LMFDB - Embedded newform 315.2.be.c.311.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.2
Character	$\chi$	$=$	315.311
Dual form			315.2.be.c.236.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03337 - 1.17397i) q^{2} +(1.49299 - 0.878053i) q^{3} +(1.75639 + 3.04216i) q^{4} -1.00000 q^{5} +(-4.06660 + 0.0326841i) q^{6} +(0.135526 + 2.64228i) q^{7} -3.55190i q^{8} +(1.45805 - 2.62185i) q^{9} +O(q^{10})$	\(q+(-2.03337 - 1.17397i) q^{2} +(1.49299 - 0.878053i) q^{3} +(1.75639 + 3.04216i) q^{4} -1.00000 q^{5} +(-4.06660 + 0.0326841i) q^{6} +(0.135526 + 2.64228i) q^{7} -3.55190i q^{8} +(1.45805 - 2.62185i) q^{9} +(2.03337 + 1.17397i) q^{10} -4.61391i q^{11} +(5.29345 + 2.99971i) q^{12} +(-5.08297 - 2.93465i) q^{13} +(2.82637 - 5.53183i) q^{14} +(-1.49299 + 0.878053i) q^{15} +(-0.657032 + 1.13801i) q^{16} +(2.10545 - 3.64675i) q^{17} +(-6.04271 + 3.61949i) q^{18} +(6.16519 - 3.55947i) q^{19} +(-1.75639 - 3.04216i) q^{20} +(2.52240 + 3.82590i) q^{21} +(-5.41657 + 9.38177i) q^{22} -1.76762i q^{23} +(-3.11876 - 5.30296i) q^{24} +1.00000 q^{25} +(6.89036 + 11.9345i) q^{26} +(-0.125273 - 5.19464i) q^{27} +(-7.80019 + 5.05316i) q^{28} +(-2.80600 + 1.62005i) q^{29} +(4.06660 - 0.0326841i) q^{30} +(3.85707 - 2.22688i) q^{31} +(-3.48010 + 2.00924i) q^{32} +(-4.05125 - 6.88852i) q^{33} +(-8.56231 + 4.94345i) q^{34} +(-0.135526 - 2.64228i) q^{35} +(10.5370 - 0.169387i) q^{36} +(3.23425 + 5.60188i) q^{37} -16.7148 q^{38} +(-10.1656 + 0.0817030i) q^{39} +3.55190i q^{40} +(-0.641710 + 1.11147i) q^{41} +(-0.637490 - 10.7407i) q^{42} +(-4.45634 - 7.71861i) q^{43} +(14.0362 - 8.10382i) q^{44} +(-1.45805 + 2.62185i) q^{45} +(-2.07513 + 3.59422i) q^{46} +(-2.79999 + 4.84972i) q^{47} +(0.0182923 + 2.27595i) q^{48} +(-6.96327 + 0.716193i) q^{49} +(-2.03337 - 1.17397i) q^{50} +(-0.0586174 - 7.29326i) q^{51} -20.6176i q^{52} +(3.81392 + 2.20197i) q^{53} +(-5.84361 + 10.7097i) q^{54} +4.61391i q^{55} +(9.38512 - 0.481374i) q^{56} +(6.07916 - 10.7276i) q^{57} +7.60752 q^{58} +(2.28980 + 3.96606i) q^{59} +(-5.29345 - 2.99971i) q^{60} +(4.18128 + 2.41406i) q^{61} -10.4571 q^{62} +(7.12526 + 3.49724i) q^{63} +12.0632 q^{64} +(5.08297 + 2.93465i) q^{65} +(0.150801 + 18.7629i) q^{66} +(5.82929 + 10.0966i) q^{67} +14.7920 q^{68} +(-1.55206 - 2.63904i) q^{69} +(-2.82637 + 5.53183i) q^{70} +3.14126i q^{71} +(-9.31256 - 5.17884i) q^{72} +(-4.62154 - 2.66824i) q^{73} -15.1876i q^{74} +(1.49299 - 0.878053i) q^{75} +(21.6569 + 12.5036i) q^{76} +(12.1912 - 0.625303i) q^{77} +(20.7663 + 11.7679i) q^{78} +(-2.13689 + 3.70121i) q^{79} +(0.657032 - 1.13801i) q^{80} +(-4.74820 - 7.64556i) q^{81} +(2.60966 - 1.50669i) q^{82} +(4.40966 + 7.63776i) q^{83} +(-7.20867 + 14.3933i) q^{84} +(-2.10545 + 3.64675i) q^{85} +20.9264i q^{86} +(-2.76685 + 4.88254i) q^{87} -16.3881 q^{88} +(0.475563 + 0.823699i) q^{89} +(6.04271 - 3.61949i) q^{90} +(7.06530 - 13.8283i) q^{91} +(5.37738 - 3.10463i) q^{92} +(3.80325 - 6.71142i) q^{93} +(11.3868 - 6.57417i) q^{94} +(-6.16519 + 3.55947i) q^{95} +(-3.43155 + 6.05549i) q^{96} +(3.34122 - 1.92905i) q^{97} +(14.9997 + 6.71835i) q^{98} +(-12.0970 - 6.72729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.03337	−	1.17397i	−1.43781	−	0.830119i	−0.440111	−	0.897943i	$-0.645061\pi$
$2$	−2.03337	−	1.17397i	−1.43781	−	0.830119i	−0.997697	+	0.0678244i	$0.978394\pi$
$3$	1.49299	−	0.878053i	0.861979	−	0.506944i
$3$	1.49299	−	0.878053i	0.861979	−	0.506944i
$4$	1.75639	+	3.04216i	0.878195	+	1.52108i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−4.06660	+	0.0326841i	−1.66018	+	0.0133432i
$7$	0.135526	+	2.64228i	0.0512239	+	0.998687i
$7$	0.135526	+	2.64228i	0.0512239	+	0.998687i
$8$		−	3.55190i		−	1.25579i
$9$	1.45805	−	2.62185i	0.486015	−	0.873950i
$10$	2.03337	+	1.17397i	0.643007	+	0.371240i
$11$		−	4.61391i		−	1.39114i	−0.718456	−	0.695572i	$-0.755151\pi$
$11$		−	4.61391i		−	1.39114i	0.718456	−	0.695572i	$-0.244849\pi$
$12$	5.29345	+	2.99971i	1.52809	+	0.865942i
$13$	−5.08297	−	2.93465i	−1.40976	−	0.813926i	−0.414397	−	0.910096i	$-0.636007\pi$
$13$	−5.08297	−	2.93465i	−1.40976	−	0.813926i	−0.995365	+	0.0961700i	$0.969341\pi$
$14$	2.82637	−	5.53183i	0.755379	−	1.47844i
$15$	−1.49299	+	0.878053i	−0.385489	+	0.226712i
$16$	−0.657032	+	1.13801i	−0.164258	+	0.284503i
$17$	2.10545	−	3.64675i	0.510647	−	0.884466i	−0.489277	−	0.872128i	$-0.662739\pi$
$17$	2.10545	−	3.64675i	0.510647	−	0.884466i	0.999924	−	0.0123378i	$-0.00392735\pi$
$18$	−6.04271	+	3.61949i	−1.42428	+	0.853122i
$19$	6.16519	−	3.55947i	1.41439	−	0.816599i	0.418592	−	0.908174i	$-0.362524\pi$
$19$	6.16519	−	3.55947i	1.41439	−	0.816599i	0.995798	+	0.0915755i	$0.0291903\pi$
$20$	−1.75639	−	3.04216i	−0.392741	−	0.680247i
$21$	2.52240	+	3.82590i	0.550432	+	0.834880i
$22$	−5.41657	+	9.38177i	−1.15482	+	2.00020i
$23$		−	1.76762i		−	0.368575i	−0.982872	−	0.184287i	$-0.941002\pi$
$23$		−	1.76762i		−	0.368575i	0.982872	−	0.184287i	$-0.0589977\pi$
$24$	−3.11876	−	5.30296i	−0.636614	−	1.08246i
$25$	1.00000			0.200000
$26$	6.89036	+	11.9345i	1.35131	+	2.34054i
$27$	−0.125273	−	5.19464i	−0.0241087	−	0.999709i
$28$	−7.80019	+	5.05316i	−1.47410	+	0.954958i
$29$	−2.80600	+	1.62005i	−0.521062	+	0.300835i	−0.737369	−	0.675490i	$-0.763932\pi$
$29$	−2.80600	+	1.62005i	−0.521062	+	0.300835i	0.216307	+	0.976325i	$0.430599\pi$
$30$	4.06660	−	0.0326841i	0.742457	−	0.00596728i
$31$	3.85707	−	2.22688i	0.692749	−	0.399959i	−0.111892	−	0.993720i	$-0.535691\pi$
$31$	3.85707	−	2.22688i	0.692749	−	0.399959i	0.804641	+	0.593761i	$0.202358\pi$
$32$	−3.48010	+	2.00924i	−0.615201	+	0.355186i
$33$	−4.05125	−	6.88852i	−0.705233	−	1.19914i
$34$	−8.56231	+	4.94345i	−1.46842	+	0.847795i
$35$	−0.135526	−	2.64228i	−0.0229080	−	0.446626i
$36$	10.5370	−	0.169387i	1.75616	−	0.0282311i
$37$	3.23425	+	5.60188i	0.531707	+	0.920944i	0.999315	+	0.0370080i	$0.0117827\pi$
$37$	3.23425	+	5.60188i	0.531707	+	0.920944i	−0.467608	+	0.883936i	$0.654884\pi$
$38$	−16.7148			−2.71150
$39$	−10.1656	+	0.0817030i	−1.62780	+	0.0130830i
$40$			3.55190i			0.561605i
$41$	−0.641710	+	1.11147i	−0.100218	+	0.173583i	−0.911774	−	0.410691i	$-0.865287\pi$
$41$	−0.641710	+	1.11147i	−0.100218	+	0.173583i	0.811556	+	0.584274i	$0.198621\pi$
$42$	−0.637490	−	10.7407i	−0.0983668	−	1.65732i
$43$	−4.45634	−	7.71861i	−0.679586	−	1.17708i	−0.975106	−	0.221741i	$-0.928826\pi$
$43$	−4.45634	−	7.71861i	−0.679586	−	1.17708i	0.295520	−	0.955337i	$-0.404507\pi$
$44$	14.0362	−	8.10382i	2.11604	−	1.22170i
$45$	−1.45805	+	2.62185i	−0.217353	+	0.390842i
$46$	−2.07513	+	3.59422i	−0.305961	+	0.529939i
$47$	−2.79999	+	4.84972i	−0.408420	+	0.707404i	−0.994713	−	0.102695i	$-0.967253\pi$
$47$	−2.79999	+	4.84972i	−0.408420	+	0.707404i	0.586293	+	0.810099i	$0.300587\pi$
$48$	0.0182923	+	2.27595i	0.00264026	+	0.328505i
$49$	−6.96327	+	0.716193i	−0.994752	+	0.102313i
$50$	−2.03337	−	1.17397i	−0.287562	−	0.166024i
$51$	−0.0586174	−	7.29326i	−0.00820808	−	1.02126i
$52$		−	20.6176i		−	2.85914i
$53$	3.81392	+	2.20197i	0.523883	+	0.302464i	0.738522	−	0.674230i	$-0.235524\pi$
$53$	3.81392	+	2.20197i	0.523883	+	0.302464i	−0.214639	+	0.976693i	$0.568858\pi$
$54$	−5.84361	+	10.7097i	−0.795214	+	1.45740i
$55$			4.61391i			0.622139i
$56$	9.38512	−	0.481374i	1.25414	−	0.0643263i
$57$	6.07916	−	10.7276i	0.805205	−	1.42091i
$58$	7.60752			0.998916
$59$	2.28980	+	3.96606i	0.298107	+	0.516337i	0.975703	−	0.219098i	$-0.0703114\pi$
$59$	2.28980	+	3.96606i	0.298107	+	0.516337i	−0.677596	+	0.735435i	$0.736978\pi$
$60$	−5.29345	−	2.99971i	−0.683381	−	0.387261i
$61$	4.18128	+	2.41406i	0.535358	+	0.309089i	0.743196	−	0.669074i	$-0.233309\pi$
$61$	4.18128	+	2.41406i	0.535358	+	0.309089i	−0.207838	+	0.978163i	$0.566643\pi$
$62$	−10.4571			−1.32805
$63$	7.12526	+	3.49724i	0.897698	+	0.440610i
$64$	12.0632			1.50790
$65$	5.08297	+	2.93465i	0.630465	+	0.363999i
$66$	0.150801	+	18.7629i	0.0185624	+	2.30956i
$67$	5.82929	+	10.0966i	0.712161	+	1.23350i	0.964044	+	0.265741i	$0.0856167\pi$
$67$	5.82929	+	10.0966i	0.712161	+	1.23350i	−0.251883	+	0.967758i	$0.581050\pi$
$68$	14.7920			1.79379
$69$	−1.55206	−	2.63904i	−0.186847	−	0.317703i
$70$	−2.82637	+	5.53183i	−0.337816	+	0.661180i
$71$			3.14126i			0.372800i	0.982474	+	0.186400i	$0.0596820\pi$
$71$			3.14126i			0.372800i	−0.982474	+	0.186400i	$0.940318\pi$
$72$	−9.31256	−	5.17884i	−1.09750	−	0.610332i
$73$	−4.62154	−	2.66824i	−0.540910	−	0.312294i	0.204538	−	0.978859i	$-0.434431\pi$
$73$	−4.62154	−	2.66824i	−0.540910	−	0.312294i	−0.745448	+	0.666564i	$0.767764\pi$
$74$		−	15.1876i		−	1.76552i
$75$	1.49299	−	0.878053i	0.172396	−	0.101389i
$76$	21.6569	+	12.5036i	2.48422	+	1.43427i
$77$	12.1912	−	0.625303i	1.38932	−	0.0712598i
$78$	20.7663	+	11.7679i	2.35132	+	1.33246i
$79$	−2.13689	+	3.70121i	−0.240419	+	0.416418i	−0.960834	−	0.277125i	$-0.910618\pi$
$79$	−2.13689	+	3.70121i	−0.240419	+	0.416418i	0.720414	+	0.693544i	$0.243952\pi$
$80$	0.657032	−	1.13801i	0.0734584	−	0.127234i
$81$	−4.74820	−	7.64556i	−0.527578	−	0.849507i
$82$	2.60966	−	1.50669i	0.288189	−	0.166386i
$83$	4.40966	+	7.63776i	0.484023	+	0.838353i	0.999832	−	0.0183510i	$-0.00584162\pi$
$83$	4.40966	+	7.63776i	0.484023	+	0.838353i	−0.515808	+	0.856704i	$0.672508\pi$
$84$	−7.20867	+	14.3933i	−0.786530	+	1.57044i
$85$	−2.10545	+	3.64675i	−0.228368	+	0.395545i
$86$			20.9264i			2.25655i
$87$	−2.76685	+	4.88254i	−0.296638	+	0.523463i
$88$	−16.3881			−1.74698
$89$	0.475563	+	0.823699i	0.0504096	+	0.0873119i	0.890129	−	0.455708i	$-0.150614\pi$
$89$	0.475563	+	0.823699i	0.0504096	+	0.0873119i	−0.839720	+	0.543020i	$0.817281\pi$
$90$	6.04271	−	3.61949i	0.636957	−	0.381528i
$91$	7.06530	−	13.8283i	0.740644	−	1.44960i
$92$	5.37738	−	3.10463i	0.560631	−	0.323680i
$93$	3.80325	−	6.71142i	0.394379	−	0.695941i
$94$	11.3868	−	6.57417i	1.17446	−	0.678074i
$95$	−6.16519	+	3.55947i	−0.632535	+	0.365194i
$96$	−3.43155	+	6.05549i	−0.350231	+	0.618036i
$97$	3.34122	−	1.92905i	0.339249	−	0.195866i	−0.320691	−	0.947184i	$-0.603915\pi$
$97$	3.34122	−	1.92905i	0.339249	−	0.195866i	0.659940	+	0.751318i	$0.270582\pi$
$98$	14.9997	+	6.71835i	1.51520	+	0.678656i
$99$	−12.0970	−	6.72729i	−1.21579	−	0.676118i
$100$	1.75639	+	3.04216i	0.175639	+	0.304216i
$101$	3.70737			0.368897			0.184448	−	0.982842i	$-0.440950\pi$
$101$	3.70737			0.368897			0.184448	+	0.982842i	$0.440950\pi$
$102$	−8.44284	+	14.8987i	−0.835966	+	1.47519i
$103$		−	14.5787i		−	1.43648i	−0.695796	−	0.718239i	$-0.744948\pi$
$103$		−	14.5787i		−	1.43648i	0.695796	−	0.718239i	$-0.255052\pi$
$104$	−10.4236	+	18.0542i	−1.02212	+	1.77036i
$105$	−2.52240	−	3.82590i	−0.246161	−	0.373370i
$106$	−5.17007	−	8.95483i	−0.502162	−	0.869770i
$107$	−0.120634	+	0.0696482i	−0.0116622	+	0.00673315i	−0.505820	−	0.862639i	$-0.668810\pi$
$107$	−0.120634	+	0.0696482i	−0.0116622	+	0.00673315i	0.494158	+	0.869372i	$0.335477\pi$
$108$	15.5829	−	9.50492i	1.49946	−	0.914611i
$109$	3.53208	−	6.11775i	0.338312	−	0.585974i	−0.645803	−	0.763504i	$-0.723477\pi$
$109$	3.53208	−	6.11775i	0.338312	−	0.585974i	0.984115	+	0.177530i	$0.0568107\pi$
$110$	5.41657	−	9.38177i	0.516449	−	0.894516i
$111$	9.74746	+	5.52372i	0.925188	+	0.524289i
$112$	−3.09599	−	1.58183i	−0.292544	−	0.149469i
$113$	−4.08371	−	2.35773i	−0.384163	−	0.221797i	0.295465	−	0.955354i	$-0.404525\pi$
$113$	−4.08371	−	2.35773i	−0.384163	−	0.221797i	−0.679628	+	0.733557i	$0.737859\pi$
$114$	−24.9550	+	14.6765i	−2.33725	+	1.37458i
$115$			1.76762i			0.164832i
$116$	−9.85688	−	5.69087i	−0.915188	−	0.528384i
$117$	−15.1054	+	9.04792i	−1.39650	+	0.836481i
$118$		−	10.7526i		−	0.989857i
$119$	9.92106	+	5.06896i	0.909462	+	0.464671i
$120$	3.11876	+	5.30296i	0.284702	+	0.484092i
$121$	−10.2881			−0.935284
$122$	−5.66805	−	9.81736i	−0.513161	−	0.888822i
$123$	0.0178657	+	2.22288i	0.00161090	+	0.200430i
$124$	13.5490	+	7.82253i	1.21674	+	0.702484i
$125$	−1.00000			−0.0894427
$126$	−10.3826	−	15.4760i	−0.924959	−	1.37871i
$127$	−17.2716			−1.53260			−0.766301	−	0.642481i	$-0.777905\pi$
$127$	−17.2716			−1.53260			−0.766301	+	0.642481i	$0.777905\pi$
$128$	−17.5688	−	10.1433i	−1.55288	−	0.896553i
$129$	−13.4306	−	7.61092i	−1.18250	−	0.670104i
$130$	−6.89036	−	11.9345i	−0.604325	−	1.04672i
$131$	−13.8881			−1.21341			−0.606703	−	0.794928i	$-0.707508\pi$
$131$	−13.8881			−1.21341			−0.606703	+	0.794928i	$0.707508\pi$
$132$	13.8404	−	24.4235i	1.20465	−	2.12579i
$133$	10.2407	+	15.8077i	0.887977	+	1.37070i
$134$		−	27.3735i		−	2.36471i
$135$	0.125273	+	5.19464i	0.0107818	+	0.447084i
$136$	−12.9529	−	7.47836i	−1.11070	−	0.641264i
$137$			8.10539i			0.692490i	0.938144	+	0.346245i	$0.112543\pi$
$137$			8.10539i			0.692490i	−0.938144	+	0.346245i	$0.887457\pi$
$138$	0.0577731	+	7.18822i	0.00491798	+	0.611902i
$139$	12.4962	+	7.21466i	1.05991	+	0.611940i	0.925408	−	0.378973i	$-0.123723\pi$
$139$	12.4962	+	7.21466i	1.05991	+	0.611940i	0.134503	+	0.990913i	$0.457056\pi$
$140$	7.80019	−	5.05316i	0.659236	−	0.427070i
$141$	0.0779538	+	9.69912i	0.00656489	+	0.816813i
$142$	3.68774	−	6.38735i	0.309468	−	0.536014i
$143$	−13.5402	+	23.4523i	−1.13229	+	1.96118i
$144$	2.02572	+	3.38191i	0.168810	+	0.281826i
$145$	2.80600	−	1.62005i	0.233026	−	0.134538i
$146$	6.26485	+	10.8510i	0.518483	+	0.898039i
$147$	−9.76724	+	7.18339i	−0.805588	+	0.592476i
$148$	−11.3612	+	19.6782i	−0.933886	+	1.61754i
$149$		−	1.00356i		−	0.0822146i	−0.999155	−	0.0411073i	$-0.986911\pi$
$149$		−	1.00356i		−	0.0822146i	0.999155	−	0.0411073i	$-0.0130885\pi$
$150$	−4.06660	+	0.0326841i	−0.332037	+	0.00266865i
$151$	−8.88680			−0.723198			−0.361599	−	0.932334i	$-0.617769\pi$
$151$	−8.88680			−0.723198			−0.361599	+	0.932334i	$0.617769\pi$
$152$	−12.6429	−	21.8981i	−1.02547	−	1.77617i
$153$	−6.49138	−	10.8373i	−0.524797	−	0.876144i
$154$	−25.5233	−	13.0406i	−2.05673	−	1.05084i
$155$	−3.85707	+	2.22688i	−0.309807	+	0.178867i
$156$	−18.1033	−	30.7819i	−1.44943	−	2.46452i
$157$	16.5964	−	9.58193i	1.32454	−	0.764721i	0.340087	−	0.940394i	$-0.389544\pi$
$157$	16.5964	−	9.58193i	1.32454	−	0.764721i	0.984449	+	0.175673i	$0.0562102\pi$
$158$	8.69018	−	5.01728i	0.691354	−	0.399153i
$159$	7.62760	−	0.0613045i	0.604908	−	0.00486177i
$160$	3.48010	−	2.00924i	0.275126	−	0.158844i
$161$	4.67055	−	0.239558i	0.368091	−	0.0188798i
$162$	0.679217	+	21.1205i	0.0533643	+	1.65938i
$163$	5.29383	+	9.16919i	0.414645	+	0.718186i	0.995391	−	0.0958986i	$-0.0305725\pi$
$163$	5.29383	+	9.16919i	0.414645	+	0.718186i	−0.580746	+	0.814085i	$0.697239\pi$
$164$	−4.50837			−0.352045
$165$	4.05125	+	6.88852i	0.315390	+	0.536271i
$166$		−	20.7072i		−	1.60719i
$167$	−2.09384	+	3.62663i	−0.162026	+	0.280637i	−0.935595	−	0.353075i	$-0.885136\pi$
$167$	−2.09384	+	3.62663i	−0.162026	+	0.280637i	0.773569	+	0.633712i	$0.218470\pi$
$168$	13.5892	−	8.95932i	1.04843	−	0.691226i
$169$	10.7244	+	18.5752i	0.824952	+	1.42886i
$170$	8.56231	−	4.94345i	0.656699	−	0.379146i
$171$	−0.343276	−	21.3541i	−0.0262510	−	1.63299i
$172$	15.6542	−	27.1138i	1.19362	−	2.06741i
$173$	10.2917	−	17.8257i	0.782461	−	1.35526i	−0.148043	−	0.988981i	$-0.547297\pi$
$173$	10.2917	−	17.8257i	0.782461	−	1.35526i	0.930504	−	0.366281i	$-0.119369\pi$
$174$	11.3580	−	6.67980i	0.861045	−	0.506395i
$175$	0.135526	+	2.64228i	0.0102448	+	0.199737i
$176$	5.25068	+	3.03148i	0.395785	+	0.228507i
$177$	6.90107	+	3.91072i	0.518716	+	0.293948i
$178$		−	2.23318i		−	0.167384i
$179$	17.6485	+	10.1894i	1.31911	+	0.761589i	0.983586	−	0.180443i	$-0.0577530\pi$
$179$	17.6485	+	10.1894i	1.31911	+	0.761589i	0.335525	+	0.942031i	$0.391086\pi$
$180$	−10.5370	+	0.169387i	−0.785380	+	0.0126253i
$181$		−	4.52616i		−	0.336427i	−0.985751	−	0.168214i	$-0.946200\pi$
$181$		−	4.52616i		−	0.336427i	0.985751	−	0.168214i	$-0.0537998\pi$
$182$	−30.6003	+	19.8237i	−2.26825	+	1.46943i
$183$	8.36229	−	0.0672094i	0.618158	−	0.00496826i
$184$	−6.27842			−0.462851
$185$	−3.23425	−	5.60188i	−0.237787	−	0.411859i
$186$	−15.6124	+	9.18189i	−1.14475	+	0.673249i
$187$	−16.8257	−	9.71435i	−1.23042	−	0.710384i
$188$	−19.6715			−1.43469
$189$	13.7087	−	1.03501i	0.997162	−	0.0752861i
$190$	16.7148			1.21262
$191$	4.31590	+	2.49179i	0.312288	+	0.180299i	0.647950	−	0.761683i	$-0.275627\pi$
$191$	4.31590	+	2.49179i	0.312288	+	0.180299i	−0.335662	+	0.941983i	$0.608960\pi$
$192$	18.0103	−	10.5922i	1.29978	−	0.764423i
$193$	3.79149	+	6.56705i	0.272917	+	0.472707i	0.969608	−	0.244665i	$-0.0786781\pi$
$193$	3.79149	+	6.56705i	0.272917	+	0.472707i	−0.696690	+	0.717372i	$0.745345\pi$
$194$	−9.05856			−0.650367
$195$	10.1656	−	0.0817030i	0.727974	−	0.00585088i
$196$	−14.4090	−	19.9254i	−1.02921	−	1.42325i
$197$			6.05244i			0.431218i	0.976480	+	0.215609i	$0.0691737\pi$
$197$			6.05244i			0.431218i	−0.976480	+	0.215609i	$0.930826\pi$
$198$	16.7000	+	27.8805i	1.18682	+	1.98138i
$199$	−9.29299	−	5.36531i	−0.658762	−	0.380337i	0.133043	−	0.991110i	$-0.457525\pi$
$199$	−9.29299	−	5.36531i	−0.658762	−	0.380337i	−0.791805	+	0.610774i	$0.790859\pi$
$200$		−	3.55190i		−	0.251157i
$201$	17.5684	+	9.95575i	1.23918	+	0.702224i
$202$	−7.53844	−	4.35232i	−0.530403	−	0.306228i
$203$	−4.66090	−	7.19469i	−0.327131	−	0.504968i
$204$	22.0843	−	12.9881i	1.54621	−	0.909351i
$205$	0.641710	−	1.11147i	0.0448189	−	0.0776287i
$206$	−17.1149	+	29.6438i	−1.19245	+	2.06538i
$207$	−4.63444	−	2.57727i	−0.322116	−	0.179133i
$208$	6.67934	−	3.85632i	0.463129	−	0.267388i
$209$	−16.4231	−	28.4456i	−1.13601	−	1.96762i
$210$	0.637490	+	10.7407i	0.0439910	+	0.741177i
$211$	−5.31170	+	9.20013i	−0.365672	+	0.633363i	−0.988884	−	0.148690i	$-0.952494\pi$
$211$	−5.31170	+	9.20013i	−0.365672	+	0.633363i	0.623211	+	0.782053i	$0.285828\pi$
$212$			15.4701i			1.06249i
$213$	2.75820	+	4.68988i	0.188989	+	0.321345i
$214$	0.327059			0.0223573
$215$	4.45634	+	7.71861i	0.303920	+	0.526405i
$216$	−18.4509	+	0.444957i	−1.25542	+	0.0302755i
$217$	6.40676	+	9.88964i	0.434919	+	0.671352i
$218$	−14.3641	+	8.29309i	−0.972856	+	0.561679i
$219$	−9.24277	+	0.0742860i	−0.624569	+	0.00501978i
$220$	−14.0362	+	8.10382i	−0.946322	+	0.546359i
$221$	−21.4039	+	12.3575i	−1.43978	+	0.831258i
$222$	−13.3355	−	22.6749i	−0.895021	−	1.52184i
$223$	−9.79885	+	5.65737i	−0.656180	+	0.378846i	−0.790820	−	0.612049i	$-0.790346\pi$
$223$	−9.79885	+	5.65737i	−0.656180	+	0.378846i	0.134640	+	0.990895i	$0.457012\pi$
$224$	−5.78061	−	8.92309i	−0.386233	−	0.596199i
$225$	1.45805	−	2.62185i	0.0972031	−	0.174790i
$226$	5.53579	+	9.58826i	0.368235	+	0.637802i
$227$	25.7220			1.70723			0.853616	−	0.520902i	$-0.174404\pi$
$227$	25.7220			1.70723			0.853616	+	0.520902i	$0.174404\pi$
$228$	43.3125	−	0.348111i	2.86844	−	0.0230542i
$229$			4.69184i			0.310046i	0.987911	+	0.155023i	$0.0495451\pi$
$229$			4.69184i			0.310046i	−0.987911	+	0.155023i	$0.950455\pi$
$230$	2.07513	−	3.59422i	0.136830	−	0.236996i
$231$	17.6523	−	11.6381i	1.16144	−	0.765731i
$232$	5.75425	+	9.96666i	0.377785	+	0.654343i
$233$	−7.96442	+	4.59826i	−0.521766	+	0.301242i	−0.737657	−	0.675176i	$-0.764068\pi$
$233$	−7.96442	+	4.59826i	−0.521766	+	0.301242i	0.215891	+	0.976418i	$0.430734\pi$
$234$	41.3368	−	0.664508i	2.70227	−	0.0434402i
$235$	2.79999	−	4.84972i	0.182651	−	0.316361i
$236$	−8.04358	+	13.9319i	−0.523592	+	0.906889i
$237$	0.0594928	+	7.40218i	0.00386447	+	0.480823i
$238$	−14.2224	−	21.9540i	−0.921901	−	1.42307i
$239$	−4.80444	−	2.77385i	−0.310774	−	0.179425i	0.336499	−	0.941684i	$-0.390757\pi$
$239$	−4.80444	−	2.77385i	−0.310774	−	0.179425i	−0.647273	+	0.762259i	$0.724090\pi$
$240$	−0.0182923	−	2.27595i	−0.00118076	−	0.146912i
$241$			1.24685i			0.0803164i	0.999193	+	0.0401582i	$0.0127862\pi$
$241$			1.24685i			0.0803164i	−0.999193	+	0.0401582i	$0.987214\pi$
$242$	20.9195	+	12.0779i	1.34476	+	0.776397i
$243$	−13.8022	−	7.24558i	−0.885413	−	0.464804i
$244$			16.9601i			1.08576i
$245$	6.96327	−	0.716193i	0.444867	−	0.0457559i
$246$	2.57325	−	4.54090i	0.164065	−	0.289517i
$247$	−41.7833			−2.65860
$248$	−7.90965	−	13.6999i	−0.502264	−	0.869946i
$249$	13.2899	+	7.53119i	0.842216	+	0.477270i
$250$	2.03337	+	1.17397i	0.128601	+	0.0742481i
$251$	−6.72351			−0.424384			−0.212192	−	0.977228i	$-0.568060\pi$
$251$	−6.72351			−0.424384			−0.212192	+	0.977228i	$0.568060\pi$
$252$	1.87560	+	27.8187i	0.118152	+	1.75241i
$253$	−8.15564			−0.512741
$254$	35.1194	+	20.2762i	2.20359	+	1.27224i
$255$	0.0586174	+	7.29326i	0.00367076	+	0.456722i
$256$	11.7526	+	20.3562i	0.734540	+	1.27226i
$257$	23.6772			1.47694			0.738472	−	0.674285i	$-0.235548\pi$
$257$	23.6772			1.47694			0.738472	+	0.674285i	$0.235548\pi$
$258$	18.3745	+	31.2429i	1.14394	+	1.94510i
$259$	−14.3634	+	9.30499i	−0.892499	+	0.578184i
$260$			20.6176i			1.27865i
$261$	0.156238	+	9.71903i	0.00967087	+	0.601593i
$262$	28.2396	+	16.3041i	1.74465	+	1.00727i
$263$			1.80050i			0.111024i	0.998458	+	0.0555118i	$0.0176790\pi$
$263$			1.80050i			0.111024i	−0.998458	+	0.0555118i	$0.982321\pi$
$264$	−24.4674	+	14.3897i	−1.50586	+	0.885622i
$265$	−3.81392	−	2.20197i	−0.234287	−	0.135266i
$266$	−2.26528	−	44.1651i	−0.138893	−	2.70794i
$267$	1.43326	+	0.812206i	0.0877142	+	0.0497062i
$268$	−20.4770	+	35.4672i	−1.25083	+	2.16651i
$269$	3.02199	−	5.23424i	0.184254	−	0.319137i	−0.759071	−	0.651008i	$-0.774346\pi$
$269$	3.02199	−	5.23424i	0.184254	−	0.319137i	0.943325	+	0.331871i	$0.107680\pi$
$270$	5.84361	−	10.7097i	0.355630	−	0.651771i
$271$	−2.31677	+	1.33759i	−0.140734	+	0.0812528i	−0.568714	−	0.822536i	$-0.692559\pi$
$271$	−2.31677	+	1.33759i	−0.140734	+	0.0812528i	0.427980	+	0.903788i	$0.359225\pi$
$272$	2.76670	+	4.79206i	0.167756	+	0.290561i
$273$	−1.59358	−	26.8493i	−0.0964480	−	1.62499i
$274$	9.51545	−	16.4812i	0.574849	−	0.995668i
$275$		−	4.61391i		−	0.278229i
$276$	5.30235	−	9.35681i	0.319164	−	0.563214i
$277$	4.19484			0.252044			0.126022	−	0.992027i	$-0.459779\pi$
$277$	4.19484			0.252044			0.126022	+	0.992027i	$0.459779\pi$
$278$	−16.9395	−	29.3401i	−1.01597	−	1.75970i
$279$	−0.214760	−	13.3595i	−0.0128574	−	0.799815i
$280$	−9.38512	+	0.481374i	−0.560868	+	0.0287676i
$281$	5.16403	−	2.98146i	0.308060	−	0.177859i	−0.337998	−	0.941147i	$-0.609750\pi$
$281$	5.16403	−	2.98146i	0.308060	−	0.177859i	0.646058	+	0.763288i	$0.276416\pi$
$282$	11.2279	−	19.8134i	0.668613	−	1.17987i
$283$	−4.59037	+	2.65025i	−0.272869	+	0.157541i	−0.630191	−	0.776440i	$-0.717023\pi$
$283$	−4.59037	+	2.65025i	−0.272869	+	0.157541i	0.357322	+	0.933981i	$0.383690\pi$
$284$	−9.55622	+	5.51729i	−0.567057	+	0.327391i
$285$	−6.07916	+	10.7276i	−0.360099	+	0.635449i
$286$	55.0645	−	31.7915i	3.25603	−	1.87987i
$287$	−3.02379	−	1.54494i	−0.178489	−	0.0911950i
$288$	0.193771	+	12.0539i	0.0114181	+	0.710281i
$289$	−0.365845	−	0.633663i	−0.0215203	−	0.0372743i
$290$	−7.60752			−0.446729
$291$	3.29460	−	5.81382i	0.193133	−	0.340812i
$292$		−	18.7459i		−	1.09702i
$293$	7.13970	−	12.3663i	0.417106	−	0.722448i	−0.578541	−	0.815653i	$-0.696378\pi$
$293$	7.13970	−	12.3663i	0.417106	−	0.722448i	0.995647	+	0.0932048i	$0.0297111\pi$
$294$	28.2934	−	3.14006i	1.65011	−	0.183132i
$295$	−2.28980	−	3.96606i	−0.133318	−	0.230913i
$296$	19.8974	−	11.4877i	1.15651	−	0.667711i
$297$	−23.9676	+	0.577997i	−1.39074	+	0.0335388i
$298$	−1.17814	+	2.04060i	−0.0682479	+	0.118209i
$299$	−5.18736	+	8.98476i	−0.299992	+	0.519602i
$300$	5.29345	+	2.99971i	0.305617	+	0.173188i
$301$	19.7908	−	12.8210i	1.14072	−	0.738988i
$302$	18.0701	+	10.4328i	1.03982	+	0.600340i
$303$	5.53507	−	3.25526i	0.317981	−	0.187010i
$304$			9.35474i			0.536531i
$305$	−4.18128	−	2.41406i	−0.239419	−	0.138229i
$306$	0.476748	+	29.6569i	0.0272538	+	1.69537i
$307$			3.32121i			0.189551i	0.995499	+	0.0947756i	$0.0302134\pi$
$307$			3.32121i			0.189551i	−0.995499	+	0.0947756i	$0.969787\pi$
$308$	23.3148	+	35.9893i	1.32848	+	2.05068i
$309$	−12.8008	−	21.7658i	−0.728214	−	1.23821i
$310$	10.4571			0.593924
$311$	2.54494	+	4.40797i	0.144310	+	0.249953i	0.929115	−	0.369790i	$-0.120570\pi$
$311$	2.54494	+	4.40797i	0.144310	+	0.249953i	−0.784805	+	0.619743i	$0.787237\pi$
$312$	0.290201	+	36.1073i	0.0164294	+	2.04417i
$313$	25.7095	+	14.8434i	1.45319	+	0.838999i	0.998661	−	0.0517342i	$-0.0164749\pi$
$313$	25.7095	+	14.8434i	1.45319	+	0.838999i	0.454527	+	0.890733i	$0.349808\pi$
$314$	−44.9954			−2.53924
$315$	−7.12526	−	3.49724i	−0.401463	−	0.197047i
$316$	−15.0129			−0.844540
$317$	9.82619	+	5.67315i	0.551894	+	0.318636i	0.749886	−	0.661568i	$-0.230109\pi$
$317$	9.82619	+	5.67315i	0.551894	+	0.318636i	−0.197992	+	0.980204i	$0.563442\pi$
$318$	−15.5817	−	8.82988i	−0.873777	−	0.495155i
$319$	7.47475	+	12.9466i	0.418505	+	0.724873i
$320$	−12.0632			−0.674355
$321$	−0.118951	+	0.209908i	−0.00663920	+	0.0117159i
$322$	−9.77817	−	4.99595i	−0.544916	−	0.278413i
$323$		−	29.9772i		−	1.66797i
$324$	14.9193	−	27.8734i	0.828850	−	1.54852i
$325$	−5.08297	−	2.93465i	−0.281952	−	0.162785i
$326$		−	24.8591i		−	1.37682i
$327$	−0.0983360	−	12.2351i	−0.00543799	−	0.676603i
$328$	3.94785	+	2.27929i	0.217983	+	0.125853i
$329$	−13.1938	−	6.74108i	−0.727396	−	0.371648i
$330$	−0.150801	−	18.7629i	−0.00830135	−	1.03287i
$331$	−7.44876	+	12.9016i	−0.409421	+	0.709138i	−0.994825	−	0.101604i	$-0.967603\pi$
$331$	−7.44876	+	12.9016i	−0.409421	+	0.709138i	0.585404	+	0.810742i	$0.300936\pi$
$332$	−15.4902	+	26.8298i	−0.850134	+	1.47248i
$333$	19.4030	−	0.311912i	1.06328	−	0.0170927i
$334$	8.51508	−	4.91619i	0.465925	−	0.269002i
$335$	−5.82929	−	10.0966i	−0.318488	−	0.551638i
$336$	−6.01122	+	0.356783i	−0.327939	+	0.0194641i
$337$	−15.4608	+	26.7789i	−0.842204	+	1.45874i	0.0458236	+	0.998950i	$0.485409\pi$
$337$	−15.4608	+	26.7789i	−0.842204	+	1.45874i	−0.888027	+	0.459790i	$0.847925\pi$
$338$		−	50.3602i		−	2.73923i
$339$	−8.16715	+	0.0656410i	−0.443579	+	0.00356513i
$340$	−14.7920			−0.802207
$341$	−10.2746	−	17.7961i	−0.556401	−	0.963715i
$342$	−24.3709	+	43.8237i	−1.31783	+	2.36971i
$343$	−2.83608	−	18.3018i	−0.153134	−	0.988205i
$344$	−27.4158	+	15.8285i	−1.47816	+	0.853415i
$345$	1.55206	+	2.63904i	0.0835604	+	0.142081i
$346$	−41.8535	+	24.1641i	−2.25006	+	1.29907i
$347$	5.15328	−	2.97525i	0.276642	−	0.159720i	−0.355260	−	0.934768i	$-0.615608\pi$
$347$	5.15328	−	2.97525i	0.276642	−	0.159720i	0.631902	+	0.775048i	$0.282274\pi$
$348$	−19.7131	+	0.158438i	−1.05673	+	0.00849318i
$349$	−9.05166	+	5.22598i	−0.484524	+	0.279740i	−0.722300	−	0.691580i	$-0.756915\pi$
$349$	−9.05166	+	5.22598i	−0.484524	+	0.279740i	0.237776	+	0.971320i	$0.423582\pi$
$350$	2.82637	−	5.53183i	0.151076	−	0.295689i
$351$	−14.6077	+	26.7718i	−0.779702	+	1.42897i
$352$	9.27043	+	16.0569i	0.494116	+	0.855834i
$353$	30.3771			1.61681			0.808406	−	0.588625i	$-0.200331\pi$
$353$	30.3771			1.61681			0.808406	+	0.588625i	$0.200331\pi$
$354$	−9.44135	−	16.0535i	−0.501802	−	0.853236i
$355$		−	3.14126i		−	0.166721i
$356$	−1.67055	+	2.89347i	−0.0885389	+	0.153354i
$357$	19.2629	−	1.14331i	1.01950	−	0.0605102i
$358$	−23.9239	−	41.4374i	−1.26442	−	2.19004i
$359$	−24.0837	+	13.9047i	−1.27109	+	0.733863i	−0.975193	−	0.221358i	$-0.928951\pi$
$359$	−24.0837	+	13.9047i	−1.27109	+	0.733863i	−0.295895	+	0.955221i	$0.595618\pi$
$360$	9.31256	+	5.17884i	0.490815	+	0.272949i
$361$	15.8397	−	27.4351i	0.833667	−	1.44395i
$362$	−5.31356	+	9.20336i	−0.279275	+	0.483718i
$363$	−15.3601	+	9.03352i	−0.806195	+	0.474137i
$364$	54.4774	−	2.79421i	2.85539	−	0.146456i
$365$	4.62154	+	2.66824i	0.241902	+	0.139662i
$366$	−17.0825	−	9.68038i	−0.892917	−	0.506001i
$367$		−	13.3298i		−	0.695808i	−0.937530	−	0.347904i	$-0.886894\pi$
$367$		−	13.3298i		−	0.695808i	0.937530	−	0.347904i	$-0.113106\pi$
$368$	2.01158	+	1.16138i	0.104861	+	0.0605413i
$369$	1.97848	+	3.30305i	0.102995	+	0.171950i
$370$			15.1876i			0.789565i
$371$	−5.30133	+	10.3759i	−0.275231	+	0.538688i
$372$	27.0972	−	0.217785i	1.40492	−	0.0112916i
$373$	37.7422			1.95422			0.977109	−	0.212740i	$-0.0682388\pi$
$373$	37.7422			1.95422			0.977109	+	0.212740i	$0.0682388\pi$
$374$	22.8086	+	39.5057i	1.17941	+	2.04279i
$375$	−1.49299	+	0.878053i	−0.0770977	+	0.0453425i
$376$	17.2257	+	9.94528i	0.888349	+	0.512888i
$377$	19.0171			0.979431
$378$	−29.0899	−	13.9890i	−1.49622	−	0.719516i
$379$	−20.8189			−1.06939			−0.534697	−	0.845044i	$-0.679574\pi$
$379$	−20.8189			−1.06939			−0.534697	+	0.845044i	$0.679574\pi$
$380$	−21.6569	−	12.5036i	−1.11098	−	0.641423i
$381$	−25.7863	+	15.1653i	−1.32107	+	0.776944i
$382$	−5.85055	−	10.1334i	−0.299340	−	0.518472i
$383$	17.0443			0.870921			0.435461	−	0.900208i	$-0.356586\pi$
$383$	17.0443			0.870921			0.435461	+	0.900208i	$0.356586\pi$
$384$	−35.1364	+	0.282399i	−1.79305	+	0.0144111i
$385$	−12.1912	+	0.625303i	−0.621322	+	0.0318684i
$386$		−	17.8043i		−	0.906216i
$387$	−26.7346	+	0.429771i	−1.35900	+	0.0218465i
$388$	11.7370	+	6.77633i	0.595854	+	0.344016i
$389$			9.35487i			0.474311i	0.971472	+	0.237155i	$0.0762151\pi$
$389$			9.35487i			0.474311i	−0.971472	+	0.237155i	$0.923785\pi$
$390$	−20.7663	−	11.7679i	−1.05154	−	0.595893i
$391$	−6.44607	−	3.72164i	−0.325992	−	0.188211i
$392$	2.54385	+	24.7328i	0.128484	+	1.24920i
$393$	−20.7348	+	12.1945i	−1.04593	+	0.615129i
$394$	7.10536	−	12.3068i	0.357963	−	0.620009i
$395$	2.13689	−	3.70121i	0.107519	−	0.186228i
$396$	−0.781534	−	48.6166i	−0.0392735	−	2.44308i
$397$	4.11541	−	2.37603i	0.206547	−	0.119250i	−0.393159	−	0.919471i	$-0.628618\pi$
$397$	4.11541	−	2.37603i	0.206547	−	0.119250i	0.599705	+	0.800221i	$0.295284\pi$
$398$	12.5974	+	21.8193i	0.631449	+	1.09370i
$399$	29.1692	+	14.6090i	1.46029	+	0.731363i
$400$	−0.657032	+	1.13801i	−0.0328516	+	0.0569006i
$401$		−	5.00405i		−	0.249890i	−0.992164	−	0.124945i	$-0.960125\pi$
$401$		−	5.00405i		−	0.249890i	0.992164	−	0.124945i	$-0.0398755\pi$
$402$	−24.0354	−	40.8685i	−1.19878	−	2.03833i
$403$	−26.1405			−1.30215
$404$	6.51158	+	11.2784i	0.323963	+	0.561121i
$405$	4.74820	+	7.64556i	0.235940	+	0.379911i
$406$	1.03101	+	20.1012i	0.0511684	+	0.997605i
$407$	25.8466	−	14.9225i	1.28117	−	0.739682i
$408$	−25.9050	+	0.208203i	−1.28249	+	0.0103076i
$409$	−0.988304	+	0.570598i	−0.0488685	+	0.0282142i	−0.524235	−	0.851574i	$-0.675649\pi$
$409$	−0.988304	+	0.570598i	−0.0488685	+	0.0282142i	0.475367	+	0.879788i	$0.342315\pi$
$410$	−2.60966	+	1.50669i	−0.128882	+	0.0744101i
$411$	7.11696	+	12.1013i	0.351054	+	0.596912i
$412$	44.3506	−	25.6058i	2.18500	−	1.26151i
$413$	−10.1691	+	6.58780i	−0.500389	+	0.324165i
$414$	6.39789	+	10.6812i	0.314439	+	0.524953i
$415$	−4.40966	−	7.63776i	−0.216462	−	0.374923i
$416$	23.5857			1.15638
$417$	24.9915	−	0.200862i	1.22384	−	0.00983625i
$418$			77.1204i			3.77208i
$419$	11.0159	−	19.0801i	0.538162	−	0.932123i	−0.460842	−	0.887482i	$-0.652452\pi$
$419$	11.0159	−	19.0801i	0.538162	−	0.932123i	0.999003	−	0.0446408i	$-0.0142143\pi$
$420$	7.20867	−	14.3933i	0.351747	−	0.702321i
$421$	−4.61938	−	8.00100i	−0.225135	−	0.389945i	0.731225	−	0.682136i	$-0.238949\pi$
$421$	−4.61938	−	8.00100i	−0.225135	−	0.389945i	−0.956360	+	0.292191i	$0.905616\pi$
$422$	21.6013	−	12.4715i	1.05153	−	0.607103i
$423$	8.63272	+	14.4123i	0.419737	+	0.700748i
$424$	7.82118	−	13.5467i	0.379830	−	0.657885i
$425$	2.10545	−	3.64675i	0.102129	−	0.176893i
$426$	−0.102669	−	12.7743i	−0.00497435	−	0.618916i
$427$	−5.81195	+	11.3753i	−0.281260	+	0.550488i
$428$	−0.423762	−	0.244659i	−0.0204833	−	0.0118260i
$429$	0.376970	+	46.9032i	0.0182003	+	2.26451i
$430$		−	20.9264i		−	1.00916i
$431$	−18.8182	−	10.8647i	−0.906440	−	0.523333i	−0.0271559	−	0.999631i	$-0.508645\pi$
$431$	−18.8182	−	10.8647i	−0.906440	−	0.523333i	−0.879284	+	0.476298i	$0.841978\pi$
$432$	5.99388	+	3.27048i	0.288381	+	0.157351i
$433$		−	10.9728i		−	0.527320i	−0.964616	−	0.263660i	$-0.915070\pi$
$433$		−	10.9728i		−	0.527320i	0.964616	−	0.263660i	$-0.0849298\pi$
$434$	−1.41721	−	27.6306i	−0.0680281	−	1.32631i
$435$	2.76685	−	4.88254i	0.132660	−	0.234100i
$436$	24.8149			1.18842
$437$	−6.29180	−	10.8977i	−0.300977	−	0.521308i
$438$	18.8812	+	10.6996i	0.902177	+	0.511249i
$439$	−9.12853	−	5.27036i	−0.435681	−	0.251540i	0.266083	−	0.963950i	$-0.414270\pi$
$439$	−9.12853	−	5.27036i	−0.435681	−	0.251540i	−0.701764	+	0.712410i	$0.747604\pi$
$440$	16.3881			0.781274
$441$	−8.27501	+	19.3009i	−0.394048	+	0.919090i
$442$	58.0293			2.76017
$443$	−29.6006	−	17.0899i	−1.40637	−	0.811966i	−0.411332	−	0.911486i	$-0.634936\pi$
$443$	−29.6006	−	17.0899i	−1.40637	−	0.811966i	−0.995036	+	0.0995193i	$0.968269\pi$
$444$	0.316305	+	39.3551i	0.0150112	+	1.86771i
$445$	−0.475563	−	0.823699i	−0.0225438	−	0.0390471i
$446$	26.5662			1.25795
$447$	−0.881176	−	1.49830i	−0.0416782	−	0.0708672i
$448$	1.63488	+	31.8744i	0.0772407	+	1.50592i
$449$			31.9314i			1.50693i	0.657486	+	0.753467i	$0.271620\pi$
$449$			31.9314i			1.50693i	−0.657486	+	0.753467i	$0.728380\pi$
$450$	−6.04271	+	3.61949i	−0.284856	+	0.170624i
$451$	5.12823	+	2.96079i	0.241479	+	0.139418i
$452$		−	16.5644i		−	0.779122i
$453$	−13.2679	+	7.80308i	−0.623381	+	0.366621i
$454$	−52.3024	−	30.1968i	−2.45467	−	1.41721i
$455$	−7.06530	+	13.8283i	−0.331226	+	0.648282i
$456$	−38.1035	−	21.5926i	−1.78436	−	1.01117i
$457$	3.94079	−	6.82565i	0.184343	−	0.319291i	−0.759012	−	0.651076i	$-0.774318\pi$
$457$	3.94079	−	6.82565i	0.184343	−	0.319291i	0.943355	+	0.331786i	$0.107651\pi$
$458$	5.50806	−	9.54024i	0.257375	−	0.445786i
$459$	−19.2073	−	10.4802i	−0.896520	−	0.489175i
$460$	−5.37738	+	3.10463i	−0.250722	+	0.144754i
$461$	2.54320	+	4.40496i	0.118449	+	0.205159i	0.919153	−	0.393900i	$-0.128875\pi$
$461$	2.54320	+	4.40496i	0.118449	+	0.205159i	−0.800704	+	0.599060i	$0.795541\pi$
$462$	−49.5564	+	2.94132i	−2.30557	+	0.136842i
$463$	12.1838	−	21.1030i	0.566229	−	0.980738i	−0.430705	−	0.902493i	$-0.641735\pi$
$463$	12.1838	−	21.1030i	0.566229	−	0.980738i	0.996934	−	0.0782450i	$-0.0249316\pi$
$464$		−	4.25769i		−	0.197658i
$465$	−3.80325	+	6.71142i	−0.176371	+	0.311234i
$466$	21.5928			1.00027
$467$	−8.88493	−	15.3892i	−0.411146	−	0.712125i	0.583870	−	0.811847i	$-0.301538\pi$
$467$	−8.88493	−	15.3892i	−0.411146	−	0.712125i	−0.995015	+	0.0997222i	$0.968205\pi$
$468$	−54.0562	−	30.0614i	−2.49875	−	1.38959i
$469$	−25.8881	+	16.7710i	−1.19540	+	0.774411i
$470$	−11.3868	+	6.57417i	−0.525234	+	0.303244i
$471$	16.3648	−	28.8782i	0.754051	−	1.33064i
$472$	14.0871	−	8.13316i	0.648409	−	0.374359i
$473$	−35.6129	+	20.5611i	−1.63749	+	0.945402i
$474$	8.56893	−	15.1212i	0.393584	−	0.694539i
$475$	6.16519	−	3.55947i	0.282878	−	0.163320i
$476$	2.00469	+	39.0845i	0.0918849	+	1.79144i
$477$	11.3341	−	6.78896i	0.518953	−	0.310845i
$478$	6.51280	+	11.2805i	0.297889	+	0.515958i
$479$	9.39651			0.429338			0.214669	−	0.976687i	$-0.431133\pi$
$479$	9.39651			0.429338			0.214669	+	0.976687i	$0.431133\pi$
$480$	3.43155	−	6.05549i	0.156628	−	0.276394i
$481$		−	37.9656i		−	1.73108i
$482$	1.46375	−	2.53530i	0.0666721	−	0.115480i
$483$	6.76274	−	4.45864i	0.307715	−	0.202875i
$484$	−18.0700	−	31.2981i	−0.821362	−	1.42264i
$485$	−3.34122	+	1.92905i	−0.151717	+	0.0875937i
$486$	19.5589	+	30.9363i	0.887212	+	1.40330i
$487$	−18.1653	+	31.4632i	−0.823148	+	1.42574i	0.0801776	+	0.996781i	$0.474451\pi$
$487$	−18.1653	+	31.4632i	−0.823148	+	1.42574i	−0.903326	+	0.428954i	$0.858882\pi$
$488$	8.57452	−	14.8515i	0.388150	−	0.672296i
$489$	15.9547	+	9.04125i	0.721495	+	0.408859i
$490$	−14.9997	−	6.71835i	−0.677616	−	0.303504i
$491$	24.4060	+	14.0908i	1.10143	+	0.635908i	0.936595	−	0.350414i	$-0.113959\pi$
$491$	24.4060	+	14.0908i	1.10143	+	0.635908i	0.164831	+	0.986322i	$0.447292\pi$
$492$	−6.73096	+	3.95859i	−0.303455	+	0.178467i
$493$			13.6437i			0.614482i
$494$	84.9607	+	49.0521i	3.82256	+	2.20696i
$495$	12.0970	+	6.72729i	0.543718	+	0.302369i
$496$			5.85252i			0.262786i
$497$	−8.30009	+	0.425722i	−0.372310	+	0.0190962i
$498$	−18.1820	−	30.9156i	−0.814754	−	1.38536i
$499$	17.2832			0.773703			0.386851	−	0.922142i	$-0.373563\pi$
$499$	17.2832			0.773703			0.386851	+	0.922142i	$0.373563\pi$
$500$	−1.75639	−	3.04216i	−0.0785482	−	0.136049i
$501$	0.0582941	+	7.25303i	0.00260439	+	0.324042i
$502$	13.6714	+	7.89317i	0.610183	+	0.352290i
$503$	43.6773			1.94747			0.973737	−	0.227677i	$-0.0731132\pi$
$503$	43.6773			1.94747			0.973737	+	0.227677i	$0.0731132\pi$
$504$	12.4218	−	25.3082i	0.553313	−	1.12732i
$505$	−3.70737			−0.164976
$506$	16.5834	+	9.57444i	0.737223	+	0.425636i
$507$	32.3214	+	18.3160i	1.43544	+	0.813442i
$508$	−30.3356	−	52.5428i	−1.34592	−	2.33121i
$509$	37.2875			1.65274			0.826370	−	0.563128i	$-0.190402\pi$
$509$	37.2875			1.65274			0.826370	+	0.563128i	$0.190402\pi$
$510$	8.44284	−	14.8987i	0.373855	−	0.659725i
$511$	6.42391	−	12.5730i	0.284177	−	0.556197i
$512$		−	14.6154i		−	0.645915i
$513$	−19.2625	−	31.5800i	−0.850461	−	1.39429i
$514$	−48.1445	−	27.7962i	−2.12356	−	1.22604i
$515$			14.5787i			0.642413i
$516$	−0.435824	−	54.2258i	−0.0191861	−	2.38716i
$517$	22.3761	+	12.9189i	0.984101	+	0.568171i
$518$	40.1298	−	2.05831i	1.76320	−	0.0904369i
$519$	−0.286528	−	35.6502i	−0.0125772	−	1.56487i
$520$	10.4236	−	18.0542i	0.457105	−	0.791730i
$521$	−0.611244	+	1.05871i	−0.0267791	+	0.0463827i	−0.879104	−	0.476629i	$-0.841858\pi$
$521$	−0.611244	+	1.05871i	−0.0267791	+	0.0463827i	0.852325	+	0.523012i	$0.175192\pi$
$522$	11.0921	−	19.9458i	0.485489	−	0.873003i
$523$	−17.9810	+	10.3813i	−0.786255	+	0.453944i	−0.838642	−	0.544682i	$-0.816650\pi$
$523$	−17.9810	+	10.3813i	−0.786255	+	0.453944i	0.0523877	+	0.998627i	$0.483317\pi$
$524$	−24.3929	−	42.2497i	−1.06561	−	1.84569i
$525$	2.52240	+	3.82590i	0.110086	+	0.166976i
$526$	2.11372	−	3.66108i	0.0921628	−	0.159631i
$527$		−	18.7543i		−	0.816951i
$528$	10.5010	−	0.0843989i	0.456999	−	0.00367299i
$529$	19.8755			0.864153
$530$	5.17007	+	8.95483i	0.224574	+	0.388973i
$531$	13.7370	−	0.220829i	0.596137	−	0.00958317i
$532$	−30.1030	+	58.9182i	−1.30513	+	2.55443i
$533$	6.52358	−	3.76639i	0.282568	−	0.163140i
$534$	−1.96085	−	3.33411i	−0.0848542	−	0.144281i
$535$	0.120634	−	0.0696482i	0.00521548	−	0.00301116i
$536$	35.8622	−	20.7051i	1.54901	−	0.894323i
$537$	35.2959	−	0.283680i	1.52313	−	0.0122417i
$538$	−12.2896	+	7.09542i	−0.529843	+	0.305905i
$539$	3.30445	+	32.1278i	0.142333	+	1.38384i
$540$	−15.5829	+	9.50492i	−0.670581	+	0.409027i
$541$	−13.0039	−	22.5234i	−0.559081	−	0.968357i	−0.997573	−	0.0696223i	$-0.977821\pi$
$541$	−13.0039	−	22.5234i	−0.559081	−	0.968357i	0.438492	−	0.898735i	$-0.355513\pi$
$542$	6.28114			0.269798
$543$	−3.97421	−	6.75753i	−0.170550	−	0.289993i
$544$			16.9214i			0.725499i
$545$	−3.53208	+	6.11775i	−0.151298	+	0.262056i
$546$	−28.2798	+	56.4653i	−1.21026	+	2.41649i
$547$	−22.0667	−	38.2207i	−0.943505	−	1.63420i	−0.758717	−	0.651420i	$-0.774174\pi$
$547$	−22.0667	−	38.2207i	−0.943505	−	1.63420i	−0.184788	−	0.982778i	$-0.559160\pi$
$548$	−24.6579	+	14.2362i	−1.05333	+	0.608142i
$549$	12.4258	−	7.44287i	0.530321	−	0.317654i
$550$	−5.41657	+	9.38177i	−0.230963	+	0.400040i
$551$	−11.5330	+	19.9758i	−0.491323	+	0.850997i
$552$	−9.37363	+	5.51278i	−0.398968	+	0.234640i
$553$	−10.0692	−	5.14466i	−0.428187	−	0.218773i
$554$	−8.52965	−	4.92460i	−0.362390	−	0.209226i
$555$	−9.74746	−	5.52372i	−0.413757	−	0.234469i
$556$			50.6871i			2.14961i
$557$	−24.0901	−	13.9084i	−1.02073	−	0.589318i	−0.106414	−	0.994322i	$-0.533937\pi$
$557$	−24.0901	−	13.9084i	−1.02073	−	0.589318i	−0.914315	+	0.405004i	$0.867270\pi$
$558$	−15.2470	+	27.4170i	−0.645455	+	1.16065i
$559$			52.3113i			2.21253i
$560$	3.09599	+	1.58183i	0.130829	+	0.0668446i
$561$	−33.6504	+	0.270455i	−1.42072	+	0.0114186i
$562$	−14.0005			−0.590576
$563$	0.491478	+	0.851264i	0.0207133	+	0.0358765i	0.876196	−	0.481954i	$-0.160073\pi$
$563$	0.491478	+	0.851264i	0.0207133	+	0.0358765i	−0.855483	+	0.517831i	$0.826740\pi$
$564$	−29.3693	+	17.2726i	−1.23667	+	0.727307i
$565$	4.08371	+	2.35773i	0.171803	+	0.0991904i
$566$	12.4452			0.523112
$567$	19.5582	−	13.5822i	0.821367	−	0.570400i
$568$	11.1575			0.468157
$569$	5.90230	+	3.40770i	0.247437	+	0.142858i	0.618590	−	0.785714i	$-0.287704\pi$
$569$	5.90230	+	3.40770i	0.247437	+	0.142858i	−0.371153	+	0.928572i	$0.621037\pi$
$570$	24.9550	−	14.6765i	1.04525	−	0.614729i
$571$	18.3531	+	31.7886i	0.768055	+	1.33031i	0.938616	+	0.344963i	$0.112108\pi$
$571$	18.3531	+	31.7886i	0.768055	+	1.33031i	−0.170562	+	0.985347i	$0.554558\pi$
$572$	−95.1276			−3.97748
$573$	8.63153	−	0.0693733i	0.360587	−	0.00289811i
$574$	4.33477	+	6.69126i	0.180930	+	0.279288i
$575$		−	1.76762i		−	0.0737149i
$576$	17.5888	−	31.6280i	0.732865	−	1.31783i
$577$	−34.0281	−	19.6461i	−1.41661	−	0.817880i	−0.420610	−	0.907242i	$-0.638184\pi$
$577$	−34.0281	−	19.6461i	−1.41661	−	0.817880i	−0.995999	+	0.0893621i	$0.971517\pi$
$578$			1.71796i			0.0714577i
$579$	11.4269	+	6.47542i	0.474885	+	0.269109i
$580$	9.85688	+	5.69087i	0.409285	+	0.236301i
$581$	−19.5835	+	12.6867i	−0.812459	+	0.526332i
$582$	−13.5244	+	7.95389i	−0.560602	+	0.329700i
$583$	10.1597	−	17.5971i	0.420771	−	0.728797i
$584$	−9.47735	+	16.4152i	−0.392175	+	0.679268i
$585$	15.1054	−	9.04792i	0.624532	−	0.374086i
$586$	−29.0353	+	16.7635i	−1.19944	+	0.692495i
$587$	−21.2148	−	36.7451i	−0.875628	−	1.51663i	−0.856093	−	0.516823i	$-0.827115\pi$
$587$	−21.2148	−	36.7451i	−0.875628	−	1.51663i	−0.0195352	−	0.999809i	$-0.506219\pi$
$588$	−39.0081	−	17.0967i	−1.60867	−	0.705054i
$589$	15.8530	−	27.4582i	0.653212	−	1.13140i
$590$			10.7526i			0.442678i
$591$	5.31436	+	9.03624i	0.218604	+	0.371701i
$592$	−8.50002			−0.349349
$593$	−19.8121	−	34.3156i	−0.813586	−	1.40917i	−0.910339	−	0.413864i	$-0.864179\pi$
$593$	−19.8121	−	34.3156i	−0.813586	−	1.40917i	0.0967528	−	0.995308i	$-0.469154\pi$
$594$	49.4135	+	26.9618i	2.02746	+	1.10626i
$595$	−9.92106	−	5.06896i	−0.406724	−	0.207807i
$596$	3.05298	−	1.76264i	0.125055	−	0.0722004i
$597$	−18.5854	+	0.149374i	−0.760649	+	0.00611349i
$598$	21.0956	−	12.1796i	0.862663	−	0.498059i
$599$	−39.8063	+	22.9822i	−1.62644	+	0.939025i	−0.641296	+	0.767294i	$0.721603\pi$
$599$	−39.8063	+	22.9822i	−1.62644	+	0.939025i	−0.985144	+	0.171731i	$0.945064\pi$
$600$	−3.11876	−	5.30296i	−0.127323	−	0.216492i
$601$	−35.9416	+	20.7509i	−1.46609	+	0.846445i	−0.999281	−	0.0379145i	$-0.987929\pi$
$601$	−35.9416	+	20.7509i	−1.46609	+	0.846445i	−0.466806	+	0.884360i	$0.654595\pi$
$602$	−55.2933	+	2.83606i	−2.25359	+	0.115589i
$603$	34.9712	−	0.562178i	1.42414	−	0.0228936i
$604$	−15.6087	−	27.0350i	−0.635109	−	1.10004i
$605$	10.2881			0.418272
$606$	−15.0764	+	0.121172i	−0.612437	+	0.00492228i
$607$			16.1390i			0.655063i	0.944840	+	0.327532i	$0.106217\pi$
$607$			16.1390i			0.655063i	−0.944840	+	0.327532i	$0.893783\pi$
$608$	−14.3036	+	24.7746i	−0.580090	+	1.00474i
$609$	−13.2760	−	6.64909i	−0.537971	−	0.269435i
$610$	5.66805	+	9.81736i	0.229493	+	0.397493i
$611$	28.4645	−	16.4340i	1.15155	−	0.664847i
$612$	21.5674	−	38.7823i	0.871810	−	1.56768i
$613$	−5.55140	+	9.61531i	−0.224219	+	0.388359i	−0.956085	−	0.293090i	$-0.905316\pi$
$613$	−5.55140	+	9.61531i	−0.224219	+	0.388359i	0.731866	+	0.681449i	$0.238650\pi$
$614$	3.89898	−	6.75323i	0.157350	−	0.272538i
$615$	−0.0178657	−	2.22288i	−0.000720414	−	0.0896350i
$616$	−2.22101	−	43.3020i	−0.0894872	−	1.74469i
$617$	−16.7252	−	9.65630i	−0.673331	−	0.388748i	0.124006	−	0.992281i	$-0.460426\pi$
$617$	−16.7252	−	9.65630i	−0.673331	−	0.388748i	−0.797338	+	0.603533i	$0.793759\pi$
$618$	0.476491	+	59.2857i	0.0191673	+	2.38482i
$619$		−	27.8193i		−	1.11815i	−0.829117	−	0.559076i	$-0.811156\pi$
$619$		−	27.8193i		−	1.11815i	0.829117	−	0.559076i	$-0.188844\pi$
$620$	−13.5490	−	7.82253i	−0.544142	−	0.314160i
$621$	−9.18216	+	0.221435i	−0.368467	+	0.00888587i
$622$		−	11.9507i		−	0.479179i
$623$	−2.11199	+	1.36820i	−0.0846151	+	0.0548158i
$624$	6.58615	−	11.6223i	0.263657	−	0.465263i
$625$	1.00000			0.0400000
$626$	−34.8513	−	60.3642i	−1.39294	−	2.41264i
$627$	−49.4962	−	28.0487i	−1.97669	−	1.12016i
$628$	58.2994	+	33.6592i	2.32640	+	1.34315i
$629$	27.2382			1.08606
$630$	10.3826	+	15.4760i	0.413654	+	0.616578i
$631$	31.3926			1.24972			0.624860	−	0.780737i	$-0.285156\pi$
$631$	31.3926			1.24972			0.624860	+	0.780737i	$0.285156\pi$
$632$	13.1463	+	7.59004i	0.522933	+	0.301916i
$633$	0.147882	+	18.3997i	0.00587777	+	0.731321i
$634$	−13.3202	−	23.0712i	−0.529012	−	0.916275i
$635$	17.2716			0.685401
$636$	13.5835	+	23.0967i	0.538622	+	0.915843i
$637$	37.4958	+	16.7944i	1.48564	+	0.665418i
$638$		−	35.1004i		−	1.38964i
$639$	8.23593	+	4.58011i	0.325808	+	0.181186i
$640$	17.5688	+	10.1433i	0.694467	+	0.400951i
$641$		−	18.8863i		−	0.745965i	−0.927838	−	0.372982i	$-0.878335\pi$
$641$		−	18.8863i		−	0.745965i	0.927838	−	0.372982i	$-0.121665\pi$
$642$	0.488296	−	0.287175i	0.0192715	−	0.0113339i
$643$	−9.74473	−	5.62612i	−0.384295	−	0.221873i	0.295391	−	0.955377i	$-0.404550\pi$
$643$	−9.74473	−	5.62612i	−0.384295	−	0.221873i	−0.679685	+	0.733504i	$0.737884\pi$
$644$	8.93208	+	13.7878i	0.351973	+	0.543315i
$645$	13.4306	+	7.61092i	0.528831	+	0.299680i
$646$	−35.1922	+	60.9546i	−1.38462	+	2.39823i
$647$	−17.9539	+	31.0971i	−0.705840	+	1.22255i	0.260547	+	0.965461i	$0.416097\pi$
$647$	−17.9539	+	31.0971i	−0.705840	+	1.22255i	−0.966387	+	0.257090i	$0.917236\pi$
$648$	−27.1563	+	16.8652i	−1.06680	+	0.662526i
$649$	18.2990	−	10.5649i	0.718299	−	0.414710i
$650$	6.89036	+	11.9345i	0.270262	+	0.468108i
$651$	18.2489	+	9.13967i	0.715229	+	0.358212i
$652$	−18.5961	+	32.2093i	−0.728278	+	1.26141i
$653$		−	40.1643i		−	1.57175i	−0.618384	−	0.785876i	$-0.712212\pi$
$653$		−	40.1643i		−	1.57175i	0.618384	−	0.785876i	$-0.287788\pi$
$654$	−14.1636	+	24.9939i	−0.553842	+	0.977339i
$655$	13.8881			0.542652
$656$	−0.843247	−	1.46055i	−0.0329233	−	0.0570248i
$657$	−13.7342	+	8.22655i	−0.535820	+	0.320948i
$658$	18.9140	+	29.1961i	0.737344	+	1.13818i
$659$	−37.9783	+	21.9268i	−1.47943	+	0.854147i	−0.999729	−	0.0232872i	$-0.992587\pi$
$659$	−37.9783	+	21.9268i	−1.47943	+	0.854147i	−0.479697	+	0.877434i	$0.659253\pi$
$660$	−13.8404	+	24.4235i	−0.538736	+	0.950683i
$661$	−3.19506	+	1.84467i	−0.124274	+	0.0717494i	−0.560848	−	0.827919i	$-0.689525\pi$
$661$	−3.19506	+	1.84467i	−0.124274	+	0.0717494i	0.436575	+	0.899668i	$0.356192\pi$
$662$	30.2921	−	17.4892i	1.17734	−	0.679736i
$663$	−21.1052	+	37.2434i	−0.819659	+	1.44641i
$664$	27.1286	−	15.6627i	1.05279	−	0.607831i
$665$	−10.2407	−	15.8077i	−0.397115	−	0.612998i
$666$	−39.8196	−	22.1442i	−1.54298	−	0.858071i
$667$	2.86363	+	4.95995i	0.110880	+	0.192050i
$668$	−14.7104			−0.569162
$669$	−9.66213	+	17.0503i	−0.373560	+	0.659203i
$670$			27.3735i			1.05753i
$671$	11.1383	−	19.2920i	0.429988	−	0.744760i
$672$	−16.4653	−	8.24642i	−0.635164	−	0.318113i
$673$	18.2345	+	31.5830i	0.702887	+	1.21744i	0.967449	+	0.253068i	$0.0814395\pi$
$673$	18.2345	+	31.5830i	0.702887	+	1.21744i	−0.264561	+	0.964369i	$0.585227\pi$
$674$	62.8750	−	36.3009i	2.42186	−	1.39826i
$675$	−0.125273	−	5.19464i	−0.00482175	−	0.199942i
$676$	−37.6724	+	65.2505i	−1.44894	+	2.50963i
$677$	15.7994	−	27.3653i	0.607219	−	1.05173i	−0.384478	−	0.923134i	$-0.625618\pi$
$677$	15.7994	−	27.3653i	0.607219	−	1.05173i	0.991697	−	0.128600i	$-0.0410482\pi$
$678$	16.6839	+	9.45448i	0.640741	+	0.363097i
$679$	5.54991	+	8.56698i	0.212986	+	0.328771i
$680$	12.9529	+	7.47836i	0.496721	+	0.286782i
$681$	38.4028	−	22.5853i	1.47160	−	0.865471i
$682$			48.2481i			1.84752i
$683$	42.4740	+	24.5224i	1.62522	+	0.938323i	0.985492	+	0.169724i	$0.0542878\pi$
$683$	42.4740	+	24.5224i	1.62522	+	0.938323i	0.639731	+	0.768599i	$0.279046\pi$
$684$	64.3595	−	38.5504i	2.46085	−	1.47401i
$685$		−	8.10539i		−	0.309691i
$686$	−15.7189	+	40.5438i	−0.600151	+	1.54797i
$687$	4.11969	+	7.00488i	0.157176	+	0.267253i
$688$	11.7118			0.446510
$689$	−12.9240	−	22.3851i	−0.492366	−	0.852804i
$690$	−0.0577731	−	7.18822i	−0.00219939	−	0.273651i
$691$	5.94072	+	3.42988i	0.225996	+	0.130479i	0.608723	−	0.793383i	$-0.291682\pi$
$691$	5.94072	+	3.42988i	0.225996	+	0.130479i	−0.382728	+	0.923861i	$0.625015\pi$
$692$	72.3047			2.74861
$693$	16.1359	−	32.8753i	0.612953	−	1.24883i
$694$	−13.9713			−0.530345
$695$	−12.4962	−	7.21466i	−0.474007	−	0.273668i
$696$	17.3423	+	9.82760i	0.657358	+	0.372514i
$697$	2.70218	+	4.68031i	0.102352	+	0.177279i
$698$	24.5405			0.928871
$699$	−7.85329	+	13.8583i	−0.297039	+	0.524170i
$700$	−7.80019	+	5.05316i	−0.294819	+	0.190992i
$701$		−	6.97938i		−	0.263607i	−0.991276	−	0.131804i	$-0.957923\pi$
$701$		−	6.97938i		−	0.263607i	0.991276	−	0.131804i	$-0.0420769\pi$
$702$	61.1321	−	37.2880i	2.30728	−	1.40735i
$703$	39.8795	+	23.0244i	1.50408	+	0.868383i
$704$		−	55.6586i		−	2.09771i
$705$	−0.0779538	−	9.69912i	−0.00293591	−	0.365290i
$706$	−61.7679	−	35.6617i	−2.32467	−	1.34215i
$707$	0.502443	+	9.79589i	0.0188963	+	0.368413i
$708$	0.223940	+	27.8629i	0.00841616	+	1.04715i
$709$	−16.5487	+	28.6633i	−0.621501	+	1.07647i	0.367705	+	0.929942i	$0.380144\pi$
$709$	−16.5487	+	28.6633i	−0.621501	+	1.07647i	−0.989206	+	0.146529i	$0.953190\pi$
$710$	−3.68774	+	6.38735i	−0.138398	+	0.239713i
$711$	6.58832	+	10.9991i	0.247081	+	0.412500i
$712$	2.92570	−	1.68915i	0.109645	−	0.0633037i
$713$	−3.93628	−	6.81783i	−0.147415	−	0.255330i
$714$	−40.5107	−	20.2892i	−1.51608	−	0.759304i
$715$	13.5402	−	23.4523i	0.506375	−	0.877068i
$716$			71.5860i			2.67529i
$717$	−9.60858	+	0.0772261i	−0.358839	+	0.00288406i
$718$	65.2946			2.43677
$719$	−4.95541	−	8.58301i	−0.184805	−	0.320092i	0.758706	−	0.651434i	$-0.225832\pi$
$719$	−4.95541	−	8.58301i	−0.184805	−	0.320092i	−0.943511	+	0.331341i	$0.892499\pi$
$720$	−2.02572	−	3.38191i	−0.0754940	−	0.126037i
$721$	38.5209	−	1.97578i	1.43459	−	0.0735820i
$722$	−64.4158	+	37.1905i	−2.39731	+	1.38409i
$723$	1.09480	+	1.86153i	0.0407159	+	0.0692310i
$724$	13.7693	−	7.94971i	0.511732	−	0.295449i
$725$	−2.80600	+	1.62005i	−0.104212	+	0.0601671i
$726$	41.8377	−	0.336258i	1.55274	−	0.0124797i
$727$	−5.94005	+	3.42949i	−0.220304	+	0.127193i	−0.606091	−	0.795395i	$-0.707263\pi$
$727$	−5.94005	+	3.42949i	−0.220304	+	0.127193i	0.385787	+	0.922588i	$0.373930\pi$
$728$	−49.1169	−	25.0952i	−1.82039	−	0.930092i
$729$	−26.9686	+	1.30149i	−0.998838	+	0.0482035i
$730$	−6.26485	−	10.8510i	−0.231873	−	0.401615i
$731$	−37.5304			−1.38811
$732$	14.8919	+	25.3213i	0.550421	+	0.935904i
$733$		−	7.87689i		−	0.290939i	−0.989363	−	0.145470i	$-0.953531\pi$
$733$		−	7.87689i		−	0.290939i	0.989363	−	0.145470i	$-0.0464693\pi$
$734$	−15.6487	+	27.1043i	−0.577603	+	1.00044i
$735$	9.76724	−	7.18339i	0.360270	−	0.264963i
$736$	3.55157	+	6.15150i	0.130913	+	0.226747i
$737$	46.5849	−	26.8958i	1.71598	−	0.990719i
$738$	−0.145305	−	9.03897i	−0.00534877	−	0.332729i
$739$	26.9795	−	46.7299i	0.992457	−	1.71899i	0.390063	−	0.920788i	$-0.372453\pi$
$739$	26.9795	−	46.7299i	0.992457	−	1.71899i	0.602395	−	0.798198i	$-0.294213\pi$
$740$	11.3612	−	19.6782i	0.417646	−	0.723385i
$741$	−62.3820	+	36.6879i	−2.29166	+	1.34776i
$742$	22.9605	−	14.8744i	0.842905	−	0.546056i
$743$	39.3208	+	22.7019i	1.44254	+	0.832851i	0.998019	−	0.0629179i	$-0.0200406\pi$
$743$	39.3208	+	22.7019i	1.44254	+	0.832851i	0.444521	+	0.895769i	$0.353374\pi$
$744$	−23.8383	−	13.5088i	−0.873954	−	0.495256i
$745$			1.00356i			0.0367675i
$746$	−76.7438	−	44.3081i	−2.80979	−	1.62223i
$747$	26.4546	−	0.425269i	0.967922	−	0.0155598i
$748$		−	68.2488i		−	2.49542i
$749$	−0.200379	−	0.309310i	−0.00732169	−	0.0113019i
$750$	4.06660	−	0.0326841i	0.148491	−	0.00119346i
$751$	25.5939			0.933936			0.466968	−	0.884274i	$-0.345346\pi$
$751$	25.5939			0.933936			0.466968	+	0.884274i	$0.345346\pi$
$752$	−3.67936	−	6.37284i	−0.134172	−	0.232393i
$753$	−10.0381	+	5.90360i	−0.365810	+	0.215139i
$754$	−38.6688	−	22.3254i	−1.40823	−	0.813044i
$755$	8.88680			0.323424
$756$	27.2265	+	39.8862i	0.990219	+	1.45065i
$757$	−12.6702			−0.460506			−0.230253	−	0.973131i	$-0.573955\pi$
$757$	−12.6702			−0.460506			−0.230253	+	0.973131i	$0.573955\pi$
$758$	42.3324	+	24.4406i	1.53758	+	0.887724i
$759$	−12.1763	+	7.16108i	−0.441972	+	0.259931i
$760$	12.6429	+	21.8981i	0.458606	+	0.794329i
$761$	−30.3457			−1.10003			−0.550015	−	0.835155i	$-0.685378\pi$
$761$	−30.3457			−1.10003			−0.550015	+	0.835155i	$0.685378\pi$
$762$	70.2366	−	0.564506i	2.54440	−	0.0204499i
$763$	16.6435	+	8.50363i	0.602534	+	0.307852i
$764$			17.5062i			0.633352i
$765$	6.49138	+	10.8373i	0.234696	+	0.391824i
$766$	−34.6573	−	20.0094i	−1.25222	−	0.722968i
$767$		−	26.8791i		−	0.970549i
$768$	35.4204	+	20.0721i	1.27812	+	0.724291i
$769$	−9.27475	−	5.35478i	−0.334456	−	0.193098i	0.323362	−	0.946275i	$-0.395187\pi$
$769$	−9.27475	−	5.35478i	−0.334456	−	0.193098i	−0.657818	+	0.753177i	$0.728520\pi$
$770$	25.5233	+	13.0406i	0.919797	+	0.469951i
$771$	35.3499	−	20.7898i	1.27309	−	0.748728i
$772$	−13.3187	+	23.0686i	−0.479349	+	0.830257i
$773$	0.0745217	−	0.129075i	0.00268036	−	0.00464252i	−0.864682	−	0.502319i	$-0.832480\pi$
$773$	0.0745217	−	0.129075i	0.00268036	−	0.00464252i	0.867362	+	0.497677i	$0.165813\pi$
$774$	54.8658	+	30.5116i	1.97211	+	1.09672i
$775$	3.85707	−	2.22688i	0.138550	−	0.0799918i
$776$	−6.85180	−	11.8677i	−0.245965	−	0.426025i
$777$	−13.2742	+	26.5041i	−0.476209	+	0.950829i
$778$	10.9823	−	19.0219i	0.393734	−	0.681968i
$779$			9.13659i			0.327352i
$780$	18.1033	+	30.7819i	0.648203	+	1.10217i
$781$	14.4935			0.518618
$782$	8.73815	+	15.1349i	0.312476	+	0.541224i
$783$	8.76708	+	14.3732i	0.313310	+	0.513658i
$784$	3.76005	−	8.39485i	0.134288	−	0.299816i
$785$	−16.5964	+	9.58193i	−0.592350	+	0.341994i
$786$	56.4773	−	0.453920i	2.01448	−	0.0161908i
$787$	−0.433622	+	0.250352i	−0.0154570	+	0.00892409i	−0.507709	−	0.861529i	$-0.669507\pi$
$787$	−0.433622	+	0.250352i	−0.0154570	+	0.00892409i	0.492252	+	0.870453i	$0.336174\pi$
$788$	−18.4125	+	10.6304i	−0.655917	+	0.378694i
$789$	1.58093	+	2.68813i	0.0562827	+	0.0957000i
$790$	−8.69018	+	5.01728i	−0.309183	+	0.178507i
$791$	5.67633	−	11.1098i	0.201827	−	0.395020i
$792$	−23.8947	+	42.9673i	−0.849060	+	1.52678i
$793$	−14.1689	−	24.5412i	−0.503151	−	0.871484i
$794$	−11.1575			−0.395966
$795$	−7.62760	+	0.0613045i	−0.270523	+	0.00217425i
$796$		−	37.6943i		−	1.33604i
$797$	−3.12062	+	5.40507i	−0.110538	+	0.191457i	−0.915987	−	0.401207i	$-0.868591\pi$
$797$	−3.12062	+	5.40507i	−0.110538	+	0.191457i	0.805449	+	0.592665i	$0.201924\pi$
$798$	−42.1613	−	63.9491i	−1.49250	−	2.26377i
$799$	11.7905	+	20.4217i	0.417117	+	0.722467i
$800$	−3.48010	+	2.00924i	−0.123040	+	0.0710373i
$801$	2.85301	−	0.0458634i	0.100806	−	0.00162050i
$802$	−5.87458	+	10.1751i	−0.207439	+	0.359294i
$803$	−12.3110	+	21.3233i	−0.434447	+	0.752484i
$804$	0.570096	+	70.9322i	0.0201057	+	2.50158i
$805$	−4.67055	+	0.239558i	−0.164615	+	0.00844331i
$806$	53.1532	+	30.6880i	1.87224	+	1.08094i
$807$	−0.0841345	−	10.4681i	−0.00296167	−	0.368496i
$808$		−	13.1682i		−	0.463256i
$809$	−25.2132	−	14.5569i	−0.886450	−	0.511792i	−0.0136704	−	0.999907i	$-0.504352\pi$
$809$	−25.2132	−	14.5569i	−0.886450	−	0.511792i	−0.872780	+	0.488114i	$0.837685\pi$
$810$	−0.679217	−	21.1205i	−0.0238653	−	0.742097i
$811$			27.1660i			0.953928i	0.878923	+	0.476964i	$0.158263\pi$
$811$			27.1660i			0.953928i	−0.878923	+	0.476964i	$0.841737\pi$
$812$	13.7010	−	26.8159i	0.480811	−	0.941053i
$813$	−2.28445	+	4.03126i	−0.0801191	+	0.141382i
$814$	−70.0741			−2.45610
$815$	−5.29383	−	9.16919i	−0.185435	−	0.321183i
$816$	8.33834	+	4.72520i	0.291900	+	0.165415i
$817$	−54.9484	−	31.7244i	−1.92240	−	1.10990i
$818$	2.67945			0.0936847
$819$	−25.9543	−	38.6865i	−0.906917	−	1.35182i
$820$	4.50837			0.157439
$821$	−4.64380	−	2.68110i	−0.162070	−	0.0935709i	0.416772	−	0.909011i	$-0.363162\pi$
$821$	−4.64380	−	2.68110i	−0.162070	−	0.0935709i	−0.578841	+	0.815440i	$0.696495\pi$
$822$	−0.264918	−	32.9614i	−0.00924006	−	1.14966i
$823$	−11.9971	−	20.7795i	−0.418191	−	0.724328i	0.577567	−	0.816344i	$-0.304002\pi$
$823$	−11.9971	−	20.7795i	−0.418191	−	0.724328i	−0.995758	+	0.0920156i	$0.970669\pi$
$824$	−51.7820			−1.80391
$825$	−4.05125	−	6.88852i	−0.141047	−	0.239828i
$826$	28.4114	−	1.45725i	0.988558	−	0.0507043i
$827$			54.2022i			1.88480i	0.334494	+	0.942398i	$0.391435\pi$
$827$			54.2022i			1.88480i	−0.334494	+	0.942398i	$0.608565\pi$
$828$	−0.299411	−	18.6254i	−0.0104053	−	0.647277i
$829$	45.9516	+	26.5302i	1.59597	+	0.921431i	0.992254	+	0.124229i	$0.0396459\pi$
$829$	45.9516	+	26.5302i	1.59597	+	0.921431i	0.603713	+	0.797202i	$0.293687\pi$
$830$			20.7072i			0.718756i
$831$	6.26286	−	3.68329i	0.217256	−	0.127772i
$832$	−61.3170	−	35.4014i	−2.12579	−	1.22732i
$833$	−12.0490	+	26.9012i	−0.417474	+	0.932071i
$834$	−51.0528	−	28.9308i	−1.76781	−	1.00179i
$835$	2.09384	−	3.62663i	0.0724602	−	0.125505i
$836$	57.6906	−	99.9231i	1.99527	−	3.45591i
$837$	−12.0510	−	19.7571i	−0.416544	−	0.682905i
$838$	−44.7987	+	25.8646i	−1.54755	+	0.893476i
$839$	22.4777	+	38.9325i	0.776016	+	1.34410i	0.934222	+	0.356692i	$0.116096\pi$
$839$	22.4777	+	38.9325i	0.776016	+	1.34410i	−0.158206	+	0.987406i	$0.550571\pi$
$840$	−13.5892	+	8.95932i	−0.468873	+	0.309126i
$841$	−9.25089	+	16.0230i	−0.318996	+	0.552518i
$842$			21.6920i			0.747555i
$843$	5.09198	−	8.98558i	0.175377	−	0.309480i
$844$	−37.3177			−1.28453
$845$	−10.7244	−	18.5752i	−0.368930	−	0.639005i
$846$	−0.634014	−	39.4399i	−0.0217979	−	1.35597i
$847$	−1.39430	−	27.1841i	−0.0479089	−	0.934056i
$848$	−5.01174	+	2.89353i	−0.172104	+	0.0993642i
$849$	−4.52632	+	7.98739i	−0.155343	+	0.274127i
$850$	−8.56231	+	4.94345i	−0.293685	+	0.169559i
$851$	9.90201	−	5.71693i	0.339437	−	0.195974i
$852$	−9.42288	+	16.6281i	−0.322823	+	0.569670i
$853$	−19.9084	+	11.4941i	−0.681652	+	0.393552i	−0.800477	−	0.599363i	$-0.795421\pi$
$853$	−19.9084	+	11.4941i	−0.681652	+	0.393552i	0.118825	+	0.992915i	$0.462087\pi$
$854$	25.1720	−	16.3071i	0.861369	−	0.558017i
$855$	0.343276	+	21.3541i	0.0117398	+	0.730294i
$856$	0.247384	+	0.428481i	0.00845541	+	0.0146452i
$857$	20.9301			0.714958			0.357479	−	0.933921i	$-0.383636\pi$
$857$	20.9301			0.714958			0.357479	+	0.933921i	$0.383636\pi$
$858$	54.2962	−	95.8139i	1.85364	−	3.27103i
$859$			2.15695i			0.0735941i	0.999323	+	0.0367971i	$0.0117155\pi$
$859$			2.15695i			0.0735941i	−0.999323	+	0.0367971i	$0.988284\pi$
$860$	−15.6542	+	27.1138i	−0.533802	+	0.924573i
$861$	−5.87103	+	0.348463i	−0.200084	+	0.0118756i
$862$	25.5095	+	44.1838i	0.868858	+	1.50491i
$863$	−28.5948	+	16.5092i	−0.973377	+	0.561980i	−0.900264	−	0.435344i	$-0.856627\pi$
$863$	−28.5948	+	16.5092i	−0.973377	+	0.561980i	−0.0731132	+	0.997324i	$0.523293\pi$
$864$	10.8732	+	17.8262i	0.369915	+	0.606459i
$865$	−10.2917	+	17.8257i	−0.349927	+	0.606092i
$866$	−12.8817	+	22.3118i	−0.437739	+	0.758186i
$867$	−1.10259	−	0.624821i	−0.0374460	−	0.0212200i
$868$	−18.8331	+	36.8604i	−0.639236	+	1.25112i
$869$	17.0770	+	9.85942i	0.579298	+	0.334458i
$870$	−11.3580	+	6.67980i	−0.385071	+	0.226467i
$871$		−	68.4278i		−	2.31859i
$872$	−21.7296	−	12.5456i	−0.735859	−	0.424848i
$873$	−0.186038	−	11.5728i	−0.00629644	−	0.391680i
$874$			29.5454i			0.999388i
$875$	−0.135526	−	2.64228i	−0.00458160	−	0.0893253i
$876$	−16.4599	−	27.9875i	−0.556129	−	0.945610i
$877$	24.6459			0.832233			0.416116	−	0.909311i	$-0.363391\pi$
$877$	24.6459			0.832233			0.416116	+	0.909311i	$0.363391\pi$
$878$	12.3744	+	21.4332i	0.417617	+	0.723334i
$879$	−0.198775	−	24.7318i	−0.00670451	−	0.834185i
$880$	−5.25068	−	3.03148i	−0.177000	−	0.102191i
$881$	−37.2965			−1.25655			−0.628276	−	0.777991i	$-0.716239\pi$
$881$	−37.2965			−1.25655			−0.628276	+	0.777991i	$0.716239\pi$
$882$	39.4847	−	29.5312i	1.32952	−	0.994368i
$883$	−5.15073			−0.173336			−0.0866679	−	0.996237i	$-0.527622\pi$
$883$	−5.15073			−0.173336			−0.0866679	+	0.996237i	$0.527622\pi$
$884$	−75.1871	−	43.4093i	−2.52882	−	1.46001i
$885$	−6.90107	−	3.91072i	−0.231977	−	0.131457i
$886$	40.1259	+	69.5002i	1.34806	+	2.33490i
$887$	−41.1889			−1.38299			−0.691494	−	0.722383i	$-0.743047\pi$
$887$	−41.1889			−1.38299			−0.691494	+	0.722383i	$0.743047\pi$
$888$	19.6197	−	34.6220i	0.658395	−	1.16184i
$889$	−2.34074	−	45.6362i	−0.0785059	−	1.53059i
$890$			2.23318i			0.0748563i
$891$	−35.2759	+	21.9078i	−1.18179	+	0.733937i
$892$	−34.4212	−	19.8731i	−1.15251	−	0.665401i
$893$			39.8659i			1.33406i
$894$	0.0328004	+	4.08107i	0.00109701	+	0.136491i
$895$	−17.6485	−	10.1894i	−0.589924	−	0.340593i
$896$	24.4205	−	47.7963i	0.815832	−	1.59676i
$897$	0.144420	+	17.9689i	0.00482204	+	0.599966i
$898$	37.4863	−	64.9282i	1.25093	−	2.16668i
$899$	−7.21530	+	12.4973i	−0.240644	+	0.416807i
$900$	10.5370	−	0.169387i	0.351233	−	0.00564622i
$901$	16.0601	−	9.27228i	0.535038	−	0.308904i
$902$	−6.95172	−	12.0407i	−0.231467	−	0.400913i
$903$	18.2900	−	36.5189i	0.608652	−	1.21527i
$904$	−8.37443	+	14.5049i	−0.278529	+	0.482427i
$905$			4.52616i			0.150455i
$906$	36.1391	−	0.290457i	1.20064	−	0.00964980i
$907$	−0.272393			−0.00904465			−0.00452233	−	0.999990i	$-0.501440\pi$
$907$	−0.272393			−0.00904465			−0.00452233	+	0.999990i	$0.501440\pi$
$908$	45.1780	+	78.2505i	1.49928	+	2.59683i
$909$	5.40551	−	9.72016i	0.179290	−	0.322397i
$910$	30.6003	−	19.8237i	1.01439	−	0.657149i
$911$	−14.0238	+	8.09667i	−0.464631	+	0.268255i	−0.713989	−	0.700156i	$-0.753114\pi$
$911$	−14.0238	+	8.09667i	−0.464631	+	0.268255i	0.249359	+	0.968411i	$0.419780\pi$
$912$	8.21396	+	13.9666i	0.271991	+	0.462479i
$913$	35.2399	−	20.3458i	1.16627	−	0.673347i
$914$	−16.0262	+	9.25271i	−0.530098	+	0.306052i
$915$	−8.36229	+	0.0672094i	−0.276449	+	0.00222187i
$916$	−14.2733	+	8.24071i	−0.471604	+	0.272281i
$917$	−1.88219	−	36.6962i	−0.0621554	−	1.21181i
$918$	26.7521	+	43.8589i	0.882951	+	1.44756i
$919$	−25.6046	−	44.3485i	−0.844618	−	1.46292i	−0.885953	−	0.463776i	$-0.846494\pi$
$919$	−25.6046	−	44.3485i	−0.844618	−	1.46292i	0.0413347	−	0.999145i	$-0.486839\pi$
$920$	6.27842			0.206993
$921$	2.91619	+	4.95853i	0.0960919	+	0.163389i
$922$		−	11.9425i		−	0.393306i
$923$	9.21852	−	15.9669i	0.303431	−	0.525558i
$924$	66.4093	+	33.2601i	2.18471	+	1.09418i
$925$	3.23425	+	5.60188i	0.106341	+	0.184189i
$926$	−49.5483	+	28.6067i	−1.62826	+	0.940075i
$927$	−38.2231	−	21.2564i	−1.25541	−	0.698151i
$928$	6.51012	−	11.2759i	0.213705	−	0.370148i
$929$	−9.77031	+	16.9227i	−0.320553	+	0.555215i	−0.980602	−	0.196008i	$-0.937202\pi$
$929$	−9.77031	+	16.9227i	−0.320553	+	0.555215i	0.660049	+	0.751223i	$0.270536\pi$
$930$	15.6124	−	9.18189i	0.511950	−	0.301086i
$931$	−40.3806	+	29.2010i	−1.32342	+	0.957024i
$932$	−27.9772	−	16.1527i	−0.916425	−	0.529098i
$933$	7.67000	+	4.34646i	0.251105	+	0.142297i
$934$			41.7224i			1.36520i
$935$	16.8257	+	9.71435i	0.550261	+	0.317693i
$936$	32.1373	+	53.6530i	1.05044	+	1.75370i
$937$		−	32.6200i		−	1.06565i	−0.846226	−	0.532825i	$-0.821130\pi$
$937$		−	32.6200i		−	1.06565i	0.846226	−	0.532825i	$-0.178870\pi$
$938$	72.3285	−	3.70982i	2.36161	−	0.121130i
$939$	51.4174	−	0.413252i	1.67794	−	0.0134860i
$940$	19.6715			0.641612
$941$	15.2357	+	26.3890i	0.496670	+	0.860257i	0.999993	−	0.00384137i	$-0.00122275\pi$
$941$	15.2357	+	26.3890i	0.496670	+	0.860257i	−0.503323	+	0.864098i	$0.667889\pi$
$942$	−67.1777	+	39.5083i	−2.18877	+	1.28725i
$943$	1.96466	+	1.13430i	0.0639783	+	0.0369379i
$944$	−6.01790			−0.195866
$945$	−13.7087	+	1.03501i	−0.445944	+	0.0336690i
$946$	96.5523			3.13919
$947$	11.0760	+	6.39475i	0.359923	+	0.207802i	0.669047	−	0.743220i	$-0.266703\pi$
$947$	11.0760	+	6.39475i	0.359923	+	0.207802i	−0.309124	+	0.951022i	$0.600036\pi$
$948$	−22.4141	+	13.1821i	−0.727976	+	0.428135i
$949$	15.6607	+	27.1252i	0.508369	+	0.880521i
$950$	−16.7148			−0.542299
$951$	19.6517	−	0.157945i	0.637252	−	0.00512172i
$952$	18.0044	−	35.2387i	0.583528	−	1.14209i
$953$			38.9878i			1.26294i	0.775401	+	0.631469i	$0.217548\pi$
$953$			38.9878i			1.26294i	−0.775401	+	0.631469i	$0.782452\pi$
$954$	−31.0164	+	0.498603i	−1.00419	+	0.0161429i
$955$	−4.31590	−	2.49179i	−0.139659	−	0.0806324i
$956$		−	19.4878i		−	0.630281i
$957$	22.5276	+	12.7660i	0.728213	+	0.412666i
$958$	−19.1066	−	11.0312i	−0.617305	−	0.356401i
$959$	−21.4167	+	1.09849i	−0.691581	+	0.0354720i
$960$	−18.0103	+	10.5922i	−0.581280	+	0.341860i
$961$	−5.58203	+	9.66836i	−0.180066	+	0.311883i
$962$	−44.5703	+	77.1980i	−1.43700	+	2.48896i
$963$	0.00671689	+	0.417835i	0.000216449	+	0.0134646i
$964$	−3.79310	+	2.18995i	−0.122167	+	0.0705334i
$965$	−3.79149	−	6.56705i	−0.122052	−	0.211401i
$966$	−18.9854	+	1.12684i	−0.610846	+	0.0362555i
$967$	14.2352	−	24.6560i	0.457772	−	0.792885i	−0.541071	−	0.840977i	$-0.681981\pi$
$967$	14.2352	−	24.6560i	0.457772	−	0.792885i	0.998843	+	0.0480923i	$0.0153141\pi$
$968$			36.5424i			1.17452i
$969$	−26.3215	−	44.7556i	−0.845570	−	1.43776i
$970$	9.05856			0.290853
$971$	0.0209533	+	0.0362922i	0.000672424	+	0.00116467i	0.866361	−	0.499418i	$-0.166453\pi$
$971$	0.0209533	+	0.0362922i	0.000672424	+	0.00116467i	−0.865689	+	0.500582i	$0.833119\pi$
$972$	−2.19990	−	54.7146i	−0.0705618	−	1.75497i
$973$	−17.3696	+	33.9961i	−0.556844	+	1.08987i
$974$	73.8735	−	42.6509i	2.36706	−	1.36662i
$975$	−10.1656	+	0.0817030i	−0.325560	+	0.00261659i
$976$	−5.49447	+	3.17223i	−0.175874	+	0.101541i
$977$	49.2937	−	28.4597i	1.57705	−	0.910508i	0.581777	−	0.813349i	$-0.302358\pi$
$977$	49.2937	−	28.4597i	1.57705	−	0.910508i	0.995269	−	0.0971590i	$-0.0309755\pi$
$978$	−21.8276	−	37.1144i	−0.697970	−	1.18679i
$979$	3.80047	−	2.19420i	0.121464	−	0.0701270i
$980$	14.4090	+	19.9254i	0.460278	+	0.636495i
$981$	−10.8899	−	18.1806i	−0.347687	−	0.580460i
$982$	−33.0842	−	57.3035i	−1.05576	−	1.82863i
$983$	−45.5401			−1.45250			−0.726251	−	0.687429i	$-0.758739\pi$
$983$	−45.5401			−1.45250			−0.726251	+	0.687429i	$0.758739\pi$
$984$	7.89544	−	0.0634572i	0.251697	−	0.00202294i
$985$		−	6.05244i		−	0.192847i
$986$	16.0173	−	27.7427i	0.510093	−	0.883508i
$987$	−25.6172	+	1.52046i	−0.815405	+	0.0483966i
$988$	−73.3877	−	127.111i	−2.33477	−	4.04395i
$989$	−13.6436	+	7.87713i	−0.433841	+	0.250478i
$990$	−16.7000	−	27.8805i	−0.530760	−	0.886100i
$991$	16.8787	−	29.2348i	0.536170	−	0.928673i	−0.462936	−	0.886392i	$-0.653204\pi$
$991$	16.8787	−	29.2348i	0.536170	−	0.928673i	0.999106	−	0.0422813i	$-0.0134626\pi$
$992$	−8.94865	+	15.4995i	−0.284120	+	0.492110i
$993$	0.207379	+	25.8024i	0.00658098	+	0.818815i
$994$	17.3769	+	8.87838i	0.551163	+	0.281605i
$995$	9.29299	+	5.36531i	0.294608	+	0.170092i
$996$	0.431259	+	53.6578i	0.0136650	+	1.70021i
$997$			13.8872i			0.439811i	0.975521	+	0.219905i	$0.0705748\pi$
$997$			13.8872i			0.439811i	−0.975521	+	0.219905i	$0.929425\pi$
$998$	−35.1431	−	20.2899i	−1.11244	−	0.642265i
$999$	28.6946	−	17.5025i	0.907858	−	0.553756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.311.2	yes	32
3.2	odd	2		945.2.be.c.206.15		32
7.5	odd	6		315.2.t.c.131.15	yes	32
9.2	odd	6		315.2.t.c.101.2	✓	32
9.7	even	3		945.2.t.c.521.15		32
21.5	even	6		945.2.t.c.341.2		32
63.47	even	6	inner	315.2.be.c.236.2	yes	32
63.61	odd	6		945.2.be.c.656.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.2	✓	32	9.2	odd	6
315.2.t.c.131.15	yes	32	7.5	odd	6
315.2.be.c.236.2	yes	32	63.47	even	6	inner
315.2.be.c.311.2	yes	32	1.1	even	1	trivial
945.2.t.c.341.2		32	21.5	even	6
945.2.t.c.521.15		32	9.7	even	3
945.2.be.c.206.15		32	3.2	odd	2
945.2.be.c.656.15		32	63.61	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03337 - 1.17397i) q^{2} +(1.49299 - 0.878053i) q^{3} +(1.75639 + 3.04216i) q^{4} -1.00000 q^{5} +(-4.06660 + 0.0326841i) q^{6} +(0.135526 + 2.64228i) q^{7} -3.55190i q^{8} +(1.45805 - 2.62185i) q^{9} +O(q^{10})\)	\(q+(-2.03337 - 1.17397i) q^{2} +(1.49299 - 0.878053i) q^{3} +(1.75639 + 3.04216i) q^{4} -1.00000 q^{5} +(-4.06660 + 0.0326841i) q^{6} +(0.135526 + 2.64228i) q^{7} -3.55190i q^{8} +(1.45805 - 2.62185i) q^{9} +(2.03337 + 1.17397i) q^{10} -4.61391i q^{11} +(5.29345 + 2.99971i) q^{12} +(-5.08297 - 2.93465i) q^{13} +(2.82637 - 5.53183i) q^{14} +(-1.49299 + 0.878053i) q^{15} +(-0.657032 + 1.13801i) q^{16} +(2.10545 - 3.64675i) q^{17} +(-6.04271 + 3.61949i) q^{18} +(6.16519 - 3.55947i) q^{19} +(-1.75639 - 3.04216i) q^{20} +(2.52240 + 3.82590i) q^{21} +(-5.41657 + 9.38177i) q^{22} -1.76762i q^{23} +(-3.11876 - 5.30296i) q^{24} +1.00000 q^{25} +(6.89036 + 11.9345i) q^{26} +(-0.125273 - 5.19464i) q^{27} +(-7.80019 + 5.05316i) q^{28} +(-2.80600 + 1.62005i) q^{29} +(4.06660 - 0.0326841i) q^{30} +(3.85707 - 2.22688i) q^{31} +(-3.48010 + 2.00924i) q^{32} +(-4.05125 - 6.88852i) q^{33} +(-8.56231 + 4.94345i) q^{34} +(-0.135526 - 2.64228i) q^{35} +(10.5370 - 0.169387i) q^{36} +(3.23425 + 5.60188i) q^{37} -16.7148 q^{38} +(-10.1656 + 0.0817030i) q^{39} +3.55190i q^{40} +(-0.641710 + 1.11147i) q^{41} +(-0.637490 - 10.7407i) q^{42} +(-4.45634 - 7.71861i) q^{43} +(14.0362 - 8.10382i) q^{44} +(-1.45805 + 2.62185i) q^{45} +(-2.07513 + 3.59422i) q^{46} +(-2.79999 + 4.84972i) q^{47} +(0.0182923 + 2.27595i) q^{48} +(-6.96327 + 0.716193i) q^{49} +(-2.03337 - 1.17397i) q^{50} +(-0.0586174 - 7.29326i) q^{51} -20.6176i q^{52} +(3.81392 + 2.20197i) q^{53} +(-5.84361 + 10.7097i) q^{54} +4.61391i q^{55} +(9.38512 - 0.481374i) q^{56} +(6.07916 - 10.7276i) q^{57} +7.60752 q^{58} +(2.28980 + 3.96606i) q^{59} +(-5.29345 - 2.99971i) q^{60} +(4.18128 + 2.41406i) q^{61} -10.4571 q^{62} +(7.12526 + 3.49724i) q^{63} +12.0632 q^{64} +(5.08297 + 2.93465i) q^{65} +(0.150801 + 18.7629i) q^{66} +(5.82929 + 10.0966i) q^{67} +14.7920 q^{68} +(-1.55206 - 2.63904i) q^{69} +(-2.82637 + 5.53183i) q^{70} +3.14126i q^{71} +(-9.31256 - 5.17884i) q^{72} +(-4.62154 - 2.66824i) q^{73} -15.1876i q^{74} +(1.49299 - 0.878053i) q^{75} +(21.6569 + 12.5036i) q^{76} +(12.1912 - 0.625303i) q^{77} +(20.7663 + 11.7679i) q^{78} +(-2.13689 + 3.70121i) q^{79} +(0.657032 - 1.13801i) q^{80} +(-4.74820 - 7.64556i) q^{81} +(2.60966 - 1.50669i) q^{82} +(4.40966 + 7.63776i) q^{83} +(-7.20867 + 14.3933i) q^{84} +(-2.10545 + 3.64675i) q^{85} +20.9264i q^{86} +(-2.76685 + 4.88254i) q^{87} -16.3881 q^{88} +(0.475563 + 0.823699i) q^{89} +(6.04271 - 3.61949i) q^{90} +(7.06530 - 13.8283i) q^{91} +(5.37738 - 3.10463i) q^{92} +(3.80325 - 6.71142i) q^{93} +(11.3868 - 6.57417i) q^{94} +(-6.16519 + 3.55947i) q^{95} +(-3.43155 + 6.05549i) q^{96} +(3.34122 - 1.92905i) q^{97} +(14.9997 + 6.71835i) q^{98} +(-12.0970 - 6.72729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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