LMFDB - Embedded newform 252.3.g.b.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,3,Mod(127,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("252.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.g (of order $2$, degree $1$, 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:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.489494783471841.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 18 x^{8} - 22 x^{7} + 33 x^{6} - 44 x^{5} + 72 x^{4} + \cdots + 64 $ x^12 - 3x^11 + 7x^10 - 11x^9 + 18x^8 - 22x^7 + 33x^6 - 44x^5 + 72x^4 - 88x^3 + 112x^2 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{19} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			127.3
Root			$-1.15503 + 0.816025i$ of defining polynomial
Character	$\chi$	$=$	252.127
Dual form			252.3.g.b.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42562 - 1.40272i) q^{2} +(0.0647610 + 3.99948i) q^{4} -1.94731 q^{5} -2.64575i q^{7} +(5.51781 - 5.79256i) q^{8} +O(q^{10})$	\(q+(-1.42562 - 1.40272i) q^{2} +(0.0647610 + 3.99948i) q^{4} -1.94731 q^{5} -2.64575i q^{7} +(5.51781 - 5.79256i) q^{8} +(2.77611 + 2.73152i) q^{10} +1.01531i q^{11} +3.44342 q^{13} +(-3.71124 + 3.77182i) q^{14} +(-15.9916 + 0.518020i) q^{16} -26.4211 q^{17} -33.7546i q^{19} +(-0.126110 - 7.78820i) q^{20} +(1.42420 - 1.44744i) q^{22} -2.98330i q^{23} -21.2080 q^{25} +(-4.90899 - 4.83015i) q^{26} +(10.5816 - 0.171342i) q^{28} -30.3904 q^{29} -0.713577i q^{31} +(23.5245 + 21.6932i) q^{32} +(37.6663 + 37.0613i) q^{34} +5.15209i q^{35} -60.0588 q^{37} +(-47.3482 + 48.1210i) q^{38} +(-10.7449 + 11.2799i) q^{40} -2.67381 q^{41} +6.69857i q^{43} +(-4.06071 + 0.0657526i) q^{44} +(-4.18473 + 4.25304i) q^{46} -24.3012i q^{47} -7.00000 q^{49} +(30.2345 + 29.7489i) q^{50} +(0.222999 + 13.7719i) q^{52} +65.8324 q^{53} -1.97712i q^{55} +(-15.3257 - 14.5988i) q^{56} +(43.3250 + 42.6291i) q^{58} -33.7709i q^{59} -81.7452 q^{61} +(-1.00095 + 1.01729i) q^{62} +(-3.10744 - 63.9245i) q^{64} -6.70539 q^{65} +62.6486i q^{67} +(-1.71106 - 105.670i) q^{68} +(7.22693 - 7.34490i) q^{70} -132.221i q^{71} +100.072 q^{73} +(85.6207 + 84.2455i) q^{74} +(135.001 - 2.18598i) q^{76} +2.68626 q^{77} -97.5751i q^{79} +(31.1406 - 1.00874i) q^{80} +(3.81183 + 3.75061i) q^{82} +87.9287i q^{83} +51.4499 q^{85} +(9.39621 - 9.54958i) q^{86} +(5.88125 + 5.60230i) q^{88} +110.387 q^{89} -9.11043i q^{91} +(11.9316 - 0.193201i) q^{92} +(-34.0878 + 34.6442i) q^{94} +65.7305i q^{95} +35.6839 q^{97} +(9.97931 + 9.81903i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8	$ 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8} + 28 q^{10} - 24 q^{13} + 14 q^{14} - 14 q^{16} + 40 q^{17} + 20 q^{20} - 88 q^{22} + 180 q^{25} - 100 q^{26} + 14 q^{28} - 72 q^{29} - 142 q^{32} - 100 q^{34} - 88 q^{37} - 128 q^{38} - 28 q^{40} + 200 q^{41} + 40 q^{44} - 24 q^{46} - 84 q^{49} + 346 q^{50} - 364 q^{52} - 104 q^{53} - 98 q^{56} + 148 q^{58} + 104 q^{61} - 64 q^{62} - 70 q^{64} - 176 q^{65} - 188 q^{68} - 84 q^{70} + 312 q^{73} - 4 q^{74} + 432 q^{76} + 224 q^{77} + 564 q^{80} + 332 q^{82} + 352 q^{85} - 160 q^{86} + 328 q^{88} + 552 q^{89} - 232 q^{92} - 144 q^{94} - 264 q^{97} + 14 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8 + 28 * q^10 - 24 * q^13 + 14 * q^14 - 14 * q^16 + 40 * q^17 + 20 * q^20 - 88 * q^22 + 180 * q^25 - 100 * q^26 + 14 * q^28 - 72 * q^29 - 142 * q^32 - 100 * q^34 - 88 * q^37 - 128 * q^38 - 28 * q^40 + 200 * q^41 + 40 * q^44 - 24 * q^46 - 84 * q^49 + 346 * q^50 - 364 * q^52 - 104 * q^53 - 98 * q^56 + 148 * q^58 + 104 * q^61 - 64 * q^62 - 70 * q^64 - 176 * q^65 - 188 * q^68 - 84 * q^70 + 312 * q^73 - 4 * q^74 + 432 * q^76 + 224 * q^77 + 564 * q^80 + 332 * q^82 + 352 * q^85 - 160 * q^86 + 328 * q^88 + 552 * q^89 - 232 * q^92 - 144 * q^94 - 264 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.42562	−	1.40272i	−0.712808	−	0.701359i
$2$	−1.42562	−	1.40272i	−0.712808	−	0.701359i
$3$		0			0
$3$		0			0
$4$	0.0647610	+	3.99948i	0.0161903	+	0.999869i
$5$	−1.94731			−0.389461			−0.194731	−	0.980857i	$-0.562383\pi$
$5$	−1.94731			−0.389461			−0.194731	+	0.980857i	$0.562383\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	5.51781	−	5.79256i	0.689727	−	0.724070i
$9$		0			0
$10$	2.77611	+	2.73152i	0.277611	+	0.273152i
$11$			1.01531i			0.0923010i	0.998934	+	0.0461505i	$0.0146954\pi$
$11$			1.01531i			0.0923010i	−0.998934	+	0.0461505i	$0.985305\pi$
$12$		0			0
$13$	3.44342			0.264878			0.132439	−	0.991191i	$-0.457719\pi$
$13$	3.44342			0.264878			0.132439	+	0.991191i	$0.457719\pi$
$14$	−3.71124	+	3.77182i	−0.265089	+	0.269416i
$15$		0			0
$16$	−15.9916	+	0.518020i	−0.999476	+	0.0323763i
$17$	−26.4211			−1.55418			−0.777090	−	0.629389i	$-0.783305\pi$
$17$	−26.4211			−1.55418			−0.777090	+	0.629389i	$0.783305\pi$
$18$		0			0
$19$		−	33.7546i		−	1.77656i	−0.459306	−	0.888278i	$-0.651902\pi$
$19$		−	33.7546i		−	1.77656i	0.459306	−	0.888278i	$-0.348098\pi$
$20$	−0.126110	−	7.78820i	−0.00630548	−	0.389410i
$21$		0			0
$22$	1.42420	−	1.44744i	0.0647362	−	0.0657929i
$23$		−	2.98330i		−	0.129709i	−0.997895	−	0.0648543i	$-0.979342\pi$
$23$		−	2.98330i		−	0.129709i	0.997895	−	0.0648543i	$-0.0206583\pi$
$24$		0			0
$25$	−21.2080			−0.848320
$26$	−4.90899	−	4.83015i	−0.188807	−	0.185775i
$27$		0			0
$28$	10.5816	−	0.171342i	0.377915	−	0.00611934i
$29$	−30.3904			−1.04794			−0.523972	−	0.851736i	$-0.675550\pi$
$29$	−30.3904			−1.04794			−0.523972	+	0.851736i	$0.675550\pi$
$30$		0			0
$31$		−	0.713577i		−	0.0230186i	−0.999934	−	0.0115093i	$-0.996336\pi$
$31$		−	0.713577i		−	0.0230186i	0.999934	−	0.0115093i	$-0.00366361\pi$
$32$	23.5245	+	21.6932i	0.735142	+	0.677914i
$33$		0			0
$34$	37.6663	+	37.0613i	1.10783	+	1.09004i
$35$			5.15209i			0.147202i
$36$		0			0
$37$	−60.0588			−1.62321			−0.811605	−	0.584207i	$-0.801406\pi$
$37$	−60.0588			−1.62321			−0.811605	+	0.584207i	$0.801406\pi$
$38$	−47.3482	+	48.1210i	−1.24600	+	1.26634i
$39$		0			0
$40$	−10.7449	+	11.2799i	−0.268622	+	0.281997i
$41$	−2.67381			−0.0652149			−0.0326075	−	0.999468i	$-0.510381\pi$
$41$	−2.67381			−0.0652149			−0.0326075	+	0.999468i	$0.510381\pi$
$42$		0			0
$43$			6.69857i			0.155781i	0.996962	+	0.0778903i	$0.0248184\pi$
$43$			6.69857i			0.155781i	−0.996962	+	0.0778903i	$0.975182\pi$
$44$	−4.06071	+	0.0657526i	−0.0922889	+	0.00149438i
$45$		0			0
$46$	−4.18473	+	4.25304i	−0.0909723	+	0.0924573i
$47$		−	24.3012i		−	0.517048i	−0.966005	−	0.258524i	$-0.916764\pi$
$47$		−	24.3012i		−	0.517048i	0.966005	−	0.258524i	$-0.0832361\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	30.2345	+	29.7489i	0.604689	+	0.594977i
$51$		0			0
$52$	0.222999	+	13.7719i	0.00428845	+	0.264844i
$53$	65.8324			1.24212			0.621061	−	0.783763i	$-0.286702\pi$
$53$	65.8324			1.24212			0.621061	+	0.783763i	$0.286702\pi$
$54$		0			0
$55$		−	1.97712i		−	0.0359477i
$56$	−15.3257	−	14.5988i	−0.273673	−	0.260692i
$57$		0			0
$58$	43.3250	+	42.6291i	0.746983	+	0.734985i
$59$		−	33.7709i		−	0.572388i	−0.958172	−	0.286194i	$-0.907610\pi$
$59$		−	33.7709i		−	0.572388i	0.958172	−	0.286194i	$-0.0923901\pi$
$60$		0			0
$61$	−81.7452			−1.34009			−0.670043	−	0.742323i	$-0.733724\pi$
$61$	−81.7452			−1.34009			−0.670043	+	0.742323i	$0.733724\pi$
$62$	−1.00095	+	1.01729i	−0.0161443	+	0.0164079i
$63$		0			0
$64$	−3.10744	−	63.9245i	−0.0485538	−	0.998821i
$65$	−6.70539			−0.103160
$66$		0			0
$67$			62.6486i			0.935054i	0.883979	+	0.467527i	$0.154855\pi$
$67$			62.6486i			0.935054i	−0.883979	+	0.467527i	$0.845145\pi$
$68$	−1.71106	−	105.670i	−0.0251626	−	1.55398i
$69$		0			0
$70$	7.22693	−	7.34490i	0.103242	−	0.104927i
$71$		−	132.221i		−	1.86226i	−0.364682	−	0.931132i	$-0.618822\pi$
$71$		−	132.221i		−	1.86226i	0.364682	−	0.931132i	$-0.381178\pi$
$72$		0			0
$73$	100.072			1.37084			0.685422	−	0.728146i	$-0.259618\pi$
$73$	100.072			1.37084			0.685422	+	0.728146i	$0.259618\pi$
$74$	85.6207	+	84.2455i	1.15704	+	1.13845i
$75$		0			0
$76$	135.001	−	2.18598i	1.77632	−	0.0287629i
$77$	2.68626			0.0348865
$78$		0			0
$79$		−	97.5751i		−	1.23513i	−0.786521	−	0.617564i	$-0.788120\pi$
$79$		−	97.5751i		−	1.23513i	0.786521	−	0.617564i	$-0.211880\pi$
$80$	31.1406	−	1.00874i	0.389257	−	0.0126093i
$81$		0			0
$82$	3.81183	+	3.75061i	0.0464857	+	0.0457391i
$83$			87.9287i			1.05938i	0.848191	+	0.529691i	$0.177692\pi$
$83$			87.9287i			1.05938i	−0.848191	+	0.529691i	$0.822308\pi$
$84$		0			0
$85$	51.4499			0.605293
$86$	9.39621	−	9.54958i	0.109258	−	0.111042i
$87$		0			0
$88$	5.88125	+	5.60230i	0.0668323	+	0.0636625i
$89$	110.387			1.24031			0.620154	−	0.784480i	$-0.287070\pi$
$89$	110.387			1.24031			0.620154	+	0.784480i	$0.287070\pi$
$90$		0			0
$91$		−	9.11043i		−	0.100115i
$92$	11.9316	−	0.193201i	0.129692	−	0.00210002i
$93$		0			0
$94$	−34.0878	+	34.6442i	−0.362636	+	0.368556i
$95$			65.7305i			0.691900i
$96$		0			0
$97$	35.6839			0.367876			0.183938	−	0.982938i	$-0.441116\pi$
$97$	35.6839			0.367876			0.183938	+	0.982938i	$0.441116\pi$
$98$	9.97931	+	9.81903i	0.101830	+	0.100194i
$99$		0			0
$100$	−1.37345	−	84.8209i	−0.0137345	−	0.848209i
$101$	56.6957			0.561344			0.280672	−	0.959804i	$-0.409443\pi$
$101$	56.6957			0.561344			0.280672	+	0.959804i	$0.409443\pi$
$102$		0			0
$103$		−	143.694i		−	1.39509i	−0.716541	−	0.697545i	$-0.754276\pi$
$103$		−	143.694i		−	1.39509i	0.716541	−	0.697545i	$-0.245724\pi$
$104$	19.0001	−	19.9462i	0.182694	−	0.191790i
$105$		0			0
$106$	−93.8518	−	92.3444i	−0.885394	−	0.871173i
$107$			170.939i			1.59756i	0.601625	+	0.798779i	$0.294520\pi$
$107$			170.939i			1.59756i	−0.601625	+	0.798779i	$0.705480\pi$
$108$		0			0
$109$	7.83710			0.0719000			0.0359500	−	0.999354i	$-0.488554\pi$
$109$	7.83710			0.0719000			0.0359500	+	0.999354i	$0.488554\pi$
$110$	−2.77334	+	2.81861i	−0.0252122	+	0.0256238i
$111$		0			0
$112$	1.37055	+	42.3098i	0.0122371	+	0.377766i
$113$	−179.807			−1.59121			−0.795607	−	0.605813i	$-0.792848\pi$
$113$	−179.807			−1.59121			−0.795607	+	0.605813i	$0.792848\pi$
$114$		0			0
$115$			5.80939i			0.0505165i
$116$	−1.96811	−	121.546i	−0.0169665	−	1.04781i
$117$		0			0
$118$	−47.3710	+	48.1443i	−0.401449	+	0.408002i
$119$			69.9036i			0.587425i
$120$		0			0
$121$	119.969			0.991481
$122$	116.537	+	114.666i	0.955223	+	0.939881i
$123$		0			0
$124$	2.85393	−	0.0462120i	0.0230156	−	0.000372677i
$125$	89.9811			0.719849
$126$		0			0
$127$			130.862i			1.03041i	0.857068	+	0.515204i	$0.172284\pi$
$127$			130.862i			1.03041i	−0.857068	+	0.515204i	$0.827716\pi$
$128$	−85.2381	+	95.4907i	−0.665923	+	0.746021i
$129$		0			0
$130$	9.55931	+	9.40578i	0.0735332	+	0.0723521i
$131$		−	190.151i		−	1.45154i	−0.687939	−	0.725768i	$-0.741485\pi$
$131$		−	190.151i		−	1.45154i	0.687939	−	0.725768i	$-0.258515\pi$
$132$		0			0
$133$	−89.3062			−0.671475
$134$	87.8784	−	89.3128i	0.655809	−	0.666514i
$135$		0			0
$136$	−145.787	+	153.046i	−1.07196	+	1.12534i
$137$	−248.425			−1.81332			−0.906662	−	0.421859i	$-0.861378\pi$
$137$	−248.425			−1.81332			−0.906662	+	0.421859i	$0.861378\pi$
$138$		0			0
$139$			88.3746i			0.635789i	0.948126	+	0.317894i	$0.102976\pi$
$139$			88.3746i			0.635789i	−0.948126	+	0.317894i	$0.897024\pi$
$140$	−20.6056	+	0.333654i	−0.147183	+	0.00238325i
$141$		0			0
$142$	−185.469	+	188.496i	−1.30612	+	1.32744i
$143$			3.49614i			0.0244485i
$144$		0			0
$145$	59.1794			0.408133
$146$	−142.664	−	140.372i	−0.977148	−	0.961454i
$147$		0			0
$148$	−3.88947	−	240.204i	−0.0262802	−	1.62300i
$149$	89.3854			0.599902			0.299951	−	0.953955i	$-0.403030\pi$
$149$	89.3854			0.599902			0.299951	+	0.953955i	$0.403030\pi$
$150$		0			0
$151$			197.560i			1.30834i	0.756346	+	0.654172i	$0.226983\pi$
$151$			197.560i			1.30834i	−0.756346	+	0.654172i	$0.773017\pi$
$152$	−195.525	−	186.251i	−1.28635	−	1.22534i
$153$		0			0
$154$	−3.82957	−	3.76807i	−0.0248674	−	0.0244680i
$155$			1.38955i			0.00896486i
$156$		0			0
$157$	195.026			1.24220			0.621101	−	0.783731i	$-0.286686\pi$
$157$	195.026			1.24220			0.621101	+	0.783731i	$0.286686\pi$
$158$	−136.870	+	139.105i	−0.866268	+	0.880409i
$159$		0			0
$160$	−45.8095	−	42.2434i	−0.286309	−	0.264021i
$161$	−7.89306			−0.0490252
$162$		0			0
$163$			119.613i			0.733823i	0.930256	+	0.366911i	$0.119585\pi$
$163$			119.613i			0.733823i	−0.930256	+	0.366911i	$0.880415\pi$
$164$	−0.173159	−	10.6938i	−0.00105585	−	0.0652064i
$165$		0			0
$166$	123.339	−	125.353i	0.743007	−	0.755136i
$167$		−	72.7649i		−	0.435718i	−0.975980	−	0.217859i	$-0.930093\pi$
$167$		−	72.7649i		−	0.435718i	0.975980	−	0.217859i	$-0.0699073\pi$
$168$		0			0
$169$	−157.143			−0.929839
$170$	−73.3478	−	72.1697i	−0.431458	−	0.424528i
$171$		0			0
$172$	−26.7908	+	0.433806i	−0.155760	+	0.00252213i
$173$	−9.89253			−0.0571822			−0.0285911	−	0.999591i	$-0.509102\pi$
$173$	−9.89253			−0.0571822			−0.0285911	+	0.999591i	$0.509102\pi$
$174$		0			0
$175$			56.1111i			0.320635i
$176$	−0.525952	−	16.2365i	−0.00298836	−	0.0922526i
$177$		0			0
$178$	−157.370	−	154.842i	−0.884101	−	0.869901i
$179$			251.994i			1.40779i	0.710305	+	0.703895i	$0.248557\pi$
$179$			251.994i			1.40779i	−0.710305	+	0.703895i	$0.751443\pi$
$180$		0			0
$181$	−299.047			−1.65219			−0.826097	−	0.563528i	$-0.809444\pi$
$181$	−299.047			−1.65219			−0.826097	+	0.563528i	$0.809444\pi$
$182$	−12.7794	+	12.9880i	−0.0702163	+	0.0713625i
$183$		0			0
$184$	−17.2809	−	16.4613i	−0.0939181	−	0.0894635i
$185$	116.953			0.632177
$186$		0			0
$187$		−	26.8256i		−	0.143452i
$188$	97.1923	−	1.57377i	0.516980	−	0.00837114i
$189$		0			0
$190$	92.2014	−	93.7064i	0.485270	−	0.493192i
$191$		−	121.179i		−	0.634444i	−0.948351	−	0.317222i	$-0.897250\pi$
$191$		−	121.179i		−	0.634444i	0.948351	−	0.317222i	$-0.102750\pi$
$192$		0			0
$193$	110.062			0.570270			0.285135	−	0.958487i	$-0.407962\pi$
$193$	110.062			0.570270			0.285135	+	0.958487i	$0.407962\pi$
$194$	−50.8716	−	50.0545i	−0.262225	−	0.258013i
$195$		0			0
$196$	−0.453327	−	27.9963i	−0.00231289	−	0.142838i
$197$	78.6134			0.399053			0.199527	−	0.979892i	$-0.436060\pi$
$197$	78.6134			0.399053			0.199527	+	0.979892i	$0.436060\pi$
$198$		0			0
$199$		−	89.9183i		−	0.451851i	−0.974145	−	0.225925i	$-0.927459\pi$
$199$		−	89.9183i		−	0.451851i	0.974145	−	0.225925i	$-0.0725405\pi$
$200$	−117.022	+	122.849i	−0.585109	+	0.614243i
$201$		0			0
$202$	−80.8263	−	79.5281i	−0.400130	−	0.393704i
$203$			80.4054i			0.396086i
$204$		0			0
$205$	5.20673			0.0253987
$206$	−201.563	+	204.853i	−0.978460	+	0.994432i
$207$		0			0
$208$	−55.0658	+	1.78376i	−0.264740	+	0.00857577i
$209$	34.2714			0.163978
$210$		0			0
$211$			146.363i			0.693663i	0.937927	+	0.346832i	$0.112742\pi$
$211$			146.363i			0.693663i	−0.937927	+	0.346832i	$0.887258\pi$
$212$	4.26337	+	263.295i	0.0201103	+	1.24196i
$213$		0			0
$214$	239.779	−	243.693i	1.12046	−	1.13875i
$215$		−	13.0442i		−	0.0606705i
$216$		0			0
$217$	−1.88795			−0.00870022
$218$	−11.1727	−	10.9932i	−0.0512509	−	0.0504277i
$219$		0			0
$220$	7.90745	−	0.128040i	0.0359429	−	0.000582002i
$221$	−90.9788			−0.411669
$222$		0			0
$223$		−	137.385i		−	0.616074i	−0.951374	−	0.308037i	$-0.900328\pi$
$223$		−	137.385i		−	0.616074i	0.951374	−	0.308037i	$-0.0996721\pi$
$224$	57.3949	−	62.2401i	0.256227	−	0.277857i
$225$		0			0
$226$	256.336	+	252.219i	1.13423	+	1.11601i
$227$			61.6479i			0.271577i	0.990738	+	0.135788i	$0.0433567\pi$
$227$			61.6479i			0.271577i	−0.990738	+	0.135788i	$0.956643\pi$
$228$		0			0
$229$	313.417			1.36863			0.684316	−	0.729186i	$-0.260101\pi$
$229$	313.417			1.36863			0.684316	+	0.729186i	$0.260101\pi$
$230$	8.14894	−	8.28196i	0.0354302	−	0.0360085i
$231$		0			0
$232$	−167.688	+	176.038i	−0.722795	+	0.758784i
$233$	142.259			0.610554			0.305277	−	0.952264i	$-0.401251\pi$
$233$	142.259			0.610554			0.305277	+	0.952264i	$0.401251\pi$
$234$		0			0
$235$			47.3220i			0.201370i
$236$	135.066	−	2.18704i	0.572313	−	0.00926710i
$237$		0			0
$238$	98.0551	−	99.6557i	0.411996	−	0.418721i
$239$		−	164.416i		−	0.687933i	−0.938982	−	0.343966i	$-0.888229\pi$
$239$		−	164.416i		−	0.687933i	0.938982	−	0.343966i	$-0.111771\pi$
$240$		0			0
$241$	69.0501			0.286515			0.143257	−	0.989685i	$-0.454242\pi$
$241$	69.0501			0.286515			0.143257	+	0.989685i	$0.454242\pi$
$242$	−171.030	−	168.283i	−0.706735	−	0.695384i
$243$		0			0
$244$	−5.29390	−	326.938i	−0.0216963	−	1.33991i
$245$	13.6311			0.0556373
$246$		0			0
$247$		−	116.231i		−	0.470571i
$248$	−4.13344	−	3.93739i	−0.0166671	−	0.0158766i
$249$		0			0
$250$	−128.278	−	126.218i	−0.513114	−	0.504873i
$251$		−	41.8933i		−	0.166906i	−0.996512	−	0.0834528i	$-0.973405\pi$
$251$		−	41.8933i		−	0.166906i	0.996512	−	0.0834528i	$-0.0265948\pi$
$252$		0			0
$253$	3.02897			0.0119722
$254$	183.562	−	186.559i	0.722686	−	0.734483i
$255$		0			0
$256$	255.463	−	16.5680i	0.997904	−	0.0647186i
$257$	−215.796			−0.839671			−0.419836	−	0.907600i	$-0.637912\pi$
$257$	−215.796			−0.839671			−0.419836	+	0.907600i	$0.637912\pi$
$258$		0			0
$259$			158.901i			0.613516i
$260$	−0.434248	−	26.8180i	−0.00167018	−	0.103146i
$261$		0			0
$262$	−266.729	+	271.083i	−1.01805	+	1.03467i
$263$		−	111.918i		−	0.425543i	−0.977102	−	0.212772i	$-0.931751\pi$
$263$		−	111.918i		−	0.425543i	0.977102	−	0.212772i	$-0.0682490\pi$
$264$		0			0
$265$	−128.196			−0.483758
$266$	127.316	+	125.271i	0.478633	+	0.470945i
$267$		0			0
$268$	−250.562	+	4.05719i	−0.934931	+	0.0151388i
$269$	131.483			0.488784			0.244392	−	0.969677i	$-0.421412\pi$
$269$	131.483			0.488784			0.244392	+	0.969677i	$0.421412\pi$
$270$		0			0
$271$		−	143.088i		−	0.528000i	−0.964523	−	0.264000i	$-0.914958\pi$
$271$		−	143.088i		−	0.528000i	0.964523	−	0.264000i	$-0.0850418\pi$
$272$	422.516	−	13.6866i	1.55337	−	0.0503186i
$273$		0			0
$274$	354.159	+	348.471i	1.29255	+	1.27179i
$275$		−	21.5327i		−	0.0783008i
$276$		0			0
$277$	−282.748			−1.02075			−0.510375	−	0.859952i	$-0.670493\pi$
$277$	−282.748			−1.02075			−0.510375	+	0.859952i	$0.670493\pi$
$278$	123.965	−	125.988i	0.445916	−	0.453195i
$279$		0			0
$280$	29.8438	+	28.4283i	0.106585	+	0.101530i
$281$	258.526			0.920021			0.460010	−	0.887913i	$-0.347846\pi$
$281$	258.526			0.920021			0.460010	+	0.887913i	$0.347846\pi$
$282$		0			0
$283$		−	471.840i		−	1.66728i	−0.552309	−	0.833640i	$-0.686253\pi$
$283$		−	471.840i		−	1.66728i	0.552309	−	0.833640i	$-0.313747\pi$
$284$	528.814	−	8.56275i	1.86202	−	0.0301505i
$285$		0			0
$286$	4.90410	−	4.98415i	0.0171472	−	0.0174271i
$287$			7.07424i			0.0246489i
$288$		0			0
$289$	409.073			1.41548
$290$	−84.3670	−	83.0120i	−0.290921	−	0.286248i
$291$		0			0
$292$	6.48074	+	400.234i	0.0221943	+	1.37066i
$293$	−348.535			−1.18954			−0.594770	−	0.803896i	$-0.702757\pi$
$293$	−348.535			−1.18954			−0.594770	+	0.803896i	$0.702757\pi$
$294$		0			0
$295$			65.7622i			0.222923i
$296$	−331.393	+	347.894i	−1.11957	+	1.17532i
$297$		0			0
$298$	−127.429	−	125.383i	−0.427615	−	0.420747i
$299$		−	10.2727i		−	0.0343570i
$300$		0			0
$301$	17.7227			0.0588795
$302$	277.121	−	281.644i	0.917619	−	0.932598i
$303$		0			0
$304$	17.4855	+	539.790i	0.0575183	+	1.77562i
$305$	159.183			0.521911
$306$		0			0
$307$			24.1654i			0.0787148i	0.999225	+	0.0393574i	$0.0125311\pi$
$307$			24.1654i			0.0787148i	−0.999225	+	0.0393574i	$0.987469\pi$
$308$	0.173965	+	10.7436i	0.000564821	+	0.0348819i
$309$		0			0
$310$	1.94915	−	1.98097i	0.00628759	−	0.00639022i
$311$		−	351.843i		−	1.13133i	−0.824635	−	0.565665i	$-0.808620\pi$
$311$		−	351.843i		−	1.13133i	0.824635	−	0.565665i	$-0.191380\pi$
$312$		0			0
$313$	−178.717			−0.570982			−0.285491	−	0.958381i	$-0.592157\pi$
$313$	−178.717			−0.570982			−0.285491	+	0.958381i	$0.592157\pi$
$314$	−278.032	−	273.566i	−0.885451	−	0.871229i
$315$		0			0
$316$	390.249	−	6.31906i	1.23497	−	0.0199970i
$317$	−101.728			−0.320910			−0.160455	−	0.987043i	$-0.551296\pi$
$317$	−101.728			−0.320910			−0.160455	+	0.987043i	$0.551296\pi$
$318$		0			0
$319$		−	30.8557i		−	0.0967263i
$320$	6.05114	+	124.481i	0.0189098	+	0.389002i
$321$		0			0
$322$	11.2525	+	11.0717i	0.0349456	+	0.0343843i
$323$			891.832i			2.76109i
$324$		0			0
$325$	−73.0280			−0.224702
$326$	167.784	−	170.522i	0.514674	−	0.523075i
$327$		0			0
$328$	−14.7536	+	15.4882i	−0.0449805	+	0.0472201i
$329$	−64.2951			−0.195426
$330$		0			0
$331$			2.78294i			0.00840768i	0.999991	+	0.00420384i	$0.00133813\pi$
$331$			2.78294i			0.00840768i	−0.999991	+	0.00420384i	$0.998662\pi$
$332$	−351.669	+	5.69435i	−1.05924	+	0.0171517i
$333$		0			0
$334$	−102.069	+	103.735i	−0.305595	+	0.310583i
$335$		−	121.996i		−	0.364167i
$336$		0			0
$337$	−303.217			−0.899755			−0.449877	−	0.893090i	$-0.648532\pi$
$337$	−303.217			−0.899755			−0.449877	+	0.893090i	$0.648532\pi$
$338$	224.025	+	220.427i	0.662797	+	0.652152i
$339$		0			0
$340$	3.33195	+	205.773i	0.00979985	+	0.605214i
$341$	0.724503			0.00212464
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	38.8018	+	36.9615i	0.112796	+	0.107446i
$345$		0			0
$346$	14.1029	+	13.8764i	0.0407600	+	0.0401053i
$347$			166.421i			0.479600i	0.970822	+	0.239800i	$0.0770819\pi$
$347$			166.421i			0.479600i	−0.970822	+	0.239800i	$0.922918\pi$
$348$		0			0
$349$	327.232			0.937629			0.468814	−	0.883297i	$-0.344681\pi$
$349$	327.232			0.937629			0.468814	+	0.883297i	$0.344681\pi$
$350$	78.7081	−	79.9929i	0.224880	−	0.228551i
$351$		0			0
$352$	−22.0254	+	23.8847i	−0.0625721	+	0.0678543i
$353$	−43.6810			−0.123742			−0.0618711	−	0.998084i	$-0.519707\pi$
$353$	−43.6810			−0.123742			−0.0618711	+	0.998084i	$0.519707\pi$
$354$		0			0
$355$			257.474i			0.725280i
$356$	7.14880	+	441.491i	0.0200809	+	1.24014i
$357$		0			0
$358$	353.477	−	359.247i	0.987366	−	1.00348i
$359$			72.4245i			0.201740i	0.994900	+	0.100870i	$0.0321625\pi$
$359$			72.4245i			0.201740i	−0.994900	+	0.100870i	$0.967837\pi$
$360$		0			0
$361$	−778.371			−2.15615
$362$	426.326	+	419.479i	1.17770	+	1.15878i
$363$		0			0
$364$	36.4369	−	0.590001i	0.100102	−	0.00162088i
$365$	−194.870			−0.533890
$366$		0			0
$367$		−	508.952i		−	1.38679i	−0.720558	−	0.693395i	$-0.756114\pi$
$367$		−	508.952i		−	1.38679i	0.720558	−	0.693395i	$-0.243886\pi$
$368$	1.54541	+	47.7077i	0.00419948	+	0.129641i
$369$		0			0
$370$	−166.730	−	164.052i	−0.450621	−	0.443383i
$371$		−	174.176i		−	0.469478i
$372$		0			0
$373$	124.672			0.334242			0.167121	−	0.985936i	$-0.446553\pi$
$373$	124.672			0.334242			0.167121	+	0.985936i	$0.446553\pi$
$374$	−37.6288	+	38.2430i	−0.100612	+	0.102254i
$375$		0			0
$376$	−140.766	−	134.090i	−0.374379	−	0.356622i
$377$	−104.647			−0.277578
$378$		0			0
$379$		−	539.605i		−	1.42376i	−0.702301	−	0.711880i	$-0.747844\pi$
$379$		−	539.605i		−	1.42376i	0.702301	−	0.711880i	$-0.252156\pi$
$380$	−262.887	+	4.25677i	−0.691809	+	0.0112020i
$381$		0			0
$382$	−169.980	+	172.754i	−0.444973	+	0.452237i
$383$		−	563.542i		−	1.47139i	−0.677313	−	0.735695i	$-0.736856\pi$
$383$		−	563.542i		−	1.47139i	0.677313	−	0.735695i	$-0.263144\pi$
$384$		0			0
$385$	−5.23097			−0.0135869
$386$	−156.906	−	154.386i	−0.406493	−	0.399964i
$387$		0			0
$388$	2.31093	+	142.717i	0.00595600	+	0.367827i
$389$	211.324			0.543248			0.271624	−	0.962403i	$-0.412439\pi$
$389$	211.324			0.543248			0.271624	+	0.962403i	$0.412439\pi$
$390$		0			0
$391$			78.8219i			0.201591i
$392$	−38.6247	+	40.5479i	−0.0985324	+	0.103439i
$393$		0			0
$394$	−112.073	−	110.273i	−0.284448	−	0.279880i
$395$			190.009i			0.481034i
$396$		0			0
$397$	271.257			0.683266			0.341633	−	0.939833i	$-0.389020\pi$
$397$	271.257			0.683266			0.341633	+	0.939833i	$0.389020\pi$
$398$	−126.130	+	128.189i	−0.316910	+	0.322083i
$399$		0			0
$400$	339.150	−	10.9862i	0.847875	−	0.0274654i
$401$	−143.015			−0.356647			−0.178323	−	0.983972i	$-0.557067\pi$
$401$	−143.015			−0.356647			−0.178323	+	0.983972i	$0.557067\pi$
$402$		0			0
$403$		−	2.45715i		−	0.00609714i
$404$	3.67167	+	226.753i	0.00908830	+	0.561270i
$405$		0			0
$406$	112.786	−	114.627i	0.277798	−	0.282333i
$407$		−	60.9783i		−	0.149824i
$408$		0			0
$409$	223.590			0.546676			0.273338	−	0.961918i	$-0.411872\pi$
$409$	223.590			0.546676			0.273338	+	0.961918i	$0.411872\pi$
$410$	−7.42280	−	7.30358i	−0.0181044	−	0.0178136i
$411$		0			0
$412$	574.702	−	9.30579i	1.39491	−	0.0225869i
$413$	−89.3493			−0.216342
$414$		0			0
$415$		−	171.224i		−	0.412588i
$416$	81.0048	+	74.6989i	0.194723	+	0.179565i
$417$		0			0
$418$	−48.8578	−	48.0731i	−0.116885	−	0.115007i
$419$		−	293.605i		−	0.700729i	−0.936614	−	0.350364i	$-0.886058\pi$
$419$		−	293.605i		−	0.700729i	0.936614	−	0.350364i	$-0.113942\pi$
$420$		0			0
$421$	−603.329			−1.43309			−0.716543	−	0.697543i	$-0.754277\pi$
$421$	−603.329			−1.43309			−0.716543	+	0.697543i	$0.754277\pi$
$422$	205.306	−	208.657i	0.486507	−	0.494449i
$423$		0			0
$424$	363.251	−	381.338i	0.856724	−	0.899382i
$425$	560.338			1.31844
$426$		0			0
$427$			216.277i			0.506505i
$428$	−683.665	+	11.0702i	−1.59735	+	0.0258649i
$429$		0			0
$430$	−18.2973	+	18.5960i	−0.0425518	+	0.0432464i
$431$		−	285.866i		−	0.663262i	−0.943409	−	0.331631i	$-0.892401\pi$
$431$		−	285.866i		−	0.663262i	0.943409	−	0.331631i	$-0.107599\pi$
$432$		0			0
$433$	−232.262			−0.536403			−0.268201	−	0.963363i	$-0.586429\pi$
$433$	−232.262			−0.536403			−0.268201	+	0.963363i	$0.586429\pi$
$434$	2.69149	+	2.64826i	0.00620159	+	0.00610198i
$435$		0			0
$436$	0.507539	+	31.3443i	0.00116408	+	0.0718906i
$437$	−100.700			−0.230435
$438$		0			0
$439$			30.1779i			0.0687423i	0.999409	+	0.0343711i	$0.0109428\pi$
$439$			30.1779i			0.0687423i	−0.999409	+	0.0343711i	$0.989057\pi$
$440$	−11.4526	−	10.9094i	−0.0260286	−	0.0247941i
$441$		0			0
$442$	129.701	+	127.618i	0.293441	+	0.288728i
$443$		−	708.628i		−	1.59961i	−0.600258	−	0.799806i	$-0.704936\pi$
$443$		−	708.628i		−	1.59961i	0.600258	−	0.799806i	$-0.295064\pi$
$444$		0			0
$445$	−214.958			−0.483051
$446$	−192.712	+	195.858i	−0.432090	+	0.439143i
$447$		0			0
$448$	−169.128	+	8.22152i	−0.377519	+	0.0183516i
$449$	69.7117			0.155260			0.0776299	−	0.996982i	$-0.475265\pi$
$449$	69.7117			0.155260			0.0776299	+	0.996982i	$0.475265\pi$
$450$		0			0
$451$		−	2.71475i		−	0.00601940i
$452$	−11.6445	−	719.135i	−0.0257622	−	1.59101i
$453$		0			0
$454$	86.4747	−	87.8863i	0.190473	−	0.193582i
$455$			17.7408i			0.0389908i
$456$		0			0
$457$	−356.679			−0.780480			−0.390240	−	0.920713i	$-0.627608\pi$
$457$	−356.679			−0.780480			−0.390240	+	0.920713i	$0.627608\pi$
$458$	−446.812	−	439.636i	−0.975572	−	0.959903i
$459$		0			0
$460$	−23.2345	+	0.376222i	−0.0505098	+	0.000817874i
$461$	−597.234			−1.29552			−0.647759	−	0.761845i	$-0.724294\pi$
$461$	−597.234			−1.29552			−0.647759	+	0.761845i	$0.724294\pi$
$462$		0			0
$463$			518.054i			1.11891i	0.828862	+	0.559453i	$0.188989\pi$
$463$			518.054i			1.11891i	−0.828862	+	0.559453i	$0.811011\pi$
$464$	485.991	−	15.7428i	1.04739	−	0.0339285i
$465$		0			0
$466$	−202.807	−	199.549i	−0.435208	−	0.428218i
$467$			546.318i			1.16985i	0.811089	+	0.584923i	$0.198875\pi$
$467$			546.318i			1.16985i	−0.811089	+	0.584923i	$0.801125\pi$
$468$		0			0
$469$	165.753			0.353417
$470$	66.3794	−	67.4629i	0.141233	−	0.143538i
$471$		0			0
$472$	−195.620	−	186.341i	−0.414448	−	0.394791i
$473$	−6.80113			−0.0143787
$474$		0			0
$475$			715.867i			1.50709i
$476$	−279.578	+	4.52703i	−0.587348	+	0.00951056i
$477$		0			0
$478$	−230.629	+	234.394i	−0.482488	+	0.490364i
$479$		−	674.246i		−	1.40761i	−0.710392	−	0.703806i	$-0.751483\pi$
$479$		−	674.246i		−	1.40761i	0.710392	−	0.703806i	$-0.248517\pi$
$480$		0			0
$481$	−206.807			−0.429953
$482$	−98.4389	−	96.8579i	−0.204230	−	0.200950i
$483$		0			0
$484$	7.76932	+	479.814i	0.0160523	+	0.991351i
$485$	−69.4875			−0.143273
$486$		0			0
$487$		−	251.723i		−	0.516886i	−0.966027	−	0.258443i	$-0.916791\pi$
$487$		−	251.723i		−	0.516886i	0.966027	−	0.258443i	$-0.0832094\pi$
$488$	−451.055	+	473.514i	−0.924293	+	0.970315i
$489$		0			0
$490$	−19.4328	−	19.1207i	−0.0396587	−	0.0390217i
$491$			181.391i			0.369433i	0.982792	+	0.184716i	$0.0591366\pi$
$491$			181.391i			0.369433i	−0.982792	+	0.184716i	$0.940863\pi$
$492$		0			0
$493$	802.946			1.62869
$494$	−163.040	+	165.701i	−0.330040	+	0.335427i
$495$		0			0
$496$	0.369647	+	11.4113i	0.000745257	+	0.0230066i
$497$	−349.823			−0.703870
$498$		0			0
$499$		−	230.573i		−	0.462069i	−0.972946	−	0.231035i	$-0.925789\pi$
$499$		−	230.573i		−	0.462069i	0.972946	−	0.231035i	$-0.0742111\pi$
$500$	5.82727	+	359.877i	0.0116545	+	0.719755i
$501$		0			0
$502$	−58.7645	+	59.7237i	−0.117061	+	0.118972i
$503$			761.117i			1.51316i	0.653903	+	0.756578i	$0.273130\pi$
$503$			761.117i			1.51316i	−0.653903	+	0.756578i	$0.726870\pi$
$504$		0			0
$505$	−110.404			−0.218622
$506$	−4.31815	−	4.24880i	−0.00853390	−	0.00839684i
$507$		0			0
$508$	−523.379	+	8.47475i	−1.03027	+	0.0166826i
$509$	−685.349			−1.34646			−0.673231	−	0.739432i	$-0.735094\pi$
$509$	−685.349			−1.34646			−0.673231	+	0.739432i	$0.735094\pi$
$510$		0			0
$511$		−	264.764i		−	0.518130i
$512$	−387.433	−	334.724i	−0.756705	−	0.653757i
$513$		0			0
$514$	307.642	+	302.700i	0.598524	+	0.588911i
$515$			279.817i			0.543334i
$516$		0			0
$517$	24.6733			0.0477240
$518$	222.893	−	226.531i	0.430295	−	0.437319i
$519$		0			0
$520$	−36.9991	+	38.8414i	−0.0711521	+	0.0746949i
$521$	1027.31			1.97181			0.985906	−	0.167298i	$-0.0535043\pi$
$521$	1027.31			1.97181			0.985906	+	0.167298i	$0.0535043\pi$
$522$		0			0
$523$			874.410i			1.67191i	0.548797	+	0.835956i	$0.315086\pi$
$523$			874.410i			1.67191i	−0.548797	+	0.835956i	$0.684914\pi$
$524$	760.505	−	12.3144i	1.45135	−	0.0235007i
$525$		0			0
$526$	−156.989	+	159.552i	−0.298459	+	0.303331i
$527$			18.8535i			0.0357751i
$528$		0			0
$529$	520.100			0.983176
$530$	182.758	+	179.823i	0.344827	+	0.339288i
$531$		0			0
$532$	−5.78356	−	357.178i	−0.0108714	−	0.671387i
$533$	−9.20705			−0.0172740
$534$		0			0
$535$		−	332.870i		−	0.622186i
$536$	362.896	+	345.683i	0.677044	+	0.644932i
$537$		0			0
$538$	−187.444	−	184.433i	−0.348409	−	0.342813i
$539$		−	7.10718i		−	0.0131859i
$540$		0			0
$541$	182.995			0.338253			0.169127	−	0.985594i	$-0.445905\pi$
$541$	182.995			0.338253			0.169127	+	0.985594i	$0.445905\pi$
$542$	−200.712	+	203.988i	−0.370317	+	0.376362i
$543$		0			0
$544$	−621.543	−	573.158i	−1.14254	−	1.05360i
$545$	−15.2612			−0.0280023
$546$		0			0
$547$			91.9279i			0.168058i	0.996463	+	0.0840291i	$0.0267789\pi$
$547$			91.9279i			0.168058i	−0.996463	+	0.0840291i	$0.973221\pi$
$548$	−16.0883	−	993.571i	−0.0293582	−	1.81309i
$549$		0			0
$550$	−30.2043	+	30.6974i	−0.0549170	+	0.0558134i
$551$			1025.81i			1.86173i
$552$		0			0
$553$	−258.159			−0.466834
$554$	403.090	+	396.615i	0.727598	+	0.715912i
$555$		0			0
$556$	−353.452	+	5.72323i	−0.635705	+	0.0102936i
$557$	−204.578			−0.367285			−0.183643	−	0.982993i	$-0.558789\pi$
$557$	−204.578			−0.367285			−0.183643	+	0.982993i	$0.558789\pi$
$558$		0			0
$559$			23.0660i			0.0412629i
$560$	−2.66889	−	82.3902i	−0.00476587	−	0.147125i
$561$		0			0
$562$	−368.559	−	362.639i	−0.655798	−	0.645265i
$563$			681.311i			1.21014i	0.796171	+	0.605072i	$0.206856\pi$
$563$			681.311i			1.21014i	−0.796171	+	0.605072i	$0.793144\pi$
$564$		0			0
$565$	350.140			0.619716
$566$	−661.859	+	672.663i	−1.16936	+	1.18845i
$567$		0			0
$568$	−765.896	−	729.570i	−1.34841	−	1.28445i
$569$	436.176			0.766566			0.383283	−	0.923631i	$-0.374793\pi$
$569$	436.176			0.766566			0.383283	+	0.923631i	$0.374793\pi$
$570$		0			0
$571$			235.145i			0.411813i	0.978572	+	0.205906i	$0.0660143\pi$
$571$			235.145i			0.411813i	−0.978572	+	0.205906i	$0.933986\pi$
$572$	−13.9827	+	0.226414i	−0.0244453	+	0.000395828i
$573$		0			0
$574$	9.92317	−	10.0851i	0.0172878	−	0.0175699i
$575$			63.2698i			0.110034i
$576$		0			0
$577$	380.151			0.658840			0.329420	−	0.944183i	$-0.393147\pi$
$577$	380.151			0.658840			0.329420	+	0.944183i	$0.393147\pi$
$578$	−583.181	−	573.814i	−1.00896	−	0.992758i
$579$		0			0
$580$	3.83251	+	236.686i	0.00660778	+	0.408080i
$581$	232.637			0.400409
$582$		0			0
$583$			66.8404i			0.114649i
$584$	552.176	−	579.670i	0.945507	−	0.992586i
$585$		0			0
$586$	496.877	+	488.897i	0.847913	+	0.834295i
$587$			364.304i			0.620620i	0.950635	+	0.310310i	$0.100433\pi$
$587$			364.304i			0.620620i	−0.950635	+	0.310310i	$0.899567\pi$
$588$		0			0
$589$	−24.0865			−0.0408939
$590$	92.2459	−	93.7516i	0.156349	−	0.158901i
$591$		0			0
$592$	960.436	−	31.1116i	1.62236	−	0.0525535i
$593$	57.6374			0.0971963			0.0485982	−	0.998818i	$-0.484525\pi$
$593$	57.6374			0.0971963			0.0485982	+	0.998818i	$0.484525\pi$
$594$		0			0
$595$		−	136.124i		−	0.228779i
$596$	5.78869	+	357.495i	0.00971257	+	0.599824i
$597$		0			0
$598$	−14.4098	+	14.6450i	−0.0240966	+	0.0244899i
$599$		−	496.778i		−	0.829346i	−0.909970	−	0.414673i	$-0.863896\pi$
$599$		−	496.778i		−	0.829346i	0.909970	−	0.414673i	$-0.136104\pi$
$600$		0			0
$601$	467.713			0.778224			0.389112	−	0.921190i	$-0.372782\pi$
$601$	467.713			0.778224			0.389112	+	0.921190i	$0.372782\pi$
$602$	−25.2658	−	24.8600i	−0.0419698	−	0.0412957i
$603$		0			0
$604$	−790.136	+	12.7942i	−1.30817	+	0.0211824i
$605$	−233.617			−0.386143
$606$		0			0
$607$		−	750.168i		−	1.23586i	−0.786233	−	0.617930i	$-0.787971\pi$
$607$		−	750.168i		−	1.23586i	0.786233	−	0.617930i	$-0.212029\pi$
$608$	732.246	−	794.060i	1.20435	−	1.30602i
$609$		0			0
$610$	−226.934	−	223.289i	−0.372022	−	0.366047i
$611$		−	83.6794i		−	0.136955i
$612$		0			0
$613$	854.291			1.39362			0.696811	−	0.717255i	$-0.254602\pi$
$613$	854.291			1.39362			0.696811	+	0.717255i	$0.254602\pi$
$614$	33.8973	−	34.4506i	0.0552073	−	0.0561085i
$615$		0			0
$616$	14.8223	−	15.5603i	0.0240622	−	0.0252603i
$617$	−272.107			−0.441015			−0.220508	−	0.975385i	$-0.570771\pi$
$617$	−272.107			−0.441015			−0.220508	+	0.975385i	$0.570771\pi$
$618$		0			0
$619$		−	414.506i		−	0.669639i	−0.942282	−	0.334819i	$-0.891325\pi$
$619$		−	414.506i		−	0.669639i	0.942282	−	0.334819i	$-0.108675\pi$
$620$	−5.55748	+	0.0899889i	−0.00896368	+	0.000145143i
$621$		0			0
$622$	−493.537	+	501.594i	−0.793469	+	0.806421i
$623$		−	292.057i		−	0.468792i
$624$		0			0
$625$	354.979			0.567967
$626$	254.782	+	250.690i	0.407000	+	0.400463i
$627$		0			0
$628$	12.6301	+	780.000i	0.0201116	+	1.24204i
$629$	1586.82			2.52276
$630$		0			0
$631$			303.910i			0.481632i	0.970571	+	0.240816i	$0.0774150\pi$
$631$			303.910i			0.481632i	−0.970571	+	0.240816i	$0.922585\pi$
$632$	−565.209	−	538.401i	−0.894319	−	0.851901i
$633$		0			0
$634$	145.026	+	142.696i	0.228747	+	0.225073i
$635$		−	254.828i		−	0.401304i
$636$		0			0
$637$	−24.1039			−0.0378398
$638$	−43.2818	+	43.9883i	−0.0678399	+	0.0689472i
$639$		0			0
$640$	165.985	−	185.950i	0.259351	−	0.290546i
$641$	−532.633			−0.830941			−0.415471	−	0.909607i	$-0.636383\pi$
$641$	−532.633			−0.830941			−0.415471	+	0.909607i	$0.636383\pi$
$642$		0			0
$643$			844.547i			1.31345i	0.754131	+	0.656724i	$0.228058\pi$
$643$			844.547i			1.31345i	−0.754131	+	0.656724i	$0.771942\pi$
$644$	−0.511163	−	31.5681i	−0.000793731	−	0.0490188i
$645$		0			0
$646$	1250.99	−	1271.41i	1.93652	−	1.96813i
$647$		−	606.314i		−	0.937116i	−0.883433	−	0.468558i	$-0.844774\pi$
$647$		−	606.314i		−	0.937116i	0.883433	−	0.468558i	$-0.155226\pi$
$648$		0			0
$649$	34.2879			0.0528319
$650$	104.110	+	102.438i	0.160169	+	0.157597i
$651$		0			0
$652$	−478.390	+	7.74627i	−0.733727	+	0.0118808i
$653$	16.8535			0.0258094			0.0129047	−	0.999917i	$-0.495892\pi$
$653$	16.8535			0.0258094			0.0129047	+	0.999917i	$0.495892\pi$
$654$		0			0
$655$			370.283i			0.565317i
$656$	42.7586	−	1.38509i	0.0651807	−	0.00211142i
$657$		0			0
$658$	91.6601	+	90.1879i	0.139301	+	0.137064i
$659$			761.139i			1.15499i	0.816394	+	0.577495i	$0.195970\pi$
$659$			761.139i			1.15499i	−0.816394	+	0.577495i	$0.804030\pi$
$660$		0			0
$661$	−982.016			−1.48565			−0.742826	−	0.669485i	$-0.766515\pi$
$661$	−982.016			−1.48565			−0.742826	+	0.669485i	$0.766515\pi$
$662$	3.90369	−	3.96741i	0.00589681	−	0.00599306i
$663$		0			0
$664$	509.332	+	485.174i	0.767066	+	0.730684i
$665$	173.906			0.261513
$666$		0			0
$667$			90.6635i			0.135927i
$668$	291.022	−	4.71233i	0.435661	−	0.00705439i
$669$		0			0
$670$	−171.126	+	173.919i	−0.255412	+	0.259581i
$671$		−	82.9968i		−	0.123691i
$672$		0			0
$673$	700.065			1.04022			0.520108	−	0.854101i	$-0.325892\pi$
$673$	700.065			1.04022			0.520108	+	0.854101i	$0.325892\pi$
$674$	432.272	+	425.329i	0.641352	+	0.631052i
$675$		0			0
$676$	−10.1767	−	628.489i	−0.0150543	−	0.929718i
$677$	712.131			1.05189			0.525946	−	0.850518i	$-0.323711\pi$
$677$	712.131			1.05189			0.525946	+	0.850518i	$0.323711\pi$
$678$		0			0
$679$		−	94.4108i		−	0.139044i
$680$	283.891	−	298.027i	0.417487	−	0.438274i
$681$		0			0
$682$	−1.03286	−	1.01627i	−0.00151446	−	0.00149014i
$683$		−	480.992i		−	0.704235i	−0.935956	−	0.352117i	$-0.885462\pi$
$683$		−	480.992i		−	0.704235i	0.935956	−	0.352117i	$-0.114538\pi$
$684$		0			0
$685$	483.760			0.706219
$686$	25.9787	−	26.4028i	0.0378698	−	0.0384880i
$687$		0			0
$688$	−3.46999	−	107.121i	−0.00504360	−	0.155699i
$689$	226.689			0.329011
$690$		0			0
$691$		−	47.0484i		−	0.0680874i	−0.999420	−	0.0340437i	$-0.989161\pi$
$691$		−	47.0484i		−	0.0680874i	0.999420	−	0.0340437i	$-0.0108385\pi$
$692$	−0.640650	−	39.5649i	−0.000925795	−	0.0571747i
$693$		0			0
$694$	233.442	−	237.253i	0.336372	−	0.341863i
$695$		−	172.092i		−	0.247615i
$696$		0			0
$697$	70.6450			0.101356
$698$	−466.508	−	459.015i	−0.668349	−	0.657615i
$699$		0			0
$700$	−224.415	+	3.63381i	−0.320593	+	0.00519116i
$701$	95.2081			0.135818			0.0679088	−	0.997692i	$-0.478367\pi$
$701$	95.2081			0.135818			0.0679088	+	0.997692i	$0.478367\pi$
$702$		0			0
$703$			2027.26i			2.88372i
$704$	64.9033	−	3.15502i	0.0921921	−	0.00448156i
$705$		0			0
$706$	62.2723	+	61.2721i	0.0882044	+	0.0867877i
$707$		−	150.003i		−	0.212168i
$708$		0			0
$709$	−408.681			−0.576419			−0.288210	−	0.957567i	$-0.593060\pi$
$709$	−408.681			−0.576419			−0.288210	+	0.957567i	$0.593060\pi$
$710$	361.164	−	367.059i	0.508682	−	0.516985i
$711$		0			0
$712$	609.097	−	639.425i	0.855473	−	0.898069i
$713$	−2.12881			−0.00298571
$714$		0			0
$715$		−	6.80806i		−	0.00952176i
$716$	−1007.84	+	16.3194i	−1.40760	+	0.0227925i
$717$		0			0
$718$	101.591	−	103.250i	0.141492	−	0.143802i
$719$			800.605i			1.11350i	0.830681	+	0.556749i	$0.187952\pi$
$719$			800.605i			1.11350i	−0.830681	+	0.556749i	$0.812048\pi$
$720$		0			0
$721$	−380.179			−0.527295
$722$	1109.66	+	1091.84i	1.53692	+	1.51224i
$723$		0			0
$724$	−19.3666	−	1196.03i	−0.0267494	−	1.65198i
$725$	644.519			0.888992
$726$		0			0
$727$		−	751.732i		−	1.03402i	−0.855980	−	0.517009i	$-0.827045\pi$
$727$		−	751.732i		−	1.03402i	0.855980	−	0.517009i	$-0.172955\pi$
$728$	−52.7727	−	50.2697i	−0.0724900	−	0.0690517i
$729$		0			0
$730$	277.810	+	273.348i	0.380561	+	0.374449i
$731$		−	176.983i		−	0.242111i
$732$		0			0
$733$	−389.015			−0.530716			−0.265358	−	0.964150i	$-0.585490\pi$
$733$	−389.015			−0.530716			−0.265358	+	0.964150i	$0.585490\pi$
$734$	−713.916	+	725.570i	−0.972638	+	0.988515i
$735$		0			0
$736$	64.7174	−	70.1807i	0.0879312	−	0.0953542i
$737$	−63.6078			−0.0863064
$738$		0			0
$739$		−	95.5532i		−	0.129301i	−0.997908	−	0.0646503i	$-0.979407\pi$
$739$		−	95.5532i		−	0.129301i	0.997908	−	0.0646503i	$-0.0205932\pi$
$740$	7.57398	+	467.750i	0.0102351	+	0.632094i
$741$		0			0
$742$	−244.320	+	248.308i	−0.329273	+	0.334647i
$743$		−	1204.73i		−	1.62144i	−0.585433	−	0.810721i	$-0.699075\pi$
$743$		−	1204.73i		−	1.62144i	0.585433	−	0.810721i	$-0.300925\pi$
$744$		0			0
$745$	−174.061			−0.233639
$746$	−177.735	−	174.880i	−0.238251	−	0.234424i
$747$		0			0
$748$	107.288	−	1.73725i	0.143434	−	0.00232253i
$749$	452.261			0.603820
$750$		0			0
$751$		−	1162.57i		−	1.54804i	−0.633164	−	0.774018i	$-0.718244\pi$
$751$		−	1162.57i		−	1.54804i	0.633164	−	0.774018i	$-0.281756\pi$
$752$	12.5885	+	388.616i	0.0167401	+	0.516777i
$753$		0			0
$754$	149.186	+	146.790i	0.197860	+	0.194682i
$755$		−	384.709i		−	0.509549i
$756$		0			0
$757$	379.147			0.500855			0.250428	−	0.968135i	$-0.419429\pi$
$757$	379.147			0.500855			0.250428	+	0.968135i	$0.419429\pi$
$758$	−756.914	+	769.270i	−0.998568	+	1.01487i
$759$		0			0
$760$	380.748	+	362.689i	0.500984	+	0.477222i
$761$	−814.146			−1.06984			−0.534918	−	0.844904i	$-0.679658\pi$
$761$	−814.146			−1.06984			−0.534918	+	0.844904i	$0.679658\pi$
$762$		0			0
$763$		−	20.7350i		−	0.0271757i
$764$	484.652	−	7.84766i	0.634361	−	0.0102718i
$765$		0			0
$766$	−790.491	+	803.394i	−1.03197	+	1.04882i
$767$		−	116.287i		−	0.151613i
$768$		0			0
$769$	−973.923			−1.26648			−0.633240	−	0.773956i	$-0.718275\pi$
$769$	−973.923			−1.26648			−0.633240	+	0.773956i	$0.718275\pi$
$770$	7.45735	+	7.33758i	0.00968487	+	0.00952932i
$771$		0			0
$772$	7.12774	+	440.191i	0.00923282	+	0.570196i
$773$	−757.451			−0.979885			−0.489943	−	0.871755i	$-0.662982\pi$
$773$	−757.451			−0.979885			−0.489943	+	0.871755i	$0.662982\pi$
$774$		0			0
$775$			15.1335i			0.0195272i
$776$	196.897	−	206.701i	0.253734	−	0.266368i
$777$		0			0
$778$	−301.266	−	296.428i	−0.387232	−	0.381012i
$779$			90.2534i			0.115858i
$780$		0			0
$781$	134.245			0.171889
$782$	110.565	−	112.370i	0.141387	−	0.143695i
$783$		0			0
$784$	111.941	−	3.62614i	0.142782	−	0.00462518i
$785$	−379.774			−0.483789
$786$		0			0
$787$		−	113.131i		−	0.143750i	−0.997414	−	0.0718749i	$-0.977102\pi$
$787$		−	113.131i		−	0.143750i	0.997414	−	0.0718749i	$-0.0228982\pi$
$788$	5.09109	+	314.413i	0.00646077	+	0.399001i
$789$		0			0
$790$	266.529	−	270.879i	0.337378	−	0.342885i
$791$			475.725i			0.601423i
$792$		0			0
$793$	−281.483			−0.354960
$794$	−386.708	−	380.497i	−0.487038	−	0.479215i
$795$		0			0
$796$	359.626	−	5.82320i	0.451791	−	0.00731558i
$797$	421.650			0.529047			0.264523	−	0.964379i	$-0.414785\pi$
$797$	421.650			0.529047			0.264523	+	0.964379i	$0.414785\pi$
$798$		0			0
$799$			642.065i			0.803586i
$800$	−498.908	−	460.070i	−0.623635	−	0.575088i
$801$		0			0
$802$	203.885	+	200.610i	0.254221	+	0.250138i
$803$			101.604i			0.126530i
$804$		0			0
$805$	15.3702			0.0190934
$806$	−3.44668	+	3.50295i	−0.00427628	+	0.00434609i
$807$		0			0
$808$	312.837	−	328.413i	0.387174	−	0.406452i
$809$	−241.212			−0.298161			−0.149081	−	0.988825i	$-0.547631\pi$
$809$	−241.212			−0.298161			−0.149081	+	0.988825i	$0.547631\pi$
$810$		0			0
$811$		−	1343.28i		−	1.65632i	−0.560491	−	0.828160i	$-0.689388\pi$
$811$		−	1343.28i		−	1.65632i	0.560491	−	0.828160i	$-0.310612\pi$
$812$	−321.579	+	5.20713i	−0.396034	+	0.00641273i
$813$		0			0
$814$	−85.5354	+	86.9316i	−0.105080	+	0.106796i
$815$		−	232.923i		−	0.285796i
$816$		0			0
$817$	226.107			0.276753
$818$	−318.754	−	313.634i	−0.389675	−	0.383416i
$819$		0			0
$820$	0.337193	+	20.8242i	0.000411211	+	0.0253953i
$821$	−1046.03			−1.27409			−0.637047	−	0.770825i	$-0.719844\pi$
$821$	−1046.03			−1.27409			−0.637047	+	0.770825i	$0.719844\pi$
$822$		0			0
$823$			410.187i			0.498404i	0.968452	+	0.249202i	$0.0801683\pi$
$823$			410.187i			0.498404i	−0.968452	+	0.249202i	$0.919832\pi$
$824$	−832.358	−	792.879i	−1.01014	−	0.962231i
$825$		0			0
$826$	127.378	+	125.332i	0.154210	+	0.151734i
$827$		−	438.443i		−	0.530161i	−0.964226	−	0.265080i	$-0.914601\pi$
$827$		−	438.443i		−	0.530161i	0.964226	−	0.265080i	$-0.0853985\pi$
$828$		0			0
$829$	−830.325			−1.00160			−0.500799	−	0.865563i	$-0.666961\pi$
$829$	−830.325			−1.00160			−0.500799	+	0.865563i	$0.666961\pi$
$830$	−240.179	+	244.100i	−0.289372	+	0.294096i
$831$		0			0
$832$	−10.7002	−	220.119i	−0.0128608	−	0.264566i
$833$	184.948			0.222026
$834$		0			0
$835$			141.696i			0.169695i
$836$	2.21945	+	137.068i	0.00265484	+	0.163956i
$837$		0			0
$838$	−411.846	+	418.568i	−0.491462	+	0.499485i
$839$			1492.60i			1.77903i	0.456910	+	0.889513i	$0.348956\pi$
$839$			1492.60i			1.77903i	−0.456910	+	0.889513i	$0.651044\pi$
$840$		0			0
$841$	82.5748			0.0981864
$842$	860.116	+	846.301i	1.02152	+	1.00511i
$843$		0			0
$844$	−585.375	+	9.47861i	−0.693572	+	0.0112306i
$845$	306.005			0.362136
$846$		0			0
$847$		−	317.409i		−	0.374744i
$848$	−1052.77	+	34.1025i	−1.24147	+	0.0402152i
$849$		0			0
$850$	−798.827	−	785.997i	−0.939796	−	0.924702i
$851$			179.173i			0.210544i
$852$		0			0
$853$	−861.696			−1.01020			−0.505098	−	0.863062i	$-0.668543\pi$
$853$	−861.696			−1.01020			−0.505098	+	0.863062i	$0.668543\pi$
$854$	303.376	−	308.329i	0.355242	−	0.361040i
$855$		0			0
$856$	990.172	+	943.208i	1.15674	+	1.10188i
$857$	−1354.69			−1.58074			−0.790369	−	0.612630i	$-0.790111\pi$
$857$	−1354.69			−1.58074			−0.790369	+	0.612630i	$0.790111\pi$
$858$		0			0
$859$		−	35.9658i		−	0.0418694i	−0.999781	−	0.0209347i	$-0.993336\pi$
$859$		−	35.9658i		−	0.0418694i	0.999781	−	0.0209347i	$-0.00666421\pi$
$860$	52.1698	−	0.844753i	0.0606626	−	0.000982271i
$861$		0			0
$862$	−400.990	+	407.535i	−0.465185	+	0.472779i
$863$			160.407i			0.185871i	0.995672	+	0.0929355i	$0.0296250\pi$
$863$			160.407i			0.185871i	−0.995672	+	0.0929355i	$0.970375\pi$
$864$		0			0
$865$	19.2638			0.0222703
$866$	331.117	+	325.799i	0.382352	+	0.376211i
$867$		0			0
$868$	−0.122265	−	7.55080i	−0.000140859	−	0.00869908i
$869$	99.0691			0.114004
$870$		0			0
$871$			215.725i			0.247676i
$872$	43.2437	−	45.3969i	0.0495914	−	0.0520606i
$873$		0			0
$874$	143.559	+	141.254i	0.164256	+	0.161617i
$875$		−	238.068i		−	0.272077i
$876$		0			0
$877$	−1496.48			−1.70636			−0.853182	−	0.521613i	$-0.825330\pi$
$877$	−1496.48			−1.70636			−0.853182	+	0.521613i	$0.825330\pi$
$878$	42.3310	−	43.0220i	0.0482130	−	0.0490000i
$879$		0			0
$880$	1.02419	+	31.6173i	0.00116385	+	0.0359288i
$881$	−627.408			−0.712154			−0.356077	−	0.934457i	$-0.615886\pi$
$881$	−627.408			−0.712154			−0.356077	+	0.934457i	$0.615886\pi$
$882$		0			0
$883$		−	1501.32i		−	1.70025i	−0.526579	−	0.850126i	$-0.676526\pi$
$883$		−	1501.32i		−	1.70025i	0.526579	−	0.850126i	$-0.323474\pi$
$884$	−5.89188	−	363.868i	−0.00666502	−	0.411615i
$885$		0			0
$886$	−994.006	+	1010.23i	−1.12190	+	1.14022i
$887$			655.427i			0.738925i	0.929246	+	0.369463i	$0.120458\pi$
$887$			655.427i			0.738925i	−0.929246	+	0.369463i	$0.879542\pi$
$888$		0			0
$889$	346.228			0.389458
$890$	306.447	+	301.525i	0.344323	+	0.338793i
$891$		0			0
$892$	549.466	−	8.89717i	0.615994	−	0.00997440i
$893$	−820.278			−0.918565
$894$		0			0
$895$		−	490.710i		−	0.548279i
$896$	252.645	+	225.519i	0.281969	+	0.251695i
$897$		0			0
$898$	−99.3821	−	97.7858i	−0.110670	−	0.108893i
$899$			21.6859i			0.0241222i
$900$		0			0
$901$	−1739.36			−1.93048
$902$	−3.80803	+	3.87019i	−0.00422176	+	0.00429068i
$903$		0			0
$904$	−992.143	+	1041.54i	−1.09750	+	1.15215i
$905$	582.336			0.643465
$906$		0			0
$907$		−	1187.82i		−	1.30962i	−0.755794	−	0.654809i	$-0.772749\pi$
$907$		−	1187.82i		−	1.30962i	0.755794	−	0.654809i	$-0.227251\pi$
$908$	−246.559	+	3.99238i	−0.271541	+	0.00439690i
$909$		0			0
$910$	24.8853	−	25.2916i	0.0273465	−	0.0277929i
$911$		−	1557.23i		−	1.70937i	−0.519150	−	0.854683i	$-0.673752\pi$
$911$		−	1557.23i		−	1.70937i	0.519150	−	0.854683i	$-0.326248\pi$
$912$		0			0
$913$	−89.2749			−0.0977820
$914$	508.488	+	500.321i	0.556332	+	0.547397i
$915$		0			0
$916$	20.2972	+	1253.50i	0.0221585	+	1.36845i
$917$	−503.093			−0.548629
$918$		0			0
$919$			813.603i			0.885313i	0.896691	+	0.442657i	$0.145964\pi$
$919$			813.603i			0.885313i	−0.896691	+	0.442657i	$0.854036\pi$
$920$	33.6512	+	32.0552i	0.0365774	+	0.0348426i
$921$		0			0
$922$	851.426	+	837.751i	0.923456	+	0.908624i
$923$		−	455.292i		−	0.493274i
$924$		0			0
$925$	1273.73			1.37700
$926$	726.684	−	738.546i	0.784756	−	0.797566i
$927$		0			0
$928$	−714.919	−	659.265i	−0.770387	−	0.710415i
$929$	−231.239			−0.248911			−0.124456	−	0.992225i	$-0.539718\pi$
$929$	−231.239			−0.248911			−0.124456	+	0.992225i	$0.539718\pi$
$930$		0			0
$931$			236.282i			0.253794i
$932$	9.21284	+	568.962i	0.00988502	+	0.610474i
$933$		0			0
$934$	766.330	−	778.839i	0.820482	−	0.833875i
$935$			52.2377i			0.0558691i
$936$		0			0
$937$	595.601			0.635647			0.317823	−	0.948150i	$-0.397048\pi$
$937$	595.601			0.635647			0.317823	+	0.948150i	$0.397048\pi$
$938$	−236.300	−	232.504i	−0.251919	−	0.247872i
$939$		0			0
$940$	−189.263	+	3.06462i	−0.201344	+	0.00326023i
$941$	−847.831			−0.900990			−0.450495	−	0.892779i	$-0.648752\pi$
$941$	−847.831			−0.900990			−0.450495	+	0.892779i	$0.648752\pi$
$942$		0			0
$943$			7.97678i			0.00845894i
$944$	17.4940	+	540.051i	0.0185318	+	0.572087i
$945$		0			0
$946$	9.69580	+	9.54007i	0.0102493	+	0.0100846i
$947$			193.623i			0.204459i	0.994761	+	0.102230i	$0.0325976\pi$
$947$			193.623i			0.204459i	−0.994761	+	0.102230i	$0.967402\pi$
$948$		0			0
$949$	344.588			0.363107
$950$	1004.16	−	1020.55i	1.05701	−	1.07426i
$951$		0			0
$952$	404.921	+	385.715i	0.425337	+	0.405163i
$953$	−1097.59			−1.15172			−0.575858	−	0.817550i	$-0.695332\pi$
$953$	−1097.59			−1.15172			−0.575858	+	0.817550i	$0.695332\pi$
$954$		0			0
$955$			235.972i			0.247091i
$956$	657.577	−	10.6477i	0.687842	−	0.0111378i
$957$		0			0
$958$	−945.777	+	961.216i	−0.987241	+	1.00336i
$959$			657.272i			0.685372i
$960$		0			0
$961$	960.491			0.999470
$962$	294.828	+	290.093i	0.306474	+	0.301552i
$963$		0			0
$964$	4.47175	+	276.164i	0.00463875	+	0.286477i
$965$	−214.325			−0.222098
$966$		0			0
$967$			1111.07i			1.14899i	0.818507	+	0.574496i	$0.194802\pi$
$967$			1111.07i			1.14899i	−0.818507	+	0.574496i	$0.805198\pi$
$968$	661.968	−	694.928i	0.683851	−	0.717901i
$969$		0			0
$970$	99.0625	+	97.4714i	0.102126	+	0.100486i
$971$		−	1113.58i		−	1.14683i	−0.819263	−	0.573417i	$-0.805617\pi$
$971$		−	1113.58i		−	1.14683i	0.819263	−	0.573417i	$-0.194383\pi$
$972$		0			0
$973$	233.817			0.240306
$974$	−353.097	+	358.861i	−0.362523	+	0.368440i
$975$		0			0
$976$	1307.24	−	42.3457i	1.33938	−	0.0433869i
$977$	630.333			0.645172			0.322586	−	0.946540i	$-0.395448\pi$
$977$	630.333			0.645172			0.322586	+	0.946540i	$0.395448\pi$
$978$		0			0
$979$			112.077i			0.114482i
$980$	0.882767	+	54.5174i	0.000900782	+	0.0556300i
$981$		0			0
$982$	254.441	−	258.594i	0.259105	−	0.263334i
$983$			1659.64i			1.68834i	0.536078	+	0.844168i	$0.319905\pi$
$983$			1659.64i			1.68834i	−0.536078	+	0.844168i	$0.680095\pi$
$984$		0			0
$985$	−153.084			−0.155416
$986$	−1144.69	−	1126.31i	−1.16095	−	1.14230i
$987$		0			0
$988$	464.864	−	7.52725i	0.470510	−	0.00761867i
$989$	19.9838			0.0202061
$990$		0			0
$991$		−	1945.49i		−	1.96316i	−0.191053	−	0.981580i	$-0.561190\pi$
$991$		−	1945.49i		−	1.96316i	0.191053	−	0.981580i	$-0.438810\pi$
$992$	15.4798	−	16.7866i	0.0156046	−	0.0169219i
$993$		0			0
$994$	498.714	+	490.704i	0.501724	+	0.493666i
$995$			175.098i			0.175978i
$996$		0			0
$997$	−142.870			−0.143300			−0.0716499	−	0.997430i	$-0.522826\pi$
$997$	−142.870			−0.143300			−0.0716499	+	0.997430i	$0.522826\pi$
$998$	−323.428	+	328.708i	−0.324077	+	0.329367i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.g.b.127.3		12
3.2	odd	2		84.3.g.a.43.10	yes	12
4.3	odd	2	inner	252.3.g.b.127.4		12
12.11	even	2		84.3.g.a.43.9	✓	12
21.20	even	2		588.3.g.d.295.10		12
24.5	odd	2		1344.3.m.e.127.3		12
24.11	even	2		1344.3.m.e.127.9		12
84.83	odd	2		588.3.g.d.295.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.g.a.43.9	✓	12	12.11	even	2
84.3.g.a.43.10	yes	12	3.2	odd	2
252.3.g.b.127.3		12	1.1	even	1	trivial
252.3.g.b.127.4		12	4.3	odd	2	inner
588.3.g.d.295.9		12	84.83	odd	2
588.3.g.d.295.10		12	21.20	even	2
1344.3.m.e.127.3		12	24.5	odd	2
1344.3.m.e.127.9		12	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42562 - 1.40272i) q^{2} +(0.0647610 + 3.99948i) q^{4} -1.94731 q^{5} -2.64575i q^{7} +(5.51781 - 5.79256i) q^{8} +O(q^{10})\)	\(q+(-1.42562 - 1.40272i) q^{2} +(0.0647610 + 3.99948i) q^{4} -1.94731 q^{5} -2.64575i q^{7} +(5.51781 - 5.79256i) q^{8} +(2.77611 + 2.73152i) q^{10} +1.01531i q^{11} +3.44342 q^{13} +(-3.71124 + 3.77182i) q^{14} +(-15.9916 + 0.518020i) q^{16} -26.4211 q^{17} -33.7546i q^{19} +(-0.126110 - 7.78820i) q^{20} +(1.42420 - 1.44744i) q^{22} -2.98330i q^{23} -21.2080 q^{25} +(-4.90899 - 4.83015i) q^{26} +(10.5816 - 0.171342i) q^{28} -30.3904 q^{29} -0.713577i q^{31} +(23.5245 + 21.6932i) q^{32} +(37.6663 + 37.0613i) q^{34} +5.15209i q^{35} -60.0588 q^{37} +(-47.3482 + 48.1210i) q^{38} +(-10.7449 + 11.2799i) q^{40} -2.67381 q^{41} +6.69857i q^{43} +(-4.06071 + 0.0657526i) q^{44} +(-4.18473 + 4.25304i) q^{46} -24.3012i q^{47} -7.00000 q^{49} +(30.2345 + 29.7489i) q^{50} +(0.222999 + 13.7719i) q^{52} +65.8324 q^{53} -1.97712i q^{55} +(-15.3257 - 14.5988i) q^{56} +(43.3250 + 42.6291i) q^{58} -33.7709i q^{59} -81.7452 q^{61} +(-1.00095 + 1.01729i) q^{62} +(-3.10744 - 63.9245i) q^{64} -6.70539 q^{65} +62.6486i q^{67} +(-1.71106 - 105.670i) q^{68} +(7.22693 - 7.34490i) q^{70} -132.221i q^{71} +100.072 q^{73} +(85.6207 + 84.2455i) q^{74} +(135.001 - 2.18598i) q^{76} +2.68626 q^{77} -97.5751i q^{79} +(31.1406 - 1.00874i) q^{80} +(3.81183 + 3.75061i) q^{82} +87.9287i q^{83} +51.4499 q^{85} +(9.39621 - 9.54958i) q^{86} +(5.88125 + 5.60230i) q^{88} +110.387 q^{89} -9.11043i q^{91} +(11.9316 - 0.193201i) q^{92} +(-34.0878 + 34.6442i) q^{94} +65.7305i q^{95} +35.6839 q^{97} +(9.97931 + 9.81903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8	\( 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8} + 28 q^{10} - 24 q^{13} + 14 q^{14} - 14 q^{16} + 40 q^{17} + 20 q^{20} - 88 q^{22} + 180 q^{25} - 100 q^{26} + 14 q^{28} - 72 q^{29} - 142 q^{32} - 100 q^{34} - 88 q^{37} - 128 q^{38} - 28 q^{40} + 200 q^{41} + 40 q^{44} - 24 q^{46} - 84 q^{49} + 346 q^{50} - 364 q^{52} - 104 q^{53} - 98 q^{56} + 148 q^{58} + 104 q^{61} - 64 q^{62} - 70 q^{64} - 176 q^{65} - 188 q^{68} - 84 q^{70} + 312 q^{73} - 4 q^{74} + 432 q^{76} + 224 q^{77} + 564 q^{80} + 332 q^{82} + 352 q^{85} - 160 q^{86} + 328 q^{88} + 552 q^{89} - 232 q^{92} - 144 q^{94} - 264 q^{97} + 14 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8 + 28 * q^10 - 24 * q^13 + 14 * q^14 - 14 * q^16 + 40 * q^17 + 20 * q^20 - 88 * q^22 + 180 * q^25 - 100 * q^26 + 14 * q^28 - 72 * q^29 - 142 * q^32 - 100 * q^34 - 88 * q^37 - 128 * q^38 - 28 * q^40 + 200 * q^41 + 40 * q^44 - 24 * q^46 - 84 * q^49 + 346 * q^50 - 364 * q^52 - 104 * q^53 - 98 * q^56 + 148 * q^58 + 104 * q^61 - 64 * q^62 - 70 * q^64 - 176 * q^65 - 188 * q^68 - 84 * q^70 + 312 * q^73 - 4 * q^74 + 432 * q^76 + 224 * q^77 + 564 * q^80 + 332 * q^82 + 352 * q^85 - 160 * q^86 + 328 * q^88 + 552 * q^89 - 232 * q^92 - 144 * q^94 - 264 * q^97 + 14 * q^98

Introduction

L-functions

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