LMFDB - Embedded newform 950.2.u.f.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.2
Character	$\chi$	$=$	950.199
Dual form			950.2.u.f.549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(1.90555 + 2.27095i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.27095 - 1.90555i) q^{6} +(-2.51922 - 1.45447i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.00513 + 5.70040i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(1.90555 + 2.27095i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.27095 - 1.90555i) q^{6} +(-2.51922 - 1.45447i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.00513 + 5.70040i) q^{9} +(-0.688430 - 1.19240i) q^{11} +(2.56734 + 1.48226i) q^{12} +(-3.44902 + 4.11038i) q^{13} +(2.73352 + 0.994919i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-5.22100 + 0.920603i) q^{17} -5.78833i q^{18} +(-2.17069 - 3.77996i) q^{19} +(-1.49748 - 8.49261i) q^{21} +(0.885029 + 1.05474i) q^{22} +(0.546254 + 1.50082i) q^{23} +(-2.78573 - 1.01392i) q^{24} +(2.68286 - 4.64685i) q^{26} +(-7.15861 + 4.13303i) q^{27} +(-2.86476 - 0.505134i) q^{28} +(0.411474 - 2.33359i) q^{29} +(-3.50252 + 6.06655i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(1.39603 - 3.83556i) q^{33} +(4.98182 - 1.81323i) q^{34} +(1.00513 + 5.70040i) q^{36} +8.31135i q^{37} +(2.79409 + 3.34560i) q^{38} -15.9067 q^{39} +(-7.13497 + 5.98695i) q^{41} +(2.94945 + 8.10355i) q^{42} +(1.99787 - 5.48910i) q^{43} +(-1.05474 - 0.885029i) q^{44} +(-0.798570 - 1.38316i) q^{46} +(-2.41402 - 0.425657i) q^{47} +(2.91947 + 0.514782i) q^{48} +(0.730994 + 1.26612i) q^{49} +(-12.0395 - 10.1024i) q^{51} +(-1.83518 + 5.04213i) q^{52} +(3.63506 + 9.98725i) q^{53} +(6.33216 - 5.31332i) q^{54} +2.90895 q^{56} +(4.44774 - 12.1324i) q^{57} +2.36959i q^{58} +(1.39863 + 7.93202i) q^{59} +(14.5150 - 5.28304i) q^{61} +(2.39587 - 6.58259i) q^{62} +(10.8232 - 12.8986i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.708783 + 4.01971i) q^{66} +(10.0911 + 1.77933i) q^{67} +(-4.59127 + 2.65077i) q^{68} +(-2.36737 + 4.10041i) q^{69} +(-2.36737 - 0.861653i) q^{71} +(-1.97973 - 5.43926i) q^{72} +(-4.37520 - 5.21416i) q^{73} +(-1.44325 - 8.18508i) q^{74} +(-3.33260 - 2.80958i) q^{76} +4.00522i q^{77} +(15.6651 - 2.76218i) q^{78} +(6.31181 - 5.29624i) q^{79} +(-6.70923 - 2.44196i) q^{81} +(5.98695 - 7.13497i) q^{82} +(0.419755 + 0.242346i) q^{83} +(-4.31181 - 7.46827i) q^{84} +(-1.01435 + 5.75264i) q^{86} +(6.08354 - 3.51233i) q^{87} +(1.19240 + 0.688430i) q^{88} +(-9.24921 - 7.76101i) q^{89} +(14.6673 - 5.33846i) q^{91} +(1.02662 + 1.22348i) q^{92} +(-20.4511 + 3.60607i) q^{93} +2.45126 q^{94} -2.96451 q^{96} +(-9.01879 + 1.59026i) q^{97} +(-0.939748 - 1.11995i) q^{98} +(7.48910 - 2.72581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 18 * q^9	$ 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	1.90555	+	2.27095i	1.10017	+	1.31113i	0.946389	+	0.323028i	$0.104701\pi$
$3$	1.90555	+	2.27095i	1.10017	+	1.31113i	0.153781	+	0.988105i	$0.450855\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−2.27095	−	1.90555i	−0.927111	−	0.777938i
$7$	−2.51922	−	1.45447i	−0.952177	−	0.549740i	−0.0584207	−	0.998292i	$-0.518606\pi$
$7$	−2.51922	−	1.45447i	−0.952177	−	0.549740i	−0.893757	+	0.448552i	$0.851940\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−1.00513	+	5.70040i	−0.335045	+	1.90013i
$10$		0			0
$11$	−0.688430	−	1.19240i	−0.207570	−	0.359521i	0.743379	−	0.668871i	$-0.233222\pi$
$11$	−0.688430	−	1.19240i	−0.207570	−	0.359521i	−0.950948	+	0.309350i	$0.899889\pi$
$12$	2.56734	+	1.48226i	0.741128	+	0.427891i
$13$	−3.44902	+	4.11038i	−0.956585	+	1.14001i	0.0334846	+	0.999439i	$0.489340\pi$
$13$	−3.44902	+	4.11038i	−0.956585	+	1.14001i	−0.990070	+	0.140575i	$0.955105\pi$
$14$	2.73352	+	0.994919i	0.730564	+	0.265903i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−5.22100	+	0.920603i	−1.26628	+	0.223279i	−0.766144	−	0.642669i	$-0.777827\pi$
$17$	−5.22100	+	0.920603i	−1.26628	+	0.223279i	−0.500134	+	0.865948i	$0.666716\pi$
$18$		−	5.78833i		−	1.36432i
$19$	−2.17069	−	3.77996i	−0.497990	−	0.867183i
$19$	−2.17069	−	3.77996i	−0.497990	−	0.867183i
$20$		0			0
$21$	−1.49748	−	8.49261i	−0.326776	−	1.85324i
$22$	0.885029	+	1.05474i	0.188689	+	0.224871i
$23$	0.546254	+	1.50082i	0.113902	+	0.312943i	0.983525	−	0.180774i	$-0.0578602\pi$
$23$	0.546254	+	1.50082i	0.113902	+	0.312943i	−0.869623	+	0.493717i	$0.835638\pi$
$24$	−2.78573	−	1.01392i	−0.568635	−	0.206966i
$25$		0			0
$26$	2.68286	−	4.64685i	0.526152	−	0.911322i
$27$	−7.15861	+	4.13303i	−1.37768	+	0.795401i
$28$	−2.86476	−	0.505134i	−0.541388	−	0.0954613i
$29$	0.411474	−	2.33359i	0.0764088	−	0.433336i	−0.922473	−	0.386061i	$-0.873835\pi$
$29$	0.411474	−	2.33359i	0.0764088	−	0.433336i	0.998882	−	0.0472746i	$-0.0150536\pi$
$30$		0			0
$31$	−3.50252	+	6.06655i	−0.629072	+	1.08958i	0.358666	+	0.933466i	$0.383232\pi$
$31$	−3.50252	+	6.06655i	−0.629072	+	1.08958i	−0.987738	+	0.156119i	$0.950102\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	1.39603	−	3.83556i	0.243018	−	0.667686i
$34$	4.98182	−	1.81323i	0.854375	−	0.310967i
$35$		0			0
$36$	1.00513	+	5.70040i	0.167522	+	0.950066i
$37$			8.31135i			1.36638i	0.730242	+	0.683189i	$0.239407\pi$
$37$			8.31135i			1.36638i	−0.730242	+	0.683189i	$0.760593\pi$
$38$	2.79409	+	3.34560i	0.453262	+	0.542728i
$39$	−15.9067			−2.54712
$40$		0			0
$41$	−7.13497	+	5.98695i	−1.11430	+	0.935005i	−0.998302	−	0.0582455i	$-0.981449\pi$
$41$	−7.13497	+	5.98695i	−1.11430	+	0.935005i	−0.115993	+	0.993250i	$0.537005\pi$
$42$	2.94945	+	8.10355i	0.455110	+	1.25040i
$43$	1.99787	−	5.48910i	0.304672	−	0.837080i	−0.689000	−	0.724761i	$-0.741950\pi$
$43$	1.99787	−	5.48910i	0.304672	−	0.837080i	0.993672	−	0.112319i	$-0.0358278\pi$
$44$	−1.05474	−	0.885029i	−0.159008	−	0.133423i
$45$		0			0
$46$	−0.798570	−	1.38316i	−0.117743	−	0.203936i
$47$	−2.41402	−	0.425657i	−0.352121	−	0.0620885i	−0.00520990	−	0.999986i	$-0.501658\pi$
$47$	−2.41402	−	0.425657i	−0.352121	−	0.0620885i	−0.346911	+	0.937898i	$0.612769\pi$
$48$	2.91947	+	0.514782i	0.421390	+	0.0743024i
$49$	0.730994	+	1.26612i	0.104428	+	0.180874i
$50$		0			0
$51$	−12.0395	−	10.1024i	−1.68587	−	1.41461i
$52$	−1.83518	+	5.04213i	−0.254494	+	0.699217i
$53$	3.63506	+	9.98725i	0.499314	+	1.37185i	0.891939	+	0.452155i	$0.149345\pi$
$53$	3.63506	+	9.98725i	0.499314	+	1.37185i	−0.392625	+	0.919699i	$0.628433\pi$
$54$	6.33216	−	5.31332i	0.861698	−	0.723051i
$55$		0			0
$56$	2.90895			0.388725
$57$	4.44774	−	12.1324i	0.589118	−	1.60698i
$58$			2.36959i			0.311142i
$59$	1.39863	+	7.93202i	0.182086	+	1.03266i	0.929642	+	0.368463i	$0.120116\pi$
$59$	1.39863	+	7.93202i	0.182086	+	1.03266i	−0.747556	+	0.664199i	$0.768773\pi$
$60$		0			0
$61$	14.5150	−	5.28304i	1.85846	−	0.676424i	0.878332	−	0.478052i	$-0.158657\pi$
$61$	14.5150	−	5.28304i	1.85846	−	0.676424i	0.980127	−	0.198371i	$-0.0635652\pi$
$62$	2.39587	−	6.58259i	0.304276	−	0.835990i
$63$	10.8232	−	12.8986i	1.36360	−	1.62508i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−0.708783	+	4.01971i	−0.0872452	+	0.494792i
$67$	10.0911	+	1.77933i	1.23282	+	0.217380i	0.751837	−	0.659349i	$-0.229168\pi$
$67$	10.0911	+	1.77933i	1.23282	+	0.217380i	0.480985	+	0.876729i	$0.340279\pi$
$68$	−4.59127	+	2.65077i	−0.556773	+	0.321453i
$69$	−2.36737	+	4.10041i	−0.284998	+	0.493631i
$70$		0			0
$71$	−2.36737	−	0.861653i	−0.280955	−	0.102259i	0.197699	−	0.980263i	$-0.436653\pi$
$71$	−2.36737	−	0.861653i	−0.280955	−	0.102259i	−0.478654	+	0.878003i	$0.658875\pi$
$72$	−1.97973	−	5.43926i	−0.233313	−	0.641022i
$73$	−4.37520	−	5.21416i	−0.512079	−	0.610272i	0.446610	−	0.894729i	$-0.352631\pi$
$73$	−4.37520	−	5.21416i	−0.512079	−	0.610272i	−0.958689	+	0.284457i	$0.908187\pi$
$74$	−1.44325	−	8.18508i	−0.167774	−	0.951496i
$75$		0			0
$76$	−3.33260	−	2.80958i	−0.382276	−	0.322281i
$77$			4.00522i			0.456437i
$78$	15.6651	−	2.76218i	1.77372	−	0.312755i
$79$	6.31181	−	5.29624i	0.710134	−	0.595873i	−0.214503	−	0.976723i	$-0.568813\pi$
$79$	6.31181	−	5.29624i	0.710134	−	0.595873i	0.924637	+	0.380850i	$0.124369\pi$
$80$		0			0
$81$	−6.70923	−	2.44196i	−0.745470	−	0.271329i
$82$	5.98695	−	7.13497i	0.661148	−	0.787926i
$83$	0.419755	+	0.242346i	0.0460741	+	0.0266009i	0.522860	−	0.852419i	$-0.324865\pi$
$83$	0.419755	+	0.242346i	0.0460741	+	0.0266009i	−0.476786	+	0.879019i	$0.658198\pi$
$84$	−4.31181	−	7.46827i	−0.470457	−	0.814855i
$85$		0			0
$86$	−1.01435	+	5.75264i	−0.109380	+	0.620323i
$87$	6.08354	−	3.51233i	0.652224	−	0.376562i
$88$	1.19240	+	0.688430i	0.127110	+	0.0733869i
$89$	−9.24921	−	7.76101i	−0.980414	−	0.822665i	0.00373759	−	0.999993i	$-0.498810\pi$
$89$	−9.24921	−	7.76101i	−0.980414	−	0.822665i	−0.984152	+	0.177328i	$0.943255\pi$
$90$		0			0
$91$	14.6673	−	5.33846i	1.53755	−	0.559622i
$92$	1.02662	+	1.22348i	0.107033	+	0.127557i
$93$	−20.4511	+	3.60607i	−2.12068	+	0.373933i
$94$	2.45126			0.252828
$95$		0			0
$96$	−2.96451			−0.302564
$97$	−9.01879	+	1.59026i	−0.915719	+	0.161466i	−0.611599	−	0.791168i	$-0.709474\pi$
$97$	−9.01879	+	1.59026i	−0.915719	+	0.161466i	−0.304120	+	0.952634i	$0.598362\pi$
$98$	−0.939748	−	1.11995i	−0.0949289	−	0.113132i
$99$	7.48910	−	2.72581i	0.752683	−	0.273954i
$100$		0			0
$101$	3.78879	+	3.17918i	0.376999	+	0.316340i	0.811523	−	0.584320i	$-0.198639\pi$
$101$	3.78879	+	3.17918i	0.376999	+	0.316340i	−0.434524	+	0.900660i	$0.643083\pi$
$102$	13.6109	+	7.85824i	1.34768	+	0.778082i
$103$	−4.77000	+	2.75396i	−0.470002	+	0.271356i	−0.716240	−	0.697854i	$-0.754139\pi$
$103$	−4.77000	+	2.75396i	−0.470002	+	0.271356i	0.246239	+	0.969209i	$0.420805\pi$
$104$	0.931747	−	5.28420i	0.0913653	−	0.518159i
$105$		0			0
$106$	−5.31410	−	9.20430i	−0.516151	−	0.894000i
$107$	5.43798	+	3.13962i	0.525710	+	0.303519i	0.739268	−	0.673412i	$-0.235172\pi$
$107$	5.43798	+	3.13962i	0.525710	+	0.303519i	−0.213558	+	0.976930i	$0.568505\pi$
$108$	−5.31332	+	6.33216i	−0.511274	+	0.609313i
$109$	5.14544	+	1.87279i	0.492844	+	0.179380i	0.576473	−	0.817117i	$-0.304429\pi$
$109$	5.14544	+	1.87279i	0.492844	+	0.179380i	−0.0836288	+	0.996497i	$0.526651\pi$
$110$		0			0
$111$	−18.8746	+	15.8377i	−1.79150	+	1.50325i
$112$	−2.86476	+	0.505134i	−0.270694	+	0.0477307i
$113$		−	3.38326i		−	0.318271i	−0.987257	−	0.159135i	$-0.949129\pi$
$113$		−	3.38326i		−	0.318271i	0.987257	−	0.159135i	$-0.0508706\pi$
$114$	−2.27340	+	12.7205i	−0.212923	+	1.19138i
$115$		0			0
$116$	−0.411474	−	2.33359i	−0.0382044	−	0.216668i
$117$	−19.9641	−	23.7923i	−1.84568	−	2.19959i
$118$	−2.75476	−	7.56865i	−0.253597	−	0.696751i
$119$	14.4919	+	5.27461i	1.32847	+	0.483522i
$120$		0			0
$121$	4.55213	−	7.88452i	0.413830	−	0.716774i
$122$	−13.3771	+	7.72328i	−1.21111	+	0.699233i
$123$	−27.1921	−	4.79470i	−2.45183	−	0.432324i
$124$	−1.21641	+	6.89863i	−0.109237	+	0.619515i
$125$		0			0
$126$	−8.41899	+	14.5821i	−0.750023	+	1.29908i
$127$	−5.27100	+	6.28174i	−0.467726	+	0.557414i	−0.947408	−	0.320028i	$-0.896308\pi$
$127$	−5.27100	+	6.28174i	−0.467726	+	0.557414i	0.479682	+	0.877442i	$0.340752\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	16.2725	−	5.92271i	1.43271	−	0.521466i
$130$		0			0
$131$	3.31008	+	18.7724i	0.289203	+	1.64015i	0.689874	+	0.723929i	$0.257666\pi$
$131$	3.31008	+	18.7724i	0.289203	+	1.64015i	−0.400671	+	0.916222i	$0.631223\pi$
$132$		−	4.08172i		−	0.355268i
$133$	−0.0294142	+	12.6798i	−0.00255054	+	1.09948i
$134$	−10.2467			−0.885184
$135$		0			0
$136$	4.06122	−	3.40777i	0.348246	−	0.292213i
$137$	−4.30123	−	11.8175i	−0.367479	−	1.00964i	−0.976317	−	0.216345i	$-0.930586\pi$
$137$	−4.30123	−	11.8175i	−0.367479	−	1.00964i	0.608838	−	0.793294i	$-0.291636\pi$
$138$	1.61938	−	4.44920i	0.137851	−	0.378741i
$139$	−6.64986	−	5.57990i	−0.564034	−	0.473281i	0.315626	−	0.948884i	$-0.397785\pi$
$139$	−6.64986	−	5.57990i	−0.564034	−	0.473281i	−0.879660	+	0.475603i	$0.842230\pi$
$140$		0			0
$141$	−3.63340	−	6.29323i	−0.305987	−	0.529985i
$142$	2.48103	+	0.437473i	0.208203	+	0.0367119i
$143$	7.27561	+	1.28289i	0.608417	+	0.107280i
$144$	2.89417	+	5.01285i	0.241181	+	0.417737i
$145$		0			0
$146$	5.21416	+	4.37520i	0.431527	+	0.362094i
$147$	−1.48234	+	4.07271i	−0.122262	+	0.335911i
$148$	2.84265	+	7.81011i	0.233664	+	0.641987i
$149$	−12.5465	+	10.5278i	−1.02785	+	0.862467i	−0.990593	−	0.136839i	$-0.956306\pi$
$149$	−12.5465	+	10.5278i	−1.02785	+	0.862467i	−0.0372549	+	0.999306i	$0.511861\pi$
$150$		0			0
$151$	12.8845			1.04852			0.524261	−	0.851557i	$-0.324341\pi$
$151$	12.8845			1.04852			0.524261	+	0.851557i	$0.324341\pi$
$152$	3.76985	+	2.18820i	0.305775	+	0.177487i
$153$		−	30.6871i		−	2.48090i
$154$	−0.695499	−	3.94437i	−0.0560449	−	0.317846i
$155$		0			0
$156$	−14.9474	+	5.44043i	−1.19675	+	0.435583i
$157$	5.60574	−	15.4017i	0.447387	−	1.22919i	−0.487150	−	0.873318i	$-0.661963\pi$
$157$	5.60574	−	15.4017i	0.447387	−	1.22919i	0.934537	−	0.355867i	$-0.115814\pi$
$158$	−5.29624	+	6.31181i	−0.421346	+	0.502141i
$159$	−15.7537	+	27.2863i	−1.24935	+	2.16394i
$160$		0			0
$161$	0.806770	−	4.57542i	0.0635824	−	0.360594i
$162$	7.03135	+	1.23982i	0.552435	+	0.0974092i
$163$	3.53398	−	2.04034i	0.276803	−	0.159812i	−0.355172	−	0.934801i	$-0.615578\pi$
$163$	3.53398	−	2.04034i	0.276803	−	0.159812i	0.631975	+	0.774989i	$0.282245\pi$
$164$	−4.65702	+	8.06620i	−0.363652	+	0.629864i
$165$		0			0
$166$	−0.455461	−	0.165774i	−0.0353506	−	0.0128666i
$167$	5.42127	+	14.8948i	0.419510	+	1.15260i	0.951984	+	0.306149i	$0.0990404\pi$
$167$	5.42127	+	14.8948i	0.419510	+	1.15260i	−0.532473	+	0.846447i	$0.678737\pi$
$168$	5.54315	+	6.60607i	0.427664	+	0.509670i
$169$	−2.74207	−	15.5510i	−0.210928	−	1.19623i
$170$		0			0
$171$	23.7291	−	8.57441i	1.81461	−	0.655701i
$172$		−	5.84138i		−	0.445401i
$173$	2.38705	−	0.420901i	0.181484	−	0.0320005i	−0.0821676	−	0.996619i	$-0.526184\pi$
$173$	2.38705	−	0.420901i	0.181484	−	0.0320005i	0.263651	+	0.964618i	$0.415073\pi$
$174$	−5.38121	+	4.51537i	−0.407948	+	0.342309i
$175$		0			0
$176$	−1.29383	−	0.470914i	−0.0975258	−	0.0354965i
$177$	−15.3481	+	18.2911i	−1.15363	+	1.37484i
$178$	10.4564	+	6.03699i	0.783739	+	0.452492i
$179$	9.04557	+	15.6674i	0.676098	+	1.17104i	0.976147	+	0.217112i	$0.0696636\pi$
$179$	9.04557	+	15.6674i	0.676098	+	1.17104i	−0.300049	+	0.953924i	$0.597003\pi$
$180$		0			0
$181$	−3.48949	+	19.7899i	−0.259371	+	1.47097i	0.525226	+	0.850963i	$0.323981\pi$
$181$	−3.48949	+	19.7899i	−0.259371	+	1.47097i	−0.784597	+	0.620006i	$0.787130\pi$
$182$	−13.5174	+	7.80430i	−1.00198	+	0.578493i
$183$	39.6566	+	22.8958i	2.93150	+	1.69250i
$184$	−1.22348	−	1.02662i	−0.0901962	−	0.0756836i
$185$		0			0
$186$	19.5142	−	7.10258i	1.43085	−	0.520786i
$187$	4.69202	+	5.59173i	0.343114	+	0.408908i
$188$	−2.41402	+	0.425657i	−0.176061	+	0.0310442i
$189$	24.0455			1.74906
$190$		0			0
$191$	−7.33371			−0.530649			−0.265324	−	0.964159i	$-0.585479\pi$
$191$	−7.33371			−0.530649			−0.265324	+	0.964159i	$0.585479\pi$
$192$	2.91947	−	0.514782i	0.210695	−	0.0371512i
$193$	−16.5147	−	19.6814i	−1.18875	−	1.41670i	−0.886033	−	0.463622i	$-0.846550\pi$
$193$	−16.5147	−	19.6814i	−1.18875	−	1.41670i	−0.302720	−	0.953079i	$-0.597895\pi$
$194$	8.60563	−	3.13219i	0.617848	−	0.224878i
$195$		0			0
$196$	1.11995	+	0.939748i	0.0799963	+	0.0671248i
$197$	−11.4157	−	6.59085i	−0.813334	−	0.469579i	0.0347781	−	0.999395i	$-0.488928\pi$
$197$	−11.4157	−	6.59085i	−0.813334	−	0.469579i	−0.848112	+	0.529816i	$0.822261\pi$
$198$	−6.90199	+	3.98487i	−0.490503	+	0.283192i
$199$	−1.78833	+	10.1421i	−0.126771	+	0.718957i	0.853468	+	0.521144i	$0.174495\pi$
$199$	−1.78833	+	10.1421i	−0.126771	+	0.718957i	−0.980240	+	0.197812i	$0.936616\pi$
$200$		0			0
$201$	15.1883	+	26.3069i	1.07130	+	1.85555i
$202$	−4.28329	−	2.47296i	−0.301371	−	0.173997i
$203$	−4.43074	+	5.28035i	−0.310977	+	0.370608i
$204$	−14.7687	−	5.37535i	−1.03401	−	0.376350i
$205$		0			0
$206$	4.21931	−	3.54042i	0.293973	−	0.246673i
$207$	−9.10434	+	1.60534i	−0.632795	+	0.111579i
$208$			5.36572i			0.372046i
$209$	−3.01285	+	5.19056i	−0.208403	+	0.359039i
$210$		0			0
$211$	−2.74895	−	15.5901i	−0.189245	−	1.07326i	−0.920379	−	0.391029i	$-0.872119\pi$
$211$	−2.74895	−	15.5901i	−0.189245	−	1.07326i	0.731133	−	0.682235i	$-0.238992\pi$
$212$	6.83168	+	8.14168i	0.469202	+	0.559173i
$213$	−2.55438	−	7.01810i	−0.175023	−	0.480873i
$214$	−5.90056	−	2.14763i	−0.403354	−	0.146809i
$215$		0			0
$216$	4.13303	−	7.15861i	0.281217	−	0.487082i
$217$	17.6473	−	10.1887i	1.19798	−	0.691652i
$218$	−5.39247	−	0.950839i	−0.365224	−	0.0643989i
$219$	3.50392	−	19.8717i	0.236773	−	1.34281i
$220$		0			0
$221$	14.2233	−	24.6355i	0.956762	−	1.65716i
$222$	15.8377	−	18.8746i	1.06296	−	1.26678i
$223$	1.12396	−	3.08806i	0.0752660	−	0.206792i	−0.896354	−	0.443339i	$-0.853794\pi$
$223$	1.12396	−	3.08806i	0.0752660	−	0.206792i	0.971620	+	0.236548i	$0.0760159\pi$
$224$	2.73352	−	0.994919i	0.182641	−	0.0664758i
$225$		0			0
$226$	0.587497	+	3.33186i	0.0390797	+	0.221632i
$227$		−	11.8147i		−	0.784172i	−0.919928	−	0.392086i	$-0.871754\pi$
$227$		−	11.8147i		−	0.784172i	0.919928	−	0.392086i	$-0.128246\pi$
$228$	0.0299760	−	12.9220i	0.00198521	−	0.855779i
$229$	11.9186			0.787604			0.393802	−	0.919195i	$-0.371160\pi$
$229$	11.9186			0.787604			0.393802	+	0.919195i	$0.371160\pi$
$230$		0			0
$231$	−9.09564	+	7.63215i	−0.598450	+	0.502159i
$232$	0.810446	+	2.22668i	0.0532084	+	0.146189i
$233$	−3.14124	+	8.63049i	−0.205790	+	0.565402i	−0.999055	−	0.0434743i	$-0.986157\pi$
$233$	−3.14124	+	8.63049i	−0.205790	+	0.565402i	0.793265	+	0.608877i	$0.208380\pi$
$234$	23.7923	+	19.9641i	1.55535	+	1.30509i
$235$		0			0
$236$	4.02719	+	6.97531i	0.262148	+	0.454054i
$237$	24.0550	+	4.24154i	1.56254	+	0.275518i
$238$	−15.1876	−	2.67799i	−0.984467	−	0.173588i
$239$	2.70456	+	4.68443i	0.174943	+	0.303011i	0.940142	−	0.340784i	$-0.110692\pi$
$239$	2.70456	+	4.68443i	0.174943	+	0.303011i	−0.765198	+	0.643795i	$0.777359\pi$
$240$		0			0
$241$	20.3709	+	17.0932i	1.31221	+	1.10107i	0.987895	+	0.155121i	$0.0495768\pi$
$241$	20.3709	+	17.0932i	1.31221	+	1.10107i	0.324311	+	0.945951i	$0.394868\pi$
$242$	−3.11384	+	8.55520i	−0.200165	+	0.549949i
$243$	1.24225	+	3.41305i	0.0796902	+	0.218947i
$244$	11.8328	−	9.92886i	0.757515	−	0.635630i
$245$		0			0
$246$	27.6116			1.76045
$247$	23.0238	+	4.11481i	1.46497	+	0.261819i
$248$		−	7.00505i		−	0.444821i
$249$	0.249510	+	1.41504i	0.0158121	+	0.0896748i
$250$		0			0
$251$	1.42144	−	0.517363i	0.0897206	−	0.0326556i	−0.296770	−	0.954949i	$-0.595909\pi$
$251$	1.42144	−	0.517363i	0.0897206	−	0.0326556i	0.386490	+	0.922293i	$0.373687\pi$
$252$	5.75893	−	15.8225i	0.362778	−	0.996725i
$253$	1.41352	−	1.68456i	0.0888670	−	0.105908i
$254$	4.10011	−	7.10160i	0.257264	−	0.445594i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−6.75923	−	1.19184i	−0.421629	−	0.0743446i	−0.0411918	−	0.999151i	$-0.513115\pi$
$257$	−6.75923	−	1.19184i	−0.421629	−	0.0743446i	−0.380438	+	0.924807i	$0.624227\pi$
$258$	−14.9968	+	8.65842i	−0.933662	+	0.539050i
$259$	12.0886	−	20.9382i	0.751152	−	1.30103i
$260$		0			0
$261$	12.8888	+	4.69113i	0.797795	+	0.290374i
$262$	−6.51958	−	17.9124i	−0.402781	−	1.10663i
$263$	13.1920	+	15.7216i	0.813454	+	0.969437i	0.999915	−	0.0130252i	$-0.00414617\pi$
$263$	13.1920	+	15.7216i	0.813454	+	0.969437i	−0.186461	+	0.982462i	$0.559702\pi$
$264$	0.708783	+	4.01971i	0.0436226	+	0.247396i
$265$		0			0
$266$	−2.17285	−	12.4923i	−0.133226	−	0.765949i
$267$		−	35.7935i		−	2.19053i
$268$	10.0911	−	1.77933i	0.616411	−	0.108690i
$269$	−13.4461	+	11.2826i	−0.819824	+	0.687914i	−0.952931	−	0.303188i	$-0.901949\pi$
$269$	−13.4461	+	11.2826i	−0.819824	+	0.687914i	0.133107	+	0.991102i	$0.457505\pi$
$270$		0			0
$271$	−8.16550	−	2.97200i	−0.496019	−	0.180536i	0.0818838	−	0.996642i	$-0.473906\pi$
$271$	−8.16550	−	2.97200i	−0.496019	−	0.180536i	−0.577902	+	0.816106i	$0.696129\pi$
$272$	−3.40777	+	4.06122i	−0.206626	+	0.246247i
$273$	40.0727	+	23.1360i	2.42531	+	1.40025i
$274$	6.28797	+	10.8911i	0.379870	+	0.657955i
$275$		0			0
$276$	−0.822180	+	4.66281i	−0.0494894	+	0.280668i
$277$	7.11964	−	4.11052i	0.427778	−	0.246977i	−0.270622	−	0.962686i	$-0.587229\pi$
$277$	7.11964	−	4.11052i	0.427778	−	0.246977i	0.698399	+	0.715708i	$0.253896\pi$
$278$	7.51777	+	4.34039i	0.450886	+	0.260319i
$279$	−31.0612	−	26.0635i	−1.85959	−	1.56038i
$280$		0			0
$281$	−15.2981	+	5.56805i	−0.912608	+	0.332162i	−0.755294	−	0.655387i	$-0.772506\pi$
$281$	−15.2981	+	5.56805i	−0.912608	+	0.332162i	−0.157314	+	0.987549i	$0.550284\pi$
$282$	4.67100	+	5.56669i	0.278154	+	0.331491i
$283$	−6.15584	+	1.08544i	−0.365927	+	0.0645228i	−0.353588	−	0.935401i	$-0.615039\pi$
$283$	−6.15584	+	1.08544i	−0.365927	+	0.0645228i	−0.0123385	+	0.999924i	$0.503928\pi$
$284$	−2.51930			−0.149493
$285$		0			0
$286$	−7.38785			−0.436853
$287$	26.6825	−	4.70484i	1.57502	−	0.277718i
$288$	−3.72067	−	4.43412i	−0.219243	−	0.261283i
$289$	10.4365	−	3.79859i	0.613914	−	0.223447i
$290$		0			0
$291$	−20.7972	−	17.4509i	−1.21915	−	1.02299i
$292$	−5.89470	−	3.40330i	−0.344961	−	0.199163i
$293$	−13.1722	+	7.60497i	−0.769528	+	0.444287i	−0.832706	−	0.553715i	$-0.813210\pi$
$293$	−13.1722	+	7.60497i	−0.769528	+	0.444287i	0.0631781	+	0.998002i	$0.479876\pi$
$294$	0.752605	−	4.26824i	0.0438928	−	0.248929i
$295$		0			0
$296$	−4.15567	−	7.19784i	−0.241544	−	0.418366i
$297$	9.85641	+	5.69060i	0.571927	+	0.330202i
$298$	10.5278	−	12.5465i	0.609856	−	0.726798i
$299$	−8.05299	−	2.93105i	−0.465716	−	0.169507i
$300$		0			0
$301$	−13.0168	+	10.9224i	−0.750278	+	0.629558i
$302$	−12.6887	+	2.23736i	−0.730154	+	0.128746i
$303$			14.6622i			0.842324i
$304$	−4.09256	−	1.50033i	−0.234724	−	0.0860498i
$305$		0			0
$306$	5.32876	+	30.2209i	0.304625	+	1.72761i
$307$	−0.417451	−	0.497498i	−0.0238252	−	0.0283937i	0.754000	−	0.656874i	$-0.228122\pi$
$307$	−0.417451	−	0.497498i	−0.0238252	−	0.0283937i	−0.777825	+	0.628480i	$0.783677\pi$
$308$	1.36987	+	3.76367i	0.0780553	+	0.214455i
$309$	−15.3436	−	5.58461i	−0.872866	−	0.317697i
$310$		0			0
$311$	−5.79261	+	10.0331i	−0.328469	+	0.568924i	−0.982208	−	0.187795i	$-0.939866\pi$
$311$	−5.79261	+	10.0331i	−0.328469	+	0.568924i	0.653740	+	0.756720i	$0.273199\pi$
$312$	13.7756	−	7.95337i	0.779892	−	0.450271i
$313$	0.620641	+	0.109436i	0.0350807	+	0.00618568i	0.191161	−	0.981559i	$-0.438775\pi$
$313$	0.620641	+	0.109436i	0.0350807	+	0.00618568i	−0.156080	+	0.987744i	$0.549886\pi$
$314$	−2.84611	+	16.1411i	−0.160615	+	0.910894i
$315$		0			0
$316$	4.11974	−	7.13560i	0.231754	−	0.401409i
$317$	−5.98705	+	7.13509i	−0.336266	+	0.400746i	−0.907508	−	0.420036i	$-0.862018\pi$
$317$	−5.98705	+	7.13509i	−0.336266	+	0.400746i	0.571241	+	0.820782i	$0.306462\pi$
$318$	10.7762	−	29.6073i	0.604298	−	1.66030i
$319$	−3.06583	+	1.11587i	−0.171654	+	0.0624768i
$320$		0			0
$321$	3.23244	+	18.3321i	0.180417	+	1.02320i
$322$			4.64600i			0.258912i
$323$	14.8130	+	17.7368i	0.824217	+	0.986904i
$324$	−7.13982			−0.396656
$325$		0			0
$326$	−3.12599	+	2.62302i	−0.173132	+	0.145275i
$327$	5.55190	+	15.2537i	0.307021	+	0.843533i
$328$	3.18559	−	8.75234i	0.175895	−	0.483267i
$329$	5.46235	+	4.58346i	0.301149	+	0.252694i
$330$		0			0
$331$	6.03292	+	10.4493i	0.331599	+	0.574347i	0.982826	−	0.184537i	$-0.0590784\pi$
$331$	6.03292	+	10.4493i	0.331599	+	0.574347i	−0.651226	+	0.758884i	$0.725745\pi$
$332$	0.477328	+	0.0841657i	0.0261968	+	0.00461920i
$333$	−47.3780	−	8.35402i	−2.59630	−	0.457797i
$334$	−7.92536	−	13.7271i	−0.433657	−	0.751115i
$335$		0			0
$336$	−6.60607	−	5.54315i	−0.360391	−	0.302404i
$337$	−0.385456	+	1.05903i	−0.0209971	+	0.0576891i	−0.949748	−	0.313014i	$-0.898661\pi$
$337$	−0.385456	+	1.05903i	−0.0209971	+	0.0576891i	0.928751	+	0.370704i	$0.120883\pi$
$338$	5.40082	+	14.8386i	0.293766	+	0.807115i
$339$	7.68321	−	6.44698i	0.417295	−	0.350152i
$340$		0			0
$341$	9.64498			0.522305
$342$	−21.8797	+	12.5647i	−1.18312	+	0.679419i
$343$			16.1098i			0.869847i
$344$	1.01435	+	5.75264i	0.0546898	+	0.310161i
$345$		0			0
$346$	−2.27769	+	0.829012i	−0.122450	+	0.0445680i
$347$	−4.40192	+	12.0942i	−0.236308	+	0.649250i	0.763686	+	0.645588i	$0.223388\pi$
$347$	−4.40192	+	12.0942i	−0.236308	+	0.649250i	−0.999993	+	0.00366167i	$0.998834\pi$
$348$	4.51537	−	5.38121i	0.242049	−	0.288463i
$349$	−4.18866	+	7.25497i	−0.224214	+	0.388350i	−0.956083	−	0.293095i	$-0.905315\pi$
$349$	−4.18866	+	7.25497i	−0.224214	+	0.388350i	0.731870	+	0.681445i	$0.238648\pi$
$350$		0			0
$351$	7.70187	−	43.6795i	0.411096	−	2.33144i
$352$	1.35594	+	0.239089i	0.0722720	+	0.0127435i
$353$	13.0798	−	7.55163i	0.696168	−	0.401933i	−0.109751	−	0.993959i	$-0.535005\pi$
$353$	13.0798	−	7.55163i	0.696168	−	0.401933i	0.805918	+	0.592027i	$0.201672\pi$
$354$	11.9387	−	20.6784i	0.634533	−	1.09904i
$355$		0			0
$356$	−11.3458	−	4.12955i	−0.601328	−	0.218866i
$357$	15.6366	+	42.9613i	0.827579	+	2.27375i
$358$	−11.6288	−	13.8586i	−0.614599	−	0.732451i
$359$	5.84746	+	33.1626i	0.308617	+	1.75025i	0.605970	+	0.795487i	$0.292785\pi$
$359$	5.84746	+	33.1626i	0.308617	+	1.75025i	−0.297353	+	0.954768i	$0.596104\pi$
$360$		0			0
$361$	−9.57624	+	16.4102i	−0.504013	+	0.863696i
$362$		−	20.0951i		−	1.05618i
$363$	26.5796	−	4.68671i	1.39507	−	0.245988i
$364$	11.9569	−	10.0330i	0.626711	−	0.525873i
$365$		0			0
$366$	−43.0300	−	15.6616i	−2.24921	−	0.818646i
$367$	2.70290	−	3.22119i	0.141090	−	0.168145i	−0.690872	−	0.722977i	$-0.742773\pi$
$367$	2.70290	−	3.22119i	0.141090	−	0.168145i	0.831962	+	0.554832i	$0.187218\pi$
$368$	1.38316	+	0.798570i	0.0721024	+	0.0416284i
$369$	−26.9564	−	46.6898i	−1.40329	−	2.43058i
$370$		0			0
$371$	5.36867	−	30.4472i	0.278727	−	1.58074i
$372$	−17.9844	+	10.3833i	−0.932446	+	0.538348i
$373$	4.63852	+	2.67805i	0.240173	+	0.138664i	0.615256	−	0.788327i	$-0.289052\pi$
$373$	4.63852	+	2.67805i	0.240173	+	0.138664i	−0.375083	+	0.926991i	$0.622386\pi$
$374$	−5.59173	−	4.69202i	−0.289141	−	0.242618i
$375$		0			0
$376$	2.30343	−	0.838381i	0.118790	−	0.0432362i
$377$	8.17274	+	9.73989i	0.420918	+	0.501630i
$378$	−23.6802	+	4.17546i	−1.21798	+	0.214763i
$379$	5.86331			0.301178			0.150589	−	0.988596i	$-0.451883\pi$
$379$	5.86331			0.301178			0.150589	+	0.988596i	$0.451883\pi$
$380$		0			0
$381$	−24.3097			−1.24542
$382$	7.22230	−	1.27349i	0.369525	−	0.0651572i
$383$	−18.6249	−	22.1962i	−0.951686	−	1.13418i	−0.990853	−	0.134942i	$-0.956915\pi$
$383$	−18.6249	−	22.1962i	−0.951686	−	1.13418i	0.0391675	−	0.999233i	$-0.487529\pi$
$384$	−2.78573	+	1.01392i	−0.142159	+	0.0517415i
$385$		0			0
$386$	19.6814	+	16.5147i	1.00176	+	0.840576i
$387$	29.2819	+	16.9059i	1.48848	+	0.859377i
$388$	−7.93099	+	4.57896i	−0.402635	+	0.232461i
$389$	0.653743	−	3.70756i	0.0331461	−	0.187981i	−0.963739	−	0.266846i	$-0.914019\pi$
$389$	0.653743	−	3.70756i	0.0331461	−	0.187981i	0.996885	+	0.0788651i	$0.0251297\pi$
$390$		0			0
$391$	−4.23365	−	7.33290i	−0.214105	−	0.370841i
$392$	−1.26612	−	0.730994i	−0.0639487	−	0.0369208i
$393$	−36.3236	+	43.2888i	−1.83228	+	2.18363i
$394$	12.3868	+	4.50841i	0.624036	+	0.227130i
$395$		0			0
$396$	6.10517	−	5.12284i	0.306796	−	0.257433i
$397$	−18.6157	+	3.28244i	−0.934293	+	0.164741i	−0.620015	−	0.784590i	$-0.712874\pi$
$397$	−18.6157	+	3.28244i	−0.934293	+	0.164741i	−0.314278	+	0.949331i	$0.601762\pi$
$398$		−	10.2986i		−	0.516222i
$399$	−28.8512	+	24.0952i	−1.44437	+	1.20627i
$400$		0			0
$401$	2.11371	+	11.9874i	0.105554	+	0.598624i	0.990998	+	0.133878i	$0.0427431\pi$
$401$	2.11371	+	11.9874i	0.105554	+	0.598624i	−0.885444	+	0.464746i	$0.846146\pi$
$402$	−19.5257	−	23.2698i	−0.973854	−	1.16059i
$403$	−12.8556	−	35.3203i	−0.640381	−	1.75943i
$404$	4.64764	+	1.69160i	0.231229	+	0.0841605i
$405$		0			0
$406$	3.44650	−	5.96952i	0.171047	−	0.296262i
$407$	9.91042	−	5.72179i	0.491241	−	0.283618i
$408$	15.4777	+	2.72914i	0.766261	+	0.135113i
$409$	4.90892	−	27.8399i	0.242731	−	1.37659i	−0.582974	−	0.812491i	$-0.698111\pi$
$409$	4.90892	−	27.8399i	0.242731	−	1.37659i	0.825705	−	0.564103i	$-0.190778\pi$
$410$		0			0
$411$	18.6408	−	32.2868i	0.919482	−	1.59259i
$412$	−3.54042	+	4.21931i	−0.174424	+	0.207870i
$413$	8.01347	−	22.0168i	0.394317	−	1.08338i
$414$	8.68726	−	3.16190i	0.426955	−	0.155399i
$415$		0			0
$416$	−0.931747	−	5.28420i	−0.0456827	−	0.259079i
$417$		−	25.7343i		−	1.26021i
$418$	2.06574	−	5.63488i	0.101039	−	0.275611i
$419$	11.5301			0.563284			0.281642	−	0.959520i	$-0.409121\pi$
$419$	11.5301			0.563284			0.281642	+	0.959520i	$0.409121\pi$
$420$		0			0
$421$	−15.9361	+	13.3719i	−0.776676	+	0.651709i	−0.942409	−	0.334462i	$-0.891445\pi$
$421$	−15.9361	+	13.3719i	−0.776676	+	0.651709i	0.165733	+	0.986171i	$0.447001\pi$
$422$	5.41437	+	14.8759i	0.263567	+	0.724145i
$423$	4.85283	−	13.3330i	0.235953	−	0.648274i
$424$	−8.14168	−	6.83168i	−0.395395	−	0.331776i
$425$		0			0
$426$	3.73426	+	6.46792i	0.180925	+	0.313372i
$427$	−44.2506	−	7.80258i	−2.14144	−	0.377593i
$428$	6.18385	+	1.09038i	0.298908	+	0.0527055i
$429$	10.9507	+	18.9671i	0.528704	+	0.915742i
$430$		0			0
$431$	2.06480	+	1.73257i	0.0994578	+	0.0834550i	0.691161	−	0.722701i	$-0.257100\pi$
$431$	2.06480	+	1.73257i	0.0994578	+	0.0834550i	−0.591703	+	0.806156i	$0.701544\pi$
$432$	−2.82716	+	7.76755i	−0.136022	+	0.373716i
$433$	−10.4904	−	28.8221i	−0.504135	−	1.38510i	−0.887203	−	0.461380i	$-0.847355\pi$
$433$	−10.4904	−	28.8221i	−0.504135	−	1.38510i	0.383068	−	0.923720i	$-0.374868\pi$
$434$	−15.6099	+	13.0983i	−0.749301	+	0.628738i
$435$		0			0
$436$	5.47566			0.262237
$437$	4.48730	−	5.32263i	0.214657	−	0.254616i
$438$			20.1783i			0.964155i
$439$	4.34601	+	24.6474i	0.207424	+	1.17636i	0.893580	+	0.448904i	$0.148185\pi$
$439$	4.34601	+	24.6474i	0.207424	+	1.17636i	−0.686156	+	0.727454i	$0.740703\pi$
$440$		0			0
$441$	−7.95213	+	2.89434i	−0.378673	+	0.137826i
$442$	−9.72930	+	26.7310i	−0.462776	+	1.27147i
$443$	22.5689	−	26.8966i	1.07228	−	1.27790i	0.113567	−	0.993530i	$-0.463772\pi$
$443$	22.5689	−	26.8966i	1.07228	−	1.27790i	0.958716	−	0.284367i	$-0.0917834\pi$
$444$	−12.3195	+	21.3381i	−0.584660	+	1.01266i
$445$		0			0
$446$	−0.570650	+	3.23631i	−0.0270210	+	0.153244i
$447$	−47.8160	−	8.43124i	−2.26162	−	0.398784i
$448$	−2.51922	+	1.45447i	−0.119022	+	0.0687175i
$449$	−1.27642	+	2.21082i	−0.0602380	+	0.104335i	−0.894572	−	0.446924i	$-0.852519\pi$
$449$	−1.27642	+	2.21082i	−0.0602380	+	0.104335i	0.834334	+	0.551260i	$0.185853\pi$
$450$		0			0
$451$	12.0507	+	4.38611i	0.567448	+	0.206534i
$452$	−1.15714	−	3.17923i	−0.0544275	−	0.149538i
$453$	24.5520	+	29.2600i	1.15355	+	1.37475i
$454$	2.05161	+	11.6353i	0.0962868	+	0.546070i
$455$		0			0
$456$	2.21436	+	12.7309i	0.103697	+	0.596177i
$457$			29.0079i			1.35693i	0.734631	+	0.678467i	$0.237355\pi$
$457$			29.0079i			1.35693i	−0.734631	+	0.678467i	$0.762645\pi$
$458$	−11.7375	+	2.06964i	−0.548459	+	0.0967081i
$459$	33.5702	−	28.1688i	1.56692	−	1.31481i
$460$		0			0
$461$	−35.2153	−	12.8173i	−1.64014	−	0.596962i	−0.653077	−	0.757291i	$-0.726522\pi$
$461$	−35.2153	−	12.8173i	−1.64014	−	0.596962i	−0.987064	+	0.160329i	$0.948745\pi$
$462$	7.63215	−	9.09564i	0.355080	−	0.423168i
$463$	−3.83218	−	2.21251i	−0.178096	−	0.102824i	0.408302	−	0.912847i	$-0.366121\pi$
$463$	−3.83218	−	2.21251i	−0.178096	−	0.102824i	−0.586398	+	0.810023i	$0.699455\pi$
$464$	−1.18479	−	2.05212i	−0.0550026	−	0.0952673i
$465$		0			0
$466$	1.59485	−	9.04485i	0.0738800	−	0.418994i
$467$	−3.74952	+	2.16478i	−0.173507	+	0.100174i	−0.584238	−	0.811582i	$-0.698607\pi$
$467$	−3.74952	+	2.16478i	−0.173507	+	0.100174i	0.410732	+	0.911756i	$0.365273\pi$
$468$	−26.8975	−	15.5293i	−1.24334	−	0.717842i
$469$	−22.8337	−	19.1597i	−1.05436	−	0.884715i
$470$		0			0
$471$	45.6584	−	16.6183i	2.10383	−	0.765731i
$472$	−5.17726	−	6.17002i	−0.238303	−	0.283998i
$473$	−7.92058	+	1.39661i	−0.364189	+	0.0642163i
$474$	−24.4260			−1.12193
$475$		0			0
$476$	15.4219			0.706862
$477$	−60.5850	+	10.6828i	−2.77400	+	0.489130i
$478$	−3.47691	−	4.14362i	−0.159030	−	0.189525i
$479$	−7.03629	+	2.56100i	−0.321496	+	0.117015i	−0.497727	−	0.867334i	$-0.665832\pi$
$479$	−7.03629	+	2.56100i	−0.321496	+	0.117015i	0.176231	+	0.984349i	$0.443610\pi$
$480$		0			0
$481$	−34.1628	−	28.6660i	−1.55769	−	1.30706i
$482$	−23.0296	−	13.2962i	−1.04897	−	0.605624i
$483$	11.9279	−	6.88657i	0.542737	−	0.313350i
$484$	1.58094	−	8.96594i	0.0718608	−	0.407543i
$485$		0			0
$486$	−1.81604	−	3.14548i	−0.0823774	−	0.142682i
$487$	−15.4397	−	8.91410i	−0.699638	−	0.403936i	0.107575	−	0.994197i	$-0.465692\pi$
$487$	−15.4397	−	8.91410i	−0.699638	−	0.403936i	−0.807213	+	0.590261i	$0.799025\pi$
$488$	−9.92886	+	11.8328i	−0.449458	+	0.535644i
$489$	11.3677	+	4.13750i	0.514065	+	0.187104i
$490$		0			0
$491$	−9.18783	+	7.70951i	−0.414641	+	0.347925i	−0.826120	−	0.563494i	$-0.809457\pi$
$491$	−9.18783	+	7.70951i	−0.414641	+	0.347925i	0.411479	+	0.911419i	$0.365012\pi$
$492$	−27.1921	+	4.79470i	−1.22591	+	0.216162i
$493$			12.5625i			0.565784i
$494$	−23.3886	−	0.0542561i	−1.05230	−	0.00244110i
$495$		0			0
$496$	1.21641	+	6.89863i	0.0546186	+	0.309757i
$497$	4.71069	+	5.61398i	0.211303	+	0.251821i
$498$	−0.491440	−	1.35022i	−0.0220219	−	0.0605048i
$499$	−6.32111	−	2.30070i	−0.282972	−	0.102993i	0.196635	−	0.980477i	$-0.436999\pi$
$499$	−6.32111	−	2.30070i	−0.282972	−	0.102993i	−0.479607	+	0.877483i	$0.659221\pi$
$500$		0			0
$501$	−23.4948	+	40.6943i	−1.04967	+	1.81809i
$502$	−1.31001	+	0.756334i	−0.0584685	+	0.0337568i
$503$	4.86312	+	0.857499i	0.216836	+	0.0382340i	0.281011	−	0.959705i	$-0.409330\pi$
$503$	4.86312	+	0.857499i	0.216836	+	0.0382340i	−0.0641748	+	0.997939i	$0.520442\pi$
$504$	−2.92388	+	16.5822i	−0.130240	+	0.738628i
$505$		0			0
$506$	−1.09952	+	1.90442i	−0.0488796	+	0.0846620i
$507$	30.0905	−	35.8604i	1.33636	−	1.59262i
$508$	−2.80464	+	7.70569i	−0.124436	+	0.341885i
$509$	18.1920	−	6.62133i	0.806345	−	0.293485i	0.0942316	−	0.995550i	$-0.469961\pi$
$509$	18.1920	−	6.62133i	0.806345	−	0.293485i	0.712113	+	0.702065i	$0.247738\pi$
$510$		0			0
$511$	3.43825	+	19.4993i	0.152099	+	0.862597i
$512$			1.00000i			0.0441942i
$513$	31.1618	+	18.0878i	1.37583	+	0.798595i
$514$	6.86350			0.302736
$515$		0			0
$516$	13.2655	−	11.1311i	0.583980	−	0.490017i
$517$	1.15433	+	3.17150i	0.0507675	+	0.139483i
$518$	−8.26912	+	22.7192i	−0.363324	+	0.998226i
$519$	5.50448	+	4.61881i	0.241620	+	0.202743i
$520$		0			0
$521$	3.76749	+	6.52549i	0.165057	+	0.285887i	0.936675	−	0.350199i	$-0.113886\pi$
$521$	3.76749	+	6.52549i	0.165057	+	0.285887i	−0.771619	+	0.636085i	$0.780553\pi$
$522$	−13.5076	−	2.38175i	−0.591211	−	0.104246i
$523$	25.8798	+	4.56331i	1.13164	+	0.199539i	0.707948	−	0.706265i	$-0.249621\pi$
$523$	25.8798	+	4.56331i	1.13164	+	0.199539i	0.423697	+	0.905804i	$0.360732\pi$
$524$	9.53099	+	16.5082i	0.416363	+	0.721162i
$525$		0			0
$526$	−15.7216	−	13.1920i	−0.685496	−	0.575199i
$527$	12.7018	−	34.8979i	0.553299	−	1.52018i
$528$	−1.39603	−	3.83556i	−0.0607544	−	0.166921i
$529$	15.6650	−	13.1445i	0.681085	−	0.571498i
$530$		0			0
$531$	−46.6215			−2.02320
$532$	4.30910	+	11.9252i	0.186823	+	0.517021i
$533$		−	49.9765i		−	2.16472i
$534$	6.21547	+	35.2497i	0.268970	+	1.52540i
$535$		0			0
$536$	−9.62879	+	3.50459i	−0.415900	+	0.151375i
$537$	−18.3430	+	50.3970i	−0.791560	+	2.17479i
$538$	11.2826	−	13.4461i	0.486429	−	0.579703i
$539$	1.00648	−	1.74327i	0.0433520	−	0.0750879i
$540$		0			0
$541$	2.24024	−	12.7051i	0.0963156	−	0.546233i	−0.898021	−	0.439953i	$-0.854995\pi$
$541$	2.24024	−	12.7051i	0.0963156	−	0.546233i	0.994336	−	0.106280i	$-0.0338939\pi$
$542$	8.55753	+	1.50892i	0.367577	+	0.0648138i
$543$	−51.5911	+	29.7862i	−2.21399	+	1.27825i
$544$	2.65077	−	4.59127i	0.113651	−	0.196849i
$545$		0			0
$546$	−43.4814	−	15.8259i	−1.86083	−	0.677287i
$547$	14.5722	+	40.0367i	0.623061	+	1.71185i	0.699369	+	0.714761i	$0.253465\pi$
$547$	14.5722	+	40.0367i	0.623061	+	1.71185i	−0.0763080	+	0.997084i	$0.524313\pi$
$548$	−8.08366	−	9.63374i	−0.345317	−	0.411533i
$549$	15.5259	+	88.0516i	0.662628	+	3.75795i
$550$		0			0
$551$	−9.71405	+	3.51013i	−0.413832	+	0.149536i
$552$		−	4.73474i		−	0.201524i
$553$	−23.6041	+	4.16204i	−1.00375	+	0.176988i
$554$	−6.29769	+	5.28439i	−0.267563	+	0.224512i
$555$		0			0
$556$	−8.15726	−	2.96900i	−0.345945	−	0.125914i
$557$	7.74009	−	9.22427i	0.327958	−	0.390845i	−0.576719	−	0.816942i	$-0.695667\pi$
$557$	7.74009	−	9.22427i	0.327958	−	0.390845i	0.904677	+	0.426097i	$0.140112\pi$
$558$	35.1152	+	20.2738i	1.48655	+	0.858258i
$559$	15.6716	+	27.1440i	0.662838	+	1.14807i
$560$		0			0
$561$	−3.75764	+	21.3107i	−0.158648	+	0.899737i
$562$	14.0988	−	8.13995i	0.594722	−	0.343363i
$563$	−38.8377	−	22.4230i	−1.63681	−	0.945015i	−0.981921	−	0.189293i	$-0.939380\pi$
$563$	−38.8377	−	22.4230i	−1.63681	−	0.945015i	−0.654893	−	0.755721i	$-0.727286\pi$
$564$	−5.56669	−	4.67100i	−0.234400	−	0.196685i
$565$		0			0
$566$	5.87384	−	2.13790i	0.246896	−	0.0898627i
$567$	13.3503	+	15.9103i	0.560660	+	0.668168i
$568$	2.48103	−	0.437473i	0.104102	−	0.0183559i
$569$	−30.1492			−1.26392			−0.631959	−	0.775002i	$-0.717749\pi$
$569$	−30.1492			−1.26392			−0.631959	+	0.775002i	$0.717749\pi$
$570$		0			0
$571$	3.87066			0.161982			0.0809910	−	0.996715i	$-0.474192\pi$
$571$	3.87066			0.161982			0.0809910	+	0.996715i	$0.474192\pi$
$572$	7.27561	−	1.28289i	0.304209	−	0.0536402i
$573$	−13.9748	−	16.6545i	−0.583804	−	0.695751i
$574$	−25.4601	+	9.26672i	−1.06268	+	0.386785i
$575$		0			0
$576$	4.43412	+	3.72067i	0.184755	+	0.155028i
$577$	13.2589	+	7.65505i	0.551976	+	0.318684i	0.749919	−	0.661530i	$-0.230093\pi$
$577$	13.2589	+	7.65505i	0.551976	+	0.318684i	−0.197942	+	0.980214i	$0.563426\pi$
$578$	−9.61837	+	5.55317i	−0.400072	+	0.230981i
$579$	13.2259	−	75.0080i	0.549651	−	3.11723i
$580$		0			0
$581$	−0.704971	−	1.22105i	−0.0292471	−	0.0506575i
$582$	23.5115	+	13.5744i	0.974584	+	0.562676i
$583$	9.40627	−	11.2100i	0.389568	−	0.464269i
$584$	6.39612	+	2.32800i	0.264673	+	0.0963332i
$585$		0			0
$586$	11.6515	−	9.77676i	0.481319	−	0.403874i
$587$	−17.8491	+	3.14728i	−0.736713	+	0.129902i	−0.529400	−	0.848372i	$-0.677583\pi$
$587$	−17.8491	+	3.14728i	−0.736713	+	0.129902i	−0.207313	+	0.978275i	$0.566472\pi$
$588$			4.33408i			0.178735i
$589$	30.5342	+	0.0708324i	1.25814	+	0.00291860i
$590$		0			0
$591$	−6.78571	−	38.4837i	−0.279127	−	1.58301i
$592$	5.34243	+	6.36686i	0.219573	+	0.261676i
$593$	9.01955	+	24.7810i	0.370389	+	1.01763i	0.975212	+	0.221275i	$0.0710217\pi$
$593$	9.01955	+	24.7810i	0.370389	+	1.01763i	−0.604823	+	0.796360i	$0.706756\pi$
$594$	−10.6948	−	3.89260i	−0.438814	−	0.159715i
$595$		0			0
$596$	−8.18914	+	14.1840i	−0.335440	+	0.580999i
$597$	−26.4400	+	15.2651i	−1.08212	+	0.624761i
$598$	8.43961	+	1.48813i	0.345121	+	0.0608542i
$599$	5.45740	−	30.9505i	0.222983	−	1.26460i	−0.643519	−	0.765430i	$-0.722526\pi$
$599$	5.45740	−	30.9505i	0.222983	−	1.26460i	0.866503	−	0.499172i	$-0.166363\pi$
$600$		0			0
$601$	8.30819	−	14.3902i	0.338898	−	0.586989i	−0.645328	−	0.763906i	$-0.723279\pi$
$601$	8.30819	−	14.3902i	0.338898	−	0.586989i	0.984226	+	0.176917i	$0.0566125\pi$
$602$	10.9224	−	13.0168i	0.445165	−	0.530527i
$603$	−20.2858	+	55.7347i	−0.826100	+	2.26969i
$604$	12.1074	−	4.40675i	0.492645	−	0.179308i
$605$		0			0
$606$	−2.54607	−	14.4395i	−0.103427	−	0.586564i
$607$		−	4.44153i		−	0.180276i	−0.995929	−	0.0901381i	$-0.971269\pi$
$607$		−	4.44153i		−	0.180276i	0.995929	−	0.0901381i	$-0.0287308\pi$
$608$	4.29091	+	0.766871i	0.174019	+	0.0311007i
$609$	−20.4344			−0.828044
$610$		0			0
$611$	10.0756	−	8.45444i	0.407616	−	0.342030i
$612$	−10.4956	−	28.8364i	−0.424260	−	1.16564i
$613$	−1.85677	+	5.10144i	−0.0749943	+	0.206045i	−0.971525	−	0.236936i	$-0.923857\pi$
$613$	−1.85677	+	5.10144i	−0.0749943	+	0.206045i	0.896531	+	0.442981i	$0.146079\pi$
$614$	0.497498	+	0.417451i	0.0200774	+	0.0168469i
$615$		0			0
$616$	−2.00261	−	3.46862i	−0.0806874	−	0.139755i
$617$	30.2620	+	5.33600i	1.21830	+	0.214819i	0.745594	−	0.666401i	$-0.232166\pi$
$617$	30.2620	+	5.33600i	1.21830	+	0.214819i	0.472707	+	0.881220i	$0.343277\pi$
$618$	16.0802	+	2.83538i	0.646842	+	0.114056i
$619$	−13.0502	−	22.6035i	−0.524530	−	0.908512i	−0.999592	−	0.0285602i	$-0.990908\pi$
$619$	−13.0502	−	22.6035i	−0.524530	−	0.908512i	0.475062	−	0.879952i	$-0.342426\pi$
$620$		0			0
$621$	−10.1134	−	8.48611i	−0.405835	−	0.340536i
$622$	3.96238	−	10.8865i	0.158877	−	0.436510i
$623$	12.0126	+	33.0045i	0.481276	+	1.32230i
$624$	−12.1853	+	10.2247i	−0.487801	+	0.409314i
$625$		0			0
$626$	−0.630216			−0.0251885
$627$	−17.5286	+	3.04886i	−0.700026	+	0.121760i
$628$		−	16.3901i		−	0.654036i
$629$	−7.65145	−	43.3935i	−0.305083	−	1.73021i
$630$		0			0
$631$	39.5529	−	14.3961i	1.57458	−	0.573099i	0.600562	−	0.799579i	$-0.294944\pi$
$631$	39.5529	−	14.3961i	1.57458	−	0.573099i	0.974016	+	0.226479i	$0.0727215\pi$
$632$	−2.81807	+	7.74258i	−0.112097	+	0.307983i
$633$	30.1659	−	35.9504i	1.19899	−	1.42890i
$634$	4.65710	−	8.06633i	0.184957	−	0.320355i
$635$		0			0
$636$	−5.47121	+	31.0288i	−0.216948	+	1.23037i
$637$	−7.72544	−	1.36220i	−0.306093	−	0.0539725i
$638$	2.82548	−	1.63129i	0.111862	−	0.0645836i
$639$	7.29129	−	12.6289i	0.288439	−	0.499591i
$640$		0			0
$641$	−13.5601	−	4.93548i	−0.535592	−	0.194940i	0.0600414	−	0.998196i	$-0.480877\pi$
$641$	−13.5601	−	4.93548i	−0.535592	−	0.194940i	−0.595634	+	0.803256i	$0.703099\pi$
$642$	−6.36667	−	17.4923i	−0.251272	−	0.690365i
$643$	−16.1189	−	19.2098i	−0.635667	−	0.757559i	0.348012	−	0.937490i	$-0.386857\pi$
$643$	−16.1189	−	19.2098i	−0.635667	−	0.757559i	−0.983679	+	0.179931i	$0.942412\pi$
$644$	−0.806770	−	4.57542i	−0.0317912	−	0.180297i
$645$		0			0
$646$	−17.6679	−	14.8951i	−0.695135	−	0.586041i
$647$			25.9344i			1.01959i	0.860297	+	0.509793i	$0.170278\pi$
$647$			25.9344i			1.01959i	−0.860297	+	0.509793i	$0.829722\pi$
$648$	7.03135	−	1.23982i	0.276217	−	0.0487046i
$649$	8.49526	−	7.12837i	0.333468	−	0.279813i
$650$		0			0
$651$	56.7658	+	20.6610i	2.22483	+	0.809770i
$652$	2.62302	−	3.12599i	0.102725	−	0.122423i
$653$	−10.2190	−	5.89996i	−0.399901	−	0.230883i	0.286540	−	0.958068i	$-0.407495\pi$
$653$	−10.2190	−	5.89996i	−0.399901	−	0.230883i	−0.686441	+	0.727185i	$0.740828\pi$
$654$	−8.11633	−	14.0579i	−0.317374	−	0.549708i
$655$		0			0
$656$	−1.61737	+	9.17254i	−0.0631475	+	0.358128i
$657$	34.1205	−	19.6995i	1.33117	−	0.768549i
$658$	−6.17528	−	3.56530i	−0.240737	−	0.138990i
$659$	−16.7858	−	14.0849i	−0.653880	−	0.548671i	0.254365	−	0.967108i	$-0.418133\pi$
$659$	−16.7858	−	14.0849i	−0.653880	−	0.548671i	−0.908246	+	0.418438i	$0.862578\pi$
$660$		0			0
$661$	−36.0396	+	13.1173i	−1.40178	+	0.510205i	−0.928705	−	0.370819i	$-0.879077\pi$
$661$	−36.0396	+	13.1173i	−1.40178	+	0.510205i	−0.473072	+	0.881024i	$0.656855\pi$
$662$	−7.75578	−	9.24297i	−0.301437	−	0.359238i
$663$	83.0491	−	14.6438i	3.22536	−	0.568718i
$664$	−0.484691			−0.0188097
$665$		0			0
$666$	48.1089			1.86418
$667$	3.72706	−	0.657182i	0.144313	−	0.0254462i
$668$	10.1887	+	12.1424i	0.394211	+	0.469802i
$669$	9.15458	−	3.33199i	0.353937	−	0.128822i
$670$		0			0
$671$	−16.2921	−	13.6707i	−0.628948	−	0.527750i
$672$	7.46827	+	4.31181i	0.288095	+	0.166332i
$673$	1.17684	−	0.679451i	0.0453640	−	0.0261909i	−0.477146	−	0.878824i	$-0.658329\pi$
$673$	1.17684	−	0.679451i	0.0453640	−	0.0261909i	0.522510	+	0.852633i	$0.324996\pi$
$674$	0.195701	−	1.10988i	0.00753812	−	0.0427508i
$675$		0			0
$676$	−7.89547	−	13.6754i	−0.303672	−	0.525975i
$677$	17.1281	+	9.88891i	0.658286	+	0.380062i	0.791624	−	0.611009i	$-0.209236\pi$
$677$	17.1281	+	9.88891i	0.658286	+	0.380062i	−0.133338	+	0.991071i	$0.542569\pi$
$678$	−6.44698	+	7.68321i	−0.247595	+	0.295072i
$679$	25.0333	+	9.11139i	0.960692	+	0.349663i
$680$		0			0
$681$	26.8307	−	22.5136i	1.02815	−	0.862724i
$682$	−9.49845	+	1.67483i	−0.363714	+	0.0641327i
$683$		−	38.4380i		−	1.47079i	−0.677640	−	0.735394i	$-0.736997\pi$
$683$		−	38.4380i		−	1.47079i	0.677640	−	0.735394i	$-0.263003\pi$
$684$	19.3655	−	16.1731i	0.740457	−	0.618396i
$685$		0			0
$686$	−2.79744	−	15.8651i	−0.106807	−	0.605731i
$687$	22.7115	+	27.0665i	0.866499	+	1.03265i
$688$	−1.99787	−	5.48910i	−0.0761681	−	0.209270i
$689$	−53.5888	−	19.5047i	−2.04157	−	0.743070i
$690$		0			0
$691$	4.00672	−	6.93985i	0.152423	−	0.264004i	−0.779695	−	0.626160i	$-0.784626\pi$
$691$	4.00672	−	6.93985i	0.152423	−	0.264004i	0.932118	+	0.362156i	$0.117959\pi$
$692$	2.09913	−	1.21193i	0.0797971	−	0.0460708i
$693$	−22.8313	−	4.02578i	−0.867291	−	0.152927i
$694$	2.23492	−	12.6748i	0.0848362	−	0.481130i
$695$		0			0
$696$	−3.51233	+	6.08354i	−0.133135	+	0.230596i
$697$	31.7401	−	37.8263i	1.20224	−	1.43277i
$698$	2.86521	−	7.87210i	0.108450	−	0.297963i
$699$	−25.5852	+	9.31225i	−0.967721	+	0.352222i
$700$		0			0
$701$	−4.88207	−	27.6876i	−0.184393	−	1.04575i	−0.926732	−	0.375722i	$-0.877395\pi$
$701$	−4.88207	−	27.6876i	−0.184393	−	1.04575i	0.742339	−	0.670025i	$-0.233716\pi$
$702$			44.3533i			1.67401i
$703$	31.4166	−	18.0413i	1.18490	−	0.680442i
$704$	−1.37686			−0.0518924
$705$		0			0
$706$	−11.5698	+	9.70819i	−0.435434	+	0.365372i
$707$	−4.92079	−	13.5198i	−0.185065	−	0.508463i
$708$	−8.16653	+	22.4374i	−0.306917	+	0.843248i
$709$	25.7736	+	21.6266i	0.967946	+	0.812204i	0.982227	−	0.187694i	$-0.0601015\pi$
$709$	25.7736	+	21.6266i	0.967946	+	0.812204i	−0.0142810	+	0.999898i	$0.504546\pi$
$710$		0			0
$711$	23.8464	+	41.3032i	0.894311	+	1.54899i
$712$	11.8906	+	2.09663i	0.445617	+	0.0785744i
$713$	−11.0181	−	1.94278i	−0.412630	−	0.0727578i
$714$	−22.8592	−	39.5934i	−0.855485	−	1.48174i
$715$		0			0
$716$	13.8586	+	11.6288i	0.517921	+	0.434587i
$717$	−5.48442	+	15.0683i	−0.204820	+	0.562737i
$718$	−11.5172	−	31.6434i	−0.429820	−	1.18092i
$719$	0.633806	−	0.531826i	0.0236370	−	0.0198338i	−0.630893	−	0.775870i	$-0.717311\pi$
$719$	0.633806	−	0.531826i	0.0236370	−	0.0198338i	0.654530	+	0.756036i	$0.272867\pi$
$720$		0			0
$721$	16.0223			0.596700
$722$	6.58115	−	17.8238i	0.244925	−	0.663334i
$723$			78.8333i			2.93184i
$724$	3.48949	+	19.7899i	0.129686	+	0.735484i
$725$		0			0
$726$	−25.3620	+	9.23101i	−0.941272	+	0.342595i
$727$	16.1735	−	44.4363i	0.599842	−	1.64805i	−0.151745	−	0.988420i	$-0.548489\pi$
$727$	16.1735	−	44.4363i	0.599842	−	1.64805i	0.751588	−	0.659633i	$-0.229288\pi$
$728$	−10.0330	+	11.9569i	−0.371848	+	0.443152i
$729$	−16.0934	+	27.8746i	−0.596052	+	1.03239i
$730$		0			0
$731$	−5.37759	+	30.4978i	−0.198897	+	1.12800i
$732$	45.0959	+	7.95162i	1.66679	+	0.293900i
$733$	−9.72810	+	5.61652i	−0.359315	+	0.207451i	−0.668780	−	0.743460i	$-0.733183\pi$
$733$	−9.72810	+	5.61652i	−0.359315	+	0.207451i	0.309465	+	0.950911i	$0.399850\pi$
$734$	−2.10248	+	3.64161i	−0.0776041	+	0.134414i
$735$		0			0
$736$	−1.50082	−	0.546254i	−0.0553210	−	0.0201352i
$737$	−4.82534	−	13.2575i	−0.177744	−	0.488347i
$738$	34.6545	+	41.2996i	1.27565	+	1.52026i
$739$	−4.49255	−	25.4785i	−0.165261	−	0.937242i	−0.948795	−	0.315893i	$-0.897696\pi$
$739$	−4.49255	−	25.4785i	−0.165261	−	0.937242i	0.783534	−	0.621349i	$-0.213415\pi$
$740$		0			0
$741$	34.5286	+	60.1269i	1.26844	+	2.20882i
$742$			30.9169i			1.13500i
$743$	42.9858	−	7.57956i	1.57700	−	0.278067i	0.684463	−	0.729047i	$-0.260037\pi$
$743$	42.9858	−	7.57956i	1.57700	−	0.278067i	0.892534	+	0.450980i	$0.148925\pi$
$744$	15.9081	−	13.3485i	0.583219	−	0.489379i
$745$		0			0
$746$	−5.03309	−	1.83189i	−0.184274	−	0.0670704i
$747$	−1.80338	+	2.14918i	−0.0659821	+	0.0786344i
$748$	6.32154	+	3.64974i	0.231138	+	0.133448i
$749$	−9.13300	−	15.8188i	−0.333713	−	0.578007i
$750$		0			0
$751$	3.63508	−	20.6156i	0.132646	−	0.752273i	−0.843824	−	0.536620i	$-0.819701\pi$
$751$	3.63508	−	20.6156i	0.132646	−	0.752273i	0.976470	−	0.215653i	$-0.0691881\pi$
$752$	−2.12285	+	1.22563i	−0.0774125	+	0.0446941i
$753$	3.88354	+	2.24216i	0.141524	+	0.0817089i
$754$	−9.73989	−	8.17274i	−0.354706	−	0.297634i
$755$		0			0
$756$	22.5954	−	8.22406i	0.821787	−	0.299106i
$757$	12.7499	+	15.1947i	0.463403	+	0.552262i	0.946247	−	0.323444i	$-0.104841\pi$
$757$	12.7499	+	15.1947i	0.463403	+	0.552262i	−0.482844	+	0.875706i	$0.660396\pi$
$758$	−5.77423	+	1.01815i	−0.209730	+	0.0369810i
$759$	6.51908			0.236628
$760$		0			0
$761$	−10.8607			−0.393700			−0.196850	−	0.980434i	$-0.563071\pi$
$761$	−10.8607			−0.393700			−0.196850	+	0.980434i	$0.563071\pi$
$762$	23.9403	−	4.22133i	0.867267	−	0.152923i
$763$	−10.2386	−	12.2019i	−0.370662	−	0.441738i
$764$	−6.89144	+	2.50828i	−0.249323	+	0.0907463i
$765$		0			0
$766$	22.1962	+	18.6249i	0.801983	+	0.672944i
$767$	−37.4275	−	21.6088i	−1.35143	−	0.780248i
$768$	2.56734	−	1.48226i	0.0926410	−	0.0534863i
$769$	−2.51395	+	14.2573i	−0.0906553	+	0.514132i	0.905337	+	0.424694i	$0.139618\pi$
$769$	−2.51395	+	14.2573i	−0.0906553	+	0.514132i	−0.995992	+	0.0894380i	$0.971493\pi$
$770$		0			0
$771$	−10.1735	−	17.6210i	−0.366389	−	0.634604i
$772$	−22.2502	−	12.8461i	−0.800802	−	0.462343i
$773$	23.0096	−	27.4218i	0.827597	−	0.986292i	−0.172402	−	0.985027i	$-0.555153\pi$
$773$	23.0096	−	27.4218i	0.827597	−	0.986292i	0.999999	−	0.00126532i	$-0.000402765\pi$
$774$	−31.7728	−	11.5643i	−1.14205	−	0.415672i
$775$		0			0
$776$	7.01537	−	5.88660i	0.251837	−	0.211317i
$777$	70.5850	−	12.4460i	2.53222	−	0.446499i
$778$			3.76475i			0.134973i
$779$	38.1182	+	13.9741i	1.36573	+	0.500675i
$780$		0			0
$781$	0.602339	+	3.41603i	0.0215534	+	0.122235i
$782$	5.44268	+	6.48633i	0.194630	+	0.231951i
$783$	6.69919	+	18.4059i	0.239409	+	0.657772i
$784$	1.37382	+	0.500029i	0.0490650	+	0.0178582i
$785$		0			0
$786$	28.2547	−	48.9386i	1.00781	−	1.74558i
$787$	12.4112	−	7.16560i	0.442411	−	0.255426i	−0.262209	−	0.965011i	$-0.584451\pi$
$787$	12.4112	−	7.16560i	0.442411	−	0.255426i	0.704620	+	0.709585i	$0.251118\pi$
$788$	−12.9814	−	2.28898i	−0.462445	−	0.0815415i
$789$	−10.5649	+	59.9168i	−0.376122	+	2.13309i
$790$		0			0
$791$	−4.92087	+	8.52320i	−0.174966	+	0.303050i
$792$	−5.12284	+	6.10517i	−0.182032	+	0.216938i
$793$	−28.3473	+	77.8835i	−1.00664	+	2.76573i
$794$	17.7629	−	6.46515i	0.630380	−	0.229440i
$795$		0			0
$796$	1.78833	+	10.1421i	0.0633857	+	0.359478i
$797$		−	17.7667i		−	0.629330i	−0.949203	−	0.314665i	$-0.898108\pi$
$797$		−	17.7667i		−	0.629330i	0.949203	−	0.314665i	$-0.101892\pi$
$798$	24.2288	−	28.7391i	0.857690	−	1.01735i
$799$	12.9955			0.459746
$800$		0			0
$801$	53.5375	−	44.9233i	1.89166	−	1.58729i
$802$	−4.16319	−	11.4383i	−0.147007	−	0.403900i
$803$	−3.20533	+	8.80657i	−0.113114	+	0.310777i
$804$	23.2698	+	19.5257i	0.820664	+	0.688619i
$805$		0			0
$806$	18.7936	+	32.5514i	0.661975	+	1.14657i
$807$	−51.2445	−	9.03580i	−1.80389	−	0.318075i
$808$	−4.87078	−	0.858850i	−0.171353	−	0.0302142i
$809$	−5.86927	−	10.1659i	−0.206353	−	0.357413i	0.744210	−	0.667946i	$-0.232826\pi$
$809$	−5.86927	−	10.1659i	−0.206353	−	0.357413i	−0.950563	+	0.310532i	$0.899493\pi$
$810$		0			0
$811$	−8.28725	−	6.95383i	−0.291005	−	0.244182i	0.485584	−	0.874190i	$-0.338607\pi$
$811$	−8.28725	−	6.95383i	−0.291005	−	0.244182i	−0.776588	+	0.630008i	$0.783052\pi$
$812$	−2.35755	+	6.47730i	−0.0827336	+	0.227309i
$813$	−8.81052	−	24.2067i	−0.308999	−	0.848967i
$814$	−8.76628	+	7.35579i	−0.307258	+	0.257820i
$815$		0			0
$816$	−15.7165			−0.550187
$817$	−25.0854	+	4.36325i	−0.877625	+	0.152651i
$818$			28.2694i			0.988415i
$819$	15.6887	+	88.9753i	0.548209	+	3.10905i
$820$		0			0
$821$	12.0721	−	4.39387i	0.421318	−	0.153347i	−0.122656	−	0.992449i	$-0.539141\pi$
$821$	12.0721	−	4.39387i	0.421318	−	0.153347i	0.543974	+	0.839102i	$0.316919\pi$
$822$	−12.7510	+	35.0332i	−0.444744	+	1.22192i
$823$	−7.30126	+	8.70130i	−0.254506	+	0.303308i	−0.878136	−	0.478411i	$-0.841213\pi$
$823$	−7.30126	+	8.70130i	−0.254506	+	0.303308i	0.623630	+	0.781720i	$0.285657\pi$
$824$	2.75396	−	4.77000i	0.0959387	−	0.166171i
$825$		0			0
$826$	−4.06854	+	23.0739i	−0.141563	+	0.802842i
$827$	−25.7071	−	4.53285i	−0.893923	−	0.157623i	−0.292228	−	0.956349i	$-0.594397\pi$
$827$	−25.7071	−	4.53285i	−0.893923	−	0.157623i	−0.601695	+	0.798726i	$0.705508\pi$
$828$	−8.00622	+	4.62239i	−0.278235	+	0.160639i
$829$	−12.3906	+	21.4611i	−0.430342	+	0.745374i	−0.996903	−	0.0786462i	$-0.974940\pi$
$829$	−12.3906	+	21.4611i	−0.430342	+	0.745374i	0.566561	+	0.824020i	$0.308274\pi$
$830$		0			0
$831$	22.9016	+	8.33551i	0.794449	+	0.289156i
$832$	1.83518	+	5.04213i	0.0636236	+	0.174804i
$833$	−4.98211	−	5.93745i	−0.172620	−	0.205720i
$834$	4.46871	+	25.3433i	0.154739	+	0.877567i
$835$		0			0
$836$	−1.05587	+	5.90799i	−0.0365182	+	0.204332i
$837$		−	57.9041i		−	2.00146i
$838$	−11.3550	+	2.00219i	−0.392251	+	0.0691644i
$839$	24.0765	−	20.2026i	0.831214	−	0.697472i	−0.124355	−	0.992238i	$-0.539686\pi$
$839$	24.0765	−	20.2026i	0.831214	−	0.697472i	0.955569	+	0.294766i	$0.0952417\pi$
$840$		0			0
$841$	21.9748	+	7.99816i	0.757751	+	0.275799i
$842$	13.3719	−	15.9361i	0.460828	−	0.549193i
$843$	−41.7961	−	24.1310i	−1.43953	−	0.831115i
$844$	−7.91528	−	13.7097i	−0.272455	−	0.471906i
$845$		0			0
$846$	−2.46385	+	13.9732i	−0.0847087	+	0.480407i
$847$	−22.9357	+	13.2419i	−0.788079	+	0.454997i
$848$	9.20430	+	5.31410i	0.316077	+	0.182487i
$849$	−14.1953	−	11.9112i	−0.487180	−	0.408793i
$850$		0			0
$851$	−12.4739	+	4.54011i	−0.427598	+	0.155633i
$852$	−4.80067	−	5.72121i	−0.164468	−	0.196005i
$853$	−39.5963	+	6.98190i	−1.35575	+	0.239056i	−0.803840	−	0.594846i	$-0.797213\pi$
$853$	−39.5963	+	6.98190i	−1.35575	+	0.239056i	−0.551913	+	0.833902i	$0.686102\pi$
$854$	44.9333			1.53759
$855$		0			0
$856$	−6.27924			−0.214620
$857$	4.70367	−	0.829384i	0.160674	−	0.0283312i	−0.0927323	−	0.995691i	$-0.529560\pi$
$857$	4.70367	−	0.829384i	0.160674	−	0.0283312i	0.253407	+	0.967360i	$0.418449\pi$
$858$	−14.0779	−	16.7774i	−0.480613	−	0.572772i
$859$	−9.73955	+	3.54491i	−0.332309	+	0.120951i	−0.502786	−	0.864411i	$-0.667692\pi$
$859$	−9.73955	+	3.54491i	−0.332309	+	0.120951i	0.170476	+	0.985362i	$0.445469\pi$
$860$		0			0
$861$	61.5292	+	51.6292i	2.09691	+	1.75952i
$862$	−2.33429	−	1.34770i	−0.0795061	−	0.0459029i
$863$	27.4609	−	15.8545i	0.934779	−	0.539695i	0.0464590	−	0.998920i	$-0.485206\pi$
$863$	27.4609	−	15.8545i	0.934779	−	0.539695i	0.888320	+	0.459225i	$0.151873\pi$
$864$	1.43539	−	8.14047i	0.0488328	−	0.276945i
$865$		0			0
$866$	15.3359	+	26.5626i	0.521135	+	0.902632i
$867$	28.5138	+	16.4624i	0.968379	+	0.559094i
$868$	13.0983	−	15.6099i	0.444585	−	0.529836i
$869$	−10.6605	−	3.88009i	−0.361631	−	0.131623i
$870$		0			0
$871$	−42.1180	+	35.3412i	−1.42711	+	1.19749i
$872$	−5.39247	+	0.950839i	−0.182612	+	0.0321995i
$873$		−	53.0091i		−	1.79409i
$874$	−3.49486	+	6.02098i	−0.118216	+	0.203663i
$875$		0			0
$876$	−3.50392	−	19.8717i	−0.118387	−	0.671403i
$877$	−4.04949	−	4.82600i	−0.136742	−	0.162962i	0.693328	−	0.720622i	$-0.256144\pi$
$877$	−4.04949	−	4.82600i	−0.136742	−	0.162962i	−0.830070	+	0.557660i	$0.811699\pi$
$878$	−8.55996	−	23.5183i	−0.288885	−	0.793705i
$879$	−42.3708	−	15.4217i	−1.42913	−	0.520162i
$880$		0			0
$881$	−26.9351	+	46.6530i	−0.907468	+	1.57178i	−0.0898984	+	0.995951i	$0.528654\pi$
$881$	−26.9351	+	46.6530i	−0.907468	+	1.57178i	−0.817570	+	0.575830i	$0.804679\pi$
$882$	7.32872	−	4.23124i	0.246771	−	0.142473i
$883$	1.94292	+	0.342590i	0.0653846	+	0.0115291i	0.206245	−	0.978500i	$-0.433876\pi$
$883$	1.94292	+	0.342590i	0.0653846	+	0.0115291i	−0.140860	+	0.990030i	$0.544987\pi$
$884$	4.93970	−	28.0144i	0.166140	−	0.942227i
$885$		0			0
$886$	−17.5555	+	30.4071i	−0.589789	+	1.02155i
$887$	−17.3589	+	20.6876i	−0.582856	+	0.694621i	−0.974216	−	0.225617i	$-0.927560\pi$
$887$	−17.3589	+	20.6876i	−0.582856	+	0.694621i	0.391360	+	0.920238i	$0.372005\pi$
$888$	8.42707	−	23.1532i	0.282794	−	0.776970i
$889$	22.4155	−	8.15856i	0.751790	−	0.273629i
$890$		0			0
$891$	1.70705	+	9.68119i	0.0571885	+	0.324332i
$892$		−	3.28624i		−	0.110031i
$893$	3.63111	+	10.0489i	0.121511	+	0.336273i
$894$	48.5536			1.62388
$895$		0			0
$896$	2.22838	−	1.86984i	0.0744451	−	0.0624669i
$897$	−8.68913	−	23.8732i	−0.290121	−	0.797102i
$898$	0.873122	−	2.39888i	0.0291365	−	0.0800518i
$899$	12.7156	+	10.6697i	0.424090	+	0.355853i
$900$		0			0
$901$	−28.1729	−	48.7970i	−0.938577	−	1.62566i
$902$	−12.6293	−	2.22689i	−0.420510	−	0.0741473i
$903$	−49.6085	−	8.74733i	−1.65087	−	0.291093i
$904$	1.69163	+	2.92999i	0.0562628	+	0.0974501i
$905$		0			0
$906$	−29.2600	−	24.5520i	−0.972097	−	0.815686i
$907$	−8.43355	+	23.1710i	−0.280031	+	0.769380i	0.717327	+	0.696737i	$0.245365\pi$
$907$	−8.43355	+	23.1710i	−0.280031	+	0.769380i	−0.997358	+	0.0726427i	$0.976857\pi$
$908$	−4.04088	−	11.1022i	−0.134101	−	0.368440i
$909$	−21.9308	+	18.4021i	−0.727399	+	0.610360i
$910$		0			0
$911$	−10.4670			−0.346787			−0.173394	−	0.984853i	$-0.555473\pi$
$911$	−10.4670			−0.346787			−0.173394	+	0.984853i	$0.555473\pi$
$912$	−4.39141	−	12.1529i	−0.145414	−	0.402424i
$913$		−	0.667352i		−	0.0220861i
$914$	−5.03718	−	28.5672i	−0.166615	−	0.944920i
$915$		0			0
$916$	11.1998	−	4.07640i	0.370053	−	0.134688i
$917$	18.9651	−	52.1063i	0.626284	−	1.72070i
$918$	−28.1688	+	33.5702i	−0.929708	+	1.10798i
$919$	−12.5834	+	21.7950i	−0.415087	+	0.718952i	−0.995438	−	0.0954150i	$-0.969582\pi$
$919$	−12.5834	+	21.7950i	−0.415087	+	0.718952i	0.580351	+	0.814367i	$0.302916\pi$
$920$		0			0
$921$	0.334319	−	1.89602i	0.0110162	−	0.0624759i
$922$	36.9060	+	6.50753i	1.21544	+	0.214314i
$923$	11.7068	−	6.75894i	0.385335	−	0.222473i
$924$	−5.93676	+	10.2828i	−0.195305	+	0.338278i
$925$		0			0
$926$	4.15816	+	1.51345i	0.136645	+	0.0497349i
$927$	−10.9042	−	29.9590i	−0.358140	−	0.983982i
$928$	1.52314	+	1.81521i	0.0499995	+	0.0595871i
$929$	3.26147	+	18.4967i	0.107005	+	0.606857i	0.990400	+	0.138228i	$0.0441408\pi$
$929$	3.26147	+	18.4967i	0.107005	+	0.606857i	−0.883395	+	0.468629i	$0.844748\pi$
$930$		0			0
$931$	3.19912	−	5.51148i	0.104847	−	0.180631i
$932$			9.18438i			0.300844i
$933$	−33.8227	+	5.96386i	−1.10731	+	0.195248i
$934$	3.31664	−	2.78299i	0.108524	−	0.0910623i
$935$		0			0
$936$	29.1855	+	10.6227i	0.953958	+	0.347212i
$937$	9.00408	−	10.7306i	0.294150	−	0.350555i	−0.598647	−	0.801013i	$-0.704295\pi$
$937$	9.00408	−	10.7306i	0.294150	−	0.350555i	0.892798	+	0.450458i	$0.148739\pi$
$938$	25.8139	+	14.9036i	0.842852	+	0.486621i
$939$	0.934141	+	1.61798i	0.0304845	+	0.0528008i
$940$		0			0
$941$	10.1772	−	57.7176i	0.331766	−	1.88154i	−0.125316	−	0.992117i	$-0.539994\pi$
$941$	10.1772	−	57.7176i	0.331766	−	1.88154i	0.457082	−	0.889424i	$-0.348894\pi$
$942$	−42.0790	+	24.2943i	−1.37101	+	0.791552i
$943$	−12.8829	−	7.43792i	−0.419523	−	0.242212i
$944$	6.17002	+	5.17726i	0.200817	+	0.168506i
$945$		0			0
$946$	7.55773	−	2.75079i	0.245723	−	0.0894359i
$947$	0.912031	+	1.08692i	0.0296370	+	0.0353200i	0.780659	−	0.624957i	$-0.214883\pi$
$947$	0.912031	+	1.08692i	0.0296370	+	0.0353200i	−0.751022	+	0.660277i	$0.770439\pi$
$948$	24.0550	−	4.24154i	0.781269	−	0.137759i
$949$	36.5223			1.18557
$950$		0			0
$951$	−27.6120			−0.895382
$952$	−15.1876	+	2.67799i	−0.492234	+	0.0867941i
$953$	23.7773	+	28.3367i	0.770223	+	0.917916i	0.998448	−	0.0556922i	$-0.0177366\pi$
$953$	23.7773	+	28.3367i	0.770223	+	0.917916i	−0.228225	+	0.973608i	$0.573292\pi$
$954$	57.8095	−	21.0410i	1.87165	−	0.681226i
$955$		0			0
$956$	4.14362	+	3.47691i	0.134014	+	0.112451i
$957$	−8.37619	−	4.83599i	−0.270764	−	0.156325i
$958$	6.48468	−	3.74393i	0.209510	−	0.120961i
$959$	−6.35254	+	36.0270i	−0.205134	+	1.16337i
$960$		0			0
$961$	−9.03536	−	15.6497i	−0.291463	−	0.504829i
$962$	38.6216	+	22.2982i	1.24521	+	0.718922i
$963$	−23.3630	+	27.8429i	−0.752862	+	0.897226i
$964$	24.9886	+	9.09512i	0.804830	+	0.292934i
$965$		0			0
$966$	−10.5508	+	8.85320i	−0.339467	+	0.284847i
$967$	−3.64316	+	0.642387i	−0.117156	+	0.0206578i	−0.231919	−	0.972735i	$-0.574500\pi$
$967$	−3.64316	+	0.642387i	−0.117156	+	0.0206578i	0.114763	+	0.993393i	$0.463389\pi$
$968$			9.10425i			0.292622i
$969$	−12.0525	+	67.4380i	−0.387183	+	2.16642i
$970$		0			0
$971$	1.26262	+	7.16068i	0.0405194	+	0.229797i	0.998342	−	0.0575637i	$-0.0183332\pi$
$971$	1.26262	+	7.16068i	0.0405194	+	0.229797i	−0.957822	+	0.287361i	$0.907222\pi$
$972$	2.33466	+	2.78234i	0.0748843	+	0.0892436i
$973$	8.63667	+	23.7291i	0.276879	+	0.760719i
$974$	16.7530	+	6.09760i	0.536801	+	0.195380i
$975$		0			0
$976$	7.72328	−	13.3771i	0.247216	−	0.428191i
$977$	9.69861	−	5.59949i	0.310286	−	0.179144i	−0.336768	−	0.941587i	$-0.609334\pi$
$977$	9.69861	−	5.59949i	0.310286	−	0.179144i	0.647054	+	0.762444i	$0.276001\pi$
$978$	−11.9135	−	2.10067i	−0.380951	−	0.0671719i
$979$	−2.88676	+	16.3716i	−0.0922613	+	0.523240i
$980$		0			0
$981$	−15.8475	+	27.4486i	−0.505971	+	0.876368i
$982$	7.70951	−	9.18783i	0.246020	−	0.293196i
$983$	−12.0730	+	33.1702i	−0.385068	+	1.05797i	0.584125	+	0.811663i	$0.301438\pi$
$983$	−12.0730	+	33.1702i	−0.385068	+	1.05797i	−0.969193	+	0.246302i	$0.920785\pi$
$984$	25.9464	−	9.44372i	0.827141	−	0.301055i
$985$		0			0
$986$	−2.18145	−	12.3716i	−0.0694714	−	0.393992i
$987$			21.1387i			0.672853i
$988$	23.0427	−	4.00795i	0.733085	−	0.127510i
$989$	9.32951			0.296661
$990$		0			0
$991$	15.8273	−	13.2807i	0.502771	−	0.421875i	−0.355806	−	0.934560i	$-0.615794\pi$
$991$	15.8273	−	13.2807i	0.502771	−	0.421875i	0.858577	+	0.512685i	$0.171349\pi$
$992$	−2.39587	−	6.58259i	−0.0760689	−	0.208998i
$993$	−12.2338	+	33.6122i	−0.388229	+	1.06665i
$994$	−5.61398	−	4.71069i	−0.178065	−	0.149414i
$995$		0			0
$996$	0.718437	+	1.24437i	0.0227645	+	0.0394293i
$997$	−44.3241	−	7.81553i	−1.40376	−	0.247520i	−0.580071	−	0.814566i	$-0.696975\pi$
$997$	−44.3241	−	7.81553i	−1.40376	−	0.247520i	−0.823687	+	0.567045i	$0.808087\pi$
$998$	6.62459	+	1.16809i	0.209698	+	0.0369754i
$999$	−34.3510	−	59.4977i	−1.08682	−	1.88242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.f.199.2		24
5.2	odd	4		950.2.l.g.351.2		12
5.3	odd	4		190.2.k.c.161.1	yes	12
5.4	even	2	inner	950.2.u.f.199.3		24
19.17	even	9	inner	950.2.u.f.549.3		24
95.13	even	36		3610.2.a.bd.1.6		6
95.17	odd	36		950.2.l.g.701.2		12
95.63	odd	36		3610.2.a.bf.1.1		6
95.74	even	18	inner	950.2.u.f.549.2		24
95.93	odd	36		190.2.k.c.131.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.131.1	✓	12	95.93	odd	36
190.2.k.c.161.1	yes	12	5.3	odd	4
950.2.l.g.351.2		12	5.2	odd	4
950.2.l.g.701.2		12	95.17	odd	36
950.2.u.f.199.2		24	1.1	even	1	trivial
950.2.u.f.199.3		24	5.4	even	2	inner
950.2.u.f.549.2		24	95.74	even	18	inner
950.2.u.f.549.3		24	19.17	even	9	inner
3610.2.a.bd.1.6		6	95.13	even	36
3610.2.a.bf.1.1		6	95.63	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.90555 + 2.27095i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.27095 - 1.90555i) q^{6} +(-2.51922 - 1.45447i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.00513 + 5.70040i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.90555 + 2.27095i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.27095 - 1.90555i) q^{6} +(-2.51922 - 1.45447i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.00513 + 5.70040i) q^{9} +(-0.688430 - 1.19240i) q^{11} +(2.56734 + 1.48226i) q^{12} +(-3.44902 + 4.11038i) q^{13} +(2.73352 + 0.994919i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-5.22100 + 0.920603i) q^{17} -5.78833i q^{18} +(-2.17069 - 3.77996i) q^{19} +(-1.49748 - 8.49261i) q^{21} +(0.885029 + 1.05474i) q^{22} +(0.546254 + 1.50082i) q^{23} +(-2.78573 - 1.01392i) q^{24} +(2.68286 - 4.64685i) q^{26} +(-7.15861 + 4.13303i) q^{27} +(-2.86476 - 0.505134i) q^{28} +(0.411474 - 2.33359i) q^{29} +(-3.50252 + 6.06655i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(1.39603 - 3.83556i) q^{33} +(4.98182 - 1.81323i) q^{34} +(1.00513 + 5.70040i) q^{36} +8.31135i q^{37} +(2.79409 + 3.34560i) q^{38} -15.9067 q^{39} +(-7.13497 + 5.98695i) q^{41} +(2.94945 + 8.10355i) q^{42} +(1.99787 - 5.48910i) q^{43} +(-1.05474 - 0.885029i) q^{44} +(-0.798570 - 1.38316i) q^{46} +(-2.41402 - 0.425657i) q^{47} +(2.91947 + 0.514782i) q^{48} +(0.730994 + 1.26612i) q^{49} +(-12.0395 - 10.1024i) q^{51} +(-1.83518 + 5.04213i) q^{52} +(3.63506 + 9.98725i) q^{53} +(6.33216 - 5.31332i) q^{54} +2.90895 q^{56} +(4.44774 - 12.1324i) q^{57} +2.36959i q^{58} +(1.39863 + 7.93202i) q^{59} +(14.5150 - 5.28304i) q^{61} +(2.39587 - 6.58259i) q^{62} +(10.8232 - 12.8986i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.708783 + 4.01971i) q^{66} +(10.0911 + 1.77933i) q^{67} +(-4.59127 + 2.65077i) q^{68} +(-2.36737 + 4.10041i) q^{69} +(-2.36737 - 0.861653i) q^{71} +(-1.97973 - 5.43926i) q^{72} +(-4.37520 - 5.21416i) q^{73} +(-1.44325 - 8.18508i) q^{74} +(-3.33260 - 2.80958i) q^{76} +4.00522i q^{77} +(15.6651 - 2.76218i) q^{78} +(6.31181 - 5.29624i) q^{79} +(-6.70923 - 2.44196i) q^{81} +(5.98695 - 7.13497i) q^{82} +(0.419755 + 0.242346i) q^{83} +(-4.31181 - 7.46827i) q^{84} +(-1.01435 + 5.75264i) q^{86} +(6.08354 - 3.51233i) q^{87} +(1.19240 + 0.688430i) q^{88} +(-9.24921 - 7.76101i) q^{89} +(14.6673 - 5.33846i) q^{91} +(1.02662 + 1.22348i) q^{92} +(-20.4511 + 3.60607i) q^{93} +2.45126 q^{94} -2.96451 q^{96} +(-9.01879 + 1.59026i) q^{97} +(-0.939748 - 1.11995i) q^{98} +(7.48910 - 2.72581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 18 * q^9	\( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Introduction

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