LMFDB - Embedded newform 950.2.l.g.701.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1511x^{6} + 4812x^{4} - 7788x^{2} + 5329 $ x^12 - 24x^10 + 264x^8 - 1511x^6 + 4812x^4 - 7788*x^2 + 5329
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			701.2
Root			$2.79086 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	950.701
Dual form			950.2.l.g.351.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(2.27095 + 1.90555i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.27095 + 1.90555i) q^{6} +(1.45447 + 2.51922i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.00513 + 5.70040i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(2.27095 + 1.90555i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.27095 + 1.90555i) q^{6} +(1.45447 + 2.51922i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.00513 + 5.70040i) q^{9} +(-0.688430 + 1.19240i) q^{11} +(-1.48226 - 2.56734i) q^{12} +(4.11038 - 3.44902i) q^{13} +(-2.73352 + 0.994919i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.920603 + 5.22100i) q^{17} -5.78833 q^{18} +(2.17069 - 3.77996i) q^{19} +(-1.49748 + 8.49261i) q^{21} +(-1.05474 - 0.885029i) q^{22} +(1.50082 + 0.546254i) q^{23} +(2.78573 - 1.01392i) q^{24} +(2.68286 + 4.64685i) q^{26} +(-4.13303 + 7.15861i) q^{27} +(-0.505134 - 2.86476i) q^{28} +(-0.411474 - 2.33359i) q^{29} +(-3.50252 - 6.06655i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-3.83556 + 1.39603i) q^{33} +(-4.98182 - 1.81323i) q^{34} +(1.00513 - 5.70040i) q^{36} -8.31135 q^{37} +(3.34560 + 2.79409i) q^{38} +15.9067 q^{39} +(-7.13497 - 5.98695i) q^{41} +(-8.10355 - 2.94945i) q^{42} +(-5.48910 + 1.99787i) q^{43} +(1.05474 - 0.885029i) q^{44} +(-0.798570 + 1.38316i) q^{46} +(0.425657 + 2.41402i) q^{47} +(0.514782 + 2.91947i) q^{48} +(-0.730994 + 1.26612i) q^{49} +(-12.0395 + 10.1024i) q^{51} +(-5.04213 + 1.83518i) q^{52} +(9.98725 + 3.63506i) q^{53} +(-6.33216 - 5.31332i) q^{54} +2.90895 q^{56} +(12.1324 - 4.44774i) q^{57} +2.36959 q^{58} +(-1.39863 + 7.93202i) q^{59} +(14.5150 + 5.28304i) q^{61} +(6.58259 - 2.39587i) q^{62} +(-12.8986 + 10.8232i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.708783 - 4.01971i) q^{66} +(-1.77933 - 10.0911i) q^{67} +(2.65077 - 4.59127i) q^{68} +(2.36737 + 4.10041i) q^{69} +(-2.36737 + 0.861653i) q^{71} +(5.43926 + 1.97973i) q^{72} +(-5.21416 - 4.37520i) q^{73} +(1.44325 - 8.18508i) q^{74} +(-3.33260 + 2.80958i) q^{76} -4.00522 q^{77} +(-2.76218 + 15.6651i) q^{78} +(-6.31181 - 5.29624i) q^{79} +(-6.70923 + 2.44196i) q^{81} +(7.13497 - 5.98695i) q^{82} +(0.242346 + 0.419755i) q^{83} +(4.31181 - 7.46827i) q^{84} +(-1.01435 - 5.75264i) q^{86} +(3.51233 - 6.08354i) q^{87} +(0.688430 + 1.19240i) q^{88} +(9.24921 - 7.76101i) q^{89} +(14.6673 + 5.33846i) q^{91} +(-1.22348 - 1.02662i) q^{92} +(3.60607 - 20.4511i) q^{93} -2.45126 q^{94} -2.96451 q^{96} +(-1.59026 + 9.01879i) q^{97} +(-1.11995 - 0.939748i) q^{98} +(-7.48910 - 2.72581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	2.27095	+	1.90555i	1.31113	+	1.10017i	0.988105	+	0.153781i	$0.0491452\pi$
$3$	2.27095	+	1.90555i	1.31113	+	1.10017i	0.323028	+	0.946389i	$0.395299\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−2.27095	+	1.90555i	−0.927111	+	0.777938i
$7$	1.45447	+	2.51922i	0.549740	+	0.952177i	0.998292	+	0.0584207i	$0.0186065\pi$
$7$	1.45447	+	2.51922i	0.549740	+	0.952177i	−0.448552	+	0.893757i	$0.648060\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.00513	+	5.70040i	0.335045	+	1.90013i
$10$		0			0
$11$	−0.688430	+	1.19240i	−0.207570	+	0.359521i	−0.950948	−	0.309350i	$-0.899889\pi$
$11$	−0.688430	+	1.19240i	−0.207570	+	0.359521i	0.743379	+	0.668871i	$0.233222\pi$
$12$	−1.48226	−	2.56734i	−0.427891	−	0.741128i
$13$	4.11038	−	3.44902i	1.14001	−	0.956585i	0.140575	−	0.990070i	$-0.455105\pi$
$13$	4.11038	−	3.44902i	1.14001	−	0.956585i	0.999439	+	0.0334846i	$0.0106605\pi$
$14$	−2.73352	+	0.994919i	−0.730564	+	0.265903i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.920603	+	5.22100i	−0.223279	+	1.26628i	0.642669	+	0.766144i	$0.277827\pi$
$17$	−0.920603	+	5.22100i	−0.223279	+	1.26628i	−0.865948	+	0.500134i	$0.833284\pi$
$18$	−5.78833			−1.36432
$19$	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
$22$	−1.05474	−	0.885029i	−0.224871	−	0.188689i
$23$	1.50082	+	0.546254i	0.312943	+	0.113902i	0.493717	−	0.869623i	$-0.335638\pi$
$23$	1.50082	+	0.546254i	0.312943	+	0.113902i	−0.180774	+	0.983525i	$0.557860\pi$
$24$	2.78573	−	1.01392i	0.568635	−	0.206966i
$25$		0			0
$26$	2.68286	+	4.64685i	0.526152	+	0.911322i
$27$	−4.13303	+	7.15861i	−0.795401	+	1.37768i
$28$	−0.505134	−	2.86476i	−0.0954613	−	0.541388i
$29$	−0.411474	−	2.33359i	−0.0764088	−	0.433336i	−0.998882	−	0.0472746i	$-0.984946\pi$
$29$	−0.411474	−	2.33359i	−0.0764088	−	0.433336i	0.922473	−	0.386061i	$-0.126165\pi$
$30$		0			0
$31$	−3.50252	−	6.06655i	−0.629072	−	1.08958i	−0.987738	−	0.156119i	$-0.950102\pi$
$31$	−3.50252	−	6.06655i	−0.629072	−	1.08958i	0.358666	−	0.933466i	$-0.383232\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−3.83556	+	1.39603i	−0.667686	+	0.243018i
$34$	−4.98182	−	1.81323i	−0.854375	−	0.310967i
$35$		0			0
$36$	1.00513	−	5.70040i	0.167522	−	0.950066i
$37$	−8.31135			−1.36638			−0.683189	−	0.730242i	$-0.739407\pi$
$37$	−8.31135			−1.36638			−0.683189	+	0.730242i	$0.739407\pi$
$38$	3.34560	+	2.79409i	0.542728	+	0.453262i
$39$	15.9067			2.54712
$40$		0			0
$41$	−7.13497	−	5.98695i	−1.11430	−	0.935005i	−0.115993	−	0.993250i	$-0.537005\pi$
$41$	−7.13497	−	5.98695i	−1.11430	−	0.935005i	−0.998302	+	0.0582455i	$0.981449\pi$
$42$	−8.10355	−	2.94945i	−1.25040	−	0.455110i
$43$	−5.48910	+	1.99787i	−0.837080	+	0.304672i	−0.724761	−	0.689000i	$-0.758050\pi$
$43$	−5.48910	+	1.99787i	−0.837080	+	0.304672i	−0.112319	+	0.993672i	$0.535828\pi$
$44$	1.05474	−	0.885029i	0.159008	−	0.133423i
$45$		0			0
$46$	−0.798570	+	1.38316i	−0.117743	+	0.203936i
$47$	0.425657	+	2.41402i	0.0620885	+	0.352121i	0.999986	+	0.00520990i	$0.00165837\pi$
$47$	0.425657	+	2.41402i	0.0620885	+	0.352121i	−0.937898	+	0.346911i	$0.887231\pi$
$48$	0.514782	+	2.91947i	0.0743024	+	0.421390i
$49$	−0.730994	+	1.26612i	−0.104428	+	0.180874i
$50$		0			0
$51$	−12.0395	+	10.1024i	−1.68587	+	1.41461i
$52$	−5.04213	+	1.83518i	−0.699217	+	0.254494i
$53$	9.98725	+	3.63506i	1.37185	+	0.499314i	0.919699	−	0.392625i	$-0.128433\pi$
$53$	9.98725	+	3.63506i	1.37185	+	0.499314i	0.452155	+	0.891939i	$0.350655\pi$
$54$	−6.33216	−	5.31332i	−0.861698	−	0.723051i
$55$		0			0
$56$	2.90895			0.388725
$57$	12.1324	−	4.44774i	1.60698	−	0.589118i
$58$	2.36959			0.311142
$59$	−1.39863	+	7.93202i	−0.182086	+	1.03266i	0.747556	+	0.664199i	$0.231227\pi$
$59$	−1.39863	+	7.93202i	−0.182086	+	1.03266i	−0.929642	+	0.368463i	$0.879884\pi$
$60$		0			0
$61$	14.5150	+	5.28304i	1.85846	+	0.676424i	0.980127	+	0.198371i	$0.0635652\pi$
$61$	14.5150	+	5.28304i	1.85846	+	0.676424i	0.878332	+	0.478052i	$0.158657\pi$
$62$	6.58259	−	2.39587i	0.835990	−	0.304276i
$63$	−12.8986	+	10.8232i	−1.62508	+	1.36360i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.708783	−	4.01971i	−0.0872452	−	0.494792i
$67$	−1.77933	−	10.0911i	−0.217380	−	1.23282i	−0.876729	−	0.480985i	$-0.840279\pi$
$67$	−1.77933	−	10.0911i	−0.217380	−	1.23282i	0.659349	−	0.751837i	$-0.270832\pi$
$68$	2.65077	−	4.59127i	0.321453	−	0.556773i
$69$	2.36737	+	4.10041i	0.284998	+	0.493631i
$70$		0			0
$71$	−2.36737	+	0.861653i	−0.280955	+	0.102259i	−0.478654	−	0.878003i	$-0.658875\pi$
$71$	−2.36737	+	0.861653i	−0.280955	+	0.102259i	0.197699	+	0.980263i	$0.436653\pi$
$72$	5.43926	+	1.97973i	0.641022	+	0.233313i
$73$	−5.21416	−	4.37520i	−0.610272	−	0.512079i	0.284457	−	0.958689i	$-0.408187\pi$
$73$	−5.21416	−	4.37520i	−0.610272	−	0.512079i	−0.894729	+	0.446610i	$0.852631\pi$
$74$	1.44325	−	8.18508i	0.167774	−	0.951496i
$75$		0			0
$76$	−3.33260	+	2.80958i	−0.382276	+	0.322281i
$77$	−4.00522			−0.456437
$78$	−2.76218	+	15.6651i	−0.312755	+	1.77372i
$79$	−6.31181	−	5.29624i	−0.710134	−	0.595873i	0.214503	−	0.976723i	$-0.431187\pi$
$79$	−6.31181	−	5.29624i	−0.710134	−	0.595873i	−0.924637	+	0.380850i	$0.875631\pi$
$80$		0			0
$81$	−6.70923	+	2.44196i	−0.745470	+	0.271329i
$82$	7.13497	−	5.98695i	0.787926	−	0.661148i
$83$	0.242346	+	0.419755i	0.0266009	+	0.0460741i	0.879019	−	0.476786i	$-0.158198\pi$
$83$	0.242346	+	0.419755i	0.0266009	+	0.0460741i	−0.852419	+	0.522860i	$0.824865\pi$
$84$	4.31181	−	7.46827i	0.470457	−	0.814855i
$85$		0			0
$86$	−1.01435	−	5.75264i	−0.109380	−	0.620323i
$87$	3.51233	−	6.08354i	0.376562	−	0.652224i
$88$	0.688430	+	1.19240i	0.0733869	+	0.127110i
$89$	9.24921	−	7.76101i	0.980414	−	0.822665i	−0.00373759	−	0.999993i	$-0.501190\pi$
$89$	9.24921	−	7.76101i	0.980414	−	0.822665i	0.984152	+	0.177328i	$0.0567453\pi$
$90$		0			0
$91$	14.6673	+	5.33846i	1.53755	+	0.559622i
$92$	−1.22348	−	1.02662i	−0.127557	−	0.107033i
$93$	3.60607	−	20.4511i	0.373933	−	2.12068i
$94$	−2.45126			−0.252828
$95$		0			0
$96$	−2.96451			−0.302564
$97$	−1.59026	+	9.01879i	−0.161466	+	0.915719i	0.791168	+	0.611599i	$0.209474\pi$
$97$	−1.59026	+	9.01879i	−0.161466	+	0.915719i	−0.952634	+	0.304120i	$0.901638\pi$
$98$	−1.11995	−	0.939748i	−0.113132	−	0.0949289i
$99$	−7.48910	−	2.72581i	−0.752683	−	0.273954i
$100$		0			0
$101$	3.78879	−	3.17918i	0.376999	−	0.316340i	−0.434524	−	0.900660i	$-0.643083\pi$
$101$	3.78879	−	3.17918i	0.376999	−	0.316340i	0.811523	+	0.584320i	$0.198639\pi$
$102$	−7.85824	−	13.6109i	−0.778082	−	1.34768i
$103$	2.75396	−	4.77000i	0.271356	−	0.470002i	−0.697854	−	0.716240i	$-0.745861\pi$
$103$	2.75396	−	4.77000i	0.271356	−	0.470002i	0.969209	+	0.246239i	$0.0791947\pi$
$104$	−0.931747	−	5.28420i	−0.0913653	−	0.518159i
$105$		0			0
$106$	−5.31410	+	9.20430i	−0.516151	+	0.894000i
$107$	−3.13962	−	5.43798i	−0.303519	−	0.525710i	0.673412	−	0.739268i	$-0.264828\pi$
$107$	−3.13962	−	5.43798i	−0.303519	−	0.525710i	−0.976930	+	0.213558i	$0.931495\pi$
$108$	6.33216	−	5.31332i	0.609313	−	0.511274i
$109$	−5.14544	+	1.87279i	−0.492844	+	0.179380i	−0.576473	−	0.817117i	$-0.695571\pi$
$109$	−5.14544	+	1.87279i	−0.492844	+	0.179380i	0.0836288	+	0.996497i	$0.473349\pi$
$110$		0			0
$111$	−18.8746	−	15.8377i	−1.79150	−	1.50325i
$112$	−0.505134	+	2.86476i	−0.0477307	+	0.270694i
$113$	−3.38326			−0.318271			−0.159135	−	0.987257i	$-0.550871\pi$
$113$	−3.38326			−0.318271			−0.159135	+	0.987257i	$0.550871\pi$
$114$	2.27340	+	12.7205i	0.212923	+	1.19138i
$115$		0			0
$116$	−0.411474	+	2.33359i	−0.0382044	+	0.216668i
$117$	23.7923	+	19.9641i	2.19959	+	1.84568i
$118$	−7.56865	−	2.75476i	−0.696751	−	0.253597i
$119$	−14.4919	+	5.27461i	−1.32847	+	0.483522i
$120$		0			0
$121$	4.55213	+	7.88452i	0.413830	+	0.716774i
$122$	−7.72328	+	13.3771i	−0.699233	+	1.21111i
$123$	−4.79470	−	27.1921i	−0.432324	−	2.45183i
$124$	1.21641	+	6.89863i	0.109237	+	0.619515i
$125$		0			0
$126$	−8.41899	−	14.5821i	−0.750023	−	1.29908i
$127$	−6.28174	+	5.27100i	−0.557414	+	0.467726i	−0.877442	−	0.479682i	$-0.840752\pi$
$127$	−6.28174	+	5.27100i	−0.557414	+	0.467726i	0.320028	+	0.947408i	$0.396308\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−16.2725	−	5.92271i	−1.43271	−	0.521466i
$130$		0			0
$131$	3.31008	−	18.7724i	0.289203	−	1.64015i	−0.400671	−	0.916222i	$-0.631223\pi$
$131$	3.31008	−	18.7724i	0.289203	−	1.64015i	0.689874	−	0.723929i	$-0.257666\pi$
$132$	4.08172			0.355268
$133$	12.6798	−	0.0294142i	1.09948	−	0.00255054i
$134$	10.2467			0.885184
$135$		0			0
$136$	4.06122	+	3.40777i	0.348246	+	0.292213i
$137$	11.8175	+	4.30123i	1.00964	+	0.367479i	0.793294	−	0.608838i	$-0.208364\pi$
$137$	11.8175	+	4.30123i	1.00964	+	0.367479i	0.216345	+	0.976317i	$0.430586\pi$
$138$	−4.44920	+	1.61938i	−0.378741	+	0.137851i
$139$	6.64986	−	5.57990i	0.564034	−	0.473281i	−0.315626	−	0.948884i	$-0.602215\pi$
$139$	6.64986	−	5.57990i	0.564034	−	0.473281i	0.879660	+	0.475603i	$0.157770\pi$
$140$		0			0
$141$	−3.63340	+	6.29323i	−0.305987	+	0.529985i
$142$	−0.437473	−	2.48103i	−0.0367119	−	0.208203i
$143$	1.28289	+	7.27561i	0.107280	+	0.608417i
$144$	−2.89417	+	5.01285i	−0.241181	+	0.417737i
$145$		0			0
$146$	5.21416	−	4.37520i	0.431527	−	0.362094i
$147$	−4.07271	+	1.48234i	−0.335911	+	0.122262i
$148$	7.81011	+	2.84265i	0.641987	+	0.233664i
$149$	12.5465	+	10.5278i	1.02785	+	0.862467i	0.990593	−	0.136839i	$-0.0436942\pi$
$149$	12.5465	+	10.5278i	1.02785	+	0.862467i	0.0372549	+	0.999306i	$0.488139\pi$
$150$		0			0
$151$	12.8845			1.04852			0.524261	−	0.851557i	$-0.324341\pi$
$151$	12.8845			1.04852			0.524261	+	0.851557i	$0.324341\pi$
$152$	−2.18820	−	3.76985i	−0.177487	−	0.305775i
$153$	−30.6871			−2.48090
$154$	0.695499	−	3.94437i	0.0560449	−	0.317846i
$155$		0			0
$156$	−14.9474	−	5.44043i	−1.19675	−	0.435583i
$157$	15.4017	−	5.60574i	1.22919	−	0.447387i	0.355867	−	0.934537i	$-0.384186\pi$
$157$	15.4017	−	5.60574i	1.22919	−	0.447387i	0.873318	+	0.487150i	$0.161963\pi$
$158$	6.31181	−	5.29624i	0.502141	−	0.421346i
$159$	15.7537	+	27.2863i	1.24935	+	2.16394i
$160$		0			0
$161$	0.806770	+	4.57542i	0.0635824	+	0.360594i
$162$	−1.23982	−	7.03135i	−0.0974092	−	0.552435i
$163$	−2.04034	+	3.53398i	−0.159812	+	0.276803i	−0.934801	−	0.355172i	$-0.884422\pi$
$163$	−2.04034	+	3.53398i	−0.159812	+	0.276803i	0.774989	+	0.631975i	$0.217755\pi$
$164$	4.65702	+	8.06620i	0.363652	+	0.629864i
$165$		0			0
$166$	−0.455461	+	0.165774i	−0.0353506	+	0.0128666i
$167$	−14.8948	−	5.42127i	−1.15260	−	0.419510i	−0.306149	−	0.951984i	$-0.599040\pi$
$167$	−14.8948	−	5.42127i	−1.15260	−	0.419510i	−0.846447	+	0.532473i	$0.821263\pi$
$168$	6.60607	+	5.54315i	0.509670	+	0.427664i
$169$	2.74207	−	15.5510i	0.210928	−	1.19623i
$170$		0			0
$171$	23.7291	+	8.57441i	1.81461	+	0.655701i
$172$	5.84138			0.445401
$173$	−0.420901	+	2.38705i	−0.0320005	+	0.181484i	−0.996619	−	0.0821676i	$-0.973816\pi$
$173$	−0.420901	+	2.38705i	−0.0320005	+	0.181484i	0.964618	+	0.263651i	$0.0849268\pi$
$174$	5.38121	+	4.51537i	0.407948	+	0.342309i
$175$		0			0
$176$	−1.29383	+	0.470914i	−0.0975258	+	0.0354965i
$177$	−18.2911	+	15.3481i	−1.37484	+	1.15363i
$178$	6.03699	+	10.4564i	0.452492	+	0.783739i
$179$	−9.04557	+	15.6674i	−0.676098	+	1.17104i	0.300049	+	0.953924i	$0.402997\pi$
$179$	−9.04557	+	15.6674i	−0.676098	+	1.17104i	−0.976147	+	0.217112i	$0.930336\pi$
$180$		0			0
$181$	−3.48949	−	19.7899i	−0.259371	−	1.47097i	−0.784597	−	0.620006i	$-0.787130\pi$
$181$	−3.48949	−	19.7899i	−0.259371	−	1.47097i	0.525226	−	0.850963i	$-0.323981\pi$
$182$	−7.80430	+	13.5174i	−0.578493	+	1.00198i
$183$	22.8958	+	39.6566i	1.69250	+	2.93150i
$184$	1.22348	−	1.02662i	0.0901962	−	0.0756836i
$185$		0			0
$186$	19.5142	+	7.10258i	1.43085	+	0.520786i
$187$	−5.59173	−	4.69202i	−0.408908	−	0.343114i
$188$	0.425657	−	2.41402i	0.0310442	−	0.176061i
$189$	−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	$0.585479\pi$
$192$	0.514782	−	2.91947i	0.0371512	−	0.210695i
$193$	−19.6814	−	16.5147i	−1.41670	−	1.18875i	−0.953079	−	0.302720i	$-0.902105\pi$
$193$	−19.6814	−	16.5147i	−1.41670	−	1.18875i	−0.463622	−	0.886033i	$-0.653450\pi$
$194$	−8.60563	−	3.13219i	−0.617848	−	0.224878i
$195$		0			0
$196$	1.11995	−	0.939748i	0.0799963	−	0.0671248i
$197$	6.59085	+	11.4157i	0.469579	+	0.813334i	0.999395	−	0.0347781i	$-0.0110724\pi$
$197$	6.59085	+	11.4157i	0.469579	+	0.813334i	−0.529816	+	0.848112i	$0.677739\pi$
$198$	3.98487	−	6.90199i	0.283192	−	0.490503i
$199$	1.78833	+	10.1421i	0.126771	+	0.718957i	0.980240	+	0.197812i	$0.0633836\pi$
$199$	1.78833	+	10.1421i	0.126771	+	0.718957i	−0.853468	+	0.521144i	$0.825505\pi$
$200$		0			0
$201$	15.1883	−	26.3069i	1.07130	−	1.85555i
$202$	2.47296	+	4.28329i	0.173997	+	0.301371i
$203$	5.28035	−	4.43074i	0.370608	−	0.310977i
$204$	14.7687	−	5.37535i	1.03401	−	0.376350i
$205$		0			0
$206$	4.21931	+	3.54042i	0.293973	+	0.246673i
$207$	−1.60534	+	9.10434i	−0.111579	+	0.632795i
$208$	5.36572			0.372046
$209$	3.01285	+	5.19056i	0.208403	+	0.359039i
$210$		0			0
$211$	−2.74895	+	15.5901i	−0.189245	+	1.07326i	0.731133	+	0.682235i	$0.238992\pi$
$211$	−2.74895	+	15.5901i	−0.189245	+	1.07326i	−0.920379	+	0.391029i	$0.872119\pi$
$212$	−8.14168	−	6.83168i	−0.559173	−	0.469202i
$213$	−7.01810	−	2.55438i	−0.480873	−	0.175023i
$214$	5.90056	−	2.14763i	0.403354	−	0.146809i
$215$		0			0
$216$	4.13303	+	7.15861i	0.281217	+	0.487082i
$217$	10.1887	−	17.6473i	0.691652	−	1.19798i
$218$	−0.950839	−	5.39247i	−0.0643989	−	0.365224i
$219$	−3.50392	−	19.8717i	−0.236773	−	1.34281i
$220$		0			0
$221$	14.2233	+	24.6355i	0.956762	+	1.65716i
$222$	18.8746	−	15.8377i	1.26678	−	1.06296i
$223$	−3.08806	+	1.12396i	−0.206792	+	0.0752660i	−0.443339	−	0.896354i	$-0.646206\pi$
$223$	−3.08806	+	1.12396i	−0.206792	+	0.0752660i	0.236548	+	0.971620i	$0.423984\pi$
$224$	−2.73352	−	0.994919i	−0.182641	−	0.0664758i
$225$		0			0
$226$	0.587497	−	3.33186i	0.0390797	−	0.221632i
$227$	11.8147			0.784172			0.392086	−	0.919928i	$-0.371754\pi$
$227$	11.8147			0.784172			0.392086	+	0.919928i	$0.371754\pi$
$228$	−12.9220	+	0.0299760i	−0.855779	+	0.00198521i
$229$	−11.9186			−0.787604			−0.393802	−	0.919195i	$-0.628840\pi$
$229$	−11.9186			−0.787604			−0.393802	+	0.919195i	$0.628840\pi$
$230$		0			0
$231$	−9.09564	−	7.63215i	−0.598450	−	0.502159i
$232$	−2.22668	−	0.810446i	−0.146189	−	0.0532084i
$233$	8.63049	−	3.14124i	0.565402	−	0.205790i	−0.0434743	−	0.999055i	$-0.513843\pi$
$233$	8.63049	−	3.14124i	0.565402	−	0.205790i	0.608877	+	0.793265i	$0.291620\pi$
$234$	−23.7923	+	19.9641i	−1.55535	+	1.30509i
$235$		0			0
$236$	4.02719	−	6.97531i	0.262148	−	0.454054i
$237$	−4.24154	−	24.0550i	−0.275518	−	1.56254i
$238$	−2.67799	−	15.1876i	−0.173588	−	0.984467i
$239$	−2.70456	+	4.68443i	−0.174943	+	0.303011i	−0.940142	−	0.340784i	$-0.889308\pi$
$239$	−2.70456	+	4.68443i	−0.174943	+	0.303011i	0.765198	+	0.643795i	$0.222641\pi$
$240$		0			0
$241$	20.3709	−	17.0932i	1.31221	−	1.10107i	0.324311	−	0.945951i	$-0.394868\pi$
$241$	20.3709	−	17.0932i	1.31221	−	1.10107i	0.987895	−	0.155121i	$-0.0495768\pi$
$242$	−8.55520	+	3.11384i	−0.549949	+	0.200165i
$243$	3.41305	+	1.24225i	0.218947	+	0.0796902i
$244$	−11.8328	−	9.92886i	−0.757515	−	0.635630i
$245$		0			0
$246$	27.6116			1.76045
$247$	−4.11481	−	23.0238i	−0.261819	−	1.46497i
$248$	−7.00505			−0.444821
$249$	−0.249510	+	1.41504i	−0.0158121	+	0.0896748i
$250$		0			0
$251$	1.42144	+	0.517363i	0.0897206	+	0.0326556i	0.386490	−	0.922293i	$-0.373687\pi$
$251$	1.42144	+	0.517363i	0.0897206	+	0.0326556i	−0.296770	+	0.954949i	$0.595909\pi$
$252$	15.8225	−	5.75893i	0.996725	−	0.362778i
$253$	−1.68456	+	1.41352i	−0.105908	+	0.0888670i
$254$	−4.10011	−	7.10160i	−0.257264	−	0.445594i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	1.19184	+	6.75923i	0.0743446	+	0.421629i	0.999151	+	0.0411918i	$0.0131155\pi$
$257$	1.19184	+	6.75923i	0.0743446	+	0.421629i	−0.924807	+	0.380438i	$0.875773\pi$
$258$	8.65842	−	14.9968i	0.539050	−	0.933662i
$259$	−12.0886	−	20.9382i	−0.751152	−	1.30103i
$260$		0			0
$261$	12.8888	−	4.69113i	0.797795	−	0.290374i
$262$	17.9124	+	6.51958i	1.10663	+	0.402781i
$263$	15.7216	+	13.1920i	0.969437	+	0.813454i	0.982462	−	0.186461i	$-0.0597017\pi$
$263$	15.7216	+	13.1920i	0.969437	+	0.813454i	−0.0130252	+	0.999915i	$0.504146\pi$
$264$	−0.708783	+	4.01971i	−0.0436226	+	0.247396i
$265$		0			0
$266$	−2.17285	+	12.4923i	−0.133226	+	0.765949i
$267$	35.7935			2.19053
$268$	−1.77933	+	10.0911i	−0.108690	+	0.616411i
$269$	13.4461	+	11.2826i	0.819824	+	0.687914i	0.952931	−	0.303188i	$-0.0980509\pi$
$269$	13.4461	+	11.2826i	0.819824	+	0.687914i	−0.133107	+	0.991102i	$0.542495\pi$
$270$		0			0
$271$	−8.16550	+	2.97200i	−0.496019	+	0.180536i	−0.577902	−	0.816106i	$-0.696129\pi$
$271$	−8.16550	+	2.97200i	−0.496019	+	0.180536i	0.0818838	+	0.996642i	$0.473906\pi$
$272$	−4.06122	+	3.40777i	−0.246247	+	0.206626i
$273$	23.1360	+	40.0727i	1.40025	+	2.42531i
$274$	−6.28797	+	10.8911i	−0.379870	+	0.657955i
$275$		0			0
$276$	−0.822180	−	4.66281i	−0.0494894	−	0.280668i
$277$	4.11052	−	7.11964i	0.246977	−	0.427778i	−0.715708	−	0.698399i	$-0.753896\pi$
$277$	4.11052	−	7.11964i	0.246977	−	0.427778i	0.962686	+	0.270622i	$0.0872293\pi$
$278$	4.34039	+	7.51777i	0.260319	+	0.450886i
$279$	31.0612	−	26.0635i	1.85959	−	1.56038i
$280$		0			0
$281$	−15.2981	−	5.56805i	−0.912608	−	0.332162i	−0.157314	−	0.987549i	$-0.550284\pi$
$281$	−15.2981	−	5.56805i	−0.912608	−	0.332162i	−0.755294	+	0.655387i	$0.772506\pi$
$282$	−5.56669	−	4.67100i	−0.331491	−	0.278154i
$283$	1.08544	−	6.15584i	0.0645228	−	0.365927i	−0.935401	−	0.353588i	$-0.884961\pi$
$283$	1.08544	−	6.15584i	0.0645228	−	0.365927i	0.999924	−	0.0123385i	$-0.00392756\pi$
$284$	2.51930			0.149493
$285$		0			0
$286$	−7.38785			−0.436853
$287$	4.70484	−	26.6825i	0.277718	−	1.57502i
$288$	−4.43412	−	3.72067i	−0.261283	−	0.219243i
$289$	−10.4365	−	3.79859i	−0.613914	−	0.223447i
$290$		0			0
$291$	−20.7972	+	17.4509i	−1.21915	+	1.02299i
$292$	3.40330	+	5.89470i	0.199163	+	0.344961i
$293$	7.60497	−	13.1722i	0.444287	−	0.769528i	−0.553715	−	0.832706i	$-0.686790\pi$
$293$	7.60497	−	13.1722i	0.444287	−	0.769528i	0.998002	+	0.0631781i	$0.0201236\pi$
$294$	−0.752605	−	4.26824i	−0.0438928	−	0.248929i
$295$		0			0
$296$	−4.15567	+	7.19784i	−0.241544	+	0.418366i
$297$	−5.69060	−	9.85641i	−0.330202	−	0.571927i
$298$	−12.5465	+	10.5278i	−0.726798	+	0.609856i
$299$	8.05299	−	2.93105i	0.465716	−	0.169507i
$300$		0			0
$301$	−13.0168	−	10.9224i	−0.750278	−	0.629558i
$302$	−2.23736	+	12.6887i	−0.128746	+	0.730154i
$303$	14.6622			0.842324
$304$	4.09256	−	1.50033i	0.234724	−	0.0860498i
$305$		0			0
$306$	5.32876	−	30.2209i	0.304625	−	1.72761i
$307$	0.497498	+	0.417451i	0.0283937	+	0.0238252i	0.656874	−	0.754000i	$-0.271878\pi$
$307$	0.497498	+	0.417451i	0.0283937	+	0.0238252i	−0.628480	+	0.777825i	$0.716323\pi$
$308$	3.76367	+	1.36987i	0.214455	+	0.0780553i
$309$	15.3436	−	5.58461i	0.872866	−	0.317697i
$310$		0			0
$311$	−5.79261	−	10.0331i	−0.328469	−	0.568924i	0.653740	−	0.756720i	$-0.273199\pi$
$311$	−5.79261	−	10.0331i	−0.328469	−	0.568924i	−0.982208	+	0.187795i	$0.939866\pi$
$312$	7.95337	−	13.7756i	0.450271	−	0.779892i
$313$	0.109436	+	0.620641i	0.00618568	+	0.0350807i	0.987744	−	0.156080i	$-0.0498859\pi$
$313$	0.109436	+	0.620641i	0.00618568	+	0.0350807i	−0.981559	+	0.191161i	$0.938775\pi$
$314$	2.84611	+	16.1411i	0.160615	+	0.910894i
$315$		0			0
$316$	4.11974	+	7.13560i	0.231754	+	0.401409i
$317$	−7.13509	+	5.98705i	−0.400746	+	0.336266i	−0.820782	−	0.571241i	$-0.806462\pi$
$317$	−7.13509	+	5.98705i	−0.400746	+	0.336266i	0.420036	+	0.907508i	$0.362018\pi$
$318$	−29.6073	+	10.7762i	−1.66030	+	0.604298i
$319$	3.06583	+	1.11587i	0.171654	+	0.0624768i
$320$		0			0
$321$	3.23244	−	18.3321i	0.180417	−	1.02320i
$322$	−4.64600			−0.258912
$323$	17.7368	+	14.8130i	0.986904	+	0.824217i
$324$	7.13982			0.396656
$325$		0			0
$326$	−3.12599	−	2.62302i	−0.173132	−	0.145275i
$327$	−15.2537	−	5.55190i	−0.843533	−	0.307021i
$328$	−8.75234	+	3.18559i	−0.483267	+	0.175895i
$329$	−5.46235	+	4.58346i	−0.301149	+	0.252694i
$330$		0			0
$331$	6.03292	−	10.4493i	0.331599	−	0.574347i	−0.651226	−	0.758884i	$-0.725745\pi$
$331$	6.03292	−	10.4493i	0.331599	−	0.574347i	0.982826	+	0.184537i	$0.0590784\pi$
$332$	−0.0841657	−	0.477328i	−0.00461920	−	0.0261968i
$333$	−8.35402	−	47.3780i	−0.457797	−	2.59630i
$334$	7.92536	−	13.7271i	0.433657	−	0.751115i
$335$		0			0
$336$	−6.60607	+	5.54315i	−0.360391	+	0.302404i
$337$	−1.05903	+	0.385456i	−0.0576891	+	0.0209971i	−0.370704	−	0.928751i	$-0.620883\pi$
$337$	−1.05903	+	0.385456i	−0.0576891	+	0.0209971i	0.313014	+	0.949748i	$0.398661\pi$
$338$	14.8386	+	5.40082i	0.807115	+	0.293766i
$339$	−7.68321	−	6.44698i	−0.417295	−	0.350152i
$340$		0			0
$341$	9.64498			0.522305
$342$	−12.5647	+	21.8797i	−0.679419	+	1.18312i
$343$	16.1098			0.869847
$344$	−1.01435	+	5.75264i	−0.0546898	+	0.310161i
$345$		0			0
$346$	−2.27769	−	0.829012i	−0.122450	−	0.0445680i
$347$	−12.0942	+	4.40192i	−0.649250	+	0.236308i	−0.645588	−	0.763686i	$-0.723388\pi$
$347$	−12.0942	+	4.40192i	−0.649250	+	0.236308i	−0.00366167	+	0.999993i	$0.501166\pi$
$348$	−5.38121	+	4.51537i	−0.288463	+	0.242049i
$349$	4.18866	+	7.25497i	0.224214	+	0.388350i	0.956083	−	0.293095i	$-0.0946853\pi$
$349$	4.18866	+	7.25497i	0.224214	+	0.388350i	−0.731870	+	0.681445i	$0.761352\pi$
$350$		0			0
$351$	7.70187	+	43.6795i	0.411096	+	2.33144i
$352$	−0.239089	−	1.35594i	−0.0127435	−	0.0722720i
$353$	−7.55163	+	13.0798i	−0.401933	+	0.696168i	−0.993959	−	0.109751i	$-0.964995\pi$
$353$	−7.55163	+	13.0798i	−0.401933	+	0.696168i	0.592027	+	0.805918i	$0.298328\pi$
$354$	−11.9387	−	20.6784i	−0.634533	−	1.09904i
$355$		0			0
$356$	−11.3458	+	4.12955i	−0.601328	+	0.218866i
$357$	−42.9613	−	15.6366i	−2.27375	−	0.827579i
$358$	−13.8586	−	11.6288i	−0.732451	−	0.614599i
$359$	−5.84746	+	33.1626i	−0.308617	+	1.75025i	0.297353	+	0.954768i	$0.403896\pi$
$359$	−5.84746	+	33.1626i	−0.308617	+	1.75025i	−0.605970	+	0.795487i	$0.707215\pi$
$360$		0			0
$361$	−9.57624	−	16.4102i	−0.504013	−	0.863696i
$362$	20.0951			1.05618
$363$	−4.68671	+	26.5796i	−0.245988	+	1.39507i
$364$	−11.9569	−	10.0330i	−0.626711	−	0.525873i
$365$		0			0
$366$	−43.0300	+	15.6616i	−2.24921	+	0.818646i
$367$	3.22119	−	2.70290i	0.168145	−	0.141090i	−0.554832	−	0.831962i	$-0.687218\pi$
$367$	3.22119	−	2.70290i	0.168145	−	0.141090i	0.722977	+	0.690872i	$0.242773\pi$
$368$	0.798570	+	1.38316i	0.0416284	+	0.0721024i
$369$	26.9564	−	46.6898i	1.40329	−	2.43058i
$370$		0			0
$371$	5.36867	+	30.4472i	0.278727	+	1.58074i
$372$	−10.3833	+	17.9844i	−0.538348	+	0.932446i
$373$	2.67805	+	4.63852i	0.138664	+	0.240173i	0.926991	−	0.375083i	$-0.122386\pi$
$373$	2.67805	+	4.63852i	0.138664	+	0.240173i	−0.788327	+	0.615256i	$0.789052\pi$
$374$	5.59173	−	4.69202i	0.289141	−	0.242618i
$375$		0			0
$376$	2.30343	+	0.838381i	0.118790	+	0.0432362i
$377$	−9.73989	−	8.17274i	−0.501630	−	0.420918i
$378$	4.17546	−	23.6802i	0.214763	−	1.21798i
$379$	−5.86331			−0.301178			−0.150589	−	0.988596i	$-0.548117\pi$
$379$	−5.86331			−0.301178			−0.150589	+	0.988596i	$0.548117\pi$
$380$		0			0
$381$	−24.3097			−1.24542
$382$	1.27349	−	7.22230i	0.0651572	−	0.369525i
$383$	−22.1962	−	18.6249i	−1.13418	−	0.951686i	−0.134942	−	0.990853i	$-0.543085\pi$
$383$	−22.1962	−	18.6249i	−1.13418	−	0.951686i	−0.999233	+	0.0391675i	$0.987529\pi$
$384$	2.78573	+	1.01392i	0.142159	+	0.0517415i
$385$		0			0
$386$	19.6814	−	16.5147i	1.00176	−	0.840576i
$387$	−16.9059	−	29.2819i	−0.859377	−	1.48848i
$388$	4.57896	−	7.93099i	0.232461	−	0.402635i
$389$	−0.653743	−	3.70756i	−0.0331461	−	0.187981i	0.963739	−	0.266846i	$-0.0859815\pi$
$389$	−0.653743	−	3.70756i	−0.0331461	−	0.187981i	−0.996885	+	0.0788651i	$0.974870\pi$
$390$		0			0
$391$	−4.23365	+	7.33290i	−0.214105	+	0.370841i
$392$	0.730994	+	1.26612i	0.0369208	+	0.0639487i
$393$	43.2888	−	36.3236i	2.18363	−	1.83228i
$394$	−12.3868	+	4.50841i	−0.624036	+	0.227130i
$395$		0			0
$396$	6.10517	+	5.12284i	0.306796	+	0.257433i
$397$	−3.28244	+	18.6157i	−0.164741	+	0.934293i	0.784590	+	0.620015i	$0.212874\pi$
$397$	−3.28244	+	18.6157i	−0.164741	+	0.934293i	−0.949331	+	0.314278i	$0.898238\pi$
$398$	−10.2986			−0.516222
$399$	28.8512	+	24.0952i	1.44437	+	1.20627i
$400$		0			0
$401$	2.11371	−	11.9874i	0.105554	−	0.598624i	−0.885444	−	0.464746i	$-0.846146\pi$
$401$	2.11371	−	11.9874i	0.105554	−	0.598624i	0.990998	−	0.133878i	$-0.0427431\pi$
$402$	23.2698	+	19.5257i	1.16059	+	0.973854i
$403$	−35.3203	−	12.8556i	−1.75943	−	0.640381i
$404$	−4.64764	+	1.69160i	−0.231229	+	0.0841605i
$405$		0			0
$406$	3.44650	+	5.96952i	0.171047	+	0.296262i
$407$	5.72179	−	9.91042i	0.283618	−	0.491241i
$408$	2.72914	+	15.4777i	0.135113	+	0.766261i
$409$	−4.90892	−	27.8399i	−0.242731	−	1.37659i	−0.825705	−	0.564103i	$-0.809222\pi$
$409$	−4.90892	−	27.8399i	−0.242731	−	1.37659i	0.582974	−	0.812491i	$-0.301889\pi$
$410$		0			0
$411$	18.6408	+	32.2868i	0.919482	+	1.59259i
$412$	−4.21931	+	3.54042i	−0.207870	+	0.174424i
$413$	−22.0168	+	8.01347i	−1.08338	+	0.394317i
$414$	−8.68726	−	3.16190i	−0.426955	−	0.155399i
$415$		0			0
$416$	−0.931747	+	5.28420i	−0.0456827	+	0.259079i
$417$	25.7343			1.26021
$418$	−5.63488	+	2.06574i	−0.275611	+	0.101039i
$419$	−11.5301			−0.563284			−0.281642	−	0.959520i	$-0.590879\pi$
$419$	−11.5301			−0.563284			−0.281642	+	0.959520i	$0.590879\pi$
$420$		0			0
$421$	−15.9361	−	13.3719i	−0.776676	−	0.651709i	0.165733	−	0.986171i	$-0.447001\pi$
$421$	−15.9361	−	13.3719i	−0.776676	−	0.651709i	−0.942409	+	0.334462i	$0.891445\pi$
$422$	−14.8759	−	5.41437i	−0.724145	−	0.263567i
$423$	−13.3330	+	4.85283i	−0.648274	+	0.235953i
$424$	8.14168	−	6.83168i	0.395395	−	0.331776i
$425$		0			0
$426$	3.73426	−	6.46792i	0.180925	−	0.313372i
$427$	7.80258	+	44.2506i	0.377593	+	2.14144i
$428$	1.09038	+	6.18385i	0.0527055	+	0.298908i
$429$	−10.9507	+	18.9671i	−0.528704	+	0.915742i
$430$		0			0
$431$	2.06480	−	1.73257i	0.0994578	−	0.0834550i	−0.591703	−	0.806156i	$-0.701544\pi$
$431$	2.06480	−	1.73257i	0.0994578	−	0.0834550i	0.691161	+	0.722701i	$0.257100\pi$
$432$	−7.76755	+	2.82716i	−0.373716	+	0.136022i
$433$	−28.8221	−	10.4904i	−1.38510	−	0.504135i	−0.461380	−	0.887203i	$-0.652645\pi$
$433$	−28.8221	−	10.4904i	−1.38510	−	0.504135i	−0.923720	+	0.383068i	$0.874868\pi$
$434$	15.6099	+	13.0983i	0.749301	+	0.628738i
$435$		0			0
$436$	5.47566			0.262237
$437$	5.32263	−	4.48730i	0.254616	−	0.214657i
$438$	20.1783			0.964155
$439$	−4.34601	+	24.6474i	−0.207424	+	1.17636i	0.686156	+	0.727454i	$0.259297\pi$
$439$	−4.34601	+	24.6474i	−0.207424	+	1.17636i	−0.893580	+	0.448904i	$0.851815\pi$
$440$		0			0
$441$	−7.95213	−	2.89434i	−0.378673	−	0.137826i
$442$	−26.7310	+	9.72930i	−1.27147	+	0.462776i
$443$	−26.8966	+	22.5689i	−1.27790	+	1.07228i	−0.284367	+	0.958716i	$0.591783\pi$
$443$	−26.8966	+	22.5689i	−1.27790	+	1.07228i	−0.993530	+	0.113567i	$0.963772\pi$
$444$	12.3195	+	21.3381i	0.584660	+	1.01266i
$445$		0			0
$446$	−0.570650	−	3.23631i	−0.0270210	−	0.153244i
$447$	8.43124	+	47.8160i	0.398784	+	2.26162i
$448$	1.45447	−	2.51922i	0.0687175	−	0.119022i
$449$	1.27642	+	2.21082i	0.0602380	+	0.104335i	0.894572	−	0.446924i	$-0.147481\pi$
$449$	1.27642	+	2.21082i	0.0602380	+	0.104335i	−0.834334	+	0.551260i	$0.814147\pi$
$450$		0			0
$451$	12.0507	−	4.38611i	0.567448	−	0.206534i
$452$	3.17923	+	1.15714i	0.149538	+	0.0544275i
$453$	29.2600	+	24.5520i	1.37475	+	1.15355i
$454$	−2.05161	+	11.6353i	−0.0962868	+	0.546070i
$455$		0			0
$456$	2.21436	−	12.7309i	0.103697	−	0.596177i
$457$	−29.0079			−1.35693			−0.678467	−	0.734631i	$-0.737355\pi$
$457$	−29.0079			−1.35693			−0.678467	+	0.734631i	$0.737355\pi$
$458$	2.06964	−	11.7375i	0.0967081	−	0.548459i
$459$	−33.5702	−	28.1688i	−1.56692	−	1.31481i
$460$		0			0
$461$	−35.2153	+	12.8173i	−1.64014	+	0.596962i	−0.987064	−	0.160329i	$-0.948745\pi$
$461$	−35.2153	+	12.8173i	−1.64014	+	0.596962i	−0.653077	+	0.757291i	$0.726522\pi$
$462$	9.09564	−	7.63215i	0.423168	−	0.355080i
$463$	−2.21251	−	3.83218i	−0.102824	−	0.178096i	0.810023	−	0.586398i	$-0.199455\pi$
$463$	−2.21251	−	3.83218i	−0.102824	−	0.178096i	−0.912847	+	0.408302i	$0.866121\pi$
$464$	1.18479	−	2.05212i	0.0550026	−	0.0952673i
$465$		0			0
$466$	1.59485	+	9.04485i	0.0738800	+	0.418994i
$467$	−2.16478	+	3.74952i	−0.100174	+	0.173507i	−0.911756	−	0.410732i	$-0.865273\pi$
$467$	−2.16478	+	3.74952i	−0.100174	+	0.173507i	0.811582	+	0.584238i	$0.198607\pi$
$468$	−15.5293	−	26.8975i	−0.717842	−	1.24334i
$469$	22.8337	−	19.1597i	1.05436	−	0.884715i
$470$		0			0
$471$	45.6584	+	16.6183i	2.10383	+	0.765731i
$472$	6.17002	+	5.17726i	0.283998	+	0.238303i
$473$	1.39661	−	7.92058i	0.0642163	−	0.364189i
$474$	24.4260			1.12193
$475$		0			0
$476$	15.4219			0.706862
$477$	−10.6828	+	60.5850i	−0.489130	+	2.77400i
$478$	−4.14362	−	3.47691i	−0.189525	−	0.159030i
$479$	7.03629	+	2.56100i	0.321496	+	0.117015i	0.497727	−	0.867334i	$-0.334168\pi$
$479$	7.03629	+	2.56100i	0.321496	+	0.117015i	−0.176231	+	0.984349i	$0.556390\pi$
$480$		0			0
$481$	−34.1628	+	28.6660i	−1.55769	+	1.30706i
$482$	13.2962	+	23.0296i	0.605624	+	1.04897i
$483$	−6.88657	+	11.9279i	−0.313350	+	0.542737i
$484$	−1.58094	−	8.96594i	−0.0718608	−	0.407543i
$485$		0			0
$486$	−1.81604	+	3.14548i	−0.0823774	+	0.142682i
$487$	8.91410	+	15.4397i	0.403936	+	0.699638i	0.994197	−	0.107575i	$-0.0343084\pi$
$487$	8.91410	+	15.4397i	0.403936	+	0.699638i	−0.590261	+	0.807213i	$0.700975\pi$
$488$	11.8328	−	9.92886i	0.535644	−	0.449458i
$489$	−11.3677	+	4.13750i	−0.514065	+	0.187104i
$490$		0			0
$491$	−9.18783	−	7.70951i	−0.414641	−	0.347925i	0.411479	−	0.911419i	$-0.365012\pi$
$491$	−9.18783	−	7.70951i	−0.414641	−	0.347925i	−0.826120	+	0.563494i	$0.809457\pi$
$492$	−4.79470	+	27.1921i	−0.216162	+	1.22591i
$493$	12.5625			0.565784
$494$	23.3886	−	0.0542561i	1.05230	−	0.00244110i
$495$		0			0
$496$	1.21641	−	6.89863i	0.0546186	−	0.309757i
$497$	−5.61398	−	4.71069i	−0.251821	−	0.211303i
$498$	−1.35022	−	0.491440i	−0.0605048	−	0.0220219i
$499$	6.32111	−	2.30070i	0.282972	−	0.102993i	−0.196635	−	0.980477i	$-0.563001\pi$
$499$	6.32111	−	2.30070i	0.282972	−	0.102993i	0.479607	+	0.877483i	$0.340779\pi$
$500$		0			0
$501$	−23.4948	−	40.6943i	−1.04967	−	1.81809i
$502$	−0.756334	+	1.31001i	−0.0337568	+	0.0584685i
$503$	0.857499	+	4.86312i	0.0382340	+	0.216836i	0.997939	−	0.0641748i	$-0.0204415\pi$
$503$	0.857499	+	4.86312i	0.0382340	+	0.216836i	−0.959705	+	0.281011i	$0.909330\pi$
$504$	2.92388	+	16.5822i	0.130240	+	0.738628i
$505$		0			0
$506$	−1.09952	−	1.90442i	−0.0488796	−	0.0846620i
$507$	35.8604	−	30.0905i	1.59262	−	1.33636i
$508$	7.70569	−	2.80464i	0.341885	−	0.124436i
$509$	−18.1920	−	6.62133i	−0.806345	−	0.293485i	−0.0942316	−	0.995550i	$-0.530039\pi$
$509$	−18.1920	−	6.62133i	−0.806345	−	0.293485i	−0.712113	+	0.702065i	$0.752262\pi$
$510$		0			0
$511$	3.43825	−	19.4993i	0.152099	−	0.862597i
$512$	−1.00000			−0.0441942
$513$	18.0878	+	31.1618i	0.798595	+	1.37583i
$514$	−6.86350			−0.302736
$515$		0			0
$516$	13.2655	+	11.1311i	0.583980	+	0.490017i
$517$	−3.17150	−	1.15433i	−0.139483	−	0.0507675i
$518$	22.7192	−	8.26912i	0.998226	−	0.363324i
$519$	−5.50448	+	4.61881i	−0.241620	+	0.202743i
$520$		0			0
$521$	3.76749	−	6.52549i	0.165057	−	0.285887i	−0.771619	−	0.636085i	$-0.780553\pi$
$521$	3.76749	−	6.52549i	0.165057	−	0.285887i	0.936675	+	0.350199i	$0.113886\pi$
$522$	2.38175	+	13.5076i	0.104246	+	0.591211i
$523$	4.56331	+	25.8798i	0.199539	+	1.13164i	0.905804	+	0.423697i	$0.139268\pi$
$523$	4.56331	+	25.8798i	0.199539	+	1.13164i	−0.706265	+	0.707948i	$0.749621\pi$
$524$	−9.53099	+	16.5082i	−0.416363	+	0.721162i
$525$		0			0
$526$	−15.7216	+	13.1920i	−0.685496	+	0.575199i
$527$	34.8979	−	12.7018i	1.52018	−	0.553299i
$528$	−3.83556	−	1.39603i	−0.166921	−	0.0607544i
$529$	−15.6650	−	13.1445i	−0.681085	−	0.571498i
$530$		0			0
$531$	−46.6215			−2.02320
$532$	−11.9252	−	4.30910i	−0.517021	−	0.186823i
$533$	−49.9765			−2.16472
$534$	−6.21547	+	35.2497i	−0.268970	+	1.52540i
$535$		0			0
$536$	−9.62879	−	3.50459i	−0.415900	−	0.151375i
$537$	−50.3970	+	18.3430i	−2.17479	+	0.791560i
$538$	−13.4461	+	11.2826i	−0.579703	+	0.486429i
$539$	−1.00648	−	1.74327i	−0.0433520	−	0.0750879i
$540$		0			0
$541$	2.24024	+	12.7051i	0.0963156	+	0.546233i	0.994336	+	0.106280i	$0.0338939\pi$
$541$	2.24024	+	12.7051i	0.0963156	+	0.546233i	−0.898021	+	0.439953i	$0.854995\pi$
$542$	−1.50892	−	8.55753i	−0.0648138	−	0.367577i
$543$	29.7862	−	51.5911i	1.27825	−	2.21399i
$544$	−2.65077	−	4.59127i	−0.113651	−	0.196849i
$545$		0			0
$546$	−43.4814	+	15.8259i	−1.86083	+	0.677287i
$547$	−40.0367	−	14.5722i	−1.71185	−	0.623061i	−0.714761	−	0.699369i	$-0.753465\pi$
$547$	−40.0367	−	14.5722i	−1.71185	−	0.623061i	−0.997084	+	0.0763080i	$0.975687\pi$
$548$	−9.63374	−	8.08366i	−0.411533	−	0.345317i
$549$	−15.5259	+	88.0516i	−0.662628	+	3.75795i
$550$		0			0
$551$	−9.71405	−	3.51013i	−0.413832	−	0.149536i
$552$	4.73474			0.201524
$553$	4.16204	−	23.6041i	0.176988	−	1.00375i
$554$	6.29769	+	5.28439i	0.267563	+	0.224512i
$555$		0			0
$556$	−8.15726	+	2.96900i	−0.345945	+	0.125914i
$557$	9.22427	−	7.74009i	0.390845	−	0.327958i	−0.426097	−	0.904677i	$-0.640112\pi$
$557$	9.22427	−	7.74009i	0.390845	−	0.327958i	0.816942	+	0.576719i	$0.195667\pi$
$558$	20.2738	+	35.1152i	0.858258	+	1.48655i
$559$	−15.6716	+	27.1440i	−0.662838	+	1.14807i
$560$		0			0
$561$	−3.75764	−	21.3107i	−0.158648	−	0.899737i
$562$	8.13995	−	14.0988i	0.343363	−	0.594722i
$563$	−22.4230	−	38.8377i	−0.945015	−	1.63681i	−0.755721	−	0.654893i	$-0.772714\pi$
$563$	−22.4230	−	38.8377i	−0.945015	−	1.63681i	−0.189293	−	0.981921i	$-0.560620\pi$
$564$	5.56669	−	4.67100i	0.234400	−	0.196685i
$565$		0			0
$566$	5.87384	+	2.13790i	0.246896	+	0.0898627i
$567$	−15.9103	−	13.3503i	−0.668168	−	0.560660i
$568$	−0.437473	+	2.48103i	−0.0183559	+	0.104102i
$569$	30.1492			1.26392			0.631959	−	0.775002i	$-0.282251\pi$
$569$	30.1492			1.26392			0.631959	+	0.775002i	$0.282251\pi$
$570$		0			0
$571$	3.87066			0.161982			0.0809910	−	0.996715i	$-0.474192\pi$
$571$	3.87066			0.161982			0.0809910	+	0.996715i	$0.474192\pi$
$572$	1.28289	−	7.27561i	0.0536402	−	0.304209i
$573$	−16.6545	−	13.9748i	−0.695751	−	0.583804i
$574$	25.4601	+	9.26672i	1.06268	+	0.386785i
$575$		0			0
$576$	4.43412	−	3.72067i	0.184755	−	0.155028i
$577$	−7.65505	−	13.2589i	−0.318684	−	0.551976i	0.661530	−	0.749919i	$-0.269907\pi$
$577$	−7.65505	−	13.2589i	−0.318684	−	0.551976i	−0.980214	+	0.197942i	$0.936574\pi$
$578$	5.55317	−	9.61837i	0.230981	−	0.400072i
$579$	−13.2259	−	75.0080i	−0.549651	−	3.11723i
$580$		0			0
$581$	−0.704971	+	1.22105i	−0.0292471	+	0.0506575i
$582$	−13.5744	−	23.5115i	−0.562676	−	0.974584i
$583$	−11.2100	+	9.40627i	−0.464269	+	0.389568i
$584$	−6.39612	+	2.32800i	−0.264673	+	0.0963332i
$585$		0			0
$586$	11.6515	+	9.77676i	0.481319	+	0.403874i
$587$	−3.14728	+	17.8491i	−0.129902	+	0.736713i	0.848372	+	0.529400i	$0.177583\pi$
$587$	−3.14728	+	17.8491i	−0.129902	+	0.736713i	−0.978275	+	0.207313i	$0.933528\pi$
$588$	4.33408			0.178735
$589$	−30.5342	+	0.0708324i	−1.25814	+	0.00291860i
$590$		0			0
$591$	−6.78571	+	38.4837i	−0.279127	+	1.58301i
$592$	−6.36686	−	5.34243i	−0.261676	−	0.219573i
$593$	24.7810	+	9.01955i	1.01763	+	0.370389i	0.796360	−	0.604823i	$-0.206756\pi$
$593$	24.7810	+	9.01955i	1.01763	+	0.370389i	0.221275	+	0.975212i	$0.428978\pi$
$594$	10.6948	−	3.89260i	0.438814	−	0.159715i
$595$		0			0
$596$	−8.18914	−	14.1840i	−0.335440	−	0.580999i
$597$	−15.2651	+	26.4400i	−0.624761	+	1.08212i
$598$	1.48813	+	8.43961i	0.0608542	+	0.345121i
$599$	−5.45740	−	30.9505i	−0.222983	−	1.26460i	−0.866503	−	0.499172i	$-0.833637\pi$
$599$	−5.45740	−	30.9505i	−0.222983	−	1.26460i	0.643519	−	0.765430i	$-0.277474\pi$
$600$		0			0
$601$	8.30819	+	14.3902i	0.338898	+	0.586989i	0.984226	−	0.176917i	$-0.0566125\pi$
$601$	8.30819	+	14.3902i	0.338898	+	0.586989i	−0.645328	+	0.763906i	$0.723279\pi$
$602$	13.0168	−	10.9224i	0.530527	−	0.445165i
$603$	55.7347	−	20.2858i	2.26969	−	0.826100i
$604$	−12.1074	−	4.40675i	−0.492645	−	0.179308i
$605$		0			0
$606$	−2.54607	+	14.4395i	−0.103427	+	0.586564i
$607$	4.44153			0.180276			0.0901381	−	0.995929i	$-0.471269\pi$
$607$	4.44153			0.180276			0.0901381	+	0.995929i	$0.471269\pi$
$608$	0.766871	+	4.29091i	0.0311007	+	0.174019i
$609$	20.4344			0.828044
$610$		0			0
$611$	10.0756	+	8.45444i	0.407616	+	0.342030i
$612$	28.8364	+	10.4956i	1.16564	+	0.424260i
$613$	5.10144	−	1.85677i	0.206045	−	0.0749943i	−0.236936	−	0.971525i	$-0.576143\pi$
$613$	5.10144	−	1.85677i	0.206045	−	0.0749943i	0.442981	+	0.896531i	$0.353921\pi$
$614$	−0.497498	+	0.417451i	−0.0200774	+	0.0168469i
$615$		0			0
$616$	−2.00261	+	3.46862i	−0.0806874	+	0.139755i
$617$	−5.33600	−	30.2620i	−0.214819	−	1.21830i	−0.881220	−	0.472707i	$-0.843277\pi$
$617$	−5.33600	−	30.2620i	−0.214819	−	1.21830i	0.666401	−	0.745594i	$-0.267834\pi$
$618$	2.83538	+	16.0802i	0.114056	+	0.646842i
$619$	13.0502	−	22.6035i	0.524530	−	0.908512i	−0.475062	−	0.879952i	$-0.657574\pi$
$619$	13.0502	−	22.6035i	0.524530	−	0.908512i	0.999592	−	0.0285602i	$-0.00909222\pi$
$620$		0			0
$621$	−10.1134	+	8.48611i	−0.405835	+	0.340536i
$622$	10.8865	−	3.96238i	0.436510	−	0.158877i
$623$	33.0045	+	12.0126i	1.32230	+	0.481276i
$624$	12.1853	+	10.2247i	0.487801	+	0.409314i
$625$		0			0
$626$	−0.630216			−0.0251885
$627$	−3.04886	+	17.5286i	−0.121760	+	0.700026i
$628$	−16.3901			−0.654036
$629$	7.65145	−	43.3935i	0.305083	−	1.73021i
$630$		0			0
$631$	39.5529	+	14.3961i	1.57458	+	0.573099i	0.974016	−	0.226479i	$-0.0727215\pi$
$631$	39.5529	+	14.3961i	1.57458	+	0.573099i	0.600562	+	0.799579i	$0.294944\pi$
$632$	−7.74258	+	2.81807i	−0.307983	+	0.112097i
$633$	−35.9504	+	30.1659i	−1.42890	+	1.19899i
$634$	−4.65710	−	8.06633i	−0.184957	−	0.320355i
$635$		0			0
$636$	−5.47121	−	31.0288i	−0.216948	−	1.23037i
$637$	1.36220	+	7.72544i	0.0539725	+	0.306093i
$638$	−1.63129	+	2.82548i	−0.0645836	+	0.111862i
$639$	−7.29129	−	12.6289i	−0.288439	−	0.499591i
$640$		0			0
$641$	−13.5601	+	4.93548i	−0.535592	+	0.194940i	−0.595634	−	0.803256i	$-0.703099\pi$
$641$	−13.5601	+	4.93548i	−0.535592	+	0.194940i	0.0600414	+	0.998196i	$0.480877\pi$
$642$	17.4923	+	6.36667i	0.690365	+	0.251272i
$643$	−19.2098	−	16.1189i	−0.757559	−	0.635667i	0.179931	−	0.983679i	$-0.442412\pi$
$643$	−19.2098	−	16.1189i	−0.757559	−	0.635667i	−0.937490	+	0.348012i	$0.886857\pi$
$644$	0.806770	−	4.57542i	0.0317912	−	0.180297i
$645$		0			0
$646$	−17.6679	+	14.8951i	−0.695135	+	0.586041i
$647$	−25.9344			−1.01959			−0.509793	−	0.860297i	$-0.670278\pi$
$647$	−25.9344			−1.01959			−0.509793	+	0.860297i	$0.670278\pi$
$648$	−1.23982	+	7.03135i	−0.0487046	+	0.276217i
$649$	−8.49526	−	7.12837i	−0.333468	−	0.279813i
$650$		0			0
$651$	56.7658	−	20.6610i	2.22483	−	0.809770i
$652$	3.12599	−	2.62302i	0.122423	−	0.102725i
$653$	−5.89996	−	10.2190i	−0.230883	−	0.399901i	0.727185	−	0.686441i	$-0.240828\pi$
$653$	−5.89996	−	10.2190i	−0.230883	−	0.399901i	−0.958068	+	0.286540i	$0.907495\pi$
$654$	8.11633	−	14.0579i	0.317374	−	0.549708i
$655$		0			0
$656$	−1.61737	−	9.17254i	−0.0631475	−	0.358128i
$657$	19.6995	−	34.1205i	0.768549	−	1.33117i
$658$	−3.56530	−	6.17528i	−0.138990	−	0.240737i
$659$	16.7858	−	14.0849i	0.653880	−	0.548671i	−0.254365	−	0.967108i	$-0.581867\pi$
$659$	16.7858	−	14.0849i	0.653880	−	0.548671i	0.908246	+	0.418438i	$0.137422\pi$
$660$		0			0
$661$	−36.0396	−	13.1173i	−1.40178	−	0.510205i	−0.473072	−	0.881024i	$-0.656855\pi$
$661$	−36.0396	−	13.1173i	−1.40178	−	0.510205i	−0.928705	+	0.370819i	$0.879077\pi$
$662$	9.24297	+	7.75578i	0.359238	+	0.301437i
$663$	−14.6438	+	83.0491i	−0.568718	+	3.22536i
$664$	0.484691			0.0188097
$665$		0			0
$666$	48.1089			1.86418
$667$	0.657182	−	3.72706i	0.0254462	−	0.144313i
$668$	12.1424	+	10.1887i	0.469802	+	0.394211i
$669$	−9.15458	−	3.33199i	−0.353937	−	0.128822i
$670$		0			0
$671$	−16.2921	+	13.6707i	−0.628948	+	0.527750i
$672$	−4.31181	−	7.46827i	−0.166332	−	0.288095i
$673$	−0.679451	+	1.17684i	−0.0261909	+	0.0453640i	−0.878824	−	0.477146i	$-0.841671\pi$
$673$	−0.679451	+	1.17684i	−0.0261909	+	0.0453640i	0.852633	+	0.522510i	$0.175004\pi$
$674$	−0.195701	−	1.10988i	−0.00753812	−	0.0427508i
$675$		0			0
$676$	−7.89547	+	13.6754i	−0.303672	+	0.525975i
$677$	−9.88891	−	17.1281i	−0.380062	−	0.658286i	0.611009	−	0.791624i	$-0.290764\pi$
$677$	−9.88891	−	17.1281i	−0.380062	−	0.658286i	−0.991071	+	0.133338i	$0.957431\pi$
$678$	7.68321	−	6.44698i	0.295072	−	0.247595i
$679$	−25.0333	+	9.11139i	−0.960692	+	0.349663i
$680$		0			0
$681$	26.8307	+	22.5136i	1.02815	+	0.862724i
$682$	−1.67483	+	9.49845i	−0.0641327	+	0.363714i
$683$	−38.4380			−1.47079			−0.735394	−	0.677640i	$-0.763003\pi$
$683$	−38.4380			−1.47079			−0.735394	+	0.677640i	$0.763003\pi$
$684$	−19.3655	−	16.1731i	−0.740457	−	0.618396i
$685$		0			0
$686$	−2.79744	+	15.8651i	−0.106807	+	0.605731i
$687$	−27.0665	−	22.7115i	−1.03265	−	0.866499i
$688$	−5.48910	−	1.99787i	−0.209270	−	0.0761681i
$689$	53.5888	−	19.5047i	2.04157	−	0.743070i
$690$		0			0
$691$	4.00672	+	6.93985i	0.152423	+	0.264004i	0.932118	−	0.362156i	$-0.117959\pi$
$691$	4.00672	+	6.93985i	0.152423	+	0.264004i	−0.779695	+	0.626160i	$0.784626\pi$
$692$	1.21193	−	2.09913i	0.0460708	−	0.0797971i
$693$	−4.02578	−	22.8313i	−0.152927	−	0.867291i
$694$	−2.23492	−	12.6748i	−0.0848362	−	0.481130i
$695$		0			0
$696$	−3.51233	−	6.08354i	−0.133135	−	0.230596i
$697$	37.8263	−	31.7401i	1.43277	−	1.20224i
$698$	−7.87210	+	2.86521i	−0.297963	+	0.108450i
$699$	25.5852	+	9.31225i	0.967721	+	0.352222i
$700$		0			0
$701$	−4.88207	+	27.6876i	−0.184393	+	1.04575i	0.742339	+	0.670025i	$0.233716\pi$
$701$	−4.88207	+	27.6876i	−0.184393	+	1.04575i	−0.926732	+	0.375722i	$0.877395\pi$
$702$	−44.3533			−1.67401
$703$	−18.0413	+	31.4166i	−0.680442	+	1.18490i
$704$	1.37686			0.0518924
$705$		0			0
$706$	−11.5698	−	9.70819i	−0.435434	−	0.365372i
$707$	13.5198	+	4.92079i	0.508463	+	0.185065i
$708$	22.4374	−	8.16653i	0.843248	−	0.306917i
$709$	−25.7736	+	21.6266i	−0.967946	+	0.812204i	−0.982227	−	0.187694i	$-0.939899\pi$
$709$	−25.7736	+	21.6266i	−0.967946	+	0.812204i	0.0142810	+	0.999898i	$0.495454\pi$
$710$		0			0
$711$	23.8464	−	41.3032i	0.894311	−	1.54899i
$712$	−2.09663	−	11.8906i	−0.0785744	−	0.445617i
$713$	−1.94278	−	11.0181i	−0.0727578	−	0.412630i
$714$	22.8592	−	39.5934i	0.855485	−	1.48174i
$715$		0			0
$716$	13.8586	−	11.6288i	0.517921	−	0.434587i
$717$	−15.0683	+	5.48442i	−0.562737	+	0.204820i
$718$	−31.6434	−	11.5172i	−1.18092	−	0.429820i
$719$	−0.633806	−	0.531826i	−0.0236370	−	0.0198338i	0.630893	−	0.775870i	$-0.282689\pi$
$719$	−0.633806	−	0.531826i	−0.0236370	−	0.0198338i	−0.654530	+	0.756036i	$0.727133\pi$
$720$		0			0
$721$	16.0223			0.596700
$722$	17.8238	−	6.58115i	0.663334	−	0.244925i
$723$	78.8333			2.93184
$724$	−3.48949	+	19.7899i	−0.129686	+	0.735484i
$725$		0			0
$726$	−25.3620	−	9.23101i	−0.941272	−	0.342595i
$727$	44.4363	−	16.1735i	1.64805	−	0.599842i	0.659633	−	0.751588i	$-0.270712\pi$
$727$	44.4363	−	16.1735i	1.64805	−	0.599842i	0.988420	+	0.151745i	$0.0484894\pi$
$728$	11.9569	−	10.0330i	0.443152	−	0.371848i
$729$	16.0934	+	27.8746i	0.596052	+	1.03239i
$730$		0			0
$731$	−5.37759	−	30.4978i	−0.198897	−	1.12800i
$732$	−7.95162	−	45.0959i	−0.293900	−	1.66679i
$733$	5.61652	−	9.72810i	0.207451	−	0.359315i	−0.743460	−	0.668780i	$-0.766817\pi$
$733$	5.61652	−	9.72810i	0.207451	−	0.359315i	0.950911	+	0.309465i	$0.100150\pi$
$734$	2.10248	+	3.64161i	0.0776041	+	0.134414i
$735$		0			0
$736$	−1.50082	+	0.546254i	−0.0553210	+	0.0201352i
$737$	13.2575	+	4.82534i	0.488347	+	0.177744i
$738$	41.2996	+	34.6545i	1.52026	+	1.27565i
$739$	4.49255	−	25.4785i	0.165261	−	0.937242i	−0.783534	−	0.621349i	$-0.786585\pi$
$739$	4.49255	−	25.4785i	0.165261	−	0.937242i	0.948795	−	0.315893i	$-0.102304\pi$
$740$		0			0
$741$	34.5286	−	60.1269i	1.26844	−	2.20882i
$742$	−30.9169			−1.13500
$743$	−7.57956	+	42.9858i	−0.278067	+	1.57700i	0.450980	+	0.892534i	$0.351075\pi$
$743$	−7.57956	+	42.9858i	−0.278067	+	1.57700i	−0.729047	+	0.684463i	$0.760037\pi$
$744$	−15.9081	−	13.3485i	−0.583219	−	0.489379i
$745$		0			0
$746$	−5.03309	+	1.83189i	−0.184274	+	0.0670704i
$747$	−2.14918	+	1.80338i	−0.0786344	+	0.0659821i
$748$	3.64974	+	6.32154i	0.133448	+	0.231138i
$749$	9.13300	−	15.8188i	0.333713	−	0.578007i
$750$		0			0
$751$	3.63508	+	20.6156i	0.132646	+	0.752273i	0.976470	+	0.215653i	$0.0691881\pi$
$751$	3.63508	+	20.6156i	0.132646	+	0.752273i	−0.843824	+	0.536620i	$0.819701\pi$
$752$	−1.22563	+	2.12285i	−0.0446941	+	0.0774125i
$753$	2.24216	+	3.88354i	0.0817089	+	0.141524i
$754$	9.73989	−	8.17274i	0.354706	−	0.297634i
$755$		0			0
$756$	22.5954	+	8.22406i	0.821787	+	0.299106i
$757$	−15.1947	−	12.7499i	−0.552262	−	0.463403i	0.323444	−	0.946247i	$-0.395159\pi$
$757$	−15.1947	−	12.7499i	−0.552262	−	0.463403i	−0.875706	+	0.482844i	$0.839604\pi$
$758$	1.01815	−	5.77423i	0.0369810	−	0.209730i
$759$	−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	$0.563071\pi$
$762$	4.22133	−	23.9403i	0.152923	−	0.867267i
$763$	−12.2019	−	10.2386i	−0.441738	−	0.370662i
$764$	6.89144	+	2.50828i	0.249323	+	0.0907463i
$765$		0			0
$766$	22.1962	−	18.6249i	0.801983	−	0.672944i
$767$	21.6088	+	37.4275i	0.780248	+	1.35143i
$768$	−1.48226	+	2.56734i	−0.0534863	+	0.0926410i
$769$	2.51395	+	14.2573i	0.0906553	+	0.514132i	0.995992	+	0.0894380i	$0.0285071\pi$
$769$	2.51395	+	14.2573i	0.0906553	+	0.514132i	−0.905337	+	0.424694i	$0.860382\pi$
$770$		0			0
$771$	−10.1735	+	17.6210i	−0.366389	+	0.634604i
$772$	12.8461	+	22.2502i	0.462343	+	0.800802i
$773$	−27.4218	+	23.0096i	−0.986292	+	0.827597i	−0.985027	−	0.172402i	$-0.944847\pi$
$773$	−27.4218	+	23.0096i	−0.986292	+	0.827597i	−0.00126532	+	0.999999i	$0.500403\pi$
$774$	31.7728	−	11.5643i	1.14205	−	0.415672i
$775$		0			0
$776$	7.01537	+	5.88660i	0.251837	+	0.211317i
$777$	12.4460	−	70.5850i	0.446499	−	2.53222i
$778$	3.76475			0.134973
$779$	−38.1182	+	13.9741i	−1.36573	+	0.500675i
$780$		0			0
$781$	0.602339	−	3.41603i	0.0215534	−	0.122235i
$782$	−6.48633	−	5.44268i	−0.231951	−	0.194630i
$783$	18.4059	+	6.69919i	0.657772	+	0.239409i
$784$	−1.37382	+	0.500029i	−0.0490650	+	0.0178582i
$785$		0			0
$786$	28.2547	+	48.9386i	1.00781	+	1.74558i
$787$	7.16560	−	12.4112i	0.255426	−	0.442411i	−0.709585	−	0.704620i	$-0.751118\pi$
$787$	7.16560	−	12.4112i	0.255426	−	0.442411i	0.965011	+	0.262209i	$0.0844510\pi$
$788$	−2.28898	−	12.9814i	−0.0815415	−	0.462445i
$789$	10.5649	+	59.9168i	0.376122	+	2.13309i
$790$		0			0
$791$	−4.92087	−	8.52320i	−0.174966	−	0.303050i
$792$	−6.10517	+	5.12284i	−0.216938	+	0.182032i
$793$	77.8835	−	28.3473i	2.76573	−	1.00664i
$794$	−17.7629	−	6.46515i	−0.630380	−	0.229440i
$795$		0			0
$796$	1.78833	−	10.1421i	0.0633857	−	0.359478i
$797$	17.7667			0.629330			0.314665	−	0.949203i	$-0.398108\pi$
$797$	17.7667			0.629330			0.314665	+	0.949203i	$0.398108\pi$
$798$	−28.7391	+	24.2288i	−1.01735	+	0.857690i
$799$	−12.9955			−0.459746
$800$		0			0
$801$	53.5375	+	44.9233i	1.89166	+	1.58729i
$802$	11.4383	+	4.16319i	0.403900	+	0.147007i
$803$	8.80657	−	3.20533i	0.310777	−	0.113114i
$804$	−23.2698	+	19.5257i	−0.820664	+	0.688619i
$805$		0			0
$806$	18.7936	−	32.5514i	0.661975	−	1.14657i
$807$	9.03580	+	51.2445i	0.318075	+	1.80389i
$808$	−0.858850	−	4.87078i	−0.0302142	−	0.171353i
$809$	5.86927	−	10.1659i	0.206353	−	0.357413i	−0.744210	−	0.667946i	$-0.767174\pi$
$809$	5.86927	−	10.1659i	0.206353	−	0.357413i	0.950563	+	0.310532i	$0.100507\pi$
$810$		0			0
$811$	−8.28725	+	6.95383i	−0.291005	+	0.244182i	−0.776588	−	0.630008i	$-0.783052\pi$
$811$	−8.28725	+	6.95383i	−0.291005	+	0.244182i	0.485584	+	0.874190i	$0.338607\pi$
$812$	−6.47730	+	2.35755i	−0.227309	+	0.0827336i
$813$	−24.2067	−	8.81052i	−0.848967	−	0.308999i
$814$	8.76628	+	7.35579i	0.307258	+	0.257820i
$815$		0			0
$816$	−15.7165			−0.550187
$817$	−4.36325	+	25.0854i	−0.152651	+	0.877625i
$818$	28.2694			0.988415
$819$	−15.6887	+	88.9753i	−0.548209	+	3.10905i
$820$		0			0
$821$	12.0721	+	4.39387i	0.421318	+	0.153347i	0.543974	−	0.839102i	$-0.316919\pi$
$821$	12.0721	+	4.39387i	0.421318	+	0.153347i	−0.122656	+	0.992449i	$0.539141\pi$
$822$	−35.0332	+	12.7510i	−1.22192	+	0.444744i
$823$	8.70130	−	7.30126i	0.303308	−	0.254506i	−0.478411	−	0.878136i	$-0.658787\pi$
$823$	8.70130	−	7.30126i	0.303308	−	0.254506i	0.781720	+	0.623630i	$0.214343\pi$
$824$	−2.75396	−	4.77000i	−0.0959387	−	0.166171i
$825$		0			0
$826$	−4.06854	−	23.0739i	−0.141563	−	0.802842i
$827$	4.53285	+	25.7071i	0.157623	+	0.893923i	0.956349	+	0.292228i	$0.0943966\pi$
$827$	4.53285	+	25.7071i	0.157623	+	0.893923i	−0.798726	+	0.601695i	$0.794492\pi$
$828$	4.62239	−	8.00622i	0.160639	−	0.278235i
$829$	12.3906	+	21.4611i	0.430342	+	0.745374i	0.996903	−	0.0786462i	$-0.0250597\pi$
$829$	12.3906	+	21.4611i	0.430342	+	0.745374i	−0.566561	+	0.824020i	$0.691726\pi$
$830$		0			0
$831$	22.9016	−	8.33551i	0.794449	−	0.289156i
$832$	−5.04213	−	1.83518i	−0.174804	−	0.0636236i
$833$	−5.93745	−	4.98211i	−0.205720	−	0.172620i
$834$	−4.46871	+	25.3433i	−0.154739	+	0.877567i
$835$		0			0
$836$	−1.05587	−	5.90799i	−0.0365182	−	0.204332i
$837$	57.9041			2.00146
$838$	2.00219	−	11.3550i	0.0691644	−	0.392251i
$839$	−24.0765	−	20.2026i	−0.831214	−	0.697472i	0.124355	−	0.992238i	$-0.460314\pi$
$839$	−24.0765	−	20.2026i	−0.831214	−	0.697472i	−0.955569	+	0.294766i	$0.904758\pi$
$840$		0			0
$841$	21.9748	−	7.99816i	0.757751	−	0.275799i
$842$	15.9361	−	13.3719i	0.549193	−	0.460828i
$843$	−24.1310	−	41.7961i	−0.831115	−	1.43953i
$844$	7.91528	−	13.7097i	0.272455	−	0.471906i
$845$		0			0
$846$	−2.46385	−	13.9732i	−0.0847087	−	0.480407i
$847$	−13.2419	+	22.9357i	−0.454997	+	0.788079i
$848$	5.31410	+	9.20430i	0.182487	+	0.316077i
$849$	14.1953	−	11.9112i	0.487180	−	0.408793i
$850$		0			0
$851$	−12.4739	−	4.54011i	−0.427598	−	0.155633i
$852$	5.72121	+	4.80067i	0.196005	+	0.164468i
$853$	6.98190	−	39.5963i	0.239056	−	1.35575i	−0.594846	−	0.803840i	$-0.702787\pi$
$853$	6.98190	−	39.5963i	0.239056	−	1.35575i	0.833902	−	0.551913i	$-0.186102\pi$
$854$	−44.9333			−1.53759
$855$		0			0
$856$	−6.27924			−0.214620
$857$	0.829384	−	4.70367i	0.0283312	−	0.160674i	−0.967360	−	0.253407i	$-0.918449\pi$
$857$	0.829384	−	4.70367i	0.0283312	−	0.160674i	0.995691	+	0.0927323i	$0.0295601\pi$
$858$	−16.7774	−	14.0779i	−0.572772	−	0.480613i
$859$	9.73955	+	3.54491i	0.332309	+	0.120951i	0.502786	−	0.864411i	$-0.332308\pi$
$859$	9.73955	+	3.54491i	0.332309	+	0.120951i	−0.170476	+	0.985362i	$0.554531\pi$
$860$		0			0
$861$	61.5292	−	51.6292i	2.09691	−	1.75952i
$862$	1.34770	+	2.33429i	0.0459029	+	0.0795061i
$863$	−15.8545	+	27.4609i	−0.539695	+	0.934779i	0.459225	+	0.888320i	$0.348127\pi$
$863$	−15.8545	+	27.4609i	−0.539695	+	0.934779i	−0.998920	+	0.0464590i	$0.985206\pi$
$864$	−1.43539	−	8.14047i	−0.0488328	−	0.276945i
$865$		0			0
$866$	15.3359	−	26.5626i	0.521135	−	0.902632i
$867$	−16.4624	−	28.5138i	−0.559094	−	0.968379i
$868$	−15.6099	+	13.0983i	−0.529836	+	0.444585i
$869$	10.6605	−	3.88009i	0.361631	−	0.131623i
$870$		0			0
$871$	−42.1180	−	35.3412i	−1.42711	−	1.19749i
$872$	−0.950839	+	5.39247i	−0.0321995	+	0.182612i
$873$	−53.0091			−1.79409
$874$	3.49486	+	6.02098i	0.118216	+	0.203663i
$875$		0			0
$876$	−3.50392	+	19.8717i	−0.118387	+	0.671403i
$877$	4.82600	+	4.04949i	0.162962	+	0.136742i	0.720622	−	0.693328i	$-0.243856\pi$
$877$	4.82600	+	4.04949i	0.162962	+	0.136742i	−0.557660	+	0.830070i	$0.688301\pi$
$878$	−23.5183	−	8.55996i	−0.793705	−	0.288885i
$879$	42.3708	−	15.4217i	1.42913	−	0.520162i
$880$		0			0
$881$	−26.9351	−	46.6530i	−0.907468	−	1.57178i	−0.817570	−	0.575830i	$-0.804679\pi$
$881$	−26.9351	−	46.6530i	−0.907468	−	1.57178i	−0.0898984	−	0.995951i	$-0.528654\pi$
$882$	4.23124	−	7.32872i	0.142473	−	0.246771i
$883$	0.342590	+	1.94292i	0.0115291	+	0.0653846i	0.990030	−	0.140860i	$-0.0449868\pi$
$883$	0.342590	+	1.94292i	0.0115291	+	0.0653846i	−0.978500	+	0.206245i	$0.933876\pi$
$884$	−4.93970	−	28.0144i	−0.166140	−	0.942227i
$885$		0			0
$886$	−17.5555	−	30.4071i	−0.589789	−	1.02155i
$887$	−20.6876	+	17.3589i	−0.694621	+	0.582856i	−0.920238	−	0.391360i	$-0.872005\pi$
$887$	−20.6876	+	17.3589i	−0.694621	+	0.582856i	0.225617	+	0.974216i	$0.427560\pi$
$888$	−23.1532	+	8.42707i	−0.776970	+	0.282794i
$889$	−22.4155	−	8.15856i	−0.751790	−	0.273629i
$890$		0			0
$891$	1.70705	−	9.68119i	0.0571885	−	0.324332i
$892$	3.28624			0.110031
$893$	10.0489	+	3.63111i	0.336273	+	0.121511i
$894$	−48.5536			−1.62388
$895$		0			0
$896$	2.22838	+	1.86984i	0.0744451	+	0.0624669i
$897$	23.8732	+	8.68913i	0.797102	+	0.290121i
$898$	−2.39888	+	0.873122i	−0.0800518	+	0.0291365i
$899$	−12.7156	+	10.6697i	−0.424090	+	0.355853i
$900$		0			0
$901$	−28.1729	+	48.7970i	−0.938577	+	1.62566i
$902$	2.22689	+	12.6293i	0.0741473	+	0.420510i
$903$	−8.74733	−	49.6085i	−0.291093	−	1.65087i
$904$	−1.69163	+	2.92999i	−0.0562628	+	0.0974501i
$905$		0			0
$906$	−29.2600	+	24.5520i	−0.972097	+	0.815686i
$907$	−23.1710	+	8.43355i	−0.769380	+	0.280031i	−0.696737	−	0.717327i	$-0.745365\pi$
$907$	−23.1710	+	8.43355i	−0.769380	+	0.280031i	−0.0726427	+	0.997358i	$0.523143\pi$
$908$	−11.1022	−	4.04088i	−0.368440	−	0.134101i
$909$	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	$0.555473\pi$
$912$	12.1529	+	4.39141i	0.402424	+	0.145414i
$913$	−0.667352			−0.0220861
$914$	5.03718	−	28.5672i	0.166615	−	0.944920i
$915$		0			0
$916$	11.1998	+	4.07640i	0.370053	+	0.134688i
$917$	52.1063	−	18.9651i	1.72070	−	0.626284i
$918$	33.5702	−	28.1688i	1.10798	−	0.929708i
$919$	12.5834	+	21.7950i	0.415087	+	0.718952i	0.995438	−	0.0954150i	$-0.0304178\pi$
$919$	12.5834	+	21.7950i	0.415087	+	0.718952i	−0.580351	+	0.814367i	$0.697084\pi$
$920$		0			0
$921$	0.334319	+	1.89602i	0.0110162	+	0.0624759i
$922$	−6.50753	−	36.9060i	−0.214314	−	1.21544i
$923$	−6.75894	+	11.7068i	−0.222473	+	0.385335i
$924$	5.93676	+	10.2828i	0.195305	+	0.338278i
$925$		0			0
$926$	4.15816	−	1.51345i	0.136645	−	0.0497349i
$927$	29.9590	+	10.9042i	0.983982	+	0.358140i
$928$	1.81521	+	1.52314i	0.0595871	+	0.0499995i
$929$	−3.26147	+	18.4967i	−0.107005	+	0.606857i	0.883395	+	0.468629i	$0.155252\pi$
$929$	−3.26147	+	18.4967i	−0.107005	+	0.606857i	−0.990400	+	0.138228i	$0.955859\pi$
$930$		0			0
$931$	3.19912	+	5.51148i	0.104847	+	0.180631i
$932$	−9.18438			−0.300844
$933$	5.96386	−	33.8227i	0.195248	−	1.10731i
$934$	−3.31664	−	2.78299i	−0.108524	−	0.0910623i
$935$		0			0
$936$	29.1855	−	10.6227i	0.953958	−	0.347212i
$937$	10.7306	−	9.00408i	0.350555	−	0.294150i	−0.450458	−	0.892798i	$-0.648739\pi$
$937$	10.7306	−	9.00408i	0.350555	−	0.294150i	0.801013	+	0.598647i	$0.204295\pi$
$938$	14.9036	+	25.8139i	0.486621	+	0.842852i
$939$	−0.934141	+	1.61798i	−0.0304845	+	0.0528008i
$940$		0			0
$941$	10.1772	+	57.7176i	0.331766	+	1.88154i	0.457082	+	0.889424i	$0.348894\pi$
$941$	10.1772	+	57.7176i	0.331766	+	1.88154i	−0.125316	+	0.992117i	$0.539994\pi$
$942$	−24.2943	+	42.0790i	−0.791552	+	1.37101i
$943$	−7.43792	−	12.8829i	−0.242212	−	0.419523i
$944$	−6.17002	+	5.17726i	−0.200817	+	0.168506i
$945$		0			0
$946$	7.55773	+	2.75079i	0.245723	+	0.0894359i
$947$	−1.08692	−	0.912031i	−0.0353200	−	0.0296370i	0.624957	−	0.780659i	$-0.285117\pi$
$947$	−1.08692	−	0.912031i	−0.0353200	−	0.0296370i	−0.660277	+	0.751022i	$0.729561\pi$
$948$	−4.24154	+	24.0550i	−0.137759	+	0.781269i
$949$	−36.5223			−1.18557
$950$		0			0
$951$	−27.6120			−0.895382
$952$	−2.67799	+	15.1876i	−0.0867941	+	0.492234i
$953$	28.3367	+	23.7773i	0.917916	+	0.770223i	0.973608	−	0.228225i	$-0.0732921\pi$
$953$	28.3367	+	23.7773i	0.917916	+	0.770223i	−0.0556922	+	0.998448i	$0.517737\pi$
$954$	−57.8095	−	21.0410i	−1.87165	−	0.681226i
$955$		0			0
$956$	4.14362	−	3.47691i	0.134014	−	0.112451i
$957$	4.83599	+	8.37619i	0.156325	+	0.270764i
$958$	−3.74393	+	6.48468i	−0.120961	+	0.209510i
$959$	6.35254	+	36.0270i	0.205134	+	1.16337i
$960$		0			0
$961$	−9.03536	+	15.6497i	−0.291463	+	0.504829i
$962$	−22.2982	−	38.6216i	−0.718922	−	1.24521i
$963$	27.8429	−	23.3630i	0.897226	−	0.752862i
$964$	−24.9886	+	9.09512i	−0.804830	+	0.292934i
$965$		0			0
$966$	−10.5508	−	8.85320i	−0.339467	−	0.284847i
$967$	−0.642387	+	3.64316i	−0.0206578	+	0.117156i	−0.993393	−	0.114763i	$-0.963389\pi$
$967$	−0.642387	+	3.64316i	−0.0206578	+	0.117156i	0.972735	+	0.231919i	$0.0745004\pi$
$968$	9.10425			0.292622
$969$	12.0525	+	67.4380i	0.387183	+	2.16642i
$970$		0			0
$971$	1.26262	−	7.16068i	0.0405194	−	0.229797i	−0.957822	−	0.287361i	$-0.907222\pi$
$971$	1.26262	−	7.16068i	0.0405194	−	0.229797i	0.998342	+	0.0575637i	$0.0183332\pi$
$972$	−2.78234	−	2.33466i	−0.0892436	−	0.0748843i
$973$	23.7291	+	8.63667i	0.760719	+	0.276879i
$974$	−16.7530	+	6.09760i	−0.536801	+	0.195380i
$975$		0			0
$976$	7.72328	+	13.3771i	0.247216	+	0.428191i
$977$	5.59949	−	9.69861i	0.179144	−	0.310286i	−0.762444	−	0.647054i	$-0.776001\pi$
$977$	5.59949	−	9.69861i	0.179144	−	0.310286i	0.941587	+	0.336768i	$0.109334\pi$
$978$	−2.10067	−	11.9135i	−0.0671719	−	0.380951i
$979$	2.88676	+	16.3716i	0.0922613	+	0.523240i
$980$		0			0
$981$	−15.8475	−	27.4486i	−0.505971	−	0.876368i
$982$	9.18783	−	7.70951i	0.293196	−	0.246020i
$983$	33.1702	−	12.0730i	1.05797	−	0.385068i	0.246302	−	0.969193i	$-0.420785\pi$
$983$	33.1702	−	12.0730i	1.05797	−	0.385068i	0.811663	+	0.584125i	$0.198562\pi$
$984$	−25.9464	−	9.44372i	−0.827141	−	0.301055i
$985$		0			0
$986$	−2.18145	+	12.3716i	−0.0694714	+	0.393992i
$987$	−21.1387			−0.672853
$988$	−4.00795	+	23.0427i	−0.127510	+	0.733085i
$989$	−9.32951			−0.296661
$990$		0			0
$991$	15.8273	+	13.2807i	0.502771	+	0.421875i	0.858577	−	0.512685i	$-0.171349\pi$
$991$	15.8273	+	13.2807i	0.502771	+	0.421875i	−0.355806	+	0.934560i	$0.615794\pi$
$992$	6.58259	+	2.39587i	0.208998	+	0.0760689i
$993$	33.6122	−	12.2338i	1.06665	−	0.388229i
$994$	5.61398	−	4.71069i	0.178065	−	0.149414i
$995$		0			0
$996$	0.718437	−	1.24437i	0.0227645	−	0.0394293i
$997$	7.81553	+	44.3241i	0.247520	+	1.40376i	0.814566	+	0.580071i	$0.196975\pi$
$997$	7.81553	+	44.3241i	0.247520	+	1.40376i	−0.567045	+	0.823687i	$0.691913\pi$
$998$	1.16809	+	6.62459i	0.0369754	+	0.209698i
$999$	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.l.g.701.2		12
5.2	odd	4		950.2.u.f.549.2		24
5.3	odd	4		950.2.u.f.549.3		24
5.4	even	2		190.2.k.c.131.1	✓	12
19.9	even	9	inner	950.2.l.g.351.2		12
95.9	even	18		190.2.k.c.161.1	yes	12
95.28	odd	36		950.2.u.f.199.2		24
95.47	odd	36		950.2.u.f.199.3		24
95.54	even	18		3610.2.a.bf.1.1		6
95.79	odd	18		3610.2.a.bd.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.131.1	✓	12	5.4	even	2
190.2.k.c.161.1	yes	12	95.9	even	18
950.2.l.g.351.2		12	19.9	even	9	inner
950.2.l.g.701.2		12	1.1	even	1	trivial
950.2.u.f.199.2		24	95.28	odd	36
950.2.u.f.199.3		24	95.47	odd	36
950.2.u.f.549.2		24	5.2	odd	4
950.2.u.f.549.3		24	5.3	odd	4
3610.2.a.bd.1.6		6	95.79	odd	18
3610.2.a.bf.1.1		6	95.54	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(2.27095 + 1.90555i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.27095 + 1.90555i) q^{6} +(1.45447 + 2.51922i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.00513 + 5.70040i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(2.27095 + 1.90555i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.27095 + 1.90555i) q^{6} +(1.45447 + 2.51922i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.00513 + 5.70040i) q^{9} +(-0.688430 + 1.19240i) q^{11} +(-1.48226 - 2.56734i) q^{12} +(4.11038 - 3.44902i) q^{13} +(-2.73352 + 0.994919i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.920603 + 5.22100i) q^{17} -5.78833 q^{18} +(2.17069 - 3.77996i) q^{19} +(-1.49748 + 8.49261i) q^{21} +(-1.05474 - 0.885029i) q^{22} +(1.50082 + 0.546254i) q^{23} +(2.78573 - 1.01392i) q^{24} +(2.68286 + 4.64685i) q^{26} +(-4.13303 + 7.15861i) q^{27} +(-0.505134 - 2.86476i) q^{28} +(-0.411474 - 2.33359i) q^{29} +(-3.50252 - 6.06655i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-3.83556 + 1.39603i) q^{33} +(-4.98182 - 1.81323i) q^{34} +(1.00513 - 5.70040i) q^{36} -8.31135 q^{37} +(3.34560 + 2.79409i) q^{38} +15.9067 q^{39} +(-7.13497 - 5.98695i) q^{41} +(-8.10355 - 2.94945i) q^{42} +(-5.48910 + 1.99787i) q^{43} +(1.05474 - 0.885029i) q^{44} +(-0.798570 + 1.38316i) q^{46} +(0.425657 + 2.41402i) q^{47} +(0.514782 + 2.91947i) q^{48} +(-0.730994 + 1.26612i) q^{49} +(-12.0395 + 10.1024i) q^{51} +(-5.04213 + 1.83518i) q^{52} +(9.98725 + 3.63506i) q^{53} +(-6.33216 - 5.31332i) q^{54} +2.90895 q^{56} +(12.1324 - 4.44774i) q^{57} +2.36959 q^{58} +(-1.39863 + 7.93202i) q^{59} +(14.5150 + 5.28304i) q^{61} +(6.58259 - 2.39587i) q^{62} +(-12.8986 + 10.8232i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.708783 - 4.01971i) q^{66} +(-1.77933 - 10.0911i) q^{67} +(2.65077 - 4.59127i) q^{68} +(2.36737 + 4.10041i) q^{69} +(-2.36737 + 0.861653i) q^{71} +(5.43926 + 1.97973i) q^{72} +(-5.21416 - 4.37520i) q^{73} +(1.44325 - 8.18508i) q^{74} +(-3.33260 + 2.80958i) q^{76} -4.00522 q^{77} +(-2.76218 + 15.6651i) q^{78} +(-6.31181 - 5.29624i) q^{79} +(-6.70923 + 2.44196i) q^{81} +(7.13497 - 5.98695i) q^{82} +(0.242346 + 0.419755i) q^{83} +(4.31181 - 7.46827i) q^{84} +(-1.01435 - 5.75264i) q^{86} +(3.51233 - 6.08354i) q^{87} +(0.688430 + 1.19240i) q^{88} +(9.24921 - 7.76101i) q^{89} +(14.6673 + 5.33846i) q^{91} +(-1.22348 - 1.02662i) q^{92} +(3.60607 - 20.4511i) q^{93} -2.45126 q^{94} -2.96451 q^{96} +(-1.59026 + 9.01879i) q^{97} +(-1.11995 - 0.939748i) q^{98} +(-7.48910 - 2.72581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Introduction

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