821i	1.07440	+	0.901532i
$634$	−2.66402	+	4.61421i	−0.105802	+	0.183254i
$635$	−26.0189	−	45.0661i	−1.03253	−	1.78839i
$636$	2.21694	−	12.5729i	0.0879073	−	0.498547i
$637$	−5.77950	+	32.7772i	−0.228992	+	1.29868i
$638$	−0.450480	−	0.780255i	−0.0178347	−	0.0308906i
$639$	7.74820	−	13.4203i	0.306514	−	0.530898i
$640$	2.83108	+	2.37556i	0.111908	+	0.0939023i
$641$	−7.78094	−	2.83203i	−0.307329	−	0.111859i	0.183752	−	0.982973i	$-0.441176\pi$
$641$	−7.78094	−	2.83203i	−0.307329	−	0.111859i	−0.491081	+	0.871114i	$0.663398\pi$
$642$	3.82687	−	1.39287i	0.151035	−	0.0549721i
$643$	28.2318	−	23.6893i	1.11336	−	0.934216i	0.115105	−	0.993353i	$-0.463279\pi$
$643$	28.2318	−	23.6893i	1.11336	−	0.934216i	0.998250	+	0.0591372i	$0.0188349\pi$
$644$	0.707578	+	4.01287i	0.0278825	+	0.158129i
$645$	−26.7425			−1.05298
$646$		0			0
$647$	−20.1901			−0.793753			−0.396876	−	0.917872i	$-0.629906\pi$
$647$	−20.1901			−0.793753			−0.396876	+	0.917872i	$0.629906\pi$
$648$	−0.541955	−	3.07358i	−0.0212900	−	0.120742i
$649$	10.8336	−	9.09046i	0.425255	−	0.356832i
$650$	−39.7980	+	14.4853i	−1.56101	+	0.568160i
$651$	1.85787	+	0.676210i	0.0728158	+	0.0265028i
$652$	−10.5502	−	8.85263i	−0.413176	−	0.346696i
$653$	11.0194	−	19.0861i	0.431221	−	0.746897i	−0.565757	−	0.824572i	$-0.691416\pi$
$653$	11.0194	−	19.0861i	0.431221	−	0.746897i	0.996979	+	0.0776744i	$0.0247495\pi$
$654$	4.35375	+	7.54091i	0.170245	+	0.294873i
$655$	10.1664	−	57.6563i	0.397232	−	2.25282i
$656$	−1.36569	+	7.74524i	−0.0533214	+	0.302401i
$657$	0.960837	+	1.66422i	0.0374858	+	0.0649273i
$658$	0.486417	−	0.842500i	0.0189625	−	0.0328441i
$659$	−20.8530	−	17.4977i	−0.812316	−	0.681614i	0.138843	−	0.990314i	$-0.455662\pi$
$659$	−20.8530	−	17.4977i	−0.812316	−	0.681614i	−0.951159	+	0.308700i	$0.900106\pi$
$660$	17.9699	+	6.54052i	0.699478	+	0.254589i
$661$	8.37102	−	3.04680i	0.325595	−	0.118507i	−0.174051	−	0.984737i	$-0.555686\pi$
$661$	8.37102	−	3.04680i	0.325595	−	0.118507i	0.499646	+	0.866230i	$0.333464\pi$
$662$	−15.7407	+	13.2080i	−0.611780	+	0.513344i
$663$	0.291099	+	1.65090i	0.0113053	+	0.0641158i
$664$	−3.28878			−0.127629
$665$		0			0
$666$	−1.95784			−0.0758648
$667$	0.357547	+	2.02775i	0.0138443	+	0.0785147i
$668$	−7.91539	+	6.64180i	−0.306255	+	0.256979i
$669$	−24.5800	+	8.94637i	−0.950316	+	0.345887i
$670$	−0.513157	−	0.186774i	−0.0198250	−	0.00721570i
$671$	−12.5932	−	10.5669i	−0.486155	−	0.407932i
$672$	0.284079	−	0.492039i	0.0109586	−	0.0189808i
$673$	−17.8505	−	30.9180i	−0.688087	−	1.19180i	−0.972456	−	0.233086i	$-0.925118\pi$
$673$	−17.8505	−	30.9180i	−0.688087	−	1.19180i	0.284370	−	0.958715i	$-0.408216\pi$
$674$	2.30647	−	13.0806i	0.0888418	−	0.503847i
$675$	−8.40038	+	47.6409i	−0.323331	+	1.83370i
$676$	−5.46334	−	9.46279i	−0.210129	−	0.363953i
$677$	13.6924	−	23.7160i	0.526243	−	0.911480i	−0.473290	−	0.880907i	$-0.656934\pi$
$677$	13.6924	−	23.7160i	0.526243	−	0.911480i	0.999533	−	0.0305727i	$-0.00973312\pi$
$678$	−9.88024	−	8.29051i	−0.379448	−	0.318395i
$679$	1.69836	+	0.618152i	0.0651770	+	0.0237225i
$680$	−0.926876	+	0.337355i	−0.0355441	+	0.0129370i
$681$	−21.7874	+	18.2818i	−0.834897	+	0.700562i
$682$	−2.43501	−	13.8096i	−0.0932414	−	0.528798i
$683$	−38.1521			−1.45985			−0.729925	−	0.683528i	$-0.760445\pi$
$683$	−38.1521			−1.45985			−0.729925	+	0.683528i	$0.760445\pi$
$684$		0			0
$685$	8.15806			0.311703
$686$	1.06062	+	6.01507i	0.0404947	+	0.229657i
$687$	12.5070	−	10.4946i	0.477173	−	0.400396i
$688$	5.29537	−	1.92736i	0.201884	−	0.0734799i
$689$	−45.7003	−	16.6335i	−1.74104	−	0.633687i
$690$	−33.4789	−	28.0921i	−1.27452	−	1.06945i
$691$	14.1029	−	24.4269i	0.536499	−	0.929244i	−0.462590	−	0.886572i	$-0.653080\pi$
$691$	14.1029	−	24.4269i	0.536499	−	0.929244i	0.999089	−	0.0426714i	$-0.0135868\pi$
$692$	4.90601	+	8.49745i	0.186498	+	0.323025i
$693$	−0.418329	+	2.37246i	−0.0158910	+	0.0901224i
$694$	5.23416	−	29.6844i	0.198686	−	1.12680i
$695$	31.5327	+	54.6162i	1.19610	+	2.07171i
$696$	0.143548	−	0.248633i	0.00544118	−	0.00942440i
$697$	−1.60796	−	1.34924i	−0.0609057	−	0.0511060i
$698$	−32.9506	−	11.9930i	−1.24720	−	0.453943i
$699$	10.4758	−	3.81286i	0.396230	−	0.144216i
$700$	−2.93471	+	2.46252i	−0.110922	+	0.0930743i
$701$	7.39998	+	41.9674i	0.279493	+	1.58509i	0.724317	+	0.689468i	$0.242155\pi$
$701$	7.39998	+	41.9674i	0.279493	+	1.58509i	−0.444823	+	0.895618i	$0.646733\pi$
$702$	−27.3298			−1.03150
$703$		0			0
$704$	−4.02967			−0.151874
$705$	1.81185	+	10.2755i	0.0682383	+	0.386998i
$706$	10.3731	−	8.70403i	0.390395	−	0.327580i
$707$	0.176822	−	0.0643578i	0.00665006	−	0.00242043i
$708$	4.23473	+	1.54132i	0.159151	+	0.0579262i
$709$	−17.3809	−	14.5843i	−0.652754	−	0.547726i	0.255151	−	0.966901i	$-0.417875\pi$
$709$	−17.3809	−	14.5843i	−0.652754	−	0.547726i	−0.907905	+	0.419176i	$0.862319\pi$
$710$	−21.1933	+	36.7079i	−0.795371	+	1.37762i
$711$	6.89310	+	11.9392i	0.258511	+	0.447755i
$712$	−1.03507	+	5.87019i	−0.0387910	+	0.219995i
$713$	−5.56490	+	31.5601i	−0.208407	+	1.18194i
$714$	0.0758187	+	0.131322i	0.00283744	+	0.00491460i
$715$	36.4233	−	63.0871i	1.36216	−	2.35932i
$716$	−6.73989	−	5.65544i	−0.251882	−	0.211354i
$717$	−26.3951	−	9.60704i	−0.985744	−	0.358781i
$718$	22.0896	−	8.03994i	0.824375	−	0.300048i
$719$	−28.9813	+	24.3182i	−1.08082	+	0.906916i	−0.995989	−	0.0894791i	$-0.971480\pi$
$719$	−28.9813	+	24.3182i	−1.08082	+	0.906916i	−0.0848319	+	0.996395i	$0.527035\pi$
$720$	−0.867101	−	4.91757i	−0.0323149	−	0.183267i
$721$	2.00709			0.0747481
$722$		0			0
$723$	−24.3503			−0.905596
$724$	2.52272	+	14.3070i	0.0937561	+	0.531717i
$725$	−1.48294	+	1.24434i	−0.0550751	+	0.0462135i
$726$	−6.32069	+	2.30054i	−0.234583	+	0.0853812i
$727$	18.3619	+	6.68318i	0.681005	+	0.247865i	0.659279	−	0.751899i	$-0.270862\pi$
$727$	18.3619	+	6.68318i	0.681005	+	0.247865i	0.0217258	+	0.999764i	$0.493084\pi$
$728$	−1.65795	−	1.39119i	−0.0614479	−	0.0515609i
$729$	−12.8701	+	22.2916i	−0.476670	+	0.825616i
$730$	−2.62814	−	4.55206i	−0.0972717	−	0.168479i
$731$	−0.261167	+	1.48115i	−0.00965961	+	0.0547824i
$732$	0.909649	−	5.15888i	0.0336216	−	0.190678i
$733$	−17.5550	−	30.4062i	−0.648410	−	1.12308i	−0.983503	−	0.180894i	$-0.942101\pi$
$733$	−17.5550	−	30.4062i	−0.648410	−	1.12308i	0.335092	−	0.942185i	$-0.391232\pi$
$734$	6.34644	−	10.9924i	0.234251	−	0.405735i
$735$	−24.7356	−	20.7557i	−0.912388	−	0.765584i
$736$	8.65391	+	3.14977i	0.318987	+	0.116102i
$737$	0.559527	−	0.203651i	0.0206104	−	0.00750158i
$738$	8.14026	−	6.83049i	0.299647	−	0.251434i
$739$	−2.82655	−	16.0302i	−0.103976	−	0.589680i	−0.991624	−	0.129157i	$-0.958773\pi$
$739$	−2.82655	−	16.0302i	−0.103976	−	0.589680i	0.887648	−	0.460523i	$-0.152338\pi$
$740$	5.35520			0.196861
$741$		0			0
$742$	−4.39915			−0.161498
$743$	5.78397	+	32.8025i	0.212193	+	1.20341i	0.885711	+	0.464237i	$0.153671\pi$
$743$	5.78397	+	32.8025i	0.212193	+	1.20341i	−0.673518	+	0.739171i	$0.735218\pi$
$744$	3.42300	−	2.87224i	0.125493	−	0.105301i
$745$	−47.0422	+	17.1220i	−1.72349	+	0.627301i
$746$	−2.48972	−	0.906183i	−0.0911550	−	0.0331777i
$747$	3.40400	+	2.85629i	0.124546	+	0.104506i
$748$	0.537746	−	0.931403i	0.0196619	−	0.0340555i
$749$	−0.701639	−	1.21528i	−0.0256373	−	0.0444052i
$750$	3.01470	−	17.0972i	0.110081	−	0.624301i
$751$	3.34445	−	18.9673i	0.122041	−	0.692127i	−0.860981	−	0.508637i	$-0.830150\pi$
$751$	3.34445	−	18.9673i	0.122041	−	0.692127i	0.983022	−	0.183490i	$-0.0587394\pi$
$752$	−1.09934	−	1.90411i	−0.0400888	−	0.0694358i
$753$	−1.86368	+	3.22800i	−0.0679164	+	0.117635i
$754$	−0.837782	−	0.702983i	−0.0305102	−	0.0256011i
$755$	31.7875	+	11.5697i	1.15687	+	0.421065i
$756$	−2.32305	+	0.845520i	−0.0844884	+	0.0307513i
$757$	−18.3433	+	15.3918i	−0.666697	+	0.559425i	−0.912086	−	0.409999i	$-0.865529\pi$
$757$	−18.3433	+	15.3918i	−0.666697	+	0.559425i	0.245389	+	0.969425i	$0.421084\pi$
$758$	3.15470	+	17.8912i	0.114584	+	0.649838i
$759$	47.6528			1.72969
$760$		0			0
$761$	−44.7968			−1.62388			−0.811941	−	0.583739i	$-0.801589\pi$
$761$	−44.7968			−1.62388			−0.811941	+	0.583739i	$0.801589\pi$
$762$	3.13966	+	17.8059i	0.113738	+	0.645040i
$763$	2.29844	−	1.92862i	0.0832090	−	0.0698207i
$764$	−11.9624	+	4.35397i	−0.432786	+	0.157521i
$765$	1.25234	+	0.455815i	0.0452785	+	0.0164800i
$766$	17.6254	+	14.7895i	0.636831	+	0.534365i
$767$	8.58341	−	14.8669i	0.309929	−	0.536813i
$768$	−0.642040	−	1.11205i	−0.0231676	−	0.0401275i
$769$	−5.51102	+	31.2546i	−0.198733	+	1.12707i	0.708269	+	0.705942i	$0.249476\pi$
$769$	−5.51102	+	31.2546i	−0.198733	+	1.12707i	−0.907002	+	0.421126i	$0.861635\pi$
$770$	1.14424	−	6.48929i	0.0412355	−	0.233858i
$771$	−14.7059	−	25.4714i	−0.529621	−	0.917330i
$772$	−8.73903	+	15.1364i	−0.314525	+	0.544772i
$773$	−17.0297	−	14.2896i	−0.612515	−	0.513961i	0.282926	−	0.959142i	$-0.408695\pi$
$773$	−17.0297	−	14.2896i	−0.612515	−	0.513961i	−0.895441	+	0.445181i	$0.853139\pi$
$774$	−7.15480	−	2.60413i	−0.257174	−	0.0936036i
$775$	−28.3127	+	10.3050i	−1.01702	+	0.370165i
$776$	3.12911	−	2.62563i	0.112328	−	0.0942547i
$777$	−0.142961	−	0.810770i	−0.00512868	−	0.0290862i
$778$	−16.5706			−0.594086
$779$		0			0
$780$	23.2130			0.831160
$781$	−8.02546	−	45.5147i	−0.287174	−	1.62864i
$782$	−1.88286	+	1.57991i	−0.0673309	+	0.0564973i
$783$	−1.17386	+	0.427251i	−0.0419504	+	0.0152687i
$784$	6.39388	+	2.32718i	0.228353	+	0.0831137i
$785$	−46.4023	−	38.9361i	−1.65617	−	1.38969i
$786$	−10.1709	+	17.6165i	−0.362783	+	0.628358i
$787$	−12.2298	−	21.1826i	−0.435945	−	0.755080i	0.561427	−	0.827526i	$-0.310253\pi$
$787$	−12.2298	−	21.1826i	−0.435945	−	0.755080i	−0.997372	+	0.0724468i	$0.976919\pi$
$788$	−4.25634	+	24.1389i	−0.151626	+	0.859913i
$789$	−1.12880	+	6.40172i	−0.0401862	+	0.227907i
$790$	−18.8544	−	32.6568i	−0.670810	−	1.16188i
$791$	−2.22213	+	3.84884i	−0.0790098	+	0.136849i
$792$	4.17085	+	3.49976i	0.148205	+	0.124358i
$793$	−18.7516	−	6.82504i	−0.665890	−	0.242364i
$794$	16.7217	−	6.08619i	0.593430	−	0.215991i
$795$	36.1440	−	30.3284i	1.28190	−	1.07564i
$796$	2.85931	+	16.2159i	0.101346	+	0.574759i
$797$	41.6933			1.47685			0.738426	−	0.674334i	$-0.235569\pi$
$797$	41.6933			1.47685			0.738426	+	0.674334i	$0.235569\pi$
$798$		0			0
$799$	0.586812			0.0207599
$800$	1.50350	+	8.52679i	0.0531569	+	0.301468i
$801$	6.16957	−	5.17689i	0.217991	−	0.182916i
$802$	−28.7748	+	10.4732i	−1.01607	+	0.369820i
$803$	5.38561	+	1.96020i	0.190054	+	0.0691740i
$804$	0.145349	+	0.121962i	0.00512605	+	0.00430127i
$805$	−7.52962	+	13.0417i	−0.265384	+	0.459659i
$806$	−8.51084	−	14.7412i	−0.299781	−	0.519237i
$807$	−4.62499	+	26.2296i	−0.162808	+	0.923327i
$808$	0.0738486	−	0.418817i	0.00259799	−	0.0147339i
$809$	24.6244	+	42.6507i	0.865748	+	1.49952i	0.866303	+	0.499519i	$0.166490\pi$
$809$	24.6244	+	42.6507i	0.865748	+	1.49952i	−0.000555336		1.00000i	$0.500177\pi$
$810$	5.76716	−	9.98901i	0.202637	−	0.350978i
$811$	39.8692	+	33.4542i	1.40000	+	1.17474i	0.961101	+	0.276197i	$0.0890741\pi$
$811$	39.8692	+	33.4542i	1.40000	+	1.17474i	0.438894	+	0.898539i	$0.355370\pi$
$812$	−0.0929607	−	0.0338349i	−0.00326228	−	0.00118737i
$813$	−7.59544	+	2.76451i	−0.266384	+	0.0969557i
$814$	−4.47302	+	3.75331i	−0.156779	+	0.131553i
$815$	−8.83840	−	50.1251i	−0.309596	−	1.75580i
$816$	0.342712			0.0119973
$817$		0			0
$818$	9.14328			0.319687
$819$	0.507796	+	2.87986i	0.0177438	+	0.100630i
$820$	−22.2657	+	18.6831i	−0.777552	+	0.652443i
$821$	39.7098	−	14.4532i	1.38588	−	0.504419i	0.461925	−	0.886919i	$-0.347159\pi$
$821$	39.7098	−	14.4532i	1.38588	−	0.504419i	0.923955	+	0.382500i	$0.124937\pi$
$822$	−2.66358	−	0.969463i	−0.0929030	−	0.0338139i
$823$	24.8789	+	20.8759i	0.867225	+	0.727688i	0.963512	−	0.267666i	$-0.0862523\pi$
$823$	24.8789	+	20.8759i	0.867225	+	0.727688i	−0.0962873	+	0.995354i	$0.530697\pi$
$824$	2.26809	−	3.92845i	0.0790127	−	0.136854i
$825$	22.4009	+	38.7995i	0.779899	+	1.35083i
$826$	0.269647	−	1.52925i	0.00938223	−	0.0532093i
$827$	−3.73615	+	21.1888i	−0.129919	+	0.736806i	0.848345	+	0.529443i	$0.177599\pi$
$827$	−3.73615	+	21.1888i	−0.129919	+	0.736806i	−0.978264	+	0.207363i	$0.933512\pi$
$828$	−6.22153	−	10.7760i	−0.216213	−	0.374492i
$829$	−2.82531	+	4.89357i	−0.0981269	+	0.169961i	−0.910909	−	0.412607i	$-0.864618\pi$
$829$	−2.82531	+	4.89357i	−0.0981269	+	0.169961i	0.812782	+	0.582567i	$0.197952\pi$
$830$	−9.31081	−	7.81270i	−0.323183	−	0.271183i
$831$	−8.65894	−	3.15160i	−0.300375	−	0.109328i
$832$	−4.59650	+	1.67299i	−0.159355	+	0.0580004i
$833$	−1.39114	+	1.16730i	−0.0482000	+	0.0404446i
$834$	−3.80499	−	21.5792i	−0.131756	−	0.747227i
$835$	−38.1871			−1.32152
$836$		0			0
$837$	−19.4427			−0.672037
$838$	2.19069	+	12.4240i	0.0756760	+	0.429180i
$839$	−8.17877	+	6.86280i	−0.282362	+	0.236930i	−0.772958	−	0.634457i	$-0.781224\pi$
$839$	−8.17877	+	6.86280i	−0.282362	+	0.236930i	0.490596	+	0.871387i	$0.336779\pi$
$840$	1.97312	−	0.718157i	0.0680792	−	0.0247788i
$841$	27.2041	+	9.90149i	0.938073	+	0.341431i
$842$	25.4751	+	21.3761i	0.877929	+	0.736670i
$843$	−1.78096	+	3.08471i	−0.0613395	+	0.106243i
$844$	−13.7402	−	23.7988i	−0.472958	−	0.819187i
$845$	7.01225	−	39.7685i	0.241229	−	1.36808i
$846$	−0.515861	+	2.92559i	−0.0177357	+	0.100584i
$847$	1.15887	+	2.00722i	0.0398192	+	0.0689689i
$848$	−4.97120	+	8.61038i	−0.170712	+	0.295682i
$849$	7.62201	+	6.39563i	0.261587	+	0.219497i
$850$	−2.17149	−	0.790356i	−0.0744813	−	0.0271090i
$851$	12.5398	−	4.56410i	0.429857	−	0.156455i
$852$	11.2817	−	9.46650i	0.386506	−	0.324317i
$853$	1.78277	+	10.1106i	0.0610410	+	0.346181i	0.999998	+	0.00214528i	$0.000682864\pi$
$853$	1.78277	+	10.1106i	0.0610410	+	0.346181i	−0.938957	+	0.344035i	$0.888206\pi$
$854$	−1.80505			−0.0617676
$855$		0			0
$856$	−3.17151			−0.108400
$857$	−6.48380	−	36.7715i	−0.221483	−	1.25609i	−0.869296	−	0.494291i	$-0.835428\pi$
$857$	−6.48380	−	36.7715i	−0.221483	−	1.25609i	0.647814	−	0.761799i	$-0.275683\pi$
$858$	−19.3891	+	16.2694i	−0.661932	+	0.555427i
$859$	22.8242	−	8.30732i	0.778751	−	0.283442i	0.0780991	−	0.996946i	$-0.475115\pi$
$859$	22.8242	−	8.30732i	0.778751	−	0.283442i	0.700652	+	0.713503i	$0.252893\pi$
$860$	19.5702	+	7.12297i	0.667339	+	0.242891i
$861$	3.42300	+	2.87224i	0.116655	+	0.0978855i
$862$	11.4957	−	19.9112i	0.391546	−	0.678178i
$863$	11.7864	+	20.4146i	0.401214	+	0.694922i	0.993873	−	0.110531i	$-0.0352552\pi$
$863$	11.7864	+	20.4146i	0.401214	+	0.694922i	−0.592659	+	0.805453i	$0.701922\pi$
$864$	−0.970209	+	5.50233i	−0.0330072	+	0.187193i
$865$	−6.29690	+	35.7115i	−0.214101	+	1.21423i
$866$	−17.3546	−	30.0591i	−0.589734	−	1.02145i
$867$	10.8689	−	18.8256i	0.369128	−	0.639349i
$868$	−1.17948	−	0.989705i	−0.0400343	−	0.0335928i
$869$	38.6367	+	14.0626i	1.31066	+	0.477041i
$870$	0.997039	−	0.362893i	0.0338028	−	0.0123032i
$871$	0.553682	−	0.464595i	0.0187608	−	0.0157422i
$872$	−1.17753	−	6.67810i	−0.0398762	−	0.226149i
$873$	−5.51908			−0.186793
$874$		0			0
$875$	−5.98217			−0.202234
$876$	0.317133	+	1.79855i	0.0107149	+	0.0607673i
$877$	−24.0830	+	20.2081i	−0.813227	+	0.682378i	−0.951376	−	0.308033i	$-0.900329\pi$
$877$	−24.0830	+	20.2081i	−0.813227	+	0.682378i	0.138149	+	0.990411i	$0.455885\pi$
$878$	34.2817	−	12.4775i	1.15695	−	0.421096i
$879$	0.944642	+	0.343822i	0.0318620	+	0.0115968i
$880$	−11.4083	−	9.57273i	−0.384575	−	0.322697i
$881$	20.8800	−	36.1653i	0.703466	−	1.21844i	−0.263776	−	0.964584i	$-0.584968\pi$
$881$	20.8800	−	36.1653i	0.703466	−	1.21844i	0.967242	−	0.253855i	$-0.0816985\pi$
$882$	−4.59673	−	7.96178i	−0.154780	−	0.268087i
$883$	0.0942980	−	0.534790i	0.00317338	−	0.0179971i	−0.983180	−	0.182639i	$-0.941536\pi$
$883$	0.0942980	−	0.534790i	0.00317338	−	0.0179971i	0.986353	+	0.164642i	$0.0526470\pi$
$884$	0.226699	−	1.28567i	0.00762470	−	0.0432418i
$885$	8.32739	+	14.4235i	0.279922	+	0.484839i
$886$	−5.87915	+	10.1830i	−0.197514	+	0.342104i
$887$	8.67530	+	7.27944i	0.291288	+	0.244420i	0.776707	−	0.629862i	$-0.216889\pi$
$887$	8.67530	+	7.27944i	0.291288	+	0.244420i	−0.485419	+	0.874282i	$0.661333\pi$
$888$	−1.74845	−	0.636385i	−0.0586743	−	0.0213557i
$889$	5.85442	−	2.13084i	0.196351	−	0.0714659i
$890$	−16.8754	+	14.1601i	−0.565664	+	0.474648i
$891$	2.18390	+	12.3855i	0.0731635	+	0.414931i
$892$	20.3706			0.682058
$893$		0			0
$894$	17.3938			0.581737
$895$	−5.64635	−	32.0221i	−0.188737	−	1.07038i
$896$	−0.338947	+	0.284410i	−0.0113234	+	0.00950147i
$897$	54.3558	−	19.7839i	1.81489	−	0.660564i
$898$	8.16689	+	2.97250i	0.272532	+	0.0991937i
$899$	−0.596006	−	0.500109i	−0.0198779	−	0.0166796i
$900$	5.84931	−	10.1313i	0.194977	−	0.337710i
$901$	−1.32678	−	2.29805i	−0.0442014	−	0.0765591i
$902$	5.50330	−	31.2108i	0.183240	−	1.03921i
$903$	0.555969	−	3.15305i	0.0185015	−	0.104927i
$904$	5.02218	+	8.69866i	0.167035	+	0.289313i
$905$	−26.8452	+	46.4973i	−0.892366	+	1.54562i
$906$	−9.00363	−	7.55494i	−0.299125	−	0.250996i
$907$	−10.2669	−	3.73686i	−0.340908	−	0.124080i	0.165892	−	0.986144i	$-0.446950\pi$
$907$	−10.2669	−	3.73686i	−0.340908	−	0.124080i	−0.506800	+	0.862064i	$0.669172\pi$
$908$	20.8136	−	7.57552i	0.690722	−	0.251402i
$909$	−0.440177	+	0.369352i	−0.0145997	+	0.0122506i
$910$	−1.38895	−	7.87715i	−0.0460434	−	0.261125i
$911$	47.4159			1.57096			0.785479	−	0.618888i	$-0.212416\pi$
$911$	47.4159			1.57096			0.785479	+	0.618888i	$0.212416\pi$
$912$		0			0
$913$	13.2527			0.438600
$914$	−2.26240	−	12.8307i	−0.0748335	−	0.424402i
$915$	14.8305	−	12.4443i	0.490282	−	0.411396i
$916$	−11.9480	+	4.34871i	−0.394772	+	0.143685i
$917$	6.58657	+	2.39732i	0.217508	+	0.0791664i
$918$	−1.14232	−	0.958516i	−0.0377020	−	0.0316358i
$919$	−2.55534	+	4.42599i	−0.0842930	+	0.146000i	−0.905090	−	0.425221i	$-0.860197\pi$
$919$	−2.55534	+	4.42599i	−0.0842930	+	0.146000i	0.820797	+	0.571220i	$0.193530\pi$
$920$	17.0175	+	29.4752i	0.561050	+	0.971767i
$921$	−6.28102	+	35.6214i	−0.206967	+	1.17377i
$922$	1.57023	−	8.90522i	0.0517128	−	0.293278i
$923$	−28.0505	−	48.5850i	−0.923295	−	1.59919i
$924$	−1.14475	+	1.98276i	−0.0376594	+	0.0652279i
$925$	9.61092	+	8.06452i	0.316005	+	0.265160i
$926$	16.6518	+	6.06077i	0.547213	+	0.199169i
$927$	−5.75939	+	2.09625i	−0.189163	+	0.0688498i
$928$	−0.171273	+	0.143715i	−0.00562233	+	0.00471769i
$929$	−7.43982	−	42.1933i	−0.244093	−	1.38432i	−0.822591	−	0.568634i	$-0.807472\pi$
$929$	−7.43982	−	42.1933i	−0.244093	−	1.38432i	0.578498	−	0.815684i	$-0.303639\pi$
$930$	16.5140			0.541514
$931$		0			0
$932$	−8.68176			−0.284381
$933$	0.862539	+	4.89170i	0.0282383	+	0.160147i
$934$	−6.03468	+	5.06370i	−0.197461	+	0.165689i
$935$	3.73501	−	1.35943i	0.122148	−	0.0444582i
$936$	6.21052	+	2.26044i	0.202997	+	0.0738849i
$937$	−2.81816	−	2.36472i	−0.0920653	−	0.0772519i	0.595593	−	0.803286i	$-0.296917\pi$
$937$	−2.81816	−	2.36472i	−0.0920653	−	0.0772519i	−0.687659	+	0.726034i	$0.741361\pi$
$938$	0.0326898	−	0.0566205i	0.00106736	−	0.00184872i
$939$	−19.5102	−	33.7926i	−0.636690	−	1.10278i
$940$	1.41101	−	8.00225i	0.0460221	−	0.261005i
$941$	3.19156	−	18.1003i	0.104042	−	0.590051i	−0.887557	−	0.460699i	$-0.847599\pi$
$941$	3.19156	−	18.1003i	0.104042	−	0.590051i	0.991599	−	0.129353i	$-0.0412900\pi$
$942$	10.5232	+	18.2267i	0.342865	+	0.593859i
$943$	−36.2143	+	62.7250i	−1.17930	+	2.04261i
$944$	−2.68845	−	2.25588i	−0.0875017	−	0.0734226i
$945$	−8.58533	−	3.12480i	−0.279281	−	0.101650i
$946$	−21.3386	+	7.76662i	−0.693779	+	0.252515i
$947$	35.8195	−	30.0561i	1.16398	−	0.976692i	0.164024	−	0.986456i	$-0.447552\pi$
$947$	35.8195	−	30.0561i	1.16398	−	0.976692i	0.999952	+	0.00976396i	$0.00310801\pi$
$948$	2.27513	+	12.9029i	0.0738927	+	0.419067i
$949$	6.95697			0.225833
$950$		0			0
$951$	6.84162			0.221855
$952$	−0.0205062	−	0.116296i	−0.000664609	−	0.00376919i
$953$	19.1933	−	16.1051i	0.621732	−	0.521695i	−0.276616	−	0.960981i	$-0.589213\pi$
$953$	19.1933	−	16.1051i	0.621732	−	0.521695i	0.898347	+	0.439286i	$0.144768\pi$
$954$	12.6234	−	4.59456i	0.408699	−	0.148754i
$955$	−44.2098	−	16.0910i	−1.43060	−	0.520694i
$956$	16.7571	+	14.0609i	0.541965	+	0.454763i
$957$	−0.578452	+	1.00191i	−0.0186987	+	0.0323871i
$958$	15.0899	+	26.1365i	0.487533	+	0.844432i
$959$	−0.169604	+	0.961871i	−0.00547679	+	0.0310604i
$960$	0.824064	−	4.67350i	0.0265965	−	0.150836i
$961$	9.44531	+	16.3598i	0.304687	+	0.527734i
$962$	−3.54395	+	6.13831i	−0.114262	+	0.197907i
$963$	3.28262	+	2.75445i	0.105781	+	0.0887609i
$964$	17.8196	+	6.48580i	0.573930	+	0.208894i
$965$	−60.6985	+	22.0924i	−1.95395	+	0.711181i
$966$	4.00820	−	3.36328i	0.128962	−	0.108212i
$967$	1.23399	+	6.99831i	0.0396825	+	0.225051i	0.998199	−	0.0599856i	$-0.0191055\pi$
$967$	1.23399	+	6.99831i	0.0396825	+	0.225051i	−0.958517	+	0.285036i	$0.907994\pi$
$968$	5.23826			0.168364
$969$		0			0
$970$	15.0961			0.484707
$971$	10.5499	+	59.8313i	0.338561	+	1.92008i	0.388764	+	0.921338i	$0.372902\pi$
$971$	10.5499	+	59.8313i	0.338561	+	1.92008i	−0.0502023	+	0.998739i	$0.515987\pi$
$972$	9.77015	−	8.19813i	0.313378	−	0.262955i
$973$	−7.09505	+	2.58239i	−0.227457	+	0.0827875i
$974$	−33.6128	−	12.2340i	−1.07702	−	0.392004i
$975$	41.6602	+	34.9570i	1.33419	+	1.11952i
$976$	−2.03977	+	3.53299i	−0.0652916	+	0.113088i
$977$	19.2706	+	33.3776i	0.616520	+	1.06784i	0.990116	+	0.140253i	$0.0447915\pi$
$977$	19.2706	+	33.3776i	0.616520	+	1.06784i	−0.373595	+	0.927592i	$0.621875\pi$
$978$	−3.07091	+	17.4160i	−0.0981968	+	0.556902i
$979$	4.17100	−	23.6549i	0.133306	−	0.756015i
$980$	12.5732	+	21.7775i	0.401638	+	0.695657i
$981$	−4.58112	+	7.93474i	−0.146264	+	0.253337i
$982$	−13.9976	−	11.7454i	−0.446683	−	0.374811i
$983$	7.05266	+	2.56696i	0.224945	+	0.0818733i	0.452034	−	0.892001i	$-0.350699\pi$
$983$	7.05266	+	2.56696i	0.224945	+	0.0818733i	−0.227089	+	0.973874i	$0.572921\pi$
$984$	9.48989	−	3.45404i	0.302527	−	0.110111i
$985$	−69.3935	+	58.2280i	−2.21106	+	1.85530i
$986$	−0.0103620	−	0.0587658i	−0.000329993	−	0.00187148i
$987$	−1.24920			−0.0397624
$988$		0			0
$989$	51.8964			1.65021
$990$	3.49413	+	19.8162i	0.111051	+	0.629801i
$991$	−16.4103	+	13.7699i	−0.521290	+	0.437415i	−0.865081	−	0.501632i	$-0.832733\pi$
$991$	−16.4103	+	13.7699i	−0.521290	+	0.437415i	0.343791	+	0.939046i	$0.388289\pi$
$992$	−3.26999	+	1.19018i	−0.103822	+	0.0377882i
$993$	24.7941	+	9.02430i	0.786816	+	0.286377i
$994$	−3.88742	−	3.26193i	−0.123301	−	0.103462i
$995$	−30.4270	+	52.7012i	−0.964602	+	1.67074i
$996$	2.11153	+	3.65727i	0.0669063	+	0.115885i
$997$	−7.11967	+	40.3776i	−0.225482	+	1.27877i	0.636279	+	0.771459i	$0.280473\pi$
$997$	−7.11967	+	40.3776i	−0.225482	+	1.27877i	−0.861761	+	0.507314i	$0.830638\pi$
$998$	3.07322	−	17.4291i	0.0972811	−	0.551709i
$999$	4.04801	+	7.01136i	0.128073	+	0.221830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.r.389.3		24
19.2	odd	18		722.2.e.s.245.2		24
19.3	odd	18		722.2.e.s.423.2		24
19.4	even	9		722.2.c.m.429.2		8
19.5	even	9	inner	722.2.e.r.415.2		24
19.6	even	9		722.2.a.n.1.3	yes	4
19.7	even	3	inner	722.2.e.r.99.3		24
19.8	odd	6		722.2.e.s.595.3		24
19.9	even	9		722.2.c.m.653.2		8
19.10	odd	18		722.2.c.n.653.3		8
19.11	even	3	inner	722.2.e.r.595.2		24
19.12	odd	6		722.2.e.s.99.2		24
19.13	odd	18		722.2.a.m.1.2	✓	4
19.14	odd	18		722.2.e.s.415.3		24
19.15	odd	18		722.2.c.n.429.3		8
19.16	even	9	inner	722.2.e.r.423.3		24
19.17	even	9	inner	722.2.e.r.245.3		24
19.18	odd	2		722.2.e.s.389.2		24
57.32	even	18		6498.2.a.ca.1.1		4
57.44	odd	18		6498.2.a.bx.1.1		4
76.51	even	18		5776.2.a.bv.1.3		4
76.63	odd	18		5776.2.a.bt.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.2	✓	4	19.13	odd	18
722.2.a.n.1.3	yes	4	19.6	even	9
722.2.c.m.429.2		8	19.4	even	9
722.2.c.m.653.2		8	19.9	even	9
722.2.c.n.429.3		8	19.15	odd	18
722.2.c.n.653.3		8	19.10	odd	18
722.2.e.r.99.3		24	19.7	even	3	inner
722.2.e.r.245.3		24	19.17	even	9	inner
722.2.e.r.389.3		24	1.1	even	1	trivial
722.2.e.r.415.2		24	19.5	even	9	inner
722.2.e.r.423.3		24	19.16	even	9	inner
722.2.e.r.595.2		24	19.11	even	3	inner
722.2.e.s.99.2		24	19.12	odd	6
722.2.e.s.245.2		24	19.2	odd	18
722.2.e.s.389.2		24	19.18	odd	2
722.2.e.s.415.3		24	19.14	odd	18
722.2.e.s.423.2		24	19.3	odd	18
722.2.e.s.595.3		24	19.8	odd	6
5776.2.a.bt.1.2		4	76.63	odd	18
5776.2.a.bv.1.3		4	76.51	even	18
6498.2.a.bx.1.1		4	57.44	odd	18
6498.2.a.ca.1.1		4	57.32	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.983662 - 0.825390i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.47284 - 1.26401i) q^{5} +(0.983662 + 0.825390i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.234623 + 1.33061i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.983662 - 0.825390i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-3.47284 - 1.26401i) q^{5} +(0.983662 + 0.825390i) q^{6} +(0.221232 - 0.383185i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.234623 + 1.33061i) q^{9} +(0.641755 - 3.63957i) q^{10} +(2.01484 + 3.48980i) q^{11} +(-0.642040 + 1.11205i) q^{12} +(3.74710 + 3.14419i) q^{13} +(0.415780 + 0.151331i) q^{14} +(-4.45940 + 1.62309i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.0463455 + 0.262838i) q^{17} -1.35114 q^{18} +3.69572 q^{20} +(-0.0986596 - 0.559526i) q^{21} +(-3.08691 + 2.59022i) q^{22} +(8.65391 - 3.14977i) q^{23} +(-1.20664 - 0.439181i) q^{24} +(6.63266 + 5.56547i) q^{25} +(-2.44575 + 4.23616i) q^{26} +(2.79360 + 4.83866i) q^{27} +(-0.0768330 + 0.435741i) q^{28} +(-0.0388245 + 0.220185i) q^{29} +(-2.37280 - 4.10980i) q^{30} +(-1.73993 + 3.01364i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.86236 + 1.76976i) q^{33} +(-0.250797 + 0.0912828i) q^{34} +(-1.25265 + 1.05110i) q^{35} +(-0.234623 - 1.33061i) q^{36} +1.44903 q^{37} +6.28106 q^{39} +(0.641755 + 3.63957i) q^{40} +(-6.02473 + 5.05535i) q^{41} +(0.533894 - 0.194322i) q^{42} +(5.29537 + 1.92736i) q^{43} +(-3.08691 - 2.59022i) q^{44} +(2.49672 - 4.32444i) q^{45} +(4.60465 + 7.97549i) q^{46} +(0.381797 - 2.16528i) q^{47} +(0.222978 - 1.26457i) q^{48} +(3.40211 + 5.89263i) q^{49} +(-4.32916 + 7.49833i) q^{50} +(0.262532 + 0.220291i) q^{51} +(-4.59650 - 1.67299i) q^{52} +(-9.34281 + 3.40050i) q^{53} +(-4.28005 + 3.59139i) q^{54} +(-2.58606 - 14.6663i) q^{55} -0.442463 q^{56} -0.223582 q^{58} +(-0.609423 - 3.45621i) q^{59} +(3.63534 - 3.05041i) q^{60} +(-3.83352 + 1.39529i) q^{61} +(-3.26999 - 1.19018i) q^{62} +(0.457965 + 0.384278i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.03879 - 15.6556i) q^{65} +(-0.898528 + 5.09581i) q^{66} +(0.0256588 - 0.145518i) q^{67} +(-0.133446 - 0.231136i) q^{68} +(5.91273 - 10.2412i) q^{69} +(-1.25265 - 1.05110i) q^{70} +(-10.7774 - 3.92267i) q^{71} +(1.26966 - 0.462117i) q^{72} +(1.08951 - 0.914211i) q^{73} +(0.251621 + 1.42701i) q^{74} +11.1180 q^{75} +1.78298 q^{77} +(1.09069 + 6.18564i) q^{78} +(7.81624 - 6.55861i) q^{79} +(-3.47284 + 1.26401i) q^{80} +(2.93278 + 1.06744i) q^{81} +(-6.02473 - 5.05535i) q^{82} +(1.64439 - 2.84817i) q^{83} +(0.284079 + 0.492039i) q^{84} +(0.171280 - 0.971376i) q^{85} +(-0.978546 + 5.54961i) q^{86} +(0.143548 + 0.248633i) q^{87} +(2.01484 - 3.48980i) q^{88} +(-4.56620 - 3.83149i) q^{89} +(4.69229 + 1.70786i) q^{90} +(2.03378 - 0.740236i) q^{91} +(-7.05473 + 5.91962i) q^{92} +(0.775931 + 4.40052i) q^{93} +2.19868 q^{94} +1.28408 q^{96} +(0.709311 + 4.02270i) q^{97} +(-5.21234 + 4.37367i) q^{98} +(-5.11630 + 1.86218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 6 * q^7 - 12 * q^8	\( 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

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