LMFDB - Embedded newform 35.3.g.a.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 70 x^{8} - 248 x^{7} + 464 x^{6} + 432 x^{5} + 1129 x^{4} + \cdots + 100 $ x^12 - 4x^11 + 8x^10 + 8x^9 + 70x^8 - 248x^7 + 464x^6 + 432x^5 + 1129x^4 - 2708x^3 + 3528x^2 + 840*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.3
Root			$0.950261 + 0.950261i$ of defining polynomial
Character	$\chi$	$=$	35.22
Dual form			35.3.g.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.950261 - 0.950261i) q^{2} +(0.269488 - 0.269488i) q^{3} -2.19401i q^{4} +(4.00169 - 2.99774i) q^{5} -0.512169 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.88593 + 5.88593i) q^{8} +8.85475i q^{9} +O(q^{10})$	\(q+(-0.950261 - 0.950261i) q^{2} +(0.269488 - 0.269488i) q^{3} -2.19401i q^{4} +(4.00169 - 2.99774i) q^{5} -0.512169 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.88593 + 5.88593i) q^{8} +8.85475i q^{9} +(-6.65129 - 0.954016i) q^{10} +16.9860 q^{11} +(-0.591259 - 0.591259i) q^{12} +(-14.0145 + 14.0145i) q^{13} +3.55555i q^{14} +(0.270553 - 1.88627i) q^{15} +2.41031 q^{16} +(1.45911 + 1.45911i) q^{17} +(8.41433 - 8.41433i) q^{18} -5.98604i q^{19} +(-6.57707 - 8.77974i) q^{20} -1.00833 q^{21} +(-16.1412 - 16.1412i) q^{22} +(12.9220 - 12.9220i) q^{23} +3.17238i q^{24} +(7.02709 - 23.9921i) q^{25} +26.6349 q^{26} +(4.81165 + 4.81165i) q^{27} +(-4.10461 + 4.10461i) q^{28} +25.1048i q^{29} +(-2.04954 + 1.53535i) q^{30} -41.5762 q^{31} +(21.2533 + 21.2533i) q^{32} +(4.57753 - 4.57753i) q^{33} -2.77308i q^{34} +(-13.0947 - 1.87822i) q^{35} +19.4274 q^{36} +(-0.676716 - 0.676716i) q^{37} +(-5.68830 + 5.68830i) q^{38} +7.55351i q^{39} +(-5.90918 + 41.1981i) q^{40} -36.8706 q^{41} +(0.958180 + 0.958180i) q^{42} +(10.2448 - 10.2448i) q^{43} -37.2674i q^{44} +(26.5443 + 35.4340i) q^{45} -24.5586 q^{46} +(-21.1237 - 21.1237i) q^{47} +(0.649550 - 0.649550i) q^{48} +7.00000i q^{49} +(-29.4763 + 16.1212i) q^{50} +0.786428 q^{51} +(30.7480 + 30.7480i) q^{52} +(-21.6352 + 21.6352i) q^{53} -9.14465i q^{54} +(67.9728 - 50.9197i) q^{55} +22.0231 q^{56} +(-1.61317 - 1.61317i) q^{57} +(23.8561 - 23.8561i) q^{58} -81.0248i q^{59} +(-4.13848 - 0.593595i) q^{60} -58.7499 q^{61} +(39.5083 + 39.5083i) q^{62} +(16.5657 - 16.5657i) q^{63} -50.0336i q^{64} +(-14.0699 + 98.0938i) q^{65} -8.69971 q^{66} +(-18.7096 - 18.7096i) q^{67} +(3.20130 - 3.20130i) q^{68} -6.96468i q^{69} +(10.6586 + 14.2282i) q^{70} +59.1919 q^{71} +(-52.1184 - 52.1184i) q^{72} +(57.8982 - 57.8982i) q^{73} +1.28611i q^{74} +(-4.57187 - 8.35931i) q^{75} -13.1334 q^{76} +(-31.7779 - 31.7779i) q^{77} +(7.17781 - 7.17781i) q^{78} +96.0718i q^{79} +(9.64532 - 7.22548i) q^{80} -77.0994 q^{81} +(35.0367 + 35.0367i) q^{82} +(-34.7065 + 34.7065i) q^{83} +2.21229i q^{84} +(10.2130 + 1.46488i) q^{85} -19.4704 q^{86} +(6.76545 + 6.76545i) q^{87} +(-99.9784 + 99.9784i) q^{88} +46.7908i q^{89} +(8.44757 - 58.8955i) q^{90} +52.4376 q^{91} +(-28.3510 - 28.3510i) q^{92} +(-11.2043 + 11.2043i) q^{93} +40.1461i q^{94} +(-17.9446 - 23.9543i) q^{95} +11.4550 q^{96} +(133.626 + 133.626i) q^{97} +(6.65183 - 6.65183i) q^{98} +150.407i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	$ 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.950261	−	0.950261i	−0.475131	−	0.475131i	0.428440	−	0.903570i	$-0.359063\pi$
$2$	−0.950261	−	0.950261i	−0.475131	−	0.475131i	−0.903570	+	0.428440i	$0.859063\pi$
$3$	0.269488	−	0.269488i	0.0898295	−	0.0898295i	−0.660764	−	0.750594i	$-0.729768\pi$
$3$	0.269488	−	0.269488i	0.0898295	−	0.0898295i	0.750594	+	0.660764i	$0.229768\pi$
$4$		−	2.19401i		−	0.548502i
$5$	4.00169	−	2.99774i	0.800339	−	0.599548i
$5$	4.00169	−	2.99774i	0.800339	−	0.599548i
$6$	−0.512169			−0.0853615
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	−5.88593	+	5.88593i	−0.735741	+	0.735741i
$9$			8.85475i			0.983861i
$10$	−6.65129	−	0.954016i	−0.665129	−	0.0954016i
$11$	16.9860			1.54418			0.772092	−	0.635511i	$-0.219211\pi$
$11$	16.9860			1.54418			0.772092	+	0.635511i	$0.219211\pi$
$12$	−0.591259	−	0.591259i	−0.0492716	−	0.0492716i
$13$	−14.0145	+	14.0145i	−1.07804	+	1.07804i	−0.0813557	+	0.996685i	$0.525925\pi$
$13$	−14.0145	+	14.0145i	−1.07804	+	1.07804i	−0.996685	+	0.0813557i	$0.974075\pi$
$14$			3.55555i			0.253968i
$15$	0.270553	−	1.88627i	0.0180369	−	0.125751i
$16$	2.41031			0.150644
$17$	1.45911	+	1.45911i	0.0858302	+	0.0858302i	0.748718	−	0.662888i	$-0.230670\pi$
$17$	1.45911	+	1.45911i	0.0858302	+	0.0858302i	−0.662888	+	0.748718i	$0.730670\pi$
$18$	8.41433	−	8.41433i	0.467463	−	0.467463i
$19$		−	5.98604i		−	0.315055i	−0.987515	−	0.157527i	$-0.949648\pi$
$19$		−	5.98604i		−	0.315055i	0.987515	−	0.157527i	$-0.0503522\pi$
$20$	−6.57707	−	8.77974i	−0.328853	−	0.438987i
$21$	−1.00833			−0.0480159
$22$	−16.1412	−	16.1412i	−0.733689	−	0.733689i
$23$	12.9220	−	12.9220i	0.561828	−	0.561828i	−0.367998	−	0.929826i	$-0.619957\pi$
$23$	12.9220	−	12.9220i	0.561828	−	0.561828i	0.929826	+	0.367998i	$0.119957\pi$
$24$			3.17238i			0.132182i
$25$	7.02709	−	23.9921i	0.281084	−	0.959683i
$26$	26.6349			1.02442
$27$	4.81165	+	4.81165i	0.178209	+	0.178209i
$28$	−4.10461	+	4.10461i	−0.146593	+	0.146593i
$29$			25.1048i			0.865683i	0.901470	+	0.432841i	$0.142489\pi$
$29$			25.1048i			0.865683i	−0.901470	+	0.432841i	$0.857511\pi$
$30$	−2.04954	+	1.53535i	−0.0683181	+	0.0511783i
$31$	−41.5762			−1.34117			−0.670584	−	0.741833i	$-0.733957\pi$
$31$	−41.5762			−1.34117			−0.670584	+	0.741833i	$0.733957\pi$
$32$	21.2533	+	21.2533i	0.664165	+	0.664165i
$33$	4.57753	−	4.57753i	0.138713	−	0.138713i
$34$		−	2.77308i		−	0.0815611i
$35$	−13.0947	−	1.87822i	−0.374136	−	0.0536634i
$36$	19.4274			0.539650
$37$	−0.676716	−	0.676716i	−0.0182896	−	0.0182896i	0.697903	−	0.716192i	$-0.254117\pi$
$37$	−0.676716	−	0.676716i	−0.0182896	−	0.0182896i	−0.716192	+	0.697903i	$0.754117\pi$
$38$	−5.68830	+	5.68830i	−0.149692	+	0.149692i
$39$			7.55351i			0.193680i
$40$	−5.90918	+	41.1981i	−0.147729	+	1.02995i
$41$	−36.8706			−0.899283			−0.449641	−	0.893209i	$-0.648448\pi$
$41$	−36.8706			−0.899283			−0.449641	+	0.893209i	$0.648448\pi$
$42$	0.958180	+	0.958180i	0.0228138	+	0.0228138i
$43$	10.2448	−	10.2448i	0.238250	−	0.238250i	−0.577875	−	0.816125i	$-0.696118\pi$
$43$	10.2448	−	10.2448i	0.238250	−	0.238250i	0.816125	+	0.577875i	$0.196118\pi$
$44$		−	37.2674i		−	0.846987i
$45$	26.5443	+	35.4340i	0.589872	+	0.787422i
$46$	−24.5586			−0.533883
$47$	−21.1237	−	21.1237i	−0.449441	−	0.449441i	0.445728	−	0.895169i	$-0.352945\pi$
$47$	−21.1237	−	21.1237i	−0.449441	−	0.449441i	−0.895169	+	0.445728i	$0.852945\pi$
$48$	0.649550	−	0.649550i	0.0135323	−	0.0135323i
$49$			7.00000i			0.142857i
$50$	−29.4763	+	16.1212i	−0.589526	+	0.322424i
$51$	0.786428			0.0154202
$52$	30.7480	+	30.7480i	0.591307	+	0.591307i
$53$	−21.6352	+	21.6352i	−0.408210	+	0.408210i	−0.881114	−	0.472904i	$-0.843206\pi$
$53$	−21.6352	+	21.6352i	−0.408210	+	0.408210i	0.472904	+	0.881114i	$0.343206\pi$
$54$		−	9.14465i		−	0.169345i
$55$	67.9728	−	50.9197i	1.23587	−	0.925813i
$56$	22.0231			0.393270
$57$	−1.61317	−	1.61317i	−0.0283012	−	0.0283012i
$58$	23.8561	−	23.8561i	0.411312	−	0.411312i
$59$		−	81.0248i		−	1.37330i	−0.726987	−	0.686651i	$-0.759080\pi$
$59$		−	81.0248i		−	1.37330i	0.726987	−	0.686651i	$-0.240920\pi$
$60$	−4.13848	−	0.593595i	−0.0689747	−	0.00989325i
$61$	−58.7499			−0.963113			−0.481556	−	0.876415i	$-0.659928\pi$
$61$	−58.7499			−0.963113			−0.481556	+	0.876415i	$0.659928\pi$
$62$	39.5083	+	39.5083i	0.637230	+	0.637230i
$63$	16.5657	−	16.5657i	0.262948	−	0.262948i
$64$		−	50.0336i		−	0.781775i
$65$	−14.0699	+	98.0938i	−0.216460	+	1.50914i
$66$	−8.69971			−0.131814
$67$	−18.7096	−	18.7096i	−0.279248	−	0.279248i	0.553561	−	0.832809i	$-0.313269\pi$
$67$	−18.7096	−	18.7096i	−0.279248	−	0.279248i	−0.832809	+	0.553561i	$0.813269\pi$
$68$	3.20130	−	3.20130i	0.0470780	−	0.0470780i
$69$		−	6.96468i		−	0.100937i
$70$	10.6586	+	14.2282i	0.152266	+	0.203260i
$71$	59.1919			0.833689			0.416845	−	0.908978i	$-0.363136\pi$
$71$	59.1919			0.833689			0.416845	+	0.908978i	$0.363136\pi$
$72$	−52.1184	−	52.1184i	−0.723867	−	0.723867i
$73$	57.8982	−	57.8982i	0.793126	−	0.793126i	−0.188875	−	0.982001i	$-0.560484\pi$
$73$	57.8982	−	57.8982i	0.793126	−	0.793126i	0.982001	+	0.188875i	$0.0604841\pi$
$74$			1.28611i			0.0173799i
$75$	−4.57187	−	8.35931i	−0.0609583	−	0.111457i
$76$	−13.1334			−0.172808
$77$	−31.7779	−	31.7779i	−0.412700	−	0.412700i
$78$	7.17781	−	7.17781i	0.0920231	−	0.0920231i
$79$			96.0718i			1.21610i	0.793899	+	0.608050i	$0.208048\pi$
$79$			96.0718i			1.21610i	−0.793899	+	0.608050i	$0.791952\pi$
$80$	9.64532	−	7.22548i	0.120566	−	0.0903186i
$81$	−77.0994			−0.951844
$82$	35.0367	+	35.0367i	0.427277	+	0.427277i
$83$	−34.7065	+	34.7065i	−0.418151	+	0.418151i	−0.884566	−	0.466415i	$-0.845545\pi$
$83$	−34.7065	+	34.7065i	−0.418151	+	0.418151i	0.466415	+	0.884566i	$0.345545\pi$
$84$			2.21229i			0.0263368i
$85$	10.2130	+	1.46488i	0.120153	+	0.0172339i
$86$	−19.4704			−0.226400
$87$	6.76545	+	6.76545i	0.0777638	+	0.0777638i
$88$	−99.9784	+	99.9784i	−1.13612	+	1.13612i
$89$			46.7908i			0.525739i	0.964831	+	0.262870i	$0.0846689\pi$
$89$			46.7908i			0.525739i	−0.964831	+	0.262870i	$0.915331\pi$
$90$	8.44757	−	58.8955i	0.0938619	−	0.654395i
$91$	52.4376			0.576237
$92$	−28.3510	−	28.3510i	−0.308164	−	0.308164i
$93$	−11.2043	+	11.2043i	−0.120476	+	0.120476i
$94$			40.1461i			0.427087i
$95$	−17.9446	−	23.9543i	−0.188890	−	0.252150i
$96$	11.4550			0.119323
$97$	133.626	+	133.626i	1.37759	+	1.37759i	0.848674	+	0.528916i	$0.177401\pi$
$97$	133.626	+	133.626i	1.37759	+	1.37759i	0.528916	+	0.848674i	$0.322599\pi$
$98$	6.65183	−	6.65183i	0.0678758	−	0.0678758i
$99$			150.407i			1.51926i
$100$	−52.6388	−	15.4175i	−0.526388	−	0.154175i
$101$	9.87747			0.0977967			0.0488983	−	0.998804i	$-0.484429\pi$
$101$	9.87747			0.0977967			0.0488983	+	0.998804i	$0.484429\pi$
$102$	−0.747312	−	0.747312i	−0.00732659	−	0.00732659i
$103$	52.5169	−	52.5169i	0.509873	−	0.509873i	−0.404614	−	0.914487i	$-0.632594\pi$
$103$	52.5169	−	52.5169i	0.509873	−	0.509873i	0.914487	+	0.404614i	$0.132594\pi$
$104$		−	164.977i		−	1.58632i
$105$	−4.03504	+	3.02272i	−0.0384289	+	0.0287878i
$106$	41.1181			0.387907
$107$	−27.1078	−	27.1078i	−0.253344	−	0.253344i	0.568996	−	0.822340i	$-0.307332\pi$
$107$	−27.1078	−	27.1078i	−0.253344	−	0.253344i	−0.822340	+	0.568996i	$0.807332\pi$
$108$	10.5568	−	10.5568i	0.0977480	−	0.0977480i
$109$		−	53.3056i		−	0.489042i	−0.969644	−	0.244521i	$-0.921369\pi$
$109$		−	53.3056i		−	0.489042i	0.969644	−	0.244521i	$-0.0786307\pi$
$110$	−112.979	−	16.2049i	−1.02708	−	0.147318i
$111$	−0.364734			−0.00328589
$112$	−4.50928	−	4.50928i	−0.0402614	−	0.0402614i
$113$	63.9956	−	63.9956i	0.566333	−	0.566333i	−0.364766	−	0.931099i	$-0.618851\pi$
$113$	63.9956	−	63.9956i	0.566333	−	0.566333i	0.931099	+	0.364766i	$0.118851\pi$
$114$			3.06586i			0.0268935i
$115$	12.9731	−	90.4470i	0.112810	−	0.786496i
$116$	55.0801			0.474828
$117$	−124.095	−	124.095i	−1.06064	−	1.06064i
$118$	−76.9948	+	76.9948i	−0.652498	+	0.652498i
$119$		−	5.45950i		−	0.0458781i
$120$	9.50997	+	12.6949i	0.0792497	+	0.105791i
$121$	167.525			1.38450
$122$	55.8277	+	55.8277i	0.457604	+	0.457604i
$123$	−9.93620	+	9.93620i	−0.0807821	+	0.0807821i
$124$			91.2185i			0.735633i
$125$	−43.8018	−	117.074i	−0.350415	−	0.936595i
$126$	−31.4835			−0.249869
$127$	−129.686	−	129.686i	−1.02115	−	1.02115i	−0.999771	−	0.0213769i	$-0.993195\pi$
$127$	−129.686	−	129.686i	−1.02115	−	1.02115i	−0.0213769	−	0.999771i	$-0.506805\pi$
$128$	37.4681	−	37.4681i	0.292720	−	0.292720i
$129$		−	5.52169i		−	0.0428038i
$130$	106.585	−	79.8447i	0.819883	−	0.614190i
$131$	124.006			0.946611			0.473305	−	0.880898i	$-0.343061\pi$
$131$	124.006			0.946611			0.473305	+	0.880898i	$0.343061\pi$
$132$	−10.0431	−	10.0431i	−0.0760844	−	0.0760844i
$133$	−11.1989	+	11.1989i	−0.0842019	+	0.0842019i
$134$			35.5580i			0.265359i
$135$	33.6788	+	4.83066i	0.249473	+	0.0357827i
$136$	−17.1765			−0.126297
$137$	135.533	+	135.533i	0.989290	+	0.989290i	0.999943	−	0.0106531i	$-0.00339104\pi$
$137$	135.533	+	135.533i	0.989290	+	0.989290i	−0.0106531	+	0.999943i	$0.503391\pi$
$138$	−6.61827	+	6.61827i	−0.0479585	+	0.0479585i
$139$			106.076i			0.763139i	0.924340	+	0.381569i	$0.124616\pi$
$139$			106.076i			0.763139i	−0.924340	+	0.381569i	$0.875384\pi$
$140$	−4.12083	+	28.7300i	−0.0294345	+	0.205214i
$141$	−11.3852			−0.0807461
$142$	−56.2478	−	56.2478i	−0.396111	−	0.396111i
$143$	−238.051	+	238.051i	−1.66469	+	1.66469i
$144$			21.3427i			0.148213i
$145$	75.2577	+	100.462i	0.519019	+	0.692839i
$146$	−110.037			−0.753677
$147$	1.88642	+	1.88642i	0.0128328	+	0.0128328i
$148$	−1.48472	+	1.48472i	−0.0100319	+	0.0100319i
$149$		−	111.939i		−	0.751269i	−0.926768	−	0.375635i	$-0.877425\pi$
$149$		−	111.939i		−	0.751269i	0.926768	−	0.375635i	$-0.122575\pi$
$150$	−3.59906	+	12.2880i	−0.0239937	+	0.0819200i
$151$	−32.7294			−0.216751			−0.108375	−	0.994110i	$-0.534565\pi$
$151$	−32.7294			−0.216751			−0.108375	+	0.994110i	$0.534565\pi$
$152$	35.2334	+	35.2334i	0.231798	+	0.231798i
$153$	−12.9201	+	12.9201i	−0.0844450	+	0.0844450i
$154$			60.3947i			0.392173i
$155$	−166.375	+	124.635i	−1.07339	+	0.804095i
$156$	16.5724			0.106234
$157$	−125.192	−	125.192i	−0.797402	−	0.797402i	0.185283	−	0.982685i	$-0.440680\pi$
$157$	−125.192	−	125.192i	−0.797402	−	0.797402i	−0.982685	+	0.185283i	$0.940680\pi$
$158$	91.2934	−	91.2934i	0.577806	−	0.577806i
$159$			11.6608i			0.0733387i
$160$	148.761	+	21.3372i	0.929756	+	0.133358i
$161$	−48.3499			−0.300310
$162$	73.2646	+	73.2646i	0.452251	+	0.452251i
$163$	−27.9402	+	27.9402i	−0.171412	+	0.171412i	−0.787600	−	0.616187i	$-0.788676\pi$
$163$	−27.9402	+	27.9402i	−0.171412	+	0.171412i	0.616187	+	0.787600i	$0.288676\pi$
$164$			80.8943i			0.493258i
$165$	4.59562	−	32.0402i	0.0278522	−	0.194183i
$166$	65.9606			0.397353
$167$	43.7279	+	43.7279i	0.261843	+	0.261843i	0.825803	−	0.563959i	$-0.190722\pi$
$167$	43.7279	+	43.7279i	0.261843	+	0.261843i	−0.563959	+	0.825803i	$0.690722\pi$
$168$	5.93497	−	5.93497i	0.0353272	−	0.0353272i
$169$		−	223.814i		−	1.32434i
$170$	−8.31297	−	11.0970i	−0.0488998	−	0.0652765i
$171$	53.0049			0.309970
$172$	−22.4771	−	22.4771i	−0.130681	−	0.130681i
$173$	17.4703	−	17.4703i	0.100984	−	0.100984i	−0.654809	−	0.755794i	$-0.727251\pi$
$173$	17.4703	−	17.4703i	0.100984	−	0.100984i	0.755794	+	0.654809i	$0.227251\pi$
$174$		−	12.8579i		−	0.0738959i
$175$	−58.0316	+	31.7386i	−0.331609	+	0.181363i
$176$	40.9416			0.232622
$177$	−21.8352	−	21.8352i	−0.123363	−	0.123363i
$178$	44.4635	−	44.4635i	0.249795	−	0.249795i
$179$		−	135.282i		−	0.755765i	−0.925854	−	0.377882i	$-0.876652\pi$
$179$		−	135.282i		−	0.755765i	0.925854	−	0.377882i	$-0.123348\pi$
$180$	77.7424	−	58.2383i	0.431902	−	0.323546i
$181$	−326.800			−1.80552			−0.902762	−	0.430141i	$-0.858464\pi$
$181$	−326.800			−1.80552			−0.902762	+	0.430141i	$0.858464\pi$
$182$	−49.8294	−	49.8294i	−0.273788	−	0.273788i
$183$	−15.8324	+	15.8324i	−0.0865159	+	0.0865159i
$184$			152.116i			0.826719i
$185$	−4.73663	−	0.679389i	−0.0256034	−	0.00367237i
$186$	21.2940			0.114484
$187$	24.7845	+	24.7845i	0.132538	+	0.132538i
$188$	−46.3456	+	46.3456i	−0.246519	+	0.246519i
$189$		−	18.0035i		−	0.0952568i
$190$	−5.71077	+	39.8149i	−0.0300567	+	0.209552i
$191$	134.550			0.704452			0.352226	−	0.935915i	$-0.385425\pi$
$191$	134.550			0.704452			0.352226	+	0.935915i	$0.385425\pi$
$192$	−13.4835	−	13.4835i	−0.0702264	−	0.0702264i
$193$	228.855	−	228.855i	1.18578	−	1.18578i	0.207552	−	0.978224i	$-0.433450\pi$
$193$	228.855	−	228.855i	1.18578	−	1.18578i	0.978224	−	0.207552i	$-0.0665497\pi$
$194$		−	253.960i		−	1.30907i
$195$	22.6435	+	30.2268i	0.116120	+	0.155009i
$196$	15.3580			0.0783574
$197$	119.505	+	119.505i	0.606624	+	0.606624i	0.942062	−	0.335438i	$-0.108884\pi$
$197$	119.505	+	119.505i	0.606624	+	0.606624i	−0.335438	+	0.942062i	$0.608884\pi$
$198$	142.926	−	142.926i	0.721848	−	0.721848i
$199$		−	40.5735i		−	0.203887i	−0.994790	−	0.101944i	$-0.967494\pi$
$199$		−	40.5735i		−	0.203887i	0.994790	−	0.101944i	$-0.0325061\pi$
$200$	99.8547	+	182.577i	0.499273	+	0.912883i
$201$	−10.0840			−0.0501694
$202$	−9.38618	−	9.38618i	−0.0464662	−	0.0464662i
$203$	46.9668	−	46.9668i	0.231363	−	0.231363i
$204$		−	1.72543i		−	0.00845798i
$205$	−147.545	+	110.529i	−0.719731	+	0.539164i
$206$	−99.8096			−0.484513
$207$	114.421	+	114.421i	0.552761	+	0.552761i
$208$	−33.7794	+	33.7794i	−0.162401	+	0.162401i
$209$		−	101.679i		−	0.486502i
$210$	6.70672	+	0.961966i	0.0319368	+	0.00458079i
$211$	−318.550			−1.50972			−0.754858	−	0.655888i	$-0.772294\pi$
$211$	−318.550			−1.50972			−0.754858	+	0.655888i	$0.772294\pi$
$212$	47.4677	+	47.4677i	0.223904	+	0.223904i
$213$	15.9515	−	15.9515i	0.0748899	−	0.0748899i
$214$			51.5190i			0.240743i
$215$	10.2852	−	71.7075i	0.0478383	−	0.333523i
$216$	−56.6420			−0.262231
$217$	77.7820	+	77.7820i	0.358442	+	0.358442i
$218$	−50.6542	+	50.6542i	−0.232359	+	0.232359i
$219$		−	31.2058i		−	0.142492i
$220$	−111.718	−	149.133i	−0.507810	−	0.677877i
$221$	−40.8976			−0.185057
$222$	0.346593	+	0.346593i	0.00156123	+	0.00156123i
$223$	72.2072	−	72.2072i	0.323799	−	0.323799i	−0.526424	−	0.850222i	$-0.676467\pi$
$223$	72.2072	−	72.2072i	0.323799	−	0.323799i	0.850222	+	0.526424i	$0.176467\pi$
$224$		−	79.5225i		−	0.355011i
$225$	212.444	+	62.2231i	0.944195	+	0.276547i
$226$	−121.625			−0.538164
$227$	128.875	+	128.875i	0.567732	+	0.567732i	0.931492	−	0.363761i	$-0.118507\pi$
$227$	128.875	+	128.875i	0.567732	+	0.567732i	−0.363761	+	0.931492i	$0.618507\pi$
$228$	−3.53930	+	3.53930i	−0.0155232	+	0.0155232i
$229$			21.6850i			0.0946941i	0.998878	+	0.0473471i	$0.0150767\pi$
$229$			21.6850i			0.0946941i	−0.998878	+	0.0473471i	$0.984923\pi$
$230$	−98.2761	+	73.6204i	−0.427287	+	0.320089i
$231$	−17.1276			−0.0741453
$232$	−147.765	−	147.765i	−0.636918	−	0.636918i
$233$	−132.855	+	132.855i	−0.570192	+	0.570192i	−0.932182	−	0.361990i	$-0.882098\pi$
$233$	−132.855	+	132.855i	−0.570192	+	0.570192i	0.361990	+	0.932182i	$0.382098\pi$
$234$			235.846i			1.00789i
$235$	−147.854	−	21.2072i	−0.629167	−	0.0902434i
$236$	−177.769			−0.753258
$237$	25.8902	+	25.8902i	0.109242	+	0.109242i
$238$	−5.18795	+	5.18795i	−0.0217981	+	0.0217981i
$239$			200.109i			0.837278i	0.908153	+	0.418639i	$0.137493\pi$
$239$			200.109i			0.837278i	−0.908153	+	0.418639i	$0.862507\pi$
$240$	0.652117	−	4.54648i	0.00271715	−	0.0189437i
$241$	225.313			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$241$	225.313			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$242$	−159.192	−	159.192i	−0.657820	−	0.657820i
$243$	−64.0822	+	64.0822i	−0.263713	+	0.263713i
$244$			128.898i			0.528269i
$245$	20.9842	+	28.0118i	0.0856498	+	0.114334i
$246$	18.8840			0.0767641
$247$	83.8915	+	83.8915i	0.339642	+	0.339642i
$248$	244.715	−	244.715i	0.986752	−	0.986752i
$249$			18.7060i			0.0751246i
$250$	−69.6280	+	152.874i	−0.278512	+	0.611498i
$251$	381.080			1.51825			0.759123	−	0.650947i	$-0.225628\pi$
$251$	381.080			1.51825			0.759123	+	0.650947i	$0.225628\pi$
$252$	−36.3453	−	36.3453i	−0.144227	−	0.144227i
$253$	219.494	−	219.494i	0.867565	−	0.867565i
$254$			246.471i			0.970358i
$255$	3.14704	−	2.35751i	0.0123413	−	0.00924513i
$256$	−271.343			−1.05993
$257$	−7.00508	−	7.00508i	−0.0272571	−	0.0272571i	0.693347	−	0.720604i	$-0.256135\pi$
$257$	−7.00508	−	7.00508i	−0.0272571	−	0.0272571i	−0.720604	+	0.693347i	$0.756135\pi$
$258$	−5.24705	+	5.24705i	−0.0203374	+	0.0203374i
$259$			2.53204i			0.00977621i
$260$	215.218	+	30.8695i	0.827763	+	0.118729i
$261$	−222.297			−0.851712
$262$	−117.838	−	117.838i	−0.449764	−	0.449764i
$263$	−318.040	+	318.040i	−1.20928	+	1.20928i	−0.238015	+	0.971261i	$0.576497\pi$
$263$	−318.040	+	318.040i	−1.20928	+	1.20928i	−0.971261	+	0.238015i	$0.923503\pi$
$264$			53.8861i			0.204114i
$265$	−21.7206	+	151.434i	−0.0819647	+	0.571448i
$266$	21.2837			0.0800138
$267$	12.6096	+	12.6096i	0.0472269	+	0.0472269i
$268$	−41.0490	+	41.0490i	−0.153168	+	0.153168i
$269$		−	192.767i		−	0.716607i	−0.933605	−	0.358303i	$-0.883355\pi$
$269$		−	192.767i		−	0.716607i	0.933605	−	0.358303i	$-0.116645\pi$
$270$	−27.4133	−	36.5941i	−0.101531	−	0.135534i
$271$	216.240			0.797932			0.398966	−	0.916966i	$-0.369369\pi$
$271$	216.240			0.797932			0.398966	+	0.916966i	$0.369369\pi$
$272$	3.51691	+	3.51691i	0.0129298	+	0.0129298i
$273$	14.1313	−	14.1313i	0.0517631	−	0.0517631i
$274$		−	257.583i		−	0.940084i
$275$	119.362	−	407.530i	0.434045	−	1.48193i
$276$	−15.2806			−0.0553643
$277$	12.5868	+	12.5868i	0.0454397	+	0.0454397i	0.729462	−	0.684022i	$-0.239771\pi$
$277$	12.5868	+	12.5868i	0.0454397	+	0.0454397i	−0.684022	+	0.729462i	$0.739771\pi$
$278$	100.800	−	100.800i	0.362591	−	0.362591i
$279$		−	368.147i		−	1.31952i
$280$	88.1297	−	66.0196i	0.314749	−	0.235784i
$281$	174.158			0.619780			0.309890	−	0.950772i	$-0.399708\pi$
$281$	174.158			0.619780			0.309890	+	0.950772i	$0.399708\pi$
$282$	10.8189	+	10.8189i	0.0383650	+	0.0383650i
$283$	−228.432	+	228.432i	−0.807178	+	0.807178i	−0.984206	−	0.177027i	$-0.943352\pi$
$283$	−228.432	+	228.432i	−0.807178	+	0.807178i	0.177027	+	0.984206i	$0.443352\pi$
$284$		−	129.867i		−	0.457280i
$285$	−11.2913	−	1.61954i	−0.0396185	−	0.00568260i
$286$	452.422			1.58189
$287$	68.9786	+	68.9786i	0.240343	+	0.240343i
$288$	−188.193	+	188.193i	−0.653446	+	0.653446i
$289$		−	284.742i		−	0.985266i
$290$	23.9504	−	166.979i	0.0825875	−	0.575791i
$291$	72.0214			0.247496
$292$	−127.029	−	127.029i	−0.435031	−	0.435031i
$293$	174.633	−	174.633i	0.596017	−	0.596017i	−0.343233	−	0.939250i	$-0.611522\pi$
$293$	174.633	−	174.633i	0.596017	−	0.596017i	0.939250	+	0.343233i	$0.111522\pi$
$294$		−	3.58518i		−	0.0121945i
$295$	−242.891	−	324.236i	−0.823361	−	1.09911i
$296$	7.96620			0.0269128
$297$	81.7307	+	81.7307i	0.275188	+	0.275188i
$298$	−106.371	+	106.371i	−0.356951	+	0.356951i
$299$			362.193i			1.21135i
$300$	−18.3404	+	10.0307i	−0.0611346	+	0.0334357i
$301$	−38.3324			−0.127350
$302$	31.1015	+	31.1015i	0.102985	+	0.102985i
$303$	2.66186	−	2.66186i	0.00878502	−	0.00878502i
$304$		−	14.4282i		−	0.0474612i
$305$	−235.099	+	176.117i	−0.770816	+	0.577433i
$306$	24.5549			0.0802448
$307$	−302.129	−	302.129i	−0.984133	−	0.984133i	0.0157433	−	0.999876i	$-0.494989\pi$
$307$	−302.129	−	302.129i	−0.984133	−	0.984133i	−0.999876	+	0.0157433i	$0.994989\pi$
$308$	−69.7210	+	69.7210i	−0.226367	+	0.226367i
$309$		−	28.3054i		−	0.0916032i
$310$	276.536	+	39.6644i	0.892050	+	0.127950i
$311$	333.217			1.07144			0.535719	−	0.844396i	$-0.320041\pi$
$311$	333.217			1.07144			0.535719	+	0.844396i	$0.320041\pi$
$312$	−44.4594	−	44.4594i	−0.142498	−	0.142498i
$313$	−356.018	+	356.018i	−1.13744	+	1.13744i	−0.148530	+	0.988908i	$0.547454\pi$
$313$	−356.018	+	356.018i	−1.13744	+	1.13744i	−0.988908	+	0.148530i	$0.952546\pi$
$314$			237.930i			0.757740i
$315$	16.6312	−	115.951i	0.0527974	−	0.368097i
$316$	210.782			0.667032
$317$	−249.198	−	249.198i	−0.786115	−	0.786115i	0.194740	−	0.980855i	$-0.437614\pi$
$317$	−249.198	−	249.198i	−0.786115	−	0.786115i	−0.980855	+	0.194740i	$0.937614\pi$
$318$	11.0809	−	11.0809i	0.0348454	−	0.0348454i
$319$			426.431i			1.33677i
$320$	−149.988	−	200.219i	−0.468712	−	0.625684i
$321$	−14.6105			−0.0455155
$322$	45.9450	+	45.9450i	0.142686	+	0.142686i
$323$	8.73430	−	8.73430i	0.0270412	−	0.0270412i
$324$			169.157i			0.522088i
$325$	237.756	+	434.719i	0.731558	+	1.33760i
$326$	53.1009			0.162886
$327$	−14.3652	−	14.3652i	−0.0439304	−	0.0439304i
$328$	217.018	−	217.018i	0.661639	−	0.661639i
$329$			79.0378i			0.240236i
$330$	−34.8136	+	26.0795i	−0.105496	+	0.0790287i
$331$	28.7478			0.0868514			0.0434257	−	0.999057i	$-0.486173\pi$
$331$	28.7478			0.0868514			0.0434257	+	0.999057i	$0.486173\pi$
$332$	76.1464	+	76.1464i	0.229357	+	0.229357i
$333$	5.99215	−	5.99215i	0.0179944	−	0.0179944i
$334$		−	83.1058i		−	0.248820i
$335$	−130.957	−	18.7835i	−0.390916	−	0.0560702i
$336$	−2.43039			−0.00723332
$337$	355.286	+	355.286i	1.05426	+	1.05426i	0.998441	+	0.0558213i	$0.0177777\pi$
$337$	355.286	+	355.286i	1.05426	+	1.05426i	0.0558213	+	0.998441i	$0.482222\pi$
$338$	−212.682	+	212.682i	−0.629237	+	0.629237i
$339$		−	34.4921i		−	0.101747i
$340$	3.21395	−	22.4073i	0.00945280	−	0.0659038i
$341$	−706.215			−2.07101
$342$	−50.3685	−	50.3685i	−0.147276	−	0.147276i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			120.600i			0.350581i
$345$	−20.8783	−	27.8705i	−0.0605168	−	0.0807841i
$346$	−33.2027			−0.0959617
$347$	−271.642	−	271.642i	−0.782830	−	0.782830i	0.197477	−	0.980307i	$-0.436725\pi$
$347$	−271.642	−	271.642i	−0.782830	−	0.782830i	−0.980307	+	0.197477i	$0.936725\pi$
$348$	14.8434	−	14.8434i	0.0426536	−	0.0426536i
$349$			603.433i			1.72903i	0.502604	+	0.864517i	$0.332375\pi$
$349$			603.433i			1.72903i	−0.502604	+	0.864517i	$0.667625\pi$
$350$	85.3051	+	24.9852i	0.243729	+	0.0713862i
$351$	−134.866			−0.384234
$352$	361.009	+	361.009i	1.02559	+	1.02559i
$353$	−69.2647	+	69.2647i	−0.196217	+	0.196217i	−0.798376	−	0.602159i	$-0.794307\pi$
$353$	−69.2647	+	69.2647i	−0.196217	+	0.196217i	0.602159	+	0.798376i	$0.294307\pi$
$354$			41.4984i			0.117227i
$355$	236.868	−	177.442i	0.667234	−	0.499837i
$356$	102.659			0.288369
$357$	−1.47127	−	1.47127i	−0.00412121	−	0.00412121i
$358$	−128.553	+	128.553i	−0.359087	+	0.359087i
$359$		−	427.886i		−	1.19188i	−0.803028	−	0.595941i	$-0.796779\pi$
$359$		−	427.886i		−	1.19188i	0.803028	−	0.595941i	$-0.203221\pi$
$360$	−364.799	−	52.3243i	−1.01333	−	0.145345i
$361$	325.167			0.900741
$362$	310.545	+	310.545i	0.857859	+	0.857859i
$363$	45.1460	−	45.1460i	0.124369	−	0.124369i
$364$		−	115.048i		−	0.316067i
$365$	58.1270	−	405.255i	0.159252	−	1.11029i
$366$	30.0898			0.0822127
$367$	−369.612	−	369.612i	−1.00712	−	1.00712i	−0.999974	−	0.00714340i	$-0.997726\pi$
$367$	−369.612	−	369.612i	−1.00712	−	1.00712i	−0.00714340	−	0.999974i	$-0.502274\pi$
$368$	31.1461	−	31.1461i	0.0846362	−	0.0846362i
$369$		−	326.480i		−	0.884770i
$370$	3.85544	+	5.14663i	0.0104201	+	0.0139098i
$371$	80.9513			0.218198
$372$	24.5823	+	24.5823i	0.0660815	+	0.0660815i
$373$	9.36361	−	9.36361i	0.0251035	−	0.0251035i	−0.694444	−	0.719547i	$-0.744349\pi$
$373$	9.36361	−	9.36361i	0.0251035	−	0.0251035i	0.719547	+	0.694444i	$0.244349\pi$
$374$		−	47.1035i		−	0.125945i
$375$	−43.3543	−	19.7461i	−0.115611	−	0.0526562i
$376$	248.665			0.661344
$377$	−351.832	−	351.832i	−0.933241	−	0.933241i
$378$	−17.1081	+	17.1081i	−0.0452594	+	0.0452594i
$379$			124.963i			0.329719i	0.986317	+	0.164859i	$0.0527170\pi$
$379$			124.963i			0.329719i	−0.986317	+	0.164859i	$0.947283\pi$
$380$	−52.5558	+	39.3706i	−0.138305	+	0.103607i
$381$	−69.8977			−0.183458
$382$	−127.858	−	127.858i	−0.334707	−	0.334707i
$383$	391.537	−	391.537i	1.02229	−	1.02229i	0.0225428	−	0.999746i	$-0.492824\pi$
$383$	391.537	−	391.537i	1.02229	−	1.02229i	0.999746	−	0.0225428i	$-0.00717620\pi$
$384$		−	20.1945i		−	0.0525897i
$385$	−222.428	−	31.9035i	−0.577734	−	0.0828662i
$386$	−434.944			−1.12680
$387$	90.7148	+	90.7148i	0.234405	+	0.234405i
$388$	293.177	−	293.177i	0.755610	−	0.755610i
$389$			68.7467i			0.176727i	0.996088	+	0.0883633i	$0.0281637\pi$
$389$			68.7467i			0.176727i	−0.996088	+	0.0883633i	$0.971836\pi$
$390$	7.20616	−	50.2406i	0.0184773	−	0.128822i
$391$	37.7094			0.0964436
$392$	−41.2015	−	41.2015i	−0.105106	−	0.105106i
$393$	33.4182	−	33.4182i	0.0850335	−	0.0850335i
$394$		−	227.122i		−	0.576452i
$395$	287.999	+	384.450i	0.729110	+	0.973291i
$396$	329.994			0.833318
$397$	501.527	+	501.527i	1.26329	+	1.26329i	0.949488	+	0.313804i	$0.101604\pi$
$397$	501.527	+	501.527i	1.26329	+	1.26329i	0.313804	+	0.949488i	$0.398396\pi$
$398$	−38.5555	+	38.5555i	−0.0968730	+	0.0968730i
$399$			6.03592i			0.0151276i
$400$	16.9375	−	57.8283i	0.0423436	−	0.144571i
$401$	−390.331			−0.973395			−0.486697	−	0.873571i	$-0.661799\pi$
$401$	−390.331			−0.973395			−0.486697	+	0.873571i	$0.661799\pi$
$402$	9.58248	+	9.58248i	0.0238370	+	0.0238370i
$403$	582.671	−	582.671i	1.44583	−	1.44583i
$404$		−	21.6712i		−	0.0536416i
$405$	−308.528	+	231.124i	−0.761798	+	0.570677i
$406$	−89.2614			−0.219856
$407$	−11.4947	−	11.4947i	−0.0282425	−	0.0282425i
$408$	−4.62886	+	4.62886i	−0.0113452	+	0.0113452i
$409$		−	44.6818i		−	0.109246i	−0.998507	−	0.0546232i	$-0.982604\pi$
$409$		−	44.6818i		−	0.109246i	0.998507	−	0.0546232i	$-0.0173958\pi$
$410$	245.237	+	35.1751i	0.598139	+	0.0857930i
$411$	73.0490			0.177735
$412$	−115.222	−	115.222i	−0.279666	−	0.279666i
$413$	−151.584	+	151.584i	−0.367030	+	0.367030i
$414$		−	217.461i		−	0.525267i
$415$	−34.8437	+	242.926i	−0.0839606	+	0.585364i
$416$	−595.709			−1.43199
$417$	28.5863	+	28.5863i	0.0685523	+	0.0685523i
$418$	−96.6216	+	96.6216i	−0.231152	+	0.231152i
$419$			360.450i			0.860263i	0.902766	+	0.430131i	$0.141533\pi$
$419$			360.450i			0.860263i	−0.902766	+	0.430131i	$0.858467\pi$
$420$	6.63187	+	8.85290i	0.0157902	+	0.0210783i
$421$	−39.1117			−0.0929020			−0.0464510	−	0.998921i	$-0.514791\pi$
$421$	−39.1117			−0.0929020			−0.0464510	+	0.998921i	$0.514791\pi$
$422$	302.706	+	302.706i	0.717313	+	0.717313i
$423$	187.045	−	187.045i	0.442188	−	0.442188i
$424$		−	254.686i		−	0.600674i
$425$	45.2605	−	24.7538i	0.106495	−	0.0582443i
$426$	−30.3163			−0.0711649
$427$	109.911	+	109.911i	0.257403	+	0.257403i
$428$	−59.4748	+	59.4748i	−0.138960	+	0.138960i
$429$			128.304i			0.299077i
$430$	−77.9145	+	58.3672i	−0.181197	+	0.135738i
$431$	220.242			0.511002			0.255501	−	0.966809i	$-0.417760\pi$
$431$	220.242			0.511002			0.255501	+	0.966809i	$0.417760\pi$
$432$	11.5976	+	11.5976i	0.0268462	+	0.0268462i
$433$	8.36944	−	8.36944i	0.0193290	−	0.0193290i	−0.697376	−	0.716705i	$-0.745649\pi$
$433$	8.36944	−	8.36944i	0.0193290	−	0.0193290i	0.716705	+	0.697376i	$0.245649\pi$
$434$		−	147.826i		−	0.340614i
$435$	47.3543	+	6.79218i	0.108861	+	0.0156142i
$436$	−116.953			−0.268240
$437$	−77.3518	−	77.3518i	−0.177006	−	0.177006i
$438$	−29.6537	+	29.6537i	−0.0677024	+	0.0677024i
$439$		−	417.501i		−	0.951028i	−0.879708	−	0.475514i	$-0.842262\pi$
$439$		−	417.501i		−	0.951028i	0.879708	−	0.475514i	$-0.157738\pi$
$440$	−100.373	+	699.793i	−0.228121	+	1.59044i
$441$	−61.9833			−0.140552
$442$	38.8634	+	38.8634i	0.0879262	+	0.0879262i
$443$	−90.6730	+	90.6730i	−0.204679	+	0.204679i	−0.802001	−	0.597322i	$-0.796231\pi$
$443$	−90.6730	+	90.6730i	−0.204679	+	0.204679i	0.597322	+	0.802001i	$0.296231\pi$
$444$			0.800229i			0.00180232i
$445$	140.267	+	187.242i	0.315206	+	0.420769i
$446$	−137.231			−0.307694
$447$	−30.1663	−	30.1663i	−0.0674861	−	0.0674861i
$448$	−93.6042	+	93.6042i	−0.208938	+	0.208938i
$449$			227.274i			0.506178i	0.967443	+	0.253089i	$0.0814466\pi$
$449$			227.274i			0.506178i	−0.967443	+	0.253089i	$0.918553\pi$
$450$	−142.749	−	261.006i	−0.317220	−	0.580012i
$451$	−626.285			−1.38866
$452$	−140.407	−	140.407i	−0.310634	−	0.310634i
$453$	−8.82019	+	8.82019i	−0.0194706	+	0.0194706i
$454$		−	244.930i		−	0.539494i
$455$	209.839	−	157.194i	0.461185	−	0.345482i
$456$	18.9900			0.0416447
$457$	197.691	+	197.691i	0.432584	+	0.432584i	0.889507	−	0.456922i	$-0.151048\pi$
$457$	197.691	+	197.691i	0.432584	+	0.432584i	−0.456922	+	0.889507i	$0.651048\pi$
$458$	20.6064	−	20.6064i	0.0449921	−	0.0449921i
$459$			14.0415i			0.0305914i
$460$	−198.441	−	28.4631i	−0.431394	−	0.0618762i
$461$	90.8584			0.197090			0.0985449	−	0.995133i	$-0.468581\pi$
$461$	90.8584			0.197090			0.0985449	+	0.995133i	$0.468581\pi$
$462$	16.2757	+	16.2757i	0.0352287	+	0.0352287i
$463$	−601.688	+	601.688i	−1.29954	+	1.29954i	−0.370850	+	0.928693i	$0.620934\pi$
$463$	−601.688	+	601.688i	−1.29954	+	1.29954i	−0.928693	+	0.370850i	$0.879066\pi$
$464$			60.5103i			0.130410i
$465$	−11.2486	+	78.4238i	−0.0241905	+	0.168653i
$466$	252.494			0.541832
$467$	−274.786	−	274.786i	−0.588406	−	0.588406i	0.348793	−	0.937200i	$-0.386591\pi$
$467$	−274.786	−	274.786i	−0.588406	−	0.588406i	−0.937200	+	0.348793i	$0.886591\pi$
$468$	−272.266	+	272.266i	−0.581764	+	0.581764i
$469$			70.0050i			0.149264i
$470$	120.348	+	160.652i	0.256059	+	0.341814i
$471$	−67.4756			−0.143260
$472$	476.906	+	476.906i	1.01039	+	1.01039i
$473$	174.018	−	174.018i	0.367902	−	0.367902i
$474$		−	49.2050i		−	0.103808i
$475$	−143.617	−	42.0644i	−0.302353	−	0.0885567i
$476$	−11.9782			−0.0251642
$477$	−191.574	−	191.574i	−0.401623	−	0.401623i
$478$	190.156	−	190.156i	0.397817	−	0.397817i
$479$			128.428i			0.268117i	0.990973	+	0.134059i	$0.0428011\pi$
$479$			128.428i			0.268117i	−0.990973	+	0.134059i	$0.957199\pi$
$480$	45.8395	−	34.3392i	0.0954989	−	0.0715400i
$481$	18.9677			0.0394339
$482$	−214.106	−	214.106i	−0.444203	−	0.444203i
$483$	−13.0297	+	13.0297i	−0.0269767	+	0.0269767i
$484$		−	367.551i		−	0.759402i
$485$	935.308	+	134.154i	1.92847	+	0.276607i
$486$	121.790			0.250596
$487$	306.248	+	306.248i	0.628846	+	0.628846i	0.947778	−	0.318932i	$-0.103324\pi$
$487$	306.248	+	306.248i	0.628846	+	0.628846i	−0.318932	+	0.947778i	$0.603324\pi$
$488$	345.797	−	345.797i	0.708601	−	0.708601i
$489$			15.0591i			0.0307957i
$490$	6.67811	−	46.5590i	0.0136288	−	0.0950185i
$491$	−242.548			−0.493987			−0.246993	−	0.969017i	$-0.579443\pi$
$491$	−242.548			−0.493987			−0.246993	+	0.969017i	$0.579443\pi$
$492$	21.8001	+	21.8001i	0.0443091	+	0.0443091i
$493$	−36.6307	+	36.6307i	−0.0743017	+	0.0743017i
$494$		−	159.438i		−	0.322748i
$495$	450.881	+	601.883i	0.910871	+	1.21592i
$496$	−100.212			−0.202039
$497$	−110.738	−	110.738i	−0.222813	−	0.222813i
$498$	17.7756	−	17.7756i	0.0356940	−	0.0356940i
$499$		−	492.667i		−	0.987308i	−0.869658	−	0.493654i	$-0.835661\pi$
$499$		−	492.667i		−	0.987308i	0.869658	−	0.493654i	$-0.164339\pi$
$500$	−256.862	+	96.1015i	−0.513724	+	0.192203i
$501$	23.5683			0.0470425
$502$	−362.125	−	362.125i	−0.721365	−	0.721365i
$503$	447.774	−	447.774i	0.890207	−	0.890207i	−0.104336	−	0.994542i	$-0.533272\pi$
$503$	447.774	−	447.774i	0.890207	−	0.890207i	0.994542	+	0.104336i	$0.0332716\pi$
$504$			195.009i			0.386923i
$505$	39.5266	−	29.6101i	0.0782705	−	0.0586338i
$506$	−417.153			−0.824414
$507$	−60.3153	−	60.3153i	−0.118965	−	0.118965i
$508$	−284.532	+	284.532i	−0.560102	+	0.560102i
$509$			545.626i			1.07196i	0.844232	+	0.535978i	$0.180057\pi$
$509$			545.626i			1.07196i	−0.844232	+	0.535978i	$0.819943\pi$
$510$	−5.23076	−	0.750264i	−0.0102564	−	0.00147111i
$511$	−216.635			−0.423944
$512$	107.975	+	107.975i	0.210888	+	0.210888i
$513$	28.8027	−	28.8027i	0.0561456	−	0.0561456i
$514$			13.3133i			0.0259014i
$515$	52.7244	−	367.589i	0.102377	−	0.713764i
$516$	−12.1146			−0.0234779
$517$	−358.808	−	358.808i	−0.694020	−	0.694020i
$518$	2.40610	−	2.40610i	0.00464498	−	0.00464498i
$519$		−	9.41609i		−	0.0181428i
$520$	−494.558	−	660.187i	−0.951074	−	1.26959i
$521$	376.509			0.722666			0.361333	−	0.932437i	$-0.382322\pi$
$521$	376.509			0.722666			0.361333	+	0.932437i	$0.382322\pi$
$522$	211.240	+	211.240i	0.404674	+	0.404674i
$523$	−189.595	+	189.595i	−0.362514	+	0.362514i	−0.864738	−	0.502223i	$-0.832515\pi$
$523$	−189.595	+	189.595i	−0.362514	+	0.362514i	0.502223	+	0.864738i	$0.332515\pi$
$524$		−	272.070i		−	0.519218i
$525$	−7.08565	+	24.1920i	−0.0134965	+	0.0460800i
$526$	604.442			1.14913
$527$	−60.6644	−	60.6644i	−0.115113	−	0.115113i
$528$	11.0333	−	11.0333i	0.0208964	−	0.0208964i
$529$			195.042i			0.368699i
$530$	164.542	−	123.261i	0.310457	−	0.232569i
$531$	717.455			1.35114
$532$	24.5704	+	24.5704i	0.0461849	+	0.0461849i
$533$	516.724	−	516.724i	0.969464	−	0.969464i
$534$		−	23.9648i		−	0.0448779i
$535$	−189.739	−	27.2149i	−0.354653	−	0.0508690i
$536$	220.247			0.410908
$537$	−36.4569	−	36.4569i	−0.0678899	−	0.0678899i
$538$	−183.179	+	183.179i	−0.340482	+	0.340482i
$539$			118.902i			0.220598i
$540$	10.5985	−	73.8915i	0.0196268	−	0.136836i
$541$	−51.3110			−0.0948447			−0.0474223	−	0.998875i	$-0.515101\pi$
$541$	−51.3110			−0.0948447			−0.0474223	+	0.998875i	$0.515101\pi$
$542$	−205.484	−	205.484i	−0.379122	−	0.379122i
$543$	−88.0687	+	88.0687i	−0.162189	+	0.162189i
$544$			62.0219i			0.114011i
$545$	−159.796	−	213.313i	−0.293204	−	0.391399i
$546$	−26.8569			−0.0491884
$547$	207.353	+	207.353i	0.379073	+	0.379073i	0.870768	−	0.491694i	$-0.163622\pi$
$547$	207.353	+	207.353i	0.379073	+	0.379073i	−0.491694	+	0.870768i	$0.663622\pi$
$548$	297.360	−	297.360i	0.542627	−	0.542627i
$549$		−	520.216i		−	0.947569i
$550$	−500.685	+	273.835i	−0.910337	+	0.497881i
$551$	150.278			0.272737
$552$	40.9936	+	40.9936i	0.0742637	+	0.0742637i
$553$	179.734	−	179.734i	0.325016	−	0.325016i
$554$		−	23.9215i		−	0.0431796i
$555$	−1.45955	+	1.09338i	−0.00262983	+	0.00197005i
$556$	232.732			0.418583
$557$	−463.357	−	463.357i	−0.831880	−	0.831880i	0.155894	−	0.987774i	$-0.450174\pi$
$557$	−463.357	−	463.357i	−0.831880	−	0.831880i	−0.987774	+	0.155894i	$0.950174\pi$
$558$	−349.836	+	349.836i	−0.626946	+	0.626946i
$559$			287.151i			0.513687i
$560$	−31.5624	−	4.52709i	−0.0563614	−	0.00808409i
$561$	13.3583			0.0238115
$562$	−165.496	−	165.496i	−0.294476	−	0.294476i
$563$	−375.952	+	375.952i	−0.667766	+	0.667766i	−0.957198	−	0.289433i	$-0.906533\pi$
$563$	−375.952	+	375.952i	−0.667766	+	0.667766i	0.289433	+	0.957198i	$0.406533\pi$
$564$			24.9792i			0.0442894i
$565$	64.2484	−	447.933i	0.113714	−	0.792802i
$566$	434.139			0.767031
$567$	144.240	+	144.240i	0.254391	+	0.254391i
$568$	−348.399	+	348.399i	−0.613379	+	0.613379i
$569$			574.205i			1.00915i	0.863369	+	0.504573i	$0.168350\pi$
$569$			574.205i			1.00915i	−0.863369	+	0.504573i	$0.831650\pi$
$570$	9.19066	+	12.2686i	0.0161240	+	0.0215239i
$571$	−1041.02			−1.82316			−0.911578	−	0.411126i	$-0.865136\pi$
$571$	−1041.02			−1.82316			−0.911578	+	0.411126i	$0.865136\pi$
$572$	522.286	+	522.286i	0.913087	+	0.913087i
$573$	36.2597	−	36.2597i	0.0632805	−	0.0632805i
$574$		−	131.095i		−	0.228389i
$575$	−219.222	−	400.831i	−0.381256	−	0.697097i
$576$	443.035			0.769158
$577$	113.000	+	113.000i	0.195840	+	0.195840i	0.798214	−	0.602374i	$-0.205778\pi$
$577$	113.000	+	113.000i	0.195840	+	0.195840i	−0.602374	+	0.798214i	$0.705778\pi$
$578$	−270.579	+	270.579i	−0.468130	+	0.468130i
$579$		−	123.347i		−	0.213035i
$580$	220.414	−	165.116i	0.380023	−	0.284683i
$581$	129.860			0.223511
$582$	−68.4392	−	68.4392i	−0.117593	−	0.117593i
$583$	−367.495	+	367.495i	−0.630352	+	0.630352i
$584$			681.569i			1.16707i
$585$	−868.596	−	124.585i	−1.48478	−	0.212967i
$586$	−331.894			−0.566372
$587$	816.530	+	816.530i	1.39102	+	1.39102i	0.823044	+	0.567978i	$0.192274\pi$
$587$	816.530	+	816.530i	1.39102	+	1.39102i	0.567978	+	0.823044i	$0.307726\pi$
$588$	4.13881	−	4.13881i	0.00703880	−	0.00703880i
$589$			248.877i			0.422541i
$590$	−77.2990	+	538.920i	−0.131015	+	0.913423i
$591$	64.4104			0.108985
$592$	−1.63109	−	1.63109i	−0.00275523	−	0.00275523i
$593$	−439.292	+	439.292i	−0.740795	+	0.740795i	−0.972731	−	0.231936i	$-0.925494\pi$
$593$	−439.292	+	439.292i	−0.740795	+	0.740795i	0.231936	+	0.972731i	$0.425494\pi$
$594$		−	155.331i		−	0.261500i
$595$	−16.3662	−	21.8472i	−0.0275062	−	0.0367180i
$596$	−245.595			−0.412072
$597$	−10.9341	−	10.9341i	−0.0183151	−	0.0183151i
$598$	344.178	−	344.178i	0.575548	−	0.575548i
$599$			580.083i			0.968419i	0.874952	+	0.484209i	$0.160893\pi$
$599$			580.083i			0.968419i	−0.874952	+	0.484209i	$0.839107\pi$
$600$	76.1119	+	22.2926i	0.126853	+	0.0371543i
$601$	−356.000			−0.592346			−0.296173	−	0.955134i	$-0.595711\pi$
$601$	−356.000			−0.592346			−0.296173	+	0.955134i	$0.595711\pi$
$602$	36.4258	+	36.4258i	0.0605079	+	0.0605079i
$603$	165.669	−	165.669i	0.274741	−	0.274741i
$604$			71.8085i			0.118888i
$605$	670.383	−	502.196i	1.10807	−	0.830076i
$606$	−5.05893			−0.00834807
$607$	−403.425	−	403.425i	−0.664622	−	0.664622i	0.291844	−	0.956466i	$-0.405731\pi$
$607$	−403.425	−	403.425i	−0.664622	−	0.664622i	−0.956466	+	0.291844i	$0.905731\pi$
$608$	127.223	−	127.223i	0.209248	−	0.209248i
$609$		−	25.3140i		−	0.0415665i
$610$	390.763	+	56.0483i	0.640594	+	0.0918825i
$611$	592.078			0.969032
$612$	28.3467	+	28.3467i	0.0463182	+	0.0463182i
$613$	142.922	−	142.922i	0.233152	−	0.233152i	−0.580855	−	0.814007i	$-0.697282\pi$
$613$	142.922	−	142.922i	0.233152	−	0.233152i	0.814007	+	0.580855i	$0.197282\pi$
$614$			574.203i			0.935183i
$615$	−9.97545	+	69.5478i	−0.0162202	+	0.113086i
$616$	374.085			0.607281
$617$	−139.583	−	139.583i	−0.226229	−	0.226229i	0.584886	−	0.811115i	$-0.301139\pi$
$617$	−139.583	−	139.583i	−0.226229	−	0.226229i	−0.811115	+	0.584886i	$0.801139\pi$
$618$	−26.8975	+	26.8975i	−0.0435235	+	0.0435235i
$619$			83.8078i			0.135392i	0.997706	+	0.0676961i	$0.0215648\pi$
$619$			83.8078i			0.135392i	−0.997706	+	0.0676961i	$0.978435\pi$
$620$	273.450	+	365.028i	0.441048	+	0.588756i
$621$	124.353			0.200246
$622$	−316.643	−	316.643i	−0.509073	−	0.509073i
$623$	87.5375	−	87.5375i	0.140510	−	0.140510i
$624$			18.2063i			0.0291767i
$625$	−526.240	−	337.189i	−0.841984	−	0.539502i
$626$	676.621			1.08086
$627$	−27.4013	−	27.4013i	−0.0437022	−	0.0437022i
$628$	−274.672	+	274.672i	−0.437376	+	0.437376i
$629$		−	1.97481i		−	0.00313960i
$630$	−125.987	+	94.3795i	−0.199980	+	0.149809i
$631$	134.361			0.212934			0.106467	−	0.994316i	$-0.466046\pi$
$631$	134.361			0.212934			0.106467	+	0.994316i	$0.466046\pi$
$632$	−565.472	−	565.472i	−0.894734	−	0.894734i
$633$	−85.8456	+	85.8456i	−0.135617	+	0.135617i
$634$			473.607i			0.747015i
$635$	−907.728	−	130.198i	−1.42949	−	0.205037i
$636$	25.5840			0.0402264
$637$	−98.1017	−	98.1017i	−0.154006	−	0.154006i
$638$	405.220	−	405.220i	0.635142	−	0.635142i
$639$			524.130i			0.820235i
$640$	37.6162	−	262.256i	0.0587753	−	0.409775i
$641$	8.24820			0.0128677			0.00643385	−	0.999979i	$-0.497952\pi$
$641$	8.24820			0.0128677			0.00643385	+	0.999979i	$0.497952\pi$
$642$	13.8838	+	13.8838i	0.0216258	+	0.0216258i
$643$	187.955	−	187.955i	0.292310	−	0.292310i	−0.545682	−	0.837992i	$-0.683730\pi$
$643$	187.955	−	187.955i	0.292310	−	0.292310i	0.837992	+	0.545682i	$0.183730\pi$
$644$			106.080i			0.164720i
$645$	−16.5526	−	22.0961i	−0.0256629	−	0.0342575i
$646$	−16.5997			−0.0256962
$647$	−827.190	−	827.190i	−1.27850	−	1.27850i	−0.941507	−	0.336994i	$-0.890590\pi$
$647$	−827.190	−	827.190i	−1.27850	−	1.27850i	−0.336994	−	0.941507i	$-0.609410\pi$
$648$	453.801	−	453.801i	0.700311	−	0.700311i
$649$		−	1376.29i		−	2.12063i
$650$	187.166	−	639.028i	0.287948	−	0.983119i
$651$	41.9227			0.0643974
$652$	61.3009	+	61.3009i	0.0940198	+	0.0940198i
$653$	−415.451	+	415.451i	−0.636219	+	0.636219i	−0.949621	−	0.313402i	$-0.898531\pi$
$653$	−415.451	+	415.451i	−0.636219	+	0.636219i	0.313402	+	0.949621i	$0.398531\pi$
$654$			27.3015i			0.0417453i
$655$	496.234	−	371.738i	0.757609	−	0.567539i
$656$	−88.8695			−0.135472
$657$	512.674	+	512.674i	0.780326	+	0.780326i
$658$	75.1065	−	75.1065i	0.114144	−	0.114144i
$659$		−	205.262i		−	0.311475i	−0.987798	−	0.155738i	$-0.950225\pi$
$659$		−	205.262i		−	0.311475i	0.987798	−	0.155738i	$-0.0497755\pi$
$660$	−70.2963	−	10.0828i	−0.106510	−	0.0152770i
$661$	453.263			0.685723			0.342862	−	0.939386i	$-0.388604\pi$
$661$	453.263			0.685723			0.342862	+	0.939386i	$0.388604\pi$
$662$	−27.3179	−	27.3179i	−0.0412658	−	0.0412658i
$663$	−11.0214	+	11.0214i	−0.0166236	+	0.0166236i
$664$		−	408.560i		−	0.615301i
$665$	−11.2431	+	78.3856i	−0.0169069	+	0.117873i
$666$	−11.3882			−0.0170994
$667$	324.405	+	324.405i	0.486365	+	0.486365i
$668$	95.9392	−	95.9392i	0.143622	−	0.143622i
$669$		−	38.9180i		−	0.0581734i
$670$	106.594	+	142.292i	0.159095	+	0.212377i
$671$	−997.926			−1.48722
$672$	−21.4304	−	21.4304i	−0.0318905	−	0.0318905i
$673$	−82.5125	+	82.5125i	−0.122604	+	0.122604i	−0.765746	−	0.643143i	$-0.777630\pi$
$673$	−82.5125	+	82.5125i	−0.122604	+	0.122604i	0.643143	+	0.765746i	$0.277630\pi$
$674$		−	675.230i		−	1.00182i
$675$	149.253	−	81.6296i	0.221116	−	0.120933i
$676$	−491.050			−0.726405
$677$	190.253	+	190.253i	0.281024	+	0.281024i	0.833517	−	0.552493i	$-0.186324\pi$
$677$	190.253	+	190.253i	0.281024	+	0.281024i	−0.552493	+	0.833517i	$0.686324\pi$
$678$	−32.7766	+	32.7766i	−0.0483430	+	0.0483430i
$679$		−	499.984i		−	0.736353i
$680$	−68.7349	+	51.4906i	−0.101081	+	0.0757214i
$681$	69.4607			0.101998
$682$	671.088	+	671.088i	0.984001	+	0.984001i
$683$	−689.089	+	689.089i	−1.00892	+	1.00892i	−0.00895579	+	0.999960i	$0.502851\pi$
$683$	−689.089	+	689.089i	−1.00892	+	1.00892i	−0.999960	+	0.00895579i	$0.997149\pi$
$684$		−	116.293i		−	0.170019i
$685$	948.653	+	136.068i	1.38489	+	0.198640i
$686$	−24.8889			−0.0362811
$687$	5.84384	+	5.84384i	0.00850632	+	0.00850632i
$688$	24.6930	−	24.6930i	0.0358910	−	0.0358910i
$689$		−	606.413i		−	0.880135i
$690$	−6.64441	+	46.3241i	−0.00962959	+	0.0671364i
$691$	624.703			0.904057			0.452029	−	0.892003i	$-0.350701\pi$
$691$	624.703			0.904057			0.452029	+	0.892003i	$0.350701\pi$
$692$	−38.3300	−	38.3300i	−0.0553902	−	0.0553902i
$693$	281.386	−	281.386i	0.406040	−	0.406040i
$694$			516.262i			0.743893i
$695$	317.989	+	424.485i	0.457539	+	0.610769i
$696$	−79.6419			−0.114428
$697$	−53.7983	−	53.7983i	−0.0771856	−	0.0771856i
$698$	573.419	−	573.419i	0.821517	−	0.821517i
$699$			71.6057i			0.102440i
$700$	69.6347	+	127.322i	0.0994781	+	0.181888i
$701$	−94.5103			−0.134822			−0.0674110	−	0.997725i	$-0.521474\pi$
$701$	−94.5103			−0.134822			−0.0674110	+	0.997725i	$0.521474\pi$
$702$	128.158	+	128.158i	0.182561	+	0.182561i
$703$	−4.05085	+	4.05085i	−0.00576223	+	0.00576223i
$704$		−	849.871i		−	1.20720i
$705$	−45.5601	+	34.1299i	−0.0646242	+	0.0484112i
$706$	131.639			0.186458
$707$	−18.4790	−	18.4790i	−0.0261373	−	0.0261373i
$708$	−47.9067	+	47.9067i	−0.0676648	+	0.0676648i
$709$			530.564i			0.748327i	0.927363	+	0.374163i	$0.122070\pi$
$709$			530.564i			0.748327i	−0.927363	+	0.374163i	$0.877930\pi$
$710$	−393.703	−	56.4700i	−0.554511	−	0.0795353i
$711$	−850.692			−1.19647
$712$	−275.407	−	275.407i	−0.386808	−	0.386808i
$713$	−537.250	+	537.250i	−0.753506	+	0.753506i
$714$			2.79619i			0.00391623i
$715$	−238.992	+	1666.22i	−0.334254	+	2.33038i
$716$	−296.809			−0.414538
$717$	53.9272	+	53.9272i	0.0752122	+	0.0752122i
$718$	−406.603	+	406.603i	−0.566300	+	0.566300i
$719$			948.213i			1.31879i	0.751795	+	0.659397i	$0.229188\pi$
$719$			948.213i			1.31879i	−0.751795	+	0.659397i	$0.770812\pi$
$720$	63.9799	+	85.4069i	0.0888609	+	0.118621i
$721$	−196.500			−0.272539
$722$	−308.994	−	308.994i	−0.427970	−	0.427970i
$723$	60.7191	−	60.7191i	0.0839822	−	0.0839822i
$724$			717.001i			0.990332i
$725$	602.316	+	176.414i	0.830781	+	0.243329i
$726$	−85.8010			−0.118183
$727$	70.0084	+	70.0084i	0.0962977	+	0.0962977i	0.753614	−	0.657317i	$-0.228309\pi$
$727$	70.0084	+	70.0084i	0.0962977	+	0.0962977i	−0.657317	+	0.753614i	$0.728309\pi$
$728$	−308.644	+	308.644i	−0.423961	+	0.423961i
$729$		−	659.356i		−	0.904466i
$730$	−440.334	+	329.862i	−0.603197	+	0.451866i
$731$	29.8965			0.0408981
$732$	34.7364	+	34.7364i	0.0474541	+	0.0474541i
$733$	493.670	−	493.670i	0.673493	−	0.673493i	−0.285027	−	0.958520i	$-0.592002\pi$
$733$	493.670	−	493.670i	0.673493	−	0.673493i	0.958520	+	0.285027i	$0.0920024\pi$
$734$			702.457i			0.957025i
$735$	13.2039	+	1.89387i	0.0179644	+	0.00257670i
$736$	549.271			0.746293
$737$	−317.802	−	317.802i	−0.431210	−	0.431210i
$738$	−310.241	+	310.241i	−0.420381	+	0.420381i
$739$		−	1057.78i		−	1.43137i	−0.698422	−	0.715686i	$-0.746114\pi$
$739$		−	1057.78i		−	1.43137i	0.698422	−	0.715686i	$-0.253886\pi$
$740$	−1.49058	+	10.3922i	−0.00201430	+	0.0140435i
$741$	45.2156			0.0610197
$742$	−76.9249	−	76.9249i	−0.103672	−	0.103672i
$743$	501.427	−	501.427i	0.674868	−	0.674868i	−0.283966	−	0.958834i	$-0.591650\pi$
$743$	501.427	−	501.427i	0.674868	−	0.674868i	0.958834	+	0.283966i	$0.0916504\pi$
$744$		−	131.895i		−	0.177279i
$745$	−335.565	−	447.946i	−0.450422	−	0.601270i
$746$	−17.7957			−0.0238549
$747$	−307.318	−	307.318i	−0.411403	−	0.411403i
$748$	54.3774	−	54.3774i	0.0726970	−	0.0726970i
$749$			101.428i			0.135418i
$750$	22.4339	+	59.9618i	0.0299119	+	0.0799491i
$751$	88.3274			0.117613			0.0588065	−	0.998269i	$-0.481270\pi$
$751$	88.3274			0.117613			0.0588065	+	0.998269i	$0.481270\pi$
$752$	−50.9147	−	50.9147i	−0.0677057	−	0.0677057i
$753$	102.697	−	102.697i	0.136383	−	0.136383i
$754$			668.665i			0.886823i
$755$	−130.973	+	98.1142i	−0.173474	+	0.129953i
$756$	−39.4999			−0.0522485
$757$	540.844	+	540.844i	0.714457	+	0.714457i	0.967464	−	0.253007i	$-0.0814196\pi$
$757$	540.844	+	540.844i	0.714457	+	0.714457i	−0.253007	+	0.967464i	$0.581420\pi$
$758$	118.748	−	118.748i	0.156659	−	0.156659i
$759$		−	118.302i		−	0.155866i
$760$	246.614	+	35.3726i	0.324492	+	0.0465429i
$761$	230.617			0.303045			0.151522	−	0.988454i	$-0.451582\pi$
$761$	230.617			0.303045			0.151522	+	0.988454i	$0.451582\pi$
$762$	66.4210	+	66.4210i	0.0871667	+	0.0871667i
$763$	−99.7256	+	99.7256i	−0.130702	+	0.130702i
$764$		−	295.204i		−	0.386393i
$765$	−12.9711	+	90.4333i	−0.0169557	+	0.118213i
$766$	−744.124			−0.971441
$767$	1135.52	+	1135.52i	1.48048	+	1.48048i
$768$	−73.1239	+	73.1239i	−0.0952134	+	0.0952134i
$769$		−	1112.96i		−	1.44729i	−0.690173	−	0.723644i	$-0.742466\pi$
$769$		−	1112.96i		−	1.44729i	0.690173	−	0.723644i	$-0.257534\pi$
$770$	181.048	+	241.681i	0.235127	+	0.313871i
$771$	−3.77558			−0.00489699
$772$	−502.109	−	502.109i	−0.650400	−	0.650400i
$773$	−510.214	+	510.214i	−0.660043	+	0.660043i	−0.955390	−	0.295347i	$-0.904565\pi$
$773$	−510.214	+	510.214i	−0.660043	+	0.660043i	0.295347	+	0.955390i	$0.404565\pi$
$774$		−	172.406i		−	0.222746i
$775$	−292.160	+	997.500i	−0.376980	+	1.28710i
$776$	−1573.03			−2.02710
$777$	0.682355	+	0.682355i	0.000878192	+	0.000878192i
$778$	65.3273	−	65.3273i	0.0839683	−	0.0839683i
$779$			220.709i			0.283323i
$780$	66.3178	−	49.6799i	0.0850228	−	0.0636922i
$781$	1005.44			1.28737
$782$	−35.8338	−	35.8338i	−0.0458233	−	0.0458233i
$783$	−120.795	+	120.795i	−0.154273	+	0.154273i
$784$			16.8722i			0.0215206i
$785$	−876.274	−	125.687i	−1.11627	−	0.160110i
$786$	−63.5120			−0.0808041
$787$	595.409	+	595.409i	0.756555	+	0.756555i	0.975694	−	0.219139i	$-0.0703247\pi$
$787$	595.409	+	595.409i	0.756555	+	0.756555i	−0.219139	+	0.975694i	$0.570325\pi$
$788$	262.195	−	262.195i	0.332735	−	0.332735i
$789$			171.416i			0.217257i
$790$	91.6540	−	639.002i	0.116018	−	0.808863i
$791$	−239.450			−0.302718
$792$	−885.284	−	885.284i	−1.11778	−	1.11778i
$793$	823.352	−	823.352i	1.03827	−	1.03827i
$794$		−	953.163i		−	1.20046i
$795$	34.9562	+	46.6631i	0.0439701	+	0.0586957i
$796$	−89.0186			−0.111832
$797$	696.032	+	696.032i	0.873315	+	0.873315i	0.992832	−	0.119517i	$-0.0381347\pi$
$797$	696.032	+	696.032i	0.873315	+	0.873315i	−0.119517	+	0.992832i	$0.538135\pi$
$798$	5.73570	−	5.73570i	0.00718760	−	0.00718760i
$799$		−	61.6438i		−	0.0771512i
$800$	659.259	−	360.562i	0.824074	−	0.450702i
$801$	−414.321			−0.517254
$802$	370.917	+	370.917i	0.462490	+	0.462490i
$803$	983.460	−	983.460i	1.22473	−	1.22473i
$804$			22.1245i			0.0275180i
$805$	−193.481	+	144.940i	−0.240349	+	0.180050i
$806$	−1107.38			−1.37392
$807$	−51.9485	−	51.9485i	−0.0643724	−	0.0643724i
$808$	−58.1380	+	58.1380i	−0.0719530	+	0.0719530i
$809$		−	771.743i		−	0.953947i	−0.878918	−	0.476973i	$-0.841734\pi$
$809$		−	771.743i		−	0.953947i	0.878918	−	0.476973i	$-0.158266\pi$
$810$	512.811	+	73.5540i	0.633100	+	0.0908075i
$811$	−1016.79			−1.25374			−0.626871	−	0.779123i	$-0.715665\pi$
$811$	−1016.79			−1.25374			−0.626871	+	0.779123i	$0.715665\pi$
$812$	−103.045	−	103.045i	−0.126903	−	0.126903i
$813$	58.2741	−	58.2741i	0.0716778	−	0.0716778i
$814$			21.8459i			0.0268378i
$815$	−28.0505	+	195.565i	−0.0344178	+	0.239957i
$816$	1.89553			0.00232296
$817$	−61.3255	−	61.3255i	−0.0750618	−	0.0750618i
$818$	−42.4594	+	42.4594i	−0.0519064	+	0.0519064i
$819$			464.322i			0.566937i
$820$	242.500	+	323.714i	0.295732	+	0.394773i
$821$	1555.27			1.89436			0.947180	−	0.320703i	$-0.103919\pi$
$821$	1555.27			1.89436			0.947180	+	0.320703i	$0.103919\pi$
$822$	−69.4157	−	69.4157i	−0.0844473	−	0.0844473i
$823$	758.352	−	758.352i	0.921449	−	0.921449i	−0.0756833	−	0.997132i	$-0.524114\pi$
$823$	758.352	−	758.352i	0.921449	−	0.921449i	0.997132	+	0.0756833i	$0.0241138\pi$
$824$			618.221i			0.750268i
$825$	−77.6579	−	141.991i	−0.0941307	−	0.172111i
$826$	288.088			0.348775
$827$	−191.726	−	191.726i	−0.231833	−	0.231833i	0.581624	−	0.813457i	$-0.302417\pi$
$827$	−191.726	−	191.726i	−0.231833	−	0.231833i	−0.813457	+	0.581624i	$0.802417\pi$
$828$	251.041	−	251.041i	0.303190	−	0.303190i
$829$			1346.18i			1.62386i	0.583752	+	0.811932i	$0.301584\pi$
$829$			1346.18i			1.62386i	−0.583752	+	0.811932i	$0.698416\pi$
$830$	263.954	−	197.733i	0.318017	−	0.238232i
$831$	6.78399			0.00816365
$832$	701.197	+	701.197i	0.842785	+	0.842785i
$833$	−10.2138	+	10.2138i	−0.0122615	+	0.0122615i
$834$		−	54.3290i		−	0.0651426i
$835$	306.070	+	43.9006i	0.366551	+	0.0525756i
$836$	−223.084			−0.266847
$837$	−200.050	−	200.050i	−0.239009	−	0.239009i
$838$	342.522	−	342.522i	0.408737	−	0.408737i
$839$		−	1182.23i		−	1.40910i	−0.709656	−	0.704548i	$-0.751150\pi$
$839$		−	1182.23i		−	1.40910i	0.709656	−	0.704548i	$-0.248850\pi$
$840$	5.95842	−	41.5415i	0.00709336	−	0.0494541i
$841$	210.749			0.250594
$842$	37.1664	+	37.1664i	0.0441406	+	0.0441406i
$843$	46.9336	−	46.9336i	0.0556745	−	0.0556745i
$844$			698.901i			0.828082i
$845$	−670.937	−	895.635i	−0.794008	−	1.05992i
$846$	−355.484			−0.420194
$847$	−313.410	−	313.410i	−0.370024	−	0.370024i
$848$	−52.1474	+	52.1474i	−0.0614946	+	0.0614946i
$849$			123.119i			0.145017i
$850$	−66.5319	−	19.4867i	−0.0782728	−	0.0229255i
$851$	−17.4891			−0.0205512
$852$	−34.9978	−	34.9978i	−0.0410772	−	0.0410772i
$853$	−782.971	+	782.971i	−0.917903	+	0.917903i	−0.996877	−	0.0789736i	$-0.974836\pi$
$853$	−782.971	+	782.971i	−0.917903	+	0.917903i	0.0789736	+	0.996877i	$0.474836\pi$
$854$		−	208.888i		−	0.244600i
$855$	212.109	−	158.895i	0.248081	−	0.185842i
$856$	319.109			0.372791
$857$	−556.260	−	556.260i	−0.649078	−	0.649078i	0.303692	−	0.952770i	$-0.401781\pi$
$857$	−556.260	−	556.260i	−0.649078	−	0.649078i	−0.952770	+	0.303692i	$0.901781\pi$
$858$	121.922	−	121.922i	0.142101	−	0.142101i
$859$		−	1126.23i		−	1.31110i	−0.755153	−	0.655548i	$-0.772438\pi$
$859$		−	1126.23i		−	1.31110i	0.755153	−	0.655548i	$-0.227562\pi$
$860$	−157.327	−	22.5659i	−0.182938	−	0.0262394i
$861$	37.1778			0.0431798
$862$	−209.287	−	209.287i	−0.242793	−	0.242793i
$863$	−8.03225	+	8.03225i	−0.00930735	+	0.00930735i	−0.711745	−	0.702438i	$-0.752095\pi$
$863$	−8.03225	+	8.03225i	−0.00930735	+	0.00930735i	0.702438	+	0.711745i	$0.252095\pi$
$864$			204.527i			0.236721i
$865$	17.5393	−	122.282i	0.0202767	−	0.141367i
$866$	−15.9063			−0.0183676
$867$	−76.7347	−	76.7347i	−0.0885059	−	0.0885059i
$868$	170.654	−	170.654i	0.196606	−	0.196606i
$869$			1631.88i			1.87788i
$870$	−38.5446	−	51.4533i	−0.0443042	−	0.0591418i
$871$	524.413			0.602081
$872$	313.753	+	313.753i	0.359808	+	0.359808i
$873$	−1183.23	+	1183.23i	−1.35536	+	1.35536i
$874$			147.009i			0.168202i
$875$	−137.080	+	300.972i	−0.156663	+	0.343968i
$876$	−68.4657			−0.0781572
$877$	−735.885	−	735.885i	−0.839093	−	0.839093i	0.149646	−	0.988740i	$-0.452186\pi$
$877$	−735.885	−	735.885i	−0.839093	−	0.839093i	−0.988740	+	0.149646i	$0.952186\pi$
$878$	−396.735	+	396.735i	−0.451863	+	0.451863i
$879$		−	94.1231i		−	0.107080i
$880$	163.836	−	122.732i	0.186177	−	0.139468i
$881$	877.809			0.996378			0.498189	−	0.867068i	$-0.333999\pi$
$881$	877.809			0.996378			0.498189	+	0.867068i	$0.333999\pi$
$882$	58.9003	+	58.9003i	0.0667804	+	0.0667804i
$883$	541.635	−	541.635i	0.613403	−	0.613403i	−0.330428	−	0.943831i	$-0.607193\pi$
$883$	541.635	−	541.635i	0.613403	−	0.613403i	0.943831	+	0.330428i	$0.107193\pi$
$884$			89.7295i			0.101504i
$885$	−152.834	−	21.9215i	−0.172694	−	0.0247701i
$886$	172.326			0.194499
$887$	748.157	+	748.157i	0.843470	+	0.843470i	0.989308	−	0.145839i	$-0.0465881\pi$
$887$	748.157	+	748.157i	0.843470	+	0.843470i	−0.145839	+	0.989308i	$0.546588\pi$
$888$	2.14680	−	2.14680i	0.00241756	−	0.00241756i
$889$			485.240i			0.545827i
$890$	44.6391	−	311.219i	0.0501563	−	0.349684i
$891$	−1309.61			−1.46982
$892$	−158.423	−	158.423i	−0.177604	−	0.177604i
$893$	−126.447	+	126.447i	−0.141598	+	0.141598i
$894$			57.3317i			0.0641294i
$895$	−405.540	−	541.356i	−0.453117	−	0.604868i
$896$	−140.193			−0.156465
$897$	97.6067	+	97.6067i	0.108815	+	0.108815i
$898$	215.970	−	215.970i	0.240501	−	0.240501i
$899$		−	1043.76i		−	1.16103i
$900$	136.518	−	466.103i	0.151687	−	0.517893i
$901$	−63.1363			−0.0700735
$902$	595.134	+	595.134i	0.659794	+	0.659794i
$903$	−10.3301	+	10.3301i	−0.0114398	+	0.0114398i
$904$			753.347i			0.833348i
$905$	−1307.75	+	979.661i	−1.44503	+	1.08250i
$906$	16.7630			0.0185022
$907$	−137.796	−	137.796i	−0.151925	−	0.151925i	0.627052	−	0.778977i	$-0.284261\pi$
$907$	−137.796	−	137.796i	−0.151925	−	0.151925i	−0.778977	+	0.627052i	$0.784261\pi$
$908$	282.753	−	282.753i	0.311402	−	0.311402i
$909$			87.4625i			0.0962184i
$910$	−348.778	−	50.0263i	−0.383272	−	0.0549739i
$911$	481.053			0.528049			0.264024	−	0.964516i	$-0.414950\pi$
$911$	481.053			0.528049			0.264024	+	0.964516i	$0.414950\pi$
$912$	−3.88823	−	3.88823i	−0.00426341	−	0.00426341i
$913$	−589.526	+	589.526i	−0.645702	+	0.645702i
$914$		−	375.716i		−	0.411068i
$915$	−15.8950	+	110.818i	−0.0173715	+	0.121112i
$916$	47.5769			0.0519399
$917$	−231.994	−	231.994i	−0.252992	−	0.252992i
$918$	13.3431	−	13.3431i	0.0145349	−	0.0145349i
$919$		−	189.464i		−	0.206163i	−0.994673	−	0.103081i	$-0.967130\pi$
$919$		−	189.464i		−	0.206163i	0.994673	−	0.103081i	$-0.0328702\pi$
$920$	456.006	+	608.723i	0.495658	+	0.661655i
$921$	−162.840			−0.176808
$922$	−86.3392	−	86.3392i	−0.0936434	−	0.0936434i
$923$	−829.547	+	829.547i	−0.898751	+	0.898751i
$924$			37.5780i			0.0406688i
$925$	−20.9912	+	11.4805i	−0.0226931	+	0.0124113i
$926$	1143.52			1.23491
$927$	465.024	+	465.024i	0.501644	+	0.501644i
$928$	−533.559	+	533.559i	−0.574956	+	0.574956i
$929$		−	145.596i		−	0.156723i	−0.996925	−	0.0783615i	$-0.975031\pi$
$929$		−	145.596i		−	0.156723i	0.996925	−	0.0783615i	$-0.0249688\pi$
$930$	85.2122	−	63.8341i	0.0916260	−	0.0686388i
$931$	41.9023			0.0450078
$932$	291.484	+	291.484i	0.312751	+	0.312751i
$933$	89.7982	−	89.7982i	0.0962467	−	0.0962467i
$934$			522.237i			0.559140i
$935$	173.478	+	24.8824i	0.185538	+	0.0266122i
$936$	1460.83			1.56072
$937$	−150.021	−	150.021i	−0.160108	−	0.160108i	0.622506	−	0.782615i	$-0.286114\pi$
$937$	−150.021	−	150.021i	−0.160108	−	0.160108i	−0.782615	+	0.622506i	$0.786114\pi$
$938$	66.5230	−	66.5230i	0.0709200	−	0.0709200i
$939$			191.886i			0.204351i
$940$	−46.5287	+	324.393i	−0.0494986	+	0.345099i
$941$	−237.719			−0.252624			−0.126312	−	0.991991i	$-0.540314\pi$
$941$	−237.719			−0.252624			−0.126312	+	0.991991i	$0.540314\pi$
$942$	64.1195	+	64.1195i	0.0680674	+	0.0680674i
$943$	−476.443	+	476.443i	−0.505242	+	0.505242i
$944$		−	195.295i		−	0.206880i
$945$	−53.9700	−	72.0446i	−0.0571111	−	0.0762377i
$946$	−330.725			−0.349603
$947$	−644.486	−	644.486i	−0.680555	−	0.680555i	0.279570	−	0.960125i	$-0.409808\pi$
$947$	−644.486	−	644.486i	−0.680555	−	0.680555i	−0.960125	+	0.279570i	$0.909808\pi$
$948$	56.8034	−	56.8034i	0.0599192	−	0.0599192i
$949$			1622.83i			1.71004i
$950$	96.5020	+	176.446i	0.101581	+	0.185733i
$951$	−134.312			−0.141233
$952$	32.1342	+	32.1342i	0.0337544	+	0.0337544i
$953$	−791.922	+	791.922i	−0.830978	+	0.830978i	−0.987651	−	0.156673i	$-0.949923\pi$
$953$	−791.922	+	791.922i	−0.830978	+	0.830978i	0.156673	+	0.987651i	$0.449923\pi$
$954$			364.091i			0.381646i
$955$	538.429	−	403.347i	0.563800	−	0.422353i
$956$	439.041			0.459248
$957$	114.918	+	114.918i	0.120082	+	0.120082i
$958$	122.040	−	122.040i	0.127391	−	0.127391i
$959$		−	507.117i		−	0.528798i
$960$	−94.3766	−	13.5367i	−0.0983090	−	0.0141008i
$961$	767.583			0.798733
$962$	−18.0243	−	18.0243i	−0.0187363	−	0.0187363i
$963$	240.033	−	240.033i	0.249256	−	0.249256i
$964$		−	494.337i		−	0.512798i
$965$	229.759	−	1601.85i	0.238092	−	1.65995i
$966$	24.7633			0.0256349
$967$	−660.928	−	660.928i	−0.683483	−	0.683483i	0.277300	−	0.960783i	$-0.410560\pi$
$967$	−660.928	−	660.928i	−0.683483	−	0.683483i	−0.960783	+	0.277300i	$0.910560\pi$
$968$	−986.039	+	986.039i	−1.01864	+	1.01864i
$969$		−	4.70759i		−	0.00485819i
$970$	−761.306	−	1016.27i	−0.784851	−	1.04770i
$971$	222.190			0.228826			0.114413	−	0.993433i	$-0.463501\pi$
$971$	222.190			0.228826			0.114413	+	0.993433i	$0.463501\pi$
$972$	140.597	+	140.597i	0.144647	+	0.144647i
$973$	198.451	−	198.451i	0.203957	−	0.203957i
$974$		−	582.031i		−	0.597568i
$975$	181.224	+	53.0792i	0.185871	+	0.0544402i
$976$	−141.605			−0.145087
$977$	−251.707	−	251.707i	−0.257633	−	0.257633i	0.566458	−	0.824091i	$-0.308313\pi$
$977$	−251.707	−	251.707i	−0.257633	−	0.257633i	−0.824091	+	0.566458i	$0.808313\pi$
$978$	14.3101	−	14.3101i	0.0146320	−	0.0146320i
$979$			794.789i			0.811838i
$980$	61.4582	−	46.0395i	0.0627124	−	0.0469790i
$981$	472.008			0.481149
$982$	230.484	+	230.484i	0.234708	+	0.234708i
$983$	641.511	−	641.511i	0.652605	−	0.652605i	−0.301014	−	0.953620i	$-0.597325\pi$
$983$	641.511	−	641.511i	0.652605	−	0.652605i	0.953620	+	0.301014i	$0.0973252\pi$
$984$		−	116.967i		−	0.118869i
$985$	836.468	+	119.977i	0.849206	+	0.121804i
$986$	69.6175			0.0706060
$987$	21.2998	+	21.2998i	0.0215803	+	0.0215803i
$988$	184.059	−	184.059i	0.186294	−	0.186294i
$989$		−	264.766i		−	0.267711i
$990$	143.491	−	1000.40i	0.144940	−	1.01051i
$991$	13.1535			0.0132730			0.00663650	−	0.999978i	$-0.497888\pi$
$991$	13.1535			0.0132730			0.00663650	+	0.999978i	$0.497888\pi$
$992$	−883.631	−	883.631i	−0.890757	−	0.890757i
$993$	7.74720	−	7.74720i	0.00780181	−	0.00780181i
$994$			210.460i			0.211730i
$995$	−121.629	−	162.363i	−0.122240	−	0.163179i
$996$	41.0411			0.0412059
$997$	−786.874	−	786.874i	−0.789241	−	0.789241i	0.192128	−	0.981370i	$-0.438461\pi$
$997$	−786.874	−	786.874i	−0.789241	−	0.789241i	−0.981370	+	0.192128i	$0.938461\pi$
$998$	−468.162	+	468.162i	−0.469100	+	0.469100i
$999$		−	6.51224i		−	0.00651875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.g.a.22.3	yes	12
3.2	odd	2		315.3.o.a.127.4		12
4.3	odd	2		560.3.bh.e.337.3		12
5.2	odd	4		175.3.g.b.43.4		12
5.3	odd	4	inner	35.3.g.a.8.3	✓	12
5.4	even	2		175.3.g.b.57.4		12
7.2	even	3		245.3.m.d.67.3		24
7.3	odd	6		245.3.m.c.177.4		24
7.4	even	3		245.3.m.d.177.4		24
7.5	odd	6		245.3.m.c.67.3		24
7.6	odd	2		245.3.g.a.197.3		12
15.8	even	4		315.3.o.a.253.4		12
20.3	even	4		560.3.bh.e.113.3		12
35.3	even	12		245.3.m.c.128.3		24
35.13	even	4		245.3.g.a.148.3		12
35.18	odd	12		245.3.m.d.128.3		24
35.23	odd	12		245.3.m.d.18.4		24
35.33	even	12		245.3.m.c.18.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.g.a.8.3	✓	12	5.3	odd	4	inner
35.3.g.a.22.3	yes	12	1.1	even	1	trivial
175.3.g.b.43.4		12	5.2	odd	4
175.3.g.b.57.4		12	5.4	even	2
245.3.g.a.148.3		12	35.13	even	4
245.3.g.a.197.3		12	7.6	odd	2
245.3.m.c.18.4		24	35.33	even	12
245.3.m.c.67.3		24	7.5	odd	6
245.3.m.c.128.3		24	35.3	even	12
245.3.m.c.177.4		24	7.3	odd	6
245.3.m.d.18.4		24	35.23	odd	12
245.3.m.d.67.3		24	7.2	even	3
245.3.m.d.128.3		24	35.18	odd	12
245.3.m.d.177.4		24	7.4	even	3
315.3.o.a.127.4		12	3.2	odd	2
315.3.o.a.253.4		12	15.8	even	4
560.3.bh.e.113.3		12	20.3	even	4
560.3.bh.e.337.3		12	4.3	odd	2

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.950261 - 0.950261i) q^{2} +(0.269488 - 0.269488i) q^{3} -2.19401i q^{4} +(4.00169 - 2.99774i) q^{5} -0.512169 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.88593 + 5.88593i) q^{8} +8.85475i q^{9} +O(q^{10})\)	\(q+(-0.950261 - 0.950261i) q^{2} +(0.269488 - 0.269488i) q^{3} -2.19401i q^{4} +(4.00169 - 2.99774i) q^{5} -0.512169 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-5.88593 + 5.88593i) q^{8} +8.85475i q^{9} +(-6.65129 - 0.954016i) q^{10} +16.9860 q^{11} +(-0.591259 - 0.591259i) q^{12} +(-14.0145 + 14.0145i) q^{13} +3.55555i q^{14} +(0.270553 - 1.88627i) q^{15} +2.41031 q^{16} +(1.45911 + 1.45911i) q^{17} +(8.41433 - 8.41433i) q^{18} -5.98604i q^{19} +(-6.57707 - 8.77974i) q^{20} -1.00833 q^{21} +(-16.1412 - 16.1412i) q^{22} +(12.9220 - 12.9220i) q^{23} +3.17238i q^{24} +(7.02709 - 23.9921i) q^{25} +26.6349 q^{26} +(4.81165 + 4.81165i) q^{27} +(-4.10461 + 4.10461i) q^{28} +25.1048i q^{29} +(-2.04954 + 1.53535i) q^{30} -41.5762 q^{31} +(21.2533 + 21.2533i) q^{32} +(4.57753 - 4.57753i) q^{33} -2.77308i q^{34} +(-13.0947 - 1.87822i) q^{35} +19.4274 q^{36} +(-0.676716 - 0.676716i) q^{37} +(-5.68830 + 5.68830i) q^{38} +7.55351i q^{39} +(-5.90918 + 41.1981i) q^{40} -36.8706 q^{41} +(0.958180 + 0.958180i) q^{42} +(10.2448 - 10.2448i) q^{43} -37.2674i q^{44} +(26.5443 + 35.4340i) q^{45} -24.5586 q^{46} +(-21.1237 - 21.1237i) q^{47} +(0.649550 - 0.649550i) q^{48} +7.00000i q^{49} +(-29.4763 + 16.1212i) q^{50} +0.786428 q^{51} +(30.7480 + 30.7480i) q^{52} +(-21.6352 + 21.6352i) q^{53} -9.14465i q^{54} +(67.9728 - 50.9197i) q^{55} +22.0231 q^{56} +(-1.61317 - 1.61317i) q^{57} +(23.8561 - 23.8561i) q^{58} -81.0248i q^{59} +(-4.13848 - 0.593595i) q^{60} -58.7499 q^{61} +(39.5083 + 39.5083i) q^{62} +(16.5657 - 16.5657i) q^{63} -50.0336i q^{64} +(-14.0699 + 98.0938i) q^{65} -8.69971 q^{66} +(-18.7096 - 18.7096i) q^{67} +(3.20130 - 3.20130i) q^{68} -6.96468i q^{69} +(10.6586 + 14.2282i) q^{70} +59.1919 q^{71} +(-52.1184 - 52.1184i) q^{72} +(57.8982 - 57.8982i) q^{73} +1.28611i q^{74} +(-4.57187 - 8.35931i) q^{75} -13.1334 q^{76} +(-31.7779 - 31.7779i) q^{77} +(7.17781 - 7.17781i) q^{78} +96.0718i q^{79} +(9.64532 - 7.22548i) q^{80} -77.0994 q^{81} +(35.0367 + 35.0367i) q^{82} +(-34.7065 + 34.7065i) q^{83} +2.21229i q^{84} +(10.2130 + 1.46488i) q^{85} -19.4704 q^{86} +(6.76545 + 6.76545i) q^{87} +(-99.9784 + 99.9784i) q^{88} +46.7908i q^{89} +(8.44757 - 58.8955i) q^{90} +52.4376 q^{91} +(-28.3510 - 28.3510i) q^{92} +(-11.2043 + 11.2043i) q^{93} +40.1461i q^{94} +(-17.9446 - 23.9543i) q^{95} +11.4550 q^{96} +(133.626 + 133.626i) q^{97} +(6.65183 - 6.65183i) q^{98} +150.407i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8	\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 24 * q^6 + 24 * q^8 + 28 * q^10 - 12 * q^11 + 16 * q^12 - 4 * q^13 - 64 * q^15 + 40 * q^16 - 12 * q^17 - 56 * q^18 + 60 * q^20 + 28 * q^21 - 68 * q^22 - 16 * q^23 + 64 * q^25 - 56 * q^26 + 164 * q^27 - 76 * q^30 - 96 * q^31 + 32 * q^32 + 124 * q^33 + 232 * q^36 - 104 * q^37 + 80 * q^38 - 124 * q^40 - 208 * q^41 - 140 * q^42 + 76 * q^43 + 92 * q^45 - 80 * q^46 - 164 * q^47 - 392 * q^48 - 52 * q^50 + 220 * q^51 + 216 * q^52 - 204 * q^53 + 116 * q^55 + 168 * q^56 - 236 * q^57 + 356 * q^58 + 152 * q^60 + 280 * q^61 + 568 * q^62 + 112 * q^63 - 192 * q^65 - 544 * q^66 + 324 * q^67 + 184 * q^68 - 112 * q^70 + 144 * q^71 - 440 * q^72 - 248 * q^73 + 108 * q^75 - 632 * q^76 - 56 * q^77 + 12 * q^78 + 60 * q^80 - 260 * q^81 - 376 * q^82 - 224 * q^83 - 324 * q^85 + 456 * q^86 + 244 * q^87 - 24 * q^88 + 780 * q^90 + 84 * q^91 - 424 * q^92 + 236 * q^93 + 52 * q^95 + 504 * q^96 + 564 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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