LMFDB - Embedded newform 396.3.g.c.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,3,Mod(199,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, 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("396.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	396.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:	$10.7902184687$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 7x^{8} + 4x^{7} - 7x^{6} + 82x^{5} - 28x^{4} + 64x^{3} + 448x^{2} - 512x + 1024 $ x^10 - 2x^9 + 7x^8 + 4x^7 - 7x^6 + 82x^5 - 28x^4 + 64x^3 + 448x^2 - 512*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.3
Root			$-0.231622 - 1.98654i$ of defining polynomial
Character	$\chi$	$=$	396.199
Dual form			396.3.g.c.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32980 - 1.49386i) q^{2} +(-0.463244 + 3.97309i) q^{4} -2.62387 q^{5} +5.65174i q^{7} +(6.55126 - 4.59140i) q^{8} +(3.48924 + 3.91971i) q^{10} -3.31662i q^{11} +2.38854 q^{13} +(8.44292 - 7.51571i) q^{14} +(-15.5708 - 3.68102i) q^{16} -3.93033 q^{17} -12.6850i q^{19} +(1.21549 - 10.4249i) q^{20} +(-4.95458 + 4.41046i) q^{22} -1.98248i q^{23} -18.1153 q^{25} +(-3.17628 - 3.56814i) q^{26} +(-22.4548 - 2.61814i) q^{28} -39.1748 q^{29} -39.6375i q^{31} +(15.2072 + 28.1557i) q^{32} +(5.22657 + 5.87137i) q^{34} -14.8295i q^{35} -32.8407 q^{37} +(-18.9496 + 16.8685i) q^{38} +(-17.1897 + 12.0473i) q^{40} -20.2535 q^{41} -11.7486i q^{43} +(13.1772 + 1.53641i) q^{44} +(-2.96155 + 2.63631i) q^{46} -13.1240i q^{47} +17.0578 q^{49} +(24.0898 + 27.0617i) q^{50} +(-1.10648 + 9.48986i) q^{52} -51.4812 q^{53} +8.70241i q^{55} +(25.9494 + 37.0260i) q^{56} +(52.0948 + 58.5218i) q^{58} +26.8316i q^{59} -95.2827 q^{61} +(-59.2129 + 52.7101i) q^{62} +(21.8381 - 60.1589i) q^{64} -6.26722 q^{65} +3.45987i q^{67} +(1.82070 - 15.6155i) q^{68} +(-22.1532 + 19.7203i) q^{70} -18.0942i q^{71} -54.0962 q^{73} +(43.6717 + 49.0595i) q^{74} +(50.3985 + 5.87624i) q^{76} +18.7447 q^{77} +97.1558i q^{79} +(40.8559 + 9.65853i) q^{80} +(26.9332 + 30.2559i) q^{82} -118.858i q^{83} +10.3127 q^{85} +(-17.5509 + 15.6234i) q^{86} +(-15.2280 - 21.7281i) q^{88} -21.4577 q^{89} +13.4994i q^{91} +(7.87655 + 0.918371i) q^{92} +(-19.6054 + 17.4523i) q^{94} +33.2838i q^{95} +0.0566354 q^{97} +(-22.6836 - 25.4820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 4 q^{5} + 12 q^{8} - 2 q^{10} - 4 q^{13} + 4 q^{14} - 40 q^{16} - 20 q^{17} + 64 q^{20} - 10 q^{25} + 36 q^{26} + 40 q^{28} - 28 q^{29} - 80 q^{32} - 88 q^{34} - 100 q^{37} - 40 q^{38}+ \cdots + 568 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 + 4 * q^5 + 12 * q^8 - 2 * q^10 - 4 * q^13 + 4 * q^14 - 40 * q^16 - 20 * q^17 + 64 * q^20 - 10 * q^25 + 36 * q^26 + 40 * q^28 - 28 * q^29 - 80 * q^32 - 88 * q^34 - 100 * q^37 - 40 * q^38 - 12 * q^40 - 100 * q^41 + 44 * q^44 - 130 * q^46 - 22 * q^49 + 198 * q^50 - 176 * q^52 - 100 * q^53 - 136 * q^56 + 116 * q^58 - 52 * q^61 - 134 * q^62 - 368 * q^64 + 184 * q^65 - 176 * q^68 - 36 * q^70 + 84 * q^73 - 362 * q^74 + 504 * q^76 + 120 * q^80 + 220 * q^82 - 216 * q^85 - 556 * q^86 - 132 * q^88 - 28 * q^89 - 152 * q^92 - 272 * q^94 - 180 * q^97 + 568 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.32980	−	1.49386i	−0.664902	−	0.746931i
$2$	−1.32980	−	1.49386i	−0.664902	−	0.746931i
$3$		0			0
$3$		0			0
$4$	−0.463244	+	3.97309i	−0.115811	+	0.993271i
$5$	−2.62387			−0.524775			−0.262387	−	0.964963i	$-0.584510\pi$
$5$	−2.62387			−0.524775			−0.262387	+	0.964963i	$0.584510\pi$
$6$		0			0
$7$			5.65174i			0.807391i	0.914893	+	0.403696i	$0.132275\pi$
$7$			5.65174i			0.807391i	−0.914893	+	0.403696i	$0.867725\pi$
$8$	6.55126	−	4.59140i	0.818908	−	0.573925i
$9$		0			0
$10$	3.48924	+	3.91971i	0.348924	+	0.391971i
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$		0			0
$13$	2.38854			0.183734			0.0918668	−	0.995771i	$-0.470717\pi$
$13$	2.38854			0.183734			0.0918668	+	0.995771i	$0.470717\pi$
$14$	8.44292	−	7.51571i	0.603066	−	0.536836i
$15$		0			0
$16$	−15.5708	−	3.68102i	−0.973176	−	0.230064i
$17$	−3.93033			−0.231196			−0.115598	−	0.993296i	$-0.536878\pi$
$17$	−3.93033			−0.231196			−0.115598	+	0.993296i	$0.536878\pi$
$18$		0			0
$19$		−	12.6850i		−	0.667631i	−0.942638	−	0.333815i	$-0.891664\pi$
$19$		−	12.6850i		−	0.667631i	0.942638	−	0.333815i	$-0.108336\pi$
$20$	1.21549	−	10.4249i	0.0607747	−	0.521244i
$21$		0			0
$22$	−4.95458	+	4.41046i	−0.225208	+	0.200475i
$23$		−	1.98248i		−	0.0861946i	−0.999071	−	0.0430973i	$-0.986277\pi$
$23$		−	1.98248i		−	0.0861946i	0.999071	−	0.0430973i	$-0.0137226\pi$
$24$		0			0
$25$	−18.1153			−0.724611
$26$	−3.17628	−	3.56814i	−0.122165	−	0.137236i
$27$		0			0
$28$	−22.4548	−	2.61814i	−0.801959	−	0.0935048i
$29$	−39.1748			−1.35086			−0.675428	−	0.737426i	$-0.736041\pi$
$29$	−39.1748			−1.35086			−0.675428	+	0.737426i	$0.736041\pi$
$30$		0			0
$31$		−	39.6375i		−	1.27863i	−0.768945	−	0.639315i	$-0.779218\pi$
$31$		−	39.6375i		−	1.27863i	0.768945	−	0.639315i	$-0.220782\pi$
$32$	15.2072	+	28.1557i	0.475225	+	0.879864i
$33$		0			0
$34$	5.22657	+	5.87137i	0.153723	+	0.172687i
$35$		−	14.8295i		−	0.423699i
$36$		0			0
$37$	−32.8407			−0.887587			−0.443793	−	0.896129i	$-0.646368\pi$
$37$	−32.8407			−0.887587			−0.443793	+	0.896129i	$0.646368\pi$
$38$	−18.9496	+	16.8685i	−0.498674	+	0.443909i
$39$		0			0
$40$	−17.1897	+	12.0473i	−0.429742	+	0.301182i
$41$	−20.2535			−0.493988			−0.246994	−	0.969017i	$-0.579443\pi$
$41$	−20.2535			−0.493988			−0.246994	+	0.969017i	$0.579443\pi$
$42$		0			0
$43$		−	11.7486i		−	0.273224i	−0.990625	−	0.136612i	$-0.956379\pi$
$43$		−	11.7486i		−	0.273224i	0.990625	−	0.136612i	$-0.0436214\pi$
$44$	13.1772	+	1.53641i	0.299483	+	0.0349183i
$45$		0			0
$46$	−2.96155	+	2.63631i	−0.0643814	+	0.0573110i
$47$		−	13.1240i		−	0.279233i	−0.990206	−	0.139617i	$-0.955413\pi$
$47$		−	13.1240i		−	0.279233i	0.990206	−	0.139617i	$-0.0445870\pi$
$48$		0			0
$49$	17.0578			0.348119
$50$	24.0898	+	27.0617i	0.481795	+	0.541234i
$51$		0			0
$52$	−1.10648	+	9.48986i	−0.0212784	+	0.182497i
$53$	−51.4812			−0.971344			−0.485672	−	0.874141i	$-0.661425\pi$
$53$	−51.4812			−0.971344			−0.485672	+	0.874141i	$0.661425\pi$
$54$		0			0
$55$			8.70241i			0.158226i
$56$	25.9494	+	37.0260i	0.463382	+	0.661179i
$57$		0			0
$58$	52.0948	+	58.5218i	0.898187	+	1.00900i
$59$			26.8316i			0.454773i	0.973805	+	0.227386i	$0.0730180\pi$
$59$			26.8316i			0.454773i	−0.973805	+	0.227386i	$0.926982\pi$
$60$		0			0
$61$	−95.2827			−1.56201			−0.781006	−	0.624524i	$-0.785293\pi$
$61$	−95.2827			−1.56201			−0.781006	+	0.624524i	$0.785293\pi$
$62$	−59.2129	+	52.7101i	−0.955047	+	0.850163i
$63$		0			0
$64$	21.8381	−	60.1589i	0.341220	−	0.939983i
$65$	−6.26722			−0.0964188
$66$		0			0
$67$			3.45987i			0.0516399i	0.999667	+	0.0258200i	$0.00821966\pi$
$67$			3.45987i			0.0516399i	−0.999667	+	0.0258200i	$0.991780\pi$
$68$	1.82070	−	15.6155i	0.0267751	−	0.229640i
$69$		0			0
$70$	−22.1532	+	19.7203i	−0.316474	+	0.281718i
$71$		−	18.0942i		−	0.254848i	−0.991848	−	0.127424i	$-0.959329\pi$
$71$		−	18.0942i		−	0.254848i	0.991848	−	0.127424i	$-0.0406710\pi$
$72$		0			0
$73$	−54.0962			−0.741043			−0.370522	−	0.928824i	$-0.620821\pi$
$73$	−54.0962			−0.741043			−0.370522	+	0.928824i	$0.620821\pi$
$74$	43.6717	+	49.0595i	0.590158	+	0.662966i
$75$		0			0
$76$	50.3985	+	5.87624i	0.663138	+	0.0773190i
$77$	18.7447			0.243438
$78$		0			0
$79$			97.1558i			1.22982i	0.788597	+	0.614910i	$0.210808\pi$
$79$			97.1558i			1.22982i	−0.788597	+	0.614910i	$0.789192\pi$
$80$	40.8559	+	9.65853i	0.510698	+	0.120732i
$81$		0			0
$82$	26.9332	+	30.2559i	0.328453	+	0.368975i
$83$		−	118.858i		−	1.43202i	−0.698090	−	0.716010i	$-0.745966\pi$
$83$		−	118.858i		−	1.43202i	0.698090	−	0.716010i	$-0.254034\pi$
$84$		0			0
$85$	10.3127			0.121326
$86$	−17.5509	+	15.6234i	−0.204080	+	0.181667i
$87$		0			0
$88$	−15.2280	−	21.7281i	−0.173045	−	0.246910i
$89$	−21.4577			−0.241098			−0.120549	−	0.992707i	$-0.538465\pi$
$89$	−21.4577			−0.241098			−0.120549	+	0.992707i	$0.538465\pi$
$90$		0			0
$91$			13.4994i			0.148345i
$92$	7.87655	+	0.918371i	0.0856147	+	0.00998229i
$93$		0			0
$94$	−19.6054	+	17.4523i	−0.208568	+	0.185663i
$95$			33.2838i			0.350356i
$96$		0			0
$97$	0.0566354			0.000583870			0.000291935	−	1.00000i	$-0.499907\pi$
$97$	0.0566354			0.000583870			0.000291935		1.00000i	$0.499907\pi$
$98$	−22.6836	−	25.4820i	−0.231465	−	0.260021i
$99$		0			0
$100$	8.39180	−	71.9736i	0.0839180	−	0.719736i
$101$	−151.041			−1.49546			−0.747728	−	0.664006i	$-0.768855\pi$
$101$	−151.041			−1.49546			−0.747728	+	0.664006i	$0.768855\pi$
$102$		0			0
$103$			8.63968i			0.0838804i	0.999120	+	0.0419402i	$0.0133539\pi$
$103$			8.63968i			0.0838804i	−0.999120	+	0.0419402i	$0.986646\pi$
$104$	15.6479	−	10.9667i	0.150461	−	0.105449i
$105$		0			0
$106$	68.4599	+	76.9058i	0.645848	+	0.725526i
$107$		−	135.015i		−	1.26183i	−0.775853	−	0.630913i	$-0.782680\pi$
$107$		−	135.015i		−	1.26183i	0.775853	−	0.630913i	$-0.217320\pi$
$108$		0			0
$109$	153.316			1.40657			0.703285	−	0.710908i	$-0.251716\pi$
$109$	153.316			1.40657			0.703285	+	0.710908i	$0.251716\pi$
$110$	13.0002	−	11.5725i	0.118184	−	0.105205i
$111$		0			0
$112$	20.8041	−	88.0022i	0.185751	−	0.785734i
$113$	138.852			1.22878			0.614389	−	0.789003i	$-0.289402\pi$
$113$	138.852			1.22878			0.614389	+	0.789003i	$0.289402\pi$
$114$		0			0
$115$			5.20177i			0.0452328i
$116$	18.1475	−	155.645i	0.156444	−	1.34177i
$117$		0			0
$118$	40.0827	−	35.6807i	0.339684	−	0.302379i
$119$		−	22.2132i		−	0.186666i
$120$		0			0
$121$	−11.0000			−0.0909091
$122$	126.707	+	142.339i	1.03858	+	1.16671i
$123$		0			0
$124$	157.483	+	18.3618i	1.27003	+	0.148079i
$125$	113.129			0.905033
$126$		0			0
$127$		−	123.765i		−	0.974530i	−0.873254	−	0.487265i	$-0.837995\pi$
$127$		−	123.765i		−	0.974530i	0.873254	−	0.487265i	$-0.162005\pi$
$128$	−118.909	+	47.3765i	−0.928980	+	0.370129i
$129$		0			0
$130$	8.33417	+	9.36236i	0.0641090	+	0.0720181i
$131$		−	98.9561i		−	0.755390i	−0.925930	−	0.377695i	$-0.876717\pi$
$131$		−	98.9561i		−	0.755390i	0.925930	−	0.377695i	$-0.123283\pi$
$132$		0			0
$133$	71.6922			0.539039
$134$	5.16857	−	4.60095i	0.0385714	−	0.0343355i
$135$		0			0
$136$	−25.7486	+	18.0457i	−0.189328	+	0.132689i
$137$	125.665			0.917265			0.458632	−	0.888626i	$-0.348340\pi$
$137$	125.665			0.917265			0.458632	+	0.888626i	$0.348340\pi$
$138$		0			0
$139$		−	201.867i		−	1.45228i	−0.687548	−	0.726139i	$-0.741313\pi$
$139$		−	201.867i		−	1.45228i	0.687548	−	0.726139i	$-0.258687\pi$
$140$	58.9187	+	6.86966i	0.420848	+	0.0490690i
$141$		0			0
$142$	−27.0303	+	24.0618i	−0.190354	+	0.169449i
$143$		−	7.92188i		−	0.0553978i
$144$		0			0
$145$	102.790			0.708895
$146$	71.9373	+	80.8122i	0.492721	+	0.553508i
$147$		0			0
$148$	15.2133	−	130.479i	0.102792	−	0.881614i
$149$	41.1801			0.276377			0.138188	−	0.990406i	$-0.455872\pi$
$149$	41.1801			0.276377			0.138188	+	0.990406i	$0.455872\pi$
$150$		0			0
$151$			119.450i			0.791059i	0.918453	+	0.395530i	$0.129439\pi$
$151$			119.450i			0.791059i	−0.918453	+	0.395530i	$0.870561\pi$
$152$	−58.2418	−	83.1027i	−0.383170	−	0.546728i
$153$		0			0
$154$	−24.9268	−	28.0020i	−0.161862	−	0.181831i
$155$			104.004i			0.670992i
$156$		0			0
$157$	121.227			0.772146			0.386073	−	0.922468i	$-0.373831\pi$
$157$	121.227			0.772146			0.386073	+	0.922468i	$0.373831\pi$
$158$	145.137	−	129.198i	0.918591	−	0.817710i
$159$		0			0
$160$	−39.9018	−	73.8769i	−0.249386	−	0.461731i
$161$	11.2044			0.0695928
$162$		0			0
$163$		−	122.252i		−	0.750012i	−0.927022	−	0.375006i	$-0.877641\pi$
$163$		−	122.252i		−	0.750012i	0.927022	−	0.375006i	$-0.122359\pi$
$164$	9.38231	−	80.4688i	0.0572092	−	0.490664i
$165$		0			0
$166$	−177.557	+	158.057i	−1.06962	+	0.952153i
$167$			143.333i			0.858280i	0.903238	+	0.429140i	$0.141183\pi$
$167$			143.333i			0.858280i	−0.903238	+	0.429140i	$0.858817\pi$
$168$		0			0
$169$	−163.295			−0.966242
$170$	−13.7139	−	15.4057i	−0.0806698	−	0.0906221i
$171$		0			0
$172$	46.6784	+	5.44249i	0.271386	+	0.0316424i
$173$	−273.225			−1.57933			−0.789667	−	0.613535i	$-0.789747\pi$
$173$	−273.225			−1.57933			−0.789667	+	0.613535i	$0.789747\pi$
$174$		0			0
$175$		−	102.383i		−	0.585045i
$176$	−12.2085	+	51.6425i	−0.0693668	+	0.293423i
$177$		0			0
$178$	28.5346	+	32.0549i	0.160306	+	0.180083i
$179$			260.106i			1.45311i	0.687110	+	0.726553i	$0.258879\pi$
$179$			260.106i			1.45311i	−0.687110	+	0.726553i	$0.741121\pi$
$180$		0			0
$181$	273.183			1.50930			0.754650	−	0.656127i	$-0.227807\pi$
$181$	273.183			1.50930			0.754650	+	0.656127i	$0.227807\pi$
$182$	20.1662	−	17.9515i	0.110803	−	0.0986348i
$183$		0			0
$184$	−9.10235	−	12.9877i	−0.0494693	−	0.0705855i
$185$	86.1699			0.465783
$186$		0			0
$187$			13.0354i			0.0697082i
$188$	52.1426	+	6.07960i	0.277354	+	0.0323383i
$189$		0			0
$190$	49.7214	−	44.2609i	0.261692	−	0.232952i
$191$			259.932i			1.36090i	0.732794	+	0.680450i	$0.238216\pi$
$191$			259.932i			1.36090i	−0.732794	+	0.680450i	$0.761784\pi$
$192$		0			0
$193$	−301.717			−1.56330			−0.781649	−	0.623719i	$-0.785621\pi$
$193$	−301.717			−1.56330			−0.781649	+	0.623719i	$0.785621\pi$
$194$	−0.0753140	−	0.0846055i	−0.000388217	−	0.000436111i
$195$		0			0
$196$	−7.90194	+	67.7722i	−0.0403160	+	0.345777i
$197$	27.4087			0.139130			0.0695652	−	0.997577i	$-0.477839\pi$
$197$	27.4087			0.139130			0.0695652	+	0.997577i	$0.477839\pi$
$198$		0			0
$199$			258.899i			1.30100i	0.759507	+	0.650499i	$0.225440\pi$
$199$			258.899i			1.30100i	−0.759507	+	0.650499i	$0.774560\pi$
$200$	−118.678	+	83.1745i	−0.593390	+	0.415873i
$201$		0			0
$202$	200.855	+	225.634i	0.994331	+	1.11700i
$203$		−	221.406i		−	1.09067i
$204$		0			0
$205$	53.1426			0.259232
$206$	12.9065	−	11.4891i	0.0626528	−	0.0557722i
$207$		0			0
$208$	−37.1914	−	8.79224i	−0.178805	−	0.0422704i
$209$	−42.0713			−0.201298
$210$		0			0
$211$			27.8516i			0.131998i	0.997820	+	0.0659990i	$0.0210234\pi$
$211$			27.8516i			0.131998i	−0.997820	+	0.0659990i	$0.978977\pi$
$212$	23.8484	−	204.539i	0.112492	−	0.964808i
$213$		0			0
$214$	−201.694	+	179.544i	−0.942497	+	0.838991i
$215$			30.8270i			0.143381i
$216$		0			0
$217$	224.021			1.03235
$218$	−203.880	−	229.033i	−0.935231	−	1.05061i
$219$		0			0
$220$	−34.5754	−	4.03134i	−0.157161	−	0.0183243i
$221$	−9.38774			−0.0424785
$222$		0			0
$223$			212.433i			0.952615i	0.879279	+	0.476308i	$0.158025\pi$
$223$			212.433i			0.952615i	−0.879279	+	0.476308i	$0.841975\pi$
$224$	−159.128	+	85.9471i	−0.710395	+	0.383692i
$225$		0			0
$226$	−184.646	−	207.426i	−0.817017	−	0.917813i
$227$			132.026i			0.581612i	0.956782	+	0.290806i	$0.0939235\pi$
$227$			132.026i			0.581612i	−0.956782	+	0.290806i	$0.906077\pi$
$228$		0			0
$229$	−274.044			−1.19670			−0.598349	−	0.801236i	$-0.704176\pi$
$229$	−274.044			−1.19670			−0.598349	+	0.801236i	$0.704176\pi$
$230$	7.77073	−	6.91733i	0.0337858	−	0.0300754i
$231$		0			0
$232$	−256.645	+	179.867i	−1.10623	+	0.775290i
$233$	−175.327			−0.752474			−0.376237	−	0.926523i	$-0.622782\pi$
$233$	−175.327			−0.752474			−0.376237	+	0.926523i	$0.622782\pi$
$234$		0			0
$235$			34.4356i			0.146535i
$236$	−106.604	−	12.4296i	−0.451712	−	0.0526677i
$237$		0			0
$238$	−33.1835	+	29.5392i	−0.139426	+	0.124114i
$239$		−	47.1871i		−	0.197436i	−0.995115	−	0.0987179i	$-0.968526\pi$
$239$		−	47.1871i		−	0.197436i	0.995115	−	0.0987179i	$-0.0314741\pi$
$240$		0			0
$241$	−9.89020			−0.0410382			−0.0205191	−	0.999789i	$-0.506532\pi$
$241$	−9.89020			−0.0410382			−0.0205191	+	0.999789i	$0.506532\pi$
$242$	14.6278	+	16.4325i	0.0604456	+	0.0679028i
$243$		0			0
$244$	44.1391	−	378.566i	0.180898	−	1.55150i
$245$	−44.7576			−0.182684
$246$		0			0
$247$		−	30.2985i		−	0.122666i
$248$	−181.992	−	259.676i	−0.733837	−	1.04708i
$249$		0			0
$250$	−150.439	−	168.999i	−0.601758	−	0.675997i
$251$			228.136i			0.908907i	0.890770	+	0.454454i	$0.150165\pi$
$251$			228.136i			0.908907i	−0.890770	+	0.454454i	$0.849835\pi$
$252$		0			0
$253$	−6.57513			−0.0259887
$254$	−184.888	+	164.584i	−0.727906	+	0.647967i
$255$		0			0
$256$	228.900	+	114.633i	0.894142	+	0.447784i
$257$	392.820			1.52848			0.764241	−	0.644931i	$-0.223114\pi$
$257$	392.820			1.52848			0.764241	+	0.644931i	$0.223114\pi$
$258$		0			0
$259$		−	185.607i		−	0.716630i
$260$	2.90325	−	24.9002i	0.0111664	−	0.0957700i
$261$		0			0
$262$	−147.827	+	131.592i	−0.564224	+	0.502260i
$263$		−	249.116i		−	0.947208i	−0.880738	−	0.473604i	$-0.842953\pi$
$263$		−	249.116i		−	0.947208i	0.880738	−	0.473604i	$-0.157047\pi$
$264$		0			0
$265$	135.080			0.509737
$266$	−95.3366	−	107.098i	−0.358408	−	0.402625i
$267$		0			0
$268$	−13.7464	−	1.60277i	−0.0512924	−	0.00598047i
$269$	71.2955			0.265039			0.132520	−	0.991180i	$-0.457693\pi$
$269$	71.2955			0.265039			0.132520	+	0.991180i	$0.457693\pi$
$270$		0			0
$271$			275.651i			1.01716i	0.861014	+	0.508581i	$0.169830\pi$
$271$			275.651i			1.01716i	−0.861014	+	0.508581i	$0.830170\pi$
$272$	61.1985	+	14.4676i	0.224994	+	0.0531898i
$273$		0			0
$274$	−167.110	−	187.726i	−0.609891	−	0.685133i
$275$			60.0816i			0.218479i
$276$		0			0
$277$	−162.557			−0.586848			−0.293424	−	0.955982i	$-0.594795\pi$
$277$	−162.557			−0.586848			−0.293424	+	0.955982i	$0.594795\pi$
$278$	−301.561	+	268.443i	−1.08475	+	0.965622i
$279$		0			0
$280$	−68.0880	−	97.1517i	−0.243171	−	0.346970i
$281$	−168.953			−0.601255			−0.300627	−	0.953742i	$-0.597196\pi$
$281$	−168.953			−0.601255			−0.300627	+	0.953742i	$0.597196\pi$
$282$		0			0
$283$			202.567i			0.715785i	0.933763	+	0.357892i	$0.116505\pi$
$283$			202.567i			0.715785i	−0.933763	+	0.357892i	$0.883495\pi$
$284$	71.8899	+	8.38205i	0.253134	+	0.0295143i
$285$		0			0
$286$	−11.8342	+	10.5345i	−0.0413783	+	0.0368341i
$287$		−	114.467i		−	0.398841i
$288$		0			0
$289$	−273.552			−0.946548
$290$	−136.690	−	153.554i	−0.471346	−	0.529496i
$291$		0			0
$292$	25.0597	−	214.929i	0.0858210	−	0.736057i
$293$	506.376			1.72825			0.864123	−	0.503281i	$-0.167874\pi$
$293$	506.376			1.72825			0.864123	+	0.503281i	$0.167874\pi$
$294$		0			0
$295$		−	70.4027i		−	0.238653i
$296$	−215.148	+	150.785i	−0.726852	+	0.509408i
$297$		0			0
$298$	−54.7615	−	61.5174i	−0.183763	−	0.206434i
$299$		−	4.73522i		−	0.0158368i
$300$		0			0
$301$	66.4003			0.220599
$302$	178.442	−	158.845i	0.590866	−	0.525977i
$303$		0			0
$304$	−46.6936	+	197.515i	−0.153597	+	0.649722i
$305$	250.010			0.819704
$306$		0			0
$307$		−	41.0747i		−	0.133794i	−0.997760	−	0.0668969i	$-0.978690\pi$
$307$		−	41.0747i		−	0.133794i	0.997760	−	0.0668969i	$-0.0213099\pi$
$308$	−8.68337	+	74.4743i	−0.0281928	+	0.241800i
$309$		0			0
$310$	155.367	−	138.305i	0.501185	−	0.446144i
$311$			469.894i			1.51091i	0.655198	+	0.755457i	$0.272585\pi$
$311$			469.894i			1.51091i	−0.655198	+	0.755457i	$0.727415\pi$
$312$		0			0
$313$	−204.777			−0.654238			−0.327119	−	0.944983i	$-0.606078\pi$
$313$	−204.777			−0.654238			−0.327119	+	0.944983i	$0.606078\pi$
$314$	−161.208	−	181.096i	−0.513401	−	0.576739i
$315$		0			0
$316$	−386.008	−	45.0068i	−1.22155	−	0.142427i
$317$	11.6988			0.0369049			0.0184524	−	0.999830i	$-0.494126\pi$
$317$	11.6988			0.0369049			0.0184524	+	0.999830i	$0.494126\pi$
$318$		0			0
$319$			129.928i			0.407298i
$320$	−57.3004	+	157.850i	−0.179064	+	0.493280i
$321$		0			0
$322$	−14.8997	−	16.7379i	−0.0462724	−	0.0519810i
$323$			49.8562i			0.154354i
$324$		0			0
$325$	−43.2690			−0.133135
$326$	−182.628	+	162.571i	−0.560207	+	0.498684i
$327$		0			0
$328$	−132.686	+	92.9919i	−0.404530	+	0.283512i
$329$	74.1732			0.225450
$330$		0			0
$331$		−	53.1038i		−	0.160434i	−0.996777	−	0.0802172i	$-0.974439\pi$
$331$		−	53.1038i		−	0.160434i	0.996777	−	0.0802172i	$-0.0255614\pi$
$332$	472.232	+	55.0601i	1.42238	+	0.165844i
$333$		0			0
$334$	214.119	−	190.604i	0.641076	−	0.570672i
$335$		−	9.07828i		−	0.0270993i
$336$		0			0
$337$	−177.750			−0.527448			−0.263724	−	0.964598i	$-0.584951\pi$
$337$	−177.750			−0.527448			−0.263724	+	0.964598i	$0.584951\pi$
$338$	217.150	+	243.940i	0.642456	+	0.721716i
$339$		0			0
$340$	−4.77730	+	40.9732i	−0.0140509	+	0.120510i
$341$	−131.463			−0.385521
$342$		0			0
$343$			373.342i			1.08846i
$344$	−53.9428	−	76.9685i	−0.156810	−	0.223746i
$345$		0			0
$346$	363.336	+	408.160i	1.05010	+	1.17965i
$347$		−	561.580i		−	1.61838i	−0.587544	−	0.809192i	$-0.699905\pi$
$347$		−	561.580i		−	1.61838i	0.587544	−	0.809192i	$-0.300095\pi$
$348$		0			0
$349$	410.932			1.17746			0.588728	−	0.808331i	$-0.299629\pi$
$349$	410.932			1.17746			0.588728	+	0.808331i	$0.299629\pi$
$350$	−152.946	+	136.149i	−0.436988	+	0.388997i
$351$		0			0
$352$	93.3818	−	50.4366i	0.265289	−	0.143286i
$353$	5.48150			0.0155283			0.00776416	−	0.999970i	$-0.497529\pi$
$353$	5.48150			0.0155283			0.00776416	+	0.999970i	$0.497529\pi$
$354$		0			0
$355$			47.4770i			0.133738i
$356$	9.94016	−	85.2533i	0.0279218	−	0.239476i
$357$		0			0
$358$	388.562	−	345.890i	1.08537	−	0.966173i
$359$			602.633i			1.67864i	0.543636	+	0.839321i	$0.317047\pi$
$359$			602.633i			1.67864i	−0.543636	+	0.839321i	$0.682953\pi$
$360$		0			0
$361$	200.091			0.554269
$362$	−363.280	−	408.098i	−1.00354	−	1.12734i
$363$		0			0
$364$	−53.6342	−	6.25351i	−0.147347	−	0.0171800i
$365$	141.942			0.388881
$366$		0			0
$367$		−	215.805i		−	0.588024i	−0.955802	−	0.294012i	$-0.905009\pi$
$367$		−	215.805i		−	0.588024i	0.955802	−	0.294012i	$-0.0949905\pi$
$368$	−7.29753	+	30.8688i	−0.0198302	+	0.0838825i
$369$		0			0
$370$	−114.589	−	128.726i	−0.309700	−	0.347908i
$371$		−	290.958i		−	0.784255i
$372$		0			0
$373$	−147.198			−0.394632			−0.197316	−	0.980340i	$-0.563223\pi$
$373$	−147.198			−0.394632			−0.197316	+	0.980340i	$0.563223\pi$
$374$	19.4731	−	17.3346i	0.0520672	−	0.0463491i
$375$		0			0
$376$	−60.2574	−	85.9785i	−0.160259	−	0.228666i
$377$	−93.5705			−0.248198
$378$		0			0
$379$		−	418.824i		−	1.10508i	−0.833487	−	0.552538i	$-0.813659\pi$
$379$		−	418.824i		−	1.10508i	0.833487	−	0.552538i	$-0.186341\pi$
$380$	−132.239	−	15.4185i	−0.347998	−	0.0405751i
$381$		0			0
$382$	388.302	−	345.658i	1.01650	−	0.904865i
$383$		−	508.317i		−	1.32720i	−0.748088	−	0.663599i	$-0.769028\pi$
$383$		−	508.317i		−	1.32720i	0.748088	−	0.663599i	$-0.230972\pi$
$384$		0			0
$385$	−49.1838			−0.127750
$386$	401.224	+	450.723i	1.03944	+	1.16768i
$387$		0			0
$388$	−0.0262360	+	0.225017i	−6.76186e−5	+	0.000579942i
$389$	−136.791			−0.351647			−0.175823	−	0.984422i	$-0.556259\pi$
$389$	−136.791			−0.351647			−0.175823	+	0.984422i	$0.556259\pi$
$390$		0			0
$391$			7.79180i			0.0199279i
$392$	111.750	−	78.3193i	0.285077	−	0.199794i
$393$		0			0
$394$	−36.4482	−	40.9448i	−0.0925080	−	0.103921i
$395$		−	254.925i		−	0.645379i
$396$		0			0
$397$	748.561			1.88554			0.942772	−	0.333438i	$-0.108209\pi$
$397$	748.561			1.88554			0.942772	+	0.333438i	$0.108209\pi$
$398$	386.759	−	344.284i	0.971755	−	0.865036i
$399$		0			0
$400$	282.070	+	66.6826i	0.705174	+	0.166707i
$401$	−233.282			−0.581750			−0.290875	−	0.956761i	$-0.593946\pi$
$401$	−233.282			−0.581750			−0.290875	+	0.956761i	$0.593946\pi$
$402$		0			0
$403$		−	94.6756i		−	0.234927i
$404$	69.9688	−	600.099i	0.173190	−	1.48539i
$405$		0			0
$406$	−330.750	+	294.426i	−0.814655	+	0.725188i
$407$			108.920i			0.267617i
$408$		0			0
$409$	−536.046			−1.31063			−0.655313	−	0.755358i	$-0.727463\pi$
$409$	−536.046			−1.31063			−0.655313	+	0.755358i	$0.727463\pi$
$410$	−70.6693	−	79.3877i	−0.172364	−	0.193629i
$411$		0			0
$412$	−34.3262	−	4.00228i	−0.0833159	−	0.00971427i
$413$	−151.645			−0.367179
$414$		0			0
$415$			311.868i			0.751488i
$416$	36.3229	+	67.2508i	0.0873147	+	0.161661i
$417$		0			0
$418$	55.9466	+	62.8487i	0.133844	+	0.150356i
$419$			408.745i			0.975524i	0.872977	+	0.487762i	$0.162187\pi$
$419$			408.745i			0.975524i	−0.872977	+	0.487762i	$0.837813\pi$
$420$		0			0
$421$	−386.634			−0.918370			−0.459185	−	0.888341i	$-0.651859\pi$
$421$	−386.634			−0.918370			−0.459185	+	0.888341i	$0.651859\pi$
$422$	41.6064	−	37.0371i	0.0985933	−	0.0877657i
$423$		0			0
$424$	−337.267	+	236.371i	−0.795441	+	0.557479i
$425$	71.1991			0.167527
$426$		0			0
$427$		−	538.513i		−	1.26115i
$428$	536.428	+	62.5451i	1.25334	+	0.146133i
$429$		0			0
$430$	46.0512	−	40.9938i	0.107096	−	0.0953345i
$431$		−	150.143i		−	0.348359i	−0.984714	−	0.174179i	$-0.944273\pi$
$431$		−	150.143i		−	0.348359i	0.984714	−	0.174179i	$-0.0557273\pi$
$432$		0			0
$433$	249.278			0.575700			0.287850	−	0.957676i	$-0.407060\pi$
$433$	249.278			0.575700			0.287850	+	0.957676i	$0.407060\pi$
$434$	−297.904	−	334.656i	−0.686414	−	0.771097i
$435$		0			0
$436$	−71.0228	+	609.138i	−0.162896	+	1.39711i
$437$	−25.1477			−0.0575462
$438$		0			0
$439$		−	308.839i		−	0.703505i	−0.936093	−	0.351753i	$-0.885586\pi$
$439$		−	308.839i		−	0.703505i	0.936093	−	0.351753i	$-0.114414\pi$
$440$	39.9562	+	57.0118i	0.0908096	+	0.129572i
$441$		0			0
$442$	12.4839	+	14.0240i	0.0282440	+	0.0317285i
$443$			187.453i			0.423145i	0.977362	+	0.211572i	$0.0678584\pi$
$443$			187.453i			0.423145i	−0.977362	+	0.211572i	$0.932142\pi$
$444$		0			0
$445$	56.3024			0.126522
$446$	317.346	−	282.494i	0.711538	−	0.633396i
$447$		0			0
$448$	340.003	+	123.423i	0.758935	+	0.275498i
$449$	144.028			0.320775			0.160388	−	0.987054i	$-0.448726\pi$
$449$	144.028			0.320775			0.160388	+	0.987054i	$0.448726\pi$
$450$		0			0
$451$			67.1732i			0.148943i
$452$	−64.3224	+	551.671i	−0.142306	+	1.22051i
$453$		0			0
$454$	197.229	−	175.569i	0.434424	−	0.386715i
$455$		−	35.4207i		−	0.0778477i
$456$		0			0
$457$	718.168			1.57148			0.785742	−	0.618554i	$-0.212281\pi$
$457$	718.168			1.57148			0.785742	+	0.618554i	$0.212281\pi$
$458$	364.425	+	409.384i	0.795687	+	0.893851i
$459$		0			0
$460$	−20.6671	−	2.40969i	−0.0449284	−	0.00523846i
$461$	−283.840			−0.615705			−0.307852	−	0.951434i	$-0.599610\pi$
$461$	−283.840			−0.615705			−0.307852	+	0.951434i	$0.599610\pi$
$462$		0			0
$463$		−	428.178i		−	0.924790i	−0.886674	−	0.462395i	$-0.846990\pi$
$463$		−	428.178i		−	0.924790i	0.886674	−	0.462395i	$-0.153010\pi$
$464$	609.984	+	144.203i	1.31462	+	0.310783i
$465$		0			0
$466$	233.150	+	261.914i	0.500322	+	0.562046i
$467$		−	415.333i		−	0.889363i	−0.895689	−	0.444681i	$-0.853317\pi$
$467$		−	415.333i		−	0.889363i	0.895689	−	0.444681i	$-0.146683\pi$
$468$		0			0
$469$	−19.5543			−0.0416936
$470$	51.4421	−	45.7926i	0.109451	−	0.0974311i
$471$		0			0
$472$	123.195	+	175.781i	0.261005	+	0.372417i
$473$	−38.9659			−0.0823803
$474$		0			0
$475$			229.792i			0.483773i
$476$	88.2550	+	10.2901i	0.185410	+	0.0216179i
$477$		0			0
$478$	−70.4911	+	62.7496i	−0.147471	+	0.131275i
$479$			176.184i			0.367816i	0.982943	+	0.183908i	$0.0588748\pi$
$479$			176.184i			0.367816i	−0.982943	+	0.183908i	$0.941125\pi$
$480$		0			0
$481$	−78.4412			−0.163079
$482$	13.1520	+	14.7746i	0.0272864	+	0.0306527i
$483$		0			0
$484$	5.09568	−	43.7039i	0.0105283	−	0.0902974i
$485$	−0.148604			−0.000306401
$486$		0			0
$487$			768.354i			1.57773i	0.614567	+	0.788865i	$0.289331\pi$
$487$			768.354i			1.57773i	−0.614567	+	0.788865i	$0.710669\pi$
$488$	−624.222	+	437.481i	−1.27914	+	0.896477i
$489$		0			0
$490$	59.5188	+	66.8617i	0.121467	+	0.136452i
$491$			187.589i			0.382055i	0.981585	+	0.191028i	$0.0611820\pi$
$491$			187.589i			0.382055i	−0.981585	+	0.191028i	$0.938818\pi$
$492$		0			0
$493$	153.970			0.312313
$494$	−45.2618	+	40.2911i	−0.0916231	+	0.0815610i
$495$		0			0
$496$	−145.906	+	617.188i	−0.294166	+	1.24433i
$497$	102.264			0.205762
$498$		0			0
$499$		−	463.814i		−	0.929487i	−0.885445	−	0.464744i	$-0.846146\pi$
$499$		−	463.814i		−	0.929487i	0.885445	−	0.464744i	$-0.153854\pi$
$500$	−52.4064	+	449.472i	−0.104813	+	0.898943i
$501$		0			0
$502$	340.803	−	303.376i	0.678891	−	0.604334i
$503$		−	516.384i		−	1.02661i	−0.858207	−	0.513304i	$-0.828421\pi$
$503$		−	516.384i		−	1.02661i	0.858207	−	0.513304i	$-0.171579\pi$
$504$		0			0
$505$	396.313			0.784777
$506$	8.74364	+	9.82234i	0.0172799	+	0.0194117i
$507$		0			0
$508$	491.730	+	57.3335i	0.967972	+	0.112861i
$509$	−163.127			−0.320486			−0.160243	−	0.987078i	$-0.551228\pi$
$509$	−163.127			−0.320486			−0.160243	+	0.987078i	$0.551228\pi$
$510$		0			0
$511$		−	305.737i		−	0.598312i
$512$	−133.147	−	494.384i	−0.260052	−	0.965594i
$513$		0			0
$514$	−522.373	−	586.818i	−1.01629	−	1.14167i
$515$		−	22.6694i		−	0.0440183i
$516$		0			0
$517$	−43.5272			−0.0841920
$518$	−277.271	+	246.821i	−0.535273	+	0.476489i
$519$		0			0
$520$	−41.0582	+	28.7753i	−0.0789581	+	0.0553372i
$521$	−794.025			−1.52404			−0.762020	−	0.647553i	$-0.775792\pi$
$521$	−794.025			−1.52404			−0.762020	+	0.647553i	$0.775792\pi$
$522$		0			0
$523$			582.806i			1.11435i	0.830394	+	0.557176i	$0.188115\pi$
$523$			582.806i			1.11435i	−0.830394	+	0.557176i	$0.811885\pi$
$524$	393.161	+	45.8408i	0.750307	+	0.0874825i
$525$		0			0
$526$	−372.144	+	331.275i	−0.707499	+	0.629800i
$527$			155.789i			0.295614i
$528$		0			0
$529$	525.070			0.992570
$530$	−179.630	−	201.791i	−0.338925	−	0.380738i
$531$		0			0
$532$	−33.2110	+	284.839i	−0.0624267	+	0.535412i
$533$	−48.3762			−0.0907621
$534$		0			0
$535$			354.264i			0.662175i
$536$	15.8857	+	22.6665i	0.0296374	+	0.0422883i
$537$		0			0
$538$	−94.8091	−	106.506i	−0.176225	−	0.197966i
$539$		−	56.5744i		−	0.104962i
$540$		0			0
$541$	−444.970			−0.822496			−0.411248	−	0.911524i	$-0.634907\pi$
$541$	−444.970			−0.822496			−0.411248	+	0.911524i	$0.634907\pi$
$542$	411.784	−	366.562i	0.759750	−	0.676313i
$543$		0			0
$544$	−59.7693	−	110.661i	−0.109870	−	0.203421i
$545$	−402.282			−0.738133
$546$		0			0
$547$		−	831.549i		−	1.52020i	−0.649806	−	0.760100i	$-0.725150\pi$
$547$		−	831.549i		−	1.52020i	0.649806	−	0.760100i	$-0.274850\pi$
$548$	−58.2137	+	499.279i	−0.106229	+	0.911093i
$549$		0			0
$550$	89.7536	−	79.8967i	0.163188	−	0.145267i
$551$			496.932i			0.901873i
$552$		0			0
$553$	−549.099			−0.992946
$554$	216.169	+	242.838i	0.390197	+	0.438335i
$555$		0			0
$556$	802.033	+	93.5135i	1.44251	+	0.168190i
$557$	−404.131			−0.725550			−0.362775	−	0.931877i	$-0.618171\pi$
$557$	−404.131			−0.725550			−0.362775	+	0.931877i	$0.618171\pi$
$558$		0			0
$559$		−	28.0621i		−	0.0502005i
$560$	−54.5875	+	230.907i	−0.0974776	+	0.412333i
$561$		0			0
$562$	224.674	+	252.392i	0.399775	+	0.449096i
$563$			11.9750i			0.0212699i	0.999943	+	0.0106350i	$0.00338528\pi$
$563$			11.9750i			0.0212699i	−0.999943	+	0.0106350i	$0.996615\pi$
$564$		0			0
$565$	−364.330			−0.644832
$566$	302.607	−	269.375i	0.534642	−	0.475927i
$567$		0			0
$568$	−83.0779	−	118.540i	−0.146264	−	0.208697i
$569$	−390.548			−0.686376			−0.343188	−	0.939267i	$-0.611507\pi$
$569$	−390.548			−0.686376			−0.343188	+	0.939267i	$0.611507\pi$
$570$		0			0
$571$		−	799.779i		−	1.40066i	−0.713817	−	0.700332i	$-0.753035\pi$
$571$		−	799.779i		−	1.40066i	0.713817	−	0.700332i	$-0.246965\pi$
$572$	31.4743	+	3.66976i	0.0550250	+	0.00641567i
$573$		0			0
$574$	−170.999	+	152.219i	−0.297907	+	0.265190i
$575$			35.9131i			0.0624576i
$576$		0			0
$577$	560.791			0.971907			0.485954	−	0.873985i	$-0.338472\pi$
$577$	560.791			0.971907			0.485954	+	0.873985i	$0.338472\pi$
$578$	363.771	+	408.650i	0.629362	+	0.707006i
$579$		0			0
$580$	−47.6168	+	408.393i	−0.0820979	+	0.704125i
$581$	671.753			1.15620
$582$		0			0
$583$			170.744i			0.292871i
$584$	−354.398	+	248.377i	−0.606846	+	0.425303i
$585$		0			0
$586$	−673.380	−	756.455i	−1.14911	−	1.29088i
$587$		−	120.056i		−	0.204525i	−0.994757	−	0.102262i	$-0.967392\pi$
$587$		−	120.056i		−	0.204525i	0.994757	−	0.102262i	$-0.0326081\pi$
$588$		0			0
$589$	−502.801			−0.853652
$590$	−105.172	+	93.6218i	−0.178257	+	0.158681i
$591$		0			0
$592$	511.356	+	120.887i	0.863778	+	0.204201i
$593$	231.649			0.390639			0.195320	−	0.980740i	$-0.437426\pi$
$593$	231.649			0.390639			0.195320	+	0.980740i	$0.437426\pi$
$594$		0			0
$595$			58.2847i			0.0979575i
$596$	−19.0764	+	163.612i	−0.0320075	+	0.274517i
$597$		0			0
$598$	−7.07376	+	6.29691i	−0.0118290	+	0.0105300i
$599$		−	475.122i		−	0.793192i	−0.917993	−	0.396596i	$-0.870191\pi$
$599$		−	475.122i		−	0.793192i	0.917993	−	0.396596i	$-0.129809\pi$
$600$		0			0
$601$	318.831			0.530500			0.265250	−	0.964180i	$-0.414546\pi$
$601$	318.831			0.530500			0.265250	+	0.964180i	$0.414546\pi$
$602$	−88.2994	−	99.1929i	−0.146677	−	0.164772i
$603$		0			0
$604$	−474.585	−	55.3345i	−0.785736	−	0.0916134i
$605$	28.8626			0.0477068
$606$		0			0
$607$			499.680i			0.823196i	0.911366	+	0.411598i	$0.135029\pi$
$607$			499.680i			0.823196i	−0.911366	+	0.411598i	$0.864971\pi$
$608$	357.154	−	192.903i	0.587425	−	0.317275i
$609$		0			0
$610$	−332.464	−	373.480i	−0.545023	−	0.612262i
$611$		−	31.3471i		−	0.0513045i
$612$		0			0
$613$	−1055.33			−1.72158			−0.860788	−	0.508963i	$-0.830029\pi$
$613$	−1055.33			−1.72158			−0.860788	+	0.508963i	$0.830029\pi$
$614$	−61.3599	+	54.6213i	−0.0999347	+	0.0889598i
$615$		0			0
$616$	122.801	−	86.0644i	0.199353	−	0.139715i
$617$	188.341			0.305253			0.152627	−	0.988284i	$-0.451227\pi$
$617$	188.341			0.305253			0.152627	+	0.988284i	$0.451227\pi$
$618$		0			0
$619$			164.992i			0.266546i	0.991079	+	0.133273i	$0.0425486\pi$
$619$			164.992i			0.266546i	−0.991079	+	0.133273i	$0.957451\pi$
$620$	−413.216	−	48.1792i	−0.666478	−	0.0777083i
$621$		0			0
$622$	701.957	−	624.867i	1.12855	−	1.00461i
$623$		−	121.273i		−	0.194660i
$624$		0			0
$625$	156.045			0.249673
$626$	272.313	+	305.908i	0.435004	+	0.488671i
$627$		0			0
$628$	−56.1576	+	481.645i	−0.0894230	+	0.766950i
$629$	129.075			0.205207
$630$		0			0
$631$			486.689i			0.771298i	0.922646	+	0.385649i	$0.126022\pi$
$631$			486.689i			0.771298i	−0.922646	+	0.385649i	$0.873978\pi$
$632$	446.081	+	636.493i	0.705825	+	1.00711i
$633$		0			0
$634$	−15.5572	−	17.4764i	−0.0245381	−	0.0275654i
$635$			324.745i			0.511409i
$636$		0			0
$637$	40.7432			0.0639611
$638$	194.095	−	172.779i	0.304224	−	0.270813i
$639$		0			0
$640$	312.004	−	124.310i	0.487506	−	0.194235i
$641$	−143.117			−0.223271			−0.111636	−	0.993749i	$-0.535609\pi$
$641$	−143.117			−0.223271			−0.111636	+	0.993749i	$0.535609\pi$
$642$		0			0
$643$		−	1037.72i		−	1.61387i	−0.590638	−	0.806937i	$-0.701124\pi$
$643$		−	1037.72i		−	1.61387i	0.590638	−	0.806937i	$-0.298876\pi$
$644$	−5.19039	+	44.5162i	−0.00805962	+	0.0691246i
$645$		0			0
$646$	74.4783	−	66.2990i	0.115291	−	0.102630i
$647$		−	383.185i		−	0.592248i	−0.955149	−	0.296124i	$-0.904306\pi$
$647$		−	383.185i		−	0.592248i	0.955149	−	0.296124i	$-0.0956942\pi$
$648$		0			0
$649$	88.9903			0.137119
$650$	57.5393	+	64.6379i	0.0885220	+	0.0994429i
$651$		0			0
$652$	485.717	+	56.6325i	0.744965	+	0.0868597i
$653$	39.5749			0.0606048			0.0303024	−	0.999541i	$-0.490353\pi$
$653$	39.5749			0.0606048			0.0303024	+	0.999541i	$0.490353\pi$
$654$		0			0
$655$			259.648i			0.396410i
$656$	315.363	+	74.5534i	0.480737	+	0.113649i
$657$		0			0
$658$	−98.6358	−	110.805i	−0.149902	−	0.168396i
$659$		−	1076.03i		−	1.63282i	−0.577470	−	0.816412i	$-0.695960\pi$
$659$		−	1076.03i		−	1.63282i	0.577470	−	0.816412i	$-0.304040\pi$
$660$		0			0
$661$	−341.729			−0.516989			−0.258494	−	0.966013i	$-0.583226\pi$
$661$	−341.729			−0.516989			−0.258494	+	0.966013i	$0.583226\pi$
$662$	−79.3297	+	70.6176i	−0.119833	+	0.106673i
$663$		0			0
$664$	−545.723	−	778.668i	−0.821872	−	1.17269i
$665$	−188.111			−0.282874
$666$		0			0
$667$			77.6632i			0.116437i
$668$	−569.473	−	66.3980i	−0.852505	−	0.0993983i
$669$		0			0
$670$	−13.5617	+	12.0723i	−0.0202413	+	0.0180184i
$671$			316.017i			0.470964i
$672$		0			0
$673$	−1090.45			−1.62028			−0.810138	−	0.586239i	$-0.800608\pi$
$673$	−1090.45			−1.62028			−0.810138	+	0.586239i	$0.800608\pi$
$674$	236.373	+	265.534i	0.350701	+	0.393967i
$675$		0			0
$676$	75.6454	−	648.785i	0.111901	−	0.959740i
$677$	68.0346			0.100494			0.0502471	−	0.998737i	$-0.483999\pi$
$677$	68.0346			0.100494			0.0502471	+	0.998737i	$0.483999\pi$
$678$		0			0
$679$			0.320089i			0.000471412i
$680$	67.5612	−	47.3498i	0.0993547	−	0.0696320i
$681$		0			0
$682$	174.820	+	196.387i	0.256334	+	0.287958i
$683$		−	1090.21i		−	1.59621i	−0.602518	−	0.798106i	$-0.705836\pi$
$683$		−	1090.21i		−	1.59621i	0.602518	−	0.798106i	$-0.294164\pi$
$684$		0			0
$685$	−329.730			−0.481358
$686$	557.721	−	496.471i	0.813004	−	0.723719i
$687$		0			0
$688$	−43.2470	+	182.936i	−0.0628590	+	0.265895i
$689$	−122.965			−0.178468
$690$		0			0
$691$		−	359.357i		−	0.520053i	−0.965601	−	0.260027i	$-0.916269\pi$
$691$		−	359.357i		−	0.520053i	0.965601	−	0.260027i	$-0.0837313\pi$
$692$	126.570	−	1085.55i	0.182904	−	1.56871i
$693$		0			0
$694$	−838.922	+	746.791i	−1.20882	+	1.07607i
$695$			529.673i			0.762119i
$696$		0			0
$697$	79.6030			0.114208
$698$	−546.459	−	613.876i	−0.782893	−	0.879478i
$699$		0			0
$700$	406.776	+	47.4283i	0.581108	+	0.0677546i
$701$	−180.147			−0.256986			−0.128493	−	0.991710i	$-0.541014\pi$
$701$	−180.147			−0.256986			−0.128493	+	0.991710i	$0.541014\pi$
$702$		0			0
$703$			416.584i			0.592580i
$704$	−199.525	−	72.4287i	−0.283416	−	0.102882i
$705$		0			0
$706$	−7.28932	−	8.18860i	−0.0103248	−	0.0115986i
$707$		−	853.644i		−	1.20742i
$708$		0			0
$709$	−1015.72			−1.43261			−0.716306	−	0.697786i	$-0.754169\pi$
$709$	−1015.72			−1.43261			−0.716306	+	0.697786i	$0.754169\pi$
$710$	70.9241	−	63.1351i	0.0998931	−	0.0889227i
$711$		0			0
$712$	−140.575	+	98.5210i	−0.197437	+	0.138372i
$713$	−78.5804			−0.110211
$714$		0			0
$715$			20.7860i			0.0290714i
$716$	−1033.42	−	120.493i	−1.44333	−	0.168286i
$717$		0			0
$718$	900.250	−	801.383i	1.25383	−	1.11613i
$719$		−	335.376i		−	0.466448i	−0.972423	−	0.233224i	$-0.925073\pi$
$719$		−	335.376i		−	0.466448i	0.972423	−	0.233224i	$-0.0749275\pi$
$720$		0			0
$721$	−48.8292			−0.0677243
$722$	−266.082	−	298.908i	−0.368535	−	0.414001i
$723$		0			0
$724$	−126.551	+	1085.38i	−0.174794	+	1.49914i
$725$	709.663			0.978845
$726$		0			0
$727$		−	818.836i		−	1.12632i	−0.826347	−	0.563161i	$-0.809585\pi$
$727$		−	818.836i		−	1.12632i	0.826347	−	0.563161i	$-0.190415\pi$
$728$	61.9811	+	88.4380i	0.0851389	+	0.121481i
$729$		0			0
$730$	−188.754	−	212.041i	−0.258568	−	0.290467i
$731$			46.1761i			0.0631684i
$732$		0			0
$733$	−248.050			−0.338404			−0.169202	−	0.985581i	$-0.554119\pi$
$733$	−248.050			−0.338404			−0.169202	+	0.985581i	$0.554119\pi$
$734$	−322.382	+	286.978i	−0.439213	+	0.390978i
$735$		0			0
$736$	55.8179	−	30.1479i	0.0758396	−	0.0409618i
$737$	11.4751			0.0155700
$738$		0			0
$739$			1074.21i			1.45360i	0.686850	+	0.726799i	$0.258993\pi$
$739$			1074.21i			1.45360i	−0.686850	+	0.726799i	$0.741007\pi$
$740$	−39.9177	+	342.360i	−0.0539428	+	0.462649i
$741$		0			0
$742$	−434.652	+	386.918i	−0.585784	+	0.521452i
$743$		−	12.5429i		−	0.0168814i	−0.999964	−	0.00844070i	$-0.997313\pi$
$743$		−	12.5429i		−	0.0168814i	0.999964	−	0.00844070i	$-0.00268679\pi$
$744$		0			0
$745$	−108.051			−0.145036
$746$	195.744	+	219.893i	0.262392	+	0.294763i
$747$		0			0
$748$	−51.7909	−	6.03859i	−0.0692392	−	0.00807298i
$749$	763.072			1.01879
$750$		0			0
$751$		−	1.16551i		−	0.00155195i	−1.00000		0.000775974i	$-0.999753\pi$
$751$		−	1.16551i		−	0.00155195i	1.00000		0.000775974i	$-0.000247000\pi$
$752$	−48.3095	+	204.351i	−0.0642414	+	0.271743i
$753$		0			0
$754$	124.430	+	139.781i	0.165027	+	0.185386i
$755$		−	313.422i		−	0.415128i
$756$		0			0
$757$	1447.87			1.91265			0.956323	−	0.292311i	$-0.0944241\pi$
$757$	1447.87			1.91265			0.956323	+	0.292311i	$0.0944241\pi$
$758$	−625.665	+	556.954i	−0.825416	+	0.734768i
$759$		0			0
$760$	152.819	+	218.051i	0.201078	+	0.286909i
$761$	−1208.38			−1.58789			−0.793943	−	0.607992i	$-0.791975\pi$
$761$	−1208.38			−1.58789			−0.793943	+	0.607992i	$0.791975\pi$
$762$		0			0
$763$			866.503i			1.13565i
$764$	−1032.73	−	120.412i	−1.35174	−	0.157607i
$765$		0			0
$766$	−759.355	+	675.962i	−0.991326	+	0.882457i
$767$			64.0882i			0.0835570i
$768$		0			0
$769$	292.708			0.380635			0.190317	−	0.981723i	$-0.439048\pi$
$769$	292.708			0.380635			0.190317	+	0.981723i	$0.439048\pi$
$770$	65.4047	+	73.4737i	0.0849412	+	0.0954204i
$771$		0			0
$772$	139.768	−	1198.75i	0.181047	−	1.55278i
$773$	−434.924			−0.562644			−0.281322	−	0.959613i	$-0.590773\pi$
$773$	−434.924			−0.562644			−0.281322	+	0.959613i	$0.590773\pi$
$774$		0			0
$775$			718.044i			0.926509i
$776$	0.371034	−	0.260036i	0.000478136	−	0.000335098i
$777$		0			0
$778$	181.905	+	204.346i	0.233811	+	0.262656i
$779$			256.915i			0.329801i
$780$		0			0
$781$	−60.0118			−0.0768397
$782$	11.6399	−	10.3616i	0.0148847	−	0.0132501i
$783$		0			0
$784$	−265.604	−	62.7901i	−0.338781	−	0.0800895i
$785$	−318.084			−0.405203
$786$		0			0
$787$		−	449.202i		−	0.570777i	−0.958412	−	0.285389i	$-0.907877\pi$
$787$		−	449.202i		−	0.570777i	0.958412	−	0.285389i	$-0.0921227\pi$
$788$	−12.6969	+	108.897i	−0.0161128	+	0.138194i
$789$		0			0
$790$	−380.822	+	339.000i	−0.482053	+	0.429114i
$791$			784.756i			0.992106i
$792$		0			0
$793$	−227.586			−0.286994
$794$	−995.439	−	1118.25i	−1.25370	−	1.40837i
$795$		0			0
$796$	−1028.63	−	119.933i	−1.29224	−	0.150670i
$797$	−165.810			−0.208043			−0.104022	−	0.994575i	$-0.533171\pi$
$797$	−165.810			−0.208043			−0.104022	+	0.994575i	$0.533171\pi$
$798$		0			0
$799$			51.5815i			0.0645576i
$800$	−275.483	−	510.048i	−0.344353	−	0.637560i
$801$		0			0
$802$	310.219	+	348.490i	0.386806	+	0.434527i
$803$			179.417i			0.223433i
$804$		0			0
$805$	−29.3991			−0.0365206
$806$	−141.432	+	125.900i	−0.175474	+	0.156203i
$807$		0			0
$808$	−989.509	+	693.490i	−1.22464	+	0.858279i
$809$	1221.43			1.50980			0.754901	−	0.655839i	$-0.227685\pi$
$809$	1221.43			1.50980			0.754901	+	0.655839i	$0.227685\pi$
$810$		0			0
$811$		−	712.821i		−	0.878940i	−0.898257	−	0.439470i	$-0.855166\pi$
$811$		−	712.821i		−	0.878940i	0.898257	−	0.439470i	$-0.144834\pi$
$812$	879.665	+	102.565i	1.08333	+	0.126312i
$813$		0			0
$814$	162.712	−	144.843i	0.199892	−	0.177939i
$815$			320.774i			0.393588i
$816$		0			0
$817$	−149.031			−0.182413
$818$	712.836	+	800.778i	0.871437	+	0.978946i
$819$		0			0
$820$	−24.6180	+	211.140i	−0.0300220	+	0.257488i
$821$	101.692			0.123864			0.0619318	−	0.998080i	$-0.480274\pi$
$821$	101.692			0.123864			0.0619318	+	0.998080i	$0.480274\pi$
$822$		0			0
$823$			936.441i			1.13784i	0.822393	+	0.568919i	$0.192638\pi$
$823$			936.441i			1.13784i	−0.822393	+	0.568919i	$0.807362\pi$
$824$	39.6682	+	56.6008i	0.0481410	+	0.0686903i
$825$		0			0
$826$	201.658	+	226.537i	0.244138	+	0.274258i
$827$			1304.16i			1.57698i	0.615049	+	0.788489i	$0.289136\pi$
$827$			1304.16i			1.57698i	−0.615049	+	0.788489i	$0.710864\pi$
$828$		0			0
$829$	793.199			0.956814			0.478407	−	0.878138i	$-0.341214\pi$
$829$	793.199			0.956814			0.478407	+	0.878138i	$0.341214\pi$
$830$	465.887	−	414.723i	0.561310	−	0.499666i
$831$		0			0
$832$	52.1610	−	143.692i	0.0626935	−	0.172707i
$833$	−67.0430			−0.0804837
$834$		0			0
$835$		−	376.087i		−	0.450404i
$836$	19.4893	−	167.153i	0.0233126	−	0.199944i
$837$		0			0
$838$	610.608	−	543.550i	0.728649	−	0.648628i
$839$			827.557i			0.986362i	0.869927	+	0.493181i	$0.164166\pi$
$839$			827.557i			0.986362i	−0.869927	+	0.493181i	$0.835834\pi$
$840$		0			0
$841$	693.667			0.824812
$842$	514.147	+	577.577i	0.610626	+	0.685959i
$843$		0			0
$844$	−110.657	−	12.9021i	−0.131110	−	0.0152868i
$845$	428.465			0.507060
$846$		0			0
$847$		−	62.1691i		−	0.0733992i
$848$	801.604	+	189.503i	0.945288	+	0.223471i
$849$		0			0
$850$	−94.6808	−	106.362i	−0.111389	−	0.125131i
$851$			65.1059i			0.0765052i
$852$		0			0
$853$	123.265			0.144508			0.0722538	−	0.997386i	$-0.476981\pi$
$853$	123.265			0.144508			0.0722538	+	0.997386i	$0.476981\pi$
$854$	−804.464	+	716.117i	−0.941995	+	0.838544i
$855$		0			0
$856$	−619.910	−	884.521i	−0.724194	−	1.03332i
$857$	119.223			0.139116			0.0695581	−	0.997578i	$-0.477841\pi$
$857$	119.223			0.139116			0.0695581	+	0.997578i	$0.477841\pi$
$858$		0			0
$859$		−	399.433i		−	0.464997i	−0.972597	−	0.232499i	$-0.925310\pi$
$859$		−	399.433i		−	0.464997i	0.972597	−	0.232499i	$-0.0746901\pi$
$860$	−122.478	−	14.2804i	−0.142417	−	0.0166051i
$861$		0			0
$862$	−224.292	+	199.660i	−0.260200	+	0.231624i
$863$			723.815i			0.838719i	0.907820	+	0.419360i	$0.137745\pi$
$863$			723.815i			0.838719i	−0.907820	+	0.419360i	$0.862255\pi$
$864$		0			0
$865$	716.908			0.828795
$866$	−331.491	−	372.387i	−0.382784	−	0.430008i
$867$		0			0
$868$	−103.776	+	890.054i	−0.119558	+	1.02541i
$869$	322.229			0.370805
$870$		0			0
$871$			8.26404i			0.00948799i
$872$	1004.41	−	703.936i	1.15185	−	0.807266i
$873$		0			0
$874$	33.4415	+	37.5672i	0.0382626	+	0.0429830i
$875$			639.376i			0.730716i
$876$		0			0
$877$	−1331.26			−1.51797			−0.758984	−	0.651110i	$-0.774304\pi$
$877$	−1331.26			−1.51797			−0.758984	+	0.651110i	$0.774304\pi$
$878$	−461.362	+	410.695i	−0.525470	+	0.467762i
$879$		0			0
$880$	32.0337	−	135.504i	0.0364019	−	0.153981i
$881$	600.014			0.681060			0.340530	−	0.940234i	$-0.389394\pi$
$881$	600.014			0.681060			0.340530	+	0.940234i	$0.389394\pi$
$882$		0			0
$883$		−	174.915i		−	0.198092i	−0.995083	−	0.0990458i	$-0.968421\pi$
$883$		−	174.915i		−	0.198092i	0.995083	−	0.0990458i	$-0.0315790\pi$
$884$	4.34882	−	37.2983i	0.00491948	−	0.0421927i
$885$		0			0
$886$	280.029	−	249.276i	0.316060	−	0.281350i
$887$			1077.58i			1.21486i	0.794374	+	0.607429i	$0.207799\pi$
$887$			1077.58i			1.21486i	−0.794374	+	0.607429i	$0.792201\pi$
$888$		0			0
$889$	699.489			0.786827
$890$	−74.8711	−	84.1079i	−0.0841248	−	0.0945033i
$891$		0			0
$892$	−844.015	−	98.4084i	−0.946205	−	0.110323i
$893$	−166.477			−0.186425
$894$		0			0
$895$		−	682.486i		−	0.762554i
$896$	−267.760	−	672.046i	−0.298839	−	0.750051i
$897$		0			0
$898$	−191.529	−	215.158i	−0.213284	−	0.239597i
$899$			1552.79i			1.72724i
$900$		0			0
$901$	202.338			0.224571
$902$	100.347	−	89.3272i	0.111250	−	0.0990324i
$903$		0			0
$904$	909.656	−	637.525i	1.00626	−	0.705227i
$905$	−716.799			−0.792043
$906$		0			0
$907$			144.563i			0.159386i	0.996819	+	0.0796932i	$0.0253941\pi$
$907$			144.563i			0.159386i	−0.996819	+	0.0796932i	$0.974606\pi$
$908$	−524.551	−	61.1603i	−0.577699	−	0.0673571i
$909$		0			0
$910$	−52.9136	+	47.1026i	−0.0581468	+	0.0517611i
$911$		−	918.460i		−	1.00819i	−0.863648	−	0.504095i	$-0.831826\pi$
$911$		−	918.460i		−	1.00819i	0.863648	−	0.504095i	$-0.168174\pi$
$912$		0			0
$913$	−394.206			−0.431770
$914$	−955.023	−	1072.84i	−1.04488	−	1.17379i
$915$		0			0
$916$	126.949	−	1088.80i	0.138591	−	1.18865i
$917$	559.274			0.609895
$918$		0			0
$919$			1564.99i			1.70293i	0.524414	+	0.851463i	$0.324284\pi$
$919$			1564.99i			1.70293i	−0.524414	+	0.851463i	$0.675716\pi$
$920$	23.8834	+	34.0782i	0.0259602	+	0.0370415i
$921$		0			0
$922$	377.451	+	424.018i	0.409383	+	0.459889i
$923$		−	43.2187i		−	0.0468242i
$924$		0			0
$925$	594.919			0.643155
$926$	−639.638	+	569.392i	−0.690754	+	0.614894i
$927$		0			0
$928$	−595.739	−	1102.99i	−0.641960	−	1.18857i
$929$	1264.32			1.36095			0.680476	−	0.732770i	$-0.261773\pi$
$929$	1264.32			1.36095			0.680476	+	0.732770i	$0.261773\pi$
$930$		0			0
$931$		−	216.378i		−	0.232415i
$932$	81.2190	−	696.587i	0.0871448	−	0.747411i
$933$		0			0
$934$	−620.449	+	552.311i	−0.664293	+	0.591339i
$935$		−	34.2034i		−	0.0365811i
$936$		0			0
$937$	1551.26			1.65556			0.827782	−	0.561049i	$-0.189602\pi$
$937$	1551.26			1.65556			0.827782	+	0.561049i	$0.189602\pi$
$938$	26.0034	+	29.2114i	0.0277222	+	0.0311423i
$939$		0			0
$940$	−136.816	−	15.9521i	−0.145549	−	0.0169703i
$941$	−1357.23			−1.44233			−0.721164	−	0.692764i	$-0.756393\pi$
$941$	−1357.23			−1.44233			−0.721164	+	0.692764i	$0.756393\pi$
$942$		0			0
$943$			40.1521i			0.0425791i
$944$	98.7675	−	417.789i	0.104627	−	0.442574i
$945$		0			0
$946$	51.8169	+	58.2096i	0.0547748	+	0.0615323i
$947$		−	17.9609i		−	0.0189661i	−0.999955	−	0.00948304i	$-0.996981\pi$
$947$		−	17.9609i		−	0.0189661i	0.999955	−	0.00948304i	$-0.00301859\pi$
$948$		0			0
$949$	−129.211			−0.136155
$950$	343.277	−	305.578i	0.361345	−	0.321661i
$951$		0			0
$952$	−101.990	−	145.525i	−0.107132	−	0.152862i
$953$	−909.911			−0.954786			−0.477393	−	0.878690i	$-0.658418\pi$
$953$	−909.911			−0.954786			−0.477393	+	0.878690i	$0.658418\pi$
$954$		0			0
$955$		−	682.029i		−	0.714166i
$956$	187.479	+	21.8592i	0.196107	+	0.0228652i
$957$		0			0
$958$	263.194	−	234.290i	0.274733	−	0.244561i
$959$			710.227i			0.740592i
$960$		0			0
$961$	−610.131			−0.634892
$962$	104.311	+	117.180i	0.108432	+	0.121809i
$963$		0			0
$964$	4.58158	−	39.2946i	0.00475267	−	0.0407620i
$965$	791.666			0.820380
$966$		0			0
$967$		−	840.940i		−	0.869638i	−0.900518	−	0.434819i	$-0.856812\pi$
$967$		−	840.940i		−	0.869638i	0.900518	−	0.434819i	$-0.143188\pi$
$968$	−72.0639	+	50.5054i	−0.0744462	+	0.0521750i
$969$		0			0
$970$	0.197615	+	0.221994i	0.000203726	+	0.000228860i
$971$			330.453i			0.340323i	0.985416	+	0.170161i	$0.0544289\pi$
$971$			330.453i			0.340323i	−0.985416	+	0.170161i	$0.945571\pi$
$972$		0			0
$973$	1140.90			1.17256
$974$	1147.81	−	1021.76i	1.17845	−	1.04904i
$975$		0			0
$976$	1483.63	+	350.737i	1.52011	+	0.359362i
$977$	−532.551			−0.545088			−0.272544	−	0.962143i	$-0.587865\pi$
$977$	−532.551			−0.545088			−0.272544	+	0.962143i	$0.587865\pi$
$978$		0			0
$979$			71.1672i			0.0726938i
$980$	20.7337	−	177.826i	0.0211568	−	0.181455i
$981$		0			0
$982$	280.232	−	249.457i	0.285369	−	0.254029i
$983$		−	498.333i		−	0.506951i	−0.967342	−	0.253476i	$-0.918426\pi$
$983$		−	498.333i		−	0.506951i	0.967342	−	0.253476i	$-0.0815737\pi$
$984$		0			0
$985$	−71.9169			−0.0730121
$986$	−204.750	−	230.010i	−0.207657	−	0.233276i
$987$		0			0
$988$	120.379	+	14.0356i	0.121841	+	0.0142061i
$989$	−23.2914			−0.0235505
$990$		0			0
$991$		−	1422.23i		−	1.43514i	−0.696484	−	0.717572i	$-0.745253\pi$
$991$		−	1422.23i		−	1.43514i	0.696484	−	0.717572i	$-0.254747\pi$
$992$	1116.02	−	602.775i	1.12502	−	0.607636i
$993$		0			0
$994$	−135.991	−	152.768i	−0.136812	−	0.153690i
$995$		−	679.318i		−	0.682731i
$996$		0			0
$997$	971.406			0.974329			0.487165	−	0.873310i	$-0.338031\pi$
$997$	971.406			0.974329			0.487165	+	0.873310i	$0.338031\pi$
$998$	−692.874	+	616.782i	−0.694263	+	0.618018i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.3.g.c.199.3		10
3.2	odd	2		44.3.b.a.23.8	yes	10
4.3	odd	2	inner	396.3.g.c.199.4		10
12.11	even	2		44.3.b.a.23.7	✓	10
24.5	odd	2		704.3.d.d.639.10		10
24.11	even	2		704.3.d.d.639.1		10
33.32	even	2		484.3.b.h.243.3		10
132.131	odd	2		484.3.b.h.243.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.b.a.23.7	✓	10	12.11	even	2
44.3.b.a.23.8	yes	10	3.2	odd	2
396.3.g.c.199.3		10	1.1	even	1	trivial
396.3.g.c.199.4		10	4.3	odd	2	inner
484.3.b.h.243.3		10	33.32	even	2
484.3.b.h.243.4		10	132.131	odd	2
704.3.d.d.639.1		10	24.11	even	2
704.3.d.d.639.10		10	24.5	odd	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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	396.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32980 - 1.49386i) q^{2} +(-0.463244 + 3.97309i) q^{4} -2.62387 q^{5} +5.65174i q^{7} +(6.55126 - 4.59140i) q^{8} +(3.48924 + 3.91971i) q^{10} -3.31662i q^{11} +2.38854 q^{13} +(8.44292 - 7.51571i) q^{14} +(-15.5708 - 3.68102i) q^{16} -3.93033 q^{17} -12.6850i q^{19} +(1.21549 - 10.4249i) q^{20} +(-4.95458 + 4.41046i) q^{22} -1.98248i q^{23} -18.1153 q^{25} +(-3.17628 - 3.56814i) q^{26} +(-22.4548 - 2.61814i) q^{28} -39.1748 q^{29} -39.6375i q^{31} +(15.2072 + 28.1557i) q^{32} +(5.22657 + 5.87137i) q^{34} -14.8295i q^{35} -32.8407 q^{37} +(-18.9496 + 16.8685i) q^{38} +(-17.1897 + 12.0473i) q^{40} -20.2535 q^{41} -11.7486i q^{43} +(13.1772 + 1.53641i) q^{44} +(-2.96155 + 2.63631i) q^{46} -13.1240i q^{47} +17.0578 q^{49} +(24.0898 + 27.0617i) q^{50} +(-1.10648 + 9.48986i) q^{52} -51.4812 q^{53} +8.70241i q^{55} +(25.9494 + 37.0260i) q^{56} +(52.0948 + 58.5218i) q^{58} +26.8316i q^{59} -95.2827 q^{61} +(-59.2129 + 52.7101i) q^{62} +(21.8381 - 60.1589i) q^{64} -6.26722 q^{65} +3.45987i q^{67} +(1.82070 - 15.6155i) q^{68} +(-22.1532 + 19.7203i) q^{70} -18.0942i q^{71} -54.0962 q^{73} +(43.6717 + 49.0595i) q^{74} +(50.3985 + 5.87624i) q^{76} +18.7447 q^{77} +97.1558i q^{79} +(40.8559 + 9.65853i) q^{80} +(26.9332 + 30.2559i) q^{82} -118.858i q^{83} +10.3127 q^{85} +(-17.5509 + 15.6234i) q^{86} +(-15.2280 - 21.7281i) q^{88} -21.4577 q^{89} +13.4994i q^{91} +(7.87655 + 0.918371i) q^{92} +(-19.6054 + 17.4523i) q^{94} +33.2838i q^{95} +0.0566354 q^{97} +(-22.6836 - 25.4820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 4 q^{5} + 12 q^{8} - 2 q^{10} - 4 q^{13} + 4 q^{14} - 40 q^{16} - 20 q^{17} + 64 q^{20} - 10 q^{25} + 36 q^{26} + 40 q^{28} - 28 q^{29} - 80 q^{32} - 88 q^{34} - 100 q^{37} - 40 q^{38}+ \cdots + 568 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 + 4 * q^5 + 12 * q^8 - 2 * q^10 - 4 * q^13 + 4 * q^14 - 40 * q^16 - 20 * q^17 + 64 * q^20 - 10 * q^25 + 36 * q^26 + 40 * q^28 - 28 * q^29 - 80 * q^32 - 88 * q^34 - 100 * q^37 - 40 * q^38 - 12 * q^40 - 100 * q^41 + 44 * q^44 - 130 * q^46 - 22 * q^49 + 198 * q^50 - 176 * q^52 - 100 * q^53 - 136 * q^56 + 116 * q^58 - 52 * q^61 - 134 * q^62 - 368 * q^64 + 184 * q^65 - 176 * q^68 - 36 * q^70 + 84 * q^73 - 362 * q^74 + 504 * q^76 + 120 * q^80 + 220 * q^82 - 216 * q^85 - 556 * q^86 - 132 * q^88 - 28 * q^89 - 152 * q^92 - 272 * q^94 - 180 * q^97 + 568 * q^98

Introduction

L-functions

Modular forms

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