LMFDB - Embedded newform 735.2.b.d.146.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(146,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("735.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.b (of order $2$, degree $1$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.7
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	735.146
Dual form			735.2.b.d.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.06288i q^{2} +(1.71189 - 0.263509i) q^{3} -2.25548 q^{4} -1.00000 q^{5} +(0.543588 + 3.53142i) q^{6} -0.527019i q^{8} +(2.86113 - 0.902197i) q^{9} +O(q^{10})$	\(q+2.06288i q^{2} +(1.71189 - 0.263509i) q^{3} -2.25548 q^{4} -1.00000 q^{5} +(0.543588 + 3.53142i) q^{6} -0.527019i q^{8} +(2.86113 - 0.902197i) q^{9} -2.06288i q^{10} +4.69211i q^{11} +(-3.86113 + 0.594339i) q^{12} +0.638688i q^{13} +(-1.71189 + 0.263509i) q^{15} -3.42378 q^{16} +4.14924 q^{17} +(1.86113 + 5.90216i) q^{18} -0.897174i q^{19} +2.25548 q^{20} -9.67925 q^{22} +6.80436i q^{23} +(-0.138874 - 0.902197i) q^{24} +1.00000 q^{25} -1.31754 q^{26} +(4.66019 - 2.29839i) q^{27} -2.14740i q^{29} +(-0.543588 - 3.53142i) q^{30} +2.33772i q^{31} -8.11688i q^{32} +(1.23641 + 8.03236i) q^{33} +8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} -11.3824 q^{37} +1.85076 q^{38} +(0.168300 + 1.09336i) q^{39} +0.527019i q^{40} -4.10624 q^{41} +3.14924 q^{43} -10.5829i q^{44} +(-2.86113 + 0.902197i) q^{45} -14.0366 q^{46} +6.80943 q^{47} +(-5.86113 + 0.902197i) q^{48} +2.06288i q^{50} +(7.10303 - 1.09336i) q^{51} -1.44055i q^{52} -2.26538i q^{53} +(4.74131 + 9.61342i) q^{54} -4.69211i q^{55} +(-0.236414 - 1.53586i) q^{57} +4.42983 q^{58} +0.508109 q^{59} +(3.86113 - 0.594339i) q^{60} +5.18398i q^{61} -4.82244 q^{62} +9.89660 q^{64} -0.638688i q^{65} +(-16.5698 + 2.55057i) q^{66} +4.82849 q^{67} -9.35851 q^{68} +(1.79301 + 11.6483i) q^{69} +1.22800i q^{71} +(-0.475475 - 1.50787i) q^{72} -14.4565i q^{73} -23.4806i q^{74} +(1.71189 - 0.263509i) q^{75} +2.02356i q^{76} +(-2.25548 + 0.347183i) q^{78} +9.08112 q^{79} +3.42378 q^{80} +(7.37208 - 5.16260i) q^{81} -8.47068i q^{82} +2.76359 q^{83} -4.14924 q^{85} +6.49650i q^{86} +(-0.565860 - 3.67611i) q^{87} +2.47283 q^{88} +13.8013 q^{89} +(-1.86113 - 5.90216i) q^{90} -15.3471i q^{92} +(0.616011 + 4.00192i) q^{93} +14.0470i q^{94} +0.897174i q^{95} +(-2.13887 - 13.8952i) q^{96} -12.9085i q^{97} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9}+O(q^{10}) $ 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9	$ 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9} - 9 q^{12} - q^{15} - 2 q^{16} + 24 q^{17} - 7 q^{18} + 6 q^{20} - 40 q^{22} - 23 q^{24} + 8 q^{25} + 12 q^{26} + 4 q^{27} - 5 q^{30} + 2 q^{33} + 9 q^{36} - 14 q^{37} + 24 q^{38} - 12 q^{39} - 30 q^{41} + 16 q^{43} - q^{45} + 14 q^{46} + 12 q^{47} - 25 q^{48} - 6 q^{51} - 10 q^{54} + 6 q^{57} + 26 q^{58} + 24 q^{59} + 9 q^{60} + 24 q^{62} + 38 q^{64} - 38 q^{66} - 8 q^{67} - 13 q^{69} + q^{72} + q^{75} - 6 q^{78} + 58 q^{79} + 2 q^{80} + 13 q^{81} + 30 q^{83} - 24 q^{85} - 61 q^{87} + 4 q^{88} + 6 q^{89} + 7 q^{90} - 36 q^{93} - 39 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9 - 9 * q^12 - q^15 - 2 * q^16 + 24 * q^17 - 7 * q^18 + 6 * q^20 - 40 * q^22 - 23 * q^24 + 8 * q^25 + 12 * q^26 + 4 * q^27 - 5 * q^30 + 2 * q^33 + 9 * q^36 - 14 * q^37 + 24 * q^38 - 12 * q^39 - 30 * q^41 + 16 * q^43 - q^45 + 14 * q^46 + 12 * q^47 - 25 * q^48 - 6 * q^51 - 10 * q^54 + 6 * q^57 + 26 * q^58 + 24 * q^59 + 9 * q^60 + 24 * q^62 + 38 * q^64 - 38 * q^66 - 8 * q^67 - 13 * q^69 + q^72 + q^75 - 6 * q^78 + 58 * q^79 + 2 * q^80 + 13 * q^81 + 30 * q^83 - 24 * q^85 - 61 * q^87 + 4 * q^88 + 6 * q^89 + 7 * q^90 - 36 * q^93 - 39 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$			2.06288i			1.45868i	0.684153	+	0.729338i	$0.260172\pi$
$2$			2.06288i			1.45868i	−0.684153	+	0.729338i	$0.739828\pi$
$3$	1.71189	−	0.263509i	0.988359	−	0.152137i
$3$	1.71189	−	0.263509i	0.988359	−	0.152137i
$4$	−2.25548			−1.12774
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.543588	+	3.53142i	0.221919	+	1.44170i
$7$		0			0
$7$		0			0
$8$		−	0.527019i		−	0.186329i
$9$	2.86113	−	0.902197i	0.953709	−	0.300732i
$10$		−	2.06288i		−	0.652340i
$11$			4.69211i			1.41472i	0.706852	+	0.707362i	$0.250115\pi$
$11$			4.69211i			1.41472i	−0.706852	+	0.707362i	$0.749885\pi$
$12$	−3.86113	+	0.594339i	−1.11461	+	0.171571i
$13$			0.638688i			0.177140i	0.996070	+	0.0885701i	$0.0282297\pi$
$13$			0.638688i			0.177140i	−0.996070	+	0.0885701i	$0.971770\pi$
$14$		0			0
$15$	−1.71189	+	0.263509i	−0.442008	+	0.0680378i
$16$	−3.42378			−0.855944
$17$	4.14924			1.00634			0.503169	−	0.864188i	$-0.332167\pi$
$17$	4.14924			1.00634			0.503169	+	0.864188i	$0.332167\pi$
$18$	1.86113	+	5.90216i	0.438672	+	1.39115i
$19$		−	0.897174i		−	0.205826i	−0.994690	−	0.102913i	$-0.967184\pi$
$19$		−	0.897174i		−	0.205826i	0.994690	−	0.102913i	$-0.0328163\pi$
$20$	2.25548			0.504340
$21$		0			0
$22$	−9.67925			−2.06362
$23$			6.80436i			1.41881i	0.704803	+	0.709403i	$0.251036\pi$
$23$			6.80436i			1.41881i	−0.704803	+	0.709403i	$0.748964\pi$
$24$	−0.138874	−	0.902197i	−0.0283476	−	0.184160i
$25$	1.00000			0.200000
$26$	−1.31754			−0.258390
$27$	4.66019	−	2.29839i	0.896854	−	0.442326i
$28$		0			0
$29$		−	2.14740i		−	0.398762i	−0.979922	−	0.199381i	$-0.936107\pi$
$29$		−	2.14740i		−	0.398762i	0.979922	−	0.199381i	$-0.0638932\pi$
$30$	−0.543588	−	3.53142i	−0.0992452	−	0.644747i
$31$			2.33772i			0.419867i	0.977716	+	0.209933i	$0.0673247\pi$
$31$			2.33772i			0.419867i	−0.977716	+	0.209933i	$0.932675\pi$
$32$		−	8.11688i		−	1.43488i
$33$	1.23641	+	8.03236i	0.215232	+	1.39825i
$34$			8.55938i			1.46792i
$35$		0			0
$36$	−6.45320	+	2.03489i	−1.07553	+	0.339148i
$37$	−11.3824			−1.87126			−0.935631	−	0.352980i	$-0.885168\pi$
$37$	−11.3824			−1.87126			−0.935631	+	0.352980i	$0.885168\pi$
$38$	1.85076			0.300233
$39$	0.168300	+	1.09336i	0.0269496	+	0.175078i
$40$			0.527019i			0.0833290i
$41$	−4.10624			−0.641287			−0.320643	−	0.947200i	$-0.603899\pi$
$41$	−4.10624			−0.641287			−0.320643	+	0.947200i	$0.603899\pi$
$42$		0			0
$43$	3.14924			0.480254			0.240127	−	0.970741i	$-0.422811\pi$
$43$	3.14924			0.480254			0.240127	+	0.970741i	$0.422811\pi$
$44$		−	10.5829i		−	1.59544i
$45$	−2.86113	+	0.902197i	−0.426511	+	0.134492i
$46$	−14.0366			−2.06958
$47$	6.80943			0.993257			0.496629	−	0.867963i	$-0.334571\pi$
$47$	6.80943			0.993257			0.496629	+	0.867963i	$0.334571\pi$
$48$	−5.86113	+	0.902197i	−0.845981	+	0.130221i
$49$		0			0
$50$			2.06288i			0.291735i
$51$	7.10303	−	1.09336i	0.994623	−	0.153101i
$52$		−	1.44055i		−	0.199768i
$53$		−	2.26538i		−	0.311173i	−0.987822	−	0.155587i	$-0.950273\pi$
$53$		−	2.26538i		−	0.311173i	0.987822	−	0.155587i	$-0.0497268\pi$
$54$	4.74131	+	9.61342i	0.645211	+	1.30822i
$55$		−	4.69211i		−	0.632683i
$56$		0			0
$57$	−0.236414	−	1.53586i	−0.0313138	−	0.203430i
$58$	4.42983			0.581665
$59$	0.508109			0.0661502			0.0330751	−	0.999453i	$-0.489470\pi$
$59$	0.508109			0.0661502			0.0330751	+	0.999453i	$0.489470\pi$
$60$	3.86113	−	0.594339i	0.498469	−	0.0767289i
$61$			5.18398i			0.663740i	0.943325	+	0.331870i	$0.107680\pi$
$61$			5.18398i			0.663740i	−0.943325	+	0.331870i	$0.892320\pi$
$62$	−4.82244			−0.612450
$63$		0			0
$64$	9.89660			1.23708
$65$		−	0.638688i		−	0.0792195i
$66$	−16.5698	+	2.55057i	−2.03960	+	0.313954i
$67$	4.82849			0.589894			0.294947	−	0.955514i	$-0.404698\pi$
$67$	4.82849			0.589894			0.294947	+	0.955514i	$0.404698\pi$
$68$	−9.35851			−1.13489
$69$	1.79301	+	11.6483i	0.215853	+	1.40229i
$70$		0			0
$71$			1.22800i			0.145737i	0.997342	+	0.0728686i	$0.0232154\pi$
$71$			1.22800i			0.145737i	−0.997342	+	0.0728686i	$0.976785\pi$
$72$	−0.475475	−	1.50787i	−0.0560353	−	0.177704i
$73$		−	14.4565i		−	1.69201i	−0.533177	−	0.846004i	$-0.679002\pi$
$73$		−	14.4565i		−	1.69201i	0.533177	−	0.846004i	$-0.320998\pi$
$74$		−	23.4806i		−	2.72957i
$75$	1.71189	−	0.263509i	0.197672	−	0.0304274i
$76$			2.02356i			0.232118i
$77$		0			0
$78$	−2.25548	+	0.347183i	−0.255382	+	0.0393108i
$79$	9.08112			1.02171			0.510853	−	0.859668i	$-0.329330\pi$
$79$	9.08112			1.02171			0.510853	+	0.859668i	$0.329330\pi$
$80$	3.42378			0.382790
$81$	7.37208	−	5.16260i	0.819120	−	0.573622i
$82$		−	8.47068i		−	0.935431i
$83$	2.76359			0.303343			0.151671	−	0.988431i	$-0.451534\pi$
$83$	2.76359			0.303343			0.151671	+	0.988431i	$0.451534\pi$
$84$		0			0
$85$	−4.14924			−0.450048
$86$			6.49650i			0.700536i
$87$	−0.565860	−	3.67611i	−0.0606666	−	0.394120i
$88$	2.47283			0.263604
$89$	13.8013			1.46294			0.731470	−	0.681874i	$-0.238835\pi$
$89$	13.8013			1.46294			0.731470	+	0.681874i	$0.238835\pi$
$90$	−1.86113	−	5.90216i	−0.196180	−	0.622142i
$91$		0			0
$92$		−	15.3471i		−	1.60004i
$93$	0.616011	+	4.00192i	0.0638774	+	0.414979i
$94$			14.0470i			1.44884i
$95$			0.897174i			0.0920481i
$96$	−2.13887	−	13.8952i	−0.218298	−	1.41817i
$97$		−	12.9085i		−	1.31066i	−0.755344	−	0.655329i	$-0.772530\pi$
$97$		−	12.9085i		−	1.31066i	0.755344	−	0.655329i	$-0.227470\pi$
$98$		0			0
$99$	4.23321	+	13.4247i	0.425453	+	1.34923i
$100$	−2.25548			−0.225548
$101$	9.03979			0.899493			0.449746	−	0.893156i	$-0.351514\pi$
$101$	9.03979			0.899493			0.449746	+	0.893156i	$0.351514\pi$
$102$	2.25548	+	14.6527i	0.223326	+	1.45083i
$103$		−	15.5206i		−	1.52929i	−0.644451	−	0.764645i	$-0.722914\pi$
$103$		−	15.5206i		−	1.52929i	0.644451	−	0.764645i	$-0.277086\pi$
$104$	0.336601			0.0330064
$105$		0			0
$106$	4.67320			0.453901
$107$		−	5.35794i		−	0.517972i	−0.965881	−	0.258986i	$-0.916612\pi$
$107$		−	5.35794i		−	0.517972i	0.965881	−	0.258986i	$-0.0833883\pi$
$108$	−10.5110	+	5.18398i	−1.01142	+	0.498828i
$109$	1.35887			0.130156			0.0650782	−	0.997880i	$-0.479270\pi$
$109$	1.35887			0.130156			0.0650782	+	0.997880i	$0.479270\pi$
$110$	9.67925			0.922881
$111$	−19.4855	+	2.99938i	−1.84948	+	0.284689i
$112$		0			0
$113$		−	11.9390i		−	1.12312i	−0.827435	−	0.561562i	$-0.810201\pi$
$113$		−	11.9390i		−	1.12312i	0.827435	−	0.561562i	$-0.189799\pi$
$114$	3.16830	−	0.487693i	0.296739	−	0.0456767i
$115$		−	6.80436i		−	0.634510i
$116$			4.84341i			0.449700i
$117$	0.576223	+	1.82737i	0.0532718	+	0.168940i
$118$			1.04817i			0.0964917i
$119$		0			0
$120$	0.138874	+	0.902197i	0.0126774	+	0.0823590i
$121$	−11.0159			−1.00144
$122$	−10.6939			−0.968183
$123$	−7.02943	+	1.08203i	−0.633822	+	0.0975636i
$124$		−	5.27267i		−	0.473500i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−16.8492			−1.49513			−0.747563	−	0.664191i	$-0.768776\pi$
$127$	−16.8492			−1.49513			−0.747563	+	0.664191i	$0.768776\pi$
$128$			4.18175i			0.369618i
$129$	5.39114	−	0.829853i	0.474664	−	0.0730645i
$130$	1.31754			0.115556
$131$	−13.8695			−1.21178			−0.605890	−	0.795548i	$-0.707183\pi$
$131$	−13.8695			−1.21178			−0.605890	+	0.795548i	$0.707183\pi$
$132$	−2.78870	−	18.1168i	−0.242725	−	1.57687i
$133$		0			0
$134$			9.96060i			0.860465i
$135$	−4.66019	+	2.29839i	−0.401085	+	0.197814i
$136$		−	2.18673i		−	0.187510i
$137$			4.33830i			0.370646i	0.982678	+	0.185323i	$0.0593332\pi$
$137$			4.33830i			0.370646i	−0.982678	+	0.185323i	$0.940667\pi$
$138$	−24.0291	+	3.69877i	−2.04549	+	0.314860i
$139$		−	10.9631i		−	0.929881i	−0.885342	−	0.464941i	$-0.846076\pi$
$139$		−	10.9631i		−	0.929881i	0.885342	−	0.464941i	$-0.153924\pi$
$140$		0			0
$141$	11.6570	−	1.79435i	0.981695	−	0.151111i
$142$	−2.53323			−0.212584
$143$	−2.99679			−0.250604
$144$	−9.79586	+	3.08892i	−0.816321	+	0.257410i
$145$			2.14740i			0.178332i
$146$	29.8221			2.46809
$147$		0			0
$148$	25.6728			2.11029
$149$			8.66656i			0.709992i	0.934868	+	0.354996i	$0.115518\pi$
$149$			8.66656i			0.709992i	−0.934868	+	0.354996i	$0.884482\pi$
$150$	0.543588	+	3.53142i	0.0443838	+	0.288339i
$151$	13.4604			1.09539			0.547694	−	0.836679i	$-0.315506\pi$
$151$	13.4604			1.09539			0.547694	+	0.836679i	$0.315506\pi$
$152$	−0.472828			−0.0383514
$153$	11.8715	−	3.74343i	0.959753	−	0.302638i
$154$		0			0
$155$		−	2.33772i		−	0.187770i
$156$	−0.379597	−	2.46605i	−0.0303921	−	0.197442i
$157$			7.81320i			0.623561i	0.950154	+	0.311781i	$0.100925\pi$
$157$			7.81320i			0.623561i	−0.950154	+	0.311781i	$0.899075\pi$
$158$			18.7333i			1.49034i
$159$	−0.596948	−	3.87807i	−0.0473410	−	0.307551i
$160$			8.11688i			0.641696i
$161$		0			0
$162$	10.6498	+	15.2077i	0.836730	+	1.19483i
$163$	16.6789			1.30639			0.653196	−	0.757189i	$-0.273428\pi$
$163$	16.6789			1.30639			0.653196	+	0.757189i	$0.273428\pi$
$164$	9.26153			0.723204
$165$	−1.23641	−	8.03236i	−0.0962547	−	0.625319i
$166$			5.70095i			0.442479i
$167$	0.465112			0.0359915			0.0179957	−	0.999838i	$-0.494271\pi$
$167$	0.465112			0.0359915			0.0179957	+	0.999838i	$0.494271\pi$
$168$		0			0
$169$	12.5921			0.968621
$170$		−	8.55938i		−	0.656475i
$171$	−0.809428	−	2.56693i	−0.0618985	−	0.196298i
$172$	−7.10303			−0.541601
$173$	−11.1842			−0.850316			−0.425158	−	0.905119i	$-0.639781\pi$
$173$	−11.1842			−0.850316			−0.425158	+	0.905119i	$0.639781\pi$
$174$	7.58338	−	1.16730i	0.574894	−	0.0884929i
$175$		0			0
$176$		−	16.0647i		−	1.21092i
$177$	0.869826	−	0.133892i	0.0653802	−	0.0100639i
$178$			28.4705i			2.13396i
$179$			0.247690i			0.0185132i	0.999957	+	0.00925660i	$0.00294651\pi$
$179$			0.247690i			0.0185132i	−0.999957	+	0.00925660i	$0.997053\pi$
$180$	6.45320	−	2.03489i	0.480993	−	0.151671i
$181$		−	14.3385i		−	1.06578i	−0.846186	−	0.532888i	$-0.821107\pi$
$181$		−	14.3385i		−	1.06578i	0.846186	−	0.532888i	$-0.178893\pi$
$182$		0			0
$183$	1.36603	+	8.87439i	0.100980	+	0.656014i
$184$	3.58602			0.264365
$185$	11.3824			0.836854
$186$	−8.25548	+	1.27076i	−0.605321	+	0.0931765i
$187$			19.4687i			1.42369i
$188$	−15.3585			−1.12013
$189$		0			0
$190$	−1.85076			−0.134268
$191$			17.0401i			1.23298i	0.787363	+	0.616490i	$0.211446\pi$
$191$			17.0401i			1.23298i	−0.787363	+	0.616490i	$0.788554\pi$
$192$	16.9419	−	2.60785i	1.22268	−	0.188205i
$193$	2.82362			0.203249			0.101624	−	0.994823i	$-0.467596\pi$
$193$	2.82362			0.203249			0.101624	+	0.994823i	$0.467596\pi$
$194$	26.6287			1.91183
$195$	−0.168300	−	1.09336i	−0.0120522	−	0.0782973i
$196$		0			0
$197$			9.59675i			0.683740i	0.939747	+	0.341870i	$0.111060\pi$
$197$			9.59675i			0.683740i	−0.939747	+	0.341870i	$0.888940\pi$
$198$	−27.6936	+	8.73260i	−1.96810	+	0.620599i
$199$		−	12.2141i		−	0.865836i	−0.901433	−	0.432918i	$-0.857484\pi$
$199$		−	12.2141i		−	0.865836i	0.901433	−	0.432918i	$-0.142516\pi$
$200$		−	0.527019i		−	0.0372659i
$201$	8.26584	−	1.27235i	0.583027	−	0.0897448i
$202$			18.6480i			1.31207i
$203$		0			0
$204$	−16.0207	+	2.46605i	−1.12168	+	0.172658i
$205$	4.10624			0.286792
$206$	32.0172			2.23074
$207$	6.13887	+	19.4681i	0.426681	+	1.35313i
$208$		−	2.18673i		−	0.151622i
$209$	4.20964			0.291187
$210$		0			0
$211$	5.64113			0.388351			0.194176	−	0.980967i	$-0.437797\pi$
$211$	5.64113			0.388351			0.194176	+	0.980967i	$0.437797\pi$
$212$			5.10950i			0.350922i
$213$	0.323591	+	2.10221i	0.0221721	+	0.144041i
$214$	11.0528			0.755554
$215$	−3.14924			−0.214776
$216$	−1.21130	−	2.45601i	−0.0824183	−	0.167110i
$217$		0			0
$218$			2.80319i			0.189856i
$219$	−3.80943	−	24.7480i	−0.257417	−	1.67231i
$220$			10.5829i			0.713501i
$221$			2.65007i			0.178263i
$222$	−6.18736	−	40.1962i	−0.415269	−	2.69779i
$223$		−	0.392378i		−	0.0262755i	−0.999914	−	0.0131378i	$-0.995818\pi$
$223$		−	0.392378i		−	0.0262755i	0.999914	−	0.0131378i	$-0.00418200\pi$
$224$		0			0
$225$	2.86113	−	0.902197i	0.190742	−	0.0601465i
$226$	24.6287			1.63827
$227$	−23.4251			−1.55478			−0.777388	−	0.629021i	$-0.783456\pi$
$227$	−23.4251			−1.55478			−0.777388	+	0.629021i	$0.783456\pi$
$228$	0.533226	+	3.46410i	0.0353137	+	0.229416i
$229$			7.72824i			0.510697i	0.966849	+	0.255348i	$0.0821902\pi$
$229$			7.72824i			0.510697i	−0.966849	+	0.255348i	$0.917810\pi$
$230$	14.0366			0.925545
$231$		0			0
$232$	−1.13172			−0.0743011
$233$			4.07982i			0.267278i	0.991030	+	0.133639i	$0.0426662\pi$
$233$			4.07982i			0.267278i	−0.991030	+	0.133639i	$0.957334\pi$
$234$	−3.76964	+	1.18868i	−0.246429	+	0.0777064i
$235$	−6.80943			−0.444198
$236$	−1.14603			−0.0746001
$237$	15.5459	−	2.39296i	1.00981	−	0.155440i
$238$		0			0
$239$			5.76281i			0.372765i	0.982477	+	0.186383i	$0.0596764\pi$
$239$			5.76281i			0.372765i	−0.982477	+	0.186383i	$0.940324\pi$
$240$	5.86113	−	0.902197i	0.378334	−	0.0582366i
$241$			20.4197i			1.31535i	0.753303	+	0.657674i	$0.228460\pi$
$241$			20.4197i			1.31535i	−0.753303	+	0.657674i	$0.771540\pi$
$242$		−	22.7244i		−	1.46078i
$243$	11.2598	−	10.7804i	0.722316	−	0.691564i
$244$		−	11.6923i		−	0.748525i
$245$		0			0
$246$	−2.23210	−	14.5009i	−0.142314	−	0.924542i
$247$	0.573014			0.0364600
$248$	1.23202			0.0782335
$249$	4.73095	−	0.728231i	0.299812	−	0.0461498i
$250$		−	2.06288i		−	0.130468i
$251$	4.42544			0.279331			0.139666	−	0.990199i	$-0.455397\pi$
$251$	4.42544			0.279331			0.139666	+	0.990199i	$0.455397\pi$
$252$		0			0
$253$	−31.9268			−2.00722
$254$		−	34.7579i		−	2.18091i
$255$	−7.10303	+	1.09336i	−0.444809	+	0.0684690i
$256$	11.1668			0.697922
$257$	−25.5077			−1.59113			−0.795565	−	0.605869i	$-0.792826\pi$
$257$	−25.5077			−1.59113			−0.795565	+	0.605869i	$0.792826\pi$
$258$	1.71189	+	11.1213i	0.106578	+	0.692381i
$259$		0			0
$260$			1.44055i			0.0893389i
$261$	−1.93738	−	6.14398i	−0.119921	−	0.380303i
$262$		−	28.6110i		−	1.76760i
$263$		−	0.357980i		−	0.0220740i	−0.999939	−	0.0110370i	$-0.996487\pi$
$263$		−	0.357980i		−	0.0220740i	0.999939	−	0.0110370i	$-0.00351325\pi$
$264$	4.23321	−	0.651613i	0.260536	−	0.0401040i
$265$			2.26538i			0.139161i
$266$		0			0
$267$	23.6264	−	3.63678i	1.44591	−	0.222568i
$268$	−10.8906			−0.665246
$269$	−8.53810			−0.520577			−0.260288	−	0.965531i	$-0.583818\pi$
$269$	−8.53810			−0.520577			−0.260288	+	0.965531i	$0.583818\pi$
$270$	−4.74131	−	9.61342i	−0.288547	−	0.585054i
$271$		−	8.43479i		−	0.512377i	−0.966627	−	0.256188i	$-0.917533\pi$
$271$		−	8.43479i		−	0.512377i	0.966627	−	0.256188i	$-0.0824667\pi$
$272$	−14.2061			−0.861369
$273$		0			0
$274$	−8.94940			−0.540653
$275$			4.69211i			0.282945i
$276$	−4.04410	−	26.2725i	−0.243426	−	1.58142i
$277$	10.1059			0.607203			0.303602	−	0.952799i	$-0.401811\pi$
$277$	10.1059			0.607203			0.303602	+	0.952799i	$0.401811\pi$
$278$	22.6156			1.35640
$279$	2.10909	+	6.68851i	0.126268	+	0.400431i
$280$		0			0
$281$			15.1554i			0.904094i	0.891994	+	0.452047i	$0.149306\pi$
$281$			15.1554i			0.904094i	−0.891994	+	0.452047i	$0.850694\pi$
$282$	3.70153	+	24.0470i	0.220423	+	1.43198i
$283$		−	23.9395i		−	1.42305i	−0.702659	−	0.711527i	$-0.748004\pi$
$283$		−	23.9395i		−	1.42305i	0.702659	−	0.711527i	$-0.251996\pi$
$284$		−	2.76973i		−	0.164354i
$285$	0.236414	+	1.53586i	0.0140039	+	0.0909766i
$286$		−	6.18202i		−	0.365551i
$287$		0			0
$288$	−7.32303	−	23.2234i	−0.431514	−	1.36845i
$289$	0.216167			0.0127157
$290$	−4.42983			−0.260129
$291$	−3.40151	−	22.0979i	−0.199400	−	1.29540i
$292$			32.6063i			1.90814i
$293$	−21.2223			−1.23982			−0.619909	−	0.784673i	$-0.712831\pi$
$293$	−21.2223			−1.23982			−0.619909	+	0.784673i	$0.712831\pi$
$294$		0			0
$295$	−0.508109			−0.0295833
$296$			5.99876i			0.348671i
$297$	10.7843	+	21.8661i	0.625769	+	1.26880i
$298$	−17.8781			−1.03565
$299$	−4.34586			−0.251328
$300$	−3.86113	+	0.594339i	−0.222922	+	0.0343142i
$301$		0			0
$302$			27.7671i			1.59782i
$303$	15.4751	−	2.38207i	0.889022	−	0.136846i
$304$			3.07172i			0.176175i
$305$		−	5.18398i		−	0.296834i
$306$	7.72225	+	24.4895i	0.441452	+	1.39997i
$307$			24.2817i			1.38583i	0.721019	+	0.692916i	$0.243674\pi$
$307$			24.2817i			1.38583i	−0.721019	+	0.692916i	$0.756326\pi$
$308$		0			0
$309$	−4.08982	−	26.5695i	−0.232662	−	1.51149i
$310$	4.82244			0.273896
$311$	−7.11716			−0.403577			−0.201789	−	0.979429i	$-0.564675\pi$
$311$	−7.11716			−0.403577			−0.201789	+	0.979429i	$0.564675\pi$
$312$	0.576223	−	0.0886974i	0.0326222	−	0.00502150i
$313$			3.54724i			0.200502i	0.994962	+	0.100251i	$0.0319646\pi$
$313$			3.54724i			0.200502i	−0.994962	+	0.100251i	$0.968035\pi$
$314$	−16.1177			−0.909575
$315$		0			0
$316$	−20.4823			−1.15222
$317$		−	21.0764i		−	1.18377i	−0.806022	−	0.591885i	$-0.798384\pi$
$317$		−	21.0764i		−	1.18377i	0.806022	−	0.591885i	$-0.201616\pi$
$318$	8.00000	−	1.23143i	0.448618	−	0.0690553i
$319$	10.0758			0.564138
$320$	−9.89660			−0.553237
$321$	−1.41187	−	9.17220i	−0.0788028	−	0.511942i
$322$		0			0
$323$		−	3.72259i		−	0.207130i
$324$	−16.6276	+	11.6441i	−0.923753	+	0.646896i
$325$			0.638688i			0.0354280i
$326$			34.4066i			1.90560i
$327$	2.32624	−	0.358076i	0.128641	−	0.0198016i
$328$			2.16407i			0.119491i
$329$		0			0
$330$	16.5698	−	2.55057i	0.912138	−	0.140404i
$331$	−14.8082			−0.813935			−0.406967	−	0.913443i	$-0.633414\pi$
$331$	−14.8082			−0.813935			−0.406967	+	0.913443i	$0.633414\pi$
$332$	−6.23321			−0.342092
$333$	−32.5666	+	10.2692i	−1.78464	+	0.562749i
$334$			0.959471i			0.0524999i
$335$	−4.82849			−0.263809
$336$		0			0
$337$	20.5062			1.11704			0.558522	−	0.829490i	$-0.311369\pi$
$337$	20.5062			1.11704			0.558522	+	0.829490i	$0.311369\pi$
$338$			25.9760i			1.41291i
$339$	−3.14603	−	20.4382i	−0.170869	−	1.11005i
$340$	9.35851			0.507536
$341$	−10.9688			−0.593995
$342$	5.29527	−	1.66975i	0.286335	−	0.0902899i
$343$		0			0
$344$		−	1.65971i		−	0.0894854i
$345$	−1.79301	−	11.6483i	−0.0965325	−	0.627124i
$346$		−	23.0716i		−	1.24034i
$347$		−	15.8313i		−	0.849871i	−0.905224	−	0.424935i	$-0.860297\pi$
$347$		−	15.8313i		−	0.849871i	0.905224	−	0.424935i	$-0.139703\pi$
$348$	1.27628	+	8.29138i	0.0684160	+	0.444465i
$349$		−	8.96019i		−	0.479628i	−0.970819	−	0.239814i	$-0.922914\pi$
$349$		−	8.96019i		−	0.479628i	0.970819	−	0.239814i	$-0.0770865\pi$
$350$		0			0
$351$	1.46796	+	2.97641i	0.0783538	+	0.158869i
$352$	38.0853			2.02995
$353$	−13.4575			−0.716271			−0.358136	−	0.933670i	$-0.616587\pi$
$353$	−13.4575			−0.716271			−0.358136	+	0.933670i	$0.616587\pi$
$354$	0.276202	+	1.79435i	0.0146800	+	0.0953685i
$355$		−	1.22800i		−	0.0651757i
$356$	−31.1286			−1.64981
$357$		0			0
$358$	−0.510954			−0.0270048
$359$		−	5.60981i		−	0.296074i	−0.988982	−	0.148037i	$-0.952704\pi$
$359$		−	5.60981i		−	0.296074i	0.988982	−	0.148037i	$-0.0472956\pi$
$360$	0.475475	+	1.50787i	0.0250597	+	0.0794716i
$361$	18.1951			0.957636
$362$	29.5787			1.55462
$363$	−18.8579	+	2.90278i	−0.989784	+	0.152356i
$364$		0			0
$365$			14.4565i			0.756689i
$366$	−18.3068	+	2.81795i	−0.956912	+	0.147297i
$367$			1.97631i			0.103163i	0.998669	+	0.0515813i	$0.0164261\pi$
$367$			1.97631i			0.103163i	−0.998669	+	0.0515813i	$0.983574\pi$
$368$		−	23.2966i		−	1.21442i
$369$	−11.7485	+	3.70464i	−0.611601	+	0.192856i
$370$			23.4806i			1.22070i
$371$		0			0
$372$	−1.38940	−	9.02623i	−0.0720370	−	0.467988i
$373$	−23.0934			−1.19573			−0.597866	−	0.801596i	$-0.703984\pi$
$373$	−23.0934			−1.19573			−0.597866	+	0.801596i	$0.703984\pi$
$374$	−40.1615			−2.07670
$375$	−1.71189	+	0.263509i	−0.0884016	+	0.0136076i
$376$		−	3.58870i		−	0.185073i
$377$	1.37152			0.0706368
$378$		0			0
$379$	−17.0645			−0.876547			−0.438273	−	0.898842i	$-0.644410\pi$
$379$	−17.0645			−0.876547			−0.438273	+	0.898842i	$0.644410\pi$
$380$		−	2.02356i		−	0.103806i
$381$	−28.8440	+	4.43993i	−1.47772	+	0.227464i
$382$	−35.1517			−1.79852
$383$	−26.6113			−1.35977			−0.679886	−	0.733318i	$-0.737971\pi$
$383$	−26.6113			−1.35977			−0.679886	+	0.733318i	$0.737971\pi$
$384$	1.10193	+	7.15869i	0.0562327	+	0.365316i
$385$		0			0
$386$			5.82479i			0.296474i
$387$	9.01036	−	2.84123i	0.458022	−	0.144428i
$388$			29.1148i			1.47808i
$389$		−	9.47953i		−	0.480631i	−0.970695	−	0.240316i	$-0.922749\pi$
$389$		−	9.47953i		−	0.480631i	0.970695	−	0.240316i	$-0.0772509\pi$
$390$	2.25548	−	0.347183i	0.114211	−	0.0175803i
$391$			28.2329i			1.42780i
$392$		0			0
$393$	−23.7430	+	3.65473i	−1.19767	+	0.184357i
$394$	−19.7970			−0.997356
$395$	−9.08112			−0.456921
$396$	−9.54790	−	30.2791i	−0.479800	−	1.52158i
$397$			12.3602i			0.620340i	0.950681	+	0.310170i	$0.100386\pi$
$397$			12.3602i			0.620340i	−0.950681	+	0.310170i	$0.899614\pi$
$398$	25.1963			1.26297
$399$		0			0
$400$	−3.42378			−0.171189
$401$			8.21563i			0.410269i	0.978734	+	0.205134i	$0.0657631\pi$
$401$			8.21563i			0.410269i	−0.978734	+	0.205134i	$0.934237\pi$
$402$	2.62471	+	17.0514i	0.130909	+	0.850449i
$403$	−1.49307			−0.0743753
$404$	−20.3890			−1.01439
$405$	−7.37208	+	5.16260i	−0.366322	+	0.256532i
$406$		0			0
$407$		−	53.4076i		−	2.64732i
$408$	−0.576223	−	3.74343i	−0.0285273	−	0.185327i
$409$			20.7355i			1.02531i	0.858596	+	0.512653i	$0.171337\pi$
$409$			20.7355i			1.02531i	−0.858596	+	0.512653i	$0.828663\pi$
$410$			8.47068i			0.418337i
$411$	1.14318	+	7.42669i	0.0563891	+	0.366332i
$412$			35.0064i			1.72464i
$413$		0			0
$414$	−40.1604	+	12.6638i	−1.97378	+	0.622390i
$415$	−2.76359			−0.135659
$416$	5.18416			0.254174
$417$	−2.88889	−	18.7677i	−0.141470	−	0.919057i
$418$			8.68398i			0.424747i
$419$	6.93924			0.339004			0.169502	−	0.985530i	$-0.445784\pi$
$419$	6.93924			0.339004			0.169502	+	0.985530i	$0.445784\pi$
$420$		0			0
$421$	−15.2162			−0.741594			−0.370797	−	0.928714i	$-0.620915\pi$
$421$	−15.2162			−0.741594			−0.370797	+	0.928714i	$0.620915\pi$
$422$			11.6370i			0.566479i
$423$	19.4826	−	6.14345i	0.947278	−	0.298705i
$424$	−1.19390			−0.0579807
$425$	4.14924			0.201268
$426$	−4.33660	+	0.667529i	−0.210109	+	0.0323419i
$427$		0			0
$428$			12.0847i			0.584137i
$429$	−5.13017	+	0.789683i	−0.247687	+	0.0381262i
$430$		−	6.49650i		−	0.313289i
$431$			31.0664i			1.49642i	0.663463	+	0.748209i	$0.269086\pi$
$431$			31.0664i			1.49642i	−0.663463	+	0.748209i	$0.730914\pi$
$432$	−15.9555	+	7.86919i	−0.767657	+	0.378607i
$433$		−	22.3083i		−	1.07207i	−0.844196	−	0.536034i	$-0.819922\pi$
$433$		−	22.3083i		−	1.07207i	0.844196	−	0.536034i	$-0.180078\pi$
$434$		0			0
$435$	0.565860	+	3.67611i	0.0271309	+	0.176256i
$436$	−3.06491			−0.146782
$437$	6.10469			0.292027
$438$	51.0521	−	7.85840i	2.43936	−	0.375489i
$439$		−	25.8799i		−	1.23518i	−0.786500	−	0.617590i	$-0.788109\pi$
$439$		−	25.8799i		−	1.23518i	0.786500	−	0.617590i	$-0.211891\pi$
$440$	−2.47283			−0.117887
$441$		0			0
$442$	−5.46677			−0.260028
$443$		−	30.9651i		−	1.47120i	−0.677418	−	0.735599i	$-0.736901\pi$
$443$		−	30.9651i		−	1.47120i	0.677418	−	0.735599i	$-0.263099\pi$
$444$	43.9490	−	6.76503i	2.08573	−	0.321054i
$445$	−13.8013			−0.654247
$446$	0.809428			0.0383275
$447$	2.28372	+	14.8362i	0.108016	+	0.701728i
$448$		0			0
$449$		−	24.2032i		−	1.14222i	−0.820874	−	0.571110i	$-0.806513\pi$
$449$		−	24.2032i		−	1.14222i	0.820874	−	0.571110i	$-0.193487\pi$
$450$	1.86113	+	5.90216i	0.0877343	+	0.278231i
$451$		−	19.2669i		−	0.907243i
$452$			26.9281i			1.26659i
$453$	23.0426	−	3.54693i	1.08264	−	0.166649i
$454$		−	48.3231i		−	2.26792i
$455$		0			0
$456$	−0.809428	+	0.124594i	−0.0379049	+	0.00583467i
$457$	−2.41452			−0.112946			−0.0564731	−	0.998404i	$-0.517986\pi$
$457$	−2.41452			−0.112946			−0.0564731	+	0.998404i	$0.517986\pi$
$458$	−15.9424			−0.744942
$459$	19.3362	−	9.53658i	0.902538	−	0.445130i
$460$			15.3471i			0.715561i
$461$	7.45376			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$461$	7.45376			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$462$		0			0
$463$	13.8862			0.645345			0.322672	−	0.946511i	$-0.395419\pi$
$463$	13.8862			0.645345			0.322672	+	0.946511i	$0.395419\pi$
$464$			7.35222i			0.341318i
$465$	−0.616011	−	4.00192i	−0.0285668	−	0.185584i
$466$	−8.41618			−0.389872
$467$	20.1384			0.931895			0.465948	−	0.884812i	$-0.345713\pi$
$467$	20.1384			0.931895			0.465948	+	0.884812i	$0.345713\pi$
$468$	−1.29966	−	4.12158i	−0.0600767	−	0.190520i
$469$		0			0
$470$		−	14.0470i		−	0.647942i
$471$	2.05885	+	13.3753i	0.0948669	+	0.616303i
$472$		−	0.267783i		−	0.0123257i
$473$			14.7766i			0.679427i
$474$	4.93639	+	32.0693i	0.226736	+	1.47299i
$475$		−	0.897174i		−	0.0411652i
$476$		0			0
$477$	−2.04382	−	6.48153i	−0.0935799	−	0.296769i
$478$	−11.8880			−0.543744
$479$	33.2377			1.51867			0.759335	−	0.650700i	$-0.225524\pi$
$479$	33.2377			1.51867			0.759335	+	0.650700i	$0.225524\pi$
$480$	2.13887	+	13.8952i	0.0976258	+	0.634226i
$481$		−	7.26983i		−	0.331476i
$482$	−42.1234			−1.91867
$483$		0			0
$484$	24.8460			1.12936
$485$			12.9085i			0.586144i
$486$	22.2387	+	23.2276i	1.00877	+	1.05363i
$487$	−32.2077			−1.45947			−0.729736	−	0.683729i	$-0.760357\pi$
$487$	−32.2077			−1.45947			−0.729736	+	0.683729i	$0.760357\pi$
$488$	2.73205			0.123674
$489$	28.5524	−	4.39504i	1.29118	−	0.198751i
$490$		0			0
$491$			22.5003i			1.01542i	0.861527	+	0.507712i	$0.169509\pi$
$491$			22.5003i			1.01542i	−0.861527	+	0.507712i	$0.830491\pi$
$492$	15.8547	−	2.44050i	0.714785	−	0.110026i
$493$		−	8.91007i		−	0.401289i
$494$			1.18206i			0.0531834i
$495$	−4.23321	−	13.4247i	−0.190268	−	0.603396i
$496$		−	8.00383i		−	0.359383i
$497$		0			0
$498$	1.50225	+	9.75939i	0.0673176	+	0.437329i
$499$	6.41404			0.287132			0.143566	−	0.989641i	$-0.454143\pi$
$499$	6.41404			0.287132			0.143566	+	0.989641i	$0.454143\pi$
$500$	2.25548			0.100868
$501$	0.796221	−	0.122561i	0.0355725	−	0.00547564i
$502$			9.12915i			0.407454i
$503$	38.0103			1.69479			0.847397	−	0.530960i	$-0.178169\pi$
$503$	38.0103			1.69479			0.847397	+	0.530960i	$0.178169\pi$
$504$		0			0
$505$	−9.03979			−0.402265
$506$		−	65.8611i		−	2.92788i
$507$	21.5562	−	3.31813i	0.957346	−	0.147363i
$508$	38.0030			1.68611
$509$	12.6996			0.562901			0.281450	−	0.959576i	$-0.409185\pi$
$509$	12.6996			0.562901			0.281450	+	0.959576i	$0.409185\pi$
$510$	−2.25548	−	14.6527i	−0.0998742	−	0.648833i
$511$		0			0
$512$			31.3992i			1.38766i
$513$	−2.06206	−	4.18100i	−0.0910422	−	0.184596i
$514$		−	52.6194i		−	2.32094i
$515$			15.5206i			0.683919i
$516$	−12.1596	+	1.87172i	−0.535297	+	0.0823977i
$517$			31.9506i			1.40518i
$518$		0			0
$519$	−19.1460	+	2.94713i	−0.840417	+	0.129365i
$520$	−0.336601			−0.0147609
$521$	−36.1940			−1.58569			−0.792843	−	0.609426i	$-0.791400\pi$
$521$	−36.1940			−1.58569			−0.792843	+	0.609426i	$0.791400\pi$
$522$	12.6743	−	3.99658i	0.554739	−	0.174926i
$523$		−	4.93499i		−	0.215792i	−0.994162	−	0.107896i	$-0.965589\pi$
$523$		−	4.93499i		−	0.215792i	0.994162	−	0.107896i	$-0.0344113\pi$
$524$	31.2823			1.36657
$525$		0			0
$526$	0.738470			0.0321988
$527$			9.69976i			0.422528i
$528$	−4.23321	−	27.5010i	−0.184227	−	1.19683i
$529$	−23.2993			−1.01301
$530$	−4.67320			−0.202991
$531$	1.45376	−	0.458415i	0.0630880	−	0.0198935i
$532$		0			0
$533$		−	2.62261i		−	0.113598i
$534$	7.50225	+	48.7384i	0.324654	+	2.10912i
$535$			5.35794i			0.231644i
$536$		−	2.54471i		−	0.109915i
$537$	0.0652685	+	0.424017i	0.00281655	+	0.0182977i
$538$		−	17.6131i		−	0.759354i
$539$		0			0
$540$	10.5110	−	5.18398i	0.452319	−	0.223083i
$541$	16.6570			0.716140			0.358070	−	0.933695i	$-0.383435\pi$
$541$	16.6570			0.716140			0.358070	+	0.933695i	$0.383435\pi$
$542$	17.4000			0.747392
$543$	−3.77834	−	24.5460i	−0.162144	−	1.05337i
$544$		−	33.6789i		−	1.44397i
$545$	−1.35887			−0.0582077
$546$		0			0
$547$	21.2868			0.910159			0.455079	−	0.890451i	$-0.349611\pi$
$547$	21.2868			0.910159			0.455079	+	0.890451i	$0.349611\pi$
$548$		−	9.78494i		−	0.417992i
$549$	4.67697	+	14.8320i	0.199608	+	0.633015i
$550$	−9.67925			−0.412725
$551$	−1.92659			−0.0820756
$552$	6.13887	−	0.944951i	0.261288	−	0.0402198i
$553$		0			0
$554$			20.8472i			0.885713i
$555$	19.4855	−	2.99938i	0.827112	−	0.127317i
$556$			24.7271i			1.04866i
$557$			19.1608i			0.811869i	0.913902	+	0.405935i	$0.133054\pi$
$557$			19.1608i			0.811869i	−0.913902	+	0.405935i	$0.866946\pi$
$558$	−13.7976	+	4.35079i	−0.584099	+	0.184184i
$559$			2.01138i			0.0850723i
$560$		0			0
$561$	5.13017	+	33.3282i	0.216596	+	1.40712i
$562$	−31.2637			−1.31878
$563$	27.2487			1.14840			0.574198	−	0.818717i	$-0.305314\pi$
$563$	27.2487			1.14840			0.574198	+	0.818717i	$0.305314\pi$
$564$	−26.2921	+	4.04711i	−1.10710	+	0.170414i
$565$			11.9390i			0.502276i
$566$	49.3843			2.07578
$567$		0			0
$568$	0.647181			0.0271551
$569$			26.2260i			1.09945i	0.835345	+	0.549726i	$0.185268\pi$
$569$			26.2260i			1.09945i	−0.835345	+	0.549726i	$0.814732\pi$
$570$	−3.16830	+	0.487693i	−0.132705	+	0.0204272i
$571$	−26.8777			−1.12479			−0.562397	−	0.826867i	$-0.690121\pi$
$571$	−26.8777			−1.12479			−0.562397	+	0.826867i	$0.690121\pi$
$572$	6.75919			0.282616
$573$	4.49023	+	29.1708i	0.187582	+	1.21863i
$574$		0			0
$575$			6.80436i			0.283761i
$576$	28.3154	−	8.92869i	1.17981	−	0.372029i
$577$			10.3123i			0.429306i	0.976690	+	0.214653i	$0.0688620\pi$
$577$			10.3123i			0.429306i	−0.976690	+	0.214653i	$0.931138\pi$
$578$			0.445928i			0.0185481i
$579$	4.83373	−	0.744051i	0.200883	−	0.0309217i
$580$		−	4.84341i		−	0.201112i
$581$		0			0
$582$	45.5853	−	7.01690i	1.88957	−	0.290860i
$583$	10.6294			0.440224
$584$	−7.61886			−0.315271
$585$	−0.576223	−	1.82737i	−0.0238239	−	0.0755523i
$586$		−	43.7790i		−	1.80850i
$587$	22.1492			0.914197			0.457098	−	0.889416i	$-0.348889\pi$
$587$	22.1492			0.914197			0.457098	+	0.889416i	$0.348889\pi$
$588$		0			0
$589$	2.09734			0.0864195
$590$		−	1.04817i		−	0.0431524i
$591$	2.52883	+	16.4286i	0.104022	+	0.675781i
$592$	38.9709			1.60170
$593$	−2.91721			−0.119796			−0.0598978	−	0.998205i	$-0.519077\pi$
$593$	−2.91721			−0.119796			−0.0598978	+	0.998205i	$0.519077\pi$
$594$	−45.1072	+	22.2467i	−1.85077	+	0.912795i
$595$		0			0
$596$		−	19.5472i		−	0.800686i
$597$	−3.21853	−	20.9092i	−0.131726	−	0.855757i
$598$		−	8.96500i		−	0.366606i
$599$			36.3212i			1.48405i	0.670374	+	0.742023i	$0.266133\pi$
$599$			36.3212i			1.48405i	−0.670374	+	0.742023i	$0.733867\pi$
$600$	−0.138874	−	0.902197i	−0.00566952	−	0.0368321i
$601$			7.15198i			0.291735i	0.989304	+	0.145868i	$0.0465974\pi$
$601$			7.15198i			0.291735i	−0.989304	+	0.145868i	$0.953403\pi$
$602$		0			0
$603$	13.8149	−	4.35625i	0.562587	−	0.177400i
$604$	−30.3595			−1.23531
$605$	11.0159			0.447858
$606$	4.91392	+	31.9233i	0.199615	+	1.29680i
$607$		−	43.6763i		−	1.77277i	−0.462951	−	0.886384i	$-0.653209\pi$
$607$		−	43.6763i		−	1.77277i	0.462951	−	0.886384i	$-0.346791\pi$
$608$	−7.28226			−0.295334
$609$		0			0
$610$	10.6939			0.432984
$611$			4.34910i			0.175946i
$612$	−26.7759	+	8.44322i	−1.08235	+	0.341297i
$613$	−14.5585			−0.588013			−0.294007	−	0.955803i	$-0.594989\pi$
$613$	−14.5585			−0.588013			−0.294007	+	0.955803i	$0.594989\pi$
$614$	−50.0903			−2.02148
$615$	7.02943	−	1.08203i	0.283454	−	0.0436318i
$616$		0			0
$617$		−	4.68442i		−	0.188588i	−0.995544	−	0.0942938i	$-0.969941\pi$
$617$		−	4.68442i		−	0.188588i	0.995544	−	0.0942938i	$-0.0300593\pi$
$618$	54.8098	−	8.43682i	2.20477	−	0.339379i
$619$			38.1546i			1.53356i	0.641908	+	0.766782i	$0.278143\pi$
$619$			38.1546i			1.53356i	−0.641908	+	0.766782i	$0.721857\pi$
$620$			5.27267i			0.211756i
$621$	15.6391	+	31.7096i	0.627576	+	1.27246i
$622$		−	14.6819i		−	0.588689i
$623$		0			0
$624$	−0.576223	−	3.74343i	−0.0230674	−	0.149857i
$625$	1.00000			0.0400000
$626$	−7.31754			−0.292468
$627$	7.20643	−	1.10928i	0.287797	−	0.0443003i
$628$		−	17.6225i		−	0.703214i
$629$	−47.2285			−1.88312
$630$		0			0
$631$	23.9959			0.955264			0.477632	−	0.878560i	$-0.341495\pi$
$631$	23.9959			0.955264			0.477632	+	0.878560i	$0.341495\pi$
$632$		−	4.78592i		−	0.190374i
$633$	9.65698	−	1.48649i	0.383831	−	0.0590827i
$634$	43.4782			1.72674
$635$	16.8492			0.668641
$636$	1.34640	+	8.74690i	0.0533883	+	0.346837i
$637$		0			0
$638$			20.7852i			0.822895i
$639$	1.10790	+	3.51347i	0.0438279	+	0.138991i
$640$		−	4.18175i		−	0.165298i
$641$		−	23.0983i		−	0.912328i	−0.889896	−	0.456164i	$-0.849223\pi$
$641$		−	23.0983i		−	0.912328i	0.889896	−	0.456164i	$-0.150777\pi$
$642$	18.9212	−	2.91252i	0.746759	−	0.114948i
$643$		−	22.7592i		−	0.897536i	−0.893648	−	0.448768i	$-0.851863\pi$
$643$		−	22.7592i		−	0.897536i	0.893648	−	0.448768i	$-0.148137\pi$
$644$		0			0
$645$	−5.39114	+	0.829853i	−0.212276	+	0.0326754i
$646$	7.67925			0.302136
$647$	−2.42699			−0.0954147			−0.0477073	−	0.998861i	$-0.515191\pi$
$647$	−2.42699			−0.0954147			−0.0477073	+	0.998861i	$0.515191\pi$
$648$	−2.72079	−	3.88522i	−0.106883	−	0.152626i
$649$			2.38410i			0.0935842i
$650$	−1.31754			−0.0516781
$651$		0			0
$652$	−37.6189			−1.47327
$653$		−	40.1558i		−	1.57142i	−0.618596	−	0.785709i	$-0.712298\pi$
$653$		−	40.1558i		−	1.57142i	0.618596	−	0.785709i	$-0.287702\pi$
$654$	0.738667	+	4.79875i	0.0288842	+	0.187646i
$655$	13.8695			0.541925
$656$	14.0589			0.548906
$657$	−13.0426	−	41.3619i	−0.508842	−	1.61368i
$658$		0			0
$659$		−	0.627454i		−	0.0244421i	−0.999925	−	0.0122211i	$-0.996110\pi$
$659$		−	0.627454i		−	0.0244421i	0.999925	−	0.0122211i	$-0.00389018\pi$
$660$	2.78870	+	18.1168i	0.108550	+	0.705196i
$661$			32.9950i			1.28336i	0.766974	+	0.641678i	$0.221761\pi$
$661$			32.9950i			1.28336i	−0.766974	+	0.641678i	$0.778239\pi$
$662$		−	30.5476i		−	1.18727i
$663$	0.698318	+	4.53662i	0.0271204	+	0.176188i
$664$		−	1.45646i		−	0.0565217i
$665$		0			0
$666$	−21.1842	−	67.1810i	−0.820869	−	2.60321i
$667$	14.6117			0.565767
$668$	−1.04905			−0.0405890
$669$	−0.103395	−	0.671707i	−0.00399749	−	0.0259697i
$670$		−	9.96060i		−	0.384812i
$671$	−24.3238			−0.939009
$672$		0			0
$673$	1.14437			0.0441121			0.0220560	−	0.999757i	$-0.492979\pi$
$673$	1.14437			0.0441121			0.0220560	+	0.999757i	$0.492979\pi$
$674$			42.3018i			1.62941i
$675$	4.66019	−	2.29839i	0.179371	−	0.0884653i
$676$	−28.4011			−1.09235
$677$	−15.9782			−0.614092			−0.307046	−	0.951695i	$-0.599341\pi$
$677$	−15.9782			−0.614092			−0.307046	+	0.951695i	$0.599341\pi$
$678$	42.1615	−	6.48988i	1.61920	−	0.249242i
$679$		0			0
$680$			2.18673i			0.0838571i
$681$	−40.1011	+	6.17273i	−1.53668	+	0.236539i
$682$		−	22.6274i		−	0.866447i
$683$			2.26463i			0.0866535i	0.999061	+	0.0433268i	$0.0137957\pi$
$683$			2.26463i			0.0866535i	−0.999061	+	0.0433268i	$0.986204\pi$
$684$	1.82565	+	5.78965i	0.0698053	+	0.221373i
$685$		−	4.33830i		−	0.165758i
$686$		0			0
$687$	2.03646	+	13.2299i	0.0776960	+	0.504752i
$688$	−10.7823			−0.411071
$689$	1.44687			0.0551213
$690$	24.0291	−	3.69877i	0.914771	−	0.140810i
$691$		−	2.77178i		−	0.105444i	−0.998609	−	0.0527218i	$-0.983210\pi$
$691$		−	2.77178i		−	0.105444i	0.998609	−	0.0527218i	$-0.0167897\pi$
$692$	25.2256			0.958934
$693$		0			0
$694$	32.6582			1.23969
$695$			10.9631i			0.415856i
$696$	−1.93738	+	0.298219i	−0.0734362	+	0.0113040i
$697$	−17.0378			−0.645351
$698$	18.4838			0.699623
$699$	1.07507	+	6.98419i	0.0406629	+	0.264166i
$700$		0			0
$701$			23.1184i			0.873169i	0.899663	+	0.436585i	$0.143812\pi$
$701$			23.1184i			0.873169i	−0.899663	+	0.436585i	$0.856188\pi$
$702$	−6.13998	+	3.02822i	−0.231738	+	0.114293i
$703$			10.2120i			0.385154i
$704$			46.4359i			1.75012i
$705$	−11.6570	+	1.79435i	−0.439027	+	0.0675791i
$706$		−	27.7612i		−	1.04481i
$707$		0			0
$708$	−1.96187	+	0.301989i	−0.0737317	+	0.0113495i
$709$	−36.0268			−1.35302			−0.676508	−	0.736435i	$-0.736508\pi$
$709$	−36.0268			−1.35302			−0.676508	+	0.736435i	$0.736508\pi$
$710$	2.53323			0.0950703
$711$	25.9822	−	8.19297i	0.974410	−	0.307260i
$712$		−	7.27357i		−	0.272589i
$713$	−15.9067			−0.595710
$714$		0			0
$715$	2.99679			0.112074
$716$		−	0.558658i		−	0.0208780i
$717$	1.51855	+	9.86529i	0.0567114	+	0.368426i
$718$	11.5724			0.431877
$719$	−17.1420			−0.639288			−0.319644	−	0.947538i	$-0.603563\pi$
$719$	−17.1420			−0.639288			−0.319644	+	0.947538i	$0.603563\pi$
$720$	9.79586	−	3.08892i	0.365070	−	0.115117i
$721$		0			0
$722$			37.5343i			1.39688i
$723$	5.38078	+	34.9562i	0.200113	+	1.30004i
$724$			32.3403i			1.20192i
$725$		−	2.14740i		−	0.0797524i
$726$	−5.98809	−	38.9016i	−0.222239	−	1.44378i
$727$		−	16.6832i		−	0.618747i	−0.950941	−	0.309374i	$-0.899881\pi$
$727$		−	16.6832i		−	0.618747i	0.950941	−	0.309374i	$-0.100119\pi$
$728$		0			0
$729$	16.4348	−	21.4219i	0.608695	−	0.793404i
$730$	−29.8221			−1.10376
$731$	13.0669			0.483298
$732$	−3.08104	−	20.0160i	−0.113879	−	0.739812i
$733$			38.0836i			1.40665i	0.710868	+	0.703326i	$0.248302\pi$
$733$			38.0836i			1.40665i	−0.710868	+	0.703326i	$0.751698\pi$
$734$	−4.07690			−0.150481
$735$		0			0
$736$	55.2302			2.03581
$737$			22.6558i			0.834537i
$738$	−7.64223	−	24.2357i	−0.281314	−	0.892128i
$739$	−22.4373			−0.825368			−0.412684	−	0.910874i	$-0.635409\pi$
$739$	−22.4373			−0.825368			−0.412684	+	0.910874i	$0.635409\pi$
$740$	−25.6728			−0.943752
$741$	0.980937	−	0.150995i	0.0360356	−	0.00554693i
$742$		0			0
$743$		−	6.39189i		−	0.234496i	−0.993103	−	0.117248i	$-0.962593\pi$
$743$		−	6.39189i		−	0.234496i	0.993103	−	0.117248i	$-0.0374072\pi$
$744$	2.10909	−	0.324649i	0.0773228	−	0.0119022i
$745$		−	8.66656i		−	0.317518i
$746$		−	47.6389i		−	1.74419i
$747$	7.90697	−	2.49330i	0.289301	−	0.0912251i
$748$		−	43.9111i		−	1.60555i
$749$		0			0
$750$	−0.543588	−	3.53142i	−0.0198490	−	0.128949i
$751$	−10.9989			−0.401355			−0.200677	−	0.979657i	$-0.564314\pi$
$751$	−10.9989			−0.401355			−0.200677	+	0.979657i	$0.564314\pi$
$752$	−23.3140			−0.850173
$753$	7.57586	−	1.16614i	0.276080	−	0.0424967i
$754$			2.82928i			0.103036i
$755$	−13.4604			−0.489873
$756$		0			0
$757$	−27.8216			−1.01119			−0.505597	−	0.862770i	$-0.668728\pi$
$757$	−27.8216			−1.01119			−0.505597	+	0.862770i	$0.668728\pi$
$758$		−	35.2021i		−	1.27860i
$759$	−54.6551	+	8.41300i	−1.98385	+	0.305373i
$760$	0.472828			0.0171513
$761$	13.0953			0.474705			0.237352	−	0.971424i	$-0.423720\pi$
$761$	13.0953			0.474705			0.237352	+	0.971424i	$0.423720\pi$
$762$	−9.15904	−	59.5017i	−0.331797	−	2.15552i
$763$		0			0
$764$		−	38.4336i		−	1.39048i
$765$	−11.8715	+	3.74343i	−0.429215	+	0.135344i
$766$		−	54.8958i		−	1.98347i
$767$			0.324523i			0.0117179i
$768$	19.1162	−	2.94254i	0.689798	−	0.106180i
$769$		−	7.74247i		−	0.279201i	−0.990208	−	0.139600i	$-0.955418\pi$
$769$		−	7.74247i		−	0.279201i	0.990208	−	0.139600i	$-0.0445818\pi$
$770$		0			0
$771$	−43.6664	+	6.72153i	−1.57261	+	0.242070i
$772$	−6.36861			−0.229211
$773$	−38.3465			−1.37923			−0.689614	−	0.724177i	$-0.742220\pi$
$773$	−38.3465			−1.37923			−0.689614	+	0.724177i	$0.742220\pi$
$774$	5.86113	+	18.5873i	0.210674	+	0.668107i
$775$			2.33772i			0.0839734i
$776$	−6.80301			−0.244214
$777$		0			0
$778$	19.5551			0.701086
$779$			3.68401i			0.131993i
$780$	0.379597	+	2.46605i	0.0135918	+	0.0882989i
$781$	−5.76192			−0.206178
$782$	−58.2411			−2.08270
$783$	−4.93557	−	10.0073i	−0.176383	−	0.357632i
$784$		0			0
$785$		−	7.81320i		−	0.278865i
$786$	−7.53928	−	48.9789i	−0.268917	−	1.74702i
$787$			24.9621i			0.889803i	0.895580	+	0.444901i	$0.146761\pi$
$787$			24.9621i			0.889803i	−0.895580	+	0.444901i	$0.853239\pi$
$788$		−	21.6453i		−	0.771080i
$789$	−0.0943310	−	0.612822i	−0.00335827	−	0.0218170i
$790$		−	18.7333i		−	0.666500i
$791$		0			0
$792$	7.07507	−	2.23098i	0.251402	−	0.0792744i
$793$	−3.31094			−0.117575
$794$	−25.4976			−0.904875
$795$	0.596948	+	3.87807i	0.0211716	+	0.137541i
$796$			27.5487i			0.976436i
$797$	5.81191			0.205868			0.102934	−	0.994688i	$-0.467177\pi$
$797$	5.81191			0.205868			0.102934	+	0.994688i	$0.467177\pi$
$798$		0			0
$799$	28.2539			0.999552
$800$		−	8.11688i		−	0.286975i
$801$	39.4874	−	12.4515i	1.39522	−	0.439954i
$802$	−16.9479			−0.598450
$803$	67.8315			2.39372
$804$	−18.6434	+	2.86976i	−0.657502	+	0.101209i
$805$		0			0
$806$		−	3.08003i		−	0.108490i
$807$	−14.6163	+	2.24987i	−0.514517	+	0.0791991i
$808$		−	4.76414i		−	0.167602i
$809$		−	1.75010i		−	0.0615301i	−0.999527	−	0.0307650i	$-0.990206\pi$
$809$		−	1.75010i		−	0.0615301i	0.999527	−	0.0307650i	$-0.00979436\pi$
$810$	−10.6498	−	15.2077i	−0.374197	−	0.534345i
$811$			28.4479i			0.998940i	0.866331	+	0.499470i	$0.166472\pi$
$811$			28.4479i			0.998940i	−0.866331	+	0.499470i	$0.833528\pi$
$812$		0			0
$813$	−2.22265	−	14.4394i	−0.0779516	−	0.506412i
$814$	110.174			3.86158
$815$	−16.6789			−0.584236
$816$	−24.3192	+	3.74343i	−0.851342	+	0.131046i
$817$		−	2.82541i		−	0.0988487i
$818$	−42.7750			−1.49559
$819$		0			0
$820$	−9.26153			−0.323427
$821$			29.9504i			1.04528i	0.852555	+	0.522638i	$0.175052\pi$
$821$			29.9504i			1.04528i	−0.852555	+	0.522638i	$0.824948\pi$
$822$	−15.3204	+	2.35825i	−0.534360	+	0.0822535i
$823$	16.1257			0.562105			0.281053	−	0.959692i	$-0.409316\pi$
$823$	16.1257			0.562105			0.281053	+	0.959692i	$0.409316\pi$
$824$	−8.17965			−0.284952
$825$	1.23641	+	8.03236i	0.0430464	+	0.279651i
$826$		0			0
$827$		−	15.9844i		−	0.555831i	−0.960605	−	0.277916i	$-0.910356\pi$
$827$		−	15.9844i		−	0.555831i	0.960605	−	0.277916i	$-0.0896436\pi$
$828$	−13.8461	−	43.9099i	−0.481185	−	1.52597i
$829$		−	20.8727i		−	0.724938i	−0.931996	−	0.362469i	$-0.881934\pi$
$829$		−	20.8727i		−	0.724938i	0.931996	−	0.362469i	$-0.118066\pi$
$830$		−	5.70095i		−	0.197883i
$831$	17.3001	−	2.66299i	0.600135	−	0.0923782i
$832$			6.32084i			0.219136i
$833$		0			0
$834$	38.7155	−	5.95943i	1.34061	−	0.206358i
$835$	−0.465112			−0.0160959
$836$	−9.49474			−0.328382
$837$	5.37300	+	10.8942i	0.185718	+	0.376559i
$838$			14.3148i			0.494497i
$839$	−14.2504			−0.491977			−0.245989	−	0.969273i	$-0.579113\pi$
$839$	−14.2504			−0.491977			−0.245989	+	0.969273i	$0.579113\pi$
$840$		0			0
$841$	24.3887			0.840989
$842$		−	31.3893i		−	1.08175i
$843$	3.99358	+	25.9443i	0.137546	+	0.893570i
$844$	−12.7234			−0.437959
$845$	−12.5921			−0.433181
$846$	12.6732	+	40.1903i	0.435714	+	1.38177i
$847$		0			0
$848$			7.75614i			0.266347i
$849$	−6.30828	−	40.9817i	−0.216499	−	1.40649i
$850$			8.55938i			0.293584i
$851$		−	77.4502i		−	2.65496i
$852$	−0.729851	−	4.74148i	−0.0250043	−	0.162440i
$853$			49.6034i			1.69839i	0.528081	+	0.849194i	$0.322912\pi$
$853$			49.6034i			1.69839i	−0.528081	+	0.849194i	$0.677088\pi$
$854$		0			0
$855$	0.809428	+	2.56693i	0.0276819	+	0.0877871i
$856$	−2.82374			−0.0965133
$857$	−5.24503			−0.179167			−0.0895834	−	0.995979i	$-0.528554\pi$
$857$	−5.24503			−0.179167			−0.0895834	+	0.995979i	$0.528554\pi$
$858$	−1.62902	−	10.5829i	−0.0556139	−	0.361295i
$859$		−	11.7458i		−	0.400763i	−0.979718	−	0.200382i	$-0.935782\pi$
$859$		−	11.7458i		−	0.400763i	0.979718	−	0.200382i	$-0.0642182\pi$
$860$	7.10303			0.242211
$861$		0			0
$862$	−64.0863			−2.18279
$863$			35.0909i			1.19451i	0.802052	+	0.597254i	$0.203741\pi$
$863$			35.0909i			1.19451i	−0.802052	+	0.597254i	$0.796259\pi$
$864$	−18.6558	−	37.8262i	−0.634683	−	1.28687i
$865$	11.1842			0.380273
$866$	46.0194			1.56380
$867$	0.370054	−	0.0569621i	0.0125677	−	0.00193454i
$868$		0			0
$869$			42.6096i			1.44543i
$870$	−7.58338	+	1.16730i	−0.257101	+	0.0395752i
$871$			3.08390i			0.104494i
$872$		−	0.716151i		−	0.0242519i
$873$	−11.6460	−	36.9328i	−0.394157	−	1.24999i
$874$			12.5933i			0.425973i
$875$		0			0
$876$	8.59208	+	55.8184i	0.290299	+	1.88593i
$877$	−16.8532			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$877$	−16.8532			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$878$	53.3871			1.80173
$879$	−36.3302	+	5.59227i	−1.22539	+	0.188623i
$880$			16.0647i			0.541542i
$881$	−51.9437			−1.75003			−0.875015	−	0.484096i	$-0.839148\pi$
$881$	−51.9437			−1.75003			−0.875015	+	0.484096i	$0.839148\pi$
$882$		0			0
$883$	14.9096			0.501748			0.250874	−	0.968020i	$-0.419282\pi$
$883$	14.9096			0.501748			0.250874	+	0.968020i	$0.419282\pi$
$884$		−	5.97717i		−	0.201034i
$885$	−0.869826	+	0.133892i	−0.0292389	+	0.00450071i
$886$	63.8774			2.14600
$887$	13.1885			0.442828			0.221414	−	0.975180i	$-0.428933\pi$
$887$	13.1885			0.442828			0.221414	+	0.975180i	$0.428933\pi$
$888$	1.58073	+	10.2692i	0.0530458	+	0.344612i
$889$		0			0
$890$		−	28.4705i		−	0.954335i
$891$	24.2235	+	34.5906i	0.811517	+	1.15883i
$892$			0.884999i			0.0296319i
$893$		−	6.10924i		−	0.204438i
$894$	−30.6053	+	4.71104i	−1.02359	+	0.157561i
$895$		−	0.247690i		−	0.00827935i
$896$		0			0
$897$	−7.43963	+	1.14518i	−0.248402	+	0.0382363i
$898$	49.9283			1.66613
$899$	5.02002			0.167427
$900$	−6.45320	+	2.03489i	−0.215107	+	0.0678295i
$901$		−	9.39958i		−	0.313146i
$902$	39.7453			1.32338
$903$		0			0
$904$	−6.29206			−0.209271
$905$			14.3385i			0.476629i
$906$	7.31689	+	47.5342i	0.243088	+	1.57922i
$907$	46.9417			1.55867			0.779337	−	0.626605i	$-0.215556\pi$
$907$	46.9417			1.55867			0.779337	+	0.626605i	$0.215556\pi$
$908$	52.8347			1.75338
$909$	25.8640	−	8.15567i	0.857854	−	0.270507i
$910$		0			0
$911$		−	45.2977i		−	1.50078i	−0.660996	−	0.750389i	$-0.729866\pi$
$911$		−	45.2977i		−	1.50078i	0.660996	−	0.750389i	$-0.270134\pi$
$912$	0.809428	+	5.25845i	0.0268028	+	0.174125i
$913$			12.9670i			0.429146i
$914$		−	4.98086i		−	0.164752i
$915$	−1.36603	−	8.87439i	−0.0451594	−	0.293378i
$916$		−	17.4309i		−	0.575932i
$917$		0			0
$918$	19.6728	+	39.8884i	0.649300	+	1.31651i
$919$	43.1822			1.42445			0.712225	−	0.701951i	$-0.247687\pi$
$919$	43.1822			1.42445			0.712225	+	0.701951i	$0.247687\pi$
$920$	−3.58602			−0.118228
$921$	6.39846	+	41.5676i	0.210837	+	1.36970i
$922$			15.3762i			0.506389i
$923$	−0.784311			−0.0258159
$924$		0			0
$925$	−11.3824			−0.374252
$926$			28.6455i			0.941349i
$927$	−14.0026	−	44.4064i	−0.459907	−	1.45850i
$928$	−17.4302			−0.572174
$929$	9.01140			0.295655			0.147827	−	0.989013i	$-0.452772\pi$
$929$	9.01140			0.295655			0.147827	+	0.989013i	$0.452772\pi$
$930$	8.25548	−	1.27076i	0.270708	−	0.0416698i
$931$		0			0
$932$		−	9.20194i		−	0.301419i
$933$	−12.1838	+	1.87544i	−0.398879	+	0.0613991i
$934$			41.5432i			1.35933i
$935$		−	19.4687i		−	0.636693i
$936$	0.963056	−	0.303680i	0.0314785	−	0.00992610i
$937$			21.9677i			0.717654i	0.933404	+	0.358827i	$0.116823\pi$
$937$			21.9677i			0.717654i	−0.933404	+	0.358827i	$0.883177\pi$
$938$		0			0
$939$	0.934731	+	6.07248i	0.0305038	+	0.198168i
$940$	15.3585			0.500939
$941$	−1.64772			−0.0537142			−0.0268571	−	0.999639i	$-0.508550\pi$
$941$	−1.64772			−0.0537142			−0.0268571	+	0.999639i	$0.508550\pi$
$942$	−27.5917	+	4.24717i	−0.898987	+	0.138380i
$943$		−	27.9403i		−	0.909862i
$944$	−1.73965			−0.0566209
$945$		0			0
$946$	−30.4823			−0.991064
$947$		−	27.3254i		−	0.887958i	−0.896037	−	0.443979i	$-0.853567\pi$
$947$		−	27.3254i		−	0.887958i	0.896037	−	0.443979i	$-0.146433\pi$
$948$	−35.0634	+	5.39727i	−1.13880	+	0.175295i
$949$	9.23321			0.299723
$950$	1.85076			0.0600467
$951$	−5.55384	−	36.0805i	−0.180095	−	1.16999i
$952$		0			0
$953$			55.2380i			1.78933i	0.446734	+	0.894667i	$0.352587\pi$
$953$			55.2380i			1.78933i	−0.446734	+	0.894667i	$0.647413\pi$
$954$	13.3706	−	4.21615i	0.432890	−	0.136503i
$955$		−	17.0401i		−	0.551405i
$956$		−	12.9979i		−	0.420382i
$957$	17.2487	−	2.65508i	0.557571	−	0.0858264i
$958$			68.5654i			2.21525i
$959$		0			0
$960$	−16.9419	+	2.60785i	−0.546797	+	0.0841679i
$961$	25.5351			0.823712
$962$	14.9968			0.483516
$963$	−4.83392	−	15.3297i	−0.155771	−	0.493994i
$964$		−	46.0562i		−	1.48337i
$965$	−2.82362			−0.0908956
$966$		0			0
$967$	−34.5930			−1.11244			−0.556218	−	0.831036i	$-0.687748\pi$
$967$	−34.5930			−1.11244			−0.556218	+	0.831036i	$0.687748\pi$
$968$			5.80556i			0.186598i
$969$	−0.980937	−	6.37266i	−0.0315122	−	0.204719i
$970$	−26.6287			−0.854995
$971$	−4.24492			−0.136226			−0.0681129	−	0.997678i	$-0.521698\pi$
$971$	−4.24492			−0.136226			−0.0681129	+	0.997678i	$0.521698\pi$
$972$	−25.3962	+	24.3150i	−0.814583	+	0.779903i
$973$		0			0
$974$		−	66.4407i		−	2.12890i
$975$	0.168300	+	1.09336i	0.00538992	+	0.0350156i
$976$		−	17.7488i		−	0.568125i
$977$			38.8911i			1.24424i	0.782924	+	0.622118i	$0.213727\pi$
$977$			38.8911i			1.24424i	−0.782924	+	0.622118i	$0.786273\pi$
$978$	9.06645	+	58.9002i	0.289913	+	1.88342i
$979$			64.7574i			2.06966i
$980$		0			0
$981$	3.88790	−	1.22597i	0.124131	−	0.0391422i
$982$	−46.4155			−1.48118
$983$	26.3768			0.841288			0.420644	−	0.907226i	$-0.361804\pi$
$983$	26.3768			0.841288			0.420644	+	0.907226i	$0.361804\pi$
$984$	0.570251	+	3.70464i	0.0181790	+	0.118100i
$985$		−	9.59675i		−	0.305778i
$986$	18.3804			0.585352
$987$		0			0
$988$	−1.29242			−0.0411174
$989$			21.4285i			0.681388i
$990$	27.6936	−	8.73260i	0.880159	−	0.277540i
$991$	−13.8167			−0.438901			−0.219450	−	0.975624i	$-0.570426\pi$
$991$	−13.8167			−0.438901			−0.219450	+	0.975624i	$0.570426\pi$
$992$	18.9750			0.602457
$993$	−25.3501	+	3.90211i	−0.804460	+	0.123830i
$994$		0			0
$995$			12.2141i			0.387213i
$996$	−10.6706	+	1.64251i	−0.338109	+	0.0520449i
$997$		−	61.3148i		−	1.94186i	−0.239368	−	0.970929i	$-0.576940\pi$
$997$		−	61.3148i		−	1.94186i	0.239368	−	0.970929i	$-0.423060\pi$
$998$			13.2314i			0.418832i
$999$	−53.0444	+	26.1613i	−1.67825	+	0.827708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.b.d.146.7		8
3.2	odd	2		735.2.b.c.146.2		8
7.2	even	3		105.2.s.c.101.4	yes	8
7.3	odd	6		105.2.s.d.26.1	yes	8
7.4	even	3		735.2.s.l.656.1		8
7.5	odd	6		735.2.s.k.521.4		8
7.6	odd	2		735.2.b.c.146.7		8
21.2	odd	6		105.2.s.d.101.1	yes	8
21.5	even	6		735.2.s.l.521.1		8
21.11	odd	6		735.2.s.k.656.4		8
21.17	even	6		105.2.s.c.26.4	✓	8
21.20	even	2	inner	735.2.b.d.146.2		8
35.2	odd	12		525.2.q.f.374.7		16
35.3	even	12		525.2.q.e.299.2		16
35.9	even	6		525.2.t.g.101.1		8
35.17	even	12		525.2.q.e.299.7		16
35.23	odd	12		525.2.q.f.374.2		16
35.24	odd	6		525.2.t.f.26.4		8
105.2	even	12		525.2.q.e.374.2		16
105.17	odd	12		525.2.q.f.299.2		16
105.23	even	12		525.2.q.e.374.7		16
105.38	odd	12		525.2.q.f.299.7		16
105.44	odd	6		525.2.t.f.101.4		8
105.59	even	6		525.2.t.g.26.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.4	✓	8	21.17	even	6
105.2.s.c.101.4	yes	8	7.2	even	3
105.2.s.d.26.1	yes	8	7.3	odd	6
105.2.s.d.101.1	yes	8	21.2	odd	6
525.2.q.e.299.2		16	35.3	even	12
525.2.q.e.299.7		16	35.17	even	12
525.2.q.e.374.2		16	105.2	even	12
525.2.q.e.374.7		16	105.23	even	12
525.2.q.f.299.2		16	105.17	odd	12
525.2.q.f.299.7		16	105.38	odd	12
525.2.q.f.374.2		16	35.23	odd	12
525.2.q.f.374.7		16	35.2	odd	12
525.2.t.f.26.4		8	35.24	odd	6
525.2.t.f.101.4		8	105.44	odd	6
525.2.t.g.26.1		8	105.59	even	6
525.2.t.g.101.1		8	35.9	even	6
735.2.b.c.146.2		8	3.2	odd	2
735.2.b.c.146.7		8	7.6	odd	2
735.2.b.d.146.2		8	21.20	even	2	inner
735.2.b.d.146.7		8	1.1	even	1	trivial
735.2.s.k.521.4		8	7.5	odd	6
735.2.s.k.656.4		8	21.11	odd	6
735.2.s.l.521.1		8	21.5	even	6
735.2.s.l.656.1		8	7.4	even	3

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.06288i q^{2} +(1.71189 - 0.263509i) q^{3} -2.25548 q^{4} -1.00000 q^{5} +(0.543588 + 3.53142i) q^{6} -0.527019i q^{8} +(2.86113 - 0.902197i) q^{9} +O(q^{10})\)	\(q+2.06288i q^{2} +(1.71189 - 0.263509i) q^{3} -2.25548 q^{4} -1.00000 q^{5} +(0.543588 + 3.53142i) q^{6} -0.527019i q^{8} +(2.86113 - 0.902197i) q^{9} -2.06288i q^{10} +4.69211i q^{11} +(-3.86113 + 0.594339i) q^{12} +0.638688i q^{13} +(-1.71189 + 0.263509i) q^{15} -3.42378 q^{16} +4.14924 q^{17} +(1.86113 + 5.90216i) q^{18} -0.897174i q^{19} +2.25548 q^{20} -9.67925 q^{22} +6.80436i q^{23} +(-0.138874 - 0.902197i) q^{24} +1.00000 q^{25} -1.31754 q^{26} +(4.66019 - 2.29839i) q^{27} -2.14740i q^{29} +(-0.543588 - 3.53142i) q^{30} +2.33772i q^{31} -8.11688i q^{32} +(1.23641 + 8.03236i) q^{33} +8.55938i q^{34} +(-6.45320 + 2.03489i) q^{36} -11.3824 q^{37} +1.85076 q^{38} +(0.168300 + 1.09336i) q^{39} +0.527019i q^{40} -4.10624 q^{41} +3.14924 q^{43} -10.5829i q^{44} +(-2.86113 + 0.902197i) q^{45} -14.0366 q^{46} +6.80943 q^{47} +(-5.86113 + 0.902197i) q^{48} +2.06288i q^{50} +(7.10303 - 1.09336i) q^{51} -1.44055i q^{52} -2.26538i q^{53} +(4.74131 + 9.61342i) q^{54} -4.69211i q^{55} +(-0.236414 - 1.53586i) q^{57} +4.42983 q^{58} +0.508109 q^{59} +(3.86113 - 0.594339i) q^{60} +5.18398i q^{61} -4.82244 q^{62} +9.89660 q^{64} -0.638688i q^{65} +(-16.5698 + 2.55057i) q^{66} +4.82849 q^{67} -9.35851 q^{68} +(1.79301 + 11.6483i) q^{69} +1.22800i q^{71} +(-0.475475 - 1.50787i) q^{72} -14.4565i q^{73} -23.4806i q^{74} +(1.71189 - 0.263509i) q^{75} +2.02356i q^{76} +(-2.25548 + 0.347183i) q^{78} +9.08112 q^{79} +3.42378 q^{80} +(7.37208 - 5.16260i) q^{81} -8.47068i q^{82} +2.76359 q^{83} -4.14924 q^{85} +6.49650i q^{86} +(-0.565860 - 3.67611i) q^{87} +2.47283 q^{88} +13.8013 q^{89} +(-1.86113 - 5.90216i) q^{90} -15.3471i q^{92} +(0.616011 + 4.00192i) q^{93} +14.0470i q^{94} +0.897174i q^{95} +(-2.13887 - 13.8952i) q^{96} -12.9085i q^{97} +(4.23321 + 13.4247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9}+O(q^{10}) \) 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9	\( 8 q + q^{3} - 6 q^{4} - 8 q^{5} + 5 q^{6} + q^{9} - 9 q^{12} - q^{15} - 2 q^{16} + 24 q^{17} - 7 q^{18} + 6 q^{20} - 40 q^{22} - 23 q^{24} + 8 q^{25} + 12 q^{26} + 4 q^{27} - 5 q^{30} + 2 q^{33} + 9 q^{36} - 14 q^{37} + 24 q^{38} - 12 q^{39} - 30 q^{41} + 16 q^{43} - q^{45} + 14 q^{46} + 12 q^{47} - 25 q^{48} - 6 q^{51} - 10 q^{54} + 6 q^{57} + 26 q^{58} + 24 q^{59} + 9 q^{60} + 24 q^{62} + 38 q^{64} - 38 q^{66} - 8 q^{67} - 13 q^{69} + q^{72} + q^{75} - 6 q^{78} + 58 q^{79} + 2 q^{80} + 13 q^{81} + 30 q^{83} - 24 q^{85} - 61 q^{87} + 4 q^{88} + 6 q^{89} + 7 q^{90} - 36 q^{93} - 39 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q + q^3 - 6 * q^4 - 8 * q^5 + 5 * q^6 + q^9 - 9 * q^12 - q^15 - 2 * q^16 + 24 * q^17 - 7 * q^18 + 6 * q^20 - 40 * q^22 - 23 * q^24 + 8 * q^25 + 12 * q^26 + 4 * q^27 - 5 * q^30 + 2 * q^33 + 9 * q^36 - 14 * q^37 + 24 * q^38 - 12 * q^39 - 30 * q^41 + 16 * q^43 - q^45 + 14 * q^46 + 12 * q^47 - 25 * q^48 - 6 * q^51 - 10 * q^54 + 6 * q^57 + 26 * q^58 + 24 * q^59 + 9 * q^60 + 24 * q^62 + 38 * q^64 - 38 * q^66 - 8 * q^67 - 13 * q^69 + q^72 + q^75 - 6 * q^78 + 58 * q^79 + 2 * q^80 + 13 * q^81 + 30 * q^83 - 24 * q^85 - 61 * q^87 + 4 * q^88 + 6 * q^89 + 7 * q^90 - 36 * q^93 - 39 * q^96 - 34 * q^99

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