LMFDB - Embedded newform 338.3.f.h.89.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,3,Mod(19,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.f (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0,0,6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.612074651904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.1
Root			$-4.71318 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.89
Dual form			338.3.f.h.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 1.36603i) q^{2} +(-2.78960 - 4.83174i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.323893 + 0.323893i) q^{5} +(-7.62134 + 2.04213i) q^{6} +(-2.05755 - 7.67890i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-11.0638 + 19.1630i) q^{9} +(0.560999 - 0.323893i) q^{10} +(-5.40655 - 1.44868i) q^{11} +11.1584i q^{12} -11.2427 q^{14} +(0.661433 - 2.46850i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.74285 + 1.00623i) q^{17} +(22.1276 + 22.1276i) q^{18} +(-4.47512 + 1.19911i) q^{19} +(-0.237106 - 0.884892i) q^{20} +(-31.3626 + 31.3626i) q^{21} +(-3.95787 + 6.85523i) q^{22} +(15.0976 - 8.71663i) q^{23} +(15.2427 + 4.08426i) q^{24} -24.7902i q^{25} +73.2415 q^{27} +(-4.11511 + 15.3578i) q^{28} +(8.25026 + 14.2899i) q^{29} +(-3.12993 - 1.80707i) q^{30} +(-9.27353 - 9.27353i) q^{31} +(5.46410 - 1.46410i) q^{32} +(8.08249 + 30.1643i) q^{33} +(2.01247 - 2.01247i) q^{34} +(1.82071 - 3.15357i) q^{35} +(38.3261 - 22.1276i) q^{36} +(-34.0501 - 9.12370i) q^{37} +6.55204i q^{38} -1.29557 q^{40} +(-15.7076 + 58.6217i) q^{41} +(31.3626 + 54.3217i) q^{42} +(45.2101 + 26.1020i) q^{43} +(7.91574 + 7.91574i) q^{44} +(-9.79026 + 2.62329i) q^{45} +(-6.38102 - 23.8143i) q^{46} +(8.73527 - 8.73527i) q^{47} +(11.1584 - 19.3269i) q^{48} +(-12.2967 + 7.09948i) q^{49} +(-33.8640 - 9.07384i) q^{50} -11.2280i q^{51} -23.4425 q^{53} +(26.8082 - 100.050i) q^{54} +(-1.28193 - 2.22036i) q^{55} +(19.4729 + 11.2427i) q^{56} +(18.2776 + 18.2776i) q^{57} +(22.5401 - 6.03961i) q^{58} +(-9.13343 - 34.0864i) q^{59} +(-3.61413 + 3.61413i) q^{60} +(-13.9421 + 24.1483i) q^{61} +(-16.0622 + 9.27353i) q^{62} +(169.915 + 45.5287i) q^{63} -8.00000i q^{64} +44.1635 q^{66} +(8.85955 - 33.0643i) q^{67} +(-2.01247 - 3.48570i) q^{68} +(-84.2329 - 48.6319i) q^{69} +(-3.64143 - 3.64143i) q^{70} +(-73.8778 + 19.7955i) q^{71} +(-16.1985 - 60.4537i) q^{72} +(-18.9304 + 18.9304i) q^{73} +(-24.9264 + 43.1738i) q^{74} +(-119.780 + 69.1548i) q^{75} +(8.95025 + 2.39821i) q^{76} +44.4971i q^{77} -142.837 q^{79} +(-0.474212 + 1.76978i) q^{80} +(-104.741 - 181.416i) q^{81} +(74.3293 + 42.9141i) q^{82} +(-91.7157 - 91.7157i) q^{83} +(85.6843 - 22.9590i) q^{84} +(0.238584 + 0.890409i) q^{85} +(52.2041 - 52.2041i) q^{86} +(46.0299 - 79.7262i) q^{87} +(13.7105 - 7.91574i) q^{88} +(-150.802 - 40.4072i) q^{89} +14.3339i q^{90} -34.8665 q^{92} +(-18.9378 + 70.6767i) q^{93} +(-8.73527 - 15.1299i) q^{94} +(-1.83784 - 1.06108i) q^{95} +(-22.3168 - 22.3168i) q^{96} +(-108.767 + 29.1440i) q^{97} +(5.19718 + 19.3961i) q^{98} +(87.5780 - 87.5780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 6 q^{5} - 6 q^{6} - 8 q^{7} - 16 q^{8} - 42 q^{9} + 18 q^{10} - 24 q^{11} + 20 q^{14} - 126 q^{15} + 16 q^{16} + 42 q^{17} + 84 q^{18} - 68 q^{19} - 12 q^{20} - 102 q^{21} - 42 q^{22} + 36 q^{23}+ \cdots + 252 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 6 * q^5 - 6 * q^6 - 8 * q^7 - 16 * q^8 - 42 * q^9 + 18 * q^10 - 24 * q^11 + 20 * q^14 - 126 * q^15 + 16 * q^16 + 42 * q^17 + 84 * q^18 - 68 * q^19 - 12 * q^20 - 102 * q^21 - 42 * q^22 + 36 * q^23 + 12 * q^24 + 72 * q^27 - 16 * q^28 - 6 * q^29 + 192 * q^30 + 32 * q^31 + 16 * q^32 - 96 * q^33 - 60 * q^34 - 78 * q^35 + 48 * q^36 + 74 * q^37 - 24 * q^40 - 120 * q^41 + 102 * q^42 + 108 * q^43 + 84 * q^44 - 138 * q^45 + 18 * q^46 + 60 * q^47 - 258 * q^49 - 106 * q^50 - 132 * q^53 + 198 * q^54 - 162 * q^55 + 12 * q^56 - 294 * q^57 + 12 * q^58 - 252 * q^59 - 120 * q^60 + 36 * q^61 + 12 * q^62 + 228 * q^63 + 108 * q^66 + 88 * q^67 + 60 * q^68 - 258 * q^69 + 156 * q^70 + 12 * q^71 + 36 * q^72 + 166 * q^73 - 32 * q^74 - 6 * q^75 + 136 * q^76 - 96 * q^79 - 24 * q^80 - 12 * q^81 + 252 * q^82 - 240 * q^83 + 336 * q^84 + 258 * q^85 + 132 * q^86 + 360 * q^87 + 12 * q^88 - 504 * q^89 - 216 * q^92 + 174 * q^93 - 60 * q^94 - 714 * q^95 - 88 * q^97 + 266 * q^98 + 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$	−2.78960	−	4.83174i	−0.929868	−	1.61058i	−0.783539	−	0.621343i	$-0.786587\pi$
$3$	−2.78960	−	4.83174i	−0.929868	−	1.61058i	−0.146330	−	0.989236i	$-0.546746\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	0.323893	+	0.323893i	0.0647786	+	0.0647786i	0.738754	−	0.673975i	$-0.235415\pi$
$5$	0.323893	+	0.323893i	0.0647786	+	0.0647786i	−0.673975	+	0.738754i	$0.735415\pi$
$6$	−7.62134	+	2.04213i	−1.27022	+	0.340355i
$7$	−2.05755	−	7.67890i	−0.293936	−	1.09699i	−0.942058	−	0.335449i	$-0.891112\pi$
$7$	−2.05755	−	7.67890i	−0.293936	−	1.09699i	0.648122	−	0.761536i	$-0.275555\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−11.0638	+	19.1630i	−1.22931	+	2.12923i
$10$	0.560999	−	0.323893i	0.0560999	−	0.0323893i
$11$	−5.40655	−	1.44868i	−0.491504	−	0.131698i	0.00455003	−	0.999990i	$-0.498552\pi$
$11$	−5.40655	−	1.44868i	−0.491504	−	0.131698i	−0.496054	+	0.868291i	$0.665218\pi$
$12$			11.1584i			0.929868i
$13$		0			0
$13$		0			0
$14$	−11.2427			−0.803049
$15$	0.661433	−	2.46850i	0.0440955	−	0.164567i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	1.74285	+	1.00623i	0.102520	+	0.0591902i	0.550384	−	0.834912i	$-0.314481\pi$
$17$	1.74285	+	1.00623i	0.102520	+	0.0591902i	−0.447863	+	0.894102i	$0.647815\pi$
$18$	22.1276	+	22.1276i	1.22931	+	1.22931i
$19$	−4.47512	+	1.19911i	−0.235533	+	0.0631108i	−0.374655	−	0.927164i	$-0.622239\pi$
$19$	−4.47512	+	1.19911i	−0.235533	+	0.0631108i	0.139122	+	0.990275i	$0.455572\pi$
$20$	−0.237106	−	0.884892i	−0.0118553	−	0.0442446i
$21$	−31.3626	+	31.3626i	−1.49346	+	1.49346i
$22$	−3.95787	+	6.85523i	−0.179903	+	0.311601i
$23$	15.0976	−	8.71663i	0.656419	−	0.378984i	−0.134492	−	0.990915i	$-0.542940\pi$
$23$	15.0976	−	8.71663i	0.656419	−	0.378984i	0.790911	+	0.611931i	$0.209607\pi$
$24$	15.2427	+	4.08426i	0.635112	+	0.170178i
$25$		−	24.7902i		−	0.991607i
$26$		0			0
$27$	73.2415			2.71265
$28$	−4.11511	+	15.3578i	−0.146968	+	0.548493i
$29$	8.25026	+	14.2899i	0.284492	+	0.492754i	0.972486	−	0.232962i	$-0.0748418\pi$
$29$	8.25026	+	14.2899i	0.284492	+	0.492754i	−0.687994	+	0.725716i	$0.741508\pi$
$30$	−3.12993	−	1.80707i	−0.104331	−	0.0602356i
$31$	−9.27353	−	9.27353i	−0.299146	−	0.299146i	0.541533	−	0.840679i	$-0.317844\pi$
$31$	−9.27353	−	9.27353i	−0.299146	−	0.299146i	−0.840679	+	0.541533i	$0.817844\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$	8.08249	+	30.1643i	0.244924	+	0.914069i
$34$	2.01247	−	2.01247i	0.0591902	−	0.0591902i
$35$	1.82071	−	3.15357i	0.0520204	−	0.0901020i
$36$	38.3261	−	22.1276i	1.06461	−	0.614655i
$37$	−34.0501	−	9.12370i	−0.920273	−	0.246586i	−0.232571	−	0.972579i	$-0.574714\pi$
$37$	−34.0501	−	9.12370i	−0.920273	−	0.246586i	−0.687702	+	0.725993i	$0.741380\pi$
$38$			6.55204i			0.172422i
$39$		0			0
$40$	−1.29557			−0.0323893
$41$	−15.7076	+	58.6217i	−0.383113	+	1.42980i	0.458007	+	0.888949i	$0.348564\pi$
$41$	−15.7076	+	58.6217i	−0.383113	+	1.42980i	−0.841120	+	0.540849i	$0.818103\pi$
$42$	31.3626	+	54.3217i	0.746730	+	1.29337i
$43$	45.2101	+	26.1020i	1.05140	+	0.607024i	0.923040	−	0.384704i	$-0.125696\pi$
$43$	45.2101	+	26.1020i	1.05140	+	0.607024i	0.128357	+	0.991728i	$0.459030\pi$
$44$	7.91574	+	7.91574i	0.179903	+	0.179903i
$45$	−9.79026	+	2.62329i	−0.217561	+	0.0582954i
$46$	−6.38102	−	23.8143i	−0.138718	−	0.517702i
$47$	8.73527	−	8.73527i	0.185857	−	0.185857i	−0.608045	−	0.793902i	$-0.708046\pi$
$47$	8.73527	−	8.73527i	0.185857	−	0.185857i	0.793902	+	0.608045i	$0.208046\pi$
$48$	11.1584	−	19.3269i	0.232467	−	0.402645i
$49$	−12.2967	+	7.09948i	−0.250952	+	0.144887i
$50$	−33.8640	−	9.07384i	−0.677280	−	0.181477i
$51$		−	11.2280i		−	0.220156i
$52$		0			0
$53$	−23.4425			−0.442311			−0.221155	−	0.975239i	$-0.570983\pi$
$53$	−23.4425			−0.442311			−0.221155	+	0.975239i	$0.570983\pi$
$54$	26.8082	−	100.050i	0.496449	−	1.85277i
$55$	−1.28193	−	2.22036i	−0.0233077	−	0.0403702i
$56$	19.4729	+	11.2427i	0.347730	+	0.200762i
$57$	18.2776	+	18.2776i	0.320660	+	0.320660i
$58$	22.5401	−	6.03961i	0.388623	−	0.104131i
$59$	−9.13343	−	34.0864i	−0.154804	−	0.577736i	−0.999122	−	0.0418940i	$-0.986661\pi$
$59$	−9.13343	−	34.0864i	−0.154804	−	0.577736i	0.844318	−	0.535842i	$-0.180006\pi$
$60$	−3.61413	+	3.61413i	−0.0602356	+	0.0602356i
$61$	−13.9421	+	24.1483i	−0.228558	+	0.395875i	−0.957381	−	0.288828i	$-0.906734\pi$
$61$	−13.9421	+	24.1483i	−0.228558	+	0.395875i	0.728823	+	0.684702i	$0.240068\pi$
$62$	−16.0622	+	9.27353i	−0.259068	+	0.149573i
$63$	169.915	+	45.5287i	2.69707	+	0.722677i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	44.1635			0.669145
$67$	8.85955	−	33.0643i	0.132232	−	0.493497i	−0.867762	−	0.496980i	$-0.834442\pi$
$67$	8.85955	−	33.0643i	0.132232	−	0.493497i	0.999994	+	0.00348324i	$0.00110875\pi$
$68$	−2.01247	−	3.48570i	−0.0295951	−	0.0512602i
$69$	−84.2329	−	48.6319i	−1.22077	−	0.704810i
$70$	−3.64143	−	3.64143i	−0.0520204	−	0.0520204i
$71$	−73.8778	+	19.7955i	−1.04053	+	0.278810i	−0.738334	−	0.674435i	$-0.764387\pi$
$71$	−73.8778	+	19.7955i	−1.04053	+	0.278810i	−0.302198	+	0.953245i	$0.597721\pi$
$72$	−16.1985	−	60.4537i	−0.224979	−	0.839634i
$73$	−18.9304	+	18.9304i	−0.259320	+	0.259320i	−0.824778	−	0.565457i	$-0.808700\pi$
$73$	−18.9304	+	18.9304i	−0.259320	+	0.259320i	0.565457	+	0.824778i	$0.308700\pi$
$74$	−24.9264	+	43.1738i	−0.336843	+	0.583430i
$75$	−119.780	+	69.1548i	−1.59706	+	0.922064i
$76$	8.95025	+	2.39821i	0.117766	+	0.0315554i
$77$			44.4971i			0.577884i
$78$		0			0
$79$	−142.837			−1.80806			−0.904029	−	0.427471i	$-0.859404\pi$
$79$	−142.837			−1.80806			−0.904029	+	0.427471i	$0.859404\pi$
$80$	−0.474212	+	1.76978i	−0.00592766	+	0.0221223i
$81$	−104.741	−	181.416i	−1.29310	−	2.23971i
$82$	74.3293	+	42.9141i	0.906455	+	0.523342i
$83$	−91.7157	−	91.7157i	−1.10501	−	1.10501i	−0.993797	−	0.111212i	$-0.964527\pi$
$83$	−91.7157	−	91.7157i	−1.10501	−	1.10501i	−0.111212	−	0.993797i	$-0.535473\pi$
$84$	85.6843	−	22.9590i	1.02005	−	0.273322i
$85$	0.238584	+	0.890409i	0.00280687	+	0.0104754i
$86$	52.2041	−	52.2041i	0.607024	−	0.607024i
$87$	46.0299	−	79.7262i	0.529080	−	0.916393i
$88$	13.7105	−	7.91574i	0.155801	−	0.0899515i
$89$	−150.802	−	40.4072i	−1.69440	−	0.454014i	−0.722883	−	0.690970i	$-0.757183\pi$
$89$	−150.802	−	40.4072i	−1.69440	−	0.454014i	−0.971520	+	0.236956i	$0.923850\pi$
$90$			14.3339i			0.159266i
$91$		0			0
$92$	−34.8665			−0.378984
$93$	−18.9378	+	70.6767i	−0.203632	+	0.759965i
$94$	−8.73527	−	15.1299i	−0.0929284	−	0.160957i
$95$	−1.83784	−	1.06108i	−0.0193457	−	0.0111693i
$96$	−22.3168	−	22.3168i	−0.232467	−	0.232467i
$97$	−108.767	+	29.1440i	−1.12131	+	0.300454i	−0.771413	−	0.636335i	$-0.780450\pi$
$97$	−108.767	+	29.1440i	−1.12131	+	0.300454i	−0.349896	+	0.936789i	$0.613783\pi$
$98$	5.19718	+	19.3961i	0.0530325	+	0.197920i
$99$	87.5780	−	87.5780i	0.884626	−	0.884626i
$100$	−24.7902	+	42.9379i	−0.247902	+	0.429379i
$101$	84.6101	−	48.8497i	0.837724	−	0.483660i	−0.0187659	−	0.999824i	$-0.505974\pi$
$101$	84.6101	−	48.8497i	0.837724	−	0.483660i	0.856490	+	0.516164i	$0.172640\pi$
$102$	−15.3377	−	4.10973i	−0.150370	−	0.0402914i
$103$			108.442i			1.05284i	0.850226	+	0.526418i	$0.176465\pi$
$103$			108.442i			1.05284i	−0.850226	+	0.526418i	$0.823535\pi$
$104$		0			0
$105$	−20.3163			−0.193488
$106$	−8.58054	+	32.0230i	−0.0809485	+	0.302104i
$107$	37.6493	+	65.2105i	0.351863	+	0.609444i	0.986576	−	0.163304i	$-0.0522151\pi$
$107$	37.6493	+	65.2105i	0.351863	+	0.609444i	−0.634713	+	0.772748i	$0.718882\pi$
$108$	−126.858	−	73.2415i	−1.17461	−	0.678162i
$109$	5.83660	+	5.83660i	0.0535468	+	0.0535468i	0.733373	−	0.679826i	$-0.237945\pi$
$109$	5.83660	+	5.83660i	0.0535468	+	0.0535468i	−0.679826	+	0.733373i	$0.737945\pi$
$110$	−3.50229	+	0.938435i	−0.0318390	+	0.00853123i
$111$	50.9030	+	189.973i	0.458586	+	1.71147i
$112$	22.4854	−	22.4854i	0.200762	−	0.200762i
$113$	57.2435	−	99.1486i	0.506580	−	0.877422i	−0.493391	−	0.869807i	$-0.664243\pi$
$113$	57.2435	−	99.1486i	0.506580	−	0.877422i	0.999971	−	0.00761416i	$-0.00242369\pi$
$114$	31.6577	−	18.2776i	0.277699	−	0.160330i
$115$	7.71328	+	2.06677i	0.0670720	+	0.0179719i
$116$		−	33.0010i		−	0.284492i
$117$		0			0
$118$	−49.9060			−0.422932
$119$	4.14076	−	15.4535i	0.0347963	−	0.129862i
$120$	3.61413	+	6.25986i	0.0301178	+	0.0521655i
$121$	−77.6570	−	44.8353i	−0.641793	−	0.370540i
$122$	27.8841	+	27.8841i	0.228558	+	0.228558i
$123$	327.063	−	87.6362i	2.65905	−	0.712489i
$124$	6.78869	+	25.3357i	0.0547475	+	0.204321i
$125$	16.1267	−	16.1267i	0.129014	−	0.129014i
$126$	124.387	−	215.444i	0.987196	−	1.70987i
$127$	−83.8081	+	48.3866i	−0.659906	+	0.380997i	−0.792241	−	0.610208i	$-0.791086\pi$
$127$	−83.8081	+	48.3866i	−0.659906	+	0.380997i	0.132335	+	0.991205i	$0.457753\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$		−	291.258i		−	2.25781i
$130$		0			0
$131$	159.613			1.21842			0.609212	−	0.793008i	$-0.291486\pi$
$131$	159.613			1.21842			0.609212	+	0.793008i	$0.291486\pi$
$132$	16.1650	−	60.3285i	0.122462	−	0.457034i
$133$	18.4156	+	31.8968i	0.138463	+	0.239825i
$134$	−41.9239	−	24.2048i	−0.312865	−	0.180632i
$135$	23.7224	+	23.7224i	0.175722	+	0.175722i
$136$	−5.49816	+	1.47323i	−0.0404277	+	0.0108326i
$137$	32.7498	+	122.224i	0.239050	+	0.892146i	0.976281	+	0.216506i	$0.0694660\pi$
$137$	32.7498	+	122.224i	0.239050	+	0.892146i	−0.737232	+	0.675640i	$0.763867\pi$
$138$	−97.2638	+	97.2638i	−0.704810	+	0.704810i
$139$	−30.2234	+	52.3485i	−0.217435	+	0.376608i	−0.954023	−	0.299733i	$-0.903102\pi$
$139$	−30.2234	+	52.3485i	−0.217435	+	0.376608i	0.736588	+	0.676341i	$0.236436\pi$
$140$	−6.30714	+	3.64143i	−0.0450510	+	0.0260102i
$141$	−66.5745	−	17.8386i	−0.472159	−	0.126515i
$142$			108.165i			0.761723i
$143$		0			0
$144$	−88.5103			−0.614655
$145$	−1.95619	+	7.30059i	−0.0134910	+	0.0503489i
$146$	18.9304	+	32.7884i	0.129660	+	0.224578i
$147$	68.6056	+	39.6095i	0.466705	+	0.269452i
$148$	49.8528	+	49.8528i	0.336843	+	0.336843i
$149$	210.878	−	56.5047i	1.41529	−	0.379226i	0.531481	−	0.847070i	$-0.321636\pi$
$149$	210.878	−	56.5047i	1.41529	−	0.379226i	0.883811	+	0.467844i	$0.154969\pi$
$150$	50.6248	+	188.934i	0.337499	+	1.25956i
$151$	73.7140	−	73.7140i	0.488172	−	0.488172i	−0.419557	−	0.907729i	$-0.637815\pi$
$151$	73.7140	−	73.7140i	0.488172	−	0.488172i	0.907729	+	0.419557i	$0.137815\pi$
$152$	6.55204	−	11.3485i	0.0431055	−	0.0746609i
$153$	−38.5650	+	22.2655i	−0.252059	+	0.145526i
$154$	60.7841	+	16.2871i	0.394702	+	0.105760i
$155$		−	6.00726i		−	0.0387565i
$156$		0			0
$157$	−127.109			−0.809611			−0.404805	−	0.914403i	$-0.632661\pi$
$157$	−127.109			−0.809611			−0.404805	+	0.914403i	$0.632661\pi$
$158$	−52.2818	+	195.118i	−0.330898	+	1.23493i
$159$	65.3952	+	113.268i	0.411291	+	0.712376i
$160$	2.24400	+	1.29557i	0.0140250	+	0.00809733i
$161$	−97.9983	−	97.9983i	−0.608685	−	0.608685i
$162$	−286.157	+	76.6755i	−1.76640	+	0.473306i
$163$	−43.7578	−	163.306i	−0.268453	−	1.00188i	−0.960103	−	0.279646i	$-0.909783\pi$
$163$	−43.7578	−	163.306i	−0.268453	−	1.00188i	0.691650	−	0.722232i	$-0.256884\pi$
$164$	85.8281	−	85.8281i	0.523342	−	0.523342i
$165$	−7.15213	+	12.3879i	−0.0433463	+	0.0750779i
$166$	−158.856	+	91.7157i	−0.956965	+	0.552504i
$167$	−161.051	−	43.1534i	−0.964375	−	0.258403i	−0.257924	−	0.966165i	$-0.583038\pi$
$167$	−161.051	−	43.1534i	−0.964375	−	0.258403i	−0.706451	+	0.707762i	$0.749705\pi$
$168$		−	125.451i		−	0.746730i
$169$		0			0
$170$	1.30365			0.00766852
$171$	26.5333	−	99.0237i	0.155166	−	0.579086i
$172$	−52.2041	−	90.4201i	−0.303512	−	0.525698i
$173$	121.663	+	70.2419i	0.703252	+	0.406023i	0.808557	−	0.588417i	$-0.200249\pi$
$173$	121.663	+	70.2419i	0.703252	+	0.406023i	−0.105305	+	0.994440i	$0.533582\pi$
$174$	−92.0599	−	92.0599i	−0.529080	−	0.529080i
$175$	−190.361	+	51.0071i	−1.08778	+	0.291469i
$176$	−5.79472	−	21.6262i	−0.0329245	−	0.122876i
$177$	−139.218	+	139.218i	−0.786543	+	0.786543i
$178$	−110.395	+	191.209i	−0.620195	+	1.07421i
$179$	273.667	−	158.002i	1.52886	−	0.882691i	0.529455	−	0.848338i	$-0.322396\pi$
$179$	273.667	−	158.002i	1.52886	−	0.882691i	0.999410	−	0.0343526i	$-0.0109369\pi$
$180$	19.5805	+	5.24659i	0.108781	+	0.0291477i
$181$			83.6580i			0.462199i	0.972930	+	0.231099i	$0.0742323\pi$
$181$			83.6580i			0.462199i	−0.972930	+	0.231099i	$0.925768\pi$
$182$		0			0
$183$	155.571			0.850116
$184$	−12.7620	+	47.6285i	−0.0693589	+	0.258851i
$185$	−8.07349	−	13.9837i	−0.0436405	−	0.0755876i
$186$	89.6145	+	51.7389i	0.481798	+	0.278166i
$187$	−7.96508	−	7.96508i	−0.0425940	−	0.0425940i
$188$	−23.8652	+	6.39466i	−0.126943	+	0.0340142i
$189$	−150.698	−	562.414i	−0.797346	−	2.97573i
$190$	−2.12216	+	2.12216i	−0.0111693	+	0.0111693i
$191$	−34.5567	+	59.8539i	−0.180925	+	0.313371i	−0.942196	−	0.335063i	$-0.891242\pi$
$191$	−34.5567	+	59.8539i	−0.180925	+	0.313371i	0.761271	+	0.648434i	$0.224576\pi$
$192$	−38.6539	+	22.3168i	−0.201322	+	0.116234i
$193$	313.603	+	84.0297i	1.62489	+	0.435387i	0.952432	−	0.304752i	$-0.0985735\pi$
$193$	313.603	+	84.0297i	1.62489	+	0.435387i	0.672454	+	0.740139i	$0.265240\pi$
$194$			159.246i			0.820855i
$195$		0			0
$196$	28.3979			0.144887
$197$	82.8586	−	309.232i	0.420602	−	1.56971i	−0.352742	−	0.935721i	$-0.614751\pi$
$197$	82.8586	−	309.232i	0.420602	−	1.56971i	0.773344	−	0.633987i	$-0.218583\pi$
$198$	−87.5780	−	151.690i	−0.442313	−	0.766109i
$199$	−149.667	−	86.4100i	−0.752093	−	0.434221i	0.0743564	−	0.997232i	$-0.476310\pi$
$199$	−149.667	−	86.4100i	−0.752093	−	0.434221i	−0.826450	+	0.563010i	$0.809643\pi$
$200$	49.5804	+	49.5804i	0.247902	+	0.247902i
$201$	−184.473	+	49.4293i	−0.917775	+	0.245917i
$202$	−35.7604	−	133.460i	−0.177032	−	0.660692i
$203$	92.7551	−	92.7551i	0.456922	−	0.456922i
$204$	−11.2280	+	19.4474i	−0.0550391	+	0.0953305i
$205$	−24.0748	+	13.8996i	−0.117438	+	0.0678028i
$206$	148.135	+	39.6926i	0.719101	+	0.192682i
$207$			385.756i			1.86355i
$208$		0			0
$209$	25.9321			0.124077
$210$	−7.43628	+	27.7526i	−0.0354108	+	0.132155i
$211$	−115.089	−	199.341i	−0.545447	−	0.944743i	−0.998579	−	0.0532988i	$-0.983026\pi$
$211$	−115.089	−	199.341i	−0.545447	−	0.944743i	0.453131	−	0.891444i	$-0.350307\pi$
$212$	40.6035	+	23.4425i	0.191526	+	0.110578i
$213$	301.736	+	301.736i	1.41660	+	1.41660i
$214$	102.860	−	27.5612i	0.480653	−	0.128791i
$215$	6.18896	+	23.0975i	0.0287858	+	0.107430i
$216$	−146.483	+	146.483i	−0.678162	+	0.678162i
$217$	−52.1297	+	90.2912i	−0.240229	+	0.416089i
$218$	10.1093	−	5.83660i	0.0463728	−	0.0267734i
$219$	144.275	+	38.6584i	0.658790	+	0.176522i
$220$			5.12770i			0.0233077i
$221$		0			0
$222$	278.139			1.25288
$223$	68.1143	−	254.206i	0.305445	−	1.13994i	−0.627116	−	0.778926i	$-0.715765\pi$
$223$	68.1143	−	254.206i	0.305445	−	1.13994i	0.932561	−	0.361012i	$-0.117569\pi$
$224$	−22.4854	−	38.9458i	−0.100381	−	0.173865i
$225$	475.055	+	274.273i	2.11136	+	1.21899i
$226$	−114.487	−	114.487i	−0.506580	−	0.506580i
$227$	−115.102	+	30.8416i	−0.507059	+	0.135866i	−0.503274	−	0.864127i	$-0.667871\pi$
$227$	−115.102	+	30.8416i	−0.507059	+	0.135866i	−0.00378487	+	0.999993i	$0.501205\pi$
$228$	−13.3801	−	49.9353i	−0.0586848	−	0.219015i
$229$	−224.372	+	224.372i	−0.979791	+	0.979791i	−0.999800	−	0.0200093i	$-0.993630\pi$
$229$	−224.372	+	224.372i	−0.979791	+	0.979791i	0.0200093	+	0.999800i	$0.493630\pi$
$230$	5.64651	−	9.78005i	0.0245501	−	0.0425219i
$231$	214.998	−	124.129i	0.930727	−	0.537356i
$232$	−45.0803	−	12.0792i	−0.194311	−	0.0520656i
$233$		−	230.683i		−	0.990054i	−0.868878	−	0.495027i	$-0.835158\pi$
$233$		−	230.683i		−	0.990054i	0.868878	−	0.495027i	$-0.164842\pi$
$234$		0			0
$235$	5.65859			0.0240791
$236$	−18.2669	+	68.1729i	−0.0774020	+	0.288868i
$237$	398.458	+	690.149i	1.68126	+	2.91202i
$238$	−19.5943	−	11.3128i	−0.0823290	−	0.0475326i
$239$	184.518	+	184.518i	0.772041	+	0.772041i	0.978463	−	0.206422i	$-0.0661820\pi$
$239$	184.518	+	184.518i	0.772041	+	0.772041i	−0.206422	+	0.978463i	$0.566182\pi$
$240$	9.87400	−	2.64573i	0.0411417	−	0.0110239i
$241$	−57.5730	−	214.865i	−0.238892	−	0.891557i	−0.976356	−	0.216170i	$-0.930643\pi$
$241$	−57.5730	−	214.865i	−0.238892	−	0.891557i	0.737464	−	0.675387i	$-0.236023\pi$
$242$	−89.6706	+	89.6706i	−0.370540	+	0.370540i
$243$	−254.784	+	441.298i	−1.04849	+	1.81604i
$244$	48.2967	−	27.8841i	0.197937	−	0.114279i
$245$	−6.28228	−	1.68333i	−0.0256419	−	0.00687074i
$246$		−	478.853i		−	1.94656i
$247$		0			0
$248$	37.0941			0.149573
$249$	−187.296	+	698.997i	−0.752191	+	2.80722i
$250$	−16.1267	−	27.9323i	−0.0645068	−	0.111729i
$251$	−218.211	−	125.984i	−0.869366	−	0.501929i	−0.00222866	−	0.999998i	$-0.500709\pi$
$251$	−218.211	−	125.984i	−0.869366	−	0.501929i	−0.867138	+	0.498069i	$0.834043\pi$
$252$	−248.773	−	248.773i	−0.987196	−	0.987196i
$253$	−94.2537	+	25.2552i	−0.372544	+	0.0998230i
$254$	35.4215	+	132.195i	0.139455	+	0.520452i
$255$	3.63666	−	3.63666i	0.0142614	−	0.0142614i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−251.399	+	145.145i	−0.978204	+	0.564767i	−0.901728	−	0.432305i	$-0.857700\pi$
$257$	−251.399	+	145.145i	−0.978204	+	0.564767i	−0.0764769	+	0.997071i	$0.524367\pi$
$258$	−397.865	−	106.608i	−1.54211	−	0.413208i
$259$			280.240i			1.08201i
$260$		0			0
$261$	−365.117			−1.39891
$262$	58.4226	−	218.036i	0.222987	−	0.832199i
$263$	53.9337	+	93.4160i	0.205071	+	0.355194i	0.950155	−	0.311777i	$-0.100924\pi$
$263$	53.9337	+	93.4160i	0.205071	+	0.355194i	−0.745084	+	0.666970i	$0.767591\pi$
$264$	−76.4935	−	44.1635i	−0.289748	−	0.167286i
$265$	−7.59285	−	7.59285i	−0.0286523	−	0.0286523i
$266$	50.3124	−	13.4812i	0.189144	−	0.0506811i
$267$	225.440	+	841.355i	0.844346	+	3.15114i
$268$	−48.4095	+	48.4095i	−0.180632	+	0.180632i
$269$	217.712	−	377.087i	0.809337	−	1.40181i	−0.103987	−	0.994579i	$-0.533160\pi$
$269$	217.712	−	377.087i	0.809337	−	1.40181i	0.913324	−	0.407234i	$-0.133507\pi$
$270$	41.0884	−	23.7224i	0.152179	−	0.0878608i
$271$	−81.2480	−	21.7703i	−0.299808	−	0.0803333i	0.105779	−	0.994390i	$-0.466266\pi$
$271$	−81.2480	−	21.7703i	−0.299808	−	0.0803333i	−0.405587	+	0.914056i	$0.632933\pi$
$272$			8.04987i			0.0295951i
$273$		0			0
$274$	178.948			0.653096
$275$	−35.9131	+	134.029i	−0.130593	+	0.487379i
$276$	97.2638	+	168.466i	0.352405	+	0.610383i
$277$	31.8797	+	18.4057i	0.115089	+	0.0664467i	0.556439	−	0.830888i	$-0.312167\pi$
$277$	31.8797	+	18.4057i	0.115089	+	0.0664467i	−0.441350	+	0.897335i	$0.645500\pi$
$278$	60.4469	+	60.4469i	0.217435	+	0.217435i
$279$	280.309	−	75.1086i	1.00469	−	0.269207i
$280$	2.66571	+	9.94856i	0.00952039	+	0.0355306i
$281$	−30.1080	+	30.1080i	−0.107146	+	0.107146i	−0.758647	−	0.651501i	$-0.774139\pi$
$281$	−30.1080	+	30.1080i	−0.107146	+	0.107146i	0.651501	+	0.758647i	$0.274139\pi$
$282$	−48.7359	+	84.4131i	−0.172822	+	0.299337i
$283$	90.8978	−	52.4799i	0.321194	−	0.185441i	−0.330731	−	0.943725i	$-0.607295\pi$
$283$	90.8978	−	52.4799i	0.321194	−	0.185441i	0.651924	+	0.758284i	$0.273962\pi$
$284$	147.756	+	39.5910i	0.520266	+	0.139405i
$285$			11.8400i			0.0415438i
$286$		0			0
$287$	482.469			1.68108
$288$	−32.3970	+	120.907i	−0.112490	+	0.419817i
$289$	−142.475	−	246.774i	−0.492993	−	0.853889i
$290$	9.25678	+	5.34441i	0.0319199	+	0.0184290i
$291$	444.233	+	444.233i	1.52657	+	1.52657i
$292$	51.7188	−	13.8580i	0.177119	−	0.0474589i
$293$	−32.5289	−	121.399i	−0.111020	−	0.414333i	0.887938	−	0.459963i	$-0.152137\pi$
$293$	−32.5289	−	121.399i	−0.111020	−	0.414333i	−0.998958	+	0.0456298i	$0.985471\pi$
$294$	79.2190	−	79.2190i	0.269452	−	0.269452i
$295$	8.08211	−	13.9986i	0.0273970	−	0.0474529i
$296$	86.3476	−	49.8528i	0.291715	−	0.168422i
$297$	−395.984	−	106.103i	−1.33328	−	0.357251i
$298$		−	308.748i		−	1.03607i
$299$		0			0
$300$	276.619			0.922064
$301$	107.413	−	400.870i	0.356853	−	1.33179i
$302$	−73.7140	−	127.676i	−0.244086	−	0.422769i
$303$	−472.058	−	272.543i	−1.55795	−	0.899480i
$304$	−13.1041	−	13.1041i	−0.0431055	−	0.0431055i
$305$	−12.3372	+	3.30575i	−0.0404499	+	0.0108385i
$306$	16.2995	+	60.8305i	0.0532663	+	0.198793i
$307$	−159.407	+	159.407i	−0.519242	+	0.519242i	−0.917342	−	0.398100i	$-0.869670\pi$
$307$	−159.407	+	159.407i	−0.519242	+	0.519242i	0.398100	+	0.917342i	$0.369670\pi$
$308$	44.4971	−	77.0712i	0.144471	−	0.250231i
$309$	523.964	−	302.511i	1.69568	−	0.978999i
$310$	−8.20607	−	2.19881i	−0.0264712	−	0.00709294i
$311$		−	461.756i		−	1.48475i	−0.669986	−	0.742374i	$-0.733700\pi$
$311$		−	461.756i		−	1.48475i	0.669986	−	0.742374i	$-0.266300\pi$
$312$		0			0
$313$	8.16759			0.0260945			0.0130473	−	0.999915i	$-0.495847\pi$
$313$	8.16759			0.0260945			0.0130473	+	0.999915i	$0.495847\pi$
$314$	−46.5251	+	173.634i	−0.148169	+	0.552974i
$315$	40.2880	+	69.7808i	0.127898	+	0.221526i
$316$	247.400	+	142.837i	0.782912	+	0.452014i
$317$	−91.6127	−	91.6127i	−0.288999	−	0.288999i	0.547685	−	0.836684i	$-0.315509\pi$
$317$	−91.6127	−	91.6127i	−0.288999	−	0.288999i	−0.836684	+	0.547685i	$0.815509\pi$
$318$	178.663	−	47.8726i	0.561833	−	0.150543i
$319$	−23.9040	−	89.2109i	−0.0749341	−	0.279658i
$320$	2.59114	−	2.59114i	0.00809733	−	0.00809733i
$321$	210.053	−	363.823i	0.654372	−	1.13341i
$322$	−169.738	+	97.9983i	−0.527137	+	0.304343i
$323$	−9.00604	−	2.41316i	−0.0278825	−	0.00747109i
$324$			418.963i			1.29310i
$325$		0			0
$326$	−239.097			−0.733426
$327$	11.9191	−	44.4827i	0.0364499	−	0.136033i
$328$	−85.8281	−	148.659i	−0.261671	−	0.453228i
$329$	−85.0505	−	49.1039i	−0.258512	−	0.149252i
$330$	14.3043	+	14.3043i	0.0433463	+	0.0433463i
$331$	−144.443	+	38.7033i	−0.436382	+	0.116928i	−0.470321	−	0.882496i	$-0.655862\pi$
$331$	−144.443	+	38.7033i	−0.436382	+	0.116928i	0.0339382	+	0.999424i	$0.489195\pi$
$332$	67.1406	+	250.572i	0.202231	+	0.754735i
$333$	551.561	−	551.561i	1.65634	−	1.65634i
$334$	−117.897	+	204.204i	−0.352986	+	0.611389i
$335$	13.5789	−	7.83975i	0.0405339	−	0.0234022i
$336$	−171.369	−	45.9181i	−0.510026	−	0.136661i
$337$			61.7332i			0.183185i	0.995797	+	0.0915923i	$0.0291956\pi$
$337$			61.7332i			0.183185i	−0.995797	+	0.0915923i	$0.970804\pi$
$338$		0			0
$339$	−638.747			−1.88421
$340$	0.477169	−	1.78082i	0.00140344	−	0.00523770i
$341$	36.7034	+	63.5721i	0.107635	+	0.186429i
$342$	−125.557	−	72.4904i	−0.367126	−	0.211960i
$343$	−195.629	−	195.629i	−0.570346	−	0.570346i
$344$	−142.624	+	38.2160i	−0.414605	+	0.111093i
$345$	−11.5309	−	43.0340i	−0.0334230	−	0.124736i
$346$	140.484	−	140.484i	0.406023	−	0.406023i
$347$	−110.431	+	191.272i	−0.318245	+	0.551216i	−0.980122	−	0.198396i	$-0.936427\pi$
$347$	−110.431	+	191.272i	−0.318245	+	0.551216i	0.661877	+	0.749612i	$0.269760\pi$
$348$	−159.452	+	92.0599i	−0.458196	+	0.264540i
$349$	281.109	+	75.3230i	0.805470	+	0.215825i	0.637984	−	0.770049i	$-0.279768\pi$
$349$	281.109	+	75.3230i	0.805470	+	0.215825i	0.167486	+	0.985874i	$0.446435\pi$
$350$			278.708i			0.796309i
$351$		0			0
$352$	−31.6629			−0.0899515
$353$	−5.10208	+	19.0412i	−0.0144535	+	0.0539412i	−0.972776	−	0.231748i	$-0.925556\pi$
$353$	−5.10208	+	19.0412i	−0.0144535	+	0.0539412i	0.958322	+	0.285689i	$0.0922223\pi$
$354$	139.218	+	241.133i	0.393271	+	0.681166i
$355$	−30.3401	−	17.5169i	−0.0854652	−	0.0493433i
$356$	220.789	+	220.789i	0.620195	+	0.620195i
$357$	−86.2185	+	23.1022i	−0.241508	+	0.0647120i
$358$	−115.665	−	431.668i	−0.323087	−	1.20578i
$359$	−275.618	+	275.618i	−0.767738	+	0.767738i	−0.977708	−	0.209970i	$-0.932663\pi$
$359$	−275.618	+	275.618i	−0.767738	+	0.767738i	0.209970	+	0.977708i	$0.432663\pi$
$360$	14.3339	−	24.8271i	0.0398165	−	0.0689642i
$361$	−294.046	+	169.768i	−0.814533	+	0.470271i
$362$	114.279	+	30.6210i	0.315688	+	0.0845883i
$363$			500.291i			1.37821i
$364$		0			0
$365$	−12.2628			−0.0335968
$366$	56.9430	−	212.514i	0.155582	−	0.580640i
$367$	−234.367	−	405.936i	−0.638603	−	1.10609i	−0.985739	−	0.168278i	$-0.946179\pi$
$367$	−234.367	−	405.936i	−0.638603	−	1.10609i	0.347136	−	0.937815i	$-0.387154\pi$
$368$	60.3906	+	34.8665i	0.164105	+	0.0947460i
$369$	−949.584	−	949.584i	−2.57340	−	2.57340i
$370$	−22.0572	+	5.91021i	−0.0596140	+	0.0159735i
$371$	48.2341	+	180.012i	0.130011	+	0.485208i
$372$	103.478	−	103.478i	0.278166	−	0.278166i
$373$	−130.407	+	225.872i	−0.349617	+	0.605555i	−0.986181	−	0.165669i	$-0.947022\pi$
$373$	−130.407	+	225.872i	−0.349617	+	0.605555i	0.636564	+	0.771224i	$0.280355\pi$
$374$	−13.7959	+	7.96508i	−0.0368875	+	0.0212970i
$375$	−122.907	−	32.9329i	−0.327752	−	0.0878209i
$376$			34.9411i			0.0929284i
$377$		0			0
$378$	−823.431			−2.17839
$379$	−55.4370	+	206.894i	−0.146272	+	0.545893i	0.853424	+	0.521218i	$0.174522\pi$
$379$	−55.4370	+	206.894i	−0.146272	+	0.545893i	−0.999696	+	0.0246758i	$0.992145\pi$
$380$	2.12216	+	3.67569i	0.00558463	+	0.00967286i
$381$	467.583	+	269.959i	1.22725	+	0.708554i
$382$	69.1133	+	69.1133i	0.180925	+	0.180925i
$383$	662.570	−	177.535i	1.72995	−	0.463538i	0.749778	−	0.661690i	$-0.230160\pi$
$383$	662.570	−	177.535i	1.72995	−	0.463538i	0.980171	+	0.198151i	$0.0634938\pi$
$384$	16.3371	+	60.9707i	0.0425444	+	0.158778i
$385$	−14.4123	+	14.4123i	−0.0374345	+	0.0374345i
$386$	229.573	−	397.633i	0.594750	−	1.03014i
$387$	−1000.39	+	577.575i	−2.58498	+	1.49244i
$388$	217.534	+	58.2880i	0.560654	+	0.150227i
$389$		−	374.691i		−	0.963216i	−0.876387	−	0.481608i	$-0.840053\pi$
$389$		−	374.691i		−	0.963216i	0.876387	−	0.481608i	$-0.159947\pi$
$390$		0			0
$391$	35.0839			0.0897286
$392$	10.3944	−	38.7923i	0.0265162	−	0.0989599i
$393$	−445.258	−	771.210i	−1.13297	−	1.96237i
$394$	−392.091	−	226.374i	−0.995155	−	0.574553i
$395$	−46.2638	−	46.2638i	−0.117123	−	0.117123i
$396$	−239.268	+	64.1116i	−0.604211	+	0.161898i
$397$	−168.880	−	630.268i	−0.425390	−	1.58758i	−0.763070	−	0.646316i	$-0.776309\pi$
$397$	−168.880	−	630.268i	−0.425390	−	1.58758i	0.337680	−	0.941261i	$-0.390358\pi$
$398$	−172.820	+	172.820i	−0.434221	+	0.434221i
$399$	102.745	−	177.959i	0.257505	−	0.446012i
$400$	85.8757	−	49.5804i	0.214689	−	0.123951i
$401$	417.539	+	111.879i	1.04125	+	0.279001i	0.738629	−	0.674112i	$-0.235473\pi$
$401$	417.539	+	111.879i	1.04125	+	0.279001i	0.302616	+	0.953113i	$0.402140\pi$
$402$			270.087i			0.671858i
$403$		0			0
$404$	−195.399			−0.483660
$405$	24.8347	−	92.6843i	0.0613202	−	0.228850i
$406$	−92.7551	−	160.656i	−0.228461	−	0.395706i
$407$	170.876	+	98.6554i	0.419843	+	0.242397i
$408$	22.4560	+	22.4560i	0.0550391	+	0.0550391i
$409$	−269.624	+	72.2456i	−0.659228	+	0.176640i	−0.572897	−	0.819627i	$-0.694181\pi$
$409$	−269.624	+	72.2456i	−0.659228	+	0.176640i	−0.0863302	+	0.996267i	$0.527514\pi$
$410$	10.1752	+	37.9743i	0.0248175	+	0.0926203i
$411$	499.195	−	499.195i	1.21459	−	1.21459i
$412$	108.442	−	187.827i	0.263209	−	0.455892i
$413$	−242.954	+	140.269i	−0.588265	+	0.339635i
$414$	526.952	+	141.196i	1.27283	+	0.341054i
$415$		−	59.4122i		−	0.143162i
$416$		0			0
$417$	337.246			0.808743
$418$	9.49181	−	35.4239i	0.0227077	−	0.0847462i
$419$	−93.7951	−	162.458i	−0.223855	−	0.387728i	0.732121	−	0.681175i	$-0.238531\pi$
$419$	−93.7951	−	162.458i	−0.223855	−	0.387728i	−0.955975	+	0.293447i	$0.905197\pi$
$420$	35.1888	+	20.3163i	0.0837829	+	0.0483721i
$421$	410.480	+	410.480i	0.975013	+	0.975013i	0.999695	−	0.0246826i	$-0.00785752\pi$
$421$	410.480	+	410.480i	0.975013	+	0.975013i	−0.0246826	+	0.999695i	$0.507858\pi$
$422$	−314.430	+	84.2513i	−0.745095	+	0.199648i
$423$	70.7492	+	264.040i	0.167256	+	0.624207i
$424$	46.8849	−	46.8849i	0.110578	−	0.110578i
$425$	24.9447	−	43.2055i	0.0586935	−	0.101660i
$426$	522.623	−	301.736i	1.22681	−	0.708302i
$427$	214.119	+	57.3731i	0.501450	+	0.134363i
$428$		−	150.597i		−	0.351863i
$429$		0			0
$430$	33.8171			0.0786444
$431$	138.478	−	516.808i	0.321295	−	1.19909i	−0.596689	−	0.802473i	$-0.703517\pi$
$431$	138.478	−	516.808i	0.321295	−	1.19909i	0.917984	−	0.396617i	$-0.129816\pi$
$432$	146.483	+	253.716i	0.339081	+	0.587305i
$433$	−140.192	−	80.9400i	−0.323769	−	0.186928i	0.329302	−	0.944225i	$-0.393187\pi$
$433$	−140.192	−	80.9400i	−0.323769	−	0.186928i	−0.653071	+	0.757296i	$0.726520\pi$
$434$	104.259	+	104.259i	0.240229	+	0.240229i
$435$	40.7315	−	10.9140i	0.0936357	−	0.0250896i
$436$	−4.27268	−	15.9459i	−0.00979974	−	0.0365731i
$437$	−57.1117	+	57.1117i	−0.130690	+	0.130690i
$438$	105.617	−	182.933i	0.241134	−	0.417656i
$439$	142.255	−	82.1308i	0.324043	−	0.187086i	−0.329150	−	0.944277i	$-0.606762\pi$
$439$	142.255	−	82.1308i	0.324043	−	0.187086i	0.653193	+	0.757191i	$0.273429\pi$
$440$	7.00457	+	1.87687i	0.0159195	+	0.00426561i
$441$		−	314.189i		−	0.712446i
$442$		0			0
$443$	309.912			0.699575			0.349788	−	0.936829i	$-0.386254\pi$
$443$	309.912			0.699575			0.349788	+	0.936829i	$0.386254\pi$
$444$	101.806	−	379.945i	0.229293	−	0.855733i
$445$	−35.7561	−	61.9313i	−0.0803507	−	0.139172i
$446$	−322.321	−	186.092i	−0.722692	−	0.417246i
$447$	−861.284	−	861.284i	−1.92681	−	1.92681i
$448$	−61.4312	+	16.4604i	−0.137123	+	0.0367420i
$449$	35.2192	+	131.440i	0.0784392	+	0.292739i	0.993991	−	0.109461i	$-0.0349124\pi$
$449$	35.2192	+	131.440i	0.0784392	+	0.292739i	−0.915552	+	0.402200i	$0.868246\pi$
$450$	548.547	−	548.547i	1.21899	−	1.21899i
$451$	169.848	−	294.186i	0.376603	−	0.652296i
$452$	−198.297	+	114.487i	−0.438711	+	0.253290i
$453$	−561.799	−	150.534i	−1.24018	−	0.332304i
$454$			168.522i			0.371193i
$455$		0			0
$456$	−73.1104			−0.160330
$457$	−58.7751	+	219.352i	−0.128611	+	0.479981i	−0.999943	−	0.0107126i	$-0.996590\pi$
$457$	−58.7751	+	219.352i	−0.128611	+	0.479981i	0.871332	+	0.490694i	$0.163257\pi$
$458$	224.372	+	388.624i	0.489895	+	0.848523i
$459$	127.649	+	73.6981i	0.278102	+	0.160562i
$460$	−11.2930	−	11.2930i	−0.0245501	−	0.0245501i
$461$	660.658	−	177.023i	1.43310	−	0.383998i	0.542987	−	0.839741i	$-0.317293\pi$
$461$	660.658	−	177.023i	1.43310	−	0.383998i	0.890111	+	0.455743i	$0.150627\pi$
$462$	−90.8689	−	339.127i	−0.196686	−	0.734042i
$463$	557.281	−	557.281i	1.20363	−	1.20363i	0.230575	−	0.973055i	$-0.425939\pi$
$463$	557.281	−	557.281i	1.20363	−	1.20363i	0.973055	−	0.230575i	$-0.0740607\pi$
$464$	−33.0010	+	57.1595i	−0.0711229	+	0.123189i
$465$	−29.0255	+	16.7579i	−0.0624205	+	0.0360385i
$466$	−315.118	−	84.4357i	−0.676219	−	0.181192i
$467$		−	91.0355i		−	0.194937i	−0.995239	−	0.0974684i	$-0.968926\pi$
$467$		−	91.0355i		−	0.194937i	0.995239	−	0.0974684i	$-0.0310745\pi$
$468$		0			0
$469$	−272.126			−0.580227
$470$	2.07119	−	7.72977i	0.00440678	−	0.0164463i
$471$	354.583	+	614.157i	0.752831	+	1.30394i
$472$	86.4397	+	49.9060i	0.183135	+	0.105733i
$473$	−206.617	−	206.617i	−0.436822	−	0.436822i
$474$	1088.61	−	291.691i	2.29664	−	0.615382i
$475$	29.7261	+	110.939i	0.0625812	+	0.233556i
$476$	−22.6255	+	22.6255i	−0.0475326	+	0.0475326i
$477$	259.362	−	449.229i	0.543737	−	0.941780i
$478$	319.594	−	184.518i	0.668607	−	0.386021i
$479$	−713.865	−	191.280i	−1.49032	−	0.399331i	−0.580477	−	0.814276i	$-0.697134\pi$
$479$	−713.865	−	191.280i	−1.49032	−	0.399331i	−0.909846	+	0.414945i	$0.863801\pi$
$480$		−	14.4565i		−	0.0301178i
$481$		0			0
$482$	−314.584			−0.652665
$483$	−200.125	+	746.879i	−0.414338	+	1.54633i
$484$	89.6706	+	155.314i	0.185270	+	0.320897i
$485$	−44.6684	−	25.7893i	−0.0920998	−	0.0531738i
$486$	509.567	+	509.567i	1.04849	+	1.04849i
$487$	−580.273	+	155.484i	−1.19153	+	0.319268i	−0.799489	−	0.600681i	$-0.794896\pi$
$487$	−580.273	+	155.484i	−1.19153	+	0.319268i	−0.392037	+	0.919949i	$0.628230\pi$
$488$	−20.4126	−	76.1808i	−0.0418291	−	0.156108i
$489$	−666.986	+	666.986i	−1.36398	+	1.36398i
$490$	−4.59895	+	7.96561i	−0.00938560	+	0.0162563i
$491$	482.376	−	278.500i	0.982436	−	0.567210i	0.0794313	−	0.996840i	$-0.474690\pi$
$491$	482.376	−	278.500i	0.982436	−	0.567210i	0.903005	+	0.429631i	$0.141356\pi$
$492$	−654.125	−	175.272i	−1.32952	−	0.356245i
$493$			33.2068i			0.0673565i
$494$		0			0
$495$	56.7318			0.114610
$496$	13.5774	−	50.6715i	0.0273738	−	0.102160i
$497$	304.015	+	526.570i	0.611700	+	1.05950i
$498$	886.292	+	511.701i	1.77970	+	1.02751i
$499$	92.7376	+	92.7376i	0.185847	+	0.185847i	0.793898	−	0.608051i	$-0.208048\pi$
$499$	92.7376	+	92.7376i	0.185847	+	0.185847i	−0.608051	+	0.793898i	$0.708048\pi$
$500$	−44.0590	+	11.8056i	−0.0881179	+	0.0236111i
$501$	240.762	+	898.535i	0.480562	+	1.79348i
$502$	−251.968	+	251.968i	−0.501929	+	0.501929i
$503$	68.4278	−	118.520i	0.136039	−	0.235627i	−0.789955	−	0.613165i	$-0.789896\pi$
$503$	68.4278	−	118.520i	0.136039	−	0.235627i	0.925994	+	0.377538i	$0.123229\pi$
$504$	−430.888	+	248.773i	−0.854937	+	0.493598i
$505$	43.2267	+	11.5826i	0.0855974	+	0.0229358i
$506$			137.997i			0.272721i
$507$		0			0
$508$	193.547			0.380997
$509$	−43.8773	+	163.752i	−0.0862029	+	0.321713i	−0.995539	−	0.0943482i	$-0.969923\pi$
$509$	−43.8773	+	163.752i	−0.0862029	+	0.321713i	0.909336	+	0.416062i	$0.136590\pi$
$510$	−3.63666	−	6.29889i	−0.00713072	−	0.0123508i
$511$	184.315	+	106.414i	0.360694	+	0.208247i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−327.765	+	87.8243i	−0.638918	+	0.171197i
$514$	106.254	+	396.544i	0.206719	+	0.771486i
$515$	−35.1237	+	35.1237i	−0.0682013	+	0.0682013i
$516$	−291.258	+	504.473i	−0.564453	+	0.977661i
$517$	−59.8823	+	34.5730i	−0.115826	+	0.0668724i
$518$	382.815	+	102.575i	0.739024	+	0.198021i
$519$		−	783.789i		−	1.51019i
$520$		0			0
$521$	161.073			0.309161			0.154580	−	0.987980i	$-0.450597\pi$
$521$	161.073			0.309161			0.154580	+	0.987980i	$0.450597\pi$
$522$	−133.642	+	498.758i	−0.256019	+	0.955476i
$523$	−67.7062	−	117.271i	−0.129457	−	0.224227i	0.794009	−	0.607906i	$-0.207990\pi$
$523$	−67.7062	−	117.271i	−0.129457	−	0.224227i	−0.923466	+	0.383679i	$0.874657\pi$
$524$	−276.459	−	159.613i	−0.527593	−	0.304606i
$525$	777.486	+	777.486i	1.48093	+	1.48093i
$526$	147.350	−	39.4822i	0.280133	−	0.0750613i
$527$	−6.83101	−	25.4937i	−0.0129621	−	0.0483751i
$528$	−88.3271	+	88.3271i	−0.167286	+	0.167286i
$529$	−112.541	+	194.926i	−0.212742	+	0.368481i
$530$	−13.1512	+	7.59285i	−0.0248136	+	0.0143261i
$531$	754.250	+	202.101i	1.42043	+	0.380604i
$532$		−	73.6625i		−	0.138463i
$533$		0			0
$534$	1231.83			2.30680
$535$	−8.92689	+	33.3156i	−0.0166858	+	0.0622721i
$536$	48.4095	+	83.8477i	0.0903162	+	0.156432i
$537$	−1526.84	−	881.524i	−2.84329	−	1.64157i
$538$	−435.423	−	435.423i	−0.809337	−	0.809337i
$539$	76.7674	−	20.5698i	0.142426	−	0.0381628i
$540$	−17.3660	−	64.8108i	−0.0321593	−	0.120020i
$541$	−127.802	+	127.802i	−0.236233	+	0.236233i	−0.815288	−	0.579055i	$-0.803422\pi$
$541$	−127.802	+	127.802i	−0.236233	+	0.236233i	0.579055	+	0.815288i	$0.303422\pi$
$542$	−59.4776	+	103.018i	−0.109737	+	0.190071i
$543$	404.213	−	233.373i	0.744408	−	0.429784i
$544$	10.9963	+	2.94646i	0.0202138	+	0.00541628i
$545$			3.78087i			0.00693737i
$546$		0			0
$547$	−161.504			−0.295254			−0.147627	−	0.989043i	$-0.547163\pi$
$547$	−161.504			−0.295254			−0.147627	+	0.989043i	$0.547163\pi$
$548$	65.4996	−	244.448i	0.119525	−	0.446073i
$549$	−308.504	−	534.344i	−0.561938	−	0.973305i
$550$	169.942	+	98.1163i	0.308986	+	0.178393i
$551$	−54.0560	−	54.0560i	−0.0981053	−	0.0981053i
$552$	265.730	−	71.2020i	0.481394	−	0.128989i
$553$	293.894	+	1096.83i	0.531454	+	1.98341i
$554$	36.8115	−	36.8115i	0.0664467	−	0.0664467i
$555$	−45.0437	+	78.0180i	−0.0811598	+	0.140573i
$556$	104.697	−	60.4469i	0.188304	−	0.108717i
$557$	574.784	+	154.013i	1.03193	+	0.276504i	0.734764	−	0.678323i	$-0.237293\pi$
$557$	574.784	+	154.013i	1.03193	+	0.276504i	0.297163	+	0.954827i	$0.403959\pi$
$558$		−	410.401i		−	0.735486i
$559$		0			0
$560$	14.5657			0.0260102
$561$	−16.2658	+	60.7046i	−0.0289942	+	0.108208i
$562$	30.1080	+	52.1486i	0.0535730	+	0.0927912i
$563$	538.929	+	311.151i	0.957244	+	0.552665i	0.895324	−	0.445416i	$-0.146944\pi$
$563$	538.929	+	311.151i	0.957244	+	0.552665i	0.0619205	+	0.998081i	$0.480277\pi$
$564$	97.4718	+	97.4718i	0.172822	+	0.172822i
$565$	50.6543	−	13.5728i	0.0896537	−	0.0240226i
$566$	−38.4179	−	143.378i	−0.0678762	−	0.253317i
$567$	−1177.57	+	1177.57i	−2.07684	+	2.07684i
$568$	108.165	−	187.347i	0.190431	−	0.329836i
$569$	−675.493	+	389.996i	−1.18716	+	0.685406i	−0.957660	−	0.287903i	$-0.907042\pi$
$569$	−675.493	+	389.996i	−1.18716	+	0.685406i	−0.229499	+	0.973309i	$0.573709\pi$
$570$	16.1737	+	4.33373i	0.0283749	+	0.00760304i
$571$			556.142i			0.973980i	0.873408	+	0.486990i	$0.161905\pi$
$571$			556.142i			0.973980i	−0.873408	+	0.486990i	$0.838095\pi$
$572$		0			0
$573$	385.598			0.672945
$574$	176.596	−	659.065i	0.307659	−	1.14820i
$575$	−216.087	−	374.273i	−0.375803	−	0.650910i
$576$	153.304	+	88.5103i	0.266153	+	0.153664i
$577$	401.975	+	401.975i	0.696663	+	0.696663i	0.963689	−	0.267026i	$-0.0860409\pi$
$577$	401.975	+	401.975i	0.696663	+	0.696663i	−0.267026	+	0.963689i	$0.586041\pi$
$578$	−389.249	+	104.299i	−0.673441	+	0.180448i
$579$	−468.819	−	1749.66i	−0.809705	−	3.02186i
$580$	10.6888	−	10.6888i	0.0184290	−	0.0184290i
$581$	−515.565	+	892.985i	−0.887376	+	1.53698i
$582$	769.434	−	444.233i	1.32205	−	0.763287i
$583$	126.743	+	33.9606i	0.217398	+	0.0582515i
$584$		−	75.7216i		−	0.129660i
$585$		0			0
$586$	−177.741			−0.303313
$587$	−173.571	+	647.776i	−0.295692	+	1.10354i	0.644974	+	0.764204i	$0.276868\pi$
$587$	−173.571	+	647.776i	−0.295692	+	1.10354i	−0.940666	+	0.339333i	$0.889799\pi$
$588$	−79.2190	−	137.211i	−0.134726	−	0.233353i
$589$	52.6201	+	30.3802i	0.0893381	+	0.0515794i
$590$	−16.1642	−	16.1642i	−0.0273970	−	0.0273970i
$591$	−1725.27	+	462.285i	−2.91924	+	0.782209i
$592$	−36.4948	−	136.200i	−0.0616466	−	0.230068i
$593$	−185.442	+	185.442i	−0.312719	+	0.312719i	−0.845962	−	0.533243i	$-0.820973\pi$
$593$	−185.442	+	185.442i	−0.312719	+	0.312719i	0.533243	+	0.845962i	$0.320973\pi$
$594$	−289.880	+	502.087i	−0.488014	+	0.845264i
$595$	6.34646	−	3.66413i	0.0106663	−	0.00615820i
$596$	−421.757	−	113.009i	−0.707646	−	0.189613i
$597$			964.199i			1.61507i
$598$		0			0
$599$	−171.466			−0.286254			−0.143127	−	0.989704i	$-0.545716\pi$
$599$	−171.466			−0.286254			−0.143127	+	0.989704i	$0.545716\pi$
$600$	101.250	−	377.869i	0.168749	−	0.629782i
$601$	−53.8259	−	93.2293i	−0.0895606	−	0.155124i	0.817765	−	0.575552i	$-0.195213\pi$
$601$	−53.8259	−	93.2293i	−0.0895606	−	0.155124i	−0.907325	+	0.420429i	$0.861880\pi$
$602$	−508.282	−	293.457i	−0.844323	−	0.487470i
$603$	535.593	+	535.593i	0.888213	+	0.888213i
$604$	−201.390	+	53.9624i	−0.333428	+	0.0893417i
$605$	−10.6307	−	39.6744i	−0.0175714	−	0.0655775i
$606$	−545.085	+	545.085i	−0.899480	+	0.899480i
$607$	−216.797	+	375.504i	−0.357162	+	0.618623i	−0.987486	−	0.157710i	$-0.949589\pi$
$607$	−216.797	+	375.504i	−0.357162	+	0.618623i	0.630323	+	0.776333i	$0.282922\pi$
$608$	−22.6969	+	13.1041i	−0.0373305	+	0.0215528i
$609$	−706.918	−	189.418i	−1.16078	−	0.311031i
$610$			18.0629i			0.0296114i
$611$		0			0
$612$	89.0621			0.145526
$613$	−166.249	+	620.451i	−0.271206	+	1.01216i	0.687135	+	0.726530i	$0.258868\pi$
$613$	−166.249	+	620.451i	−0.271206	+	1.01216i	−0.958341	+	0.285626i	$0.907799\pi$
$614$	159.407	+	276.102i	0.259621	+	0.449677i
$615$	134.318	+	77.5486i	0.218403	+	0.126095i
$616$	−88.9941	−	88.9941i	−0.144471	−	0.144471i
$617$	400.004	−	107.181i	0.648304	−	0.173713i	0.0803421	−	0.996767i	$-0.474399\pi$
$617$	400.004	−	107.181i	0.648304	−	0.173713i	0.567962	+	0.823055i	$0.307732\pi$
$618$	−221.453	−	826.475i	−0.358339	−	1.33734i
$619$	693.205	−	693.205i	1.11988	−	1.11988i	0.128120	−	0.991759i	$-0.459106\pi$
$619$	693.205	−	693.205i	1.11988	−	1.11988i	0.991759	−	0.128120i	$-0.0408943\pi$
$620$	−6.00726	+	10.4049i	−0.00968913	+	0.0167821i
$621$	1105.77	−	638.419i	1.78063	−	1.02805i
$622$	−630.771	−	169.015i	−1.01410	−	0.271728i
$623$			1241.13i			1.99219i
$624$		0			0
$625$	−609.308			−0.974893
$626$	2.98955	−	11.1571i	0.00477563	−	0.0178229i
$627$	−72.3403	−	125.297i	−0.115375	−	0.199836i
$628$	220.159	+	127.109i	0.350572	+	0.202403i
$629$	−50.1636	−	50.1636i	−0.0797513	−	0.0797513i
$630$	110.069	−	29.4928i	0.174712	−	0.0468140i
$631$	−136.067	−	507.808i	−0.215637	−	0.804767i	−0.985941	−	0.167091i	$-0.946563\pi$
$631$	−136.067	−	507.808i	−0.215637	−	0.804767i	0.770305	−	0.637676i	$-0.220104\pi$
$632$	285.673	−	285.673i	0.452014	−	0.452014i
$633$	−642.108	+	1112.16i	−1.01439	+	1.75697i
$634$	−158.678	+	91.6127i	−0.250281	+	0.144500i
$635$	−42.8170	−	11.4728i	−0.0674283	−	0.0180674i
$636$		−	261.581i		−	0.411291i
$637$		0			0
$638$	−130.614			−0.204724
$639$	438.026	−	1634.74i	0.685487	−	2.55827i
$640$	−2.59114	−	4.48799i	−0.00404866	−	0.00701249i
$641$	936.399	+	540.630i	1.46084	+	0.843416i	0.999050	−	0.0435728i	$-0.0138741\pi$
$641$	936.399	+	540.630i	1.46084	+	0.843416i	0.461790	+	0.886989i	$0.347207\pi$
$642$	−420.107	−	420.107i	−0.654372	−	0.654372i
$643$	381.388	−	102.193i	0.593138	−	0.158931i	0.0502511	−	0.998737i	$-0.483998\pi$
$643$	381.388	−	102.193i	0.593138	−	0.158931i	0.542887	+	0.839806i	$0.317331\pi$
$644$	71.7397	+	267.736i	0.111397	+	0.415740i
$645$	94.3363	−	94.3363i	0.146258	−	0.146258i
$646$	−6.59288	+	11.4192i	−0.0102057	+	0.0176768i
$647$	−275.454	+	159.033i	−0.425740	+	0.245801i	−0.697530	−	0.716555i	$-0.745718\pi$
$647$	−275.454	+	159.033i	−0.425740	+	0.245801i	0.271790	+	0.962357i	$0.412384\pi$
$648$	572.314	+	153.351i	0.883200	+	0.236653i
$649$			197.521i			0.304347i
$650$		0			0
$651$	581.685			0.893525
$652$	−87.5156	+	326.613i	−0.134226	+	0.500939i
$653$	201.115	+	348.341i	0.307986	+	0.533447i	0.977922	−	0.208972i	$-0.0670117\pi$
$653$	201.115	+	348.341i	0.307986	+	0.533447i	−0.669936	+	0.742419i	$0.733678\pi$
$654$	−56.4018	−	32.5636i	−0.0862413	−	0.0497914i
$655$	51.6977	+	51.6977i	0.0789278	+	0.0789278i
$656$	−234.487	+	62.8305i	−0.357449	+	0.0957783i
$657$	−153.322	−	572.206i	−0.233367	−	0.870937i
$658$	−98.2079	+	98.2079i	−0.149252	+	0.149252i
$659$	−292.874	+	507.272i	−0.444421	+	0.769760i	−0.998012	−	0.0630290i	$-0.979924\pi$
$659$	−292.874	+	507.272i	−0.444421	+	0.769760i	0.553591	+	0.832789i	$0.313257\pi$
$660$	24.7757	−	14.3043i	0.0375390	−	0.0216731i
$661$	−781.140	−	209.306i	−1.18176	−	0.316650i	−0.386133	−	0.922443i	$-0.626189\pi$
$661$	−781.140	−	209.306i	−1.18176	−	0.316650i	−0.795623	+	0.605793i	$0.792856\pi$
$662$			211.479i			0.319454i
$663$		0			0
$664$	366.863			0.552504
$665$	−4.36646	+	16.2958i	−0.00656610	+	0.0245050i
$666$	−551.561	−	955.332i	−0.828170	−	1.43443i
$667$	249.119	+	143.829i	0.373492	+	0.215636i
$668$	235.794	+	235.794i	0.352986	+	0.352986i
$669$	−1418.27	+	380.024i	−2.11998	+	0.568048i
$670$	−5.73910	−	21.4186i	−0.00856582	−	0.0319681i
$671$	110.362	−	110.362i	0.164473	−	0.164473i
$672$	−125.451	+	217.287i	−0.186682	+	0.323343i
$673$	373.474	−	215.625i	0.554939	−	0.320394i	−0.196173	−	0.980569i	$-0.562851\pi$
$673$	373.474	−	215.625i	0.554939	−	0.320394i	0.751112	+	0.660175i	$0.229518\pi$
$674$	84.3291	+	22.5959i	0.125117	+	0.0335251i
$675$		−	1815.67i		−	2.68988i
$676$		0			0
$677$	6.72056			0.00992697			0.00496348	−	0.999988i	$-0.498420\pi$
$677$	6.72056			0.00992697			0.00496348	+	0.999988i	$0.498420\pi$
$678$	−233.798	+	872.544i	−0.344834	+	1.28694i
$679$	447.588	+	775.244i	0.659186	+	1.14174i
$680$	−2.25799	−	1.30365i	−0.00332057	−	0.00191713i
$681$	470.109	+	470.109i	0.690321	+	0.690321i
$682$	100.276	−	26.8687i	0.147032	−	0.0393970i
$683$	−31.7287	−	118.413i	−0.0464549	−	0.173372i	0.938801	−	0.344461i	$-0.111938\pi$
$683$	−31.7287	−	118.413i	−0.0464549	−	0.173372i	−0.985256	+	0.171089i	$0.945272\pi$
$684$	−144.981	+	144.981i	−0.211960	+	0.211960i
$685$	−28.9801	+	50.1949i	−0.0423067	+	0.0732773i
$686$	−338.839	+	195.629i	−0.493934	+	0.285173i
$687$	1710.02	+	458.197i	2.48911	+	0.666954i
$688$			208.816i			0.303512i
$689$		0			0
$690$	−63.0061			−0.0913133
$691$	−24.3539	+	90.8900i	−0.0352444	+	0.131534i	−0.981307	−	0.192451i	$-0.938356\pi$
$691$	−24.3539	+	90.8900i	−0.0352444	+	0.131534i	0.946062	+	0.323985i	$0.105023\pi$
$692$	−140.484	−	243.325i	−0.203011	−	0.351626i
$693$	−852.699	−	492.306i	−1.23045	−	0.710398i
$694$	220.862	+	220.862i	0.318245	+	0.318245i
$695$	−26.7445	+	7.16616i	−0.0384813	+	0.0103110i
$696$	67.3925	+	251.512i	0.0968283	+	0.361368i
$697$	−86.3632	+	86.3632i	−0.123907	+	0.123907i
$698$	205.786	−	356.432i	0.294823	−	0.510648i
$699$	−1114.60	+	643.513i	−1.59456	+	0.920620i
$700$	380.722	+	102.014i	0.543889	+	0.145735i
$701$		−	716.506i		−	1.02212i	−0.859545	−	0.511060i	$-0.829253\pi$
$701$		−	716.506i		−	1.02212i	0.859545	−	0.511060i	$-0.170747\pi$
$702$		0			0
$703$	163.319			0.232317
$704$	−11.5894	+	43.2524i	−0.0164623	+	0.0614380i
$705$	−15.7852	−	27.3408i	−0.0223904	−	0.0387813i
$706$	24.1433	+	13.9392i	0.0341973	+	0.0197438i
$707$	−549.201	−	549.201i	−0.776805	−	0.776805i
$708$	380.351	−	101.915i	0.537219	−	0.143947i
$709$	256.439	+	957.045i	0.361692	+	1.34985i	0.871851	+	0.489772i	$0.162920\pi$
$709$	256.439	+	957.045i	0.361692	+	1.34985i	−0.510159	+	0.860080i	$0.670413\pi$
$710$	−35.0338	+	35.0338i	−0.0493433	+	0.0493433i
$711$	1580.31	−	2737.18i	2.22266	−	3.84977i
$712$	382.418	−	220.789i	0.537104	−	0.310097i
$713$	−220.842	−	59.1745i	−0.309737	−	0.0829937i
$714$			126.233i			0.176796i
$715$		0			0
$716$	−632.006			−0.882691
$717$	376.810	−	1406.27i	0.525537	−	1.96133i
$718$	275.618	+	477.384i	0.383869	+	0.664881i
$719$	−150.591	−	86.9435i	−0.209445	−	0.120923i	0.391609	−	0.920132i	$-0.371919\pi$
$719$	−150.591	−	86.9435i	−0.209445	−	0.120923i	−0.601053	+	0.799209i	$0.705252\pi$
$720$	−28.6679	−	28.6679i	−0.0398165	−	0.0398165i
$721$	832.716	−	223.126i	1.15495	−	0.309467i
$722$	124.279	+	463.814i	0.172131	+	0.642402i
$723$	−877.566	+	877.566i	−1.21378	+	1.21378i
$724$	83.6580	−	144.900i	0.115550	−	0.200138i
$725$	354.249	−	204.526i	0.488619	−	0.282104i
$726$	683.410	+	183.119i	0.941336	+	0.252230i
$727$		−	729.011i		−	1.00277i	−0.865225	−	0.501383i	$-0.832825\pi$
$727$		−	729.011i		−	1.00277i	0.865225	−	0.501383i	$-0.167175\pi$
$728$		0			0
$729$	957.649			1.31365
$730$	−4.48851	+	16.7514i	−0.00614865	+	0.0229471i
$731$	52.5295	+	90.9838i	0.0718598	+	0.124465i
$732$	−269.457	−	155.571i	−0.368111	−	0.212529i
$733$	−762.465	−	762.465i	−1.04020	−	1.04020i	−0.999157	−	0.0410404i	$-0.986933\pi$
$733$	−762.465	−	762.465i	−1.04020	−	1.04020i	−0.0410404	−	0.999157i	$-0.513067\pi$
$734$	−640.304	+	171.569i	−0.872348	+	0.233745i
$735$	9.39166	+	35.0501i	0.0127778	+	0.0476873i
$736$	69.7330	−	69.7330i	0.0947460	−	0.0947460i
$737$	−95.7992	+	165.929i	−0.129985	+	0.225141i
$738$	−1644.73	+	949.584i	−2.22863	+	1.28670i
$739$	−592.703	−	158.814i	−0.802033	−	0.214904i	−0.165557	−	0.986200i	$-0.552942\pi$
$739$	−592.703	−	158.814i	−0.802033	−	0.214904i	−0.636476	+	0.771296i	$0.719609\pi$
$740$			32.2940i			0.0436405i
$741$		0			0
$742$	263.556			0.355197
$743$	−43.1002	+	160.852i	−0.0580084	+	0.216490i	−0.988846	−	0.148944i	$-0.952413\pi$
$743$	−43.1002	+	160.852i	−0.0580084	+	0.216490i	0.930837	+	0.365434i	$0.119079\pi$
$744$	−103.478	−	179.229i	−0.139083	−	0.240899i
$745$	86.6036	+	50.0006i	0.116246	+	0.0671149i
$746$	260.814	+	260.814i	0.349617	+	0.349617i
$747$	2772.27	−	742.829i	3.71121	−	0.994416i
$748$	5.83084	+	21.7610i	0.00779525	+	0.0290923i
$749$	423.279	−	423.279i	0.565126	−	0.565126i
$750$	−89.9742	+	155.840i	−0.119966	+	0.207787i
$751$	116.272	−	67.1297i	0.154823	−	0.0893871i	−0.420587	−	0.907252i	$-0.638176\pi$
$751$	116.272	−	67.1297i	0.154823	−	0.0893871i	0.575410	+	0.817865i	$0.304842\pi$
$752$	47.7304	+	12.7893i	0.0634713	+	0.0170071i
$753$			1405.78i			1.86691i
$754$		0			0
$755$	47.7509			0.0632462
$756$	−301.397	+	1124.83i	−0.398673	+	1.48787i
$757$	598.217	+	1036.14i	0.790247	+	1.36875i	0.925814	+	0.377980i	$0.123381\pi$
$757$	598.217	+	1036.14i	0.790247	+	1.36875i	−0.135567	+	0.990768i	$0.543285\pi$
$758$	262.331	+	151.457i	0.346083	+	0.199811i
$759$	384.957	+	384.957i	0.507190	+	0.507190i
$760$	5.79785	−	1.55353i	0.00762875	−	0.00204412i
$761$	9.05420	+	33.7907i	0.0118978	+	0.0444031i	0.971620	−	0.236549i	$-0.0760164\pi$
$761$	9.05420	+	33.7907i	0.0118978	+	0.0444031i	−0.959722	+	0.280952i	$0.909350\pi$
$762$	539.918	−	539.918i	0.708554	−	0.708554i
$763$	32.8095	−	56.8277i	0.0430007	−	0.0744793i
$764$	119.708	−	69.1133i	0.156686	−	0.0904625i
$765$	−19.7026	−	5.27929i	−0.0257550	−	0.00690104i
$766$		−	970.071i		−	1.26641i
$767$		0			0
$768$	89.2673			0.116234
$769$	−64.5729	+	240.989i	−0.0839700	+	0.313380i	−0.995117	−	0.0987009i	$-0.968531\pi$
$769$	−64.5729	+	240.989i	−0.0839700	+	0.313380i	0.911147	+	0.412081i	$0.135198\pi$
$770$	14.4123	+	24.9628i	0.0187173	+	0.0324192i
$771$	1402.61	+	809.794i	1.81920	+	1.05032i
$772$	−459.147	−	459.147i	−0.594750	−	0.594750i
$773$	533.020	−	142.822i	0.689547	−	0.184764i	0.103003	−	0.994681i	$-0.467155\pi$
$773$	533.020	−	142.822i	0.689547	−	0.184764i	0.586544	+	0.809917i	$0.300488\pi$
$774$	422.814	+	1577.96i	0.546272	+	2.03871i
$775$	−229.892	+	229.892i	−0.296635	+	0.296635i
$776$	159.246	−	275.822i	0.205214	−	0.355441i
$777$	1354.04	−	781.758i	1.74266	−	1.00612i
$778$	−511.838	−	137.146i	−0.657889	−	0.176281i
$779$		−	281.175i		−	0.360943i
$780$		0			0
$781$	428.101			0.548145
$782$	12.8416	−	47.9255i	0.0164215	−	0.0612858i
$783$	604.261	+	1046.61i	0.771726	+	1.33667i
$784$	−49.1866	−	28.3979i	−0.0627381	−	0.0362218i
$785$	−41.1697	−	41.1697i	−0.0524455	−	0.0524455i
$786$	−1216.47	+	325.952i	−1.54767	+	0.414697i
$787$	−182.321	−	680.430i	−0.231665	−	0.864587i	−0.979624	−	0.200841i	$-0.935632\pi$
$787$	−182.321	−	680.430i	−0.231665	−	0.864587i	0.747958	−	0.663746i	$-0.231034\pi$
$788$	−452.748	+	452.748i	−0.574553	+	0.574553i
$789$	300.908	−	521.187i	0.381379	−	0.660567i
$790$	−80.1312	+	46.2638i	−0.101432	+	0.0585617i
$791$	−879.134	−	235.563i	−1.11142	−	0.297804i
$792$			350.312i			0.442313i
$793$		0			0
$794$	−922.776			−1.16219
$795$	−15.5056	+	57.8677i	−0.0195039	+	0.0727896i
$796$	172.820	+	299.333i	0.217111	+	0.376047i
$797$	−118.158	−	68.2188i	−0.148254	−	0.0855945i	0.424038	−	0.905644i	$-0.360612\pi$
$797$	−118.158	−	68.2188i	−0.148254	−	0.0855945i	−0.572292	+	0.820050i	$0.693946\pi$
$798$	−205.489	−	205.489i	−0.257505	−	0.257505i
$799$	24.0140	−	6.43453i	0.0300550	−	0.00805322i
$800$	−36.2954	−	135.456i	−0.0453692	−	0.169320i
$801$	2442.77	−	2442.77i	3.04965	−	3.04965i
$802$	305.660	−	529.419i	0.381122	−	0.660123i
$803$	129.772	−	74.9240i	0.161609	−	0.0933051i
$804$	368.945	+	98.8586i	0.458887	+	0.122958i
$805$		−	63.4819i		−	0.0788596i
$806$		0			0
$807$	−2429.32			−3.01031
$808$	−71.5209	+	266.920i	−0.0885160	+	0.330346i
$809$	50.0507	+	86.6904i	0.0618674	+	0.107157i	0.895300	−	0.445463i	$-0.146961\pi$
$809$	50.0507	+	86.6904i	0.0618674	+	0.107157i	−0.833433	+	0.552621i	$0.813628\pi$
$810$	−117.519	−	67.8496i	−0.145085	−	0.0837649i
$811$	−143.367	−	143.367i	−0.176778	−	0.176778i	0.613172	−	0.789950i	$-0.289893\pi$
$811$	−143.367	−	143.367i	−0.176778	−	0.176778i	−0.789950	+	0.613172i	$0.789893\pi$
$812$	−253.412	+	67.9014i	−0.312083	+	0.0836224i
$813$	121.461	+	453.299i	0.149399	+	0.557564i
$814$	197.311	−	197.311i	0.242397	−	0.242397i
$815$	38.7209	−	67.0666i	0.0475103	−	0.0822903i
$816$	38.8949	−	22.4560i	0.0476653	−	0.0275196i
$817$	−233.620	−	62.5982i	−0.285948	−	0.0766196i
$818$			394.757i			0.482588i
$819$		0			0
$820$	55.5983			0.0678028
$821$	−76.5922	+	285.846i	−0.0932914	+	0.348168i	−0.996755	−	0.0804969i	$-0.974349\pi$
$821$	−76.5922	+	285.846i	−0.0932914	+	0.348168i	0.903463	+	0.428665i	$0.141016\pi$
$822$	−499.195	−	864.631i	−0.607293	−	1.05186i
$823$	−213.860	−	123.472i	−0.259854	−	0.150027i	0.364414	−	0.931237i	$-0.381269\pi$
$823$	−213.860	−	123.472i	−0.259854	−	0.150027i	−0.624268	+	0.781210i	$0.714603\pi$
$824$	−216.884	−	216.884i	−0.263209	−	0.263209i
$825$	747.778	−	200.366i	0.906397	−	0.242868i
$826$	102.684	+	383.223i	0.124315	+	0.463950i
$827$	450.766	−	450.766i	0.545062	−	0.545062i	−0.379947	−	0.925008i	$-0.624058\pi$
$827$	450.766	−	450.766i	0.545062	−	0.545062i	0.925008	+	0.379947i	$0.124058\pi$
$828$	385.756	−	668.149i	0.465889	−	0.806943i
$829$	−782.813	+	451.957i	−0.944286	+	0.545184i	−0.891301	−	0.453411i	$-0.850207\pi$
$829$	−782.813	+	451.957i	−0.944286	+	0.545184i	−0.0529848	+	0.998595i	$0.516873\pi$
$830$	−81.1585	−	21.7464i	−0.0977814	−	0.0262004i
$831$		−	205.379i		−	0.247147i
$832$		0			0
$833$	−28.5750			−0.0343037
$834$	123.441	−	460.686i	0.148010	−	0.552382i
$835$	−38.1861	−	66.1403i	−0.0457319	−	0.0792099i
$836$	−44.9157	−	25.9321i	−0.0537269	−	0.0310193i
$837$	−679.207	−	679.207i	−0.811478	−	0.811478i
$838$	−256.253	+	68.6628i	−0.305791	+	0.0819365i
$839$	−249.753	−	932.092i	−0.297680	−	1.11096i	−0.939066	−	0.343737i	$-0.888307\pi$
$839$	−249.753	−	932.092i	−0.297680	−	1.11096i	0.641386	−	0.767218i	$-0.278360\pi$
$840$	40.6326	−	40.6326i	0.0483721	−	0.0483721i
$841$	284.366	−	492.537i	0.338129	−	0.585656i
$842$	710.973	−	410.480i	0.844386	−	0.487506i
$843$	229.464	+	61.4846i	0.272199	+	0.0729355i
$844$			460.358i			0.545447i
$845$		0			0
$846$	386.581			0.456951
$847$	−184.502	+	688.571i	−0.217830	+	0.812953i
$848$	−46.8849	−	81.2071i	−0.0552888	−	0.0957631i
$849$	−507.138	−	292.796i	−0.597335	−	0.344872i
$850$	−49.8895	−	49.8895i	−0.0586935	−	0.0586935i
$851$	−593.604	+	159.056i	−0.697537	+	0.186905i
$852$	−220.886	−	824.359i	−0.259256	−	0.967558i
$853$	−103.615	+	103.615i	−0.121471	+	0.121471i	−0.765229	−	0.643758i	$-0.777374\pi$
$853$	−103.615	+	103.615i	−0.121471	+	0.121471i	0.643758	+	0.765229i	$0.277374\pi$
$854$	156.746	−	271.492i	0.183543	−	0.317907i
$855$	40.6670	−	23.4791i	0.0475638	−	0.0274610i
$856$	−205.720	−	55.1224i	−0.240327	−	0.0643953i
$857$			497.605i			0.580636i	0.956930	+	0.290318i	$0.0937612\pi$
$857$			497.605i			0.580636i	−0.956930	+	0.290318i	$0.906239\pi$
$858$		0			0
$859$	763.167			0.888437			0.444218	−	0.895918i	$-0.353481\pi$
$859$	763.167			0.888437			0.444218	+	0.895918i	$0.353481\pi$
$860$	12.3779	−	46.1950i	0.0143929	−	0.0537151i
$861$	−1345.90	−	2331.16i	−1.56318	−	2.70751i
$862$	−655.286	−	378.330i	−0.760193	−	0.438897i
$863$	299.561	+	299.561i	0.347115	+	0.347115i	0.859034	−	0.511919i	$-0.171065\pi$
$863$	299.561	+	299.561i	0.347115	+	0.347115i	−0.511919	+	0.859034i	$0.671065\pi$
$864$	400.199	−	107.233i	0.463193	−	0.124112i
$865$	16.6548	+	62.1566i	0.0192541	+	0.0718573i
$866$	−161.880	+	161.880i	−0.186928	+	0.186928i
$867$	−794.898	+	1376.80i	−0.916837	+	1.58801i
$868$	180.582	−	104.259i	0.208044	−	0.120114i
$869$	772.253	+	206.924i	0.888668	+	0.238118i
$870$		−	59.6351i		−	0.0685461i
$871$		0			0
$872$	−23.3464			−0.0267734
$873$	644.886	−	2406.75i	0.738701	−	2.75687i
$874$	57.1117	+	98.9203i	0.0653452	+	0.113181i
$875$	−157.017	−	90.6537i	−0.179448	−	0.103604i
$876$	−211.233	−	211.233i	−0.241134	−	0.241134i
$877$	1212.64	−	324.925i	1.38271	−	0.370496i	0.510605	−	0.859816i	$-0.329422\pi$
$877$	1212.64	−	324.925i	1.38271	−	0.370496i	0.872104	+	0.489320i	$0.162755\pi$
$878$	−60.1239	−	224.385i	−0.0684783	−	0.255564i
$879$	−495.828	+	495.828i	−0.564082	+	0.564082i
$880$	5.12770	−	8.88144i	0.00582694	−	0.0100926i
$881$	−487.059	+	281.204i	−0.552848	+	0.319187i	−0.750270	−	0.661132i	$-0.770077\pi$
$881$	−487.059	+	281.204i	−0.552848	+	0.319187i	0.197422	+	0.980319i	$0.436743\pi$
$882$	−429.190	−	115.001i	−0.486610	−	0.130387i
$883$		−	325.309i		−	0.368413i	−0.982888	−	0.184207i	$-0.941028\pi$
$883$		−	325.309i		−	0.368413i	0.982888	−	0.184207i	$-0.0589715\pi$
$884$		0			0
$885$	−90.1835			−0.101902
$886$	113.436	−	423.347i	0.128031	−	0.477819i
$887$	−744.398	−	1289.33i	−0.839231	−	1.45359i	−0.890539	−	0.454907i	$-0.849672\pi$
$887$	−744.398	−	1289.33i	−0.839231	−	1.45359i	0.0513079	−	0.998683i	$-0.483661\pi$
$888$	−481.751	−	278.139i	−0.542513	−	0.313220i
$889$	543.996	+	543.996i	0.611919	+	0.611919i
$890$	−97.6874	+	26.1753i	−0.109761	+	0.0294104i
$891$	303.472	+	1132.57i	0.340597	+	1.27112i
$892$	−372.184	+	372.184i	−0.417246	+	0.417246i
$893$	−28.6169	+	49.5659i	−0.0320458	+	0.0555050i
$894$	−1491.79	+	861.284i	−1.66867	+	0.963404i
$895$	139.814	+	37.4632i	0.156217	+	0.0418583i
$896$			89.9415i			0.100381i
$897$		0			0
$898$	192.441			0.214300
$899$	56.0085	−	209.026i	0.0623009	−	0.232510i
$900$	−548.547	−	950.111i	−0.609496	−	1.05568i
$901$	−40.8567	−	23.5886i	−0.0453459	−	0.0261805i
$902$	−339.696	−	339.696i	−0.376603	−	0.376603i
$903$	−2236.54	+	599.278i	−2.47678	+	0.663652i
$904$	83.8103	+	312.784i	0.0927105	+	0.346000i
$905$	−27.0962	+	27.0962i	−0.0299406	+	0.0299406i
$906$	−411.266	+	712.333i	−0.453936	+	0.786240i
$907$	227.634	−	131.425i	0.250975	−	0.144900i	−0.369236	−	0.929336i	$-0.620381\pi$
$907$	227.634	−	131.425i	0.250975	−	0.144900i	0.620210	+	0.784435i	$0.287047\pi$
$908$	230.205	+	61.6832i	0.253530	+	0.0679330i
$909$			2161.85i			2.37827i
$910$		0			0
$911$	−1043.25			−1.14517			−0.572584	−	0.819846i	$-0.694059\pi$
$911$	−1043.25			−1.14517			−0.572584	+	0.819846i	$0.694059\pi$
$912$	−26.7603	+	99.8706i	−0.0293424	+	0.109507i
$913$	362.999	+	628.732i	0.397589	+	0.688644i
$914$	278.127	+	160.576i	0.304296	+	0.175685i
$915$	50.3885	+	50.3885i	0.0550694	+	0.0550694i
$916$	612.996	−	164.252i	0.669209	−	0.179314i
$917$	−328.413	−	1225.66i	−0.358139	−	1.33659i
$918$	147.396	−	147.396i	0.160562	−	0.160562i
$919$	408.478	−	707.504i	0.444481	−	0.769863i	−0.553535	−	0.832826i	$-0.686722\pi$
$919$	408.478	−	707.504i	0.444481	−	0.769863i	0.998016	+	0.0629627i	$0.0200549\pi$
$920$	−19.5601	+	11.2930i	−0.0212610	+	0.0122750i
$921$	1214.90	+	325.531i	1.31911	+	0.353454i
$922$		−	967.271i		−	1.04910i
$923$		0			0
$924$	−496.517			−0.537356
$925$	−226.178	+	844.108i	−0.244517	+	0.912550i
$926$	−557.281	−	965.238i	−0.601815	−	1.04237i
$927$	−2078.08	−	1199.78i	−2.24173	−	1.29426i
$928$	66.0021	+	66.0021i	0.0711229	+	0.0711229i
$929$	−1445.30	+	387.266i	−1.55575	+	0.416863i	−0.931317	−	0.364211i	$-0.881339\pi$
$929$	−1445.30	+	387.266i	−1.55575	+	0.416863i	−0.624438	+	0.781074i	$0.714672\pi$
$930$	12.2676	+	45.7834i	0.0131910	+	0.0492295i
$931$	46.5161	−	46.5161i	0.0499635	−	0.0499635i
$932$	−230.683	+	399.554i	−0.247513	+	0.428706i
$933$	−2231.09	+	1288.12i	−2.39130	+	1.38062i
$934$	−124.357	−	33.3213i	−0.133144	−	0.0356759i
$935$		−	5.15967i		−	0.00551836i
$936$		0			0
$937$	−1671.65			−1.78404			−0.892020	−	0.451996i	$-0.850712\pi$
$937$	−1671.65			−1.78404			−0.892020	+	0.451996i	$0.850712\pi$
$938$	−99.6052	+	371.732i	−0.106189	+	0.396302i
$939$	−22.7843	−	39.4636i	−0.0242645	−	0.0420273i
$940$	−9.80096	−	5.65859i	−0.0104266	−	0.00601977i
$941$	87.2271	+	87.2271i	0.0926962	+	0.0926962i	0.751934	−	0.659238i	$-0.229121\pi$
$941$	87.2271	+	87.2271i	0.0926962	+	0.0926962i	−0.659238	+	0.751934i	$0.729121\pi$
$942$	968.740	−	259.573i	1.02839	−	0.275555i
$943$	273.835	+	1021.97i	0.290387	+	1.08374i
$944$	99.8120	−	99.8120i	0.105733	−	0.105733i
$945$	133.352	−	230.972i	0.141113	−	0.244415i
$946$	−357.871	+	206.617i	−0.378299	+	0.218411i
$947$	−1430.15	−	383.208i	−1.51019	−	0.404654i	−0.593692	−	0.804693i	$-0.702330\pi$
$947$	−1430.15	−	383.208i	−1.51019	−	0.404654i	−0.916498	+	0.400038i	$0.868997\pi$
$948$		−	1593.83i		−	1.68126i
$949$		0			0
$950$	162.426			0.170975
$951$	−187.085	+	698.212i	−0.196725	+	0.734187i
$952$	22.6255	+	39.1886i	0.0237663	+	0.0411645i
$953$	736.584	+	425.267i	0.772911	+	0.446240i	0.833912	−	0.551897i	$-0.186096\pi$
$953$	736.584	+	425.267i	0.772911	+	0.446240i	−0.0610010	+	0.998138i	$0.519429\pi$
$954$	−518.725	−	518.725i	−0.543737	−	0.543737i
$955$	−30.5789	+	8.19360i	−0.0320198	+	0.00857968i
$956$	−135.076	−	504.112i	−0.141293	−	0.527314i
$957$	−364.361	+	364.361i	−0.380732	+	0.380732i
$958$	−522.586	+	905.145i	−0.545496	+	0.944827i
$959$	871.161	−	502.965i	0.908405	−	0.524468i
$960$	−19.7480	−	5.29146i	−0.0205708	−	0.00551194i
$961$		−	789.003i		−	0.821023i
$962$		0			0
$963$	−1666.18			−1.73019
$964$	−115.146	+	429.730i	−0.119446	+	0.445778i
$965$	74.3572	+	128.790i	0.0770541	+	0.133462i
$966$	947.004	+	546.753i	0.980335	+	0.565997i
$967$	133.506	+	133.506i	0.138062	+	0.138062i	0.772760	−	0.634698i	$-0.218875\pi$
$967$	133.506	+	133.506i	0.138062	+	0.138062i	−0.634698	+	0.772760i	$0.718875\pi$
$968$	244.985	−	65.6434i	0.253083	−	0.0678134i
$969$	13.4635	+	50.2466i	0.0138943	+	0.0518541i
$970$	−51.5786	+	51.5786i	−0.0531738	+	0.0531738i
$971$	−693.721	+	1201.56i	−0.714439	+	1.23745i	0.248736	+	0.968571i	$0.419985\pi$
$971$	−693.721	+	1201.56i	−0.714439	+	1.23745i	−0.963175	+	0.268874i	$0.913349\pi$
$972$	882.596	−	509.567i	0.908021	−	0.524246i
$973$	464.165	+	124.373i	0.477045	+	0.127824i
$974$			849.579i			0.872257i
$975$		0			0
$976$	−111.536			−0.114279
$977$	362.725	−	1353.71i	0.371264	−	1.38558i	−0.487464	−	0.873143i	$-0.662078\pi$
$977$	362.725	−	1353.71i	0.371264	−	1.38558i	0.858728	−	0.512432i	$-0.171255\pi$
$978$	666.986	+	1155.25i	0.681990	+	1.18124i
$979$	756.780	+	436.927i	0.773014	+	0.446300i
$980$	9.19789	+	9.19789i	0.00938560	+	0.00938560i
$981$	−176.422	+	47.2721i	−0.179839	+	0.0481876i
$982$	−203.876	−	760.876i	−0.207613	−	0.774823i
$983$	457.371	−	457.371i	0.465280	−	0.465280i	−0.435101	−	0.900382i	$-0.643287\pi$
$983$	457.371	−	457.371i	0.465280	−	0.465280i	0.900382	+	0.435101i	$0.143287\pi$
$984$	−478.853	+	829.398i	−0.486639	+	0.842884i
$985$	126.996	−	73.3209i	0.128930	−	0.0744375i
$986$	45.3613	+	12.1545i	0.0460054	+	0.0123271i
$987$			547.922i			0.555139i
$988$		0			0
$989$	910.087			0.920210
$990$	20.7653	−	77.4971i	0.0209750	−	0.0782799i
$991$	75.8147	+	131.315i	0.0765033	+	0.132508i	0.901739	−	0.432281i	$-0.142291\pi$
$991$	75.8147	+	131.315i	0.0765033	+	0.132508i	−0.825236	+	0.564788i	$0.808958\pi$
$992$	−64.2489	−	37.0941i	−0.0647670	−	0.0373933i
$993$	589.942	+	589.942i	0.594100	+	0.594100i
$994$	830.585	−	222.555i	0.835598	−	0.223898i
$995$	−20.4884	−	76.4636i	−0.0205913	−	0.0768478i
$996$	1023.40	−	1023.40i	1.02751	−	1.02751i
$997$	239.901	−	415.520i	0.240623	−	0.416771i	−0.720269	−	0.693695i	$-0.755982\pi$
$997$	239.901	−	415.520i	0.240623	−	0.416771i	0.960892	+	0.276924i	$0.0893150\pi$
$998$	160.626	−	92.7376i	0.160948	−	0.0929234i
$999$	−2493.88	−	668.233i	−2.49638	−	0.668902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.f.h.89.1		8
13.2	odd	12		338.3.d.g.239.4		8
13.3	even	3		338.3.d.g.99.4		8
13.4	even	6		338.3.f.i.319.1		8
13.5	odd	4		26.3.f.b.15.1	yes	8
13.6	odd	12	inner	338.3.f.h.19.1		8
13.7	odd	12		338.3.f.j.19.1		8
13.8	odd	4		338.3.f.i.249.1		8
13.9	even	3		26.3.f.b.7.1	✓	8
13.10	even	6		338.3.d.f.99.4		8
13.11	odd	12		338.3.d.f.239.4		8
13.12	even	2		338.3.f.j.89.1		8
39.5	even	4		234.3.bb.f.145.2		8
39.35	odd	6		234.3.bb.f.163.2		8
52.31	even	4		208.3.bd.f.145.2		8
52.35	odd	6		208.3.bd.f.33.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.7.1	✓	8	13.9	even	3
26.3.f.b.15.1	yes	8	13.5	odd	4
208.3.bd.f.33.2		8	52.35	odd	6
208.3.bd.f.145.2		8	52.31	even	4
234.3.bb.f.145.2		8	39.5	even	4
234.3.bb.f.163.2		8	39.35	odd	6
338.3.d.f.99.4		8	13.10	even	6
338.3.d.f.239.4		8	13.11	odd	12
338.3.d.g.99.4		8	13.3	even	3
338.3.d.g.239.4		8	13.2	odd	12
338.3.f.h.19.1		8	13.6	odd	12	inner
338.3.f.h.89.1		8	1.1	even	1	trivial
338.3.f.i.249.1		8	13.8	odd	4
338.3.f.i.319.1		8	13.4	even	6
338.3.f.j.19.1		8	13.7	odd	12
338.3.f.j.89.1		8	13.12	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-2.78960 - 4.83174i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.323893 + 0.323893i) q^{5} +(-7.62134 + 2.04213i) q^{6} +(-2.05755 - 7.67890i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-11.0638 + 19.1630i) q^{9} +(0.560999 - 0.323893i) q^{10} +(-5.40655 - 1.44868i) q^{11} +11.1584i q^{12} -11.2427 q^{14} +(0.661433 - 2.46850i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.74285 + 1.00623i) q^{17} +(22.1276 + 22.1276i) q^{18} +(-4.47512 + 1.19911i) q^{19} +(-0.237106 - 0.884892i) q^{20} +(-31.3626 + 31.3626i) q^{21} +(-3.95787 + 6.85523i) q^{22} +(15.0976 - 8.71663i) q^{23} +(15.2427 + 4.08426i) q^{24} -24.7902i q^{25} +73.2415 q^{27} +(-4.11511 + 15.3578i) q^{28} +(8.25026 + 14.2899i) q^{29} +(-3.12993 - 1.80707i) q^{30} +(-9.27353 - 9.27353i) q^{31} +(5.46410 - 1.46410i) q^{32} +(8.08249 + 30.1643i) q^{33} +(2.01247 - 2.01247i) q^{34} +(1.82071 - 3.15357i) q^{35} +(38.3261 - 22.1276i) q^{36} +(-34.0501 - 9.12370i) q^{37} +6.55204i q^{38} -1.29557 q^{40} +(-15.7076 + 58.6217i) q^{41} +(31.3626 + 54.3217i) q^{42} +(45.2101 + 26.1020i) q^{43} +(7.91574 + 7.91574i) q^{44} +(-9.79026 + 2.62329i) q^{45} +(-6.38102 - 23.8143i) q^{46} +(8.73527 - 8.73527i) q^{47} +(11.1584 - 19.3269i) q^{48} +(-12.2967 + 7.09948i) q^{49} +(-33.8640 - 9.07384i) q^{50} -11.2280i q^{51} -23.4425 q^{53} +(26.8082 - 100.050i) q^{54} +(-1.28193 - 2.22036i) q^{55} +(19.4729 + 11.2427i) q^{56} +(18.2776 + 18.2776i) q^{57} +(22.5401 - 6.03961i) q^{58} +(-9.13343 - 34.0864i) q^{59} +(-3.61413 + 3.61413i) q^{60} +(-13.9421 + 24.1483i) q^{61} +(-16.0622 + 9.27353i) q^{62} +(169.915 + 45.5287i) q^{63} -8.00000i q^{64} +44.1635 q^{66} +(8.85955 - 33.0643i) q^{67} +(-2.01247 - 3.48570i) q^{68} +(-84.2329 - 48.6319i) q^{69} +(-3.64143 - 3.64143i) q^{70} +(-73.8778 + 19.7955i) q^{71} +(-16.1985 - 60.4537i) q^{72} +(-18.9304 + 18.9304i) q^{73} +(-24.9264 + 43.1738i) q^{74} +(-119.780 + 69.1548i) q^{75} +(8.95025 + 2.39821i) q^{76} +44.4971i q^{77} -142.837 q^{79} +(-0.474212 + 1.76978i) q^{80} +(-104.741 - 181.416i) q^{81} +(74.3293 + 42.9141i) q^{82} +(-91.7157 - 91.7157i) q^{83} +(85.6843 - 22.9590i) q^{84} +(0.238584 + 0.890409i) q^{85} +(52.2041 - 52.2041i) q^{86} +(46.0299 - 79.7262i) q^{87} +(13.7105 - 7.91574i) q^{88} +(-150.802 - 40.4072i) q^{89} +14.3339i q^{90} -34.8665 q^{92} +(-18.9378 + 70.6767i) q^{93} +(-8.73527 - 15.1299i) q^{94} +(-1.83784 - 1.06108i) q^{95} +(-22.3168 - 22.3168i) q^{96} +(-108.767 + 29.1440i) q^{97} +(5.19718 + 19.3961i) q^{98} +(87.5780 - 87.5780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{5} - 6 q^{6} - 8 q^{7} - 16 q^{8} - 42 q^{9} + 18 q^{10} - 24 q^{11} + 20 q^{14} - 126 q^{15} + 16 q^{16} + 42 q^{17} + 84 q^{18} - 68 q^{19} - 12 q^{20} - 102 q^{21} - 42 q^{22} + 36 q^{23}+ \cdots + 252 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^5 - 6 * q^6 - 8 * q^7 - 16 * q^8 - 42 * q^9 + 18 * q^10 - 24 * q^11 + 20 * q^14 - 126 * q^15 + 16 * q^16 + 42 * q^17 + 84 * q^18 - 68 * q^19 - 12 * q^20 - 102 * q^21 - 42 * q^22 + 36 * q^23 + 12 * q^24 + 72 * q^27 - 16 * q^28 - 6 * q^29 + 192 * q^30 + 32 * q^31 + 16 * q^32 - 96 * q^33 - 60 * q^34 - 78 * q^35 + 48 * q^36 + 74 * q^37 - 24 * q^40 - 120 * q^41 + 102 * q^42 + 108 * q^43 + 84 * q^44 - 138 * q^45 + 18 * q^46 + 60 * q^47 - 258 * q^49 - 106 * q^50 - 132 * q^53 + 198 * q^54 - 162 * q^55 + 12 * q^56 - 294 * q^57 + 12 * q^58 - 252 * q^59 - 120 * q^60 + 36 * q^61 + 12 * q^62 + 228 * q^63 + 108 * q^66 + 88 * q^67 + 60 * q^68 - 258 * q^69 + 156 * q^70 + 12 * q^71 + 36 * q^72 + 166 * q^73 - 32 * q^74 - 6 * q^75 + 136 * q^76 - 96 * q^79 - 24 * q^80 - 12 * q^81 + 252 * q^82 - 240 * q^83 + 336 * q^84 + 258 * q^85 + 132 * q^86 + 360 * q^87 + 12 * q^88 - 504 * q^89 - 216 * q^92 + 174 * q^93 - 60 * q^94 - 714 * q^95 - 88 * q^97 + 266 * q^98 + 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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