LMFDB - Embedded newform 1350.3.k.a.899.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,3,Mod(449,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1350.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1350.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$36.7848356886$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.899
Dual form			1350.3.k.a.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(7.22999 + 4.17423i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(7.22999 + 4.17423i) q^{7} -2.82843 q^{8} +(-0.825765 - 0.476756i) q^{11} +(8.39780 - 4.84847i) q^{13} +(10.2247 - 5.90326i) q^{14} +(-2.00000 + 3.46410i) q^{16} -18.8776 q^{17} +24.6969 q^{19} +(-1.16781 + 0.674235i) q^{22} +(0.476756 + 0.825765i) q^{23} -13.7135i q^{26} -16.6969i q^{28} +(11.8485 + 6.84072i) q^{29} +(-1.52270 - 2.63740i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-13.3485 + 23.1202i) q^{34} +46.6969i q^{37} +(17.4634 - 30.2474i) q^{38} +(9.45459 - 5.45861i) q^{41} +(39.0105 + 22.5227i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(22.6435 - 39.2196i) q^{47} +(10.3485 + 17.9241i) q^{49} +(-16.7956 - 9.69694i) q^{52} +94.3879 q^{53} +(-20.4495 - 11.8065i) q^{56} +(16.7563 - 9.67423i) q^{58} +(-16.2650 + 9.39063i) q^{59} +(-6.54541 + 11.3370i) q^{61} -4.30686 q^{62} +8.00000 q^{64} +(64.9912 - 37.5227i) q^{67} +(18.8776 + 32.6969i) q^{68} -18.0204i q^{71} +7.90918i q^{73} +(57.1918 + 33.0197i) q^{74} +(-24.6969 - 42.7764i) q^{76} +(-3.98018 - 6.89388i) q^{77} +(-21.8712 + 37.8820i) q^{79} -15.4393i q^{82} +(65.1662 - 112.871i) q^{83} +(55.1691 - 31.8519i) q^{86} +(2.33562 + 1.34847i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(0.953512 - 1.65153i) q^{92} +(-32.0227 - 55.4650i) q^{94} +(95.1576 + 54.9393i) q^{97} +29.2699 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} - 36 q^{11} + 72 q^{14} - 16 q^{16} + 80 q^{19} + 36 q^{29} + 76 q^{31} - 48 q^{34} + 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{56} + 252 q^{59} + 124 q^{61} + 64 q^{64} + 144 q^{74} - 80 q^{76} - 28 q^{79} + 216 q^{86} + 824 q^{91} - 168 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 - 36 * q^11 + 72 * q^14 - 16 * q^16 + 80 * q^19 + 36 * q^29 + 76 * q^31 - 48 * q^34 + 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^56 + 252 * q^59 + 124 * q^61 + 64 * q^64 + 144 * q^74 - 80 * q^76 - 28 * q^79 + 216 * q^86 + 824 * q^91 - 168 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	7.22999	+	4.17423i	1.03286	+	0.596319i	0.917801	−	0.397040i	$-0.129963\pi$
$7$	7.22999	+	4.17423i	1.03286	+	0.596319i	0.115054	+	0.993359i	$0.463296\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$		0			0
$11$	−0.825765	−	0.476756i	−0.0750696	−	0.0433414i	0.461995	−	0.886882i	$-0.347134\pi$
$11$	−0.825765	−	0.476756i	−0.0750696	−	0.0433414i	−0.537065	+	0.843541i	$0.680467\pi$
$12$		0			0
$13$	8.39780	−	4.84847i	0.645984	−	0.372959i	−0.140932	−	0.990019i	$-0.545010\pi$
$13$	8.39780	−	4.84847i	0.645984	−	0.372959i	0.786916	+	0.617060i	$0.211676\pi$
$14$	10.2247	−	5.90326i	0.730339	−	0.421661i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−18.8776			−1.11045			−0.555223	−	0.831701i	$-0.687367\pi$
$17$	−18.8776			−1.11045			−0.555223	+	0.831701i	$0.687367\pi$
$18$		0			0
$19$	24.6969			1.29984			0.649919	−	0.760003i	$-0.274803\pi$
$19$	24.6969			1.29984			0.649919	+	0.760003i	$0.274803\pi$
$20$		0			0
$21$		0			0
$22$	−1.16781	+	0.674235i	−0.0530822	+	0.0306470i
$23$	0.476756	+	0.825765i	0.0207285	+	0.0359028i	0.876204	−	0.481941i	$-0.160068\pi$
$23$	0.476756	+	0.825765i	0.0207285	+	0.0359028i	−0.855475	+	0.517844i	$0.826735\pi$
$24$		0			0
$25$		0			0
$26$		−	13.7135i		−	0.527444i
$27$		0			0
$28$		−	16.6969i		−	0.596319i
$29$	11.8485	+	6.84072i	0.408568	+	0.235887i	0.690174	−	0.723643i	$-0.257534\pi$
$29$	11.8485	+	6.84072i	0.408568	+	0.235887i	−0.281606	+	0.959530i	$0.590867\pi$
$30$		0			0
$31$	−1.52270	−	2.63740i	−0.0491195	−	0.0850774i	0.840420	−	0.541935i	$-0.182308\pi$
$31$	−1.52270	−	2.63740i	−0.0491195	−	0.0850774i	−0.889540	+	0.456858i	$0.848975\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$	−13.3485	+	23.1202i	−0.392602	+	0.680007i
$35$		0			0
$36$		0			0
$37$			46.6969i			1.26208i	0.775751	+	0.631040i	$0.217372\pi$
$37$			46.6969i			1.26208i	−0.775751	+	0.631040i	$0.782628\pi$
$38$	17.4634	−	30.2474i	0.459562	−	0.795985i
$39$		0			0
$40$		0			0
$41$	9.45459	−	5.45861i	0.230600	−	0.133137i	−0.380249	−	0.924884i	$-0.624162\pi$
$41$	9.45459	−	5.45861i	0.230600	−	0.133137i	0.610849	+	0.791747i	$0.290828\pi$
$42$		0			0
$43$	39.0105	+	22.5227i	0.907220	+	0.523784i	0.879536	−	0.475833i	$-0.157853\pi$
$43$	39.0105	+	22.5227i	0.907220	+	0.523784i	0.0276845	+	0.999617i	$0.491187\pi$
$44$			1.90702i			0.0433414i
$45$		0			0
$46$	1.34847			0.0293145
$47$	22.6435	−	39.2196i	0.481776	−	0.834460i	−0.518005	−	0.855377i	$-0.673325\pi$
$47$	22.6435	−	39.2196i	0.481776	−	0.834460i	0.999781	+	0.0209170i	$0.00665856\pi$
$48$		0			0
$49$	10.3485	+	17.9241i	0.211193	+	0.365797i
$50$		0			0
$51$		0			0
$52$	−16.7956	−	9.69694i	−0.322992	−	0.186480i
$53$	94.3879			1.78090			0.890452	−	0.455077i	$-0.150388\pi$
$53$	94.3879			1.78090			0.890452	+	0.455077i	$0.150388\pi$
$54$		0			0
$55$		0			0
$56$	−20.4495	−	11.8065i	−0.365169	−	0.210831i
$57$		0			0
$58$	16.7563	−	9.67423i	0.288901	−	0.166797i
$59$	−16.2650	+	9.39063i	−0.275679	+	0.159163i	−0.631466	−	0.775404i	$-0.717546\pi$
$59$	−16.2650	+	9.39063i	−0.275679	+	0.159163i	0.355787	+	0.934567i	$0.384213\pi$
$60$		0			0
$61$	−6.54541	+	11.3370i	−0.107302	+	0.185852i	−0.914676	−	0.404187i	$-0.867554\pi$
$61$	−6.54541	+	11.3370i	−0.107302	+	0.185852i	0.807375	+	0.590039i	$0.200888\pi$
$62$	−4.30686			−0.0694654
$63$		0			0
$64$	8.00000			0.125000
$65$		0			0
$66$		0			0
$67$	64.9912	−	37.5227i	0.970018	−	0.560040i	0.0707765	−	0.997492i	$-0.477452\pi$
$67$	64.9912	−	37.5227i	0.970018	−	0.560040i	0.899242	+	0.437452i	$0.144119\pi$
$68$	18.8776	+	32.6969i	0.277612	+	0.480837i
$69$		0			0
$70$		0			0
$71$		−	18.0204i		−	0.253808i	−0.991915	−	0.126904i	$-0.959496\pi$
$71$		−	18.0204i		−	0.253808i	0.991915	−	0.126904i	$-0.0405041\pi$
$72$		0			0
$73$			7.90918i			0.108345i	0.998532	+	0.0541725i	$0.0172521\pi$
$73$			7.90918i			0.108345i	−0.998532	+	0.0541725i	$0.982748\pi$
$74$	57.1918	+	33.0197i	0.772863	+	0.446212i
$75$		0			0
$76$	−24.6969	−	42.7764i	−0.324960	−	0.562847i
$77$	−3.98018	−	6.89388i	−0.0516907	−	0.0895309i
$78$		0			0
$79$	−21.8712	+	37.8820i	−0.276850	+	0.479519i	−0.970600	−	0.240697i	$-0.922624\pi$
$79$	−21.8712	+	37.8820i	−0.276850	+	0.479519i	0.693750	+	0.720216i	$0.255957\pi$
$80$		0			0
$81$		0			0
$82$		−	15.4393i		−	0.188284i
$83$	65.1662	−	112.871i	0.785135	−	1.35989i	−0.143783	−	0.989609i	$-0.545927\pi$
$83$	65.1662	−	112.871i	0.785135	−	1.35989i	0.928918	−	0.370284i	$-0.120740\pi$
$84$		0			0
$85$		0			0
$86$	55.1691	−	31.8519i	0.641502	−	0.370371i
$87$		0			0
$88$	2.33562	+	1.34847i	0.0265411	+	0.0153235i
$89$			145.300i			1.63258i	0.577642	+	0.816290i	$0.303973\pi$
$89$			145.300i			1.63258i	−0.577642	+	0.816290i	$0.696027\pi$
$90$		0			0
$91$	80.9546			0.889611
$92$	0.953512	−	1.65153i	0.0103643	−	0.0179514i
$93$		0			0
$94$	−32.0227	−	55.4650i	−0.340667	−	0.590053i
$95$		0			0
$96$		0			0
$97$	95.1576	+	54.9393i	0.981007	+	0.566384i	0.902574	−	0.430535i	$-0.141675\pi$
$97$	95.1576	+	54.9393i	0.981007	+	0.566384i	0.0784327	+	0.996919i	$0.475008\pi$
$98$	29.2699			0.298672
$99$		0			0
$100$		0			0
$101$	−127.772	−	73.7695i	−1.26507	−	0.730391i	−0.291022	−	0.956716i	$-0.593995\pi$
$101$	−127.772	−	73.7695i	−1.26507	−	0.730391i	−0.974052	+	0.226326i	$0.927329\pi$
$102$		0			0
$103$	89.3186	−	51.5681i	0.867171	−	0.500661i	0.000763745	−	1.00000i	$-0.499757\pi$
$103$	89.3186	−	51.5681i	0.867171	−	0.500661i	0.866407	+	0.499338i	$0.166424\pi$
$104$	−23.7526	+	13.7135i	−0.228390	+	0.131861i
$105$		0			0
$106$	66.7423	−	115.601i	0.629645	−	1.09058i
$107$	36.0408			0.336830			0.168415	−	0.985716i	$-0.446135\pi$
$107$	36.0408			0.336830			0.168415	+	0.985716i	$0.446135\pi$
$108$		0			0
$109$	148.272			1.36030			0.680149	−	0.733074i	$-0.261915\pi$
$109$	148.272			1.36030			0.680149	+	0.733074i	$0.261915\pi$
$110$		0			0
$111$		0			0
$112$	−28.9199	+	16.6969i	−0.258214	+	0.149080i
$113$	−85.5439	−	148.166i	−0.757025	−	1.31121i	−0.944361	−	0.328910i	$-0.893319\pi$
$113$	−85.5439	−	148.166i	−0.757025	−	1.31121i	0.187336	−	0.982296i	$-0.440015\pi$
$114$		0			0
$115$		0			0
$116$		−	27.3629i		−	0.235887i
$117$		0			0
$118$			26.5607i			0.225091i
$119$	−136.485	−	78.7995i	−1.14693	−	0.662180i
$120$		0			0
$121$	−60.0454	−	104.002i	−0.496243	−	0.859518i
$122$	9.25660	+	16.0329i	0.0758738	+	0.131417i
$123$		0			0
$124$	−3.04541	+	5.27480i	−0.0245597	+	0.0425387i
$125$		0			0
$126$		0			0
$127$		−	78.0908i		−	0.614888i	−0.951566	−	0.307444i	$-0.900526\pi$
$127$		−	78.0908i		−	0.614888i	0.951566	−	0.307444i	$-0.0994737\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−202.704	+	117.031i	−1.54736	+	0.893369i	−0.549019	+	0.835810i	$0.684999\pi$
$131$	−202.704	+	117.031i	−1.54736	+	0.893369i	−0.998342	+	0.0575598i	$0.981668\pi$
$132$		0			0
$133$	178.559	+	103.091i	1.34255	+	0.775119i
$134$		−	106.130i		−	0.792017i
$135$		0			0
$136$	53.3939			0.392602
$137$	74.9156	−	129.758i	0.546829	−	0.947136i	−0.451660	−	0.892190i	$-0.649168\pi$
$137$	74.9156	−	129.758i	0.546829	−	0.947136i	0.998489	−	0.0549460i	$-0.0174987\pi$
$138$		0			0
$139$	−42.2650	−	73.2052i	−0.304065	−	0.526656i	0.672988	−	0.739654i	$-0.265011\pi$
$139$	−42.2650	−	73.2052i	−0.304065	−	0.526656i	−0.977053	+	0.212998i	$0.931677\pi$
$140$		0			0
$141$		0			0
$142$	−22.0704	−	12.7423i	−0.155425	−	0.0897348i
$143$	−9.24614			−0.0646584
$144$		0			0
$145$		0			0
$146$	9.68673	+	5.59264i	0.0663475	+	0.0383057i
$147$		0			0
$148$	80.8815	−	46.6969i	0.546496	−	0.315520i
$149$	100.030	−	57.7524i	0.671343	−	0.387600i	−0.125242	−	0.992126i	$-0.539971\pi$
$149$	100.030	−	57.7524i	0.671343	−	0.387600i	0.796585	+	0.604526i	$0.206638\pi$
$150$		0			0
$151$	32.3865	−	56.0950i	0.214480	−	0.371490i	−0.738632	−	0.674109i	$-0.764528\pi$
$151$	32.3865	−	56.0950i	0.214480	−	0.371490i	0.953112	+	0.302619i	$0.0978610\pi$
$152$	−69.8535			−0.459562
$153$		0			0
$154$	−11.2577			−0.0731016
$155$		0			0
$156$		0			0
$157$	−18.0292	+	10.4092i	−0.114836	+	0.0663005i	−0.556318	−	0.830970i	$-0.687786\pi$
$157$	−18.0292	+	10.4092i	−0.114836	+	0.0663005i	0.441482	+	0.897270i	$0.354453\pi$
$158$	30.9305	+	53.5732i	0.195763	+	0.339071i
$159$		0			0
$160$		0			0
$161$			7.96036i			0.0494433i
$162$		0			0
$163$		−	133.060i		−	0.816320i	−0.912910	−	0.408160i	$-0.866171\pi$
$163$		−	133.060i		−	0.816320i	0.912910	−	0.408160i	$-0.133829\pi$
$164$	−18.9092	−	10.9172i	−0.115300	−	0.0665684i
$165$		0			0
$166$	−92.1589	−	159.624i	−0.555174	−	0.961590i
$167$	147.255	+	255.053i	0.881765	+	1.52726i	0.849377	+	0.527787i	$0.176978\pi$
$167$	147.255	+	255.053i	0.881765	+	1.52726i	0.0323885	+	0.999475i	$0.489689\pi$
$168$		0			0
$169$	−37.4847	+	64.9254i	−0.221803	+	0.384174i
$170$		0			0
$171$		0			0
$172$		−	90.0908i		−	0.523784i
$173$	34.6322	−	59.9847i	0.200186	−	0.346732i	−0.748402	−	0.663245i	$-0.769179\pi$
$173$	34.6322	−	59.9847i	0.200186	−	0.346732i	0.948588	+	0.316513i	$0.102512\pi$
$174$		0			0
$175$		0			0
$176$	3.30306	−	1.90702i	0.0187674	−	0.0108354i
$177$		0			0
$178$	177.955	+	102.742i	0.999747	+	0.577204i
$179$			47.4829i			0.265268i	0.991165	+	0.132634i	$0.0423435\pi$
$179$			47.4829i			0.265268i	−0.991165	+	0.132634i	$0.957657\pi$
$180$		0			0
$181$	242.879			1.34187			0.670935	−	0.741516i	$-0.265893\pi$
$181$	242.879			1.34187			0.670935	+	0.741516i	$0.265893\pi$
$182$	57.2435	−	99.1487i	0.314525	−	0.544773i
$183$		0			0
$184$	−1.34847	−	2.33562i	−0.00732864	−	0.0126936i
$185$		0			0
$186$		0			0
$187$	15.5885	+	9.00000i	0.0833607	+	0.0481283i
$188$	−90.5739			−0.481776
$189$		0			0
$190$		0			0
$191$	−6.52270	−	3.76588i	−0.0341503	−	0.0197167i	0.482828	−	0.875715i	$-0.339610\pi$
$191$	−6.52270	−	3.76588i	−0.0341503	−	0.0197167i	−0.516978	+	0.855999i	$0.672943\pi$
$192$		0			0
$193$	−299.172	+	172.727i	−1.55011	+	0.894959i	−0.551983	+	0.833856i	$0.686129\pi$
$193$	−299.172	+	172.727i	−1.55011	+	0.894959i	−0.998131	+	0.0611031i	$0.980538\pi$
$194$	134.573	−	77.6959i	0.693676	−	0.400494i
$195$		0			0
$196$	20.6969	−	35.8481i	0.105597	−	0.182899i
$197$	77.2247			0.392004			0.196002	−	0.980604i	$-0.437204\pi$
$197$	77.2247			0.392004			0.196002	+	0.980604i	$0.437204\pi$
$198$		0			0
$199$	−153.485			−0.771280			−0.385640	−	0.922649i	$-0.626019\pi$
$199$	−153.485			−0.771280			−0.385640	+	0.922649i	$0.626019\pi$
$200$		0			0
$201$		0			0
$202$	−180.698	+	104.326i	−0.894542	+	0.516464i
$203$	57.1095	+	98.9166i	0.281328	+	0.487274i
$204$		0			0
$205$		0			0
$206$		−	145.857i		−	0.708042i
$207$		0			0
$208$			38.7878i			0.186480i
$209$	−20.3939	−	11.7744i	−0.0975784	−	0.0563369i
$210$		0			0
$211$	25.7804	+	44.6529i	0.122182	+	0.211625i	0.920628	−	0.390441i	$-0.127678\pi$
$211$	25.7804	+	44.6529i	0.122182	+	0.211625i	−0.798446	+	0.602066i	$0.794344\pi$
$212$	−94.3879	−	163.485i	−0.445226	−	0.771154i
$213$		0			0
$214$	25.4847	−	44.1408i	0.119087	−	0.206265i
$215$		0			0
$216$		0			0
$217$		−	25.4245i		−	0.117164i
$218$	104.844	−	181.596i	0.480938	−	0.833009i
$219$		0			0
$220$		0			0
$221$	−158.530	+	91.5274i	−0.717331	+	0.414151i
$222$		0			0
$223$	271.263	+	156.614i	1.21642	+	0.702303i	0.964151	−	0.265353i	$-0.0854886\pi$
$223$	271.263	+	156.614i	1.21642	+	0.702303i	0.252273	+	0.967656i	$0.418822\pi$
$224$			47.2261i			0.210831i
$225$		0			0
$226$	−241.955			−1.07060
$227$	−38.1356	+	66.0528i	−0.167998	+	0.290982i	−0.937716	−	0.347403i	$-0.887064\pi$
$227$	−38.1356	+	66.0528i	−0.167998	+	0.290982i	0.769718	+	0.638384i	$0.220397\pi$
$228$		0			0
$229$	−60.7724	−	105.261i	−0.265382	−	0.459655i	0.702282	−	0.711899i	$-0.252165\pi$
$229$	−60.7724	−	105.261i	−0.265382	−	0.459655i	−0.967664	+	0.252244i	$0.918831\pi$
$230$		0			0
$231$		0			0
$232$	−33.5125	−	19.3485i	−0.144451	−	0.0833986i
$233$	151.021			0.648157			0.324079	−	0.946030i	$-0.394946\pi$
$233$	151.021			0.648157			0.324079	+	0.946030i	$0.394946\pi$
$234$		0			0
$235$		0			0
$236$	32.5301	+	18.7813i	0.137839	+	0.0795816i
$237$		0			0
$238$	−193.019	+	111.439i	−0.811002	+	0.468232i
$239$	−75.9620	+	43.8567i	−0.317833	+	0.183501i	−0.650426	−	0.759570i	$-0.725410\pi$
$239$	−75.9620	+	43.8567i	−0.317833	+	0.183501i	0.332593	+	0.943070i	$0.392076\pi$
$240$		0			0
$241$	−100.894	+	174.753i	−0.418647	+	0.725118i	−0.995804	−	0.0915158i	$-0.970829\pi$
$241$	−100.894	+	174.753i	−0.418647	+	0.725118i	0.577157	+	0.816633i	$0.304162\pi$
$242$	−169.834			−0.701794
$243$		0			0
$244$	26.1816			0.107302
$245$		0			0
$246$		0			0
$247$	207.400	−	119.742i	0.839675	−	0.484787i
$248$	4.30686	+	7.45969i	0.0173664	+	0.0300794i
$249$		0			0
$250$		0			0
$251$		−	52.6261i		−	0.209666i	−0.994490	−	0.104833i	$-0.966569\pi$
$251$		−	52.6261i		−	0.209666i	0.994490	−	0.104833i	$-0.0334307\pi$
$252$		0			0
$253$		−	0.909185i		−	0.00359362i
$254$	−95.6413	−	55.2185i	−0.376541	−	0.217396i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	40.3532	+	69.8939i	0.157017	+	0.271961i	0.933791	−	0.357818i	$-0.116479\pi$
$257$	40.3532	+	69.8939i	0.157017	+	0.271961i	−0.776775	+	0.629778i	$0.783146\pi$
$258$		0			0
$259$	−194.924	+	337.618i	−0.752602	+	1.30355i
$260$		0			0
$261$		0			0
$262$			331.015i			1.26342i
$263$	−231.872	+	401.614i	−0.881641	+	1.52705i	−0.0321259	+	0.999484i	$0.510228\pi$
$263$	−231.872	+	401.614i	−0.881641	+	1.52705i	−0.849515	+	0.527564i	$0.823106\pi$
$264$		0			0
$265$		0			0
$266$	252.520	−	145.792i	0.949323	−	0.548092i
$267$		0			0
$268$	−129.982	−	75.0454i	−0.485009	−	0.280020i
$269$		−	43.4762i		−	0.161622i	−0.996729	−	0.0808109i	$-0.974249\pi$
$269$		−	43.4762i		−	0.161622i	0.996729	−	0.0808109i	$-0.0257510\pi$
$270$		0			0
$271$	−342.636			−1.26434			−0.632169	−	0.774830i	$-0.717835\pi$
$271$	−342.636			−1.26434			−0.632169	+	0.774830i	$0.717835\pi$
$272$	37.7552	−	65.3939i	0.138806	−	0.240419i
$273$		0			0
$274$	−105.947	−	183.505i	−0.386667	−	0.669726i
$275$		0			0
$276$		0			0
$277$	42.4352	+	24.5000i	0.153196	+	0.0884477i	0.574638	−	0.818407i	$-0.305143\pi$
$277$	42.4352	+	24.5000i	0.153196	+	0.0884477i	−0.421442	+	0.906855i	$0.638476\pi$
$278$	−119.544			−0.430013
$279$		0			0
$280$		0			0
$281$	17.8791	+	10.3225i	0.0636266	+	0.0367349i	0.531476	−	0.847073i	$-0.321638\pi$
$281$	17.8791	+	10.3225i	0.0636266	+	0.0367349i	−0.467849	+	0.883808i	$0.654971\pi$
$282$		0			0
$283$	−46.2533	+	26.7043i	−0.163439	+	0.0943616i	−0.579489	−	0.814980i	$-0.696748\pi$
$283$	−46.2533	+	26.7043i	−0.163439	+	0.0943616i	0.416049	+	0.909342i	$0.363414\pi$
$284$	−31.2122	+	18.0204i	−0.109902	+	0.0634521i
$285$		0			0
$286$	−6.53801	+	11.3242i	−0.0228602	+	0.0395950i
$287$	91.1421			0.317568
$288$		0			0
$289$	67.3633			0.233091
$290$		0			0
$291$		0			0
$292$	13.6991	−	7.90918i	0.0469148	−	0.0270862i
$293$	−7.46196	−	12.9245i	−0.0254674	−	0.0441109i	0.853011	−	0.521893i	$-0.174774\pi$
$293$	−7.46196	−	12.9245i	−0.0254674	−	0.0441109i	−0.878478	+	0.477782i	$0.841441\pi$
$294$		0			0
$295$		0			0
$296$		−	132.079i		−	0.446212i
$297$		0			0
$298$		−	163.348i		−	0.548149i
$299$	8.00740	+	4.62307i	0.0267806	+	0.0154618i
$300$		0			0
$301$	188.030	+	325.678i	0.624685	+	1.08199i
$302$	−45.8014	−	79.3304i	−0.151660	−	0.262683i
$303$		0			0
$304$	−49.3939	+	85.5527i	−0.162480	+	0.281423i
$305$		0			0
$306$		0			0
$307$			65.9092i			0.214688i	0.994222	+	0.107344i	$0.0342346\pi$
$307$			65.9092i			0.214688i	−0.994222	+	0.107344i	$0.965765\pi$
$308$	−7.96036	+	13.7878i	−0.0258453	+	0.0447654i
$309$		0			0
$310$		0			0
$311$	216.659	−	125.088i	0.696652	−	0.402213i	−0.109447	−	0.993993i	$-0.534908\pi$
$311$	216.659	−	125.088i	0.696652	−	0.402213i	0.806099	+	0.591780i	$0.201575\pi$
$312$		0			0
$313$	−369.268	−	213.197i	−1.17977	−	0.681140i	−0.223808	−	0.974633i	$-0.571849\pi$
$313$	−369.268	−	213.197i	−1.17977	−	0.681140i	−0.955961	+	0.293493i	$0.905182\pi$
$314$			29.4416i			0.0937631i
$315$		0			0
$316$	87.4847			0.276850
$317$	−231.990	+	401.818i	−0.731829	+	1.26756i	0.224272	+	0.974527i	$0.427999\pi$
$317$	−231.990	+	401.818i	−0.731829	+	1.26756i	−0.956101	+	0.293038i	$0.905334\pi$
$318$		0			0
$319$	−6.52270	−	11.2977i	−0.0204473	−	0.0354158i
$320$		0			0
$321$		0			0
$322$	9.74941	+	5.62883i	0.0302777	+	0.0174808i
$323$	−466.219			−1.44340
$324$		0			0
$325$		0			0
$326$	−162.965	−	94.0878i	−0.499892	−	0.288613i
$327$		0			0
$328$	−26.7416	+	15.4393i	−0.0815293	+	0.0470710i
$329$	327.424	−	189.038i	0.995210	−	0.574585i
$330$		0			0
$331$	−236.401	+	409.459i	−0.714203	+	1.23704i	0.249063	+	0.968487i	$0.419877\pi$
$331$	−236.401	+	409.459i	−0.714203	+	1.23704i	−0.963266	+	0.268549i	$0.913456\pi$
$332$	−260.665			−0.785135
$333$		0			0
$334$	416.499			1.24700
$335$		0			0
$336$		0			0
$337$	264.663	−	152.803i	0.785349	−	0.453422i	−0.0529735	−	0.998596i	$-0.516870\pi$
$337$	264.663	−	152.803i	0.785349	−	0.453422i	0.838323	+	0.545174i	$0.183537\pi$
$338$	53.0114	+	91.8184i	0.156838	+	0.271652i
$339$		0			0
$340$		0			0
$341$			2.90383i			0.00851564i
$342$		0			0
$343$		−	236.287i		−	0.688884i
$344$	−110.338	−	63.7038i	−0.320751	−	0.185186i
$345$		0			0
$346$	−48.9773	−	84.8312i	−0.141553	−	0.245177i
$347$	−66.8373	−	115.766i	−0.192615	−	0.333618i	0.753501	−	0.657446i	$-0.228363\pi$
$347$	−66.8373	−	115.766i	−0.192615	−	0.333618i	−0.946116	+	0.323828i	$0.895030\pi$
$348$		0			0
$349$	−49.3786	+	85.5262i	−0.141486	+	0.245061i	−0.928056	−	0.372440i	$-0.878521\pi$
$349$	−49.3786	+	85.5262i	−0.141486	+	0.245061i	0.786570	+	0.617500i	$0.211855\pi$
$350$		0			0
$351$		0			0
$352$		−	5.39388i		−	0.0153235i
$353$	163.058	−	282.424i	0.461919	−	0.800068i	−0.537137	−	0.843495i	$-0.680494\pi$
$353$	163.058	−	282.424i	0.461919	−	0.800068i	0.999057	+	0.0434270i	$0.0138276\pi$
$354$		0			0
$355$		0			0
$356$	251.666	−	145.300i	0.706928	−	0.408145i
$357$		0			0
$358$	58.1545	+	33.5755i	0.162443	+	0.0937863i
$359$		−	418.736i		−	1.16639i	−0.812331	−	0.583197i	$-0.801801\pi$
$359$		−	418.736i		−	1.16639i	0.812331	−	0.583197i	$-0.198199\pi$
$360$		0			0
$361$	248.939			0.689581
$362$	171.741	−	297.464i	0.474423	−	0.821725i
$363$		0			0
$364$	−80.9546	−	140.217i	−0.222403	−	0.385213i
$365$		0			0
$366$		0			0
$367$	−162.143	−	93.6135i	−0.441808	−	0.255078i	0.262557	−	0.964917i	$-0.415434\pi$
$367$	−162.143	−	93.6135i	−0.441808	−	0.255078i	−0.704364	+	0.709839i	$0.748768\pi$
$368$	−3.81405			−0.0103643
$369$		0			0
$370$		0			0
$371$	682.423	+	393.997i	1.83942	+	1.06199i
$372$		0			0
$373$	−390.603	+	225.515i	−1.04719	+	0.604597i	−0.921862	−	0.387518i	$-0.873333\pi$
$373$	−390.603	+	225.515i	−1.04719	+	0.604597i	−0.125331	+	0.992115i	$0.539999\pi$
$374$	22.0454	−	12.7279i	0.0589449	−	0.0340319i
$375$		0			0
$376$	−64.0454	+	110.930i	−0.170334	+	0.295026i
$377$	132.668			0.351905
$378$		0			0
$379$	489.666			1.29200			0.645998	−	0.763339i	$-0.276442\pi$
$379$	489.666			1.29200			0.645998	+	0.763339i	$0.276442\pi$
$380$		0			0
$381$		0			0
$382$	−9.22450	+	5.32577i	−0.0241479	+	0.0139418i
$383$	51.5281	+	89.2492i	0.134538	+	0.233027i	0.925421	−	0.378941i	$-0.123712\pi$
$383$	51.5281	+	89.2492i	0.134538	+	0.233027i	−0.790883	+	0.611968i	$0.790378\pi$
$384$		0			0
$385$		0			0
$386$			488.546i			1.26566i
$387$		0			0
$388$		−	219.757i		−	0.566384i
$389$	29.6816	+	17.1367i	0.0763024	+	0.0440532i	0.537666	−	0.843158i	$-0.319306\pi$
$389$	29.6816	+	17.1367i	0.0763024	+	0.0440532i	−0.461363	+	0.887211i	$0.652640\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.0230179	−	0.0398682i
$392$	−29.2699	−	50.6969i	−0.0746681	−	0.129329i
$393$		0			0
$394$	54.6061	−	94.5806i	0.138594	−	0.240052i
$395$		0			0
$396$		0			0
$397$			8.27245i			0.0208374i	0.999946	+	0.0104187i	$0.00331643\pi$
$397$			8.27245i			0.0208374i	−0.999946	+	0.0104187i	$0.996684\pi$
$398$	−108.530	+	187.980i	−0.272689	+	0.472311i
$399$		0			0
$400$		0			0
$401$	−358.636	+	207.059i	−0.894355	+	0.516356i	−0.875364	−	0.483464i	$-0.839378\pi$
$401$	−358.636	+	207.059i	−0.894355	+	0.516356i	−0.0189903	+	0.999820i	$0.506045\pi$
$402$		0			0
$403$	−25.5747	−	14.7656i	−0.0634608	−	0.0366391i
$404$			295.078i			0.730391i
$405$		0			0
$406$	161.530			0.397857
$407$	22.2630	−	38.5607i	0.0547003	−	0.0947438i
$408$		0			0
$409$	−163.106	−	282.508i	−0.398792	−	0.690729i	0.594785	−	0.803885i	$-0.297237\pi$
$409$	−163.106	−	282.508i	−0.398792	−	0.690729i	−0.993577	+	0.113156i	$0.963904\pi$
$410$		0			0
$411$		0			0
$412$	−178.637	−	103.136i	−0.433585	−	0.250331i
$413$	−156.795			−0.379648
$414$		0			0
$415$		0			0
$416$	47.5051	+	27.4271i	0.114195	+	0.0659305i
$417$		0			0
$418$	−28.8413	+	16.6515i	−0.0689983	+	0.0398362i
$419$	−468.325	+	270.388i	−1.11772	+	0.645317i	−0.940818	−	0.338912i	$-0.889941\pi$
$419$	−468.325	+	270.388i	−1.11772	+	0.645317i	−0.176903	+	0.984228i	$0.556608\pi$
$420$		0			0
$421$	−141.848	+	245.689i	−0.336932	+	0.583584i	−0.983854	−	0.178973i	$-0.942723\pi$
$421$	−141.848	+	245.689i	−0.336932	+	0.583584i	0.646922	+	0.762556i	$0.276056\pi$
$422$	72.9179			0.172791
$423$		0			0
$424$	−266.969			−0.629645
$425$		0			0
$426$		0			0
$427$	−94.6464	+	54.6441i	−0.221654	+	0.127972i
$428$	−36.0408	−	62.4245i	−0.0842075	−	0.145852i
$429$		0			0
$430$		0			0
$431$			257.429i			0.597282i	0.954365	+	0.298641i	$0.0965334\pi$
$431$			257.429i			0.597282i	−0.954365	+	0.298641i	$0.903467\pi$
$432$		0			0
$433$		−	476.272i		−	1.09994i	−0.835186	−	0.549968i	$-0.814640\pi$
$433$		−	476.272i		−	1.09994i	0.835186	−	0.549968i	$-0.185360\pi$
$434$	−31.1385	−	17.9778i	−0.0717477	−	0.0414236i
$435$		0			0
$436$	−148.272	−	256.815i	−0.340074	−	0.589026i
$437$	11.7744	+	20.3939i	0.0269437	+	0.0466679i
$438$		0			0
$439$	−278.931	+	483.123i	−0.635379	+	1.10051i	0.351056	+	0.936355i	$0.385823\pi$
$439$	−278.931	+	483.123i	−0.635379	+	1.10051i	−0.986435	+	0.164154i	$0.947511\pi$
$440$		0			0
$441$		0			0
$442$			258.879i			0.585698i
$443$	−415.923	+	720.400i	−0.938879	+	1.62619i	−0.171312	+	0.985217i	$0.554801\pi$
$443$	−415.923	+	720.400i	−0.938879	+	1.62619i	−0.767567	+	0.640969i	$0.778533\pi$
$444$		0			0
$445$		0			0
$446$	383.623	−	221.485i	0.860142	−	0.496603i
$447$		0			0
$448$	57.8399	+	33.3939i	0.129107	+	0.0745399i
$449$			729.927i			1.62567i	0.582492	+	0.812836i	$0.302078\pi$
$449$			729.927i			1.62567i	−0.582492	+	0.812836i	$0.697922\pi$
$450$		0			0
$451$	−10.4097			−0.0230814
$452$	−171.088	+	296.333i	−0.378513	+	0.655603i
$453$		0			0
$454$	53.9319	+	93.4128i	0.118793	+	0.205755i
$455$		0			0
$456$		0			0
$457$	−614.563	−	354.818i	−1.34478	−	0.776407i	−0.357272	−	0.934000i	$-0.616293\pi$
$457$	−614.563	−	354.818i	−1.34478	−	0.776407i	−0.987504	+	0.157594i	$0.949626\pi$
$458$	−171.890			−0.375307
$459$		0			0
$460$		0			0
$461$	7.96990	+	4.60142i	0.0172883	+	0.00998140i	0.508619	−	0.860992i	$-0.330156\pi$
$461$	7.96990	+	4.60142i	0.0172883	+	0.00998140i	−0.491331	+	0.870973i	$0.663489\pi$
$462$		0			0
$463$	47.8024	−	27.5987i	0.103245	−	0.0596085i	−0.447488	−	0.894290i	$-0.647681\pi$
$463$	47.8024	−	27.5987i	0.103245	−	0.0596085i	0.550733	+	0.834681i	$0.314348\pi$
$464$	−47.3939	+	27.3629i	−0.102142	+	0.0589717i
$465$		0			0
$466$	106.788	−	184.962i	0.229158	−	0.396914i
$467$	−625.811			−1.34007			−0.670033	−	0.742331i	$-0.733720\pi$
$467$	−625.811			−1.34007			−0.670033	+	0.742331i	$0.733720\pi$
$468$		0			0
$469$	626.514			1.33585
$470$		0			0
$471$		0			0
$472$	46.0045	−	26.5607i	0.0974672	−	0.0562727i
$473$	−21.4757	−	37.1969i	−0.0454031	−	0.0786405i
$474$		0			0
$475$		0			0
$476$			315.198i			0.662180i
$477$		0			0
$478$			124.045i			0.259509i
$479$	267.856	+	154.647i	0.559199	+	0.322854i	0.752824	−	0.658222i	$-0.228691\pi$
$479$	267.856	+	154.647i	0.559199	+	0.322854i	−0.193625	+	0.981076i	$0.562024\pi$
$480$		0			0
$481$	226.409	+	392.151i	0.470704	+	0.815283i
$482$	142.685	+	247.139i	0.296028	+	0.512736i
$483$		0			0
$484$	−120.091	+	208.003i	−0.248122	+	0.429759i
$485$		0			0
$486$		0			0
$487$		−	28.3337i		−	0.0581800i	−0.999577	−	0.0290900i	$-0.990739\pi$
$487$		−	28.3337i		−	0.0581800i	0.999577	−	0.0290900i	$-0.00926095\pi$
$488$	18.5132	−	32.0658i	0.0379369	−	0.0657086i
$489$		0			0
$490$		0			0
$491$	−822.461	+	474.848i	−1.67507	+	0.967105i	−0.710348	+	0.703851i	$0.751462\pi$
$491$	−822.461	+	474.848i	−1.67507	+	0.967105i	−0.964727	+	0.263254i	$0.915204\pi$
$492$		0			0
$493$	−223.670	−	129.136i	−0.453693	−	0.261940i
$494$		−	338.682i		−	0.685592i
$495$		0			0
$496$	12.1816			0.0245597
$497$	75.2214	−	130.287i	0.151351	−	0.262147i
$498$		0			0
$499$	−280.113	−	485.170i	−0.561349	−	0.972284i	−0.997379	−	0.0723525i	$-0.976949\pi$
$499$	−280.113	−	485.170i	−0.561349	−	0.972284i	0.436030	−	0.899932i	$-0.356384\pi$
$500$		0			0
$501$		0			0
$502$	−64.4535	−	37.2122i	−0.128393	−	0.0741280i
$503$	897.832			1.78495			0.892477	−	0.451094i	$-0.148966\pi$
$503$	897.832			1.78495			0.892477	+	0.451094i	$0.148966\pi$
$504$		0			0
$505$		0			0
$506$	−1.11352	−	0.642891i	−0.00220063	−	0.00127053i
$507$		0			0
$508$	−135.257	+	78.0908i	−0.266254	+	0.153722i
$509$	−170.454	+	98.4114i	−0.334879	+	0.193343i	−0.658005	−	0.753013i	$-0.728600\pi$
$509$	−170.454	+	98.4114i	−0.334879	+	0.193343i	0.323126	+	0.946356i	$0.395266\pi$
$510$		0			0
$511$	−33.0148	+	57.1833i	−0.0646082	+	0.111905i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	114.136			0.222055
$515$		0			0
$516$		0			0
$517$	−37.3964	+	21.5908i	−0.0723334	+	0.0417617i
$518$	275.664	+	477.464i	0.532170	+	0.921746i
$519$		0			0
$520$		0			0
$521$			375.837i			0.721377i	0.932686	+	0.360688i	$0.117458\pi$
$521$			375.837i			0.721377i	−0.932686	+	0.360688i	$0.882542\pi$
$522$		0			0
$523$		−	91.1827i		−	0.174345i	−0.996193	−	0.0871727i	$-0.972217\pi$
$523$		−	91.1827i		−	0.174345i	0.996193	−	0.0871727i	$-0.0277832\pi$
$524$	405.409	+	234.063i	0.773681	+	0.446685i
$525$		0			0
$526$	327.916	+	567.967i	0.623415	+	1.07979i
$527$	28.7450	+	49.7878i	0.0545445	+	0.0944739i
$528$		0			0
$529$	264.045	−	457.340i	0.499141	−	0.864537i
$530$		0			0
$531$		0			0
$532$		−	412.363i		−	0.775119i
$533$	52.9318	−	91.6806i	0.0993092	−	0.172009i
$534$		0			0
$535$		0			0
$536$	−183.823	+	106.130i	−0.342953	+	0.198004i
$537$		0			0
$538$	−53.2473	−	30.7423i	−0.0989727	−	0.0571419i
$539$		−	19.7348i		−	0.0366137i
$540$		0			0
$541$	−38.8490			−0.0718096			−0.0359048	−	0.999355i	$-0.511431\pi$
$541$	−38.8490			−0.0718096			−0.0359048	+	0.999355i	$0.511431\pi$
$542$	−242.280	+	419.641i	−0.447011	+	0.774246i
$543$		0			0
$544$	−53.3939	−	92.4809i	−0.0981505	−	0.170002i
$545$		0			0
$546$		0			0
$547$	403.606	+	233.022i	0.737854	+	0.426000i	0.821289	−	0.570513i	$-0.193256\pi$
$547$	403.606	+	233.022i	0.737854	+	0.426000i	−0.0834344	+	0.996513i	$0.526589\pi$
$548$	−299.662			−0.546829
$549$		0			0
$550$		0			0
$551$	292.621	+	168.945i	0.531072	+	0.306615i
$552$		0			0
$553$	−316.257	+	182.591i	−0.571893	+	0.330182i
$554$	60.0125	−	34.6482i	0.108326	−	0.0625419i
$555$		0			0
$556$	−84.5301	+	146.410i	−0.152033	+	0.263328i
$557$	695.042			1.24783			0.623916	−	0.781492i	$-0.285541\pi$
$557$	695.042			1.24783			0.623916	+	0.781492i	$0.285541\pi$
$558$		0			0
$559$	436.803			0.781400
$560$		0			0
$561$		0			0
$562$	25.2848	−	14.5982i	0.0449908	−	0.0259755i
$563$	−273.537	−	473.780i	−0.485857	−	0.841528i	0.514011	−	0.857783i	$-0.328159\pi$
$563$	−273.537	−	473.780i	−0.485857	−	0.841528i	−0.999868	+	0.0162552i	$0.994826\pi$
$564$		0			0
$565$		0			0
$566$			75.5313i			0.133447i
$567$		0			0
$568$			50.9694i			0.0897348i
$569$	215.954	+	124.681i	0.379533	+	0.219123i	0.677615	−	0.735417i	$-0.263014\pi$
$569$	215.954	+	124.681i	0.379533	+	0.219123i	−0.298082	+	0.954540i	$0.596347\pi$
$570$		0			0
$571$	−36.9166	−	63.9414i	−0.0646525	−	0.111981i	0.831887	−	0.554945i	$-0.187261\pi$
$571$	−36.9166	−	63.9414i	−0.0646525	−	0.111981i	−0.896540	+	0.442963i	$0.853927\pi$
$572$	9.24614	+	16.0148i	0.0161646	+	0.0279979i
$573$		0			0
$574$	64.4472	−	111.626i	0.112277	−	0.194470i
$575$		0			0
$576$		0			0
$577$		−	43.9092i		−	0.0760991i	−0.999276	−	0.0380496i	$-0.987886\pi$
$577$		−	43.9092i		−	0.0760991i	0.999276	−	0.0380496i	$-0.0121145\pi$
$578$	47.6330	−	82.5028i	0.0824101	−	0.142738i
$579$		0			0
$580$		0			0
$581$	942.302	−	544.038i	1.62186	−	0.936382i
$582$		0			0
$583$	−77.9423	−	45.0000i	−0.133692	−	0.0771870i
$584$		−	22.3706i		−	0.0383057i
$585$		0			0
$586$	−21.1056			−0.0360164
$587$	−220.194	+	381.386i	−0.375117	+	0.649721i	−0.990345	−	0.138628i	$-0.955731\pi$
$587$	−220.194	+	381.386i	−0.375117	+	0.649721i	0.615228	+	0.788349i	$0.289064\pi$
$588$		0			0
$589$	−37.6061	−	65.1357i	−0.0638474	−	0.110587i
$590$		0			0
$591$		0			0
$592$	−161.763	−	93.3939i	−0.273248	−	0.157760i
$593$	347.232			0.585551			0.292776	−	0.956181i	$-0.405421\pi$
$593$	347.232			0.585551			0.292776	+	0.956181i	$0.405421\pi$
$594$		0			0
$595$		0			0
$596$	−200.060	−	115.505i	−0.335671	−	0.193800i
$597$		0			0
$598$	11.3242	−	6.53801i	0.0189367	−	0.0109331i
$599$	−684.083	+	394.956i	−1.14204	+	0.659359i	−0.946936	−	0.321423i	$-0.895839\pi$
$599$	−684.083	+	394.956i	−1.14204	+	0.659359i	−0.195107	+	0.980782i	$0.562505\pi$
$600$		0			0
$601$	353.455	−	612.201i	0.588111	−	1.01864i	−0.406369	−	0.913709i	$-0.633205\pi$
$601$	353.455	−	612.201i	0.588111	−	1.01864i	0.994480	−	0.104929i	$-0.0334614\pi$
$602$	531.829			0.883438
$603$		0			0
$604$	−129.546			−0.214480
$605$		0			0
$606$		0			0
$607$	−1033.39	+	596.628i	−1.70246	+	0.982913i	−0.759193	+	0.650866i	$0.774406\pi$
$607$	−1033.39	+	596.628i	−1.70246	+	0.982913i	−0.943263	+	0.332048i	$0.892261\pi$
$608$	69.8535	+	120.990i	0.114891	+	0.198996i
$609$		0			0
$610$		0			0
$611$		−	439.145i		−	0.718731i
$612$		0			0
$613$		−	629.181i		−	1.02640i	−0.858270	−	0.513198i	$-0.828461\pi$
$613$		−	629.181i		−	1.02640i	0.858270	−	0.513198i	$-0.171539\pi$
$614$	80.7219	+	46.6048i	0.131469	+	0.0759036i
$615$		0			0
$616$	11.2577	+	19.4988i	0.0182754	+	0.0316539i
$617$	−96.3648	−	166.909i	−0.156183	−	0.270516i	0.777306	−	0.629122i	$-0.216586\pi$
$617$	−96.3648	−	166.909i	−0.156183	−	0.270516i	−0.933489	+	0.358606i	$0.883252\pi$
$618$		0			0
$619$	−76.4773	+	132.463i	−0.123550	+	0.213994i	−0.921165	−	0.389172i	$-0.872761\pi$
$619$	−76.4773	+	132.463i	−0.123550	+	0.213994i	0.797615	+	0.603166i	$0.206095\pi$
$620$		0			0
$621$		0			0
$622$		−	353.803i		−	0.568814i
$623$	−606.515	+	1050.51i	−0.973539	+	1.68622i
$624$		0			0
$625$		0			0
$626$	−522.224	+	301.506i	−0.834223	+	0.481639i
$627$		0			0
$628$	36.0585	+	20.8184i	0.0574180	+	0.0331503i
$629$		−	881.525i		−	1.40147i
$630$		0			0
$631$	44.8786			0.0711229			0.0355615	−	0.999367i	$-0.488678\pi$
$631$	44.8786			0.0711229			0.0355615	+	0.999367i	$0.488678\pi$
$632$	61.8610	−	107.146i	0.0978814	−	0.169535i
$633$		0			0
$634$	328.083	+	568.256i	0.517481	+	0.896303i
$635$		0			0
$636$		0			0
$637$	173.809	+	100.348i	0.272855	+	0.157533i
$638$	−18.4490			−0.0289169
$639$		0			0
$640$		0			0
$641$	209.106	+	120.727i	0.326219	+	0.188342i	0.654161	−	0.756355i	$-0.273022\pi$
$641$	209.106	+	120.727i	0.326219	+	0.188342i	−0.327942	+	0.944698i	$0.606355\pi$
$642$		0			0
$643$	−685.380	+	395.704i	−1.06591	+	0.615403i	−0.927061	−	0.374910i	$-0.877674\pi$
$643$	−685.380	+	395.704i	−1.06591	+	0.615403i	−0.138849	+	0.990314i	$0.544340\pi$
$644$	13.7878	−	7.96036i	0.0214096	−	0.0123608i
$645$		0			0
$646$	−329.666	+	570.999i	−0.510319	+	0.883899i
$647$	294.028			0.454448			0.227224	−	0.973842i	$-0.427035\pi$
$647$	294.028			0.454448			0.227224	+	0.973842i	$0.427035\pi$
$648$		0			0
$649$	17.9082			0.0275935
$650$		0			0
$651$		0			0
$652$	−230.467	+	133.060i	−0.353477	+	0.204080i
$653$	−384.156	−	665.379i	−0.588295	−	1.01896i	−0.994456	−	0.105155i	$-0.966466\pi$
$653$	−384.156	−	665.379i	−0.588295	−	1.01896i	0.406161	−	0.913802i	$-0.366867\pi$
$654$		0			0
$655$		0			0
$656$			43.6689i			0.0665684i
$657$		0			0
$658$		−	534.681i		−	0.812585i
$659$	−373.204	−	215.469i	−0.566318	−	0.326964i	0.189359	−	0.981908i	$-0.439359\pi$
$659$	−373.204	−	215.469i	−0.566318	−	0.326964i	−0.755678	+	0.654944i	$0.772692\pi$
$660$		0			0
$661$	−506.136	−	876.653i	−0.765712	−	1.32625i	−0.939869	−	0.341534i	$-0.889053\pi$
$661$	−506.136	−	876.653i	−0.765712	−	1.32625i	0.174157	−	0.984718i	$-0.444280\pi$
$662$	334.322	+	579.062i	0.505018	+	0.874717i
$663$		0			0
$664$	−184.318	+	319.248i	−0.277587	+	0.480795i
$665$		0			0
$666$		0			0
$667$			13.0454i			0.0195583i
$668$	294.510	−	510.106i	0.440883	−	0.763631i
$669$		0			0
$670$		0			0
$671$	10.8099	−	6.24112i	0.0161102	−	0.00930123i
$672$		0			0
$673$	487.755	+	281.606i	0.724748	+	0.418433i	0.816498	−	0.577349i	$-0.195913\pi$
$673$	487.755	+	281.606i	0.724748	+	0.418433i	−0.0917499	+	0.995782i	$0.529246\pi$
$674$		−	432.192i		−	0.641235i
$675$		0			0
$676$	149.939			0.221803
$677$	−175.068	+	303.227i	−0.258594	+	0.447897i	−0.965865	−	0.259044i	$-0.916592\pi$
$677$	−175.068	+	303.227i	−0.258594	+	0.447897i	0.707272	+	0.706942i	$0.249926\pi$
$678$		0			0
$679$	458.659	+	794.421i	0.675492	+	1.16999i
$680$		0			0
$681$		0			0
$682$	3.55645	+	2.05332i	0.00521474	+	0.00301073i
$683$	−502.818			−0.736190			−0.368095	−	0.929788i	$-0.619990\pi$
$683$	−502.818			−0.736190			−0.368095	+	0.929788i	$0.619990\pi$
$684$		0			0
$685$		0			0
$686$	−289.392	−	167.080i	−0.421854	−	0.243557i
$687$		0			0
$688$	−156.042	+	90.0908i	−0.226805	+	0.130946i
$689$	792.650	−	457.637i	1.15044	−	0.664205i
$690$		0			0
$691$	−188.159	+	325.902i	−0.272300	+	0.471638i	−0.969450	−	0.245287i	$-0.921118\pi$
$691$	−188.159	+	325.902i	−0.272300	+	0.471638i	0.697150	+	0.716925i	$0.254451\pi$
$692$	−138.529			−0.200186
$693$		0			0
$694$	−189.044			−0.272398
$695$		0			0
$696$		0			0
$697$	−178.480	+	103.045i	−0.256069	+	0.147841i
$698$	69.8318	+	120.952i	0.100046	+	0.173284i
$699$		0			0
$700$		0			0
$701$		−	489.681i		−	0.698546i	−0.937021	−	0.349273i	$-0.886429\pi$
$701$		−	489.681i		−	0.698546i	0.937021	−	0.349273i	$-0.113571\pi$
$702$		0			0
$703$			1153.27i			1.64050i
$704$	−6.60612	−	3.81405i	−0.00938370	−	0.00541768i
$705$		0			0
$706$	−230.598	−	399.408i	−0.326626	−	0.565733i
$707$	−615.862	−	1066.70i	−0.871092	−	1.50878i
$708$		0			0
$709$	237.014	−	410.521i	0.334294	−	0.579014i	−0.649055	−	0.760741i	$-0.724836\pi$
$709$	237.014	−	410.521i	0.334294	−	0.579014i	0.983349	+	0.181728i	$0.0581689\pi$
$710$		0			0
$711$		0			0
$712$		−	410.969i		−	0.577204i
$713$	1.45192	−	2.51479i	0.00203635	−	0.00352706i
$714$		0			0
$715$		0			0
$716$	82.2429	−	47.4829i	0.114864	−	0.0663170i
$717$		0			0
$718$	−512.844	−	296.091i	−0.714268	−	0.412383i
$719$		−	108.122i		−	0.150379i	−0.997169	−	0.0751894i	$-0.976044\pi$
$719$		−	108.122i		−	0.150379i	0.997169	−	0.0751894i	$-0.0239561\pi$
$720$		0			0
$721$	861.030			1.19422
$722$	176.026	−	304.886i	0.243804	−	0.422280i
$723$		0			0
$724$	−242.879	−	420.678i	−0.335468	−	0.581047i
$725$		0			0
$726$		0			0
$727$	385.027	+	222.296i	0.529611	+	0.305771i	0.740858	−	0.671662i	$-0.234419\pi$
$727$	385.027	+	222.296i	0.529611	+	0.305771i	−0.211247	+	0.977433i	$0.567752\pi$
$728$	−228.974			−0.314525
$729$		0			0
$730$		0			0
$731$	−736.423	−	425.174i	−1.00742	−	0.581634i
$732$		0			0
$733$	620.388	−	358.181i	0.846368	−	0.488651i	−0.0130556	−	0.999915i	$-0.504156\pi$
$733$	620.388	−	358.181i	0.846368	−	0.488651i	0.859424	+	0.511264i	$0.170823\pi$
$734$	−229.305	+	132.390i	−0.312405	+	0.180367i
$735$		0			0
$736$	−2.69694	+	4.67123i	−0.00366432	+	0.00634679i
$737$	−71.5567			−0.0970918
$738$		0			0
$739$	−933.362			−1.26301			−0.631504	−	0.775373i	$-0.717562\pi$
$739$	−933.362			−1.26301			−0.631504	+	0.775373i	$0.717562\pi$
$740$		0			0
$741$		0			0
$742$	965.093	−	557.196i	1.30066	−	0.750939i
$743$	−7.95550	−	13.7793i	−0.0107073	−	0.0185455i	0.860622	−	0.509244i	$-0.170075\pi$
$743$	−7.95550	−	13.7793i	−0.0107073	−	0.0185455i	−0.871329	+	0.490699i	$0.836742\pi$
$744$		0			0
$745$		0			0
$746$			637.852i			0.855030i
$747$		0			0
$748$		−	36.0000i		−	0.0481283i
$749$	260.574	+	150.443i	0.347896	+	0.200858i
$750$		0			0
$751$	−404.916	−	701.334i	−0.539169	−	0.933867i	−0.998949	−	0.0458347i	$-0.985405\pi$
$751$	−404.916	−	701.334i	−0.539169	−	0.933867i	0.459781	−	0.888033i	$-0.347928\pi$
$752$	90.5739	+	156.879i	0.120444	+	0.208615i
$753$		0			0
$754$	93.8105	−	162.484i	0.124417	−	0.215497i
$755$		0			0
$756$		0			0
$757$			689.637i			0.911013i	0.890232	+	0.455506i	$0.150542\pi$
$757$			689.637i			0.911013i	−0.890232	+	0.455506i	$0.849458\pi$
$758$	346.246	−	599.716i	0.456789	−	0.791182i
$759$		0			0
$760$		0			0
$761$	825.393	−	476.541i	1.08462	−	0.626204i	0.152479	−	0.988307i	$-0.451274\pi$
$761$	825.393	−	476.541i	1.08462	−	0.626204i	0.932138	+	0.362103i	$0.117941\pi$
$762$		0			0
$763$	1072.01	+	618.924i	1.40499	+	0.811172i
$764$			15.0635i			0.0197167i
$765$		0			0
$766$	145.743			0.190266
$767$	−91.0604	+	157.721i	−0.118723	+	0.205634i
$768$		0			0
$769$	−328.348	−	568.715i	−0.426980	−	0.739552i	0.569623	−	0.821906i	$-0.307089\pi$
$769$	−328.348	−	568.715i	−0.426980	−	0.739552i	−0.996603	+	0.0823545i	$0.973756\pi$
$770$		0			0
$771$		0			0
$772$	598.344	+	345.454i	0.775057	+	0.447479i
$773$	278.021			0.359665			0.179832	−	0.983697i	$-0.442445\pi$
$773$	278.021			0.359665			0.179832	+	0.983697i	$0.442445\pi$
$774$		0			0
$775$		0			0
$776$	−269.146	−	155.392i	−0.346838	−	0.200247i
$777$		0			0
$778$	41.9762	−	24.2350i	0.0539539	−	0.0311503i
$779$	233.499	−	134.811i	0.299743	−	0.173056i
$780$		0			0
$781$	−8.59133	+	14.8806i	−0.0110004	+	0.0190533i
$782$	−25.4558			−0.0325522
$783$		0			0
$784$	−82.7878			−0.105597
$785$		0			0
$786$		0			0
$787$	711.833	−	410.977i	0.904489	−	0.522207i	0.0258350	−	0.999666i	$-0.491776\pi$
$787$	711.833	−	410.977i	0.904489	−	0.522207i	0.878654	+	0.477459i	$0.158442\pi$
$788$	−77.2247	−	133.757i	−0.0980009	−	0.169743i
$789$		0			0
$790$		0			0
$791$		−	1428.32i		−	1.80572i
$792$		0			0
$793$			126.941i			0.160077i
$794$	10.1316	+	5.84950i	0.0127602	+	0.00736713i
$795$		0			0
$796$	153.485	+	265.843i	0.192820	+	0.333974i
$797$	−661.257	−	1145.33i	−0.829683	−	1.43705i	−0.898287	−	0.439409i	$-0.855188\pi$
$797$	−661.257	−	1145.33i	−0.829683	−	1.43705i	0.0686043	−	0.997644i	$-0.478145\pi$
$798$		0			0
$799$	−427.454	+	740.372i	−0.534986	+	0.926624i
$800$		0			0
$801$		0			0
$802$			585.650i			0.730238i
$803$	3.77075	−	6.53113i	0.00469583	−	0.00813341i
$804$		0			0
$805$		0			0
$806$	−36.1681	+	20.8817i	−0.0448736	+	0.0259078i
$807$		0			0
$808$	361.395	+	208.652i	0.447271	+	0.258232i
$809$			235.681i			0.291324i	0.989334	+	0.145662i	$0.0465311\pi$
$809$			235.681i			0.291324i	−0.989334	+	0.145662i	$0.953469\pi$
$810$		0			0
$811$	−587.362			−0.724244			−0.362122	−	0.932131i	$-0.617948\pi$
$811$	−587.362			−0.724244			−0.362122	+	0.932131i	$0.617948\pi$
$812$	114.219	−	197.833i	0.140664	−	0.243637i
$813$		0			0
$814$	−31.4847	−	54.5331i	−0.0386790	−	0.0669940i
$815$		0			0
$816$		0			0
$817$	963.439	+	556.242i	1.17924	+	0.680835i
$818$	−461.334			−0.563978
$819$		0			0
$820$		0			0
$821$	817.453	+	471.956i	0.995679	+	0.574856i	0.906967	−	0.421202i	$-0.138392\pi$
$821$	817.453	+	471.956i	0.995679	+	0.574856i	0.0887121	+	0.996057i	$0.471725\pi$
$822$		0			0
$823$	1399.27	−	807.871i	1.70021	−	0.981617i	0.754676	−	0.656097i	$-0.227794\pi$
$823$	1399.27	−	807.871i	1.70021	−	0.981617i	0.945535	−	0.325520i	$-0.105539\pi$
$824$	−252.631	+	145.857i	−0.306591	+	0.177010i
$825$		0			0
$826$	−110.871	+	192.034i	−0.134226	+	0.232486i
$827$	582.354			0.704177			0.352088	−	0.935967i	$-0.385472\pi$
$827$	582.354			0.704177			0.352088	+	0.935967i	$0.385472\pi$
$828$		0			0
$829$	−877.121			−1.05805			−0.529024	−	0.848607i	$-0.677442\pi$
$829$	−877.121			−1.05805			−0.529024	+	0.848607i	$0.677442\pi$
$830$		0			0
$831$		0			0
$832$	67.1824	−	38.7878i	0.0807480	−	0.0466199i
$833$	−195.354	−	338.363i	−0.234519	−	0.406198i
$834$		0			0
$835$		0			0
$836$			47.0976i			0.0563369i
$837$		0			0
$838$			764.772i			0.912616i
$839$	−984.778	−	568.562i	−1.17375	−	0.677666i	−0.219191	−	0.975682i	$-0.570342\pi$
$839$	−984.778	−	568.562i	−1.17375	−	0.677666i	−0.954561	+	0.298016i	$0.903675\pi$
$840$		0			0
$841$	−326.909	−	566.223i	−0.388715	−	0.673274i
$842$	200.604	+	347.456i	0.238247	+	0.412656i
$843$		0			0
$844$	51.5607	−	89.3058i	0.0610909	−	0.105813i
$845$		0			0
$846$		0			0
$847$		−	1002.57i		−	1.18368i
$848$	−188.776	+	326.969i	−0.222613	+	0.385577i
$849$		0			0
$850$		0			0
$851$	−38.5607	+	22.2630i	−0.0453122	+	0.0261610i
$852$		0			0
$853$	−276.970	−	159.909i	−0.324701	−	0.187466i	0.328785	−	0.944405i	$-0.393361\pi$
$853$	−276.970	−	159.909i	−0.324701	−	0.187466i	−0.653486	+	0.756939i	$0.726694\pi$
$854$			154.557i			0.180980i
$855$		0			0
$856$	−101.939			−0.119087
$857$	398.984	−	691.061i	0.465559	−	0.806372i	−0.533668	−	0.845694i	$-0.679187\pi$
$857$	398.984	−	691.061i	0.465559	−	0.806372i	0.999227	+	0.0393225i	$0.0125200\pi$
$858$		0			0
$859$	−233.901	−	405.128i	−0.272294	−	0.471627i	0.697155	−	0.716921i	$-0.254449\pi$
$859$	−233.901	−	405.128i	−0.272294	−	0.471627i	−0.969449	+	0.245293i	$0.921116\pi$
$860$		0			0
$861$		0			0
$862$	315.284	+	182.030i	0.365759	+	0.211171i
$863$	1304.85			1.51199			0.755994	−	0.654578i	$-0.227154\pi$
$863$	1304.85			1.51199			0.755994	+	0.654578i	$0.227154\pi$
$864$		0			0
$865$		0			0
$866$	−583.312	−	336.775i	−0.673571	−	0.388886i
$867$		0			0
$868$	−44.0365	+	25.4245i	−0.0507333	+	0.0292909i
$869$	36.1209	−	20.8544i	0.0415661	−	0.0239982i
$870$		0			0
$871$	363.855	−	630.216i	0.417744	−	0.723554i
$872$	−419.378			−0.480938
$873$		0			0
$874$	33.3031			0.0381042
$875$		0			0
$876$		0			0
$877$	−323.682	+	186.878i	−0.369079	+	0.213088i	−0.673056	−	0.739592i	$-0.735019\pi$
$877$	−323.682	+	186.878i	−0.369079	+	0.213088i	0.303977	+	0.952679i	$0.401685\pi$
$878$	394.469	+	683.240i	0.449281	+	0.778177i
$879$		0			0
$880$		0			0
$881$		−	229.979i		−	0.261043i	−0.991445	−	0.130522i	$-0.958335\pi$
$881$		−	229.979i		−	0.261043i	0.991445	−	0.130522i	$-0.0416652\pi$
$882$		0			0
$883$			1381.79i			1.56488i	0.622728	+	0.782439i	$0.286024\pi$
$883$			1381.79i			1.56488i	−0.622728	+	0.782439i	$0.713976\pi$
$884$	317.060	+	183.055i	0.358665	+	0.207076i
$885$		0			0
$886$	588.204	+	1018.80i	0.663888	+	1.14989i
$887$	−438.090	−	758.794i	−0.493901	−	0.855461i	0.506075	−	0.862490i	$-0.331096\pi$
$887$	−438.090	−	758.794i	−0.493901	−	0.855461i	−0.999975	+	0.00702852i	$0.997763\pi$
$888$		0			0
$889$	325.969	−	564.596i	0.366670	−	0.635091i
$890$		0			0
$891$		0			0
$892$		−	626.454i		−	0.702303i
$893$	559.224	−	968.605i	0.626231	−	1.08466i
$894$		0			0
$895$		0			0
$896$	81.7980	−	47.2261i	0.0912924	−	0.0527077i
$897$		0			0
$898$	893.974	+	516.136i	0.995517	+	0.574762i
$899$		−	41.6655i		−	0.0463465i
$900$		0			0
$901$	−1781.82			−1.97760
$902$	−7.36077	+	12.7492i	−0.00816050	+	0.0141344i
$903$		0			0
$904$	241.955	+	419.078i	0.267649	+	0.463581i
$905$		0			0
$906$		0			0
$907$	−1021.97	−	590.037i	−1.12676	−	0.650537i	−0.183644	−	0.982993i	$-0.558789\pi$
$907$	−1021.97	−	590.037i	−1.12676	−	0.650537i	−0.943119	+	0.332456i	$0.892123\pi$
$908$	152.542			0.167998
$909$		0			0
$910$		0			0
$911$	−1100.13	−	635.158i	−1.20760	−	0.697210i	−0.245368	−	0.969430i	$-0.578909\pi$
$911$	−1100.13	−	635.158i	−1.20760	−	0.697210i	−0.962235	+	0.272220i	$0.912242\pi$
$912$		0			0
$913$	−107.624	+	62.1367i	−0.117880	+	0.0680578i
$914$	−869.123	+	501.788i	−0.950900	+	0.549002i
$915$		0			0
$916$	−121.545	+	210.522i	−0.132691	+	0.229827i
$917$	−1954.07			−2.13093
$918$		0			0
$919$	−1316.63			−1.43268			−0.716340	−	0.697751i	$-0.754184\pi$
$919$	−1316.63			−1.43268			−0.716340	+	0.697751i	$0.754184\pi$
$920$		0			0
$921$		0			0
$922$	11.2711	−	6.50740i	0.0122247	−	0.00705791i
$923$	−87.3713	−	151.332i	−0.0946602	−	0.163956i
$924$		0			0
$925$		0			0
$926$		−	78.0610i		−	0.0842991i
$927$		0			0
$928$			77.3939i			0.0833986i
$929$	543.424	+	313.746i	0.584956	+	0.337724i	0.763100	−	0.646280i	$-0.223676\pi$
$929$	543.424	+	313.746i	0.584956	+	0.337724i	−0.178145	+	0.984004i	$0.557009\pi$
$930$		0			0
$931$	255.576	+	442.670i	0.274517	+	0.475478i
$932$	−151.021	−	261.576i	−0.162039	−	0.280660i
$933$		0			0
$934$	−442.515	+	766.459i	−0.473785	+	0.820620i
$935$		0			0
$936$		0			0
$937$			469.789i			0.501375i	0.968068	+	0.250688i	$0.0806567\pi$
$937$			469.789i			0.501375i	−0.968068	+	0.250688i	$0.919343\pi$
$938$	443.012	−	767.320i	0.472295	−	0.818039i
$939$		0			0
$940$		0			0
$941$	−805.984	+	465.335i	−0.856518	+	0.494511i	−0.862845	−	0.505469i	$-0.831320\pi$
$941$	−805.984	+	465.335i	−0.856518	+	0.494511i	0.00632656	+	0.999980i	$0.497986\pi$
$942$		0			0
$943$	9.01506	+	5.20485i	0.00955998	+	0.00551946i
$944$		−	75.1250i		−	0.0795816i
$945$		0			0
$946$	−60.7423			−0.0642097
$947$	−1.81556	+	3.14465i	−0.00191717	+	0.00332064i	−0.866982	−	0.498339i	$-0.833944\pi$
$947$	−1.81556	+	3.14465i	−0.00191717	+	0.00332064i	0.865065	+	0.501659i	$0.167277\pi$
$948$		0			0
$949$	38.3474	+	66.4197i	0.0404083	+	0.0699892i
$950$		0			0
$951$		0			0
$952$	386.037	+	222.879i	0.405501	+	0.234116i
$953$	719.641			0.755132			0.377566	−	0.925983i	$-0.376761\pi$
$953$	719.641			0.755132			0.377566	+	0.925983i	$0.376761\pi$
$954$		0			0
$955$		0			0
$956$	151.924	+	87.7133i	0.158916	+	0.0917504i
$957$		0			0
$958$	378.806	−	218.704i	0.395413	−	0.228292i
$959$	1083.28	−	625.431i	1.12959	−	0.652170i
$960$		0			0
$961$	475.863	−	824.218i	0.495175	−	0.857667i
$962$	640.380			0.665676
$963$		0			0
$964$	403.576			0.418647
$965$		0			0
$966$		0			0
$967$	29.2491	−	16.8870i	0.0302473	−	0.0174633i	−0.484800	−	0.874625i	$-0.661108\pi$
$967$	29.2491	−	16.8870i	0.0302473	−	0.0174633i	0.515047	+	0.857162i	$0.327774\pi$
$968$	169.834	+	294.161i	0.175448	+	0.303886i
$969$		0			0
$970$		0			0
$971$		−	970.472i		−	0.999456i	−0.866182	−	0.499728i	$-0.833433\pi$
$971$		−	970.472i		−	0.999456i	0.866182	−	0.499728i	$-0.166567\pi$
$972$		0			0
$973$		−	705.697i		−	0.725279i
$974$	−34.7015	−	20.0349i	−0.0356278	−	0.0205697i
$975$		0			0
$976$	−26.1816	−	45.3479i	−0.0268254	−	0.0464630i
$977$	785.151	+	1359.92i	0.803635	+	1.39194i	0.917209	+	0.398406i	$0.130437\pi$
$977$	785.151	+	1359.92i	0.803635	+	1.39194i	−0.113574	+	0.993529i	$0.536230\pi$
$978$		0			0
$979$	69.2724	−	119.983i	0.0707584	−	0.122557i
$980$		0			0
$981$		0			0
$982$			1343.07i			1.36769i
$983$	387.939	−	671.930i	0.394648	−	0.683551i	−0.598408	−	0.801192i	$-0.704200\pi$
$983$	387.939	−	671.930i	0.394648	−	0.683551i	0.993056	+	0.117641i	$0.0375331\pi$
$984$		0			0
$985$		0			0
$986$	−316.318	+	182.626i	−0.320809	+	0.185219i
$987$		0			0
$988$	−414.800	−	239.485i	−0.419838	−	0.242393i
$989$			42.9513i			0.0434290i
$990$		0			0
$991$	870.454			0.878359			0.439180	−	0.898399i	$-0.355269\pi$
$991$	870.454			0.878359			0.439180	+	0.898399i	$0.355269\pi$
$992$	8.61371	−	14.9194i	0.00868318	−	0.0150397i
$993$		0			0
$994$	−106.379	−	184.254i	−0.107021	−	0.185366i
$995$		0			0
$996$		0			0
$997$	−1078.20	−	622.499i	−1.08144	−	0.624372i	−0.150159	−	0.988662i	$-0.547978\pi$
$997$	−1078.20	−	622.499i	−1.08144	−	0.624372i	−0.931286	+	0.364290i	$0.881312\pi$
$998$	−792.279			−0.793867
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.3.k.a.899.4		8
3.2	odd	2		450.3.k.a.299.1		8
5.2	odd	4		1350.3.i.b.251.2		4
5.3	odd	4		54.3.d.a.35.1		4
5.4	even	2	inner	1350.3.k.a.899.1		8
9.4	even	3		450.3.k.a.149.4		8
9.5	odd	6	inner	1350.3.k.a.449.1		8
15.2	even	4		450.3.i.b.101.1		4
15.8	even	4		18.3.d.a.11.2	yes	4
15.14	odd	2		450.3.k.a.299.4		8
20.3	even	4		432.3.q.d.305.1		4
40.3	even	4		1728.3.q.c.1601.1		4
40.13	odd	4		1728.3.q.d.1601.2		4
45.4	even	6		450.3.k.a.149.1		8
45.13	odd	12		18.3.d.a.5.2	✓	4
45.14	odd	6	inner	1350.3.k.a.449.4		8
45.22	odd	12		450.3.i.b.401.1		4
45.23	even	12		54.3.d.a.17.1		4
45.32	even	12		1350.3.i.b.1151.2		4
45.38	even	12		162.3.b.a.161.1		4
45.43	odd	12		162.3.b.a.161.4		4
60.23	odd	4		144.3.q.c.65.2		4
120.53	even	4		576.3.q.f.65.2		4
120.83	odd	4		576.3.q.e.65.1		4
180.23	odd	12		432.3.q.d.17.1		4
180.43	even	12		1296.3.e.g.161.4		4
180.83	odd	12		1296.3.e.g.161.2		4
180.103	even	12		144.3.q.c.113.2		4
360.13	odd	12		576.3.q.f.257.2		4
360.203	odd	12		1728.3.q.c.449.1		4
360.283	even	12		576.3.q.e.257.1		4
360.293	even	12		1728.3.q.d.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.2	✓	4	45.13	odd	12
18.3.d.a.11.2	yes	4	15.8	even	4
54.3.d.a.17.1		4	45.23	even	12
54.3.d.a.35.1		4	5.3	odd	4
144.3.q.c.65.2		4	60.23	odd	4
144.3.q.c.113.2		4	180.103	even	12
162.3.b.a.161.1		4	45.38	even	12
162.3.b.a.161.4		4	45.43	odd	12
432.3.q.d.17.1		4	180.23	odd	12
432.3.q.d.305.1		4	20.3	even	4
450.3.i.b.101.1		4	15.2	even	4
450.3.i.b.401.1		4	45.22	odd	12
450.3.k.a.149.1		8	45.4	even	6
450.3.k.a.149.4		8	9.4	even	3
450.3.k.a.299.1		8	3.2	odd	2
450.3.k.a.299.4		8	15.14	odd	2
576.3.q.e.65.1		4	120.83	odd	4
576.3.q.e.257.1		4	360.283	even	12
576.3.q.f.65.2		4	120.53	even	4
576.3.q.f.257.2		4	360.13	odd	12
1296.3.e.g.161.2		4	180.83	odd	12
1296.3.e.g.161.4		4	180.43	even	12
1350.3.i.b.251.2		4	5.2	odd	4
1350.3.i.b.1151.2		4	45.32	even	12
1350.3.k.a.449.1		8	9.5	odd	6	inner
1350.3.k.a.449.4		8	45.14	odd	6	inner
1350.3.k.a.899.1		8	5.4	even	2	inner
1350.3.k.a.899.4		8	1.1	even	1	trivial
1728.3.q.c.449.1		4	360.203	odd	12
1728.3.q.c.1601.1		4	40.3	even	4
1728.3.q.d.449.2		4	360.293	even	12
1728.3.q.d.1601.2		4	40.13	odd	4

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1350.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(7.22999 + 4.17423i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(7.22999 + 4.17423i) q^{7} -2.82843 q^{8} +(-0.825765 - 0.476756i) q^{11} +(8.39780 - 4.84847i) q^{13} +(10.2247 - 5.90326i) q^{14} +(-2.00000 + 3.46410i) q^{16} -18.8776 q^{17} +24.6969 q^{19} +(-1.16781 + 0.674235i) q^{22} +(0.476756 + 0.825765i) q^{23} -13.7135i q^{26} -16.6969i q^{28} +(11.8485 + 6.84072i) q^{29} +(-1.52270 - 2.63740i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-13.3485 + 23.1202i) q^{34} +46.6969i q^{37} +(17.4634 - 30.2474i) q^{38} +(9.45459 - 5.45861i) q^{41} +(39.0105 + 22.5227i) q^{43} +1.90702i q^{44} +1.34847 q^{46} +(22.6435 - 39.2196i) q^{47} +(10.3485 + 17.9241i) q^{49} +(-16.7956 - 9.69694i) q^{52} +94.3879 q^{53} +(-20.4495 - 11.8065i) q^{56} +(16.7563 - 9.67423i) q^{58} +(-16.2650 + 9.39063i) q^{59} +(-6.54541 + 11.3370i) q^{61} -4.30686 q^{62} +8.00000 q^{64} +(64.9912 - 37.5227i) q^{67} +(18.8776 + 32.6969i) q^{68} -18.0204i q^{71} +7.90918i q^{73} +(57.1918 + 33.0197i) q^{74} +(-24.6969 - 42.7764i) q^{76} +(-3.98018 - 6.89388i) q^{77} +(-21.8712 + 37.8820i) q^{79} -15.4393i q^{82} +(65.1662 - 112.871i) q^{83} +(55.1691 - 31.8519i) q^{86} +(2.33562 + 1.34847i) q^{88} +145.300i q^{89} +80.9546 q^{91} +(0.953512 - 1.65153i) q^{92} +(-32.0227 - 55.4650i) q^{94} +(95.1576 + 54.9393i) q^{97} +29.2699 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} - 36 q^{11} + 72 q^{14} - 16 q^{16} + 80 q^{19} + 36 q^{29} + 76 q^{31} - 48 q^{34} + 252 q^{41} - 48 q^{46} + 24 q^{49} - 144 q^{56} + 252 q^{59} + 124 q^{61} + 64 q^{64} + 144 q^{74} - 80 q^{76} - 28 q^{79} + 216 q^{86} + 824 q^{91} - 168 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 - 36 * q^11 + 72 * q^14 - 16 * q^16 + 80 * q^19 + 36 * q^29 + 76 * q^31 - 48 * q^34 + 252 * q^41 - 48 * q^46 + 24 * q^49 - 144 * q^56 + 252 * q^59 + 124 * q^61 + 64 * q^64 + 144 * q^74 - 80 * q^76 - 28 * q^79 + 216 * q^86 + 824 * q^91 - 168 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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