LMFDB - Embedded newform 208.3.bd.e.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,3,Mod(33,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

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

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

chi := DirichletCharacter("208.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	208.bd (of order $12$, degree $4$, 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:	$5.66758949869$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.44991500544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 38x^{6} + 555x^{4} - 3674x^{2} + 9409 $ x^8 - 38x^6 + 555x^4 - 3674*x^2 + 9409
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.2
Root			$2.83160 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.145
Dual form			208.3.bd.e.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.982786 + 1.70224i) q^{3} +(5.05105 - 5.05105i) q^{5} +(-0.383239 + 0.102689i) q^{7} +(2.56826 - 4.44836i) q^{9} +(3.51976 - 13.1359i) q^{11} +(-9.67036 + 8.68816i) q^{13} +(13.5622 + 3.63397i) q^{15} +(12.3415 + 7.12539i) q^{17} +(-0.873186 - 3.25878i) q^{19} +(-0.551442 - 0.551442i) q^{21} +(14.3562 - 8.28854i) q^{23} -26.0262i q^{25} +27.7864 q^{27} +(22.3938 + 38.7872i) q^{29} +(-35.2730 + 35.2730i) q^{31} +(25.8196 - 6.91835i) q^{33} +(-1.41707 + 2.45444i) q^{35} +(9.58504 - 35.7719i) q^{37} +(-24.2932 - 7.92262i) q^{39} +(-10.8895 - 2.91782i) q^{41} +(51.5199 + 29.7450i) q^{43} +(-9.49646 - 35.4413i) q^{45} +(-54.6357 - 54.6357i) q^{47} +(-42.2989 + 24.4213i) q^{49} +28.0110i q^{51} -63.3563 q^{53} +(-48.5717 - 84.1287i) q^{55} +(4.68905 - 4.68905i) q^{57} +(-31.1381 + 8.34343i) q^{59} +(-29.0686 + 50.3483i) q^{61} +(-0.527462 + 1.96852i) q^{63} +(-4.96111 + 92.7298i) q^{65} +(100.204 + 26.8497i) q^{67} +(28.2181 + 16.2917i) q^{69} +(19.7845 + 73.8369i) q^{71} +(-53.5296 - 53.5296i) q^{73} +(44.3027 - 25.5782i) q^{75} +5.39564i q^{77} -129.990 q^{79} +(4.19371 + 7.26372i) q^{81} +(-48.6837 + 48.6837i) q^{83} +(98.3284 - 26.3470i) q^{85} +(-44.0166 + 76.2390i) q^{87} +(-4.08744 + 15.2545i) q^{89} +(2.81388 - 4.32268i) q^{91} +(-94.7089 - 25.3772i) q^{93} +(-20.8707 - 12.0497i) q^{95} +(-3.73635 - 13.9442i) q^{97} +(-49.3937 - 49.3937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{5} - 4 q^{7} - 6 q^{9} - 24 q^{11} + 18 q^{13} + 60 q^{15} - 54 q^{17} + 50 q^{19} - 54 q^{21} + 24 q^{23} - 36 q^{27} + 108 q^{29} - 176 q^{31} + 114 q^{33} + 30 q^{35} + 104 q^{37} - 120 q^{39}+ \cdots + 182 q^{97}+O(q^{100}) $ 8 * q + 6 * q^5 - 4 * q^7 - 6 * q^9 - 24 * q^11 + 18 * q^13 + 60 * q^15 - 54 * q^17 + 50 * q^19 - 54 * q^21 + 24 * q^23 - 36 * q^27 + 108 * q^29 - 176 * q^31 + 114 * q^33 + 30 * q^35 + 104 * q^37 - 120 * q^39 - 168 * q^41 + 198 * q^43 + 6 * q^45 + 96 * q^47 - 162 * q^49 - 72 * q^53 - 126 * q^55 + 318 * q^57 - 18 * q^61 - 180 * q^63 - 72 * q^65 + 326 * q^67 - 498 * q^69 + 162 * q^71 - 98 * q^73 + 240 * q^75 - 192 * q^79 + 240 * q^81 - 408 * q^83 + 318 * q^85 - 36 * q^87 + 54 * q^89 - 280 * q^91 - 66 * q^93 - 312 * q^95 + 182 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{12}\right)$

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			0
$2$		0			0
$3$	0.982786	+	1.70224i	0.327595	+	0.567412i	0.982034	−	0.188703i	$-0.0604284\pi$
$3$	0.982786	+	1.70224i	0.327595	+	0.567412i	−0.654439	+	0.756115i	$0.727095\pi$
$4$		0			0
$5$	5.05105	−	5.05105i	1.01021	−	1.01021i	0.0102623	−	0.999947i	$-0.496733\pi$
$5$	5.05105	−	5.05105i	1.01021	−	1.01021i	0.999947	−	0.0102623i	$-0.00326663\pi$
$6$		0			0
$7$	−0.383239	+	0.102689i	−0.0547484	+	0.0146698i	−0.286089	−	0.958203i	$-0.592355\pi$
$7$	−0.383239	+	0.102689i	−0.0547484	+	0.0146698i	0.231341	+	0.972873i	$0.425689\pi$
$8$		0			0
$9$	2.56826	−	4.44836i	0.285362	−	0.494262i
$10$		0			0
$11$	3.51976	−	13.1359i	0.319978	−	1.19418i	−0.599286	−	0.800535i	$-0.704549\pi$
$11$	3.51976	−	13.1359i	0.319978	−	1.19418i	0.919264	−	0.393641i	$-0.128785\pi$
$12$		0			0
$13$	−9.67036	+	8.68816i	−0.743874	+	0.668320i
$13$	−9.67036	+	8.68816i	−0.743874	+	0.668320i
$14$		0			0
$15$	13.5622	+	3.63397i	0.904145	+	0.242265i
$16$		0			0
$17$	12.3415	+	7.12539i	0.725973	+	0.419141i	0.816947	−	0.576712i	$-0.195665\pi$
$17$	12.3415	+	7.12539i	0.725973	+	0.419141i	−0.0909741	+	0.995853i	$0.528998\pi$
$18$		0			0
$19$	−0.873186	−	3.25878i	−0.0459572	−	0.171514i	0.939133	−	0.343554i	$-0.111631\pi$
$19$	−0.873186	−	3.25878i	−0.0459572	−	0.171514i	−0.985090	+	0.172040i	$0.944964\pi$
$20$		0			0
$21$	−0.551442	−	0.551442i	−0.0262592	−	0.0262592i
$22$		0			0
$23$	14.3562	−	8.28854i	0.624181	−	0.360371i	−0.154314	−	0.988022i	$-0.549317\pi$
$23$	14.3562	−	8.28854i	0.624181	−	0.360371i	0.778495	+	0.627651i	$0.215983\pi$
$24$		0			0
$25$		−	26.0262i		−	1.04105i
$26$		0			0
$27$	27.7864			1.02912
$28$		0			0
$29$	22.3938	+	38.7872i	0.772199	+	1.33749i	0.936355	+	0.351054i	$0.114177\pi$
$29$	22.3938	+	38.7872i	0.772199	+	1.33749i	−0.164156	+	0.986434i	$0.552490\pi$
$30$		0			0
$31$	−35.2730	+	35.2730i	−1.13784	+	1.13784i	−0.149004	+	0.988837i	$0.547607\pi$
$31$	−35.2730	+	35.2730i	−1.13784	+	1.13784i	−0.988837	+	0.149004i	$0.952393\pi$
$32$		0			0
$33$	25.8196	−	6.91835i	0.782413	−	0.209647i
$34$		0			0
$35$	−1.41707	+	2.45444i	−0.0404878	+	0.0701269i
$36$		0			0
$37$	9.58504	−	35.7719i	0.259055	−	0.966807i	−0.706734	−	0.707479i	$-0.749832\pi$
$37$	9.58504	−	35.7719i	0.259055	−	0.966807i	0.965789	−	0.259328i	$-0.0835010\pi$
$38$		0			0
$39$	−24.2932	−	7.92262i	−0.622903	−	0.203144i
$40$		0			0
$41$	−10.8895	−	2.91782i	−0.265597	−	0.0711665i	0.123563	−	0.992337i	$-0.460568\pi$
$41$	−10.8895	−	2.91782i	−0.265597	−	0.0711665i	−0.389160	+	0.921170i	$0.627235\pi$
$42$		0			0
$43$	51.5199	+	29.7450i	1.19814	+	0.691745i	0.960140	−	0.279521i	$-0.0901756\pi$
$43$	51.5199	+	29.7450i	1.19814	+	0.691745i	0.237998	+	0.971266i	$0.423509\pi$
$44$		0			0
$45$	−9.49646	−	35.4413i	−0.211033	−	0.787584i
$46$		0			0
$47$	−54.6357	−	54.6357i	−1.16246	−	1.16246i	−0.983935	−	0.178527i	$-0.942867\pi$
$47$	−54.6357	−	54.6357i	−1.16246	−	1.16246i	−0.178527	−	0.983935i	$-0.557133\pi$
$48$		0			0
$49$	−42.2989	+	24.4213i	−0.863243	+	0.498394i
$50$		0			0
$51$			28.0110i			0.549235i
$52$		0			0
$53$	−63.3563			−1.19540			−0.597701	−	0.801719i	$-0.703919\pi$
$53$	−63.3563			−1.19540			−0.597701	+	0.801719i	$0.703919\pi$
$54$		0			0
$55$	−48.5717	−	84.1287i	−0.883122	−	1.52961i
$56$		0			0
$57$	4.68905	−	4.68905i	0.0822640	−	0.0822640i
$58$		0			0
$59$	−31.1381	+	8.34343i	−0.527765	+	0.141414i	−0.512856	−	0.858475i	$-0.671412\pi$
$59$	−31.1381	+	8.34343i	−0.527765	+	0.141414i	−0.0149089	+	0.999889i	$0.504746\pi$
$60$		0			0
$61$	−29.0686	+	50.3483i	−0.476534	+	0.825382i	−0.999638	−	0.0268870i	$-0.991441\pi$
$61$	−29.0686	+	50.3483i	−0.476534	+	0.825382i	0.523104	+	0.852269i	$0.324774\pi$
$62$		0			0
$63$	−0.527462	+	1.96852i	−0.00837242	+	0.0312463i
$64$		0			0
$65$	−4.96111	+	92.7298i	−0.0763247	+	1.42661i
$66$		0			0
$67$	100.204	+	26.8497i	1.49559	+	0.400741i	0.911619	−	0.411035i	$-0.134833\pi$
$67$	100.204	+	26.8497i	1.49559	+	0.400741i	0.583968	+	0.811777i	$0.301499\pi$
$68$		0			0
$69$	28.2181	+	16.2917i	0.408958	+	0.236112i
$70$		0			0
$71$	19.7845	+	73.8369i	0.278656	+	1.03996i	0.953352	+	0.301861i	$0.0976079\pi$
$71$	19.7845	+	73.8369i	0.278656	+	1.03996i	−0.674696	+	0.738095i	$0.735725\pi$
$72$		0			0
$73$	−53.5296	−	53.5296i	−0.733282	−	0.733282i	0.237987	−	0.971268i	$-0.423513\pi$
$73$	−53.5296	−	53.5296i	−0.733282	−	0.733282i	−0.971268	+	0.237987i	$0.923513\pi$
$74$		0			0
$75$	44.3027	−	25.5782i	0.590703	−	0.341042i
$76$		0			0
$77$			5.39564i			0.0700732i
$78$		0			0
$79$	−129.990			−1.64544			−0.822719	−	0.568449i	$-0.807544\pi$
$79$	−129.990			−1.64544			−0.822719	+	0.568449i	$0.807544\pi$
$80$		0			0
$81$	4.19371	+	7.26372i	0.0517742	+	0.0896756i
$82$		0			0
$83$	−48.6837	+	48.6837i	−0.586551	+	0.586551i	−0.936696	−	0.350145i	$-0.886132\pi$
$83$	−48.6837	+	48.6837i	−0.586551	+	0.586551i	0.350145	+	0.936696i	$0.386132\pi$
$84$		0			0
$85$	98.3284	−	26.3470i	1.15681	−	0.309965i
$86$		0			0
$87$	−44.0166	+	76.2390i	−0.505938	+	0.876310i
$88$		0			0
$89$	−4.08744	+	15.2545i	−0.0459263	+	0.171399i	−0.985080	−	0.172099i	$-0.944945\pi$
$89$	−4.08744	+	15.2545i	−0.0459263	+	0.171399i	0.939153	+	0.343498i	$0.111612\pi$
$90$		0			0
$91$	2.81388	−	4.32268i	0.0309218	−	0.0475020i
$92$		0			0
$93$	−94.7089	−	25.3772i	−1.01838	−	0.272873i
$94$		0			0
$95$	−20.8707	−	12.0497i	−0.219692	−	0.126839i
$96$		0			0
$97$	−3.73635	−	13.9442i	−0.0385190	−	0.143755i	0.943988	−	0.329979i	$-0.107042\pi$
$97$	−3.73635	−	13.9442i	−0.0385190	−	0.143755i	−0.982507	+	0.186224i	$0.940375\pi$
$98$		0			0
$99$	−49.3937	−	49.3937i	−0.498926	−	0.498926i
$100$		0			0
$101$	−0.332715	+	0.192093i	−0.00329421	+	0.00190191i	−0.501646	−	0.865073i	$-0.667272\pi$
$101$	−0.332715	+	0.192093i	−0.00329421	+	0.00190191i	0.498352	+	0.866975i	$0.333939\pi$
$102$		0			0
$103$			10.1674i			0.0987130i	0.998781	+	0.0493565i	$0.0157170\pi$
$103$			10.1674i			0.0987130i	−0.998781	+	0.0493565i	$0.984283\pi$
$104$		0			0
$105$	−5.57072			−0.0530545
$106$		0			0
$107$	28.2273	+	48.8911i	0.263806	+	0.456926i	0.967250	−	0.253825i	$-0.0816886\pi$
$107$	28.2273	+	48.8911i	0.263806	+	0.456926i	−0.703444	+	0.710751i	$0.748355\pi$
$108$		0			0
$109$	86.1609	−	86.1609i	0.790467	−	0.790467i	−0.191103	−	0.981570i	$-0.561206\pi$
$109$	86.1609	−	86.1609i	0.790467	−	0.790467i	0.981570	+	0.191103i	$0.0612065\pi$
$110$		0			0
$111$	70.3122	−	18.8401i	0.633443	−	0.169731i
$112$		0			0
$113$	33.5007	−	58.0250i	0.296467	−	0.513495i	−0.678858	−	0.734269i	$-0.737525\pi$
$113$	33.5007	−	58.0250i	0.296467	−	0.513495i	0.975325	+	0.220774i	$0.0708583\pi$
$114$		0			0
$115$	30.6479	−	114.380i	0.266503	−	0.994605i
$116$		0			0
$117$	13.8121	+	65.3307i	0.118052	+	0.558382i
$118$		0			0
$119$	−5.46146	−	1.46339i	−0.0458946	−	0.0122974i
$120$		0			0
$121$	−55.3749	−	31.9707i	−0.457644	−	0.264221i
$122$		0			0
$123$	−5.73520	−	21.4040i	−0.0466276	−	0.174017i
$124$		0			0
$125$	−5.18324	−	5.18324i	−0.0414659	−	0.0414659i
$126$		0			0
$127$	12.2590	−	7.07775i	0.0965277	−	0.0557303i	−0.450959	−	0.892545i	$-0.648918\pi$
$127$	12.2590	−	7.07775i	0.0965277	−	0.0557303i	0.547487	+	0.836814i	$0.315585\pi$
$128$		0			0
$129$			116.932i			0.906450i
$130$		0			0
$131$	134.167			1.02418			0.512089	−	0.858932i	$-0.328872\pi$
$131$	134.167			1.02418			0.512089	+	0.858932i	$0.328872\pi$
$132$		0			0
$133$	0.669278	+	1.15922i	0.00503216	+	0.00871596i
$134$		0			0
$135$	140.350	−	140.350i	1.03963	−	1.03963i
$136$		0			0
$137$	−61.0842	+	16.3675i	−0.445870	+	0.119470i	−0.474766	−	0.880112i	$-0.657467\pi$
$137$	−61.0842	+	16.3675i	−0.445870	+	0.119470i	0.0288964	+	0.999582i	$0.490801\pi$
$138$		0			0
$139$	134.588	−	233.114i	0.968261	−	1.67708i	0.267676	−	0.963509i	$-0.413744\pi$
$139$	134.588	−	233.114i	0.968261	−	1.67708i	0.700586	−	0.713568i	$-0.252922\pi$
$140$		0			0
$141$	39.3076	−	146.698i	0.278778	−	1.04041i
$142$		0			0
$143$	80.0898	+	157.609i	0.560068	+	1.10216i
$144$		0			0
$145$	309.028	+	82.8038i	2.13123	+	0.571060i
$146$		0			0
$147$	−83.1416	−	48.0018i	−0.565589	−	0.326543i
$148$		0			0
$149$	46.0924	+	172.019i	0.309345	+	1.15449i	0.929141	+	0.369727i	$0.120549\pi$
$149$	46.0924	+	172.019i	0.309345	+	1.15449i	−0.619796	+	0.784763i	$0.712785\pi$
$150$		0			0
$151$	18.9917	+	18.9917i	0.125773	+	0.125773i	0.767191	−	0.641418i	$-0.221654\pi$
$151$	18.9917	+	18.9917i	0.125773	+	0.125773i	−0.641418	+	0.767191i	$0.721654\pi$
$152$		0			0
$153$	63.3926	−	36.5997i	0.414331	−	0.239214i
$154$		0			0
$155$			356.332i			2.29891i
$156$		0			0
$157$	−99.6292			−0.634581			−0.317291	−	0.948328i	$-0.602773\pi$
$157$	−99.6292			−0.634581			−0.317291	+	0.948328i	$0.602773\pi$
$158$		0			0
$159$	−62.2657	−	107.847i	−0.391608	−	0.678285i
$160$		0			0
$161$	−4.65071	+	4.65071i	−0.0288864	+	0.0288864i
$162$		0			0
$163$	32.2814	−	8.64978i	0.198045	−	0.0530661i	−0.158433	−	0.987370i	$-0.550644\pi$
$163$	32.2814	−	8.64978i	0.198045	−	0.0530661i	0.356478	+	0.934304i	$0.383977\pi$
$164$		0			0
$165$	95.4713	−	165.361i	0.578614	−	1.00219i
$166$		0			0
$167$	−5.23878	+	19.5514i	−0.0313699	+	0.117074i	−0.979835	−	0.199806i	$-0.935969\pi$
$167$	−5.23878	+	19.5514i	−0.0313699	+	0.117074i	0.948465	+	0.316880i	$0.102635\pi$
$168$		0			0
$169$	18.0316	−	168.035i	0.106696	−	0.994292i
$170$		0			0
$171$	−16.7388	−	4.48514i	−0.0978876	−	0.0262289i
$172$		0			0
$173$	−92.5187	−	53.4157i	−0.534790	−	0.308761i	0.208175	−	0.978092i	$-0.433248\pi$
$173$	−92.5187	−	53.4157i	−0.534790	−	0.308761i	−0.742965	+	0.669330i	$0.766581\pi$
$174$		0			0
$175$	2.67259	+	9.97424i	0.0152719	+	0.0569957i
$176$		0			0
$177$	−44.8046	−	44.8046i	−0.253133	−	0.253133i
$178$		0			0
$179$	−247.149	+	142.692i	−1.38072	+	0.797159i	−0.992245	−	0.124299i	$-0.960332\pi$
$179$	−247.149	+	142.692i	−1.38072	+	0.797159i	−0.388476	+	0.921459i	$0.626998\pi$
$180$		0			0
$181$			286.491i			1.58282i	0.611285	+	0.791411i	$0.290653\pi$
$181$			286.491i			1.58282i	−0.611285	+	0.791411i	$0.709347\pi$
$182$		0			0
$183$	−114.273			−0.624442
$184$		0			0
$185$	−132.271	−	229.100i	−0.714978	−	1.23838i
$186$		0			0
$187$	137.038	−	137.038i	0.732823	−	0.732823i
$188$		0			0
$189$	−10.6488	+	2.85334i	−0.0563430	+	0.0150970i
$190$		0			0
$191$	−24.0138	+	41.5931i	−0.125727	+	0.217765i	−0.922017	−	0.387150i	$-0.873460\pi$
$191$	−24.0138	+	41.5931i	−0.125727	+	0.217765i	0.796290	+	0.604915i	$0.206793\pi$
$192$		0			0
$193$	14.1623	−	52.8544i	0.0733798	−	0.273857i	−0.919481	−	0.393134i	$-0.871391\pi$
$193$	14.1623	−	52.8544i	0.0733798	−	0.273857i	0.992861	+	0.119277i	$0.0380576\pi$
$194$		0			0
$195$	−162.724	+	82.6886i	−0.834480	+	0.424044i
$196$		0			0
$197$	216.454	+	57.9987i	1.09875	+	0.294410i	0.762256	−	0.647275i	$-0.224092\pi$
$197$	216.454	+	57.9987i	1.09875	+	0.294410i	0.336496	+	0.941685i	$0.390758\pi$
$198$		0			0
$199$	−139.201	−	80.3674i	−0.699500	−	0.403857i	0.107661	−	0.994188i	$-0.465664\pi$
$199$	−139.201	−	80.3674i	−0.699500	−	0.403857i	−0.807161	+	0.590331i	$0.798997\pi$
$200$		0			0
$201$	52.7750	+	196.959i	0.262562	+	0.979895i
$202$		0			0
$203$	−12.5652	−	12.5652i	−0.0618974	−	0.0618974i
$204$		0			0
$205$	−69.7413	+	40.2652i	−0.340202	+	0.196415i
$206$		0			0
$207$		−	85.1485i		−	0.411346i
$208$		0			0
$209$	−45.8805			−0.219524
$210$		0			0
$211$	168.202	+	291.334i	0.797164	+	1.38073i	0.921456	+	0.388483i	$0.127001\pi$
$211$	168.202	+	291.334i	0.797164	+	1.38073i	−0.124292	+	0.992246i	$0.539666\pi$
$212$		0			0
$213$	−106.244	+	106.244i	−0.498798	+	0.498798i
$214$		0			0
$215$	410.473	−	109.986i	1.90918	−	0.511562i
$216$		0			0
$217$	9.89587	−	17.1401i	0.0456031	−	0.0789868i
$218$		0			0
$219$	38.5118	−	143.728i	0.175853	−	0.656293i
$220$		0			0
$221$	−181.254	+	38.3202i	−0.820153	+	0.173395i
$222$		0			0
$223$	58.5729	+	15.6946i	0.262659	+	0.0703792i	0.387745	−	0.921767i	$-0.373254\pi$
$223$	58.5729	+	15.6946i	0.262659	+	0.0703792i	−0.125086	+	0.992146i	$0.539921\pi$
$224$		0			0
$225$	−115.774	−	66.8420i	−0.514550	−	0.297076i
$226$		0			0
$227$	−14.8051	−	55.2535i	−0.0652208	−	0.243407i	0.925618	−	0.378460i	$-0.123546\pi$
$227$	−14.8051	−	55.2535i	−0.0652208	−	0.243407i	−0.990838	+	0.135053i	$0.956880\pi$
$228$		0			0
$229$	−100.531	−	100.531i	−0.439000	−	0.439000i	0.452675	−	0.891675i	$-0.350470\pi$
$229$	−100.531	−	100.531i	−0.439000	−	0.439000i	−0.891675	+	0.452675i	$0.850470\pi$
$230$		0			0
$231$	−9.18465	+	5.30276i	−0.0397604	+	0.0229557i
$232$		0			0
$233$			366.815i			1.57431i	0.616754	+	0.787156i	$0.288448\pi$
$233$			366.815i			1.57431i	−0.616754	+	0.787156i	$0.711552\pi$
$234$		0			0
$235$	−551.935			−2.34866
$236$		0			0
$237$	−127.752	−	221.273i	−0.539038	−	0.933641i
$238$		0			0
$239$	−15.4013	+	15.4013i	−0.0644407	+	0.0644407i	−0.738593	−	0.674152i	$-0.764509\pi$
$239$	−15.4013	+	15.4013i	−0.0644407	+	0.0644407i	0.674152	+	0.738593i	$0.264509\pi$
$240$		0			0
$241$	153.249	−	41.0631i	0.635890	−	0.170386i	0.0735487	−	0.997292i	$-0.476568\pi$
$241$	153.249	−	41.0631i	0.635890	−	0.170386i	0.562341	+	0.826906i	$0.309901\pi$
$242$		0			0
$243$	116.796	−	202.296i	0.480640	−	0.832494i
$244$		0			0
$245$	−90.3007	+	337.007i	−0.368574	+	1.37554i
$246$		0			0
$247$	36.7568	+	23.9271i	0.148813	+	0.0968710i
$248$		0			0
$249$	−130.717	−	35.0255i	−0.524967	−	0.140665i
$250$		0			0
$251$	−234.064	−	135.137i	−0.932527	−	0.538395i	−0.0449172	−	0.998991i	$-0.514302\pi$
$251$	−234.064	−	135.137i	−0.932527	−	0.538395i	−0.887610	+	0.460596i	$0.847636\pi$
$252$		0			0
$253$	−58.3474	−	217.755i	−0.230622	−	0.860693i
$254$		0			0
$255$	141.485	+	141.485i	0.554842	+	0.554842i
$256$		0			0
$257$	211.966	−	122.378i	0.824769	−	0.476180i	−0.0272894	−	0.999628i	$-0.508688\pi$
$257$	211.966	−	122.378i	0.824769	−	0.476180i	0.852058	+	0.523447i	$0.175354\pi$
$258$		0			0
$259$			14.6934i			0.0567314i
$260$		0			0
$261$	230.052			0.881426
$262$		0			0
$263$	26.0425	+	45.1070i	0.0990211	+	0.171509i	0.911280	−	0.411788i	$-0.135096\pi$
$263$	26.0425	+	45.1070i	0.0990211	+	0.171509i	−0.812259	+	0.583297i	$0.801762\pi$
$264$		0			0
$265$	−320.016	+	320.016i	−1.20761	+	1.20761i
$266$		0			0
$267$	−29.9839	+	8.03417i	−0.112299	+	0.0300905i
$268$		0			0
$269$	27.7456	−	48.0568i	0.103144	−	0.178650i	−0.809835	−	0.586658i	$-0.800443\pi$
$269$	27.7456	−	48.0568i	0.103144	−	0.178650i	0.912978	+	0.408008i	$0.133777\pi$
$270$		0			0
$271$	−53.8417	+	200.940i	−0.198678	+	0.741476i	0.792606	+	0.609734i	$0.208724\pi$
$271$	−53.8417	+	200.940i	−0.198678	+	0.741476i	−0.991284	+	0.131742i	$0.957943\pi$
$272$		0			0
$273$	10.1237	+	0.541623i	0.0370830	+	0.00198397i
$274$		0			0
$275$	−341.878	−	91.6059i	−1.24319	−	0.333112i
$276$		0			0
$277$	−139.256	−	80.3992i	−0.502728	−	0.290250i	0.227112	−	0.973869i	$-0.427072\pi$
$277$	−139.256	−	80.3992i	−0.502728	−	0.290250i	−0.729839	+	0.683619i	$0.760405\pi$
$278$		0			0
$279$	66.3168	+	247.498i	0.237695	+	0.887088i
$280$		0			0
$281$	−132.843	−	132.843i	−0.472752	−	0.472752i	0.430052	−	0.902804i	$-0.358495\pi$
$281$	−132.843	−	132.843i	−0.472752	−	0.472752i	−0.902804	+	0.430052i	$0.858495\pi$
$282$		0			0
$283$	−218.526	+	126.166i	−0.772176	+	0.445816i	−0.833650	−	0.552293i	$-0.813753\pi$
$283$	−218.526	+	126.166i	−0.772176	+	0.445816i	0.0614742	+	0.998109i	$0.480420\pi$
$284$		0			0
$285$		−	47.3692i		−	0.166208i
$286$		0			0
$287$	4.47290			0.0155850
$288$		0			0
$289$	−42.9575	−	74.4046i	−0.148642	−	0.257456i
$290$		0			0
$291$	20.0643	−	20.0643i	0.0689496	−	0.0689496i
$292$		0			0
$293$	287.318	−	76.9867i	0.980608	−	0.262753i	0.267308	−	0.963611i	$-0.413866\pi$
$293$	287.318	−	76.9867i	0.980608	−	0.262753i	0.713301	+	0.700858i	$0.247199\pi$
$294$		0			0
$295$	−115.137	+	199.423i	−0.390295	+	0.676011i
$296$		0			0
$297$	97.8014	−	365.000i	0.329298	−	1.22896i
$298$		0			0
$299$	−66.8171	+	204.882i	−0.223469	+	0.685224i
$300$		0			0
$301$	−22.7989	−	6.10895i	−0.0757439	−	0.0202955i
$302$		0			0
$303$	−0.653976	−	0.377573i	−0.00215834	−	0.00124612i
$304$		0			0
$305$	107.485	+	401.139i	0.352409	+	1.31521i
$306$		0			0
$307$	−385.654	−	385.654i	−1.25620	−	1.25620i	−0.952892	−	0.303310i	$-0.901908\pi$
$307$	−385.654	−	385.654i	−1.25620	−	1.25620i	−0.303310	−	0.952892i	$-0.598092\pi$
$308$		0			0
$309$	−17.3074	+	9.99242i	−0.0560109	+	0.0323379i
$310$		0			0
$311$			91.9643i			0.295705i	0.989009	+	0.147853i	$0.0472361\pi$
$311$			91.9643i			0.295705i	−0.989009	+	0.147853i	$0.952764\pi$
$312$		0			0
$313$	−324.502			−1.03675			−0.518374	−	0.855154i	$-0.673462\pi$
$313$	−324.502			−1.03675			−0.518374	+	0.855154i	$0.673462\pi$
$314$		0			0
$315$	7.27883	+	12.6073i	0.0231074	+	0.0400232i
$316$		0			0
$317$	125.476	−	125.476i	0.395825	−	0.395825i	−0.480933	−	0.876757i	$-0.659702\pi$
$317$	125.476	−	125.476i	0.395825	−	0.395825i	0.876757	+	0.480933i	$0.159702\pi$
$318$		0			0
$319$	588.326	−	157.642i	1.84428	−	0.494174i
$320$		0			0
$321$	−55.4828	+	96.0990i	−0.172844	+	0.299374i
$322$		0			0
$323$	12.4436	−	46.4401i	0.0385250	−	0.143777i
$324$		0			0
$325$	226.120	+	251.682i	0.695753	+	0.774407i
$326$		0			0
$327$	231.344	+	61.9884i	0.707474	+	0.189567i
$328$		0			0
$329$	26.5490	+	15.3281i	0.0806960	+	0.0465899i
$330$		0			0
$331$	28.5043	+	106.380i	0.0861158	+	0.321389i	0.995523	−	0.0945179i	$-0.0301310\pi$
$331$	28.5043	+	106.380i	0.0861158	+	0.321389i	−0.909407	+	0.415907i	$0.863464\pi$
$332$		0			0
$333$	−134.509	−	134.509i	−0.403932	−	0.403932i
$334$		0			0
$335$	641.756	−	370.518i	1.91569	−	1.10602i
$336$		0			0
$337$			70.0627i			0.207901i	0.994582	+	0.103951i	$0.0331484\pi$
$337$			70.0627i			0.207901i	−0.994582	+	0.103951i	$0.966852\pi$
$338$		0			0
$339$	131.696			0.388484
$340$		0			0
$341$	339.192	+	587.497i	0.994697	+	1.72287i
$342$		0			0
$343$	27.4498	−	27.4498i	0.0800285	−	0.0800285i
$344$		0			0
$345$	224.821	−	60.2407i	0.651656	−	0.174611i
$346$		0			0
$347$	198.543	−	343.887i	0.572170	−	0.991027i	−0.424173	−	0.905581i	$-0.639435\pi$
$347$	198.543	−	343.887i	0.572170	−	0.991027i	0.996343	−	0.0854462i	$-0.0272316\pi$
$348$		0			0
$349$	37.1748	−	138.738i	0.106518	−	0.397531i	−0.891995	−	0.452045i	$-0.850694\pi$
$349$	37.1748	−	138.738i	0.106518	−	0.397531i	0.998513	+	0.0545146i	$0.0173612\pi$
$350$		0			0
$351$	−268.704	+	241.413i	−0.765539	+	0.687785i
$352$		0			0
$353$	347.277	+	93.0527i	0.983789	+	0.263605i	0.714639	−	0.699493i	$-0.246591\pi$
$353$	347.277	+	93.0527i	0.983789	+	0.263605i	0.269149	+	0.963098i	$0.413258\pi$
$354$		0			0
$355$	472.887	+	273.021i	1.33207	+	0.769074i
$356$		0			0
$357$	−2.87641	−	10.7349i	−0.00805716	−	0.0300697i
$358$		0			0
$359$	−136.661	−	136.661i	−0.380670	−	0.380670i	0.490673	−	0.871344i	$-0.336751\pi$
$359$	−136.661	−	136.661i	−0.380670	−	0.380670i	−0.871344	+	0.490673i	$0.836751\pi$
$360$		0			0
$361$	302.778	−	174.809i	0.838720	−	0.484235i
$362$		0			0
$363$		−	125.681i		−	0.346230i
$364$		0			0
$365$	−540.761			−1.48154
$366$		0			0
$367$	−73.2216	−	126.823i	−0.199514	−	0.345568i	0.748857	−	0.662732i	$-0.230603\pi$
$367$	−73.2216	−	126.823i	−0.199514	−	0.345568i	−0.948371	+	0.317163i	$0.897270\pi$
$368$		0			0
$369$	−40.9465	+	40.9465i	−0.110966	+	0.110966i
$370$		0			0
$371$	24.2806	−	6.50597i	0.0654464	−	0.0175363i
$372$		0			0
$373$	107.966	−	187.002i	0.289452	−	0.501345i	−0.684227	−	0.729269i	$-0.739860\pi$
$373$	107.966	−	187.002i	0.289452	−	0.501345i	0.973679	+	0.227924i	$0.0731937\pi$
$374$		0			0
$375$	3.72908	−	13.9171i	0.00994421	−	0.0371123i
$376$		0			0
$377$	−553.545	−	180.525i	−1.46829	−	0.478846i
$378$		0			0
$379$	306.392	+	82.0974i	0.808422	+	0.216616i	0.639278	−	0.768976i	$-0.279233\pi$
$379$	306.392	+	82.0974i	0.808422	+	0.216616i	0.169143	+	0.985591i	$0.445900\pi$
$380$		0			0
$381$	24.0960	+	13.9118i	0.0632441	+	0.0365140i
$382$		0			0
$383$	−159.079	−	593.690i	−0.415349	−	1.55010i	−0.784136	−	0.620590i	$-0.786893\pi$
$383$	−159.079	−	593.690i	−0.415349	−	1.55010i	0.368786	−	0.929514i	$-0.379773\pi$
$384$		0			0
$385$	27.2536	+	27.2536i	0.0707887	+	0.0707887i
$386$		0			0
$387$	264.633	−	152.786i	0.683807	−	0.394796i
$388$		0			0
$389$		−	738.319i		−	1.89799i	−0.315286	−	0.948997i	$-0.602101\pi$
$389$		−	738.319i		−	1.89799i	0.315286	−	0.948997i	$-0.397899\pi$
$390$		0			0
$391$	236.236			0.604185
$392$		0			0
$393$	131.858	+	228.385i	0.335516	+	0.581131i
$394$		0			0
$395$	−656.584	+	656.584i	−1.66224	+	1.66224i
$396$		0			0
$397$	418.554	−	112.151i	1.05429	−	0.282497i	0.310268	−	0.950649i	$-0.399581\pi$
$397$	418.554	−	112.151i	1.05429	−	0.282497i	0.744025	+	0.668152i	$0.232914\pi$
$398$		0			0
$399$	−1.31551	+	2.27854i	−0.00329703	+	0.00571062i
$400$		0			0
$401$	−88.4912	+	330.254i	−0.220676	+	0.823575i	0.763414	+	0.645909i	$0.223521\pi$
$401$	−88.4912	+	330.254i	−0.220676	+	0.823575i	−0.984091	+	0.177666i	$0.943145\pi$
$402$		0			0
$403$	34.6450	−	647.561i	0.0859677	−	1.60685i
$404$		0			0
$405$	57.8721	+	15.5068i	0.142894	+	0.0382883i
$406$		0			0
$407$	−436.160	−	251.817i	−1.07165	−	0.618715i
$408$		0			0
$409$	−194.342	−	725.295i	−0.475164	−	1.77334i	−0.620769	−	0.783994i	$-0.713179\pi$
$409$	−194.342	−	725.295i	−0.475164	−	1.77334i	0.145605	−	0.989343i	$-0.453487\pi$
$410$		0			0
$411$	−87.8940	−	87.8940i	−0.213854	−	0.213854i
$412$		0			0
$413$	11.0766	−	6.39506i	0.0268198	−	0.0154844i
$414$		0			0
$415$			491.807i			1.18508i
$416$		0			0
$417$	529.086			1.26879
$418$		0			0
$419$	22.5991	+	39.1428i	0.0539358	+	0.0934196i	0.891733	−	0.452562i	$-0.149490\pi$
$419$	22.5991	+	39.1428i	0.0539358	+	0.0934196i	−0.837797	+	0.545982i	$0.816157\pi$
$420$		0			0
$421$	114.370	−	114.370i	0.271664	−	0.271664i	−0.558106	−	0.829770i	$-0.688472\pi$
$421$	114.370	−	114.370i	0.271664	−	0.271664i	0.829770	+	0.558106i	$0.188472\pi$
$422$		0			0
$423$	−383.358	+	102.720i	−0.906284	+	0.242838i
$424$		0			0
$425$	185.447	−	321.203i	0.436345	−	0.755772i
$426$		0			0
$427$	5.97003	−	22.2804i	0.0139813	−	0.0521790i
$428$		0			0
$429$	−189.577	+	291.228i	−0.441905	+	0.678853i
$430$		0			0
$431$	476.518	+	127.683i	1.10561	+	0.296247i	0.765047	−	0.643975i	$-0.222716\pi$
$431$	476.518	+	127.683i	1.10561	+	0.296247i	0.340563	+	0.940222i	$0.389382\pi$
$432$		0			0
$433$	479.798	+	277.012i	1.10808	+	0.639750i	0.938331	−	0.345738i	$-0.112371\pi$
$433$	479.798	+	277.012i	1.10808	+	0.639750i	0.169748	+	0.985488i	$0.445705\pi$
$434$		0			0
$435$	162.757	+	607.417i	0.374154	+	1.39636i
$436$		0			0
$437$	−39.5461	−	39.5461i	−0.0904945	−	0.0904945i
$438$		0			0
$439$	−216.740	+	125.135i	−0.493712	+	0.285045i	−0.726113	−	0.687575i	$-0.758675\pi$
$439$	−216.740	+	125.135i	−0.493712	+	0.285045i	0.232401	+	0.972620i	$0.425342\pi$
$440$		0			0
$441$			250.881i			0.568891i
$442$		0			0
$443$	351.926			0.794415			0.397207	−	0.917729i	$-0.369979\pi$
$443$	351.926			0.794415			0.397207	+	0.917729i	$0.369979\pi$
$444$		0			0
$445$	56.4056	+	97.6973i	0.126754	+	0.219545i
$446$		0			0
$447$	−247.518	+	247.518i	−0.553732	+	0.553732i
$448$		0			0
$449$	−230.991	+	61.8939i	−0.514457	+	0.137848i	−0.506701	−	0.862122i	$-0.669135\pi$
$449$	−230.991	+	61.8939i	−0.514457	+	0.137848i	−0.00775542	+	0.999970i	$0.502469\pi$
$450$		0			0
$451$	−76.6567	+	132.773i	−0.169970	+	0.294398i
$452$		0			0
$453$	−13.6636	+	50.9933i	−0.0301625	+	0.112568i
$454$		0			0
$455$	−7.62100	−	36.0471i	−0.0167494	−	0.0792244i
$456$		0			0
$457$	−595.464	−	159.554i	−1.30298	−	0.349133i	−0.460406	−	0.887708i	$-0.652296\pi$
$457$	−595.464	−	159.554i	−1.30298	−	0.349133i	−0.842578	+	0.538575i	$0.818963\pi$
$458$		0			0
$459$	342.927	+	197.989i	0.747117	+	0.431348i
$460$		0			0
$461$	58.2997	+	217.577i	0.126464	+	0.471968i	0.999888	−	0.0149920i	$-0.00477229\pi$
$461$	58.2997	+	217.577i	0.126464	+	0.471968i	−0.873424	+	0.486960i	$0.838106\pi$
$462$		0			0
$463$	−31.6428	−	31.6428i	−0.0683430	−	0.0683430i	0.672109	−	0.740452i	$-0.265389\pi$
$463$	−31.6428	−	31.6428i	−0.0683430	−	0.0683430i	−0.740452	+	0.672109i	$0.765389\pi$
$464$		0			0
$465$	−606.561	+	350.198i	−1.30443	+	0.753114i
$466$		0			0
$467$			228.839i			0.490018i	0.969521	+	0.245009i	$0.0787910\pi$
$467$			228.839i			0.490018i	−0.969521	+	0.245009i	$0.921209\pi$
$468$		0			0
$469$	−41.1594			−0.0877598
$470$		0			0
$471$	−97.9143	−	169.593i	−0.207886	−	0.360069i
$472$		0			0
$473$	572.066	−	572.066i	1.20944	−	1.20944i
$474$		0			0
$475$	−84.8134	+	22.7257i	−0.178555	+	0.0478436i
$476$		0			0
$477$	−162.716	+	281.832i	−0.341123	+	0.590842i
$478$		0			0
$479$	159.775	−	596.288i	0.333559	−	1.24486i	−0.571863	−	0.820349i	$-0.693779\pi$
$479$	159.775	−	596.288i	0.333559	−	1.24486i	0.905423	−	0.424511i	$-0.139554\pi$
$480$		0			0
$481$	218.101	+	429.203i	0.453432	+	0.892314i
$482$		0			0
$483$	−12.4872	−	3.34595i	−0.0258535	−	0.00692743i
$484$		0			0
$485$	−89.3054	−	51.5605i	−0.184135	−	0.106310i
$486$		0			0
$487$	−133.652	−	498.797i	−0.274440	−	1.02422i	−0.956216	−	0.292663i	$-0.905459\pi$
$487$	−133.652	−	498.797i	−0.274440	−	1.02422i	0.681776	−	0.731561i	$-0.261208\pi$
$488$		0			0
$489$	46.4497	+	46.4497i	0.0949892	+	0.0949892i
$490$		0			0
$491$	186.731	−	107.809i	0.380307	−	0.219571i	−0.297645	−	0.954677i	$-0.596201\pi$
$491$	186.731	−	107.809i	0.380307	−	0.219571i	0.677952	+	0.735106i	$0.262868\pi$
$492$		0			0
$493$			638.258i			1.29464i
$494$		0			0
$495$	−498.980			−1.00804
$496$		0			0
$497$	−15.1644	−	26.2655i	−0.0305119	−	0.0528482i
$498$		0			0
$499$	81.3789	−	81.3789i	0.163084	−	0.163084i	−0.620847	−	0.783931i	$-0.713211\pi$
$499$	81.3789	−	81.3789i	0.163084	−	0.163084i	0.783931	+	0.620847i	$0.213211\pi$
$500$		0			0
$501$	−38.4297	+	10.2972i	−0.0767059	+	0.0205533i
$502$		0			0
$503$	−245.576	+	425.350i	−0.488223	+	0.845627i	−0.999908	−	0.0135460i	$-0.995688\pi$
$503$	−245.576	+	425.350i	−0.488223	+	0.845627i	0.511685	+	0.859173i	$0.329021\pi$
$504$		0			0
$505$	−0.710288	+	2.65083i	−0.00140651	+	0.00524917i
$506$		0			0
$507$	303.757	−	134.449i	0.599126	−	0.265185i
$508$		0			0
$509$	−731.107	−	195.900i	−1.43636	−	0.384871i	−0.545102	−	0.838369i	$-0.683509\pi$
$509$	−731.107	−	195.900i	−1.43636	−	0.384871i	−0.891257	+	0.453498i	$0.850176\pi$
$510$		0			0
$511$	26.0115	+	15.0177i	0.0509031	+	0.0293889i
$512$		0			0
$513$	−24.2627	−	90.5495i	−0.0472957	−	0.176510i
$514$		0			0
$515$	51.3562	+	51.3562i	0.0997208	+	0.0997208i
$516$		0			0
$517$	−909.995	+	525.386i	−1.76015	+	1.01622i
$518$		0			0
$519$		−	209.985i		−	0.404595i
$520$		0			0
$521$	−493.093			−0.946436			−0.473218	−	0.880945i	$-0.656908\pi$
$521$	−493.093			−0.946436			−0.473218	+	0.880945i	$0.656908\pi$
$522$		0			0
$523$	−295.949	−	512.598i	−0.565867	−	0.980111i	−0.996968	−	0.0778071i	$-0.975208\pi$
$523$	−295.949	−	512.598i	−0.565867	−	0.980111i	0.431101	−	0.902304i	$-0.358125\pi$
$524$		0			0
$525$	−14.3519	+	14.3519i	−0.0273370	+	0.0273370i
$526$		0			0
$527$	−686.658	+	183.989i	−1.30296	+	0.349126i
$528$		0			0
$529$	−127.100	+	220.144i	−0.240265	+	0.416151i
$530$		0			0
$531$	−42.8562	+	159.942i	−0.0807086	+	0.301208i
$532$		0			0
$533$	130.656	−	66.3931i	0.245132	−	0.124565i
$534$		0			0
$535$	389.529	+	104.374i	0.728091	+	0.195091i
$536$		0			0
$537$	−485.789	−	280.471i	−0.904636	−	0.522292i
$538$		0			0
$539$	171.914	+	641.593i	0.318950	+	1.19034i
$540$		0			0
$541$	359.655	+	359.655i	0.664796	+	0.664796i	0.956507	−	0.291710i	$-0.0942243\pi$
$541$	359.655	+	359.655i	0.664796	+	0.664796i	−0.291710	+	0.956507i	$0.594224\pi$
$542$		0			0
$543$	−487.675	+	281.559i	−0.898112	+	0.518525i
$544$		0			0
$545$		−	870.406i		−	1.59707i
$546$		0			0
$547$	−279.253			−0.510517			−0.255258	−	0.966873i	$-0.582161\pi$
$547$	−279.253			−0.510517			−0.255258	+	0.966873i	$0.582161\pi$
$548$		0			0
$549$	149.312	+	258.615i	0.271970	+	0.471066i
$550$		0			0
$551$	106.845	−	106.845i	0.193911	−	0.193911i
$552$		0			0
$553$	49.8171	−	13.3484i	0.0900851	−	0.0241382i
$554$		0			0
$555$	259.988	−	450.313i	0.468447	−	0.811374i
$556$		0			0
$557$	219.899	−	820.673i	0.394791	−	1.47338i	−0.427344	−	0.904089i	$-0.640551\pi$
$557$	219.899	−	820.673i	0.394791	−	1.47338i	0.822135	−	0.569292i	$-0.192783\pi$
$558$		0			0
$559$	−756.646	+	159.968i	−1.35357	+	0.286169i
$560$		0			0
$561$	367.950	+	98.5919i	0.655882	+	0.175743i
$562$		0			0
$563$	−8.83856	−	5.10294i	−0.0156990	−	0.00906384i	0.492130	−	0.870522i	$-0.336218\pi$
$563$	−8.83856	−	5.10294i	−0.0156990	−	0.00906384i	−0.507829	+	0.861458i	$0.669552\pi$
$564$		0			0
$565$	−123.873	−	462.301i	−0.219244	−	0.818231i
$566$		0			0
$567$	−2.35309	−	2.35309i	−0.00415008	−	0.00415008i
$568$		0			0
$569$	463.691	−	267.712i	0.814923	−	0.470496i	−0.0337397	−	0.999431i	$-0.510742\pi$
$569$	463.691	−	267.712i	0.814923	−	0.470496i	0.848663	+	0.528935i	$0.177408\pi$
$570$		0			0
$571$		−	80.7627i		−	0.141441i	−0.997496	−	0.0707204i	$-0.977470\pi$
$571$		−	80.7627i		−	0.141441i	0.997496	−	0.0707204i	$-0.0225298\pi$
$572$		0			0
$573$	−94.4018			−0.164750
$574$		0			0
$575$	−215.719	−	373.636i	−0.375163	−	0.649802i
$576$		0			0
$577$	−315.472	+	315.472i	−0.546746	+	0.546746i	−0.925498	−	0.378752i	$-0.876353\pi$
$577$	−315.472	+	315.472i	−0.546746	+	0.546746i	0.378752	+	0.925498i	$0.376353\pi$
$578$		0			0
$579$	103.889	−	27.8370i	0.179429	−	0.0480778i
$580$		0			0
$581$	13.6582	−	23.6567i	0.0235081	−	0.0407173i
$582$		0			0
$583$	−222.999	+	832.244i	−0.382503	+	1.42752i
$584$		0			0
$585$	399.754	+	260.223i	0.683340	+	0.444826i
$586$		0			0
$587$	−1034.86	−	277.289i	−1.76296	−	0.472383i	−0.775645	−	0.631169i	$-0.782575\pi$
$587$	−1034.86	−	277.289i	−1.76296	−	0.472383i	−0.987313	+	0.158786i	$0.949242\pi$
$588$		0			0
$589$	145.747	+	84.1470i	0.247448	+	0.142864i
$590$		0			0
$591$	114.001	+	425.456i	0.192895	+	0.719892i
$592$		0			0
$593$	−83.2716	−	83.2716i	−0.140424	−	0.140424i	0.633400	−	0.773824i	$-0.281659\pi$
$593$	−83.2716	−	83.2716i	−0.140424	−	0.140424i	−0.773824	+	0.633400i	$0.781659\pi$
$594$		0			0
$595$	−34.9777	+	20.1944i	−0.0587861	+	0.0339402i
$596$		0			0
$597$		−	315.936i		−	0.529206i
$598$		0			0
$599$	816.105			1.36244			0.681222	−	0.732076i	$-0.261449\pi$
$599$	816.105			1.36244			0.681222	+	0.732076i	$0.261449\pi$
$600$		0			0
$601$	−134.337	−	232.679i	−0.223523	−	0.387152i	0.732353	−	0.680926i	$-0.238422\pi$
$601$	−134.337	−	232.679i	−0.223523	−	0.387152i	−0.955875	+	0.293773i	$0.905089\pi$
$602$		0			0
$603$	376.788	−	376.788i	0.624856	−	0.624856i
$604$		0			0
$605$	−441.187	+	118.216i	−0.729234	+	0.195398i
$606$		0			0
$607$	−77.2134	+	133.737i	−0.127205	+	0.220325i	−0.922593	−	0.385776i	$-0.873934\pi$
$607$	−77.2134	+	133.737i	−0.127205	+	0.220325i	0.795388	+	0.606101i	$0.207267\pi$
$608$		0			0
$609$	9.04000	−	33.7378i	0.0148440	−	0.0553986i
$610$		0			0
$611$	1003.03	+	53.6629i	1.64162	+	0.0878279i
$612$		0			0
$613$	156.303	+	41.8812i	0.254980	+	0.0683218i	0.384045	−	0.923314i	$-0.374531\pi$
$613$	156.303	+	41.8812i	0.254980	+	0.0683218i	−0.129065	+	0.991636i	$0.541197\pi$
$614$		0			0
$615$	−137.082	−	79.1441i	−0.222897	−	0.128690i
$616$		0			0
$617$	224.930	+	839.450i	0.364554	+	1.36054i	0.868024	+	0.496523i	$0.165390\pi$
$617$	224.930	+	839.450i	0.364554	+	1.36054i	−0.503469	+	0.864013i	$0.667943\pi$
$618$		0			0
$619$	169.456	+	169.456i	0.273757	+	0.273757i	0.830611	−	0.556854i	$-0.187992\pi$
$619$	169.456	+	169.456i	0.273757	+	0.273757i	−0.556854	+	0.830611i	$0.687992\pi$
$620$		0			0
$621$	398.906	−	230.308i	0.642360	−	0.370867i
$622$		0			0
$623$		−	6.26587i		−	0.0100576i
$624$		0			0
$625$	598.293			0.957268
$626$		0			0
$627$	−45.0907	−	78.0994i	−0.0719150	−	0.124560i
$628$		0			0
$629$	373.183	−	373.183i	0.593295	−	0.593295i
$630$		0			0
$631$	−1034.16	+	277.102i	−1.63892	+	0.439147i	−0.956480	−	0.291797i	$-0.905747\pi$
$631$	−1034.16	+	277.102i	−1.63892	+	0.439147i	−0.682438	+	0.730943i	$0.739080\pi$
$632$		0			0
$633$	−330.612	+	572.638i	−0.522295	+	0.904641i
$634$		0			0
$635$	26.1708	−	97.6709i	0.0412139	−	0.153812i
$636$		0			0
$637$	196.869	−	603.663i	0.309057	−	0.947665i
$638$		0			0
$639$	379.265	+	101.624i	0.593529	+	0.159036i
$640$		0			0
$641$	−325.961	−	188.193i	−0.508519	−	0.293594i	0.223706	−	0.974657i	$-0.428185\pi$
$641$	−325.961	−	188.193i	−0.508519	−	0.293594i	−0.732225	+	0.681063i	$0.761518\pi$
$642$		0			0
$643$	151.996	+	567.258i	0.236386	+	0.882205i	0.977519	+	0.210847i	$0.0676221\pi$
$643$	151.996	+	567.258i	0.236386	+	0.882205i	−0.741133	+	0.671358i	$0.765711\pi$
$644$		0			0
$645$	590.629	+	590.629i	0.915704	+	0.915704i
$646$		0			0
$647$	538.312	−	310.795i	0.832013	−	0.480363i	−0.0225284	−	0.999746i	$-0.507172\pi$
$647$	538.312	−	310.795i	0.832013	−	0.480363i	0.854541	+	0.519383i	$0.173838\pi$
$648$		0			0
$649$			438.395i			0.675493i
$650$		0			0
$651$	38.9021			0.0597574
$652$		0			0
$653$	−215.178	−	372.699i	−0.329522	−	0.570749i	0.652895	−	0.757448i	$-0.273554\pi$
$653$	−215.178	−	372.699i	−0.329522	−	0.570749i	−0.982417	+	0.186700i	$0.940221\pi$
$654$		0			0
$655$	677.686	−	677.686i	1.03463	−	1.03463i
$656$		0			0
$657$	−375.597	+	100.641i	−0.571685	+	0.153182i
$658$		0			0
$659$	−100.548	+	174.154i	−0.152576	+	0.264269i	−0.932174	−	0.362011i	$-0.882090\pi$
$659$	−100.548	+	174.154i	−0.152576	+	0.264269i	0.779598	+	0.626281i	$0.215424\pi$
$660$		0			0
$661$	−143.054	+	533.885i	−0.216421	+	0.807693i	0.769241	+	0.638959i	$0.220635\pi$
$661$	−143.054	+	533.885i	−0.216421	+	0.807693i	−0.985662	+	0.168734i	$0.946032\pi$
$662$		0			0
$663$	−243.364	−	270.876i	−0.367065	−	0.408561i
$664$		0			0
$665$	9.23585	+	2.47474i	0.0138885	+	0.00372141i
$666$		0			0
$667$	642.978	+	371.223i	0.963985	+	0.556557i
$668$		0			0
$669$	30.8488	+	115.129i	0.0461118	+	0.172092i
$670$		0			0
$671$	559.057	+	559.057i	0.833170	+	0.833170i
$672$		0			0
$673$	−530.404	+	306.229i	−0.788119	+	0.455021i	−0.839300	−	0.543669i	$-0.817035\pi$
$673$	−530.404	+	306.229i	−0.788119	+	0.455021i	0.0511810	+	0.998689i	$0.483701\pi$
$674$		0			0
$675$		−	723.173i		−	1.07137i
$676$		0			0
$677$	271.670			0.401285			0.200642	−	0.979665i	$-0.435697\pi$
$677$	271.670			0.401285			0.200642	+	0.979665i	$0.435697\pi$
$678$		0			0
$679$	2.86383	+	4.96029i	0.00421771	+	0.00730529i
$680$		0			0
$681$	79.5042	−	79.5042i	0.116746	−	0.116746i
$682$		0			0
$683$	1125.63	−	301.611i	1.64806	−	0.441597i	0.688993	−	0.724768i	$-0.258053\pi$
$683$	1125.63	−	301.611i	1.64806	−	0.441597i	0.959069	+	0.283171i	$0.0913864\pi$
$684$		0			0
$685$	−225.866	+	391.212i	−0.329732	+	0.571112i
$686$		0			0
$687$	72.3270	−	269.928i	0.105279	−	0.392908i
$688$		0			0
$689$	612.678	−	550.450i	0.889228	−	0.798911i
$690$		0			0
$691$	−522.444	−	139.988i	−0.756069	−	0.202588i	−0.139861	−	0.990171i	$-0.544666\pi$
$691$	−522.444	−	139.988i	−0.756069	−	0.202588i	−0.616209	+	0.787583i	$0.711332\pi$
$692$		0			0
$693$	24.0017	+	13.8574i	0.0346345	+	0.0199963i
$694$		0			0
$695$	−497.657	−	1857.28i	−0.716053	−	2.67235i
$696$		0			0
$697$	−113.602	−	113.602i	−0.162987	−	0.162987i
$698$		0			0
$699$	−624.405	+	360.501i	−0.893284	+	0.515738i
$700$		0			0
$701$			349.407i			0.498441i	0.968447	+	0.249221i	$0.0801744\pi$
$701$			349.407i			0.498441i	−0.968447	+	0.249221i	$0.919826\pi$
$702$		0			0
$703$	−124.942			−0.177727
$704$		0			0
$705$	−542.434	−	939.524i	−0.769410	−	1.33266i
$706$		0			0
$707$	0.107784	−	0.107784i	0.000152452	−	0.000152452i
$708$		0			0
$709$	−857.862	+	229.863i	−1.20996	+	0.324208i	−0.806746	−	0.590898i	$-0.798774\pi$
$709$	−857.862	+	229.863i	−1.20996	+	0.324208i	−0.403214	+	0.915106i	$0.632107\pi$
$710$		0			0
$711$	−333.847	+	578.240i	−0.469546	+	0.813278i
$712$		0			0
$713$	−214.024	+	798.748i	−0.300174	+	1.12026i
$714$		0			0
$715$	1200.63	+	391.555i	1.67920	+	0.547630i
$716$		0			0
$717$	−41.3529	−	11.0805i	−0.0576750	−	0.0154540i
$718$		0			0
$719$	−1101.34	−	635.861i	−1.53177	−	0.884369i	−0.999280	−	0.0379340i	$-0.987922\pi$
$719$	−1101.34	−	635.861i	−1.53177	−	0.884369i	−0.532492	−	0.846435i	$-0.678744\pi$
$720$		0			0
$721$	−1.04408	−	3.89656i	−0.00144810	−	0.00540438i
$722$		0			0
$723$	220.510	+	220.510i	0.304994	+	0.304994i
$724$		0			0
$725$	1009.48	−	582.824i	1.39239	−	0.803896i
$726$		0			0
$727$		−	215.990i		−	0.297098i	−0.988905	−	0.148549i	$-0.952540\pi$
$727$		−	215.990i		−	0.297098i	0.988905	−	0.148549i	$-0.0474603\pi$
$728$		0			0
$729$	534.627			0.733371
$730$		0			0
$731$	423.890	+	734.199i	0.579877	+	1.00438i
$732$		0			0
$733$	367.788	−	367.788i	0.501757	−	0.501757i	−0.410227	−	0.911984i	$-0.634550\pi$
$733$	367.788	−	367.788i	0.501757	−	0.501757i	0.911984	+	0.410227i	$0.134550\pi$
$734$		0			0
$735$	−662.412	+	177.493i	−0.901241	+	0.241487i
$736$		0			0
$737$	705.391	−	1221.77i	0.957111	−	1.65777i
$738$		0			0
$739$	128.451	−	479.386i	0.173817	−	0.648695i	−0.822933	−	0.568139i	$-0.807664\pi$
$739$	128.451	−	479.386i	0.173817	−	0.648695i	0.996750	−	0.0805562i	$-0.0256696\pi$
$740$		0			0
$741$	−4.60556	+	86.0840i	−0.00621532	+	0.116173i
$742$		0			0
$743$	77.8650	+	20.8639i	0.104798	+	0.0280806i	0.310837	−	0.950463i	$-0.399391\pi$
$743$	77.8650	+	20.8639i	0.104798	+	0.0280806i	−0.206039	+	0.978544i	$0.566057\pi$
$744$		0			0
$745$	1101.69	+	636.062i	1.47878	+	0.853774i
$746$		0			0
$747$	91.5301	+	341.595i	0.122530	+	0.457289i
$748$		0			0
$749$	−15.8384	−	15.8384i	−0.0211460	−	0.0211460i
$750$		0			0
$751$	−88.7495	+	51.2396i	−0.118175	+	0.0682284i	−0.557922	−	0.829893i	$-0.688401\pi$
$751$	−88.7495	+	51.2396i	−0.118175	+	0.0682284i	0.439747	+	0.898122i	$0.355068\pi$
$752$		0			0
$753$		−	531.244i		−	0.705503i
$754$		0			0
$755$	191.856			0.254114
$756$		0			0
$757$	−502.999	−	871.219i	−0.664463	−	1.15088i	−0.979431	−	0.201781i	$-0.935327\pi$
$757$	−502.999	−	871.219i	−0.664463	−	1.15088i	0.314967	−	0.949102i	$-0.398006\pi$
$758$		0			0
$759$	313.328	−	313.328i	0.412817	−	0.412817i
$760$		0			0
$761$	−634.206	+	169.935i	−0.833386	+	0.223305i	−0.650190	−	0.759772i	$-0.725311\pi$
$761$	−634.206	+	169.935i	−0.833386	+	0.223305i	−0.183195	+	0.983077i	$0.558644\pi$
$762$		0			0
$763$	−24.1725	+	41.8679i	−0.0316808	+	0.0548728i
$764$		0			0
$765$	135.332	−	505.066i	0.176905	−	0.660217i
$766$		0			0
$767$	228.628	−	351.217i	0.298080	−	0.457910i
$768$		0			0
$769$	542.013	+	145.232i	0.704828	+	0.188858i	0.593392	−	0.804914i	$-0.297788\pi$
$769$	542.013	+	145.232i	0.704828	+	0.188858i	0.111436	+	0.993772i	$0.464455\pi$
$770$		0			0
$771$	416.634	+	240.544i	0.540381	+	0.311989i
$772$		0			0
$773$	−26.8805	−	100.319i	−0.0347742	−	0.129779i	0.946357	−	0.323124i	$-0.104733\pi$
$773$	−26.8805	−	100.319i	−0.0347742	−	0.129779i	−0.981131	+	0.193345i	$0.938066\pi$
$774$		0			0
$775$	918.022	+	918.022i	1.18454	+	1.18454i
$776$		0			0
$777$	−25.0117	+	14.4405i	−0.0321901	+	0.0185850i
$778$		0			0
$779$			38.0341i			0.0488243i
$780$		0			0
$781$	1039.55			1.33105
$782$		0			0
$783$	622.242	+	1077.75i	0.794689	+	1.37644i
$784$		0			0
$785$	−503.232	+	503.232i	−0.641060	+	0.641060i
$786$		0			0
$787$	−485.028	+	129.963i	−0.616300	+	0.165137i	−0.553445	−	0.832885i	$-0.686687\pi$
$787$	−485.028	+	129.963i	−0.616300	+	0.165137i	−0.0628551	+	0.998023i	$0.520021\pi$
$788$		0			0
$789$	−51.1885	+	88.6611i	−0.0648777	+	0.112371i
$790$		0			0
$791$	−6.88028	+	25.6776i	−0.00869821	+	0.0324622i
$792$		0			0
$793$	−156.330	−	739.439i	−0.197138	−	0.932457i
$794$		0			0
$795$	−859.249	−	230.235i	−1.08082	−	0.289604i
$796$		0			0
$797$	957.425	+	552.769i	1.20129	+	0.693563i	0.960841	−	0.277100i	$-0.0893734\pi$
$797$	957.425	+	552.769i	1.20129	+	0.693563i	0.240445	+	0.970663i	$0.422707\pi$
$798$		0			0
$799$	−284.988	−	1063.59i	−0.356681	−	1.33115i
$800$		0			0
$801$	57.3601	+	57.3601i	0.0716106	+	0.0716106i
$802$		0			0
$803$	−891.572	+	514.749i	−1.11030	+	0.641033i
$804$		0			0
$805$			46.9819i			0.0583626i
$806$		0			0
$807$	109.072			0.135158
$808$		0			0
$809$	636.533	+	1102.51i	0.786815	+	1.36280i	0.927909	+	0.372807i	$0.121605\pi$
$809$	636.533	+	1102.51i	0.786815	+	1.36280i	−0.141094	+	0.989996i	$0.545062\pi$
$810$		0			0
$811$	−242.696	+	242.696i	−0.299256	+	0.299256i	−0.840722	−	0.541467i	$-0.817869\pi$
$811$	−242.696	+	242.696i	−0.299256	+	0.299256i	0.541467	+	0.840722i	$0.317869\pi$
$812$		0			0
$813$	−394.962	+	105.830i	−0.485808	+	0.130172i
$814$		0			0
$815$	119.365	−	206.745i	0.146460	−	0.253675i
$816$		0			0
$817$	51.9459	−	193.865i	0.0635813	−	0.237289i
$818$		0			0
$819$	−12.0020	−	23.6189i	−0.0146545	−	0.0288387i
$820$		0			0
$821$	553.739	+	148.374i	0.674469	+	0.180723i	0.579767	−	0.814782i	$-0.303144\pi$
$821$	553.739	+	148.374i	0.674469	+	0.180723i	0.0947017	+	0.995506i	$0.469810\pi$
$822$		0			0
$823$	912.674	+	526.933i	1.10896	+	0.640259i	0.938560	−	0.345116i	$-0.112161\pi$
$823$	912.674	+	526.933i	1.10896	+	0.640259i	0.170401	+	0.985375i	$0.445494\pi$
$824$		0			0
$825$	−180.058	−	671.986i	−0.218252	−	0.814529i
$826$		0			0
$827$	−1026.38	−	1026.38i	−1.24109	−	1.24109i	−0.959548	−	0.281547i	$-0.909153\pi$
$827$	−1026.38	−	1026.38i	−1.24109	−	1.24109i	−0.281547	−	0.959548i	$-0.590847\pi$
$828$		0			0
$829$	515.278	−	297.496i	0.621565	−	0.358861i	−0.155913	−	0.987771i	$-0.549832\pi$
$829$	515.278	−	297.496i	0.621565	−	0.358861i	0.777478	+	0.628910i	$0.216499\pi$
$830$		0			0
$831$		−	316.061i		−	0.380338i
$832$		0			0
$833$	−696.045			−0.835588
$834$		0			0
$835$	72.2937	+	125.216i	0.0865792	+	0.149960i
$836$		0			0
$837$	−980.110	+	980.110i	−1.17098	+	1.17098i
$838$		0			0
$839$	330.829	−	88.6454i	0.394314	−	0.105656i	−0.0562135	−	0.998419i	$-0.517903\pi$
$839$	330.829	−	88.6454i	0.394314	−	0.105656i	0.450527	+	0.892763i	$0.351236\pi$
$840$		0			0
$841$	−582.462	+	1008.85i	−0.692583	+	1.19959i
$842$		0			0
$843$	95.5742	−	356.688i	0.113374	−	0.423117i
$844$		0			0
$845$	−757.676	−	939.833i	−0.896658	−	1.11223i
$846$		0			0
$847$	24.5048	+	6.56605i	0.0289313	+	0.00775212i
$848$		0			0
$849$	−429.528	−	247.988i	−0.505923	−	0.292095i
$850$		0			0
$851$	−158.892	−	592.993i	−0.186712	−	0.696819i
$852$		0			0
$853$	−1098.53	−	1098.53i	−1.28784	−	1.28784i	−0.936094	−	0.351749i	$-0.885587\pi$
$853$	−1098.53	−	1098.53i	−1.28784	−	1.28784i	−0.351749	−	0.936094i	$-0.614413\pi$
$854$		0			0
$855$	−107.203	+	61.8937i	−0.125384	+	0.0723903i
$856$		0			0
$857$		−	513.231i		−	0.598870i	−0.954117	−	0.299435i	$-0.903202\pi$
$857$		−	513.231i		−	0.598870i	0.954117	−	0.299435i	$-0.0967981\pi$
$858$		0			0
$859$	−454.733			−0.529375			−0.264687	−	0.964334i	$-0.585269\pi$
$859$	−454.733			−0.529375			−0.264687	+	0.964334i	$0.585269\pi$
$860$		0			0
$861$	4.39590	+	7.61393i	0.00510558	+	0.00884312i
$862$		0			0
$863$	477.014	−	477.014i	0.552739	−	0.552739i	−0.374491	−	0.927230i	$-0.622183\pi$
$863$	477.014	−	477.014i	0.552739	−	0.552739i	0.927230	+	0.374491i	$0.122183\pi$
$864$		0			0
$865$	−737.122	+	197.511i	−0.852164	+	0.228337i
$866$		0			0
$867$	84.4362	−	146.248i	0.0973889	−	0.168683i
$868$		0			0
$869$	−457.532	+	1707.53i	−0.526504	+	1.96494i
$870$		0			0
$871$	−1202.29	+	610.946i	−1.38035	+	0.701430i
$872$		0			0
$873$	−71.6249	−	19.1918i	−0.0820445	−	0.0219838i
$874$		0			0
$875$	2.51868	+	1.45416i	0.00287849	+	0.00166190i
$876$		0			0
$877$	199.068	+	742.933i	0.226988	+	0.847130i	0.981598	+	0.190957i	$0.0611592\pi$
$877$	199.068	+	742.933i	0.226988	+	0.847130i	−0.754610	+	0.656173i	$0.772174\pi$
$878$		0			0
$879$	413.422	+	413.422i	0.470332	+	0.470332i
$880$		0			0
$881$	−623.881	+	360.198i	−0.708151	+	0.408851i	−0.810376	−	0.585910i	$-0.800737\pi$
$881$	−623.881	+	360.198i	−0.708151	+	0.408851i	0.102225	+	0.994761i	$0.467404\pi$
$882$		0			0
$883$		−	1193.49i		−	1.35163i	−0.737073	−	0.675813i	$-0.763793\pi$
$883$		−	1193.49i		−	1.35163i	0.737073	−	0.675813i	$-0.236207\pi$
$884$		0			0
$885$	−452.621			−0.511436
$886$		0			0
$887$	664.890	+	1151.62i	0.749595	+	1.29834i	0.948017	+	0.318219i	$0.103085\pi$
$887$	664.890	+	1151.62i	0.749595	+	1.29834i	−0.198423	+	0.980117i	$0.563582\pi$
$888$		0			0
$889$	−3.97133	+	3.97133i	−0.00446719	+	0.00446719i
$890$		0			0
$891$	110.177	−	29.5217i	0.123655	−	0.0331333i
$892$		0			0
$893$	−130.338	+	225.753i	−0.145956	+	0.252802i
$894$		0			0
$895$	−527.620	+	1969.10i	−0.589519	+	2.20012i
$896$		0			0
$897$	−414.424	+	87.6166i	−0.462012	+	0.0976774i
$898$		0			0
$899$	−2158.04	−	578.245i	−2.40049	−	0.643209i
$900$		0			0
$901$	−781.915	−	451.439i	−0.867830	−	0.501042i
$902$		0			0
$903$	−12.0076	−	44.8129i	−0.0132974	−	0.0496267i
$904$		0			0
$905$	1447.08	+	1447.08i	1.59898	+	1.59898i
$906$		0			0
$907$	466.237	−	269.182i	0.514043	−	0.296783i	−0.220451	−	0.975398i	$-0.570753\pi$
$907$	466.237	−	269.182i	0.514043	−	0.296783i	0.734494	+	0.678615i	$0.237420\pi$
$908$		0			0
$909$			1.97338i			0.00217094i
$910$		0			0
$911$	1029.58			1.13016			0.565080	−	0.825036i	$-0.308845\pi$
$911$	1029.58			1.13016			0.565080	+	0.825036i	$0.308845\pi$
$912$		0			0
$913$	468.151	+	810.861i	0.512761	+	0.888128i
$914$		0			0
$915$	−577.198	+	577.198i	−0.630817	+	0.630817i
$916$		0			0
$917$	−51.4182	+	13.7775i	−0.0560721	+	0.0150245i
$918$		0			0
$919$	−108.919	+	188.653i	−0.118519	+	0.205280i	−0.919181	−	0.393836i	$-0.871148\pi$
$919$	−108.919	+	188.653i	−0.118519	+	0.205280i	0.800662	+	0.599116i	$0.204481\pi$
$920$		0			0
$921$	277.459	−	1035.49i	0.301258	−	1.12431i
$922$		0			0
$923$	−832.831	−	542.138i	−0.902309	−	0.587365i
$924$		0			0
$925$	−931.005	−	249.462i	−1.00649	−	0.269689i
$926$		0			0
$927$	45.2284	+	26.1126i	0.0487901	+	0.0281690i
$928$		0			0
$929$	−165.737	−	618.540i	−0.178404	−	0.665813i	−0.995947	−	0.0899448i	$-0.971331\pi$
$929$	−165.737	−	618.540i	−0.178404	−	0.665813i	0.817543	−	0.575868i	$-0.195336\pi$
$930$		0			0
$931$	116.518	+	116.518i	0.125154	+	0.125154i
$932$		0			0
$933$	−156.545	+	90.3812i	−0.167787	+	0.0968716i
$934$		0			0
$935$		−	1384.37i		−	1.48061i
$936$		0			0
$937$	676.936			0.722450			0.361225	−	0.932479i	$-0.382359\pi$
$937$	676.936			0.722450			0.361225	+	0.932479i	$0.382359\pi$
$938$		0			0
$939$	−318.916	−	552.379i	−0.339634	−	0.588263i
$940$		0			0
$941$	−965.935	+	965.935i	−1.02650	+	1.02650i	−0.0268595	+	0.999639i	$0.508551\pi$
$941$	−965.935	+	965.935i	−1.02650	+	1.02650i	−0.999639	+	0.0268595i	$0.991449\pi$
$942$		0			0
$943$	−180.516	+	48.3690i	−0.191427	+	0.0512927i
$944$		0			0
$945$	−39.3753	+	68.2001i	−0.0416670	+	0.0721694i
$946$		0			0
$947$	−452.017	+	1686.95i	−0.477314	+	1.78136i	0.135108	+	0.990831i	$0.456862\pi$
$947$	−452.017	+	1686.95i	−0.477314	+	1.78136i	−0.612422	+	0.790531i	$0.709805\pi$
$948$		0			0
$949$	982.724	+	52.5764i	1.03554	+	0.0554019i
$950$		0			0
$951$	336.907	+	90.2740i	0.354266	+	0.0949253i
$952$		0			0
$953$	−282.434	−	163.063i	−0.296363	−	0.171105i	0.344445	−	0.938807i	$-0.388067\pi$
$953$	−282.434	−	163.063i	−0.296363	−	0.171105i	−0.640808	+	0.767701i	$0.721400\pi$
$954$		0			0
$955$	88.7940	+	331.384i	0.0929780	+	0.346999i
$956$		0			0
$957$	846.542	+	846.542i	0.884579	+	0.884579i
$958$		0			0
$959$	21.7291	−	12.5453i	0.0226581	−	0.0130816i
$960$		0			0
$961$		−	1527.38i		−	1.58936i
$962$		0			0
$963$	289.980			0.301122
$964$		0			0
$965$	−195.436	−	338.505i	−0.202524	−	0.350782i
$966$		0			0
$967$	354.860	−	354.860i	0.366970	−	0.366970i	−0.499401	−	0.866371i	$-0.666447\pi$
$967$	354.860	−	354.860i	0.366970	−	0.366970i	0.866371	+	0.499401i	$0.166447\pi$
$968$		0			0
$969$	91.2814	−	24.4588i	0.0942017	−	0.0252413i
$970$		0			0
$971$	−216.415	+	374.842i	−0.222878	+	0.386037i	−0.955681	−	0.294405i	$-0.904879\pi$
$971$	−216.415	+	374.842i	−0.222878	+	0.386037i	0.732802	+	0.680441i	$0.238212\pi$
$972$		0			0
$973$	−27.6414	+	103.159i	−0.0284084	+	0.106022i
$974$		0			0
$975$	−206.196	+	632.259i	−0.211483	+	0.648471i
$976$		0			0
$977$	−708.038	−	189.718i	−0.724707	−	0.194185i	−0.122436	−	0.992476i	$-0.539071\pi$
$977$	−708.038	−	189.718i	−0.724707	−	0.194185i	−0.602271	+	0.798292i	$0.705737\pi$
$978$		0			0
$979$	185.996	+	107.385i	0.189986	+	0.109688i
$980$		0			0
$981$	−161.991	−	604.558i	−0.165128	−	0.616267i
$982$		0			0
$983$	1120.30	+	1120.30i	1.13968	+	1.13968i	0.988508	+	0.151171i	$0.0483044\pi$
$983$	1120.30	+	1120.30i	1.13968	+	1.13968i	0.151171	+	0.988508i	$0.451696\pi$
$984$		0			0
$985$	1386.27	−	800.366i	1.40739	−	0.812554i
$986$		0			0
$987$			60.2569i			0.0610505i
$988$		0			0
$989$	986.171			0.997140
$990$		0			0
$991$	−304.820	−	527.964i	−0.307588	−	0.532759i	0.670246	−	0.742139i	$-0.266189\pi$
$991$	−304.820	−	527.964i	−0.307588	−	0.532759i	−0.977834	+	0.209381i	$0.932855\pi$
$992$		0			0
$993$	−153.070	+	153.070i	−0.154149	+	0.154149i
$994$		0			0
$995$	−1109.05	+	297.169i	−1.11462	+	0.298662i
$996$		0			0
$997$	−35.3004	+	61.1421i	−0.0354066	+	0.0613260i	−0.883186	−	0.469023i	$-0.844606\pi$
$997$	−35.3004	+	61.1421i	−0.0354066	+	0.0613260i	0.847779	+	0.530350i	$0.177939\pi$
$998$		0			0
$999$	266.333	−	993.970i	0.266600	−	0.994965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.bd.e.145.2		8
4.3	odd	2		52.3.k.a.41.1	yes	8
12.11	even	2		468.3.cd.b.145.1		8
13.7	odd	12	inner	208.3.bd.e.33.2		8
52.3	odd	6		676.3.g.d.577.3		8
52.7	even	12		52.3.k.a.33.1	✓	8
52.11	even	12		676.3.g.d.437.3		8
52.15	even	12		676.3.g.c.437.3		8
52.23	odd	6		676.3.g.c.577.3		8
156.59	odd	12		468.3.cd.b.397.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.3.k.a.33.1	✓	8	52.7	even	12
52.3.k.a.41.1	yes	8	4.3	odd	2
208.3.bd.e.33.2		8	13.7	odd	12	inner
208.3.bd.e.145.2		8	1.1	even	1	trivial
468.3.cd.b.145.1		8	12.11	even	2
468.3.cd.b.397.1		8	156.59	odd	12
676.3.g.c.437.3		8	52.15	even	12
676.3.g.c.577.3		8	52.23	odd	6
676.3.g.d.437.3		8	52.11	even	12
676.3.g.d.577.3		8	52.3	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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.bd (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.982786 + 1.70224i) q^{3} +(5.05105 - 5.05105i) q^{5} +(-0.383239 + 0.102689i) q^{7} +(2.56826 - 4.44836i) q^{9} +(3.51976 - 13.1359i) q^{11} +(-9.67036 + 8.68816i) q^{13} +(13.5622 + 3.63397i) q^{15} +(12.3415 + 7.12539i) q^{17} +(-0.873186 - 3.25878i) q^{19} +(-0.551442 - 0.551442i) q^{21} +(14.3562 - 8.28854i) q^{23} -26.0262i q^{25} +27.7864 q^{27} +(22.3938 + 38.7872i) q^{29} +(-35.2730 + 35.2730i) q^{31} +(25.8196 - 6.91835i) q^{33} +(-1.41707 + 2.45444i) q^{35} +(9.58504 - 35.7719i) q^{37} +(-24.2932 - 7.92262i) q^{39} +(-10.8895 - 2.91782i) q^{41} +(51.5199 + 29.7450i) q^{43} +(-9.49646 - 35.4413i) q^{45} +(-54.6357 - 54.6357i) q^{47} +(-42.2989 + 24.4213i) q^{49} +28.0110i q^{51} -63.3563 q^{53} +(-48.5717 - 84.1287i) q^{55} +(4.68905 - 4.68905i) q^{57} +(-31.1381 + 8.34343i) q^{59} +(-29.0686 + 50.3483i) q^{61} +(-0.527462 + 1.96852i) q^{63} +(-4.96111 + 92.7298i) q^{65} +(100.204 + 26.8497i) q^{67} +(28.2181 + 16.2917i) q^{69} +(19.7845 + 73.8369i) q^{71} +(-53.5296 - 53.5296i) q^{73} +(44.3027 - 25.5782i) q^{75} +5.39564i q^{77} -129.990 q^{79} +(4.19371 + 7.26372i) q^{81} +(-48.6837 + 48.6837i) q^{83} +(98.3284 - 26.3470i) q^{85} +(-44.0166 + 76.2390i) q^{87} +(-4.08744 + 15.2545i) q^{89} +(2.81388 - 4.32268i) q^{91} +(-94.7089 - 25.3772i) q^{93} +(-20.8707 - 12.0497i) q^{95} +(-3.73635 - 13.9442i) q^{97} +(-49.3937 - 49.3937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{5} - 4 q^{7} - 6 q^{9} - 24 q^{11} + 18 q^{13} + 60 q^{15} - 54 q^{17} + 50 q^{19} - 54 q^{21} + 24 q^{23} - 36 q^{27} + 108 q^{29} - 176 q^{31} + 114 q^{33} + 30 q^{35} + 104 q^{37} - 120 q^{39}+ \cdots + 182 q^{97}+O(q^{100}) \) 8 * q + 6 * q^5 - 4 * q^7 - 6 * q^9 - 24 * q^11 + 18 * q^13 + 60 * q^15 - 54 * q^17 + 50 * q^19 - 54 * q^21 + 24 * q^23 - 36 * q^27 + 108 * q^29 - 176 * q^31 + 114 * q^33 + 30 * q^35 + 104 * q^37 - 120 * q^39 - 168 * q^41 + 198 * q^43 + 6 * q^45 + 96 * q^47 - 162 * q^49 - 72 * q^53 - 126 * q^55 + 318 * q^57 - 18 * q^61 - 180 * q^63 - 72 * q^65 + 326 * q^67 - 498 * q^69 + 162 * q^71 - 98 * q^73 + 240 * q^75 - 192 * q^79 + 240 * q^81 - 408 * q^83 + 318 * q^85 - 36 * q^87 + 54 * q^89 - 280 * q^91 - 66 * q^93 - 312 * q^95 + 182 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more