LMFDB - Embedded newform 336.4.q.j.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{1345})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 337x^{2} + 336x + 112896 $ x^4 - x^3 + 337x^2 + 336x + 112896
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$9.41856 + 16.3134i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.4.q.j.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(-10.4186 - 18.0455i) q^{5} +(18.3371 + 2.59808i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(-10.4186 - 18.0455i) q^{5} +(18.3371 + 2.59808i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(7.58144 - 13.1314i) q^{11} +2.16288 q^{13} -62.5114 q^{15} +(59.6742 - 103.359i) q^{17} +(-16.7557 - 29.0217i) q^{19} +(34.2557 - 43.7441i) q^{21} +(0.325758 + 0.564230i) q^{23} +(-154.593 + 267.763i) q^{25} -27.0000 q^{27} -163.208 q^{29} +(-111.663 + 193.406i) q^{31} +(-22.7443 - 39.3943i) q^{33} +(-144.163 - 357.970i) q^{35} +(-84.2670 - 145.955i) q^{37} +(3.24432 - 5.61932i) q^{39} -323.023 q^{41} -221.557 q^{43} +(-93.7670 + 162.409i) q^{45} +(254.023 + 439.980i) q^{47} +(329.500 + 95.2825i) q^{49} +(-179.023 - 310.076i) q^{51} +(88.2557 - 152.863i) q^{53} -315.951 q^{55} -100.534 q^{57} +(227.464 - 393.979i) q^{59} +(-19.3258 - 33.4732i) q^{61} +(-62.2670 - 154.615i) q^{63} +(-22.5341 - 39.0302i) q^{65} +(70.8958 - 122.795i) q^{67} +1.95455 q^{69} -602.742 q^{71} +(551.150 - 954.619i) q^{73} +(463.778 + 803.288i) q^{75} +(173.138 - 221.096i) q^{77} +(-58.1515 - 100.721i) q^{79} +(-40.5000 + 70.1481i) q^{81} +568.928 q^{83} -2486.88 q^{85} +(-244.812 + 424.028i) q^{87} +(191.580 + 331.825i) q^{89} +(39.6610 + 5.61932i) q^{91} +(334.989 + 580.217i) q^{93} +(-349.140 + 604.728i) q^{95} +334.701 q^{97} -136.466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 5 q^{5} - 18 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 5 * q^5 - 18 * q^9	$ 4 q + 6 q^{3} - 5 q^{5} - 18 q^{9} + 67 q^{11} + 82 q^{13} - 30 q^{15} + 92 q^{17} + 43 q^{19} + 27 q^{21} + 148 q^{23} - 435 q^{25} - 108 q^{27} + 154 q^{29} - 520 q^{31} - 201 q^{33} - 650 q^{35} - 7 q^{37} + 123 q^{39} - 852 q^{41} + 214 q^{43} - 45 q^{45} + 576 q^{47} + 1318 q^{49} - 276 q^{51} + 243 q^{53} + 1010 q^{55} + 258 q^{57} - 7 q^{59} - 224 q^{61} + 81 q^{63} + 570 q^{65} + 687 q^{67} + 888 q^{69} - 944 q^{71} + 921 q^{73} + 1305 q^{75} - 371 q^{77} - 526 q^{79} - 162 q^{81} + 442 q^{83} - 5840 q^{85} + 231 q^{87} - 774 q^{89} - 1345 q^{91} + 1560 q^{93} - 1910 q^{95} + 3906 q^{97} - 1206 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 5 * q^5 - 18 * q^9 + 67 * q^11 + 82 * q^13 - 30 * q^15 + 92 * q^17 + 43 * q^19 + 27 * q^21 + 148 * q^23 - 435 * q^25 - 108 * q^27 + 154 * q^29 - 520 * q^31 - 201 * q^33 - 650 * q^35 - 7 * q^37 + 123 * q^39 - 852 * q^41 + 214 * q^43 - 45 * q^45 + 576 * q^47 + 1318 * q^49 - 276 * q^51 + 243 * q^53 + 1010 * q^55 + 258 * q^57 - 7 * q^59 - 224 * q^61 + 81 * q^63 + 570 * q^65 + 687 * q^67 + 888 * q^69 - 944 * q^71 + 921 * q^73 + 1305 * q^75 - 371 * q^77 - 526 * q^79 - 162 * q^81 + 442 * q^83 - 5840 * q^85 + 231 * q^87 - 774 * q^89 - 1345 * q^91 + 1560 * q^93 - 1910 * q^95 + 3906 * q^97 - 1206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$		0			0
$5$	−10.4186	−	18.0455i	−0.931864	−	1.61404i	−0.780132	−	0.625615i	$-0.784848\pi$
$5$	−10.4186	−	18.0455i	−0.931864	−	1.61404i	−0.151732	−	0.988422i	$-0.548485\pi$
$6$		0			0
$7$	18.3371	+	2.59808i	0.990111	+	0.140283i
$7$	18.3371	+	2.59808i	0.990111	+	0.140283i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	7.58144	−	13.1314i	0.207808	−	0.359934i	−0.743216	−	0.669052i	$-0.766700\pi$
$11$	7.58144	−	13.1314i	0.207808	−	0.359934i	0.951024	+	0.309118i	$0.100034\pi$
$12$		0			0
$13$	2.16288			0.0461442			0.0230721	−	0.999734i	$-0.492655\pi$
$13$	2.16288			0.0461442			0.0230721	+	0.999734i	$0.492655\pi$
$14$		0			0
$15$	−62.5114			−1.07602
$16$		0			0
$17$	59.6742	−	103.359i	0.851361	−	1.47460i	−0.0286202	−	0.999590i	$-0.509111\pi$
$17$	59.6742	−	103.359i	0.851361	−	1.47460i	0.879981	−	0.475009i	$-0.157555\pi$
$18$		0			0
$19$	−16.7557	−	29.0217i	−0.202317	−	0.350423i	0.746958	−	0.664871i	$-0.231514\pi$
$19$	−16.7557	−	29.0217i	−0.202317	−	0.350423i	−0.949274	+	0.314449i	$0.898180\pi$
$20$		0			0
$21$	34.2557	−	43.7441i	0.355962	−	0.454560i
$22$		0			0
$23$	0.325758	+	0.564230i	0.00295327	+	0.00511522i	0.867498	−	0.497440i	$-0.165727\pi$
$23$	0.325758	+	0.564230i	0.00295327	+	0.00511522i	−0.864545	+	0.502555i	$0.832393\pi$
$24$		0			0
$25$	−154.593	+	267.763i	−1.23674	+	2.14210i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−163.208			−1.04507			−0.522535	−	0.852618i	$-0.675014\pi$
$29$	−163.208			−1.04507			−0.522535	+	0.852618i	$0.675014\pi$
$30$		0			0
$31$	−111.663	+	193.406i	−0.646943	+	1.12054i	0.336906	+	0.941538i	$0.390620\pi$
$31$	−111.663	+	193.406i	−0.646943	+	1.12054i	−0.983849	+	0.179000i	$0.942714\pi$
$32$		0			0
$33$	−22.7443	−	39.3943i	−0.119978	−	0.207808i
$34$		0			0
$35$	−144.163	−	357.970i	−0.696228	−	1.72880i
$36$		0			0
$37$	−84.2670	−	145.955i	−0.374417	−	0.648509i	0.615823	−	0.787885i	$-0.288824\pi$
$37$	−84.2670	−	145.955i	−0.374417	−	0.648509i	−0.990240	+	0.139376i	$0.955490\pi$
$38$		0			0
$39$	3.24432	−	5.61932i	0.0133207	−	0.0230721i
$40$		0			0
$41$	−323.023			−1.23043			−0.615216	−	0.788359i	$-0.710931\pi$
$41$	−323.023			−1.23043			−0.615216	+	0.788359i	$0.710931\pi$
$42$		0			0
$43$	−221.557			−0.785746			−0.392873	−	0.919593i	$-0.628519\pi$
$43$	−221.557			−0.785746			−0.392873	+	0.919593i	$0.628519\pi$
$44$		0			0
$45$	−93.7670	+	162.409i	−0.310621	+	0.538012i
$46$		0			0
$47$	254.023	+	439.980i	0.788362	+	1.36548i	0.926970	+	0.375136i	$0.122404\pi$
$47$	254.023	+	439.980i	0.788362	+	1.36548i	−0.138608	+	0.990347i	$0.544263\pi$
$48$		0			0
$49$	329.500	+	95.2825i	0.960641	+	0.277791i
$50$		0			0
$51$	−179.023	−	310.076i	−0.491533	−	0.851361i
$52$		0			0
$53$	88.2557	−	152.863i	0.228733	−	0.396177i	−0.728700	−	0.684833i	$-0.759875\pi$
$53$	88.2557	−	152.863i	0.228733	−	0.396177i	0.957433	+	0.288656i	$0.0932084\pi$
$54$		0			0
$55$	−315.951			−0.774596
$56$		0			0
$57$	−100.534			−0.233615
$58$		0			0
$59$	227.464	−	393.979i	0.501920	−	0.869351i	−0.498077	−	0.867133i	$-0.665960\pi$
$59$	227.464	−	393.979i	0.501920	−	0.869351i	0.999998	−	0.00221868i	$-0.000706227\pi$
$60$		0			0
$61$	−19.3258	−	33.4732i	−0.0405641	−	0.0702591i	0.845031	−	0.534718i	$-0.179582\pi$
$61$	−19.3258	−	33.4732i	−0.0405641	−	0.0702591i	−0.885595	+	0.464459i	$0.846249\pi$
$62$		0			0
$63$	−62.2670	−	154.615i	−0.124522	−	0.309201i
$64$		0			0
$65$	−22.5341	−	39.0302i	−0.0430001	−	0.0744784i
$66$		0			0
$67$	70.8958	−	122.795i	0.129273	−	0.223908i	−0.794122	−	0.607758i	$-0.792069\pi$
$67$	70.8958	−	122.795i	0.129273	−	0.223908i	0.923395	+	0.383851i	$0.125402\pi$
$68$		0			0
$69$	1.95455			0.00341015
$70$		0			0
$71$	−602.742			−1.00750			−0.503749	−	0.863850i	$-0.668046\pi$
$71$	−602.742			−1.00750			−0.503749	+	0.863850i	$0.668046\pi$
$72$		0			0
$73$	551.150	−	954.619i	0.883660	−	1.53054i	0.0364183	−	0.999337i	$-0.488405\pi$
$73$	551.150	−	954.619i	0.883660	−	1.53054i	0.847242	−	0.531207i	$-0.178262\pi$
$74$		0			0
$75$	463.778	+	803.288i	0.714034	+	1.23674i
$76$		0			0
$77$	173.138	−	221.096i	0.256246	−	0.327223i
$78$		0			0
$79$	−58.1515	−	100.721i	−0.0828172	−	0.143444i	0.821642	−	0.570004i	$-0.193058\pi$
$79$	−58.1515	−	100.721i	−0.0828172	−	0.143444i	−0.904459	+	0.426561i	$0.859725\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	568.928			0.752385			0.376193	−	0.926542i	$-0.377233\pi$
$83$	568.928			0.752385			0.376193	+	0.926542i	$0.377233\pi$
$84$		0			0
$85$	−2486.88			−3.17341
$86$		0			0
$87$	−244.812	+	424.028i	−0.301686	+	0.522535i
$88$		0			0
$89$	191.580	+	331.825i	0.228173	+	0.395207i	0.957267	−	0.289207i	$-0.0933915\pi$
$89$	191.580	+	331.825i	0.228173	+	0.395207i	−0.729094	+	0.684414i	$0.760058\pi$
$90$		0			0
$91$	39.6610	+	5.61932i	0.0456879	+	0.00647325i
$92$		0			0
$93$	334.989	+	580.217i	0.373513	+	0.646943i
$94$		0			0
$95$	−349.140	+	604.728i	−0.377063	+	0.653093i
$96$		0			0
$97$	334.701			0.350348			0.175174	−	0.984538i	$-0.443951\pi$
$97$	334.701			0.350348			0.175174	+	0.984538i	$0.443951\pi$
$98$		0			0
$99$	−136.466			−0.138539
$100$		0			0
$101$	7.37121	−	12.7673i	0.00726201	−	0.0125782i	−0.862372	−	0.506276i	$-0.831022\pi$
$101$	7.37121	−	12.7673i	0.00726201	−	0.0125782i	0.869634	+	0.493698i	$0.164355\pi$
$102$		0			0
$103$	−420.710	−	728.691i	−0.402464	−	0.697088i	0.591559	−	0.806262i	$-0.298513\pi$
$103$	−420.710	−	728.691i	−0.402464	−	0.697088i	−0.994023	+	0.109174i	$0.965180\pi$
$104$		0			0
$105$	−1146.28	−	162.409i	−1.06538	−	0.150948i
$106$		0			0
$107$	−357.835	−	619.789i	−0.323301	−	0.559974i	0.657866	−	0.753135i	$-0.271459\pi$
$107$	−357.835	−	619.789i	−0.323301	−	0.559974i	−0.981167	+	0.193161i	$0.938126\pi$
$108$		0			0
$109$	−300.009	+	519.632i	−0.263630	+	0.456621i	−0.967204	−	0.254001i	$-0.918253\pi$
$109$	−300.009	+	519.632i	−0.263630	+	0.456621i	0.703574	+	0.710622i	$0.251587\pi$
$110$		0			0
$111$	−505.602			−0.432339
$112$		0			0
$113$	622.644			0.518349			0.259174	−	0.965831i	$-0.416550\pi$
$113$	622.644			0.518349			0.259174	+	0.965831i	$0.416550\pi$
$114$		0			0
$115$	6.78787	−	11.7569i	0.00550410	−	0.00953339i
$116$		0			0
$117$	−9.73296	−	16.8580i	−0.00769070	−	0.0133207i
$118$		0			0
$119$	1362.79	−	1740.26i	1.04980	−	1.34059i
$120$		0			0
$121$	550.544	+	953.569i	0.413632	+	0.716431i
$122$		0			0
$123$	−484.534	+	839.238i	−0.355195	+	0.615216i
$124$		0			0
$125$	3837.90			2.74618
$126$		0			0
$127$	180.076			0.125820			0.0629100	−	0.998019i	$-0.479962\pi$
$127$	180.076			0.125820			0.0629100	+	0.998019i	$0.479962\pi$
$128$		0			0
$129$	−332.335	+	575.621i	−0.226825	+	0.392873i
$130$		0			0
$131$	108.930	+	188.672i	0.0726508	+	0.125835i	0.900062	−	0.435761i	$-0.143521\pi$
$131$	108.930	+	188.672i	0.0726508	+	0.125835i	−0.827411	+	0.561596i	$0.810187\pi$
$132$		0			0
$133$	−231.850	−	575.707i	−0.151158	−	0.375339i
$134$		0			0
$135$	281.301	+	487.228i	0.179337	+	0.310621i
$136$		0			0
$137$	1300.93	−	2253.27i	0.811283	−	1.40518i	−0.100683	−	0.994919i	$-0.532103\pi$
$137$	1300.93	−	2253.27i	0.811283	−	1.40518i	0.911966	−	0.410265i	$-0.134564\pi$
$138$		0			0
$139$	2651.55			1.61800			0.808998	−	0.587811i	$-0.200010\pi$
$139$	2651.55			1.61800			0.808998	+	0.587811i	$0.200010\pi$
$140$		0			0
$141$	1524.14			0.910322
$142$		0			0
$143$	16.3977	−	28.4017i	0.00958914	−	0.0166089i
$144$		0			0
$145$	1700.40	+	2945.17i	0.973863	+	1.68678i
$146$		0			0
$147$	741.801	−	713.142i	0.416209	−	0.400129i
$148$		0			0
$149$	−290.511	−	503.180i	−0.159729	−	0.276659i	0.775042	−	0.631910i	$-0.217729\pi$
$149$	−290.511	−	503.180i	−0.159729	−	0.276659i	−0.934771	+	0.355251i	$0.884395\pi$
$150$		0			0
$151$	−307.695	+	532.943i	−0.165827	+	0.287221i	−0.936949	−	0.349467i	$-0.886363\pi$
$151$	−307.695	+	532.943i	−0.165827	+	0.287221i	0.771122	+	0.636688i	$0.219696\pi$
$152$		0			0
$153$	−1074.14			−0.567574
$154$		0			0
$155$	4653.47			2.41145
$156$		0			0
$157$	153.466	−	265.811i	0.0780122	−	0.135121i	−0.824380	−	0.566037i	$-0.808476\pi$
$157$	153.466	−	265.811i	0.0780122	−	0.135121i	0.902392	+	0.430916i	$0.141809\pi$
$158$		0			0
$159$	−264.767	−	458.590i	−0.132059	−	0.228733i
$160$		0			0
$161$	4.50756	+	11.1927i	0.00220649	+	0.00547893i
$162$		0			0
$163$	1757.25	+	3043.65i	0.844408	+	1.46256i	0.886135	+	0.463428i	$0.153381\pi$
$163$	1757.25	+	3043.65i	0.844408	+	1.46256i	−0.0417271	+	0.999129i	$0.513286\pi$
$164$		0			0
$165$	−473.926	+	820.864i	−0.223607	+	0.387298i
$166$		0			0
$167$	−1123.30			−0.520502			−0.260251	−	0.965541i	$-0.583805\pi$
$167$	−1123.30			−0.520502			−0.260251	+	0.965541i	$0.583805\pi$
$168$		0			0
$169$	−2192.32			−0.997871
$170$		0			0
$171$	−150.801	+	261.195i	−0.0674389	+	0.116808i
$172$		0			0
$173$	−765.299	−	1325.54i	−0.336327	−	0.582536i	0.647412	−	0.762141i	$-0.275852\pi$
$173$	−765.299	−	1325.54i	−0.336327	−	0.582536i	−0.983739	+	0.179605i	$0.942518\pi$
$174$		0			0
$175$	−3530.45	+	4508.35i	−1.52501	+	1.94742i
$176$		0			0
$177$	−682.392	−	1181.94i	−0.289784	−	0.501920i
$178$		0			0
$179$	1706.72	−	2956.12i	0.712659	−	1.23436i	−0.251197	−	0.967936i	$-0.580824\pi$
$179$	1706.72	−	2956.12i	0.712659	−	1.23436i	0.963856	−	0.266425i	$-0.0858426\pi$
$180$		0			0
$181$	1286.71			0.528399			0.264200	−	0.964468i	$-0.414892\pi$
$181$	1286.71			0.528399			0.264200	+	0.964468i	$0.414892\pi$
$182$		0			0
$183$	−115.955			−0.0468394
$184$		0			0
$185$	−1755.88	+	3041.28i	−0.697811	+	1.20864i
$186$		0			0
$187$	−904.833	−	1567.22i	−0.353839	−	0.612868i
$188$		0			0
$189$	−495.102	−	70.1481i	−0.190547	−	0.0269975i
$190$		0			0
$191$	527.648	+	913.913i	0.199891	+	0.346222i	0.948493	−	0.316798i	$-0.102608\pi$
$191$	527.648	+	913.913i	0.199891	+	0.346222i	−0.748602	+	0.663020i	$0.769274\pi$
$192$		0			0
$193$	2385.42	−	4131.67i	0.889670	−	1.54095i	0.0494044	−	0.998779i	$-0.484268\pi$
$193$	2385.42	−	4131.67i	0.889670	−	1.54095i	0.840266	−	0.542175i	$-0.182399\pi$
$194$		0			0
$195$	−135.205			−0.0496523
$196$		0			0
$197$	1622.31			0.586725			0.293363	−	0.956001i	$-0.405226\pi$
$197$	1622.31			0.586725			0.293363	+	0.956001i	$0.405226\pi$
$198$		0			0
$199$	−1775.07	+	3074.51i	−0.632318	+	1.09521i	0.354759	+	0.934958i	$0.384563\pi$
$199$	−1775.07	+	3074.51i	−0.632318	+	1.09521i	−0.987077	+	0.160249i	$0.948770\pi$
$200$		0			0
$201$	−212.688	−	368.386i	−0.0746359	−	0.129273i
$202$		0			0
$203$	−2992.77	−	424.028i	−1.03474	−	0.146605i
$204$		0			0
$205$	3365.43	+	5829.10i	1.14659	+	1.98596i
$206$		0			0
$207$	2.93183	−	5.07807i	0.000984425	−	0.00170507i
$208$		0			0
$209$	−508.129			−0.168172
$210$		0			0
$211$	−4653.39			−1.51826			−0.759129	−	0.650941i	$-0.774375\pi$
$211$	−4653.39			−1.51826			−0.759129	+	0.650941i	$0.774375\pi$
$212$		0			0
$213$	−904.114	+	1565.97i	−0.290840	+	0.503749i
$214$		0			0
$215$	2308.30	+	3998.10i	0.732209	+	1.26822i
$216$		0			0
$217$	−2550.06	+	3256.40i	−0.797739	+	1.01870i
$218$		0			0
$219$	−1653.45	−	2863.86i	−0.510181	−	0.883660i
$220$		0			0
$221$	129.068	−	223.553i	0.0392854	−	0.0680442i
$222$		0			0
$223$	4649.53			1.39621			0.698107	−	0.715993i	$-0.254026\pi$
$223$	4649.53			1.39621			0.698107	+	0.715993i	$0.254026\pi$
$224$		0			0
$225$	2782.67			0.824495
$226$		0			0
$227$	2075.86	−	3595.49i	0.606958	−	1.05128i	−0.384780	−	0.923008i	$-0.625723\pi$
$227$	2075.86	−	3595.49i	0.606958	−	1.05128i	0.991739	−	0.128274i	$-0.0409438\pi$
$228$		0			0
$229$	−2131.82	−	3692.41i	−0.615172	−	1.06551i	−0.990354	−	0.138558i	$-0.955753\pi$
$229$	−2131.82	−	3692.41i	−0.615172	−	1.06551i	0.375182	−	0.926951i	$-0.377580\pi$
$230$		0			0
$231$	−314.716	−	781.470i	−0.0896398	−	0.222584i
$232$		0			0
$233$	−1524.95	−	2641.29i	−0.428768	−	0.742647i	0.567996	−	0.823031i	$-0.307719\pi$
$233$	−1524.95	−	2641.29i	−0.428768	−	0.742647i	−0.996764	+	0.0803838i	$0.974385\pi$
$234$		0			0
$235$	5293.10	−	9167.92i	1.46929	−	2.54489i
$236$		0			0
$237$	−348.909			−0.0956290
$238$		0			0
$239$	−3987.20			−1.07912			−0.539562	−	0.841946i	$-0.681410\pi$
$239$	−3987.20			−1.07912			−0.539562	+	0.841946i	$0.681410\pi$
$240$		0			0
$241$	312.324	−	540.961i	0.0834795	−	0.144591i	−0.821263	−	0.570550i	$-0.806730\pi$
$241$	312.324	−	540.961i	0.0834795	−	0.144591i	0.904742	+	0.425959i	$0.140063\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−1713.50	−	6938.69i	−0.446822	−	1.80937i
$246$		0			0
$247$	−36.2405	−	62.7704i	−0.00933574	−	0.0161700i
$248$		0			0
$249$	853.392	−	1478.12i	0.217195	−	0.376193i
$250$		0			0
$251$	1328.78			0.334152			0.167076	−	0.985944i	$-0.446568\pi$
$251$	1328.78			0.334152			0.167076	+	0.985944i	$0.446568\pi$
$252$		0			0
$253$	9.87887			0.00245486
$254$		0			0
$255$	−3730.32	+	6461.10i	−0.916085	+	1.58671i
$256$		0			0
$257$	1613.09	+	2793.96i	0.391525	+	0.678141i	0.992651	−	0.121013i	$-0.0386144\pi$
$257$	1613.09	+	2793.96i	0.391525	+	0.678141i	−0.601126	+	0.799154i	$0.705281\pi$
$258$		0			0
$259$	−1166.01	−	2895.32i	−0.279740	−	0.694620i
$260$		0			0
$261$	734.437	+	1272.08i	0.174178	+	0.301686i
$262$		0			0
$263$	1625.31	−	2815.11i	0.381067	−	0.660028i	−0.610148	−	0.792288i	$-0.708890\pi$
$263$	1625.31	−	2815.11i	0.381067	−	0.660028i	0.991215	+	0.132260i	$0.0422233\pi$
$264$		0			0
$265$	−3677.99			−0.852593
$266$		0			0
$267$	1149.48			0.263471
$268$		0			0
$269$	−1413.02	+	2447.42i	−0.320273	+	0.554729i	−0.980544	−	0.196298i	$-0.937108\pi$
$269$	−1413.02	+	2447.42i	−0.320273	+	0.554729i	0.660271	+	0.751027i	$0.270441\pi$
$270$		0			0
$271$	−1198.38	−	2075.66i	−0.268622	−	0.465268i	0.699884	−	0.714257i	$-0.253235\pi$
$271$	−1198.38	−	2075.66i	−0.268622	−	0.465268i	−0.968506	+	0.248989i	$0.919902\pi$
$272$		0			0
$273$	74.0909	−	94.6133i	0.0164256	−	0.0209753i
$274$		0			0
$275$	2344.07	+	4060.05i	0.514010	+	0.890292i
$276$		0			0
$277$	−910.233	+	1576.57i	−0.197439	+	0.341974i	−0.947697	−	0.319170i	$-0.896596\pi$
$277$	−910.233	+	1576.57i	−0.197439	+	0.341974i	0.750258	+	0.661145i	$0.229929\pi$
$278$		0			0
$279$	2009.93			0.431296
$280$		0			0
$281$	3083.81			0.654679			0.327339	−	0.944907i	$-0.393848\pi$
$281$	3083.81			0.654679			0.327339	+	0.944907i	$0.393848\pi$
$282$		0			0
$283$	1277.38	−	2212.49i	0.268313	−	0.464732i	−0.700113	−	0.714032i	$-0.746867\pi$
$283$	1277.38	−	2212.49i	0.268313	−	0.464732i	0.968426	+	0.249300i	$0.0802005\pi$
$284$		0			0
$285$	1047.42	+	1814.19i	0.217698	+	0.377063i
$286$		0			0
$287$	−5923.31	−	839.238i	−1.21826	−	0.172608i
$288$		0			0
$289$	−4665.53	−	8080.94i	−0.949630	−	1.64481i
$290$		0			0
$291$	502.051	−	869.578i	0.101137	−	0.175174i
$292$		0			0
$293$	−1846.47			−0.368163			−0.184081	−	0.982911i	$-0.558931\pi$
$293$	−1846.47			−0.368163			−0.184081	+	0.982911i	$0.558931\pi$
$294$		0			0
$295$	−9479.39			−1.87089
$296$		0			0
$297$	−204.699	+	354.549i	−0.0399927	+	0.0692694i
$298$		0			0
$299$	0.704576	+	1.22036i	0.000136277	+	0.000236038i
$300$		0			0
$301$	−4062.71	−	575.621i	−0.777977	−	0.110227i
$302$		0			0
$303$	−22.1136	−	38.3019i	−0.00419272	−	0.00726201i
$304$		0			0
$305$	−402.693	+	697.485i	−0.0756005	+	0.130944i
$306$		0			0
$307$	−7041.50			−1.30905			−0.654527	−	0.756039i	$-0.727132\pi$
$307$	−7041.50			−1.30905			−0.654527	+	0.756039i	$0.727132\pi$
$308$		0			0
$309$	−2524.26			−0.464726
$310$		0			0
$311$	−1343.00	+	2326.14i	−0.244869	+	0.424126i	−0.962095	−	0.272715i	$-0.912078\pi$
$311$	−1343.00	+	2326.14i	−0.244869	+	0.424126i	0.717226	+	0.696841i	$0.245412\pi$
$312$		0			0
$313$	−1109.59	−	1921.87i	−0.200377	−	0.347063i	0.748273	−	0.663391i	$-0.230883\pi$
$313$	−1109.59	−	1921.87i	−0.200377	−	0.347063i	−0.948650	+	0.316328i	$0.897550\pi$
$314$		0			0
$315$	−2141.37	+	2734.50i	−0.383024	+	0.489117i
$316$		0			0
$317$	−1110.63	−	1923.67i	−0.196780	−	0.340833i	0.750703	−	0.660640i	$-0.229715\pi$
$317$	−1110.63	−	1923.67i	−0.196780	−	0.340833i	−0.947483	+	0.319807i	$0.896382\pi$
$318$		0			0
$319$	−1237.35	+	2143.16i	−0.217174	+	0.376157i
$320$		0			0
$321$	−2147.01			−0.373316
$322$		0			0
$323$	−3999.53			−0.688978
$324$		0			0
$325$	−334.366	+	579.138i	−0.0570685	+	0.0988455i
$326$		0			0
$327$	900.028	+	1558.89i	0.152207	+	0.263630i
$328$		0			0
$329$	3514.94	+	8727.94i	0.589012	+	1.46257i
$330$		0			0
$331$	2077.03	+	3597.52i	0.344906	+	0.597394i	0.985337	−	0.170622i	$-0.0545775\pi$
$331$	2077.03	+	3597.52i	0.344906	+	0.597394i	−0.640431	+	0.768016i	$0.721244\pi$
$332$		0			0
$333$	−758.403	+	1313.59i	−0.124806	+	0.216170i
$334$		0			0
$335$	−2954.53			−0.481860
$336$		0			0
$337$	−254.167			−0.0410841			−0.0205420	−	0.999789i	$-0.506539\pi$
$337$	−254.167			−0.0410841			−0.0205420	+	0.999789i	$0.506539\pi$
$338$		0			0
$339$	933.966	−	1617.68i	0.149634	−	0.259174i
$340$		0			0
$341$	1693.13	+	2932.59i	0.268880	+	0.465714i
$342$		0			0
$343$	5794.53	+	2603.27i	0.912173	+	0.409806i
$344$		0			0
$345$	−20.3636	−	35.2708i	−0.00317780	−	0.00550410i
$346$		0			0
$347$	−3112.32	+	5390.69i	−0.481493	+	0.833970i	−0.999774	−	0.0212401i	$-0.993239\pi$
$347$	−3112.32	+	5390.69i	−0.481493	+	0.833970i	0.518282	+	0.855210i	$0.326572\pi$
$348$		0			0
$349$	9732.21			1.49270			0.746352	−	0.665552i	$-0.231804\pi$
$349$	9732.21			1.49270			0.746352	+	0.665552i	$0.231804\pi$
$350$		0			0
$351$	−58.3977			−0.00888046
$352$		0			0
$353$	−712.807	+	1234.62i	−0.107476	+	0.186153i	−0.914747	−	0.404027i	$-0.867610\pi$
$353$	−712.807	+	1234.62i	−0.107476	+	0.186153i	0.807271	+	0.590180i	$0.200943\pi$
$354$		0			0
$355$	6279.71	+	10876.8i	0.938852	+	1.62614i
$356$		0			0
$357$	−2477.16	−	6151.02i	−0.367241	−	0.911896i
$358$		0			0
$359$	−2883.25	−	4993.93i	−0.423877	−	0.734177i	0.572438	−	0.819948i	$-0.305998\pi$
$359$	−2883.25	−	4993.93i	−0.423877	−	0.734177i	−0.996315	+	0.0857714i	$0.972665\pi$
$360$		0			0
$361$	2867.99	−	4967.51i	0.418136	−	0.724233i
$362$		0			0
$363$	3303.26			0.477621
$364$		0			0
$365$	−22968.7			−3.29381
$366$		0			0
$367$	5772.67	−	9998.56i	0.821065	−	1.42213i	−0.0838244	−	0.996481i	$-0.526713\pi$
$367$	5772.67	−	9998.56i	0.821065	−	1.42213i	0.904890	−	0.425646i	$-0.139953\pi$
$368$		0			0
$369$	1453.60	+	2517.71i	0.205072	+	0.355195i
$370$		0			0
$371$	2015.51	−	2573.78i	0.282048	−	0.360172i
$372$		0			0
$373$	3239.79	+	5611.47i	0.449731	+	0.778957i	0.998368	−	0.0571033i	$-0.0181864\pi$
$373$	3239.79	+	5611.47i	0.449731	+	0.778957i	−0.548637	+	0.836061i	$0.684853\pi$
$374$		0			0
$375$	5756.85	−	9971.15i	0.792753	−	1.37309i
$376$		0			0
$377$	−353.000			−0.0482239
$378$		0			0
$379$	−611.996			−0.0829449			−0.0414725	−	0.999140i	$-0.513205\pi$
$379$	−611.996			−0.0829449			−0.0414725	+	0.999140i	$0.513205\pi$
$380$		0			0
$381$	270.114	−	467.851i	0.0363211	−	0.0629100i
$382$		0			0
$383$	2180.41	+	3776.57i	0.290897	+	0.503848i	0.974022	−	0.226453i	$-0.0727130\pi$
$383$	2180.41	+	3776.57i	0.290897	+	0.503848i	−0.683125	+	0.730301i	$0.739380\pi$
$384$		0			0
$385$	−5793.63	−	820.864i	−0.766937	−	0.108663i
$386$		0			0
$387$	997.006	+	1726.86i	0.130958	+	0.226825i
$388$		0			0
$389$	6573.46	−	11385.6i	0.856781	−	1.48399i	−0.0182021	−	0.999834i	$-0.505794\pi$
$389$	6573.46	−	11385.6i	0.856781	−	1.48399i	0.874983	−	0.484154i	$-0.160872\pi$
$390$		0			0
$391$	77.7575			0.0100572
$392$		0			0
$393$	653.580			0.0838899
$394$		0			0
$395$	−1211.71	+	2098.74i	−0.154349	+	0.267340i
$396$		0			0
$397$	4239.02	+	7342.20i	0.535895	+	0.928198i	0.999119	+	0.0419565i	$0.0133591\pi$
$397$	4239.02	+	7342.20i	0.535895	+	0.928198i	−0.463224	+	0.886241i	$0.653308\pi$
$398$		0			0
$399$	−1843.51	−	261.195i	−0.231305	−	0.0327722i
$400$		0			0
$401$	−1401.50	−	2427.47i	−0.174533	−	0.302299i	0.765467	−	0.643475i	$-0.222508\pi$
$401$	−1401.50	−	2427.47i	−0.174533	−	0.302299i	−0.939999	+	0.341176i	$0.889175\pi$
$402$		0			0
$403$	−241.513	+	418.313i	−0.0298527	+	0.0517064i
$404$		0			0
$405$	1687.81			0.207081
$406$		0			0
$407$	−2555.46			−0.311227
$408$		0			0
$409$	3192.69	−	5529.91i	0.385987	−	0.668548i	−0.605919	−	0.795526i	$-0.707194\pi$
$409$	3192.69	−	5529.91i	0.385987	−	0.668548i	0.991906	+	0.126978i	$0.0405278\pi$
$410$		0			0
$411$	−3902.78	−	6759.82i	−0.468395	−	0.811283i
$412$		0			0
$413$	5194.62	−	6633.48i	0.618912	−	0.790344i
$414$		0			0
$415$	−5927.41	−	10266.6i	−0.701121	−	1.21438i
$416$		0			0
$417$	3977.32	−	6888.93i	0.467075	−	0.808998i
$418$		0			0
$419$	−4831.66			−0.563346			−0.281673	−	0.959510i	$-0.590889\pi$
$419$	−4831.66			−0.563346			−0.281673	+	0.959510i	$0.590889\pi$
$420$		0			0
$421$	7475.37			0.865385			0.432693	−	0.901542i	$-0.357564\pi$
$421$	7475.37			0.865385			0.432693	+	0.901542i	$0.357564\pi$
$422$		0			0
$423$	2286.20	−	3959.82i	0.262787	−	0.455161i
$424$		0			0
$425$	18450.4	+	31957.1i	2.10583	+	3.64740i
$426$		0			0
$427$	−267.413	−	664.012i	−0.0303068	−	0.0752548i
$428$		0			0
$429$	−49.1932	−	85.2051i	−0.00553630	−	0.00958914i
$430$		0			0
$431$	3495.97	−	6055.19i	0.390707	−	0.676725i	−0.601836	−	0.798620i	$-0.705564\pi$
$431$	3495.97	−	6055.19i	0.390707	−	0.676725i	0.992543	+	0.121895i	$0.0388972\pi$
$432$		0			0
$433$	−7699.26			−0.854510			−0.427255	−	0.904131i	$-0.640519\pi$
$433$	−7699.26			−0.854510			−0.427255	+	0.904131i	$0.640519\pi$
$434$		0			0
$435$	10202.4			1.12452
$436$		0			0
$437$	10.9166	−	18.9081i	0.00119499	−	0.00206979i
$438$		0			0
$439$	4706.16	+	8151.31i	0.511646	+	0.886198i	0.999909	+	0.0135008i	$0.00429758\pi$
$439$	4706.16	+	8151.31i	0.511646	+	0.886198i	−0.488262	+	0.872697i	$0.662369\pi$
$440$		0			0
$441$	−740.097	−	2996.97i	−0.0799154	−	0.323612i
$442$		0			0
$443$	−3129.09	−	5419.74i	−0.335593	−	0.581263i	0.648006	−	0.761635i	$-0.275603\pi$
$443$	−3129.09	−	5419.74i	−0.335593	−	0.581263i	−0.983598	+	0.180372i	$0.942270\pi$
$444$		0			0
$445$	3991.97	−	6914.29i	0.425252	−	0.736559i
$446$		0			0
$447$	−1743.07			−0.184439
$448$		0			0
$449$	−11633.8			−1.22279			−0.611396	−	0.791325i	$-0.709392\pi$
$449$	−11633.8			−1.22279			−0.611396	+	0.791325i	$0.709392\pi$
$450$		0			0
$451$	−2448.98	+	4241.75i	−0.255694	+	0.442874i
$452$		0			0
$453$	923.085	+	1598.83i	0.0957402	+	0.165827i
$454$		0			0
$455$	−311.807	−	774.246i	−0.0321269	−	0.0797741i
$456$		0			0
$457$	6552.31	+	11348.9i	0.670688	+	1.16167i	0.977709	+	0.209963i	$0.0673343\pi$
$457$	6552.31	+	11348.9i	0.670688	+	1.16167i	−0.307022	+	0.951703i	$0.599332\pi$
$458$		0			0
$459$	−1611.20	+	2790.69i	−0.163844	+	0.283787i
$460$		0			0
$461$	−2594.63			−0.262134			−0.131067	−	0.991373i	$-0.541840\pi$
$461$	−2594.63			−0.262134			−0.131067	+	0.991373i	$0.541840\pi$
$462$		0			0
$463$	14136.2			1.41893			0.709465	−	0.704741i	$-0.248937\pi$
$463$	14136.2			1.41893			0.709465	+	0.704741i	$0.248937\pi$
$464$		0			0
$465$	6980.20	−	12090.1i	0.696127	−	1.20573i
$466$		0			0
$467$	7795.12	+	13501.5i	0.772409	+	1.33785i	0.936239	+	0.351363i	$0.114282\pi$
$467$	7795.12	+	13501.5i	0.772409	+	1.33785i	−0.163830	+	0.986489i	$0.552385\pi$
$468$		0			0
$469$	1619.06	−	2067.52i	0.159405	−	0.203559i
$470$		0			0
$471$	−460.398	−	797.432i	−0.0450404	−	0.0780122i
$472$		0			0
$473$	−1679.72	+	2909.36i	−0.163285	+	0.282817i
$474$		0			0
$475$	10361.2			1.00085
$476$		0			0
$477$	−1588.60			−0.152489
$478$		0			0
$479$	−4226.75	+	7320.95i	−0.403184	+	0.698336i	−0.994108	−	0.108391i	$-0.965430\pi$
$479$	−4226.75	+	7320.95i	−0.403184	+	0.698336i	0.590924	+	0.806727i	$0.298763\pi$
$480$		0			0
$481$	−182.259	−	315.683i	−0.0172772	−	0.0299249i
$482$		0			0
$483$	35.8408	+	5.07807i	0.00337643	+	0.000478386i
$484$		0			0
$485$	−3487.10	−	6039.83i	−0.326476	−	0.565474i
$486$		0			0
$487$	−2005.53	+	3473.69i	−0.186611	+	0.323219i	−0.944118	−	0.329607i	$-0.893084\pi$
$487$	−2005.53	+	3473.69i	−0.186611	+	0.323219i	0.757507	+	0.652827i	$0.226417\pi$
$488$		0			0
$489$	10543.5			0.975038
$490$		0			0
$491$	−13927.9			−1.28016			−0.640079	−	0.768309i	$-0.721098\pi$
$491$	−13927.9			−1.28016			−0.640079	+	0.768309i	$0.721098\pi$
$492$		0			0
$493$	−9739.33	+	16869.0i	−0.889731	+	1.54106i
$494$		0			0
$495$	1421.78	+	2462.59i	0.129099	+	0.223607i
$496$		0			0
$497$	−11052.6	−	1565.97i	−0.997535	−	0.141335i
$498$		0			0
$499$	−1973.77	−	3418.68i	−0.177071	−	0.306695i	0.763805	−	0.645447i	$-0.223329\pi$
$499$	−1973.77	−	3418.68i	−0.177071	−	0.306695i	−0.940876	+	0.338751i	$0.889995\pi$
$500$		0			0
$501$	−1684.95	+	2918.43i	−0.150256	+	0.260251i
$502$		0			0
$503$	13725.3			1.21666			0.608331	−	0.793684i	$-0.291839\pi$
$503$	13725.3			1.21666			0.608331	+	0.793684i	$0.291839\pi$
$504$		0			0
$505$	−307.190			−0.0270688
$506$		0			0
$507$	−3288.48	+	5695.82i	−0.288060	+	0.498935i
$508$		0			0
$509$	−3915.05	−	6781.07i	−0.340926	−	0.590502i	0.643679	−	0.765296i	$-0.277407\pi$
$509$	−3915.05	−	6781.07i	−0.340926	−	0.590502i	−0.984605	+	0.174794i	$0.944074\pi$
$510$		0			0
$511$	12586.7	−	16073.0i	1.08963	−	1.39145i
$512$		0			0
$513$	452.403	+	783.586i	0.0389359	+	0.0674389i
$514$		0			0
$515$	−8766.39	+	15183.8i	−0.750084	+	1.29918i
$516$		0			0
$517$	7703.43			0.655312
$518$		0			0
$519$	−4591.80			−0.388357
$520$		0			0
$521$	2953.69	−	5115.95i	0.248376	−	0.430199i	−0.714700	−	0.699431i	$-0.753437\pi$
$521$	2953.69	−	5115.95i	0.248376	−	0.430199i	0.963075	+	0.269232i	$0.0867700\pi$
$522$		0			0
$523$	3954.03	+	6848.58i	0.330588	+	0.572595i	0.982627	−	0.185590i	$-0.0594196\pi$
$523$	3954.03	+	6848.58i	0.330588	+	0.572595i	−0.652039	+	0.758185i	$0.726086\pi$
$524$		0			0
$525$	6417.36	+	15934.9i	0.533479	+	1.32468i
$526$		0			0
$527$	13326.8	+	23082.7i	1.10156	+	1.90797i
$528$		0			0
$529$	6083.29	−	10536.6i	0.499983	−	0.865995i
$530$		0			0
$531$	−4094.35			−0.334613
$532$		0			0
$533$	−698.659			−0.0567773
$534$		0			0
$535$	−7456.26	+	12914.6i	−0.602546	+	1.04364i
$536$		0			0
$537$	−5120.15	−	8868.36i	−0.411454	−	0.712659i
$538$		0			0
$539$	3749.28	−	3604.43i	0.299616	−	0.288040i
$540$		0			0
$541$	1970.52	+	3413.04i	0.156598	+	0.271235i	0.933640	−	0.358214i	$-0.116614\pi$
$541$	1970.52	+	3413.04i	0.156598	+	0.271235i	−0.777042	+	0.629449i	$0.783281\pi$
$542$		0			0
$543$	1930.06	−	3342.97i	0.152536	−	0.264200i
$544$		0			0
$545$	12502.7			0.982670
$546$		0			0
$547$	1828.71			0.142943			0.0714717	−	0.997443i	$-0.477230\pi$
$547$	1828.71			0.142943			0.0714717	+	0.997443i	$0.477230\pi$
$548$		0			0
$549$	−173.932	+	301.259i	−0.0135214	+	0.0234197i
$550$		0			0
$551$	2734.67	+	4736.58i	0.211435	+	0.366216i
$552$		0			0
$553$	−804.650	−	1998.02i	−0.0618756	−	0.153643i
$554$		0			0
$555$	5267.65	+	9123.83i	0.402881	+	0.697811i
$556$		0			0
$557$	−11266.0	+	19513.3i	−0.857011	+	1.48439i	0.0177556	+	0.999842i	$0.494348\pi$
$557$	−11266.0	+	19513.3i	−0.857011	+	1.48439i	−0.874767	+	0.484544i	$0.838985\pi$
$558$		0			0
$559$	−479.201			−0.0362577
$560$		0			0
$561$	−5429.00			−0.408579
$562$		0			0
$563$	11677.9	−	20226.6i	0.874179	−	1.51412i	0.0165446	−	0.999863i	$-0.494733\pi$
$563$	11677.9	−	20226.6i	0.874179	−	1.51412i	0.857635	−	0.514260i	$-0.171933\pi$
$564$		0			0
$565$	−6487.05	−	11235.9i	−0.483031	−	0.836634i
$566$		0			0
$567$	−924.903	+	1181.09i	−0.0685049	+	0.0874800i
$568$		0			0
$569$	10443.8	+	18089.2i	0.769468	+	1.33276i	0.937852	+	0.347036i	$0.112812\pi$
$569$	10443.8	+	18089.2i	0.769468	+	1.33276i	−0.168384	+	0.985721i	$0.553855\pi$
$570$		0			0
$571$	11872.6	−	20564.0i	0.870147	−	1.50714i	0.00830301	−	0.999966i	$-0.497357\pi$
$571$	11872.6	−	20564.0i	0.870147	−	1.50714i	0.861844	−	0.507173i	$-0.169310\pi$
$572$		0			0
$573$	3165.89			0.230815
$574$		0			0
$575$	−201.440			−0.0146098
$576$		0			0
$577$	−1227.20	+	2125.57i	−0.0885422	+	0.153360i	−0.906895	−	0.421356i	$-0.861554\pi$
$577$	−1227.20	+	2125.57i	−0.0885422	+	0.153360i	0.818353	+	0.574716i	$0.194887\pi$
$578$		0			0
$579$	−7156.26	−	12395.0i	−0.513651	−	0.889670i
$580$		0			0
$581$	10432.5	+	1478.12i	0.744945	+	0.105547i
$582$		0			0
$583$	−1338.21	−	2317.85i	−0.0950652	−	0.164658i
$584$		0			0
$585$	−202.807	+	351.272i	−0.0143334	+	0.0248261i
$586$		0			0
$587$	−18567.5			−1.30556			−0.652780	−	0.757547i	$-0.726397\pi$
$587$	−18567.5			−1.30556			−0.652780	+	0.757547i	$0.726397\pi$
$588$		0			0
$589$	7483.95			0.523550
$590$		0			0
$591$	2433.47	−	4214.89i	0.169373	−	0.293363i
$592$		0			0
$593$	−8556.47	−	14820.2i	−0.592533	−	1.02630i	−0.993890	−	0.110375i	$-0.964795\pi$
$593$	−8556.47	−	14820.2i	−0.592533	−	1.02630i	0.401357	−	0.915922i	$-0.368539\pi$
$594$		0			0
$595$	−45602.2	−	6461.10i	−3.14203	−	0.445175i
$596$		0			0
$597$	5325.20	+	9223.52i	0.365069	+	0.632318i
$598$		0			0
$599$	11632.4	−	20147.9i	0.793469	−	1.37433i	−0.130338	−	0.991470i	$-0.541606\pi$
$599$	11632.4	−	20147.9i	0.793469	−	1.37433i	0.923807	−	0.382859i	$-0.125060\pi$
$600$		0			0
$601$	25322.3			1.71867			0.859334	−	0.511416i	$-0.170879\pi$
$601$	25322.3			1.71867			0.859334	+	0.511416i	$0.170879\pi$
$602$		0			0
$603$	−1276.13			−0.0861821
$604$		0			0
$605$	11471.7	−	19869.6i	0.770897	−	1.33523i
$606$		0			0
$607$	−10867.2	−	18822.5i	−0.726665	−	1.25862i	−0.958285	−	0.285814i	$-0.907736\pi$
$607$	−10867.2	−	18822.5i	−0.726665	−	1.25862i	0.231620	−	0.972806i	$-0.425597\pi$
$608$		0			0
$609$	−5590.81	+	7139.41i	−0.372005	+	0.475046i
$610$		0			0
$611$	549.420	+	951.624i	0.0363784	+	0.0630092i
$612$		0			0
$613$	6786.19	−	11754.0i	0.447131	−	0.774454i	−0.551067	−	0.834461i	$-0.685779\pi$
$613$	6786.19	−	11754.0i	0.447131	−	0.774454i	0.998198	+	0.0600072i	$0.0191124\pi$
$614$		0			0
$615$	20192.6			1.32397
$616$		0			0
$617$	−8497.12			−0.554427			−0.277213	−	0.960808i	$-0.589411\pi$
$617$	−8497.12			−0.554427			−0.277213	+	0.960808i	$0.589411\pi$
$618$		0			0
$619$	−11491.5	+	19903.8i	−0.746173	+	1.29241i	0.203472	+	0.979081i	$0.434777\pi$
$619$	−11491.5	+	19903.8i	−0.746173	+	1.29241i	−0.949645	+	0.313329i	$0.898556\pi$
$620$		0			0
$621$	−8.79548	−	15.2342i	−0.000568358	−	0.000984425i
$622$		0			0
$623$	2650.91	+	6582.46i	0.170476	+	0.423308i
$624$		0			0
$625$	−20661.3	−	35786.4i	−1.32232	−	2.29033i
$626$		0			0
$627$	−762.193	+	1320.16i	−0.0485471	+	0.0840861i
$628$		0			0
$629$	−20114.3			−1.27505
$630$		0			0
$631$	15717.9			0.991635			0.495817	−	0.868427i	$-0.334869\pi$
$631$	15717.9			0.991635			0.495817	+	0.868427i	$0.334869\pi$
$632$		0			0
$633$	−6980.08	+	12089.9i	−0.438283	+	0.759129i
$634$		0			0
$635$	−1876.13	−	3249.55i	−0.117247	−	0.203078i
$636$		0			0
$637$	712.669	+	206.084i	0.0443280	+	0.0128185i
$638$		0			0
$639$	2712.34	+	4697.91i	0.167916	+	0.290840i
$640$		0			0
$641$	−14553.7	+	25207.7i	−0.896780	+	1.55327i	−0.0651930	+	0.997873i	$0.520766\pi$
$641$	−14553.7	+	25207.7i	−0.896780	+	1.55327i	−0.831587	+	0.555395i	$0.812567\pi$
$642$		0			0
$643$	3112.26			0.190880			0.0954398	−	0.995435i	$-0.469574\pi$
$643$	3112.26			0.190880			0.0954398	+	0.995435i	$0.469574\pi$
$644$		0			0
$645$	13849.8			0.845482
$646$		0			0
$647$	−3928.80	+	6804.87i	−0.238728	+	0.413489i	−0.960349	−	0.278799i	$-0.910064\pi$
$647$	−3928.80	+	6804.87i	−0.238728	+	0.413489i	0.721622	+	0.692288i	$0.243397\pi$
$648$		0			0
$649$	−3449.01	−	5973.86i	−0.208606	−	0.361317i
$650$		0			0
$651$	4635.28	+	11509.8i	0.279064	+	0.692944i
$652$		0			0
$653$	9761.01	+	16906.6i	0.584958	+	1.01318i	0.994881	+	0.101057i	$0.0322224\pi$
$653$	9761.01	+	16906.6i	0.584958	+	1.01318i	−0.409923	+	0.912120i	$0.634444\pi$
$654$		0			0
$655$	2269.79	−	3931.38i	0.135401	−	0.234522i
$656$		0			0
$657$	−9920.69			−0.589107
$658$		0			0
$659$	−664.061			−0.0392536			−0.0196268	−	0.999807i	$-0.506248\pi$
$659$	−664.061			−0.0392536			−0.0196268	+	0.999807i	$0.506248\pi$
$660$		0			0
$661$	−7960.82	+	13788.5i	−0.468442	+	0.811365i	−0.999349	−	0.0360650i	$-0.988518\pi$
$661$	−7960.82	+	13788.5i	−0.468442	+	0.811365i	0.530908	+	0.847430i	$0.321851\pi$
$662$		0			0
$663$	−387.205	−	670.658i	−0.0226814	−	0.0392854i
$664$		0			0
$665$	−7973.36	+	10181.9i	−0.464953	+	0.593739i
$666$		0			0
$667$	−53.1665	−	92.0870i	−0.00308638	−	0.00534576i
$668$		0			0
$669$	6974.30	−	12079.8i	0.403052	−	0.698107i
$670$		0			0
$671$	−586.068			−0.0337182
$672$		0			0
$673$	24631.0			1.41078			0.705391	−	0.708819i	$-0.250771\pi$
$673$	24631.0			1.41078			0.705391	+	0.708819i	$0.250771\pi$
$674$		0			0
$675$	4174.01	−	7229.59i	0.238011	−	0.412247i
$676$		0			0
$677$	−8546.39	−	14802.8i	−0.485177	−	0.840350i	0.514678	−	0.857383i	$-0.327911\pi$
$677$	−8546.39	−	14802.8i	−0.485177	−	0.840350i	−0.999855	+	0.0170329i	$0.994578\pi$
$678$		0			0
$679$	6137.45	+	869.578i	0.346883	+	0.0491478i
$680$		0			0
$681$	−6227.57	−	10786.5i	−0.350428	−	0.606958i
$682$		0			0
$683$	−9581.79	+	16596.1i	−0.536804	+	0.929771i	0.462270	+	0.886739i	$0.347035\pi$
$683$	−9581.79	+	16596.1i	−0.536804	+	0.929771i	−0.999074	+	0.0430322i	$0.986298\pi$
$684$		0			0
$685$	−54215.2			−3.02402
$686$		0			0
$687$	−12790.9			−0.710339
$688$		0			0
$689$	190.886	−	330.625i	0.0105547	−	0.0182813i
$690$		0			0
$691$	4047.94	+	7011.23i	0.222852	+	0.385991i	0.955673	−	0.294431i	$-0.0951300\pi$
$691$	4047.94	+	7011.23i	0.222852	+	0.385991i	−0.732821	+	0.680422i	$0.761797\pi$
$692$		0			0
$693$	−2502.39	−	354.549i	−0.137169	−	0.0194346i
$694$		0			0
$695$	−27625.3	−	47848.5i	−1.50775	−	2.61150i
$696$		0			0
$697$	−19276.1	+	33387.2i	−1.04754	+	1.81439i
$698$		0			0
$699$	−9149.70			−0.495098
$700$		0			0
$701$	12354.7			0.665664			0.332832	−	0.942986i	$-0.391996\pi$
$701$	12354.7			0.665664			0.332832	+	0.942986i	$0.391996\pi$
$702$		0			0
$703$	−2823.90	+	4891.14i	−0.151501	+	0.262408i
$704$		0			0
$705$	−15879.3	−	27503.8i	−0.848297	−	1.46929i
$706$		0			0
$707$	168.337	−	214.965i	0.00895470	−	0.0114350i
$708$		0			0
$709$	−1914.41	−	3315.85i	−0.101406	−	0.175641i	0.810858	−	0.585243i	$-0.199001\pi$
$709$	−1914.41	−	3315.85i	−0.101406	−	0.175641i	−0.912264	+	0.409602i	$0.865668\pi$
$710$		0			0
$711$	−523.364	+	906.492i	−0.0276057	+	0.0478145i
$712$		0			0
$713$	−145.500			−0.00764241
$714$		0			0
$715$	−683.363			−0.0357431
$716$		0			0
$717$	−5980.81	+	10359.1i	−0.311516	+	0.539562i
$718$		0			0
$719$	611.500	+	1059.15i	0.0317178	+	0.0549368i	0.881449	−	0.472280i	$-0.156569\pi$
$719$	611.500	+	1059.15i	0.0317178	+	0.0549368i	−0.849731	+	0.527217i	$0.823236\pi$
$720$		0			0
$721$	−5821.42	−	14455.1i	−0.300695	−	0.746654i
$722$		0			0
$723$	−936.972	−	1622.88i	−0.0481969	−	0.0834795i
$724$		0			0
$725$	25230.8	−	43701.1i	1.29248	−	2.23864i
$726$		0			0
$727$	−6368.21			−0.324875			−0.162437	−	0.986719i	$-0.551936\pi$
$727$	−6368.21			−0.324875			−0.162437	+	0.986719i	$0.551936\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−13221.2	+	22899.9i	−0.668954	+	1.15866i
$732$		0			0
$733$	12577.0	+	21784.0i	0.633753	+	1.09769i	0.986778	+	0.162079i	$0.0518199\pi$
$733$	12577.0	+	21784.0i	0.633753	+	1.09769i	−0.353024	+	0.935614i	$0.614847\pi$
$734$		0			0
$735$	−20597.5	−	5956.24i	−1.03367	−	0.298910i
$736$		0			0
$737$	−1074.98	−	1861.93i	−0.0537281	−	0.0930597i
$738$		0			0
$739$	−5369.55	+	9300.34i	−0.267283	+	0.462948i	−0.968159	−	0.250335i	$-0.919459\pi$
$739$	−5369.55	+	9300.34i	−0.267283	+	0.462948i	0.700876	+	0.713283i	$0.252793\pi$
$740$		0			0
$741$	−217.443			−0.0107800
$742$		0			0
$743$	−28166.3			−1.39074			−0.695370	−	0.718652i	$-0.744760\pi$
$743$	−28166.3			−1.39074			−0.695370	+	0.718652i	$0.744760\pi$
$744$		0			0
$745$	−6053.42	+	10484.8i	−0.297691	+	0.515617i
$746$		0			0
$747$	−2560.18	−	4434.36i	−0.125398	−	0.217195i
$748$		0			0
$749$	−4951.41	−	12294.8i	−0.241549	−	0.599791i
$750$		0			0
$751$	14328.5	+	24817.7i	0.696211	+	1.20587i	0.969771	+	0.244018i	$0.0784657\pi$
$751$	14328.5	+	24817.7i	0.696211	+	1.20587i	−0.273559	+	0.961855i	$0.588201\pi$
$752$		0			0
$753$	1993.18	−	3452.28i	0.0964613	−	0.167076i
$754$		0			0
$755$	12823.0			0.618113
$756$		0			0
$757$	−23604.1			−1.13330			−0.566648	−	0.823960i	$-0.691760\pi$
$757$	−23604.1			−1.13330			−0.566648	+	0.823960i	$0.691760\pi$
$758$		0			0
$759$	14.8183	−	25.6661i	0.000708657	−	0.00122743i
$760$		0			0
$761$	−2315.48	−	4010.54i	−0.110297	−	0.191041i	0.805593	−	0.592470i	$-0.201847\pi$
$761$	−2315.48	−	4010.54i	−0.110297	−	0.191041i	−0.915890	+	0.401429i	$0.868514\pi$
$762$		0			0
$763$	−6851.35	+	8749.10i	−0.325079	+	0.415123i
$764$		0			0
$765$	11191.0	+	19383.3i	0.528902	+	0.916085i
$766$		0			0
$767$	491.977	−	852.129i	0.0231607	−	0.0401155i
$768$		0			0
$769$	33276.8			1.56046			0.780228	−	0.625495i	$-0.215103\pi$
$769$	33276.8			1.56046			0.780228	+	0.625495i	$0.215103\pi$
$770$		0			0
$771$	9678.55			0.452094
$772$		0			0
$773$	11469.4	−	19865.6i	0.533668	−	0.924340i	−0.465558	−	0.885017i	$-0.654147\pi$
$773$	11469.4	−	19865.6i	0.533668	−	0.924340i	0.999227	−	0.0393231i	$-0.0125202\pi$
$774$		0			0
$775$	−34524.6	−	59798.3i	−1.60020	−	2.77164i
$776$		0			0
$777$	−9271.29	−	1313.59i	−0.428064	−	0.0606498i
$778$		0			0
$779$	5412.47	+	9374.67i	0.248937	+	0.431171i
$780$		0			0
$781$	−4569.66	+	7914.88i	−0.209366	+	0.362633i
$782$		0			0
$783$	4406.62			0.201124
$784$		0			0
$785$	−6395.58			−0.290787
$786$		0			0
$787$	−6757.23	+	11703.9i	−0.306060	+	0.530112i	−0.977497	−	0.210950i	$-0.932344\pi$
$787$	−6757.23	+	11703.9i	−0.306060	+	0.530112i	0.671437	+	0.741062i	$0.265678\pi$
$788$		0			0
$789$	−4875.92	−	8445.34i	−0.220009	−	0.381067i
$790$		0			0
$791$	11417.5	+	1617.68i	0.513223	+	0.0727155i
$792$		0			0
$793$	−41.7993	−	72.3985i	−0.00187180	−	0.00324205i
$794$		0			0
$795$	−5516.98	+	9555.69i	−0.246122	+	0.426296i
$796$		0			0
$797$	10473.4			0.465480			0.232740	−	0.972539i	$-0.425231\pi$
$797$	10473.4			0.465480			0.232740	+	0.972539i	$0.425231\pi$
$798$		0			0
$799$	60634.5			2.68472
$800$		0			0
$801$	1724.22	−	2986.43i	0.0760576	−	0.131736i
$802$		0			0
$803$	−8357.02	−	14474.8i	−0.367264	−	0.636119i
$804$		0			0
$805$	155.015	−	197.953i	0.00678705	−	0.00866698i
$806$		0			0
$807$	4239.06	+	7342.27i	0.184910	+	0.320273i
$808$		0			0
$809$	−11784.0	+	20410.5i	−0.512117	+	0.887013i	0.487784	+	0.872964i	$0.337805\pi$
$809$	−11784.0	+	20410.5i	−0.512117	+	0.887013i	−0.999901	+	0.0140486i	$0.995528\pi$
$810$		0			0
$811$	6704.22			0.290280			0.145140	−	0.989411i	$-0.453637\pi$
$811$	6704.22			0.290280			0.145140	+	0.989411i	$0.453637\pi$
$812$		0			0
$813$	−7190.31			−0.310178
$814$		0			0
$815$	36616.0	−	63420.8i	1.57375	−	2.72581i
$816$		0			0
$817$	3712.34	+	6429.95i	0.158970	+	0.275343i
$818$		0			0
$819$	−134.676	−	334.414i	−0.00574599	−	0.0142678i
$820$		0			0
$821$	−12269.7	−	21251.8i	−0.521579	−	0.903401i	−0.999685	−	0.0250988i	$-0.992010\pi$
$821$	−12269.7	−	21251.8i	−0.521579	−	0.903401i	0.478106	−	0.878302i	$-0.341323\pi$
$822$		0			0
$823$	−15558.5	+	26948.1i	−0.658973	+	1.14137i	0.321909	+	0.946771i	$0.395675\pi$
$823$	−15558.5	+	26948.1i	−0.658973	+	1.14137i	−0.980882	+	0.194604i	$0.937658\pi$
$824$		0			0
$825$	14064.4			0.593528
$826$		0			0
$827$	−31244.9			−1.31377			−0.656887	−	0.753989i	$-0.728127\pi$
$827$	−31244.9			−1.31377			−0.656887	+	0.753989i	$0.728127\pi$
$828$		0			0
$829$	−2115.75	+	3664.58i	−0.0886405	+	0.153530i	−0.906937	−	0.421267i	$-0.861586\pi$
$829$	−2115.75	+	3664.58i	−0.0886405	+	0.153530i	0.818296	+	0.574797i	$0.194919\pi$
$830$		0			0
$831$	2730.70	+	4729.71i	0.113991	+	0.197439i
$832$		0			0
$833$	29510.9	−	28370.8i	1.22748	−	1.18006i
$834$		0			0
$835$	11703.2	+	20270.5i	0.485037	+	0.840109i
$836$		0			0
$837$	3014.90	−	5221.96i	0.124504	−	0.215648i
$838$		0			0
$839$	38670.4			1.59124			0.795621	−	0.605795i	$-0.207145\pi$
$839$	38670.4			1.59124			0.795621	+	0.605795i	$0.207145\pi$
$840$		0			0
$841$	2247.96			0.0921710
$842$		0			0
$843$	4625.72	−	8011.97i	0.188989	−	0.327339i
$844$		0			0
$845$	22840.8	+	39561.5i	0.929880	+	1.61060i
$846$		0			0
$847$	7617.94	+	18916.1i	0.309038	+	0.767372i
$848$		0			0
$849$	−3832.15	−	6637.48i	−0.154911	−	0.268313i
$850$		0			0
$851$	54.9014	−	95.0920i	0.00221151	−	0.00383045i
$852$		0			0
$853$	−19944.4			−0.800565			−0.400282	−	0.916392i	$-0.631088\pi$
$853$	−19944.4			−0.800565			−0.400282	+	0.916392i	$0.631088\pi$
$854$		0			0
$855$	6284.52			0.251376
$856$		0			0
$857$	−6941.10	+	12022.3i	−0.276667	+	0.479201i	−0.970554	−	0.240882i	$-0.922563\pi$
$857$	−6941.10	+	12022.3i	−0.276667	+	0.479201i	0.693887	+	0.720084i	$0.255897\pi$
$858$		0			0
$859$	−2078.58	−	3600.21i	−0.0825614	−	0.143000i	0.821788	−	0.569793i	$-0.192977\pi$
$859$	−2078.58	−	3600.21i	−0.0825614	−	0.143000i	−0.904349	+	0.426793i	$0.859643\pi$
$860$		0			0
$861$	−11065.4	+	14130.3i	−0.437987	+	0.559304i
$862$		0			0
$863$	−8118.96	−	14062.5i	−0.320246	−	0.554683i	0.660292	−	0.751009i	$-0.270432\pi$
$863$	−8118.96	−	14062.5i	−0.320246	−	0.554683i	−0.980539	+	0.196326i	$0.937099\pi$
$864$		0			0
$865$	−15946.6	+	27620.4i	−0.626823	+	1.08569i
$866$		0			0
$867$	−27993.2			−1.09654
$868$		0			0
$869$	−1763.49			−0.0688403
$870$		0			0
$871$	153.339	−	265.591i	0.00596521	−	0.0103320i
$872$		0			0
$873$	−1506.15	−	2608.73i	−0.0583913	−	0.101137i
$874$		0			0
$875$	70376.0	+	9971.15i	2.71902	+	0.385242i
$876$		0			0
$877$	8244.70	+	14280.2i	0.317450	+	0.549840i	0.979955	−	0.199218i	$-0.0638401\pi$
$877$	8244.70	+	14280.2i	0.317450	+	0.549840i	−0.662505	+	0.749057i	$0.730507\pi$
$878$		0			0
$879$	−2769.70	+	4797.26i	−0.106279	+	0.184081i
$880$		0			0
$881$	45411.7			1.73662			0.868309	−	0.496023i	$-0.165207\pi$
$881$	45411.7			1.73662			0.868309	+	0.496023i	$0.165207\pi$
$882$		0			0
$883$	2206.85			0.0841070			0.0420535	−	0.999115i	$-0.486610\pi$
$883$	2206.85			0.0841070			0.0420535	+	0.999115i	$0.486610\pi$
$884$		0			0
$885$	−14219.1	+	24628.2i	−0.540078	+	0.935443i
$886$		0			0
$887$	14073.1	+	24375.3i	0.532727	+	0.922710i	0.999270	+	0.0382111i	$0.0121659\pi$
$887$	14073.1	+	24375.3i	0.532727	+	0.922710i	−0.466543	+	0.884498i	$0.654501\pi$
$888$		0			0
$889$	3302.07	+	467.851i	0.124576	+	0.0176504i
$890$		0			0
$891$	614.097	+	1063.65i	0.0230898	+	0.0399927i
$892$		0			0
$893$	8512.65	−	14744.3i	0.318998	−	0.552520i
$894$		0			0
$895$	−71126.1			−2.65641
$896$		0			0
$897$	4.22746			0.000157359
$898$		0			0
$899$	18224.3	−	31565.4i	0.676101	−	1.17104i
$900$		0			0
$901$	−10533.2	−	18244.0i	−0.389469	−	0.674579i
$902$		0			0
$903$	−7589.58	+	9691.81i	−0.279696	+	0.357169i
$904$		0			0
$905$	−13405.6	−	23219.3i	−0.492396	−	0.852856i
$906$		0			0
$907$	−2521.12	+	4366.71i	−0.0922960	+	0.159861i	−0.908477	−	0.417935i	$-0.862754\pi$
$907$	−2521.12	+	4366.71i	−0.0922960	+	0.159861i	0.816181	+	0.577797i	$0.196087\pi$
$908$		0			0
$909$	−132.682			−0.00484134
$910$		0			0
$911$	−29647.3			−1.07822			−0.539110	−	0.842235i	$-0.681239\pi$
$911$	−29647.3			−1.07822			−0.539110	+	0.842235i	$0.681239\pi$
$912$		0			0
$913$	4313.29	−	7470.84i	0.156352	−	0.270809i
$914$		0			0
$915$	1208.08	+	2092.46i	0.0436480	+	0.0756005i
$916$		0			0
$917$	1507.28	+	3742.71i	0.0542799	+	0.134782i
$918$		0			0
$919$	−5945.64	−	10298.1i	−0.213415	−	0.369646i	0.739366	−	0.673304i	$-0.235125\pi$
$919$	−5945.64	−	10298.1i	−0.213415	−	0.369646i	−0.952781	+	0.303658i	$0.901792\pi$
$920$		0			0
$921$	−10562.2	+	18294.3i	−0.377891	+	0.654527i
$922$		0			0
$923$	−1303.66			−0.0464902
$924$		0			0
$925$	52108.3			1.85223
$926$		0			0
$927$	−3786.39	+	6558.22i	−0.134155	+	0.232363i
$928$		0			0
$929$	19594.3	+	33938.3i	0.691999	+	1.19858i	0.971182	+	0.238340i	$0.0766032\pi$
$929$	19594.3	+	33938.3i	0.691999	+	1.19858i	−0.279183	+	0.960238i	$0.590063\pi$
$930$		0			0
$931$	−2755.74	−	11159.2i	−0.0970093	−	0.392832i
$932$		0			0
$933$	4028.99	+	6978.41i	0.141375	+	0.244869i
$934$		0			0
$935$	−18854.1	+	32656.3i	−0.659461	+	1.14222i
$936$		0			0
$937$	9716.23			0.338757			0.169379	−	0.985551i	$-0.445824\pi$
$937$	9716.23			0.338757			0.169379	+	0.985551i	$0.445824\pi$
$938$		0			0
$939$	−6657.57			−0.231375
$940$		0			0
$941$	3497.93	−	6058.60i	0.121179	−	0.209888i	−0.799054	−	0.601259i	$-0.794666\pi$
$941$	3497.93	−	6058.60i	0.121179	−	0.209888i	0.920233	+	0.391371i	$0.127999\pi$
$942$		0			0
$943$	−105.227	−	182.259i	−0.00363380	−	0.00629393i
$944$		0			0
$945$	3892.40	+	9665.20i	0.133989	+	0.332708i
$946$		0			0
$947$	7489.62	+	12972.4i	0.257001	+	0.445139i	0.965437	−	0.260636i	$-0.0839323\pi$
$947$	7489.62	+	12972.4i	0.257001	+	0.445139i	−0.708436	+	0.705775i	$0.750599\pi$
$948$		0			0
$949$	1192.07	−	2064.73i	0.0407758	−	0.0706258i
$950$		0			0
$951$	−6663.78			−0.227222
$952$		0			0
$953$	29393.3			0.999100			0.499550	−	0.866285i	$-0.333499\pi$
$953$	29393.3			0.999100			0.499550	+	0.866285i	$0.333499\pi$
$954$		0			0
$955$	10994.7	−	19043.3i	0.372543	−	0.645264i
$956$		0			0
$957$	3712.06	+	6429.48i	0.125386	+	0.217174i
$958$		0			0
$959$	29709.5	−	37938.6i	1.00038	−	1.27748i
$960$		0			0
$961$	−10041.7	−	17392.7i	−0.337072	−	0.583825i
$962$		0			0
$963$	−3220.52	+	5578.10i	−0.107767	+	0.186658i
$964$		0			0
$965$	−99410.6			−3.31621
$966$		0			0
$967$	7133.95			0.237241			0.118621	−	0.992940i	$-0.462153\pi$
$967$	7133.95			0.237241			0.118621	+	0.992940i	$0.462153\pi$
$968$		0			0
$969$	−5999.30	+	10391.1i	−0.198891	+	0.344489i
$970$		0			0
$971$	−4844.06	−	8390.16i	−0.160096	−	0.277295i	0.774807	−	0.632198i	$-0.217847\pi$
$971$	−4844.06	−	8390.16i	−0.160096	−	0.277295i	−0.934903	+	0.354903i	$0.884514\pi$
$972$		0			0
$973$	48621.8	+	6888.93i	1.60200	+	0.226977i
$974$		0			0
$975$	1003.10	+	1737.41i	0.0329485	+	0.0570685i
$976$		0			0
$977$	−10652.8	+	18451.3i	−0.348838	+	0.604205i	−0.986043	−	0.166489i	$-0.946757\pi$
$977$	−10652.8	+	18451.3i	−0.348838	+	0.604205i	0.637205	+	0.770694i	$0.280090\pi$
$978$		0			0
$979$	5809.79			0.189665
$980$		0			0
$981$	5400.17			0.175753
$982$		0			0
$983$	−18640.4	+	32286.1i	−0.604818	+	1.04758i	0.387262	+	0.921970i	$0.373421\pi$
$983$	−18640.4	+	32286.1i	−0.604818	+	1.04758i	−0.992080	+	0.125606i	$0.959913\pi$
$984$		0			0
$985$	−16902.1	−	29275.4i	−0.546748	−	0.946996i
$986$		0			0
$987$	27948.3	+	3959.82i	0.901320	+	0.127703i
$988$		0			0
$989$	−72.1740	−	125.009i	−0.00232052	−	0.00401927i
$990$		0			0
$991$	−25698.5	+	44511.2i	−0.823755	+	1.42678i	0.0791128	+	0.996866i	$0.474791\pi$
$991$	−25698.5	+	44511.2i	−0.823755	+	1.42678i	−0.902867	+	0.429919i	$0.858542\pi$
$992$		0			0
$993$	12462.2			0.398263
$994$		0			0
$995$	73974.6			2.35694
$996$		0			0
$997$	17186.9	−	29768.6i	0.545953	−	0.945618i	−0.452594	−	0.891717i	$-0.649501\pi$
$997$	17186.9	−	29768.6i	0.545953	−	0.945618i	0.998546	−	0.0539007i	$-0.0171655\pi$
$998$		0			0
$999$	2275.21	+	3940.78i	0.0720565	+	0.124806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.j.193.1		4
4.3	odd	2		42.4.e.c.25.1	✓	4
7.2	even	3	inner	336.4.q.j.289.1		4
7.3	odd	6		2352.4.a.ca.1.1		2
7.4	even	3		2352.4.a.bq.1.2		2
12.11	even	2		126.4.g.g.109.2		4
28.3	even	6		294.4.a.m.1.1		2
28.11	odd	6		294.4.a.n.1.2		2
28.19	even	6		294.4.e.l.79.2		4
28.23	odd	6		42.4.e.c.37.1	yes	4
28.27	even	2		294.4.e.l.67.2		4
84.11	even	6		882.4.a.v.1.1		2
84.23	even	6		126.4.g.g.37.2		4
84.47	odd	6		882.4.g.bf.667.1		4
84.59	odd	6		882.4.a.z.1.2		2
84.83	odd	2		882.4.g.bf.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.c.25.1	✓	4	4.3	odd	2
42.4.e.c.37.1	yes	4	28.23	odd	6
126.4.g.g.37.2		4	84.23	even	6
126.4.g.g.109.2		4	12.11	even	2
294.4.a.m.1.1		2	28.3	even	6
294.4.a.n.1.2		2	28.11	odd	6
294.4.e.l.67.2		4	28.27	even	2
294.4.e.l.79.2		4	28.19	even	6
336.4.q.j.193.1		4	1.1	even	1	trivial
336.4.q.j.289.1		4	7.2	even	3	inner
882.4.a.v.1.1		2	84.11	even	6
882.4.a.z.1.2		2	84.59	odd	6
882.4.g.bf.361.1		4	84.83	odd	2
882.4.g.bf.667.1		4	84.47	odd	6
2352.4.a.bq.1.2		2	7.4	even	3
2352.4.a.ca.1.1		2	7.3	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-10.4186 - 18.0455i) q^{5} +(18.3371 + 2.59808i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(-10.4186 - 18.0455i) q^{5} +(18.3371 + 2.59808i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(7.58144 - 13.1314i) q^{11} +2.16288 q^{13} -62.5114 q^{15} +(59.6742 - 103.359i) q^{17} +(-16.7557 - 29.0217i) q^{19} +(34.2557 - 43.7441i) q^{21} +(0.325758 + 0.564230i) q^{23} +(-154.593 + 267.763i) q^{25} -27.0000 q^{27} -163.208 q^{29} +(-111.663 + 193.406i) q^{31} +(-22.7443 - 39.3943i) q^{33} +(-144.163 - 357.970i) q^{35} +(-84.2670 - 145.955i) q^{37} +(3.24432 - 5.61932i) q^{39} -323.023 q^{41} -221.557 q^{43} +(-93.7670 + 162.409i) q^{45} +(254.023 + 439.980i) q^{47} +(329.500 + 95.2825i) q^{49} +(-179.023 - 310.076i) q^{51} +(88.2557 - 152.863i) q^{53} -315.951 q^{55} -100.534 q^{57} +(227.464 - 393.979i) q^{59} +(-19.3258 - 33.4732i) q^{61} +(-62.2670 - 154.615i) q^{63} +(-22.5341 - 39.0302i) q^{65} +(70.8958 - 122.795i) q^{67} +1.95455 q^{69} -602.742 q^{71} +(551.150 - 954.619i) q^{73} +(463.778 + 803.288i) q^{75} +(173.138 - 221.096i) q^{77} +(-58.1515 - 100.721i) q^{79} +(-40.5000 + 70.1481i) q^{81} +568.928 q^{83} -2486.88 q^{85} +(-244.812 + 424.028i) q^{87} +(191.580 + 331.825i) q^{89} +(39.6610 + 5.61932i) q^{91} +(334.989 + 580.217i) q^{93} +(-349.140 + 604.728i) q^{95} +334.701 q^{97} -136.466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 5 q^{5} - 18 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 5 * q^5 - 18 * q^9	\( 4 q + 6 q^{3} - 5 q^{5} - 18 q^{9} + 67 q^{11} + 82 q^{13} - 30 q^{15} + 92 q^{17} + 43 q^{19} + 27 q^{21} + 148 q^{23} - 435 q^{25} - 108 q^{27} + 154 q^{29} - 520 q^{31} - 201 q^{33} - 650 q^{35} - 7 q^{37} + 123 q^{39} - 852 q^{41} + 214 q^{43} - 45 q^{45} + 576 q^{47} + 1318 q^{49} - 276 q^{51} + 243 q^{53} + 1010 q^{55} + 258 q^{57} - 7 q^{59} - 224 q^{61} + 81 q^{63} + 570 q^{65} + 687 q^{67} + 888 q^{69} - 944 q^{71} + 921 q^{73} + 1305 q^{75} - 371 q^{77} - 526 q^{79} - 162 q^{81} + 442 q^{83} - 5840 q^{85} + 231 q^{87} - 774 q^{89} - 1345 q^{91} + 1560 q^{93} - 1910 q^{95} + 3906 q^{97} - 1206 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 5 * q^5 - 18 * q^9 + 67 * q^11 + 82 * q^13 - 30 * q^15 + 92 * q^17 + 43 * q^19 + 27 * q^21 + 148 * q^23 - 435 * q^25 - 108 * q^27 + 154 * q^29 - 520 * q^31 - 201 * q^33 - 650 * q^35 - 7 * q^37 + 123 * q^39 - 852 * q^41 + 214 * q^43 - 45 * q^45 + 576 * q^47 + 1318 * q^49 - 276 * q^51 + 243 * q^53 + 1010 * q^55 + 258 * q^57 - 7 * q^59 - 224 * q^61 + 81 * q^63 + 570 * q^65 + 687 * q^67 + 888 * q^69 - 944 * q^71 + 921 * q^73 + 1305 * q^75 - 371 * q^77 - 526 * q^79 - 162 * q^81 + 442 * q^83 - 5840 * q^85 + 231 * q^87 - 774 * q^89 - 1345 * q^91 + 1560 * q^93 - 1910 * q^95 + 3906 * q^97 - 1206 * q^99

Introduction

L-functions

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