LMFDB - Embedded newform 52.3.k.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,3,Mod(33,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([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("52.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	52.k (of order $12$, degree $4$, 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:	$1.41689737467$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.1
Root			$-2.83160 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	52.41
Dual form			52.3.k.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.982786 - 1.70224i) q^{3} +(5.05105 - 5.05105i) q^{5} +(0.383239 - 0.102689i) q^{7} +(2.56826 - 4.44836i) q^{9} +O(q^{10})$	\(q+(-0.982786 - 1.70224i) q^{3} +(5.05105 - 5.05105i) q^{5} +(0.383239 - 0.102689i) q^{7} +(2.56826 - 4.44836i) q^{9} +(-3.51976 + 13.1359i) q^{11} +(-9.67036 + 8.68816i) q^{13} +(-13.5622 - 3.63397i) q^{15} +(12.3415 + 7.12539i) q^{17} +(0.873186 + 3.25878i) q^{19} +(-0.551442 - 0.551442i) q^{21} +(-14.3562 + 8.28854i) q^{23} -26.0262i q^{25} -27.7864 q^{27} +(22.3938 + 38.7872i) q^{29} +(35.2730 - 35.2730i) q^{31} +(25.8196 - 6.91835i) q^{33} +(1.41707 - 2.45444i) q^{35} +(9.58504 - 35.7719i) q^{37} +(24.2932 + 7.92262i) q^{39} +(-10.8895 - 2.91782i) q^{41} +(-51.5199 - 29.7450i) q^{43} +(-9.49646 - 35.4413i) q^{45} +(54.6357 + 54.6357i) q^{47} +(-42.2989 + 24.4213i) q^{49} -28.0110i q^{51} -63.3563 q^{53} +(48.5717 + 84.1287i) q^{55} +(4.68905 - 4.68905i) q^{57} +(31.1381 - 8.34343i) q^{59} +(-29.0686 + 50.3483i) q^{61} +(0.527462 - 1.96852i) q^{63} +(-4.96111 + 92.7298i) q^{65} +(-100.204 - 26.8497i) q^{67} +(28.2181 + 16.2917i) q^{69} +(-19.7845 - 73.8369i) q^{71} +(-53.5296 - 53.5296i) q^{73} +(-44.3027 + 25.5782i) q^{75} +5.39564i q^{77} +129.990 q^{79} +(4.19371 + 7.26372i) q^{81} +(48.6837 - 48.6837i) q^{83} +(98.3284 - 26.3470i) q^{85} +(44.0166 - 76.2390i) q^{87} +(-4.08744 + 15.2545i) q^{89} +(-2.81388 + 4.32268i) q^{91} +(-94.7089 - 25.3772i) q^{93} +(20.8707 + 12.0497i) q^{95} +(-3.73635 - 13.9442i) q^{97} +(49.3937 + 49.3937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$

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	0.654439	−	0.756115i	$-0.272905\pi$
$3$	−0.982786	−	1.70224i	−0.327595	−	0.567412i	−0.982034	+	0.188703i	$0.939572\pi$
$4$		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	−0.231341	−	0.972873i	$-0.574311\pi$
$7$	0.383239	−	0.102689i	0.0547484	−	0.0146698i	0.286089	+	0.958203i	$0.407645\pi$
$8$		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	$0.295451\pi$
$11$	−3.51976	+	13.1359i	−0.319978	+	1.19418i	−0.919264	+	0.393641i	$0.871215\pi$
$12$		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	0.985090	−	0.172040i	$-0.0550358\pi$
$19$	0.873186	+	3.25878i	0.0459572	+	0.171514i	−0.939133	+	0.343554i	$0.888369\pi$
$20$		0			0
$21$	−0.551442	−	0.551442i	−0.0262592	−	0.0262592i
$22$		0			0
$23$	−14.3562	+	8.28854i	−0.624181	+	0.360371i	−0.778495	−	0.627651i	$-0.784017\pi$
$23$	−14.3562	+	8.28854i	−0.624181	+	0.360371i	0.154314	+	0.988022i	$0.450683\pi$
$24$		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	$-0.452393\pi$
$31$	35.2730	−	35.2730i	1.13784	−	1.13784i	0.988837	−	0.149004i	$-0.0476066\pi$
$32$		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	−0.237998	−	0.971266i	$-0.576491\pi$
$43$	−51.5199	−	29.7450i	−1.19814	−	0.691745i	−0.960140	+	0.279521i	$0.909824\pi$
$44$		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	$0.0571331\pi$
$47$	54.6357	+	54.6357i	1.16246	+	1.16246i	0.178527	+	0.983935i	$0.442867\pi$
$48$		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	0.0149089	−	0.999889i	$-0.495254\pi$
$59$	31.1381	−	8.34343i	0.527765	−	0.141414i	0.512856	+	0.858475i	$0.328588\pi$
$60$		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	−0.583968	−	0.811777i	$-0.698501\pi$
$67$	−100.204	−	26.8497i	−1.49559	−	0.400741i	−0.911619	+	0.411035i	$0.865167\pi$
$68$		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	$-0.902392\pi$
$71$	−19.7845	−	73.8369i	−0.278656	−	1.03996i	0.674696	−	0.738095i	$-0.264275\pi$
$72$		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	$-0.192456\pi$
$79$	129.990			1.64544			0.822719	+	0.568449i	$0.192456\pi$
$80$		0			0
$81$	4.19371	+	7.26372i	0.0517742	+	0.0896756i
$82$		0			0
$83$	48.6837	−	48.6837i	0.586551	−	0.586551i	−0.350145	−	0.936696i	$-0.613868\pi$
$83$	48.6837	−	48.6837i	0.586551	−	0.586551i	0.936696	+	0.350145i	$0.113868\pi$
$84$		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	$-0.984283\pi$
$103$		−	10.1674i		−	0.0987130i	0.998781	−	0.0493565i	$-0.0157170\pi$
$104$		0			0
$105$	−5.57072			−0.0530545
$106$		0			0
$107$	−28.2273	−	48.8911i	−0.263806	−	0.456926i	0.703444	−	0.710751i	$-0.251645\pi$
$107$	−28.2273	−	48.8911i	−0.263806	−	0.456926i	−0.967250	+	0.253825i	$0.918311\pi$
$108$		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	−0.547487	−	0.836814i	$-0.684415\pi$
$127$	−12.2590	+	7.07775i	−0.0965277	+	0.0557303i	0.450959	+	0.892545i	$0.351082\pi$
$128$		0			0
$129$			116.932i			0.906450i
$130$		0			0
$131$	−134.167			−1.02418			−0.512089	−	0.858932i	$-0.671128\pi$
$131$	−134.167			−1.02418			−0.512089	+	0.858932i	$0.671128\pi$
$132$		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	$0.586256\pi$
$139$	−134.588	+	233.114i	−0.968261	+	1.67708i	−0.700586	+	0.713568i	$0.747078\pi$
$140$		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	0.641418	−	0.767191i	$-0.278346\pi$
$151$	−18.9917	−	18.9917i	−0.125773	−	0.125773i	−0.767191	+	0.641418i	$0.778346\pi$
$152$		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	−0.356478	−	0.934304i	$-0.616023\pi$
$163$	−32.2814	+	8.64978i	−0.198045	+	0.0530661i	0.158433	+	0.987370i	$0.449356\pi$
$164$		0			0
$165$	95.4713	−	165.361i	0.578614	−	1.00219i
$166$		0			0
$167$	5.23878	−	19.5514i	0.0313699	−	0.117074i	−0.948465	−	0.316880i	$-0.897365\pi$
$167$	5.23878	−	19.5514i	0.0313699	−	0.117074i	0.979835	+	0.199806i	$0.0640313\pi$
$168$		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	0.388476	−	0.921459i	$-0.373002\pi$
$179$	247.149	−	142.692i	1.38072	−	0.797159i	0.992245	+	0.124299i	$0.0396683\pi$
$180$		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	−0.796290	−	0.604915i	$-0.793207\pi$
$191$	24.0138	−	41.5931i	0.125727	−	0.217765i	0.922017	+	0.387150i	$0.126540\pi$
$192$		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	0.807161	−	0.590331i	$-0.201003\pi$
$199$	139.201	+	80.3674i	0.699500	+	0.403857i	−0.107661	+	0.994188i	$0.534336\pi$
$200$		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	$-0.872999\pi$
$211$	−168.202	−	291.334i	−0.797164	−	1.38073i	0.124292	−	0.992246i	$-0.460334\pi$
$212$		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	0.125086	−	0.992146i	$-0.460079\pi$
$223$	−58.5729	−	15.6946i	−0.262659	−	0.0703792i	−0.387745	+	0.921767i	$0.626746\pi$
$224$		0			0
$225$	−115.774	−	66.8420i	−0.514550	−	0.297076i
$226$		0			0
$227$	14.8051	+	55.2535i	0.0652208	+	0.243407i	0.990838	−	0.135053i	$-0.0431204\pi$
$227$	14.8051	+	55.2535i	0.0652208	+	0.243407i	−0.925618	+	0.378460i	$0.876454\pi$
$228$		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	−0.674152	−	0.738593i	$-0.735491\pi$
$239$	15.4013	−	15.4013i	0.0644407	−	0.0644407i	0.738593	+	0.674152i	$0.235491\pi$
$240$		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	0.887610	−	0.460596i	$-0.152364\pi$
$251$	234.064	+	135.137i	0.932527	+	0.538395i	0.0449172	+	0.998991i	$0.485698\pi$
$252$		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	0.812259	−	0.583297i	$-0.198238\pi$
$263$	−26.0425	−	45.1070i	−0.0990211	−	0.171509i	−0.911280	+	0.411788i	$0.864904\pi$
$264$		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	$-0.791276\pi$
$271$	53.8417	−	200.940i	0.198678	−	0.741476i	0.991284	−	0.131742i	$-0.0420570\pi$
$272$		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	−0.0614742	−	0.998109i	$-0.519580\pi$
$283$	218.526	−	126.166i	0.772176	−	0.445816i	0.833650	+	0.552293i	$0.186247\pi$
$284$		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	$0.0980917\pi$
$307$	385.654	+	385.654i	1.25620	+	1.25620i	0.303310	+	0.952892i	$0.401908\pi$
$308$		0			0
$309$	−17.3074	+	9.99242i	−0.0560109	+	0.0323379i
$310$		0			0
$311$		−	91.9643i		−	0.295705i	−0.989009	−	0.147853i	$-0.952764\pi$
$311$		−	91.9643i		−	0.295705i	0.989009	−	0.147853i	$-0.0472361\pi$
$312$		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	0.909407	−	0.415907i	$-0.136536\pi$
$331$	−28.5043	−	106.380i	−0.0861158	−	0.321389i	−0.995523	+	0.0945179i	$0.969869\pi$
$332$		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	$0.360565\pi$
$347$	−198.543	+	343.887i	−0.572170	+	0.991027i	−0.996343	+	0.0854462i	$0.972768\pi$
$348$		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	0.871344	−	0.490673i	$-0.163249\pi$
$359$	136.661	+	136.661i	0.380670	+	0.380670i	−0.490673	+	0.871344i	$0.663249\pi$
$360$		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	0.948371	−	0.317163i	$-0.102730\pi$
$367$	73.2216	+	126.823i	0.199514	+	0.345568i	−0.748857	+	0.662732i	$0.769397\pi$
$368$		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	−0.169143	−	0.985591i	$-0.554100\pi$
$379$	−306.392	−	82.0974i	−0.808422	−	0.216616i	−0.639278	+	0.768976i	$0.720767\pi$
$380$		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	$0.213107\pi$
$383$	159.079	+	593.690i	0.415349	+	1.55010i	−0.368786	+	0.929514i	$0.620227\pi$
$384$		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	0.837797	−	0.545982i	$-0.183843\pi$
$419$	−22.5991	−	39.1428i	−0.0539358	−	0.0934196i	−0.891733	+	0.452562i	$0.850510\pi$
$420$		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	−0.340563	−	0.940222i	$-0.610618\pi$
$431$	−476.518	−	127.683i	−1.10561	−	0.296247i	−0.765047	+	0.643975i	$0.777284\pi$
$432$		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	−0.232401	−	0.972620i	$-0.574658\pi$
$439$	216.740	−	125.135i	0.493712	−	0.285045i	0.726113	+	0.687575i	$0.241325\pi$
$440$		0			0
$441$			250.881i			0.568891i
$442$		0			0
$443$	−351.926			−0.794415			−0.397207	−	0.917729i	$-0.630021\pi$
$443$	−351.926			−0.794415			−0.397207	+	0.917729i	$0.630021\pi$
$444$		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	0.740452	−	0.672109i	$-0.234611\pi$
$463$	31.6428	+	31.6428i	0.0683430	+	0.0683430i	−0.672109	+	0.740452i	$0.734611\pi$
$464$		0			0
$465$	−606.561	+	350.198i	−1.30443	+	0.753114i
$466$		0			0
$467$		−	228.839i		−	0.490018i	−0.969521	−	0.245009i	$-0.921209\pi$
$467$		−	228.839i		−	0.490018i	0.969521	−	0.245009i	$-0.0787910\pi$
$468$		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	$0.306221\pi$
$479$	−159.775	+	596.288i	−0.333559	+	1.24486i	−0.905423	+	0.424511i	$0.860446\pi$
$480$		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	$0.0945414\pi$
$487$	133.652	+	498.797i	0.274440	+	1.02422i	−0.681776	+	0.731561i	$0.738792\pi$
$488$		0			0
$489$	46.4497	+	46.4497i	0.0949892	+	0.0949892i
$490$		0			0
$491$	−186.731	+	107.809i	−0.380307	+	0.219571i	−0.677952	−	0.735106i	$-0.737132\pi$
$491$	−186.731	+	107.809i	−0.380307	+	0.219571i	0.297645	+	0.954677i	$0.403799\pi$
$492$		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	−0.783931	−	0.620847i	$-0.786789\pi$
$499$	−81.3789	+	81.3789i	−0.163084	+	0.163084i	0.620847	+	0.783931i	$0.286789\pi$
$500$		0			0
$501$	−38.4297	+	10.2972i	−0.0767059	+	0.0205533i
$502$		0			0
$503$	245.576	−	425.350i	0.488223	−	0.845627i	−0.511685	−	0.859173i	$-0.670979\pi$
$503$	245.576	−	425.350i	0.488223	−	0.845627i	0.999908	+	0.0135460i	$0.00431195\pi$
$504$		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	$0.0247918\pi$
$523$	295.949	+	512.598i	0.565867	+	0.980111i	−0.431101	+	0.902304i	$0.641875\pi$
$524$		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	$-0.417839\pi$
$547$	279.253			0.510517			0.255258	+	0.966873i	$0.417839\pi$
$548$		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	0.507829	−	0.861458i	$-0.330448\pi$
$563$	8.83856	+	5.10294i	0.0156990	+	0.00906384i	−0.492130	+	0.870522i	$0.663782\pi$
$564$		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	$0.0225298\pi$
$571$			80.7627i			0.141441i	−0.997496	+	0.0707204i	$0.977470\pi$
$572$		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	0.987313	−	0.158786i	$-0.0507580\pi$
$587$	1034.86	+	277.289i	1.76296	+	0.472383i	0.775645	+	0.631169i	$0.217425\pi$
$588$		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	$-0.738551\pi$
$599$	−816.105			−1.36244			−0.681222	+	0.732076i	$0.738551\pi$
$600$		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	−0.795388	−	0.606101i	$-0.792733\pi$
$607$	77.2134	−	133.737i	0.127205	−	0.220325i	0.922593	+	0.385776i	$0.126066\pi$
$608$		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	0.556854	−	0.830611i	$-0.312008\pi$
$619$	−169.456	−	169.456i	−0.273757	−	0.273757i	−0.830611	+	0.556854i	$0.812008\pi$
$620$		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	0.682438	−	0.730943i	$-0.260920\pi$
$631$	1034.16	−	277.102i	1.63892	−	0.439147i	0.956480	+	0.291797i	$0.0942530\pi$
$632$		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	$-0.932378\pi$
$643$	−151.996	−	567.258i	−0.236386	−	0.882205i	0.741133	−	0.671358i	$-0.234289\pi$
$644$		0			0
$645$	590.629	+	590.629i	0.915704	+	0.915704i
$646$		0			0
$647$	−538.312	+	310.795i	−0.832013	+	0.480363i	−0.854541	−	0.519383i	$-0.826162\pi$
$647$	−538.312	+	310.795i	−0.832013	+	0.480363i	0.0225284	+	0.999746i	$0.492828\pi$
$648$		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	−0.779598	−	0.626281i	$-0.784576\pi$
$659$	100.548	−	174.154i	0.152576	−	0.264269i	0.932174	+	0.362011i	$0.117910\pi$
$660$		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	−0.959069	−	0.283171i	$-0.908614\pi$
$683$	−1125.63	+	301.611i	−1.64806	+	0.441597i	−0.688993	+	0.724768i	$0.741947\pi$
$684$		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	0.616209	−	0.787583i	$-0.288668\pi$
$691$	522.444	+	139.988i	0.756069	+	0.202588i	0.139861	+	0.990171i	$0.455334\pi$
$692$		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	$0.0120777\pi$
$719$	1101.34	+	635.861i	1.53177	+	0.884369i	0.532492	+	0.846435i	$0.321256\pi$
$720$		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	$0.0474603\pi$
$727$			215.990i			0.297098i	−0.988905	+	0.148549i	$0.952540\pi$
$728$		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	$0.192336\pi$
$739$	−128.451	+	479.386i	−0.173817	+	0.648695i	−0.996750	+	0.0805562i	$0.974330\pi$
$740$		0			0
$741$	−4.60556	+	86.0840i	−0.00621532	+	0.116173i
$742$		0			0
$743$	−77.8650	−	20.8639i	−0.104798	−	0.0280806i	0.206039	−	0.978544i	$-0.433943\pi$
$743$	−77.8650	−	20.8639i	−0.104798	−	0.0280806i	−0.310837	+	0.950463i	$0.600609\pi$
$744$		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	−0.439747	−	0.898122i	$-0.644932\pi$
$751$	88.7495	−	51.2396i	0.118175	−	0.0682284i	0.557922	+	0.829893i	$0.311599\pi$
$752$		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	0.0628551	−	0.998023i	$-0.479979\pi$
$787$	485.028	−	129.963i	0.616300	−	0.165137i	0.553445	+	0.832885i	$0.313313\pi$
$788$		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	−0.541467	−	0.840722i	$-0.682131\pi$
$811$	242.696	−	242.696i	0.299256	−	0.299256i	0.840722	+	0.541467i	$0.182131\pi$
$812$		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	−0.170401	−	0.985375i	$-0.554506\pi$
$823$	−912.674	−	526.933i	−1.10896	−	0.640259i	−0.938560	+	0.345116i	$0.887839\pi$
$824$		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	$0.0908474\pi$
$827$	1026.38	+	1026.38i	1.24109	+	1.24109i	0.281547	+	0.959548i	$0.409153\pi$
$828$		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	−0.450527	−	0.892763i	$-0.648764\pi$
$839$	−330.829	+	88.6454i	−0.394314	+	0.105656i	0.0562135	+	0.998419i	$0.482097\pi$
$840$		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	$-0.414731\pi$
$859$	454.733			0.529375			0.264687	+	0.964334i	$0.414731\pi$
$860$		0			0
$861$	4.39590	+	7.61393i	0.00510558	+	0.00884312i
$862$		0			0
$863$	−477.014	+	477.014i	−0.552739	+	0.552739i	−0.927230	−	0.374491i	$-0.877817\pi$
$863$	−477.014	+	477.014i	−0.552739	+	0.552739i	0.374491	+	0.927230i	$0.377817\pi$
$864$		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	$0.236207\pi$
$883$			1193.49i			1.35163i	−0.737073	+	0.675813i	$0.763793\pi$
$884$		0			0
$885$	−452.621			−0.511436
$886$		0			0
$887$	−664.890	−	1151.62i	−0.749595	−	1.29834i	−0.948017	−	0.318219i	$-0.896915\pi$
$887$	−664.890	−	1151.62i	−0.749595	−	1.29834i	0.198423	−	0.980117i	$-0.436418\pi$
$888$		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	−0.734494	−	0.678615i	$-0.762580\pi$
$907$	−466.237	+	269.182i	−0.514043	+	0.296783i	0.220451	+	0.975398i	$0.429247\pi$
$908$		0			0
$909$			1.97338i			0.00217094i
$910$		0			0
$911$	−1029.58			−1.13016			−0.565080	−	0.825036i	$-0.691155\pi$
$911$	−1029.58			−1.13016			−0.565080	+	0.825036i	$0.691155\pi$
$912$		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	−0.800662	−	0.599116i	$-0.795519\pi$
$919$	108.919	−	188.653i	0.118519	−	0.205280i	0.919181	+	0.393836i	$0.128852\pi$
$920$		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	$-0.543138\pi$
$947$	452.017	−	1686.95i	0.477314	−	1.78136i	0.612422	−	0.790531i	$-0.290195\pi$
$948$		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	−0.866371	−	0.499401i	$-0.833553\pi$
$967$	−354.860	+	354.860i	−0.366970	+	0.366970i	0.499401	+	0.866371i	$0.333553\pi$
$968$		0			0
$969$	91.2814	−	24.4588i	0.0942017	−	0.0252413i
$970$		0			0
$971$	216.415	−	374.842i	0.222878	−	0.386037i	−0.732802	−	0.680441i	$-0.761788\pi$
$971$	216.415	−	374.842i	0.222878	−	0.386037i	0.955681	+	0.294405i	$0.0951214\pi$
$972$		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	$-0.951696\pi$
$983$	−1120.30	−	1120.30i	−1.13968	−	1.13968i	−0.151171	−	0.988508i	$-0.548304\pi$
$984$		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	0.977834	−	0.209381i	$-0.0671447\pi$
$991$	304.820	+	527.964i	0.307588	+	0.532759i	−0.670246	+	0.742139i	$0.733811\pi$
$992$		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	52.3.k.a.41.1	yes	8
3.2	odd	2		468.3.cd.b.145.1		8
4.3	odd	2		208.3.bd.e.145.2		8
13.2	odd	12		676.3.g.c.437.3		8
13.3	even	3		676.3.g.d.577.3		8
13.7	odd	12	inner	52.3.k.a.33.1	✓	8
13.10	even	6		676.3.g.c.577.3		8
13.11	odd	12		676.3.g.d.437.3		8
39.20	even	12		468.3.cd.b.397.1		8
52.7	even	12		208.3.bd.e.33.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.3.k.a.33.1	✓	8	13.7	odd	12	inner
52.3.k.a.41.1	yes	8	1.1	even	1	trivial
208.3.bd.e.33.2		8	52.7	even	12
208.3.bd.e.145.2		8	4.3	odd	2
468.3.cd.b.145.1		8	3.2	odd	2
468.3.cd.b.397.1		8	39.20	even	12
676.3.g.c.437.3		8	13.2	odd	12
676.3.g.c.577.3		8	13.10	even	6
676.3.g.d.437.3		8	13.11	odd	12
676.3.g.d.577.3		8	13.3	even	3

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	52.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.982786 - 1.70224i) q^{3} +(5.05105 - 5.05105i) q^{5} +(0.383239 - 0.102689i) q^{7} +(2.56826 - 4.44836i) q^{9} +O(q^{10})\)	\(q+(-0.982786 - 1.70224i) q^{3} +(5.05105 - 5.05105i) q^{5} +(0.383239 - 0.102689i) q^{7} +(2.56826 - 4.44836i) q^{9} +(-3.51976 + 13.1359i) q^{11} +(-9.67036 + 8.68816i) q^{13} +(-13.5622 - 3.63397i) q^{15} +(12.3415 + 7.12539i) q^{17} +(0.873186 + 3.25878i) q^{19} +(-0.551442 - 0.551442i) q^{21} +(-14.3562 + 8.28854i) q^{23} -26.0262i q^{25} -27.7864 q^{27} +(22.3938 + 38.7872i) q^{29} +(35.2730 - 35.2730i) q^{31} +(25.8196 - 6.91835i) q^{33} +(1.41707 - 2.45444i) q^{35} +(9.58504 - 35.7719i) q^{37} +(24.2932 + 7.92262i) q^{39} +(-10.8895 - 2.91782i) q^{41} +(-51.5199 - 29.7450i) q^{43} +(-9.49646 - 35.4413i) q^{45} +(54.6357 + 54.6357i) q^{47} +(-42.2989 + 24.4213i) q^{49} -28.0110i q^{51} -63.3563 q^{53} +(48.5717 + 84.1287i) q^{55} +(4.68905 - 4.68905i) q^{57} +(31.1381 - 8.34343i) q^{59} +(-29.0686 + 50.3483i) q^{61} +(0.527462 - 1.96852i) q^{63} +(-4.96111 + 92.7298i) q^{65} +(-100.204 - 26.8497i) q^{67} +(28.2181 + 16.2917i) q^{69} +(-19.7845 - 73.8369i) q^{71} +(-53.5296 - 53.5296i) q^{73} +(-44.3027 + 25.5782i) q^{75} +5.39564i q^{77} +129.990 q^{79} +(4.19371 + 7.26372i) q^{81} +(48.6837 - 48.6837i) q^{83} +(98.3284 - 26.3470i) q^{85} +(44.0166 - 76.2390i) q^{87} +(-4.08744 + 15.2545i) q^{89} +(-2.81388 + 4.32268i) q^{91} +(-94.7089 - 25.3772i) q^{93} +(20.8707 + 12.0497i) q^{95} +(-3.73635 - 13.9442i) q^{97} +(49.3937 + 49.3937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9	\( 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9} + 24 q^{11} + 18 q^{13} - 60 q^{15} - 54 q^{17} - 50 q^{19} - 54 q^{21} - 24 q^{23} + 36 q^{27} + 108 q^{29} + 176 q^{31} + 114 q^{33} - 30 q^{35} + 104 q^{37} + 120 q^{39} - 168 q^{41} - 198 q^{43} + 6 q^{45} - 96 q^{47} - 162 q^{49} - 72 q^{53} + 126 q^{55} + 318 q^{57} - 18 q^{61} + 180 q^{63} - 72 q^{65} - 326 q^{67} - 498 q^{69} - 162 q^{71} - 98 q^{73} - 240 q^{75} + 192 q^{79} + 240 q^{81} + 408 q^{83} + 318 q^{85} + 36 q^{87} + 54 q^{89} + 280 q^{91} - 66 q^{93} + 312 q^{95} + 182 q^{97}+O(q^{100}) \) 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

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Representations

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Database

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